Class. 
 Book. 
 
 ki 
 
The Publishers and the Author will be grateful to 
 any of the readers of this volume who will kindly call 
 their attention to any errors of omission or of commis- 
 sion that they may find therein. It is intended to make 
 our 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 Author 
 may be aided in his task of revision, from time to time, 
 by the kindly criticism of his readers. 
 
 JOHN WILEY & SONS. 
 43 & 45 East Nineteenth Street. 
 
WORKS OF WILLIAM KENT 
 
 PUBLISHED BY 
 
 JOHN WILEY & SONS. 
 
 The Mechanical Engineers' Pocket-Book. 
 
 A Reference Book of Rules, Tables, Data, and 
 Formula?, for the Use of Engineers, Mechanics, 
 and Students, xl + 1461 pages, 16mo, morocco, 
 $5.00 net. 
 
 Steam=Boiler Economy. 
 
 A treatise on the Theory and Practice of Fuel 
 Economy in the Operation of Steam-Boilers. 
 xiv + 458 pages, 136 figures, 870, cloth, $4.00. 
 
THE 
 
 MECHANICAL ENGINEERS' 
 POCKET-BOOK. 
 
 A REFERENCE-BOOK OF BULES, TABLES, DATA, 
 AND FORMULA K< FOR THE, ,U$E OF 
 ENGINEERS, MECHAJflGS^ 
 AND STUDENTS. 
 
 WILLIAM KENT, M.E., Sc.D., 
 
 Consulting Engineer. 
 Member Amer. Soc'y Mechl. Engrs. and Amer. Inst. Mining Engrs. 
 
 EIGHTH EDITION, REWRITTEN. 
 TOTAL ISSUE EIGHTY-ONE THOUSAND. 
 
 XTbr A fTy^ 
 
 OF THE 
 
 Ns5ft/FF BO 
 
 NEW YORK: 
 
 JOHN WILEY & SONS. 
 
 London: CHAPMAN & HALL, Limited. 
 
 1910. 
 

 By tranafer from 
 U.S. Tariff Board 
 
 1 .'* 
 
 Copyright, 1895, 1902, 1910, 
 
 BY 
 
 WILLIAM KENT. 
 
 Eighth Edition entered at Stationers* Hall 
 
 TYPOGRAPHY BY 
 
 PRESS OF 
 
 Stanbopc lpres^ br aun worth & co. 
 
 K.gilson company BOOKBINDERS AND PRINTERS 
 
 boston. U.S.A. BROOKLYN, N. Y. 
 
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 ferum, 4 tlfe' ScVap-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 formulae 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. 
 
IV PREFACE. 
 
 The author desires to express his obligation to the many persons who 
 have assisted him in the preparation of the work, to manufacturers who 
 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. The thanks of the author are also due to the following 
 gentlemen who have given assistance in revising manuscript or proofs 
 of the sections named: Prof. De Volson "Wood, mechanics and turbines; 
 Mr. Frank Richards, compressed air; Mr. Alfred R. Wolff, windmills; 
 Mr. Alex. C. Humphreys, illuminating gas; Mr. Albert E. Mitchell, loco- 
 motives; Prof. James E. Denton, refrigerating-machinery; Messrs. Joseph 
 Wetzler and Thomas W. Varley, electrical engineering; and Mr. Walter 
 S. Dix, for valuable contributions on several subjects, and suggestions 
 as to their treatment. 
 
 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 have 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 1417.) 
 
 MATHEMATICS. 
 Arithmetic. 
 
 PAGE 
 
 Arithmetical and Algebraical Signs 1 
 
 Greatest Common Divisor 2 
 
 Least Common Multiple 2 
 
 Fractions 2 
 
 Decimals 3 
 
 Table. Decimal Equivalents of Fractions of One Inch 3 
 
 Table. Products of Fractions expressed in Decimals 4 
 
 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 13 
 
 Compound Interest Table, 3, 4, 5, and 6 per cent 14 
 
 Equation of Payments 14 
 
 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 18 
 
 Solid or Cubic Measure 18 
 
 Liquid Measure 18 
 
 The Miners' Inch 18 
 
 Apothecaries' Fluid Measure 18 
 
 Dry Measure 19 
 
 Shipping Measure 19 
 
 Avoirdupois Weight 19 
 
 Troy Weight 19 
 
 Apothecaries' Weight 20 
 
 To Weigh Correctly on an Incorrect Balance 20 
 
 Circular Measure 20 
 
 Measure of Time 20 
 
 V 
 
VI CONTENTS. 
 
 PAGE 
 
 Board and Timber Measure 20 
 
 Table. Contents in Feet of Joists, Scantlings, and Timber 21 
 
 French or Metric Measures 22 
 
 British and French Equivalents 22 
 
 Metric Conversion Tables 23 
 
 Compound Units 
 
 of Pressure and Weight 27 
 
 of Water, Weight, and Bulk 28 
 
 of Air, Weight, and Volume 28 
 
 of Work, Power, and Duty 28 
 
 of Velocity 28 
 
 Wire and Sheet Metal Gauges 29 
 
 Twist-drill and Steel-wire Gauges 30 
 
 Circular-mil Wire Gauge 31 
 
 New U. S. Standard Wire and Sheet Gauge, 1893 31 
 
 Decimal Gauge 33 
 
 Algebra. 
 
 Addition, Multiplication, etc 34 
 
 Powers of Numbers 34 
 
 Parentheses, Division 35 
 
 Simple Equations and Problems 35 
 
 Equations containing two or more Unknown Quantities 36 
 
 Elimination 36 
 
 Quadratic Equations 36 
 
 Theory of Exponents 37 
 
 Binomial Theorem 38 
 
 Geometrical Problems of Construction 38 
 
 of Straight Lines 38 
 
 of Angles 39 
 
 of Circles 40 
 
 of Triangles 42 
 
 of Squares and Polygons 42 
 
 of the Ellipse 46 
 
 of the Parabola 49 
 
 of the Hvperbola '. 50 
 
 of the Cycloid 51 
 
 of the Tractrix or Schiele Anti-friction Curve 51 
 
 of the Spiral 52 
 
 of Rings inside a Circle 52 
 
 of Arc of a Large Circle 52 
 
 of the Catenary . 53 
 
 of the Involute 53 
 
 of plotting Angles 54 
 
 Geometrical Propositions 54 
 
 Mensuration, Plane Surfaces. 
 
 Quadrilateral, Parallelogram, etc 55 
 
 Trapezium and Trapezoid . 55 
 
 Triangles 55 
 
 Polygons. Table of Polygons 56 
 
 Irregular Figures 57 
 
 Properties of the Circle 58 
 
 Values of n and its Multiples, etc 58 
 
 Relations of arc, chord, etc 59 
 
 Relations of circle to inscribed square, etc 60 
 
 Formulas for a Circular Curve 60 
 
 Sectors and Segments 61 
 
 Circular Ring 61 
 
 The Ellipse 61 
 
 The Helix 62 
 
 The Spiral 62 
 
 Surfaces and Volumes of Similar Solids »* 
 
CONTENTS. 
 
 Mensuration, Solid Bodies. 
 
 PAGE 
 
 Prism - 63 
 
 Pyramid 63 
 
 Wedge 63 
 
 Rectangular Prismoid 63 
 
 Cylinder . 63 
 
 Cone 63 
 
 Sphere 63 
 
 Spherical Triangle 64 
 
 Spherical Polygon 64 
 
 The Prismoid 64 
 
 The Prismoidal Formula 64 
 
 Polyedron 64 
 
 Spherical Zone 65 
 
 Spherical Segment 65 
 
 Spheroid or Ellipsoid 65 
 
 Cylindrical Ring 65 
 
 Solids of Revolution 65 
 
 Spindles 65 
 
 Frustrum of a Spheroid 65 
 
 Parabolic Conoid 66 
 
 Volume of a Cask 66 
 
 Irregular Solids 66 
 
 Plane Trigonometry. 
 
 Solution of Plane Triangles 67 
 
 Sine, Tangent, Secant, etc 67 
 
 Signs of the Trigonometric Functions 68 
 
 Trigonometrical Formulae 69 
 
 Solution of Plane Right-angled Triangles 70 
 
 Solution of Oblique-angled Triangles 70 
 
 Analytical Geometry. 
 
 Ordinates and Abscissas 71 
 
 Equations of a Straight Line, Intersections, etc 71 
 
 Equations of the Circle 72 
 
 Equations of the Ellipse 72 
 
 Equations of the Parabola r ........ . 73 
 
 Equations of the Hyperbola , 73 
 
 Logarithmic Curves 74 
 
 Differential Calculus. 
 
 Definitions 74 
 
 Differentials of Algebraic Functions 75 
 
 Formulae for Differentiating 75 
 
 Partial Differentials 76 
 
 Integrals . . . . 76 
 
 Formulae for Integration 76 
 
 Integration between Limits 77 
 
 Quadrature of a Plane Surface 77 
 
 Quadrature of Surfaces of Revolution 78 
 
 Cubature of Volumes of Revolution 78 
 
 Second, Third, etc., Differentials 78 
 
 Maclaurin's and Taylor's Theorems 79 
 
 Maxima and Minima 79 
 
 Differential of an Exponential Function 80 
 
 Logarithms 80 
 
 Differential Forms which have Known Integrals . 81 
 
 Exponential Functions 81 
 
 Circular Functions ....;.... 82 
 
 The Cycloid 82 
 
 Integral Calculus 83 
 
V1U CONTENTS. 
 
 The Slide Rule. 
 
 PAGE 
 
 Examples solved by the Slide Rule 83 
 
 Logarithmic Ruled Paper. 
 
 Plotting on Logarithmic Paper 85 
 
 Mathematical Tables. 
 
 Formula for Interpolation 87 
 
 Reciprocals of Numbers 1 to 2000 '. 88 
 
 Squares, Cubes, Square Roots, and Cube Roots from 0.1 to 1600. . . 94 
 
 Squares and Cubes of Decimals a ; . 109 
 
 Fifth Roots and Fifth Powers 110 
 
 Circumferences and Areas of Circles Ill 
 
 Circumferences of Circles in Feet and Inches' from 1 inch to 32 feet 
 
 11 inches in diameter \20 
 
 Areas of the Segments of a Circle 121 
 
 Lengths of Circular Arcs, Degrees Given 122 
 
 Lengths of Circular Arcs, Height of Arc Given 124 
 
 Spheres . . . . 125 
 
 Contents of Pipes and Cylinders, Cubic Feet and Gallons 127 
 
 Cylindrical Vessels, Tanks, Cisterns, etc 128 
 
 Gallons in a Number of Cubic Feet 129 
 
 Cubic Feet in a Number of Gallons 129 
 
 Square Feet in Plates 3 to 32 feet long and 1 inch wide 130 
 
 Capacities of Rectangular Tanks in Gallons 132 
 
 Number of Barrels in Cylindrical Cisterns and Tanks 133 
 
 Logarithms 134 
 
 Table of Logarithms 136 
 
 Hyperbolic Logarithms 163 
 
 Natural Trigonometrical Functions 166 
 
 Logarithmic Trigonometrical Functions 169 
 
 Materials. 
 
 Chemical Elements 170 
 
 Specific Gravity and Weight of Materials 171 
 
 The Hydrometer 172 
 
 Metals, Properties of 174 
 
 Aluminum 174 
 
 Antimony 175 
 
 Bismuth 175 
 
 Cadmium 175 
 
 Copper 175 
 
 Gold 175 
 
 Iridium 175 
 
 Iron 175 
 
 Lead 175 
 
 Magnesium 176 
 
 Manganese 176 
 
 Mercury 176 
 
 Nickel 176 
 
 Platinum 176 
 
 Silver 176 
 
 Tin 176 
 
 Zinc 177 
 
 Miscellaneous Materials. 
 
 Order of Malleability, etc., of Metals 177 
 
 Measures and Weights of Various Materials 177 
 
 Formulae and Table for Calculating Weight of Rods, Plates, etc .... 178 
 
 Commercial Sizes of Iron and Steel Bars 179 
 
 Weights of Iron Bars 180 
 
 of Iron and Steel Sheets 181 
 
 of Flat Rolled Iron 182 
 
 of Plate Iron 184 
 
 of Steel Blooms 185 
 
 
CONTENTS. IX 
 
 PAGE 
 
 Sizes and Weights of Roofing Materials 186 
 
 Terra-cotta 186 
 
 Tiles 186 
 
 Tin Plates 187 
 
 Slates 189 
 
 Pine Shingles 189 
 
 Sky-light Glass 190 
 
 Weights of Various Roof-coverings 190 
 
 " Cast-iron Pipes or Columns 191 
 
 Weights and Thickness of Cast-iron Pipes 192 
 
 Safe Pressures on Cast-iron Pipe 194 
 
 Cast-iron Pipe Fittings 196 
 
 Standard Pipe Flanges 197 
 
 Straight-way Gate Valves 199 
 
 Forged Steel Flanges 200 
 
 Standard Hose Couplings 207 
 
 Standard Sizes of Welded Pipe 208 
 
 Wrought-iron Welded Tubes 209 
 
 Shelby Cold-drawn Tubing 210 
 
 Riveted Iron Pipes 211 
 
 Weight of Iron for Riveted Pipe 212 
 
 Spiral Riveted Pipe 212 
 
 Riveted Hydraulic Pipe ■ 212 
 
 Coiled Pipes , 214 
 
 Forged Steel Flanges for Riveted Pipe 214 
 
 Seamless Brass Tubing , 215, 216 
 
 Copper Tubing 216 
 
 Lead and Tin-lined Lead Pipe - 217 
 
 Wooden Stave Pipe 218 
 
 Weight of Copper Rods 218 
 
 Weight of Copper and Brass Wire and Plates 219 
 
 " " Sheet and Bar Brass 220 
 
 " " Aluminium Sheets and Bars 220 
 
 Whitworth Screw-threads 220 
 
 Screw-thread, U. S. Standard 221 
 
 Automobile Screws and Nuts 222 
 
 International Screw-thread 222 
 
 Limit-gauges for Screw-threads 223 
 
 Size of Iron for Standard Bolts 223 
 
 Sizes of Screw-threads for Bolts and Taps 224 
 
 Set Screws and Tap Screws • • • 225 
 
 Acme Screw-thread 226 
 
 Machine Screws, A.S.M.E. Standard 226 
 
 Standard Taps 227 
 
 Machine Screw Heads 228 
 
 Weight of Bolts with Heads 229 
 
 Round Head Rivets 229 
 
 Track Bolts 230 
 
 Washers 230 
 
 Weights of Cone-head Rivets 231 
 
 Sizes of Turnbuckles 231 
 
 Tinners' Rivets 232 
 
 Material Required per Mile of Railroad Track 232 
 
 Railway Spikes 233 
 
 Boat Spikes 233 
 
 Wrought Spikes 233 
 
 Cut Nails 234 
 
 Wood Screws 234 
 
 Lag Screws 234 
 
 Wire Nails 235, 236 
 
 Steel Wire, Size, Strength, etc 237 
 
 Galvanized Iron Telegraph Wire 238 
 
 Tests of Telegraph Wire 238 
 
 Specifications for Galvanized Iron Wire 239 
 
 Strength of Piano Wire 239 
 
 Plough-steel Wire 239 
 
 Copper Wire Table, Edison or Circular-mil Gauge 240 
 
X CONTENTS. 
 
 PAGE 
 
 Insulated Wire 241 
 
 Copper Telegraph Wire 241 
 
 Stranded Copper Feed Wire 242 
 
 Rule for Resistance of Copper Wire 242 
 
 Wires of Different Metals . . '. '. . .'.'.'.'.'.'. '.'.'.'..* \ 243 
 
 Specirications for Copper Wire . . . , .' . . 243 
 
 Wire Ropes . . 244 
 
 Transmission or Haulage Rope ' . 245 
 
 Plough-steel Ropes 246 
 
 Lang Lay Rope . . . 246 
 
 Galvanized Iron Wire Rope 247 
 
 Cable Traction Ropes 247 
 
 Flat Wire Ropes 248 
 
 Galvanized Steel Cables 248 
 
 Steel Hawsers 249 
 
 Galvanized Steel-wire Strand 249 
 
 Notes on use of Wire Rope . '. 250 
 
 Locked Wire Rope ........ , 250 
 
 Chains and. Chain Cables 251 
 
 Sizes of Fire Brick 253 
 
 Weights of Logs, Lumber,, etc 254, 255 
 
 Fire Clay„ in Analysis 255 
 
 Refractoriness of American Fire-brick 255 
 
 Slag Bricks and Slag Blocks 256 
 
 Magnesia Bricks. 257 
 
 Asbestos , , 257 
 
 Strength of Materials. 
 
 Stress and Strain 258 
 
 Elastic Limit ....." 259 
 
 Yield Point 259 
 
 Modulus of Elasticity 260 
 
 Resilience 260 
 
 Elastic Limit and Ultimate Stress 261 
 
 Repeated Stresses 261 
 
 Repeated Shocks 262 
 
 Stresses due to Sudden Shocks 263 
 
 Increasing Tensile Strength of Bars by Twisting 264 
 
 Tensile Strength 265 
 
 Measurement of Elongation 265 
 
 Shapes of Test Specimens ..." 266 
 
 Compressive Strength 267 
 
 Columns, Pillars, or Struts 269 
 
 Hodgkinson's Formula. Euler's Formula 269 
 
 Gordon's Formula. Rankine's Formula. . 270 
 
 Wrought-iron Columns 271 
 
 Built Columns ..;'..' 271 
 
 The Straight-line Formula 271 
 
 Working Strains in Bridge Members . 272 
 
 Strength of Cast-iron Columns 274 
 
 Safe Load on Cast-iron Columns 276 
 
 Strength of Brackets on Cast-iron Columns 277 
 
 Eccentric Loading of Columns 278 
 
 Moment of Inertia 279 
 
 Radius of Gyration . 279 
 
 Elements of Usual Sections 280 
 
 Transverse Strength . : 282 
 
 Formulge for Flexure of Beams 282 
 
 Safe Loads on Steel Beams . . . / 284 
 
 Beams of Uniform Strength :...... 286 
 
 Properties of Rolled Structural Shapes . 287 
 
 " Steel I Beams . . . 288 
 
 Spacing of Steel I Beams 291 
 
 Properties of Steel Channels 292 
 
 " " T Shapes 294 
 
 " '* Angles 295 
 
 " •' Z-bars . 299 
 
CONTENTS. XI 
 
 PAGE 
 
 Dimensions of Z-bar Columns ; 300 
 
 Dimensions and Safe Load on Channel Columns 305 
 
 Bethlehem Special, Girder and H-beams 306 
 
 Torsional Strength 311 
 
 Elastic Resistance to Torsion 311 
 
 Combined Stresses 312 
 
 Stress due to Temperature 312 
 
 Strength of Flat Plates 313 
 
 Thickness of Flat Cast-iron Plates 313 
 
 Strength of Unstayed Flat Surfaces 314 
 
 Unbraced Heads of Boilers 314 
 
 Strength of Stayed Surfaces 315 
 
 Stresses in Steel Plating under Water Pressure 315 
 
 Spherical Shells and Domed Heads 316 
 
 Thick Hollow Cylinders under Tension 316 
 
 Thin Cylinders under Tension 317 
 
 Carrying Capacity of Steel Rollers and Balls 317 
 
 Resistance of Hollow Cylinders to Collapse 318 
 
 Collapsing Pressure of Tubes or Flues 319 
 
 Formula for Corrugated Furnaces 193 
 
 Hollow Copper Balls 322 
 
 Holding Power of Nails, Spikes, Bolts, and Screws 323 
 
 Cut versus Wire Nails 324 
 
 Strength of Wrought-iron Bolts 325, 326 
 
 Initial Strain on Bolts , 325 
 
 Stand Pipes and their Design , 327 
 
 Riveted Steel Water-pipes . ., 329 
 
 Kirkaldy's Tests of Materials . 330 
 
 Cast Iron. 330 
 
 Iron Castings 330 
 
 Iron Bars, Forgings, etc 330 
 
 Steel Rails and Tires r 331 
 
 ; Steel Axles, Shafts, Spring Steel 332 
 
 Riveted Joints . 333 
 
 Welds.. . . .'. ; 333 
 
 Copper, Brass, Bronze, etc . . . . 334 
 
 Wire-rope 334 
 
 Wire. 335 
 
 Ropes, Hemp, and Cotton . 335 
 
 Belting-Canvas ... 335 
 
 Stones, Brick, Cement 335 
 
 Wood 336 
 
 Tensile Strength of Wire 336 
 
 Watertown Testing-machine Tests 337 
 
 Riveted Joints , 337. 
 
 Wrought-iron Bars, Compression Tests 1 . . 337 
 
 Steel Eye-bars 338 
 
 Wrought-iron Columns 338 
 
 Cold Drawn Steel 339 
 
 Tests of Steel Angles 340 
 
 Shearing Strength 340 
 
 Relation of Shearing to Tensile Strength 340 
 
 Strength of Iron and Steel Pipe 341 
 
 Threading Tests of Pipe 341 
 
 Old Tubes used as Columns 341 
 
 Methods of Testing Hardness of Metals 342 
 
 Holding Power of Boiler-tubes 342 
 
 Strength of Glass 343 
 
 Strength of Ice 344 
 
 Copper at High Temperatures 344 
 
 Strength of Timber ...;...... 344 
 
 Expansion of Timber 345 
 
 Tests of American Woods. 346 
 
 Shearing Strength of Woods 347 
 
 Strength of Brick, Stone, etc 347 
 
 "Flagging. 350 
 
 " " Lime and Cement Mortar 350. 
 
Xll CONTENTS. 
 
 PAGE 
 
 Moduli of Elasticity of Various Materials 351 
 
 Tests of Portland Cement 351 
 
 Factors of Safety 352 
 
 Properties of Cork 355 
 
 Vulcanized India- Rubber 356 
 
 Nickel 357 
 
 Aluminum, Properties and Uses 357 
 
 Alloys. 
 
 Alloys of Copper and Tin, Bronze 360 
 
 Alloys of Copper and Zinc, Brass 362 
 
 Variation in Strength of Bronze 362 
 
 Copper-tin-zinc Alloys 363 
 
 Liquation, or Separation of Metals 364 
 
 Alloys used in Brass Foundries 366 
 
 Tobin Bronze 368 
 
 Copper-zinc-iron Alloys 369 
 
 Alloys of Copper, Tin and Lead 369 
 
 Phosphor Bronze 370 
 
 Aluminum Alloys 371 
 
 Alloys for Casting under Pressure 371 
 
 The Thermit Process 372 
 
 Caution as to Strength of Alloys 373 
 
 Alloys -of Aluminum, Silicon and Iron 374 
 
 Tungsten-aluminum Alloys 375 
 
 Aluminum-tin Alloys 375 
 
 Manganese Alloys 376 
 
 Manganese Bronze 377 
 
 German Silver 378 
 
 Copper-nickel Alloys 378 
 
 Alloys of Bismuth , 379 
 
 Fusible Alloys *« 380 
 
 Bearing Metal Alloys 380 
 
 Bearing Metal Practice, 1907 382 
 
 White Metal for Engine Bearings 382 
 
 Alloys containing Antimony 383 
 
 White-metal Alloys 383 
 
 Type-metal 384 
 
 Babbitt metals 384 
 
 Solders 385 
 
 Ropes and Cables. 
 
 Strength of Hemp, Iron, and Steel Ropes 386 
 
 Rope for Hoisting or Transmission 386 
 
 Flat Ropes 387 
 
 Cordage, Technical Terms of , . 388 
 
 Splicing of Ropes 388 
 
 Cargo Hoisting 390 
 
 Working Loads for Manila Rope 390 
 
 Knots 391 
 
 Life of Hoisting and Transmission Rope 391 
 
 Efficiency of Rope Tackles 391 
 
 Splicing Wire Ropes 393 
 
 Springs. 
 
 Laminated Steel Springs 394 
 
 Helical Steel Springs 395 
 
 Carrying Capacity of Springs 396 
 
 Elliptical Springs 399 
 
 Springs to Resist Torsional Force 399 
 
 Helical Springs for Cars, etc 400 
 
 Phosphor-bronze Springs 401 
 
 Chromium-Vanadium Spring Steel 401 
 
 Test of a Vanadium Steel Spring — 401 
 
CONTENTS. 
 
 Riveted Joints. 
 
 PAGE 
 
 Fairbairn's Experiments 401 
 
 Loss of Strength by Punching 401 
 
 Strength of Perforated Plates 402 
 
 Hand vs. Hydraulic Riveting 402 
 
 Formulas for Pitch of Rivets 404 
 
 Proportions of Joints 405 
 
 Efficiencies of Joints 405 
 
 Diameter of Rivets 406 
 
 Shearing Resistance of Rivet Iron and Steel 407 
 
 Strength of Riveted Joints 408 
 
 Riveting Pressures 412 
 
 Iron and Steel. 
 
 Classification of Iron and Steel 413 
 
 Grading of Pig Iron 414 
 
 Manufacture of Cast Iron 414 
 
 Influence of Silicon Sulphur, Phos. and Mn on Cast Iron 415 
 
 Microscopic Constituents 416 
 
 Analyses of Cast Iron 416 
 
 Specifications for Pig Iron and Castings 418 
 
 Specifications for Cast-iron Pipe 419 
 
 Strength of Cast Iron 421, 427 
 
 Strength in relation to Cross-section 422 
 
 Shrinkage of Cast Iron 423 
 
 White Iron Converted into Gray 424 
 
 Mobility of Molecules of Cast Iron 424 
 
 Castings from Blast Furnace Metal . 425 
 
 Effect of Cupola Melting 425 
 
 Additions of Titanium, etc., to Cast Iron 426 
 
 " Semi-steel " 428 
 
 Permanent Expansion of Cast Iron by Heating 429 
 
 Mixture of Cast Iron with Steel 429 
 
 Bessemerized Cast Iron 429 
 
 Bad Cast Iron 429 
 
 Malleable Cast Iron 429 
 
 Design of Malleable Castings 433 
 
 Specifications for Malleable Iron 433 
 
 Strength of Malleable Cast Iron 434 
 
 Wrought Iron 435 
 
 Chemistry of Wrought Iron 436 
 
 Influence of Rolling on Wrought Iron 437 
 
 Specifications for Wrought Iron 437 
 
 Stay-bolt Iron 438 
 
 Tenacity of Iron at High Temperatures 439 
 
 Effect of Cold on Strength of Iron 440 
 
 Expansion of Iron by Heat 441 
 
 Durability of Cast Iron 441 
 
 Corrosion of Iron and Steel 442 
 
 Corrosion of Iron and Steel Pipes 443 
 
 Electrolytic Theory, and Prevention of Corrosion 444 
 
 Chrome Paints, Anti-corrosive 445 
 
 Corrosion Caused by Stray Electric Currents 446 
 
 Electrolytic Corrosion due to Overstrain 446 
 
 Preservative Coatings; Paints, etc 447 
 
 Inoxydation Processes, Bower-Barff , etc 448 
 
 Aluminum Coatings 449 
 
 Galvanizing 449 
 
 Sherardizing, Galvanizing by Cementation 450 
 
 Lead Coatings '. 450 
 
 Manufacture of Steel 451 
 
 Crucible, Bessemer and Open Hearth Steel 451 
 
 Steel. 
 
 Relation between Chemical and Physical Properties 452 
 
 Electric Conductivity 453 
 
 Variation in Strength 454 
 
XIV CONTENTS. 
 
 PAGE 
 
 Bending Tests of Steel 454 
 
 Effect of Heat Treatment and of Work 454 
 
 Hardening Soft Steel 455 
 
 Effect of Cold Rolling 455 
 
 Comparison of Full-sized and Small Pieces 455 
 
 Recalescence of Steel 455 
 
 Critical Point . 456 
 
 Metallography 456 
 
 Burning, Overheating, and Restoring Steel 457 
 
 Working Steel at a Blue Heat 458 
 
 Oil Tempering and Annealing 458 
 
 Brittleness due to Long-continued Heating 458 
 
 Influence of Annealing upon Magnetic Capacity 459 
 
 Treatment of Structural Steel 459 
 
 May Carbon be Burned out of Steel ? ., 461 
 
 Effect of Nicking a Bar 461 
 
 Specific Gravity 461 
 
 Welding of Steel 461 
 
 Occasional Failures 462 
 
 Segregation in Ingots and Plates 462 
 
 Endurance of Steel under Repeated Stresses 463 
 
 The Thermit Welding Process 463 
 
 Oxy-acetylene Welding and Cutting of Metals 464 
 
 Hydraulic Forging. . 464 
 
 Fluid-compressed Steel 464 
 
 Steel Castings 464 
 
 Crucible Steel 466 
 
 Effect of Heat on Grain 466 
 
 Heating and Forging 467 
 
 Tempering Steel 468 
 
 Kinds of Steel used for Different Purposes 469 
 
 High-speed Tool Steel 469 
 
 Manganese Steel 470 
 
 Chrome Steel 470 
 
 Nickel Steel 472 
 
 Aluminum Steel 472 
 
 Tungsten Steel 472 
 
 Copper Steel 475 
 
 Nickel- Vanadium Steel 475 
 
 Static and Dynamic Properties of Steel 476 
 
 Strength and Fatigue Resistance of Steels 477 
 
 Chromium-Vanadium Steel 478 
 
 Heat Treatment of Alloy Steels 479 
 
 Specifications for Steel ; 480 
 
 High-strength Steel for Shipbuilding 483 
 
 Fire-box Steel 484 
 
 Steel Rails 484 
 
 MECHANICS. 
 
 Matter, Weight, Mass 487 
 
 Force, Unit of Force 488 
 
 Inertia • 488 
 
 Newton's Laws of Motion 488 
 
 Resolution of Forces 489 
 
 Parallelogram of Forces 489 
 
 Moment of a Force 490 
 
 Statical Moment, Stability 490 
 
 Stability of a Dam 491 
 
 Parallel Forces 491 
 
 Couples 491 
 
 Equilibrium of Forces 492 
 
 Center of Gravity 492 
 
 Moment of Inertia 493 
 
 Centers of Oscillation and Percussion 494 
 
 Center and Radius of Gyration .- 494 
 
 The Pendulum 496 
 
CONTENTS. XV 
 
 PAGE 
 
 Conical Pendulum 496 
 
 Centrifugal Force 497 
 
 Velocity, Acceleration, Falling Bodies 497 
 
 Value of g 498 
 
 Angular Velocity 498 
 
 Height due to Velocity 499 
 
 Parallelogram of Velocities 499 
 
 Velocity due to Falling a Given Height 500 
 
 Mass, Force of Acceleration 501 
 
 Formulae for Accelerated Motion 501 
 
 Motion on Inclined Planes 502 
 
 Momentum, Vis- Viva 502 
 
 Work, Foot-pound 502 
 
 Fundamental Equations in Dynamics . 502 
 
 Power, Horse-power 503 
 
 Energy 503 
 
 Work of Acceleration 504 
 
 Work of Accelerated Rotation 504 
 
 Force of a Blow 504 
 
 Impact of Bodies 505 
 
 Energy of Recoil of Guns 506 
 
 Conservation of Energy 506 
 
 Sources of Energy 506 
 
 Perpetual Motion 507 
 
 Efficiency of a Machine 507 
 
 Animal-power, Man-power 507 
 
 Man-wheel, Tread Mills 508 
 
 Work of a Horse 508 
 
 Horse-gin 509 
 
 Resistance of Vehicles 509 
 
 Elements of Mechanics. 
 
 The Lever 510 
 
 The Bent Lever 511 
 
 The Moving Strut 511 
 
 The Toggle-joint , 511 
 
 The Inclined Plane 512 
 
 The Wedge 512 
 
 The Screw 512 
 
 The Cam 512 
 
 The Pulley 513 
 
 Differential Pulley 513 
 
 Differential Windlass 514 
 
 Differential Screw 514 
 
 Wheel and Axle 514 
 
 Toothed-wheel Gearing 514 
 
 Endless Screw, Worm Gear . 514 
 
 Stresses in Framed Structures. 
 
 Cranes and Derricks 515 
 
 Shear Poles and Guys 516 
 
 King Post Truss or Bridge 517 
 
 Queen Post Truss 517 
 
 Burr Truss 518 
 
 Pratt or Whipple Truss 518 
 
 Method of Moments 519 
 
 Howe Truss : 520 
 
 Warren Girder 520 
 
 Roof Truss 521 
 
 The Economical Angle 522 
 
 HEAT. 
 
 Thermometers and Pyrometers 523 
 
 Centigrade and Fahrenheit degrees compared 524 
 
 Copper-ball Pyrometer 526 
 
 Thermo-electric Pyrometer 526 
 
 Temperatures in Furnaces 527 
 
CONTENTS. 
 
 PAGE 
 
 „ ir's Fire-clay Pyrometer 528 
 
 Wiborgh Air Pyrometer 528 
 
 Mesure and Nouel's Pyrometer 529 
 
 Uehling and Steinbart Pyrometer 530 
 
 Air-thermometer 530 
 
 High Temperatures judged by Color 531 
 
 Boiling-points of Substances 532 
 
 Melting-points 532 
 
 Unit of Heat 532 
 
 Mechanical Equivalent of Heat 532 
 
 Heat of Combustion 533 
 
 Heat Absorbed by Decomposition 534 
 
 Specific Heat 534 
 
 Thermal Capacity of Gases 537 
 
 Expansion by Heat 538 
 
 Absolute Temperature, Absolute Zero 540 
 
 Latent Heat of Fusion 541 
 
 Latent Heat of Evaporation 542 
 
 Total Heat of Evaporation 542 
 
 Evaporation and Drying 542 
 
 Evaporation from Reservoirs 543 
 
 Evaporation by the Multiple System 543 
 
 Resistance to Boiling 543 
 
 Manufacture of Salt 543 
 
 Solubility of Salt 544 
 
 Salt Contents of Brines 545 
 
 Concentration of Sugar Solutions 545 
 
 Evaporating by Exhaust Steam 545 
 
 Drying in Vacuum 546 
 
 Driers and Drying 547 
 
 Design of Drying Apparatus 550 
 
 Humidity Table 551 
 
 Radiation of Heat 551 
 
 Black-body Radiation : 552 
 
 Conduction and Convection of Heat 553 
 
 Rate of External Conduction 554 
 
 Heat Conduction of Insulating Materials 555, 556 
 
 Heat Resistance, Reciprocal of Heat Conductivity 556 
 
 Steam-pipe Coverings 558 
 
 Transmission through Plates . . 561 
 
 Transmission in Condenser Tubes 563 
 
 Transmission of Heat in Feed-water Heaters 564 
 
 Transmission through Cast-iron Plates 565 
 
 Heating Water by Steam Coils 565 
 
 Transmission from Air or Gases to Water 566 
 
 Transmission from Flame to Water 567 
 
 Cooling of Air 568 
 
 Transmission from Steam or Hot Water to Air 569 
 
 Thermodynamics 572 
 
 Entropy 573 
 
 Reversed Carnot Cycle, Refrigeration 574 
 
 Principal Equations of a Perfect Gas 575 
 
 Construction of the Curve PV n = C 576 
 
 Temperature-Entropy Diagram of Water and Steam 576 
 
 PHYSICAL PROPERTIES OF GASES. 
 
 Expansion of Gases 577 
 
 Boyle and Marriotte's Law 577 
 
 Law of Charles, Avogadro's Law 578 
 
 Saturation Point of Vapors 578 
 
 Law of Gaseous Pressure 578 
 
 Flow of Gases 579 
 
 Absorption by Liquids 579 
 
 Liquefaction of Gases, Liquid Air 579 
 
 AIR. 
 
 Properties of Air 580 
 
 Afr-manorneter. 581 
 
CONTENTS. XV11 
 
 PAGE 
 
 Barometric Pressures 581 
 
 Pressure at Different Altitudes 582 
 
 Leveling by the Barometer and by Boiling Water 582 
 
 To find Difference in Altitude 582 
 
 Moisture in Atmosphere 583 
 
 Weight of Air and Mixtures of Air and Vapor 584, 586 
 
 Specific Heat of Air 587 
 
 Flow of Air. 
 
 Flow of Air through Orifices 588 
 
 Flow of Air in Pipes 591 
 
 Effects of Bends in Pipe 593 
 
 Flow of Compressed Air 593 
 
 Tables of Flow of Air 594 
 
 Loss of Pressure in Pipes 595 
 
 Anemometer Measurements 596 
 
 Equalization of Pipes 597 
 
 Wind. 
 
 Force of the Wind 597 
 
 Wind Pressure in Storms 598 
 
 Windmills 599 
 
 Capacity of Windmills 601 
 
 Economy of Windmills 601 
 
 Electric Power from Windmills 603 
 
 Compressed Air. 
 
 Heating of Air by Compression 604 
 
 Loss of Energy in Compressed Air 604 
 
 Volumes and Pressures 605 
 
 Loss due to Heating 606 
 
 Horse-power Required for Compression 606 
 
 Work of Adiabatic Compression of Air 607 
 
 Compressed-air Engines 608 
 
 Compound Air-compression 609 
 
 Table for Adiabatic Compression 610 
 
 Mean Effective Pressures 610 
 
 Mean and Terminal Pressures 611 
 
 Air-compression at Altitudes 611 
 
 Popp Compressed-air System : 612 
 
 Small Compressed-air Motors 612 
 
 Efficiency of Air-heating Stoves 612 
 
 Efficiency of Compressed-air Transmission 613 
 
 Efficiency of Compressed-air Engines 613 
 
 Air-compressors 614 
 
 Requirements of Rock-drills 616 
 
 Steam Required to Compress 1 Cu. Ft. of Air 617 
 
 Compressed air for Pumping Plants 617 
 
 Compressed air for Hoisting Engines 618 
 
 Practical Results with Air Transmission 619 
 
 Effect of Intake Temperature 619 
 
 Compressed air Motors with Return Circuit 620 
 
 Intercoolers for Air-compressors 620 
 
 Centrifugal Air-compressors 620 
 
 High-pressure Centrifugal Fans 621 
 
 Test of a Hydraulic Air-compressor 622 
 
 Pneumatic Postal Transmission 624 
 
 Mekarski Compressed-air Tramways 624 
 
 Compressed Air Working Pumps in Mines 625 
 
 Compressed Air for Street Railways , 625 
 
 Fans and Blowers. 
 
 Centrifugal Fans 626 
 
 Best Proportions of Fans 626 
 
 Pressure due to Velocity , 627 
 
 Experiments with Blowers 629 
 
XV111 CONTENTS. 
 
 PAGE 
 
 Blast Area or Capacity Area 629 
 
 Quantity of Air Delivered 630 
 
 Efficiency of Fans and Positive Blowers 631 
 
 Capacity of Fans and Blowers 632 
 
 Table of Centrifugal Fans 632 
 
 Steel Pressure Blowers for Cupolas 633 
 
 Sturtevant Steel Pressure-blower 635 
 
 Effect of Resistance on Capacity of Fans 636 
 
 Sirocco Fans 636 
 
 Multivane Fans 638 
 
 Methods of Testing Fans 639 
 
 Efficiency of Fans 641 
 
 Diameter of Blast-pipes 643 
 
 Centrifugal Ventilators for Mines 644 
 
 Experiments on Mine Ventilators 645 
 
 Disk Fans 647 
 
 Efficiency of Disk Fans 648 
 
 Positive Rotary Blowers 649 
 
 Steam-jet Blowers „ 651 
 
 Blowing Engines 652 
 
 Steam-jet for Ventilation . 652 
 
 HEATING AND VENTILATION. 
 
 Ventilation 653 
 
 Quantity of Air Discharged through a Ventilating Duct 655 
 
 Heating and Ventilating of Large Buildings 656 
 
 Standards for Calculating Heating Problems 658 
 
 Heating Value of Coal 658 
 
 Heat Transmission through Walls, etc 659 
 
 Allowance for Exposure and Leakage 660 
 
 Heating by Hot-air Furnaces 661 
 
 Carrying Capacity of Air-pipes 662 
 
 Volume of Air at Different Temperatures 663 
 
 Sizes of Pipes Used in Furnace Heating 663 
 
 Furnace Heating with Forced Air Supply 664 
 
 Rated Capacity of Boilers for House Heating 664 
 
 Capacity of Grate Surface 665 
 
 Steam Heating, Rating of Boilers 665 
 
 Testing Cast-iron Heating Boilers 667 
 
 Proportioning House Heating Boilers 667 
 
 Coefficient of Transmission in Direct Radiation 668 
 
 Heat Transmitted in Indirect Radiation 669 
 
 Short Rules for Computing Radiating Surface 669 
 
 Carrying Capacity of Steam Pipes in Low Pressure Heating 669 
 
 Proportioning Pipes to Radiating Surface 671 
 
 Sizes of Pipes in Steam Heating Plants 672 
 
 Resistance of Fittings 672 
 
 Removal of Air, Vacuum Systems 673 
 
 Overhead Steam-pipes 673 
 
 Steam-consumption in Car-heating 673 
 
 Heating a Greenhouse by Steam 673 
 
 Heating a Greenhouse by Hot Water 674 
 
 Velocity of Flow in Hot-water Heating 674 
 
 Hot-water Heating 674 
 
 Sizes of Pipe for Hot-water Heating 675 
 
 Sizes of Flow and Return Pipes 678 
 
 Heating by Hot-water, with Forced Circulation 678 
 
 Blower Svstem of Heating and Ventilating 678 
 
 Advantages and Disadvantages of the Plenum System 678 
 
 Heat Radiated from Coils in the Blower System 679 
 
 Test of Cast-iron Heaters for Hot-blast Work 680 
 
 Factory Heating by the Fan System 681 
 
 Artificial Cooling of Air 681 
 
 Capacities of Fans for Hot-blast Heating 682 
 
 Relative Efficiency of Fans and Heated Chimneys 683 
 
 Heating a Building to 70° F .. ..,..., •. • 683 
 
CONTENTS. XIX 
 
 ™ . PAGE 
 
 Heating by Electricity 684 
 
 Mine-ventilation 685 
 
 ; Friction of Air in Underground Passages 685 
 
 Equivalent Orifices 686 
 
 WATER. 
 
 Expansion of Water . . . . . 687 
 
 Weight of Water at Different Temperatures 687, 688 
 
 Pressure of Water due to its Weight 689, 690 
 
 Head Corresponding to Pressures 689 
 
 Buoyancy 690 
 
 Boiling-point 690 
 
 Freezing-point . 690 
 
 Sea-water . . -...=.- 690 
 
 Ice and Snow . .' 691 
 
 Specific Heat of Water ... . . . 691 
 
 Compressibility of Water ..-. . 691 
 
 Impurities- of Water .... . . . . .-. .-. 691 
 
 Causes of Incrustation 692 
 
 Means for Preventing Incrustation 692 
 
 •Analyses of Boiler-scale -..-...• 693 
 
 Hardness of Water 694 
 
 Purifying Feed-water 7\ 694 
 
 Softening Hard Water , 695 
 
 Hydraulics. Flow of Water. 
 
 Formulae for Discharge through Orifices and Weirs 697 
 
 Flow of Water from Orifices ' 698 
 
 Flow in Open and Closed Channels 699 
 
 General Formulae for Flow 699 
 
 Chezy's Formula 699 
 
 Values of the Coefficient c . 699, 703 
 
 Table, Fall in Feet per mile, etc. 700 
 
 Values of Vr for Circular Pipes 701 
 
 Kutter's Formula 701 
 
 D'Arcy's Formula 704 
 
 Velocity of Water in Open Channels 704 
 
 Mean Surface and Bottom Velocities 704 
 
 Safe Bottom and Mean Velocities . 705 
 
 Resistance of Soil to Erosion 705 
 
 Abrading and Transporting Power of Water 705 
 
 Grade of Sewers 706 
 
 Flow of Water in a 20-inch Pipe 706 
 
 Table of Flow of Water in Circular Pipes 707-711 
 
 Short Formulae 710 
 
 Flow of Water in House-service pipes 712 
 
 Flow of Water through Nozzles 713 
 
 Loss of Head 714 
 
 Values of the Coefficient of Friction 715 
 
 Resistance at the Inlet of a Pipe 715 
 
 Flow of Water in Riveted Pipes 716 
 
 Cox's Formula 717 
 
 Exponential Formulae 718 
 
 Friction Loss in Clean Cast-iron Pipe 719 
 
 Approximate Hydraulic Formulae 720 
 
 Compound Pipes, and Pipes with Branches 720 
 
 Effect of Bend and Curves 721 
 
 Hydraulic Grade-line 721 
 
 Long Pipe Lines 721 
 
 Rifled Pipes for Conveying Oils 721 
 
 Loss of Pressure Caused by Valves, etc 721 
 
 Air-bound Pipes .. , 722 
 
 Vertical Jets 722 
 
 Water Delivered through Meters 722 
 
 ■ Fire Streams , 722 
 
 Water Hammer . . 722 
 
XX CONTENTS. 
 
 PAGE 
 
 Price Charged for Water in Cities 722 
 
 Hydrant Pressures required with Different Lengths and Sizes of 
 
 Hose 723 
 
 Friction Losses in Hose 725 
 
 Pump Inspection Table , 725 
 
 Rated Capacity of Steam Fire-engines 725 
 
 The Siphon . 726 
 
 Measurement of Flowing Water 727 
 
 Piezometer 727 
 
 Pitot Tube Gauge 727 
 
 Maximum and Mean Velocities in Pipes 727 
 
 The Venturi Meter 728 
 
 Measurement of Discharge by Means of Nozzles 728 
 
 Flow through Rectangular Orifices 729 
 
 Measurement of an Open Stream 729 
 
 Miners' Inch Measurements 730 
 
 Flow of Water over Weirs 731 
 
 Francis's Formula for Weirs 731 
 
 Weir Table , 732 
 
 Bazin's Experiments 733 
 
 The Cippoleti, or Trapezoidal Weir 733 
 
 Water-power. 
 
 Power of a Fall of Water 734 
 
 Horse-power of a Running Stream 734 
 
 Current Motors 734 
 
 Bernoulli's Theorem 734 
 
 Maximum Efficiency of a Long Conduit 735 
 
 Mill-power 735 
 
 Value of Water-power 735 
 
 Water Wheels; Turbine Wheels. 
 
 Water Wheels 737 
 
 Proportions of Turbines 737 
 
 Tests of Turbines 742 
 
 Dimensions of Turbines 743 
 
 Rating and Efficiency of Turbines 743 
 
 Rating Table for Turbines 746 
 
 Turbines of 13,500 H.P. each 747 
 
 The Fall-increaser for Turbines 747 
 
 Tangential or Impulse Water Wheel 748 
 
 The Pelton Water Wheel 748 
 
 Considerations in the Choice of a Tangential Wheel 749 
 
 Control of Tangential Water Wheels 750 
 
 Tangential Water-wheel Table 751 
 
 Amount of Water Required to Develop a given Horse- Power 753 
 
 Efficiency of the Doble Nozzle 753 
 
 Water Plants Operating under High Pressure 754 
 
 Formulae for Calculating the Power of Jet Water Wheels 754 
 
 The Power of Ocean Waves. 
 
 Utilization of Tidal Power 756 
 
 Pumps. 
 
 Theoretical Capacity of a Pump 757 
 
 Depth of Suction 757 
 
 The Deane Pump 758 
 
 Amount of Water Raised by a Single-acting Lift-pump 759 
 
 Proportioning the Steam-cylinder of a Direct-acting Pump 759 
 
 Speed of Water through Pipes and Pump-passages 759 
 
 Sizes of Direct-acting Pumps 759 
 
 Efficiency of Small Pumps 759 
 
 The Worthington Duplex Pump 760 
 
 Speed of Piston 760 
 
 Speed of Water through Valves 761 
 
CONTENTS. XXI 
 
 PAGE 
 
 Boiler-feed Pumps - 761 
 
 Pump Valves 762 
 
 The Worthington High-duty Pumping Engine 762 
 
 The d'Auria Pumping Engine 762 
 
 A 72,000,000-Gallon Pumping Engine 762 
 
 The Screw Pumping Engine 763 
 
 Finance of Pumping Engine Economy 763 
 
 Cost of Pumping 1000 Gallons per minute 764 
 
 Centrifugal Pumps 764 
 
 Design of a Four-stage Turbine Pump 765 
 
 Relation of Peripheral Speed to Head 766 
 
 Tests of De Laval Centrifugal Pump 768 
 
 A High-duty Centrifugal Pump 770 
 
 Rotary Pumps 770 
 
 Tests of Centrifugal and Rotary Pumps 770 
 
 Duty Trials of Pumping Engines 771 
 
 Leakage Tests of Pumps 772 
 
 Notable High-duty Pump Records 774 
 
 Vacuum Pumps 775 
 
 The Pulsometer 775 
 
 Pumping by Compressed Air 776 
 
 The Jet Pump 776 
 
 The Injector 776 
 
 Air-lift Pump 776 
 
 Air-lifts for Deep Oil-wells 777 
 
 The Hydraulic Ram 778 
 
 Quantity of Water Delivered by the Hydraulic Ram 778 
 
 Hydraulic Pressure Transmission. 
 
 Energy of Water under Pressure 779 
 
 Efficiency of Apparatus 780 
 
 Hydraulic Presses 781 
 
 Hydraulic Power in London 781 
 
 Hydraulic Riveting Machines : 782 
 
 Hydraulic Forging 782 
 
 Hydraulic Engine 783 
 
 FUEL. 
 
 Theory of Combustion 784 
 
 Analyses of the Gases of Combustion 785 
 
 Temperature of the Fire 785 
 
 Classification of Solid Fuels 786 
 
 Classification of Coals 786 
 
 Analyses of Coals 787 
 
 Caking and Non-caking Coals 788 
 
 Cannel Coals 788 
 
 Rhode Island Graphitic Anthracite 788 
 
 Analysis and Heating Value of Coals 789 
 
 Approximate Heating Values 791 
 
 Tests of the U. S. Geological Survey 791 
 
 Lord and Haas's Tests 792 
 
 Sizes of Anthracite Coal 792 
 
 Space occupied by Anthracite 793 
 
 Bernice Basin, Pa., Coal 793 
 
 Connellsville Coal and Coke 793 
 
 Bituminous Coals of the United States 794 
 
 Western Lignites 796 
 
 Analysis of Foreign Coals 796 
 
 Sampling Coal for Analyses 797 
 
 Relative Value of Steam Coals 797 
 
 Calorimetric Tests of Coals 797 
 
 Purchase of Coal Under Specifications 799 
 
 Evaporative Power of Bituminous Coals 799 
 
 Weathering of Coal 800 
 
 Pressed Fuel , 801 
 
XX11 CONTENTS. 
 
 PAGE 
 
 Coke . 801 
 
 Experiments in Coking 802 
 
 Coal Washing 802 
 
 Recovery of By-products in Coke Manufacture 802 
 
 Generation of Steam from the Waste Heat and Gases from Coke- 
 ovens 803 
 
 Products of the Distillation of Coal 803 
 
 Wood as Fuel 804 
 
 Heating Value of Wood „ 804 
 
 Composition of Wood 805 
 
 Charcoal 805 
 
 Yield of Charcoal from a Cord of Wood 806 
 
 Consumption of Charcoal in Blast Furnaces 806 
 
 Absorption of Water and of Gases by Charcoal 806 
 
 Composition of Charcoals 807 
 
 Miscellaneous Solid Fuels 807 
 
 Dust-fuel — Dust Explosions 807 
 
 Peat or Turf 808 
 
 Sawdust as Fuel 808 
 
 Wet Tan-bark as Fuel 808 
 
 Straw as Fuel 808 
 
 Bagasse as Fuel in Sugar Manufacture 809 
 
 Liquid Fuel. 
 
 Products of Distillation of Petroleum 810 
 
 Lima Petroleum 810 
 
 Value of Petroleum as Fuel 811 
 
 Fuel Oil Burners 812 
 
 Oil vs. Coal as Fuel 812 
 
 Alcohol as Fuel 813 
 
 Specific Gravity of Ethyl Alcohol 813 
 
 Vapor Pressures of Saturation of Alcohol and other Liquids 814 
 
 Fuel Gas. 
 
 Carbon Gas 814 
 
 Anthracite Gas 815 
 
 Bituminous -Gas 816 
 
 Water Gas 817 
 
 Natural Gas in Ohio and Indiana 817 
 
 Natural Gas as a Fuel for Boilers -. 817 
 
 Producer-gas from One Ton of Coal 818 
 
 Proportions of Gas Producers and Scrubbers 819 
 
 Combustion of Producer-gas 819 
 
 Gas Producer Practice 820 
 
 Capacity of Producers 821 
 
 High Temperature Required for Production of C0 2 822 
 
 The Mond Gas Producer 822 
 
 Relative Efficiency of Different Coals in Gas-engine Tests 823 
 
 Use of Steam in Producers and Boiler Furnaces 824 
 
 Gas Fuel for Small Furnaces 824 
 
 Gas Analyses by Volume and by Weight 824 
 
 Blast-furnace Gas 825 
 
 Acetylene and Calcium Carbide. 
 
 Acetvlene 825 
 
 Calcium Carbide 826 
 
 Acetylene Generators and Burners 826 
 
 The Acetylene Blowpipe 827 
 
 Illuminating Gas. 
 
 Coal-gas 828 
 
 Water-gas 829 
 
 Analyses of Water-gas and Coal-gas 830 
 
 Calorific Equivalents of Constituents 830 
 
 Efficiency of a Water-gas Plant . , 830 
 
CONTENTS. XX111 
 
 PAGE 
 
 Space Required for a Water-gas Plant — .... 832 
 
 Fuel-value of Illuminating Gas 833 
 
 Flow of Gas in Pipes . . 834 
 
 Services for Lamps 834 
 
 STEAM. 
 
 Temperature and Pressure 836 
 
 Total Heat 836 
 
 Latent Heat of Steam 836 
 
 Specific Heat of Saturated Steam 837 
 
 The Mechanical Equivalent of Heat 837 
 
 Pressure of Saturated Steam 837 
 
 Volume of Saturated Steam 837 
 
 Volume of Superheated Steam . 837 
 
 Specific Density of Gaseous Steam 838 
 
 Specific Heat of Superheated Steam 838 
 
 Regnault's Experiments '..".'.'. 838 
 
 Table of the Properties of Saturated Steam . 839 
 
 Table of the Properties of Superheated Steam 843 
 
 Flow of Steam. 
 
 Napier's Approximate Rule 844 
 
 Flow of Steam through a Nozzle 844 
 
 Flow of Steam in Pipes 845 
 
 Table of Flow of Steam in Pipes 846 
 
 Carrying Capacity of Extra Heavy Steam Pipes 847 
 
 Flow of Steam in Long Pipes, Ledoux's Formula 847 
 
 Resistance to Flow by Bends, Valves, etc 848 
 
 Sizes of Steam-pipes for Stationary Engines 848 
 
 Sizes of Steam-pipes for Marine Engines 848 
 
 Proportioning Pipes for Minimum Loss by Radiation and Friction . . .849 
 
 Available Maximum Efficiency of Expanded Steam 850 
 
 Steam-pipes. 
 
 Bursting-tests of Copper Steam-pipes 851 
 
 Failure of a Copper Steam-pipe 851 
 
 Wire-wound Steam-pipes 851 
 
 Materials for Pipes and Valves for Superheated Steam 851 
 
 Riveted Steel Steam-pipes 852 
 
 Valves in Steam-pipes 852 
 
 The Steam Loop 852 
 
 Loss from an Uncovered Steam-pipe 853 
 
 Condensation in an Underground Pipe Line 853 
 
 Steam Receivers in Pipe Lines . . . 853 
 
 Equation of Pipes 853 
 
 Identification of Power House Piping by Colors 854 
 
 THE STEAM-BOILER. 
 
 The Horse-power of a Steam-boiler 854 
 
 Measures for Comparing the Duty of Boilers 855 
 
 Steam-boiler Proportions 855 
 
 Unit of Evaporation 855 
 
 Heating-surface . . . 856 
 
 Horse-power, Builders'. Rating . 857 
 
 Grate-surface 857 
 
 Areas of Flues 858 
 
 Air-passages Through Grate-bars 858 
 
 Performance of Boilers . . . 858 
 
 Conditions which Secure Economy 859 
 
 Air Leakage in Boiler Settings 859 
 
 Efficiency of a Boiler . . 860 
 
 Autographic C0 2 Recorders 860 
 
 Relation of Efficiency to Rate of Driving, Air Supply, etc 862 
 
 Tests of Steam-boilers . . 864 
 
XXIV CONTENTS. 
 
 PAGE 
 
 Boilers at the Centennial Exhibition 864 
 
 High Rates of Evaporation 865 
 
 Economy Effected by Heating the Air 865 
 
 Maximum Boiler Efficiency with Cumberland Coal 865 
 
 Boilers Using Waste Gases 865 
 
 Rules for Conducting Boiler Tests 866 
 
 Heat Balance in Boiler Tests 872 
 
 Table of Factors of Evaporation 874 
 
 Strength of Steam-boilers. 
 
 Rules for Construction 879 
 
 Shell-plate Formulae 880 
 
 Rules for Flat Plates 880 
 
 Furnace Formula?- 881 
 
 Material for Stays 882 
 
 Loads allowed on Stays 882 
 
 Girders 882 
 
 Tube Plates . < 882 
 
 Material for Tubes 883 
 
 Holding Power of Boiler Tubes 883 
 
 Iron versus Steel Boiler Tubes 883 
 
 Rules for Construction of Boilers in Merchant Vessels in U. S 884 
 
 Safe-working Pressures 887 
 
 Flat-stayed Surfaces 888 
 
 Diameter of Stay-bolts 888 
 
 Strength of Stays 888 
 
 Boiler Attachments, Furnaces, etc. 
 
 Fusible Plugs 889 
 
 Steam Domes 889 
 
 Height of Furnace 889 
 
 Mechanical Stokers 889 
 
 The Hawley Down-draught Furnace 890 
 
 Under-feed Stokers 890 
 
 Smoke Prevention 890 
 
 Burning Illinois Coal without Smoke 892 
 
 Conditions of Smoke Prevention 893 
 
 Forced Combustion 894 
 
 Fuel Economizers 894 
 
 Thermal Storage 897 
 
 Incrustation and Corrosion 897 
 
 Boiler-scale Compounds 898 
 
 Removal of Hard Scale 900 
 
 Corrosion in Marine Boilers 900 
 
 Use of Zinc 901 
 
 Effect of Deposit on Flues 901 
 
 Dangerous Boilers 901 
 
 Safety-valves. 
 
 Rules for Area of Safety-valves 902 
 
 Spring-loaded Safety-valves 904 
 
 The Injector. 
 
 Equation of the Injector 906 
 
 Performance of Injectors 907 
 
 Boiler-feeding Pumps 908 
 
 Feed-water Heaters. 
 
 Percentage of Saving Due to Use of Heaters 909 
 
 Strains Caused by Cold Feed-water 909 
 
 Calculation of Surface of Heaters and Condensers 910 
 
 Open vs. Closed Feed-water Heaters 911 
 
 Steam Separators. 
 
 Efficiency of Steam Separators 911 
 
CONTENTS. XXV 
 
 Determination of Moisture in Steam. 
 
 Steam Calorimeters 912 
 
 Coil Calorimeter 913 
 
 Throttling Calorimeters 913 
 
 Separating Calorimeters 914 
 
 Identification of Dry Steam 915 
 
 Usual Amount of Moisture in Steam 915 
 
 Chimneys. 
 
 Chimney Draught Theory 915 
 
 Force or Intensity of Draught 916 
 
 Rate of Combustion Due to Height of Chimney 918 
 
 High Chimneys not Necessary „ 919 
 
 Height of Chimneys Required for Different Fuels 919 
 
 Protection of Chimney from Lightning 920 
 
 Table of Size of Chimneys 921 
 
 Some Tall Brick Chimneys 922 
 
 Stability of Chimneys 924 
 
 Steel Chimneys 925 
 
 Reinforced Concrete Chimneys 927 
 
 Sheet-iron Chimneys 928 
 
 THE STEAM ENGINE. 
 
 Expansion of Steam 929 
 
 Mean and Terminal Absolute Pressures 930 
 
 Calculation of Mean Effective Pressure •. . 931 
 
 Mechanical Energy of Steam Expanded Adiabatically 933 
 
 Measures for Comparing the Duty of Engines 933 
 
 Efficiency, Thermal Units per Minute 934 
 
 Real Ratio of Expansion 935 
 
 Effect of Compression 935 
 
 Clearance in Low- and High-speed Engines 936 
 
 Cylinder-condensation 936 
 
 Water-consumption of Automatic Cut-off Engines 937 
 
 Experiments on Cylinder-condensation 937 
 
 Indicator Diagrams 938 
 
 Errors of Indicators 939 
 
 Pendulum Indicator Rig 939 
 
 The Manograph 939 
 
 The Lea Continuous Recorder , 940 
 
 Indicated Horse-power 940 
 
 Rules for. Estimating Horse-power 940 
 
 Horse-power Constants 941 
 
 Table of Engine Constants 942 
 
 To Draw Clearance on Indicator-diagram 944 
 
 To Draw Hyperbola Curve on Indicator-diagram 944 
 
 Theoretical Water Consumption 945 
 
 Leakage of Steam 946 
 
 Compound Engines. 
 
 Advantages of Compounding 946 
 
 Woolf and Receiver Types of Engines 947 
 
 Combined Diagrams 949 
 
 Proportions of Cylinders in Compound Engines 950 
 
 Receiver Space 950 
 
 Formula for Calculating Work of Steam 951 
 
 Calculation of Diameters of Cylinders 952 
 
 Triple-expansion Engines 953 
 
 Proportions of Cylinders 953 
 
 Formulge for Proportioning Cylinders 953 
 
 Types of Three-stage Expansion Engines 956 
 
 Sequence of Cranks 956 
 
 Velocity of Steam through Passages 956 
 
 A Double-tandem Triple-expansion Engine 956 
 
 Quadruple-expansion Engines 956 
 
XXVI CONTENTS. 
 
 Steam-engine Economy. 
 
 PAGE 
 
 Economic Performance of Steam-engines 957 
 
 Feed-water Consumption of Different Types 957 
 
 Sizes and Calculated Performances of Vertical High-speed Engine . 959 
 
 The Willans Law, Steam Consumption at Different Loads 962 
 
 Relative Economy of Engines under Variable Loads 963 
 
 Steam Consumption of Various Sizes 963 
 
 Steam Consumption in Small Engines 964 
 
 Steam Consumption at Various Speeds 964 
 
 Capacity and Economy of Steam fire Engines 964 
 
 Economy Tests of High-speed Engines 965 
 
 Limitation of Engine Speed 966 
 
 British High-speed Engines 966 
 
 Advantage of High Initial and Low-back Pressure 967 
 
 Comparison of Compound and Single-cylinder Engines 968 
 
 Two-cylinder and Three-cylinder Engines 9"" 
 
 The Lentz Compound Engine 9 
 
 Steam Consumption of Different Types of Engine 9 
 
 Steam Consumption of Engines with Superheated Steam 969 
 
 Efficiency of Non-condensing Compound Engines 971 
 
 Economy of Engines under Varying Loads 971 
 
 Effect of Water in Steam on Efficiency 972 
 
 Influence of Vacuum and Superheat on Steam Consumption 972 
 
 Practical Application of Superheated Steam 973 
 
 Performance of a Quadruple Engine < 974 
 
 Influence of the Steam-jacket 975 
 
 Best Economy of the Piston Steam Engine 977 
 
 Highest Economy of Pumping-engines 978 
 
 Sulphur-dioxide Addendum to Steam-engine 978 
 
 Standard Dimensions of Direct-connected Generator Sets 979 
 
 Dimensions of Parts of Large Engines 979 
 
 Large Rolling-mill Engines 980 
 
 Counterbalancing Engines 980 
 
 Preventing Vibrations of Engines 980 
 
 Foundations Embedded in Air 980 
 
 Most Economical Point of Cut-off 981 
 
 Type of Engine used when Exhaust-steam is used for Heating .... 981 
 
 Cost of Steam-power . . 981, 982 
 
 Cost of Coal for Steam-power 983 
 
 Relative Commercial Economy of Compound and Triple-expansion 
 
 Engines 984 
 
 Power-plant Economics 984 
 
 Economy of Combination of Gas Engines and Turbines 986 
 
 Analysis of Operating Costs of Power-plants 987 
 
 Storing Steam Heat in Hot Water 987 
 
 Utilizing the Sun's Heat as a Source of Power 988 
 
 Rules for Conducting Steam-engine Tests 988 
 
 Dimensions of Parts of Engines. 
 
 Cylinder 996 
 
 Clearance of Piston 996 
 
 Thickness of Cylinder 997 
 
 Cylinder Heads 998 
 
 Cylinder-head Bolts 999 
 
 The Piston . . 999 
 
 Piston Packing-rings 1000 
 
 Fit of Piston-rod 1001 
 
 Diameter of Piston-rods 1002 
 
 Piston-rod Guides 1002 
 
 The Connecting-rod 1003 
 
 Connecting-rod Ends 1005 
 
 Tapered Connecting-rods 1005 
 
 The Crank-pin 1005 
 
 Crosshead-pin or Wrist-pin 1009 
 
 The Crank-arm 1009 
 
 The Shaft, Twisting Resistance 1010 
 
CONTENTS. XXV11 
 
 PAGE 
 
 Resistance to Bending . * . . . . 1012 
 
 Equivalent Twisting Moment 1012 
 
 Fly-wheel Shafts 1013 
 
 Length of Shaft-bearings 1015 
 
 Crank-shafts with Center-crank and Double-crank Arms 1017 
 
 Crank-shaft with two Cranks Coupled at 90° 10 IS 
 
 Crank-shaft with three Cranks at 120° 1019 
 
 Valve-stem or Valve-rod 1019 
 
 Size of Slot-link 1020 
 
 The Eccentric 1020 
 
 The Eccentric-rod 1020 
 
 Reversing-gear ' 1020 
 
 Current Practice in Engine Proportions, 1897 1021 
 
 Current Practice in Steam-engine Design, 1909 1022 
 
 Shafts and Bearings of Engines 1023 
 
 Calculating the Dimensions of Bearings 1024 
 
 Engine-frames or Bed-plates 1025 
 
 Fly-wheels. 
 
 Weight of Fly-wheels 1026 
 
 Weight of Fly-wheels for Alternating-current Units 1028 
 
 Centrifugal Force in Fly-wheels 1029 
 
 Diameters for Various Speeds 1030 
 
 Strains in the Rims 1031 
 
 Arms of Fly-wheels and Pulleys ' . . . . 1032 
 
 Thickness of Rims 10^2 
 
 A Wooden Rim Fly-wheel 1033 
 
 Wire-wound Fly-wheels 1034 
 
 The Slide-valve. 
 
 Definitions, Lap, Lead, etc 1034 
 
 Sweet's Valve-diagram 1036 
 
 The Zeuner Valve-diagram 1036 
 
 Port Opening, Lead, and Inside Lead 1089 
 
 Crank Angles for Connecting-rods of Different Lengths 1040 
 
 Ratio of Lap and of Port-opening to Valve-travel 1041 
 
 Relative Motions of Crosshead and Crank 1042 
 
 Periods of Admission or Cut-off for Various Laps and Travels 1042 
 
 Piston- valves 1043 
 
 Setting the Valves of an Engine 1043 
 
 To put an Engine on its Center , 1043 
 
 Link-motion 1044 
 
 The Walschaert Valve-gear 1046 
 
 Governors. 
 
 Pendulum or Fly-ball Governors 1047 
 
 To Change the Speed of an Engine 1048 
 
 Fly-wheel or Shaft Governors 1048 
 
 The Rites Inertia Governor 1048 
 
 Calculation of Springs for Shaft-governors 1048 
 
 Condensers, Air-pumps, Circulating-pumps, etc. 
 
 The Jet Condenser 1050 
 
 Quantity of Cooling water 1050 
 
 Ejector Condensers 1051 
 
 The Barometric Condensers 1051 
 
 The Surface Condenser 1051 
 
 Coefficient of Heat Transference in Condensers 1052 
 
 The Power Used for Condensing Apparatus . 1053 
 
 Vacuum, Inches of Mercury and Absolute Pressure 1053 
 
 Temperatures, Pressures and Volumes of Saturated Air 1054 
 
 Condenser Tubes . . 1054 
 
 Bimetallic Condenser Tubes ...:." 1055 
 
 Tube-plates 1055 
 
 Spacing of Tubes ; . . 1055 
 
XXV111 CONTENTS. 
 
 PAGE 
 
 Air-pump 1055 
 
 Area through Valve-seats 1056 
 
 The Leblanc Condenser 1057 
 
 Circulating-pump 1057 
 
 Feed-pumps for Marine Engines 1057 
 
 An Evaporative Surface Condenser 1057 
 
 Continuous Use of Condensing Water 1058 
 
 Increase of Power by Condensers 1058 
 
 Advantage of High Vacuum in Reciprocating Engines 1059 
 
 The Choice of a Condenser 1059 
 
 Cooling Towers 1060 
 
 Tests of a Cooling Tower and Condenser 1061 
 
 Evaporators and Distillers 1061 
 
 Rotary Steam Engines — Steam Turbines. 
 
 Rotary Steam Engines 1062 
 
 Impulse and Reaction Turbines 1062 
 
 The DeLaval Turbine 1062 
 
 The Zolley or Rateau Turbine 1062 
 
 The Parsons Turbine 1062 
 
 The Westinghouse Double-flow Turbine 1063 
 
 Mechanical Theory of the Steam Turbine 1063 
 
 Heat Theory of the Steam Turbine 1064 
 
 Velocity of Steam in Nozzles 1065 
 
 Speed of the Blades 1066 
 
 Comparison of Impulse and Reaction Turbines 1066 
 
 Loss due to Windage 1066 
 
 Efficiency of the Machine 1067 
 
 Steam Consumption of Turbines 1067 
 
 The Largest Steam Turbine 1068 
 
 Steam Consumption of Small Steam Turbines 1069 
 
 Low-pressure Steam Turbines 1069 
 
 Tests of a 15,000 K.W. Steam-engine Turbine Unit 1071 
 
 Reduction Gear for Steam Turbines 1071 
 
 Naphtha Engines — Hot-air Engines. 
 
 Naphtha Engines 1071 
 
 Hot-air or Caloric Engines 1071 
 
 Test of a Hot-air Engine 1071 
 
 Internal Combustion Engines. 
 
 Four-cycle and Two-cycle Gas-engines 1072 
 
 Temperatures and Pressures Developed 1072 
 
 Calculation of the Power of Gas-engines 1073 
 
 Pressures and Temperatures at End of Compression 1074 
 
 Pressures and Temperature at Release 1075 
 
 " " " after Combustion 1075 
 
 Mean Effective Pressures 1076 
 
 Sizes of Large Gas-engines 1076 
 
 Engine Constants for Gas-engines 1077 
 
 Rated Capacity of Automobile Engines 1077 
 
 Estimate of the Horse-power of a Gas-engine 1077 
 
 Oil and Gasoline Engines 1077 
 
 The Diesel Oil Engine 1078 
 
 The De La Vergne Oil Engine 1078 
 
 Alcohol Engines 1078 
 
 Ignition 1078 
 
 Timing 1079 
 
 Governing 1079 
 
 Gas and Oil Engine Troubles 1079 
 
 Conditions of Maximum Efficiency 1079 
 
 Heat Losses in the Gas-engine 1080 
 
 Economical Performance of Gas-engines 1080 
 
 Utilization of Waste Heat from Gas-engines 1081 
 
 Rules for Conducting Tests of Gas and Oil Engines 1081 
 
contents. xxix 
 
 locomotives. pagb 
 
 Resistance of Trains 1084 
 
 Resistance of Electric Railway Cars and Trains 1086 
 
 Efficiency of the Mechanism of a Locomotive 1087 
 
 Adhesion 1087 
 
 Tractive Force 1087 
 
 Size of Locomotive Cylinders 1088 
 
 Horse-power of a Locomotive 1089 
 
 Size of Locomotive Boilers 1089 
 
 Wootten's Locomotive 1090 
 
 Grate-surface, Smokestacks, and Exhaust-nozzles 1091 
 
 Fire-brick Arches 1091 
 
 Economy of High Pressures 1092 
 
 Leading American Types . 1092 
 
 Classification of Locomotives 1092 
 
 Steam Distribution for High Speed 1093 
 
 Formulae for Curves 1093 
 
 Speed of Railway Trains 1094 
 
 Performance of a High-speed Locomotive 1094 
 
 Fuel Efficiency of American Locomotives 1095 
 
 Locomotive Link-motion 1095 
 
 Dimensions of Some American Locomotives 1096 
 
 The Mallet Compound Locomotive 1096 
 
 Indicated Water Consumption 1098 
 
 Indicator Tests of a Locomotive at High-speed 1098 
 
 Locomotive Testing Apparatus 1099 
 
 Weights and Prices 'of Locomotives 1100 
 
 Waste of fuel in Locomotives 1101 
 
 Advantages of Compounding 1101 
 
 Depreciation of Locomotives 1101 
 
 Average Train Loads 1101 
 
 Tractive Force of Locomotives, 1893 and 1905 1101 
 
 Superheating in Locomotives 1102 
 
 Counterbalancing Locomotives 1102 
 
 Narrow-gauge Railways 1103 
 
 Petroleum-burning Locomotives 1103 
 
 Fireless Locomotives 1 103 
 
 Self-propelled Railway Cars 1103 
 
 Compressed-air Locomotives 1104 
 
 Air Locomotives with Compound Cylinders 1105 
 
 SHAFTING. 
 
 Diameters to Resist Torsional Strain 1106 
 
 Deflection of Shafting 1107 
 
 Horse-power Transmitted by Shafting 1108 
 
 Flange Couplings 1109 
 
 Effect of Cold Rolling 1109 
 
 Hollow Shafts 1109 
 
 Sizes of Collars for Shafting 1109 
 
 Table for Laying Gut Shafting 1110 
 
 PULLETS. 
 
 Proportions of Pulleys 1111 
 
 Convexity of Pulleys 1112 
 
 Cone or Step Pulleys 1112 
 
 Burmester's Method for Cone Pulleys 1113 
 
 Speeds of Shafts with Cone Pulleys 1114 
 
 Speeds in Geometrical Progression 1114 
 
 BELTING. 
 
 Theory of Belts and Bands 1115 
 
 Centrifugal Tension 1115 
 
 Belting Practice, Formulae for Belting 1116 
 
 Horse-power of a Belt one inch wide 1117 
 
XXX CONTENTS. 
 
 PAGE 
 
 A. F. Nagle's Formula 1117 
 
 Width of Belt for Given Horse-power 1118 
 
 Belt Factors 1119 
 
 Taylor's Rules for Belting 1120 
 
 Barth's Studies on Belting 1123 
 
 Notes on Belting 1123 
 
 Lacing of Belts 1124 
 
 Setting a Belt on Quarter-twist. 1124 
 
 To Find the Length of Belt 1125 
 
 To Find the Angle of the Arc of Contact 1125 
 
 To Find the Length of Belt when Closely Rolled 1125 
 
 To Find the Approximate Weight of Belts 1125 
 
 Relations of the Size and Speeds of Driving and Driven Pulleys 1125 
 
 Evils of Tight Belts 1126 
 
 Sag of Belts 1126 
 
 Arrangements of Belts and Pulleys 1126 
 
 Care of Belts 1127 
 
 Strength of Belting 1127 
 
 Adhesion, Independent of Diameter 1127 
 
 Endless Belts 1 127 
 
 Belt Data 1127 
 
 Belt Dressing 1128 
 
 Cement for Cloth or Leather 1128 
 
 Rubber Belting 1128 
 
 Steel Belts 1129 
 
 Roller Chain and Sprocket Drives 1129 
 
 Belting versus Chain Drives 1132 
 
 A 350 H.P. Silent Chain Drive 1132 
 
 GEARING. 
 
 Pitch, Pitch-circle, etc 1133 
 
 Diametral and Circular Pitch 1133 
 
 Diameter of Pitch-line of Wheels from 10 to 100 Teeth 1134 
 
 Ohordal Pitch 1 135 
 
 Proportions of Teeth 1 135 
 
 Gears with Short Teeth 1135 
 
 Formulae for Dimensions of Teeth 1136 
 
 Width of Teeth 1136 
 
 Proportion of Gear-wheels 1137 
 
 Rules for Calculating the Speed of Gears and Pulleys 1 137 
 
 Milling Cutters for Interchangeable Gears 1138 
 
 Forms of the Teeth. 
 
 The Cycloidal Tooth 1138 
 
 The Involute Tooth 1140 
 
 Approximation by Circular Arcs 1142 
 
 Stepped Gears 1143 
 
 Twisted Teeth 1143 
 
 Spiral Gears 1 143 
 
 Worm Gearing 1143 
 
 The Hindley Worm 1144 
 
 Teeth of Bevel-wheels 1144 
 
 Annular and Differential Gearing 1145 
 
 Efficiency of Gearing 1146 
 
 Efficiency of Worm Gearing 1147 
 
 Efficiency of Automobile Gears 1148 
 
 Strength of Gear Teeth. 
 
 Various Formulas for Strength 1148 
 
 Comparison of Formulae 1150 
 
 Raw-hide Pinions 1153 
 
 Maximum Speed of Gearing 1153 
 
 A Heavy Machine-cut Spur-gear 1153 
 
 Frictional Gearing 1154 
 
 Frictional Grooved Gearing 1154 
 
CONTENTS. XXXi 
 
 PAGE 
 
 Power Transmitted by Friction Drives 1154 
 
 Friction Clutches 1 155 
 
 Coil Friction Clutches 1156 
 
 HOISTING AND CONVEYING. 
 
 Working Strength of Blocks 1157 
 
 Chain-blocks 1157 
 
 Efficiency of Hoisting Tackle 1158 
 
 Proportions of Hooks 1 159 
 
 Iron versus Steel Hooks 1 159 
 
 Heavy Crane Hooks 1 159 
 
 Strength of Hooks and Shackles 1161 
 
 Power of Hoisting Engines 1 162 
 
 Effect of Slack Rope on Strain in Hoisting 1162 
 
 Limit of Depth for Hoisting 1162 
 
 Large Hoisting Records 1 163 
 
 Pneumatic Hoisting 1163 
 
 Counterbalancing of Winding-engines 1163 
 
 Cranes. 
 
 Classification of Cranes 1165 
 
 Position of the Inclined Brace in a Jib Crane 1166 
 
 Electric Overhead Traveling Cranes . 1166 
 
 Power Required to Drive Cranes 1166 
 
 Dimensions, Loads and Speeds of Electric Cranes 1167 
 
 Notable Crane Installations 1168 
 
 Electric versus Hydraulic Cranes 1168 
 
 A 150-ton Pillar Crane 1168 
 
 Compressed-air Traveling Cranes 1168 
 
 Power Required for Traveling Cranes and Hoists 1169 
 
 Lifting Magnets 1169 
 
 Telpherage 1171 
 
 Coal-handling Machinery. 
 
 Weight of Overhead Bins 1172 
 
 Supply-pipes from Bins 1172 
 
 Types of Coal Elevators 1172 
 
 Combined Elevators and Conveyors 1172 
 
 Coal Conveyors 1173 
 
 Horse-power of Conveyors 1173 
 
 Weight of Chain and of Flights 1174 
 
 Bucket, Screw, and Belt Conveyors 1175 
 
 Capacity of Belt Conveyors 1175 
 
 Belt Conveyor Construction 1176 
 
 Horse-power to Drive Belt Conveyors 1176 
 
 Relative Wearing Power of Conveyor Belts 1177 
 
 Wire-rope Haulage. 
 
 Self-acting Inclined Plane 1177 
 
 Simple Engine Plane . . . 1178 
 
 Tail-rope System 1178 
 
 Endless Rope System 1178 
 
 Wire-rope Tramways . 1179 
 
 Stress in Hoisting-ropes on Inclined Planes 1179 
 
 An Aerial Tramway 21 miles long 1180 
 
 Formulae for Deflection of a Wire Cable 1180 
 
 Suspension Cableways and Cable Hoists 1181 
 
 Tension Required to Prevent Wire Slipping on Drums 1182 
 
 Taper Ropes of Uniform Tensile Strength 1183 
 
 WIRE-ROPE TRANSMISSION. 
 
 Working Tension of Wire Ropes 1183 
 
 Breaking Strength of Wire Ropes 1184 
 
 Sheaves for Wire-rope Transmission 1184 
 
XXX11 CONTENTS. 
 
 1, PAGE 
 
 Bending Stresses of Wire Ropes 1 184 
 
 Horse-power Transmitted 1185 
 
 Diameters of Minimum Sheaves 1186 
 
 Deflections of the Rope : 1187 
 
 Limits of Span 1187 
 
 Long-distance Transmission 1188 
 
 Inclined Transmissions 1188 
 
 Bending Curvature of Wire Ropes 1188 
 
 ROPE DRIVING. 
 
 Formulae for Rope Driving 1189 
 
 Horse-power of Transmission at Various Speeds 1191 
 
 Sag of the Rope between Pulleys 1191 
 
 Tension on the Slack Part of the Rope 1192 
 
 Data of Manila Transmission Rope 1193 
 
 Miscellaneous Notes on Rope-driving 1193 
 
 Cotton Ropes 1194 
 
 FRICTION AND LUBRICATION. 
 
 Coefficient of Friction 1194 
 
 Rolling Friction : 1194 
 
 Friction of Solids 1195 
 
 Friction of Rest 1195 
 
 Laws of Unlubricated Friction 1195 
 
 Friction of Tires Sliding on Rails 1195 
 
 Coefficient of Rolling Friction . 1195 
 
 Laws of Fluid Friction 1196 
 
 Angles of Repose of Building Materials 1196 
 
 Coefficient of Friction of Journals 1196 
 
 Friction of Motion 1197 
 
 Experiments on Friction of a Journal 1197 
 
 Coefficients of Friction of Journal with Oil Bath 1197, 1199 
 
 Coefficients of Friction of Motion and of Rest 1198 
 
 Value of Anti-friction Metals 1199 
 
 Cast-iron for Bearings 1199 
 
 Friction of Metal Under Steam-pressure 1200 
 
 Morin's Laws of Friction 1200 
 
 Laws of Friction of well-lubricated Journals 1201 
 
 Allowable Pressures on Bearing-surface 1203 
 
 Oil-pressure in a Bearing 1204 
 
 Friction of Car-journal Brasses 1204 
 
 Experiments on Overheating of Bearings 1205 
 
 Moment of Friction and Work of Friction 1205 j 
 
 Tests of Large Shaft Bearings 1206 
 
 Clearance between Journal and Bearing 1206 
 
 Allowable Pressures on Bearings 1206 
 
 Bearing Pressures for Heavy Intermittent Loads 1207 
 
 Bearings for Very High Rotative Speed 1208 
 
 Thrust Bearings in Marine Practice 1208 
 
 Bearings for Locomotives • 1208 
 
 Bearings of Corliss Engines 1208 
 
 Temperature of Engine Bearings 1209 
 
 Pivot Bearings 1209 
 
 The Schiele Curve 1209 
 
 Friction of a Flat Pivot-bearing 1209 
 
 Mercury-bath Pivot 1209 
 
 Ball Bearings, Roller Bearings, etc • 1210 
 
 Friction Rollers 1210 
 
 Conical Roller Thrust Bearings 1211 
 
 The Hyatt Roller Bearing 1211 
 
 Notes on Ball Bearings 1212 
 
 Saving of Power by use of Ball Bearings 1214 
 
 Knife-edge Bearings 1214 
 
 Friction of Steam-engines 1215 1 
 
 Distribution of the Friction of Engines 1215: 
 
contents. xxxiii 
 
 Friction Brakes and Friction Clutches. PAGE 
 
 Friction Brakes 1216 
 
 Friction Clutches - 1216 
 
 Magnetic and Electric Brakes 1217 
 
 Design of Band Brakes *. 1217 
 
 Friction of Hydraulic Plunger Packing 1217 
 
 Lubrication. 
 
 Durability of Lubricants 1218 
 
 Qualifications of Lubricants 1219 
 
 Examination of Oils 1219 
 
 Specifications for Petroleum Lubricants 1219 
 
 Penna. R. R. Specifications 1220 
 
 Grease Lubricants 1221 
 
 Testing Oil for Steam Turbines 1221 
 
 Quantity of Oil to run an Engine 1221 
 
 Cylinder Lubrication 1222 
 
 Soda Mixture for Machine Tools 1223 
 
 Water as a Lubricant 1223 
 
 Acheson's Deflocculated Graphite 1223 
 
 Solid Lubricants 1223 
 
 Graphite, Soapstone, Metaline 1223 
 
 THE FOUNDRY. 
 
 Cupola Practice 1224 
 
 Melting Capacity of Different Cupolas 1225 
 
 Charging a Cupola 1225 
 
 Improvement of Cupola Practice 1226 
 
 Charges in Stove Foundries 1227 
 
 Foundry Blower Practice . . 1227 
 
 Results of Increased Driving 1229 
 
 Power Required for a Cupola Fan 1230 
 
 Utilization of Cupola Gases 1230 
 
 Loss of Iron in Melting 1230 
 
 Use of Softeners 1230 
 
 Weakness of Large Castings 1230 
 
 Shrinkage of Castings 1231 
 
 Growth of Cast Iron by Heating 1231 
 
 Hard Iron due to Excessive Silicon 1231 
 
 Ferro Alloys for Foundry Use 1232 
 
 Dangerous Ferro-silicon 1232 
 
 Quality of Foundry Coke 1232 
 
 Castings made in Permanent Cast-iron Molds 1232 
 
 Weight of Castings from Weight of Pattern 1233 
 
 Molding Sand 1233 
 
 Foundry Ladles , 1234 
 
 THE MACHINE SHOP. 
 
 Speed of Cutting Tools 1235 
 
 Table of Cutting Speeds 1235 
 
 Spindle Speeds of Lathes 1236 
 
 Rule for Gearing Lathes 1236 
 
 Change-gears for Lathes 1237 . 
 
 Quick Change Gears 1237 
 
 Metric Screw-threads . • 1238 
 
 Cold Chisels 1238 
 
 Setting the Taper in a Lathe 1238 
 
 Tavlor's Experiments on Tool Steel * . 1238 
 
 Proper Shape of Lathe Tool 1238 
 
 Forging and Grinding Tools 1240 
 
 Best Grinding Wheel for Tools 1240 
 
 Chatter 1241 
 
 Use of Water on Tool 1241 
 
 Interval between Grindings 1241 
 
 Effect of Feed and Depth of Cut on Speed 1241 
 
XXXIV CONTENTS. 
 
 PAGE 
 
 Best High Speed Tool Steel — Heat Treatment 1242 
 
 Best Method of Treating Tools in Small Shops 1243 
 
 Quality of Different Tool Steels 1243 
 
 Parting and Thread Tools 1243 
 
 Durability of Cutting Tools 1243 
 
 Economical Cutting Speeds 1243- 1245 
 
 New High Speed Steels, 1909 1246 
 
 Use of a Magnet to Determine Hardening Temperature 1246 
 
 Case-hardening, Cementation, Harveyizing 1246 
 
 Change of Shape due to Hardening and Tempering 1247 
 
 Milling Cutters 1247 
 
 Teeth of Milling Cutters 1247 
 
 Keyways in Milling Cutters 1248 
 
 Power Required for Milling 1249 
 
 Extreme Results with Milling Machines 1249 
 
 Speed of Cutters 1250 
 
 Typical Milling Jobs 1251 
 
 Milling with or against Feed 1252 
 
 Modern Milling Practice 1252 
 
 Lubricant for Milling ^utters 1252 
 
 Milling-machine vs. Planer 1252 
 
 Drills, Speed of Drills • 1253 
 
 High-speed Steel Drills 1253 
 
 Power Required to Drive High-speed Drills 1253 
 
 Extreme Results with Radial Drills , 1254 
 
 Experiments on Twist Drills 1254 
 
 Resistance Overcome in Cutting Metal 1256 
 
 Heavy Work on a Planer 1256 
 
 Horse-power to run Lathes 1256-1260 
 
 Power required for Machine Tools 1256-1260 
 
 Power used by Machine Tools 1258 
 
 Size of Motors for Machine Tools 1260 
 
 Horse-power Required to Drive Shafting 1261 
 
 Power used in Maehine-shops 1261 
 
 Power Required to Drive Machines in Groups 1262 
 
 Abrasive Processes. 
 
 The Cold Saw 1262 
 
 Reese's Fusing-disk 1262 
 
 Cutting Stone with Wire 1262 
 
 The Sand-blast 1262 
 
 Emery-wheels 1263-1267 
 
 Grindstones 1264-1268 
 
 Various Tools and Processes. 
 
 Efficiency of a Screw 1268 
 
 Tap Drills 1269 
 
 Efficiency of Screw Bolts 1270 
 
 Efficiency of a Differential Screw 1270 
 
 Taper Bolts, Pins, Reamers, etc 1270 
 
 Morse Tapers 1271 
 
 The Jarno Taper 1271 
 
 Punches, Dies, Presses 1272 
 
 Clearance between Punch and Die 1272 
 
 Size of Blanks for Drawing-press 1272 
 
 Pressure of Drop-press 1273 
 
 Flow of Metals 1273 
 
 Forcing and Shrinking Fits 1273 
 
 Shaft Allowances for Electrical Machinery 1274 
 
 Running Fits 1274 
 
 Force Required to Start Force and Shrink Fits 1275 
 
 Proportioning Parts of Machines in Series 1276 
 
 Keys for Gearing, etc 1276 
 
 Holding-power of Set-screws 1278 
 
 Holding-power of Keys 1279 
 
CONTENTS. XXXV 
 
 DYNAMOMETERS. 
 
 PAGE 
 
 Traction Dynamometers 1280 
 
 The Prony Brake 1280 
 
 The Alden Dynamometer 1281 
 
 Capacity of Friction-brakes 1281 
 
 Transmission Dynamometers 1282 
 
 ICE MAKING OR REFRIGERATING MACHINES. 
 
 Operations of a Refrigerating-Machine 1283 
 
 Pressures, etc., of Available Liquids 1284 
 
 Properties of Ammonia and Sulphur Dioxide Gas 1285 
 
 Solubility of Ammonia 1288 
 
 Properties of Saturated Vapors 1288 
 
 Heat Generated by Absorption of Ammonia 1288 
 
 Cooling Effect, Compressor Volume and Power Required, with 
 
 different Cooling Agents 1289 
 
 Ratios of Condenser, Mean Effective, and Vaporizer Pressures. . . . 1289 
 
 Properties of Brine used to absorb Refrigerating Effect 1290 
 
 Chloride-of-calcium Solution 1290 
 
 Ice-melting Effect 1291 
 
 Ether-machines 1291 
 
 Air-machines 1291 
 
 Carbon Dioxide Machines 1292 
 
 Methyl Chloride Machines 1292 
 
 Sulphur-dioxide Machines s 1292 
 
 Machines Using Vapor of Water 1292 
 
 Ammonia Compression-machines 1292 
 
 Dry, Wet and Flooded Systems 1292 
 
 Ammonia Absorption-machines 1293 
 
 Relative Performance of Compression and Absorption Machines . . 1294 
 
 Efficiency of a Refrigerating-machine 1295 
 
 Cylinder-heating 1296 
 
 Volumetric Efficiency 1296 
 
 Pounds of Ammonia per Ton of Refrigeration 1297, 1298 
 
 Mean Effective Pressure, and Horse-power 1297 
 
 The Voorhees Multiple Effect Compressor 1297 
 
 Size and Capacities of Ammonia Machines 1299 
 
 Piston Speeds and Revolutions per Minute 1300 
 
 Condensers for Refrigerating-machines 1300 
 
 Cooling Tower Practice in Refrigerating Plants 1301 
 
 Test Trials of Refrigerating-machines 1302 
 
 Comparison of Actual and Theoretical Capacity 1302 
 
 Performance of Ammonia Compression-machines 1303 
 
 Economy of Ammonia Compression-machines 1304 
 
 Form of Report of Test 1306 
 
 Temperature Range 1306 
 
 Metering the Ammonia 1307 
 
 Performance of Ice-making Machines 1307 
 
 Performance of a 75-ton Refrigerating-machine 1309, 1311 
 
 Ammonia Compression-machine.. Results of Tests 1312 
 
 Performance of a Single-acting Ammonia Compressor 1312 
 
 Performance of Ammonia Absorption-machine 1312 
 
 Means for Applying the Cold 1314 
 
 Artificial Ice-manufacture 1314 
 
 Test of the New York Hygeia Ice-making Plant 1315 
 
 An Absorption Evaporator Ice-making System 1315 
 
 Ice-making with Exhaust Steam 1316 
 
 Tons of Ice per Ton of Coal 1316 
 
 Standard Ice Cans or Molds 1316 
 
 MARINE ENGINEERING 
 
 Rules for Measuring and Obtaining Tonnage of Vessels 1316 
 
 The Displacement of a Vessel 1317 
 
 Coefficient of Fineness 1317 
 
 Coefficient of Water-lines 1317 
 
XXXVI CONTENTS. 
 
 PAGE 
 
 Resistance of Ships 1317 
 
 Coefficient of Performance of Vessels 1318 
 
 Defects of the Common Formula for Resistance 1318 
 
 Rankine's Formula 1 319 
 
 E. R. Mumford's Method . 
 Dr. Kirk's Method. 
 
 1319 
 1320 
 1320 
 
 To find the I.H.P. from the Wetted Surface 
 
 Relative Horse-power required for Different Speeds of Vessels i*m 
 
 Resistance per Horse-power for Different Speeds ' ' ' io 2 i 
 
 Estimated Displacement, Horse-power, etc., of Steam-vessels ' ' 1322 
 
 Speed of Boats with Internal Combustion Engines '.".':'. 1322 
 
 The Screw-propeller 
 
 Pitch and Size of Screw 1324 
 
 Propeller Coefficients 1325 
 
 Efficiency of the Propeller 1326 
 
 Pitch-ratio and Slip for Screws of Standard Form 1326 
 
 Table for Calculating Dimensions of Screws 1327 
 
 Marine Practice 
 
 Dimensions and Performance of Notable Atlantic Steamers 1328 
 
 Relative Economv of Turbines and Reciprocating Engines 1328 
 
 Marine Practice, 1901 1329 
 
 Comparison of Marine Engines, 1872, 1881, 1891, 1901 1329 
 
 Turbines and Boilers of the " Lusitania " 1330 
 
 Performance of the " Lusitania," 1908 - 1330 
 
 Relation of Horse-power to Speed 1331 
 
 Reciprocating Engines with a Low-pressure Turbine 1331 
 
 The Paddle-wheel 
 
 Paddle-wheels with Radial Floats 1331 
 
 Feathering Paddle-wheels 1331 
 
 Efficiency of Paddle-wheels 1332 
 
 Jet Propulsion 
 
 Reaction of a Jet 1332 
 
 CONSTRUCTION OF BUILDINGS 
 
 Foundations 
 
 Bearing Power of Soils 1333 
 
 Bearing Power of Piles 1334 
 
 Safe Strength of Brick Piers 1334 
 
 Thickness of Foundation Walls 1334 
 
 Masonry 
 
 Allowable Pressures on Masonry 1334 
 
 Crushing Strength of Concrete , . 1334 
 
 Beams and Girders 
 
 Safe Loads on Beams 1335 
 
 Maximum Permissible Stresses in Structural Materials 1335 
 
 Safe Loads on Wooden Beams 1336 
 
 Walls 
 
 Thickness of Walls of Buildings 1336 
 
 Walls of Warehouses, Stores, Factories, and Stables 1337 
 
 Floors, Columns and Posts 
 
 Strength of Floors, Roofs, and Supports 1337 
 
 Columns and Posts 1337 
 
 Fireproof Buildings 1338 
 
 Iron and Steel Columns 1338 
 
 Lintels, Bearings, and Supports 1338 
 
CONTENTS. XXXV11 
 
 PAGE 
 
 Strains on Girders and Rivets 1338 
 
 Maximum Load on Floors 1339 
 
 Strength of Floors 1339 
 
 Mill Columns 1341 
 
 Safe Distributed Loads on Southern-pine Beams 1341 
 
 Maximum Spans for 1, 2 and 3 inch Plank 1342 
 
 Approximate Cost of 31ill Buildings 1342 
 
 ELECTRICAL ENGINEERING 
 
 C. G. S. System of Physical Measurement 1344 
 
 Practical Units used in Electrical Calculations 1345 
 
 Relations of Various Units 1346 
 
 Units of the Magnetic Circuit 1346 
 
 Equivalent Electrical, and Mechanical Units 1347 
 
 Permeability 1348 
 
 Analogies between Flow of Water and Electricity 1348 
 
 Electrical Resistance 
 
 Laws of Electrical Resistance 1349 
 
 Electrical Conductivity of Different Metals and Alloys 1349 
 
 Conductors and Insulators 1350 
 
 Resistance Varies with Temperature 1350 
 
 Annealing 1351 
 
 Standard of Resistance of Copper Wire 1351 
 
 Direct Electric Currents 
 
 Ohm's Law 1351 
 
 Series and Parallel or Multiple Circuits 1352 
 
 Resistance of Conductors in Series and Parallel 1352 
 
 Internal Resistance 1353 
 
 Power of the Circuit 1353 
 
 Electrical, Indicated, and Brake Horse-power 1353 
 
 Heat Generated by a Current 1354 
 
 Heating of Conductors 1354 
 
 Heating of Coils 1355 
 
 Fusion of Wires 1355 
 
 Allowable Carrying Capacity of Copper Wires 1355 
 
 Underwriters' Insulation • 1355 
 
 Drop of Voltage in Wires Carrying Allowed Currents 1356 
 
 Wiring Table for Motor Service 1356 
 
 Copper-wire Table 1357, 1358 
 
 Electric Transmission, Direct-Currents 
 
 Section of Wire Required for a Given Current 1359 
 
 Weight of Copper for a Given Power 1359 
 
 Short-circuiting 1360 
 
 Economy of Electric Transmission 1360 
 
 Wire Table for 110, 220, 500, 1000, and 2000 volt Circuits 1360 
 
 Efficiency of Electric Systems 1361 
 
 Resistances of Pure Aluminium Wire 1362 
 
 Systems of Electrical Distribution 1363 
 
 Table of Electrical Horse-powers 1364 
 
 Cost of Copper for Long-distance Transmission 1365 
 
 Electric Railways 
 
 Electric Railway Cars and Motors 1366 
 
 A 4000-H.P. Electric Locomotive 1366 
 
 Electric Lighting. — Ilhimination 
 
 Illumination 1367 
 
 Terms, Units, Definitions 1367 
 
 Relative Color Values of Illuminants 1367 
 
 Relation of Illumination to Vision 1367 
 
XXXV111 CONTENTS. 
 
 _^ PAGE 
 
 Arc Lamps , 1368 
 
 Illumination by Arc Lamps at Different Distances 1368 
 
 Data of Some Arc Lamps 1369 
 
 Watts per Square Foot Required for Arc Lighting 1369 
 
 The Mercury Vapor Lamp 1369 
 
 Incandescent Lamps 1370 
 
 Rating of Incandescent Lamps 1370 
 
 Incandescent Lamp Characteristics 1370 
 
 Variation in Candle-power Efficiency and Life 1371 
 
 Performance of Tantalum and Tungsten Lamps 1372 
 
 Specifications for Lamps 1372 
 
 Special Lamps 1372 
 
 Nernst Lamp 1372 
 
 Cost of Electric Lighting 1373 
 
 Electric Welding 1374 
 
 Electric Heaters 1375 
 
 Electric Furnaces " 1376 
 
 Silundum 1377 
 
 Electric Batteries 
 
 Description of Storage-batteries or Accumulators 1378 
 
 Sizes and Weights of Storage-batteries 1379 
 
 Efficiency of a Storage Cell 1380 
 
 Rules for Care of Storage-batteries .* 1380 
 
 Electrolysis 1381 
 
 Electro-chemical Equivalents 1382 
 
 The Magnetic Circuit 
 
 Lines and Loops of Force '. 1383 
 
 Values of B and H 1384 
 
 Tractive or Lifting Force of a Magnet 1384 
 
 Determining the Polarity of Electro-magnets 1385 
 
 Determining the Direction of a Current 1385 
 
 Dynamo-electric Machines 
 
 Kinds of Machines as regards Manner of Winding 1385 
 
 Moving Force of a Dynamo-electric Machine 1386 
 
 Torque of an Armature 1386 
 
 Torque, Horse-power and Revolutions 1386 
 
 Electro-motive Force of the Armature Circuit 1386 
 
 Strength of the Magnetic Field 1387 
 
 Alternating Currents 
 
 Maximum, Average and Effective Values 1388 
 
 Frequency 1388 
 
 Inductance 1389 
 
 Capacity 1389 
 
 Power Factor 1389 
 
 Reactance, Impedance, Admittance 1390 
 
 Skin Effect 1390 
 
 Ohm's Law Applied to Alternating Current Circuits 1390 
 
 Impedance Polygons 1390 
 
 Self-inductance of Lines and Circuits 1393 
 
 Capacity of Conductors 1394 
 
 Single-phase and Polyphase Currents 1394 
 
 Measurement of Power in Polyphase Circuits 1395 
 
 Alternating Current Circuits 
 
 Calculation of Alternating Current Circuits 1396 
 
 Relative Weight of Copper Required in Different Systems 1398 
 
 Rule for Size of Wires for Three-phase Transmission Lines 1398 
 
 Notes on High-tension Transmission 1398 
 
CONTENTS. XXXIX 
 
 Transformers, Converters, etc. 
 
 PAGE 
 
 Transformers 1400 
 
 Converters 1401 
 
 Mercury Arc Rectifiers . . 1401 
 
 Electric Motors 
 
 Classification of Motors 1401 
 
 The Auxiliary-pole Type of Motors 1402 
 
 Speed of Electric Motors 1403 
 
 Speed Control of Motors. Rheostats 1404 
 
 Selection of Motors for Different Kinds of Service 1405 
 
 The Electric Drive in the Machine Shop 1407 
 
 Choice of Motors for Machine Tools 1407 
 
 Alternating Current Motors 
 
 Synchronous Motors 1408 
 
 Induction Motors 1409 
 
 Induction Motor Applications 1409 
 
 Alternating Current Motors for Variable Speed 1412 
 
 Sizes of Electric Generators and Motors 
 
 Direct-connected Engine-driven Generators 1412 
 
 Belt-driven Generators 1412 
 
 Belt-driven Motors 1413 
 
 Belt-driven Alternators 1413 
 
 Machines with Commutating Poles 1413 
 
 Small Engine-driven Alternators 1414 
 
 Railway Motors 1414 
 
 Small Polyphase, Single-phase, and Direct-current Motors 1415 
 
 Symbols Used in Electrical Diagrams 1416 
 
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 En- 
 gineers. 
 
 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. 
 
 Kapp's Electric Transmission of Energy. 
 
 Lanza's Applied Mechanics. 
 
 Machy. Machinery. 
 
 Merriman's Strength of Materials. 
 
 Modern Mechanism. Supplementary volume of Appleton's Cyclopaedia of 
 Mechanics. 
 
 Peabody's Thermodynamics. 
 
 Proc. A. S. H. V. E. Proceedings Am. Soc'y of Heating and Ventilating 
 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 (Lon- 
 don). 
 
 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. Stevens Institute 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 Letters 
 
 
 
 
 
 A 
 
 a 
 
 Alpha 
 
 H 
 
 V 
 
 Eta 
 
 N v 
 
 Nu 
 
 T 
 
 T 
 
 Tau 
 
 B 
 
 
 
 Beta 
 
 © 
 
 &e 
 
 Theta 
 
 a i 
 
 Xi 
 
 Y 
 
 V 
 
 Upsilon 
 
 r 
 
 V 
 
 Gamma 
 
 I 
 
 i 
 
 Iota 
 
 o 
 
 Omicron 
 
 <D 
 
 4> 
 
 Phi 
 
 A 
 
 5 
 
 Delta 
 
 K 
 
 K 
 
 Kappa 
 
 n tt 
 
 Pi 
 
 X 
 
 X 
 
 Chi 
 
 E 
 
 6 
 
 Epsilou 
 
 A 
 
 \ 
 
 Lambda 
 
 p p 
 
 Kho 
 
 * 
 
 ^ 
 
 Psi 
 
 Z 
 
 i 
 
 Zeta 
 
 M 
 
 f* 
 
 Mu 
 
 2 <rs 
 
 Sigma 
 
 o 
 
 O) 
 
 Omega 
 
 Arithmetical and Algebraical Signs and Abbreviations. 
 
 4- plus (addition). 
 + positive. 
 
 — minus (subtraction). 
 
 — negative. 
 
 ± plus or minus. 
 T minus or plus. 
 = equals. 
 X multiplied by. 
 ab or a.b = a X b. 
 -v- divided by. 
 / divided by. 
 
 £ = a/6 = a h- 6. 15-16 = J|- 
 
 O 9 p lb 
 
 2- ^0.002- — 
 
 V square root. 
 
 ^/ cube root. 
 
 tf 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. 
 
 □ square. 
 
 G round. 
 
 ° degrees, arc or thermometer. 
 
 'minutes or feet. 
 
 * seconds or inches. 
 
 ' " '" accents to distinguish letters, 
 as a', a", a'". 
 
 fli, 0,2, a 3 , at, a c , read a sub 1, a sub 
 6, etc. 
 
 ( ) [ ] \ \ parenthesis, brackets, 
 
 braces, vinculum ; denoting 
 that the numbers enclosed are 
 to be taken toget her; 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. 
 
 -. a- 2 = 
 
 a 2 
 
 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. 
 1 
 
 sin a -1 
 
 sin 
 
 log = logarithm, 
 loge or hyp log == hyperbolic loga- 
 rithm. 
 % per cent. 
 A angle. 
 
 L right angle. 
 J. 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. 
 
 7r, 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 friction. 
 E., coefficient of elasticity. 
 R., 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. 
 1. p., low pressure. 
 A.W.G., American Wire Gauge 
 
 (Brown & Sharpe). 
 B.W.G., Birmingham Wire 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 bv the last 
 remainder, until there is no remainder, and the last divisor is the greatest 
 common measure required. 
 
 LEAST COMMON 31ULTIPLE 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 
 13/ 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 = 3_ i _5 = 34 = 12 = 3 
 
 4 /4 4 ' 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. 
 
 by all the denominators except its own for the new numerator, and all 
 the denominators together for the common denominator: 
 
 21 
 42' 
 
 To add fractions. — Reduce them to a common denominator, then 
 add the numerators and place their sum over the common denominator: 
 
 7 
 
 42 
 
 42 
 
 = 111/42. 
 
 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 = 1_ 
 
 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' -f 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 + 0.25 = 6. 0.1 -J- 0.3 = 0.10000 -*• 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 
 
 .953125 
 
 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 
 
 1-2 
 
 .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 
 
rH 
 
 
 ARITHMETIC. 
 
 o 
 
 Uilffl 
 
 o m 
 oo t>. 
 i>. en 
 
 00 ON 
 
 t-lOO-* 
 
 nO en © 
 mom 
 no «s r>. 
 t>. 00 -co 
 
 
 — o r>. in 
 o o — cN 
 
 vO — vO — 
 
 «© t>. r> oq 
 
 n|* 
 
 in T en — © 
 O) On nO en © 
 no © in © in 
 in vq n© t>. |>» 
 
 M|50 
 
 Hh 
 
 fo nO no no in m 
 eN in ao — T r* 
 r^ — in o T co 
 T m in \0 •© no 
 
 io|oo 
 
 vO l>» 00 00 On On O 
 
 O On oo r>. vO m m 
 
 On CN vO © T 00 tM 
 
 en ■* ->r in in in no 
 
 J® 
 
 ■^TNOrxONOCNlcriin 
 
 no — no — r»«^t>.c^ 
 — inoor^inONCNiNO 
 en en en ■* ->r "T in in 
 
 ■h|(M 
 
 
 oenmoooenmooo 
 O — cn) en in no r-»« oo © 
 inoo — •*t>.0<nNOO 
 
 
 < 
 
 
 too — Too — moocNin 
 
 — oONOmoooinfNOt>. 
 On — T l>« © cn in ao — en 
 
 — tNeN«NtncnencnTT 
 
 
 cc]w 
 
 
 vO — inON-^-oocnrv. — voo 
 © T r^ © t r>. — Too — m 
 Tnooo — mmoootNint-N 
 — — — tNcMcNCNentncncn 
 
 
 ■* 
 
 rxfNjt^tNaOcnoo-TON-q-om 
 i->t-NNONOinm-<T-q-cnenmcs| 
 On — mint>.ON — mint^.ON"- 
 © — — — ; — — CNj cvj cm cs cn| en 
 
 H« 
 
 
 in — t^mONOcsONin — r->^ro 
 cN]oo<nONin©NO — r>. en oo T © 
 vOt^ON©eNTint>.oo© — en>n 
 
 OOO — — — — — — N N N N 
 
 
 * 
 
 © 
 
 ONNOcnOooincNONNOcn"— oom 
 NOooOfNcninh>ooOfN"^-mr>. 
 T in r^ ao on © — CNjTinNor>,oo 
 OOOOO — — — — — — — — 
 
 
 H» 
 
 no -«r 
 m en 
 — <s 
 
 o o 
 
 m — ONi>.incn — Onoonot«n© 
 — ONNOTCNJ-Oooinm — ft N m 
 
 rnmTmNOt->t>>a0ON©© — e» 
 © © © © © © © © O — — — — 
 
 
 J 50 
 
 On 00 t-> 
 
 o o — 
 
 O O O 
 
 NOinTeneneN — OOoot>.NOin 
 inONtnr-'i'— inONcnNOO^aofNi 
 
 ©©©©©©©©OO©©© 
 
 
 tH 
 
 in o m 
 
 nO fM 00 
 o — — 
 
 ©in©in©in©tn©in©in 
 ©csln^OfNiint-NOfNinr^© 
 in — i->enONoeNooin — t>.cno 
 cscncnTminNONOixooaoON© 
 
 "7 
 
 O 
 
 ^^«pH*^e 8 »»^H B .«g-*»$«N.$H»$*H 
 
COMPOUND NUMBERS. 
 
 decimal point in the numerator, and reduce the fraction thus formed to its 
 lowest terms: 
 
 «-£■ 
 
 3333 1 
 10000 = 3* neaFly - 
 
 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 
 
 78975 , , , . .. . % 117 
 
 ■ QQQnn = (reduced to its lowest 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. 
 
 3 yards to inches: 3 X 36 = 108 inches. 
 
 0.04 square feet to square inches: .04 X 144 = 5.76 sq. in. 
 
 If 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, +1 = 10, 10 X 12 = 120, +7 = 127 in. 
 
 Reduction ascending. — To express a number of a lower denomina- 
 tion in terms 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 -s- 12 = 10 feet + 7 inches; 10 feet -=-3 = 3 yards + 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 
 
 = 319/36 = 3.5277 + yards. 
 
 Decimals of a Foot Equivalent to Inches and Fractions 
 of an Inch. 
 
 Inches 
 
 
 
 H 
 
 K 
 
 % 
 
 l A 
 
 H 
 
 H 
 
 %■ 
 
 
 
 
 
 .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 _di vide by the first. 
 
 2 : 4 : : 3 : what number? Ans. — £— = 6. 
 
 Algebraic expression of proportion. — a : b : : c : d; - = -; ad =■ be; 
 
 , ... be , be , ad ad 
 
 from which a =• ~? ; d= — ;&= — ; c = -r- • 
 d a c b 
 
 From the above equations may also be derived the following: 
 
 & : a : : d : e a + b 
 
 a : c : :b : d a + b 
 
 a : b = c : d a — b 
 
 a — b 
 
 a : :c + d : c a + b : a — b : : c + d ; 
 6 : : c + d : d a n : b"> : : c n : d™ 
 
 y~a\ ^jb: :^/c y~d 
 
 b::c - d 
 a : :c — d 
 
 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 = "^2 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 = — — — = 15 men. 
 
 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 term and 3 days the first term. 3:1:: 
 15 men : 5 men. 
 
POWERS OF NUMBERS. 
 
 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 kind 
 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 be greater. 
 
 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 
 Days 
 Hours 
 
 4: 
 
 3 : 
 
 10 : 
 
 3 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. 
 
 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 h- 2 2 » 2 1 = 2; 2 2 -t- 2* = 2~ 2 = j 2 = | • 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^, 2i, 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 0#5 , 2 1-6 ; 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. 
 
 0) 
 
 T3 % 
 N O 
 
 3^ 
 
 C<~1 Q 
 
 4th 
 
 5th 
 
 6th 
 
 7th 
 
 8th 
 
 9th 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Power. 
 
 Ph 
 
 P4 
 
 Ph 
 
 
 
 
 
 
 
 1 
 
 2 
 
 1 
 
 4 
 
 1 
 8 
 
 1 
 16 
 
 1 
 
 32 
 
 1 
 64 
 
 1 
 128 
 
 1 
 256 
 
 1 
 
 512 
 
 3 
 
 9 
 
 27 
 
 81 
 
 243 
 
 729 
 
 2187 
 
 6561 
 
 19683 
 
 4 
 
 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 3. 
 
 
 
 01 
 
 i 
 
 CD 
 
 
 P4 
 
 1 
 
 
 3- 
 
 to 
 
 o 
 
 i 
 
 
 
 1 
 
 9 
 
 512 
 
 18 
 
 262144 
 
 27 
 
 134217728 
 
 36 
 
 68719476736 
 
 1 
 
 2 
 
 10 
 
 1024 
 
 19 
 
 52428S 
 
 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 ty y f 
 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* = \J2, <\/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: _ 
 
 V2 6 = 2§ = 2* = 2 3 = 8. 
 
 The 6th power of 2, as in the table above, is 64; V64 = 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. 
 
CUBE ROOT. 
 
 SQUARE ROOT. 
 
 3.1415926536 LL77245 + 
 
 1 
 
 271214 
 1189 
 34712515 
 |2429 
 3542 8692 
 7084 
 160865 
 141776 
 
 35444 
 
 35448511908936 
 
 11772425 
 
 CUBE ROOT. 
 
 1,881,365.963.6251 12345 
 
 1 
 
 300 XI 2 = 300 881 
 30 X 1 X 2 = 60 
 
 2 2 = 4 
 
 364J728 
 
 300 X 122 
 30 X 12 
 
 = 43200 
 X 3 = 1080 
 
 32 = 9 
 
 44289 
 
 153365 
 
 300 X 123 2 = 4538700 
 
 30 X 123 X 4 = 14760 
 
 42= 16 
 
 300 X 1234 2 =456826800 
 
 30X1234X5= 185100 
 
 5 2 = 25 
 
 457011925 
 
 2285059625 
 
 To extract the square root of a fraction, extract the root of a numerator 
 and denominator separately. 
 
 a decimal, 
 
 VI 
 
 sjl 
 
 ■■ V.4444 + = 0.6 
 
 3 + . 
 
 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, etc. 
 P = mean value or price per unit of A. 
 AP = aw + bx + cy + dz, etc. 
 p _ aw + bx 4- cy 4- oz 
 
 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 ail 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- 
 
 binati0n? 9X8X7 = 504 = S4 
 
 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 I-, 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 formulse: 
 
 Let a = first term, I «= last term, d = common difference, n = number 
 of terms, s = sum of the terms: 
 
 I = a + (n — l)d, 
 
 2s 
 = — — a, 
 n 
 
 s = -ft [2a 4- (n - l)d], 
 
 = (Z + a)|, 
 a ^l - (n - l)d, 
 
 
 -!<*±v/(' + H ! - 
 
 , l - a 
 
 I 2 - a* - 
 
 2s - I - a 
 
 I — a , , 
 r - — -7— 4- 1, 
 
 d 
 
 =. 2s 
 *~ I + a' 
 
 ■ 2ds, 
 
 ~\d± \f2ds + (c 
 s (n — l)d 
 n + 2 
 I + a I 2 - a 2 
 2 + 2d * 
 
 \n\2l - in - l)d]. 
 
 s 
 n 
 2s 
 n 
 2(s - 
 
 (ft - l)d 
 
 2 
 
 L 
 
 - an) , 
 
 n (ft 
 2{nl 
 n(n 
 
 -1) ' 
 
 - s) 
 
 - 1) 
 
 d - 
 
 2a ± V(2a - 
 
 «-H* 
 
 dy + 
 
 21 4- d ± ^{21 4- d) 2 - 
 
GEOMETRICAL PROGRESSION. 
 
 11 
 
 GEOMETRICAL PROGRESSION. 
 
 in a 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: 
 
 I = ar n ~ l , 
 
 log I = log a + (n ■ 
 m = arm-i 
 
 _ a + (r — l)-s 
 r 
 l)logr, l(s - t)n-i - 
 
 log m = log a + (m — 1) log r. 
 
 . (r - l)srw 
 
 a(s - a)n-i = 
 
 rl — a 
 
 ~<Jl n ~ n V«" lrn-l 
 
 log a = log I — (n — .1) log r. 
 
 r n . 
 
 log r ..== '- 
 
 log r 
 
 log Z — log a 
 
 " log ( 
 
 ■ a) - log (s - 
 
 log I — log a 
 i - 1 
 
 i — l ■' ' s- I 
 
 log [a + (r — l)s] — log a 
 
 logr 
 logZ - logRr - (r - l)s] 
 
 0. 
 
 + 1. 
 
 Population of the United States. 
 
 (A problem in geometrical progression.) 
 
 Year. 
 
 Population. 
 
 1860 
 
 31,443,321 
 
 1870 
 
 39,818,449* 
 
 1880 
 
 50,155,783 
 
 1890 
 
 62,622,250 
 
 1900 
 
 76,295,220 
 
 1905 
 
 Est. 83,577,000 
 
 1910 
 
 " 91,554,000 
 
 Increase in 10 Annual Increase,; 
 Years, per cent. per cent. 
 
 26.63 
 25.96 
 
 24.86 
 21.834 
 
 Est. 20.0 
 
 2.39 
 2.33 
 2.25 
 1.994 
 Est. 1.840 
 " 1.840 
 
 Estimated Population in Each Year from 1870 to 1909. 
 (Based on the above rates of increase, in even thousands.) 
 
 1870.... 
 
 39,818 
 
 1880 
 
 50, 1 56 
 
 1890 
 
 62,622 
 
 1900... 
 
 76,295 
 
 1871 
 
 40,748 
 
 1881 
 
 51,281 
 
 1891 
 
 63,871 
 
 1901... 
 
 77,699 
 
 1872 
 
 41,699 
 
 1882 
 
 52,433 
 
 1892;... 
 
 65, 1 45 
 
 1902... 
 
 79,129 
 
 1873 
 
 42,673 
 
 1883 
 
 53,610 
 
 1893 
 
 66,444 
 
 1903... 
 
 80,585 
 
 1874.... 
 
 43,670 
 
 1884 
 
 54,813 
 
 1894 
 
 67,770 
 
 1904... 
 
 82,067 
 
 1875.... 
 
 44,690 
 
 1885.... 
 
 56,043 
 
 1895 
 
 69,122 
 
 1905... 
 
 83,577 
 
 1876.... 
 
 45,373 
 
 1886 
 
 57,301 
 
 1896.... 
 
 70,500 
 
 1906... 
 
 85,115 
 
 1877.... 
 
 46,800 
 
 1887 
 
 58,588 
 
 1897 
 
 71,906 
 
 1907... 
 
 86,681 
 
 1878 
 
 47,893 
 
 1888 
 
 59,903 
 
 1898 
 
 73,341 
 
 1908. . . 
 
 88,276 
 
 1879 
 
 49,01 1 
 
 1889 
 
 61,247 
 
 1899 
 
 74,803 
 
 1909... 
 
 89,900 
 
 * Corrected by addition of 1,260,078, estimated error of the census of 
 1870, Census Bulletin No. 16, Dec. 12, 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 r 
 
 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. h- 10 = .00857703 = logr, 
 
 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 lbs. of fuel with 75% 
 efficiency will do as much work as 75 lbs. with 60% efficiency. The 
 saving of fuel is 15 lbs. which is 20% of 75 lbs. 
 
 INTEREST AND DISCOUNT. 
 
 Interest is money paid for the use of money for a given time; the 
 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. 
 Formulae: 
 
 = interest = principal X time X rate per cent = i = 
 
 ptr . 
 
 a — amount = principal + interest = p + jrrr ; 
 
 inn* 
 r = rate = 
 
 pi 
 . . , lOOi ptr . 
 
 p - pnncipal - -^ = a - — : 
 
 lOOi 
 
INTEREST AND DISCOUNT. 13 
 
 If the rate is expressed decimally as a per cent, — thus, 6 per cent 
 = .06, — the formulae become 
 
 i = prt;a = p(l + rt); r =~; *=-; p=l = — ^—. 
 pV pr tr 1 + rt 
 
 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. 
 
 T * 4-u i- • • -j -x principal X rate X no. of days 
 
 If the time is given in days, interest = — l^, - ^- *±. 
 
 obo 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 100 Dollars for Different Times and Bates. 
 
 Time 2% 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= 3 ^ year .00551 .0083* .0111* .01381 .01661 .0222| .02775 
 1 day= 3 &5 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: 
 
 = amount = p(l + r) n ;r = rate = 
 
 . . , a . log a — log p 
 
 V - principal - (1 + f)n ; no. of years- n= lQg (1 + r) • 
 
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.) 
 
 i 
 
 Per cent 
 
 ,9 
 
 Per cent 
 
 & 
 
 3 
 
 4 
 
 5 
 
 6 
 
 3 
 
 4 
 
 5 
 
 6 
 
 i 
 
 1.03 
 
 1.04 
 
 1.05 
 
 1.06 
 
 16 
 
 1 .6047 
 
 1.8730 
 
 2.1829 
 
 2.5403 
 
 2 
 
 1 .0609 
 
 1.0816 
 
 1.1025 
 
 1.1236 
 
 17 
 
 1.6528 
 
 1 .9479 
 
 2.2920 
 
 2.6928 
 
 3 
 
 1.0927 
 
 1.1249 
 
 1.1576 
 
 1.1910 
 
 18 
 
 1 .7024 
 
 2.0258 
 
 2.4066 
 
 2.8543 
 
 4 
 
 1.1255 
 
 1 . 1 699 
 
 1.2155 
 
 1 .2625 
 
 19 
 
 1.7535 
 
 2.1068 
 
 2.5269 
 
 3.0256 
 
 5 
 
 1.1593 
 
 1.2166 
 
 1.2763 
 
 1.3382 
 
 20 
 
 1.8061 
 
 2.1911 
 
 2.6533 
 
 3.2071 
 
 6 
 
 1.1941 
 
 1 .2653 
 
 1.3401 
 
 1.4185 
 
 21 
 
 1 .8603 
 
 2.2787 
 
 2.7859 
 
 3.3995 
 
 7 
 
 1 .2299 
 
 1.3159 
 
 1.4071 
 
 1.5036 
 
 22 
 
 1.9161 
 
 2.3699 
 
 2.9252 
 
 3.6035 
 
 8 
 
 1 .2668 
 
 1.3686 
 
 1.4774 
 
 1.5938 
 
 23 
 
 1.9736 
 
 2.4647 
 
 3.0715 
 
 3.8197 
 
 9 
 
 1 .3048 
 
 1 .4233 
 
 1.5513 
 
 1 .6895 
 
 24 
 
 2.0328 
 
 2.5633 
 
 3.2251 
 
 4.0487 
 
 10 
 
 1.3439 
 
 1 .4802 
 
 1 .6289 
 
 1.7908 
 
 25 
 
 2.0937 
 
 2.6658 
 
 3.3863 
 
 4.2919 
 
 11 
 
 1 .3842 
 
 1.5394 
 
 1.7103 
 
 1 .8983 
 
 30 
 
 2.4272 
 
 3.2433 
 
 4.3219 
 
 5.7435 
 
 12 
 
 1.4258 
 
 1.6010 
 
 1.7958 
 
 2.0122 
 
 35 
 
 2.8138 
 
 3.9460 
 
 5.5159 
 
 7.6862 
 
 13 
 
 1.4685 
 
 1.6651 
 
 1.8856 
 
 2.1329 
 
 40 
 
 3.2620 
 
 4.8009 
 
 7.0398 
 
 10.2858 
 
 14 
 
 1.5126 
 
 1.7317 
 
 1 .9799 
 
 2.2609 
 
 45 
 
 3.7815 
 
 5.8410 
 
 8.9847 
 
 13.7648 
 
 15 
 
 1.5580 
 
 1 .8009 
 
 2.0789 
 
 2.3965 
 
 50 
 
 4.3838 
 
 7.1064 
 
 1 1 .4670 
 
 18.4204 
 
 At compound interest at 3 per cent money will double itself in 23 1/2 years, 
 at 4 per cent in 1 7 2/3 years, at 5 per cent in 14.2 years, and at 6 per cent in 
 1 1.9 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- 
 ment. 
 
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 equal 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 the 
 amount will be 1 + i. At the end of n years it will be (1 + i) n . 
 
 2. The sum which in-n years will amount to 1 is or (1 + i) ~ n t 
 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 
 1 - (l + t)-» 
 
 (l + i) n -l 
 
 5. The annuity which 1 will purchase for any number of years n is 
 
 1 - (1 + i)~ n 
 
 6. The annuity which would amount to 1 in n years is 
 
 (1 + i) n - 1 
 
 Amounts, Present Values, etc., at 5% Interest. 
 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 Years 
 
 (1 + i) n 
 
 vW n 
 
 (l+i)^-1 
 
 i-a+;r n 
 
 i 
 
 i 
 
 
 i 
 
 X 
 
 ]-{\ + i)- n 
 
 (\+i)n-\ 
 
 1 . . 
 
 1.05 
 
 .952381 
 
 1.00 
 
 .952381 
 
 1.05 
 
 1.00 
 
 2. . 
 
 1.1025 
 
 .907029 
 
 2.05 
 
 1.859410 
 
 .537805 
 
 .487805 
 
 3. . 
 
 1.157625 
 
 .863838 
 
 3.1525 
 
 2.723248 
 
 .367209 
 
 .317209 
 
 4. . 
 
 1.215506 
 
 .822702 
 
 4.310125 
 
 3.545951 
 
 .282012 
 
 .232012 
 
 5. . 
 
 1 .276282 
 
 .783526 
 
 5.525631 
 
 4.329477 
 
 .230975 
 
 .180975 
 
 6. . 
 
 1.340096 
 
 .746215 
 
 6.801913 
 
 5.075692 
 
 .197017 
 
 .147018 
 
 7. . 
 
 1.407100 
 
 .710681 
 
 8.142008 
 
 5.786373 
 
 .172820 
 
 .122820 
 
 8. . 
 
 1.477455 
 
 .676839 
 
 9.549109 
 
 6.463213 
 
 .154722 
 
 .104722 
 
 9. . 
 
 1.551328 
 
 .644609 
 
 1 1 .026564 
 
 7.107822 
 
 .140690 
 
 .090690 
 
 10. . 
 
 1.628895 
 
 .613913 
 
 12.577893 
 
 7.721735 
 
 .129505 
 
 .079505 
 
16 
 
 ARITHMETIC. 
 
 
 © 
 
 485.43 
 314.10 
 228.60 
 177.39 
 143.36 
 
 119.13 
 101.03 
 87.02 
 75.87 
 66.79 
 
 59.28 
 52.96 
 
 47.58 
 42.96 
 38.95 
 
 35.44 
 32.36 
 29.62 
 27.18 
 18.23 
 
 12.65 
 8.97 
 6.46 
 4.70 
 3.44 
 
 
 10 
 
 486.62 
 315.63 
 230.29 
 179.13 
 145.18 
 
 120.96 
 102.86 
 88.83 
 77.67 
 68.57 
 
 61.03 
 
 54.68 
 49.28 
 44.62 
 40.58 
 
 37.04 
 33.92 
 31.15 
 28.68 
 19.55 
 
 13.80 
 9.97 
 7.32 
 5.43 
 4.06 
 
 
 10 
 
 487.80 
 317.21 
 232.01 
 180.98 
 147.02 
 
 122.82 
 104.72 
 90.69 
 79.50 
 70.39 
 
 62.83 
 56.45 
 51.02 
 46.34 
 42.27 
 
 38.70 
 35.54 
 32.75 
 30.24 
 20.95 
 
 15.05 
 11.07 
 8.28 
 6.26 
 4.78 
 
 
 ■>* 
 
 489.00 
 318.77 
 233.74 
 182.79 
 148.88 
 
 124.67 
 106.60 
 92.57 
 81.38 
 72.25 
 
 64.67 
 58.27 
 52.82 
 48.11 
 44.01 
 
 40.42 
 37.24 
 34.40 
 31.87 
 22.44 
 
 16.39 
 12.27 
 9.34 
 7.20 
 5.60 
 
 
 <* 
 
 490.20 
 320.36 
 235.50 
 184.63 
 150.79 
 
 126.61 
 108.53 
 94.49 
 83.29 
 
 74.15 
 
 66.55 
 60.14 
 54.67 
 49.94 
 45.82 
 
 42.20 
 38.99 
 36.14 
 33.58 
 24.01 
 
 17.83 
 13.58 
 10.52 
 8.26 
 6.55 
 
 CD 
 
 CO 
 
 490.80 
 321.13 
 236.38 
 185.56 
 151.73 
 
 127.59 
 109.50 
 95.46 
 84.26 
 75.12 
 
 67.51 
 61.10 
 55.62 
 50.88 
 46.75 
 
 43.12 
 39.90 
 37.04 
 34.47 
 24.84 
 
 18.60 
 14.29 
 11.17 
 8.85 
 7.09 
 
 a 
 1 
 
 01 
 
 eo 
 
 491.40 
 321.94 
 237.26 
 186.49 
 152.67 
 
 128.57 
 110.48 
 96.44 
 85.24 
 76.09 
 
 68.48 
 62.06 
 56.57 
 51.82 
 47.68 
 
 44.04 
 40.82 
 37.94 
 35.36 
 25.67 
 
 19.37 
 1.5.00 
 11.83 
 9.45 
 7.63 
 
 "etl 
 
 CO 
 
 492.00 
 322.75 
 238.14 
 187.42 
 153.64 
 
 129.54 
 111.47 
 97.44 
 86.24 
 77.08 
 
 69.47 
 63.05 
 57.55 
 52.79 
 48.64 
 
 44.99 
 41.76 
 38.87 
 36.29 
 26.55 
 
 20.19 
 15.77 
 12.54 
 10.12 
 8.25 
 
 CO 
 
 492.61 
 323.56 
 239.02 
 188.35 
 154.61 
 
 130.51 
 112.46 
 98.44 
 87.24 
 78.07 
 
 70.46 
 64.03 
 58.53 
 53.77 
 49.61 
 
 45.95 
 
 42.71 
 39.81 
 37.22 
 27.43 
 
 21.02 
 16.54 
 13.26 
 10.78 
 8.87 
 
 
 (M 
 
 493.22 
 324.35 
 239.93 
 189.30 
 155.58 
 
 131.50 
 113.46 
 99.45 
 88.24 
 79.09 
 
 71.47 
 65.04 
 59.53 
 
 54.77 
 50.60 
 
 46.94 
 43.69 
 40.78 
 38.18 
 28.35 
 
 .21.90 
 17.37 
 14.05 
 11.52 
 9.56 
 
 
 « 
 
 493.83 
 325.14 
 240.84 
 190.24 
 156.56 
 
 132.49 
 114.47 
 100.46 
 89.25 
 80.11 
 
 72.49 
 66.03 
 60.54 
 55.77 
 51.60 
 
 47.93 
 44.67 
 41.76 
 39.14 
 29.27 
 
 22.78 
 18.20 
 14.84 
 12.27 
 10.26 
 
 
 N 
 
 494.43 
 325.94 
 241.74 
 191.18 
 157.53 
 
 133.51 
 115.48 
 101.48 
 90.29 
 81.14 
 
 73.52 
 67.08 
 61.56 
 56.79 
 52.62 
 
 48.94 
 45.67 
 42.76 
 40.14 
 30.24 
 
 23.70 
 19.09 
 15.68 
 13.07 
 11.02 
 
 
 N 
 
 495.05 
 326.72 
 242.63 
 192.16 
 158.53 
 
 134.52 
 116.51 
 102.52 
 91.33 
 82.18 
 
 74.56 
 68.12 
 62.60 
 57.83 
 53.65 
 
 49.97 
 46.70 
 43.78 
 41.15 
 31.22 
 
 24.65 
 20.00 
 16.55 
 13.91 
 11.82 
 
 
 
 
 £$ 
 
 
 
 
 
 
 s- 
 
 
 
 
 
 
 kH° 
 
 eNen^mvo 
 
 MOOO- 
 
 eNen^-invO 
 
 NOOOOm 
 — — — (N(N 
 
 omomo 
 tfientTift 
 
WEIGHTS AND MEASURES. 
 
 17 
 
 TABLES FOB CALCULATING SINKING-FUNDS AND 
 PBESENT 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 100 Years. 
 
 3 
 
 V 
 
 
 
 Rate of Interest, per cent. 
 
 
 
 
 2V2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 5 
 
 51/2 
 
 6 
 
 5 
 
 
 5 
 
 20 
 25 
 
 iO 
 J5 
 40 
 *5 
 >0 
 )0 
 
 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 
 14,877.27 
 17,413.01 
 
 19,600.21 
 21,487.04 
 23,114.36 
 24,518.49 
 25,729.58 
 31,598.81 
 
 4,514.92 
 8,316.45 
 11,517.23 
 14,212.12 
 16,481.28 
 
 18,391.85 
 20,000.43 
 21,354.83 
 22,495.23 
 23,455.21 
 27,655.36 
 
 4,451.68 
 8,110.74 
 11,118.06 
 13,590.21 
 15,621.93 
 
 17,291.86 
 18,664.37 
 19,792.65 
 20,719.89 
 21,482.08 
 24,504.96 
 
 4,389.91 
 7,912.67 
 10,739.42 
 13,007.88 
 14,828.12 
 
 16,288.77 
 17,460.89 
 18,401.49 
 19,156.24 
 19,761.93 
 21,949.21 
 
 4,329.45 
 7,721.73 
 10,379.53 
 12,462.13 
 14,093.86 
 
 15,372.36 
 16,374.36 
 17,159.01 
 17,773.99 
 18,255.86 
 19,847.90 
 
 4,268.09 
 7,537.54 
 10,037.48 
 11,950.26 
 13,413.82 
 14,533.63 
 15,390.48 
 16,044.92 
 16,547.65 
 16,931.97 
 18,095.83 
 
 4,212.40 
 7,360.19 
 9,712.30 
 11,469.96 
 12,783.38 
 
 13,764.85 
 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; 51/2 yards, or 16 1/2 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. 
 
 6080.26 feet, or 1.15156 stat-1 
 ute miles J 
 
 3 nautical miles 
 60 nautical miles, or 69.168 
 statute miles 
 360 degrees 
 
 = 1 nautical mile, or knot.* 
 
 = 1 league. 
 
 = 1 degree (at the equator). 
 
 = circumference of the earth at the equator. 
 
 * The British Admiralty takes the round figure of 60S0 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 I _ -, _„„„,.,. f ~„* 
 
 inches ] ~ 1 S( l uare t00t - 
 9 square feet = 1 square yard. 
 
 30 1/4 square yards, or 2721/4 square feet ■— 1 square rod. 
 
 10 sq. chains, or 160 sq. rods, or 4840 sq. ) _ , Q „ ro 
 
 yards, or 43560 sq. feet J ~~ i acre ' 
 640 acres = 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 in 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. 
 1000 2 or 1,000,000 circular mils = 1 circular inch. 
 
 1 square inch = 1,273,239 circular mils. 
 
 The mil and circular mil are used in electrical calculations involving 
 the 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 = I6V2 X IV2 XI foot = 243/ 4 cubic feet. 
 
 Liquid Measure. 
 
 4 gills = 1 pint. 
 2 pints = 1 quart. 
 
 4 miartq - 1 gallon { U - S - 231 cubic in ches. 
 4 quarts - 1 gallon j Eng _ 2 ?7.274 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 8.3356 lbs. 
 
 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 lbs. 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 foot 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 IV4 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 IV2 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 MEASUKES. 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, I8V2 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 1V4 struck bushels. 
 
 The British Imperial bushel is based on the Imperial gallon, and contains 
 8 such gallons, or 2218.192 cubic inches = 1.2837 cubic feet. The English 
 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 
 internal 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: 
 
 1 U. S. shipping ton. 
 
 31.16 Imp. bushels. 
 
 32.143 C. S. 
 ( 1 British shipping ton. 
 42 cubic feet = \ 32.719 Imp. bushels. 
 (33.75 U.S. 
 
 Carpenter's Rule. — Weight a vessel will carry = length of keel X 
 breadth at main beam X depth of hold in feet -e- 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 beam. 
 
 Measures of Weight. — Avoirdupois, or Commercial 
 Weight. 
 
 16 drachms, or 437.5 grains = 1 ounce, oz. 
 16 ounces, or 7000 grains = 1 pound, lb. 
 28 pounds • = 1 quarter, qr. 
 
 4 quarters = 1 hundredweight, cwt. = 112 lbs. 
 
 20 hundred weight = 1 ton of 2240 lbs., 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, lb. = 5760 grains. 
 
 Troy weight is used for weighing gold and silver. The grain is the same 
 
 Avoird 
 
 weighing c 
 
 in Avoirdupois, Troy, and Apothecaries' weights. A" carat, used in 
 weighing diamonds = 3.168 grains = 0.205' i 
 
20 ARITHMETIC. 
 
 Apothecaries' Weight. 
 
 20 grains = 1 scruple, 3 
 3 scruples = 1 drachm, 5 = 60 grains. 
 8 drachms = 1 ounce, § = 480 grains. 
 
 12 ounces = 1 pound, lb. = 5760 grains. 
 
 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 this 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. 
 360 " = 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 56s. 555 sidereal time; 
 24 hours sidereal time = 23* 5Qm 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. 
 
WEIGHTS AND MEASURES. 
 
 21 
 
 When either of the dimensions are in inches, multiply as above and 
 divide the product by 12. 
 
 n 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 
 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. 
 
 12 14 16 18 20 22 24 26 28 
 
 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 
 
 84 
 
 91 
 
 98 
 
 105 
 
 4X4 
 
 16 
 
 19 
 
 21 
 
 24 
 
 27 
 
 29 
 
 32 
 
 35 
 
 37 
 
 40 
 
 4X6 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 52 
 
 56 
 
 60 
 
 4X8 
 
 32 
 
 37 
 
 43 
 
 48 
 
 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 
 
 88 
 
 96 
 
 104 
 
 112 
 
 120 
 
 4 X 14 
 
 56 
 
 65 
 
 75 
 
 84 
 
 93 
 
 103 
 
 112 
 
 121 
 
 131 
 
 140 
 
 6X6 
 
 36 
 
 42 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 84 
 
 90 
 
 6X8 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 88 
 
 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 
 
 6 X 14 
 
 84 
 
 93 
 
 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 
 
 280 
 
 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 
 
22 
 
 ARITHMETIC. 
 
 FRENCH OR METRIC MEASURES. 
 
 The metric unit of length is the metre = 39.37 inches. 
 
 The metric unit of weight is the gram = 15. 432. grains. 
 
 The following prefixes are used for subdivisions and multiples: Milli = 
 Viooo, Centi = Vioo, Deci = i/io, Deca = 10, Hecto = 100, Kilo -= 1000, 
 Myria = 10,000. 
 
 FRENCH AND BRITISH (AND AMERICAN) 
 EQUIVALENT MEASURES. 
 
 French. • 
 
 1 metre 
 0.3048 metre 
 
 1 centimetre 
 2.54 centimetres 
 
 1 millimetre 
 25.4 millimetres 
 
 1 kilometre 
 
 French. 
 
 1 square metre 
 
 0.836 square metre 
 0.0929 square metre 
 
 1 square centimetre 
 6.452 square centimetres 
 
 1 square millimetre 
 645.2 square millimetres 
 
 1 centiare = 1 sq. metre 
 
 1 are = 1 sq. decametre 
 
 1 hectare =100 ares 
 
 1 sq. kilometre 
 
 1 sq. myriametre 
 
 Measures of Length. 
 
 British and U. S. 
 = 39.37 inches, or 3.28083 feet, or 1.09361 yards. 
 = 1 foot. 
 = 0.3937 inch. 
 = 1 inch. 
 
 = 0.03937 inch, or 1/25 inch, nearly. 
 = 1 inch. 
 = 1093.61 yards, or 0.62137 mile. 
 
 Of Surface. 
 
 British and U. S. 
 f 10.764 square feet, 
 ' \ 1.196 square yards. 
 = 1 square yard. 
 = 1 square foot. 
 » 0.155 square inch. 
 : 1 square inch. 
 
 = 0.00155 sq. in. = 1973.5 cire. mils. 
 = 1 square inch. 
 = 10.764 square feet. 
 = 1076.41 " 
 
 > 107641 " " = 2.4711 acres. 
 = 0.386109 sq. miles = 247.11 " 
 « 38.6109 " 
 
 French. 
 
 1 cubic metre 
 
 0.7645 cubic metre 
 0.02832 cubic metre 
 
 1 cubic decimetre = 
 
 Of Volume. 
 
 British and U. S. 
 . (35.314 cubic feet, 
 
 \ 1.308 cubic yards. 
 : 1 cubic yard. 
 ■■ 1 cubic foot. 
 ( 61 .023 cubic inches; 
 ( 0.0353 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 centilitre = 0.610 
 
 1 decilitre = 6.102 
 
 1 litre = 1 cubic decimetre =61.023 " £ =1.05671 quarts, U.S. 
 
 1 hectolitre or decistere =3.5314 cubic feet =2.8375 bushels, " 
 
 1 stere, kilolitre, or cubic metre = 1.308 cubic yards = 28.37 bushels, 
 
 Of Capacity. 
 
 French. British and U. S. 
 
 61.023 cubic inches, 
 0.03531 cubic foot, 
 0.2642 gallon (American), 
 2.202 pounds of water at 62° F. 
 = 1 cubic foot. 
 = 1 gallon (British). 
 = 1 gallon (American). 
 
 1 litre (=1 cubic decimetre) = 
 
 28.317 litres 
 4.543 litres 
 3.785 litres 
 
WEIGHTS AND MEASURES. 
 
 23 
 
 Of Weight. 
 
 British and U. S. 
 = 15.432 grains. 
 = 1 grain. 
 
 = 1 ounce avoirdupois. 
 =±= 2.2046 pounds. 
 • = 1 pound. 
 
 (0.9842 ton of 2240 pounds, 
 
 ] 19.68 cwts., 
 
 ( 2204.6 pounds. 
 
 } 1 ton of 2240 pounds. 
 
 French. 
 
 1 gramme 
 
 0.0648 gramme 
 
 28.35 gramme 
 
 1 kilogramme 
 
 0.4536 kilogramme 
 
 1 tonne or metric ton = 
 
 1000 kilogrammes 
 
 1.016 metric tons 
 
 1016 kilogrammes 
 
 Mr. O. H. Titmann, in Bulletin No. 9 of the U. S. Coast and Geodetic 
 
 urvey, discusses the work of various authorities who have compared the 
 
 ard and the metre, and by referring all the observations to a common 
 
 tandard has succeeded in reconciling the discrepancies within very 
 
 iarrow limits. The following are his results for the number of inches in a 
 
 netre according to the comparisons of the authorities named: 1817. 
 
 iassler, 39.36994 in. 1818. Kater, 39.36990 in. 1835. Baily, 39.36973 
 
 a. 1866. Clarke, 39.36970 in. 1885. Comstock, 39.36984 in. The mean 
 
 if these is 39.36982 in. 
 
 The value of the metre is now defined in the U. S. laws as 39.37 inches. 
 
 French and British Equivalents of Compound Units. 
 
 French. 
 gramme per square millimetre 
 
 kilogramme per square 
 
 British. 
 =" 1.422 lbs. per sq. in. 
 = 1422.32 " " " " 
 centimetre = 14.223 ° " " " 
 
 ..0335 kg. per sq. cm. = 1 atmosphere = 14.7 " " " 
 
 K070308 kilogramme per square centimetre = 1 lb. per square inch. 
 l kilogrammetre = 7.2330 foot-pounds. 
 
 L gramme per litre = 0.062428 lb. per cu. ft. = 58.349 grains per U. S gal. 
 
 of water at 62° F. 
 L 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 U. S. Weights and Measures — 
 Customary to Metric. 
 
 1 = 
 
 2 = 
 
 3 = 
 
 4 = 
 
 5 = 
 
 6 = 
 
 7 = 
 
 8 = 
 
 9 = 
 
 Inches to Milli- 
 metres. 
 
 Feet to Metres. 
 
 Yards to Metres. 
 
 Miles to Kilo- 
 metres. 
 
 25.4001 
 50.8001 
 76.2002 
 101.6002 
 127.0003 
 
 152.4003 
 177.8004 
 203.2004 
 228.6005 
 
 0.304801 
 0.609601 
 0.914402 
 1.219202 
 1 .524003 
 
 1.828804 
 2.133604 
 2.438405 
 2.743205 
 
 0.914402 
 1 .828804 
 2.743205 
 3.657607 
 4.572009 
 
 5.486411 
 6.400813 
 7.315215 
 8.229616 
 
 1.60935 
 3.21869 
 4.82804 
 6.43739 
 8.04674 
 
 9.65608 
 1 1 .26543 
 12.87478 
 14.48412 
 
24 
 
 ARITHMETIC. 
 
 SQUARE. 
 
 
 Square Inches to 
 Square Centi- 
 metres. 
 
 Square Feet to 
 Square Deci- 
 metres. 
 
 Square Yards to 
 Square Metres. 
 
 Acres to 
 Hectares. 
 
 1 = 
 
 6.452 
 
 9.290 
 
 0.836 
 
 4047 
 
 2 = 
 
 12.903 
 
 18.581 
 
 1.672 
 
 0.8094 
 
 3 = 
 
 19.355 
 
 27.871 
 
 2.508 
 
 1.2141 
 
 4 = 
 
 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 
 
 
 Cubic Inches to 
 Cubic Centi- 
 metres. 
 
 Cubic Feet to 
 
 Cubic Yards to 
 
 Bushels to 
 
 
 Cubic Metres. 
 
 Cubic Metres. 
 
 Hectolitres. 
 
 1 = 
 
 16.387 
 
 0.02832 
 
 0.765 
 
 0.35242 
 
 2 = 
 
 32.774 
 
 0.05663 
 
 1.529 
 
 0.70485 
 
 3 = 
 
 49.161 
 
 0.08495 
 
 2.294 
 
 1.05727 
 
 4 = 
 
 65.549 
 
 0.11327 
 
 3.058 
 
 1 .40969 
 
 5 = 
 
 81.936 
 
 0.14158 
 
 3.823 
 
 1.76211 
 
 6 = 
 
 98.323 
 
 0.16990 
 
 4.587 
 
 2.11454 
 
 7 = 
 
 114.710 
 
 0.19822 
 
 5.352 
 
 2.46696 
 
 8 = 
 
 131.097 
 
 0.22654 
 
 6.116 
 
 2.81938 
 
 9 = 
 
 147.484 
 
 0.25485 
 
 6.881 
 
 3.17181 
 
 
 Fluid Drachms 
 
 
 
 
 
 to Millilitres or 
 Cubic Centi- 
 
 Fluid Ounces to 
 Millilitres. 
 
 Quarts to Litres. 
 
 Gallons to 
 Litres. 
 
 
 metres. 
 
 
 
 
 1 = 
 
 3.70 
 
 29.57 
 
 0.94636 
 
 3.78544 
 
 2 = 
 
 7.39 
 
 59.15 
 
 1 .89272 
 
 7.57088 
 
 3 = 
 
 11.09 
 
 88.72 
 
 2.83908 
 
 11.35632 
 
 4 = 
 
 14.79 
 
 118.30 
 
 3.78544 
 
 15.14176 
 
 5 = 
 
 18.48 
 
 147.87 
 
 4.73180 
 
 18.92720 
 
 6 = 
 
 22.18 
 
 177.44 
 
 5.67816 
 
 22.71264 
 
 7 = 
 
 25.88 
 
 207.02 
 
 6.62452 
 
 26.49808 
 
 8 = 
 
 29.57 
 
 236.59 
 
 7.57088 
 
 30.28352 
 
 9 = 
 
 33.28 
 
 266.16 
 
 8.51724 
 
 34.06896 
 

 METRIC CONVERSION TABLES. 
 WEIGHT. 
 
 25 
 
 
 Grains to Milli- 
 grammes. 
 
 Avoirdupois 
 Ounces to 
 Grammes. 
 
 Avoirdupois 
 Pounds to Kilo- 
 grammes. 
 
 Troy Ounces to 
 Grammes. 
 
 1 = 
 
 2 = 
 
 3 = 
 
 4 = 
 
 5 = 
 
 6 = 
 
 7 = 
 
 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 = 20.1 169 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. 
 
 - 
 
 
 
 
 
 
 Tables for Converting IT. S. Weights and Measures — 
 Metric to Customary. 
 
 
 Metres to 
 Inches. 
 
 Metres to 
 Feet. 
 
 Metres to 
 Yards. 
 
 Kilometres to 
 Miles. 
 
 1 = 
 
 2 = 
 
 3 = 
 
 4 = 
 
 5 = 
 
 6 = 
 
 7 = 
 
 8 = 
 
 9 = 
 
 39.3700 
 78.7400 
 118.1100 
 157.4800 
 196.8500 
 
 236.2200 
 275.5900 
 314.9600 
 354.3300 
 
 3.28083 
 6.56167 
 9.84250 
 13.12333 
 16.40417 
 
 19.68500 
 22.96583 
 26.24667 
 29.52750 
 
 1.093611 
 2.187222 
 3.280833 
 4.374444 
 5.468056 
 
 6.561667 
 7.655278 
 8.748889 
 9.842500 
 
 0.62137 
 1 .24274 
 1.86411 
 2.48548 
 3.10685 
 
 3.72822 
 4.34959 
 4.97096 
 5.59233 
 
 SQUARE. 
 
 Square Centi- 
 metres to 
 Square Inches. 
 
 O550 
 0.3100 
 0.4650 
 0.6200 
 0.7750 
 
 0.9300 
 1 .0850 
 1 .2400 
 1.3950 
 
 Square Metres 
 to Square Feet. 
 
 WJ64 
 21.528 
 32.292 
 43.055 
 53.819 
 
 64.583 
 75.347 
 86.111 
 96.874 
 
 Square Metres 
 to Square Yards. 
 
 U96 
 2.392 
 3.588 
 4.784 
 5.980 
 
 7.176 
 8.372 
 9.568 
 10.764 
 
 Hectares to 
 Acres. 
 
 2A7) 
 4.942 
 7.413 
 9.884 
 12.355 
 
 14.826 
 17.297 
 19.768 
 22.239 
 
26 
 
 ARITHMETIC. 
 
 
 Cubic Centi- 
 metres to Cubic 
 Inches. 
 
 Cubic Deci- 
 metres to Cubic 
 Inches. 
 
 Cubic Metres to 
 Cubic Feet. 
 
 Cubic Metres t 
 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 
 
 7 = 
 
 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 
 
 
 Millilitres or 
 Cubic Centi- 
 metres toFluid 
 
 Centilitres 
 to Fluid 
 
 Litres to 
 Quarts. 
 
 Dekalitres 
 to 
 
 Hektolitres 
 to 
 
 
 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 
 
 7 = 
 
 1.89 
 
 2.368 
 
 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 
 
 
 Milligrammes 
 to Grains. 
 
 Kilogrammes 
 to Grains. 
 
 Hectogrammes 
 ( 1 00 grammes) 
 to Ounces Av. 
 
 Kilogrammes 
 to Pounds 
 Avoirdupois. 
 
 1 = 
 
 2 = 
 
 3 = 
 
 4 = 
 
 5 = 
 
 6 = 
 
 7 = 
 
 8 = 
 
 9 = 
 
 0.01543 
 0.03086 
 0.04630 
 0.06173 
 0.07716 
 
 0.09259 
 0.10803 
 0.12346 
 0.13889 
 
 15432.36 
 30864.71 
 46297.07 
 61729.43 
 77161.78 
 
 92594.14 
 108026.49 
 123458.85 
 138891.21 
 
 3.5274 
 7.0548 
 10.5822 
 14.1096 
 17.6370 
 
 21.1644 
 24.6918 
 28.2192 
 31.7466 
 
 2.20462 
 4.40924 
 6.61386 
 8.81849 
 11.02311 
 
 13.22773 
 15.43235 
 17.63697 
 19.84159 
 
WEIGHTS AND MEASURES. 
 
 27 
 
 WEIGHT — (Continued). 
 
 
 Quintals to 
 Pounds Av. 
 
 Milliers or Tonnes to 
 Pounds Av. 
 
 Grammes to Ounces. 
 Troy. 
 
 1 = 
 
 2 = 
 
 3 = 
 
 4 = 
 
 5 = 
 
 6 = 
 
 7 = 
 
 8 = 
 
 9 = 
 
 220.46 
 440.92 
 661.38 
 881.84 
 1102.30 
 
 1322.76 
 1543.22 
 1763.68 
 1982.14 
 
 2204.6 
 4409.2 
 6613.8 
 8818.4 
 11023.0 
 
 13227.6 
 15432.2 
 17636.8 
 19841.4 
 
 0.03215 
 0.06430 
 0.09645 
 0.12860 
 0.16075 
 
 0.19290 
 0.22505 
 0.25721 
 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 0° 
 Centigrade, on a platinum-iridium bar deposited at the International 
 Bureau. 
 
 The International Standard Kilogramme is a mass of platinum-iridium 
 deposited at the same place, and its weight in vacuo is the same as that of 
 the Kilogramme des Archives. 
 
 Copies of these international standards are deposited in the office of 
 standard weights and measures of the U. S. Coast and Geodetic Survey. 
 
 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 40 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. 
 
 COMPOUND UNITS. 
 
 Measures of Pressure and Weight. 
 
 1 lb. per square inch. 
 
 1 ounce per sq. in. 
 
 1 atmosphere (14.7 lbs. per sq.in.) = 
 
 144 lbs. per square foot. 
 
 2.0355 ins. of mercury at 32° F. 
 2.0416 " " " " 62° F. 
 
 2.309 ft. of water at 62° F. 
 27.71 ins. " " " 62° F. 
 0.1276 in. of mercury at 62° F. 
 1.732 ins. of water at 62° F. 
 2116.3 lbs. per square foot. 
 
 33.947 ft. of water at 62° F. 
 30 ins. of mercury at 62° F. 
 
 29.922 ins. of mercury at 32° F. 
 760 millimetres of mercury at 32° F. 
 
28 ARITHMETIC. 
 
 COMPOUND UNITS — (Continued). 
 
 ( 0.03609 lb. or .5774 oz. per sq.in. 
 1 inch of water at 62° F. = < 5.196 lbs. per square foot. 
 
 ( 0.0736 in. of mercury at 62° F. 
 
 1 inch of water at 32° F. -\ $%&£&* *Wffik. 
 
 Hoot of water a, 62= F. -{ ^gj lb. per square inch. 
 
 ( 0.491 lb. or 7.86 oz. per sq. in. 
 1 inch of mercury at 62° F. = \ 1.132 ft. of water at 62° F. 
 
 ( 13.58 ins. " " " 62° F. 
 
 "Weight of One Cubic Foot of Pure Water. 
 
 At 32° F. (freezing-point) 62.418 lbs. 
 
 " 39.1° F. (maximum density) 62.425 " 
 
 " 62° F. (standard temperature) 62.355 " 
 
 " 212° F. (boiling-point, under 1 atmosphere) 59.76 " 
 
 American gallon = 231 cubic ins. of water at 62° F. = 8.3356 lbs. 
 British " = 277.274 " " " " " " - 10 lbs. 
 
 Weight and Volume of Air. 
 
 1 cubic ft. of air at 32° F. and atmospheric pressure weighs 0.080728 lb. 
 
 (0.0005606 lb. per sq. in. 
 1 ft. in height of air at 32° F„ = \ 0.008970 ounces per sq. in. 
 
 (0.015534 inches of water at 62° F. 
 For air at any other temperature T° Fahr. multiply by 460 -h (460 + T). 
 1 lb. pressure per sq. ft. = 12.387 ft. of air at 32° F. 
 
 1 " " " sq. in. = 1784. " " " " 
 
 1 ounce " " l! " = 111.48 " " " " 
 
 1 inch of water at 62° F. == 64.37 " " " " 
 
 For air at any other temperature multiply by (460 + T) -*- 460. 
 1 atmosphere = 14.696 lb. per sq. in. == 760 mm. or 29.921 in. of mercury. 
 
 Measures of Work, Power, and Duty. 
 
 Work. — The sustained exertion of pressure through space. 
 
 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 
 ft.-lbs. per minute, or 550 ft.-lbs. per second = 1,980,000 ft.-lbs. per hour. 
 
 Heat unit = heat required to raise 1 lb. of water 1° F. (from 39° to 40°). 
 
 33000 
 Horse-power expressed in heat units = ' ' R = 42.416 heat units per 
 
 minute = 0.707 heat unit per second = 2545 heat units per hour. 
 
 1 lb. of fne! per H. P. per honr - { ^i'^a/Sinits' ^ ^ * ^ 
 
 1,000,000 ft.-lbs. per lb. of fuel = 1.98 lbs. of fuel per H. P. per hour. 
 
 5^80 ^2 
 Velocity. — Feet per second = „~^ = ^ X miles per hour. 
 3600 15 
 
 Gross tons per mile = ooln = i"7 * bs - per yard ( sm ^ e rail.) 
 
WIRE AND SHEET-METAL GAUGES. 
 
 29 
 
 WIRE AND SHEET-METAL GAUGES COMPARED. 
 
 
 
 sis, 
 
 
 T3„»fi 
 
 — . a5o 
 
 British Imperial 
 
 "S * -si 
 
 
 
 £ * * 
 .8 gc? 
 
 rt a 5 
 
 ■ago 
 
 £Meo 
 
 Standard 
 Wire Gauge. 
 
 (Legal Standard 
 
 =3 n * » 
 
 CO ixS SS 
 
 || 
 
 S-2 2 
 
 - |sl 
 
 03 
 
 3|S 
 
 v& 
 
 
 in Great Britain 
 
 since 
 
 March 1, 1884.) 
 
 
 |5 
 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 millim. 
 
 inch. 
 
 
 0000000 
 
 
 
 .49 
 
 
 .500 
 
 12.7 
 
 .5 
 
 7/0 
 
 000000 
 
 
 
 .46 
 
 
 .464 
 
 11.78 
 
 .469 
 
 % 
 
 00000 
 
 
 
 .43 
 
 
 .432 
 
 10.97 
 
 .438 
 
 5/0 
 
 0000 
 
 .454 
 
 .46 
 
 .393 
 
 
 .4 
 
 10.16 
 
 .406 
 
 4/0 
 
 000 
 
 .425 
 
 .40964 
 
 .362 
 
 
 .372 
 
 9.45 
 
 .375 
 
 3/0 
 
 00 
 
 .38 
 
 .3648 
 
 .331 
 
 
 .348 
 
 8.84 
 
 .344 
 
 2/0 
 
 
 
 .34 
 
 .32486 
 
 .307 
 
 
 .324 
 
 8.23 
 
 .313 
 
 
 
 1 
 
 .3 
 
 .2893 
 
 .283 
 
 .227 
 
 .3 
 
 7.62 
 
 .281 
 
 1 
 
 2 
 
 .284 
 
 .25763 
 
 .263 
 
 .219 
 
 .276 
 
 7.01 
 
 .266 
 
 2 
 
 3 
 
 .259 
 
 .22942 
 
 .244 
 
 .212 
 
 .252 
 
 6.4 
 
 .25 
 
 3 
 
 4 
 
 .238 
 
 .2043 1 
 
 .225 
 
 .207 
 
 .232 
 
 5.89 
 
 .234 
 
 4 
 
 5 
 
 .22 
 
 .18194 
 
 .207 
 
 .204 
 
 .212 
 
 5.38 
 
 .219 
 
 5 
 
 6 
 
 .203 
 
 .16202 
 
 .192 
 
 .201 
 
 .192 
 
 4.88 
 
 .203 
 
 6 
 
 —7 
 
 .18 
 
 .14428 
 
 .177 
 
 .199 
 
 .176 
 
 4.47 
 
 .188 
 
 7 
 
 8 
 
 .165 
 
 .12849 
 
 .162 
 
 .197 
 
 .16 
 
 4.06 
 
 .172 
 
 8 
 
 9 
 
 .148 
 
 .11443 
 
 .148 
 
 .194 
 
 .144 
 
 3.66 
 
 .156 
 
 9 
 
 10 
 
 .134 
 
 .10189 
 
 .135 
 
 .191 
 
 .128 
 
 3.23 
 
 .141 
 
 10 
 
 11 
 
 .12 
 
 .09074 
 
 .12 
 
 .188 
 
 .116 
 
 2.95 
 
 .125 
 
 11 
 
 _12 
 
 .109 
 
 .08081 
 
 .105 
 
 .185 
 
 .104 
 
 2.64 
 
 .109 
 
 12 
 
 13 
 
 .095 
 
 .07196 
 
 .092 
 
 .182 
 
 .092 
 
 2.34 
 
 .094 
 
 13 
 
 14 
 
 .033 
 
 .06403 
 
 .08 
 
 .180 
 
 .08 
 
 2.03 
 
 .078 
 
 14 
 
 15 
 
 .072 
 
 .05707 
 
 .072 
 
 .178 
 
 .072 
 
 1.83 
 
 .07 
 
 15 
 
 "16 
 
 .065 
 
 .05032 
 
 .063 
 
 .175 
 
 .064 
 
 1.63 
 
 .0625 
 
 16 
 
 17 
 
 .058 
 
 .04526 
 
 .054 
 
 .172 
 
 .056 
 
 1.42 
 
 .0563 
 
 17 
 
 13 
 
 .049 
 
 .0403 
 
 .047 
 
 .168 
 
 .048 
 
 1.22 
 
 .05 
 
 18 
 
 19 
 
 .042 
 
 .03589 
 
 .041 
 
 164 
 
 .04 
 
 1.02 
 
 .0438 
 
 19 
 
 20 
 
 .035 
 
 .03196 
 
 .035 
 
 .161 
 
 .036 
 
 .91 
 
 .0375 
 
 20 
 
 21 
 
 .032 
 
 .02846 
 
 .032 
 
 .157 
 
 .032 
 
 .81 
 
 .0344 
 
 21 
 
 22 
 
 .028 
 
 .02535 
 
 .028 
 
 .155 
 
 .028 
 
 .71 
 
 .0313 
 
 22 
 
 23 
 
 .025 
 
 .02257 
 
 .025 
 
 .153 
 
 .024 
 
 .61 
 
 .0281 
 
 23 
 
 24 
 
 .022 
 
 .0201 
 
 .023 
 
 .151 
 
 .022 
 
 .56 
 
 .025 
 
 24 
 
 25 
 
 .02 
 
 .0179 
 
 .02 
 
 .148 
 
 .02 
 
 .51 
 
 .0219 
 
 25 
 
 26 
 
 .018 
 
 .01594 
 
 .018 
 
 .146 
 
 .018 
 
 .46 
 
 .0188 
 
 26 
 
 - 27 
 
 .016 
 
 .01419 
 
 .017 
 
 .143 
 
 .0164 
 
 .42 
 
 .0172 
 
 27 
 
 28 
 
 .014 
 
 .01264 
 
 .016 
 
 .139 
 
 .0148 
 
 .38 
 
 .0156 
 
 28 
 
 29 
 
 .013 
 
 .01126 
 
 .015 
 
 .134 
 
 .0136 
 
 .35 
 
 .0141 
 
 29 
 
 30 
 
 .012 
 
 .01002 
 
 .014 
 
 .127 
 
 .0124 
 
 .31 
 
 .0125 
 
 30 
 
 31 
 
 .01 
 
 .00893 
 
 .013 
 
 .120 
 
 .0116 
 
 .29 
 
 .0109 
 
 31 
 
 32 
 
 .009 
 
 .00795 
 
 .013 
 
 .115 
 
 .0108 
 
 .27 
 
 .0101 
 
 32 
 
 33 
 
 .008 
 
 .00708 
 
 .011 
 
 .112 
 
 .01 
 
 .25 
 
 .0094 
 
 33 
 
 34 
 
 .007 
 
 .0063 
 
 .01 
 
 .110 
 
 .0092 
 
 .23 
 
 .0086 
 
 34 
 
 35 
 
 .005 
 
 .00561 
 
 .00 
 
 .108 
 
 .0084 
 
 .21 
 
 .0078 
 
 35 
 
 ~ 36 
 
 .004 
 
 .005 
 
 .009 
 
 .106 
 
 .0076 
 
 .19 
 
 .007 
 
 36 
 
 37 
 
 
 .00445 
 
 .0085 
 
 .103 
 
 .0068 
 
 .17 
 
 .0066 
 
 37 
 
 38 
 
 
 .00396 
 
 .008 
 
 .101 
 
 .006 
 
 .15 
 
 .0063 
 
 38 
 
 39 
 
 
 .00353 
 
 .0075 
 
 .099 
 
 .0052 
 
 .13 
 
 
 39 
 
 40 
 
 
 .00314 
 
 .007 
 
 .097 
 
 .0048 
 
 .12 
 
 
 40 
 
 41 
 
 
 
 
 .095 
 
 .0044 
 
 .11 
 
 
 41 
 
 42 
 
 
 
 
 .092 
 
 .004 
 
 .10 
 
 
 42 
 
 43 
 
 
 
 
 .088 
 
 .0036 
 
 .09 
 
 
 43 
 
 44 
 
 
 
 
 .085 
 
 .0032 
 
 .08 
 
 
 44 
 
 45 
 
 
 
 
 .081 
 
 .0028 
 
 .07 
 
 
 45 
 
 46 
 
 
 
 
 .079 
 
 .0024 
 
 .06 
 
 
 46 
 
 47 
 
 
 
 
 .077 
 
 .002 
 
 .05 
 
 
 47 
 
 48 
 
 
 
 
 .075 
 
 .0016 
 
 .04 
 
 
 48 
 
 49 
 
 
 
 
 .092 
 
 .0012 
 
 .03 
 
 
 49 
 
 50 
 
 
 
 
 .069 
 
 .001 
 
 .025 
 
 
 50 
 
30 
 
 ARITHMETIC. 
 
 
 EDISON, OR CIRCULAR MIL GAUGE, FOR ELEC- 
 TRICAL 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 
 5 
 8 
 12 
 15 
 
 20 
 25 
 30 
 35 
 40 
 
 45 
 50 
 55 
 60 
 65 
 
 3,000 
 5,000 
 8,000 
 12,000 
 15,000 
 
 20,000 
 25,000 
 30,000 
 35,000 
 40,000 
 
 45,000 
 50,000 
 55,000 
 60,000 
 65,000 
 
 54.78 
 70.72 
 89.45 
 109.55 
 122.48 
 
 141.43 
 
 158.12 
 173.21 
 187.09 
 200.00 
 
 212.14 
 
 223.61 
 234.53 
 244.95 
 254.96 
 
 70 
 75 
 80 
 85 
 90 
 
 95 
 100 
 110 
 120 
 130 
 
 140 
 150 
 160 
 
 170 
 
 180 
 
 70,000 
 75,000 
 80,000 
 85,000 
 90,000 
 
 95,000 
 100,000 
 110,000 
 120,000 
 130,000 
 
 140,000 
 150,000 
 160,000 
 170,000 
 180,000 
 
 264.58 
 273.87 
 282.85 
 291.55 
 300.00 
 
 308.23 
 316.23 
 33 1 .67 
 346.42 
 360.56 
 
 374.17 
 387.30 
 400.00 
 412.32 
 424.27 
 
 190 
 200 
 220 
 240 
 260 
 
 280 
 300 
 320 
 340 
 360 
 
 190,000 
 200,000 
 220,000 
 240,000 
 260,000 
 
 280,000 
 300,000 
 320,000 
 340,000 
 360,000 
 
 435.89 
 447.22 
 469.05 
 489.90 
 509.91 
 
 529.16 
 547.73 
 565.69 
 583.10 
 600.00 
 
 TWIST DRILL AND STEEL WIRE GAUGE. 
 
 (Morse Twist Drill and Machine Co.) 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 
 inch. 
 
 1 
 
 .2230 
 
 11 
 
 .1910 
 
 7,1 
 
 .1590 
 
 31 
 
 .1200 
 
 41 
 
 .0960 
 
 51 
 
 .0670 
 
 ?. 
 
 .2210 
 
 12 
 
 .1890 
 
 22 
 
 .1570 
 
 32 
 
 .1160 
 
 42 
 
 .0935 
 
 52 
 
 .0635 
 
 3 
 
 .2130 
 
 13 
 
 .1850 
 
 23 
 
 .1540 
 
 33 
 
 .1130 
 
 43 
 
 .0890 
 
 53 
 
 .0595 
 
 4 
 
 .2090 
 
 14 
 
 .1820 
 
 7,4 
 
 .1520 
 
 34 
 
 .1110 
 
 44 
 
 .0860 
 
 54 
 
 .0550 
 
 5 
 
 .2055 
 
 15 
 
 .1800 
 
 7.5 
 
 .1495 
 
 35 
 
 .1100 
 
 45 
 
 .0820 
 
 55 
 
 .0520 
 
 6 
 
 .2040 
 
 16 
 
 .1770 
 
 26 
 
 .1470 
 
 36 
 
 .1065 
 
 46 
 
 .0810 
 
 56 
 
 .0465 
 
 7 
 
 .2010 
 
 17 
 
 .1730 
 
 27 
 
 .1440 
 
 37 
 
 .1040 
 
 47 
 
 .0785 
 
 57 
 
 .0430 
 
 8 
 
 .1990 
 
 18 
 
 .1695 
 
 28 
 
 .1405 
 
 38 
 
 .1015 
 
 48 
 
 .0760 
 
 58 
 
 .0420 
 
 9 
 
 .1960 
 
 19 
 
 .1660 
 
 29 
 
 .1360 
 
 39 
 
 .0995 
 
 49 
 
 .0730 
 
 59 
 
 .0410 
 
 10 
 
 .1935 
 
 20 
 
 .1610 
 
 30 
 
 .1285 
 
 40 
 
 .0980 
 
 50 
 
 .0700 
 
 60 
 
 .0400 
 
 STUBS' STEEL WIRE GAUGE. 
 
 (For Nos. 1 to 50 see table on page 29.) 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 inch. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 No. 
 
 Size. 
 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 inch. 
 
 Z 
 
 .413 
 
 P 
 
 .323 
 
 W 
 
 .257 
 
 51 
 
 .066 
 
 61 
 
 .038 
 
 71 
 
 .026 
 
 Y 
 
 .404 
 
 o 
 
 .316 
 
 b) 
 
 .250 
 
 52 
 
 .063 
 
 62 
 
 .037 
 
 72 
 
 .024 
 
 X 
 
 .397 
 
 N 
 
 .302 
 
 1) 
 
 .246 
 
 53 
 
 .058 
 
 63 
 
 .036 
 
 73 
 
 .023 
 
 W 
 
 .386 
 
 M 
 
 .295 
 
 C 
 
 .242 
 
 54 
 
 .055 
 
 64 
 
 .035 
 
 74 
 
 .022 
 
 V 
 
 .377 
 
 r, 
 
 .290 
 
 B 
 
 .238 
 
 55 
 
 .050 
 
 65 
 
 .033 
 
 75 
 
 .020 
 
 u 
 
 .368 
 
 K 
 
 .281 
 
 A 
 
 .234 
 
 56 
 
 .045 
 
 66 
 
 .032 
 
 76 
 
 .018 
 
 T 
 
 .358 
 
 .1 
 
 .277 
 
 1 
 
 (See 
 
 57 
 
 .042 
 
 67 
 
 .031 
 
 77 
 
 .016 
 
 s 
 
 .348 
 
 T 
 
 .272 
 
 to 
 
 {page 
 
 58 
 
 .041 
 
 68 
 
 .030 
 
 78 
 
 .015 
 
 H, 
 
 .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 
 
 THE EDISON OR CIRCULAR 3IIL 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 cm., 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 cm, 
 
 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 
 specity 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 
 
 Slates. This has given rise to much misunderstanding and friction 
 etween 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 
 
32 
 
 
 
 ARITHMETIC. 
 
 
 
 
 
 U. S. STANDARD GAUGE FOR SHEET AND PLATE 
 
 
 IRON AND STEEL, 
 
 1893. 
 
 
 
 S3 S. 
 
 BO 
 
 
 Approximate 
 
 Thickness in 
 
 Decimal 
 
 Parts of an 
 
 Inch. 
 
 li 1 
 
 ■Ha -£ 
 oo-S S 
 
 < •* 
 
 Weight per 
 
 Square Foot 
 
 in Ounces 
 
 Avoirdupois. 
 
 Weight per 
 
 Square Foot 
 
 in Pounds 
 
 Avoirdupois. 
 
 Hi 
 
 >• & 
 
 Hi 
 
 II! 
 
 as .3 
 
 6^ • 
 en £.22 
 
 ill 
 -.S'2 
 
 0000000 
 
 1-2 
 
 0.5 
 
 12.7 
 
 320 
 
 20. 
 
 9.072 
 
 97.65 
 
 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 
 
 1.984 
 
 21.36 
 
 47.09 
 
 13 
 
 3-32 
 
 0.09375 
 
 2.38125 
 
 60 
 
 3.75 
 
 1.701 
 
 18.31 
 
 40.36 
 
 14 
 
 5-64 
 
 0.078125 
 
 1.984375 
 
 50 
 
 3.125 
 
 1.417 
 
 15.26 
 
 33.64 
 
 15 
 
 9-128 
 
 0.0703125 
 
 1.7859375 
 
 45 
 
 2.8125 
 
 1.276 
 
 13.73 
 
 30.27 
 
 16 
 
 1-16 
 
 0.0625 
 
 1.5875 
 
 40 
 
 2.5 
 
 1.134 
 
 12.21 
 
 26.91 
 
 17 
 
 9-160 
 
 0.05625 
 
 1 .42875 
 
 36 
 
 2.25 
 
 1.021 
 
 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 
 
 1.75 
 
 0.7938 
 
 8.544 
 
 18.84 
 
 20 
 
 3-80 
 
 0.0375 
 
 0.9525 
 
 24 
 
 1.50 
 
 0.6804 
 
 7.324 
 
 16.15 
 
 21 
 
 1 1-320 
 
 0.034375 
 
 0.873125 
 
 22 
 
 1.375 
 
 0.6237 
 
 6.713 
 
 14.80 
 
 22 
 
 1-32 
 
 0.03125 
 
 0.793750 
 
 20 
 
 1.25 
 
 0.567 
 
 6.103 
 
 13.46 
 
 23 
 
 9-320 
 
 0.028125 
 
 0.714375 
 
 18 
 
 1.125 
 
 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 
 
 2 746 
 
 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 
 
 6V2 
 
 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 
 
 5V2 
 
 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 
 
 41/2 
 
 0.28125 
 
 0.1276 
 
 1.373 
 
 3.03 
 
 37 
 
 1 7-2560 
 
 0.00664062 
 
 0.16867187 
 
 41/4 
 
 0.26562 
 
 0.1205 
 
 1.297 
 
 2.87 
 
 38 
 
 1-160 
 
 0.00625 
 
 0.15875 
 
 4 
 
 0.25 
 
 0.1134 
 
 1.221 
 
 2.69 
 
 
 
 
 
 
 
 
 
 
THE DECIMAL GAUGE. 
 
 33 
 
 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. 
 
 
 
 2 
 
 Weight per 
 
 
 
 
 Weight per 
 
 • 
 
 a 
 
 . 
 
 Square Foot 
 
 • 
 
 § 
 
 ! 
 
 Square Foot 
 
 O 
 
 in Pounds. 
 
 3 
 
 
 
 .2 
 
 in Pounds. 
 
 ■£-5 
 ££ 
 *fi 
 
 go 
 a 
 a 
 < 
 
 3 
 
 ^ 
 
 vO 
 
 £§ 
 
 a 
 
 &* 
 
 •& 
 
 "3 • 
 
 a 
 
 i 
 
 • 
 
 00 3 
 
 
 a 
 
 *g 
 
 i 
 
 Sri 
 
 §> 
 
 01 
 
 Q 
 
 2 
 
 a 
 a 
 < - 
 
 a 
 
 
 Oi 
 
 Q 
 
 aS 
 
 a 
 < 
 
 
 a 
 a 
 < 
 
 TO 
 
 fife 
 
 a 
 
 "i Ja ri 
 
 0.002 
 
 1/500 
 
 0.05 
 
 0.08 
 
 0.082 
 
 0.060 
 
 i/is- 
 
 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 /l00 
 
 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 
 
 11/100 
 
 2.79 
 
 4.40 
 
 4.488 
 
 0.022 
 
 U/500 
 
 0.56 
 
 0.88 
 
 0.898 
 
 0.125 
 
 1/8 
 
 3.18 
 
 5.00 
 
 5.100 
 
 0.025 
 
 1/40 
 
 0.64 
 
 1.00 
 
 1.020 
 
 0.135 
 
 27/200 
 
 3.43 
 
 5.40 
 
 5.508 
 
 0.028 
 
 7/250 
 
 0.71 
 
 1.12 
 
 1.142 
 
 0.150 
 
 3/20 
 
 3.81 
 
 6.00 
 
 6.120 
 
 0.032 
 
 1/32 + 
 
 0.81 
 
 1.28 
 
 1.306 
 
 0.165 
 
 33/200 
 
 4.19 
 
 6.60 
 
 6.732 
 
 0.036 
 
 9/250 
 
 0.91 
 
 1.44 
 
 1.469 
 
 0.180 
 
 9/50 
 
 4.57 
 
 7.20 
 
 7.344 
 
 0.040 
 
 1/25 
 
 1.02 
 
 1.60 
 
 1.632 
 
 0.200 
 
 1/5 
 
 5.08 
 
 8.00 
 
 8.160 
 
 0.045 
 
 9 /200 
 
 1.14 
 
 1.80 
 
 1.836 
 
 0.220 
 
 H/50 
 
 5.59 
 
 8.80 
 
 8.976 
 
 0.050 
 
 1/20 
 
 1.27 
 
 2.00 
 
 2.040 
 
 0.240 
 
 6 /25 
 
 6.10 
 
 9.60 
 
 9.792 
 
 0.055 
 
 11/200 
 
 1.40 
 
 2.20 
 
 2.244 
 
 0.250 
 
 1/4 
 
 6.35 10.00 
 
 10.200 
 
 '■9 
 
 ^OlMALGA^I^ 
 
 
 STANDARD O 
 
34 
 
 ALGEBRA. 
 
 Addition. — Add a, 6, and - c. Ans. a + b - c. 
 
 Add 2a and - 3a. Ans. - a. Add 2ab, - 3ab, — c, — 3c. Ans, 
 
 — ab — 4c. Add a 2 and 2a. Ans. a 2 4 2a. 
 
 Subtraction. — Subtract a from 6. Ans. b — a. Subtract - a from 
 
 — 6. Ans. — & + a. 
 
 Subtract b + c from a. Ans. a - 6 — c. Subtract 3a 2 & - 9c from 
 4a 2 6 4 c. Ans. a 2 b + 10c. Rule: Change the signs of the subtrahend 
 and proceed as in addition. 
 
 Multiplication. — Multiply a by 6. Ans. ab. Multiply ab by a + b. 
 Ans. a 2 6 + ab 1 . 
 
 Multiply a+ b by a + b. Ans.- (a +6) (a 4 6) = a 2 4- 2a6 4 6 2 . 
 
 Multiply — a by - b. Ans. ab. Multiply -a by 6. Ans. - ab. 
 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 Xa 3 = a 5 ; a 2 b 2 X ab = a 3 6 3 ; - lab X 2ac = - 14a 2 6c. 
 
 To multiply a polynomial by a monomial, multiply each term of the 
 polynomial by the monomial and add the partial products: (6a — 3b) 
 X 3c = 18ac - 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 + 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 + 6)2 = a 2 4 2ab 4 6 2 ; (a - 6) 2 = a 2 - 2a6 + 6 2 ; 
 (a + 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: ( — — I = a6 4 ( — — I • 
 
 The square of the sum of two quantities is equal to four times their 
 products, plus the square of their difference: (a 4- 6) 2 = 4a6 + (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 + (a - 6) 2 . 
 
 The square of a trinomial = square of each term + twice the product 
 of each term by each of the terms that follow it: (a + 6 + c) 2 = a 2 4- 6 2 
 4 c 2 + 2a6 + 2ac 4- 26c; (a - 6 - c) 2 = a 2 + 6 2 + c* - 2a6- 2ac + 26c. 
 
 The square of (any number + 1/2) = square of the number 4- the number 
 + 1/4: = the number X (the number 4- 1) + 1/4: (a + V2) 2 = a 2 + a + 1/4, 
 = a(a+ 1)4- 1/4. (4V 2 ) 2 = 4 2 + 4 + l/ 4 = 4 X 5 +1/4= 20l/ 4 . 
 
 The product of any number 4- 1/2 by any other number 4- 1/2 = product 
 of the numbers 4 half their sum 4 1/4. (a 4 1/2) X (6 4- 1/2) = a6 4 l?2(& 46) 
 4 1/4. 41/2 X 6V2 = 4 X 6 4- 1/2(4 4- 6) 4- 1/4 = 24 + 5 4- 1/4 = 291/4. 
 
 Square, cube, 4th power, etc., of a binomial a+b. 
 
 (a 4 6) 2 = a 2 4- 2a6 + 6 2 ; (a 4 6) 3 = a 3 4- 3a 2 6 4 3a6 2 + 6 3 
 (a + b)* = a 4 4- 4a 3 6 4- 6a 2 6 2 4- 4a& 3 4- 6*. 
 
 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. 
 
35 
 
 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 value 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) = l— a+b+c. When a parenthesis is within a 
 parenthesis remove the inner one first: a — [& - {c — (d — e)}] = a — [ft — 
 {c — d + e} ] = 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 + b X a + b = a + ab + b; while (a + b) 
 X (a + b) = a 2 + 2ab + b 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 -h b = ac; 
 abc h- — b = — 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: 
 
 9 , . a 2 bx a, 
 
 a 2 bx -5- aby = —. — = - , 
 
 aby y a 3 'a 5 a 2 
 
 To divide a polynomial by a monomial, divide each term of the poly- 
 nomial by the monomial: (Sab — I2ac) -j- 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 — 6 2 ) -4- (a +6). 
 
 The difference of two equal odd powers of any two numbers is divisible 
 by their difference and also by their sum: 
 
 (a* -&s) -5- (a-b) =a 2 +ab +b 2 ; (a 3 - & 3 ) -s- (a +6) =a 2 -ab +b 2 . 
 
 The difference of two equal even powers of two numbers is divisible by 
 their difference and also by their sum: (a 2 — b 2 ) -f- (a — o) = a + b. 
 
 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 byx 4- y or by x — y, 
 but is divisible by x 2 + y 2 . 
 
 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 
 
36 ALGEBRA. 
 
 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 8x - 29 = 26 - 3x. 8x + 3x — 29 + 26; llz = 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, x + 14 the greater, x + x + 14 = 48. 
 2x = 34, x = 17; x + 14 = 31, ans. 
 
 Find a number whose treble exceeds 50 as much as its double falls short 
 of 40. Let x = the number. 3x — 50 = 40 — 2x; 5x = 90; x = 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. 
 
 c n1v „ | 2x + 3y = 7. Multiply by 2: 4x + 6y =14 
 
 &olve \ 4k - 5y = 3. Subtract : 4x - by = 3 lly - 11 ; y = 1. 
 
 Substituting value of y in first equation, 2x + 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. 
 
 Solve ! 2x + 3 V = 8 " (1 >- From (1 > we find x = 8 ~o 3V - 
 bolve (3x + 7y = 7. (2). 2 
 
 Substitute this value in (2):3( 8 ~ 3y ) +7y = 7; =24-9y + 14?/ = 14, 
 
 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 other. 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 
 
 x = ik + *y. From (2) we end x = i^l. 
 
 Equating these values of x, 1— y = "t v ; 19y = — 19; y = - 1. 
 
 Substitute this value of y in (1): 2x + 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, 
 and the known quantities on the other; divide by the coefficient of the 
 unknown quantity and extract the square root of each side of the resulting 
 equation; _ 
 
 Solve 3x 2 - 15 = 0. 3z 2 = 15; x 2 = 5; x = ^5. 
 
 A root like ^5, which is indicated, but which can be found only approxi- 
 mately, is called a surd. 
 
ALGEBRA. 37 
 
 Solve 3x 2 + 15 = 0. 3x = - 15; x 2 = - 5; x = V~5. 
 
 The square root of — 5 cannot be found even approximately, for the 
 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 2 x 2 ± 2dbx = 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±b, 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:r 2 — 4.r= 32. To make the coefficient of x 2 a square number, 
 
 multiply by 3 : 9x 2 - 12s = 96; 12x -e- (2 X 3x) = 2; 2 2 = 4. 
 
 Complete the square: 9a; 2 — 12x + 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 t o the form ax 2 +bx+c=0. 
 
 — b ± *^b 2 — Aac 
 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, x 2 + (x + l) 2 = 481. 2z 2 + 
 2x + 1 = 481. 
 
 x 2 + x = 240. Completing the square, x 2 +x + 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. — ^Ja when n is a positive integer is one of n 
 
 n /~m 
 -qual factors of a. *\ja means a is to be raised to the mth power and the 
 
 nth root extracted. 
 
 ( Vaf 
 
 ' means that the nth root of a is to be taken and the result 
 raised to the mth power. 
 
 ya m = ( Vo ) 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 s = a 1 - 5 . 
 
 To extract the root of a quantity raised to an indicated power, divide 
 the exponent by the index of the required root; as, 
 
 m 
 yaJ 1 = a » ; \/a 6 = a 6 /3 = a 2 . 
 
 Subtracting 1 from the exponent of a is equivalent to dividing by a: 
 
 a 2 ~i= a 1 = a; a 1 "* = a = -= 1; a - 1 = a" 1 = -; a ~ l -i = a~2= I. 
 a a a 2 
 
 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: 
 
 VoJb = v^i x Vb = a Vb. 
 
38 
 
 GEOMETRICAL PROBLEMS. 
 
 A factor outside the radical sign may be raised to the corresponding 
 power and placed under it : 
 
 Binomial Theorem. — To obtain any power, as the nth, of an expres- 
 sion of the form x + a s 
 {a + x) n_ n n^„ n n-i,._ u n(n - l)a ^ n(w-l)(n-: 
 
 etc. 
 
 ri = a n + na a 
 
 l x + 
 
 - x 2 + 
 
 1.2 1.2.3. 
 
 The following laws hold for any term in the expansion of (a + x) n . 
 
 x 3 -\ 
 
 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 + 1. 
 
 The last factor of the numerator will be n — r +2. 
 
 The last factor of the denominator will be = r — 1. 
 
 n(n - l)(n - 2) . . (n - r+ 2) „n-r + i .M. 
 1.2.3....&— 1) a X 
 
 Hence the rth term = 
 
 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 25, 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 I), 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, 
 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, 8» 
 10, or 9, 12, 15. 
 
GEOMETRICAL PROBLEMS. 
 
 39 
 
 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 C, D, and draw the 
 parallel lines C D touching the arcs. 
 
 I I 
 
 _<! A— 
 
 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, A22, 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 / 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 I, 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 I; 
 draw the perpendicular / H equal to 
 / F, and join H F to form the angle at 
 F, The angle at H is also 45°. 
 
40 
 
 GEOMETRICAL PROBLEMS. 
 
 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 D. 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 points 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. 
 
 Fig. 14. 
 
 Fig. 15, 
 
 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, F G, 
 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 A H, B G. 
 Through the third point C draw 
 A E, BF, 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, B M, 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 B C 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, which is the tangent required. 
 
GEOMETRICAL PROBLEMS. 
 
 41 
 
 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 EF, 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, CD, by 
 the line N O. From a point P in this 
 line draw the perpendicular PB to the 
 line A B, and on P describe the circle 
 BD, touching the lines and cutting 
 the centre line at E. From E draw 
 E F perpendicular to the centre line, 
 cutting AB 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 F C 
 which bisects the angle of the 
 lines (Fig. 18). — Through F draw 
 DA at right angles to FC\ bisect 
 the angles A and D, as in Problem 
 11, by lines cutting at C, and from 
 C with radius C F draw the arc H FG 
 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 £F at right 
 angles to AB; 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 AB, 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 C H and bisect it with the per- 
 pendicular L I, cutting E F at /. 
 On the centre I, with radius IF, 
 describe the arc FA as required. 
 
 Fig. 20. 
 
42 
 
 GEOMETRICAL PROBLEMS. 
 
 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 a 
 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, and 
 D B to form the square. 
 
 25. To construct a rectangle 
 with given base E F and height E H 
 
 (Fig. 25). — On the base E F draw 
 the perpendiculars E H, F G 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 
 
GEOMETRICAL PROBLEMS. 
 
 43 
 
 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. 
 
 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 i 5; 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. 
 
44 
 
 GEOMETRICAL PROBLEMS. 
 
 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, 
 with the radius g A, describe a circle; 
 with the same radius set off the arcs 
 AG, 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 A C B. 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, 
 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, 
 B F; bisect the external angles yl 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 square 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. 
 
 45 
 
 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 ef, 
 etc., and join A e, e B, etc., to form 
 the octagon, 
 
 39. To describe an octagon 
 about a circle (Fig. 39). — Describe 
 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, 6, 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, 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 C, 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 
 
46 
 
 GEOMETRICAL PROBLEMS. 
 
 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 Dis 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 
 
 Angle 
 
 Number 
 
 Angle 
 
 Number 
 
 Angle 
 
 of Sides. 
 
 at Centre. 
 
 of Sides. 
 
 at Centre. 
 
 of Sides. 
 
 at Centre. 
 
 No. 
 
 Degrees. 
 
 No. 
 
 Degrees. 
 
 No. 
 
 Degrees. 
 
 3 
 
 120 
 
 9 
 
 40 
 
 15 
 
 24 
 
 4 
 
 90 
 
 10 
 
 36 
 
 16 
 
 221/2 
 
 5 
 
 72 
 
 11 
 
 328/u 
 
 17 
 
 21 3/ 17 
 
 6 
 
 60 
 
 12 
 
 30 
 
 18 
 
 20 
 
 7 
 
 513/7 
 
 13 
 
 279/ 13 
 
 19 
 
 19 
 
 8 
 
 45 
 
 14 
 
 25 5/ 7 
 
 20 
 
 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 D, 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 H, 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 D, half the conjugate axis. 
 
 Fig. 45, 
 
GEOMETRICAL PROBLEMS. 
 
 47 
 
 Place the slip so as to bring the point 5 on the line A B of the transverse 
 axis, and the point 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 point c on the conjugate axis, any number of 
 points in the curve may be found, through which the curve may be 
 
 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. 
 By 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', for the foci. Divide 
 A C into a number of parts at the 
 points 1, 2, 3, etc. With the radius 
 A I on F and F' as centres, describe 
 arcs, and with the radius B I 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', b', etc. 
 From a, b, etc., draw perpendiculars 
 to A B; and from a' , b' , 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. 
 
 6th Method (Fig. 49). — When the 
 transverse and conjugate diameters 
 are given, AB,C D, 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, cutting the 
 circumference at I, 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 GC, cutting the 
 lines O E, Or, etc., at L, M, N, etc. 
 
4S 
 
 GEOMETRICAL PROBLEMS. 
 
 ^-~~c 
 
 c \ 
 
 
 V \ 
 
 
 77i 
 
 /e V 
 
 D 
 
 Fig. 50. 
 
 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 ac; 
 set off O e equal to 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 & 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 f 
 and lay off e g equal to e f, and use g b 
 as radius for the arc at each extrem- 
 Fig. 51. ity of the major axis. 
 
 The method is not considered applicable for cases in which the minor 
 axis is 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 a 
 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 6 at a. Thus the five 
 centres D, a. b, H, H' 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. 
 
 Uh 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. 
 
GEOMETRICAL PROBLEMS. 
 
 49 
 
 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 f 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 b d. Join e h, and draw c k 
 and b I parallel to e h. Take a k for the longest radius ( = R) t 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 b arnd c d (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 gh as a 
 radius, draw the arc h k; 
 with the centre e and 
 radius e f draw the arc f 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 to 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 
 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 D C, drawn across 
 the figure at right angles to the axis is a 
 double ordinate, and either half of it is an 
 ordinate. 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. 
 
 K 
 
 
 e 
 
 L 
 
 E 
 
 
 A 
 
 G 
 
 n/ 
 
 F 
 
 \ 
 
 
 J 
 
 
 
 
 
 J 
 
 o 
 
 
 \™ 
 
 1 
 
 
 
 
 
 D 
 
 B 
 b 
 
 
 "«^ 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 b. Set off A e, A F, each equal to 
 B b; and draw K eL 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, 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). 
 
50 
 
 GEOMETRICAL PROBLEMS. 
 
 d cbaBabcd 
 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 G, 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 and B D into any number of 
 equal parts, say five, at a, b, 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, dinC E 
 and D F draw lines to the vertex A, 
 cutting the perpendiculars at e, f,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' F 
 the distance between them. Take a 
 ruler longer than the distance F' F, 
 and fasten one of its extremities at 
 the focus F' . At the other extrem- 
 ity, II, 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 r 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' II as a 
 radius describe the arc of a circle. 
 Then with F as a centre and iV H as a radius describe an arc intersecting 
 the arc before described at p and q. These will be points of the hyper- 
 bola, for F' a — 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. 
 
 Th,e Equilateral Hyperbola. — The transverse axis of a hyperbola is 
 
 Fig. 58. 
 
GEOMETRICAL PROBLEMS. 
 
 51 
 
 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 pi, and vi are the 
 ordinate and abscissa of any other point, pv = pivi; or pv = a constant. 
 
 48. The Cycloid (Fig. 
 .60). — If a circle A d 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 = Al, 2b = A2, 3c = 
 A3, etc. The points A, a, b, 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 U" B is the epicycloid. 
 
 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 = 
 radius 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., 
 the axis. From O set off on R a 
 small distance, oa; with radius R and 
 centre a cut the axis at 1, join a 1, 
 and set off a like small distance a b\ 
 from 6 with radius R cut axis at 2, 
 join 6 2, and so on, thus finding 
 points o, a, b, c, d, etc., through which 
 the curve is to be drawn- 
 
 Fig. 63 8 
 
52 
 
 GEOMETRICAL PROBLEMS. 
 
 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). 
 
 This 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 
 corresponding to the scale upon which the 
 
 Fig. 64. 
 
 the distances 1, 2, 3, 4, etc . 
 curve is drawn, as shown in Fig. 
 
 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, construcfa 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 
 Yig. 65. eacn arc °f tne external # 
 
 forming a quadrant of a spire. 
 
 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 1/2-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 
 given ring. We have now to find 
 the 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 
 and C D ; since the polygon has twelve 
 sides the angle A C D = 30° and 
 ACB = 15°. One half of the side 
 A D is equal to A B. We now give 
 the following proportion: The sine 
 of the angle A C B is to A B as 1 is to 
 the required radius. From this we 
 get 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 he 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 
 size, or on a smaller scale if more convenient, and erect a perpendicular at 
 one end, thus making rectangular axes of coordinates. Erect perpen- 
 diculars at points 1, 2, 3, and 4 feet from the first perpendicular. Find 
 values of y in the formula of the circle, x 2 + y 2 — R 2 , by substituting for 
 
GEOMETRICAL PROBLEMS. 
 
 53 
 
 x the values 0, 1, 2, 3, and 4, etc and fo r R 2 the square of the radius, or 
 400. The values will be y = V '#» _ x i = V 4 00, ^399, ^396, V39I, 
 
 V384; = 20, 19.975, 19.90, 19.774, 19.596. 
 Subtract the smallest, „„„„ „ * 4 
 
 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 
 
 »-l(^.~ 5 ). 
 
 in which e is the 
 
 base" of the Napierian system of log- 
 arithms. 
 
 To plot the catenary. — Let 
 (Fig. 67) be the origin of coordinates. 
 Assigning to a any value a% 3, the 
 equation becomes 
 
 ,-§(.C-S). 
 
 To find the lowest point of the 
 curve. 
 
 . Put a; - 0; .\ y=^ (e°+e- 
 
 ; (1.396 +0.717) =3.17. 
 
 (e 3 + e 3 )= I (1.948 +0.513) =3.69. 
 
 Then put x = l; .'. V 
 Put z = 2; .'. y- 
 
 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' . 
 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 
 y = a>. 
 
 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 and 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 \a t perpendicular to CI; 2 a 2 perpendicular to C2; and 
 so on. Make la x equal to bb x ; 2 a 2 equal to b b 2 ; 3 03 equal to 6 6 3 ; and 
 so on. Join the points A, a u a 2 , az, etc., by a curve; this curve will be 
 the required involute. 
 
 Fig. 68. 
 
54 GEOMETRICAL PROPOSITIONS. 
 
 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 be 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 0° 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 off at the rate of 1 by scale for each degree. 
 
 Angle. Chord. Angle. Chord. Angle. Chord. 
 
 1° 0.999 40° 39.192 30° 73.658 
 
 10° 9.98S 50° 48.429 90° 81.029 
 
 20° 19.899 60° 57.296 100° 87.782 
 
 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 is 
 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, the 
 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. 
 
MENSURATION — PLANE SURFACES, 55 
 
 Degree of 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 1/2 n 
 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^ degrees further and a 100 ft. chord 
 is measured from the point already found to 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, 
 
 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 = ^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 sides 
 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, hay- 
 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°. 
 
 Hypothe nuge of a right-angled triangle, the side opposite the right 
 angle, = v sum of the squares of the other two si des. If a and b are the 
 two sides and c the hypothenuse, c 2 =a 2 + & 2 ; a = V c 2 — & 2 = v / ( c +6)(c — 6). 
 
 If the two sides are equal, side = hyp 4- 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 
 
 a 2 v's 
 one of its sides multiplied by the square root of 3, = — -r- , a being the 
 
 side; or a 2 X 0.433013. 
 
56 
 
 MENSURATION. 
 
 Area of a triangle given, to find base: Base = twice area -s- perpendicular 
 height. 
 
 Area of a triangle given, to find height: Height = twice area -h 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 by drawing the 
 perpendicular. Half this difference being added to or subtracted ^from 
 half the base will give the two divisions thereof. As each side and its 
 opposite division of the base constitutes a right-angled triangle, th e 
 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.S6G03, what is the area of a similar 
 triangle whose height = 1? 0.86603 2 : l 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 polygons 
 
 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 
 
 
 
 
 Jl 
 
 Radius of Cir- 
 cun. scribed 
 
 1> • 
 
 03 6 
 
 
 
 
 d 
 
 
 i 
 
 Circle. 
 
 •gll 
 
 
 a5 
 
 < 
 
 
 
 
 |d2 
 
 tacj 
 d"^ 
 
 i 
 
 m 
 6 
 
 >> 
 I 
 "3 
 
 a 
 
 II 
 
 of 
 
 K3 
 
 o 
 w 
 
 2 11 
 
 c £ 
 gg 
 
 
 
 .S'm 
 
 3 " • 
 
 111 
 
 6 
 
 "oj 
 Oi 
 
 T3> 
 d 
 
 fc 
 
 & 
 
 -S3 
 
 < 
 
 Ph 
 
 w. 
 
 ti 
 
 A 
 
 < 
 
 < 
 
 3 
 
 Triangle. 
 
 0.4330 
 
 0.5773 
 
 2.000 
 
 0.5773 
 
 0.2887 
 
 1.732 
 
 120° 
 
 60° 
 
 4 
 
 Square 
 
 1.0000 
 
 1 . 0000 
 
 1.414 
 
 0.7071 
 
 0.5000 
 
 1.4142 
 
 90 
 
 90 
 
 5 
 
 Pentagon 
 
 1 . 7205 
 
 0.7265 
 
 1.236 
 
 0.8506 
 
 0.6382 
 
 1.1756 
 
 72 
 
 108 
 
 6 
 
 Hexagon 
 
 2.5981 
 
 0.8660 
 
 1.155 
 
 1 . 0000 
 
 0.866 
 
 1 . 0000 
 
 60 
 
 120 
 
 7 
 
 Heptagon 
 
 3.6339 
 
 0.7572 
 
 1.11 
 
 1 . 1 524 
 
 1.0333 
 
 0.8677 
 
 51 26' 
 
 1284-7 
 
 8 
 
 Octagon 
 
 4.8284 
 
 0.8284 
 
 1.082 
 
 1 . 3066 
 
 1.2071 
 
 0.7653 
 
 45 
 
 135 
 
 9 
 
 Nonagon 
 
 6.1818 
 
 0.7688 
 
 1.064 
 
 1.4619 
 
 1.3737 
 
 684 
 
 40 
 
 140 
 
 10 
 
 Decagon 
 
 7.6942 
 
 0.8123 
 
 1.051 
 
 1.613 
 
 1.5388 
 
 0.618 
 
 36 
 
 144 
 
 11 
 
 Undecagon 
 
 9.3656 
 
 0.7744 
 
 1.042 
 
 1.7747 
 
 1 . 7028 
 
 0.5634 
 
 32 43' 
 
 147 3-11 
 
 12 
 
 Dodecagon 
 
 11.1962 
 
 0.8038 
 
 1.035 
 
 1.9319 
 
 1.666 
 
 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. of 
 circumscribed circle. ' 
 
AREA OF IRREGULAR FIGURES. 
 
 57 
 
 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° -h no. of s" n 
 
 of sides sin (180°/n) 
 
 No. 
 
 sin (180° In) 
 
 No. 
 
 sin (180°/n) 
 
 3 0.86603 
 
 9 
 
 0.34202 
 
 15 
 
 0.20791 
 
 4 .70711 
 
 10 
 
 .30902 
 
 16 
 
 .19509 
 
 5 .58778 
 
 11 
 
 .28173 
 
 17 
 
 .18375 
 
 6 .50000 
 
 12 
 
 .25882 
 
 18 
 
 .17365 
 
 7 .43388 
 
 13 
 
 .23931 
 
 19 
 
 .16458 
 
 8 .38268 
 
 14 
 
 .22252 
 
 20 
 
 .15643 
 
 To find the area of an irregular 
 figure (Fig. 69). — Draw ordinates 
 across 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. 
 
 In a figure of very irregular outline, 
 
 1 
 
 1 i 2 v, i. 
 
 5 6 7 I: 9 K 
 
 - Length 
 
 Fig. 69. 
 
 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. — DiJ'ide 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 B\ add together the odd ordinates, 
 except the first and last, and call the sum C. Then, 
 
 area of the figure ■■ 
 
 -4B+ 2C 
 
 X D. 
 
 4th Method: Durand's Rule. — Add together 4/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 
 obtain 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 the 
 
58 
 
 MENSURATION. 
 
 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 word "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 + sum of the other ordinates) Vio of (sum of penultimates 
 - sum of first and last) and multiplying by the common distance between 
 the ordinates. 
 
 5th 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. 
 
 1th 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. 
 
 Approximations, — = 3.143; ^ = 3.1415929. 
 
 The ratio of circum. to diam. is represented by the symbol k (called Pi). 
 Area = 0.7854 X square of the diameter. 
 
 Multiples of v. 
 
 Ik = 3.14159265359 
 2k = 6.28318530718 
 3k = 9.42477796077 
 4rr = 12.56637061436 
 5k = 15.70796326795 
 6k = 18.84955592154 
 In = 21.99114857513 
 8k = 25.13274122872 
 9k = 28.27433388231 
 
 1/47! 
 
 Multiples of -• 
 
 = 0.7853982 
 X 2 = 1.5707963 
 X 3 = 2.3561945 
 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 1/4* = 1.27324. 
 Multiples of 1/tt. 
 1/k = 0.31831 
 2/k = 0.63662 
 2>/k = 0.95493 
 4/tt = 1.27324 
 
 5/tt = 1.59155 
 6/k - 1.90986 
 
 -ence 
 
 = reciprocal of k = 0.3183099. 
 
 1/k 
 8/k 
 9/k 
 10/k 
 12 A 
 
 = 2.22817 
 = 2.54648 
 = 2.86479 
 = 3.18310 
 = 3.81972 
 
 k/12 = 
 
 tt/360 = 
 360A = 
 
 K 2 — 
 1/tt* = 
 
 0.261799 
 0.0087266 
 114.5915 
 9.86960 
 0.101321 
 
 k/2 
 
 =. 1.570796 
 
 V* = 
 
 1.772453 
 
 k/3 
 
 = 1.047197 
 
 v£- 
 
 0.564189 
 
 k/Q 
 
 = 0.523599 
 
 Log k = 
 
 0.4971498' 
 
 
 
 Log tt/4 = 
 
 1.895090 
 
 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, 
 
THE CIRCLE. 59 
 
 C = nD; =2nR; = ~ ; = 2^71; = 3.545VJ; 
 
 4 = Z) 2 X.7854;= ^ ; = 4# 2 X.7854; = ;r# 2 ; =^D 2 ; =^ ; = .07958C 2 ; = ~- 
 
 £>=-; = 0.31831C; = 2 J - ; = 1.12838 V^T; 
 
 R = £ ; = (U59155C; = 4/- ; = 0.564189 ^A. 
 
 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, 
 
 8c — C 9 f X 10F 
 
 Length of the arc = L = (very nearly), = "' _ 27 y +2c, nearly, 
 
 Vq* + 4F 2 X 1072 
 
 '- 2c, nearly. 
 
 15C 2 + 33 F 2 
 
 Chord of the arc C, = 2 V C 2 _ y 2 . = Vd 2 - (D - 2V) 2 ; = 8c - 3L 
 = 2\/R2 _ ^ R _ F)2 . = 2 V(D - V) X V. 
 arc, c = 
 
 Diameter of the circle, D = 
 
 Chord of half the arc, c = 1/2 ^ C 2 + 4 V 2 ; = Vd x V; = (3L + C) • 
 
 c 2 1/4 C 2 + F 2 
 
 y 
 
 Rise of the arc, V = ^ ; = 1/2 (D - Vd 2 - C 2 ), 
 
 (or if V is greater than radius 1/2 (I> + V/)2 - C 2 ) ; 
 
 = Vc 2 - i/ 4 C 2 . 
 
 Half the chord of the arc is a mean proportional b etween the rise and 
 the diameter minus the rise: 1/2 C = v'l' X ( D — V). 
 
 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, V = height of the arc, or 
 middle ordinate, x = abscissa, or distance measured on the chord from its 
 central point, y.= or dinate, or d istance fr om the arc to the chord at the 
 point x, V = R - V#2 _ i/ 4C . 2; y = Vr.2 _ X 2 _ (K _ v). 
 
 Length of a Circular Arc. — Huyghens's Approximation. 
 
 Length of the arc, L = (8c — C) -4- 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. 
 
 In the measurement of an arc which is descrihed 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 ansrle, bisect it and measure 
 each half as before — in this case making 5 = length of the chord of half the 
 arc, and 6 = length of the chord of one fourth the arc ; then L = (166 — 27?) ■*■ 3. 
 
 Formulas for a Circular Curve. 
 
 J. C. Locke, Eng. News, March 16, 1908. 
 c = V272a, = vV + 6 2 , 
 = \ // 2E (72 - V(72 + 6) (72 - b) 
 
 = 2V W (272 - m), = 2R sin l/ 2 /, 
 = 2Tcosy 2 I. 
 
 = R exsec 1/2/, = R tan 1/2 ^ tan 1/4 7", 
 = T tan 1/4/. 
 
 ^ x ^p.Su / 7 —* 
 
 = R sin I, = 
 
 = q2 + &2 
 2a ' 
 
 a cot 1/2 1- 
 
 _c 2 __d 2 __ c 2 + An. 
 "2a' 
 
 2m ' 
 
 8m 
 
 m 
 
 Fig. 70. 
 
 / 2 J KmT= ^R{2R - ^(272 + c) (272 - c)) f = 272 sin 1/4/. 
 = 72 T 
 
 _^1 
 : 2R 
 ■■ R sin 1/2/ tan 1/4/, 
 
 \/( # + !)(#- |), = £ vers 1/2/, 
 1/2 c tan 1/4/. 
 
 2S'- K - V(fi 
 
 + b) (72 - 6), = 272 
 
 (sin 
 
 V2/) 2 , 
 
 = 72 
 
 vers 
 
 /, 
 
 72 sin 7" tan 1/2/, = 
 
 6 tan 1/2/, = I 7 sin 7 
 
 
 
 
 
 
 72 tan 1/2 /. 7" 
 
 = | X 57.295780°. 
 
 
 *-r 
 
 X 57. 
 
 2957 
 
 SO 
 
 772 X 0.01745329, 
 
 8d - c 
 3 
 
 
 
 
 
 
 Area of Segment 
 
 L72 72 2 sin I 
 
 2 2 
 
 L72 
 
 2 
 
 726 
 
 2 ' 
 
 
 
 
 Relation of the Circle to its Equal, Inscribed, and Circum- 
 scribed Squares. 
 
 = side of equal square. 
 
 Diameter of circle X 0.88623 ) = 6 
 
 Circumference of circle X 0.28209 J 
 
 Circumference of circle X 1.1284 = perimeter of equal square. 
 
 Diameter of circle X 0.7071 ) 
 
 Circumference of circle X 0.2250S \ = side of inscribed square. 
 
 Area of circle X 0.90031 -s- diameter 3 
 
 Area of circle X 1.2732 = area of circumscribed square. 
 
 Area of circle X 0.63662 = area of inscribed square. 
 
 Side of square X 1.4142 = diam. of circumscribed circle. 
 
 X 4.4428 = circum. 
 
 X 1.1284 = diam. of equal circle. 
 
 X 3.5449 = circum. 
 
 Perimeter of square X 0.88023 = 
 
 Square inches X 1.2732 = circular inches. 
 
MENSURATION. 61 
 
 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. Multiolv the number of degrees in the arc by the square of the 
 radius and by 0.00S727. 
 
 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: Area of segment = 1/2 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: 
 
 1 fsquare of half the chord , . . , . 1 
 = 2 L height ' + height J • 
 
 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 <?, area = h^ l.766dh 
 
 " " " " 1/4 <* to l/id, area = h\ / 0.0l7d 2 + \.7dh - h 2 
 
 (approx.). Greatest error 0.23%, when h = Vid. 
 
 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 tzR 2 ; 
 and the area of the smaller, itr 2 . 
 
 Their difference, or the area of the ring, is n(R 2 — r 2 ). 
 The Ellipse. — Area of an ellipse = product of its semi-axes X3. 14159 
 = product of its axes X0. 785398. 
 
 , / D 2 + d 2 
 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, 
 
 , D 2 + d 2 (D - 
 Circumference = 3.1416 - 
 
 v/ 1 
 
62 MENSURATION. 
 
 When D is more than 5rf, the divisor S.8 is to be replaced by the following: 
 
 ForZ>A? = 6 7 8 9 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 
 
 1 + T + 64 + ^6 + i^t4 + •••) , 
 in which A = r^jr- — Ingenieurs Taschenbuch, 1896. (a and b, semi-axes.) 
 
 Carl G. Barth (Machinery, Sept., 1900) gives as a very close approxi- 
 mation to this formula 
 
 , , , A $4 - 3.4 * 
 C=.(a+ft) 64 _ 16A2 . 
 
 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 of 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 of 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 ot 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, 
 
 V(c 2 + h 2 )n = 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 i. 
 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 = nn — - — , d and d' being the inner and outer diameters. 
 
 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. 
 
 K 
 
 Or, length = 4/ m -^r— + h 2 . 
 
 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 
 
MENSURATION. 63 
 
 c' a cube or other solid, and I the side of a similar body of different size, 
 S, s, the surfaces and V, v. the volumes respectively, S : s :: L 2 : P; 
 V : v :: U : Z 3 . 
 
 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 prismoid 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 frustum of a cone: Add together the areas of 
 the two bases and a mean proportional between them, and multiply 
 the sum by one third of the altitude. Or, Vol. = 0.261Sa(b 2 + c 2 + bc)\ 
 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. 
 " " " = 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 */6; that is, by 0.5236.. 
 Value of n/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. 
 
64 MENSURATION. 
 
 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 I 
 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 Prismoidal Formula. 
 
 Let A = area of the base of a prism, wedge, or pyramid; 
 Ai, Ai, A m = the two end and the middle areas of a prismoid, or of any of 
 its elementary solids; h = altitude of the prismoid or elementary solid; 
 V = its volume; 
 
 V ■ 
 For a prism, A\, A m and Ai are equal, 
 For a wedge with parallel ends, Ai = 0, A m = -x Av,V= ~{Ai+2A:)= — • 
 For a cone or pyramid, Ai = 0, A m = -j Av, V = - (Ai + Ai) = -r- • 
 
 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; or, multiply the square of one of the 
 edges by the surface of a similar solid whose edge is unity. 
 
 A Table op theS 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 
 
 Icosaedron t . , . . , , . 20 8.6602540 2.1816950 
 
MENSURATION. 65 
 
 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; Vint 2 = sectional area; 1/2 (d +d') = mean 
 diameter = M ; nt = circumference of section; n M = mean circum- 
 ference of ring; surface = ntXn M; = 1/4 n 2 (d 2 - d' 2 ); = 9.86965 t M; 
 = 2.46741 (d 2 - d' 2 )- volume = 1/4 n t 2 M n; = 2.467241 t 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 whose 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. 
 
 Spheripal 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 revolv- 
 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 curve other than a circle, when the 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. 
 
66 MENSURATION. 
 
 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 frustum 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. 
 
 Volume of a cycloidal spindle = five eighths of the volume of the circum- 
 scribing cylinder. — Multiply the product of the square of twice the dia- 
 meter of the generating circle and 3.927 by its circumference, and divide 
 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 
 0.3927. 
 
 Volume of a frustum of a parabolic conoid. ■ — Multiply half the sum of 
 trie 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- 
 tent of each part; the sum of the contents is the cubic contents of the solid. 
 
PLANE TRIGONOMETRY. 67 
 
 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 180°. 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 = — 
 c 
 The tangent of the angle A is the quotient of the opposite side divided by 
 
 the adjacent side. Tan A = r~ 
 
 The secant of the angle A is the quotient of the hypothenuse divided by the 
 
 adjacent side. Sec A = — • 
 
 The cosine (cos), cotangent (cot), and cosecant (cosec) 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 
 
m 
 
 PLANE TRIGONOMETRY. 
 
 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 defined, divided by the radius of the 
 circle. 
 
 If ICA (Fig. 71) is an angle in the first quadrant, and CF = radius, 
 
 FG „_„ CG KF 
 
 The sine of the angle = 
 
 Rad 
 
 I A 
 Rad " 
 
 Cosec = 
 
 Secant 
 
 CL 
 Rad ' 
 
 Cos = 
 
 = SLL 
 
 Rad ' 
 
 Versin = 
 
 Rad 
 
 Rad 
 
 "Rad 
 PL 
 
 Rad ' 
 
 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 FA. 
 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, + — — + 
 
 Tangent and cotangent, + — + — 
 
 The values of the functions are as follows for the angles specified: 
 
 Angle 
 
 Sine 
 
 Cosine 
 Tangent . . . 
 Cotangent . 
 
 Secant ..'.'. 
 Cosecant . . 
 Versed sine 
 
 o 
 
 
 
 
 
 o 
 
 o 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 30 
 
 45 
 
 60 
 
 90 
 
 120 
 
 135 
 
 150 
 
 ISO 
 
 270 
 
 
 1 
 
 1 
 
 V-A 
 
 
 V3 
 
 1 
 
 1 
 
 
 
 (1 
 
 
 
 
 1 
 
 
 
 
 1) 
 
 1 
 
 
 2 
 
 v 2 
 
 2 
 
 
 
 V 2 
 
 
 
 
 1 
 
 V3 
 
 1 
 
 1 
 
 
 
 1 
 
 1 
 
 Vf 
 
 -1 
 
 
 
 
 2 
 
 v 2 
 
 2 
 
 
 2 
 
 v 2 
 
 2 
 
 
 
 1 
 
 1 
 
 N/3 
 
 on 
 
 -V3 
 
 -1 
 
 1 
 
 
 
 00 
 
 00 
 
 V 3 
 
 1 
 
 1 
 V/3 
 
 
 
 1 
 V3 
 
 -1 
 
 v 3 
 -V3 
 
 00 
 
 
 
 1 
 
 2 
 
 a/2 
 
 2 
 
 00 
 
 -2 
 
 -V2 
 
 2 
 
 -1 
 
 CO 
 
 00 
 
 2 
 
 Vi 
 
 Vi 
 
 1 
 
 V3 
 
 V£ 
 
 2 
 
 00 
 
 -1 
 
 n 
 
 2-V3 
 
 x/2-1 
 
 1 
 
 1 
 
 3 
 
 vT+i 
 
 2+V3 
 
 
 1 
 
 
 2 
 
 v 2 
 
 - 
 
 
 2 
 
 V2 
 
 2 
 
 
 360 
 
 
 1 
 
 
PLANE TRIGONOMETRY. 69 
 
 TRIGONOMETRICAL FORMULAE. 
 
 The following relations are deduced from the properties of similar 
 triangles (Radius = 1): 
 
 cos A : sin A : : 1 : tan A, whence tan A = r ; 
 
 cos A 
 
 • a a cos A 
 
 sin A : cos A : : 1 : cot A, cotan A = -: — -. ; 
 
 sin A 
 
 cos A : 1 : : 1 : sec A, " sec A = -? ; 
 
 cos A 
 
 sin A : 1 : : 1 : cosec A, " cosec A = -: — — ; 
 
 sin A 
 
 tan A : 1 : : 1 : cot A " tan A = — - — -.■ 
 
 cot A 
 
 The sum of the square of the sine of an arc and the square of its cosine 
 equals unity. Sin 2 A + cos 2 A = 1. 
 
 Also, 1 + tan 2 A = sec 2 A; 1 + 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 + B = C, and 
 their difference A — B by D. 
 
 sin (A + B) = sin A cos B + cos A sin B; (1) 
 
 cos (A + B) = cos A cos 5 — sin A sin 5; (2) 
 
 sin (A — B) = sin A cos B — cos A sin B ; (3) 
 
 cos (A — B) = cos A cos 5 + 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 5; . . . . (5) 
 
 sin (A + B) — sin (A - B) = 2 cos A sin B; . . . . (6) 
 
 cos (A + B) + cos (A - B) = 2 cos A cos B; . . . . (7) 
 
 cos (A - B) - cos (A + 5) = 2 sin A sin 5 (8) 
 
 If we put A + 5 = C, and A - B = Z>, then A = i/ 2 (C + £>) and 5 = 
 V2(C — D), and we have 
 
 sin C + sin D = 2 sin i/ 2 (C + D) cos 1/2 (C - D) ; . . (9) 
 
 sin C - sin Z) = 2 cos 1/2 (C + £>) sin 1/2 (C -£>);. . (10) 
 
 cosC + cosD = 2 cos 1/2 (C + D) cos 1/2 (C - D); . . (11) 
 
 cos D - cos C = 2 sin 1/2 (C + Z>) sin 1/2 (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 of 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 + sin B = 2 sin V 2 (A + B) cos y 2 (A-B) = tan 1/2 (A + B) 
 sin A - sin B 2 cos 1/2 (A + B) sin 1/2 (A-B)~ tan 1/2 (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 + cos B 2 cos 1/2 (A + B) cos 1/2 (A - B) = cot 1/2 (A + £) 
 cos B - cos A 2 sin 1/2 (A + B) sin 1/2 (A - B) tan 1/2 (A - B) ' K ' 
 
 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 + B) = tan A + tan B . 
 sin (A - B) tan A - tan B ' * ' 
 
PLANE TRIGONOMETRY. 
 
 sin (A + B) 
 cos A cos B 
 sin (A - B) 
 cos A cos 5 * 
 cos (A + B) 
 cos A cos B 
 cos (A - B) 
 cos A cos # 
 
 Functions of twice an angle : 
 sin 2 A — 2 sin A cos A. ; 
 
 . _ . 2 tan A 
 
 tan 2A = — tt—t ; 
 
 1 - tan 2 A 
 
 Functions of half an angle: 
 
 = tan A + tan B; 
 tan A ~ tan B; 
 1 —tan A tan 5; 
 1 + tan A tan B; 
 
 tan (A + £) = 
 tan (A - B) = 
 cot (A + B) = 
 cot (A - B) = 
 
 tan A + tan B . 
 1 -tan A tan .8 ' 
 tan A — tan i? 
 1 + tan A tan B ' 
 cot A cot B — 1 . 
 cot B + cot A ' 
 cot A cot .B + 1 
 cot B — cot A " 
 
 sinV 2 A=± 
 
 tan 1/2-4 = 
 
 
 cos A 
 
 cos 2 A 
 cot 2A 
 
 = cos 2 A — sin 2 A; 
 cot 2 A — 1 
 2 cot A 
 
 cos V2-4 
 cot 1/2 A 
 
 , / 1 -f cos A , 
 ~* V 2 
 
 < 4 /l + cos A 
 
 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, b, and 
 c the sides opposite these angles, respectively, then we have 
 
 1. sin A = cos B = - ; 3. tan A — cot B — 
 
 2. cos A = sin 5 < 
 
 4. cot A = tan 5 : 
 
 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 leg 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 the following proportion: 
 
ANALYTICAL GEOMETRY. 71 
 
 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, b, and the included angle A, ta find the remaining side 
 a and the remaining angles B and C. 
 
 From either of the unknown angles, as B, dra * a perpendicular Be to 
 the opposite side. 
 
 Then 
 
 Ae = c cos A, Be = c sin A, eC = b — Ac Be -s- 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, Y 
 
 XX' being the axis of abscissas or axis of X, I 
 
 and YY' the axis of ordinates or axis of Y . / p 
 
 A, the intersection, is called the origin of co- -j 
 
 ordinates. The distance of any point P / c / 
 
 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 x' — / ' x 
 
 axis of X, measured parallel to the axis of /AD 
 
 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 y 
 
 a right angle, in which case the axes of X jr IG 72 
 
 and Y are called rectangular coordinates. 
 
 The abscissa of a point is designated by the letter x and the ordinate 
 byy. 
 
 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 ± 5, in which a is the tangent of the 
 angle the line makes with the axis of X, 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 
 
72 ANALYTICAL GEOMETRY. 
 
 of a straight line, as Ay + Bx +C^0, which can be reduced to the foria 
 y = ax ± b. 
 
 Equation of the distance between two points: 
 
 D - vV - x') 2 + iv" - y') 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, o, 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: 
 
 y" — y' 
 
 y - y = x » __ X M - x )- 
 
 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: 
 
 T7 a' — a 
 tang V = r— — t • 
 1 + 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. 
 Equation of an intersection of two lines, whose equations are 
 y = ax + b, and y — a'x + b', 
 ab' — a'b 
 a — a' 
 Equation of a perpendicular from a given point to a given line: 
 
 y ~ y' = - - (x - x'). 
 
 Equation of the length of the perpendicular P: 
 p _ y' - ax' - b 
 Vi + a 2 
 
 The circle. — Equation of a circle, the origin of coordinates being at 
 the centre, and radius = R: 
 
 x 2 + y z = R 2 . 
 
 If 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 - x') 2 + (y - y') 2 = R 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: 
 
 A 2y2 + B 2 X 2 = .4252, 
 
 in which 4 is half the transverse axis and B half the conjugate axis. 
 
ANALYTICAL GEOMETRY. 73 
 
 Equation of the ellipse when the origin is at the vertex of the transverse 
 axis: 
 
 y 2 = ~(2Ax - x 2 ). 
 
 The eccentricity of an ellipse is the distance from the centre to either 
 focus, divided by the semi-transverse axis, or 
 
 , VII 
 
 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 
 
 2B 2 
 2A : 2B :: 2B : parameter; or parameter = — -.— 
 
 Any ordinate of a circle circumscribing an ellipse is to the corresponding 
 ordinate of the ellipse as the semi -transverse 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 2 xx" = A 2 B 2 , 
 
 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 ~ V = B 2 jr»(x - * )• 
 
 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 + x"), 
 
 y"x" being coordinates of the point of tangency. 
 Equation of the normal: 
 
 y - y" = - y(z - 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 point of tangency to the focus. 
 
 The hyperbola. — Equation of the hyperbola referred to rectangular 
 coordinates, origin at the centre: 
 
 A 2 y 2 - B 2 x 2 = - A 2 B 2 , 
 
 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: 
 
 A 2 
 Conjugate and equilateral hyperbolas. — If on the conjugate axis, 
 
74 DIFFERENTIAL CALCULUS. 
 
 as a transverse, and a focal distance equal to V A 2 + B 2 , 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 2 — x 2 = —A' 1 
 when A is the transverse axis, and x 2 — y 2 = — B 2 when B is the trans- 
 verse axis. 
 
 The parameter of the transverse axis is a third proportional to the trans- 
 verse axis and its conjugate. 
 
 2 A : 2B :: 25 : 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 asymDtotes 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, 
 PV = a constant. This equation is that of the expansion of a perfect 
 gas, in which P = absolute pressure, V = volume. 
 
 Curve of Expansion of Gases. —PV 71 = a constant, or PiVi n = P 2 V2 n , 
 in which Vi and Vi are the volumes at the pressures Pi and Pt. When 
 these are given, the exponent n may be found from the formula 
 
 = log Pi - log P 2 
 
 log Vi — 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 ■■= 0, 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, -j-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. 
 
DIFFERENTIAL CALCULUS. 75 
 
 In any curve whose equation is y = f(x), the differential coefficient 
 
 ~ = tan a; hence, the rate of increase of the function, or the ascension of 
 
 dx 
 
 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 + 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: 
 
 ... j,j d(uv) du dv 
 
 d(uv) = vdu+ udv. = 1- 
 
 uv u v 
 
 The differential of the product of any number of 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 + us dt + ut ds. 
 
 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: 
 
 _ ?u\ = vdu-udv . 
 
 \V / V 2 
 
 If the denominator is constant, dv = 0, and dt = -^ = — . 
 
 If the numerator is constant, du = 0, and dt = — • 
 
 v 2 
 
 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 = U V2, or v - ^u, dv = -^=; = \%r 1 l2dn. 
 
 2^u 
 
 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. 
 
 ft w ( x \ — Vdx-xdy 
 
 1. d (a) = 0. 
 
 2. d {ax) = a dx. 
 
 3. d (x + y) = dx + dy. 
 
 4. d {x — y) = dx — dy. 
 
 5. d (xy) = xdy + y dx. 
 
 \yf y 
 
 7. d (x m ) = mx m ~ 
 
 8. d (Vx) = -$* 
 
 2 v x 
 
 (.1. 
 
 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 
 
76 DIFFERENTIAL CALCULUS. 
 
 binomial raised to a power less 1, intr- 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 ~ 1 x n ~ 1 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 . 
 
 dx 
 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 r 
 function of two or more variables under the supposition that only ont 
 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 = / (xy), the partial differentials are — dx, -rdy. 
 
 , dy + -j- dz; = 2x dx + 3y 2 dy — dz. 
 dx dy dz ' 
 
 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 /, which is 
 
 read "the integral of." Thus fix dx = x 2 ; read, the integral of 2x dx 
 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: J3x 2 dx = X s . (Applicable in all cases except 
 when m = — 1. For fx dx see formula 2, page 81.) 
 
 The integral of the product of a constant by the differential of a vari- . 
 able is equal to the constant multiplied by the integral of the differential: 
 
 The integral of the algebraic sum of any number of differentials is 
 equal to the algebraic sum of their integrals: 
 
 = 2ax 2 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 -{■ 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 = a dx ;/dy = aj~dx. Integrating, 
 
 y = ax ± C. 
 
DIFFERENTIAL CALCULUS. 77 
 
 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 
 variable. 
 
 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 
 
 I dy = a I d 
 
 is read: Integral of the differential of y, taken between the limits x' and 
 x": the least limit, or the limit corresponding to the subtractive integral, 
 being placed below. 
 
 Integrate du = 9x 2 dx between the limits x = 1 and x = 3, u being equal 
 
 to 81 when x = 0. /du = /9.r 2 dx = 3.r 3 + C; C = 81 when x = 0, then 
 du = 3(3)3 + 81, minus 3(1)3+ 81 = 78> 
 
 Jx= 
 
 Integration of particular forms. 
 
 To integrate a differential of the form du = (a + bx n ) m x n - 1 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 
 
 /« 
 
 (ra+ l)nb 
 
 __ hypothen 
 which the base is dx and the perpendicular dy. 
 
 The differential of an arc is the hypothenuse of a right-angle triangle of 
 
 is dx '- ' 
 
 If z is an arc, dz = Vdx 2 + dy* z ^f^dx^ + dy 2 . 
 
 Quadrature of a plane figure. 
 
 The differential of the area of a plane surface is equal to the ordinate into 
 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 ot the com- 
 mon parabola wnose equation is 
 
 y 2 = %px; whence?/ = A ^ / 2px. 
 
78 DIFFERENTIAL CALCULUS. 
 
 Substituting this value of y in the differential equation ds = y dx givea 
 
 fds = fV^pdx = ^Tv §x h dx = ^^x B/2 + C; 
 Xx = |xy + C. 
 
 If we estimate the area from the principal vertex, x = 0, y = 0, and 
 C = 0; and denoting the particular integral by s', s' = k^2/- 
 
 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 = 2ny\ / dx°~ + dy 2 ; 
 
 in which y is the radius of a circle of the bounding surface in a plane per- 
 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 = ny 2 dx. 
 
 The area of a circle described by any ordinate y is Try 2 ; hence the differ- 
 ential of a volume of revolution is equal to 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 = 
 2 1 
 
 - nR 2 X D = - tiD 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: 
 
m 
 
 DIFFEKENTIAL CALCULUS 79 
 
 ■ -p- Dividing by dx, we have for the second differential 
 
 coefficient -r-g, which is read : second differential of u divided by the square 
 
 of the differential of x (or dx squared). 
 d 3 u 
 The third differential coefficient -r-^ 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 
 whose 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 
 
 • j. dy 
 any point -r- = <*>• 
 
 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 2 + Dx s + Ex i , etc., in which 
 A, B, C, etc., are independent of x: 
 
 . . , (du\ , 1 (d\i\ . , 1 (d 3 u\ , , . 
 
 U = (U) +[-r-) X +— tt X 2 + - — - -rl-r-rj X s + etc. 
 
 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 
 
 + rn(n^(m-2 lam - ix3+e ^ 
 
 1 = 1 _ X_ X? _ Xf X H 
 
 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' = f(x ± y): 
 
 dx 2 1.2 dx 3 1 . 2 . 3 
 
 du . , 
 , — is whau -y- y 
 dx dx 
 
 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, 
 
80 DIFFERENTIAL CALCULUS. 
 
 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 ; 
 
 dv x , . x . . . 
 
 ~ == — -; making — - = gives x = 0. 
 
 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 of 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 *^2. r = radius. 
 
 The altitude of a cylinder inscribed in a sphere when the volume is a 
 maximum is 2r -s- V3. 
 
 Maxima and Minima without the Calculus. — In the equation 
 y = a + bx + ex 2 , in which a, b, 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 + 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 k dx (2) 
 
 in which A; is a constant dependent on a. 
 
 1 
 
 The relation between a and k is a k = e; whence a = e k .... (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 
 always by log. 
 
 k = Nap. log a, log a = k log a (4) 
 
DIFFERENTIAL CALCULUS. 81 
 
 The common logarithm of e, = log 2.7182818 . . . = 0.4342945 . . . , 
 is called the modulus of the common system, and is denoted by M. 
 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 t = 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 
 
 — = — — = k dx. 
 
 u a x 
 
 If we make a = 10, the base of the common system, x = log u, and 
 
 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.) 
 
 1. J a x ladx = a x +C; 
 
 2. C$2 = C 'dxx" 1 = lx + C; 
 
 3. C (xy x ~ 1 dy + y x ly X dx) = y x +C; 
 
 4. f . dX = Kx+^x* ± a2)4-C; 
 J v x 2 ± a 2 
 
 5. f . dX =l(x ± a+ V X 2 ± 2ax) + C; 
 J VxJ ± 2ax 
 
 J a 2 - x 2 \a - xf 
 
82 
 
 DIFFERENTIAL CALCULUS. 
 
 J x 2 — a- \x + a) 
 
 r -ma* _ IV^- a \^ 
 
 J x^a 2 + x 2 \v a 2 + a; 2 +a/ 
 
 / 2adx f a - Va 2 - xA 
 
 x V«2 - x' 2 \ a + V a 2 - x 2 ) 
 
 J x~ 2 dx ( 1 + Vl + a 2 x 2 \ 
 
 x+ x - \ I 
 
 Circular functions. — Let z denote an arc in the first quadrant, y its 
 sine, x its cosine, v 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 " " " " " x is the cosine, 
 tan~~M " " " " " t is the tangent, 
 
 (read "arc whose sine is y, ,J etc.), — we have the following differential 
 forms which have known integrals (r = radius): 
 
 cos zdz = sin z + C; 
 sin zdz = cos z+ C; 
 
 /- . 
 
 f-7 dy — = sin -i y + C; 
 
 J VI - 2/2 
 
 r - dx 
 
 S 
 
 = cos -1 x+ C; 
 
 ^2v - 
 dt 
 
 /if 
 
 J V r 2 
 
 / — r dx 
 \/ r 2 _ #2 
 
 = = versin — 1 v + C ; 
 v 2 
 
 = tan -1 £ + C; 
 — = sin -1 y + C; 
 = cos -1 x + C\ 
 
 J sin z dz = versin z+ C; 
 
 C-^r =tanz+C; 
 J cos 2 z 
 
 /r dv . , , 
 
 . = versin -1 v + C 
 
 V2rv + v 2 
 
 f-^5 = tan -1 *+<7; 
 J r 2 + * 2 
 
 /tfu . . u , _ 
 
 . = sin -1 - + C; 
 
 Va 2 -u 2 a 
 
 . = cos- 1 - + C; 
 
 Va 2 - z*2 a 
 
 «/ V2 aw — u 2 
 
 / a du 
 a 2 + x 
 
 versin — 1 — -I 
 
 -w 2 
 
 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. 
 
THE SLIDE RULE. 
 
 83 
 
 The transcendental equation of the cycloid is 
 
 V2ry 
 
 and the differential equation is dx -- 
 
 V dx 
 
 V2ry - 
 
 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 
 thenumbers. 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," consisting of a transparent 
 strip of celluloid with a 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 
 
 i: **— 
 
 U^~il 
 
 
 
 
 
 
 :\ _jLa :§§ 
 
 
 
 
 14-31 
 
 
 1 Jit 
 
 
 ; M* ^ 
 
 
 
 
 I *W || 
 
 
 r | Jjf^ "^ 
 
 
 
 
 : ' T=f- «H^- 
 
 
 [\ M || 
 
 
 
 
 ; § i[ 
 
 
 
 
 - \ 3" *j=^ 
 
 
 :jl|[ % 
 
 
 j 3 t§L 1 r 
 
 
 ■ iB 
 
 
 
 I- I 
 
 ~ c " > ii- 
 
 
 H 
 
 Z* j [ 
 
 
 3 
 
 H"]p 
 
 * 
 
 r ,< -% 
 
 F \ f 
 
 1 
 
 
 
 
 \ ' -1 
 
 =- jr 
 
 1 
 
 -" =-: 
 
 r \r~ 
 
 s 
 
 :: \ 
 
 ^"jr 
 
 1 
 
 l\ "^F" "H '- 
 
 I 
 
 '- N — jfl^e 1 L 
 
 i 
 
 ■A ^|p"H^ 
 
 
 ■A -Mf^it 
 
 
 :| A ^F 
 
 
 %%i 
 
 
 itME 
 
 
 fit 
 
 
 ? 1~Th- 
 
 
 i ifW\ 
 
 
 ijjU it 
 
 
84 THE SLIDE RULE. 
 
 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 
 slide 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 D, 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 Z>„ 
 
 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 D 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 left 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. 
 
 Example, = 8.9 nearly. Set 3 on C over 4 on D, set 
 
 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^ 
 
 V46 = 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. 
 
 Example. — 2 3 = 8. Set the index of C over 2 on D, and above 2 
 on B read the result 8on4„ 
 
 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, 
 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, and 
 coinciding with an angle on T will be found the tangent on D. Sines and 
 tangents can be multiplied or divided like numbers. 
 
LOGARITHMIC RULED PAPER. 85 
 
 LOGARITHMIC RULED PAPER. 
 
 W. F. Durand {Eng. News, Sept. 28, 1893.) 
 
 As plotted on ordinal 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 ali relationships which involve multiplication, divisioH, 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 + 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 of 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 11 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 n, 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 
 to 10 may be made to serve for any number whatever from to oo. Thus 
 to express graphically the locus of the equation: y — a* 3 /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 O, 
 OF will give the value of x ,3 /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 x 3 ^ 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 x 3 /2 where x lies between 10 and the value at (7, 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, which 
 
8 
 
 t£ 
 
 ir 
 o 
 
 fr 
 
 a 
 gi 
 
 m 
 
 H 
 
 6 LO 
 
 ikes us finally to the 
 g this, the same ser 
 -ders. 
 
 The value of ar/2 f 
 om one or another 
 and 1. The locatic 
 tention to the nun 
 ven line may be mar 
 ade. Thus, in Fig. 
 
 Q 
 
 GARITH1V 
 
 opposite ( 
 ies of lines 
 
 >r any valu 
 of these lii 
 n of the d 
 bers invol 
 ked on it, t 
 2 we marl 
 
 2 G 
 
 IIC RULE 
 
 orner and < 
 would resi 
 
 e of x betw 
 ies, and lik 
 ecimal poin 
 ved. The 
 hus enablin 
 c OF as - 
 
 3 Q 
 
 D PA] 
 
 jomple 
 lit for 
 
 een 1 a 
 ewise f 
 t is re 
 limitin 
 g a pro 
 - 4.6, j 
 
 I F 
 
 J EJ 
 es 
 
 1UI 
 
 nd 
 or 
 idi 
 ? ^ 
 
 3D 
 
 R. 
 
 th 
 nb 
 
 CO 
 
 an 
 
 y 
 
 B 
 
 ch 
 
 as 
 
 3 eye 
 
 srs o 
 
 may 
 y va 
 :ounr 
 ies o 
 oice 
 4.6 
 
 > 
 
 le. 
 E si 
 
 thii 
 
 ue 
 1 b 
 f i 
 o t 
 
 P 
 
 cc 
 
 s b 
 be 
 
 fc 
 e r 
 L0, 
 
 8 
 
 ollow- 
 seding. 
 
 e read 
 
 tween 
 little 
 r any 
 eadily 
 IG as 
 
 9 1( 
 
 
 -/ ■""' ■ .1 :- 
 
 
 . r • "/i ■ 
 
 
 
 
 
 
 
 
 8 t 
 P_ 
 
 V ; 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /l.j "; o 
 
 (i - 
 
 '-■ / 
 
 
 
 
 
 
 
 
 
 !) - 
 
 
 / 
 
 
 
 ^fSP 
 
 
 
 
 :■: 
 
 — 
 
 
 
 
 ¥ 
 
 4 - 
 
 
 
 
 E= 
 
 -f~A 
 
 
 
 
 
 /.:': 
 
 
 
 / 
 
 
 " : :'". 1 
 
 
 
 
 l.____ 
 
 
 |||e||e 
 
 rrfefet 
 
 — 
 
 
 — 
 
 
 ^: 
 
 / 
 
 
 
 
 1 ' 
 
 
 
 ~^~ i i < i h 
 
 1j 
 
 t-~~z 
 
 tfffl 
 
 
 
 
 
 / 
 
 
 
 
 . i.J C 
 
 
 
 
 ; M M / 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ! 1 / 
 
 
 
 
 
 
 
 
 
 
 
 
 ^A 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 /■■'■' 
 
 
 ! 
 
 1 
 
 
 
 
 
 
 
 
 L. 
 
 
 
 1 
 
 
 
 
 
 
 
 
 : H 
 
 
 
 i 
 
 
 
 .... 
 
 V 
 
 
 
 
 
 
 
 
 j/| 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Iff 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 | 
 
 
 
 
 
 
 
 
 
 T 
 
 ' / 
 
 
 
 
 / 
 
 A 
 
 
 A 
 
 
 
 _ ■ -t 
 
 / Mi 
 
 
 = ====== 
 
 
 -.j 7 : 
 
 
 
 / 
 
 
 ::..|: 
 
 
 1 i | 
 
 
 
 -^J 
 
 /--44frTTf- 
 
 
 
 ^ — W 1 ' 
 
 
 
 
 
 
 
 
 
 
 
 "A"/ 
 
 — H 
 
 
 / 
 
 
 .7. ..... 
 
 
 -/■ 
 
 
 
 
 
 - 
 
 
 
 / / 
 
 ' 
 
 
 / 
 
 
 
 
 / 
 
 
 
 
 
 .....j . 
 
 
 
 / / 
 
 
 
 / 
 
 
 
 / 
 
 
 
 
 1 
 
 
 
 
 
 / / 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 ' / 
 
 / . 
 
 
 
 / 
 
 K 
 
 . ... 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 / 
 
 w 
 
 
 
 
 
 
 
 
 
 
 it 
 
 
 
 -J- '■ 
 
 Twit 
 
 
 
 
 
 
 
 
 1 / 
 
 
 
 
 
 / 
 
 I/Ill 
 
 ..... y 
 
 
 
 
 1 
 
 
 !.r.t; .|l 
 
 
 
 1( 
 
 d( 
 
 VI 
 
 
 
 ot 
 
 se 
 th 
 al 
 w 
 
 — 
 alt 
 
 llH 
 
 F i 
 Tl 
 her 
 t 
 
 e o 
 
 tl 
 11 1 
 
 21.5, 
 
 with 
 is bet 
 or va 
 e prir 
 , and 
 f lines 
 ther i 
 ere w 
 >e n li 
 
 and AE as 
 ^.E will s 
 ween 0.215 
 ues betweei 
 iciples invo 
 in general if 
 
 may be dr 
 lto n parts, 
 ill be (m -+- 
 nes correspc 
 
 •l 
 
 2 
 ;r 
 
 in 
 l C 
 
 V€ 
 tl 
 
 IW 
 
 an 
 n 
 
 n< 
 
 ft 
 
 1.5 - 1C 
 fe for vj 
 d 0.1, 5 
 .046 anc 
 d in thi 
 le expon 
 n by dh 
 d joining 
 - 1) lin< 
 ing to t 
 
 3 ■ P 1 
 
 Fig. 74. 
 
 0. If valu 
 dues of x I 
 D for values 
 I 0.001. 
 3 case may 
 ent be repfe 
 iding one s 
 I the points 
 is, and oppc 
 le n differei 
 
 es c 
 
 <"{ V 
 
 be 
 
 be 
 
 sen 
 de 
 of c 
 
 >sitt 
 it t 
 
 B 
 
 f x 
 r eer 
 twe 
 
 rea 
 ted 
 >f t 
 ivi 
 to 
 egi 
 
 le£ 
 
 l 
 en 
 
 dil 
 
 by 
 he 
 ^io 
 an 
 mi 
 
 S 1 
 
 ar 
 
 0.1 
 
 y t 
 
 m 
 
 sq 
 i a 
 
 v I 
 >gf 
 
 ha 
 
 (1 
 a 
 
 xt 
 /re 
 
 la 
 s i 
 oi 
 
 
 
 n 
 0. 
 
 id 
 
 en 
 tl 
 re 
 l I 
 nt 
 f t 
 
 1 a 
 215 
 0. 
 
 dec 
 le c 
 int. 
 lg. 
 on 
 he 
 
 3 
 
 re 
 , / 
 
 346 
 
 t( 
 
 on 
 o r 
 
 74 
 
 X 
 
 9 10 
 C 
 
 to be 
 3 for 
 , and 
 
 ) any 
 plete 
 i and 
 . In 
 there 
 root 
 
INTERPOLATION. 87 
 
 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 , we have a constant term as a mufti- 
 
 Iplier, giving an equation in the more general form y =5x n , or Bx min, 
 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 term's of their diameters, being 
 
 ; the locus of the equation A = 1/4 *■ d 2 or y = 1/4 "" x 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. 
 
 a.-», + (»-l)rf 1+ (B -»<"- 2 U + (n -»(»-«(» -8) A+ . . . 
 
 at = the first term of the series; n, number of the required term; a n , the 
 required' term; d u a\, d 3 , first terms of successive orders of differences 
 between a t , a%, 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 u a 2 ,'az, 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 ; f or log 40 rr , n = 1 .7 • n - 1 = 7 • n — 2 
 = - 0.3; n - 3 = - 1.3. ' ' 
 
 a n =1.6021+0.7 (0.0107) | (°- 7 H ~0-3)( -0.0003) ( (0.7) (-0.3) (-1.3) (0.0002 ) 
 2 6 
 
 = 1.6021 4- 0.00749 + 0.000031 -h 0.000009 = 1.6096. +. 
 
MATHEMATICAL TABLES. 
 
 
 
 RECIPROCALS 
 
 OF NUMBERS. 
 
 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 ~~64 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 1 
 
 1 .00000000 
 
 01562500 
 
 127 
 
 •00787402 
 
 190 
 
 .00526316 
 
 253 
 
 .00395257 
 
 2 
 
 .50000000 
 
 5 
 
 01538461 
 
 8 
 
 ■00781250 
 
 1 
 
 .00523560 
 
 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 
 
 01 449275 
 
 2 
 
 00757576 
 
 5 
 
 .00512820 
 
 8 
 
 .00387597 
 
 7 
 
 .14285714 
 
 70 
 
 01428571 
 
 3 
 
 •00751880 
 
 6 
 
 .005-10204 
 
 9 
 
 .00386100 
 
 8 
 
 .12500C00 
 
 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 
 
 .00378788 
 
 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 
 
 .00490196 
 
 7 
 
 .0037,4532 
 
 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 
 
 1 
 
 .04761905 
 
 4 
 
 •01190476 
 
 7 
 
 ■00680272 
 
 210 
 
 .00476190 
 
 3 
 
 .00366300 
 
 2 
 
 .04545455 
 
 5 
 
 •01176471 
 
 6 
 
 ■00675676 
 
 li 
 
 .00473934 
 
 4 
 
 .00364963 
 
 3 
 
 .04347826 
 
 6 
 
 •01162791 
 
 9 
 
 ■00671141 
 
 12 
 
 .00471698 
 
 5 
 
 .00363636 
 
 4 
 
 .04166667 
 
 7 
 
 •01149425 
 
 150 
 
 .00666667 
 
 13 
 
 .00469484 
 
 6 
 
 .00362319 
 
 5 
 
 .04000000 
 
 8 
 
 •01136364 
 
 1 
 
 .00662252 
 
 14 
 
 .00467290 
 
 7 
 
 .00361011 
 
 6 
 
 .03846154 
 
 9 
 
 01123595 
 
 2 
 
 .00657895 
 
 15 
 
 .00465116 
 
 8 
 
 .00359712 
 
 7 
 
 .03703704 
 
 90 
 
 ■01111111 
 
 3 
 
 .00653595 
 
 16 
 
 .00462963 
 
 9 
 
 .00358423 
 
 e 
 
 .03571429 
 
 1 
 
 ■01098901 
 
 4 
 
 .00649351 
 
 17 
 
 .00460829 
 
 280 
 
 .00357143 
 
 ? 
 
 .03448276 
 
 2 
 
 ■01086956 
 
 5 
 
 00645161 
 
 IS 
 
 .00458716 
 
 1 
 
 .00355872 
 
 3C 
 
 .03333333 
 
 3 
 
 •01075269 
 
 6 
 
 .00641026 
 
 19 
 
 .00456621 
 
 2 
 
 .00354610 
 
 1 
 
 .03225806 
 
 4 
 
 ■01063830 
 
 7 
 
 .00636943 
 
 220 
 
 .00454545 
 
 3 
 
 .00353357 
 
 2 
 
 .03125000 
 
 5 
 
 •01052632 
 
 8 
 
 .00632911 
 
 1 
 
 .00452489 
 
 4 
 
 .00352113 
 
 3 
 
 .03030303 
 
 6 
 
 •01041667 
 
 9 
 
 .00628931 
 
 2 
 
 .00450450 
 
 5 
 
 .00350877 
 
 4 
 
 .02941176 
 
 7 
 
 •01030928 
 
 160 
 
 .00625000 
 
 3 
 
 .00448430 
 
 6 
 
 .00349650 
 
 5 
 
 .02857143 
 
 8 
 
 •01020408 
 
 1 
 
 .00621118 
 
 4 
 
 .00446429 
 
 7 
 
 .00348432 
 
 £ 
 
 .027/7778 
 
 9 
 
 •01010101 
 
 2 
 
 .00617284 
 
 5 
 
 .00444444 
 
 8 
 
 .00347222 
 
 J 
 
 .02702703 
 
 100 
 
 •01000000 
 
 3 
 
 .00613497 
 
 6 
 
 .00442478 
 
 9 
 
 .00346021 
 
 £ 
 
 .02631579 
 
 1 
 
 •00990099 
 
 4 
 
 .00609756 
 
 7 
 
 .00440529 
 
 290 
 
 .00344828 
 
 c 
 
 .02564103 
 
 2 
 
 00980392 
 
 5 
 
 .00606061 
 
 8 
 
 .00438596 
 
 1 
 
 .00343643 
 
 4C 
 
 .02500000 
 
 3 
 
 ■00970874 
 
 6 
 
 .00602410 
 
 9 
 
 .00436681 
 
 2 
 
 .00342466 
 
 1 
 
 .02439024 
 
 4 
 
 ■00961538 
 
 7 
 
 .00598802 
 
 230 
 
 .00434783 
 
 3 
 
 .00341297 
 
 2 
 
 .02380952 
 
 5 
 
 ■00952381 
 
 8 
 
 .00595238 
 
 1 
 
 .00432900 
 
 4 
 
 .00340136 
 
 3 
 
 .02325581 
 
 6 
 
 ■00943396 
 
 9 
 
 00591716 
 
 2 
 
 .00431034 
 
 5 
 
 .00338983 
 
 4 
 
 .02272727 
 
 7 
 
 ■00934579 
 
 170 
 
 .00588235 
 
 3 
 
 .00429184 
 
 6 
 
 .00337838 
 
 5 
 
 .02222222 
 
 8 
 
 ■00925926 
 
 1 
 
 .00584795 
 
 4 
 
 .00427350 
 
 7 
 
 .00336700 
 
 e 
 
 .02173913 
 
 9 
 
 ■00917431 
 
 2 
 
 .00581395 
 
 5 
 
 .00425532 
 
 8 
 
 .00335570 
 
 7 
 
 .02127660 
 
 110 
 
 ■00909091 
 
 3 
 
 .00578035 
 
 6 
 
 .00423729 
 
 9 
 
 .00334448 
 
 e 
 
 .02083333 
 
 11 
 
 ■00900901 
 
 4 
 
 .00574713 
 
 7 
 
 .00421941 
 
 300 
 
 .00333333 
 
 ? 
 
 .02040816 
 
 12 
 
 ■00892857 
 
 5 
 
 .00571429 
 
 8 
 
 .00420168 
 
 1 
 
 .00332226 
 
 5C 
 
 .02000000 
 
 13 
 
 .00884956 
 
 6 
 
 .00568182 
 
 9 
 
 .00418410 
 
 2 
 
 .00331126 
 
 1 
 
 .01960784 
 
 14 
 
 .00877193 
 
 7 
 
 .00564972 
 
 240 
 
 .00416667 
 
 3 
 
 .00330033 
 
 2 
 
 .01923077 
 
 15 
 
 .00869565 
 
 8 
 
 .00561798 
 
 1 
 
 .00414938 
 
 4 
 
 00328947 
 
 3 
 
 .01886792 
 
 16 
 
 ■00862069 
 
 9 
 
 .00558659 
 
 2 
 
 .00413223 
 
 5 
 
 .00327869 
 
 4 
 
 .01851852 
 
 17 
 
 .00854701 
 
 180 
 
 .00555556 
 
 3 
 
 .00411523 
 
 6 
 
 .00326797 
 
 5 
 
 .01818182 
 
 18 
 
 .00847458 
 
 1 
 
 .00552486 
 
 4 
 
 .00409836 
 
 7 
 
 .00325733 
 
 6 
 
 .01785714 
 
 19 
 
 .00840336 
 
 2 
 
 .00549451 
 
 5 
 
 .00408163 
 
 6 
 
 .00324675 
 
 7 
 
 .01754386 
 
 120 
 
 .00833333 
 
 3 
 
 .00546448 
 
 6 
 
 .00406504 
 
 9 
 
 .00323625 
 
 fi 
 
 .01724138 
 
 1 
 
 .00826446 
 
 4 
 
 .00543478 
 
 7 
 
 .00404858 
 
 310 
 
 .00322531 
 
 9 
 
 .01694915 
 
 2 
 
 .00819672 
 
 5 
 
 .00540540 
 
 8 
 
 .00403226 
 
 1! 
 
 .00321543 
 
 6C 
 
 .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 
 
 2 .00396825 
 
 15 .00317460 
 
RECIPROCALS OF NUMBERS. 
 
 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 
 
 .00303642 
 
 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 
 
 .00218813 
 
 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 
 
 I 
 
 .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 
 
 A 
 
 .00247525 
 
 9 
 
 .00213220 
 
 4 
 
 .00187266 
 
 9 
 
 .00166945 
 
 340 
 
 .002941 18 
 
 5 
 
 .00246914 
 
 470 
 
 .00212766 
 
 5 
 
 .00186916 
 
 600 
 
 .00166667 
 
 1 
 
 .00293255 
 
 6 
 
 .00246305 
 
 1. 
 
 .00212314 
 
 6 
 
 .00186567 
 
 1 
 
 .00166389 
 
 2 
 
 .00292398 
 
 / 
 
 .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 
 
 .00236533 
 
 14 
 
 .00241546 
 
 9 
 
 .00208763 
 
 4 
 
 .00183823 
 
 9 
 
 .00164204 
 
 350 
 
 ,00285714 
 
 15 
 
 .00240964 
 
 480 
 
 .00208333 
 
 5 
 
 .00183486 
 
 610 
 
 .00163934 
 
 1 
 
 .00284900 
 
 16 
 
 .00240385 
 
 1 
 
 .00207900 
 
 6 
 
 .C018>150 
 
 11 
 
 .00163666 
 
 2 
 
 .00284091 
 
 17 
 
 .00239308 
 
 2 
 
 .00207469 
 
 7 
 
 .00182815 
 
 12 
 
 .00163399 
 
 3 
 
 .00283286 
 
 13 
 
 .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 
 
 4100202429 
 
 9 
 
 .00178891 
 
 4 
 
 00160256 
 
 5 
 
 .00273973 
 
 430 
 
 .00232553 
 
 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 
 
 Q 
 
 .00200401 
 
 4 
 
 .00177305 
 
 9 
 
 00158982 
 
 370 
 
 .00270270 
 
 5 
 
 .00229835 
 
 500 
 
 .00200000 
 
 5 
 
 .00176991 
 
 6301.00158730 
 
 1 
 
 .00269542 
 
 6 
 
 .00229358 
 
 1 
 
 .00199601 
 
 6 
 
 .00176678 
 
 1 
 
 00158479 
 
 2 
 
 .00268817 
 
 7 
 
 .00223833 
 
 2 
 
 .00199203 
 
 7 
 
 .00176367 
 
 2 
 
 00158228 
 
 3 
 
 .00268096 
 
 8 
 
 .00228310 
 
 3 
 
 .00198807 
 
 8 
 
 .00176056 
 
 3 
 
 00157978 
 
 4 
 
 .00267380 
 
 9 
 
 .00227790 
 
 4 
 
 .00198413 
 
 9 
 
 .00175747 
 
 4 
 
 .00157729 
 
 5 
 
 .00266667 
 
 440 
 
 .00227273 
 
 5 
 
 .00198020 
 
 570 
 
 .00175439 
 
 5 
 
 .00157480 
 
 6 
 
 .00265957 
 
 1 
 
 .00226757 
 
 6 
 
 .00197623 
 
 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 
 
 4 
 
 .00174216 
 
 9 
 
 .00156494 
 
 380 
 
 .00263158 
 
 5 .00224719 
 
 510 .00196078 
 
 5 .00173913 
 
 640 .00156250 
 
MATHEMATICAL TABLES. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 641 
 
 .00156006 
 
 706 
 
 .00141643 
 
 771 
 
 .00129702 
 
 830 
 
 .00119617 
 
 90! 
 
 .00110988 
 
 2 
 
 .00155763 
 
 7 
 
 .00141443 
 
 2 
 
 .00129534 
 
 7 
 
 .00119474 
 
 2 
 
 .00110865 
 
 3 
 
 .00155521 
 
 8 
 
 .00141243 
 
 3 
 
 .00129366 
 
 8 
 
 .001 19332 
 
 3 
 
 .00110742 
 
 4 
 
 .00155279 
 
 9 
 
 .00141044 
 
 A 
 
 .00129199 
 
 9 
 
 .00119189 
 
 A 
 
 .00110619 
 
 5 
 
 .00155039 
 
 710 
 
 .00140845 
 
 5 
 
 .00129032 
 
 840 
 
 .00119048 
 
 5 
 
 .00110497 
 
 6 
 
 .00154799 
 
 11 
 
 .00140647 
 
 6 
 
 .00128866 
 
 1 
 
 .001 18906 
 
 6 
 
 .00110375 
 
 7 
 
 .00154559 
 
 12 
 
 .00140449 
 
 7 
 
 .00128700 
 
 2 
 
 .00118765 
 
 7 
 
 .00110254 
 
 8 
 
 .00154321 
 
 13 
 
 .00140252 
 
 8 
 
 .00128535 
 
 3 
 
 .001 18624 
 
 £ 
 
 .00110132 
 
 9 
 
 .00154083 
 
 14 
 
 .00140056 
 
 9 
 
 .00128370 
 
 4 
 
 .00118483 
 
 9 
 
 .00110011 
 
 650 
 
 .00153846 
 
 15 
 
 .00139860 
 
 78 J 
 
 .00128205 
 
 5 
 
 .001 18343 
 
 9iC 
 
 .00109890 
 
 1 
 
 .00153610 
 
 16 
 
 .00139665 
 
 1 
 
 .00128041 
 
 6 
 
 .00118203 
 
 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 
 
 .00138839 
 
 5 
 
 .0012738S 
 
 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 
 
 3 
 
 .00126904 
 
 3 
 
 .00117233 
 
 18 
 
 .00103932 
 
 9 
 
 .00151745 
 
 4 
 
 .00138121 
 
 9 
 
 .00126743 
 
 4 
 
 .00117096 
 
 19 
 
 00108814 
 
 660 
 
 .00151515 
 
 5 
 
 .00137931 
 
 790 
 
 .00126582 
 
 5 
 
 .00116959 
 
 928 
 
 .00108696 
 
 1 
 
 .00151236 
 
 6 
 
 .00137741 
 
 1 
 
 .00126422 
 
 6 
 
 .00116822 
 
 1 
 
 .00103578 
 
 2 
 
 .00151057 
 
 7 
 
 .00137552 
 
 2 
 
 .00126263 
 
 7 
 
 .00116636 
 
 2 
 
 .00108460 
 
 3 
 
 .00150330 
 
 8 
 
 .00137363 
 
 3 
 
 .00126103 
 
 8 
 
 .00116550 
 
 3 
 
 .00103342 
 
 4 
 
 .00150602 
 
 9 
 
 .00137174 
 
 4 
 
 .00125945 
 
 9 
 
 .00116414 
 
 4 
 
 .00108225 
 
 5 
 
 .00150376 
 
 730 
 
 .00136936 
 
 5 
 
 .00125786 
 
 860 
 
 .00116279 
 
 5 
 
 .00103108 
 
 6 
 
 .00150150 
 
 1 
 
 .00136799 
 
 6 
 
 .00125623 
 
 1 
 
 .00116144 
 
 6 
 
 .00107991 
 
 7 
 
 .00149925 
 
 2 
 
 .00136612 
 
 7 
 
 .00125470 
 
 2 
 
 .00116009 
 
 7 
 
 .00107375 
 
 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 
 
 008 
 
 .00125000 
 
 5 
 
 .00115607 
 
 930 
 
 .00107527 
 
 1 
 
 .00149031 
 
 6 
 
 .00135870 
 
 1 
 
 .00124844 
 
 6 
 
 .00115473 
 
 1 
 
 .00107411 
 
 2 
 
 ,00148809 
 
 7 
 
 .00135635 
 
 2 
 
 .00124688 
 
 7 
 
 .00115340 
 
 2 
 
 .00107296 
 
 3 
 
 .00148588 
 
 8 
 
 .00135501 
 
 3 
 
 .00124533 
 
 8 
 
 .00115207 
 
 3 
 
 .00107181 
 
 4 
 
 .00148368 
 
 9 
 
 .00135318 
 
 4 
 
 .00124373 
 
 9 
 
 .00115075 
 
 A 
 
 .00107066 
 
 5 
 
 .00148148 
 
 740 
 
 .00135135 
 
 5 
 
 .00124224 
 
 870 
 
 .00114942 
 
 5 
 
 .00106952 
 
 6 
 
 .00147929 
 
 1 
 
 .00134953 
 
 6 
 
 .00124069 
 
 1 
 
 .00114811 
 
 6 
 
 .00106338 
 
 7 
 
 .00147710 
 
 2 
 
 .00134771 
 
 7 
 
 .00123916 
 
 2 
 
 .00114679 
 
 7 
 
 .00106724 
 
 8 
 
 .00147493 
 
 3 
 
 .00134589 
 
 8 
 
 .00123762 
 
 3 
 
 .00114547 
 
 8 
 
 .00106610 
 
 9 
 
 .00147275 
 
 A 
 
 .00134409 
 
 9 
 
 00123609 
 
 4 
 
 .00114416 
 
 9 
 
 .00106496 
 
 680 
 
 .00147059 
 
 5 
 
 .00134228 
 
 810 
 
 .00123457 
 
 5 
 
 .00114286 
 
 940 
 
 .00106383 
 
 1 
 
 .00146843 
 
 6 
 
 .00134048 
 
 11 
 
 .00123305 
 
 6 
 
 .00114155 
 
 1 
 
 .00106270 
 
 2 
 
 .00146628 
 
 7 
 
 .00133869 
 
 12 
 
 .00123153 
 
 7 
 
 .00114025 
 
 2 
 
 .00106157 
 
 3 
 
 .00146413 
 
 6 
 
 .00133690 
 
 13 
 
 .00123001 
 
 8 
 
 .00113395 
 
 3 
 
 .00106044 
 
 4 
 
 .00146199 
 
 9 
 
 .00133511 
 
 14 
 
 .00122850 
 
 9 
 
 .00113766 
 
 4 
 
 .00105932 
 
 5 
 
 .00145985 
 
 750 
 
 .00133333 
 
 15 
 
 .00122699 
 
 880 
 
 .00113636 
 
 5 
 
 .00105820 
 
 6 
 
 .00145773 
 
 1 
 
 .00133156 
 
 16 
 
 .00122549 
 
 1 
 
 .00113507 
 
 6 
 
 00105703 
 
 7 
 
 .00145560 
 
 2 
 
 .00132979 
 
 17 
 
 .00122399 
 
 2 
 
 .00113379 
 
 7 
 
 .00105597 
 
 8 
 
 .00145349 
 
 3 
 
 .00132802 
 
 18 
 
 .00122249 
 
 3 
 
 .00113250 
 
 8 
 
 .00105485 
 
 9 
 
 .00145137 
 
 4 
 
 .00132626 
 
 19 
 
 .00122100 
 
 4 
 
 .00113122 
 
 9 
 
 .00105374 
 
 690 
 
 .00144927 
 
 5 
 
 .00132450 
 
 820 
 
 .00121951 
 
 5 
 
 .00112994 
 
 930 
 
 .00105263 
 
 1 
 
 .00144718 
 
 6 
 
 .00132275 
 
 1 
 
 .00121803 
 
 6 
 
 .00112367 
 
 1 
 
 .00105152 
 
 2 
 
 .00144509 
 
 7 
 
 .00132100 
 
 2 
 
 .00121654 
 
 7 
 
 .00112740 
 
 2 
 
 .00105042 
 
 3 
 
 .00144300 
 
 8 
 
 .00131926 
 
 • 3 
 
 .00121507 
 
 8 
 
 .00112613 
 
 3 
 
 .00104932 
 
 4 
 
 .00144092 
 
 9 
 
 .00131752 
 
 4 
 
 .00121359 
 
 9 
 
 .001 12486 
 
 4 
 
 .00104822 
 
 5 
 
 .00143385 
 
 760 
 
 .00131579 
 
 5 
 
 .00121212 
 
 890 
 
 .00112360 
 
 5 
 
 .00104712 
 
 6 
 
 .00143678 
 
 1 
 
 .00131406 
 
 6 
 
 .00121065 
 
 1 
 
 .00112233 
 
 6 
 
 00104602 
 
 7 
 
 .00143472 
 
 2 
 
 .00131234 
 
 7 
 
 .00120919 
 
 2 
 
 00112103 
 
 1 
 
 .00104493 
 
 8 
 
 .00143266 
 
 3 
 
 .00131062 
 
 8 
 
 .00120773 
 
 3 
 
 .00111932 
 
 8 
 
 .00104384 
 
 9 
 
 .00143061 
 
 4 
 
 .00130390 
 
 9 
 
 .00120627 
 
 4 
 
 .00111857 
 
 9 
 
 .00104275 
 
 700 
 
 .00142857 
 
 5 
 
 .00130719 
 
 830 
 
 .00120432 
 
 5 
 
 .00111732 
 
 960 
 
 .00104167 
 
 1 
 
 .00142653 
 
 6 
 
 .00130548 
 
 1 
 
 .00120337 
 
 6 
 
 .00111607 
 
 1 
 
 .00104058 
 
 2 
 
 .00142450 
 
 7 
 
 .00130378 
 
 2 
 
 .00120192 
 
 / 
 
 .00111433 
 
 2 
 
 .00103950 
 
 3 
 
 .00142247 
 
 8 
 
 .00130209 
 
 3 
 
 00120043 
 
 8 
 
 .00111359 
 
 3 
 
 .00103842 
 
 4 
 
 .00142045 
 
 9 
 
 .00130039 
 
 4 
 
 .00119904 
 
 9 
 
 .00111235 
 
 4 
 
 .00103734 
 
 5 .00141844 
 
 770 .00129370 
 
 5 .00119760 
 
 900 .001 11111 
 
 5 .00103627 
 
RECIPROCALS OF NUMBERS. 
 
 91 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 966 
 
 .00103520 
 
 1031 
 
 .000969932 
 
 1096 
 
 .000912409 
 
 1161 
 
 .000861326 
 
 '226 
 
 .000815661 
 
 7 
 
 .00103413 
 
 2 
 
 .000968992 
 
 7 
 
 .000911577 
 
 2 
 
 .000860585 
 
 7 
 
 .000814996 
 
 8 
 
 .00103306 
 
 3 
 
 .000968054 
 
 8 
 
 .000910747 
 
 3 
 
 .000859845 
 
 8 
 
 .000814332 
 
 9 
 
 .00103199 
 
 4 
 
 .000967113 
 
 9 
 
 .000909918 
 
 4 
 
 .000359106 
 
 9 
 
 .000813670 
 
 970 
 
 .00103093 
 
 5 
 
 .000966184 
 
 1100 
 
 .000909091 
 
 5 
 
 .000858369 
 
 1233 
 
 .000813008 
 
 1 
 
 .00102937 
 
 6 
 
 .000965251 
 
 1 
 
 .000903265 
 
 6 
 
 .000857633 
 
 1 
 
 .000812348 
 
 2 
 
 .00102881 
 
 7 
 
 .000964320 
 
 2 
 
 .000907441 
 
 7 
 
 .000856898 
 
 2 
 
 .000811638 
 
 3 
 
 .00102775 
 
 8 
 
 .000963391 
 
 3 
 
 .000906618 
 
 8 
 
 .000856164 
 
 3 
 
 .000811030 
 
 4 
 
 .00102669 
 
 9 
 
 .000962464 
 
 4 
 
 .000905797 
 
 9 
 
 .000855432 
 
 4 
 
 .000810373 
 
 5 
 
 .00102564 
 
 1040 
 
 .000961538 
 
 5 
 
 .000904977 
 
 1170 
 
 .000354701 
 
 5 
 
 .000809717 
 
 6 
 
 .00102459 
 
 1 
 
 .000960615 
 
 6 
 
 .000904159 
 
 1 
 
 .00085397! 
 
 6 
 
 .000309061 
 
 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 
 
 11 
 
 .000900090 
 
 6 
 
 .0C035034C 
 
 1 
 
 .000305302 
 
 2 
 
 .00101833 
 
 ■ 7 
 
 .000955110 
 
 12 
 
 .000899231 
 
 7 
 
 .000849618 
 
 2 
 
 .000805153 
 
 3 
 
 .00101729 
 
 8 
 
 .000954198 
 
 13 
 
 .000898473 
 
 8 
 
 .000848396 
 
 3 
 
 .000804505 
 
 4 
 
 .00101626 
 
 9 
 
 .000953289 
 
 14 
 
 .000897666 
 
 9 
 
 .000848 176 
 
 4 
 
 .000303858 
 
 5 
 
 .00101523 
 
 1050 
 
 .000952331 
 
 15 
 
 .000396861 
 
 1130 
 
 .000347457 
 
 5 
 
 .000303213 
 
 6 
 
 .00101420 
 
 1 
 
 .000951475 
 
 16 
 
 .000896057 
 
 1 
 
 .O0OS4674C 
 
 6 
 
 .000802568 
 
 7 
 
 .00101317 
 
 2 
 
 .000950570 
 
 17 
 
 .000395255 
 
 2 
 
 .000346024 
 
 7 
 
 .000801925 
 
 8 
 
 .00101215 
 
 3 
 
 .000949668 
 
 18 
 
 .000894454 
 
 3 
 
 .000345308 
 
 8 
 
 .000801282 
 
 9 
 
 .00101112 
 
 4 
 
 .000948767 
 
 19 
 
 .000393655 
 
 4 
 
 .000344595 
 
 9 
 
 .000800640 
 
 990 
 
 .00101010 
 
 5 
 
 .000947867 
 
 M23 
 
 .000392857 
 
 5 
 
 .0333^333: 
 
 !250 
 
 .000800000 
 
 1 
 
 .00100908 
 
 6 
 
 .000946970 
 
 1 
 
 .000392061 
 
 6 
 
 .000343 17C 
 
 1 
 
 .000799360 
 
 2 
 
 .00100806 
 
 7 
 
 .000946074 
 
 2 
 
 .000891266 
 
 7 
 
 .03034246C 
 
 2 
 
 .000793722 
 
 3 
 
 .00100705 
 
 8 
 
 .000945180 
 
 3 
 
 .000890472 
 
 8 
 
 .00034175! 
 
 3 
 
 .000798085 
 
 4 
 
 .00100604 
 
 9 
 
 .000944287 
 
 4 
 
 .000389680 
 
 9 
 
 .000341043 
 
 4 
 
 .000797448 
 
 5 
 
 .00100502 
 
 1060 
 
 .000943396 
 
 5 
 
 .000SS3389 
 
 1190 
 
 .000340336 
 
 5 
 
 .000796813 
 
 6 
 
 .00100402 
 
 1 
 
 .000942507 
 
 6 
 
 .000888099 
 
 1 
 
 .000339631 
 
 6 
 
 .000796178 
 
 7 
 
 .00100301 
 
 2 
 
 .000941620 
 
 7 
 
 .000887311 
 
 2 
 
 .000333926 
 
 7 
 
 .000795545 
 
 8 
 
 .00100200 
 
 3 
 
 .000940734 
 
 ■ 8 
 
 .000886525 
 
 3 
 
 .000338222 
 
 8 
 
 .000794913 
 
 9 
 
 .00100100 
 
 4 
 
 .000939350 
 
 9 
 
 .000885740 
 
 4 
 
 .000837521 
 
 9 
 
 .000794281 
 
 1000 
 
 .00100000 
 
 5 
 
 .000938967 
 
 1130 
 
 .000884956 
 
 5 
 
 .000836820 
 
 1260 
 
 .000793651 
 
 1 
 
 .000999001 
 
 6 
 
 .000933036 
 
 1 
 
 .000384173 
 
 6 
 
 .000836120 
 
 1 
 
 .000793021 
 
 2 
 
 .000998004 
 
 7 
 
 .00093720; 
 
 2 
 
 .000383392 
 
 7 
 
 .000335422 
 
 2 
 
 .000792393 
 
 3 
 
 .000997009 
 
 8 
 
 .000936330 
 
 3 
 
 .000832612 
 
 8 
 
 .000334724 
 
 3 
 
 .000791766 
 
 4 
 
 .000996016 
 
 9 
 
 .000935454 
 
 4 
 
 .000381834 
 
 9 
 
 .000834028 
 
 4 
 
 .000791139 
 
 5 
 
 .000995025 
 
 1070 
 
 .000934579 
 
 5 
 
 .000881057 
 
 1200 
 
 .000833333 
 
 5 
 
 .000790514 
 
 6 
 
 .000994036 
 
 1 
 
 .000933707 
 
 6 
 
 .000330232 
 
 1 
 
 .000832639 
 
 ■ 6 
 
 .000789889 
 
 7 
 
 .000993049 
 
 2 
 
 000932336 
 
 7 
 
 .000379503 
 
 2 
 
 .000331947 
 
 7 
 
 000789266 
 
 . 8 
 
 .000992063 
 
 3 
 
 .000931966 
 
 8 
 
 .000378735 
 
 3 
 
 .000331255 
 
 8 
 
 .000788643 
 
 9 
 
 .000991080 
 
 4 
 
 .000931095 
 
 9 
 
 .000377963 
 
 4 
 
 .000330565 
 
 9 
 
 .000733022 
 
 1010 
 
 .000990099 
 
 5 
 
 .000930233 
 
 IMG 
 
 .000877193 
 
 5 
 
 .000329875 
 
 1270 
 
 .000787402 
 
 11 
 
 .000989120 
 
 6 
 
 .000929368 
 
 1 
 
 .000376424 
 
 6 
 
 .000829187 
 
 1 
 
 .000786782 
 
 12 
 
 .000988142 
 
 7 
 
 .000923505 
 
 2 
 
 .000375657 
 
 7 
 
 .000328500 
 
 2 
 
 .000786163 
 
 13 
 
 .000987167 
 
 8 
 
 .000927644 
 
 3 
 
 .000374891 
 
 8 
 
 .000827815 
 
 3 
 
 .000785546 
 
 14 
 
 .000986193 
 
 9 
 
 .000926784 
 
 4 
 
 .000874126 
 
 9 
 
 .000827130 
 
 4 
 
 .000784929 
 
 15 
 
 .000985222 
 
 1030 
 
 .000925926 
 
 5 
 
 .000873362 
 
 1210 
 
 .000826446 
 
 5 
 
 .000784314 
 
 16 
 
 .000984252 
 
 1 
 
 .000925069 
 
 6 
 
 .000872600 
 
 11 
 
 .000325764 
 
 6 
 
 000783699 
 
 17 
 
 .000983284 
 
 2 
 
 .000924214 
 
 7 
 
 .000871840 
 
 12 
 
 .000325082 
 
 7 
 
 .000783085 
 
 18 
 
 .000982318 
 
 3 
 
 .000923361 
 
 8 
 
 .000871080 
 
 13 
 
 .000324402 
 
 8 
 
 .000782473 
 
 19 
 
 .000981354 
 
 4 
 
 .000922509 
 
 9 
 
 .000870322 
 
 14 
 
 000323723 
 
 9 
 
 .000781861 
 
 1020 
 
 .000980392 
 
 5 
 
 .000921659 
 
 1150 
 
 .000869565 
 
 15 
 
 .000323045 
 
 1230 
 
 .000781250 
 
 1 
 
 .OC0979432 
 
 6 
 
 000920310 
 
 1 
 
 000868810 
 
 16 
 
 .000322368 
 
 1 
 
 .000780640 
 
 2 
 
 .000978474 
 
 7 
 
 .000919963 
 
 2 
 
 .000863056 
 
 17 
 
 .000321693 
 
 2 
 
 .000780031 
 
 3 
 
 .000977517 
 
 8 
 
 .000919118 
 
 3 
 
 .000367303 
 
 18 
 
 .000321018 
 
 3 
 
 .000779423 
 
 4 
 
 .000976562 
 
 9 
 
 .000918274 
 
 4 
 
 .000866551 
 
 19 
 
 .000320344 
 
 4 
 
 .000778816 
 
 5 
 
 .000975610 
 
 1090 
 
 .000917431 
 
 5 
 
 .000865801 
 
 1220 
 
 .000319672 
 
 5 
 
 .000778210 
 
 6 
 
 .000974659 
 
 1 
 
 .000916590 
 
 6 
 
 .000865052 
 
 1 
 
 .000319001 
 
 6 
 
 .000777605 
 
 7 
 
 .000973710 
 
 2 
 
 .00091575 
 
 7 
 
 .000864304 
 
 2 
 
 .000318331 
 
 7 
 
 .000777001 
 
 8 
 
 .000972763 
 
 3 
 
 .000914913 
 
 8 
 
 .000863558 
 
 3 
 
 .000817661 
 
 8 
 
 .000776397 
 
 9 
 
 .000971817 
 
 4 
 
 .00091407 
 
 9 
 
 .000362813 
 
 4 
 
 .000316993 
 
 9 
 
 ,000775795 
 
 1030 .000970874 
 
 5 .000913242 
 
 1160 
 
 .000862069 
 
 5 
 
 .000816326 
 
 1290 .000775194 
 
92 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 No. 
 
 Recipro- 
 cal. 
 
 1291 
 
 .000774593 
 
 1356 
 
 .000737463 
 
 1421 
 
 .000703730 
 
 1 4oc 
 
 .000672948 
 
 !5H! 
 
 .000644745 
 
 2 
 
 .000773994 
 
 7 
 
 .000736920 
 
 2 
 
 .000703235 
 
 7 
 
 .000672495 
 
 2 
 
 .000644330 
 
 3 
 
 .000773395 
 
 8 
 
 .000736377 
 
 3 
 
 .000702741 
 
 8 
 
 .000672043 
 
 3 
 
 .000643915 
 
 4 
 
 .000772797 
 
 9 
 
 .000735835 
 
 4 
 
 .000702247 
 
 9 
 
 .000671592 
 
 4 
 
 .000643501 
 
 5 
 
 .000772201 
 
 '>.: 
 
 .000735294 
 
 5 
 
 .000701754 
 
 1490 
 
 .000671141 
 
 5 
 
 .000643067 
 
 6 
 
 .000771605 
 
 1 
 
 .000734754 
 
 6 
 
 .000701262 
 
 1 
 
 .000670691 
 
 6 
 
 .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 
 
 .000668896 
 
 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 
 
 3 
 
 .000639795 
 
 4 
 
 .000766871 
 
 9 
 
 .000730460 
 
 4 
 
 .000697350 
 
 9 
 
 .000667111 
 
 4 
 
 :C0G639386 
 
 5 
 
 .000766283 
 
 
 .000729927 
 
 5 
 
 .000696364 
 
 1500 
 
 .000666667 
 
 5 
 
 :000638978 
 
 6 
 
 .00076569} 
 
 1 
 
 .000729395 
 
 6 
 
 .000696379 
 
 1 
 
 .000666223 
 
 6 
 
 ;000638570 
 
 7 
 
 .000765111 
 
 2 
 
 .000728863 
 
 7 
 
 .000695894 
 
 2 
 
 .000665779 
 
 7 
 
 .000638162 
 
 8 
 
 .000764526 
 
 3 
 
 .000723332 
 
 8 
 
 .000695410 
 
 3 
 
 .000665336 
 
 8 
 
 .000637755 
 
 9 
 
 .000763942 
 
 4 
 
 .000727802 
 
 9 
 
 .000694927 
 
 4 
 
 .000664894 
 
 9 
 
 .000637349 
 
 1310 
 
 .000763359 
 
 5 
 
 .000727273 
 
 1440 
 
 .000694444 
 
 5 
 
 .000664452 
 
 15/6 
 
 .000636943 
 
 11 
 
 .000762776 
 
 6 
 
 .000726744 
 
 1 
 
 .000693962 
 
 6 
 
 .00066401 1 
 
 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 
 
 .00069252! 
 
 9 
 
 .00066269! 
 
 4 
 
 .000635324 
 
 15 
 
 .000760456 
 
 132C 
 
 .GG0724638 
 
 5 
 
 .000692041 
 
 15 ;G 
 
 .000662252 
 
 5 
 
 .000634921 
 
 16 
 
 .00075987C 
 
 1 
 
 .0007241 13 
 
 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 
 
 !450 
 
 .000689655 
 
 15 
 
 .000660066 
 
 I5EC 
 
 .000632911 
 
 1 
 
 .000757002 
 
 6 
 
 .000721501 
 
 1 
 
 .000689180 
 
 16 
 
 .000659631 
 
 1 
 
 .000632511 
 
 2 
 
 .000756430 
 
 7 
 
 .000720980 
 
 2 
 
 .000688705 
 
 17 
 
 .000659196 
 
 2 
 
 0C0632I11 
 
 3 
 
 .000755856 
 
 8 
 
 .000720461 
 
 3 
 
 .00068823! 
 
 18 
 
 .000658761 
 
 3 
 
 .000631712 
 
 4 
 
 .000755287 
 
 9 
 
 .000719942 
 
 4 
 
 .000687758 
 
 19 
 
 .000658323 
 
 4 
 
 .000631313 
 
 5 
 
 .000754717 
 
 
 .000719424 
 
 5 
 
 .000687285 
 
 1520 
 
 .000657895 
 
 5 
 
 .000630915 
 
 6 
 
 .000754 MS 
 
 1 
 
 .000718907 
 
 6 
 
 .000686813 
 
 1 
 
 .000657462 
 
 6 
 
 .000630517 
 
 7 
 
 .000753579 
 
 2 
 
 .000718391 
 
 7 
 
 .000686341 
 
 2 
 
 .000657030 
 
 7 
 
 CCC630120 
 
 8 
 
 .000753012 
 
 3 
 
 .000717875 
 
 8 
 
 .000635871 
 
 3 
 
 .000656598 
 
 8 
 
 .000629723 
 
 9 
 
 .000752445 
 
 4 
 
 .000717360 
 
 9 
 
 .000685401 
 
 4 
 
 .000656168 
 
 9 
 
 .000629327 
 
 1330 
 
 .00075 18SC 
 
 5 
 
 .000716346 
 
 i46C 
 
 .000634932 
 
 5 
 
 .000655738 
 
 1590 
 
 .00062893 \ 
 
 1 
 
 .000751315 
 
 6 
 
 .000716332 
 
 1 
 
 .000684463 
 
 6 
 
 .000655308 
 
 1 
 
 .000628536 
 
 2 
 
 .000750750 
 
 7 
 
 .000715820 
 
 2 
 
 .000683994 
 
 7 
 
 .000654879 
 
 2 
 
 .0CC628141 
 
 3 
 
 .000750187 
 
 8 
 
 .000715303 
 
 3 
 
 .000633527 
 
 8 
 
 .000654450 
 
 3 
 
 .000627746 
 
 4 
 
 .000749625 
 
 9 
 
 .000714796 
 
 4 
 
 .000683060 
 
 9 
 
 .000654022 
 
 4 
 
 .000627353 
 
 5 
 
 .000749064 
 
 uoc 
 
 .000714286 
 
 5 
 
 .000682594 
 
 i53r 
 
 .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 
 
 !450 
 
 .000680272 
 
 5 
 
 .000651466 
 
 1600 
 
 .000625000 
 
 1 
 
 .000745712 
 
 6 
 
 .00071 1238 
 
 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 
 
 J54G 
 
 .000649351 
 
 1610 
 
 .000621118 
 
 6 
 
 .000742942 
 
 11 
 
 .000708717 
 
 6 
 
 .000677507 
 
 1 
 
 .000648929 
 
 12 
 
 .000620347 
 
 7 
 
 .000742390 
 
 12 
 
 .000703215 
 
 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 
 
 143C 
 
 .000675676 
 
 5 
 
 .000647249 
 
 1620 
 
 .000617284 
 
 1 
 
 .000740192 
 
 16 
 
 .000706215 
 
 1 
 
 .000675219 
 
 6 
 
 .000646830 
 
 2 
 
 .000616523 
 
 2 
 
 .000739645 
 
 17 
 
 .000705716 
 
 2 
 
 .000674764 
 
 7 
 
 .000646412 
 
 4 
 
 .000615763 
 
 3 
 
 .000739098 
 
 18 
 
 .000705219 
 
 3 
 
 .000674309 
 
 8 
 
 .000645995 
 
 6 .000615006 
 
 4 
 
 .000738552 
 
 19 
 
 .000704722 
 
 4 
 
 .000673854 
 
 9 
 
 .000645578 
 
 8 .000614250 
 
 5 
 
 .000738007 
 
 1420 .000704225 
 
 5 .000673401 
 
 1550 
 
 .000645161 16301.000613497 
 
RECIPROCALS OF NUMBERS. 
 
 93 
 
 N Recipro- N Recipro- N Recipro- N Recipro- N Recipro- 
 
 cal cal. ' cal. ' cal. ' cal. 
 
 1632 
 4 
 6 
 
 1640 
 2 
 4 
 
 1530 
 2 
 4 
 6 
 
 (560 
 2 
 
 15 50 
 2 
 4 
 6 
 
 1690 
 2 
 
 1700 
 
 2 
 4 
 
 .000612745 
 .00061 1995 
 .00061 1247 
 .000610500 
 .000609756 
 .000609013 
 .000603272 
 .000607533 
 .000505796 
 .00050606! 
 .000505327 
 .000504595 
 .000503365 
 .000503 '36 
 .000502 110 
 .000301585 
 .000300962 
 .000300240 
 ;000>99520 
 ,000593302 
 .000593086 
 ;on0597371 
 ,000596658 
 .000595947 
 000395238 
 000594530 
 .000393324 
 .000593120 
 .000592417 
 .000591716 
 :00059i0!7 
 .000590319 
 .000389622 
 .000383923 
 .000533235 
 .000587544 
 .000536354 
 
 .000586166 
 
 .000585480 
 
 .000584795 
 
 .0005841 12 
 
 .000583430 
 
 .000582750 
 
 .000582072 
 
 .000531395 
 
 .000530720 
 
 .000580046 
 
 .000579374 
 
 .000578704 
 
 .000578035 
 
 .000577367 
 
 .000576701 
 
 .000576037 
 
 .000575374 
 
 .000574713 
 
 .000574053 
 
 .000573394 
 
 .000572737 
 
 .000572082 
 
 .000571429 
 
 .000570776 
 
 .000570125 
 
 000569476 
 
 .000563323 
 
 .000563132 
 
 .000567537 
 
 .000566393 
 
 .000566251 
 
 .00056561 
 
 .000564972 
 
 .000564334 
 
 .000563693 
 
 .000563063 
 
 .000562430 
 
 .000561798 
 .000561167 
 .000560538 
 .000559910 
 .000559284 
 .000558659 
 .000558035 
 .000557413 
 .000556793 
 .000556174 
 .000555556 
 .000554939 
 .000554324 
 .000553710 
 .000553097 
 .000552486 
 .000551876 
 .000551268 
 .000550661 
 .000550055 
 .000549451 
 .000548848 
 .000548246 
 .000547645 
 .000547046 
 .000546448 
 .000545851 
 .000545256 
 .000544662 
 .000544069 
 .000543478 
 .000542838 
 .000542299 
 .000541711 
 .000541 125 
 .000540540 
 .000539957 
 
 .000539374 
 
 .000538793 
 
 .000538213 
 
 .000537634 
 
 .000537057 
 
 .000536480 
 
 .000535905 
 
 .000535332 
 
 .000534759 
 
 .000534188 
 
 .000533618 
 
 .000533049 
 
 .00053248 
 
 .000531915 
 
 .000531350 
 
 .000530785 
 
 .000530222 
 
 .000529661 
 
 .000529100 
 
 .000528541 
 
 .000527983 
 
 .000527426 
 
 .000526870 
 
 .000526316 
 
 .000525762 
 
 .000525210 
 
 .000524659 
 
 .000524109 
 
 .000523560 
 
 .000523012 
 
 .000522466 
 
 .000521920 
 
 .000521376 
 
 .000520833 
 
 .000520291 
 
 .000519750 
 
 .000519211 
 
 2000 
 
 .000518672 
 .000518135 
 .000517599 
 .000517063 
 .000516528 
 .000515996 
 .000515464 
 .000514933 
 .000514403 
 .000513874 
 .000513347 
 .000512820 
 .000512295 
 .000511770 
 .000511247 
 .000510725 
 .000510204 
 .000509684 
 .000509165 
 .000508647 
 .000508130 
 .000507614 
 .000507099 
 .000506585 
 .000506073 
 .000505561 
 .000505051 
 .000504541 
 .000504032 
 .000503524 
 .000503018 
 .000502513 
 .000502008 
 .000501504 
 .000501002 
 .000500501 
 .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. .0006105 The table of multiples is made by continuous addi- 
 
 2. .0012210 tion of 6105. The tenth line is written to check the 
 
 3. .0018315 accuracy of the addition, but it is not afterwards used. 
 
 4. .0024420 Operation: 
 
 5. .0030525 Dividend 9871 
 
 6. .0036630 Take from table 1 0006105 
 
 7. .0042735 7 0.042735 
 
 8. .0048840 8 00.48840. 
 
 9. .0054945 9 005.4945 
 
 10. .0061050 — - 
 
 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. 
 
94 
 
 
 MATHEMATICAL TABLES. 
 
 
 
 
 SQUARES, 
 
 CUBES 
 
 , SQUARE ROOTS AND CUBE ROOTS OF 
 
 
 
 NUMBERS 
 
 FROM 0.1 TO 1600. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 0.1 
 
 .01 
 
 .001 
 
 .3162 
 
 .4642 
 
 3.1 
 
 9.61 
 
 29.791 
 
 1.761 
 
 1.458 
 
 .15 
 
 .0225 
 
 .0034 
 
 .3873 
 
 .5313 
 
 .2 
 
 10.24 
 
 32.768 
 
 1.789 
 
 1.474 
 
 .2 
 
 .04 
 
 .008 
 
 .4472 
 
 .5848 
 
 .3 
 
 10.89 
 
 35.937 
 
 1.817 
 
 1 .489 
 
 .25 
 
 .0625 
 
 .0156 
 
 .500 
 
 .6300 
 
 .4 
 
 11.56 
 
 39.304 
 
 1.844 
 
 1.504 
 
 .3 
 
 .09 
 
 .027 
 
 .5477 
 
 .6694 
 
 .5 
 
 12.25 
 
 42.875 
 
 1.871 
 
 1.518 
 
 .35 
 
 .1225 
 
 .0429 
 
 .5916 
 
 .7047 
 
 .6 
 
 12.96 
 
 46.656 
 
 1.897 
 
 1.533 
 
 .4 
 
 16 
 
 .064 
 
 .6325 
 
 .7368 
 
 .7 
 
 13.69 
 
 50.653 
 
 1.924 
 
 1.547 
 
 .45 
 
 . .2025 
 
 .0911 
 
 .6708 
 
 .7663 
 
 .8 
 
 14.44 
 
 54.872 
 
 1.949 
 
 1.560 
 
 .5 
 
 .25 
 
 .125 
 
 .7071 
 
 .7937 
 
 .9 
 
 15.21 
 
 59.319 
 
 1.975 
 
 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. 
 
 1. 
 
 1. 
 
 1. 
 
 .9 
 
 24.01 
 
 !'1 7.649 
 
 2.214 
 
 1.698 
 
 1.05 
 
 1.1025 
 
 1.158 
 
 1.025 
 
 1.016. 
 
 5. 
 
 25. 
 
 125. 
 
 2.2361 
 
 1.7100 
 
 1.1 
 
 1.21 
 
 1.331 
 
 1.049 
 
 1.032 
 
 .1 
 
 26.01 
 
 132.651 
 
 2.258 
 
 1.721 
 
 1.15 
 
 1.3225 
 
 1.521 
 
 1.072 
 
 1.048 
 
 .2 
 
 27.04 
 
 140.608 
 
 2.280 
 
 1.732 
 
 1.2 
 
 1.44 
 
 1.728 
 
 1.095 
 
 1.063 
 
 .3 
 
 28.09 
 
 148.877 
 
 2.302 
 
 1.744 
 
 1.25 
 
 1.5625 
 
 1.953 
 
 1.118 
 
 1.077 
 
 .4 
 
 29.16 
 
 157.464 
 
 2.324 
 
 1.754 
 
 1.3 
 
 1.69 
 
 2.197 
 
 1.140 
 
 1.091 
 
 .5 
 
 30.25 
 
 166.375 
 
 2.345 
 
 1 .765 
 
 1.35 
 
 1.8225 
 
 2.460 
 
 1.162 
 
 1.105 
 
 .6 
 
 31.36 
 
 175.616 
 
 2.366 
 
 1.776 
 
 1.4 
 
 1.96 
 
 2.744 
 
 1.183 
 
 1.119 
 
 .7 
 
 32.49 
 
 185.193 
 
 2.387 
 
 1.786 
 
 1.45 
 
 2.1025 
 
 3.049 
 
 1.204 
 
 1.132 
 
 .8 
 
 33.64 
 
 195.112 
 
 2.408 
 
 1.797 
 
 1.5 
 
 2.25 
 
 3.375 
 
 1 .2247 
 
 1.1447 
 
 .9 
 
 34.81 
 
 205.379 
 
 2.429 
 
 1.807 
 
 1.55 
 
 2.4025 
 
 3.724 
 
 1.245 
 
 1.157 
 
 3. 
 
 36. 
 
 216. • 
 
 2.4495 
 
 1.8171 
 
 1.6 
 
 2.56 
 
 4.096 
 
 1.265 
 
 1.170 
 
 .1 
 
 37.21 
 
 226.981 
 
 2.470 
 
 1.827 
 
 1.65 
 
 2.7225 
 
 4.492 
 
 1.285 
 
 1.182 
 
 .2 
 
 38.44 
 
 238.328 
 
 2.490 
 
 1 .837 
 
 1.7 
 
 2.89 
 
 4.913 
 
 1.304 
 
 1.193 
 
 .3 
 
 39.69 
 
 250.047 
 
 2.510 
 
 1.847 
 
 1.75 
 
 3.0625 
 
 5.359 
 
 1.323 
 
 1.205 
 
 .4 
 
 40.96 
 
 262.144 
 
 2.530 
 
 1.85/ 
 
 1.8 
 
 3.24 
 
 5.832 
 
 1.342 
 
 1.216 
 
 .5 
 
 42.25 
 
 274.625 
 
 2.550 
 
 1.866 
 
 1.85 
 
 3.4225 
 
 6.332 
 
 1.360 
 
 1.228 
 
 .6 
 
 43.56 
 
 287.496 
 
 2.569 
 
 1.876 
 
 1.9 
 
 3.61 
 
 6.859 
 
 1.378 
 
 1.239 
 
 .7 
 
 44.89 
 
 300.763 
 
 2.588 
 
 1.885 
 
 1.95 
 
 3.8025 
 
 7.415 
 
 1.396 
 
 1.249 
 
 .8 
 
 46.24 
 
 314.432 
 
 2.608 
 
 1.895 
 
 2. 
 
 4. 
 
 8. 
 
 1.4142 
 
 1.2599 
 
 .9 
 
 47.61 
 
 328.509 
 
 2.627 
 
 1.904 
 
 .1 
 
 4.41 
 
 9.261 
 
 1.449 
 
 1.281 
 
 7. 
 
 49. 
 
 343. 
 
 2.6458 
 
 1.9129 
 
 .2 
 
 4.84 
 
 10.648 
 
 1.483 
 
 1.301 
 
 J 
 
 50.41 
 
 357.911 
 
 2.665 
 
 1.922 
 
 .3 
 
 5.29 
 
 12.167 
 
 1.517 
 
 1.320 
 
 .2 
 
 51.84 
 
 373.248 
 
 2.683 
 
 1.931 
 
 .4 
 
 5.76 
 
 13.824 
 
 1.549 
 
 1.339 
 
 .3 
 
 53.29 
 
 389.017 
 
 2.702 
 
 1.940 
 
 .5 
 
 6.25 
 
 15.625 
 
 1.581 
 
 • 1.357 
 
 .4 
 
 54.76 
 
 405.224 
 
 2.720 
 
 1.949 
 
 .6 
 
 6.76 
 
 17.576 
 
 1.612 
 
 1.375 
 
 .5 
 
 56.25 
 
 421.875 
 
 2.739 
 
 1.957 
 
 .7 
 
 7.29 
 
 19.683 
 
 1.643 
 
 1.392 
 
 .6 
 
 57.76 
 
 438.976 
 
 2.757 
 
 1.966 
 
 .8 
 
 7.84 
 
 21.952 
 
 1.673 
 
 1.409 
 
 .7 
 
 59.29 
 
 456.533 
 
 2.775 
 
 1.975 
 
 .9 
 
 8.41 
 
 24.389 
 
 1.703 
 
 1.426 
 
 .8 
 
 60.84 
 
 474.552 
 
 2.793 
 
 1.983 
 
 3. 
 
 9. 
 
 27. 
 
 1.7321 
 
 1 .4422 
 
 .9 
 
 62.41 
 
 493.039 
 
 2.811 
 
 1.992 
 
 
 
 
 
 
 
 
 
 
 „ 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 
 
 95 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 
 Root. 
 
 Cube 
 Root. 
 
 No 
 
 Square Cube. 
 
 Sq. 
 
 Root. 
 
 Cube 
 Root. 
 
 8. 
 
 64. 
 
 512. 
 
 2.828- 
 
 i 2. 
 
 45 
 
 2025 
 
 9112: 
 
 6.7082 
 
 3.5569 
 
 .1 
 
 65.61 
 
 531.44 
 
 2.846 
 
 2.008 
 
 46 
 
 2116 
 
 97336 6.7823 
 
 3.5830 
 
 .2 
 
 67.24 
 
 551.36J 
 
 2.864 
 
 2.017 
 
 47 
 
 2209 
 
 103823 
 
 6.8557 
 
 3.6088 
 
 .3 
 
 68.89 
 
 571.78} 
 
 2.881 
 
 2.025 
 
 48 
 
 2304 
 
 110592 
 
 6.9282 
 
 3.6342 
 
 .4 
 
 70.56 
 
 592.70^ 
 
 2.898 
 
 2.033 
 
 49 
 
 2401 
 
 117649 
 
 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 
 
 157464 
 
 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 
 
 262 1 44 
 
 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 
 
 3 1 4432 
 
 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. 1 793 
 
 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 
 
 512000 
 
 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 
 
 1024 
 
 32768 
 
 5.6569 
 
 3.1748 
 
 87 
 
 7569 
 
 658503 
 
 9.3276 
 
 4.4310 
 
 33 
 
 1089 
 
 35937 
 
 5.7446 
 
 3.2075 
 
 88 
 
 7744 
 
 681472 
 
 9.3808 
 
 4.44&v> 
 
 34 
 
 1156 
 
 39304 
 
 5.8310 
 
 3.2396 
 
 89 
 
 7921 
 
 704969 
 
 9.4340 
 
 4.4647 
 
 35 
 
 1225 
 
 42875 
 
 5.9161 
 
 3.2711 
 
 90 
 
 8100 
 
 729000 
 
 9.4868 
 
 4.4814 
 
 36 
 
 1296 
 
 46656 
 
 6. 
 
 3.3019 
 
 91 
 
 8281 
 
 753571 
 
 9.5394 
 
 4.4979 
 
 37 
 
 1369 
 
 50653 
 
 6.0828 
 
 3.3322 
 
 92 
 
 8464 
 
 778688 
 
 9.5917 
 
 4.5144 
 
 38 
 
 1444 
 
 54872 
 
 6.1644 
 
 3.3620 
 
 93 
 
 8649 
 
 804357 
 
 9.6437 
 
 4.5307 
 
 39 
 
 1521 
 
 39319 
 
 6.2450 
 
 3.3912 
 
 94 
 
 8836 
 
 830584 
 
 9.6954 
 
 4.5468 
 
 40 
 
 1600 
 
 54000 
 
 6.3246 
 
 3.4200 
 
 95 
 
 9025 
 
 857375 
 
 9.7468 
 
 4.5629 
 
 41 
 
 1681 
 
 58921 
 
 6 4031 
 
 3.4482 
 
 96 
 
 9216 
 
 884736 
 
 9.7980 
 
 4.5789 
 
 42 
 
 1764 
 
 74088 
 
 6.4807 
 
 3.4760 
 
 97 
 
 9409 
 
 912673 
 
 9.8489 
 
 4.5947 
 
 43 
 
 1849 
 
 79507 
 
 6.5574 
 
 3.5034 
 
 98 
 
 9604 
 
 941192 
 
 9.8995 
 
 4.6104 
 
 44 
 
 1936 
 
 35184 
 
 6.6332 
 
 3.5303 
 
 99 1 9801 
 
 970299 
 
 9.9499 
 
 4.6261 
 
MATHEMATICAL TABLES. 
 
 No. 
 
 Sq. 
 
 Cube 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 10T 
 
 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 
 
 1 0. 1 489 
 
 4.6875 
 
 158 
 
 24964 
 
 3944312 
 
 12.5698 
 
 5.4061 
 
 104 
 
 10816 
 
 1 124864 
 
 10.1980 
 
 4.7027 
 
 159 
 
 2528! 
 
 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 
 
 4251528 
 
 12.7279 
 
 5.4514 
 
 103 
 
 11664 
 
 1259712 
 
 10.3923 
 
 4.7622 
 
 163 
 
 26569 
 
 4330747 
 
 12.7671 
 
 5.4626 
 
 10? 
 
 11881 
 
 1295029 
 
 10.4403 
 
 4.7769 
 
 164 
 
 26896 
 
 4410944 
 
 12.8062 
 
 5.4737 
 
 110 
 
 12100 
 
 1331000 
 
 10.4881 
 
 4.7914 
 
 165 
 
 2/225 
 
 4492125 
 
 12.8452 
 
 5.4848 
 
 II! 
 
 12321 
 
 1367631 
 
 10.5357 
 
 4.8059 
 
 166 
 
 27556 
 
 4574296 
 
 12.8841 
 
 5.4959 
 
 112 
 
 12544 
 
 1 404928 
 
 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 
 
 1520375 
 
 10.7238 
 
 4.8629 
 
 170 
 
 28900 
 
 4913000 
 
 13.0384 
 
 5.5397 
 
 116 
 
 13456 
 
 1560396 
 
 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 
 
 1 19 
 
 14161 
 
 1685159 
 
 10.9087 
 
 4.9187 
 
 174 
 
 30276 
 
 5268024 
 
 13.1909 
 
 5.5828 
 
 120 
 
 14400 
 
 1 728000 
 
 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 
 
 11.0454 
 
 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 
 
 11.2694 
 
 5.0265 
 
 182 
 
 33124 
 
 6028568 
 
 13.4907 
 
 5.6671 
 
 123 
 
 16384 
 
 2097152 
 
 11.3137 
 
 5.0397 
 
 183 
 
 33489 
 
 6128487 
 
 13.5277 
 
 5.6774 
 
 129 
 
 16641 
 
 2146639 
 
 11.3578 
 
 5.0528 
 
 184 
 
 33856 
 
 6229504 
 
 13.5647 
 
 5.6877 
 
 130 
 
 16900 
 
 2197000 
 
 11.4018 
 
 5.0658 
 
 185 
 
 34225 
 
 6331625 
 
 13.6015 
 
 5.6980 
 
 131 
 
 17161 
 
 2243091 
 
 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 
 
 17639 
 
 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 
 
 133 
 
 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 
 
 1 1 .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 
 
 2863283 
 
 11.9164 
 
 5.2171 
 
 197 
 
 38809 
 
 7645373 
 
 14.0357 
 
 5.8186 
 
 143 
 
 20449 
 
 2924207 
 
 11.9583 
 
 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 
 
 12.0416 
 
 5.2536 
 
 200 
 
 40000 
 
 8000000 
 
 14.1421 
 
 5.8480 
 
 146 
 
 21316 
 
 3112136 
 
 12.0330 
 
 5.2656 
 
 201 
 
 40401 
 
 8120601 
 
 14.1774 
 
 5.8578 
 
 147 
 
 21609 
 
 3176523 
 
 12.1244 
 
 5.2776 
 
 202 
 
 40804 
 
 8242408 
 
 14.2127 
 
 5.8675 
 
 143 
 
 21904 
 
 3241792 
 
 12.1655 
 
 5.2896 
 
 203 
 
 41209 
 
 8365427 
 
 14.2478 
 
 5.8771 
 
 !49 
 
 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 
 
 22301 
 
 3442951 
 
 12.2882 
 
 5.3251 
 
 206 
 
 42436 
 
 8741816 
 
 14.3527 
 
 5.9059 
 
 152 
 
 23104 
 
 3511803 
 
 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 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 97 
 
 No. 
 
 Sq. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 5T9439 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 210 
 
 44100 
 
 9261000 
 
 14.4914 
 
 265 
 
 70225 
 
 18609625 
 
 16.2788 
 
 6.4232 
 
 211 
 
 44521 
 
 9393931 
 
 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 
 
 10218313 
 
 14.7309 
 
 6.0092 
 
 272 
 
 73984 
 
 20123648 
 
 1 6.4924 
 
 6.4792 
 
 218 
 
 47524 
 
 10360232 
 
 14.7648 
 
 6.0185 
 
 273 
 
 74529 
 
 20346417 
 
 16.5227 
 
 6.4872 
 
 219 
 
 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 
 
 10941048 
 
 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 
 
 6.1446 
 
 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 
 
 15.3948 
 
 6.1885 
 
 292 
 
 85264 
 
 24897088 
 
 17.0880 
 
 6.6343 
 
 233 
 
 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 
 
 6.2231 
 
 296 
 
 87616 
 
 25934336 
 
 17.2047 
 
 6.6644 
 
 242 
 
 58564 
 
 14172488 
 
 15.5563 
 
 6.2317 
 
 297 
 
 88209 
 
 26193073 
 
 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 
 
 243 
 
 61504 
 
 15252992 
 
 15.7480 
 
 6.2828 
 
 303 
 
 91809 
 
 27818127 
 
 17.4069 
 
 6.7166 
 
 249 
 
 62001 
 
 1 5438249 
 
 15.7797 
 
 6.2912 
 
 304 
 
 92416 
 
 28094464 
 
 17.4356 
 
 6.7240 
 
 250 
 
 62500 
 
 15625000 
 
 15.8114 
 
 6.2996 
 
 305 
 
 93025 
 
 28372625 
 
 17.4642 
 
 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 
 
 17.6068 
 
 6.7679 
 
 256 
 
 65536 
 
 16777216 
 
 16.0000 
 
 6.3496 
 
 311 
 
 . 96721 
 
 3008023 1 
 
 17.6352 
 
 6.7752 
 
 257 
 
 66049 
 
 16974593 
 
 16.0312 
 
 63579 
 
 312 
 
 97344 
 
 30371328 
 
 17.6635 
 
 6.7824 
 
 253 
 
 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 
 
 6.3907 
 
 316 
 
 99856 
 
 31554496 
 
 17.7764 
 
 6.8113 
 
 262 
 
 68644 
 
 1 7984723 
 
 16.1864 
 
 6.3988 
 
 317 
 
 100489 
 
 31855013 
 
 17.8045 
 
 6.8185 
 
 263 
 
 69169 
 
 18191447 
 
 16.2173 
 
 J6.4070 
 
 318 
 
 101124 
 
 32157432 
 
 17.8326 
 
 6.8256 
 
 264 
 
 69696 
 
 18399744 
 
 16.2481 
 
 "6.4151 
 
 319 
 
 101761 
 
 32461759 
 
 17.8606 
 
 6.8328 
 
MATHEMATICAL TABLES. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 19.3649 
 
 Cube 
 Rcot. 
 
 320 
 
 1 02400 
 
 32768000 
 
 17.8885 
 
 6.8399 
 
 375 
 
 1 40625 
 
 52734375 
 
 7.2112 
 
 321 
 
 103041 
 
 33076161 17.9165 
 
 6.8470 
 
 376 
 
 141376 
 
 53157376 
 
 19.3907 
 
 7.2177 
 
 322 
 
 103684 
 
 33386248117.9444 
 
 6.8541 
 
 377 
 
 142129 
 
 53582633 
 
 19.4165 
 
 7.2240 
 
 323 
 
 104329 
 
 33698267! 17.9722 
 
 6.8612 
 
 378! 142884 
 
 54010152 
 
 19.4422 
 
 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 
 
 19.4936 
 
 7.2432 
 
 326 
 
 106276 
 
 34645976j18.0555j6.8824 
 
 381 
 
 145161 
 
 55306341 
 
 19.5192 
 
 7.2495 
 
 327 
 
 106929 
 
 34965783 i 18.0831 16.8894 
 
 382 
 
 145924 
 
 55 742968 
 
 19.5448 
 
 7.2558 
 
 328 
 
 107584 
 
 35287552 18.1 108 6.8964 
 
 383 146689 
 
 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 
 
 3851148225 
 
 57066625 
 
 19.6214 
 
 7.2748 
 
 331 
 
 109561 
 
 36264691 
 
 18.1934 
 
 6.9174 
 
 386H48996 
 
 57512456 
 
 19.6469 
 
 7.2811 
 
 3 32 
 
 110224 
 
 36594368 
 
 18.2209 
 
 6.9244 
 
 387J149769 
 
 57960603 
 
 19.6723 
 
 7.2874 
 
 333 
 
 110389 
 
 36926037 
 
 18.2483 
 
 6.9313 
 
 3831150544 
 
 58411072 
 
 19.6977 
 
 7.2936 
 
 334 
 
 111556 
 
 37259704 
 
 18.2757 
 
 6.9382 
 
 389 151321 
 
 58863869 
 
 197231 
 
 7.2999 
 
 335 
 
 112225 
 
 37595375 
 
 18.3030 
 
 6.9451 
 
 390 152100 
 
 593 1 9000 
 
 19.7484 
 
 7.3061 
 
 336 
 
 112896 
 
 37933056 
 
 18.3303 
 
 6.9521 
 
 391 152381 
 
 59776471 
 
 19.7737 
 
 7.3124 
 
 337 
 
 113569 
 
 38272753 18.3576 
 
 6.9589 
 
 392 ! 153664 
 
 60256288 
 
 197990 
 
 7.3186 
 
 333 
 
 114244 
 
 38614472i18.3848l6.9658 
 
 393:154449 
 
 60598457 
 
 19.8242 
 
 7.3248 
 
 339 
 
 114921 
 
 38958219 
 
 18.4120 6.9727 
 
 394 
 
 155236 
 
 61162984 
 
 19.8494 
 
 7.3310 
 
 340 
 
 1 1 5600 
 
 39304000 
 
 18.4391 6.9795 
 
 395 
 
 156025 
 
 61629875 
 
 19.8746 
 
 7.3372 
 
 341 
 
 116281 
 
 39651821 
 
 18.46626.9864 
 
 396 
 
 156816 
 
 62099136 
 
 19.8997 
 
 7.3434 
 
 342 
 
 116964 
 
 40001683 
 
 1 8.4932 J6. 9932 
 
 397 
 
 157609 
 
 62570773 
 
 19.9249 
 
 7.3496 
 
 343 
 
 1 1 7649 
 
 40353607 
 
 18.52037-0000 
 
 398 
 
 158404 
 
 63044792 
 
 19.9499 
 
 7.35^8 
 
 344 
 
 118336 
 
 40707584 
 
 18.5472 7.0068 
 
 399 
 
 159201 
 
 63521199 
 
 19.9750 
 
 7.3619 
 
 345 
 
 119025 
 
 41063625 
 
 1 8.5742|7.0i 36 
 
 400 160000 
 
 64000000 
 
 2O.CC0O 
 
 7.3681 
 
 346 
 
 119716 
 
 41421736 
 
 18.6011 17.0203 
 
 401 i 160801 
 
 64481201 
 
 20.0250 
 
 7.3742 
 
 347 
 
 120409 
 
 41731923 
 
 ',8.62797.0271 
 
 402! 161604 
 
 64964808 20.0499 
 
 7.3£03 
 
 348 
 
 121104 
 
 42144192 
 
 18.65487.0338 
 
 403 162 -'09 
 
 65450827 20.0749 
 
 7.3864 
 
 349 
 
 121801 
 
 42503549 
 
 18.6815 
 
 7.0406 
 
 404 
 
 163216 
 
 65939264 
 
 20.0998 
 
 7.3925 
 
 359 
 
 122500 
 
 42375000 18.7033 
 
 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 
 
 43614208118.7617 
 
 7.0607 
 
 407 165649 
 
 67419143(20.1742 
 
 7.4108 
 
 353 
 
 124609 
 
 43986977 
 
 18.7883 
 
 7.0674 
 
 408 
 
 166464 
 
 67917312 
 
 20.1990 
 
 7.^169 
 
 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 
 
 20.2485 
 
 7.4290 
 
 356 
 
 126736 
 
 45118016 
 
 18.8680 
 
 7.0873 
 
 411 
 
 1 6892 1 
 
 69426531 
 
 20.2731 
 
 7.4350 
 
 357 
 
 127449 
 
 45499293 118.8944! 7.0940 
 
 412| 169744 
 
 69934528 
 
 20.2978 
 
 7.4410 
 
 353 
 
 123164 
 
 45882712| 18.92097.1006 
 
 413j 170569 
 
 70444997 
 
 20.3224 
 
 7.4470 
 
 359 
 
 128881 
 
 46268279 18.9473 1 7. 1072 
 
 414 
 
 171396 
 
 70957944 
 
 20.3470 
 
 7.4530 
 
 360 
 
 129600 
 
 46656000; 18.9737 7.1138 
 
 415 
 
 172225 
 
 71473375 
 
 20.3715 
 
 7.4590 
 
 361 
 
 130321 
 
 47045881I19.0000 7.1204 
 
 416 
 
 173056 
 
 71991296 
 
 20.3961 
 
 7.4650 
 
 36? 
 
 131044 
 
 47437928 
 
 19.0263 
 
 7.1269 
 
 417 
 
 173889 
 
 72511713 
 
 20.4206 
 
 7.4710 
 
 363 
 
 1 3 1 769 
 
 47832147 
 
 19.0526 
 
 7.1335 
 
 418 
 
 174724 
 
 73034632 
 
 20.4450 
 
 7.4770 
 
 364 
 
 132496 
 
 43228544 
 
 19.0788 
 
 7.1400 
 
 419 
 
 175561 
 
 73560059 
 
 20.4695 
 
 7.4829 
 
 365 
 
 133225 
 
 4S627125 
 
 19.1050 
 
 7.1466 
 
 420 
 
 1 76400 
 
 74088000 
 
 20.4939 
 
 7.4889 
 
 366 133956 
 
 49027896 
 
 19.1311 
 
 7.1531 
 
 421 
 
 177241 
 
 74618461 
 
 20.5183 
 
 7.4948 
 
 367 
 
 134639 
 
 49430863 
 
 19.1572 
 
 7.1596 
 
 422 
 
 1 78084 
 
 75151448 
 
 20.5426 
 
 7.5007 
 
 363 
 
 135424 
 
 49836032 
 
 19.18337.1661 
 
 423 
 
 1 78929 
 
 75686967 
 
 20.5670 
 
 7.5067 
 
 369 
 
 . 136161 
 
 50243409 19.2094 7.1 726 
 
 424 
 
 179776 
 
 76225024 
 
 20.5913 
 
 7.5126 
 
 370 
 
 136900 
 
 506530001 19.235417. 1791 
 
 425)180625 
 
 76765625 
 
 20.6155 
 
 7.5185 
 
 371 137641 
 
 5106431 l!l9.2614;7. 1855 
 
 4261181476 
 
 77308776 
 
 20.6398 
 
 7.5244 
 
 372i 138384 
 
 51478348 19.2873|7. 1920 
 
 427; 182329 
 
 77854^8320.6640 
 
 7 5302 
 
 373 139129 
 
 51895117 19.3132(7.1984 
 
 428,183184 
 
 7840275270.6882 
 
 7.5361 
 
 374 1 139876 
 
 5231362419.33917.2048 
 
 429 184041 
 
 78953589 207123 
 
 7.5420 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 99 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube, 
 
 Sq. 
 Root. 
 
 Cube 
 Root, 
 
 430 
 
 184900 
 
 79507000 
 
 20.7364 7.547 
 
 485 
 
 235225 
 
 114084125 
 
 22.0227 
 
 7.8568 
 
 431 
 
 185761 
 
 80062991 
 
 20.7605 
 
 7.5537 
 
 486 
 
 236196 
 
 114791256 
 
 22.0454 
 
 7.8622 
 
 432 
 
 186624 
 
 80621568 
 
 20.7846 
 
 7.5595 
 
 487 
 
 237169 
 
 115501303 
 
 22.0681 
 
 7.8676 
 
 433 
 
 187489 
 
 81182737 
 
 20.8087 
 
 7.5654 
 
 488 
 
 238144 
 
 116214272 
 
 22.0907 
 
 7.8730 
 
 434 
 
 188356 
 
 81746504 
 
 20.8327 
 
 7.5712 
 
 489 
 
 239121 
 
 116930169 
 
 22.1133 
 
 7.8784 
 
 435 
 
 189225 
 
 82312875 
 
 20.8567 
 
 7.5770 
 
 490 
 
 240100 
 
 1 1 7649000 
 
 22.1359 
 
 7.8837 
 
 436 
 
 1 90096 
 
 82381856 
 
 20.8806 
 
 7.5828 
 
 491 
 
 241081 
 
 118370771 
 
 22.1585 
 
 7.8891 
 
 457 
 
 190969 
 
 83453453 
 
 20.9045 
 
 7.5886 
 
 492 
 
 242064 
 
 119095438 
 
 22.1811 
 
 7.8944 
 
 43 J 
 
 191844 
 
 84027672 
 
 20.9284 
 
 7.5944 
 
 493 
 
 243049 
 
 119823157 
 
 22.2036 
 
 7.8998 
 
 439 
 
 192721 
 
 846045 1 9 
 
 20.9523 
 
 7.6001 
 
 494 
 
 244036 
 
 120553784 
 
 22.2261 
 
 7.9051 
 
 440 
 
 193600 
 
 85 1 84000 
 
 20.9762 
 
 7.6059 
 
 495 
 
 245025 
 
 121287375 
 
 22.2486 
 
 7.9105 
 
 441 
 
 1944S1 
 
 85766121 
 
 21.0000 
 
 7.6117 
 
 496 
 
 246016 
 
 122023936 
 
 22.2711 
 
 7.9158 
 
 442 
 
 195364 
 
 86350888 
 
 21.0238 
 
 7.6174 
 
 497 
 
 247009 
 
 122763473 
 
 22.2935 
 
 7.9211 
 
 443 
 
 196249 
 
 86938307 
 
 21.0476 
 
 7.6232 
 
 498 
 
 248004 
 
 123505992 
 
 22.3159 
 
 7.9264 
 
 444 
 
 197136 
 
 87528384 
 
 21.0713 
 
 7.6289 
 
 499 
 
 249001 
 
 124251499 
 
 22.3383 
 
 7.9317 
 
 445 
 
 198025 
 
 88121125 
 
 21.0950 
 
 7.6346 
 
 500 
 
 250000 
 
 125000000 
 
 22.3607 
 
 7.9370 
 
 44o 
 
 198916 
 
 88716536 
 
 21.1187 
 
 7.6403 
 
 501 
 
 251001 
 
 125751501 
 
 22.3830 
 
 7.9423 
 
 447 
 
 199809 
 
 893 1 4623 
 
 21.1424 
 
 7.6460 
 
 502 
 
 252004 
 
 126506008 
 
 22.4054 
 
 7.9476 
 
 443 
 
 200704 
 
 89915392 
 
 21.1660 
 
 7.6517 
 
 503 
 
 253009 
 
 127263527 
 
 22.4277 
 
 7.9528 
 
 449 
 
 201601 
 
 905 1 8849 
 
 21.1896 
 
 7.6574 
 
 504 
 
 254016 
 
 128024064 
 
 22.4499 
 
 7.9581 
 
 450 
 
 202500 
 
 91125000 
 
 21.2132 
 
 7.6631 
 
 505 
 
 255025 
 
 128787625 
 
 22.4722 
 
 7.9634 
 
 451 
 
 203401 
 
 91733851 
 
 21.2368 
 
 7.6688 
 
 506 
 
 256036 
 
 129554216 
 
 22.4944 
 
 7.9686 
 
 452 
 
 204304 
 
 92345408 
 
 21.2603 
 
 7.6744 
 
 507 
 
 257049 
 
 130323843 
 
 22.5167 
 
 7 9739 
 
 453 
 
 205209 
 
 92959677 
 
 21.2838 
 
 7.6800 
 
 508 
 
 258064 
 
 131096512 
 
 22.5389 
 
 7.9791 
 
 434 
 
 206116 
 
 93576664 
 
 21.3073 
 
 7.6857 
 
 509 
 
 259081 
 
 131872229 
 
 22.5610 
 
 7.9843 
 
 455 
 
 207025 
 
 94196375 
 
 21.3307 
 
 7.6914 
 
 510 
 
 260100 
 
 132651000 
 
 22.5832 
 
 7.9896 
 
 456 
 
 207936 
 
 94818816 
 
 21.3542 
 
 7.6970 
 
 511 
 
 261121 
 
 13343283 1 
 
 22.6053 
 
 7.9948 
 
 457 
 
 208849 
 
 95443993 
 
 21.3776 
 
 7.7026 
 
 512 
 
 262144 
 
 134217728 
 
 22.6274 
 
 8.0000 
 
 4j3 
 
 209764 
 
 96071912 
 
 21.4009 
 
 7.7082 
 
 513 
 
 263169 
 
 135005697 
 
 22.6495 
 
 8.0052 
 
 459 
 
 210681 
 
 96702579 
 
 2 1 .4243 
 
 7.7138 
 
 514 
 
 264196 
 
 135796744 
 
 22.6716 
 
 8.0104 
 
 460 
 
 211600 
 
 97336000 
 
 21.4476 
 
 7.7194 
 
 515 
 
 265225 
 
 136590875 
 
 22.6936 
 
 8.0156 
 
 461 
 
 212521 
 
 97972181 
 
 21.4709 
 
 7.7250 
 
 516 
 
 266256 
 
 137338096 
 
 22.7156 
 
 8.0208 
 
 40? 
 
 213444 
 
 98611128 
 
 21.4942 
 
 7.7306 
 
 517 
 
 267289 
 
 138188413 
 
 22.7376 
 
 8.0260 
 
 463 
 
 214369 
 
 99252847 
 
 21.5174 
 
 7.7362 
 
 518 
 
 268324 
 
 138991832 
 
 22.7596 
 
 8.0311 
 
 464 
 
 215296 
 
 99897344 
 
 21.5407 
 
 7.7418 
 
 519 
 
 269361 
 
 139798359 
 
 22.7816 
 
 8.0363 
 
 465 
 
 216225 
 
 100544625 
 
 21.5639 
 
 7.7473 
 
 520 
 
 270400 
 
 140608000 
 
 22.8035 
 
 8.0415 
 
 466 
 
 217156 
 
 101194696 
 
 21.587C 
 
 7.7529 
 
 521 
 
 27144! 
 
 141420761 
 
 22.8254 
 
 8.0466 
 
 467 
 
 218089 
 
 101847563 
 
 21.6102 
 
 7.7584 
 
 522 
 
 272484 
 
 142236646 
 
 22.8473 
 
 8.0517 
 
 468 
 
 219024 
 
 102503232 
 
 21.6333 
 
 7.7639 
 
 523 
 
 273529 
 
 143055667 
 
 22.8692 
 
 8.0569 
 
 469 
 
 21996! 
 
 103161709 
 
 21.6564 
 
 7.7695 
 
 524 
 
 274576 
 
 143877824 
 
 22.8910 
 
 8.062P 
 
 470 
 
 220900 
 
 103823000 
 
 21.6795 
 
 7.7750 
 
 525 
 
 275625 
 
 144703125 
 
 22.9129 
 
 8.0671 
 
 47! 
 
 221341 
 
 104437111 
 
 21.7025 
 
 7.7805 
 
 526 
 
 276676 
 
 145531576 
 
 22.9347 
 
 8.0723 
 
 472 
 
 222/34 
 
 105154048 
 
 21.7256 
 
 7.7860 
 
 527 
 
 277729 
 
 146363183 
 
 22.9565 
 
 8.0774 
 
 473 
 
 223 729 
 
 105823317 
 
 21.7486 
 
 7.7915 
 
 528 
 
 278784 
 
 147197952 
 
 22.9783 
 
 8.0825 
 
 474 
 
 224676 
 
 106496424 
 
 21.7715 
 
 7.7970 
 
 529 
 
 279841 
 
 148035889 
 
 23.0000 
 
 8.0876 
 
 475 
 
 225625 
 
 107171875 
 
 21.7945 
 
 7.8025 
 
 530 
 
 280900 
 
 14887700C 
 
 23.0217 
 
 8.0927 
 
 476 
 
 226576 
 
 107850176 
 
 21.8174 
 
 7.8079 
 
 531 
 
 281961 
 
 149721291 
 
 23.0434 
 
 8.0978 
 
 477 
 
 227529 
 
 103531333 
 
 21.8403 
 
 7.8134 
 
 532 
 
 283024 
 
 150568766 
 
 23.0651 
 
 8.1028 
 
 478 
 
 228484 
 
 109215352 
 
 2 1 .8632 
 
 7.8188 
 
 533 
 
 284089 
 
 151419437 
 
 23.0868 
 
 8.1079 
 
 479 
 
 229441 
 
 109902239 
 
 21.8861 
 
 7.8243 
 
 534 
 
 285156 
 
 152273304 
 
 23.1084 
 
 8.1130 
 
 4S0 
 
 230400 
 
 110592000 
 
 21.9089 
 
 7.8297 
 
 535 
 
 286225 
 
 153130375 
 
 23.1301 
 
 8.1180 
 
 431 
 
 231361 
 
 1 11284641 
 
 21.9317 
 
 7.8352 
 
 536 
 
 287296 
 
 153990656 
 
 23.1517 
 
 8.1231 
 
 432 
 
 232324 
 
 1 1 1980168 
 
 21.9545 
 
 7.8406 
 
 537 
 
 238369 
 
 154854153 
 
 23.1733 
 
 8.1281 
 
 433 
 
 233239 
 
 112678537 
 
 21.9773 
 
 7.8460 
 
 538 
 
 289444 
 
 155720372 
 
 23.1948 
 
 8.1332 
 
 484 
 
 234256 
 
 1 13379904 
 
 22.0000 
 
 7.8514 
 
 539 
 
 1290521 
 
 156590819 
 
 23.2164 
 
 8.1382 
 
MATHEMATICAL TABLES. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 540 
 
 291600 
 
 157464000 
 
 23.2379 
 
 8.1433 
 
 595 
 
 354025 
 
 2106448/5 24. 
 
 8.4103 
 
 541 
 
 292681 
 
 158340421 
 
 23.2594 
 
 8.1483 
 
 596 
 
 355216 
 
 211708736 
 
 24.4131 
 
 8.4155 
 
 542 
 
 293764 
 
 1 59220088 
 
 23.2809 
 
 8.1533 
 
 597 
 
 356409 
 
 212776173 
 
 24.4336 
 
 8.4202 
 
 543 
 
 294349 
 
 160103007 
 
 23.3024 
 
 8.1583 
 
 598 
 
 357604 
 
 213847192 
 
 24.4540 
 
 8.4249 
 
 544 
 
 295936 
 
 160989184 
 
 23.3238 
 
 8.1633 
 
 599 
 
 358801 
 
 214921799 
 
 24.4745 
 
 8.4296 
 
 545 
 
 297025 
 
 161878625 
 
 23.3452 
 
 8.1683 
 
 600 
 
 360000 
 
 216000000 
 
 24.4949 
 
 8.4343 
 
 546 
 
 298116 
 
 162771336 
 
 23.3666 
 
 8.1733 
 
 601 
 
 361201 
 
 217081801 
 
 24.5153 
 
 8.4390 
 
 547 
 
 299209 
 
 163667323 
 
 23.3380 
 
 8. 1 783 
 
 602 
 
 362404 
 
 218167208 
 
 24.5357 
 
 8.4437 
 
 543 
 
 300304 
 
 164566592 
 
 23.4094 
 
 8.1833 
 
 603 
 
 363609 
 
 219256227 
 
 24.5561 
 
 8.4484 
 
 549 
 
 301401 
 
 165469149 
 
 23.4307 
 
 8.1882 
 
 604 
 
 364816 
 
 220348864 
 
 24.5764 
 
 8.4530 
 
 550 
 
 302500 
 
 166375000 
 
 23.4521 
 
 8.1932 
 
 605 
 
 366025 
 
 221445125 
 
 24.5967 
 
 8.4577 
 
 551 
 
 303601 
 
 167284151 
 
 23.4734 
 
 8.1982 
 
 606 
 
 367236 
 
 222545016 
 
 24.6171 
 
 8.4623 
 
 552 
 
 304704 
 
 163196608 
 
 23.4947 
 
 8.2031 
 
 607 
 
 36S449 
 
 223648543 
 
 24.6374 
 
 8.4670 
 
 553 
 
 305809 
 
 169112377 
 
 23.5160 
 
 8.2081 
 
 608 
 
 369664 
 
 224755712 
 
 24.6577 
 
 8.4716 
 
 554 
 
 306916 
 
 170031464 
 
 23.5372 
 
 8.2130 
 
 609 
 
 370881 
 
 225866529 
 
 24.6779 
 
 8.4763 
 
 555 
 
 308025 
 
 170953875 
 
 23.5584 
 
 8.2180 
 
 610 
 
 372100 
 
 226981000 
 
 24.6982 
 
 8.4809 
 
 556 
 
 309136 
 
 171879616 
 
 23.5797 
 
 8.2229 
 
 611 
 
 373321 
 
 228099131 
 
 24.7184 
 
 8.4856 
 
 557 
 
 310249 
 
 1 72808693 
 
 23.6008 
 
 8.2278 
 
 612 
 
 374544 
 
 229220928 
 
 24.7386 
 
 8.4902 
 
 553 
 
 311364 
 
 173741112 
 
 23.6220 
 
 8.2327 
 
 613 
 
 375769 
 
 230346397 
 
 24.7588 
 
 8.4948 
 
 559 
 
 312481 
 
 174676879 
 
 23.6432 
 
 8.2377 
 
 614 
 
 376996 
 
 231475544 
 
 24.7790 
 
 8.4994 
 
 560 
 
 313600 
 
 175616000 
 
 23.6643 
 
 8.2426 
 
 635 
 
 378225 
 
 232608375 
 
 24.7992 
 
 8.5040 
 
 561 
 
 314721 
 
 176558481 
 
 23.6854 
 
 8.2475 
 
 616 
 
 379456 
 
 233744896 
 
 24.8193 
 
 8.5086 
 
 562 
 
 315844 
 
 177504328 
 
 23.7065 
 
 8.2524 
 
 617 
 
 380689 
 
 234885113 
 
 24.8395 
 
 8.5132 
 
 563 
 
 316969 
 
 178453547 
 
 23.7276 
 
 8.2573 
 
 618 
 
 381924 
 
 236029032 
 
 24.8596 
 
 8.5178 
 
 564 
 
 318096 
 
 179406144 
 
 23.7487 
 
 8.2621 
 
 619 
 
 383161 
 
 237176659 
 
 24.8797 
 
 8.5224 
 
 565 
 
 319225 
 
 180362125 
 
 23.7697 
 
 8.2670 
 
 620 
 
 384400 
 
 238328000 
 
 24.8998 
 
 8.5270 
 
 566 
 
 320356 
 
 181321496 
 
 23.7908 
 
 8.2719 
 
 621 
 
 385641 
 
 239483061 
 
 24.9199 
 
 8.5316 
 
 567 
 
 321489 
 
 182284263 
 
 23.8118 
 
 8.2768 
 
 622 
 
 386884 
 
 240641848 
 
 24.9399 
 
 8.5362 
 
 568 
 
 322624 
 
 1*3250432 
 
 23.8328 
 
 8.2816 
 
 623 
 
 388129 
 
 241804367 
 
 24.9600 
 
 8.5408 
 
 569 
 
 323761 
 
 i 84220009 
 
 23.8537 
 
 8.2865 
 
 624 
 
 389376 
 
 242970624 
 
 24.9800 
 
 8.5453 
 
 570 
 
 324900 
 
 185193000 
 
 23.8747 
 
 8.2913 
 
 625 
 
 390625 
 
 244140625 
 
 25.0000 
 
 8.5499 
 
 571 
 
 326041 
 
 186169411 
 
 23.8956 
 
 8.2962 
 
 626 
 
 391876 
 
 245314376 
 
 25.0200 
 
 8.5544 
 
 572 
 
 327184 
 
 187149248 
 
 23.9165 
 
 8.3010 
 
 627 
 
 393129 
 
 246491833 
 
 25.0400 
 
 8 5590 
 
 573 
 
 328329 
 
 188132517 
 
 23.9374 
 
 8.3059 
 
 628 
 
 394384 
 
 247673152 
 
 25.0599 
 
 8.5635 
 
 574 
 
 329476 
 
 189119224 
 
 23.9583 
 
 8.3107 
 
 629 
 
 395641 
 
 248858189 
 
 25.0799 
 
 8.5681 
 
 575 
 
 330625 
 
 190109375 
 
 23.9792 
 
 8.3155 
 
 630 
 
 396900 
 
 250047000 
 
 25.0998 
 
 8.5726 
 
 576 
 
 331776 
 
 191102976 
 
 24.0000 
 
 8.3203 
 
 631 
 
 398161 
 
 251239591 
 
 25.1197 
 
 8.5772 
 
 577 
 
 332929 
 
 192100033 
 
 24.0208 
 
 8.3251 
 
 632 
 
 399424 
 
 252435968 
 
 25.1396 
 
 8.5817 
 
 
 334034 
 
 193100552 
 
 24.0416 
 
 8.3300 
 
 633 
 
 400639 
 
 253636137 
 
 25.1595 
 
 8.5862 
 
 579 
 
 335241 
 
 194104539 
 
 24.0624 
 
 8.3348 
 
 634 
 
 401956 
 
 254840104 
 
 25.1794 
 
 8.5907 
 
 580 
 
 336400 
 
 195112000 
 
 24.0832 
 
 8.3396 
 
 635 
 
 403225 
 
 256047875 
 
 25.1992 
 
 8.5952 
 
 581 
 
 337561 
 
 196122941 
 
 24.1039 
 
 8.3443 
 
 636 
 
 404496 
 
 257259456 
 
 25.2190 
 
 8.5997 
 
 582 
 
 338724 
 
 197137368 
 
 24.1247 
 
 8.3491 
 
 637 
 
 405769 
 
 258474853 
 
 25.2389 
 
 8.6043 
 
 583 
 
 339889 
 
 198155287 
 
 24.1454 
 
 8.3539 
 
 638 
 
 407044 
 
 259694072 
 
 25.2587 
 
 8.6039 
 
 584 
 
 341056 
 
 199176704 
 
 24.1661 
 
 8.3587 
 
 639 
 
 408321 
 
 260917119 
 
 25.2784 
 
 8.6132 
 
 585 
 
 342225 
 
 200201625 
 
 24.1868 
 
 8.3634 
 
 640 
 
 409600 
 
 262144000 
 
 25.2982 
 
 8.6177 
 
 586 
 
 343396 
 
 201230056 
 
 24.2074 
 
 8.3682 
 
 641 
 
 410881 
 
 263374721 
 
 25.3180 
 
 8.6222 
 
 587 
 
 344569 
 
 202262003 
 
 24.2281 
 
 8.3730 
 
 642 
 
 412164 
 
 264609288 
 
 25.3377 
 
 8.6267 
 
 583 
 
 345744 
 
 203297472 
 
 24.2487 
 
 8.3777 
 
 643 
 
 413449 
 
 265847707 
 
 25.3574 
 
 8.6312 
 
 589 
 
 34692 1 
 
 204336469 
 
 24.2693 
 
 8.3825 
 
 644 
 
 414736 
 
 267089934 
 
 25.3772 
 
 8.6357 
 
 590 
 
 348100 
 
 205379000 
 
 24.2899 
 
 8.3872 
 
 645 
 
 416025 
 
 268336125 
 
 25.3969 
 
 8.6401 
 
 591 
 
 349281 
 
 206425071 
 
 24.3105 
 
 8.3919 
 
 646 
 
 417316 
 
 269586136 
 
 25.4165 
 
 8.6446 
 
 592 
 
 350464 
 
 207474688 
 
 24.3311 
 
 8.3967 
 
 647 
 
 4 1 8609 
 
 270840n?3 
 
 25.4362 
 
 8 6490 
 
 593 
 
 351649 
 
 208527857 24.3516 
 
 8.4014 
 
 648 
 
 419904 
 
 272097792 
 
 25.4555 
 
 8.6535 
 
 594 352836 209584584 24.37218.4061 
 
 649 421201273359449 25.4755 8.6579 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 101 
 
 \ T o 
 
 Square. 
 422500 
 
 Cube. 
 
 Sq. 
 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 350 
 
 274625000 
 
 25.4951 
 
 8.6624 
 
 705 
 
 497025 
 
 350402625 
 
 26.5518 
 
 8.9001 
 
 551 
 
 423801 
 
 275894451 
 
 25.5147 
 
 8.6668 
 
 706 
 
 498436 
 
 351895816 
 
 26.5707 
 
 8.9043 
 
 552 
 
 425104 
 
 277167808 
 
 25.5343 
 
 8.6713 
 
 707 
 
 499849 
 
 353393243 
 
 26.5895 
 
 8.9085 
 
 d53 
 
 426409 
 
 278445077 
 
 25.5539 
 
 8.6757 
 
 708 
 
 501264 
 
 354894912 
 
 26.6083 
 
 8.9127 
 
 354 
 
 427716 
 
 279726264 
 
 25.5734 
 
 8.6801 
 
 709 
 
 502681 
 
 356400829 
 
 26.6271 
 
 8.9169 
 
 >55 
 
 429025 
 
 281011375 
 
 25.5930 
 
 8.6845 
 
 710 
 
 504100 
 
 357911000 
 
 26.6458 
 
 8.9211 
 
 )56 
 
 430336 
 
 282300416 
 
 25.6125 
 
 8.6890 
 
 711 
 
 505521 
 
 359425431 
 
 26.6646 
 
 8.9253 
 
 ?57 
 
 431649 
 
 283593393 
 
 25.6320 
 
 8.6934 
 
 712 
 
 506944 
 
 360944128 
 
 26.6833 
 
 8.9295 
 
 )5S 
 
 432964 
 
 284890312 
 
 25.6515 
 
 8.6978 
 
 713 
 
 508369 
 
 362467097 
 
 26.7021 
 
 8.9337 
 
 )59 
 
 434281 
 
 286191179 
 
 25.6710 
 
 8.7022 
 
 714 
 
 509796 
 
 363994344 
 
 26.7208 
 
 8.9378 
 
 >60 
 
 435600 
 
 287496000 
 
 25.6905 
 
 8.7066 
 
 715 
 
 511225 
 
 365525875 
 
 26.7395 
 
 8.9420 
 
 61 
 
 43692 1 
 
 288804781 
 
 25.7099 
 
 8.7110 
 
 716 
 
 512656 
 
 367061696 
 
 26 7582 
 
 8.9462 
 
 62 
 
 438244 
 
 290117528 
 
 25.7294 
 
 8.7154 
 
 717 
 
 514089 
 
 368601813 
 
 26.7769 
 
 8.9503 
 
 33 
 
 439569 
 
 291434247 
 
 25.7488 
 
 8.7198 
 
 718 
 
 515524 
 
 370146232 
 
 26.7955 
 
 8.9545 
 
 64 
 
 440896 
 
 292754944 
 
 25.7682 
 
 8.7241 
 
 719 
 
 516961 
 
 371694959 
 
 26.8142 
 
 8.9587 
 
 65 
 
 442225 
 
 294079625 
 
 25.7876 
 
 8.7285 
 
 720 
 
 518400 
 
 373248000 
 
 26.8328 
 
 8.9628 
 
 66 
 
 443556 
 
 295408296 
 
 25.8070 
 
 8.7329 
 
 721 
 
 519841 
 
 374805361 
 
 26.8514 
 
 8.9670 
 
 67 
 
 444889 
 
 296740963 
 
 25 8263 
 
 8.7373 
 
 722 
 
 521284 
 
 376367048 
 
 26.8701 
 
 8.9711 
 
 6S 
 
 446224 
 
 298077632 
 
 25.8457 
 
 8.7416 
 
 723 
 
 522729 
 
 377933067 
 
 26.8887 
 
 8.9752 
 
 69 
 
 447561 
 
 299418309 
 
 25.8650 
 
 8.7460 
 
 724 
 
 524176 
 
 379503424 
 
 26.9072 
 
 8.9794 
 
 70 
 
 448900 
 
 300763000 
 
 25.8844 
 
 8.7503 
 
 725 
 
 525625 
 
 381078125 
 
 26.9258 
 
 8.9835 
 
 71 
 
 450241 
 
 302111711 
 
 25.9037 
 
 8.7547 
 
 726 
 
 527076 
 
 382657176 
 
 26.9444 
 
 8.9876 
 
 72 
 
 451584 
 
 303464448 
 
 25.9230 
 
 8.7590 
 
 727 
 
 528529 
 
 384240583 
 
 26.9629 
 
 8.9918 
 
 73 
 
 452929 
 
 304821217 
 
 25.9422 
 
 8.7634 
 
 728 
 
 529984 
 
 385828352 
 
 26.9815 
 
 8.9959 
 
 74 
 
 454276 
 
 306182024 
 
 25.9615 
 
 8.7677 
 
 729 
 
 531441 
 
 387420489 
 
 27.0000 
 
 9.0000 
 
 75 
 
 455625 
 
 307546875 
 
 25.9808 
 
 8.7721 
 
 730 
 
 532900 
 
 389017000 
 
 27.0185 
 
 9.0041 
 
 76 
 
 456976 
 
 308915776 
 
 26.0000 
 
 8.7764 
 
 731 
 
 534361 
 
 390617891 
 
 27.0370 
 
 9.0082 
 
 77 
 
 458329 
 
 310288733 
 
 26.0192 
 
 8.7807 
 
 732 
 
 535824 
 
 392223168 
 
 27.0555 
 
 9.0123 
 
 78 
 
 459684 
 
 311665752 
 
 26.0384 
 
 8.7850 
 
 733 
 
 537289 
 
 393832837 
 
 27.0740 
 
 9.0164 
 
 79 
 
 461041 
 
 313046839 
 
 26.0576 
 
 8.7893 
 
 734 
 
 538756 
 
 395446904 
 
 27.0924 
 
 9.0205 
 
 80 
 
 462400 
 
 314432000 
 
 26.0768 
 
 8.7937 
 
 735 
 
 540225 
 
 397065375 
 
 27.1109 
 
 9.0246 
 
 31 
 
 463761 
 
 315821241 
 
 26.0960 
 
 8.7980 
 
 736 
 
 541696 
 
 398688256 
 
 27.1293 
 
 9.0287 
 
 82 
 
 465124 
 
 317214568 
 
 26.1151 
 
 8.8023 
 
 737 
 
 543169 
 
 400315553 
 
 27.1477 
 
 9.0328 
 
 83 
 
 466489 
 
 318611987 
 
 26.1343 
 
 8.8066 
 
 738 
 
 544644 
 
 401947272 
 
 27.1662 
 
 9.0369 
 
 34 
 
 467856 
 
 320013504 
 
 26.1534 
 
 8.8109 
 
 739 
 
 546121 
 
 403583419 
 
 27.1846 
 
 9.0410 
 
 85 
 
 469225 
 
 321419125 
 
 26.1725 
 
 8.8152 
 
 740 
 
 547600 
 
 405224000 
 
 27.2029 
 
 9.0450 
 
 36 
 
 470596 
 
 322828856 
 
 26.1916 
 
 8.8194 
 
 741 
 
 54908 1 
 
 406869021 
 
 27.2213 
 
 9 0491 
 
 87 
 
 471969 
 
 324242703 
 
 26.2107 
 
 8.8237 
 
 742 
 
 550564 
 
 408518488 
 
 27.2397 
 
 9.0532 
 
 38 
 
 473344 
 
 325660672 
 
 26.2298 
 
 8.8280 
 
 743 
 
 552049 
 
 410172407 
 
 27.2580 
 
 9.0572 
 
 39 
 
 474721 
 
 327082769 
 
 26.2488 
 
 8.8323 
 
 744 
 
 553536 
 
 411830784 
 
 27.2764 
 
 9.0613 
 
 90 
 
 476100 
 
 328509000 
 
 26.2679 
 
 8.8366 
 
 745 
 
 555025 
 
 413493625 
 
 27.2947 
 
 9.0654 
 
 91 
 
 477481 
 
 329939371 
 
 26.2869 
 
 8.8408 
 
 746 
 
 556516 
 
 415160936 
 
 27.3130 
 
 9.0694 
 
 92 
 
 478864 
 
 331373888 
 
 26.3059 
 
 8.8451 
 
 747 
 
 558009 
 
 416832723 
 
 27.3313 
 
 9.0735 
 
 93 
 
 480249 
 
 332812557 
 
 26.3249 
 
 8.8493 
 
 748 
 
 559504 
 
 418508992 
 
 27.3496 
 
 9.0775 
 
 94 
 
 481636 
 
 334255384 
 
 26.3439 
 
 8.8536 
 
 749 
 
 561001 
 
 420189749 
 
 27.3679 
 
 9.0816 
 
 95 
 
 483025 
 
 335702375 
 
 26.3629 
 
 8.8578 
 
 750 
 
 562500 
 
 421875000 
 
 27.3861 
 
 9.0856 
 
 96 
 
 484416 
 
 337153536 
 
 26.3818 
 
 8.8621 
 
 751 
 
 564001 
 
 423564751 
 
 27.4044 
 
 9.0896 
 
 97 
 
 485809 
 
 338608873 
 
 26.4008 
 
 8.8663 
 
 752 
 
 565504 
 
 425259008 
 
 27.4226 
 
 9.0937 
 
 93 
 
 487204 
 
 340068392 
 
 26.4197 
 
 8.8706 
 
 753 
 
 567009 
 
 426957777 
 
 27.4408 
 
 9.0977 
 
 99 
 
 488601 
 
 341532099 
 
 26.4386 
 
 8.8748 
 
 754 
 
 568516 
 
 42866106-1 
 
 27.4591 
 
 9.1017 
 
 00 
 
 490000 
 
 343000000 
 
 26.4575 
 
 8.8790 
 
 755 
 
 570025 
 
 430368875 
 
 27.4773 
 
 9.1057 
 
 01 
 
 491401 
 
 344472101 
 
 26.4764 
 
 8.8833 
 
 756 
 
 571536 
 
 432081216 
 
 27.4955 
 
 9.1098 
 
 02 
 
 492804 
 
 345948408 
 
 26.4953 
 
 8.8875 
 
 757 
 
 573049 
 
 433798093 
 
 27.5136 
 
 9.1138 
 
 03 
 
 494209 
 
 347428927 
 
 26.5141 
 
 8.8917 
 
 758 
 
 574564 
 
 435519512 
 
 27.5318 
 
 9.1178 
 
 ?04 
 
 495616 
 
 348913664 
 
 26.5330 
 
 8.8959 
 
 759 
 
 576081 
 
 437245479 
 
 27.5500 
 
 9.1218 
 
102 
 
 MATHEMATICAL TABLES. 
 
 No 
 
 . Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 76C 
 
 ) 57760C 
 
 43897600C 
 
 27.5681 
 
 9.1258 
 
 815 
 
 664225 
 
 541343375 
 
 28.5482 
 
 9.3408 
 
 76 
 
 579121 
 
 440711081 
 
 27.5862 
 
 9.1298 
 
 816 
 
 665856 
 
 543338496 
 
 28.5657 
 
 9.3447 
 
 762 
 
 580644 
 
 442450725 
 
 27.6043 
 
 9.1338 
 
 817 
 
 667489 
 
 545338513 
 
 28.5832 
 
 9.3485 
 
 763 
 
 582 1 69 
 
 444194945 
 
 27.6225 
 
 9.1378 
 
 815 
 
 669124 
 
 547343432 
 
 28.6007 
 
 9.3523 
 
 76- 
 
 583696 
 
 44594374^ 
 
 27.6405 
 
 9.1418 
 
 819 
 
 670761 
 
 549353259 
 
 28.6182 
 
 9.3561 
 
 765 
 
 585225 
 
 447697125 
 
 27.6586 
 
 9.1458 
 
 82C 
 
 672400 
 
 55136800C 
 
 28.6356 
 
 9.3599 
 
 766 
 
 586756 
 
 449455096 
 
 27.6767 
 
 9.1498 
 
 821 
 
 674041 
 
 55338766 
 
 28.653 
 
 9.3637 
 
 767 
 
 583289 
 
 451217663 
 
 27.6948 
 
 9.1537 
 
 822 
 
 675684 
 
 555412248 
 
 28.6705 
 
 9.3675 
 
 76e 
 
 589824 
 
 452984832 
 
 27.7128 
 
 9.1577 
 
 823 
 
 677329 
 
 557441767 
 
 28.688C 
 
 9.3713 
 
 769 
 
 591361 
 
 454756609 
 
 27.7308 
 
 9.1617 
 
 824 
 
 678976 
 
 559476224 
 
 28.705^ 
 
 9.3751 
 
 770 
 
 592900 
 
 456533000 
 
 27.7489 
 
 9.1657 
 
 825 
 
 680625 
 
 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 
 
 28.775C 
 
 9.3902 
 
 774 
 
 599076 
 
 463684824 
 
 27.8209 
 
 9.1815 
 
 829 
 
 687241 
 
 569722789 
 
 28.792^ 
 
 9.3940 
 
 775 
 
 600625 
 
 465484375 
 
 27.8388 
 
 9.1855 
 
 830 
 
 688900 
 
 571787000 
 
 28.8097 
 
 9.3978 
 
 776 
 
 602176 
 
 46728S576 
 
 27.8568 
 
 9.1894 
 
 831 
 
 690561 
 
 573856191 
 
 28.8271 
 
 9.4016 
 
 777 
 
 603729 
 
 469097433 
 
 27.8747 
 
 9.1933 
 
 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 
 
 28.9137 
 
 9.4204 
 
 782 
 
 611524 
 
 478211768 
 
 27.9643 
 
 9.2130 
 
 837 
 
 700569 
 
 586376253 
 
 28.9310 
 
 9.4241 
 
 783 
 
 613039 
 
 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 
 
 783 
 
 620944 
 
 439303372 
 
 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 
 
 793 
 
 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 
 
 628349 
 
 498677257 
 
 28.1603 
 
 9.2560 
 
 848 
 
 719104 
 
 609800192 
 
 29.1204 
 
 9.4652 
 
 794 
 
 630436 
 
 500566184 
 
 28. 1 780 
 
 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 
 
 28.2312 
 
 9.2716 
 
 852 
 
 725904 
 
 618470208 
 
 29.1890 
 
 9.4801 
 
 793 
 
 636804 
 
 508169592 
 
 28.2489 
 
 9.2754 
 
 853 
 
 727609 
 
 620650477 
 
 29.2062 
 
 9.4838 
 
 799 
 
 638401 
 
 510082399 
 
 28.2666 
 
 9.2793 
 
 854 
 
 729316 
 
 622835864 
 
 29.2233 
 
 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 
 
 5 1 5849608 
 
 28.3196 
 
 9.2909 
 
 857 
 
 734449 
 
 629422793 
 
 29.2746 
 
 9.4986 
 
 803 
 
 644809 
 
 517781627 
 
 28.3373 
 
 9.2948 
 
 853 
 
 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 
 
 542735647 
 
 29.3769 
 
 9.5207 
 
 809 
 
 654481 
 
 529475129 
 
 28.4429 9.3179 
 
 864 
 
 746496 
 
 544972544 
 
 29.3939 
 
 9.5244 
 
 810 
 
 656100 
 
 531441000 
 
 28.4605'9.3217 
 
 865 
 
 748225 
 
 547214625 
 
 29.4109 
 
 9.5231 
 
 811 
 
 657721 
 
 533411731 
 
 28.4781 9.3255 
 
 866 
 
 749956 
 
 349461896 
 
 29.4279 
 
 9.5317 
 
 812 
 
 659344 i 
 
 535387328 
 
 28.4956 9.3294 
 
 867 
 
 751689 
 
 d5 171 4363 
 
 29.4449 
 
 9.5354 
 
 813 
 
 6609691 
 
 537367797 
 
 28.5132 9.3332 
 
 868 
 
 753424 653972032! 
 
 29.4618 
 
 9.5391 
 
 814 
 
 662596! 
 
 5393531441 
 
 28.5307i9.3370 
 
 869 
 
 755161 Io56234909|. 
 
 29.4783 9.5427 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 103 
 
 No. 
 
 Square 
 
 Cube. 
 
 Sq. 
 
 Root. 
 
 Cube 
 Roo : . 
 
 No. 
 ^925 
 
 Square 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 870 
 
 75690C 
 
 65850300C 
 
 29.4958 
 
 9.5464 
 
 855625 
 
 791453125 
 
 30.4136 
 
 9.7435 
 
 871 
 
 758641 
 
 66077631 
 
 29.5127 
 
 9.5501 
 
 92C 
 
 857476 
 
 794022776 
 
 30.4302 
 
 9.7470 
 
 872 
 
 760384 
 
 603054845 
 
 29.5296 
 
 9.5537 
 
 92/ 
 
 859329 
 
 796597983 
 
 30.446/ 
 
 9.7505 
 
 873 
 
 762129 
 
 6653386H 
 
 29.5466 
 
 9.5574 
 
 92£ 
 
 861184 
 
 799178752 
 
 30.463 
 
 9.7540 
 
 874 
 
 763876 
 
 66762762^ 
 
 29.5635 
 
 9.5610 
 
 92? 
 
 863041 
 
 801765089 
 
 30.4795 
 
 9.7575 
 
 875 
 
 765625 
 
 669921875 
 
 29.5804 
 
 9.5647 
 
 93C 
 
 864900 
 
 80435700C 
 
 30.495? 
 
 9.7610 
 
 876 
 
 767376 
 
 67222 137<: 
 
 29.5973 
 
 9.5683 
 
 931 
 
 866761 
 
 806954491 
 
 30.5123 
 
 9.7645 
 
 877 
 
 769129 
 
 674526133 
 
 29.6142 
 
 9.5719 
 
 932 
 
 868624 
 
 809557568 
 
 30.528/ 
 
 9.7680 
 
 876 
 
 770884 
 
 676836152 
 
 29.63 1 1 
 
 9.5756 
 
 933 
 
 870489 
 
 812166237 
 
 30.545C 
 
 9.7715 
 
 879 
 
 772641 
 
 679151439 
 
 29.6479 
 
 9.5792 
 
 934 
 
 872356 
 
 814780504 
 
 30.5614 
 
 9.7750 
 
 880 
 
 774400 
 
 68147200C 
 
 29.6648 
 
 9.5828 
 
 935 
 
 874225 
 
 817400375 
 
 30.5778 
 
 9.7785 
 
 881 
 
 776161 
 
 683797841 
 
 29.6816 
 
 9.5865 
 
 936 
 
 876096 
 
 820025856 
 
 30.5941 
 
 9.7819 
 
 882 
 
 777924 
 
 686128969 
 
 29.6985 
 
 9.5901 
 
 937 
 
 877969 
 
 822656953 
 
 30.6105 
 
 9.7854 
 
 883 
 
 779689 
 
 688465387 
 
 29.7153 
 
 9.5937 
 
 938 
 
 879844 
 
 825293672 
 
 30.6268 
 
 9.7889 
 
 884 
 
 781456 
 
 690807104 
 
 29.7321 
 
 9.5973 
 
 939 
 
 881721 
 
 827936019 
 
 30.6431 
 
 9.7924 
 
 885 
 
 783225 
 
 693154125 
 
 29.7489 
 
 9.6010 
 
 940 
 
 883600 
 
 830584000 
 
 30.6594 
 
 9.7959 
 
 836 
 
 784996 
 
 695506456 
 
 29.7658 
 
 9.6046 
 
 941 
 
 885481 
 
 833237621 
 
 30.6757 
 
 9.7993 
 
 887 
 
 786769 
 
 697864103 
 
 29.7825 
 
 9.6082 
 
 942 
 
 887364 
 
 835896888 
 
 30.6920 
 
 9.8028 
 
 833 
 
 788544 
 
 700227072 
 
 29.7993 
 
 9.6118 
 
 943 
 
 889249 
 
 838561807 
 
 30.7083 
 
 9.8063 
 
 889 
 
 790321 
 
 702595369 
 
 29.8161 
 
 9.6154 
 
 944 
 
 891136 
 
 841232384 
 
 30.7246 
 
 9.8097 
 
 890 
 
 792100 
 
 704969000 
 
 29.8329 
 
 9.6190 
 
 945 
 
 393025 
 
 843908625 
 
 30.7409 
 
 9.8132 
 
 89": 
 
 793881 
 
 707347971 
 
 29.8496 
 
 9.6226 
 
 946 
 
 894916 
 
 846590536 
 
 30.7571 
 
 9.8167 
 
 892 
 
 795664 
 
 70973228S 
 
 29.8664 
 
 9.6262 . 
 
 947 
 
 896809 
 
 849278123 
 
 30.7734 
 
 9.8201 
 
 893 
 
 797449 
 
 712121957 
 
 29.8831 
 
 9.6293 
 
 943 
 
 898704 
 
 851971392 
 
 30.7896 
 
 9.8236 
 
 894 
 
 799236 
 
 714516984 
 
 29.8998 
 
 9.6334 
 
 949 
 
 900601 
 
 854670349 
 
 30.8058 
 
 9.8270 
 
 895 
 
 801025 
 
 716917375 
 
 29.9166 
 
 9.6370 
 
 950 
 
 902500 
 
 857375000 
 
 30.8221 
 
 9.8305 
 
 696 
 
 802816 
 
 719323136 
 
 29.9333 
 
 9.6406 
 
 951 
 
 904401 
 
 860085351 
 
 30.8383 
 
 9.8339 
 
 697 
 
 804609 
 
 721734273 
 
 29.9500 
 
 9.6442 
 
 952 
 
 906304 
 
 862801408 
 
 30.8545 
 
 9.8374 
 
 893 
 
 806404 
 
 724150792 
 
 29.9666 
 
 9.6477 
 
 953 
 
 908209 
 
 865523177 
 
 30.8707 
 
 9.8408 
 
 899 
 
 808201 
 
 726572699 
 
 29.9833 
 
 9.6513 
 
 954 
 
 910116 
 
 868250664 
 
 30.8869 
 
 9.8443 
 
 900 
 
 810000 
 
 729000000 
 
 30.0000 
 
 9.6549 
 
 955 
 
 912025 
 
 870983875 
 
 30.9031 
 
 9.8477 
 
 901 
 
 811801 
 
 731432701 
 
 30.0167 
 
 9.6585 
 
 956 913936 
 
 873722816 
 
 30.9192 
 
 9.8511 
 
 002 
 
 813604 
 
 733870808 
 
 30.0333 
 
 9.6620 
 
 957 915849 
 
 876467493 
 
 30.9354 
 
 9.8546 
 
 903 
 
 815409 
 
 736314327 
 
 30.0500 
 
 9.6656 
 
 958 917764 
 
 879217912 
 
 30.9516 
 
 9.8580 
 
 904 
 
 817216 
 
 738763264 
 
 30.0666 
 
 9.6692 
 
 959 919681 
 
 881974079 
 
 30.9677 
 
 9.8614 
 
 905 
 
 819025 
 
 741217625 
 
 30.0832 
 
 9.6727 
 
 960 921600 
 
 884736000 
 
 30.9839 
 
 9.8648 
 
 906 
 
 820836 
 
 743677416 
 
 30.0998 
 
 9.6763 
 
 961 1923521 
 
 887503681 
 
 3 1 .0000 
 
 9.8683 
 
 907 
 
 822649 
 
 746142643 
 
 30.1164 
 
 9.6799 
 
 962 925444 
 
 890277128 
 
 31.0161 
 
 9.8717 
 
 903 
 
 824464 
 
 748613312 
 
 30.1330 
 
 9.6834 
 
 963 
 
 927369 
 
 893056347 
 
 31.0322 
 
 9.8751 
 
 909 
 
 826281 
 
 751089429 
 
 30.1496 
 
 9.6870 
 
 964 
 
 929296 
 
 895841344 
 
 31.0483 
 
 9.8785 
 
 910 
 
 828100 
 
 753571000 
 
 30.1662 
 
 9.6905 
 
 965 
 
 931225 
 
 898632125 
 
 31.0644 
 
 9.8819 
 
 91! 
 
 829921 
 
 756058031 
 
 30.1828 
 
 9.6941 
 
 966 
 
 933156 
 
 901428696 
 
 3 1 .0805 
 
 9.8854 
 
 912 
 
 83 1 744 
 
 758550528 
 
 30.1993 
 
 9.6976 
 
 967 
 
 935089 
 
 90423 1 063 
 
 31.0966 
 
 9.8888 
 
 913 
 
 833569 
 
 761048497 
 
 30.2159 
 
 9.7012 
 
 963 
 
 937024 
 
 907039232 
 
 31.1127 
 
 9.8922 
 
 914 
 
 835396 
 
 763551944 
 
 30.2324 
 
 9.7047 
 
 969 
 
 938961 
 
 909853209 
 
 31.1288 
 
 9.8956 
 
 915 
 
 837225 
 
 766060875 
 
 30.2490 
 
 9.7082 
 
 970 
 
 940900 
 
 912673000 
 
 31.1448 
 
 9.8990 
 
 916 
 
 839056 
 
 768575296 
 
 30.2655 
 
 9.7118 
 
 971 
 
 942841 
 
 915498611 
 
 31.1609 
 
 9.9024 
 
 917 
 
 840889 
 
 771095213 
 
 30.2820 
 
 9.7153 
 
 972 
 
 944784 
 
 918330048 
 
 31.1769 
 
 9.9058 
 
 918 
 
 842724 
 
 773620632 
 
 30.2985 
 
 9.7188 
 
 973 
 
 946729 
 
 921167317 
 
 3 1 . 1 929 
 
 9.9092 
 
 919 
 
 844561 
 
 776151559 
 
 30.3150 
 
 9.7224 
 
 974 
 
 948676 
 
 924010424 
 
 31.2090 
 
 9.9126 
 
 920 
 
 846400 
 
 778688000 
 
 30.3315 
 
 9.7259 
 
 975 
 
 950625 
 
 926859375 
 
 31.2250 
 
 9.9160 
 
 921 
 
 843241 
 
 781229961 
 
 30.3430 
 
 9.7294 
 
 976 
 
 952576, 
 
 929714176 
 
 31.2410 
 
 99194 
 
 922 
 
 850084 
 
 783777443 
 
 30.3645 
 
 9.7329 
 
 977 
 
 954529 
 
 932574833 31.2570 
 
 9.9227 
 
 923 
 
 851929 
 
 786330467 
 
 30.33091 
 
 9.7364 
 
 978 956484! 
 
 935441352131.2730 
 
 9.9261 
 
 924 
 
 853776 
 
 788889024 
 
 30.3974, 
 
 9.7400 
 
 979J 958441; 
 
 938313739131.2890 
 
 9.9295 
 
104 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 9.9329 
 
 No. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 "930 
 
 960400 
 
 941192000 
 
 31.3050 
 
 1035 
 
 1071225 
 
 1108717875 
 
 32.1714 
 
 10.1153 
 
 931 
 
 962361 
 
 944076141 
 
 31.3209 
 
 9.9363 
 
 1036 
 
 1073296 
 
 1111934656 
 
 32.1870 
 
 10.1186 
 
 932 
 
 964324 
 
 946966168 
 
 31.3369 
 
 9.9396 
 
 1037 
 
 1075369 
 
 1115157653 
 
 32.2025 
 
 10.1218 
 
 933 
 
 966289 
 
 949862087 
 
 31.3528 
 
 9.9430 
 
 1038 
 
 1077444 
 
 1118386872 
 
 32.2180 
 
 10.1251 
 
 934 
 
 968256 
 
 952763904 
 
 31.3688 
 
 9.9464 
 
 1039 
 
 1079521 
 
 1121622319 
 
 32.2335 
 
 10.1283 
 
 735 
 
 970225 
 
 955671625 
 
 31.3847 
 
 9.9497 
 
 1040 
 
 1081600 
 
 1124864000 
 
 32.2490 
 
 10.1316 
 
 936 
 
 972196 
 
 958585256 
 
 31.4006 
 
 9.9531 
 
 1041 
 
 1083681 
 
 1128111921 
 
 32.2645 
 
 10 1348 
 
 937 
 
 974169 
 
 961504803 
 
 31.4166 
 
 9.9565 
 
 1042 
 
 1085764 
 
 1131366088 
 
 32.2800 
 
 10.1381 
 
 93S 
 
 976144 
 
 964430272 
 
 31.4325 
 
 9.9598 
 
 1043 
 
 1087849 
 
 1134626507 
 
 32.2955 
 
 10.1413 
 
 939 
 
 978121 
 
 967361569 
 
 31.4484 
 
 9.9632 
 
 1044 
 
 1089936 
 
 1137893184 
 
 32.3110 
 
 10.1446 
 
 990 
 
 980100 
 
 970299000 
 
 31.4643 
 
 9.9666 
 
 1045 
 
 1092025 
 
 1141166125 
 
 32.3265 
 
 10.1478 
 
 991 
 
 982081 
 
 973242271 
 
 31.4802 
 
 9.9699 
 
 1046 
 
 1094116 
 
 1144445336 
 
 32.3419 
 
 10.1510 
 
 992 
 
 984064 
 
 976191488 
 
 31.4960 
 
 9.9733 
 
 1047 
 
 1096209 
 
 1 147730823 
 
 32.3574 
 
 10.1543 
 
 993 
 
 986049 
 
 979146657 
 
 31.5119 
 
 9.9766 
 
 1043 
 
 1098304 
 
 1151022592 
 
 32.3728 
 
 10.1575 
 
 994 
 
 988036 
 
 982107784 
 
 31.5278 
 
 9.9800 
 
 1049 
 
 1100401 
 
 1154320649 
 
 32.3883 
 
 10.1607 
 
 995 
 
 990025 
 
 985074875 
 
 31.5436 
 
 9.9833 
 
 1050 
 
 1 102500 
 
 1157625000 
 
 32.4037 
 
 10.1640 
 
 996 
 
 992016 
 
 988047936 
 
 31.5595 
 
 9.9866 
 
 1051 
 
 1 104601 
 
 1160935651 
 
 32.4191 
 
 10.1672 
 
 997 
 
 994009 
 
 991026973 
 
 31.5753 
 
 9.9900 
 
 1052 
 
 1106704 
 
 1164252608 
 
 32.4345 
 
 10.1704 
 
 998 
 
 996004 
 
 99401 1992 
 
 31.5911 
 
 9.9933 
 
 1053 
 
 1 108809 
 
 1167575877 
 
 32.4500 
 
 10.1736 
 
 999 
 
 998001 
 
 997002999 
 
 31.6070 
 
 9.9967 
 
 1054 
 
 1110916 
 
 1170905464 
 
 32.4654 
 
 10.1769 
 
 1000 
 
 1000000 
 
 1000000000 
 
 31.6228 
 
 10.0000 
 
 1055 
 
 1113025 
 
 1174241375 
 
 32.4808 
 
 10.1801 
 
 1001 
 
 1002001 
 
 1003003001 
 
 31.6386 
 
 10.0033 
 
 1056 
 
 1115136 
 
 1177583616 
 
 32.4962 
 
 10.1833 
 
 1002 
 
 1004004 
 
 1006012008 
 
 31.6544 
 
 10.0067 
 
 1057 
 
 1117249 
 
 1180932193 
 
 32.5115 
 
 10.1865 
 
 1003 
 
 1006009 
 
 1009027027 
 
 31.6702 
 
 10.0100 
 
 1058 
 
 1119364 
 
 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 
 
 1 191016000 
 
 32.5576 
 
 10.1961 
 
 1006 
 
 1012036 
 
 1018108216 
 
 31.7175 
 
 10.0200 
 
 1061 
 
 1125721 
 
 1 194389981 
 
 32.5730 
 
 10.1993 
 
 1007 
 
 1014049 
 
 1021147343 
 
 31.7333 
 
 10.0233 
 
 1062 
 
 1 127844 
 
 1 197770328 
 
 32.5883 
 
 10.2025 
 
 1008 
 
 1016064 
 
 1024192512 
 
 31.7490 
 
 10.0266 
 
 1063 
 
 1129969 
 
 1201157047 
 
 32.6036 
 
 10.2057 
 
 1009 
 
 1018081 
 
 1027243729 
 
 31.7648 
 
 10.0299 
 
 1064 
 
 1 132096 
 
 1204550144 
 
 32.6190 
 
 10.2089 
 
 1010 
 
 T020100 
 
 1030301000 
 
 31.7805 
 
 10.0332 
 
 1065 
 
 1134225 
 
 1207949625 
 
 32.6343 
 
 10.2121 
 
 1011 
 
 1022121 
 
 1033364331 
 
 31.7962 
 
 10.0365 
 
 1066 
 
 1136356 
 
 1211355496 
 
 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 
 
 1068 
 
 1140624 
 
 1218186432 
 
 32.6303 
 
 10.2217 
 
 1014 
 
 1028196 
 
 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 
 
 1048772096 
 
 31.8748 
 
 10.0531 
 
 1071 
 
 1147041 
 
 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 
 
 1164241 
 
 1256216039 
 
 32.8481 
 
 10.2567 
 
 1025 
 
 1050625 
 
 1076890625 
 
 32.0156 
 
 10.0826 
 
 1030 
 
 1166400 
 
 1259712000 
 
 32.8634 
 
 10.2599 
 
 1026 
 
 1052676 
 
 1030045576 
 
 32.0312 
 
 10.0859 
 
 1081 
 
 1168561 
 
 12632 I 444 I 
 
 32.8786 
 
 10.2630 
 
 1027 
 
 1054729 
 
 1033206683 
 
 32.0468 
 
 10.0892 
 
 1032 
 
 1170724 
 
 1266723368 
 
 32.8938 
 
 10.2662 
 
 1028 
 
 1056784 
 
 1036373952 
 
 32.0624 
 
 10.0925 
 
 1083 
 
 1172889 
 
 1270238787 
 
 32.9090 
 
 10.2693 
 
 1029 
 
 1058341 
 
 1089547389 
 
 32.0780 
 
 10.0957 
 
 1034 
 
 1175056 
 
 1273760704 
 
 32.9242 
 
 10.2725 
 
 1030 
 
 1060900 
 
 1092727000 
 
 32.0936 
 
 10.0990 
 
 1035 
 
 1177225 
 
 1277289125 
 
 32.9393 
 
 10.2757 
 
 1031 
 
 1062961 
 
 1095912791 
 
 32.1092 
 
 10.1023 
 
 1086 
 
 1179396 
 
 1230824056 
 
 32.9545 
 
 10.2788 
 
 1032 
 
 1065024 
 
 1099104763 
 
 32.1243 
 
 10.1055 
 
 1037 
 
 1181569 
 
 1284365503 
 
 32.9697 
 
 10.2820 
 
 1033 
 
 10IS70S9 
 
 1 102302937 
 
 32.1403 
 
 10.1088 
 
 1038 
 
 1183744 
 
 1287913472 
 
 32.9848 
 
 10.2851 
 
 1034 
 
 1069156 1105507304 
 
 32.1559'10.1121 
 
 1089 
 
 1185921 1291467969 33.0000 10.2883 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 105 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 1188100 
 1190281 
 1192464 
 1194649 
 1196336 
 
 1199025 
 1201216 
 1203409 
 1205604 
 1099 1207801 
 
 1210000 
 1212201 
 1214404 
 1216609 
 1218816 
 
 1221025 
 1223236 
 1225449 
 1227664 
 1229881 
 
 1232100 
 1234321 
 1236544 
 1238769 
 1240996 
 
 1243225 
 1245456 
 12476S9 
 1249924 
 1252161 
 
 1254400 
 1256641 
 1258884 
 1261129 
 1263376 
 
 1265625 
 1267876 
 1270129 
 1272384 
 1274641 
 
 1276900 
 1279161 
 1281424 
 1283689 
 1285956 
 
 1288225 
 1290496 
 1292769 
 1295044 
 1139 1297321 
 
 1295029000 
 1298596571 
 1302170688 
 1305751357 
 1309338584 
 
 1312932375 
 1316532736 
 1320139673 
 1323753192 
 1327373299 
 
 1331000000 
 1334633301 
 1338273208 
 1341919727 
 1345572864 
 
 1349232625 
 1352899016 
 1356572043 
 1360251712 
 1363938029 
 
 1367631000 
 1371330631 
 1375036928 
 1378749897 
 1382469544 
 
 1386195875 
 1389928896 
 1393668613 
 1397415032 
 1401168159 
 
 1404928000 
 1408694561 
 1412467848 
 1416247867 
 1420034624 
 
 1423828125 
 1427628376 
 1431435383 
 1435249152 
 1439069689 
 
 33.015 
 33.0303 
 33.0454 
 33.0606 
 33.0757 
 
 33.0 
 
 33.1059 
 
 33.1210 
 
 33.1361 
 
 33.1512 
 
 33.1662 
 33.1813 
 33.1964 
 33.2114 
 33.2264 
 
 33.2415 
 33.2566 
 33.2716 
 33.2866 
 33.3017 
 
 33.3167 
 33.3317 
 33.3467 
 33.3617 
 33.3766 
 
 33.3916 
 33.4066 
 33.4215 
 33.4365 
 33.4515 
 
 33.4664 
 33.4813 
 33.4963 
 33.5112 
 
 10.2914 
 10.2946 
 10.297: 
 10.3009 
 10.3040 
 
 10.307 
 10.3103 
 10.3134 
 10.3165 
 10.3197 
 
 10.3228 
 10.3259 
 10.3290 
 10.3322 
 10 3353 
 
 10.3384 
 10.3415 
 10.3447 
 10.3478 
 10.3509 
 
 10.3540 
 10.3571 
 10.3602 
 10.3633 
 10.3664 
 
 10.3695 
 10.3726 
 10.3757 
 10.3788 
 10.3819 
 
 0.3850 
 10.388; 
 10.3912 
 10.3943 
 
 1442897000 
 1446731091 
 1450571968 
 1454419637 
 1458274104 
 
 33.5261 10.3973 
 
 33.5410 10.4004 
 33.5559 10.4035 
 33.5708 10.4066 
 33.5857 10.4097 
 33.6006 10.4127 
 
 33.6155 
 33.6303 
 33.6452 
 33.6601 
 33.6749 
 
 1462135375 33.6398 
 1466003456 33.7046 
 1469878353133.7174 
 1473760072:33.7342 
 1477648619 33.7491 
 
 1299600 1481544000133.7639 
 1301881 1485446221,33.7787 
 1304164 1489355238 33.7935 
 1306449 1493271207|33.8033 
 13087361 1497193934:33.8231 
 
 10.4158 
 10.4189 
 10.4219 
 10.4250 
 10.4281 
 
 10.4311 
 
 10.4342 
 10.4373 
 10.4404 
 10.4434 
 
 10.4464 
 10 4495 
 10 4525 
 10.4556 
 10.4536 
 
 1155 
 1156 
 1157 
 1158 
 1159 
 
 1160 
 1161 
 1162 
 1163 
 
 1311025 
 1313316 
 1315609 
 1317904 
 1320201 
 
 1322500 
 1324801 
 1327104 
 1329409 
 1331716 
 
 1334025 
 1336336 
 1338649 
 1340964 
 1343281 
 
 1345600 
 1347921 
 1350244 
 1352569 
 
 1164 
 
 1354896 
 
 1165 
 
 1357225 
 
 1166 
 
 1359556 
 
 1167 
 
 1361889 
 
 1168 
 
 1364224 
 
 1169 
 
 1366561 
 
 1170 
 
 1368900 
 
 1171 
 
 1371241 
 
 1172 
 
 1373584 
 
 1173 
 
 1375929 
 
 1174 
 
 1378276 
 
 1175 
 
 1380625 
 
 1176 
 
 1382976 
 
 1177 
 
 1385329 
 
 1178 
 
 1387684 
 
 1179 
 
 1390041 
 
 1180 
 
 1392400 
 
 1181 
 
 1394761 
 
 1182 
 
 1397124 
 
 1183 
 
 1399489 
 
 1184 
 
 1401856 
 
 1185 
 
 1404225 
 
 1186 
 
 1406596 
 
 1187 
 
 1408969 
 
 1188 
 
 1411344 
 
 1189 
 
 1413721 
 
 1190 
 
 1416100 
 
 1191 
 
 1418481 
 
 1192 
 
 1420864 
 
 1193 
 
 1423249 
 
 1194 
 
 1425636 
 
 1195 
 
 1428025 
 
 1196 
 
 1430416 
 
 1197 
 
 1432809 
 
 1198 
 
 1435204 
 
 1199 
 
 1437601 
 
 1501123625 
 1505060136 
 1509003523 
 1512953792 
 1516910949 
 
 1520875000 
 152434595 
 1528323808 
 1532808577 
 1536800264 
 
 1540798875 
 1544804416 
 1548816893 
 1552836312 
 1556862679 
 
 1560896000 
 156493628 
 1568983523 
 1573037747 
 1577098944 
 
 1531167125 
 1585242296 
 1589324463 
 1593413632 
 1597509809 
 
 1601613000 
 1605723211 
 1609840448 
 1613964717 
 1618096024 
 
 1622234375 
 1626379776 
 1630532233 
 1634691752 
 1638858339 
 
 1643032000 
 1647212741 
 1651400568 
 1655595487 
 1659797504 
 
 33.8378 
 33.8526 
 33.8674 
 33.8321 
 33.8969 
 
 33.9116 
 
 33.9264 
 
 33.941 
 
 33.9559 
 
 33.9706 
 
 10.4617 
 10.4647 
 10.4678 
 10.4708 
 10.4739 
 
 10.4769 
 10.4799 
 10.4830 
 10.4860 
 10.4890 
 
 1664006625 
 1668222856 
 1672446203 
 1676676672 
 1680914269 
 
 1685159000 
 1689410871 
 1693669838 
 1697936057 
 702209384 
 
 1706489875 
 710777536 
 1715072373 
 1719374392 
 723683599 
 
 33.9853 10.492! 
 
 34.0147 
 34.0294 
 34.0441 
 
 34.0588 
 34.0735 
 34.0881 
 34.1028 
 34.1174 
 
 34.132 
 34.1467 
 34.1614 
 34.1760 
 34.1906 
 
 34.2053 
 34.2199 
 34.2345 
 34.2491 
 34.2637 
 
 34.2783 
 34.2929 
 34.3074 
 34.3220 
 34.3366 
 
 34.3511 
 
 34.3657 
 34.3802 
 34.3948 
 34.4093 
 
 34.4233 
 34.4384 
 34.4529 
 34.4674 
 34.4819 
 
 34.4964 
 34.5109 
 
 34.5254 
 34.5393 
 
 34.5543 10.6088 
 
 34.5688 
 34.5832 
 34.5977 
 34.6121 
 34.6266 
 
 10.4981 
 10.5011 
 10.5042 
 
 10.5072 
 10.5102 
 10.5132 
 10.5162 
 10.5192 
 
 10.5223 
 10.5253 
 10.5283 
 10.5313 
 10.5343 
 
 10.5373 
 10.5403 
 10.5433 
 10.5463 
 10.5493 
 
 10.5523 
 10.5553 
 10.5583 
 10.5612 
 10.5642 
 
 10.5672 
 10.5702 
 10.5732 
 10.5762 
 10.5791 
 
 10.5821 
 10.5851 
 10.5881 
 10.5910 
 10.5940 
 
 10.5970 
 10.6000 
 10.6029 
 10.6059 
 
 10.6118 
 10.6148 
 10.6177 
 10.6207 
 10.6235 
 
106 
 
 MATHEMATICAL TABLES. 
 
 . Square. 
 
 Cube. 
 
 Sq. 
 Root. 
 
 Cube 
 Root. 
 
 No. 
 
 Square. 
 
 10.6266 
 
 1255 
 
 1575025 
 
 10.6295 
 
 1256 
 
 1577536 
 
 10.6325 
 
 1257 
 
 1580049 
 
 10.6354 
 
 1258 
 
 1582564 
 
 10.6384 
 
 1259 
 
 1585081 
 
 10.6413 
 
 1260 
 
 1587600 
 
 10.6443 
 
 1261 
 
 1590121 
 
 10.5472 
 
 1262 
 
 1592644 
 
 10.6501 
 
 1263 
 
 1595169 
 
 10.6530 
 
 1264 
 
 1597696 
 
 10.6560 
 
 1265 
 
 1600225 
 
 10.6590 
 
 1266 
 
 1602756 
 
 10.6619 
 
 1267 
 
 1605289 
 
 10.6648 
 
 1268 
 
 1607824 
 
 10.6678 
 
 1269 
 
 1610361 
 
 10.6707 
 
 1270 
 
 1612900 
 
 10.6736 
 
 1271 
 
 1615441 
 
 10.6765 
 
 1272 
 
 1617984 
 
 10.6795 
 
 1273 
 
 1620529 
 
 10.6324 
 
 1274 
 
 1623076 
 
 10.6353 
 
 1275 
 
 1625625 
 
 10.6382 
 
 1276 
 
 1628176 
 
 10.6911 
 
 1277 
 
 1630729 
 
 10.6940 
 
 1278 
 
 1633284 
 
 10.6970 
 
 1279 
 
 1635841 
 
 10.6999 
 
 1280 
 
 1638400 
 
 10.7028 
 
 1281 
 
 1640961 
 
 10.7057 
 
 1232 
 
 1643524 
 
 30.7086 
 
 1283 
 
 1646089 
 
 10.7115 
 
 1284 
 
 1648656 
 
 10.7144 
 
 1285 
 
 1651225 
 
 10.7173 
 
 1286 
 
 1653796 
 
 10.7202 
 
 1287 
 
 1656369 
 
 10.7231 
 
 1288 
 
 1658944 
 
 10.7260 
 
 1289 
 
 1661521 
 
 10.7289 
 
 1290 
 
 1664100 
 
 10.7318 
 
 1291 
 
 1666681 
 
 10.7347 
 
 1292 
 
 1669264 
 
 10.7376 
 
 1293 
 
 1671849 
 
 10.7405 
 
 1294 
 
 1674436 
 
 10.7434 
 
 1295 
 
 1677025 
 
 10.7463 
 
 1296 
 
 1679616 
 
 10.7491 
 
 1297 
 
 1632209 
 
 10.7520 
 
 1298 
 
 1684804 
 
 10.7549 
 
 1299 
 
 1687401 
 
 10.7578 
 
 1300 
 
 1690000 
 
 10.7607 
 
 1301 
 
 169260! 
 
 10.7635 
 
 1302 
 
 1695204 
 
 10.7664 
 
 1303 
 
 1697809 
 
 10.7693 
 
 1304 
 
 1700416 
 
 10.7722 
 
 1305 
 
 1703025 
 
 10.7750 
 
 1306 
 
 1705636 
 
 10.7779 
 
 1307 
 
 1703249 
 
 10.7803 
 
 1308 
 
 1710364 
 
 10.7837 
 
 1309 
 
 1713481 
 
 Cube. 
 
 Sq. 
 Root 
 
 Cube 
 Root. 
 
 1440000 
 1442401 
 1444304 
 1447209 
 1449616 
 
 1452025 
 1454436 
 1455349 
 1459264 
 1461 5! 
 
 1451100 
 
 14555 21 
 1 46394 < 
 1471369 
 1473796 
 
 1476225 
 1478656 
 1431039 
 1433524 
 1485961 
 
 1438400 
 1490341 
 1493234 
 1495729 
 1493176 
 
 1500625 
 1503076 
 1505529 
 1507984 
 1510441 
 
 1512900 
 1515361 
 1517824 
 1520289 
 1522756 
 
 1525225 
 1527696 
 1530169 
 1532644 
 153512 
 
 1537690 
 1540031 
 1542564 
 1545049 
 1547536 
 
 1550025 
 1552516 
 155500? 
 1557504 
 1560301 
 
 1562503 
 
 155503 
 
 1557504 
 
 1570009 
 
 1572516 
 
 1 728000000 
 1732323601 
 1736654403 
 1740992427 
 1745337664 
 
 1749690125 
 1754049316 
 1758416743 
 1762790912 
 1767172329 
 
 1771561000 
 177595693! 
 1780360128 
 1734770597 
 1789133344 
 
 1793613375 
 1793045696 
 1802435313 
 806932232 
 
 34.6410 
 34.6554 
 34.6699 
 34.6343 
 34.6987 
 
 34.7131 
 
 34.7275 
 34.7419 
 34.7563 
 34.7707 
 
 34.7851 
 34.7994 
 34.8138 
 34.8281 
 
 34.8425 
 
 34.8569 
 34.8712 
 
 34.8355 
 34.8999 
 
 1811336459 34.9142 
 
 1815343000 
 1820316361 
 1824793043 
 1829276567 
 1833767424 
 
 1838265625 
 1342771176 
 1847234033 
 1851S04352 
 1856331939 
 
 1860867000 
 1865409391 
 1869959163 
 1874516337 
 1879030904 
 
 1883652875 
 1838232256 
 1892819053 
 1897413272 
 1902014919 
 
 1906624000 
 1911240521 
 1915864488 
 1920495907 
 1925134784 
 
 1929781125 
 1934434936 
 1939096223 
 1943764992 
 1948441249 
 
 1953125000 
 1957016251 
 1962515008 
 1967221277 
 1971935064 
 
 34.9235 
 34.9423 
 34.9571 
 34.9714 
 34.9857 
 
 35.0000 
 35.0143 
 35.0236 
 35.0428 
 35.0571 
 
 35.0714 
 35.0856 
 35.0999 
 35.1141 
 35.1233 
 
 35.1426 
 35.1568 
 35.1710 
 35.1852 
 35.1994 
 
 35.2136 
 35.2278 
 35.2420 
 35.2562 
 35.2704 
 
 35.2846 
 35.2987 
 35.3129 
 35.3270 
 35.3412 
 
 35.3553 
 35.3695 
 35.3836 
 35.3977 
 35.4119 
 
 1976656375 
 1981385216 
 1986121593 
 1990865512 
 1995616979 
 
 2000376000 
 2005142581 
 2009916728 
 2014698447 
 2019487744 
 
 2024284625 
 2029089096 
 2033901163 
 2038720832 
 2043548109 
 
 2048383000 
 205322551 1 
 2058075648 
 2062933417 
 2067798824 
 
 2072671875 
 2077552576 
 2082440933 
 2087336952 
 2092240639 
 
 2097152000 
 210207104 
 2106997768 
 2111932187 
 2116874304 
 
 2121824125 
 2126781656 
 2131746903 
 2136719872 
 2141700569 
 
 35.4260 
 35.4401 
 35.4542 
 35.4683 
 35.4824 
 
 35.4965 
 35.5106 
 35.5246 
 35.5387 
 35.5528 
 
 35.5668 
 35.5809 
 35.5949 
 35.6090 
 35.6230 
 
 35.6371 
 35.6511 
 35.6651 
 35.6791 
 35.6931 
 
 35.7071 
 
 35.7211 
 35.7351 
 35.7491 
 35.7631 
 
 35.7771 
 35.7911 
 35.8050 
 35.8190 
 35.8329 
 
 35.8469 
 35.8608 
 35.8748 
 35.8887 
 35.9026 
 
 2146689000 35.9166 
 2151685171 35.9305 
 2156639038 35.9444 
 2161700757 35.9583 
 2166720184 35.9722 
 
 2171747375 
 2176782336 
 2181825073 
 2186875592 
 2191933399 
 
 2197000000 
 2-02073901 
 2207155603 
 2212245127 
 2217342464 
 
 2222447625 
 2227560616 
 2232681443 
 2237810112 
 2242946629 
 
 35.9861 
 36.0000 
 36.0139 
 36.0278 
 36.0416 
 
 36.0555 
 36.0694 
 36.0332 
 36.0971 
 36.1109 
 
 36.1243 
 36.1386 
 36.1525 
 36.1663 
 36.1801 
 
 10.7865 
 10.7894 
 10.7922 
 10.7951 
 10.7980 
 
 10.8008 
 10.8037 
 10.8065 
 10.8094 
 10.8122 
 
 10.8151 
 
 10.8179 
 10.8208 
 10.8236 
 10.8265 
 
 10.8293 
 10.8322 
 10.8350 
 10.8378 
 10.8407 
 
 10.8435 
 10.8463 
 10.8492 
 10.8520 
 10.8548 
 
 10.8577 
 10.8605 
 10.3633 
 10.8661 
 10.8690 
 
 10.8718 
 10.8746 
 10.8774 
 10.8802 
 10.8831 
 
 10.8859 
 10.8887 
 10.8915 
 10.8943 
 10.8971 
 
 10.8999 
 10.9027 
 10.9055 
 10.9083 
 10.9111 
 
 10.9139 
 10.9167 
 10.9195 
 10.9223 
 10.9251 
 
 10.9279 
 10.9307 
 10.9335 
 10.9363 
 10.9391 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 107 
 
 Square, 
 
 1716100 
 1718721 
 1721344 
 1723969 
 1726596 
 
 1729225 
 1731856 
 1734489 
 1737124 
 1739761 
 
 1742400 
 174504! 
 1747684 
 1750329 
 1752976 
 
 1755625 
 1753276 
 1760929 
 1763584 
 1766241 
 
 1768900 
 1771561 
 1774224 
 1776889 
 1779556 
 
 1782225 
 1784396 
 1787569 
 1790244 
 1792921 
 
 1795600 
 1798281 
 1800964 
 1803649 
 1806336 
 
 1809025 
 1811716 
 1814409 
 1817104 
 1819801 
 
 1322500 
 1825201 
 1327904 
 1330609 
 1833316 
 
 1836025 
 1338736 
 1841449 
 1844164 
 184688 
 
 1849600 
 1852321 
 1855044 
 1857769 
 1860496 
 
 Cube. 
 
 2248091000 
 2253243231 
 2258403328 
 2263571297 
 2268747144 
 
 2273930875 
 2279122496 
 2284322013 
 2289529432 
 2294744759 
 
 2299968000 
 2305199161 
 2310438248 
 2315685267 
 2320940224 
 
 2326203125 
 2331473976 
 2336752783 
 2342039552 
 2347334289 
 
 2352637000 
 2357947691 
 2363266368 
 2368593037 
 2373927704 
 
 2379270375 
 2384621056 
 2389979753 
 2395346472 
 2400721219 
 
 2406104000 
 2411494821 
 2416893688 
 2422300607 
 2427715584 
 
 2433138625 36.6742 
 2438569736 36.6879 
 2444003923 36.7015 
 2449456192 36.7151 
 2454911549 36.7287 
 
 Sq. 
 Root. 
 
 36.1939 
 36.2077 
 36.2215 
 36.2353 
 36.2491 
 
 36.2629 
 36.2767 
 36.2905 
 36.3043 
 36.31 
 
 36.3318 
 36.3456 
 36.3593 
 36.3731 
 36.3868 
 
 36.4005 
 36.4143 
 36.4280 
 36.4417 
 36.4555 
 
 36.4692 
 36.4829 
 36.4966 
 36.5103 
 36.5240 
 
 36.5377 
 
 36.5513 
 36.5650 
 36.5787 
 36.5923 
 
 36.6060 
 36.6197 
 36.6333 
 36.6469 
 
 36.6606 
 
 Cube 
 Root. 
 
 1460375000 
 2465846551 
 2471326208 
 2476313977 
 24323G9864 
 
 2487813875 
 2493326016 
 2498846293 
 2504374712 
 2509911279 
 
 2515456000 
 2521008881 
 2.526569928 
 2532139147 
 2537716544 
 
 36.7423 
 36.7560 
 36.7696 
 36.7831 
 36.7967 
 
 36.8103 
 36.8239 
 36.8375 
 36.8511 
 36.8646 
 
 36.8782 
 36.8917 
 36.905: 
 36.9188 
 36.9324 
 
 10.9418 
 10.9446 
 10.9474 
 10.9502 
 10.9530 
 
 10.9557 
 10.9585 
 10.9613 
 10.9640 
 10.9668 
 
 10.9696 
 10.9724 
 10.9752 
 10.9779 
 10. 
 
 10.9834 
 10.9862 
 10.9890 
 10.9917 
 0.9945 
 
 0.9972 
 1 1 .0000 
 1 1 .0028 
 1 1 .0055 
 1 1 .0083 
 
 11.0110 
 
 1.0138 
 11.0165 
 11.0193 
 1 1 .0220 
 
 1 .0247 
 11.0275 
 1 1 .0302 
 1 1 .0330 
 1 1 .0357 
 
 1 1 .0384 
 11.0412 
 1 1 .0439 
 1 1 .0466 
 11.0494 
 
 11.0521 
 1 1 .0548 
 1 1 .0575 
 1 1 .0603 
 1 1 .0630 
 
 11.0657 
 11.0684 
 11.0712 
 1 1 .0739 
 1 1 .0766 
 
 1 1 .0793 
 1 1 .0820 
 1 1 .0847 
 1 1 .0875 
 i 1 .0902 
 
 Square. 
 
 1365 
 1366 
 1367 
 1368 
 1369 
 
 1370 
 137 
 1372 
 1373 
 1374 
 
 1375 
 1376 
 1377 
 1378 
 1379 
 
 1380 
 1381 
 
 1382 
 1383 
 1384 
 
 1385 
 1386 
 1387 
 1388 
 1389 
 
 1390 
 139 
 
 1392 
 1393 
 1394 
 
 1395 
 
 1396 
 1397 
 1398 
 1399 
 
 1400 
 1401 
 
 1402 
 1403 
 1404 
 
 1405 
 1406 
 
 !407 
 
 
 1409 
 
 1410 
 1411 
 1412 
 
 1413 
 1414 
 
 1415 
 1416 
 1417 
 
 1413 
 1419 
 
 1863225 
 1865956 
 1868689 
 1871424 
 1874161 
 
 1876900 
 1879641 
 
 1882384 
 1885129 
 1887876 
 
 Cube. 
 
 Sq. 
 Root 
 
 2543302125 
 2548895896 
 2554497863 
 2560108032 
 2565726409 
 
 2571353000 
 257698781 1 
 2582630848 
 2588282117 
 2593941624 
 
 1890625 2599609375 
 1893376 2605285376 
 1896129 2610969633 
 1898884 2616662152 
 1901641 2622362939 
 
 1904400 
 1907161 
 1909924 
 1912689 
 1915456 
 
 1918225 
 1920996 
 1923769 
 1926544 
 192932 
 
 1932100 
 1934881 
 1937664 
 1940449 
 1943236 
 
 1946025 
 1948816 
 1951609 
 1954404 
 1957201 
 
 1960000 
 1962801 
 1965604 
 1968409 
 1971216 
 
 1974025 
 1976836 
 1979649 
 1982464 
 1985281 
 
 1988100 
 1990921 
 1993744 
 1996569 
 1999396 
 
 2002225 
 2005056 
 2007889 
 2010724 
 2013561 
 
 2628072000 
 2633789341 
 2639514968 
 2645248887 
 2650991104 
 
 2656741625 
 2662500456 
 2668267603 
 2674043072 
 2679326869 
 
 2685619000 
 269141947 
 2697228288 
 2703045457 
 2708870984 
 
 2714704875 
 2720547136 
 2726397773 
 2732256792 
 2738124199 
 
 2744000000 
 274988420 
 2755776808 
 2761677827 
 2767587264 
 
 2773505125 
 2779431416 
 2785366143 
 2791309312 
 2797260929 
 
 2803221000 
 2809189531 
 2815166528 
 2821151997 
 2827145944 
 
 2833148375 
 2839159296 
 2845178713 
 2851206632 
 2857243059 
 
 36.9459 
 36.9594 
 36.9730 
 36.9865 
 37.0000 
 
 37.0135 
 37.0270 
 37.0405 
 37.0540 
 37.0675 
 
 37.0810 
 37.0945 
 37.1080 
 37.1214 
 37.1349 
 
 37.1484 
 37.1618 
 37.1753 
 37.1887 
 37.202 
 
 37.2156 
 37.2290 
 37.2424 
 37.2559 
 37.2693 
 
 37.2827 
 37.2961 
 37.3095 
 37.3229 
 37.3363 
 
 37.3497 
 37.3631 
 37.3765 
 37.3898 
 37.4032 
 
 37.4166 
 37.4299 
 37.4433 
 37.4566 
 37.4700 
 
 37.4833 
 37.4967 
 37.5100 
 37.5233 
 37.5366 
 
 37.5500 
 37.5633 
 37.5766 
 37.5899 
 37.6032 
 
 37.6165 
 37.6298 
 37.6431 
 37.6563 
 37.6696 
 
 Cube 
 Root. 
 
 1T0929 
 1 1 .0956 
 1 1 .0983 
 11.1010 
 11.1037 
 
 11.1064 
 11.1091 
 11.1118 
 11.1145 
 11.1172 
 
 11.1199 
 11.1226 
 11.1253 
 11.1280 
 11.1307 
 
 H.1334 
 11.1361 
 11.1387 
 11.1414 
 11.1441 
 
 11.1468 
 11.1495 
 11.1522 
 11.1548 
 11.1575 
 
 11.1602 
 11.1629 
 11.1655 
 11.1682 
 11.1709 
 
 11.1736 
 
 11.1762 
 11.1789 
 11.1816 
 11.1842 
 
 11.1869 
 11.1896 
 11.1922 
 11.1949 
 11.1975 
 
 1 1 .2002 
 1 1 .2028 
 1 1 .2055 
 1 1 .2082 
 11.2108 
 
 11.2135 
 11.2161 
 11.2188 
 11.2214 
 11.2240 
 
 11.2267 
 11.2293 
 11.2320 
 1 1 2346 
 1 1 2373 
 
108 
 
 MATHEMATICAL TABLES. 
 
 . Square. 
 
 2016400 
 2019241 
 2022034 
 2024929 
 2027776 
 
 2030625 
 2033476 
 2036329 
 2039184 
 2042041 
 
 2044900 
 2047761 
 2050624 
 2053439 
 2056356 
 
 2059225 
 2062096 
 2064969 
 2067844 
 2070721 
 
 2073600 
 2076431 
 2079364 
 2082249 
 2085136 
 
 2033025 
 2090916 
 2093309 
 2096704 
 2099601 
 
 2102500 
 2105401 
 2103304 
 2111209 
 2114116 
 
 2117025 
 2119936 
 2122349 
 2125764 
 212868 
 
 2131600 
 2134521 
 2137444 
 2140369 
 2143296 
 
 2146225 
 2149156 
 2152089 
 2155024 
 2157961 
 
 2160900 
 2163841 
 2166784 
 2169779 
 2172676 
 
 Cube. 
 
 2363288000 
 2869341461 
 2875403448 
 2881473967 
 2887553024 
 
 2893640625 
 2899736776 
 2905841483 
 2911954752 
 2918076589 
 
 2924207000 
 2930345991 
 2936493568 
 2942649737 
 2948814504 
 
 2954987875 
 2961169856 
 2967360453 
 2973559672 
 2979767519 
 
 2985984000 
 2992209121 
 2993442888 
 3004685307 
 3010936384 
 
 3017196125 
 3023464536 
 3029741623 
 3036027392 
 3042321849 
 
 3048625000 
 3054936851 
 3061257403 
 3067586677 
 3073924664 
 
 3030271375 
 3086626816 
 3092990993 
 3099363912 
 3105745579 
 
 3112136000 
 31 18535 "" 
 
 3124943128 
 3131359847 
 3137785344 
 
 3144219625 
 3150662696 
 3157114563 
 3163575232 
 3170044709 
 
 3176523000 
 3183010111 
 3189506048 
 3196010817 
 3202524424 
 
 Sq. 
 Root. 
 
 37.6829 
 37.6962 
 37.7094 
 37.7227 
 37.7359 
 
 37.7492 
 37.7624 
 37.7757 
 37.7889 
 37.8021 
 
 37.8153 
 37.8286 
 37.8418 
 37.8550 
 37.8682 
 
 37.8814 
 37.8946 
 37.9078 
 37.9210 
 37.9342 
 
 37.9473 
 37.9605 
 37.9737 
 37.9368 
 38.0000 
 
 38.0132 
 38.0263 
 38.0395 
 38.0526 
 38.0657 
 
 38.0789 
 38.0920 
 38.1051 
 38.1182 
 38.1314 
 
 38.1445 
 38.1576 
 38.1707 
 38.1838 
 38.1969 
 
 38.2099 
 38.2230 
 38.236 
 38.2492 
 33.2623 
 
 38.2753 
 38.2884 
 38.3014 
 38.3145 
 33.3275 
 
 383406 
 383536 
 383667 
 38.3797 
 38.3927 
 
 Cube 
 Root. 
 
 1 1 .2399 
 1 1 .2425 
 1 1 .2452 
 1 1 .2478 
 11.2505 
 
 11.2531 
 1 1 .2557 
 11.2583 
 11.2610 
 11.2636 
 
 11.2662 
 11.2639 
 11.2715 
 1 1 .2741 
 11.2767 
 
 11.2793 
 11.2820 
 11.2846 
 1 1 .2872 
 
 ii.r" 
 
 1 1 .2924 
 11.2950 
 1 1 .2977 
 11.3003 
 11.3029 
 
 11.3055 
 11.3081 
 11.3107 
 11.3133 
 11.3159 
 
 11.3185 
 11.3211 
 1 1 .3237 
 1 1 .3263 
 1 1 .3289 
 
 11.3315 
 1 1 .3341 
 1 1 .3367 
 1 1 .3393 
 11.3419 
 
 11.3445 
 11.3471 
 1 1 .3496 
 1 1 .3522 
 11.3548 
 
 1 1 .3574 
 1 1 .3600 
 1 1 .3626 
 1 1 .3652 
 11.3677 
 
 1 1 .3703 
 1 1 .3729 
 11.3755 
 1 1 .3780 
 1 1 .3806 
 
 1475 
 1476 
 1477 
 1478 
 1479 
 
 1480 
 148 
 1432 
 1483 
 1484 
 
 1485 
 1486 
 1487 
 1488 
 1489 
 
 1490 
 1491 
 
 1492 
 1493 
 1494 
 
 1495 
 1496 
 1497 
 1498 
 
 1499 
 
 1500 
 150 
 1502 
 1503 
 1504 
 
 1505 
 1506 
 1507 
 
 1503 
 1509 
 
 1510 
 1511 
 1512 
 1513 
 1514 
 
 1515 
 1516 
 1517 
 1518 
 
 1519 
 
 1520 
 1521 
 1522 
 1523 
 1524 
 
 1525 
 1526 
 1527 
 1528 
 1529 
 
 Square. 
 
 2175625 
 2178576 
 2181529 
 2184484 
 2187441 
 
 2190400 
 2193361 
 2196324 
 2199289 
 2202256 
 
 2205225 
 2208196 
 2211169 
 2214144 
 221712 
 
 2220100 
 2223081 
 2226064 
 2229049 
 2232036 
 
 2235025 
 2238016 
 2241009 
 2244004 
 2247001 
 
 2250000 
 2253001 
 2256004 
 2259009 
 2262016 
 
 2265025 
 2268036 
 2271049 
 2274064 
 2277081 
 
 2280100 
 2283121 
 2286144 
 2239169 
 2292196 
 
 2295225 
 2298256 
 2301289 
 2304324 
 2307361 
 
 2310400 
 2313441 
 2316434 
 2319529 
 2322576 
 
 2325625 
 2328676 
 2331729 
 2334784 
 2337841 
 
 Cube. 
 
 3209046875 
 3215578176 
 3222118333 
 3228667352 
 3235225239 
 
 3241792000 
 3248367641 
 3254952168 
 3261545587 
 3268147904 
 
 3274759125 
 3281379256 
 3288008303 
 3294646272 
 3301293169 
 
 3307949000 
 3314613771 
 3321287488 
 3327970157 
 3334661784 
 
 3341362375 
 3348071936 
 3354790473 
 3361517992 
 3368254499 
 
 3375000000 
 3381754501 
 3388518008 
 3395290527 
 3402072064 
 
 3408862625 
 3415662216 
 3422470843 
 3429288512 
 3436115229 
 
 3442951000 
 3449795831 
 3456649728 
 3463512697 
 3470384744 
 
 3477265875 
 3484156096 
 3491055413 
 3497963832 
 3504881359 
 
 3511808000 
 3518743761 
 3525688648 
 3532642667 
 3539605824 
 
 3546578125 
 3553559576 
 3560550183 
 3567549952 
 3574558889 
 
 Sq. 
 Root. 
 
 38.4057 
 38.4187 
 38.4318 
 38.4448 
 38.4578 
 
 38.4708 
 38.4838 
 38.4968 
 38.5097 
 38.5227 
 
 38.5357 
 38.5487 
 38.5616 
 38.5746 
 38.5876 
 
 38.6005 
 38.6135 
 38.6264 
 38.6394 
 38.6523 
 
 38.6652 
 38.6782 
 38.691 1 
 38.7040 
 38.7169 
 
 38.7298 
 38.7427 
 38.7556 
 38.7685 
 38.7814 
 
 38.7943 
 38.8072 
 38.8201 
 38.8330 
 38.8458 
 
 38.8587 
 38.8716 
 38.8844 
 38.8973 
 38.9102 
 
 38.9230 
 38.9358 
 38.9487 
 38.9615 
 38.9744 
 
 38.9872 
 39.0000 
 39.0128 
 39.0256 
 39.0384 
 
 39.0512 
 39.0640 
 39.0768 
 39.0896 
 39.1024 
 
 Cube 
 Root. 
 
 1 1 .3832 
 1 1 .3858 
 1 1 3883 
 11.3909 
 11.3935 
 
 11.3960 
 11.3986 
 11.4012 
 11.4037 
 11.4063 
 
 11.4089 
 11.4114 
 11.4140 
 11.4165 
 11.4191 
 
 11.4216 
 1 1 .4242 
 1 1 .4268 
 1 1 .4293 
 11.4319 
 
 11.4344 
 11.4370 
 11.4395 
 11.4421 
 lt.4446 
 
 11.4471 
 11.4497 
 11.4522 
 1 1 .4548 
 1 1,4573 
 
 11.4598 
 11.4624 
 11.4649 
 11.4675 
 11.4700 
 
 11.4725 
 11.4751 
 11.4776 
 11.4801 
 1.4826 
 
 11.4852 
 11.4877 
 1 1 .4902 
 11.4927 
 11.4953 
 
 1 1 .4978 
 11.5003 
 11.5028 
 11.5054 
 11.5079 
 
 11.5104 
 11.5129 
 11.5154 
 11.5179 
 11.5204 
 
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 109 
 
 Square. 
 
 2340900 
 2343961 
 2347024 
 2350089 
 2353156 
 
 2356225 
 2359296 
 2362369 
 2365444 
 2368521 
 
 2371600 
 2374681 
 2377764 
 2380849 
 2383936 
 
 2387025 
 23901 16 
 2393209 
 2396304 
 2399401 
 
 2402500 
 2405601 
 2408704 
 2411809 
 2414916 
 
 2418025 
 2421136 
 2424249 
 2427364 
 2430481 
 
 2433600 
 2436721 
 2439844 
 2442969 
 2446096 
 
 Cube. 
 
 3581577000 
 3588604291 
 3595640768 
 3602686437 
 3609741304 
 
 3616805375 
 3623878656 
 3630%! 153 
 3638052872 
 3645153819 
 
 3652264000 
 365938342 
 3666512088 
 3673650007 
 3680797184 
 
 3687953625 
 3695119336 
 3702294323 
 3709478592 
 3716672149 
 
 3723875000 
 3731087151 
 3738308608 
 3745539377 
 3752779464 
 
 3760028875 
 3767287616 
 3774555693 
 3781833112 
 3789119879 
 
 3796416000 
 3803721481 
 381 1036328 
 3818360547 
 3825694144 
 
 Sq. 
 Root. 
 
 39.1152 
 39.1280 
 39.1408 
 39.1535 
 39.1663 
 
 39.1791 
 39.1918 
 39.2046 
 39.2173 
 39.2301 
 
 39.2428 
 39.2556 
 39.2683 
 39.2810 
 39.2938 
 
 39.3065 
 39.3192 
 39.3319 
 39.3446 
 39.3573 
 
 39.3700 
 
 39.3827 
 39.3954 
 39.4081 
 39.4208 
 
 39.4335 
 39.4462 
 39.4583 
 39.4715 
 39.4842 
 
 39.4968 
 39.5095 
 39.5221 
 39.5348 
 39.5474 
 
 Cube 
 Root. 
 
 1 1 .5230 
 11.5255 
 11.5280 
 1 1 .5305 
 1 1 .5330 
 
 11.5355 
 1 1 .5380 
 1 1 .5405 
 1 1 .5430 
 1 1 .5455 
 
 11.5480 
 1 1 .5505 
 11.5530 
 11.5555 
 11.5580 
 
 1 1 .5605 
 11.5630 
 11.5655 
 1 1 .5680 
 11.5705 
 
 1 1 .5729 
 11.5754 
 1 1 .5779 
 1 1 .5804 
 1 1 .5829 
 
 1 1 .5854 
 1 1 .5879 
 1 1 .5903 
 1 1 .5928 
 11.5953 
 
 11.5978 
 1 1 .6003 
 1 1 .6027 
 1 1 .6052 
 11.6077 
 
 1565 
 1566 
 1567 
 
 1568 
 1569 
 
 1570 
 1571 
 1572 
 1573 
 1574 
 
 1575 
 1576 
 1577 
 1578 
 1579 
 
 1580 
 1581 
 1582 
 1583 
 1584 
 
 1585 
 1586 
 1587 
 1583 
 1539 
 
 1590 
 159! 
 1592 
 1593 
 1594 
 
 1595 
 1596 
 1597 
 1593 
 1599 
 
 Square. 
 
 2449225 
 2452356 
 2455489 
 2458624 
 2461761 
 
 2464900 
 246804 
 2471184 
 2474329 
 2477476 
 
 2480625 
 24837-76 
 2486929 
 2490084 
 2493241 
 
 2496400 
 2499561 
 2502724 
 2505889 
 2509056 
 
 2512225 
 2515396 
 2518569 
 2521744 
 2524921 
 
 2528100 
 2531281 
 2534464 
 2537649 
 2540836 
 
 2544025 
 2547216 
 2550409 
 2553604 
 2556801 
 
 Cube. 
 
 3833037125 
 3840389496 
 3847751263 
 3855123432 
 3862503009 
 
 3869893000 
 38772924! 1 
 3884701248 
 3892119517 
 3899547224 
 
 3906984375 
 3914430976 
 3921887033 
 3929352552 
 3936827539 
 
 3944312000 
 1951805941 
 
 3959309368 
 3966822287 
 3974344704 
 
 3981876625 
 3989418056 
 3996969003 
 4004529472 
 4012099469 
 
 4019679000 
 4027268071 
 4034S66683 
 4042474857 
 4050092584 
 
 4057719875 
 4065356736 
 4073003173 
 4080659192 
 4088324799 
 
 2560000 4096000000 40.0000 1 1 .6961 
 
 Sq. 
 Root. 
 
 39.5601 
 39.5727 
 39.5854 
 39.5980 
 39.6106 
 
 39.6232 
 39.6358 
 39.6485 
 39.661 1 
 39.6737 
 
 39.6863 
 39.6989 
 39.7115 
 39.7240 
 39.7366 
 
 39.7492 
 39.7618 
 39.7744 
 39.7869 
 39.7995 
 
 39.8121 
 39.8246 
 39.8372 
 39.8497 
 39.8623 
 
 39.8748 
 39.8873 
 39.8999 
 39.9124 
 39.9249 
 
 39.9375 
 39.9500 
 39.9625 
 39.9750 
 39.9875 
 
 Cube 
 Root. 
 
 11.6102 
 11.6126 
 11.6151 
 11.6176 
 1 1 .6200 
 
 1 1 .6225 
 1 1 .6250 
 1 1 .6274 
 1 1 .6299 
 11.6324 
 
 1 1 .6348 
 1 1 .6373 
 1 1 .6398 
 1 1 .6422 
 1 1 .6447 
 
 11.6471 
 1 1 .6496 
 1 1 .6520 
 1 1 .6545 
 1 1 .6570 
 
 11.6594 
 11.6619 
 1 1 .6643 
 11.6668 
 1 1 .6692 
 
 11.6717 
 
 1 1 .6741 
 1 1 .6765 
 1 1 .6790 
 11.6814 
 
 1 1 .6839 
 1 1 .6863 
 1 1 .6888 
 11.6912 
 1 1 .6936 
 
 SQUARES AND CUBES OF DECIMALS. 
 
 No. 
 
 Square 
 
 Cube. 
 
 No. 
 
 Square 
 
 Cube. 
 
 No. 
 
 Square. 
 
 Cube. 
 
 1 
 
 .01 
 
 .001 
 
 01 
 
 .0001 
 
 .000 001 
 
 .001 
 
 .00 00 01 
 
 .000 000 001 
 
 7 
 
 .04 
 
 .008 
 
 02 
 
 .0004 
 
 .000 008 
 
 .002 
 
 .00 00 04 
 
 .000 000 008 
 
 3 
 
 .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 
 
 1.2 
 
 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. 
 
110 
 
 MATHEMATICAL TABLES. 
 
 FIFTH ROOTS AND FIFTH POWERS. 
 
 (Abridged from Trautwine.) 
 
 u 
 
 
 u 
 
 
 u 
 
 u 
 
 
 u 
 
 
 0+» 
 
 
 Z ■:' 
 
 
 O-ti 
 
 
 z - 
 
 
 °-s 
 
 
 
 Power. 
 
 - ■■* 
 
 Power. 
 
 . O 
 
 o o 
 
 Power. 
 
 . 
 z z 
 
 Power. 
 
 . o 
 o o 
 
 Power. 
 
 £f§ 
 
 
 £& 
 
 
 £Ph 
 
 
 ■',- 
 
 
 z* 
 
 
 .10 
 
 .000010 
 
 3.7 
 
 693.440 
 
 9.8 
 
 90392 
 
 2!. 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 
 
 2.2.2 
 
 5392186 
 
 42 
 
 130691232 
 
 .25 
 
 .000977 
 
 4.0 
 
 1024.00 
 
 10.2 
 
 110408 
 
 12, i 
 
 5639493 
 
 43 
 
 . 147003443 
 
 .30 
 
 .002430 
 
 4.1 
 
 1158.56 
 
 10.4 
 
 121665 
 
 12.6 
 
 5895793 
 
 44 
 
 164916224 
 
 .35 
 
 .005252 
 
 4.2 
 
 1306.91 
 
 10.6 
 
 133823 
 
 11.?. 
 
 6161327 
 
 45 
 
 184523125 
 
 .40 
 
 .010240 
 
 4.3 
 
 1470.08 
 
 10.8 
 
 146933 
 
 2; i 
 
 6436343 
 
 46 
 
 205962976 
 
 .45 
 
 .018453 
 
 4.4 
 
 1649.16 
 
 11.0 
 
 161051 
 
 -' 
 
 6721093 
 
 47 
 
 229345007 
 
 .50 
 
 .031250 
 
 4.5 
 
 1845.28 
 
 11.2 
 
 176234 
 
 l-.A 
 
 7015834 
 
 48 
 
 254803963 
 
 .55 
 
 .050328 
 
 4.6 
 
 2059.63 
 
 11.4 
 
 192541 
 
 -. 
 
 7320825 
 
 49 
 
 282475249 
 
 .60 
 
 .077760 
 
 4.7 
 
 2293.45 
 
 11.6 
 
 210034 
 
 :3 
 
 7636332 
 
 50 
 
 312500000 
 
 .65 
 
 .116029 
 
 4.8 
 
 2548.04 
 
 11.8 
 
 228776 
 
 2-: C 
 
 7962624 
 
 51 
 
 345025251 
 
 .70 
 
 .168070 
 
 4.9 
 
 2824.75 
 
 12.0 
 
 248832 
 
 24.2 
 
 8299976 
 
 52 
 
 380204032 
 
 .75 
 
 .237305 
 
 5.0 
 
 3125.00 
 
 12.2 
 
 27027 1 
 
 24.-: 
 
 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 
 
 9381200 
 
 55 
 
 503234375 
 
 .90 
 
 .590490 
 
 5.3 
 
 4181.95 
 
 12.8 
 
 343597 
 
 25.0 
 
 9765625 
 
 56 
 
 550731776 
 
 .95 
 
 .773781 
 
 5.4 
 
 4591.65 
 
 13.0 
 
 371293 
 
 2 5.2 
 
 10162550 
 
 57 
 
 601692057 
 
 1.00 
 
 1 .00000 
 
 5.5 
 
 5032.84 
 
 13.2 
 
 400746 
 
 5. 
 
 10572278 
 
 58 
 
 656356768 
 
 1.05 
 
 1.27628 
 
 5.6 
 
 5507.32 
 
 13.4 
 
 432040 
 
 : 
 
 10995116 
 
 -59 
 
 714924299 
 
 1.10 
 
 1.61051 
 
 5.7 
 
 6016.92 
 
 13.6 
 
 465259 
 
 ■: P 
 
 11431377 
 
 60 
 
 777600000 
 
 1.15 
 
 2.01135 
 
 5.3 
 
 6563.57 
 
 13.8 
 
 500490 
 
 
 11881376 
 
 61 
 
 844596301 
 
 1.20 
 
 2.48832 
 
 5.9 
 
 7149.24 
 
 14.0 
 
 537824 
 
 :1.2 
 
 12345437 
 
 62 
 
 916132332 
 
 1.25 
 
 3.05176 
 
 6.0 
 
 7776.00 
 
 14.2 
 
 577353 
 
 :•'.■.-: 
 
 12823886 
 
 63 
 
 992436543 
 
 1.30 
 
 3.71293 
 
 6.1 
 
 8445.96 
 
 14.4 
 
 619174 
 
 22,2 
 
 13317055 
 
 64 
 
 1073741824 
 
 1.35 
 
 4.48403 
 
 6.2 
 
 9161.33 
 
 14.6 
 
 663383 
 
 26.8 
 
 13825281 
 
 65 
 
 1160290625 
 
 1.40 
 
 5.37824 
 
 6.3 
 
 9924.37 
 
 14.8 
 
 710032 
 
 a c. 
 
 14348907 
 
 66 
 
 1252332576 
 
 1.45 
 
 6.4097 3 
 
 6.4 
 
 10737 
 
 15.0 
 
 759375 
 
 '7.2 
 
 14888280 
 
 67 
 
 1350125107 
 
 1.50 
 
 7.59375 
 
 6.5 
 
 11603 
 
 15.2 
 
 811368 
 
 . - 
 
 15443752 
 
 68 
 
 1453933568 
 
 1.55 
 
 8.94661 
 
 6.6 
 
 12523 
 
 15.4 
 
 866171 
 
 27.6 
 
 16015681 
 
 69 
 
 1564031349 
 
 1.60 
 
 10.4858 
 
 o.7 
 
 13501 
 
 15.6 
 
 923896 
 
 2 7.8 
 
 16604430 
 
 70 
 
 1680700000 
 
 1.65 
 
 12.2298 
 
 6.8 
 
 14539 
 
 15.8 
 
 934658 
 
 28.0 
 
 17210368 
 
 71 
 
 1804229351 
 
 1.70 
 
 14.1986 
 
 
 15640 
 
 16.0 
 
 1048576 
 
 _J _ 
 
 17833868 
 
 72 
 
 1934917632 
 
 1.75 
 
 16.4131 
 
 2 
 
 16807 
 
 16.2 
 
 1115771 
 
 
 18475309 
 
 73 
 
 2073071593 
 
 1.80 
 
 18.8957 
 
 7.1 
 
 18042 
 
 16.4 
 
 1186367 
 
 L 3/; 
 
 19135075 
 
 74 
 
 2219006624 
 
 1.85 
 
 21.6700 
 
 7.2 
 
 19349 
 
 16.6 
 
 1260493 
 
 
 19813557 
 
 75 
 
 2373046875 
 
 1.90 
 
 24.7610 
 
 7.3 
 
 20731 
 
 16.8 
 
 1338278 
 
 29.0 
 
 20511149 
 
 76 
 
 2535525376 
 
 1.95 
 
 28.1951 
 
 7 4 
 
 22190 
 
 17.0 
 
 1419357 
 
 29 2 
 
 21228253 
 
 77 
 
 2706784157 
 
 2.00 
 
 32.0000 
 
 7.5 
 
 23730 
 
 17.2 
 
 1505366 
 
 1~:, 
 
 21965275 
 
 78 
 
 2887174368 
 
 2.05 
 
 36.2051 
 
 7.6 
 
 25355 
 
 17.4 
 
 1 594947 
 
 2 
 
 22722628 
 
 79 
 
 3077056399 
 
 2.10 
 
 40.8410 
 
 7.7 
 
 27068 
 
 17.6 
 
 1688742 
 
 29; 
 
 23500728 
 
 80 
 
 3276800000 
 
 2.15 
 
 45.9401 
 
 7.8 
 
 28872 
 
 17.8 
 
 1 786899 
 
 
 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 
 
 48875930 
 
 90 
 
 5904900000 
 
 2.70 
 
 143.489 
 
 8.3 
 
 52773 
 
 19.8 
 
 3043 1 68 
 
 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 
 
 26.0 
 
 60466176 
 
 93 
 
 6956883693 
 
 3.00 
 
 243.000 
 
 9.1 
 
 62403 
 
 20.4 
 
 3533059 
 
 26 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 
 
 4034101 
 
 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 
 
 4433166 
 
 39.0 
 
 90224199 
 
 99 
 
 9509900499 
 
 3.60 
 
 604.662 
 
 9.7'85873 21.6 4701850 
 
 39.5 96158012 
 
 
 
CIRCUMFERENCES AND AREAS OP CIRCLES. 
 CIRCUMFERENCES AND AREAS OF CIRCLES. 
 
 Ill 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 V64 
 
 . 04909 
 
 .00019 
 
 3 3 /8 
 
 7.4613 
 
 4.4301 
 
 6V8 
 
 19.242 
 
 29 465 
 
 V32 
 
 .09818 
 
 .00077 
 
 7/16 
 
 7.6576 
 
 4.6664 
 
 1/4 
 
 19.635 
 
 30 680 
 
 3/64 
 
 .14726 
 
 .00173 
 
 1/2 
 
 7.8540 
 
 4.9087 
 
 3/8 
 
 20.028 
 
 31 919 
 
 1/16 
 
 .19635 
 
 .00307 
 
 9/16 
 
 8.0503 
 
 5.1572 
 
 1/2 
 
 20.420 
 
 33. 183 
 
 3 /32 
 
 .29452 
 
 . 00690 
 
 5/8 
 
 8.2467 
 
 5.4119 
 
 5/8 
 
 20.813 
 
 34.472 
 
 1/8 
 
 .39270 
 
 .01227 
 
 . U/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 
 
 7. 
 
 21.991 
 
 38.485 
 
 7/32 
 
 .68722 
 
 .03758 
 
 7/8 
 
 9.0321 
 
 6.4918 
 
 1/8 
 
 22.384 
 
 39.871 
 
 
 
 
 15/16 
 
 9.2284 
 
 6.7771 
 
 1/4 
 
 22.776 
 
 41.282 
 
 V4 
 
 . 78540 
 
 . 04909 
 
 
 
 
 3 /s 
 
 23.169 
 
 42.718 
 
 9 /32 
 
 .88357 
 
 . 062 1 3 
 
 3. 
 
 9.4248 
 
 7.0686 
 
 1/2 
 
 23.562 
 
 44. 179 
 
 5/16 
 
 .98175 
 
 .07670 
 
 Vl6 
 
 9.6211 
 
 7.3662 
 
 5/8 
 
 23.955 
 
 45.664 
 
 H/32 
 
 1.0799 
 
 .09281 
 
 1/8 
 
 9.8175 
 
 7 . 6699 
 
 3/ 4 
 
 24.347 
 
 47.173 
 
 3/8 
 
 1.1781 
 
 .11045 
 
 3/16 
 
 10.014 
 
 7.9798 
 
 7/8 
 
 24.740 
 
 48.707 
 
 13/32 
 
 1.2763 
 
 .12962 
 
 V4 
 
 10.210 
 
 8.2958 
 
 8. 
 
 25.133 
 
 50.265 
 
 7/16 
 
 1.3744 
 
 .15033 
 
 5/16 
 
 10.407 
 
 8.6179 
 
 1/8 
 
 25.525 
 
 51.849 
 
 15/32 
 
 1.4726 
 
 .17257 
 
 3/8 
 
 10.603 
 
 8 . 9462 
 
 1/4 
 
 25.918 
 
 53.456 
 
 
 
 
 7/16 
 
 10.799 
 
 9.2806 
 
 3/8 
 
 26.311 
 
 55.088 
 
 1/2 
 
 1.5708 
 
 .19635 
 
 1/2 
 
 10.996 
 
 9.6211 
 
 1/2 
 
 26.704 
 
 56.745 
 
 17/32 
 
 1 . 6690 
 
 .22166 
 
 9/16 
 
 11.192 
 
 9.9678 
 
 5 /8 
 
 27.096 
 
 58.426 
 
 9/16 
 
 1.7671 
 
 .24850 
 
 5/8 
 
 11.388 
 
 10.321 
 
 3/4 
 
 27.489 
 
 60.132 
 
 19/32 
 
 1.8653 
 
 .27688 
 
 U/16 
 
 11.585 
 
 10.680 
 
 7/8 
 
 27.882 
 
 61.862 
 
 5/8 
 
 1.9635 
 
 .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 
 
 11.793 
 
 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 
 
 23/32 
 
 2.4544 
 
 .47937 
 
 1/8 
 
 12.959 
 
 13.364 
 
 3/4 
 
 30.631 
 
 74.662 
 
 13/16 
 
 2.5525 
 
 .51849 
 
 3 /l6 
 
 13.155 
 
 13.772 
 
 7 /8 
 
 31.023 
 
 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 
 
 1/8 
 
 31.809 
 
 80.516 
 
 29/32 
 
 2.8471 
 
 .64504 
 
 3/8 
 
 13.744 
 
 15.033 
 
 1/4 
 
 32.201 
 
 82 . 5 1 6 
 
 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 
 
 1/2 
 
 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/g 
 
 34.165 
 
 92 . 886 
 
 1/8 
 
 3.5343 
 
 .9940 
 
 3/ 4 
 
 14.923 
 
 17.721 
 
 11. 
 
 34.558 
 
 95.033 
 
 3/16 
 
 3.7306 
 
 1.1075 
 
 13/16 
 
 15.119 
 
 18.190 
 
 1/8 
 
 34.950 
 
 97.205 
 
 1/4 
 
 3.9270 
 
 1.2272 
 
 7/8 
 
 15.315 
 
 18.665 
 
 1/4 
 
 35.343 
 
 99.402 
 
 5/16 
 
 4.1233 
 
 1.3530 
 
 15/16 
 
 15.512 
 
 19.147 
 
 3/8 
 
 35.736 
 
 101.62 
 
 3/8 
 
 4.3197 
 
 1.4849 
 
 5. 
 
 1 5 . 708 
 
 19.635 
 
 1/2 
 
 36. 128 
 
 103.87 
 
 7/16 
 
 4.5160 
 
 1.6230 
 
 Vl6 
 
 1 5 . 904 
 
 20.129 
 
 5/8 
 
 36.521 
 
 106.14 
 
 1/2 
 
 4.7124 
 
 1.7671 
 
 1/8 
 
 16.101 
 
 20.629 
 
 3/4 
 
 36.914 
 
 1C8.43 
 
 9/16 
 
 4.9087 
 
 1.9175 
 
 3 /l6 
 
 16.297 
 
 21.135 
 
 7/8 
 
 37.306 
 
 110.75 
 
 % 
 
 5.1051 
 
 2.0739 
 
 1/4 
 
 16.493 
 
 21.648 
 
 12. 
 
 37.699 
 
 113.10 
 
 U/16 
 
 5.3014 
 
 2.2365 
 
 5/16 
 
 16.690 
 
 22 . 1 66 
 
 1/8 
 
 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 
 
 2. 
 
 6.2832 
 
 3.1416 
 
 U/16 
 
 1 7 . 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 
 
 1/8 
 
 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 
 
MATHEMATICAL TABLES. 
 
 Diam. 
 
 Circura. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 13-3/s 
 
 42.804 
 
 145.80 
 
 217/s 
 
 68.722 
 
 375.83 
 
 30 V8 
 
 94.640 
 
 712.76 
 
 3/ 4 
 
 43.197 
 
 148.49 
 
 22. 
 
 69.115 
 
 380.13 
 
 1/4 
 
 95.033 
 
 718.69 
 
 7/8 
 
 43.590 
 
 1 5 1 . 20 
 
 1/8 
 
 69.503 
 
 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 
 
 Vs 
 
 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 
 
 1/2 
 
 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 
 
 1/8 
 
 97.782 
 
 760.87 
 
 3/ 4 
 
 46.338 
 
 170.87 
 
 23. 
 
 72.257 
 
 4 1 5 . 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 
 
 1/8 
 
 47.517 
 
 179.67 
 
 3/8 
 
 73.435 
 
 429.13 
 
 5/8 
 
 99.353 
 
 785.51 
 
 V4 
 
 47.909 
 
 1 82 . 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 
 
 1/2 
 
 48.695 
 
 188.69 
 
 3/ 4 
 
 74.613 
 
 443.01 
 
 32. 
 
 100.531 
 
 804.25 
 
 5/8 
 
 49.0*7 
 
 191.75 
 
 7/8 
 
 75.006 
 
 447.69 
 
 1/8 
 
 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 
 
 1/8 
 
 50.658 
 
 204.22 
 
 3/8 
 
 76.576 
 
 466.64 
 
 5/8 
 
 1 02 . 494 
 
 835.97 
 
 1/4 
 
 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 
 
 1/2 
 
 51.836 
 
 213.82 
 
 3/4 
 
 77.754 
 
 481.11 
 
 33. 
 
 103.673 
 
 855.30 
 
 5/8 
 
 52.229 
 
 2 1 7 . 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 
 
 1/2 
 
 105.243 
 
 881.41 
 
 1/8 
 
 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 
 
 1/8 
 
 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 
 
 l/ 2 
 
 103.385 
 
 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 
 
 1/8 
 
 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 
 
 1 1 3 . 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 
 
 1/8 
 
 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 
 
 1/4 
 
 91.892 
 
 671.96 
 
 1/2 
 
 117.810 
 
 1104.5 
 
 '-'a 
 
 66.366 
 
 350.50 
 
 3/8 
 
 92.284 
 
 677.71 
 
 5 /8 
 
 118.202 
 
 1111.8 
 
 V4 
 
 66.759 
 
 354.66 
 
 1/2 
 
 92.677 
 
 683.49 
 
 3/4 
 
 118.596 
 
 1119.2 
 
 3/8 
 
 67.152 
 
 358.84 
 
 5/8 
 
 93.070 
 
 689.30 
 
 7/8 
 
 118.988 
 
 1126.7 
 
 1/2 
 
 67.544 
 
 363.05 
 
 3/4 
 
 93.462 
 
 695.13 
 
 38. 
 
 119.381 
 
 1134.1 
 
 5/8 
 
 67.937 
 
 367.28 
 
 7/8 
 
 93.855 
 
 700.98 
 
 1/8 
 
 119.773 
 
 1141.6 
 
 3/4 
 
 63.330 
 
 371 .54 
 
 30. 
 
 94.248 
 
 706 . 86 
 
 1/4 
 
 120.166 
 
 1149.1 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 
 
 113 
 
 Diana. 
 
 Circuin. 
 
 Area. 
 
 Diana. 
 
 Circum. 
 
 Area. 
 
 Diam 
 
 I Circum. 
 
 I Area. 
 
 383/s 
 
 120.559 
 
 1156.6 
 
 465/s 
 
 146.477 
 
 1707.4 
 
 547/ 8 
 
 172.395 
 
 1 2365.0 
 
 V2 
 
 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 
 
 Vs 
 
 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 
 
 1 73 . 966 
 
 2408.3 
 
 39. 
 
 122.522 
 
 1194.6 
 
 V4 
 
 1 48 . 440 
 
 1753.5 
 
 1/2 
 
 174.358 
 
 2419.2 
 
 V8 
 
 122.915 
 
 1202.3 
 
 3/8 
 
 148.833 
 
 1762.7 
 
 5/8 
 
 174.751 
 
 2430. 1 
 
 V4 
 
 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 
 
 1 78 1 . 4 
 
 7/8 
 
 175.536 
 
 2452.0 
 
 V2 
 
 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 
 
 V4 
 
 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 
 
 V2 
 
 177.500 
 
 2507.2 
 
 Vs 
 
 126.056 
 
 1264.5 
 
 3/8 
 
 151.975 
 
 1837.9 
 
 5 /8 
 
 177.893 
 
 2518.3 
 
 V4 
 
 126.449 
 
 1272.4 
 
 V2 
 
 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 
 
 V2 
 
 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 
 
 Vs 
 
 179.463 
 
 2563.0 
 
 3/4 
 
 128.020 
 
 1304.2 
 
 49. 
 
 153.938 
 
 1885.7 
 
 V4 
 
 179.856 
 
 2574.2 
 
 7/8 
 
 128.413 
 
 1312.2 
 
 Vs 
 
 154.331 
 
 1895.4 
 
 3/8 
 
 180.249 
 
 2585.4 
 
 41. 
 
 128.805 
 
 1320.3 
 
 1/4 
 
 154.723 
 
 1905.0 
 
 V2 
 
 180.642 
 
 2596.7 
 
 Vs 
 
 129.198 
 
 1328.3 
 
 3/8 
 
 155.116 
 
 1914.7 
 
 5/8 
 
 181.034 
 
 2608.0 
 
 Va 
 
 129.591 
 
 1336.4 
 
 1/2 
 
 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 
 
 V2 
 
 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 
 
 V4 
 
 157.865 
 
 1983.2 
 
 V2 
 
 183.783 
 
 2687.8 
 
 Vs 
 
 132.340 
 
 1393.7 
 
 3/8 
 
 158.258 
 
 1993. 1 
 
 5 /8 
 
 184.176 
 
 2699.3 
 
 1/4 
 
 132.732 
 
 1402.0 
 
 V2 
 
 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 
 
 V2 
 
 133.518 
 
 1418.6 
 
 3/4 
 
 159.436 
 
 2022.8 
 
 59. 
 
 185.354 
 
 2734.0 
 
 5 /8 
 
 133.910 
 
 1427.0 
 
 7/8 
 
 159.829 
 
 2032.8 
 
 1/8 
 
 185.747 
 
 2745.6 
 
 3/4 
 
 134.303 
 
 1435.4 
 
 51. 
 
 160.22! 
 
 2042.8 
 
 V4 
 
 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 
 
 V4 
 
 161.007 
 
 2062.9 
 
 v 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 
 
 • V2 
 
 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 
 
 V 2 
 
 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 
 
 52. 
 
 163.363 
 
 2123.7 
 
 V4 
 
 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 
 
 V2 
 
 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 
 
 V2 
 
 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 
 
 Vs 
 
 192.030 
 
 2934.5 
 
 3/4 
 
 140.586 
 
 1572.8 
 
 53. 
 
 166.504 
 
 2206.2 
 
 1/4 
 
 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 
 
 V2 
 
 193.208 
 
 2970.6 
 
 V8 
 
 141.764 
 
 1599.3 
 
 3/8 
 
 167.683 
 
 2237.5 
 
 5/8 
 
 193.601 
 
 2982.7 
 
 V4 
 
 142.157 
 
 1608.2 
 
 V2 
 
 168.075 
 
 2248.0 
 
 3/4 
 
 193.993 
 
 2994.8 
 
 3/8 
 
 142.550 
 
 1617.0 
 
 5/8 
 
 168.468 
 
 2258.5 
 
 7/8 
 
 194.386 
 
 3006.9 
 
 V2 
 
 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. 
 
 1 69 . 646 
 
 2290.2 
 
 1/4 
 
 195.564 
 
 3043.5 
 
 7/8 
 
 144.121 
 
 1652.9 
 
 Vs 
 
 170.039 
 
 2300.8 
 
 3/8 
 
 195.957 
 
 3055.7 
 
 46. 
 
 144.513 
 
 1661.9 
 
 V4 
 
 170.431 
 
 2311.5 
 
 1/2 
 
 196.350 
 
 3068.0 
 
 Vs 
 
 144.906 
 
 1670.9 
 
 3/8 
 
 170.824 
 
 2322.1 
 
 5/8 
 
 196.742 
 
 3080.3 
 
 1/4 
 
 145.299 
 
 1680.0 
 
 V2 
 
 171.217 
 
 2332.8 
 
 3/4 
 
 197.135 
 
 3092.6 
 
 3/8 
 
 145.691 
 
 1689. 1 
 
 5/8 
 
 171.609 
 
 2343.5 
 
 7/8 
 
 197.528 
 
 3 1 04 9 
 
 V2 
 
 146.084 
 
 1698.2 
 
 3/ 4 
 
 1 72 . 002 
 
 2354.3 
 
 63. 
 
 197.920 
 
 3117.2 
 
114 
 
 MATHEMATICAL TABLES. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 Diam.l Circum. 
 
 Area. 
 
 63 V8 
 
 198.313 
 
 3129.6 
 
 713/8 
 
 224.23 1 
 
 4001. 1 
 
 795/ 8 
 
 250.149 
 
 49/9.5 
 
 V4 
 
 198.706 
 
 3 1 42 . 
 
 1/2 
 
 224.624 
 
 4015.2 
 
 3/4 
 
 250.542 
 
 4995.1 
 
 3 /8 
 
 199.098 
 
 3154.5 
 
 5/8 
 
 225.017 
 
 4029.2 
 
 7/8 
 
 250.935 
 
 5010.9 
 
 V2 
 
 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 
 
 72. 
 
 226.195 
 
 4071.5 
 
 1/4 
 
 252.113 
 
 5053.0 
 
 7 /8 
 
 200.669 
 
 3204.4 
 
 1/8 
 
 226.587 
 
 4085.7 
 
 3 /8 
 
 252.506 
 
 5073.8 
 
 64. 
 
 201.062 
 
 3217.0 
 
 1/4 
 
 226.980 
 
 4099.8 
 
 1/2 
 
 252.393 
 
 50S9.6 
 
 V8 
 
 201.455 
 
 3229.6 
 
 3/8 
 
 227.373 
 
 4114.0 
 
 5/8 
 
 253.291 
 
 5105.4 
 
 V4 
 
 201.847 
 
 3242 . 2 
 
 1/2 
 
 227.765 
 
 4128.2 
 
 3/ 4 
 
 253.634 
 
 5121.2 
 
 3/8 
 
 202.240 
 
 3254.8 
 
 5 /8 
 
 228.158 
 
 4142.5 
 
 7/8 
 
 254.076 
 
 5137. 1 
 
 V2 
 
 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 
 
 Vs 
 
 254.862 
 
 5168.9 
 
 3/ 4 
 
 203.418 
 
 3292.8 
 
 73. 
 
 229.336 
 
 4185.4 
 
 V4 
 
 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 
 
 Vt 
 
 204.989 
 
 3343.9 
 
 1/2 
 
 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 
 
 23 1 . 692 
 
 4271.8 
 
 82. 
 
 257.611 
 
 5281.0 
 
 5 /8 
 
 206.167 
 
 3382.4 
 
 7/8 
 
 232.085 
 
 4286.3 
 
 Vs 
 
 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 
 
 Vs 
 
 207.738 
 
 3434.2 
 
 3/8 
 
 233.656 
 
 4344.5 
 
 5/8 
 
 259.574 
 
 5361.8 
 
 V4 
 
 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 
 
 V2 
 
 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 
 
 V4 
 
 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 
 
 V8 
 
 210.879 
 
 3538.8 
 
 3/8 
 
 236.798 
 
 4462.2 
 
 5/8 
 
 262.716 
 
 5492.4 
 
 V4 
 
 211.272 
 
 3552.0 
 
 1/2 
 
 237.190 
 
 4477.0 
 
 3/4 
 
 263 . 1 08 
 
 5503.8 
 
 3/8 
 
 211.665 
 
 3565.2 
 
 5/8 
 
 237.583 
 
 4491.8 
 
 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 
 
 233.368 
 
 4521.5 
 
 Vs 
 
 264.236 
 
 5558.3 
 
 3/4 
 
 212.843 
 
 3605.0 
 
 76c 
 
 238.761 
 
 4536.5 
 
 1/4 
 
 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 
 
 1/4 
 
 239.546 
 
 4566.4 
 
 1/2 
 
 265.465 
 
 5607.9 
 
 1/8 
 
 214.021 
 
 3645.0 
 
 3/8 
 
 239.939 
 
 4581.3 
 
 5 /8 
 
 265.857 
 
 5624.5 
 
 1/4 
 
 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 
 
 1/4 
 
 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 
 
 242.633 
 
 4686.9 
 
 1/2 
 
 263.606 
 
 5741.5 
 
 1/8 
 
 217.163 
 
 3752.8 
 
 3/8 
 
 243.081 
 
 4702.1 
 
 5/8 
 
 263.999 
 
 5758.3 
 
 1/4 
 
 217.555 
 
 3766.4 
 
 1/2 
 
 243.473 
 
 4717.3 
 
 3/4 
 
 269.392 
 
 5775.1 
 
 3/8 
 
 217.948 
 
 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 
 
 Vs 
 
 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 
 
 1/2 
 
 271.748 
 
 5876.5 
 
 1/8 
 
 220.304 
 
 3862.2 
 
 3/8 
 
 246.222 
 
 4824.4 
 
 5/8 
 
 272.140 
 
 5893.5 
 
 1/4 
 
 220.697 
 
 3876.0 
 
 l/ 2 
 
 246.615 
 
 4839.8 
 
 3/ 4 
 
 272.533 
 
 5910.6 
 
 3/8 
 
 221.090 
 
 3889.8 
 
 5/8 
 
 247.003 
 
 4855.2 
 
 7/8 
 
 272.926 
 
 5927.6 
 
 1/2 
 
 221.482 
 
 3903.6 
 
 3/4 
 
 247.400 
 
 4870.7 
 
 87. 
 
 273.319 
 
 5944.7 
 
 5/8 
 
 221.875 
 
 3917.5 
 
 7/8 
 
 247.793 
 
 4886.2 
 
 1/8 
 
 273.711 
 
 5961.8 
 
 3/4 
 
 222.268 
 
 3931.4 
 
 7 a 
 
 248. 186 
 
 4901.7 
 
 1/4 
 
 274.104 
 
 5978.9 
 
 7/8 
 
 222.660 
 
 3945.3 
 
 1/8 
 
 243.579 
 
 4917.2 
 
 3/8 
 
 274.497 
 
 5996.0 
 
 71. 
 
 223.053 
 
 3959 2 
 
 1/4 
 
 248.971 
 
 4932.7 
 
 1/2 
 
 274.889 
 
 60 1 3 . 2 
 
 1/8 
 
 223.446 
 
 3973 1 
 
 3/8 
 
 249.364 
 
 4948 . 3 
 
 5/8 
 
 275.282 
 
 6030.4 
 
 1/4 
 
 223.838 
 
 3987.1 
 
 1/2 249.75 7 
 
 4963.9 
 
 3/4 
 
 275.675 
 
 6047.6 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 115 
 
 Area. Diam. Circum. Area. Diani. Circum. Area 
 
 276.067 
 
 276.460 
 
 276.853 
 
 277.246, 
 
 277.633! 
 
 278.031 
 
 278.424 
 
 278.816 
 
 279.209 
 
 279.602 
 
 279.994 
 
 280.387 
 
 280.780 
 
 281. 173 
 
 281.565 
 
 281.958 
 
 282.351 
 
 282.743 
 
 283. 136 
 
 283.529 
 
 283.921 
 
 284.314 
 
 284.707 
 
 285.100 
 
 285.492 
 
 285.835 
 
 286.278 
 
 286.670 
 
 237.063 
 
 287.456 
 
 2S7.848 
 
 288.241 
 
 288.634 
 
 239.027 
 
 289.419 
 
 239.812 
 
 290.205 
 
 290.597 
 
 290.990 
 
 291.333 
 
 291.775 
 
 292.168 
 
 292.561 
 
 292.954 
 
 293.346 
 
 293.739 
 
 294.132 
 
 294.524 
 
 294. 91 7 
 
 295.310 
 
 295.702 
 
 296.095 
 
 296.488 
 
 296.881 
 
 297.273 
 
 297.666 
 
 293.059 
 
 298.451 
 
 298.844 
 
 299.237 
 
 299.629 
 
 300.022 
 
 300.415 
 
 300.807 
 
 6064.9 
 
 6082.1 
 
 6099.4 
 
 6116.7 
 
 6134. 1 
 
 6151.4 
 
 6168.8 
 
 6186.2 
 
 6203 . 7 
 
 6221.1 
 
 6238.6 
 
 6256.1 
 
 6273.7 
 
 6291.2 
 
 6308.8 
 
 6326.4 
 
 6344.1 
 
 6361.7 
 
 6379.4 
 
 6397.1 
 
 6414.9 
 
 6432.6 
 
 6450.4 
 
 6468.2 
 
 6436.0 
 
 6503.9 
 
 6521.8 
 
 6539.7 
 
 6557.6 
 
 6575.5 
 
 6593.5 
 
 66H.5 
 
 6629.6 
 
 6647.6 
 
 6665 . 7 
 
 6683.8 
 
 6701.9 
 
 6720.1 
 
 6738.2 
 
 6756.4 
 
 6774.7 
 
 6792.9 
 
 6811.2 
 
 6829.5 
 
 6847.8 
 
 6366.1 
 
 6834.5 
 
 6902 . 9 
 
 6921.3 
 
 6939.8 
 
 6958.2 
 
 6976.7 
 
 6995 . 3 
 
 7013.8 
 
 7032.4 
 
 7051.0 
 
 7069.6 
 
 7088 . 2 
 
 7106.9 
 
 7125.6 
 
 7144.3 
 
 7163.0 
 
 7181.8 
 
 7200.6 
 
 95 7/ 8 
 96. 
 
 V8 
 
 V4 
 
 Vs 
 
 1/4 
 3/8 
 1/2 
 5/8 
 3/4 
 7/8 
 100 
 101 
 102 
 103 
 104 
 105 
 106 
 107 
 108 
 109 
 110 
 111 
 112 
 113 
 114 
 115 
 116 
 117 
 118 
 119 
 120 
 121 
 122 
 123 
 124 
 125 
 126 
 127 
 128 
 129 
 
 301.200 
 
 301.593 
 
 301.986 
 
 302.378 
 
 302.771 
 
 303. 164 
 
 303.556 
 
 303.949 
 
 304.342 
 
 304.734 
 
 305.127 
 
 305.520 
 
 305.913 
 
 306.305 
 
 306.698 
 
 307.091 
 
 307.483 
 
 307.876 
 
 308.269 
 
 308.661 
 
 309.054 
 
 309.447 
 
 309.840 
 
 310.232 
 
 310.625 
 
 311.018 
 
 311.410 
 
 311.803 
 
 312. 196 
 
 312.538 
 
 312.981 
 
 313.374 
 
 313.767 
 
 314.159 
 
 317.30 
 
 320.44 
 
 323.58 
 
 326.73 
 
 329.87 
 
 333.01 
 
 336.15 
 
 339.29 
 
 342.43 
 
 345.58 
 
 343.72 
 
 351.86 
 
 355.00 
 
 353.14 
 
 361.28 
 
 364.42 
 
 367.57 
 
 370:71 
 
 373.85 
 
 376.99 
 
 380.13 
 
 383.27 
 
 386.42 
 
 389.56 
 
 392.70 
 
 395.84 
 
 398.98 
 
 402. 12 
 
 405.27 
 
 7219.4 
 7238.2 
 7257.1 
 7276.0 
 7294.9 
 7313.8 
 7332.8 
 7351.8 
 7370.8 
 7389.8 
 7408 . 9 
 7428.0 
 7447.1 
 7466.2 
 7435.3 
 7504.5 
 7523.7 
 7543.0 
 7562.2 
 7581.5 
 7600.8 
 
 7620. 1 
 7639.5 
 7658.9 
 7678.3 
 7697.7 
 7717.1 
 7736.6 
 7756.1 
 7775.6 
 7795.2 
 7814.8 
 7834.4 
 7854.0 
 8011.85 
 8171.28 
 8332.29 
 8494.87 
 8659.01 
 8324.73 
 
 8992 . 02 
 9160. ._ 
 9331.32 
 9503.32 
 9676.89 
 9852.03 
 
 10028.75 
 10207.03 
 10386.89 
 10568.32 
 10751.32 
 10935.88 
 11122.02 
 11309.73 
 I 1499.01 
 11689.87 
 11882.29 
 12076.28 
 12271.85 
 12468.98 
 12667.69 
 12867.96 
 13069.81 
 
 130 
 
 131 
 132 
 133 
 134 
 135 
 136 
 137 
 138 
 139 
 140 
 141 
 142 
 143 
 144 
 145 
 146 
 147 
 148 
 149 
 150 
 151 
 152 
 153 
 154 
 155 
 156 
 157 
 158 
 159 
 160 
 161 
 162 
 163 
 164 
 165 
 166 
 167 
 168 
 169 
 170 
 171 
 172 
 173 
 174 
 175 
 176 
 177 
 178 
 179 
 180 
 181 
 182 
 183 
 184 
 185 
 186 
 187 
 188 
 189 
 190 
 191 
 192 
 
 408.41 
 
 411.55 
 
 414.69 
 
 417.83 
 
 420.97 
 
 424. 12 
 
 427.26 
 
 430.40 
 
 433.54 
 
 436.68 
 
 439.82 
 
 442 . 96 
 
 446. 11 
 
 449.25 
 
 452.39 
 
 455.53 
 
 458.67 
 
 461.81 
 
 464.96 
 
 468.10 
 
 471.24 
 
 474.38 
 
 477.52 
 
 480.66 
 
 483.81 
 
 486.95 
 
 490.09 
 
 493.23 
 
 496.37 
 
 499.51 
 
 502.65 
 
 505.80 
 
 508.94 
 
 512.08 
 
 5 1 5 . 22 
 
 518.36 
 
 521.50 
 
 524.65 
 
 527.79 
 
 530.93 
 
 534.07 
 
 537.21 
 
 540.35 
 
 543.50 
 
 546.64 
 
 549.78 
 
 552.92 
 
 556.06 
 
 559.20 
 
 562.35 
 
 565.49 
 
 568.63 
 
 571.77 
 
 574.91 
 
 578.05 
 
 581.19 
 
 584.34 
 
 587.48 
 
 590.62 
 
 593.76 
 
 596.90 
 
 600.04 
 
 603.19 
 
 13273.23 
 
 13478.22 
 
 13684.78 
 
 13892.91 
 
 14102.61 
 
 14313.88 
 
 14526.72 
 
 14741. 14 
 
 14957. 12 
 
 15174.68 
 
 15393.80 
 
 15614.50 
 
 15836.77 
 
 16060.61 
 
 16286.02 
 
 16513.00 
 
 16741.55 
 
 16971.67 
 
 17203.36 
 
 17436.62 
 
 17671.46 
 
 17907.86 
 
 18145.84 
 
 18385.39 
 
 18626.50 
 
 18869.19 
 
 19113.45 
 
 19359.28 
 
 19606.68 
 
 19855.65 
 
 20106.19 
 
 20358.31 
 
 20611.99 
 
 20867.24 
 
 21124.07 
 
 21382.46 
 
 21642.43 
 
 21903.97 
 
 22167.08 
 
 22431.76 
 
 22698.01 
 
 22965.83 
 
 23235.22 
 
 23506. 18 
 
 23778.71 
 
 24052.82 
 
 24328.49 
 
 24605.74 
 
 24884.56 
 
 25164.94 
 
 25446.90 
 
 25730.43 
 
 26015.53 
 
 26302.20 
 
 26590.44 
 
 26880.25 
 
 27171.63 
 
 27464.59 
 
 27759.11 
 
 28055.21 
 
 28352.87 
 
 28652. 11 
 
 28952 . 92 
 
116 
 
 MATHEMATICAL TABLES. 
 
 Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. 
 
 606.33 
 609.47 
 612.61 
 615.75 
 618.89 
 622.04 
 625. 18 
 628.32 
 63 1 . 46 
 634.60 
 637.74 
 640.88 
 644.03 
 647. 17 
 650.31 
 653.45 
 656.59 
 659.73 
 662.88 
 666.02 
 669. 16 
 672.30 
 675.44 
 678.58 
 681.73 
 684.87 
 688.01 
 691.15 
 694.29 
 697.43 
 700.58 
 703.72 
 706.86 
 710.00 
 713.14 
 716.28 
 719.42 
 722.57 
 725.71 
 728.85 
 731.99 
 735.13 
 738.27 
 741.42 
 744.56 
 747.70 
 750.84 
 753.98 
 757. 12 
 760.27 
 763.41 
 766.55 
 769 . 69 
 772.83 
 775.97 
 779.11 
 782.26 
 785.40 
 783.54 
 791.68 
 794.82 
 797.96 
 801. 11 
 804.25 
 807.39 
 810.53 
 813.67 
 
 29255.30 
 
 29559.25 
 
 29864.77 
 
 30171.86 
 
 30480.52 
 
 30790.75 
 
 31102.55 
 
 31415.93 
 
 31730.87 
 
 32047.39 
 
 32365.47 
 
 32685. 13 
 
 33006.36 
 
 33329. 16 
 
 33653.53 
 
 33979.47 
 
 34306 
 
 34636.06 
 
 34966.71 
 
 35298.94 
 
 35632,73 
 
 35963.09 
 
 36305.03 
 
 36643.54 
 
 36983.61 
 
 37325.26 
 
 37668. 
 
 38013.27 
 
 38359.63 
 
 38707.56 
 
 39057.07 
 
 39408. 14 
 
 39760.78 
 
 401 15.00 
 
 40470.78 
 
 40828. 14 
 
 41187.07 
 
 41547.56 
 
 4190^.63 
 
 42273.27 
 
 42638.48 
 
 43005.26 
 
 43373.61 
 
 43743.54 
 
 44115.03 
 
 44488 . 09 
 
 44862.73 
 
 45238.93 
 
 45616.71 
 
 45996.06 
 
 46376 
 
 46759.47 
 
 47143.52 
 
 47529. 16 
 
 47916.36 
 
 48305. 13 
 
 48695.47 
 
 49087.39 
 
 49480.87 
 
 49875.92 
 
 50272.55 
 
 50670.75 
 
 51070.52 
 
 51471.85 
 
 51874.76 
 
 52279.24 
 
 52685 29 
 
 260 
 
 261 
 
 262 
 
 263 
 
 264 
 
 265 
 
 266 
 
 267 
 
 268 
 
 269 
 
 270 
 
 271 
 
 272 
 
 273 
 
 274 
 
 275 
 
 276 
 
 277 
 
 278 
 
 279 
 
 280 
 
 281 
 
 282 
 
 283 
 
 284 
 
 285 
 
 286 
 
 287 
 
 288 
 
 289 
 
 290 
 
 291 
 
 292 
 
 293 
 
 294 
 
 295 
 
 296 
 
 297 
 
 298 
 
 299 
 
 300 
 
 301 
 
 302 
 
 303 
 
 304 
 
 305 
 
 306 
 
 307 
 
 303 
 
 309 
 
 310 
 
 311 
 
 312 
 
 313 
 
 314 
 
 315 
 
 316 
 
 317 
 
 318 
 
 319 
 
 320 
 
 321 
 
 322 
 
 323 
 
 324 
 
 325 
 
 326 
 
 816.81 
 819.96 
 823. 10 
 826.24 
 829.33 
 832.52 
 835.66 
 838.81 
 841.95 
 845.09 
 848.23 
 851.37 
 854.5! 
 857.65 
 860.80 
 863.94 
 867.08 
 870.22 
 873.36 
 876.50 
 879.65 
 882.79 
 885.93 
 889.07 
 892.2 
 895.35 
 893.50 
 901.64 
 904.78 
 907.92 
 911.06 
 914.20 
 917.35 
 920.49 
 923.6: 
 926.77 
 929.91 
 933.05 
 936. 19 
 939.34 
 942.48 
 945.62 
 948.76 
 951.90 
 955.04 
 958. 19 
 961.33 
 964.47 
 967.61 
 970.75 
 973.89 
 977.04 
 930. 18 
 983.32 
 986.46 
 989.60 
 992.74 
 995.88 
 999.03 
 1002.17 
 1005.31 
 1008.45 
 1011.59 
 1014.73 
 1017.8^ 
 1021.02 
 1024. 16 
 
 53092 
 53502 
 53912 
 54325 
 54739 
 55154 
 55571 
 55990 
 56410 
 56832 
 57255 
 57680 
 58106 
 58534 
 58964 
 59395 
 59823 
 60262 
 60698 
 61 136 
 61575 
 62015 
 62458 
 62901 
 63347 
 63793 
 64242 
 64692 
 65144 
 65597 
 66051 
 66508 
 66966 
 67425 
 67886 
 68349 
 68813 
 69279 
 69746 
 70215 
 70685 
 71157 
 71631 
 72106 
 72583 
 73061 
 73541 
 74022 
 74506 
 74990 
 75476. 
 75964, 
 76453. 
 76944. 
 77437. 
 77931. 
 78426 
 78923 
 79422 
 79922 
 80424 
 80928 
 81433 
 81939 
 82447 
 82957 
 83468 
 
 327 
 
 328 
 
 329 
 
 330 
 
 331 
 
 332 
 
 333 
 
 334 
 
 335 
 
 336 
 
 337 
 
 338 
 
 339 
 
 340 
 
 341 
 
 342 
 
 343 
 
 344 
 
 345 
 
 346 
 
 347 
 
 348 
 
 349 
 
 350 
 
 351 
 
 352 
 
 353 
 
 354 
 
 355 
 
 356 
 
 357 
 
 358 
 
 359 
 
 3fiO 
 
 361 
 
 362 
 
 363 
 
 364 
 
 365 
 
 366 
 
 367 
 
 368 
 
 369 
 
 370 
 
 371 
 
 372 
 
 373 
 
 374 
 
 375 
 
 376 
 
 377 
 
 378 
 
 379 
 
 380 
 
 381 
 
 382 
 
 383 
 
 384 
 
 385 
 
 386 
 
 387 
 
 388 
 
 389 
 
 390 
 
 391 
 
 392 
 
 393 
 
 1027.30 
 
 1030.44 
 
 1033.58 
 
 1036.73 
 
 1039.87 
 
 1043.0 
 
 1046. 15 
 
 1049.29 
 
 1052.43 
 
 1055.58 
 
 1058.72 
 
 1061.86 
 
 1065.00 
 
 1068. 14 
 
 1071.28 
 
 1074.42 
 
 1077.57 
 
 1080.71 
 
 1083.85 
 
 1086.99 
 
 1090.13 
 
 1093.27 
 
 1096.42 
 
 1099.56 
 
 1102.70 
 
 1105.84 
 
 1108.98 
 
 1112. 12 
 
 1115.27 
 
 1118.41 
 
 1121.55 
 
 1124.69 
 
 1127.83 
 
 1130.97 
 
 1134.11 
 
 1137-26 
 
 1140.40 
 
 1143.54 
 
 1146.68 
 
 1149.82 
 
 1152.96 
 
 1156.11 
 
 1159.25 
 
 1162.39 
 
 1165.53 
 
 1168.67 
 
 1171.8 
 
 1174.96 
 
 1178. 10 
 
 1181.24 
 
 1184.38 
 
 1187.52 
 
 1190.66 
 
 1193.81 
 
 1196.95 
 
 1200.09 
 
 1203.23 
 
 1206.37 
 
 1209.51 
 
 1212.65 
 
 1215.80 
 
 1218.94 
 
 1222.08 
 
 1225.22 
 
 1228.36 
 
 1231.50 
 
 1234.65 
 
 Area. 
 
 83981.84 
 
 84496.28 
 
 85012.28 
 
 85529.86 
 
 86049.01 
 
 86569.73 
 
 87092.02 
 
 87615.88 
 
 88141.31 
 
 88668.31' 
 
 89196.88 
 
 89727.03 
 
 90258.74 
 
 90792.03 
 
 91326.88 
 
 91863.31 
 
 92401.31 
 
 92940.88 
 
 93482.02 
 
 94024.73 
 
 94569.01 
 
 95114.86 
 
 95662.28 
 
 96211.28 
 
 96761.84 
 
 97313.97 
 
 97867.68 
 
 98422.96 
 
 98979.80 | 
 
 99538.22 
 
 1 00098. 2| 
 
 100659.77 ;; 
 
 101222.90 I 
 
 101787.60 
 
 102353. 8J I 
 
 102921.72 ji 
 
 103491. 13 I 
 
 104062. 12 ji 
 
 104634.67 
 
 105208.80 J 
 
 105784.49 
 
 106361.76 ! 
 
 106940.60 
 
 107521.01 II 
 
 108102.9) 
 
 108686.51 ! 
 
 109271.66 | 
 
 09853.35 
 
 10446.62 
 
 11 1036.45 
 
 111627.86 
 
 1220.83 
 
 112815.38 
 
 13411.49 
 
 114009. 13 
 
 1 14603.44 
 
 115209.27 
 
 115811.67 
 
 116415.64 
 
 117021.18 
 
 117628.30 
 
 118236.98 
 
 118847.24 
 
 119459.06 
 
 120072.46 
 
 120687.46 
 
 121303.96 
 
CIRCUMFERENCES AND AREAS OP CIRCLES. 
 
 117 
 
 Diam. Circum Area. Diam. Circum. Area. Diam. Circum. Area 
 
 1237 
 
 1240 
 
 1244 
 
 1247 
 
 1250 
 
 1253 
 
 1256 
 
 1259 
 
 1262 
 
 1266 
 
 1269 
 
 1272 
 
 1275 
 
 1278 
 
 1281 
 
 1284 
 
 1288 
 
 1291 
 
 1294 
 
 1297 
 
 1300 
 
 1303 
 
 1306 
 
 1310 
 
 1313 
 
 1316 
 
 1319 
 
 1322 
 
 1325 
 
 1328 
 
 1332 
 
 1335 
 
 1338 
 
 1341. 
 
 1344 
 
 1347 
 
 1350 
 
 1354 
 
 1357 
 
 1360 
 
 1363. 
 
 1366 
 
 1369 
 
 1372 
 
 1376 
 
 1379. 
 
 1382 
 
 1385 
 
 1388 
 
 1391 
 
 1394 
 
 1398 
 
 1401 
 
 1404 
 
 1407 
 
 1410 
 
 1413 
 
 1416 
 
 1420 
 
 1423 
 
 1426 
 
 1429 
 
 1432 
 
 1435 
 
 1438 
 
 1441 
 
 1445 
 
 121922.07 
 
 122541.75 
 123163.00 
 123785.82 
 124410.21 
 125036.17 
 125663.71 
 126292.81 
 1 26923 . 48 
 127555.73 
 128189.55 
 128824.93 
 129461 
 130100.42 
 130740.52 
 131382. 19 
 132025.43 
 132670.24 
 133316.63 
 133964.58 
 134614. 10 
 135265.20 
 135917.86 
 136572.10 
 137227.91 
 137885.29 
 138544.24 
 139204.76 
 139866.85 
 140530.51 
 141195.74 
 141862.54 
 142530.92 
 143200.86 
 143872.38 
 144545.46 
 145220.12 
 145896.35 
 146574.15 
 147253.52 
 147934.46 
 148616.97 
 149301.05 
 149986.70 
 150673.93 
 151362.72 
 152053.08 
 44 1 152745. 02 
 5S 153438.53 
 154133.60 
 154830.25 
 155528.47 
 156228.26 
 156929.62 
 157632.55 
 158337.06 
 159043.13 
 159750.77 
 160459.99 
 161170.77 
 161883.13 
 162597.05 
 163312.55 
 164029.62 
 164748.26 
 165468.47 
 166190.25 
 
 461 
 462 
 463 
 464 
 465 
 466 
 467 
 468 
 469 
 470 
 471 
 472 
 473 
 474 
 475 
 476 
 477 
 478 
 479 
 480 
 481 
 482 
 483 
 484 
 485 
 486 
 487 
 488 
 489 
 490 
 491 
 492 
 493 
 494 
 495 
 496 
 497 
 498 
 499 
 500 
 501 
 502 
 503 
 504 
 505 
 506 
 507 
 508 
 500 
 510 
 511 
 512 
 513 
 514 
 515 
 516 
 517 
 518 
 519 
 520 
 521 
 522 
 523 
 524 
 525 
 526 
 527 
 
 1448.27 
 
 1451.42 
 
 1454.56 
 
 1457.70 
 
 1460.84 
 
 1463.98 
 
 1467. 12 
 
 1470.27 
 
 1473.41 
 
 1476.55 
 
 1479.69 
 
 1482.83 
 
 1485.97 
 
 1489.11 
 
 1492.26 
 
 1495.40 
 
 1498.54 
 
 1501.68 
 
 1504.82 
 
 1507.96 
 
 1511.11 
 
 1514.25 
 
 1517.39 
 
 1520.53 
 
 1523.67 
 
 1526.81 
 
 1529.96 
 
 1533 
 
 1536.24 
 
 1539.38 
 
 1542.52 
 
 1545.66 
 
 1548.81 
 
 1551.95 
 
 1555.09 
 
 1558.23 
 
 1561.37 
 
 1564.51 
 
 1567.65 
 
 1570.80 
 
 1573.94 
 
 1577. 05 
 1580.22 
 1583.36 
 1586.50 
 1589.65 
 1592.79 
 1595.93 
 1599.07 
 1602.21 
 1605.35 
 1608.50 
 1611 .64 
 1614.78 
 1617.92 
 
 1 62 1 . 06 
 1624.20 
 1627.34 
 1630.49 
 1633.63 
 1636.77 
 1639.91 
 1643.05 
 1646. 19 
 1649.34 
 1652.48 
 1655.62 
 
 166913.60 
 
 167638.53 
 
 168365.02 
 
 169093.08 
 
 169822.72 
 
 170553.92 
 
 171286.70 
 
 172021.05 
 
 172756.9! 
 
 173494.45 
 
 174233.51 
 
 174974. 14 
 
 175716.35 
 
 176460.12 
 
 177205.46 
 
 177952.3: 
 
 178700.86 
 
 179450.91 
 
 180202.54 
 
 180955.74 
 
 181710.50 
 
 182466.84 
 
 183224.75 
 
 183984.23 
 
 184745.28 
 
 185507.90 
 
 186272.10 
 
 187037.86 
 
 187805.19 
 
 188574.10 
 
 189344.5: 
 
 190116.62 
 
 190890.2 
 
 191665.43 
 
 192442.18 
 
 193220.51 
 
 194000.41 
 
 194781.85 
 
 195564.93 
 
 196349.54 
 
 197135.72 
 
 197923.48 
 
 198712.80 
 
 199503.70 
 
 200296.1 
 
 201090.20 
 
 201885.81 
 
 202682.99 
 
 203481.74 
 
 204282.06 
 
 205083.95 
 
 205887.42 
 
 206692.45 
 
 207499.05 
 
 208307.23 
 
 209116.97 
 
 209928.29 
 
 210741.18 
 
 211555.63 
 
 212371.66 
 
 213189.26 
 
 214008.43 
 
 214829. 17 
 
 215651 .49 
 
 216475.37 
 
 217300.82 
 
 218127.85 
 
 528 
 
 529 
 
 530 
 
 531 
 
 532 
 
 533 
 
 534 
 
 535 
 
 536 
 
 537 
 
 538 
 
 539 
 
 540 
 
 541 
 
 542 
 
 543 
 
 544 
 
 545 
 
 546 
 
 547 
 
 548 
 
 549 
 
 550 
 
 551 
 
 552 
 
 553 
 
 554 
 
 555 
 
 556 
 
 557 
 
 558 
 
 559 
 
 560 
 
 561 
 
 562 
 
 563 
 
 564 
 
 565 
 
 566 
 
 567 
 
 568 
 
 569 
 
 570 
 
 571 
 
 572 
 
 573 
 
 574 
 
 575 
 
 576 
 
 577 
 
 578 
 
 579 
 
 580 
 
 581 
 
 582 
 
 583 
 
 584 
 
 585 
 
 586 
 
 587 
 
 588 
 
 589 
 
 590 
 
 591 
 
 592 
 
 593 
 
 594 
 
 1658.76 
 
 1661.90 
 
 1665.04 
 
 1 668 . 1 . 
 
 1671.33 
 
 1674.47 
 
 1677.61 
 
 1680.75 
 
 1 683 . 89 
 
 1687.04 
 
 1690.18 
 
 1693.32 
 
 1696.46 
 
 1699.60 
 
 1702.74 
 
 1705.88 
 
 1709.03 
 
 1712.17 
 
 1715.31 
 
 1718.45 
 
 1721.59 
 
 1724.73 
 
 1727.88 
 
 1 73 1 . 02 
 
 1734.16 
 
 1737.30 
 
 1740.44 
 
 1743.58 
 
 1746.73 
 
 1749.87 
 
 1753.0 
 
 1756.15 
 
 1759.29 
 
 1762.43 
 
 1765.58 
 
 1768.72 
 
 1771.86 
 
 1775.00 
 
 1778.14 
 
 1781.28 
 
 1784.42 
 
 1787.57 
 
 1790.71 
 
 1793.85 
 
 1796.99 
 
 1800.13 
 
 1803.27 
 
 1806.42 
 
 1809.56 
 
 1812.70 
 
 1815.84 
 
 1818.98 
 
 1822.12 
 
 1825.27 
 
 1828.41 
 
 1831.55 
 
 1834.69 
 
 .837.83 
 
 1840.97 
 
 1844.11 
 
 1847.26 
 
 1850.40 
 
 1853.54 
 
 1856.68 
 
 1859.82 
 
 1862.96 
 
 1866.11 
 
 218956.44 
 219786.61 
 220618.34 
 221451.65 
 222286.53 
 223122.98 
 223961. CO 
 224800.59 
 225641.75 
 226484.48 
 227328.79 
 228174.66 
 229022. 10 
 229871.12 
 230721.71 
 231573.86 
 232427.59 
 233282.89 
 234139.76 
 234998.20 
 235858.21 
 236719.79 
 237582.94 
 238447.67 
 239313.96 
 240181.83 
 241051.26 
 241922.27 
 242794.85 
 243668.99 
 244544.71 
 245422.00 
 246300.86 
 247181.30 
 248063.30 
 248946.87 
 249832.01 
 250718.73 
 251607.01 
 252496.87 
 253388.30 
 254281.29 
 255175.86 
 256072.00 
 256969.71 
 257868.99 
 258769.85 
 259672.27 
 260576.26 
 261481.83 
 262388.96 
 263297.67 
 264207.94 
 265119.79 
 266033.21 
 266948.20 
 267864.76 
 268782.89 
 269702.59 
 270623.86 
 271546.70 
 272471.12 
 273397.10 
 274324.66 
 275253.78 
 276184.48 
 277116.75 
 
118 
 
 MATHEMATICAL TABLES. 
 
 Diam 
 
 Circum. 
 
 Area. 
 
 Dkm 
 
 Circum 
 
 Area. 
 
 Diam. 
 
 Circum. 
 
 Area. 
 
 595 
 
 1869.25 
 
 278050.58 
 
 663 
 
 2082 . 88 
 
 345236.69 
 
 731 
 
 2296.50 
 
 419686. 15 
 
 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 
 
 2312.21 
 
 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 
 
 237475.36 
 
 673 
 
 2114.29 
 
 355729.60 
 
 741 
 
 2327.92 
 
 431247.21 
 
 606 
 
 1903.81 
 
 283426.48 
 
 674 
 
 2117.43 
 
 356787.54 
 
 742 
 
 233 1 . 06 
 
 432411.95 
 
 607 
 
 1906.95 
 
 239379. 17 
 
 675 
 
 2120.58 
 
 357847.04 
 
 743 
 
 2334.20 
 
 433578.27 
 
 608 
 
 1910.09 
 
 290333.43 
 
 676 
 
 2123.72 
 
 358908.11 
 
 744 
 
 2337.34 
 
 434746.16 
 
 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 
 
 630 
 
 2136.28 
 
 3631:8.11 
 
 748 
 
 2349.91 
 
 439433.41 
 
 613 
 
 1925.80 
 
 295128.28 
 
 631 
 
 2139.42 
 
 364237.04 
 
 749 
 
 2353.05 
 
 440609.16 
 
 614 
 
 1928.94 
 
 296091.97 
 
 632 
 
 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 
 
 634 
 
 2148.85 
 
 367453.24 
 
 752 
 
 2362.48 
 
 444145.80 
 
 617 
 
 1938.36 
 
 298992.44 
 
 635 
 
 2151.99 
 
 368528.45 
 
 753 
 
 2365.62 
 
 445327.83 
 
 618 
 
 1941.50 
 
 299962.41 
 
 686 
 
 2155.13 
 
 369605.23 
 
 754 
 
 2368.76 
 
 445511.42 
 
 619 
 
 1944.65 
 
 300933.95 
 
 637 
 
 2158.27 
 
 370683.59 
 
 755 
 
 2371.90 
 
 447696.59 
 
 620 
 
 1947.79 
 
 301907.05 
 
 633 
 
 2161.42 
 
 371763.51 
 
 756 
 
 2375.04 
 
 448883.32 
 
 621 
 
 1950.93 
 
 302881.73 
 
 639 
 
 2164.56 
 
 372845.00 
 
 757 
 
 2378.19 
 
 450071.63 
 
 622 
 
 1954.07 
 
 303857.98 
 
 090 
 
 2167.70 
 
 373928.07 
 
 758 
 
 2381.33 
 
 451261.51 
 
 623 
 
 1957.21 
 
 304835. 8G 
 
 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 
 
 1969.73 
 
 308762.75 
 
 695 
 
 2183.41 
 
 379366.95 
 
 763. 
 
 2397.04 
 
 457234.46 
 
 628 
 
 1972.92 
 
 309748. 4/ 
 
 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 
 
 3 1 6692 . 1 7 
 
 703 
 
 2208.54 
 
 388150.84 
 
 771 
 
 2422. 1, 
 
 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 
 
 2423.45 
 
 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 
 
 399272.03 
 
 781 
 
 2453.58 
 
 479062.25 
 
 646 
 
 2029.47 
 
 327759.22 
 
 714 
 
 2243.10 
 
 00392.84 
 
 782 
 
 2456.73 
 
 480289.83 
 
 647 
 
 2032.61 
 
 328774.74 
 
 715 
 
 2246.24 
 
 401515.18 
 
 703 
 
 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 
 
 40489 1 . 60 
 
 786 
 
 2469.29 
 
 485215.84 
 
 651 
 
 2045. 18 
 
 332852.53 
 
 719 
 
 2258.81 
 
 406020.22 
 
 787 
 
 2472.43 
 
 486451.28 
 
 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 
 
 655 
 
 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 
 
 653 
 
 2067. 17 
 
 340049.13 
 
 726 
 
 2280.80 
 
 413964.52 
 
 794 
 
 2494.42 
 
 495143.28 
 
 659 
 
 2070.3 1 
 
 341083.50 
 
 727 
 
 2283.94 
 
 415105.71 
 
 795 
 
 2497.57 
 
 496391.27 
 
 660 
 
 2073.45 
 
 342119.44 
 
 728 
 
 2287.08 
 
 416248.46 
 
 796 
 
 2500.71 
 
 497640.84 
 
 661 
 
 2076 59 
 
 343156.95 
 
 729 
 
 2290.22 
 
 417392.79 
 
 797 
 
 2503.85^ 
 
 498891.98 
 
 662 2079. 731344196.03 
 
 730 
 
 2293.36 
 
 418538.68 
 
 798 2506.99 500144.69 
 
CIRCUMFERENCES AND AREAS OF CIRCLES. 
 
 110 
 
 Area. 
 
 Circum.l Area. 
 
 Diam. Cireum. 
 
 2937.39 
 2940.53 
 2943.67 
 2946.81 
 2949.96 
 2953.10 
 2956.24 
 2959.38 
 2^62.52 
 2965.66 
 2968.81 
 2971.95 
 2975.09 
 2978.23 
 2981.37 
 2984.51 
 2987.65 
 2990.80 
 2993.94 
 2997 . 08 
 3000.22 
 3003.36 
 3006.50 
 3009.65 
 3012.79 
 3015.93 
 3019.07 
 3022.21 
 3025.35 
 3028.50 
 3031.64 
 3034.78 
 3037.92 
 3041.06 
 3044.20 
 3047.34 
 3050.49 
 3053.63 
 3056.77 
 3059.91 
 3063.05 
 3066.19 
 3069.34 
 3072.48 
 3075.62 
 3078.76 
 3081.90 
 3085.04 
 3088.19 
 3091.33 
 3094.47 
 3097.61 
 3100.75 
 3103.89 
 3107.04 
 3110.18 
 3113.32 
 3116.46 
 3119.60 
 3122.74 
 3125.88 
 3129.03 
 3132.17 
 3135.31 
 3138.45 
 3141.59 
 
 Area. 
 
 799 
 800 
 
 801 
 802 
 803 
 804 
 805 
 806 
 807 
 808 
 809 
 810 
 811 
 812 
 813 
 814 
 815 
 816 
 817 
 818 
 819 
 820 
 821 
 822 
 823 
 824 
 825 
 826 
 827 
 828 
 829 
 830 
 831 
 832 
 833 
 834 
 835 
 836 
 837 
 838 
 839 
 840 
 841 
 842 
 843 
 844 
 845 
 846 
 847 
 848 
 849 
 850 
 851 
 852 
 853 
 854 
 855 
 856 
 857 
 858 
 859 
 860 
 861 
 862 
 863 
 864 
 865 
 866 
 
 2510 
 
 2513 
 
 2516 
 
 2519 
 
 2522 
 
 2525 
 
 2528 
 
 2532 
 
 2535 
 
 2538. 
 
 2541. 
 
 2544. 
 
 2547. 
 
 2550. 
 
 2554. 
 
 2557. 
 
 2560. 
 
 2563 
 
 2566 
 
 2569 
 
 2572. 
 
 2576 
 
 2579 
 
 2582 
 
 2585 
 
 2588. 
 
 2591 
 
 2594. 
 
 2598 
 
 2601. 
 
 2604 
 
 2607. 
 
 2610. 
 
 2613. 
 
 2616. 
 
 2620. 
 
 2623. 
 
 2626. 
 
 2629. 
 
 2632. 
 
 2635. 
 
 2638. 
 
 2642 
 
 2645. 
 
 2648 
 
 2651. 
 
 2654 
 
 2657. 
 
 2660 
 
 2664. 
 
 2667. 
 
 2670 
 
 2673 
 
 2676 
 
 2679 
 
 2682. 
 
 2686. 
 
 2689. 
 
 2692, 
 
 2695, 
 
 2698. 
 
 2701. 
 
 2704 
 
 2708 
 
 2711 
 
 2714 
 
 2717 
 
 2720 
 
 13 501398 
 27 502654 
 42 503912 
 56J505171 
 
 506431 
 
 507693 
 
 508957 
 
 5 1 0222 
 
 511489 
 
 512758 
 
 514028 
 
 515299 
 
 516572 
 
 517847 
 
 519123 
 
 520401 
 
 521681 
 
 522962 
 
 524244 
 
 525528 
 
 5268 1 4 
 
 528101. 
 
 529390 
 
 530680. 
 
 531972 
 
 533266. 
 
 534561 
 
 535858. 
 
 537156 
 
 538456. 
 
 539757 
 
 541060. 
 
 542365 
 
 543671. 
 
 544979. 
 
 546288. 
 
 547599. 
 
 548911. 
 
 550225. 
 
 551541. 
 
 552858. 
 
 554176. 
 
 555497 
 
 556819 
 
 558142 
 
 559467. 
 
 560793 
 
 562122. 
 
 563451 
 
 564782. 
 
 566115. 
 
 567450. 
 
 568786. 
 
 570123. 
 
 571462. 
 
 572803. 
 
 574145. 
 
 575489, 
 
 576834, 
 
 578181, 
 
 579530, 
 
 580880. 
 
 582232, 
 
 5G3585, 
 
 584940 
 
 586296 
 
 587654 
 
 589014 
 
 867 
 868 
 869 
 870 
 871 
 872 
 873 
 874 
 875 
 876 
 877 
 878 
 879 
 880 
 881 
 882 
 883 
 884 
 885 
 886 
 887 
 
 890 
 891 
 892 
 893 
 894 
 895 
 896 
 897 
 898 
 899 
 900 
 901 
 902 
 903 
 904 
 905 
 906 
 907 
 908 
 909 
 910 
 911 
 912 
 913 
 914 
 915 
 916 
 917 
 918 
 919 
 920 
 921 
 922 
 923 
 924 
 925 
 926 
 927 
 928 
 929 
 930 
 931 
 932 
 933 
 934 
 
 2723.761590375 
 2726.90J591737, 
 2730.041593102. 
 2733.19,594467. 
 2736.331595835, 
 2739.47!597204. 
 2742.611598574. 
 2745.75 599946. 
 2748.89 601320. 
 2752.04 602695. 
 2755.181604072. 
 2758.32 605450. 
 
 935 
 936 
 937 
 938 
 939 
 940 
 941 
 
 2761.46 
 2764.60 
 2767.74 
 2770.88 
 2774.03 
 2777,17 
 2780.31 
 2703.45 
 2786.59 
 2789.73 
 2792.88 
 2796.02 
 2799.16 
 2802.30 
 2805.44 
 2808.58 
 2811.73 
 2814.87 
 2818.01 
 2821.15 
 2824.29 
 2827.43 
 2830.58 
 2833.72 
 2836.86 
 2840.00 
 2843.14 
 2846.28 
 2849.42 
 2852.57 
 2855.71 
 2858.85 
 2861.99 
 2865.13 
 2868.27 
 2871.42 
 2874.56 
 2877.70 
 2880.84 
 2883.98 
 2887.12 
 2890.27 
 2893.41 
 2896.55 
 2899.69 
 2902.83 
 2905.97 
 2909.11 
 2912.26 
 2915.40 
 
 606830. J 
 
 6082 12.: 
 
 609595. 
 
 610980J 
 
 612366. 
 
 613754. 
 
 615143. 
 
 616534.. 
 
 617926.' 
 
 619321. 
 
 620716j 
 
 622113. 
 
 623512. 
 
 624913J 
 
 6:6314.' 
 
 627718 
 
 629123.. 
 
 630530.; 
 
 631938.4 
 
 633348.; 
 
 634759. 
 
 636172.5 
 
 637587J 
 
 639003.0 
 
 640420.; 
 
 641839.9 
 
 643260.: 
 
 644683J 
 
 646107J 
 
 647532. 
 
 648959. 
 
 650388.2 
 
 6518 ' 
 
 653250.2 
 
 654683. f 
 
 656118 
 
 657554.' 
 
 658993.' 
 
 660432. 
 
 661873., 
 
 66331 6. ( 
 
 664761 . 
 
 t 66206.' 
 
 667654. 
 
 669103 
 
 670554. 
 
 672006.: 
 
 673460.1 
 
 674915. 
 
 676372.: 
 
 2918.54J677830.J 
 2921.68|679290.i 
 2924.82 680752. 
 2927.96 ! 682215.i 
 2931 . 11 683680. 
 2934.25 6851 46. i 
 
 81 
 
 942 
 
 47 
 
 943 
 
 70 
 
 944 
 
 50 
 
 945 
 
 88 
 
 946 
 
 rV 
 
 947 
 
 4 
 
 948 
 
 
 949 
 
 
 950 
 
 31 
 
 951 
 
 11 
 
 952 
 
 4;-', 
 
 953 
 
 : 
 
 954 
 
 9^ 
 
 955 
 
 01 
 
 956 
 
 66 
 
 957 
 
 89 
 
 958 
 
 68 
 
 959 
 
 04 
 
 960 
 
 9f 
 
 961 
 
 -:■<; 
 
 962 
 
 5( 
 
 963 
 
 ?.} 
 
 964 
 
 
 965 
 
 
 966 
 
 58 
 
 967 
 
 51 
 
 968 
 
 01 
 
 969 
 
 09 
 
 970 
 
 73 
 
 971 
 
 95 
 
 972 
 
 73 
 
 973 
 
 09 
 
 974 
 
 01 
 
 975 
 
 51 
 
 976 
 
 58 
 
 977 
 
 17. 
 
 978 
 
 -n 
 
 979 
 
 21 
 
 980 
 
 56 
 
 981 
 
 48 
 
 982 
 
 98 
 
 983 
 
 04 
 
 984 
 
 68 
 
 985 
 
 88 
 
 986 
 
 66 
 
 987 
 
 01 
 
 988 
 
 92 
 
 989 
 
 41 
 
 990 
 
 47 
 
 991 
 
 1(1 
 
 992 
 
 30 
 
 993 
 
 08 
 
 994 
 
 ■■:; 
 
 995 
 
 3; 
 
 996 
 
 r-l 
 
 997 
 
 87 
 
 998 
 
 50 
 
 999 
 
 69 
 
 1000 
 
 686614.71 
 688084. 19 
 689555.24 
 691027.86 
 692502.05 
 693977.82 
 695455. 15 
 696934.06 
 698414.53 
 699896.58 
 701380.19 
 702865.38 
 704352.14 
 705840.47 
 707330.37 
 708821.84 
 710314.88 
 711809.50 
 713305.68 
 714803.43 
 716302.76 
 717803.66 
 719306.12 
 720810.16 
 722315.77 
 723822*. 95 
 725331.70 
 726842.02 
 728353.91 
 729867.37 
 731382.40 
 732899.01 
 734417.18 
 735936.93 
 737458.24 
 738981.13 
 740505.59 
 742031.62 
 743559.22 
 745088.39 
 746619. 13 
 748151.44 
 749685 -.32 
 751220.78 
 752757.80 
 754296.40 
 755836.56 
 757378.30 
 758921.61 
 760466.48 
 762012.93 
 763560.95 
 765110.54 
 766661 .70 
 768214.44 
 769768.74 
 771324.61 
 772882.06 
 774441.07 
 776001.66 
 777563.82 
 779127.54 
 780692 . 84 
 782259.71 
 783828.15 
 785398.16 
 
120 CIRCUMFERENCE OP CIRCLES, FEET AND INCHES. 
 
 OONlAiAMOOO- 
 
 ■XOCOO CAT 
 
 T\Q t>>0 — © CN -3- m r^ O — ON'fifilMJOONf mrsOvOOf 
 
 -NtvOMJ- 
 
 ^ "$• vO r» O © - 
 
 ^Tr^N^-ON'TmtN^-ON'rmN 
 
 u — TOO — Tt^OcAvOOcA^OC- 
 
 l-miniri\OvOvOf>.r«.r^coooooooo^OO^O 
 
 vOoOO — — mmvOooO- — cat \O0O© — — CA T ^O CO 0\ — — tr\T \OQ0& — 
 
 - — — cseNCNCMcncAcATTTir 
 
 nvO^OOtstNlNOOOOoOtoaaO^O 
 
 ^oooo-cc,ifii>,cooo-^ift^cooo-t(MnvOooO' tnm>oooo 
 
 ocntu-u^oo©^ 
 
 ni\0»OONc<MnN00OO- CAint^OO©© — C 
 
 +J — ■'^-r^OcA^OC^cAvOO^C- 
 
 +a tf\NO(A^O>Nin!>NiACCI- T rv — ^■tsOff\vOO>(A'00>Nin!0.- moo- 
 
 -; — CN fN CN <* 
 
 rivO»OvO*OtsNNOOOOooaoao 
 
 H >o go o ■ NTj-vOr^o — — fNTvOr*o*-- ©<NT>oi>»t>— ■©NT»ni>.0'>--© 
 
 -Tj-hN,— 
 
 -ivOvOvcot^r^r^ooooooo^o^o^o 
 
 ^ cA T nO GO C - * ■ 
 
 +-j ca vo o n »**> o* n «■* * 
 
 - (NT vO GO C> — — CNT vO r>0^ - 
 
 -oiT \Dr-> o 
 
 '.-cAin-oioo- 
 ; ca vo o^ cs in go — 
 
 nvOoOO ^^-OCOO- 
 
 at\0 ooo* — — cat o 
 
 fl-s 
 
 o — N«i-iriiOMOO>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 (diam. of circle ~- rise of given segment). 
 
 Given chord and rise, to find diameter. Diam. = (square of half chord -s- 
 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 
 
 
 Rise 
 
 
 Rise 
 
 
 Rise 
 
 
 Rise 
 
 
 -*- 
 
 Area. 
 
 -j- 
 
 Area. 
 
 -L- 
 
 Area. 
 
 -i- 
 
 Area, 
 
 -^ 
 
 Area. 
 
 Diam. 
 
 
 Diam: 
 
 
 Diam. 
 
 .04514 
 
 Diam. 
 
 
 Diam. 
 
 
 .001 
 
 .00004 
 
 .054 
 
 •01646 
 
 .107 
 
 .16 
 
 .08111 
 
 .213 
 
 .12235 
 
 .002 
 
 .00012 
 
 .055 
 
 .01691 
 
 .108 
 
 .04576 
 
 .161 
 
 .08185 
 
 .214 
 
 .12317 
 
 .003 
 
 .00022 
 
 .056 
 
 .01737 
 
 .109 
 
 .04638 
 
 .162 
 
 .03258 
 
 .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 
 
 .003 
 
 .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 
 
 .09231. 
 
 .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 
 
 .033 
 
 .03108 
 
 .136 
 
 .06407 
 
 .189 
 
 .10312 
 
 .242 
 
 . 1 4666 
 
 .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 
 
 .00327 
 
 .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 
 
 .15263 
 
 .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 
 
 J 1262 
 
 .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 
 
 .1 
 
 .04087 
 
 .153 
 
 .07603 
 
 .206 
 
 .11665 
 
 .259 
 
 .16139 
 
 .048 
 
 .01382 
 
 .101 
 
 .04148 
 
 .154 
 
 .07675 
 
 .207 
 
 .11746 
 
 .26 
 
 J 6226 
 
 .049 
 
 .01425 
 
 .102 
 
 .04208 
 
 .155 
 
 .07747 
 
 .203 
 
 .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 
 
MATHEMATICAL TABLES. 
 
 Rise 
 
 
 Rise 
 
 
 Rise 
 
 
 Rise 
 
 
 Rise 
 
 
 
 Area. 
 
 -H 
 
 Area. 
 
 ■*■ 
 
 Area. 
 
 •*" 
 
 Area. 
 
 -i- 
 
 Area. 
 
 Diam. 
 
 
 Diam. 
 
 
 Diam. 
 
 
 Diam. 
 
 
 Diam. 
 
 
 .266 
 
 .16755 
 
 .313 
 
 .21015 
 
 .36 
 
 .25455 
 
 .407 
 
 .30024 
 
 .454 
 
 .34676 
 
 .267 
 
 .16843 
 
 .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 
 
 .31008 
 
 .464 
 
 .35673 
 
 .277 
 
 .17733 
 
 .324 
 
 .22040 
 
 .371 
 
 .26514 
 
 .418 
 
 .31107 
 
 .465 
 
 .35773 
 
 .278 
 
 .17823 
 
 .325 
 
 .22134 
 
 .372 
 
 .26611 
 
 .419 
 
 .31205 
 
 .466 
 
 .35873 
 
 .279 
 
 .17912 
 
 .326 
 
 .22228 
 
 .373 
 
 .26708 
 
 .42 
 
 .31304 
 
 .467 
 
 .35972 
 
 .23 
 
 .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 
 
 .3 1 699 
 
 .471 
 
 .36372 
 
 .284 
 
 .18362 
 
 .331 
 
 .22697 
 
 .378 
 
 .27192 
 
 .425 
 
 .31798 
 
 .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 
 
 .283 
 
 .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 
 
 .23332 
 
 .39 
 
 .28359 
 
 .437 
 
 .32987 
 
 .484 
 
 .37670 
 
 .297 
 
 .19542 
 
 .344 
 
 .23927 
 
 .391 
 
 .28457 
 
 .438 
 
 .33086 
 
 .485 
 
 .37770 
 
 .293 
 
 .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 
 
 .33334 
 
 .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 
 
 .24493 
 
 .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 
 
 .303 
 
 .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 61. 
 
 LENGTHS OF CIRCULAR ARCS. 
 
 (Degrees being given. Radius of Circle =■ 1.) 
 
 Formula. — Length of arc — ~ 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 78° 20'. 
 
 Factor from table for 78° 1 .3613568 
 
 Factor from table for 20' .0058178 
 
 Factor. 1.3671746 
 
 1.3671746X55 = 75.19 feet. 
 
LENGTHS OF CIRCULAR ARCS. 
 
 123 
 
 Factors for Lengths of Circular Arcs. 
 
 Degrees. 
 
 Minutes. 
 
 1 
 
 .0174533 
 
 61 
 
 1.0646508 
 
 121. 
 
 2.1118484 
 
 1 
 
 .0002909 
 
 2 
 
 .0349066 
 
 62 
 
 1.0821041 
 
 122 
 
 2.1293017 
 
 2 
 
 .0005818 
 
 3 
 
 .0523599 
 
 63 
 
 1.0995574 
 
 123 
 
 2.1467550 
 
 3 
 
 .0008727 
 
 4 
 
 .0698 1 32 
 
 64 
 
 1.1170107 
 
 124 
 
 2. 1 642083 
 
 4 
 
 .001 1636 
 
 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 
 
 .0026180 
 
 10 
 
 .1745329 
 
 70 
 
 1.2217305 
 
 130 
 
 2.2689280 
 
 10 
 
 .0029089 
 
 11 
 
 .1919862 
 
 71 
 
 1.2391838 
 
 131 
 
 2.2863813 
 
 11 
 
 .003 1 998 
 
 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 
 
 1.4311700 
 
 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 
 
 .0078540 
 
 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 
 
 .0087266 
 
 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 
 
 1.9722221 
 
 173 
 
 3.0194196 
 
 53 
 
 .0154171 
 
 54 
 
 .9424778 
 
 114 
 
 1 .9896753 
 
 174 
 
 3.0368729 
 
 54 
 
 .0157080 
 
 55 
 
 .95993 1 1 
 
 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 TABLES. 
 
 
 
 LENGTHS OF CIRCULAR 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 -*- 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. 1 
 
 .001 
 
 1 .00002 
 
 .15 
 
 1 .05896 
 
 .238 
 
 1.14480 
 
 .326 
 
 1 .26288 
 
 .414 
 
 1.407811 
 
 .005 
 
 1 .00007 
 
 .152 
 
 1.06051 
 
 .24 
 
 1.14714 
 
 .328 
 
 1 .26588 
 
 .416 
 
 1.41141 
 
 .01 
 
 1 .00027 
 
 .154 
 
 1 .06209 
 
 .242 
 
 1.14951 
 
 .33 
 
 1 .26892 
 
 .418 
 
 1.4150 
 
 .015 
 
 1.00061 
 
 .156 
 
 1 .06368 
 
 .244 
 
 1.15189 
 
 .332 
 
 1.27196 
 
 .42 
 
 1.4186 
 
 .02 
 
 1.00107 
 
 .158 
 
 1.06530 
 
 .246 
 
 1.15428 
 
 .334 
 
 1.27502 
 
 .422 
 
 1 .4222 
 
 .025 
 
 1.00167 
 
 .16 
 
 1 .06693 
 
 .248 
 
 1.15670 
 
 .336 
 
 1.27810 
 
 .424 
 
 1.4258: 
 
 .03 
 
 1 .00240 
 
 .162 
 
 1.06353 
 
 .25 
 
 1.15912 
 
 .338 
 
 1.28118 
 
 .426 
 
 1.4294. 
 
 .035 
 
 1.00327 
 
 .164 
 
 1.07025 
 
 .252 
 
 1.16156 
 
 .34 
 
 1 .28428 
 
 .428 
 
 I.4330 1 
 
 .04 
 
 1.00426 
 
 .166 
 
 1.07194 
 
 .254 
 
 1.16402 
 
 .342 
 
 1 .28739 
 
 .43 
 
 1.4367.1 
 
 .045 
 
 1.00539 
 
 .163 
 
 1 .07365 
 
 .256 
 
 1.16650 
 
 .344 
 
 1 .29052 
 
 .432 
 
 1 .4-403'! 
 
 .05 
 
 1.00665 
 
 .17 
 
 1.07537 
 
 .258 
 
 1.16899 
 
 .346 
 
 1.29366 
 
 .434 
 
 1.4440 
 
 055 
 
 1.00305 
 
 .172 
 
 1.07711 
 
 .26 
 
 1.17150 
 
 .348 
 
 1.29681 
 
 .436 
 
 1.4477; 
 
 .05 
 
 1.O0957 
 
 .174 
 
 1.07833 
 
 .262 
 
 1.17403 
 
 .35 
 
 1 .29997 
 
 .438 
 
 1.4514:1 
 
 .055 
 
 1.01123 
 
 .176 
 
 1.03066 
 
 .264 
 
 1.17657 
 
 .352 
 
 1.30315 
 
 .44 
 
 1.4551:1 
 
 .0/ 
 
 1.01302 
 
 .178 
 
 1.03246 
 
 .266 
 
 1.17912 
 
 .354 
 
 1 .30634 
 
 .442 
 
 1.4588:1 
 
 .075 
 
 1.01493 
 
 .18 
 
 1.03423 
 
 .268 
 
 1.18169 
 
 .356 
 
 1.30954 
 
 .444 
 
 1.4625:i 
 
 .03 
 
 1.01693 
 
 .182 
 
 1.03611 
 
 .27 
 
 1.18429 
 
 .358 
 
 1.31276 
 
 .446 
 
 1.46621! 
 
 .035 
 
 1.01916 
 
 .184 
 
 1.08797 
 
 .272 
 
 1.18689 
 
 .36 
 
 1.31599 
 
 .448 
 
 1 .4700; 
 
 .09 
 
 1.02146 
 
 .186 
 
 1.08934 
 
 .274 
 
 1.18951 
 
 .362 
 
 1.31923 
 
 .45 
 
 1.4737; 
 
 .095 
 
 1.02339 
 
 .188 
 
 1.09174 
 
 .276 
 
 1.19214 
 
 .364 
 
 1 .32249 
 
 .452 
 
 1.4775; 
 
 .10 
 
 1.02646 
 
 .19 
 
 1 .09365 
 
 .278 
 
 1.19479 
 
 .366 
 
 1.32577 
 
 .454 
 
 1.4813 j 
 
 .102 
 
 1.02752 
 
 .192 
 
 1.09557 
 
 .28 
 
 1.19746 
 
 .368 
 
 1 .32905 
 
 .456 
 
 1.4850' 1 
 
 .104 
 
 1 .02860 
 
 .194 
 
 1.09752 
 
 .282 
 
 1.20014 
 
 .37 
 
 1.33234 
 
 .458 
 
 1.4888<l 
 
 .106 
 
 1 .02970 
 
 .196 
 
 1 .09949 
 
 .284 
 
 1 .20284 
 
 .372 
 
 1.33564 
 
 .46 
 
 1.4926' I 
 
 .108 
 
 1.03032 
 
 .198 
 
 1.10147 
 
 .286 
 
 1.20555 
 
 .374 
 
 1 .33896 
 
 .462 
 
 1 .4965;] 
 
 .11 
 
 1.03196 
 
 .20 
 
 1.10347 
 
 .288 
 
 1 .20827 
 
 .376 
 
 1 .34229 
 
 .464 
 
 1.5003; 
 
 .112 
 
 1.03312 
 
 .202 
 
 1.10548 
 
 .29 
 
 1.21102 
 
 .378 
 
 1 .34563 
 
 .466 
 
 1.504 If 
 
 .114 
 
 1.03430 
 
 .204 
 
 1.10752 
 
 .292 
 
 1.21377 
 
 .38 
 
 1 .34899 
 
 .468 
 
 1.5080( 
 
 .116 
 
 1.03551 
 
 .206 
 
 1.10958 
 
 .294 
 
 1.21654 
 
 .382 
 
 135237 
 
 .47 
 
 1.5118; 
 
 .118 
 
 1.03672 
 
 .203 
 
 1.11165 
 
 .296 
 
 1.21933 
 
 .384 
 
 1.35575 
 
 .472 
 
 1.51571 
 
 .12 
 
 1.03797 
 
 .21 
 
 1.21374 
 
 .293 
 
 1.22213 
 
 .386 
 
 1.35914 
 
 .474 
 
 1.5195^ 
 
 .122 
 
 1.03923 
 
 .212 
 
 1.11584 
 
 .30 
 
 1 .22495 
 
 .388 
 
 1.36254 
 
 .476 
 
 1.5234( 
 
 .124 
 
 1.04051 
 
 .214 
 
 1.11796 
 
 .302 
 
 1 .22778 
 
 .39 
 
 1.36596 
 
 .478 
 
 1.52736 
 
 .126 
 
 1.04181 
 
 .216 
 
 1.12011 
 
 .304 
 
 1 .23063 
 
 .392 
 
 1 .36939 
 
 .48 
 
 1.53126 
 
 .128 
 
 1.04313 
 
 .218 
 
 1.12225 
 
 .306 
 
 1.23349 
 
 .394 
 
 1 .37283 
 
 .482 
 
 1.53516] 
 
 .13 
 
 1.04447 
 
 .22 
 
 1.12444 
 
 303 
 
 1.23636 
 
 .396 
 
 1.37628 
 
 .484 
 
 1.5391C! 
 
 .132 
 
 1.04534 
 
 .222 
 
 1.12664 
 
 .31 
 
 1 .23926 
 
 .398 
 
 1 .37974 
 
 .486 
 
 1 54302! 
 
 .134 
 
 1.04722 
 
 .224 
 
 1.12885 
 
 .312 
 
 1.24216 
 
 .40 
 
 1 .38322 
 
 .488 
 
 1.54696] 
 
 .136 
 
 1.04362 
 
 .226 
 
 1.13108 
 
 .314 
 
 1 .24507 
 
 .402 
 
 1.38671 
 
 .49 
 
 1.550911 
 
 .138 
 
 1.05003 
 
 .228 
 
 1.13331 
 
 .316 
 
 1.24801 
 
 .404 
 
 1.39021 
 
 .492 
 
 1.55487' 
 
 .14 
 
 1.05147 
 
 .23 
 
 1.13557 
 
 .318 
 
 1 .25095 
 
 .406 
 
 1.39372 
 
 .494 
 
 1.55854 
 
 .142 
 
 1.05293 
 
 .232 
 
 1.13785 
 
 .32 
 
 1.25391 
 
 .408 
 
 1.39724 
 
 .496 
 
 1.56282 
 
 144 
 
 1.05441 
 
 .234 
 
 1.1^015 
 
 .322 
 
 1 .25689 
 
 .41 
 
 1.40077 
 
 .498 
 
 1.56681 
 
 145 
 
 1.05591 
 
 .236 
 
 1.14247 
 
 .324 
 
 1 .25988 
 
 .412 
 
 1 .40432 
 
 .50 
 
 1.57080 
 
 .143 
 
 1.05743 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 SPHEKES. 
 
 
 
 125 
 
 
 
 SPHERES. 
 
 
 (Some errors of 1 
 
 n the last figure only. From Trautwine.) 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 V32 
 
 .00307 
 
 .00002 
 
 31/4 
 
 33.183 
 
 17.974 
 
 9 7/ 8 
 
 306.36 
 
 "504.21 
 
 Vi6 
 
 .01227 
 
 .00013 
 
 5/16 
 
 34.472 
 
 19.031 
 
 10. 
 
 314.16 
 
 523.60 
 
 3/32 
 
 .02761 
 
 .00043 
 
 3/8 
 
 35.784 
 
 20.129 
 
 1/8 
 
 322.06 
 
 543.48 
 
 1/8 
 
 .04909 
 
 .00102 
 
 7/16 
 
 37.122 
 
 21.268 
 
 1/4 
 
 330.06 
 
 563.86 
 
 5 /32 
 
 .07670 
 
 .00200 
 
 1/2 
 
 38.484 
 
 22.449 
 
 3/8 
 
 338.16 
 
 584.74 
 
 3/16 
 
 .11045 
 
 .00345 
 
 9/16 
 
 39.872 
 
 23.674 
 
 1/3 
 
 346.36 
 
 606.13 
 
 7/32 
 
 .15033 
 
 .00548 
 
 5/8 
 
 41.283 
 
 24.942 
 
 5/8 
 
 354.66 
 
 628.04 
 
 1/4 
 
 .19635 
 
 .00818 
 
 H/16 
 
 42.719 
 
 26.254 
 
 3/4 
 
 363.05 
 
 650.46 
 
 9/32 
 
 .2485 1 
 
 .01165 
 
 3/4 
 
 44.179 
 
 27.611 
 
 7/8 
 
 371.54 
 
 673.42 
 
 5/16 
 
 .30680 
 
 .01598 
 
 13/16 
 
 45.664 
 
 29.016 
 
 11. 
 
 380.13 
 
 696.91 
 
 U/32 
 
 .37123 
 
 .02127 
 
 7/8 
 
 47.173 
 
 30.466 
 
 1/8 
 
 388.83 
 
 720.95 
 
 3/8 
 
 .44179 
 
 .02761 
 
 15/16 
 
 48.708 
 
 31.965 
 
 1/4 
 
 397.61 
 
 745.51 
 
 13/32 
 
 .51848 
 
 .03511 
 
 4. 
 
 50.265 
 
 33.510 
 
 3/8 
 
 406.49 
 
 770.64- 
 
 7/16 
 
 .60132 
 
 .04385 
 
 1/8 
 
 53.456 
 
 36.751 
 
 1/2 
 
 415.48 
 
 796.33 
 
 15/32 
 
 .69028 
 
 .05393 
 
 1/4 
 
 56.745 
 
 40.195 
 
 5 /8 
 
 424.50 
 
 822.58 
 
 1/2 
 
 .78540 
 
 .06545 
 
 3/8 
 
 60.133 
 
 43.847 
 
 3/4 
 
 433.73 
 
 849.40 
 
 9/16 
 
 .99403 
 
 .09319 
 
 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 
 
 1/2 
 
 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 
 
 .43143 
 
 1/4 
 
 86.591 
 
 75.767 
 
 1/4 
 
 551.55 
 
 1218.0 
 
 
 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 
 
 .74551 
 
 5/8 
 
 99.401 
 
 93.189 
 
 14. 
 
 615.75 
 
 1436.8 
 
 3/16 
 
 4.4301 
 
 .87681 
 
 3/4 
 
 103.87 
 
 99.541 
 
 1/4 
 
 637.95 
 
 1515.1 
 
 1/4 
 
 4.9088 
 
 1 .0227 
 
 7/8 
 
 108.44 
 
 106.18 
 
 1/2 
 
 660.52 
 
 1596.3 
 
 5/16 
 
 5.4119 
 
 1.1839 
 
 6. 
 
 113.10 
 
 113.10 
 
 3/4 
 
 683.49 
 
 1680.3 
 
 3/8 
 
 5.9396 
 
 1.3611 
 
 1/8 
 
 117.87 
 
 120.31 
 
 15. 
 
 706.85 
 
 1767.2 
 
 7/16 
 
 6.4919 
 
 1.5553 
 
 1/4 
 
 122.72 
 
 127.83 
 
 1/4 
 
 730.63 
 
 1857.0 
 
 1/2 
 
 7.0686 
 
 1.7671 
 
 3/8 
 
 127.68 
 
 135.66 
 
 1/2 
 
 754.77 
 
 1949.8 
 
 9/16 
 
 7.6699 
 
 1 .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 
 
 11/16 
 
 8.9461 
 
 2.5161 
 
 3/4 
 
 143.14 
 
 161.03 
 
 1/4 
 
 829.57 
 
 2246.8 
 
 3/4 
 
 9.6211 
 
 2.8062 
 
 7/8 
 
 148.49 
 
 170.14 
 
 1/2 
 
 855.29 
 
 2352.1 
 
 13/16 
 
 10.321 
 
 3.1177 
 
 7. 
 
 153.94 
 
 179.59 
 
 3/ 4 
 
 881.42 
 
 2460.6 
 
 7/8 
 
 1 1 .044 
 
 3.4514 
 
 1/8 
 
 159.49 
 
 189.39 
 
 17. 
 
 907.93 
 
 2572.4 
 
 15/16 
 
 11.793 
 
 3.8083 
 
 1/4 
 
 165.13 
 
 199.53 
 
 1/4 
 
 934.83 
 
 2687.6 
 
 
 12.566 
 
 4.1888 
 
 3/8 
 
 170.87 
 
 210.03 
 
 1/2 
 
 962.12 
 
 2806.2 
 
 Vl6 
 
 13.364 
 
 4.5939 
 
 1/2 
 
 176.71 
 
 220.89 
 
 3/4 
 
 989.80 
 
 2928.2 
 
 1/8 
 
 14.186 
 
 5.0243 
 
 5/8 
 
 182.66 
 
 232.13 
 
 18. 
 
 1017.9 
 
 3053.6 
 
 3/16 
 
 15.033 
 
 5.4809 
 
 3/4 
 
 188.69 
 
 243.73 
 
 1/4 
 
 1046.4 
 
 3182.6 
 
 1/4 
 
 15.904 
 
 5.9641 
 
 7/8 
 
 194.83 
 
 255.72 
 
 1/2 
 
 1075.2 
 
 3315.3 
 
 5/16 
 
 16.800 
 
 6.4751 
 
 8. 
 
 201.06 
 
 268.08 
 
 3/4 
 
 1104.5 
 
 3451.5 
 
 3/8 
 
 17.721 
 
 7.0144 
 
 1/8 
 
 207.39 
 
 280.85 
 
 19. 
 
 1134.1 
 
 3591.4 
 
 7/18 
 
 18.666 
 
 7.5829 
 
 1/4 
 
 213.82 
 
 294.01 
 
 1/4 
 
 1164.2 
 
 3735.0 
 
 1/2 
 
 19.635 
 
 8.1813 
 
 3/8 
 
 220.36 
 
 307.58 
 
 1/2 
 
 1194.6 
 
 3882.5 
 
 9/16 
 
 20.629 
 
 8.8103 
 
 1/2 
 
 226.98 
 
 321.56 
 
 3/4 
 
 1225.4 
 
 4033.7 
 
 5/8 
 
 21.648 
 
 9.4708 
 
 5/8 
 
 233.71 
 
 335.95 
 
 20. 
 
 1256.7 
 
 4188.8 
 
 H/16 
 
 22.691 
 
 10.164 
 
 3/4 
 
 240.53 
 
 350.77 
 
 1/4 
 
 1288.3 
 
 4347.8 
 
 3/4 
 
 23.758 
 
 10.889 
 
 7/8 
 
 247.45 
 
 366.02 
 
 1/?. 
 
 1320.3 
 
 4510.9 
 
 13/16 
 
 24.850 
 
 1 1 .649 
 
 9. 
 
 254.47 
 
 381.70 
 
 3/4 
 
 1352.7 
 
 4677.9 
 
 7/8 
 
 25.967 
 
 12.443 
 
 1/8 
 
 261.59 
 
 397.83 
 
 21. 
 
 1385.5 
 
 4849.1 
 
 15/16 
 
 27.109 
 
 13.272 
 
 1/4 
 
 268.81 
 
 414.41 
 
 1/4 
 
 1418.6 
 
 5024.3 
 
 
 28.274 
 
 14.137 
 
 3/8 
 
 270.12 
 
 43 1 .44 
 
 1/2 
 
 1452.2 
 
 5203.7 
 
 1/16 
 
 29.465 
 
 15.039 
 
 1/2 
 
 283.53 
 
 448.92 
 
 3/4 
 
 1486.2 
 
 5387.4 
 
 1/8 
 
 30.680 
 
 15.979 
 
 5/8 
 
 291.04 
 
 466.87 
 
 22. 
 
 1520.5 
 
 55753 
 
 3/16 
 
 31.919 
 
 16.957 
 
 3/ 4 
 
 289.65 
 
 435.31 
 
 1/4 '1555.3 
 
 5767.6 
 
126 
 
 
 MATHEMATICAL TABLES. 
 
 
 
 
 
 SPHERES — Continued. 
 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 Diam. 
 
 Sur- 
 face. 
 
 Vol- 
 ume. 
 
 22 1/2 
 
 1590.4 
 
 5964.1 
 
 40 1/2 
 
 5153.1 
 
 34783 
 
 70 1/2 
 
 15615 
 
 183471 
 
 3/4 
 
 1626.0 
 
 6165.2 
 
 41. 
 
 5281.1 
 
 36087 
 
 71. 
 
 15837 
 
 18740? 
 
 23. 
 
 1661.9 
 
 6370.6 
 
 1/2 
 
 5410.7 
 
 37423 
 
 1/2 
 
 16061 
 
 19138? 
 
 V4 
 
 1698.2 
 
 6580.6 
 
 43. 
 
 5541.9 
 
 38792 
 
 
 16286 
 
 195433 
 
 V2 
 
 1735.0 
 
 6795.2 
 
 1/2 
 
 5674.5 
 
 40194 
 
 ' 1/2 
 
 16513 
 
 199532 
 
 3/ 4 
 
 1772.1 
 
 7014.3 
 
 43. 
 
 5808.8 
 
 41630 
 
 73. 
 
 16742 
 
 203689 
 
 24. 
 
 1809.6 
 
 7238.2 
 
 V2 
 
 5944.7 
 
 43099 
 
 1/2 
 
 16972 
 
 207903 
 
 1/4 
 
 1847.5 
 
 7466.7 
 
 44. 
 
 6082.1 
 
 44602 
 
 74. 
 
 17204 
 
 212175 
 
 1/2 
 
 1885.8 
 
 7700.1 
 
 V2 
 
 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 
 
 1/2 
 
 6503.9 
 
 49321 
 
 1/2 
 
 17908 
 
 225341 
 
 1/4 
 
 2002.9 
 
 8429.2 
 
 46. 
 
 6647.6 
 
 50965 
 
 78. 
 
 18146 
 
 229848 
 
 V2 
 
 2042.8 
 
 8682.0 
 
 1/2 
 
 6792.9 
 
 52645 
 
 1/2 
 
 18386 
 
 234414 
 
 3/4 
 
 2083.0 
 
 8939.9 
 
 47. 
 
 6939.9 
 
 54362 
 
 77. 
 
 18626 
 
 239041 
 
 26. 
 
 2123.7 
 
 9202.8 
 
 v 2 
 
 7088.3 
 
 56115 
 
 1/2 
 
 18869 
 
 243728 
 
 • 1/4 
 
 2164.7 
 
 9470.8 
 
 48. 
 
 7238.3 
 
 57906 
 
 78. 
 
 19114 
 
 248475 
 
 V2 
 
 2206.2 
 
 9744.0 
 
 V2 
 
 7389.9 
 
 59734 
 
 1/2 
 
 19360 
 
 253284 
 
 3 /4 
 
 2248.0 
 
 10022 
 
 49. 
 
 7543.1 
 
 61601 
 
 79. 
 
 19607 
 
 258155 
 
 27. 
 
 2290.2 
 
 10306 
 
 V2 
 
 7697.7 
 
 63506 
 
 1/2 
 
 19856 
 
 26308S 
 
 V4 
 
 2332.8 
 
 10595 
 
 50. 
 
 7854.0 
 
 65450 
 
 80. 
 
 20106 
 
 268083 
 
 V2 
 
 2375.8 
 
 10889 
 
 1/2 
 
 8011.8 
 
 67433 
 
 1/2 
 
 20358 
 
 273141 
 
 3/4 
 
 2419.2 
 
 11189 
 
 51. 
 
 8171.2 
 
 69456 
 
 81. 
 
 20612 
 
 278263 
 
 28. 
 
 2463.0 
 
 11494 
 
 V2 
 
 8332.3 
 
 71519 
 
 1/2 
 
 20867 
 
 283447 
 
 Vi 
 
 2507.2 
 
 11805 
 
 52. 
 
 8494.8 
 
 73622 
 
 82. 
 
 21124 
 
 288696 
 
 V2 
 
 2551.8 
 
 12121 
 
 V2 
 
 8658.9 
 
 75767 
 
 1/2 
 
 21382 
 
 294010 
 
 3/4 
 
 2596.7 
 
 12443 
 
 53. 
 
 8824.8 
 
 77952 
 
 83. 
 
 21642 
 
 299388 
 
 29. 
 
 2642.1 
 
 12770 
 
 V2 
 
 8992.0 
 
 80178 
 
 1/2 
 
 21904 
 
 304831- 
 
 V4 
 
 2687.8 
 
 13103 
 
 54. 
 
 9160.8 
 
 82448 
 
 84. 
 
 22167 
 
 310340 
 
 V2 
 
 2734.0 
 
 13442 
 
 1/2 
 
 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 
 
 V4 
 
 2874.8 
 
 14494 
 
 58. 
 
 9852.0 
 
 91953 
 
 86. 
 
 23235 
 
 333039 
 
 . V2 
 
 2922.5 
 
 14856 
 
 V2 
 
 10029 
 
 94438 
 
 1/2 
 
 23506 
 
 338882 
 
 3/4 
 
 2970.6 
 
 15224 
 
 57. 
 
 10207 
 
 96967 
 
 87. 
 
 23779 
 
 344792 
 
 31c 
 
 3019.1 
 
 15599 
 
 1/2 
 
 10387 
 
 99541 
 
 1/2 
 
 24053 
 
 350771 
 
 V4 
 
 3068.0 
 
 15979 
 
 58. 
 
 10568 
 
 102161 
 
 88. 
 
 24328 
 
 356819 
 
 V2 
 
 3117.3 
 
 16366 
 
 1/2 
 
 10751. 
 
 104826 
 
 1/2 
 
 24606 
 
 362935 
 
 3/4 
 
 3166.9 
 
 16758 
 
 59. 
 
 10936 
 
 107536 
 
 89. 
 
 24885 
 
 369122 
 
 32. 
 
 3217.0 
 
 17157 
 
 1/2 
 
 11122 
 
 110294 
 
 1/2 
 
 25165 
 
 375378 
 
 V4 
 
 3267.4 
 
 17563 
 
 60. 
 
 11310 
 
 113098 
 
 90. 
 
 25447 
 
 381704 
 
 V2 
 
 3318.3 
 
 17974 
 
 1/2 
 
 11499 
 
 115949 
 
 1/2 
 
 25730 
 
 388102 
 
 3/4 
 
 3369.6 
 
 18392 
 
 61. 
 
 11690 
 
 118847 
 
 91. 
 
 26016 
 
 394570 
 
 33. 
 
 3421.2 
 
 18817 
 
 V2 
 
 11882 
 
 121794 
 
 1/2 
 
 26302 
 
 401109 
 
 V4 
 
 3473.3 
 
 19248 
 
 63. 
 
 12076 
 
 124789 
 
 92. 
 
 26590 
 
 407721 
 
 V2 
 
 3525.7 
 
 19685 
 
 1/2 
 
 12272 
 
 127832 
 
 1/2 
 
 26880 
 
 414405 
 
 3/4 
 
 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 
 
 V2 
 
 3739.3 
 
 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 
 
 1/2 
 
 28652 
 
 456047 
 
 36. 
 
 4071.5 
 
 24429 
 
 66. 
 
 13685 
 
 150533 
 
 98. 
 
 28953 
 
 463248 J 
 
 V2 
 
 4185.5 
 
 25461 
 
 1/2 
 
 13893 
 
 1 53980 
 
 1/2 
 
 29255 
 
 470524 
 
 37. 
 
 4300.9 
 
 26522 
 
 67. 
 
 14103 
 
 157480 
 
 97. 
 
 29559 
 
 477874 
 
 V2 
 
 4417.9 
 
 27612 
 
 1/2 
 
 .14314 
 
 161032 
 
 1/2 
 
 29865 
 
 485302 
 
 38. 
 
 4536.5 
 
 28731 
 
 68. 
 
 14527 
 
 164637 
 
 98. 
 
 30172 
 
 492803 J 
 
 1/2 
 
 4656.7 
 
 29880 
 
 1/2 
 
 14741 
 
 168295 
 
 1/2 
 
 30481 
 
 500388 
 
 39. 
 
 4778.4 
 
 31059 
 
 69. 
 
 14957 
 
 172007 
 
 99. 
 
 30791 
 
 508047 
 
 V2 
 
 4901.7 
 
 32270 
 
 1/2 
 
 15175 
 
 175774 
 
 V? 
 
 31103 
 
 515785 
 
 40. 
 
 5026.5 
 
 33510 
 
 70. 
 
 15394 
 
 179595 100. 
 
 31416 
 
 523 593 
 
 
 
 
 
 
 
 
 
 
CAPACITY OF CYLINDRICAL VESSELS. 
 
 127 
 
 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 
 
 .5 
 
 1 
 
 For 1 Foot in 
 
 
 For 1 Foot in 
 
 83 i 
 
 i-s 
 
 , | a 
 
 Length . 
 
 Len 
 
 gth. 
 
 .5 
 
 Length. 
 
 Cu.Ft. 
 
 U.S. 
 
 Cu.Ft. 
 
 U.S. 
 
 Cu.Ft. 
 
 U.S. 
 
 also 
 
 Gals., 
 
 also 
 
 Gals., 
 
 also 
 
 Gals.. 
 
 5 
 
 Area in 
 
 231 
 
 5 
 
 Area in 
 
 231 
 
 fl M 
 
 Area in 
 
 231 
 
 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 
 
 2 074 
 
 15.51 
 
 3/8 
 
 .0008 
 
 .0057 
 
 71/4 
 
 .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 
 
 211/2 
 
 2.521 
 
 18.86 
 
 5/8 
 
 .0021 
 
 .0159 
 
 81/4 
 
 .3712 
 
 2.777 
 
 22 
 
 2.640 
 
 19.75 
 
 H/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 
 
 13/16 
 
 .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 
 
 10l/ 2 
 
 .6013 
 
 4.498 
 
 29 
 
 4.587 
 
 34.31 
 
 2 
 
 .0218 
 
 .1632 
 
 103/4 
 
 .6303 
 
 4.715 
 
 30 
 
 4.909 
 
 36.72 
 
 |2l/ 4 
 
 .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 
 
 IH/2 
 
 .7213 
 
 5.396 
 
 33 
 
 5.940 
 
 44.43 
 
 3 
 
 .0491 
 
 .3672 
 
 1 1 3/4 
 
 .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 
 
 131/2 
 
 .994 
 
 7.436 
 
 38 
 
 7.876 
 
 58.92 
 
 41/4 
 
 .0985 
 
 .7369 
 
 14 
 
 1.069 
 
 7.997 
 
 39 
 
 8.296 
 
 62.06 
 
 41/2 
 
 .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 
 
 1.020 
 
 151/2 
 
 1.310 
 
 9.801 
 
 42 
 
 9.621 
 
 71.97 
 
 51/4 
 
 .1503 
 
 1.125 
 
 16 
 
 1.396 
 
 10.44 
 
 43 
 
 10.085 
 
 75.44 
 
 51/2 
 
 .1650 
 
 1.234 
 
 161/2 
 
 1.485 
 
 11.11 
 
 44 
 
 10.559 
 
 78.99 
 
 53/4 
 
 .1803 
 
 1.349 
 
 17 
 
 1.576 
 
 11.79 
 
 45 
 
 11.045 
 
 82.62 
 
 6 
 
 .1963 
 
 1.469 
 
 171/2 
 
 1.670 
 
 12.49 
 
 46 
 
 11.541 
 
 86.33 
 
 61/ 4 
 
 .2131 
 
 1.594 
 
 18 
 
 1.768 
 
 13.22 
 
 47 
 
 12.048 
 
 90.10 
 
 61/2 
 
 .2304 
 
 1.724 
 
 181/2 
 
 1.867 
 
 13.96 
 
 48 
 
 12.566 
 
 94.00 
 
 To find the capacity of pipes greater than the largest given in the table, 
 look in the table for a pipe of one-half the given size, and multiply its capa- 
 city by 4; or one of one-third its size, and multiply its capacity by 9, etc. 
 
 To find the weight of water in any of the given sizes, multiply the capacity 
 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. S. 
 gallons: Square the diameter, multiply by the length and by 0.0034. If d = 
 
 rf2vn 78^4. V / 
 
 diameter, I = length, gallons = OQ , = 0.0034 &1. If D and L are 
 
 in feet, gallons = 5.875 D 2 L. 
 
 231 
 
128 
 
 
 MATHEMATICAL 
 
 TABLES. 
 
 
 
 CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC. 
 
 Diameter in 
 
 Feet and Inches, Area in Square Feet, and V. S. 
 
 
 Gallons Capacity 
 
 for One Foot in Depth. 
 
 
 1 gallon = 231 cubic inches 
 
 1 cubic foot 
 7.4805 
 
 D. 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 1 
 
 .922 
 
 6.89 
 
 5 9 
 
 25.97 
 
 194.25 
 
 19 3 
 
 291.04 
 
 2177.1 
 
 1 2 
 
 1.069 
 
 8.00 
 
 5 10 
 
 26.73 
 
 199.92 
 
 19 6 
 
 298.65 
 
 2234.0 
 
 1 3 
 
 1.227 
 
 9.18 
 
 5 11 
 
 27.49 
 
 205.67 
 
 19 9 
 
 306.35 
 
 2291.7 
 
 1 4 
 
 1.396 
 
 10.44 
 
 G 
 
 28.27 
 
 211.51 
 
 20 
 
 314.16 
 
 2350.1 
 
 1 5 
 
 1.576 
 
 11.79 
 
 6 3 
 
 30.68 
 
 229.50 
 
 20 3 
 
 322.06 
 
 2409.2 
 
 1 6 
 
 1.767 
 
 13.22 
 
 6 6 
 
 33.18 
 
 248.23 
 
 20 6 
 
 330.C6 
 
 2469.1 
 
 I 7 
 
 1.969 
 
 14.73 
 
 6 9 
 
 35.78 
 
 267.69 
 
 20 9 
 
 338.16 
 
 2529.6 
 
 1 8 
 
 2.182 
 
 16.32 
 
 7 
 
 38.48 
 
 287.88 
 
 21 
 
 346.36 
 
 2591.0 
 
 1 9 
 
 2.405 
 
 17.99 
 
 7 3 
 
 41.28 
 
 308.81 
 
 21 3 
 
 354.66 
 
 2653.0 
 
 1 10 
 
 2.640 
 
 19.75 
 
 7 6 
 
 44.18 
 
 330.48 
 
 21 6 
 
 363.05 
 
 2715.8 
 
 1 11 
 
 2.885 
 
 21.58 
 
 7 9 
 
 47.17 
 
 352.88 
 
 21 9 
 
 371.54 
 
 2779.3 
 
 2 
 
 3.142 
 
 23.50 
 
 8 
 
 50.27 
 
 376.01 
 
 22 
 
 380.13 
 
 2843.6 
 
 2 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 
 
 3 1 
 
 7.467 
 
 55.86 
 
 11 3 
 
 99.40 
 
 743.58 
 
 25 3 
 
 500.74 
 
 3745.8 
 
 3 2 
 
 7.876 
 
 58.92 
 
 11 6 
 
 103.87 
 
 776.99 
 
 25 6 
 
 510.71 
 
 3820.3 
 
 3 3 
 
 8.296 
 
 62.06 
 
 11 9 
 
 108.43 
 
 811.14 
 
 25 9 
 
 520.77 
 
 3895.6 
 
 3 4 
 
 8.727 
 
 65.28 
 
 12 
 
 113.10 
 
 846.03 
 
 26 
 
 530.93 
 
 3971.6 
 
 3 5 
 
 9.168 
 
 68.58 
 
 12 3 
 
 117.86 
 
 881.65 
 
 26 3 
 
 541.19 
 
 4048.4 
 
 3 6 
 
 9.621 
 
 71.97 
 
 12 6 
 
 122.72 
 
 918.00 
 
 26 6 
 
 551.55 
 
 4125.9 
 
 3 7 
 
 10.085 
 
 75.44 
 
 12 9 
 
 127.68 
 
 955.09 
 
 . 26 9 
 
 562.00 
 
 4204.1 
 
 3 8 
 
 10.559 
 
 78.99 
 
 13 
 
 132.73 
 
 992.91 
 
 27 
 
 572.56 
 
 4283.0 
 
 3 9 
 
 1 1 .045 
 
 82.62 
 
 13 3 
 
 137.89 
 
 1031.5 
 
 27 3 
 
 583.21 
 
 4362.7 
 
 3 10 
 
 11.541 
 
 86.33 
 
 13 6 
 
 143.14 
 
 1070.8 
 
 27 6 
 
 593.96 
 
 4443.1 
 
 3 11 
 
 12.048 
 
 90.13 
 
 13 9 
 
 148.49 
 
 1110.8 
 
 27 9 
 
 604.81 
 
 4524.3 
 
 4 
 
 12.566 
 
 94.00 
 
 14 
 
 153.94 
 
 1151.5 
 
 28 
 
 615.75 
 
 4606.2 
 
 4 1 
 
 13.095 
 
 97.96 
 
 14 3 
 
 159.48 
 
 1193.0 
 
 28 3 
 
 626.80 
 
 4688.8 
 
 4 2 
 
 13.635 
 
 102.00 
 
 14 6 
 
 165.13 
 
 1235.3 
 
 28 6 
 
 637.94 
 
 4772.1 
 
 4 3 
 
 14.186 
 
 106.12 
 
 14 9 
 
 170.87 
 
 1278.2 
 
 28 9 
 
 649.18 
 
 4856.2 
 
 4 4 
 
 14.748 
 
 110.32 
 
 15 
 
 176.71 
 
 1321.9 
 
 29 
 
 660.52 
 
 4941.0 
 
 4 5 
 
 15.321 
 
 114.61 
 
 15 3 
 
 182.65 
 
 1366.4 
 
 29 3 
 
 671.96 
 
 5026.6 
 
 4 6 
 
 15.90 
 
 118.97 
 
 15 6 
 
 188.69 
 
 1411.5 
 
 29 6 
 
 683.49 
 
 5112.9 
 
 4 7 
 
 16.50 
 
 123.42 
 
 15 9 
 
 194.83 
 
 1457.4 
 
 29 9 
 
 695.13 
 
 5199.9 
 
 4 8 
 
 17.10 
 
 127.95 
 
 16 
 
 201.06 
 
 1504.1 
 
 30 
 
 706.86 
 
 5287.7 
 
 4 9 
 
 17.72 
 
 132.56 
 
 16 3 
 
 207.39 
 
 1551.4 
 
 30 3 
 
 718.69 
 
 5376.2 
 
 4 10 
 
 18.35 
 
 137.25 
 
 16 6 
 
 213.82 
 
 1599.5 
 
 30 6 
 
 730.62 
 
 5465.4 
 
 4 11 
 
 18.99 
 
 142.02 
 
 16 9 
 
 220.35 
 
 1648.4 
 
 30 9 
 
 742.64 
 
 5555.4 
 
 5 
 
 19.63 
 
 146.88 
 
 17 
 
 226.98 
 
 1697.9 
 
 31 
 
 754.77 
 
 5646.1 
 
 5 1 
 
 20.29 
 
 151.82 
 
 17 3 
 
 233.71 
 
 1748.2 
 
 31 3 
 
 766.99 
 
 5737.5 
 
 5 2 
 
 20.97 
 
 156.83 
 
 17 6 
 
 240.53 
 
 1 799.3 
 
 31 6 
 
 779.31 
 
 5829.7 
 
 5 3 
 
 21.65 
 
 161.93 
 
 17 9 
 
 247.45 
 
 1851.1 
 
 31 9 
 
 791.73 
 
 5922.6 
 
 5 4 
 
 22.34 
 
 167.12 
 
 18 
 
 254.47 
 
 1903.6 
 
 32 
 
 804.25 
 
 6016.2 
 
 5 5 
 
 23.04 
 
 172.38 
 
 18 3 
 
 261.59 
 
 1956.8 
 
 32 3 
 
 816.86 
 
 6110.6 
 
 5 6 
 
 23.76 
 
 177.72 
 
 18 6 
 
 268.80 
 
 2010.8 
 
 32 6 
 
 829.58 
 
 6205.7 
 
 5 7 
 
 24.48 
 
 183.15 
 
 18 9 
 
 276.12 
 
 2065.5 
 
 32 9 
 
 842.39 
 
 6301.5 
 
 
 
 
 
 
 
 
 
 
GALLONS AND CUBIC FEET. 
 
 129 
 
 GALLONS AND CUBIC FEET. 
 
 United States Gallons in a given Number of Cubic Feet. 
 
 cubic foot = 7.480519 U.S. gallons; 1 gallon = 231 cu.in. = 0.13368056cu.ft. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 0.1 
 0.2 
 0.3 
 0.4 
 0.5 
 
 0.75 
 1.50 
 
 2.24 
 2.99 
 3.74 
 
 50 
 60 
 70 
 80 
 90 
 
 374.0 
 448.8 
 523.6 
 598.4 
 673.2 
 
 8,000 
 9,000 
 10,000 
 20,000 
 30,000 
 
 59,844.2 
 
 67,324.7 
 
 74,805.2 
 
 149,610.4 
 
 224.415.6 
 
 0.6 
 0.7 
 0.8 
 0.9 
 
 1 
 
 4.49 
 5.24 
 5.98 
 6.73 
 
 7.48 
 
 100 
 200 
 300 
 400 
 500 
 
 748.0 
 1,496.1 
 2,244.2 
 2,992.2 
 3,740.3 
 
 40,000 
 50,000 
 60,000 
 70,000 
 80,000 
 
 299,220.8 
 374,025.9 
 448,831.1 
 523,636.3 
 598,441.5 
 
 2 
 3 
 
 4 
 
 5 
 6 
 
 14.96 
 
 22.44 
 29.92 
 37.40 
 44.88 
 
 600 
 700 
 800 
 900 
 1,000 
 
 4,488.3 
 5,236.4 
 5,984.4 
 6,732.5 
 7,480.5 
 
 90,000 
 100,000 
 200,000 
 300,000 
 400,000 
 
 673,246. 
 
 748,051.9 
 1,496,103.8 
 2,244,155.7 
 2,992,207.6 
 
 7 
 8 
 9 
 10 
 20 
 
 52.36 
 
 59.84 
 67.32 
 74.80 
 149.6 
 
 2,000 
 3,000 
 4,000 
 5,000 
 6,000 
 
 14,961.0 
 22,441.6 
 29,922.1 
 37,402.6 
 44,883.1 
 
 500,000 
 600,000 
 700,000 
 800,000 
 900,000 
 
 3,740,259.5 
 4,488,3.11.4 
 5,236,363.3 
 5,984,415.2 
 6,732,467.1 
 
 30 
 40 
 
 224.4 
 299.2 
 
 7,000 
 
 52,363.6 
 
 1,000,000 
 
 7,480,519.0 
 
 Cubic Feet in a given Number of Gallons. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 Gallons. 
 
 Cubic Ft. 
 
 1 
 
 .134 
 
 1,000 
 
 133.681 
 
 1,000,000 
 
 133,680.6 
 
 2 
 
 .267 
 
 2,000 
 
 267.361 
 
 2,000,000 
 
 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 1 
 
 Cu. ft. per sec. 
 Cu. ft. per min. 
 U. S. Gals, per min. 
 " 24hrs. 
 Pounds of water ) 
 (at 62° F.) per min. J 
 The gallon is a troublesome and unnecessary measure, 
 engineers and pump manufacturers would stop using it, and use cubic 
 feet instead, many tedious calculations would be saved, 
 
 7.480519 
 10,771.95 
 
 62.355 
 
 448.31 
 646,317 
 3741.3 
 
 1.5472 
 92.834 
 694.444 
 1,000,000 
 
 5788.66 
 
 2.2801 
 133.681 
 1,000. 
 1,440,000 
 
 8335.65 
 If hydraulic 
 
130 
 
 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. lsq.in.= 
 
 0.00694/9 sq.ft. 
 
 Ft. and 
 
 Ins. 
 
 Square 
 
 Ft. and 
 
 Ins. 
 Long. 
 
 Ins. 
 
 Square 
 
 Ft. and 
 
 Ins. 
 Long. 
 
 Ins. 
 
 Square 
 Feet. : 
 
 Ins. 
 Long. 
 
 Long. 
 
 Feet. 
 
 Long. 
 
 Feet. 
 
 Long. 
 
 3. 
 
 36 
 
 .25 
 
 7. 10 
 
 94 
 
 .6528 
 
 12. 8 
 
 152 
 
 1.056 
 
 1 
 
 37 
 
 .2569 
 
 11 
 
 95 
 
 .6597 
 
 9 
 
 153 
 
 1.063 
 
 2 
 
 38 
 
 .2639 
 
 8. 
 
 96 
 
 .6667 
 
 10 
 
 154 
 
 1.069 
 
 3 
 
 39 
 
 .2708 
 
 1 
 
 97 
 
 .6736 
 
 11 
 
 155 
 
 1.076 
 
 4 
 
 40 
 
 .2778 
 
 2 
 
 98 
 
 .6806 
 
 13. 
 
 156 
 
 1.083 
 
 5 
 
 41 
 
 .2847 
 
 3 
 
 99 
 
 .6875 
 
 1 
 
 157 
 
 1.09 
 
 6 
 
 42 
 
 .2917 
 
 4 
 
 100 
 
 .6944 
 
 2 
 
 158 
 
 1.097 
 
 7 
 
 43 
 
 .2986 
 
 5 
 
 101 
 
 .7014 
 
 3 
 
 159 
 
 1.104 
 
 8 
 
 44 
 
 .3056 
 
 6 
 
 102 
 
 .7083 
 
 4 
 
 160 
 
 1.114 
 
 9 
 
 45 
 
 . .3125 
 
 7 
 
 103 
 
 .7153 
 
 5 
 
 161 
 
 1.118 
 
 10 
 
 46 
 
 .3194 
 
 8 
 
 104 
 
 .7222 
 
 6 
 
 162 
 
 1.125 
 
 11 
 
 47 
 
 .3264 
 
 9 
 
 105 
 
 .7292 
 
 7 
 
 163 
 
 1.132 
 
 4. 
 
 48 
 
 .3333 
 
 10 
 
 106 
 
 .7361 
 
 8 
 
 164 
 
 1.139 
 
 1 
 
 49 
 
 .3403 
 
 11 
 
 107 
 
 .7431 
 
 9 
 
 165 
 
 1.146 
 
 2 
 
 50 
 
 .3472 
 
 9. 
 
 108 
 
 .75 
 
 10 
 
 166 
 
 1.153 
 
 3 
 
 51 
 
 .3542 
 
 1 
 
 109 
 
 .7569 
 
 11 
 
 167 
 
 1.159 
 
 4 
 
 52 
 
 .36.1 1 
 
 2 
 
 110 
 
 .7639 
 
 14. 
 
 168 
 
 1.167 
 
 5 
 
 53 
 
 .3681 
 
 3 
 
 111 
 
 .7708 
 
 1 
 
 169 
 
 1.174 
 
 6 
 
 54 
 
 .375 
 
 4 
 
 112 
 
 .7778 
 
 2 
 
 170 
 
 1.181 
 
 7 
 
 55 
 
 .3819 
 
 5 
 
 113 
 
 .7847 
 
 3 
 
 171 
 
 1.188 
 
 8 
 
 56 
 
 .3889 
 
 6 
 
 114 
 
 .7917 
 
 4 
 
 172 
 
 1.194 
 
 9 
 
 57 
 
 .3958 
 
 7 
 
 115 
 
 .7986 
 
 5 
 
 173 
 
 1.201 
 
 10 
 
 58 
 
 .4028 
 
 8 
 
 116 
 
 .8056 
 
 6 
 
 174 
 
 1.208 
 
 11 
 
 59 
 
 .4097 
 
 9 
 
 117 
 
 .8125 
 
 7 
 
 175 
 
 1.215 
 
 5. 
 
 60 
 
 .4167 
 
 10 
 
 118 
 
 .8194 
 
 8 
 
 176 
 
 1.222 
 
 1 
 
 61 
 
 .4236 
 
 11 
 
 119 
 
 .8264 
 
 9 
 
 177 
 
 1.229 
 
 2 
 
 62 
 
 .4306 
 
 10. o 
 
 120 
 
 .8333 
 
 10 
 
 178 
 
 1.236 
 
 3 
 
 63 
 
 .4375 
 
 1 
 
 121 
 
 .8403 
 
 11 
 
 179 
 
 1.243 
 
 4 
 
 64 
 
 .4444 
 
 2 
 
 122 
 
 .8472 
 
 15. 
 
 180 
 
 1.25 
 
 5 
 
 65 
 
 .4514 
 
 3 
 
 123 
 
 .8542 
 
 1 
 
 181 
 
 1.257 
 
 6 
 
 66 
 
 .4583 
 
 4 
 
 124 
 
 .8611 
 
 2 
 
 182 
 
 1.264 
 
 7 
 
 67 
 
 .4653 
 
 5 
 
 125 
 
 .8681 
 
 3 
 
 183 
 
 1.271 
 
 8 
 
 68 
 
 .4722 
 
 6 
 
 126 
 
 .875 
 
 4 
 
 184 
 
 1.278 
 
 9 
 
 69 
 
 .4792 
 
 7 
 
 127 
 
 .8819 
 
 5 
 
 185 
 
 1.285 
 
 10 
 
 70 
 
 .4861 
 
 8 
 
 128 
 
 .8889 
 
 6 
 
 186 
 
 1.292 
 
 11 
 
 71 
 
 .4931 
 
 9 
 
 129 
 
 .8958 
 
 7 
 
 187 
 
 1.299 
 
 6. 
 
 72 
 
 .5 
 
 10 
 
 130 
 
 .9028 
 
 8 
 
 188 
 
 1.306 
 
 1 
 
 73 
 
 .5069 
 
 11 
 
 131 
 
 .9097 
 
 9 
 
 189 
 
 . 1.313 
 
 2 
 
 74 
 
 .5139 
 
 11. o 
 
 132 
 
 .9167 
 
 10 
 
 190 
 
 1.319 
 
 3 
 
 75 
 
 .5208 
 
 1 
 
 133 
 
 .9236 
 
 11 
 
 191 
 
 1.326 
 
 4 
 
 76 
 
 .5278 
 
 2 
 
 134 
 
 .9306 
 
 16. 
 
 192 
 
 1.333 
 
 5 
 
 77 
 
 .5347 
 
 3 
 
 135 
 
 .9375 
 
 1 
 
 193 
 
 1.34 
 
 6 
 
 78 
 
 .5417 
 
 4 
 
 136 
 
 .9444 
 
 2 
 
 194 
 
 1.347 
 
 7 
 
 79 
 
 .5486 
 
 5 
 
 137 
 
 .9514 
 
 3 
 
 195 
 
 1.354 
 
 8 
 
 80 
 
 .5556 
 
 6 
 
 138 
 
 .9583 
 
 4 
 
 196 
 
 1.361 
 
 9 
 
 81 
 
 .5625 
 
 7 
 
 139 
 
 .9653 
 
 5 
 
 197 
 
 1.368 
 
 10 
 
 82 
 
 .5694 
 
 8 
 
 140 
 
 .9722 
 
 6 
 
 198 
 
 1.375 
 
 11 
 
 83 
 
 .5764 
 
 9 
 
 141 
 
 .9792 
 
 7 
 
 199 
 
 1.382 
 
 7. 
 
 84 
 
 .5834 
 
 10 
 
 142 
 
 .9861 
 
 8 
 
 200 
 
 1.389 
 
 1 
 
 85 
 
 .5903 
 
 11 
 
 143 
 
 .9931 
 
 9 
 
 201 
 
 1.396 
 
 2 
 
 86 
 
 .5972 
 
 12. 
 
 144 
 
 1.000 
 
 10 
 
 202 
 
 1.403 i 
 
 3 
 
 87 
 
 .6042 
 
 t 
 
 145 
 
 1.007 
 
 11 
 
 203 
 
 1.41 
 
 4 
 
 88 
 
 .6111 
 
 2 
 
 146 
 
 1.014 
 
 17. 
 
 204 
 
 1.417 
 
 5 
 
 89 
 
 .6181 
 
 3 
 
 147 
 
 1.021 
 
 1 
 
 205 
 
 1.424 
 
 6 
 
 90 
 
 .625 
 
 4 
 
 148 
 
 1.028 
 
 2 
 
 206 
 
 1.431 
 
 7 
 
 91 
 
 .6319 
 
 5 
 
 149 
 
 1.035 
 
 3 
 
 207 
 
 1.438 
 
 8 
 
 92 
 
 .6389 
 
 6 
 
 150 
 
 1.042 
 
 4 
 
 208 
 
 1.444 
 
 9 
 
 93 
 
 .6458 
 
 7 
 
 151 
 
 1.049 
 
 5 
 
 209 
 
 1.451 
 
 
 
 
 
 
 
 
 
 
NUMBER OF SQUARE FEET IN PLATES. 
 
 131 
 
 
 SQUARE FEET 
 
 IN PLATES.— 
 
 Continued. 
 
 
 Ft .and 
 
 Ins. 
 
 Long. 
 
 Ins. 
 
 Square 
 
 Ft. and 
 
 Ins. 
 Long. 
 
 Ins. 
 
 Square 
 
 Ft. and 
 Ins. 
 Long. 
 
 Ins. 
 
 Square 
 
 Long. 
 
 Feet. 
 
 Long. 
 
 Feet. 
 
 Long 
 
 Feet. 
 
 17. 6 
 
 210 
 
 1.458 
 
 22. 5 
 
 269 
 
 1.868 
 
 27o 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 
 
 II 
 
 275 
 
 1.91 
 
 10 
 
 334 
 
 2.319 
 
 1 
 
 217 
 
 1.507 
 
 23. 
 
 276 
 
 1.917 
 
 11 
 
 335 
 
 2.326 
 
 2 
 
 218 
 
 1.514 
 
 1 
 
 211 
 
 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 
 
 i 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 
 
 1 
 
 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 
 
 1 
 
 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 
 
 1 
 
 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 
 
 11 
 
 251 
 
 1.743 
 
 10 
 
 310 
 
 2.153 
 
 9 
 
 369 
 
 2.563 
 
 21. 
 
 252 
 
 1.75 
 
 11 
 
 311 
 
 2.16 
 
 10 
 
 370 
 
 2.569 
 
 1 
 
 253 
 
 1.757 
 
 26. 
 
 312 
 
 2.167 
 
 11 
 
 371 
 
 2.576 
 
 2 
 
 254 
 
 1.764 
 
 1 
 
 313 
 
 2.174 
 
 31. 
 
 372 
 
 2.583 
 
 3 
 
 255 
 
 1.771 
 
 2 
 
 314 
 
 2.181 
 
 1 
 
 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 
 
 2.61 1 
 
 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. 
 
 264 
 
 1.833 
 
 11 
 
 323 
 
 2.243 
 
 10 
 
 382 
 
 2.653 
 
 1 
 
 265 
 
 1.84 
 
 27. 
 
 324 
 
 2.25 
 
 11 
 
 333 
 
 2.66 
 
 2 
 
 266 
 
 1.847 
 
 1 
 
 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.(81 
 
132 
 
 MATHEMATICAL TABLES, 
 
 CAPACITIES OP RECTANGULAR TANKS IN TJ. S. 
 GALLONS, FOR EACH FOOT IN DEPTH. 
 
 1 cubic foot = 7.4805 U. S. gallons. 
 
 Width 
 
 of 
 Tank. 
 
 Length of Tank. 
 
 feet. ft. in. feet. ft. in 
 2 2 6 3 3 6 
 
 feet. ft. in 
 4 4 6 
 
 feet. ft. in. feet. ft. in. 
 5 5 6 6 6 6 
 
 feet. 
 
 7 
 
 ft. 
 2 
 2 
 3 
 3 
 4 
 
 4 
 5 
 5 
 6 
 6 
 
 37.40 
 46.75 
 
 52.36 
 65.45 
 78.54 
 91.64 
 
 59.84 
 74.80 
 89.77 
 104.73 
 1 19.69 
 
 67.32 
 84.16 
 100.99 
 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 
 170.1 
 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 
 
 
 Length of Tank. 
 
 Width 
 
 
 of 
 
 
 
 
 
 
 
 
 
 
 Tank. 
 
 ft. in 
 
 feet. 
 
 ft. in 
 
 feet. 
 
 ft. in 
 
 feet. 
 
 ft. in 
 
 feet. 
 
 ft. in 
 
 feet. 
 
 
 7 6 
 
 8 
 
 8 6 
 
 9 
 
 9 6 
 
 10 
 
 10 6 
 
 11 
 
 11 6 
 
 12 
 
 ft. in. 
 2 
 
 112.21 
 
 119.69 
 
 127.17 
 
 134.65 
 
 142.13 
 
 149.61 
 
 157.09 
 
 164.57 
 
 172.05 
 
 179.53 
 
 2 6 
 
 140.26 
 
 149.61 
 
 158.96 
 
 168.31 
 
 177.66 
 
 187.01 
 
 196.36 
 
 205.71 
 
 215.06 
 
 224.41 
 
 3 
 
 168.31 
 
 179.53 
 
 190.75 
 
 202.97 
 
 213.19 
 
 224.41 
 
 235.63 
 
 246.86 
 
 258.07 
 
 269.30 
 
 3 6 
 
 196.36 
 
 209.45 
 
 222.54 
 
 235.63 
 
 248.73 
 
 261.82 
 
 274.9C 
 
 288.00 
 
 301.09 
 
 314.18 
 
 4 
 
 224.41 
 
 239.37 
 
 254.34 
 
 269.30 
 
 284.26 
 
 299.22 
 
 314.18 
 
 329.14 
 
 344.10 
 
 359.06 
 
 4 6 
 
 252.47 
 
 269.30 
 
 286.13 
 
 302.96 
 
 319.79 
 
 336.62 
 
 353.45 
 
 370.28 
 
 387.11 
 
 403.94 
 
 5 
 
 280.52 
 
 299.22 
 
 317.92 
 
 336.62 
 
 355.32 
 
 374.03 
 
 392.72 
 
 411.43 
 
 430.13 
 
 448.83 
 
 5 6 
 
 308.57 
 
 329.14 
 
 349.71 
 
 370.28 
 
 390.85 
 
 411.43 
 
 432.00 
 
 452.57 
 
 473.1' 
 
 493.71 
 
 6 
 
 336.62 
 
 359.06 
 
 381.50 
 
 403.94 
 
 426.39 
 
 448.83 
 
 471.27 
 
 493.71 
 
 516.15 
 
 538.59 
 
 6 6 
 
 364.67 
 
 388.98 
 
 413.30 
 
 437.60 
 
 461.92 
 
 486.23 
 
 510.54 
 
 534.85 
 
 559.16 
 
 583.47 
 
 7 
 
 392.72 
 
 418.91 
 
 445.09 
 
 471 .27 
 
 497.45 
 
 523.64 
 
 549.81 
 
 575.99 
 
 602.18 
 
 628.36 
 
 7 6 
 
 420.78 
 
 448.83 
 
 476.88 
 
 504.93 
 
 532.98 
 
 561.04 
 
 589.08 
 
 617.14 
 
 645.19 
 
 673.24 
 
 8 
 
 
 478.75 
 
 508.67 
 
 538.59 
 
 568.51 
 
 598.44 
 
 628.36 
 
 658.28 
 
 688.20 
 
 718.12 
 
 8 6 
 
 
 
 540.46 
 
 572.25 
 
 604.05 
 
 635.84 
 
 667.63 
 
 699.42 
 
 731.21 
 
 763.00 
 
 9 
 
 
 
 
 605.92 
 
 639.58 
 
 673.25 
 
 706.90 
 
 740.56 
 
 774.23 
 
 807.89 
 
 9 6 
 
 
 
 
 
 675.11 
 
 710.65 
 
 746. 1 7 
 
 781.71 
 
 817.24 
 
 852.77 
 
 10 
 
 
 
 
 
 
 748.05 
 
 785.45 
 
 822.86 
 
 860.26 
 
 897.66 
 
 10 6 
 
 
 
 
 
 
 
 824.73 
 
 864.00 
 
 903.26 
 
 942.56 
 
 11 
 
 
 
 
 
 
 
 
 905.14 
 
 946.27 
 
 987.43 
 
 11 6 
 
 
 
 
 
 
 
 
 
 989.29 
 
 1032.3 
 
 12 
 
 
 
 
 
 
 
 ... j ... 
 
 
 1077.2 
 
CAPACITY OF CYLINDRICAL CISTERNS AND TANKS. 133 
 
 NUMBER OF BARRELS (31 1-2 GALLONS) IN 
 CISTERNS AND TANKS. 
 
 I barrel = 3 1 J^ j 
 
 31.5X 231 
 1728 
 
 = 4.21094 cu. ft. Reciprocal = 0.2 37 477 
 
 Depth 
 
 in 
 Feet. 
 
 
 
 
 Diameter 
 
 in Feet 
 
 
 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 13 
 
 13 
 
 14 
 
 1 
 
 4.663 
 
 6.714 
 
 9.139 
 
 11.937 
 
 15.108 
 
 18.652 
 
 22.569 
 
 26.859 
 
 31.522 
 
 36.557 
 
 5 
 
 23.3 
 
 33.6 
 
 45.7 
 
 59.7 
 
 75.5 
 
 93.3 
 
 112.8 
 
 134.3 
 
 157.6 
 
 182.8 
 
 6 
 
 28.0 
 
 40.3 
 
 54.8 
 
 71.6 
 
 90.6 
 
 111.9 
 
 135.4 
 
 161.2 
 
 189.1 
 
 219.3 
 
 7 
 
 32.6 
 
 47.0 
 
 64.0 
 
 83.6 
 
 105.8 
 
 130.6 
 
 158.0 
 
 188.0 
 
 220.7 
 
 255.9 
 
 8 
 
 37.3 
 
 53.7 
 
 73.1 
 
 95.5 
 
 120.9 
 
 149.2 
 
 180.6 
 
 214.9 
 
 252.2 
 
 292.5 
 
 9 
 
 42.0 
 
 60.4 
 
 62.3 
 
 107.4 
 
 136.0 
 
 167.9 
 
 203.1 
 
 241.7 
 
 283.7 
 
 329.0 
 
 10 
 
 46.6 
 
 67.1 
 
 91.4 
 
 119.4 
 
 151.1 
 
 186.5 
 
 225.7 
 
 268.6 
 
 315.2 
 
 365.6 
 
 11 
 
 51.3 
 
 73.9 
 
 100.5 
 
 131.3 
 
 166.2 
 
 205.2 
 
 248.3 
 
 295.4 
 
 346.7 
 
 402.1 
 
 12 
 
 56.0 
 
 80.6 
 
 109.7 
 
 143.2 
 
 181.3 
 
 223.8 
 
 270.8 
 
 322.3 
 
 378.3 
 
 438.7 
 
 13 
 
 60.6 
 
 87.3 
 
 118.8 
 
 155.2 
 
 196.4 
 
 242.5 
 
 293.4 
 
 349.2 
 
 409.8 
 
 475.2 
 
 14 
 
 65.3 
 
 94.0 
 
 127.9 
 
 167.1 
 
 211.5 
 
 261.1 
 
 316.0 
 
 376.0 
 
 441.3 
 
 511.8 
 
 15 
 
 69.9 
 
 100.7 
 
 137.1 
 
 179.1 
 
 226.6 
 
 279.8 
 
 338.5 
 
 402.9 
 
 472.8 
 
 548.4 
 
 16 
 
 74.6 
 
 107.4 
 
 146.2 
 
 191.0 
 
 241.7 
 
 298.4 
 
 361.1 
 
 429.7 
 
 504.4 
 
 584.9 
 
 17 
 
 79.3 
 
 114.1 
 
 155.4 
 
 202.9 
 
 256.8 
 
 317.1 
 
 383.7 
 
 456.6 
 
 535.9 
 
 621.5 
 
 18 
 
 83.9 
 
 120.9 
 
 164.5 
 
 214.9 
 
 271.9 
 
 335.7 
 
 406.2 
 
 483.5 
 
 567.4 
 
 658.0 
 
 19 
 
 88.6 
 
 127.6 
 
 173.6 
 
 226.8 
 
 287.1 
 
 354.4 
 
 428.8 
 
 510.3 
 
 598.9 
 
 694.6 
 
 20 
 
 93.3 
 
 134.3 
 
 182.8 
 
 238.7 
 
 302.2 
 
 373.0 
 
 451.4 
 
 537.2 
 
 630.4 
 
 731.1 
 
 Depth 
 
 
 
 
 Diameter 
 
 in Feet. 
 
 
 
 
 Feet. 
 
 15 
 
 1G 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 1 
 5 
 6 
 7 
 8 
 
 41.966 
 209.8 
 251.8 
 293.8 
 335.7 
 
 47.748 
 238.7 
 286.5 
 334.2 
 382.0 
 
 53.903 
 269.5 
 323.4 
 377.3 
 431.2 
 
 60.431 
 302.2 
 362.6 
 423.0 
 
 483.4 
 
 67.332 
 336.7 
 404.0 
 471.3 
 538.7 
 
 74.606 
 373.0 
 447.6 
 522.2 
 596.8 
 
 82.253 
 411.3 
 493.5 
 575.8 
 658.0 
 
 90.273 
 451.4 
 541.6 
 631.9 
 722.2 
 
 9 
 10 
 11 
 12 
 13 
 
 377.7 
 419.7 
 461.6 
 503.6 
 545.6 
 
 429.7 
 477.5 
 525.2 
 573.0 
 620.7 
 
 485.1 
 539.0 
 592.9 
 646.8 
 700.7 
 
 543.9 
 604.3 
 664.7 
 725.2 
 785.6 
 
 606.0 
 673.3 
 740.7 
 808.0 
 875.3 
 
 671.5 
 746.1 
 820.7 
 895.3 
 969.9 
 
 740.3 
 
 822.5 
 904.8 
 987.0 
 1069.3 
 
 812.5 
 902.7 
 993.0 
 1083.3 
 1173.5 
 
 14 
 15 
 16 
 17 
 18 
 
 587.5 
 629.5 
 671.5 
 713.4 
 755.4 
 
 668.5 
 716.2 
 764.0 
 811.7 
 859.5 
 
 754.6 
 
 808.5 
 862.4 
 916.4 
 970.3 
 
 846.0 
 906.5 
 966.9 
 1027.3 
 1087.8 
 
 942.6 
 1010.0 
 1077.3 
 1144.6 
 1212.0 
 
 1044.5 
 1119.1 
 1193.7 
 1268.3 
 1342.9 
 
 1151.5 
 1233.8 
 1316.0 
 1398.3 
 1480.6 
 
 1263.8 
 1354.1 
 1444.4 
 1534.5 
 1624.9 
 
 19 
 20 
 
 797.4 
 839.3 
 
 907.2 
 955.0 
 
 1024.2 
 1078.1 
 
 1148.2 
 1208.6 
 
 1279.3 
 1346.6 
 
 1417.5 
 1492.1 
 
 1562.8 
 1645.1 
 
 1715.2 
 1805.5 
 
134 
 
 MATHEMATICAL TABLES. 
 
 NUMBER OF BARRELS (31 1-3 GALLONS) IN CISTERNS 
 AND TANKS. — Continued. 
 
 Depth 
 
 
 
 
 Diametei 
 
 in Feet 
 
 
 
 
 Feet. 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 1 
 5 
 6 
 7 
 8 
 
 98.666 
 
 493.3 
 
 592.0 
 
 690.7 
 
 789.3 
 
 107.432 
 537.2 
 644.6 
 752.0 
 859.5 
 
 116.571 
 582.9 
 699.4 
 816.0 
 932.6 
 
 126.083 
 630.4 
 756.5 
 882.6 
 
 1008.7 
 
 135.968 
 679.8 
 815.8 
 951.8 
 
 1087.7 
 
 146.226 
 731.1 
 
 877.4 
 1023.6 
 1169.8 
 
 157.858 
 784.3 
 941.1 
 1098.0 
 1254.9 
 
 167.863 
 839.3 
 1007.2 
 1175.0 
 1342.9 
 
 9 
 10 
 11 
 12 
 13 
 
 888.0 
 986.7 
 1085.3 
 1184.0 
 1282.7 
 
 966.9 
 
 1074.3 
 1181.8 
 1289.2 
 1396.6 
 
 1049.1 
 
 1165.7 
 1282.3 
 1398.8 
 1515.4 
 
 1134.7 
 1260.8 
 1386.9 
 1513.0 
 1639.1 
 
 1223.7 
 1359.7 
 1495.6 
 1631.6 
 1767.6 
 
 1316.0 
 1462.2 
 1608.5 
 1754.7 
 1900.9 
 
 1411.7 
 1568.6 
 1725.4 
 1882.3 
 2039.2 
 
 1510.8 
 1678.6 
 1846.5 
 2014.4 
 2182.2 
 
 14 
 15 
 16 
 17 
 18 
 
 1381.3 
 1480.0 
 1578.7 
 1677.3 
 1776.0 
 
 1504.0 
 1611.5 
 1718.9 
 1826.3 
 1933.8 
 
 1632.0 
 1748.6 
 1865.1 
 1981.7 
 2098.3 
 
 1765.2 
 1891.2 
 2017.3 
 2143.4 
 2269.5 
 
 1903.6 
 2039.5 
 2175.5 
 2311.5 
 2447.4 
 
 2047.2 
 2193.4 
 2339.6 
 2485.8 
 2632.0 
 
 2196.0 
 2352.9 
 2509.7 
 2666.6 
 2823.4 
 
 2350.1 
 2517.9 
 2685.8 
 2853.7 
 3021.5 
 
 19 
 20 
 
 1874.7 
 1973.3 
 
 2041.2 
 2148.6 
 
 2214.8 
 2321.4 
 
 2395.6 
 2521.7 
 
 2583.4 
 2719.4 
 
 2778.3 
 2924.5 
 
 2980.3 
 3137.2 
 
 3189.4 
 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 x. 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 4- is 0, from 
 10 to 99.99 + is 1, from 100 to 999 + 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 
 
 " " 200 " 2.30103 
 
 " " 20 " 1.30103 
 
 " " 2 " 0.30103 
 
 log of 0.2 is - 1.30103, or 9.30103 - 10 
 " " 0.02 " - 2.30103, " 8.30103 - 10 
 " " 0.002 " - 3.30103, " 7.30103 - 10 
 " " 0.0002 " - 4.30103, " 6.30103 - 10 
 
LOGARITHMS OF NUMBERS- 135 
 
 The minus sign is frequently written above the characteristic thus: 
 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 
 jmall table on page 136. 
 
 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, 
 vhich 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 
 point, then prefix the index according to rule; the index is one less than 
 the number of figures to the left of the decimal point. 
 
 Required log of 3.141593. 
 
 log of 3.141 =0.497068. Diff. = 138 
 
 From proportional parts 5 = 690 
 
 09 = 1242 
 
 003 = 041 
 
 log 3.141593 0.4971498 
 
 To find the number corresponding to a given log. — Find in the 
 
 table the log nearest to the 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 than the given 
 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 U 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 h- 138 = 0.59 + 
 The index being 0, the number is therefore 3.14159 +. 
 
 To multiply two numbers by the 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/6 = 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 
 by the index of the root. The quotient is the log of the root. 
 
136 
 
 LOGARITHMS OF NUMBERS. 
 
 To find the reciprocal of a number. — Subtract the decimal part 
 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 iound 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 loga:ithm 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 — 6+ 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 
 
 (596 \ 2 - 4 5 
 j , which means divide 526 by 1011 and raise the 
 
 quotient to the 2.45 power. 
 
 log 526 == 2.720986 
 log 1011 = 3.004751 
 log of quotient = 
 Multiply by 
 
 10 
 
 = 9.716235- 
 2.45 
 .48581175 
 3.8864940 
 19.432470 
 23.80477575 - (10 X 2.45) = 1.30477575 = 0.20173, Ans. 
 
 Logarithms of Numbers from 1 to 100. 
 

 
 
 
 LOGARITHMS OF NUMBERS. 
 
 
 
 
 137 
 
 No. 100 L. 000.] 
 
 
 [No. 109 L. 040. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 346! 
 
 9 
 
 "389 
 
 Diff. 
 
 100 
 
 000000 
 
 0434 
 
 0868 
 
 1301 
 
 1734 
 
 2166 
 
 2598 
 
 3029 
 
 'l 432 
 
 1 
 
 4321 
 
 4751 
 
 5181 
 
 5609 
 
 6038 
 
 6466 
 
 6894 
 
 7321 
 
 7748 
 
 8174 428 
 
 2 
 
 86^ ft 
 
 9026 
 
 9451 
 
 9876 
 
 
 
 
 
 
 
 
 
 
 0300 
 
 4521 
 
 0724 
 
 1147 
 5360 
 
 1570 
 5779 
 
 1993 
 6197 
 
 2415 424 
 6616 420 
 
 3 
 
 012837 
 
 3259 
 
 3680 
 
 4100 
 
 4940 
 
 i 4 
 
 70^ 
 
 7451 
 
 7868 
 
 8284 
 
 8700 
 
 9116 
 
 9532 
 
 9947 
 
 
 
 
 
 
 0361 
 
 0775 416 
 
 
 
 
 
 
 
 
 
 
 5 
 
 021189 
 
 1603 
 
 2016 
 
 2428 
 
 2841 
 
 3252 
 
 3664 
 
 4075 
 
 4486 
 
 4896 412 
 
 6 
 
 5306 
 
 5715 
 
 6125 
 
 6533 
 
 6942 
 
 7350 
 
 7757 
 
 8164 
 
 8571 
 
 8978 408 
 
 7 
 
 
 9789 
 
 
 
 
 
 
 
 
 
 
 
 
 0195 
 
 4227 
 
 0600 
 
 4628 
 
 1004 
 5029 
 
 1408 
 5430 
 
 1812 
 5830 
 
 2216 
 6230 
 
 2619 
 6629 
 
 3021 404 
 7028 400 
 
 8 
 
 033424 
 
 3826 
 
 9 
 
 74 9A 
 
 7825 
 
 8223 
 
 8620 
 
 9017 
 
 9414 
 
 9811 
 
 
 
 
 
 04 
 
 
 0207 
 
 0602 
 
 0998 397 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 303.8 
 
 8 
 
 9 
 
 434 
 
 43.4 
 
 86.8 
 
 130.2 
 
 173.6 
 
 217.0 
 
 260.4 
 
 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 
 
 338.8 
 
 431 
 
 43.1 
 
 86.2 
 
 129.3 
 
 172.4 
 
 215.5 
 
 258.6 
 
 301.7 
 
 344.8 
 
 337.9 
 
 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 
 
 293.2 
 
 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 
 
 378.0 
 
 419 
 
 41.9 
 
 83.8 
 
 125.7 
 
 167.6 
 
 209.5 
 
 251.4 
 
 293.3 
 
 335.2 
 
 377.1 
 
 413 
 
 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 
 
 411 
 
 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 
 
 403 
 
 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 
 
 393 
 
 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 
 
 7< 
 
 ).0 
 
 
 18.5 
 
 158.( 
 
 ) 
 
 197.5 
 
 
 237.0 
 
 276.5 1 
 
 316.0 ' 
 
 355.5 
 
138 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 110 L. 041.] 
 
 [No. 119 L. 078. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 110 
 
 1 
 2 
 
 04)393 
 5323 
 
 9218 
 
 1787 
 5714 
 9606 
 
 2182 
 6105 
 9993 
 
 2576 
 6495 
 
 2969 
 6885 
 
 3362 
 7275 
 
 3755 
 7664 
 
 4148 
 8053 
 
 4540 
 8442 
 
 4932 
 8830 
 
 393 
 
 390 
 
 0380 
 4230 
 8046 
 
 0766 
 4613 
 8426 
 
 1153 
 4996 
 8805 
 
 1538 
 5378 
 9185 
 
 1924 
 5760 
 9563 
 
 2309 
 6142 
 9942 
 
 2694 
 6524 
 
 386 
 383 
 
 3 
 4 
 
 053078 
 6905 
 
 3463 
 7286 
 
 3846 
 7666 
 
 0320 
 4083 
 7815 
 
 379 
 376 
 373 
 
 5 
 
 6 
 7 
 
 060693 
 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 
 
 370 
 366 
 363 
 
 8 
 9 
 
 071882 
 
 5547 
 
 2250 
 5912 
 
 2617 
 6276 
 
 2985 
 6640 
 
 3352 
 7004 
 
 Proportional Parts. 
 
 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 
 
 118.2 
 
 157.6 
 
 197.0 
 
 236.4 
 
 275.8 
 
 315.2 
 
 354.6 
 
 393 
 
 39.3 
 
 78.6 
 
 117.9 
 
 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 
 
 351.0 
 
 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 
 
 346.5 
 
 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 
 
 190.0 
 
 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 
 
 1.11.9 
 
 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 
 
 321.3 
 
 356 
 
 35.6 
 
 71.2 
 
 106.8 
 
 142.4 
 
 178.0 
 
 213.6 
 
 249.2 
 
 284.8 
 
 320.4 
 
LOGARITHMS OF NUMBERS. 
 
 139 
 
 No. 120 L. 079.] 
 
 
 
 
 
 
 
 [No 
 
 134 L 
 
 . 130. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 120 
 
 079181 
 
 9543 
 
 
 
 
 
 
 
 
 
 
 
 0266 
 3861 
 7426 
 
 0626 
 4219 
 7781 
 
 0987 
 4576 
 8136 
 
 1347 
 4934 
 8490 
 
 1707 
 5291 
 8845 
 
 2067 
 5647 
 9198 
 
 2426 
 6004 
 9552 
 
 360 
 357 
 
 355 
 
 1 
 
 2 
 3 
 
 082785 
 6360 
 9905 
 
 3144 
 6716 
 
 3503 
 7071 
 
 0258 
 3772 
 7257 
 
 0611 
 4122 
 7604 
 
 0963 
 4471 
 7951 
 
 1315 
 4320 
 8298 
 
 1667 
 5169 
 8644 
 
 2018 
 5518 
 8990 
 
 2370 
 5866 
 9335 
 
 2721 
 6215 
 9681 
 
 3071 
 6562 
 
 352 
 349 
 
 4 
 5 
 
 093422 
 6910 
 
 0026 
 3462 
 6871 
 
 346 
 343 
 341 
 
 6 
 7 
 8 
 
 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 
 
 338 
 335 
 
 333 
 
 9 
 
 130 
 
 110590 
 
 3943 
 7271 
 
 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 
 
 330 
 328 
 325 
 
 2 
 3 
 4 
 
 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 
 
 323 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 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 
 
 69.4 
 
 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 
 
 307.3 
 
 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 
 
 33y 
 
 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 
 
 239.8 
 
140 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 135 L. 130.] 
 
 
 
 
 
 
 
 [No 
 
 . 149 L. 175. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 135 
 
 6 
 7 
 8 
 
 130334 
 3539 
 6721 
 9879 
 
 0o55 
 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 
 
 321 
 318 
 316 
 
 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 
 
 314 
 311 
 
 309 
 
 9 
 140 
 
 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 
 
 307 
 305 
 30? 
 
 2 
 3 
 4 
 
 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 
 
 301 
 299 
 297 
 295 
 
 5 
 6 
 
 7 
 
 161368 
 4353 
 
 7317 
 
 1667 
 4650 
 7613 
 
 1967 
 4947 
 7908 
 
 2266 
 5244 
 8203 
 
 2564 
 5541 
 8497 
 
 2863 
 5838 
 8792 
 
 8 
 9 
 
 1 70262 
 3186 
 
 0555 
 
 3478 
 
 0848 
 3769 
 
 1141 
 4060 
 
 1434 
 4351 
 
 1726 
 4641 
 
 2019 
 4932 
 
 2311 
 5222 
 
 2603 
 5512 
 
 2895 
 5802 
 
 293 
 291 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 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 
 
 288.0 
 
 319 
 
 31.9 
 
 63.8 
 
 95.7 
 
 127.6 
 
 159.5 
 
 191.4 
 
 223.3 
 
 255.2 
 
 28>.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 
 
 180 6 
 
 210.7 
 
 240.8 
 
 270.9 
 
 300 
 
 30.0 
 
 60.0 
 
 90.0 
 
 120.0 
 
 150.0 
 
 180.0 
 
 210.0 
 
 240.0 
 
 270.G 
 
 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 
 
 143.0 
 
 177.6 
 
 207.2 
 
 236.8 
 
 266.4 
 
 295 
 
 29.5 
 
 59.0 
 
 8S.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 
 
 261.0 
 
 289 
 
 28.9 
 
 57.8 
 
 86.7 
 
 115.6 
 
 144.5 i 
 
 173.4 
 
 202.3 
 
 231.2 
 
 260.1 
 
 288 
 
 28.8 
 
 57.6 
 
 86.4 
 
 115.2 
 
 144.0 
 
 172.8 
 
 20'. 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 
 
 257.4 
 
LOGARITHMS OF NUMBERS. 
 
 141 
 
 No. 150 L. 176.] 
 
 
 
 
 
 
 
 [No. 
 
 169 L. 230 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 DiflF. 
 
 150 
 
 176091 
 8977 
 
 6381 
 9264- 
 
 6670 
 9552 
 
 6959 
 
 7248 
 
 7536 
 
 7825 
 
 8113 
 
 8401 
 
 8689 
 
 289 
 
 ' 
 
 
 0126 
 2985 
 5825 
 8647 
 
 0413 
 3270 
 6108 
 8928 
 
 0699 
 3555 
 6391 
 9209 
 
 0986 
 3839 
 6674 
 9490 
 
 1272 
 4123 
 6956 
 9771 
 
 1558 
 4407 
 7239 
 
 287 
 285 
 283 
 
 2 
 3 
 4 
 
 181844 
 4691 
 7521 
 
 2129 
 4975 
 7803 
 
 2415 
 5259 
 8084 
 
 2700 
 5542 
 8366 
 
 0051 
 2846 
 5623 
 6382 
 
 281 
 279 
 278 
 276 
 
 5 
 6 
 7 
 8 
 
 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 
 
 274 
 272 
 
 271 
 269 
 
 9 
 
 160 
 
 1 
 2 
 
 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 
 
 267 
 266 
 264 
 262 
 
 3 
 
 4 
 5 
 
 212188 
 4844 
 7484 
 
 2454 
 5109 
 7747 
 
 6 
 7 
 8 
 9 
 
 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 
 
 261 
 259 
 258 
 
 0193 
 
 256 
 
 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 
 
 284 
 
 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 
 
 247.3 
 
 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 
 
 253 
 
 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 
 
 1530 
 
 178.5 
 
 204.0 
 
 229.5 
 
142 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 170 L. 230. 
 
 
 
 
 
 
 
 
 [No 
 
 . 189 L. 278. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 170 
 1 
 
 2 
 3 
 
 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 
 
 0050 
 
 254-1 
 5019 
 7482 
 9932 
 
 0300 
 2790 
 5266 
 7728 
 
 250 
 
 249 
 248 
 246 
 
 4 
 5 
 6 
 7 
 
 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 
 
 245 
 243 
 242 
 
 241 
 239 
 
 8 
 9 
 
 180 
 
 1 
 
 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 
 
 2 
 3 
 4 
 5 
 6 
 
 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 
 
 238 
 237 
 235 
 234 
 
 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 
 
 233 
 232 
 230 
 229 
 
 7 
 8 
 9 
 
 271842 
 4158 
 6462 
 
 2074 
 4389 
 6692 
 
 2306 
 4620 
 6921 
 
 Proportional, Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 1 
 
 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 
 
 169.4 
 
 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 
 
 92.0 
 
 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 
 
LOGARITHMS OP NUMBERS. 
 
 143 
 
 No. 190 L. 278.] 
 
 
 
 
 
 
 
 [No 
 
 214 L 
 
 .332. 
 
 N. 
 
 
 
 1 
 
 2 1 3 1 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diflf. 
 
 190 
 
 278754 
 
 8982 
 
 9211 
 
 943S 
 
 9667 
 
 9895 
 
 
 
 
 
 
 0123 
 2396 
 4656 
 6905 
 9143 
 
 0351 
 2622 
 4882 
 7130 
 9366 
 
 0576 
 
 2845 
 5107 
 7354 
 9589 
 
 0806 
 3075 
 
 5332 
 7578 
 9812 
 
 228 
 .227 
 226 
 225 
 223 
 
 1 
 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 
 
 5 
 6 
 7 
 8 
 9 
 
 290035 
 2256 
 4466 
 6665 
 8853 
 
 0257 
 
 2478 
 4687 
 6884 
 9071 
 
 0480 
 2699 
 4907 
 7104 
 9289 
 
 0702 
 2920 
 5 127 
 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 
 
 2331 
 
 4491 
 6639 
 8778 
 
 0378 
 
 2547 
 4706 
 6854 
 8991 
 
 0595 
 
 2764 
 4921 
 7068 
 9204 
 
 0813 
 
 2980 
 5136 
 7282 
 9417 
 
 218 
 
 217 
 216 
 215 
 213 
 
 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 
 
 0056 
 2177 
 4289 
 6390 
 8481 
 
 0268 
 2389 
 4499 
 6599 
 8689 
 
 0481 
 2600 
 4710 
 6809 
 8898 
 
 0693 
 2812 
 4920 
 7018 
 9106 
 
 0906 
 3023 
 5130 
 7227 
 9314 
 
 1118 
 3234 
 5340 
 7436 
 9522 
 
 1330 
 3445 
 5551 
 7646 
 9730 
 
 1542 
 3656 
 5760 
 7854 
 9938 
 
 212 
 21J 
 210 
 209 
 208 
 
 5 
 6 
 7 
 8 
 
 311754 
 3867 
 5970 
 8063 
 
 1966 
 4078 
 6180 
 8272 
 
 9 
 
 210 
 
 1 
 
 2 
 3 
 
 320146 
 
 2219 
 4282 
 6336 
 8380 
 
 0354 
 
 2426 
 4488 
 6541 
 8583 
 
 0562 
 
 2633 
 4694 
 6745 
 8787 
 
 0769 
 
 2839 
 4899 
 6950 
 8991 
 
 0977 
 
 3046 
 5105 
 7155 
 9194 
 
 1184 
 
 3252 
 5310 
 7359 
 9398 
 
 1391 
 
 3458 
 5516 
 7563 
 9601 
 
 1598 
 
 3665 
 5721 
 7767 
 9805 
 
 1805 
 
 3871 
 5926 
 7972 
 
 0008 
 2034 
 
 2012 
 
 4077 
 6131 
 8176 
 
 207 
 
 206 
 205 
 204 
 
 0211 
 2236 
 
 203 
 202 
 
 4 
 
 330414 1 0617 
 
 0819 
 
 1022 
 
 1225 
 
 14271 1630 
 
 1832 
 
 
 
 
 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 
 
 111.0 
 
 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 
 
 20/ 
 
 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 1 
 
 40.4 1 
 
 60.6 
 
 80.8 1 
 
 101.0 1 
 
 121.2 
 
 141.4 1 
 
 161.6 
 
 181.8 
 
144 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 215 L. 332.] 
 
 [No. 239 L. 380. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 "4253 
 6260 
 8257 
 
 Diff. 
 
 215 
 6 
 
 7 
 8 
 
 332438 
 4454 
 6460 
 8456 
 
 2640 
 4655 
 6660 
 8656 
 
 2842 
 4856 
 6860 
 8855 
 
 3044 
 5057 
 7060 
 9054 
 
 3246 
 5257 
 7260 
 9253 
 
 3447 
 5458 
 7459 
 9451 
 
 3649 
 5658 
 7659 
 9650 
 
 3850 
 5859 
 7858 
 9849 
 
 4051 
 6059 
 8058 
 
 202 
 201 
 200 
 
 0047 
 2028 
 
 3999 
 5962 
 7915 
 9860 
 
 0246 
 2225 
 
 4196 
 6157 
 8110 
 
 199 
 198 
 
 197 
 196 
 195 
 
 9 
 
 220 
 
 1 
 
 2 
 3 
 
 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 
 
 194 
 193 
 193 
 192 
 191 
 190 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 350248 
 2183 
 4108 
 6026 
 7935 
 9835 
 
 0442 
 2375 
 4301 
 6217 
 8125 
 
 0636 
 2568 
 4493 
 6408 
 8316 
 
 0215 
 
 2105 
 
 3988 
 5862 
 7729 
 9587 
 
 0829 
 2761 
 4685 
 6599 
 8506 
 
 1023 
 2954 
 4876 
 6790 
 8696 
 
 1216 
 3147 
 5068 
 6981 
 8886 
 
 1410 
 3339 
 5260 
 7172 
 9076 
 
 1796 
 
 3724 
 5643 
 7554 
 9456 
 
 0025 
 
 1917 
 3800 
 5675 
 7542 
 9401 
 
 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 
 
 1539 
 
 3424 
 5301 
 7169 
 9030 
 
 189 
 
 188 
 188 
 187 
 186 
 
 230 
 
 1 
 
 2 
 3 
 4 
 
 361728 
 3612 
 5433 
 7356 
 9216 
 
 0143 
 1991 
 3831 
 5664 
 7488 
 9306 
 
 0328 
 2175 
 4015 
 5846 
 7670 
 9487 
 
 0513 
 2360 
 4198 
 6029 
 7852 
 9668 
 
 0698 
 
 2544 
 4382 
 6212 
 8034 
 9849 
 
 0883 
 2728 
 4565 
 6394 
 8216 
 
 185 
 184 
 184 
 183 
 182 
 
 5 
 6 
 7 
 8 
 9 
 
 371063 
 2912 
 4743 
 6577 
 8398 
 
 38 
 
 1253 
 3096 
 4932 
 6759 
 8580 
 
 1437 
 3280 
 5115 
 6942 
 8761 
 
 1622 
 3464 
 5298 
 7124 
 8943 
 
 1806 
 3647 
 5481 
 7306 
 9124 
 
 0030 
 
 181 
 
 
 
 
 
 Proportional 
 
 Parts. 
 
 
 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 202 
 
 20.2 
 
 40.4 
 
 60.6 
 
 80.8 
 
 101.0 
 
 121.2 
 
 141.4 
 
 161.6 
 
 181.8 
 
 ?,01 
 
 20.1 
 
 40.2 
 
 60.3 
 
 80.4 
 
 100.5 
 
 120.6 
 
 140.7 
 
 160.8 
 
 180.9 
 
 7.00 
 
 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 
 
 179.1 
 
 193 
 
 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 
 
 156.0 
 
 175. S 
 
 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 
 
 19.0 
 
 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 
 
 183 
 
 18.8 
 
 37.6 
 
 56.4 
 
 75.2 
 
 94.0 
 
 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 
 
 144.0 
 
 162.0 
 
 179 
 
 17.9 
 
 35.8 
 
 53.7 
 
 71.6 
 
 89.5 
 
 107.4 
 
 125.3 
 
 143.2 
 
 161.1 
 
LOGARITHMS OF NUMBERS. 
 
 145 
 
 No. 240 L. 380.] 
 
 
 
 
 
 
 
 [No 
 
 269 L. 431. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 T656 
 3456 
 5249 
 7034 
 8811 
 
 9 
 
 Diff. 
 
 240 
 1 
 
 2 
 3 
 4 
 5 
 
 3802 1 1 
 2017 
 3815 
 5606 
 7390 
 9166 
 
 0392 
 2197 
 3995 
 5785 
 7568 
 9343 
 
 0573 
 2377 
 4174 
 5964 
 7746 
 9520 
 
 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 
 
 181 
 180 
 179 
 178 
 
 178 
 
 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 
 
 177 
 176 
 176 
 175 
 174 
 
 173 
 
 6 
 
 7 
 8 
 9 
 
 250 
 
 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 
 2039 
 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 
 
 173 
 
 172 
 171 
 171 
 
 170 
 169 
 
 2 
 3 
 4 
 5 
 6 
 7 
 
 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 
 
 1114 
 2796 
 4472 
 
 6141 
 
 7804 
 9460 
 
 1283 
 2964 
 4639 
 
 6308 
 7970 
 9625 
 
 1451 
 3132 
 4806 
 
 6474 
 8135 
 9791 
 
 169 
 168 
 167 
 
 167 
 166 
 165 
 
 8 
 9 
 
 260 
 1 
 
 2 
 3 
 
 411620 
 3300 
 
 4973 
 6641 
 8301 
 
 
 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 
 74S6 
 9106 
 
 1110 
 
 2754 
 4392 
 6023 
 7648 
 9268 
 
 1275 
 2918 
 4555 
 6186 
 7811 
 9429 
 
 1439 
 3082 
 4718 
 6349 
 7973 
 9591 
 
 165 
 164 
 164 
 163 
 162 
 162 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 421604 
 3246 
 4882 
 6511 
 8135 
 9752 
 
 43 
 
 0075 
 
 0236 
 
 0398 
 
 0559 
 
 0720 
 
 0881 
 
 1042 
 
 1203 
 
 161 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 178 
 
 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 
 
 123.9 
 
 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 
 
 i36.8 
 
 153.9 
 
 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 
 
 83.0 
 
 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 
 
 145.8 
 
 161 
 
 16.1 
 
 32.2 
 
 48.3 
 
 64.4 
 
 80.5 
 
 96.6 
 
 112.7 
 
 128.8 
 
 144.9 
 
146 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 270 L. 431.] 
 
 [No. 299 L. 476. 
 
 N. 
 
 
 
 1 
 
 2 ■ 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 270 
 1 
 
 2 
 3 
 4 
 5 
 
 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 
 
 2167 
 3770 
 5367 
 6957 
 8542 
 
 2328 
 3930 
 5526 
 7116 
 8701 
 
 2433 
 40?0 
 5685 
 7275 
 8359 
 
 2649 
 4249 
 5844 
 7433 
 9017 
 
 2809 
 4409 
 6004 
 7592 
 9175 
 
 161 
 160 
 159 
 159 
 
 153 
 
 
 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 
 
 158 
 157 
 157 
 156 
 
 155 
 
 155 
 
 6 
 
 7 
 8 
 9 
 
 280 
 
 440909 
 2480 
 4045 
 5604 
 
 7158 
 8706 
 
 1066 
 2637 
 4201 
 5760 
 
 7313 
 8361 
 
 1224 
 2793 
 4357 
 5915 
 
 7468 
 9015 
 
 1381 
 2950 
 4513 
 6071 
 
 7623 
 9170 
 
 1536 
 3106 
 4669 
 6226 
 
 7778 
 9324 
 
 
 0095 
 1633 
 3165 
 4692 
 6214 
 7731 
 9242 
 
 0748 
 2248 
 
 3744 
 5234 
 6719 
 8200 
 9675 
 
 154 
 154 
 153 
 153 
 152 
 152 
 151 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 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 
 682! 
 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 
 
 0597 
 2098 
 
 3594 
 5085 
 6571 
 8052 
 9527 
 
 0146 
 1649 
 
 3146 
 4639 
 6126 
 7608 
 9035 
 
 0296 
 1799 
 
 3296 
 
 4788 
 6274 
 7756 
 9233 
 
 0447 
 1948 
 
 3445 
 4936 
 6423 
 7904 
 9380 
 
 151 
 150 
 
 150 
 149 
 149 
 
 148 
 148 
 
 9 
 
 290 
 1 
 
 2 
 3 
 4 
 5 
 
 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 
 4503 
 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 
 
 147 
 146 
 146 
 146 
 145 
 
 f 
 
 8 
 9 
 
 471292 
 2756 
 4216 
 5671 
 
 1438 
 2903 
 4362 
 5816 
 
 Proportional Parts. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 16.1 
 
 32.2 
 
 48.3 
 
 64.4 
 
 80.5 
 
 96.6 
 
 112.7 
 
 16.0 
 
 32.0 
 
 48.0 
 
 64.0 
 
 80.0 
 
 96.0 
 
 112.0 
 
 15.9 
 
 31.8 
 
 47.7 
 
 63.6 
 
 79.5 
 
 95.4 
 
 111.3 
 
 15.8 
 
 31.6 
 
 47.4 
 
 63.2 
 
 79.0 
 
 94.8 
 
 110.6 
 
 15.7 
 
 31.4 
 
 47.1 
 
 62.8 
 
 78.5 
 
 94.2 
 
 109.9 
 
 15.6 
 
 31.2 
 
 46.8 
 
 62.4 
 
 78.0 
 
 93.6 
 
 109.2 
 
 15.5 
 
 31.0 
 
 46.5 
 
 62.0 
 
 77.5 
 
 93.0 
 
 108.5 
 
 15.4 
 
 30.8 
 
 46.2 
 
 61.6 
 
 77.0 
 
 92.4 
 
 107.8 
 
 15.3 
 
 30.6 
 
 45.9 
 
 61.2 
 
 76.5 
 
 91.8 
 
 107.1 
 
 15.2 
 
 30.4 
 
 45.6 
 
 60.8 
 
 76.0 
 
 91.2 
 
 106.4 
 
 15.1 
 
 30.2 
 
 45.3 
 
 60.4 
 
 75.5 
 
 90.6 
 
 105.7 
 
 15.0 
 
 30.0 
 
 45.0 
 
 60.0 
 
 75.0 
 
 90.0 
 
 105.0 
 
 14.9 
 
 29.8 
 
 44.7 
 
 59.6 
 
 74.5 
 
 89.4 
 
 104.3 
 
 14.8 
 
 29.6 
 
 44.4 
 
 59.2 
 
 74.0 
 
 88.8 
 
 103.6 
 
 14.7 
 
 29.4 
 
 44.1 
 
 58.8 
 
 73.5 
 
 88.2 
 
 102.9 
 
 14.6 
 
 29.2 
 
 43.8 
 
 58.4 
 
 73.0 
 
 87.6 
 
 102.2 
 
 14.5 
 
 29.0 
 
 43.5 
 
 58.0 
 
 72.5 
 
 87.0 
 
 101.5 
 
 14.4 
 
 28.8 
 
 43.2 
 
 57.6 
 
 72.0 
 
 86.4 
 
 100.8 
 
 14.3 
 
 28.6 
 
 42.9 
 
 57.2 
 
 71.5 
 
 85.8 
 
 100.1 
 
 14.2 
 
 28.4 
 
 42.6 
 
 56.8 
 
 71.0 
 
 85.2 
 
 99.4 
 
 14.1 
 
 28.2 
 
 42.3 
 
 56.4 
 
 70.5 
 
 84.6 
 
 98.7 
 
 14.0 
 
 28.0 
 
 42.0 
 
 56.0 
 
 70.0 
 
 84.0 
 
 98.0 
 
 128.8 
 128.0 
 127.2 
 126.4 
 125.6 
 124.8 
 124.0 
 123.2 
 122.4 
 121.6 
 120.8 
 
 120.0 
 119.2 
 118.4 
 117.6 
 116.8 
 116.0 
 115.2 
 114.4 
 113.6 
 112.8 
 112.0 
 
 144.9 
 144.0 
 143. 1 
 142.2 
 141.3 
 140.4 
 139.5 
 138.6 
 137.7 
 136.8 
 135.9 
 
 135.0 
 134.1 
 133.2 
 132.3 
 131.4 
 130.5 
 129.6 
 128.7 
 127.8 
 126.9 
 126.0 
 

 
 
 LOGARITHMS OF NUMBERS. 
 
 
 
 147 
 
 No. 300 L. 477 
 
 ] 
 
 
 
 
 [No. 339 L. 531. 
 
 •N. 
 
 
 
 1 
 
 2 
 
 3 1 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 300 
 
 477121 
 
 726f 
 
 7411 
 
 7555 
 
 770C 
 
 7844 
 
 7989 
 
 8133 
 
 8278 
 
 8422 
 
 145 
 
 1 
 
 8566 
 
 8711 
 
 8855 
 
 8999 
 
 9143 
 
 9287 
 
 9431 
 
 9575 
 
 9719 
 
 9863 
 
 144 
 
 ?. 
 
 480007 
 
 0151 
 
 0294 
 
 0438 
 
 0582 
 
 0725 
 
 0369 
 
 1012 
 
 1156 
 
 1299 
 
 144 
 
 3 
 
 1443 
 
 1586 
 
 1729 
 
 1872 
 
 2016 
 
 2159 
 
 2302 
 
 2445 
 
 2538 
 
 2731 
 
 143 
 
 4 
 
 2874 
 
 3016 
 
 3159 
 
 3302 
 
 3445 
 
 3587 
 
 373C 
 
 3872 
 
 4015 
 
 4157 
 
 143 
 
 5 
 
 4300 
 
 444? 
 
 4585 
 
 4727 
 
 4869 
 
 5011 
 
 5153 
 
 5295 
 
 5437 
 
 5579 
 
 142 
 
 6 
 
 5721 
 
 5863 
 
 6005 
 
 6147 
 
 6289 
 
 6430 
 
 6572 
 
 6714 
 
 6855 
 
 6997 
 
 142 
 
 7 
 
 7138 
 
 728( 
 
 7421 
 
 7563 
 
 7704 
 
 7845 
 
 7986 
 
 8127 
 
 8269 
 
 8410 
 
 141 
 
 8 
 
 8551 
 
 8692 
 
 8833 
 
 8974 
 
 9114 
 
 9255 
 
 9396 
 
 9537 
 
 9677 
 
 9818 
 
 141 
 
 9 
 
 9958 
 
 0099 
 1502 
 
 0239 
 1642 
 
 0380 
 1782 
 
 0520 
 1922 
 
 0661 
 2062 
 
 0801 
 2201 
 
 0941 
 2341 
 
 1081 
 2481 
 
 1222 
 2621 
 
 140 
 
 310 
 
 491362 
 
 140 
 
 1 
 
 2760 
 
 29<)( 
 
 3040 
 
 3179 
 
 3319 
 
 3458 
 
 3597 
 
 3737 
 
 3876 
 
 4015 
 
 139 
 
 2 
 
 4155 
 
 429^ 
 
 4433 
 
 4572 
 
 4711 
 
 4850 
 
 4989 
 
 5128 
 
 5267 
 
 5406 
 
 139 
 
 3 
 
 5544 
 
 5683 
 
 5822 
 
 5960 
 
 6099 
 
 623S 
 
 6376 
 
 6515 
 
 6653 
 
 6791 
 
 139 
 
 4 
 
 6930 
 
 7068 
 
 7206 
 
 7344 
 
 7483 
 
 7621 
 
 7759 
 
 7897 
 
 8035 
 
 8173 
 
 138 
 
 5 
 
 8311 
 
 8448 
 
 8586 
 
 8724 
 
 8862 
 
 8999 
 
 9137 
 
 9275 
 
 9412 
 
 9550 
 
 138 
 
 6 
 
 9687 
 501059" 
 
 9824 
 
 9962 
 
 0099 
 1470 
 
 0236 
 1607 
 
 0374 
 1744 
 
 0511 
 1880 
 
 0648 
 2017 
 
 0785 
 2154 
 
 0922 
 2291 
 
 137 
 
 7 
 
 1196 
 
 1333 
 
 137 
 
 8 
 
 2427 
 
 2564 
 
 2700 
 
 2837 
 
 2973 
 
 3109 
 
 3246 
 
 3382 
 
 3518 
 
 3655 
 
 136 
 
 9 
 
 3791 
 
 3927 
 
 4063 
 
 4199 
 
 4335 
 
 4471 
 
 4607 
 
 4743 
 
 4878 
 
 5014 
 
 136 
 
 320 
 
 5150 
 
 5286 
 
 5421 
 
 5557 
 
 5693 
 
 5828 
 
 5964 
 
 6099 
 
 6234 
 
 6370 
 
 136 
 
 1 
 
 6505 
 
 6640 
 
 6776 
 
 6911 
 
 7046 
 
 7181 
 
 7316 
 
 7451 
 
 7586 
 
 7721 
 
 135 
 
 2 
 
 7856 
 
 7991 
 
 8126 
 
 8260 
 
 8395 
 
 8530 
 
 8664 
 
 8799 
 
 8934 
 
 9068 
 
 135 
 
 3 
 
 9203 
 
 9337 
 
 9471 
 
 9606 
 
 9740 
 
 9374 
 
 0009 
 1349 
 
 0143 
 1482 
 
 0277 
 1616 
 
 0411 
 1750 
 
 134 
 
 4 
 
 510545 
 
 0679 
 
 0813 
 
 0947 
 
 1031 
 
 1215 
 
 134 
 
 5 
 
 1883 
 
 2017 
 
 2151 
 
 2284 
 
 2418 
 
 2551 
 
 2684 
 
 2818 
 
 2951 
 
 3084 
 
 133 
 
 6 
 
 3218 
 
 3351 
 
 3484 
 
 3617 
 
 3750 
 
 3383 
 
 4016 
 
 4149 
 
 4282 
 
 4415 
 
 133 
 
 7 
 
 4548 
 
 4681 
 
 4813 
 
 4946 
 
 5079 
 
 5211 
 
 5344 
 
 5476 
 
 5609 
 
 5741 
 
 133 
 
 8 
 
 5874 
 
 6006 
 
 6139 
 
 6271 
 
 6403 
 
 6535 
 
 6668 
 
 6800 
 
 693?, 
 
 7064 
 
 132 
 
 9 
 
 7196 
 
 7328 
 
 7460 
 
 7592 
 
 7724 
 
 7355 
 
 7987 
 
 8119 
 
 8251 
 
 8382 
 
 132 
 
 330 
 
 8514 
 
 8646 
 
 8777 
 
 8909 
 
 9040 
 
 9171 
 
 9303 
 
 9434 
 
 9566 
 
 9697 
 
 131 
 
 1 
 
 9823 
 
 9959 
 
 0090 
 1400 
 
 0221 
 1530 
 
 0353 
 1661 
 
 0484 
 1792 
 
 0615 
 1922 
 
 0745 
 2053 
 
 0876 
 2183 
 
 1007 
 2314 
 
 131 
 
 2 
 
 521138 
 
 1269 
 
 131 
 
 3 
 
 2444 
 
 2575 
 
 2705 
 
 2835 
 
 2966 
 
 3096 
 
 3226 
 
 3356 
 
 3486 
 
 3616 
 
 130 
 
 4 
 
 3746 
 
 3876 
 
 4006 
 
 4136 
 
 4266 
 
 4396 
 
 4526 
 
 4656 
 
 4785 
 
 4915 
 
 130 
 
 5 
 
 5045 
 
 5174 
 
 5304 
 
 5434 
 
 5563 
 
 5693 
 
 58?.?, 
 
 5951 
 
 6081 
 
 6210 
 
 129 
 
 6 
 
 6339 
 
 6469 
 
 6598 
 
 6727 
 
 6856 
 
 6985 
 
 7114 
 
 7243 
 
 7372 
 
 7501 
 
 129 
 
 7 
 
 7630 
 
 7759 
 
 7888 
 
 8016 8145 
 
 8274 
 
 8402 
 
 8531 
 
 8660 
 
 8788 
 
 129 
 
 8 
 
 8917 
 
 9045 
 
 9174 
 
 9302 
 
 9430 
 0712 
 
 9559 
 
 9687 
 0968 
 
 9815 
 1096 
 
 9943 
 
 0072 
 
 128 
 
 9 
 
 530200 ' 
 
 0328 
 
 0456 
 
 05841 
 
 0840 
 
 1223^ 
 
 1351 
 
 128 
 
 
 
 
 Proportional Parts. 
 
 
 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 139 
 
 13.9 
 
 27.8 
 
 41.7 
 
 55.6 
 
 69.5 
 
 83.4 
 
 97.3 
 
 111.2 
 
 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 
 
 13? 
 
 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 
 
 104.0 
 
 117.0 
 
 129 
 
 12.9 
 
 25.8 
 
 38.7 
 
 51.6 
 
 64.5 
 
 77.4 
 
 90.3 
 
 103.2 
 
 116.1 
 
 178 
 
 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 
 
148 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 340 L. 531.] 
 
 
 
 
 
 
 
 [No. 
 
 379 L 
 
 579. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 340 
 1 
 
 2 
 3 
 4 
 5 
 6 
 
 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 
 8443 
 9703 
 
 2245 
 3518 
 4787 
 6053 
 7315 
 8574 
 9829 
 
 1080 
 2327 
 3571 
 
 4812 
 6049 
 
 7282 
 8512 
 9739 
 
 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 
 
 0079 
 1330 
 2576 
 3820 
 
 5060 
 6296 
 7529 
 8758 
 9984 
 
 0204 
 1454 
 2701 
 3944 
 
 5183 
 6419 
 7652 
 8881 
 
 7 
 8 
 9 
 
 350 
 1 
 
 2 
 3 
 
 4 
 
 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 
 
 1205 
 2452 
 3696 
 
 4936 
 6172 
 7405 
 8635 
 9861 
 
 0106 
 1328 
 2547 
 3762 
 4973 
 6182 
 
 7387 
 8589 
 9787 
 
 123 
 122 
 122 
 121 
 121 
 121 
 
 120 
 120 
 120 
 
 5 
 6 
 7 
 8 
 9 
 
 360 
 1 
 
 2 
 3 
 
 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 
 
 0265 
 1459 
 2650 
 3837 
 5021 
 6202 
 7379 
 
 8554 
 9725 
 
 0717 
 1938 
 3155 
 4368 
 5578 
 
 6785 
 
 7988 
 9188 
 
 0840 
 2060 
 3276 
 4- 59 
 5699 
 
 6905 
 8108 
 9308 
 
 0962 
 2181 
 3398 
 4610 
 5820 
 
 7026 
 8228 
 9428 
 
 1034 
 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 
 
 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 
 
 119 
 119 
 119 
 119 
 118 
 118 
 118 
 
 117 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 370 
 
 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 
 7377 
 8525 
 9669 
 
 117 
 117 
 116 
 116 
 116 
 115 
 115 
 115 
 114 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 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 
 
 2 
 
 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 
 
LOGARITHMS OF NUMBERS. 
 
 149 
 
 tfo. 3S0 L. 579.] 
 
 
 
 
 
 
 
 
 [No. 
 
 414 L 
 
 617. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 380 
 
 1 
 
 2 
 3 
 4 
 5 
 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 
 
 1 
 
 2 
 3 
 4 
 
 5/9784 
 
 9698 
 
 
 
 0241 
 1381 
 2518 
 3652 
 4783 
 5912 
 7037 
 8160 
 9279 
 
 
 
 
 
 
 
 0012 
 1153 
 2291 
 3426 
 4557 
 5636 
 6812 
 7935 
 9056 
 
 0126 
 1267 
 2404 
 3539 
 4670 
 5799 
 6925 
 8047 
 9167 
 
 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 
 
 114 
 
 113 
 112 
 
 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 
 
 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 
 9226 
 
 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 
 
 0646 
 1734 
 
 2819 
 3902 
 4982 
 6059 
 7133 
 8205 
 9274 
 
 0842 
 
 1955 
 3064 
 4171 
 5276 
 6377 
 7476 
 8572 
 9665 
 
 0755 
 1843 
 
 2928 
 4010 
 5089 
 6166 
 7241 
 8312 
 9381 
 
 0447 
 1511 
 2572 
 
 3630 
 4686 
 5740 
 6790 
 7839 
 
 0953 
 
 2066 
 3175 
 4282 
 5386 
 6487 
 7586 
 8681 
 9774 
 
 
 591065 
 2177 
 3286 
 4393 
 5496 
 6597 
 7695 
 8791 
 9883 
 
 111 
 
 110 
 109 
 
 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 
 6811 
 7884 
 8954 
 
 0428 
 1517 
 
 2603 
 3686 
 4766 
 5844 
 6919 
 7991 
 9061 
 
 0537 
 1625 
 
 2711 
 
 3794 
 4874 
 5951 
 7026 
 8098 
 9167 
 
 0864 
 1951 
 
 3036 
 4118 
 5197 
 6274 
 7348 
 8419 
 9488 
 
 600973 
 
 2060 
 
 3144 
 4226 
 5305 
 6381 
 7455 
 8526 
 9594 
 
 1082 
 
 2169 
 
 3253 
 4334 
 5413 
 6439 
 7562 
 8633 
 9701 
 
 108 
 107 
 
 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 
 
 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 
 
 106 
 105 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 118 
 
 1.1.8 
 
 23.6 
 
 35.4 
 
 47.2 
 
 5-9.0 
 
 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 
 
 91.2 
 
 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 
 
150 
 
 LOGARITHMS OF NUMBERS. 
 
 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 
 1072 
 
 
 7 
 
 620136 
 
 0240 
 
 0344 
 
 0448 
 
 0552 
 
 0656 
 
 0760 
 
 0864 
 
 0968 
 
 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 
 
 4232 
 
 4335 
 
 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 
 
 7356 
 
 7463 
 
 7571 
 
 7673 
 
 7775 
 
 7878 
 
 7930 
 
 8082 
 
 8185 
 
 8287 
 
 
 5 
 
 8389 
 
 8491 
 
 8593 
 
 8695 
 
 8797 
 
 8900 
 
 9002 
 
 9104 
 
 9206 
 
 9308 
 
 102 
 
 6 
 
 9410 
 
 9512 
 
 9613 
 
 9715 
 
 9317 
 
 9919 
 
 0021 
 1038 
 
 0123 
 1139 
 
 0224 
 1241 
 
 0326 
 1342 
 
 
 7 
 
 630423 
 
 0530 
 
 0631 
 
 0733 
 
 0335 
 
 0936 
 
 
 8 
 
 1444 
 
 1545 
 
 1647 
 
 1748 
 
 1849 
 
 1951 
 
 2052 
 
 2153 
 
 2255 
 
 2356 
 
 
 9 
 
 2457 
 
 2559 
 
 2660 
 
 2761 
 
 2862 
 
 2963 
 
 3064 
 
 3165 
 
 3266 
 
 3367 
 
 
 430 
 
 3463 
 
 3569 
 
 3670 
 
 3771 
 
 3872 
 
 3973 
 
 4074 
 
 4175 
 
 4276 
 
 4376 
 
 101 
 
 1 
 
 4477 
 
 4578 
 
 4679 
 
 4779 
 
 4880 
 
 4981 
 
 5081 
 
 5132 
 
 5283 
 
 5383 
 
 
 2 
 
 5434 
 
 5584 
 
 5635 
 
 5785 
 
 5886 
 
 5986 
 
 6087 
 
 6187 
 
 6287 
 
 6388 
 
 
 3 
 
 6433 
 
 6588 
 
 6638 
 
 6789 
 
 6389 
 
 6939 
 
 70S9 
 
 7189 
 
 7290 
 
 7390 
 
 
 4 
 
 7490 
 
 7590 
 
 7690 
 
 7790 
 
 7890 
 
 7990 
 
 8090 
 
 8190 
 
 8290 
 
 8389 
 
 1(»U 
 
 5 
 
 8439 
 
 8589 
 
 8639 
 
 8789 
 
 8838 
 
 8988 
 
 9088 
 
 9188 
 
 9287 
 
 9387 
 
 
 6 
 
 9486 
 
 9586 
 
 9636 
 
 9785 
 
 9885 
 
 9984 
 
 0084 
 1077 
 
 0183 
 1177 
 
 0283 
 1276 
 
 0382 
 1375 
 
 
 7 
 
 640431 
 
 0581 
 
 0680 
 
 0779 
 
 0879 
 
 0978 
 
 
 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 
 650303 
 
 9432 
 
 9530 
 
 9627 
 
 9724 
 
 9821 
 
 9919 
 
 0016 
 0987 
 
 0113 
 1084 
 
 0210 
 1181 
 
 
 7 
 
 0405 
 
 0502 
 
 0599 
 
 0696 
 
 0793 
 
 0890 
 
 
 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 
 
 350?, 
 
 3598 
 
 3695 
 
 3791 
 
 3888 
 
 3984 
 
 4080 
 
 
 1 
 
 4177 
 
 4273 
 
 4369 
 
 4465 
 
 4562 
 
 4658 
 
 4754 
 
 4850 
 
 4946 
 
 5042 
 
 
 2 
 
 5138 
 
 5235 
 
 5331 
 
 5427 
 
 5523 
 
 5619 
 
 5715 
 
 5310 
 
 5906 
 
 6002 
 
 96 
 
 3 
 
 6093 
 
 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 
 9916 
 
 9060 
 
 9155 
 0106 
 1055 
 
 9250 
 
 9346 
 
 9441 
 
 9536 
 
 9631 
 
 9726 
 0676 
 1623 
 
 9821 
 0771 
 1718 
 
 
 7 
 
 0011 
 0960 
 
 0201 
 1150 
 
 0296 
 1245 
 
 0391 
 1339 
 
 0486 
 1434 
 
 0581 
 1529 
 
 95 
 
 8 
 
 660365 
 
 
 9 
 
 1813 
 
 1907 
 
 2002 
 
 2096 
 
 2191 
 
 2286 
 
 2380 
 
 2475 
 
 2569 
 
 2663 
 
 
 Proportional, Parts. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 10.5 
 
 21.0 
 
 31.5 
 
 42.0 
 
 52.5 
 
 63.0 
 
 73.5 
 
 84.0 
 
 10.4 
 
 20.8 
 
 31.2 
 
 41.6 
 
 52.0 
 
 62.4 
 
 72.8 
 
 83.2 
 
 10.3 
 
 20.6 
 
 30.9 
 
 41.2 
 
 51.5 
 
 61.8 
 
 72.1 
 
 82.4 
 
 10.2 
 
 20.4 
 
 30.6 
 
 40.8 
 
 51.0 
 
 61.2 
 
 71.4 
 
 81.6 
 
 10.1 
 
 20.2 
 
 30.3 
 
 40.4 
 
 50.5 
 
 60.6 
 
 70.7 
 
 80.8 
 
 10.0 
 
 20.0 
 
 30.0 
 
 40.0 
 
 50.0 
 
 60.0 
 
 70.0 
 
 80.0 
 
 9.9 
 
 19.8 
 
 29.7 
 
 39.6 
 
 49.5 
 
 59.4 
 
 69.3 
 
 79.2 
 
LOGARITHMS OP NUMBERS. 
 
 151 
 
 No. 460 L. 632.] 
 
 
 
 
 
 
 
 [No 
 
 499 L. 698 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 Tl35 
 4078 
 5018 
 5956 
 6892 
 7826 
 8759 
 9689 
 
 5 
 
 6 
 
 3324 
 4266 
 5206 
 6143 
 7079 
 8013 
 8945 
 9875 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 460 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 
 662758 
 3701 
 4642 
 5581 
 6518 
 7453 
 8336 
 9317 
 
 2852 
 3795 
 4736 
 5675 
 6612 
 7546 
 8479 
 9410 
 
 2947 
 3889 
 4830 
 5769 
 6705 
 7640 
 8572 
 9503 
 
 3041 
 3983 
 4924 
 5862 
 6799 
 7733 
 8665 
 9596 
 
 3230 
 4172 
 5112 
 6050 
 6986 
 7920 
 8852 
 9782 
 
 3418 
 4360 
 5299 
 6237 
 7173 
 8106 
 9038 
 9967 
 
 3512 
 4454 
 5393 
 6331 
 7266 
 8199 
 9131 
 
 3607 
 4548 
 5487 
 6424 
 7360 
 8293 
 9224 
 
 94 
 
 0060 
 0988 
 1913 
 
 2836 
 3758 
 4677 
 5595 
 6511 
 7424 
 8336 
 9246 
 
 0153 
 1080 
 2005 
 
 2929 
 3850 
 4769 
 5687 
 6602 
 7516 
 8427 
 9337 
 
 0245 
 1151 
 
 2055 
 2957 
 3857 
 4756 
 5652 
 6547 
 7440 
 8331 
 9220 
 
 93 
 
 92 
 91 
 
 8 
 9 
 
 470 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 670246 
 1173 
 
 2098 
 3021 
 3942 
 4861 
 5778 
 6694 
 7607 
 8518 
 9423 
 
 0339 
 1265 
 
 2190 
 3113 
 
 4034 
 4953 
 5870 
 6785 
 7698 
 8609 
 9519 
 
 0431 
 1358 
 
 2283 
 3205 
 4126 
 5045 
 5962 
 6876 
 7789 
 8700 
 9610 
 
 0524 
 1451 
 
 2375 
 3297 
 4218 
 5137 
 6053 
 6968 
 7881 
 8791 
 9700 
 
 C617 
 1543 
 
 2467 
 3390 
 4310 
 5228 
 6145 
 7059 
 7972 
 8882 
 9791 
 
 0710 
 1636 
 
 2560 
 3482 
 4402 
 5320 
 6236 
 7151 
 8063 
 8973 
 9882 
 
 0802 
 1728 
 
 2652 
 3574 
 4494 
 5412 
 6328 
 7242 
 8154 
 9064 
 9973 
 
 0895 
 1821 
 
 2744 
 3666 
 4586 
 5503 
 6419 
 7333 
 8245 
 9155 
 
 0063 
 0970 
 
 1874 
 2777 
 3677 
 4576 
 5473 
 6368 
 7261 
 8153 
 9042 
 9930 
 
 0154 
 1060 
 
 1964 
 2867 
 3767 
 4666 
 5563 
 6458 
 7351 
 8242 
 9131 
 
 
 9 
 
 480 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 680336 
 
 1241 
 2145 
 3047 
 3947 
 4845 
 5742 
 6636 
 7529 
 8420 
 9309 
 
 0426 
 
 1332 
 2235 
 3137 
 4037 
 4935 
 5831 
 6726 
 7618 
 8509 
 9398 
 
 0517 
 
 1422 
 2326 
 3227 
 4127 
 5025 
 5921 
 6815 
 7707 
 8598 
 9486 
 
 0607 
 
 1513 
 
 2416 
 3317 
 4217 
 5114 
 6010 
 6904 
 7796 
 8687 
 9575 
 
 0698 
 
 1603 
 2506 
 3407 
 4307 
 5204 
 6100 
 6994 
 7886 
 8776 
 9664 
 
 0789 
 
 1693 
 2596 
 3497 
 4396 
 5294 
 6189 
 7083 
 7975 
 8865 
 9753 
 
 0879 
 
 1784 
 2686 
 3587 
 4486 
 5383 
 6279 
 7172 
 8064 
 8953 
 9841 
 
 90 
 89 
 
 0019 
 
 0905 
 1789 
 2671 
 3551 
 4430 
 5307 
 6182 
 7055 
 7926 
 8796 
 
 0107 
 
 0993 
 1877 
 2759 
 3639 
 4517 
 5394 
 6269 
 7142 
 8014 
 8883 
 
 
 490 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 690196 
 1081 
 1965 
 2847 
 3727 
 4605 
 5482 
 6356 
 7229 
 8100 
 
 0285 
 1170 
 2053 
 2935 
 3815 
 4693 
 5569 
 6444 
 7317 
 8188 
 
 0373 
 1258 
 2142 
 3023 
 3903 
 4781 
 5657 
 6531 
 7404 
 8275 
 
 0462 
 1347 
 2230 
 3111 
 3991 
 4868 
 5744 
 6618 
 7491 
 8362 
 
 0550 
 1435 
 2318 
 3199 
 4078 
 4956 
 5832 
 6706 
 7578 
 8449 
 
 0639 
 1524 
 2406 
 3287 
 4166 
 5044 
 5919 
 6793 
 7665 
 8535 
 
 0728 
 1612 
 2494 
 3375 
 4254 
 5131 
 6007 
 6880 
 7752 
 8622 
 
 0816 
 1700 
 2583 
 3463 
 4342 
 5219 
 6094 
 6968 
 7839 
 8709 
 
 88 
 87 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 98 
 
 9.8 
 
 19.6 
 
 29.4 
 
 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 
 
 86 
 
 8.6 
 
 17.2 
 
 25.8 
 
 34.4 
 
 43.0 
 
 51.6 
 
 60.2 
 
 68.8 
 
 77.4 
 
152 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 500 L. 698.1 
 
 [No. 544 L. 736. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 698970 
 
 9057 
 
 9144 
 
 9231 
 
 9317 
 
 9404 
 
 9491 
 
 9578 
 
 9664 
 
 9751 
 
 9838 
 
 9924 
 
 
 
 
 
 
 
 
 
 0011 
 0877 
 
 0098 
 0963 
 
 0184 
 1050 
 
 0271 
 1136 
 
 0358 
 1222 
 
 0444 
 1309 
 
 0531 
 1395 
 
 0617 
 1482 
 
 700704 
 
 0790 
 
 1568 
 
 1654 
 
 1741 
 
 1827 
 
 1913 
 
 1999 
 
 2086 
 
 2172 
 
 2258 
 
 2344 
 
 2431 
 
 2517 
 
 2603 
 
 2689 
 
 2775 
 
 2861 
 
 2947 
 
 3033 
 
 3119 
 
 3205 
 
 3291 
 
 3377 
 
 3463 
 
 3549 
 
 3635 
 
 3721 
 
 3807 
 
 3893 
 
 3979 
 
 4065 
 
 4151 
 
 4236 
 
 4322 
 
 4408 
 
 4494 
 
 4579 
 
 4665 
 
 4751 
 
 4837 
 
 4922 
 
 5008 
 
 5094 
 
 5179 
 
 5265 
 
 5350 
 
 5436 
 
 5522 
 
 5607 
 
 5693 
 
 5778 
 
 5864 
 
 5949 
 
 6035 
 
 6120 
 
 6206 
 
 6291 
 
 6376 
 
 6462 
 
 6547 
 
 6632 
 
 • 6718 
 
 6803 
 
 6888 
 
 6974 
 
 7059 
 
 7144 
 
 7229 
 
 7315 
 
 7400 
 
 7485 
 
 7570 
 
 7655 
 
 7740 
 
 7826 
 
 7911 
 
 7996 
 
 8081 
 
 8166 
 
 8251 
 
 8336 
 
 8421 
 
 8506 
 
 8591 
 
 8676 
 
 8761 
 
 8846 
 
 8931 
 
 9015 
 
 9100 
 
 9185 
 
 9270 
 
 9355 
 
 9440 
 
 9524 
 
 9609 
 
 9694 
 
 9779 
 
 9863 
 
 9948 
 
 
 0033 
 0879 
 
 710117 
 
 0202 
 
 0287 
 
 0371 
 
 0456 
 
 0540 
 
 0625 
 
 •0710 
 
 0794 
 
 0963 
 
 1048 
 
 1132 
 
 1217 
 
 1301 
 
 1385 
 
 1470 
 
 1554 
 
 1639 
 
 1723 
 
 1807 
 
 1892 
 
 1976 
 
 2060 
 
 2144 
 
 2229 
 
 2313 
 
 2397 
 
 2481 
 
 2566 
 
 2650 
 
 2734 
 
 2818 
 
 2902 
 
 2986 
 
 3070 
 
 3154 
 
 3238 
 
 3323 
 
 3407 
 
 3491 
 
 3575 
 
 3659 
 
 3742 
 
 3826 
 
 3910 
 
 3994 
 
 4078 
 
 4162 
 
 4246 
 
 4330 
 
 4414 
 
 4497 
 
 4581 
 
 4665 
 
 4749 
 
 4833 
 
 4916 
 
 5000 
 
 5084 
 
 5167 
 
 5251 
 
 5335 
 
 5418 
 
 5502 
 
 5586 
 
 5669 
 
 5753 
 
 5836 
 
 5920 
 
 6003 
 
 6087 
 
 6170 
 
 6254 
 
 6337 
 
 6421 
 
 6504 
 
 6588 
 
 6671 
 
 6754 
 
 6838 
 
 6921 
 
 7004 
 
 7088 
 
 7171 
 
 7254 
 
 7338 
 
 7421 
 
 7504 
 
 7587 
 
 7671 
 
 7754 
 
 7837 
 
 7920 
 
 8003 
 
 8086 
 
 8169 
 
 8253 
 
 8336 
 
 8419 
 
 8502 
 
 8585 
 
 8668 
 
 8751 
 
 8834 
 
 8917 
 
 9000 
 
 9083 
 
 9165 
 
 9248 
 
 9331 
 
 9414 
 
 9497 
 
 9580 
 
 9663 
 
 9745 
 
 9828 
 
 9911 
 
 9994 
 
 
 
 0077 
 0903 
 
 720159 
 
 0242 
 
 0325 
 
 0407 
 
 0490 
 
 0573 
 
 0655 
 
 0738 
 
 0821 
 
 0986 
 
 1068 
 
 1151 
 
 1233 
 
 1316 
 
 1398 
 
 1481 
 
 1563 
 
 1646 
 
 1728 
 
 1811 
 
 1893 
 
 1975 
 
 2058 
 
 2140 
 
 2222 
 
 2305 
 
 2387 
 
 2469 
 
 2552 
 
 2634 
 
 2716 
 
 2798 
 
 2881 
 
 2963 
 
 3045 
 
 3127 
 
 3209 
 
 3291 
 
 3374 
 
 3456 
 
 3538 
 
 3620 
 
 3702 
 
 3784 
 
 3866 
 
 3948 
 
 4030 
 
 4112 
 
 4194 
 
 4276 
 
 4358 
 
 4440 
 
 4522 
 
 4604 
 
 4685 
 
 4767 
 
 4849 
 
 4931 
 
 5013 
 
 5095 
 
 5176 
 
 5258 
 
 5340 
 
 5422 
 
 5503 
 
 5585 
 
 5667 
 
 5748 
 
 5830 
 
 5912 
 
 5993 
 
 6075 
 
 6156 
 
 6238 
 
 6320 
 
 6401 
 
 6483 
 
 6564 
 
 6646 
 
 6727 
 
 6809 
 
 6890 
 
 6972 
 
 7053 
 
 7134 
 
 7216 
 
 7297 
 
 7379 
 
 7460 
 
 7541 
 
 7623 
 
 7704 
 
 7785 
 
 7866 
 
 7948 
 
 8029 
 
 8110 
 
 8191 
 
 8273 
 
 8354 
 
 8435 
 
 8516 
 
 8597 
 
 8678 
 
 8759 
 
 8841 
 
 8922 
 
 9003 
 
 9084 
 
 9165 
 
 9246 
 
 9327 
 
 9408 
 
 9489 
 
 9570 
 
 9651 
 
 9732 
 
 9813 
 
 9893 
 
 9974 
 
 
 
 
 
 
 
 
 
 
 
 0055 
 0863 
 
 0136 
 0944 
 
 0217 
 1024 
 
 0298 
 1105 
 
 0378 
 1186 
 
 0459 
 1266 
 
 0540 
 1347 
 
 0621 
 1428 
 
 0702 
 1508 
 
 730782 
 
 1589 
 
 1669 
 
 1750 
 
 1830 
 
 1911 
 
 1991 
 
 2072 
 
 2152 
 
 2233 
 
 2313 
 
 2394 
 
 2474 
 
 2555 
 
 2635 
 
 2715 
 
 2796 
 
 2876 
 
 2956 
 
 3037 
 
 3117 
 
 3197 
 
 3278 
 
 3358 
 
 3438 
 
 3518 
 
 3598 
 
 3679 
 
 3759 
 
 3839 
 
 3919 
 
 3999 
 
 4079 
 
 4160 
 
 4240 
 
 4320 
 
 4400 
 
 4480 
 
 4560 
 
 4640 
 
 4720 
 
 4800 
 
 4880 
 
 4960 
 
 5040 
 
 5120 
 
 5200 
 
 5279 
 
 5359 
 
 5439 
 
 5519 
 
 5599 
 
 5679 
 
 5759 
 
 5838 
 
 5918 
 
 5998 
 
 6078 
 
 6157 
 
 6237 
 
 6317 
 
 Proportional, Parts. 
 
 Diff. 
 
 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 
 
LOGARITHMS OF NUMBERS. 
 
 153 
 
 No. 545 L. 736.] 
 
 
 
 
 
 
 
 [No 
 
 . 584 L. 767. 
 
 N. 
 
 
 
 1 
 
 ~6476 
 7272 
 8067 
 8860 
 9651 
 
 2 
 
 ~6556 
 7352 
 8146 
 8939 
 9731 
 
 3 
 
 ~6635 
 7431 
 8225 
 9018 
 9810 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 545 
 6 
 7 
 8 
 9 
 
 736397 
 7193 
 7987 
 8781 
 9572 
 
 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 
 
 0284 
 
 1073 
 1860 
 2647 
 3431 
 4215 
 4997 
 5777 
 6556 
 7334 
 8110 
 
 8885 
 9659 
 
 
 0047 
 
 0836 
 1624 
 2411 
 3196 
 3980 
 4762 
 5543 
 6323 
 7101 
 7878 
 
 8653 
 9427 
 
 0126 
 
 0915 
 1703 
 2489 
 3275 
 4058 
 4840 
 5621 
 6401 
 7179 
 7955 
 
 8731 
 9504 
 
 0205 
 
 0994 
 1782 
 2568 
 3353 
 4136 
 4919 
 5699 
 6479 
 7256 
 8033 
 
 8808 
 9582 
 
 79 
 78 
 
 550 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 560 
 
 2 
 
 740363 
 1152 
 1939 
 2725 
 3510 
 4293 
 5075 
 5855 
 6634 
 7412 
 
 8188 
 8963 
 9736 
 
 0442 
 1230 
 2018 
 2804 
 3588 
 4371 
 5153 
 5933 
 6712 
 7489 
 
 8266 
 9040 
 9814 
 
 0521 
 1309 
 2096 
 2882 
 3667 
 4449 
 5231 
 6011 
 6790 
 7567 
 
 8343 
 9118 
 9891 
 
 0600 
 
 1388 
 2175 
 2961 
 3745 
 4528 
 5309 
 6089 
 6868 
 7645 
 
 8421 
 9i95 
 9968 
 
 0678 
 1467 
 2254 
 3039 
 3823 
 4606 
 5387 
 6167 
 6945 
 7722 
 
 8498 
 9272 
 
 0757 
 1546 
 2332 
 3118 
 3902 
 4684 
 5465 
 6245 
 7023 
 7800 
 
 8576 
 9350 
 
 0045 
 0817 
 1587 
 2356 
 3123 
 3889 
 4654 
 5417 
 
 6180 
 6940 
 7700 
 8458 
 9214 
 9970 
 
 0123 
 0894 
 1664 
 2433 
 3200 
 3966 
 4730 
 5494 
 
 6256 
 7016 
 7775 
 8533 
 9290 
 
 0200 
 0971 
 1741 
 2509 
 3277 
 4042 
 4807 
 5570 
 
 6332 
 7092 
 7851 
 8609 
 9366 
 
 0277 
 1048 
 1818 
 2586 
 3353 
 4119 
 4883 
 5646 
 
 6408 
 7168 
 7927 
 8685 
 9441 
 
 0354 
 1125 
 1895 
 2663 
 3430 
 4195 
 4960 
 5722 
 
 6484 
 7244 
 8003 
 8761 
 9517 
 
 0431 
 1202 
 1972 
 2740 
 3506 
 4272 
 5036 
 5799 
 
 6560 
 7320 
 8079 
 8836 
 9592 
 
 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 570 
 1 
 
 2 
 3 
 4 
 5 
 
 750508 
 1279 
 2048 
 2816 
 3583 
 4348 
 5112 
 
 5875 
 6636 
 7396 
 8155 
 8912 
 9668 
 
 0586 
 1356 
 2125 
 2893 
 3660 
 4425 
 5189 
 
 5951 
 6712 
 7472 
 8230 
 8988 
 9743 
 
 0663 
 1433 
 2202 
 2970 
 3736 
 4501 
 5265 
 
 6027 
 6788 
 7548 
 8306 
 9063 
 9819 
 
 0740 
 1510 
 2279 
 3047 
 3813 
 4578 
 5341 
 
 6103 
 6864 
 7624 
 8382 
 9139 
 9894 
 
 77 
 76 
 
 0045 
 0799 
 1552 
 2303 
 3053 
 
 3802 
 4550 
 5296 
 6041 
 6785 
 
 0121 
 0875 
 1627 
 2378 
 3128 
 
 3877 
 4624 
 5370 
 6115 
 6859 
 
 0196 
 0950 
 1702 
 2453 
 3203 
 
 3952 
 4699 
 5445 
 6190 
 6933 
 
 0272 
 1025 
 1778 
 2529 
 3278 
 
 4027 
 4774 
 5520 
 6264 
 7007 
 
 0347 
 1101 
 1853 
 2604 
 3353 
 
 4101 
 4848 
 5594 
 6338 
 7082 
 
 
 6 
 7 
 
 8 
 9 
 
 580 
 1 
 
 2 
 3 
 4 
 
 760422 
 1176 
 1928 
 2679 
 
 3428 
 4176 
 4923 
 5669 
 6413 
 
 0498 
 1251 
 2003 
 2754 
 
 3503 
 4251 
 4998 
 5743 
 6487 
 
 0573 
 1326 
 2078 
 2829 
 
 3578 
 4326 
 5072 
 5818 
 6562 
 
 0649 
 1402 
 2153 
 2904 
 
 3653 
 4400 
 5147 
 5892 
 6636 
 
 0724 
 1477 
 2228 
 2978 
 
 3727 
 4475 
 5221 
 5966 
 6710 
 
 75 
 
 Proportional. Parts. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 83 
 
 8.3 
 
 16.6 
 
 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 
 
 59.2 
 
 66.6 
 
154 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 585 L.767J 
 
 
 
 
 
 
 
 [No 
 
 629 1 
 
 .799. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7601 
 8342 
 9082 
 9820 
 
 7 
 
 8 
 
 9 
 
 Difif. 
 
 585 
 6 
 7 
 8 
 
 767156 
 7898 
 8638 
 9377 
 
 7230 
 7972 
 8712 
 9451 
 
 7304 
 8046 
 8786 
 9525 
 
 7379 
 8120 
 8860 
 9599 
 
 7453 
 8194 
 8934 
 9673 
 
 7527 
 8268 
 9008 
 9746 
 
 7675 
 8416 
 9156 
 9894 
 
 7749 
 8490 
 9230 
 9968 
 
 7823 
 8564 
 9303 
 
 74 
 
 0042 
 0778 
 
 1514 
 2248 
 2981 
 3713 
 4444 
 5173 
 5902 
 6629 
 7354 
 8079 
 
 8802 
 9524 
 
 
 9 
 
 590 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 600 
 
 1 
 2 
 
 770115 
 
 0852 
 1587 
 2322 
 3055 
 3786 
 4517 
 5246 
 5974 
 6701 
 7427 
 
 8151 
 8874 
 9596 
 
 0189 
 
 0926 
 1661 
 2395 
 3128 
 3860 
 4590 
 5319 
 6047 
 6774 
 7499 
 
 8224 
 8947 
 9669 
 
 0263 
 
 0999 
 1734 
 2468 
 3201 
 3933 
 4663 
 5392 
 6120 
 6846 
 7572 
 
 8296 
 9019 
 9741 
 
 0336 
 
 1073 
 1808 
 2542 
 3274 
 4006 
 4736 
 5465 
 6193 
 6919 
 7644 
 
 8368 
 9091 
 9813 
 
 0410 
 
 1146 
 1881 
 2615 
 3348 
 4079 
 4809 
 5538 
 6265 
 6992 
 7717 
 
 8441 
 9163 
 9885 
 
 0484 
 
 1220 
 1955 
 2688 
 3421 
 4152 
 4882 
 5610 
 6338 
 7064 
 7789 
 
 8513 
 9236 
 9957 
 
 0557 
 
 1293 
 2028 
 2762 
 3494 
 4225 
 4955 
 5683 
 6411 
 7137 
 7862 
 
 8585 
 9308 
 
 0631 
 
 1367 
 2102 
 2835 
 3567 
 4298 
 5028 
 5756 
 6483 
 7209 
 7934 
 
 8658 
 9380 
 
 0705 
 
 1440 
 2175 
 2908 
 3640 
 4371 
 5100 
 5829 
 6556 
 7282 
 8006 
 
 8730 
 9452 
 
 73 
 
 0029 
 0749 
 1468 
 2186 
 2902 
 3618 
 .4332 
 5045 
 
 5757 
 6467 
 7177 
 7885 
 8593 
 9299 
 
 0101 
 0821 
 1540 
 2258 
 2974 
 3689 
 4403 
 5116 
 
 5828 
 6538 
 7248 
 7956 
 8663 
 9369 
 
 0173 
 0893 
 1612 
 2329 
 3046 
 3761 
 4475 
 5187 
 
 5899 
 6609 
 7319 
 8027 
 8734 
 9440 
 
 0245 
 0965 
 1684 
 2401 
 3117 
 3832 
 4546 
 5259 
 
 5970 
 6680 
 7390 
 8098 
 8804 
 9510 
 
 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 610 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 
 780317 
 1037 
 1755 
 2473 
 3189 
 3904 
 4617 
 
 5330 
 6041 
 6751 
 7460 
 8168 
 8875 
 9581 
 
 0389 
 1109 
 1827 
 2544 
 3260 
 3975 
 4689 
 
 5401 
 6112 
 6822 
 7531 
 8239 
 8946 
 9651 
 
 0461 
 1181 
 1899 
 2616 
 3332 
 4046 
 4760 
 
 5472 
 6183 
 6893 
 7602 
 8310 
 9016 
 9722 
 
 0533 
 1253 
 1971 
 2683 
 3403 
 4118 
 4831 
 
 5543 
 6254 
 6964 
 7673 
 8381 
 9087 
 9792 
 
 0605 
 
 1324 
 2042 
 2759 
 3475 
 4189 
 4902 
 
 5615 
 6325 
 7035 
 7744 
 8451 
 9157 
 9863 
 
 0677 
 1396 
 2114 
 2831 
 3546 
 4261 
 4974 
 
 5686 
 6396 
 7106 
 7815 
 8522 
 9228 
 9933 
 
 72 
 71 
 
 0004 
 0707 
 1410 
 2111 
 
 2812 
 3511 
 4209 
 4906 
 5602 
 6297 
 6990 
 7683 
 8374 
 9065 
 
 0074 
 0778 
 1480 
 2181 
 
 2882 
 3581 
 4279 
 4976 
 5672 
 6366 
 7060 
 7752 
 8443 
 9134 
 
 0144 
 0848 
 1550 
 2252 
 
 2952 
 3651 
 4349 
 5045 
 5741 
 6436 
 7129 
 7821 
 8513 
 9203 
 
 0215 
 0918 
 1620 
 2322 
 
 3022 
 3721 
 4418 
 5115 
 5811 
 6505 
 7198 
 7890 
 8582 
 9272 
 
 
 7 
 
 8 
 9 
 
 620 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 790285 
 0988 
 1691 
 
 2392 
 3092 
 3790 
 4488 
 5185 
 5880 
 6574 
 7268 
 7960 
 8651 
 
 0356 
 1059 
 1761 
 
 2462 
 3162 
 3860 
 4558 
 5254 
 5949 
 6644 
 7337 
 8029 
 8720 
 
 0426 
 1129 
 1831 
 
 2532 
 3231 
 3930 
 4627 
 5324 
 6019 
 6713 
 7406 
 8098 
 8789 
 
 0496 
 1199 
 1901 
 
 2602 
 3301 
 4000 
 4697 
 5393 
 6088 
 6782 
 7475 
 8167 
 8858 
 
 0567 
 1269 
 1971 
 
 2672 
 3371 
 4070 
 4767 
 5463 
 6158 
 6852 
 7545 
 8236 
 8927 
 
 0637 
 1340 
 2041 
 
 2742 
 3441 
 4139 
 4836 
 5532 
 6227 
 6921 
 7614 
 8305 
 8996 
 
 70 
 69 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 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 
 
 59.2 
 
 66.6 
 
 73 
 
 7.3 
 
 14.6 
 
 21.9 
 
 29.2 
 
 36.5 
 
 43.8 
 
 51.1 
 
 58.4 
 
 65.7 
 
 72 
 
 7.2 
 
 14.4 
 
 21.6 
 
 28.8 
 
 36.0 
 
 43.2 
 
 50.4 
 
 57.6 
 
 64.8 
 
 71 
 
 7.1 
 
 14.2 
 
 21.3 
 
 28.4 
 
 35.5 
 
 42.6 
 
 49.7 
 
 56.8 
 
 63.9 
 
 70 
 
 7.0 
 
 14.0 
 
 21.0 
 
 28.0 
 
 35.0 
 
 42.0 
 
 49.0 
 
 56.0 
 
 63.0 
 
 69 
 
 6.9 
 
 13.8 
 
 20.7 
 
 27.6 
 
 34.5 
 
 41.4 
 
 48.3 
 
 55.2 
 
 62.1 
 
LOGARITHMS OF NUMBERS. 
 
 155 
 
 No. 630 L. 799.] 
 
 
 
 
 
 
 
 [No 
 
 . 674 L. 829. 
 
 N. 
 
 
 
 1 
 
 3 
 
 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 
 
 31S4 
 
 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 
 0703 
 
 0098 
 0770 
 
 0165 
 
 0837 
 
 
 6 
 
 810233 
 
 0300 
 
 0367 
 
 0434 
 
 0501 
 
 0569 
 
 0636 
 
 
 7 
 
 0904 
 
 0971 
 
 1039 
 
 1106 
 
 1173 
 
 1240 
 
 1307 
 
 1374 
 
 1441 
 
 1508 
 
 67 
 
 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 
 
 6 
 
 7 
 
 8 
 
 9 
 
 68 
 
 6.8 
 
 13.6 
 
 20.4 
 
 27.2 
 
 34.0 
 
 40.8 
 
 47.6 
 
 54.4 
 
 61.2 
 
 67 
 
 6.7 
 
 13.4 
 
 20.1 
 
 26.8 
 
 33.5 
 
 40.2 
 
 46.9 
 
 53.6 
 
 60.3 
 
 66 
 
 6.6 
 
 13.2 
 
 19.8 
 
 26.4 
 
 33.0 
 
 39.6 
 
 46.2 
 
 52.8 
 
 59.4 
 
 65 
 
 6.5 
 
 13.0 
 
 19.5 
 
 26.0 
 
 32.5 
 
 39.0 
 
 45.5 
 
 52.0 
 
 58.5 
 
 64 
 
 6.4 
 
 12.8 
 
 19.2 
 
 25.6 
 
 32.0 
 
 38.4 
 
 44.8 
 
 51.2 
 
 57.6 
 
156 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 675 L. 829.] 
 
 
 
 
 
 
 
 [No 
 
 . 719 L. 857. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 675 
 
 829304 
 9947 
 
 9368 
 
 9432 
 
 9497 
 
 9561 
 
 9625 
 
 9690 
 
 9754 
 
 9818 
 
 9882 
 
 
 6 
 
 0011 
 
 0075 
 
 0139 
 
 0204 
 
 0268 
 
 0332 
 
 0396 
 
 0460 
 
 0525 
 
 
 7 
 
 830589 
 
 0653 
 
 0717 
 
 0781 
 
 0845 
 
 0909 
 
 0973 
 
 1037 
 
 1102 
 
 1166 
 
 
 8 
 
 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 
 
 
 
 9478 
 
 9541 
 
 9604 
 
 9657 
 
 9729 
 
 9792 
 
 9855 
 
 9918 
 
 9981 
 
 
 
 ' 
 
 
 
 
 
 0043 
 0671 
 
 
 2 
 
 840106 
 
 0169 
 
 0232 
 
 0294 
 
 0357 
 
 0420 
 
 0482 
 
 0545 
 
 0608 
 
 
 3 
 
 0733 
 
 0796 
 
 0859 
 
 0921 
 
 0934 
 
 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 
 
 3432 
 
 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 
 
 8S66 
 
 8928 
 
 8989 
 
 905! 
 
 9112 
 
 9174 
 
 9235 
 
 9297 
 
 9358 
 
 
 7 
 
 9419 
 
 9431 
 
 9542 
 
 9604 
 
 9665 
 
 9726 
 
 9788 
 
 9849 
 
 9911 
 
 9972 
 
 
 6 
 
 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 
 
 2963 
 
 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 
 
 473! 
 
 4792 
 
 4852 
 
 
 6 
 
 4913 
 
 4974 
 
 5034 
 
 5095 
 
 5156 
 
 5216 
 
 5277 
 
 5337 
 
 5398 
 
 5459 
 
 
 7 
 
 5519 
 
 5580 
 
 5640 
 
 570! 
 
 5761 
 
 5822 
 
 5882 
 
 5943 
 
 6003 
 
 6064 
 
 
 8 
 
 6124 
 
 6185 
 
 6245 
 
 6306 
 
 6366 
 
 6427 
 
 6487 
 
 6548 
 
 6608 
 
 6668 
 
 
 9 
 
 6729 
 
 6789 
 
 6850 
 
 6910 
 
 6970 
 
 7031 
 
 7091 
 
 7152 
 
 7212 
 
 7272 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 65 
 
 6.5 
 
 13.0 
 
 19.5 
 
 26.0 
 
 32.5 
 
 39.0 
 
 45.5 
 
 52.0 
 
 58.5 
 
 64 
 
 6.4 
 
 12.8 
 
 19.2 
 
 25.6 
 
 32.0 
 
 38.4 
 
 44.8 
 
 51.2 
 
 57.6 
 
 63 
 
 6.3 
 
 12.6 
 
 18.9 
 
 25.2 
 
 31.5 
 
 37.8 
 
 44.1 
 
 50.4 
 
 56.7 
 
 67 
 
 6.2 
 
 12.4 
 
 18.6 
 
 24.8 
 
 31.0 
 
 37.2 
 
 43.4 
 
 49.6 
 
 55.8 
 
 61 
 
 6.1 
 
 12.2 
 
 18.3 
 
 24.4 
 
 30.5 
 
 36.6 
 
 42.7 
 
 48.8 
 
 54.9 
 
 60 
 
 6.0 
 
 12.0 
 
 18.0 
 
 24.0 
 
 30.0 
 
 36.0 
 
 42.0 
 
 48.0 
 
 54.0 
 
LOGARITHMS OF NUMBERS. 
 
 157 
 
 No. 720 L. 857 
 
 ] 
 
 
 
 
 
 
 
 [No 
 
 . 764 L. 883. 
 
 N. 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 720 
 1 
 
 2 
 3 
 4 
 
 857332 
 7935 
 8537 
 9138 
 9739 
 
 7393 
 7995 
 8597 
 9198 
 9799 
 
 7453 
 8056 
 8657 
 9258 
 9859 
 
 7513 
 8116 
 8718 
 9318 
 9918 
 
 7574 
 3176 
 8778 
 9379 
 9978 
 
 7634 
 8236 
 8838 
 9439 
 
 0038 
 0637 
 1236 
 1833 
 2430 
 3025 
 
 3620 
 4214 
 4808 
 5400 
 5992 
 6583 
 7173 
 7762 
 8350 
 8938 
 
 9525 
 
 7694 
 8297 
 8898 
 9499 
 
 7755 
 8357 
 8958 
 9559 
 
 7815 
 8417 
 9018 
 9619 
 
 7875 
 8477 
 9078 
 9679 
 
 60 
 
 0098 
 0697 
 1295 
 1893 
 2489 
 3085 
 
 3680 
 4274 
 4867 
 5459 
 6051 
 6642 
 7232 
 7821 
 8409 
 8997 
 
 9584 
 
 0158 
 0757 
 1355 
 1952 
 2549 
 3144 
 
 3739 
 
 4333 
 4926 
 5519 
 6110 
 6701 
 7291 
 7880 
 8468 
 9056 
 
 9642 
 
 0218 
 0817 
 1415 
 2012 
 2608 
 3204 
 
 3799 
 
 4392 
 4985 
 5578 
 6169 
 6760 
 7350 
 7939 
 8527 
 9114 
 
 9701 
 
 0278 
 0877 
 1475 
 2072 
 2668 
 3263 
 
 3858 
 4452 
 5045 
 5637 
 6228 
 6819 
 7409 
 7998 
 8586 
 9173 
 
 9760 
 
 
 5 
 6 
 
 7 
 8 
 9 
 
 730 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 740 
 
 860338 
 0937 
 1534 
 2131 
 2728 
 
 3323 
 3917 
 4511 
 5104 
 5696 
 6287 
 6878 
 7467 
 8056 
 8644 
 
 9232 
 9318 
 
 0398 
 0996 
 1594 
 2191 
 2787 
 
 3382 
 3977 
 4570 
 5163 
 5755 
 6346 
 6937 
 7526 
 8115 
 8703 
 
 9290 
 9877 
 
 0453 
 1056 
 1654 
 2251 
 2847 
 
 3442 
 4036 
 4630 
 5222 
 5814 
 6405 
 6996 
 7535 
 8174 
 8762 
 
 9349 
 9935 
 
 0518 
 1116 
 1714 
 2310 
 2906 
 
 3501 
 4096 
 4689 
 5282 
 5874 
 6465 
 7055 
 7644 
 8233 
 8821 
 
 9408 
 
 0578 
 1176 
 1773 
 2370 
 2966 
 
 3561 
 
 4155 
 4748 
 5341 
 5933 
 6524 
 7114 
 7703 
 8292 
 8879 
 
 9466 
 
 59 
 
 
 
 0053 
 063-S 
 
 1223 
 1806 
 2389 
 2972 
 3553 
 4134 
 4714 
 
 5293 
 5871 
 6449 
 7026 
 7602 
 8177 
 8752 
 9325 
 9898 
 
 0111 
 0696 
 128! 
 1865 
 2448 
 3030 
 3611 
 4192 
 4772 
 
 5351 
 5929 
 6507 
 7083 
 7659 
 8234 
 8809 
 9383 
 9956 
 
 0170 
 0755 
 1339 
 1923 
 2506 
 3088 
 3669 
 4250 
 4830 
 
 5409 
 5987 
 6564 
 7141 
 7717 
 8292 
 8866 
 9440 
 
 0228 
 0313 
 1398 
 1931 
 2564 
 3146 
 3727 
 4308 
 4888 
 
 5466 
 6045 
 6622 
 7199 
 7774 
 8349 
 8924 
 9497 
 
 0287 
 0372 
 1456 
 2040 
 2622 
 3204 
 3785 
 4366 
 4945 
 
 5524 
 61-02 
 6680 
 7256 
 7832 
 8407 
 8981 
 9555 
 
 0345 
 0930 
 1515 
 2098 
 2681 
 3262 
 3844 
 4424 
 5003 
 
 '5582 
 6160 
 6737 
 7314 
 7889 
 8464 
 9039 
 9612 
 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 .9 
 
 750 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 870404 
 0989 
 1573 
 2156 
 2739 
 3321 
 3902 
 4482 
 
 5061 
 5640 
 6218 
 6795 
 7371 
 7947 
 8522 
 9096 
 9669 
 
 0462 
 1047 
 1631 
 2215 
 2797 
 3379 
 3960 
 4540 
 
 5119 
 5698 
 6276 
 6853 
 7429 
 8004 
 8579 
 9153 
 9726 
 
 0521 
 1106 
 1690 
 2273 
 2855 
 3437 
 4018 
 4598 
 
 5177 
 
 5756 
 6333 
 6910 
 7487 
 8062 
 8637 
 9211 
 9784 
 
 0579 
 1164 
 1748 
 2331 
 2913 
 3495 
 4076 
 4656 
 
 5235 
 5813 
 6391 
 6968 
 7544 
 8119 
 8694 
 9268 
 9841 
 
 58 
 
 0013 
 0585 
 
 1156 
 
 1727 
 2297 
 2866 
 3434 
 
 0070 
 0642 
 
 1213 
 1784 
 2354 
 2923 
 3491 
 
 0127 
 0699 
 
 1271 
 1841 
 2411 
 2980 
 3548 
 
 0185 
 0756 
 
 1328 
 1898 
 2468 
 3037 
 3605 
 
 
 9 
 
 760 
 1 
 
 2 
 3 
 4 
 
 880242 
 
 0814 
 1385 
 1955 
 2525 
 3093 
 
 0299 
 
 0871 
 
 1442 
 2012 
 2581 
 3150 
 
 0356 
 
 0928 
 1499 
 2069 
 2638 
 3207 
 
 0413 
 
 0985 
 1556 
 2126 
 2695 
 3264 
 
 0471 
 
 1042 
 1613 
 2183 
 2752 
 3321 
 
 0528 
 
 1099 
 1670 
 2240 
 2809 
 3377 
 
 57 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 59 
 
 5.9 
 
 11.8 
 
 17.7 
 
 23.6 
 
 29.5 
 
 35.4 
 
 41.3 
 
 47.2 
 
 53.1 
 
 58 
 
 5.8 
 
 11.6 
 
 17.4 
 
 23.2 
 
 29.0 
 
 34.8 
 
 40.6 
 
 46.4 
 
 52.2 
 
 57 
 
 5.7 
 
 11.4 
 
 17.1 
 
 22.8 
 
 28.5 
 
 34.2 
 
 39.9 
 
 45.6 
 
 51.3 
 
 56 
 
 5.6 
 
 11.2 
 
 16.8 
 
 22.4 
 
 28.0 
 
 33.6 
 
 39.2 
 
 44.8 
 
 50.4 
 
158 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 765 L. 883.] 
 
 [No. 5 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 4172 
 
 883661 
 
 3718 
 
 3775 
 
 3832 
 
 3888 
 
 3945 
 
 4002 
 
 4059 
 
 4115 
 
 4229 
 
 4285 
 
 4342 
 
 4399 
 
 4455 
 
 4512 
 
 4569 
 
 4625 
 
 4682 
 
 4739 
 
 4795 
 
 4852 
 
 4909 
 
 4965 
 
 5022 
 
 5078 
 
 5135 
 
 5192 
 
 5248 
 
 5305 
 
 5361 
 
 5418 
 
 5474 
 
 5531 
 
 5587 
 
 5644 
 
 5700 
 
 5757 
 
 5813 
 
 5870 
 
 5926 
 
 5983 
 
 6039 
 
 6096 
 
 6152 
 
 6209 
 
 6265 
 
 6321 
 
 6378 
 
 6434 
 
 6491 
 
 6547 
 
 6604 
 
 6660 
 
 6716 
 
 6773 
 
 6829 
 
 6885 
 
 6942 
 
 6998 
 
 7054 
 
 7111 
 
 7167 
 
 7223 
 
 7280 
 
 7336 
 
 7392 
 
 7449 
 
 7505 
 
 7561 
 
 7617 
 
 7674 
 
 7730 
 
 7786 
 
 7842 
 
 7898 
 
 7955 
 
 8011 
 
 8067 
 
 8123 
 
 8179 
 
 8236 
 
 8292 
 
 8348 
 
 8404 
 
 8460 
 
 8516 
 
 8573 
 
 8629 
 
 8685 
 
 8741 
 
 8797 
 
 8853 
 
 8909 
 
 8965 
 
 9021 
 
 9077 
 
 9134 
 
 9190 
 
 9246 
 
 9302 
 
 9358 
 
 9414 
 
 9470 
 
 9526 
 
 9582 
 
 9638 
 
 9694 
 
 9750 
 
 9806 
 
 9862 
 
 9918 
 
 9974 
 
 
 
 
 
 
 
 
 0030 
 0589 
 
 0086 
 0645 
 
 0141 
 0700 
 
 0197 
 0756 
 
 0253 
 0812 
 
 0309 
 0868 
 
 0365 
 0924 
 
 890421 
 
 0477 
 
 0533 
 
 0980 
 
 1035 
 
 1091 
 
 1147 
 
 1203 
 
 1259 
 
 1314 
 
 1370 
 
 1426 
 
 1482 
 
 1537 
 
 1593 
 
 1649 
 
 1705 
 
 1760 
 
 1816 
 
 1872 
 
 1928 
 
 1983 
 
 2039 
 
 2095 
 
 2150 
 
 2206 
 
 2262 
 
 2317 
 
 2373 
 
 2429 
 
 2484 
 
 2540 
 
 2595 
 
 2651 
 
 2707 
 
 2762 
 
 2818 
 
 2873 
 
 2929 
 
 2985 
 
 3040 
 
 3096 
 
 3151 
 
 3207 
 
 3262 
 
 3318 
 
 3373 
 
 3429 
 
 3484 
 
 3540 
 
 3595 
 
 3651 
 
 3706 
 
 3762 
 
 3817 
 
 3873 
 
 3928 
 
 3984 
 
 4039 
 
 4094 
 
 4150 
 
 4205 
 
 4261 
 
 4316 
 
 4371 
 
 4427 
 
 4482 
 
 4538 
 
 4593 
 
 4648 
 
 4704 
 
 4759 
 
 4814 
 
 4870 
 
 4925 
 
 4980 
 
 5036 
 
 5091 
 
 5146 
 
 5201 
 
 5257 
 
 5312 
 
 5367 
 
 5423 
 
 5478 
 
 5533 
 
 5588 
 
 5644 
 
 5699 
 
 5754 
 
 5809 
 
 5864 
 
 5920 
 
 5975 
 
 6030 
 
 6085 
 
 6140 
 
 6195 
 
 6251 
 
 6306 
 
 6361 
 
 6416 
 
 6471 
 
 6526 
 
 6581 
 
 6636 
 
 6692 
 
 6747 
 
 6802 
 
 6857 
 
 6912 
 
 6967 
 
 7022 
 
 7077 
 
 7132 
 
 7187 
 
 7242 
 
 7297 
 
 7352 
 
 7407 
 
 7462 
 
 7517 
 
 7572 
 
 7627 
 
 7682 
 
 7737 
 
 7792 
 
 7847 
 
 7902 
 
 7957 
 
 8012 
 
 8067 
 
 8122 
 
 8176 
 
 8231 
 
 8286 
 
 8341 
 
 8396 
 
 8451 
 
 8506 
 
 8561 
 
 8615 
 
 8670 
 
 8725 
 
 8780 
 
 8835 
 
 8890 
 
 8944 
 
 8999 
 
 9054 
 
 9109 
 
 9164 
 
 9218 
 
 9273 
 
 9328 
 
 9383 
 
 9437 
 
 9492 
 
 9547 
 
 9602 
 
 9656 
 
 9711 
 
 9766 
 
 9821 
 
 9875 
 
 9930 
 
 9985 
 
 
 
 
 
 
 
 0039 
 0586 
 
 0094 
 0640 
 
 0149 
 0695 
 
 0203 
 0749 
 
 0258 
 0804 
 
 0312 
 0859 
 
 900367 
 
 0422 
 
 0476 
 
 0531 
 
 0913 
 
 0968 
 
 1022 
 
 1077 
 
 1131 
 
 1186 
 
 1240 
 
 1295 
 
 1349 
 
 1404 
 
 1458 
 
 1513 
 
 1567 
 
 1622 
 
 1676 
 
 1731 
 
 1785 
 
 1840 
 
 1894 
 
 1948 
 
 2003 
 
 2057 
 
 2112 
 
 2166 
 
 2221 
 
 2275 
 
 2329 
 
 2384 
 
 2438 
 
 2492 
 
 2547 
 
 2601 
 
 2655 
 
 2710 
 
 2764 
 
 2818 
 
 2873 
 
 2927 
 
 2981 
 
 3036 
 
 3090 
 
 3144 
 
 3199 
 
 3253 
 
 3307 
 
 3361 
 
 3416 
 
 3470 
 
 3524 
 
 3578 
 
 3633 
 
 3687 
 
 3741 
 
 3795 
 
 3849 
 
 3904 
 
 3958 
 
 4012 
 
 4066 
 
 4120 
 
 4174 
 
 4229 
 
 4283 
 
 4337 
 
 4391 
 
 4445 
 
 4499 
 
 4553 
 
 4607 
 
 4661 
 
 4716 
 
 4770 
 
 4824 
 
 4878 
 
 4932 
 
 4986 
 
 5040 
 
 5094 
 
 5148 
 
 5202 
 
 5256 
 
 5310 
 
 5364 
 
 5418 
 
 5472 
 
 5526 
 
 5580 
 
 5634 
 
 5688 
 
 5742 
 
 5796 
 
 5850 
 
 5904 
 
 5958 
 
 6012 
 
 6066 
 
 6119 
 
 6173 
 
 6227 
 
 6281 
 
 6335 
 
 6389 
 
 6443 
 
 6497 
 
 6551 
 
 6604 
 
 6658 
 
 6712 
 
 6766 
 
 6820 
 
 6874 
 
 6927 
 
 6981 
 
 7035 
 
 7089 
 
 7143 
 
 7196 
 
 7250 
 
 7304 
 
 7358 
 
 7411 
 
 7465 
 
 7519 
 
 7573 
 
 7626 
 
 7680 
 
 7734 
 
 7787 
 
 7841 
 
 7895 
 
 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. 
 
 
 
 159 
 
 No. 810 L. 908.] 
 
 
 
 
 
 [No. 854 L. 931. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 810 
 
 908485 
 
 8539 
 
 8592 
 
 8646 
 
 8699 
 
 8753 
 
 8807 
 
 8860 
 
 8914 
 
 8967 
 
 
 1 
 
 9021 
 
 9074 
 
 9128 
 
 9181 
 
 9235 
 
 9289 
 
 9342 
 
 9396 
 
 9449 
 
 9503 
 
 
 2 
 
 9556 
 
 9610 
 
 9663 
 
 9716 
 
 9770 
 
 9823 
 
 9877 
 
 9930 
 
 9984 
 
 
 
 
 
 
 
 0037 
 0571 
 
 
 3 
 
 910091 
 
 0144 
 
 0197 
 
 0251 
 
 0304 
 
 0358 
 
 0411 
 
 0464 
 
 0518 
 
 
 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 
 
 
 I 
 
 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 
 
 
 I 
 
 9601 
 
 9653 
 
 9706 
 
 9758 
 
 9810 
 
 9862 
 
 9914 
 
 9967 
 
 
 
 
 
 0019 
 0541 
 
 0071 
 0593 
 
 
 2 
 
 920123 
 
 0176 
 
 0228 
 
 0280 
 
 0332 
 
 0384 
 
 0436 
 
 0489 
 
 
 3 
 
 0645 
 
 0697 
 
 0749 
 
 0801 
 
 0853 
 
 0906 
 
 0958 
 
 1010 
 
 1062 
 
 1114 
 
 52 
 
 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 
 1 
 
 9419 
 9930 
 
 9470 
 9981 
 
 9521 
 
 9572 
 
 9623 
 
 9674 
 
 9725 
 
 9776 
 
 9827 
 
 9879 
 
 51 
 
 
 0032 
 0542 
 
 0083 
 0592 
 
 0134 
 0643 
 
 0185 
 0694 
 
 0236 
 0745 
 
 0287 
 0796 
 
 0338 
 0847 
 
 0389 
 0898 
 
 2 
 
 930440 
 
 0491 
 
 
 3 
 
 0949 
 
 1000 
 
 1051 
 
 1102 
 
 1153 
 
 1204 
 
 1254 
 
 1305 
 
 1356 
 
 1407 
 
 
 4 
 
 1458 
 
 1509 
 
 1560 
 
 1610 
 
 1661 
 
 1712 
 
 1763 
 
 1814 
 
 1865 
 
 1915 
 
 
 Proportional Parts. 
 
 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 
 
 6 
 
 31.8 
 31.2 
 30.6 
 30.0 
 
 37.1 
 36.4 
 35.7 
 35.0 
 
 8 
 
 42.4 
 41.6 
 40.8 
 40.0 
 
160 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 855 L. 931.] 
 
 
 
 
 
 
 
 [No 
 
 . 899 L. 954. 
 
 N. 
 
 
 
 1 
 
 2 
 
 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 
 
 8 
 
 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 
 0467 
 
 
 1 
 
 940018 
 
 0068 
 
 0118 
 
 0168 
 
 0218 
 
 0267 
 
 0317 
 
 0367 
 
 0417 
 
 
 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 
 
 
 5 
 
 2008 
 
 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 
 
 
 890 
 I 
 
 9390 
 
 9878 
 
 9439 
 9926 
 
 9488 
 9975 
 
 9536 
 
 9585 
 
 9634 
 
 9683 
 
 9731 
 
 97.80 
 
 9829 
 
 
 
 0024 
 0511 
 
 0073 
 0560 
 
 0121 
 0608 
 
 0170 
 0657 
 
 0219 
 0706 
 
 0267 
 0754 
 
 0316 
 0303 
 
 
 2 
 
 950365 
 
 0414 
 
 0462 
 
 
 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 
 
 3033 
 
 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. 
 
 5.1 
 5.0 
 4.9 
 
 4.8 
 
 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 
 
 8 
 
 40.8 
 40.0 
 39.2 
 38.4 
 
LOGARITHMS OF NUMBERS. 
 
 161 
 
 No. 900 L. 954.] 
 
 
 
 
 
 
 
 [No 
 
 944 L 
 
 .975. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 900 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 910 
 
 1 
 2 
 
 954243 
 4725 
 5207 
 5683 
 6168 
 6649 
 7128 
 7607 
 8086 
 8564 
 
 9041 
 9518 
 9995 
 
 4291 
 4773 
 5255 
 5736 
 6216 
 6697 
 7176 
 7655 
 8134 
 8612 
 
 9089 
 9566 
 
 4339 
 4821 
 5303 
 5784 
 6265 
 6745 
 7224 
 7703 
 8181 
 8659 
 
 9137 
 
 9614 
 
 4387 
 4869 
 5351 
 5832 
 6313 
 6793 
 7272 
 7751 
 8229 
 8707 
 
 9185 
 9661 
 
 4435 
 4918 
 5399 
 5880 
 6361 
 6840 
 7320 
 7799 
 8277 
 8755 
 
 9232 
 9709 
 
 4484 
 4966 
 5447 
 5928 
 6409 
 6888 
 7368 
 7847 
 8325 
 8803 
 
 9280 
 9757 
 
 4532 
 5014 
 5495 
 5976 
 6457 
 6936 
 7416 
 7894 
 8373 
 8850 
 
 9328 
 9804 
 
 4580 
 5062 
 5543 
 6024 
 6505 
 6984 
 7464 
 7942 
 8421 
 8898 
 
 9375 
 9852 
 
 4628 
 5110 
 5592 
 6072 
 6553 
 7032 
 7512 
 7990 
 8468 
 8946 
 
 9423 
 9900 
 
 4677 
 5158 
 5640 
 6120 
 6601 
 7080 
 7559 
 8038 
 8516 
 8994 
 
 9471 
 9947 
 
 48 
 
 0042 
 0518 
 0994 
 1469 
 1943 
 2417 
 2890 
 3363 
 
 3835 
 4307 
 4778 
 5249 
 5719 
 6189 
 6658 
 7127 
 7595 
 8062 
 
 8530 
 8996 
 9463 
 
 9928 
 
 0090 
 0566 
 1041 
 1516 
 1990 
 2464 
 2937 
 3410 
 
 3882 
 4354 
 4825 
 5296 
 5766 
 6236 
 6705 
 7173 
 7642 
 8109 
 
 8576 
 9043 
 9509 
 9975 
 
 0138 
 0613 
 1089 
 1563 
 2038 
 2511 
 2985 
 3457 
 
 3929 
 4401 
 4872 
 5343 
 5813 
 6283 
 6752 
 7220 
 7688 
 8156 
 
 8623 
 9090 
 9556 
 
 0185 
 0661 
 1136 
 1611 
 2085 
 2559 
 3032 
 3504 
 
 3977 
 4448 
 4919 
 5390 
 5860 
 6329 
 6799 
 7267 
 7735 
 8203 
 
 8670 
 9136 
 9602 
 
 0233 
 0709 
 1184 
 1658 
 2132 
 2606 
 3079 
 3552 
 
 4024 
 4495 
 4966 
 5437 
 5907 
 6376 
 6845 
 7314 
 7782 
 8249 
 
 8716 
 
 9183 
 9649 
 
 0280 
 0756 
 1231 
 1706 
 2180 
 2653 
 3126 
 3599 
 
 4071 
 
 4542 
 5013 
 5484 
 5954 
 6423 
 6892 
 7361 
 7829 
 8296 
 
 8763 
 9229 
 9695 
 
 0328 
 0804 
 1279 
 1753 
 2227 
 2701 
 3174 
 3646 
 
 4118 
 4590 
 5061 
 5531 
 6001 
 6470 
 6939 
 7408 
 7875 
 8343 
 
 8810 
 9276 
 9742 
 
 0376 
 0851 
 1326 
 1801 
 2275 
 2748 
 3221 
 3693 
 
 4165 
 4637 
 5108 
 5578 
 6048 
 6517 
 6986 
 7454 
 7922 
 8390 
 
 8856 
 9323 
 9789 
 
 0423 
 0899 
 1374 
 1848 
 2322 
 2795 
 3268 
 3741 
 
 4212 
 4684 
 5155 
 5625 
 6095 
 6564 
 7033 
 7501 
 7969 
 8436 
 
 8903 
 9369 
 9835 
 
 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 920 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 930 
 
 1 
 
 2 
 3 
 
 960471 
 0946 
 1421 
 1895 
 2369 
 2843 
 3316 
 
 3788 
 4260 
 4731 
 5202 
 5672 
 6142 
 6611 
 7080 
 7548 
 8016 
 
 8483 
 8950 
 9416 
 
 9882 
 
 47 
 
 0021 
 0486 
 
 0951 
 1-415 
 1879 
 2342 
 2804 
 
 3266 
 3728 
 4189 
 4650 
 5110 
 
 0068 
 0533 
 0997 
 1461 
 1925 
 2388 
 2851 
 
 3313 
 
 3774 
 4235 
 4696 
 5156 
 
 0114 
 0579 
 1044 
 1508 
 1971 
 2434 
 2897 
 
 3359 
 3820 
 4281 
 4742 
 5202 
 
 0161 
 0626 
 1090 
 1554 
 2018 
 2481 
 2943 
 
 3405 
 3866 
 
 4327 
 4788 
 
 5248 
 
 0207 
 0672 
 1137 
 1601 
 2064 
 2527 
 2989 
 
 3451 
 3913 
 
 4374 
 4834 
 5294 
 
 0254 
 0719 
 1183 
 1647 
 2110 
 2573 
 3035 
 
 3497 
 3959 
 4420 
 4880 
 5340 
 
 0300 
 0765 
 1229 
 1693 
 2157 
 2619 
 3082 
 
 3543 
 4005 
 4466 
 4926 
 5386 
 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 940 
 1 
 
 2 
 3 
 
 4 
 
 970347 
 0812 
 1276 
 1740 
 2203 
 2666 
 
 3128 
 3590 
 4051 
 4512 
 4972 
 
 0393 
 
 0858 
 1322 
 1786 
 2249 
 2712 
 
 3174 
 3636 
 4097 
 
 4558 
 5018 
 
 0440 
 0904 
 1369 
 
 1832 
 2295 
 2758 
 
 3220 
 3682 
 4143 
 4604 
 5064 
 
 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 
 
162 
 
 LOGARITHMS OF NUMBERS. 
 
 No. 945 L. 975.] 
 
 [No. 
 
 N. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 945 
 6 
 7 
 8 
 9 
 
 950 
 
 1 
 2 
 3 
 
 4 
 
 975432 
 5891 
 6350 
 6808 
 7266 
 
 7724 
 
 8181 
 8637 
 9093 
 9548 
 
 5478 
 5937 
 6396 
 6854 
 7312 
 
 7769 
 
 8226 
 8683 
 9138 
 9594 
 
 5524 
 5983 
 6442 
 6900 
 7358 
 
 7815 
 
 8272 
 8728 
 9184 
 9639 
 
 5570 
 6029 
 6488 
 6946 
 7403 
 
 7861 
 
 8317 
 8774 
 9230 
 9685 
 
 5616 
 6075 
 6533 
 6992 
 7449 
 
 7906 
 8363 
 8819 
 9275 
 9730 
 
 5662 
 6121 
 6579 
 7037 
 7495 
 
 7952 
 8409 
 8865 
 9321 
 9776 
 
 5707 
 6167 
 6625 
 7083 
 7541 
 
 7998 
 8454 
 8911 
 9366 
 9821 
 
 5753 
 6212 
 6671 
 7129 
 7586 
 
 8043 
 8500 
 8956 
 9412 
 9867 
 
 5799 
 6258 
 6717 
 7175 
 7632 
 
 8089 
 8546 
 9002 
 9457 
 9912 
 
 5845 
 6304 
 6763 
 7220 
 7678 
 
 8135 
 8591 
 9047 
 9503 
 9958 
 
 
 5 
 6 
 
 7 
 8 
 9 
 
 960 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 970 
 
 1 
 2 
 
 A 
 
 5 
 6 
 
 7 
 
 980003 
 0458 
 0912 
 1366 
 1819 
 
 2271 
 2723 
 3175 
 3626 
 4077 
 4527 
 4977 
 5426 
 5875 
 6324 
 
 6772 
 7219 
 7666 
 8113 
 8559 
 9005 
 9450 
 9895 
 
 0049 
 0503 
 0957 
 1411 
 1864 
 
 2316 
 2769 
 3220 
 3671 
 4122 
 4572 
 5022 
 5471 
 5920 
 6369 
 
 6817 
 7264 
 7711 
 8157 
 8604 
 9049 
 9494 
 9939 
 
 0094 
 0549 
 1003 
 1456 
 1909 
 
 2362 
 2814 
 3265 
 3716 
 4167 
 4617 
 5067 
 5516 
 5965 
 6413 
 
 6861 
 7309 
 7756 
 8202 
 8648 
 9094 
 9539 
 9983 
 
 0140 
 0594 
 1048 
 1501 
 1954 
 
 2407 
 2859 
 3310 
 3762 
 4212 
 4662 
 5112 
 5561 
 6010 
 6458 
 
 6906 
 7353 
 7800 
 8247 
 8693 
 9138 
 9583 
 
 0185 
 0640 
 1093 
 1547 
 2000 
 
 2452 
 2904 
 3356 
 3807 
 4257 
 4707 
 5157 
 5606 
 6055 
 6503 
 
 6951 
 
 7398 
 7845 
 8291 
 8737 
 9183 
 9628 
 
 0231 
 0685 
 1139 
 1592 
 2045 
 
 2497 
 2949 
 3401 
 3852 
 4302 
 4752 
 5202 
 5651 
 6100 
 6548 
 
 6996 
 7443 
 7890 
 8336 
 8782 
 9227 
 9672 
 
 0276 
 0730 
 1184 
 1637 
 2090 
 
 2543 
 2994 
 3446 
 3897 
 4347 
 4797 
 5247 
 5696 
 6144 
 6593 
 
 7040 
 7488 
 7934 
 8381 
 8826 
 9272 
 9717 
 
 0322 
 0776 
 1229 
 1683 
 2135 
 
 2588 
 3040 
 3491 
 3942 
 4392 
 4842 
 5292 
 5741 
 6189 
 6637 
 
 7085 
 7532 
 7979 
 8425 
 8871 
 9316 
 9761 
 
 0367 
 0821 
 1275 
 1728 
 2181 
 
 2633 
 3085 
 3536 
 3987 
 4437 
 4887 
 5337 
 5786 
 6234 
 6682 
 
 7130 
 7577 
 8024 
 8470 
 8916 
 9361 
 9806 
 
 0412 
 0867 
 1320 
 1773 
 2226 
 
 2678 
 3130 
 3581 
 4032 
 4482 
 4932 
 5382 
 5830 
 6279 
 6727 
 
 7175 
 7622 
 8068 
 8514 
 8960 
 9405 
 9850 
 
 45 
 
 0028 
 0472 
 0916 
 
 1359 
 1802 
 2244 
 2686 
 3127 
 3568 
 4009 
 4449 
 4889 
 5328 
 
 0072 
 0516 
 0960 
 
 1403 
 1846 
 2288 
 2730 
 3172 
 3613 
 4053 
 4493 
 4933 
 5372 
 
 0117 
 0561 
 1004 
 
 1448 
 1890 
 2333 
 2774 
 3216 
 3657 
 4097 
 4537 
 4977 
 5416 
 
 0161 
 0605 
 1049 
 
 1492 
 1935 
 2377 
 2819 
 3260 
 3701 
 4141 
 4581 
 5021 
 5460 
 
 0206 
 0650 
 1093 
 
 1536 
 1979 
 2421 
 2863 
 3304 
 3745 
 4185 
 4625 
 5065 
 5504 
 
 0250 
 0694 
 1137 
 
 1580 
 2023 
 2465 
 2907 
 3348 
 3789 
 4229 
 4669 
 5108 
 5547 
 
 0294 
 0738 
 1182 
 
 1625 
 2067 
 2509 
 2951 
 3392 
 3833 
 4273 
 4713 
 5152 
 5591 
 
 
 8 
 9 
 
 980 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 990339 
 0783 
 
 1226 
 1669 
 2111 
 2554 
 2995 
 3436 
 3877 
 4317 
 4757 
 5196 
 
 0383 
 0827 
 
 1270 
 1713 
 2156 
 
 2598 
 3039 
 3480 
 3921 
 4361 
 4801 
 5240 
 
 0428 
 0871 
 
 1315 
 
 1758 
 2200 
 2642 
 3083 
 3524 
 3965 
 4405 
 4845 
 5284 
 
 44 
 
 Proportional Parts. 
 
 Diff. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 46 
 
 4.6 
 
 9.2 
 
 13.8 
 
 18.4 
 
 23.0 
 
 27.6 
 
 32.2 
 
 36.8 
 
 41.4 
 
 45 
 
 4.5 
 
 9.0 
 
 13.5 
 
 18.0 
 
 22.5 
 
 27.0 
 
 31.5 
 
 36.0 
 
 40.5 
 
 44 
 
 4.4 
 
 8.8 
 
 13.2 
 
 17.6 
 
 22.0 
 
 26.4 
 
 30.8 
 
 35.2 
 
 39.6 
 
 43 
 
 4.3 
 
 8.6 
 
 12.9 
 
 17.2 
 
 21.5 
 
 25.8 
 
 30.1 
 
 34.4 
 
 38.7 
 
HYPERBOLIC LOGARITHMS. 
 
 163 
 
 No. 990 L. 995.] 
 
 [No. 999 L. 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 
 
 1.89 
 
 .6366 
 
 2.33 
 
 .8458 
 
 2.77 
 
 1.0188 
 
 1.02 
 
 .0198 
 
 1.46 
 
 .3784 
 
 1.90 
 
 .6419 
 
 2.34 
 
 .8502 
 
 2.78 
 
 1 .0225 
 
 1.03 
 
 .0296 
 
 1.47 
 
 .3853 
 
 1.91 
 
 .6471 
 
 2.35 
 
 .8544 
 
 2.79 
 
 1 .0260 
 
 1.04 
 
 .0392 
 
 1.48 
 
 .3920 
 
 1.92 
 
 .6523 
 
 2.36 
 
 .8587 
 
 2.80 
 
 1 .0296 
 
 1.05 
 
 .0488 
 
 1.49 
 
 .3988 
 
 1.93 
 
 .6575 
 
 2.37 
 
 .8629 
 
 2.81 
 
 1 .0332 
 
 1.06 
 
 .0583 
 
 1.50 
 
 .4055 
 
 1.94 
 
 .6627 
 
 2.38 
 
 .8671 
 
 2.82 
 
 1 .0367 
 
 1.07 
 
 .0677 
 
 1.51 
 
 .4121 
 
 1.95 
 
 .6678 
 
 2.39 
 
 .8713 
 
 2.83 
 
 1 .0403 
 
 1.08 
 
 .0770 
 
 1.52 
 
 .4187 
 
 1.96 
 
 .6729 
 
 2.40 
 
 .8755 
 
 2.84 
 
 1 .0438 
 
 1.09 
 
 .0862 
 
 1.53 
 
 .4253 
 
 1.97 
 
 .6780 
 
 2.41 
 
 .8796 
 
 2.85 
 
 1.0473 
 
 1.10 
 
 .0953 
 
 1.54 
 
 .4318 
 
 1.98 
 
 .6831 
 
 2.42 
 
 .8838 
 
 2.86 
 
 1 .0508 
 
 1.11 
 
 .1044 
 
 1.55 
 
 .4383 
 
 1.99 
 
 .6881 
 
 2.43 
 
 .8879 
 
 2.87 
 
 1.0543 
 
 1.12 
 
 .1133 
 
 1.56 
 
 .4447 
 
 2.00 
 
 .6931 
 
 2.44 
 
 .8920 
 
 2.88 
 
 1.0578 
 
 1.13 
 
 .1222 
 
 1.57 
 
 .4511 
 
 2.01 
 
 .6981 
 
 2.45 
 
 .8961 
 
 2.89 
 
 1.0613 
 
 1.14 
 
 .1310 
 
 1.58 
 
 .4574 
 
 2.02 
 
 .7031 
 
 2.46 
 
 .9002 
 
 2.90 
 
 1 .0647 
 
 1.15 
 
 .1398 
 
 1.59 
 
 .4637 
 
 2.03 
 
 .7080 
 
 2.47 
 
 .9042 
 
 2.91 
 
 1 .0682 
 
 1.16 
 
 .1484 
 
 1.60 
 
 .4700 
 
 2.04 
 
 .7129 
 
 2.48 
 
 .9083 
 
 2.92 
 
 1.0716 
 
 1.17 
 
 .1570 
 
 1.61 
 
 .4762 
 
 2.05 
 
 .7178 
 
 2.49 
 
 .9123 
 
 2.93 
 
 1.0750 
 
 1.18 
 
 .1655 
 
 1.62 
 
 .4824 
 
 2.06 
 
 .7227 
 
 2.50 
 
 .9163 
 
 2.94 
 
 1 .0784 
 
 1.19 
 
 .1740 
 
 1.63 
 
 .4886 
 
 2.07 
 
 .7275 
 
 2.51 
 
 .9203 
 
 2.95 
 
 1.0818 
 
 1.20 
 
 .1823 
 
 1.64 
 
 .4947 
 
 2.08 
 
 .7324 
 
 2.52 
 
 .9243 
 
 2.96 
 
 1 .0852 
 
 1.21 
 
 .1906 
 
 1.65 
 
 .5008 
 
 2.09 
 
 .7372 
 
 2.53 
 
 .9282 
 
 2.97 
 
 1 .0886 
 
 1.22 
 
 .1988 
 
 1.66 
 
 .5068 
 
 2.10 
 
 .7419 
 
 2.54 
 
 .9322 
 
 2.98 
 
 1.0919 
 
 1.23 
 
 .2070 
 
 1.67 
 
 .5128 
 
 2.11 
 
 .7467 
 
 2.55 
 
 .9361 
 
 2.99 
 
 1 .0953 
 
 1.24 
 
 .2151 
 
 1.68 
 
 .5188 
 
 2.12 
 
 .7514 
 
 2.56 
 
 .9400 
 
 3.00 
 
 1 .0986 
 
 1.25 
 
 .2231 
 
 1.69 
 
 .5247 
 
 2.13 
 
 .7561 
 
 2.57 
 
 .9439 
 
 3.01 
 
 1.1019 
 
 1.26 
 
 .2311 
 
 1.70 
 
 .5306 
 
 2.14 
 
 .7608 
 
 2.58 
 
 .9478 
 
 3.02 
 
 1.1056 
 
 1.27 
 
 .2390 
 
 1.71 
 
 .5365 
 
 2.15 
 
 .7655 
 
 2.59 
 
 .9517 
 
 3.03 
 
 1.1081 
 
 1.28 
 
 .2469 
 
 1.72 
 
 .5423 
 
 2.16 
 
 .7701 
 
 2.60 
 
 .9555 
 
 3.04 
 
 1.1113 
 
 1.29 
 
 .2546 
 
 1.73 
 
 .5481 
 
 2.17 
 
 .7747 
 
 2.61 
 
 .9594 
 
 3.05 
 
 1.1154 
 
 1.30 
 
 .2624 
 
 1.74 
 
 .5539 
 
 2.18 
 
 .7793 
 
 2.62 
 
 .9632 
 
 3.06 
 
 1.1187 
 
 1.31 
 
 .2700 
 
 1.75 
 
 .5596 
 
 2.19 
 
 .7839 
 
 2.63 
 
 .9670 
 
 3.07 
 
 1.1219 
 
 1.32 
 
 .2776 
 
 1.76 
 
 .5653 
 
 2.20 
 
 .7885 
 
 2.64 
 
 .9708 
 
 3.08 
 
 1.1246 
 
 1.33 
 
 .2852 
 
 1.77 
 
 .5710 
 
 2.21 
 
 .7930 
 
 2.65 
 
 .9746 
 
 3.09 
 
 1.1284 
 
 1.34 
 
 .2927 
 
 1.78 
 
 .5766 
 
 2.22 
 
 .7975 
 
 2.66 
 
 .9783 
 
 3.10 
 
 1.1312 
 
 1.35 
 
 .3001 
 
 1.79 
 
 .5822 
 
 2.23 
 
 .8020 
 
 2.67 
 
 .9821 
 
 3.11 
 
 1.1349 
 
 1.36 
 
 .3075 
 
 1.80 
 
 .5878 
 
 2.24 
 
 .8065 
 
 2.68 
 
 .9858 
 
 3.12 
 
 1.1378 
 
 1.37 
 
 .3148 
 
 1.81 
 
 .5933 
 
 2.25 
 
 .8109 
 
 2.69 
 
 .9895 
 
 3.13 
 
 1.1410 
 
 1.38 
 
 .3221 
 
 1.82 
 
 .5988 
 
 2.26 
 
 .8154 
 
 2.70 
 
 .9933 
 
 3.14 
 
 1.1442 
 
 1.39 
 
 .3293 
 
 1.83 
 
 .6043 
 
 2.27 
 
 .8198 
 
 2.71 
 
 .9969 
 
 3.15 
 
 1.1474 
 
 1.40 
 
 .3365 
 
 1.84 
 
 .6098 
 
 2.28 
 
 .8242 
 
 2.72 
 
 1 .0006 
 
 3.16 
 
 1.1506 
 
 1.41 
 
 .3436 
 
 1.85 
 
 .6152 
 
 2.29 
 
 .8286 
 
 2.73 
 
 1 .0043 
 
 3.17 
 
 1.1537 
 
 1.42 
 
 .3507 
 
 1.86 
 
 .6206 
 
 2.30 
 
 .8329 
 
 2.74 
 
 1 .0080 
 
 3.18 
 
 1.1569 
 
 1.43 
 
 .3577 
 
 1.87 
 
 .6259 
 
 2.31 
 
 .8372 
 
 2.75 
 
 1.0116 
 
 3.19 
 
 1.1600 
 
 1.44 
 
 .3646 
 
 1.88 
 
 .6313 
 
 2.32 
 
 .8416 
 
 2.76 
 
 1.0152 
 
 3.20 
 
 1.1632 
 
164 
 
 MATHEMATICAL TABLES. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 3.21 
 
 1.1663 
 
 3.87 
 
 1.3533 
 
 4.53 
 
 1.5107 
 
 5.19 
 
 1 .6467 
 
 5.85 
 
 1.7664 
 
 3.22 
 
 1.1694 
 
 3.88 
 
 1.3558 
 
 4.54 
 
 1.5129 
 
 5.20 
 
 1.6487 
 
 5.86 
 
 1.7681 
 
 3.23 
 
 1.1725 
 
 3.89 
 
 1.3584 
 
 4.55 
 
 1.5151 
 
 5.21 
 
 1.6506 
 
 5.87 
 
 1 .7699 
 
 3.24 
 
 1.1756 
 
 3.90 
 
 1.3610 
 
 4.56 
 
 1.5173 
 
 5.22 
 
 1.6525 
 
 5.88 
 
 1.7716 
 
 3.25 
 
 1.1787 
 
 3.91 
 
 1.3635 
 
 4.57 
 
 1.5195 
 
 5.23 
 
 1.6544 
 
 5.89 
 
 1.7733 
 
 3.26 
 
 1.1817 
 
 3.92 
 
 1.3661 
 
 4.58 
 
 1.5217 
 
 5.24 
 
 1 .6563 
 
 5.90 
 
 1.7750 
 
 3.27 
 
 1.1848 
 
 3.93 
 
 1.3686 
 
 4.59 
 
 1.5239 
 
 5.25 
 
 1.6582 
 
 5.91 
 
 1.7766 
 
 3.28 
 
 1.1878 
 
 3.94 
 
 1.3712 
 
 4.60 
 
 1.5261 
 
 5.26 
 
 1.6601 
 
 5.92 
 
 1.7783 
 
 3.29 
 
 1.1909 
 
 3.95 
 
 1.3737 
 
 4.61 
 
 1.5282 
 
 5.27 
 
 1 .6620 
 
 5.93 
 
 1.7800 
 
 3.30 
 
 1.1939 
 
 3.96' 
 
 1.3762 
 
 4.62 
 
 1.5304 
 
 5.28 
 
 1 .6639 
 
 5.94 
 
 1.7817 
 
 3.31 
 
 1.1969 
 
 3.97 
 
 1.3788 
 
 4.63 
 
 1.5326 
 
 5.29 
 
 1 .6658 
 
 5.95 
 
 1.7834 
 
 3.32 
 
 1.1999 
 
 3.98 
 
 1.3813 
 
 4.64 
 
 1.5347 
 
 5.30 
 
 1 .6677 
 
 5.96 
 
 1.7851 
 
 3.33 
 
 1 .2030 
 
 3.99 
 
 1.3838 
 
 4.65 
 
 1.5369 
 
 5.31 
 
 1 .6696 
 
 5.97 
 
 1.7867 
 
 3.34 
 
 1 .2060 
 
 4.00 
 
 1.3863 
 
 4.66 
 
 1.5390 
 
 5.32 
 
 1.6715 
 
 5.98 
 
 1 .7884 
 
 3.35 
 
 1 .2090 
 
 4.01 
 
 1.3888 
 
 4.67 
 
 1.5412 
 
 5.33 
 
 1.6734 
 
 5.99 
 
 1.7901 
 
 3.36 
 
 1.2119 
 
 4.02 
 
 1.3913 
 
 4.68 
 
 1.5433 
 
 5.34 
 
 1.6752 
 
 6.00 
 
 1.7918 
 
 3.37 
 
 1.2149 
 
 4.03 
 
 1.3938 
 
 4.69 
 
 1.5454 
 
 5.35 
 
 1.6771 
 
 6.01 
 
 1.7934 
 
 3.38 
 
 1.2179 
 
 4.04 
 
 1 .3962 
 
 4.70 
 
 1.5476 
 
 5.36 
 
 1 .6790 
 
 6.02 
 
 1.7951 
 
 3.39 
 
 1 .2208 
 
 4.05 
 
 1.3987 
 
 4.71 
 
 1.5497 
 
 5.37 
 
 1 .6808 
 
 6.03 
 
 1.7967 
 
 3.40 
 
 1.2238 
 
 4.06 
 
 1.4012 
 
 4.72 
 
 1.5518 
 
 5.38 
 
 1 .6827 
 
 6.04 
 
 1.7984 
 
 3.41 
 
 1 .2267 
 
 4.07 
 
 1.4036 
 
 4.73 
 
 1.5539 
 
 5.39 
 
 1 .6845 
 
 6.05 
 
 1.8001 
 
 3.42 
 
 1 .2296 
 
 4.08 
 
 1.4061 
 
 4.74 
 
 1.5560 
 
 5.40 
 
 1 .6864 
 
 606 
 
 1.8017 
 
 3.43 
 
 1.2326 
 
 4.09 
 
 1 .4085 
 
 4.75 
 
 1.5581 
 
 5.41 
 
 1 .6882 
 
 6.07 
 
 1.8034 
 
 3.44 
 
 1.2355 
 
 4.10 
 
 1.4110 
 
 4.76 
 
 1.5602 
 
 5.42 
 
 1.6901 
 
 6.08 
 
 1 .8050 
 
 3.45 
 
 1.2384 
 
 4.11 
 
 1.4134 
 
 4.77 
 
 1.5623 
 
 5.43 
 
 1.6919 
 
 6.09 
 
 1 .8066 
 
 3.46 
 
 1.2413 
 
 4.12 
 
 1.4159 
 
 4.78 
 
 1.5644 
 
 5.44 
 
 1 .6938 
 
 6.10 
 
 1 .8083 
 
 3.47 
 
 1 .2442 
 
 4.13 
 
 1.4183 
 
 4.79 
 
 1.5665 
 
 5.45 
 
 1.6956 
 
 6.11 
 
 1 .8099 
 
 3.48 
 
 1 .2470 
 
 4.14 
 
 1 .4207 
 
 4.80 
 
 1.5686 
 
 5.46 
 
 1 .6974 
 
 6.12 
 
 1.8116 
 
 3.49 
 
 1.2499 
 
 4.15 
 
 1 .423 1 
 
 4.81 
 
 1.5707 
 
 5.47 
 
 1 .6993 
 
 6.13 
 
 1.8132 
 
 3.50 
 
 1.2528 
 
 4.16 
 
 1.4255 
 
 4.82 
 
 1.5728 
 
 5.48 
 
 1.7011 
 
 6.14 
 
 1.8148 
 
 3.51 
 
 1.2556 
 
 4.17 
 
 1 .4279 
 
 4.83 
 
 1.5748 
 
 5.49 
 
 1 .7029 
 
 6.15 
 
 1.8165 
 
 3.52 
 
 1.2585 
 
 4.18 
 
 1 .4303 
 
 4.84 
 
 1.5769 
 
 5.50 
 
 1.7047 
 
 6.16 
 
 1.8181 
 
 3.53 
 
 1.2613 
 
 4.19 
 
 1.4327 
 
 4.85 
 
 1.5790 
 
 5.51 
 
 1 .7066 
 
 6.17 
 
 1.8197 
 
 3.54 
 
 1.2641 
 
 4.20 
 
 1.4351 
 
 4.86 
 
 1.5810 
 
 5.52 
 
 1.7084 
 
 6.18 
 
 1.8213 
 
 3.55 
 
 1 .2669 
 
 4.21 
 
 1.4375 
 
 4.87 
 
 1.5831 
 
 5.53 
 
 1.7102 
 
 6.19 
 
 1 .8229 
 
 3.56 
 
 1 .2698 
 
 4.22 
 
 1.4398 
 
 4.88 
 
 1.5851 
 
 5.54 
 
 1.7120 
 
 6.20 
 
 1.8245 
 
 3.57 
 
 1.2726 
 
 4.23 
 
 1 .4422 
 
 4.89 
 
 1.5872 
 
 5.55 
 
 1.7138 
 
 6.21 
 
 1.8262 
 
 3.58 
 
 1.2754 
 
 4.24 
 
 1 .4446 
 
 4.90 
 
 1.5892 
 
 5.56 
 
 1.7156 
 
 6.22 
 
 1.8278 
 
 3.59 
 
 1.2782 
 
 4.25 
 
 1 .4469 
 
 4.91 
 
 1.5913 
 
 5.57 
 
 1.7174 
 
 6.23 
 
 1.8294 
 
 3.60 
 
 1 .2809 
 
 4.26 
 
 1 .4493 
 
 4.92 
 
 1.5933 
 
 5.58 
 
 1.7192 
 
 6.24 
 
 1.8310 
 
 3.61 
 
 1.2837 
 
 4.27 
 
 1.4516 
 
 4.93 
 
 1.5953 
 
 5.59 
 
 1.7210 
 
 6.25 
 
 1.8326 
 
 3.62 
 
 1.2865 
 
 4.28 
 
 1 .4540 
 
 4.94 
 
 1.5974 
 
 5.60 
 
 1.7228 
 
 6.26 
 
 1.8342 
 
 3.63 
 
 1 .2892 
 
 4.29 
 
 1.4563 
 
 4.95 
 
 1.5994 
 
 5.61 
 
 1.7246 
 
 6.27 
 
 1.8358 
 
 3.64 
 
 1 .2920 
 
 4.30 
 
 1 .4586 
 
 4.96 
 
 1.6014 
 
 5.62 
 
 1.7263 
 
 6.28 
 
 1.8374 
 
 3 65 
 
 1.2947 
 
 4.31 
 
 1 .4609 
 
 4.97 
 
 1.6034 
 
 5.63 
 
 1.7281 
 
 6.29 
 
 1.8390 
 
 3.66 
 
 1.2975 
 
 4.32 
 
 1.4633 
 
 4.98 
 
 1.6054 
 
 5.64 
 
 1 .7299 
 
 6.30 
 
 1 .8405 
 
 3.67 
 
 1.3002 
 
 4.33 
 
 1.4656 
 
 4.99 
 
 1.6074 
 
 5.65 
 
 1.7317 
 
 6.31 
 
 1.8421 
 
 3.68 
 
 1 .3029 
 
 4.34 
 
 1 .4679 
 
 5.00 
 
 1 .6094 
 
 5.66 
 
 1.7334 
 
 6.32 
 
 1.8437 
 
 3.69 
 
 1.3056 
 
 4.35 
 
 1 .4702 
 
 5.01 
 
 1.6114 
 
 5.67 
 
 1.7352 
 
 6.33 
 
 1.8453 
 
 3.70 
 
 1.3083 
 
 4.36 
 
 1 .4725 
 
 5.02 
 
 1.6134 
 
 5.68 
 
 1.7370 
 
 6.34 
 
 1 .8469 
 
 3.71 
 
 1.3110 
 
 4.37 
 
 1 .4748 
 
 5.03 
 
 1.6154 
 
 5.69 
 
 1.7387 
 
 6.35 
 
 1 .8485 
 
 3.72 
 
 1.3137 
 
 4.38 
 
 1.4770 
 
 5.04 
 
 1.6174 
 
 5.70 
 
 1 .7405 
 
 6.36 
 
 1.8500 
 
 3.73 
 
 1.3164 
 
 4.39 
 
 1.4793 
 
 5.05 
 
 1.6194 
 
 5.71 
 
 1.7422 
 
 6.37 
 
 1.8516 
 
 3.74 
 
 1.3191 
 
 4.40 
 
 1.4816 
 
 5.06 
 
 1.6214 
 
 5.72 
 
 1.7440 
 
 6.38 
 
 1.8532 
 
 3.75 
 
 1.3218 
 
 4.41 
 
 1.4839 
 
 5.07 
 
 1.6233 
 
 5.73 
 
 1.7457 
 
 6.39 
 
 1.8547 
 
 3.76 
 
 1.3244 
 
 4.42 
 
 1.4861 
 
 5.08 
 
 1.6253 
 
 5.74 
 
 1.7475 
 
 6.40 
 
 1.8563 
 
 3.77 
 
 1.3271 
 
 4.43 
 
 1 .4884 
 
 5.09 
 
 1.6273 
 
 5.75 
 
 1 .7492 
 
 6.41 
 
 1.8579 
 
 3.78 
 
 1.3297 
 
 4.44 
 
 1 .4907 
 
 5.10 
 
 1 .6292 
 
 5.76 
 
 1.7509 
 
 6.42 
 
 1.8594 
 
 3.79 
 
 1.3324 
 
 4.45 
 
 1 .4929 
 
 5.11 
 
 1.6312 
 
 5.77 
 
 1.7527 
 
 6.43 
 
 1.8610 
 
 3.80 
 
 1.3350 
 
 4.46 
 
 1.4951 
 
 5.12 
 
 1.6332 
 
 5.78 
 
 1.7544 
 
 6.44 
 
 1.8625 
 
 3.81 
 
 1.3376 
 
 4.47 
 
 1.4974 
 
 5.13 
 
 1.6351 
 
 5.79 
 
 1.7561 
 
 6.45 
 
 1.8641 
 
 3.82 
 
 1.3403 
 
 4.48 
 
 1 .4996 
 
 5.14 
 
 1.6371 
 
 5.80 
 
 1.7579 
 
 6.46 
 
 1 .8656 
 
 3.83 
 
 1.3429 
 
 4.49 
 
 1.5019 
 
 5.15 
 
 1.6390 
 
 5.81 
 
 1.7596 
 
 6.47 
 
 1.8672 
 
 3.84 
 
 1.3455 
 
 4.50 
 
 1.5041 
 
 5.16 
 
 1 .6409 
 
 5.82 
 
 1.7613 
 
 6.43 
 
 1.8687 
 
 3.85 
 
 1.3481 
 
 4.51 
 
 1.5063 
 
 5.17 
 
 1 .6429 
 
 5.83 
 
 1.7630 
 
 6.49 
 
 1.8703 
 
 3.86 
 
 1.3507 
 
 4.52 
 
 1.5085 
 
 5.18 
 
 1 .6448 
 
 5.84 
 
 1.7647 
 
 6.50 
 
 1.8713 
 
HYPERBOLIC LOGARITHMS. 
 
 165 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No. 
 
 Log. 
 
 No 
 
 Log. 
 
 6.51 
 
 1.8733 
 
 7.15 
 
 1.9671 
 
 7.79 
 
 2.0528 
 
 8.66 
 
 2.1587 
 
 9.94 
 
 2.2966 
 
 6.52 
 
 1.8749 
 
 7.16 
 
 1.9685 
 
 7.80 
 
 2.0541 
 
 8.68 
 
 2.1610 
 
 9.96 
 
 2.2986 
 
 6.53 
 
 1.8764 
 
 7.17 
 
 1 .9699 
 
 7.81 
 
 2.0554 
 
 8.70 
 
 2.1633 
 
 9.98 
 
 2.3006 
 
 6.54 
 
 1.8779 
 
 7.18 
 
 1.9713 
 
 7.82 
 
 2.0567 
 
 8.72 
 
 2.1656 
 
 10.00 
 
 2.3026 
 
 6.55 
 
 1.8795 
 
 7.19 
 
 1.9727 
 
 7.83 
 
 2.0580 
 
 8.74 
 
 2.1679 
 
 10.25 
 
 2.3279 
 
 6.56 
 
 1.8810 
 
 7.20 
 
 1.9741 
 
 7.84 
 
 2.0592 
 
 8.76 
 
 2.1702 
 
 10.50 
 
 2.3513 
 
 6.57 
 
 1.8825 
 
 7.21 
 
 1.9754 
 
 7.85 
 
 2.0605 
 
 8.78 
 
 2.1725 
 
 10.75 
 
 2.3749 
 
 6.58 
 
 1 .8840 
 
 7.22 
 
 1 .9769 
 
 7.86 
 
 2.0618 
 
 8.80 
 
 2.1743 
 
 11.00 
 
 2.3979 
 
 6.59 
 
 1.8856 
 
 7.23 
 
 1.9782 
 
 7.87 
 
 2.0631 
 
 8.82 
 
 2.1770 
 
 11.25 
 
 2.4201 
 
 6.60 
 
 1.8871 
 
 7.24 
 
 1.9796 
 
 7.88 
 
 2.0643 
 
 8.84 
 
 2.1793 
 
 11.50 
 
 2.4430 
 
 6.61 
 
 1 .8886 
 
 7.25 
 
 1.9810 
 
 7.89 
 
 2.0656 
 
 8.86 
 
 2.1815 
 
 11.75 
 
 2.4636 
 
 6.62 
 
 1.8901 
 
 7.26 
 
 1.9824 
 
 7.90 
 
 2.0669 
 
 8.88 
 
 2.1838 
 
 12.00 
 
 2.4849 
 
 6.63 
 
 1.8916 
 
 7.27 
 
 1 .9838 
 
 7.91 
 
 2.0681 
 
 8.90 
 
 2.1861 
 
 12.25 
 
 2.5052 
 
 6.64 
 
 1.8931 
 
 7.28 
 
 1.9851 
 
 7.92 
 
 2.0694 
 
 8.92 
 
 2.1883 
 
 12.50 
 
 2.5262 
 
 6.65 
 
 1 .8946 
 
 7.29 
 
 1 .9865 
 
 7.93 
 
 2.0707 
 
 8.94 
 
 2.1905 
 
 12.75 
 
 2.5455 
 
 6.66 
 
 1.8961 
 
 7.30 
 
 1.9879 
 
 7.94 
 
 2.0719 
 
 8.96 
 
 2.1928 
 
 13.00 
 
 2.5649 
 
 6.67 
 
 1.8976 
 
 7.31 
 
 1 .9892 
 
 7.95 
 
 2.0732 
 
 8.98 
 
 2.1950 
 
 13.25 
 
 2.5840 
 
 6.68 
 
 1.8991 
 
 7.32 
 
 1 .9906 
 
 7.96 
 
 2.0744 
 
 9.00 
 
 2.1972 
 
 13.50 
 
 2.6027 
 
 6.69 
 
 1 .9006 
 
 7.33 
 
 1 .9920 
 
 7.97 
 
 2.0757 
 
 9.02 
 
 2.1994 
 
 13.75 
 
 2.6211 
 
 6.70 
 
 1.9021 
 
 7.34 
 
 1 .9933 
 
 7.98 
 
 2.0769 
 
 9.04 
 
 2.2017 
 
 14.00 
 
 2.6391 
 
 6.71 
 
 1 .9036 
 
 7.35 
 
 1 .9947 
 
 7.99 
 
 2.0782 
 
 9.06 
 
 2.2039 
 
 14.25 
 
 2.6567 
 
 6.72 
 
 1.9051 
 
 7.36 
 
 1.9961 
 
 8.00 
 
 2.0794 
 
 9.08 
 
 2.2061 
 
 14.50 
 
 2.6740 
 
 6.73 
 
 1 .9066 
 
 7.37 
 
 1 .9974 
 
 8.01 
 
 2.0807 
 
 9.10 
 
 2.2083 
 
 14.75 
 
 2.6913 
 
 6.74 
 
 1.9081 
 
 7.38 
 
 1 .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 
 
 9.24 
 
 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 
 
 1.9315 
 
 7.54 
 
 2.0202 
 
 8.18 
 
 2.1017 
 
 9.44 
 
 2.2450 
 
 26 
 
 3.2581 
 
 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 
 
 3.7136 
 
 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 
 
 5.8501 
 
 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 
 
166 
 
 MATHEMATICAL TABLES. 
 
 
 
 NATURAL TRIGONOMETRICAL FUNCTIONS. 
 
 
 
 • 
 
 M. 
 
 Sine. 
 
 Co- 
 vers. 
 
 Cosec. 
 
 Tang. 
 
 Cotan. 
 
 Se- 
 cant. 
 
 Ver. 
 Sin. 
 
 Cosine. 
 
 
 
 ~0~ 
 
 ~0 
 
 .00000 
 
 1 .0000 
 
 Infinite 
 
 .00000 
 
 Infinite 
 
 1 .0000 
 
 .00000 
 
 1 .0000 
 
 90 
 
 
 
 
 15 
 
 .00436 
 
 .99564 
 
 229.18 
 
 .00436 
 
 229.18 
 
 1 .0000 
 
 .00001 
 
 .99999 
 
 
 45 
 
 
 30 
 
 .00873 
 
 .99127 
 
 114.59 
 
 .00873 
 
 114.59 
 
 1 .0000 
 
 .00004 
 
 .99996 
 
 
 30 
 
 
 45 
 
 .01309 
 
 .98691 
 
 76.397 
 
 .01309 
 
 76.390 
 
 1.0001 
 
 .00009 
 
 .99991 
 
 
 15 
 
 1 
 
 
 
 .01745 
 
 .98255 
 
 57.299 
 
 .01745 
 
 57.290 
 
 1.0001 
 
 .00015 
 
 .99985 
 
 89 
 
 
 
 
 15 
 
 .02181 
 
 .97819 
 
 45.840 
 
 .02182 
 
 45.829 
 
 1 .0002 
 
 .00024 
 
 .99976 
 
 
 45 
 
 
 30 
 
 .02618 
 
 .97382 
 
 38.202 
 
 .02618 
 
 38.188 
 
 1 .0003 
 
 .00034 
 
 .99966 
 
 
 30 
 
 
 45 
 
 .03054 
 
 .96946 
 
 32.746 
 
 .03055 
 
 32.730 
 
 1 .0005 
 
 .00047 
 
 .99953 
 
 
 15 
 
 3 
 
 
 
 .03490 
 
 .96510 
 
 28.654 
 
 .03492 
 
 28.636 
 
 1 .0006 
 
 .00061 
 
 .99939 
 
 88 
 
 
 
 
 15 
 
 .03926 
 
 .96074 
 
 25.471 
 
 .03929 
 
 25.452 
 
 1 .0008 
 
 .00077 
 
 .99923 
 
 
 45 
 
 
 30 
 
 .04362 
 
 .95638 
 
 22.926 
 
 .04366 
 
 22.904 
 
 1 .0009 
 
 .00095 
 
 .99905 
 
 
 30 
 
 
 45 
 
 .04798 
 
 .95202 
 
 20.843 
 
 .04803 
 
 20.819 
 
 1.0011 
 
 .00115 
 
 .99885 
 
 
 15 
 
 3 
 
 
 
 .05234 
 
 .94766 
 
 19.107 
 
 .05241 
 
 19.081 
 
 1.0014 
 
 .00137 
 
 .99863 
 
 87 
 
 
 
 
 15 
 
 .05669 
 
 .94331 
 
 17.639 
 
 .05678 
 
 17.611 
 
 1.0016 
 
 .00161 
 
 .99839 
 
 
 45 
 
 
 30 
 
 .06105 
 
 .93895 
 
 16.380 
 
 .06116 
 
 16.350 
 
 1.0019 
 
 .00187 
 
 .99813 
 
 
 30 
 
 
 45 
 
 .06540 
 
 .93460 
 
 15.290 
 
 .06554 
 
 15.257 
 
 1.0021 
 
 .00214 
 
 .99786 
 
 
 15 
 
 4 
 
 
 
 .06976 
 
 .93024 
 
 14.336 
 
 .06993 
 
 14.301 
 
 1.0024 
 
 .00244 
 
 .99756 
 
 86 
 
 
 
 
 15 
 
 .07411 
 
 .92589 
 
 13.494 
 
 .07431 
 
 13.457 
 
 1 .0028 
 
 .00275 
 
 .99725 
 
 
 45 
 
 
 30 
 
 .07846 
 
 .92154 
 
 12.745 
 
 .07870 
 
 12.706 
 
 1.0031 
 
 .00308 
 
 .99692 
 
 
 30 
 
 
 45 
 
 .08281 
 
 .91719 
 
 12.076 
 
 .08309 
 
 12.035 
 
 1 .0034 
 
 .00343 
 
 .99656 
 
 
 15 
 
 5 
 
 
 
 .08716 
 
 .91284 
 
 11.474 
 
 .08749 
 
 11.430 
 
 1.0038 
 
 .00381 
 
 .99619 
 
 85 
 
 
 
 
 15 
 
 .09150 
 
 .90850 
 
 10.929 
 
 .09189 
 
 10.883 
 
 1 .0042 
 
 .00420 
 
 .99580 
 
 
 45 
 
 
 30 
 
 .09585 
 
 .90415 
 
 10.433 
 
 .09629 
 
 10.385 
 
 1 .0046 
 
 .00460 
 
 .99540 
 
 
 30 
 
 
 45 
 
 .10019 
 
 .89981 
 
 9.9812 
 
 .10069 
 
 9.9310 
 
 1.0051 
 
 .00503 
 
 .99497 
 
 
 15 
 
 6 
 
 
 
 .10453 
 
 .89547 
 
 9.5668 
 
 .10510 
 
 9.5144 
 
 1.0055 
 
 .00548 
 
 .99452 
 
 84 
 
 
 
 
 15 
 
 .10887 
 
 .89113 
 
 9.1855 
 
 .10952 
 
 9.1309 
 
 1 .0060 
 
 .00594 
 
 .99406 
 
 
 45 
 
 
 30 
 
 .11320 
 
 .88680 
 
 8.8337 
 
 .11393 
 
 8.7769 
 
 1 .0065 
 
 .00643 
 
 .99357 
 
 
 30 
 
 
 45 
 
 .11754 
 
 .88246 
 
 8.5079 
 
 .11836 
 
 8.4490 
 
 1 .0070 
 
 .00693 
 
 .99307 
 
 
 15 
 
 7 
 
 
 
 .12187 
 
 .87813 
 
 8.2055 
 
 .12278 
 
 8.1443 
 
 1.0075 
 
 .00745 
 
 .99255 
 
 83 
 
 
 
 
 15 
 
 .12620 
 
 .87380 
 
 7.9240 
 
 .12722 
 
 7.8606 
 
 1.0081 
 
 .00800 
 
 .99200 
 
 
 45 
 
 
 30 
 
 .13053 
 
 .86947 
 
 7.6613 
 
 .13165 
 
 7.5958 
 
 1 .0086 
 
 .00856 
 
 .99144 
 
 
 30 
 
 
 45 
 
 .13485 
 
 .86515 
 
 7.4156 
 
 .13609 
 
 7.3479 
 
 1 .0092 
 
 .00913 
 
 .99086 
 
 
 15 
 
 8 
 
 
 
 .13917 
 
 .86083 
 
 7.1853 
 
 .14054 
 
 7.1154 
 
 1 .0098 
 
 .00973 
 
 .99027 
 
 82 
 
 
 
 
 15 
 
 .14349 
 
 .85651 
 
 6.9690 
 
 .14499 
 
 6.8969 
 
 1.0105 
 
 .01035 
 
 .98965 
 
 
 45 
 
 
 30 
 
 .14781 
 
 .85219 
 
 6.7655 
 
 .14945 
 
 6.6912 
 
 1.0111 
 
 .01098 
 
 .98902 
 
 
 30 
 
 
 45 
 
 .15212 
 
 .84788 
 
 6.5736 
 
 .15391 
 
 6.4971 
 
 1.0118 
 
 .01164 
 
 .98836 
 
 
 15 
 
 9 
 
 
 
 .15643 
 
 .84357 
 
 6.3924 
 
 .15838 
 
 6.3138 
 
 1.0125 
 
 .01231 
 
 .98769 
 
 81 
 
 
 
 
 15 
 
 .16074 
 
 .83926 
 
 6.2211 
 
 .16286 
 
 6.1402 
 
 1.0132 
 
 .01300 
 
 .98700 
 
 
 45 
 
 
 30 
 
 .16505 
 
 .83495 
 
 6.0589 
 
 .16734 
 
 5.9758 
 
 1.0139 
 
 .01371 
 
 .98629 
 
 
 30 
 
 
 45 
 
 .16935 
 
 .83065 
 
 5.9049 
 
 .17183 
 
 5.8197 
 
 1.0147 
 
 .01444 
 
 .98556 
 
 
 15 
 
 10 
 
 
 
 .17365 
 
 .82635 
 
 5.7588 
 
 .17633 
 
 5.6713 
 
 1.0154 
 
 .01519 
 
 .98481 
 
 80 
 
 
 
 
 15 
 
 .17794 
 
 .82206 
 
 5.6198 
 
 .18083 
 
 5.5301 
 
 1.0162 
 
 .01596 
 
 .98404 
 
 
 45 
 
 
 30 
 
 .18224 
 
 .81776 
 
 5.4874 
 
 .18534 
 
 5.3955 
 
 1.0170 
 
 .01675 
 
 .98325 
 
 
 30 
 
 
 45 
 
 .18652 
 
 .81348 
 
 5.3612 
 
 .18986 
 
 5.2672 
 
 1.0179 
 
 .01755 
 
 .98245 
 
 
 15 
 
 11 
 
 
 
 .19081 
 
 .80919 
 
 5.2408 
 
 .19438 
 
 5.1446 
 
 1.0187 
 
 .01837 
 
 .98163 
 
 79 
 
 
 
 
 15 
 
 .19509 
 
 .80491 
 
 5.1258 
 
 .19891 
 
 5.0273 
 
 1.0196 
 
 .01921 
 
 .98079 
 
 
 45 
 
 
 30 
 
 .19937 
 
 .80063 
 
 5.0158 
 
 .20345 
 
 4.9152 
 
 1.0205 
 
 .02008 
 
 .97992 
 
 
 30 
 
 
 45 
 
 .20364 
 
 .79636 
 
 4.9106 
 
 .20800 
 
 4.8077 
 
 1.0214 
 
 .02095 
 
 .97905 
 
 
 15 
 
 13 
 
 
 
 .20791 
 
 .79209 
 
 4.8097 
 
 .21256 
 
 4.7046 
 
 1 .0223 
 
 .02185 
 
 .97815 
 
 78 
 
 
 
 
 15 
 
 .21218 
 
 .78782 
 
 4.7130 
 
 .21712 
 
 4.6057 
 
 1.0233 
 
 .02277 
 
 .97723 
 
 
 45 
 
 
 30 
 
 .21644 
 
 .78356 
 
 4.6202 
 
 .22169 
 
 4.5107 
 
 1 .0243 
 
 .02370 
 
 .97630 
 
 
 30 
 
 
 45 
 
 .22070 
 
 .77930 
 
 4.5311 
 
 .22628 
 
 4.4194 
 
 1.0253 
 
 .02466 
 
 .97534 
 
 
 15 
 
 13 
 
 
 
 .22495 
 
 .77505 
 
 4.4454 
 
 .23087 
 
 4.3315 
 
 1 .0263 
 
 .02563 
 
 .97437 
 
 77 
 
 
 
 
 15 
 
 .22920 
 
 .77080 
 
 4.3630 
 
 .23547 
 
 4.2468 
 
 1.0273 
 
 .02662 
 
 .97338 
 
 
 45 
 
 
 30 
 
 .23345 
 
 .76655 
 
 4.2837 
 
 .24008 
 
 4.1653 
 
 1 .0284 
 
 .02763 
 
 .97237 
 
 
 30 
 
 
 45 
 
 .23769 
 
 .76231 
 
 4.2072 
 
 .24470 
 
 4.0867 
 
 1 .0295 
 
 .02866 
 
 .97134 
 
 
 15 
 
 14 
 
 
 
 24192 
 
 .75808 
 
 4.1336 
 
 .24933 
 
 4.0108 
 
 1.0306 
 
 .02970 
 
 .97030 
 
 76 
 
 
 
 
 15 
 
 .24615 
 
 .75385 
 
 4.0625 
 
 .25397 
 
 3.9375 
 
 1.0317 
 
 .03077 
 
 .96923 
 
 
 45 
 
 
 30 
 
 .25038 
 
 .74962 
 
 3.9939 
 
 .25862 
 
 3.8667 
 
 1 .0329 
 
 .03185 
 
 .96815 
 
 
 30 
 
 
 45 
 
 .25460 
 
 .74540 
 
 3.9277 
 
 .26328 
 
 3.7983 
 
 1.0341 
 
 .03295 
 
 .96705 
 
 
 15 
 
 15 
 
 
 
 .25882 
 
 .74118 
 
 3.8637 
 
 .26795 
 
 3.7320 
 
 1.0353 
 
 03407 
 
 .96593 
 
 75 
 
 
 
 
 Co- 
 sine. 
 
 Ver. 
 Sin. 
 
 Secant. 
 
 Cotan 
 
 Tang. 
 
 Cosec. 
 
 Co- 
 vers. 
 
 Sine. 
 
 :\i. 
 
 From 75° to 90° read from bottom of table upwards. 
 
NATURAL TRIGONOMETRICAL FUNCTIONS. 
 
 167 
 
 " 
 
 M. 
 
 Sine. 
 
 Co- 
 vers. 
 
 Cosec. 
 
 Tang. Cotan. 
 
 Secant. 
 
 Ver. 
 
 Sin. 
 
 Cosine. 
 
 
 
 15 
 
 
 
 .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 
 
 1.0390 
 
 .03754 
 
 .96246 
 
 74 
 
 15 
 
 16 
 
 
 
 .27564 
 
 .72436 
 
 3.6280 
 
 .28674 
 
 3.4874 
 
 1 .0403 
 
 .03874 
 
 .96126 
 
 
 
 
 
 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 
 
 73 
 
 
 
 
 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 
 
 .6703 1 
 
 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 
 
 
 15 
 
 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 
 
 
 15 
 
 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 .0743 
 
 .06958 
 
 .93042 
 
 
 30 
 
 
 45 
 
 .37056 
 
 .62944 
 
 2.6986 
 
 .39896 
 
 2.5065 
 
 1 .0766 
 
 .07119 
 
 .92881 
 
 
 15 
 
 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 
 
 5.1079 
 
 .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 
 
 1.1150 
 
 .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 
 
 28 
 
 
 
 .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. 
 
 Cotan. 
 
 Tang. 
 
 Cosec. 
 
 Co- 
 vers. 
 
 Sine. 
 
 • 
 
 M. 
 
 From 60° to 75° read from bottom of table upwards. 
 
168 
 
 MATHEMATICAL TABLES. 
 
 ° 
 
 M. 
 
 ~~ 0" 
 
 Sine. 
 
 Co- 
 vers. 
 
 Cosec. 
 
 Tang. 
 
 Co tan. 
 
 Secant. 
 
 Ver. 
 Sin. 
 
 Cosine 
 
 
 
 3tT 
 
 .50000 
 
 .50000 
 
 2.0000 
 
 .57735 
 
 1.7320 
 
 1.1547 
 
 .13397 
 
 .86603 
 
 60 
 
 
 
 
 15 
 
 .50377 
 
 .49623 
 
 1 .9850 
 
 .58318 
 
 1.7147 
 
 1.1576 
 
 .13616 
 
 .86384 
 
 
 45 
 
 
 30 
 
 .50754 
 
 .49246 
 
 1.9703 
 
 .58904 
 
 1 .6977 
 
 1.1606 
 
 .13837 
 
 .86163 
 
 
 30 
 
 
 45 
 
 .51129 
 
 .48871 
 
 1.9558 
 
 .59494 
 
 1 .6808 
 
 1.1636 
 
 .14059 
 
 .85941 
 
 
 15 
 
 31 
 
 
 
 .51504 
 
 .48496 
 
 1.9416 
 
 .60086 
 
 1 .6643 
 
 1.1666 
 
 .14283 
 
 .85717 
 
 59 
 
 
 
 
 15 
 
 .51877 
 
 .48123 
 
 1.9276 
 
 .60681 
 
 1 .6479 
 
 1.1697 
 
 .14509 
 
 .85491 
 
 
 45 
 
 
 30 
 
 .52250 
 
 .47750 
 
 1.9139 
 
 .61280 
 
 1.6319 
 
 1.1728 
 
 .14736 
 
 .85264 
 
 
 30 
 
 
 45 
 
 .52621 
 
 .47379 
 
 1 .9004 
 
 .61882 
 
 1.6160 
 
 1.1760 
 
 .14965 
 
 .85035 
 
 
 15 
 
 33 
 
 
 
 .52992 
 
 .47008 
 
 1.8871 
 
 .62487 
 
 1 .6003 
 
 1.1792 
 
 .15195 
 
 .84805 
 
 58 
 
 
 
 
 15 
 
 .53361 
 
 .46639 
 
 1.8740 
 
 .63095 
 
 1 .5849 
 
 1.1824 
 
 .15427 
 
 .84573 
 
 
 45 
 
 
 30 
 
 .53730 
 
 .46270 
 
 1.8612 
 
 .63707 
 
 1.5697 
 
 1.1857 
 
 .15661 
 
 .84339 
 
 
 30 
 
 
 45 
 
 .54097 
 
 .45903 
 
 1 .8485 
 
 .64322 
 
 1.5547 
 
 1.1890 
 
 .15896 
 
 .84104 
 
 
 15 
 
 33 
 
 
 
 .54464 
 
 .45536 
 
 1.8361 
 
 .64941 
 
 1.5399 
 
 1.1924 
 
 .16133 
 
 .83867 
 
 57 
 
 
 
 
 15 
 
 .54829 
 
 .45171 
 
 1.8238 
 
 .65563 
 
 1.5253 
 
 1.1958 
 
 .16371 
 
 .83629 
 
 
 45 
 
 
 30 
 
 .55194 
 
 .44806 
 
 1.8118 
 
 .66188 
 
 1.5108 
 
 1.1992 
 
 .16611 
 
 .83389 
 
 
 30 
 
 
 45 
 
 .55557 
 
 .44443 
 
 1 .7999 
 
 .66818 
 
 1 .4966 
 
 1.2027 
 
 .16853 
 
 .83147 
 
 
 15 
 
 34 
 
 
 
 .55919 
 
 .44081 
 
 1.7883 
 
 .67451 
 
 1 .4826 
 
 1 .2062 
 
 .17096 
 
 .82904 
 
 56 
 
 
 
 
 15 
 
 .56280 
 
 .43720 
 
 1.7768 
 
 .68087 
 
 1 .4687 
 
 1 .2098 
 
 .17341 
 
 .82659 
 
 
 45 
 
 
 30 
 
 .56641 
 
 .43359 
 
 1.7655 
 
 .68728 
 
 1.4550 
 
 1.2134 
 
 .17587 
 
 .82413 
 
 
 30 
 
 
 45 
 
 .57000 
 
 .43000 
 
 1.7544 
 
 .69372 
 
 1.4415 
 
 1.2171 
 
 .17835 
 
 .82165 
 
 
 15 
 
 35 
 
 
 
 .57358 
 
 .42642 
 
 1.7434 
 
 .70021 
 
 1.4281 
 
 1 .2208 
 
 .18085 
 
 .81915 
 
 55 
 
 
 
 
 15 
 
 .57715 
 
 .42285 
 
 1.7327 
 
 .70673 
 
 1.4150 
 
 1.2245 
 
 .18336 
 
 .81664 
 
 
 45 
 
 
 30 
 
 .58070 
 
 .41930 
 
 1.7220 
 
 .71329 
 
 1.4019 
 
 1 .2283 
 
 .18588 
 
 .81412 
 
 
 30 
 
 
 45 
 
 .58425 
 
 .41575 
 
 1.7116 
 
 .71990 
 
 1.3891 
 
 1.2322 
 
 .18843 
 
 .81157 
 
 
 15 
 
 36 
 
 
 
 .58779 
 
 .41221 
 
 1.7013 
 
 .72654 
 
 1.3764 
 
 1.2361 
 
 .19098 
 
 .80902 
 
 54 
 
 
 
 
 15 
 
 .59131 
 
 .40869 
 
 1.6912 
 
 .73323 
 
 1.3638 
 
 1 .2400 
 
 .19356 
 
 .80644 
 
 
 45 
 
 
 30 
 
 .59482 
 
 .40518 
 
 1.6812 
 
 .73996 
 
 1.3514 
 
 1 .2440 
 
 .19614 
 
 .80386 
 
 
 30 
 
 
 45 
 
 .59832 
 
 .40168 
 
 1.6713 
 
 .74673 
 
 1.3392 
 
 1 .2480 
 
 .19875 
 
 .80125 
 
 
 15 
 
 37 
 
 
 
 .60181 
 
 .39819 
 
 1.6616 
 
 .75355 
 
 1.3270 
 
 1.2521 
 
 .20136 
 
 .79864 
 
 53 
 
 
 
 
 15 
 
 .60529 
 
 .39471 
 
 1.6521 
 
 .76042 
 
 1.3151 
 
 1.2563 
 
 .20400 
 
 .79600 
 
 
 45 
 
 
 30 
 
 .60876 
 
 .39124 
 
 1.6427 
 
 .76733 
 
 1.3032 
 
 1 .2605 
 
 .20665 
 
 .79335 
 
 
 30 
 
 
 45 
 
 .61222 
 
 .38778 
 
 1.6334 
 
 .77428 
 
 1.2915 
 
 1 .2647 
 
 .20931 
 
 .79069 
 
 
 15 
 
 38 
 
 
 
 .61566 
 
 .38434 
 
 1.6243 
 
 .78129 
 
 1 .2799 
 
 1 .2690 
 
 .21199 
 
 .78801 
 
 52 
 
 
 
 
 15 
 
 .61909 
 
 .38091 
 
 1.6153 
 
 .78834 
 
 1 .2685 
 
 1.2734 
 
 .21468 
 
 .78532 
 
 
 45 
 
 
 30 
 
 .62251 
 
 .37749 
 
 1 .6064 
 
 .79543 
 
 1.2572 
 
 1.2778 
 
 .21739 
 
 .78261 
 
 
 30 
 
 
 45 
 
 .62592 
 
 .37403 
 
 1.5976 
 
 .80258 
 
 1 .2460 
 
 1 2822 
 
 .22012 
 
 .77988 
 
 
 15 
 
 39 
 
 
 
 .62932 
 
 .37068 
 
 1.5890 
 
 .80978 
 
 1.2349 
 
 1 .2868 
 
 .22285 
 
 .77715 
 
 51 
 
 
 
 
 15 
 
 .63271 
 
 .36729 
 
 1.5805 
 
 .81703 
 
 1.2239 
 
 1.2913 
 
 .22561 
 
 .77439 
 
 
 45 
 
 
 30 
 
 .63608 
 
 .36392 
 
 1.5721 
 
 .82434 
 
 1.2131 
 
 1 .2960 
 
 .22838 
 
 .77162 
 
 
 30 
 
 
 45 
 
 .63944 
 
 .36056 
 
 1.5639 
 
 .83169 
 
 1 .2024 
 
 1.3007 
 
 .23116 
 
 .76884 
 
 
 15 
 
 40 
 
 
 
 .64279 
 
 .35721 
 
 1.5557 
 
 .83910 
 
 1.1918 
 
 1.3054 
 
 .23396 
 
 .76604 
 
 50 
 
 
 
 
 15 
 
 .64612 
 
 .35388 
 
 1.5477 
 
 .84656 
 
 1.1812 
 
 1.3102 
 
 .23677 
 
 .76323 
 
 
 45 
 
 
 30 
 
 .64945 
 
 .35055 
 
 1.5398 
 
 .85408 
 
 1.1708 
 
 1.3151 
 
 .23959 
 
 .76041 
 
 
 30 
 
 
 45 
 
 .65276 
 
 .34724 
 
 1.5320 
 
 .86165 
 
 1 . 1 606 
 
 1 .3200 
 
 .24244 
 
 .75756 
 
 
 15 
 
 41 
 
 
 
 .65606 
 
 .34394 
 
 1.5242 
 
 .86929 
 
 1.1504 
 
 1.3250 
 
 .24529 
 
 .75471 
 
 49 
 
 
 
 
 15 
 
 .65935 
 
 .34065 
 
 1.5166 
 
 .87698 
 
 1.1403 
 
 1.3301 
 
 .24816 
 
 .75184 
 
 
 45 
 
 
 30 
 
 .66262 
 
 .33738 
 
 1.5092 
 
 .88472 
 
 1.1303 
 
 1.3352 
 
 .25104 
 
 .74896 
 
 
 30 
 
 
 45 
 
 .66588 
 
 .33412 
 
 1.5018 
 
 .89253 
 
 1.1204 
 
 1.3404 
 
 .25394 
 
 .74606 
 
 
 15 
 
 42 
 
 
 
 .66913 
 
 .33087 
 
 1.4945 
 
 .90040 
 
 1.1106 
 
 1.3456 
 
 .25686 
 
 .74314 
 
 48 
 
 
 
 
 15 
 
 .67237 
 
 .32763 
 
 1.4873 
 
 .90834 
 
 1.1009 
 
 1.3509 
 
 .25978 
 
 .74022 
 
 
 45 
 
 
 30 
 
 .67559 
 
 .32441 
 
 1 .4802 
 
 .91633 
 
 1.0913 
 
 1.3563 
 
 .26272 
 
 .73728 
 
 
 30 
 
 
 45 
 
 .67880 
 
 .32120 
 
 1.4732 
 
 .92439 
 
 1.0818 
 
 1.3618 
 
 .26568 
 
 .73432 
 
 
 15 
 
 43 
 
 
 
 .68200 
 
 .31800 
 
 1 .4663 
 
 .93251 
 
 1 .0724 
 
 1.3673 
 
 .26865 
 
 .73135 
 
 47 
 
 
 
 
 15 
 
 .68518 
 
 .31482 
 
 1.4595 
 
 .94071 
 
 1 .0630 
 
 1.3729 
 
 .27163 
 
 .72837 
 
 
 45 
 
 
 30 
 
 .68835 
 
 .31165 
 
 1.4527 
 
 .94896 
 
 1.0538 
 
 1.3786 
 
 .27463 
 
 .72537 
 
 
 30 
 
 
 45 
 
 .69151 
 
 .30849 
 
 1.4461 
 
 .95729 
 
 1 .0446 
 
 1.3843 
 
 .27764 
 
 .72236 
 
 
 15 
 
 44 
 
 
 
 .69466 
 
 .30534 
 
 1 .4396 
 
 .96569 
 
 1.0355 
 
 1.3902 
 
 .28066 
 
 .71934 
 
 46 
 
 
 
 
 15 
 
 .69779 
 
 .30221 
 
 1.4331 
 
 .97416 
 
 1 .0265 
 
 1.3961 
 
 .28370 
 
 .71630 
 
 
 45 
 
 
 30 
 
 .70091 
 
 .29909 
 
 1 .4267 
 
 .98270 
 
 1.0176 
 
 1 .4020 
 
 .28675 
 
 .71325 
 
 
 30 
 
 
 45 
 
 .70401 
 
 .29599 
 
 1 .4204 
 
 .99131 
 
 1 .0088 
 
 1.4081 
 
 .28981 
 
 .71019 
 
 
 15 
 
 45 
 
 
 
 .70711 
 
 .29289 
 
 1.4142 
 
 1 .0000 
 
 1 .0000 
 
 1.4142 
 
 .29289 
 
 .70711 
 
 45 
 
 
 
 
 
 Cosine 
 
 Ver. 
 Sin. 
 
 Se- 
 cant. 
 
 Cotan. 
 
 Tang. 
 
 Cosec. 
 
 Co- 
 Verc. 
 
 Sine. 
 
 
 
 M. 
 
 From 45° to 60° read from bottom of table upwards. 
 
LOGARITHMIC TRIGONOMETRICAL FUNCTIONS. 169 
 
 LOGARITHMIC SINES, ETC. 
 
 
 Sine. 
 
 Cosec. 
 
 Versin. 
 
 Tangent 
 
 Co tan. 
 
 Covers. 
 
 Secant. 
 
 Cosine. 
 
 
 
 
 In.Neg. 
 
 Infinite. 
 
 In.Neg. 
 
 In.Neg. 
 
 Infinite. 
 
 1 0.00000 
 
 1 0.00000 
 
 10.00000 
 
 90 
 
 1 
 
 8.24186 
 
 11.75814 
 
 6.18271 
 
 8.24192 
 
 11.75808 
 
 9.99235 
 
 10.00007 
 
 9.99993 
 
 89 
 
 2 
 
 8.54282 
 
 11.45718 
 
 6.78474 
 
 8.54308 
 
 11.45692 
 
 9.98457 
 
 10.00026 
 
 9.99974 
 
 88 
 
 3 
 
 8.71880 
 
 11.28120 
 
 7.13687 
 
 8.71940 
 
 1 1 .28060 
 
 9.97665 
 
 10.00060 
 
 9.99940 
 
 87 
 
 4 
 
 8.84358 
 
 11.15642 
 
 7.38667 
 
 8.84464 
 
 11.15536 
 
 9.96860 
 
 10.00106 
 
 9.99894 
 
 86 
 
 5 
 
 8.94030 
 
 11.05970 
 
 7.58039 
 
 8.94195 
 
 1 1 .05805 
 
 9.96040 
 
 10.00166 
 
 9.99834 
 
 85 
 
 6 
 
 9.01923 
 
 10.98077 
 
 7.73863 
 
 9.02162 
 
 10.97838 
 
 9.95205 
 
 10.00239 
 
 9 99761 
 
 84 
 
 7 
 
 9.08589 
 
 10.91411 
 
 7.87238 
 
 9.08914 
 
 10.91086 
 
 9.94356 
 
 10.00325 
 
 9.99675 
 
 83 
 
 8 
 
 9.14356 
 
 10.85644 
 
 7.98820 
 
 9.14780 
 
 10.85220 
 
 9.93492 
 
 10.00425 
 
 9.99575 
 
 82 
 
 9 
 
 9.19433 
 
 10.80567 
 
 8.09032 
 
 9.19971 
 
 10.80029 
 
 9.92612 
 
 50.00538 
 
 9.99462 
 
 81 
 
 10 
 
 9.23967 
 
 10.76033 
 
 8.18162 
 
 9.24632 
 
 10.75368 
 
 9.91717 
 
 10.00665 
 
 9.99335 
 
 80 
 
 11 
 
 9.28060 
 
 10.71940 
 
 8.26418 
 
 9.28865 
 
 10.71135 
 
 9.90805 
 
 10.00805 
 
 9.99195 
 
 79 
 
 12 
 
 9.31788 
 
 10.68212 
 
 8.33950 
 
 9.32747 
 
 10.67253 
 
 9.89877 
 
 10.00960 
 
 9.99040 
 
 78 
 
 13 
 
 9.35209 
 
 10.64791 
 
 8.40875 
 
 9.36336 
 
 10.63664 
 
 9.88933 
 
 10.01128 
 
 9.98872 
 
 77 
 
 14 
 
 9.38368 
 
 10.61632 
 
 8.47282 
 
 9.39677 
 
 10.60323 
 
 9.87971 
 
 10.01310 
 
 9.98690 
 
 76 
 
 15 
 
 9.41300 
 
 10.58700 
 
 8.53243 
 
 9.42805 
 
 10.57195 
 
 9.86992 
 
 10.01506 
 
 9.98494 
 
 75 
 
 16 
 
 9.44034 
 
 10.55966 
 
 8.58814 
 
 9.45750 
 
 10.54250 
 
 9.85996 
 
 10.01716 
 
 9.98284 
 
 74 
 
 17 
 
 9.46594 
 
 10.53406 
 
 8.64043 
 
 9.48534 
 
 10.51466 
 
 9.84981 
 
 10.01940 
 
 9.98060 
 
 73 
 
 18 
 
 9.48998 
 
 10.51002 
 
 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 
 
 9.60931 
 
 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 
 
 10J2893 
 
 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 
 
 9.44S18 
 
 9.98484 
 
 10.01516 
 
 9.48479 
 
 10.14307 
 
 9.85693 
 
 46 
 
 45 
 
 9.84949 
 
 10.15052 
 
 9.46671 
 
 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. 
 
170 
 
 MATERIALS. 
 
 MATERIALS. 
 
 THE CHEMICAL ELEMENTS. 
 
 Common Elements (42). 
 
 s a 
 
 
 «;£ 
 
 o"° 
 
 
 2-? 
 
 g"o 
 
 
 oi 
 
 Name. 
 
 !•» 
 
 al 
 
 Name. 
 
 a-| c 
 
 al 
 
 Name. 
 
 ■% bfl 
 
 P 
 
 
 & 
 
 
 
 
 6" 
 
 
 ^ 
 
 Al 
 
 Aluminum 
 
 27.1 
 
 F 
 
 Fluorine 
 
 19. 
 
 Pd 
 
 Palladium 
 
 106.5 
 
 Sb 
 
 Antimony 
 
 120.2 
 
 Au 
 
 Gold 
 
 197.2 
 
 P 
 
 Phosphorus 
 
 31. 
 
 As 
 
 Arsenic 
 
 75.0 
 
 H 
 
 Hydrogen 
 
 1.01 
 
 Pt 
 
 Platinum 
 
 194.8 
 
 Ba 
 
 Barium 
 
 137.4 
 
 I 
 
 Iodine 
 
 127.0 
 
 K 
 
 Potassium 
 
 39.1 
 
 Bi 
 
 Bismuth 
 
 209.5 
 
 Ir 
 
 Iridium 
 
 193.0 
 
 Si 
 
 Silicon 
 
 28.4 
 
 B 
 
 Boron 
 
 11.0 
 
 Fe 
 
 Iron 
 
 55.9 
 
 Ag 
 
 Silver 
 
 107.9 
 
 Br 
 
 Bromine 
 
 80.0 
 
 Pb 
 
 Lead 
 
 206.9 
 
 Na 
 
 Sodium 
 
 23. 
 
 Cd 
 
 Cadmium 
 
 112.4 
 
 Li 
 
 Lithium 
 
 7.03 
 
 Sr 
 
 Strontium 
 
 87.6 
 
 Ca 
 
 Calcium 
 
 40.1 
 
 Mg 
 
 Magnesium 
 
 24.36 
 
 S 
 
 Sulphur 
 
 32.1 
 
 C 
 
 Carbon 
 
 12. 
 
 Mn 
 
 Manganese 
 
 55. 
 
 Sn 
 
 Tin 
 
 119. 
 
 CI 
 
 Chlorine 
 
 35.4 
 
 Hg 
 
 Mercury 
 
 200. 
 
 Ti 
 
 Titanium 
 
 48.1 
 
 Cr 
 
 Chromium 
 
 52.1 
 
 Ni 
 
 Nickel 
 
 58.7 
 
 W 
 
 Tungsten 
 
 184.0 
 
 Co 
 
 Cobalt 
 
 59. 
 
 N 
 
 Nitrogen 
 
 14.04 
 
 Va 
 
 Vanadium 
 
 51.2 
 
 Cu 
 
 Copper 
 
 63.6 
 
 O 
 
 Oxygen 
 
 16. 
 
 Zn 
 
 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. (See Jour. Am. 
 Chem. Soc, March, 1896.) 
 
 Rare Elements (27). 
 
 Beryllium, Be. 
 Csesium, Cs. 
 Cerium, Ce. 
 Erbium, Er. 
 Gallium, Ga. 
 Germanium, Ge. 
 Glucinum, G. 
 
 Indium, In. 
 Lanthanum, La. 
 Molybdenum, Mo. 
 Niobium, Nb. 
 Osmium, Os. 
 Rhodium, R. 
 Rubidium, Rb. 
 
 Ruthenium, Ru. 
 Samarium, Sm. 
 Scandium, Sc. 
 Selenium, Se. 
 Tantalum, Ta. 
 Tellurium, Te. 
 Terbium, Tb. 
 
 Thallium, Tl. 
 Thorium, Th. 
 Uranium, U. 
 Ytterbium, Yr. 
 Yttrium, Y. 
 Zirconium, Zr. 
 
 Elements recently discovered (1900-1905): 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; PraBsodymium, Pr, 140.5; 
 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. 
 
 To find the specific gravity of a substance. 
 
 W = weight of body in air; w = weight of body submerged in water. 
 
 Specific gravity = 
 
 W 
 
SPECIFIC GRAVITY. 
 
 171 
 
 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 lbs. per cubic foot. Some experi- 
 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 
 0.036085. 
 
 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, 
 lbs. 
 
 Weight 
 per 
 Cubic 
 Inch, 
 
 lbs. 
 
 
 2.56 to 2.71 
 6.66 to 6.86 
 9.74 to 9.90 
 
 7.8 to 8.6 
 
 8.52 to 8.96 
 
 8.6 to 8.7 
 1.58 
 5.0 
 8.5 to 8.6 
 19.245 to 19.361 
 8.69 to 8.92 
 22.38 to 23. 
 
 6.85 to 7.48 
 7.4 to 7.9 
 
 11.07 to 11.44 
 7. to 8. 
 1 .69 to 1 .75 
 13.60 to 13.62 
 
 13.58 
 13.37 to 13.38 
 8.279 to 8.93 
 20.33 to 22.07 
 
 0.865 
 10.474 to 10.511 
 
 0.97 
 7.69* to 7.932f 
 7.291 to 7.409 
 
 5.3 
 17. to 17.6 
 
 6.86 to 7.20 
 
 2.67 
 6.76 
 9.82 
 
 (8.60 
 J8.40 
 18.36 
 1.8.20 
 
 8.853 
 
 8.65 
 
 1.58 
 
 5.0 
 
 8.55 
 
 19.258 
 8.853 
 
 22.38 
 7.218 
 7.70 
 
 11.38 
 8. 
 1.75 
 
 13.62 
 
 13.58 
 
 13.38 
 8.8 
 
 21.5 
 0.865 
 
 10.505 
 0.97 
 7.854 
 7.350 
 5.3 
 
 17.3 
 7.00 
 
 166.5 
 421.6 
 612.4 
 
 536.3 
 
 523.8 
 521.3 
 511.4 
 
 552. 
 539. 
 98.5 
 311.8 
 533.1 
 
 1200.9 
 552. 
 
 1396. 
 450. 
 480. 
 709.7 
 499. 
 109. 
 849.3 
 846.8 
 834.4 
 548.7 
 
 1347.0 
 53.9 
 655.1 
 60.5 
 489.6 
 458.3 
 330.5 
 
 1078.7 
 436.5 
 
 0.0963 
 
 
 0.2439 
 
 
 0.3544 
 
 Brass: Copper + Zinc^ 
 80 20 
 70 30l. . 
 60 40 
 50 50* 
 
 Rrm^p/CoP-' 95 to 80 1 
 Bronze \Tin, 5 to 20/ 
 
 0.3103 
 0.3031 
 0.3017 
 0.2959 
 
 0.3195 
 0.3121 
 
 
 0.0570 
 
 
 0.1804 
 
 Cobalt. 
 
 0.3085 
 
 Gold, pure 
 
 0.6949 
 0.3195 
 
 
 0.8076 
 
 
 0.2604 
 
 Iron, Wrought 
 
 0.2779 
 0.4106 
 
 
 0.2887 
 
 
 0.0641 
 
 ( 32° 
 Mercury < 60° 
 
 1212° 
 
 0.4915 
 0.4900 
 0.4828 
 0.3175 
 
 
 0.7758 
 
 
 0.0312 
 
 
 0.3791 
 
 
 0.0350 
 
 Steel 
 
 0.2834 
 
 Tin 
 
 0.2652 
 
 
 0.1913 
 
 
 0.6243 
 
 
 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. 
 
172 
 
 MATERIALS. 
 
 Specific Gravity of Liquids at 60° F. 
 
 Acid, Muriatic 1 .200 
 
 " Nitric 1.217 
 
 " Sulphuric. 1.849 
 
 Alcohol, pure 0.794 
 
 95 percent 0.816 
 
 50 per cent 0.934 
 
 Ammonia, 27.9 per cent .. . 0.891 
 
 Bromine 2.97 
 
 Carbon disulphide. .1 1 .26 
 
 Ether, Sulphuric 0.72 
 
 Oil, Linseed, 0.94 
 
 Oil, Olive 0.92 
 
 " Palm 0.97 
 
 " Petroleum 0.78 to 0.88 
 
 " Rape 0.92 
 
 " Turpentine 0.87 
 
 " Whale 0.92 
 
 Tar I. 
 
 Vinegar 1 .08 
 
 Water 1 . 
 
 Water, Sea ............ . 1.026 to 1.03 
 
 Compression of the following Fluids under a Pressure of 15 lbs. 
 per Square Inch. 
 
 Water 0.00004663 
 
 Alcohol... 0.0000216 
 
 Ether.... 0.00006158 
 
 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 instrument 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. 
 
 r„ rni11 u /Heavy liquids, Sp. gr. 
 * ormulse \Light liquids, Sp. gr. 
 
 145 ■«- (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 
 Lighter 
 
 than 
 Water, 
 Sp. Gr. 
 
 0.0 
 1.0 
 2.0 
 3.0 
 4.0 
 5.0 
 6.0 
 7.0 
 8.0 
 9.0 
 10.0 
 11.0 
 12.0 
 13.0 
 14.0 
 15.0 
 16.0 
 17.0 
 
 1.000 
 1.007 
 1.014 
 1 021 
 1.028 
 1.036 
 1.043 
 1.051 
 1.058 
 1.066 
 1.074 
 1.082 
 1.090 
 1.099 
 1.107 
 1.115 
 1.124 
 1.133 
 1.142 
 
 ' Y.666' 
 0.993 
 0.986 
 0.979 
 0.972 
 0.966 
 0.959 
 0.952 
 0.946 
 
 19.0 
 20.0 
 21.0 
 22.0 
 23.0 
 24.0 
 25.0 
 26.0 
 27.0 
 28.0 
 29.0 
 30.0 
 31.0 
 32.0 
 33 
 34.0 
 35.0 
 36.0 
 37.0 
 
 1.151 
 1.160 
 1.169 
 1.179 
 1.189 
 1.198 
 1.208 
 1.219 
 1.229 
 1.239 
 1.250 
 1.261 
 1.272 
 1.283 
 1.295 
 1.306 
 1.318 
 1.330 
 1.343 
 
 0.940 
 0.933 
 0.927 
 0.921 
 0.915 
 0.909 
 0.903 
 0.897 
 0.892 
 0.886 
 0.881 
 0.875 
 0.870 
 0.864 
 0,859 
 0.854 
 0.849 
 0.843 
 0.838 
 
 38.0 
 39.0 
 40.0 
 41.0 
 42.0 
 44.0 
 46.0 
 48.0 
 50.0 
 52.0 
 54.0 
 56.0 
 58.0 
 60.0 
 65.0 
 70.0 
 75.0 
 
 1.355 
 1.368 
 1.381 
 1 394 
 1.408 
 1.436 
 1.465 
 1.495 
 1.526 
 1.559 
 1.593 
 1.629 
 1 .667 
 1.706 
 1.813 
 1.933 
 2.071 
 
 0.833 
 
 0.828 
 0.824 
 0.819 
 0.814 
 0.805 
 0.796 
 0.787 
 0.778 
 0.769 
 761 
 0.753 
 0.745 
 0.737 
 0.718 
 0.700 
 0.683 
 
 18.0 
 
 
 
 
 
 
 
 
SPECIFIC GRAVITY. 
 
 173 
 
 Specific Gravity and Weight of Gases at Atmospheric Pressure 
 and 32° F. 
 
 (For other temperatures and pressures see Physical Properties of Gases.) 
 
 
 Density, 
 Air = 1 . 
 
 Density, 
 H = 1. 
 
 Grammes 
 per Litre. 
 
 Lbs. per 
 Cu. Ft. 
 
 Cubic Ft. 
 per Lb. 
 
 Air 
 
 Oxygen, O 
 
 Hydrogen, H 
 
 Nitrogen, N 
 
 Carbon monoxide, CO . 
 Carbon dioxide, CO2 . . 
 Methane,marsh-gas, CPU 
 
 Ethylene, C2H4 
 
 Acetylene, C2H2 
 
 Ammonia, NH3 
 
 Water vapor, H2O .... 
 
 1 .0000 
 1.1052 
 0.0692 
 0.9701 
 0.9671 
 1.5197 
 0.5530 
 0.9674 
 ■ 0.8982 
 0.5889 
 0.6218 
 
 14.444 
 15.963 
 
 1.000 
 14.012 
 13.968 
 21.950 
 
 7.987 
 13.973 
 12.973 
 
 8.506 
 
 8.981 
 
 1 .293 1 
 1.4291 
 0.0895 
 1 .2544 
 1.2505 
 1 .9650 
 0.7150 
 1.2510 
 1.1614 
 0.7615 
 0.8041 
 
 0.080728 
 
 0.08921 
 
 0.00559 
 
 0.0783 1 
 
 0.07807 
 
 0.12267 
 
 0.04464 
 
 0.07809 
 
 0.07251 
 
 0.04754 
 
 0.05020 
 
 12.388 
 1 1 .209 
 178.931 
 12.770 
 12.810 
 8.152 
 22.429 
 12.805 
 13.792 
 21.036 
 19.922 
 
 Specific Gravity and Weight of Wood. 
 
 
 
 
 
 
 
 
 „- 
 
 
 Specific 
 
 
 
 
 
 Specific 
 
 
 ^ 
 
 
 Gravity 
 
 
 M~ O 
 
 'S0P-1 
 
 
 Gravity 
 
 
 lT3o 
 
 
 . Avge- 
 
 
 
 Avge. 
 
 
 Alder 
 
 0.56 to 0.80 
 
 0,68 
 
 42 
 
 Hornbeam. . 
 
 0.76 
 
 76 
 
 47 
 
 Apple 
 
 0.73 to 0.79 
 
 0.76 
 
 47 
 
 Juniper .... 
 
 0.56 
 
 0.56 
 
 35 
 
 Ash 
 
 0.60 to 0.84 
 
 0.72 
 
 45 
 
 Larch 
 
 0.56 
 
 56 
 
 35 
 
 Bamboo .... 
 
 0.31 to 0.40 
 
 0.35 
 
 22 
 
 Lignum vita 1 
 
 0.65 to 1 .33 
 
 1.00 
 
 62 
 
 Beech 
 
 0.62 to 0.85 
 
 73 
 
 46 
 
 Linden . . . 
 
 0.604 
 
 
 37 
 
 Birch ...... 
 
 0.56 to 0.74 
 
 65 
 
 41 
 
 Locust 
 
 0.728 
 
 
 46 
 
 Box 
 
 0.91 to 1.33 
 
 1.12 
 
 70 
 
 Mahogany. . 
 
 0.56 to 1.06 
 
 081 
 
 51 
 
 Cedar. ....... 
 
 0.49 to 0.75 
 
 0,62 
 
 39 
 
 Maple 
 
 0.57 to 0.79 
 
 68 
 
 42 
 
 Cherry. ..... 
 
 0.61 to 0.72 
 
 0.66 
 
 41 
 
 Mulberry. . . 
 
 0.56 to 0.90 
 
 0,73 
 
 46 
 
 Chestnut. . . . 
 
 0.46 to 0.66 
 
 56 
 
 35 
 
 Oak, Live . . 
 
 0.96 to 1 .26 
 
 1 11 
 
 69 
 
 Cork: 
 
 0.24 
 
 24 
 
 15 
 
 Oak, White. 
 
 0.69 to 0.86 
 
 77 
 
 48 
 
 Cvpress ..... 
 
 0.41 to 0.66 
 
 0.53 
 
 33 
 
 Oak, Red . . 
 
 0.73 to 0.75 
 
 74 
 
 46 
 
 Dogwood . . . 
 
 0.76 
 
 0.76 
 
 47 
 
 Pine, White 
 
 0.35 to 0.55 
 
 45 
 
 28 
 
 Ebony 
 
 1.13 to 1.33 
 
 1.23 
 
 76 
 
 " Yellow 
 
 0.46 to 0.76 
 
 61 
 
 38 
 
 Elm........ 
 
 0.55 to 0.78 
 
 0.61 
 
 38 
 
 Poplar 
 
 0.38 to 0.58 
 
 48 
 
 30 
 
 Fir 
 
 0.48 to 0.70 
 0.84 to 1 .00 
 
 0.59 
 0.92 
 
 37 
 57 
 
 Spruce 
 
 Sycamore . . 
 
 0.40 to 0.50 
 0.59 to 0.62 
 
 0.45 
 60 
 
 28 
 
 Gum 
 
 37 
 
 Hackmatack 
 
 0.59 
 
 59 
 
 37 
 
 Teak 
 
 0.66 to 0.98 
 
 82 
 
 51 
 
 Hemlock. . . . 
 
 0.36 to 0.41 
 
 38 
 
 24 
 
 Walnut 
 
 0.50 to 0.67 
 
 58 
 
 36 
 
 Hickory 
 
 0.69 to 0.94 
 
 0.77 
 
 48 
 
 Willow .... 
 
 0.49 to 0.59 
 
 0,54 
 
 34 
 
 Holly 
 
 0.76 
 
 0.76 
 
 47 
 
 
 
 
 
174 
 
 MATERIALS. 
 
 Weight and Specific Gravity of Stones, Brick, Cement, etc. 
 Water = 1.00.) 
 
 
 Lb. per Cu. Ft. 
 
 Sp. Gr. 
 
 
 87 
 100 
 112 
 125 
 135 
 
 140 to 150 
 136 
 100 
 112 
 
 92 
 115 
 
 120 to 150 
 120 to 155 
 72 to 80 
 90 to 110 
 250 
 
 156 to 172 
 180 to 196 
 
 160 to 170 
 100 to 120 
 130 to 150 
 200 to 220 
 
 55 to 57 
 
 50 to 60 
 140 to 185 
 150 
 
 160 to 180 
 140 to 160 
 140 to 180 
 175 
 
 90 to 100 
 104 to 120 
 
 72 
 
 93 to 113 
 165 
 
 90 to 110 
 118 to 129 
 140 to 150 
 170 to 180 
 166 to 175 
 135 to 200 
 170 to 200 
 110 to 120 
 
 1 39 
 
 Brick, Soft 
 
 1.6 
 
 
 1.79 
 
 " Hard 
 
 2 
 
 
 2 16 
 
 Fire 
 
 2 24 to 2 4 
 
 
 2 18 
 
 
 1 6 
 
 
 1.79 
 
 
 2.8 to 3.2 
 
 
 3.05 to 3.15 
 
 
 
 " " in barrel 
 
 
 Clay 
 
 1 .92 to 2.4 
 
 
 1 .92 to 2.48 
 
 
 1.15 to 1.28 
 
 
 1 .44 to 1 .76 
 
 
 4. 
 
 Glass 
 
 2.5 to 2.75 
 
 " flint 
 
 2.88 to 3.14 
 
 
 2.56 to 2.72 
 
 Granite/ 
 
 1 6 to 1.92 
 
 
 2.08 to 2.4 
 
 
 3.2 to 3.52 
 
 
 0.88 to 0.92 
 
 
 0.8 to 0.96 
 
 
 2.30 to 2.90 
 
 
 2.4 
 
 
 2.56 to 2.88 
 
 
 2.24 to 2.56 
 
 
 2.24 to 2.88 
 
 
 2.80 
 
 
 1 .44 to 1 .6 
 
 
 1 .67 to 1 .92 
 
 Pitch 
 
 1.15 
 
 
 1.50 to 1.81 
 
 
 2.64 
 
 
 1 .44 to 1 .76 
 
 
 1.89 to 2.07 
 
 
 2.24 to 2.4 
 
 Slate 
 
 2.72 to 2.88 
 
 
 2.65 to 2.8 
 
 
 2.16 to 3.4 
 
 Trap 
 
 2.72 to 3.4 
 
 Tile 
 
 1 .76 to 1 .92 
 
 
 
 PROPERTIES OF THE USEFUL METALS. 
 
 Aluminum, Al. — 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 357. 
 
PROPERTIES OF THE USEFUL METALS. 175 
 
 Antimony (Stibium), Sb. — At. wt. 120.2. Sp. gr. 6.7 to 6.8. A 
 brittle metal of a bluish-white color and highly crystalline or laminated 
 structure. Melts at 842° F. Heated in the open air it burns with a 
 bluish-white flame. Its chief use is for the manufacture of certain alloys, 
 as type-metal (antimony 1, lead 4), britannia (antimony 1, tin 9), and 
 various anti-friction metals (see Alloys). Cubical expansion by heat 
 from 32° to 212° F., 0.0070. Specific heat 0.050. 
 
 Bismuth, Bi. — At. wt. 208.5. Bismuth is of a peculiar light reddish 
 color, highly crystalline, and so brittle that it can readily be pulverized. 
 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 
 ordinary temperatures. Coefficient of cubical expansion from 32° to 
 21 2°, 0*.0040. Conductivity for heat about 1/56 and for electricity only 
 about V80 of that of silver. Its tensile strength is about 6400 lbs. 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 
 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 lbs. per square inch. Heat conductivity 73.6% of that 
 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, 
 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 cold 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 about 2500° F. Conductivity for heat 11.9, and for electricity 
 12 to 14.8, silver being 100. Expansion in bulk bv 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 lbs. per square inch. Its elasticity is very low, and the metal 
 
176 MATERIALS. 
 
 flows under very slight strain. Lead dissolves to some extent in pure 
 water, but water containing carbonates or sulphates forms over it a 
 film of insoluble salt which prevents further action. 
 
 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 two thirds as much as aluminum. In the form of 
 filings, wire, or 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, winch 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, In. — 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. 194.8. 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 lbs. per square 
 inch. Fuses at 442° F. Not sensiblv volatile when melted at ordinary 
 heats. Heat conductivity 14.5, electric conductivity 12.4: silver being 
 100 in each case. Expansion of volume bv 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. 
 
MEASURES AND WEIGHTS OF VARIOUS MATERIALS. 177 
 
 Zinc, Zn. — At. wt. 65.4. Sp. gr. 7.14. Melts at 780° F. Volatilizes 
 land burns in the air when melted, with bluish-white fumes of zinc oxide, 
 ilt is ductile and malleable, but to a much less extent than copper, and 
 jits tenacity, about 5000 to 6000 lbs. 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 
 
 Gold 
 
 Silver 
 
 Aluminum 
 
 Copper 
 
 Tin 
 
 Lead 
 
 Zinc 
 
 Platinum 
 
 Iron 
 
 Ductility. 
 
 Tenacity. 
 
 Infusibility 
 
 Platinum 
 
 Iron 
 
 Platinum 
 
 Silver 
 
 Copper 
 
 Iron 
 
 Iron 
 
 Aluminum 
 
 Copper 
 Gold 
 
 Copper 
 Gold 
 
 Platinum 
 
 Silver 
 
 Silver 
 
 Aluminum 
 
 Zinc 
 
 Aluminum 
 
 Zinc 
 
 Gold 
 
 Zinc 
 
 Tin 
 
 Tin 
 
 Lead 
 
 Lead 
 
 Lead 
 
 Tin 
 
 MEASURES AND WEIGHTS OF VARIOUS MATERIALS 
 (APPROXIMATE). 
 
 Brickwork. — Brickwork is estimated by the thousand, and for 
 various thicknesses of wall runs as follows: 
 
 8i/4-in. wall, or 1 brick in thickness, 14 bricks per superficial foot. 
 123/4 " " " 11/2" " " 21 " 
 
 17 " " " 2 " " " 28 " 
 
 211/2 " " " 21/2 " " " 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 
 41/2 lbs. 
 
 Fuel. — A bushel of bituminous coal weighs 76 pounds and contains 
 26S8 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 eubic feet bituminous coal when broken down = 1 ton, 2240 lbs. 
 
 34 to 41 " " anthracite prepared for market. . . =1 ton, 2240 lbs. 
 
 123 " " of charcoal =1 ton, 2240 dbs. 
 
 70.9 " " "coke = 1 ton, 2240 ibs. 
 
 1 cubic foot of anthracite coal = 55 to 66 lbs. 
 
 1 " " " bituminous coal = 50 to 55 lbs. 
 
 1 " " Cumberland (semi-bituminous) coal =53 lbs. 
 
 1 " " Cannel coal = 50.3 lbs. 
 
 1 " " Charcoal (hardwood) = 18.5 lbs. 
 
 1 " " " (pine) =18 lbs. 
 
 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. 
 
178 MATERIALS. 
 
 Ores, Earths, etc. 
 
 13 cubic feet of ordinary gold or silver ore, in mine 
 
 20 " " " broken quartz 
 
 18 feet of gravel in bank 
 
 27 cubic feet of gravel when dry 
 
 25 " " " sand . 
 18 " 
 27 " 
 17 " 
 
 
 1 ton = 2000 lbs. 
 ■■ 1 ton = 2000 lbs. 
 
 . . . =1 ton. 
 
 =1 ton. 
 
 = 1 ton.; 
 
 1 earth in bank =1 ton. 
 
 earth when dry =1 ton.; 
 
 clay = 1 ton. 
 
 Cement. — Portland, per bbl. net, 376 lbs., per bag, net 94 lbs. 
 
 Nat ural, per bbl. net, 282 lbs., per bag net 94 lbs. 
 
 Lime. — A struck bushel 72 to 75 lbs. 
 
 Grain. — A struck bushel of wheat = 60 lbs.; of corn = 56 lbs.; of i 
 oats = 30 lbs. 
 
 Salt. — A struck bushel of salt, coarse, Syracuse, N. Y. = 56 lbs.; 
 Turk's Island = 76 to 80 lbs. 
 
 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 = bt; of round rods 
 = 0.7854 D 2 ; of tubes = 0.7854 (Z> 2 - d 2 ) = 3.1416 (Dt - t 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 (£ 2 - d 2 ) = 37.699 (Dt - P), 
 in cu. in. 
 
 Weight per foot length = volume X weight per cubic inch of mate- 
 rial. Weight of a sphere = diam. 3 X 0.5236 X weight per cubic inch. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ® a 
 
 tH O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 § ° m 
 
 °a^ 
 5^ M 
 Wo § 
 
 
 Material. 
 
 > 
 
 6 
 
 3 
 O ^ 
 
 if 
 
 
 g^3 
 
 m u^ 
 
 «w ® -- 
 
 o a-g 
 .S>5 § 
 
 O <D - 
 g oa'M 
 
 3 
 
 a^ 
 bo" 
 
 
 a- 
 
 02 ^ 
 
 JdCQ 
 
 
 a 
 m 
 
 (D&h 
 
 4>-C£ 
 
 ^Wf-1 
 
 «P£W 
 
 
 13 J- 
 
 Stfi^ 
 
 
 
 £ 
 
 & 
 
 £ 
 
 & 
 
 £ 
 
 tf£ 
 
 £ 
 
 £ 
 
 
 
 
 
 s 2 X 
 
 MY 
 
 
 
 7) 2 X 
 
 £> 3 X 
 
 
 7.218 
 7.7 
 
 450. 
 480. 
 
 37.5 
 40. 
 
 31/8 
 31/3 
 
 31/8 
 31/3 
 
 .2604 
 .2779 
 
 15^16 
 1. 
 
 2.454 
 2.618 
 
 .1363 
 
 Wrought iron 
 
 .1455 
 
 Steel 
 
 7.854 
 
 489.6 
 
 40.8 
 
 3.4 
 
 3.4 
 
 .2833 
 
 1.02 
 
 2.670 
 
 .1484 
 
 Copper & Bronze ) 
 (copper and tin) 1 
 
 8.855 
 
 552. 
 
 46. 
 
 3.833 
 
 3.833 
 
 .3195 
 
 1.15 
 
 3.011 
 
 .1673 
 
 Brass | 35 zinc J 
 
 8.393 
 
 523.2 
 
 43.6 
 
 3.633 
 
 3.633 
 
 .3029 
 
 1.09 
 
 2.854 
 
 .1586 
 
 11.38 
 2.67 
 2.62 
 0.481 
 
 709.6 
 166.5 
 163.4 
 30.0 
 
 59.1 
 13.9 
 13.6 
 
 2.5 
 
 4.93 
 1.16 
 1.13 
 0.21 
 
 4.93 
 1.16 
 1.13 
 0.21 
 
 .4106 
 .0963 
 .0945 
 .0174 
 
 1.48 
 0.347 
 0.34 
 1-16 
 
 3.870 
 0.908 
 0.891 
 0.164 
 
 .2150 
 
 
 .0504 
 
 
 .0495 
 
 Pine wood, dry. . . . 
 
 .0091 
 
 Weight per cylindrical in., 
 last col.-*- 12. 
 
 1 in. long, — coefficient of D 2 in next to 
 
SIZES OF IRON AND STEEL BARS. 
 
 179 
 
 For 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 - t 2 ). 
 
 For hollow spheres use the coefficient of D s 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 IRON AND STEEL BARS. 
 
 Flats. 
 
 Width. 
 
 Thickness. 
 
 Width. 
 
 Thickness . 
 
 Width. 
 
 Thickness. 
 
 3/4 
 
 1/8 to 5/ 8 
 
 17/8 
 
 1/2 to 1 1/2 
 
 4 
 
 1/4 to 2 
 
 7/8 
 
 1/8 to 3/ 4 
 
 2 
 
 1/8 to 1 3/ 4 
 
 41/2 
 
 1/4 to 2 
 
 1 
 
 1/8 to 15/16 
 
 21/4 
 
 1/4 to 1 3/ 4 
 
 5 
 
 1/4 to 2 
 
 U/8 
 
 1/8 to 1 
 
 23/ 8 
 
 1/4 to 1 1/8 
 
 51/2 
 
 1/4 to 2 
 
 U/4 
 
 1/8 to 1 1/8 
 
 21/2 
 
 3/16 to 1 3/4 
 
 6 
 
 1/4 to 2 
 
 13/8 
 
 1/8 to 1 1/8 
 
 25/ 8 
 
 1/4 to 1 1/8 
 
 61/2 
 
 1/4 to 2 
 
 U/2 
 
 1/8 to 1 l/ 4 
 
 23/ 4 
 
 1/4 to 1 1/8 
 
 7 
 
 1/4 to 2 
 
 15/8 
 
 1/4 to 1 1/4 
 
 3 
 
 1/4 to 2 
 
 71/2 
 
 1/4 to 2 
 
 13/ 4 
 
 3/16 to 1 1/2 
 
 31/2 
 
 1/4 to 2 
 
 
 
 Commercial Sizes of Iron and Steel Bars. 
 
 Rounds: Iron. 1/4 to 13/s in., advancing by 1/16 in.; 13/ 8 in. to 5 in., 
 advancing by l/s in. Steel. 1/4 in. to li/s in., advancing by 1/32 in.; 
 11/8 in. to 2 in., advancing by Vie in.; 2 in. to 4 in., advancing by i/ 8 in.; 
 4 to 63/ 4 in., advancing by 1/4 in. Also the following intermediate sizes: 
 
 23/64, 2 5/64, 29/ 64 , 31/64, 33/ 64 , 35/ 64 , 39/ 64 , 47/ 64 , 53/^, 55/ 64 , 63/ 64 , \7/ m and 115/ 32 
 
 in. 
 
 Squares: Iron. 5/i 6 to 11/4 in., advancing by Vie in.; 11/4 to 3 in., 
 advancing by Vs in. Steel. 1/4 to 2 in., advancing by Vi6in.; 2 l/s in.; 
 21/4 to 4 in., advancing by 1/4 in.; 41/2 in.; 5 in. 
 
 Half rounds: Iron. 7/ m , i/ 2 , 5/ 8 , u/ 16 , 3/ 4i i, n/ 8 , ii/ 4j n/ 2 , 13/4, and 
 
 2 in. Steel. 3/ 8 , 25/ 64 , 13/ 32t 7/ 16 , 29/ 64 , 15/ 32 , l/ 2 , 33/04, 17/ 32 , 9/i6, l 9 /32, 5 / 8 , 2 V 32 , 
 11/16, 23 /32, 3/4, 25/ 32 , 13/ 16 , 27/ 32 , 7/ 8 , 29/ 32 , 15/i 6 , 1, 1 1/ 32 , 1 1/ 8? 1 1/ 4? 1 3/ 8 , 1 l/ 2 , 
 
 13/4, 2, 21/2, and 3 in. Weights of half rounds, one half of corresponding 
 rounds. See table, page 180. 
 
 Ovals: Iron. 1/2 X 1/4, VsXS/ie, 3 / 4 x 3/ 8 , and 7/ 8 x7/i 6 in. Steel. 
 
 5/8 X 5/i 6 , I/2 X 3/ 8 , 17/32 X 9/ 32 , 9/i 6 X 3/ 8l 19/ 32 X 9/ 32 , 3/ 4 X 5/i 6 , 3/ 4 X 3/ 8 , 7/ 8 X 5/i 6l 
 
 7/8 X 7/i6, 1 X 1/2, and 1 l/s X 9/i6 in. 
 
 Half Ovals: Iron. 1/2 X Vs, 5 / 8 X5/ 32 , 3/ 4 x3/ie, 7/ 8 X7/ 32) 1 1/2 X 1/2. 
 
 13/4X5/8, 17/ 8 X 5/ 8 in. 
 
 Round Edge Flats: Iron. 1 1/2 X 1/2, l 3 / 4 X5/ 8 , 17/ 8 X5/ 8 in. Steel. 
 
 1 X 3/i6, 1 X 1/4, 1 X 5/16, 1 X 3/ 8 , 1 X 7/i6, 1 Vi X 3/ 16 , 1 1/ 4 X l/ 4 , U/4 X 5/ le> 
 
 H/4X 3/ 8 , H/4X 7/i 6 in.; H/2X 1/4 to H/2X 1 in., advancing by i/i 6 in.; 
 13/4X1/4 to 13/ 4 x 1 in., advancing by i/i 6 in.; 2X 1/4 to 2 X 1 in., 
 advancing by Vi6 in.; 21/4X 1/4 to 21/4X 1 in., advancing by 1/16 in.; 
 21/2 X 1/4 to 21/2X 1 in., advancing by i/i 6 in.; 23/ 4 x 1/4 to 23/ 4 x 1 in., 
 advancing by i/iein.; 3 X 1/4 to 3 X 1 in., advancing by Vie in. 
 
 Bands: Iron. 1/2 toll/s in., advancing by l/s in., 7 to 16 B. W. G.; 
 11/4 to 5 in.; advancing by 1/4 in., 7 to 16 gauge up to 3 in., 4 to 14 gauge, 
 31/4 to 5 in. 
 
180 
 
 MATERIALS. 
 
 WEIGHTS OF SQUARE AND ROUND BARS OF WROUGHT 
 IRON IN POUNDS PER LINEAL FOOT. 
 
 Iron weighing 480 lb. per cubic foot. For steel add 2 per cent. 
 
 °K A 
 
 *S«8 ^ 
 
 «*tfM 
 
 o 
 
 •j-SjM 
 
 ^PQ o 
 
 O j_ • 
 
 •s £ 5P 
 
 «** w 
 
 m% % 
 
 ^ffl O 
 
 °«§ 
 
 X$ 4> 
 
 °W O 
 
 M V CD 
 
 °«§ 
 
 °PQ S 
 
 
 
 
 gQ.S 
 
 
 SPe ■ 
 
 2Q.S 
 
 j3 gi-} 
 '53 3,*^ 
 
 bJ3 c 
 
 M5 
 
 
 
 
 
 H/16 
 
 24.03 
 
 18.91 
 
 3/8 
 
 96.30 
 
 75.64 
 
 1/16 
 
 0.013 
 
 0.010 
 
 3/4 
 
 25.21 
 
 19.80 
 
 7/16 
 
 98.55 
 
 77.40 
 
 1/8 
 
 .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 /l6 
 
 .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 
 
 90.36 
 
 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 
 
 1/2 
 
 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 
 
 1/16 
 
 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 
 
 7 
 
 163.3 
 
 128.3 
 
 3/16 
 
 4.70! 
 
 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 
 
 142.4 
 
 3/8 
 
 6.302 
 
 4.950 
 
 Vl6 
 
 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 
 
 8 
 
 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 
 
 1/2 
 
 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 
 
 11/16 
 
 73.24 
 
 57.52 
 
 1/2 
 
 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 /l6 
 
 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 
 
 1/2 
 
 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 
 
 19.80 
 
 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 IRON AND STEEL SHEETS. 
 
 181 
 
 WEIGHT OF IRON AND STEEL 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. 
 p. 32.) 
 
 (See 
 
 ' 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. 
 
 15.30 
 
 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 
 
 0.2655 
 
 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 
 
 1.96 
 
 2.00 
 
 15 
 
 0.0703 
 
 2.8125 
 
 2.869 
 
 19 
 
 .042 
 
 1.68 
 
 1.71 
 
 16 
 
 0.0625 
 
 2.5 
 
 2.55 
 
 20 
 
 .035 
 
 1.40 
 
 1.43 
 
 17 
 
 0.0563 
 
 2.25 
 
 2.295 
 
 21 
 
 .032 
 
 1.28 
 
 1.31 
 
 18 
 
 0.05 
 
 2. 
 
 2.04 
 
 22 
 
 .028 
 
 1.12 
 
 1.14 
 
 19 
 
 0.0438 
 
 1.75 
 
 1.785 
 
 23 
 
 .025 
 
 1.00 
 
 1.02 
 
 20 
 
 0.0375 
 
 1.50 
 
 1.53 
 
 24 
 
 .022 
 
 .88 
 
 .898 
 
 21 
 
 0.0344 
 
 1.375 
 
 1.402 
 
 25 
 
 .02 
 
 .80 
 
 .816 
 
 22 
 
 0.0312 
 
 1.25 
 
 1.275 
 
 26 
 
 .018 
 
 .72 
 
 .734 
 
 23 
 
 0.0281 
 
 1.125 
 
 1.147 
 
 27 
 
 .016 
 
 .64 
 
 .653 
 
 24 
 
 0.025 
 
 1. 
 
 1.02 
 
 28 
 
 .014 
 
 .56 
 
 .571 
 
 25 
 
 0.0219 
 
 0.875 
 
 0.892 
 
 29 
 
 .013 
 
 .52 
 
 .530 
 
 26 
 
 0.0188 
 
 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 
 
 Specific gravity 
 
 Weight per cubic foot . 
 
 Iron. Steel. 
 
 7.7 7.854 
 
 480. 489.6 
 
 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. 
 
182 
 
 MATERIALS. 
 
 -oooeooc 
 > oo ao oo at 
 
 -©OooOrNiOm^frc^cN — OOoOIn 
 
 niOlNOOOi© — CNcON"U" 
 
 <*i vO © "* oo — mo 
 q m_ in tj- co co cn — 
 n id in oo' d o — co 
 
 PnO in in oo oo © — 
 
 Nodofo.ts 
 
 oj CN CN CN CN CN CN CN <o 
 
 fiNOmNOf 
 
 nvOtNOOO^OO- 
 
 nco — ooooomco — © 
 
 into — c 
 in code 
 
 oo iO If to — c 
 ©'— "cn'co'co'-< 
 
 cojvooocNma 
 in -<r — oo vq c 
 © — cn cn to n 
 
 in in to — O oo oc 
 ^(Nooqinto — 
 'm' id in in code 
 
 on- — oor> 
 
 n cn cn cn cn to 
 
 n oo — N- in o c* 
 
 toto^r 
 n d id In 
 
 OOOvO 
 aq-<t_ 
 
 odd© 
 
 CO — a^O^NONiA 
 © — <N CN c 
 
 \OiOIn0O00Oi©©- 
 
 CNm oo O tou - 
 vqcojoqin — t^ 
 
 © — — CN to' C> 
 
 ootomooOt<- 
 to. o iq cn aq in — 
 r'm'm'vdvdi<oc 
 
 0©cO- . 
 O O -O (N 
 
 oqin- 
 
 om oo © com oo © 
 OtNoom — incoO 
 n' id id r-s," oo' od d ©' 
 
 O — — CN CN CO T T if 
 
 niOiOINOOOOOiOiOO- 
 
 © — — CNCNcOcON-N-ininvOoOINtNOOOOOiOi©© — — CNtOCOTN-inm' 
 O00 
 
 iOto — con- — oomcNOnOcoooiOcoorNTj' — oo^ - — comcNOOoOcooooOco© 
 •"* Oi "T oo to oo tN in cn vO — oO © in O in Oi T Oi to oo to in cn in — iO — in © «n i © 
 O* "— — 'cNCN'co'co'VN-'inin'ddtNiN'tNao'co'dd©'©' — ■— ' cn cn co' co V ' 
 
 toONiOOmat^N- 
 
 vOCNOOiOCNOnntNOOm — oCtOtNCOOoOcOOOoOCNOnn — OON - - tNN - © I-- 
 to IN O T 00 — in Oi CN iO O to In — N - 00 tN in Oi tN oO i O to , IN — . IT 00 CN | in i OO .to oO 
 d '—" — — cn'cn'cn'cWco't't V in m' m' id id od IN In OO CO 00 Oioooooo© — — 
 
 — cNtomiOooooo — to-^imoooooo — to-^-moOooOiO — toN-miOcoooo 
 to_ iq o> cn in oo — in oo — n- in o to ■■o © to iO oo cn m aq — in oo_ — "T in o to -© © 
 <-> — ' — cn cn cn co' to' to' T ' ^f " N" m i m" m" m" od iO iO in in r> oo oo oo oo oo oo o 
 
 ©' 
 
 lOcoiooN-OootNoo-^-OoOrooim — in to Oi m — iNtoOoin — in co oo in — r, .. , 
 cn in in o to in oo o to iO oo — to iO c> — N- iO oo cn N - in oo coi^ in in o cn in oq o co 
 ' — ' — *-' — ' cm' cn cn cn ico' to' co' co' -* ' N - 't' N" in'min'moo lOooiNtNiNrNoooo 
 
 coin m co 
 
 o — cNto^rmioiNooooooo — cNtoco^J-mooiNtNooooo — NcQjjjjin^.^ 
 
 CNN-iOOOOCNN-iOOOOtNinrNOi — CO in rN Oi — co m IN O -CN ^ oO oq O CN ■* oO 
 
 ' — — ' — ' — ' — ' cn cn cn cn cn co to to co co ^' ^' ^' ^' in in in in' in od od id oo' 
 
 
WEIGHTS OF FLAT WROUGHT IRON. 
 
 183 
 
 
 « 
 
 oooooooooooooooooooooooo 
 
 in © «n © in O In © m O m o <n , © in o ; © ; © © O O O ; q ; O 
 pj in r%'o <N m' r>.' o' cn m' r>." o eN m' r--.' ©' in o m' ©' m o in o 
 ^^X — — — eNvNvNCNencnenen^r^-mmvovOt^t^oo 
 
 3 
 
 2.29 
 
 4.58 
 6.88 
 9.17 
 11.46 
 13.75 
 16.04 
 18.33 
 20.63 
 22.92 
 25.21 
 27.50 
 29.79 
 32.08 
 34.38 
 36.67 
 41.25 
 45.83 
 50.42 
 55.00 
 59.58 
 64.17 
 68.75 
 73.33 
 
 b 
 
 2.08 
 4.17 
 6.25 
 
 8.33 
 10.42 
 12.50 
 14.58 
 16.67 
 18.75 
 20.83 
 22.92 
 25.00 
 27.08 
 29.17 
 31.25 
 33.33 
 37.50 
 41.67 
 45.83 
 50.00 
 54.17 
 58.33 
 62.50 
 66.67 
 
 05 
 
 1.88 
 3.75 
 5.63 
 7.50 
 9.38 
 11.25 
 13.13 
 15.00 
 16.88 
 18.75 
 20.63 
 22.50 
 24.38 
 26.25 
 28.13 
 30.00 
 33.75 
 37.50 
 41.25 
 45.00 
 48.75 
 52.50 
 56.25 
 60.00 
 
 So 
 
 1.77 
 3.54 
 5.31 
 7.08 
 8.85 
 10.63 
 12.40 
 14.17 
 15.94 
 17.71 
 19.48 
 21.25 
 23.02 
 24.79 
 26.56 
 28.33 
 31.88 
 35.42 
 33.96 
 42.50 
 46.04 
 49.58 
 53.13 
 56.67 
 
 00 
 
 1.67 
 3.33 
 5.00 
 6.67 
 8.33 
 10.00 
 11.67 
 13.33 
 15.00 
 16.67 
 18.33 
 20.00 
 21.67 
 23.33 
 25.00 
 26.67 
 30.00 
 33.33 
 36.67 
 40.00 
 43.33 
 46.67 
 50.00 
 53.33 
 
 r« 
 
 1.56 
 3.13 
 4.69 
 6.25 
 7.81 
 9.38 
 10.94 
 12.50 
 14.06 
 15.63 
 17.19 
 18.75 
 20.31 
 21.88 
 23.44 
 25.00 
 28.13 
 31.25 
 34.38 
 37.50 
 40.63 
 43.75 
 46.88 
 50.00 
 
 r» 
 
 1.46 
 2.92 
 4.38 
 5.83 
 7.29 
 8.75 
 10.21 
 11.67 
 13.13 
 14.58 
 16.04 
 17.50 
 18.96 
 20.42 
 21.88 
 23.33 
 26.25 
 29.17 
 32.08 
 35.00 
 37.92 
 40.83 
 43.75 
 46.67 
 
 CO 
 
 1.41 
 
 2.81 
 
 4.22 
 
 5.63 
 
 7.03 
 
 8.44 
 
 9.84 
 
 11.25 
 
 12.66 
 
 14.06 
 
 15.47 
 
 16.88 
 
 18.28 
 
 19.69 
 
 21.09 
 
 22.50 
 
 25.31 
 
 28.13 
 
 30.94 
 
 33.75 
 
 36.56 
 
 39.38 
 
 42.19 
 
 45.00 
 
 CO 
 
 1.35 
 2.71 
 4.06 
 
 5.42 
 6.77 
 8.13 
 9.48 
 10.83 
 12.19 
 13.54 
 14.90 
 16.25 
 17.60 
 18.96 
 20.31 
 21.67 
 24.38 
 27.08 
 29.79 
 32.50 
 35.21 
 37.92 
 40.63 
 43.33 
 
 CO 
 
 1.30 
 2.60 
 3.91 
 5.21 
 6.51 
 7.81 
 9.11 
 10.42 
 11.72 
 13.02 
 14.32 
 15.63 
 16.93 
 18.23 
 19.53 
 20.83 
 23.44 
 26.04 
 28.65 
 31.25 
 33.85 
 36.46 
 39.06 
 41.67 
 
 b 
 
 1.25 
 2.50 
 3.75 
 5.00 
 6.25 
 7.50 
 8.75 
 10.00 
 11.25 
 12.50 
 13.75 
 15.00 
 16.25 
 17.50 
 18.75 
 20.00 
 22.50 
 25.00 
 27.50 
 30.00 
 32.50 
 35.00 
 37.50 
 40.00 
 
 w 
 
 1.20 
 
 2.40 
 
 3.59 
 
 4.79 
 
 5.99 
 
 7.19 
 
 8.39 
 
 9.58 
 
 10.78 
 
 11.98 
 
 13.18 
 
 14.38 
 
 15.57 
 
 16.77 
 
 17.97 
 
 19.17 
 
 21.56 
 
 23.96 
 
 26.35 
 
 28.75 
 
 31.15 
 
 33.54 
 
 35.94 
 
 38.33 
 
 »0 
 
 1.15 
 
 2.29 
 
 3.44 
 
 4.58 
 
 5.73 
 
 6.88 
 
 8.02 
 
 9.17 
 
 10.31 
 
 11.46 
 
 12.60 
 
 13.75 
 
 14.90 
 
 16.04 
 
 17.19 
 
 18.33 
 
 20.63 
 
 22.92 
 
 25.21 
 
 27.50 
 
 29.79 
 
 32.08 
 
 34.38 
 
 36.67 
 
 10 
 
 1.09 
 2.19 
 
 3.28 
 
 4.38 
 
 5.47 
 
 6.56 
 
 7.66 
 
 8.75 
 
 9.84 
 
 10.94 
 
 12.03 
 
 13.13 
 
 14.22 
 
 15.31 
 
 16.41 
 
 17.50 
 
 19.69 
 
 21.88 
 
 24.06 
 
 26.25 
 
 28.44 
 
 30.63 
 
 32.81 
 
 35.00 
 
 W5 
 
 1.04 
 
 2.08 
 
 3.13 
 
 4.17 
 
 5.21 
 
 6.25 
 
 7.29 
 
 8.33 
 
 9.38 
 
 10.42 
 
 11.46 
 
 12.50 
 
 13.54 
 
 14.58 
 
 15.63 
 
 16.67 
 
 18.75 
 
 20.83 
 
 22.92 
 
 25.00 
 
 27.08 
 
 29.17 
 
 31.25 
 
 33.33 
 
 
 i! 
 
 cocD«oir>c©222 
 
 T 
 
 ~ 
 
 rs-a 
 
 > 
 
 o 
 
 
 O 
 
 -£ 
 
 x£ 
 
 - 
 
 M 
 
 
 a; 
 
 
 c< 
 
 — 
 
 £^£S 
 
 
 R 
 
 
 
 
 s 
 
 
 "3 
 
 Z%$'* 
 
 ■§ 
 
 A 1.13 £ u 
 
 >> 
 
 
 o> 
 
 1*11 
 
 a 
 
 C^ g-Q 
 
 
 
 V 
 
 
 S 
 
 
 ■jj-j 
 
 x-S-x 
 
 
 t>r 5 Xt 
 
 O 
 
 _h £vO<N 
 
 
 
 
 ^5 --C 
 
 
 tr.+- b£ M 
 
 3 
 
 'loll 
 
 * 
 
 
 
184 
 
 
 40.00 
 
 43.33 
 
 46.67 
 
 50.00 
 
 53.33 
 
 56.67 
 
 60.00 
 
 63.33 
 
 66.67 
 
 70.00 g 
 
 73.33 > 
 
 76.67 t-3 
 
 80.00 H 
 
 83.33 ft 
 
 86.67 £ 
 
 90.00 £ 
 
 93.33 5 
 
 96.67 
 
 00.0 
 
 06.7 
 
 13.3 
 
 20.0 
 
 26.7 
 
 33.3 
 
 40 
 
 46.7 
 
 53.3 
 
 60.0 
 
 66.7 
 
 73.3 
 
 80.0 
 
 86.7 
 
 
 
 s 
 
 OmfMDOCMA^Ot^inooOtfMntoomm 
 
 m q rx ao q — ; cn tn^/O^aqo — Ntnin^OrsOtniftcoot'iinoootniAcootf 
 tx' o en <i ©' en ' >0 O cn m co — m oo — -T rx ©' cn ©' voVi cd m' — ' rx cn ©' vd cn oc i m' — 
 r r V T)-'<r-<TmmmmvO^OvOr>t-«.t>.flOoocoo^O^OO — — cNcncn^-mmvO-Orxoc 
 
 
 
 £ 
 
 O O so rx q q q t q N^OO.C^i»t>\qiriiritfi--qa3iNintfvNOcONiAcfit 
 iTih,Oc^^O^NinoD— 'tt > >ONinoO'- , tINtf\0 1 ifiO\0(SOO' , to'iri — rstfio 
 rAcA^^^^^ in ^^^^ t ^ r ^ I ^ t>,0 O a OO s O N 0-— ■— tS<NcriTr->rininvO< 
 
 
 
 1 
 
 0-NtAcAinminiMOiOOOONmT>nintstoo 
 
 n cn 0\ q en p rx "<r — ; cq q q © rx "T — oo q CN q O q q q rx cn O O "f oo en tx - 1 
 r^ in rx o en cc — ^' o o^' cn in ix ©' en in cd ^ \d cn tx cn cd en o^ t' ©' m' ©' vd — ' r 
 ^cncn^r-<3-N-^-ininininvOO>orxrxrxrxoococ>c>©©. cn en en n- t m u 
 
 
 . 
 
 £ 
 
 OOOOOOOOOOOOOOOOOOOOOOO 
 
 q in q q q q q m q m q q q m q q q m q q q q q q q q q q q q o o c 
 ©CN'n rx ONin^o'Niri^'o'Nift'NO'Nifio'in'o'inbirio'ifiOino'ino'u 
 ciMnf r it f lT1"t'tminininvO>0\OvOrNr>t>.oOoOO>i>00- — <N CN en en -T •» 
 
 3 
 
 ©ONcoaoixNOm-^-cneneN — O (Mo on in \0 m en — o O rx m 
 
 m_ ix q en q q cn m oq — ; ■* rx q cm m co — ->t tx en q q q q cn co T q q cn oq en c 
 
 rx' o' cn V -o co' — ' en m' co' ©' cn m' ix o' — ' ■*' -6 od en ix' cn rx — ' ^d © m' ©' -*r o' en oo f 
 
 eNjeNSenenenen'<rTj--q--q-ininininin\OvO^O'Ot^t^OOOOO^O > -00 — — — eSeNe 
 
 £ 
 
 O(0rsmte,(SO00r>UMeiNOC0MTitfiNOt>^OrMnOr>Cl 
 
 © q — cn en •>* in m O rx oo O O O — CN en N - in vO co O <— en in q oq © cn en in ix 1 1 
 
 m rx O- -- en in rx' o' — ' en" m' rx' ©' cn tj-' vd co' o' eN >© ©' m' o' en ix — in ©' ■*' oo cn \0 < ■ 
 
 NfNjNtf|ce\cnrrirA , t"1"^"fininifMnm\O^0>Ot>r>r>oD00ai^OOO--M 
 
 2 
 
 ©coqcnOGOmrx©comenOoomenOGOm©m©in©m©mOinO 
 
 in i en CN ! — O q ix , q in en cn — © co ix -O in en cn © ix in i cn © . rx in eN iq rx m ; cn , © ■ ; 
 
 <M -3- --O no © — en in rx' a- — ' en m' \d od ©' eN '■S - <> ©' en" rx -- m' od eN \D o' cn rx — m' 1 1 
 
 eNeNeNeNenenenenenen^r-^--^--^--^-ininininvOvO^Or->t^r^oOoOO^O N O v -0©'' 
 
 5 
 
 ©rxcn©rxcn©rxcnorxcn©rxcnorxen©cnrx©cnrx©cnrx©enrx©cnr 
 ©qen©\Oen©vOen©NOen©^Oen©vOen©envOOenvO©envO©e<*iqOeni 
 
 q — m 'n vO - rd ©" — ' en' in ^6 od ©' — ' en m' \d od O en \d C i en \0 ' O en <©' O en vO © en : 
 (s leNf>leNeNeNenenenenenen-<3--^-'T'^-^r'1 - mininvOsOvOt^r>.t~«GOGOGOO^O^ 1 
 
 cs 
 
 OvONcOtnOMn- i^cnco^-OvOeNoOeno^int^aOOeNeninr>GOO-- eninvOJ 
 in iO» -T q en r> eN r^. — o © in o -<r O^ en go eN r^ vO m in tj- en eN — ; q q & q r% q < 
 ^.° TO d — ' en V sd I-n' o' ©' CN en in' vd P^.' cK O CN en vO o' CN in GO — -<r t-> p CN m CO -; ; 
 CN>4CNeN(N(NCNenenenenenenen-^ T TTrN-N m ininin\0^O'O^ rs-l^ t^ GO . 
 
 .00 
 
 ©'nOm©mO'n©m©m©momOmO©©©©©0©0©00©0$ 
 ©r^in r> © cn in t^ ocn m t^ ©csm t-> ©CN in ©m ©m qm qm© inqmq J 
 in so v»' -O ©' — ' cn' f\ in vo' r>.' od ©' — ' cn en m' ■■6 rx' ©' cn in i< ©' cn m' t--' ©' cn in tx p ; 
 — ' — cn cn tN (N eNeNeNeNcncncnmenencnT'<J-TTmmmmvO'0^0*©f> 
 
 ec 
 
 3i-(0tAN-in»cf\(0N'OO^c0enN-iriff 1 NOC^rNiA^NO5tNir;rA : 
 
 ■ n in in q q i-n [^ t>s, co co c> c> o © o •— •— cn cn en ■*_ in in q t>. q o_ q q — ; cn en 
 CN en ■* in \D r-> od o' O — ' CN en in vO tx cd o' C i — " en i in r^ C> — ' en iflrs © CN N" vO CO : 
 — — — — ■ ■— — cNeNeNeNeNCNCNCNeNcncncncncncn-'l-TT r rmmmmm» 
 
 5 
 
 Ornt5 0enrx©enr^©enrx©entx©entx©rxen©rxenor>;en©t>»cnor>.| 
 © ao q >n en — © co o m en — O co O m en — © O en © q en q q en q q en q q • 
 
 d ©' — cn en t' m' in vo' r>i cd o' ©' ©' — ' CN cn ^r m! *6 od ©' — '■ en m' \6 cd O •- en in -O ; 
 — _ — — . , (scNCNCNCNCNCNCNCNenenenenenen-^rT'^ -, T T r 
 
 2 
 
 DcnmcOOenm!x©enmoO©CNinooOensnOmOmOm©mpin©inO. 
 n — ix en © q cn co in — rx en O vO cn co in — tx © CN in ix q cn q t->. q cN q tx q 
 x, GO GO O O © — — cN en en ^ in in O O tx cd 00 O ^ CN en in vO tx co © — CN en in J 
 
 
 
 -9° 
 
 OCNcn intxooonienintxoo©cNeninixco©entx©enix©fntxOcntx©en. , 
 © ^ q cn q © q o en ix — m © n- oo cn q q q q — _ q q q q q — ; q q q q q « 
 m' m" in vd O ix rx rx cd GO o' O © O O — ' — " CN CN cn ^ '^ in O tx cd O^ O O •- nj en J 
 
 s 
 
 O — CNenenirmorxaocooo — cNenen^inixnoocNeninrxcoocNeninixl 
 in tx q — q q rx q — q q rx © cN ->r q q O CN q O q q q rx — q © tj- q cN q r 
 cn cn N en en en en en ■^-' ■*' T -<r in in m m' m' vd ^d vd rx tx rx' oo co o s O O O -^ ^ g 
 
 ^ A 
 
WEIGHTS OF STEEL BLOOMS. 
 
 185 
 
 WEIGHTS OF STEEL BLOOMS. 
 
 Soft steel. 1 cubic inch = 0.284 lb. 1 cubic foot = 490.75 lbs. 
 
 
 
 
 
 Lengths. 
 
 
 Size, 
 Inches 
 
 
 
 
 
 
 
 1" 
 
 6" 
 
 12" 
 
 18" 
 
 24" 
 
 30" 
 
 36" 
 
 42" 
 
 48" 
 
 54" 
 
 60" 
 
 66" 
 
 12 X6 
 
 20.45 
 
 123 
 
 245 
 
 368 
 
 491 
 
 613 
 
 736 
 
 859 
 
 982 
 
 1 104 
 
 1227 
 
 1350 
 
 X5 
 
 17.04 
 
 102 
 
 204 
 
 307 
 
 409 
 
 511 
 
 613 
 
 716 
 
 818 
 
 920 
 
 1022 
 
 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 
 
 X3 
 
 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 
 
 118! 
 
 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 
 
 238 
 
 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 
 
 51/2X51/2 
 
 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 
 
 7.1C 
 
 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 
 
 j 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 
 
 3.4C 
 
 20 
 
 41 
 
 61 
 
 82 
 
 102 
 
 122 
 
 143 
 
 163 
 
 184 
 
 204 
 
 224 
 
 131/2X31/2 
 
 3.4S 
 
 21 
 
 42 
 
 63 
 
 84 
 
 104 
 
 125 
 
 146 
 
 167 
 
 188 
 
 209 
 
 230 
 
 X3 
 
 2.9e 
 
 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 
 
186 
 
 MATERIALS. 
 
 SIZES AND WEIGHTS OF ROOFING MATERIALS. 
 
 Corrugated Iron or Steel Plates. —Weight per 100 Sq. Ft., Lb. 
 
 (American Sheet and Tin Plate Co., 1905.) 
 
 SCHEDULE OF WEIGHTS. 
 
 Corruga- 
 tions. 
 
 5/8 
 
 in. 
 
 U/4 
 
 <3/ 8 in. 
 
 2x1/ 
 
 2 in. 
 
 21/ 2 X 
 
 1/2 in. 
 
 3x3/ 4 in. 
 
 5x7/ 8 in. 
 
 U. S.Std. 
 
 T3 
 
 a 
 
 i. 
 
 h 
 
 T3 
 
 h 
 
 'i 
 
 a 
 
 ^3 
 
 c 
 
 T3 
 
 
 Sheet 
 Metal 
 Gauge. 
 
 
 - 
 
 
 <* — 
 
 d tsj 
 
 .3 
 "3 
 
 -3-~ 
 
 
 
 g 
 
 
 
 g ■ 
 — <o 
 
 -« 
 
 28 
 
 72 
 
 87 
 
 72 
 
 87 
 
 68 
 
 85 
 
 68 
 
 85 
 
 68 
 
 85 
 
 68 
 
 85 
 
 27 
 
 79 
 
 94 
 
 79 
 
 94 
 
 76 
 
 91 
 
 76 
 
 91 
 
 76 
 
 91 
 
 76 
 
 91 
 
 26 
 
 86 
 
 101 
 
 86 
 
 101 
 
 83 
 
 98 
 
 83 
 
 98 
 
 83 
 
 98 
 
 83 
 
 98 
 
 25 
 
 100 
 
 115 
 
 100 
 
 115 
 
 96 
 
 11! 
 
 96 
 
 111 
 
 96 
 
 111 
 
 96 
 
 111 
 
 24 
 
 114 
 
 129 
 
 114 
 
 129 
 
 110 
 
 124 
 
 110 
 
 124 
 
 110 
 
 124 
 
 110 
 
 124 
 
 23 
 
 
 
 128 
 !42 
 156 
 170 
 
 143 
 157 
 171 
 185 
 
 123 
 136 
 
 150 
 163 
 217 
 
 271 
 
 138 
 151 
 165 
 
 178 
 232 
 286 
 
 123 
 136 
 150 
 163 
 217 
 271 
 
 138 
 151 
 165 
 178 
 232 
 286 
 
 123 
 136 
 150 
 163 
 217 
 271 
 
 138 
 151 
 165 
 178 
 232 
 286 
 
 123 
 136 
 150 
 163 
 
 217 
 271 
 
 138 
 
 22 
 
 
 
 151 
 
 21 
 
 
 
 165 
 
 20 
 
 
 
 178 
 
 18 
 
 
 
 232 
 
 16 
 
 
 
 
 
 286 
 
 
 
 
 
 
 
 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 11/2 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 gauge corrugated iron is generally used for applying to wooden 
 buildings; but for applying to iron framework No. 24 gauge or heavier 
 should be adopted. 
 
 Galvanizing sheet iron adds about 21/2 oz. to its weight per square foot. 
 
 Corrugated Arches. 
 
 For corrugated curved sheets for floor and ceiling construction in fire- . 
 proof buildings, No. 16, 18, or 20 gauge 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 11/4X3/8, 21/2 X 1/2, 3X 3/4 and 
 5 X 7/8 in. corrugations, and in the same width of sheet as above men- 
 tioned. 
 
 Terra-Cotta. 
 
 Porous terra-cotta roofing 3 in. thick weighs 16 lb. per square foot and 
 2 in. thick, 12 lb. per square foot. 
 
 Ceiling made of the same material 2 in. thick weighs 11 lb. per square 
 foot. 
 
 Tiles. 
 
 Flat tiles 6V4 X 101/2 X 5/ 8 in. weigh from 1480 to 1850 lb. 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 lb. per square of roof.] 
 
 Pan-tiles 141/2X 10 1/2 laid 10 in. to the weather weigh 850 lb. per,; 
 square. 
 
SIZE AND WEIGHT OF ROOFING MATERIALS. 
 
 187 
 
 Standard Weights and Gauges of Tin Plates. 
 
 American Sheet and Tin Plate Co., Pittsburg, Pa. 
 
 rrade term. 
 
 56 1b. 
 
 60 1b. 
 
 65 1b. 
 
 70 1b. 
 
 75 1b. 
 
 80 1b. 
 
 85 1b. 
 
 90 1b. 
 
 95 1b. 
 
 Nearest wire 
 
 
 
 
 
 
 
 
 
 
 gauge No. 
 
 height per 
 
 sq.ft., lb.. 
 
 38 
 
 37 
 
 35 
 
 35 
 
 34 
 
 33 
 
 32 
 
 31 
 
 31 
 
 0.257 
 
 0.275 
 
 0.298 
 
 0.322 
 
 0.345 
 
 0.367 
 
 0.390 
 
 0.413 
 
 0.436 
 
 height, box, 
 
 
 
 
 
 
 
 
 
 
 14x20 in., 
 
 
 
 
 
 
 
 
 
 
 lb 
 
 56 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 85 
 
 90 
 
 95 
 
 1001b. 
 301/2 
 0.459 
 
 100 
 
 Trade term 
 
 Nearest wire gauge 
 
 No 
 
 iVeight per sq. ft., 
 
 lb 
 
 height, box, 14x20, 
 
 lb 
 
 IC 
 
 IXL 
 
 IX 
 
 IXX 
 
 IXXX 
 
 IXXXX 
 
 30 
 
 28 
 
 28 
 
 27 
 
 26 
 
 25 
 
 0.491 
 
 0.588 
 
 0.619 
 
 0.712 
 
 0.803 
 
 0.895 
 
 107 
 
 128 
 
 135 
 
 155 
 
 175 
 
 195 
 
 IXXXXX 
 
 24 
 
 0.987 
 
 215 
 
 Trade term 
 
 height, per sq. ft., lb 
 
 Nearest equivalent in I 
 
 plates 
 
 21/2x17 in. 100 sheets, per 
 
 box. lbs 
 
 7x25 in. 50 sheets, per 
 
 box, lbs 
 
 5x21 in. 100 sheets, per 
 
 box, lbs 
 
 DC 
 
 0.637 
 
 DX 
 
 0.826 
 
 IX 
 
 IXXX 
 
 94 
 
 122 
 
 94 
 
 122 
 
 140 
 
 181 
 
 DXX 
 0.962 
 
 DXXX 
 
 1.10 
 
 xxxx 
 
 1-6 X 
 
 142 
 
 162 
 
 142 
 
 162 
 
 211 
 
 241 
 
 DXXXX 
 1.23 
 
 1-7 X 
 
 182 
 
 182 
 
 271 
 
 Sizes and Net Weight per Box of 100-lb. (0.459 lb. per sq. ft.) 
 Tin Plates. 
 
 
 Sheets 
 
 Weight 
 
 
 Sheets 
 
 Weight 
 
 Sheets. 
 
 per 
 Box. 
 
 per 
 Box. 
 
 Sheets. 
 
 per 
 Box. 
 
 per 
 Box. 
 
 xl4 
 
 225 
 
 100 
 
 15x15 
 
 225 
 
 161 
 
 4 x20 
 
 112 
 
 100 
 
 16x16 
 
 225 
 
 183 
 
 ) x28 
 
 112 
 
 200 
 
 17x17 
 
 225 
 
 206 
 
 3 x20 
 
 225 
 
 143 
 
 18x18 
 
 112 
 
 116 
 
 1 x22 
 
 225 
 
 172 
 
 19x19 
 
 112 
 
 129 
 
 11/2x23 
 
 225 
 
 189 
 
 20x20 
 
 112 
 
 143 
 
 2 Xl2 
 
 225 
 
 103 
 
 21x21 
 
 112 
 
 158 
 
 2 X24 
 
 112 
 
 103 
 
 22x22 
 
 112 
 
 172 
 
 3 X13 
 
 225 
 
 121 
 
 23x23 
 
 112 
 
 189 
 
 J X26 
 
 112 
 
 121 
 
 24x24 
 
 112 
 
 204 
 
 4 xl4 
 
 225 
 
 140 
 
 26x26 
 
 112 
 
 241 
 
 4 x28 
 
 112 
 
 140 
 
 16x20 
 
 112 
 
 114 
 
 Size of 
 
 Sheets. 
 
 14 x3I 
 
 111/ 4 x223/ 4 
 
 13l/ 4 x 173/4 
 
 131/ 4 x191/ 4 
 
 131/oXl91/-> 
 
 13l/ 2 x193/4 
 
 14 X 183/4 
 
 14 X 191/4 
 
 14 X21 
 
 14 X22 
 
 14 X221/4 
 
 151/ 2 x23 
 
 Sheets 
 
 Weight 
 
 per 
 
 per 
 
 Box. 
 
 Box. 
 
 112 
 
 155 
 
 112 
 
 91 
 
 112 
 
 84 
 
 112 
 
 91 
 
 112 
 
 94 
 
 112 
 
 95 
 
 124 
 
 103 
 
 120 
 
 103 
 
 112 
 
 105 
 
 112 
 
 110 
 
 112 
 
 in 
 
 112 
 
 127 
 
 For weight per box of other than 100-lb. plates, multiply by the 
 Igures in the fourth line of the two upper tables, and divide by 100. 
 Ihus for IX plates 20 X 28 in., 200 X 135 -*- 100 = 270. 
 I Tin Plates are made of soft sheet steel coated with tin. The words 
 [charcoal" and "coke" plates are trade terms retained from the time 
 
188 
 
 MATERIALS. 
 
 when high-grade tin plates were made from charcoal iron and lower 
 grade from coke iron (sheet iron made with coke as fuel). The terms 
 are now used to distinguisli the percentage of tin coating, and the finish. 
 Coke plates, with light coating, are used for cans. Charcoal plates are 
 designated by letters A to AAAAA, the latter having the heaviest 
 coating and the highest polish. Plates lighter than 65-lb. per base box 
 (14 X 20 in., 112 plates) are called taggers tin. 
 
 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: 
 
 IC 14 X 20 IC 20 X 28 IX 14 X 20 IX 20 X 28 . 
 Black plates 95 to 100 lb. 190 to 200 lb. 125 to 130 lb. 250 to 260 lb.. 
 After coating 115 to 120 230 to 240 145 to 150 290 to 300 
 
 Long terne sheets are made in gauges, Nos. 20 to 30, from 20 to 40 in 
 wide and up to 120 in. long. Continuous roofing tin, 10, 14, 20 and 28 in 
 wide, is made from terne coated sheets 72, 84 and 96 in. long, single lock 
 seam and soldered. 
 
 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 370 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. Co., 1903.) 
 
 
 Material Desired. 
 
 
 Tin Plate. 
 
 No. I Terne. 
 
 No. 2 Terne, 
 
 
 Pure tin 
 0.023 lb. 
 
 0.496 " 
 0.625 " 
 0.716 " 
 0.808 " 
 0.900 " 
 
 26 tin, 74 lead 
 0.46 1b. 
 
 0.519 " 
 
 0.648 " 
 0.739 " 
 0.831 " 
 0.923 " 
 
 16tin,841eat 
 0.023 lb. 
 
 0.496 " 
 0.625 " 
 0.716 " 
 0.808 " 
 0.900 " 
 
 Amount of coating per sq. ft 
 
 Weight per sq. ft. of — 
 
 Grade IC 
 
 Grade IX 
 
 Grade IXX 
 
 Grade IXX 
 
 Grade IXXX 
 
 
 
 Will be r 
 
 ejected if less than 
 
 Amount of coating per sq. ft 
 
 Weight per sq. ft. of — 
 
 Grade IC 
 
 0.0183 1b. 
 
 0.468 " 
 0.590 " 
 0.676 " 
 0.763 " 
 0.850 " 
 
 0.0413 1b. 
 
 0.490 ** 
 0.612 " 
 0.699 " 
 0.787 " 
 0.874 " 
 
 0.0183 1b. 
 
 0.468 " 
 0.590 " 
 
 0.676 " 
 0.763 " 
 0.850 " j 
 
 Grade IX 
 
 Grade IXX 
 
 Grade IXXX 
 
 Grade IXXXX 
 
 
 Each sheet in a shipment of tin or terne plate must (1) be cut as near! 
 exact to size ordered as possible; (2) must be rectangular and flat and frel 
 from flaws; (3) must double seam successfully under reasonable treatmen a 
 (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; («'! 
 must be so nearly like every other sheet in the shipment, both in thickne 
 and in uniformity and amount of coating, that no difficulty will arise il 
 the shops, due to varying thickness of sheets. • 
 
SIZE AND WEIGHT OF ROOFING MATERIALS. 189 
 
 Number and superficial area of slate required for one square of roof. 
 (1 square = 100 square feet.) 
 
 Size, 
 Inches. 
 
 Num- 
 ber per 
 Square. 
 
 Area in 
 Sq. Ft. 
 
 Size, 
 Inches. 
 
 Num- 
 ber per 
 Square. 
 
 Area in 
 
 Sq.Ft. 
 
 Size, 
 Inches. 
 
 Num- 
 ber per 
 Square. 
 
 Area in 
 Sq. Ft. 
 
 6x12 
 7x12 
 8x12 
 9x12 
 7x14 
 8x14 
 9x14 
 10x14 
 8x16 
 
 533 
 457 
 400 
 355 
 374 
 327 
 291 
 261 
 277 
 
 267 
 "254" 
 "246" 
 
 9x16 
 10x16 
 
 9x18 
 10x18 
 12x18 
 10x20 
 11x20 
 12x20 
 14x20 
 
 246 
 221 
 213 
 192 
 160 
 169 
 154 
 141 
 121 
 
 "240" 
 
 "240" 
 235 
 
 16x20 
 12x22 
 14x22 
 12x24 
 14x24 
 16x24 
 14x26 
 16x26 
 
 137 
 126 
 108 
 114 
 98 
 86 
 89 
 78 
 
 23 T ' " 
 
 "228" 
 
 "225" 
 
 
 
 
 
 As slate is usually laid, the number of square feet of roof covered by one 
 slate can be obtained from the following formula: 
 
 width X (length - 3 inches) ,, , . . , . ■ . , 
 
 ■ ^r = the number of square feet of roof covered. 
 
 Weight of slate of various lengths and thicknesses required for one 
 square of roof: based on the number of slate required for one square of 
 roof, taking the weight of a cubic foot of slate at 175 pounds. 
 
 Length 
 
 
 Weight 
 
 in Pounds per Square for the Thickness. 
 
 
 Inches. 
 
 1/8 In. 
 
 3/ieIn. 
 
 1/4 In. 
 
 3/8 In. 
 
 1/2 In. 
 
 5/8 In. 
 
 3/ 4 In. 
 
 lln. 
 
 12 
 
 483 
 
 724 
 
 967 
 
 1450 
 
 1936 
 
 2419 
 
 2902 
 
 3872 
 
 14 
 
 460 
 
 688 
 
 920 
 
 1379 
 
 1842 
 
 2301 
 
 2760 
 
 3683 
 
 16 
 
 445 
 
 667 
 
 890 
 
 1336 
 
 1784 
 
 2229 
 
 2670 
 
 3567 
 
 18 
 
 434 
 
 650 
 
 869 
 
 1303 
 
 1740 
 
 2174 
 
 2607 
 
 3480 
 
 20 
 
 425 
 
 637 
 
 851 
 
 1276 
 
 1704 
 
 2129 
 
 2553 
 
 3408 
 
 22 
 
 418 
 
 626 
 
 836 
 
 1254 
 
 1675 
 
 2093 
 
 2508 
 
 3350 
 
 24 
 
 412 
 
 617 
 
 825 
 
 1238 
 
 1653 
 
 2066 
 
 2478 
 
 3306 
 
 26 
 
 407 
 
 610 
 
 815 
 
 1222 
 
 1631 
 
 2039 
 
 2445 
 
 3263 
 
 Pine Shingles. 
 
 Number and weight of shingles required to cover one square of roof: 
 
 [nches exposed to weather 
 
 Number of shingles per square of roof 
 
 Weight of shingles on one square, pound. . . . 
 
 41/2 
 
 51/2 
 655 
 157 
 
 600 
 144 
 
 The number of shingles per square is for common gable-roofs, 
 nip-roofs add five per cent to these figures. 
 
190 
 
 MATERIALS. 
 
 Skylight Glass. 
 
 The weights of various sizes and thicknesses of fluted or rough plate- 
 glass required for one square of roof. 
 
 Dimensions in 
 Inches. 
 
 Thickness in 
 Inches. 
 
 Area in Square 
 Feet. 
 
 Weight in Lbs. per 
 Square of Roof. 
 
 I2x 48 
 15 x 60 
 20x100 
 94x156 
 
 3/16 
 V4 
 3/8 
 
 1/2 
 
 3.997 
 
 6.246 
 
 13.880 
 
 101.768 
 
 250 
 350 
 500 
 700 
 
 In the above table no allowance is made for lap. 
 
 If ordinary window-glass is used, single thick glass (about Vie inch) 
 will weigh about 82 lb. per square, and double thick glass (about Vs inch) 
 will weigh about 164 lb. 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 of. 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. 
 
 APPROXIMATE WEIGHT OF MATERIALS FOR ROOFS. 
 
 American Sheet and Tin Plate Co. 
 
 Corrugated galvanized iron, No. 20, unboarded 
 
 Copper, 16 oz. standing seam. 
 
 Felt and asphalt, without sheathing. ..... 
 
 Glass, 1/8 in. thick 
 
 Hemlock sheathing, 1 in. thick. 
 
 Lead, about 1/8 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/ig in. thick, 3 in. double lap 
 
 Slate, 1/8 in. thick, 3 in. double lap 
 
 Shingles, 6 in. X 18 in., 1/3 to weather 
 
 Skylight of glass, 3/jg to 1/2 in., inc. frame 
 
 Slag roof, 4-ply 
 
 Terne plate, IC, without sheathing 
 
 Terne plate, IX, without sheathing 
 
 Tiles (plain), 10 l/ 2 in. X 6 1/4 in. X 5/ 8 - 51/4U1. to weather . 
 
 Tiles (Spanish) Hl/2 in. X 1 1/ 2 in. - 71/4 in. to weather 
 
 White pine sheathing, 1 in. thick 
 
 Yellow pine sheathing, I in. thick 
 
 Average 
 Weight, 
 Lb. per 
 Sq. Ft. 
 
 21/4 
 
 U/4 
 
 2 
 
 13/4 
 
 2 
 
 6 to 8 
 
 6 to 8 
 
 10 
 
 1/2 
 
 21/2 
 
 63/ 4 
 
 41/2 
 2 
 4 to 10 
 4 
 1/2 
 
 18 5/8 
 8 1/2 
 21/2 
 
WEIGHT OF CAST-IRON PIPES OR COLUMNS. 
 
 191 
 
 WEIGHT OF CAST-IRON PIPES OR COLUMNS. 
 
 In Pounds per Lineal Foot. 
 
 Cast iron = 450 lbs. per cubic foot. 
 
 Jo.re. 
 
 Thick. 
 
 of 
 Metal. 
 
 Weight 
 per Foot. 
 
 Bore. 
 
 Thick. 
 
 of 
 Metal. 
 
 Weight 
 per Foot. 
 
 Bore. 
 
 Thick. 
 
 of 
 Metal. 
 
 Weight 
 per Foot. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 Ins. 
 
 Ins. 
 
 Lbs. 
 
 3 
 
 3 /8 
 
 12.4 
 
 10 
 
 3/4 
 
 79.2 
 
 22 
 
 3/4 
 
 167.5 
 
 
 1/2 
 
 17.2 
 
 10 1/ 2 
 
 1/2 
 
 54.0 
 
 
 7/8 
 
 196.5 
 
 
 5/8 
 
 22.2 
 
 
 5/8 
 
 68.2 
 
 23 
 
 3/4 
 
 174.9 
 
 3 1/2 
 
 3/8 
 
 14.3 
 
 
 3/4 
 
 82.8 
 
 
 7/8 
 
 205.1 
 
 
 1/2 
 
 19.6 
 
 11 
 
 1/2 
 
 56.5 
 
 
 
 235.6 
 
 
 5/8 
 
 25.3 
 
 
 5/8 
 
 71.3 
 
 24 
 
 3/4 
 
 182.2 
 
 4 
 
 3/8 
 
 16.1 
 
 
 3/4 
 
 86.5 
 
 
 7/8 
 
 213.7 
 
 
 1/2 
 
 22.1 
 
 111/2 
 
 1/2 
 
 58.9 
 
 
 
 245.4 
 
 
 5/8 
 
 28.4 
 
 
 5/S 
 
 74.4 
 
 25 
 
 3/4 
 
 189.6 
 
 41/2 
 
 3/8 
 
 18.0 
 
 
 3/4 
 
 90.2 
 
 
 7/8 
 
 222.3 
 
 
 1/2 
 
 24.5 
 
 12 
 
 1/2 
 
 61.4 
 
 
 
 255.3 
 
 
 5/8 
 
 31.5 
 
 
 5/8 
 
 77.5 
 
 26 
 
 3/4 
 
 197.0 
 
 
 3/8 
 
 19.8 
 
 
 3/4 
 
 93.9 
 
 
 7/8 
 
 230.9 
 
 1 
 
 • 1/2 
 
 27.0 
 
 121/2 
 
 1/2 
 
 63.8 
 
 
 
 265.1 
 
 
 5/8 
 
 34.4 
 
 
 5/8 
 
 80.5 
 
 27 
 
 3/4 
 
 204.3 
 
 51/2 
 
 3/8 
 
 21.6 
 
 
 3/4 
 
 97.6 
 
 
 7/8 
 
 239.4 
 
 
 1/2 
 
 29.4 
 
 13 
 
 1/2 
 
 66.3 
 
 
 
 274.9 
 
 
 5/8 
 
 37.6 
 
 
 5/8 
 
 83.6 
 
 28 
 
 3/4 
 
 211.7 
 
 6 
 
 3/8 
 
 23.5 
 
 
 3/4 
 
 101.2 
 
 
 7/8 
 
 248.1 
 
 
 1/2 
 
 31.9 
 
 14 
 
 1/2 
 
 71.2 
 
 
 
 284.7 
 
 
 5/8 
 
 40.7 
 
 
 5/8 
 
 89.7 
 
 29 
 
 3/4 
 
 219.1 
 
 61/2 
 
 3/8 
 
 25.3 
 
 
 3/4 
 
 108.6 
 
 
 7/8 
 
 256.6 
 
 
 1/2 
 
 34.4 
 
 15 
 
 5/8 
 
 95.9 
 
 
 
 294.5 
 
 
 5/8 
 
 43.7 
 
 
 3/4 
 
 116.0 
 
 30 
 
 7/8 
 
 265.2 
 
 7 
 
 3/8 
 
 27.2 
 
 
 7/8 
 
 136.4 
 
 
 
 304.3 
 
 
 1/2 
 
 36.8 
 
 16 
 
 5/8 
 
 102.0 
 
 
 U/8 
 
 343.7 
 
 
 5/8 
 
 46.8 
 
 
 3/4 
 
 123.3 
 
 31 
 
 7/8 
 
 273.8 
 
 71/2 
 
 3/8 
 
 29.0 
 
 
 7/8 
 
 145.0 
 
 
 
 314.2 
 
 
 1/2 
 
 39.3 
 
 17 
 
 5/8 
 
 108.2 
 
 
 U/8 
 
 354.8 
 
 
 5/8 
 
 49.9 
 
 
 3/4 
 
 130.7 
 
 32 
 
 7/8 
 
 282.4 
 
 3 
 
 3/8 
 
 30.8 
 
 
 7/8 
 
 153.6 
 
 
 
 324.0 
 
 
 1/2 
 
 41.7 
 
 18 
 
 5/8 
 
 114.3 
 
 
 11/8 
 
 365.8 
 
 
 5/8 
 
 52.9 
 
 
 3/ 4 
 
 138.1 
 
 33 
 
 7/8 
 
 291.0 
 
 51/2 
 
 1/2 
 
 44.2 
 
 
 7/8 
 
 162.1 
 
 
 
 333.8 
 
 
 5/8 
 
 56.0 
 
 19 
 
 5/8 
 
 120.4 
 
 
 U/8 
 
 376.9 
 
 
 3/4 
 
 68.1 
 
 
 3/4 
 
 145.4 
 
 34 
 
 7/8 
 
 299.6 
 
 ;> 
 
 1/2 
 
 46.6 
 
 
 7/8 
 
 170.7 
 
 
 
 343.7 
 
 
 5/8 
 
 59.1 
 
 20 
 
 5/8 
 
 126.6 
 
 
 U/8 
 
 388.0 
 
 
 3/4 
 
 71.8 
 
 
 ?/4 
 
 152.8 
 
 35 
 
 7/8 
 
 308.1 
 
 ! 'V2 
 
 1/2 
 
 49.1 
 
 
 7/8 
 
 179.3 
 
 
 
 353.4 
 
 
 5/8 
 
 62.1 
 
 21 
 
 5/8 
 
 132.7 
 
 
 U/8 
 
 399.0 
 
 
 3/4 
 
 75.5 
 
 
 3/4 
 
 160.1 
 
 36 
 
 7/8 
 
 316.6 
 
 il 
 
 1/2 
 
 51.5 
 
 
 7/8 
 
 187.9 
 
 
 
 363.1 
 
 
 5/8 
 
 65.2 
 
 22 
 
 5/8 
 
 138.8 
 
 
 U/8 
 
 410.0 
 
 The weight of the two flanges may be reckoned = weight of one foot. 
 
192 
 
 MATERIALS. 
 
 STANDARD THICKNESSES AND WEIGHTS OF CAST-IRON 
 PIPE. 
 
 
 (U. S. Cast-iron Pipe & Fd' 
 
 y Co., 1908.) 
 
 
 
 Class A. 
 
 100 ft. Head. 
 
 43 lb. Pressure. 
 
 Class B. 
 
 200 ft. Head. 
 
 86 lb. Pressure. 
 
 side Diam. Ins. 
 
 Thick- 
 ness, Ins. 
 
 Wt. per 
 
 Thick- 
 ness, Ins. 
 
 Wt. per 
 
 
 Ft. 
 
 L'gth. 
 
 Ft. 
 
 L'gth. 
 
 3 
 
 0.39 
 
 .42 
 
 .44 
 
 .46 
 
 .50 
 
 .54 
 
 .57 
 
 .60 
 
 .64 
 
 .67 
 
 .76 
 
 .88 
 
 .99 
 
 1.10 
 
 1.26 
 
 1.35 
 
 1.39 
 
 1.62 
 
 1.72 
 
 14.5 
 
 20.0 
 
 30.8 
 
 42.9 
 
 57.1 
 
 72.5 
 
 89.6 
 
 108.3 
 
 129.2 
 
 150.0 
 
 204.2 
 
 291.7 
 
 391.7 
 
 512.5 
 
 666.7 
 
 800.0 
 
 916.7 
 
 1283.4 
 
 1633.4 
 
 175 
 240 
 370 
 515 
 685 
 870 
 1075 
 1300 
 1550 
 1-800 
 2450 
 3500 
 4700 
 6150 
 8000 
 9600 
 11000 
 15400 
 19600 
 
 0.42 
 
 .45 
 
 .48 
 
 .51 
 
 .57 
 
 .62 
 
 .66 
 
 .70 
 
 .75 
 
 .80 
 
 .89 
 
 1.03 
 
 1.15 
 
 1.28 
 
 1.42 
 
 1.55 
 
 1.67 
 
 1.95 
 
 2.22 
 
 16.2 
 21.7 
 33.3 
 47.5 
 63.8 
 82.1 
 102.5 
 125.0. 
 150.0 
 175.0 
 233.3 
 333.3 
 454.2 
 591.7 
 750.0 
 933.3 
 1104.2 
 1545.8 
 2104.2 
 
 194 
 260 
 400 
 570 
 765 
 985 
 
 4 
 
 6... 
 
 8 
 
 10 
 
 12 
 
 14 
 
 1230 
 
 16.. . 
 
 1500 
 
 18 .. 
 
 1800 
 
 20.... 
 
 2100 i 
 
 24.... *. 
 
 2800 
 
 30 
 
 4000 
 
 36 
 
 5450 
 
 42 
 
 7100 
 
 48 
 
 9000 
 
 54 
 
 11200 
 
 60 
 
 13250 , 
 
 72 
 
 18550 
 
 84 
 
 25250 
 
 
 
 
 Class C. 
 
 300 ft. Head. 
 
 130 lb. Pressure. 
 
 Class D. 
 
 400 ft. Head. 
 
 173 lb. Pressure. 
 
 sideDiam. Ins. 
 
 Thick- 
 ness, Ins 
 
 Wt. per 
 
 Thick- 
 ness, Ins. 
 
 Wt. per 
 
 
 Ft. 
 
 L'gth. 
 
 Ft. 
 
 L'gth. 
 
 3 
 
 0.45 
 
 .48 
 
 .51 
 
 .56 
 
 .62 
 
 .68 
 
 .74 
 
 .80 
 
 .87 
 
 .92 
 
 1.04 
 
 1.20 
 
 1.36 
 
 1.54 
 
 1.71 
 
 1.90 
 
 2.00 
 
 2.39 
 
 17.1 
 
 23.3 
 
 35.8 
 
 52.1 
 
 70.8 
 
 91.7 
 
 116.7 
 
 143.8 
 
 175.0 
 
 208.3 
 
 279.2 
 
 400.0 
 
 545.8 
 
 716.7 
 
 908.3 
 
 1141.7 
 
 1341.7 
 
 1904.2 
 
 205 
 
 280 
 
 430 
 
 625 
 
 850 
 
 1100 
 
 1400 
 
 1725 
 
 2100 
 
 2500 
 
 3350 
 
 4800 
 
 6550 
 
 8600 
 
 10900 
 
 13700 
 
 16100 
 
 22850 
 
 0.48 
 
 .52 
 
 .55 
 
 .60 
 
 .68 
 
 .75 
 
 .82 
 
 .89 
 
 .96 
 
 1.03 
 
 1.16 
 
 1.37 
 
 1.58 
 
 1.78 
 
 1.96 
 
 2.23 
 
 2.38 
 
 18.0 
 
 25.0 
 
 38.3 
 
 55.8 
 
 76.7 
 
 100.0 
 
 129.2 
 
 158.3 
 
 191.7 
 
 229.2 
 
 306.7 
 
 450.0 
 
 625.0 
 
 825.0 
 
 1050.0 
 
 1341.7 
 
 1583.3 
 
 216 l 
 
 4 
 
 300 1 
 
 6 
 
 460 \ 
 
 8 
 
 670 lit 
 
 10 
 
 920 1 
 
 12 
 
 1200 
 
 14 . . 
 
 1550 
 
 16... 
 
 1900 
 
 18 
 
 2300 
 
 20 
 
 2750 
 
 24 
 
 3680 1 
 
 30 
 
 5400 1 
 
 36 
 
 7500 
 
 42 
 
 9900 
 
 48 
 
 12600 
 
 54 ... 
 
 16100 
 
 60 
 
 72 
 
 19000 
 
 84 
 
 ::: 1 
 
 
 
 The above w 
 sockets; propor 
 
 eights ar 
 tionate al 
 
 i per leng 
 owance t( 
 
 th to lay 
 
 ) be made 
 
 12 feet, i 
 for any v 
 
 ncluding 
 ariation. 
 
 1 
 
 i 
 
THICKNESS OF CAST-IRON WATER-PIPES. 
 
 193 
 
 Standard Thicknesses and Weights of Cast-iron Pipe. 
 
 FOR FIRE-LINES AND OTHER HIGH-PRESSURE SERVICE. 
 (U. S. Cast-Iron Pipe & Fd'y Co., 1908.) 
 
 i d 
 
 Class E. 
 
 Class F. 
 
 Class G. 
 
 
 Class H. 
 
 500 ft. Head. 
 
 600 ft. Head. 
 
 700 ft. Head. 
 
 800 ft iit-i.l 
 
 •3 s 
 
 217 1b. 
 
 260 lb. 
 
 304 lb. 
 
 
 347 lb. 
 
 •'- c 
 
 Wt. per 
 
 v a 
 
 Wt. per 
 
 v C 
 
 Wt. per 
 
 Jk c ' 
 
 Wt. per 
 
 $1 
 
 IS r f 
 
 rn OB 
 
 
 z ' 
 
 
 IS £ 
 
 
 is •/■ 
 
 
 Ft. 
 
 L'gth 
 
 Ft. 
 
 L'gth 
 
 Ft. 
 
 L'gth 
 
 Ft. 
 
 L'gth 
 
 
 c 
 
 
 
 
 
 
 C 
 
 
 
 c 
 
 
 
 i 6 
 
 n 5,s 
 
 41.7 
 
 500 
 
 61 
 
 43.3 
 
 520 
 
 65 
 
 47.1 
 
 565 
 
 69 
 
 49.6 
 
 595 
 
 8 
 
 66 
 
 61.7 
 
 740 
 
 71 
 
 65.7 
 
 790 
 
 75 
 
 70.8 
 
 850 
 
 80 
 
 75.0 
 
 900 
 
 J 10 
 
 74 
 
 86.3 
 
 1035 
 
 80 
 
 92.1 
 
 1105 
 
 86 
 
 100.9 
 
 1210 
 
 .92 
 
 106.7 
 
 1280 
 
 12 
 
 87 
 
 113.8 
 
 1365 
 
 89 
 
 122.1 
 
 1465 
 
 97 
 
 135.4 
 
 1625 
 
 1 04 
 
 143.8 
 
 1725 
 
 14 
 
 Q0 
 
 145.0 
 
 1740 
 
 99 
 
 157.5 
 
 1890 
 
 1 07 
 
 174.2 
 
 2090 
 
 1 16 
 
 186.7 
 
 2240 
 
 16 
 
 98 
 
 179. i 
 
 2155 
 
 1 08 
 
 195.4 
 
 2345 
 
 1 18 
 
 219.2 
 
 2620 
 
 1 7.7 
 
 232.5 
 
 2790 
 
 18 
 
 1 07 
 
 220.4 
 
 2645 
 
 1 17 
 
 238.4 
 
 •2860 
 
 1 78 
 
 267.1 
 
 3205 
 
 1 39 
 
 286.7 
 
 3440 
 
 20 
 
 1 15 
 
 263.0 
 
 3155 
 
 1 27 
 
 286.3 
 
 3435 
 
 1 39 
 
 320.8 
 
 3850 
 
 1 51 
 
 344.6 
 
 4135 
 
 24 
 
 1 31 
 
 359.6 
 
 4315 
 
 1 45 
 
 392.9 
 
 4715 
 
 
 
 
 
 
 
 30 
 
 1 55 
 
 521.7 
 
 6260 
 
 1 73 
 
 585.4 
 
 7025 
 
 
 
 
 
 
 
 36 
 
 1.80 
 
 725.0 
 
 8700 
 
 2.02 
 
 820.0 
 
 9840 
 
 
 
 
 
 
 
 The above weights are per length to lay 12 feet, including standard 
 iockets; proportionate allowance to be made for any variation. 
 
 Weight of Underground Pipes. (Adopted by the Natl. Fire Pro- 
 action Association, 1905). Weights are not to be less than those specified 
 when the normal pressures do not exceed 125 lbs. per sq. in. When the 
 lormal pressures are in excess of 125 lbs. heavier pipes should be used. 
 The weights given include sockets. 
 
 Pipe, ins 
 
 Weights per foot, lbs 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 32 
 
 48 
 
 67 
 
 87 
 
 109 
 
 133 
 
 THICKNESS OF CAST-IRON WATER-PIPES. 
 
 P. H. Baermann, in a paper read before the Engineers' Club of Phila- 
 ielphia in 1882, gave twenty different formulas for determining the thick- 
 iess of cast-iron pipes under pressure. The formulas are of three classes: 
 
 1. Depending upon the diameter only. 
 
 2. Those depending upon the diameter and head, and which add a con- 
 stant. 
 
 3. Those depending upon the diameter and head, contain an additive 
 or subtractive term depending upon the diameter, and add a constant. 
 
 I The more modern formulas are of the third class, and are as follows: 
 
 .! = 0.00008/id + O.Old + 0.36 Shedd, No. 1. 
 
 = 0.00006/id + 0.0133d + 0.296 Warren Foundry, No. 2. 
 
 ; = 0.000058/id + 0.0152d -I- 0.312 Francis, No. 3. 
 
 = 0.000048/id + 0.013d + 0.32 . Dupuit, - No. 4. 
 
 ! = 0.00004/wZ + 0.1 ^d + 0.15 Box, No. 5. 
 
 ! = 0.000135/id + 0.4 - O.OOlld Whitman, No. 6. 
 
 J = 0.00006(ft + 230)d + 0.333 - 0.0033d Fanning, No. 7. 
 
 ! = 0.00015ftd 4- 0.25 - 0.0052d Meggs, No. 8. 
 
194 
 
 MATERIALS. 
 
 In which t - thickness in inches, A = head in feet, d = diameter in inches. 
 For ft = 100 ft., and d = 10 in., formulae 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. 72-1) says: "Cast-iron pipes should be 
 made of a soft and tough quality of iron. Great attention should be paid 
 to molding them correctly, 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 f = 18,000, and a 
 factor of safety of 5 is used, the above expressed in terms of d and hi 
 becomes t = 0.5d X 0.433ft ■*- 3600 = 0.00006dft. 
 
 "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 Bursting 
 Strength of Cast-iron Cylinders, under "Cast Iron.") 
 
 The most common defect of cast-iron pipes is due to the "shifting oi 
 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 oi 
 every pipe for uniformity of thickness. 
 
 Safe Pressures and Equivalent Heads of Water for Cast-iron Pipe 
 of Different Sizes and Thicknesses. 
 
 (Calculated by F. H. Lewis, from Fanning's Formula.) 
 
 
 Size of Pipe. 
 
 
 4" 
 
 6" 
 
 8" 
 
 10" 
 
 12" 
 
 14" 
 
 16" 
 
 18" 
 
 20" 
 
 Thickness. 
 
 *3 
 
 
 i-3 
 
 
 
 
 3 
 
 
 3 
 h! 
 
 
 3 
 
 
 1 
 
 
 Hi 
 
 
 J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 Uh 
 
 
 Uh 
 
 
 Uh 
 
 
 ft 
 
 
 ft 
 
 
 ft 
 
 
 ft 
 
 
 Uh 
 
 
 Uh 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 
 d 
 
 
 
 
 
 
 
 
 d 
 
 
 d 
 
 
 
 
 
 
 d 
 
 
 d 
 
 
 d 
 
 
 
 
 
 
 ^ 
 
 
 d 
 
 
 5 
 
 
 d 
 
 
 
 
 TS 
 
 
 
 
 
 
 — 
 
 
 —■ 
 
 
 — 
 
 
 — 
 
 
 
 
 -) 
 
 
 
 
 ft 
 49 
 
 a; 
 112 
 
 ft 
 18 
 
 O 
 ft 
 
 42 
 
 CD 
 ft 
 
 X 
 
 9 
 ft 
 
 03 
 
 CD 
 ft 
 
 
 0^ 
 
 ft 
 
 
 ft 
 
 8) 
 
 ft 
 
 CD 
 
 7/16 
 
 112 
 
 258 
 
 l/ 2 ........ 
 
 224 
 
 516 
 
 124 
 
 
 74 
 
 171 
 
 44 
 
 101 
 
 24 
 
 55 
 
 
 
 
 
 
 
 
 
 9/16 
 
 336 
 
 774 
 
 199 
 
 458 
 
 130 
 
 300 
 
 89 
 
 205 
 
 62 
 
 143 
 
 42 
 
 97 
 
 
 
 
 
 
 
 5/8 
 
 
 
 774 
 
 631 
 
 186 
 
 4?:-) 
 
 13?, 
 
 304 
 
 99 
 
 228 
 
 74 
 
 1 70 
 
 56 
 
 129 
 
 41 
 
 95 
 
 
 
 ll/l 6 
 
 
 
 
 
 
 
 177 
 
 224 
 
 516 
 
 137 
 174 
 212 
 249 
 
 316 
 401 
 
 488 
 574 
 
 106 
 138 
 170 
 
 202 
 234 
 266 
 
 316 
 392 
 465 
 538 
 612 
 
 84 
 112 
 140 
 168 
 196 
 224 
 
 194 
 258 
 323 
 387 
 452 
 516 
 
 66 
 91 
 116 
 141 
 166 
 191 
 216 
 
 152 
 210 
 
 267 
 325 
 382 
 440 
 497 
 
 51 
 
 74 
 96 
 119 
 14! 
 164 
 209 
 256 
 
 lit 
 
 17( 
 221 
 27^ 
 32! 
 37c 
 481 
 58< 
 
 3/ 4 
 
 
 
 
 
 
 
 13/ 16 
 
 
 
 
 
 
 
 7 /8 
 
 
 
 
 
 
 
 
 
 15 /l6- • • • 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 1 l/ 8 
 
 
 
 
 
 
 
 
 
 
 
 ' Vi 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
THICKNESS OF CAST-IRON WATER-PIPES. 
 
 195 
 
 Safe Pressures, etc., for Cast-iron Pipe. — (Continued.) 
 
 
 
 
 
 
 
 
 
 Size of Pipe. 
 
 
 
 
 
 
 
 
 
 22" 
 
 24" 
 
 27" 
 
 30" 
 
 33" 
 
 36" 
 
 42" 
 
 48" 
 
 60" 
 
 Thickness. 
 
 ja 
 
 h! 
 
 
 hi 
 
 
 HH 
 
 
 
 
 h! 
 
 
 ja 
 h1 
 
 
 ,3 
 
 Hi 
 
 
 ja 
 
 
 Hi 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 U^ 
 
 
 l*t 
 
 
 l=q 
 
 Ti 
 
 Uh 
 
 
 ^ 
 
 
 (^ 
 
 m 
 
 Uh 
 
 
 [hh 
 
 ■~ 
 
 Uh 
 
 
 
 
 
 rt 
 
 
 fl 
 
 
 
 
 
 
 C 
 
 
 
 
 fl 
 
 
 (3 
 
 
 3 
 
 
 a 
 
 
 3 
 
 
 
 
 
 
 3 
 
 
 
 
 " 
 
 
 
 
 
 
 T5 
 
 
 T5 
 
 
 
 
 — 
 
 
 — 
 
 
 
 
 
 
 
 
 TJ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 «( 
 
 
 
 
 rt 
 
 
 rt 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ph 
 40 
 
 a 
 
 92 
 
 Ph 
 30 
 
 69 
 
 Ph 
 19 
 
 64 
 
 Ph 
 
 W 
 
 Ph 
 
 a 
 
 Ph 
 
 W 
 
 Ph- 
 
 a 
 
 Ph 
 
 a 
 
 Ph 
 
 a 
 
 H/16 
 
 
 3/4 
 
 60 
 
 138 
 
 49 
 
 113 
 
 36 
 
 83 
 
 24 
 
 55 
 
 
 
 
 
 
 
 
 
 
 
 13/16 
 
 80 
 
 184 
 
 68 
 
 157 
 
 52 
 
 120 
 
 39 
 
 90 
 
 
 
 
 
 
 
 
 
 
 
 7/8 
 
 101 
 
 233 
 
 86 
 
 198 
 
 69 
 
 159 
 
 54 
 
 124 
 
 42 
 
 97 
 
 32 
 
 74 
 
 
 
 
 
 
 
 15/16 
 
 121 
 
 279 
 
 105 
 
 14 ! 
 
 85 
 
 196 
 
 69 
 
 159 
 
 55 
 
 127 
 
 44 
 
 101 
 
 
 
 
 
 
 
 1 
 
 142 
 187, 
 
 327 
 419 
 
 124 
 161 
 
 286 
 371 
 
 102 
 135 
 
 235 
 311 
 
 84 
 114 
 
 194 
 263 
 
 69 
 96 
 
 159 
 
 221 
 
 57 
 
 82 
 
 131 
 
 189 
 
 38 
 
 59 
 
 88 
 
 136 
 
 24 
 43 
 
 55 
 99 
 
 
 
 11/8 
 
 
 1 1/4 
 
 224 
 
 516 
 
 199 
 
 458 
 
 169 
 
 389 
 
 144 
 
 12 
 
 124 
 
 16 
 
 107 
 
 247 
 
 81 
 
 187 
 
 62 
 
 143 
 
 34 
 
 78 
 
 13/ 8 
 
 
 
 237 
 
 "746 
 
 202 
 
 465 
 
 174 
 
 401 
 
 151 
 
 .348 
 
 132 
 
 304 
 
 103 
 
 237 
 
 81 
 
 187 
 
 49 
 
 113 
 
 1 l/ 2 
 
 
 
 
 
 236 
 
 544 
 
 204 
 234 
 
 470 
 538 
 
 178 
 205 
 733 
 
 410 
 
 472 
 537 
 
 157 
 182 
 ?07 
 
 3*2 
 4.9 
 
 477 
 
 124 
 145 
 167 
 
 286 
 334 
 
 385 
 
 99 
 Ufa 
 
 136 
 
 228 
 :\ 
 313 
 
 64 
 79 
 94 
 
 147 
 
 1 5/ 8 
 
 
 
 
 
 18"? 
 
 13/ 4 
 
 
 
 
 
 
 
 ?17 
 
 1 7/ 8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 188 
 
 433 
 
 155 
 
 357 
 
 100 
 
 ?51 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 710 
 
 484 
 
 174 
 
 40! 
 
 174 
 
 ^86 
 
 2 1/8 
 
 21/4 
 
 21/2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 193 
 
 ^45 
 
 no 
 
 3?n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ?1? 
 
 488 
 
 |S4 
 
 355 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 184 
 
 474 
 
 2 3/ 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 214 
 
 48? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Note. — The absolute safe static pressure which may 
 be put upon pipe is given by the formula P = 2TS/5D, 
 in which formula P is the pressure per square inch; T, 
 the thickness of the shell; S, the ultimate strength per 
 square inch of the metal in tension; and D, the inside 
 diameter of the pipe. In the tables *S is taken as 18,000 
 pounds per square inch, with a working strain of one- 
 fifth this amount or 3600 pounds per square inch. The 
 formula for the absolute safe static pressure then is: 
 P = 7200/D. 
 
 It is, however, usual to allow for "water-ram" by 
 increasing the thickness enough to provide for 100 
 pounds additional static pressure, and, to insure suffi- 
 cient metal for good casting and for wear and tear, a 
 further increase equal to 0.333 (1 - 0.01 D). 
 
 The expression for the thickness then becomes 
 
 (P + 100)P 
 
 + 0.333 
 
 - 0.333 (1 
 
 
 100. 
 
 7200 
 and for safe working pressure 
 
 p = ?f°(r- 
 
 The additional section provided as above represents 
 an increased value under static pressure for the different 
 sizes of pipe as follows (see table in margin). So that 
 to test the pipes up to one-fifth of the ultimate strength 
 of the material, the pressures in the marginal table 
 should be added to the pressure-values given in the 
 table above. 
 
 Size 
 
 
 of 
 
 Lbs. 
 
 Pipe. 
 
 
 4" 
 
 676 
 
 6 
 
 476 
 
 8 
 
 346 
 
 10 
 
 316 
 
 12 
 
 276 
 
 14 
 
 248 
 
 16 
 
 226 
 
 18 
 
 209 
 
 20 
 
 196 
 
 22 
 
 185 
 
 24 
 
 176 
 
 27 
 
 165 
 
 30 
 
 156 
 
 33 
 
 149 
 
 36 
 
 143 
 
 42 
 
 133 
 
 48 
 
 126 
 
 60 
 
 116 
 
196 
 
 MATERIALS. 
 
 / 
 
 CAST-IRON PIPE-FITTINGS. 
 
 Approximate Weights (The Massilon Iron & Steel Co.). 
 
 m 
 
 0) 
 
 
 Hi 
 
 m 
 
 
 Ol 
 
 o> 
 
 
 
 g 
 
 
 rg 
 
 P 
 
 4) 
 
 A 
 
 o 
 
 
 
 a 
 
 o 
 
 03 
 
 -g 
 
 a 
 
 e 
 
 1 
 
 
 o 
 
 H 
 
 
 O 
 
 H 
 
 M 
 
 D 
 
 H 
 
 
 Q 
 
 H 
 
 3x3 
 
 85 
 
 65 
 
 14x14 
 
 665 
 
 525 
 
 20x12 
 
 900 
 
 800 
 
 36x36 
 
 4160 
 
 3490 
 
 4x4 
 
 115 
 
 90 
 
 14x10 
 
 530 
 
 445 
 
 20x8 
 
 730 
 
 665 
 
 36x30 
 
 3475 
 
 3010 
 
 4x3 
 
 105 
 
 85 
 
 14x6 
 
 390 
 
 350 
 
 20x3 
 
 565 
 
 545 
 
 36x24 
 
 2920 
 
 2585 
 
 6x6 
 
 165 
 
 130 
 
 14x3 
 
 330 
 
 310 
 
 24x24 
 
 1800 
 
 1565 
 
 36x20 
 
 2550 
 
 2315 
 
 6x3 
 
 125 
 
 105 
 
 16x16 
 
 810- 
 
 735 
 
 24x18 
 
 1480 
 
 1280 
 
 36x18 
 
 2370 
 
 2175 
 
 8x8 
 
 290 
 
 230 
 
 16x12 
 
 715 
 
 615 
 
 24x14 
 
 1215 
 
 1085 
 
 36x16 
 
 2240 
 
 2070 
 
 8x6 
 
 230 
 
 195 
 
 16x8 
 
 585 
 
 520 
 
 24x10 
 
 1035 
 
 945 
 
 36x14 
 
 2060 
 
 1930 
 
 8x4 
 
 205 
 
 175 
 
 16x3 
 
 415 
 
 395 
 
 24x6 
 
 840 
 
 800 
 
 36x12 
 
 1940 
 
 1835 
 
 8x3 
 
 185 
 
 165 
 
 18x18 
 
 1055 
 
 860 
 
 24x3 
 
 725 
 
 705 
 
 36x10 
 
 1810 
 
 1730 
 
 10x10 
 
 380 
 
 300 
 
 18x14 
 
 865 
 
 735 
 
 30x30 
 
 2850 
 
 2415 
 
 36x8 
 
 1700 
 
 1635 
 
 10x6 
 
 280 
 
 240 
 
 18x10 
 
 695 
 
 610 
 
 30x20 
 
 2020 
 
 1790 
 
 36x6 
 
 1555 
 
 1515 
 
 10x3 
 
 225 
 
 205 
 
 18x6 
 
 550 
 
 510 
 
 30x16 
 
 1755 
 
 1585 
 
 36x4 
 
 1445 
 
 1415 
 
 12x12 
 
 495 
 
 395 
 
 18x3 
 
 455 
 
 435 
 
 30x12 
 
 1475 
 
 1370 
 
 36x3 
 
 1380 
 
 1360 
 
 12x8 
 
 405 
 
 345 
 
 20x20 
 
 1335 
 
 1100 
 
 30x8 
 
 1255 
 
 1190 
 
 
 
 
 12x3 
 
 275 
 
 255 
 
 20x16 
 
 1 1C0 
 
 935 
 
 30x4 
 
 1030 
 
 1005 
 
 
 
 
 These tables are greatly abridged from the original, many intermediate 
 sizes being omitted. 
 
 4) 
 
 Branches. 
 
 a 
 
 B 
 
 ranches. 
 
 J3 
 
 Branches. 
 
 c 
 
 30° 
 
 45° 
 
 60° 
 
 30° 
 
 45° 
 
 60° 
 
 30° 
 
 45° 
 
 60° 
 
 3x3 
 
 70 
 
 70 
 
 60 
 
 14x3 
 
 360 
 
 295 
 
 305 
 
 24x16 
 
 1865 
 
 1520 
 
 1345 
 
 4x4 
 
 115 
 
 95 
 
 85 
 
 16x16 
 
 1185 
 
 910 
 
 815 
 
 24x12 
 
 1500 
 
 1235 
 
 1100 
 
 4x3 
 
 100 
 
 80 
 
 75 
 
 16x12 
 
 885 
 
 710 
 
 635 
 
 24x8 
 
 1175 
 
 1055 
 
 915 
 
 6x6 
 
 180 
 
 145 
 
 130 
 
 16X8 
 
 670 
 
 560 
 
 520 
 
 24x3 
 
 825 
 
 770 
 
 695 
 
 6x3 
 
 135 
 
 105 
 
 100 
 
 16x3 
 
 460 
 
 385 
 
 385 
 
 30x30 
 
 4445 
 
 3390 
 
 2905 
 
 8x8 
 
 310 
 
 250 
 
 230 
 
 18x18 
 
 1415 
 
 1080 
 
 935 
 
 30x20 
 
 3005 
 
 2365 
 
 2220 
 
 8x6 
 
 240 
 
 205 
 
 190 
 
 18x14 
 
 1105 
 
 865 
 
 770 
 
 30x16 
 
 2475 
 
 2025 
 
 1770 
 
 8x3 
 
 135 
 
 160 
 
 150 
 
 18x10 
 
 850 
 
 670 
 
 635 
 
 30x12 
 
 1990 
 
 1695 
 
 1495 
 
 10x10 
 
 450 
 
 370 
 
 320 
 
 18x6 
 
 630 
 
 510 
 
 500 
 
 30x8 
 
 1630 
 
 1400 
 
 1250 
 
 10x6 
 
 300 
 
 255 
 
 235 
 
 18x3 
 
 510 
 
 435 
 
 410 
 
 30x3 
 
 1180 
 
 1125 
 
 960 
 
 10x3 
 
 235 
 
 195 
 
 190 
 
 20x20 
 
 1935 
 
 1455 
 
 1400 
 
 36x36 
 
 6595 
 
 4565 
 
 4115 
 
 12x12 
 
 650 
 
 545 
 
 445 
 
 20x16 
 
 1550 
 
 1190 
 
 1045 
 
 36x24 
 
 4405 
 
 3335 
 
 2990 
 
 12x8 
 
 470 
 
 385 
 
 345 
 
 20x12 
 
 1195 
 
 935 
 
 860 
 
 36x18 
 
 3370 
 
 2695 
 
 2360 
 
 12x3 
 
 300 
 
 255 
 
 240 
 
 20x8 
 
 930 
 
 750 
 
 690 
 
 36x14 
 
 2805 
 
 2340 
 
 2050 
 
 14x14 
 
 830 
 
 650 
 
 565 
 
 20x3 
 
 635 
 
 550 
 
 520 
 
 36x10 
 
 2295 
 
 2040 
 
 1760 
 
 14x10 
 
 625 
 
 505 
 
 455 
 
 24x24 
 
 2795 
 
 2140 
 
 1840 
 
 36x6 
 
 1860 
 
 1610 
 
 1415 
 
 14x6 
 
 450 
 
 365 
 
 355 
 
 24x18 
 
 2035 
 
 1675 
 
 ?450 
 
 36x3 
 
 1505 
 
 1360 
 
 1245 
 
 Split Tees. 
 
 3x3 
 4x4 
 
 10x8 
 10x3 
 
 165 
 
 125 
 220 
 180 
 
 12x3 
 14x8 
 14x3 
 
 275 
 235 
 
 325 
 
 285 
 
 16x3 
 18x8 
 18x3 
 
 380 
 340 
 
 485 
 
 555 
 780 
 1130 
 
 1090 
 1460 
 1420 
 
CAST-IRON PIPE-FITTINGS. 
 
 Split E 
 
 197 
 
 <B 
 
 Branches. 
 
 s 
 
 -S 
 
 o 
 
 c 
 
 Branches. 
 
 1 
 a 
 
 Branches. 
 
 a 
 
 30° 
 
 45° 
 
 60° 
 
 30° 
 
 45° 
 
 60° 
 
 30° 
 
 45° 
 
 60° 
 
 3 
 
 4 
 6 
 
 50 
 60 
 
 85 
 
 8 
 10 
 
 110 
 165 
 
 12 
 14 
 
 220 
 270 
 
 16 
 
 18 
 
 325 
 430 
 
 20 
 
 24 
 
 540 
 725 
 
 30 
 36 
 
 1075 
 1405 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Taper 
 
 Plugs 
 
 
 
 
 
 
 3 
 4 
 6 
 
 7 
 10 
 20 
 
 8 
 10 
 
 25 
 40 
 
 12 
 14 
 
 60 
 80 
 
 16 
 
 18 
 
 • 95 
 135 
 
 20 
 24 
 
 170 
 260 
 
 30 
 36 
 
 430 
 600 
 
 
 
 
 
 
 
 
 
 
 
 
 4x3 
 
 50 
 
 10x8 
 
 175 
 
 14x12 
 
 295 
 
 16x6 
 
 220 
 
 20x14 
 
 430 
 
 30x24 
 
 865 
 
 6x4 
 
 70 
 
 10x3 
 
 115 
 
 14x8 
 
 220 
 
 18x16 
 
 435 
 
 20x10 
 
 380 
 
 30x18 
 
 825 
 
 6x3 
 
 60 
 
 12x10 
 
 230 
 
 14x4 
 
 165 
 
 18x12 
 
 345 
 
 24x20 
 
 645 
 
 36x30 
 
 1455 
 
 8x6 
 
 100 
 
 12x6 
 
 165 
 
 16x14 
 
 355 
 
 18x8 
 
 280 
 
 24x16 
 
 555 
 
 36x18 
 
 950 
 
 8x3 
 
 55 
 
 12x3 
 
 140 
 
 16x10 
 
 290 
 
 20x18 
 
 520 
 
 24x12 
 
 485 
 
 
 
 3x4 
 
 55 
 
 4x14 
 
 210 
 
 8x14 
 
 235 
 
 12x14 
 
 300 
 
 16x18 
 
 455 
 
 20x36 
 
 1310 
 
 3x8 
 
 95 
 
 6x8 
 
 115 
 
 8x18 
 
 320 
 
 12x18 
 
 385 
 
 16x30 
 
 965 
 
 24x30 
 
 940 
 
 3x12 
 
 165 
 
 6x12 
 
 195 
 
 10x12 
 
 245 
 
 12x24 
 
 510 
 
 18x20 
 
 485 
 
 24x36 
 
 1380 
 
 4x6 
 
 75 
 
 6x16 
 
 275 
 
 10x16 
 
 335 
 
 14x16 
 
 375 
 
 18x36 
 
 1220 
 
 30x38 
 
 1475 
 
 4x10 
 
 150 
 
 8x10 
 
 190 
 
 10x20 
 
 410 
 
 14x24 
 
 600 
 
 20x24 
 
 700 
 
 
 
 
 o 
 
 T3 
 
 C 
 
 CD 
 
 o & 
 
 o ^ 
 
 -£2 cd 
 cn' 
 
 
 CD 
 
 a 
 'a 
 w. 
 
 8 
 
 a o 
 
 p 
 
 >-i a 
 o "a 
 
 o 
 
 o 
 
 ^a 
 
 o 'a 
 
 f* a 
 o a 
 
 o 
 
 a 
 
 6 
 
 > 
 
 m 
 
 3 
 
 50 
 
 40 
 
 35 
 
 75 
 
 50 
 
 355 
 
 50 
 
 55 
 
 65 
 
 70 
 
 20 
 
 35 
 
 4 
 
 60 
 
 50 
 
 45 
 
 105 
 
 70 
 
 370 
 
 70 
 
 75 
 
 85 
 
 95 
 
 25 
 
 45 
 
 6 
 
 95 
 
 70 
 
 60 
 
 145 
 
 115 
 
 395 
 
 95 
 
 105 
 
 120 
 
 125 
 
 40 
 
 60 
 
 8 
 
 155 
 
 115 
 
 100 
 
 210 
 
 190 
 
 450 
 
 160 
 
 175 
 
 205 
 
 210 
 
 60 
 
 75 
 
 10 
 
 215 
 
 160 
 
 130 
 
 360 
 
 295 
 
 485 
 
 200 
 
 235 
 
 270 
 
 290 
 
 85 
 
 100 
 
 12 
 
 290 
 
 210 
 
 170 
 
 450 
 
 420 
 
 575 
 
 265 
 
 300 
 
 380 
 
 425 
 
 110 
 
 17.5 
 
 14 
 
 355 
 
 260 
 
 210 
 
 595 
 
 500 
 
 690 
 
 320 
 
 360 
 
 480 
 
 520 
 
 145 
 
 150 
 
 16 
 
 495 
 
 355 
 
 280 
 
 640 
 
 775 
 
 890 
 
 415 
 
 500 
 
 615 
 
 755 
 
 165 
 
 175 
 
 18 
 
 575 
 
 405 
 
 320 
 
 880 
 
 910 
 
 1080 
 
 475 
 
 565 
 
 735 
 
 875 
 
 235 
 
 200 
 
 20 
 
 745 
 
 515 
 
 410 
 
 1160 
 
 1195 
 
 1190 
 
 580 
 
 725 
 
 950 
 
 1135 
 
 290 
 
 240 
 
 74 
 
 1040 
 
 715 
 
 555 
 
 1590 
 
 1680 
 
 1785 
 
 830 
 
 1000 
 
 1330 
 
 1600 
 
 435 
 
 345 
 
 30 
 
 1580 
 
 1060 
 
 800 
 
 2450 
 
 2345 
 
 2410 
 
 1145 
 
 1470 
 
 2005 
 
 2270 
 
 680 
 
 475 
 
 36 
 
 2230 
 
 1490 
 
 1120 
 
 3540 
 
 3495 
 
 3225 
 
 1600 
 
 2070 
 
 2720 
 
 3315 
 
 1015 
 
 630 
 
 STANDARD PIPE FLANGES (CAST IRON). 
 
 Adopted August, 1894, at a conference of committees of the American 
 Society of Mechanical Engineers, and the Master Steam and Hot Water 
 Fitters' Association, with representatives of leading manufacturers and 
 users of pipe, -^- Trans, A. S. M. E,, xxi, 29. 
 
198 
 
 
 
 
 MATERIALS. 
 
 
 
 
 
 
 
 The list is divided 
 
 into two 
 
 groups; for medium and high pressures, • 
 
 ti 
 
 e first ranging up 
 
 to 75 lbs 
 
 per square inch, 
 
 and the second up to 
 
 200 lbs. 
 
 
 
 
 
 
 ■Sjt 
 
 °3. 
 
 03 
 
 m 
 
 .a 
 
 40 
 
 
 
 
 
 
 -a 
 
 <u 
 
 
 I 
 
 6 
 
 3 
 
 a 1 
 
 02 
 
 la 
 
 a 
 
 
 
 m 
 
 
 
 <D 
 
 
 
 Ol 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 I? 
 .2 ^ 
 
 o3 • 
 v •/, 
 
 zi 
 
 J. z 
 
 rt 
 
 °8 
 
 0) 
 
 s 
 
 03 
 
 Q 
 
 .z-d 
 .d ° 
 
 bJO 
 
 d 
 
 J5 
 
 a 
 
 03 
 
 5 
 
 "0 o5 
 
 
 ffl 
 "0 
 
 <x> 
 
 
 1 
 
 a 
 
 -d* 
 ftfl 
 
 d 
 
 d a,. 
 
 03 
 
 H2 oo 
 
 _5 d* 
 
 .r - 
 
 32 
 
 (3 
 
 M 
 
 d 
 
 £5 
 
 dT3 
 
 
 5-1 
 
 PQ 
 
 — 
 
 i 
 
 s 
 
 5 
 
 "0 
 
 "0 
 
 n 
 
 & d! 
 
 Oi CTi 
 
 2 
 
 0.409 
 
 7/16 
 
 460 
 
 1/8 
 
 6 
 
 5/8 
 
 2 
 
 43/4 
 
 4 
 
 5/8 
 
 2 
 
 82! 
 
 21/2 
 
 .429 
 
 7 16 
 
 550 
 
 1/8 
 
 7 
 
 U/16 
 
 21/ 4 
 
 51/2 
 
 4 
 
 5/8 
 
 21/4 
 
 1051 
 
 3 
 
 .448 
 
 7/16 
 
 690 
 
 1/8 
 
 71/2 
 
 3/4 
 
 21/4 
 
 6 
 
 4 
 
 5/8 
 
 21/2 
 
 1331 
 
 31/2 
 
 .466 
 
 1/2 
 
 700 
 
 1/8 
 
 81/2 
 
 13/16 
 
 21/2 
 
 7 
 
 4 
 
 5/8 
 
 
 2531 
 
 4 
 
 .486 
 
 1/2 
 
 800 
 
 1/8 
 
 9 
 
 15/16 
 
 21/2 
 
 71/2 
 
 4 
 
 3/ 4 
 
 23/4 
 
 2101 
 
 41/ 2 
 
 .498 
 
 1/2 
 
 900 
 
 1/8 
 
 91/4 
 
 15/16 
 
 23/s 
 
 73/4 
 
 8 
 
 3/4 
 
 3 
 
 143(: 
 
 5 
 
 .525 
 
 1/2 
 
 1000 
 
 1/8 
 
 10 
 
 15/16 
 
 21/2 
 
 81/2 
 
 8 
 
 3/4 
 
 3 
 
 163( 
 
 6 
 
 .563 
 
 9/16 
 
 1060 
 
 1/8 
 
 11 
 
 1 
 
 21/2 
 
 91/2 
 
 8 
 
 3/4 
 
 3 
 
 236( 
 
 7 
 
 .60 
 
 5/8 
 
 1120 
 
 1/8 
 
 121/2 
 
 1 Vie 
 
 23/4 
 
 103/4 
 
 8 
 
 3/4 
 
 31/4 
 
 320( 
 
 8 
 
 .639 
 
 5/8 
 
 1280 
 
 1/8 
 
 131/2 
 
 1 1/8 
 
 23/4 
 
 113/4 
 
 8 
 
 3/ 4 
 
 31/2 
 
 419C 
 
 9 
 
 .678 
 
 11/16 
 
 1310 
 
 3/16 
 
 15 
 
 1 1/8 
 
 3 
 
 131/4 
 
 12 
 
 3/4 
 
 > 
 
 3610 
 
 10 
 
 .713 
 
 3/ 4 
 
 1330 
 
 3/16 
 
 16 
 
 1 3/16 
 
 3 
 
 141/ 4 
 
 12 
 
 7/8 
 
 35/s 
 
 297C: 
 
 12 
 
 .79 
 
 i-Vie 
 
 1470 
 
 3/16 
 
 19 
 
 1 1/4 
 
 31/2 
 
 17 
 
 12 
 
 7/8 
 
 33/4 
 
 428C 
 
 14 
 
 .864 
 
 7/8 
 
 1600 
 
 3/16 
 
 21 
 
 1 3/8 
 
 31/2 
 
 183/4 
 
 12 
 
 1 
 
 41/4 
 
 4280. 
 
 15 
 
 .904 
 
 15/16 
 
 1600 
 
 3/16 
 
 221/4 
 
 1 3/8 
 
 35/s 
 
 20 
 
 16 
 
 1 
 
 41/4 
 
 366C 
 
 16 
 
 .946 
 
 1 
 
 1600 
 
 
 231/2 
 
 1 7/ie 
 
 33/ 4 
 
 211/4 
 
 16 
 
 1 
 
 41/4 
 
 4210 
 
 18 
 
 1.02 
 
 H/16 
 
 1690 
 
 
 25 
 
 1 9/16 
 
 31/2 
 
 223/4 
 
 16 
 
 U/8 
 
 43/4 
 
 4540 
 
 20 
 
 1.09 
 
 U/8 
 
 1780 
 
 3/16 
 
 271/2 
 
 1 H/16 
 
 33/ 4 
 
 25 
 
 20 
 
 U/8 
 
 5 
 
 449C 
 
 22 
 
 1.18 
 
 13/16 
 
 1850 
 
 1/4 
 
 291/ 2 
 
 1 13/16 
 
 33/4 
 
 271/4 
 
 20 
 
 U/4 
 
 51/2 
 
 4320 
 
 24 
 
 1.25 
 
 U/4 
 
 1920 
 
 1/4 
 
 31 1/ 2 32 
 
 U/4 1 7/ 8 
 
 3 3/4 4 
 
 291/ 4 291/2 
 
 20 
 
 U/4 
 
 51/0 
 
 513C 
 
 26 
 
 1.30 
 
 15/16 
 
 1980 
 
 1/4 
 
 333/ 4 341/4 
 
 13/8 2 
 
 3 7/8 41/8 
 
 311/4313/4 
 
 24 
 
 U/4 
 
 53/4 
 
 503C 
 
 28 
 
 1.38 
 
 1.3/8 
 
 2040 
 
 1/4 
 
 36 361/2 
 
 17/16 2 l/i 6 
 
 4 41/4 
 
 331/2 34 
 
 28 
 
 U/4 
 
 6 
 
 500C 
 
 30 
 
 1.48 
 
 U/2 
 
 2000 
 
 1/4 
 
 38 383/4 
 
 1 1/2 2 1/8 
 
 4 43/ 8 
 
 35 1/2 36 
 
 28 
 
 13/8 
 
 6I/4 
 
 459C 
 
 36 
 
 1.71 
 
 13/4 
 
 1920 
 
 1/4 
 
 441/2 453/4 
 
 13/4 2 3/ 8 
 
 41/4 47/s 
 
 42 423/4 
 
 32 
 
 13/8 
 
 6I/2 
 
 579C 
 
 42 
 
 1.87 
 
 2 
 
 2100 
 
 1/4 
 
 51 523/4 
 
 1 7/8 2 5/ 8 
 
 41/2 53/s 
 
 481/ 2 491/ 2 
 
 36 
 
 U/2 
 
 71/4 
 
 570C 
 
 48 
 
 2.17 
 
 21/4 
 
 2130 
 
 1/4 
 
 571/2 591/2 
 
 2 2 3/4 
 
 43/4 53/4 
 
 543/ 4 56 
 
 44 
 
 U/2 
 
 73/4 
 
 609C 
 
 Notes. — Sizes up to 24 inches are designed for 200 lbs. or less. 
 
 Sizes from 24 to 48 inches are divided into two scales, one for 200 lbs. 
 the other for less. 
 
 The sizes of bolts given are for high pressure. For medium pressures 
 the diameters are Vs in. less for pipes 2 to 20 in. diameter inclusive, and 
 1/4 in. less for larger sizes, except 48-in. pipe, for which the size of bolt is 
 13/8 in. 
 
 When two lines of figures occur under one heading, the single columns 
 are for both medium and high pressures. Beginning with 24 inches, the 
 left-hand columns are for medium and the right-hand lines are for high 
 pressures. 
 
 The sudden increase in diameters at 16 inches is due to the possible 
 insertion of wrought-iron pipe, making with a nearly constant width of 
 gasket a greater diameter desirable. 
 
 When wrought-iron pipe is used, if thinner flanges than those given 
 are sufficient, it is proposed that bosses be used, to bring the nuts up to 
 the standard lengths. This avoids the use of a reinforcement around the 
 pipe. 
 
 Figures in the 3d, 4th, 5th, and last columns refer only to pipe for 
 high pressure. 
 
 In drilling valve flanges a vertical line parallel to the spindles should 
 be midway between two holes on the upper side of the flanges. 
 
STANDARD STRAIGHT-WAY GATE VALVES. 
 
 199 
 
 FLANGE DIMENSIONS, ETC., FOB EXTRA HEAVY ] 
 FITTINGS (UP TO 250 LBS. PRESSURE). 
 
 Adopted by a Conference of Manufacturers, June 28, 1901. 
 
 Size of 
 
 Diam. of 
 
 Thickness 
 
 Diameter of 
 
 Number of 
 
 Size of 
 
 Pipe. 
 
 Flange. 
 
 of Flange. 
 
 Bolt Circle. 
 
 Bolts. 
 
 Bolts. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 
 Inches. 
 
 2 
 
 61/2 
 
 7/8 
 
 5 
 
 4 
 
 5/8 
 
 21/2 
 
 71/2 
 
 1 
 
 5 7/ 8 
 
 4 
 
 3/4 
 
 3 
 
 81/4 
 
 H/8 
 
 65/s 
 
 8 
 
 5/8 
 
 31/2 
 
 9 
 
 13/16 
 
 71/4 
 
 8 
 
 5/8 
 
 4 
 
 10 
 
 11/4 
 
 77/s 
 
 8 
 
 3/4 
 
 41/2 
 
 101/2 
 
 15/16 
 
 8I/2 
 
 8 
 
 3/4 
 
 5 
 
 11 
 
 13/s 
 
 91/4 
 
 8 
 
 3/4 
 
 6 
 
 '21/2 
 
 17/16 
 
 105/ 8 
 
 12 
 
 3/4 
 
 7 
 
 14 
 
 H/2 
 
 H7/8 
 
 12 
 
 7/8 
 
 8 
 
 15 
 
 15/8 
 
 13 
 
 12 
 
 7/8 
 
 9 
 
 16 
 
 13/4 
 
 14 
 
 12 
 
 7/8 
 
 10 
 
 171/2 
 
 17/8 
 
 151/4 
 
 16 
 
 7/8 
 
 12 
 
 20 
 
 2 
 
 173/4 
 
 16 
 
 7/8 
 
 14 
 
 221/2 
 
 21/8 
 
 20 
 
 20 
 
 7/8 
 
 15 
 
 231/2 
 
 23/ie 
 
 21 
 
 20 
 
 1 
 
 16 
 
 25 
 
 21/4 
 
 221/2 
 
 20 
 
 1 
 
 18 
 
 27 
 
 23/ 8 
 
 241/2 
 
 24 
 
 1 
 
 20 
 
 291/2 
 
 21/2 
 
 26 3/4 
 
 24 
 
 H/8 
 
 22 
 
 3U/2 
 
 25/ 8 
 
 28 3/4 
 
 28 
 
 H/8 
 
 24 
 
 34 
 
 23/ 4 
 
 311/4 
 
 28 
 
 H/8 
 
 STANDARD STRAIGHT-WAY GATE VALVES. 
 
 (Crane Co.) 
 
 Iron Body. Brass Trimmings. Wedge Gate. 
 
 Dimensions in Inches: A, nominal size; D, 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; 0, diam. of wheel; S, center to top of rising stem, 
 open; P, size of by-pass; F, end to end, hub; T, diam. of hub; X, number 
 of turns to open. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 K 
 
 N 
 
 
 
 S 
 
 Y 
 
 P 
 
 X 
 
 U/2 
 
 61/2 
 
 51/4 
 
 9/16 
 
 5 
 
 101/2 
 
 51/2 
 
 
 
 6 
 
 2 
 
 7 
 
 6 
 
 5/8 
 
 57/16 
 
 113/4 
 
 51/2 
 
 14 
 
 
 
 7 
 
 21/2 
 
 71/2 
 
 7 
 
 H/16 
 
 57/8 
 
 123/4 
 
 51/2 
 
 153/ 4 
 
 
 
 8 
 
 3 
 
 8 
 
 71/2 
 
 3/4 
 
 61/8 
 
 141/4 
 
 61/2 
 
 181/2 
 
 
 
 101/4 
 
 31/2 
 
 81/2 
 
 8 1/2 
 
 13/16 
 
 61/2 
 
 151/4 
 
 71/2 
 
 203/4 
 
 
 
 101/ 8 
 
 4 
 
 9 
 
 9 
 
 15/16 
 
 67/s 
 
 161/4 
 
 9 
 
 231/2 
 
 
 
 8 3/4 
 
 41/2 
 
 91/2 
 
 91/4 
 
 15/16 
 
 71/4 
 
 175/s 
 
 9 
 
 243/4 
 
 
 
 9 
 
 5 
 
 10 
 
 10 
 
 15/16 
 
 75/ie 
 
 19 
 
 10 
 
 28 
 
 
 
 11 
 
 6 
 
 101/2 
 
 11 
 
 1 
 
 73/4 
 
 203/4 
 
 10 
 
 313/4 
 
 
 
 125/s 
 
 7 
 
 11 
 
 121/2 
 
 U/16 
 
 8I/4 
 
 23 
 
 12 
 
 371/4 
 
 
 
 151/4 
 
 8 
 
 111/2 
 
 131/2 
 
 U/8 
 
 EU/16 
 
 26 
 
 14 
 
 41 
 
 
 
 16 
 
 9 
 
 12 
 
 15 
 
 U/8 
 
 91/4 
 
 28 
 
 14 
 
 441/4 
 
 
 
 183/4 
 
 10 
 
 13 
 
 16 
 
 13/16 
 
 97/ 8 
 
 301/4 
 
 16 
 
 491/2 
 
 
 
 201/2 
 
 12 
 
 14 
 
 19 
 
 U/4 
 
 H5/8 
 
 351/4 
 
 18 
 
 571/4 
 
 
 
 241/8 
 
 14 
 
 15 
 
 21 
 
 13/8 
 
 
 391/4 
 
 20 
 
 66I/9 
 
 191/2 
 
 2 
 
 211/4 
 
 15 
 
 15 
 
 221/4 
 
 13/8 
 
 
 4U/8 
 
 20 
 
 693/ 4 
 
 21 
 
 2 
 
 3H/2 
 
 16 
 
 16 
 
 231/2 
 
 17/16 
 
 
 423/4 
 
 22 
 
 743/4 
 
 233/4 
 
 3 
 
 331/4 
 
 18 
 
 17 
 
 25 
 
 19/16 
 
 
 483/4 
 
 24 
 
 86 
 
 243/4 
 
 3 
 
 351/2 
 
 20 
 
 18 
 
 27 1/2 
 
 1 H/16 
 
 
 521/2 
 
 24 
 
 91 
 
 2 73/4 
 
 4 
 
 421/4 
 
 22 
 
 19 
 
 291/2 
 
 1 13/16 
 
 
 551/2 
 
 27 
 
 100 
 
 29 
 
 4 
 
 46 
 
 24 
 
 20 
 
 32 
 
 17/8 
 
 
 62 
 
 30 
 
 109 
 
 301/2 
 
 4 
 
 50 
 
 26 
 
 23 
 
 341/4 
 
 2 
 
 
 657/ 8 
 
 30 
 
 1171/2 
 
 32 
 
 4 
 
 65 
 
 28 
 
 26 
 
 351/2 
 
 21/16 
 
 
 70 
 
 36 
 
 125 
 
 33 
 
 4 
 
 80 
 
 30 
 
 30 
 
 383/4 
 
 21/8 
 
 
 751/2 
 
 36 
 
 133 
 
 34 
 
 4 
 
 921/2 
 
 36 
 
 36 
 
 453/4 
 
 23/8 
 
 
 83 
 
 
 1581/2 
 
 39 
 
 6 
 
 108 
 
200 
 
 MATERIALS. 
 
 EXTRA HEAVY STRAIGHT-WAT GATE VALVES. 
 
 Ferrosteel. Hard Metal Seats. Wedge Gate. 
 
 A 
 
 5 
 
 K 
 
 C 
 
 D 
 
 N 
 
 83/ 4 
 
 S 
 
 
 5 
 
 P 
 
 Y 
 
 X 
 
 U/4 
 
 61/2 
 
 51/2 
 
 5 
 
 3/ 4 
 
 105/ 8 
 
 12 
 
 11/2 
 
 71/2 
 
 61/4 
 
 6 
 
 13/1 fi 
 
 9b/« 
 
 121/4 
 
 51/9 
 
 
 
 11 
 
 2 
 
 81/2 
 
 7 
 
 61/2 
 
 V/8 
 
 101/9, 
 
 133/4 
 
 61/9 
 
 
 
 14 
 
 21/ 2 
 
 91/2 
 
 8 
 
 71/2 
 
 I 
 
 127/8 
 
 16 
 
 71/9 
 
 
 
 15 
 
 3 
 
 111/8 
 
 9 
 
 81/4 
 
 1 1/8 
 
 l4b/ 8 
 
 191/9 
 
 9 
 
 
 
 14 
 
 31/2 
 
 117/8 
 
 10 
 
 9 
 
 13/16 
 
 151/, 
 
 22 
 
 10 
 
 
 
 16 
 
 4 
 
 12 
 
 11 
 
 10 
 
 H/4 
 
 i;3 /4 
 
 241/9 
 
 12 
 
 
 
 18 
 
 41/2 
 
 131/4 
 
 121/4 
 
 101/2 
 
 Itylfi 
 
 l83 /4 
 
 27 
 
 12 
 
 
 
 21 
 
 5 
 
 15 
 
 131/2 
 
 11 
 
 I 3/8 
 
 201/4 
 
 2y3/ 4 
 
 14 
 
 
 
 23 
 
 6 
 
 15 7/s 
 
 157/s 
 
 121/2 
 
 IV/i fi 
 
 23 
 
 341/ 8 
 
 16 
 
 U/4 
 
 13 
 
 28 
 
 7 
 
 I6I/4 
 
 161/4 
 
 14 
 
 IV? 
 
 243/4 
 
 38 
 
 18 
 
 H/ 4 
 
 141/8 
 
 30 
 
 8 
 
 161/2 
 
 I6I/2 
 
 15 
 
 15/8 
 
 283/ 4 
 
 423/4 
 
 20 
 
 IV?, 
 
 157/8 
 
 34 
 
 9 
 
 17 
 
 17 
 
 16 
 
 13/4 
 
 301/, 
 
 47 
 
 20 
 
 H/2 
 
 163/s 
 
 40 
 
 10 
 
 18 
 
 18 
 
 171/2 
 
 17/8 
 
 3i3/ 4 
 
 523/ 4 
 
 22 
 
 11/?, 
 
 167/ s 
 
 39 
 
 12 
 
 193/ 4 
 
 
 20 
 
 2 
 
 3/1/4 
 
 60 
 
 24 
 
 2 
 
 197/8 
 
 46 
 
 14 
 
 221/2 
 
 
 221/2 
 
 21/8 
 
 423/4 
 
 67 3/ 4 
 
 24 
 
 2 
 
 205/s 
 
 52 
 
 15 
 
 221/2 
 
 
 231/2 
 
 23/ « 
 
 423/4 
 
 6/3/ 4 
 
 24 
 
 2 
 
 205/ 8 
 
 52 
 
 16 
 
 24 
 
 
 25 
 
 21/4 
 
 
 751/4 
 
 27 
 
 3 
 
 251/4 
 
 60 
 
 18 
 
 26 
 
 
 27 
 
 23/8 
 
 
 821/4 
 
 30 
 
 3 
 
 261/9 
 
 67 
 
 20 
 
 28 
 
 
 291/2 
 
 21/? 
 
 
 9U/9 
 
 30 
 
 4 
 
 301/9 
 
 74 
 
 22 
 
 291/2 
 
 
 3H/2 
 
 25/8 
 
 
 101 
 
 36 
 
 4 
 
 321/4 
 
 82 
 
 24 
 
 31 
 
 
 34 
 
 23/4 
 
 
 109 
 
 36 
 
 4 
 
 33 
 
 88 
 
 For dimensions of Medium Valves and Extra Heavy Hydraulic Valves, 
 See Crane Company's catalogue. 
 
 FORGED AND ROLLED STEEL FLANGES. 
 
 Dimensions in Inches. (American Spiral Pipe Works, 1908.) 
 
 f A 
 
 > 1 ' 
 
 ' 
 
 
 
 
 
 
 Standard Companion Flanges. 
 
 Standard Shrink Flanges. 
 
 "3 0> 
 
 ■§a 
 
 li ® 
 
 , . 
 
 
 
 
 -Sa 
 
 a 
 
 , . 
 
 *3 
 
 "o . 
 
 S|S 
 
 is 
 
 £ 
 
 .2 <B 
 
 -a fl 
 
 &M 
 
 a 3 
 
 ii^ 
 
 ■?s 
 
 *Q 
 
 .2 i> 
 
 ftK 
 
 .gW 
 
 £ 
 
 
 
 < 
 
 H 
 
 Q 
 
 Q 
 
 £ 
 
 
 
 ffl 
 
 H 
 
 A 
 
 Q 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 2 
 
 6 
 
 21/8 
 
 5/8 
 
 1 
 
 31/8 
 
 4 
 
 9 
 
 *3/ 8 
 
 15/16 
 
 23/ir 
 
 5 3/4 
 
 21/9 
 
 7 
 
 21/?, 
 
 H/16 
 
 U/lfi 
 
 35/8 
 
 41/?, 
 
 9 1/4 
 
 47/s 
 
 I'/lR 
 
 21/4 
 
 61/8 
 
 3 
 
 nh 
 
 31,'s 
 
 3/4 
 
 I 1/8 
 
 45/ lfi 
 
 5 
 
 10 
 
 5 7/, fi 
 
 iVifi 
 
 25/ 1fi 
 
 6 7/s 
 
 31/?, 
 
 81/?, 
 
 35/s 
 
 13/16 
 
 13/16 
 
 4 V/8 
 
 6 
 
 11 
 
 61/9 
 
 1 
 
 27/ 16 
 
 7 7/s 
 
 4 
 
 9 
 
 41/8 
 
 15/16 
 
 I 8/1 6 
 
 53/8 
 
 7 
 
 121/9 
 
 yi/9 
 
 11/16 
 
 21/9 
 
 9 
 
 41/9 
 
 9 1/4 
 
 4^/8 
 
 l/<6 
 
 U/4 
 
 5 13/, fi 
 
 8 
 
 131/9 
 
 8 1/9 
 
 11/8 
 
 25/8 
 
 101 
 
 5 
 
 10 
 
 51/8 
 
 15/16 
 
 i*»/tfl 
 
 67/ie 
 
 9 
 
 15 
 
 91/9 
 
 11/8 
 
 23/ 4 
 
 111/8 
 
 6 
 
 11 
 
 63/i 6 
 
 1 
 
 1 V/,6 
 
 '»/l« 
 
 10 
 
 16 
 
 105/8 
 
 is/m 
 
 3 
 
 121/8 
 
 7 
 
 121/9, 
 
 '8/lfl 
 
 11/16 
 
 11/9 
 
 85/8 
 
 12 
 
 19 
 
 125/8 
 
 11/4 
 
 33/s 
 
 147/ 
 
 8 
 
 131/9 
 
 83/, 6 
 
 11/8 
 
 15/8 
 
 9H/16 
 
 14 
 
 21 
 
 13 7/8 
 
 13/8 
 
 33/s 
 
 15 7/8 
 
 9 
 
 15 
 
 93/, 6 
 
 11/8 
 
 13/4 
 
 10 5/8 
 
 15 
 
 221/ 4 
 
 147/8 
 
 13/8 
 
 31/? 
 
 16 
 
 10 
 
 16 
 
 I0b/i 6 
 
 13/16 
 
 IV/8 
 
 1 ! 15/, 6 
 
 16 
 
 231/2 
 
 l5 7/ 8 
 
 17/0 
 
 35/8 
 
 l«?/4 
 
 12 
 
 19 
 
 I2b/ ]fi 
 
 I l/ 4 
 
 21/, 6 
 
 141/8 
 
 18 
 
 25 
 
 177/s 
 
 l»/tfi 
 
 3 V/8 
 
 201/8 
 
 14 
 
 21 
 
 131/2 
 
 13/8 
 
 23/i 6 
 
 15 7/i 6 
 
 20 
 
 271/2 
 
 197/8 
 
 1 U/1G 
 
 41/8 
 
 221/4 
 
FORGED AND ROLLED STEEL FLANGES. 
 
 201 
 
 FORGED AND ROLLED STEEL FLANGES. 
 
 — Continued 
 
 ExtraHeavy Companion Flanges. 
 
 Extra Heavy High Hub Flanges. 
 
 "o3 <D 
 
 83 rt 
 
 § 
 
 
 
 4 
 
 "3 -a5 
 
 .9 <B' =1 
 
 Is 
 
 
 13 o 
 
 "3 
 
 
 B 
 
 O 
 
 pq 
 
 H 
 
 « 
 
 A 
 
 fc 
 
 o 
 
 m 
 
 H 
 
 Q 
 
 Q 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 2 
 
 6V9 
 
 21/8 
 
 7/8 
 
 13/8 
 
 33/ 8 
 
 4 
 
 10 
 
 43/8 
 
 U/8 
 
 31/8 
 
 53/4 
 
 21/2 
 
 71/9 
 
 21/?, 
 
 1 
 
 1 Vlfl 
 
 41/16 
 
 41/?, 
 
 101/9, 
 
 47/s 
 
 H/4 
 
 31/4 
 
 6I/4 
 
 3 
 
 81/4 
 
 31/8 
 
 1 
 
 19/16 
 
 4 11/ie 
 
 5 
 
 11 
 
 57/16 
 
 U/4 
 
 31/4 
 
 7 
 
 31/2 
 
 9 
 
 3b/ 8 
 
 U/8 
 
 lb/8 
 
 !>*>/ifl 
 
 6 
 
 121/? 
 
 61/?, 
 
 11/4 
 
 31/4 
 
 715/16 
 
 4 
 
 10 
 
 41/8 
 
 H/8 
 
 13/4 
 
 5 13/ t R 
 
 7 
 
 14 
 
 /I/? 
 
 Itylfi 
 
 33/8 
 
 91/8 
 
 41/2 
 
 101/9, 
 
 45/ 8 
 
 11/4 
 
 U3/fi 
 
 61/4 
 
 8 
 
 15 
 
 81/?, 
 
 13/8 
 
 3V? 
 
 105/i 6 
 
 5 
 
 11 
 
 5 1/s 
 
 H/4 
 
 IV/8 
 
 613/6 
 
 9 
 
 16 
 
 91/?, 
 
 IV/16 
 
 35/8 
 
 113/ 8 
 
 6 
 
 121/9 
 
 63/, 6 
 
 H/4 
 
 2 
 
 /V/8 
 
 10 
 
 171/?, 
 
 105/ 8 
 
 11/?, 
 
 33/4 
 
 125/ 8 
 
 7 
 
 14 
 
 73/46 
 
 1 b/ifi 
 
 21/16 
 
 91/8 
 
 11 
 
 l83/ 4 
 
 H<>/8 
 
 1 »/l 6 
 
 37/8 
 
 135/ 8 
 
 8 
 
 15 
 
 83/| « 
 
 13/8 
 
 23/. 6 
 
 10 1/8 
 
 12 
 
 20 
 
 l25/ 8 
 
 H>/8 
 
 4 
 
 143/4 
 
 9 
 
 16 
 
 93/,fi 
 
 1 Vl6 
 
 21/4 
 
 iia/ifl 
 
 14 
 
 221/9, 
 
 I3V/8 
 
 I 3/4 
 
 43/ 8 
 
 163/i 6 
 
 10 
 
 M 1/9, 
 
 IOb/iB 
 
 U/?, 
 
 23/s 
 
 129/16 
 
 15 
 
 231/3 
 
 147/s 
 
 I 13/16 
 
 41/9 
 
 171/ 4 
 
 12 
 
 20 
 
 I2b/ 1fi 
 
 l*>/8 
 
 29/16 
 
 1 4o/8 
 
 16 
 
 25 
 
 liV/ R 
 
 IV/8 
 
 43/4 
 
 18l/ 2 
 
 14 
 
 221/9, 
 
 131/9, 
 
 13/4 
 
 2H/16 
 
 1 5 13/, 6 
 
 18 
 
 27 
 
 l7V/ 8 
 
 2 
 
 5 
 
 203/4 
 
 15 
 
 231/9, 
 
 141/9, 
 
 1 13/1R 
 
 213/16 
 
 i/a/i« 
 
 20 
 
 291/ ? , 
 
 197/8 
 
 21/4 
 
 Wi 
 
 221/2 
 
 16 
 
 25 
 
 151/2 
 
 IV/8 
 
 31/16 
 
 I8I/4 
 
 
 
 
 
 
 
 Forged Steel Flanges for Riveted Pipe. 
 
 Riveted Pipe Manufacturers' Standard.* 
 
 
 „ - 
 
 1 1 
 
 *. 
 
 Si 
 
 1 
 
 "Si: 
 
 .2 02 
 
 
 1® 
 
 
 
 
 •2p2 
 
 
 3 
 
 6 
 
 5/16 
 
 
 4 
 
 7/16 
 
 43/4 
 
 16 
 
 2U/4 
 
 5/8 
 
 3/4 
 
 12 
 
 1/? 
 
 191/4 
 
 4 
 
 y 
 
 W16 
 
 9/16 
 
 8 
 
 V/16 
 
 510/16 
 
 18 
 
 231/4 
 
 5/8 
 
 3/4 
 
 16 
 
 5/8 
 
 2U/4 
 
 5 
 
 8 
 
 •V16 
 
 9/16 
 
 8 
 
 7/16 
 
 61b/ifi 
 
 20 
 
 251/ 4 
 
 5/8 
 
 3/4 
 
 16 
 
 5/8 
 
 231/8 
 
 6 
 
 9 
 
 3/8 
 
 9/16 
 
 8 
 
 1/?, 
 
 /'/R 
 
 22 
 
 281/4 
 
 H/16 
 
 3/4 
 
 16 
 
 5/8 
 
 26 
 
 ■J 
 
 10 
 
 3/8 
 
 9/16 
 
 8 
 
 v* 
 
 9 
 
 24 
 
 30 
 
 H/16 
 
 V/8 
 
 16 
 
 5/8 
 
 2/3/ 4 
 
 8 
 
 II 
 
 3/8 
 
 S>/8 
 
 8 
 
 i/? 
 
 10 
 
 26 
 
 32 
 
 
 I 3/8 
 
 24 
 
 3/4 
 
 293/4 
 
 9 
 
 13 
 
 3/8 
 
 t>/8 
 
 8 
 
 V? 
 
 IU/4 
 
 28 
 
 34 
 
 
 I 3/8 
 
 28 
 
 3/4 
 
 313/4 
 
 10 
 
 14 
 
 3/8 
 
 H/16 
 
 8 
 
 Vl 
 
 121/4 
 
 3U 
 
 36 
 
 
 I 3/8 
 
 28 
 
 3/4 
 
 333/4 
 
 11 
 
 15 
 
 7/16 
 
 
 12 
 
 V?, 
 
 133/8 
 
 32 
 
 38 
 
 
 
 28 
 
 3/4 
 
 35 3/4 
 
 12 
 
 16 
 
 7/16 
 
 3/4 
 
 12 
 
 V? 
 
 Ul/ 4 
 
 34 
 
 40 
 
 
 
 28 
 
 3/4 
 
 373/ 4 
 
 13 
 
 YJ 
 
 7/16 
 
 
 12 
 
 1/? 
 
 151/4 
 
 36 
 
 42 
 
 
 U/? 
 
 32 
 
 3/4 
 
 393/ 4 
 
 14 
 
 18 
 
 Vi« 
 
 3/4 
 
 12 
 
 1/?, 
 
 161/4 
 
 40 
 
 46 
 
 
 IV? 
 
 32 
 
 3/4 
 
 433/4 
 
 15 
 
 19 
 
 «/l6 
 
 3/4 
 
 12 
 
 1/2 
 
 I///16 
 
 
 
 
 
 
 
 
 * 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 198), 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. 
 
202 
 
 MATERIALS. 
 
 The Rockwood Pipe Joint. — The 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. 
 
 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 -, in which D = outside diameter of the tubes, and n 
 
 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 - 4- d, in which 
 
 n n 
 
 d is the diameter at the bottom of the thread at the end of the pipe. 
 
 {Continued on page 207). 
 
 Forms of Cast-Iron Flanges. (See tables on pages 203 to 206). 
 
 (1) Elbow. (2) 45° (3) Side (4) Long (5) Tee. (6) Side 
 Elbow. Outlet Turn Elbow. Outlet T. 
 
 Elbow. 
 
 (7) Single (8) Lateral. (9) Double (10) Double 
 Sweep T. Sweep T. Branch 
 
 Elbow. 
 
 (11) Cross. (12) Re- 
 ducing 
 
 Cross. 
 
 (13) Re- (14) Red. T (15) Red. (16) Reduc- 
 ducing with Side Single ing Lateral. 
 Tee. Outlet. Sweep 
 
 Tee. 
 
STANDARD CAST-IRON FLANGED FITTINGS. 
 
 203 
 
 *o"]2S 
 
 n 
 
 ȣ 
 
 — "£ 
 
 1— -<r — 
 
 ^ 
 
 »2?§ 
 
 o=og 
 
 — -o 
 
 -1°, 
 
 *r 
 
 GO-*-*" — 
 
 00 
 
 -a 
 
 -a 
 
 — ■* 00 
 
 N 
 
 ™<SOv 
 
 : 
 
 S 2 
 
 -a 
 
 ^ 
 
 o 
 
 N | 
 
 ■2S 
 
 <o sO 
 
 fe 
 
 ^S§ 
 
 ooootn 
 
 2 <oin 
 
 -2 
 
 ?ff 
 
 00 
 
 0OOM>t 
 
 2 
 
 ^m 
 
 — 00 
 
 ^|f 
 
 r* 
 
 r^ooGocN 
 
 o£§ 
 
 5oo 
 
 mo 
 
 vOvO 00 00 — 
 
 f« = 
 
 — 00 
 
 *«! 
 
 in 
 
 in t-s. i~%. o oo ■f o 
 
 Sh 00 
 
 mOO 
 
 "*■<*■ r->. t->. o 
 
 1 
 
 ti-o* 
 
 3 00 
 
 iu? 
 
 T 
 
 J^D^C* 
 
 1 
 
 ^-Os 
 
 3 ■"»■ 
 
 "^"^ 
 
 s 
 
 ^OO 
 
 
 r^co 
 
 CO ,5- 
 
 
 <n 
 
 -^ 
 
 
 m£ 
 
 ^ 
 
 " (NO 
 
 S 
 
 0-n.n 
 
 
 ^ 
 
 S^r 
 
 
 N 
 
 &■ ^-^J- 
 
 
 L 
 
 '" rf 
 
 cmt 
 
 § 
 
 oo^r-r 
 
 
 £jlT> 
 
 -C 
 
 ^^■t? 
 
 i 
 
 Iff 
 
 
 (N^ 
 
 
 ^1 
 
 GGGGGGGGG • G G G 
 
 T3 m3 
 
 ■Si's&a 
 
 
 c3 bjo 
 A G 
 
 ft 
 
 & 
 
 O 
 
 M 
 
 
 5 
 
 
 0.2 
 
 G ^ 
 
 •< 
 £ 
 
 H 
 
 ft 
 
 <| 
 
 O G 
 
 fl 
 
 ft 
 
 t» T3 
 
 G ® 
 
 § 
 
 P4 
 
 R 
 
 fl 
 
 
 G Jr g 
 
 A 
 
 H 
 
 S CD 
 
 =35 
 
 ft 
 
 
 
 a 
 
 <p .G 
 
 oa 
 
 
 ■& a 
 
 fc 
 
 
 **a 
 
 O 
 
 H 
 
 © £ ■ 
 
 CA. 
 
 hJ 
 
 > G 
 
 
 & 
 
 
 S 
 
 
 
 
 
 G <" 
 
 R 
 
 
 - H 
 
 P 
 
 
 ■* & 
 
 
 
 •* 33 
 
 fa ° 
 
 f g N _, 
 
 
 fcfafa 
 o o o 
 
 u G G 
 .2G<99 
 
 coO<!<PQ 
 

 "T TCMfM 
 
 -* 
 
 1 
 
 M •*> 00 -^ 
 
 
 ~J Q© © 
 
 
 it 
 
 — cA <n ~ "° S 
 
 
 op-ff 
 
 On 
 
 <o 
 
 ofl^fll 
 
 
 25J2J5 
 
 s 
 
 § 
 
 ir^^^^g 
 
 
 orso* 
 
 rr 
 
 
 0>NNO-iAN 
 
 
 £©£.« 
 
 1 
 
 o 
 
 sg£©-£- 
 
 
 n-Os^J-^J- 
 
 
 00 
 
 tONNO mo 
 
 a 
 p 
 
 c 
 
 Pi 
 
 c 
 
 IQ 
 
 Ci 
 
 o 
 p 
 
 6B 
 
 CNnOcAcO 
 
 On 
 
 NO 
 
 BONO 1AI> 
 
 ©Cn — — 
 
 ■•o 
 
 1 
 
 ^ffvO^lf 
 
 On — ©© 
 
 2 
 
 — 
 
 S 2 ^N^^ 
 
 GOOOO 
 
 *r 
 
 tN 
 
 *iA-N -3- fA 
 
 ^ £ OnOn 
 
 1 
 
 o 
 
 vo^r — m ^ — 
 
 P 
 
 ^r>SS 
 
 | 
 
 On 
 
 
 mvoooco 
 
 o 
 
 00 
 
 m — — oo coo 
 
 d 
 
 
 
 
 
 ££ 
 
 
 nvov© oo v© to>" 
 
 ^ o o r>. \o 
 
 0—00 K-nnO 
 
 a d d ri p 
 
 pi d d '■ r 
 
 ■ 
 
 
 ■ : : o r A M 
 
 
 
 to Face, 
 to Face, 
 to Face, 
 to Face 
 aclius Ell 
 of Lon 
 Flls 
 
 2 -mm: 
 
 "o 
 ffl 
 
 - • 
 
 -2 2 bf- 2 -2° += fi ffl^ Jd»- 
 
 ajT-^r^ « c S rf a?Z £ « d <d £P+> 
 
 £0> 
 
 
 I 3 
 
 
 s 
 
 
 
 
 1 
 
 & 
 
 ^ 
 
 O IA On 
 
 
 <N 
 
 ^ T3 
 
 <N~, - - 
 
 
 o 
 
 
 
 
 H 
 
 
 
 
 o 
 
 U 
 
 
 
 
 73 
 
 •S2 
 
 
 
 
 
 
 ft 
 
 
 
 
 SI 
 
 N T) 
 
 
 
 
 
 
 
 
 fe 
 
 
 
 
 fi 
 
 s 
 
 -S2 
 
 
 H 
 
 => t/i 
 
 
 
 ft 
 
 N C 
 
 
 
 Q 
 
 
 
 
 ft 
 
 
 
 
 
 
 
 
 
 fz? 
 
 
 
 
 <1 
 
 | 
 
 ^- ~j- 
 
 
 
 3 S 
 
 
 
 h * ' 
 
 ~ "g 
 
 
 
 ©- « 
 
 
 
 
 >z;H 
 
 ^ 
 
 
 
 Sh 
 
 V 
 
 
 
 ^ 
 
 73 
 
 
 
 H v 
 
 oS t , 
 
 
 # ri 
 
 
 
 
 , 
 
 
 
 
 ^ o 
 
 
 
 
 p> « 
 
 o 
 
 
 
 
 
 
 
 ft£ 
 
 a 
 
 M CM 
 
 
 «!« u 
 
 "i n f 
 
 -» — ro 
 
 
 « M 
 
 
 
 
 H tT 
 
 
 
 
 M ^ 
 
 
 
 
 ft H 
 
 O 
 
 
 
 ft H 
 
 
 
 
 OP 
 
 
 
 
 o 
 
 
 
 
 ^ J "! 
 
 r 5 r 
 
 nj — m 
 
 
 O^ 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ i 
 
 ON 
 
 
 
 ss 
 
 V 
 
 
 
 pS 
 
 s 
 
 .(N « 
 
 
 J ^ - 
 
 J M ? 
 
 O CS| 
 
 
 <! 
 
 T3 
 
 
 
 ft 
 
 OO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 c 
 
 S 00 On — 
 
 
 o 
 w 
 
 NO 
 
 
 . 
 
 w 
 
 a c 
 
 d a 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 • o 
 
 
 o 
 
 
 
 
 
 
 01 
 
 
 
 « 
 
 ' e3 
 
 - 
 
 ert 
 
 
 
 ft 
 
 "fa 
 
 In 
 
 Uh 
 
 
 
 
 o 
 
 o 
 
 
 c 
 
 
 
 
 
 
 
 £ 
 
 O g 
 
 dJ 
 
 ss 
 
 
 
 °fa£ 
 
 d c CZ 
 
 
 
 ca 3 oj 3 
 
 
 2 K 
 
 N<<p: 
 
 V«9o 
 
 
 >■ iL 
 
 CQ<J 
 
 < 
 
 p 
 
 
 
HYDRAULIC FERROSTEEL FLANGED FITTINGS. 
 
 
 i-Tw" ^r^r 
 
 
 tj- a^ <si -^ — r>. so 
 
 
 
 
 
 
 
 
 vOsO c<>i ro, 
 
 (Mm -<r "" in 
 
 
 
 
 
 
 
 
 NinNO-'O- 
 
 
 
 
 
 
 
 
 
 CMm™£'~'' § 
 
 tf-Ct^tn 
 
 
 
 
 
 
 
 OOOO 
 
 OONvO-'CN 
 cMin <t> t)- 
 
 
 -SJ S .5 -^-^ 
 
 
 
 
 23- S?"""' '* 
 
 
 
 
 
 
 
 
 vO vO GO 00 
 
 2^-^-^^ 
 
 
 .N.0O JO _« 
 
 
 
 "3-Tj-r^r^ 
 
 l^^ — ^ — ^^ 
 
 
 
 
 
 
 
 
 
 CMCMvOO 
 
 
 
 
 
 
 
 
 ©©mm 
 
 in oo — oo — m v© 
 
 
 
 
 
 
 
 
 
 oooo-tt 
 
 Tt- VO S 00 — 1T\ I" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — CM °^0 — m c> 
 
 
 
 
 
 
 
 
 
 
 cm^cmS 
 
 Off.-0-iftN 
 — CM CM CM 
 
 
 ^^m^o 40^ 
 
 
 
 OvOCOOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N e -«i 
 
 
 ;?-<! ^j- 
 
 
 
 
 
 
 
 
 
 
 
 Ift^^ft 
 
 00 CM — sO — -3- O 
 
 
 
 
 
 
 
 
 too^i- 
 
 1^ — *H CM — Tf 00 
 
 
 
 
 
 
 
 
 
 cm jt cm cm 
 
 t^O — CM WM>. 
 
 
 
 d d d d 
 
 d d d 
 
 d d d 
 
 
 
 
 
 
 
 
 
 
 : : ;"S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fefefetti 
 
 ^«i§ 
 
 
 
 
 
 
 
 § ® OJ 
 
 fll 
 
 «St.ffl°g 
 
 
 
 
 c 
 
 
 a 
 
 <1<3fQW 
 
 QH2 
 
 
 ^£ 
 
 
 fc 
 
 OOOvOOO'- 
 
 
 « 
 
 
 w 
 
 
 
 
 
 H 
 
 
 ft 
 
 
 N 
 
 
 
 n 
 
 ^SmS^ 
 
 
 
 pq 
 
 NOOO^O 
 
 H 
 
 
 M 
 
 
 w 
 
 Qco*m» 
 
 
 
 1 
 
 OO sO ^T CM 00 
 
 
 
 K 
 
 vOCMCM — r-s 
 
 
 
 H 
 
 
 & 
 
 ^■Noom 
 
 J 
 
 
 < 
 
 NOMOJ 
 
 X 
 
 
 
 
 
 
 w 
 
 
 
 
 
 
 
 00 00 CM vO — 
 
 
 
 - 
 
 sOOOCMnO© 
 
 
 
 R 
 
 
 
 
 *r^o©ino 
 
 h 
 
 
 c 
 2 
 
 Nmco^-to 
 
 5 
 
 o^roo^r^ 
 
 
 cm — cm — — 
 
 « 
 
 42 
 
 
 
 
 
 
 
 32 
 
 vCOtNt 
 
 c 
 
 CN ' - '- 
 
 * 
 
 -5-5 
 
 
 
 £ 
 
 
 
 
 - 
 
 TTOCM — ^ 
 
 J 
 
 — CM — — 
 
 - 
 
 NCOOO- 
 
 s 
 
 — CM 
 
 X 
 £ 
 
 d '■ d d d 
 
 
 
 > 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -5j 
 
 
 a 
 
 
 -& 
 
 
 
 12 §§1 
 
 
 
 
 M ® & c 
 
 ^ 
 
 
 
 
 
 /" 
 
 
 ffe^fe 
 
 
 
 
 /^ 0> *■" ** 
 
 Q y 0> 0) 
 
 H 
 
 
 3 
 
 
 "fels 
 
 < 
 
 SS^oo 
 
 
 a: 
 
 'J2< 
 
 < 
 
 PC 
 
 
 H I • 
 
 o * ^ 
 
 3 S i 
 
 © 613 C 
 
 3 -S O 
 
 M 
 H 
 
 H 
 H 
 
 
 
 
 -5^ 
 
 
 
 
 
 
 
 •OT 0> 
 
 — CM 
 
 — CM CM 
 
 
 
 
 
 
 
 O — 
 — CM 
 
 jncMvooo 
 
 
 
 
 
 
 
 O00 
 
 mo -or^ 
 
 ~ 
 
 ' -<N '~ 
 
 
 
 
 
 
 
 00 t^ 
 
 CMI^ ^T^ 
 
 ~ 
 
 
 
 -5-5 
 
 
 
 t^O 
 
 
 ~~ 
 
 — , 
 
 
 -5 
 
 
 
 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 -5-5 
 
 .£>~£! -5 42 
 
 
 
 
 
 "" 
 
 "" 
 
 
 
 
 
 
 
 
 00 00 in 
 
 *~ 
 
 ~ 
 
 
 
 
 
 c^O 
 
 
 "~ 
 
 "~ 
 
 
 ^^2 40^ 
 
 
 
 MO 
 
 
 "~ 
 
 
 « ■* 
 
 <M TH 00 
 
 
 
 
 
 CM 00 
 
 vOOOvOTJ- 
 
 N 
 
 "* N 
 
 
 
 
 
 CMt-N 
 
 vOCOvOfA 
 
 W M 
 
 M TJ< 00 ^n 
 
 
 
 
 
 
 mt^inrn 
 
 d d 
 
 d d d d 
 
 
 
 
 
 
 
 
 
 
 
 
 ojo a> 
 
 
 
 
 
 
 oj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 O 
 
 
 
 
 
 
 "t 
 
 XI 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 I 
 
 c 
 
 is 
 
 
 
 swS^ 
 
 
 cS* 8 a^ 
 
 
 
 
 
 u< ; 
 
 
 
 <** 
 
 fl oj ^ <S 
 
 
 x^ 
 
 1s°s 
 
 
 
 
 
 Ph S3 §5 
 
 g § d 
 
 oil! 
 
 zc 
 
 c 
 
 
 
 C 
 
 p: 
 
 O 
 
 
206 
 
 MATERIALS. 
 
 
 asP? 
 
 o^co 
 
 OOO^NIN 
 
 vO vO o -o 
 
 m^rcoo 
 
 Tr^rsO ' 
 
 Not'" 
 
 off- 
 
 atat 
 
 oorar>Tr 
 
 NO*t 
 
 **,££ 
 
 ■ntega 
 
 fffw 
 
 * ££ }« 
 
 fff^ 
 
 mc^S^ 
 
 cqtNO-ra 
 
 NOGON 
 
 •«« ° ° 
 
 : ode* 
 
 
 ^r -<i-o 
 
 DC 
 
 H 
 
 H 
 
 g 
 
 p 
 
 Q 
 
 1 
 
 r - 
 
 
 
 03 
 fe 
 
 
 oc 
 
 H 
 
 s 
 
 _££ 
 
 5$ s 
 
 Or^t->, 
 
 CO ^5 
 
 vOOvO 
 
 (VlvOvO 
 
 §3^ 
 
 g — ir, 
 
 as* 
 
 &°=^ 
 
 -tst 
 
 gU^ 
 
 
 JS* 
 
 Jj^ 
 
 2 = «n 
 
 WON 
 
 §oS 
 
 a : : 
 
 2^ 
 
 o o o 
 
 fa w *-« 
 
 ■*" a fl 
 
 05 0) 0) 
 
 
 
 a? a? a? a) 
 
 £999 
 
 3° °Q 
 
 aj a) a> 5 
 
 AAVdJl 
 
NATIONAL STANDARD HOSE COUPLINGS. 
 
 207 
 
 {Continued jrom page 202.) The sizes for the diameters at the bottom 
 and top of the thread at the end of the pipe are as follows: 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 Diam. 
 
 of Pipe, 
 
 at Bot- 
 
 at Top 
 
 of Pipe, 
 
 at Bot- 
 
 at Top 
 
 of Pipe, 
 
 at Bot- 
 
 at Top 
 
 Nomi- 
 
 tom of 
 
 of 
 
 Nomi- 
 
 tom of 
 
 of 
 
 Nomi- 
 
 tom of 
 
 of 
 
 nal. 
 
 Thread. 
 
 Thread. 
 
 nal. 
 
 Thread . 
 
 Thread. 
 
 nal. 
 
 Thread. 
 
 Thread. 
 
 in. 
 
 in. 
 
 in 
 
 m. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 Vs 
 
 0.334 
 
 0.393 
 
 21/2 
 
 2.620 
 
 2.820 
 
 8 
 
 8.334 
 
 8.534 
 
 1/4 
 
 .433 
 
 .522 
 
 3 
 
 3.241 
 
 3.441 
 
 9 
 
 9.327 
 
 9.527 
 
 3/8 
 
 .568 
 
 .658 
 
 31/2 
 
 3.738 
 
 3.938 
 
 10 
 
 10.445 
 
 10.645 
 
 1/2 
 
 .701 
 
 .815 
 
 4 
 
 4.234 
 
 4.434 
 
 11 
 
 11.439 
 
 11.639 
 
 3/ 4 
 
 .911 
 
 1.025 
 
 41/2 
 
 4.731 
 
 4.931 
 
 12 
 
 12.433 
 
 12.633 
 
 1 
 
 1.144 
 
 1.283 
 
 5 
 
 5.290 
 
 5.490 
 
 13 
 
 13.675 
 
 13.875 
 
 H/4 
 
 1.488 
 
 1.627 
 
 6 
 
 6.346 
 
 6.546 
 
 14 
 
 14.669 
 
 14.869 
 
 11/2 
 
 1.727 
 
 1.866 
 
 7 
 
 7.340 
 
 7.540 
 
 15 
 
 15.663 
 
 15.863 
 
 2 
 
 2.223 
 
 2.339 
 
 
 
 
 
 
 
 Having the taper, length of full-threaded portion, and the sizes at bot- 
 tom 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 -*- n, n 
 being the number of threads per inch. 
 
 Taper of conical tube ends, 1 in 32 to axis of tube = 3/ 4 inch to the 
 foot total taper. 
 
 NATIONAL STANDARD HOSE COUPLINGS. 
 
 Dimensions in Inches. 
 
 A 
 
 21/2 
 
 1/4 
 
 31/16 
 
 2.8715 
 
 1 
 
 71/2 
 
 7/8 
 
 3.0925 
 
 3 
 
 1/4 
 
 35/ 8 
 3.3763 
 
 U/8 
 
 6 
 
 1 
 3.6550 
 
 31/2 
 
 1/4 
 41/4 
 4.0013 
 U/8 
 
 6 
 
 1 
 4.28 
 
 41/2 
 
 1/4 
 
 5?/ 4 
 
 5.3970 
 
 TS/S 
 
 4 
 
 11/4 
 5.80 
 
 B, 
 
 C 
 
 D 
 
 E 
 
 N 
 
 F 
 
 G 
 
 
 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 21/2-in., 3-in., and 31/2-in. 
 couplings, and 0.02 in. in like manner for the 41/2 in. couplings. 
 • A = inside diameter of hose couplings, N = number of threads per 
 inch. 
 
 DIMENSIONS OF STANDARD WELDED PIPE. 
 
 Referring to the table on the next page, the weights per foot are based 
 upon steel weighing 0.2833 ib. per cu. in. and up to and including 15 ins on 
 - an average lengtn of 20 ft. in. including the coupling, although shipping 
 lengths of small sizes will usually average less than 20 ft. Long. Above 
 15 ins. the weignts given are for plain end pipe. All dimensions and 
 weights are nominal. The imits of variation in weight are 5 per cent above 
 and 5 per cent below. Taper of threads is s/ 4 hi. in the diameter per ft 
 length. Weigat of contained water is based on a temperature of 62° F. and 
 0.036085 lb. to tne cubic men. 
 
208 
 
 MATERIALS. 
 
 £ 2 
 
 eg a 
 
 •8di(J 
 
 JO -!»J -Ulf X 
 
 -nob J9^A\ 
 
 •9did jo 
 
 •%j -utf x m 
 
 paufB^uoo 
 
 5u 01I Ti§ -g - n 
 
 •^iLiCj' - ° ^ Li rr "^ "i ,— — - tNu^rMOTr-jr-.in — r^r^omo 1 ^ — — 
 
 ? H 3 X ^ S3 £: 3 2£ _ C2 °. °°. — ovc — iNvoooTinrNO^^a 
 
 ;} O -J CN £< u-\ — mSdmSM?;- 
 
 J2S2;!^ tlNOr>tK ~ vo <n m o — a \o om<mn * oo oo ^ - co i 
 iOOOOOOO — — NmiftvDODOinoiAiMnnlnftS ?S-S-_ _ 
 
 •^oojoiqno 
 
 -uoo 9drd 
 jo q^Saai 
 
 5S 
 
 ^-NtOOO- 
 
 -i — r^o^j- — rr 
 
 9013 jjng 
 
 \T3U 
 
 ■•i9}xg 
 
 -J9JUJ 
 
 a^xg; 
 
 •aj -uit 
 J9d adij 
 jo m§i3A\. 
 
 ,0000000000c 
 £o 
 
 NO>v001-0>OOf 
 
 -1 T ir\ vO t~s O* - 
 
 MvOO^CT* 
 
 So- 
 
 o-^-oc^t^r^oor->o^ooor^or^oooooo-^-v©r^ovou 
 
 -N^tNO^NinOOOCOONOOlf\tfMNa>N^ — ■*' T 
 
 30000 C* 
 
 
 £=>" ' 
 
 
 
 
 
 
 
 
 
 
 ___ 
 
 — CM CS i fi 
 
 
 .554 
 .866 
 1.358 
 2.164 
 2.835 
 4.430 
 6.492 
 9.621 
 12.566 
 15.904 
 19.635 
 24.306 
 
 ■"«■ 
 
 1 
 
 00 
 
 1 
 
 90.763 
 108.434 
 127.676 
 153.938 
 176.715 
 201.062 
 254.469 
 314.159 
 380.133 
 452.389 
 
 Ft. 
 14.200 
 10.494 
 7.748 
 6.141 
 4.636 
 3.641 
 2.768 
 2.372 
 
 I 
 
 1.547 
 1.245 
 1.077 
 .949 
 
 .848 
 
 r-. 
 
 3 
 
 
 
 00 TT 
 
 WNN^ 
 
 <n 00 vo 
 
 t o om vo a 
 
 ^■^OOOtNO^O 
 
 - — NOiNinm — o* r» 
 
 ^' , to^^omao'<rrsoo^Doo^o^O'*mwo^c^»o^^oooo^.^^voo^N 
 
 ■(OMnNmOtN'0-vO-1100000tiri**N»-fNO 
 
 - — NN(^1'irnntNOvON'<rintsOtAr>ot< 
 
 OvOOUIOOOOOOOOOC 
 
 cs^j"if^oO' — socMr^.sooovocsio^r^ 
 [~o' "— — 'NcicKiPlt^OkoV 
 
 ^ ^o so 1^, r^. 00 ^ 
 
 •qom J9d 
 
 sprojqx 
 
 JQ'°N 
 
 OflO-OiMmOinTft^vOvOr- 
 
 •p3U 
 
 -J9^UJ 
 
 •JBU 
 
 .\0 ^OO^ CS N'I'OO ' — < 
 
 r\^^rmsoisrsooo- 
 
 ^3 
 
 --NN^Ttif 
 
 ■Jtmvoooo 
 
 33 
 
 - — — MtSf^rrc^^-if^vOrsOOa.0 — P. 
 
LAP-WELDED BOILER-TUBES. 
 
 209 
 
 WROUGHT-IRON WELDED TUBES, EXTRA STRONG. 
 
 Standard Dimensions. 
 
 (National Tube Co., 1902.) 
 
 Nominal 
 Diameter. 
 
 Actual 
 
 Outside 
 
 Diameter. 
 
 Thickness, 
 Extra 
 Strong. 
 
 Thickness, 
 Double 
 Extra 
 Strong. 
 
 Actual Inside 
 
 Diameter, 
 
 Extra 
 
 Strong. 
 
 Actual Inside 
 
 Diameter, 
 
 Double Extra 
 
 Strong. 
 
 Inches. 
 
 Vs 
 
 Inches. 
 0.405 
 0.54 
 0.675 
 0.84 
 1.05 
 1.315 
 1.66 
 1.9 
 2.375 
 2.875 
 3.5 
 4.0 
 4.5 
 
 Inches. 
 0.100 
 0.123 
 0.127 
 0.149 
 0.157 
 0.182 
 0.194 
 0.203 
 0.221 
 0.280 
 0.304 
 0.321 
 0.341 
 
 Inches. 
 
 Inches. 
 0.205 
 0.294 
 0.421 
 0.542 
 0.736 
 0.951 
 1.272 
 1.494 
 1.933 
 2.315 
 2.892 
 3.358 
 3.818 
 
 Inches. 
 
 1/4 
 
 
 
 3 /8 
 
 
 
 1/2 
 3/4 
 
 1 
 
 11/4 
 
 1 1/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 0.298 
 0.314 
 0.364 
 0.388 
 0.406 
 0.442 
 0.560 
 0.608 
 0.642 
 0.682 
 
 0.244 
 0.422 
 0.587 
 0.884 
 1.088 
 1.491 
 1.755 
 2.284 
 2.716 
 3.136 
 
 STANDARD SIZES, ETC., OF LAP-WELDED CHARCOAL-IRON 
 BOILER-TUBES. 
 
 (National Tube Co.) 
 
 1 
 
 5 
 
 a 
 5 
 
 ~ t 
 
 — » 
 
 Si 
 a o> 
 
 is a 
 
 Internal 
 
 External 
 
 
 2^ 
 
 
 eta 
 
 1, 
 
 
 z ~ 
 
 CO 
 
 sa 
 3 s 
 
 Area. 
 
 Area. 
 
 r <u c 
 
 
 ©£' . « 
 
 C fc a 
 
 5*1 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 sq. in. 
 
 sq.ft. 
 
 sq.in. 
 
 sq.ft. 
 
 ft. 
 
 ft. 
 
 ft. 
 
 lb. 
 
 1 
 
 0.810 
 
 .095 
 
 2.545 
 
 3.142 
 
 0.515 
 
 .0036 
 
 0.785 
 
 .0055 
 
 4.479 
 
 3.820 
 
 4.149 
 
 0.90 
 
 11/4 
 
 1.060 
 
 .095 
 
 3.330 
 
 3.927 
 
 0.882 
 
 .0061 
 
 1.227 
 
 .0085 
 
 3.604 
 
 3.056 
 
 3.330 
 
 1.15 
 
 11/2 
 
 1.310 
 
 .095 
 
 4.115 
 
 4.712 
 
 1.348 
 
 .0094 
 
 1.767 
 
 .0123 
 
 2.916 
 
 2.547 
 
 2.732 
 
 1.40 
 
 13/ 4 
 
 1.560 
 
 .095 
 
 4.901 
 
 5.498 
 
 1.911 
 
 .0133 
 
 2.405 
 
 .0167 
 
 2.448 
 
 2.183 
 
 2.316 
 
 1.65 
 
 2 
 
 1.810 
 
 .095 
 
 5.686 
 
 6.283 
 
 2.573 
 
 .0179 
 
 3.142 
 
 .0218 
 
 2.110 
 
 1.910 
 
 2.010 
 
 1.91 
 
 21/4 
 
 2.060 
 
 .095 
 
 6.472 
 
 7.069 
 
 3.333 
 
 .0231 
 
 3.976 
 
 .0276 
 
 1.854 
 
 1.698 
 
 1.776 
 
 2.16 
 
 21/2 
 
 2.282 
 
 .109 
 
 7.169 
 
 7.854 
 
 4.090 
 
 .0284 
 
 4.909 
 
 .0341 
 
 1.674 
 
 1.528 
 
 1.601 
 
 2.75 
 
 23/4 
 
 2.532 
 
 .109 
 
 7.955 
 
 8.639 
 
 5.035 
 
 .0350 
 
 5.940 
 
 .0412 
 
 1.508 
 
 1.389 
 
 1.449 
 
 3.04 
 
 3 
 
 2.782 
 
 .109 
 
 8.740 
 
 9.425 
 
 6.079 
 
 .0422 
 
 7.069 
 
 .0491 
 
 1.373 
 
 1.273 
 
 1.322 
 
 3.33 
 
 31/4 
 
 3.010 
 
 .120 
 
 9.456 
 
 10.210 
 
 7.116 
 
 .0494 
 
 8.296 
 
 .0576 
 
 1.269 
 
 1.175 
 
 1.222 
 
 3.96 
 
 31/2 
 
 3.260 
 
 .120 
 
 10.242 
 
 10.996 
 
 8.347 
 
 .0580 
 
 9.621 
 
 .0668 
 
 1.172 
 
 1.091 
 
 1.132 
 
 4.28 
 
 33/4 
 
 3.510 
 
 .120 
 
 11.027 
 
 11.781 
 
 9.676 
 
 .0672 
 
 1 1 .045 
 
 .0767 
 
 1.088 
 
 1.019 
 
 1.054 
 
 4.60 
 
 4 
 
 3.732 
 
 .134 
 
 11.724 
 
 12.566 
 
 10.939 
 
 .0760 
 
 12.566 
 
 .0873 
 
 1.024 
 
 0.955 
 
 0.990 
 
 5.47 
 
 41/2 
 
 4.232 
 
 .134 
 
 13.295 
 
 14.137 
 
 14.066 
 
 .0977 
 
 15.904 
 
 .1104 
 
 0.903 
 
 0.849 
 
 0.876 
 
 6.17 
 
 5 
 
 4.704 
 
 .148 
 
 14.778 
 
 15.708 
 
 17.379 
 
 .1207 
 
 19.635 
 
 .1364 
 
 0.812 
 
 0.764 
 
 0.788 
 
 7.58 
 
 6 
 
 5.670 
 
 .165 
 
 17.813 
 
 18.850 
 
 25.250 
 
 .1750 
 
 28.274 
 
 .1963 
 
 0.674 
 
 0.637 
 
 0.656 
 
 10.16 
 
 7 
 
 6.670 
 
 .165 
 
 20.954 
 
 21.991 
 
 34.942 
 
 .2427 
 
 38.485 
 
 .2673 
 
 0.573 
 
 0.546 
 
 0.560 
 
 11.90 
 
 8 
 
 7.670 
 
 .165 
 
 24.096 
 
 25.133 
 
 46.204 
 
 .3209 
 
 50.266 
 
 .3491 
 
 0.498 
 
 0.477 
 
 0.488 
 
 13.65 
 
 9 
 
 8.640 
 
 .180 
 
 27.143 
 
 28.274 
 
 58.630 
 
 .4072 
 
 63.617 
 
 .4418 
 
 0.442 
 
 0.424 
 
 0.433 
 
 16.76 
 
 10 
 
 9.594 
 
 .203 
 
 30.141 
 
 31.416 
 
 72.292 
 
 .5020 
 
 78.540 
 
 .5454 
 
 0.398 
 
 0.382 
 
 0.390 
 
 21.00 
 
 11 
 
 10.560 
 
 .220 
 
 33.175 
 
 34.558 
 
 87.583 
 
 .6082 
 
 95.033 
 
 .6600 
 
 0.362 
 
 0.347 
 
 0.355 
 
 25.00 
 
 12 
 
 11.542 
 
 .229 
 
 36.260 
 
 37.699 
 
 104.629 
 
 .7266 
 
 113.098 
 
 .7854 
 
 0.331 
 
 0.318 
 
 0.325 
 
 28.50 
 
 13 
 
 12.524 
 
 .238 
 
 39.345 
 
 40.841 
 
 123.190 
 
 .8555 
 
 132.733 
 
 .9217 
 
 0.305 
 
 0.294 
 
 0.300 
 
 32.06 
 
 14 
 
 13.504 
 
 .248 
 
 42.424 
 
 43.982 
 
 143.224 
 
 .9946 
 
 153.938 
 
 1 .0690 
 
 0.283 
 
 0.273 
 
 0.278 
 
 36.00 
 
 15 
 
 14.482 
 
 .259 
 
 45.497 
 
 47.124 
 
 164.721 
 
 1.1439 
 
 176.715 
 
 1 .2272 
 
 0.264 
 
 0.255 
 
 0.260 
 
 40.60 
 
 16 
 
 15.458 
 
 .271 
 
 48.563 
 
 50.266 
 
 187.671 
 
 1 .3033 
 
 201.062 
 
 1.3963 
 
 0.247 
 
 0.239 
 
 0.243 
 
 45.20 
 
 17 
 
 16.432 
 
 .284 
 
 51.623 
 
 53.407 
 
 212.066 
 
 1.4727 
 
 226.981 
 
 1.5763 
 
 0.232 
 
 0.225 
 
 0.229 
 
 49.90 
 
 18 
 
 17.416 
 
 .292 
 
 54.714 
 
 56.549 
 
 238.225 
 
 1.6543 
 
 254.470 
 
 1.767! 
 
 0.219 
 
 0.212 
 
 0.216 
 
 54.82 
 
 19 
 
 18.400 
 
 .300 
 
 57.805 
 
 59.690 
 
 265.905 
 
 1.8466 283.529 
 
 1.9690 
 
 0.208 
 
 0.201 
 
 0.205 
 
 59.48 
 
 20 
 
 19.360 
 
 .320 
 
 60.821 
 
 62.832 
 
 294.375 
 
 2.0443 314.159 
 
 2.1817 
 
 0.197 
 
 0.191 
 
 0.194 
 
 66.77 
 
 21 
 
 20.320 
 
 .340 
 
 63.837 65.974 324.294 
 
 2.2520'346.361 
 
 2.4053 0.188 
 
 0.182 
 
 0.185 73.40 
 
210 
 
 COLD-DRAWN SEAMLESS STEEL TUBES. 
 
 c 
 PI 
 
 £ 
 
 
 c3 
 0> 
 W) 
 
 O 
 
 m 
 
 a; 
 
 C 
 
 H 
 
 ~ | 
 
 
 
 
 O 
 
 Otsm 
 
 §£:* SKo 
 
 ?4 
 
 3SS 
 
 cfltfll^ ■"*■ "*• •t 
 
 s 
 
 
 
 
 •O 
 
 2S^ 
 
 O ^"OO — ir\<N 
 
 £ 
 
 tNI^r sO 
 
 O — rA vOOOia 
 
 & 
 
 
 
 
 o 
 
 OOO 
 
 rr, t)- Tf tt ^j- u-s 
 
 OOO OOO 
 
 00 
 
 o<Ni^r 
 
 vOOOO N^CO 
 
 £ 
 
 
 
 2S 
 
 in — OO 
 
 £-w 
 
 rn©r^ mOJ 
 
 oo 
 
 22£ 
 
 r^o^o 
 
 <si tj-it^ r^o r^ 
 
 ;? 
 
 
 
 £ So£ 
 
 ®gS 
 
 orvivo 
 
 O n-v \0 O <"A O 
 -OOm r^Ot^ 
 
 m vOCOO 
 
 ONM 
 
 t*rN 
 
 00 O — C4 -3- -O 
 
 
 
 # 
 
 
 
 
 
 ^KK 
 
 ££K KK£ 
 
 mou-s mm^ 
 
 inuMn 
 
 ^^■rr ^^ts 
 
 oo^O 
 
 — CMro 
 
 tirwo NOOO 
 
 
 
 s 
 
 
 
 £££ §SS 
 
 O ^j-i^. 
 
 o^i-t^ 
 
 — ^J-00 — tj- — 
 
 ^cnc^ ^-.n^ 
 
 r^oooo 
 
 o-o — 
 
 ™«-m^ tinN 
 
 
 
 £ 
 
 
 ss 
 
 s§s 55?; 
 
 — oo-r 
 
 0*m 
 
 O -O r*1 O -O O 
 
 ™™ 
 
 ™«™ ^-^-^ 
 
 * ,OIN 
 
 GO OOO 
 
 OO— «SN^ 
 
 1 
 
 
 £S2 
 
 — O O 0O*lT\ 
 
 £5;°. 
 
 O vOCN 
 
 cacmo or^^r 
 
 — ™ 
 
 ^™ m-r^p 
 
 ininv0 
 
 r^r^oo 
 
 »0>0 O-N 
 
 s 
 
 2 
 
 OOrAOO 
 
 £g£ 1222 
 
 2^2 
 
 22 — 
 
 c<-\ ■* ■<*■ T tt -*■ 
 
 vO — vO — vO ^O 
 
 
 
 
 ^•^^ 
 
 vO*IN 
 
 r*. oo oo o o o 
 
 1 
 
 o" 
 
 8^2 
 
 So©3 ^oo^ 
 
 £&£: 
 
 vOOOO 
 
 -* 00 <N! -O O O 
 
 
 
 <— C^(N C-JH»irf>i 
 
 cn-fT 
 
 U-MT1VO 
 
 ■O^O^ r^oooo 
 
 ;? 
 
 
 8^S 
 
 or^-* r-*.©f 
 
 r^©rr 
 
 ££3 
 
 s 
 
 o 
 
 
 c-qrsXN 
 
 <^<r^ 
 
 ^TT 
 
 u-, 
 
 8 
 
 Iks 
 
 t^O^S 
 
 |£<C- O — O 
 
 — vO — 
 
 2^ : 
 
 
 
 
 
 o 
 
 - 
 
 "-^ 
 
 NNN 
 
 m^ • 
 
 
 
 
 s 
 
 pi. 
 
 SSi 
 
 OMN^O rA CJ> vD 
 
 r<M> • 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 oo$ 
 
 ■— °. 
 
 o 
 
 r^o vO 
 
 S!c?S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 si 
 
 d 
 
 SSS 
 
 £s§ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 KjO 
 
 5S^ 
 
 cQ^S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 3-1 
 
 Sf£ 
 
 i? ;? 
 
 ir£r Jr ST ^ 
 
 £L 
 
 ««« 
 
 ^j- -r -<r • ->r m «"> 
 
RIVETED IRON PIPE. 
 
 211 
 
 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 
 feet, and diameter, d, in inches, multiply the length in feet by the diam- 
 eter in inches and by 0.2618. Or, S = 3 - 14 ^ dL = 0.2618 dL. For the 
 
 diameters in the table below, multiply the length in feet by the figures 
 given opposite the diameter. 
 
 Inches, 
 Diameter. 
 
 Square Feet 
 per Foot 
 Length. 
 
 Inches, 
 Diameter. 
 
 Square Feet 
 per Foot 
 Length. 
 
 Inches, 
 Diameter. 
 
 Square 
 Feet per 
 
 Foot 
 Length. 
 
 1/4 
 
 0.0654 
 
 21/4 
 
 0.5890 
 
 5 
 
 1 .3090 
 
 1/2 
 
 .1309 
 
 21/2 
 
 .6545 
 
 6 
 
 1.5708 
 
 3/ 4 
 
 .1963 
 
 23/ 4 
 
 .7199 
 
 7 
 
 1.8326 
 
 1 
 
 .2618 
 
 3 
 
 .7854 
 
 8 
 
 2.0944 
 
 U/4 
 
 .3272 
 
 31/4 
 
 .8508 
 
 9 
 
 2.3562 
 
 11/2 
 
 .3927 
 
 31/2 
 
 .9163 
 
 10 
 
 2.6180 
 
 13/4 
 
 .4581 
 
 3 3/4 
 
 .9817 
 
 11 
 
 2.8798 
 
 2 
 
 .5236 
 
 4 
 
 1.0472 
 
 12 
 
 3.1416 
 
 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 
 
 ^i §r ^ 
 
 Number Square Feet of 
 
 ^iljf 
 
 Iron Required to Make 
 
 6& ^» 
 
 Iron Required to Make 
 
 
 100 Lineal Feet Punched 
 
 100 Lineal Feet Punched 
 
 
 and Formed Sheets 
 
 and Formed Sheets 
 
 when put Together. 
 
 £ a "^ 
 
 when put Together. 
 
 2c ^ 
 
 
 Approxima 
 Rivets 1 ] 
 Required 
 Lineal Fee 
 and Form 
 
 
 
 Diam- 
 eter in 
 Inches. 
 
 Width 
 of Lap 
 
 in 
 Inches. 
 
 Square 
 Feet. 
 
 Diam- 
 eter in 
 Inches. 
 
 Width 
 of Lap 
 
 in 
 Inches. 
 
 Square 
 Feet. 
 
 Approxim 
 Rivets 1 
 Requirec 
 Lineal Fe 
 and Forr 
 
 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 
 
 H/2 
 
 178 
 
 1900 
 
 18 
 
 U/2 
 
 506 
 
 3200 
 
 7 
 
 H/2 
 
 206 
 
 2000 
 
 20 
 
 U/2 
 
 562 
 
 3500 
 
 8 
 
 H/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 
 
 U/2 
 
 314 
 
 2500 
 
 28 
 
 U/2 
 
 779 
 
 4400 
 
 12 
 
 1 1/2 
 
 343 
 
 2600 
 
 30 
 
 U/2 
 
 836 
 
 4600 
 
 13 
 
 U/2 
 
 369 
 
 2700 
 
 36 
 
 U/2 
 
 998 
 
 5200 
 
212 
 
 MATERIALS. 
 
 Weight and Strength of Riveted Hydraulic Pipe. 
 
 (Abner Doble Co., San Francisco, 1906.) 
 S = Safe head in feet. W = "Weight in pounds. 
 
 Thickne 
 
 
 
 
 
 
 
 
 4-in. 
 
 5-in. 
 
 
 7-m. 
 
 8-in. 
 
 Gauge. 
 
 In. 
 
 
 
 
 
 
 
 
 S 
 
 W 
 
 8 
 
 W 
 
 8 
 
 W 
 
 ,S' 
 
 W 
 
 8 
 
 W 
 
 18 
 
 0.050 
 
 555 
 
 2.8 
 
 444 
 
 3.5 
 
 370 
 
 4.1 
 
 317 
 
 4.7 
 
 277 
 
 5.3 
 
 16 
 
 .062 
 
 693 
 
 3.7 
 
 555 
 
 4.4 
 
 462 
 
 5.2 
 
 396 
 
 5.9 
 
 346 
 
 6.7 
 
 14 
 
 .078 
 
 866 
 
 4.4 
 
 693 
 
 5.5 
 
 578 
 
 6.4 
 
 495 
 
 7.3 
 
 433 
 
 8.2 
 
 12 
 
 .109 
 .140 
 
 
 
 
 
 .808. 
 
 8.8 
 
 693 
 
 10.0 
 
 606 
 777 
 
 11.5 
 
 10 
 
 
 
 
 
 14.5 
 
 
 9-in. 
 
 10-in. 
 
 11-in. 
 
 12-in. 
 
 14-in. 
 
 16 
 
 0.062 
 
 308 
 
 7.5 
 
 277 
 
 8.3 
 
 252 
 
 9.0 
 
 231 
 
 9.9 
 
 198 
 
 11.4 
 
 14 
 
 .078 
 
 385 
 
 9.2 
 
 346 
 
 10.2 
 
 314 
 
 11.0 
 
 289 
 
 12.2 
 
 248 
 
 14.0 
 
 12 
 
 .109 
 
 539 
 
 12.6 
 
 485 
 
 14.2 
 
 439 
 
 15.2 
 
 404 
 
 16.7 
 
 346 
 
 19.2 
 
 10 
 
 .140 
 
 693 
 
 16.4 
 
 623 
 
 18.0 
 
 565 
 
 19.3 
 
 519 
 
 21.0 
 
 445 
 
 24.2 
 
 8 
 
 .171 
 3/16 
 
 
 
 761 
 832 
 
 21.5 
 23.5 
 
 693 
 757 
 
 23.5 
 25.5 
 
 635 
 693 
 
 25.6 
 27.7 
 
 543 
 594 
 
 29.3 
 
 
 
 
 31.9 
 
 
 
 
 
 
 15-in. 
 
 16-in. 
 
 18-in. 
 
 20-in. 
 
 22-in. 
 
 16 
 
 0.062 
 
 185 
 
 12.0 
 
 173 
 
 12.8 
 
 154 
 
 14.5 
 
 139 
 
 16.0 
 
 126 
 
 17.7 
 
 14 
 
 .078 
 
 231 
 
 14.0 
 
 217 
 
 16.0 
 
 193 
 
 17.8 
 
 173 
 
 19.6 
 
 157 
 
 21.2 
 
 12 
 
 .109 
 
 323 
 
 20.3 
 
 303 
 
 21.5 
 
 270 
 
 24.4 
 
 242 
 
 27.3 
 
 220 
 
 29.2 
 
 10 
 
 .140 
 
 415 
 
 25.7 
 
 388 
 
 27.3 
 
 346 
 
 30.7 
 
 311 
 
 34.5 
 
 283 
 
 37.1 
 
 8 
 
 .171 
 
 507 
 
 30.4 
 
 475 
 
 33.3 
 
 422 
 
 38.4 
 
 380 
 
 41.5 
 
 346 
 
 45.2 
 
 
 3/16 
 
 555 
 
 34.0 
 
 520 
 
 36.0 
 
 462 
 
 40.5 
 
 416 
 
 45.0 
 
 378 
 
 49.0 
 
 
 1/4 
 
 739 
 
 45.5 
 
 693 
 
 48.2 
 
 616 
 
 54.1 
 
 555 
 
 59.6 
 
 505 
 
 65 5 
 
 
 5 /l6 
 
 3/8 
 7/16 
 
 
 
 866 
 
 60.6 
 
 770 
 924 
 
 67.7 
 81.3 
 
 693 
 831 
 970 
 
 74.6 
 89.5 
 105.0 
 
 631 
 
 757 
 883 
 
 81.5 
 
 
 
 
 98.0 
 
 
 
 
 
 
 114.5 
 
 
 24-in. 
 
 26-in. 
 
 30-in. 
 
 36-in. 
 
 42-in. 
 
 14 
 
 0.078 
 
 144 
 
 23.7 
 
 133 
 
 25.5 
 
 
 
 
 
 
 
 12 
 
 .109 
 
 202 
 
 32.5 
 
 186 
 
 34.5 
 
 162 
 
 39.5 
 
 134 
 
 47.7 
 
 
 
 10 
 
 .140 
 
 259 
 
 40.5 
 
 239 
 
 43.7 
 
 208 
 
 50.3 
 
 173 
 
 60.0 
 
 148 
 
 69.5 
 
 8 
 
 .171 
 
 317 
 
 49.2 
 
 293 
 
 53.0 
 
 254 
 
 60.5 
 
 211 
 
 75.0 
 
 181 
 
 84.7 
 
 
 3/16 
 
 346 
 
 53.0 
 
 320 
 
 57.5 
 
 277 
 
 65.5 
 
 231 
 
 79.0 
 
 198 
 
 91.5 
 
 
 1/4 
 
 462 
 
 71.0 
 
 427 
 
 76.5 
 
 370 
 
 87.5 
 
 308 
 
 105.5 
 
 264 
 
 122.0 
 
 
 5 /l6 
 
 578 
 
 88.5 
 
 533 
 
 95.5 
 
 462 
 
 109.0 
 
 385 
 
 130.0 
 
 330 
 
 151.0 
 
 
 3/8 
 
 693 
 
 106.0 
 
 640 
 
 114.5 
 
 555 
 
 130.5 
 
 462 
 
 156.0 
 
 396 
 
 180.5 
 
 
 Vl 6 
 
 808 
 
 124.5 
 
 747 
 
 134.0 
 
 647 
 
 151.5 
 
 539 
 
 182.5 
 
 462 
 
 211.0 
 
 
 1/2 
 
 924 
 
 142.0 
 
 854 
 
 153.0 
 
 739 
 
 174.5 
 
 616 
 
 207.0 
 
 528 
 
 240.5 
 
 
 5/8 
 3/4 
 7/8 
 
 
 
 1066 
 
 191.0 
 
 924 
 1108 
 
 220.0 
 264.0 
 
 770 
 924 
 1078 
 
 260.0 
 312.5 
 366.0 
 
 660 
 792 
 924 
 
 302.0 
 
 
 
 
 361.5 
 
 
 
 
 
 
 424.0 
 
 
 
 
 
 
 
 
 
 48-in. 
 
 54-in. 
 
 60-in. 
 
 66-in. 
 
 72-in. 
 
 8 
 
 0.171 
 
 158 
 
 98.0 
 
 141 
 
 110.0 
 
 127 
 
 121.0 
 
 
 
 
 
 
 3/16 
 
 173 
 
 106.0 
 
 154 
 
 119.0 
 
 139 
 
 131.0 
 
 127 
 
 144.5 
 
 115 
 
 158.0 
 
 
 1/4 
 
 231 
 
 142.0 
 
 205 
 
 159.0 
 
 185 
 
 175.0 
 
 168 
 
 193.0 
 
 154 
 
 211.0 
 
 
 5 /l6 
 
 289 
 
 177.0 
 
 256 
 
 198.0 
 
 231 
 
 218.0 
 
 210 
 
 239.0 
 
 193 
 
 260.0 
 
 
 3/8 
 
 346 
 
 212.0 
 
 308 
 
 237.0 
 
 277 
 
 261.0 
 
 252 
 
 286.5 
 
 231 
 
 312.0 
 
 
 7/16 
 
 404 
 
 249.0 
 
 359 
 
 277.5 
 
 323 
 
 303.0 
 
 294 
 
 334.0 
 
 270 
 
 365.0 
 
 
 1/2 
 
 462 
 
 284.0 
 
 411 
 
 316.5 
 
 370 
 
 349.0 
 
 336 
 
 382.0 
 
 308 
 
 414.0 
 
 
 5/8 
 
 578 
 
 354.0 
 
 513 
 
 399.5 
 
 462 
 
 440.0 
 
 420 
 
 480.0 
 
 385 
 
 520.0 
 
 
 3/- 4 
 
 693 
 
 430.0 
 
 616 
 
 479.5 
 
 555 
 
 528.0 
 
 504 
 
 577.5 
 
 462 
 
 624.0 
 
 
 7/8 
 
 808 
 
 505.0 
 
 719 
 
 563.5 
 
 647 
 
 620.0 
 
 588 
 
 677.0 
 
 539 
 
 732.0 
 
 
 1 
 
 924 
 
 582.0 
 
 822 
 
 647.5 
 
 739 
 
 712.0 
 
 672 
 
 777.5 
 
 616 
 
 840.0 
 
 Pipe made of sheet steel plate, ultimate tensile strength 55,000 lbs. 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. 
 
SPIRAL RIVETED PIPE. 
 
 213 
 
 WEIGHT OF ONE SQUARE FOOT OF SHEET-IRON FOR 
 RIVETED PIPE. 
 
 Thickness by the Birmingham Wire-Gauge. 
 
 No. of 
 Gauge. 
 
 Weight 
 in Lbs., 
 Black. 
 
 Weight 
 in Lbs., 
 
 No. of 
 
 Thick- 
 
 Galvan- 
 ized. 
 
 Gauge. 
 
 In. 
 
 0.91 
 
 18 
 
 0.049 
 
 1.16 
 
 16 
 
 .065 
 
 1.40 
 
 14 
 
 .083 
 
 1.67 
 
 12 
 
 .10? 
 
 Weight 
 in Lbs., 
 Black. 
 
 Weight 
 
 in Lbs., 
 
 Galvan- 
 
 zed. 
 
 22 
 20 
 
 0.018 
 .022 
 .028 
 .035 
 
 1.82 
 2.50 
 3.12 
 4.37 
 
 2.16 
 2.67 
 3.34 
 4.73 
 
 SPIRAL RIVETED PIPE. 
 
 Approximate Bursting Strength. Pounds per Square Inch. 
 
 (American Spiral Pipe Works.) 
 
 Inside 
 Diam. 
 Inches. 
 
 
 
 Thickness. — U.S. Standard Gauge. 
 
 
 
 
 
 
 
 
 
 
 
 No.20. 
 
 No, 18. 
 
 No. 16. 
 
 No. 14. 
 
 No. 12. 
 
 No. 10. 
 
 No, 8. 
 
 No. 6. 
 
 No. 3 
 (1/4"). 
 
 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 
 
214 
 
 MATERIALS. 
 
 FORGED STEEL FLANGES FOR RIVETED PIPE. 
 
 (American Spiral Pipe Works.) 
 
 1 . 8 
 
 ® m OC 
 
 3ai 
 
 ci"* 3 
 
 Q 0> 
 
 
 
 'o^ 
 
 laJ 
 
 
 <D 
 
 6 & 
 
 
 *" " 
 
 3 S g 
 
 Isl 
 
 °5 
 pq 
 
 3 3/, 6 
 
 fq OH 
 
 
 .2pq 
 
 | S - 
 
 3-2 C 
 
 
 35 OKH 
 
 So 
 12 
 
 S"o 
 
 •-PQ 
 
 3 
 
 6 
 
 4 3/ 4 
 
 4 
 
 7/16 
 
 16 
 
 211/4 
 
 161/ 4 
 
 191/4 
 
 1/? 
 
 4 
 
 7 
 
 43/16 
 
 >Wl« 
 
 8 
 
 V/16 
 
 18 
 
 231/4 
 
 IS-Vlfi 
 
 2ll/ 4 
 
 16 
 
 5/8 
 
 5 
 
 8 
 
 53/lfi 
 
 61Vt« 
 
 8 
 
 '//in 
 
 20 
 
 25l/ 4 
 
 20o/ 1fi 
 
 231/s 
 
 16 
 
 5/8 
 
 6 
 
 9 
 
 63/16 
 
 r// H 
 
 8 
 
 1/7 
 
 22 
 
 281/4 
 
 223/ 8 
 
 26 
 
 16 
 
 5/8 
 
 7 
 
 10 
 
 73/ 1fi 
 
 9 
 
 8 
 
 i/^ 
 
 24 
 
 30 
 
 243/ 8 
 
 273/4 
 
 16 
 
 5/8 
 
 8 
 
 11 
 
 8 3/ t 6 
 
 10 
 
 8 
 
 V? 
 
 26 
 
 32 
 
 263/ 8 
 
 293/ 4 
 
 24 
 
 3/4 
 
 9 
 
 13 
 
 91/4 
 
 IU/4 
 
 8 
 
 V? 
 
 28 
 
 34 
 
 283/ 8 
 
 3l3/ 4 
 
 28 
 
 3/4 
 
 10 
 
 14 
 
 101/4 
 
 l2 1/ 4 
 
 8 
 
 1/7! 
 
 30 
 
 36 
 
 303/ 8 
 
 333/4 
 
 28 
 
 3/4 
 
 11 
 
 15 
 
 IU/4 
 
 13 3/8 
 
 12 
 
 1/?, 
 
 32 
 
 38 
 
 323/ s 
 
 33 3/ 4 
 
 28 
 
 3/4 
 
 12 
 
 16 
 
 l21/ 4 
 
 14 1/4 
 
 12 
 
 1/?, 
 
 34 
 
 40 
 
 343/ 8 
 
 37 3/ 4 
 
 28 
 
 3/4 
 
 I) 
 
 17 
 
 131/4 
 
 l3 1/ 4 
 
 12 
 
 V? 
 
 36 
 
 42 
 
 3&3/ 8 
 
 393/ 4 
 
 32 
 
 3/4 
 
 14 
 
 18 
 
 141/4 
 
 I6I/4 
 
 12 
 
 1/? 
 
 40 
 
 46 
 
 4l)3/ 8 
 
 433/ 4 
 
 32 
 
 3/4 
 
 13 
 
 19 
 
 ID 1/4 
 
 U''/16 
 
 12 
 
 V2 
 
 
 
 
 
 
 
 BENT AND COILED PIPES. 
 
 (National Pipe Bending Co., New Haven, Conn.) 
 Coils and Bends of Iron and Steel Pipe. 
 
 Size of pipe Inches 
 
 Least outside diameter 
 of coil Inches 
 
 1/4 
 2 
 
 3/8 
 
 21/2 
 
 1/2 
 31/2 
 
 3/4 
 
 41/2 
 
 1 
 6 
 
 11/4 
 
 8 
 
 11/2 
 12 
 
 2 
 16 
 
 21/2 
 24 
 
 3 
 
 32 
 
 Size of pipe Inches 
 
 Least outside diameter 
 of coil Inches 
 
 31/2 
 40 
 
 4 
 
 48 
 
 41/2 
 52 
 
 5 
 
 58 
 
 6 
 66 
 
 7 
 
 80 
 
 8 
 92 
 
 9 
 
 105 
 
 10 
 130 
 
 12 
 
 156 
 
 Lengths continuous welded up to 3-in. pipe or coupled as desired. 
 
 Coils and Bends of Drawn Brass and Copper Tubing. 
 
 Size of tube, outside diameter. .Inches 
 Least outside diameter of coil. .Inches 
 
 1/4 
 1 
 
 3/8 
 U/2 
 
 V 2 
 2 
 
 5/8 
 21/2 
 
 3/4 1 
 3 4 
 
 11/4 
 6 
 
 13/8 
 7 
 
 Size of tube, outside diameter. .Inches 
 Least outside diameter of coil. .Inches 
 
 I l/ 2 
 8 
 
 1 5/8 
 9 
 
 13/4 
 10 
 
 2 
 
 12 
 
 21/4 
 14 
 
 23/s 
 16 
 
 21/2 
 18 
 
 23/4 
 20 
 
 Lengths continuous brazed, soldered, or coupled as desired. 
 
SEAMLESS BRASS TUBES. 
 
 215 
 
 90° Bends in Iron or Steel Pipe. 
 
 (Whitlock Goil Pipe Co., Hartford, Conn.) 
 
 
 3 
 
 12 
 3 
 15 
 
 31/2 
 13 
 
 31/ 2 
 161/2 
 
 4 
 15 
 
 31/2 
 I8I/2 
 
 41/2 
 17 
 
 4 
 21 
 
 5 
 
 20 
 4 
 24 
 
 6 
 
 23 
 4 
 27 
 
 7 
 
 8 
 
 30 
 5 
 33 
 
 9 
 36 
 
 5 
 41 
 
 10 
 
 42 
 6 
 48 
 
 f? 
 
 
 26 
 5 
 31 
 
 48 
 
 End 
 
 6 
 
 
 54 
 
 
 
 Size pipe, O.D 
 
 14 
 60 
 7 
 67 
 
 16 
 70 
 7 
 77 
 
 18 
 80 
 7 
 87 
 
 20 
 90 
 8 
 98 
 
 22 
 
 100 
 
 8 
 
 108 
 
 24 
 
 110 
 
 8 
 
 118 
 
 26 
 120 
 
 10 
 130 
 
 28 
 140 
 
 10 
 150 
 
 30 
 160 
 
 End 
 
 10 
 
 
 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. 
 
 Flexibility of Pipe Bends. (Valve World, Feb., 1906.) — So far as 
 can be ascertained, no thorough attempt has ever been made to determine 
 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 have adopted five diameters of the pipe as a standard 
 radius, which come nearer than any other to suiting average requirements, 
 and at the same time produce 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 lbs. 
 per foot, with extra heavy cast-iron flanges screwed on and refaced. It 
 was connected by elbows to two straight pipes, N, 67 ft., >S, 82 ft., which 
 were firmly anchored at their outer ends. Steam was then let into the 
 pipes with results as follows: 
 
 m. 
 
 80 lbs. Expansion, Total 1 7/ 8 
 
 50 lbs. Expansion, iV, 7/ 8) S, H/s. Total 2 
 
 100 lbs. Expansion, JV, 13/i 6 , S, H/2- Total 2H/16 in. 
 
 150 lbs. Expansion, N, U/8, S, 17/ 8 . Total 3 
 
 200 lbs. Expansion, JV, H/2, S, 17/ 8 . Total 33/ 8 
 
 Flange broke. 
 
 Flange broke at 
 208 lbs. 
 
 Quarter bend, full weight pipe. Straight pipe 148 ft., one end. 80 lbs. 
 Total expansion 13/ 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 lty 8 in. 
 
 SEAMLESS BRASS TUBE, IRON-PIPE SIZES. 
 
 (For actual dimensions see tables of Wrought-iron Pipe.) 
 
 Nominal 
 
 Weight 
 
 Nom. 
 
 Weight 
 
 Nom. 
 
 Weight 
 
 Nom. 
 
 Weight 
 
 Size. 
 
 per Foot. 
 
 Size. 
 
 per Foot. 
 
 Size. 
 
 per Foot. 
 
 Size. 
 
 per Foot. 
 
 ins. 
 
 lbs. 
 
 ins. 
 
 lbs. 
 
 ins. 
 
 lbs. 
 
 ins. 
 
 lbs. 
 
 1/8 
 
 .25 
 
 3/4 
 
 1.25 
 
 2 
 
 4.0 
 
 4 
 
 12.70 
 
 1/4 
 
 .43 
 
 1 
 
 1.70 
 
 21/2 
 
 5.75 
 
 41/2 
 
 13.90 
 
 3/8 
 
 .62 
 
 U/4 
 
 2.50 
 
 3 
 
 8.30 
 
 5 
 
 15.75 
 
 1/2 
 
 .90 
 
 11/2 
 
 3. 
 
 31/2 
 
 10.90 
 
 6 
 
 18.31 
 
216 
 
 MATERIALS. 
 
 WEIGHT PER FOOT OF SEA31LESS BRASS TUBES. 
 
 (Waterbury Brass Co., 1908.) 
 
 A.W.G. 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 .24 
 
 26 
 
 In* 
 
 .20431 
 
 .16202 
 
 .12849 
 
 .10189 
 
 
 .064084 
 
 .05082 
 
 .04030; 
 
 .03196: 
 
 •025345 
 
 .0201 
 
 .01594 
 
 In.t 
 
 V8 
 
 
 
 
 
 
 
 0.043 
 
 0.039 
 
 0.034 
 
 0.028 
 
 0.024 
 
 0.020 
 
 3/16 
 
 
 
 
 
 
 0.090 
 
 .08 
 
 .068 
 
 .057 
 
 .047 
 
 .038 
 
 .032 
 
 1/4 
 
 
 
 
 0.'l74 
 
 0J6 
 
 .14 
 
 .12 
 
 .097 
 
 .080 
 
 .065 
 
 .053 
 
 .043 
 
 5/16 
 
 
 
 
 .25 
 
 .22 
 
 .18 
 
 .15 
 
 .13 
 
 .104 
 
 .084 
 
 .067 
 
 .054 
 
 3/8 
 
 
 
 0.36 
 
 .32 
 
 .27 
 
 .23 
 
 .19 
 
 .15 
 
 .126 
 
 .102 
 
 .082 
 
 .066 
 
 1/2 
 
 
 0.63 
 
 .55 
 
 .47 
 
 .39 
 
 .32 
 
 .26 
 
 .21 
 
 .17 
 
 .139 
 
 .111 
 
 .089 
 
 5/8 
 
 0.99 
 
 .87 
 
 .74 
 
 .61 
 
 .51 
 
 .42 
 
 .34 
 
 .27 
 
 .22 
 
 .174 
 
 .140 
 
 .112 
 
 3/ 4 
 
 1.29 
 
 1.10 
 
 .92 
 
 .76 
 
 .62 
 
 .51 
 
 .41 
 
 .33 
 
 .26 
 
 .211 
 
 .169 
 
 .135 
 
 7/8 
 
 1.58 
 
 1.33 
 
 1.11 
 
 .91 
 
 .74 
 
 .60 
 
 .48 
 
 .39 
 
 .31 
 
 .248 
 
 .198 
 
 .158 
 
 1 
 
 1.88 
 
 1.57 
 
 1.29 
 
 1.06 
 
 .86 
 
 .69 
 
 .56 
 
 .45 
 
 .36 
 
 .285 
 
 .227 
 
 .181 
 
 U/8 
 
 2.17 
 
 1.80 
 
 1.48 
 
 1.20 
 
 .97 
 
 .79 
 
 .63 
 
 .50 
 
 .40 
 
 .321 
 
 .256 
 
 
 11/4 
 
 2.47 
 
 2.03 
 
 1.66 
 
 1.35 
 
 1.09 
 
 .88 
 
 .70 
 
 .56 
 
 .45 
 
 .358 
 
 .285 
 
 
 13/8 
 
 2.76 
 
 2.27 
 
 1.85 
 
 1.50 
 
 1.21 
 
 .97 
 
 .78 
 
 .62 
 
 .50 
 
 .395 
 
 .314 
 
 
 H/2 
 
 3.05 
 
 2.50 
 
 2.03 
 
 1.64 
 
 1.32 
 
 1.06 
 
 .85 
 
 .68 
 
 .54 
 
 .43 
 
 .343 
 
 
 13/4 
 
 3.64 
 
 2.97 
 
 2.40 
 
 1.94 
 
 1.56 
 
 1.25 
 
 1.00 
 
 .79 
 
 .63 
 
 .50 
 
 .401 
 
 
 2 
 
 4.23 3.44 2.77 2.23 1.79 1.43 
 
 1.14 .91 .73 
 
 .58 
 
 .459 
 
 
 A.W.G. 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 In* 
 
 .25763 
 
 .20431 
 
 .X6202 
 
 .12849 
 
 .0x89 
 
 .080808 
 
 .064084 
 
 .05082 
 
 .040303 
 
 •025347 
 
 .01594 
 
 TnT 
 21/4 
 
 5.92 
 
 4.82 
 
 3.90 
 
 3.15 
 
 2.53 
 
 2.02 
 
 1.62 
 
 1.29 
 
 1.03 
 
 0.82 
 
 0.65 
 
 
 21/2 
 
 6.67 
 
 5.41 
 
 4.37 
 
 3.52 
 
 2.82 
 
 2.26 
 
 1.80 
 
 1.44 
 
 1.14 
 
 .91 
 
 
 73 
 
 
 23/4 
 
 7.41 
 
 6.00 
 
 4.84 
 
 3.89 
 
 3.11 
 
 2.49 
 
 1.99 
 
 1.58 
 
 1.26 
 
 1.00 
 
 
 80 
 
 
 3 
 
 8.16 
 
 6.59 
 
 5.31 
 
 4.26 
 
 3.41 
 
 2.72 
 
 2.17 
 
 1.73 
 
 1.38 
 
 1.09 
 
 
 87 
 
 
 31/4 
 
 8.90 
 
 7.18 
 
 5.77 
 
 4.63 
 
 3.70 
 
 2.96 
 
 2.36 
 
 1.88 
 
 1.49 
 
 1.19 
 
 
 ■ 
 
 
 31/2 
 
 9.64 
 
 7.77 
 
 6.24 
 
 5.00 
 
 4.00 
 
 3.19 
 
 2.54 
 
 2.02 
 
 1.61 
 
 1.28 
 
 1 
 
 02 
 
 
 33/4 
 
 10.39 
 
 8.36 
 
 6.71 
 
 5.37 
 
 4.29 
 
 3.42 
 
 2.73 
 
 2.17 
 
 1.72 
 
 1.37 
 
 1 
 
 09 
 
 
 4 
 
 11.13 
 
 8.95 
 
 7.18 
 
 5.74 
 
 4.58 
 
 3.66 
 
 2.91 
 
 2.32 
 
 1.84 
 
 1.46 
 
 1 
 
 16 
 
 
 41/4 
 
 11.87 
 
 9.54 
 
 7.64 
 
 6.11 
 
 4.88 
 
 3.89 
 
 3.10 
 
 2.46 
 
 1.96 
 
 1.55 
 
 
 
 
 41/2 
 
 12.62 
 
 10.13 
 
 8.11 
 
 6.48 
 
 5.17 
 
 4.12 
 
 3.28 
 
 2.61 
 
 2.07 
 
 1.64 
 
 
 
 
 43/4 
 
 13.36 
 
 10.72 
 
 8.58 
 
 6.85 
 
 5.47 
 
 4.36 
 
 3.47 
 
 2.76 
 
 2.19 
 
 1.74 
 
 
 
 
 5 
 
 14.10 
 
 11.31 
 
 9.05 
 
 7.22 
 
 5.76 
 
 4.59 
 
 3.65 
 
 2.90 
 
 2.31 
 
 1.83 
 
 
 
 
 51/4 
 
 14.85 
 
 11.90 
 
 9.51 
 
 7.59 
 
 6.05 
 
 4.82 
 
 3.84 
 
 3.05 
 
 2.42 
 
 
 
 
 
 51/2 
 
 15.59 
 
 12.49 
 
 9.98 
 
 7.97 
 
 6.35 
 
 5.06 
 
 4.02 
 
 3.20 
 
 2.54 
 
 
 
 
 
 53/4 
 
 16.33 
 
 13.08 
 
 10.45 
 
 8.34 
 
 6.64 
 
 5.29 
 
 4.21 
 
 3.34 
 
 2.65 
 
 
 
 
 
 6 
 
 17.08 
 
 13.67 
 
 10.92 
 
 8.71 
 
 6.94 
 
 5.52 
 
 4.39 
 
 3.49 
 
 2.77 
 
 
 
 
 
 6I/4 
 
 17.82 
 
 14.26 
 
 11.38 
 
 9.08 
 
 7.23 
 
 5.76 
 
 4.58 
 
 3.64 
 
 
 
 
 
 
 61/ 2 
 
 18.56 
 
 14.84 
 
 11.85 
 
 9.45 
 
 7.52 
 
 5.99 
 
 4.76 
 
 3.78 
 
 
 
 
 
 
 63/ 4 
 
 19.31 
 
 15.43 
 
 12.32 
 
 9.82 
 
 7.82 
 
 6.22 
 
 4.95 
 
 3.93 
 
 
 
 
 
 
 7 
 
 20.05 
 
 16.02 
 
 12.79 
 
 10.19 
 
 8.1! 
 
 6.46 
 
 5.13 
 
 4.08 
 
 
 
 
 
 
 71/4 
 
 20.79 
 
 16.61 
 
 13.25 
 
 10.56 
 
 8.41 
 
 6.69 
 
 5.32 
 
 
 
 
 
 
 
 71/2 
 
 21.54 
 
 17.20 
 
 13.72 
 
 10.93 
 
 8.70 
 
 6.92 
 
 5.50 
 
 
 
 
 
 
 
 73/4 
 
 22.28 
 
 17.79 
 
 14.19 
 
 11.30 
 
 8.99 
 
 7.15 
 
 5.69 
 
 
 
 
 
 
 
 8 
 
 23.03 
 
 18.48 
 
 14.66 11.67 9.29 7.39 5.87 ... 
 
 
 
 
 
 * Thickness of Wall. t Outside diameter. 
 
 Seamless brass tubes are made from l/s in. to 1 in. outside diameter, 
 
 varying by Vi6in., and from lVsin. to 8 in. outside diameter, varying by 
 
 1/8 in., and in all gauges from No. 2 to No. 26 A. W. G. within 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 gauge numbers. 
 
 For copper tubing add 5% to the weights given above. 
 
 A.W.G. 2 4 6 8 10 12 14 16 18 20 22 24 26 
 
 Lb.pe 
 
 •ft. 1. 
 
 532 .9( 
 
 37.60 
 
 61 .38 
 
 1 .239 
 
 7.1507 
 
 .0948 . 
 
 0596 .C 
 
 375 .02 
 
 36 .014 
 
 1 .00 
 
 93 
 
 .0059 
 
 i 
 
WEIGHT OF LEAD PIPE. 
 
 217 
 
 LEAD AND TIN LINED LEAD PIPE. 
 
 (United Lead Co., New York, 1908.) 
 
 
 
 
 m ^ 
 
 
 
 
 jg a 
 
 Cali- 
 ber. 
 
 Letter. 
 
 Weight 
 per Foot 
 and Rod. 
 
 
 Cali- 
 ber. 
 
 Letter. 
 
 Weight 
 per Foot. 
 
 .2 2 
 
 3/ 8 in. 
 
 E 
 
 7 lbs. per rod 
 
 5 
 
 1 in. 
 
 E 
 
 1 1/2 lbs. per foot 
 
 10 
 
 
 D 
 
 I oz. per foot 
 
 6 
 
 
 D 
 
 2 
 
 
 
 11 
 
 •* 
 
 C 
 
 12" " " 
 
 8 
 
 
 C 
 
 21/2 
 
 ' " 
 
 
 14 
 
 " 
 
 B 
 
 1 lb. " " 
 
 12 
 
 
 B 
 
 31/4 
 
 
 
 17 
 
 
 A 
 
 1 1/4 " " " 
 
 16 
 
 
 A 
 
 4 
 
 
 
 21 
 
 •« 
 
 AA 
 
 1 1/2 " " " 
 
 19 
 
 
 AA 
 
 43/4 
 
 ' " ' 
 
 
 24 
 
 
 AAA 
 
 1 3/4 " " » 
 
 27 
 
 
 AAA 
 
 6 
 
 
 
 30 
 
 7/16 in. 
 
 
 13oz. " " 
 
 1 lb. " " 
 
 
 1 V4 in. 
 
 E 
 D 
 
 2 
 
 21/2 
 
 
 
 10 
 12 
 
 1/2 in. 
 
 E 
 
 9 lbs. per rod 
 
 7 
 
 
 C 
 
 3 
 
 
 
 14 
 
 
 D 
 
 3/4 lb. per foot 
 
 9 
 
 
 B 
 
 33/ 4 - 
 
 
 
 16 
 
 
 C 
 
 1 " " " 
 
 11 
 
 
 A 
 
 43/4 
 
 
 
 19 
 
 " 
 
 B 
 
 1 1/4 " " " 
 
 13 
 
 
 AA 
 
 53/4 
 
 
 
 25 
 
 " 
 
 Spc'l 
 
 ll/ 2 " " " 
 
 14 
 
 
 AAA 
 
 63/4 
 
 
 
 28 
 
 J " 
 
 A 
 
 13/ 4 " " «« 
 
 16 
 
 U/2 in. 
 
 E 
 
 3 
 
 
 
 12 
 
 " 
 
 AA 
 
 2 " " " 
 
 19 
 
 
 D 
 
 31/2 
 
 
 
 14 
 
 
 Spc'l 
 
 21/ 2 " " " 
 
 23 
 
 
 C 
 
 41/4 
 
 
 
 17 
 
 
 AAA 
 
 3 ■« ,, « 
 
 25 
 
 
 B 
 
 5 
 
 
 
 19 
 
 5/8 in. 
 
 E 
 
 I 2 " per rod 
 
 8 
 
 " 
 
 A 
 
 6V2 
 
 
 
 23 
 
 
 D 
 
 1 " per foot 
 
 9 
 
 " 
 
 AA 
 
 71/2 
 
 
 
 25 
 
 *• 
 
 C 
 
 11/2" " " 
 
 13 
 
 
 Spc'l 
 
 8 
 
 
 
 27 
 
 " 
 
 B 
 
 2 " " " 
 
 16 
 
 
 AAA 
 
 8 1/2 
 
 
 
 28 
 
 " 
 
 A 
 
 21/2 " " " 
 
 20 
 
 13/4 in. 
 
 D 
 
 4 ' 
 
 
 
 13 
 
 " 
 
 AA 
 
 23/4 " " " 
 
 22 
 
 
 C 
 
 B 
 
 Spc'l 
 
 A 
 
 5 ' 
 
 6 * 
 6V2; 
 
 
 
 17 
 19 
 21 
 23 
 
 3/4 in. 
 
 AAA 
 
 E 
 
 31/ 2 " " «' 
 1 " " " 
 
 25 
 . 8 
 
 
 
 
 
 D 
 
 1 1/4 " " " 
 
 10 
 
 " 
 
 AA 
 
 81/ 2 * 
 
 
 
 27 
 
 " 
 
 C 
 
 13/4" " » 
 
 12 
 
 " 
 
 AAA 
 
 10 ' 
 
 1 •< 
 
 
 30 
 
 •' 
 
 Spc'l 
 
 2 " " " 
 
 14 
 
 2 in. 
 
 D 
 
 43/4' 
 
 
 
 15 
 
 " 
 
 B 
 A 
 
 21/4" " " 
 3 .. .. „ 
 
 16 
 20 
 
 ;; 
 
 C 
 B 
 A 
 
 6 
 
 7 ' 
 
 8 ' 
 
 
 
 18 
 
 22 
 25 
 
 
 AA 
 
 31/2" " " 
 
 23 
 
 
 AA 
 
 9 ' 
 
 
 
 27 
 
 
 AAA 
 
 43/4 " " " 
 
 30 
 
 
 AAA 
 
 113/4" " " 
 
 30 
 
 WEIGHT OF LEAD PIPE WHICH SHOULD BE USED FOR A 
 GIVEN HEAD OF WATER. 
 
 (United Lead Co., New York, 1908.) 
 
 Head or 
 Number 
 
 Pres- 
 sure 
 per sq. 
 inch. 
 
 Caliber and Weight per Foot. 
 
 of Feet 
 Fall. 
 
 Letter. 
 
 3/8 inch. 
 
 1/2 inch. 
 
 5/8 inch. 
 
 3/4 inch. 
 
 1 inch. 
 
 11/4 in. 
 
 30 ft. 
 
 50 ft. 
 
 75 ft. 
 100 ft. 
 150 ft. 
 200 ft. 
 
 15 1b. 
 25 1b. 
 38 1b. 
 50 1b. 
 75 1b. 
 100 lb. 
 
 D 
 C 
 B 
 A 
 AA 
 AAA 
 
 10 oz. 
 12 oz. 
 1 lb. 
 
 11/4 lb. 
 1 1/2 lb. 
 13/4 lb. 
 
 3/4 lb. 
 1 lb. 
 11/4 lb. 
 
 1 3/4 lb. 
 
 2 lb. 
 
 3 lb. 
 
 1 lb. 
 11/2 lb. 
 
 2 lb. 
 21/2 lb. 
 23/4 lb. 
 3 1/2 lb. 
 
 1 1/4 lb. 
 13/4 lb. 
 21/4 lb. 
 3 lb. 
 31/2 lb. 
 43/4 lb. 
 
 2 lb. 
 21/2 lb. 
 31/4 lb. 
 4 lb. 
 43/4 lb. 
 6 lb. 
 
 21/2 lb. 
 3 lb. 
 33/4 lb. 
 43/4 lb. 
 53/4 lb. 
 63/4 lb. 
 
 
 
 
 
 
 
 
 
 
218 
 
 MATERIALS. 
 
 To find the thickness of lead pipe required when the head ol 
 water is given. (Chad wick 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. 
 
 Example. — Required thickness of half-inch pipe for a head of 25 
 feet. 
 
 25 X 0.50 -*■ 750 = 0.16 inch. 
 
 1 1/2 in., 2 and 3 pounds per foot. 
 
 2 "3 and 4 pounds per foot. 
 
 3 " 31/2, 5, and 6pounds perfoot. 
 3V2 " 4 pounds per foot. 
 
 LEAD WASTE-PIPE. 
 
 4 in., 5, 6, and 8 pounds per foot. 
 41/2 " 6 and 8 pounds per foot. 
 
 5 " 8, 10, and 12 pounds perfoot. 
 
 6 " 12 pounds per foot. 
 
 COMMERCIAL SIZES OF LEAD AND TIN TUBING. 
 
 1/8 inch. 1/4 inch. 
 
 SHEET LEAD. 
 
 Weight per square foot, 2l/ 2 , 3, 31/ 2 , 4, 4l/ 2 , 5, 6, 8, 9, 10 lb. and upwards. 
 Other weights rolled to order. 
 
 BLOCK-TIN PIPE. 
 
 3/g in., 4, 5, 6 and 8 oz. perfoot. 
 1/2 " 6, 71/2 and 10 " " 
 5/ 8 " 8 and 10 " " 
 
 3/4 " 10 and 12 " " 
 
 U/4 " 
 
 1 1/2 " 
 
 , 15 and 18 oz. perfoot. 
 11/4 and 11/2 lb." " 
 2 and 21/2 lb. " " 
 21/2 and 3 lb. " " 
 
 TIN-LINED AND LEAD-LINED IRON PIPE. 
 
 Iron and steel pipes are frequently lined with tin or lead for use as water 
 service pipes, ventilation pipes, and for carrying corrosive liquids. See 
 catalogue of Lead Lined Iron Pipe Co., Wakefield, Mass. 
 
 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 with 
 upset and threaded ends. When buried below the hydraulic grade line j 
 and kept full of water, these pipes are practically indestructible. For the | 
 economic design and use of stave pipe see paper by A. L. Adams, Trans. 
 A.S.C.E., vol. xli. 
 
 
 WEIGHT 
 
 PER 
 
 FT. OF 
 
 COPPER RODS, LB. 
 
 
 
 
 (Waterbury Brass Co., 1908.) 
 
 
 
 In. 
 
 Round. 
 
 Square. 
 
 In. 
 
 Round . 
 
 Square. 
 
 In. 
 
 Round. 
 
 Square. 
 
 1/8 
 
 0.047 
 
 0.060 
 
 11/8 
 
 3.831 
 
 4.88 
 
 21/8 
 
 13.668 
 
 17.42 
 
 1/4 
 
 .189 
 
 .241 
 
 U/4 
 
 4.723 
 
 6.01 
 
 21/4 
 
 15.325 
 
 19.51 
 
 3/8 
 
 .426 
 
 .542 
 
 13/8 
 
 5.723 
 
 7.24 
 
 23/8 
 
 17.075 
 
 21.74 
 
 v% 
 
 .757 
 
 .964 
 
 11/2 
 
 6.811 
 
 8.67 
 
 2l/ 2 
 
 18.916 
 
 24.09 
 
 5/8 
 
 1.182 
 
 1.51 
 
 15/8 
 
 7.993 
 
 10.18 
 
 25/8 
 
 20.856 
 
 26.56 
 
 3/4 
 
 1.703 
 
 2.17 
 
 13/4 
 
 9.27 
 
 11.80 
 
 23/4 
 
 22.891 
 
 29.05 
 
 7/8 
 
 2.318 
 
 2.95 
 
 17/8 
 
 10.642 
 
 13.55 
 
 27/8 
 
 25.019 
 
 31.86 
 
 1 
 
 3.03 
 
 3.86 
 
 2 
 
 12.108 
 
 15.42 
 
 3 
 
 27.243 
 
 34.69 
 
 To find the weight of octagon rod, multiply the weight of round rod by 
 1.084. 
 
 To find the weight of hexagon rod, multiply the weight of round rod by 
 1.12. 
 
WEIGHT OF COPPER AND BRASS WIRE AND PLATES. 219 
 
 ooo^-ooNoo^OtNT-aiNin^ 
 
 
 -Ovt^in^r^tNCM — , OOC 
 
 MO 
 'So 
 
 - '5 |Q o rj t> oj 
 
 3 O O O O O 00 
 
 •'O'^tsoo'rotmNNmooo-om'O^l " u-, 
 C^rr^tA— O^ O^ — vONOa*0\OP p l , 00 , T0 1 iA 
 
 QOOlflNOtMntN OOOrslXvOirMTl'^TAf^rr : w 
 
 ii fN (N CN CN — — — — O O O O O O O © O !0 -^ 'T 
 
 ^ooooooooooooooooooog .£> & 
 
 Z6 
 
 & £ 
 
 £-a 
 
 O PI 
 
 s3 
 
 £- 
 
 0<f\— O00tANtO>nMeoO*B0>O001"t0C 
 
 K vom*ovtno»Msov- momoO'l-Of^T — 
 
 ->o^vOT -, r-'rcsioo<N — vo>ooo>o«tM» 
 
 o — t^t-^u-ifStsoor^ooifsr^-^-o^inoo — m n o> -o in oo N 
 
 -a>^ooomcoinm>ooinN^ , oiAvOooiNmuM)0'0\oo> 
 
 i-JorsOOOfnoom-a-tNintt^Nf- 
 
 ,lftO00ifM'iatA'tNtO»O' , tO>N' 
 
 °TOO — mom(NOr- "- — 
 
 
 ■J o^ r> O T tA tf»> 
 
 
 
 ^N — TNOOarnO^^fOvOOO-OMinOa'O 
 3-^TA0NO(NT-^-00t^.a0O^OO00<Np^00ON 
 
 ^No»>0'<tN-oo^oo^.^Olf^^n'r'r^M 
 
 -1NN------0000000000 
 
 so — N^'tmvoiNooo'O- 
 
220 
 
 MATERIALS. 
 
 WEIGHT OF SHEET AND BAR BRASS. 
 
 Thickness, 
 
 Sheets 
 
 Square 
 
 Round' 
 
 Thickness, 
 
 Sheets 
 
 Square 
 
 Round 
 
 Side or 
 
 per 
 
 Bars 1 
 
 Bars 1 
 
 Side or 
 
 per 
 
 Bars 1 
 
 Bars 1 
 
 Diam., 
 
 sq ft., 
 
 ft. long, 
 
 ft. long. 
 
 Diam., 
 
 sq. ft., 
 
 ft. long, 
 
 ft. long, 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 1/16 
 
 2.72 
 
 0.014 
 
 0.011 
 
 1 Vl6 
 
 46.32 
 
 4.10 
 
 3.22 
 
 1/8 
 
 5.45 
 
 .056 
 
 .045 
 
 1 1/8 
 
 49.05 
 
 4.59 
 
 3.61 
 
 3/16 
 
 8.17 
 
 .128 
 
 .100 
 
 1 3/i 6 
 
 51.77 
 
 5.12 
 
 4.02 
 
 1/4 
 
 10.90 
 
 .227 
 
 .178 
 
 1 1/4 
 
 54.50 
 
 5.67 
 
 4.45 
 
 5/16 
 
 13.62 
 
 .355 
 
 .278 
 
 1 5/i 6 
 
 57.22 
 
 6.26 
 
 4.91 
 
 3/8 
 
 16.35 
 
 .510 
 
 .401 
 
 1 3/ 8 
 
 59.95 
 
 6.86 
 
 5.39 
 
 7/16 
 
 19.07 
 
 .695 
 
 .545 
 
 1 7/16 
 
 62.67 
 
 7.50 
 
 5.89 
 
 1/2 
 
 21.80 
 
 .907 
 
 .712 
 
 1 1/2 
 
 65.40 
 
 8.16 
 
 6.41 
 
 9/16 
 
 24.52 
 
 1.15 
 
 .902 
 
 1 9/16 
 
 68.12 
 
 8.86 
 
 6.95 
 
 5/8 
 
 27.25 
 
 1.42 
 
 1.11 
 
 1 5/ 8 
 
 70.85 
 
 9.59 
 
 7.53 
 
 11/16 
 
 29.97 
 
 1.72 
 
 1.35 
 
 1 H/16 
 
 73.57 
 
 10.34 
 
 8.12 
 
 3/4 
 
 32.70 
 
 2.04 
 
 1.60 
 
 1 3/4 
 
 76.30 
 
 11.12 
 
 8.73 
 
 13/16 
 
 35.42 
 
 2.40 
 
 1.88 
 
 1 13/16 
 
 79.02 
 
 11.93 
 
 9.36 
 
 7/8 
 
 38 15 
 
 2.78 
 
 2.18 
 
 1 7/ 8 
 
 81.75 
 
 12.76 
 
 10.01 
 
 15/16 
 
 40.87 
 
 3.19 
 
 2.50 
 
 1 15/16 
 
 84.47 
 
 13.63 
 
 10.70 
 
 1 
 
 43.60 
 
 3.63 
 
 2.85 
 
 2 
 
 87.20 
 
 14.52 
 
 11.40 
 
 WEIGHT OF ALUMINUM SHEETS, SQUARE AND ROUND BARS. 
 
 (Specific Gravity 2.68; 1 cu. in. = 0.0973 lb.) 
 
 Thickness 
 
 Sheets 
 
 Round 
 
 Square 
 
 Thickness 
 
 Sheets 
 
 Round 
 
 Square 
 
 or 
 
 per 
 
 Bars 
 
 Bars 
 
 or 
 
 per 
 
 Bars 
 
 Bars 
 
 Diameter, 
 
 Sq.Ft., 
 
 per Ft., 
 
 per Ft., 
 
 Diameter, 
 
 Sq.Ft., 
 Lbs. 
 
 per Ft., 
 
 per Ft., 
 
 Inches. 
 
 Lbs 
 
 Lbs. 
 
 Lbs. 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 1/16 
 
 0.876 
 
 0.004 
 
 0.005 
 
 3/4 
 
 10.508 
 
 0.516 
 
 0.657 
 
 1/8 
 
 1.751 
 
 .014 
 
 .018 
 
 7/8 
 
 12.260 
 
 .702 
 
 .894 
 
 1/4 
 
 3.503 
 
 .057 
 
 .073 
 
 1 
 
 14.011 
 
 .917 
 
 1.168 
 
 3/8 
 
 5.254 
 
 -129 
 
 .164 
 
 11/4 
 
 17.514 
 
 1.433 
 
 1.824 
 
 1/2 
 
 7.006 
 
 .229 
 
 .292 
 
 11/2 
 
 21.017 
 
 2.063 
 
 2.627 
 
 5/8 
 
 8.757 
 
 .358 
 
 .456 
 
 2 
 
 28.022 
 
 3.668 
 
 4.671 
 
 For further particulars regarding aluminum, see pp. 174, 357. 
 
 SCREW-THREADS, WHITWORTH 
 
 (ENGLISH) STANDARD. 
 
 d 
 
 4 
 
 i 
 
 ,d 
 
 s 
 
 4 
 
 g 
 
 JS 
 
 a 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 Ph 
 
 s 
 
 P4 
 
 Q 
 
 Oh 
 
 s 
 
 (U 
 
 Q 
 
 s 
 
 1/4 
 
 20 
 
 5/8 
 
 11 
 
 1 
 
 8 
 
 13/4 
 
 5 
 
 3 
 
 3V? 
 
 5/16 
 
 18 
 
 U/16 
 
 11 
 
 H/8 
 
 y 
 
 17/8 
 
 41/2 
 
 31/4 
 
 31/4 
 
 3/8 
 
 16 
 
 3/4 
 
 10 
 
 11/ 4 
 
 7 
 
 2 
 
 41/2 
 
 31/2 
 
 31/4 
 
 7/16 
 
 14 
 
 13/16 
 
 10 
 
 13/8 
 
 6 
 
 21/4 
 
 4 
 
 33/4 
 
 3 
 
 1/2 
 
 12 
 
 7/8 
 
 9 
 
 11/2 
 
 6 
 
 21/2 
 
 4 
 
 4 
 
 3 
 
 9/16 
 
 12 
 
 15/16 
 
 9 
 
 15/8 
 
 i> 
 
 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. 
 

 
 
 
 SCREW- 
 
 rHREADS. 
 
 
 
 
 221 
 
 SCREW-THREADS, SEIXERS OR U. S. STANDARD. 
 
 Bolts and Threads. 
 
 Hex. Nuts and Heads. 
 
 
 ffl 
 
 i 
 
 
 "SJS 
 1? 
 
 "o 
 
 is 
 
 cS O " 
 
 OT3 OB 
 
 5*1 
 
 M M 
 
 £ ° 
 
 i 
 
 ft-g 
 J* 
 
 1 
 
 QJ3 
 
 
 
 
 1°' 
 
 s 
 
 . Ins. 
 
 H 
 
 5 
 
 ? 
 
 < 
 
 < OB 
 
 W 
 
 w 
 
 Hi 
 
 H 
 
 H 
 
 yA 
 
 
 Ins. 
 
 Ins. 
 
 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 
 1/4 
 
 20 
 
 0.185 
 
 0.0062 
 
 0.049 
 
 0.027 
 
 1/2 
 
 7/16 
 
 37/64 
 
 1/4 
 
 3/16 
 
 7/10 
 
 5/16 
 
 18 
 
 .240 
 
 .0074 
 
 .077 
 
 .045 
 
 19/32 
 
 17/32 
 
 11/16 
 
 5/16 
 
 1/4 
 
 1°/12 
 
 3/8 
 
 16 
 
 .294 
 
 .0078 
 
 .110 
 
 .068 
 
 11/16 
 
 5/8 
 
 51/64 
 
 3/8 
 
 5/16 
 
 63/64 
 
 7/16 
 
 14 
 
 .344 
 
 .0089 
 
 .150 
 
 .093 
 
 25/32 
 
 23/32 
 
 9/10 
 
 7/16 
 
 3/8 
 
 17/64 
 
 1/2 
 
 13 
 
 .400 
 
 .0096 
 
 .196 
 
 .126 
 
 7/8 
 
 13/16 
 
 1 
 
 1/2 
 
 7/16 
 
 1 15/64 
 
 9/16 
 
 12 
 
 .454 
 
 .0104 
 
 .249 
 
 .162 
 
 i < V 32 
 
 29/3 2 
 
 11/8 
 
 9/16 
 
 1/2 
 
 1 23/ 6 4 
 
 5/8 
 
 11 
 
 .507 
 
 .0113 
 
 .307 
 
 .202 
 
 H/16 
 
 1 
 
 17/32 
 
 5/8 
 
 9/16 
 
 11/2 
 
 3/ 4 
 
 10 
 
 .620 
 
 .0125 
 
 .442 
 
 .302 
 
 H/4 
 
 '3/16 
 
 17/16 
 
 3/ 4 
 
 11/16 
 
 1 4 9/64 
 
 7/8 
 
 9 
 
 .731 
 
 .0138 
 
 .601 
 
 .420 
 
 17/16 
 
 13/8 
 
 1 21/32 
 
 7/8 
 
 13/16 
 
 21/32 
 
 1 
 
 8 
 
 .837 
 
 .0156 
 
 .785 
 
 .550 
 
 15/ 8 
 
 '9/16 
 
 17/8 
 
 1 
 
 15/16 
 
 219/64 
 
 J 1/8 
 
 7 
 
 .940 
 
 .0178 
 
 .994 
 
 .694 
 
 1 13/ ia 
 
 I3/4 
 
 23/32 
 
 11/8 
 
 11/16 
 
 29/ie 
 
 1/4 
 
 7 
 
 1.065 
 
 .0178 
 
 1.227 
 
 .893 
 
 2 
 
 1 15/16 
 
 25/16 
 
 11/4 
 
 13/16 
 
 253/64 
 
 3/8 
 
 6 
 
 1.160 
 
 .0208 
 
 1.485 
 
 1.057 
 
 23/ie 
 
 21/8 
 
 217/32 
 
 '3/8 
 
 15/16 
 
 33/32 
 
 1/2 
 
 6 
 
 1.284 
 
 .0208 
 
 1.767 
 
 1.295 
 
 23/ 8 
 
 25/i 6 
 
 23/4 
 
 U/2 
 
 17/16 
 
 323/64 
 
 5/8 
 
 51/2 
 
 1.389 
 
 .0227 
 
 2.074 
 
 1.515 
 
 29/16 
 
 21/2 
 
 231/32 
 
 15/8 
 
 19/16 
 
 35/8 
 
 13/4 
 
 5 
 
 1.491 
 
 .0250 
 
 2.405 
 
 1.746 
 
 23/ 4 
 
 211/16 
 
 33/16 
 
 13/4 
 
 1 H/I6 
 
 357/64 
 
 17/g 
 
 5 
 
 1.616 
 
 .0250 
 
 2.761 
 
 2.051 
 
 215/ie 
 
 27/8 
 
 313/32 
 
 17/8 
 
 1 13/16 
 
 45/32 
 
 2 
 
 41/2 
 
 1.712 
 
 .0277 
 
 3.142 
 
 2.302 
 
 31/8 
 
 31/16 
 
 35/8 
 
 2 
 
 1 15/16 
 
 427/ 6 4 
 
 21/4 
 
 41/2 
 
 1.962 
 
 .0277 
 
 3.976 
 
 3.023 
 
 31/2 
 
 37/i 6 
 
 4Vl6 
 
 21/4 
 
 23/ 16 
 
 461/64 
 
 21/2 
 
 4 
 
 2.176 
 
 .0312 
 
 4.909 
 
 3.719 
 
 37/ 8 
 
 313/16 
 
 41/2 
 
 21/2 
 
 27/i 6 
 
 531/64 
 
 23/4 
 
 4 
 
 2.426 
 
 .0312 
 
 5.940 
 
 4.620 
 
 41/4 
 
 43/ie 
 
 429/32 
 
 23/4 
 
 2U/16 
 
 6 
 
 3 
 
 31/2 
 
 2.629 
 
 .0357 
 
 7.069 
 
 5.428 
 
 45/s 
 
 89 /i6 
 
 53/s 
 
 3 
 
 215/ie 
 
 617/32 
 
 31/4 
 
 31/2 
 
 2.879 
 
 .0357 
 
 8.296 
 
 6.510 
 
 5 
 
 415/16 
 
 5*3/16 
 
 31/4 
 
 33/16 
 
 71/16 
 
 31/2 
 
 31/4 
 
 3.100 
 
 .0384 
 
 9.621 
 
 7.548 
 
 53/s 
 
 55 /l6 
 
 67/64 
 
 31/2 
 
 3 7/16 
 
 739/64 
 
 33/4 
 
 3 
 
 3.317 
 
 .0413 
 
 11.045 
 
 8.641 
 
 53/4 
 
 511/16 
 
 621/32 
 
 33/4 
 
 3U/16 
 
 81/8 
 
 4 
 
 3 
 
 3.567 
 
 .0413 
 
 12.566 
 
 9.993 
 
 61/8 
 
 6 Vl6 
 
 73/32 
 
 4 
 
 315/16 
 
 841/ 6 4 
 
 41/4 
 
 27/ 8 
 
 3.798 
 
 .0435 
 
 14.186 
 
 11.329 
 
 6 1/2 
 
 67/ 8 
 
 71/4 
 
 75/s 
 
 8 
 
 83/ 8 
 
 83/4 
 
 91/8 
 
 67 /l6 
 
 79/16 
 
 41/4 
 
 43/16 
 
 93/i 6 
 
 41/2 
 
 23/ 4 
 
 4.028 
 
 .0454 
 
 15.904 
 
 12.743 
 
 6l3/i 6 
 
 731/32 
 
 41/2 
 
 47/16 
 
 93/ 4 
 
 43/4 
 
 25/ 8 
 
 4.256 
 
 .0476 
 
 17.721 
 
 14.226 
 
 73 /l6 
 
 813/32 
 
 43/4 
 
 4H/16 
 
 IOI/4 
 
 5 
 
 21/2 
 
 4.480 
 
 .0500 
 
 19.635 
 
 15.763 
 
 7 9/16 
 
 827/3 2 
 
 5 
 
 415/ie 
 
 1049/ 6 4 
 
 51/4 
 
 21/2 
 
 4.730 
 
 .0500 
 
 21.648 
 
 17.572 
 
 713/16 
 
 99/32 
 
 51/4 
 
 5 3/i 6 
 
 1 1 23/ e4 
 
 5l/ 2 
 
 23/s 
 
 4.953 
 
 .0526 
 
 23 . 758 
 
 19.267 
 
 85/i 6 
 
 923/32 
 
 51/2 
 
 57/i 6 
 
 117/8 
 
 53/4 
 
 23/ 8 
 
 5.203 
 
 .0526 
 
 25.967 
 
 21.262 
 
 8H/16 
 
 05/32 
 
 53/4 
 
 5H/16 
 
 123/s 
 
 6 
 
 21/4 
 
 5.423 
 
 .0555 
 
 28.274 23.098 
 
 91/16 
 
 019/32 
 
 6 
 
 515/16 
 
 1215/16 
 
 In 1864 a committee of the Franklin Institute recommended the adop- 
 tion of the system of screw-threads and bolts which was devised by Mr. 
 William Sellers of Philadelphia. This system is now in general use in 
 the United States, and it is commonly called the United States Standard. 
 
 The rule for proportioning the thread is as follows: Divide the pitch, 
 or, what is the same thing, the side of the thread, into eight equal parts; 
 take off one part from the top and fill in one part in the bottom of the 
 thread ; then the flat top and bottom will equal one-eighth of the pitch, 
 the wearing surface will be three-quarters of the pitch, and the diameter 
 of screw at bottom of the thread will be expressed by the formula, 
 diam. of bolt - (1.299 -^ no. of threads per inch). 
 
 For a sharp V-thread with angle of 60 degrees the formula is, 
 diam. of bolt - (1.733 -5- no. of threads per inch). 
 
 The angle of the thread in the Sellers system is 60 degrees. 
 
222 
 
 MATERIALS. 
 
 Thickness of Nuts and Bolt Heads. — In the above table the thickness 
 of nuts and heads (rough) is given as equal to the diameter of the bolt. 
 Many manufacturers make the thickness of nuts about 7/ 8) and of bolt 
 heads 3/ 4 , of the diam. of the bolt. 
 
 Automobile Screws and Nuts. — The Association of Licensed Auto- 
 mobile M'f'rs (1906) 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 lbs. per sq. in., tensile strength 
 not less than 100,000 lbs. per sq. in. U. S. Standard thread is used, the 
 threaded portion of screws being li/ 2 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 -*■ 8 = flat top. 
 
 D 
 
 P 
 
 B 
 
 Ai 
 
 H 
 
 K 
 
 / 
 
 A 
 
 c 
 
 E 
 
 d 
 
 1/4 
 
 28 
 
 3/8 
 
 7/32 
 
 3/16 
 
 Vlfi 
 
 3/3? 
 
 9/32 
 
 3/3? 
 
 5/64 
 
 1/16 
 
 Wir 
 
 24 
 
 }/2 . 
 
 17/64 
 
 15/64 
 
 1/lfi 
 
 Vlk 
 
 21/64 
 
 3/32 
 
 5/64 
 
 1/16 
 
 3/8 
 
 24 
 
 9/16 
 
 2V64 
 
 9 /32 
 
 3/32 
 
 1/8 
 
 13/32 
 
 1/8 
 
 1/8 
 
 3/3? 
 
 V/16 
 
 20 
 
 U/16 
 
 3/8 
 
 21/64 
 
 3 /32 
 
 1/8 
 
 29/64 
 
 1/8 
 
 1/8 
 
 3/3? 
 
 V? 
 
 20 
 
 3/4 
 
 7/16 
 
 3 /8 
 
 3/37! 
 
 1/8 
 
 9/16 
 
 3/16 
 
 1/8 
 
 3/3? 
 
 «/1« 
 
 18 
 
 7/8 
 
 3V64 
 
 27/64 
 
 3/32 
 
 1/8 
 
 39/64 
 
 3/16 
 
 5 /32 
 
 1/8 
 
 5/8 
 
 18 
 
 15/16 
 
 35/64 
 
 15/32 
 
 3/39, 
 
 VS 
 
 23/32 
 
 1/4 
 
 5/3? 
 
 1/8 
 
 H/tfi 
 
 16 
 
 1 
 
 19/32 
 
 33/64 
 
 3/3? 
 
 1/8 
 
 49/64 
 
 1/4 
 
 5/32 
 
 1/8 
 
 3/4 
 
 16 
 
 »l/8 
 
 21/32 
 
 9/16 
 
 3/3?, 
 
 1/8 
 
 13/16 
 
 V4 
 
 5 /32 
 
 1/8 
 
 7/8 
 
 14 
 
 H/4 
 
 49/64 
 
 21/32 
 
 3/3? 
 
 1/8 
 
 29/32 
 
 1/4 
 
 5/32 
 
 1/8 
 
 1 
 
 14 
 
 17/16 
 
 7/8 
 
 3/4 
 
 3/32 
 
 1/8 
 
 1 
 
 1/4 
 
 5 /32 
 
 1/8 
 
 INTERNATIONAL STANDARD THREAD (METRIC SYSTEM). 
 
 P = pitch, = 1 — no. of threads per millimeter. 
 
 Depth of thread = 0.6495 P. 
 
 Flat top and bottom of thread = one-eighth pitch. 
 
 Diam. at bottom of thread = diam. of bolt - 1.299 P. 
 Diam., mm. 6 7 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 471/2°. 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/n of the pitch. 
 
 Number 1 2 3 4 5 6 
 
 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 0.59 0.53 
 
SIZE OF ROUGH IRON FOR U. S. STANDARD BOLTS. 223 
 
 Number 7 
 
 Diameter, mm 2.5 
 
 Pitch, mm 0.48 
 
 0.43 
 
 9 
 
 10 
 
 12 
 
 14 
 
 19 
 
 1.9 
 
 1.7 
 
 1.3 
 
 1.0 
 
 .79 
 
 0.39 
 
 0.35 
 
 0.28 
 
 0.23 
 
 0.19 
 
 LIMIT GAUGES FOR IRON FOR SCREW-THREADS. 
 
 In adopting 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-gauges for inspecting iron with two 
 openings, one larger and the other smaller than the standard size, and 
 then specify that the iron should enter the large end and not enter the 
 small one. The following table of dimensions for the limit-gauges was 
 adopted by the Master Car-Builders' Association in 1883. 
 
 Size of 
 
 Large 
 
 Small 
 
 Differ- 
 
 Size of 
 
 Large 
 
 Small 
 
 Differ- 
 
 Iron. 
 
 End of 
 
 End of 
 
 Iron. 
 
 End of 
 
 End of 
 
 In. 
 
 Gauge. 
 
 Gauge. 
 
 
 In. 
 
 Gauge. 
 
 Gauge. 
 
 
 1/4 
 
 0.2550 
 
 0.2450 
 
 0.010 
 
 5/8 
 
 0.6330 
 
 0.6170 
 
 0.016 
 
 5 /l6 
 
 0.3180 
 
 0.3070 
 
 0.011 
 
 3/ 4 
 
 0.7585 
 
 0.7415 
 
 0.017 
 
 3/8 
 
 0.3810 
 
 0.3690 
 
 0.012 
 
 7/8 
 
 0.8840 
 
 0.8660 
 
 0.018 
 
 7/16 
 
 0.4440 
 
 0.4310 
 
 0.013 
 
 1 
 
 1.0095 
 
 0.9905 
 
 0.019 
 
 V2 
 
 0.5070 
 
 0.4930 
 
 0.014 
 
 H/8 
 
 1.1350 
 
 1.1150 
 
 0.020 
 
 9 /l6 
 
 0.5700 
 
 0.5550 
 
 0.015 
 
 H/4 
 
 1.2605 
 
 1.2395 
 
 0.021 
 
 Caliper gauges with the above dimensions, and standard reference 
 gauges for testing them, are made by the Pratt & Whitney Co. 
 
 THE MAXIMUM VARIATION IN SIZE OF ROUGH IRON 
 FOR U. S. STANDARD BOLTS. 
 
 Am. Mach., May 12, 1892. 
 
 By the adoption of the Sellers or U. S. Standard, thread taps and dies 
 keep their size much longer in use when flatted in accordance with this 
 system than when made sharp "V", though it has been found advisable 
 in practice in most cases to make the taps of somewhat larger outside 
 diameter than the nominal size, thus carrying the threads further towards 
 the V-shape and giving corresponding clearance to the tops of the threads 
 when in the nuts or tapped holes. 
 
 Makers of taps and dies often have calls for taps and dies, U. S. Stand- 
 ard, "for rough iron." 
 
 An examination of rough iron will show that much of it is rolled out of 
 round to an amount exceeding the limit of variation in size allowed. 
 
 In view of this it may be desirable to know what the extreme varia- 
 tion in iron may be, consistent with the maintenance of U. S. Standard 
 threads, i.e., threads which are standard when measured upon the angles, 
 the only place where it seems advisable to have them fit closely. Mr. 
 Chas. A. Bauer, the general manager of the Warder, Bushnell & Glessner 
 Co., at Springfield, Ohio, in 1884 adopted a plan which may be stated as 
 follows: All bolts, whether cut from rough or finished stock, are stand- 
 ard size at the bottom and at the sides or angles of the threads, the vari- 
 ation for fit of the nut and allowance for wear of taps being made in the 
 machine taps. Nuts are punched with holes of such size as to give 85 
 per cent of a full thread, experience showing that the metal of wrought 
 nuts will then crowd into the threads of the taps sufficiently to give 
 practically a full thread, while if punched smaller some of the metal will 
 be cut out by the tap at the bottom of the threads, which is of course 
 undesirable. Machine taps are made enough larger than the nominal 
 
224 
 
 MATERIALS. 
 
 to bring the tops of the threads up sharp, plus the amount allowed for 
 fit and wear of taps. This allows the iron to be enough above the nomi- 
 nal diameter to bring the threads up full (sharp) at top, while if it is 
 small the only effect is to give a flat at top of threads; neither condition 
 affecting the actual size of the thread at the point at which it is intended 
 to bear. Limit gauges are furnished to the mills, by which the iron is 
 rolled, the maximum size being shown in the third column of the table 
 The minimum diameter is not given, the tendency in rolling being nearly 
 always to exceed the nominal diameter. 
 
 In making the taps the threaded portion is turned to the size given in 
 the eighth column of the table, which gives 6 to 7 thousandths of an inch 
 allowance for fit and wear of tap. Just above the threaded portion of the 
 tap a place is turned to the size given in the ninth column, these sizes 
 being the same as those of the regular U. S. Standard bolt, at the bottom 
 of the thread, plus the amount allowed for fit and wear of tap; or, in other 
 words, d' = U. S. Standard d + (Z)' — D). Gauges like the one in the 
 cut, Fig. 75, are furnished for this sizing. In finishing the threads of the 
 
 Fig. 75. 
 
 tap a tool is used which has a removable cutter finished accurately to 
 gauge by grinding, this tool being correct U. S. Standard as to angle, 
 and flat at the point. It is fed in and the threads chased until the flat 
 point just touches the portion of the tap which has been turned to size 
 §'. Care having been taken with the form of the tool, with its grinding 
 on the top face (a fixture being provided for this to insure its being ground 
 properly), and also with the setting of the tool properly in the lathe, the 
 result is that the threads of the tap are correctly sized without further 
 attention. 
 
 STANDARD SIZES OF SCREW-THREADS FOR BOLTS 
 AND TAPS. 
 
 (Chas. A. Bauer.) 
 
 A 
 
 n 
 
 D 
 
 d 
 
 h 
 
 / 
 
 D'-D 
 
 D' 
 
 d' 
 
 H 
 
 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 1/4 
 
 20 
 
 0.2608 
 
 0.1855 
 
 0.0379 
 
 0.0062 
 
 0.006 
 
 0.2668 
 
 0.1915 
 
 0.2024 
 
 &/10 
 
 18 
 
 0.3245 
 
 0.2403 
 
 0.0421 
 
 0.0070 
 
 0.006 
 
 0.3305 
 
 0.2463 
 
 0.2589 
 
 3/8 
 
 16 
 
 0.3885 
 
 0.293S 
 
 0.0474 
 
 0.0078 
 
 0.006 
 
 0.3945 
 
 0.2998 
 
 0.3139 
 
 7/1*5 
 
 14 
 
 0.4530 
 
 0.3447 
 
 0.0541 
 
 0.0089 
 
 0.006 
 
 0.4590 
 
 0.3507 
 
 0.3670 
 
 V? 
 
 13 
 
 0.5166 
 
 0.4000 
 
 0.0582 
 
 0.0096 
 
 0.006 
 
 0.5226 
 
 0.4060 
 
 0.4236 
 
 «/lfi 
 
 12 
 
 0.5805 
 
 0.4543 
 
 0.0631 
 
 0.0104 
 
 0.007 
 
 0.5875 
 
 0.4613 
 
 0.4802 
 
 5 /s 
 
 11 
 
 0.6447 
 
 0.5069 
 
 0.0689 
 
 0.0114 
 
 0.007 
 
 0.0517 
 
 0.5139 
 
 0.5346 
 
 3/4 
 
 10 
 
 0.7717 
 
 0.6201 
 
 0.0758 
 
 0.0125 
 
 0.007 
 
 0.7787 
 
 0.6271 
 
 0.6499 
 
 7/R 
 
 9 
 
 0.8991 
 
 0.7307 
 
 0.0842 
 
 0.0139 
 
 0.007 
 
 0.9061 
 
 0.7377 
 
 0.7630 
 
 1 
 
 8 
 
 1.0271 
 
 0.8376 
 
 0.0947 
 
 0.0156 
 
 0.007 
 
 1.0341 
 
 0.8446 
 
 0.8731 
 
 11/8 
 
 7 
 
 1.1559 
 
 0.9394 
 
 0.1083 
 
 0.0179 
 
 0.007 
 
 1.1629 
 
 0.9464 
 
 0.9789 
 
 11/4 
 
 7 
 
 1.2809 
 
 1.0644 
 
 0.1083 
 
 0.0179 
 
 0.007 
 
 1.2879 
 
 1.0714 
 
 1.1039 
 
 A — nominal diameter of bolt. 
 D = actual diameter of bolt. 
 d = diameter of bolt at bottom of 
 
 thread. 
 n = number of threads per inch. 
 / = flat of bottom of thread. 
 h = depth of thread. 
 
 D' and d' = diameters of tap. 
 
 H = hole in nut before tapping. 
 
 D = A + 0.2165/n. 
 
 d = A- 1.29904/n. 
 
 h = 0.7577/n = (D - d)/2. 
 
 f = 0.125/w. 
 
 H = D'_i^? = .D'-o.85(2ft). 
 
STANDARD SET-SCREWS AND CAP-SCREWS. 225 
 
 STANDARD SET-SCREWS AND CAP-SCREWS. 
 
 American, Hartford, and Worcester Machine-Screw Companies. 
 (Compiled by W. S. Dix, 1895.) 
 
 (See tables below) 
 
 Diameter of screw 
 
 Threads per inch 
 
 Size of tap drill * 
 
 (A) 
 
 (B) 
 
 (C) 
 
 (D) 
 
 (E) 
 
 (F) 
 
 1/8 
 
 3/16 
 
 1/4 
 
 Wifi 
 
 3/8 
 
 7/16 
 
 40 
 
 24 
 
 20 
 
 18 
 
 16 
 
 14 
 
 No. 43 
 
 No. 30 
 
 No. 5 
 
 17/64 
 
 21/64 
 
 3/8 
 
 (H) 
 
 (I) 
 
 (J) 
 
 (K) 
 
 (L) 
 
 (M) 
 
 9/16 
 
 Ws 
 
 3/ 4 
 
 V/8 
 
 1 
 
 1 
 
 12 
 
 11 
 
 10 
 
 9 
 
 8 
 
 7 
 
 31/64 
 
 17/32 
 
 21/32 
 
 49/64 
 
 7/8 
 
 63/64 
 
 (G) 
 
 1/2 
 
 12 
 
 27/64 
 
 Diameter of screw. 
 Threads per inch . . 
 Size of tap drill * . . . 
 
 (N) 
 
 IV 
 
 7 
 
 H/8 
 
 * For cast iron. For numbers of twist-drills, see page 30. 
 
 Set-screws. 
 
 Hex. Head Cap-screws. 
 
 Sq. Head Cap-screws. 
 
 Short 
 
 Diam. 
 
 of Head. 
 
 Long 
 Diam. 
 ofH'd. 
 
 Lengths 
 (under 
 Head). 
 
 Short 
 Diam. 
 
 of 
 Head. 
 
 Long 
 Diam. 
 
 of 
 Head. 
 
 Lengths 
 (under 
 Head). 
 
 Short 
 Diam. 
 
 of 
 Head. 
 
 Long 
 Diam. 
 
 of 
 Head. 
 
 Lengths 
 (under 
 Head)... 
 
 (C) 1/4 
 
 (D) 5/i6 
 
 (E) 3/ 8 
 
 (F) 7/ie 
 
 (G) 1/2 
 (H) 9/ 16 
 (I) S/g 
 (J) 3/4 
 (K) 7/s 
 (L) 1 
 (M) H/8 
 (N) H/4 
 
 0.35 
 
 .44 
 
 .53 
 
 .62 
 
 .71 
 
 .80 
 
 .89 
 
 1.06 
 
 1.24 
 
 1.42 
 
 1.60 
 
 1.77 
 
 3/ 4 to 3 
 
 3/4 to 3 1/ 4 
 3/ 4 to 31/ 2 
 3/ 4 to 33/4 
 3/ 4 to 4 
 3/ 4 to 41/4 
 3/4 to 41/2 
 
 1 to 43/ 4 
 
 1 1/4 to 5 
 
 1 1/2 to 5 
 
 1 3/ 4 to 5 
 2 to 5 
 
 7/16 
 1/2 
 9 /l6 
 5/8 
 3/4 
 13/16 
 7/8 
 1 
 
 U/8 
 U/4 
 13/8 
 1 1/2 
 
 0.51 
 .58 
 .65 
 .72 
 .87 
 .94 
 1.01 
 1.15 
 1.30 
 1.45 
 1.59 
 1.73 
 
 3/4 to 3 
 
 3/4 to 3 1/4 
 3/4 to 3 1/ 2 
 3/ 4 to 3 3/ 4 
 3/ 4 to 4 
 3/ 4 to 41/4 
 
 1 to 41/2 
 1 1/4 to 43/4 
 1 1/2 to 5 
 
 1 3/ 4 to 5 
 
 2 to 5 
 2 to 5 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9 /l6 
 
 5/8 
 
 11/16 
 
 3/4 
 
 7/8 
 
 U/8 
 
 11/4 
 
 13/ 8 
 
 H/2 
 
 0.53 
 
 .62 
 
 .71 
 
 .80 
 
 .89 
 
 .98 
 
 1.06 
 
 1.24 
 
 1.60 
 
 1.77 
 
 1.95 
 
 2.13 
 
 3/ 4 to 3 
 3/4 to 3 1/ 4 
 3/4 to 3 1/ 2 
 3/4 to 33/ 4 
 3/ 4 to 4 
 3/4 to 41/4 
 
 1 to 41/2 
 1 1/4 to 43/ 4 
 1 1/2 to 5 
 
 1 3/ 4 to 5 
 
 2 to 5 
 21/4 to 5 
 
 Round and Fillister Head 
 Cap-screws. 
 
 Flat Head Cap-screws. 
 
 Button-head Cap- 
 screws. 
 
 Diam. of 
 Head. 
 
 Lengths 
 
 (under 
 
 Head). 
 
 Diam. of 
 Head. 
 
 Lengths 
 
 (including 
 
 Head). 
 
 Diam. of 
 Head. 
 
 Lengths 
 (under 
 Head). 
 
 (A) 3/ie 
 
 (B) 1/4 
 
 (C) 3/8 
 
 (D) 7/ie 
 
 (E) 9/16 
 
 (F) 5/8 
 
 (G) 3/4 
 (H) 13/16 
 (I) 7/ 8 
 (J) 1 
 (K) U/8 
 (L) 1 1/4 
 
 3/ 4 to 21/2 
 3/4 to 23/4 
 3/4 to 3 
 3/ 4 to 31/4 
 3/ 4 to 3 1/2 
 3/ 4 to 33/ 4 
 3/4 to 4 
 
 1 to 41/4 
 U/4 to 41/2 
 1 1/2 to 43/4 
 1 3/ 4 to 5 
 
 2 to 5 
 
 1/4 
 3/8 
 
 15/32 
 5/8 
 3/4 
 
 13/16 
 7/8 
 1 
 
 U/8 
 
 13/8 
 
 3/4 to 1 3/4 
 3/4 to 2 
 3/ 4 to 21/4 
 3/ 4 to 23/4 
 3/ 4 to 3 
 
 1 to 3 
 1 1/4 to 3 
 1 1/2 to 3 
 1 3/ 4 to 3 
 
 2 to 3 
 
 7/32 (-225) 
 5/16 
 7/16 
 9/16 
 5/8 
 3/4 
 13/16 
 15/16 
 
 U/4 
 
 3/4 to 13/4 
 3/4 to 2 
 3/4 to 21/ 4 
 3/ 4 to 21/2 
 3/4 to 23/ 4 
 3/4 to 3 
 1 to 3 
 
 1 1/4 to 3 
 
 1 1/2 to 3 
 
 1 3/ 4 to 3 
 
 Threads are U. S. Standard. Cap-screws are threaded 3/ 4 length up 
 to and including 1 inch diameter X 4 inches long, and 1/2 length above. 
 Lengths increase by 1/4 inch each regular size between the limits given. 
 Lengths of heads, except flat and button, equal diameter of screws. 
 
 The angle of the cone of the flat-head screw is 76 degrees, the sides 
 making angles of 52 degrees with the top. 
 
226 
 
 MATERIALS. 
 
 THE ACME SCREW THREAD. 
 
 The Acme Thread is an adaptation of the commonly used style of worm j 
 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 -*- No. of Threads per in.) - 0.0052. 
 
 Width of screw or nut thread = 0.3707 -s- No. of Threads per in. 
 
 Diam. of Tap = Diam. of Screw + 0.020. 
 
 : Diam. of Screw- XT „ „„ r^, 1 ,^ ._ + 0.020. 
 
 Diam. of Tap or ) 
 Screw at Root J 
 
 Depth of Thread = (1 
 
 No. of Threads per in. 
 - 2 X No. of Threads per in.) + 0.010. 
 
 MACHINE SCREWS.— A. £.M.#. Standard. 
 
 The 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 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 of the diameter 
 as expressed by the formula 
 
 Threads per inch = D + 002 m 
 
 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 
 
 Mini- 
 
 Maxi- 
 
 Dif- 
 fer- 
 
 Mini- 
 
 Maxi- 
 
 Dif- 
 fer- 
 
 Mini- 
 
 Maxi- 
 
 Dif- 
 
 
 Thds. 
 
 mum. 
 
 mum. 
 
 
 mum. 
 
 mum. 
 
 
 mum. 
 
 mum. 
 
 
 
 
 
 ence. 
 
 
 
 ence. 
 
 
 
 ence. 
 
 
 per In. 
 
 
 
 
 
 
 
 
 
 
 
 
 0.060-80 
 
 0.0572 
 
 0.060 
 
 0.0028 
 
 0.0505 
 
 0.0519 
 
 0.0014 
 
 0.0410 
 
 0.0438 
 
 0.0028 
 
 I 
 
 .073-72 
 
 .070 
 
 .073 
 
 .003 
 
 .0625 
 
 .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 
 
 .C048 
 
 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. 
 
 227 
 
 A.S.M.E. STANDARD TAPS. 
 
 (Corbin Screw Corporation.) 
 
 Size. 
 
 Outside Diameters. 
 
 Pitch Diameters. 
 
 Root Diameters. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Tap 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Out. 
 
 
 
 
 
 
 
 
 
 
 Drill 
 
 No. 
 
 Dia. 
 
 and 
 Thds. 
 
 per 
 Inch. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Mini- 
 mum. 
 
 Maxi- 
 mum. 
 
 Dif- 
 fer- 
 ence. 
 
 Di- 
 am- 
 eters. 
 
 
 
 0.060-80 
 
 0.0609 
 
 0.0632 
 
 0.0023 
 
 0.0528 
 
 0.0538 
 
 0.001 
 
 0.0447 
 
 0.0466 
 
 0.0019 
 
 0.0465 
 
 1 
 
 .073-72 
 
 .074 
 
 .0765 
 
 .0025 
 
 .065 
 
 .066 
 
 .001 
 
 .056 
 
 .058 
 
 .002 
 
 .0595 
 
 2 
 
 .086-64 
 
 .0871 
 
 .0898 
 
 .0027 
 
 .0770 
 
 .0781 
 
 .0011 
 
 .0668 
 
 .0689 
 
 .0021 
 
 .070 
 
 3 
 
 .099-56 
 
 .1002 
 
 .1033 
 
 .0031 
 
 .0886 
 
 .0897 
 
 .0011 
 
 .077 
 
 .0793 
 
 .0023 
 
 .0785 
 
 4 
 
 .112-48 
 
 .1133 
 
 .1168 
 
 .0035 
 
 .0998 
 
 .101 
 
 .0012 
 
 .0852 
 
 .0887 
 
 .0025 
 
 .089 
 
 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 
 
 .110 
 
 7 
 
 .151-36 
 
 .1525 
 
 .1569 
 
 .0044 
 
 .1345 
 
 .1359 
 
 .0014 
 
 .1164 
 
 .1193 
 
 .0029 
 
 .120 
 
 8 
 
 .164-36 
 
 .1655 
 
 .1699 
 
 .0044 
 
 .1475 
 
 .1489 
 
 .0014 
 
 .1294 
 
 .1323 
 
 .0029 
 
 .136 
 
 9 
 
 .177-32 
 
 .1786 
 
 .1835 
 
 .0049 
 
 .1583 
 
 .1598 
 
 .0015 
 
 .138 
 
 .1411 
 
 .0031 
 
 .1405 
 
 10 
 
 .190-30 
 
 .1916 
 
 .1968 
 
 .0052 
 
 .170 
 
 .1716 
 
 .0016 
 
 .1483 
 
 .1515 
 
 .0032 
 
 .152 
 
 12 
 
 .216-28 
 
 .2176 
 
 .2232 
 
 .0056 
 
 .1944 
 
 .1961 
 
 .0017 
 
 .1712 
 
 .1745 
 
 .0033 
 
 .173 
 
 14 
 
 .242-24 
 
 .2438 
 
 .250 
 
 .0062 
 
 .2167 
 
 .2184 
 
 .0017 
 
 .1897 
 
 .1932 
 
 .0035 
 
 .1935 
 
 16 
 
 .268-22 
 
 .2698 
 
 .2765 
 
 .0067 
 
 .2403 
 
 .2421 
 
 .0018 
 
 .2108 
 
 .2144 
 
 .0036 
 
 .213 
 
 18 
 
 .294-20 
 
 .2959 
 
 .3031 
 
 .0072 
 
 .2634 
 
 .2652 
 
 .0018 
 
 .2309 
 
 .2346 
 
 .0037 
 
 .234 
 
 20 
 
 .320-20 
 
 .3219 
 
 .3291 
 
 .0072 
 
 .2894 
 
 .2912 
 
 .0018 
 
 .2569 
 
 .2606 
 
 .0037 
 
 .261 
 
 22 
 
 .346-18 
 
 .3479 
 
 .3559 
 
 .0080 
 
 .3118 
 
 .3138 
 
 .0020 
 
 .2757 
 
 .2796 
 
 .0039 
 
 .281 
 
 24 
 
 .372-16 
 
 .374 
 
 .3828 
 
 .0088 
 
 .3334 
 
 .3354 
 
 .0020 
 
 .2928 
 
 .2968 
 
 .004C 
 
 .2968 
 
 26 
 
 .398-16 
 
 .400 
 
 .4088 
 
 .0088 
 
 .3594 
 
 .3614 
 
 .002C 
 
 .3188 
 
 .3228 
 
 .004C 
 
 .323 
 
 28 
 
 .424-14 
 
 .4261 
 
 .4359 
 
 .0098 
 
 .3797 
 
 .3818 
 
 .0021 
 
 .3333 
 
 .3374 
 
 .0041 
 
 .339 
 
 30 
 
 .450-14 
 
 .4521 
 
 .4619 
 
 .0098 
 
 .4057 
 
 .4078 
 
 .0021 
 
 .3593 
 
 .3634 
 
 .0041 
 
 .368 
 
 SPECIAL TAPS. 
 
 1 
 
 0.073-64 
 
 0.0741 
 
 0.0768 
 
 0.0027 
 
 0.064 
 
 0.0651 
 
 0.0011 
 
 0.0538 
 
 0.0559 
 
 0.0021 
 
 0.055 
 
 2 
 
 .086-56 
 
 .0872 
 
 .0903 
 
 .0031 
 
 .0756 
 
 .0767 
 
 .0011 
 
 .064 
 
 .0663 
 
 .0023 
 
 .067 
 
 3 
 
 .099-48 
 
 .1003 
 
 .1038 
 
 .0035 
 
 .0868 
 
 .088 
 
 .0012 
 
 .0732 
 
 .0757 
 
 .0025 
 
 .076 
 
 4 
 
 .112-40 
 
 .1134 
 
 .1175 
 
 .0041 
 
 .0972 
 
 .0986 
 
 .0014 
 
 .0809 
 
 .0837 
 
 .0028 
 
 .082 
 
 
 36 
 
 .1135 
 
 .1179 
 
 .0044 
 
 .0955 
 
 .0969 
 
 .0014 
 
 .0774 
 
 .0803 
 
 .0029 
 
 .081 
 
 5 
 
 .125-40 
 
 .1264 
 
 .1305 
 
 .0041 
 
 .1102 
 
 .1116 
 
 .0014 
 
 .0939 
 
 .0967 
 
 .C028 
 
 .098 
 
 
 36 
 
 .1255 
 
 .1309 
 
 .0044 
 
 .1085 
 
 .1099 
 
 .0014 
 
 .0904 
 
 .0933 
 
 .0029 
 
 .0935 
 
 6 
 
 .138-36 
 
 .1395 
 
 .1439 
 
 .0044 
 
 .1215 
 
 .1229 
 
 .0014 
 
 .1034 
 
 .1063 
 
 .0029 
 
 .1065 
 
 
 32 
 
 .1396 
 
 .1445 
 
 .0049 
 
 .1193 
 
 .1208 
 
 .0315 
 
 .099 
 
 .1021 
 
 .0031 
 
 .1015 
 
 7 
 
 .151-32 
 
 .1526 
 
 .1575 
 
 .0049 
 
 .1323 
 
 .1338 
 
 .0315 
 
 .112 
 
 .1151 
 
 .0031 
 
 .116 
 
 
 30 
 
 .1526 
 
 .1578 
 
 .0052 
 
 .131 
 
 .1326 
 
 .0016 
 
 .1093 
 
 .1125 
 
 .0032 
 
 .113 
 
 8 
 
 .164-32 
 
 .1656 
 
 .1705 
 
 .0049 
 
 .1453 
 
 .1468 
 
 .0015 
 
 .125 
 
 .1281 
 
 .0031 
 
 .1285 
 
 
 30 
 
 .1656 
 
 .1708 
 
 .0052 
 
 .144 
 
 .1456 
 
 .0016 
 
 .1223 
 
 .1255 
 
 ."032 
 
 .1285 
 
 9 
 
 .177-30 
 
 .1786 
 
 .1838 
 
 .0052 
 
 .1569 
 
 .1585 
 
 .0016 
 
 .1353 
 
 .1385 
 
 .0032 
 
 .1405 
 
 
 24 
 
 .1788 
 
 .185 
 
 .0962 
 
 .1517 
 
 .1534 
 
 .0017 
 
 .1247 
 
 .1282 
 
 .0035 
 
 .1285 
 
 10 
 
 .190-32 
 
 .1916 
 
 .1965 
 
 .0049 
 
 .1713 
 
 .1728 
 
 .0015 
 
 .151 
 
 .1541 
 
 .0031 
 
 .154 
 
 
 24 
 
 .1918 
 
 .198 
 
 .:062 
 
 .1647 
 
 .1664 
 
 .0017 
 
 .1377 
 
 .1412 
 
 .0035 
 
 .1405 
 
 12 
 
 .216-24 
 
 .2178 
 
 .224 
 
 .0062 
 
 .1907 
 
 . 1 ?24 
 
 .0017 
 
 .1637 
 
 .1672 
 
 .C035 
 
 .166 
 
 14 
 
 .242-20 
 
 .2439 
 
 .2511 
 
 .0072 
 
 .2114 
 
 .2132 
 
 .0018 
 
 .1789 
 
 .1826 
 
 .0037 
 
 .182 
 
 16 
 
 .268-20 
 
 .2699 
 
 .2771 
 
 .0072 
 
 .2374 
 
 .2392 
 
 .0018 
 
 .2049 
 
 .2086 
 
 .0037 
 
 .209 
 
 18 
 
 .294-18 
 
 .2959 
 
 .3039 
 
 .0080 
 
 .2598 
 
 .2618 
 
 .0020 
 
 .2237 
 
 .2276 
 
 .0039 
 
 .228 
 
 20 
 
 .320-18 
 
 .3219 
 
 .3299 
 
 .0080 
 
 .2858 
 
 .2878 
 
 .0020 
 
 .2497 
 
 .2536 
 
 .0039 
 
 .257 
 
 22 
 
 .346-16 
 
 .348 
 
 .3568 
 
 .0088 
 
 .3074 
 
 .3094 
 
 .0020 
 
 .2668 
 
 .2708 
 
 .0040 
 
 .272 
 
 24 
 
 .372-18 
 
 .3739 
 
 .3819 
 
 .0080 
 
 .3378 
 
 .3398 
 
 .0020 
 
 .3017 
 
 .3056 
 
 .0039 
 
 .3125 
 
 26 
 
 .398-14 
 
 .4001 
 
 .4099 
 
 .0098 
 
 .3537 
 
 .3558 
 
 .0021 
 
 .3073 
 
 .3114 
 
 .0041 
 
 .316 
 
 28 
 
 .424-16 
 
 .426 
 
 .4348 
 
 .0088 
 
 .3854 
 
 .3874 
 
 .0020 
 
 .3448 
 
 .3488 
 
 .0040 
 
 .348 
 
 30 
 
 .450-16 
 
 .452 
 
 .4608 
 
 .0088 
 
 .4114 
 
 .4134 
 
 .0020 
 
 .3708 
 
 .3748 
 
 .0040 
 
 .377 
 
228 
 
 MATERIALS. 
 
 DIMENSIONS OF MACHINE SCREW HEADS, A.S.M.E. 
 STANDARD. 
 
 ROUND HEAD. 
 
 (2) 
 
 H3 
 
 OVAL. FILLISTER FLAT FILLI8- 
 HEAD. TER HEAD. 
 
 (3) (4) 
 
 Dimensions. 
 
 A=Diam.ofBody. D 
 B = Diameter of 
 
 Head, and r ad. 
 
 of oval (3). 
 C = H eight of i a-O.OC 
 
 Head or Side > — ■ _ on 
 
 of Head (3). ) 1 - 739 
 E= Width of Slot, 1/3C 
 F= Height of ) 
 
 Head (3). J 
 
 Width of Slot = 0.173 A + 0.015. 
 
 (1) (2) (3) (4) 
 
 2A-0.008 1.85A- 0.005 1.64A-0.009 1.64A- 0.009 
 
 0.7A 0.66A-0.002 0.66A- 0.002. 
 V2C+O.OI 1/ 2 F I/2C 
 0.134B]+C 
 
 A 
 
 B 
 
 B 
 
 B 
 
 C! 
 
 C 
 
 C 
 
 D 
 
 0~025~ 
 
 E 
 
 E 
 
 E 
 
 E 
 
 F 
 
 (1) 
 
 (2) 
 
 106 
 
 (3,4) 
 
 (1) 
 
 (2) 
 
 (3,4) 
 
 (1) 
 
 (2) 
 
 oToTT 
 
 (3) 
 
 (4) 
 
 0.019 
 
 (3) 
 
 0.060 
 
 11?. 
 
 0.0894 
 
 029 
 
 042 
 
 0.0376 
 
 0.010 
 
 0.025 
 
 0.0496 
 
 073 
 
 138 
 
 130 
 
 .1107 
 
 .037 
 
 .051 
 
 .0461 
 
 .028 
 
 .012 
 
 .035 
 
 .030 
 
 023 
 
 .0609 
 
 086 
 
 164 
 
 154 
 
 .132 
 
 ,045 
 
 ,060 
 
 .0548 
 
 .030 
 
 .015 
 
 .040 
 
 .036 
 
 027 
 
 .0725 
 
 099 
 
 190 
 
 178 
 
 .153 
 
 052 
 
 069 
 
 .0633 
 
 .032 
 
 .017 
 
 .044 
 
 .042 
 
 .032 
 
 .0838 
 
 .112 
 
 .216 
 
 .202 
 
 .1747 
 
 .060 
 
 .078 
 
 .0719 
 
 .034 
 
 .020 
 
 .049 
 
 .048 
 
 .036 
 
 .0953 
 
 .125 
 
 242 
 
 226 
 
 .196 
 
 067 
 
 087 
 
 .0805 
 
 .037 
 
 022 
 
 .053 
 
 .053 
 
 .040 
 
 .1068 
 
 ,138 
 
 262 
 
 250 
 
 .217 
 
 075 
 
 096 
 
 .089 
 
 .039 
 
 .025 
 
 .058 
 
 .059 
 
 .044 
 
 .1180 
 
 .151 
 
 294 
 
 274 
 
 .2386 
 
 ,082 
 
 .105 
 
 .0976 
 
 .041 
 
 .027 
 
 .062 
 
 .065 
 
 .049 
 
 .1296 
 
 .164 
 
 320 
 
 298 
 
 .2599 
 
 090 
 
 114 
 
 .1062 
 
 .043 
 
 .030 
 
 .067 
 
 .071 
 
 053 
 
 .1410 
 
 .177 
 
 .346 
 
 .322 
 
 .2813 
 
 .097 
 
 .123 
 
 .1148 
 
 .046 
 
 .032 
 
 .071 
 
 .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 
 
 472 
 
 443 
 
 .3879 
 
 .135 
 
 169 
 
 .1577 
 
 .057 
 
 .045 
 
 .094 
 
 .105 
 
 .079 
 
 .2097 
 
 268 
 
 .528 
 
 491 
 
 .4305 
 
 .150 
 
 .187 
 
 .1748 
 
 .061 
 
 .050 
 
 .103 
 
 .116 
 
 .087 
 
 .2325 
 
 294 
 
 .580 
 
 .539 
 
 .4731 
 
 .164 
 
 .205 
 
 .192 
 
 .066 
 
 .055 
 
 .112 
 
 .128 
 
 .096 
 
 .2554 
 
 320 
 
 632 
 
 587 
 
 .5158 
 
 179 
 
 224 
 
 .2092 
 
 .070 
 
 .060 
 
 .122 
 
 .140 
 
 104 
 
 .2783 
 
 .346 
 
 682 
 
 635 
 
 .5584 
 
 .194 
 
 .242 
 
 .2263 
 
 .075 
 
 .065 
 
 .131 
 
 .150 
 
 .113 
 
 .3011 
 
 „372 
 
 .732 
 
 ,683 
 
 .601 
 
 .209 
 
 .260 
 
 .2435 
 
 .079 
 
 .070 
 
 .140 
 
 .162 
 
 .122 
 
 .3240 
 
 .398 
 
 .788 
 
 .731 
 
 .6437 
 
 .224 
 
 .278 
 
 .2606 
 
 .084 
 
 .075 
 
 .149 
 
 .173 
 
 .130 
 
 .3469 
 
 .424 
 
 .840 
 
 .779 
 
 .6863 
 
 .239 
 
 .296 
 
 .2778 
 
 .088 
 
 .080 
 
 .158 
 
 .185 
 
 .139 
 
 .3698 
 
 .450 
 
 .892 
 
 .827 
 
 .727 
 
 .254 
 
 .315 
 
 .295 
 
 .093 
 
 .085 
 
 .167 
 
 .201 
 
 .147 
 
 .4024 
 

 WEIGHT OF 
 WEIGHT OF 
 
 100 BOLTS WITH SQUARE 
 
 100 BOLTS WITH SQUARE 
 
 (Hoopes & Townsend.) 
 
 HEADS. 
 HEADS. 
 
 220 
 
 
 am. 
 3hes. 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 H/8 
 
 11/4 
 
 13/8 
 
 11/2 
 
 13/4 
 
 2 I 
 
 agth. 
 ches. 
 
 H/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 51/2 
 
 6 
 
 61/ 2 
 
 7 
 '71/2 
 
 8 
 
 9 
 10 
 II 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 
 lbs. 
 3.9 
 4.6 
 5.4 
 6.2 
 6.9 
 7.6 
 8.3 
 9.0 
 9.7 
 10.4 
 11.1 
 11.8 
 12.5 
 13.2 
 
 lbs. 
 6.2 
 7.2 
 8.2 
 9.3 
 10.4 
 11.5 
 12.6 
 13.7 
 14.8 
 15.9 
 17.0 
 18.1 
 19.2 
 20.3 
 
 lbs. 
 9.7 
 11.3 
 12.9 
 14.5 
 16.1 
 17.7 
 19.2 
 20.7 
 22.2 
 23.7 
 25.2 
 2o.7 
 28.2 
 29.7 
 33.1 
 36.5 
 40.0 
 43.5 
 
 lbs. 
 14.7 
 16.5 
 18.5 
 20.5 
 22.6 
 24.7 
 26.8 
 28.9 
 31.0 
 33.1 
 35.2 
 37.3 
 39.4 
 41.5 
 45.7 
 49.9 
 54.1 
 58.3 
 
 lbs. 
 20.4 
 22.4 
 25.0 
 27.8 
 30.6 
 33.4 
 36.2 
 39.0 
 41.8 
 44.6 
 47.4 
 50.2 
 53.1 
 56.0 
 61.5 
 67.0 
 72.5 
 78.0 
 83.5 
 89.0 
 94.5 
 100.0 
 105.5 
 111.0 
 116.5 
 122.0 
 
 lbs. 
 
 26.0 
 29.0 
 32.2 
 35.4 
 38.7 
 42.0 
 45.3 
 48.6 
 51.9 
 55.2 
 58.5 
 61.8 
 65.1 
 68.5 
 75.2 
 81.9 
 88.7 
 95.5 
 102.3 
 109.1 
 116.0 
 123.0 
 130.0 
 137.0 
 
 144:0 
 
 151.0 
 
 lbs. 
 37.0 
 39.9 
 44.1 
 48.3 
 52.5 
 56.7 
 60.9 
 65.1 
 69.2 
 73.4 
 77.6 
 81.8 
 86.0 
 90.0 
 98.0 
 106.3 
 114.6 
 122.9 
 131.2 
 139.5 
 148.0 
 
 156:5 
 
 165.0 
 173.5 
 182.0 
 190.5 
 198.0 
 206.0 
 215.0 
 224.0 
 
 lbs. 
 58.0 
 63.2 
 69.0 
 75.2 
 81.4 
 87.6 
 93.8 
 100.0 
 106.1 
 112.2 
 118.3 
 124.4 
 130.5 
 136.6 
 148.8 
 161.0 
 173.2 
 184.4 
 196.6 
 208.8 
 221.0 
 233.2 
 245.4 
 257.6 
 269.8 
 282.0 
 294.0 
 306.0 
 318.0 
 330.0 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 97.7 
 105.6 
 113.8 
 122.0 
 130.2 
 138.4 
 146.6 
 154.9 
 163.2 
 171.5 
 179.8 
 187.1 
 195.4 
 212.0 
 229.0 
 246.0 
 263.0 
 280.0 
 297.0 
 314.0 
 331.0 
 348.0 
 365.0 
 382.0 
 399.0 
 416.0 
 437.0 
 454.0 
 470.0 
 
 145 
 153 
 163 
 174 
 185 
 196 
 207 
 218 
 229 
 240 
 251 
 262 
 273 
 295 
 317 
 339 
 361 
 383 
 405 
 427 
 449 
 471 
 493 
 515 
 537 
 559 
 581 
 603 
 625 
 
 
 
 
 
 
 
 
 
 
 
 
 
 240 
 253 
 267 
 281 
 295 
 309 
 323 
 337 
 351 
 365 
 379 
 407 
 435 
 463 
 491 
 519 
 547 
 575 
 603 
 631 
 659 
 687 
 715 
 743 
 771 
 799 
 827 
 855 
 
 309 
 325 
 342 
 359 
 376 
 394 
 412 
 430 
 448 
 466 
 484 
 518 
 552 
 586 
 620 
 655 
 690 
 725 
 760 
 795 
 830 
 865 
 900 
 935 
 970 
 1005 
 1040 
 1075 
 
 350 
 370 
 390 
 410 
 430 
 450 
 470 
 490 
 510 
 530 
 550 
 590 
 630 
 670 
 710 
 751 
 793 
 835 
 877 
 919 
 961 
 1003 
 1045 
 1087 
 1129 
 1171 
 1213 
 1?Vi 
 
 480 
 500 
 520 
 545 
 570 
 595 
 620 
 645 
 670 
 695 
 725 
 775 
 825 
 875 
 925 
 975 
 1025 
 1075 
 1125 
 1175 
 1225 
 1275 
 1325 
 1375 
 1425 
 1475 
 1525 
 157S 
 
 
 
 
 
 800 
 833 
 866 
 900 
 934 
 968 
 1002 
 1036 
 1070 
 1138 
 1206 
 1274 
 1342 
 1410 
 1478 
 1548 
 1616 
 1684 
 1752 
 1820 
 1888 
 1956 
 2024 
 2092 
 2160 
 ??7fi 
 
 1370 
 1414 
 1458 
 1502 
 1546 
 1590 
 1634 
 1722 
 
 
 
 1810 
 
 
 
 1898 
 
 
 
 1986 
 
 
 
 2074 
 
 
 
 
 
 2162 
 
 
 
 
 
 2250 
 
 
 
 
 
 2338 
 
 
 
 
 
 2426 
 
 
 
 
 
 2514 
 
 
 
 
 
 2602 
 
 
 
 
 
 2690 
 
 
 
 
 
 2778 
 
 
 
 
 
 
 
 2866 
 
 
 
 
 
 
 
 2954 
 
 
 
 
 
 
 
 3042 
 
 
 
 
 
 
 
 3130 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ROUND HEAD RIVETS. 
 
 
 
 
 
 
 
 Approximate Number in One Pound. (Garland Nut & Rivet Co.) 
 
 si 
 
 7/16 
 
 3/8 
 
 5/13 
 
 1/4 
 
 7/32 
 
 3/16 
 
 r, /32 
 
 1/8 
 
 - - 
 
 7/16 
 
 3/8 
 
 5/16 
 
 1/4 
 
 7/32 
 
 3/16 
 
 f) /32 
 
 1/8 
 
 CJ 
 
 
 
 
 
 
 
 
 
 3^ 
 
 
 
 
 
 
 
 
 
 3/s 
 
 
 
 68 
 
 103 
 
 145 
 
 184 
 
 194 
 
 204 
 
 13/8 
 
 10 l/o 
 
 15 
 
 22 
 
 34 
 
 46 
 
 65 
 
 76 
 
 87 
 
 v? 
 
 
 31 
 
 51 
 
 80 
 
 108 
 
 155 
 
 165 
 
 175 
 
 1 3/,, 
 
 10 
 
 14 
 
 21 
 
 32 
 
 43 
 
 62 
 
 72 
 
 81 
 
 5/8 
 
 
 28 
 
 45 
 
 70 
 
 94 
 
 135 
 
 148 
 
 160 
 
 17/s 
 
 91/o 
 
 13 
 
 20 
 
 30 
 
 41 
 
 58 
 
 69 
 
 
 3/ 4 
 
 17 
 
 24 
 
 39 
 
 63 
 
 84 
 
 119 
 
 132 
 
 144 
 
 2 
 
 9 
 
 12 
 
 19 
 
 29 
 
 39 
 
 55 
 
 67 
 
 
 7/8 
 
 15 
 
 22 
 
 35 
 
 56 
 
 75 
 
 106 
 
 121 
 
 135 
 
 21/1 
 
 81/4 
 
 11 
 
 17 
 
 27 
 
 35 
 
 49 
 
 
 
 1 
 
 14 
 
 20 
 
 32 
 
 50 
 
 68 
 
 96 
 
 111 
 
 126 
 
 2 l/o 
 
 73/ 4 
 
 10 
 
 16 
 
 24 
 
 32 
 
 45 
 
 
 
 H/8 
 
 13 
 
 19 
 
 30 
 
 46 
 
 62 
 
 88 
 
 102 
 
 116 
 
 23/.« 
 
 71/4 
 
 9 
 
 14 
 
 22 
 
 29 
 
 42 
 
 
 
 U/4 
 
 12 
 
 18 
 
 28 
 
 43 
 
 57 
 
 81 
 
 94 
 
 108 
 
 3 
 
 63/ 4 
 
 8 
 
 13 
 
 20 
 
 21 
 
 39 
 
 
 
 13/8 
 
 111/9 
 
 17 
 
 26 
 
 40 
 
 53 
 
 74 
 
 87 
 
 100 
 
 i 1/9 
 
 6 
 
 7 
 
 11 
 
 18 
 
 lb 
 
 34 
 
 
 
 H/2 
 
 11 
 
 16 
 
 24 
 
 37 
 
 50 
 
 69 
 
 81 
 
 93 
 
 4 
 
 5 
 
 6 
 
 10 
 
 16 
 
 20 
 
 30 
 
 
 
 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 6/33 U/ M 3/ 16 
 
 Approx. diam 094 .109 .125 .140 .155 .170 .185 
 
 Size 7/32 1/4 9 /32 5 / 16 3/ 8 7/ 16 
 
 Approx. diam 215 .245 .275 .305 .365 .425 
 
230' 
 
 MATERIALS. 
 
 
 With United 
 
 TRACK BOLTS. 
 
 States Standard Hexagon Nuts. 
 
 
 
 Wt.of 
 
 Rail. 
 
 Lb. per 
 
 Yard. 
 
 Bolts. 
 
 Nuts. 
 
 No. in 
 Keg, 
 200 
 Lb. 
 
 Kegs 
 per 
 Mile. 
 
 Wt. of 
 
 Rail. 
 
 Lbs. per 
 
 Yard. 
 
 
 Nuts. 
 
 No. in 
 Keg, 
 200 
 Lb. 
 
 375 
 410 
 435 
 465 
 715 
 760 
 800 
 820 
 
 Kegs 
 per 
 Mile. 
 
 45 to 85 | 
 
 3/ 4 x41/4 
 
 3/ 4 x4 
 
 3/4X33/4 
 
 3/4X31/2 
 
 3/4x31/4 
 
 3/4 X 3 
 
 11/4 
 U/4 
 U/4 
 11/4 
 U/4 
 U/4 
 
 230 
 240 
 254 
 260 
 266 
 283 
 
 6.3 
 6. 
 
 5.7 
 5.5 
 5.4 
 5.1 
 
 30 to 40 J 
 20 to 30 J 
 
 U/16 
 U/16 
 U/16 
 U/16 
 
 7/8 
 7/8 
 7/8 
 7/8 
 
 4. 
 3.7 
 3.3 
 3.1 
 
 2. 
 2. 
 2. 
 2. 
 
 WROUGHT WASHERS, MANUFACTURERS' STANDARD. 
 
 (Upson Nut Co., Cleveland, 1906.) 
 
 Diam. 
 
 Hole. 
 
 Thick- 
 ness 
 B.W.G. 
 
 Bolt. 
 
 No. in 
 200 Lb. 
 
 Diam. 
 
 Hole. 
 
 Thick- 
 ness 
 B.W.G. 
 
 Bolt. 
 
 No. in 
 200 Lb 
 
 In. 
 
 In. 
 
 No. 
 
 In. 
 
 
 In. 
 
 In. 
 
 No. 
 
 In. 
 
 
 »/ifi 
 
 1/4 
 
 18 
 
 3/16 
 
 85200 
 
 21/? 
 
 1 V16 
 
 9 
 
 1 
 
 1200 
 
 3/4 
 
 W1R 
 
 16 
 
 1/4 
 
 34800 
 
 23/4 
 
 11/4 
 
 9 
 
 U/8 
 
 888 
 
 7/8 
 
 a/« 
 
 16 
 
 5/16 
 
 26200 
 
 3 
 
 13/8 
 
 9 
 
 U/4 
 
 900 
 
 1 
 
 7/lfi 
 
 14 
 
 3/8 
 
 14400 
 
 31/4 
 
 U/9, 
 
 8 
 
 13/ 8 
 
 600 
 
 U/4 
 
 V? 
 
 14 
 
 7/16 
 
 8400 
 
 31/2 
 
 15/8 
 
 8 
 
 11/2 
 
 570 
 
 m 
 
 a/16 
 
 12 
 
 1/2 
 
 5800 
 
 33/4 
 
 13/ 4 
 
 8 
 
 15/8 
 
 460 
 
 11/2 
 
 Vr 
 
 12 
 
 9/16 
 
 4600 
 
 4 
 
 17/8 
 
 8 
 
 13/4 
 
 432 
 
 13/4 
 
 11/16 
 
 10 
 
 5/8 
 
 2600 
 
 41/4 
 
 2 
 
 8 
 
 17/8 
 
 366 
 
 2 
 
 13/1 fl 
 
 10 
 
 3/4 
 
 2200 
 
 41/2 
 
 21/8 
 
 8 
 
 2 
 
 356 
 
 21/4 
 
 l°/l6 
 
 9 
 
 7/8 
 
 1600 
 
 
 
 
 
 
 
 
 
 SIZES OF CAST WASHERS. 
 
 
 
 
 
 (Upson Nut Co., Cleveland, 1906.) 
 
 
 
 Diam. 
 
 Hole. 
 
 Thick. 
 
 Bolt. 
 
 Weight. 
 Lbs. 
 
 Diam. 
 
 Hole. 
 
 Thick. 
 
 Bolt. 
 
 Weight. 
 Lbs. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 
 21/4 
 
 5/8 
 
 H/16 
 
 1/2 
 
 1/2 
 
 4 
 
 11/ 8 
 
 15/16 
 
 1 
 
 15/ 8 
 
 23/4 
 
 3/4 
 
 3/4 
 
 5/8 
 
 5/8 
 
 41/2 
 
 U/4 
 
 1 
 
 U/8 
 
 21/4 
 
 3 
 
 7/8 
 
 13/16 
 
 3/4 
 
 3/4 
 
 5 
 
 13/ 8 
 
 U/8 
 
 U/4 
 
 3 
 
 31/2 
 
 1 
 
 7/8 
 
 7/8 
 
 U/4 
 
 6 
 
 13/4 
 
 U/4 
 
 11/2 
 
 5 
 
TURNBUCKLES. 
 
 231 
 
 CONE-HEAD BOILER RIVETS, Vf EIGHT PER 100. 
 
 . (Hoopes & Townsend.) 
 
 Diam., in., 
 Scant. 
 
 1/2 
 
 9 /l6 
 
 5/8 
 
 H/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 1 
 
 11/8* 
 
 11/4* 
 
 Length. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 3/4 inch 
 
 8.75 
 9.35 
 10.00 
 10.70 
 11.40 
 12.10 
 
 13.7 
 14.4 
 15.2 
 16.0 
 16.8 
 17.6 
 
 16.20 
 17.22 
 18.25 
 19.28 
 20.31 
 21.34 
 
 
 
 
 
 
 
 
 7/8 " 
 
 
 
 
 
 
 
 
 1 
 
 2K70 
 23.10 
 24.50 
 25.90 
 
 '26:55 
 28.00 
 29.45 
 30.90 
 
 
 
 
 
 
 1 1/8 " 
 
 
 
 
 
 
 11/4 " 
 
 37.0' 
 38.6 
 
 "'46' 
 
 48 
 
 '"60" 
 63 
 
 
 
 '3/8 " 
 
 '95' 
 
 
 11/2 " 
 
 12.80 
 
 18.4 
 
 22.37 
 
 27.30 
 
 32.35 
 
 40.2 
 
 50 
 
 65 
 
 98 
 
 " 133 * 
 
 15/8 " 
 
 13.50 
 
 19.2 
 
 23.40 
 
 28.70 
 
 33.80 
 
 41.9 
 
 52 
 
 67 
 
 101 
 
 137 
 
 13/4 " 
 
 14.20 
 
 20.0 
 
 24.43 
 
 30.10 
 
 35.25 
 
 43.5 
 
 54 
 
 69 
 
 104 
 
 141 
 
 17/8 " 
 
 14.90 
 
 20.8 
 
 25.46 
 
 31.50 
 
 36.70 
 
 45.2 
 
 56 
 
 71 
 
 107 
 
 145 
 
 2 
 
 15.60 
 
 21.6 
 
 26.49 
 
 32.90 
 
 38.15 
 
 47.0 
 
 58 
 
 74 
 
 110 
 
 149 
 
 21/8 " 
 
 16.30 
 
 22.4 
 
 27.52 
 
 34.30 
 
 39.60 
 
 48.7 
 
 60 
 
 77 
 
 114 
 
 153 
 
 21/4 " 
 
 17.00 
 
 23.2 
 
 28.55 
 
 35.70 
 
 41.05 
 
 50.3 
 
 62 
 
 80 
 
 118 
 
 157 
 
 23/8 " 
 
 17.70 
 
 24.0 
 
 29.58 
 
 37.10 
 
 42.50 
 
 51.9 
 
 64 
 
 83 
 
 121 
 
 161 
 
 21/2 " 
 
 18.40 
 
 24.8 
 
 30.61 
 
 38.50 
 
 43.95 
 
 53.5 
 
 66 
 
 86 
 
 124 
 
 165 
 
 25/8 " 
 
 19.10 
 
 25.6 
 
 31.64 
 
 39.90 
 
 45.40 
 
 55.1 
 
 68 
 
 89 
 
 17,7 
 
 169 
 
 23/ 4 " 
 
 19.80 
 
 26.4 
 
 32.67 
 
 41.30 
 
 46.85 
 
 56.8 
 
 70 
 
 92 
 
 130 
 
 173 
 
 27/8 " 
 
 20.50 
 
 27.2 
 
 33.70 
 
 42.70 
 
 48.30 
 
 58.4 
 
 72 
 
 95 
 
 133 
 
 177 
 
 3 
 
 21.20 
 
 28.0 
 
 34.73 
 
 44.10 
 
 49.75 
 
 60.0 
 
 74 
 
 98 
 
 137 
 
 181 
 
 31/4 " 
 
 22.60 
 
 29.7 
 
 36.79 
 
 46.90 
 
 52.65 
 
 63.3 
 
 78 
 
 103 
 
 144 
 
 189 
 
 31/2 " 
 
 24.00 
 
 31.5 
 
 38.85 
 
 49.70 
 
 55.55 
 
 66.5 
 
 82 
 
 108 
 
 151 
 
 197 
 
 33/4 " 
 
 25.40 
 
 33.3 
 
 40.91 
 
 52.50 
 
 58.45 
 
 69.8 
 
 86 
 
 113 
 
 158 
 
 205 
 
 4 
 
 26.80 
 
 35.2 
 
 42.97 
 
 55.30 
 
 61.35 
 
 73.0 
 
 90 
 
 118 
 
 165 
 
 2'3 
 
 41/4 " 
 
 28.20 
 
 36.9 
 
 45.03 
 
 58.10 
 
 64.25 
 
 76.3 
 
 94 
 
 124 
 
 172 
 
 221 
 
 41/2 " 
 
 29.60 
 
 38.6 
 
 47.09 
 
 60.90 
 
 67.15 
 
 79.5 
 
 98 
 
 130 
 
 179 
 
 229 
 
 43/4 " 
 
 31.00 
 
 40.3 
 
 49.15 
 
 63.70 
 
 70.05 
 
 82.8 
 
 102 
 
 136 
 
 186 
 
 237 
 
 5 
 
 32.40 
 
 42.0 
 
 51.27 
 
 66.50 
 
 72.95 
 
 86.0 
 
 106 
 
 142 
 
 193 
 
 245 
 
 51/4 " 
 
 33.80 
 
 43.7 
 
 53.27 
 
 69.20 
 
 75.85 
 
 89.3 
 
 110 
 
 148 
 
 200 
 
 254 
 
 51/2 " 
 
 35.20 
 
 45.4 
 
 55.33 
 
 72.00 
 
 78.75 
 
 92.5 
 
 114 
 
 154 
 
 206 
 
 263 
 
 53/4 «' 
 
 36.60 
 
 47.1 
 
 57.39 
 
 74.80 
 
 81.65 
 
 95.7 
 
 118 
 
 160 
 
 212 
 
 272 
 
 6 
 
 38.00 
 
 48.8 
 
 59.45 
 
 77.60 
 
 84.55 
 
 99.0 
 
 122 
 
 166 
 
 218 
 
 281 
 
 6I/2 " 
 
 40.80 
 
 52.0 
 
 63.57 
 
 83.30 
 
 90.35 
 
 105.5 
 
 130 
 
 177 
 
 231 
 
 297 
 
 7 
 
 43.60 
 
 55.2 
 
 67.69 
 
 88.90 
 
 95.15 
 
 112.0 
 
 138 
 
 188 
 
 245 
 
 314 
 
 Heads 
 
 5.50 
 
 8.40 
 
 11.50 
 
 13.20 
 
 18.00 
 
 23.0 
 
 29.0 
 
 38.0 
 
 56.0 
 
 77.5 
 
 * These two sizes are calculated for exact diameter. 
 
 TURNBUCKLES. 
 
 (Cleveland City Forge and Iron Co.) 
 Standard sizes made with right and left threads. D = 
 
 outside diameter 
 
 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. 
 
232 
 
 MATERIALS. 
 
 TINNERS' RIVETS. FLAT HEADS. 
 
 Garland Nut & Rivet Co. 
 
 gd 
 
 a a 
 
 is 
 
 ■ o 
 
 sfri 
 
 .g 
 
 k 
 
 I s 
 
 -g 
 M • 
 
 C S3 
 
 
 ia 
 
 to • 
 
 S3.C 
 
 0> . 
 
 Q 
 
 h1 
 
 £ 
 
 .Q 
 
 1-} 
 
 fc~ 
 
 Q 
 
 ^ 
 
 £~ 
 
 Q 
 
 Hi 
 
 £- 
 
 0.070 
 
 Vs 
 
 4 oz. 
 
 0.115 
 
 13/fi 4 
 
 1 lb. 
 
 0.160 
 
 5/16 
 
 3 lbs. 
 
 0.225 
 
 7/16 
 
 8 
 
 .080 
 
 9/64 
 
 6 
 
 .120 
 
 7/3? 
 
 H/4 
 
 .163 
 
 *V«4 
 
 31/2 
 
 .230 
 
 ^9/64 
 
 9 
 
 .090 
 
 5/32 
 
 8 
 
 .125 
 
 15/fi 4 
 
 H/?, 
 
 .173 
 
 11/3?, 
 
 4 
 
 .233 
 
 l°/32 
 
 10 
 
 .094 
 
 U/(M 
 
 10 
 
 .133 
 
 1/4 
 
 13/4 
 
 .185 
 
 8/8 
 
 5 
 
 .253 
 
 1/2 
 
 12 
 
 .101 
 
 3 /l6 
 
 12 
 
 .140 
 
 17/64 
 
 2 
 
 .200 
 
 &/«4 
 
 6 
 
 .275 
 
 33/ fi4 
 
 14 
 
 .109 
 
 3/16 
 
 14 
 
 .147 
 
 9/32 
 
 21/2 
 
 .215 
 
 13/32 
 
 7 
 
 .293 
 
 l>/32 
 
 16 
 
 MATERIAL REQUIRED FOR ONE MILE OF SINGLE TRACK 
 RAILROAD. 
 
 (American Bureau of Inspection and Tests, 1908.) 
 Cross Ties. 
 
 33-Foot Rail. 
 
 30-Foot Rail. 
 
 Spacing of 
 Ties, Center 
 to Center. 
 
 Ties per 
 Rail. 
 
 Ties per Mile. 
 
 Ties per Rail. 
 
 Ties per Mile. 
 
 20 
 18 
 16 
 
 3200 
 2880 
 2560 
 
 18 
 16 
 14 
 
 3168 
 2816 
 2464 
 
 1 ft. 6 in. 
 
 1 " 9 " 
 
 2 " " 
 
 Weight per 
 
 Yard. 
 
 Lb. 
 
 Gross Tons 
 Per Mile. 
 
 Weight per 
 
 Yard. 
 
 Lb. 
 
 Gross Tons 
 Per Mile. 
 
 Weight per 
 
 Yard. 
 
 Lb. 
 
 Gross Tons 
 per Mile. 
 
 100 
 90 
 85 
 80 
 75 
 72 
 70 
 
 1571/7 
 1413/ 7 
 133 4/ 7 
 125 5/ 7 
 1176/7 
 1131/7 
 110 
 
 67 
 65 
 60 
 56 
 52 
 50 
 45 
 
 1052/7 
 1021/7 
 942/7 
 88 
 
 815/7 
 78 4/7 
 705/ 7 
 
 40 
 35 
 30 
 25 
 20 
 16 
 12 
 
 626/7 
 55 
 
 471/7 
 392/7 
 313/7 
 251/7 
 I86/7 
 
 Decimal 1 
 5/ 7 =0.714. 
 
 Equivalent fo 
 B/7 = 0.857. 
 
 r i/ 7 = 0.143 
 
 2/ 7 = 0.286. 
 
 3/ 7 = 0.429. 
 
 4/ 7 = 0.571. 
 
233 
 
 To find gross tons per mile of track multiply weight of rail (pounds per 
 yard) by 11 and divide by 7. To find feet of rail per gross ton divide 6720 
 by weight of rail per yard. 
 
 Splices and Bolts. 
 
 Length of Rails 
 Used. 
 
 Number of Joints 
 or Rails. 
 
 Number of Bolts 
 
 Using Four-Hole 
 
 Splices. 
 
 Number of Bolts 
 
 Using Six-Hole 
 
 Splices. 
 
 33 ft. 
 30 " 
 
 320 
 352 
 
 1280 
 1408 
 
 1920 
 2112 
 
 Spikes. 
 
 
 °o 
 
 Kegs per Mile (4 Spikes to a Tie). 
 
 
 Using 33-Ft. 
 
 Using 30-Ft. 
 
 
 
 Under Head. 
 
 »03 
 
 Rails. 
 
 Rails. 
 
 No 
 
 
 
 20 I 18 1 16 
 
 18 | 16 I 14 
 
 £6 
 
 
 < 
 
 Ties per Rail. 
 
 Ties per Rail. 
 
 
 $"£ 
 
 6 x5/ 8 
 
 260 
 
 49.2 
 
 44.3 
 
 39.4 
 
 48.7 
 
 43.3 
 
 37.9 
 
 40.6 
 
 Hi 
 
 6 X9/16 
 
 350 
 
 36.6 
 
 32.9 
 
 29.3 
 
 36.2 
 
 32.2 
 
 28.2 
 
 30.2 
 
 w - 
 
 51/2X5/ 8 
 
 290 
 
 44.1 
 
 39.7 
 
 35.3 
 
 43.7 
 
 38.8 
 
 34.0 
 
 36.4 
 
 g»s 
 
 51/2X 9 /16 
 
 375 
 
 34.1 
 
 30.7 
 
 27.3 
 
 33.8 
 
 30.0 
 
 26.3 
 
 28.2 
 
 
 5 X9/1 6 
 
 400 
 
 32.0 
 
 28.8 
 
 25.6 
 
 31.7 
 
 28.2 
 
 24.6 
 
 26.4 
 
 * 
 
 5 Xl/2 
 
 450 
 
 28.5 
 
 25.6 
 
 22.8 
 
 28.2 
 
 25.0 
 
 21.9 
 
 23.5 
 
 "E 
 
 41/2X1/2 
 
 530 
 
 24.2 
 
 21.8 
 
 19.3 
 
 23.9 
 
 21.3 
 
 18.6 
 
 19.9 
 
 
 
 41/ 2 x7/i6 
 
 680 
 
 18.8 
 
 17.0 
 
 15.1 
 
 18.6 
 
 16.6 
 
 14.5 
 
 15.5 
 
 M 
 
 
 12800 
 
 11520 
 
 10240 
 
 12672 
 
 11264 
 
 9856 
 
 10560 
 
 
 
 
 WROUGHT SPIKES. 
 
 Number of Nails in Keg of 150 Pounds. 
 
 Length, 
 Inches. 
 
 1/4 in. 
 
 5 /l6 in- 
 
 3 /8in. 
 
 Length, 
 Inches. 
 
 1/4 in. 
 
 5 /l6 in. 
 
 3 /8 in. 
 
 7 /l6in. 
 
 1/2 in 
 
 3 
 
 2250 
 1890 
 1650 
 1464 
 1380 
 1292 
 
 
 
 7 
 8 
 9 
 10 
 11 
 12 
 
 1161 
 
 662 
 635 
 573 
 
 482 
 455 
 424 
 391 
 
 445 
 384 
 300 
 270 
 249 
 236 
 
 306 
 
 31/2 
 4 
 
 41/2 
 
 1208 
 1135 
 1064 
 930 
 
 868 
 
 "742' 
 570 
 
 256 
 240 
 222 
 
 
 
 203 
 
 6 
 
 
 
 
 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 
 
 1/2 
 
 
 2375 
 2050 
 1825 
 
 
 
 
 5 " 
 
 1230 
 1175 
 990 
 
 880 
 
 940 
 800 
 650 
 600 
 
 525 
 
 475 
 
 
 6 " 
 
 450 
 
 7 " 
 
 375 
 
 8 " .... 
 
 
 335 
 
 9 " 
 
 
 300 
 
 10 " 
 
 
 
 275 
 
234 
 
 MATERIALS. 
 
 LENGTH 
 
 AND 
 
 NUMBER 
 
 OF 
 
 CUT 
 
 NAILS TO 
 
 THE POUND. 
 
 Size. 
 
 a 
 1-1 
 
 a 
 
 
 
 a 
 a 
 
 
 
 O 
 
 
 
 c 
 
 6 
 a 
 
 73 
 
 m 
 
 a 
 
 '1 
 O 
 
 n 
 
 
 5 
 
 O 
 
 H 
 
 03 
 
 M 
 
 » 
 
 
 
 3/ 4 
 
 3/4 In. 
 
 
 
 
 
 
 sou 
 
 500 
 376 
 224 
 180 
 
 
 
 
 
 7/ 8 
 
 7/8 
 
 1 
 
 11/4 
 
 11/2 
 
 13/4 
 
 2 
 
 21/4 
 
 21/2 
 
 23/4 
 
 3 
 
 31/4 
 
 31/2 
 
 4 
 
 .41/2 
 
 51/2 
 6 
 
 
 
 
 
 
 
 
 
 
 2d 
 
 800 
 
 480 
 
 288 
 
 200 
 
 168 
 
 124 
 
 88 
 
 70 
 
 58 
 
 44 
 
 34 
 
 23 
 
 18 
 
 14 
 
 10 
 
 8 
 
 
 
 1100 
 720 
 523 
 410 
 268 
 188 
 146 
 130 
 102 
 76 
 62 
 54 
 
 1000 
 
 760 
 
 368 
 
 
 
 
 
 3d 
 
 
 
 
 
 
 
 4d 
 
 
 
 398 
 
 
 
 
 5d 
 
 
 
 
 130 
 96 
 
 82 
 68 
 
 
 6d 
 
 95 
 
 74 
 62 
 53 
 46 
 42 
 38 
 33 
 20 
 
 84 
 64 
 48 
 36 
 30 
 24 
 20 
 16 
 
 
 
 224 
 
 126 
 98 
 75 
 65 
 55 
 40 
 27 
 
 
 7d 
 
 
 
 
 8d 
 
 
 
 128 
 110 
 91 
 71 
 
 54 
 40 
 33 
 27 
 
 
 9d 
 
 
 
 
 lOd 
 
 
 
 
 28 
 
 12d 
 
 
 
 
 16d 
 
 
 
 
 22 
 
 20d 
 
 
 
 141/ 2 
 121/2 
 
 91/2 
 
 8 
 
 30d 
 
 
 
 
 
 40d 
 
 
 
 
 
 
 
 50d 
 
 
 
 
 
 
 
 
 60d 
 
 
 
 
 
 
 
 
 
 6 
 
 
 DIMENSIONS OF 
 
 WOOD SCREWS. 
 
 
 No. 
 
 Threads 
 per In. 
 
 Diam. of 
 Body. 
 
 Lengths. 
 
 No. 
 
 Threads 
 per In. 
 
 Diam. of 
 Body. 
 
 Lengths, 
 
 
 
 In. 
 
 In. 
 
 
 
 In. 
 
 In. 
 
 2 
 
 56 
 
 0.0842 
 
 3/16-1/2 
 
 12 
 
 20, 24 
 
 0.2158 
 
 3/8-13/4 
 
 3 
 
 48 
 
 .0973 
 
 3 /l6- 5 /8 
 
 14 
 
 20, 24 
 
 .2421 
 
 3/8-2 
 
 4 
 
 32, 36, 40 
 
 .1105 
 
 3/16-3/4 
 
 16 
 
 16, 18, 20 
 
 .2684 
 
 3/8-21/4 
 
 5 
 
 32, 36, 40 
 
 . 1 236 
 
 3/16-7/8 
 
 18 
 
 16, 18 
 
 .2947 
 
 1/2-21/2 
 
 6 
 
 30, 32 
 
 .1368 
 
 3/16-1 
 
 20 
 
 16, 18 
 
 .3210 
 
 1/2-23/4 
 
 7 
 
 30, 32 
 
 .1500 
 
 1/4-1 1/8 
 
 22 
 
 16, 18 
 
 .3474 
 
 1/2-3 
 
 8 
 
 30, 32 
 
 .1631 
 
 1/4-1 1/4 
 
 24 
 
 14, 16 
 
 .3737 
 
 1/2-3 
 
 9 
 
 24, 30, 32 
 
 .1763 
 
 1/4-13/8 
 
 26 
 
 14, 16 
 
 .4000 
 
 3/4-3 
 
 10 
 
 24, 30, 32 
 
 .1894 
 
 1/4-1 1/2 
 
 28 
 
 14, 16 
 
 .4263 
 
 7/3-8 
 
 
 
 
 
 30 
 
 14, 16 
 
 .4520 
 
 13- 
 
 WEIGHTS AND 
 
 DIMENSIONS OF LAG SCREWS. 
 
 Length in 
 Inches. 
 
 Diameter in Inches. 
 
 3/8 
 Lb. per 100. 
 
 7/16 
 Lb. per 100. 
 
 1/2 
 Lb. per 100. 
 
 5/8 
 Lb. per 100. 
 
 3/ 4 
 Lb. per 100. 
 
 H/2 
 
 6.88 
 7.50 
 8.25 
 9.25 
 9.62 
 10.82 
 11.50 
 13.31 
 14.82 
 16.50 
 17.37 
 18.82 
 
 
 
 
 
 13/ 4 
 
 11.75 
 12.62 
 12.88 
 13.28 
 16.62 
 18.18 
 18.88 
 19.50 
 21.25 
 23.56 
 25.31 
 
 16.88 
 17.18 
 18.07 
 19.18 
 22.00 
 24.00 
 26.82 
 28.25 
 30.37 
 33.88 
 35.37 
 38.94 
 44.37 
 
 
 
 2 
 
 
 
 21/4 
 
 
 
 21/0 
 
 
 
 3 
 
 34.07 
 35.88 
 39.25 
 42.62 
 47.75 
 51.62 
 55.12 
 61.88 
 68.75 
 77.00 
 90.00 
 
 
 31/2 
 
 
 4 
 
 64 00 
 
 41/2 
 
 67 88 
 
 5 : 2 
 
 71 37 
 
 51/2 
 
 79 37 
 
 6... 
 
 86.62 
 
 7 
 
 92.75 
 
 8 
 
 
 
 97.50 
 
 9 
 
 
 
 108.75 
 
 10 
 
 
 
 
 124.75 
 
STEEL WIRE NAILS. 
 
 235 
 
 GO 
 
 
 
 
 
 T3T3X3'w5-C'O-CJ'C-dX)'0T5T3-d 
 tm>OMO»oN>oooooo 
 
 — — — CNr^TirtvO 
 
 •saqouj 'q^Sua^j 
 
 
 •S85[ldg 8JJAV 
 
 
 
 
 
 
 
 
 • -^-*^r3 — — 2°° 
 
 •Surajq 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •ooo'Bqo^ 
 
 
 
 
 
 
 
 r^. r^ ir> rr^ Q\ Q\ \C 
 
 
 
 
 
 
 
 
 • 8T Suiqg 
 
 
 
 
 
 ?4 
 
 §SlE~z s 
 
 
 
 
 
 
 
 
 Sugoog paqj-Bg 
 
 
 SS^S 
 
 
 
 
 
 
 
 
 
 •Sm^is 
 
 
 
 T 
 
 § 
 
 22° 
 
 
 
 
 
 
 
 
 
 e3 
 O . 
 
 >> 
 
 > 
 
 
 
 
 
 
 
 \0 — or^^oiTMn-^-f^Cvlc^ — — — 
 
 M. 
 
 3 
 
 
 
 
 
 
 
 tN^NNNISOm — 00 — t^m 
 
 O 
 ffl 
 
 >> 
 
 > 
 
 K 
 
 
 
 
 
 
 
 <T 
 
 <N 
 
 vO ■TftANO 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 CO 
 
 
 O : MOB|0 
 
 
 
 
 
 •spB-igSniJOOfj 
 
 
 
 
 
 
 
 
 "A f^ O^ O^ ^O iA 1" d 
 
 
 
 
 
 •xog paqJT3g 
 
 puB q-joorag 
 
 puB 'Suisbq 
 
 
 
 o 
 o 
 
 ^ 3 -q- tj- rQ £5 — — 
 
 
 
 qajj^g 
 
 \0 vom o oo o r>. ■ 
 T o r-* o vO o m • 
 
 
 
 
 
 
 
 
 
 
 •8UIJ 
 
 N-COO 
 
 
 o • 
 
 
 
 
 
 
 
 
 
 
 •gtnqstui j paqj-sg 
 puB qaoouig 
 
 
 
 1 
 
 o 
 
 tOO>COaN-nON 
 OOOOl^OONN — ©^ \C 
 
 
 
 
 
 •80U8J 
 
 
 
 
 
 • ^ n aoo >c in t tn m 
 
 
 
 
 
 •qouyio 
 
 
 
 
 
 TTmr^ovooocsior^ 
 
 
 
 
 
 •sp-Bjg pu-e 
 
 Sft'B^J UOTIIUIOQ 
 
 
 
 00 
 
 CO 
 
 -^55oo>«*tmN'-'-- 
 
 •saqouj 'q^Suaq; 
 
 — — — — — — {Mr^CN!Cvlr<* 1 r<-\rA^l-" , Tir\mvO 
 
 
 
 CO 
 
 
 
 
 : 
 
 i 
 
 c 
 
 = 
 
 
 
 — 
 
 - 
 
 X 
 
 00O> 
 
 i 
 
 o 
 
 a 
 
 I 
 
 -z 
 
 
 
236 
 
 NUMBER OF WIRE NAILS PER POUND. 
 
 M 
 
 l-l 
 
 a | 
 
 »5!<£j4?\ ;:."'.;::;: 
 
 
 
 
 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. 
 
 = | 
 
 f^-*mso i i i* : i : i i i 
 
 
 
 
 © 
 
 t^in*NO. i i ''■ ''■ 
 
 
 
 
 o> 
 
 Tfin*ts»o ; ; 
 
 
 
 
 CO | 
 
 >nloco- ::::::: 
 
 
 
 
 - 1 
 
 vONOOO^ — f^lACO 
 
 
 
 
 * 1 
 
 SOOO — r^tnco — inu. • • • 
 
 
 
 
 in 1 
 
 ooa — rnmoo — mom — O • 
 
 
 
 
 "f 1 
 
 O>Orntr\O^00mO'»OinC 
 
 
 
 
 " ! 
 
 o-^*o»tn>o-is^NNam 
 
 
 
 1 
 
 Ntn^O^MOOi^f\^0* — ONt^ 
 
 
 «' 
 
 f in o^ N ia o if\ — o i^ o» m m rsco vO 
 • — « — i — NNrnr^^tirnriOCOOr^tMA 
 
 ^ 
 
 ^Ntfl>00>ONOOO'NO'm1-1 , tO ■ • 
 
 
 
 
 
 N 
 
 O-OONOOintANinvOrA^NI-OOOOO-O • 
 CN cm cs m en tj- m vcin oo o <N in o -o m m r> r~^ • 
 
 
 
 
 
 I 
 
 OONO^iAO^OOtAON 
 minNN^-O-UMO-tNcnOOOinOMS 
 
 
 
 
 
 
 NaoOI-OO-NOinoOiAOi^NW^-OOoMO 
 NNrOtinvOtM»0-tANOOrMAtM»vOMNr> 
 
 
 
 
 > 
 
 ^tinNONinO>ONinCO-0>OM»-^'OinfriO 
 
 
 
 - 
 
 57 
 
 65 
 
 76 
 
 90 
 
 106 
 
 123 
 
 149 
 
 172 
 
 207 
 
 248 
 
 314 
 
 411 
 
 536 
 
 710 
 
 876 
 
 1143 
 
 1558 
 
 2069 
 
 2667 
 
 3750 
 
 4444 
 
 
 £ 
 
 100 
 120 
 141 
 164 
 200 
 229 
 276 
 333 
 418 
 548 
 714 
 947 
 1168 
 1523 
 2077 
 2758 
 3556 
 5000 
 5926 
 7618 
 
 £ 
 
 169 
 197 
 ?39 
 275 
 331 
 397 
 502 
 658 
 857 
 1136 
 1402 
 1828 
 2495 
 3310 
 4267 
 6000 
 7111 
 9143 
 
 £ 
 
 211 
 247 
 299 
 345 
 414 
 496 
 628 
 822 
 1072 
 1420 
 1752 
 2280 
 3116 
 4138 
 5334 
 7500 
 8888 
 11428 
 
 £ 
 
 
 
 
 5 0>^*»«NNOON 
 
 
 
 
 -i — ^-Mfl^iANO'-m 
 
 
 
 
 > 
 
 
 
 
 
 
 
 3$$2SS8£8 
 
 
 
 
 
 CO 
 
 
 
 
 
 
 
 9 
 
 '1 
 
 8g 
 
 es" To 
 
 222E 
 
 vOlNOOO 
 
 c 
 
 
 
 1 
 
PROPERTIES OF STEEL WIRE. 
 
 PROPERTIES OF STEEL WIRE. 
 
 (John A. Roebling'sISons Co., 1908.) 
 
 No., 
 
 Diam., 
 
 in. 
 
 Area, 
 square 
 inches. 
 
 Breaking 
 strain, 100, 
 000 lb. per 
 
 sq. inch. 
 
 Weight 
 
 n pounds. 
 
 Feet in 
 2000 lb. 
 
 Roebling 
 Gauge. 
 
 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 
 
 0.393 
 
 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 
 
 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 
 
 0.011310 
 
 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 
 
 0.000491 
 
 49 
 
 1.65 
 
 8.71 
 
 
 24 
 
 0.023 
 
 0.000415 
 
 42 
 
 1.40 
 
 7.37 
 
 
 25 
 
 0.020 
 
 0.000314 
 
 31 
 
 1.06 
 
 5.58 
 
 
 26 
 
 0.018 
 
 0.000254 
 
 25 
 
 0.855 
 
 4.51 
 
 
 27 
 
 0.017 
 
 0.000227 
 
 23 
 
 .763 
 
 4.03 
 
 
 28 
 
 0.016 
 
 0.000201 
 
 20 
 
 .676 
 
 3.57 
 
 
 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 lb. per cu. ft. for steel 
 wire. Iron wire is a trifle lighter. The breaking strains are calculated for 
 100,000 lb. per sq. in. throughout, simply for convenience, so that the 
 breaking strains of 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 lb., has a breaking strain of 407 X ] 5 ° 
 
 ■■ 610.51b. 
 
 ' 100,000 
 
238 
 
 MATERIALS. 
 
 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 lbs.) would be about 91/2 ohms; and 
 No. 14 steel wire, 6500 lbs. weight per mile-ohm (95 lbs. 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 locations 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. 
 
 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 lbs. 
 
 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 lbs. 
 
 The "Steel" wire is well suited for telephone or short telegraph lines, 
 and the weight per mile-ohm is about 6500 lbs. 
 
 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 Co. 
 
 
 
 Wei 
 
 ? ht. 
 
 
 Resist 
 
 ance. 
 
 Ratio of 
 Breaking 
 
 Size 
 
 Diam., 
 Inch. 
 
 
 
 Length. 
 
 Feet 
 
 per 
 pound. 
 
 Temp. 75.8° Fahr. 
 
 of 
 
 Grains 
 
 Pounds 
 
 Weight to 
 
 Wire 
 
 Feet 
 
 Ohms 
 
 Weight 
 
 
 
 per foot. 
 
 per mile. 
 
 per ohm 
 
 per mile. 
 
 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 
 
 596.7 
 
 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 
 
" PLOUGH "-STEEL WIRE. 
 
 239 
 
 Joints in Telegraph Wires. — The fewer the joints in a line the 
 better. All joints should be carefully made and well soldered over, for 
 a bad joint may cause as much resistance to the electric current as several 
 miles of wire. 
 
 
 SPECIFICATIONS 
 
 FOR GALVANIZED 
 
 IRON WIRE. 
 
 
 
 Issued by the British Postal Telegraph Authorities. 
 
 Weight 
 Mile 
 
 per 
 
 Diameter. 
 
 Tests for Strength and 
 Ductility. 
 
 ID 43 
 
 rd a 
 
 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 T3 
 
 a 
 
 T3 
 
 
 SO +5 
 
 '5 
 H ■ 
 
 SO 
 
 ^o 
 
 M 
 
 ,5 
 
 ?1 
 
 "C to 
 
 
 Allowed. 
 
 w. 
 
 Allowed. 
 
 
 c = 
 
 1«2 
 
 S+3 
 
 1 
 
 
 .5 
 
 
 II X 
 
 ■= 
 
 
 
 u 
 
 
 ffl 
 
 'A 
 
 W fn 
 
 
 w t; 
 
 IS 
 
 rt 
 
 
 a* 
 & 
 
 d 
 
 03 
 
 3 
 
 d 
 
 03 
 
 d 
 
 d 
 
 §'53 
 
 oil 
 
 d 
 
 x 
 
 ll 
 
 3 
 
 § 
 
 tf 
 
 m 
 
 § 
 
 ^ 
 
 § 
 
 i-T 
 
 3 
 
 ^ 
 
 i 
 
 § 
 
 O 
 
 lb. 
 
 lb. 
 
 lb. 
 
 mils. 
 
 mils. 
 
 mils. 
 
 lb. 
 
 
 lb. 
 
 
 lb 
 
 
 
 
 800 
 
 767 
 
 833 
 
 242 
 
 23; 
 
 24/ 
 
 2480 
 
 15 
 
 2550 
 
 14 
 
 2620 
 
 n 
 
 6.75 
 
 5400 
 
 600 
 
 571 
 
 629 
 
 209 
 
 204 
 
 214 
 
 1860 
 
 17 
 
 1910 
 
 16 
 
 1960 
 
 is 
 
 9.00 
 
 5400 
 
 430 
 
 424 
 
 477 
 
 181 
 
 176 
 
 186 
 
 1390 
 
 19 
 
 1425 
 
 18 
 
 1460 
 
 17 
 
 12.00 
 
 5400 
 
 400 
 
 377 
 
 424 
 
 l/l 
 
 166 
 
 176 
 
 1240 
 
 21 
 
 1270 
 
 20 
 
 1300 
 
 19 
 
 13.50 
 
 5400 
 
 200 
 
 190 
 
 213 
 
 121 
 
 118 
 
 125 
 
 620 
 
 30 
 
 638 
 
 28 
 
 655 
 
 26 
 
 27.00 5400 
 
 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 
 13 
 14 
 15 
 
 16 
 17 
 
 0.029 
 .031 
 .033 
 .035 
 .037 
 .039 
 
 225 
 250 
 285 
 305 
 340 
 360 
 
 18 
 19 
 20 
 21 
 22 
 
 0.041 
 .043 
 .045 
 .047 
 .052 
 
 395 
 425 
 500 
 540 
 650 
 
 These strengths range from 300,000 to 340,000 lbs. per sq. in. The 
 composition of this wire is as follows: Carbon, 0.570; silicon, 090- 
 sulphur, 0.011; phosphorus, 0.018; manganese, 0.425. 
 
 " PLOUGH "-STEEL WIRE. 
 
 The term "plough," given in England to steel wire of high quality 
 was derived from the fact that such wire is used for the construction of 
 ropes used for ploughing purposes. It is to be hoped that the term will 
 not be used in this country, as it tends to confusion of terms. Plough- 
 steel is known here in some steel-works as the quality of plate steel used 
 for the mold-boards of ploughs, for which a very ordinary grade is 
 good enough. 
 
 Experiments by Dr. Percy on the English plough-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. 
 
240 
 
 COPPER WIRE TABLE. 
 
 *3l 
 
 S£8aSS?9SSSSSR8ffiSS|2§§|RSgg||§||||§|| 
 
 >p?sl 
 
 OK>6"fNO«>O0P00O 
 
 SsfSEIISssSa^S 
 
 S — O OOOO OO OQOOOOQpOOOQOOoSOOOdO 
 
 i§ssg§§s§ss§sssllsg§gss§s§ssss 
 
 1B'TON--Oars-iA!nnlNO > 0-NiAt>-0>6tO'00'0 > 0-NNJ«)2 
 
 ^i — oooooooo£ : - - " : - : • ■'■'. ; - ". ooooooooooo 
 
 3 © O © O © O O O O O O O O © © O O O O © © © © © O © © © © © © © © © © © 
 
 
 O£00NN r^i^TOOOOO — C 
 
 00(N^>OmtSO'<S-<M<AOOmOI^'q 
 
 
 •> — vOr^©r^r^<M-"T^c>rvi'«t-ir" 1 aov©»^ir\t^©Tt-GO»r%fnC'ie>r>. , !rcvico'«raO\0 — c>f^>oc>GC 
 
 iANtinar^NNt^'<rOOtnNiftN^'^S^OO^^"NflOinO^>ON , OiA— O C'l'T *© — 
 
 rq r*.' oo — ' •■J- u-i o eW f\ — ' T — r-i oo oo r^ <s u-.' wi' so «i' •* o- wi t' n •» r*i ir> -*' — ' -o o-' c>>\oVi i>« <«i a 
 — — — — — <S{slr>l{"JW«*ir>>©t>.00O© — r^^e>£j<QeJ>f > 
 
 £°i82?£ 
 
 0^t>.©i*-iOO©C>>OrjONsOCqHaO^-fi)r>.0>ir>0*r> 
 
 _ jS©rjcoS| 
 
 ■Z 8 
 
 Srs it c 
 
 5 s 
 
 54.78 
 70.72 
 89.45 
 109.55 
 122.48 
 141.43 
 158.12 
 173.21 
 187.09 
 200.00 
 212.14 
 223.61 
 234.53 
 244.95 
 254196 
 264.58 
 273.87 
 282.85 
 291.55 
 300.00 
 308.23 
 316.23 
 331 .67 
 346.42 
 360.56 
 374.17 
 387.30 
 400.00 
 412.32 
 424.27 
 435.89 
 447.22 
 469.05 
 489.90 
 509.91 
 529.16 
 547.73 
 565 69 
 583.10 
 600.00 
 
 
 ^«ON'C'Coo'ei0 9.N«NO--©ooifi-<e»ONNo«on«*obi«N«-wm 
 
 N oo vO m — — — © oo <> "J 2} © i»» t> «s ^ £ **» e> >£ ^ u> » © N >» ir\ r>» oo e* © <S f» «"> ws m «* fi! "T 
 
 — ■— — — — — — — — — — — — r4rSCv»<s|tM?5<s£l«*><«M*\<*»WS'«"»'* 
 
 ii||l|||||||l|||i||||p|||||l|||l||||||l 
 
 £31 
 u»5 
 
 9C ^£SS^9?9SSSSSi;.8SS$8Sgg§SSg8Sg§||'||§|| 
 
BARE AND INSULATED COPPER WIRE. 
 
 241 
 
 Sizes, Weights and Strengths of Hard-Copper Telegraph and 
 Telephone Wire. 
 
 (J. A. Roebling's Sons Co., 1908.) 
 
 02 
 
 _d 
 
 5 
 -2 
 
 
 ance, ln- 
 ational 
 s per mile 
 °F. 
 
 x. size, 
 ing gauge 
 B.B.iron 
 of equal 
 ance. 
 
 
 d 
 
 a 
 
 
 of C £ . 
 
 x. size, 
 ing gauge 
 B.B.iron 
 of equal 
 ance. 
 
 W "• 
 
 
 
 
 "S H SR 
 
 
 ^ -! 
 
 
 <D 
 
 
 .sEJh 
 
 °J2 • "E 
 
 So 
 
 02 
 
 S 
 
 
 2 = 
 
 
 ^W £-p 
 
 1 « 
 
 so 
 
 32 
 
 rt 
 
 5 
 
 f" 
 
 zi ■'- 
 - =. 
 
 pq 
 
 
 9 
 
 0.114 
 
 208 
 
 653 
 
 4.39 
 
 2 
 
 13 
 
 0.072 
 
 83 
 
 274 
 
 11.01 
 
 6 1/2 
 
 10 
 
 0.102 
 
 166 
 
 340 
 
 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 
 
 103 
 
 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 
 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 
 
 
 
 
 Weather- 
 
 
 
 
 Weather- 
 
 
 
 i 
 
 v proof. 
 
 s s ° 
 
 bi 
 
 a 
 
 6 
 
 proof. 
 
 
 hi) 
 
 ■So 
 
 J2 • 
 
 3 3 
 
 S'8 
 
 3"0 
 3 '3 
 
 || 
 
 -9 => 
 
 m 
 
 pq 
 
 Qpq 
 
 Hpq 
 
 ^(^Pm 
 
 w pq 
 
 PQ 
 
 Qpq 
 
 Hpq 
 
 E^Ph 
 4550 
 
 ojpq 
 
 0000 
 
 641 
 
 723 
 
 767 
 
 862 
 
 925 
 
 3384 
 
 3817 
 
 4050 
 
 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 
 
 80 
 
 169 
 
 241 
 
 280 
 
 315 
 
 420 
 
 12 
 
 20 
 
 30 
 
 35 
 
 42 
 
 55 
 
 106 
 
 158 
 
 185 
 
 220 
 
 290 
 
 14 
 
 \2A 
 
 20 
 
 25 
 
 30 
 
 40 
 
 66 
 
 107 
 
 130 
 
 160 
 
 210 
 
 16 
 
 7.9 
 
 16 
 
 20 
 
 24 
 
 30 
 
 42 
 
 83 
 
 105 
 
 130 
 
 160 
 
 18 
 
 4.t 
 
 12 
 
 16 
 
 19 
 
 24 
 
 25 
 
 64 
 
 85 
 
 100 
 
 130 
 
 20 
 
 3.1 
 
 9 
 
 12 
 
 
 
 16 
 
 48 
 
 65 
 
 
 
MATERIALS. 
 
 Stranded Copper Feed Wire, Weight in Pounds. 
 
 (John A. Roebling's Sons Co., 1908.) 
 
 
 Weight 
 
 per 1000 Feet. 
 
 Weight per Mile. 
 
 
 Weather- 
 
 
 
 
 Weather- 
 
 
 
 
 
 proof 
 
 
 
 
 proof 
 
 
 
 
 
 
 
 
 
 
 
 "^ 5rt 
 
 
 03 
 
 a3o!§ 
 
 03 
 
 c3 
 
 PQ 
 
 3:2 
 
 QPQ 
 
 ~2 
 
 a % 
 
 - "> 2 
 £js:pm 
 
 a 
 
 a5 
 
 o3 
 
 pq 
 
 03 . 
 
 3 a 
 
 11 
 
 C u 
 
 
 PQ 
 
 | 
 
 53 
 
 2,000,000 
 
 6100 
 
 6690 
 
 7008 
 
 
 7540 
 
 32208 
 
 35323 
 
 37000 
 
 
 39800 
 
 1,750,000 
 
 5338 
 
 5894 
 
 6193 
 
 
 6700 
 
 28184 
 
 31119 
 
 32700 
 
 
 35400 
 
 1,500,000 
 
 4575 
 
 5098 
 
 5380 
 
 
 5830 
 
 24156 
 
 26915 
 
 28400 
 
 
 30800 
 
 1,250,000 
 
 3813 
 
 4264 
 
 4508 
 
 
 4940 
 
 20132 
 
 22516 
 
 23800 
 
 
 20000 
 
 1,000,000 
 
 3050 
 
 3456 
 
 3674 
 
 3860 
 
 3980 
 
 16104 
 
 18246 
 
 19400 
 
 20400 
 
 26100 
 
 900,000 
 
 2745 
 
 3127 
 
 3332 
 
 3520 
 
 3640 
 
 14493 
 
 16513 
 
 17600 
 
 18600 
 
 11000 
 
 800,000 
 
 2440 
 
 2799 
 
 2992 
 
 3180 
 
 3280 
 
 12883 
 
 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 
 
 2460 
 
 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 
 
 Approximate Rules for the Resistance of Copper Wire. — The 
 
 resistance 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 = l/ioooinch.) 
 
 A No. 10 Wire, A.W.G., 0.1019 in. diameter (practically 0.1 in.), 
 1000 ft. in length, has a resistance of 1 ohm at 68° F. and weighs 31.4 
 lbs. 
 
 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 
 
 Relative resistance 
 
 section or weight . 
 
 See wire table, A.W.G. , under Electrical Engineering. 
 
 000 1 
 
 4 
 
 7 
 
 10 
 
 16 8 
 
 4 
 
 2 
 
 1 
 
 1/16 1/8 
 
 1/4 
 
 1/2 
 
 1 
 
 13 16 19 22 
 
 1/2 1/4 1/8 Vl6 
 
WIRES OF DIFFERENT METALS AND ALLOYS. 243 
 
 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 
 
 Approximate Equiv- 
 
 C 
 
 £ 
 
 -g'S J 3' ; 
 
 i° 
 
 Mile. 
 
 alent Diameter, mils. 
 
 
 
 »^rt a 
 
 ■s® 
 
 
 
 
 
 
 
 
 0) - 
 
 
 
 
 
 
 
 
 ■a'H 
 
 a o3 
 
 so 
 
 a 
 
 3 
 
 a 
 
 '5 
 
 B 
 3 
 B 
 
 1 
 
 03 
 -3 
 
 CI 
 
 03 
 
 B 
 3 
 B 
 'B 
 
 i 
 
 B 
 3 
 
 a 
 1 
 
 c 
 
 i 
 
 3 m 
 a. s 
 
 '3 £ 
 
 3 13 >fe 
 3^o 
 
 .aggs 
 
 oj o3|> c3 
 
 a-g£ 
 1^ 
 
 , 100 
 
 971/2 
 
 1021/2 
 
 79 
 
 78 
 
 80 
 
 330 
 
 30 
 
 9.10 
 
 50 
 
 150 
 
 1461/4 
 
 1533/ 4 
 
 97 
 
 951/2 
 
 98 
 
 490 
 
 25 
 
 6.05 
 
 50 
 
 200 
 
 195 
 
 205 
 
 112 
 
 IIOI/2 
 
 1131/4 
 
 650 
 
 20 
 
 4.53 
 
 50 
 
 400 
 
 390 
 
 410 
 
 158 
 
 1551/2 
 
 160 1/4 
 
 1300 
 
 10 
 
 2.27 
 
 50 
 
 WIRES OF DIFFERENT METALS AND ALLOYS. 
 
 (J. Bucknall Smith's Treatise on Wire.) 
 
 Brass Wire is commonly composed of an alloy of 1 3/4 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 without 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 1/8 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 de- 
 posits of verdigris. It has great toughness, even when its tensile 
 strength is over 60 tons per square inch. 
 
 Aluminum Wire. — Specific gravity 0.268. Tensile strength only 
 about 10 tons per square inch. It has been drawn as fine as 11,400 
 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. 
 
 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 28 to 55 
 tons per square inch of section. The conductivity decreases as the ten- 
 sile 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. 
 
244 
 
 MATERIALS. 
 
 Composed of 
 
 WIRE ROPES. 
 STANDARD HOISTING ROPE. 
 
 } Strands and a Hemp Center, 19 Wires to the Strand. 
 (John A. Roebling's Sons Co., 1908.) 
 
 See also pamphlets of John A. Roebling's Sons Co., Trenton Iron Co., 
 A. Leschen & Sons Rope Co., and other makers. 
 
 SWEDISH IRON. 
 
 03 
 
 s 
 
 01 
 
 ' s .s 
 
 jO 
 
 
 HI 
 
 5odS 
 
 "3 o 
 
 .2 ID 
 
 
 .5 
 
 '3 
 
 jP 
 
 
 *!§ 
 
 | 60 G 
 O.S£ 
 
 0> 
 
 .2 a? 
 
 3 0) 
 
 0) 
 
 2 
 
 1 
 
 Q 
 
 a 
 a 
 
 a 
 
 O to 
 
 £;s2 
 
 03 02 
 
 £ 60 £ 
 
 J2.2-2 
 
 
 0) 
 T3 
 
 | 
 
 a° 
 
 a 
 
 O co 
 
 £ 6J0C 
 flfl o 
 
 H 
 
 <! 
 
 S 
 
 < 
 
 <! 
 
 a 
 
 H 
 
 3 
 
 -< 
 
 «! 
 
 5 
 
 s 
 
 
 23/4 
 
 85/s 
 
 11.95 
 
 114 
 
 22.8 
 
 16 
 
 8 
 
 i 
 
 3 
 
 1.58 
 
 iy 
 
 3.40 
 
 51/4 
 
 
 21/, 
 
 /7/ 8 
 
 9.85 
 
 95 
 
 18.9 
 
 15 
 
 9 
 
 7/8 
 
 23/4 
 
 1.20 
 
 13 
 
 2.60 
 
 41/2 
 
 1 
 
 21/ 4 
 
 >l/8 
 
 8.00 
 
 78 
 
 15.60 
 
 13 
 
 10 
 
 3/4 
 
 21/4 
 
 0.89 
 
 97 
 
 1.94 
 
 4 
 
 2 
 
 2 
 
 6I/4 
 
 6.30 
 
 62 
 
 12.40 
 
 12 
 
 101/4 
 
 b/8 
 
 2 
 
 0.62 
 
 6.8 
 
 1.36 
 
 31/2 
 
 3 
 
 13/4 
 
 !>l/ ? 
 
 4.85 
 
 48 
 
 9.60 
 
 10 
 
 101/2 
 
 y/ifi 
 
 IS/4 
 
 0.50 
 
 5.5 
 
 1.10 
 
 23/ 4 
 
 4 
 
 1 V8 
 
 3 
 
 4.15 
 
 42 
 
 8.40 
 
 81/9, 
 
 103/4 
 
 1/9 
 
 U/?, 
 
 0.39 
 
 4.4 
 
 0.88 
 
 21/4 
 
 5 
 
 U/ ? 
 
 43/ 4 
 
 3.55 
 
 36 
 
 7.20 
 
 71/9 
 
 10a 
 
 V/1B 
 
 H/4 
 
 0.30 
 
 3.4 
 
 0.68 
 
 2 
 
 5 V* 
 
 13/s 
 
 41/4 
 
 3.00 
 
 31 
 
 6.20 
 
 7 
 
 106 
 
 3/8 
 
 H/8 
 
 0.22 
 
 2.5 
 
 0.50 
 
 H/2 
 
 6 
 
 U/4 
 
 4 
 
 2.45 
 
 25 
 
 5.00 
 
 61/9 
 
 \0c 
 
 W16 
 
 1 
 
 0.15 
 
 1.7 
 
 0.34 
 
 1 
 
 y 
 
 H/8 
 
 31/2 
 
 2.00 
 
 21 
 
 4.20 
 
 6 
 
 lOrf 
 
 1/4 
 
 3/ 4 
 
 0.10 
 
 1.2 
 
 0.24 
 
 3/4 
 
 CAST STEEL. 
 
 
 23/ 4 
 
 85/s 
 
 11.95 
 
 228 
 
 45.6 
 
 10 
 
 8 
 
 i 
 
 3 
 
 1.58 
 
 34 
 
 6.80 
 
 4 
 
 
 
 77/ 8 
 
 9.85 
 
 190 
 
 37.9 
 
 91/9 
 
 9 
 
 ■7/8 
 
 23/ 4 
 
 1.20 
 
 26 
 
 5.20 
 
 31/ 2 
 
 1 
 
 21/4 
 
 A/8 
 
 8.00 
 
 156 
 
 31.2 
 
 8 V? 
 
 10 
 
 3/ 4 
 
 21/4 
 
 0.89 
 
 19.4 
 
 3.88 
 
 3 
 
 2 
 
 2 
 
 6I/4 
 
 6.30 
 
 124 
 
 24.8 
 
 8 
 
 101/4 
 
 *>/8 
 
 2 
 
 62 
 
 13.6 
 
 2.72 
 
 21/4 
 
 3 
 
 13/4 
 
 51/?, 
 
 4:85 
 
 96 
 
 19.2 
 
 71/4 
 
 101/9 
 
 »/lB 
 
 13/4 
 
 0.50 
 
 11.0 
 
 2.20 
 
 13/4 
 
 4 
 
 lb/8 
 
 5 
 
 4.15 
 
 84 
 
 16.8 
 
 6I/4 
 
 l03/ 4 
 
 i/„ 
 
 11/9, 
 
 0.39 
 
 8.8 
 
 1.76 
 
 H/2 
 
 5 
 
 11/, 
 
 43/ 4 
 
 3.55 
 
 72 
 
 14.4 
 
 53/ 4 
 
 10a 
 
 V/lfi 
 
 U/4 
 
 0.30 
 
 6.8 
 
 1.36 
 
 U/4 
 
 51/2 
 
 l3/ 8 
 
 41/4 
 
 3.00 
 
 62 
 
 12.4 
 
 51/? 
 
 106 
 
 3/8 
 
 11/8 
 
 0.22 
 
 5.0 
 
 1.00 
 
 
 6 
 
 H/4 
 
 4 
 
 2.45 
 
 50 
 
 10.0 
 
 5 
 
 m 
 
 *>/m 
 
 1 
 
 0.15 
 
 3.4 
 
 0.68 
 
 2/3 
 
 y 
 
 H/8 
 
 31/2 
 
 2.00 
 
 42 
 
 8.40 
 
 41/2 
 
 10rf 
 
 1/4 
 
 3/4 
 
 0.10 
 
 2.4 
 
 0.48 
 
 1/2 
 
 .This rope is almost universally employed for hoisting purposes on 
 account of its flexibility. It is made of 6 strands, each of which is 
 formed by twisting 19 wires together, and a hemp core or center. Some- 
 times the hemp center is replaced by a wire strand, which 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 its use is not generally advised. 
 This rope is very pliable, and will wind on moderate-sized drums and 
 pass over reasonably small sheaves without injury. Where it is possi- 
 ble, drums and sheaves larger than those indicated in the lists should 
 be adopted, particularly when high speeds are employed or when the 
 working strain is greater than one-fifth of the breaking strain, as the 
 bending of a rope around a sheave is more destructive the heavier the 
 strain on the rope and the smaller the sheave. The working strains for 
 these tables have been calculated at about one-fifth the breaking strains. 
 It is necessary, however, in some cases, — where the speed of the rope is 
 - to take it at one-eighth or one-tenth of the breaking strain, 
 
TRANSMISSION OR HAULAGE ROPE. 
 
 245 
 
 Before deciding upon iron or steel for ropes, it is better to have advice 
 from the manufacturers of wire rope. 
 
 In substituting steel for iron, it is well to use the same size of rope, 
 thereby taking full advantage of the increased wearing capacity of steel 
 over iron. The best steel is the only one to use, as inferior grades are 
 not as serviceable as good iron, because the constant vibrations to which 
 ropes are subjected cause the poor steel to become brittle and unsafe. 
 
 TRANSMISSION OR HAULAGE ROPE. 
 
 Composed of 6 Strands and a Hemp Center, 7 Wires to the Strand. 
 
 SWEDISH IRON. 
 
 
 
 .a 
 
 
 MO 
 
 .a§ 
 
 MO 
 
 eg 
 
 a 
 
 
 
 .a 
 
 
 MO 
 .So 
 
 ,ai 
 
 a 
 
 a 
 
 .a 
 
 o 
 
 a 
 
 a 
 
 3 
 o 
 
 '3 
 
 X 
 
 O 
 
 a 
 
 O 03 
 
 O w 
 
 a."* 3 
 
 24 
 
 o of 
 
 5 
 3 
 
 3 
 03 
 
 | 
 
 a 
 
 '3 
 o 
 
 2 
 
 05 
 
 a 
 
 ffl o 
 
 x.a" 
 
 13 tS 
 
 O 03 
 
 tsg 
 
 fig- 
 
 „ > 
 
 2 
 
 a 
 a 
 
 % 
 
 ow£ 
 
 2w2 
 
 .as 
 
 g 
 
 a 
 
 ■+i 
 
 #$2 
 
 -2w£ 
 
 .as 
 
 H 
 
 Q 
 
 < 
 
 < 
 
 < 
 
 § 
 
 H 
 
 Q 
 
 < 
 
 b 
 
 < 
 
 <J 
 
 s 
 
 11 
 
 1V-, 
 
 43/ 4 
 
 3.55 
 
 34 
 
 6.80 
 
 13 
 
 19 
 
 5/8 
 
 2 
 
 0.62 
 
 6.6 
 
 1.32 
 
 51/i 
 
 12 
 
 13/8 
 
 41/4 
 
 3.00 
 
 29 
 
 5.80 
 
 12 
 
 2U 
 
 9/16 
 
 13/4 
 
 0.50 
 
 5.3 
 
 1.06 
 
 41A> 
 
 13 
 
 U/4 
 
 4 
 
 2.45 
 
 24 
 
 4.80 
 
 103/4 
 
 21 
 
 V? 
 
 HA. 
 
 0.39 
 
 4.2 
 
 0.84 
 
 4 
 
 14 
 
 11/8 
 
 31/9 
 
 2.00 
 
 20 
 
 4.00 
 
 91/9 
 
 22 
 
 ■Vlfl 
 
 U/4 
 
 0.30 
 
 3.3 
 
 0.66 
 
 31/ 4 
 
 15 
 
 1 
 
 3 
 
 1.58 
 
 16 
 
 3.20 
 
 8I/2 
 
 23 
 
 3/8 
 
 H/8 
 
 0.22 
 
 2.4 
 
 0.48 
 
 23/,, 
 
 16 
 
 7/8 
 
 23/4 
 
 1.20 
 
 12 
 
 2.40 
 
 71/9, 
 
 24 
 
 •>Mfi 
 
 1 
 
 0.15 
 
 1.7 
 
 0.34 
 
 2 I'm 
 
 \1 
 
 3/ 4 
 
 21/4 
 
 0.89 
 
 9.3 
 
 1.86 
 
 63/4 
 
 2b 
 
 9/3? 
 
 V* 
 
 0.125 
 
 1.4 
 
 0.28 
 
 21/4 
 
 Id 
 
 H/16 
 
 21/8 
 
 0.75 
 
 7.9 
 
 1.58 
 
 6 
 
 
 
 
 
 
 
 
 CAST STEEL. 
 
 11 
 
 11/9 
 
 43/ 4 
 
 3.55 
 
 68 
 
 13.6 
 
 81/9, 
 
 19 
 
 5/8 
 
 2 
 
 0.62 
 
 13.2 
 
 2.64 
 
 31/9 
 
 12 
 
 13/ 8 
 
 41/4 
 
 3.00 
 
 58 
 
 11.6 
 
 8 
 
 20 
 
 9/16 
 
 I 3/ 4 
 
 0.50 
 
 10.6 
 
 2.12 
 
 3 
 
 13 
 
 U/4 
 
 4 
 
 2.45 
 
 48 
 
 9.60 
 
 71/4 
 
 21 
 
 1/9 
 
 I 1/., 
 
 0.39 
 
 8.4 
 
 1.68 
 
 21/9 
 
 14 
 
 U/8 
 
 31/9 
 
 2.00 
 
 40 
 
 8.00 
 
 6I/4 
 
 22 
 
 '','16 
 
 11/4 
 
 0.30 
 
 6.6 
 
 1.32 
 
 21/,, 
 
 15 
 
 1 
 
 3 
 
 1.58 
 
 32 
 
 6.40 
 
 53/4 
 
 23 
 
 3/8 
 
 11/8 
 
 0.22 
 
 4.8 
 
 0.96 
 
 ?, 
 
 16 
 
 7/8 
 
 23/ 4 
 
 1.20 
 
 24 
 
 4.80 
 
 5 
 
 24 
 
 5/1 fi 
 
 1 
 
 0.15 
 
 3.4 
 
 0.68 
 
 I3/4 
 
 17 
 
 3/4 
 
 21/4 
 
 0.89 
 
 18.6 
 
 3.72 
 
 41/2 
 
 25 
 
 9/3- 
 
 7/8 
 
 0.125 
 
 2.8 
 
 0.56 
 
 11/o 
 
 18 
 
 H/16 
 
 21/8 
 
 0.75 
 
 15.8 
 
 3.16 
 
 4 
 
 
 
 
 
 
 
 
 This rope is much stiffer than standard hoisting rope. It is made of 
 6 strands, each of which is composed of 7 wires, and a hemp core or 
 center. It may have, if it is desired, a wire center, which adds from 7 
 to 10 per cent to its strength, but it is then open to the objections 
 already noted on page 226. The wires of this variety of rope are 1 2/3 
 times greater in diameter than those of the standard hoisting rope, 
 and hence the rope is much less pliable, and will not bend around as 
 small sheaves. It is well adapted for haulages and transmissions, 
 because the wires are large and are not quickly worn through. It will 
 resist the rough usage of mine haulages and the great wear due to pass- 
 ing over a large number of pulleys and rollers. The wires are fewer in 
 number, however, and a greater factor of safety is desirable than for 
 hoisting rope, because the breakage of one or two wires takes away con- 
 siderable amount of the total strength. In using steel, instead of iron 
 rope, it is necessary to have the best quality. For transmissions, the 
 sizes from li/s in. diameter down give excellent satisfaction, when prop- 
 erly selected. Both the regular and Lang constructions are extensively 
 used for haulages and inclined planes. 
 
246 
 
 MATERIALS. 
 
 PLOUGH-STEEL ROPE. 
 
 Composed of 6 Strands and a Hemp Center. 
 
 19 WIRES TO THE STRAND. 
 
 
 
 ,3 
 
 
 bjjo 
 So 
 
 Mo 
 
 • So 
 
 s 
 
 3 
 
 
 
 .s 
 
 
 M§ 
 
 Mo 
 
 s 
 
 ^ 
 
 
 g 
 
 
 J2^>, 
 
 -fifCS 
 
 P*> 
 
 h - 
 
 
 n 
 
 
 
 JiJtN 
 
 «*i 
 
 
 
 3 
 
 J2 
 
 
 
 
 
 
 
 
 
 O m 
 
 B 
 
 3 
 
 .9 
 
 
 h a 
 
 £§ 
 
 0)"* 3 
 
 "3 oj" 
 
 g S3 
 
 a 
 
 3 
 
 .g 
 
 _Sh 
 
 
 fn 3 
 ffl ° 
 
 
 °> 
 
 0> 
 
 I 
 
 o 
 
 ft 
 
 x.S 
 
 JO 3 
 
 s i- 
 
 £ 
 
 | 
 
 X 
 
 S 
 
 ft 
 
 O 03 • 
 
 ,Q 3 
 
 2 u 
 
 F, 
 
 a 
 
 -4 
 
 Sm£ 
 
 -2££ 
 
 .So 
 
 03 
 
 ft 
 
 -J 
 
 $n£ 
 
 -2r/5£ 
 
 .S o 
 
 H 
 
 P 
 
 <J 
 
 £ 
 
 <J 
 
 <J 
 
 § 
 
 H 
 
 P 
 
 ^ 
 
 £ 
 
 <! 
 
 k<! 
 
 3 
 
 
 23/4 
 
 85/r 
 
 11.95 
 
 305 
 
 61.0 
 
 11 
 
 8 
 
 1 
 
 3 
 
 1.58 
 
 44 
 
 8.80 
 
 41/4 
 
 
 21/ ? 
 
 77/s 
 
 9.85 
 
 254 
 
 50.8 
 
 10 
 
 9 
 
 7/8 
 
 23/4 
 
 1.20 
 
 34 
 
 6.80 
 
 33/4 
 
 1 
 
 21/4 
 
 71/8 
 
 8.00 
 
 208 
 
 41.6 
 
 9 
 
 10 
 
 3/4 
 
 2l/ 4 
 
 0.89 
 
 25 
 
 5.00 
 
 31/9 
 
 2 
 
 2 
 
 61/4 
 
 6 30 
 
 165 
 
 33.0 
 
 8 
 
 101/4 
 
 O/S 
 
 2 
 
 62 
 
 18 
 
 3.60 
 
 3 
 
 5 
 
 l3/ 4 
 
 5l/ ? 
 
 4.85 
 
 128 
 
 25.6 
 
 71/9 
 
 101/9 
 
 9/16 
 
 l3/ 4 
 
 0.50 
 
 14.5 
 
 2.90 
 
 21/9 
 
 4 
 
 I&/8 
 
 5 
 
 4 15 
 
 111 
 
 22.2 
 
 6 
 
 103/4 
 
 1/9 
 
 11/9 
 
 0.39 
 
 11.4 
 
 2.28 
 
 2 
 
 5 
 
 ll/o 
 
 43/4 
 
 3.55 
 
 96 
 
 19.2 
 
 51/9 
 
 10a 
 
 7/tt 
 
 11/4 
 
 0.30 
 
 8.85 
 
 1.77 
 
 11/, 
 
 1)1/9 
 
 l3/ 8 
 
 41/4 
 
 3.00 
 
 82 
 
 16.4 
 
 »V4 
 
 10& 
 
 3/8 
 
 H/8 
 
 0.22 
 
 6.55 
 
 1.31 
 
 1 
 
 6 
 
 11/4 
 
 4 
 
 2,45 
 
 67 
 
 13.4 
 
 5 
 
 10c 
 
 Wl6 
 
 1 
 
 15 
 
 4.50 
 
 0.90 
 
 7/ s 
 
 7 
 
 H/8 
 
 31/2 
 
 2.00 
 
 56 
 
 11.2 
 
 41/2 
 
 lOd 
 
 1/4 
 
 3/4 
 
 0.10 
 
 3.00 
 
 0.60 
 
 2/3 
 
 7 WIRES TO THE STRAND. 
 
 11 
 
 11/9 
 
 43/4 
 
 3 55 
 
 91 
 
 18.2 
 
 81/ 2 
 
 19 
 
 5/fl 
 
 2 
 
 0.62 
 
 17 
 
 3.40 
 
 3 
 
 12 
 
 13/8 
 
 /1/4 
 
 3.00 
 
 78 
 
 15.6 
 
 8 
 
 20 
 
 9/16 
 
 13/4 
 
 0.50 
 
 14 
 
 2.80 
 
 23/4 
 
 13 
 
 U/4 
 
 4 
 
 2.45 
 
 64 
 
 12.8 
 
 71/ 4 
 
 21 
 
 !/•> 
 
 11/9 
 
 0.39 
 
 11 
 
 2.20 
 
 21/9 
 
 14 
 
 H/8 
 
 31/9, 
 
 2.00 
 
 53 
 
 10.6 
 
 61/4 
 
 22 
 
 V/16 
 
 H/4 
 
 0.30 
 
 8.55 
 
 1.71 
 
 2 
 
 15 
 
 1 
 
 3 
 
 1.58 
 
 42 
 
 8.40 
 
 51/9 
 
 23 
 
 3/8 
 
 11/8 
 
 0.22 
 
 6.35 
 
 1.27 
 
 11/9 
 
 16 
 
 7/8 
 
 23/4 
 
 1.20 
 
 32 
 
 6.40 
 
 5 
 
 24 
 
 ■V16 
 
 1 
 
 0.15 
 
 4.35 
 
 0.87 
 
 H/4 
 
 17 
 
 3/4 
 
 21/4 
 
 0.89 
 
 24 
 
 4.80 
 
 4 
 
 25 
 
 Ufa 
 
 '7/8 
 
 0.125 
 
 3.65 
 
 0.73 
 
 1 
 
 18 
 
 H/16 
 
 21/8 
 
 0.75 
 
 21 
 
 4.20 
 
 31/2 
 
 
 
 
 
 
 
 
 Plough-steel wire is made of high grade of crucible steel, and will 
 stand a strain of from 95 to 175 tons per sq. in. Plough-steel ropes are 
 used instead of cast-steel or iron where it is necessary to reduce the 
 dead weight, as, for instance, with heavy or extremely long ropes when 
 the weight of the rope is a large item. They are also employed when 
 the load on the rope of an existing plant has been materially Increased 
 and the sheaves and drums cannot be altered to meet the new require- 
 ments. In this case a plough-steel rope of the same size can be used 
 with an increase in strength of 50 to 100 per cent. Plough-steel is, 
 therefore, applicable to conditions involving great wear and rough 
 usage. It is advisable to reduce all bends to a minimum and to use 
 somewhat larger drums and sheaves than are suitable for the ordinary 
 cast-steel rope, having a strength of 60 to 80 tons per sq. in. It is well 
 to obtain advice upon the adaptability of plough-steel ropes before 
 using them. 
 
 " LANG LAY » ROPE. 
 
 In wire rope, as ordinarily made, the component strands are laid up 
 into rope in a direction opposite to that in which the wires are laid into 
 strands; that is, if the wires in the strands are laid from right to left, 
 the strands are laid into rope from left to right. In the "Lang Lay," 
 sometimes known as "Universal Lay," the wires are laid into strands 
 and the strands into rope in the same direction; that is, if the wire is laid 
 in the strands from right to left, the strands are also laid into rope from 
 right to left. Its use has been found desirable under certain conditions 
 
GALVANIZED IRON WIRE ROPE. 
 
 247 
 
 and for certain purposes, mostly for haulage plants, inclined planes, and 
 street railway cables, although it has also been used for vertical hoists 
 in mines, etc. Its advantages are that it is somewhat more flexible 
 than rope of the same diameter and composed of the same number of 
 wires laid up in the ordinary manner; and (especially) that owing to the 
 fact that the wires are laid more axially in the rope, longer surfaces of 
 the wire are exposed to wear, and the endurance of the rope is thereby 
 increased. (Trenton Iron Co.) 
 
 CABLE-TRACTION ROPES. 
 
 According to English practice, cable-traction ropes, of about 31/2 in' 
 circumference, are commonly constructed with six strands of 7 or 15 
 wires, the lays in the strands varying from, say, 3 in. to 31/2 in., and 
 the lays in the ropes from, say, 7 1/2 in. to 9 in. In the United States, how- 
 ever, strands of 19 wires are generally preferred, as being more flexible; 
 but, on the other hand, the smaller external wires wear out more rapidly. 
 The Market-street Street Railway Company, San Francisco, has used 
 ropes 11/4 in. diam., composed of six strands of 19 steel wires, weighing 
 21/2 lb. per foot, the longest continuous length being 24,125 ft. The 
 Chicago City Railroad Co. has employed cables of identical construction, 
 the longest length being 27,700 ft. On the New York and Brooklyn 
 Bridge cable-railway steel ropes 11,500 ft. long, containing 114 wires, 
 have been used. 
 
 GALVANIZED IRON WIRE ROPE. 
 
 For Ships' Rigging and Derrick Guys. 
 Composed of 6 Strands and a Hemp Center, 7 or 12 Wires to the Strand. 
 
 2 
 
 
 J2 
 
 4a2 
 
 r 2& 
 
 2' 
 
 
 ,fl 
 
 Mi 
 
 - a o 1 
 
 ^ 
 
 .2 
 
 4»" 
 
 . UJ rA 
 
 .2|h_c 
 
 t3 
 
 a 
 
 J 
 
 w »i 
 
 r <3 M 
 
 £ 
 
 2 
 
 3 
 
 OS 
 
 O GO 
 
 d m C 
 
 
 
 2 
 
 3 
 
 a 
 
 p 52 
 
 d a 
 
 < 
 
 
 
 s 
 
 a-2-S 
 
 b 
 
 £2 
 < 
 
 5 
 
 js* 
 
 < 
 
 O 
 
 13/4 
 
 51/2 
 
 4.85 
 
 44 
 
 11 
 
 1 
 
 3 
 
 1.44 
 
 13 
 
 53/4 
 
 UV16 
 
 51/4 
 
 4.40 
 
 40 
 
 101/2 
 
 v/s 
 
 23/4 
 
 1.21 
 
 11 
 
 51/4 
 
 1 5/8 
 
 5 
 
 4.00 
 
 36 
 
 10 
 
 13/16 
 
 21/2 
 
 1.00 
 
 9.0 
 
 5 
 
 1 V? 
 
 43/4 
 
 3.60 
 
 32 
 
 91/2 
 
 3/4 
 
 21/4 
 
 0.81 
 
 7.3 
 
 43/4 
 
 1 V/16 
 
 41/2 
 
 3.25 
 
 29 
 
 9 
 
 t»/R 
 
 2 
 
 0.64 
 
 5.8 
 
 41/2 
 
 1 3/ 8 
 
 41/4 
 
 2.90 
 
 26 
 
 8 1/2 
 
 9/16 
 
 13/4 
 
 0.49 
 
 4.4 
 
 33/4 
 
 1 1/4 
 
 4 
 
 2.55 
 
 23 
 
 8 
 
 1/7 
 
 11/2 
 
 0.36 
 
 3.2 
 
 3 
 
 1 3/ 1fi 
 
 33/4 
 
 2.25 
 
 20 
 
 71/2 
 
 V/16 
 
 11/4 
 
 0.25 
 
 2.3 
 
 21/2 
 
 U/8 
 
 31/2 
 
 1.95 
 
 18 
 
 6 1/2 
 
 3/8 
 
 U/8 
 
 0.20 
 
 1.8 
 
 21/4 
 
 1 Vl6 
 
 31/4 
 
 1.70 
 
 15 
 
 6 
 
 Wl6 
 
 I 
 
 0.16 
 
 1.4 
 
 2 
 
 
 
 
 5 St 
 
 RANDS, ' 
 
 * WlR 
 
 esEach 
 
 
 
 
 9 /32 
 
 7/8 
 
 0.123 
 
 1.1 
 
 13/4 
 
 7/32 
 
 5/8 
 
 0.063 
 
 0.56 
 
 11/4 
 
 1/4 
 
 3/4 
 
 0.090 
 
 0.81 
 
 11/2 
 
 3/16 
 
 1/2 
 
 0.040 
 
 0.36 
 
 U/8 
 
 Galvanized wire rope has almost entirely superseded manila rope for 
 shrouds and stays aboard ship. It is cheaper in first cost, is not affected 
 by weather, and does not stretch and contract with changes in atmos- 
 pheric conditions; on the other hand, it is quite as elastic as manila rope. 
 It is only 1/5 or 1/6 as large by bulk as a manila rope of equal strength, 
 and offers only half as much surface to the wind, and weighs less. It is 
 much less liable to accidents by cutting or chafing. 
 
 If galvanized rope of greater strength than that shown in the table 
 is desired, galvanized open hearth, cast-steel or plough-steel wire rope 
 can be obtained. 
 
248 
 
 MATERIALS. 
 
 STEEL FLAT ROPES. 
 
 (J. A. Roebling's Sons Co.) 
 
 Steel-wire Flat Ropes are composed of a number of strands, alter- 
 nately twisted to the right and left, laid alongside of each other, and 
 sewed together with soft iron wires. These ropes are used at times in 
 place of round ropes in the shafts of mines. They wind upon them- 
 selves on a narrow winding-drum, which takes up less room than one 
 necessary for a round rope. The soft-iron sewing-wires wear out sooner 
 •than the steel strands, and then it becomes necessary to sew the rope 
 with new iron wires. 
 
 _fl 
 
 s 
 
 lS8 
 
 i 
 
 .5 
 
 J" 
 
 J) -r 
 
 
 a a) 
 -3 
 
 a 
 
 
 
 03 
 
 a 
 
 "11 
 
 
 M . 
 
 O oa • 
 
 Sofii 
 
 -fl.H 
 
 .fl 
 
 2 M O! 
 
 i a 
 
 g.S3£ 
 
 s^oQw 
 
 §£ 
 
 - 5)^5 
 
 
 =3^02^, 
 
 £ 
 
 < 
 
 <! 
 
 £ 
 
 £ 
 
 <9*> 
 
 < 
 
 3/8X2 
 
 1.19 
 
 18 
 
 3.6 
 
 1/2 x 3 
 
 2.38 
 
 36 
 
 7.2 
 
 3/8X21/2 
 
 1.86 
 
 28 
 
 5.6 
 
 1/2X31/2 
 
 2.97 
 
 45 
 
 9.0 
 
 3/8X3 
 
 2.00 
 
 30 
 
 6.0 
 
 1/2X4 
 
 3.30 
 
 50 
 
 10. a 
 
 3/8 X 31/2 
 
 2.50 
 
 38 
 
 7.6 
 
 1/2X41/2 
 
 4.00 
 
 60 
 
 12.0 
 
 3/8 X 4 
 
 2.86 
 
 43 
 
 8.6 
 
 1/2 x 5 
 
 4.27 
 
 64 
 
 12.8 
 
 3/8 X 41/ 2 
 
 3.12 
 
 47 
 
 9.4 
 
 1/2X51/2 
 
 4.82 
 
 72 
 
 14.4 
 
 3/8X5 
 
 3.40 
 
 50 
 
 10.0 
 
 1/2 X 6 
 
 5.10 
 
 77 
 
 15.4 
 
 3/8 X 51/2 
 
 3.90 
 
 55 
 
 11.0 
 
 1/2X7 
 
 5.90 
 
 89 
 
 17.8 
 
 GALVANIZED STEEL CABLES. 
 
 For Suspension Bridges. (Roebling's.) 
 Composed of 6 Strands — With Wire Center. 
 
 
 
 Approx. 
 
 
 
 Appro. 
 
 
 
 Appro. 
 
 Diam., 
 
 Wt. per 
 foot, 
 
 Breaking 
 Strain, 
 
 Diam., 
 
 Wt. per 
 foot, 
 
 Break- 
 ing 
 
 Diam., 
 
 Wt. per 
 foot, 
 
 Break- 
 ing 
 
 
 lb. 
 
 tons 
 (20001b.). 
 
 
 lb. 
 
 Strain, 
 tons. 
 
 
 lb. 
 
 Strain, 
 tons. 
 
 23/ 4 
 
 12.7 
 
 310 
 
 21/4 
 
 6.52 
 
 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 
 
 11/2 
 
 3.70 
 
 90 
 
 2S/ 8 
 
 9.50 232 
 
 17/8 
 
 5.90 
 
 144 
 
 13/8 
 
 3.10 
 
 75 
 
 GALVANIZED CAST-STEEL YACHT RIGGLNG. 
 
 6 Strands and a Hemp Center. 7 or 19 Wires to the Strand. 
 
 i 
 
 
 J2 
 
 o3 ,£ 
 
 I1| 
 
 £18 
 
 i 
 
 03 
 
 
 £ 
 
 
 111 
 
 £ag 
 
 3 
 
 .s 
 
 £ 
 
 n-SS 
 
 fl 
 
 .£ 
 
 £ 
 
 
 o^| 
 
 O 
 
 s 
 
 ft 
 
 
 S^ 
 
 2 
 
 a 
 
 01 
 
 a 
 
 °&^ 
 
 N* 
 
 ft . 
 
 w 
 
 
 ft bH fl 
 
 
 a . 
 
 
 
 awfl 
 
 O oj o< 
 
 ac 
 
 
 
 £ 
 
 ft A 9, 
 
 glw 
 
 as 
 
 
 
 £ 
 
 ac 
 
 s §w 
 
 H/4 
 
 4 
 
 2 55 
 
 53 
 
 13 
 
 5/8 
 
 2 
 
 0.64 
 
 14.0 
 
 6 
 
 13/16 
 
 33/ 4 
 
 2.25 
 
 47 
 
 12 
 
 9/16 
 
 13/4 
 
 0.49 
 
 10.8 
 
 51/4 
 
 11/8 
 
 3l/„ 
 
 1.95 
 
 41 
 
 11 
 
 1/2 
 
 11/2 
 
 0.36 
 
 8.1 
 
 43/4 
 
 11/16 
 
 31/4 
 
 1.70 
 
 36 
 
 10 
 
 15/32 
 
 13/8 
 
 0.30 
 
 6.8 
 
 41/2 
 
 1 
 
 3 
 
 1.44 
 
 31 
 
 9 
 
 7/16 
 
 11/4 
 
 0.25 
 
 5.7 
 
 41/4 
 
 7/8 
 
 23/4 
 
 1.21 
 
 26 
 
 8 1/2 
 
 3/8 
 
 H/8 
 
 0.20 
 
 4.5 
 
 33/4 
 
 13/16 
 
 21/9 
 
 1.00 
 
 22 
 
 8 
 
 5/16 
 
 1 
 
 0.16 
 
 3.7 
 
 3 
 
 3/4 
 
 21/4 
 
 0.81 
 
 17.6 
 
 7 
 
 
 
 
 
 
GALVANIZED STEEL HAWSERS. 
 
 249 
 
 GALVANIZED STEEL-WIRE STRAND. 
 
 For Smokestack Guys, Signal Strand, etc. 
 
 (J. A. Roebling's Sons Co., 1908.) 
 This strand is composed of 7 wires, twisted together into a single strand. 
 
 Diam., in. 
 
 Wt. per. 
 1000 ft., lb. 
 
 Approx. 
 Breaking 
 Strain, lb. 
 
 Diam., in. 
 
 Wt. per 
 1000 ft. 
 
 Approx. 
 Breaking 
 Strain, lb. 
 
 I/9 
 
 510 
 415 
 295 
 210 
 125 
 
 8500 
 6500 
 5000 
 3800 
 2300 
 
 7/39 
 
 95 
 75 
 55 
 32 
 20 
 
 1800 
 
 7/ 16 
 
 3/ 16 
 
 1400 
 
 3 /8 ••• 
 
 0/39 
 
 900 
 
 5 /l6 
 
 l/ 8 
 
 500 
 
 1/4 . 
 
 3/ 32 
 
 400 
 
 
 
 
 Galvanized strand is made on application of wire of any strength from 
 60,000 lb. to 350,000 lb. per sq. in. When used to run over sheaves or 
 pulleys the use of soft-iron stock is advisable. 
 
 FLEXIBLE STEEL-WIRE HAWSERS. 
 
 These hawsers are extensively used. They are made with six strands of 
 twelve wires each, hemp centers being inserted in the individual strands as 
 well as in the completed rope. The material employed is crucible cast 
 steel, galvanized, and guaranteed to fulfill Lloyd's requirements. They 
 are only one-third the weight of hempen hawsers, and are sufficiently 
 pliable to work round any bitts to which hempen rope of equivalent 
 strength can be applied. 
 
 13-inch tarred Russian hemp hawser weighs about 39 lbs. per fathom. 
 
 10-inch white manila hawser weighs about 20 lbs. per fathom. 
 
 1 1/8-inch stud chain weighs about 68 lbs. per fathom. 
 
 4-inch galvanized steel hawser weighs about 12 lbs. per fathom. 
 
 Each of the above named has about the same tensile strength. 
 
 GALVANIZED STEEL HAWSERS. 
 
 For Mooring, Sea or Lake Towing. 
 
 Composed of 6 Strands and a Hemp Center, each Strand consisting of 
 12 Wires and a Hemp Core or of 37 Wires. 
 
 
 
 Wt. per 
 
 ft., lb. 
 
 Approx. Breaking Strain, 
 tons (2000 lb.). 
 
 Approx. 
 
 Circum., 
 
 
 
 
 
 
 
 Diam., in. 
 
 m. 
 
 12-Wire 
 
 37-Wire 
 
 12-Wire 
 
 37-Wire 
 
 
 
 Strand. 
 
 Strand. 
 
 Strand. 
 
 Strand. 
 
 21/16 
 
 6 1/2 
 
 4.56 
 
 6.76 
 
 83 
 
 179 
 
 2 
 
 6 1/4 
 
 4.20, 
 
 6.25 
 
 77 
 
 166 
 
 1 15/ 16 
 
 6 
 
 3.88 
 
 5.76 
 
 71 
 
 155 
 
 1 13/16 
 
 53/4 
 
 3.56 
 
 5.29 
 
 66 
 
 142 
 
 13/4 
 
 51/2 
 
 3.25 
 
 4.85 
 
 61 
 
 131 
 
 1 H/I6 
 
 51/4 
 
 2.95 
 
 4.41 
 
 57 
 
 120 
 
 15/8 
 
 5 
 
 2.70 
 
 4.00 
 
 53 
 
 109 
 
 11/2 
 
 43/4 
 
 2.42 
 
 3.60 
 
 45 
 
 99 
 
 17/16 
 
 41/2 
 
 2.18 
 
 3.24 
 
 42 
 
 90 
 
 13/s 
 
 41/4 
 
 1.94 
 
 2.90 
 
 39 
 
 81 
 
 11/4 
 
 4 
 
 1.72 
 
 2.55 
 
 32 
 
 72 
 
 13/16 
 
 33/ 4 
 
 1.51 
 
 2.25 
 
 29 
 
 62 
 
 11/8 
 
 31/2 
 
 1.32 
 
 1.95 
 
 27 
 
 55 
 
 11/16 
 
 31/4 
 
 1.14 
 
 1.69 
 
 24 
 
 46 
 
 1 
 
 3 
 
 .97 
 
 1.44 
 
 21.5 
 
 40 
 
 7/8 
 
 23/4 
 
 .81 
 
 1.21 
 
 16.4 
 
 34 
 
 13/16 
 
 21/2 
 
 .67 
 
 1.00 
 
 14.4 
 
 28 
 
 3/4 
 
 r 
 
 21/4 
 
 .54 
 
 .81 
 
 12.3 
 
 23 
 
 
 
 
 
 
 
250 MATERIALS. 
 
 Notes on the Use of Wire Rope. (J. A. Roebling's Sons Co.) 
 (See also notes under various tables of wire ropes.) 
 
 Several kinds of wire rope are manufactured. The most pliable 
 variety contains nineteen wires to the strand. The ropes with twelve 
 wires and seven wires in the strand are stiffer, and are better adapted for 
 standing rope, guys, and rigging. Orders should state the use of the 
 rope, and advice will be given. 
 
 Wire rope is as pliable as new hemp rope of the same strength; the 
 former will therefore run over the same-sized sheaves and pulleys as the 
 latter. But the greater the diameter of the sheaves, pulleys, or drums, 
 the longer wire rope will last. The minimum size of drum is given in 
 the table. Experience has demonstrated that the wear increases with 
 the speed. It is, therefore, better to increase the load than the speed. 
 
 Wire rope must 'not be coiled or uncoiled like hemp rope. — When 
 mounted on a reel, the latter should be mounted on a spindle or flat 
 turn-table to pay off the rope. When forwarded in a small coil, without 
 reel, roll -it over the ground like a wheel, and run off the rope in that 
 wav. All untwisting or kinking must be avoided. 
 
 To preserve wire rope, apply raw linseed -oil with a piece of sheepskin, 
 wool inside; or mix the oil with equal parts of Spanish brown or lamp- 
 black. 
 
 To preserve wire rope under water or under ground, take mineral or 
 vegetable tar, and add one bushel of fresh-slacked lime to one barrel of 
 tar, which will neutralize the acid. Boil it well, and saturate the rope 
 with the hot tar. To give the mixture body, add some sawdust. 
 
 The grooves of cast-iron pulleys and sheaves should be filled with 
 well-seasoned blocks of hard wood, set on end, to be renewed when 
 worn out. This end-wood will save wear and increase adhesion. The 
 smaller pulleys or rollers which support the ropes on inclined planes 
 should be constructed on the same plan. When large sheaves run at 
 high velocity, the grooves should be lined with leather, set on end, or 
 with India rubber. This is done in the case of sheaves used in the 
 transmission of power between distant points by means of rope, which 
 frequently runs at the rate of 4000 feet per minute. 
 
 Locked Wire Rope. 
 
 Fig. 77 shows what is known as the Patent Locked Steel Wire Rope 
 made by the Trenton Iron Co. It is claimed to wear two to three times 
 
 as long as an ordinary wire rope of equal diameter and of like material, 
 with an increased life for sheaves and rollers. Sizes made are from 1/2 
 to 2 inches diameter, with a minimum diameter of sheave of 4 and 12 
 feet respectively. 
 
251 
 
 CHAINS. 
 
 Weight per Foot, Proof Test and Breaking Weight. 
 
 (Pennsylvania Railroad Specifications, 1903.) 
 
 Nominal 
 
 Diameter 
 
 of Wire. 
 
 Inches. 
 
 5/32 
 3/16 
 3/16 
 
 V4 
 5/16 
 3/8 
 3/8 
 7/16 
 7/16 
 1/2 
 1/2 
 5/8 
 5/8 
 3/4 
 3/4 
 7/8 
 1 
 1 
 
 H/8 
 H/4 
 U/2 
 13/4 
 2 
 
 Description, 
 
 Twisted chain . 
 
 Perfection twisted chain 
 Straight-link chain. 
 
 Crane chain 
 
 Straight-link chain . . . 
 
 Crane chain 
 
 Straight-link chain . . . 
 
 Crane chain 
 
 Straight-link chain . . . 
 
 Crane chain 
 
 Straight-link chain . . . 
 Crane chain 
 
 Straight-link chain . 
 Crane chain 
 
 Maximum 
 
 Length of 
 
 100 Links 
 
 Inches. 
 
 1031/ 8 
 96l/ 4 
 l5ll/ 4 
 102 
 1143/ 4 
 1143/4 
 1135/ 8 
 1271/ 2 
 1261/4 
 153 
 1511/2 
 1781/9 
 176 3/4 
 204 
 202 
 2521/2 
 277 ?/ 4 
 2801/-, 
 303 
 3531/2 
 4165/ 8 
 4793/ 4 
 5551/ 2 
 
 \\ eight 
 
 Lbs. 
 
 0.20 
 0.35 
 0.27 
 0.70 
 1.10 
 1.60 
 1.60 
 2.07 
 2.07 
 2.50 
 2.60 
 4.08 
 4.18 
 5.65 
 5.75 
 7.70 
 9.80 
 9.80 
 12.65 
 15.50 
 22.50 
 30.00 
 39.00 
 
 Proof 
 Test. 
 Lbs. 
 
 1,600 
 2,500 
 3,600 
 4,140 
 4,900 
 5,635 
 6,400 
 7,360 
 10,000 
 11,500 
 14,400 
 16,560 
 22,540 
 29,440 
 25,600 
 38,260 
 46,000 
 66,240 
 90, 1 60 
 117,760 
 
 Breaking 
 
 Weight. 
 Lbs. 
 
 3,200 
 5,000 
 7,200 
 8,280 
 9,800 
 11,270 
 12,800 
 14,720 
 20,000 
 23,000 
 28,800 
 33,120 
 45,080 
 58,880 
 51,200 
 76,520 
 92,000 
 132,480 
 180,320 
 235,520 
 
 A.11 chain must stand the proof 
 ft. long out of each 200 ft. is 
 
 Elongation of all sizes, 10 per cent 
 test without deformation. A piece 
 tested to destruction. 
 
 British Admiralty Proving Tests of Chain Cables. — Stud-links. 
 Minimum size in inches and 16ths. Proving test in tons of 2240 lbs. 
 Min. Size: ft I i§ i if 1 1th H 1 r 3 s H li 6 s If 
 Test, tons: 8* 10.1 11.9 13f 15f 18 20.3 22f 25A 28.1 31 34 
 Min. Size: 1 T 7 H 1* 1 T 9 6 IS Ui 1* Ul If lit 2 2| 
 Test, tons: 37 5 3 5 40£ 43 9 47| 51* 55.1 59.1 63* 67JJ 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. 
 
252 
 
 MATERIALS. 
 
 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. 
 
 1 
 
 71,172 
 
 33,840 
 
 19/16 
 
 162,283 
 
 77,159 
 
 11/16 
 
 79,544 
 
 37,820 
 
 15/8 
 
 174,475 
 
 82,956 
 
 U/8 
 
 88,445 
 
 42,053 
 
 1 11/16 
 
 187,075 
 
 88,947 
 
 13/16 
 
 97,731 
 
 46,468 
 
 13/4 
 
 200,074 
 
 95,128 
 
 U/4 
 
 107,440 
 
 51,084 
 
 1 13/16 
 
 213,475 
 
 101,499 
 
 1 5 /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 
 
 66,138 
 
 2 
 
 256,040 
 
 121,737 
 
 H/2 
 
 150,485 
 
 71,550 
 
 
 
 
 Pitch, Breaking, Proof and Working Strains of Chains. 
 
 (Bradlee & Co., Philadelphia.) 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 8/16 
 
 5/8 
 
 H/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 15/16 
 
 H/16 
 
 U/8 
 
 13/16 
 
 U/4 
 
 15/16 
 
 13/8 
 
 17/16 
 
 11/2 
 
 19/16 
 
 13/ 4 
 
 2 
 
 21/ 4 
 
 21/2 
 
 2 3/4 
 
 3 
 
 25 /32 
 27/32 
 31/32 
 15/32 
 1 H/32 
 1 15/3 2 
 1 23/3 2 
 1 13/16 
 1 15/16 
 21/16 
 23/ie 
 27/i 6 
 21/2 
 25/ 8 
 23/4 
 31/16 
 31/8 
 33/8 
 39/i 6 
 3H/16 
 37/8 
 4 
 
 43/ 4 
 53/4 
 63/4 
 7 
 
 71/4 
 73/4 
 
 3/4 
 1 
 
 U/2 
 2 
 
 21/2 
 33/io 
 41/10 
 5 
 
 62/io 
 67/io 
 83/s 
 9 
 
 101/9 
 
 12 
 
 135/s 
 
 137/io 
 
 16 
 
 161/-> 
 
 191/4 
 
 197/io 
 
 23 
 
 25 
 
 31 
 
 40 
 
 523/4 
 
 641/2 
 
 73 
 
 86 
 
 15/16 
 
 U/8 
 
 15/16 
 
 U/2 
 
 1 13/16 
 
 2 
 
 23/16 
 
 23/ 8 
 
 29/ie 
 
 23/4 
 
 215/ie 
 
 33/i 6 
 
 33/8 
 
 39/ie 
 
 313/i 6 
 
 4 
 
 43/ie 
 
 43/ 8 
 
 49/ie 
 
 43/ 4 
 
 51/8 
 
 55/ie 
 
 57/s 
 
 63/4 
 
 75/8 
 
 83/s 
 
 91/8 
 
 97/8 
 
 D. B. G. Special Crane. 
 
 1,932 
 
 2,898 
 4,186 
 5,796 
 7,728 
 9,660 
 11,914 
 14,490 
 17,388 
 20,286 
 22,484 
 25,872 
 29,568 
 33,264 
 37,576 
 41,888 
 46,200 
 50,512 
 55,748 
 60,368 
 66,528 
 70,762 
 82,320 
 107,520 
 136,080 
 168,000 
 193,088 
 217,728 
 
 3,864 
 5,796 
 8,372 
 11,592 
 15,456 
 19,320 
 23,828 
 28,9 
 34,776 
 40,572 
 44,968 
 51,744 
 59,136 
 66,538 
 75,152 
 83,776 
 92,400 
 101,024 
 111,496 
 120,736 
 133,056 
 141,524 
 164,640 
 215,040 
 272,160 
 336,000 
 386,176 
 435,456 
 
 1,288 
 1,932 
 2,790 
 3,864 
 5,152 
 6,440 
 7,942 
 9,660 
 11,592 
 13,524 
 14,989 
 17,248 
 19,712 
 22,176 
 25,050 
 27,925 
 30,800 
 33,674 
 37,165 
 40,245 
 44,352 
 47,174 
 54,880 
 71,680 
 90,720 
 112,000 
 128,725 
 145,152 
 
 1,680 
 2,520 
 3,640 
 5,040 
 6,720 
 8,400 
 10,360 
 12,600 
 15,120 
 17,640 
 20,440 
 23,520 
 26,880 
 30,240 
 34,160 
 38,080 
 42,000 
 45,920 
 50,680 
 54,880 
 60,480 
 65,520 
 
 <~ 
 
 3,360 
 5,040 
 7,280 
 10,080 
 13,440 
 16,800 
 20,720 
 25,200 
 30,240 
 35,280 
 40,880 
 47,040 
 53,760 
 60,480 
 68,320 
 76,160 
 84,000 
 91,840 
 101,360 
 109,760 
 120,960 
 131,140 
 
 1,12 
 1,68 
 2,420 
 3,360 
 4,487 
 5,600 
 6,900 
 8,400 
 10,087 
 11,760 
 13,620 
 15,680 
 17,927 
 20,160 
 22,770 
 25,380 
 28,003 
 30,617 
 33,780 
 36,583 
 40,327 
 43,187 
 
 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. 
 
SIZES OF FIRE-BRICK. 
 
 253 
 
 9x4^x2)^ , 
 
 9-inch straight ... 9 X 4 1/2 X 2 V 2 inches. 
 
 Soap 9x21/4X21/2 
 
 Checker 9X3 X3 
 
 'Kev \ NO. 1 Split 9X41/2X1V4 
 
 _!___— -} No. 2 Split 9X41/2X2 
 
 -^7aH- 2 T Jamb 9 X 4V 2 X 2 1/2 
 
 : -"-' — -'- No. 1 key 9 X 21/2 thick X 4V 2 to 4 inches 
 
 wide. 112 bricks to circle 12 feet inside 
 diam. 
 
 No. 2 key 9 X 2V 2 thick X 41/2 to 3V 2 inches 
 
 Wedge \ wide. 65 bricks to circle 6 ft. inside diam. 
 
 x No. 3 key 9 X 21/2 thick X4i/ 2 to 3 inches wide. 
 
 41 bricks to circle 3 ft. inside diam. 
 * - g-^ No. 4 key 9X2 1/2 thick X 4 V 2 to 2 1/4 inches 
 
 wide. 26 bricks to circle IV2 ft. inside diam. 
 
 v No. 1 wedge (or bullhead) 9 X 4 1/2 wide 2 XV2 
 
 Arch \ to 2 in. thick, tapering lengthwise. 
 
 7 102 bricks to circle 5 ft. inside diam. 
 
 :4>$x (2>£:1K/ No. 2 wedge 9 X 41/2 X 21/2 to 1 1/2 in. thick. 
 
 / 63 bricks to circle 21/2 ft. inside diam. 
 
 ■ ' No. 1 arch 9 X 4V 2 X 2V 2 to 2 in. thick, 
 
 tapering breadthwise. 72 bricks to circle 4 ft. 
 inside diam. 
 ,No.l Skew\ No. 2 arch 9 X 4l/ 2 X 2i/ 2 to 1 1/ 2 . 
 
 42 bricks to circle 2 ft. inside diam. 
 No. 1 skew 9 to 7 X 41/2 to 2V 2 . 
 
 ( m*Ui*ZX / Bevel on one end. 
 
 '■ No. 2 skew 9 X 2i/ 2 X 4V 2 to 2i/ 2 . 
 
 Equal bevel on both edges. 
 
 ~ __. — \ No. 3 skew 9 X 2i/ 2 X 4i/ 2 to H/ 2 . 
 
 jno.^ sKew \ Taper on one edge. 
 
 / 24-inch circle 8 1/4 to 5i/ 8 X 4V 2 X 2l/ 2 . 
 
 *2tex(il4-2Xt Edges curved, 9 bricks line a 24-inch circle. 
 
 n I 36-inch circle 83/ 4 ,to 6i/ 2 X 4i/ 2 X 2i/ 2 . 
 
 -* 13 bricks line a 36-inch circle. 
 
 48-inch circle. ... 83/ 4 to 71/4X 4i/ 2 X 2i/ 2 . 
 17 bricks line a 48-inch circle. 
 No 3 Skew — \ 13 1/2-inch straight . . 13 1/2 X 2 1/ 2 X 6. 
 
 131/2-inch key No. 1, 13i/ 2 X 2 1/2 X 6 to 5 inch. 
 2Xx(i\4-U£Y 1 90 bricks turn a 12-ft. circle. 
 
 ' * . 2-2/ 3 1/2-inch key No. 2, 1 3 1/2 X 2 1/2 X 6 to 4 3/ 8 inch. 
 
 52 bricks turn a 6-ft. circle. 
 in. Cirdfl Bridge wall, No. 1, 13 X 6V2X 6. 
 
 ~~S% -\ Bridge wall, No. 2, 13 X 6 1/2 X 3. 
 
 \ Mill tile 18, 20, or 24 X 6 X 3. 
 
 ^\ M \ Stock-hole tiles ... 18, 20, or 24 X 9 X 4. 
 1 18-inch block .... 18X9X6. 
 
 Flat back 9 X 6 X 2 1/2. 
 
 Flat back arch ... 9 X 6 X 3 1/2 to 21/2. 
 
 22-inch radius, 56 bricks to circle. 
 CuDoia^^ Locomotive tile. . .32 X 10 X 3. I 36 X 8 X 3. 
 34 X 10 X 3. 40 X 10 X 3. 
 
 34 X 8 X 3. I 
 Tiles, slabs, and blocks, various sizes 12 to 30 
 in. long, 8 to 30 in. wide, 2 to 6 in. thick. 
 Cupola brick, 4 and 6 in. high, 4 and 6 in. radial width, to line shells 
 23 to 66 in. diameter. 
 
 A 9-inch straight brick weighs 7 lb. and contains 100 cubic inches. 
 ( = 120 lb. per cubic foot. Specific gravity 1.93.) 
 
 One cubic foot of wall requires 17 9-inch bricks, one cubic yard re- 
 quires 460. Where keys, wedges, and other "shapes" are used, add 10 
 per cent in estimating the number required. 
 
 One ton of fire-clay should be sufficient to lay 3000 ordinary bricks. 
 To secure the best results, fire-bricks should be laid in the same clay 
 
254 
 
 MATERIALS. 
 
 from which they are manufactured. 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 required should be 
 stated. 
 
 NUMBER OF FIRE-BRICK REQUIRED FOR VARIOUS 
 CIRCLES. 
 
 Diam. 
 
 Key Bricks. 
 
 Arch Bricks. 
 
 Wedge Bricks. 
 
 of 
 Circle. 
 
 d 
 
 d 
 
 c 
 
 d 
 
 *3 
 
 o 
 
 c 
 
 Iz; 
 
 d 
 5 
 
 
 o 
 
 d 
 
 d 
 
 .5 
 
 ON 
 
 "3 
 
 o 
 H 
 
 ft. in. 
 1 6 
 
 25 
 17 
 9 
 
 
 
 
 25 
 30 
 34 
 38 
 42 
 46 
 51 
 55 
 59 
 63 
 67 
 71 
 76 
 80 
 84 
 
 92 
 97 
 101 
 105 
 109 
 113 
 117 
 
 
 
 
 
 
 
 
 
 2 
 
 13 
 25 
 38 
 32 
 25 
 19 
 13 
 6 
 
 
 
 42 
 31 
 ?,1 
 
 
 
 42 
 49 
 57 
 64 
 72 
 80 
 87 
 95 
 102 
 110 
 117 
 125 
 132 
 140 
 147 
 155 
 162 
 170 
 177 
 185 
 193 
 
 
 
 
 
 2 6 
 
 
 
 18 
 36 
 54 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 72 
 
 72 
 72 
 72 
 72 
 72 
 
 15 
 23 
 30 
 38 
 45 
 53 
 60 
 68 
 75 
 83 
 90 
 98 
 105 
 113 
 121 
 
 60 
 
 48 
 36 
 24 
 12 
 
 
 
 60 
 
 3 
 
 
 
 20 
 40 
 59 
 79 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 98 
 
 "8" 
 
 15 
 
 23 
 
 30 
 
 38 
 
 46 
 
 53 
 
 61 
 
 68 
 
 76 
 
 83 
 
 91 
 
 98 
 106 
 
 68 
 
 3 6 
 
 4 
 
 4 6 
 
 5 
 
 5 6 
 
 6 
 
 10 
 
 21 
 32 
 42 
 53 
 63 
 58 
 52 
 47 
 42 
 37 
 31 
 26 
 21 
 16 
 11 
 5 
 
 ' 9 " 
 
 19 
 
 29 
 
 38 
 47 
 
 66 
 
 76 
 
 85 
 
 94 
 104 
 113 
 113 
 
 1 
 
 ) 
 
 76 
 83 
 91 
 98 
 106 
 113 
 
 6 6 
 
 
 
 121 
 
 7 
 
 
 
 128 
 
 7 6 
 
 
 
 136 
 
 8 
 
 
 
 144 
 
 8 6 
 
 
 
 151 
 
 9 
 
 
 
 159 
 
 9 6 
 
 
 
 166 
 
 10 
 
 
 
 174 
 
 10 6 
 
 
 
 181 
 
 11 
 
 
 
 189 
 
 11 6 
 
 
 
 196 
 
 12 
 
 
 
 204 
 
 12 6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch 
 brick as may be needed in addition. 
 
 WEIGHTS OF LOGS, LUMBER, ETC. 
 
 Weight of Green Logs to Scale 1000 Feet, Board Measure. 
 
 Yellow pine (Southern) 8,000 to 10 
 
 Norway pine (Michigan) 7,000 to 8 
 
 White nine rMichiearrt i off of stum P 7 - 000 to 7 
 
 wnite pine (.Micmgan) J QUt of water 7000 to 
 
 White pine (Pennsylvania), bark off 5,000 to 
 
 Hemlock (Pennsylvania), bark off 6,000 to 7,000 ' 
 
 Four acres of water are required to store 1,000,000 feet of logs. 
 
 000 lb. 
 000 " 
 ,000 " 
 ,000 " 
 ,000 " 
 
 Weight of 1000 Feet of Lumber, Board Measure. 
 
 Yellow or Norway pine Dry, 3,000 lb. 
 
 White pine " 2,500" 
 
 Green, 5, 
 
 4', 
 
 0001b. 
 ,000 " 
 
ANALYSES OF FIRE CLAYS. 
 
 255 
 
 Weight of 1 Cord of Seasoned Wood, 138 Cu. Ft. per Cord. 
 
 Hickory or sugar maple 4 500 lb 
 
 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 " 
 
 ANALYSES OF FIRE CLAYS. 
 
 Brand. 
 
 73 
 
 '3 
 < 
 
 u 
 
 H 
 
 6 
 
 c n 
 go 
 
 
 O 
 
 s 
 
 O 
 6 
 
 S 
 
 3 
 
 .2 
 
 93 
 
 C 
 o 
 
 q 
 
 73 
 
 c 
 
 X< 
 
 H 
 
 o ft 
 Eh 
 
 o 
 i-1 
 
 
 
 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 
 73.82 
 
 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 
 15.88 
 
 12.744 
 10.50 
 14.575 
 9.68 
 
 Y.W 
 
 5.98 
 3.03 
 10.56 
 14.70 
 1.94 
 6.87 
 13.63 
 13.30 
 10.45 
 6.45 
 
 1.50 
 1.12 
 1.08 
 0.59 
 1.60 
 1.67 
 1.57 
 1.01 
 2.00 
 0.30 
 0.33 
 1.20 
 1.25 
 2.03 
 2.56 
 2.95 
 
 0.13 
 
 1 
 02 Trop.fi 
 
 1.65 
 1.92 
 1.47 
 0.88 
 2.79 
 3.97 
 4.33 
 4.02 
 4.73 
 
 
 Mt. Savage 2 
 
 1.15 
 1.53 
 
 
 0.80 
 0.247 
 
 
 Mt. Savage 3 
 
 Tr. 
 0.17 
 0.40 
 
 0.11 
 0.12 
 0.30 
 
 
 Strasburg, O 
 
 0.45 
 1.15 
 
 0.29 
 
 2.30 
 
 2.24 
 
 0.20 
 
 
 Woodbridge, N. J. . 
 
 0.28 
 3.01 
 0.07 
 0.20 
 0.23 
 0.17 
 0.08 
 0.08 
 0.41 
 Tr. 
 
 0.24 
 
 
 Clearfield Co., Pa. . 
 
 L46 
 
 1.02 
 
 0.12 
 1.00 
 1.15 
 0.47 
 0.41 
 0.02 
 0.07 
 Tr. 
 
 2.54 
 
 
 
 
 
 
 Clinton Co., Pa. ... 
 
 Clarion Co., Pa 
 
 Farrandsville, Pa. . 
 St. Louis Co., Mo.. . 
 Stourbridge, Eng. . . 
 
 2.52 
 1.74 
 1.26 
 1.07 
 0.90 
 
 4.55 
 3.47 
 3.59 
 5.14 
 
 3.85 
 
 SO 2 0.l9 
 6.20 
 
 1 Mass. Inst, of Technology 1871. 2 Report on Clays of New Jersey. 
 Prof. G. H. Cook, 1877. 3 Second Geological Survey of Penna., 1878, 
 * Dr. Otto Wuth (2 samples), 1885. 6 Flint clay from Clearfield 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., 1907. 
 
 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 fusion-point of 
 almost any of the New Jersey fire-bricks could be reduced four or five 
 cones by grinding the brick sufficiently fine to pass through a 100-mesb 
 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. 
 
256 
 
 MATERIALS. 
 
 
 Locality. 
 
 Si0 2 . 
 
 AI2O3. 
 
 FesOs- 
 
 Ti0 2 . 
 
 13 
 
 < 
 
 i 
 
 °.2 
 
 " 2 3 
 
 flrv. 
 
 O 
 
 1 .. 
 
 
 Per 
 
 cent. 
 
 51.59 
 
 54.90 
 
 53.05 
 
 93.57 
 
 44.77 
 
 68.70 
 
 61.28 
 
 74.83 
 
 67.19 
 
 60.76 
 
 60.58 
 
 Per 
 
 cent. 
 38.26 
 38.19 
 41.16 
 2.53 
 43.08 
 20.75 
 27.13 
 16.40 
 25.05 
 31.66 
 32.49 
 
 Per 
 
 cent. 
 1.84 
 2.18 
 2.65 
 0.62 
 2.78 
 1.20 
 2.90 
 3.26 
 2.83 
 5.67 
 2.25 
 
 Per 
 cent. 
 1.97 
 1.55 
 1.80 
 0.27 
 2.54 
 5.54 
 1.37 
 0.77 
 0.71 
 1.58 
 1.69 
 
 Per 
 cent. 
 6.34 
 3.18 
 1.34 
 3.01 
 6.83 
 3.81 
 7.31 
 4.74 
 4.22 
 0.33 
 2.99 
 
 Per 
 cent. 
 10.25 
 6.91 
 5.79 
 3.90 
 12.15 
 10.55 
 11.58 
 8.77 
 7.76 
 7.58 
 6.93 
 
 No. 
 32 to 33 
 
 2.... 
 3.... 
 4 .. 
 
 Kentucky 
 
 Pennsylvania 
 
 32 to 33 
 32 to 33 
 32 to 33 
 
 5 ... 
 
 
 31 to 32 
 
 6.... 
 
 
 31 to 32 
 
 40.... 
 41.... 
 42 
 
 Pennsylvania 
 
 Pennsylvania. 
 
 26 
 26 
 26 
 
 43 ... . 
 
 
 26 
 
 44.... 
 
 Kentucky 
 
 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. 
 
 43 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- 
 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, Eng. 
 News, April 30, 1903. 
 
MAGNESIA BRICKS. 257 
 
 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 
 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., 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). 
 
 Grecian. Styrian. 
 
 Crude. Calcined. Crude. Calcined. 
 
 Carbonate of magnesia 97.00% 92.50% . 
 
 Magnesia 94.00% 85.50% 
 
 Silica 1.25 2.75 1.50 3.00 
 
 Alumina 0.40 0.70 0.50 1.00 
 
 Iron Oxide 0.40 0.80 3.90 8.00 
 
 Lime 0.75 1.50 1.25 2.50 
 
 Loss 0.40 0.50 
 
 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. 
 
 ASBESTOS. 
 
 The following analyses of asbestos'are given 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 sample 
 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. 
 
258 STRENGTH OF MATERIALS. 
 
 STRENGTH OF 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; others call the external 
 force a strain, and the internal force a stress; this confusion 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 deformation 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. 259 
 
 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 Limit. — 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 
 lbs. 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 only 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 eye. 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 of 
 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 observable by ordinary instruments or by the drop of 
 the beam. With this definition it is practically synonymous with yield- 
 point. 
 
260 STRENGTH OF MATERIALS. 
 
 Coefficient (or Modulus) of Elasticity. — 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 by 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 -*- I = the 
 elongation of a unit of length. 
 
 7? = Z u. * = U. 
 
 k ' I k\ 
 
 The coefficient of elasticity is sometimes defined as the figure express- 
 ing the load which would be necessary to elongate a piece of one square' 
 inch section to double its original length, provided the piece would not 
 break, and the ratio of extension to the force producing it remained con- 
 stant. This definition follows from the formula above given, thus: 
 If k = one square inch, I 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 
 limit it decreases rapidly. 
 
 In cast iron there is generally no apparent limit of elasticity, the defor- 
 mations increasing at a faster rate than the stresses, and 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 
 steel, 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 
 stress, supported at the ends and loaded in the middle, 
 
 3 I 
 
 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, 
 E = modulus of elasticity, A = deflection, I, b, and d = length, breadth, 
 and depth in inches. Substituting for P in (2) its value in (1), A= 1/6 Rl 2 
 + Ed. 
 
 The elastic resilience = half the product of the load and deflection = 
 1/2 P A, and the elastic resilience per cubic inch = 1/2 PA -r- Ibd. 
 
 Substituting the values of P and a, this reduces to elastic resilience per 
 1 R 2 
 cubic inch= rr. tt > which is independent of the dimensions; and therefore 
 
 18 hi 
 the elastic resilience per cubic inch for transverse strain may be used as a 
 modulus expressing one valuable quality of a material. 
 
ELEVATION OP THE ELASTIC LIMIT. 261 
 
 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. 
 
 1 P 2 
 
 Then elastic resilience per cubic inch = 1/2 Pe = ^ jjr 
 
 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 materia], without 
 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 beyond 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 experiments 
 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 
 
 Eossibly for years if the bar is left at rest under its load. On the other 
 and, 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 its primitive breaking- 
 
262 STRENGTH OF MATERIALS. 
 
 down point the elastic limit begins to rise again, and may, if left a suffi- 
 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 8V2 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 
 place, and the first, in spite of its having been strained beyond its elastic 
 limits, and not subsequently annealed, would be as strong as the other. 
 
 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. 
 
STRESSES DUE TO SUDDEN FORCES AND SHOCKS. 263 
 
 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 continuous vibration assumes a crystalline 
 structure, and that the cohesive powers are much deteriorated, but we 
 are ignorant of the causes of this change." We are still ignorant, not 
 only of the causes of this change, but of the conditions under which it 
 takes place. Who knows whether wrought iron subjected to very slight 
 continuous vibration will endure forever? or whether to insure final 
 rupture each of the continuous small shocks must amount at least to a 
 certain percentage of single heavy shock (both measured in foot-pounds), 
 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 lbs.). 
 
 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 
 1000 foot-pounds, how many times would it be likely to bear the repetition 
 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 
 carbon under impact. Some small steel pitmans were made, the specifi- 
 cations for which required that the unloaded machine should run 41/2 
 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 machine 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. I. M. E., vol. viii, p. 76, from which the above 
 extract is taken.) 
 
 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 
 
264 STRENGTH OF MATERIALS, 
 
 the mean stress 1/2 Q multiplied by the total elongation y, or TF=i/2 QV- 
 Whence, neglecting the work that may be dissipated in heat, 
 
 V2 Qy = Ph + Py. 
 If e be the elongation due to the static l oad P, within the elastic limit 
 y = -pe; whence Q = P (l + y 1 + 2 -Y which gives the momentary 
 maximu m stres s. Substituting this value of Q, there results y = e 
 (l + y 1 + 2 -J, 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 lbs. this will be compressed about 0.012 
 in., supposing that no lateral flexure occurs; but if a weight of 5000 lbs. 
 drops upon its end from the small height of 0.048 in. there will be produced 
 the stress of 20,000 lbs. 
 
 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. 
 
 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 
 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 c 
 
 No. of turns per foot 3 43/ 4 5 53/ 4 57/ 8 
 
 Yield point, lbs. 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 5 1/2 
 
 Yield point, lbs. 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 V2 5 /8 3/ 4 7/ 8 1 1 1/ 8 1 1/4 
 
 No. of turns per ft 4 3 1/2 3 21/4 1 1/2 1 V4 1 7 /s 3 /4 
 
 Yield point, increase %* Ill 82 64 83 85.5 77 82 64 ^59 
 
 Ult. strength " %* 37 38.6 41 33.5 34.3 29.7 22.8 20.1 28.9 
 
 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 lbs. 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. . 
 
 * Average of two tests each.] 
 
TENSILE STRENGTH. 
 
 265 
 
 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 
 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 the 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 1/4-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. 
 
 1.00 in. long 
 
 0.50 in. long 
 
 0.25 in. long 
 
 Semicircular groove, 0.4 
 
 in. radius 
 
 Semicircular groove, 1/8 
 
 in. radius 
 
 V-shaped groove 
 
 Elastic Limit, 
 Lbs. per Sq. In. 
 
 64,900 
 65,320 
 68,000 
 
 75,000 
 
 86,000, about 
 90,000, about 
 
 Tensile Strength, 
 Lbs. per Sq. In. 
 
 Contraction of 
 Area, per cent. 
 
 94,400 
 97,800 
 102,420 
 
 49.0 
 43.4 
 39.6 
 
 116,380 
 
 31.6 
 
 134,960 
 117,000 
 
 23.0 
 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 lbs. T. S. Aver. 57,566 lbs. 
 
 4 grooved " 64,341 to 67,400 " " " 65,452 " 
 
 Excess of the short or grooved specimen, 21 per cent, or 12,114 lbs. 
 
 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): 
 
266 STRENGTH OF MATERIALS. 
 
 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 + 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 4- spaces. 
 
 • Shapes of Specimens for Tensile Tests. — The shapes shown in 
 Fig. 78 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. 
 
 f< 16-'to-20" : 
 
 Y 16- f to-2Q- H 
 
 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. 
 
 Fig. 78. 
 
 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. 
 
 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 
 
COMPRESSIVE STRENGTH. 267 
 
 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. 
 
 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 compressive 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 as 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 rupture, 
 may vary with every size and shape of specimen experimented upon. 
 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 the 
 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 
 
268 STRENGTH OF MATERIALS. 
 
 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 1 
 
 " (mean) 85,500 
 
 Fnriteh " " i 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 11/2 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 definition 
 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 regards length, viz., 
 from one to five diameters. In some metals a specimen five diameters 
 long would bend, and give a much lower apparent strength than a speci- 
 men 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 weight 
 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 desirable: 
 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 
 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 above. 
 
 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 ordi- 
 nary 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 calculation 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 3/ 4 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 H/2 inches in height was 
 
COLUMNS, PILLARS, OR STRUTS. 269 
 
 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 Mechan- 
 ical Engineers say (vol. xi, p. 624): 
 
 "Although compression tests have heretofore been made on diminutive 
 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 deter- 
 mined 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 structures, 
 which have always been and are now designed according to empirical for- 
 mulas 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, lbs. 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 
 
 m„A ,-vf rui,,™™ length of the column of the column exceed- 
 
 ivinaoi column. exceeding 15 times its ing 30 times its diam- 
 
 diameter. eter. 
 
 W3-55 
 
 P = 98,920 j— j 
 
 Solid cylindrical col- 1 
 
 umns of cast iron . . . ) 
 Solid cylindrical col- \ 
 
 umns of wrought iron ) 
 
 These formulae apply only in cases in which the length is so great that 
 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. 
 
 P/a = it 2 E (r/l) 2 for columns with round or hinged ends. For columns 
 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 
 quality of the iron being about as follows: tensile strength per sq. in., 
 49,600 lbs., elastic limit 32,000 lbs., elongation 18% in 8 ins. 
 
270 
 
 STRENGTH OP MATERIALS. 
 
 The following table gives the average results. 
 
 Ratio I It 
 Length to 
 Least Ra- 
 dius of 
 Gyration. 
 
 Ultimate Load, P/a, in Pounds per Square Inch. 
 
 Fixed Ends. 
 
 Flat Ends. 
 
 Hinged Ends. 
 
 Round Ends. 
 
 20 
 40 
 60 
 80 
 100 
 120 
 140 
 160 
 180 
 200 
 220 
 240 
 260 
 280 
 300 
 320 
 360 
 400 
 
 46,000 
 40,000 
 36,000 
 32,000 
 30,000 
 28,000 
 25,500 
 23,000 
 20,000 
 17,500 
 15,000 
 13,000 
 11,000 
 10,000 
 9,000 
 8,000 
 6,500 
 5,200 
 
 46,000 
 40,000 
 36,000 
 32,000 
 29,800 
 26,300 
 23,500 
 20,000 
 16,800 
 14,500 
 12,700 
 11,200 
 9,800 
 8,500 
 7,200 
 6,000 
 4,300 
 3,000 
 
 46,000 
 
 40,000 
 
 36,000 
 
 31,500 
 
 28,000 
 
 24,300 
 
 21,000 
 
 16,500 
 
 12,800 
 
 10,800 
 
 8,800 
 
 7,500 
 
 6,500 
 
 5,700 
 
 5,000 
 
 4,500 
 
 3,500 
 
 2,500 
 
 44,000 
 
 36,500 
 
 30,500 
 
 25,000 
 
 20,500 
 
 16,500 
 
 12,800 
 
 9,500 
 
 7,500 
 
 6,000 
 
 5,000 
 
 4,300 
 
 3,800 
 
 3,200 
 
 2,800 
 
 2,500 
 
 1,900 
 
 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 = — f 1 +<£ (-) ) 
 
 or — = — — , /T/ .„ • Applying Rankine's formula to the results of 
 
 a 1+0 (l/ry 
 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 4> for Rankine's Formula. 
 
 Material. 
 
 Both Ends 
 Fixed. 
 
 Fixed and 
 Round. 
 
 Both Ends 
 Round. 
 
 
 1/3,000 
 1 /5,000 
 1/36,000 
 1 /25.000 
 
 1.78/3,000 
 1.78/5,000 
 1 .78/36,000 
 1.78/25,000 
 
 4/3,000 
 
 
 4/5,000 
 
 Wrought Iron 
 
 Steel 
 
 4/36,000 
 4/25,000 
 
 
 
 The value to be taken for 5 is the ultimate compressive strength of the 
 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, <j> = 1/36,000 to 
 1/40,000. 
 
 For solid cast-iron columns, S = 80,000, <b = 1/6,400. 
 
 IP 
 
 For hollow cast-iron columns, P/a = 80,000 -r 1 + ™ -g (d — outside 
 
 diam. in inches;. 
 
 800 c 
 
COLUMNS, PILLARS, OR STRUTS. 271 
 
 The coefficient of l 2 /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, £ = 67,000 lbs., = 1/22,400; 
 for strong steel, S = 114,000 lbs., <j> = 1/14,400. Prof. Burr considers 
 these only loose approximations. (See Straight-line Formula, below). 
 
 For dry timber, Rankine gives *S = 7200 lbs., 4> = 1/3000. 
 
 The Straight-line Formula. — The results of computations by Euler's 
 or Rankine's formulas give a curved line when plotted on a diagram 
 with values of l/r as abscissas and value of P la 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 la = 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 lbs., 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 5 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 la = 17,000 - 90 l/r lbs. 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 formulas: 
 
 p = Ultimate %^$j^ 
 Kind of Strut. lb^ner^'in ] /5 Ultimate, 
 
 Flat-end iron channels and I-beams . . . 40000 - 1 10 - (5) 8000 - 22 - (6) 
 
 r r 
 
 Flat-end mild-steel angles 52000-180- (7) 10400-36- (8) 
 
 Flat-end high-steel angles 76000-290 - (9) 15200-58- (10) 
 
 r r 
 
 Pin-end solid wrought-iron columns . . . 32000 - 80 -] 6400 - 16-1 
 
 * (ID r j\(X2) 
 
 d) 6400 - 55 d) 
 
 ir ' l 
 
 32000- 277 -U 6400-55 
 
" 
 
 
 20 " " 
 40 " " 
 20 " " 
 
 ~ 
 
 200 
 200 
 200 
 
 I 
 d 
 
 
 6 and - 
 a 
 
 = 
 
 65 
 
 272 STRENGTH OF MATERIALS. 
 
 Equations (1) to (4) are to be used only between - =40 and - = 
 
 (5) and (6) " " " " 
 
 " (7) to (10) " " " " 
 
 (11) and (12) " " " " 
 
 Built Columns (Burr). — Steel columns, properly made, of steel 
 ranging in specimens from 65,000 to 73,000 lbs. 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 -j- 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 centre 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 dis- 
 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." 
 
 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 „ a • x, 
 
 for square-end compression members; 
 
 for compression members with one pin and one square 
 end; 
 
 for compression members with pin-bearings; 
 
 p = 
 
 1 
 
 + 
 
 I 2 
 
 40,000 r 2 
 8000 
 
 1 
 
 + 
 
 I 2 
 
 p = 
 
 30,000 r 2 
 8000 
 
 1 
 
 + 
 
 I 2 
 20,000 r 2 
 
WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 273 
 
 (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 Phoenix Bridge Co. (Standard Specifications, 1895) gives the follow- 
 ing: 
 
 The greatest working stresses in pounds per square inch shall be as 
 follows : 
 
 Tension. 
 
 Steel. Iron. 
 
 p_ 8 , 5 oo \i + " in - s f ess 1 , P,ates 7 P- 7,000 Tl + "in. ^1 
 L Max. stressj shapes net. |_ Max. stressj 
 
 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%. 
 6,000 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%. 
 
274 STRENGTH OF MATERIALS. 
 
 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 — ^ 
 
 1 + 
 For one end hinged, b = 
 
 36,000 r 2 
 P 
 
 For both ends hinged, b -- 
 
 24,000 r 2 
 P 
 
 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 
 
 10,000 ( 
 
 min. total stress x 
 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 CAST-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 "short" pillars, 0.733 ft. to 2.251 ft. long, with exter- 
 
THE STRENGTH OF CAST-IRON COLUMNS. 
 
 275 
 
 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 lbs. 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 lbs. 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 for 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, 190 1/4 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 frictional 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 frictional 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. 
 
 Num- 
 ber. 
 
 Diam. 
 Inches. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Max. 
 
 Min. 
 
 Average. 
 
 Pounds. 
 
 Pounds 
 per Sq. In. 
 
 1 
 
 15 
 
 1 
 
 
 1 
 
 1,356,000 
 
 30,830 
 
 2 
 
 15 
 
 15/16 
 
 
 11/8 
 
 1,330,000 
 
 27,700 
 
 3 
 
 15 
 
 H/4 
 
 
 11/8 
 
 1,198,000 
 
 24,900 
 
 4 
 
 151/8 
 
 17/32 
 
 
 H/8 
 
 1,246,000 
 
 25,200 
 
 5 
 
 15 
 
 1 H/16 
 
 
 1 H/64 
 
 1,632,000 
 
 32,100 
 
 6 
 
 15 
 
 11/4 
 
 11/8 
 
 13/16 
 
 2,082,000 + 
 
 40,400 + 
 
 7 
 
 73/ 4 to8l/ 4 
 
 H/4 
 
 5/8 
 
 1 
 
 651,000 
 
 31,900 
 
 8 
 
 8 
 
 13/32 
 
 
 13/64 
 
 612,800 
 
 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 
 duplicates of Nos. 3 and 4. Nos. 1 and 2 were made by a foundry in New 
 York with no knowledge of their ultimate use. Nos. 5 and 6 were made 
 
276 
 
 STRENGTH OP MATERIALS. 
 
 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 = ~ i - !!"* to tnese columns gives for the breaking strength per square 
 
 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 for 
 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 1 1 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 lid. 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 lbs. per 
 sq. in. and a factor of safety of 5. 
 
 Thick- 
 
 
 
 
 
 
 Diameter, Inches. 
 
 
 
 
 
 ness, 
 Inches. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 13 
 
 13 
 
 14 
 
 15 
 
 16 
 
 18 
 
 5/8 
 3/ 4 
 
 Vs 
 
 11/8 
 
 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 
 93.1 
 
 69.6 
 
 78.5 
 87.2 
 95.7 
 103.9 
 
 76.5 
 86.4 
 96.1 
 105.5 
 114.7 
 123.7 
 
 94.2 
 104.9 
 115.3 
 125.5 
 135.5 
 
 102.1 
 113.8 
 125.2 
 136.3 
 147.3 
 168.4 
 
 110.0 
 122.6 
 135.0 
 147.1 
 159.0 
 182.1 
 204.2 
 
 131.4 
 144.8 
 157.9 
 170.8 
 195.8 
 219.9 
 
 
 11/ 4 
 
 
 
 164.4 
 
 1 3 /8 
 
 
 
 
 179.5 
 
 1V2 
 
 
 
 
 
 194.4 
 
 13/ 4 
 
 
 
 
 
 
 
 223.3 
 
 2 
 
 
 
 
 
 
 
 
 
 251.3 
 
 
 
 
 
 
 
 
 
 
 
 
THE STRENGTH OF CAST-IRON COLUMNS. 277 
 
 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 2000 Pounds for Cast-iron Columns. 
 
 (By the Building Laws of New York City, Boston, and Chicago, 1897.) 
 
 
 New York. 
 ( 8a 
 
 Boston. 
 5 a 
 
 Chicago. 
 5 a 
 
 Square columns . . . 
 
 I * + 500d 2 
 ( 8a 
 
 I 2 
 1 + 1067d 2 
 
 5a 
 
 1 + 800 d 2 
 5a 
 
 Round columns . . . 
 
 ■ < I 2 
 I 1 + 400¥ 2 
 
 1 +-^- 
 800 d 2 
 
 I 2 
 1 + 600 d 2 
 
 a = sectional area in square inches; Z= 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 11/2 inches diameter, 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 lbs., averaging 4200 lbs., for a load con- 
 centrated at the end of the shelf, and 4100 to 10,900 lbs., averaging 8000 
 lbs., 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: 
 
 I = length of column in inches; 
 r = least radius of gyration in inches; 
 ■"■ ' 36000 r 2 a= area °f column in square inches. 
 
 For riveted or other steel columns, if more than 60 r in length: 
 
 s = 17,000 - 521. 
 
 r 
 
 If less than 60 r in length: S = 13,500 a. 
 For wooden posts: 
 
 no. a = area of post in square inches; 
 
 d = least side of rectangular post in inches; 
 
 I 2 
 1 + o£7Tw2 I = len £tb of P° st in inches, 
 
 Jbua ( 600 for white or Norway pine; 
 
 J 800 for oak; 
 900 for long-leaf yellow pine. 
 
278 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 eige 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. 
 
 Then M = p (l + ^) and m = p (l - ^V 
 
 When d = ~ w then M = 2p and m = O. 
 b 
 
 When d is greater than 1 /6 w, 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\ 
 c\ = distance of most compressed and ci = that of least compressed 
 
 fibre from above stated axis; 
 si = maximum and S2 = minimum pressure ner unit of area. Then 
 
 P , (Pd)ci , P (Pd)c2 
 
 Si = a + -r~ and S2 = i--t— 
 
 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 used 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 lbs. 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. 
 
MOMENT OF INERTIA AND RADIUS OF GYRATION. 279 
 
 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, I, 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 see 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, I = moment of inertia and A = area 
 
 R =^TJa. I/A = R*. 
 
 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 
 
 d = diameter, or outside diameter; di = inside diameter; b = breadth; 
 h = depth; bi, hi, inside breadth and depth; 
 
 Solid rectangle I = Vnbh 3 ; Hollow rectangle I = i/uibh 3 - bihi 3 ); 
 Solid square I = V12& 4 ; Hollow square I =-- 1/12(0* — bi*); 
 Solid cylinder I = Ve^d 4 ; Hollow cylinder / = i/ei^Cd 4 — di 4 ). 
 
 Moment of Inertia about any Axis. — If 6 = breadth and h = 
 depth of a rectangular section its moment of inertia about its central 
 axis (parallel to the breadth) is 1/12 bh 3 ; and about one side is 1/3 bh 3 . If 
 a parallel axis exterior to the section is taken, and d = distance of this 
 axis from the farthest side and di = its distance from the nearest side, 
 [d — di = h), the moment of inertia about this axis is 1/3 b (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 I about a parallel axis passing through its centre of gravity + (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. Mack., Dec. 15, 1898) gives the following formula for 
 the moment of inertia of any rectangular element of a built up beam: 
 / = V3 (h 3 — hi 3 )b, I = moment of inertia about any axis parallel to the 
 neutral axis, h = distance from the assumed axis to the farthest fiber, 
 hi = distance to nearest fiber, b = breadth of element. The sum of the 
 moments of inertia of all 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 
 /. For a solid shaft J = 1/32 *d 4 ; for a hollow shaft, J = 1/32 Jt(d i - di 4 ), 
 in which d is the outside and d 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 poiar moment of inertia as the actual area. 
 
 For a solid circular section R p 2 = i/8D 2 ; for a hollow circular sec- 
 tion R p 2 = i/ 8 (cZ 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 
 
280 STRENGTH OP 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 
 
 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 ar ound an other axis parallel to above; d = distance 
 between axes: R = ^d 2 + r 2 . , 
 
 When r is small, R may be taken as equal to d without material error. 
 
 Graphical 31ethod 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= Viiom. of inertia -*- Area = 1/4 ^D 2 + d 2 
 in which A = area and D = diameter of outer circle, a = area an d d = 
 diameter of inner circle, and G = radius of gyration. \^D 2 + d 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 e quals the hypothenuse 
 and d equals the altitude, the base will equal VD 2 — d 2 . Calling the 
 value of this expression for the base B, the area will equal 0.7854J5 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 
 
 V- 
 
 Mom. of inertia 1 
 
 = 7y= ^D 2 + d 2 , = 0.28867 V ' D 2 + d 2 ' 
 
 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. 
 
 281 
 
 Shape of Section. 
 
 Moment 
 of Inertia. 
 
 Section 
 Modulus. 
 
 Square of 
 
 Least 
 Radius of 
 
 Cyration. 
 
 Least 
 Radius of 
 Gyration. 
 
 - 
 
 — - 
 
 4 
 
 "7 
 
 Solid Rect- 
 angle. 
 
 bh 3 * 
 12 
 
 bh 2 * 
 6 
 
 (Least side) 2 * 
 
 Least side * 
 
 12 
 
 3.46 
 
 .-b- 
 
 
 
 
 Hollow Rect- 
 angle. 
 
 12 
 
 bht-bjij* 
 
 6/i 
 
 h 2 +h t 2 * 
 12 
 
 
 - 
 
 m 
 
 r 
 
 h+h 1 
 4.89 
 
 -*-h 
 
 
 
 
 Solid Circle. 
 
 1/64 nD* 
 = 0.0491 D 4 
 
 1/32 *D 3 
 = 0.0982 Z) 3 
 
 D 2 * 
 16 
 
 D* 
 4 
 
 t 5 ^! 
 
 Hollow Circle. 
 A, area of 
 large section ; 
 a, area of 
 small section. 
 
 AD 2 -ad 2 
 16 
 
 .4D 2 -ad 2 
 
 D 2 +d 2 * 
 16 
 
 D+d 
 
 8D 
 
 5.64 
 
 m 
 
 Solid Triangle. 
 
 bh? ■ 
 36 
 
 fc/t 2 
 24 
 
 The least of 
 the two ; 
 h 2 b 2 
 T8° r 24 
 
 The least 
 
 of the two ; 
 
 h b 
 
 4.24 ° r 4.9 
 
 
 
 Even Angle. 
 
 Ah? 
 10.2 
 
 7.2 
 
 b 2 
 25 
 
 
 
 
 
 b 
 5 
 
 
 
 
 '-6-H 
 
 
 
 e 
 
 Uneven Angle. 
 
 Ah 2 
 9.5 
 
 .4/i 
 6.5 
 
 (hb) 2 
 
 hb 
 
 I3(/i 2 +fe 2 ) 
 
 2.6(h+b) 
 
 -e 
 
 Even Cross. 
 
 .4 ft 2 
 19 
 
 .4/i 
 9.5 
 
 h 2 
 22.5 
 
 h 
 4.74 
 
 
 o 
 
 Even Tee. 
 
 Ah 2 
 11.1 
 
 .4/i 
 8 
 
 6 2 
 22.5 
 
 6 
 4.74 
 
 
 
 
 c 
 
 fert 
 
 I Beam. 
 
 Ah 2 
 6.66 
 
 Ah 
 3.2 
 
 6 2 
 21 
 
 b 
 4.58 
 
 
 Channel. 
 
 .4/i 2 
 7.34 
 
 J/i 
 3.67 
 
 b 2 
 12.5 
 
 
 3 
 
 :i ! v 
 
 6 
 3.54 
 
 ° 
 
 m 
 
 Deck Beam. 
 
 Ah 2 
 6.9 
 
 Ah 
 4 
 
 6 2 
 36.5 
 
 b 
 6 
 
 
 
 
 
 
 
 luneyen angle, — -= ; even tee, 77-5 ; deck beam, — ; all other shapes 
 given in the table, - or — • 
 
282 STRENGTH OF MATERIALS. 
 
 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, I the length, b the breadth, and d the depth, 
 
 a . bd 2 ,~. I 3 
 
 S varies as — - and D vanes as t—- 
 I ba 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: 
 
 p 3 PI 
 K 2bd*' 
 
 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 I 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 lbs. 
 
 Coefficient ot transverse strength = . ^—r—. — : — r — ——5 — -r-. — : — - — - , 
 
 breadth in inches X(depthininches) 2 ' 
 
 * . = — th of the modulus of rupture. 
 
 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 $ the shearing unit stress, then 
 resisting shear = AS S ; and if the vertical shear = V, then V= ASs. 
 
 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, cousidered 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 shortest distance from that fibre to said axis, and / = 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 
 
TRANSVERSE STRENGTH OF BEAMS. 
 
 283 
 
 
 
 
 
 
 
 
 
 "n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S. &q 
 
 
 
 
 
 
 o 
 I" 1 
 
 £i^ 
 
 fe|S £1^ 
 
 l|5 
 
 mloo 
 
 *IS 
 
 aP*Psi 
 
 & l 5 f 
 
 
 
 
 -I0O -j^ 
 
 i 1 * 
 
 + 
 
 ft. 
 
 Q,|S 
 
 feir 
 
 ' Oslo 5 
 
 Mil 
 
 
 Q 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 -1™ 
 
 
 
 
 
 "S ^ 
 
 
 
 
 
 
 
 
 
 
 S3 u. 
 
 
 
 
 
 
 
 
 
 m 
 
 
 
 
 
 
 
 -■I >-S 1 
 
 
 
 
 o " 
 
 «|« 
 
 03|« Q*|« 
 
 3|« 
 
 S|« 
 
 ai|° 
 
 *j|« o-|o ^ 
 
 «|° 
 
 03 
 
 o 
 
 § tf 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 c 
 
 
 II II 
 
 ii 
 
 11 
 
 II 
 
 
 ii 
 
 11 
 
 o3 
 
 1 . 
 
 
 
 
 ~o 
 
 
 
 ft^ 
 
 
 ffl 
 
 
 £ 
 
 fe £ 
 
 s 
 
 "C^ 
 
 ft^ 
 
 £ fe 
 
 "^T^ 
 
 S 
 
 
 §co 
 
 
 — Its _ i^r 
 
 _ . 
 
 — |0O 
 
 -|0C 
 
 -l-O lc 
 
 ^ IcA 
 
 — |0O 
 
 
 So 
 
 
 
 
 + 
 
 
 1- 
 
 " > 
 
 
 
 "3 
 
 
 
 
 ft. 
 
 
 
 -CL- 
 
 
 
 1 
 
 
 
 
 ^riS 
 
 
 
 tA |00 
 
 
 
 ou 
 
 
 
 
 CO l^ 1 
 
 
 
 
 
 s 
 
 o3 
 0) 
 
 PQ 
 
 o o 
 
 SIS 
 
 s ^ tt; ^ 
 
 LA 1^ 
 
 ^ IcA 
 
 — ICO 
 + 
 
 -12 
 
 -i 
 
 -1 
 
 C CO 
 
 - z 
 
 a d 
 
 § 
 
 00 
 
 d 
 
 
 03 
 
 
 
 
 
 -I-* 
 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 M 
 
 CUD 
 
 -6 
 
 Ik 
 
 nu «u 
 
 HU 
 
 S|~ 
 
 2U 
 
 N l ^1 
 
 
 ^3 | 
 
 o3 
 
 o3 
 
 o 
 
 §1 
 
 Oil 51 
 
 SI 
 
 Oil 
 
 Oil 
 
 ok>S 
 
 
 oil 
 
 o> 
 
 J 
 
 — i>o 
 
 ^_ iff, (N ]rA 
 
 ■* ItO 
 
 "^ IcA 
 
 ^T I (A 
 
 Oil <vjl 
 
 
 ^IrA 
 
 £ 
 
 be 
 
 II 
 
 II II 
 
 II 
 
 || 
 
 II 
 
 II 1 
 
 
 II 
 
 
 3 
 
 ft. 
 
 &S ^ 
 
 fe 
 
 ^ 
 
 ft, 
 
 ft, £ 
 
 
 f^. 
 
 
 0) 
 
 
 
 
 + 
 
 
 
 
 
 
 ffl 
 
 
 
 
 eg 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 >3 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iO 
 
 M 
 
 1 =3 
 
 
 
 
 ■3 
 
 
 
 O 
 
 
 
 
 00 
 01 
 
 03 
 
 a 
 
 o 
 
 "3 3 
 
 
 
 O 
 "ol 
 
 s 
 
 
 
 X2 T3* 
 
 
 
 
 s s 
 
 « .2 
 
 "o3 
 
 o3 
 O 
 
 XJ o3 
 
 ■'g q 
 
 > 
 
 1 
 
 
 3 
 ■3 „ 
 
 X3 T3 
 
 03 
 
 o 
 
 1 -c 
 
 ft o- 
 
 "£ «^ 
 
 ° c 
 a c 
 
 ft o 
 
 a 
 
 - 
 
 
 
 
 
 O 
 
 "S o3 
 
 
 X c 
 
 m *" 
 
 _o 
 
 
 c3 
 O 
 S3 
 
 o 
 
 fa 
 
 o 
 
 -3 -a 
 
 1 ts 
 
 T3 
 
 03 
 
 3 O 
 
 o3 - 
 
 S3 
 0) 
 
 o 
 
 JO 
 
 fa 1 
 
 % 1 
 
 o3 7 
 
 o ^ 
 
 | 
 o 
 
 
 
 "o3 
 T3 
 
 -! o 
 
 o 
 
 O 3 
 
 "ol 
 T3 
 
 CQ = 
 a? a 
 
 03 « 
 
 3 _ 
 
 
 
 S 
 
 a S 
 
 1 
 
 l| 
 
 X 
 
 £ E 
 
 M 1 
 
 I 
 
 
 
 
 03 3 
 
 03 
 
 o3 
 
 
 
 .H — 
 
 o3 
 
 
 
 fc 
 
 
 W • 02 
 
 <r 
 
 
 02 
 
 
 fa 
 
 cr 
 
 a 
 
 2 fa 
 
 
 a 
 
 2 
 
284 
 
 STRENGTH OF MATERIALS. 
 
 Concerning the formula, M = SI/c, p. 282, Prof. Merriman, Eng. 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 lbs. for steel. (For iron the loads should 
 be one-eighth less, corresponding to a fibre strain of 14,000 lbs. 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 
 
 Greatest Safe Load in Pounds. 
 
 Deflection in Inches. 
 
 Section. 
 
 Load in 
 Middle. 
 
 Load 
 Distributed. 
 
 Load in 
 Middle. 
 
 Load 
 Distributed. 
 
 Solid Rect- 
 
 890 A D 
 L 
 
 1780AD 
 L 
 
 wL 3 
 32AD 2 
 
 wL 3 
 
 angle. 
 
 52AD 2 
 
 Hollow 
 
 890 (A D-ad) 
 L 
 
 1780( A D-ad) 
 L 
 
 wL 3 
 
 wL 3 
 
 Rectangle. 
 
 32( AD 2 -ad 2 ) 
 
 52(AD 2 -ad 2 ) 
 
 Solid 
 
 Cylinder. 
 
 667AD 
 L 
 
 \333AD 
 L 
 
 wL 3 
 24 AD 2 
 
 wU 
 3SAD 2 
 
 Hollow 
 
 667 (A D-ad) 
 L 
 
 \333(AD-ad) 
 L 
 
 wL 3 
 
 wL 3 
 
 Cylinder. 
 
 24( A D-'-aa 2 ) 
 
 38(AD 2 -ad 2 ) 
 
 Even- 
 legged 
 Angle or 
 Tee. 
 
 885AD 
 L 
 
 1770AD 
 L 
 
 wL s 
 32 AD 2 
 
 wL 3 
 52AD 2 
 
 Channel or 
 Z bar 
 
 1525AD 
 L 
 
 3050 AD 
 L 
 
 wL 3 
 53AD* 
 
 wL 3 
 85AD 2 
 
 Deck 
 
 \380AD 
 L 
 
 2760AD 
 L 
 
 wL 3 
 
 wL 3 
 
 Beam. 
 
 50 AD 2 
 
 80 AD 2 
 
 I Beam. 
 
 1695 AD 
 L 
 
 3390AD 
 L 
 
 iv L 3 
 58 AD- 
 
 wTJ 
 95 A D- 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 V 
 
 The above formula} for the strength and stiffness of rolled beams of 
 various sections are intended for convenient application in cases where 
 strict accuracy is not required, 
 
TRANSVERSE STRENGTH OF BEAMS. 
 
 ■285 
 
 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 tne 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 d ©flection 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: 
 
 Proportion of Calculated Load 
 forming Greatest Safe Load. 
 
 Length of Beam. 
 
 
 20 times flange width. 
 
 Whole calculated load 
 
 30 " 
 
 9-10 
 
 40 " 
 
 8-10 
 
 50 " 
 
 7-10 
 
 60 " 
 
 6-10 
 
 70 " 
 
 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 
 in page 283, 
 
 P = load at middle; 
 W = total load, distributed uniformly; 
 I = length, b = breadth, d = depth, in inches; 
 
 E = modulus of elasticity; 
 
 R = modulus of rupture, or stress per square inch of extreme fiber; 
 
 / = moment of inertia; 
 
 c = distance between neutral axis and extreme fibre. 
 For breaking load of circular section, replace bd 2 by 0.59d 3 . 
 
286 
 
 STRENGTH OF MATERIALS. 
 
 The value of R at rupture, or the modulus of rupture (see page 268), 
 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 OF 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. 
 
 Fixed at one end, loaded at the other2 
 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 2 
 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. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 287 
 
 PROPERTIES OF ROLLED STRUCTURAL STEEL. 
 
 Explanation of Tables of the Properties of I-Beams, Channels, 
 Angles, Z-Bars, Tees, Trough and Corrugated Plates. 
 
 (The Carnegie Steel Co.) 
 
 The tables for I-beams and channels are calculated for all standard 
 weights to which each pattern is rolled. The tables for angles are cal- 
 culated for the minimum intermediate and maximum weights of the 
 various shapes, while the properties of Z-bars are given for thicknesses 
 differing by Vi6 inch. For tees, each shape can be rolled to one weight 
 only. 
 
 Columns headed C in the tables for I-beams and channels give coeffi- 
 cients by the help of which the safe uniformly distributed load may be 
 readily determined. To do this, divide the coefficient given by the span 
 or distance between supports in feet. 
 
 If a section is to be selected (as will usually be the case), intended to 
 carry a certain load for a length of span already determined on,_ascertain 
 the coefficient which this load and span will require, and refer to the table 
 for a section having a coefficient of this value. The coefficient is obtained 
 by multiplying the load, in pounds uniformly distributed, by the span 
 length in feet. 
 
 In case the load is not uniformly distributed, but is concentrated at the 
 middle of the span, multiply the load by 2, and then consider it as uni- 
 formly distributed. The deflection will be 8/ 10 of the deflection for the 
 latter load. 
 
 For other cases of loading obtain the bending moment in foot-pounds; 
 this multiplied by 8 will give the coefficient required. 
 
 If the loads are quiescent, the coefficients for a fiber stress of 16,000 
 
 gounds per square inch for steel may be used; but if moving loads are to 
 e provided for, a coefficient of 12,500 pounds should be taken. Inas- 
 much as the effects of impact may be very considerable (the stresses pro- 
 duced in an unyielding inelastic material by a load suddenly applied being 
 double those produced by the same load in a quiescent state), it will 
 sometimes be advisable to use still smaller fiber stresses than those given 
 in the tables. In such cases the coefficients may be determined by 
 ^ proportion. Thus, for a fiber stress of 8000 pounds per square inch the 
 coefficient will equal the coefficient for 16,000 pounds fiber stress, from 
 the table, divided by 2. 
 
 The section moduli are used to determine the fiber stress per square 
 inch in a beam, or other shape, subjected to bending or transverse stresses, 
 by simply dividing the bending moment expressed in inch-pounds by the 
 section modulus. 
 
 In the case of T-shapes with the neutral axis parallel to the flange, there 
 will be two section moduli, and the smaller is given. The fiber stress cal- 
 culated from it will, therefore, give the larger of the two stresses in the 
 extreme fibers, since these stresses are equal to the bending moment 
 divided by the section modulus of the section. 
 
 For Z-bars the coefficient (C) may be applied for cases where the bars 
 are subjected to transverse loading, as in the case of roof-purlins. 
 
 For angles, there will be two section moduli for each position of the 
 neutral axis, since the distance between the neutral axis and the extreme 
 fibers has a different value on one side of the axis from what it has on the 
 other. The section modulus given in the table is the smaller of these two 
 values. 
 
 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 con- 
 sisting 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 between 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 intro- 
 ducing a slight error on the side of safety. 
 
 (For much other important information concerning rolled structural 
 shapes, see the " Pocket Companion" of The Carnegie Steel Co., Pittsburg, 
 Pa., price $2.) 
 
288 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Standard I-Beams — Steel. 
 
 
 
 
 
 
 
 , 
 
 i -+j«*-i 
 
 , 
 
 1 -^42 
 
 — i n 
 
 ^o 
 
 
 
 
 
 • 
 
 
 ip 
 
 3 a o 
 
 .3.33 
 
 J go 
 ill 
 
 0-" IB 
 
 
 
 | 
 02 
 
 PQ 
 "8 
 
 Q 
 in. 
 
 o 
 
 o 
 
 En 
 
 tu 
 
 ft 
 
 1 
 
 53 
 lbs. 
 
 d 
 
 .2 
 
 o 
 
 <d 
 02 
 
 i 
 
 OJ 
 
 M 
 
 a 
 
 'M 
 H 
 
 PI 
 
 Moment of Inert 
 tral Axis Co 
 with Center 
 Web. 
 
 «Of) 
 
 <$ H > 
 
 |ll 
 f &o 
 
 o oj 
 
 III 
 
 m 
 
 £ o . 
 
 'S j ft 
 
 o 
 
 
 sq.in. 
 
 in. 
 
 in 
 
 / 
 
 If 
 
 r 
 
 r' 
 
 S 
 
 c* 
 
 B] 
 
 
 100 
 
 29.41 
 
 0.75 
 
 
 2380.3 
 
 48.56 
 
 9.00 
 
 1.28 
 
 198.4 
 
 2115800 
 
 
 
 95 
 
 27.94 
 
 0.69 
 
 7.19 
 
 2309.6 
 
 47.10 
 
 9.09 
 
 1.30 
 
 192.5 
 
 2052900 
 
 >• 
 
 
 90 
 
 26.47 
 
 0.63 
 
 7.13 
 
 2239.1 
 
 45.70 
 
 9.20 
 
 1.31 
 
 186.6 
 
 1 990300 
 
 " 
 
 
 85 
 
 25.00 
 
 0.57 
 
 7.07 
 
 2168.6 
 
 44.35 
 
 9.31 
 
 1.33 
 
 180.7 
 
 1 927600 
 
 « 
 
 
 80 
 
 23.32 
 
 0.50 
 
 7.00 
 
 2087.9 
 
 42.86 
 
 9.46 
 
 1.36 
 
 174.0 
 
 1855900 
 
 B2 
 
 20 
 
 100 
 
 29.41 
 
 33 
 
 7.28 
 
 1655.8 
 
 52.65 
 
 7.50 
 
 1.34 
 
 165.6 
 
 1766100 
 
 
 
 95 
 
 27.94 
 
 0.81 
 
 721 
 
 1606.8 
 
 50.78 
 
 7.58 
 
 1.35 
 
 160.7 
 
 1713900 
 
 
 
 90 
 
 26.47 
 
 0.74 
 
 7.14 
 
 1557.8 
 
 48.98 
 
 7.67 
 
 1.36 
 
 155.8 
 
 1661600 
 
 
 
 85 
 
 25.00 
 
 0.66 
 
 7.06 
 
 1508.7 
 
 47.25 
 
 7.77 
 
 1.37 
 
 150.9 
 
 1 609300 
 
 
 
 80 
 
 23.73 
 
 0.60 
 
 7.00 
 
 1466.5 
 
 '45.81 
 
 7.86 
 
 1.39 
 
 146.7 
 
 1 564300 
 
 B3 
 
 20 
 
 75 
 
 22.06 
 
 0.65 
 
 6.40 
 
 1268.9 
 
 30.25 
 
 7.58 
 
 1.17 
 
 126.9 
 
 1353500 
 
 
 
 70 
 
 20.59 
 
 0.58 
 
 6.33 
 
 1219.9 
 
 29.04 
 
 7.70 
 
 1.19 
 
 122.0 
 
 1301200 
 
 
 
 65 
 
 19.0S 
 
 0.50 
 
 6.25 
 
 1169.6 
 
 27.86 
 
 7.83 
 
 1.21 
 
 117.0 
 
 1247600 
 
 B80 
 
 18 
 
 70 
 
 20.59 
 
 0.72 
 
 6.26 
 
 921.3 
 
 24.62 
 
 6.69 
 
 1.09 
 
 102.4 
 
 1091900 
 
 
 
 65 
 
 19.12 
 
 
 6.18 
 
 881.5 
 
 23.47 
 
 6.79 
 
 1.11 
 
 97.9 
 
 1044800 
 
 
 
 60 
 
 17.65 
 
 0.56 
 
 6.10 
 
 841.8 
 
 22.38 
 
 6.91 
 
 1.13 
 
 93.5 
 
 997700 
 
 
 
 55 
 
 15.93 
 
 0.46 
 
 6.00 
 
 795.6 
 
 21.19 
 
 7.07 
 
 1.15 
 
 88.4 
 
 943000 
 
 B4 
 
 15 
 
 100 
 
 29.41 
 
 1.18 
 
 6.77 
 
 900.5 
 
 50.98 
 
 5.53 
 
 1.31 
 
 120.1 
 
 1280700 
 
 
 
 95 
 
 27.94 
 
 1 .09 
 
 6,68 
 
 872.9 
 
 48.37 
 
 5.59 
 
 1.32 
 
 116.4 
 
 1241500 
 
 
 
 90 
 
 26.47 
 
 9.99 
 
 6.58 
 
 845.4 
 
 45.91 
 
 5.65 
 
 1.32 
 
 112.7 
 
 1202300 
 
 
 
 85 
 
 25.00 
 
 
 , 18 
 
 817.8 
 
 43.57 
 
 5.72 
 
 1.32 
 
 109.0 
 
 1163000 
 
 " 
 
 
 80 
 
 23.81 
 
 0.81 
 
 6.40 
 
 795.5 
 
 41.76 
 
 5.78 
 
 1.32 
 
 106.1 
 
 1131300 
 
 J5 
 
 15 
 
 75 
 
 22.05 
 
 0.88 
 
 6.29 
 
 691.2 
 
 30.68 
 
 5.60 
 
 1.18 
 
 92.2 
 
 983000 
 
 
 
 70 
 
 20.59 
 
 0.78 
 
 6.19 
 
 663.6 
 
 29.00 
 
 5.68 
 
 1.19 
 
 88.5 
 
 943800 
 
 
 
 65 
 
 19.12 
 
 0.69 
 
 6.10 
 
 636.0 
 
 27.42 
 
 5.77 
 
 1.20 
 
 84.8 
 
 904600 
 
 
 
 60 
 
 17.67 
 
 0.59 
 
 6.00 
 
 609.0 
 
 25.96 
 
 5.87 
 
 1.21 
 
 81.2 
 
 866100 
 
 $7 
 
 15 
 
 55 
 
 16.18 
 
 
 5.75 
 
 511.0 
 
 17.06 
 
 5.62 
 
 1.02 
 
 68.1 
 
 726800 
 
 
 
 50 
 
 14.71 
 
 0.56 
 
 5.65 
 
 483.4 
 
 16.04 
 
 5.73 
 
 1.04 
 
 64.5 
 
 687500 
 
 
 
 45 
 
 13.24 
 
 0.46 
 
 5.55 
 
 455.8 
 
 15.00 
 
 5.87 
 
 1.07 
 
 60.8 
 
 648200 
 
 
 
 42 
 
 12.48 
 
 0.41 
 
 5.50 
 
 441.7 
 
 14.62 
 
 5.95 
 
 1.08 
 
 58.9 
 
 628300 
 
 38 
 
 12 
 
 55 
 
 16.18 
 
 0.82 
 
 5.61 
 
 321.0 
 
 17.46 
 
 4.45 
 
 1.04 
 
 53.5 
 
 570600 
 
 
 
 50 
 
 14.71 
 
 0.70 
 
 5.49 
 
 303.3 
 
 16.12 
 
 4.54 
 
 1.05 
 
 50.6 
 
 539200 
 
 
 
 45 
 
 13.24 
 
 0.58 
 
 5.37 
 
 285.7 
 
 14.89 
 
 4.65 
 
 1.06 
 
 47.6 
 
 507900 
 
 
 
 40 
 
 11.84 
 
 0.46 
 
 5.25 
 
 268.9 
 
 13.81 
 
 4.77 
 
 1.08 
 
 44.8 
 
 478100 
 
 S? 
 
 12 
 
 35 
 
 10.29 
 
 0.44 
 
 5.09 
 
 228.3 
 
 10.07 
 
 4.71 
 
 0.99 
 
 38.0 
 
 405800 
 
 
 
 31.5 
 
 9.26 
 
 0.35 
 
 5.00 
 
 215.8 
 
 9.50 
 
 4.83 
 
 1.01 
 
 36.0 
 
 383700 
 
 311 
 
 10 
 
 40 
 
 11.76 
 
 0.75 
 
 5.10 
 
 158.7 
 
 9.50 
 
 3.67 
 
 0.90 
 
 31.7 
 
 338500 
 
 
 
 35 
 
 10.29 
 
 0.60 
 
 4.95 
 
 146.4 
 
 8.52 
 
 3.77 
 
 0.91 
 
 29.3 
 
 312400 
 
 
 
 30 
 
 8.82 
 
 0.4 b 
 
 4.81 
 
 134.2 
 
 7.65 
 
 3.90 
 
 0.93 
 
 26.8 
 
 286300 
 
 
 
 25 
 
 7.37 
 
 0.31 
 
 4.66 
 
 122.1 
 
 6.89 
 
 4.07 
 
 0.97 
 
 24.4 
 
 260500 
 
 313 
 
 9 
 
 35 
 
 10.29 
 
 0.73 
 
 4.77 
 
 111.8 
 
 7.31 
 
 3.29 
 
 0.84 
 
 24.8 
 
 265000 
 
 
 
 30 
 
 8.82 
 
 0.57 
 
 4.61 
 
 101.9 
 
 6.42 
 
 3.40 
 
 0.85 
 
 22.6 
 
 241500 
 
 
 
 25 
 
 7.35 
 
 0.41 
 
 4.45 
 
 91.9 
 
 5.65 
 
 3.54 
 
 0.S8 
 
 20.4 
 
 217900 
 
 
 
 21 
 
 6.31 
 
 0.29 
 
 4.33 
 
 84.9 
 
 5.16 
 
 3.67 
 
 0.90 
 
 18.9 
 
 201300 
 
 315 
 
 8 
 
 25.5 
 
 7.50 
 
 0.54 
 
 4.27 
 
 68.4 
 
 4.75 
 
 3.02 
 
 0.80 
 
 17.1 
 
 182500 
 
 
 
 23 
 
 6.76 
 
 0.45 
 
 4.18 
 
 64.5 
 
 4.39 
 
 3.09 
 
 0.81 
 
 16.1 
 
 1 72000 
 
 
 
 20.5 
 
 6.03 
 
 9 36 
 
 4.09 
 
 60.6 
 
 4.07 
 
 3.17 
 
 0.82 
 
 15.1 
 
 161600 
 
 
 
 18 
 
 5.33 
 
 0.27 
 
 4.00 
 
 56.9 
 
 3.78 
 
 3.27 
 
 0.84 
 
 14.2 
 
 151700 
 
 * This coefficient used for buildings; for bridges use 12,500 pounds per 
 square inch, or multiply value in this column by 0.78125. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 289 
 
 Properties of Carnegie 
 
 Standard I-Beams — 
 
 Steel. 
 
 Conti 
 
 nued. 
 
 
 
 
 
 
 
 
 3 c ° 
 
 § =■ U 
 
 M 
 
 "c5 o 
 
 eg 
 
 c 
 
 c 
 
 S 
 
 i' 
 
 w 
 
 ft 
 
 2 
 
 "o 
 
 o 
 
 ft 
 
 i 
 
 S3 
 
 _o 
 
 01 
 
 W 
 'o 
 o> 
 
 < 
 
 t 
 
 
 St! 
 
 •J ft° 
 
 0) 0> cS 
 
 o>_ +J 
 
 m 
 
 a> 53 
 
 -"8 fl 
 
 Si 
 
 ill 
 
 3 
 
 d § 53 
 .2ftO 
 ts 53 ■£ 
 
 r 
 
 ego" 
 .2-2 © 
 
 >> ^ 
 
 S3 
 I- 1 
 
 3 u 
 Oi e« 
 
 S Is 
 o Bo 
 
 .2. £-3 
 
 5 
 
 c 
 
 ©<,_ 
 
 £ ° 
 o to • 
 
 S 53 ^ 
 O 
 
 
 in. 
 
 lbs. 
 
 sq.ra. 
 
 in. 
 
 in. 
 
 / 
 
 /' 
 
 / 
 
 c* 
 
 H17 
 
 7 
 
 20 
 
 5.88 
 
 46 
 
 3.87 
 
 42.2 
 
 3.24 
 
 2.68 
 
 0.74 
 
 12.1 
 
 128600 
 
 
 
 17.5 
 
 5.15 
 
 035 
 
 3.76 
 
 39 2 
 
 2.94 
 
 2.76 
 
 0.76 
 
 11.2 
 
 1 1 9400 
 
 " 
 
 
 15 
 
 4.42 
 
 0.25 
 
 3.66 
 
 36.2 
 
 2.67 
 
 2.86 
 
 0.78 
 
 10.4 
 
 110400 
 
 H19 
 
 6 
 
 l71/ 4 
 
 5.07 
 
 0.48 
 
 3.58 
 
 26.2 
 
 2.36 
 
 2.27 
 
 0.68 
 
 8.7 
 
 93100 
 
 
 
 143/^ 
 
 4.34 
 
 35 
 
 3 45 
 
 24.0 
 
 2.09 
 
 2.35 
 
 0.69 
 
 8.0 
 
 85300 
 
 " 
 
 
 121/^ 
 
 3.61 
 
 23 
 
 3.33 
 
 21.8 
 
 1.85 
 
 2.46 
 
 072 
 
 7.3 
 
 77500 
 
 R21 
 
 5 
 
 143/^ 
 
 4.34 
 
 0.50 
 
 3.29 
 
 15.2 
 
 1.70 
 
 1.87 
 
 0.63 
 
 6.1 
 
 64600 
 
 
 
 121/4 
 
 3.60 
 
 0.36 
 
 3.15 
 
 13.6 
 
 1.45 
 
 1.94 
 
 0.63 
 
 5.4 
 
 58100 
 
 
 " 
 
 93/„ 
 
 2 87 
 
 21 
 
 3 00 
 
 12.1 
 
 1.23 
 
 2.05 
 
 0.65 
 
 4.8 
 
 51600 
 
 B23 
 
 4 
 
 105 
 
 3.09 
 
 41 
 
 2 88 
 
 7.1 
 
 1.01 
 
 1.52 
 
 0.57 
 
 3.6 
 
 38100 
 
 
 
 9.5 
 
 2.79 
 
 0.34 
 
 2.81 
 
 6.7 
 
 0.93 
 
 1.55 
 
 0.58 
 
 3.4 
 
 36000 
 
 " 
 
 
 8.5 
 
 2.50 
 
 0.26 
 
 2.73 
 
 6.4 
 
 0.85 
 
 1.59 
 
 0.58 
 
 3.2 
 
 33900 
 
 " 
 
 " 
 
 7.5 
 
 2.21 
 
 19 
 
 2 66 
 
 6.0 
 
 0.77 
 
 1.64 
 
 0.59 
 
 3.0 
 
 31800 
 
 B77 
 
 3 
 
 75 
 
 2.21 
 
 36 
 
 2 52 
 
 2.9 
 
 0.60 
 
 1.15 
 
 0.52 
 
 1.9 
 
 20700 
 
 
 
 65 
 
 1.91 
 
 26 
 
 2 42 
 
 2.7 
 
 53 
 
 1.19 
 
 0.52 
 
 1.8 
 
 19100 
 
 " 
 
 
 5.5 
 
 1.63 
 
 0.17 
 
 2.33 
 
 2.5 
 
 0.46 
 
 1.23 
 
 0.53 1 1.7 
 
 17600 
 
 Lightest weight in each section is standard ; others are special. 
 
 L = safe loads in pounds, uniformly distributed; I = span in feet. 
 M = moments of forces in foot-pounds; C = coefficient given above. 
 
 L = ~ ; M = | ; C = LI =8 M = ^ ; / = fiber stress. 
 
 
 Properties of Carnegie 
 
 Trough Plates — 
 
 Steel. 
 
 
 Section 
 Index. 
 
 Size, in 
 Inches. 
 
 Weight 
 per 
 Foot. 
 
 Area 
 
 of Sec- 
 tion. 
 
 Thick- 
 ness in 
 Inches. 
 
 Moment of 
 
 Inertia, 
 
 Neutral 
 
 Axis 
 
 Parallel to 
 Length. 
 
 Section 
 Modulus, 
 Axis as 
 before. 
 
 Radius 
 of Gyra- 
 tion, 
 Axis as 
 before. 
 
 M10 
 
 Mil 
 M12 
 M13 
 M14 
 
 91/2X33/4 
 91/2X33/4 
 91/2X33/4 
 91/2X33/4 
 91/2X33/4 
 
 lb. 
 16.32 
 18.02 
 19.72 
 21.42 
 23.15 
 
 sq. in. 
 4.8 
 5.3 
 5.8 
 6.3 
 6.8 
 
 1/2 
 9/16 
 
 5/8 
 U/16 
 
 3/4 
 
 / 
 3.68 
 4.13 
 4.57 
 5.02 
 5.46 
 
 S 
 
 1.38 
 1.57 
 1.77 
 1.96 
 2.15 
 
 0.91 
 0.91 
 0.90 
 0.90 
 
 0.90 
 
 Properties of Carnegie Corrugated Plates 
 
 ed Plates 
 
 — Steel. 
 
 Moment of 
 
 
 Inertia, 
 
 Section 
 
 Neutral 
 
 Modulus, 
 
 Axis 
 
 Axis as 
 
 Parallel to 
 
 before. 
 
 Length. 
 
 
 / 
 
 8 
 
 0.64 
 
 0.80 
 
 0.95 
 
 1.13 
 
 1.25 
 
 1.42 
 
 4.79 
 
 3.33 
 
 5.81 
 
 3.90 
 
 6.82 
 
 4.46 
 
 Section 
 Index. 
 
 M30 
 M31 
 M32 
 M33 
 M34 
 M35 
 
 Size, in 
 Inches. 
 
 83/4 XI 1/2 
 83/4 XI 9/16 
 8 3/4 XI 5/s 
 12 3/ ]6 X23/ 4 
 123/ 16 X213/ 10 
 123/ l6 x27/ 8 
 
 Weight 
 
 Area 
 
 Thick- 
 
 per 
 
 of Sec- 
 
 ness in 
 
 Foot. 
 
 tion. 
 
 Inches. 
 
 lb. 
 
 sq. in. 
 
 
 8.01 
 
 2.4 
 
 1/4 
 
 10.10 
 
 3.0 
 
 5/16 
 
 12.00 
 
 3.5 
 
 3/8 - 
 
 17.75 
 
 5.2 
 
 % 
 
 20.71 
 
 6.1 
 
 7/16 
 
 23.67 
 
 7.0 
 
 1/2 
 
 Radius 
 of Gyra- 
 tion, 
 Axis as 
 before. 
 
 0.52 
 0.57 
 0.62 
 0.96 
 0.98 
 0.99 
 
STRENGTH OF MATERIALS. 
 
 - * ^ "S 
 
 ^- 
 
 2s 
 
 com 
 
 — vO 
 
 N 
 
 o 
 
 
 
 t^ON 
 
 ^■cn 
 
 3 
 
 1.14 
 1.06 
 0.99 
 0.94 
 0.88 
 0.84 
 0.80 
 0.76 
 
 in 
 
 ON— 1 
 
 vOO 
 
 int' 
 
 
 s 
 
 som 
 
 CSJCS 
 
 
 oo t>. vq in ■* <rv N N 
 
 vO 
 
 ^ 
 
 N- 
 
 r>vd 
 
 T 
 
 
 n-'cA 
 
 incvj 
 
 00 
 
 r>. oo N oo m T * m 
 r>. m tj- n — © O; oq 
 
 IN <N tN «N IN f-i — ' — ' 
 
 
 jQ 
 
 ^ro 
 
 o> 
 oq 
 
 o 
 
 <3 
 
 so'ifi 
 
 NO 
 
 o>q 
 
 
 T 00 mm r>. — vO m 
 
 00 
 
 j£5 
 
 00 
 
 
 T 
 GO 
 
 d 
 
 CO 
 On' 
 
 COIN 
 
 ON 
 vo'nO 
 
 S 
 
 NvDtO-0>a- 
 
 ■^ o t->. i- (N ov r» vq 
 
 ifMn'tV^CMflfl 
 
 n«MOwoi-«M 
 
 — — OO OO < 
 
 r>vD l^. 00 OvO —IN c 
 
 ivors»o>o- 
 
 Jv — Ov NOvOC 
 
 -r> in ovmcnc 
 
 t^tl-l-tAf 
 
 o o Ov oo oo r«. r-> vc -o vO 
 
 
 "fr Ov fs OO — in (N o 
 
 \u — in i— rs.<^Ov\Orn — oOvO"^ 
 
 O ©' Ov Ov oo' oo K. r>.' r> t>.' vd \d vd 
 
 q m <n ov 
 
 - O O Ov Ov Ov 00 00 00 l>«° 
 
 > so tsooao • 
 
 2o 
 
 
 
 6.18 
 .4.17 
 .2.44 
 .0.94 
 9.63 
 8.48 
 7.45 
 6.53 
 5.71 
 4.96 
 4.28 
 3.66 
 3.09 
 2.57 
 
 2.08 
 1.64 
 1.22 
 0.83 
 0.47 
 
 0.13 
 9.82 
 9.52 
 9.24 
 8.98 
 8.73 
 
 
 
 O 
 vO 
 
 6.09 
 3.31 
 0.93 
 8.87 
 7.07 
 5.47 
 4.06 
 2.79 
 1.65 
 0.62 
 9.68 
 8.83 
 8.04 
 7.32 
 
 6.66 
 6.04 
 5.47 
 4.93 
 4.43 
 
 3.97 
 3.53 
 3.12 
 2.74 
 2.37 
 2.03 
 
 
 
 o 
 
 00 
 
 47.14 
 43.51 
 40.40 
 37.71 
 35.35 
 33.27 
 31.42 
 29.77 
 28.28 
 26.94 
 25.71 
 24.59 
 23.57 
 22.63 
 
 .1.76 
 '0.95 
 >0.20 
 9.51 
 8.86 
 
 8.25 
 7.68 
 7.14 
 6.64 
 6.16 
 5.71 
 
 
 
 - ov r>« vo -<r m cv 
 
 co oo O Ov Ov o 
 
 nrvi — © OOvoo oor>.rN 
 
 oo vO r> t oo — if 
 
 — — 0C - 
 
 m'o'ir 
 
 vOvOir 
 
 J O Ov Ov Ov O ( 
 
 !_; 
 
 xj 
 
 dOOOOvOOOO-O'tOaoOintsN 
 mmcslooommoOT — — cove- 
 
 Ov^nTOO 
 vOm — OOv 
 
 fOM 
 OO — 
 
 0> — 00 
 CNinr-N 
 
 ^r 
 
 o 
 
 00 
 
 rs— vo — oot- oOvO^TMOoor^ 
 NN>0»OinininvTvftttnvc^ 
 
 inTcocviO 
 commence 
 
 CMtNCs] 
 
 I^NvOin 
 CSINCM 
 
 
 
 
 
 
 Nt^tmvOtsooO'O- (Nro-^-in 
 
 _, ____^_ fslfNJ , Nf sj f M< N 
 
 vONCOOvO 
 CM <N CN CM CO 
 
 
 fmvo 
 
 .23 <u 
 
 «g.a 
 
 
 
 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 291 
 
 ,_; 
 
 
 O O 
 
 o 
 
 CO 
 
 CN 
 
 CO 
 
 in 
 
 tN 
 
 o 
 
 o 
 
 
 
 
 
 
 
 
 en 
 
 ^ jQ 1 t> tT 
 
 en 
 
 cs 
 
 tN 
 
 *" 
 
 — 
 
 — — o 
 
 
 
 
 
 
 
 • 
 
 
 t> oo 
 
 IT. 
 
 o 
 
 O 
 
 tN 
 
 o 
 
 tN O xO 
 
 ir 
 
 tN 
 
 — o 
 
 
 
 
 ^r 
 
 E£ 
 
 (N CO 
 
 xO 
 
 in 
 
 en 
 
 en 
 
 eN 
 
 <N , 
 
 "~ 
 
 "" 
 
 — o 
 
 
 
 
 • 
 
 IP! 
 
 xO en 
 
 m 
 
 „_ 
 
 *r 
 
 <N 
 
 en 
 
 
 
 
 
 ^r 
 
 en 
 
 N - 
 
 *. 
 
 
 o -<r 
 
 o 
 
 CO 
 
 o 
 
 in 
 
 ^r 
 
 en en CN 
 
 tN 
 
 N 
 
 "" "* 
 
 "~ 
 
 "" 
 
 ' 
 
 ^ 
 
 ™. 43" 
 
 O in 
 
 CO 
 
 _ 
 
 o 
 
 CO 
 
 T 
 
 t*o 
 
 T 
 
 O 
 
 r^ t 
 
 IN 
 
 o 
 
 00 sO 
 
 
 
 
 
 o 
 
 
 xO 
 
 Xltt 
 
 
 
 
 
 
 
 <o 
 
 - 
 
 
 
 "" 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 £ 
 
 (N r^ 
 
 in 
 
 en 
 
 sO 
 
 _ 
 
 _ 
 
 ^ 
 
 m vO 
 
 O 
 
 en 
 
 eo ^r 
 
 _ 
 
 CO 
 
 m en 
 
 
 
 -* o 
 
 
 r^ 
 
 
 
 
 so m 
 
 
 T 
 
 
 
 
 
 
 
 T en 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 42 
 
 f> — 
 
 o 
 
 ^ 
 
 r^ 
 
 <N 
 
 m 
 
 mo 
 
 ^ 
 
 r^ 
 
 o 
 
 en r> 
 
 (N 
 
 CO 
 
 T — 
 
 
 
 O eN 
 
 
 
 Of) 
 
 
 
 o o 
 
 
 V2 
 
 
 m T 
 
 "* 
 
 
 
 CO 
 
 £ 
 
 
 ^ 
 
 IN 
 
 
 "" 
 
 
 " 
 
 
 
 
 
 
 
 
 
 43 
 
 m o 
 
 _ 
 
 IT. 
 
 o 
 
 _ 
 
 o 
 
 O O en 
 
 O 
 
 o 
 
 o eg 
 
 vO 
 
 O 
 
 vO 00 
 
 
 
 O m 
 
 
 
 T 
 
 o 
 
 xO 
 
 tj- — o 
 
 f> 
 
 
 
 
 m 
 
 T en 
 
 0> 
 
 <N 
 
 
 
 en 
 
 tN 
 
 tN 
 
 
 " ~ 
 
 
 
 
 
 
 
 CJ r> BJ . 
 
 U « £ "£ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ri S g 8 
 
 in xO 
 
 r^ 
 
 CD 
 
 r> 
 
 r> 
 
 
 fN en -^r 
 
 
 
 
 
 o 
 
 — IN 
 
 •2 & g& 
 
 
 
 
 
 
 
 
 
 
 
 
 tN 
 
 tN eN 
 
 S*«g.s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 43 
 
 — T 
 
 en 
 
 xO 
 
 CN 
 
 o 
 
 o 
 
 Nm 0> 
 
 ■* 
 
 t> 
 
 m <n O 
 
 ■o 
 
 en 
 
 — o* 
 
 
 00 m 
 
 
 
 o 
 
 o 
 
 
 
 
 T 
 
 -* T en 
 
 
 en 
 
 en tN 
 
 b 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 xO t^ 
 
 xO 
 
 — 
 
 c 
 
 en 
 
 CO 
 
 vO vO 
 
 r^ 
 
 O 
 
 en 
 
 r>. — i>. 
 
 en 
 
 On 
 
 vO en 
 
 M * 
 
 — ' 42 
 
 xO eN 
 
 O 
 
 ^ 
 
 £ 
 
 2 
 
 ~ 
 
 o o 
 
 CO 
 
 ^ 
 
 ^ 
 
 vO sO^ 
 
 "" 
 
 ^r 
 
 -<r ■* 
 
 eN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <n en 
 
 ■* 
 
 en 
 
 r> 
 
 in 
 
 CO 
 
 (N O 
 
 CO 
 
 o 
 
 o 
 
 en t^ — 
 
 vO 
 
 — 
 
 r> en 
 
 
 
 
 "* 
 
 
 a> 
 
 xO 
 
 T 
 
 
 O 
 
 CT> 
 
 o 
 
 
 vO 
 
 vO 
 
 
 
 
 m eN 
 
 <N 
 
 tN 
 
 
 
 
 
 
 
 
 
 
 
 
 ^r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 43 
 
 xO in 
 
 — 
 
 O 
 
 m 
 
 r> 
 
 ■* 
 
 T t> N 
 
 o 
 
 o 
 
 o — 
 
 en 
 
 *c 
 
 o 
 
 m O 
 
 
 
 
 
 tr 
 
 
 ON 
 
 i^ in ^r 
 
 
 
 o o 
 
 O 
 
 CO 
 
 CO 
 
 r>, t*s 
 
 
 
 
 
 
 nj 
 
 IN 
 
 
 
 
 
 
 
 
 
 
 HJ 
 
 ■<af 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 12 2 
 
 fN 
 
 m 
 
 CO 
 
 o 
 
 1^ 
 
 ON* 
 
 o 
 
 ■* 
 
 0,00 
 
 O 
 
 O 
 
 en O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O Ox 
 
 - 
 
 o ho « 
 
 T 
 
 en 
 
 en 
 
 
 CN 
 
 CS (N — 
 
 
 
 --J- 
 
 
 
 
 42 
 
 -o o 
 
 t^ 
 
 en 
 
 tN 
 
 tN 
 
 o> 
 
 en en C^ 
 
 ■>T 
 
 ^5- 
 
 V© — 
 
 r^ 
 
 m 
 
 T 
 
 in xO 
 
 
 
 
 
 
 
 
 
 
 
 O 00 
 
 
 
 
 en tN 
 
 
 
 
 
 
 ^r 
 
 
 
 
 CM 
 
 CN 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 42 
 
 in oo 
 
 
 o 
 
 CO 
 
 o 
 
 
 — \0 ^r 
 
 
 
 ^r — t> 
 
 O 
 
 o 
 
 
 
 
 
 
 
 
 o 
 
 vO en — 
 
 O 
 
 
 sO m en 
 
 eN 
 
 
 — o 
 
 
 m 
 
 vo m 
 
 ^r 
 
 T 
 
 
 en 
 
 cm 
 
 N N N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4J5 
 
 o oo 
 
 
 
 
 tN 
 
 
 vO CN en 
 
 CO 
 
 NO 
 
 r> O m 
 
 
 
 00 Ox 
 
 
 
 
 
 
 
 
 T — CO 
 
 
 
 — O 00 
 
 
 
 ^r en 
 
 
 
 
 xO 
 
 
 t 
 
 ^xt 
 
 
 
 
 (M 
 
 
 
 
 
 ^ 
 
 xO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v£) vO 
 
 cc 
 
 un 
 
 — 
 
 — 
 
 en 
 
 en — in 
 
 en 
 
 vO 
 
 NO- 
 
 in 
 
 o 
 
 xO ■* 
 
 
 42 
 
 
 
 
 
 
 on 
 
 en O m 
 
 
 O 
 
 
 
 o 
 
 
 
 
 
 
 
 xD 
 
 
 ^r 
 
 
 
 n) 
 
 CS tN tN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O CO 
 
 
 
 
 tN 
 
 
 tt T5- — 
 
 ■* 
 
 
 
 
 
 — xO 
 
 
 42 
 
 
 
 
 
 N- 
 
 i^ 
 
 — vO (N 
 
 on 
 
 
 N 0>N 
 
 
 
 CN O 
 
 
 
 
 
 co 
 
 
 xo 
 
 
 in TT ^T 
 
 
 
 
 
 
 
 t 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 cn 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 «jc^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ox O — 
 
 
 en 
 
 til* 
 
 
 CO 
 
 Ox O 
 
 i§ £ g-fa 
 
 
 
 
 
 
 
 — es es 
 
 
 
 CN fS CN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 ^ 
 
 » 3 fi 
 
 3 OQ ■- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 e. 
 
 O ^ 
 
 0X'J2 — 
 oOO 
 
 yi 
 
 >43^ 
 
 cp O 3 
 
 ,9P 
 
 
 ■a 
 
 fa o'O 
 
292 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Standard Channels — Steel. 
 
 
 
 
 
 
 "3 ° 
 
 "H ^ 
 
 3 3 
 
 h-B 
 
 "3° 
 
 o§ 
 
 >_d 
 
 1 
 
 1 
 j 
 
 o 
 
 o 
 
 fa 
 
 I 
 
 1 
 1 
 
 c 
 ,o 
 
 <u 
 
 m 
 "o 
 
 < 
 
 a 
 IS 
 
 0) 
 
 M 
 
 C 
 
 flj 
 
 1-1 So 
 
 Hi 
 
 30 
 
 M go 
 «- 03 o> 
 
 gls 
 111 
 
 &PhO 
 '■B S O 
 
 m & 
 
 3 fc. 
 
 *| 
 
 3 c a 
 H P. c 
 
 73 £7 CD 
 
 - : 
 
 "§0 
 
 8 ° 
 
 M « a 
 •4^02 w 
 
 •sfeft 
 
 
 0^ 
 <B73 
 
 if 
 
 So 
 g| 
 
 in. 
 
 lbs. 
 
 sq. in. 
 
 in. 
 
 in. 
 
 / 
 
 r 
 
 r' 
 
 S 
 
 c* 
 
 X 
 
 15 
 
 55. 
 
 16.18 
 
 0.82 
 
 3.82 
 
 430.2 
 
 12.19 
 
 5.16 
 
 0.868 
 
 57.4 
 
 611900 
 
 0.823 
 
 
 50. 
 
 14.71 
 
 0.72 
 
 3.72 
 
 402.7 
 
 11.22 
 
 5.23 
 
 0.873 
 
 53.7 
 
 572700 
 
 0.803 
 
 
 45. 
 
 13.24 
 
 0.62 
 
 3.62 
 
 375.1 
 
 10.29 
 
 5.32 
 
 0.882 
 
 50.0 
 
 533500 
 
 0.788 
 
 
 40. 
 
 11.76 
 
 0.52 
 
 3.52 
 
 347.5 
 
 9.39 
 
 5.43 
 
 0.893 
 
 46.3 
 
 494200 
 
 0.783 
 
 " 
 
 35. 
 
 10.29 
 
 0.43 
 
 3.43 
 
 320.0 
 
 8.48 
 
 5.58 
 
 0.908 
 
 42.7 
 
 455000 
 
 0.789 
 
 " 
 
 33. 
 
 9.90 
 
 0.40 
 
 3.40 
 
 312.6 
 
 8.23 
 
 5.62 
 
 0.912 
 
 41.7 
 
 444500 
 
 0.794 
 
 12 
 
 40. 
 
 11.76 
 
 0.76 
 
 3.42 
 
 197.0 
 
 6.63 
 
 4.09 
 
 0.751 
 
 32.8 
 
 350200 
 
 0.722 
 
 " 
 
 35. 
 
 10.29 
 
 0.64 
 
 3.30 
 
 179.3 
 
 5.90 
 
 4.17 
 
 0.757 
 
 29.9 
 
 318800 
 
 0.694 
 
 " 
 
 30. 
 
 8.82 
 
 0.51 
 
 3.17 
 
 161.7 
 
 5.21 
 
 4.28 
 
 0.768 
 
 26.9 
 
 287400 
 
 0.677 
 
 
 25. 
 
 7.35 
 
 0.39 
 
 3.05 
 
 144.0 
 
 4.53 
 
 4.43 
 
 0.785 
 
 24.0 
 
 256100 
 
 0.678 
 
 " 
 
 20.5 
 
 6.03 
 
 0.28 
 
 2.94 
 
 128.1 
 
 3.91 
 
 4.61 
 
 0.805 
 
 21.4 
 
 227800 
 
 0.704 
 
 10 
 
 35. 
 
 10.29 
 
 0.82 
 
 3.18 
 
 115.5 
 
 4.66 
 
 3.35 
 
 0.672 
 
 23.1 
 
 246400 
 
 0.695 
 
 " 
 
 30. 
 
 8.82 
 
 0.68 
 
 3.04 
 
 103.2 
 
 3.90 
 
 3.42 
 
 0.672 
 
 20.6 
 
 220300 
 
 0.651 
 
 
 25. 
 
 7.35 
 
 0.53 
 
 2.89 
 
 91.0 
 
 3.40 
 
 3.52 
 
 0.680 
 
 18.2 
 
 194100 
 
 0.620 
 
 " 
 
 20. 
 
 5.88 
 
 0.38 
 
 2.74 
 
 78.7 
 
 2.85 
 
 3.66 
 
 0.696 
 
 15.7 
 
 168000 
 
 0.609 
 
 
 15. 
 
 4.46 
 
 0.24 
 
 2.60 
 
 66.9 
 
 2.30 
 
 3.87 
 
 0.718 
 
 13.4 
 
 142700 
 
 0.639 
 
 9 
 
 25. 
 
 7.35 
 
 0.62 
 
 2.82 
 
 70.7 
 
 2.98 
 
 3.10 
 
 0.637 
 
 15.7 
 
 167600 
 
 0.615 
 
 " 
 
 20. 
 
 5.88 
 
 0.45 
 
 2.65 
 
 60.8 
 
 2.45 
 
 3.21 
 
 0.646 
 
 13.5 
 
 144100 
 
 0.585 
 
 " 
 
 15. 
 
 4.41 
 
 0.29 
 
 2.49 
 
 50.9 
 
 1.95 
 
 3.40 
 
 0.665 
 
 11.3 
 
 120500 
 
 0.590 
 
 " 
 
 131/4 
 
 3.89 
 
 0.23 
 
 2.43 
 
 47.3 
 
 1.77 
 
 3.49 
 
 0.674 
 
 10.5 
 
 112200 
 
 0.607 
 
 8 
 
 2H/4 
 
 6.25 
 
 0.58 
 
 2.62 
 
 47.8 
 
 2.25 
 
 2.77 
 
 0.600 
 
 11.9 
 
 127400 
 
 0.587 
 
 
 183/4 
 
 5.51 
 
 0.49 
 
 2.53 
 
 43.8 
 
 2.01 
 
 2.82 
 
 0.603 
 
 11.0 
 
 116900 
 
 0.567 
 
 
 161/4 
 
 4.78 
 
 0.40 
 
 2.44 
 
 39.9 
 
 1.78 
 
 2.89 
 
 0.610 
 
 10.0 
 
 106400 
 
 0.556 
 
 " 
 
 133/4 
 
 4.04 
 
 0.31 
 
 2.35 
 
 36.0 
 
 1.55 
 
 2.98 
 
 0.619 
 
 9.0 
 
 96000 
 
 0.557 
 
 
 1H/4 
 
 3.35 
 
 0.22 
 
 2.26 
 
 32.3 
 
 1.33 
 
 3.11 
 
 0.630 
 
 8.1 
 
 86100 
 
 0.576 
 
 7 
 
 193/4 
 
 5.81 
 
 0.63 
 
 2.51 
 
 33.2 
 
 1.85 
 
 2.39 
 
 0.565 
 
 9.5 
 
 101100 
 
 0.583 
 
 " 
 
 171/4 
 
 5.07 
 
 0.53 
 
 2.41 
 
 30.2 
 
 1.62 
 
 2.44 
 
 0.564 
 
 8.6 
 
 92000 
 
 0.555 
 
 
 143/4 
 
 4.34 
 
 0.42 
 
 2.30 
 
 27.2 
 
 1.40 
 
 2.50 
 
 0.568 
 
 7.8 
 
 82800 
 
 0.535 
 
 
 121/4 
 
 3.60 
 
 0.32 
 
 2.20 
 
 24.2 
 
 1.19 
 
 2.59 
 
 0.575 
 
 6.9 
 
 73700 
 
 0.528 
 
 
 93/4 
 
 2.85 
 
 0.21 
 
 2.09 
 
 21.1 
 
 0.98 
 
 2.72 
 
 0.586 
 
 6.0 
 
 66800 
 
 0.546 
 
 6 
 
 15.5 
 
 4.56 
 
 0.56 
 
 2.28 
 
 19.5 
 
 1.28 
 
 2.07 
 
 0.529 
 
 6.5 
 
 69500 
 
 0.546 
 
 
 13. 
 
 3.82 
 
 0.44 
 
 2.16 
 
 17.3 
 
 1.07 
 
 2.13 
 
 0.529 
 
 5.8 
 
 61600 
 
 0.517 
 
 " 
 
 10.5 
 
 3.09 
 
 0.32 
 
 2.04 
 
 15.1 
 
 0.88 
 
 2.21 
 
 0.534 
 
 5.0 
 
 53800 
 
 0.503 
 
 
 8. 
 
 2.38 
 
 0.20 
 
 1.92 
 
 13.0 
 
 0.70 
 
 2.34 
 
 0.542 
 
 4.3 
 
 46200 
 
 0.517 
 
 5 
 
 11.5 
 
 3.38 
 
 0.48 
 
 2.04 
 
 10.4 
 
 0.82 
 
 1.75 
 
 0.493 
 
 4.2 
 
 44400 
 
 0.508 
 
 
 9. 
 
 2.65 
 
 0.33 
 
 1.89 
 
 8.9 
 
 0.64 
 
 1.83 
 
 0.493 
 
 3.5 
 
 37900 
 
 0.481 
 
 " 
 
 6.5 
 
 1.95 
 
 0.19 
 
 1.75 
 
 7.4 
 
 0.48 
 
 1.95 
 
 0.498 
 
 3.0 
 
 31600 
 
 0.489 
 
 4 
 
 71/4 
 
 2.13 
 
 0.33 
 
 1.73 
 
 4.6 
 
 0.44 
 
 1.46 
 
 0.455 
 
 2.3 
 
 24400 
 
 0.463 
 
 " 
 
 61/4 
 
 1.84 
 
 0.25 
 
 1.65 
 
 4.2 
 
 0.38 
 
 1.51 
 
 0.454 
 
 2.1 
 
 22300 
 
 0.458 
 
 
 51/4 
 
 1.55 
 
 0.18 
 
 1.58 
 
 3.8 
 
 0.32 
 
 1.56 
 
 0.453 
 
 1.9 
 
 20200 
 
 0.464 
 
 3 
 
 6. 
 
 1.76 
 
 0.36 
 
 1.60 
 
 2.1 
 
 0.31 
 
 1.08 
 
 0.421 
 
 1.4 
 
 14700 
 
 0.459 
 
 
 5. 
 
 1.47 
 
 0.26 
 
 1.50 
 
 1.8 
 
 0.25 
 
 1.12 
 
 0.415 
 
 1.2 
 
 13100 
 
 0.443 
 
 " 
 
 4. 
 
 1.19 
 
 0.17 
 
 1.41 
 
 1.6 
 
 0.20 
 
 1.17 
 
 0.409 
 
 1.1 
 
 11600 
 
 0.443 
 
 * Used for buildings; for bridges use 12,500 pounds, or multiply coeffi- 
 cient in this column by 0.78125. 
 
 L = safe load in pounds, uniformly distributed; I = span in feet; 
 M = moment of forces in foot-pounds; C = coefficient given above. 
 
 • 7 " r - 7 • * - T 7 - ° ■*' - ^ ; /,= fiber stress. 
 
 L = 
 
 M = £■ ; C ■■ 
 
 LI ■- 
 
 \M -- 
 
 12 ' 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 
 
 293 
 
 vOen — ©O00 rvNvOOu 
 
 — . — : —. — . P °. °. °. °. °. °. °. °. °. °. °. 
 dddddd ddddd dddoo 
 
 •<r •■*• ^ ttwc 
 
 ooooo ooooo ooooo 
 
 oooooo ooooo ooooo ooooo 
 
 DOOO OOOOO 
 
 vOeNJO^O^ren eN - 
 CN CN — — — ; — — - 
 
 o'do'do'd o'c 
 
 ^ o 00 oo t> 
 
 ooooo 
 
 ooooo ooooo 
 
 oooooo ooooo ooooo ooooo 
 
 lUgl8A4. UT 8SB9J0UI •£ © vO en © 00 
 x i- • • en en eN cn cn — 
 
 •q T ^j9Aajojppv ooo'doo 
 
 ooooo ooooo ooooo 
 
 u 
 
 Sa 
 
 6.68 
 5.57 
 4.77 
 4.18 
 3.71 
 3.34 
 
 3.04 
 2.78 
 2.57 
 2.39 
 2.23 
 
 2.09 
 1.96 
 1.86 
 1.76 
 1.67 
 
 ONinof 
 
 •q|A.i8Aa'jojppv 
 
 eNm©vO en- 
 Ten en eN CN eN 
 
 do" oo'o'd 
 
 0.19 
 
 0.18 
 0.16 
 0.15 
 0.14 
 
 0.13 
 0.12 
 0.11 
 0.11 
 0.11 
 
 0.10 
 0.10 
 0.09 
 0.09 
 0.08 
 
 U 
 
 GO 
 
 
 8.61 
 
 7.18 
 6.15 
 5.38 
 4.78 
 4.31 
 
 — on 
 On in 
 
 -oors 
 
 2.69 
 2.53 
 2.39 
 2.27 
 2.15 
 
 2.05 
 1.96 
 1.87 
 1.79 
 1.72 
 
 •^tjSraAi. m as-eajoiiT 
 
 T 
 
 — OOOt^vO 
 
 mTeneNeN 
 
 0.11 
 0.11 
 0.10 
 0.10 
 0.09 
 
 0.09 
 0.09 
 0.08 
 0.08 
 0.08 
 
 •qjA\i8A8 jo j ppy 
 
 ' "d 
 
 d ©" d o" © 
 
 d ©' © © d 
 
 U 
 
 
 3 
 
 OooeN — JT 
 
 — ocNm — 
 
 vO m -T cn <N 
 
 vOcnOrAN 
 — ©©On CO 
 
 ON 
 
 m'£ 
 
 : : : : :m 
 
 mi-1-Tm 
 
 enencnCNeN 
 
 eNcseNeNCN 
 
 tNfNCN 
 
 \0 in T ■>»■ en 
 
 ^<N — — © ©OONONQN 
 
 •qj AJ8A9 
 
 joippy 
 
 : : : : .^ 
 
 •© 
 
 © © © © © 
 
 © © © © © 
 
 © d ©' © © 
 
 o'dc'oo 
 
 u 
 
 © 
 
 — j§ 
 
 ! '. '. '. !»• 
 
 6.49 
 5.95 
 5.49 
 5.10 
 4.76 
 
 4.46 
 4.20 
 3.96 
 3.76 
 3.57 
 
 3.40 
 3.24 
 3.10 
 2.97 
 
 2.85 
 
 ■"3- -3- m vO 00 
 r>. vo m t en 
 
 •qj AjaAa'-ioj ppy ' 
 
 en 
 
 © 
 
 0.29 
 0.26 
 0.24 
 0.23 
 0.21 
 
 © 00 00 f> vO 
 
 © © © © © 
 
 mTTTrenen 
 © © © © © 
 
 © ©' © © © 
 
 U 
 
 Si 
 
 ON 
 
 en 
 
 10.35 
 9.49 
 8.76 
 8.14 
 7.59 
 
 7.12 
 6.70 
 6.33 
 5.99 
 5.70 
 
 5.42 
 5.18 
 4.95 
 4.75 
 4.56 
 
 4.38 
 4.22 
 4.07 
 3.93 
 3.80 
 
 -juSiaAi ux aseajatri 
 •qj ^t8A8joj ppy 
 
 ON 
 
 ©' 
 
 0.35 
 0.33 
 0.30 
 0.28 
 0.26 
 
 0.24 
 0.23 
 0.22 
 0.21 
 0.20 
 
 ON GO t^ vO O 
 ©' © © © © 
 
 in t tj- m en 
 
 © ©odd 
 
 U 
 
 en j§ 
 
 CN 
 
 20.20 
 18.52 
 17.10 
 15.87 
 14.82 
 
 13.89 
 13.07 
 12.35 
 11.70 
 11.11 
 
 10.58 
 10.10 
 9.66 
 9.26 
 8.89 
 
 8.55 
 8.23 
 7.94 
 7.66 
 7.41 
 
 •^aaj m 
 uaaA^aq 
 
 s^joddng 
 aou^siQ 
 
 m vo t>ooON©» 
 
 — cNenTm 
 
 vONCOOO 
 
 — eNenTm 
 
 fNMfNCSCN 
 
 ^rsoooo 
 cN<N(NfNen 
 
STRENGTH OF MATERIALS. 
 
 Properties of Carnegie T-Shapes. — Steel. 
 
 
 
 
 
 
 
 
 
 
 1 
 
 132 
 >> 
 
 So 
 
 | 
 
 
 
 
 
 s 
 
 bO 
 
 "8 
 
 d 
 
 m 
 t 
 
 V ■ 
 
 u M 
 Gv 
 
 $ g 
 
 ~1 
 
 So 
 
 *-> ® * 
 goo 
 
 0+ .>t-i 
 
 3° So 
 
 ^ M ?3 
 
 m «'£ 
 
 <> 
 C ^ 8 
 O M-2 
 
 J 11 
 
 SJOD 
 
 8 Oy- 
 
 og MO 
 
 Hi 
 
 III 
 
 2S 
 1^ 
 
 xg . 
 <•& g 
 .p "8 » 
 
 3.5£ 
 
 Sg£ 
 
 :>efric. of Strength for Fibe 
 Stress of 12,0001b. per sq. in. 
 Neutral Axis thro' C. of G 
 Parallel to Flange. 
 
 B3 
 
 £ 
 
 < 
 
 Q*~ 
 
 s 
 
 j 
 
 & 
 
 § 
 
 w 
 
 ^ 
 
 O 
 
 in. 
 
 lb. 
 
 sq.in. 
 
 in. 
 
 / 
 
 s 
 
 r 
 
 /' 
 
 S' 
 
 r' 
 
 c 
 
 5 X3 
 
 13.6 
 
 3.99 
 
 0.75 
 
 2.6 
 
 1.18 
 
 0.82 
 
 5.6 
 
 2.22 
 
 1.19 
 
 9410 
 
 5 X21/2 
 
 11.0 
 
 3.24 
 
 0.65 
 
 1.6 
 
 0.86 
 
 0.71 
 
 4.3 
 
 1.70 
 
 1.16 
 
 6900 
 
 41/2X31/2 
 
 15.9 
 
 4.65 
 
 1.11 
 
 5.1 
 
 2.13 
 
 1.04 
 
 3.7 
 
 1.65 
 
 0.90 
 
 17020 
 
 41/2X3 
 
 8.6 
 
 2.55 
 
 0.73 
 
 1.8 
 
 0.81 
 
 0.87 
 
 2.6 
 
 1.16 
 
 1.03 
 
 6490 
 
 41/2X3 
 
 10.0 
 
 3.00 
 
 0.75 
 
 2.1 
 
 0.94 
 
 0.86 
 
 3.1 
 
 1.38 
 
 1.04 
 
 7540 
 
 41/2X21/2 
 
 8.0 
 
 2.40 
 
 0.58 
 
 1.1 
 
 0.56 
 
 0.69 
 
 2.6 
 
 1.16 
 
 1.07 
 
 4520 
 
 41/2X21/2 
 
 9.3 
 
 2.79 
 
 0.60 
 
 1.2 
 
 0.65 
 
 0.68 
 
 3.1 
 
 1.38 
 
 1.08 
 
 5220 
 
 4 X5 
 
 15.7 
 
 4.56 
 
 1.56 
 
 10.7 
 
 3.10 
 
 1.54 
 
 2.8 
 
 1.41 
 
 0.79 
 
 24800 
 
 4 X5 
 
 12.3 
 
 3.54 
 
 1.51 
 
 8.5 
 
 2.43 
 
 1.56 
 
 2.1 
 
 1.06 
 
 0.78 
 
 19410 
 
 4 X4i/ 2 
 
 14.8 
 
 4.29 
 
 1.37 
 
 8.0 
 
 2.55 
 
 1.37 
 
 2.8 
 
 1.41 
 
 0.81 
 
 20400 
 
 4 X4i/ 2 
 
 11.6 
 
 3.36 
 
 1.31 
 
 6.3 
 
 1.98 
 
 1.38 
 
 2.1 
 
 1.06 
 
 0.80 
 
 15840 
 
 4 X4 
 
 13.9 
 
 4.02 
 
 1.18 
 
 5.7 
 
 2.02 
 
 1.20 
 
 2.8 
 
 1.40 
 
 0.84 
 
 16170 
 
 4 X4 
 
 10.9 
 
 3.21 
 
 1.15 
 
 4.7 
 
 1.64 
 
 1.23 
 
 2.2 
 
 1.09 
 
 0.84 
 
 13100 
 
 4 X3 
 
 9.3 
 
 2.73 
 
 0.78 
 
 2.0 
 
 0.88 
 
 0.86 
 
 2.1 
 
 1.05 
 
 0.88 
 
 7070 
 
 4 X21/ 2 
 
 8.7 
 
 2.52 
 
 0.63 
 
 1.2 
 
 0.62 
 
 0.69 
 
 2.1 
 
 1.05 
 
 0.92 
 
 4980 
 
 4 x2i/ 2 
 
 7.4 
 
 2.16 
 
 0.60 
 
 1.0 
 
 0.55 
 
 0.70 
 
 1.8 
 
 0.88 
 
 0.91 
 
 4380 
 
 4 X2 
 
 7.9 
 
 2.31 
 
 0.48 
 
 0.60 
 
 0.40 
 
 0.52 
 
 2.1 
 
 1.05 
 
 0.96 
 
 3180 
 
 4 X2 
 
 6.7 
 
 1.95 
 
 0.51 
 
 0.54 
 
 0.34 
 
 0.51 
 
 1.8 
 
 0.88 
 
 0.95 
 
 2700 
 
 31/2X4 
 
 12.8 
 
 3.75 
 
 1.25 
 
 5.5 
 
 1.98 
 
 1.21 
 
 1.89 
 
 1.08 
 
 0.72 
 
 15870 
 
 31/2X4 
 
 10.0 
 
 2.91 
 
 1.19 
 
 4.3 
 
 1.55 
 
 1.22 
 
 1.42 
 
 0.81 
 
 0.70 
 
 12380 
 
 31/2X31/2 
 
 11.9 
 
 3.45 
 
 1.06 
 
 3.7 
 
 1.52 
 
 1.04 
 
 1.89 
 
 1.08 
 
 0.74 
 
 12160 
 
 31/2X31/2 
 
 9.3 
 
 2.70 
 
 1.01 
 
 3.0 
 
 1.19 
 
 1.05 
 
 1.42 
 
 0.81 
 
 0.73 
 
 9530 
 
 31/2X3 
 
 11.0 
 
 3.21 
 
 0.88 
 
 2.4 
 
 1.13 
 
 0.87 
 
 1.88 
 
 1.08 
 
 0.77 
 
 9050 
 
 31/2X3 
 
 8.7 
 
 2.49 
 
 0.83 
 
 1.9 
 
 0.88 
 
 0.88 
 
 1.41 
 
 0.81 
 
 0.75 
 
 7040 
 
 31/2X3 
 
 7.7 
 
 2.28 
 
 0.78 
 
 1.6 
 
 0.72 
 
 0.89 
 
 1.18 
 
 0.68 
 
 0.76 
 
 5790 
 
 3 X4 
 
 11.9 
 
 3.48 
 
 1.32 
 
 5.2 
 
 1.94 
 
 1.23 
 
 1.21 
 
 0.81 
 
 0.59 
 
 15480 
 
 3 X4 
 
 10.6 
 
 3.12 
 
 1.32 
 
 4.8 
 
 1.78 
 
 1.25 
 
 1.09 
 
 0.72 
 
 0.60 
 
 14270 
 
 3 X4 
 
 9.3 
 
 2.73 
 
 1.29 
 
 4.3 
 
 1.57 
 
 1.26 
 
 0.93 
 
 0.62 
 
 0.59 
 
 12540 
 
 3 X31/2 
 
 11.0 
 
 3.21 
 
 1.12 
 
 3.5 
 
 1.49 
 
 1.06 
 
 1.20 
 
 0.80 
 
 0.62 
 
 11910 
 
 3 X31/2 
 
 9.8 
 
 2.88 
 
 1.11 
 
 3.3 
 
 1.37 
 
 1.08 
 
 1.31 
 
 0.88 
 
 0.68 
 
 10990 
 
 3 X3 
 
 10.1 
 
 2.94 
 
 0.93 
 
 2.3 
 
 1.10 
 
 0.88 
 
 1.20 
 
 0.80 
 
 0.64 
 
 8780 
 
 3 X3 
 
 9.0 
 
 2.67 
 
 0.92 
 
 2.1 
 
 1.01 
 
 0.90 
 
 1.08 
 
 0.72 
 
 0.64 
 
 8110 
 
 3 X3 
 
 7.9 
 
 2.28 
 
 0.88 
 
 1.8 
 
 0.86 
 
 0.90 
 
 0.90 
 
 0.60 
 
 0.63 
 
 6900 
 
 3 X2l/ 2 
 
 7.2 
 
 2.10 
 
 0.71 
 
 1.1 
 
 0.60 
 
 0.72 
 
 0.89 
 
 0.60 
 
 0.66 
 
 4800 
 
 23/4X2 
 
 7.4 
 
 2.16 
 
 0.53 
 
 1.1 
 
 0.75 
 
 0.71 
 
 0.62 
 
 0.45 
 
 0.54 
 
 6000 
 
 21/2X3 
 
 7.2 
 
 2.10 
 
 0.97 
 
 1.8 
 
 0.87 
 
 0.92 
 
 0.54 
 
 0.43 
 
 0.51 
 
 6960 
 
 21/2X23/4 
 
 6.8 
 
 1.98 
 
 0.87 
 
 1.4 
 
 0.73 
 
 0.84 
 
 0.66 
 
 0.53 
 
 0.58 
 
 5860 
 
 21/2X21/2 
 
 6.5 
 
 1.89 
 
 0.76 
 
 1.0 
 
 0.59 
 
 0.74 
 
 0.52 
 
 0.42 
 
 0.53 
 
 4700 
 
 2 1/2 X HA 
 
 3.0 
 
 0.84 
 
 0.29 
 
 0.094 
 
 0.09 
 
 0.31 
 
 0.29 
 
 0.23 
 
 0.58 
 
 710 
 
 21/4X21/4 
 
 5.0 
 
 1.44 
 
 0.69 
 
 0.66 
 
 0.42 
 
 0.68 
 
 0.33 
 
 0.30 
 
 0.48 
 
 3360 
 
 2 X2 
 
 4.4 
 
 1.26 
 
 0.63 
 
 0.45 
 
 0.33 
 
 0.60 
 
 0.23 
 
 0.23 
 
 0.43 
 
 2610 
 
 2 X 1 1/2 
 
 3.2 
 
 0.90 
 
 0.42 
 
 0.16 
 
 0.15 
 
 0.42 
 
 0.18 
 
 0.18 
 
 0.45 
 
 1200 
 
 13/4Xl3/ 4 
 
 3.2 
 
 0.90 
 
 0.54 
 
 0.23 
 
 0.19 
 
 0.51 
 
 0.12 
 
 0.14 
 
 0.37 
 
 1540 
 
 H/2XH/2 
 
 2.6 
 
 0.75 
 
 0.42 
 
 0.15 
 
 0.14 
 
 0.49 
 
 0.08 
 
 0.10 
 
 0.34 
 
 1150 
 
 H/4XI 1/4 
 
 2.1 
 
 0.60 
 
 0.40 
 
 0.08 
 
 0.10 
 
 0.36 
 
 0.05 
 
 0.07 
 
 0.27 
 
 760 
 
 1 XI 
 
 1.3 
 
 0.36 
 
 0.32 
 
 0.03 
 
 0.05 
 
 0.29 
 
 0.02 
 
 0.04 
 
 0.21 
 
 370 
 
 Some light weight T's of the smaller sizes are omitted. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 
 
 295 
 
 Properties of Carnegie Standard and Special Angles with Equal 
 
 Legs. Minimum, Intermediate, and Maximum Thicknesses 
 
 and Weights. 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 3 G£ 
 
 gOp 
 
 3 js 
 
 3 G*> 
 
 ir.- 
 
 
 0) 
 
 xi 
 C 
 
 I 
 
 
 U 
 
 •2 a 
 
 3 rt « 
 
 't, ^ 
 
 
 .2 s . .■ 
 
 £■£'> 1 
 
 i 6 |i 
 
 • 
 
 7 
 
 Cm 
 
 
 ■8*1 
 
 
 l§ 1 
 
 Cl ,« tH ffl 
 
 3-gSl 
 
 a 
 o 
 
 1 
 
 S 
 
 a 
 a 
 
 13 
 
 a 
 1 
 
 
 
 oment of 
 tral Axis 
 ter of G 
 to Flang 
 
 action Mc 
 Axis thri 
 Gravity 
 Flange. - 
 
 adius of ( 
 tral Axis 
 ter of G 
 to Flang 
 
 
 S 
 
 H 
 
 1 
 
 < 
 
 S 
 
 § 
 
 CO 
 
 « 
 
 J 
 
 8 X8 
 
 I 1/8 
 
 56.9 
 
 16.73 
 
 2.41 
 
 97.97 
 
 17.53 
 
 2.42 
 
 1.55 
 
 8 X8 
 
 13/16 
 
 42.0 
 
 12.34 
 
 2.30 
 
 74.71 
 
 13.11 
 
 2.46 
 
 1.57 
 
 8 X8 
 
 1/2 
 
 26.4 
 
 7.75 
 
 2.19 
 
 48.63 
 
 8.37 
 
 2.50 
 
 1.58 
 
 6 X6 
 
 1 
 
 37.4 
 
 11.00 
 
 1.86 
 
 35.46 
 
 8.57 
 
 1.80 
 
 1.16 
 
 6 X6 
 
 11/16 
 
 26.5 
 
 7.78 
 
 1.75 
 
 26.19 
 
 6.17 
 
 1.83 
 
 1.17 
 
 6 X6 
 
 3/8 
 
 14.9 
 
 4.36 
 
 1.64 
 
 15.39 
 
 3.53 
 
 1.88 
 
 1.19 
 
 *5 X5 
 
 1 
 
 30.6 
 
 9.00 
 
 1.61 
 
 19.64 
 
 5.80 
 
 1.48 
 
 0.96 
 
 *5 X5 
 
 11/16 
 
 21.8 
 
 6.42 
 
 1.50 
 
 14.68 
 
 4.20 
 
 1.51 
 
 0.97 
 
 *5 X5 
 
 3/8 
 
 12.3 
 
 3.61 
 
 1.39 
 
 8.74 
 
 2.42 
 
 1.56 
 
 0.99 
 
 4 X4 
 
 13/16 
 
 19.9 
 
 5.84 
 
 1.29 
 
 8.14 
 
 3.01 
 
 1.18 
 
 0.77 
 
 4 X4 
 
 9/16 
 
 14.3 
 
 4.18 
 
 1.21 
 
 6.12 
 
 2.19 
 
 1.21 
 
 0.78 
 
 4 X4 
 
 5 /l6 
 
 8.2 
 
 2.40 
 
 1.12 
 
 3.71 
 
 1.29 
 
 1.24 
 
 0.79 
 
 3V2X31/2 
 
 13/16 
 
 17.1 
 
 5.03 
 
 1.17 
 
 5.25 
 
 2.25 
 
 1.02 
 
 0.67 
 
 31/2X31/2 
 
 9/16 
 
 12.4 
 
 3.62 
 
 1.08 
 
 3.99 
 
 1.65 
 
 1.05 
 
 0.68 
 
 31/2X31/2 
 
 5/16 
 
 7.2 
 
 2.09 
 
 0.99 
 
 2.45 
 
 0.98 
 
 1.08 
 
 0.69 
 
 3 X3 
 
 5/8 
 
 11.5 
 
 3.36 
 
 0.98 
 
 2.62 
 
 1.30 
 
 0.88 
 
 0.57 
 
 3 X3 
 
 7/16 
 
 8.3 
 
 2.43 
 
 0.91 
 
 1.99 
 
 0.95 
 
 0.91 
 
 0.58 
 
 3 X3 
 
 1/4 
 
 4.9 
 
 1.44 
 
 0.84 
 
 1.24 
 
 0.58 
 
 0.93 
 
 0.59 
 
 *2 3/ 4 x2 3/4 
 
 1/2 
 
 8.5 
 
 2.50 
 
 0.87 
 
 1.67 
 
 0.89 
 
 0.82 
 
 0.52 
 
 *2 3/4X23/ 4 
 
 3/8 
 
 6.6 
 
 1.92 
 
 0.82 
 
 1.33 
 
 0.69 
 
 0.83 
 
 0.53 
 
 *2 3/4X2 3/4 
 
 1/4 
 
 4.5 
 
 1.31 
 
 0.78 
 
 0.93 
 
 0.48 
 
 0.85 
 
 0.55 
 
 21/2X21/2 
 
 1/2 
 
 7.7 
 
 2.25 
 
 0.81 
 
 1.23 
 
 0.73 
 
 0.74 
 
 0.47 
 
 21/2X21/2 
 
 3/8 
 
 5.9 
 
 1.73 
 
 0.76 
 
 0.98 
 
 0.57 
 
 0.75 
 
 0.48 
 
 21/2X21/2 
 
 3/16 
 
 3.1 
 
 0.90 
 
 0.69 
 
 0.55 
 
 0.30 
 
 0.78 
 
 0.49 
 
 *2 1/4X2 1/4 
 
 1/2 
 
 6.8 
 
 2.00 
 
 0.74 
 
 0.87 
 
 0.58 
 
 0.66 
 
 0.48 
 
 *2 1/4X2 1/4 
 
 3/8 
 
 5.3 
 
 1.55 
 
 0.70 
 
 0.70 
 
 0.45 
 
 0.67 
 
 0.43 
 
 *2 1/4X2 1/4 
 
 3/16 
 
 2.8 
 
 0.81 
 
 0.63 
 
 0.39 
 
 0.24 
 
 0.70 
 
 0.44 
 
 2 X2 
 
 7/16 
 
 5.3 
 
 1.56 
 
 0.66 
 
 0.54 
 
 0.40 
 
 0.59 
 
 0.39 
 
 2 X2 
 
 5/16 
 
 4.0 
 
 1.15 
 
 0.61 
 
 0.42 
 
 0.30 
 
 0.60 
 
 0.39 
 
 2 X2 
 
 3/16 
 
 2.5 
 
 0.72 
 
 0.57 
 
 0.28 
 
 0.19 
 
 0.62 
 
 0.40 
 
 13/4X13/4 
 
 7/16 
 
 4.6 
 
 1.30 
 
 0.59 
 
 0.35 
 
 0.30 
 
 0.51 
 
 0.33 
 
 13/4X13/4 
 
 5/16 
 
 3.4 
 
 1.00 
 
 0.55 
 
 0.27 
 
 0.23 
 
 0.52 
 
 0.34 
 
 13/4X13/4 
 
 3/16 
 
 2.2 
 
 0.62 
 
 0.51 
 
 0.18 
 
 0.14 
 
 0.54 
 
 0.35 
 
 H/2XH/2 
 
 3/8 
 
 3.4 
 
 0.99 
 
 0.51 
 
 0.19 
 
 0.19 
 
 0.44 
 
 0.29 
 
 II/2XH/2 
 
 1/4 
 
 2.4 
 
 0.69 
 
 0.47 
 
 0.14 
 
 0.134 
 
 0.45 
 
 0.29 
 
 II/2XH/2 
 
 1/8 
 
 1.3 
 
 0.36 
 
 0.42 
 
 0.08 
 
 0.070 
 
 0.46 
 
 0.30 
 
 II/4XH/4 
 
 5/16 
 
 2.4 
 
 0.69 
 
 0.42 
 
 0.09 
 
 0.109 
 
 0.36 
 
 0.23 
 
 II/4XH/4 
 
 1/4 
 
 2.0 
 
 0.56 
 
 0.40 
 
 0.077 
 
 0.091 
 
 0.37 
 
 0.24 
 
 II/4XH/4 
 
 1/8 
 
 1.1 
 
 0.30 
 
 0.35 
 
 0.044 
 
 0.049 
 
 0.38 
 
 0.25 
 
 1 XI 
 
 1/4 
 
 1.5 
 
 0.44 
 
 0.34 
 
 0.037 
 
 0.056 
 
 0.29 
 
 0.19 
 
 1 XI 
 
 3/16 
 
 1.2 
 
 0.34 
 
 0.32 
 
 0.030 
 
 0.044 
 
 0.30 
 
 0.19 
 
 1 XI 
 
 1/8 
 
 0.8 
 
 0.24 
 
 0.30 
 
 0.022 
 
 0.031 
 
 0.31 
 
 0.20 
 
 * 7/s X 7/ 8 
 
 3/16 
 
 1.0 
 
 0.29 
 
 0.29 
 
 0.019 
 
 0.033 
 
 0.26 
 
 0.18 
 
 * 7/s X 7/ 8 
 
 1/8 
 
 0.7 
 
 0.21 
 
 0.26 
 
 0.014 
 
 0.023 
 
 0.26 
 
 0.19 
 
 3/4 X 3/ 4 
 
 3/16 
 
 0.9 
 
 0.25 
 
 0.26 
 
 0.012 
 
 0.024 
 
 0.22 
 
 0.16 
 
 3/4 x 3/4 1 
 
 1/8 
 
 0.6 
 
 0.17 ' 
 
 0.23 1 
 
 0.009 
 
 0.017 
 
 0.23 
 
 0.17 
 
 Angles marked * are special. 
 
296 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Carnegie Standard and Special Angles with 
 
 Unequal Legs; Minimum, Intermediate, and Maximum 
 
 Thicknesses, and Weights. 
 
 8 
 
 
 
 
 Moment of 
 
 Section 
 
 Radius of Gyra- 
 
 i 
 
 c 
 
 1 
 
 1 
 
 O 
 
 O 
 
 ■g a 
 
 Inertia. — /. 
 
 Modul 
 
 as.— S 
 
 tion. — r. 
 
 C 
 
 T 
 
 1 
 
 o3 Si) 
 
 Ph C 
 
 O 
 
 
 =3 M 
 
 Ph a 
 
 
 
 o3 M 
 
 Ph C 
 
 
 o3 -2 
 Png 
 
 . a 
 
 m 
 
 a> «; 
 
 a; 1- 1 
 
 <o • 
 
 < . 
 
 <Jo • 
 
 < • 
 
 <lo . 
 
 <o ■ 
 
 %.$ 
 
 
 
 CO CD 
 
 -^ <d 
 
 -£ CD 
 
 +j <u 
 
 ■H CD 
 
 -U CD 
 
 +3 CD 
 
 tiQ 
 
 I 
 
 6 
 
 2 
 
 a 3 
 
 MO 
 '53 Ph 
 
 03 a 1 
 
 CDCB 
 
 .-3 M 
 
 ?3_ C 
 
 — bJO 
 
 
 13 M 
 
 =3_ a 
 
 .-5 M 
 
 ?3_ C 
 
 §3 
 
 Q 
 
 H 
 
 £ 
 
 < 
 
 6.02 
 
 A. 92 
 
 39.96 
 
 1.79 
 
 £ 
 
 I 
 
 2.58 
 
 £ 
 
 8 X31/2 
 
 n/20 
 
 20.5 
 
 7.99 
 
 0.90 
 
 0.74 
 
 ♦7 X31/2 
 
 1 
 
 32.3 
 
 9.50 
 
 7.53 
 
 45.37 
 
 2.96 
 
 10.58 
 
 0.89 
 
 2.19 
 
 0.88 
 
 *7 X31/2 
 
 3/ 4 
 
 24.9 
 
 7.31 
 
 6.08 
 
 35.99 
 
 2.31 
 
 8.22 
 
 0.91 
 
 2.22 
 
 0.88 
 
 *7 X31/2 
 
 7/16 
 
 15.0 
 
 4.40 
 
 3.95 
 
 22.56 
 
 1.47 
 
 5.01 
 
 0.95 
 
 2.26 
 
 0.89 
 
 6 X4 
 
 1 
 
 30.6 
 
 9.00 
 
 10.75 
 
 30.75 
 
 3.79 
 
 8.02 
 
 1.09 
 
 1.85 
 
 0.85 
 
 6 X4 
 
 11/16 
 
 21.8 
 
 6.41 
 
 8.11 
 
 22.82 
 
 2.76 
 
 5.78 
 
 1.13 
 
 1.89 
 
 0.86 
 
 6 X4 
 
 3/8 
 
 12.3 
 
 3.61 
 
 4.90 
 
 13.47 
 
 1.60 
 
 3.32 
 
 1.17 
 
 1.93 
 
 0.88 
 
 6 X31/2 
 
 1 
 
 28.9 
 
 8.50 
 
 7.21 
 
 29.24 
 
 2.90 
 
 7.83 
 
 0.92 
 
 1.85 
 
 0.74 
 
 6 X3V2 
 
 11/16 
 
 20.6 
 
 6.06 
 
 5.47 
 
 21.74 
 
 2.11 
 
 5.65 
 
 0.95 
 
 1.89 
 
 0.75 
 
 6 X31/2 
 
 3/8 
 
 11.7 
 
 3.42 
 
 3.34 
 
 12.86 
 
 1.23 
 
 3.25 
 
 0.99 
 
 1.94 
 
 0.77 
 
 *5 X4 
 
 7/8 
 
 24.2 
 
 7.11 
 
 9.23 
 
 16.42 
 
 3.31 
 
 4.99 
 
 1.14 
 
 1.52 
 
 0.84 
 
 *5 X4 
 
 5 /8 
 
 17.8 
 
 5.23 
 
 7.14 
 
 12.61 
 
 2.48 
 
 3.73 
 
 1.17 
 
 1.55 
 
 0.84 
 
 *5 X4 
 
 3/8 
 
 11.0 
 
 3.23 
 
 4.67 
 
 8.14 
 
 1.57 
 
 2.34 
 
 1.20 
 
 1.59 
 
 0.86 
 
 5 X31/2 
 
 7/8 
 
 22.7 
 
 6.67 
 
 6.21 
 
 15.67 
 
 2.52 
 
 4.88 
 
 0.96 
 
 1.53 
 
 0.75 
 
 5 X31/2 
 
 5/8 
 
 16.8 
 
 4.92 
 
 4.83 
 
 12.03 
 
 1.90 
 
 3.65 
 
 0.99 
 
 1.56 
 
 0.75 
 
 5 X31/2 
 
 5/16 
 
 8.7 
 
 2.56 
 
 2.72 
 
 6.60 
 
 1.02 
 
 1.94 
 
 1.03 
 
 1.61 
 
 0.76 
 
 5 X3 
 
 13/16 
 
 19.9 
 
 5.84 
 
 3.71 
 
 13.98 
 
 1.74 
 
 4.45 
 
 0.80 
 
 1.55 
 
 0.64 
 
 5 X3 
 
 9/16 
 
 14.3 
 
 4.18 
 
 2.83 
 
 10.43 
 
 1.27 
 
 3.23 
 
 0.82 
 
 1.58 
 
 0.65 
 
 5 X3 
 
 5/16 
 
 8.2 
 
 2.40 
 
 1.75 
 
 6.26 
 
 0.75 
 
 1.89 
 
 0.85 
 
 1.61 
 
 0.66 
 
 ♦41/2X3 
 
 13/16 
 
 18.5 
 
 5.43 
 
 3.60 
 
 10.33 
 
 1.71 
 
 3.62 
 
 0.81 
 
 1.38 
 
 0.64 
 
 *4i/2X3 
 
 9/16 
 
 13.3 
 
 3.90 
 
 2.75 • 
 
 7.75 
 
 1.25 
 
 2.64 
 
 0.85 
 
 1.41 
 
 0.64 
 
 ♦41/2X3 
 
 5/16 
 
 7.7 
 
 2.25 
 
 1.73 
 
 4.69 
 
 0.76 
 
 1.54 
 
 0.88 
 
 1.44 
 
 0.66 
 
 ♦4 X31/2 
 
 13/16 
 
 18.5 
 
 5.43 
 
 5.49 
 
 7.77 
 
 2.30 
 
 2.92 
 
 1.01 
 
 1.19 
 
 0.72 
 
 ♦4 X31/2 
 
 9/16 
 
 13.3 
 
 3.90 
 
 4.17 
 
 5.86 
 
 1.68 
 
 2.15 
 
 1.03 
 
 1.23 
 
 0.72 
 
 ♦4 X31/2 
 
 5/16 
 
 7.7 
 
 2.25 
 
 2.59 
 
 3.56 
 
 1.01 
 
 1.26 
 
 1.07 
 
 1.26 
 
 0.73 
 
 4 X3 
 
 13/16 
 
 17.1 
 
 5.03 
 
 3.47 
 
 7.34 
 
 1.68 
 
 2.87 
 
 0.83 
 
 1.21 
 
 0.64 
 
 4 X3 
 
 9/16 
 
 12.4 
 
 3.62 
 
 2.66 
 
 5.55 
 
 1.23 
 
 2.09 
 
 0.86 
 
 1.24 
 
 0.64 
 
 4 X3 
 
 5/16 
 
 7.2 
 
 2.09 
 
 1.65 
 
 3.38 
 
 0.74 
 
 1.23 
 
 0.89 
 
 1.27 
 
 0.65 
 
 • 31/2X3 
 
 13/16 
 
 15.8 
 
 4.62 
 
 3.33 
 
 4.98 
 
 1.65 
 
 2.20 
 
 0.85 
 
 1.04 
 
 0.62 
 
 31/2X3 
 
 5/16 
 
 6.6 
 
 1.93 
 
 1.58 
 
 2.33 
 
 0.72 
 
 0.96 
 
 0.90 
 
 1.10 
 
 0.63 
 
 31/2X21/2 
 
 11/16 
 
 12.5 
 
 3.65 
 
 1,72 
 
 4.13 
 
 0.99 
 
 1.85 
 
 0.67 
 
 1.06 
 
 0.53 
 
 31/2X21/2 
 
 1/4 
 
 4.9 
 
 1.44 
 
 0.78 
 
 1.80 
 
 0.41 
 
 0.75 
 
 0.74 
 
 1.12 
 
 0.54 
 
 ♦31/4X2 
 
 9/16 
 
 9.0 
 
 2.64 
 
 0.75 
 
 2.64 
 
 0.53 
 
 1.30 
 
 0.53 
 
 1.00 
 
 0.44 
 
 ♦31/4X2 
 
 1/4 
 
 4.3 
 
 1.25 
 
 0.40 
 
 1.36 
 
 0.26 
 
 0.63 
 
 0.57 
 
 1.04 
 
 0.45 
 
 3 X21/2 
 
 9/16 
 
 9.5 
 
 2.78 
 
 1.42 
 
 2.28 
 
 0.82 
 
 1.15 
 
 0.72 
 
 0.91 
 
 0.52 
 
 3 X21/2 
 
 1/4 
 
 4.5 
 
 1.31 
 
 0.74 
 
 1.17 
 
 0.40 
 
 0.56 
 
 0.75 
 
 0.95 
 
 0.53 
 
 ♦3 X2 
 
 1/2 
 
 7.7 
 
 2.25 
 
 0.67 
 
 1.92 
 
 0.47 
 
 1.00 
 
 0.55 
 
 0.92 
 
 0.43 
 
 ♦3 X2 
 
 1/4 
 
 4.1 
 
 1.19 
 
 0.39 
 
 1.09 
 
 0.25 
 
 0.54 
 
 0.57 
 
 0.95 
 
 0.43 
 
 21/2X2 
 
 1/2 
 
 6.8 
 
 2.00 
 
 0.64 
 
 1.14 
 
 0.46 
 
 0.70 
 
 0.56 
 
 0.75 
 
 0.42 
 
 21/2X2 
 
 3/16 
 
 2.8 
 
 0.81 
 
 0.29 
 
 0.51 
 
 0.20 
 
 0.29 
 
 0.60 
 
 0.79 
 
 0.43 
 
 ♦21/4XU/2 
 
 1/2 
 
 5.6 
 
 1.63 
 
 0.26 
 
 0.75 
 
 0.26 
 
 0.54 
 
 0.40 
 
 0.68 
 
 0.39 
 
 ♦21/4XU/2 
 
 3/8 
 
 4.4 
 
 1.27 
 
 0.21 
 
 0.61 
 
 0.20 
 
 0.42 
 
 0.41 
 
 0.69 
 
 0.39 
 
 ♦21/4XU/2 
 
 3/16 
 
 2.3 
 
 0.67 
 
 0.12 
 
 0.34 
 
 0.11 
 
 0.23 
 
 0.43 
 
 0.72 
 
 040 
 
 ♦2 X 1 3/ 8 
 
 1/4 
 
 2.7 
 
 0.78 
 
 0.12 
 
 0.37 
 
 0.12 
 
 0.23 
 
 0.39 
 
 0.63 
 
 0.30 
 
 ♦2 X 1 % 
 
 3/16 
 
 2.1 
 
 0.60 
 
 0.09 
 
 0.24 
 
 0.09 
 
 0.18 
 
 0.40 
 
 0.63 
 
 031 
 
 ♦13/8X1 
 
 1/4 
 
 1.9 
 
 0.53 
 
 0.04 
 
 0.09 
 
 0.05 
 
 0.09 
 
 0.27 
 
 0.41 
 
 22 
 
 ♦13/sXl 
 
 1/8 1 
 
 1.0 
 
 0.28 
 
 0.02 
 
 0.051 0.03 
 
 0.06 
 
 0.29 
 
 0.44 
 
 0.22 
 
 Angles marked * are special. A few of the smaller intermediate sizes 
 are omitted, 
 
PROPERTIES 
 
 OF 
 
 ROLLED 
 
 STRUCTURAL STEEL. 297 
 
 Safe Loads (Tons, 2000 Lb.) Uniformly Distributed for 
 
 Carnegie 
 
 Standard and Special Angl 
 
 es With Equal Legs. 
 
 Size of Angle. 
 
 Distance between Supports in Feet. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 8 X8 XI 1/8 
 8 X8 XV2 
 
 93.49 
 44.64 
 
 46.74 
 22.32 
 
 31.16 
 
 14.88 
 
 23.37 
 11.16 
 
 18.70 
 8.93 
 
 15.58 
 7.44 
 
 13.36 
 6.38 
 
 11.69 
 5.58 
 
 10.39 
 4.96 
 
 9.35 
 4.46 
 
 6 X6 XI 
 6 X6 X3/ 8 
 *5 X5 XI 
 *5 X5 X3/8 
 
 45.72 
 18.82 
 30.91 
 12.91 
 
 22.86 
 9.41 
 
 15.45 
 6.45 
 
 15.24 
 6.27 
 
 10.30 
 4.30 
 
 11.43 
 4.70 
 7.73 
 3.23 
 
 9.14 
 3.76 
 6.18 
 2.58 
 
 7.62 
 3.14 
 5.15 
 2.15 
 
 6.53 
 2.69 
 4.42 
 1.84 
 
 5.72 
 2.35 
 3.86 
 1.61 
 
 5.08 
 2.09 
 3.43 
 1.43 
 
 4.57 
 1.88 
 3.09 
 1.29 
 
 4 X4 X WIG 
 4 X4 X 5 /i6 
 
 31/2X31/2X13/16 
 31/2X31/2X5/16 
 
 16.05 
 6.88 
 
 12.00 
 5.20 
 
 8.03 
 
 3.44 
 6.00 
 2.60 
 
 5.35 
 
 2.29 
 4.00 
 1.73 
 
 4.01 
 1.72 
 3.00 
 1.30 
 
 3.21 
 1.38 
 2.40 
 1.04 
 
 2.68 
 1.15 
 2.00 
 0.87 
 
 2.29 
 0.98 
 1.71 
 0.74 
 
 2.01 
 0.86 
 1.50 
 0.65 
 
 1.78 
 0.76 
 1.33 
 0.58 
 
 1.61 
 0.69 
 1.20 
 0.52 
 
 3 X3 X5/ 8 
 3 X3 Xi/4 
 
 *2 3/4X2 3/4 X 1/2 
 *2 3/4X2 3/4X1/4 
 
 6.93 
 3.09 
 
 4.75 
 2.56 
 
 3.47 
 1.55 
 2.37 
 1.28 
 
 2.31 
 1.03 
 1.58 
 0.85 
 
 1.73 
 0.77 
 1.19 
 0.64 
 
 1.39 
 
 0.62 
 0.95 
 0.51 
 
 1.16 
 0.52 
 0.79 
 0.43 
 
 0.99 
 0,44 
 0.68 
 0.37 
 
 0.87 
 0.39 
 0.59 
 0.32 
 
 0.77 
 0.34 
 0.53 
 0.28 
 
 0.69 
 0.31 
 0.47 
 0.26 
 
 21/2X21/2X1/2 
 2V2X21/2X3/16 
 *2 1/4X21/4XV2 
 *21/ 4 X21/4X3/16 
 
 3.89 
 1.61 
 3.09 
 1.30 
 
 1.95 
 0.81 
 1.55 
 0.65 
 
 1.29 
 0.54 
 1.03 
 0.43 
 
 0.97 
 0.40 
 0.77 
 0.32 
 
 0.78 
 0.32 
 0.62 
 0.26 
 
 0.65 
 0.27 
 0.52 
 0.22 
 
 0.56 
 0.23 
 0.44 
 0.19 
 
 0.49 
 0.20 
 0.39 
 0.16 
 
 0.43 
 0.18 
 0.34 
 0.14 
 
 0.39 
 0.16 
 0.31 
 0.13 
 
 2 X2 X7/16 
 2 X2 X3/i6 
 13/4X13/4X7/16 
 13/4X13/4X3/16 
 
 2.13 
 1.01 
 1.60 
 0.75 
 
 1.07 
 0.51 
 0.80 
 0.37 
 
 0.71 
 0.34 
 0.53 
 0.25 
 
 0.53 
 0.25 
 0.40 
 0.19 
 
 0.43 
 0.20 
 0.32 
 0.15 
 
 0.36 
 0.17 
 0.27 
 0.12 
 
 0.30 
 0.14 
 0.23 
 0.11 
 
 0.27 
 0.13 
 0.20 
 0.093 
 
 0.24 
 0.11 
 0.18 
 0.083 
 
 0.21 
 0.10 
 0.16 
 0.075 
 
 11/2X11/2X3/8 
 II/2XII/2XV8 
 11/4X1 1/4 X.5/16 
 11/4X1 I/4XV8 
 
 1.01 
 0.38 
 0.58 
 0.26 
 
 0.51 
 0.19 
 0.29 
 0.13 
 
 0.34 
 0.13 
 0.19 
 0.087 
 
 0.25 
 0.096 
 0.150 
 0.065 
 
 0.20 
 0.077 
 0.120 
 0.052 
 
 0.17 
 0.064 
 0.097 
 0.044 
 
 0.14 
 0.055 
 0.083 
 0.037 
 
 0.130 
 0.048 
 0.073 
 0.033 
 
 0.110 
 0.043 
 0.065 
 0.029 
 
 0.100 
 0.038 
 0.058 
 0.026 
 
 1 XI Xl/4 
 1 XI XV8 
 
 0.30 
 0.17 
 
 0.15 
 
 0.083 
 
 0.100 
 0.055 
 
 0.075 
 0.041 
 
 0.060 
 0.033 
 
 0.050 
 0.028 
 
 0.043 
 0.024 
 
 0.037 
 0.021 
 
 0.033 
 0.018 
 
 0.030 
 0.017 
 
 * 7/ 8 X 7/ 8X 3/ 16 
 
 * 7/ 8 X 7/8X1/8 
 3/4 X 3/ 4 X3/i6 
 3/4 X 3/4X1/8 
 
 0.18 
 0.12 
 0.13 
 0.091 
 
 0.088 
 0.061 
 0.064 
 0.045 
 
 0.059 
 0.041 
 0.043 
 0.030 
 
 0.044 
 0.031 
 0.032 
 0.023 
 
 0.035 
 0.025 
 0.026 
 0.018 
 
 0.029 
 0.020 
 0.021 
 0.015 
 
 0.025 
 0.018 
 0.018 
 0.013 
 
 0.022 
 0.015 
 0.016 
 0.011 
 
 0.020 
 0.014 
 0.014 
 0.010 
 
 0.018 
 0.012 
 0.013 
 0.009 
 
 Safe loads given include weight of angle. Maximum fiber stress, 
 16,000 pounds per square inch. Neutral axis through center of gravity 
 parallel to one leg. Angles marked * are s 
 
298 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads in Tons (2000 Lb.) Uniformly Distributed for Stand- 
 ard Carnegie Angles with Unequal Legs. 
 
 
 
 
 (Short Leg Vertical.) 
 
 
 
 
 
 
 Distance between Supports in Feet. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 6 x4 xl 
 
 20 21 
 
 10.11 
 
 6.74 
 
 5.05 
 
 4.04 
 
 3.37 
 
 2.89 
 
 2.53 
 
 2.25 
 
 2 02 
 
 6 x4 x3/ 8 
 
 8,53 
 
 4.27 
 
 2.84 
 
 2.13 
 
 1.71 
 
 1.42 
 
 1.22 
 
 1.07 
 
 0.95 
 
 85 
 
 6 x3l/ 2 xl 
 
 15.47 
 
 7.74 
 
 5.16 
 
 3.87 
 
 3.09 
 
 2.58 
 
 2.21 
 
 1.93 
 
 1.72 
 
 1 55 
 
 6 x3i/ 2 x3/ 8 
 
 6,56 
 
 3.28 
 
 2.19 
 
 1.64 
 
 1.31 
 
 1.09 
 
 0.94 
 
 0.82 
 
 0.73 
 
 66 
 
 5 x3l/ 2 x7/ 8 
 
 13,44 
 
 6.72 
 
 4.48 
 
 3.36 
 
 2.69 
 
 2.24 
 
 1.92 
 
 1.68 
 
 1.49 
 
 1 14 
 
 5 X 3 1/2X5/16 
 
 5,44 
 
 2.72 
 
 1.81 
 
 1.36 
 
 1.09 
 
 0.91 
 
 0.78 
 
 0.68 
 
 0.60 
 
 54 
 
 5 x3 xi3/ 16 
 
 9 28 
 
 4.64 
 
 3.09 
 
 2.32 
 
 1.86 
 
 1.55 
 
 1.33 
 
 1.16 
 
 1.03 
 
 0.93 
 
 5 x3 x'/ie 
 
 4,00 
 
 2.00 
 
 1.33 
 
 1.00 
 
 0.80 
 
 0.67 
 
 0.57 
 
 0.50 
 
 0.44 
 
 0.40 
 
 4 x3 xl3/ 16 
 
 8 96 
 
 4.48 
 
 2.99 
 
 2.24 
 
 1.79 
 
 1 <9 
 
 1.28 
 
 1.12 
 
 1.00 
 
 0.90 
 
 4 x3 x"Vi6 
 
 3.95 
 
 1.97 
 
 1.32 
 
 0.99 
 
 0.79 
 
 0.65 
 
 0.56 
 
 0.49 
 
 0.44 
 
 0.39 
 
 3 1/ 2 X 3 xl3/ 16 
 
 8.80 
 
 4.40 
 
 2.93 
 
 2.20 
 
 1.76 
 
 1.47 
 
 1.26 
 
 1.10 
 
 0.98 
 
 0.88 
 
 31/ 3 x3 X5/ 16 
 
 3 84 
 
 1.92 
 
 1.28 
 
 0.96 
 
 0.77 
 
 0.64 
 
 0.55 
 
 0.48 
 
 0.43 
 
 38 
 
 3l/ 2 x2l/ 2 x ll/i 6 
 
 5 28 
 
 2.64 
 
 1.76 
 
 1.32 
 
 1.06 
 
 0.88 
 
 0.75 
 
 0.66 
 
 0.59 
 
 53 
 
 31/2X21/2 X l/ 4 
 
 2 19 
 
 1.09 
 
 0.73 
 
 0.55 
 
 0.44 
 
 0.36 
 
 0.31 
 
 0.27 
 
 0.24 
 
 22 
 
 3 X21/ 2 x9/ 16 
 
 4.37 
 
 2.19 
 
 1.46 
 
 1.09 
 
 0.87 
 
 0.73 
 
 0.62 
 
 0.55 
 
 0.49 
 
 44 
 
 3 x 21/2x1/4 
 
 2.13 
 
 1.07 
 
 0.71 
 
 0.53 
 
 0.43 
 
 0.36 
 
 0.30 
 
 0.27 
 
 0.24 
 
 0.21 
 
 2l/ 2 x2 xl/2 
 
 2.45 
 
 1.23 
 
 0.82 
 
 0.61 
 
 0.49 
 
 0.41 
 
 0.35 
 
 0.31 
 
 0.27 
 
 0.25 
 
 21/2X2 X3/ 16 
 
 1.07 
 
 0.53 
 
 0.36 
 
 0.27 
 
 0.21 
 
 0.18 
 
 0.15 
 
 0.13 
 
 0.12 
 
 0.11 
 
 Safe loads given include weight of angle. Maximum fiber stress, 
 16,000 lb. persq. in. Neutral axis through center of gravity parallel to 
 long leg. 
 
 Safe Loads in Tons (2000 Lb.) Uniformly Distributed for Stand- 
 ard Carnegie Angles with Unequal Legs. 
 
 (Long Leg Vertical.) 
 
 
 
 
 Distance between Supports in 
 
 Feet. 
 
 
 
 Size of Angle. 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 6 x4 x 1 
 
 42,77 
 
 21.39 
 
 14 26 
 
 10.69 
 
 8.55 
 
 7.13 
 
 6.11 
 
 5.35 
 
 4.75 
 
 4 28 
 
 6 x4 x3/ 8 
 
 17,71 
 
 8.85 
 
 5 90 
 
 4.43 
 
 3.54 
 
 2.95 
 
 2.53 
 
 2.21 
 
 1.97 
 
 1 77 
 
 6 x3l/ 2 x 1 
 
 41.76 
 
 20.88 
 
 13 92 
 
 10.44 
 
 8.35 
 
 6.96 
 
 5.97 
 
 5.22 
 
 4,64 
 
 4.18 
 
 6 x3i/ 2 x3/ 8 
 
 17.33 
 
 8.67 
 
 5.78 
 
 4.33 
 
 3.47 
 
 2.89 
 
 2.48 
 
 2.17 
 
 1.93 
 
 1 73 
 
 5 x31/ 2 x7/ 8 
 
 26.03 
 
 13.01 
 
 8.68 
 
 6.51 
 
 5.21 
 
 4.34 
 
 3.72 
 
 3.25 
 
 2.89 
 
 2 60 
 
 5 X3l/ 2 X5/ 16 
 
 10.35 
 
 5.18 
 
 3.45 
 
 2.59 
 
 2.07 
 
 1.73 
 
 1.48 
 
 1.29 
 
 1.15 
 
 1 04 
 
 5 x3 xl3/ 16 
 
 23 73 
 
 11.87 
 
 7 91 
 
 5.93 
 
 4.75 
 
 3.96 
 
 3.39 
 
 2.97 
 
 2.64 
 
 7, 37 
 
 5 x3 x5/i 6 
 
 10 08 
 
 5.04 
 
 3 36 
 
 2.52 
 
 2.02 
 
 1.68 
 
 1.44 
 
 1.26 
 
 1.12 
 
 1 01 
 
 4 X3 X 13/i 6 
 
 15.31 
 
 7.65 
 
 5 10 
 
 3.83 
 
 3.06 
 
 2.55 
 
 2.19 
 
 1.91 
 
 1.70 
 
 1 53 
 
 4 X3 x5/i 6 
 
 6.56 
 
 3.28 
 
 2.19 
 
 1.64 
 
 1.31 
 
 1.10 
 
 0.94 
 
 0.82 
 
 0.73 
 
 66 
 
 31/2X3 X 13/i 6 
 
 11.73 
 
 5.87 
 
 3.91 
 
 2.93 
 
 2.35 
 
 1.96 
 
 1.68 
 
 1.47 
 
 1.30 
 
 1 17 
 
 31/2X3 x5/i 6 
 
 3.12 
 
 2.56 
 
 1.71 
 
 1.28 
 
 1.02 
 
 0.85 
 
 0.73 
 
 0.64 
 
 0.57 
 
 0.51 
 
 3 1/ 2 X21/ 2 X11/16 
 
 9 87 
 
 4.93 
 
 3 29 
 
 2.47 
 
 1.97 
 
 1.64 
 
 1.41 
 
 1.23 
 
 1.10 
 
 99 
 
 31/2X21/2X1/4 
 
 4 00 
 
 2.00 
 
 1.33 
 
 1.00 
 
 0.80 
 
 0.67 
 
 0.57 
 
 0.50 
 
 0.44 
 
 40 
 
 3 X2i/ 2 x9/ 16 
 
 6.13 
 
 3.07 
 
 2.04 
 
 1.53 
 
 1.23 
 
 1.02 
 
 0.88 
 
 0.77 
 
 0.68 
 
 61 
 
 3 x 21/3x1/4 
 
 2.99 
 
 1.50 
 
 1.00 
 
 0.75 
 
 0.60 
 
 0.50 
 
 0.43 
 
 0.37 
 
 0.33 
 
 0.30 
 
 21/2X2 Xl/ 2 
 
 3 73 
 
 1.87 
 
 1 24 
 
 0.93 
 
 0.75 
 
 0.62 
 
 0.53 
 
 0.47 
 
 0.41 
 
 37 
 
 21/2X2 X3/i 6 
 
 1.55 
 
 0.77 
 
 0.52 
 
 0.39 
 
 0.31 
 
 0.26 
 
 0.22 
 
 0.19 
 
 0.17 
 
 0.16 
 
 Safe loads given include weight of angle. Maximum fiber stress, 
 16,000 lb. per sq. in. Neutral axis through center of gravity parallel to 
 short leg. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 299 
 
 Properties of Carnegie Z-Bars. 
 
 
 
 
 
 
 .2 i 
 
 ■a a 
 
 fi 
 
 •pfl 
 
 +=■ i 
 
 *-' m 
 
 to bb 
 
 33 aS 
 
 
 
 
 
 
 
 n <v 
 
 rf a; 
 
 
 §o 
 
 SB a 
 
 J3 CG 
 
 t 
 a 
 
 12 
 
 1 
 
 o 
 
 o 
 
 03 
 
 1 
 
 .2 
 
 Xfl 
 C3 
 
 . G 
 
 .go 
 
 m 
 
 if 
 
 «»3 
 
 Pn 
 
 Jo 
 
 5 c « 
 
 <3 
 
 is 
 
 V o 
 
 £0 
 
 ,/0 
 
 log 
 
 1~* 
 
 £ & 
 
 Ph 
 
 • SO 
 pi 
 
 O"o£ 
 
 J-91 
 
 o 2"^ 
 PI 
 
 35 
 o| 
 
 O £ 
 3 
 
 ?'6J 
 
 t,<N'Pn a 
 ^ to<J 03 
 
 §cq-.S£ 
 
 Q 
 
 ? 
 
 E- 
 
 s 
 
 < 
 
 § 
 
 § 
 
 02 
 
 03 
 
 cd 
 
 tf 
 
 P3 
 
 o 
 
 in. 
 
 in. 
 
 in. 
 
 lb. 
 
 sq.in. 
 
 / 
 
 I 
 
 s 
 
 s 
 
 r 
 
 r 
 
 r 
 
 c 
 
 ) 
 
 31/2 
 
 3/8 
 
 15.6 
 
 4.59 
 
 25.32 
 
 9.11 
 
 8.44 
 
 2.75 
 
 2.35 
 
 1.41 
 
 0.83 
 
 67,500 
 
 >Vl6 
 
 3 9/16 
 
 7/16 
 
 18.3 
 
 5.39 
 
 29.80 
 
 10.95 
 
 9.83 
 
 3.27 
 
 2.35 
 
 1.43 
 
 0.84 
 
 78,600 
 
 >Vs 
 
 35/8 
 
 1/2 
 
 21.0 
 
 6.19 
 
 34.36 
 
 12.87 
 
 11.22 
 
 3.81 
 
 2.36 
 
 1.44 
 
 0.84 
 
 89,800 
 
 5 
 
 31/2 
 
 9/16 
 
 22.7 
 
 6.68 
 
 34.64 
 
 12.59 
 
 11.52 
 
 3.91 
 
 2.28 
 
 1.37 
 
 0.81 
 
 92,400 
 
 3Vl6 
 
 3 9/16 
 
 5/8 
 
 25.4 
 
 7.46 
 
 38.86 
 
 14.42 
 
 12.82 
 
 4.43 
 
 2.28 
 
 1.39 
 
 0.82 
 
 102,600 
 
 >Vs 
 
 3 5/8 
 
 11/16 
 
 28.0 
 
 8.25 
 
 43.18 
 
 16.34 
 
 14.10 
 
 4.98 
 
 2.29 
 
 1.41 
 
 0.84 
 
 112,800 
 
 s 
 
 31/2 
 
 3/ 4 
 
 29.3 
 
 8.63 
 
 42.12 
 
 15.44 
 
 14.04 
 
 4.94 
 
 2.21 
 
 1.34 
 
 0.81 
 
 112,300 
 
 s Vie 
 
 3 9/i 6 
 
 13/16 
 
 31.9 
 
 9.40 
 
 46.13 
 
 17.27 
 
 15.22 
 
 5.47 
 
 2.22 
 
 1.36 
 
 0.82 
 
 121,800 
 
 51/8 
 
 3 5/8 
 
 7/8 
 
 34.6 
 
 10.17 
 
 50.22 
 
 19.18 
 
 16.40 
 
 6.02 
 
 2.22 
 
 1.37 
 
 0.83 
 
 131,200 
 
 5 
 
 31/4 
 
 5/16 
 
 11.6 
 
 3.40 
 
 13.36 
 
 6.18 
 
 5.34 
 
 2.00 
 
 1.98 
 
 1.35 
 
 0.75 
 
 42,700 
 
 i Vie 
 
 3 5/ie 
 
 3/8 
 
 13.9 
 
 4.10 
 
 16.18 
 
 7.65 
 
 6.39 
 
 2.45 
 
 1.99 
 
 1.37 
 
 0.76 
 
 51,100 
 
 >Vs 
 
 3 3/ 8 
 
 7/16 
 
 16.4 
 
 4.81 
 
 19.07 
 
 9.20 
 
 7.44 
 
 2.92 
 
 1.99 
 
 1.38 
 
 0.77 
 
 59,500 
 
 
 31/ 4 
 
 1/2 
 
 17.9 
 
 5.25 
 
 19.19 
 
 9.05 
 
 7.68 
 
 3.02 
 
 1.91 
 
 1.31 
 
 0.74 
 
 61,400 
 
 'Vie 
 
 3 5/i 6 
 
 9/16 
 
 20.2 
 
 5.94 
 
 21.83 
 
 10.51 
 
 8.62 
 
 3.47 
 
 1.91 
 
 1.33 
 
 0.75 
 
 69,000 
 
 >Vs 
 
 3 3/8 
 
 5 /8 
 
 22.6 
 
 6.64 
 
 24.53 
 
 12.06 
 
 9.57 
 
 3.94 
 
 1.92 
 
 1.35 
 
 0.76 
 
 76,600 
 
 
 31/4 
 
 11/16 
 
 23.7 
 
 6.96 
 
 23.68 
 
 11.37 
 
 9.47 
 
 3.91 
 
 1.84 
 
 1.28 
 
 0.73 
 
 75,800 
 
 1 1/16 
 
 3 5/ie 
 
 3/4 
 
 26.0 
 
 7.64 
 
 26.16 
 
 12.83 
 
 10.34 
 
 4.37 
 
 1.85 
 
 1.30 
 
 0.75 
 
 82,700 
 
 '1/8 
 
 3 3/ 8 
 
 13/16 
 
 28.3 
 
 8.33 
 
 28.70 
 
 14.36 
 
 11.20 
 
 4.84 
 
 1.86 
 
 1.31 
 
 0.76 
 
 89,600 
 
 \ 
 
 31/16 
 
 V4 
 
 8.2 
 
 2.41 
 
 6.28 
 
 4.23 
 
 3.14 
 
 1.44 
 
 1.62 
 
 1.33 
 
 0.67 
 
 25,100 
 
 H/16 
 
 31/8 
 
 5/16 
 
 10.3 
 
 3.03 
 
 7.94 
 
 5.46 
 
 3.91 
 
 1.84 
 
 1.62 
 
 1.34 
 
 0.68 
 
 31,300 
 
 »V 8 
 
 3 3/ie 
 
 3/8 
 
 12.4 
 
 3.66 
 
 9.63 
 
 6.77 
 
 4.67 
 
 2.26 
 
 1 62 
 
 1.36 
 
 0.69 
 
 37,400 
 
 1 
 
 31/16 
 
 7/16 
 
 13.8 
 
 4.05 
 
 9.66 
 
 6.73 
 
 4.83 
 
 2.37 
 
 1.55 
 
 1.29 
 
 0.66 
 
 38,600 
 
 H/ie 
 
 31/8 
 
 1/2 
 
 15.8 
 
 4.66 
 
 11.18 
 
 7.96 
 
 5.50 
 
 2.77 
 
 1.55 
 
 1.31 
 
 0.67 
 
 44,000 
 
 ♦1/8 
 
 3 3/ie 
 
 9/16 
 
 1.7.9 
 
 5.27 
 
 12.74 
 
 9.26 
 
 6.18 
 
 3.19 
 
 1.55 
 
 1.33 
 
 0.69 
 
 49,400 
 
 \ 
 
 3Vl6 
 
 5/8 
 
 18.9 
 
 5.55 
 
 12.11 
 
 8.73 
 
 6.05 
 
 3.18 
 
 1.48 
 
 1.25 
 
 0.66 
 
 48,400 
 
 i Vie 
 
 31/8 
 
 11/16 
 
 20.9 
 
 6.14 
 
 13.52 
 
 9.95 
 
 6.65 
 
 3.58 
 
 1.48 
 
 1.27 
 
 0.67 
 
 53,200 
 
 H/8 
 
 3 3/16 
 
 3/4 
 
 23.0 
 
 6.75 
 
 14.97 
 
 11.24 
 
 7.26 
 
 4.00 
 
 1.49 
 
 1.29 
 
 0.69 
 
 58,100 
 
 
 2H/16 
 
 1/4 6.7 
 
 1.97 
 
 2.87 
 
 2.81 
 
 1.92 
 
 1.10 
 
 1.21 
 
 1.19 
 
 0.55 
 
 15,400 
 
 Vl6 
 
 2 3/4 
 
 5/16 8.4 
 
 2.48 
 
 3.64 
 
 3.64 
 
 2.38 
 
 1.40 
 
 1.21 
 
 1.21 
 
 0.56 
 
 19,000 
 
 > 
 
 211/16 
 
 3/8 9.7 
 
 286 
 
 3.85 
 
 3.92 
 
 2.57 
 
 1.57 
 
 1.16 
 
 1.17 
 
 0.55 
 
 2,6000 
 
 Vl6 
 
 23/ 4 
 
 7/16 11.4 
 
 3.36 
 
 4.57 
 
 4.75 
 
 2.98 
 
 1.88 
 
 1.17 
 
 1.19 
 
 0.56 
 
 23,800 
 
 
 2 11/16 
 
 1/2 12.5 
 
 3.69 
 
 4.59 
 
 4.85 
 
 3.06 
 
 1.99 
 
 1.12 
 
 1.15 
 
 0.55 
 
 24,500 
 
 1/16 
 
 23/4 
 
 9/16 J 
 
 14.2 
 
 4.18 
 
 5.26 
 
 5.70 
 
 3.43 
 
 2.31 
 
 1.12 
 
 1.17 
 
 0.56 
 
 27,400 
 
300 
 
 STRENGTH OF MATERIALS. 
 
 D 
 
 mensions of 6, 8 
 
 , and 
 
 10-Inch Carnegie 
 
 Z-Bar Columns. 
 
 %~ 
 
 A. 
 
 B. 
 
 C. 
 
 D. 
 
 c^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 6 
 
 8 
 
 10 
 
 6 
 
 8 
 
 10 
 
 6 
 
 8 
 
 10 
 
 6 
 
 8 
 
 10 
 
 h^ 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 31/s 
 
 m. 
 
 41/8 
 
 m. 
 
 in. 
 
 5 9/, 6 
 
 m. 
 
 67/ 16 
 
 in. 
 
 in. 
 
 31/8 
 
 in. 
 
 35/s 
 
 in. 
 
 in. 
 !'4 
 
 123/4 
 
 155/ 16 
 
 
 
 5/16 
 
 I27/ S 
 
 153/8 
 
 b H/i 6 
 
 3V/ m 
 
 4v/ m 
 
 55/ 3 9, 
 
 i»/lfl 
 
 6 V/! o 
 
 69/ 1R 
 
 31/8 
 
 3 5/8 
 
 35/8 
 
 3/8 
 
 I2b/ H 
 
 151/2 
 
 613/10 
 
 3 3/ 1fi 
 
 45/16 
 
 51/4 
 
 5V/ 1fi 
 
 bV/ 1R 
 
 69/16 
 
 31/s 
 
 35/8 
 
 3i>/8 
 
 7/10 
 
 I2H/1 
 
 3 151/16 
 
 blb/16 
 
 3 9/3? 
 
 47/3? 
 
 5H/3? 
 
 jV/lfi 
 
 61/4 
 
 6»/lfl 
 
 31/8 
 
 3 5/8 
 
 35/8 
 
 1/7 
 
 !27/ 1fi 
 
 153/16 
 
 l61/ ? 
 
 31/4 
 
 45/ifi 
 
 51/4 
 
 5ty|fi 
 
 61/4 
 
 63/8 
 
 31/8 
 
 35/8 
 
 35/ 8 
 
 9/10 
 
 12 9/10 
 
 15 5/ 16 
 
 I6b/ S 
 
 311/32 
 
 4l3/ 3? 
 
 5 U/3? 
 
 55/ 16 
 
 61/4 
 
 63/ 8 
 
 31/8 
 
 35/ 8 
 
 35/ 8 
 
 B/8 
 
 
 14 7/ 8 
 
 I 6 3/ 4 
 
 
 4 5/, o 
 
 5 7/10 
 
 
 61/16 
 
 6 3/8 
 
 
 3 5/8 
 
 35/ 8 
 
 11/16 
 
 
 15 
 
 I63/ S 
 
 
 413/JW 
 
 5 H/3? 
 
 
 61/16 
 
 63/ 1fi 
 
 
 35/s 
 
 35/ a 
 
 3/4 
 
 
 151/8 
 
 \bl/ ?l 
 
 
 41/2 
 
 5V/io 
 
 
 61/16 
 
 63/,o 
 
 
 35/ 8 
 
 3W8 
 
 13/10 
 
 
 
 165/ 8 
 
 
 ... 517/3 2 
 
 
 
 63/16 
 
 
 
 35/ 8 
 
 c3 
 
 IS 
 
 E. 
 
 F. 
 
 G. 
 
 H. 
 
 I. 
 
 6 
 
 8 
 
 10 
 
 6 
 
 8 and 
 
 6 
 
 8 
 
 10 
 
 6 
 
 Sand 
 
 6 
 
 8 
 
 10 
 
 
 m. 
 
 iii. 
 
 in. 
 
 in. 
 
 10 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 10 in. 
 
 in. 
 
 m. 
 
 in. 
 
 1/4 
 
 3 
 
 Mh 
 
 
 15/8 
 
 17/8 
 
 211/10 
 
 31/16 
 
 
 8V ? , 
 
 10 
 
 31/4 
 
 41/4 
 
 
 W10 
 
 3 
 
 »v, 
 
 31/. 
 
 15/8 
 
 IV/8 
 
 23/4 
 
 31/8 
 
 31/4 
 
 81/7, 
 
 10 
 
 33/s 
 
 43/8 
 
 5t>/l6 
 
 3/8 
 
 3 
 
 
 31/' 
 
 15/8 
 
 IV/8 
 
 2H/10 
 
 33/ 16 
 
 35/ 16 
 
 8V ? 
 
 10 
 
 33/8 
 
 41/?, 
 
 5V/ 1f , 
 
 Vw 
 
 3 
 
 Jl/o 
 
 3V- 
 
 1 5/8 
 
 Wh 
 
 23/4 
 
 31/16 
 
 3 3/8 
 
 81/9 
 
 10 
 
 31/2 
 
 4V/ 16 
 
 59/m 
 
 i/?, 
 
 3 
 
 U/ ? 
 
 31/- 
 
 15/8 
 
 IV/8 
 
 2H/16 
 
 31/8 
 
 31/ 4 
 
 81/9 
 
 10 
 
 31/2 
 
 49/ 16 
 
 5 V? 
 
 9/16 
 
 3 
 
 1 
 
 3V- 
 
 15/8 
 
 IV/8 
 
 23/ 4 
 
 3 8/10 
 
 3 5/! 6 
 
 81/9 
 
 10 
 
 35/s 
 
 4H/16 
 
 5 5/ 8 
 
 *»/« 
 
 
 ii/., 
 
 3 1/- 
 
 
 IV/8 
 
 
 31/16 
 
 3 3/8 
 
 
 10 
 
 
 45/ 8 
 
 53/ 4 
 
 11/10 
 
 
 il/9 
 
 3 1/. 
 
 
 IV/8 
 
 
 31/8 
 
 3 1/4 
 
 
 10 
 
 
 43/ 4 
 
 5H/16 
 
 3/4 
 13/16 
 
 ::: 
 
 51/2 
 
 3V: 
 31/3 
 
 
 IV/8 
 17/8 
 
 
 3 3/ie 
 
 3 5/ie 
 3 3/s 
 
 
 10 
 10 
 
 
 47/ 8 
 
 513/ie 
 515/16 
 
 fi in m] I 4 z " bars - 3 " 3 Vie in- deep, 
 
 o-in. coi. | x web plate 6 in x tMck Qf z _ bars> 
 
 a in onl i 4. Z-bars, 4.-4 1/s in. deep, 
 
 s-in. coi. 1 1 web plate 7 in x thick _ of z _ bars _ 
 
 i n in nni 1 4 Z-bars, 5-51/s in. deep, 
 
 lU-m. coi. y 1 web plate 7 in x thick# of z-bars. 
 
 All rivets or bolts 3/ 4 inch diameter. 
 
 Dimensions of 14-Inch Carnegie Z-Bar Columns. 
 
 
 A. Inches. 
 
 B. Inches. 
 
 •R8 
 
 d 
 
 
 ® s 
 
 d 
 
 d 
 
 
 d 
 
 d 
 
 
 >£ 
 
 • S on 
 
 3-° 
 
 
 S • 
 
 ■s'h 
 
 e? "» 
 
 ^co 
 
 M 2 
 
 x4 
 
 w-.Q 
 
 XN 
 
 xj 
 
 xii 
 
 -^ o3 
 
 xjS 
 
 xj 
 
 SiM 
 
 %** 
 
 XN 
 
 <?.s 
 
 > N 
 
 >^ 
 
 XN 
 
 <CS3 
 
 ^N3 
 
 H 
 
 vO 
 
 vO 
 
 vO 
 
 vO 
 
 o 
 
 ^o 
 
 ^O 
 
 vO 
 
 3/8 
 
 199/i 6 
 
 197/16 
 
 199/is 
 
 193/ 4 
 
 627/3, 
 
 63/4 
 
 627/32 
 
 615/10 
 
 7/16 
 
 1911/ie 
 
 191/2 
 
 195/ 8 
 
 1913/iG 
 
 baa/a,. 
 
 6 13/1R 
 
 6 29/32 
 
 7 
 
 1/9 
 
 193/4 
 
 195/s 
 
 193/4 
 
 197/g 
 
 Mi/r> 
 
 67/8 
 
 631/39 
 
 7Vie 
 
 9/16 
 
 197/s 
 
 193/4 
 
 197/s 
 
 20 
 
 > 1/37 
 
 615/ifi 
 
 7Vs? 
 
 71/8 
 
 5/8 
 
 1915/i 6 
 
 1913/ 16 
 
 1915/ie 
 
 201/ie 
 
 / 3/39 
 
 7 
 
 73/3? 
 
 73/ie 
 
 11/16 
 
 201/16 
 
 197/s 
 
 201/ie 
 
 201/g 
 
 >5/39 
 
 71/16 
 
 7 5/ s? 
 
 71/4 
 
 3/4 
 
 201/8 
 
 20 
 
 201/s 
 
 201/4 
 
 /''/m 
 
 71/8 
 
 yv/jw 
 
 7b/i« 
 
 13/10 
 
 201/4 
 
 201/ie 
 
 203/ 16 
 
 20 5/i 6 
 
 ^9/39 
 
 /3/ 1fi 
 
 yy/37 
 
 73/g 
 
 7/8 
 
 205/ 16 
 
 201/s 
 
 201/4 
 
 20 7/i 6 
 
 ' H/32 
 
 71/4 
 
 ^ H/32 
 
 77/16 
 
 ^.i=d 
 
 1 Web Plate, 8 in.X thick, of Z-bars. 
 
 2 Side Plates 14 in. wide 4 Z-bars. 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 301 
 
 Notes on Tables of Z-Bar and Channel Columns. 
 
 (Carnegie Steel Co., 1903.) 
 
 The tables of safe loads for steel Z-bar and channel columns are com- 
 piled on the basis of an allowable stress per square inch of 12,000 pounds, 
 with a factor of safety of 4 for lengths of 90 radii and under and an allow- 
 able stress deduced from the formula 17,100 — 57 I -s- r for lengths greater 
 than 90 radii; I = length in feet; r = radius of gyration in inches. Calcu- 
 lations are made by means of Gordon's formula, modified for steel. The 
 values used in these tables should be used only where the loads are mostly 
 statical and equal or nearly so on opposite sides of the column. If the 
 eccentricity is great or the load subject to sudden changes the values 
 should be reduced according to circumstances. The safe loads given in 
 the tables on channel columns range in value from I -*- r= 90 to about 
 
 1 -r- r = 125. The size and spacing of lattice bars of channel columns 
 should be proportioned to the sections composing the column. They 
 should not be less than 11/2 inch X 5 /i6 inch for 6-inch channels; 13/4 X 5 /ie 
 inch for 7- and 8-inch channels; 2 X 5/i 6 inch for 9- and 10-inch channels; 
 
 2 X 3 /8 inch for 12-inch channels. 
 
 Safe Loads in Tons (2000 Lb.) on Carnegie Z-Bar Columns 
 (Square Ends). 
 
 Dimensions and form of columns given in tables, p. 300. 
 6-INCH Z-BAR COLUMN. 
 
 Length 
 of 
 
 Col. 
 Feet. 
 
 
 
 
 Thiol 
 
 mess of Metal, 
 
 Inch. 
 
 
 
 1/4 
 
 5/ie 
 
 3/S 
 
 7/16 
 
 1/2 
 
 9/16 
 
 5/8 
 
 11/16 
 
 3/4 
 
 13/16 
 
 r (min) 
 
 = 1.86 
 55.9 
 
 1.90 
 
 1.88 
 
 1.93 
 
 1.90 
 
 1.95 
 
 
 
 
 
 12 
 
 and under 
 
 70.3 
 
 81.6 
 
 95.8 
 
 105.7 
 
 119.8 
 
 
 
 
 
 14 
 
 55.7 
 
 70.3 
 
 81.6 
 
 95. e 
 
 105.7 
 
 .119.6 
 
 
 
 
 
 16 
 
 52.3 
 
 66.5 
 
 76.6 
 
 91.3 
 
 99.9 
 
 114.8 
 
 
 
 
 
 18 
 
 48.fi 
 
 62.3 
 
 71.7 
 
 85.6 
 
 93.6 
 
 107.fi 
 
 
 
 
 
 20 
 
 45.4 
 
 58.1 
 
 66.7 
 
 79.9 
 
 87.2 
 
 iocs 
 
 
 
 
 
 22 
 
 42.0 
 
 53.9 
 
 61.8 
 
 74.3 
 
 80.9 
 
 93 .e 
 
 
 
 
 
 24 
 
 38.6 
 
 49.7 
 
 56.9 
 
 68.6 
 
 74.6 
 
 86.fi 
 
 
 
 
 
 26 
 
 35.2 
 
 45.5 
 
 51.9 
 
 63.0 
 
 68.2 
 
 79.8 
 
 
 
 
 
 28 
 
 31.7 
 
 41.3 
 
 47.0 
 
 57.3 
 
 61.9 
 
 72.8 
 
 
 
 
 
 30 
 
 28.3 
 
 37.1 
 
 42.0 
 
 51.7 
 
 55.5 
 
 65.8 
 
 
 
 
 
 
 
 
 8- 
 
 [NCH 
 
 Z-BAR 
 
 COLL 
 
 MN. 
 
 
 
 r (min) 
 
 = 2.47 
 67.5 
 
 2.52 
 
 2.57 
 
 2.49 
 
 2.55 
 
 2.60 
 
 2.52 
 
 2.58 
 
 2.63 
 
 
 18 
 
 84.8 
 
 102.4 
 
 114.2 
 
 131.2 
 
 148.5 
 
 157.5 
 
 174.3 
 
 191.2 
 
 
 20 
 
 65.0 
 
 82.5 
 
 100.5 
 
 110.5 
 
 128.2 
 
 146.4 
 
 153.3 
 
 171.3 
 
 189.6 
 
 
 22 
 
 61.9 
 
 78 7 
 
 95.9 
 
 105.3 
 
 122.4 
 
 139.9 
 
 146.2 
 
 163.5 
 
 181.3 
 
 
 24 
 
 58.8 
 
 74.8 
 
 91.3 
 
 100.1 
 
 116.5 
 
 133.4 
 
 139.1 
 
 155.8 
 
 173.0 
 
 
 26 
 
 55.7 
 
 71.0 
 
 86.8 
 
 94.8 
 
 110.6 
 
 126.9 
 
 132.0 
 
 148.1 
 
 164.7 
 
 
 28 
 
 52.6 
 
 67.1 
 
 82.3 
 
 89.6 
 
 104.7 
 
 120.3 
 
 124.8 
 
 140.4 
 
 156.4 
 
 
 30 
 
 49.4 
 
 63.3 
 
 77.7 
 
 84.4 
 
 93.8 
 
 113.8 
 
 117.7 
 
 132.7 
 
 148.2 
 
 
 32 
 
 46.3 
 
 59.5 
 
 73.2 
 
 79.2 
 
 93.0 
 
 107.3 
 
 110.6 
 
 125.0 
 
 139.9 
 
 
 34 
 
 43.2 
 
 55.6 
 
 68.7 
 
 74.0 
 
 87.1 
 
 100.8 
 
 103.5 
 
 117.3 
 
 131.6 
 
 
 36 
 
 40.1 
 
 51.8 
 
 64.1 
 
 68.7 
 
 81.2 
 
 94.3 
 
 96.4 
 
 109.6 
 
 123.3 
 
 
 38 
 
 37.0 
 
 48.0 
 
 59.6 
 
 63.5 
 
 75.3 
 
 87.8 
 
 89.4 
 
 101.9 
 
 115.0 
 
 
 40 
 
 33.9 
 
 44.1 
 
 55.0 
 
 58.3 
 
 69.5 
 
 81.3 
 
 82.2 
 
 94.2 
 
 106.7 
 
 
302 
 
 STRENGTH OF MATERIALS. 
 
 Safe Loads in Tons (2000 Lb.) on Carnegie Z-Bar Columns 
 (Square Ends). (Continued) 
 
 10-INCH Z-BAR COLUMN. 
 
 r (min) 
 
 = 
 
 3.08 
 94.7 
 
 3.13 
 
 3.18 
 
 3.10 
 
 3.15 
 
 3.21 
 
 3.13 
 
 3.18 
 
 3.25 
 
 22 
 
 
 
 114.2 
 
 133.9 
 
 147.0 
 
 166 2 
 
 185.6 
 
 196.0 
 
 214.9 
 
 234.0 
 
 24 
 
 
 
 
 92.8 
 
 112.6 
 
 133.1 
 
 144.6 
 
 164.8 
 
 185.3 
 
 193.6 
 
 213.9 
 
 234.0 
 
 26 
 
 
 
 
 89.3 
 
 108.6 
 
 128.3 
 
 139.2 
 
 158.7 
 
 178.7 
 
 186.5 
 
 206.2 
 
 226.6 
 
 28 
 
 
 
 
 85.8 
 
 104.4 
 
 123.5 
 
 133.8 
 
 152.7 
 
 172.1 
 
 179.3 
 
 198.5 
 
 218.4 
 
 30 
 
 
 
 
 82.3 
 
 100.2 
 
 118.7 
 
 128.4 
 
 146.7 
 
 165.5 
 
 172.2 
 
 190.8 
 
 210.2 
 
 32 
 
 
 
 
 78.8 
 
 96.1 
 
 113.8 
 
 123.0 
 
 140.7 
 
 158.9 
 
 165.0 
 
 183.1 
 
 202.0 
 
 34 
 
 
 
 
 75.3 
 
 91.9 
 
 109.1 
 
 117.6 
 
 134.7 
 
 152.3 
 
 157.9 
 
 175.4 
 
 193.8 
 
 36 
 
 
 
 
 71.8 
 
 87.8 
 
 104.3 
 
 112.2 
 
 128.7 
 
 145.7 
 
 150.7 
 
 167.8 
 
 185.6 
 
 38 
 
 
 
 
 68.3 
 
 83.6 
 
 99.5 
 
 106.8 
 
 122.7 
 
 139.1 
 
 143.6 
 
 160.0 
 
 177.4 
 
 40 
 
 
 
 
 64.8 
 
 79.4 
 
 94.7 
 
 101.4 
 
 116.7 
 
 132.5 
 
 136.5 
 
 152.3 
 
 169.1 
 
 42 
 
 
 
 
 61.3 
 
 75.3 
 
 89.9 
 
 96.0 
 
 110.6 
 
 125.9 
 
 129.4 
 
 144.6 
 
 160.9 
 
 44 
 
 
 
 
 57.7 
 
 71.1 
 
 85.1 
 
 90 6 
 
 104 6 
 
 119.3 
 
 122.2 
 
 136.9 
 
 152.7 
 
 46 
 
 
 
 
 54.2 
 
 67.0 
 
 80.3 
 
 85.2 
 
 98.6 
 
 112.7 
 
 115.1 
 
 129.2 
 
 144.5 
 
 48 
 
 
 
 
 50.7 
 
 62.8 
 
 75.5 
 
 79.8 
 
 926 
 
 106.1 
 
 107.9 
 
 121.5 
 
 136.3 
 
 50 
 
 
 
 
 47.2 
 
 58.6 
 
 70.7 
 
 74.4 
 
 86.6 
 
 99.5 
 
 100.8 
 
 113.8 
 
 128.1 
 
 Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 
 Columns (Square Ends). 
 
 Dimensions and form of column given in table, p. S00. 
 
 Section: 4 Z-bars 6l/ 8 X U/i6 in- 1 Web Plate 8 X U/i6 in. 2 Side Plate 
 14 in. wide. 
 
 
 vO 
 
 <3 
 
 in 
 
 in 
 
 Tf 
 
 t 
 
 m 
 
 ■^r 
 
 rs 
 
 
 o a 
 
 cn a 
 
 
 3; a 
 
 o a 
 
 o a 
 
 <s a 
 
 oo C 
 
 -r q 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n . 
 
 
 <N " 
 
 
 II £ 
 
 II g* 
 
 II §? 
 
 II cr 
 
 II 5* 
 
 II O" 
 
 II g 1 
 
 II O* 
 
 II a 1 
 
 So 
 
 Length of 
 
 do 
 
 ®<x> 
 
 
 jC 
 
 So 
 
 SoO 
 
 Jm 
 
 ®r^ 
 
 
 ^£ 
 
 £© 
 
 "S£ 
 
 i^' 
 
 tf^O 
 
 
 fflO* 
 
 
 
 in Feet. 
 
 £ 
 
 PLl 10 
 
 Ph ,| 
 
 An^ 
 
 S' 
 
 (^m 
 
 ^7 
 
 Ph^ 
 
 Ph 
 
 
 x~£ 
 
 J^ 
 
 X;5 
 
 »VQ 
 
 x-° 
 
 y=2 
 
 X-0 
 
 x£ 
 
 .00 II 
 
 x£ 
 
 
 T 
 
 t 
 
 •* 
 
 <♦ 
 
 1- 
 
 T 
 
 T 
 
 f 
 
 T 
 
 r (min.) = 
 
 3.80 
 
 3.81 
 
 3.82 
 
 3.82 
 
 3.83 
 
 3.84 
 
 3.85 
 
 3.85 
 
 3.85 
 
 28 
 and under 
 
 294.0 
 
 304.5 
 
 315.0 
 
 325.5 
 
 336.0 
 
 346.5 
 
 357.0 
 
 367.5 
 
 378.0 
 
 30 
 
 286.6 
 
 297.2 
 
 307.7 
 
 318.3 
 
 328.9 
 
 339.5 
 
 350.0 
 
 360.4 
 
 370.9 
 
 32 
 
 277.8 
 
 288.1 
 
 298.3 
 
 308.6 
 
 3189 
 
 329.2 
 
 339.4 
 
 349.5 
 
 359.7 
 
 34 
 
 269.0 
 
 278.9 
 
 288.9 
 
 298.9 
 
 308.9 
 
 318.9 
 
 328.8 
 
 338.6 
 
 348.6 
 
 36 
 
 260.1 
 
 269.8 
 
 279.5 
 
 289.2 
 
 298.9 
 
 308.6 
 
 318.2 
 
 327.7 
 
 337.4 
 
 38 
 
 251.3 
 
 260.7 
 
 270.1 
 
 279.5 
 
 289.0 
 
 298.3 
 
 307.6 
 
 316.8 
 
 326.2 
 
 40 
 
 242.5 
 
 251.6 
 
 260.7 
 
 269.7 
 
 278.9 
 
 288.0 
 
 297.0 
 
 306.0 
 
 315.0 
 
 42 
 
 233.7 
 
 242.5 
 
 251.3 
 
 260.1 
 
 269.0 
 
 277.8 
 
 286.4 
 
 295.1 
 
 303.8 
 
 44 
 
 224.9 
 
 233.3 
 
 241.9 
 
 250.4 
 
 258.9 
 
 267.4 
 
 275.8 
 
 284.2 
 
 292.3 
 
 46 
 
 216.0 
 
 224.3 
 
 232.4 
 
 240.7 
 
 249.0 
 
 257.2 
 
 265.2 
 
 273.3 
 
 281.6 
 
 48 
 
 207.2 
 
 215.1 
 
 223.0 
 
 230.9 
 
 238.9 
 
 246.9 
 
 254.6 
 
 262.4 
 
 270.5 
 
 50 
 
 198.4 
 
 206.0 
 
 213.6 
 
 221.3 
 
 229.0 
 
 236.5 
 
 244.0 
 
 251.5 
 
 259.1 
 
PROPERTIES OF ROLLED STRUCTURAL STEEL. 303 
 
 Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 
 
 Columns (Square Ends). (Continued) 
 
 Section: 4 Z-bars 6 X 3/4 in. 1 Web Plate 8 X 3/ 4 in. 2 Side Plates 1 4 in . wide. 
 
 
 ■a- 
 
 * 
 
 m 
 
 ^r 
 
 CN 
 
 eg 
 
 — 
 
 — 
 
 
 
 
 
 
 
 
 
 o a 
 
 m C 
 
 o . 
 
 
 
 
 
 o 5 
 
 
 
 
 
 
 
 
 
 
 
 
 <N . 
 
 
 
 
 
 II » 
 
 II & 
 
 ll Sf 
 
 II o- 
 
 ll 5* 
 
 II & 
 
 II CO 
 
 II S* 
 
 7 °* 
 
 Length of 
 Column 
 
 !-■ 
 
 ^S 
 
 as"* 
 
 ta ' 
 
 
 $00 
 
 fa""* 
 
 QJ^ 
 
 K>© 
 
 in Feet. 
 
 S H 
 
 %ll 
 
 E || 
 
 &H J 
 
 S ii 
 
 53 II 
 
 Ph ii 
 
 Pw^ 
 
 E ii 
 
 
 OT-J2 
 
 ^_Q 
 
 
 TO _Q 
 
 W ,£3 
 
 3 -Q 
 
 m _Q 
 
 2 JD 
 
 c?:2 
 
 
 
 
 
 
 
 
 
 X" 
 
 X 
 
 
 T 
 
 T 
 
 Z 
 
 ^r 
 
 2 
 
 ^r 
 
 2 
 
 ■a- - 
 
 2 
 
 r (min.) = 
 
 3.75 
 
 3.76 
 
 3.77 
 
 3.78 
 
 3.79 
 
 3.80 
 
 3.80 
 
 3.81 
 
 3.82 
 
 28 
 and under 
 
 306 
 
 316.5 
 
 327.0 
 
 337.5 
 
 348.0 
 
 358.5 
 
 369.0 
 
 379.5 
 
 390.0 
 
 30 
 
 296.7 
 
 307.2 
 
 317.8 
 
 328.3 
 
 338.9 
 
 349.4 
 
 359.9 
 
 370.5 
 
 381.1 
 
 32 
 
 287.4 
 
 297.6 
 
 307.9 
 
 318.2 
 
 328.4 
 
 338.7 
 
 348.9 
 
 359.1 
 
 369.4 
 
 34 
 
 278.1 
 
 288.0 
 
 298.0 
 
 308.0 
 
 318.0 
 
 327.9 
 
 337.8 
 
 347.8 
 
 357.8 
 
 36 
 
 268.8 
 
 278.4 
 
 288.2 
 
 297.9 
 
 307.4 
 
 317.2 
 
 326.8 
 
 336.4 
 
 346.1 
 
 38 
 
 259.5 
 
 268.8 
 
 278.3 
 
 287.7 
 
 297.0 
 
 306.4 
 
 315.7 
 
 325.1 
 
 334.5 
 
 40 
 
 250.2 
 
 2593 
 
 268.4 
 
 277.5 
 
 286.5 
 
 295.6 
 
 304.7 
 
 313.7 
 
 322.8 
 
 42 
 
 240.9 
 
 249.7 
 
 258.5 
 
 267.3 
 
 276.1 
 
 284.8 
 
 293.6 
 
 302.4 
 
 311.2 
 
 44 
 
 231.6 
 
 240.1 
 
 248.6 
 
 257.1 
 
 265.6 
 
 274.1 
 
 282.5 
 
 291.0 
 
 299.6 
 
 46 
 
 222.4 
 
 230.5 
 
 238.7 
 
 246.9 
 
 255.1 
 
 263.4 
 
 271.5 
 
 279.7 
 
 287.9 
 
 48 
 
 213.0 
 
 220.9 
 
 228.8 
 
 236.8 
 
 244.7 
 
 252.6 
 
 
 
 276.2 
 
 50 
 
 203.7 
 
 211.3 
 
 219.0 
 
 226.6 
 
 234.2 
 
 241.8 
 
 
 
 264.6 
 
 Section: 4 Z-bars 61/ieX 13 /l6 in. 1 Web Plate 8 X 13/16 in. 2 Side Plates 
 14 in. wide. 
 
 
 ■o 
 
 in 
 
 in 
 
 ^r 
 
 ■*r 
 
 en 
 
 en 
 
 <N 
 
 OJ 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 00 
 
 O 
 
 & 
 
 o 
 
 o 
 
 
 <N 
 
 Ol 
 
 en 
 
 
 1-a 
 
 II .s 
 
 7 
 
 k U 
 
 " fi- 
 ll - 5 
 
 l ii-s 
 
 •;-a 
 
 °H -S 
 
 N a' 
 
 II"! 
 
 Length of 
 
 S3? 
 
 CD d* 
 
 g.S 
 
 1 ST 
 
 8i" 
 
 £ cr 
 
 s £f 
 
 cS g* 
 
 o* 
 
 Column 
 
 s^o 
 
 3^ 
 
 e3 a 1 
 
 — 0O 
 
 cjvO 
 
 rim 
 
 o3 — . 
 
 ^ao 
 
 1$o 
 
 in Feet. 
 
 &£ 
 
 Phvo 
 
 5" 
 
 Pna>" 
 
 QLi — 
 
 Sen 
 
 ss 
 
 Ph'O 
 
 Eg 
 
 jw II 
 
 
 
 
 
 
 
 
 
 
 
 
 xS 
 
 x£ 
 
 x II 
 
 05 -Q 
 X — 
 
 X-Q 
 
 X-' 
 
 x£ 
 
 x£ 
 
 x:2 
 
 
 ■* 
 
 t 
 
 "■*■ 
 
 1- 
 
 ^r 
 
 ■a- 
 
 -<r 
 
 ■* 
 
 f 
 
 (min.) = 
 
 3.73 
 
 3.74 
 
 3.75 
 
 3.76 
 
 3.77 
 
 3.78 
 
 3.78 
 
 3.79 
 
 3.80 
 
 26 
 
 and under 
 
 327.5 
 
 338.0 
 
 348.5 
 
 359.0 
 
 369.5 
 
 380.0 
 
 390.5 
 
 401.0 
 
 411.5 
 
 28 
 
 326.7 
 
 337.5 
 
 348.5 
 
 359.0 
 
 369.5 
 
 380.0 
 
 390.5 
 
 401.0 
 
 411.5 
 
 30 
 
 316.7 
 
 827.2 
 
 337.7 
 
 348.3 
 
 358.9 
 
 369.5 
 
 380.0 
 
 390.6 
 
 401.1 
 
 32 
 
 306.6 
 
 318.0 
 
 327.2 
 
 337.4 
 
 347.7 
 
 358.0 
 
 368.2 
 
 378.5 
 
 388.8 
 
 34 
 
 296.6 
 
 306.6 
 
 316.6 
 
 326.5 
 
 336.5 
 
 346.5 
 
 356.4 
 
 366.4 
 
 376.4 
 
 36 
 
 286.7 
 
 296.4 
 
 306.0 
 
 315.7 
 
 325.3 
 
 335.0 
 
 344.7 
 
 354.3 
 
 364.0 
 
 38 
 
 276.7 
 
 236.0 
 
 295.4 
 
 304.8 
 
 314.2 
 
 323.6 
 
 332.9 
 
 342.3 
 
 351.7 
 
 40 
 
 266.6 
 
 275.7 
 
 284.8 
 
 293.9 
 
 303.0 
 
 312.1 
 
 321.2 
 
 330.3 
 
 339.3 
 
 42 
 
 256.6 
 
 265.5 
 
 274.3 
 
 283.0 
 
 291.8 
 
 300.6 
 
 309.4 
 
 318.2 
 
 327.0 
 
 44 
 
 246.6 
 
 255.2 
 
 263.6 
 
 272.2 
 
 280.6 
 
 289.2 
 
 297.6 
 
 306.1 
 
 314.6 
 
 46 
 
 236.6 
 
 244.9 
 
 253.0 
 
 261.3 
 
 269.5 
 
 277.7 
 
 285.8 
 
 294.0 
 
 302.3 
 
 48 
 
 226 7 
 
 234.6 
 
 242.5 
 
 250.4 
 
 258.3 
 
 266.2 
 
 274.1 
 
 282.0 
 
 290.0 
 
 50 
 
 216.6 
 
 224.3 
 
 231.9 
 
 239.5 
 
 247.1 
 
 254.8 
 
 262.3 
 
 269.9 
 
 277.6 
 
304 
 
 STRENGTH OF MATERIALS. 
 
 Safe Load in Tons (2000 Lb.) on 14-Inch Carnegie Z-Bar 
 Columns (Square Ends). (Continued) 
 
 Section: 4 Z-bars 61/8 X7/ 8 in. 1 Web Plate 8X7/8 in. 2 Side Plates 14 in. wide. 
 
 
 0O 
 
 00 
 
 r^ 
 
 r^ 
 
 vO 
 
 vO 
 
 m 
 
 ir\ 
 
 ■<r 
 
 
 
 
 On" 
 
 
 
 
 
 On' 
 
 
 
 2d 
 
 o 
 
 O . 
 
 ?3 d 
 
 Sd 
 
 N.d 
 
 c3 d 
 
 (N d 
 
 J5.s 
 
 
 
 *!? d" 
 
 
 
 
 
 
 
 
 Length of 
 
 03 °" 
 
 Is 1 
 
 w & 
 
 |? 
 
 II ^ 
 
 to O* 
 
 
 
 II £ 
 
 Column 
 
 ^ 00 
 
 ^°" 
 
 J^. 
 
 r ^^ t - 
 
 eSiW 
 
 ^S 
 
 "cloo' 
 
 -S^ - 
 
 "S«m* 
 
 in Feet. 
 
 E«" 
 
 £<£ 
 
 Pnso 
 
 ss 
 
 £<= 
 
 PhS 
 
 E^ 
 
 ss 
 
 S^ 
 
 
 x£ 
 
 x£ 
 
 
 Sll 
 
 x£ 
 
 2 || 
 
 x~' 
 
 xfi 
 
 X- 
 
 x~' 
 
 
 <«■ 
 
 T 
 
 t 
 
 ^r 
 
 f 
 
 ^ 
 
 ■>r 
 
 T 
 
 *r 
 
 r (min.) = 
 
 3.71 
 
 3.72 
 
 3.73 
 
 3.74 
 
 3.75 
 
 3.76 
 
 '3.77 
 
 3.77 
 
 3.78 
 
 26 
 and under 
 
 349.1 
 
 359.6 
 
 370.1 
 
 380.6 
 
 391.1 
 
 401.6 
 
 412.1 
 
 422.6 
 
 433.1 
 
 28 
 
 347.4 
 
 358.3 
 
 369.1 
 
 380.0 
 
 390.9 
 
 401.6 
 
 412.1 
 
 422.6 
 
 433.1 
 
 30 
 
 336.7 
 
 347.2 
 
 357.9 
 
 368.4 
 
 378.9 
 
 389.5 
 
 400.1 
 
 410.7 
 
 421.2 
 
 32 
 
 326.0 
 
 336.3 
 
 346.6 
 
 356.8 
 
 367.1 
 
 377.3 
 
 387.6 
 
 397.9 
 
 408.2 
 
 34 
 
 315.3 
 
 325.2 
 
 335.2 
 
 345.2 
 
 355.1 
 
 365.2 
 
 375.2 
 
 385.1 
 
 395.1 
 
 36 
 
 304.5 
 
 314.2 
 
 324.0 
 
 333.6 
 
 343.3 
 
 353.0 
 
 362.7 
 
 372.4 
 
 382.0 
 
 38 
 
 293.8 
 
 303.2 
 
 312.6 
 
 322.0 
 
 331.4 
 
 340.8 
 
 350.2 
 
 359.6 
 
 369.0 
 
 40 
 
 283.1 
 
 292.2 
 
 301.3 
 
 310.4 
 
 319.5 
 
 328.6 
 
 337.7 
 
 346.8 
 
 355.9 
 
 42 
 
 272.3 
 
 281.2 
 
 290.0 
 
 298.8 
 
 307.6 
 
 316.4 
 
 325.2 
 
 334.0 
 
 342.8 
 
 44 
 
 261.6 
 
 270.2 
 
 278.7 
 
 287.2 
 
 295.7 
 
 304.2 
 
 312.7 
 
 321.2 
 
 329.8 
 
 46 
 
 250.9 
 
 259.1 
 
 267.4 
 
 275.6 
 
 283.8 
 
 292.1 
 
 300.3 
 
 308.5 
 
 316.7 
 
 48 
 
 240.2 
 
 248.1 
 
 256.1 
 
 264.0 
 
 272.0 
 
 279.8 
 
 287.8 
 
 295.7 
 
 303.6 
 
 50 
 
 229.5 
 
 237.1 
 
 244.8 
 
 252.4 
 
 260.0 
 
 267.6 
 
 275.3 
 
 283.0 
 
 290.6 
 
PKOPERTIES OF ROLLED STRUCTURAL STEEL. 305 
 
 Dimensions of and Safe Loads on Carnegie Channel 
 Columns, Tons (2000 Lb.). 
 
 Column comprises 2 Channels Latticed or with 2 Side 
 Plates. ' (Square Ends.) 
 
 h 
 
 x> 
 a 
 
 -o 1 
 55 8 
 
 
 15 
 o 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ?« 
 
 
 
 
 
 
 
 
 
 
 
 w 
 
 
 5,5 
 
 o . 
 
 
 So 
 
 o 
 
 a 
 
 § 
 
 o 
 
 M x 
 
 T3 
 
 5 
 
 x> 
 
 01 
 
 5 
 
 XI 
 
 5 
 
 s 
 
 5 
 
 5 
 
 s 
 
 3 
 
 ^ 
 
 £ 
 
 pq 
 
 6 
 
 ^ 
 
 h-1 
 
 ■51 
 
 <~ 
 
 M~ 
 
 2.32 
 
 2.32 
 
 2.32 
 
 2.32 
 
 ^~ 
 
 s? 
 
 
 
 
 
 
 
 2.33 
 
 2.32 
 
 2.32 
 
 2.32 
 
 2.32 
 
 
 
 
 
 
 
 16 
 
 28 6 
 
 52.6 
 
 58.6 
 
 64.6 
 
 70.6 
 
 76.6 
 
 82 6 
 
 88 6 
 
 94 6 
 
 
 
 
 
 
 
 18 
 
 28 1 
 
 51.7 
 
 57.5 
 
 63.^ 
 
 69.3 
 
 75.2 
 
 81 1 
 
 87 f 
 
 92 9 
 
 
 
 8 
 
 8 
 
 3 7/ 8 
 
 53/4 
 
 20 
 
 26 7 
 
 49.1 
 
 54.7 
 
 60.3 
 
 65.fi 
 
 71.4 
 
 77.( 
 
 82 6 
 
 88.2 
 
 
 
 
 
 
 
 22 
 
 25 3 
 
 46,5 
 
 51.6 
 
 57.1 
 
 62.4 
 
 67,7 
 
 73 f 
 
 78.2 
 
 83.5 
 
 
 6 
 
 
 
 
 24 
 
 23.9 
 
 43.9 
 
 48.9 
 
 53.9 
 
 58.9 
 
 63.9 
 
 68.9 
 
 73.9 
 
 78.9 
 
 
 
 
 
 
 r = 
 
 2.00 
 
 2.12 
 
 "847 
 84.2 
 
 2.13 
 
 2.14 
 
 2.15 
 
 2.16 
 
 2.17 
 
 2.18 
 
 2.18 
 
 
 
 
 
 
 14 
 16 
 
 54.7 
 53 
 
 90.7 
 90 4 
 
 
 
 
 
 96 7 
 
 107.7 
 
 108 7 
 
 1)4 7 
 
 120 7 
 
 126 7 
 
 
 
 15.5 
 
 8 
 
 »"'/« 
 
 53/ 4 
 
 18 
 
 49.9 
 
 79.7 85.6 
 
 91 5 
 
 97. A 
 
 103 3 
 
 109.2 
 
 115.1 
 
 121.0 
 
 
 
 
 
 
 
 20 
 
 46.8 
 
 75.1 80.7 
 
 86 4 
 
 92 ,0 
 
 97 6 
 
 103 2 
 
 mjt 
 
 114.^ 
 
 
 
 
 
 
 
 22 
 
 
 70.51 75.9 
 
 81.2 
 
 86.5 
 
 91.8 
 
 97.1 
 
 102.5 
 
 107.8 
 
 
 
 
 
 
 
 r = 
 
 3.11 
 
 3.03 
 
 3.02 
 
 3.01 
 
 3.00 
 
 2.99 
 
 2.98 
 
 2.98 
 
 2.97 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 22 
 
 40.2 
 
 70 2 
 
 77 7 
 
 85 2 
 
 92,7 
 
 100.7 
 
 107.7 
 
 115 2 
 
 122 7 
 
 
 
 
 
 
 
 24 
 
 39 6 
 
 68 4 
 
 75 5 
 
 82 7 
 
 89 8 
 
 97 
 
 104 1 
 
 111 7, 
 
 118 4 
 
 
 
 Hl/4 
 
 10 
 
 .l/o 
 
 71/9 
 
 26 
 
 33.1 
 
 65 7 
 
 72 6 
 
 794 
 
 86,3 
 
 93.1 
 
 100,1 
 
 106 8 
 
 1137 
 
 
 
 
 
 
 
 28 
 
 36 6 
 
 63.1 
 
 69 7 
 
 76 2 
 
 82 8 
 
 89 3 
 
 95 9 
 
 107 4 
 
 109 
 
 
 8 
 
 
 
 
 
 30 
 
 35.2 
 
 60.5 66.7 
 
 73 
 
 79 2 
 
 85 5 
 
 91 a 
 
 98 
 
 104.2 
 
 
 
 
 
 
 r = 
 
 2.77 
 
 2.83 
 
 2.84 
 
 2.84 
 
 2.84 
 
 2.84 
 
 2.84 
 
 2.85 
 
 2.85 1 
 
 
 
 
 
 
 20 
 
 75 
 
 135 
 
 142 5 
 
 150 
 
 157 5 
 
 165 
 
 172 5 
 
 180 
 
 187.5 . . . 
 
 
 
 
 
 
 22 
 
 72 9 
 
 132 6 
 
 140 
 
 147 5 
 
 154 9 
 
 162 3 
 
 169 8 
 
 177 2 
 
 184.7 ... 
 
 
 211/4 
 
 10 
 
 51/9, 
 
 71/9 
 
 24 
 
 69.8 
 
 27 2 
 
 134 3 
 
 141 5 
 
 148 6 
 
 1557 
 
 162,9 
 
 l ;o,o 
 
 177.1 ... 
 
 
 
 
 
 
 26 
 
 66.7 
 
 21 7 
 
 128 6 
 
 135 4 
 
 142.3 
 
 149.1 
 
 155.9 
 
 162.8 
 
 169.6 
 
 
 
 
 
 
 28 
 
 63.7 
 
 116.3 
 
 122.9 
 
 129.4 
 
 136.0 
 
 142.5 
 
 149.0 
 
 155.6 
 
 162.1 
 
 
 
 
 
 
 
 r = 
 
 3.87 
 
 
 3.74 
 
 3.72 
 
 3.70 
 
 3.68 
 
 3.67 
 
 3.65 
 
 3.64 
 
 3.63 
 
 
 
 
 
 
 26 
 
 
 
 
 107 5 
 
 1165 
 
 17.5 5 
 
 134 5 
 
 143 5 
 
 152 5 
 
 161 5 
 
 
 
 
 
 
 28 
 
 53 5 
 
 
 98 5 
 
 107 
 
 1157 
 
 124 4 
 
 133 1 
 
 141 8 
 
 150 5 
 
 159?. 
 
 
 
 
 
 
 30 
 
 52 6 
 
 
 95 3 
 
 103 7 
 
 1122 
 
 120 5 
 
 128 9 
 
 137,3 
 
 145.7 
 
 154 2 
 
 
 15 
 
 12 
 
 7 
 
 91/2 
 
 32 
 
 51 
 
 
 92 3 
 
 1004 
 
 108 6 
 
 1167 
 
 124 8 
 
 132.9 
 
 141.0 
 
 149.1 
 
 
 
 
 
 34 
 
 49 5 
 
 
 89 3 
 
 97.1 
 
 105.0 
 
 112,8 
 
 120.6 
 
 128.4 
 
 136.2 
 
 144.0 
 
 
 
 
 
 
 36 
 
 47.9 
 
 
 86 3 
 
 93 8 
 
 101 4 
 
 108 9 
 
 1164 
 
 123 9 
 
 131 4 
 
 139,0 
 
 n 
 
 
 
 
 
 38 
 
 46.3 
 
 
 83.3 
 
 90.5 
 
 97.8 
 
 105.0J 
 
 112.2 
 
 119.4 
 
 126.7 
 
 133.9 
 
 
 
 
 
 •I 
 
 8 
 
 dl 
 
 8 
 
 .8 
 
 rif 
 
 .8 
 
 4 
 
 
 
 
 
 
 
 
 
 •2 o3 
 
 
 — o3 
 
 03 
 
 
 
 
 
 
 
 
 
 
 
 
 
 SE 
 
 | S 
 
 .SP-i 
 
 ^Ah 
 
 ^5 
 
 §s 
 
 s^ 
 
 
 
 
 
 
 r~ 
 
 3.35 
 
 
 3.45 
 
 3.45 
 
 3.45 
 
 3.45 
 
 3.45 
 
 3.45 
 
 3.45 
 
 3.45 
 
 
 
 
 
 
 ~?T 
 
 123 5 
 
 
 ?40l 
 
 249~5 
 
 258~5 
 
 2673 
 
 2853 
 
 3033 
 
 3273 
 
 339.5 
 
 
 
 
 
 
 76 
 
 121 3 
 
 
 239 3 
 
 248 2 
 
 257.2 
 
 266.2 
 
 284.1 
 
 302.1 
 
 320.0 
 
 338.0 
 
 
 
 
 
 
 78 
 
 117 I 
 
 
 731 3 
 
 740 
 
 7.48 7 
 
 257 3 
 
 274 7 
 
 292.1 
 
 309.4 
 
 326.8 
 
 
 35 
 
 12 
 
 / 
 
 yi/ 2 
 
 30 
 
 112.9 
 
 
 723 3 
 
 731 7 
 
 7,40 1 
 
 748 5 
 
 265 2 
 
 282.0 
 
 298.8 
 
 315.5 
 
 
 
 
 
 
 3? 
 
 108 7 
 
 
 715 4 
 
 2?3 5 
 
 731 6 
 
 239 6 
 
 255.8 
 
 272.0 
 
 288.1 
 
 304.3 
 
 
 
 
 
 
 34 
 
 104 5 
 
 
 207 4 
 
 7.15 7. 
 
 7.7.3 
 
 730 8 
 
 246 3 
 
 262.0 
 
 277.5 
 
 293.1 
 
 
 
 
 36 
 
 
 . . . 199.5 
 
 207.0 
 
 214.5 
 
 222.0 
 
 236.9 
 
 251.9 
 
 266.9 
 
 28 1. s> 
 
 To above weights of column shaft add weights of rivets and lattice bars. 
 
306 
 
 STRENGTH OF MATERIALS. 
 
 Dimensions of and Safe Loads on Carnegie Channel 
 Columns, Tons (3000 Lb.). 
 
 Column comprises 2 Channels Latticed or with 2 Side 
 Plates. (Square Ends.) 
 
 c 
 
 "53 
 
 t3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 "^ i 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 °~? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 o . 
 J:2 
 
 ' 3 I 
 
 s 
 
 c 
 
 6_ 
 
 o 
 
 if -: 
 ^ 
 
 & 
 
 "S 
 
 5 
 
 o> 
 
 5 
 
 s 
 
 5 
 
 "5 
 5 
 
 5 
 
 o> 
 
 5 
 
 c3 
 
 to 
 
 
 
 
 
 
 
 r = 
 
 4.61 
 
 
 4.40 
 
 4.38 
 
 4.35 
 
 4.33 
 
 4.32 
 
 4.30 
 
 4.29 
 
 4.27 
 
 
 
 
 
 
 1>2 
 
 
 
 124.9 
 
 T35~4 
 
 145.9 
 
 15674 
 
 166^9 
 
 17774 
 
 187.9 
 
 198.4 
 
 
 
 
 
 
 34 
 
 72.4 
 
 
 123.0 
 
 133.0 
 
 142.9 
 
 152.9 
 
 162.8 
 
 172.8 
 
 182.8 
 
 192.7 
 
 
 
 
 
 
 36 
 
 70.9 
 
 
 119.7 
 
 129.4 
 
 139.1 
 
 148.8 
 
 158.4 
 
 168.1 
 
 177.8 
 
 187.4 
 
 12 
 
 201/2 
 
 14 
 
 8I/4 
 
 11 1/4 
 
 38 
 
 69.1 
 
 
 116.5 
 
 125.9 
 
 135.3 
 
 144.6 
 
 154.0 
 
 163.4 
 
 172.8 
 
 182.1 
 
 
 
 
 
 
 40 
 
 67.3 
 
 
 113.3 
 
 122.4 
 
 131.5 
 
 140.5 
 
 149.6 
 
 158.7 
 
 167.8 
 
 176.8 
 
 
 
 
 
 
 42 
 
 65.5 
 
 
 110.0 
 
 118.8 
 
 127.6 
 
 136.4 
 
 145.2 
 
 154.0 
 
 162.8 
 
 171.5 
 
 
 
 
 
 
 44 
 
 63.7 
 
 
 106.8 
 
 115.3 
 
 123.8 
 
 132.3 
 
 140.8 
 
 149.3 
 
 157.8 
 
 166.2 
 
 
 
 
 
 
 
 
 S 
 
 E 
 
 5 
 
 5 
 
 s 
 
 5 
 
 ■5 
 
 5 
 
 
 
 
 
 
 
 
 "eg 
 
 1-3 
 
 
 ,a> 
 
 
 ; 
 
 rt" 
 
 rt- 
 
 jj- 
 
 dr 
 
 
 
 
 
 
 
 
 
 — - — 
 
 — — — 
 
 — =i — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r = 
 
 4.09 
 
 4.12 
 
 4.11 
 
 4.11 
 
 4.11 
 
 4.10 
 
 4.10 
 
 4.10 
 
 4.09 
 
 
 
 
 
 
 
 30 
 
 141.1 
 
 277.6 
 
 233.1 
 
 293.6 
 
 309.1 
 
 330.1 
 
 351.1 
 
 372.1 
 
 393.1 
 
 
 
 
 
 
 
 32 
 
 133.2 
 
 272.6 
 
 232.8 
 
 293.0 
 
 303.2 
 
 323.7 
 
 344.1 
 
 364.6 
 
 385.0 
 
 
 
 
 
 
 
 34 
 
 134.2 
 
 264.9 
 
 274.8 
 
 284.8 
 
 294.7 
 
 314.5 
 
 334.4 
 
 354.2 
 
 374.1 
 
 
 12 
 
 40 
 
 14 
 
 8I/4 
 
 111/4 
 
 36 
 
 130.3 
 
 257.2 
 
 266.8 
 
 276.5 
 
 286.1 
 
 305.4 
 
 324.6 
 
 343.9 
 
 363.1 
 
 
 
 
 
 
 
 33 
 
 126.3 
 
 249.5 
 
 258.8 
 
 268.2 
 
 277.5 
 
 296.2 
 
 314.9 
 
 333.5 
 
 352.2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 To above weights of column shaft, add weights of rivets and lattice bars. 
 
 Bethlehem "Special," "Girder" and "H" Steel Beams. These 
 beams are rolled on the Grey universal beam mill, and have wider 
 flanges than the standard American forms of I-beams, which are rolled 
 in grooved rolls. The special I-beams from 8 to 24 in. in depth have 
 the same section modulus or coefficient of strength as the standard 
 forms, but on account of putting a larger proportion of metal in the 
 flanges they are 10% lighter. For equal weights of sections they have 
 a coefficient of strength about 5% greater than the standard shapes. 
 The 26, 28 and 30-in. beams are respectively equal in coefficient of 
 strength to two 20-in. 65 lb., two 20-in. 80 lb., and two 24-in. 80 lb. 
 standard beams. 
 
 The girder beams from 8 to 24 in. in depth have a coefficient of 
 strength equal to that of two standard I-beams of minimum weight of 
 the same depth, but weigh 121/2% less than the two combined. 
 
 The rolled H, or column sections are designed especially for columns of 
 buildings. All shapes having the same section number are rolled from 
 the same main rolls without change. Thus the 12-in. H column is rolled 
 in 35 different weights, the sectional areas ranging from 11.76 to 79.06 
 sq. in. 
 
 The flanges of the special and girder beams have a uniform slope of 
 12V2%, and the flanges of the H sections a uniform slope of 2%. 
 
PROPERTIES OF BETHLEHEM GIRDER BEAMS. 
 
 307 
 
 The tables of special and girder beams give the sections and weights 
 usually rolled. Intermediate and heavier weights may be obtained 
 by special arrangement. 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 in the tables are based on a maxi- 
 mum fiber stress of 16,000 lb. per sq. in., which is allowable for quies- 
 cent loads, as in buildings. For moving loads the fiber stress of 12,500 
 lb. 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 lb. per sq. in. the 
 coefficients would be one half those given in the tables. 
 
 For further information see handbook of Structural Steel Shapes, 
 Bethlehem Steel Co., South Bethlehem, Pa., 1907. 
 
 PROPERTIES OF BETHLEHEM GIRDER BEAMS. 
 
 8 
 
 03 
 
 o 
 
 o 
 
 O (B 
 1| 
 
 < 
 
 'o . 
 
 be 
 
 a 
 
 s 
 
 o o 
 G 
 
 rG 1 "" 1 
 
 T3 
 
 Neutral Axis 
 Perpendicular to 
 Web at Center. 
 
 Coeffic'nts of Strength 
 
 for Fiber Stz-ess of 
 
 ~ 16,000 Lbs. per Sq. 
 
 In. for Buildings. 
 
 rj O • 
 x = — 
 
 !£" 
 
 X G 
 o3 O 
 
 Neutral 
 Axis Coinci- 
 dent with 
 Center Line 
 of Web. 
 
 Q 
 
 G oj 
 CD •- 
 
 1 s 
 
 I 
 
 3 >>G 
 
 IS'l 
 
 r 
 
 s 
 
 a os 
 
 § ° v 
 
 V 
 
 
 30 
 
 30 
 
 200.0 
 175.0 
 
 58.85 
 51.35 
 
 0.75 
 
 .68 
 
 15.00 
 12.00 
 
 9154.7 
 7851.8 
 
 12.47 
 12.37 
 
 610.3 
 523.5 
 
 6,510,000 
 5,583,500 
 
 95.2 
 81.1 
 
 599.7 
 
 346.4 
 
 3.19 
 2.60 
 
 28 
 28 
 
 180.0 
 162.5 
 
 52.98 
 47.81 
 
 .69 
 .65 
 
 14.35 
 12.00 
 
 7269.0 
 6465 . 1 
 
 11.72 
 11.63 
 
 519.2 
 461.8 
 
 5,538,200 
 4,925,800 
 
 81.3 
 73.8 
 
 507.6 
 328.2 
 
 3.09 
 2.62 
 
 26 
 26 
 
 160.0 
 150.0 
 
 47.00 
 44.13 
 
 .63 
 .62 
 
 13.60 
 12.00 
 
 5618.7 
 5200.4 
 
 10.93 
 10.86 
 
 432.2 
 400.0 
 
 4,610,200 
 4,267,000 
 
 68.3 
 66.6 
 
 414.5 
 306.5 
 
 2.97 
 2.63 
 
 24 
 24 
 
 140.0 
 120.0 
 
 41.03 
 35.31 
 
 .56 
 .51 
 
 13.00 
 12.00 
 
 4241.9 
 3630.7 
 
 10.17 
 
 10.14 
 
 353.5 
 302.6 
 
 3,770,700 
 3,227,200 
 
 54.9 
 46.5 
 
 338.3 
 240.0 
 
 2.87 
 2.61 
 
 20 
 20 
 
 140.0 
 112.0 
 
 41.28 
 32.88 
 
 .64 
 .52 
 
 12.50 
 12.00 
 
 2938.3 
 2368.9 
 
 8.44 
 8.49 
 
 293.8 
 236.9 
 
 3,134,200 
 2,526,700 
 
 62.4 
 45.6 
 
 334.3 
 232.8 
 
 2.85 
 2.66 
 
 18 
 
 92.0 
 
 27.09 
 
 .47 
 
 11.50 
 
 1595.3 
 
 7.67 
 
 177.3 
 
 1,890,800 
 
 37.1 
 
 172.4 
 
 2.52 
 
 15 
 
 15 
 15 
 
 140.0 
 104.0 
 73.0 
 
 41.28 
 30.58 
 21.52 
 
 .80 
 .60 
 
 .42 
 
 11.75 
 11.25 
 10.50 
 
 1591.5 
 1219.7 
 886.5 
 
 6.21 
 6.32 
 6.42 
 
 212.2 
 162.6 
 118.2 
 
 2,263,500 
 1,734,700 
 1,260,900 
 
 67.3 
 47.4 
 28.8 
 
 319.2 
 203.3 
 116.6 
 
 2.78 
 2.58 
 2.33 
 
 12 
 
 12 
 
 70.0 
 55.0 
 
 20.60 
 16.12 
 
 .445 
 .35 
 
 10.00 
 9.75 
 
 540.9 
 432.0 
 
 5.12 
 5.18 
 
 90.2 
 72.0 
 
 961,600 
 768,000 
 
 28.0 
 
 19.7 
 
 109.5 
 76.1 
 
 2.31 
 2.17 
 
 10 
 9 
 8 
 
 44.0 
 38.0 
 32.5 
 
 12.95 
 11.18 
 9.52 
 
 .30 
 .29 
 
 .28 
 
 9.00 
 8.50 
 8.00 
 
 244.3 
 169.8 
 113.9 
 
 4.34 
 3.90 
 3.46 
 
 48.9 
 37.7 
 
 28.5 
 
 521,200 
 402,500 
 303,800 
 
 14.3 
 12.8 
 11.4 
 
 53.6 
 
 40.7 
 30.3 
 
 2.03 
 1.91 
 1.78 
 
 W = Safe load in pounds uniformly distributed including weight of beam. 
 L = Span in feet. M = Moment offerees in foot-pounds. /= fiber stress, 
 W= C/L; M = C/8 ; C = WL = 8 M = 2/ 3 fS, 
 
308 
 
 STRENGTH OF MATERIALS. 
 
 Properties of Bethlehem Sp2cial I Beams. 
 
 s 
 
 ffl i 
 
 o 
 
 o ■ 
 
 O <u 
 
 0) fl 
 
 02 h-1 
 
 < 
 
 o 
 
 H 
 
 a 
 
 Neutral Axis 
 Perpendicular to 
 Web at Center. 
 
 Coeffic'ntsof Strength 
 
 for Fiber Stress of 
 
 O 16,000 Lbs. per Sq. 
 
 In. for Buildings. 
 
 02.S 
 
 3 0-^ 
 cS go 
 
 Neutral 
 Axis Coin- 
 cident with 
 Center Line 
 
 of Web. 
 
 ° c 
 
 03 
 
 Q 
 
 <x> .5 
 
 o o> 
 
 i 
 
 r 
 
 .0,3 . 
 
 z : ~ 
 
 S 
 
 1 i 
 i' 
 
 2 >A 
 r' 
 
 30 
 
 28 
 26 
 24 
 
 120.0 
 105.0 
 90.0 
 84.0 
 
 35.25 
 31.04 
 26.63 
 24.79 
 
 0.52 
 .48 
 .44 
 
 .45 
 
 10.00 
 9.60 
 9.15 
 8.85 
 
 5271 
 4089 
 3043 
 2392 
 
 12.23 
 11.43 
 10.71 
 9.82 
 
 351.4 
 292.1 
 234.1 
 199.3 
 
 3,748,200 
 3,115,700 
 2,496,900 
 2,125,900 
 
 48.7 
 41.5 
 34.9 
 36.3 
 
 149.7 
 122.6 
 93.4 
 82.0 
 
 2.11 
 1.98 
 1.87 
 1.82 
 
 24 
 24 
 
 82.0 
 72.0 
 
 24.33 
 21.21 
 
 .50 
 .37 
 
 8.83 
 8.70 
 
 2240 
 2091 
 
 9.60 
 9.93 
 
 186.7 
 174.2 
 
 1,991,600 
 1,858,100 
 
 43.8 
 24.4 
 
 71.1 
 67.7 
 
 1.71 
 1.79 
 
 20 
 20 
 
 82.0 
 72.0 
 
 24.23 
 21.43 
 
 .57 
 .43 
 
 8.51 
 8.37 
 
 1561 
 1468 
 
 8.03 
 8.28 
 
 156.1 
 146.8 
 
 1,665,400 
 1,565,800 
 
 51.5 
 32.7 
 
 71.5 
 67.6 
 
 1.72 
 1.78 
 
 20 
 20 
 20 
 20 
 
 68.0 
 63.0 
 60.0 
 58.5 
 
 19.95 
 
 18.55 
 17.65 
 17.15 
 
 .49 
 .42 
 .375 
 .35 
 
 7.69 
 7.62 
 7.58 
 7.55 
 
 1270 
 1223 
 1193 
 1176 
 
 7.98 
 8.12 
 8.22 
 8.28 
 
 127.0 
 122.3 
 119.3 
 117.6 
 
 1,354,600 
 1,304,500 
 1,272,600 
 1,254,800 
 
 40.4 
 31.1 
 25.3 
 
 22.2 
 
 45.7 
 44.3 
 43.4 
 43.0 
 
 1.51 
 1.54 
 1.57 
 
 1.58 
 
 18 
 18 
 18 
 
 58.5 
 52.5 
 48.5 
 
 17.29 
 15.40 
 14.23 
 
 .48 
 .373 
 .31 
 
 7.47 
 7.37 
 7.30 
 
 883.6 
 832.9 
 801.3 
 
 7.15 
 7.35 
 7.50 
 
 98.2 
 92.5 
 89.0 
 
 1,047,500 
 987,200 
 949,800 
 
 37.4 
 24.8 
 17.4 
 
 35.9 
 34.4 
 33.4 
 
 1.44 
 1.49 
 1.53 
 
 15 
 
 72.0 
 
 21.27 
 
 .54 
 
 7.15 
 
 797.9 
 
 6.13 
 
 106.4 
 
 1,134,800 
 
 41.2 
 
 55.1 
 
 1.61 
 
 15 
 15 
 
 64.0 
 54.0 
 
 18.85 
 15.85 
 
 .60 
 .40 
 
 7.20 
 7.00 
 
 666.8 
 610.5 
 
 5.95 
 6.21 
 
 88.9 
 81.4 
 
 948,100 
 868,100 
 
 46.6 
 26.5 
 
 40.8 
 37.2 
 
 1.47 
 1.53 
 
 15 
 15 
 15 
 
 46.0 
 42.0 
 38.0 
 
 13.46 
 12.41 
 11.21 
 
 .43 
 .36 
 
 .28 
 
 6.81 
 6.74 
 6.66 
 
 484.6 
 464.9 
 442.4 
 
 5.99 
 6.12 
 6.28 
 
 64.6 
 62.0 
 59.0 
 
 689,200 
 661,200 
 629,200 
 
 29.1 
 22.1 
 14.2 
 
 24.2 
 23.4 
 22.5 
 
 1.34 
 1.37 
 1.42 
 
 12 
 
 36.0 
 
 10.63 
 
 .31 
 
 6.30 
 
 270.2 
 
 5.04 
 
 45.0 
 
 480,300 
 
 16.2 
 
 20.4 
 
 1.38 
 
 12 
 12 
 
 31.0 
 28.5 
 
 9.13 
 8.41 
 
 .31 
 
 .25 
 
 6.16 
 6.10 
 
 225.2 
 216.6 
 
 4.97 
 5.07 
 
 37.5 
 36.1 
 
 400,300 
 385,000 
 
 16.0 
 11.2 
 
 14.7 
 14.2 
 
 1.27 
 1.30 
 
 10 
 10 
 10 
 
 27.5 
 24.5 
 22.5 
 
 8.05 
 7.15 
 6.65 
 
 34 
 .25 
 .20 
 
 5.94 
 5.85 
 5.80 
 
 134.6 
 127.1 
 122.8 
 
 4.09 
 4.22 
 4.27 
 
 26.9 
 25.4 
 24.6 
 
 287,300 
 271,300 
 262,000 
 
 16.7 
 10.6 
 7.3 
 
 11.7 
 11.1 
 10.8 
 
 1.20 
 1.24 
 1.27 
 
 9 
 9 
 9 
 
 23.0 
 21.0 
 19.0 
 
 6.76 
 6.22 
 5.68 
 
 .31 
 .25 
 .19 
 
 5.50 
 
 5.44 
 5.38 
 
 92.4 
 
 88.8 
 85.1 
 
 3.70 
 3.78 
 3.87 
 
 20.5 
 19.7 
 
 18.9 
 
 219,100 
 210,300 
 201,800 
 
 13.8 
 10.0 
 6.5 
 
 8.5 
 8.2 
 7.9 
 
 1.12 
 1.15 
 1.18 
 
 8 
 8 
 8 
 
 21.25 
 18.00 
 16.25 
 
 6.25 
 5.37 
 4.81 
 
 .36 
 .25 
 .18 
 
 5.37 
 5.26 
 5.19 
 
 64.7 
 60.0 
 57.0 
 
 3.22 
 3.34 
 
 3.44 
 
 16.2 
 15.0 
 14.3 
 
 172,500 
 160,000 
 152,000 
 
 15.3 
 9.5 
 5.7 
 
 6.8 
 6.4 
 6.1 
 
 1.05 
 1.09 
 1.12 
 
 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 = CIS; C = WL = 8M = 2/ 3 /£. 
 
PROPERTIES OF BETHLEHEM GIRDER BEAMS. 
 
 309 
 
 Dimensions and Properties of Bethlehem Rolled Steel. 
 14-Ineh H Columns. 
 
 Table greatly condensed from original.* 
 
 
 3" 
 
 Dimensions in 
 
 a 
 
 Axis Perpen. to 
 
 Axis Center of 
 
 fl3 
 
 
 
 Inches. 
 
 2 »3 
 
 Web. 
 
 
 Web. 
 
 J2 
 B 
 3 
 
 3 
 
 o 
 
 01 
 
 m 
 
 18 
 
 o§3 
 
 1- 
 '53^ 
 
 
 
 oj"S 
 
 
 
 
 .3 
 a 
 
 CD 
 
 Q 
 
 03 M 
 
 
 i— * 
 
 3 0j 
 
 is 
 
 3 
 
 Jl 
 
 .2 
 - * 
 
 B ® 
 
 O 3 
 
 .2-2 
 
 It 
 
 H14s 
 
 42.6 
 
 133/ 8 
 
 V? 
 
 8.00 
 
 0.33 
 
 12.53 
 
 400.8 
 
 59.9 
 
 5.66 
 
 43.6 
 
 10.9 
 
 1.87 
 
 93.7 
 
 14 
 
 13/16 
 
 13.00 
 
 .51 
 
 27.56 
 
 1004.7 
 
 143.5 
 
 6.04 
 
 288.5 
 
 44.4 
 
 3.24 
 
 H14 
 
 98.8 
 
 14 
 
 13/1 fi 
 
 14.00 
 
 .51 
 
 29.06 
 
 1070.6 
 
 153.0 
 
 6.07 
 
 355.9 
 
 50.8 
 
 3.50 
 
 162.2 
 
 15 
 
 I -Vie 
 
 14.31 
 
 .82 
 
 47.71 
 
 1894.0 
 
 252.5 
 
 6.31 
 
 625.1 
 
 87.4 
 
 3.62 
 
 H14a 
 
 164.4 
 
 15 
 
 1 5/1 B 
 
 14 57 
 
 87, 
 
 48 36 
 
 1924.7 
 
 256.6 
 
 6 32 
 
 659.8 
 
 90.6 
 
 3.69 
 
 222.3 
 
 157/ 8 
 
 1 3/ 4 
 
 14.84 
 
 1.09 
 
 65.39 
 
 2774.5 
 
 349.5 
 
 6.51 
 
 936.6 
 
 126.2 
 
 3.78 
 
 H14b 
 
 230.8 
 
 16 
 
 1 13/1 fi 
 
 14 88 
 
 1 13 
 
 67 89 
 
 2905.9 
 
 363.2 
 
 6 55 
 
 978.7 
 
 131.5 
 
 3.80 
 
 291.2 
 
 167/ 8 
 
 2 1/4 
 
 15.16 
 
 1.41 
 
 85.63 
 
 3897.7 
 
 462.0 
 
 6.75 
 
 1290.7 
 
 170.3 
 
 3.88 
 
 13-Inch H Columns. 
 
 41.2 
 86.6 
 
 123/g 
 13 
 
 1/2 
 13/16 
 
 8.00 
 12.04 
 
 0.33 
 .51 
 
 12.12 
 
 25.48 
 
 334.5 
 793.6 
 
 54.1 
 122.1 
 
 5.25 
 5.58 
 
 43.2 
 229.9 
 
 10.8 
 38.2 
 
 91.5 
 150.5 
 
 13 
 14 
 
 13/16 
 1 5/16 
 
 13.00 
 13.31 
 
 .51 
 .82 
 
 26.93 
 44.27 
 
 847.9 
 1511.4 
 
 130.5 
 215.9 
 
 5.61 
 
 5.84 
 
 286.7 
 504.9 
 
 44.1 
 75.9 
 
 156.4 
 219.8 
 
 14 
 15 
 
 1 5/ie 
 1 13/16 
 
 14.00 
 14.31 
 
 .82 
 
 1.13 
 
 45.99 
 64.64 
 
 1581.6 
 2404.9 
 
 225.9 
 320.7 
 
 5.86 
 6.10 
 
 585.1 
 870.2 
 
 83.6 
 121.6 
 
 226.5 
 285.9 
 
 15 
 
 157/ 8 
 
 1 13/16 
 
 2 1/4 
 
 14.88 
 15.16 
 
 1.13 
 1.41 
 
 66.62 
 84.09 
 
 2492.7 
 3361.9 
 
 332.4 
 423.6 
 
 6.12 
 6.32 
 
 975.8 
 1287.6 
 
 131.2 
 169.9 
 
 12-Inch H Columns. 
 
 40.0 
 73.4 
 
 111/2 
 12 
 
 1/2 
 3/4 
 
 8.00 
 11.04 
 
 0.33 
 .47 
 
 78.0 
 132.5 
 
 12 
 13 
 
 3/4 
 11/4 
 
 12.00 
 12.31 
 
 .47 
 .78 
 
 138.1 
 197.1 
 
 13 
 14 
 
 11/4 
 13/4 
 
 13.00 
 13.31 
 
 .78 
 1.09 
 
 204.9 
 268.8 
 
 14 
 15 
 
 13/4 
 
 21/4 
 
 14.00 
 14.32 
 
 1.09 
 1.41 
 
 11.76 
 21.60 
 
 40.61 
 57.96 
 
 60.27 
 79.06 
 
 282.1 
 572.8 
 
 1198.8 
 1862.2 
 
 1950.8 
 2777.0 
 
 41.9 
 95.5 
 
 102.6 
 175.6 
 
 184.4 
 266.0 
 
 278.7 
 370.3 
 
 42.8 
 163.7 
 
 446.4 
 676.6 
 
 784.8 
 1086.2 
 
 * Only the minimum and maximum weights of each section number 
 are given here. The original table gives many intermediate weights. 
 
310 
 
 STRENGTH OF MATERIALS. 
 
 Dimensions and Properties of Bethlehem Rolled Steel. 
 11-Ineh H Columns. 
 
 J2 
 
 o 
 
 01 o 
 
 'o £ 
 •g ft 
 
 'IS 
 
 Dimensions in 
 Inches. 
 
 
 
 Axis 
 
 Perpen. to 
 
 Web. 
 
 Axis 
 
 Center of 
 Web. 
 
 a 
 m 
 
 ft 
 & 
 
 
 8) 
 
 «° 
 
 8.00 
 10.03 
 
 11.00 
 11.31 
 
 12.00 
 12.32 
 
 0.32 
 .43 
 
 .43 
 
 .74 
 
 .74 
 
 1.06 
 
 %£ 
 
 v If 
 
 as 
 £L M 
 
 234.1 
 401.2 
 
 434.6 
 843.1 
 
 889.4 
 1417.0 
 
 3 
 
 "S o 
 l § 
 
 44.1 
 73.0 
 
 79.0 
 140.5 
 
 148.2 
 218.0 
 
 oo 
 
 
 
 11 
 
 HI1 s 
 
 H1I 
 
 Hlla 
 
 38.4 
 61.3 
 
 65.5 
 115.5 
 
 120.9 
 175.8 
 
 I05/ 8 
 11 
 
 11 
 12 
 
 12 
 13 
 
 1/2 
 U/16 
 
 H/16 
 • 3 /l6 
 
 1 3/ie 
 Hl/16 
 
 11.30 
 
 18.02 
 
 19.26 
 33.98 
 
 35.54 
 51.70 
 
 4.55 
 4.72 
 
 4.75 
 4.98 
 
 5.00 
 
 5.24 
 
 42.4 
 112.6 
 
 147.0 
 280.7 
 
 333.5 
 517.9 
 
 10.6 
 
 22.4 
 
 26.7 
 49.6 
 
 55.6 
 84.1 
 
 1.94 
 2.50 
 
 2.76 
 2.87 
 
 3.06 
 3.17 
 
 
 
 
 
 10-Inch H Columns. 
 
 
 
 
 
 HlOs 
 
 37.2 
 50.6 
 
 9 3/ 4 
 10 
 
 1/2 
 5/8 
 
 8.00 
 9.04 
 
 0.32 
 .40 
 
 10.95 
 
 14.88 
 
 192.0 
 272.5 
 
 39.4 
 54.5 
 
 4.19 
 
 4.28 
 
 41.9 
 75.1 
 
 ,0.5 
 16.6 
 
 1.96 
 2.25 
 
 H10 
 
 54.1 
 99.7 
 
 10 
 
 11 
 
 5/8 
 H/8 
 
 10.00 
 10.31 
 
 .39 
 .70 
 
 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 
 
 HlOa 
 
 104.7 
 155.2 
 
 11 
 
 12 
 
 H/8 
 15 /8 
 
 11.00 
 11.32 
 
 .70 
 
 1.02 
 
 30.80 
 45.64 
 
 643.6 
 1053.6 
 
 117.0 
 175.6 
 
 4.57 
 4.80 
 
 243.7 
 387.2 
 
 44.3 
 68.4 
 
 2.81 
 2.91 
 
 
 
 
 
 9-Inch H Columns. 
 
 
 
 
 
 H9s 
 
 28.8 
 40.6 
 
 8 3/ 4 
 9 
 
 7/16 
 9/16 
 
 7.00 
 8.04 
 
 0.28 
 .36 
 
 8.46 
 11.95 
 
 119.3 
 177.0 
 
 27.3 
 39.3 
 
 3.76 
 3.85 
 
 24.7 
 47.6 
 
 7.0 
 11.8 
 
 1.71 
 2.00 
 
 H9 
 
 43.8 
 85.3 
 
 9 
 10 
 
 9/16 
 U/16 
 
 9.00 
 9.32 
 
 .35 
 .67 
 
 12.88 
 25.08 
 
 194.7 
 424.6 
 
 43.3 
 84.9 
 
 3.89 
 4.11 
 
 65.9 
 140.9 
 
 14.6 
 30.2 
 
 2.26 
 2.37 
 
 H9a 
 
 90.0 
 135.6 
 
 10 
 11 
 
 U/16 
 19/16 
 
 10.00 
 10.31 
 
 .67 
 .98 
 
 26.46 
 39.87 
 
 452.6 
 762.8 
 
 90.5 
 138.7 
 
 4.14 
 4.38 
 
 173.1 
 281.6 
 
 34.6 
 54.6 
 
 2.56 
 2.66 
 
 8-Inch H Columns. 
 
 27.7 
 31.8 
 
 77/g 
 8 
 
 7/16 
 
 1/2 
 
 7.00 
 7.04 
 
 0.28 
 .32 
 
 8.15 
 9.35 
 
 93.6 
 109.1 
 
 23.8 
 27.3 
 
 3.39 
 3.42 
 
 24.4 
 28.5 
 
 7.0 
 8.1 
 
 34.6 
 71.6 
 
 8 
 9 
 
 1/2 
 1 
 
 8.00 
 8.32 
 
 .31 
 .63 
 
 10.17 
 21.05 
 
 121.5 
 285.6 
 
 30.4 
 63.5 
 
 3.46 
 3.68 
 
 41.1 
 94.4 
 
 10.3 
 
 22.7 
 
 76.0 
 117.1 
 
 9 
 10 
 
 1 
 
 11/2 
 
 9.00 
 9.31 
 
 .63 
 .94 
 
 22.35 
 34.45 
 
 306.8 
 535.9 
 
 68.2 
 107.2 
 
 3.70 
 3.94 
 
 118.9 
 199.3 
 
 26.4 
 42.8 
 
TORSIONAL STRENGTH. 311 
 
 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 
 
 c = 1/2 d; 
 
 StITp 
 
 3 s; ^=y-s" 
 
 For hollow sMafts of external diameter d and internal diameter d lt 
 Pa = 0.1963 ,, * S; d 
 
 For a rectangular bar in which b and d are the long and short sides of 
 the rectangle, Pa = 0.2222 bd 2 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 S is about the same as the 
 direct shearing resistance, and may be taken at 20,000 to 25,000 lbs. per 
 square inch for cast iron, 45,000 lbs. for wrought iron, and 50,000 to 
 150,000 lbs. 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, 6 = angle through which the free end of the shaft is twisted, 
 measured in arc of radius = 1. 
 
 For a cylindrical shaft, 
 
 _ n6Gd\ ._ 32 Pal . 32 Pal . 32 
 
 Fa -"32T' d -~nd*G' G -~e^F' v- 10 - 186 - 
 If a = angle of torsion in degrees, 
 
 _a^. 180 6 180 X 32 Pal _ 583.6 Pal 
 
 ~ 180' a it nWG d 4 G 
 
 The value of G is given by different authorities as from 1/3 to 2/5 of E, 
 the modulus of elasticity for tension. For steel it is generally taken as 
 12,000,000 lbs. per sq. in. 
 
312 STRENGTH OF MATERIALS. 
 
 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 -5- 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 -s- A) + S. A beam to resist com- 
 bined tension and flexure should be designed so that (P -f- A) \ + S shall 
 not exceed the proper allowable working unit stress. 
 
 Combined Compression and Flexure. — If P -s- 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 -h A) + S. 
 
 Combined Tension (or Compression) and 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 = ± vV+ V4P 2 , Maximum shearing unit stress; 
 Max. t = V2P+^v 2 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 = V2S 4- V ' S s 2 + 1/1S 2 ; 
 Max. shear s = ±^S S 2 + 1/4SP. 
 
 Equivalent bending moment = 1/2 M 4- 1/2 ^ M 2 + T 2 , where M = bending 
 moment and T= torsional moment. 
 
 Formula for diameter of a round shaft subjected to transverse load 
 while transmitting a given horse-power (see also Shafts of Engines): 
 
 31 , 16 ./A 
 
 16 M , 16 JM 2 , 402,500,000/7 2 
 
 d 3 = — h -r Vt ^ 9 ' 
 
 * n 2 n 2 
 
 where M = maximum bending moment of the transverse forces in 
 pound-inches, H = horse-power transmitted, n = No. of revs, per minute, 
 and t = the safe allowable tensile or compressive working strength of 
 the material. 
 
 Gues t's For mula for maximum tension or compression unit stress is 
 t = *SS S 2 +S 2 {Phil. Mag., July, 1900). It is claimed by many writers to 
 be more accurate th an Ran kine's formula, given above. Equivalent 
 bending moment = v'mHP. (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 
 
 7id z " n 2 d 2 rM* 
 
 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 = dl. 
 
 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.. ..(=0.0000065. 
 
STRENGTH OF FLAT PLATES. 313 
 
 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 = 1 X 0.0000065 X 100 X 
 30,000,000 = 19,500 lbs. Suppose the bar is under tension of 19,500 
 lbs. 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, 
 
 5r 2 , t/ErZp 6 ft 2 
 
 For a circular plate fixed at the edge, uniformly loaded, 
 
 t/2£5- p , 
 
 ▼ 3 / ' p 
 
 _w.. 
 
 ' 3f 2 i 
 
 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 Vp t = 0.0163300 r ^p_ 
 
 Wrought iron t = 0.0117850 r \ / p_ t = 0.^)105410 r ^p 
 
 Steel t = 0.0091287 r Vp t = 0.0081649 r ^p 
 
 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 r : 
 
 \6 7 / Ttt* Ttt" 
 
 
 - = 10 20 30 40 
 
 50; 
 
 c = 4.07 5.00 5.53 5.92 
 
 6.22; 
 
 f=V /cP p = ^. 
 
 
 The above formulse 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 formula 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 of 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.] 
 
314 STRENGTH OF MATERIALS. 
 
 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 Vp, and for circular plates T = 0.00439 flVp, where T = 
 thickness of plate, S = side of the square, D = diameter of the circle, 
 and p = pressure in lbs. per sq. in. Professor Harkness, however, 
 doubts the value of the rules, and says that no satisfactory theoretical 
 solution has yet been obtained. 
 
 The Strength of Unstayed Flat Surfaces. — Robert Wilson 
 (Eng'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 Ion? 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., applv only within the elasiic 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 comes largely from theory. 
 Experiments have been made on small plates Vi6 of an inch thick, 
 
STRENGTH OF FLAT PLATES. 315 
 
 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 well 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 ot 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 
 given below, with the calculated pressure, by his rule, for comparison. 
 
 1. An unstayed flat boiler-head is 341/2 inches in diameter and 9/ ]6 
 inch thick. What is its bursting pressure? The area of a circle 341/2 
 inches in diameter is 935 square inches: then 9/i6 x 44,800 X 10 = 
 252,000, and 252,000 -*- 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 +- 935 
 = 180 pounds, calculated bursting pressure. This head actually burst 
 at 200 pounds. 
 
 3. Head 26 1/4 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 28 1/2 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. . 
 Plate bulged 
 
 10 
 
 20 
 
 40 
 
 80 
 
 120 
 
 140 
 
 170 
 
 200 
 
 L/32 
 
 1/16 
 
 1/8 
 
 1/4 
 
 3/8 
 
 1/2 
 
 5/8 
 
 3/4 
 
 The pressure was now reduced to zero, and the end sprang back 3/ 16 
 inch, leaving it with- a permanent set of 9/ 16 inch. The pressure of 
 200 lbs. 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 lbs. per square inch. Each stay supports pa 2 lbs. The 
 greatest stress on the plate is 
 
 ' 9P ' 
 
 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 between the frames or other 
 rigid supports, and let d represent the depth m 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 t/d, D should not be greater than 
 
316 
 
 STRENGTH OF MATERIALS. 
 
 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- 
 
 Depth 
 
 Spacing of 
 
 Thick- 
 
 Depth of 
 Water. 
 
 Maximum Spac- 
 
 ness of 
 
 below 
 
 Frames should 
 
 ness of 
 
 ing of Rigid 
 
 Plating. 
 
 Water. 
 
 not exceed 
 
 Plating. 
 
 Stiff en ers. 
 
 in. 
 
 ft. 
 
 in. 
 
 in. 
 
 ft. 
 
 ft. in. 
 
 V2 
 
 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 
 
 1/4 
 
 10 
 
 " 20 
 
 1/4 
 
 10 
 
 9 8 
 
 1/4 
 
 5 
 
 " 40 
 
 1/8 
 
 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 V4^d' 2 p. Let *S' = safe tensile stress per 
 square inch, and t the thickness of metal in inches; then the resistance 
 to the pressure will be ndt S. Since the resistance must be equal to the 
 pressure, 
 
 1/4 7td 2 p = 7tdtS. Whence t = £| . 
 
 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 h- 25; but the thickness of a hemispherical 
 head of the same diameter is t = pd -*- AS. Hence if we make the 
 radius of curvature of a domed head equal to the diameter of the boiler, 
 
 we shall have t = -j~ = -^ , or the thickness of such a domed head 
 
 will be equal to the thickness of the shell. 
 
 THICK HOLLOW CYLINDERS UNDER TENSION. 
 
 Lamp's formula, which is generally used, gives 
 
 f ( h + p \h 
 l \\T^p) 
 
 h = P : 
 
 t = thickness; n= inside and ri = outside radius; 
 h = maximum allowable hoop tension at the 
 
 interior of the cylinder; 
 p = intensity of interior pressure; 
 s = tension at the exterior of the cylinder. 
 
 •■ p - 
 
 2n 2 
 
STEEL ROLLERS AND BALLS. 317 
 
 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. 
 
 s = p 9 2n , = 4000 X .J? X \ 6 g = 4000 lbs. per sq. in. 
 T2 2 — TV 48-16 
 
 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 
 for 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. 
 
 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 ^-r— = — ^ — ; 
 
 4Ttc 
 
 whence p = —rz — • 
 
 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. — (Merri- 
 man, Mech. of Matls.) 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/ s idS (2 S/£)i 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<2, 
 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 Crandall 
 
318 STRENGTH OF MATERIALS. 
 
 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 
 Roller Bearings.) 
 
 Spherical Rollers. — With the same notat ion as above, d being the 
 diameter of the sphere, S = ^WElV.i nd?\ W = 1/4 nd 2 S 2 /E. The 
 diameter of a sphe re to ca rry a given load with an allowable unit- 
 stress S is d = 2 \/WE/xS 2 . 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 lbs. per square inch, t = thickness of cylinder, 
 d = diameter, and I = length, all in inches; or, 
 
 p = 806,300 j^, if Lis in feet .... (2) 
 
 He recommends the simpler formula 
 
 Id 
 
 (3) 
 
 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 (3) was until about 1 908 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., 
 
 P- 8 -^- (4) 
 
 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 t 2 
 
 (L+l)d {o) 
 
 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. (6) 
 
 In formulae (4), (5), (6) 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 (4) is the same as formula (3), 
 with a factor of safety of 9. In formula (5) the length L is increased 
 by 1; the influence which this addition has on the value of P is, of 
 course, greater for short tubes than for long ones. 
 
 Nystrom has deduced from Fairbairn's experiments the following 
 formula for the collapsing strength of flues: 
 
 4 TV 
 
 P = 7-' (7) 
 
 rfVL 
 where p, t, and d have the same meaning as in formula (1), L is the length 
 in feet, and T is the tensile strength of the metal in pounds per square 
 inch. 
 
 If we assign to T the value 50,000, and express the length of the flue in 
 inches-, equation (7) assumes the following form, viz., 
 
 V = 692,800 -!—-- • (8) 
 
 dVl 
 
RESISTANCE OF HOLLOW CYLINDERS. 319 
 
 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.) 
 
 Formulae (1), (4), and (8) 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/i6 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. At the collapsing pres- 
 sures the flues experienced compressions ranging from 1.53 to 2.17 tons, 
 or a mean compression of 1.82 tons per square inch of section. From 
 these data Clark deduced the following formula "for the average resist- 
 ing force of common boiler-flues," viz., 
 
 p . (2 («|0?_5oo) (9) 
 
 where p is the collapsing pressure in pounds per square inch, and d and t 
 are the diameter and thickness expressed in inches. 
 
 Clark (S. E., vol. i. p. 643) says : The resistance to collapse of plain- 
 riveted flues is directly as the square of the thickness of the plate, and 
 inversely as the square of the diameter. The support of the two ends 
 of the flue does not practically extend over a length of tube greater than 
 twice or three times the diameter. The collapsing pressure of long 
 tubes is therefore practically independent of the length. Instances of 
 collapsed flues of Cornish and Lancashire boilers collated by Clark, 
 showed that the resistance to collapse of flues of 3/ 8 -inch plates, 18 to 
 43 feet long, and 30 to 50 inches diameter, varied as the 1.75 power of 
 the diameter. Thus, 
 
 for diameters of 30 35 40 45 50 inches, 
 
 the collapsing pressures were 76 58 45 37 30 lbs. per sq. in. 
 
 for 7/ 16 -inch plates the collapsing 
 
 pressures were 60 49 42 lbs. per sq. in. 
 
 C. R. Roelker, in Van Nostrand's Magazine, March, 1881, says that 
 Nystrom's formula, (8), 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. 
 
 For collapsing pressures of plain iron flue-tubes of Cornish and Lanca- 
 shire steam-boilers, Clark gives: 
 
 200,000 P 
 
 For short lengths the longitudinal tensile resistance may be effective in 
 augmenting the resistance to collapse. Flues efficiently fortified by 
 flange-joints or hoops at intervals of 3 feet may be enabled to resis't 
 from 50 lbs. to 60 lbs. or 70 lbs. pressure per square inch more than 
 plain tubes, according to the thickness of the plates. 
 
 (For strength of Segmental Crowns of Furnaces and Cylinders see 
 Clark, S. E., vol. i. pp. 649-651 and pp. 627, 628.) 
 
 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 formulas for these furnaces in 1891 as follows: 
 
 Board of Trade formula is altered from 
 
 T = thickness in inches; 
 D = mean diameter of furnace; 
 WP = working pressure in pounds per square inch. 
 
WP. 
 
 320 STRENGTH OF MATERIALS. 
 
 Lloyd's formula is altered from 
 
 1000 X {T - 2) _ 1234 X (T - 2) 
 
 D ■ D 
 
 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., 
 
 xxvii, 730) made two series of tests on Bessemer steel lap-welded tubes 
 3 to 10 ins. diam. One series was made on tubes 85/ 8 in. outside diam. 
 with the different commercial thicknesses of wall, and in lengths of 21/2, 
 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 not less than 
 about six diameters of tube. 
 
 2. The formulae, based upon this research, for the collapsing pres- 
 sures of modern lap-welded Bessemer steel tubes, for all lengths greater 
 than six diameters, are as follows: 
 
 p= 1,000 (1 - yi -1600^,) (a) 
 
 P =• 86,670 I - 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 - 
 
 less than 0.023, while formula B is for values greater than these. When 
 applying these formula?, 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 lbs. for the relatively thinnest to 35,000 lbs. 
 per sq. in. for the relatively thickest walls. Since the average yield 
 point of the material was 37,000 and the tensile strength 58,000 lbs. 
 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, t 
 
 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 by 
 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 = [2E/(1 -m*)](t/D)*, ....... (1) 
 
 in which P = collapsing pressure in lbs. per sq. in. 
 
 E = modulus of elasticity in lbs. per sq. in. 
 
 m = Poisson's ratio of lateral to transverse deformation. 
 
 t = thickness of tube wall in ins. 
 D = external tube diameter in ins. 
 
RESISTANCE OF HOLLOW CYLINDERS. 
 
 321 
 
 Collapsing Pressure of Lap-Welded Steel Tubes. 
 Outside Diameter, 85/ 8 In.; Length of Pipe, 20 Ft. 
 
 Thick- 
 
 Length, 
 
 Bursting 
 Pressure, 
 
 Aver- 
 
 Outside 
 
 Diam. 
 
 In. 
 
 Thick- 
 
 Bursting 
 
 Aver- 
 
 In. 
 
 Ft. 
 
 Lbs. per 
 Sq. In. 
 
 age. 
 
 ness. 
 
 Pressure. 
 
 age. 
 
 0.176 
 
 2.21 
 
 815-1085 
 
 977 
 
 3 
 
 0.112 
 
 1550-2175 
 
 1860 
 
 0.180 
 
 4.70 
 
 525-705 
 
 792 
 
 3 
 
 0.143 
 
 2575-3350 
 
 2962 
 
 0.181 
 
 10.08 
 
 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 
 
 
 
 
 
 
 2 In. 
 
 21/2 
 In. 
 
 3 In. 
 
 4 In. 
 
 5 In. 
 
 6 In. 
 
 7 In. 
 
 8 In. 
 
 9 In. 
 
 10 In. 
 
 11 In. 
 
 0.10 
 
 2947 
 
 3814 
 4671 
 5548 
 
 2081 
 2774 
 3468 
 4161 
 
 1503 
 2081 
 2659 
 3236 
 
 781 
 1214 
 1647 
 2081 
 
 
 
 
 
 
 
 
 0.12 
 
 694 
 1041 
 1387 
 
 400 
 636 
 925 
 
 
 
 
 
 
 0.14 
 
 400 
 595 
 
 286 
 400 
 
 217 
 
 297 
 
 
 
 0.16 
 
 232 
 
 187 
 
 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 
 
 0.34 
 
 
 
 8437 
 9014 
 9592 
 
 5981 
 6414 
 6848 
 7281 
 7714 
 8148 
 8581 
 9014. 
 9448 
 
 4508 
 4854 
 5201 
 5548 
 5894 
 6241 
 6588 
 6934 
 7281 
 
 3525 
 3814 
 4103 
 4392 
 4681 
 4970 
 5259 
 5543 
 5887 
 
 2824 
 3071 
 3319 
 3567 
 3814 
 4062 
 4309 
 4557 
 4805 
 
 2297 
 2514 
 2731 
 2947 
 3164 
 3381 
 3598 
 3814 
 4031 
 
 1888 
 2081 
 2273 
 2466 
 2659 
 2851 
 3044 
 3236 
 3429 
 
 1561 
 1734 
 1907 
 2081 
 2254 
 2427 
 2601 
 2774 
 2947 
 
 1293 
 
 36 
 
 
 
 1450 
 
 38 
 
 
 
 1608 
 
 0.40 
 
 
 
 i766 
 
 0.42 
 
 
 
 
 1923 
 
 0.44 
 
 
 
 
 2081 
 
 46 
 
 
 
 
 2238 
 
 48 
 
 
 
 
 2396 
 
 0.50 
 
 
 
 
 2554 
 
 
 
 
 
 
322 STRENGTH OF MATERIALS. 
 
 For thick tubes a special case of Lame's general formula is 
 
 P = 2u[(t/D) - (t/DT-], (2) 
 
 in which u = ultimate compressive strength in lbs. 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 (t/D) 3 (3) 
 
 For thick steel tubes, P = 80,000 [(t/D) - (t/D) 2 ] .... (4) 
 
 For thin brass tubes, P = 32,090,000 (t/D) 3 (5) 
 
 For thick brass tubes, P = 22,000 [(t/D) - (t/D) 2 ] .... (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 = (D m in/2>max) 3 , and that for variation in 
 thickness = C 2 = (tmin/^aver.) 3 . From Stewart's twenty-five experiments 
 C t = 0.967 and Ci = 0.712. The correction factor C = C x Ci = 0.69; 
 and (1) becomes 
 
 P = C [2 22/(1 - m 2 )](t/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 (t/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- 
 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)[l - C(t/D)] (8) 
 
 in which t = average thickness, and C = d, Ci, C t being equal to 
 
 Dmin/Dmax: C 2 = Average /Urn- 
 
 From Stewart's experiments, average ellipticity C t = 0.9874, and 
 average variation in thickness C 2 = 0.9022; .\ C = 0.9874 X 0.5022 
 = 0.89. 
 
 We have then, for thick lap-welded steel flues, 
 
 P = 2w c 0.89 (t/D) [1 - 0.89 (t/D)] 
 and for thin lap-welded steel flues, 
 
 P = 0.69 [2 E/(l - m?)} (t/D) 3 
 in which E = 30,000,000, m = 0.295, and u c = 38,500 lbs. per sq. in. 
 
 The experimental data of Stewart and Carman have made it possible 
 to correct the rational formulas of Love and Lame" 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 
 
HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 323 
 
 made use of afterwards to secure the float to its stem. The original 
 thickness of the metal may be anything up to about Vi6 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. 
 
 1. lluckness 16,000 
 
 _ _, . , diameter X ^pressure 
 
 2. Thickness = t^ttt^ 
 
 1240 
 
 These rules give the same result for a pressure of 166 lbs. only. Ex- 
 ample: Required the thickness of a 5-inch copper ball to sustain 
 
 Pressures of 50 100 150 166 200 250 lbs.per sq.in. 
 
 Answer by first rule. . ..0156 .0312 .0469 .0519 .0625 .0781 inch. 
 Answer by second rule .0285 .0403 .0494 .0518 .0570 .0637 " 
 
 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 1/4 in. sq. 6 X 1/4 . 6 X 1/2 5 X3/8 
 
 Length driven in 41/4 in. 5 in. 5 in. 4 1/4 in. 
 
 Pounds resistance to drawing. Av'ge. lbs. 857 821 1691 1202 
 
 From fi to Q tests earh (Max. " 1159 923- 2129 1556 
 
 *rom b to 9 tests eacn j Min .. ?66 76Q n2Q 68? 
 
 A. M. Wellington found the force required to draw spikes 9/i6 X 9 /i6 in., 
 driven 41/4 inches into seasoned oak, to be 4281 lbs. ; same spikes, etc., 
 in unseasoned oak, 6523 lbs. 
 
 " Professor W. R. Johnson found that a plain spike 3/ 8 inch square 
 driven 33/s inches into seasoned Jersey yellow pine or unseasoned chest- 
 nut required about 2000 lbs. force to extract it; from seasoned white 
 oak about 4000 and from well-seasoned locust 6000 lbs." 
 
 Experiments in Germany, by Funk, give from 2465 to 3940 lbs. (mean 
 of many experiments about 3000 lbs.) as the force necessary to extract a 
 plain 1/2-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 V10 part greater. Similar spikes 9/ 16 inches 
 square, 7 inches long, driven 6 inches deep, required from 3700 to 6745 
 lbs. to extract them from pine; the mean of the results being 4S73 lbs. 
 In all 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 about 300 to 400 lbs. 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 i5/i6-in. hole, lbs 26,400 19,200 
 
 1 in. round " " 34 " " i3/i 6 -in. " " 16,800 18,720 
 
 1 in. square " " 18 " " i5/i 6 -in. " " 14,600 15,600 
 
 1 in. round ". " 22 " " i3/i 6 -in. " " 13,200 14,400 
 
324 STRENGTH OP MATERIALS. 
 
 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 1/ 8 in 7805 8110 
 
 Average of all bolts 8383 8598 
 
 Round drift-bolts should be driven in holes 13/ 16 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 lbs. 
 
 " 4 threads per in. 5 in. in wood. " " 2743 " 
 
 " D'blethr'd,3perin.,4in. in " " " 2730 " 
 
 Lag-screw, 7 per in., 11/2 "" " " 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 lbs.; ash, 
 790 lbs.; oak, 760 lbs.; mahogany, 770 lbs.; elm, 665 lbs.; sycamore, 
 830 lbs. 
 
 Tests of Lag-screws in Various Woods were made by A. J. Cox, 
 University of Iowa, 1891: 
 
 Kind of Wood Size Hole Length JSjx No 
 
 Kind 01 w 00a. gcrew _ ^tioie in Tie. i| s Tests. 
 
 Seasoned white oak 5/ 8 in. 1/2 in. 41/2 in. 8037 3 
 
 " 9/ 16 " 7/ 16 " 3 " 6480 1 
 
 " 1/2 " 3 /8 " 41/2 " 8780 2 
 
 Yellow-pine stick 5/ 8 " i/ 2 " 4 " 3800 2 
 
 White cedar, unseasoned. .. . 5/ 8 " 1/2 " 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, both 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 (H 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. The 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, 495. Yellow pine, wire, 318; cut, 
 662. White oak, wire, 940; cut, 1216. Chestnut, cut, 683. Laurel, 
 wire, 651; cut, 1200. 
 
STRENGTH OF WROUGHT IRON BOLTS. 
 
 325 
 
 Experiments by F. W. Clay. (Eng'g News, Jan. 11, 1894.) 
 
 w™^i f Tenacity of 6d nails > 
 
 wooa - 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 WROUGHT IRON BOLTS. 
 
 (Computed by A. F. Nagle.) 
 
 
 
 Dia. 
 
 Dia. 
 
 No. 
 
 of 
 
 
 Thr. 
 
 Root. 
 
 V9, 
 
 13 
 
 0.400 
 
 9/16 
 
 12 
 
 0.454 
 
 5/8 
 
 11 
 
 0.507 
 
 3/4 
 
 10 
 
 0.620 
 
 7/8 
 
 9 
 
 0.731 
 
 1 
 
 8 
 
 0.337 
 
 H/8 
 
 7 
 
 0.940 
 
 U/4 
 
 7 
 
 1.065 
 
 13/8 
 
 6 
 
 1.160 
 
 11/2 
 
 6 
 
 1.284 
 
 15/8 
 
 51/2 
 
 1.389 
 
 13/ 4 
 
 5 
 
 1.491 
 
 17/8 
 
 5 
 
 1.616 
 
 2 
 
 41/2 
 
 1.712 
 
 21/ 4 
 
 41/2 
 
 1.962 
 
 21/9, 
 
 4 
 
 2.176 
 
 23/ 4 
 
 4 
 
 2.426 
 
 3 
 
 31/2 
 
 2.629 
 
 31/7 
 
 31/4 
 
 3.100 
 
 4 
 
 3 
 
 3.567 
 
 Area 
 
 at 
 Root. 
 
 0.126 
 0.162 
 0.202 
 0.302 
 0.420 
 0.550 
 0.694 
 0.893 
 1.057 
 1.295 
 1.515 
 1.746 
 2.051 
 2.302 
 3.023 
 3.719 
 4.620 
 5.428 
 7.548 
 9.963 
 
 Stress upon Bolt upon Basis of 
 
 per 
 Sq. In. 
 
 378 
 
 486 
 
 606 
 
 906 
 
 1,260 
 
 1,650 
 
 2,082 
 
 2,679 
 
 3,171 
 
 3,885 
 
 4,545 
 
 5,238 
 
 6,153 
 
 6,906 
 
 9,069 
 
 11,157 
 
 13,860 
 
 16,284 
 
 22,644 
 
 29,889 
 
 4,000 
 lb. 
 
 504 
 
 648 
 
 808 
 
 1,208 
 
 1,680 
 
 2,200 
 
 2,776 
 
 3,572 
 
 4,228 
 
 5,180 
 
 6,060 
 
 6,984 
 
 8,204 
 
 9,208 
 
 12,092 
 
 14,876 
 
 18,480 
 
 21,712 
 
 30,192 
 
 39,852 
 
 5,000 
 lb. 
 
 630 
 
 810 
 
 1,010 
 
 1,510 
 
 2,100 
 
 2,750 
 
 3,470 
 
 4,465 
 
 - 5,285 
 
 6,475 
 
 7,575 
 
 8,730 
 
 10,255 
 
 11,510 
 
 15,165 
 
 18,595 
 
 23,100 
 
 27,140 
 
 37,740 
 
 49,815 
 
 7,500 
 lb. 
 
 945 
 
 1,215 
 
 1,515 
 
 2,265 
 
 3,150 
 
 4,125 
 
 5,205 
 
 6,698 
 
 7,927 
 
 9,712 
 
 11,362 
 
 13,095 
 
 15,382 
 
 17,265 
 
 22,672 
 
 27,892 
 
 34,650 
 
 40,710 
 
 56,610 
 
 74,722 
 
 10,000 
 lb. 
 
 1,260 
 
 1,620 
 
 2,020 
 
 3,020 
 
 4,200 
 
 5,500 
 
 6,940 
 
 8,930 
 
 10,570 
 
 12,950 
 
 15,150 
 
 17,460 
 
 20,510 
 
 23,020 
 
 30,230 
 
 37,190 
 
 46,200 
 
 54,280 
 
 75,480 
 
 99,630 
 
 6,400 
 
 8,200 
 
 10,200 
 
 15,200 
 
 21,100 
 
 27,500 
 
 34,500 
 
 44,000 
 
 52,000 
 
 63,000 
 
 74,000 
 
 84,000 
 
 99,000 
 
 110,000 
 
 143,000 
 
 174,000 
 
 214,000 
 
 248,000 
 
 337,000 
 
 433,000 
 
 The U. S. or Sellers System of Screw Threads is used in the above table. 
 
 The "Probable Breaking Load" is based upon wrought iron running from 
 51,000 lbs. per sq. in. for 1/2 inch diam. down to 43,500 lbs. for 4 in. diam. 
 
 For soft steel bolts add 20% to this column. 
 
 When it is known what load is to be put upon a bolt, and the judgment 
 of the engineer has determined what stress is safe to put upon the iron, 
 look down in the proper column of said stress until the required load is 
 found. The area at the bottom of the thread will give the equivalent 
 area of a flat bar to that of the bolt. 
 
 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 Pi = the load after- 
 wards added. The greatest load may vary but little from Pi or Pi, 
 according as the former or the latter is greater, or it may approach the 
 value Pi 4- Pi, 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 Pi, 
 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 4- Pi. 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.) 
 
326 
 
 STRENGTH OF MATERIALS. 
 
 Forrest E. Cardullo (Machinery' 1 s Reference Series No. 22, 190S) 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, 3 /4, 1 and 11/4 in. bolts showed that the 
 stress produced is often sufficient to break a 1/2-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 1/2-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. 
 
 ^ 
 
 "3 £ 
 
 A 
 
 
 j 
 
 <- 
 
 j 
 
 \ 
 
 „. 
 
 ~o 
 
 c3 
 
 
 "0 
 
 
 *o 
 
 *o 
 
 *5 03 
 
 "O rn 
 
 m 
 
 -^ 3 
 
 02 g 
 
 ffl 73 
 
 W 03 
 
 W03 
 
 W 03 
 
 m 1 
 
 W-3 
 
 "o 
 
 8 g* 
 
 ^*G 
 
 3 
 
 1=1 
 
 
 a 
 
 ■Si 
 
 
 <U 03 
 
 ■**& A 
 
 bOeo 
 
 ^ 03 
 
 -3 _: 
 
 •B eU 
 
 £°m 
 
 ^ a »5 
 
 ^ & 03 
 
 si 
 
 .S-S 
 
 «3 $ « 
 
 £H.S 
 
 •§3 
 
 5o » 
 
 
 eg £ 
 
 £^02 
 
 £«02 
 
 MO S 
 
 Mo a 
 
 CO E 
 
 03.RJ += 
 
 £-02 
 
 Q 
 
 < 
 
 
 02 
 
 02 
 
 02 
 
 02 
 
 02 
 
 02 
 
 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 
 
 11/8 
 
 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 
 
 13/8 
 
 1 .057 
 
 0.710 
 
 3,550 
 
 4,260 
 
 4,970 
 
 5,680 
 
 7,100 
 
 8,520 
 
 11/3 
 
 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 
 
 13,260 
 
 13/ 4 
 
 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 -5- (1 + nd), where d = external diameter 
 of the screw. T X E = 2 nnLP -h (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 
 load 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. 327 
 
 STAND-PIPES AND THEIR DESIGN. 
 
 (Freeman C. Coffin, New England Water Works Assoc, Eng. News, 
 March 16, 1893.) See also papers bv A. H. Howland, Eng. Club of Phil., 
 1887; B. F. Stephens, Amer. Water Works Assoc., Eng. Neivs, 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-pressure when empty. 
 
 The following table gives the height of stand-pipes beyond which they 
 are not safe against wind-pressures of 40 and 50 lbs. 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 lbs 45 70 150 
 
 " 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; 
 V = pressure in lbs. 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 lbs. per sq. in., which they consider much 
 too high for safety. Taking 20,000 as a permissible maximum stress, 
 they give the formulse for safe load P = 8000 d 2 for open links and 
 P = 10,000 d 2 for stud links. Thev 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 251. 
 
328 STRENGTH OF MATERIALS. 
 
 Then the total strain on each side per vertical inch 
 
 = 0.434 Hd = pd . OAteHdf _ 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 
 (Hiv) 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 i:ti 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 lbs. per square inch, a 
 factor of safety of 4, and efficiencv 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 
 -H3.6D; which will give safe heights for thicknesses up to 5/ 8 to 3/ 4 of an 
 irich. 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, whenrf = 
 diameter of stand- pipe in inches; x = any unknown height of stand- 
 pipe; x = VgOTzdt = 15.85 ^dt. 
 
 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 n/i6 of an inch, based on a tensile 
 strength of 60,000 lbs. 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 Vl6 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 lbs. 
 per square inch ; an ultimate tensile strength of from 56,000 to 66,000 lbs. 
 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 Laboratorv. 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. 
 
 329 
 
 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 
 stiffeners. 
 
 Heights of Stand-pipes for Various Diameters and Thicknesses of 
 Plates. 
 
 Thickness 
 of Plate 
 in Frac- 
 tions of 
 an Inch. 
 
 3/i 6 
 
 
 
 
 
 Diameters in Feet. 
 
 
 
 
 
 
 5 
 
 50 
 55 
 60 
 70 
 75 
 80 
 85 
 
 6 
 55 
 
 7 
 60 
 
 8 
 65 
 
 9 
 
 55 
 65 
 75 
 90 
 100 
 110 
 115 
 125 
 130 
 
 10 
 
 50 
 60 
 70 
 85 
 100 
 115 
 120 
 130 
 135 
 145 
 150 
 
 12 
 
 35 
 50 
 55 
 70 
 85 
 100 
 115 
 130 
 145 
 155 
 165 
 
 14 
 
 15 
 
 16 
 
 18 
 
 20 
 
 25 
 
 7/32 
 
 40 
 50 
 60 
 75 
 85 
 100 
 110 
 120 
 135 
 145 
 160 
 
 40 
 
 45 
 55 
 70 
 80 
 90 
 100 
 115 
 125 
 135 
 150 
 160 
 
 
 
 
 
 V4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9/l 6 
 
 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 
 
 5/ 8 
 
 
 
 
 65 
 
 11/16 
 
 
 
 
 
 75 
 
 3/ 4 
 
 
 
 
 
 
 80 
 
 13/i 6 
 
 
 
 
 
 
 90 
 
 17/ 8 
 
 
 
 
 
 
 
 
 95 
 
 •Vi ...... 
 
 
 
 
 
 
 
 
 
 105 
 
 1 
 
 
 
 
 
 
 
 
 
 
 110 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Heights to nearest 5 feet. Rings are to build 5 feet vertically. 
 
 WROUGHT -IRON AND STEEL WATER-PD?ES. 
 
 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 11 1/2-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/i 6 , and 3/ 8 inches, the pipe made of these 
 thicknesses having a weight of 160, 185, and 225 lbs. per foot, respec- 
 tively. At the works all the pipe was tested to pressure IV2 times that 
 to which it is to be subjected when in place. 
 
 An important discussion of the design of large riveted steel pipes to 
 
330 STRENGTH OF MATERIALS. 
 
 resist not only the internal pressure but also the external pressure from 
 moist earth in which thev are laid, together uith notes on the design of f 
 pipe 18 ft. diam. t,000 ft. long for the Ontario Water Power Co., Niagari 
 Falls, by Joseph Mayer, will be found in Eng. News, April 26, 1906. 
 
 a 
 
 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 oL.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 2 = 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., 
 40,693, 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. 
 
 Lowraoor Iron Bars. — Three rolled bars 21/2 inches diameter; ten- 
 sile 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. 
 
 331 
 
 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, SOS 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 Forging?, 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., 55,4S5 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. 
 
 
 67,294 
 60,753 
 75,936 
 64,044 
 63,745 
 65,930 
 63,980 
 
 38,294 
 36,030 
 44,166 
 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% 
 15 
 30 
 100 
 35 
 
 
 
 Lowest T. S 
 
 Highest T.S. and E. L.. . . 
 
 Lowest E. L 
 
 Greatest Contraction 
 
 Greatest Extension 
 
 Least Contr. and Ext 
 
 70% 
 85 
 70 
 
 65 
 100 
 
 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 lbs. per sq. in., 0.018 to 
 0.024; mean, 0.020 inch; at 20,000 lbs. per sq. in., 0.049 to 0.063; mean, 
 0.055 inch; at 30,000 lbs. per sq. in., 0.083 to 0.100; mean, 0.090; set at 
 30,000 pounds per sq. in., to 0.0G2; mean, 0. 
 
 The mean extension between 10,000 to 30,000 lbs. per sq. in. increased 
 regularly at the rate of 0.007 inch for each 2000 lbs. 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 lbs. 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. 
 
332 
 
 STRENGTH OF MATERIALS. 
 
 Elastic stress 
 Pounds. 
 Hardest. . . 34,200 
 Softest .... 32,000 
 
 Mean 32,763 
 
 All uncracked at 
 
 Ultimate stress. Deflection at 50,000 
 
 Pounds. 
 60,960 
 56,740 
 59,209 
 inches deflection. 
 
 Pounds. 
 3.24 ins. 
 3.76 " 
 3.53 " 
 
 Ultimate 
 
 Deflection. 
 
 8 ins. 
 
 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. 
 
 Highest . 
 
 Mean 
 
 Lowest. . 
 
 E. L. 
 
 69,250 
 52,869 
 41,700 
 
 T. S. 
 119,079 
 104,112 
 
 90,523 
 
 Contr. 
 31 9 
 29.5 
 45.5 
 
 Ext. in 
 
 5 inches. 
 
 18.1 
 
 19.7 
 
 23.7 
 
 Vickers, Sons & Co. — 70 Tests. 
 
 Highest . 
 Mean. . . . 
 Lowest. . 
 
 E. L. 
 
 58,600 
 51,066 
 43,700 
 
 T. S. 
 120,789 
 101,264 
 
 87,697 
 
 Contr. 
 11.8 
 17.6 
 24.7 
 
 Ext. in 
 
 5 inches. 
 
 8.4 
 
 12.4 
 
 16.0 
 
 Note the correspondence between Krupp's and Vickers' 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. 
 
 Highest . 
 Mean 
 Lowest. . 
 
 E. L. 
 
 49,800 
 36,267 
 31,800 
 
 Vickers, Sons & 
 
 Highest . 
 Mean . . . 
 Lowest. . 
 
 E. L. 
 
 42,600 
 37,618 
 30,250 
 
 Tree Co. — 157 Tests. 
 
 
 
 Ext. in 
 
 T. S. Contr. 
 
 5 inches. 
 
 99,009 21.1 
 
 16.0 
 
 72,099 33.0 
 
 23.6 
 
 61,382 34.8 
 
 25.3 
 
 Co. — 125 Tests. 
 
 
 
 Ext. in 
 
 T. S. Contr. 
 
 5 inches. 
 
 83,701 18.9 
 
 13.2 
 
 70,572 41.6 
 
 27.5 
 
 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. Hollow shaft, Whitvvorth, T. S., 61,290; E. L., 
 30,575; contr., 52.8; ext. in 10 inches, 28.6. Solid shaft, Vickers', 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 lbs., 0.18 per cent; set at 40,000 lbs., 2.04 per cent; set at 50,000 
 lbs., 3.82 per cent. 
 
 Thrusting tests, Vickers', ultimate, 44,602; elastic, 22,250; set at 
 30,000 lbs., 2.29 per cent; set at 40,000 lbs., 4.69 per cent. 
 
kirkaldy's tests. 333 
 
 Shearing strength of the Whitworth shaft, mean of four tests, 40,654 
 lbs. per square inch, or 66.3 per cent of the pulling stress. Specific 
 gravity of the Whitworth steel, 7.867; of the Vickers', 7.856. 
 
 Spring Steel. — Untempered, 6 tests, average, E. L., 67,916: T. S., 
 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 12.25X1.01 14.00X0.77 
 Plates, gross sectional area square inches: 
 
 3.375 6.63 9.165 12.372 10.780 
 
 Stress, total, pounds: 
 
 199,320 332,640 423,180 528,000 455,210 
 
 Stress per square inch of gross area, joint: 
 
 59,058 50,172 46,173 42,696 42,227 
 
 Stress per square inch of plates, solid: 
 
 70,765 65,300 64,050 62,280 68,045 
 
 Ratio of strength of joint to solid plate: 
 
 83.46 76.83 72.09 68.55 62.06 
 
 Ratio net area of plate to gross: 
 
 73.4 65.5 62.7 64.7 72.9 
 
 Where fractured: 
 
 plate at plate at plate at plate at rivets 
 
 holes. holes. holes. holes. sheared 
 
 Rivets, diameter, area and number: 
 
 0.45, 0.159, 24 0.64, 0.321, 21 0.95, 0.708, 12 1.08, 0.916, 12 0.95,0.708, 12 
 Rivets, total area: 
 
 3.816 6.741 8.496 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 lbs. 
 
 Strength of welded bars varied from 17,816 to 44,586 lbs. 
 
 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 lbs. 
 
 Strength of welded plate from 26,442 to 38,931 lbs. 
 
 Ratio of weld to solid 57.7 to 83.9% 
 
 Chain Links. — 216 Tests. 
 
 Strength of solid bar from 49,122 to 57,875 lbs. 
 
 Strength of welded bar from 39,575 to 48,824 lbs. 
 
 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 82.1% 
 
 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. 
 
334 
 
 STRENGTH OF MATERIALS. 
 
 Cast Copper. —4 tests, average, E. L., 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. 
 
 Description. 
 
 Galvanized. . 
 Ungalvanized 
 Ungalvanized 
 Galvanized . . . 
 Ungalvanized 
 Ungalvanized 
 Galvanized. . . 
 Galvanized. . . 
 Galvanized. . . 
 Ungalvanized 
 Ungalvanized 
 Ungalvanized 
 Galvanized. . . 
 Galvanized. . . 
 Ungalvanized 
 Ungalvanized 
 Galvanized . . . 
 Galvanized. . 
 Ungalvanized 
 Galvanized . . 
 Galvanized. . 
 
 <B 
 
 
 
 
 C 
 
 a^ 
 
 
 
 aj 
 
 
 
 
 
 
 
 
 
 
 . c 
 
 O Bi 
 
 
 7.70 
 
 53.00 
 
 6 
 
 19 
 
 0.1563 
 
 7.00 
 
 53.10 
 
 7 
 
 19 
 
 0.1495 
 
 6.38 
 
 42.50 
 
 7 
 
 19 
 
 0.1347 
 
 7.10 
 
 37.57 
 
 6 
 
 30 
 
 0.1004 
 
 6.18 
 
 40.46 
 
 7 
 
 19 
 
 0.1302 
 
 6.19 
 
 40.33 
 
 7 
 
 19 
 
 0.1316 
 
 4.92 
 
 20.86 
 
 6 
 
 30 
 
 0.0728 
 
 5.36 
 
 18.94 
 
 6 
 
 12 
 
 0. 1 1 04 
 
 4.82 
 
 21.50 
 
 6 
 
 7 
 
 0. 1 693 
 
 3.65 
 
 12.21 
 
 6 
 
 19 
 
 0.0755 
 
 3.50 
 
 12.65 
 
 7 
 
 7 
 
 0.122 
 
 3.82 
 
 14.12 
 
 6 
 
 7 
 
 0.135 
 
 4.11 
 
 11.35 
 
 6 
 
 12 
 
 0.080 
 
 3.31 
 
 7.27 
 
 6 
 
 17. 
 
 0.068 
 
 3.02 
 
 8.62 
 
 6 
 
 7 
 
 0.105 
 
 2.68 
 
 6.26 
 
 6 
 
 6 
 
 0.0963 
 
 2.87 
 
 5.43 
 
 6 
 
 12 
 
 0.0560 
 
 2.46 
 
 3.85 
 
 6 
 
 12 
 
 0.0472 
 
 1.75 
 
 2.80 
 
 6 
 
 7 
 
 0.0619 
 
 2.04 
 
 2.72 
 
 6 
 
 12 
 
 0.0378 
 
 1.76 
 
 1.85 
 
 6 
 
 12 
 
 0.0305 
 
 Hemp Core. 
 
 Main 
 Main and Strands 
 
 Wire Core 
 
 Main and Strands 
 
 Wire Core 
 
 Wire Core 
 
 Main and Strands 
 
 Main and Strands 
 
 Main 
 
 Main 
 Wire Core 
 
 Main 
 Main and Strands 
 Main and Strands 
 
 Main 
 Main and Strands 
 Main and Strands 
 Main and Strands 
 
 Main 
 Main and Strands 
 
 Main 
 
 IP 
 
 P«2 
 
 339,780 
 314,860 
 295,920 
 272,750 
 268,470 
 221,820 
 190,890 
 136,550 
 129,710 
 110,180 
 101,440 
 98,670 
 75,110 
 55,095 
 49,555 
 41,205 
 38,555 
 28,075 
 24,552 
 20,415 
 14,634 
 
kirkaldy's tests. 335 
 
 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 0.3 percent; 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* I. T n 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 30S9 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; 
 crossways, 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 
 Railwav. 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 
 being from different lots. The different specimens in each lot gave 
 results which generally agreed within 30 per cent. 
 
336 
 
 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. 
 
 Pitch pine. 
 
 Dantzic fir . . 
 
 English oak 
 
 American white oak . . 
 
 Sizes abt. in 
 square. 
 
 11 1/2 to 121/2 
 12 to 13 
 
 41/2 X 12 
 41/2 X 12 
 
 
 
 S= 
 
 Span, 
 
 Ultimate 
 
 LW 
 
 inches. 
 
 Stress. 
 
 4BD 2 
 
 
 45,856 
 
 1096 
 
 144 
 
 to 
 
 to 
 
 
 80,520 
 
 1403 
 
 
 37,948 
 
 657 
 
 144 
 
 to 
 
 to 
 
 
 54,152 
 
 790 
 
 
 32,856 
 
 1505 
 
 120 
 
 to 
 
 to 
 
 
 39,084 
 
 1779 
 
 
 23,624 
 
 1190 
 
 120 
 
 to 
 
 to 
 
 
 26,952 
 
 1372 
 
 5438 
 2478 
 
 3423 
 2473 
 
 4437 
 2656 
 
 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 lbs. per sq. in. were as follows: 
 
 Cement Cement 1 Cement, 1 Cement, 1 Cement, 
 
 alone, alone, 2 Sand, 3 Sand, 4 Sand, 
 
 Age. Pulling. Thrusting. Thrusting. Thrusting. Thrusting. 
 
 10 days 376 2910 893 407 228 
 
 20 days 420 3342 1023 494 275 
 
 30 days 451 3724 1172 594 338 
 
 Portland Cement. — Various samples pulling tests, 2 X 21/2 inches 
 cross-section, all aged 10 days, 180 tests; ranges 87 to 643 pounds per 
 square inch. 
 
 TENSILE STRENGTH OF WIRE. 
 
 (From J. Bucknall Smith's Treatise on Wire.) 
 
 Tons per sq. Pounds per 
 in. sectional sq. in. sec- 
 area, tional area. 
 
 Black or annealed iron wire 25 56,000 
 
 Bright hard drawn 35 78,400 
 
 Bessemer, steel wire 40 89,600 
 
 Mild Siemens-Martin steel wire 60 134,000 
 
 High carbon ditto (or "improved") 80 179,200 
 
 Crucible cast-steel "improved" wire 100 224,000 
 
 "Improved" cast-steel "plough" 120 268,800 
 
 Special qualities of tempered and improved 
 
 cast steel wire may attain 150 to 170 336,000 to 380,800 
 
MISCELLANEOUS TESTS OF MATERIALS. 
 
 337 
 
 MISCELLANEOUS TESTS OF MATERIALS. 
 Reports of Work of the Watertown Testing-machine in 1883. 
 
 TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES. 
 
 
 
 5 
 
 
 
 
 
 -S O CD 
 
 A * 
 
 43' 
 
 
 5 
 
 1 
 
 > 
 
 CD'" 
 
 5 
 
 J 
 
 Co 
 
 Stem 
 
 %^£ 
 
 B £ » 
 •2-g G 
 Qg~ 
 
 3 
 P4 
 
 'oi'o 
 
 > 
 
 d 
 
 6 
 
 "o-S 
 
 s 
 
 Tensile Streng 
 
 Joint in Net Se 
 
 tion of Plate p 
 
 square inch, 
 
 pounds. 
 
 biS5 
 £ <a G 
 
 G-g.G 
 
 «fH G 
 
 o <u 
 
 &° 
 
 .£Ph 
 
 * 
 
 3/8 
 
 H/16 
 
 3/4 
 
 101/2 
 
 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 
 
 * 
 
 1/9 
 
 3/4 
 
 13/16 
 
 10 
 
 5 
 
 2 
 
 35,650 
 
 44,615 
 
 45.6 X 
 
 * 
 
 V? 
 
 3/4 
 
 13/16 
 
 10 
 
 5 
 
 2 
 
 35,150 
 
 44,615 
 
 44.9 J 
 
 * 
 
 3/8 
 
 11/16 
 
 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 § 
 
 * 
 
 1/9 
 
 3/4 
 
 .13/16 
 
 10 
 
 5 
 
 2 
 
 46,400 
 
 44,615 
 
 59.4 § 
 
 * 
 
 !/•> 
 
 3/4 
 
 13/16 
 
 10 
 
 5 
 
 2 
 
 46,140 
 
 44,615 
 
 59.2 § 
 
 * 
 
 5/8 
 
 1 
 
 H/16 
 
 101/2 
 
 4 
 
 25/ 8 
 
 44,260 
 
 44,635 
 
 57.2 § 
 
 * 
 
 5/8 
 
 1 
 
 1-1/16 
 
 101/2 
 
 4 
 
 25/ 8 
 
 42,350 
 
 44,635 
 
 54.9 § 
 
 * 
 
 3/4 
 
 U/8 
 
 13/16 
 
 11 .9 
 
 4 
 
 2.9 
 
 42,310 
 
 46,590 
 
 52.1 § 
 
 * 
 
 3/4 
 
 U/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 t 
 
 t 
 
 3/8 
 
 3/4 
 
 13/16 
 
 101/2 
 
 6 
 
 13/4 
 
 60,830 
 
 53,330 
 
 59.1 % 
 
 t 
 
 1/9 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 47,530 
 
 57,215 
 
 40.2 X 
 
 t 
 
 1/9 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 49,840 
 
 57,215 
 
 42.3 X 
 
 t 
 
 3/8 
 
 H/16 
 
 3/4 
 
 10 
 
 5 
 
 2 
 
 62,770 
 
 53,330 
 
 71.7 § 
 
 t 
 
 3/8 
 
 H/16 
 
 3/4 
 
 10 
 
 5 
 
 2 
 
 61,210 
 
 53,330 
 
 69.8 § 
 
 t 
 
 1/9 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 68,920 
 
 57,215 
 
 57.1 § 
 
 t 
 
 1/9 
 
 15/16 
 
 1 
 
 10 
 
 5 
 
 2 
 
 66,710 
 
 57,215 
 
 55.0 § 
 
 t 
 
 5/8 
 
 1 
 
 H/16 
 
 91/2 
 
 4 
 
 23/g 
 
 62,180 
 
 52,445 
 
 63.4 § 
 
 t 
 
 5/8 
 
 1 
 
 H/16 
 
 91/2 
 
 4 
 
 23/ 8 
 
 62,590 
 
 52,445 
 
 63.8 § 
 
 t 
 
 3/4 
 
 U/8 
 
 13/16 
 
 10 
 
 4 
 
 21/2 
 
 54,650 
 
 51,545 
 
 54.0 § 
 
 t 
 
 3/4 
 
 U/8 
 
 13/16 
 
 10 
 
 4 
 
 21/2 
 
 54,200 
 
 51,545 
 
 53.4 § 
 
 t Steel. 
 
 X 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. 
 
 Tested with Two 
 Pin Ends, Pins U/2 
 in. Diana. Com- 
 pressive Strength, 
 lbs. per sq. in. 
 
 Tested with Two 
 Flat Ends. Com- 
 pressive Strength, 
 lbs. per sq. in. 
 
 Tested with One 
 Flat and One Pin 
 End. Compressive 
 Strength, lbs. per 
 sq. in. 
 
 
 (28,260 
 \ 3 1 ,990 
 (26,310 
 \ 26,640 
 ( 24,030 
 \ 25,380 
 ( 20,660 
 1 20,200 
 ( 16,520 
 X 17,840 
 ( 13,010 
 X 15,700 
 
 
 
 
 
 
 
 
 60 
 
 
 
 
 
 
 
 90 
 
 VoVs 
 oooo 
 
 (25,120 
 
 120 
 
 < 22,450 
 (21,870 
 
 
 
 
 
 
 
 
 
 
 
 
 
338 
 
 STRENGTH OF MATERIALS, 
 
 Tested 
 Ends. 
 
 with Two Pin 
 Length of Bars 
 
 Diameter Comp 
 
 of Pins. per sq. : 
 
 7/ 8 inch 16 
 
 1 1/8 inches 17, 
 
 17/s " 21 
 
 .21/4 " ....: 
 
 . Str., 
 n., lbs. 
 250 
 740 
 
 400 
 
 210 
 
 COMPRESSION OF WROUGHT-IRON COLUMNS, 
 BOX AND SOLID WEB. 
 
 ALL TESTED WITH PIN ENDS. 
 
 Columns made of 
 
 6-inch channel, solid web 
 
 6 " " " " 
 
 6 " " " " 
 
 8 " " " " 
 
 8 " " " " 
 
 8-inch channels, with 5/ig-in. continuous 
 
 plates ." 
 
 5/i6-inch continuous plates and angles.. 
 
 Width of plates, 12 in., 1 in. and 7.35 in 
 7/i6-inch continuous plates and angles.. 
 
 Plates 1 2 in. wide 
 
 8-inch channels, latticed 
 
 8 " " " 
 
 8 " " " 
 
 8-inch channels, latticed, swelled sides . . 
 
 10-inch channels, latticed, swelled sides. 
 10 " " " 
 
 io " •• 'I 
 
 * 10-inch channels, latticed one side; con 
 tinuous plate one side 
 
 t 10-inch channels, latticed one side; con 
 tinuous plate one side 
 
 10.0 
 15.0 
 20.0 
 20.0 
 
 26.8 
 13.3 
 20.0 
 26.8 
 13.4 
 20.0 
 26.8 
 16.8 
 25.0 
 16.7 
 25.0 
 
 25.0 
 
 25.0 
 
 9.83 f 
 9.977 
 9.762 
 16.281 
 16.141 
 
 19.417 
 
 16.163 
 
 20.954 
 7.628 
 7.621 
 7.673 
 7.624 
 7.517 
 7.702 
 1 1 .944 
 12.175 
 12.366 
 1 1 .932 
 
 17.622 
 
 17.721 
 
 432 
 
 592 
 
 755 
 
 1,290 
 
 1,645 
 
 1,940 
 
 1,765 
 
 2,242 
 
 679 
 
 924 
 
 1,255 
 
 684 
 
 921 
 
 1,280 
 
 1,470 
 
 1,926 
 
 1,549 
 
 1,962 
 
 1,848 
 
 1,827 
 
 
 30,220 
 21,050 
 16,220 
 22,540 
 17,570 
 
 25,290 
 
 28,020 
 
 25,770 
 33,910 
 34,120 
 29,870 
 33,530 
 33,390 
 30,770 
 33,740 
 32,440 
 31,130 
 32,740 
 
 26,190 
 
 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 6 1/2 X 1 inch. Chemical tests gave carbon 0.27 
 to 0.30; manganese, 0.64 to 0.73; phosphorus, 0.074 to 0.09S. 
 
MISCELLANEOUS TESTS OF IRON AND STEEL. 339 
 
 Gauged 
 
 Elastic 
 
 Tensile 
 
 Elongation 
 
 Length, 
 
 limit, lbs. 
 
 strength per 
 
 per cent, in 
 
 inches. 
 
 per sq. in. 
 
 sq. in., lbs. 
 
 Gauged Length. 
 
 160 
 
 37,4S0 
 
 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 
 
 6S,290 
 
 13.9 
 
 The average tensile strength of the 3/4-inch test pieces was 71,310 lbs., 
 that of the eye-bars 67,230 lbs., a decrease of 5.7%. The average elastic 
 limit of the test pieces was 45,150 lbs., that of the eye-bars 36,402 lbs., a 
 decrease of 19.4%. The elastic limit of the test pieces was 63.3% of 
 the ultimate strength, that of the eve-bars 54.2% of the ultimate strength. 
 
 Tests of 11 full-sized eye bars, 15 X 1 1/4 to 2i/i 6 in., 20.5 to 21.4 ft. long 
 between centers of pins, made bv the Phoenix Iron Co., are reported in 
 Eng. News, Feb. 2, 1905. The average T.S. of the bars was 58,300 lbs. 
 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 lbs. per square in.; elongation 23.9%. 
 
 2. Diameter reduced in compression dies (one pass) .094in.; T. S. 70,420; 
 
 el. 2.7% in 20 in. 
 
 3. " " " " " " " 0.222in.;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 lbs.; 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 coid-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., IS in. long. The reduction in diameter 
 from the hot-rolled to the cold-rolled or cold-drawn bar was 1/16 in. in 
 each case. 
 
 Cold Rolled Steel Shafting (Jones & Laughlins) m/i6in. diam. — 
 Torsion tests of 12 samples gave apparent outside fiber stress, calculated 
 from maximum twisting moment, 70,700 to 82,900 lbs. per sq. in.; fiber 
 stress at elastic limit, 32,500 to 38,800 lbs. 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 lbs. 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 lbs. 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 lbs. 
 per sq. in.; apparent outside fiber stress at maximum load, 45,350 to 
 58,340. Shea?ing modulus of elasticity, 10,220,000 to 11,700,000. Turns 
 per foot betwem jaws at fracture, 1.08 to 1.42. 
 
340 
 
 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_= 0.3£ for a flat knife, 
 d = 0.25t for a 4° bevel knife, and d = 0.16 Vjs f or an 8° bevel knife. 
 The ultimate pressure per inch of width in flat steel bars is approxi- 
 mately "0,000 lbs. X t. The energy consumed in foot-pounds per inch 
 width of steel bars is, approximately: 1" thick, 1300 ft. -lbs.; IV2", 
 2500; 13/4", 3700; 1W, 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. Few 
 hot-rolled steel the, resistance per square inch for rectangular sections 
 varies from 4400 lbs. to 20,500 lbs., 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 lbs. per square 
 inch — as a decrease of 1000 lbs. will henceforth mean a considerable 
 increase in cross-section and temperature. 
 
 Relation of Shearing to Tensile Strength of Different 31etals. 
 E. G. Izod, in a paper presented to the Institution of Mechl. Engrs. 
 {Am. Mac.h., Jan. 18, 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 
 
 • 
 
 
 a 
 
 6 
 
 c 
 
 Cast iron. A 
 
 9.7 
 13.4 
 11.3 
 
 33.1 
 
 13.4 
 
 19.7 
 12.1 
 7.5 
 16.0 
 
 12.5 
 
 2.2 
 
 8.0 
 7.8 
 6.5 
 35.0 
 
 152 
 111 
 122 
 
 60 
 
 128 
 
 93 
 103 
 126 
 
 74 
 
 Rolled phosphor- 
 
 39.5 
 6.4 
 12.7 
 26.0 
 
 26.9 
 24.9 
 42.1 
 56.3 
 61.3 
 
 11,7 
 
 25.5 
 9.6 
 
 22.5 
 
 34.7 
 43.0 
 26.0 
 15.0 
 11.0 
 
 61 
 
 
 
 70 
 
 Cast aluminum- 
 bronze 
 
 Cast phosphor- 
 
 Aluminum alloy 
 
 Wrought t-iron bar. . 
 Mild-steel,0.14 car- 
 
 59 
 75 
 
 78 
 
 Cast phosphor- 
 
 Crucible steel, 0.12 C 
 0.48 C 
 
 74 
 68 
 
 
 0.71 C. . . 
 
 65 
 
 
 0.77 C 
 
 6? 
 
 Yellow brass 
 
 
 
 a. Tensile strength of the metal, gross tons per sq. in.; 6. elongation 
 in 2 in.%; c. ratio shearing -r- 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 407 and 412, 
 
STRENGTH OF IRON AND STEEL PIPE. 
 
 341 
 
 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 lbs. and four steel rings at 5300 (defective 
 weld) 18,000, 29,000 and 35,000 lbs. 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 
 lbs. 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 lbs.; 1 in., 172 lbs.; 
 IV2 in., 300 lbs.; 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 lbs.; 1 in., 
 154, 136, 107 lbs.; 1 1/2 in. 256, 250, 258 lbs. The number of turns in 
 6 feet for the nine lots were respectively, 41/2, 53/4, 21/2; 6 1/4, 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 ll/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 lbs. pull, steel pipe 100 to 111 lbs. 
 Improved die, iron pipe 58 to 62 lbs. pull, steel pipe, 60 to 65 lbs. 
 
 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 
 
 3/4 in. steel 
 
 112 
 
 
 81 
 
 1 in. steel 
 
 1 in. iron 
 
 259 
 173 
 
 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 
 lbs., and the maximum load per sq. in. from 17,100 to 27,500 lbs. Six 
 new tubes also were tested, with maximum loads 55,600 to 64,800 lbs., 
 and maximusa loads per sq. in. 31,600 to 38,100 lbs. The relation of 
 the strength p^r sq. in. of the old tubes to the ratio l/r was very variable, 
 being expressed approximately by the formula S = 41,000 — €00 l/r 
 ± 5000. That of the new tubes is approximately S = 52,000 - 300 l/r 
 ± 2000. 
 
342 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 3/ 4 inch thick, gave results 
 ranging from 5850 to 46,000 lbs. Out of 48 tests 5 gave figures under 
 10,000 lbs., 12 between 10,000 and 20,000 lbs., 18 between 20,000 and 
 30,000 lbs., 10 between 30,000 and 40,000 lbs., and 3 over 40,000 lbs. 
 
 Experiments by Yarrow & Co., on steel tubes, 2 to 21/4 inches diameter, 
 gave results similarly varying, ranging from 7900 to 41,715 lbs., the 
 majority ranging from 20,000 to 30,000 lbs. In 15 experiments on 
 4 and 5 inch tubes the strain ranged from 20,720 to 68,040 lbs. 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 of 
 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/? 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 lbs. The frictional resistance of such tubes is about 
 750 lbs. per sq. in. of tube-bearing area in sheets 5/ 8 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 lbs. The elastic limit of the tube was reached at 
 about 34,000 lbs. 
 
 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, in 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 lbs.) 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 /ormulse: 
 
 H = K (r 4- Vr* - R*) -5- 2 n rR*, or H = K -f- 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 R and d. 
 
STRENGTH OF GLASS. 
 
 343 
 
 R 
 
 H 
 
 R 
 
 H 
 
 R 
 
 H 
 
 d 
 
 H 
 
 d 
 
 H 
 
 d 
 
 H 
 
 1.00 
 
 955 
 
 2.40 
 
 398 
 
 3.80 
 
 251 
 
 2.00 
 
 946 
 
 3.20 
 
 364 
 
 4.60 
 
 170 
 
 1.20 
 
 796 
 
 2.60 
 
 367 
 
 4.00 
 
 239 
 
 2.10 
 
 857 
 
 3.40 
 
 321 
 
 4.80 
 
 156 
 
 1.40 
 
 682 
 
 2.80 
 
 341 
 
 4.20 
 
 227 
 
 2.20 
 
 782 
 
 3.60 
 
 286 
 
 5.00 
 
 143 
 
 1.60 
 
 597 
 
 3.00 
 
 318 
 
 4.40 
 
 217 
 
 2.40 
 
 652 
 
 3.80 
 
 255 
 
 5.50 
 
 116 
 
 1.80 
 
 531 
 
 3.20 
 
 298 
 
 4.60 
 
 208 
 
 2.60 
 
 555 
 
 4.00 
 
 228 
 
 6.00 
 
 95 
 
 2.00 
 
 477 
 
 3.40 
 
 281 
 
 4.80 
 
 199 
 
 2.80 
 
 477 
 
 4.20 
 
 207 
 
 6.50 
 
 80 
 
 2.20 
 
 434 
 
 3.60 
 
 265 
 
 4.95 
 
 193 
 
 3.00 
 
 ' 418 
 
 4.40 
 
 187 
 
 6.95 
 
 68 
 
 The hardness of steel, as determined by the Brinell method, has a 
 direct 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 H 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. .) 
 
 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 onto 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 Green White Crown 
 Glass. 
 
 Mean specific gravity 3.078 
 
 Mean tensile strength, lbs. per sq. in., bars 2,413 
 
 do. thin plates 4,200 
 
 Mean crush'g strength, lbs. p. sq. in., cyl'drs 27,582 
 
 do. cubes 13,130 
 
 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 lbs. and a mean compressive strength of 30,150 
 lbs. 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 lbs., b = 
 breadth, d = depth, and I = length, in inches. Actual tests will prob- 
 ably show wide variations in both directions from the mean calculated 
 strength. 
 
 Glass. 
 
 Glass. 
 
 2.528 
 2,896 
 4,800 
 39,876 
 20,206 
 
 2.450 
 2,546 
 6,000 
 31,003 
 21,867 
 
344 
 
 STRENGTH OF MATERIALS. 
 
 STRENGTH OF ICE. 
 
 Experiments at the University of Illinois in 1895 (The Technograph, 
 vol. ix) gave 620 lbs. per sq. in. as the average crushing strength of cubes 
 of manufactured ice tested at 23° F., and 906 lbs. for cubes tested at 
 14° F. Natural ice, at 12° F., tested with the direction of pressure parallel 
 to the original water surface, gave a mean of 1070 lbs., and tested with 
 the pressure perpendicular to this surface 1845 lbs. The range of varia- 
 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 lbs. per sq. in. The tensile strength of 34 samples tested at 19 to 
 23° F. was from 102 to 256 lbs. per sq. in. 
 
 STRENGTH OF COPPER AT HIGH TE31PERATURES. 
 
 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 lbs. per sq. in. 
 
 Temperature, 
 Fahr. 
 
 Tensile Strength 
 in lbs. 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 lbs. 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. 
 
 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: 
 
 Specific gravity . , 
 Transverse strength, 
 
 3WL 
 
 h 2bh? 
 
 do. do. at elast. limit 
 
 Mod. of elast., thous. lbs. 
 
 Relative elast. resilience, 
 
 inch-pounds per cub. in. 
 
 Crushing endwise, str. 
 
 per sq. in.-lbs 
 
 Crushing across grain, 
 
 strength per sq. in., lbs. 
 
 Tensile strength per sq. 
 
 in 
 
 Shearing strength (with 
 grain) , mean per sq . in . 
 
 
 
 
 Av'g 
 of all 
 Butt 
 
 Butt Logs. 
 
 Middle Logs. 
 
 Top Logs. 
 
 
 
 
 Logs. 
 
 0.449 to 1 .039 
 
 0.575 to 0.859 
 
 0.484 to 0.907 
 
 0.767 
 
 4,762 to 16,200 
 
 7,640 to 17,128 
 
 4,268 to 15,554 
 
 12,614 
 
 4,930 to 13,110 
 l,119to 3,117 
 
 5,540 to 11,790 
 1,136 to 2,982 
 
 2,553 to 11,950 
 842 to 2,697 
 
 9,460 
 1,926 
 
 0.23 to 4.69 
 
 1.34 to 4.21 
 
 0.09 to 4.65 
 
 2.98 
 
 4,781 to 9,850 
 
 5,030 to 9,300 
 
 4,587 to 9,100 
 
 7,452 
 
 675 to 2,094 
 
 656 to 1,445 
 
 584 to 1,766 
 
 1,598 
 
 8,600 to 31,890 
 
 6,330 to 29,500 
 
 4, 170 to 23,280 
 
 17,359 
 
 464 to 1,299 
 
 539 to 1,230 
 
 484 to 1,1 56 
 
 866 
 
 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. ■ 
 
STRENGTH OF TIMBER. 345 
 
 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. 
 
 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 elastic 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 
 Carolina to Texas. Prof. Johnson says it is probably the strongest timber 
 in large sizes to be had in the United States. In small selected speci- 
 mens, other species, as oak and hickory, may exceed it in strength and 
 toughness. The other Southern yellow pines, viz., the Cuban, short- 
 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 
 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 
 is given as follows by different authors: Hatfield, 9900 lbs. per square 
 inch; Rankine, 11,100; Laslett, 9045; Trautwine, 8100; Rodman, 6168. 
 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 
 rupture from 2995 to 5666 lbs.; the average being 4613 lbs. These 
 were average beams, ordered from dealers of good repute. Two beams 
 of selected stock, seasoned four years, gave 7562 and 8748 lbs. The 
 modulus of elasticity ranged from 897,000 to 1,588,000, averaging 
 1,294,000. 
 
 Time tests show much smaller values for both modulus of rupture and 
 modulus of elasticity. A beam tested to 5800 lbs. 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 factors 
 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 fraction 
 of its span, say about 1/300 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, 
 and 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. 
 
346 
 
 STRENGTH OF MATERIALS. 
 
 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 = ~prj, ; P = load in pounds at the middle, I = length, in 
 
 inches, b = breadth, d — depth: 
 
 Name of Wood. 
 
 Transverse Tests. 
 Modulus of 
 Rupture. 
 
 Comp 
 
 Para 
 
 Grain, 
 
 per squ 
 
 Min. 
 
 ression 
 llel to 
 pounds 
 are inch. 
 
 
 Min. 
 
 Max. 
 
 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 
 
 White wood, Basswood (Tilia Ameri- 
 cana) 
 
 Sugar-maple, Rock-maple (Acer sac- 
 
 6,480 
 9,940 
 
 Red maple (Acer rubrum) 
 
 Locust (Robinia pseudacacia) 
 
 Wild cherry (Primus serotina) 
 
 Sweet gum (Liquidambar styraciflua) . 
 
 Dogwood (Cornus florida) 
 
 Sour gum, Pepperidgd(Nyssa sylvatica) 
 Persimmon (Diospyros Virginiana) . . 
 White ash (Fraxunis Americana) .... 
 Sassafras (Sassafras officinale) 
 
 7,500 
 1 1 ,940 
 9,120 
 7,620 
 9,400 
 7,480 
 8,080 
 8,830 
 5,970 
 8,790 
 
 White elm (Ulmus Americana) 
 
 Sycamore; Button wood (Platanus 
 
 8,040 
 7,340 
 
 Butternut; white walnut (Juglans 
 
 6,810 
 
 Black walnut (Juglans nigra) 
 
 Shellbark hickory (Carya alba) 
 
 8,850 
 10,280 
 8,470 
 
 
 9,070 
 
 
 8,970 
 
 Black oak (Quercus tinctoria) 
 
 Chestnut (Castanea vulgaris) 
 
 8,550 
 6,650 
 7,840 
 
 Canoe-birch, paper-birch (Betula pa- 
 
 8,590 
 
 Cottonwood (Popidus monilifera) .... 
 
 White cedar ( Thuja occidentalis) 
 
 Red cedar (Juniperus Virginiana) . . . 
 Cypress (Saxodium Distichum) 
 
 6,510 
 5,810 
 7,040 
 7,140 
 5,600 
 
 
 4,680 
 
 
 10,600 
 
 
 5,300 
 
 Hemlock (Tsuga Canadensis) 
 
 7,420 
 9,800 
 
 Tamarack (Larix Americana) 
 
 10,700 
 
THE STRENGTH OF BRICK, STONE, ETC. 
 
 347 
 
 Shearing Strength of American Woods, adapted for Pins or 
 Tree-nails. 
 
 J. C. Trautwine {Jour. Franklin Inst.). (Shearing across the grain.) 
 
 per 
 
 sq. in. 
 
 per 
 
 sq. in. 
 
 Ash 
 
 .6280 
 
 Hickory 
 
 . 6045 
 
 Beech 
 
 5223 
 
 Hickory 
 
 . 7285 
 
 Birch 
 
 .5595 
 
 Maple 
 
 . 6355 
 
 Cedar (white) 
 
 1372 
 
 Oak 
 
 . 4425 
 
 
 1519 
 
 Oak (live) 
 
 8480 
 
 Cedar (Central American) . . . 
 
 3410 
 
 Pine (white) 
 
 . 2480 
 
 Cherry 
 
 2945 
 
 Pine (Northern yellow) 
 
 . 4340 
 
 Chestnut 
 
 1536 
 
 Pine (Southern yellow) 
 
 . 5735 
 
 Dogwood 
 
 6510 
 
 Pine (very resinous yellow) . . 
 
 . 5053 
 
 Ebony 
 
 7750 
 
 Poplar 
 
 . 4418 
 
 Gum 
 
 5890 
 
 Spruce 
 
 . 3255 
 
 Hemlock 
 
 2750 
 
 Walnut (black) 
 
 . 4728 
 
 Locust 
 
 7176 
 
 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 16 ft. length between supports, showed great varia- 
 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 lbs. 
 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 sapwood. 
 It is recommended that heartwood should finally contain about 6 lbs. 
 of oil per cubic foot, and sapwood about 10 lbs. 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. 
 
 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 lbs. per sq. in. Now, taking recent tests in 
 
348 
 
 STRENGTH OF MATERIALS. 
 
 experiments made at Watertown Arsenal, the strength ran from 5000 to 
 22,000 lbs. 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 lbs. per square inch. The average crushing strength of ten varie- 
 ties of paving-brick much used in the West, I find to be 7150 lbs. 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 lbs. 
 per sq. in. In one instance it reached 4973 lbs. 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 lbs., and the brick crushed at 364,300 
 lbs., or 11,130 lbs. per sq. in. This indicates almost as great compressive 
 strength as granite paving-blocks, which is from 12,000 to 20,000 lbs. 
 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 lbs. per 
 sq. in. A soft brick will crush under 450 to 600 lbs. 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 lbs. per sq. in.). 
 
 Weight of Bricks. — Per cubic foot, best pressed brick, 150 lbs.; 
 good pressed brick, 131 lbs.; common hard brick, 125 lbs.; good common 
 brick, 118 lbs.; soft inferior brick, 100 lbs. 
 
 Absorption of Water. — A brick will in a few minutes absorb 1/2 to 
 3/4 lb. of water, the last being 1/7 of the weight of a hand-molded one, 
 or 1/3 of its bulk. 
 
 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 lbs.; a second, 12,995 to 22,351; a 
 third, 10,390 to 12,709. Other tests gave results from 5960 to 10,250 
 lbs. 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, lbs. per sq. in. 
 
 (Tech. 
 
 Quar. 
 
 XII, No 
 
 . 3, 1899.) 38 tests. 
 
 
 
 No. 
 Test. 
 
 Aver- 
 age. 
 
 Maxi- 
 mum. 
 
 Mini- 
 mum. 
 
 Per cent Wai 
 Absorbed. 
 
 er 
 
 On broad surface 
 Bay State, light hard 
 
 Same, tested on edge . . 
 
 On broad surface 
 Dover River, soft 
 
 71 
 
 67 
 
 38 
 
 36 
 
 36 
 
 36 
 
 36 
 
 16 
 16 
 
 7039 
 6241 
 
 5350 
 
 8070 
 
 2190 
 
 3600 
 
 5360 
 
 7940 
 6430 
 
 11,240 
 10,840 
 
 8630 
 
 10,940 
 
 3060 
 
 4950 
 
 8810 
 
 9770 
 10,230 
 
 3587 
 3325 
 
 3930 
 
 5850 
 
 1370 
 
 2080 
 
 3310 
 
 6570 
 3830 
 
 15.15 to 19.3av. 
 13.67 to 18.2 " 
 
 14.0 to 18.6 " 
 
 4.7 to 10.1 " 
 
 !7.8 to 22.0 " 
 
 16.6 to 23.4 " 
 
 8.3 to 16.7 " 
 
 7.6 to 12.9 " 
 6.2 to 18.7 " 
 
 7.5 
 7.4 
 
 11 6 
 
 Dover River, hard 
 
 7 
 
 Central N. Y., soft 
 
 19.9 
 
 Central N. Y., me- 
 dium burned 
 
 Central N. Y., hard 
 
 18.6 
 12 5 
 
 Another lot,* hard 
 
 10 6 
 
 Same,* tested on edge 
 
 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. 
 
THE STRENGTH OF BRICK, STONE, ETC. 349 
 
 Strength of Common Red Brick. — Tests of 67 samples of Hudson 
 River macnine-molded brick were made by I. H. Woolson, Eng. News. 
 April 13, 1905. The crushing strength, in lbs. per sq. in., of 15 pale biick 
 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 lbs. 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 3S,446 lbs. 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. 
 
 Crushing Strength of Masonry Materials. (From Howe's "Re- 
 taining-Wafls.") — 
 
 tons per sq. ft. tons per sq. ft. 
 
 Brick, best pressed . 40 to 300 Limestones and marbles 250 to 1000 
 
 Chalk 20 to 30 Sandstone 150 to 550 
 
 Granite 300 to 1200 Soapstone 400 to 800 
 
 Strength of Granite. — The crushing strength of granite is commonly 
 rated at 12,000 to 15,000 lbs. 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 lbs. Samples of granite from a quarry on the 
 Connecticut River, tested at the Watertown Arsenal, have shown a 
 strength of 35,965 lbs. per sq. in. (Engineering News, Jan. 12, 1893). 
 
 Ordinary granite ranges from 20,000 to 30,000 lbs. compressive strength 
 per sq. in. A granite from Asheville, N.C., tested at the Watertown 
 Arsenal, gave 51,900 lbs. — Eng. News, Mar. 14, 1907. 
 
 Strength of Avondale, Pa., Limestone. (Engineering Nei»*, 
 Feb. 9, 1893.) — Crushing strength of 2-in. cubes: light stone 12,112, 
 gray stone 18,040, lbs. 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 lbs. 
 
 Modulus of rupture 2,200 " 
 
 Light stone, section SV4 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 tested for transverse strength, on 
 supports 7 in. apart, loaded in the middle: and half bricks were tested by 
 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 li/8-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 
 
350 
 
 STRENGTH OF MATERIALS. 
 
 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 to 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 sa'nd-lime 
 bricks adhered to the mortar better, were cracked less, and were not so 
 brittle. 
 
 Designation of Brick. 
 
 A 
 
 272 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 Modulus of ) 
 Rupture J 
 
 As received 
 
 424 
 
 377 
 
 262 
 
 190 
 
 301 
 
 365 
 
 Dried 
 
 320 
 
 505 
 
 406 
 
 334 
 
 197 
 
 570 
 
 494 
 
 
 Increase, % 
 
 15.0 
 
 16.0 
 
 7.1 
 
 21.5 
 
 3.5 
 
 47.2 
 
 26.2 
 
 
 Wet 
 
 248 
 
 349 
 
 345 
 
 241 
 
 243 
 
 250 
 
 485 
 
 " 
 
 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 
 
 lbs. per sq. in. ) 
 
 Increase, % 
 
 30.2 
 
 17.1 
 
 20.7 
 
 22.3 
 
 13.5 
 
 24.8 
 
 16.3 
 
 
 Wet 
 
 1611 
 
 2174 
 
 2097 
 
 1923 
 
 1108 
 
 2063 
 
 2183 
 
 
 After freez- 
 
 
 
 
 
 
 
 
 
 ing 
 
 1596 
 
 1619 
 
 2265 
 
 1174 
 
 1167 
 
 1851 
 
 1739 
 
 
 After fire 1807 
 
 2814 
 
 2573 
 
 2069 
 
 1089 
 
 2051 
 
 4885 
 
 % of lime in brick 
 
 b 
 
 10 
 
 5 
 
 41/* 
 
 41/7 
 
 5 
 
 8 
 
 Pressure for hardening, lbs.. . . 
 
 120 
 
 135 
 
 150 
 
 125 
 
 120 
 
 150 
 
 125 
 
 Hours in hardening, lbs 
 
 10 
 
 8 
 
 7 
 
 10 
 
 10 
 
 7 
 
 10 
 
 Transverse Strength of Flagging. 
 
 (N. J. Steel & Iron Co.'s Book.) 
 Experiments made by R. G. Hatfield and Others. 
 
 6 = width of the stone in inches; d = its thickness in inches; I — dis- 
 tance between bearings in inches. 
 
 The breaking loads in tons of 2000 lbs., for a weight placed at the center 
 of the space, will be as follows: 
 
 bd 2 
 I 
 
 Bluestone flagging 0.744 
 
 Quincy granite 0.624 
 
 Little Falls freestone 0.576 
 
 Belleville, N. J., freestone. . 0.480 
 Granite (another quarry). . . 0.432 
 Connecticut freestone 0.312 
 
 X 
 
 bd 2 
 I 
 
 X 
 
 Dorchester freestone 0.264 
 
 Aubigny freestone 0.216 
 
 Caen freestone 0.144 
 
 Glass 1.000 
 
 Slate 1.2 to 2.7 
 
 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 
 
 80 X 36 
 midway between the beams = — — — X 0.624 »= 49.92 tons, 
 oo 
 
 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 
 
VARIOUS MATERIALS. 
 
 351 
 
 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, 
 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. 
 
 
 4 
 5 
 
 8 
 81/2 
 
 10 
 91/2 
 
 13 
 12 
 
 18 
 17 
 
 21 
 17 
 
 26 
 
 20 per cent Rosendale 
 
 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 
 
 I6I/2 
 
 211/2 
 
 221/9 
 
 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 
 
 I8I/2 
 
 221/2 
 
 27 
 
 29 
 
 3H/2 
 
 33 
 
 80 " " Portland. 
 
 87 
 
 91 
 
 103 
 
 124 
 
 94 
 
 210 
 
 145 
 
 100 " " Rosendale 
 
 18 
 
 23 
 
 26 
 
 31 
 
 34 
 
 46 
 
 48 
 
 100 " " 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. 
 
 6 Mos. 
 
 1 Year. 
 
 Neat cement: 
 Tension, lbs. 
 per sq. in... 
 
 268-312 
 ( 8650 
 { to 
 ( 10,250 
 
 56-75 
 ( 1200 
 \ to 
 ( 1585 
 
 454-532 
 13,080 
 
 to 
 14,860 
 
 79-92 
 1750 
 to 
 1885 
 
 780-820 
 23,640 
 
 to 
 34,820 
 
 185-211 
 3780 
 to 
 4420 
 
 915-920 
 211-230 
 
 950-1100 
 34,000 
 
 to 
 38,500 
 
 217-240 
 7850 
 to 
 8250 
 
 1036-1190 
 
 996-1248 
 36,150 
 
 to 
 50,000 
 
 Compression, 
 lbs. per sq. in 
 
 
 3 sand, 1 cem. 
 Tens 
 
 300-382 
 
 280-383 
 
 
 8000 
 
 3 sand, 1 cem. 
 
 
 to 
 
 Comp. 
 
 
 10,000 
 
 
 
 
 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 
 
 f)er square inch at any point of the test by the elongation per inch of 
 ength produced by that stress; or if P = pounds of stress applied, 
 K = the sectional area, I = length of the portion of the bar in which the 
 measurement is made, and A. = the elongation in that length, the modu- 
 lus of elasticity E = — ■*• - = — • The modulus is generally measured 
 
 A ( /1A 
 
 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 
 
352 STRENGTH OF MATERIALS. 
 
 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 near 
 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 earlv writers for iron and steel, 
 viz., 40,000,000 and 42,000,000, are undoubtedly erroneous. The modulus 
 of elasticity of steel (within the elastic limit) is remarkably constant, 
 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. Johnson, 
 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 
 testing." 
 
 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 lbs. 
 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 lbs. per sq. in., 25,000,000: at 2000 lbs., 
 16,666,000; at 4000 lbs., 15,384,000; at 6000 lbs., 13,636,000; at 8000 
 lbs., 12,500,000; at 12,000 lbs., 11,250,000; at 15,000 lbs., 10,000,000; 
 at 20,000 lbs., 8,000 000; at 23,000 lbs., 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": 
 
 Dead Load, Live Load, Live Load, 
 
 Greatest. Mean. 
 
 Iron and steel 3 6 from 6 to 40 
 
 Timber 4 to 5 
 
 Masonry 4 
 
 The great factor of safety, 40, is for shafts in millwork which transmit 
 very variable efforts. 
 
FACTORS OF SAFETY. 353 
 
 Unwin gives the following " factors of safety which have been adopted 
 in certain cases for different materials." They "include an allowance 
 for ordinary contingencies." 
 
 , Live Load. > 
 
 Dead In Temporary In Permanent In Structures 
 Load. Structures. Structures, subj. to Shocks. 
 Wrought iron and steel 3 4 4 to 5 10 
 
 Cast iron 3 4 5 10 
 
 Timber 4 10 
 
 Brickwork .... 6 .... 
 
 Masonry 20 20 to 30 
 
 Unwin says that "these numbers fairly represent practice based on 
 experience in many actual cases, but they are not very trustworthy." 
 
 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 261 to 264. 
 
 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 of the steel being from 50,000 to 60,000 lbs. per 
 sq. in., an allowable working stress of 10,000 lbs. per sq. in. on the plates 
 and 6000 lbs. per sq. in. on the stay-bolts may be specified instead. So 
 also in the use of formulae for columns (see page 271) 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 in 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. 
 
 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. 
 
351 STRENGTH OF MATERIALS. 
 
 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, Ma^h'y, Jan,. 
 
 1906.) The apparent factor of safety is the product of four factors, or, 
 
 F = a X b X c X d. 
 
 a is the ratio of the ultimate strength of the material to its elastic limit, 
 rot 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 - Vi/P), 
 where / is the "carrying strength" when the load varies repeatedly 
 between a maximum value, p, and a minimum value, pi, and U is the 
 ultimate strength of the material. The quantities p and pi 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, 
 b = U/f = 2 - pi/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. If 
 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 IV2 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 the failure of the piece, this factor must be made 
 larger. Thus, while it is IV2 to 2 in most ordinary steel constructions, 
 it is rarely less than 2 1/2 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 
 
THE MECHANICAL PROPERTIES OF CORK. 355 
 
 forgings, hardened steel, and the like, also for materials subject to hidden 
 detects, such as internal haws in lorgings, spongy places in castings, etc. 
 It will be smaller tor ductile and larger tor brittle materials. It will be 
 smaller as we are sure that the piece lias received uniform treatment, and 
 as the tests we have give more uniform results and more accurate : ndi- 
 cations of the real strength and quality of the pjece 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. r ~~a~ h^°c d~~^ F 
 
 Boilers 2 1 1 21/4-3 4 1/ 2 - 6 
 
 Piston and connecting rods for double- 
 acting engines 1 1/ 3 -2 3 2 1 1/ 2 13 1/2-I8 
 
 Piston and connecting rod for single-acting 
 
 engines 1 1/2-2 2 2 1 1/ 2 9 -12 
 
 Shaft carrying bandwheel, flv-wheel, or 
 
 'armature 1 1/>-2 3 I 1 l/ 2 63/ 4 - 9 
 
 Lathe spindles 2 2 2 1 1/ 2 12 
 
 Mill shafting. 2 3 22 24 
 
 Steel work in buildings 2 I 1 2 4 
 
 Steel work in bridges 2 1 I 21/ 2 5 
 
 Steel work for small work 2 1 2 1 1/ 2 6 
 
 Cast iron wheel rims 2 1 110 20 
 
 Steel wheel rims i 2 1 I 4 8 
 
 Materials. Minimum Values. 
 
 Cast iron and other castings , 2 1 12 4 
 
 Wrought iron or mild steel. 2 1 1 1 1/ 2 3 
 
 Oil tempered or nickel steel 1 1/2 1 I I V2 2 1/4 
 
 Hardened steel 1 1/2 1 1 2 3 
 
 Bronze and brass, rolled or forged 2 1 1 1 1/2 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 
 deformation or "permanent set" takes place very quickly. This prop- 
 erty is common to all solid elastic substances when strained beyond their 
 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. 
 
356 STRENGTH OF MATERIALS. 
 
 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 by 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 L. 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 folio wng, 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. Mach., 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, lbs 30 50 80 120 150 200 320 430 
 
 Stretch per in. of 
 
 length, in 0.5 1. 2.2 4 5 6 7 7.5 
 
 Stretch per 10 lbs. 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 pize of 
 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 
 
ALUMINUM — ITS PROPERTIES AND USES. 357 
 
 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 sub- 
 stitutes, sulphide substitutes, oxidized (blown) oils, sulphur in substitutes, 
 chlorine in substitutes. F. Residue. 
 
 4. Extraction with nitro-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. 
 
 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 malle- 
 able 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 perceptibly. 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. Commercial 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 iron in being cold- 
 short. Cast bars are likely to be porous or spongy, but, after hammer- 
 ing or rolling, are compact and tough. 
 
 The average results of several tests are as follows: Castings, tensile 
 strength, 85,000 lbs. 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%. (See also page 473.) 
 
 Nickel readily takes up carbon, and the porous nature of the metal 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 amor- 
 phous 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. 
 
 (By Alfred E. Hunt, Pres't of the Pittsburgh Reduction Co.) 
 The specific gravity of pure aluminum in a cast state is 2.58; in rolled 
 bars Of large section it is 2.6; in very thin sheets subjected to high com- 
 pression under chilled rolls, it is as much as 2.7. Taking the weight of a 
 given bulk of cast aluminum as 1, wrought iron is 2.90 times heavier; struc- 
 tural steel, 2.95 times; copper, 3.60; ordinary high brass, 3.45. Most wood 
 suitable for use in structures has about one third the weight of aluminum, 
 which weighs 0.092 lb. to the cubic inch. 
 
 Pure aluminum is practically not acted upon by boiling water or steam. 
 Carbonic oxide or hydrogen sulphide does not act upon it at any tempera- 
 ture under 600° F. It is not acted upon by most organic secretions. 
 
 Hydrochloric acid is the best solvent for aluminum, and strong solutions 
 of caustic alkalies readily dissolve it. Ammonia has a slight solvent action, 
 and concentrated sulphuric acid dissolves aluminum upon heating, with 
 evolution of sulphurqus acid gas, Dilute sulphuric acid acts but slowly on 
 
358 STRENGTH OF MATERIALS, 
 
 the metal, though the presence of any chlorides in the solution allows rapid 
 decomposition. Nitric acid, either concentrated or dilute, has very littie 
 action upon the metal, and sulphur has no action unless the metal is at a 
 red heat. Sea-water has very little effect on aluminum. Strips of the 
 metal placed on the sides of a wooden ship corroded less than 1/1000 inch 
 after six months' exposure to sea-water, corroding less than copper sheets 
 similarly placed. 
 
 In malleability pure aluminum is only exceeded by gold and silver. In 
 ductility it stands seventh in the series, being exceeded by gold, silver, 
 platinum, iron, very soft steel, and copper. Sheets of aluminum have been 
 rolled down to a thickness of 0.0005 inch, 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 down into the very finest wire. By the Mannesmann process 
 aluminum tubes have been made in Germany. 
 
 Aluminum stands very high in the series as an electro-positive metal, and 
 contact with other metals should be avoided, as it would establish a gal- 
 vanic couple. 
 
 The electrical conductivity of aluminum is only surpassed by pure 
 copper, silver, and gold. With silver taken at 100 the electrical conduc- 
 tivity of aluminum is 54.20; that of gold on the same scale is 78; zinc is 
 29.90; iron is only 16, and platinum 10.60. Pure aluminum has no polar- 
 ity, and the metal in the market is absolutely non-magnetic. 
 
 Sound castings can be made of aluminum in either dry or "green" sand 
 moulds, or in metal "chills." It must not be heated much beyond its 
 melting-point, and must be poured with care, owing to the ready absorp- 
 tion of occluded gases and air. The shrinkage in cooling is 17/64 inch per 
 foot, or a little more than ordinary brass. It should be melted in plumbago 
 crucibles, and the metal becomes molten at a temperature of 1215° F. 
 
 The coefficient of linear expansion, as tested on s/g-inch round aluminum 
 rods, is 0.00002295 per degree centigrade between the freezing and boiling 
 point of water. The mean specific heat of aluminum is higher than that of 
 any other metal, excepting only magnesium and the alkali metals. From 
 zero to the melting-point it is 0.2185; water being taken as 1, and the latent 
 heat of fusion at 28.5 heat units. The coefficient of thermal conductivity 
 of unannealed aluminum is 37.96; of annealed aluminum, 38.37. As a 
 conductor of heat alumnium ranks fourth, being exceeded only by silver, 
 copper, and gold. 
 
 Aluminum, under tension, and section for section, is about as strong as 
 cast iron. The tensile strength of aluminum 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 Reduct'n 
 
 Form. Tension, Tension, of Area in 
 
 lbs. lbs. Tension. 
 
 Castings 6,500 15,000 15 
 
 Sheet 12,000 24,000 35 
 
 Wire 16,000-30,000 30,000-65,000 60 
 
 Bars 14,000 28,000 40 
 
 The elastic limit per square inch under compression in cylinders, with 
 length twice the diameter, is 3500. The ultimate strength per square inch 
 under compression in cylinders of same form is 12,000. The modulus of 
 elasticity of cast aluminum is about 11,000,000. 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 this porosity. Its maximum shearing stress in 
 castings is about 12,000, and in forgings about 16,000, or about that of pure 
 copper. 
 
 Pure aluminum is too soft and lacking in tensile strength and rigidity for 
 many purposes. Valuable allovs 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. 
 
 Plates and bars of these alloys have a tensile strength of from 40,000 to 
 
ALUMINUM — ITS PROPERTIES AND USES. 359 
 
 50,000 pounds per square inch, an elastic limit of 55% to 60% of the 
 ultimate tensile strength, an elongation of 20% in 2 inches, and a 
 red tCtio.i of area of 25 f . 
 
 This metal is especially capable of withstanding the punishment and 
 distortion to which structural material is ordinarily subjected. Some 
 aluminum alloys have as much resilience and spring as the hardest of hard- 
 drawn brass. 
 
 Their specific gravity is about 2.80 to 2.85, where pure aluminum has a 
 specific gravity of 2.72. 
 
 In castings, more of the hardening elements are necessary in order to give 
 the maximum stiffness and rigidity, together with the strength and duc- 
 tility of the metal; the favorite alloy material being zinc, iron, manganese, 
 and copper. Tin added to the alloy reduces the shrinkage, and alloys of 
 aluminum and tin can be made which have less shrinkage than cast iron. 
 
 The tensile strength of hardened aluminum-alloy castings is from 20,000 
 to 25,000 pounds per square inch. 
 
 Alloys of aluminum and copper form two series, both valuable. The 
 first is aluminum bronze, containing from 5% to 11 1/2% of aluminum; and 
 the second is copper-hardened aluminum, containing from 2% to 15% of 
 copper. Aluminum-bronze is a very dense, fine-grained, and strong alloy, 
 having good ductility as compared with tensile strength. The 10% bronze 
 in forged bars will give 100,000 lbs. tensile strength per square inch, with 
 60,003 lbs. elastic limit per square inch, and 10% elongation in 8 inches. 
 The 5 % to 7 1/2% bronze has a specific gravity of 8 to 8.30, as compared with 
 7.50 for the 10% to 11 1/2% bronze, a tensile strength of 70,000 to 80,000 
 lbs., an elastic limit of 40,000 lbs. per square inch, and an elongation of 
 30% in 8 inches. 
 
 Aluminum is used by steel manufacturers to prevent the retention of 
 the occluded gases in the steel, and thereby produce a solid ingot. The 
 proportions of the dose range from 1/2 lb. to several pounds of aluminum 
 per ton of steel. Aluminum is also used in giving extra fluidity to steel 
 used in castings, making them sharper and sounder. Added to cast iron, 
 aluminum causes the iron to be softer, free from shrinkage, and lessens the 
 tendency to "chill." 
 
 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 composition is 
 deduced: Aluminum, 85.74%; tin, 12.94%; silicon, 1.32%; iron, none. 
 
 The metal can be readily electrically welded, but soldering is still not 
 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 success. 
 A pure nickel soldering-bit should be used, as it does not discolor aluminum 
 as copper bits do. 
 
 Aluminum Wire. — Tension tests. Diam. 0.128"in. 14 tests. E.L. 
 12,509 to 19,100; T. S. 25,800 to 26,900 lbs. 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 outride fiber stress, lbs. per sq. in. 15,900 to 18,300 lbs. 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 fiber stress, 20,700 
 to 21,500 lbs. 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. 
 
360 
 
 ALLOYS. 
 
 AIXOYS OF COPPER ANI> TIN. 
 
 (Extract from Report of IT. g. Test Board.*) 
 
 
 Mean 
 
 Corn- 
 
 A . 
 
 
 
 *r 
 
 03 fl 
 
 a 
 
 Torsion 
 
 
 position by 
 
 "S.S 
 c . 
 
 la 
 
 *d 
 
 l-s 
 
 £ J2 
 
 '". 
 
 Tests. 
 
 0/ 
 
 £ 
 
 Analysis. 
 
 
 Oft.S 
 
 D 03 05 
 
 ill 
 
 a o a 
 
 - a 
 
 bjo Mas 
 
 c a a 
 
 a ■ M 
 
 'Hog 
 
 , . 
 
 Cop- 
 per. 
 
 Tin. 
 
 =11 
 
 m 
 
 
 
 
 H 
 
 H 
 
 w 
 
 H 
 
 Q 
 
 O 
 
 < 
 
 1 
 
 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 
 
 160 
 
 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 
 
 IOO' 
 
 9 
 
 82.70 
 
 17.34 
 
 
 
 
 67,930 
 
 0.63 
 
 
 
 
 10 
 
 80.95 
 
 18.84 
 
 32,980 
 
 
 ' 0.04 
 
 56,715 
 
 0.49 
 
 78,000 
 
 190 
 
 16* 
 
 1! 
 
 77.56 
 
 22.25 
 
 
 
 0. 
 
 29,926 
 
 0.16 
 
 
 
 
 12 
 
 76.63 
 
 23.24 
 
 22,6 io 
 
 22,6 io 
 
 0. 
 
 32,210 
 
 0.19 
 
 114,000 
 
 122 
 
 '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 
 
 "is 
 
 T.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 
 
 *i6 
 
 T 
 
 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 
 
 
 6,400 
 
 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/ 8 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, and all the alloys containing less than 
 
ALLOYS OF COPPER AND TIN. 361 
 
 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 possibly 
 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. 
 
362 
 
 ALLOYS. 
 
 ALLOYS OF COPPER AND ZINC. (U. S. Test Board.) 
 
 
 
 
 
 Elastic 
 
 T 
 
 v 
 
 
 Torsional 
 
 
 Mean Com- 
 position by 
 
 Tensile 
 
 Limit 
 %of 
 
 
 verse 
 Test 
 Modu- 
 lus of 
 Rup- 
 ture. 
 
 i^s 
 
 Crush- 
 ing 
 Str'gth 
 per sq. 
 in., lbs. 
 
 Tests. 
 
 
 
 
 No. 
 
 Analysis. 
 
 Str'gth, 
 lbs. per 
 sq. in. 
 
 B reak- 
 ing 
 
 Load, 
 lbs. per 
 
 sq. in. 
 
 ! J 
 
 o ti 
 
 .2 h 1 
 
 o c • 
 
 
 
 Cop- 
 per. 
 
 Zinc. 
 
 
 1 
 
 97.83 
 
 1.88 
 
 27,240 
 
 
 
 
 
 
 130 
 
 357 
 
 2 
 
 82,93 
 
 16.98 
 
 32,600 
 
 26.1 
 
 26.7 
 
 23, 1 97 
 
 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 
 
 
 
 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 1 7,400 
 
 172 
 
 38 
 
 16 
 
 48.99 
 
 50.82 
 
 26,050 
 
 100 
 
 0.8 
 
 40,189 
 
 0.61 
 
 
 176 
 
 16 
 
 17 
 
 47.56 
 
 52.28 
 
 24, 1 50 
 
 100 
 
 0.8 
 
 48,471 
 
 1.17 
 
 1 2 i ,000 
 
 155 
 
 13 
 
 18 
 
 43 36 
 
 56.22 
 
 9,170 
 
 100 
 
 
 17,691 
 
 0.10 
 
 
 88 
 
 2 
 
 19 
 
 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 east 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-pound er howitzer): Specific gravitv, 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 is 
 found in guns are mostly of a negative character. They expose defects 
 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, tested 
 at Washington, D.C., in 1875-6, showed a variation in tensile strength 
 from 29,800 to 51,400 lbs. 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 of 
 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 the 
 
ALLOYS OF COPPER, TIN AND ZINC. 
 
 363 
 
 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 
 
 ALLOTS 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- 
 port. 
 
 Cu. 
 
 Sn. 
 
 Zn. 
 
 Modulus 
 of 
 Rup- 
 ture. 
 
 Deflec- 
 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, 1 1 7 
 
 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 
 
 
 » 
 
 67.5 
 
 2.5 
 
 30 
 
 58,343 
 
 2.91 
 
 34,720 
 
 45,850 
 
 7.27 
 
 3.09 
 
 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 
 
 B 
 
 65 
 
 2.5 
 
 32.5 
 
 56,949 
 
 2.36 
 
 41,350 
 
 38,300 
 
 3.26 
 
 3.02 
 
 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 
 
 6,820 
 
 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 . 1 5 
 
 2.Y9 
 
 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 
 
 3J3 
 
 3.' 15 
 
 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 
 
364 
 
 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 transverse-test bar, one half bein6 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: 
 
 Per 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 lbs. 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 4- (3 X tin) 
 = 55. 
 
 All alloys Iving to the rear of the rid^e. 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. 
 
 365 
 
 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. 79. 
 
 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 lbs. 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 lbs. per sq. in. + 500 2. 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, 
 lbs. per 
 sq. in. 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength 
 lbs. per 
 sq. in. 
 
 1 
 
 52 
 
 47 
 
 66,000 
 
 8 
 
 31 
 
 61 
 
 55,500 
 
 2 
 
 49 
 
 49 
 
 64,500 
 
 9 
 
 28 
 
 63 
 
 54,000 
 
 3 
 
 46 
 
 51 
 
 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 
 
366 
 
 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 + 4t = 50 would have greater ductility, together 
 with considerable strength, as follows, the strength being calculated as 
 before, tensile strength in lbs. per sq. in. = 40,000 + 500 z. 
 
 
 
 
 Tensile 
 
 
 
 
 Tensile 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength, 
 lbs. per 
 sq. in. 
 
 Tin. 
 
 Zinc. 
 
 Copper. 
 
 Strength, 
 lbs. per 
 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 . . 
 
 lbs. 
 87 
 
 16 
 16 
 
 64 
 
 32 
 
 20 
 
 16 
 60 
 
 92 
 90 
 
 16 
 50 
 
 lbs. 
 5 
 
 ...£.. 
 
 8 
 1 
 
 1 
 
 *40" 
 
 3 
 
 50 
 
 lbs. 
 8 
 
 4 
 
 4 
 3 
 
 H/2 
 21/2 
 
 lbs. 
 
 " "i/2 ' 
 4 
 
 1 
 
 For parts of engines on 
 board naval vessels. 
 
 Bells for ships and factories. 
 
 For plumbers, ship and house 
 brass work. 
 
 For bearing bushes for shaft- 
 ing. 
 
 For pumps and other hydrau- 
 lic purposes. 
 
 Castings subjected to steam 
 pressure. 
 
 For heavy bearings. 
 
 Brass (yellow) 
 
 Bush metal 
 
 Steam metal 
 
 Hard gun metal. . . 
 
 Phosphor bronze . . 
 
 8phc 
 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 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 lbs. per sq. in., elongation 27% in 1 inch, sp. gr. 
 8.696. (W. J. Keep, Trans, A, I, M, E., 1890.) 
 
ALLOYS OF COPPER, TIN, AND ZINC, 
 
 367 
 
 Composition of Various Grades of Rolled Brass, Etc 
 
 
 Trade Name. 
 
 Copper. 
 
 Zinc. 
 
 Tin. 
 
 Lead. 
 
 Nickel. 
 
 
 61.5 
 
 60 
 
 662/3 
 
 80 
 
 60 
 
 60 
 
 662/3 
 
 6H/2 
 
 38.5 
 
 40 
 
 331/3 
 
 20 
 
 40 
 
 40 
 
 331/3 
 
 201/2 
 
 Ti/2 
 
 Ti/2 
 
 11/2 to 2 
 
 
 
 
 
 
 
 
 
 
 Drill rod 
 
 
 
 
 
 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 331/3 per cent zinc and common high brass with 38 1/2 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.) 
 
 U. S. Navy Dept. journal boxes ) _ 
 
 and guide-gibs J 
 
 Tobin bronze 
 
 Naval brass 
 
 Composition, U. S. Navy 
 
 Brass bearings (J. Rose) 
 
 Gun metal 
 
 Tough brass for engines 
 
 Bronze for rod-boxes (Lafond) 
 
 " " pieces subject to shock 
 
 Red brass parts 
 
 " v " per cent 
 
 Bronze for pump casings (Lafond).. 
 " " eccentric straps. 
 
 " shrill whistles 
 
 " " low-toned whistles 
 
 Art bronze, dull red fracture 
 
 Gold bronze 
 
 Bearing metal 
 
 English brass of a.d. 1504 . 
 
 Copper. 
 
 Tin. 
 
 182.8 
 
 1 
 13.8 
 
 58.22 
 
 2.30 
 
 62 
 
 I 
 
 88 
 
 10 
 
 (64 
 
 8 
 
 187.7 
 
 11.0 
 
 92.5 
 
 5 
 
 91 
 
 7 
 
 87.75 
 
 9.75 
 
 85 
 
 5 
 
 83 
 
 2 
 
 (13 
 1 76.5 
 
 2 
 
 11.8 
 
 82 
 
 16 
 
 83 
 
 15 
 
 20 
 
 1 
 
 87 
 
 4.4 
 
 88 
 
 10 
 
 84 
 
 14 
 
 80 
 
 18 
 
 81 
 
 17 
 
 97 
 
 2 
 
 89.5 
 
 2.1 
 
 89 
 
 8 
 
 89 
 
 21/2 
 
 86 
 
 14 
 
 851/4 
 
 123/4 
 
 80 
 
 18 
 
 79 
 
 18 
 
 74 
 
 91/2 
 
 64 
 
 3 
 
 1/4 parts. 
 
 3.4 per cent. 
 39.48 " " 
 37 " " 
 
 2 " " 
 
 1 parts. 
 
 1 .3 per cent 
 
 2.5 " " 
 
 2 ." " 
 
 2.5 " " 
 10 " " 
 15 " «' 
 
 2 parts. 
 11 .7 per cent. 
 
 2 slightly malleable. 
 
 1.50 0.50 lead. 
 
 1 1 
 
 4.3 4.3 " 
 
 2 
 
 2 
 
 2.0 antimony. 
 
 2.0 " 
 
 1 
 
 5.6 2.8 lead. 
 
 81/2 
 
 "l" 
 
 2 
 
 21/2 1/2 lead. 
 
 91/2 7 lead. 
 291/2 3 1/2 lead. 
 
368 
 
 " 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 lbs. per sq. in., when cold, and about 30,600 lbs. 
 when heated to 407° F., corresponding to steam of 250 lbs. pressure. 
 
 Tobin Bronze. — This alloy is practically a sterro or delta metal with 
 the addition of a small amount of lead, which tends to render copper 
 softer and more ductile. (F. L. Garrison, J. F. I., 1891.) 
 
 The following analyses of Tobin bronze were made by Dr. Chas. B. 
 Dudley: 
 
 Test Bar 
 
 (Rolled), per 
 
 cent. 
 
 Copper. 
 • Zinc. . . 
 Tin.... 
 Iron. . 
 Lead. . . 
 
 61.20 
 37.14 
 0.90 
 0.18 
 0.35 
 
 Dr. Dudley writes. " We tested the test bars and found 78,500 tensile 
 strength with 40V2% elongation in two inches, and 15% in eight inches. 
 This high tensile strength can only be obtained when the metal is manip- 
 ulated. Such high results could hardly be expected with cast metal." 
 
 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 lbs. per sq. in., and as rolled 79,000 lbs.; cold rolled it 
 gave 104,000 lbs. 
 
 A circular of Ansonia Brass & Copper Co. gives the following: — The 
 tensile strength of six Tobin bronze one-inch round rolled rods, turned 
 down to a diameter of 5/8 of an inch, tested by Fairbanks, averaged 79,600 
 lbs. per sq. in., and the elastic limit obtained on three specimens aver- 
 aged 54,257 lbs. per sq. in. 
 
 At a cherry-red heat Tobin bronze can be forged and stamped as 
 readily as steel. Bolts and nuts can be forged from it, either by hand 
 or by machinery. Its great tensile strength, and resistance to the corro- 
 sive action of sea-water, render it a most suitable metal for condenser 
 plates, steam-launch shafting, ship sheathing and fastenings, nails, hull 
 plates for steam yachts, torpedo and life boats, and ship deck fittings. 
 
 The Navy Department has specified its use for certain purposes in the 
 machinery of the new cruisers. Its specific gravity is 8.071. The 
 weight of a cubic inch is 0.291 lb. 
 
 Special Alloys. (Engineering, March 24, 1893.) 
 Japanese Alloys for art work: 
 
 
 Copper. 
 
 Silver. 
 
 Gold. 
 
 Lead. 
 
 Zinc. 
 
 Iron. 
 
 Shaku-do 
 
 Shibu-ichi 
 
 94.50 
 
 67.31 
 
 1.55 
 32.07 
 
 3.73 
 traces. 
 
 0.11 
 0.52 
 
 trace. 
 
 trace. 
 
 Gilbert's Alloy for cera-perduta process, for casting in plaster-of- 
 paris. 
 
 Copper 91.4 Tin 5.7 Lead 2.9 Very fusible. 
 
ALLOYS OF COPPER, TIN, AND LEAD. 369 
 
 COPPER-ZINC-IRON 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 of 
 copper-zinc-iron, and copper-zinc-tin-iron 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. 
 
 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- 
 
370 
 
 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 couid 
 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, % 
 Zinc, % . . . 
 Lead, % . . 
 
 T. S. per sq. in.* . . 
 Elonga. in 1 in.,% . 
 Elonga. in 8 in.,%. 
 Red. of area, %.. . . 
 
 P.R.. 
 
 60.0 
 
 92% 
 
 60.0 
 37.5 
 2.5 
 
 65% 
 
 60.0 
 35.0 
 5.0 
 
 61% 
 
 60.0 
 30.0 
 10.0 
 
 * Thousands of pounds. C, casting; A, annealed sheet; H, hard 
 rolled sheet; P. R., possible reduction in rolling. 
 
 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 SPECIAE 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. 
 
 Three samples of phosphor-bronze tested by Kirkaldy gave: 
 
 Elastic limit, lbs. per sq. in 23,800 24,700 16,100 
 
 Tensile strength, lbs. per sq. in. . 52,625 46,100 44,448 
 Elongation, per cent 8.40 1.50 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 in. diam. 
 Apparent outside fiber stress, 77,500 to 86,700 lbs. per sq. in.; average 
 number of turns per inch of length, 0.76 to 1.50. — Tech. Quar., vol. xii, 
 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. 381.) 
 
ALUMINUM ALLOYS. 
 
 371 
 
 Deoxidized Bronze. — This alloy resembles phosphor bronze some- 
 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, 
 Wires. 
 
 Silicon-bronze, and Phosphor-bronze 
 
 (Engineering, Nov. 23, 1883.) 
 
 Description of Wire. 
 
 Tensile Strength. 
 
 Relative Conductivity. 
 
 
 39,827 lbs. per sq. in. 
 
 41,696 " " " " 
 108,080 " " " " 
 102,390 " " " " 
 
 
 Silicon bronze (telegraph) 
 
 " (telephone) 
 
 Phosphor bronze (telephone) . . 
 
 96 " " 
 34 " " 
 
 26 " " 
 
 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 lbs. per sq. in., and from 50% to 
 60% elongation. The 5% bronze has a tensile strength of about 75,000 
 lbs. and about 8% elongation. More than 5% or 5V2% 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 lbs. per sq. in.; with an elongation of over 60%. 
 
 ALLOTS 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 
 
 , 
 
 14.75 
 19 
 12 
 30.8 
 
 5.25 
 
 5 
 
 10.6 
 20.4 
 
 6.25 
 1. 
 
 3.4 
 2.6 
 
 73.75 
 72.7 
 73.8 
 46.2 
 
 
 
 
 2 
 3 
 
 2 
 
 0.3 
 
 0.2." 
 
 4 
 
 
 
 
 
 
 
 
 Nos. 1 and 2 suitable for ordinary work, such as could be performed by 
 average brass castings. No. 3 and 4 are harder. 
 
 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. 
 
372 
 
 The tenacity of castings of A No. 2 grade metal varies between 75,000 
 and 90,000 lbs. 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 71/2%, 5%, 21/2%, and ii/4% 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. 
 
 The Thermit Process. — When finely divided aluminum is mixed 
 with a metallic oxide and ignited the aluminum burns with great rapidity 
 and intense heat, the chemical reaction being Al + Fe203 = AI2O3 + 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 463. 
 
 Tests of Aluminum Bronzes. 
 
 (John H. J. Dagger, British Association, 1889.) 
 
 Per cent 
 
 Tensile Strength. 
 
 Elonga- 
 tion, 
 per cent. 
 
 Specific 
 Gravity. 
 
 of 
 Aluminum. 
 
 Tons per 
 square inch. 
 
 Pounds per 
 square inch. 
 
 It 
 
 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 
 
 10 
 
 7.69 
 
 71/2 
 
 5-31/2 
 
 21/-> 
 
 8.00 
 8.37 
 8.69 
 
 U/4 
 
 
 
 
 Both physical and chemical tests made of samples cut from various 
 sections of 21/2%, 5%, 71/2%, or 10% aluminized copper castings tend to 
 prove that the aluminum unites itself with each particle of copper with 
 uniform proportion in each case, so that we have a product that is free 
 from liquation and highly homogeneous. (P. C. Cole, Iron Age, Jan. 16, 
 1890.) 
 
 Casting. — The melting point of aluminum bronze varies slightly with 
 the amount of aluminum contained, the higher grades melting at a 
 somewhat lower temperature than the lower grades. The A No. 1 grades 
 melt at about 1700° F., a little higher than ordinary bronze or brass. 
 
 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 maids 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, swedged, 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 
 ins. outside diameter, 0.05 in. thick, showed a yield point of 68,700, and a 
 tensile strength of 96,000 lbs. per sq. in. with an elongation of 4.9% in 
 10 in.; heated to bright red and plunged in water, the Y. P. reduced to 
 24,200 and the T. S. to 47,600 lbs. per sq. in., and the elongation in 10 
 ins. increased to 64.9%. 
 
ALUMINUM ALLOYS. 
 
 373 
 
 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. — To solder aluminum bronze with ordinary soft (pewter) 
 solder: Cleanse well the parts to be joined free from grease and dirt. 
 Then place the parts to be soldered in a strong solution of sulphate of 
 copper and place in the bath a rod of soft iron touching the parts to be 
 joined. After a while a coppery-like surface will be seen on the metal. 
 Remove from bath, rinse quite clean, and brighten the surfaces. These 
 surfaces can then be tinned by using a fluid consisting of zinc dissolved 
 in hydrochloric acid, in the ordinary way, with common soft solder. 
 
 Mierzinski recommends ordinary hard solder, and says that Hulot uses 
 an alloy of the usual half-and-half lead-tin solder, with 12.5%, 25% or 
 50% of zinc amalgam. 
 
 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 screw of the United States gunboat Petrel is cast from this brass 
 mixed with a trifle less zinc in order to increase its ductility. 
 
 Tests of Aluminum Brass. 
 
 (Cowles E. S. & Al. Co.) 
 
 Specimen (Castings) 
 
 Diameter 
 
 of Piece, 
 
 Inch. 
 
 Area, 
 sq. in. 
 
 Tensile 
 
 Strength, 
 
 lbs. per 
 
 sq. in. 
 
 Elastic 
 Limit, 
 lbs. per 
 sq. in. 
 
 Elonga 
 tion, 
 per ct. 
 
 Remarks. 
 
 15%A grade Bronze ) 
 17% Zinc | 
 
 0.465 
 0.465 
 0.460 
 
 0.1698 
 0.1698 
 0.1661 
 
 41,225 
 78,327 
 72,246 
 
 17,668 
 
 41 1/2 
 
 21/2 
 
 21/2 
 
 S3 bC 
 
 68% Copper ) 
 
 1 part A Bronze . . . ) 
 
 
 1 part Copper ) 
 
 1 part A Bronze . . . ) 
 
 I part Zinc j 
 
 1 part Copper ) 
 
 
 The first brass on the above list is an extremely tough metal with low 
 elastic limit, made purposely so as to "upset" easily. The other, which 
 is called Aluminum brass No. 2, is very hard. 
 
 We have not in this country or in England any official standard by 
 which to judge of the physical characteristics of cast metals. There are 
 two conditions that are absolutely necessary to be known before we can 
 make a fair comparison of different materials; namely, whether the 
 casting was made in dry or green sand or in a chill, and whether it was 
 attached to a larger casting or cast by itself. It has also been found that 
 chill-castings give higher results than sand-castings, and that bars cast 
 by themselves purposely for testing almost invariably run higher than 
 test-bars attached to castings. It is also a fact that bars cut out from 
 castings are generallv weaker than bars cast alone. (E. H. Cowles.) 
 
 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 in method of moulding and casting, 
 temperature of pouring, size and shape of casting, depth of "sinking 
 head," etc. 
 
374 
 
 Aluminum Hardened by Addition of Copper. 
 
 Tests of rolled sheets 0.04 inch thick. (The Engineer, Jan. 2, 1891.) 
 
 Al. 
 Per cent. 
 
 Cu. 
 Per cent. 
 
 Sp. Gr. 
 Calculated. 
 
 Sp. Gr. 
 Determined. 
 
 Tensile Strength 
 lbs. per 
 sq. in. 
 
 100 
 
 
 
 2.67 
 2.71 
 2.77 
 
 2.82 
 2.85 
 
 26,535 
 43,563 
 44,130 
 54,773 
 50,374 
 
 98 
 96 
 94 
 92 
 
 2 
 4 
 6 
 
 8 
 
 2.78 
 2.90 
 3.02 
 3.14 
 
 Tests of Aluminum Alloys. 
 
 (Engineer Harris, U. S. N., Trans. A. I. M. E., vol. xviii.) 
 
 Composition. 
 
 Tensile 
 Strength 
 per sq. 
 in., lbs. 
 
 Elastic 
 Limit, 
 lbs. per 
 sq. in. 
 
 Elonga- 
 tion, 
 per ct. 
 
 Reduc- 
 tion of 
 Area, 
 per ct' 
 
 Copper. 
 
 Alumi- 
 num. 
 
 Silicon. 
 
 Zinc. 
 
 Iron. 
 
 91.5G% 
 88.50 
 91.50 
 90.00 
 
 6.5G% 
 
 9.33 
 
 6.50 
 
 9.00 
 
 3.33 
 
 3.33 
 
 6.50 
 
 6.50 
 
 9.33 
 
 6.50 
 
 1.73% 
 
 1.66 
 
 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 
 17,000 
 
 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 
 
 63.00 
 63.00 
 91.50 
 93.00 
 
 33.33% 
 33.33 
 
 "6!25" 
 
 9.88 
 4.33 
 23.59 
 15.5 
 
 88.50 
 92.00 
 
 
 0.50 
 
 3.30 
 19.19 
 
 
 
 
 
 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. 
 The density of the allovs of silicon is approximately the same as that of 
 aluminum. — La Melallurgie, 1892. 
 
ALUMINUM ALLOYS. 375 
 
 Tungsten and Aluminum. — Mr. Leinhardt Mannesmann says that 
 the addition of a little tungsten to pure aluminum or its alloys com- 
 municates a remarkable resistance to the action of cold and hot Mater, 
 salt water and other reagents. When the proportion of tungsten is 
 sufficient the alloys offer great resistance to tensile strains. An alloy of 
 aluminum and tungsten called partinium, from the name of its inventor, 
 M. Partin, has been used in France since 1898 for motor-car bodies. Its 
 properties are stated as follows: 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, Copper, and Tin. — Prof. R. C. Carpenter, Trans. 
 A. S. M. E., vol. xix., finds the following alloys of maximum strength iai 
 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 lbs. 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. — Like the copper alloys, the zinc alloys can 
 be divided into two classes, (1) those containing a relatively snail amount 
 of aluminum, and (2) those containing less than 35% of zinc. The first 
 class is used largely in galvanizing baths to produce greater fluidity, while 
 the second class embraces the zinc casting alloys. Prof. Carpenter finds 
 that the strongest alloy of these metals consists of two parts of alumi- 
 num and one part of zinc. Its tensile strength is 24,000 to 26,000 lbs. 
 per sq. in.; has but little ductility, is readily cut with machine-tools, and 
 is a good substitute for hard cast brass. 
 
 Aluminum and Tin. — M. Bourbouze has compounded an alloy of 
 aluminum and tin, by fusing together 100 parts of the former vith 10 
 parts of the latter. This alloy is paler than aluminum, and has a specific 
 gravity of 2.85. The alloy is not as easily attacked by several reagents 
 as aluminum is, and it can also be worked more readily. Another 
 advantage is that it can be soldered as easily as bronze, without fuither 
 preliminary preparations. Prof. Carpenter found that aluminum-tin 
 alloys with from 2 to 10% Al are as a rule weaker than pure aluminum 
 and of little practical value. 
 
 Aluminum with Nickel, German Silver or Titanium. — J. W. 
 Richards, Jour. Frank. Inst., 1895, says that an addition of 5% of nickel 
 or German silver, or 2% of titanium to aluminum increases the tensile 
 strength to 20,000-30,000 lbs. per sq. in. in castings and to 40,000-50,000 
 lbs. in sheet. For purposes where the requirements are fine color, 
 strength, hardness and springiness the German-silver alloy is recom- 
 mended. 
 
 Aluminum-Antimony Alloys. — Dr. C. R, Alder Wright describes 
 some aluminum-antimony alloys in a communication read before the 
 Society of Chemical Industry. The results of his researches do not dis- 
 close the existence of a commercially useful alloy of these two metals, 
 and have greater scientific than practical interest. A remarkable point 
 is that the alloy with the chemical composition Al Sb has a higher melt- 
 ing-point than either aluminum or antimony alone, and that when al urm - 
 num is added to pure antimony the melting-point goes up from that of 
 antimony (450° C.) to a certain temperature rather above that of silver 
 (1000° C). 
 
 Aluminum and Cast Iron. — Aluminum alloys readily with cast 
 iron, up to 14 to 15% Al, but the metal decreases in strength as the Al 
 is increased. Mixtures with greater percentages of Al are granular, 
 and have practically no coherence. — Trans. A. I. M. E., vol. xviu., 
 A. S. M. E., vol. xix. 
 
 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 lbs. 
 per sq. in., and a sp. gr. slightly above 3. It has very little ductility. 
 
376 
 
 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 lbs. per sq. in. — A. S. M E., 
 vol. xix. 
 
 Aluminum and 31agnesium. — Magnalium. — An alloy containing 
 90 to 98% of aluminum, the balance being mainly magnesium, has been 
 patented under the trade name of "magnalium." Its specific gravity is 
 only 2.5; it is whiter, harder and stronger than aluminum, and can be 
 forged, rolled, drawn, machined and filed. It takes a high polish and 
 resists oxidation better than any other light metals or alloys. The 
 tensile strength of cast magnalium, class X, is reported at 18,400 to 
 21,300 lbs. per sq. in., with a reduction of area of 3.75%; hard rolled 
 plates, class Z, 52,200 lbs. per sq. in., with 3.7% reduction; annealed 
 plates, 42,200 lbs. per sq. in., 17.8% reduction. Made by the Magna- 
 lium Syndicate of Berlin. The price is said to be about twice that of 
 aluminum. — (Mach'y, July, 1908.) 
 
 Prof. Carpenter (A. S. M. E., vol. xix) found that additions of Mn 
 increased the strength of Al up to 10% Mn. Larger additions made 
 brittle alloys. 
 
 Resistance of Aluminum Alloys to Corrosion. — J. W. Richards, 
 Jour. Frank. Inst., 1895, gives the following table showing the relative j 
 resistance to corrosion of aluminum (99% pure) and alloys of aluminum | 
 with different metals, when immersed in the liquids named. The J 
 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. 
 
 150° F. 
 
 Strong 
 Acetic 
 Acid. 
 140° F. 
 
 Car- 
 bonic 
 Acid. 
 Water. 
 77° F. 
 
 3 per cent copper 
 
 3 per cent German silver 
 
 3 per cent nickel 
 
 2 per cent titanium 
 
 99 per cent aluminum . . . 
 
 265.0 
 1534.4 
 
 580.3 
 73.4 
 34.6 
 
 53.3 
 130.6 
 180.0 
 
 4.3 
 5.8 
 
 36.1 
 97.7 
 83.0 
 18.6 
 9.6 
 
 0.1 
 
 0.05 
 
 0.13 
 
 0.06 
 
 0.04 
 
 0.4 
 0.6 
 0.75 
 0.20 
 0.15 
 
 0.0 
 0.01 
 0.04 
 0.0 
 0.01 
 
 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. 
 
 ALLOTS 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 the; 
 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 copper 
 more radical in its action even than nickel. In other words, it was| 
 found that 181/2% 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 
 
ALLOYS OF MANGANESE AND COPPER. 
 
 377 
 
 silver, producing an ingot which is a mass of blow-holes, and which 
 swells up above the mold before cooling. 
 
 4. That the ahoy 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 
 process into a metal of superior casting qualities, and the non-corrodi- 
 bility 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 lbs. 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. I., 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 lbs. per sq, in., tensile strength of about 60,000 lbs. 
 per sq. in. with an elongation of 8% to 10% in sand castings. When 
 rolled, the E. L. is about 80,000 lbs. per sq. in., tensile strength 95,000 to 
 106,000 lbs. per sq. in., with an elongation of 12% to 15%. 
 
 Compression tests made at United States Navy 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 lb. 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° with the direction of stress. 
 
 A test on a specimen 1 x 1 x 1 inch was made from a piece of the 
 same pouring-gate. Under stress of 150,000 pounds it was flattened to 
 0.72 inch high by about ll/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 vacht 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 copper. 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 
 56.11 
 60.00 
 56.00 
 
 37.52 
 41.34 
 38.00 
 42.38 
 
 1.41 
 1.30 
 1.25 
 1.25 
 
 0.75 
 0.75 
 0.65 
 0.75 
 
 0.47 
 
 6;5o" 
 
 0.01 
 0.01 
 0.10 
 0.12 
 
 O.Ui 
 
 " 2 
 
 " 3 
 
 0.02 
 
 " 4 
 
 
 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. 
 The mixture for No. 3, allowing for volatilization of some zinc is: copper: 
 60 lbs.; zinc, 39 lbs.; "steel alloy," 2 lbs. That for No. 4 is: copper. 
 56 lbs.; zinc, 43 lbs.; "steel alloy," 2 lbs.; aluminum, 0.5 lb. The steel 
 alloy is made by melting wrought iron, 18 lbs.; ferro-manganese 
 (80 Fe, 20 Mn), 4 lbs.; tin, 10 lbs. The iron and ferro-manganese are 
 first melted and then the tin is added. In making the bronzes about 
 15 lbs. of the copper is first melted under charcoal, the steel alloy is 
 
378 
 
 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 iron, 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 lbs. 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 ALLOTS. 
 
 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 
 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. 
 
 
 51.6 
 50.2 
 51.1 
 52 to 55 
 75 to 66 
 40.4 
 
 8 
 
 2 
 
 8 
 
 8 
 
 25.8 
 
 14.8 
 
 13.8 
 
 18 to 25 
 
 25 to 33 
 
 31.6 
 
 3 
 
 1 
 
 2 
 
 3 
 
 22.6 
 3.1 
 
 3.2 
 
 
 
 31.9 
 
 
 31.9 
 
 " " 
 
 20 to 30 
 
 Nickel " 
 
 
 
 
 
 6.5 parts 
 6.5 " 
 
 
 
 
 
 1 
 
 
 
 3.5 " 
 
 
 
 3.5 " 
 
 
 
 
 Nickel-copper Alloys. — (F. L. Sperry, A. I. M. E., 1895.) 
 
 - 
 
 Copper. 
 
 Nickel. 
 
 Zinc. 
 
 Iron. 
 
 Cobalt. 
 
 
 52 to 63 
 
 50 
 
 65.4 
 
 50 
 50 to 60 
 45.7 to 60 
 
 52.5 
 
 50 
 
 88 
 
 75 
 
 22 to 6 
 18.7 to 20 
 
 16.8 
 
 50 
 25 to 20 
 31.6 to 15 
 
 17.7 
 
 25 
 
 12 
 
 25 
 
 26 to 31 
 
 31.3 to 30 
 
 13.4 
 
 
 
 
 
 
 
 3.4 
 
 
 Christofle 
 
 
 
 25 to 20 
 25.4 to 17 
 28.8 
 25 
 
 
 
 English, Sheffield 
 
 to 2.6 
 
 to 3.4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ALLOYS OF BISMUTH. 
 
 379 
 
 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 roofing. 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 lbs. per sq. in., and in rolled sheets as 
 high as 108,000 lbs. 
 
 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 
 .00003. This same material is also much used to form one element of 
 base-metal thermo-couples. 
 
 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 
 somewhat 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. 
 
 
 50 
 50 
 50 
 50 
 50 
 50 
 50 
 
 31.25 
 28.10 
 25.00 
 25.00 
 25.00 
 26.90 
 20.55 
 
 18.75 
 24.10 
 25.00 
 25.00 
 12.50 
 12.78 
 21.10 
 
 
 
 202° F. 
 
 
 
 
 203° " 
 
 
 
 
 201° " 
 
 D' Arcet's with mercury 
 Wood's 
 
 10.40 
 ' 14.03 
 
 250.0 
 
 113° " 
 149° " 
 149° " 
 
 Guthrie's " Eutectic ". 
 
 "Very low.'? 
 
 The action of heat upon some of these alloys is remarkable. Thus, 
 Lipowitz's alloy, which solidifies at 149° F., contracts 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. 
 
380 
 
 FUSIBLE ALLOTS. 
 
 (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, bismuth 5, melts at 202 ' 
 
 BEARING-METAL ALLOTS. 
 
 (C. B. Dudley, Jour. F. I., 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 I 
 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 j 
 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 lb! 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 I 
 sound castings. This is a principal element of value in phosphor- 
 bronze. 
 
 (4) Good bearing-metals should show small friction. It is true that J 
 friction is almost wholly a question of the lubricant used; but the metal j ( 
 of the bearing has certainly some influence. 
 
 (5) Other things being equal, the best bearing-metal is that which I 
 wears slowest. 
 
 The principal constituents of bearing-metal alloys are copper, tin, W 
 lead, zinc, antimony, iron, and aluminum. The following table gives I 
 the constituents of most of the prominent bearing-metals as analyzed at : 
 the Pennsylvania Railroad laboratory at Altoona. 
 
BEARING-METAL ALLOYS. 
 
 381 
 
 Analyses of Bearing-metal Alloys. 
 
 Metal. 
 
 Copper. 
 
 Tin. 
 
 Lead. 
 
 Zinc. 
 
 Anti- 
 mony. 
 
 Iron. 
 
 
 70.20 
 1.60 
 
 4.25 
 98.13 
 
 14.75 
 
 10.20 
 
 
 55 
 
 
 
 
 87.92 
 84.87 
 
 1.15 
 67.73 
 80.69 
 14.57 
 12.40 
 
 5.10 
 83.55 
 
 78.44 
 0.31 
 15.06 
 12.52 
 
 "85l57 
 
 12.08 
 15.10 
 
 
 
 
 trace 
 9.91 
 14.38 
 
 
 
 4.01 
 
 
 
 16.73 
 
 18.83 
 
 ? (1) 
 
 
 
 
 75.47 
 77.83 
 92.39 
 trace 
 
 9.72 
 9.60 
 2.37 
 
 • (2) 
 
 
 trace 
 
 
 trace(3) 
 0.07 
 
 
 
 trace 
 
 0.98 
 38.40 
 
 16.45 
 19.60 
 
 
 American anti-friction 
 
 65 
 
 
 59.66 
 75.80 
 76.41 
 90.52 
 81.24 
 
 2J6 
 9.20 
 
 10.60 
 9.58 
 
 10.98 
 
 11 
 
 
 
 
 
 
 
 
 
 
 (5) 
 
 
 7.27 
 88.32 
 
 "84 J3" 
 94.40 
 9.61 
 15.00 
 
 
 
 (6) 
 
 
 "42!67' 
 trace 
 
 11.93 
 
 "i4J8' 
 6.03 
 
 
 Harrington bronze 
 
 55.73 
 
 0.97 
 
 0.68 
 61 
 
 
 
 
 
 
 79.17 
 
 76.80 
 
 10.22 
 8.00 
 
 ...(7) 
 
 Ex. B. metal 
 
 
 
 (*\ 
 
 Other constituents: 
 
 (1) No graphite. 
 
 (2) Possible trace of carbon. 
 
 (3) Trace of phosphorus. 
 
 (4) Possible trace of bismuth. 
 
 (5) No manganese. 
 
 (6) Phosphorus or arsenic, 0.37. 
 
 (7) Phosphorus, 0.94. 
 
 (8) Phosphorus, 0.20. 
 
 * Dr. H. C. Torrey says this analysis is erroneous and that Magnolia 
 metal always contains tin. 
 
 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 lb. 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 having 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 lb. 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. , — A \ of 
 
 Copper. 
 
 Standard 79.70 
 
 Copper-tin 87.50 
 
 Same, second experiment , 
 
 Same, third experiment 
 
 Arsenic-bronze 89.20 
 
 Arsenic-bronze 79.20 
 
 Arsenic-bronze 79.70 
 
 "K" bronze 77.00 
 
 Same, second experiment , 
 
 Alloy "B" 77.00 
 
 Tin. 
 
 10.00 
 
 12.50 
 
 Lead. 
 9.50 
 
 Phos. Arsenic. Wear. 
 
 0.80 
 
 10.00 
 10.00 
 10.00 
 10.50 
 
 7.00 
 9.50 
 12.50 
 
 0.80 
 0.80 
 0.80 
 
 100 
 148 
 153 
 147 
 142 
 115 
 101 
 92 
 92.7 
 86.5 
 
382 ALLOYS. 
 
 The old copper-tin alloy of 7 to 1 has repeatedly proved its inferiority 
 to the phosphor-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 ii 
 practically takes the place of phosphorus in a copper-tin alloy, and three 
 tests were made with arsenic-bron2es as noted above. As the propor- i 
 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. I 
 The result was that the metal wore 7.30% slower than the phosphor-! 
 bronze. No trouble from heating was experienced with the "K" bronze j 
 more than with the standard. Dr. Dudley continues: 
 
 At about this time we began to find evidences that wear of bearing- 
 metal alloys varie 1 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. j 
 91/2 parts copper o 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 i 
 lead on this copper-tin alloy seems to be much the same as a still further 
 diminution of tin. However, the tendency of 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 tin is also necessary to keep the lead alloyed with the copper. I 
 
 Bearings were cast of the metal noted in the table as alloy "B/" and it i 
 wore 13.5% slower tha.n the standard phosphor-bronze. This metal is i 
 now the standarrl bearingr-metal of the Pennsylvania Railroad, being | 
 slightly changed in composition to allow the use of phosphor-bronze 
 scrap. The formula adopted is: Copper, 105 lbs.; phosphor-bronze, j 
 60 lbs.; tin, 93/4 lbs.; lead, 251/4 lbs. By using ordinary care in the | 
 foundry, keeping the metal well covered with charcoal during the melt- I 
 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 j 
 taken from the fire. 
 
 It is not known whether the use of a little zinc, or possibly some other 1 
 combination, might not give still better results. For the present, how- j 
 ever, this alloy is considered to fulfill the various conditions required for i| 
 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 of 
 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- 1 ' 
 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 , 
 Compressive strength of about 15,000 lbs. per sq. in., and is found to 
 operate without distortion in the bearings of the heaviest locomotives, 
 not only for driving brasses, but also for rod brasses and bushings, and 
 for bearings of cars of 100,000 lbs. 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%, j 
 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. 
 
 383 
 
 ALLOYS CONTAINING ANTIMONY. 
 
 Various Analyses of 
 
 Babbitt Metal and other 
 ing Antimony. 
 
 Alloys 
 
 CONTAIN- 
 
 Tin. 
 
 Copper. 
 
 Antimony. 
 
 Zinc. 
 
 Lead. 
 
 Bismuth. 
 
 Babbitt metal 1 
 
 50 
 
 = 89.3 
 96 
 
 = 88.9 
 .85.7 
 .81.9 
 .81.0 
 .70.5 
 .22 
 .45.5 
 .89.3 
 .85 
 
 1 
 
 1.8 
 4 
 
 3.7 
 1.0 
 
 "2" 
 
 4 
 10 
 1.5 
 1.8 
 5 
 
 5 parts 
 8.9 per ct. 
 
 
 
 
 for light duty ) 
 
 
 
 
 Harder Babbitt ) 
 
 8 parts 
 
 7.4per ct. 
 10.1 
 16. 2 
 16 
 
 25.5 
 62 
 13 
 
 7.1 
 10 
 
 
 
 
 
 
 
 
 2.9 
 1.9 
 1 
 
 
 
 
 
 
 «« 
 
 
 
 
 
 
 
 6 
 
 
 
 " Babbitt " 
 
 40.0 
 
 
 Plate pewter 
 
 White metal 
 
 
 1 8 
 
 Bearings 
 
 an Ger. locomotives. 
 
 * 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 
 
 70 
 80 
 
 25 
 
 11.12 
 20 
 8 
 
 
 
 83.33' 
 10 
 12 
 
 10 
 
 2 
 
 5.55 
 
 3 
 
 
 
 4 
 
 
 
 
 
 
 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 
 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. 
 
 
 86 
 70 
 55 
 16 
 
 71/2 
 85 
 
 1 
 15 
 
 18 
 
 
 
 71/2 
 
 2 
 
 101/2 
 231/2 
 
 
 
 7 
 
 
 
 2 . 
 41/2 
 31/2 
 
 5 
 7 
 
 71/2 
 
 27 
 
 2. Richards' 
 
 3. Babbitt's 
 
 
 
 
 4. Fenton's 
 
 79 
 
 871/2 
 
 6. German Navy 
 
 
 
 "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 
 
384 ALLOYS. 
 
 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 of 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. Boxes 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 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-friction properties of either. 
 The antimony hardens the lead, and when mixed in the proportion of 80 
 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. 
 
 It is difficult at the present time to determine the exact formulas 
 used by the original Babbitt, the inventor of the recessed box, as a num- 
 ber of different formulas are given for that composition. Tin, copper, 
 
SOLDERS. 385 
 
 and antimony were the ingredients, and from the best sources of infor- 
 mation the original proportions were as follows: 
 
 Another writer gives: 
 
 50 parts tin == 89.3% 83.3% 
 
 2 parts copper = 3.6% 8.3% 
 
 4 parts antimony = 7.1 % 8.3 % 
 
 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 H/2 to lead 1 334° F. 
 
 2 " " 1 340 
 
 " 3 " " 1 356 
 
 " 4 " " 1 365 
 
 " 5 " " 1 378 
 
 " 6 " " 1 381 
 
 1 to lead 25 . . . 
 
 . . . 558< 
 
 1 " " 10... 
 
 ... 541 
 
 1 " " 5... 
 
 ...511 
 
 1 " " 3... 
 
 ...482 
 
 1 " " 2... 
 
 ...441 
 
 1 " " 1... 
 
 ...370 
 
 The melting point of the tin-lead alloys decreases almost proportionately 
 to the increase of tin, from 619°F, the melting point of pure lead, to 356°F 
 when the alloy contains 68% of tin, and then increases to 44S°F., the melt- 
 ing point of pure tin. Alloys on either side of the 68% mixture begin to 
 sorten materially at 356°F, 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 Brinell's method. The results are as follows: 
 
 % Tin 
 Hardness 
 
 
 3.90 
 
 10 
 10.10 
 
 20 
 12.16 
 
 30 
 14.46 
 
 40 
 15.76 
 
 50 
 14.90 
 
 60 
 14.58 
 
 % Tin 
 Hardness 
 
 66 
 16.66 
 
 67 
 15.40 
 
 68 
 14.58 
 
 70 
 15.84 
 
 80 
 15.20 
 
 90 
 13.25 
 
 100 
 4.14 
 
 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 of 
 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, 12 1/2 brass, 1 zinc. 
 
 Silver solder: Yellow brass 70 parts, zinc 7, tin 11 1/2. 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; 
 
 melts at 536° 
 
 to 572° F 
 
 100 " 
 
 zinc 5; 
 
 536 
 
 to 612 
 
 " 1000 " 
 
 copper 10 to 15; 
 
 662 
 
 to 842 
 
 " 1000 " 
 
 nickel 10 to 15; 
 
 " - 662 
 
 to 842 
 
 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. 
 
386 
 
 ROPES AJJD CABLES. 
 
 ROPES AND CABLES. 
 
 STRENGTH OF ROPES. 
 
 (A. S. Newell & Co., Birkenhead. Klein's Translation of Weisbach, 
 vol. iii, part 1, sec. 2.) 
 
 Hemp. 
 
 Iron. 
 
 Steel. 
 
 Tensile 
 Strength, 
 
 
 Weight 
 
 
 Weight 
 
 
 Weight 
 
 Girth. 
 
 per 
 
 Girth. 
 
 per 
 
 Girth. 
 
 per 
 
 Gross tona. 
 
 Inches. 
 
 Fathom. 
 Pounds. 
 
 Inches. 
 
 Fathom. 
 Pounds. 
 
 Inches. 
 
 Fathom. 
 Pounds. 
 
 
 23/4 
 
 2 
 
 1 
 
 H/2 
 
 1 
 H/2 
 
 1 
 
 1 
 
 2 
 3 
 
 3 3/ 4 
 
 4 
 
 15/8 
 
 2 
 
 
 
 4 
 
 
 
 13/4 
 
 21/2 
 
 11/2 
 
 H/2 
 
 5 
 
 41/2 
 
 5 
 
 17/8 
 
 3 
 
 
 
 6 
 
 
 
 2 
 
 31/2 
 
 . 15/8 
 
 2 
 
 7 
 
 51/2 
 
 7 
 
 21/8 
 21/4 
 
 4 
 
 41/2 
 
 13/ 4 
 
 21/2 
 
 8 
 9 
 
 6 
 
 9 
 
 23/ 8 
 21/2 
 
 5 
 51/2 
 
 17/8 
 
 3 
 
 10 
 11 
 
 61/2 
 
 10 
 
 25/8 
 
 6 
 
 2 
 
 31/2 
 
 12 
 
 
 
 23/4 
 
 61/2 
 
 21/8 
 
 4 
 
 13 
 
 7 
 
 12 
 
 27/8 
 3 
 
 7 
 71/2 
 
 21/4 
 
 41/2 
 
 14 
 15 
 
 71/2 
 
 14 
 
 31/8 
 31/4 
 
 8 
 81/2 
 
 23/8 
 
 5 
 
 16 
 17 
 
 8 
 
 16 
 
 33/8 
 
 9 
 
 21/2 
 
 51/2 
 
 18 
 
 
 
 31/2 
 
 10 
 
 25/8 
 
 6 
 
 20 
 
 81/2 
 
 18 
 
 35/ 8 
 33/4 
 
 11 
 12 
 
 23/4 
 
 61/2 
 
 22 
 24 
 
 91/2 
 
 22 
 
 37/s 
 
 13 
 
 31/4 
 
 8 
 
 26 
 
 10 
 
 26 
 
 4 
 
 14 
 
 
 
 28 
 
 11 
 
 30 
 
 41/4 
 43/s 
 
 15 
 16 
 
 33/s 
 
 9 
 
 30 
 32 
 
 
 
 41/2 
 
 18 
 
 31/2 
 
 10 
 
 36 
 
 12 
 
 34 
 
 45/ 8 
 
 20 
 
 33/4 
 
 12 
 
 40 
 
 Length Sufficient to Cause the Maximum Working Stress. 
 (Weisbach.) 
 
 Hempen rope, dry and untarred 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 iower end. It is evident 
 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 rone internally. 
 
STRENGTH OF ROPES. 
 
 387 
 
 The "Stevedore "rope used by theC.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 varn 
 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 s;rands 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 wall 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) 2 . 
 
 Flat Ropes. (Weisbach.) 
 
 Iron 
 
 
 Steel. 
 
 
 Iron 
 
 
 Steel. 
 
 
 
 u 
 
 
 
 
 M 
 
 
 u 
 
 re 
 
 O 
 
 
 s 
 
 ft8 
 •-P ° 
 
 §"5 
 
 %S 
 v a 03 
 
 — a> 03 
 
 03 £ O 
 
 H 
 
 
 -^ ° 
 
 
 
 £■ a 
 jj) a 03 
 
 In. 
 
 Lbs. 
 
 In. 
 
 Lbs. 
 
 
 In. 
 
 Lbs. 
 
 In. 
 
 Lbs. 
 
 
 21/4X1/2 
 
 11 
 
 
 
 20 
 
 3 3/4X11/, 6 
 
 22 
 
 21/2X1/2 
 
 13 
 
 40 
 
 21/2X1/2 
 
 13 
 
 
 
 23 
 
 4 X ll/i 6 
 
 25 
 
 23/4X3/8 
 
 15 
 
 45 
 
 23/4X5/ 8 
 
 15 
 
 
 
 27 
 
 41/4X3/4 
 
 28 
 
 3 x3/ 4 
 
 16 
 
 50 
 
 3 x5/ 8 
 
 16 
 
 2 xl/ 2 
 
 10 
 
 28 
 
 41/ 2 x3/4 
 
 32 
 
 31/ 4 x3/8 
 
 18 
 
 56 
 
 31/4X5/8 
 
 18 
 
 21/4X1/2 
 
 11 
 
 32 
 
 45/ 8 x3/ 4 
 
 34 
 
 31/2X3/8 
 
 20 
 
 60 
 
 31/2X5/8 
 
 20 
 
 21/4X1/2 
 
 12 
 
 36 
 
 
 
 
 
 
OOO ROPES AND CABLES. 
 
 The Technical Words relating to Cordage most frequently heard 
 
 are: 
 
 Yarn. — Fibres twisted together. 
 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. 
 Ha wsers 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 Ropes. — 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. 80. 
 
 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 s.\rand 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 s rands off to a length of about twenty inches for convenience 
 in manipulation. 
 
 The rope now assumes the form shown in Fig. 81 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. 82, 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. 83. 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 
 
STRENGTH OF ROPES. 389 
 
 Fig. 83. 
 Splicing of Ropes. 
 
390 
 
 ROPES AND CABLES. 
 
 draw into the body of the rope or wear off, so that the locality of the 
 splice can scarcely be detected. 
 
 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 Rope (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 
 
 7,100 
 
 200 
 
 400 
 
 1000 
 
 40 
 
 12 
 
 8 
 
 H/8 
 
 9,000 
 
 250 
 
 500 
 
 1250 
 
 45 
 
 13 
 
 9 
 
 H/4 
 
 11,000 
 
 300 
 
 600 
 
 1500 
 
 50 
 
 14 
 
 10 
 
 13/8 
 
 13,400 
 
 380 
 
 750 
 
 1900 
 
 55 
 
 15 
 
 11 
 
 U/2 
 
 15,800 
 
 450 
 
 900 
 
 2200 
 
 60 
 
 16 
 
 12 
 
 15/8 
 
 18,800 
 
 530 
 
 1100 
 
 2600 
 
 65 
 
 17 
 
 13 
 
 13/ 4 
 
 21,800 
 
 620 
 
 1250 
 
 3000 
 
 70 
 
 18 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 ton 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 11/4-inch diameter rope is too small and a 13/4- 
 inch rope is too large for economy. The Pennsylvania Railroad Company 
 
STRENGTH OF ROPES. 391 
 
 uses 11/2-inch rope, running over 14-inch diameter sheaves for hoisting 
 freight on lighters in New York harbor, and handle 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 1/2-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 lbs. 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 H/2 
 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. S 
 
 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 . 
 
 Efficiency of Rope Tackles. Robert Grimshaw in 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, lbs 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 breakMg 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 lbs. = circumference 2 X a coefficient which varies 
 from 900 for 1/2" to 700 for 2" diameter rope, as below: 
 
 Circumference .-. H/ 2 2 2 1/2 23/ 4 3 3 1/2 33/ 4 41/4 4 1/2 5 5 1/2 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 £ looks as though it would give way, but it will not; 
 the greater the strain the tighter it will hold. The wail 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. 
 
392 
 
 ROPES AND CABLES. 
 
 "Varieties of Knots. — A great number of knots have been devised of 
 which a tew only are illustrated, but those selected are the most frequently 
 used. In the cut, Fig. 84, 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: 
 
 A. Bight of a rope. 
 
 B. Simple or Overhand knot. 
 
 C. Figure 8 knot. 
 
 D. Double knot. 
 
 E. Boat knot. 
 
 F. Bowline, first step. 
 
 G. Bowline, second step. 
 H. Bowline completed. 
 I. Square or reef knot. 
 
 J. Sheet bend or weaver's knot. 
 
 K. Sheet bend with a toggle. 
 
 L. Carrick bend. 
 
 M. Stevedore knot completed. 
 
 N. Stevedore knot commenced. 
 
 /O. Slip knot. . 
 
 P. Flemish loop. 
 
 Q. Chain knot with toggle. 
 
 R. Half-hitch. 
 
 S. Timber-hitch. 
 
 T. Clove-hitch. 
 
 U. Rolling-hitch. 
 
 V. Timber-hitch and half-hitch. 
 
 W. Black wall-hitch. 
 
 X. Fisherman's bend. 
 
 Y. Round turn and half-hitch 
 
 Z. Wall knot commenced. 
 
 AA. Wall knot completed. 
 
 BB. Wall knot crown commenced. 
 
 CC. Wall knot crown completed. 
 
 Fig. 84. — Knots. 
 
STRENGTH OF ROPES. 
 
 393 
 
 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 
 wnicn 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 1/2-inch 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. 85, 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. 86. 
 
 (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. 87. 
 
 (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. 87. 
 
 There are now four strands laid in place terminating at A and B, with 
 the eight remaining at MM', as in Fig. 87. 
 
 It will be well after laying each pair of strands to tie them temporarily 
 at the points A and B. 
 
 Fig. 88. Splicing Wire Rope. Fig. 89. 
 
 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. 88. 
 
 All methods of rope-splicing 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. 88, and 
 by a hand-clamp applied near A, open up the rope by untwisting suffi- 
 cientlv 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. 89. 
 
 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 nearlv as strong as the original rope 
 and smooth everywhere. After running a few days, the splice, if well 
 made, cannot be found except bv close examination. 
 
 The above instructions have been adopted by the leading rope manu- 
 facturers of America. 
 
394 
 
 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 flat bars, plates, or "leaves," of regularly varying lengths, super- 
 posed one upon the other. 
 
 Laminated Steel Springs. — Clark (Rules, Tables and Data) gives 
 the following from his work on Railway Machinery, 1855: 
 
 . _ 1.66 L\ _ Wn . _ 1.66 L 3 . 
 
 U 3 n 11.3 L AW3 
 
 A = elasticity, or deflection, in sixteenths of an inch per ton of load; 
 • s = working strength, or load, in tons (2240 lbs.) ; 
 L = span, when loaded in inches; 
 
 6 = breadth of plates, in inches, taken as uniform; 
 
 t = thickness of plates, in sixteenths of an inch; 
 n = number of 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 is 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: 
 
 D Snbh* , ' 6 PI 3 . 
 
 P = -GT and f = EnW 3 '' 
 
 8 = max. direct fiber-strain in plate; b = width of plates; 
 
 n = number of plates in spring; ft = 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/ = '^ ,,„ • (G. R. Henderson, 
 
 Enbh 3 
 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 lbs. **- 1120; 
 As = 16/; L = 21; t = 16ft; then 
 
 Ao ,_. 1.66 X 8 Z-'XP . PI 3 ' 
 
 AS = 16 /= 4096 X 1120 Xttftfts ' Whence ^ 5,527,133 ' 
 
 which corresponds with Reuleaux's formula for deflection if in the latter 
 
 we take E = 33,162,800. 
 
 Also s 
 
 which corresponds with Reuleaux's formula for working load when S in 
 the latter is taken at 76,120. 
 
395 
 
 The value of E is usually taken at 30,000,000 and S at 80,000, in which 
 case Reuleaux's formulae become 
 
 13,333 nbh" 1 
 
 and / = 
 
 PP 
 
 ),000,OOOw&7i 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 of coil, = 1/2 (D — d). 
 n = number of coils. 
 P = load applied to the spring, lbs. 
 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 compression, for load P. 
 W = safe carrying capacity of spring, lbs. 
 
 64 PR* 
 Gd* ' 
 
 Fn 
 
 64 PR 3 n . 
 Gd* ' 
 
 W 
 
 0.1963 Sd s 
 R 
 
 Sd? 
 I 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 lbs. per sq. in. 
 Taking G at 12,000,000 and S at 60,000 the above formulas become 
 
 PR 3 
 '' 187,500 d 4 ' 
 
 W = 11,781 
 
 If P = W, then F = 0.06285 
 
 R* 
 
 For square steel the values found 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 formulas for springs from torsional formulas see 
 paper by J. W. Cloud, Trans. A. S. M. E., vol. 173. Mr. Cloud takes 
 S = 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 h- d, we have the following compari- 
 son of the specified values of capacity and compression with those ob- 
 tained from. the. formulas. 
 
 No. 
 
 d, in. 
 
 D 
 
 D-d 
 
 W t 
 
 W 
 
 H 
 
 h 
 
 H-h 
 
 Fn 
 
 n 
 
 T. 
 
 1/4 
 
 11/2 
 
 11/4 
 
 400 
 
 295 
 
 9 
 
 6 
 
 3 
 
 3.20 
 
 24 
 
 S. 
 
 1/9 
 
 3 
 
 21/9 
 
 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. 
 
 1 
 
 5 
 
 4 
 
 8100 
 
 5890 
 
 101/2 
 
 8 
 
 21/o 
 
 2.76 
 
 8 
 
 I. 
 
 U/4 
 
 8 
 
 6 3/4 
 
 10000 
 
 6788 
 
 9 
 
 53/4 
 
 31/ 4 
 
 3.86 
 
 43/5 
 
 C. 
 
 IVs 
 
 47/ 8 
 
 3 3/ 4 
 
 16000 
 
 8946 
 
 43/ 8 
 
 3 3/ 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 lbs. per square inch of section with 3/ 8 -mch 
 wire, and about 50,000 with 1/2-inch wire. Hence the work that can be 
 done by springs of wire is four or five times as great as Rankine allows. 
 
396 
 
 For 3/ 8 -inch wire and under, 
 
 Maximum load in lbs. 
 
 12,000 X (diam. of wire) 3 . 
 
 Mean radius of springs 
 
 -..-...' n . 180,000 X (diam.) 4 
 
 Weight in lbs. to deflect spring 1 in. = = r- 1 — -. — -. — w . , .„ • 
 
 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 1/4-inch wire; 
 11,000,000 for n/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: 
 
 W = 0.3927 2J^?V F = 8 P ^Ed*^ 3 ' f ° r r0Und SteeL 
 
 ,Sf73 P (D — d)3 
 
 W = 0.471 ~^- d , F = 4.712 K mi a) , for square steel. 
 
 W = carrying capacity in pounds, 
 
 8 = 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 to allow a great amount of deflection, will not be affected by sudden 
 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 -s- 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 7/ 16 " 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. TF= 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 
 
397 
 
 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-sixth; for 14 million subtract one-sixth.) 
 
 d 
 
 in. 
 .065 
 
 D 
 
 w 
 
 F 
 
 0.25 
 
 35 
 
 0.0236 
 
 0.50 
 15 
 
 0.3075 
 
 0.75 
 9 
 
 1.228 
 
 1.00 
 
 7 
 
 3.053 
 
 1.25 
 
 5 
 
 6.214 
 
 1.50 
 
 4.5 
 
 11.04 
 
 1.75 
 
 3.8 
 17.87 
 
 2.00 
 3.3 
 
 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 
 0.3548 
 
 3.25 
 123 
 
 0.4607 
 
 3.50 
 113 
 
 0.5859 
 
 
 5/16 
 
 D 
 W 
 
 F 
 
 1.50 
 605 
 0.0117 
 
 1.75 
 500 
 0.0207 
 
 2.00 
 426 
 0.0336 
 
 2.25 
 371 
 0.0508 
 
 2.50 
 329 
 0.0732 
 
 2.75 
 295 
 0.1012 
 
 3.00 
 267 
 0.1357 
 
 3.25 
 245 
 0.1771 
 
 3.50 
 226 
 0.2263 
 
 3.75 
 
 209 
 0.2839 
 
 4.00 
 195 
 
 0.3503 
 
 3/8 
 
 D 
 W 
 
 F 
 
 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 
 0.2363 
 
 7/16 
 
 D 
 W 
 
 F 
 
 2.00 
 1263 
 0.0069 
 
 2.25 
 
 1089 
 0.0108 
 
 2.50 
 957 
 0.0160 
 
 2.75 
 853 
 0.0225 
 
 3.00 
 770 
 0.0306 
 
 3.25 
 
 702 
 0.0405 
 
 3.50 
 644 
 0.0529 
 
 3.75 
 
 596 
 0.0661 
 
 4.00 
 
 544 
 0.0823 
 
 4.50 
 486 
 0.1220 
 
 5.00 
 432 
 0.1728 
 
 1/2 
 
 D. 
 W 
 F 
 
 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 
 
 9/16 
 
 D 
 W 
 
 F 
 
 2.50 
 2163 
 0.0048 
 
 2.75 
 1916 
 0.0070 
 
 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 
 
 1315 
 
 0.0366 
 
 5.50 
 1180 
 0.0506 
 
 11/16 
 
 D 
 W 
 
 F 
 
 3.00 
 3311 
 0.0037 
 
 3.25 
 2988 
 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 
 
 3/4 
 
 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 
 
 6.0Q 
 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 gauges, 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. 
 
398 
 
 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 
 
 0.625 
 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 
 
 3125 
 
 9.2 
 0.294 
 
 0.375 
 
 74.5 
 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 
 0.128 
 
 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 
 2.38 
 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 
 0.5)2 
 
 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. 5 
 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.l 
 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. 
 
SPRINGS TO RESIST TORSIONAL FORCE. 
 
 399 
 
 ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. 
 
 Pennsylvania Railroad Specifications, 1896. 
 
 c 
 
 
 CD 
 
 
 m ■ 
 
 
 * -i 
 
 ri 
 
 "S c 
 
 
 
 
 
 > 
 
 — 5 
 
 r a, 
 
 8-8 
 
 ^ 
 
 £~ 
 
 40 
 
 113/4 
 
 40 
 
 151/9 
 
 36 
 
 113/4 
 
 40 
 
 
 40 
 
 
 42 
 
 
 35 
 
 ?13/ 4 
 
 32 
 
 nh 
 
 36 
 
 91/2 
 
 40 
 
 151/2 
 
 40 
 
 151/2 
 
 34 
 
 151/9, 
 
 30 
 
 91/2 
 
 40 
 
 91/?, 
 
 36 
 
 151/9, 
 
 30 
 
 151/9, 
 
 36 
 
 91/9 
 
 42 
 
 
 22 
 
 101/9 
 
 22 
 
 101/2 
 
 24 
 
 101/2 
 
 24 
 
 101/9, 
 
 36 
 
 10 
 
 36 
 
 10 
 
 Plates, 
 No. Size, In 
 
 Ins. high. lbs. 
 (a) (6) 
 
 Ins. lbs. 
 
 (a) 
 
 aS 
 
 E I, Triple 
 
 E 2, Quadruple . 
 
 E 3, Triple 
 
 E 4, Singlet-... 
 E 5, " t-... 
 E6. " t .-. 
 
 E 7, Triple 
 
 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, " 
 
 E 21, " .... 
 
 E 22, " 
 
 E 23, " .... 
 
 E 24, " .... 
 
 3 X 11/32 
 3x3/ 8 
 ' 3x11/32 
 3x11/32 
 3 x3/ 8 
 
 • 31/ 2 x3/ 8 
 
 • 3 X ll/3 2 
 
 3 x3/ 8 
 
 4 X 11/32 
 
 33/4 
 33/4 
 
 15/16* 
 
 93/s 
 93/4 
 95/ 8 
 
 21/ 2 91/ 2 11,f 
 
 4,800 
 6,650 
 6,000 
 free 
 3,000 
 4,375 
 
 3x3/ 8 
 3x3/8 
 4X3/8 
 • 4 X U/39 
 , 3X11/32 
 3 'X 11/32 
 4x3/ 8 
 31/ 2 x3/8 
 4I/9XH/39 
 4I/2XH/32 
 41/2X3.8 
 41/ 2 x3/8 
 4x3/8 
 4x3/ 8 
 
 31/2 
 
 33/4 
 33/4 
 
 8,000 
 87/ 16 5,400 
 8,000 
 
 93/4 
 93/4 
 
 93/4 11,820 
 
 3 3/ 8 
 37/16 
 
 41/2 101/8 8, 
 23/ 4 
 I* 
 13/16 
 
 13/16 
 
 10,600 
 13,100 
 5,600 
 6,840 
 
 1 
 1 
 
 21/4 
 21/4 
 
 000 
 ,070 
 .... 5,250 
 67/i 6 13,800 
 71/g 15,600 
 71/4 15,750 
 8I/2 18,000 
 8 8,750 
 
 8 7,500 
 
 5,500 
 8,000 
 8,000 
 2,350 
 4,970 
 6,350 
 
 6,000 
 10,000 
 12,200 
 15,780 
 10,600 
 8,600 
 21/2 14,370 
 23/ 4 15,500 
 2 9,540 
 7,300 
 
 28,800 
 32,930 
 U/4 10,750 
 11/4 9,500 
 
 (a) Between bands; (b) overall; 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 ■- 
 
 Round helical spring . .P ■■ 
 
 Round bar, in torsion P ■■ 
 
 Flat bar, in torsion P -- 
 
 Sbh\ 
 6 R ' 
 
 
 ' = **= 12 JW 
 
 SxdK 
 32 R' 
 
 
 f ~ R * ~ K Ed*' 
 
 Snd*. 
 16R' 
 
 
 
 S b% 2 . 
 3R \Zb°-+ h 2 ' 
 
 f ~ R * ~ ~~g~ ~~m? 
 
 P = force applied at end of radius or lever-arm R; ■& = angular motion 
 at end of radius R; S = permissible maximum stress, = 4 /s of permissible 
 stress in flexure: E = modulus of elasticity in tension; G = torsional 
 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. 311. 
 
400 
 
 HELICAL SPRINGS — SIZES AND CAPACITIES. 
 
 (Selected from Specifications of Penna. R. R. Co., 1899.) 
 
 
 
 
 
 
 
 Test. Height and 
 
 "So 
 
 
 c 
 
 u 
 
 
 ^ 
 
 
 
 
 Loads. 
 
 a 
 
 
 oS 
 
 PQ 
 
 oS 
 
 pq 
 
 .5 
 
 
 
 0J 
 
 '53 
 
 a 
 
 oS 
 
 
 
 m 
 
 d 
 O 
 
 a 
 
 a 
 
 A 
 
 
 
 «| 
 
 03 
 
 &0 H3 
 
 fl PI 
 
 a 
 
 oS 
 
 I 
 
 
 
 Jjo 
 
 30 
 
 f 
 
 12 
 
 "0 
 
 
 *2 
 
 OS 
 O 
 
 
 PM 
 
 Q 
 
 h3 
 
 H 
 
 fc 
 
 
 
 Eh 
 
 GQ 
 
 
 k! 
 
 
 
 
 
 lbs. oz. 
 
 
 
 
 ' 
 
 
 
 H 26 
 
 9/64 
 
 571/2 
 
 59 
 
 4 
 
 1 
 
 53/4 
 
 3 
 
 31/ 4 
 
 110 
 
 130 
 
 H 18 
 
 H/64 
 
 75 
 
 761/4 
 
 8 
 
 1 
 
 8 
 
 5 
 
 6 
 
 170 
 
 270 
 
 H 55 
 
 3/16 
 
 451/g 
 
 465/ 16 
 
 55/8 
 
 1 
 
 41/2 
 
 35/i 6 
 
 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 
 
 201/ 2 
 
 227/ 16 
 
 31/ 2 
 
 1 15/32 
 
 HI/16 
 
 19/64 
 
 13/8 
 
 110 
 
 200 
 
 H 1 
 
 1/4 
 
 451/2 
 
 47 
 
 10 
 
 11/4 
 
 51/8 
 
 35/ 8 
 
 43/s 
 
 250 
 
 500 
 
 H 5 
 
 1/4 
 
 251/ 4 
 
 281/4 
 
 6 
 
 21/4 
 
 21/4 
 
 U/8 
 
 11/2 
 
 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 I4l/ 2 
 
 1 U/16 
 
 191/s 
 
 13 
 
 141/8 
 
 587 
 
 700 
 
 H 68!* 
 
 3/8 
 
 991/2 
 
 1031/4 
 
 3 11/2 
 
 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 80 2 
 
 13/32 
 
 1923/s 
 
 1953/4 
 
 7 H/2 
 
 29/16 
 
 18 
 
 119/16 
 
 151/2 
 
 380 
 
 975 
 
 H 43 
 
 7/16 
 
 96 
 
 l025/i 6 
 
 4 1 
 
 47/i 6 
 
 815/16 
 
 33/s 
 
 51/8 
 
 450 
 
 660 
 
 H 64 
 
 7/16 
 
 755/ 8 
 
 781/2 
 
 3 3 
 
 29/32 
 
 75/s 
 
 55/8 
 
 53/4 
 
 1350 
 
 1440 
 
 H 53 2 
 
 15/32 
 
 1695^ 
 
 I729/i 6 
 
 8 4 
 
 217/32 
 
 16 1/2 
 
 121/4 
 
 151/2 
 
 330 
 
 1410 
 
 H 27 2 
 
 1/2 
 
 903/4 
 
 951/ 8 
 
 5 
 
 31/4 
 
 8 1/2 
 
 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 
 
 81 1/2 
 
 851/ 2 
 
 5 2 
 
 31/32 
 
 8 
 
 59/16 
 
 67/ie 
 
 1200 
 
 1900 
 
 H 86 3 
 
 17/32 
 
 I535/ 8 
 
 159 
 
 9 10 
 
 4 
 
 133/4 
 
 71/2 
 
 87/ie 
 
 1156 
 
 1360 
 
 H 63 
 
 9/16 
 
 98 
 
 103 
 
 6 15 
 
 33/4 
 
 91/8 
 
 51/2 
 
 7 
 
 1050 
 
 1800 
 
 H 33 3 
 
 9/16 
 
 80 1/4 
 
 847/g 
 
 5 10l/ 9 
 
 31/4 
 
 8 
 
 53/s 
 
 613/ie 
 
 1000 
 
 2200 
 
 H 59 2 
 
 5/8 
 
 741/4 
 
 773/4 
 
 6 7 
 
 27/s 
 
 81/4 
 
 69/16 
 
 71/4 
 
 2100 
 
 3500 . 
 
 H 8O1 
 
 5/8 
 
 1921/9 
 
 1973/4 
 
 16 11 
 
 315/16 
 
 18 
 
 119/16 
 
 151/2 
 
 900 
 
 2315 
 
 H 72 2 
 
 21/32 
 
 601/s 
 
 631/2 
 
 5 117/g 
 
 23/4 
 
 75/16 
 
 6 
 
 63/g 
 
 3260 
 
 4240 
 
 H 15 2 
 
 H/16 
 
 557/8 
 
 593/4 
 
 5 14 
 
 31/2 
 
 53/4 
 
 45/16 
 
 53/16 
 
 1400 
 
 3500 
 
 H 41 
 
 11/16 
 
 1171/2 
 
 1231/2 
 
 12 10 
 
 41/2 
 
 07/s 
 
 63/4 
 
 85/8 
 87/£ 
 
 1500 
 
 2720 
 
 H 40 
 
 3/4 
 
 1771/2 
 
 1865/ 8 
 
 22 21/2 
 
 6 1/2 
 
 6 
 
 73/s 
 
 1900 
 
 2300 
 
 H 70 
 
 3/4 
 
 62 
 
 66 
 
 7 12 
 
 3 3/s 
 
 7 
 
 55/s 
 
 61/4 
 
 2750 
 
 5050 
 
 H 17 2 
 
 13/16 
 
 100 
 
 1063/4 
 
 14 12 
 
 51/8 
 
 91/8 
 
 6 
 
 75/8 
 
 1700 3700 
 
 H 66 2 
 
 13/16 
 
 1051/4 
 
 1103/s 
 
 15 7 
 
 45/32 
 
 07/s 
 
 81/8 
 
 87/s 
 
 3670 5040 
 
 H 37 
 
 27/32 
 
 77 
 
 817/s 
 
 12 21/2 
 
 315/16 
 
 8 1/2 
 
 6H/16 
 
 71/2 
 
 3300 
 
 6250 
 
 H 87 2 
 
 27/32 
 
 13013/ 16 
 
 13715/ 16 
 
 20 9 
 
 5 3/8 
 
 21/4 
 
 73/4 
 
 87/ie 
 
 3540 
 
 4165 
 
 H 12 2 
 
 7/8 
 
 85 
 
 9H/2 
 
 14 7 
 
 5 
 
 8 1/2 
 
 53/4 
 
 73/s 
 
 2000 
 
 5200 
 
 H 33 2 
 
 7/8 
 
 82 
 
 8811/i 6 
 
 13 15 
 
 51/8 
 
 8 
 
 53/s 
 
 613/ie 
 
 2250 
 
 5000 
 
 H 2 
 
 15/16 
 
 46 
 
 523/s 
 
 8 151/4 
 
 5 
 
 45/ 8 
 
 33/s 
 
 4 
 
 3250 
 
 7000 
 
 H 16 
 
 15/16 
 
 85 
 
 927/ 8 
 
 16 10 
 
 6 
 
 8 
 
 5 
 
 6 
 
 3600 
 
 5100 
 
 H 10 
 
 1 
 
 85 
 
 92 
 
 18 14 
 
 51/2 
 
 8 1/2 
 
 6 
 
 7 
 
 4500 
 
 7000 
 
 H 42 x 
 
 1 
 
 36 
 
 427/g 
 
 8 
 
 5 3/8 
 
 35/8 
 
 25/s 
 
 33/ 8 
 
 1795 
 
 7180 
 
 H 4 
 
 U/16 
 
 987/s 
 
 105 
 
 24 12 
 
 5 
 
 07/s 
 
 8 1/2 
 
 93/ 8 
 
 6000 
 
 9570 
 
 H 861 
 
 U/16 
 
 1535/8 
 
 1641/2 
 
 38 9 
 
 8 
 
 33/4 
 
 71/2 
 
 87/i 6 
 
 4624 
 
 5440 
 
 H 3 
 
 11/8 
 
 353/ 8 
 
 4II/4 
 
 9 15 
 
 47/s 
 
 41/8 
 
 33/s 
 
 33/4 
 
 6000 
 
 12000 
 
 H 14i 
 
 U/8 
 
 51 
 
 587/s 
 
 14 4 
 
 61/8 
 
 51/8 
 
 3H/16 
 
 43/16 
 
 5000 
 
 8950 
 
 H 6! 
 
 13/16 
 
 991/g 
 
 1093/ 4 
 
 31 1 
 
 8 
 
 91/8 
 
 51/2 
 
 7 
 
 4550 
 
 7750 
 
 H 47 
 
 13/16 
 
 731/ 2 
 
 791/2 
 
 23 
 
 5 7/16 
 
 8I/4 
 
 69/16 
 
 71/4 
 
 7400 
 
 12500 
 
 H 9 
 
 11/4 
 
 971/2 
 
 108 
 
 33 12 
 
 8 
 
 9 
 
 53/4 
 
 71/2 
 
 4000 
 
 9100 
 
 H 72i 
 
 11/4 
 
 621/s 
 
 683/4 
 
 21 8I/2 
 
 53/s 
 
 75/i 6 
 
 6 
 
 63/ 8 
 
 10700 
 
 14875 
 
 H 8 
 
 15/16 
 
 96 
 
 106 1/2 
 
 36 12 
 
 8 
 
 91/8 
 
 6 
 
 71/4 
 
 6350 
 
 10600 
 
 H 62 
 
 1 5/16 
 
 70 
 
 771/16 
 
 26 12 
 
 513/16 
 
 8 
 
 6 1/2 
 
 71/4 
 
 7900 
 
 15800 
 
 H 12i 
 
 13/8 
 
 87 
 
 973/s 
 
 36 7 
 
 8 
 
 8 1/2 
 
 53/4 
 
 73/s 
 
 5000 
 
 12200 
 
 H 39i 
 
 13/s 
 
 755/ 8 
 
 831/2 
 
 31 11 
 
 63/g 
 
 83/s 
 
 65/ 8 
 
 71/2 
 
 8150 
 
 16300 
 
 H 28i 
 
 1 13/32 
 
 8411/ie 
 
 95 
 
 37 3 
 
 8 
 
 81/4 
 
 53/4 
 
 67/s 
 
 7325 
 
 13250 
 
 * The subscript 1 means the outside coil of a concentric group or 
 cluster; 2 and 3 are inner coils. 
 
RIVETED JOINTS. 401 
 
 Phosphor-Bronze Springs. Wilfred Lewis (Engs'. Club, Phila., 1887) 
 made some tests of a helical spring of phosphor-bronze wire, 0.12 in. 
 diameter, 1V4 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 lbs. A load of 30 lbs. gradually applied gave a permanent 
 set. With a load of 21 lbs. in 30 hours the spring lengthened from 20 Vs 
 inches to 21 1/8 inches, and in 200 hours to 21 1/4 inches. It was concluded 
 that 21 lbs. 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., 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 lbs. 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 3 /D lbs. WnD 3 -*- 1,468,000 d* 
 
 West Bromwich Spring 28,400 d 3 /D " WnD 3 -s- 1,575,000 d* 
 
 Turton & Piatt Spring 44,200 d s /D " WnD 3 -i- 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 lbs., reached its elastic limit at 85,000 lbs., or 
 234,000 lbs. 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 lbs. and reached an elastic limit at 
 65,000 lbs., or 180,000 lbs. 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., 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 V\ 3 /s V2 3 /4 
 
 Loss of tenacity, per cent 8 18 26 33 
 
 When 7/8-in. punched holes were reamed out to lVsin. 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 Institution 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 
 
402 
 
 RIVETED JOINTS. 
 
 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 3/4-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 
 
 Perforated by punching and drilling- 
 Perforated by punching only 
 
 1.110 
 0.927 
 
 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 of 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. 
 
 Total breaking load. Tons 
 Load at which visible slip began 
 
 Hand. . . . . 
 Hydraulic 
 
 Hand 
 
 Hydraulic 
 
 86.01 
 
 82.16 
 
 149.2 
 
 85.75 
 
 82.70 
 
 145.5 
 
 21.7 
 
 25.0 
 
 31.7 
 
 47.5 
 
 53.7 
 
 49:7 
 
 193.6 
 183.1 
 25.0 
 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. 
 
RIVETED JOINTS. 
 
 403 
 
 The metal between the rivet-holes has a considerably greater tensile 
 resistance per square inch than the imperforated 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 -in C h 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 lbs.] 
 
 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 8V2% 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-\- rf/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 upon 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 
 3/ 4 " 
 3/4 " 
 1 inch 
 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 
 
404 
 
 RIVETED JOINTS. 
 
 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 -4- t), 
 and of pitch p to diameter of hole (p -s- d) in joints of maximum strength 
 in 3/s-inch plate. 
 
 For Single-riveted Plates. 
 
 Original Tenacity of 
 Plate. 
 
 Shearing Resistance 
 of Rivets. 
 
 Ratio. 
 d+t 
 
 Ratio. 
 p + d 
 
 Ratio. 
 Plate Area 
 Rivet Area 
 
 Tons per 
 Sq. In. 
 
 Lbs. per 
 Sq. In. 
 
 Tons per 
 Sq. In. 
 
 Lbs. per 
 Sq. In. 
 
 30 
 
 28 
 30 
 28 
 
 67,200 
 62,720 
 67,200 
 62,720 
 
 22 
 22 
 24 
 24 
 
 49,200 
 49,200 
 53,760 
 53,760 
 
 2.48 
 2.48 
 2.28 
 2.28 
 
 2.30 
 2.40 
 2.27 
 2.36 
 
 0.667 
 0.785 
 0.713 
 0.690 
 
 This table shows that the diameter of the hole should be 2V3 times the 
 thickness of the plate, and the pitch of the rivets 23/s 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 best 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 
 
 " 30 " " " 24 " " " 0.570 
 
 " 28 " " " .24 " " " 0.606 
 
 d 2 
 Or, in the mean, the pitch p = 0.56 -r + d. With too small rivets this 
 
 gives pitches often considerably smaller in proportion than 23/g 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 \ __ _ , 1rt & , j. 
 " 28 " " " 22 " " j ' t 
 
 (12 
 
 " 30 ' 22 " " p = 1.06 - + d°, 
 
 d? 
 " 28 24 " " p = 1.24y+a\ 
 
RIVETED JOINTS. 
 
 4D5 
 
 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 belong to joints of 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 tplates 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. 
 
406 
 
 RIVETED JOINTS. 
 
 The pitch is as wide as is allowable without impairing the tightness ot 
 the joint under steam. 
 
 For single-riveted lap-joints in the circular seams of boilers which have 
 double-riveted longitudinal lap-joints, 
 
 d = t X 2.25; v = dX 2.25 = tX 5 (nearly) ; I = 1X6. 
 
 For double-riveted lap-joints: 
 
 d = 2.25t; p = Si; s = 4.5* ; I = 10.5L 
 
 Single- riveted Joints. 
 
 Double-riveted Joints. 
 
 t 
 
 d 
 
 V 
 
 I 
 
 t 
 
 d 
 
 V 
 
 s 
 
 I 
 
 3/16 
 
 7/16 
 
 15/16 
 
 U/8 
 
 3/16 
 
 7/16 
 
 U/2 
 
 7/8 
 
 2 
 
 V4 
 
 0/16 
 
 U/4 
 
 U/2 
 
 1/4 
 
 9/16 
 
 2 
 
 13/16 
 
 23/4 
 
 6/16 
 
 11/16 
 
 1 9/16 
 
 17/8 
 
 5/16 
 
 11/16 
 
 21/2 
 
 U/2 
 
 33/a 
 
 3/8 
 
 13/16 
 
 1 7/ 8 
 
 21/4 
 
 3/8 
 
 13/16 
 
 3 
 
 13/ 4 
 
 4 
 
 7/16 
 
 1 
 
 2 3/ 16 
 
 25/8 
 
 7/16 
 
 1 
 
 31/2 
 
 2 
 
 45/8 
 
 1/2 
 
 11.8 
 
 2 1/2 
 
 3 
 
 1/2 
 
 U/8 
 
 4 
 
 21/4 
 
 51/4 
 
 9/16 
 
 11/4 
 
 213/i 6 
 
 3 3/8 
 
 9/16 
 
 H/4 
 
 41/2 
 
 21/2 
 
 57/a 
 
 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" 
 3/8 
 3/4 
 3/4 
 3/4 
 3/4 
 
 1 
 
 1 
 
 1 
 
 0.8" 
 
 0.7 
 
 1.1 
 
 1.6 
 
 1.1 
 
 1.6 
 
 1.3 
 
 1.75 
 
 1.3 
 
 3.62 
 3.93 
 2.82 
 3.41 
 4.00 
 3.94 
 2.42 
 3.00 
 3.92 
 
 75.2 
 
 Butt 
 
 Lap 
 
 Lap 
 
 Butt 
 
 Butt 
 
 76.5 
 68.0 
 73.6 
 72.4 
 76.1 
 
 Lap 
 
 Lap 
 
 Butt 
 
 63.0 
 70.2 
 76.1 
 
 Diameter of Rivets for Different Thicknesses of Plates. 
 
 Thickness 
 of Plate. 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 3/4 
 13/16 
 
 3/4 
 ...... 
 
 15/16 
 H/16 
 
 9/16 
 
 3/4 
 13/16 
 
 7/8 
 3/4 
 
 5/8 
 
 3/4 
 7/8 
 7/8 
 
 H/16 
 
 3/8 
 
 7/8 
 7/8 
 13/16 
 
 3/4 
 
 7/8 
 
 15/16 
 1 
 7/8 
 
 13/16 
 
 7/8 
 1 
 1 
 
 7/8 
 
 I 
 
 1 1/8 
 Us 
 1 
 
 15/16 
 
 1 
 
 13/16 
 
 U/8 
 
 1 
 
 Diam. (1). 
 Diam. (2). 
 Diam. (3). 
 Diam. (4). 
 
 • 5/ 8 
 . 5/ 8 
 
 . 1/2 
 
 5/8 
 5/8 
 5/8 
 5/8 
 7/8 
 3/4 
 1/2 
 
 5/8 
 3/ 4 
 3/4 
 5/8 
 15/16 
 7/8 
 9/16 
 
 1 
 
 U/4 
 U/8 
 11/16 
 
 Diam. (5). 
 
 . 3/ 4 
 . H/16 
 
 . 3/ 8 
 
 
 1 
 
 3/4 
 
 1 
 
 13/16 
 
 
 
 
 
 
 
 Diam. (7). 
 
 
 
 
 
 
 
RIVETED JOINTS. 
 
 407 
 
 (1) Lloyd's Rules. (2) Liverpool Rules. (3) English Dock-yards. 
 (4) French Veritas. (5) Hartford Steam Boiler 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 
 
 w A d 2 
 
 (p - d)t X I.IQT = - c/ 2 X | T, whence p = 0.571 ~ + 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 404, ante. » 
 
 
 > 
 
 Pitch. 
 
 Efficiency. 
 
 
 0> 
 > 
 
 Pitch. 
 
 Efficiency. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 bi> 
 
 
 bi) 
 
 ti) 
 
 
 
 bi) 
 
 M 
 
 bi) 
 
 bi 
 
 
 
 c 
 
 a 
 
 
 
 
 
 a 
 
 E 
 
 c 
 
 
 PI 
 
 
 
 
 
 a>'$ 
 
 a 
 
 
 
 o>'£ 
 
 
 0>+3 
 
 
 
 "So > 
 
 as 
 
 3£ 
 
 ■52 
 
 
 
 flJS 
 
 c3 O 
 
 Q^ 5 
 
 o> "2 
 
 bfi> 
 
 11 
 
 "bb> 
 
 ■S£ 
 
 11 
 
 Q 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 % 
 
 % 
 
 in 
 
 in. 
 
 in. 
 
 in. 
 
 % 
 
 % 
 
 3/16 
 
 7/16 
 
 1.020 
 
 1.603 
 
 57.1 
 
 72.7 
 
 V2' 
 
 3/4 
 
 1.392 
 
 2.035 
 
 46.1 
 
 63.1 
 
 3/16 
 
 1/2 
 
 1.261 
 
 2.023 
 
 60.5 
 
 75.3 
 
 1/2 
 
 7/8 
 
 1.749 
 
 2.624 
 
 50.0 
 
 66.6 
 
 1/4 
 
 1/2 
 
 1.071 
 
 1.642 
 
 53.3 
 
 69.6 
 
 1/2 
 
 1 
 
 2.142 
 
 3.284 
 
 53.3 
 
 70.0 
 
 1/4 
 
 9 /l6 
 
 1.285 
 
 2.008 
 
 56.2 
 
 72.0 
 
 1/2 
 
 11/8 
 
 2.570 
 
 4.016 
 
 56.2 
 
 72.0 
 
 5/16 
 
 9/16 
 
 1.137 
 
 1.712 
 
 50.5 
 
 67.1 
 
 9/16 
 
 3/4 
 
 1.321 
 
 1.892 
 
 43.2 
 
 60.3 
 
 5/16 
 
 5/8 
 
 1.339 
 
 2.053 
 
 53.3 
 
 69.5 
 
 9/16 
 
 7/8 
 
 1.652 
 
 2.429 
 
 47.0 
 
 64.0 
 
 5/16 
 
 11/16 
 
 1.551 
 
 2.415 
 
 55.7 
 
 71.5 
 
 9/16 
 
 1 
 
 2.015 
 
 3.030 
 
 50.4 
 
 67.0 
 
 3/8 
 
 5/8 
 
 1.218 
 
 1.810 
 
 48.7 
 
 65.5 
 
 9/16 
 
 1V8 
 
 2.410 
 
 3.694 
 
 53.3 
 
 69.5 
 
 3/8 
 
 3/4 
 
 1.607 
 
 2.463 
 
 53.3 
 
 69.5 
 
 9/16 
 
 11/4 
 
 2.836 
 
 4.422 
 
 55.9 
 
 71.5 
 
 3/8 
 
 7/8 
 
 2.041 
 
 3.206 
 
 5" 1 
 
 72.7 
 
 5/8 
 
 3/4 
 
 1.264 
 
 1.778 
 
 40.7 
 
 57.8 
 
 7/16 
 
 5/8 
 
 1.136 
 
 1.647 
 
 45.') 
 
 62.0 
 
 5/8 
 
 7/8 
 
 1.575 
 
 2.274 
 
 44.4 
 
 61.5 
 
 7/16 
 
 3/ 4 
 
 1.484 
 
 2.218 
 
 49. i 
 
 66.2 
 
 5/8 
 
 1 
 
 1.914 
 
 2.827 
 
 47.7 
 
 64.6 
 
 7/16 
 
 7/8 
 
 1.869 
 
 2.864 
 
 53.2 
 
 69.4 
 
 5/8 
 
 11/8 
 
 2.281 
 
 3.438 
 
 50.7 
 
 67.3 
 
 7/16 
 
 1 
 
 2.305 
 
 3.610 
 
 56.6 
 
 72.3 
 
 5/8 
 
 11/4 
 
 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 1/7% weaker in a drilled 
 t^an 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. 
 
408 
 
 RIVETED JOINTS. 
 
 Shearing, 16.5 
 
 Ratio, 0.62 
 
 20.2 
 
 0.79 
 
 19.0 
 
 0.85 
 
 22.1 
 
 " 0.77 
 
 The shearing resistance of a bar, when sheared in circumstances which 
 prevent friction, is usualiy less than the tenacity of the bar. The ioi« 
 lowing results show the decrease: 
 
 Harkort, iron Tenacity, 26.4 
 
 Lavalley, iron. " 25.4 
 
 Greig and Eyth, iron. " 22.2 
 Greig and Eyth, steel " 28.8 
 
 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 siiow that for iron the ratio of the 
 shearing resistance and tenacity aepends 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. CardulkO 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. 
 
 / = the tensile strength of the plate in pounds per sq. in. 
 
 s = 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. 90 and 91)= the pitch in single and double lap riveting = twice 
 
 (p"""@ w 
 
 © © © © © 
 
 MM 1 
 
 &._©_©_ 
 
 Fig. 90. 
 Triple Riveting. 
 
 Fig. 91. 
 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 grouD 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, = 0.7854 d 2 (ns + 
 ms") . 
 
 C = the strength of the rivets or the plates against crushing, = 
 dtc (n + m). 
 
THE STRENGTH OF RIVETED JOINTS. 409 
 
 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 Vi6in. 
 
 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) -s- p. 
 
 The maximum possible efficiency for a well-designed joint is 
 
 m + n + (/ -*- c) 
 
 Empirical formula for the diameter of the rivet-hole when the crush- 
 ing strength is unknown. Assuming that c = 1.4/, and s"= 1.75 s, we have 
 by equating C and S, and substituting, 
 
 s{n+ 1.75 m) 
 
 Margin. The distance from the center of any rivet-hole to the edge of 
 the plate should be not less than 1 1/2(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 3/ 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.. 
 
 Lap Joints 
 
 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 Vi6in. 
 
 Calculation of Triple-riveted Butt and Strap Joints. — Formulae: 
 T = ft (p-d), S = -0.7854 d 2 (ns + ms"), C = dtc (m + n) (notation on 
 preceding page), n = 1, m .= 4. 
 
 Take / = 55,000; * = 0.8/, = 44,000; s" = 1.75s = 77,000, c = 1.4 / 
 = 77,000. 
 
 Then T = 55,000 1 (p-d), S = 276,460 rf 2 , C = 385,000 dt. 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 (]=] 
 
 1 31 
 
 2.62 
 
 3.47 
 
 4.14 
 
 c= 
 
 1.75 
 
 3.50 
 
 4.63 
 
 5.52 
 
410 RIVETED JOINTS. 
 
 For maximum strength, T = S = C; dividing by 55,000 1, (p- d) = 
 5.027 d 2 = 7dt; whence d = 1.3925$; p = 3d. 
 
 Thickness of plate, < =5/ie 3 /8 7 /i6 V2 9 /i6 5 /s 
 
 Diam. rivet hole, 
 
 d= 1.3925$. .... 0.4353 0.5222 0.6092 0.6962 0.7833 0.8703 
 Pitch of outer row, 
 
 p = 8d. ....... 3.4816 A 1776 4.8736 5.5696 6.2664 6.9624 
 
 T= 55,000 t(p-d) 52,360 75,390 102,610 134,020 169,630 209,420 
 5= 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, — ■ —77- = _ , ' , 
 
 n + m + f/c 5+1/1.4 
 = 87.5 per cent. 
 Diameter of rivet-hole, next largest 16th, 7/ 16 9/ 16 5/ 8 3/4 13/ 16 7/ 8 
 
 For the same thickness of plates the Hartford Steam Boiler Inspection 
 and Insurance Co. gives the following proportions: 
 Thickness, t, 5/ 16 3/ 8 7/ 16 i/ 2 9/ 16 5/ 8 
 
 Diam. rivet-hole, d, 3/ 4 13/ 16 15/ 16 1 n/ 16 n/ 16 
 
 Pitch of outer row, p, 6 1/4 6 1/2 63/ 4 71/2 73/ 4 72/4 
 
 Using the same values for /, s, s" and c, we obtain: 
 
 T= 94,530 117,300 139,860 178,750 207,850 229,880 
 
 S = 155,400 168,400 194,300 207,300 220,200 220,200 
 
 C= 90,030 117,300 157,900 192,500 230,000 255,500 
 
 Strength of solid 
 
 plate, fvt = 107,360 134,060 162,420 206,250 239,770 266,400 
 
 Efficiency T, S or 
 
 C, lowest -h 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 = 15.4 dt; whence d = 
 1.32485$, p = 16.4 d. Efficiency (p - d)+p = 93.9 per cent. Check by 
 
 Cardullo's formula — ; -—rr = 71 — , in/ ■ = 93.9 per cent. 
 
 n+ m + f/c 11+ 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 8 1/2". 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 IV2. 
 
 Distance between rows of rivets 
 
 = 2 X diam. of rivet or = [(diam. X 4) + 1] -*- 2, if chain, and 
 
 V[(pitch X 11) + (diam. X 4)1 X (pitch + diam. X 4)' . 
 = — ^ i j~ — if zigzag. 
 
 Diagonal pitch = (pitch X 6 + diam. X 4) -f 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 
 
THE STRENGTH OF RIVETED JOINTS 
 
 411 
 
 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 /l6 
 
 3/8 
 
 7/16 
 
 1/2 
 
 Diam. rivet-hole. 
 Pitch 
 
 3/4 H/I6 
 2Vl6 21/16 
 U/8 H/32 
 
 13/16 3/4 
 21/8 21/8 
 17/32 U/8 
 
 15/16 13/16 
 23/ 8 21/8 
 113/32 17/3 2 
 
 1 15/16 
 27/ie 23/s 
 U/2 U3/32 
 
 I 1/16 I 
 
 21/2 21/2 
 19/32 U/2 
 
 Center to edge . . 
 
 Double-riveted Lap Joints. 
 
 
 
 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 
 
 
 3/ 4 
 27/8 
 1 15/16 
 U/8 
 0.74 
 
 13/16 
 27/8 
 1 15/16 
 17/32 
 0.72 
 
 15 /l6 
 31/ 4 
 2 3/, 6 
 1 13/32 
 0.70 
 
 1 
 
 31/4 
 
 23/16 
 
 U/2 
 
 0.70 
 
 U/l6 
 
 Pitch 
 
 3.32 
 
 Dist. bet. rows 
 
 2.2 
 1 19/32 
 0.68 
 
 
 
 
 Triple-riveted Lap Joints. 
 
 Thickness 
 
 Diam. rivet-hole. . 
 
 Pitch 
 
 Dist. bet. rows. . . . 
 Inner row to edge 
 Efficiency 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 H/16 
 
 3/ 4 
 
 13/16 
 
 15/16 
 
 3 
 
 31/8 
 
 31/4 
 
 33/4 
 
 2 
 
 2Vi6 
 
 23/18 
 
 21/2 
 
 U/32 
 
 U/8 
 
 17/32 
 
 1 13/32 
 
 7/ 
 
 0.76 
 
 0.75 
 
 0.75 
 
 1 
 
 315/ie 
 25/s 
 U/2 
 0.75 
 
 Triple-riveted Butl-slrap Joints. 
 
 Thickness 
 
 Diam. rivet-hole 
 
 Pitch, inner rows. . . . 
 Dist. bet. inner rows. 
 Dist. outer to 2d row 
 Edge to nearest row. 
 Efficiency % 
 
 5/16 
 
 3/8 
 
 7/16 
 
 1/2 
 
 9 /l6 
 
 3/ 4 
 
 13/16 
 
 15/16 
 
 1 
 
 11/16 
 
 31/8 
 
 31/4 
 
 3 3/8 
 
 33/4 
 
 37/s 
 
 21/8 
 
 2 3/ 16 
 
 21/4 
 
 23/8 
 
 2 5/8 
 
 23/s 
 
 21/2 
 
 23/4 
 
 3 
 
 3 3/! 6 
 
 U/4 
 
 17/32 
 
 1 13/32 
 
 U/2 
 
 1 19/32 
 
 88 (?) 
 
 87.5 
 
 86 
 
 86.6 
 
 85.4 
 
 U/16 
 37/ 8 
 25/ 8 
 3 3/16 
 1 19/32 
 84(?j 
 
 The distance to the edge of the plate is from the center of rivet-holes. 
 
4.12 
 
 RIVETED JOINTS. 
 
 Pressure Required to Drive Hot Rivets. 
 
 Philadelphia, give the following table (1897): 
 
 -R. D. Wood & Co. 
 
 Power to Dkive Rivets Hot. 
 
 Size. 
 
 Girder- 
 
 Tank- 
 
 Boiler- 
 
 Size. 
 
 Girder- 
 
 Tank- 
 
 Boiler- 
 
 work. 
 
 work. 
 
 work. 
 
 work. 
 
 work. 
 
 work. 
 
 in. 
 
 tons. 
 
 tons. 
 
 tons. 
 
 in. 
 
 tons. 
 
 tons. 
 
 tons. 
 
 1/2 
 
 9 
 
 15 
 
 20 
 
 H/8 
 
 38 
 
 60 
 
 75 
 
 5/8 
 
 12 
 
 18 
 
 25 
 
 H/4 
 
 45 
 
 70 
 
 100 
 
 3/4 
 
 15 
 
 22 
 
 33 
 
 U/2 
 
 60 
 
 85 
 
 125 
 
 7/8 
 1 
 
 22 
 30 
 
 30 
 
 45 
 
 45 
 60 
 
 13/4 
 
 75 
 
 100 
 
 150 
 
 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 lbs. At 10,000 lbs. the rivet swelled and filled the hole with- 
 out forming a head. At 20,000 lbs. the head was formed and the plates 
 were slightly pinched. At 30,000 lbs. the rivet was well set. At 40,000 
 lbs. 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 lbs. From these experiments the conclusion might 
 be drawn that the pressure required for cold riveting was about 300,000 
 lbs. per square inch of rivet section. In hot riveting, until recently there 
 was never any call for a pressure exceeding 60,000 lbs., but now pressures 
 as high as 150,000 lbs. are not uncommon, and even 300,000 lbs. 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 lbs. per sq. in. press- 
 ure, but it hardened and increased its resistance as it flowed until it reached 
 a maximum of about 100,000 lbs. 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 bv Oscar Textor, with results as follows: 
 
 P. 0.008 to 0.027, av. 6.015; 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 
 high strength. Ten bars and two rivets gave tensile strength, 46,735 to 
 55,380, av. 52,195 lbs. 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 of 
 area. 65.6%. Eight bars in single shear gave shearing strength 35,660 
 to 50 190 av. 44,478 lbs. per sq. in.; seven bars in double shear gave 
 39,170 to 53,900, av. 45,720 lbs. The shearing strength averaged 86.3% 
 of the tensile strength. 
 
IRON AND STEEL. 
 
 413 
 
 
 
 
 
 5? L"^ 
 
 
 
 
 
 o ^ 
 
 
 
 
 « 
 
 
 
 
 s 
 
 cX! 
 
 g o3^ 
 
 
 
 -B 
 
 H 
 
 -3 mS 
 
 
 
 S 
 
 2 
 
 
 
 s 
 
 ^ 
 
 o 
 
 ined 
 ct p: 
 shea 
 
 ed st 
 
 
 >> 
 
 
 
 03 £ ~3 
 
 
 
 
 
 3^ §12 
 
 °.SSa 
 
 
 3 -S 
 
 
 oo 
 
 
 tocS 
 
 
 
 
 
 
 
 
 
 Is 
 
 
 
 S "S 2 § oi — 
 
 
 S ° 
 
 s 
 
 O 
 
 'btained by dir 
 is from ores, as C 
 Chenot, and ot] 
 is irons. 
 
 btained by indir 
 is from cast iron, 
 ■hearth and pudd 
 
 
 o 
 
 1 
 
 e 
 1 
 
 S 
 
 o 
 p 
 o 
 
 03 
 
 
 
 
 ' £ 
 
 
 
 K^ 
 
 ^ 
 
 ° £ .SO « >>» 
 
 
 
 
 C^ 
 
 eala^lco 
 
 £ 
 
 
 
 
 a"3 & &«•- 
 
 
 
 
 ,n 
 
 c 
 
 
 
 
 
 g 
 
 
 
 j 
 
 . - c3 
 
 .2 3 2« 
 
 
 
 
 H 
 
 
 
 
 a 
 
 
 
 
 w 
 
 ) Cruci 
 )Bessei 
 and 
 ) Open 
 stei 
 ) Mitis 
 
 
 $ 
 
 « 
 
 
 CS C S 
 
 
 03 
 
 
 
 
 
 s 
 
 § 
 
 
 
 
 03 O ^ 
 _2^5 3 <» 
 
 
 
 
 
 
 12 
 '3 
 
 33 
 
 l 
 
 
 
 03 
 
 
 
 _q 03 c3 <U 
 
 "3 c ^"3 
 
 
 § O 
 
 
 
 :p£'§ ■ 
 
 
 ^£ 
 
 
 
 o3^ ~ 
 
 
 
 fc 
 
 §°-.S 
 
 
 
 
 O 
 
 ^0°M 
 
 
 
 
 ^Q 
 
 
 
 
 
 o 
 
 
 <! 
 
 
 
 
 i^ 
 
 o 
 
 o 
 
 
 O 
 
 e 
 
 
 o3 
 
 a 
 
 T3 
 4) 
 
 bJO 
 
 
 
 g 
 
 '-S • 
 
 
 
 
 '3 
 
 .2 >> 
 
 .2 
 
 .2 
 
 
 O 
 
 M"^ 
 
 o 
 
 .2 
 
 CD 
 
 B 
 
 ct 
 
 o 
 
 w 
 
 5 
 
 cc 
 
 > 
 
 w 3 ft ,H^3 
 
 CD OJ £ "^ M .So 
 
 1 1 ! °m 
 
 1 i i §t§i 
 
 m » ■£ £-.3 >>> 
 
 T3P, . CI Og^a 
 
 O +^ pTI CD 
 
 lp 
 
 2^- 
 "2^ 
 
 P O £ a, 
 
 .2o£ o ST!®-* 
 
 III f S||l 
 
 _ a 
 
 60 2|, § i'3 
 
 0) > g" . C CD' 
 
 t 1- T 
 
 S|5l 
 
 cdx: oj _ 
 
 S "^ '> ^ ~ ' «3 ^ to i^ 
 '>co3^'a — "eS & ° 
 5 3^^S SIS® 
 
 ! cud" 
 
 c5-S 
 
 - r- 
 
 o S 3 a 3 
 
 ■c-3 o — 
 
 t«H as 3 
 
 fio,„§c 
 
 bj^ 
 
 ££ 
 
 = 12 > 2 
 
 
 Tx.-cPcd'O >d°^ 
 
 (^ o3 o3 • p O rj 
 
 o.>^.2.E; = 
 • w .-a-2-2 ^ Sf,a M 
 
 «5o3C»o3'3^£J-ro- t; ' OT 
 
 m .2 5 ££3,3 
 
414 
 
 IRON AND STEEL. 
 
 CAST IRON. 
 
 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 giaded 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 silicized 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. I. & S. A., Feb., 1892): 
 
 
 No. 1. 
 
 No. 2. 
 
 No. 3. 
 
 No. 4. 
 
 No.4B. 
 
 No. 5. 
 
 
 92.37 
 3.52 
 0.13 
 2.44 
 1.25 
 0.02 
 0.28 
 
 92.31 
 2.99 
 0.37 
 2.52 
 1.08 
 0.02 
 0.72 
 
 94.66 
 2.50 
 1.52 
 0.72 
 0.26 
 
 trace 
 0.34 
 
 94.48 
 2.02 
 1.98 
 0.56 
 0.19 
 0.08 
 0.67 
 
 94.08 
 2.02 
 1.43 
 0.92 
 0.04 
 0.04 
 2.02 
 
 94.68 
 
 Graphitic carbon 
 
 Combined carbon 
 
 0.41 
 
 
 0.04 
 
 
 0.02 
 
 
 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. 
 
CAST IRON. 415 
 
 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 soft, 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. The total C in cast iron usually 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 alloy is 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. 
 
416 IRON AND STEEL. 
 
 Aluminum. — 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 
 gray iron it softens and weakens it. 
 
 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 Ikon. — 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 remelting. Since Mn, Ti, and Va all act as 
 deoxidizers, it should be possible by additions to the ladle of alloys of 
 FeMn, FeVa, or FeTi, 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, increased 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 Metallography, under Steel.) 
 
 Ferrite, iron free from carbon. It is found in miid steel in small amounts 
 in gray cast iron, and in malleable cast iron. 
 
 Cementite, Fe 3 C. 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 laminee 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 
 respectively. 
 
 Martensite, 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 417.) 
 
 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. Mack., 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. 
 
CAST IRON. 
 
 417 
 
 Analyses of Cast Iron. 
 
 (Abbreviations, TC, total carbon; GC, graphitic carbon; CC, combined 
 carbon.) 
 
 No. 
 
 TC 
 
 GC 
 
 CC 
 
 Silicon. 
 
 Man- 
 ganese. 
 
 Phos- 
 phorus . 
 
 Sul- 
 phur. 
 
 
 1 
 
 3.98 
 
 0.39 
 
 3.59 
 
 0.38 
 
 0.13 
 
 0.20 
 
 0.038 
 
 Melts at 2048° F. 
 
 2 
 
 3 78 
 
 1.76 
 
 2.01 
 
 0.69 
 
 0.44 
 
 0.53 
 
 0.031 
 
 Melts at 2156° F. 
 
 3 
 
 3.88 
 
 2.60 
 
 1.28 
 
 1.52 
 
 0.49 
 
 0.45 
 
 0.035 
 
 Melts at 221 l°F. 
 
 4 
 
 4.03 
 
 3.47 
 
 0.56 
 
 2.01 
 
 0.49 
 
 0.39 
 
 0.034 
 
 Melts at 2248° F. 
 
 5 
 
 3.56 
 
 3.43 
 
 0.13 
 
 2.40 
 
 0.90 
 
 0.08 
 
 0.032 
 
 Melts at 2280° F. 
 
 6 
 
 4.39 
 
 0.13 
 
 4.26 
 
 0.65 
 
 0.40 
 
 0.25 
 
 0.038 
 
 Melts at 2000° F. 
 
 7 
 
 4 45 
 
 2 99 
 
 1.46 
 
 0.67 
 
 0.41 
 
 0.26 
 
 0.039 
 
 Melts at 2237° F. 
 
 8 
 
 3 . 30 
 
 2.80 
 
 0.50 
 
 2.00 
 
 0.60 
 
 0.08 
 
 0.03 
 
 Swedish char- 
 coal pig. 
 
 9 
 
 
 2.25-2.5 
 
 0.6-0.8 
 
 0.8-1.2 
 
 0.4-0.8 
 
 0.15-0.4 
 
 
 For engine cylin- 
 ders. 
 
 10 
 
 3 . 40 
 
 3.40 
 
 trace 
 
 2.90 
 
 0.50 
 
 1.65 
 
 0.04 
 
 English, high P. 
 
 No. 1. 
 English, high P. 
 
 No. 3. 
 For thin orna- 
 
 11 
 
 3.40 
 
 3.20 
 
 0.20 
 
 2.60 
 
 0.50 
 
 1.58 
 
 0.04 
 
 12 
 
 
 3.2-3.6 
 
 0.1-0.15 
 
 2.5-2.8 
 
 up to 
 
 1.3-1.5 
 
 .03-. 04 
 
 
 
 
 
 
 1.0 
 
 
 
 mental work. 
 
 13 
 
 
 Y. 0-3. 2 
 
 0.4-0.5 
 
 2-2.3 
 
 up to 
 1.0 
 
 1-1.3 
 
 .06-. 08 
 
 For medium size 
 castings. 
 
 14 
 
 
 2.8-3.0 
 
 0.4-0.6 
 
 1.2-1.5 
 
 0.6-0.9 
 
 0.4-0.6 
 
 .06-. 08 
 
 Heavy machin- 
 ery castings. 
 
 15 
 
 
 2.5-2.8 
 
 0.6-0.8 
 
 1.0-1.3 
 
 0.5-0.7 
 
 0.4-0.7 
 
 .08-. 12 
 
 Cylinders and 
 hydraulic work. 
 
 16 
 
 
 
 
 1.2-1.8 
 
 0.4-1.0 
 
 0.4-0.7 
 
 to .06 
 
 For' hydraulic 
 
 
 
 
 
 cylinders. 
 
 17 
 
 
 2.7-3.0 
 
 0.5-0.8 
 
 0.5-0.7 
 
 0.3-0.5 
 
 0.3-0.5 
 
 .05-. 07 
 
 For car wheels. 
 
 18 
 
 
 2.6-3.1 
 
 0.6-1.0 
 
 0.6-0.7 
 
 0.1-0.3 
 
 0.3-0.5 
 
 .05-. 08 
 
 For car wheels. 
 
 19 
 
 
 2.5-3.0 
 
 0.4-0.9 
 
 1.3-1.7 
 
 0.5-1.0 
 
 0.3-0.4 
 
 .03 max 
 
 Charcoal pig. 1/4 
 in. chill. 
 
 20 
 
 
 2.3-2.7 
 
 0.5-1.0 
 
 1.0-1.5 
 
 0.5-1.0 
 
 0.3 0.4 
 
 .03 " 
 
 Ditto 1/2 in. chill. 
 
 21 
 
 
 2.0-2.5 
 
 0.8-1.2 
 
 0.8-1.2 
 
 0.5-1.0 
 
 0.3-0.4 
 
 .035 " 
 
 Ditto 3/4 in. chill. 
 
 22 
 
 
 1.8-2.2 
 
 0.9-1.4 
 
 0.5-1.0 
 
 0.3-0.7 
 
 0.3-0.4 
 
 .035 " 
 
 Ditto 1 in. chill. 
 
 23 
 
 3! 87 
 
 3.44 
 
 0.43 
 
 1.67 
 
 0.29 
 
 0.095 
 
 0.032 
 
 Series A. Am. 
 F' dm en's Assn. 
 
 24 
 
 3.82 
 
 3.23 
 
 0.59 
 
 1.95 
 
 0.39 
 
 0.405 
 
 0.042 
 
 Series B. ditto. 
 
 25 
 
 3.84 
 
 3.52 
 
 0.32 
 
 2.04 
 
 0.39 
 
 0.578 
 
 0.044 
 
 Series C. ditto. 
 
 26 
 
 
 2.8-3.2 
 
 0.5-0.7 
 
 1.3-1.5 
 
 0.3-0.6 
 
 0.5-0.8 
 
 .06-. 10 
 
 For locomotive 
 cylinders. 
 
 27 
 
 
 2.3-2.4 
 
 0.8-1.0 
 
 1.8-2.0 
 
 0.8-1.0 
 
 0.6-0.8 
 
 .06-. 10 
 
 " Semi-steel." 
 
 28 
 
 
 2.4-2.6 
 
 0.8-1.0 
 
 0.9-1.0 
 
 0.6-0.7 
 
 0.1-0.3 
 
 .04-. 06 
 
 li Semi-steel." 
 
 29 
 
 4J3 
 
 3.08 
 
 1.25 
 
 0.73 
 
 0.44 
 
 0.43 
 
 0.08 
 
 A strong car 
 wheel, Cu, 0.03. 
 
 30 
 
 3.17 
 
 2.72 
 
 0.45 
 
 1.99 
 
 0.39 
 
 0.65 
 
 0.13' 
 
 Automobile cyl- 
 inders. 
 
 31 
 
 3.34 
 
 2.57 
 
 0.77 
 
 1.89 
 
 0.39 
 
 0.70 
 
 0.09 
 
 Ditto. 
 
 32 
 
 3.5 
 
 2.9 
 
 0.6 
 
 0.7 
 
 0.4 
 
 5 
 
 0.08 
 
 Good car wheel. 
 
 33 
 
 3.55 
 
 3.0 
 
 0.55 
 
 2.75 
 
 2.39 
 
 0.86 
 
 0.014 
 
 Scotch irons. 
 
 34 
 
 
 
 
 3.10 
 
 1.80 
 
 0.90 
 
 
 " Am. Scotch " 
 
 
 
 
 
 Ohio irons. 
 
 35 
 
 
 
 
 0.75-1.5 
 
 to 0.6 
 
 to 0:22 
 
 to 0.04 
 
 Pig for malle- 
 
 
 
 
 
 able castings. 
 
 36 
 
 
 
 
 2-25 
 1.2-1.5 
 
 to 0.7 
 0.5-0.8 
 
 to 0.7 
 0.35-0.6 
 
 to 0.15 
 to 0.09 
 
 Brake-shoes. 
 
 37 
 
 
 
 
 Hard iron for 
 
 
 
 
 
 
 
 
 
 heavy work. 
 
 38 
 
 
 
 
 1.5-2 
 
 0.5-0.8 
 
 J. 35-0. 6 
 
 to 0.08 
 
 Medium iron for 
 
 
 
 
 
 general work. 
 
 39 
 
 
 
 
 2.2-2.8 
 
 to 0.7 
 
 to 0.7 
 
 to 0.085 
 
 Soft iron cast'gs 
 
 
 
 
 
418 IRON AND STEEL. 
 
 23 to 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 lb. on 11/4-in. round bar, 12 in. 
 between supports; deflection, 0.1 in. minimum; stirinkage, 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 XI X 24 in. of the 
 low Si semi-steel showing 2800 to 3000 lb. transverse strength, with 
 7/i 6 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 cooled 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 (-listings, 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 heavv. The transverse strength of the arbitration bar shall not 
 be under 2500 lb. for light, 2900 lb. for medium, and 3300 lb. 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 lb. per sq. in. for 
 light, 21,000 lb. for medium, and 24,000 lb. 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 constant 15.646, the factor for R/P 
 for a 11/4-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 by J. W. Keep, A.S.M.E., 1907. See Table of Analyses, 
 Nos. 37-39, page 417. Transverse test, lxl x 12-in. bar, hard iron castings. 
 No. 37, 2400 to 2600 lb.; tensile test of same bar, 22,000 to 25,000 lb. 
 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. 
 
 Standard Specifications for Foundry Pig Iron. 
 
 (American Foundrymen's Association, May, 1909.) 
 
 Analysis. — It is recommended that found-y pig be bought by analysis. 
 
 Sampling. — Each carload or its equivalent shall be considered as a 
 Jinit. One pig of machine-cast, or one-half pig of sand-cast iron shall be 
 iaken to every four tons in the car, and shall be so chosen from different 
 parts of the car as to represent as nearly as possible 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. 
 
 * Formula, ViPl = RI/c; see page 283. 7=1/64 n-0 4 ; c=l/2tZ; d = H/4in.; 
 1 = 12 in. 
 

 
 CAST IRON. 
 
 
 
 419 
 
 Silicon 
 
 Sulphur 
 (max.) Code 
 
 Total Carbon 
 (min J Code 
 
 Manganese 
 % Code ' 
 
 Phosp 
 
 HORUS 
 
 
 % 
 
 Code 
 
 % Code 
 
 0.04 Sa 
 
 3.00 Ca 
 
 0.20 Ma 
 
 0.20 
 
 Pa 
 
 1 . 00 La 
 
 0.05 Se 
 
 3.20 Ce 
 
 0.40 Me 
 
 0.40 
 
 Pe 
 
 1 . 50 Le 
 
 0.06 Si 
 
 3.40 Ci 
 
 0.60 Mi 
 
 0.60 
 
 Pi 
 
 2.00 Li 
 
 0.07 So 
 
 3.60 Co 
 
 0.80 Mo 
 
 0.80 
 
 Po 
 
 2.50 Lo 
 
 . 08 Su 
 
 3.80 Cu 
 
 1.00 Mu 
 
 1.00 
 
 Pu 
 
 3.00 Lu 
 
 0.09 Sy 
 0.10 Sh 
 
 
 1 . 25 My 
 1 . 50 Mh 
 
 1.25 
 
 a 
 
 
 
 1.50 
 
 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 con- 
 tract; "B," or Base, represents the price agreed upon for a p g of 2.00 Si 
 and under 0.05 S. "C" is a constant differential to be determined at 
 the time the contract is made. 
 
 Sul-, 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-6C 
 
 0.08 B + 2C B + 1C B B-1C B-2C B-3C B-4C B-5C B-6C 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 
 
 Specifications for Metal for Cast-iron Pipe.— Proc. A.S.T.M ., 1905, 
 A.I.M.E., 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 lb. and show a deflection of not less than 0.30 in, 
 before breaking. For pipes larger than 12 in., 2000 lb. and 0.32 in. 
 The corresponding moduli of rupture are respectivelv 34,200 and 36,000 
 Vo. Four grades of pig are specified: No. 1, Si, 2.75; S, 0.035. No 2. 
 Si, 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. 
 
 Tensile Tests of Cast-iron Bars. 
 
 (American Foundrymen's Association, 1899.) 
 
 Square Bars. 
 
 Round Bars. 
 
 Size, in... 
 (A)g,c. 
 ' g. m. 
 " d. s.. 
 " d. m. 
 (B)g.c. 
 g. m. 
 " d. c 
 d. m. 
 
 (C) i 
 
 d. c. . 
 d. m. 
 
 0.5x0.5 
 15,900 
 
 14,600 
 '17,100 
 
 16,300 
 17*766 
 
 13,600 
 15,800 
 14,700 
 
 1x1 
 13,900 
 15,400 
 12,900 
 13,800 
 15,200 
 17,600 
 15,100 
 18,400 
 16,000 
 18,500 
 16,000 
 17,100 
 16,100 
 15,500 
 14,800 
 16,800 
 
 1.5x1.5 
 12,100 
 12,900 
 12,300 
 13,400 
 12,900 
 15,000 
 13,300 
 15,000 
 12,500 
 15,100 
 12,200 
 14,100 
 13,400 
 13,400 
 12,500 
 14,200 
 
 2x2 
 10,600 
 10,900 
 
 9,800 
 12,100 
 11,500 
 11,800 
 11,100 
 12,100 
 11,100 
 11,700 
 11,300 
 
 9,800 
 11,300 
 11,000 
 10,900 
 11,400 
 
 0.56 
 16,000 
 
 14,300 
 'l 6,566 ' 
 
 16,700 
 17,800 
 
 13,400 
 15,800 
 16,300 
 
 1.13 
 13,800 
 13,800 
 13,700 
 13,600 
 15,900 
 19,000 
 16,200 
 16,900 
 15,900 
 17,400 
 15,900 
 17,700 
 16,000 
 15,700 
 15,200 
 16,400 
 
 1.69 
 12,000 
 13,500 
 11,700 
 13,200 
 13,100 
 15,400 
 13,200 
 15,100 
 14,200 
 15,000 
 14,000 
 15,900 
 13,900 
 13,800 
 13,000 
 14,600 
 
 2.15 
 11,000 
 12,200 
 10,500 
 10,600 
 1 1 ,400 
 12,500 
 11,000 
 13,100 
 12,000 
 11,600 
 11,600 
 10,400 
 11,600 
 11,200 
 11,200 
 11,700 
 
420 
 
 IRON AND STEEL. 
 
 Transverse Tests of 
 
 Dast-Iron Bars. Modulus of Rupture. 
 
 Size * 
 
 0.5x0.5 
 
 1x1 
 
 1.5x1.5 
 
 2x2 
 
 2.5x2.5 
 
 3x3 
 
 3.5x3.5 
 
 4x4 
 
 Diam. f 
 
 0.56 
 
 1.13 
 
 1.69 
 
 2.15 
 
 2.82 
 
 3.38 
 
 3.95 
 
 4.51 
 
 (A) r.d.c 
 
 31,100 
 
 33,400 
 
 33,900 
 
 31,700 
 
 27,000 
 
 26,600 
 
 23,400 
 
 22,600 
 
 " r. d.m. . . 
 
 
 27,800 
 
 38,000 
 
 32,300 
 
 28,000 
 
 28,600 
 
 22,400 
 
 22,900 
 
 (B) s.g.c... 
 
 44,400 
 
 39,100 
 
 39,500 
 
 33,900 
 
 31,900 
 
 29,700 
 
 27,200 
 
 27,600 
 
 " s.g.m... 
 
 
 37,400 
 
 40,300 
 
 34,700 
 
 35,800 
 
 33,500 
 
 30,100 
 
 27,100 
 
 " s.d.c... 
 
 35,500 
 
 38,300 
 
 34,000 
 
 32,900 
 
 31,900 
 
 30,200 
 
 29,300 
 
 25,900 
 
 " s.d.m. .. 
 
 
 30,200 
 
 36,200 
 
 33,300 
 
 35,200 
 
 30,900 
 
 28,100 
 
 25,800 
 
 " r.g.c. . .. 
 
 36,400 
 
 46,200 
 
 41,200 
 
 41,400 
 
 41,300 
 
 36,300 
 
 34,800 
 
 31,000 
 
 ' r.g.m... 
 
 
 40,000 
 
 44,800 
 
 38,800 
 
 37,100 
 
 32,900 
 
 32,700 
 
 32,300 
 
 " r d. c. . . . 
 
 37,800 
 
 49,000 
 
 44,300 
 
 39,200 
 
 40,700 
 
 31,800 
 
 35,300 
 
 31,100 
 
 r. d.m. 
 
 
 39,100 
 
 37,800 
 
 37,700 
 
 33,900 
 
 32,800 
 
 32,000 
 
 31,200 
 
 (C) s.g.c... 
 
 51,800 
 
 39,200 
 
 33,600 
 
 37,900 
 
 32,200 
 
 31,100 
 
 31,300 
 
 29,200 
 
 " s.g. m. .. 
 
 
 
 40,200 
 
 37,000 
 
 33,700 
 
 33,300 
 
 32,300 
 
 27,900 
 
 " s. d. c. ... 
 
 48,000 
 
 39,100 
 
 38,800 
 
 35,100 
 
 31,200 
 
 29,300 
 
 29,300 
 
 27,800 
 
 " s. d. m. 
 
 
 
 38,900 
 
 35,400 
 
 33,500 
 
 32,700 
 
 29,100 
 
 25,500 
 
 " r. g. c. . . . 
 
 62,800 
 
 48,500 
 
 39,000 
 
 44,500 
 
 41,400 
 
 41,200 
 
 35,000 
 
 32,300 
 
 " r. g. m. . . 
 
 
 55,700 
 
 49,200 
 
 42,900 
 
 41,500 
 
 36,500 
 
 34,100 
 
 36,000 
 
 " r. d. c. . . . 
 
 53,000 
 
 50,400 
 
 44,000 
 
 40,200 
 
 39,500 
 
 37,800 
 
 35,200 
 
 32,100 
 
 " r. d.m. . . 
 
 
 47,900 
 
 51,300 
 
 38,000 
 
 38,900 
 
 36,300 
 
 32,200 
 
 33,500 
 
 Av. (B)s. ... 
 
 39,900 
 
 36,200 
 
 37,500 
 
 33,700 
 
 33,700 
 
 31,100 
 
 28,700 
 
 26,600 
 
 " r. . . . 
 
 37,100 
 
 43,600 
 
 42,000 
 
 39,300 
 
 38,200 
 
 33,400 
 
 33,700 
 
 31,400 
 
 " (C)s 
 
 49,900 
 
 39,100 
 
 37,900 
 
 36,300 
 
 32,600 
 
 31,600 
 
 30,500 
 
 27,600 
 
 " r 
 
 57,900 
 
 50,600 
 
 45,900 
 
 41,400 
 
 40,400 
 
 37,900 
 
 34,100 
 
 33,200 
 
 "(B)&(C)g. 
 
 48,800 
 
 43,100 
 
 41,000 
 
 38,800 
 
 36,800 
 
 33,900 
 
 32,200 
 
 30,400 
 
 ' d. 
 
 43,300 
 
 41,600 
 
 40,700 
 
 36,500 
 
 35,600 
 
 32,700 
 
 31,300 
 
 30,400 
 
 Gen'l av 
 
 46,100 
 
 42,400 
 
 40,800 
 
 37,700 
 
 36,200 
 
 33,400 
 
 31,700 
 
 29,900 
 
 Equiv. load. . 
 
 320 
 
 2356 
 
 7650 
 
 16,756 
 
 31,424- 
 
 50,100 
 
 75,516 
 
 106,311 
 
 * Size of square bars as cast, in. t Diam. of round bars as cast, in. 
 Compression Tests of Cast-iron Bars. 
 
 Size, in.. . 
 
 (A) (1)... 
 
 (2>... 
 
 0.5x0.5 
 29,570 
 
 1x1 
 20,010 
 21,990 
 
 1.5x1.5 
 17,180 
 17,920 
 17,180 
 
 2x2 
 13,810 
 13,750 
 13,880 
 
 2.5x2.5 
 10,950 
 12,040 
 11,430 
 10,950 
 15,060 
 18,270 
 15,940 
 
 '17,840 
 19,800 
 18,050 
 
 3x3 
 9,830 
 11,200 
 10,270 
 10,430 
 13,790 
 17,000 
 14,410 
 13,900 
 15,950 
 18,170 
 16,850 
 16,040 
 
 3.5x3.5 
 9,350 
 10,770 
 9,830 
 9,540 
 13,160 
 15,970 
 15,200 
 13,560 
 15,880 
 17,100 
 16,510 
 16,080 
 
 4x4 
 9,100 
 10,340 
 
 " (3)... 
 
 
 9,950 
 
 " (4). 
 
 
 
 9,570 
 
 (B) (I)... 
 
 " (2)... 
 
 (3)... 
 
 . 38,360 
 
 23,000 
 12,440 
 
 20,980 
 24,820 
 20,980 
 
 18,130 
 21,640 
 18,740 
 15,060 
 18,010 
 21,750 
 19,340 
 17,840 
 
 12,430 
 16,140 
 13,950 
 
 " (4)... 
 
 
 
 13,760 
 
 (C) (0... 
 " (2)... 
 
 38,360 
 
 24,890 
 27,900 
 
 20,750 
 22,060 
 20,750 
 
 14,220 
 16,410 
 
 " (3)... 
 
 
 15 250 
 
 '* (4)... 
 
 
 
 14,880 
 
 Notes on the Tables of Tests. — The machined bars were cut to 
 the next size smaller than the size they were cast. The transverse bars 
 were 12in. long between supports. (A), (B), (C), three qualities of iron; 
 for analyses see page 417; r, round bars; s, square bars; <7, 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 i in. cubes cut from the bars. Multiply by 4 to obtain lbs. 
 per sq. in. (1) Cube cut from the middle of the bar; (2) first J 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 11/4 in. square, and afterwards planed down to 1 in. square. 
 
CAST IKON. 421 
 
 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 " " =28,175 11,000 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 
 slow cooling tends to cause segregation of the chemical constituents and 
 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, IV2, 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.I.M.E., xxvi, 1017. 
 
 Theory of the Relation of Strength to Chemical Constitution. — 
 J. E. Johnston, Jr. (Am. Mach., 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. withO C to 125,0001b. with 1.20 C. With higher C it rapidlv 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 2.0 2.5 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 15.4 19.9 28.5 38 42.9 52.1 58 56.1 36 28.7 30 
 
 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 GC The sq. root of 3.4 is 1.9, and of 2.4 is 
 1.55. The ratio of these to V6.25 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/ 8 in. 
 and one say 2 or 21/2 in. diameter, in order to show the effect of rapid 
 and slow cooling. 
 
422 
 
 IRON AND STEEL. 
 
 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 1/2-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. Foundry men'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 
 
 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 1/2-in. x 12-in. bar. 
 
 
 Size of Square Cast Bars. 
 
 
 Size of Square Cast Bars. 
 
 If 
 
 73 U 
 
 1/2 in. 
 
 1 in. 
 
 2 in. 
 
 3 in. 
 
 4 in. 
 
 1/2 in. 
 
 1 in. 
 
 2 in. 
 
 3 in. 
 
 4 in. 
 
 *ft 
 
 Strength of a 1/2-in. x 12-in. 
 Section, lb. 
 
 Strength of a 1/2-in. X 12-in. 
 Section, lb. 
 
 1.00 
 
 1.50 
 2.00 
 
 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 
 
 
 
 
 
 
 
 
 
 
 350 
 
 
 ! 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 (U 250 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 __ 
 
 
 
 
 
 
 *••>- 
 
 --. 
 
 __ 
 
 
 - I nches S quare 
 Fig. 92. 
 Fig. 92 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 1/2-in. bars, we find 
 
 Si, per cent 1 1.5 2 2.5 3 3.5 
 
 2-in, weaker than 1/2-in. .percent. . 20 30 35 46 53 57 
 
CAST IRON. 
 
 423 
 
 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 1/2-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 (^4. 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: 
 
 
 Size of Square Bars. 
 
 0^ 
 Ah 
 
 Size of Square Bars. 
 
 a c 
 
 g8 
 
 V2 in. 
 
 1 in. 
 
 2 in. 
 
 3 in. 
 
 4 in. 
 
 1/2 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 
 
 0.142 
 .130 
 .118 
 
 0.121 
 .109 
 .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 
 needed to bring the quality of the casting to an accepted standard of 
 excellence." 
 
 A shrinkage of l/s 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. L & S. I., 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 hy 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- 
 
424 IRON AND STEEL. 
 
 ure by the removal of the sand while yet in the act of contracting; 
 Manges, 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 butt. Some of 
 his figures are: Point of pig, 2.328 Si; butt of same, 2.157; point of pig, 
 1.834; butt of same, 1.787. 
 
 White Iron Converted into Gray by Heating. (A. E. Outerbridge, 
 Jr., Proc. Am. Socy. for Testing Mat'ls, 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 its carbon removed 
 by oxidation, while the converted cast iron retains its original total 
 carbon, although in a changed form. The tensile strength of the new 
 metal is high, 40,000 to 50,000 lb. 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 TC, 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, GC, 0.72; CC, 2.60; Si, 0.71; Mn, 0.11; S, 0.045; P, 0.04 
 After annealing, GC, 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.l.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 
 2J40°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 graphite 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.l.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 1/2-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 
 
CAST IRON. 425 
 
 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 HVi6in. and its cross-section 
 1/8 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 Vsin. per foot. The strength 
 and deflection of the cast-iron bars was greatly decreased by the treatment, 
 1250 as compared with 2150 lb., 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. 
 
 Grate-bars of boiler furnaces grow longer in use, as do also cast-iron 
 pipes in ovens for heating air. 
 
 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 GC and CC vary in 
 an erratic manner. The metal charged into the cupola should contain 
 more GC, Si and Mn than are desired in the castings. Fairbairn (Manu- 
 facture of Iron, 1865) found that remelting up to 12 times increased the 
 strength and the deflection, but after 18 remeltings the strength was only 
 5/8 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 pis; 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 
 
426 
 
 IRON AND STEEL. 
 
 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 Si02, which goes into the 
 slag. 
 
 Experiments with Titanium added to cast iron in the ladle are 
 reported by R. Moldenke, Proc. Am. Fdrymen's 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: 
 
 White Iron. Lbs. 
 
 Original iron 
 
 Plus0.05Ti... 
 PlusO.lOTi... 
 Plus 0.05 Ti and C 
 PlusO.lOTiandC 
 Plus0.15TiandC 
 
 9 tests 
 4 tests 
 
 3 tests 
 6 tests 
 6 tests 
 
 4 tests 
 
 1720-2260 av. 2020 
 
 2750-3140 
 2880-3150 
 2850-3230 
 2850-3150 
 3030-3270 
 
 Average of treated iron . 
 Increase over original. . . 
 
 3100 
 3030 
 3070 
 2990 
 3190 
 
 . 3070 
 
 . 52% 
 
 8 tests 
 1 1 tests 
 
 1920-2110 av. 2050 
 2210-2660 " 2400 
 
 9 tests 
 10 tests 
 10 tests 
 
 2230-2720 " 2420 
 2320-2460 " 2400 
 2280-2620 " 2520 
 
 2430 
 18% 
 
 Modulus of rupture, treated iron, 48,030 
 
 The test bars were H/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 H/2 in. deep 
 gave but 1 in. chill when the iron was treated in the ladle. The original 
 iron crushed at 173,000 lbs. per sq. in. and stood 445 in Brinel's test 
 for hardness, soft steel running about 105. The treated piece ran 
 298,000 lbs. per sq. in. and showed a hardness of 557. Testing the soft 
 metal below the chilled portion for hardness gave 332 for the original 
 and 322 for the treated piece. 
 
 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 0.1S 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 following are average results: 
 
CAST IRON. 
 
 427 
 
 Gray Machinery Iron. 
 
 Remelted Car Wheels. 
 
 Added Per cent. 
 
 Breaking 
 
 Strength, 
 lbs. 
 
 Deflec- 
 tion, In. 
 
 Added Per cent. 
 
 Breaking 
 
 Strength, 
 
 lbs. 
 
 Deflec- 
 tion, In. 
 
 Va. 
 
 Mn. 
 
 Va. 
 
 Mn. 
 
 0.0 
 0.0 
 0.05 
 
 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 
 
 0^05' 
 0.05 
 0.10 
 0.10 
 0.15 
 0.15 
 
 0.0 
 0.50 
 
 0^50 
 
 0.50 
 
 "o!50 
 
 1470 
 2790 
 3020 
 2970 
 2800 
 3030 
 2950 
 3920 
 
 3069 
 
 0.050 
 0.070 
 0.060 
 
 0.05 
 0.10 
 
 0.50 
 
 0.090 
 0.055 
 
 0.10 
 0.15 
 
 0.50 
 
 0.090 
 0.070 
 
 
 Viar>5 
 
 095 
 
 Average treated 
 
 2224 
 
 
 Mod. of ri 
 
 ipture 
 
 . 35,800 
 
 
 
 
 48,020 
 
 
 The bars were 11/4 in. diam. 12 in. between supports. 
 
 The burnt gray iron was increased in breaking strength from 1310 to 
 2220 lbs. by the addition of 0.05% Va, and the burnt white iron from 
 1440 to 1910 lbs. by the addition of 0.05 Va and 0.50 Mn. 
 
 Strength of Cast-iron Beams. — C. H. Benjamin, MacWy, 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 
 beins: 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 hollow 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 of 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. 
 
 Bursting Strength of Cast-iron Cylinders. — C. H. 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 lbs. 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 lbs. 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, assuming 
 each half of pipe as a beam fixed at the ends, ranging from 12,800 lbs. to 
 23,303 lbs. per sq. in. 
 
 Bars 2 in. wide cut from the pipes gave moduli of rupture ranging from 
 28,400 to 51,400 lbs. per sq. in. Four of the tests, bars and pipes : 
 
 Moduli of rupture of bar 28,400 
 
 Fiber stress of pipe 18,300 
 
 34,400 
 12,800 
 
 40,000 
 14,500 
 
 51,400 
 26,300 
 
428 
 
 IRON AND STEEL. 
 
 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 of 
 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, lbs. 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 lbs. T. S., and of cast iron of 22,000 lbs. 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: 
 Bursting Strength of Pipe-Fittings. Pounds per Square Inch. 
 
 Inside Diam. 
 Thickness. 
 
 6 
 
 3/4 
 
 8 
 13/16 
 
 10 
 15/16 
 
 12 
 
 1 
 
 14 
 
 H/8 
 
 16 
 13/16 
 
 18 
 11/4 
 
 20 
 « 5 /l6 
 
 24 
 11/2 
 
 B, Ferro-steel 
 
 calculated 
 
 B, Cast iron 
 
 calculated 
 
 2733 
 
 2680 
 1687 
 1790 
 3266 
 2275 
 
 2250 
 2180 
 1350 
 1450 
 2725 
 1625 
 
 2160 
 2010 
 1306 
 1340 
 2350 
 1541 
 
 2033 
 1870 
 1380 
 1190 
 2133 
 1275 
 
 1825 
 1570 
 1100 
 1060 
 
 1700 
 1450 
 1025 
 980 
 
 1450 
 1350 
 600 
 920 
 
 1275 
 1280 
 750 
 870 
 
 1300 
 1220 
 700 
 820 
 
 
 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 
 lbs. T. S. per square inch, one sample giving 42,281 lbs. Muirkirk, Md., 
 iron tested at the Washington Navy Yard showed: average for No. 2 
 iron, 21,601 lbs.; No. 3, 23,959 lbs.; No. 4, 41,329 lbs.; 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 lbs. to 41,882 lbs. Char- 
 coal pig iron from Shelby, Ala. (tests made in August, 1891), showed a 
 strength of 34,800 lbs. for No. 3; No. 4, 39,675 lbs.; No. 5, 46,450 lbs.; 
 and a mixture of equal parts of Nos. 2, 3, 4, and 5, 41,470 lbs. (Bull. 
 I. & 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 
 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 GC to CC, but the TC is unchanged, for any 
 reduction made by the steel is balanced by absorption of C from the fuel. 
 
MALLEABLE CAST IRON. 429 
 
 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 lbs. {Jour. C. I. W., iii, p. 184): 
 
 lbs. per sq. in. 
 
 Charcoal iron with 2V2% steel 22,467 
 
 " 33/4% steel 26,733 
 
 " 61/4% steel and 6 1/4% anthracite 24,400 
 
 " 7V 3 % 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 31/2 minutes), 
 chilled in a chill test mold over an inch deep, just as a test of cold 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 lbs. 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 lbs. per square inch in sound 
 pieces to 1000 lbs. 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 
 for 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 629/ 64 j n . 
 
 The results were: Cast-steel flange, no change. Cast-iron flange, 
 outside 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. 
 
 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 /i6 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 
 
 * 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, 1906; C. H. Day, Am. Mach., April 5, 1906. 
 
430 IRON AND STEEL. 
 
 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 seldom 
 over 175 lbs. in weight, or 3 ft. in length, or 3/ 4 in. in thickness. The 
 great majority of even the heavier castings do not exceed 10 lbs. 
 
 When properly made, malleable cast iron should have a tensile strength 
 of 42,000 to 48,000 lbs. 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 lbs., with a deflection of at least 1/2 in. 
 
 While the strength of malleable iron should be as stated, much of it 
 will fall as low as 35,000 lbs. 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 lbs. per sq. in. has been reached, with a load of 5000 lbs. and 
 a deflection of 21/2 in. in the transverse test. This high strength is not 
 desirable, as the softness of the casting is sacrificed, and its resistance 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. 
 
 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 ia to be used for; P not over 0.225, Mn 
 not over 0.20, S not over 0.05. The total carbon can be from 2.75 upward, 
 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 1/2 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 .00 and still leave the metal white in fracture. 
 
 Pig Iron for 31alleable 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 being melted by this process. Prior to about 1885, 
 the standard furnace was one of 5 tons capacity. At present (1908) we 
 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, Manganese is also oxidized in the furnace. 
 
MALLEABLE CAST tRON. 
 
 431 
 
 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 0.07%; 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 as in ordi- 
 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. 
 
 
 0.63 
 0.61 
 0.61 
 
 0.043 
 0.049 
 0.065 
 
 0.147 
 0.145 
 0.150 
 
 0.21 
 0.21 
 0.21 
 
 2.54 
 0.24 
 0.25 
 
 Trace 
 
 
 1 65 
 
 Annealed in coke 
 
 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- 
 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. 
 
432 IRON AND STEEL. 
 
 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, 
 0.1o% perhaps even less. Cut in another 1/16 in. 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 Jess 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 
 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- 
 sidered 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 
 
MALLEABLE CAST IRON. 433 
 
 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 31alleable 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: 
 
 (1) Endeavor to keep the metal in different parts of the casting at a 
 uniform thickness. In a small casting, of, say, 10 lbs. weight. 1/4-in. 
 metal is about the practical thickness. -Via in. for a casting of 15 to 20 
 lbs., and 3/ 8 to 1/2 in. for castings of 40 lbs. 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 lbs. per sq. in.; 3/ 8 to 3/ 4 in. thick, not less than 3S,000: and over 
 3/4 in., not less than 36,000 lbs. per sq. in. Test bars 5/s 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/s-in. bars, 45,095; 7/8-m. bars, 
 41,316 lbs. 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 lbs. 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 IS tons (40,320 lbs.) per square 
 inch, a minimum elongation of 4i/2 c o in three inches and a bending angle 
 of at least 90° over a 1-in. radius, the bar being 1 X 3 / 8 in. in section. 
 
 The specifications of the American Society for Testing Materials 
 include the following: 
 
 Cupola iron is not recommended for heavy or important castings. 
 
 Castings for which physical requirements are specified shall not con- 
 tain over 0.06 sulphur or over 0.225 phosphorus. 
 
 The Standard Test Bar is 1 in. square and 14 in. long, cast without 
 chills and left perfectly free in the mold. Three bars shall be cast in one 
 mold, heavy risers insuring sound bars. "Where the full heat goes into 
 castings which are subject to specification, one mold shall be poured 
 two minutes after tapping into the first ladle, and another mold from 
 the last iron of the heat. 
 
 The tensile strength of a standard test bar shall not be less than 40,000 
 lbs. per sq. in. The elongation in 2 in. shall not be less than 21/2%. 
 
434 
 
 IRON AND STEEL. 
 
 The transverse strength of a standard test bar on supports 12 inches 
 apart shall not be less than 3000 lbs., deflection being at least 1/2 in. 
 
 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 of malleable cast iron was about 35,000 lbs. 
 per sq. in., with an elongation of about 2% in 2 in. The transverse 
 strength was perhaps 2800 lbs., 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 lbs. per sq. in., with an elongation of 5% in 2 in., and the 
 transverse strength, about 3500 lbs., with a deflection of 1/2 inch. These 
 average figures were greatly exceeded in establishments where special 
 attention was given to the niceties of the process. The tensile strength 
 here would run 52,000 lbs. per sq. in. regularly, with 7% elongation in 
 2 in., and the transverse strength, 5000 and over, with 1 1/2 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. 
 
 Bars cast by Buhl Malleable Co., Detroit, Mich. Reported by Chas. H. 
 Day, Am. Mach., April 5, 1906. The castings were all made at the same 
 time. The figures here given are the maximum and minimum results 
 from three bars of each section. 
 
 
 Tensile Tests. 
 
 
 Compression Tests. 
 
 Section. 
 
 Area, 
 
 Tensile 
 St'gth, 
 lbs. per 
 sq. in. 
 
 Elong. 
 in 8 in., 
 
 Red. of 
 Area, 
 
 Area, 
 
 L'gth, 
 
 Comp. 
 Str., 
 
 Final 
 
 
 sq. in. 
 
 %. 
 
 %. 
 
 sq. in. 
 
 in. 
 
 lbs. per 
 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 
 
 " 
 
 1.050 
 
 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 
 0.575 
 
 34,600 
 37,200 
 
 4.20 
 
 4.80 
 
 3.10 
 3.50 
 
 
 
 
 
 Broke in flaw. 
 
WROUGHT IRON. 
 
 435 
 
 The rectangular sections were approximately 1/4 X 3 /4 in. The star 
 sections were square crosses, 1 inch wide, with arms about 1/4 in. thick. 
 
 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, 
 
 0.25x1.52 
 0.5 xl.53 
 
 0.78x2 
 
 0.88x1.54 
 
 1.52x1.54 
 
 Tensile 
 
 Elastic 
 
 St'gth, 
 
 Limit, 
 
 lbs. per 
 
 lbs. per 
 
 sq. m. 
 
 sq. m. 
 
 34,700 
 
 21,100 
 
 32,800 
 
 17,000 
 
 25,100 
 
 15,400 
 
 33,600 
 
 19,300 
 
 28,200 
 
 
 Elonga- 
 tion, % 
 in 4 in. 
 
 Size of 
 Section, 
 
 0.29x2.78 
 0.39x2.82 
 0.53x2.76 
 0.8 X2.76 
 1.03x2.82 
 
 Tensile 
 St'gth, 
 lbs. per 
 sq. in. 
 
 28,160 
 32,060 
 27,875 
 25,120 
 28,720 
 
 Elastic 
 Limit, 
 lbs. per 
 
 22,650 
 20,595 
 19,520 
 18,390 
 18,220 
 
 Elong. 
 in 8 in., 
 
 %• 
 
 0.6 
 1.5 
 1.1 
 
 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. 
 
 Elong. in 8 in., 1/2-in. bars, 4.75%; 1-in. bars, 4.32%; turned bars, 
 3 73%. 
 ' Modulus of elasticity, 1/2-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, 1/2-in. sq., 93,000 to 114,500 lbs. per sq. in. Mean, 
 101,900 lbs. per sq. in. 
 
 Short blocks, 1 in. sq., 137,600 to 165,300 lbs. per sq. in. Mean, 
 152,800 lbs. per sq. in. 
 
 Ratio of final to original length, l/2in., 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 lbs. per sq. in.: 1 in. 
 X 15 in., 27,500 lbs. 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, 1/2-in. 
 bars, 34,163 lbs. per sq. in. 1-in. bars, 36,125 lbs. persq. in. Length 
 between supports, 20 in. The bars did not break, but failed by bending. 
 The 1/2-in. bars could be bent nearly double. 
 
 WROUGHT IRON. 
 
 The Manufacture of Wrought Iron. — When iron ore, which is an 
 oxide of iron, Fe203 or Fe30 4 , 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- 
 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 
 
436 
 
 IRON AND STEEL. 
 
 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 
 ia a reverb eratory furnace is desiiiconized and decarbonized by the 
 oxygen derived from iron ore or iron scale in the bottom of the furnace, 
 and fro n the oxidizing flame of the furnace. The temperature being too 
 lov to maintain the iron, when low in carbon, in a melted condition, 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 becomes of a pasty condition, and the lumps so formed when 
 gathered together make the "puddle-ball" which is consolidated into 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 an I 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. 
 
 Influence of Chemical Composition on the Properties of Wrought 
 Iron. (Beardslee on Wrought Iron and Chain Cables. Abridgment by 
 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 tests 
 by A. L. Holley the following figures are taken: 
 
 Brand. 
 
 Average 
 Tensile 
 Strength. 
 
 Chemical Composition. 
 
 S. 
 
 P. 
 
 Si. 
 
 C. 
 
 Mn. 
 
 Slag. 
 
 L 
 
 P 
 B 
 J 
 O 
 C 
 
 66,598 
 54,363 
 52,764 
 51,754 
 
 51,134 
 50,765 
 
 trace 
 (0.009 
 {0.001 
 
 0.008 
 (0.003 
 {0.005 
 (0.004 
 { . 005 
 
 0.007 
 
 (0.065 
 {0.084 
 0.250 
 0.095 
 0.231 
 0.140 
 0.291 
 0.067 
 0.078 
 0.169 
 
 0.080 
 0.105 
 0.182 
 0.028 
 0.156 
 0.182 
 0.321 
 0.065 
 0.073 
 0.154 
 
 0.212 
 0.512 
 0.033 
 0.066 
 0.015 
 0.027 
 0.051 
 0.045 
 0.042 
 0.042 
 
 0.005 
 0.029 
 0.033 
 0.009 
 0.017 
 trace 
 0.053 
 0.007 
 0.005 
 0.021 
 
 0.192 
 0.452 
 0.848 
 1.214 
 
 ' 6.678' 
 1.724 
 1.168 
 0.974 
 
 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. 
 
WROUGHT IRON. 
 
 437 
 
 Order of Qualities Graded from No. 1 to No. 19. 
 
 Brand. 
 
 Tensile 
 Strength. 
 
 Reduction of 
 Area. 
 
 Elongation. 
 
 Welding Power. 
 
 L 
 P 
 B 
 J 
 
 O 
 
 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 the 
 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 had 
 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 confusing. 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." 
 
 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 lbs. per sq. in., brand 
 L, which was really a steel, not being considered. Some specimens of L 
 gave figures as high as 70,000 lbs. 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.: 
 Area of pile, sq. in.: 
 Bar per cent of pile: 
 Tensile strength, lb.: 
 Elastic limit, lb.: 
 
 2 
 
 1 
 
 1/2 
 
 1'4 
 
 72 
 
 25 
 
 9 
 
 3 
 
 4.36 
 
 3.14 
 
 2.17 
 
 1.6 
 
 48,280 
 
 51,128 
 
 52,275 
 
 59,585 
 
 31,892 
 
 36,467 
 
 39,126 
 
 
 
 3 
 
 80 80 
 
 15.7 8.83 
 
 46,322 47,761 
 
 23.430 26,400 
 
 Specifications for Wrought Iron. (F. H. Lewis, Engineers' Club oi 
 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 aiong 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- 
 section shall not be less than 1/2 square inch. The elongation shall be 
 measured after breaking on an original length of 8 inches. 
 
 3. The tests shall show not less than the following results: 
 
 For bar iron in tension 
 
 For shape iron in tension. . . 
 For plates under 36 in. wide 
 For plates over 36 in. wide . 
 
 T. S. 
 
 
 
 
 
 
 in 8 in. 
 
 = 50,000; 
 
 E 
 
 L. 
 
 = 26,000; 
 
 E 
 
 L. 
 
 18% 
 15% 
 
 = 48,000; 
 
 
 
 = 26,000, 
 
 
 
 = 48,000; 
 
 
 
 = 26,000; 
 
 
 ** 
 
 12% 
 
 = 46,000; 
 
 
 
 = 25,000; 
 
 
 
 10% 
 
438 IRON AND STEEL. 
 
 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) pounds per square inch will be allowed. 
 
 5. All iron shall bend, cold, 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 
 of 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. R. It. 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 lbs. or exceeds 53,000 lbs. per sq. in., or if a single specimen falls 
 below 45,000 lbs. 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 lbs. 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 lbs. 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 1/8 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 lbs. 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 lbs. per square inch of: 
 
 _ 9 „ _ 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 an elongation of 20% in 8 in. 
 
 Plate iron 8 to 24 inches wide, T. S. 48,000, E. L. 26,000 lbs. per sq. in., 
 elong. 12%. Plates over 24 inches wide, T. S. 46,000, E. L. 26,000 lbs. 
 per sq. in. Plates 24 to 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 lbs. per sq. in. of: 
 _ 7000 X area of original bar 
 circumference of original bar ' 
 
METALS AT VARIOUS TEMPERATURES. 439 
 
 with 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 loss 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 tins point, up to 500° F., 
 there is little, if any, further loss of strength; the temperature at which 
 this great change and loss of strength takes place, although uniform in 
 the specimens cast from the same pot, varies about 100° in the same 
 composition cast at different temperatures, or with some varying condi- 
 tions in the foundry 'process. The temperature at which the change took 
 place 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 Landore steel is not affected by temperature up to 500°, 
 but its ductility is reduced more than one-half. (Iron, Oct. 6, 1877.) 
 
 Tensile Strength of Iron and Steel at High Temperatures. — 
 James E. Howard's tests (Iron Age, April 10, 1S90) show that the tensile 
 strength of steel diminishes as the temperature increases from 0° until a 
 minimum is reached between 200° and 300° F., the total decrease being 
 about 4000 lbs. per square inch in the softer steels, and from 6000 to 
 8000 lbs. in steels of over 80,000 lbs. tensile strength. From this mini- 
 mum point the strength increases up to 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 lbs. per square inch above the mini- 
 mum strength at from 200° to 300°. From this maximum, the strength 
 of all the steel decreases steadily af a rate approximating 10,000 lbs. 
 decrease per 100° increase of temperature. A strength of 20,000 lbs. 
 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 0° up 
 to a maximum at from 400 to 600° F., the increase being from 8000 to 
 10,000 lbs. per square inch, and then decreases steadily till a strength of 
 only 6000 lbs. per square inch is shown at 1500° F. 
 
 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 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, lbs 55,366 63,080 65,343 
 
 contr. of area % 26 23 21 
 
 Soft open-hearth steel, tensile strength, lbs 54,600 66,083 64,350 
 
 " contr. % 47 38 33 
 
 " Crucible steel, tensile strength, lbs 64,000 69,266 68,600 
 
 contr. % 36 30 21 
 
 Strength of Wrought Iron and Steel at High Temperatures. 
 (Jour. F. I., cxii, 1881, p. 241.) — Kollmann's experiments at Oberhausen 
 
440 
 
 IRON AND STEEL. 
 
 included tests of the tensile strength of iron and steel at temperatures 
 ranging between 7U° and 2000° F. Three kinds of metal were tested, 
 viz., fibrous iron of 52,464 lbs. T. S., 38,280 lbs. E. L., and 17.5% 
 elong.; fine-grained iron of 56,s«j2 lbs. T. S., 39,113 lbs. E. L., and 20% 
 elong.; and Bessemer steei of 84,826 lbs. T. S., 55,029 lbs. 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 
 
 Fibrous 
 
 Fine-grained 
 
 Bessemer 
 
 Franklin In- 
 
 Degrees F. 
 
 Iron, %. 
 
 Iron, %. 
 
 Steel, %. 
 
 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 
 18.0 
 13.5 
 7.0 
 4.5 
 3.5 
 
 30.5 
 28.0 
 19.0 
 12.5 
 8.5 
 5.0 
 
 26.5 
 22.0 
 15.0 
 10.0 
 7.5 
 5.0 
 
 
 1200 
 
 
 1400 
 
 
 1600 
 
 
 1800 
 
 
 2000 
 
 
 
 
 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% for 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.), I 
 but their ductility was increased about 1% in iron and 3% in steel. 
 
 2. When 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: 
 
 
 Reduction of 
 Force of Im- 
 pact, %. 
 
 Reduction of 
 
 Flexibility, 
 
 %. 
 
 
 3 
 
 31/2 
 41/2 
 21 
 
 18 
 
 
 17 
 
 
 15 
 
 (Sast iron, about 
 
 not taken 
 
DURABILITY OF IRON, CORROSION, ETC. 
 
 441 
 
 The experience of railways in Russia, Canada, and other countries 
 where the winter is severe, is 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 lb. T. S. and 62,800 lb. 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. hist. C. E., 1891.) — Axles 6 ft. 6 in. long be- 
 tween centers of journals, total length 7 ft. 3V2 in., diameter at middle 
 4V2 in., at wheel-sets 51/8 in., journals 33/4 x 7 in., were tested by impact 
 at temperatures of 0° and 100° F. Between the blows each axle was 
 half turned over, and was 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, re = extent of deflections between bearings 
 
 then F (mean force) = W/x = liw/x . 
 
 The results of these experiments show that whereas at 0° F. a total 
 average Vnean 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 0° F. was only 
 about 42% of what it was at 100° F. 
 
 The average total deflection at 0° 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 0° F., compared with the warm axles at 100° F. 
 
 EXPANSION OF IRON AND STEEL BY HEAT. 
 
 James E. Howard, engineer in charge of the IT. S. testing-machine at 
 Watertown, Mass., gives the following results of tests made on bars 35 
 inches long (Iron Age, April 10, 1890): 
 
 
 C. 
 
 Mn. 
 
 Si. 
 
 Coeffi. of 
 
 Expansion 
 
 per degree 
 
 F. 
 
 
 c. 
 
 Mn. 
 
 Si. 
 
 .07 
 .08 
 .17 
 .19 
 
 .28 
 
 Coeffi. of 
 
 Expansion 
 
 per degree 
 
 F. 
 
 
 
 
 
 0.0000067302 
 .0000067561 
 .0000066259 
 .0000065149 
 .0000066597 
 .0000066202 
 
 Steel 
 
 0.57 
 .71 
 .81 
 
 .89 
 .97 
 
 0.93 
 
 .58 
 .56 
 .57 
 .SO 
 
 0.G00C063891 
 
 Steel 
 
 0.C9 
 .20 
 .31 
 .37 
 .51 
 
 0.11 
 .45 
 .57 
 .70 
 .58 
 
 m 
 
 
 .0000064716 
 
 
 
 0000062167 
 
 
 
 .0000062335 
 
 
 
 .C000061700 
 
 
 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 
 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 apparentlv crystalline fracture. See " Resistance of Metals to Repeated 
 Shocks," p. 262. 
 
442 IRON AND STEEL. 
 
 Walter H. Finley (Am. Mack., April 27, 1905) relates a case of fail- 
 ures of H/8-in. wrougnt-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 entirely 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 from brittle pins was entirely 
 avoided." 
 
 Durability of Cast Iron. — Frederick Graff, 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'g News, April 23, 1887, and March 26, 1892.) 
 
 Tests of Iron after Forty Years' Service. — A square link 12 inches 
 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 WsX 8 inches, taken from each link (Stah? und Eisen, 1890): 
 
 Old Link T. S., 21.8 tons; E. L., 11.1 tons; Elong., 14.05% 
 
 New Link " 22.2 " " 11.9 " " 13.42% 
 
 Durability of Iron in Bridges. (G. Lindenthal, Eng'g, May 2, 1884, 
 p. 139.) — The Old Monongahela suspension bridge in Pittsburg, built 
 in 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 lbs. 
 per sq. in. The elastic limit was from 67,100 to 78,600 lbs. 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 lbs.; E. L., 81,550 lbs.; reduction, 57%. Iron 
 rods used as stays or suspenders showed: T. S., 43,770 to 49,720 lbs. 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 1/2 in., and from 5/g in. diam- 
 eter to 5/i6 inch. 
 
 Wire ropes exposed to drip in colliery shafts are very liable to corrosion. 
 
 Corrosive Agents in the Atmosphere. — The experiments of F. 
 Crace Calvert (Chemical News, March 3, 1871) show that carbonic acid, 
 in the presence of moisture, is the agent which determines the oxidation 
 of iron in the atmosphere. He subjected perfectly cleaned blades of iron 
 
DURABILITY OF IRON, CORROSION, ETC. 443 
 
 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. Tins 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, 
 hist., 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 chloride 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. 691, and Incrustation and 
 Corrosion, p. 897.) 
 
 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 conveving water at a temperature varving 
 from 160° to 212° F. In one year 913/32 lbs. of wrought iron lost 203/4 oz., 
 and 913/32 lbs. of steel 247/§ 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 
 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 
 
444 IRON AND STEEL. 
 
 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 unconfmed 
 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, 
 and Proc. A. S. T. M., 1906. 
 
 Corrosion of Fence Wire. (A. S. Cushman, Farmers' Bulletin, No. 
 239, U. S. Dept. of Agriculture, 1905.) — "A large number of letters were 
 received from all over the country 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 
 steel 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. Cush- 
 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 inliuences. 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 is 
 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 
 and wiped with a clean cloth without disturbing this new surface condi- 
 tion. No visible change has been effected, for the polished surfaces 
 
DURABILITY OF IRON, CORROSION, ETC. 445 
 
 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. Chromatid 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 even weeks before the inhibiting effect is over- 
 come. 
 
 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 extremelv rapid corrosion bv electrolysis. 
 
 Chrome Paints. — G. B. Heckel (Jour. F. I., 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 
 lbs. American vermilion, 10 lbs. red lead, 5 lbs. Venetian red. Zinc 
 oxide and lamp-black to produce the required tint or shade. Grind in 
 1 1/3 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 practically safe, because of its well-known 
 chemical stability. 
 
446 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 over- 
 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. 
 
PRESERVATIVE COATINGS. 447 
 
 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- 
 strained 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 on (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 
 graphite paints give very good results. There are many grades of lamp- 
 black; 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, 
 and 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 to a con- 
 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 paint to preserve it. 
 Asphaltum is sometimes substituted in part or in whole for the fossil 
 resin, 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 
 
448 IRON AND STEEL. 
 
 also been simply dissolved in solvents, as benzine or carbon disulphide, 
 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 
 pores 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 metal 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 (Fe30 4 ) 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. Bv a further improvement known 
 as the "Wells Process," the work is finished in one operation, the steam 
 
PRESERVATIVE COATINGS. 449 
 
 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 cannot 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 exten- 
 sively used for small hardware. (See F. S. Barff, Jour. I. & S. Inst., 1877, 
 p. 356; A. S. Bower, Trans. A. I. M. E. 18S2, 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. & 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 implies, 
 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. Buffington 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 
 would 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 21/2 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. The Aluminum Co. of America makes 
 " bi-metallic " tubing composed of aluminum and other metal tubes 
 placed one inside the other and drawn down together to the required 
 size. 
 
 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. Alfred 
 Sans: Trans. Am. Foundn/mcn's Assoc, 1907. Iron Age, May 23d and 
 30th, 1907, and Proc. Eng. Soc. of W. Penna., Nov., 1907.) 
 
 The Penna. R. R. Specifications for galvanized sheets for car roofs 
 
450 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 
 tney 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 several 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 Ornamentation 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 other corroding liquids. 
 
STEEL. 451 
 
 • STEEL. 
 
 The Manufacture of Steel. (See Classification of Iron and Steel, 
 p. 413.) 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 over 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 ore; 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- 
 dom from objectionable elements, such as phosphorus, in the mixture, 
 on the complete removal of oxide, slag and blowholes by "dead-melting" 
 or "killing" before pouring, and on the kind and quantity of different 
 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. 
 
452 
 
 STEEL. 
 
 Relation between the Chemical Composition and Physical 
 Character of Steel. 
 
 W. R. Webster {Trans. A.I. M. E., vols, xxi and xxii, 1893-4) gives re- 
 sults 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 
 strength of 34,750 lbs. 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 lbs. for each 0.01%. 
 
 Sulphur, " " 500 " " " 0.01%, 
 
 Phosphorus, the effect is higher in high-carbon than in low-carbon steels. 
 With carbon hun- 
 
 dredths % 9 10 
 
 Each 0.01% Phas 
 an effect of lbs .. 900 1000 1100 
 Manganese, the effect decreases ai 
 .00 .15 .20 .25 
 
 12 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 Mn bein 
 cent . . 
 
 per 
 
 to 
 
 to 
 
 to 
 
 1200 1300 1400 1500 1500 1500 
 
 the per cent of manganese increases. 
 
 .30 .35 .40 .45 .50 .55 
 
 to 
 
 to 
 
 to to 
 
 to 
 
 to 
 .65 
 
 . .15 .20 .25 .30 .35 .40 .45 .50 .55 
 Strength incr. 
 
 for 0.01%... 240 240 220 200 180 160 140 120 100 100 lbs. 
 Total increase 
 
 fromO 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. 
 
 Carbon. 
 
 0.06 
 
 .08 
 
 .10 
 
 .12 
 
 .14 
 
 .16 
 
 .18 
 
 .20 
 
 .22 
 
 .24 
 
 Phos. .005 
 
 39,950 
 
 41,550 
 
 43,250 
 
 44,953 
 
 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 
 
 58,159 
 
 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 
 
 47,550 
 
 49,150 
 
 52,750 
 
 56,359 
 
 59,950 
 
 62,550 
 
 64,150 
 
 65,750 
 
 57,350 
 
 68,950 
 
 0.001 P.= 
 
 80 lbs. 
 
 80 lbs. 
 
 100 1b. 
 
 1201b. 
 
 1401b. 
 
 1501b. 
 
 150 lb. 
 
 1501b. 
 
 1501b. 
 
 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. 
 
 453 
 
 Thickness, in 
 
 3/ 4 * 
 
 -2000 
 -1000 
 
 U/16 
 
 -17I>0 
 - 750 
 
 5/8 9 /l6 
 -1500-1250 
 
 - 500 - 25C 
 
 1/2 
 -1UO0 
 
 
 
 7/16 
 
 -500 
 ±500 
 
 3/8 
 
 + 1000 
 
 5/16 
 
 + 3000 
 
 
 + 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 lbs. 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 lbs. T. S. from a specified 
 figure (equal to a total range of 10,000 lbs.), 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 
 Basic steel, 41,500 
 
 1000 C 
 770 C ■ 
 
 1000 P + xMn = Ultimate strength. 
 1000 P + yMn = Ultimate strength. 
 
 The values of xMn and yMn are given by Mr. Campbell in a table, 
 but they may be found from the formulse xMn = 8 CMn - 320 C and 
 yMn = 90 Mn + 4 CMn - 2700 - 120 C, or, combining the formulse 
 we have: 
 
 Ult. strength, acid steel, 40,000 
 basic " 38,800 - 
 
 680 C - 
 650 C • 
 
 1000 P +8 CMn. 
 
 1000 P + 90 Mn+4CMn 
 
 In these formulse 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 lbs. per sq. in. A piece of American nail-rod steel showed 
 45,021 lbs. 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 lbs. per sq. 
 in.; remelted and forged, 47,040 lbs. The analvsis of the cast bar was: 
 C, 0.08; Si, 0.04; S, 0.02; P, 0.02; Mn, 0.01; Fe, 99.82. 
 
 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 of Prof. Ledebur, given in Stahl und Eisen, May, 1892, 
 p. 193. The variation in O may make a difference in strength of nearly 
 1/2 ton per sq. in. (Jour. I. and^S. I., 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 
 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 + 6.2*S ± 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 + 43 ± 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: C, 0.15; Mn, 0.30; P, 0.06; S, 0.06; Si, 0.05; 
 none of these figures to be exceeded. 
 
454 
 
 STEEL. 
 
 Range of Variation in Strength of Bessemer and Open-Hearth 
 Steels. 
 
 The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bessemer 
 and open-hearth steel, from which the following figures are selected: 
 
 Kind of Steel. 
 
 H 
 'o 
 
 6 
 
 Elastic Limit. 
 
 Ultimate 
 Strength. 
 
 Elongation 
 
 per cent 
 in 8 Inches. 
 
 
 High't. 
 
 Lowest. 
 
 High't. 
 
 Lowest. 
 
 High't. 
 
 Lowest. 
 
 (a) Bess, structural. 
 (6) " 
 
 (c) Bess, angles 
 
 (d) 0. H. fire-box... 
 
 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 
 30.25 
 34.30 
 36.00 
 30.00 
 
 23.75 
 23.15 
 26.25 
 25.62 
 
 (e) 0. H. bridge 
 
 
 
 22.75 
 
 
 
 
 
 Requirements of Specifications. 
 
 (a) E. L., 35,000; T. S., 62,000 to 70,000; elong., 22% in 8 in. 
 
 (b) E. L., 40,000; T. 8., 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 lbs. 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 lbs. 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 
 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., 1902.) 
 
EFFECT OF HEAT TREATMENT ON STEEL. 
 
 455 
 
 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 1 1/2 hi* 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%. 
 
 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 1/4 in. thick plate. 
 
 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/ig 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%. 
 
 Effect of Annealing on Rolled Bars. (Campbell, Mfr. of Iron and 
 Steel, p. 275.) — 
 
 Ultimate 
 
 Elastic 
 
 Elong. in 
 
 Red. Area, 
 
 Elaa. 
 
 Strength. 
 
 Limit. 
 
 8 in., %. 
 
 %• 
 
 Ratio. 
 
 Natural. 
 
 An- 
 
 Nat- 
 
 An- 
 
 Nat- 
 
 An- 
 
 Nat- 
 
 An- 
 
 Nat- 
 
 An- 
 
 nealed. 
 
 ural. 
 
 nealed. 
 
 ural. 
 
 nealed. 
 
 ural. 
 
 nealed. 
 
 ural. 
 
 nealed. 
 
 •-§(58,568 
 
 54,098 
 
 40,300 
 
 31,823 
 
 29.7 
 
 28.8 
 
 60.8 
 
 62.7 
 
 68.8 
 
 58.8 
 
 .£ cj62,187 
 
 58,364 
 
 42,606 
 
 35,120 
 
 28.0 
 
 28.6 
 
 62.2 
 
 63.5 
 
 68.5 
 
 60.2 
 
 *g 170,530 
 
 65,500 
 
 49,000 
 
 37,685 
 
 26.9 
 
 23.4 
 
 61.1 
 
 55.3 
 
 69.5 
 
 57.5 
 
 w ^ 176,616 
 
 69,402 
 
 51,108 
 
 40,505 
 
 24.5 
 
 23.0 
 
 53.7 
 
 56.5 
 
 66.7 
 
 58.4 
 
 w[ 58, 130 
 
 51,418 
 
 40,400 
 
 30,393 
 
 30.1 
 
 31.1 
 
 61.8 
 
 60.5 
 
 69.5 
 
 59.1 
 
 4» ta J 62,089 
 
 55,021 
 
 42,441 
 
 31,576 
 
 30.1 
 
 30.4 
 
 60.9 
 
 60.0 
 
 68.4 
 
 57.4 
 
 "5=169,420 
 <n d 175,865 
 
 60,850 
 
 45,090 
 
 34,000 
 
 25.6 
 
 26.5 
 
 59.3 
 
 52.1 
 
 65.0 
 
 55.9 
 
 67,618 
 
 49,691 
 
 39,403 
 
 24.7 
 
 26.3 
 
 54.4 
 
 51.4 
 
 65.5 
 
 58.3 
 
 The bars were rolled from 4X 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. 
 
 *' Recalescence " 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 
 
456 STEEL. 
 
 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 cool 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. I. 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 action, 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, A^ 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 x . 
 It is the constituent which confers hardness on steel. In steels cooled 
 slowly to below Ar t the structure is composed entirely of ferrite, or 
 entirely of pearlite, or of pearlite mixed with ferrite or cementite. Ferrite 
 is iron free from carbon and forms almost the whole of a low-carbon steel, 
 while cementite is considered to be a compound of iron and carbon, Fe3C, 
 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 cooled 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 HEAT TREATMENT ON STEEL. 
 
 457 
 
 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 
 
 1 15400 
 
 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 
 
 1 00300 
 
 98000 
 
 94000 
 
 94350 
 
 95000 
 
 92350 
 
 65300 
 
 E.L 
 
 98100 
 
 78300 
 
 75700 
 
 50500 
 
 48750 
 
 47900 
 
 48600 
 
 45200 
 
 43100 
 
 50600 
 
 EI. in 2 in. 
 
 7.2 
 
 8.0 
 
 11.5 
 
 16.5 
 
 10.0 
 
 13.5 
 
 11. 
 
 7.5 
 
 6.0 
 
 2.0 
 
 (4) T. S. . . 
 
 157700 
 
 128100 
 
 1 1 7000 
 
 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 
 
 15.0 
 
 11.5 
 
 7.5 
 
 3.5 
 
 3.0 
 
 (5) T.S... 
 
 141100 
 
 105400 
 
 97800 
 
 86800 
 
 96600 
 
 111800 
 
 115900 
 
 111500 
 
 106100 
 
 112600 
 
 E.L 
 
 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 Ar x and Ac x were determined, and the six steels gave 
 practically identical results; thus Ar x ranged from 696 to 708, averaging 
 704° C, and Ac! 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 
 
 1 
 
 800 
 1070 
 
 2 
 
 760 
 1070 
 
 3 
 
 715-760 
 
 1070 
 
 4 
 
 760 
 1070 
 
 5 
 715 
 
 855 
 
 6 
 
 
 715° C 
 
 Very coarse fracture 
 
 800° C 
 
 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 can be restored by heat treatment or mechanical work. Seven lots of 
 nickel steel bars, containing 3.8% Ni, and C as in the table, were heated 
 to various temperatures in a muffle furnace, with results as below. 
 
 %c. 
 
 
 IOOJt 
 
 90246 
 
 26.0 
 
 99109 
 
 21.0 
 
 115421 
 
 16.5 
 
 135194 
 
 14.0 
 
 156827 
 
 7.5 
 
 168697 
 
 3.5 
 
 145642 
 
 10.5 
 
 1000b 
 71800 
 
 26.0 
 78600 
 
 25.0 
 89000 
 
 20.5 
 108960 
 
 15.0 
 130336 
 
 97510 
 15.0 
 
 63950 
 23.6 
 
 1100b 
 
 71700 
 
 25.5 
 
 78800 
 
 24.0 
 
 89400 
 
 19.0 
 
 111840 
 
 14.0 
 
 138112 
 
 3.5 
 
 98183 
 
 1.0 
 
 66640 
 
 25.0 
 
 120ub 
 74000 
 
 11.0 
 84900 
 
 11.5 
 99600 
 
 7.0 
 109600 
 
 3.0 
 83117 
 
 0.5 
 90729 
 
 0.5 
 97894 
 
 8.0 
 
 13C0b 
 71320 
 
 7.0 
 79600 
 
 5.0 
 85200 
 
 2.0 
 66800 
 
 0.5 
 46648 
 
 0.0 
 60600 
 
 0.0 
 35480 
 
 1.0 
 
 1200c 
 71487 
 
 10.5 
 81487 
 
 15.5 
 96040 
 
 10.0 
 102705 
 
 6.0 
 114107 
 
 5.5 
 
 95103 
 
 1.5 
 
 89045 
 
 17.5 
 
 1200d 
 
 0.41 
 
 T. S 
 
 74989 
 
 
 El. % in 2 in 
 
 25.0 
 
 0.51 
 
 T.S 
 
 80795 
 
 
 El. % in 2 in 
 
 22.5 
 
 0.63 
 
 T.S 
 
 89842 
 
 
 El. % in 2 in 
 
 21.0 
 
 0.79 
 
 T.S 
 
 90214 
 
 
 El. % in 2 in 
 
 21.0 
 
 0.97 
 
 T.S 
 
 103476 
 
 
 El. % in 2 in 
 
 18.0 
 
 1.24 
 
 T.S 
 
 106304 
 
 
 El. in 2 in 
 
 3.5 
 
 1.48 
 
 T. S 
 
 74592 
 
 
 El. in 2 in 
 
 24.0 
 
458 STEEL. 
 
 a. Heated to 1000 C, which took 1 hr. 25 min., held there 25 min. 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 
 steel much 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 work- 
 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 
 steel. 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 Forgings. — 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. (Hadfield 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 in 
 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 
 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° O, 
 finally reached a condition of coarse crystallization, so that it was unable 
 
TREATMENT OF STRUCTURAL STEEL. 459 
 
 to bear the strain upon it. This phenomenon of 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.) 
 
 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 finds 
 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; 
 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 i/s in. 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/s 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- 
 
460 STEEL. 
 
 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 463.] 
 
 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- 
 pose of securing homogeneity of structure that is supposed to be impaired 
 by 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: "Annealing is of advan- 
 tage to all steel above 64,000 lbs. 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 lbs. 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 
 to be avoided, because the edges of the holes are thereby strained beyond 
 the yield-point. Reaming drilled holes is not necessary, particularly 
 when sharp drills are used and neat work is done. A slight counter- 
 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., Aug., 
 1887, p. 326.) — In Prof. TJnwin's report the results of the greater number 
 of the experiments made on iron and steel plates 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% in iron plates and from 11% to 
 33% in the case of mild steel. 
 
MISCELLANEOUS NOTES ON STEEL. 461 
 
 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. Ifithe 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 bar, 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 lbs. 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 lbs. 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. 
 Height of fall 21 26 30 40 50 
 
 The weight was then shifted so as to fall directly on the sleeve-nut, and 
 the test proceeded as follows: 
 
 Stress on specimen in lbs. per square inch 65,350 65,350 68,800 
 
 Height of fall, feet 3 6 6 
 
 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 lbs. (average of several authori- 
 ties), this figure gives 489.775 lbs. ns the weight of a cubic foot of steel, 
 or the even figure, 490 lbs., may bo 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 lbs. per square foot one inch thick. Taking this 
 
462 
 
 weight and adding 2% gives almost exactly the weight of steel boiler- 
 plate given above (40 X 12 X 1.02 = 489.6 lbs. 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 
 purposes. One of the most marked, however, was the following: A 
 12-in. I-beam weighing 30 lbs. 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." 
 
 Segregation in Steel Ingots. (A. Pourcel, Trans. A.I. 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 
 segregation. 
 
 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. 
 
 
 C. 
 
 Mn. 
 
 Si. 
 
 S. 
 
 P. 
 
 Top 
 
 0.92 
 0.37 
 
 0.535 
 
 0.498 
 
 0.043 
 0.006 
 
 0.161 
 0.025 
 
 0.261 
 
 
 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. 
 
 
 0.14 
 0.11 
 
 0.053 
 0.036 
 
 0.072 
 0.027 
 
 0.576 
 
 
 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 5 /i6 in. was rolled from a 16 X 18-in. ingot, weighing 
 
MISCELLANEOUS NOTES ON STEEL. 
 
 463 
 
 2800 lbs., the ladle test of which showed 0.18 C. Test pieces from the 
 
 plate gave the following: 
 
 Top of Ingot: 
 
 Tensile Strength 56,730 67,420 67,050 66,980 56,440 
 
 Carbon 0.13 0.25 0.27 0.25 0.13 
 
 Bottom of Ingot: 
 
 Tensile Strength 56,120 57,720 58,400 58,140 56,900 
 
 Carbon 0.13 0.13 0.16 0.16 0.14 
 
 1 2 3 4 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 
 results as follows: (1) 0.55 C, T. S., 111,200; E. L., 59,000; Elong., 12%; 
 Red. of area, 33.5%. (2) 0.82 C, T. S., 142,000; E. L., 64,000; Elong., 
 7%; Red. of area, 11.8%. 
 
 Fiber stress 
 
 No. of rotations be- 
 fore rupture. 
 
 60,000 
 f(l) 12,490 
 \(2) 37,250 
 
 50,000 
 33,160 
 213,150 
 
 45,000 
 166,240 
 605,640 
 
 40,000 
 
 455,000 
 
 202,000,000 
 
 35,000 30,000 
 
 900,720 |76,326,240 
 Not broken. 
 
 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%, 
 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 do 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 ductilitv of the piece." 
 
 Welding of Steel.— A. E. Hunt (A. I. 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 in the 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 finelv 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 forcings, 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 
 
464 
 
 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. 
 
 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 forgings. 
 
 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 Lilienberg's 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. I., 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 speeimens: 
 
 Bed-plates up to 24,000 lbs.; stern-posts up to 54,000 lbs.; stems up to 
 21,000 lbs.; hydraulic cylinders up to 11,000 lbs.; shaft-struts up to 32,000 
 lbs.; hawse-pipes up to 7500 lbs.; stern-pipes up to 8000 lbs. 
 
STEEL CASTINGS. 
 
 465 
 
 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 lbs., 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. E.,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 smoother 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 3/ 8 to 1/2 in. for finish, as a large mass of metal 
 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 con- 
 taining about 0.60% of carbon. Such castings, properly annealed, have 
 worn well and seldom broken. Miscellaneous gearing should contain 
 
466 STEEL. 
 
 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 lbs. 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 almost 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 3456789 10 11 12 
 
 O 0.302 .490 .529 .649 .801 .841 .867 .871 .955 1.005 1.058 1.079 
 
 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 C is 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 
 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 
 reduced the sp. 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 
 
CRUCIBLE STEEL. 467 
 
 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 very injurious; and, 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 good chance for a 
 crack to be seen. Many a costly tool is ruined by inattention to this point. 
 
 The effect of too 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 the cooling bath, to do the work quickly and uniformly 
 all over, is very 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. 
 
 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 brought 
 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 
 (Elertrot. 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 
 
468 STEEL. 
 
 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 special 
 regulating transformer serves to regulate the current, and thus also the 
 temperature. 
 
 A test was made with a furnace, the bath of which was 6 1/2 X 6 1/2 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. diameter, H/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/ 8 in. bore, was heated in 243 seconds to 850° C. 
 
 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 hotter than the 
 outside; that is, that the inside shall be in a state of semi-fusion, while the 
 outside is hard and firm. Now let 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 
 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 in 
 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 very strong, nicely 
 refined, and will hold a keen, strong edge. 
 
 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 
 
CRUCIBLE STEEL. 469 
 
 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 not desired, as in the case of taps 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 steel- 
 maker that his steel is too high, so as to prevent a recurrence of the 
 trouble. 
 
 For descriptions of various methods of tempering steel, see "Tempering 
 of Metals," by Joshua Rose, in App. Cyc. Mech., vol. ii, p. 863; also, 
 "Wrinkles and Recipes," from the Scientific American. In both of 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. Flat drills for brass. 
 
 Slight turning tools. Wood-boring cutters. 
 
 Hammer faces. Drifts. 
 
 Planer tools for steel. Coopers' tools. 
 
 Ivory-cutting tools. Edging cutters; light purple, 530° F. 
 
 Planer tools for iron. Augers. 
 
 Paper-cutters. Dental and surgical instruments. 
 
 Wood-engraving tools. Cold chisels for steel. 
 
 Bone-cutting tools. Axes; dark purple, 550° F. 
 Milling-cutters; straw yellow, 460° F. Gimlets. 
 
 Wire-drawing dies. Cold chisels for cast iron. 
 
 Boring-cutters. Saws for bone and ivory. 
 
 Leather-cutting dies. Needles. 
 
 Screw-cutting dies. Firmer-chisels. 
 
 Inserted saw-teeth. Hack-saws. 
 
 Taps. Framing-chisels. 
 
 Rock-drills. Cold chisels for wrought iron. 
 
 Chasers. Molding and planing cutters to be 
 Punches and dies. filed. 
 
 Penknives. Circular saws for metal. 
 
 Reamers. Screw-drivers. 
 
 Half-round bits. Springs. 
 
 Planing and molding cutters. Saws for wood. 
 Stone-cutting tools; brown yellow, Dark blue, 570° F. 
 
 500° F. Pale blue, 610°. 
 
 Gouges. Blue tinged with green, 630°. 
 
 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; 
 
470 
 
 Steel. 
 
 C. 
 
 W. 
 
 Cr. 
 
 Mn. 
 
 Si. 
 
 Mo. 
 
 P. 
 
 s. 
 
 
 0.70 
 0.25 
 0.75 
 0.49 
 0.65 
 0.60 
 0.55 
 0.66 
 
 14.91 
 17.27 
 14.83 
 17.60 
 
 2.95 
 2.69 
 2.90 
 5.11 
 
 0.01 
 Trace 
 0.08 
 
 
 
 0.013 
 
 0.035 
 
 0.02 
 
 0.01 
 
 0.016 
 
 0.019 
 
 0.008 
 
 b 
 c 
 
 d 
 
 0.179 
 
 "b.\k" 
 
 Trace 
 0.01 
 0.007 
 
 
 0.19 
 
 0.039 
 
 9.60 
 
 0.005 
 
 f 
 
 13.00 
 17.81 
 19.03 
 
 2.88 
 2.48 
 
 0.0! 
 
 I 
 
 0.11 
 
 0.090 
 0.036 
 
 
 
 
 0.015 
 
 
 
 1 
 
 
 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 "ALLOT" 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 yellow 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. 
 
 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. 
 
"alloy" steels. 471 
 
 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, where 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 screen 
 shells to screen these crushings; gears, sprockets, link belts, etc., when 
 used in the vicinity of ore, stone and coal crushers or other places where 
 they are subjected to the hard, grinding wear of the gritty particles of 
 dust with which they are usually covered. 
 
 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 castings 
 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 lbs.; E. L., not less than 90,000 
 lbs.; Red. of area, not less than 50%; Elong. in 2 in., not less than 20%. 
 
 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. 
 
472 STEEL. 
 
 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, without 
 danger of an extraordinary brittleness in the cold metal or an increased 
 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 speci- 
 men from Sheffield, used for chisels, contained 9.3% of tungsten, 0.7% of 
 silver, and 0,6% of carbon. This steel, though used with advantage 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 sam- 
 ples 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 re- 
 tains 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. — R. A. Hadfield (Trans. A. I. M. E., 1890) says: 
 Aluminum appears to be of service as an addition to baths of molten iron or 
 steel unduly saturated with oxides, and these in properly regulated steel 
 manufacture should not often occur. Speaking generally, its role appears 
 to be similar to that of silicon. The statement that aluminum lowers the 
 melting-point of iron seems to have no foundation in fact. If any increase 
 of heat or fluidity takes place by the addition of small amounts of alumi- 
 num, it may be due to evolution of heat from oxidation of the aluminum, 
 as the calorific value of this metal is very high — in fact, higher than 
 silicon. According to Berthollet, the conversion of aluminum to A1 2 3 
 equals 7900 cal.; silicon to Si0 2 is stated as 7800. 
 
 The action of aluminum may be classed along with that of silicon, 
 sulphur, phosphorus, arsenic, and copper, as giving no increase of hardness 
 to iron, in contradistinction to carbon, manganese, chromium, tungsten, 
 and nickel. Its special advantage seems to be that it combines in itself 
 the advantages of both silicon and manganese; but so long as alloys con- 
 taining these metals are so cheap and aluminum dear, its extensive use 
 seems hardly probable. 
 
 J. E. Stead, in discussion of Mr. Hadfield's paper, said: Every one of our 
 trials has indicated that aluminum can kill the most fiery steel, providing, 
 of course, that it is added in sufficient quantity to combine with all the 
 oxygen which the steel contains. The metal will then be absolutely 
 dead, and will pour like dead-melted silicon steel. If the aluminum is 
 added as metallic aluminum, and not as a compound, and if the addition 
 is made just before the steel is cast, 0.1% is ample to obtain perfect solidity 
 in the steel. 
 
 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 H/4-in. square 
 
473 
 
 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 or 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.f 
 
 El., % 
 in 2 in. 
 
 
 5,119 
 9,243 
 17,064 
 
 12,557 
 21,045 
 18,059 
 16,921 
 
 40,669 
 72,522 
 72,806 
 71,860 
 
 23,989,140 
 29,506,500 
 26,870,800 
 
 18.2 
 
 ^ (Raw 
 
 43.9 
 
 
 48.6 
 
 
 45.0 
 
 
 
 
 
 * Limit of Proportionality. t Modulus of Elasticity. 
 
 Annealed Cast Bars of Nickel Steel with C 0.15 to 0.20. (Hadfield.) 
 — The proportion of Ni used in soft steels for armor and for engine- 
 forgings 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 Forging s" Compared. 
 (Bethlehem Steel Co.) 
 
 c. 
 
 Ni. 
 
 T.S. 
 
 E L. 
 
 El., 
 
 %• 
 
 Red. 
 Area, 
 
 %• 
 
 C. 
 
 Ni. 
 
 T.S. 
 
 E. L. 
 
 El., 
 
 %• 
 
 Red. 
 Area, 
 
 %. 
 
 0.20 
 
 
 
 55000 
 
 28000 
 
 34 
 
 60 
 
 0.20 
 
 3.5 
 
 85000 
 
 48000 
 
 26 
 
 55 
 
 0.30 
 
 
 
 75000 
 
 37000 
 
 30 
 
 50 
 
 0.30 
 
 3.5 
 
 95000 
 
 60000 
 
 22 
 
 48 
 
 0.40 
 
 
 
 85000 
 
 43000 
 
 25 
 
 45 
 
 0.40 
 
 3.5 
 
 110000 
 
 72000 
 
 18 
 
 40 
 
 0.50 
 
 
 
 95000 
 
 48000 
 
 21 
 
 40 
 
 0.50 
 
 3.5 
 
 125000 
 
 85000 
 
 13 
 
 32 
 
 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 lbs. 
 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 in Ni are entirely different in physical properties from low- 
 nickel steels, 
 
474 
 
 Effect of Ni on Hardness. — Gun barrels with 4.5% Ni and 0.30 C are 
 soft and very ductile; T. S. 80,000, elong. 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 
 
 Nickel 
 
 E. L., tons 
 
 Shortening* .. . 
 
 0.17 
 7.65 
 
 0.16 
 9.51 
 70 
 3 
 
 0.18 
 11.39 
 100 
 
 0.23 
 13. 
 
 0.19 
 19.64 
 80 
 
 0.16 
 24.51 
 50 
 
 0.14 
 29.07 
 24 
 
 * 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, 
 has 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, 17in. outside, 11 in. inside diam., length 38 ft. 11" 
 in., weight per foot, 449 lbs. 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 lbs. 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 lbs. 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%. 
 
 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. I. 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 
 
"alloy" steels. 475 
 
 Tor 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 540. 
 
 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 i) 10-6 
 between temperatures 0° 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 540. 
 
 Copper Steels. — Pierre Breuil (Jour. Land S. I., 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 steels. 
 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 constituents 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 lbs., an 
 elastic limit of 70,000 lbs., and an elongation of 23.5%. With 1% Va, 
 the T. S. increased to 119,500 lbs., and the E. L. to 91,000 lbs., 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 lbs. and an E. L. of 172,000 lbs. per sq. in., 
 the elong. being 6%, while with 1% Va the T. S. rose to 220,000 lbs. 
 and the E. L. to 176,000 lbs., the elongation remaining unchanged. 
 When the Va is increased above 1 % the tensile strength falls off, and the 
 material begins to show evidence of brittleness. 
 
 Similar effects are produced for steels of the higher carbon, but in a 
 lesser c n 
 
 When the nickel-vanadium steels are subjected to a tempering process 
 the beneficial effects of the Va are still further emphasized. The temper- 
 ing experiments of M. Guillet were conducted by heating the steel to a 
 temperature of 850° O, and cooling in water at 20° C. The T. S. and 
 
476 
 
 the E. L. were increased, being nearly doubled for the low nickel con- 
 tent. Thus while the 0.20 C steel with 2% of Ni, untempered, and 
 containing 0.7% of Va, gave a T. S. of 91,000 lbs., with an E. L. of 70,000 
 lbs., the same steel, tempered from 850° C, showed a T. S. of 168,000 lbs. 
 and an E. L. of 150,000 lbs., the resistance to shock and the hardness 
 being also increased. 
 
 Static and Dynamic Properties of Steels. (W. L. Turner, Iron Age, 
 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 "intermolecular 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 steel 
 is the case of the staying of a locomotive fire-box. Something is re- 
 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 
 satisfactory. 
 
 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 2V4 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 the 
 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 
 appear to undergo much alteration 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. 
 
' ALLOY STEELS. 
 
 477 
 
 Hi 
 
 -<N — NNtA-X 
 
 Dsoooaooo 
 
 -Ols-OtsTTa 
 
 
 -^r>00*moiriO>0>in inrAMNMnooooo — en cs oo o \o u 
 
 3 rn C>1 ■* m in O 00 "*■ ■* O C-l in t~% in — OO •'T O^ m '0»0*'*tOOP 
 
 0m\OvOvO'C>o>ot , tN so vo in — \© vo ■•© T >•© -mifivommu 
 
 
 momooooooomo 
 nj-rmmmToomcNioomvO 
 
 OOOmOmOOO mOOOOOu 
 
 OinifM»vOooir-N OvO*»Ntu 
 m CN CM cn rs tN cn cn _ _ _ , 
 
 oooooooooooo 
 o^t'o'o"©"— "tCu-T— oo'o'tN 
 
 88g§||8 
 
 vo oo '— T" o** r-s o 
 
 
 O — — t (A O N IN m * m «■ 
 
 ooooooooo ooooooo 
 
 ^•^MONt^mOO OOOOOOO 
 
 — »— o^ oo in •— • cn — o Of^^oo^cA^fi 
 
 — n — cfiiso^o^mo — in — o^ cn en "^ 
 
 O N vO ^O vO O N O^ OO OO^"Nm00cA 
 
 oo § 
 
 «s 1 
 
 O 1 - \0 in QO O 
 
 in — tN o O oo oo in -"Tin o oo "£ 
 oooooooooooo F5 
 
 iflinOONrNNNf m ONONISN'* 
 1 1 in lAts N is N m is mMAisNtNtn 
 
 O © O © © O © © © P5 O © © © O © © 
 
 n — ■«■ oo oo vo vo m vo co a^ rs — 
 
 > O T r~> r-s o o o ■* o o vO 
 
 pun rN w ^f fMS in f^ O "*?" rn CN m "*T rn 
 
 OOO— OOOOO — OOOOOO 
 
 03 g "5 
 
 
 ^o^^^h ddddddrH 
 
 .9° >•£>£;>££ 
 
 b> M "^ U LZ2 O O (rf t-r+3 03 S-i •— • -* £_< Q, t-t t-4"-* E-i £-t 
 
 C L n 03 oj-i o3 — 
 
 •5^t>>£>£ 
 a fc< &-.A i ^ i 
 
 — N m ■>r in * r> oo o> o - n 
 
 1*in*N00O>O- 
 
 ^m-*m>ONoo 
 
 a g 
 
 03 o3 
 
 of 
 
 1 
 
 
 OQ 
 
 © ° 
 
 0) 
 
 - So 
 
 43 
 
 
 
 few •!• 
 
 2 
 
 ?nt< 
 
 o 
 
 3^X 
 
 
 Si* 
 
 ^■5x 
 
 
 s 
 
 
 llTs 
 
 *1>£; 
 
 o,-gft 
 
 p^ 
 
 c © aS 
 
 
 ong. 
 of: E 
 
 ; T, 
 
 2 in. 
 duct 
 tigue- 
 pered 
 
 xs^a 
 
 d m-2 
 
 cn£3n j 
 
 rt CJO 8 - 1 
 
 J£r8 
 
 © o3 r 
 
 mi 
 
 ■■5 3 o S © 
 
 w. c$S h 
 
 1 2 K § a 
 
 n-^ © W.3 
 
 2- ft « 
 
 S © -d 
 
 • Si- •** 
 
478 
 
 STEEL. 
 
 Comparative Effects of Cr and Va. 
 
 Inst. M. E., 1904. 
 
 Sankey and J. Kent Smith, Proc. 
 
 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 
 
 +52.6 
 
 34.4 
 
 25.0 
 
 55.5 
 
 ... 0.1 
 
 34.8 
 
 28.5 
 
 31 
 
 60.0 
 
 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 
 
 +32.2 
 
 17.7 
 
 34. 
 
 52.6 
 
 * Tons, of 2240 lbs., per sq. in. + 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: 
 
 As rolled 
 
 Annealed l/ 2 hr. at 800° C 
 
 Soaked 12 hours at 800° C 
 
 Water quenched at 800° C 
 
 Oil quenched at 800° C 
 
 Oil quenched at 800°, reheated to 
 
 350° 
 
 Water quenched at 1200° C 
 
 Oil quenched at 1200° C 
 
 Tens. 
 
 Yield 
 
 El. in 
 
 Red. 
 
 Im- 
 
 Str. 
 
 Point. 
 
 2 in. 
 
 Area. 
 
 pact. 
 
 121,200 
 
 82,650 
 
 24.0% 
 
 44.9% 
 
 3.1 
 
 87,360 
 
 47,260 
 
 34.5 
 
 53.1 
 
 15.6 
 
 86,020 
 
 68,100 
 
 33.7 
 
 51.5 
 
 11.2 
 
 167,100 
 
 135,070 
 
 7.5 
 
 16.6 
 
 1.2 
 
 122,080 
 
 82,880 
 
 22.0 
 
 35.2 
 
 2.4 
 
 132,830 
 
 111,550 
 
 23.0 
 
 50.8 
 
 9.0 
 
 209,440 
 
 191,520 
 
 1.2 
 
 1.5 
 
 * 
 
 140,220 
 
 118,500 
 
 8.5 
 
 21.5 
 
 3.0 
 
 1906 
 2237 
 
 174 
 296 
 
 * 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 3/ 4 in. broad, notched so that 0.137 in. in 
 depth remained to be broken through. The figures represent ft.-lbs. 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: 
 
 
 Shearing Stress. 
 
 Twist 
 Angle. 
 
 
 
 Elastic. 
 
 Ulti- 
 mate. 
 
 No. of 
 
 Twists. 
 
 
 45,700 
 38,528 
 
 99,900 
 90,272 
 
 1410° 
 1628° 
 
 3.92 
 
 Annealed l/ 2 hr. at 800° C. 
 
 4.52 
 
 
 
"alloy" steels. 479 
 
 Heat-treatment 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 and 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 
 
480 
 
 treatment is shown by the table below. The composition of the alloy 
 was: Ni, 2.43; Cr, 0.42; Si, 0.26; C, 0.23; Mn, 0.43; P, 0.025; S, 0.022. 
 
 
 
 
 1* 
 
 |l 
 ft? 
 
 OHM 
 
 ao 
 
 a— 
 
 H 03 
 
 Tensile Strength . 
 E. L 
 
 227,000 
 
 208,000 
 
 4 
 
 219,000 
 
 203,500 
 
 6 
 
 195,500 
 
 150,000 
 
 8 
 
 172,000 
 
 148,500 
 
 11 
 
 156,500 
 
 125,000 
 
 13 
 
 141,000 
 
 102,000 
 
 15 
 
 109,500 
 70,500 
 
 Elong.,% in 2 in. 
 
 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. 1881. 1882. 1885. 1887. 1888. 
 
 Elastic limit,. . . 50,000 40 @ 45,000 40,000 40,000 40,000 38,000 
 
 Tensile strength 80,000 70 @ 80,000 70,000 70,000 67@75,000 63 @ 70,000 
 Elongation in 8 in. 12% 18% 18% 18% 20% 22% 
 
 Reduction of area 20% 30% 45% 42% 42% 45% 
 
 F. H. Lewis (IronAae, 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 lbs. 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 segrt gations 
 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 
 
 Ehosphorus are kept low, the effect of these segregations is inconsiderable; 
 ut 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 lbs. 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 lbs., or in some cases to 64,000 lbs., 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 the following limits: 
 
VABIOUS SPECIFICATIONS FOR STEEL. 
 
 481 
 
 Elements Considered. 
 
 Phosphorus, f Basic . . 
 
 Max \ Acid. . . , 
 
 Sulphur, Max 
 
 Tensile strength, lbs. 
 
 per sq. in 
 
 Elong.: Min. % in 8 in. 
 Elong.:Min. % in 2 in. 
 Fracture 
 
 Cold bend without 
 fracture 
 
 Structural Steel 
 
 0.04% 
 0.08% 
 0.05% 
 
 Desired 
 
 60,000 
 
 1,500,000* 
 
 tens. str. 
 
 22 
 
 Silky 
 
 0.04% 
 0.04% 
 0.04% 
 
 Desired 
 
 50,000 
 
 1,500,000 
 
 tens. str. 
 
 Silky 
 
 180° flat* 
 
 Steel Castings. 
 
 0.05% 
 0.08% 
 0.05% 
 
 Not less than 
 65,000 
 
 18 
 
 Silky or fine 
 
 granular 
 
 * The following modifications will be allowed in the requirements for 
 elongation for structural steel: For each Vi6 inch in thickness below 
 5/i6 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 tne 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. 
 
 t 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 lbs. 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 lbs. 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 lbs. 
 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 
 11/2 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 lbs. per sq. 
 in. of gross section. 
 
482 
 
 Caebon 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 and 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 lbs. per sq. in.; E. L., 55,000 lbs. min.; elong. in 
 8 ins., min., = 1,600,000 -i- T. S.; min. red. of area, 40%. 
 
 Specimens . cut from the finished material shall show the following 
 physical properties: 
 
 T. S., lbs. per sq. 
 
 Min.E.L. 
 lbs. per 
 sq. in. 
 
 Min. 
 Elong., 
 % in 8 in. 
 
 Min. Red. 
 of Area, 
 
 %• 
 
 Shapes and universal mill 
 plates 
 
 Eye-bars, pins and rollers 
 
 Sheared plates 
 
 Rivet rods 
 
 High-carbon steel for 
 trusses 
 
 60,000 to 68,000 
 64,000 to 72,000 
 60,000 to 68,000 
 50,000 to 58,000 
 
 85,000 to 95,000 
 
 33,0001 
 35,000 
 33,000 
 30,000 
 
 45,000 J 
 
 44 
 50 
 
 Nickel rivet steel: T. S., 70,000 to 80,000; E. L., min., 45,000; elong., 
 min., 1,600,000 -e- 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. 
 
 Solid or hollow forgings, no diam. 
 or thickness of section to exceed 
 10 in. 
 
 Solid or hollow forgings, diam. 
 not to exceed 20 in. or thickness 
 of section 15 in. 
 
 Solid forgings, over 20 in 
 
 Solid forgings 
 
 Solid or hollow forgings, diam. or 
 thickness not over 3 in. 
 
 Solid rectangular sections, thick- 
 ness not over 6 in., or hollow 
 with walls not over 6 in. thick. 
 
 Solid rect. sections, thickness not 
 over 10 in., or hollow with walls 
 not over 10 in. thick. 
 
 Locomotive forgings 
 
 Kind of 
 Steel. 
 
 Tensile 
 Strength. 
 
 Elast. 
 Limit. 
 
 El. in 
 2 in., 
 
 %. 
 
 Red 
 Area, 
 
 IS: 
 
 fC.A. 
 
 Jn.a. 
 
 58,000 
 75,000 
 80,000 
 80,000 
 
 29,000* 
 37,500* 
 40,000 
 50,000 
 
 28 
 18 
 22 
 25 
 
 35(a) 
 30(c) 
 35(b) 
 45(a) 
 
 (C.A. 
 JN.A. 
 
 75 000 
 80,000 
 
 37,500 
 45,000 
 
 23 
 25 
 
 35(b) 
 45(a) 
 
 C.A. 
 
 N.A. 
 )C.O. 
 JN.O. 
 
 70,000 
 80,000 
 90,000 
 95,000 
 
 35,000 
 45,000 
 55,000 
 65,000 
 
 24 
 24 
 20 
 21 
 
 30(c) 
 40(a) 
 45(b) 
 50(b) 
 
 (c.o. 
 
 jN.O. 
 
 85,000 
 90,000 
 
 50,000 
 60,000 
 
 22 
 22 
 
 45(b) 
 50(b) 
 
 )c.o. 
 
 jN.O. 
 
 80,000 
 85,000 
 
 45,000 
 55,000 
 
 23 
 24 
 
 40(b) 
 45(b) 
 
 
 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 2 inches. 
 
VARIOUS SPECIFICATIONS FOR STEEL. 
 
 483 
 
 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 1S0° without fracture on 
 outside of bent portion, as follows: (a) around a diam. of 1/2 in.; (b) 
 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., 1906, p. 175.) — 
 
 For Hull. Construction. 
 
 Tens. Strength. 
 
 E. L. 
 
 El. in 
 8 in., %. 
 
 
 58,000 to 60,000 
 60,000 to 75,000 
 55,000 to 65,000 
 
 1/2 T. S. 
 
 22* I8t 
 
 
 \5 
 
 
 
 20 
 
 
 
 
 In plates 18 lbs. per sq. ft. and over. 
 
 f In plates under 18 lbs. 
 
 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 lbs. 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 in. and over, 25%. 
 
 Cold Bending and Quenching Tests. Rivet steel and all steel of 
 52,000 to 62,000 lbs. 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 IV2 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 lbs. per sq. in. for normal high-tensile steel, and 81,984 lbs. 
 for the same annealed, as compared with 66,304 lbs. 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. 
 
 
 
 
 c3 
 
 3 
 
 C. 
 
 Mn. 
 
 Si. 
 
 P. 
 
 s. 
 
 Cu. 
 
 
 (1) 
 
 1899 
 1901 
 1899 
 1904 
 1902 
 1906 
 1906 
 
 0.12 
 1.00 
 0.40 
 0.45 
 0.45 
 0.18 
 0.18 
 
 0.35 
 
 0.25 
 
 0.50 
 
 0.60- 
 
 0.50 
 
 0.40- 
 
 0.40- 
 
 0.05 
 
 0.15- 
 
 0.05 
 
 0.05- 
 
 0.05 
 
 0.05- 
 
 0.02- 
 
 0.04- 
 0.03- 
 0.05- 
 0.03- 
 0.03- 
 0.04- 
 0.03- 
 
 0.03- 
 0.03- 
 0.04- 
 0.04- 
 0.02- 
 0.03- 
 0.02- 
 
 
 
 0.03- 
 
 
 (2) 
 (3) 
 (4) 
 (5) 
 (6) 
 
 
 
 
 Billets or blooms for forging 
 
 0.05- 
 0.03- 
 
 Fire-box sheets 
 
 0.03- 
 
484 STEEL. 
 
 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 lbs. 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 lbs. per sq. in.; elong. in 8 ins. 
 = 1,500,000 -*- 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 lbs. per sq. in.; elong. in 8 ins. 18%. Pins will 
 be rejected if the T. S. is below 80,000 or above 95,000, if the elongation 
 is less than 12%, or if 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 2S*% in 8 in. Sheets will be rejected if the T. S. is les^ 
 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, describe I 
 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 
 of 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 pin showed 88,000 lbs. strength and 22% elon- 
 gation, and the piece from the opposite side showed 106,000 lbs. 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 lbs. 
 
 Specifications for Steel Rails. (Adopted by the manufacturers of the 
 U. S. and Canada. In effect Jan. 1, 1909.)— Bessemer rails: 
 Wt. per yard, lbs. 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 ft. apart. The anvil weighs at least 20,000 lbs., 
 and the tup, or falling weight, 2000 lbs. The rail should not break when 
 the drop is as follows: 
 
 Weight per yard, lbs 71 to 80 81 to 90 91 to 100 
 
 Height of drop, feet 16 17 18 
 
 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 FOR STEEL. 
 
 485 
 
 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 lbs. 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 6U/16 inches for a 33-ft. 75-lb. rail, with an 
 increase of Vie in. for each increase of 5 lbs. in the weight of the section. 
 
 Open-hearth rails; chemical specifications: 
 
 Weight per yard, lbs. . . 50 to 60 61 to 70 71 to 80 81 to 90 90 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.& 
 
 Tens. 
 
 Str. 
 
 Yield 
 Pt. 
 
 El. in 
 2 in. 
 
 Red. 
 Area. 
 
 
 0.06 
 0.06 
 0.04 
 
 
 
 
 
 Driving and engine truck, C. S.* 
 
 Driving and engine truck, N. S.f 
 
 80,000 
 80,000 
 
 40,000 
 50,000 
 
 20% 
 25% 
 
 25% 
 45% 
 
 * Carbon steel. 
 
 t Nickel steel, 3 to 4 % Ni. 
 
 % 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 
 rests on supports 3 ft. apart, the tup weighs 1640 lbs., the anvil supported 
 on springs, 17,500 lbs.; 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, 
 
 Number of blows 
 
 Height of drop, ft.... 
 Deflection, in 
 
 41/4" 
 
 24 
 8I/4, 
 
 43/8 
 
 26 
 8I/4 
 
 4 5 7/16 
 
 281/2 
 81/4 
 
 45/ 8 
 
 31 
 
 43/4 
 34 
 
 53/8 
 
 43 
 
 7 
 
 57/8 
 
 43 
 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., 119,000; 
 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 lbs. 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 -f 
 2D), D being internal diameter and T thickness of tire at center of 
 tread. 
 
 Splice-bars. (A. S. T. M., 1901.) — Tensile strength of a specimen 
 cut from the head of the bar, 54,000 to 64,000 lbs.; yield point, 32,000 
 lbs. 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. 
 
486 
 
 STEEL. 
 
 Specifications for Steel Used in Automobile Construction. 
 
 (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. 
 
 (1) 
 
 (2) 
 (3) 
 
 (4) 
 
 0.40-0.55 
 
 0.20-O.35 
 
 0.25 
 
 0.25-0.35 
 
 0.45-0.55 
 0.28-0.36 
 0.85-1.00 
 0.50 
 
 0.40- 
 
 0.40- 
 
 0.40 
 
 0.60 
 
 1.1-1.3 
 
 0.3-0.6 
 
 0.25-0.5 
 
 1.50- 
 
 0.80+ 
 0.80 + 
 1.50 
 
 1.50+ 
 
 1.50 + 
 3.50 
 1.50 + 
 
 0.04- 
 
 0.04- 
 
 0.015 
 
 0.03 
 
 0.065- 
 0.05- 
 0.03- 
 0.04- 
 
 0.04- 
 
 0.04- 
 
 0.025 
 
 0.04 
 
 0.06- 
 
 0.06- 
 
 0.03- 
 
 0.06- 
 
 f 90000 + 
 i 180000 + 
 / 85000 + 
 1130000 + 
 
 120000 
 
 f 85000 + 
 
 1100000 + 
 
 85000 + 
 
 75000 + 
 
 65000 + 
 140000 + 
 65000 + 
 100000 + 
 105000 
 60000 + 
 70000 + 
 55000 + 
 40000 + 
 
 18 + 
 8+ 
 20 + 
 12+ 
 20 
 25 + 
 20+ 
 15 + 
 25 + 
 
 35+a 
 20 +b 
 50 + a 
 30+b 
 58c 
 50+a 
 50+b 
 45 + c 
 
 
 
 
 ft 
 
 
 
 
 
 30.0 
 
 
 
 
 
 
 
 
 
 
 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 l/i6-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 hour* 
 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 stee! (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. 
 
 85,000 
 70,000 
 60,000 
 
 Y. P. 
 
 El. in 2 
 in. 
 
 Red. 
 Area. 
 
 
 38,250 
 31,500 
 27,000 
 
 15% 
 18 % 
 22% 
 
 20% 
 
 
 25% 
 
 
 30% 
 
 
 
FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 487 
 
 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 1/2 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 lbs., 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 lbs. 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 lbs., nor if the elongation is less than 12%, nor 
 if castings have blow-holes and shrinkage cracks. Castings weighing 80 
 lbs. or more must have cast with them a strip to be used as a test-piece. 
 The dimensions of this strip must be 3/ 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 w r eights, 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, as 
 
488 MECHANICS. 
 
 determined by the first method of weighing given above, by 32.2, the 
 value of g, the acceleration due to gravity, at London, expressed by 
 the formula M = Wig. 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, exactly 
 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 statement in such 
 books that the engineers' unit of mass is 32.2 lbs. is an error. There is 
 no such unit. Whenever the term " mass " is represented by M in engi- 
 neering calculations it is equivalent to Wig, in which W is the quantity 
 of matter in pounds, and g = 32.2. 
 
 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 force; 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 repul- 
 sion) of one body upon another, and always implies the existence of a 
 simultaneous equal and opposite force exerted by that other body on the 
 first body, i.e., the reaction. In no case should we call anything a force 
 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. For some scientific purposes, as in electro-dynamics, 
 forces are sometimes expressed in "absolute units." The absolute unit of 
 force is that force which acting on a unit of mass during a unit of time pro- 
 duces a unit of velocity. In the French C. G. S., or centimeter-gram- 
 second system, it is the force which acting on the mass whose weight is one 
 gram at Paris will produce in one second a velocity of one centimeter per 
 second. This unit is called a "dyne " = 1/981 gram at Paris. 
 
 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, 
 " 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. 
 
 * 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 = M V, 
 F = MVIT, F = i/ 2 IF 2 v S. Force is not these things; 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, 
 
FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 489 
 
 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. 
 
 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 Mne, 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 to 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. 93, is the resultant of OQ 
 and OP. 
 
 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 
 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. 94, to be urged in the directions Al, A 2, 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 A 2 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 Ah' 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 bv that force to its original position, 
 supposing the forces to act successively, but if they had acted 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 
 
490 
 
 MECHANICS. 
 
 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 in 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 OR, Fig. 95, 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. 
 
 ^d 
 
 Fig. 96. 
 
 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. 96 (from Trautwine), if the weights n and m 
 represent forces, their moments about the point / are respectively nX 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, 
 dXfh. 
 
 If 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 X fc, or s X 
 ft, or yX fb, or d X hf. 
 
 The moment of the resultant of any number of forces acting together in 
 the 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 edge. 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 
 
 
FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 491 
 
 the body into the coefficient of friction between the base of the body and 
 its supporting piane. 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 lbs. 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, 
 or 62.4 H 2 -s- 2. The center of gravity of a triangle being 1/3 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 H 3 ■* 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. 96 the resultant of the forces n and m acts vertically 
 downward at /, and is equal to n + m. 
 
 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 appli- 
 
 N 
 
 £*4 
 
 Fig 
 
 >Q 
 
 97. 
 
 >R 
 
 W*z -v 
 
 m/ i: 
 
 
 
 S6 £- 
 
 Fig. 98. 
 
 -^-R 
 
 
 cation of the components, inversely as the components. Thus in Fig. 96, 
 m: n:: af:fc; and in Fig. 97, 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 differe- 1 R 
 
 nee of the intensities of the two forces. 
 
 Thus the resultant of the two forces Q and P, 
 Fig. 98, is equal to Q - P = R. Of any two par- 
 allel forces and their resultant each is propor- 
 tional to the distance between the other two; 
 thus in both Figs. 97 and 98, P:Q:R:: SN: 
 SM: MN. 
 
 Couples. — If P and Q be equal and act in 
 opposite directions, #=0; that is, they have no 
 resultant. Two such forces constitute what is 
 
 m 
 
 called a couple. , rg 
 
 The tendency of a couple is to produce rota- ' -p. Qq 
 
 tion; the measure of this tendency, called the ya ' 
 
 moment of the couple, is the product of one of the forces by the distance 
 between the two. 
 
 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 applica- 
 tion of two other forces is required, forming a second couple. Thus in 
 Fig. 99, P and Q, forming a couple, may be balanced by 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 5 need not be parallel to P and Q, but if not, then their 
 components parallel to PQ are to be taken instead of the forces themselves. 
 
492 Mechanics. 
 
 Equilibrium of Forces. — A system of forces applied at points of a 
 solid body will be in 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 compo- 
 nents of the forces in the direction of any three rectangular axes must be 
 separately equal to 0. 
 
 2. The algebraic sum of the moments of the forces, with respect to any 
 three rectangular axes, must be separately equal to 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 mo- 
 ments 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 connected 
 together, is that point about which, if suspended, .all the 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 heaviness through- 
 out, 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 the 
 centers of magnitude of the several equal parts from that plane.) 
 
 If a body be suspended at its center of gravity, it will be in equilibrium 
 in all positions. If it be suspended at a point out of its center of gravity, it 
 will swing into a position such that its center of gravity, is vertically 
 beneath its point of suspension. 
 
 To find the center of gravity of any plane figure mechanically, suspend 
 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. Then the 
 center of gravity of the surface will be at the point of intersection of the 
 two marks of the plumb-line. 
 
 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 op- 
 posite 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 
 required. 
 
 Of a sector of a circle: On the radius which bisects the arc, 2 cr-e-3 I 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, 0.6002 r from the center. 
 
 Of a segment of a circle: c 3 -f- 12 a from the center, c = chord, a = area. 
 
 Of a parabolic surface: In the axis, 3/ 5 of its length from the vertex. 
 
 Of a semi-parabola (surface): 3/ 5 length of the axis from the vertex, and 
 3/8 of the semi-base from the axis. 
 
 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 = - — ■ . 9 , ' — -. — ■ — 75-.- 
 4 4 (a 2 + aa' + a' 2 ) 
 
MOMENT OF INERTIA. 493 
 
 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, whose 
 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 
 sum 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 of the 
 three planes. 
 
 MOMENT OF INERTIA. 
 
 The moment of inertia of the weight of a body with respect to an axis la 
 the algebraic sum of the products obtained by multiplying 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 = /, the weight of any 
 element of the body = w, and its distance from the axis = r, we have 
 1 = 2 (vrr 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 parts into which the body is 
 divided. 
 
 Moments of Inertia of Regular Solids. — Rod, or bar, of uniform 
 thickness, with respect to an axis perpendicular to the length of the rod, 
 
 /= w (| +d*) (1) 
 
 W == weight of rod, 21 = length, d = distance of center of gravity from 
 
 axis. 
 
 Thin circular plate, axis in its ) r _ w ( r 2_ , ^ \ fo \ 
 
 own plane, J l ~ w U ) ( ; 
 
 r = radius of plate. 
 
 Circular plate, axis perpendicular to ) j = w M + rf2 \ ,^ 
 
 ttl© pi£LLC, ) \2 * / 
 
 Circular ring, axis perpendicular to) T _ w (r^+r^ . ^ 2 \ (a\ 
 
 its own plane, I ' \ 2 /.' ' ' ' " K } 
 
 r and r' are the exterior and interior radii of the ring. 
 Cylinder, axis perpendicular to the) i ^-n? ( r2 ,V , ^\ /n 
 
 axis of the cylinder. ) ~ 1 4 + 3 + / ' ' ' * { } 
 
 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, 2wr 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- 
 sections of beams under strain. In this case / = 2ar 2 , in which a is any 
 elementary area, and r its distance from the center. (See under Strength 
 of Materials, p. 279.) Some writers call 2mr 2 =2w 2 -*- g the moment of 
 inertia. 
 
494 MECHANICS. 
 
 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. 
 
 For 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 
 
 2r_ 2 
 " 5h' 
 
 from center of the sphere, I = radius of oscillation = h+ h' = h + ~ 
 
 If the sphere vibrate about an axis tangent to its surface, h = r, and 
 Z = r+2/ 5 r. If h = 10 r, I = 10 r+ ■£=• 
 
 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 flatwise, or perpendicular to the plane of 
 the figure: 
 
 In an isosceles triangle the radius of oscillation is equal to 3/ 4 of the 
 height of the triangle. 
 
 In a circle, 5/8 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 body were 
 concentrated at the point. This point 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, / = 2w 2 = its moment of inertia, and k = its radius of gyration, 
 
 / =Wk* = 2w 2 ; k = \^7p' 
 
 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 of inertia is known, divide it by the weight 
 and extract the square root. For radius of gyration of an area, as a cross- 
 section of a beam, divide the moment of inertia of the area by the area 
 and extract the square root. 
 
CENTER AND RADIUS OF GYRATION. 
 
 495 
 
 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. to > i. _ 7 4 A. h , _ ./l* 
 length, )k-L \-, k - y- 
 
 (2) Circular plate, axis in 
 its plane, 
 
 (3) Circular plate, axis per- ) fr 
 pen. to plane, J 
 
 (4) Circular ring, axis per- 
 pen. to plane, 
 
 (5) Cylinder, axis 
 pen. to length, 
 
 
 Principal Radii of Gyration and Squares of Radii of Gyration. 
 
 (For radii of gyration of sections of columns, see page 281.) 
 
 Surface or Solid. 
 
 Parallelogram: ) axis at its base 
 
 height 7i ) " mid-height 
 
 Straight rod: ) „_• . „, ■, 
 
 i „-i 7 „i, .t; ■ ( axis at end 
 
 iss&i&n •■ *^ 
 
 Rectangular prism: 
 
 axes 2 a, 2 b, 2 c, referred to axis 2 a... . 
 Parallelopiped: length I, base b, axis at ) 
 
 one end, at mid-breadth ) 
 
 Hollow square tube: 
 
 out. side h, inner h', axis mid-length . . . 
 
 very thin, side = h, axis mid-length . . . 
 Thin rectangular tube: sides &, h, axis ) 
 
 mid-length J 
 
 Thin circ. plate: rad. r, diam. h, ax. diam. 
 Flat circ. ring: diams. h, h', axis diam.. . 
 Solid circular cylinder: length I, axis di- ) 
 
 ameter at mid-length ) 
 
 Circular plate: solid wheel of uniform j 
 
 thickness, or cylinder of any length, > 
 
 referred to axis of cyl ) 
 
 Hollow circ. cylinder, or flat ring: 
 
 I, length; R, r, outer and inner radii. 
 
 Axis, 1, longitudinal axis; 2, diam. at 
 
 mid-length ! 
 
 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) 
 
 polar axis a J 
 
 Paraboloid: r = rad. of base, rev. on axis 
 Ellipsoid: semi-axes a,b,c; revolving on ) 
 
 axis 2 a J 
 
 Spherical shell: radii R, r, revolving on ) 
 
 its diam J 
 
 Same: very thin, radius r 
 
 Solid cone: r = rad. of base, rev. on axis. . 
 
 Rad. of Gyration. %%%$% 
 
 0.5773/* 
 0.2886 h 
 0.5773 1 
 
 0.2886 I 
 
 0.577 V&2 . 
 
 0.289 V4Z 2 + 62 
 
 0.289 V^ +h'2 
 .403 h 
 
 0.289A %/ h -r^ 
 1/4 V h? + h' 2 
 
 0.289 Vp + 3r 2 
 
 0.7071 r 
 0.7071 iVF 
 
 289\//2 + 3 (iJ2 +r 2) 
 
 1/3 ft 2 
 1/12 h 2 
 
 Vl2 1 2 
 
 (b 2 + c 2 ) + 3 
 
 4P + b 2 
 
 12 
 
 (h 2 +h' 2 ) + \2 
 
 h 2 + 6 
 
 ¥ h + 3b 
 
 12' h + b 
 
 l/ 4 r 2 = ft 2 + 16 
 
 (h 2 + h' 2 ) -h 16 
 
 P. -J* 
 
 12 + 4 
 
 1/2 r 2 
 
 (R 2 + r 2 ) +2 
 I 2 , R 2 - ' 
 
 0.289 Vp + 6ft2 
 
 r 
 
 r 
 0.7071 r 
 0.6325 r 
 0.6325 r 
 0.5773 r 
 
 0.4472V&2 + C 2 
 
 l R 5 - r 5 
 
 ^ 
 
 0.8165r 
 
 0.5477r 
 
496 MECHANICS. 
 
 THE PENDULUM. 
 
 A body of any form suspended from a fixed axis about which it oscillates 
 by the force of gravity is called a compound pendulum. The ideal body 
 concentrated at the center of oscillation, suspended from the center of sus- 
 pension 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 
 21/2° 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 = 
 
 acceleration = 32.16, T = n \ — ; since it is constant, Too — =.• At a given 
 
 * 9 _ Vg 
 
 location g is constant and T oo vz. if I be constant, then for any location 
 
 T oo —j=.- If T be constant, gT 2 = ir 2 l; I oo g; g = ?—■ From this equation 
 
 v g 
 the force of gravity at any place may be determined if the length of the 
 simple pendulum, vibrating seconds, at that place is known. At New 
 York this length is 39.1017 inches = 3.2585 ft., whence g = 32.16 ft. At \ 
 London the length is 39.1393 inches. At the equator 39.0152 or 39.0168 
 inches, according to different authorities. 
 
 Time of vibration of a pendulum of a given length at New York 
 
 -t- i/ ~ T ~ = -^L, 
 
 ▼ 39.1017 6.253 
 
 t being in seconds and I in inches. Length of a pendulum having a given 
 time of vibration, I = t 2 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, vibrating 
 seconds, when the weight of the lower bob and the distances of the 
 weights from the point of suspension are given: 
 
 (39.1XP)-J>». 
 (39.1 X d) + d 2 
 
 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 unti< 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 be- 
 ing 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 
 
 -Vl 
 
 V^; /*=|^= 0.8146 £ 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 steam-engines. (See Governors.) 
 
VELOCITY, ACCELERATION; FALLING BODIES. 497 
 
 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 " hying 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 = 32.16, 
 then 
 
 2nRN „ Wv 2 Wv 2 W4ir 2 RN 2 WRN 2 nnno „ nWDW ,u 
 V - -60- ; F - 1R = 32-16^ = -36007- = ^93T = - 000341 ° WRN ^' 
 
 If n = number of revolutions per second, F = 1.2276 WRn 2 . 
 (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 
 second, if the velocity is uniform, 
 
 S xx S 
 
 v = r ; s = vt; t = — 
 
 i v 
 
 If the velocity varies uniformly, the mean velocity v m =1/2 (v x + v 2 ), in which 
 Vi is the velocity at the beginning and v 2 the velocity at the end of the time t. 
 
 S = l/ 2 (^ +V 2 )t (1) 
 
 If vi = 0, then s = 1/2 v 2 t. v 2 = 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. Unit of acceleration = a = 1 foot per second in one second. For 
 uniformly varying velocity, the acceleration is a constant quantity, and 
 
 a= Vll^l . V2 = Vl + at; Vt = v 2 -at\t= V2 ~ Vi ■ . . . (2) 
 
 If the body start from rest, v x = 0; then if v TO = mean velocity 
 
 v n = I 2 ; v 2 = 2v m ; a= j; v 2 = at; v 2 -at = 0; t=\ 
 
 Combining (1) and (2), we have 
 
 v 2 2 -v t 2 . , at 2 . at 2 
 
 s = 2a ; s = Vit+—; s = v 2 t — -• 
 
 If Vi = 0, s=y 2 v 2 t. 
 
 Retarded Motion. ■ — If the body start with a velocity Vi and come to 
 rest, v 2 = 0; then s=V2Vit. 
 
 In any case, if the change in velocity is v, 
 
 v . v 2 a ... 
 
 s = -t; s = — ; s = -t-. 
 2 2a 2 
 
 For a body starting from or ending at rest, we have the equations 
 
 . v , at 2 , 
 
 v = at; s = -t; s = — ; v 2 = 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, 
 
 v=gt = S2.1Qt = ^2~gh = 8.02 ^h = ^j ; 
 &-J# 2 _i«ns*2_ v * v * - £■ 
 
498 
 
 MECHANICS. 
 
 : V 9 4.01 
 
 g 32.16 
 
 u = space fallen through in the jPth second = g (T - 1/2). 
 
 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 -j- 2 = 16.08 feet; the acquired velocity is g = 
 
 32.16 ft. per sec; the distance fallen in two seconds is h = g — = 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 12 3 4 5 6 
 
 Acceleration, g 32.16X111 1 1 1 
 
 Velocity acquired at end of time, v 32.16 x 12 3 4.5 6 
 
 Height of fall in each second, u — - — x 1 3 5 7 9 11 
 
 Total height of fall, 
 
 9 16 25 36 
 
 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 Paris, lat. 48° 50' N., g = 980.87 cm. = 32.181 ft. 
 
 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 0° 10° 20° 30° 40° 50° 60° 
 
 Value of VJ^.. 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, _£_is generally taken 
 at 32.16. and V2g at 8.02. In England g = 32.2. \/2g = 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 = 32.089 
 
 Fig. 100 represents graphically the velocity, space, etc., of a body falling 
 for six seconds. The vertical line at the left is the time in seconds, the 
 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 = 1/2 9= 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 h, u and v adjoining the cut are to 
 be multiplied by 16.08 to obtain the actual 
 velocities and heights for the given times 
 
 Angular and Linear Velocity of a 
 Turning Body. — Let r — radius of a 
 turning body in feet, n = number of revo- 25 9 10 5" 
 lutions per minute, i>= linear velocity of 
 a point on the circumference in feet per 
 second, and 60 v = velocity in feet per 36 11 12 6- 
 minute. 
 
 v = 2 -IgZL 60v = 2»rrn 
 bO 
 
 t 
 
 3 4 2" 
 
 I 
 
 \3\ 
 
 16 
 
 K 
 
 Fig. 100. 
 
PARALLELOGRAM OF VELOCITIES. 
 
 499 
 
 Angular 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 
 
 angle = — degrees = 57.3°. 2wX 57.3° = 360°, or the circumference. 
 If A = angular velocity, v = Ar, A = ■ 
 
 r DU 
 
 called a radian. 
 
 Height Corresponding to a Given Acquired Velocity. 
 
 >> 
 
 
 >> 
 
 
 >> 
 
 
 >> 
 
 
 >> 
 
 
 £> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^3 
 
 
 m 
 
 
 
 
 A 
 
 
 A 
 
 
 -a 
 
 ja 
 
 .SP 
 
 JO 
 
 _M 
 
 _o 
 
 .£? 
 
 ^o 
 
 _M 
 
 _o 
 
 .SP 
 
 o 
 
 .SP 
 
 "a5 
 
 > 
 
 '53 
 
 w 
 
 "a 
 
 > 
 
 w 
 
 "53 
 
 > 
 
 '53 
 
 w 
 
 "53 
 > 
 
 & 
 
 "53 
 
 > 
 
 '53 
 
 i> 
 
 & 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 feet 
 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 per 
 
 feet. 
 
 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 
 
 0.048 
 
 19 
 
 5.61 
 
 40 
 
 24.9 
 
 61 
 
 57.9 
 
 82 
 
 104.5 
 
 115 
 
 205 
 
 2 
 
 0.062 
 
 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 
 
 350 
 
 4 
 
 0.248 
 
 24 
 
 8.94 
 
 45 
 
 31.4 
 
 66 
 
 67.7 
 
 87 
 
 117.7 
 
 175 
 
 476 
 
 4.5 
 
 0.314 
 
 25 
 
 9.71 
 
 •46 
 
 32.9 
 
 67 
 
 69.8 
 
 88 
 
 120.4 
 
 200 
 
 622 
 
 5 
 
 0.388 
 
 26 
 
 10.5 
 
 47 
 
 34.3 
 
 68 
 
 71.9 
 
 89 
 
 123.2 
 
 300 
 
 1399 
 
 6 
 
 0.559 
 
 27 
 
 11.3 
 
 48 
 
 35.8 
 
 69 
 
 74.0 
 
 90 
 
 125.9 
 
 400 
 
 2488 
 
 7 
 
 0.761 
 
 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 
 
 11 
 
 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 
 
 Parallelogram of Velocities. — The principle of the composition 
 and resolution of forces may also be applied to velocities or to distances 
 moved in given intervals of time. Referring 
 to Fig. 93, page 489, if a body at O has a 
 force applied to it which acting alone would a ri 
 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 velocitv. 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. 101 shows the 
 
 resultant velocities, also the path traversed „„<f„ rm 
 
 by a body acted on by two forces, one of which would carry it at a uniform 
 velocitv over the intervals 1. 2. 3, B and the other of vvhich would carry it 
 by an accelerated motion over the i ntervals a,b,c,Dm the same times. At 
 
 Fig. 101. 
 
500 
 
 MECHANICS. 
 
 Falling Bodies: Velocity Acquired by a Body Falling a Given 
 Height. 
 
 
 >> 
 
 
 >> 
 
 
 >> 
 
 
 >> 
 
 
 £ 
 
 
 >> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -Q 
 
 
 
 
 J3 
 
 
 ,c 
 
 
 
 
 a 
 
 o 
 
 M 
 
 o 
 
 _M 
 
 o 
 
 _bJ) 
 
 o 
 
 M 
 
 o 
 
 ,M 
 
 _o 
 
 
 
 'S 
 
 
 
 
 '3 
 
 
 '3 
 
 
 
 
 K 
 
 > 
 
 w 
 
 > 
 
 K 
 
 > 
 
 K 
 
 f> 
 
 K 
 
 > 
 
 w 
 
 > 
 
 feet. 
 
 feet 
 
 feet. 
 
 feet 
 
 feet. 
 
 feet 
 
 feet. 
 
 feet 
 
 feet. 
 
 feet 
 
 feet. 
 
 feet 
 
 
 p. sec. 
 
 
 p. sec. 
 
 
 p. sec. 
 
 
 p. sec. 
 
 
 p. sec. 
 
 
 p. sec. 
 
 0.005 
 
 .57 
 
 0.39 
 
 5.01 
 
 1.20 
 
 8.79 
 
 5. 
 
 17.9 
 
 23. 
 
 38.5 
 
 72 
 
 68.1 
 
 0.010 
 
 .80 
 
 0.40 
 
 5.07 
 
 1.22 
 
 8.87 
 
 .2 
 
 18.3 
 
 .5 
 
 38.9 
 
 73 
 
 68.5 
 
 0.015 
 
 .98 
 
 0.41 
 
 5.14 
 
 1.24 
 
 8.94 
 
 .4 
 
 18.7 
 
 24. 
 
 39.3 
 
 74 
 
 69.0 
 
 0.020 
 
 1.13 
 
 0.42 
 
 5.20 
 
 1.26 
 
 9.01 
 
 .6 
 
 19.0 
 
 .5 
 
 39.7 
 
 75 
 
 69.5 
 
 0.025 
 
 1.27 
 
 0.43 
 
 5.26 
 
 1.28 
 
 9.08 
 
 .8 
 
 19.3 
 
 25 
 
 40.1 
 
 76 
 
 69.9 
 
 0.030 
 
 1.39 
 
 0.44 
 
 5.32 
 
 1.30 
 
 9.15 
 
 6. 
 
 19.7 
 
 26 
 
 40.9 
 
 77 
 
 70.4 
 
 0.035 
 
 1.50 
 
 0.45 
 
 5.38 
 
 1.32 
 
 9.21 
 
 .2 
 
 20.0 
 
 27 
 
 41.7 
 
 78 
 
 70.9 
 
 0.040 
 
 1.60 
 
 0.46 
 
 5.44 
 
 1.34 
 
 9.29 
 
 .4 
 
 20.3 
 
 28 
 
 42.5 
 
 79 
 
 71.3 
 
 0.045 
 
 1.70 
 
 0.47 
 
 5.50 
 
 1.36 
 
 9.36 
 
 .6 
 
 20.6 
 
 29 
 
 43.2 
 
 80 
 
 71.8 
 
 0.050 
 
 1.79 
 
 0.48 
 
 5.56 
 
 1.38 
 
 9.43 
 
 .8 
 
 20.9 
 
 30 
 
 43.9 
 
 81 
 
 72.2 
 
 0.055 
 
 1.88 
 
 0.49 
 
 5.61 
 
 1.40 
 
 9.49 
 
 7. 
 
 21.2 
 
 31 
 
 44.7 
 
 82 
 
 72.6 
 
 0.060 
 
 1.97 
 
 0.50 
 
 5.67 
 
 1.42 
 
 9.57 
 
 .2 
 
 21.5 
 
 32 
 
 45.4 
 
 83 
 
 73.1 
 
 0.065 
 
 2.04 
 
 0.51 
 
 5.73 
 
 1.44 
 
 9.62 
 
 .4 
 
 21.8 
 
 33 
 
 46.1 
 
 84 
 
 73.5 
 
 0.070 
 
 2.12 
 
 0.52 
 
 5.78 
 
 1.46 
 
 9.70 
 
 .6 
 
 22.1 
 
 34 
 
 46.8 
 
 85 
 
 74.0 
 
 0.075 
 
 2.20 
 
 0.53 
 
 5.84 
 
 1.48 
 
 9.77 
 
 .8 
 
 22.4 
 
 35 
 
 47.4 
 
 86 
 
 74.4 
 
 0.080 
 
 2.27 
 
 0.54 
 
 5.90 
 
 1.50 
 
 9.82 
 
 8. 
 
 22.7 
 
 36 
 
 48.1 
 
 87 
 
 74.8 
 
 0.085 
 
 2.34 
 
 0.55 
 
 5.95 
 
 1.52 
 
 9.90 
 
 .2 
 
 23.0 
 
 37 
 
 48.8 
 
 88 
 
 75.3 
 
 0.090 
 
 2.41 
 
 0.56 
 
 6.00 
 
 1.54 
 
 9.96 
 
 .4 
 
 23.3 
 
 38 
 
 49.4 
 
 89 
 
 75.7 
 
 0.095 
 
 2.47 
 
 0.57 
 
 6.06 
 
 1.56 
 
 10.0 
 
 .6 
 
 23.5 
 
 39 
 
 50.1 
 
 90 
 
 76.1 
 
 0.100 
 
 2.54 
 
 0.58 
 
 6.11 
 
 1.58 
 
 10.1 
 
 .8 
 
 23.8 
 
 40 
 
 50.7 
 
 91 
 
 76.5 
 
 0.105 
 
 2.60 
 
 0.59 
 
 6.16 
 
 1.60 
 
 10.2 
 
 9. 
 
 24.1 
 
 41 
 
 51.4 
 
 92 
 
 76.9 
 
 0.110 
 
 2.66 
 
 0.60 
 
 6.21 
 
 1.65 
 
 10.3 
 
 .2 
 
 24.3 
 
 42 
 
 52.0 
 
 93 
 
 77.4 
 
 0.115 
 
 2.72 
 
 0.62 
 
 6.32 
 
 1.70 
 
 10.5 
 
 .4 
 
 24.6 
 
 43 
 
 52.6 
 
 94 
 
 77.8 
 
 0.120 
 
 2.78 
 
 0.64 
 
 6.42 
 
 1.75 
 
 10.6 
 
 .6 
 
 24.8 
 
 44 
 
 53.2 
 
 95 
 
 78.2 
 
 0.125 
 
 2.84 
 
 0.66 
 
 6.52 
 
 1.80 
 
 10.8 
 
 .8 
 
 25.1 
 
 45 
 
 53.8 
 
 96 
 
 78.6 
 
 0.130 
 
 2.89 
 
 0.68 
 
 6.61 
 
 1.90 
 
 11.1 
 
 10. 
 
 25.4 
 
 46 
 
 54.4 
 
 97 
 
 79.0 
 
 0.14 
 
 3.00 
 
 0.70 
 
 6.71 
 
 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 
 
 0.17 
 
 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. 
 
 30.0 
 
 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 
 
 1.00 
 
 8.02 
 
 3.5 
 
 15.0 
 
 18. 
 
 34.0 
 
 62 
 
 63.2 
 
 550 
 
 188 
 
 0.30 
 
 4.39 
 
 1.02 
 
 8.10 
 
 3.6 
 
 15.2 
 
 .5 
 
 34.5 
 
 63 
 
 63.7 
 
 600 
 
 197 
 
 0.31 
 
 4.47 
 
 1.04 
 
 8.18 
 
 3.7 
 
 15.4 
 
 19. 
 
 35.0 
 
 64 
 
 64.2 
 
 700 
 
 212 
 
 0.32 
 
 4.54 
 
 1.06 
 
 8.26 
 
 3.8 
 
 15.6 
 
 .5 
 
 35.4 
 
 65 
 
 64.7 
 
 800 
 
 227 
 
 0.33 
 
 4.61 
 
 1.08 
 
 8.34 
 
 3.9 
 
 15.8 
 
 20. 
 
 35.9 
 
 66 
 
 65.2 
 
 900 
 
 241 
 
 0.34 
 
 4.68 
 
 1.10 
 
 8.41 
 
 4. 
 
 16.0 
 
 .5 
 
 36.3 
 
 67 
 
 65.7 
 
 1000 
 
 254 
 
 0.35 
 
 4.74 
 
 1.12 
 
 8.49 
 
 .2 
 
 16.4 
 
 21. 
 
 36.8 
 
 68 
 
 66.1 
 
 2000 
 
 359 
 
 0.36 
 
 4.81 
 
 1.14 
 
 8.57 
 
 .4 
 
 16.8 
 
 .5 
 
 37.2 
 
 69 
 
 66.6 
 
 3000 
 
 439 
 
 0.37 
 
 4.88 
 
 1.16 
 
 8.64 
 
 .6 
 
 17.2 
 
 22. 
 
 37.6 
 
 70 
 
 67.1 
 
 4000 
 
 507 
 
 0.38 
 
 4.94 
 
 1.18 
 
 8.72 
 
 .8 
 
 17.6 
 
 .5 
 
 38.1 
 
 71 
 
 67.6 
 
 5000 
 
 567 
 
FORCE OP ACCELERATION. 501 
 
 the end of the respective intervals the body will be found at C lt C 2 , C3, C, 
 and the mean velocity during each intervals is represented by the distances 
 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. 
 Mass — Force of Acceleration. — The mass of a body, m = w/g, is a 
 constant quantity. If g = the acceleration due to gravity, and w = 
 
 weight, then the mass m = — ; w = mg. If the weight w is taken to be the 
 
 resultant of the force of gravity on the particles of a body such as may 
 be measured by a spring balance, or by the extension or deflection of a 
 rod of metal loaded with the given weight, then the weight varies accord- 
 ing to the variation in the force of gravity at different places, and the value 
 of g is that at the place where the body is weighed ; but if w is the weight 
 as weighed on a platform scale, then g = 32.2, the English value. In either 
 case m = w/g is a constant. 
 
 Force has been defined 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 required to produce an 
 acceleration of 32.2 ft. per second per second in a pound of free mass. 
 
 Force equals the product of the mass by the acceleration, or / = ma. 
 
 Also, if v = the velocity acquired in the time t,ft = mv;f = mv -*- t; the 
 acceleration being uniform. 
 
 The force required to produce an acceleration of g (that is, 32.16 ft. per 
 
 sec. in one second) is / = mg = — g = w, or the weight of the body. Also, 
 / = ma = m -^—. — - . in which v 2 is the velocity at the end, and vi the 
 velocity at the beginning of the time t, and / = mg = — 2 ■■ . — -f a; 
 
 weight of the body as that acceleration is to the acceleration produced by 
 gravity. (The weight w is the weight where g is measured.) 
 
 Example. — Tension in a cord lifting a weight. A weight of 100 lbs. 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? Mean velocity = v m =20 ft. per sec; final 
 
 velocity = v 2 = 2 v m = 40; acceleration a = y = — = 10. Force / = 
 
 ma = — = — X 10 = 31.1 lbs. 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 lbs., making a total of 131.1 lbs. 
 
 The Resistance to Acceleration is the same as the force required to pro- 
 duce the acceleration = — V<2 ~ ■♦ 
 g t 
 
 Formulae for Accelerated Motion. — For cases of uniformly accel- 
 erated motion other than those of falling bodies, we have the formulae 
 
 already given, / = — a, = — V2 ~ — • If the body starts from rest, Vi = 0. 
 
 IV v vt 
 
 Vi = v, and/ = - j ; fgt = wv. We also have s = -■ Transforming and 
 
 substituting for g its value 32.16, we obtain 
 
 32.16.ft _ 64.32 /g. 
 
 / = 
 
 64.32 s 32.16 4 16.08 1 2 ' 
 
 wv 2 = 16.08 .ft 2 = vt m= _ Rn9 k /fs = 32.16.ft 
 '64.32/ w 2* 
 
 32.16/ 4. 
 
 .01 V / 
 
 y « 
 
502 MECHANICS. 
 
 For any change in velocity, f=w r 2 ' ~ ^ *" ■ ) • 
 
 (See also Work of Acceleration, under Work.) 
 
 Motion on Inclined Planes. — The velocity acquired by a body 
 descending 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 
 
 V g sin a 4.01 Vh 
 
 FUNDAMENTAL EQUATIONS IN DYNAMICS. 
 
 (1) FS = 1/2 MV 2 = WH. Force into space equals energy, or work. 
 
 (2) FT = MV. Force into time equals momentum, 
 
 (3) F = M A = M V/T. Force equals mass into acceleration. 
 
 (4) 7 = V2 gH. Falling bodies. 
 
 The sign = here means "numerically equivalent to," the proper units 
 of each elementary quantity being chosen. 
 
 M = mass = Wig; W = weight in pounds, g = 32.2; F = force in 
 pounds, exerted on a mass free to move; S = space, or distance in feet 
 through which F is exerted; T = time in seconds; H = height in feet 
 through which a body falls, or in eq. (1) is lifted; A = acceleration in feet 
 per second per second, = V/T; V = velocity in feet per second acquired at 
 the end of the time T, the space S, or the height of fall H. 
 
 By these four equations and their algebraic transformations practically 
 all problems in dynamics (except those relating to impact) may be solved. 
 
 MOMENTUM, VIS-VITA. 
 
 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, 
 
 w 
 ..= mv = — v. 
 
 Since the moving force = product of mass by acceleration, / = ma; 
 
 v mv 
 
 and if the velocity acquired in t seconds = v, or a = j, f = — — ; ft = 
 
 mv; that is, the product of a constant force into the time in which it acts 
 equals numerically the momentum. 
 
 Since ft = mv, if t = 1 second mv = f, whence momentum might be de- 
 fined as numerically equivalent to the number of pounds of force that will 
 stop a moving body in 1 second, or the number of pounds of force which 
 acting during 1 second will give it the given velocity. 
 
 Vis- viva, or living force, is a term used by early writers on Mechanics 
 to denote the energy stored in a moving body. Some defined it as the 
 
 product of the mass into the square of the velocity, mv 2 , =— v 2 ; others as 
 
 one-half of this quantity, or lfomv 2 , or the same as what is now known as 
 energy. The term is now obsolete, its place being taken by the word 
 energy. 
 
 WORK, ENERGY, POWER. 
 
 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, 
 
WORK, ENERGY, POWER. 503 
 
 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 following 
 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 lbs. per sq. in. 
 
 The work performed in lifting a body is the product of the weight ot 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 performed 
 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 second 
 = 1,980,000 foot-pounds per hour. 
 
 Expressions for Force, Work, Power, etc. 
 
 The fundamental conceptions in Dynamics are: 
 
 Mass, Force, Time, Space, represented by the letters M, F, T, S. 
 
 Mass = weight -*■ g. If the weight of a body is determined by a spring 
 balance standardized at London it will vary with the latitude, and the 
 value of g to be taken in order to find the mass is that of the latitude 
 where the weighing is done. If the weight is determined by a balance 
 or by a platform scale, as is customary in engineering and in commerce, 
 the London value of g, = 32.2, is to be taken. 
 
 Velocity = space divided by time, V = S -s- T, if V be uniform. 
 V = 2S -s- T if V be uniformly accelerated. 
 
 Work = force multiplied by space = FS = i/ 2 MV 2 = FVT (V uniform). 
 
 Power = rate of work = work divided by time = FS •*■ T = P = 
 product of force into uniform velocity == FV. 
 
 Power exerted for a certain time produces work; PT = FS = FVT. 
 
 Effort is a force which acts on a body in the direction of its motion. 
 
 Resistance is that which is opposed to an acting force. It is equal 
 and opposite to the force. 
 
 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 distance 
 through which it is capable of acting, or by the product of the pressure it 
 exerts into the distance through which that pressure is capable of acting. 
 Potential energy may also exist as stored heat, or as stored chemical 
 energy, as in fuel, gunpowder, etc., or as electrical energy, the measure of 
 these energies being the amount of work that they are capable of perform- 
 ing. 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. 
 
504 MECHANICS. 
 
 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 
 
 v 2 
 bodies, h, the height due to the velocity, = — ; and if w = the weight, the 
 
 energy = 1/2 fnv 2 = wv 2 -4- 2g = wh. Since energy is the capacity for perform- 
 ing work, the units of work and energy are equivalent, or FS = i/2 mv 2 = wh. 
 Energy exerted = work done. 
 
 The actual energy of a rotating body whose angular velocity is A and 
 A 2 1 
 moment of inertia 2w 2 = /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 — , 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 accelera- 
 tion, or / = ma = — — • . If the distance traversed in the time t = s, 
 
 then work = fs = -t— s. 
 
 9 t 
 
 Example. — What work is required to move a body weighing 100 lbs. 
 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 = 2v m = 40; 
 
 initial velocity vi = 0; acceleration, a = — — - = — = 10; force = 
 
 -a= ^L X 10 = 31.1 lbs.; distance 80 ft.; work = fs = 31.1 X SO = 
 
 2488 foot-pounds. 
 
 The energy stored in the body moving at the final velocity of 40. ft. 
 per second is 
 
 1/2 mv 2 = I %2 = ^x^Te = 2488 f00t -P° urKls ' 
 which equals the work of acceleration, 
 
 . W V2 10 Vo V2 . 1 w „ 
 
 If a body of the weight W falls from a height H, the work of acceleration 
 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 A t to A 2 , the increase of the 
 velocity of the particle is vi — Vi=r (Ai — At), and the work of accelerat- 
 ing it is 
 
 w v£ — -t>i 2 _ wr 2 A2 2 — Ai 2 
 9 2 ~ g 2 
 
 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 2w 2 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 falling 
 hammer strike? " The question cannot be answered directly, and it 
 is based upon a misconception or ignorance of fundamental mechanical 
 
IMPACT. 505 
 
 laws. The energy, or capacity of 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 -i-2ji= Wv 2 -*- 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 lbs. 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 to motion imparted to the 
 body struck, penetration against friction, or against resistance to shearing 
 or 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 m 3 and m 2 are the masses of the two bodies and v x and v 2 
 their respective velocities before impact, and v their common velocity 
 after impact, (mi + m 2 )v = niiVi + m 2 v 2 , 
 
 _ m x v x + m 2 V2 
 
 rrti + m 2 
 
 m,\V\ — m 2 v 2 
 
 If the bodies move in opposite directions, v= ; — — , or the velocity 
 
 mi + tn 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. 
 
 y2miVi 1 + l/2m 2 t> 2 2 — V2 (m x + m 2 ) v 2 =1/2 mi (vi — v) 2 + 1/2 mi (vi — v) 2 ; 
 in which vi — v is the velocity lost by mi and v — vi the velocity gained 
 by mi. 
 
 Example. — Let mi = 10, mi = 8, v x = 12, vi = 15. 
 
 10 X 12 8X15 
 
 If the bodies collide they will come to rest, for v= " = 0. 
 
 The energy loss is 
 1/2 10 X 144+ I/28 X 225 -1/2 18 X = 1/2 10(12 - 0)2+1/28(15- 0) 2 = 
 1620 ft.-lbs. 
 
 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, v 2 their velocities after impact; then 
 
 f 
 
 m-iVi + mivi m 2 e (v t — v 2 ) 
 
 Ul 
 
 mi + mi mi + m 2 
 
 Vi 
 
 mivi + mivi m\e (v t — vi) 
 pi\ + mi mi + mi 
 
506 MECHANICS. 
 
 If the bodies are perfectly elastic, their relative velocities before and 
 after impact are the same. That is, vi' — 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. 
 
 mxVi + m 2 v 2 = m 1 v 1 + 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 
 momentum of the projectile (because both are acted on by equal force, 
 the pressure of the gases in the gun, for equal time), we have WV = wv, 
 or V = wv -5- 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 lbs., we find the velocity of recoil = 
 
 , 7 2000 X 400 n . , , , 
 
 V = — t- n nhn — =16 feet per second. 
 
 Now the energy of a body in motion is WV 2 -*■ 2 g. 
 
 Therefore the energy of recoil = 5 °'°°°* 162 = 198,800 foot-pounds. 
 
 Ji X O — .— 
 
 400 X 2000 2 
 The energy of the projectile is - QO = 24,844,000 foot-pounds. 
 
 Z X oZ.JL 
 
 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 heat 
 which is radiated into the atmosphere, increasing its temperature. Thus 
 
ANIMAL POWER. 
 
 507 
 
 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- 
 phere, apparently is lost. But the carbon dioxide generated by the com- 
 bustion 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. 
 
 lbs. 
 
 V, 
 
 ft. per 
 
 sec. 
 
 T" 
 3600 
 
 (hours 
 per 
 day). 
 
 RV, 
 ft.-lbs. 
 per sec. 
 
 RVT, 
 
 ft.-lbs. 
 per day. 
 
 1. Raising his own weight up 
 
 143 
 
 40 
 
 44 
 
 143 
 6 
 
 132 
 
 26.5 
 (12.5 
 ^ 18.0 
 (20.0 
 
 13.2 
 
 15 
 
 0.5 
 
 0.75 
 0.55 
 
 0.13 
 
 1.3 
 
 0.075 
 
 2.0 
 5.0 
 2.5 
 14.4 
 2.5 
 ? 
 
 8 
 
 6 
 6 
 
 6 
 
 10 
 
 10 
 
 8 
 ? 
 
 8 
 
 2 min. 
 
 10 
 
 8? 
 
 71.5 
 
 30 
 
 24.2 
 
 18.5 
 7.8 
 
 9.9 
 
 53 
 62.5 
 
 45 
 288 
 33 
 
 ? 
 
 2,059,200 
 
 648,000 
 522,720 
 
 399,600 
 
 280,800 
 
 2. Hauling up weights with rope, 
 and lowering the rope un- 
 
 3. Lifting weights by hand 
 
 4. Carrying weights up-stairs 
 
 and returning unloaded 
 
 5. Shoveling up earth to a 
 
 6. Wheeling earth in barrow up 
 slope of 1 in 12, 1/2 horiz. 
 veloc. 0.9 ft. per sec, and re- 
 
 356,400 
 
 7. Pushing or pulling horizon- 
 tally (capstan or oar) 
 
 1,526,400 
 
 8. Turning a crank or winch 
 
 1,296,000 
 
 
 1,188,000 
 
 
 480,000 
 
 
 
 Explanation. — R, resistance; V, effective velocity = distance 
 through which R is overcome -h 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. 
 
508 
 
 MECHANICS. 
 
 Performance of a Man in Transporting Loads Horizontally. 
 
 (Rankine.) 
 
 Kind of Exertion. 
 
 
 
 T" 
 
 LV, 
 
 L, 
 
 V, 
 
 3600 
 
 lbs. 
 
 lbs. 
 
 ft.-sec. 
 
 (hours 
 per 
 
 con- 
 veyed 
 
 
 
 day). 
 
 1 foot. 
 
 140 
 
 5 
 
 10 
 
 700 
 
 224 
 
 12/3 
 
 10 
 
 373 
 
 132 
 
 12/3 
 
 10 
 
 220 
 
 90 
 
 21/2 
 
 7 
 
 225 
 
 140 
 
 12/3 
 
 6 
 
 233 
 
 ( 252 
 
 
 
 
 
 
 \ 126 
 
 11.7 
 
 
 1474.2 
 
 I o 
 
 23.1 
 
 
 
 
 LVT, 
 lbs. con- 
 veyed 
 1 foot. 
 
 11. Walking unloaded, viana- 
 
 porting his own weight 
 
 12. Wheeling load L in 2-whld. 
 
 barrow, return unloaded . . 
 
 13. Ditto in 1-wh. barrow, ditto. . 
 
 14. Traveling with burden. ..... . 
 
 15. Carrying burden, returning 
 
 unloaded 
 
 16. Carrying burden, for 30 sec- 
 
 onds only 
 
 13,428,000 
 7,920,000 
 5,670,000 
 
 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 lbs. 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 lbs. at the 
 handle of a crane for short periods; 
 but that for continuous work a 
 force of 15 lbs. is all that should 
 be assumed, moving through 220 
 feet per minute. 
 
 Man-wheel. — Fig.102 is a sketeh 
 of a very efficient man-power hoist- 
 ing-machine which the author saw 
 Fig. 102. in Berne, Switzerland, in 1889. 
 
 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. 
 
 1. Cantering and trotting, draw- 
 
 ing a light railway carriage 
 (thoroughbred) 
 
 2. Horse drawing cart or boat, 
 
 walking (draught-horse) . . . 
 
 3. Horse drawing a gin or mill, 
 
 walking 
 
 4. Ditto, trotting 
 
 min. 221/2 
 mean 301/2 
 max. 50 
 
 100 
 66 
 
 V. 
 
 T" 
 
 3600 
 
 RV. 
 
 J H2/3 
 
 4 
 
 4471/2 
 
 3.6 
 
 8 
 
 432 
 
 3.0 
 6.5 
 
 8 
 41/2 
 
 300 
 429 
 
 8,640,000 
 6,950,000 
 
ANIMAL POWER. 
 
 509 
 
 Explanation. — R, resistance, in lbs.; V, velocity, in feet per second; 
 T" ■*■ 3600, hours work per day; RV, work per second; RVT, 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 4 32/55o = 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 
 
 T500 
 
 750 
 
 1500 
 270 
 180 
 
 3.6 
 
 . 7.2 
 
 2.0 
 3.6 
 7.2 
 
 10 
 41/2 
 
 10 
 10 
 7 
 
 5400 
 5400 
 
 3000 
 972 
 1296 
 
 194,400,000 
 
 
 87,480,000 
 
 7. Walking with cart, going 
 
 loaded, returning empty; 
 V, mean velocity 
 
 8. Carrying burden, walking . . 
 
 108,000,000 
 34,992,000 
 32,659,200 
 
 
 
 Explanation. — L, load in lbs. ; V, 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 common 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, 31ules, 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 Gay frier & 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: 
 
 W 
 
 r = IL [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. 
 
510 MECHANICS. 
 
 ELEMENTS OF 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. d 
 
 is overcome. The specific result may be to 
 change the character or direction of mo- 
 tion, as from circular to rectilinear, or vice 
 
 \ 6* 
 
 6w 
 
 a 
 
 Ow 
 
 versa, to change the velocity, or to overcome L (\w 
 
 a great resistance by the application of a W 
 moderate force. In all cases the total energy p 1n „ 
 
 exerted equals the total work done, the latter G - IUd ' 
 
 including the overcoming of all the frictional 
 resistances of the machine as well as the use- 
 ful work performed. No increase of power 
 can be obtained from any machine, since this 
 
 is impossible according to the law of conser- _] B 
 
 vationof energy. In a frictionless machine the 
 product of the force exerted at the driving- 
 point into the velocity of the driving-point, 
 cr the distance it moves in a given interval 
 of time, equals the product of the resistance 
 into the distance through which the resist- Fl 104 
 
 ance is overcome in the same time. 
 
 The most simple machines, or elementary 
 machines, are reducible to three classes, viz., 
 the Lever, the Cord, and the Inclined Plane. 
 
 The first class includes every machine con- 
 sisting of a solid body capable of revolving B 
 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. vJW 
 
 The third class includes every machine in jr IG jq5 
 
 which 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. 103 ) 
 
 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. 104.) 
 
 In a lever of the third order, the point of action of the force is between 
 that of the load and the fulcrum. (Fig. 105.) 
 
 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 P X 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 Vwis the velocity of W, and Vp is the velocity of P, W : P : : Vp: 
 Vw, and P X Vp = W X Vw. 
 
 If Sp 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- 
 
ELEMENTS OF MACHINES. 
 
 511 
 
 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. 96, p. 490), 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 force 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 m 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. 106) 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 
 to become infinite as the angle ap- 
 proaches zero. If a =the angle, P X cos a = R X sin a. 
 cos a = 0.99619, sin a = 0.08716, R = 11.44 P. 
 
 The stone-crusher (Fig. 107) 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. 106. 
 
 If a = 5 degrees, 
 
 Fig. 107. 
 
 Fig. 108. 
 
 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 ratio of 
 the resistance to the applied force is R : P ' : : cos a : 2 sin a ; 2 R sin a 
 = P cos a. The ratio varies when the angle varies, becoming infinite 
 when the angle becomes zero. 
 
512 
 
 MECHANICS. 
 
 Fig. 109. 
 
 The toggle-joint is used where great resistances are to be overcome 
 through very small distances, as in stone-crushers (Fig. 108). 
 
 The Inclined Plane, as a mechanical element, is supposed perfectly 
 hard and smooth, unless friction be 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. 109), 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 
 angle of the direction of the applied force with the angle of the plane. 
 P : W : : sin i : cos e; PX 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, 
 IF the resistance, and Pthe applied force or pressure on the head of the 
 
 wedge. Then, friction neglected, P; W : : t : I; P = -— ; W = -r- 
 
 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 
 the power transmitted is 
 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 
 a way that the height of jr IG ] 
 
 the plane is radial to the 
 cylinder, such as the ordinary lifting-cam, used in stamp-mills (Fig. 110), 
 
ELEMENTS OF MACHINES. 
 
 513 
 
 or it may be an inclined plane curved edgewise, and rotating in a plane 
 parallel to its base (Fig. 111). The relation of the weight to the applied 
 force is calculated in the same manner as in the case of the screw. 
 
 Pulleys or Blocks. — P = force applied, or pull; W = load lifted, 
 or resistance. In the simple pulley A (Fig. 112) 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 = 2 P. 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 7 = 
 velocity of W, and v = velocity of P, then in all cases VW = 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. 113.)— 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 = AB, during the same time the point C or the cord CE will 
 
514 
 
 MECHANICS. 
 
 threads wind the same way. 
 
 Si s 2 r 
 
 Fig. 115. 
 
 Fig. 114. 
 
 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. 
 
 The Differential Windlass (Fig. 114) 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. 115) is a com- 
 pound screw of different pitches, in which the 
 . JVi and N2 are the 
 
 two nuts; S1S1, 
 
 the longer-pitched 
 
 thread; S 2 Sn. the 
 
 short er-pi t ch ed 
 
 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. 
 
 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, 17 = 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. 116). 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 
 they act in a given time. If R, Ri, Ri 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, f X 
 R X Ri X R2 = W X r X n X ri, 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. 
 
 Endless Screw, or Worm-gear. (Fig. 117.) — 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 
 
 J)itch-circle of the wheel. The ratio of the applied force to the weight 
 ifted 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, 
 
STRESSES IN FRAMED STRUCTURES. 
 
 515 
 
 and also of the teeth on the cog-wheel, d = diameter of the axle, and 
 
 6 283 v D 
 D = diameter of the pitch-line of the cog-wheel, v = - L -r — -r X V; 
 
 V= vXtd -T- 6.283 rD. Pv = WV+ friction. 
 
 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. 118 and 119.) — 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 b 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 
 
 J 
 
 t 
 
 rl 
 
 T/ // 
 // 
 
 -^ 
 
 — \ 
 
 *- % 
 
 © 
 
 Fig. 118. 
 
 Fig. 120 
 
 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 in T *= 
 
 P X -77 » and the compression in B = P X -ry Also, if a = the angle 
 
 the inclined member makes with the mast, the other member being 
 
516 
 
 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=PX T/A', and Compression in B = PX B/A', hold true 
 even if the triangle is not right-angled, as in Fig. 120; but the trigono- 
 metrical relations above 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. 121.) — The strain in B is, as 
 before, P X B/A', A' being that portion of the vertical included between 
 B and T, wherever T may be attached to A. If, however, 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 
 «*. — ?L_ 
 
 T 
 
 Fig. 121. 
 
 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 -r- /. 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 ■*■ 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. 
 
 3. Shear-poles with Guys. 
 (Fig. 122.) — 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. 120. 
 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. 123.) — Sup- 
 pose the braces are used to 
 Compressive stress on AD = 1/2 P X AD 
 AB. This is true only if CB and BD 
 
 Fig. 122. 
 
 sustain a single load P. 
 v i5; on Ci = 1/2 PX CA 
 
STRESSES IN FRAMED STRUCTURES. 
 
 517 
 
 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. 124), then, by the principle 
 of the lever, find the reactions of the abutments Pi and R 2 . If P is the 
 load applied at the point B on the lever CD, the fulcrum being D, 
 then Bi X CD = P X BD and Ri X CD = P X BC; Ri = PX BD + CD; 
 P 2 = PX BC + CD. 
 
 The strain on AC = Ri X AC -*> AS, and on AD = #2 X AD -*- AS. 
 
 The strain on the tie = RiX CB + AB = R2X BD + AB. 
 
 When CP = BD, Ri — R2. The strain on CB and BD is the same, 
 whether the braces are of equal length or not, and is equal to 1/2 P X 
 1/2 CD •*■ AB. 
 
 Fig. 125. 
 
 Fig. 124. 
 
 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. 125.) — 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 A B = P. Com- 
 pression in each of the inclined braces 
 = l/ 2 P X AD -4- AB. Tension in the tie 
 CD = 1/2 P X BD + 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. 126.) — 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 = V2 P 
 X AD h- AB. Compression on CD = 
 1/2 P X BD + AB. 
 
 Queen-post Truss. (Fig. 127.) — 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 P2, 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 P2 
 only are considered to affect the 
 members of the truss. Strain in 
 the vertical ties BE and CF each 
 equals Pi or P2. Strain on AB and 
 CD each = Pi X CD +- CF. Strain 
 on the tie AE or EF or PD = Pi X 
 t-, , 07 FD-i- CF. Thrust on BC = tension 
 
 Fig. 127. on EF ^ 
 
 For stability to resist heavy unequal loads the queen-post truss should 
 have diagonal braces from B to F and from C to E. 
 
 Fig. 126. 
 
518 
 
 MECHANICS. 
 
 Inverted Queen-post Truss. (Fig. 128.) — Compression on EB and 
 FC each = Pi or P 2 . Compression on AB or BC or CD = Pi X AP -*-#P. 
 Tension on A E or FD = Pi X AP -*- 
 PP. Tension on EF = compression 
 on BC. For stability to resist 
 unequal loads, ties rhouid be run 
 from C to E and from B to P. 
 
 Burr Truss of Five Panels. 
 (Fig. 129.) — Four-fifths of the load 
 may be taken as concentrated at the 
 points P, K, L and P, 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, P2 concentrated at E, and the loads P 3 , P 4 concentrated at P 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 
 
 Fig. 128. 
 
 Fig. 129. 
 
 strain on BE or CF = Pi + P 2 . That portion of the truss between E 
 and P may be considered as a smaller queen-post truss, supporting the 
 loads P 2 , Pz at K and L. The strain on EG or HF = P 2 X EG + 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 
 P2 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 AB or CD, = (Pi + P 2 ) 
 X tan angle ABE, or (Pi + P 2 ) x AE ^ 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. 130.) — 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 l/e to the abutment 0, on the principle 
 of the lever. As the five-sixths must be transmitted through J A 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, J A, and AH the figure 4, and on KD, 
 DL, LE, etc., the figure 2. The load P 2 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: 
 
 Tension on diagonals \ AJ BH BK CJ CL DK DM EL EN FM F0 GN 
 .tension on aiagonaisj 15 10 x 6 3 3 6 1 10 ,0 15 
 
 Compression on verticals {*$ f Q J C f D Q L E f ™ <*> 
 
 Each of the figures in the first line is to be multiplied by Ve P X secant 
 of angle HAJ, or l/e P X AJ •*■ AH, to obtain the tension, and each 
 
STRESSES IN FRAMED STRUCTURES. 
 
 519 
 
 figure in the lower line is to be multiplied by l/ 6 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 f the load P is 
 carried through JB and the strut BH, which latter then receives a strain 
 = 15 /6 P X secant of HBJ. 
 
 OOO 
 
 fi f 2 P 3 P 4 h 
 
 Fig. 130. 
 
 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 15/6 P X tan A JB. 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 
 WL 
 equal to ^j-> 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, P2, 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 V6P secant would be seed 
 X (5/e Pi + 4/e P2 + 3/ 6 P 3 + 2/ 6 P 4 + 1/6 P 5 ). 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, 
 
 _. [(n-x) + (n-x) 2 -(x-l) + (x-l)*] P r(x-l) + (x-l)* 
 
 Strain on verticals = 
 
 2ft 
 
 For a uniformly distributed load, leave out the last term, 
 [r (x - 1) + (x - 1) 2 J v2ji. 
 
 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, 
 
 3d, 4th, etc., it is P secant X ^ » 1 -~ < 1+ ^ +3 , etc., P being the total 
 load in one panel. 
 
 Strain in the Chords — Method of 31oments. — 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. 130) 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) = H. Depth of the truss = D. 
 
520 
 
 MECHANICS. 
 
 By the method of moments we take the difference of the moments, about 
 the point 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 Wx/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 -5- 2 L. Moment of the 
 
 Wx Wx 2 W / x 2 \ 
 
 stress in the chord = HD = — — — -5-^- - whence H — — I x - -=-!• 
 
 If x = or L, H ■■ 
 
 Itx 
 
 2 
 ■ L/2, 
 
 II 
 
 WL 
 8D' 
 
 which is the horizontal 
 
 strain at the middle of the chords, as before given. 
 
 Fig. 131. 
 
 The Howe Truss. (Fig. 131.) — 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. 132.) — 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. 132. 
 
 On the principle of the lever, the load Pi being 1/10 of the length of the 
 span from the line of the nearest support a, transmits 9/io of its weight to 
 a and 1/10 to g. Write 9 on the right hand of the strut la, to represent the 
 compression, and 1 on the right hand of 16, 2c, 3d, etc., to represent com- 
 pression, and on the left hand of b2, c3, etc., to represent tension. The 
 load Pi transmits T/\.o of its weight to a and 3/i to g. Write 7 on each 
 member from 2 to a, and 3 on each member from 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 
 sum, to show whether the difference represents tension or compression. 
 The results are as follows: Compression, la, 25; 2b, 15; 3c, 5; 3d, 5; 4e, 15; 
 5a, 25. Tension, lb, 15; 2c, 5; 4d, 5;5e, 15. Each of these figures is to 
 
STRESSES IN FRAMED STRUCTURES. 
 
 521 
 
 be multiplied by 1/10 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. 133. 
 
 In the truss shown in Fig. 133 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 P a , P 2 , 
 P 3 , Pa 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 P X 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 = P2 = 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 + Pi X 12.5 = 0; 38.4 Y = 75 ,; Y = 
 
 75 P h- 38.4 = 1.953 P. 
 
 - Zz + 3.5 PX 37.5 - PiX 25 - P 2 X 12.5 - P 3 X = 0; 15 Z = 
 
 93.75 P;Z = 6.25 P. 
 In the same manner the forces exerted in the other members have been 
 found as follows: EG = 6.73 P;G J = 8.07 P; J A = 9A2P;JH = 1.35 P; 
 GF = 1.59 P; AH = 8.75 P; HF = 7.50 P. 
 
 The Fink Roof-truss. (Fig. 134.) — An analysis by Prof. P. H. 
 hilbrick {Van N„ Mag., Aug., 1880) gives the following results: 
 W= total load on roof; 
 JV== No. of panels on both rafters; 
 W/N= P = load at each joint b, d, f, etc.; 
 V= reaction at A = 1/2 W = 1/2 NP = 4P; 
 AD= S; AC = L; CD = D; 
 ti,h,tz= tension on De, eg, gA, respectively; 
 ci, C2, c 3 , c 4 = compression on Cb, bd, df, and fA. 
 
522 
 
 MECHANICS. 
 
 Strains in 
 
 1, orDe = h= 2PS + D; 
 
 2, " eg = k = 3 PS -s- Z>; 
 
 3, " gA = t s =7frPS -*- D; 
 
 4, "A/ = c 4 =7/ 2 PL + D; 
 
 5, " /d = c 3 = 7/ 2 PL/D-PD/L; 
 
 6, " eft = c 2 \=y2PL/D-2PD/L; 
 
 7, or &C = c t = 7/ 2 PL/D - 3 PD/L; 
 
 8, " bcoxfg= PS -h L; 
 9," de =2PSh- L; 
 
 10, " cd or dg= 1/2 PS -^ D; 
 11," ec =PS -v- D; 
 
 12," cC =3/2 PS •*• Z>. 
 
 Exampm:. — 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, 6, C, etc. (and 2 tons each at A and B, which trans- 
 mit no strain to the truss me mbers). Here W = 32tons, P = 4 tons, 
 S= 32 ft., D = 16 ft., L = ^S 2 + Z> 2 = 2.236 X D. L + D = 2.236, 
 D -*- L = 0.4472, £-i-D = 2, S -i- L = 0.8944. The strains on the 
 numbered members then are as follows: 
 
 1, 2X4X2 =16 tons; 
 
 2, 3X4X2 =24 
 
 3, 7/ 2 X4X2 =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. 135, 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 9 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 9 
 
 =v/H- r ' 
 
 in which C and T represent 
 
 Fig. 135. 
 
 the crushing and the tensile strength respectively of 
 
 the material employed. It is applicable to any 
 
 material. For C = T, 9 = 543/ 4 °. For C = 0.4 T (yellow pine), 9 = 
 
 49 3/4 . For Cj= 0.8 T (soft steel), 9 = 531/4°. For C = 6 T (cast iron), 
 
 0= 691/4°. 
 
PYROMETRY. 523 
 
 HEAT. 
 
 THERM031ETERS. 
 
 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. 
 
 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 lbs. per sq. in., is taken at 212°, the distance between these 
 two points being divided into 180°. In the Centigrade and Reaumur 
 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 =4/9 deg. Reaumur. 
 
 1 Centigrade degree = 9/5 deg. Fahrenheit =4/5 deg. Reaumur. 
 
 1 Rdaumur 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.X2 = 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 mercury 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) 4- 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.) j 
 
 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. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 €. 
 
 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 
 
 i 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. 
 
 111 
 
 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 
 
 4- 1.4 
 
 49 
 
 120.2 
 
 115 
 
 239. 
 
 181 
 
 357.8 
 
 247 
 
 476.6 
 
 520 
 
 968 
 
 1180 
 
 2156 
 
 -16 
 
 3.2 
 
 50 
 
 122. 
 
 116 
 
 240.8 
 
 182 
 
 359.6 
 
 248 
 
 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 
 
 580 
 
 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. 
 
 600 
 
 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.F 
 
 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 
 
 158. 
 
 136 
 
 276.8 
 
 202 
 
 395.6 
 
 268 
 
 514.4 
 
 730 
 
 1346 
 
 1390 
 
 2534 
 
 5 
 
 41. 
 
 71 
 
 159.8 
 
 137 
 
 278.6 
 
 203 
 
 397.4 
 
 26*9 
 
 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 
 
 1:436 
 
 1440 
 
 2624 
 
 10 
 
 50. 
 
 76 
 
 168.8 
 
 142 
 
 287.6 
 
 208 
 
 406.4 
 
 274 
 
 525.2 
 
 790 
 
 1454 
 
 1450 
 
 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 
 
 830 
 
 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. 
 
 850 
 
 1562 
 
 1510 
 
 2750 
 
 "7 
 
 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 
 
 370 
 
 1598 
 
 1530 
 
 2786 
 
 19 
 
 66.2 
 
 85 
 
 185. 
 
 151 
 
 303.8 
 
 217 
 
 422.6 
 
 283 
 
 541.4 
 
 380 
 
 1616 
 
 1540 
 
 2804 
 
 20 
 
 68. 
 
 86 
 
 186.8 
 
 152 
 
 305.6 
 
 218 
 
 424.4 
 
 284 
 
 543.2 
 
 890 
 
 1634 
 
 1550 
 
 2822 
 
 21 
 
 69.8 
 
 87 
 
 188.6 
 
 153 
 
 307.4 
 
 219 
 
 426.2 
 
 285 
 
 545. 
 
 900 
 
 1652 
 
 1600 
 
 2912 
 
 22 
 
 71.6 
 
 88 
 
 190.4 
 
 154 
 
 309.2 
 
 220 
 
 428. 
 
 286 
 
 546.8 
 
 910 
 
 1670 
 
 1650 
 
 3002 
 
 23 
 
 73.4 
 
 89 
 
 192.2 
 
 155 
 
 311. 
 
 221 
 
 429.8 
 
 287 
 
 548.6 
 
 920 
 
 1688 
 
 1700 
 
 3092 
 
 24 
 
 75.2 
 
 90 
 
 194. 
 
 156 
 
 312.8 
 
 222 
 
 431.6 
 
 288 
 
 550.4 
 
 930 
 
 1706 
 
 1750 
 
 3182 
 
 25 
 
 77. 
 
 91 
 
 195.8 
 
 157 
 
 314.6 
 
 223 
 
 433.4 
 
 289 
 
 552.2 
 
 940 
 
 1724 
 
 1800 
 
 3272 
 

 TEMPERATURES 
 
 , FAHRENHEIT AND CENTIGRADE 
 
 • 
 
 F. 
 
 C. 
 
 F. 
 26 
 
 C. 
 -3.3 
 
 F. 
 
 C. 
 33.3 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 
 F. 
 
 C. 
 143.3 
 
 F. 
 
 C. 
 
 -40 
 
 -40. 
 
 92 
 
 158 
 
 70. 
 
 224 
 
 106.7 
 
 290 
 
 360 
 
 182.2 
 
 -39 
 
 -39.4 
 
 27 
 
 -2.8 
 
 93 
 
 33.9 
 
 159 
 
 70.6 
 
 225 
 
 107.2 
 
 291 
 
 143.9 
 
 370 
 
 187.8 
 
 -38 
 
 -38.9 
 
 28 
 
 -2.2 
 
 94 
 
 34.4 
 
 160 
 
 71.1 
 
 226 
 
 107.8 
 
 292 
 
 144.4 
 
 380 
 
 193.3 
 
 -37 
 
 -38.3 
 
 29 
 
 -1.7 
 
 95 
 
 35. 
 
 161 
 
 71.7 
 
 227 
 
 108.3 
 
 293 
 
 145. 
 
 390 
 
 198.9 
 
 -36 
 
 -37.8 
 
 30 
 
 -1.1 
 
 96 
 
 35.6 
 
 162 
 
 72.2 
 
 228 
 
 108.9 
 
 294 
 
 145.6 
 
 400 
 
 204.4 
 
 -35 
 
 -37.2 
 
 31 
 
 -0.6 
 
 97 
 
 36.1 
 
 163 
 
 72.8 
 
 229 
 
 109.4 
 
 295 
 
 146.1 
 
 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 
 
 I 10.6 
 
 297 
 
 147.2 
 
 430 
 
 221.1 
 
 -32 
 
 -35.6 
 
 34 
 
 1.1 
 
 100 
 
 37.8 
 
 166 
 
 74.4 
 
 232 
 
 111.1 
 
 298 
 
 147.8 
 
 440 
 
 226.7 
 
 -31 
 
 -35. 
 
 35 
 
 ].7 
 
 101 
 
 38.3 
 
 167 
 
 75. 
 
 233 
 
 111.7 
 
 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 
 
 -32.2 
 
 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 
 
 111 
 
 43.9 
 
 177 
 
 80.6 
 
 243 
 
 117.2 
 
 309 
 
 153.9 
 
 550 
 
 287.8 
 
 -20 
 
 -28.9 
 
 46 
 
 7.8 
 
 112 
 
 :■: : 
 
 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 
 
 159.4 
 
 650 
 
 343.3 
 
 -10 
 
 -23.3 
 
 56 
 
 13.3 
 
 122 
 
 50. 
 
 188 
 
 86.7 
 
 254 
 
 123.3 
 
 320 
 
 160. 
 
 660 
 
 348.9 
 
 - 9 
 
 -22.8 
 
 57 
 
 13.9 
 
 123 
 
 50.6 
 
 189 
 
 87.2 
 
 255 
 
 123.9 
 
 321 
 
 160.6 
 
 670 
 
 354.4 
 
 - 8 
 
 -22.2 
 
 58 
 
 14.4 
 
 124 
 
 51.1 
 
 190 
 
 87.8 
 
 256 
 
 124.4 
 
 322 
 
 161.1 
 
 680 
 
 360. 
 
 - 7 
 
 -21.7 
 
 59 
 
 15. 
 
 125 
 
 51.7 
 
 191 
 
 83.3 
 
 257 
 
 125. 
 
 323 
 
 161.7 
 
 690 
 
 365.6 
 
 - 6 
 
 -21.1 
 
 60 
 
 15.6 
 
 126 
 
 52.2 
 
 192 
 
 88.9 
 
 258 
 
 125.6 
 
 324 
 
 162.2 
 
 700 
 
 371.1 
 
 - 5 
 
 -20.6 
 
 61 
 
 16.1 
 
 127 
 
 52.8 
 
 193 
 
 89.4 
 
 259 
 
 126.1 
 
 325 
 
 162.8 
 
 710 
 
 376.7 
 
 - 4 
 
 -20. 
 
 62 
 
 16.7 
 
 128 
 
 53.3 
 
 194 
 
 90. 
 
 260 
 
 126.7 
 
 326 
 
 163.3 
 
 720 
 
 382.2 
 
 - 3 
 
 -19.4 
 
 63 
 
 17.2 
 
 129 
 
 53.9 
 
 195 
 
 90.6 
 
 261 
 
 127.2 
 
 327 
 
 163.9 
 
 730 
 
 387.8 
 
 - 2 
 
 -18.9 
 
 64 
 
 17.8 
 
 130 
 
 54.4 
 
 196 
 
 91.1 
 
 262 
 
 127.8 
 
 328 
 
 164.4 
 
 740 
 
 393.3 
 
 - 1 
 
 -18.3 
 
 65 
 
 18.3 
 
 131 
 
 55. 
 
 197 
 
 91.7 
 
 263 
 
 128.3 
 
 329 
 
 165. 
 
 750 
 
 398.9 
 
 
 
 -17.8 
 
 66 
 
 18.9 
 
 132 
 
 55.6 
 
 198 
 
 92.2 
 
 264 
 
 128.9 
 
 330 
 
 165.6 
 
 760 
 
 404.4 
 
 + 1 
 
 -17.2 
 
 67 
 
 19.4 
 
 133 
 
 56.1 
 
 199 
 
 92.8 
 
 265 
 
 129.4 
 
 331 
 
 166.1 
 
 770 
 
 410. 
 
 2 
 
 -16.7 
 
 68 
 
 20. 
 
 134 
 
 56.7 
 
 200 
 
 93.3 
 
 266 
 
 130. 
 
 332 
 
 166.7 
 
 780 
 
 415.6 
 
 3 
 
 -16.1 
 
 69 
 
 20.6 
 
 135 
 
 57.2 
 
 201 
 
 93.9 
 
 267 
 
 130.6 
 
 333 
 
 67.2 
 
 790 
 
 421.1 
 
 4 
 
 -15.6 
 
 70 
 
 21.1 
 
 136 
 
 57.8 
 
 202 
 
 94.4 
 
 268 
 
 131.1 
 
 334 
 
 67.8 
 
 800 
 
 426.7 
 
 5 
 
 -15. 
 
 71 
 
 21.7 
 
 137 
 
 58.3 
 
 203 
 
 95. 
 
 269 
 
 131.7 
 
 335 
 
 68.3 
 
 810 
 
 432.2 
 
 6 
 
 -14.4 
 
 72 
 
 22.2 
 
 138 
 
 58.9 
 
 204 
 
 95.6 
 
 270 
 
 132.2 
 
 336 
 
 68.9 
 
 820 
 
 437.8 
 
 7 
 
 -13.9 
 
 73 
 
 22.8 
 
 139 
 
 59.4 
 
 205 
 
 96.1 
 
 271 
 
 132.8 
 
 337 
 
 69.4 
 
 830 
 
 443.3 
 
 8 
 
 -13.3 
 
 74 
 
 23.3 
 
 140 
 
 50. 
 
 206 
 
 96.7 
 
 272 
 
 133.3 
 
 338 
 
 70. 
 
 840 
 
 448.9 
 
 9 
 
 -12.8 
 
 75 
 
 23.9 
 
 141 
 
 50.6 
 
 207 
 
 97.2 
 
 273 
 
 133.9 
 
 339 
 
 70.6 
 
 850 
 
 454.4 
 
 10 
 
 -12.2 
 
 76 
 
 24.4 
 
 142 
 
 51.1 
 
 208 
 
 97.8 
 
 274 
 
 134.4 
 
 340 
 
 71.1 
 
 860 
 
 460. 
 
 11 
 
 -11.7 
 
 77 
 
 25. 
 
 143 
 
 51.7 
 
 209 
 
 98.3 
 
 275 
 
 135. 
 
 341 
 
 71.7 
 
 870 
 
 465.6 
 
 12 
 
 -11.1 
 
 78 
 
 25.6 
 
 144 
 
 52.2 
 
 210 
 
 98.9 
 
 276 
 
 135.6 
 
 342 
 
 72.2 
 
 880 
 
 471.1 
 
 13 
 
 -10.6 
 
 79 
 
 26.1 
 
 145 
 
 52.8 
 
 211 
 
 99.4 
 
 277 
 
 136.1 
 
 343 
 
 72.8 
 
 890 
 
 476.7 
 
 14 
 
 -10. 
 
 80 
 
 26.7 
 
 146 
 
 53.3 
 
 212 
 
 100. 
 
 278 
 
 136.7 
 
 344 
 
 73.3 
 
 900 
 
 482.2 
 
 15 
 
 - 9.4 
 
 81 
 
 27.2 
 
 147 
 
 53.9 
 
 213 
 
 100.6 
 
 279 
 
 137.2 
 
 345 
 
 73.9 
 
 910 
 
 487.8 
 
 16 
 
 - 8.9 
 
 82 
 
 27.8 
 
 148 
 
 54 4 
 
 214 
 
 101.1 
 
 280 
 
 137.8 
 
 346 
 
 74.4 
 
 920 
 
 493.3 
 
 17 
 
 - 8.3 
 
 83 
 
 28.3 
 
 149 
 
 55. 
 
 215 
 
 101.7 
 
 281 
 
 138.3 
 
 347 
 
 75. 
 
 930 
 
 498.9 
 
 18 
 
 - 7.8 
 
 84 
 
 28.9 
 
 150 
 
 55.6 
 
 216 
 
 102.2 
 
 282 
 
 138.9 
 
 348 
 
 75.6 
 
 940 
 
 504.4 
 
 19 
 
 - 7.2 
 
 85 
 
 29.4 
 
 151 
 
 56.1 
 
 217 
 
 102.8 
 
 283 
 
 139.4 
 
 349 
 
 76.1 
 
 950 
 
 510. 
 
 20 
 
 - 6.7 
 
 86 
 
 30. 
 
 152 
 
 56.7 
 
 218 
 
 103.3 
 
 284 
 
 140. 
 
 350 
 
 76.7 
 
 960 
 
 515.6 
 
 21 
 
 - 6.1 
 
 87 
 
 30.6 
 
 153 
 
 57.2 
 
 219 
 
 103.9 
 
 285 
 
 140.6 
 
 351 
 
 77.2 
 
 970 
 
 521.1 
 
 22 
 
 - 5.6 
 
 88 
 
 31.1 
 
 154 
 
 57.8 
 
 220 
 
 104.4 
 
 286 
 
 141.1 
 
 352 
 
 77.8 
 
 980 
 
 526.7 
 
 23 
 
 - 5. 
 
 89 
 
 31.7 
 
 155 
 
 38.3 
 
 221 
 
 105. 
 
 287 
 
 141.7 
 
 353 
 
 78.3 
 
 990 
 
 532.2 
 
 24 
 
 - 4.4 
 
 90 
 
 32.2 
 
 156 
 
 58.9 
 
 222 
 
 105.6 
 
 288 
 
 142.2 
 
 354 
 
 78.9 
 
 1000 
 
 537.8 
 
 25 
 
 - 3.9 
 
 91 
 
 32.8 
 
 157 
 
 39.4 
 
 223 
 
 106.1 
 
 289 
 
 142.8 
 
 355 
 
 179.4 
 
 1010 
 
 543.3 
 
526 
 
 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 Wanner'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 Hol- 
 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 Fury'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.) 
 
 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, 
 t = 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 
 ' W(T - t) , _ 
 
 wS 
 
 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., 
 xviii, 728. 
 
 For accuracy corrections are required for variations in the specific heat 
 of the 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. 
 
 Le 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. 
 
PYROMETRY. 
 
 527 
 
 The principle upon which this pyrometer is constructed is the measure- 
 ment of a current of electricity produced by heating a couple composed 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 winch 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 1/2 
 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 uncorrected 
 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, Proc. Inst. M. E., 1892, 
 says: The electromotive force produced by heating the thermo-junction 
 to any given temperature is'measured by the movement of the spot of light 
 on the 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. 
 
 C. 
 
 Deg. F 
 
 Deg. C. 
 
 212 
 
 100 
 
 Water boils. 
 
 1733 
 
 945 
 
 Silver melts. 
 
 618 
 
 326 
 
 Lead melts. 
 
 1859 
 
 1015 
 
 Potassium sulphate 
 
 676 
 
 358 
 
 Mercury boils. 
 
 
 
 melts. 
 
 779 
 
 415 
 
 Zinc melts. 
 
 1913 
 
 1045 
 
 Gold melts. 
 
 838 
 
 448 
 
 Sulphur boils. 
 
 1929 
 
 1054 
 
 Copper melts. 
 Palladium melts. 
 
 1157 
 
 625 
 
 Aluminum melts. 
 
 2732 
 
 1500 
 
 1229 
 
 665 
 
 Selenium boils. 
 
 3227 
 
 1775 
 
 Platinum melts. 
 
 The Temperatures Developed in Industrial Furnaces. — M. Le 
 
 Chatelier states that by means of his pyrometer he has discovered that 
 the temperatures which occur in melting steel and in other industrial 
 operations have been hitherto overestimated. He finds the melting 
 heat of white cast iron 1135° (2075° F.), and that of gray cast iron 1220° 
 (2228° F.). Mild steel melts at 1475° (2687° F.), and hard steel at 1410° 
 (2570° 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. Boberts- Austen (Recent Advances in Pyrometry, Trans. A.T.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 2993 
 
 Steel, 0.3% carbon, pouring into large mold 1580 2876 
 
 Reheating furnace, interior . 930 1706 
 
 Cupola furnace, No. 2 cast iron, pouring into ladle 1600 2912 
 
 The following determinations have been effected by M. Le Chatelier: 
 Bessemer Process. Six-ton Converter. 
 
 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 
 
528 
 
 HEAT. 
 
 Open-hearth Furnace (Semi-mild Steel). Deg. C. Deg. F. 
 
 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 carbon and 3.43% graphite. 
 The results of the whole series may be expressed 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 thermom- 
 eter. The openings in the arms are adjusted so that the proportion 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 con- 
 nection be discontinued, and there be then forced into the globe contain- 
 ing 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 tem- 
 perature T. Before the introduction of V , we have the two separate 
 air-volumes, V at the temperature T, and V at the temperature 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. (Catalog, Stowe-Fuller Co., 1907.) — Seger cones were 
 developed in Germany by Dr. Herman A. Seger. They comprise a series 
 of triangular pyramids about 3 in. high and 5/ 8 in. wide at the base, each a 
 trifle less fusible than the next. When the series is placed in a furnace 
 whose temperature is gradually raised, one cone after another will bend 
 as its temperature of plasticity is reached. The temperature at which 
 it bends so far that its apex touches the surface supporting it, determines 
 a point on Seger's scale. Seger used as his standard, Zettlitz kaolin 
 and Rackonitz shale clay of the following analyses: 
 
 Zettlitz kaolin. . 
 Rackonitz clay. . 
 
 46.87 
 52.50 
 
 Alu- 
 
 38.56 
 45.22 
 
 Iron 
 Oxide. 
 
 0.83 
 0.81 
 
 Mag- 
 nesia. 
 
 / Potash) 
 I Soda. J 
 
 1.06 
 
 trace 
 
 Loss 
 on Ig- 
 nition. 
 
 12.73 
 0.78 
 
PYROMETRY. 
 
 Rackomtz shale clay consists of 99.27% clay substance and 0.73% 
 sand. The melting-point of a cone depends on the ratio of alumina to 
 silica and the amount of fluxes contained. The following table shows the 
 chemical formulae, mixtures and melting-points of Seger cones from 1 to 
 36. The temperatures corresponding to the melting-points of cones 
 21 to 26 are attained in the iron and steel industries. Cones 26 to 36 
 serve to determine the refractoriness of clays. 
 
 
 Chemical Composition. 
 
 Mixture. 
 
 Melting- 
 Point. 
 
 
 
 G 
 O 
 
 o 
 
 6 
 
 
 6 
 fa 
 
 6 
 < 
 
 d 
 
 1 
 
 a 
 
 fa 
 
 o3 
 
 3 
 
 So 
 
 .2.S 
 
 fa 
 
 "I 
 O 
 
 1 
 
 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 
 78 
 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 0.3 
 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0.7 
 0,7 
 0.7 
 0.7 
 0.7 
 0.7 
 
 0.2 
 0.1 
 0.05 
 
 0.3 
 0.4 
 0.45 
 0.5 
 0.5 
 0.6 
 0.7 
 0.8 
 0.9 
 1.0 
 1.2 
 1.4 
 1.6 
 1.8 
 2.1 
 2.4 
 2.7 
 3.1 
 3.5 
 3.9 
 4.4 
 4.9 
 5.4 
 6.0 
 6.6 
 7.2 
 20.0 
 1.0 
 1.0 
 1.0 
 1.0 
 1.0 
 1.0 
 1.0 
 1.0 
 
 4 
 
 4 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 10 
 12 
 14 
 16 
 18 
 21 
 24 
 27 
 31 
 35 
 39 
 44 
 49 
 54 
 60 
 66 
 72 
 200 
 10 
 
 8 
 
 6 
 
 5 
 
 4 
 
 3 
 
 2.5 
 
 2 
 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 83.55 
 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35^ 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 35 
 
 66 
 
 60 
 
 57 
 
 54 
 
 84 
 
 108 
 
 132 
 
 156 
 
 180 
 
 204 
 
 252 
 
 300 
 
 348 
 
 396 
 
 468 
 
 540 
 
 612 
 
 708 
 
 804 
 
 900 
 
 1020 
 
 1140 
 
 1260 
 
 1404 
 
 1548 
 
 1692 
 
 4764 
 
 240 
 
 180 
 
 120 
 
 90 
 
 60 
 
 30 
 
 15 
 
 16.0 
 8.0 
 4.0 
 
 "n'M 
 
 19.43 
 25.90 
 25.90 
 38.85 
 51.80 
 64.75 
 77.70 
 90.65 
 116.55 
 142.45 
 168.35 
 194.25 
 233.10 
 271.95 
 310.80 
 362.60 
 414.40 
 466.20 
 530.95 
 595.70 
 660.45 
 738.15 
 815.85 
 893.55 
 2551.13 
 129.50 
 129.5 
 129.5 
 129.5 
 129.5 
 129.5 
 129.5 
 
 2102 
 2138 
 2174 
 2210 
 2246 
 2282 
 2318 
 2354 
 2390 
 2426 
 2462 
 2498 
 2534 
 2570 
 2606 
 2642 
 2678 
 2714 
 2750 
 2786 
 2822 
 2858 
 2894 
 2930 
 2966 
 3002 
 3038 
 3074 
 3110 
 3146 
 3182 
 3218 
 3254 
 3290 
 3326 
 3362 
 
 1150 
 1170 
 1190 
 1210 
 1230 
 1250 
 1270 
 1290 
 1310 
 1330 
 1350 
 1370 
 1390 
 1410 
 1430 
 1450 
 1470 
 1490 
 1510 
 1530 
 1550 
 1570 
 1590 
 1610 
 1630 
 1650 
 1670 
 1690 
 
 ?q 
 
 
 
 
 
 
 1710 
 
 30 
 
 
 
 
 
 
 1730 
 
 31 
 
 
 
 
 
 
 1750 
 
 M 
 
 
 
 
 
 
 1770 
 
 33 
 
 
 
 
 
 
 1790 
 
 34 
 
 
 
 
 
 
 1810 
 
 35 
 
 
 
 
 Zettlitz 
 
 
 1830 
 
 36 
 
 
 
 
 
 1850 
 
 
 
 
 
 
 
 
 
 
 
 Mesure and IVouel's Pyrometric Telescope. (H. M. Howe, E. and 
 M. J., June 7, 1890.) — Mesure and Nouel's telescope gives an immediate 
 determination of the temperature of incandescent bodies, and is therefore 
 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 neek, can be used by foreman or heater 
 at anv 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 
 
530 
 
 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 apertures 
 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 f , and the corresponding absolute 
 temperatures by T and T', we should have 
 
 T 
 p \ p' \: T : T' and T' = p' - • 
 
 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. 
 
 The temperature of 32° F. is fixed as the point of melting ice, in which 
 case T = 460 + 32 == 492° F. This temperature can be produced by sur- 
 rounding the bulb in melting ice and leaving it several minutes, so that the 
 temperature of the confined air shall acquire that of the surrounding ice. 
 When the air is at that temperature, note the reading of the attached 
 manometer h, and that of a barometer; the sum will be the value of p 
 corresponding to the absolute temperature of 492° F. The constant of 
 the instrument, K = 492 -*■ p, once obtained, can be used in all future 
 determinations. 
 
PYROMETRY. 
 
 531 
 
 High Temperatures judged by Color. — The temperature of a body 
 can be approximately judged by 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, 
 but which is now replaced by the tables of H. M. Howe and of Maunsel 
 
 White and F. W. Taylor (Trans. 
 below. 
 
 A. S. M. E., 1899), which are given 
 
 Howe. 
 Lowest red vis- 
 ible in dark . . 
 Lowest red vis- 
 ible in day- 
 light 
 
 Dull red 550 to 625 
 
 Full cherry .... 700 
 
 Light red 850 
 
 Tull 
 
 470 
 
 475 
 
 3 F. White and Taylor. ° C. °F. 
 Dark blood-red, black- 
 
 878 red 990 
 
 Dark red, blood-red, low 
 
 red 556 1050 
 
 887 Dark cherry-red 635 1175 
 
 1022 to 1157 Medium cherry- red 1250 
 
 1292 Cherry, full red 746 1375 
 
 1562 Light cherry, light red*. 843 1550 
 
 Full yellow 950 to 1000 1742 to 1832 Orange, free scaling heat 899 1650 
 
 Light yellow. . . 1050 1922 Light orange 941 1725 
 
 White 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 
 1000 
 1100 
 1200 
 1300 
 1400 
 1500 
 
 F. Colors. 
 
 1832 Bright cherry-red. 
 
 2012 Orange-red. 
 
 2192 Orange-yellow. 
 
 2372 Yellow-white. 
 
 2552 White welding heat. 
 
 2732 Brilliant white. 
 
 1600 2912 Dazzling white (bluish 
 white). 
 
 °C. °F. Colors. 
 
 400 752 Red, visible in the dark. 
 474 885 Red, visible in the twilight. 
 525 975 Red, visible in the day- 
 light. 
 581 1077 Red, visible in the sun- 
 light. 
 700 1292 Dark red. 
 800 1472 Dull cherry- red. 
 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. 
 
 Yellow at 225 
 
 Orange at 243 
 
 Red at 265 
 
 Violet at 277 
 
 The Halcomb Steel Co. 
 colors of steel: 
 
 Colors. 
 
 Fahr. 
 437 
 473 
 509 
 531 
 
 Indigo at 
 
 Blue at 
 
 Green at 
 
 "Oxide-gray" . 
 
 Cent. 
 288 
 293 
 332 
 400 
 
 Fahr. 
 550 
 559 
 630 
 752 
 
 (1908) gives the following heats and temper 
 
 221.1 
 
 430 
 
 226.7 
 
 440 
 
 232.2 
 
 450 
 
 237.8 
 
 460 
 
 243.3 
 
 470 
 
 248.9 
 
 480 
 
 254.4 
 
 490 
 
 260.0 
 
 500 
 
 430 Very pale yellow. 
 Light yellow. 
 Pale straw-yellow. 
 Straw-yellow. 
 Deep straw-yellow. 
 Dark yellow. 
 Yellow-b rown . 
 Brown-yellow. 
 
 Cent. Fahr. 
 265.6 510 
 271.1 
 276.7 
 282.2 
 287.8 
 293.3 
 
 315.6 
 
 Colors. 
 Spotted red-brown. 
 Brown-purple. 
 Light purple. 
 Full purple. 
 Dark purple. 
 Full blue. 
 Dark blue. 
 Very dark blue. 
 
532 HEAT. 
 
 BOILING-POINTS AT ATMOSPHERIC PRESSURE. 
 
 14.7 lbs. per square inch. 
 
 Ether, sulphuric 100° F. Saturated brine 226° F. 
 
 Carbon bisulphide 118 Nitric acid 248 
 
 Ammonia 140 Oil of turpentine 315 
 
 Chloroform 140 Aniline 363 
 
 Bromine 145 Naphthaline 428 
 
 Wood spirit 150 Phosphorus 554 
 
 Alcohol 173 Sulphur 833 
 
 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. 
 
 MELTING-POINTS OF VARIOUS SUBSTANCES. 
 
 The following figures are given by Clark (on the authority of Pouillet. 
 Claudel, and Wilson), except those marked *, which are given by Prof. 
 Roberts-Austen, and those marked t, which are given by Dr. J. A. Harker. 
 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*, 620t 
 
 Bromine + 9.5 Zinc 779*, 786f 
 
 Turpentine 14 Antimony 1150, 1169f 
 
 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 1733*, 1751f 
 
 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*, 3110f 
 
 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. 580. 
 
 QUANTITATIVE MEASURE3IENT 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 lb. of pure water 
 from 62° to 63° F. (Peabody), or i/iso of the heat required to raise the 
 temperature of 1 lb. of water from 32° to 212° F. (Marks and Davis, see 
 Steam, p. 840). 
 
 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 lb. of 
 water 1° C. 1 lb. calorie = o/ 5 B.T.U. = 0.4536 calorie. The heat of 
 combustion of carbon, to CO2, 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 lb. 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 
 
HEAT OF COMBUSTION. 
 
 533 
 
 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 (Proc. Am. Acad. Arts and 
 Sciences, 1880; see also Wood's Thermodynamics) give higher figures, and 
 the most probable average is now considered to be 778. 
 
 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 lb. carbon burned to C0 2 = 14,600 heat-units. 1 lb. 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 0® C. . 
 
 " to steam at 100° C 
 
 Carbon (wood charcoal) to car- 
 bonic acid, CO2; ordinary tem- 
 
 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 
 
 1 2,431 
 
 ( 2,385 
 
 5,607 
 
 (13,120 
 
 \ 13,108 
 
 ( 13,063 
 
 (11,858 
 
 { 11,942 
 
 (11,957 
 
 ( 10,102 
 
 X 9,915 
 
 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 
 
 Favre and Silbermann. 
 
 Andrews. 
 
 Thomsen. 
 
 Favre and Silbermann. 
 
 Andrews. 
 
 
 
 black diamond to CO2 .... 
 
 
 Carbon to carbonic oxide, CO 
 
 Carbonic oxide to CO2 per unit of 
 CO 
 
 Favre and Silbermann. 
 
 Andrews. 
 
 Thomsen. 
 
 Favre and Silbermann. 
 
 Thomsen. 
 
 Andrews. 
 
 Favre and Silbermann. 
 
 Andrews. 
 Thomsen. 
 
 Favre and Silbermann. 
 
 CO to CO2 per unit of C=21/ 3 x2403 
 
 Marsh-gas, Methane, CH 4 ,to water 
 
 and CO2 
 
 Olefiant gas, Ethylene, C2H4, to 
 
 Benzole gas,C6H6,to water and CO2 
 
 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 14,000, 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 lb. 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 lb. 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 lb. of hydrogen and 8 lbs. 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 lbs. of steam, or 9 X 969.7 = 8727 B.T.U., leaving 
 as the "low" heating value 53,273 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 
 products of combustion are not often discharged at 212°. In steam- 
 
534 HEAT. 
 
 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 lb. of H is burned in twice the quantity of air required 
 for complete combustion, or 2 X (8 O + 26.56 N) = 69.12 lbs. 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 
 
 9 lbs. water heated fromJ62° to 212° 1352 B.T.U. 
 
 Latent heat of 9 lbs. H 2 at 212°, 9 X 969.7 8727 
 
 Superheated steam, 9 lbs. 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.- £^f 14,600 C + 62,000 (h - ^ + 4500 s] ; 
 
 in which C, H, O, and S are respectively the percentages of the several 
 elements. The term H — Vs 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 lb. of carbon is burned to 
 CO2, 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 + 
 C = 2 CO, the result is the same as if the 2 lbs. C had been burned directly 
 to 2 CO, generating 2 X 4450 = 8900 B.T.U. The 2 lbs. C burned to CO2 
 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 lbs. of water be injected into a large bed of glowing 
 coal, it will be decomposed into 1 lb. H and 8 lbs. 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 lbs. of O will combine with 6 lbs. 
 C, forming 14 lbs. 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 lbs. CO, to be evolved later if it is burned to CO2 
 with an additional supply of 8 lbs. O. 
 
 SPECIFIC HEAT. 
 
 Thermal Capacity. — The thermal capacity of a body between two 
 temperatures 7'o and T\ is the quantity of heat required to raise the tem- 
 perature from 7 1 o to T\. 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, 
 and is then immersed in a mass of liquid of which the weight, specific 
 
SPECIFIC HEAT. 
 
 535 
 
 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 d, w', and t' 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 d X vf X (T — V) = heat-units gained by the 
 cold liquid. If there is no heat lost by radiation or conduction, these 
 must be equal, and 
 
 cw (t - T) = did (T-f) or c = C ^ a (r _~[ ) - 
 
 , 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. 
 1 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 0.0951 
 
 Gold 0.0324 
 
 Wrought iron . 1138 
 
 Glass 0.1937 
 
 Cast iron 0.1298 
 
 Lead 0.0314 
 
 Platinum 0.0324 
 
 Silver 0.0570 
 
 Tin 0.0582 
 
 Steel (soft) 0.1165 
 
 Steel (hard) 0.1175 
 
 Zinc . 0956 
 
 Brass 0.0939 
 
 Ice . 5040 
 
 Sulphur 0.2026 
 
 Charcoal . 2410 
 
 Alumina 0.1970 
 
 Phosphorus . 1887 
 
 Water 1.0000 
 
 Lead (melted). 
 Sulphur " 
 
 Bismuth " 
 
 Tin " . . 
 
 Sulphuric acid. 
 
 . 0402 
 . 2340 
 . 0308 
 0.0637 
 . 3350 
 
 Mercury 0.0333 
 
 Alcohol (absolute) . 7000 
 
 Fusel oil . 5640 
 
 Benzine 0.4500 
 
 Ether 0.5034 
 
 Gases. 
 Constant Pressure. 
 
 Air.... 0.23751 
 
 Oxygen . 21751 
 
 Hydrogen 3 . 40900 
 
 Nitrogen . 24380 
 
 Superheated steam* 0. 4805 
 
 Carbonic acid . . 217 
 
 defiant gas (CH 2 ) 0. 404 
 
 Carbonic oxide . 2479 
 
 Ammonia . 508 
 
 Ether 0.4797 
 
 Alcohol 0.4534 
 
 Acetic acid . 4125 
 
 Chloroform . 1567 
 
 * See Superheated Steam, page 833. 
 
 Constant Volume. 
 0.16847 
 0.15507 
 2.41226 
 0.17273 
 0.346 
 0.1535 
 0.173 
 0.1758 
 0.299 
 0.3411 
 0.3200 
 
536 
 
 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 0.0567 
 
 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, Comptes Rendus, 1887.) 
 
 1382' to 1832° F 0.213 
 
 1749' to 1843° F , 0.218 
 
 1922 D to 2192° F 0.199 
 
 Brass 0.0939 
 
 Copper, 32° to 212° F 0.094 
 
 32° to 572° F 0.1013 
 
 Zinc, 32° to 212° F 0.0927 
 
 32° to 572° F 0.1015 
 
 Nickel 0.1086 
 
 Aluminum, 0° 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. 
 
 Otheb Solids. 
 
 Brickwork and masonry, about . 20 
 
 Marble 0.210 
 
 Chalk 0.215 
 
 Quicklime 0. 217 
 
 Magnesian limestone 0. 217 
 
 Silica 0.191 
 
 Corundum . 198 
 
 Stones generally 0. 2 to 0. 22 
 
 Coal 0.20 to 0.241 
 
 Coke . 203 
 
 Graphite 0. 202 
 
 Sulphate of lime 0. 197 
 
 Magnesia . 222 
 
 Soda 0.231 
 
 Quartz 0.188 
 
 River sand 0. 195 
 
 Woods. 
 
 Pine (turpentine). 0.467 I Oak. . 
 
 Fir 0.650 | Pear. 
 
 0.570 
 0.500 
 
 Liquids. 
 
 Alcohol, density 0.793 
 
 Sulphuric acid, density 1.87. 
 
 1.30. 
 
 Hydrochloric acid 
 
 0.622 
 0.335 
 0.661 
 0.600 
 
 Olive oil 
 
 Benzine 
 
 Turpentine, density 0.872. . 
 Bromine 
 
 0.310 
 0.393 
 0.472 
 1.111 
 
 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. 
 
 °F. 
 
 Sp. Ht, 
 
 °C. 
 
 °F. 
 
 Sp. Ht. 
 
 °C. 
 
 °F. 
 248 
 
 Sp. Ht. 
 
 
 
 V. 
 
 1.0G94 
 
 35 
 
 95 
 
 0.99735 
 
 70 
 
 158 
 
 1.00150 
 
 17.0 
 
 1.01620 
 
 5 
 
 41 
 
 1.00530 
 
 40 
 
 (04 
 
 0.99735 
 
 75 
 
 167 
 
 1.00275 
 
 140 
 
 284 
 
 1 .02230 
 
 10 
 
 50 
 
 1 . 00^30 
 
 45 
 
 113 
 
 0.90760 
 
 80 
 
 176 
 
 1.00415 
 
 160 
 
 320 
 
 1.02850 
 
 15 
 
 59 
 
 1.00030 
 
 50 
 
 122 
 
 0. 99800 
 
 85 
 
 188 
 
 1.00557 
 
 180 
 
 356 
 
 1.03475 
 
 7.0 
 
 68 
 
 0.99895 
 
 55 
 
 131 
 
 0.99850 
 
 90 
 
 194 
 
 1.00705 
 
 700 
 
 392 
 
 1.04100 
 
 7.5 
 
 77 
 
 0.99806 
 
 60 
 
 140 
 
 0.99940 
 
 95 
 
 203 
 
 1.00855 
 
 220 
 
 428 
 
 1.04760 
 
 30 
 
 86 
 
 0.99759 
 
 65 
 
 149 
 
 1.00040 
 
 '00 
 
 212 
 
 1.01010 
 
 
 
 
SPECIFIC HEAT. 
 
 537 
 
 Specific Heat of Salt Solution. (Schuller.) 
 
 Per cent salt in solution ... 5 
 
 Specific heat 0.9306 
 
 10 
 0.S909 
 
 15 20 
 0.8606 0.S490 
 
 25 
 O.S073 
 
 Specific Heat of Air.- 
 
 pressure 
 
 Between - 30° C. and 
 
 Regnault gives for the mean value at constant 
 
 10° C 0.23771 
 
 100° C 0.23741 
 
 200° C. 0.23751 
 
 Hanssen uses 0.1686 for the specific heat of air at constant volume. 
 The value of this constant has never been found to any degree of accuracy 
 by direct experiment. Prof. Wood gives 0.2375 h- 1.406 = 0.16S9. 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 h- 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's 
 " 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 0° and 100° C., the 
 thermal capacity at a temperature above 100° C. The specific heats of 
 gases under constant pressure between 0° 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 0° (— 273° C.) to a temperature T (= 273° + t) may be 
 expressed by the formula Q = 0.001 aT + 0.000,001 bT*, in which a is a 
 constant, 6.5, for all gases, and b has the following values for different 
 gases: 2 , N 2 , H 2 , CO, 0.6; H2O vapor, 2.9; C0 2 , 3.7; CH4, 6.0. 
 
 Specific Heats of Gases per Kilogram. 
 
 Under Constant 
 Pressure. 
 
 Under Constant 
 Volume. 
 
 Oxygen 
 
 Nitrogen and Carbon Monoxid< 
 
 Hydrogen 
 
 Water Vapor 
 
 Carbon Dioxide 
 
 Methane 
 
 0.213+ 38x10-6* 
 0.243+ 42xl0~6£ 
 3. 400 + 600 x 10- *t 
 0.447 + 324x10-6* 
 0.193+168x10-6^ 
 0.608 + 748x10-6* 
 
 0.150+ 38x10-6£ 
 0.171+ 42X10-H 
 2. 400+600x!0-6£ 
 0.335 + 324x10-6* 
 0.150+168x10-6* 
 0.491 + 748x10-6* 
 
538 
 
 Thermal Capacities of Gases per Kilogram in Centigrade Degrees. 
 
 Under Constant 
 Pressure. 
 
 Under Constant 
 Volume. 
 
 Oxygen 
 
 Nitrogen and Carbon Monoxide 
 
 Hydrogen 
 
 Water Vapor 
 
 Carbon Dioxide 
 
 Methane or Marsh Gas 
 
 0.213 t + 19x10~6{2 
 0.243 * + 21x10-6*2 
 3.400 £+300x10-0 P 
 0.447 £ + 162x10-6^2 
 0.193£+ 84x10-6*2 
 0.608 £+374x10-6*2 
 
 0.150 * + 19xl0-6£2 
 0.243 * + 21x10-6*2 
 2.400 £+300x10-6*2 
 0.335 £ + 162x10-6*2 
 0.150*+ 84x10-6*2 
 0.491 £+3,4x10-6*2 
 
 Thermal Capacities op Gases per Kilogram. 
 
 Temperatures. 
 
 o 2 
 
 N 2 , CO 
 
 H 2 
 
 H 2 
 
 C0 2 
 
 CH 4 
 
 Degrees Centigrade. 
 200 
 
 
 
 47.3 
 88.0 
 134.0 
 181.0 
 232.0 
 284.0 
 334.0 
 391.0 
 444.0 
 503.0 
 558.0 
 6 0.0 
 681.0 
 735.0 
 810.0 
 
 i 
 
 
 
 50 
 100 
 154 
 207 
 264 
 325 
 383 
 445 
 508 
 575 
 637 
 708 
 777 
 850 
 921 
 
 
 700 
 1400 
 2150 
 2900 
 3700 
 4550 
 5350 
 6250 
 7100 
 8050 
 8950 
 9900 
 10900 
 11900 
 12950 
 
 
 
 100 
 203 
 326 
 461 
 609 
 770 
 943 
 1130 
 1330 
 154'. 
 1751 
 1985 
 2241 
 2520 
 2799 
 
 
 
 43.1 
 91.0 
 145.0 
 208.0 
 277.0 
 354.0 
 435.0 
 523.0 
 618.0 
 728.0 
 840.0 
 950.0 
 1070.0 
 1200.0 
 1355.0 
 
 
 136.6 
 
 400 
 
 600 
 
 303.0 
 499.0 
 
 800 
 
 726.0 
 
 1000 
 
 982.0 
 
 1200.... 
 
 1269.0 
 
 1400 
 
 1584.0 
 
 1600 
 
 1931.0 
 
 1800 
 
 2000 
 
 2307.0 
 712.0 
 
 2200 
 
 3148.0 
 
 >400 
 
 3614.0 
 
 2600 
 
 4109.0 
 
 2800 
 
 4635.0 
 
 3000 
 
 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 0° C. for every increase in 
 temperature of 1° C. In Fahrenheit units it increases 1/491.2= 0.003620 
 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. 
 
 1°F. 
 
 100° C. 
 
 1°F. 
 
 
 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 
 
 
 
 If the volume is kept constant, the pressure varies directly as the abso- 
 lute temperature. 
 
EXPANSION BY HEAT. 
 
 539 
 
 Lineal Expansion of Solids at Ordinary Temperatures. 
 
 (Mostly British Board of Trade; from Clark.) 
 
 For 
 l°Fahr. 
 Length 
 
 = 1. 
 
 For 
 1°Cent. 
 Length 
 
 Expan- 
 sion 
 from 
 32° to 
 212° F. 
 
 Accord- 
 ing to 
 Other 
 
 Author- 
 ties. 
 
 Aluminum (cast) 
 
 Antimony (cryst.) 
 
 Brass, cast 
 
 Brass, plate 
 
 Brick 
 
 Brick (fire) 
 
 Bronze (Copper, 17; Tin, 2l/ 2 ; Zinc, 1) . . 
 
 Bismuth 
 
 Cement, Portland (mixed), pure 
 
 Concrete: cement-mortar and pebbles. . 
 
 Copper 
 
 Ebonite 
 
 Glass, English flint 
 
 Glass, thermometer 
 
 Glass, hard 
 
 Granite, gray, dry 
 
 Granite, red, dry 
 
 Gold, pure 
 
 Iridium, pure 
 
 Iron, wrought 
 
 Iron, cast 
 
 Lead 
 
 Magnesium 
 
 Marbles, various { ^° m 
 
 Masonry, brick { *™ m 
 
 Mercury (cubic expansion) 
 
 Nickel 
 
 Pewter 
 
 Plaster, white 
 
 Platinum 
 
 Platinum, 85 %, Iridium, 15 % 
 
 Porcelain 
 
 Quartz, parallel to maj. axis, 0° to 40° C 
 Quartz, perpend, to maj. axis, 0° to 40°C 
 
 Silver, pure 
 
 Slate 
 
 Steel, cast 
 
 Steel, tempered 
 
 Stone (sandstone), dry 
 
 Stone (sandstone), Rauville 
 
 Tin 
 
 Wedgwood ware 
 
 Wood, pine 
 
 Zinc 
 
 Zinc, 8, Tin, 1 
 
 0.00001234 
 0.00000627 
 0.00000957 
 0.00001052 
 0.00000306 
 0.00000300 
 0.00000986 
 0.00000975 
 0.00000594 
 0.00000795 
 0.00000887 
 0.00004278 
 0.00000451 
 0.00000499 
 0.00000397 
 00000438 
 0.00000498 
 0.00000786 
 0.00000356 
 0.00000648 
 0.00000556 
 0.00001571 
 
 0.00002221 
 0.00001129 
 0.00001722 
 0.00001894 
 0.O0OOO55O 
 0.00000540 
 J. 0000 1774 
 3.00001755 
 3.00001070 
 3.00001430 
 0.00001596 
 3 . 00007700 
 3.00000812 
 . 00000897 
 00000714 
 .00000789 
 0.0000089^ 
 0.00001415 
 0.0000064 
 0.00001166 
 0.00001001 
 0.00002828 
 
 0.002221 
 
 0.001129 
 
 0.001722 
 
 0.001894 
 
 0.000550 
 
 0.005400 
 
 0.001774 
 
 0.001755 
 
 0.001070 
 
 0.001430 
 
 0.001596 
 
 0.007700 
 
 0.000812 
 
 0.000897 
 
 0.00071 
 
 0.000789 
 
 0. 000897 
 
 0.001415 
 
 0.000641 
 
 0.001166 
 
 0.001001 
 
 0.002828 
 
 0.001083 
 0.001868 
 
 0.001235 
 0.001110 
 
 0.00000308 
 0.00000786 
 0.00000256 
 0.00000494 
 0.00009984 
 0.00000695 
 0.00001129 
 0.00000922 
 0.00000479 
 0.00000453 
 0.00000200 
 0.00000434 
 0.00000788 
 0.00001079 
 0.00000577 
 0.00000636 
 0.00000689 
 0.00000652 
 0.00000417 
 0.00001163 
 0.00000489 
 0.00000276 
 0.00001407 
 0.00001496 
 
 0.00000554 
 0.00001415 
 0.00000460 
 
 00000890 
 0.00017971 
 0.00001251 
 
 .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 
 
 0.000554 
 0.001415 
 0.000460 
 0.000890 
 0.017971 
 0.001251 
 0.002033 
 0.001660 
 0.000863 
 0.000815 
 0.000360 
 0.00078! 
 0.001419 
 0.001943 
 0.001038 
 0.001144 
 0.001240 
 0.001174 
 0.000750 
 0.002094 
 
 0.000496 
 0.002532 
 0.002692 
 
 0.018018 
 0.001279 
 
 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 Hiffh Temperatures. (Charpy and Grenet, 
 Comptes Rendus, 1902.) — Coefficients of expansion (for 1° C.) of annealed 
 carbon and nickel steels at temperatures at which there is no transforma- 
 
540 
 
 tion of the steel. The results seein to show that iron and carbide of iron 
 have appreciably the same coefficient of expansion. [See also p. 474.] 
 
 Composition 
 of Steels. 
 
 Mean Coefficients of Expansion 
 from 
 
 Coeffs. between 
 
 f! 
 
 \l.i 
 
 Si 
 
 P 
 
 1.5° to 200 
 
 3 200° to 500° 500° to 650° 
 
 
 
 o 03 
 
 ) 01 
 
 n rn 
 
 013 
 
 11.8X10""" 
 
 14.3X10" 
 
 > 17.0X10 " 6 
 
 24.5X10- 6 
 
 880° & 950° 
 
 2,5 
 
 ) 04 
 
 05 
 
 010 
 
 11.5 
 
 14.5 
 
 17.5 
 
 23.3 
 
 800° & 950° 
 
 64 
 
 ) 12 
 
 14 
 
 009 
 
 12.1 
 
 14.1 
 
 16.5 
 
 23.3 
 
 720° & 950° 
 
 93 
 
 ) 10 
 
 05 
 
 005 
 
 11.6 
 
 14.9 
 
 16.0 
 
 27.5 
 
 
 1 23 
 
 ) 10 
 
 08 
 
 005 
 
 11.9 
 
 14.3 
 
 16.5 
 
 33.8 
 
 
 1 50 
 
 ) 04 
 
 09 
 
 0<G 
 
 11.5 
 
 14.9 
 
 16.5 
 
 36.7 
 
 
 3.50 
 
 3.03 
 
 0.07 
 
 0.005 
 
 11.2 
 
 14.2 
 
 18.0 
 
 33.3 
 
 
 Nickel Steels. 
 
 Mean Coefficients of Expansion from 
 
 Ni 
 
 
 
 Mr, 
 
 15° to 100° 
 
 00° to 200° 
 
 200° to 400° 
 
 400° to 600° 
 
 600° to 900° 
 
 26 9 
 
 0.35 
 
 30 
 
 11.0x10-6 
 
 18.0x10-6 
 
 18.7x10-6 
 
 22.0x10-6 
 
 23.0X10- 6 
 
 28,9 
 
 0.35 
 
 36 
 
 10.0 
 
 21.5 
 
 19.0 
 
 20.0 
 
 22.7 
 
 30 1 
 
 0.35 
 
 0.34 
 
 9.5 
 
 14.0 
 
 19.5 
 
 19.0 
 
 21.3 
 
 34 7 
 
 0.36 
 
 36 
 
 2.0 
 
 2.5 
 
 11.75 
 
 19.5 
 
 ;o.7 
 
 36 1 
 
 0.39 
 
 39 
 
 1.5 
 
 1.5 
 
 11.75 
 
 17.0 
 
 20.3 
 
 32. e 
 
 0.29 
 
 0.66 
 
 8.0 
 
 14.0 
 
 18.0 
 
 21.5 
 
 22.3 
 
 35 f> 
 
 0.31 
 
 0,69 
 
 2.5 
 
 2.5 
 
 12.5 
 
 13.75 
 
 1\3 
 
 37 < 
 
 0.30 
 
 69 
 
 2.5 
 
 1.5 
 
 8.5 
 
 19.75 
 
 18.3 
 
 25 A 
 
 1.01 
 
 79 
 
 12.5 
 
 18.5 
 
 19.75 
 
 21.0 
 
 35.0 
 
 29 4 
 
 0.99 
 
 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 temperature 
 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 accurate survey work, etc. The Bureau of Stand- 
 ards found its coefficient of expansion to range from 0.000,000,374 to 
 0.000,000,44 for 1° C, or about V28 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 been 
 rolled, and which is used for fire-proofing, etc. It can also be used instead 
 of platinum for the electric connections passing through the glass plugs in 
 the base of incandescent electric lights. (Stoughton's " Metallurgy of 
 
 Expansion of Liquids from 33° to 212° F. — Apparent expansion 
 in glass (Clark). Volume at 212°, volume at 32° being 1: 
 
 Water 1.0466 
 
 Water saturated with salt . 1.05 
 
 Mercury 1.0182 
 
 Alcohol 1.11 
 
 Nitric acid 1.11 
 
 Olive and linseed oils 1 . 08 
 
 Turpentine and ether 1 .07 
 
 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. 
 
LATENT HEATS OF FUSION. 541 
 
 If the volume of a perfect gas increases V273 of its volume at 0° C. for 
 every increase of temperature of 1° C.,and decreases V273 of its volume 
 for every decrease of temperature of 1° C„ then at -273° C. the volume 
 of the imaginary gas would be reduced to nothing. This point -273° C , 
 or 491.2° F. below the melting-point of ice on the air-thermometer, or 
 492.66° F. below on a perfect gas-thermometer = -459.2° F. (or 
 — 460.66°), is called the absolute zero; and absolute temperatures are 
 temperatures measured, on either the Fahrenheit or Centigrade scale, 
 from this zero. The freezing-point, 32° F., corresponds to 491.2° F. 
 absolute. If p be the pressure and v the volume of a gas at the tem- 
 perature of 32° F. = 491.2° on the absolute scale = T , and p the pressure, 
 and v the volume of the same quantity of gas at any other absolute tem- 
 perature T, then 
 
 pv _ T_ = t + 459 . 2 . pv = p v 
 p Vo T 491.2 ' T ~ T ' 
 
 The value of p v ■*■ T for air is 53.37, and pv = 53.37 T, calculated as 
 follows by Prof. Wood: 
 
 A cubic foot of dry air at 32° F. at the sea-level weighs 0.080728 lb. 
 
 The volume of one pound is v = nori _ 00 = 12.387 cubic feet. The 
 pressure per square foot is 2116.2 lbs. 
 
 Wo = 2116.2 X 12.387 26214 ro 
 To 491.13 491.13 °° 
 
 The figure 491.13 is the number of degrees that the absolute zero is below 
 the melting-point of ice, by the air-thermometer. On the absolute scale, 
 whose divisions would be indicated by a perfect gas-thermometer, the 
 calculated value approximately is -192.66, which would make pv = 53.21 T. 
 Prof. Thomson considers that — 273.1° C, = — 459.4° F., is the most 
 probable value of the absolute zero. See Heat in Ency. Brit. 
 
 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 transferred 
 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 produced 
 in the body and rejected into the atmosphere or other surrounding bodies. 
 
 The following are examples in British thermal units per pound, as 
 given in Landolt and Bornstein's Phi/sikalische-Chemische Tabellen (Berlin, 
 1894). 
 
 Snhqtanrps Latent Heat s,,bstanrpq Latent Heat 
 
 bubstances. of Fusion bubstances. of Fusion> 
 
 Bismuth 22.75 Silver 37.93 
 
 Cast iron, gray ... 41 . 4 Beeswax 76 . 14 
 
 Cast iron, white . . 59 . 4 Paraffine 63 . 27 
 
 Lead 9 . 66 Spermaceti 66 . 56 
 
 Tin 25.65 Phosphorus 9.06 
 
 Zinc 50.63 Sulphur 16.86 
 
 Prof. Wood considers 144 heat-units as the most reliable value for the 
 latent heat of fusion of ice. Person gives 142.65. 
 
542 HEAT. 
 
 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 
 in the body; and in order that the operation of condensation 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 lbs. on the square inch: 
 
 (,„!,„,„,... Boiling-point under Latent Heat in 
 
 toUDSiance. 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 0° to 100° C. 
 
 Fori kg.,Z = 94.210 (365 - 1° C.) 0.31249. 
 
 Fori lb., £ = 141.124 (689 -£° 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, 
 ft = 1150 + 0.3745 (t- 21-2) -0.000550 (f-212) 2 . 
 
 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. 
 
EVAPORATION AND DRYING. 543 
 
 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 Reservoir, 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 
 
 " 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 
 
 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 l/s in. per day throughout the year. 
 
 When the pan was in the air the average evaporation was less than 3/ 16 
 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 0.0S8 to 0.16 in. per day during the irriga- 
 ting 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 l/e to 1/5 
 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 graduated so that 
 the liquid is boiled at a constant and low temperature. 
 
 A series distilling apparatus of high efficiency is described by W. P. 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 efficiency of 
 approximately 60 lbs. of water per pound of coal. 
 
 Tests of Yaryan six-effect machines have shown as high as 44 lbs. 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. News, 
 Mar. 29, 1900, and in Jour. Am. Soc'y of Naval Engineers, Feb., 1900. 
 
 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 V32 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/ 32 to 3/32. 
 
 Methods of Evaporation Employed in the Manufacture of Salt. 
 (F. E. Engelhardt, Chemist Onondaga 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 
 
544 
 
 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 lbs. of water per pound of coal. By 
 the pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single 
 effect, 86 bu. per ton of anthracite dust (2000 lbs.). With a double 
 effect nearly double that amount can be produced. 
 
 Solubility of Common Salt in Pure Water. (Andrese.) 
 
 32 50 86 104 140 176 
 
 35.63 35.69 36.03 36.32 37.06 38.00 
 26.27 26.30 26.49 26.64 27.04 27.54 
 
 Temp, of brine, F 
 
 100 parts water dissolve parts. 
 100 parts brine contain salt . . . 
 
 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 of 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. 
 
 1 
 
 o> 
 
 a 
 
 o 
 
 03 
 O) 
 
 g> 
 SB 
 
 bfl 
 
 "o3 
 4) 
 
 Mo 
 ft 
 
 *.£ 
 
 .2 3 
 
 o3_ 
 
 °£ . 
 
 '3 . 
 
 ® cm 
 
 O «3 
 
 0> 0) 
 
 3 OS 
 
 eg 3O 
 
 of coal required to 
 duce a bushel of 
 ;, 1 lb. coal evapo- 
 ing 6 lbs. of water. 
 
 §"3 
 
 03.^ ft 
 
 -■85 
 ■si's 
 
 "c3 
 
 o3 
 ffl 
 
 ft 
 
 0) 
 
 ga 
 
 !-s 
 
 O 1 " 
 
 £o>03 
 
 3 all 
 
 
 1 
 
 0.26 
 
 1.002 
 
 0.265 
 
 8.347 
 
 0.022 
 
 2,531 
 
 21,076 
 
 3,513 
 
 0.569 
 
 2 
 
 0.52 
 
 1.003 
 
 0.530 
 
 8.356 
 
 0.044 
 
 1,264 
 
 10,510 
 
 1,752 
 
 1.141 
 
 4 
 
 1.04 
 
 1.007 
 
 1.060 
 
 8.389 
 
 0.088 
 
 629.7 
 
 5,227 
 
 871.2 
 
 2.295 
 
 6..... 
 
 1.56 
 
 1.010 
 
 1.590 
 
 8.414 
 
 0.133 
 
 418.6 
 
 3,466 
 
 577.7 
 
 3.462 
 
 8 
 
 2.08 
 
 1.014 
 
 2.120 
 
 8.447 
 
 0.179 
 
 312.7 
 
 2,585 
 
 430.9 
 
 4.641 
 
 10 
 
 2.60 
 
 1.017 
 
 2.650 
 
 8.472 
 
 0.224 
 
 249.4 
 
 2,057 
 
 342.9 
 
 5.833 
 
 12 
 
 3.12 
 
 1.021 
 
 3.180 
 
 8.506 
 
 0.270 
 
 207.0 
 
 1,705 
 
 284.2 
 
 7.038 
 
 14 
 
 3.64 
 
 1.025 
 
 3.710 
 
 8.539 
 
 0.316 
 
 176.8 
 
 1,453 
 
 242.2 
 
 8.256 
 
 16 
 
 4.16 
 
 1.028 
 
 4.240 
 
 8.564 
 
 0.364 
 
 154.2 
 
 1,265 
 
 210.8 
 
 9.488 
 
 18 
 
 4.68 
 
 1.032 
 
 4.770 
 
 8.597 
 
 0.410 
 
 136.5 
 
 1,118 
 
 186.3 
 
 10.73 
 
 20 
 
 5.20 
 
 1.035 
 
 5.300 
 
 8.622 
 
 0.457 
 
 122.5 
 
 1,001 
 
 176.8 
 
 11.99 
 
 30 
 
 7.80 
 
 1.054 
 
 7.950 
 
 8.781 
 
 0.698 
 
 80.21 
 
 648.4 
 
 108.1 
 
 18.51 
 
 40 
 
 10.40 
 
 1.073 
 
 10.600 
 
 8.939 
 
 0.947 
 
 59.09 
 
 472.3 
 
 78.71 
 
 25.41 
 
 50 
 
 13.00 
 
 1.093 
 
 13.250 
 
 9.105 
 
 1.206 
 
 46.41 
 
 366.6 
 
 61.10 
 
 32.73 
 
 60 
 
 15.60 
 
 1.114 
 
 15.900 
 
 9.280 
 
 1.475 
 
 37.94 
 
 296.2 
 
 49.36 
 
 40.51 
 
 70 
 
 18.20 
 
 1.136 
 
 18.550 
 
 9.454 
 
 1.755 
 
 31.89 
 
 245.9 
 
 40.98 
 
 48.80 
 
 80 
 
 20.80 
 
 1.158 
 
 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 
 
 109 
 
 26.00 
 
 1.205 
 
 26.500 
 
 10.039 
 
 2.660 
 
 21.04 
 
 155.3 
 
 25.88 
 
 77.26 
 
EVAPORATION AND DRYING. 545 
 
 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 
 P \ rt parltvpsim diSSOlVe ) i15 386 371 368 370 375 417 452 
 P ^^Z^t^!}^ «* 470 466 468 474 528 572 
 
 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 
 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 18S9 was 
 69.38 degrees of the saliuometer. 
 
 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 lbs. 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 lbs. 
 
 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. — 43/4 in. copper coils, 528 square feet of surface; 
 steam in coils, 15 lbs.; temperature in pan, 141° to 148°; density of feed, 
 25° Baumd, 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 lbs. 
 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 6.123 3.6 2.26 1.5 .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 1.6 1.39 1.2 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 2.6 2.38 2.18 1.9 
 
 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 1' 6", 
 
 * For other sugar data, see Bagasse as Fuel, under Fuel. 
 
546 HEAT. 
 
 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 lbs. 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 
 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., 18S9. The three essential requirements 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 through 
 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., 
 under atmospheiic 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 
 bv 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 
 
EVAPORATION AND DRYING. 547 
 
 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 agaii\. 
 
 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 this tem- 
 perature and that of the heating surfaces is amply 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 food-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, 17 3/ 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, andj design different machines for each 
 group. 
 
 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 
 
548 HEAT, 
 
 must be kept above 212° F M 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 crystallization, breaking up chemical combinations, or on 
 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- 
 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 con- 
 stantly 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 be 
 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 
 
EVAPORATION AND DRYING. 
 
 549 
 
 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 
 
 Performance of Different Types of Driers. 
 
 (W. B. Ruggies.) 
 
 Type of drier 
 
 Material 
 
 Moisture, initial, per cent 
 
 Moisture, final, per cent 
 
 Calorific value of fuel, B.T.TJ 
 
 Fuel consumed per hour, lbs 
 
 Water evaporated per hour, lbs.. 
 Water evap. per pound fuel, lbs.. 
 
 Material dried per hour, lbs ' 
 
 Fuel per ton dried material, lbs. . . 
 Heat lost in exhaust air, per cent 
 Heat lost by radiation, etc., per 
 
 centi 
 
 Heat used to evaporate water, 
 
 per cent 
 
 Heat used to raise temperature of 
 
 material, per cent 
 
 Total efficiency, per cent 
 
 
 
 .. 
 
 
 
 
 3i 
 
 -fi£ 
 
 Jfi'1 
 
 »."§ 
 
 
 
 
 -g-c-s 
 
 
 
 Is* 
 
 o a 1 
 
 Is 
 
 III 
 
 'Mg 
 
 Sand. 
 
 Coal. 
 
 Cement 
 slurry. 
 
 Lime- 
 stone. 
 
 4.58 
 
 10.2 
 
 61.2 
 
 3.6 
 
 
 
 
 
 40.7 
 
 0.5 
 
 12100 
 
 12290 
 
 13200 
 
 13180 
 
 398 
 
 213.6 
 
 667 
 
 460 
 
 2196 
 
 924.2 
 
 4057 
 
 1325 
 
 5.3 
 
 4.3 
 
 6.1 
 
 2.3 
 
 36460 
 
 8300 
 
 7680 
 
 41400 
 
 21.8 
 
 51.3 
 
 17.3 
 
 22.2 
 
 11.3 
 
 42.8 
 
 38.4 
 
 38.2 
 
 7.6 
 
 7.7 
 
 12.5 
 
 15.6 
 
 52.5 
 
 39.4 
 
 52.0 
 
 24.4 
 
 28.6 
 
 10.1 
 
 7.1 
 
 21.8 
 
 
 81.1 
 
 49.5 
 
 59.1 
 
 46.2 
 
 in r~ 
 Nitrate 
 of soda. 
 7.2 
 0.3 
 13600 
 87 
 349 
 
 4.0 
 4581 
 38.0 
 40.7 
 
 13.8 
 
 33.1 
 
 12.4 
 45.5 
 
 Performance of a Steam Drier. 
 
 Material: Starch feed. Moisture, initial 39.8%, final 0.22%. Dried 
 material per hour, 831 lbs. Water evaporated per hour, 548 lbs. Steam 
 consumed per hour, 793 lbs. Water evaporated per pound steam, 
 0.691 lb. Temperature of material, moist, 58°, dry, 212°. Steam pres- 
 sure, 98 lbs. gauge. 
 
 Total heat to evaporate 548 lbs. water at 58° into steam, 
 
 548 X (154.2 + 969.7) = 615,897 B.T.TJ. 
 Heat supplied by 793 lbs. steam condensed to water at 212°, 
 
 793 X (1188.2 - 180.3) = 799,265 B.T.U. 
 Heat used to evaporate water, 
 
 (615,897 ■*■ 799,265) = 77.1%. 
 Heat used to raise temp, of material, 
 
 (831 X 154 X 0.492) = 62,963 = 7.9%. 
 . 100 - (77.1 
 
 Loss by radiation 
 Total efficiency . 
 
 - 7.9) = 15%. 
 , , 85.0%, 
 
550 
 
 Water Evaporated and Heat Required for Drying. 
 
 M = percentage of moisture in material to be dried. 
 
 Q = lbs. water evaporated per ton (2000 lbs.) of dry material. 
 
 H = 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 
 
 150.5 
 
 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 = 
 
 100 
 
 • M' 
 
 H = 1120 Q 4- 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.lthen 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 allowance for the fact that the moist, warm air on leaving 
 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 + 0.04% CO2 = 
 
 001293052 
 1 + 0.00367 X Temp. C. (in Kg * per CU " m<) - Density ° f Water Vap ° r 
 =0.62186 X density of air. Density at partial pressure -*■ density at 760 
 m.m. = partial pressure -5- 760 m.m. Specific heat of water vapor = 0.475; 
 sp. ht. of air = 0.2373. Kg. per cu. meter X 0.062428 = lbs. 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 586.) 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. 
 
RADIATION OF HEAT. 
 
 551 
 
 Humidity Table. 
 
 
 Vapor 
 
 Temp. 
 F. 
 
 Tension, 
 
 Milli- 
 
 meters of 
 
 
 (Mercury. 
 
 32 
 
 4.569 
 
 35 
 
 5.152 
 
 40 
 
 6.264 
 
 45 
 
 7.582 
 
 50 
 
 9.140 
 
 55 
 
 10.980 
 
 60 
 
 13.138 
 
 65 
 
 15.660 
 
 70 
 
 18.595 
 
 75 
 
 22.008 
 
 80 
 
 25.965 
 
 85 
 
 30.573 
 
 90 
 
 35.774 
 
 95 
 
 41.784 
 
 100 
 
 48.679 
 
 105 
 
 56.534 
 
 110 
 
 65.459 
 
 115 
 
 75.591 
 
 120 
 
 87.010 
 
 125 
 
 99.024 
 
 130 
 
 114.437 
 
 135 
 
 130.702 
 
 140 
 
 148.885 
 
 145 
 
 169.227 
 
 150 
 
 191.860 
 
 155 
 
 216.983 
 
 160 
 
 244.803 
 
 165 
 
 275.592 
 
 170 
 
 309.593 
 
 175 
 
 347.015 
 
 180 
 
 388.121 
 
 185 
 
 433.194 
 
 190 
 
 482.668 
 
 195 
 
 536.744 
 
 200 
 
 595.771 
 
 205 
 
 660.116 
 
 210 
 
 730.267 
 
 Lbs. 
 Water 
 Vapor 
 per lb. 
 
 Air. 
 
 .003761 
 
 .0042435 
 
 .0050463 
 
 .0062670 
 
 .0075697 
 
 .0091163 
 
 .010939 
 
 .013081 
 
 .015597 
 
 .018545 
 
 .021998 
 
 .026026 
 
 .030718 
 
 .036174 
 
 .042116 
 
 .049973 
 
 .058613 
 
 .068662 
 
 .080402 
 
 .094147 
 
 .11022 
 
 .12927 
 
 .15150 
 
 .17816 
 
 .21005 
 
 .24534 
 
 .29553 
 
 .35286 
 
 .42756 
 
 .52285 
 
 .64942 
 
 .82430 
 
 1.00805 
 
 1 .4994 
 
 2.2680 
 
 4.2272 
 15.8174 
 
 Humid 
 Heat, 
 B.T.U. 
 
 Humid 
 Volume 
 cu.ft 
 
 .2391 
 .2393 
 .2398 
 .2403 
 .2409 
 .2416 
 .2425 
 .2435 
 .2447 
 .2461 
 .2478 
 .2497 
 .2519 
 .2545 
 .2575 
 .2610 
 .2651 
 .2699 
 .2755 
 .2820 
 .2896 
 .2987 
 .3093 
 .3219 
 .3371 
 .3553 
 .3776 
 .4054 
 .4405 
 .4856 
 .5458 
 .6288 
 .7519 
 .9494 
 1.3147 
 2.1562 
 15.9148 
 
 12.462 
 12.549 
 12.695 
 12.843 
 12.999 
 13.159 
 13.326 
 13.501 
 13.683 
 13.876 
 14.081 
 14.301 
 14.539 
 14.793 
 15.071 
 15.376 
 15.711 
 16.084 
 16.499 
 16.968 
 17.499 
 18.103 
 18.800 
 19.609 
 20.559 
 21.687 
 23.045 
 24.708 
 26.790 
 29.454 
 32.967 
 37.796 
 44.918 
 56.302 
 77.304 
 131.028 
 562.054 
 
 Density, lbs. 
 
 per cu.ft. at 760 
 
 Millimeters. 
 
 Dry 
 Air. 
 
 .080726 
 .080231 
 .079420 
 .078641 
 .077867 
 .077109 
 .076363 
 .075635 
 .074921 
 .074218 
 .073531 
 .072852 
 .072189 
 .071535 
 .070894 
 .070264 
 .069647 
 .069040 
 .068443 
 .067857 
 .067380 
 .066713 
 .066156 
 ,065601 
 .065154 
 .064539 
 .064016 
 .063502 
 .062997 
 .062500 
 .062015 
 .061529 
 .061053 
 .060588 
 .060127 
 .059674 
 .059228 
 
 Sat'd 
 Mix. 
 
 .080556 
 .080085 
 .079181 
 .078348 
 .077511 
 .076685 
 .075865 
 .075039 
 .074219 
 .073471 
 .072644 
 .071744 
 .070894 
 .070051 
 .069179 
 .068288 
 .067383 
 .066447 
 .065477 
 .064480 
 .063449 
 .062374 
 .061255 
 .060104 
 .058865 
 .057570 
 .056218 
 .054795 
 .053305 
 ,051708 
 .050035 
 .048265 
 .046391 
 .044405 
 .042308 
 .040075 
 .037323 
 
 Volume in cu. 
 ft. per lb. of 
 
 Dry 
 Air. 
 
 12.388 
 12.464 
 12.590 
 12.718 
 12.842 
 12.968 
 13.095 
 13.222 
 13.348 
 13.474 
 13.600 
 13.726 
 13.852 
 13.979 
 14.106 
 14.232 
 14.358 
 14.484 
 14.611 
 14.736 
 14.863 
 14.989 
 15.116 
 15.242 
 15.368 
 15,494 
 15.621 
 15.748 
 15.874 
 16.000 
 16.126 
 16.253 
 16.379 
 16.505 
 16.631 
 16.758 
 16.884 
 
 Sat'd 
 Mix. 
 
 12.414 
 12.496 
 12.629 
 12.763 
 12.901 
 13.041 
 13.180 
 13.325 
 13.471 
 13.624 
 13.777 
 13.938 
 14.106 
 14.275 
 14.455 
 14.643 
 14.840 
 15.050 
 15.272 
 15.509 
 15.761 
 16.032 
 16.325 
 16.643 
 16,993 
 17,370 
 17,788 
 18.250 
 18.761 
 19.339 
 19.987 
 20.719 
 21.557 
 22.521 
 23.638 
 24.954 
 26.796 
 
 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 of 
 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 
 
552 
 
 of steam pipes and boilers should be smooth and of a light color: uncovered 
 pipes and steam-cylinder covers should be polished. 
 
 The quantity of heat radiated by a body is also a measure of its heat- 
 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. 
 The reflecting power of a body is therefore the complement of its absorb- 
 ing power, which latter is the same as its radiating power. 
 
 The relative radiating and reflecting power of different bodies has been 
 determined by experiment, as shown in the table below, but as far as 
 quantities of heat are concerned, 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. 
 
 
 u 
 
 
 
 . 
 
 
 
 °.« 
 
 bfl 
 
 
 MS 
 
 W) 
 
 
 ■ji^ 
 
 .s • 
 
 
 •J^ss 
 
 
 
 .2 s ! 
 
 
 
 ,c3 O £ • 
 
 o & 
 
 
 ^-Q O 
 
 
 
 "$£> o 
 
 cfl O 
 
 
 
 ^ 
 
 
 #& 
 
 $P* 
 
 
 100 
 
 
 
 Zinc, polished 
 
 Steel, polished 
 
 Platinum, polished. 
 
 19 
 
 81 
 
 
 100 
 100 
 
 
 
 
 17 
 
 24 
 
 83 
 
 Carbonate of lead . . . 
 
 76 
 
 Writing-paper 
 
 98 
 
 2 
 
 Platinum in sheet . . 
 
 17 . 
 
 83 
 
 Ivory, jet, marble... 
 
 93 to 98 
 
 7 to 2 
 
 Tin 
 
 15 
 
 85 
 
 Ordinary glass 
 
 90 
 
 10 
 
 Brass, cast, dead 
 
 
 
 Ice 
 
 85 
 
 15 
 
 polished 
 
 11 
 
 89 
 
 Gum lac 
 
 72 
 
 28 
 
 Brass, bright pol- 
 
 
 
 Silver-leaf on glass . . 
 
 27 
 
 73 
 
 ished 
 
 7 
 
 93 
 
 Cast iron, bright pol- 
 
 
 
 Copper, varnished. . 
 
 14 
 
 86 
 
 
 25 
 23 
 
 75 
 
 77 
 
 Copper, hammered . 
 Gold, plated 
 
 7 
 5 
 
 93 
 
 Mercury, about 
 
 95 
 
 Wrought iron, pol- 
 
 
 
 Gold on polished 
 
 
 
 
 23 
 
 77 
 
 
 3 
 
 97 
 
 
 Silver, polished 
 
 
 
 
 
 
 3 
 
 97 
 
 
 
 
 Experiments of Dr. A. M. Mayer give the following: The relative radia- 
 tions from a cube of cast iron, having faces rough, as from the foundry, 
 Elaned, " drawfiled," and polished, and from the same surfaces oiled, are as 
 elow (Prof. Thurston, in Trans. A. S. M. E., vol. xvi): 
 
 
 Rough. 
 
 Planed. 
 
 Drawfiled. 
 
 Polished. 
 
 
 100 
 100 
 
 60 
 32 
 
 49 
 20 
 
 45 
 
 
 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 does not seriously affect rough castings. 
 
 " Black Body " Radiation. Stefan and Boltzman's Law. (Eng'g, 
 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, 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 553 
 
 and is identical with the radiation inside an inclosure all parts of which 
 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 (2' 4 — T *), 
 where E = total energy radiated by the body at T to the body at T , 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 Kuribaum, as below (T = 
 290 degrees C, abs. in all cases). 
 
 T=492. 654. 795. 1108. 1481. 1761, 
 
 b (Black body 109.1 108.4 109.9 109.0 110.7 
 
 ™ m * Polished platinum.. 4.28 6.56 8.14 12.18 16.69 19.64 
 Ti ~ r * (l r0 n oxide 33.1 33.1 36.6 46.9 653 
 
 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 betw r een 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' and T the temperatures 
 on the two faces, and q the quantitv in thermal units transmitted per 
 
 T' — T 
 hour per square foot of area, q = — (Rankine.) 
 
 Peclet gives the following values of r: 
 
 Gold, platinum, silver. 0.0016 J Lead....... 0.0090 
 
 Copper 0.0018 Marble . 0.0716 
 
 Iron 0.0043 Brick.. 0.1500 
 
 Zinc . 0.0045 I 
 
 Relative Heat-conducting Power of Metals. 
 
 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. 
 
 tW.&F 
 
 Cadmium 
 
 . 577 
 
 
 Wrought iron. 
 
 . 436 
 
 119 
 
 Tin 
 
 .. 422 
 
 145 
 
 Steel 
 
 . 397 
 
 116 
 
 Platinum 
 
 . 380 
 
 84 
 
 Sodium 
 
 . 365 
 
 
 Cast iron 
 
 . 359 
 
 
 Lead 
 
 . 287 
 
 85 
 
 Antimony: 
 
 
 
 cast horizontally. 
 
 . 215 
 
 
 cast vertically. . . 
 
 . 192 
 
 
 Bismuth 
 
 . 61 
 
 18 
 
 \ 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 
 
554 HEAT. 
 
 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' 
 the coefficient of external resistance of the two surfaces, x the thickness of 
 the plate, and T' and T the temperatures of the two fluids in contact 
 
 T' — T 
 
 with the two surfaces, the rate of conduction is a = — — — Accord- 
 
 e + e' + rx 
 
 ing to Peclet, e+ e f = -r-y ^-y • in which the constants A and 
 
 A. [1 -f- ±S ( i — 1 )\ 
 
 B have the following values: 
 
 B for polished metallic surfaces 0.0028 
 
 B for rough metallic surfaces and for non-metallic surfaces . . 0.0037 
 
 A foe 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 Peclet 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: 
 
 , _ a 
 e+ e - (r _ T y 
 
 which gives for the rate of conduction, per square foot of surface per hour, 
 
 a 
 
 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 wholly, 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 
 the conduction of heat through that plate; and in these formula? it is 
 implied 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 motions of the two fluid masses 
 should, if possible, be in opposite directions, in order that the hottest par- 
 ticles of each fluid may be in 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. 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 555 
 
 Coefficients of Heat Conduction at Different Temperatures for 
 Various Insulating Materials. 
 
 (B.T.U. per hour = Area of surface in square feet X coefficient 4- thick- 
 ness in inches.) 
 
 Lb. per 
 cu. ft. 
 
 M aterials. 
 
 32° 
 F. 
 
 212° 
 F. 
 
 392° 
 F. 
 
 572° 
 F. 
 
 752° 
 F. 
 
 10. 
 
 
 0.250 
 0.266 
 0.306 
 0.314 
 0.379 
 
 0.403 
 
 0.387 
 0.403 
 0.411 
 0.419 
 0.476 
 
 0.508 
 
 0.443 
 
 
 
 8.5 
 
 
 
 
 6.3 
 
 
 
 
 
 9.18 
 
 Silk, tufted 
 
 
 
 
 5.06 
 
 
 
 
 
 11.86 
 
 Charcoal (carbonized cabbage 
 
 
 
 
 13.42 
 
 Sawdust (0.443 at 1 12° F.) 
 
 
 
 
 10. 
 
 Peat refusef (0.443 at 77° F.) 
 
 
 
 
 
 
 21.85 
 
 Kieselguhr (infusorial earth), 
 
 0.419 
 
 0.532 
 
 0.596 
 
 0.629 
 
 
 12.49 
 
 Asphalt-cork composition (0.492 
 at65°F.) 
 
 
 25.28 
 
 
 0.484 
 0.516 
 
 0.613 
 0.629 
 
 J. 653 
 3.742 
 
 
 
 12.49 
 
 
 0.854 
 
 0.961 
 
 12.17 
 
 Peat refusef (0.564 at 68° F.) 
 
 
 36.2 
 
 Kieselguhr, dry and compacted 
 (0.669 at 302° F.; 0.991 at 662° F.) . 
 
 
 
 
 
 
 43.07 
 
 Composition,^ compacted (0.806 
 at 302° F.; 0.967 at 428° F.) 
 
 
 
 
 
 
 22.47 
 
 Porous blast-furnace slag (0.766 
 at 112° F.) 
 
 
 
 
 
 
 35.96 
 
 34.33 
 
 Asbestos (1.644 at 1112° F.) 
 
 Slag concrete || (1.532 at 112° F.). 
 
 1.048 
 
 1.346 
 
 1.451 
 
 1.499 
 
 1.548 
 
 18.23 
 
 Pumice 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, f Hygroscopic; measurements made in moist zones, t 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 (J) mixed 
 with water and compacted. || 1 part cement, 9 parts porous blast-furnace 
 slag, by volume. 
 
 Heat Resistance, the Reciprocal of Heat Conductivity. (W. 
 Kent, Trans. A. S. M. E., xxiv, 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. 
 
556 
 
 HEAT. 
 
 We then have for the three cases, 
 
 Resistance of one piece A 4- 2 a =» 10 
 
 of two pieces in contact .... 2A+2c+2a=-16 
 of the thin piece 1/2 A + 2 a = 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, 2A+4a+s= 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. 
 Starr's figures are given in terms of the B.T.U. transmitted per sq. ft. of 
 surface per day per degree of difference of temperatures of the air adjacent 
 to each surface. The writer's figures, those in the last column of the table 
 given herewith, 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. 
 
 Heat Conducting and Resisting Values of Different Insulating 
 Materials. 
 
 Insulating Material. 
 
 Conductance, 
 B.T.U. per 
 sq. ft. per 
 Day per De- 
 gree of Differ- 
 ence of Tem- 
 perature. 
 
 Coefficient 
 
 of Heat 
 
 Resistance. 
 
 C. 
 
 1. 
 
 2. 
 
 3. 
 4. 
 
 5/8-in. oak board, 1 in. lampblack, 7/g-in. pine 
 
 board (ordinary family refrigerator) 
 
 7/s-in. board, I in. pitch, 7/s-in. board 
 
 7/g-in. board, 2 in. pitch, 7/s-in. board 
 
 7/s-in. board, paper, 1 in. mineral wool, paper, 
 
 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 
 
 5. 
 
 7/8-in. board, paper, 21/oin. mineral wool, 
 
 6.63 
 
 6. 
 
 7/8-in. board, paper, 2 1/2 in. calcined pumice, 
 
 7.10 -» 
 
 7 
 
 
 6.15 
 
 8. 
 
 7/8-in. board, paper, 3 in., sheet cork, 7/s-in. 
 
 11.43 
 
 9. 
 
 Two 7/8-in. boards, paper, solid, no air space, 
 
 5.61 
 
 10. 
 
 Two 7/8-in. boards, paper, 1 in. air space, 
 
 6.47 
 
 11. 
 
 Two 7/ 8 -in. boards, paper, 1 in. hair felt, 
 
 7.23 
 
 12. 
 
 Two 7/8-in. boards, paper, 8 in. mill shav- 
 
 17.78 
 
 n 
 
 
 13 33 
 
 14 
 
 
 11.43 
 
 15. 
 1ft 
 
 Two 7/8-in. boards, paper, 3 in. air, 4 in. 
 sheet cork, paper, two 7/g-in. boards 
 
 20.00 
 26.67 
 
 17 
 
 
 14.12 
 
 18 
 
 
 7.27 
 
 19. 
 
 20. 
 21. 
 
 Four double 7/s-in. boards (8 boards), with 
 paper between, three 8-in. air spaces ...._. 
 
 Four 7/g-in. boards, with three quilts of 1/4-m 
 hair between, papers separating boards . . 
 
 7/s-in. board, 6 in. patented silicated straw- 
 board, finished inside with thin cement.. 
 
 8.89 
 9.52 
 9.68 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 537 
 
 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, li/2iri. 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 U/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/g-in. boards and two sheets of paper. This 
 would indicate that one 7/ 8 -in. board 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 
 indicates a difference in the conditions of the experiments. The average 
 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 expressed 
 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: 
 
 Thickness, 
 in. 
 
 }< 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 C 
 
 K, revised. 
 K, original. 
 Difference.. 
 
 1.50 
 0.667 
 0.68 
 0.013 
 
 2.30 
 0.435 
 0.46 
 0.025 
 
 3.10 
 0.323 
 0.32 
 0.003 
 
 3.90 
 0.256 
 0.26 
 0.004 
 
 4.70 
 0.213 
 0.23 
 0.017 
 
 5.50 
 0.182 
 0.20 
 0.018 
 
 6.30 
 0.159 
 0.174 
 0.015 
 
 7.10 
 0.141 
 0.15 
 0.009 
 
 7.90 
 0.127 
 0.129 
 0.002 
 
 8.70 
 0.115 
 0.115 
 0.0 
 
 The following additional .values of C are computed from Mr. Wolff's 
 figures for K : 
 
 K C 
 Wooden beam construction, planked over or 
 ceiled : 
 
 As flooring . 083 12. 05 
 
 As ceiling . 104 9.71 
 
 Fireproof construction, Moored over: 
 
 As flooring . 124 8 . 06 
 
 As ceiling . 145 6 . 90 
 
 Single window 1 . 030 . 97 
 
 Single skylight 1.118 . 89 
 
 Double window . 518 1 . 93 
 
 Double skylight 0.621 1.61 
 
 Door 0.414 2.42 
 
 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 
 
&8 
 
 of resistance with a different definition may be found — viz., that obtained 
 from the formula a= (T - t)' 2 h- 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 inch 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 inch 
 thick, 
 parts in 
 1000. 
 
 tJ8 
 Us 
 
 If 
 
 .Si ft 
 
 < 
 
 
 8.1 
 9.6 
 
 10.4 
 10.3 
 9.8 
 10.6 
 11.9 
 13.9 
 35.7 
 12.4 
 42.6 
 13.7 
 15.4 
 14.5 
 15.7 
 20.6 
 30.9 
 49.0 
 48.0 
 62.1 
 13. 
 14. 
 21. 
 21.7 
 14.6 
 18. 
 18.7 
 16.7 
 22. 
 21. 
 27. 
 30.9 
 
 1.35 
 1.60 
 1.73 
 1.72 
 1.63 
 1.77 
 1.98 
 2.32 
 5.95 
 2.07 
 7.10 
 2.28 
 2.57 
 2.42 
 2.62 
 3.43 
 5.15 
 8.17 
 8.00 
 10.35 
 2.17 
 2.33 
 3.50 
 3.62 
 2.43 
 3. 
 
 3.12 
 2.78 
 3.67 
 3.50 
 4.50 
 5.15 
 
 56 
 
 50 
 
 20 
 185 
 
 56 
 244 
 
 53 
 119 
 506 
 
 23 
 285 
 
 60 
 150 
 
 60 
 112 
 253 
 368 
 
 81 
 
 
 
 529 
 
 944 
 
 
 950 
 
 
 980 
 
 
 815 
 
 
 944 
 
 
 756 
 
 
 947 
 
 
 881 
 
 
 494 
 
 10. Loose calcined magnesia 
 
 1 1 . Compressed calcined magnesia . . 
 
 12. Light carbonate of magnesia. . . . 
 
 13. Compressed carb. of magnesia.. . 
 
 977 
 715 
 940 
 850 
 940 
 
 
 888 
 
 16. Ground chalk (Paris white) 
 
 747 
 632 
 
 
 919 
 
 
 1000 
 
 20. Sand 
 
 471 
 
 
 
 22. Paper 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 It will be observed 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 heated by steam to 310° F. The substances 
 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 com- 
 parison. 
 
CONDUCTION AND CONVECTION OF HEAT. 559 
 
 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 lbs. 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: 
 
 Kind of Covering. 
 
 M 
 
 > 
 o 
 O 
 
 "o 
 
 01 . 
 
 .3 O 
 
 JS C 
 
 Jg 
 
 =•= 
 
 ° a 
 
 3& 
 
 4) 
 
 ft 
 
 0) 
 ft . 
 
 B.T.U. per sq. ft. per 
 hour per degree of av- 
 erage difference of 
 temperature. 
 
 J ft 
 
 s§ 
 
 8-^ 
 SK 
 
 a °?£ 
 
 lag* 
 
 CO 
 
 ""■ > 
 o 
 
 w 
 
 o 
 
 o © <0 
 
 . ft 
 
 o.S" 
 
 ~ °-% 
 
 
 
 0.846 
 0.120 
 0.080 
 0.089 
 0.157 
 0.109 
 
 12.27 
 1.74 
 1.16 
 1.29 
 2.28 
 1.59 
 
 2.706 
 0.384 
 0.256 
 0.285 
 0.502 
 0.350 
 
 '6!726 
 
 0.766 
 0.757 
 0.689 
 0.737 
 
 100. 
 14.2 
 9.5 
 10.5 
 18.6 
 12.9 
 
 2.819 
 
 
 1.25 
 1.60 
 1.30 
 1.30 
 1.70 
 
 0.400 
 
 
 0.267 
 
 
 297 
 
 Fire-felt 
 
 523 
 
 Manville sectional 
 
 0.564 
 
 Manv. sect and hair-felt 
 
 2.40 
 
 0.066 
 
 0.96 
 
 0.212 
 
 0.780 
 
 7.8 
 
 0.221 
 
 Manville wool-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 
 
 0.33t) 
 
 Hair-felt 
 
 0.82 
 0.75 
 
 0.132 
 0.298 
 
 1.91 
 
 4.32 
 
 0.422 
 0.953 
 
 0.714 
 0.548 
 
 15.6 
 35.2 
 
 0.439 
 
 
 0.993 
 
 
 0.75 
 
 0.275 
 
 3.99 
 
 0.879 
 
 0.571 
 
 32.5 
 
 0.919 
 
 
 
 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. Solid sectional covering, 1 1/2 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. 
 
560 HEAT. 
 
 No. 4. Solid 1-in. sectional, granulated cork molded under pressure 
 and baked at 500° F.; i/s 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, Vs 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 1/4-in. square indentations, which serve to keep the asbestos 
 layers from coming in close contact with one another; i/s 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 1 1/2-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 li/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; Vs in. asbestos next to pipe. Made in Germany. 
 
 No. 16. 2 1/2-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. 2 1/2-in. covering, 85% magnesia. Put on in a 2-in. molded 
 section wired on; next to the pipe and over this a 1/2-in. layer of magnesia 
 plaster. 
 
 No. 18. 2 1/2-in. covering, 85% carbonate of magnesia. Put on in two 
 solid 1-in. molded sections with 1/2-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 lb. 
 steam pressure. 
 
CONDUCTION AND CONVECTION OF HEaI. 
 
 561 
 
 Electrical Test of Steam-Pipe Coverings. 
 
 Covering. 
 
 Solid cork 
 
 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] 
 
 Aver. 
 Thick- 
 ness. 
 
 1.68 
 1.18 
 1.20 
 1.19 
 1.48 
 1.12 
 1.26 
 1.24 
 1.70 
 1.22 
 1.29 
 1.51 
 
 2.71 
 
 2.45 
 2.50 
 2.24 
 2.34 
 2.20 
 
 B.T.U. 
 Loss 
 
 per sq. 
 ft. at 
 160 1b. 
 Pres. 
 
 B.T.U. 
 per sq. 
 ft. per 
 Hr. per 
 
 Deg. 
 Diff. of 
 Temp. 
 
 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 
 
 1.387 
 1.412 
 1.465 
 1.555 
 1.568 
 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 
 
 0.289 
 0.294 
 0.305 
 0.324 
 0.314 
 2.708 
 
 Per 
 cent 
 Heat 
 
 Saved 
 by 
 
 Cover- 
 ing. 
 
 87.1 
 84.5 
 84.2 
 83.6 
 83.7 
 83.2 
 83.1 
 80.3 
 78.8 
 78.5 
 78.4 
 
 88.7 
 89.0 
 88.7 
 88.0 
 87.9 
 
 Transmission of Heat, through Solid Plates, from Water to Water. 
 
 (Clark, S. E.) — M. Peclet 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. Peclet'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, 21 1/4 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 with 
 the equivalent quantities of heat-units: 
 
562 
 
 Water at 212°. 
 
 Copper . 665 lb. 
 
 Brass .577 " 
 
 Wrought iron . 387 " 
 
 Cast iron 327 " 
 
 Heat-units. 
 
 Ratio 
 
 642.5 
 556.8 
 373.6 
 315.7 
 
 1.00 
 0.87 
 
 .58 
 .49 
 
 Whitham, "Steam Engine Design," p. 283, also Trans. A. S. M. E., ix, 
 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- 
 
 
 
 
 densed per 
 
 mitted per 
 
 
 
 
 square foot 
 
 square foot 
 
 
 
 
 per degree 
 
 per degree 
 
 
 
 *£ 
 
 difference of 
 
 difference of 
 
 
 
 3 
 
 temperature 
 
 temperature 
 
 
 <s 
 
 CO 
 
 per hour. 
 
 per hour. 
 
 Remarks. 
 
 
 35 
 
 
 
 
 0) 
 
 
 
 
 
 
 
 
 eS 
 
 Jl 
 
 ^2 
 
 
 .SP 
 
 Bj-I-'H 
 
 
 w 
 
 O 
 
 ffi a 
 
 ^- 
 
 W* 
 
 &tm 
 
 
 Laurens . 
 
 Copper coils . . 
 2 Copper coils 
 
 0.292 
 
 0.981 
 1.20 
 
 315 
 
 974 
 1120 
 
 
 Havrez . . 
 
 Copper coil . . . 
 
 6.268 
 
 1.26 
 
 280 
 
 1200 
 
 
 
 
 
 0.24 
 
 
 215 
 
 ( Steam pressure 
 \ =100. 
 ( Steam pressure 
 \ =10. 
 
 
 
 
 0.22 
 
 
 208.2 
 
 
 
 
 Box 
 
 Iron tube 
 
 0.235 
 0.196 
 0.206 
 
 
 230 
 207 
 210 
 
 
 
 Havrez . . 
 
 Cast-iron boiler 
 
 0.077 
 
 0.105 
 
 82 
 
 100 
 
 
 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. 
 
 563 
 
 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 lbs. Gauge 
 
 Pressure. 
 
 U/2-in. Pipe; 
 
 Steam inside, 
 
 10 lbs. 
 
 Pressure. 
 
 1 1/2-in. Pipe; 
 
 Steam outside, 
 
 10 lbs. 
 
 Pressure. 
 
 1 1/2-in. Pipe; 
 
 Steam inside, 
 
 60 lbs 
 
 Pressure. 
 
 80 
 
 265 
 269 
 272 
 277 
 281 
 299 
 313 
 
 128 
 130 
 137 
 145 
 158 
 174 
 
 200 
 230 
 260 
 267 
 271 
 270 
 
 
 100 
 120 
 140 
 160 
 180 
 200 
 
 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. . . . 
 
 Heat-units transmitted per hour 
 per square foot of surface per 
 degree of mean diff. of temp 
 
 Vertical Tube. Horizontal Tube. 
 
 128 151.9 152.9 111.6 146.2 150.4 
 
 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- 
 ing 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 of 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. 
 
564 
 
 
 Tubes. 
 
 Velocity of Water, Feet per 
 Second. 
 
 
 Authority. 
 
 0.5 
 
 .| 2 1 3] 4 1 5 ■:■]« 
 
 
 B.T.U. per sq. ft. per hr. per 
 deg. diff. 
 
 
 
 
 325 
 420 
 540 
 500 
 365 
 560 
 
 400 
 470 
 370 
 530 
 590 
 
 465 
 525 
 405 
 560 
 
 520 
 560 
 435 
 585 
 
 550 
 585 
 460 
 615 
 
 
 
 
 
 
 
 
 
 470 
 
 
 
 
 650 
 
 5. Hepburn 
 
 6. Hepburn . . . 
 
 1 1/4-in. horiz. copper. . . . 
 1 1/4-in. horiz. corrugated 
 1 1/2-in. horiz. corrugated 
 
 250 
 360 
 '.60 
 
 
 
 
 
 
 
 
 
 
 
 8. Weighton... 
 
 9. Allen 
 
 380 
 225 
 
 615 
 
 290 
 
 760 
 365 
 
 865 
 
 940 
 
 
 
 
 
 
 
 
 
 
 
 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: 
 
 1 1/4-in. smooth tubes { Jj Z i|§ " 5 570 6?0 
 
 1 1/2-in. corrugated tubes { JjZ 3? £ 4 f \ 4 J| 7 || 
 
 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 
 F — I 
 
 to be D = -r = f-r= =7 j-^ =7-, • (This formula was derived by 
 
 hyp. log [(S - I) -*- (S - F)] 
 Cecil P. Poole in 1899, Power, Dec, 1906.) 
 
 The following table is calculated from the formula: 
 
 Degrees of 
 
 Difference Between Steam Temperature and Actual 
 Average Temperature of Water. 
 
 
 Vacuum Heaters Between Engine and Condenser. 
 
 Initial 
 
 26" Vac. Temp. 126° F. 
 
 24" Vac. Temp. 141° F. 
 
 Temperature 
 of Water. 
 
 Final Temp, of Water. 
 
 Final Temp, of Water. 
 
 
 105 
 
 110 
 
 115 
 
 120 
 
 105 
 
 110 
 
 115 
 
 120 
 
 125 
 
 130 
 
 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 
 
 24.5 
 
 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 
 37.5 
 
 46.1 
 43.2 
 40.1 
 36.9 
 33.6 
 
 40.6 
 
 50 
 
 37.9 
 
 60 
 
 70 
 
 80 
 
 35.0 
 
 32.2 
 29.2 
 
 
 
 
 
CONDUCTION AND CONVECTION OF HEAT. 
 
 565 
 
 
 Atmospheric Heaters. 
 
 Initial Temp. 
 
 Atmos. Press. Temp. 
 212° F. 
 
 o 
 a 
 Be 
 
 ~3 
 
 Atmos. Press. Temp. 
 212° F. 
 
 of Water. 
 
 Final Temp, of Water. 
 
 Final Temp, of Water. 
 
 
 192 
 
 196 
 
 200 
 
 204 
 
 208 
 
 210 
 
 192 
 
 196 
 
 200 
 
 204 
 
 208 
 
 210 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 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 
 ^4.5 
 23.5 
 ?.?. 5 
 
 
 
 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, / = 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 
 Temp. 
 
 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. 
 
 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 
 
 289 
 415 
 565 
 695 
 
 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: 
 
 Mean temp, diff., deg. F 5 6 8 11 15 18 
 
 B.T.U. per sq. ft. per hr. per deg. 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. 
 
566 
 
 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: 
 
 Character of Plate6, each plate 8.4 in. 
 by 5.4 in., exposed surface 27 sq. ft. 
 
 Cast iron — untreated skin on, but 
 
 clean, free from rust, 
 
 Cast iron — nitric acid, I % sol., 9 days . . 
 1% sol., 18 days 
 1% sol., 40 days 
 5% sol., 9 days.. 
 5% sol., 40 days 
 Plate of pine.wood, same dimensions as 
 the plate of cast iron 
 
 Increase 
 in Tem- 
 perature 
 of 3.125 
 lbs. of 
 Water 
 each 
 Minute. 
 
 Proportionate 
 
 Thermal Units 
 
 Transmitted for 
 
 each Degree of 
 
 Difference of 
 
 Temperature per 
 
 Square Foot per 
 
 Hour. 
 
 13.90 
 11.5 
 9.7 
 9.6 
 9.93 
 10.6 
 
 0.33 
 
 113.2 
 97.7 
 80.08 
 77.8 
 87.0 
 77.4 
 
 Rela- 
 tive 
 Trans- 
 mission 
 
 of 
 Heat. 
 
 100.0 
 86.3 
 70.7 
 68.7 
 76. 8 
 68. 5 
 
 1.6 
 
 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: 
 
 cro 
 
 f 170. 
 
 
 152. 
 
 fen"©- 
 
 169. 
 
 ft3 <u^- 
 
 162. 
 
 wjZ two 1 " 
 
 
 •Sfc-S 1 ' 
 
 166. 
 
 3 Pus ** 
 
 
 ss'i 
 
 113. 
 
 117. 
 
 As finished — greasy. 
 
 washed with benzine and dried. 
 Oiled with lubricating oil. 
 After exposure to nitric acid sixteen hours, then oiled 
 
 (linseed oil). 
 After exposure to hydrochloric acid twelve hours, then 
 oiled (linseed oil). 
 After exposure to sulphuric acid 1, water 2, for 48 
 hours, then oiled, varnished, and allowed to dry for 
 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 1/30 inch in thickness, 
 
CONDUCTION AND CONVECTION OF HEAT. 567 
 
 equal quantities of water were evaporated to dryness, in the times as 
 follows: 
 
 Water. Iron Vessel. Copper Vessel. Iron V^S?? 1 *' 
 
 4 ounces 19 minutes 18.5 minutes 
 
 11 " 33 " 30.75 " 
 
 5 J/2 " 50 44 " 
 
 4 " 35.7 " 36.83 minutes 
 
 Two other vessels of iron sides 1/30 inch thick, one having a 1/4-Itich 
 copper bottom and the other a 1/4-inch lead bottom, were tested against 
 the iron and copper vessel, 1/33 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 Eng. 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 (Power, 
 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. Bleehynden'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 w r ater 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. 235, and it is shown 
 that the value of a in Rankine's formula q =(T\— T) 2 -=-a, which a is the 
 reciprocal of Mr. Bleehynden's constant and is a function of the thickness 
 of the plate. One of the plates, A, originally 1.187 in. thick, was reduced 
 
568 
 
 in four successive operations, by machining to 0.125 in. Another, B, was 
 tested in four thicknesses. The othe; 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 ■+- 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 = lb. of air per hour; S a = specific 
 heat of air; T ai = temp, of hot inlet air; T ao =temp. of cooled outlet air; 
 d = actual average diff. of temp, between "the air and the water; U = 
 B.T.U. absorbed by the water per degree of diff. of temp, per sq. ft. per 
 hour. W = lb. of water per hour; T Wl = temp, of inlet water; T w% = 
 temp, of outlet water. Then 
 
 AdU = KS a (T, 
 
 rf = [(r ai -r a2 )-(r, 
 
 AU = 
 T W2 = 
 
 «i 
 
 T a2 ); A = KS a (T ai - T tt2 ) + dU. 
 -T^Jl+iog [(T ai -T W2 ) + (T a2 -T Wl ). 
 
 KS a W T ai - T W2 
 
 W-KS a l ° g eT a2 - T Wl ' 
 {S a K + W)(T ai -T a2 ) + T Wl . 
 
 The more cooling water used, the lower is the temperature T wy Also 
 the less T W2 is, the larger d becomes and the less surface is needed. About 
 10 is the largest value of W IK 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 IK = 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 lb. 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. 
 
 T 
 
 T a 2 
 
 T w 
 
 T W2 
 
 K 
 
 W 
 
 B a 
 
 B w 
 
 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 
 
 4152 
 
 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 
 
 7.8) 
 
 239.3 
 
 57.5 
 
 51.0 
 
 95.2 
 
 130.0 
 
 125.70 
 
 "612 
 
 5556 
 
 9.70 
 
 9.3T 
 
 246.0 
 
 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. 
 
 569 
 
 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 IS, 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 
 
 Velocity over cooling surface 
 
 Initial temperature of air 
 
 Drop in temperature 
 
 Average temp, of water 
 
 Average temp, of air 
 
 Difference 
 
 B.T.U. per hour per sq. ft. per degree 
 difference 
 
 268 
 
 268 
 
 469 
 
 469 
 
 636 
 
 638. 
 
 638 
 
 1116 
 
 1116 
 
 1514 
 
 72° 
 
 72° 
 
 72° 
 
 74° 
 
 74° 
 
 8° 
 
 12° 
 
 8° 
 
 10° 
 
 8° 
 
 50° 
 
 43° 
 
 48° 
 
 48° 
 
 50° 
 
 68° 
 
 66° 
 
 68° 
 
 69° 
 
 70° 
 
 18° 
 
 23° 
 
 20° 
 
 21° 
 
 20° 
 
 6.5 
 
 7.6 
 
 10.2 
 
 12.1 
 
 13.8 
 
 636 
 
 1514 
 
 74° 
 
 10° 
 
 44° 
 
 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 Peclet's 
 experiments. 
 
 Heat Units Radiated per Hour, per Square Foot of Surface, 
 for 1° Fahrenheit Excess in Temperature. 
 
 Glass 0.5948 
 
 Cast iron, new 0.6480 
 
 Common steam-pipe, in- 
 ferred 0.6400 
 
 Cast and sheet iron, rusted . . 0.6S68 
 Wood, building stone, and 
 brick 0.7358 
 
 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 
 
 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 lonsrer proportional to the difference in tem- 
 perature, but must be calculated by a complex formula established experi- 
 mentally by Dulong and Petit. Box has computed a table from this 
 
570 
 
 formula, which greatly facilitates its application, and which is given 
 below: 
 
 Factors for Reduction to Dulong's Law of Radiation. • 
 
 Differences in Tem- 
 
 Temperature of the Air 
 
 an the Fahrenheit Scale. 
 
 perature between 
 Radiating Body 
 
 
 
 
 
 
 
 
 
 
 
 
 and the Air. 
 
 32° 
 
 50° 
 
 59° 
 
 68° 
 
 86° 
 
 IQ4° 
 
 122° 
 
 140° 
 
 158° 
 
 176° 
 
 194° 
 
 212 c 
 
 Deg. Fahr. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 18 
 
 1.00 
 
 1.07 
 
 1.12 
 
 1.16 
 
 1.25 
 
 1.36 
 
 1.47 
 
 1.58 
 
 1.70 
 
 1.85 
 
 1.99 
 
 2.15 
 
 36 
 
 1.03 
 
 1.11 
 
 1.16 
 
 1.21 
 
 1.30 
 
 1.40 
 
 1.52 
 
 1.68 
 
 1.76 
 
 1.91 
 
 2.06 
 
 2.23 
 
 54 . 
 
 1.07 
 
 1.16 
 
 1.20 
 
 1.25 
 
 1.35 
 
 1.45 
 
 1.58 
 
 1.70 
 
 1.83 
 
 l.9=> 
 
 2.14 
 
 2.31 
 
 72 
 
 1.12 
 
 1.20 
 
 1.25 
 
 1.30 
 
 1.40 
 
 1.52 
 
 1.64 
 
 1.76 
 
 1.90 
 
 2.07 
 
 2.23 
 
 2.40 
 
 90 
 
 1.16 
 
 1.25 
 
 1.31 
 
 1.36 
 
 1.46 
 
 1.58 
 
 1.71 
 
 1.84 
 
 1.98 
 
 2.15 
 
 2.33 
 
 2.51 
 
 108 
 
 1.21 
 
 1.31 
 
 1.36 
 
 1.42 
 
 1.52 
 
 1.65 
 
 1.78 
 
 1.92 
 
 2.07 
 
 2.28 
 
 2.42 
 
 2.62 
 
 126 
 
 1.26 
 
 1.36 
 
 1.42 
 
 1.48 
 
 1.60 
 
 1.72 
 
 1.86 
 
 2.00 
 
 2.16 
 
 2.34 
 
 2.52 
 
 2.72 
 
 144 
 
 1.32 
 
 1.42 
 
 1.48 
 
 1.54 
 
 1.65 
 
 1.79 
 
 1.94 
 
 2.08 
 
 2.24 
 
 2.44 
 
 2.64 
 
 2.83 
 
 162 
 
 1.37 
 
 1.48 
 
 1.54 
 
 1.60 
 
 1.73 
 
 1.86 
 
 2.02 
 
 2.17 
 
 2.34 
 
 2.54 
 
 2.74 
 
 2.96 
 
 180 
 
 1.44 
 
 1.55 
 
 1.61 
 
 1.68 
 
 1.81 
 
 1.95 
 
 2.11 
 
 2.27 
 
 2.46 
 
 2.66 
 
 2.87 
 
 3.10 
 
 198 
 
 1.50 
 
 1.62 
 
 1.69 
 
 1.75 
 
 1.89 
 
 2.04 
 
 2.21 
 
 2.38 
 
 2.56 
 
 2.78 
 
 3.00 
 
 3.24 
 
 216 
 
 1.58 
 
 1.69 
 
 1.76 
 
 1.83 
 
 1.97 
 
 2.13 
 
 2.32 
 
 2.48 
 
 2.68 
 
 2.91 
 
 3.13 
 
 3.38 
 
 234 
 
 1.64 
 
 1.77 
 
 1.84 
 
 1.90 
 
 2.06 
 
 2.23 
 
 2.43 
 
 2.52 
 
 2.80 
 
 3 03 
 
 3.28 
 
 3 46 
 
 252 
 
 1.71 
 
 1.85 
 
 1.92 
 
 2.00 
 
 2.15 
 
 2.33 
 
 2.52 
 
 2.71 
 
 2.92 
 
 3.18 
 
 3.43 
 
 3.70 
 
 270 
 
 1.79 
 
 1.93 
 
 2.01 
 
 2.09 
 
 2.26 
 
 2.44 
 
 2.64 
 
 2.84 
 
 3.06 
 
 3.32 
 
 3.58 
 
 3.87 
 
 288 
 
 1.89 
 
 2.03 
 
 2.12 
 
 2.20 
 
 2.37 
 
 2.56 
 
 2.78 
 
 2.99 
 
 3.22 
 
 3.50 
 
 3.77 
 
 4.07 
 
 306 
 
 1.98 
 
 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 
 
 2.98 
 
 3.10 
 
 3,23 
 
 3.47 
 
 3.76 
 
 4.10 
 
 4.32 
 
 4.61 
 
 5.12 
 
 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 In ;hes. 
 
 Heat 
 Units 
 Lost. 
 
 2 
 3 
 4 
 5 
 6 
 
 0.728 
 0.626 
 0.574 
 0.544 
 0.523 
 
 7 
 8 
 9 
 10 
 12 
 
 0.509 
 0.498 
 489 
 482 
 0.472 
 
 18 
 24 
 36 
 48 
 
 0.455 
 0.447 
 438 
 434 
 
 
 
 
THERMODYNAMICS. 
 
 571 
 
 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 Peclet 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 
 
 
 Difference 
 
 
 Difference 
 
 
 in Temp, 
 between Hot 
 
 
 in Temp. 
 
 
 in Temp. 
 
 
 Factor. 
 
 between Hot 
 
 Factor. 
 
 between Hot 
 
 Factor. 
 
 Body and 
 
 
 Body and 
 
 
 Body and 
 
 
 Air. 
 
 
 Air. 
 
 
 Air. 
 
 
 18° F. 
 
 0.94 
 
 180° F. 
 
 1.62 
 
 342° F. 
 
 1.87 
 
 36° 
 
 1.11 
 
 198° 
 
 1.65 
 
 360° 
 
 1.90 
 
 54° 
 
 1.22 
 
 216° 
 
 1.68 
 
 378° 
 
 1.92 
 
 72° 
 
 1.30 
 
 234° 
 
 1.72 
 
 396° 
 
 1.94 
 
 90° 
 
 1.37 
 
 252° 
 
 1.74 
 
 414° 
 
 1.96 
 
 108° 
 
 1.43 
 
 270° 
 
 1.77 
 
 432° 
 
 1.98 
 
 126° 
 
 1.49 
 
 288° 
 
 1.80 
 
 450° 
 
 2.00 
 
 144° 
 
 1.53 
 
 306° 
 
 1.83 
 
 468° 
 
 2.02 
 
 162° 
 
 1.58 
 
 324° 
 
 1.85 
 
 
 
 
 
 
 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 211/32 
 in. external diameter, steam pressure 60 lbs., temperature of the air in the 
 room 68° Fahr. 
 
 Temperature corresponding to 60 lbs. 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 211/32-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 211/32 in. diam. under the above 
 conditions (Trans. A. S. M. E., 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 
 
572 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 ratio 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 - = x „ — - 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.) Qx and T\ = quantity and 
 absolute temperature of the heat received; Qi and Ti = quantity and 
 absolute temperature of the heat rejected. 
 Ti — Ti 
 The expression ^ represents the efficiency of a perfect heat 
 
 engine which receives all its heat at the absolute temperature T\, and 
 rejects heat at the temperature Ti, 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 lbs. gauge 
 pressure) and rejects heat at 100° F. (temperature of a condenser, pressure 
 1 lb. above vacuum)? 
 
 388 + 459.2 
 
 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\, volume vi 
 and absolute temperature T\ be enclosed in an ideal cylinder, having non- 
 conducting walls but the bottom a perfect con- 
 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 
 pv or pressure-volume diagram, Fig. 136, and 
 let 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 T\, or isothermally, to p 2 w>. or B. 
 
 F , Q /> 2 - Remove the source of heat and put a non- 
 
 r ig. ido. conducting cover on the bottom, and let the gas 
 
 expand adiabatically, or without transmission of heat, to pzm, or C, while 
 
 its temperature is being reduced to T-i. 
 
 3. Apply to the bottom of the cvlinder a cold body, or refrigerator, of 
 the temperature T2, and let the gas be compressed by the piston isother- 
 mally to the point D, or p 4 ?>4, 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 pivi, 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 v\/v\ = m/vz. 
 
 The area aABCc represents the work done by the gas on the piston; 
 
 p 
 
 A 
 
 
 
 ( 
 
 \\b 
 
 
 D^ 
 
 "l C 
 
 a 
 
 d 
 
 b \c 
 
THERMODYNAMICS. 573 
 
 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 = pm log e {V2/v\), where pi = the 
 initial absolute pressure in lbs. 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 (i>2/m). 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 1 — (— ) \ . y being the ratio of the specific heat at constant 
 
 pressure to the specific heat at constant volume. For air y = 1.406. 
 The loss of intrinsic energy = K v (Ti — Ti) ft.-lbs. K v = specific heat 
 at constant volume X 778. 
 
 3a. CDdc is the work of isothermal compression, = Wz = piv\ logg 
 (vz/vt) = heat rejected = JJ% = RTi log e (vz/vt). 
 
 4a. DAad is the work of adiabatic compression 
 
 = Wi 
 
 ■v^-en 
 
 which is the same as Wi and therefore, being negative, cancels it, and the 
 
 net work ABCD = Wi — Wz. The gain of intrinsic energy is K v (Ti — Ti). 
 
 Comparing la and 3a, we have pm = pivi;pzvz = pm; vi/vz = vi/vi =r. 
 
 Wi = pivi logg r = RTi log e r; Wz = pm log e r = RTi log e r. 
 
 R(Ti-T2)\og e r _ Ti-Tz _T 1 
 
 RTi\og e r ~~ T\ "* T\ 
 
 M 7-1 Vx-Vt 
 
 >&"-■ 
 
 Ui 
 
 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 = I -t^p, which may be interpreted thus: increase of entropy 
 
 between the temperatures T* and Ti 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 0<£, theta-phi, diagram, is one in which the abscissas, or horizontal 
 distances, represent entropy, 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 
 manv cases it simplifies calculations and makes it possible to use alge- 
 braic or graphical methods instead of the more difficult methods of the 
 calculus. 
 
574 HEAT. 
 
 The Carnot Cycle in the Temperature-Entropy Diagram. — Let a 
 
 pound of gas having a temperature Ti and entropy E be subjected to the 
 four operations described above. (1) Ti being 
 constant, heat (area aABc, Fig. 137) 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 Tr, 
 entropy constant ; adiabatic expansion. (3) Heat 
 is rejected at the constant temperature T z , 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 Ti to T\\ no heat transferred as heat; 
 adiabatic compression. The area aJL.Bc repre- 
 sents the total heat added during the cycle, the 
 area cCDa the heat rejected; the difference, or the 
 Fig 137 area ^4 i?CD, 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 (Ti — T2) **- Ti. It 
 appears from this diagram that the efficiency may be increased by in- 
 creasing T\ or by decreasing T2; also that since Ti 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 Ti and Ti, 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 — Tt. 
 
 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 T\ (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 
 lbs. per sq. ft. V = volume in cu. ft. P0F0, pressure and volume at 
 32° F. T, absolute temperature = t° F. + 459.4. C p , specific heat at 
 constant pressure. C v , specific heat at constant volume. K p = C p X 778; 
 K v = C v X 778 ; specific heats taken in foot-pounds of energy. R, a 
 constant, =? K p — K v . y = C p /C v . r = ratio of isothermal expansion 
 or compression = P2/Pior V1/V2. 
 
 For air: C p = 0.2375; C v = 0.1689; K p = 184.8; K v = 131.4; 
 R = 53.35; y = 1.406. 
 
 Boyle's Law, PV = constant when T is constant. P1V1 = P2V2. 
 For 1 lb. air P V = 2116.2 X 12.387 = 26,224 ft.-lbs. 
 
 Charles's Law, P1V1/T1 = P2V2/T2; P1F1 = P F X 7\/T : T = 32 
 + 459.4 = 491.4; P1V1 for air = 26,224 h- 491.4 = 53.35. 
 
 General Equation, PV = RT. R is a constant which is different for 
 different gases. 
 
 Internal or Intrinsic Energy K v (Ti - 1\) = R (Ti- To) + (y — 1) 
 = P\V\ -f- (v — 1) == amount of heat in a body, measured above abso- 
 lute zero. For air at 32° F., K v (Ti - T ) = 131.4 X 491.4 = 64,570 
 ft.-lbs. When air is expanded or compressed isothermally, PV = con- 
 stant, and the internal energy remains constant, the work done in expan- 
 sion = the heat added, and the work done in compression = the heat 
 rejected. 
 
THERMODYNAMICS. 575 
 
 Work done by Adiabatic Expansion, no transmission of heat, from Pi Vi to 
 p 2 7 2 = p l y l \\ - (Vi/Vi) y \ -*- (y - 1), = (PiVi - P2V2) +'(y - 1) 
 
 = P1V1 { 1 - (P*/Pi)~ } - (7 - 1). 
 
 "FTorfc 0/ Adiabatic Compression from PiFi to P2F2 (P2 here being the 
 higher pressure) = Pi V\ {( Vi/ V2) 7_1 - 1} -*- (7 - 1) = (Pj F 2 -P1F1) + 7 - 1 
 
 =PiVi {(P2/P1) y -}}-*■ (v-i). 
 
 Loss 0/ Intrinsic Energy in adiabatic expansion, or gain in compression 
 ==K v (Ti— a^), Ti being the higher temperature. 
 
 TForfc of Isothermal Expansion, temperature constant, = heat expended 
 = Pi Vi log e Vt/ Vi = Pi Vi log e r= RT log e r. 
 
 Work of Isothermal Compression from Pi to P2 = PiFi log e Pi/P 2 
 = PTlog e r= heat discharged. 
 
 Relation between Pressure, Volume and Temperature: 
 
 7-1 
 
 t 2 = ri (£*) v = r 1 (-ft) 7-1 , Pi vv = p 2 v»y . 
 
 For air, v = 1,406; 7 - 1 = 0.406; 1/7 = 0.711; 1/(7 - 1) = 2.463; 
 7/(7-1) = 3.463; (7 - l)/7 = 0.289. 
 
 Differential Equations of a Perfect Gas. Q = quantity of heat. 4> == 
 entropy. 
 
 , v jyur. d<f> = C v -yr + (C p -C v ) -y-o 
 
 T dT dP 
 
 upui -r (v v -C p ) p dV. d<f>=C p -Y + (C v - C p ) -p- • 
 
 T T dP dV 
 
 dQ=C vp -dP+C pp -dV. d^C v a -f+c p ?y> 
 
 02 - 41 - c v iog e Q + (Cp - cy iog 6 £ • 
 ^ - 0i <r c p iog e |> + (c v - c p ) iog e £ 
 
 2 -0i = CVog e g+c-plogg^. 
 
 Work of Isothermal Expansion, W= P1V1 C 2 ~ = PiFi log. =&'• 
 
 J Ti " F i 
 
 Heat supplied during isothermal expansion, 
 
 J*Vz dy y 
 
 v ^-={C v -CJTi\og e g. 
 
 Heat added = work done= ARTilog e Vi/Vi = AP1F1 log e V2/V1; (A — 
 1/778). 
 
 Work of adiabatic expansion, 
 
 w- fW-v™ pff.^h-Y^V, 
 
 JFi JFi FY V- 1 I W ) 
 
576 
 
 Fig. 138. 
 
 Construction of the Curve PV n = C. (Am. Mach., June 21, 1900.) — 
 Referring to Fig. 138, on a system of rectangular coordinates YOX lay 
 
 off OB = pi and BA = vi. 
 Draw OJ, extended, at 
 any convenient angle a, 
 say 15°, with OX, and OC 
 at an angle /3 with OY. /3 
 is found from the equation 
 1 + tan § =[l + tan a] n . 
 Draw AJ parallel to YO. 
 From B draw BC at 45° 
 with BO, and draw CE 
 parallel to OX. From J 
 draw JH at 45° with AJ, 
 and draw HE and HJi 
 parallel to YO. The inter- 
 section of CE and HE is 
 the second point on the 
 curve, or P2V2. From Ji 
 draw JiHi at 45° to #«/i 
 and draw the vertical 
 JiHiR. Draw DK at 45° 
 to DOi and i£.R parallel 
 to OX. R is the third 
 point on the curve, and 
 so on. 
 
 Conversely, if we have 
 a curve for which we wish 
 to derive an exponent, we can, by working backward, locate the lines 
 OC and OJ, measure the angles a and 0, and solve for n. 
 
 The smaller the angle a is taken the more closely the points of the curve 
 may be located. If a = the curve is the isothermal curve, pv = con- 
 stant. If a = 15° and = 21 c 30' the curve is the adiabatic for air, 
 n = 1.41. (See Index of the Curve of an Air Diagram, p. 611). 
 
 Temperature-Entropy Diagram of Water and Steam. — The line 
 OA, Fig. 139, is the origin from which entropy is measured on horizontal 
 lines, 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 lb. of water at 
 32° F. or 492° abs., B the state at 
 212°, and C at 392° F., correspond- 
 ing to about 226 lbs. 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 Ti are 
 respectively the lower and the 
 higher temperatures, the addition of 
 entropy, <j>, is approximately Q -4- 1/ 2 (T 2 + Ti) = 180 -^ 1/2 (672 + 492) 
 = 0.3093. More accurately it is i = log e (T2/T1) = 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 
 of water, taking into account the variation in specific heat, will be found 
 in Peabody's Steam Tables.' 
 
 J^et the 1 lb. of water at the state B have heat added to it at the con- 
 
 P.° Abs. 
 392-1852 
 
 212- 
 
 672 
 
 32- 
 
 
 T 
 
 d 
 
 ■ Entropy - 
 
 Fig. 139. 
 
PHYSICAL PROPERTIES OF GASES. 577 
 
 stant 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 = 969.7 B.T.U., and it will be represented on the diagram by 
 the rectangle bBFf. Dividing by T 2 = 672, the absolute temperature, 
 gives fa - fa = 1.443 = BF. Adding fa = 0.312 gives fa = 1.755, the 
 entropy of 1 lb. steam at 212° F. measured from water at 32° F. 
 
 In like manner if we take L = 835 for steam at 852° abs., fa — fa = 
 0.980 = CE, and fa = entropy of water at 852° = 0.558, the sum fa = 
 1.538 = 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 lb. The state point D thus represents wet 
 steam having a dryness fraction of CD IDE. 
 
 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 BCEe, and a dryness 
 fraction Be/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 FJ 
 until it cuts the line EFG lt 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., 
 such as are given in Peabody's Steam Tables, Ripper's Steam Engine, 
 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 lbs. 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 Law. — 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 p\ = pressure at a volumelvi, pivi = 
 
 = a constant. 
 
578 PHYSICAL PROPERTIES OF GASES. 
 
 The constant, C, varies with the temperature, everything else remaining 
 the same. 
 
 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 v be the volume of a gas 
 at 32° F., and vi the volume at any other temperature, ti, then 
 
 (ti+ 459.2\. /, • tx - 32° 
 
 ,-(i 
 
 491.2 )' -- V^ 491.2 r°' 
 or vi = [1 + 0.002036 (h - 32°)] v . 
 If the pressure also change from p to pi, 
 
 Po /ti+ 459. 2\ 
 
 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 density of CO2 is 
 1/2 (12 4- 32) = 22. 
 
 Avogadro's Law. — Equal volumes of all gases, under the same con- 
 ditions 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. marsh- 
 gas, CH 4 , 
 
 = 1/2 (12 + 4) X 0.00559 = 0.0447 lb. 
 
 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. 
 
 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, portion 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 s 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 lb. 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, on each 
 square inch of the interior of the vessel, then will each additional 0.080728 
 lb. 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, 0.12344 lb. of carbonic- 
 acid gas, at 32°, being inclosed in a vessel of one cubic foot in capacitv, 
 exerts a pressure of one atmosphere; consequently, if 0.080728 lb. of air 
 and 0.12344 lb. 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 lb. 
 
PHYSICAL PROPERTIES OF GASES. 579 
 
 of air, at 212°, be inclosed in a vessel of one cubic foot; it will exert a 
 pressure of 
 
 21 9 -t- 4-^Q 9 
 32 + 459 2 = 1 ' 366 atmos P heres - 
 
 Let 0.03797 lb. 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 
 lb. of air and 0.03797 lb. of steam be mixed and inclosed together, at 212°, 
 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 0.591 lb. 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 or less 
 degree. Water will, for example, absorb its own volume of carbonic-acid 
 gas, 430 times its volume of ammonia, 2 V3 times its volume of chlorine, 
 and only about V20 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 cvlinder 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 
 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 which 
 the vapor cannot be liquefied by compression. The critical pressure is 
 the pressure of the vapor at the critical temperature. 
 
580 
 
 
 
 
 
 Temp, 
 of 
 
 
 
 
 
 
 Criti- 
 
 Satu- 
 
 
 
 
 
 Criti- 
 
 cal 
 
 rated 
 
 Freez- 
 
 Density of 
 
 
 
 cal 
 
 Pres- 
 
 Vapor 
 
 ing 
 
 Liquid at 
 
 
 
 Temp. 
 
 sure in 
 
 at 
 
 Point. 
 
 Temperature 
 
 
 
 Deg. F. 
 
 Atmo- 
 spheres 
 
 Atmos. 
 Pres- 
 sure 
 
 Deg. F. 
 
 Deg. F. 
 
 Given. 
 
 
 H 2 
 
 689 
 
 200 
 
 212 
 
 32 
 
 1 at 39° F. 
 
 Ammonia 
 
 NH 4 
 
 266 
 
 115 
 
 — 27 
 
 —107 
 
 0. 6364 at 32° F. 
 
 
 C 2 Ho 
 
 98.6 
 
 
 —121 
 
 —113.8 
 
 
 Carbon Dioxide. . . . 
 
 C0 2 
 
 88 
 
 75 
 
 —112 
 
 — 69 
 
 0.83 at 32° F. 
 
 
 C 2 H 4 
 CH 4 
 
 50 
 —115.2 
 
 51.7 
 54.9 
 
 —150 
 -263.4 
 
 —272 
 —302.4 
 
 
 
 1 0.415 1 
 
 
 1 at— 263° F. | 
 
 
 o 2 
 
 —182 
 
 50.8 
 
 —294.5 
 
 
 J 1.124 I 
 
 
 \ at — 294° F. 1 
 
 
 A 
 
 —185.8 
 
 50.6 
 
 —304.6 
 
 —309.3 
 
 f about 1 .5 ) 
 
 
 I at —305° F. J 
 
 
 CO 
 
 -219.1 
 —220 
 
 35.5 
 39 
 
 —310 
 —312.6 
 
 —340.6 
 
 
 Air 
 
 f 0.933 ) 
 \ at —313° F.f 
 
 
 N 2 
 
 —231 
 
 35 
 
 —318 
 
 —353.2 
 
 i 0.885 ) 
 tat— 318° F. } 
 
 
 
 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: 
 
 
 By Volume. 
 
 By Weight 
 
 
 
 N 
 
 O 
 
 Ar 
 
 N 
 
 O 
 
 Ar 
 
 1 
 
 79.3 
 79.09 
 78.122 
 78.06 
 
 23.7 
 20.91 
 20.941 
 21. 
 
 
 77 
 
 76.85 
 75.539 
 75.5 
 
 23 
 
 23.15 
 23.024 
 23.2 
 
 
 2 
 
 
 
 3 
 
 0.937 
 0.94 
 
 1.437 
 
 4 
 
 1.3 
 
 
 
 (1) Values formerly given in works on physics. (2) Average results 
 of several determinations, Hempel's Gas Analysis. (3) Sir Wm. Ramsay, 
 Bull. U. S. Geol. Survey, No. 330. (4) A. Leduc, Comptes Rendus, 1896, 
 Jour. F. /., 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 lbs. per sq. in., or 2116.3 lbs. per sq. ft., is 
 080728 lb. per cubic foot. Volume of 1 lb. = 12.387 cu. ft. At any 
 other temperature and barometric pressure its weight in lbs. per cubic 
 
AIR. 
 
 581 
 
 foot is W ■■ 
 
 1.3253 X B 
 
 where B = height of the barometer, T= tem- 
 
 459.2+ T ' 
 
 perature Fahr., and 1.3253 = weight in lbs. of 459.2 eu. ft. of air at 0° F. 
 and one inch barometric pressure. Air expands 1/491.2 of its volume at 
 32° F. for every increase of 1° F., and its volume varies inversely as the 
 pressure. 
 
 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 i>o be that volume, at the temperature of 32° Fahrenheit, and mean 
 pressure of the atmosphere, p ; let vi be the volume of the air at the tem- 
 perature t, and under the absolute pressure to be measured pi; then 
 
 (JL± 459.2°) povo 
 
 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 
 3/4 mile, 12.66; at 1 mile, 12.02; at IV4 mile, 11.42; at 1 1/2 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. 
 
 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. 
 
 Pressure of the Atmosphere per Square Inch and per Square Foot 
 at Various Readings of the Barometer. 
 
 Rule. — Barometer in inches X 0.4908 = 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. 
 
 lbs. 
 
 lbs* 
 
 in. 
 
 lbs. 
 
 lbs.* 
 
 28.00 
 
 13.74 
 
 1978 
 
 29.75 
 
 14.60 
 
 2102 
 
 28.25 
 
 13.86 
 
 1995 
 
 30.00 - 
 
 14.72 
 
 2119 
 
 28.50 
 
 13.98 
 
 2013 
 
 30.25 - 
 
 14.84 
 
 2136 
 
 28.75 
 
 14.11 
 
 2031 
 
 30.50 
 
 14.96 
 
 2154 
 
 29.00 
 
 14.23 
 
 2049 
 
 30.75 
 
 15.09 
 
 2172 
 
 29.25 
 
 14.35 
 
 2066 
 
 31.00 
 
 15.21 
 
 2190 
 
 29.50 
 
 14.47 
 
 2083 
 
 
 
 
 * Decimals omitted. 
 For lower pressures see table of the Properties of Steam. 
 
582 
 
 AIR. 
 
 Barometric Readings corresponding with Different 
 Altitudes, in French and English Measures. 
 
 Alti- 
 tude. 
 
 Read- 
 
 
 Reading 
 
 
 Reading 
 
 
 Reading 
 
 ing of 
 
 Altitude. 
 
 of 
 
 Alti- 
 
 of 
 
 Altitude. 
 
 of 
 
 Barom- 
 
 
 Barom- 
 
 tude. 
 
 Barom- 
 
 
 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. I 
 
 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 
 
 Boiling Point of Water. — JTemperature in degrees F., barometer in 
 in. of mercury. 
 
 In. 
 
 .0 
 
 .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 
 
 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 1/4 of an inch within a few 
 hours, corresponding to a difference of elevation of nearly 100 feet. No 
 formula can possibly be devised that shall embrace these sources of 
 error. 
 
 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 out 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 for 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 about 
 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. 
 
AIR. 
 
 583 
 
 
 „ 
 
 O -K 
 
 
 
 
 
 . 
 
 
 fl <U j< 
 
 p§ ft s* 
 
 PQ 
 
 Altitud 
 above 
 
 Sea leve 
 Feet. 
 
 PQ a .H fa 
 
 85 
 
 PQ 
 
 Altitud 
 
 above 
 
 Sea leve 
 
 Feet. 
 
 Boiling 
 point 
 
 in Deg 
 Fahr. 
 
 a . 
 
 PQ 
 
 ^ 02 
 
 184° 
 
 16.79 
 
 15,221 
 
 196 
 
 21.71 
 
 8,4^1 
 
 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 
 
 211 
 
 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 
 
 26/4 
 
 3,115 
 
 213 
 
 30.59 
 
 —511 
 
 195 
 
 21.26 
 
 9,031 
 
 207 
 
 27.18 
 
 2,589 
 
 
 
 
 
 
 Corrections for Temperature. 
 
 Mean temp. F. in shade. 0, 10° I 20° 30° 40° I 50° 60° I 70° I 80° I 90° I 100° 
 Multiply by ^33 .9541.975 .996 1.0161 1.036 1 .058J 1 .079[l . 1 00 [ 1 . 1 21 1 1 .1 42 
 
 Moisture in the Atmosphere. — Atmospheric air always contains a 
 smalt quantity of carbonic acid (see Ventilation), and a varying quantity 
 of aqueous vapor or moisture. The relative humidity of the air at any time 
 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 
 by 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 the 
 following table, condensed from the Hygrometric Tables of the U. S. 
 Weather Bureau: 
 
 
 
 
 
 
 
 Relative 
 
 Humidity, 
 
 Per 
 
 Cent. 
 
 
 
 
 
 
 
 
 
 ic 
 
 Difference between the Dry and Wet Thermometers, Deg. F. 
 
 » Or' 
 
 £ « • 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 26 
 
 23 
 
 30 
 
 Relative Humidity, Saturation being 100. (Barometer = 30 ins.) 
 
 32 
 
 89 
 
 79 
 
 69 
 
 59 
 
 49 
 
 39 
 
 30 
 
 20 
 
 11 
 
 2 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 40 
 
 92 
 
 83 
 
 75 
 
 68 
 
 60 
 
 52 
 
 45 
 
 37 
 
 29 
 
 23 
 
 15 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 93 
 
 87 
 
 80 
 
 74 
 
 67 
 
 61 
 
 55 
 
 49 
 
 43 
 
 38 
 
 3227 
 
 21 
 
 16 
 
 11 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 60 
 
 94 
 
 89 
 
 83 
 
 78 
 
 73 
 
 68 
 
 63 
 
 58 
 
 53 
 
 48 
 
 43 39 
 
 34 
 
 30 
 
 26 
 
 21 
 
 17 
 
 13 
 
 9 
 
 5 
 
 1 
 
 
 
 
 
 
 
 70 
 
 95 
 
 90 
 
 8ft 
 
 81 
 
 77 
 
 72 
 
 68 
 
 64 
 
 59 
 
 55 
 
 51 
 
 48 
 
 44 
 
 40 
 
 36 
 
 33 
 
 29 
 
 25 
 
 22 
 
 19 
 
 15 
 
 12 
 
 9 
 
 6 
 
 
 
 
 80 
 
 96 
 
 91 
 
 87 
 
 83 
 
 79 
 
 75 
 
 72 
 
 68 
 
 64 
 
 61 
 
 57 
 
 54 
 
 50 
 
 47 
 
 44 
 
 41 
 
 38 
 
 35 
 
 32 
 
 29 
 
 26 
 
 23 
 
 20 
 
 18 
 
 12 
 
 7 
 
 
 90 
 
 96 
 
 92 
 
 89 
 
 85 
 
 81 
 
 78 
 
 74 
 
 71 
 
 68 
 
 65 
 
 61 
 
 58 
 
 55 
 
 52 
 
 49 
 
 47 
 
 44 
 
 41 
 
 39 
 
 36 
 
 34 
 
 31 
 
 29 
 
 26 
 
 22 
 
 17 
 
 13 
 
 100 
 
 96 
 
 93 
 
 8? 
 
 86 
 
 83 
 
 80 
 
 77 
 
 73 
 
 70 
 
 68 
 
 65 
 
 62 
 
 59 
 
 56 
 
 54 
 
 51 
 
 49 
 
 46 
 
 44 
 
 41 
 
 39 
 
 37 
 
 35 
 
 33 
 
 28 
 
 24 
 
 21 
 
 110 
 
 97 
 
 93 
 
 90 
 
 87 
 
 84 
 
 81 
 
 78 
 
 75 
 
 73 
 
 70 
 
 67 
 
 65 
 
 62 
 
 60 
 
 57 
 
 55 
 
 52 
 
 50 
 
 48 
 
 46 
 
 44 
 
 42 
 
 40 
 
 38 
 
 34 
 
 30 
 
 26 
 
 120 
 
 97 
 
 94 
 
 91 
 
 88 
 
 85 
 
 87 
 
 80 
 
 77 
 
 74 
 
 7? 
 
 69 
 
 67 
 
 65 
 
 62 
 
 60 
 
 58 
 
 55 
 
 53 
 
 51 
 
 49 
 
 47 
 
 45 
 
 43 
 
 41 
 
 38 
 
 34 
 
 31 
 
 140 
 
 97 
 
 95 
 
 52 
 
 89 
 
 87 
 
 84 
 
 2 
 
 79 
 
 77 
 
 75 
 
 73 
 
 70 
 
 68 
 
 66 
 
 64 
 
 62 
 
 :0 
 
 58 
 
 56 
 
 54 
 
 53 
 
 51 
 
 49 
 
 47 
 
 44 
 
 41 
 
 38 
 
 Moistnre in Air at FHfferent Pressures and Temperatures. (H. M. 
 
 Prevost Murphy, Enn. News, June 18, 1908.) — 1. The maximum amount 
 of moisture that pure air can contain depends only on its temperature 
 and oressure, and has an unvarying value for each condition. 
 
584 air. 
 
 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 of 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 Lb. 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 = "' " — • 
 
 H = 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 + 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, 
 
 n ah so. 0092 * 
 = - 6113+ 850=T 
 Values of K and H corresponding to the various temperatures t are 
 given in the table below. 
 w ., + ,, .. . . 1.325271 M 2.698192 P 
 
 Weight of 1 cu. ft. pure dry air- 4592+ ^ = 4 59.2-M ' 
 
 M = absolute pressure in inch of mercury. 
 
 P = absolute pressure in pounds per square inch. 
 
AIR. 
 
 585 
 
 W= maximum weight, in lbs., of water vapor, that 1 lb. of pure air 
 can contain, when the temperature of the mixture is t, and the total, or 
 observed, absolute pressure in pounds per square inch is P, 
 
 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 pressures 
 and temperatures; the value of K being correct for all temperatures up 
 to the critical steam temperature of 689° F. 
 
 Values of "K" and " H" Corresponding to Temperatures t from 
 - 30° to 434° F. 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K 
 
 H 
 
 t 
 
 K 
 
 H 
 
 -30 
 
 .6082 
 
 .0099 
 
 64 
 
 .6188 
 
 .5962 
 
 158 
 
 .6323 
 
 9.177 
 
 252 
 
 .6501 
 
 62.97 
 
 344 
 
 .6739 
 
 254.2 
 
 -28 
 
 .6084 
 
 .0111 
 
 66 
 
 .6190 
 
 .6393 
 
 160 
 
 .6326 
 
 9.628 
 
 254 
 
 .6505 
 
 65.21 
 
 346 
 
 .6745 
 
 261.0 
 
 -26 
 
 .6086 
 
 .0123 
 
 68 
 
 .6193 
 
 .6848 
 
 162 
 
 .6330 
 
 10.10 
 
 256 
 
 .6510 
 
 67.49 
 
 348 
 
 .6751 
 
 268.0 
 
 -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 
 
 .6763 
 
 282.2 
 
 -20 
 
 .6092 
 
 .0168 
 
 74 
 
 .6201 
 
 8391 
 
 168 
 
 .6340 
 
 11.63 
 
 262 
 
 .6523 
 
 74.75 
 
 354 
 
 .6770 
 
 289.6 
 
 -18 
 
 .6094 
 
 .0186 
 
 76 
 
 .6203 
 
 8969 
 
 170 
 
 .6343 
 
 12.18 
 
 264 
 
 .6528 
 
 77.30 
 
 356 
 
 .6776 
 
 297.1 
 
 -16 
 
 .6096 
 
 .0206 
 
 78 
 
 .6206 
 
 9585 
 
 172 
 
 .6346 
 
 12.75 
 
 266 
 
 .6532 
 
 79.93 
 
 358 
 
 .6783 
 
 304.8 
 
 -14 
 
 .6098 
 
 .0227 
 
 80 
 
 .6209 
 
 1.024 
 
 174 
 
 .6350 
 
 13.34 
 
 268 
 
 .6537 
 
 82.62 
 
 360 
 
 .6789 
 
 312.6 
 
 -12 
 
 .6100 
 
 .0250 
 
 82 
 
 .6211 
 
 1.092 
 
 176 
 
 .6353 
 
 13.96 
 
 270 
 
 .6541 
 
 85.39 
 
 362 
 
 .6795 
 
 320.6 
 
 -10 
 
 .6102 
 
 .0275 
 
 84 
 
 .6214 
 
 1.165 
 
 178 
 
 .6357 
 
 14.60 
 
 272 
 
 .6546 
 
 88.26 
 
 364 
 
 .6803 
 
 328.7 
 
 - 8 
 
 .6104 
 
 .0303 
 
 86 
 
 .6217 
 
 1.242 
 
 180 
 
 .6360 
 
 15.27 
 
 274 
 
 .6551 
 
 91.18 
 
 366 
 
 .6809 
 
 337.0 
 
 - 6 
 
 .6107 
 
 .0332 
 
 88 
 
 .6219 
 
 1.324 
 
 182 
 
 .6364 
 
 15.97 
 
 276 
 
 .6555 
 
 94.18 
 
 368 
 
 .6816 
 
 345.4 
 
 - 4 
 
 .6109 
 
 .0365 
 
 90 
 
 .6222 
 
 1.410 
 
 184 
 
 .6367 
 
 16.68 
 
 278 
 
 .6560 
 
 97.26 
 
 370 
 
 6822 
 
 354.0 
 
 - 2 
 
 6111 
 
 .0400 
 
 92 
 
 .6225 
 
 1.501 
 
 186 
 
 .637! 
 
 17.43 
 
 280 
 
 .6565 
 
 100.4 
 
 372 
 
 6829 
 
 362.8 
 
 
 
 .6113 
 
 .0439 
 
 94 
 
 .6227 
 
 1.597 
 
 188 
 
 .6374 
 
 18.20 
 
 282 
 
 .6570 
 
 103.7 
 
 374 
 
 .6836 
 
 371.8 
 
 2 
 
 .6115 
 
 .0481 
 
 96 
 
 .6230 
 
 1.698 
 
 190 
 
 .6377 
 
 19.00 
 
 284 
 
 .6575 
 
 107.0 
 
 376 
 
 .6843 
 
 380.9 
 
 4 
 
 .6117 
 
 0526 
 
 98 
 
 .6233 
 
 1.805 
 
 192 
 
 .6381 
 
 19.83 
 
 286 
 
 .6580 
 
 110.4 
 
 378 
 
 .6850 
 
 390.2 
 
 6 
 
 .6120 
 
 0576 
 
 100 
 
 .6236 
 
 1.918 
 
 194 
 
 .6385 
 
 20.69 
 
 288 
 
 .6584 
 
 113.9 
 
 380 
 
 6857 
 
 399.6 
 
 8 
 
 .6122 
 
 0630 
 
 102 
 
 .6238 
 
 2.036 
 
 196 
 
 .6389 
 
 21.58 
 
 290 
 
 .6590 
 
 117.5 
 
 382 
 
 6865 
 
 409.3 
 
 10 
 
 .6124 
 
 0690 
 
 104 
 
 .6241 
 
 2.161 
 
 198 
 
 .6393 
 
 22.50 
 
 292 
 
 .6594 
 
 121.2 
 
 384 
 
 6871 
 
 419.1 
 
 12 
 
 .6126 
 
 .0754 
 
 106 
 
 .6244 
 
 2.294 
 
 200 
 
 .6396 
 
 23.46 
 
 294 
 
 .66C0 
 
 125.0 
 
 386 
 
 .6879 
 
 429.1 
 
 14 
 
 .6128 
 
 .0824 
 
 108 
 
 .6247 
 
 2.432 
 
 202 
 
 .6400 
 
 24.44 
 
 296 
 
 .6604 
 
 128.8 
 
 388 
 
 6886 
 
 439.3 
 
 16 
 
 .6131 
 
 .0^00 
 
 110 
 
 6250 
 
 2.578 
 
 204 
 
 .6404 
 
 25.47 
 
 298 
 
 .6610 
 
 132.8 
 
 390 
 
 6893 
 
 449.6 
 
 18 
 
 .6133 
 
 .0983 
 
 112 
 
 6253 
 
 2.731 
 
 206 
 
 .6407 
 
 26.53 
 
 300 
 
 .6615 
 
 136.8 
 
 392 
 
 6901 
 
 460.2 
 
 20 
 
 .6135 
 
 .1074 
 
 114 
 
 .6256 
 
 2.892 
 
 208 
 
 .6411 
 
 27.62 
 
 302 
 
 .6620 
 
 141.0 
 
 394 
 
 6908 
 
 470.9 
 
 22 
 
 .6137 
 
 .1172 
 
 116 
 
 .6258 
 
 3.061 
 
 210 
 
 .6415 
 
 28.75 
 
 304 
 
 .6625 
 
 145.3 
 
 396 
 
 6915 
 
 481.9 
 
 24 
 
 .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.H 
 
 308 
 
 .6636 
 
 154.1 
 
 400 
 
 6931 
 
 504.4 
 
 28 
 
 .6144 
 
 .1523 
 
 122 
 
 .6267 
 
 3.621 
 
 216 
 
 .6426 
 
 32.38 
 
 310 
 
 .6641 
 
 1587 
 
 402 
 
 .6939 
 
 515.9 
 
 30 
 
 .6147 
 
 .1661 
 
 124 
 
 .6270 
 
 3.826 
 
 218 
 
 .6430 
 
 33.67 
 
 3:2 
 
 .6647 
 
 163.3 
 
 404 
 
 .6947 
 
 527.6 
 
 32 .6149 
 
 .1811 
 
 126 
 
 .6275 
 
 4.042 
 
 220 
 
 .6434 
 
 35.01 
 
 314 
 
 .6652 
 
 168.1 
 
 406 
 
 .6955 
 
 539.5 
 
 34 
 
 .6151 
 
 .1960 
 
 128 
 
 .6276 
 
 4.267 
 
 222 
 
 .6438 
 
 36.38 
 
 316 
 
 .6658 
 
 173.0 
 
 408 
 
 .6962 
 
 551.6 
 
 36 
 
 .6154 
 
 .2120 
 
 130 
 
 .6279 
 
 4.503 
 
 224 
 
 .6442 
 
 37.80 
 
 318 
 
 .6663 
 
 178.0 
 
 410 
 
 .6970 
 
 564.0 
 
 38 
 
 .6156 
 
 2292 
 
 132 
 
 .6282 
 
 4.750 
 
 226 
 
 .6446 
 
 39.27 
 
 320 
 
 .6669 
 
 183.1 
 
 412 
 
 .6979 
 
 576.5 
 
 40 
 
 .6158 
 
 >76 
 
 134 
 
 .6285 
 
 5.008 
 
 228 
 
 .6451 
 
 40.78 
 
 322 
 
 .6674 
 
 188.3 
 
 414 
 
 .6987 
 
 589.3 
 
 42 
 
 .6161 
 
 .2673 
 
 136 
 
 6288 
 
 5.280 
 
 230 
 
 .6455 
 
 42.34 
 
 324 
 
 .6680 
 
 193.7 
 
 416 
 
 6995 
 
 602.2 
 
 44 
 
 .6163 
 
 .2883 
 
 138 
 
 .6291 
 
 5.563 
 
 232 
 
 .6458 
 
 43.95 
 
 326 
 
 .6686 
 
 199.2 
 
 418 
 
 .7003 
 
 615.4 
 
 46 
 
 .6166 
 
 .3109 
 
 140 
 
 .6294 
 
 5.859 
 
 234 
 
 .6463 
 
 45.61 
 
 328 
 
 .6691 
 
 204.8 
 
 420 
 
 .7012 
 
 628.8 
 
 48 
 
 .6168 
 
 .3350 
 
 142 
 
 .6298 
 
 6.167 
 
 236 
 
 .6467 
 
 47.32 
 
 330 
 
 .6697 
 
 210.5 
 
 422 
 
 .7021 
 
 642.5 
 
 50 
 
 .6170 
 
 3608 
 
 144 
 
 .6301 
 
 6.490 
 
 238 
 
 .6471 
 
 49.08 
 
 332 
 
 .6703 
 
 216.4 
 
 424 
 
 .7029 
 
 656.3 
 
 52 
 
 .6173 
 
 .3883 
 
 146 
 
 .6304 
 
 6. £27 
 
 240 
 
 .6475 
 
 50.89 
 
 334 
 
 .6709 
 
 222.4 
 
 426 
 
 .7037 
 
 670.4 
 
 54 
 
 .6175 
 
 .4176 
 
 148 
 
 .6307 
 
 7.178 
 
 242 
 
 .6479 
 
 52.77 
 
 336 
 
 .6715 
 
 228.5 
 
 428 
 
 .7046 
 
 684.7 
 
 56 
 
 .6178 
 
 .4490 
 
 150 
 
 .6310 
 
 7.545 
 
 244 
 
 .6484 
 
 54.69 
 
 338 
 
 .6721 
 
 234.7 
 
 430 
 
 .7055 
 
 699.2 
 
 58 
 
 .6180 
 
 .4824 
 
 152 
 
 .6313 
 
 7.929 
 
 246 
 
 .6488 
 
 56.67 
 
 340 
 
 .6727 
 
 241.1 
 
 432 
 
 .7064 
 
 713.9 
 
 60 
 
 .6183 
 
 .5180 
 
 154 
 
 .6317 
 
 8.328 
 
 248 
 
 .6492 
 
 58.71 
 
 342 
 
 .6733 
 
 247.6 
 
 434 
 
 .7073 
 
 728.9 
 
 62 
 
 .6185 
 
 .5559 
 
 156 
 
 .6320 
 
 8.7441 250 
 
 .6496 
 
 60.81 
 
 
 
 
 
 
 
586 
 
 Applications of the Formulae and Tables. 
 
 Example 1. — How low must the relative humidity be, when the 
 atmospheric pressure is 14.7 lb. 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 lb. per sq. in.? 
 
 Ans. — The maximum amount of moisture that 1 lb. of pure air can 
 contain at 90 lb. gauge, = 104.7 lb. (absolute pressure) and 60° F., is 
 
 W = 
 
 KH 
 
 0.6183X0.5180 
 
 2.036 P-H 2.036X104.7-0.5180 
 
 = 0.0015061b. 
 
 The maximum weight of moisture that 1 lb. of air can contain at 60° 
 F. and 14.7 lb. (absolute pressure) is 
 
 W (at 14.7) = 
 
 0.6183X0.5180 
 2.036X14.7-0.5180 
 
 = 0.01089 1b. 
 
 In order that no moisture may be deposited, the relative humidity 
 must not be above 
 
 (0.001506 -*- 0.01089) X 100 = 13.83%. 
 
 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. 
 
 tt fl 03 
 S 03 03 
 
 ft^H 5 
 KS 
 
 03 ^ 
 
 O o >> 
 M.2 03 
 
 U O § 
 
 o ft" 
 fa 03 03 
 
 Elastic Force 
 of the Air 
 
 alone, when 
 Saturated, Ins. 
 
 of Mercury. 
 
 Weight of the 
 Vapor in 1 Cu. 
 Ft. of the Mix- 
 ture, or Wt. of 1 
 Cu. Ft. of Satu- 
 rated Steam. 
 
 2c& u 
 
 •& - 03 
 
 .£p.5"J3 
 
 "5 u +> 
 
 log 
 
 55 a 
 
 
 
 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 
 
 0.0775169 
 
 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 
 
 0.023526 
 
 92 
 
 0.071940 
 
 1.501 
 
 28.420 
 
 0.002247 
 
 0.068331 
 
 0.070578 
 
 0.032877 
 
 102 
 
 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. 1 18548 
 
 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 
 
 . 063834 
 
 10.097 
 
 19.824 
 
 0.013636 
 
 0.042293 
 
 0.055929 
 
 0.322407 
 
 172 
 
 0.062822 
 
 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. 
 
air. 587 
 
 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. 
 
 w KH 0.6 196 X 0.7332 . M ___ ., 
 
 W = 2.036 P- H ~ 2WX 14.7 - 0.7332 = °- 01556 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: 
 
 o ni ccc _ KH = K.H 
 
 2.036 X 89.7 -if 182.63 - H 
 
 9 849 
 
 or H — n ni ' " 7 - r > , and the temperature which satisfies this equation 
 0.0155b + K 
 
 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 lb. 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 lb. gauge in order to cause 1 lb. of 
 water to be deposited when the air is cooled to 82° F.? 
 
 Ans. — Weight of moisture mixed with 1 lb. of air at 82° F., and 
 atmospheric pressure = 0.023526 lb. For 100 lb. gauge pressure, 
 
 IF— ™ = °- 6211 X 1092 = 0002918 1b 
 
 2.036 P - H 2.036 X 114.6963 - 1.092 »- w ^ iai »- 
 
 Weight of moisture deposited by each lb. of compressed air = 0.023526 
 - 0.002918 = 0.020608 lb. Each cu. ft. of the moist atmosphere con- 
 tains 0.070595 lb. of pure, air, therefore the number of cu. ft. that must 
 be delivered to cause 1 lb. of water to be deposited is 
 
 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 
 lb. of water vapor and the weight of 1 cu. ft. of the mixture is 0.072256 lb., 
 consequently the volume of the mixture is 
 
 1.023526 -h 0.072256 = 14.165 cu. ft. 
 
 For 100 lb. gauge pressure and 82° F. as shown in Example 3, 1 lb. 
 of air can hold 0.002918 lb. of water in suspension, having deposited 
 0.020608 lb. in the reservoir. The weight of 1 cu. ft. of water vapor at 
 82° is 0.001661 lb., consequently -by Dalton's law the volume of the mix- 
 ture of 1 lb. of air and 0.002918 lb. of water vapor at 100 lb. 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 lb. absolute when expanded to atmospheric pressure will be 
 
 (114.6963 -r 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 + 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 lb. of air at 32° F. and pressure of 14.7 lbs. per sq. in. = 
 12.387 cu. ft. = a column 1 sq. ft. area X 12.387 ft. high. Raising tem- 
 
588 air. 
 
 perature 1° F. expands it 1/492, or to 12.4122 ft. high — a rise of 0.02522 
 foot. 
 
 Work done = 2116 lbs. per sq. ft. X .02522 = 53.37 foot-pounds, or 
 53.37 -*- 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 -h 0.1689 = 1.406. (See Specific Heat, p. 534.) 
 
 Flow of Air through Orifices. — The theoretical velocity in feet per 
 second of jlow of any fluid, liquid, or gas through an orifice is v =\ / 2 gh 
 = 8.02 Vft, 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 differences 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 pi into a reservoir of the pressure pi, Weisbach gives the following 
 values for the coefficient of flow, obtained from his experiments. 
 
 Flow of Air through an Orifice. 
 Coefficient c in formula v = c V2 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 Air through a Short Tube. 
 
 Diam. 1 cm., = 0.394 in., length 3 cm. = 1.181 in. 
 
 Ratio of pressures pi-^-pi. . . 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 = cy^X773.2 X 
 or, simplified, 
 
 V = 352 Cy (1 + .00203 (t 
 
 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 ^h. 
 
 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 0.79 
 
 Short cylindrical mouthpieces C = 0.81 to 0.84 
 
 The same rounded at the inner end C = 0.92 to 0.93 
 
 Conical converging mouthpieces C = 0.90 to 0.99 
 
FLOW OF AIR THROUGH ORIFICES. 589 
 
 R. 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 
 
 -=V^f^-f:[(#-@r] • • • a> 
 
 W = weight of gas discharged per second in pounds. 
 A = area of cross section of jet in square feet. 
 Pi = pressure inside orifice in pounds per square foot. 
 . P2 = pressure outside orifice. 
 
 Vi = specific volume of gas inside orifice in cu. ft. per lb. 
 y = ratio of the specific heat at constant pressure to that at constant 
 volume. 
 
 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 2 Pi\/(pj ~ (jrj 
 
 (2) 
 
 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 introducing 
 a coefficient of discharge (generally less than unity) depending 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 approxi- 
 mate formula for the ideal discharge: 
 
 V£- 
 
 (3) 
 
 in which d = diam. in inches, i = difference of pressures measured in 
 inches of water, P = mean absolute pressure in lbs. 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 
 
 pp \/i 
 
 W = 0.6299 d* U ~ (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 lbs. 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 
 pf the box and orifice is at least 20 : 1. 
 
590 
 
 AIR. 
 
 Mean Discharge in Pounds per Square Foot of Orifice per Second 
 as Found from Experiments. 
 
 Diameter 
 
 1-inch 
 
 Head 
 
 Discharge 
 
 per Sq. Ft. 
 
 2-inch Head 
 
 3-inch Head 
 
 4-inch 
 
 Head 
 
 Discharge 
 
 per Sq. Ft. 
 
 5-inch 
 
 Head 
 
 Discharge 
 
 per Sq. Ft. 
 
 Orifice, 
 Inches. 
 
 Discharge 
 per Sq. Ft. 
 
 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 
 
 Coefficients of Discharge for Various Heads and Diameters of 
 Orifice. 
 
 Diameter 
 
 of Orifice, 
 
 Inches. 
 
 1-inch 
 
 2-inch 
 
 3-inch 
 
 4-inch 
 
 5-inch 
 
 Head. 
 
 Head. 
 
 Head. 
 
 Head. 
 
 Head. 
 
 5 /l6 
 
 0.603 
 
 0.606 
 
 0.610 
 
 0.613 
 
 0.616 
 
 V2 
 
 0.602 
 
 0.605 
 
 0.608 
 
 0.610 
 
 0.613 
 
 1 
 
 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. 
 
 ^ 
 W3 
 
 0.3125 
 
 0.500 
 
 1.000 
 
 1.500 
 
 2.000 
 
 2.500 
 
 3.000 
 
 3.500 
 
 4.000 
 
 4.500 
 
 5.000 
 
 V? 
 
 0.00114 
 
 0.00293 
 
 0.0117 
 
 0.0263 
 
 0.0468 
 
 0.0732 
 
 0.105 
 
 0.143 
 
 0.187 
 
 0.237 
 
 0.292 
 
 I 
 
 0.00162 
 
 0.00416 
 
 0.0166 
 
 0.0373 
 
 0.0663 
 
 0.103 
 
 0.149 
 
 0.202 
 
 0.264 
 
 0.334 
 
 0.413 
 
 Mh 
 
 0.00199 
 
 0.00510 
 
 0.0203 
 
 0.0457 
 
 0.0811 
 
 0.127 
 
 0.182 
 
 0.248 
 
 0.323 
 
 0.409 
 
 0.505 
 
 2 
 
 0.00231 
 
 0.00590 
 
 0.0235 
 
 0.0528 
 
 0.0937 
 
 0.146 
 
 0.210 
 
 0.285 
 
 0.373 
 
 0.471 
 
 0.582 
 
 2V> 
 
 0.00259 
 
 0.00662 
 
 0.0263 
 
 0.1591 
 
 0.105 
 
 0.163 
 
 0.235 
 
 0.319 
 
 0.416 
 
 0.526 
 
 0.649 
 
 3 
 
 0.00285 
 
 0.00726 
 
 0.0289 
 
 0.0648 
 
 0.115 
 
 0.179 
 
 0.257 
 
 0.349 
 
 0.455 
 
 0.575 
 
 0.710 
 
 3V-> 
 
 0.00308 
 
 0.00786 
 
 0.0312 
 
 0.0700 
 
 0.124 
 
 0.193 
 
 0.277 
 
 0.377 
 
 0.491 
 
 0.621 
 
 0.766 
 
 4 
 
 0.00330 
 
 0.00842 
 
 0.0334 
 
 0.0749 
 
 0.133 
 
 0.206 
 
 0.296 
 
 0.402 
 
 0.525 
 
 0.663 
 
 0.817 
 
 41/9 
 
 0.00351 
 
 0.00895 
 
 0.0355 
 
 0.0794 
 
 0.141 
 
 0.219 
 
 0.314 
 
 0.426 
 
 0.556 
 
 0.702 
 
 0.865 
 
 5 
 
 0.00371 
 
 0.00945 
 
 0.0375 
 
 0.0838 
 
 0.148 
 
 0.231 
 
 0.331 
 
 0.449 
 
 0.586 
 
 0.739 
 
 0.912 
 
 5V-> 
 
 0.00390 
 
 0.00993 
 
 0.0393 
 
 0.0879 
 
 0.155 
 
 0.242 
 
 0.347 
 
 0.471 
 
 0.613 
 
 0.774 
 
 0.953 
 
 6 
 
 0.00408 
 
 0.01049 
 
 0.0411 
 
 0.0918 
 
 0.162 
 
 0.252 
 
 0.362 
 
 0.492 
 
 0.640 
 
 0.808 
 
 0.995 
 
FLOW OF AIR IN PIPES. 
 
 591 
 
 Flow of Air in Pipes. — Hawksley (Proc. Inst. C 
 that his formula for flow of water in pipes, v = 48 
 
 E., xxxiil. 55) states 
 
 i/'-r~ i ma y also be 
 employed for flow of air. In this case H = height n feet of a column of 
 air required to produce the pressure causing the flow, or the loss of head 
 for a given flow; v = velocity in feet per second, D = diameter in feet, 
 L = length in feet. 
 
 If the head is expressed in inches of water, h, the air being taken at 
 62°F., its weight per cubic foot at atmospheric pressure = 0.0761 lb. 
 
 Then /f= jlfy v ? = 68.3 h. If d = diameter in inches, D= ^ , and 
 
 the formula becomes v = 114.5 
 
 V^. 
 
 rf = diameter in inches, and L=length in feet 
 The quantity in cubic feet per second s 
 
 in which /i=inches of water column, 
 
 Lv 2 , Lv 2 
 
 o,8 Ml f^=o.e 2 , 5 ^ :rf = V ' ^ ;ft =^ T . 
 
 The horse-power required to drive air through a pipe is the volume Q in 
 cubic feet per second multiplied by the pressure in pounds per square foot 
 and divided by 550. Pressure in pounds per square foot = P = inches 
 of water column X 5.196, whence horse-power = 
 
 H.P. 
 
 = QP_ 
 
 550 
 
 Qh 
 105.9 
 
 Q*L 
 
 Volume of Air Transmitted in Cubic Feet per Minute in 
 Pipes of Various Diameters. 
 
 o ■ 
 
 Actual Diameter of Pipe in Inches. 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 16 
 
 20 
 
 24 
 
 > 
 
 
 
 2.95 
 
 
 
 
 
 
 
 
 
 
 i 
 
 327 
 
 1 .31 
 
 5.24 
 
 8.18 
 
 11 78 
 
 20,94 
 
 32.73 
 
 47.12 
 
 83.77 
 
 1309 
 
 188.5 
 
 2 
 
 655 
 
 2.62 
 
 5.89 
 
 10.47 
 
 16.36 
 
 23.56 
 
 4L89 
 
 65.45 
 
 94.25 
 
 167.5 
 
 261.8 
 
 377.0 
 
 3 
 
 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 
 
 ■> 
 
 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 
 
 10 5 
 
 23 5 
 
 41.9 
 
 65,4 
 
 94 
 
 167 
 
 262 
 
 377 
 
 670 
 
 1047 
 
 1508 
 
 9 
 
 2 95 
 
 11 78 
 
 26 5 
 
 47 
 
 73 
 
 106 
 
 188 
 
 294 
 
 424 
 
 754 
 
 1178 
 
 1696 
 
 in 
 
 3 27 
 
 13.1 
 
 29 4 
 
 52 
 
 82 
 
 118 
 
 209 
 
 327 
 
 471 
 
 833 
 
 1309 
 
 1885 
 
 12 
 
 3 93 
 
 15 7 
 
 35 3 
 
 63 
 
 98 
 
 141 
 
 251 
 
 393 
 
 565 
 
 1005 
 
 1571 
 
 2262 
 
 15 
 
 4 91 
 
 19 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 
 
 2D 
 
 6 54 
 
 26.2 
 
 59 
 
 105 
 
 164 
 
 235 
 
 419 
 
 654 
 
 942 
 
 1675 
 
 2618 
 
 3770 
 
 ?A 
 
 7 85 
 
 31 4 
 
 71 
 
 125 
 
 196 
 
 283 
 
 502 
 
 785 
 
 1131 
 
 2010 
 
 3141 
 
 4524 
 
 75 
 
 8 18 
 
 37 7 
 
 73 
 
 131 
 
 204 
 
 294 
 
 523 
 
 818 
 
 1178 
 
 2094 
 
 3272 
 
 4712 
 
 7* 
 
 9.16 
 
 36 6 
 
 8? 
 
 146 
 
 229 
 
 330 
 
 586 
 
 916 
 
 1319 
 
 2346 
 
 3665 
 
 5278 
 
 30 
 
 9.8 
 
 39.3 
 
 88 
 
 157 
 
 245 
 
 353 
 
 628 
 
 982 
 
 1414 
 
 2513 
 
 3927 
 
 5655 
 
592 air. 
 
 In Hawksley's formula and its derivatives the numerical coefficients are 
 constant. It is scarcely possible, however, that they can be accurate 
 except within a limited range of conditions. In the case of water it is 
 found that the coefficient of friction, on which the loss of head depends 
 varies with the length and diameter of the pipe, and with the velocity as 
 well as with the condition of the interior surface. In the case of air and 
 other gases we have, in addition, the decrease in density and consequent 
 increase in volume and in velocity due to the progressive loss of head from 
 one end of the pipe to the other. 
 
 Clark states that according to the experiments of D'Aubuisson and those 
 of a Sardinian commission on the resistance of air through long conduits 
 or pipes, the diminution of pressure is very nearly directly as the length, 
 and as the square of the velocity and inversely as the diameter. The 
 resistance is not varied by the density. 
 
 If these statements are correct, then the formulae h — — r and h = ~-r. 
 
 cd c'd 5 
 
 and their derivatives are correct in form, and they may be used when the 
 numerical coefficients c and c' are obtained by experiment. 
 
 If we take the forms of the above formulae as correct, and let C be a 
 variable coefficient, depending upon the length, diameter, and condition 
 of surface of the pipe, and possibly also upon the velocity, the tempera- 
 ture and the density, to be determined by future experiments, then for 
 h = head in inches of water, d = diameter in inches, L = length in feet, 
 v = velocity in feet per second, and Q = quantity in cubic feet per 
 
 second: 
 
 „Jhd , Lv 2 . Lv* 
 
 \ L ; d ~ C 2 /* ; h ~ C*d ; 
 
 . 33683 Q 2 L . 33683 Q 2 L 
 
 = V — c*h' h = cw ' 
 
 For difference or loss of pressure p in pounds per square inch, 
 h = 27.71 p; *Jh = 5.264 Vp; 
 
 V = 5.264 C Vf* ^L- -J^_ 
 
 ' L * 27.71 C 2 p' * 21.11 C 2 d' 
 
 Q = 0.02871 C ^~; d = i/- 3 
 
 1213 Q 2 L . 1213 Q*L 
 
 C 2 p ' P C 2 d 5 
 
 (For other formulae for flow of air, see Mine Ventilation.) 
 Loss of Pressure in Ounces per Square Inch. — B. F. 
 
 Company uses the following formulae: 
 
 .-■V^ 
 
 in which pi = loss of pressure in ounces per square inch, v = velocity of 
 air in feet per second, and L = length of pipe in feet. If p is taken in 
 pounds per square inch, these formulae reduce to 
 
 J dpi. j 0.0000025 L& 
 
 p = 0.0000025 -~; v = 632.5 T 
 
 I v 2 
 These are deduced from the common formula (Weisbach's), p=f-j-^— • 
 
 in which /= 0.000 1608. They correspond to the formulae given above 
 when C is taken at 120.15, Hawksley's formula for the same notation 
 giving 114.5. Using the notation given in the formulae for compressed 
 air, where Q is taken in cu. ft. per minute, Sturtevant's formula gives a 
 value of C = 57.1, Hawksley's 54.4. The figure 60 is commonly used, 
 assuming a density of air of 0.761 lb. per cu. ft. 
 
 The following table is condensed from one given in the catalogue of 
 B. F. Sturtevant Company. 
 
AIR. 
 
 593 
 
 Loss of Pressure in Pipes 100 ft. Long,* in Ounces per Sq. In. 
 
 *g 
 
 
 
 
 Diameter of Pipe in Inches. 
 
 
 
 
 
 
 1 
 
 2 
 
 5 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 12 
 
 600 
 
 0.400 
 
 0.200 
 
 0.133 
 
 0.100 
 
 0.080 
 
 0.067 
 
 0.057 
 
 0.050 
 
 0,044 
 
 0.040 
 
 036 
 
 0.033 
 
 1700 
 
 1.600 
 
 0.800 
 
 0.533 
 
 0.400 
 
 0.320 
 
 0.267 
 
 0.229 
 
 0.200 
 
 0.178 
 
 0.160 
 
 145 
 
 0.133 
 
 1800 
 
 3.600 
 
 1.800 
 
 1.200 
 
 0.900 
 
 0.720 
 
 0.600 
 
 0.514 
 
 0.450 
 
 0.400 
 
 0.360 
 
 327 
 
 0.300 
 
 7400 
 
 6.400 
 
 3.200 
 
 2.133 
 
 1.600 
 
 1.280 
 
 1 .067 
 
 0.914 
 
 0.800 
 
 0.711 
 
 0.640 
 
 582 
 
 0.533 
 
 3000 
 
 10.0 
 
 5.0 
 
 3.333 
 
 2.5 
 
 2.0 
 
 1.667 
 
 1.429 
 
 1.250 
 
 1.111 
 
 1.000 
 
 909 
 
 0.833 
 
 1600 
 
 14.4 
 
 7.2 
 
 4.8 
 
 3.6 
 
 2.88 
 
 2.4 
 
 2.057 
 
 1.8 
 
 1.6 
 
 1.44 
 
 1,309 
 
 1.200 
 
 4700 
 
 
 9.8 
 
 6.553 
 
 4.9 
 
 3.92 
 
 3.267 
 
 2.8 
 
 2.45 
 
 2 178 
 
 1 96 
 
 1 782 
 
 1.633 
 
 4800 
 
 
 12.8 
 
 8.533 
 
 6.4 
 
 5.12 
 
 4.267 
 
 3.657 
 
 3.2 
 
 2 844 
 
 2 56 
 
 2 327 
 
 2.133 
 
 6000 
 
 
 20. 
 
 13.333 
 
 10.0 
 
 8.0 
 
 6.667 
 
 5.714 
 
 5.0 
 
 4.444 
 
 4.0 
 
 3.636 
 
 3.333 
 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 6011 
 
 .029 
 
 .026 
 
 .022 
 
 .020 
 
 .018 
 
 .017 
 
 .014 
 
 .012 
 
 .011 
 
 .010 
 
 .009 
 
 .008 
 
 l?00 
 
 .114 
 
 .100 
 
 .089 
 
 .080 
 
 .073 
 
 ..067 
 
 .057 
 
 .050 
 
 044 
 
 .040 
 
 036 
 
 .033 
 
 1800 
 
 .257 
 
 .225 
 
 .200 
 
 .180 
 
 .164 
 
 .156 
 
 .129 
 
 .112 
 
 .100 
 
 .090 
 
 .082 
 
 .075 
 
 7,400 
 
 .457 
 
 .400 
 
 .356 
 
 .320 
 
 .291 
 
 .267 
 
 .239 
 
 .200 
 
 .178 
 
 .160 
 
 .145 
 
 .133 
 
 3600 
 
 1.029 
 
 .900 
 
 .800 
 
 .720 
 
 .655 
 
 .600 
 
 .514 
 
 .450 
 
 .400 
 
 .360 
 
 .327 
 
 .300 
 
 47,00 
 
 1.400 
 
 1.225 
 
 1.089 
 
 .980 
 
 .891 
 
 .817 
 
 .700 
 
 .612 
 
 .544 
 
 .490 
 
 .445 
 
 .408 
 
 4800 
 
 1.829 
 
 1.600 
 
 1.422 
 
 1.280 
 
 1.164 
 
 1.067 
 
 .914 
 
 .800 
 
 711 
 
 640 
 
 582 
 
 .533 
 
 6000 
 
 2.857 
 
 2.500 
 
 2.222 
 
 2.000 
 
 1.818 
 
 1.667 
 
 1.429 
 
 1.250 
 
 1.111 
 
 1.000 
 
 .909 
 
 .833 
 
 * For any other length the loss is proportional to the length. 
 
 Effect of Bends in Pipes. (Norwalk Iron Works Co.) 
 Radius of elbow, in diameter 
 
 of pipe = 5 3 2 1 1/2 1 1/4 1 3/4 l/ 2 
 
 Equivalent lengths of straight 
 
 pipe, diams. 7.85 8.24 9.03 10.36 12.72 17.51 35.09 121.2 
 
 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 li/ 2 2 2i/ 2 3 3i/ 2 4 5 6 7 8 10 
 Globe Valves ..... 2 4 7 10 13 16 20 28 36 44 53 70 
 Elbows and Tees .23 5 7 9 11 13 19 24 30 35 47 
 
 Compressed-air Transmission. (Frank Richards, Am. Mach., March 
 8, 1894.) — The volume of. free air transmitted may be assumed to be 
 directly as the number of atmospheres to which the air is compressed. 
 Thus, if the air transmitted be at 75 pounds gauge-pressure, or six atmos- 
 pheres, the volume of free air will be six times the amount given in the 
 table (page 591). It is generally considered that for economical trans- 
 mission the velocity in main pipes should not exceed 20 feet per second. 
 In the smaller distributing pipes the velocity should be decidedly less 
 than this. 
 
 The loss of power in the transmission of compressed air in general is not 
 a serious one, or at all to be compared with the losses of power in the opera- 
 tion of compression and in the re-expansion or final application of the 
 air. 
 
 The formulas for loss by friction are all unsatisfactory. The statements 
 of observed facts in this line are in a more or less chaotic state, and self- 
 evidently unreliable. 
 
 A statement of the friction of air flowing through a pipe involves at least 
 all the following factors: Unit of time, volume of air, pressure of air, diam- 
 
594 
 
 eter of pipe, length of pipe, and the difference or pressure at the ends of 
 the pipe or the head required to maintain the flow. Neither of these 
 factors can be allowed its independent and absolute value, but is subject to 
 modifications in deference to its associates. The flow of air being assumed 
 to be uniform at the entrance to the pipe, the volume and flow are not 
 uniform after that. The air is constantly losing some of its pressure and 
 its volume is constantly increasing. The velocity of flow is therefore also 
 somewhat accelerated continually. This also modifies the use of the 
 length of the pipe as a constant factor. 
 
 Then, besides the fluctuating values of these factors, there is the condi- 
 tion of the pipe itself. The actual diameter of the pipe, especially in the 
 smaller sizes, is different from the nominal diameter. The pipe may be 
 straight, or it may be crooked and have numerous elbows. 
 
 Formulae for Flow of Compressed Air in Pipes. — The formulae on 
 pages 591 and 592 are for air at or near atmospheric pressure. For com- 
 pressed air the density has to be taken into account. A common formula 
 for the flow of air, gas, or steam in pipes is 
 
 4& 
 
 in which Q — volume in cubic feet per minute, p = difference of pressure 
 in lbs. per sq. in. causing the flow, d = diameter of pipe in in., L = length 
 of pipe in ft., w = density of the entering gas or steam in lbs. per cu. ft., 
 and c = a coefficient found by experiment. Mr. F. A. Halsey in calculat- 
 ing a table for the Rand Drill Co.'s Catalogue takes the value of c at 58, 
 basing it upon the experiments made by order of the Italian government 
 preliminary to boring the Mt. Cenis tunnel. These experiments were made 
 with pipes of 3281 feet in length and of approximately 4, 8, and 14 in. 
 diameter. The volumes of compressed air passed ranged between 16.64 
 and 1200 cu. ft. per minute. The value of c is quite constant throughout 
 the range and shows little disposition to change with the varying diameter 
 of the pipe. It is of course probable, says Mr. Halsey, that c would be 
 smaller if determined for smaller sizes of pipe, but to offset that the actual 
 sizes of small commercial pipe are considerably larger than the nominal 
 sizes, and as these calculations are commoniy made for the nominal 
 diameters it is probable that in those small sizes the loss would really be 
 less than shown by the table. The formula is of course strictly applicable 
 to fluids which do not change their density, but within the change of 
 density admissible in the transmission of air for power purposes it is prob- 
 able that the errors introduced by this change are less than those due to 
 errors of observation in the present state of knowledge of the subject. 
 Mr. Halsey's table is condensed below. 
 
 
 Cubic feet of free air compressed to a gauge-pressure of 80 lbs. 
 and passing through the pipe each minute. 
 
 
 50 
 
 100 
 
 200 
 
 400 
 
 800 
 
 1000 
 
 1500 
 
 2000 
 
 3000 
 
 4000 
 
 5000 
 
 ii 
 
 5 
 
 Loss of pressure in lbs. per square inch for each 1000 ft. of 
 straight pipe. 
 
 H/4 
 
 H/2 
 2 
 
 21/2 
 3 
 
 31/2 
 
 3.61 
 1.45 
 0.20 
 0.12 
 
 5.8 
 1.05 
 0.35 
 0.14 
 
 4.30 
 1.41 
 0.57 
 0.26 
 0.14 
 
 5.80 
 2.28 
 1.05 
 0.54 
 0.18 
 
 4.16 
 2.12 
 0.68 
 0.28 
 0.07 
 
 6.4 
 3.27 
 1.08 
 0.43 
 0.10 
 
 7.60 
 2.43 
 1.00 
 0.24 
 0.08 
 
 4.32 
 1.75 
 0.42 
 0.14 
 
 9.6 
 3.91 
 0.93 
 0.30 
 0.12 
 
 7.10 
 1.68 
 0.55 
 0.22 
 0.10 
 
 
 4 
 
 
 
 
 5 
 
 
 
 
 6 
 
 
 
 
 10.7 
 
 8 
 
 
 
 
 
 2.59 
 
 10 
 
 
 
 
 
 0.84 
 
 12 
 
 
 
 
 
 
 
 0.34 
 
 14 
 
 
 
 
 
 
 
 
 
 0.16 
 
 
 
 
 
 
 
 
 
 
 
 
595 
 
 To apply the formula given above to air of different pressures it may be 
 given other forms, as follows: 
 
 Let Q = the volume in cubic feet per minute of the compressed air; Q\ = 
 the volume before compression, or "free air," both being taken at mean 
 atmospheric temperature of 62° F.; wi = weight per cubic foot of Qi = 
 0.0761 lb.; r = atmospheres, or ratio of absolute pressures, = (gauge- 
 pressure + 14.7) -s- 14.7; w = weight per cu. ft. of Q; p = difference of 
 pressure, in lbs. per sq. in., causing the flow; d = diam. of pipe in in.; 
 L = length of pipe in ft.; c = experimental constant. Then 
 
 ▼ wL' 
 
 Q = 3.625 c 
 
 fl 
 
 ■■ rwi = 0.0761 r; 
 pd^r \ 
 
 I - WO.O 
 
 .LQ*r 
 
 7lqv = 
 
 V c 2 p 
 
 pd r °r 
 
 y/ox 
 
 c 2 pr 
 
 - 0.0761^= 0.0761 ^ 2 - 
 c 2 d 3 c 2 rfV 
 
 The value of c according to the Mt. Cenis experiments is about 58 for 
 pipes 4, 8, and 14 in. diameter, 3281 ft. long. In the St. Gothard experi- 
 ments it ranged from 62.8 to 73.2 (see table below) for pipes 5.91 and 7.87 
 in. diameter, 1713 and 15,092 ft. long. Values derived from Darcy's 
 formula for flow of water in pipes, ranging from 45.3 for 1 in. diameter to 
 63.2 for 24 in., are given under "Flow of Steam," p. 845. For approxi- 
 mate calculations the value 60 may be used for all pipes of 4 in. diameter 
 and upwards. Using c = 60, the above formulae become 
 
 Q - 
 
 217.5 
 
 /pdfi 
 rL' 
 
 = 217.5 
 
 LQH 
 
 <l 
 
 f pd 5 r 
 
 V —• 
 
 LQi* 
 
 p == 0.00002114 
 
 LQ*r 
 
 ,W 
 
 Loss of Pressure in Compressed Air Pipe-main, at St. 
 Tunnel. (E. Stockalper.) 
 
 Gothard 
 
 
 03 
 
 a 
 
 03 
 
 Q 
 a 
 "3 
 
 Volume per second 
 of free air, or equi- 
 valent volume at 
 atmospheric pres- 
 sure and 32° F. 
 
 03 03 'S 
 
 tC OJ g 
 
 ftftC 
 o> S v 
 
 asa 
 
 "o O o3 
 
 > 
 
 fl 03 U 
 H3 ft*; 
 
 c3 0^> 
 03 13 — ' 
 
 2 
 
 o . 
 
 MM 
 
 .2 a 
 >>8 
 . n ® 
 
 O °3 
 
 O (L, 
 
 Observed Pressures. 
 
 
 03 
 
 s 
 
 ft 
 
 43 M 
 
 c3 G 
 
 g.2'3. 
 
 03 
 
 43 ft 
 
 *'ft 
 
 03^ 
 
 g § 
 
 Loss of 
 Pressure. 
 
 «S| a| 9 
 
 lbs. 
 per 
 sq.in. 
 
 % 
 
 II 
 IS 
 
 > 
 
 No. 
 
 '{ 
 
 2 ! 
 
 in. 
 7.87 
 5.91 
 7.87 
 5.91 
 7.87 
 5.91 
 
 cu.ft. 
 } 33.056 { 
 
 j 22.002 { 
 
 1 18.364 { 
 
 cu.ft. 
 6.534 
 7.063 
 5.509 
 5.863 
 5.262 
 5.580 
 
 den. 
 .00650 
 .00603 
 .00514 
 .00482 
 .00449 
 .00423 
 
 lbs. 
 
 2.669 
 
 2.669 
 
 1.776 
 
 1.776 
 
 1.483 
 
 1.483 
 
 feet. 
 19.32 
 37.14 
 16.30 
 
 i 5 " 58 
 
 29.34 
 
 5.60 
 5.24 
 4.35 
 4.13 
 3.84 
 3.65 
 
 at. 
 5.24 
 5.00 
 4.13 
 
 5.292 
 3.528 
 3.234 
 
 6.4 
 4.6 
 5.1 
 
 73.2 
 63.9 
 70.7 
 
 A 
 
 3.65 
 3.54 
 
 2.793 
 1.617 
 
 5.0 
 3.0 
 
 67.6 
 
 62.8 
 
 The length of the pipe 7.87 in. in diameter was 15,092 ft., and of the 
 smaller pipe 1712.6 ft. The mean temperature of the air in the large pipe 
 was 70°F. and in the small pipe 80° F. 
 
 Flow of Air in Long Pipes with Large Differences of Pressure..— The 
 formulae given above are applicable strictly only to cases in which the 
 
596 
 
 difference of pressure at the two ends of the pipe is small, and the density 
 of the air, therefore, nearly constant. For long pipes with considerable 
 difference of pressure the density decreases and the velocity increases 
 during the flow from one end of the pipe to the other. Church (Mechs. of 
 Eng'g, p. 790) develops a formula for flow in long pipes under the assump- 
 tions of uniform decrease of density and of constant temperature, the 
 loss of heat by adiabatic expansion being in great part made up by the 
 heat generated by friction. Using the same notation as above Church's 
 
 4 fl W 2 Vi 
 formula is 1/2 [Pi 2 — P2 2 ] = % 9W "77 • f Dein S tne coefficient of friction, 
 
 A the area of the pipe in square inches, and w the density of air at the 
 entrance. The value of /is given at 0.004 to 0.005. 
 
 J. E. Johnson, Jr. (Am. Mach., July 27, 1899) gives Church's formula 
 in a simpler form as follows: Px 2 — p 2 2 = KQ 2 L -s- d 5 , in which p x and 
 p 2 are the initial and final pressures in lbs. 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 
 Pi 2 - P2 2 = 0.0005 V^ X Q 2 L/dK 
 
 Measurement of the Velocity of Air in Pipes by an Anemometer. 
 — Tests were made by B. Donkin, Jr. (Inst. Civil Engrs., 1892), to com- 
 pare the velocity of air in pipes from 8 in. to 24 in. diam., as shown by an 
 anemometer 23/4 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. 
 
 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 
 Wm. 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. 
 8 ft. square. 
 
 1712 
 
 1795 
 
 1859 
 
 1329 
 
 1622 
 
 1685 
 
 1782 
 
 1091 
 1049 
 
 1477 
 
 1344 
 
 1524 
 
 1262 
 
 1356 
 
 1293 
 
 1333 
 
 1170 
 
 1209 
 1104 
 
 1288 
 
 948 
 
 1177 
 
 1134 
 
 1049 
 
 1106 
 
 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; 
 
AIR. 
 
 597 
 
 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. 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 6 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 24 
 
 2 
 
 577 
 
 ~T~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 15.6 
 
 2.8 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 32.0 
 
 5.7 
 
 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 
 
 43.0 
 
 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 
 
 3.1 
 
 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 
 
 19.0 
 
 10.9 
 
 7.1 
 
 4.7 
 
 3.4 
 
 2.5 
 
 1.9 
 
 1.2 
 
 
 
 
 
 
 14 
 
 733 
 
 130 
 
 47.0 
 
 22.9 
 
 13.1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3.0 
 
 2.3 
 
 1.5 
 
 1 
 
 
 
 
 
 15 
 
 871 
 
 154 
 
 55.9 
 
 27.2 
 
 15.6 
 
 9.9 
 
 6.7 
 
 4.8 
 
 3.6 
 
 2.8 
 
 1.7 
 
 1.2 
 
 
 
 
 
 16 
 
 
 181 
 
 65.7 
 
 32.0 
 
 18.3 
 
 11.7 
 
 7.9 
 
 5.7 
 
 4.2 
 
 3.2 
 
 2.1 
 
 1.4 
 
 1 
 
 
 
 
 17 
 
 
 211 
 
 76.4 
 
 37.2 
 
 21.3 
 
 13.5 
 
 9.2 
 
 6.6 
 
 4.9 
 
 3.8 
 
 2.4 
 
 1.6 
 
 1.2 
 
 
 
 
 18 
 
 
 243 
 
 88.2 
 
 43.0 
 
 24.6 
 
 15.6 
 
 10.6 
 
 7.6 
 
 5.7 
 
 4.3 
 
 2.8 
 
 1.9 
 
 1.3 
 
 1 
 
 
 
 19 
 
 
 278 
 
 101 
 
 49.1 
 
 28.1 
 
 17.8 
 
 12.1 
 
 8.7 
 
 6.5 
 
 5.0 
 
 3.2 
 
 2.1 
 
 1.5 
 
 1.1 
 
 
 
 20 
 
 
 316 
 
 115 
 
 55.9 
 
 32.0 
 
 20.3 
 
 13.8 
 
 9.9 
 
 7.4 
 
 5.7 
 
 3.6 
 
 2.4 
 
 1.7 
 
 1.3 
 
 1 
 
 
 22 
 
 
 401 
 
 146 
 
 70.9 
 
 40.6 
 
 25.7 
 
 17.5 
 
 12.5 
 
 9.3 
 
 7.2 
 
 4.6 
 
 3.1 
 
 2.2 
 
 1.7 
 
 1.3 
 
 
 24 
 
 
 499 
 
 181 
 
 88.2 
 
 50.5 
 
 32.0 
 
 21.8 
 
 15.6 
 
 11.6 
 
 8.9 
 
 5.7 
 
 3.8 
 
 2.8 
 
 2.1 
 
 1.6 
 
 1 
 
 26 
 
 
 609 
 
 221 
 
 108 
 
 61.7 
 
 39.1 
 
 26.6 
 
 19.0 
 
 14.2 
 
 10.9 
 
 7.1 
 
 ■ 4.7 
 
 3.4 
 
 2.5 
 
 1.9 
 
 1.2 
 
 28 
 
 
 733 
 
 266 
 
 130 
 
 74.2 
 
 47.0 
 
 32.0 
 
 22.9 
 
 17.1 
 
 13.1 
 
 8.3 
 
 5.7 
 
 4.1 
 
 3.0 
 
 2.3 
 
 1.5 
 
 30 
 
 
 871 
 
 316 
 
 154 
 
 88.2 
 
 55.9 
 
 38.0 
 
 27.2 
 
 20.3 
 
 15.6 
 
 9.9 
 
 6.7 
 
 4.8 
 
 3.6 
 
 2.8 
 
 1.7 
 
 36 
 
 
 
 499 
 733 
 
 243 
 357 
 499 
 670 
 871 
 
 130 
 205 
 286 
 383 
 499 
 
 88.2 
 
 130 
 
 181 
 
 243 
 
 316 
 
 60.0 
 88.2 
 123 
 165 
 215 
 
 43.0 
 63.2 
 88.2 
 118 
 154 
 
 32.0 
 47.0 
 62.7 
 88.2 
 115 
 
 24.6 
 36.2 
 50.5 
 67.8 
 88.2 
 
 15.6 
 19.0 
 32.0 
 43.0 
 55.9 
 
 10.6 
 15.6 
 21.8 
 29.2 
 38.0 
 
 7.6 
 11.2 
 15.6 
 20.9 
 27.2 
 
 5.7 
 8.3 
 11.6 
 15.6 
 20.3 
 
 4.3 
 6.4 
 8.9 
 12.0 
 15.6 
 
 2.8 
 
 42 
 
 
 
 4.1 
 
 48 
 
 
 
 5.7 
 
 54 
 
 
 
 
 7.6 
 
 60 
 
 
 
 
 9.9 
 
 WIND. 
 
 Force of the Wind. — Smeaton in 1759 published a table of the 
 velocity and pressure of wind, as follows: 
 
 Velocity and Force of Wind, in Founds per Square Inch. 
 
 0)73 
 
 45 * m 
 
 
 I* 
 
 1.47 
 
 
 
 0.005 
 
 2.93 
 
 0.020 
 
 4.4 
 
 0.044 
 
 5.87 
 
 0.079 
 
 7.33 
 
 0.123 
 
 8.8 
 
 0.177 
 
 10.25 
 
 0.241 
 
 11.75 
 
 0.315 
 
 13.2 
 
 0.400 
 
 14.67 
 
 0.492 
 
 17.6 
 
 0.708 
 
 20.5 
 
 0.964 
 
 22.00 
 
 1.107 
 
 23.45 
 
 1.25 
 
 Common Appella- 
 tion of the 
 Force of Wind. 
 
 Hardly perceptible. 
 Just perceptible. 
 
 Gentle, pleasant 
 wind. 
 
 ■ Pleasant, brisk gale 
 
 m 3 
 
 a 
 
 
 
 
 
 
 S 03 
 
 pmcu 
 
 18 
 
 26.4 
 
 1.55 
 
 20 
 
 29.34 
 
 1.968 
 
 25 
 
 36.67 
 
 3.075 
 
 30 
 
 44.00 
 
 4.429 
 
 35 
 
 51.34 
 
 6.027 
 
 40 
 
 58.68 
 
 7.873 
 
 45 
 
 66.01 
 
 9.963 
 
 50 
 
 73.35 
 
 12.30 
 
 55 
 
 80.7 
 
 14.9 
 
 60 
 
 88.00 
 
 17.71 
 
 65 
 
 95.3 
 
 20.85 
 
 70 
 
 102.5 
 
 24.1 
 
 75 
 
 110.00 
 
 27.7 
 
 80 
 
 117.36 
 
 31.49 
 
 100 
 
 146.67 
 
 49.2 
 
 Common Appella- 
 tion of the 
 Force of Wind. 
 
 Very brisk. 
 High wind. 
 ^Very high storm. 
 
 Great storm. 
 
 | Hurricane. 
 
 I Immense hurri- 
 
598 air. 
 
 The pressures per square foot in the above table correspond to the 
 formula P — 0.005 V 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 V 2 
 
 As determined by Prof. Martin P — 0.004 V 2 
 
 " Whipple and Dines P = 0.0029 V 2 
 
 At 60 miles per hour these formulas give for the pressure per square foot, 
 18, 14.4, and 10.44 lbs., 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 = fV 2 , are discredited. 
 
 Experiments by M. Eiffel on plates let fall from the Eiffel tower in Paris 
 gave coefficients of V 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. = — 'j-^- -; 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, i> = 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 
 found by experiment, and substituting the above value of d, he obtains 
 
 D 0.017431 X V A u o, 1CC ir, 
 
 P = ,- - , and when p = 21 16.5 lb. per sq. ft., or average 
 
 t x y-i*> _ . 018743 
 
 V 2 
 
 u ... .... i i r. 36.8929 
 
 atmospheric pressure at the sea-level, P = . , an ex- 
 
 UL^lb 
 
 v 2 
 pression in which the pressure is shown to vary with the temperature; 
 and he gives a table showing the relation between velocity and pressure 
 for temperatures from 0° 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 0° F. they are about 10 per cent greater, and for 100°, 
 10 per cent less. 
 
 Prof. 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 quection 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 hour, 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 large as railway carriages, houses, or bridges never exceeded two- 
 thirds of that upon small 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 
 
WINDMILLS. 599 
 
 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 of 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 lb. per 
 sq. ft., and there are numerous instances in which it was between 30 and 
 40 lb. 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 lb. 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, 
 s = sectional area of the cylinder, or annular cylinder of wind, through 
 which the sail, or part of the sail, sweeps in one revolution, c = a coeffi- 
 cient to be found by experience; then Q =cvs. Rankine, from experi- 
 mental data given by Smeaton, and taking c to include an allowance for 
 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 
 
 E -D^J2- 9 =C \l sin2 ^ -%V ~ COS2A + /) -/}, 
 
 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° 
 
 F-fi) = ratio of speed of greatest 
 efficiency, for a given 
 weather-angle, to that 
 
 of the wind . . .' =2.63 1.86 1.41 
 
 E = efficiency = . 24 . 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 12 3 4 5 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 
 
600 AIR. 
 
 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 second; 
 
 n = number of revolutions of the windmill per minute; 
 
 60. &it fo, b x be the breadth of the sail or blade at distances Z , h, It, 
 l s , 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; 
 
 Vo, vi, V2, v 3 , v x = the velocity of the sail in feet per second at dis- 
 tances la, Zi, h, h, I, respectively, from the axis of the shaft; 
 
 a , ai, <Z2, az, a x = the angles of impulse for maximum effect at dis- 
 tances To, h, h, h, 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 
 
 - to) Kc* 
 550 g 
 
 (I - Z ) KcUN „ . ( I . vo V 
 
 Xmean of j v (sin a cos a)b cos a 
 
 / v x \ 
 
 r (sin a cos a) b x 
 
 fWX 0.05236 nD 
 l > ~ -550 
 
 2 sin 2 a x - 1 n fw X 0.05236 nD . 
 sin 2 a r °x) 550 
 
 The effective horse-power of a windmill of shape of sail for maximum 
 effect equals 
 
 N (Z-Z )Kdc 3 v „/2sin 2 a -l, 2 sin 2 01 - 1 . 
 
 • — n "' X mean of I r-^ 6 , — — ^— s 5i . . . 
 
 2200 g \ sin 2 a sin 2 ai . 
 
 in 2 a x - 1 v 
 
 sin 2 a x b x)~ 
 
 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 a, c, d, and e, but since improvement in the present angles is possible, 
 it is better to give the formulae 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. 
 
WINDMILLS. 
 
 601 
 
 
 
 
 Capacity of 
 
 the Windmill. 
 
 
 
 
 _; 
 
 a 
 
 J 
 
 
 
 h 
 
 3.53 . 
 
 i 
 
 S? 
 
 ^ • 
 
 Gallons of Water raised per Minute 
 
 3 cS 
 
 O 3 a)T3 
 
 "8 
 
 ^W 
 
 "s-s 
 
 
 to an Elevation of 
 
 a 
 .2 
 
 ^S 
 
 
 
 
 
 srage No. o 
 er Day 
 hich this 
 ill be obta 
 
 03 
 
 a 
 
 
 3 03 
 
 
 
 
 — o o 
 
 
 25 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 
 
 > 
 
 ri 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 > ft? P 
 < 
 
 wheel 
 
 
 
 
 
 
 
 
 
 
 
 81/2 ft. 
 10 " 
 
 16 
 16 
 16 
 
 70 to 75 
 60 to 65 
 55 to 60 
 
 6.162 
 19.179 
 33.941 
 
 3.016 
 9.563 
 17.952 
 
 
 
 
 
 0.04 
 0.12 
 0.21 
 
 8 
 
 6.638 
 11.851 
 
 4.750 
 8.485 
 
 
 
 8 
 
 12 " 
 
 5.680 
 
 
 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 the 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. 
 
 Economy of the Windmill. 
 
 
 
 64 
 
 11 
 o o 
 <i ft 
 
 a Z . 
 
 ige Number of 
 rs per Day during 
 h this Quantity 
 be raised. 
 
 Expense of Actual Useful Power 
 
 4S 
 
 
 1 
 'js . 
 
 03 o 
 
 fe u 
 
 r* 03 
 
 «M ft 
 
 o . 
 
 Developed, in Cents, per Hour. 
 
 Designe 
 tion o: 
 Mill. 
 
 Interest on 
 b Cost (First 
 , including 
 
 of Windmill, 
 p, and Tower, 
 oer Annum). 
 
 Repairs and 
 -eciation (5% 
 irst Cost per 
 
 am). 
 
 I 
 
 a 
 
 03 
 < 
 
 O 
 
 o 
 to 
 
 "3 
 o 
 H 
 
 o . 
 
 
 °c3 
 
 ■a o 
 
 
 »^S c 
 
 pto a 
 
 
 
 
 S £ 2 
 
 
 "3 
 
 O 
 
 
 33 Oj3 — 
 
 fc.s o o3^ 
 
 *< »Va 
 
 to 
 
 
 
 l aS 
 
 wheel 
 
 
 
 
 
 
 
 
 
 
 81/2 f 
 
 t. 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 
 
 4 12743 
 
 1.34 
 
 8 
 
 2.05 
 
 2.05 
 
 0.06 
 
 0.10 
 
 4.26 
 
 3.2 
 
12. 
 
 16. 
 
 20. 
 
 25. 
 
 30 
 
 10.2 
 
 19.3 
 
 25.3 
 
 28.1 
 
 25 
 
 20.2 
 
 26.1 
 
 28. 
 
 27.5 
 
 
 4.8 
 
 12.7 
 
 18.8 
 
 23.3 
 
 25 
 
 6.2 
 
 11.9 
 
 14.7 
 
 16. 
 
 
 602 air. 
 
 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 lbs. The velocity of the wind in each 
 test 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, 
 0.142; B, 0.176; C, 0.261. The work of wheel C was 674.5 ft. lb. 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 
 
 Strikes per min., Mill No. 1, 8-ft. wheel 
 Strokes per min., Mill No. 2, 8-ft. wheel 
 Strokes per min., Mill No. 3, 12-ft. wheel 
 Strokes per min., Mill No. 4, 12-ft. wheel 
 
 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 
 pumps of unknown and variable efficiency. The variations are largely 
 due 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 
 Supply and Irrigation Papers of the U. S. Geological Survey, Mr. Murphy's 
 in pamphlets Nos. 41 and 42 of the same Papers, and Prof. King'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 7/g 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 IV4 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 
 
WINDMILLS. 603 
 
 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 0.0110.088 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 
 
 16 ft 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 experiments 
 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 exten-. 
 sion of the Murphy tests: 
 
 ck™ ~t ™ni 25-mile 30-mile 35-mile 40-mile 
 
 Size ot mill. wind wind ^^ ^jncL 
 
 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. 
 
 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- 
 
604 
 
 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 
 
 Elant, and of a more recent one at Marblehead Neck, Mass., see Lieut. 
 ewis'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 of 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 
 equilibrium with the surrounding atmosphere, expands and does work in 
 virtue of its intrinsic energy. 
 
 The intrinsic energy of a fluid is the energy which it is capable of exert- 
 ing against a piston in changing from a given state as to temperature and 
 volume to a total privation of heat and indefinite expansion. 
 
 Adiabatic and Isothermal Compression. — Air may be compressed 
 either adiabatically , in which all the heat resulting from compression is 
 retained in the air compressed, or isothermally , in which the heat is removed 
 as rapidly as produced, by means of some form of refrigerator. 
 
COMPRESSED AIR. 
 
 605 
 
 Volumes, Mean Pressures per Stroke, Temperatures, etc., In the 
 Operation of Air-compression from 1 Atmosphere and 60° Fahr. 
 
 (F. Richards, Am. Mach., March 30, 1893.) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i- a 
 
 
 o s 
 
 <D O 
 
 o 
 
 
 
 "3 a 
 
 
 © a 
 
 <D O 
 
 
 e 
 
 
 <% 
 
 < 
 
 ft o 
 
 as 
 
 a 
 
 o3 
 
 
 § 
 
 < 
 
 ft o 
 
 as. 
 
 3 
 
 3 
 
 0) 
 
 ^H 
 
 jH-13 
 
 2 
 
 £ u 
 
 17 
 
 3 
 
 <2 
 
 *& 
 
 u 
 
 I s 
 
 o 
 > 
 
 £ 
 
 2 *-> 
 
 '£ 
 
 6 
 
 h 
 bo 
 
 3 
 
 o 
 
 n 
 
 o 
 
 a 
 3 
 
 
 P o 
 
 "o 
 
 u <o 
 
 
 ol 
 
 .o 
 
 a 
 
 a 
 
 a3 
 
 i 
 
 bfl 
 3 
 
 s 
 
 -3 
 
 a 
 
 
 
 a 
 < 
 
 '^1 
 
 a§ 
 
 Oh 'oT H 
 
 all 
 
 5p 
 
 flgo 
 
 a 
 
 a 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 1 
 
 80 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 
 1 
 
 1 
 
 1 
 
 
 
 
 
 60° 
 
 6.442 
 
 .1552 
 
 .266 
 
 27.38 
 
 36.64 
 
 432 
 
 1 
 
 1.068 
 
 .9363 
 
 .95 
 
 .96 
 
 .975 
 
 71 
 
 85 
 
 6.782 
 
 .1474 
 
 .2566 
 
 28.16 
 
 37.94 
 
 447 
 
 2 
 
 1. 136 
 
 .8803 
 
 .91 
 
 J. 87 
 
 1.91 
 
 80.4 
 
 90 
 
 7.122 
 
 .1404 
 
 .248 
 
 28.89 
 
 39.18 
 
 459 
 
 3 
 
 1.204 
 
 .8305 
 
 .876 
 
 2.72 
 
 2.8 
 
 88.9 
 
 95 
 
 7.462 
 
 .134 
 
 .24 
 
 29.57 
 
 40.4 
 
 472 
 
 4 
 
 1.272 
 
 .7861 
 
 .84 
 
 3.53 
 
 3.67 
 
 98 
 
 100 
 
 7.802 
 
 .1281 
 
 .2324 
 
 30.21 
 
 41.6 
 
 485 
 
 5 
 
 1.34 
 
 .7462 
 
 .81 
 
 4.3 
 
 4.5 
 
 106 
 
 105 
 
 8.142 
 
 .1228 
 
 .2254 
 
 30.81 
 
 42.78 
 
 496 
 
 10 
 
 1.68 
 
 .5952 
 
 .69 
 
 7.62 
 
 8.27 
 
 145 
 
 110 
 
 8.483 
 
 .1178 
 
 .2189 
 
 31.39 
 
 43.91 
 
 507 
 
 15 
 
 2.02 
 
 .495 
 
 .606 
 
 10.33 
 
 11.51 
 
 178 
 
 115 
 
 8.823 
 
 .1133 
 
 .2129 
 
 31.98 
 
 44.98 
 
 518 
 
 20 
 
 2.36 
 
 .4237 
 
 .543 
 
 12.62 
 
 14.4 
 
 207 
 
 120 
 
 9.163 
 
 .1091 
 
 .2073 
 
 32.54 
 
 46.04 
 
 529 
 
 25 
 
 2.7 
 
 .3703 
 
 .494 
 
 14.59 
 
 17.01 
 
 234 
 
 125 
 
 9.503 
 
 .1052 
 
 .2020 
 
 33.07 
 
 47.06 
 
 540 
 
 30 
 
 3.04 
 
 .3289 
 
 .4538 
 
 16.34 
 
 19.4 
 
 252 
 
 130 
 
 9.843 
 
 .1015 
 
 .1969 
 
 33.57 
 
 48.1 
 
 550 
 
 35 
 
 3.381 
 
 .2957 
 
 .42 
 
 17.92 
 
 21.6 
 
 281 
 
 135 
 
 10.183 
 
 .0981 
 
 .1922 
 
 34.05 
 
 49.1 
 
 560 
 
 40 
 
 3.721 
 
 .2687 
 
 .393 
 
 19.32 
 
 23.66 
 
 302 
 
 140 
 
 10.523 
 
 .095 
 
 .1878 
 
 34.57 
 
 50.02 
 
 570 
 
 45 
 
 4.061 
 
 .2462 
 
 .37 
 
 20.57 
 
 25.59 
 
 321 
 
 145 
 
 10.864 
 
 .0921 
 
 .1837 
 
 35.09 
 
 51. 
 
 580 
 
 50 
 
 4.401 
 
 .2272 
 
 .35 
 
 21.69 
 
 27.39 
 
 339 
 
 150 
 
 11.204 
 
 .0892 
 
 .1796 
 
 35.48 
 
 51.89 
 
 589 
 
 55 
 
 4.741 
 
 .2109 
 
 .331 
 
 22.76 
 
 29.11 
 
 357 
 
 160 
 
 11.88 
 
 .0841 
 
 .1722 
 
 36.29 
 
 53.65 
 
 607 
 
 60 
 
 5.081 
 
 .1968 
 
 .3144 
 
 23.78 
 
 30.75 
 
 375 
 
 170 
 
 12.56 
 
 .0796 
 
 .1657 
 
 37.2 
 
 55.39 
 
 624 
 
 65 
 
 5.422 
 
 .1844 
 
 .301 
 
 24.75 
 
 32.32 
 
 389 
 
 180 
 
 13.24 
 
 .0755 
 
 .1595 
 
 37.96 
 
 57.01 
 
 640 
 
 70 
 
 5.762 
 
 .1735 
 
 .288 
 
 25.67 
 
 33.83 
 
 405 
 
 190 
 
 13.93 
 
 .0718 
 
 .154 
 
 38.68 
 
 58.57 
 
 657 
 
 75 
 
 6.102 
 
 .1639 
 
 .276 
 
 26.55 
 
 35.27 
 
 420 
 
 200 
 
 14.61 
 
 .0685 
 
 .149 
 
 39.42 
 
 60.14 
 
 672 
 
 Column 3 gives the volume of air after compression to the given pressure 
 and after it is cooled to its initial temperature. After compression air 
 loses its heat very rapidly, and this column may be taken to represent the 
 volume of air after compression available for the purpose for which the 
 air has been compressed. 
 
 Column 4 gives the volume of air more nearly as the compressor has to 
 deal with it. In any compressor the air will lose some of its heat during 
 compression. The slower the compressor runs the cooler the air and the 
 smaller the volume. 
 
 Column 5 gives the mean effective resistance to be overcome by the air- 
 cylinder piston in the stroke of compression, supposing the air to remain 
 constantly at its initial temperature. Of course it will not so remain, but 
 this column is the ideal to be kept in view in economical air-compression. 
 
 Column 6 gives the mean effective resistance to be overcome by the pis- 
 ton, supposing that there is no cooling of the air. The actual mean effec- 
 tive pressure will be somewhat less than as given in this column; but for 
 computing the actual power required for operating air-compressor cylin- 
 ders, the figures in this column may be taken and a certain percentage 
 added — say 10 per cent — and the result will represent very closely the 
 power required by the compressor. 
 
 The mean pressures given being for compression from one atmosphere 
 upward, they will not be correct for computations in compound com- 
 pression or for any other initial pressure. 
 
606 
 
 AIR. 
 
 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 pm = p v , or pi = p — , pct'o 
 
 being the pressure and volume at the beginning of compression, and 
 P1V1 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 
 
 curve, with the equation p\ ■■- 
 
 °©r 
 
 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 compression, 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. 
 
 Horse-power required to com- 
 press and deliver One Cubic Foot 
 6t 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. 
 
 Gauge- 
 
 Air not 
 
 pressure. 
 
 cooled. 
 
 5 
 
 0.0196 
 
 10 
 
 0.0361 
 
 20 
 
 0.0628 
 
 30 
 
 0.0846 
 
 40 
 
 0.1032 
 
 50 
 
 0.1195 
 
 60 
 
 0. 1342 
 
 70 
 
 0.1476 
 
 80 
 
 0.1599 
 
 90 
 
 0.1710 
 
 100 
 
 0.1815 
 
 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 not 
 
 Air constant 
 
 pressure. 
 
 cooled. 
 
 temperature 
 
 5 
 
 0.0263 
 
 0.0251 
 
 10 
 
 0.0606 
 
 0.0559 
 
 20 
 
 0.1483 
 
 0.1300 
 
 30 
 
 0.2573 
 
 0.2168 
 
 40 
 
 0.3842 
 
 0.3138 
 
 50 
 
 0.5261 
 
 0.4166 
 
 60 
 
 0.6818 
 
 0.5266 
 
 70 
 
 0.8508 
 
 0.6456 
 
 80 
 
 1.0302 
 
 0.7700 
 
 90 
 
 1.2177 
 
 0.8979 
 
 100 
 
 1.4171 
 
 1.0291 
 
 Air constant 
 temperature. 
 
 0.0188 
 
 0.0333 
 
 0.0551 
 
 0.0713 
 
 0.0843 
 
 0.0946 
 
 0.1036 
 
 0.1120 
 
 0.1195 
 
 0.1261 
 
 0.1318 
 
 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. 
 
 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 pi and corresponding volume v% 
 and absolute temperature Tr, or let compressed air of an initial pressure, 
 volume, and temperature pi, Vt, and Ti be expanded to pi, vi, and Tk, there 
 being no transmission of heat from or into the air during the operation. 
 
COMPRESSED AIR. 607 
 
 Then the following equations express the relations between pressure, 
 volume, and temperature (see works on Thermodynamics): 
 
 vi = /P2\ 071 . P2 = MV- 41 . vi = /TjV- 
 
 V2 \Pl) ' pX \V2/ ' V2 \tJ 
 
 T2 _ M\°-« Tj. _ /P2\°-- 9 V2 = (T2\ 3 
 
 Ti W ' Tx \px) ' px \tJ 
 
 The exponents are derived from the ratio c^. -*- c v = k of the specific 
 heats of air at constant pressure and constant volume. Taking k = 
 1.406, I -r- fe= 0.711; l-'l= 0.406; 1 4- (k - 1) = 2.463; fc ■*■ 
 (ft - 1) = 3.463; (k - 1) -j- k = 0.289. 
 
 Work of Adiabatic Compression of Air. — If air is compressed in a 
 cylinder without clearance from a volume vi and pressure px to a smaller 
 volume V2 and higher pressure p>, work equal to pxVx 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 V2, and then in expelling the volume V2 from the cylinder 
 
 against the pressure p 2 . If the compression is adiabatic, p t Vi — P2V2 — 
 constant, k = 1.406. 
 
 The work of compression of a given quantity of air is 
 
 PiVi \ tyA*- 1 _ -, j _ Ptvi J (PA k I , 
 
 k-ll Kvz) ) ~ k - 1 | W ) 
 
 2.463 Vl vx { g) 041 - 1 } = 2.463 ft* { (f)^- 1 } • 
 The work of expulsion is P2V2 = PxVx I 
 
 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 
 
 pwx 
 
 ffective pressure during the stroke is 
 
 px and P2 are absolute pressures above a vacuum in atmospheres or in 
 pounds per square inch or 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. 
 
 P2 ■*• px = 6; 6 029 - 1 = 0.681; 3.463 X 0.681 = 2.358 atmospheres 
 X 14.7 = 34.661b. per sq. in. mean effective pressure, X 144 = 4991 lb. 
 per sq. ft., XI ft. stroke =4991 ft .-lb.,-*- 550 ft.-lb. per second = 9.08 H.P. 
 
 If R = ratio of pressures = P2 + Px, and if Vi = 1 cubic foot, the work 
 done in compressing 1 cubic foot from px to P2 is, in foot-pounds, 
 
 3.463 Pi (E 029 - 1), 
 
 Px being taken in lb. per sq. ft. For compression at the sea level Pi may 
 be taken at 14 lbs. per sq. in. = 2016 lb. 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 P t (E°- 29 - 1); P x being the pressure of the free air in 
 pounds per sq. in., absolute. 
 
 Example. To compress 100 cu. ft. from 1 to 6 atmospheres. Fi = 1.47; 
 R = 6; 1.511 X 14.7 X 0.68.1 = 15.13 H.P. 
 
608 air. 
 
 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 
 and the re-expansion of the air in clearance-spaces tends to reduce the 
 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 P1V1 (R - 29 - 1), 
 
 in which P t ■= initial absolute pressure in lb. per sq. ft., and V t = 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 vi and pressure 
 Vi is equal to the mechanical equivalent of the heating (or cooling). If 
 t\ is the higher and fa the lower temperature, Fahr., the work done is 
 c v J (ti — k) 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 pound of air =■ 
 53.37. 
 
 The work during expansion is 
 
 2.463 ** [l -(g)" 29 ] - 2.463 «, [(g) °' 2 " - l], 
 
 in which pivi are the initial and P2V2 the final pressures and volumes. 
 Compressed-air Engines, Adiabatic Expansion. — Let the initial 
 
 pressure and volume taken into the cylinder be p x lb. per sq. ft. and v x 
 cubic feet; let expansion take place to pi and vi according to the adiabatic 
 law pivi 1 - 41 = P2V2 1 - il ; then 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 pm, the work during expansion is 2.463 piVi 1 — 
 
 (p 2 \ 0.29-1 
 — J , and the negative or back pressure work is — p 3 V2. The total 
 
 work is piVi + 2.463 PtVi 1 — (— J — p 3 V2, and the mean effective pres- 
 
 sure is the total work divided by v%. 
 
 If the air is expanded down to the back-pressure pz the total work is 
 
 3.463^, { 1 -(g) 0!9 }, 
 
 or, in terms of the final pressure and volume, 
 
 3.463^2 {(g) 029 -l}. 
 and the mean effective pressure is 
 
 3.463 P3 {(g)°;%l}. 
 
 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. (Seep. 931, under "Steam-engine.") 
 
COMPRESSED AIR. 
 
 609 
 
 Mean Effective Pressures of Air Compressed Adiabatically. 
 
 (F. A. Halsey, Am. Mach., Mar. 10, 1898.) 
 
 
 
 M.E.P. from 
 
 
 
 M.E.P. from 
 
 R. 
 
 P> 29 . 
 
 14 lbs. 
 Initial. 
 
 R. 
 
 fio.29. 
 
 14 lbs. 
 Initial. 
 
 1.25 
 
 1.067 
 
 3.24 
 
 4.75 
 
 1.570 
 
 27.5 
 
 1.50 
 
 1.125 
 
 6.04 
 
 5 
 
 1.594 
 
 28.7 
 
 1.75 
 
 1.176 
 
 8.51 
 
 5.25 
 
 1.617 
 
 29.8 
 
 2 
 
 1.223 
 
 10.8 
 
 5.5 
 
 1.639 
 
 30.8 
 
 2.25 
 
 1.265 
 
 12.8 
 
 5.75 
 
 1.660 
 
 31.8 
 
 2.5 
 
 1.304 
 
 14.7 
 
 6 
 
 1.681 
 
 32.8 
 
 2.75 
 
 1.341 
 
 16.4 
 
 6.25 
 
 1.701 
 
 33.8 
 
 3 
 
 1.375 
 
 18.1 
 
 6.5 
 
 1.720 
 
 34.7 
 
 3.25 
 
 1.407 
 
 19.6 
 
 6.75 
 
 1.739 
 
 35.6 
 
 3.5 
 
 1.438 
 
 21.1 
 
 7 
 
 1.757 
 
 36.5 
 
 3.75 
 
 1.467 
 
 22.5 
 
 7.25 
 
 1.775 
 
 37.4 
 
 4 
 
 1.495 
 
 23.9 
 
 7.5 
 
 1.793 
 
 38.3 
 
 4.25 
 
 1.521 
 
 25.2 
 
 8 
 
 1.827 
 
 39.9 
 
 4.5 
 
 1.546 
 
 26.4 
 
 
 
 
 R = final -4- initial absolute pressure. 
 
 M.E.P. = mean effective pressure, lb. per sq. in., based on 14 lb. initial. 
 
 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 W 2 . Total work 
 
 Wt + W 2 = 3.46 PiVt [rjO-29 + #0.29 x r t -<■■» - 2]. 
 ri = ratio of pressures in 1. p. cyl., r 2 = ratio in h.p. cyl., R = nr 2 . When 
 n = r 2 = Vp, the sum W t + 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 r x = ^R, to the following: 
 Wi + W 2 = 6.92 PiFi [fl°-»5 _ i]. 
 Dividing by V t gives the mean effective pressure reduced to the low- 
 pressure cylinder M.E.P. = 6.92 P x [i2°-i« - 1]. 
 
 In the above equation 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 intercooling, and with equal ratio of com- 
 
 Rression in each cylinder, = 3.022 P x (R° 145 — 1); Pi being the pressure in 
 )s. per sq. in., absolute, of the free air, and R the 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.) 
 
 R. 
 
 #0.145. 
 
 M.E.P. 
 from 
 14 lbs. 
 
 Initial. 
 
 Ultimate 
 Saving 
 
 by Com- 
 pound- 
 ing, %. 
 
 R. 
 
 #0.145. 
 
 M.E.P. 
 
 from 
 14 lbs. 
 Initial. 
 
 Ultimate 
 Saving 
 
 by Com- 
 pound- 
 ing, %. 
 
 5.0 
 
 1 .263 
 
 25.4 
 
 11.5 
 
 9.0 
 
 1.375 
 
 36.3 
 
 15.8 
 
 5.5 
 
 1.280 
 
 27.0 
 
 12.3 
 
 9.5 
 
 1.386 
 
 37.3 
 
 16.2 
 
 6.0 
 
 1.296 
 
 28.6 
 
 12.8 
 
 10 
 
 1.396 
 
 38.3 
 
 16.6 
 
 6.5 
 
 1.312 
 
 30.1 
 
 13.2 
 
 11 
 
 1.416 
 
 40.2 
 
 17.2 
 
 7.0 
 
 1.326 
 
 31.5 
 
 13.7 
 
 12 
 
 1.434 
 
 41.9 
 
 17.8 
 
 7.5 
 
 1.336 
 
 32.8 
 
 14.3 
 
 13 
 
 1.451 
 
 43.5 
 
 18.4 
 
 8.0 
 
 1.352 
 
 34.0 
 
 14.8 
 
 14 
 
 1.466 
 
 45.0 
 
 19.0 
 
 8.5 
 
 1.364 
 
 35.2 
 
 15.3 
 
 15 
 
 1.481 
 
 46.4 
 
 19.4 
 
610 
 
 AIR. 
 
 R = final -*■ initial absolute pressure. 
 
 M.E.P. = mean effective pressure, lb. per sq. in., based on 14 lb. absolute 
 Initial pressure reduced to the low-pressure cylinder. 
 
 Table for Adiabatic Compression or Expansion of Air. 
 
 (Proc. Inst. M.E., Jan., 1881, p. 123.) 
 
 Absolute Pressure. 
 
 Absolute Temperature. 
 
 Volume. 
 
 Ratio of 
 
 Ratio of 
 
 Ratio of 
 
 Ratio of 
 
 Ratio of 
 
 Ratio of 
 
 Greater 
 
 Less to 
 
 Greater 
 
 Less to 
 
 Greater 
 
 Less to 
 
 to Less. 
 
 Greater. 
 
 to Less. 
 
 Greater. 
 
 to Less. 
 
 Greater. 
 
 (Expan 
 
 (Compres 
 
 (Expan- 
 
 (Compres- 
 
 (Compres- 
 
 (Expan- 
 
 sion.) 
 
 sion.) 
 
 sion.) 
 
 sion.) 
 
 sion.) 
 
 sion.) 
 
 1.2 
 
 0.833 
 
 1.054 
 
 0.948 
 
 1.138 
 
 0.879 
 
 1.4 
 
 0.714 
 
 1.102 
 
 0.907 
 
 1.270 
 
 0.788 
 
 1.6 
 
 0.625 
 
 1.146 
 
 0.873 
 
 1.396 
 
 0.716 
 
 1.8 
 
 0.556 
 
 1.186 
 
 0.843 
 
 1.518 
 
 0.659 
 
 2.0 
 
 0.500 
 
 1.222 
 
 0.818 
 
 1.636 
 
 0.611 
 
 2.2 
 
 0.454 
 
 1.257 
 
 0.796 
 
 1.750 
 
 0.571 
 
 2.4 
 
 0.417 
 
 1.289 
 
 0.776 
 
 1.862 
 
 0.537 
 
 2.6 
 
 0.385 
 
 1.319 
 
 0.758 
 
 1.971 
 
 0.507 
 
 2.8 
 
 0.357 
 
 1.348 
 
 0.742 
 
 2.077 
 
 0.481 
 
 3.0 
 
 0.333 
 
 1.375 
 
 0.727 
 
 2.182 
 
 0.458 
 
 3.2 
 
 0.312 
 
 1.401 
 
 0.714 
 
 2.284 
 
 0.438 
 
 3.4 
 
 0.294 
 
 1.426 
 
 0.701 
 
 2.384 
 
 0.419 
 
 3.6 
 
 0.278 
 
 1.450 
 
 0.690 
 
 2.483 
 
 0.403 
 
 3.8 
 
 0.263 
 
 1.473 
 
 0.679 
 
 2.580 
 
 0.388 
 
 4.0 
 
 0.250 
 
 1.495 
 
 0.669 
 
 2.676 
 
 0.374 
 
 4.2 
 
 0.238 
 
 1.516 
 
 0.660 
 
 2.770 
 
 0.361 
 
 4.4 
 
 0.227 
 
 1.537 
 
 0.651 
 
 2.863 
 
 0.349 
 
 4.6 
 
 0.217 
 
 1.557 
 
 0.642 
 
 2.955 
 
 0.338 
 
 4.8 
 
 0.208 
 
 1.576 
 
 0.635 
 
 3.046 
 
 0.328 
 
 5.0 
 
 0.200 
 
 1.595 
 
 0.627 
 
 3.135 
 
 0.319 
 
 6.0 
 
 0.167 
 
 1.681 
 
 0.595 
 
 3.569 
 
 0.280 
 
 7.0 
 
 0.143 
 
 1.758 
 
 0.569 
 
 3.981 
 
 0.251 
 
 8.0 
 
 0.125 
 
 1.828 
 
 0.547 
 
 4.377 
 
 0.228 
 
 9.0 
 
 0.111 
 
 1.891 
 
 0.529 
 
 4.759 
 
 0.210 
 
 10.0 
 
 0.100 
 
 1.950 
 
 0.513 
 
 5.129 
 
 0.195 
 
 Mean Effective Pressures for the Compression Part only of the 
 Stroke when Compressing and Delivering Air from One Atmos- 
 phere to given Gauge-pressure in a Single Cylinder. (F. Richards, 
 Am. Mach., Dec. 14, 1893.) 
 
 Gauge- 
 
 Adiabatic 
 
 Isothermal 
 
 Gauge- 
 
 Adiabatic 
 
 Isothermal 
 
 Pressure. 
 
 Compression. 
 
 Compression. 
 
 Pressure. 
 
 Compression. 
 
 Compression. 
 
 1 
 
 0.44 
 
 0.43 
 
 45 
 
 13.95 
 
 12.62 
 
 2 
 
 0.96 
 
 0.95 
 
 50 
 
 15.05 
 
 13.48 
 
 3 
 
 1.41 
 
 )4 
 
 55 
 
 15.98 
 
 14.3 
 
 4 
 
 1.86 
 
 1.84 
 
 60 
 
 16.89 
 
 15.05 
 
 5 
 
 2.26 
 
 2.22 
 
 65 
 
 17.88 
 
 15.76 
 
 10 
 
 4.26 
 
 4.14 
 
 70 
 
 18.74 
 
 16.43 
 
 15 
 
 5.99 
 
 5.77 
 
 75 
 
 19.54 
 
 17.09 
 
 20 
 
 7.58 
 
 7.2 
 
 80 
 
 20.5 
 
 17.7 
 
 25 
 
 9.05 
 
 8.49 
 
 85 
 
 21.22 
 
 18.3 
 
 30 
 
 10.39 
 
 9.66 
 
 90 
 
 22.0 
 
 18.87 
 
 35 
 
 11.59 
 
 10.72 
 
 95 
 
 22.77 
 
 19.4 
 
 40 
 
 12.8 
 
 11.7 
 
 100 
 
 23.43 
 
 19.92 
 
AIR COMPRESSION AT ALTITUDES. 
 
 611 
 
 The mean effective pressure for compression only is always lower than 
 the mean effective pressure for the whole work. 
 
 To find the Index of the Curve of an Air-diagram. If PiVx be 
 pressure and volume at one point on the curve, and PV the pressure and 
 
 volume at another point, then -=- = {r/) > 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 -s- log r. (See also graphic method on page 576.) 
 
 Mean and Terminal Pressures of Compressed Air used Expansively 
 for Gauge Pressures from 60 to 100 lb. 
 
 (Frank Richards, Am. Mach., April 13, 1893.) 
 
 J 
 
 
 
 
 
 Initial Pressure. 
 
 
 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 o 
 M 
 
 'o 
 
 3 2 
 
 § ft 
 
 H ft 
 
 gft 
 
 "c3 ® 
 
 i 6 
 la 
 
 *3 g 
 
 H ft 
 
 6 
 
 dig 
 
 §^g 
 
 ft 
 
 "3 ai 
 H ft 
 
 
 "3 ? 
 
 w 
 
 .25 
 
 23.6 
 
 io.es 
 
 28.74 
 
 12.07 
 
 33.89 
 
 JS.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 
 
 6.11 
 
 # 
 
 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 
 
 1 
 
 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 
 
 * 
 
 51.92 
 
 23.69 
 
 60.84 
 
 28.85 
 
 69.76 
 
 34.01 
 
 78.69 
 
 39.16 
 
 87.61 
 
 44.32 
 
 .!• 
 
 53.67 
 
 27.94 
 
 62.83 
 
 33.03 
 
 71.99 
 
 38.68 
 
 81.14 
 
 44.33 
 
 90.32 
 
 49.97 
 
 54.93 
 
 30.39 
 
 64.25 
 
 36.44 
 
 73.57 
 
 42.49 
 
 82.9 
 
 48.54 
 
 92.22 
 
 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 
 
 Jo 
 
 59.15 
 
 47.14 
 
 69.03 
 
 55.43 
 
 78.92 
 
 63.81 
 
 88.81 
 
 72. 
 
 98.7 
 
 80.28 
 
 59.46 
 
 49.65 
 
 69.38 
 
 58.27 
 
 79.31 
 
 66.89 
 
 89.24 
 
 75.52 
 
 99.17 
 
 87.82 
 
 Pressures in italics are absolute; all others are gauge pressures. 
 
 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- 
 
 Barometric 
 Pressure. 
 
 Gauge Pressure (Pounds). 
 
 
 tude, 
 Feet. 
 
 
 
 
 
 
 In. of 
 Mercury. 
 
 Lb. per 
 Sq. In. 
 
 60 
 
 80 
 
 100 
 
 125 
 
 150 
 
 1,000 
 
 28.88 
 
 14.20 
 
 1.032 
 
 1.033 
 
 1.034 
 
 1.035 
 
 1.036 
 
 2,000 
 
 27.80 
 
 13.67 
 
 1.064 
 
 1.066 
 
 1.068 
 
 1.071 
 
 1.072 
 
 3,000 
 
 26.76 
 
 13.16 
 
 1.097 
 
 1.102 
 
 1.105 
 
 1.107 
 
 1.109 
 
 4,000 
 
 25.76 
 
 12.67 
 
 1 .132 
 
 1.139 
 
 1.142 
 
 1.147 
 
 1.149 
 
 5,000 
 
 24.79 
 
 12.20 
 
 1.168 
 
 1.178 
 
 1.182 
 
 1.187 
 
 1.190 
 
 6,000 
 
 23.86 
 
 11.73 
 
 1.206 
 
 1.218 
 
 1.224 
 
 1.231 
 
 1.234 
 
 7,000 
 
 22.97 
 
 11.30 
 
 1.245 
 
 1.258 
 
 1.267 
 
 1.274 
 
 1.278 
 
 8,000 
 
 22.11 
 
 10.87 
 
 1.287 
 
 1.300 
 
 1.310 
 
 1.319 
 
 1.326 
 
 9,000 
 
 21.29 
 
 10.46 
 
 1.329 
 
 1.346 
 
 1.356 
 
 1.366 
 
 1.374 
 
 10,000 
 
 20.49 
 
 10.07 
 
 1.373 
 
 1.394 
 
 1.404 
 
 1,416 
 
 1.424 
 
612 
 
 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 
 
 
 
 0.1533 
 
 0.1824 
 
 0.2075 
 
 0.1354 
 
 0.1580 
 
 0.1765 
 
 0.1964 
 
 0.2138 
 
 1,000 
 
 0.1511 
 
 0.1795 
 
 0.2040 
 
 0.1332 
 
 0.1553 
 
 0.1734 
 
 0.1926 
 
 0.2093 
 
 2,000 
 
 0.1489 
 
 0.1766 
 
 0.2006 
 
 0.1310 
 
 0.1524 
 
 0.1700 
 
 0.1887 
 
 0.2048 
 
 3,000 
 
 0.1469 
 
 0.1739 
 
 0.1971 
 
 0.1286 
 
 0.1493 
 
 0.1666 
 
 0.1848 
 
 0.2003 
 
 4,000 
 
 0.1448 
 
 0.1712 
 
 0.1939 
 
 0.1263 
 
 0.1464 
 
 0.1635 
 
 0.1810 
 
 0.1963 
 
 5,000 
 
 0.1425 
 
 0.1685 
 
 0.1906 
 
 0.1241 
 
 0.1438 
 
 0.1600 
 
 0.1772 
 
 0.1921 
 
 6,000 
 
 0.1402 
 
 0.1656 
 
 0.1872 
 
 0.1218 
 
 0.1409 
 
 0.1566 
 
 0.1737 
 
 0.1879 
 
 7,000 
 
 0.1379 
 
 0.1628 
 
 0.1839 
 
 0.1197 
 
 0.1383 
 
 0.1536 
 
 0.1700 
 
 0.1838 
 
 8,000 
 
 0.1358 
 
 0.1600 
 
 0.1807 
 
 0.1173 
 
 0.1358 
 
 0.1504 
 
 0. 1662 
 
 0.1797 
 
 9,000 
 
 0.1337 
 
 0.1572 
 
 0.1774 
 
 0.1151 
 
 0.1329 
 
 0.1473 
 
 0.1627 
 
 0.1758 
 
 10,000 
 
 0.1316 
 
 0.1547 
 
 0.1743 
 
 0.1132 
 
 0.1303 
 
 0.1442 
 
 0.1592 
 
 0.1717 
 
 Example. — Required the volume of free air which when compressed 
 to 100 lb. 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 lb. 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. Also 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 
 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 
 
COMPRESSED AIR TRANSMISSION. 613' 
 
 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 lb. per sq. in. and its temperature 54° F., and 988 cu. ft. when the air 
 was heated to 338° F., its pressure being 72 lb. 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 lb. 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 lb. 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, " .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 assumed 
 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 
 Motor Working with Pressure Reduced to 41/2 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 
 mains. 
 
 The fall of pressure in mains between central station and Paris (say 5 
 kilometres) reduces the possibility of work from 0.52 to 0.51 I.H.P. 
 
 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 -f- 0.39 = 1.38. 
 
 In this process additional heat is supplied by. the combustion of about 
 0.39 lb. 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-power 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 -4- 0.845 = 0.61. 
 
 Efficiency of transmission through mains 0.51 -4- 0.52 = 0.98. 
 
 Efficiency of reducing valve 0.50 -4- 0.51 = 0.98. 
 
 The combined efficiency of the mains and reducing valve between 5 and 
 4V2 atmospheres is thus 0.98 X 0.98 = 0.96. If the reduction had been 
 
614 
 
 AIR. 
 
 to 4, 3V2, or 3 atmospheres, the corresponding efficiencies would have 
 been 0.93, 0.89, and 0.85 respectively. 
 
 Indicated efficiency of motor 0.39 -4- 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-Sergeant Standard Air Compressors. 
 
 (Ingersoll-Rand Co., 1908.) 
 
 
 Diam.of Cyl., In. 
 
 a 
 
 Si 
 
 
 02 
 
 £ 
 > 
 
 
 MS 
 
 | 
 
 
 ft 
 
 0> 
 
 
 
 w 
 
 el'd 
 
 Class and Type. 
 
 Steam. 
 
 Air. 
 
 .So 
 
 
 
 r-; 
 
 bfl 
 
 i 
 
 h5 
 
 it 
 
 A-1* 
 Straight Line 
 Steam Driven. 
 
 10 
 
 12 
 
 14 
 16 
 18 
 20 
 
 22 
 24 
 
 
 10,1/4 
 
 12l/ 4 
 HI/4 
 I6I/4 
 I8I/4 
 20l/ 4 
 221/4 
 241/4 
 
 
 12 
 14 
 18 
 18 
 24 
 24 
 24 
 30 
 
 160 
 155 
 120 
 120 
 94 
 94 
 94 
 80 
 
 177 
 285 
 381 
 498 
 656 
 807 
 973 
 1223 
 
 50-100 
 50-100 
 50-100 
 50-100 
 50-100 
 50-100 
 50-100 
 50-100 
 
 23- 35 
 37- 57 
 50- 76 
 65-100 
 86-131 
 106-161 
 127-194 
 161-242 
 
 113 
 200 
 340 
 340 
 520 
 520 
 520 
 710 
 
 A-2* 
 Straight Line 
 Steam Driven 
 Compound Air. 
 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 26 
 
 
 71/2 
 91/4 
 IOI/4 
 121/4 
 131/4 
 141,4 
 151/4 
 I6I/4 
 
 121/4 
 Ml/4 
 I.6I/4 
 
 2OI/4 
 221/4 
 241/4 
 261/4 
 
 12 
 14 
 18 
 
 18 
 24 
 24 
 24 
 30 
 
 160 
 155 
 135 
 135 
 110 
 110 
 110 
 90 
 
 252 
 375 
 550 
 702 
 940 
 1131 
 1333 
 1606 
 
 90-110 
 90-110 
 90-110 
 90-110 
 90-110 
 90-110 
 90-110 
 90-110 
 
 40- 45 
 60- 66 
 89- 97 
 113-124 
 151-166 
 182-193 
 214-236 
 258-284 
 
 145 
 230 
 435 
 435 
 640 
 640 
 640 
 950 
 
 B,* Straight line, belt driven. .Same as A-1 in sizes up to 16 1/4 X ISin. 
 
 C, Duplex Corliss Steam, Duplex air. j ?f S n f ^l manWo 22nd" 
 
 C-2, Compound Corliss Steam .Compound air.f ] a rd lize^ 
 
 
 
 
 IOI/4 
 I21/4 
 HI/4 
 I6I/4 
 I8I/4 
 201/4 
 
 
 12 
 
 14 
 
 18 
 18 
 24 
 24 
 
 160 
 155 
 120 
 120 
 100 
 100 
 
 352 
 568 
 763 
 994 
 1338 
 1674 
 
 60-100 
 60-100 
 65-100 
 70-100 
 70-100 
 70-100 
 
 50- 67 
 81-108 
 113-146 
 154-189 
 207-256 
 259-320 
 
 240 
 
 D-1* 
 
 
 
 400 
 
 
 
 
 6?5 
 
 
 
 
 6?5 
 
 
 
 
 1050 
 
 
 
 
 105Q 
 
 
 
 
 IOI/4 
 HI/4 
 
 HI/4 
 151/4 
 171/4 
 18 1/4 
 201/ 4 
 
 16 1/4 
 I81/ 4 
 221/4 
 251/4 
 281/4 
 301/4 
 321/4 
 
 12 
 14 
 18 
 18 
 
 24 
 24 
 24 
 
 160 
 155 
 120 
 120 
 100 
 100 
 100 
 
 444 
 638 
 925 
 1205 
 1622 
 1857 
 2130 
 
 80-100 
 80-100 
 80-100 
 80-100 
 80-100 
 80-100 
 80 
 
 65- 72 
 93-104 
 134-150 
 174-194 
 235-263 
 269-300 
 309 
 
 ?40 
 
 
 
 
 400 
 
 D-2J 
 
 
 
 6?5 
 
 
 
 
 6?5 
 
 
 
 
 1050 
 
 
 
 
 1050 
 
 
 
 
 1050 
 
 E.* Straight line, belt driven 
 
 same sizes as F-1. 
 
 
 
 F-1* 
 Straight Line 
 Steam Driven. 
 
 6 
 8 
 
 10 
 12 
 
 
 6 
 
 8 
 10 
 121/4 
 
 1 6 
 
 8 
 
 10 
 
 1 12 
 
 150 
 150 
 150 
 150 
 
 29 
 69 
 134 
 233 
 
 45-100 
 50-100 
 55-100 
 60-100 
 
 4- 6 
 
 91/2-14 
 19-27 
 35-47 
 
 21 
 32 
 46 
 63 
 
 * Built in intermediate sizes for lower pressures. 
 
 t Most economical form of compressor, t For sea level; also built with 
 larger low pressure cylinders for altitudes of 5,000 and 10,000 ft. 
 
AIR COMPRESSORS. 
 
 615 
 
 Ingersoll-Sergeant Standard Air Compressors.— Continued. 
 
 
 Diam.of Cyl., In. 
 
 G 
 aT 
 
 o 
 
 OS 
 
 G 
 
 ft 
 > 
 
 
 
 o 
 ft 
 
 i ■ 
 
 1 
 
 55- 70 
 85-114 
 119-152 
 160-200 
 218-267 
 273-335 
 328-402 
 
 
 Class and Type. 
 
 Steam. 
 
 Air. 
 
 -.2 
 
 4 
 
 9 
 
 o 
 
 fa 
 
 4 
 
 o 
 
 h3 
 
 fa 
 
 G-1* 
 
 Duplex and Half 
 
 Duplex 
 
 Steam Driven. 
 
 10 
 
 12 
 14 
 16 
 18 
 20 
 22 
 
 
 IOI/4 
 121/4 
 141/ 4 
 I6I/4 
 I8I/4 
 201/ 4 
 221/4 
 
 
 12 
 14 
 
 18 
 18 
 24 
 24 
 24 
 
 160 
 155 
 120 
 120 
 100 
 100 
 100 
 
 352 
 568 
 763 
 994 
 1338 
 1674 
 2010 
 
 50-100 
 60-100 
 55-100 
 70-100 
 70-100 
 70-100 
 70-100 
 
 330 
 480 
 800 
 800 
 1450 
 1450 
 1450 
 
 G-2f 
 Duplex Steam, 
 Compound Air. 
 
 10 
 
 12 
 14 
 16 
 18 
 20 
 22 
 22 
 
 
 101/4 
 11 1/4 
 
 141/4 
 151/4 
 171/4 
 I8I/4 
 201/4 
 221/4 
 
 I6I/4 
 I8I/4 
 221/ 4 
 251/4 
 281/4 
 301/4 
 321/4 
 341/4 
 
 12 
 
 14 
 18 
 18 
 24 
 24 
 24 
 24 
 
 160 
 153 
 120 
 120 
 100 
 100 
 100 
 100 
 
 444 
 638 
 925 
 1205 
 1622 
 1857 
 2130 
 2390 
 
 80-100 
 
 80-100 
 
 80-100 
 
 80-100 
 
 80-100 
 
 100 
 
 100 
 
 80 
 
 67- 75 
 
 97-108 
 
 140-157 
 
 182-204 
 
 245-274 
 
 314 
 
 360 
 
 361 
 
 330 
 480 
 800 
 800 
 1475 
 1475 
 1475 
 1475 
 
 H-1* 
 
 Duplex Steam, 
 
 Duplex Air. 
 
 6 
 8 
 
 10 
 12 
 14 
 16 
 
 
 6 
 
 8I/4 
 101/4 
 121/4 
 141/4 
 161/4 
 
 
 6 
 8 
 
 10 
 12 
 14 
 16 
 
 150 
 150 
 150 
 150 
 140 
 135 
 
 58 
 140 
 272 
 472 
 680 
 986 
 
 50-100 
 55-100 
 60-100 
 60-100 
 65-100 
 70-100 
 
 71/2-1H/2 
 20- 28 
 40- 54 
 70- 94 
 106-136 
 160-197 
 
 115 
 150 
 180 
 220 
 383 
 585 
 
 H-2'j 
 
 Duplex Steam, 
 Compound Air. 
 
 6 
 8 
 
 10 
 12 
 14 
 16 
 
 
 7 
 
 91/4 
 101/4 
 121/4 
 141/4 
 I6I/4 
 
 10 
 
 141/4 
 161/4 
 
 I8I/4 
 221/4 
 251/4 
 
 6 
 8 
 10 
 12 
 14 
 16 
 
 150 
 150 
 150 
 150 
 140 
 135 
 
 81 
 215 
 348 
 526 
 841 
 1205 
 
 80-100 
 80-100 
 80-100 
 80-100 
 80-100 
 80-100 
 
 121/2-141/2 
 
 33-37 
 
 53-59 
 
 80-90 
 129-144 
 182-204 
 
 115 
 150 
 180 
 220 
 383 
 585 
 
 
 
 
 6 
 
 8I/4 
 101/4 
 121/4 
 141/4 
 161/4 
 
 
 6 
 8 
 10 
 12 
 14 
 16 
 
 150 
 150 
 150 
 150 
 140 
 135 
 
 58 
 140 
 272 
 472 
 680 
 986 
 
 50-100 
 55-100 
 60-100 
 60-100 
 65-100 
 70-100 
 
 7-11 
 19-27 
 39-53 
 67-90 
 101-130 
 153-190 
 
 83 
 
 
 
 
 1?5 
 
 Duplex 
 Belt Driven. 
 
 
 
 135 
 
 
 
 17? 
 
 
 
 315 
 
 
 
 
 479 
 
 
 
 
 
 
 
 
 7 
 
 91/4 
 IOI/4 
 121/4 
 141/4 
 161/ 4 
 
 10 
 
 141/4 
 161/4 
 I8I/4 
 221/4 
 251/4 
 
 6 
 8 
 10 
 12 
 
 14 
 16 
 
 150 
 150 
 150 
 
 81 
 215 
 348 
 
 80-100 
 80-100 
 80-100 
 80-100 
 
 12-14 
 31-35 
 51-57 
 
 77-86 
 
 83 
 
 
 
 
 1?5 
 
 J-2J 
 
 Duplex Compound 
 
 Belt Driven. 
 
 
 
 135 
 
 
 
 150 526 
 140! 841 
 
 117 
 
 
 
 80-1001 12-138 
 
 315 
 
 
 
 
 135 
 
 1 1205 
 
 80-1 00 
 
 I 176-198 
 
 429 
 
 * Built in intermediate sizes for lower pressures. 
 
 t For sea level ; also built with larger low pressure cylinders for alti- 
 tudes of 5,000 and 10,000 ft. 
 
 X For sea level; also built in the 4 largest sizes with larger low pressure 
 cylinders for altitudes of 5,000 and 10,000 ft. 
 
 Many other styles of compressors are also built. Among them are the 
 following: 
 
 Rand-Corliss, compound condensing steam, compound air; capacities. 
 750 to 7670 cu. ft. of free air per min.; steam cylinders, 10 and IS to 28 and 
 52 in.; air cylinders, 11 1/2 and 18 to 33 and 52 in.; stroke 30 to 48 in.; 
 I.H. P., from 114 to 1166. 
 
616 
 
 AIR. 
 
 "Vertical duplex single acting, belt driven; capacities, 16.6 to 321 cu. ft. 
 of free air per min. ; air cylinders, 4V2 to 12 in. ; stroke 41/2 to 14in. ; I.H.P., 
 2.5 to 66. 
 
 Duplex steam, non condensing, compound air; capacities, 343 to 2209 
 cu. ft. of free air per min. ; steam cylinders, 10 to 20 in. ; air cylinders, 9 
 and 14 to 19 and 30 in.; stroke, 16 to 30 in.; I.H.P., 53 to 380. 
 
 Compound steam, non condensing, duplex air; capacities, 349 to 1962 
 cu. ft. of free air per min.; steam cylinders, 10 and 16 to 20 and 32 in.; 
 air cylinders, 10 to 20 in.; stroke, 16 to 30 in.; I.H.P., 62 to 392. 
 
 Straight line, steam driven; capacities, 42 to 630 cu. ft. of free air per 
 min.; steam cylinders, 6 to 12 in.; air cylinders, 6 to 19 in.; stroke, 8 to 
 16 in.; I.H.P., 8.2 to 54. 
 
 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. 
 
 
 Size and Cylinder Diameter of Drill. 
 
 
 A 35 
 
 A 32 
 A 86 
 
 B 
 
 C 
 
 D 
 
 D 
 
 D 
 
 E 
 
 F 
 
 F 
 
 G 
 
 H 
 
 H9 
 
 ?„ a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2" 
 
 21/4" 
 
 21/2" 
 
 23/ 4 " 
 
 3" 
 
 31/8" 
 
 33/ie" 
 
 31/4" 
 
 31/2" 
 
 35/ 8 " 
 
 41/4" 
 
 5" 
 
 51/2" 
 
 60 
 
 50 
 
 60 
 
 68 
 
 82 
 
 90 
 
 95 
 
 97 
 
 100 
 
 108 
 
 113 
 
 130 
 
 150 
 
 164 
 
 70 
 
 56 
 
 68 
 
 77 
 
 93 
 
 102 
 
 108 
 
 110 
 
 113 
 
 124 
 
 129 
 
 147 
 
 170 
 
 181 
 
 80 
 
 63 
 
 76 
 
 86 
 
 104 
 
 114 
 
 120 
 
 123 
 
 127 
 
 131 
 
 143 
 
 164 
 
 190 
 
 207 
 
 90 
 
 70 
 
 84 
 
 95 
 
 115 
 
 126 
 
 133 
 
 136 
 
 141 
 
 152 
 
 159 
 
 182 
 
 210 
 
 230 
 
 100 
 
 77 
 
 92 
 
 104 
 
 126 
 
 138 
 
 146 
 
 149 
 
 154 
 
 166 
 
 174 
 
 199 
 
 240 
 
 252 
 
 Table II. — multipliers to give capacity of compressor to operate 
 FROM 1 TO 70 rock drills at various altitudes. 
 
 < > 
 
 
 
 
 
 
 
 Number of Drills. 
 
 
 
 
 
 
 it 
 
 < 
 
 1 
 1. 
 
 2 
 
 1.8 
 
 3 
 
 2.7 
 
 4 
 
 3.4 
 
 5 
 
 4.1 
 
 6 
 
 4.8 
 
 7 
 
 5.4 
 
 8 
 
 6.0 
 
 9 
 
 6.5 
 
 10 
 7.1 
 
 15 
 
 20 
 11.7 
 
 25 
 13.7 
 
 30 
 
 40 
 21,4 
 
 50 
 
 
 
 9.5 
 
 15.8 
 
 25.5 
 
 1000 
 
 1 03 
 
 1.85 
 
 2.78 
 
 3.5 
 
 4.22 
 
 4.94 
 
 5.56 
 
 6.18 
 
 6.69 
 
 7.3 
 
 9.78 
 
 12.05 
 
 14.1 
 
 16.3 
 
 22.0 
 
 26.26 
 
 2000 
 
 1.07 
 
 1.92 
 
 2.89 
 
 3.64 
 
 4.39 
 
 5.14 
 
 5.78 
 
 6.42 
 
 6.95 
 
 7.60 
 
 10.17 
 
 12.52 
 
 14.66 
 
 16.9 
 
 22.9 
 
 27.28 
 
 300C 
 
 1.10 
 
 1 98 
 
 2.97 
 
 3.74 
 
 4.51 
 
 5.28 
 
 5.94 
 
 6.6 
 
 7.15 
 
 7.81 
 
 10.45 
 
 12.87 
 
 15.07 
 
 17.38 
 
 23.54 
 
 28.05 
 
 5000 
 
 1 17 
 
 2 10 
 
 3 16 
 
 3.98 
 
 48 
 
 5 62 
 
 6.32 
 
 7.02 
 
 7.61 
 
 8.31 
 
 11.12 
 
 13.69 
 
 16.03 
 
 18,49 
 
 25.04 
 
 29.84 
 
 8000 
 
 1 26 
 
 2 27 
 
 3 40 
 
 4.28 
 
 5 17 
 
 6.05 
 
 6.8 
 
 7.56 
 
 8.19 
 
 8.95 
 
 11.97 
 
 14.74 
 
 17.26 
 
 19.9 
 
 26.96 
 
 32.13 
 
 10000 
 
 1 32 
 
 238 
 
 3.56 
 
 4,49 
 
 5.41 
 
 6.34 
 
 7.13 
 
 7.92 
 
 8.58 
 
 9.37 
 
 12.54 
 
 15.44 
 
 18.08 
 
 20.86 
 
 28.25 
 
 33.66 
 
 15000 
 
 1.43 
 
 2.57 
 
 3.86 
 
 4.86 
 
 5.86 
 
 6.86 
 
 7.72 
 
 8.58 
 
 9.3 
 
 10.15 
 
 13.58 
 
 16.73 
 
 19.59 
 
 22.59 
 
 30.6 
 
 36.49 
 
 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 lb. per 
 sq. in. From Table I, we find that one 5-inch " H " drill operating at 80 lb. 
 gauge pressure requires 190 cu. ft. of free air per minute. From Table 
 II, 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. 
 
COMPRESSED AIR. 
 
 617 
 
 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 
 or pipe line losses. 
 
 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 lbs. 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. 
 
 Steam per I.H.P. Hour. Lbs. 
 
 Gauge 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Pres- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 sure. 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 36 
 
 40 
 
 20 
 
 1.36 
 
 1 58 
 
 1 82 
 
 2 04 
 
 2 26 
 
 2 49 
 
 2 72 
 
 2 94 
 
 3 17 
 
 3 40 
 
 3 61 
 
 4 08 
 
 4.54 
 
 30 
 
 1,84 
 
 2 14 
 
 2 45 
 
 2.76 
 
 3.06 
 
 3,37 
 
 3 68 
 
 3 98 
 
 4 29 
 
 4 60 
 
 4 90 
 
 5,51 
 
 6.12 
 
 40 
 
 2 26 
 
 2 64 
 
 3 02 
 
 3.39 
 
 3.77 
 
 4.15 
 
 4 52 
 
 4 90 
 
 5.26 
 
 5 65 
 
 6 03 
 
 6.78 
 
 7.50 
 
 50 
 
 2.62 
 
 3 06 
 
 3 50 
 
 3.93 
 
 4.36 
 
 4.80 
 
 5.25 
 
 5.68 
 
 6.10 
 
 6.55 
 
 7.00 
 
 8.86 
 
 8.71 
 
 60 
 
 2.92 
 
 3 4! 
 
 3 90 
 
 4.38 
 
 4.80 
 
 5.36 
 
 5.85 
 
 6,32 
 
 6.80 
 
 7 30 
 
 7.80 
 
 8.76 
 
 9.71 
 
 70 
 
 3 22 
 
 3 76 
 
 4 30 
 
 4 83 
 
 5 36 
 
 5 90 
 
 6.45 
 
 6 97 
 
 7 50 
 
 8 05 
 
 8 60 
 
 9 66 
 
 10.70 
 
 80 
 
 3.50 
 
 4 08 
 
 4 67 
 
 5 25 
 
 5.84 
 
 6 42 
 
 7 00 
 
 7 59 
 
 8 15 
 
 8 75 
 
 9 34 
 
 10.50 
 
 11.61 
 
 90 
 
 3.72 
 
 4 34 
 
 4 96 
 
 5 58 
 
 6.20 
 
 6 82 
 
 7.45 
 
 8 05 
 
 8.66 
 
 9 30 
 
 9 94 
 
 11.15 
 
 12.35 
 
 100 
 
 3.96 
 
 4 61 
 
 5 29 
 
 5.95 
 
 6.60 
 
 7.25 
 
 7,92 
 
 8 58 
 
 9 22 
 
 9 90 
 
 10 56 
 
 11 88 
 
 13.15 
 
 110 
 
 4.18 
 
 4 87 
 
 5 58 
 
 6 26 
 
 6 96 
 
 7 66 
 
 8.36 
 
 9 05 
 
 9.75 
 
 10 45 
 
 11 15 
 
 12 52 
 
 13,90 
 
 120 
 
 4.38 
 
 5.11 
 
 5.85 
 
 6.57 
 
 7.30 
 
 8.04 
 
 8.76 
 
 9.50 
 
 10.20 
 
 10.95 
 
 11.66 
 
 13.13 
 
 14.55 
 
 Two-Stage Compression. 
 
 70 
 
 2 82 
 
 3 25 
 
 3 76 
 
 4 23 
 
 4,69 
 
 5,16 
 
 5.63 
 
 6,10 
 
 6 56 
 
 7 04 
 
 7.50 
 
 8.45 
 
 9 35 
 
 80 
 
 3.01 
 
 3 51 
 
 4 03 
 
 4 52 
 
 5,02 
 
 5.53 
 
 6.03 
 
 6.53 
 
 7.03 
 
 7.53 
 
 8.03 
 
 9.05 
 
 10.01 
 
 90 
 
 3.19 
 
 3,72 
 
 4.26 
 
 4.79 
 
 5.32 
 
 5.85 
 
 6.38 
 
 6.91 
 
 7.44 
 
 7.98 
 
 8.50 
 
 9.57 
 
 10.60 
 
 100 
 
 3 37 
 
 3 93 
 
 4 50 
 
 5 05 
 
 5 61 
 
 6,19 
 
 6 74 
 
 7 30 
 
 7 85 
 
 8 42 
 
 8 99 
 
 10,10 
 
 11.20 
 
 110 
 
 3 54 
 
 4 14 
 
 4 74 
 
 5 32 
 
 5.91 
 
 6.51 
 
 7.10 
 
 7 70 
 
 8.27 
 
 8.86 
 
 9.46 
 
 10.64 
 
 11.80 
 
 120 
 
 3,69 
 
 4 30 
 
 4,93 
 
 5 54 
 
 6.15 
 
 6.78 
 
 7.38 
 
 8,00 
 
 8.61 
 
 9.24 
 
 9 85 
 
 11.05 
 
 12.27 
 
 130 
 
 3.83 
 
 4 46 
 
 5 11 
 
 5,75 
 
 6 38 
 
 7.03 
 
 7.66 
 
 8.30 
 
 8.92 
 
 9,57 
 
 10.20 
 
 11,48 
 
 12.72 
 
 140 
 
 3 96 
 
 4 62 
 
 5 29 
 
 5 94 
 
 6 60 
 
 7 26 
 
 7 92 
 
 8 60 
 
 9 23 
 
 9 90 
 
 10 56 
 
 11 88 
 
 13 15 
 
 150 
 
 4.10 
 
 4.76 
 
 5.46 
 
 6.14 
 
 6.81 
 
 7.50 
 
 6.74 
 
 8.86 
 
 9.55 
 
 10.20 
 
 10.90 
 
 12.26 
 
 13.60 
 
 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 
 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 example: The ratio between 
 cylinders being 2 to 1, required to pump 100 gallons, height of lift 250 
 
618 
 
 AIR. 
 
 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 
 
 i j. i ( 
 
 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 
 
 
 
 
 1 to 1 | 
 
 
 
 
 1 1/2 to 1 { 
 
 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 
 
 1 3/ 4 to 1 | 
 
 
 
 2 88 
 
 r 
 
 
 
 55 
 
 2 to 1 J 
 
 
 
 
 7 98 
 
 21/4 to 1 { 
 
 
 
 
 44.0 
 
 
 
 
 
 3 15 
 
 ( 
 
 
 
 
 
 35 ?. 
 
 2 1/ 2 to I | 
 
 
 
 
 
 
 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 lbs. 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 60 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 
 5 
 
 61/4 
 7 
 
 8I/4 
 8 1/2 
 10 
 
 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 
 6,000 
 
 75 
 80 
 125 
 151 
 170 
 238 
 330 
 
 - 
 
COMPRESSED AIR. 
 
 619 
 
 Double-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 
 5 
 
 6I/4 
 
 81/4 
 81/2 
 
 10 
 
 121/4 
 
 14 
 
 6 
 8 
 8 
 10 
 10 
 12 
 12 
 15 
 18 
 
 200 
 160 
 160 
 125 
 125 
 110 
 110 
 100 
 90 
 
 6 
 8 
 12 
 20 
 30 
 40 
 50 
 75 
 100 
 
 11.8 
 12.6 
 19.8 
 24.2 
 33.6 
 37.8 
 52.4 
 89.2 
 125. 
 
 1,000 
 1,650 
 2,500 
 3,500 
 6,000 
 8 000 
 10,000 
 
 150 
 160 
 250 
 302 
 340 
 476 
 660 
 1,125 
 1,587 
 
 Practical Results with Compressed Air. — ■ Compressed-air System 
 at the Chqpin 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 itself, 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 of 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 315°, 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 0° 32° 62° 75° 80° 90° 100° 110° 
 
 Volume discharged, cubic ft. 1135 1060 1000 975 966 949 932 916 
 
620 
 
 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 air entering it. The difference of these temperatures 
 for given temperatures of the entering water and air is diminished by in- 
 creasing 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 quantity of air to area of sur- 
 face, 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. — (Eng. News, Nov. 19, 1908.) The 
 General Electric Co. has placed on the market a line of centrifugal air 
 compressors with pressure ratings from 0.75 to 4.0 lbs. per sq. in. and 
 capacities from 750 to 28,000 cu. ft. of free air per minute. The com- 
 pressor consists essentially of a rotating impeller surrounded by a suit- 
 able casing with an intake opening at the center and a discharge opening 
 at the circumference. It is similar to the centrifugal pump, the efficiency 
 depending largely upon the design of the impeller and casing. 
 
 The compressors are driven by Curtis steam turbines or by electric 
 motors especially designed for them. With "squirrel-cage" induction 
 motors, since the speed cannot be varied, care must be taken to specify 
 a pressure sufficiently high to cover the operating requirements, because 
 at constant speed the pressure cannot be varied without altering the 
 design of the impeller. For foundry cupola service direct-current motors 
 can be compound wound so as to automatically increase the speed should 
 the volume of air delivered decrease, thus increasing the pressure of the 
 air and preventing undue reduction of flow of air through the cupola 
 when it chokes up. Further adjustments of pressure can be made by 
 changing the speed of the motor by means of the field rheostat. 
 
 Standard 
 
 Single 
 
 -Stage Centrifugal Air 
 
 Compressors (1909). 
 
 
 Standard Con- 
 
 Minimum Speed 
 
 Maximum Speed 
 
 
 
 ditions. 
 
 Conditions. 
 
 Conditions. 
 
 Pipe 
 
 R.P.M. 
 
 
 
 
 
 
 
 Diam- 
 
 Lbs. 
 
 per Sq. 
 
 In. 
 
 Cu. Ft. 
 per Min. 
 
 Lbs. 
 
 per Sq. 
 
 In. 
 
 Cu. Ft. 
 per Min. 
 
 Lbs. 
 
 per Sq. 
 
 In. 
 
 Cu. Ft. 
 per Min. 
 
 eter 
 Inches. 
 
 3450 
 
 1.0 
 
 800 
 
 0.75 
 
 1,100 
 
 1.25 
 
 600 
 
 10 
 
 3450 
 
 1.0 
 
 1,600 
 
 0.75 
 
 2,100 
 
 1.25 
 
 1,300 
 
 12 
 
 3450 
 
 1.0 
 
 3,200 
 
 0.75 
 
 4,100 
 
 1.25 
 
 2,600 
 
 12 
 
 3450 
 
 1.0 
 
 4,500 
 
 0.75 
 
 5,900 
 
 1.25 
 
 3,800 
 
 16 
 
 3450 
 
 1.0 
 
 7,200 
 
 0.75 
 
 8,800 
 
 1.25 
 
 6,000 
 
 20 
 
 3450 
 
 1.0 
 
 10,200 
 
 0.75 
 
 12,000 
 
 1.25 
 
 8,700 
 
 26 
 
 1725 
 
 1.0 
 
 25,000 
 
 0.75 
 
 31,000 
 
 1.25 
 
 21,000 
 
 36 
 
 3450 
 
 2.0 
 
 750 
 
 1.5 
 
 1,000 
 
 2.50 
 
 500 
 
 8 
 
 3450 
 
 2.0 
 
 1,600 
 
 1.5 
 
 2,100 
 
 2.50 
 
 1,200 
 
 10 
 
 3450 
 
 2.0 
 
 2,500 
 
 1.5 
 
 3,300 
 
 2.50 
 
 1,900 
 
 12 
 
 3450 
 
 2.0 
 
 4,200 
 
 1.5 
 
 5,400 
 
 2.50 
 
 3,300 
 
 16 
 
 3450 
 
 2.0 
 
 6,200 
 
 1.5 
 
 8,000 
 
 2.50 
 
 5,000 
 
 20 
 
 1725 
 
 2.0 
 
 15,000 
 
 1.5 
 
 19,000 
 
 2.50 
 
 11,000 
 
 26 
 
 1725 
 
 2.0 
 
 28,000 
 
 1.5 
 
 36,000 
 
 2.50 
 
 24,000 
 
 36 
 
 3450 
 
 3.25 
 
 1,250 
 
 2.5 
 
 1,800 
 
 4.00 
 
 900 
 
 8 
 
 3450 
 
 3.25 
 
 2,400 
 
 2.5 
 
 3,200 
 
 4.00 
 
 1,900 
 
 12 
 
 3450 
 
 3.25 
 
 3,800 
 
 2.5 
 
 5,000 
 
 4.00 
 
 3,000 
 
 14 
 
 3450A.C.&tur. 
 
 3.25 
 
 9,000 
 
 2.5 
 
 11,500 
 
 4.00 
 
 7,500 
 
 24 
 
 1725 D.C. 
 
 3.25 
 
 9,000 
 
 2.5 
 
 11.000 
 
 4.00 
 
 6,400 
 
 24 
 
 3450A.C.&tur. 
 
 3.25 
 
 18,000 
 
 2.5 
 
 23; 000 
 
 4.00 
 
 15,000 
 
 26 
 
 1725 D.C. 
 
 3.25 
 
 18,000 
 
 2.5 
 
 23,500 
 
 4.00 
 
 14,000 
 
 26 
 
HIGH-PRESSURE CENTRIFUGAL FANS. 621 
 
 Multi-stage compressors have been built of the following sizes. 
 
 Cu. ft. free air per min. Pressures. Rated speed. 
 
 22,500 10 to 25 lbs. 1,800 r.p.m. 
 
 8,000 8 to 15 lbs. 3,750 r.p.m. 
 
 3,450 25 to 35 lbs. 3,450 r.p.m. 
 
 From a curve of the load characteristics of a compressor rated at 1.7 
 lbs. pressure and 750 cu. ft. per min. the following figures are derived. 
 The actual efficiency is not given: 
 
 Delivery, cu. ft. per min.* 200 400 600 700 800 900 1000 
 
 Discharge pressure, lbs. per sq. in. 1.641.75 1.82 1.811.80 1.72 1.00 1.46 
 
 Effy. per cent of maximum 49 77 95 99 100 99 96 
 
 * Reduced to atmospheric pressure and 60° F. 
 
 As in the case of centrifugal pumps, the pressure depends on the 
 
 Seripheral velocity of the impeller. The volume of free air delivered is 
 mited, however, by the capacity of the driver, and hence must be re- 
 duced proportionately to the increase in pressure, otherwise the driver 
 might become overloaded. 
 
 The power required to drive centrifugal compressors varies approxi- 
 mately with the volume of air delivered when operating at a constant 
 speed. This gives flexibility and economy to the centrifugal type where 
 variable loads are required, satisfactory efficiency being obtained between 
 the limits of 25% and 125% of the rated load. 
 
 When the compressor is operated as an exhauster against atmospheric 
 pressure, the rated pressure P in lbs. per square inch must be multiplied 
 by 14.7 and then divided by 14.7 + P. The result represents the vacuum 
 obtained in lbs. per square inch below atmosphere. 
 
 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 8i/4lbs. 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 lb. 
 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. ft. per sec; in the second test it was 
 46 cu. ft. 
 
2d. 
 
 3d. 
 
 4th. 
 
 23.37 
 
 38.69 
 
 66.44 
 
 39.98 
 
 66.44 
 
 102.60 
 
 4660 
 
 4660 
 
 4660 
 
 67.8 
 
 63. 
 
 66. 
 
 205. 
 
 216. 
 
 215.6 
 
 122. 
 
 114.8 
 
 105.8 
 
 137.2 
 
 153. 
 
 149.6 
 
 60.5 
 
 54. 
 
 46.2 
 
 2d. 
 
 3d. 
 
 4th. 
 
 21.31 
 
 37.33 
 
 65.12 
 
 38.22 
 
 65.12 
 
 99.66 
 
 5000 
 
 4840 
 
 4840 
 
 69.8 
 
 64.4 
 
 68.5 
 
 208.4 
 
 208.4 
 
 199.6 
 
 131. 
 
 123.8 
 
 100.4 
 
 66.6 
 
 58.7 
 
 48.6 
 
 622 
 
 First Test. 
 Stages. 1st. 
 
 Abs. pressure at inlet, lbs. per sq. in. ... 15. 18 
 
 Abs. pressure at discharge 24. 10 
 
 Speed, revs, per rain 4660 
 
 Temperature of air at inlet, deg. F. ... 57.2 
 Temperature of air at discharge, deg. F. 171 . 
 
 Adiabatic rise in temp., deg. F 106. 
 
 Actual rise in temperature, deg. F. ... 113.8 
 Efficiency, per cent 60 . 5 
 
 Second Test. 
 Stages. 1st. 
 
 Abs. pressure at inlet, lbs. per sq. in. . . . 15. 18 
 
 Abs. pressure at discharge 23 . 52 
 
 Speed, revs, per min 5000 
 
 Temp, of air at inlet, deg. F 55. 
 
 Temp, of air at discharge, deg. F 160. 7 
 
 Adiabatic rise in temp., deg. F 102.2 
 
 Efficiency, per cent 62 . 3 
 
 The Gutehoffnungshiitte Co. in Germany have in 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 up 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. I., 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 150 ft.; 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 bv 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-in. 
 pipes. 
 
HYDRAULIC AIR COMPRESSION. 
 
 623 
 
 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, winch 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 lbs. 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 
 
 Flow of water, cu. ft. per min.. . 
 
 Available head in ft 
 
 Gross water, H.P 
 
 Cu. ft. air, at atmos. press., per 
 
 minute 
 
 Pressure of air at comp., lbs 
 
 Effective work in compressing, 
 
 H.P 
 
 Efficiency of compressor, % 
 
 Temp, of external air, deg. F — 
 Temp, of water and comp. air, 
 
 deg. F t 
 
 Ratio of water to air, volumes... 
 Moisture in external air, p. c. of 
 
 saturation 
 
 Moisture in comp. air, p. c. of 
 
 saturation 
 
 1 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 
 
 3772 
 20.54 
 146.3 
 
 3628 
 20.00 
 136.9 
 
 4066 
 20.35 
 156.2 
 
 4.292 
 19.51 
 158.1 
 
 4408 
 19.93 
 165.8 
 
 4700 
 19.31 
 171.4 
 
 864 
 
 51.: 
 
 901 
 53.7 
 
 967 
 53.2 
 
 1148 
 53.3 
 
 1091 
 53.7 
 
 1103 
 52.9 
 
 83.3 
 56.8 
 68.3 
 
 88.2 
 64.4 
 57.7 
 
 94.3 
 60.3 
 66.4 
 
 111.74 
 70.7 
 65.2 
 
 107 
 64.5 
 59.7 
 
 106.8 
 62.2 
 65 
 
 66 
 4.37 
 
 65.5 
 4.03 
 
 66.4 
 4.20 
 
 66.5 
 3.74 
 
 67 
 4.04 
 
 66.5 
 4.26 
 
 61 
 
 77.5 
 
 71 
 
 68 
 
 90 
 
 60.5 
 
 51.5 
 
 44 
 
 38.5 
 
 35 
 
 29 
 
 31.2 
 
 10 
 
 5058 
 18.75 
 179.1 
 
 1165 
 53.3 
 
 113.4 
 63.3 
 
 64.2 
 
 66 
 4.34 
 
 30 
 
 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 30 3/4-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, Cascade 
 
 Ont. Conn. Range, 
 
 Wash. 
 
 Head of water 14 ft. 18* ft. 45 ft. 
 
 Gauge pressure 25 lbs. 85 lbs. 85 lbs. 
 
 Diam. of shaft 42 in. 24 ft. 
 
 Diam. of compressor pipe 18 ft. 13 ft. 3 ft. 
 
 Depth below tailrace 64 ft. 215 ft. 
 
 Horse-power 1365 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 the up- 
 flow pipe is 4'ft. 9 in. 
 
624 
 
 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 downfiow 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. 
 
 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 1/4 and 
 3-inch lead pipes laid in cast-iron pipes for protection. The carriers 
 used in 21/4-inch tubes are but 11/4 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 21/2 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 6i/s inches, the tubes being of cast iron bored to size. -The 
 lengths of the outgoing and return tubes are 2928 feet each. The pressure 
 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's 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 ar€ 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 mi nut es, 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 261/4 X 18 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 thev 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 svstem 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. 
 
 The Mekarski Compressed-air Tramwav at Berne, Switzerland. 
 (Eng'g 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 lb. per sq. in. 
 
OPERATION OF PUMPS BY COMPRESSED AIR. 625 
 
 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. Taking the resistance 
 due to the grooved rails and to curves under unfavorable conditions at 
 
 30 lb. per ton of car weight, the engine has to overcome on the steepest 
 grade, 5%, a total resistance of about 0.63 ton, and has to develop 25 
 H.P. At the maximum authorized working pressure in cylinders of 176 
 lb. per sq. in. the motors can develop a tractive force of 0.64 ton. This 
 maximum is, therefore, just sufficient to take the car up the 5.2% grade, 
 while on the flatter sections of the line the working pressure does not 
 exceed 73 to 147 lb. per sq. in. Sand has to be frequently used to increase 
 the adhesion on the 2% to 5% grades. 
 
 < Between the two car frames are suspended ten horizontal compressed- 
 air storage-cylinders, varying in length according to the available space, 
 but of uniform inside diameter of 17.7 in., composed of riveted 0.27-in. 
 sheet iron, and tested up to 588 lb. per sq. in., and having a collective 
 capacity of 64.25 cu. ft., and two further small storage-cylinders of 
 5.3 cu. ft. capacity each, a total capacity for the 12 storage-cylinders 
 per car of 75 cu. ft., divided into two groups, the working and the reserve 
 battery, of 49 cu. ft. and 26 cu. ft. capacity respectively. 
 
 From the results of six official trips, the pressure and the mean con- 
 sumption of air during a double trip per motor car are as follows: 
 
 Pressure of air in storage-cylinders at starting, 440 lb. per sq. in. ; at end 
 of up-trip, 176 lb., reserve, 260 lb.; at end of down-trip, 103 lb., reserve, 
 176 lb. Consumption of air during up-trip, 92 lb., during down-trip, 
 
 31 lb. The working experience of 1891 showed that the air consumption 
 per motor car for a double trip was from 103 to 154 lb., mean 123 lb., 
 and. per car mile from 28 to 42 lb., mean 35 lb. 
 
 The disadvantages 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 one motor car, which necessitates the car 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 lb. per sq. in. as against only 440 lb. at Berne. 
 
 For description of the Mekarski system as used at Nantes, France, 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 lb. 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 lb. 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 lb. per sq. in. 65%. By wire-drawing to 100 lbs. 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 31ine 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. 
 
626 
 
 Air Mag., Feb., 1899) states the relations of simple or single-cylinder 
 pumps to be A/W = l hh/p, where A = area of air cylinder, sq. in., W 
 = area of water cylinder, sq. in., h = head, ft., and p = air pressure, lb. 
 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 = 
 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 and 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 pumps 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 BLOWERS. 
 
 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. His results are presented here merely for purposes of reference and 
 comparison. The experiments were made on fans of the " paddle-wheel" 
 type, and have no bearing on the more modern multivane fans of the 
 "Sirocco" type. 
 
 From his experiments Mr. Buckle deduced the following proportions for 
 a fan: 1. The width of the vanes should be one-fourth the diameter; 
 2. The diameter of the inlet opening in the sides of the fan chest should 
 be one-half the diameter of the. fan; 3. The length of the vanes should be 
 one-fourth the diameter of the fan. These rules do not agree with those 
 adopted by modern manufacturers, nor do the rules adopted by different 
 manufacturers agree among themselves. An examination of 18 commer- 
 cial sizes of fans, of the ordinary steel-plate type, built by two prominent 
 manufacturers, A and B, shows the following proportions based on the 
 diameter of the fan wheel, D, in inches: 
 
 Proportions of Fans, Rectangular Blades. 
 
 
 
 A 
 
 Max. 
 
 A 
 
 Min. 
 
 A 
 
 Av. 
 
 B 
 
 Max. 
 
 B 
 
 Min. 
 
 B 
 
 Av. 
 
 Buckle. 
 
 Diam. inlet 
 Width of blade . 
 
 0.666D 
 0.435D 
 
 0.618D 
 0.380D 
 
 0.636D 
 0.398D 
 
 0.495D 
 0.366D 
 
 0.430D 
 0.333D 
 
 0.476D 
 0.356D 
 
 0.5D 
 0.25D 
 
 The rules laid down by Buckle do not give a fan the highest commer- 
 cial efficiency without loss of mechanical efficiency. By commercial effi- 
 ciency is meant the ratio of the volume of air delivered per revolution to 
 the cubical contents of the wheel, if the wheel be considered a solid whose 
 dimensions are those of the wheel. This ratio is also known as the volu- 
 metric efficiency. 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 
 
FANS AND BLOWERS. 627 
 
 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 vanes varies from 4 to 8, while with 
 multivane fans it is 60 or more. The number of vanes 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 de- 
 creases the depth of the blade, thus diminishing the capacity and pressure. 
 To overcome this decrease, the number of blades is increased to the limit 
 placed by constructional considerations. A properly proportioned fan is 
 one in which a balance is obtained between these two features of maxi- 
 mum inlet and maximum number of blades. Generally speaking, in a 
 purely centrifugal fan, increased pressure is obtained with the increase in 
 depth of the blade. This appears to be due to the greater area of blade 
 working on the air. A smaller wheel, with a greater number of blades, 
 aggregating a larger blade area, gives a higher pressure than a larger 
 wheel with less total blade area. 
 
 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 formulae 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 
 
 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 
 equal 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 q the acceleration 
 due to gravity. The pressure of the air is increased by increasing the 
 number of revolutions per minute of the fan. Wolff, in his "The Wind- 
 mill as a Prime Mover," p. 17, argues that it is an error to take // = v 2 
 ■*■ 2 g, the formula according to him being H = v 2 -s- 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 being twice that 
 due the height calculated from the formula h = v 2 -*- 2 g. (See Hawksley, 
 Proc. Inst. M. E., 1882.) Later authorities and manufacturers, however, 
 base all their calculations on the former formula. 
 
 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." D. K. Clark (R. T. & D., p. 924), paraphrasing Buckle, appar- 
 ently, says: " It further appears that the pressure generated at the circum- 
 ference is one-ninth greater than that which is due to the actual circumfer- 
 ential velocity of the fan." The two statements, however, are not in 
 
 harmony, for if „ = oWi^?, H = Q -^^= 1.234^and not ff g - 
 
 If we take the pressure as that equal to a head or column of air of twice 
 the height due the velocity, as stated by Trowbridge, the paradoxical 
 statements of Buckle and Clark — which would indicate that the actual 
 pressure is greater than the theoretical — are explained, and the formula 
 
 becomes H = 0.617 — and v = 1.273 ^gH = 0.9 ^2gH, in which H is 
 
 the head of a column producing the pressure, which is equal to twice the 
 theoretical head due the velocity of a falling body (k = v 2 /2 g), multiplied 
 by the coefficient 0.617. The difference between 1 and this coefficient ex- 
 presses the loss of pressure due to friction, to the fact that the inner por- 
 tions of the blade have a smaller velocity than the outer edge, and probably 
 to other causes. The coefficient 1 .273 means that the tip of the blade must 
 be given a velocity 1.273 times that theoretically required to produce the 
 head H. 
 
628 air. 
 
 Commenting on the above paragraphs and the formulae below, 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 fan outlet is wholly 
 dependent upon the load on the fan, and, therefore, 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 forwara it is possible to obtain a much higher pressure 
 than if the blade is running 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 concaved 
 in the direction of rotation has the highest efficiency, all other things being 
 equal, the noise of operation is increased. A blade convex in the direction 
 of rotation runs more quietly, and in most situations it is necessary to 
 sacrifice efficiency in order to obtain quiet operation. 
 
 To convert the head H expressed in feet to pressure in lb. per sq. in. 
 multiply it by the weight of a cubic foot of air at the pressure and tempera- 
 ture of the air expelled from the fan (about 0.08 lb. 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 c olum n. Taking 0.08 as the weight of 1 cu. ft. of air, and 
 v - 0.9 ^2 gH, 
 
 p lb. per sq. in. = 0.00001066 v 2 ; v = 310 VP_nearly; 
 
 pi ounces per sq. in. = 0.0001706 v 2 ; v= 80 \/Pi " 
 p 2 inches of mercury = 0.00002169 v 2 \ v = 220 VP2 " 
 ps inches of water = 0.0002954 v 2 ; v= 60 VP3 " 
 
 in which v = velocity of tips of blades in feet per second. 
 
 Testing the above formula by one of Buckle's expeiiments with a vane 
 14 inches long, we have p = 0.00001066 v 2 = 9.56 oz. The experiment 
 gave 9.4 oz. 
 
 Testing it by the experiment of H. I. Snell, given below, in which the 
 circumferential speed was about 150 ft. per second, we obtain 3.85 ounces, 
 while the experiment gave from 2.38 to 3.50 ounces, according to the 
 amount of opening for discharge. _ 
 
 Taking the formula v = 80 Vp x> 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 
 
 A rule in App. Cyc. Mech., article " Blowers," gives the following veloci- 
 ties of circumference for different densities of blast in ounces: 3,170 ; 4, 180; 
 5, 195; 6, 205; 7, 215. 
 
 The same article gives the following tables, the first of which shows that 
 the density of blast is not constant for a given velocity, but depends on the 
 ratio of area of nozzle to area of blades: 
 
 Velocity of circumference, feet per second.. . 150 150 150 170 200 200 220 
 
 Area of nozzle -5- area of blades 2 1 1/2 1/4 1/2 Ve Vs 
 
 Density of blast, oz. per square inch 12 3 4 4 6 6 
 
 Quantity of Air op 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. 642. 
 
 Density, Velocity, 
 
 ounces feet per 
 
 per sq. in. minute. 
 
 1 5,000 
 
 2 7,000 
 
 3 8,600 
 
 4 10,000 
 
 Density, Velocity, 
 
 ounces feet per 
 
 per sq. in. minute. 
 
 5 11,000 
 
 6 12,250 
 
 7 13,200 
 
 8 14,150 
 
 Density, Velocity, 
 
 ounces feet per 
 
 per sq. in. minute. 
 
 9 15,000 
 
 10 15,800 
 
 11 16,500 
 
 12 17,300 
 
FANS AND BLOWERS. 
 
 629 
 
 " 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 -4- 3, in winch 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. Snow. 
 
 Experiments with Blowers. (Henry I. Snell, Trans. A. S. M. E., ix. 
 51.) — The following tables give velocities of air discharging through an 
 aperture of any size under the given pressures into the atmosphere. The 
 volume discharged can be obtained by multiplying the area of discharge 
 opening by the velocity, and this product by the coefficient of contraction: 
 0.65 for a thin plate and 0.93 when the orifice is a conical tube with a con- 
 vergence of about 3.5 degrees, as determined by the experiments of Weis- 
 bach. 
 
 The tables are calculated for a barometric pressure of 14.69 lb . ( = 
 235 oz.), and for a temperature of 50° Fahr., from the formula V = "^2 gh. 
 
 Allowances have been made for the effect of the compression of the air, 
 but none for the heating effect due to the compression. 
 
 At a temperature of 50 degrees, a cubic foot of air weighs 0.078 lb., and 
 calling g = 32.1602, the above formula may be reduced to 
 
 V x = 60 \ / 31.5812 X (235 + P)X P, 
 
 where V t = velocity in feet per minute, P = pressure above atmosphere, 
 or the pressure shown by gauge, in oz. per square inch. 
 
 
 Corre- 
 
 
 
 Corre- 
 
 
 Pressure 
 
 sponding 
 
 Velocity due 
 
 Pressure 
 
 sponding 
 
 Velocity due 
 
 per sq. in., 
 
 Pressure, 
 
 to Pressure, 
 
 per sq. in., 
 
 Pressure, 
 
 to Pressure, 
 
 in. of water. 
 
 oz. per sq. 
 in. 
 
 ft. per min. 
 
 in. of water. 
 
 oz. per sq. 
 in. 
 
 ft. per min. 
 
 V32 
 
 0.01817 
 
 696.78 
 
 5/8 
 
 0.36340 
 
 3118.38 
 
 Vl6 
 
 0.03634 
 
 987.66 
 
 3/ 4 
 
 0.43608 
 
 3416.64 
 
 1/8 
 
 0.07268 
 
 1393.75 
 
 7/8 
 
 0.50870 
 
 3690.62 
 
 3/16 
 
 0.10902 
 
 1707.00 
 
 1 
 
 0.58140 
 
 3946.17 
 
 1/4 
 
 0.14536 
 
 1971.30 
 
 11/4 
 
 0.7267 
 
 4362.62 
 
 5/16 
 
 0.18170 
 
 2204.16 
 
 11/2 
 
 0.8721 
 
 4836.06 
 
 3/8 
 
 0.21804 
 
 2414.70 
 
 13/4 
 
 1.0174 
 
 5224.98 
 
 1/2 
 
 0.29072 
 
 2788.74 
 
 2 
 
 1.1628 
 
 5587.58 
 
 Pres- 
 sure, 
 oz.per 
 sq. in. 
 
 0.25 
 0.50 
 0.75 
 1.00 
 1.25 
 1.50 
 1.75 
 2.00 
 
 Velocity 
 due to 
 
 Pressure ; 
 ft. per. 
 min. 
 
 2,582 
 3,658 
 4,482 
 5,178 
 5,792 
 6,349 
 6,861 
 7,338 
 
 Pres- 
 sure, 
 oz.per 
 sq. in. 
 
 2.25 
 2.50 
 2.75 
 3.00 
 3.50 
 4.00 
 4.50 
 5.00 
 
 Velocity 
 due to 
 
 Pressure 
 ft. per 
 min. 
 
 7,787 
 8,213 
 8,618 
 9,006 
 9,739 
 10,421 
 11,065 
 11,676 
 
 Pres- 
 sure, 
 oz.per 
 sq. in. 
 
 5.50 
 6.00 
 6.50 
 7.00 
 7.50 
 8.00 
 9.00 
 10.00 
 
 Velocity 
 due to 
 
 Pressure, 
 ft. per 
 
 12,259 
 12,817 
 13,354 
 13,873 
 14,374 
 14,861 
 15,795 
 16,684 
 
 Pres- 
 sure, 
 oz. per 
 
 11.00 
 12.00 
 13.00 
 14.00 
 15.00 
 16.00 
 
 Velocity 
 due to 
 Pressure, 
 ft. per 
 min. 
 
 17,534 
 18,350 
 19,138 
 19,901 
 20,641 
 21,360 
 
630 
 
 Pressure in 
 ounces per 
 square inch. 
 
 Velocity in feet 
 per minute. 
 
 Pressure in ounces 
 per square inch. 
 
 Velocity in feet 
 per minute. 
 
 0.01 
 0.02 
 0.03 
 0.04 
 0.05 
 
 516.90 
 722.64 
 895.26 
 1033.86 
 1155.90 
 
 0.06 
 0.07 
 0.08 
 0.09 
 0.10 
 
 1266.24 
 1367.76 
 1462.20 
 1550.70 
 1635.00 
 
 Experiments on a Fan with Varying Discharge-opening. 
 Revolutions nearly constant. 
 
 © 
 ft 
 w 
 
 3 
 
 .2© 
 
 © • 
 || 
 
 3 
 © 
 
 I 
 
 <! © ■ 
 
 ftS 
 
 'ot3 © 
 
 1 
 
 o 
 
 Izj'S © 
 
 heoret. Vol. per 
 min. that may be 
 discharged with 
 1 H.P.at corresp. 
 Pressure. 
 
 O © 
 
 3 3 
 
 o.S 
 
 ©S 
 
 © a 
 
 © s 
 
 > 3 
 
 n 
 
 © bfl « 
 
 3^ 3 
 ■£ © e 
 
 ft 
 1 
 
 o 
 
 • ft 
 3g| 
 
 .£ * 3 
 
 J ©S 
 
 K 
 
 < 
 
 o 
 
 > 
 
 W 
 
 < 
 
 H 
 
 H 
 
 1519 
 
 
 6 
 
 3.50 
 3.50 
 
 
 406 
 
 0.80 
 1.15 
 
 
 1048 
 1048 
 
 
 1479 
 
 353 
 
 0.337 
 
 1480 
 
 10 
 
 3.50 
 
 676 
 
 1.30 
 
 520 
 
 1048 
 
 0.496 
 
 1471 
 
 20 
 
 3.50 
 
 1353 
 
 1.95 
 
 694 
 
 1048 
 
 0.66 
 
 1485 
 
 28 
 
 3.50 
 
 1894 
 
 2.55 
 
 742 
 
 1048 
 
 0.709 
 
 1485 
 
 36 
 
 3.40 
 
 2400 
 
 3.10 
 
 774 
 
 1078 
 
 0.718 
 
 1465 
 
 40 
 
 3.25 
 
 2605 
 
 3.30 
 
 790 
 
 1126 
 
 0.70 
 
 1468 
 
 44 
 
 3.00 
 
 2752 
 
 3.55 
 
 115 
 
 1222 
 
 0.635 
 
 1500 
 
 48 
 
 3.00 
 
 3002 
 
 3.80 
 
 790 
 
 1222 . 
 
 0.646 
 
 1426 
 
 89.5 
 
 2.38 
 
 3972 
 
 4.80 
 
 827 
 
 1544 
 
 0.536 
 
 The fan wheel was 23 in. diam., 65/s in. wide at its periphery, and had 
 an inlet 12 1/2 in. diam. on either side, which was partially obstructed by 
 the pulleys, which were 59/i6 in. diam. It had eight blades, each of an 
 area of 45.49 sq. in. The discharge of air was through a conical tin tube 
 with sides tapered at an angle of 31/2 degrees. The actual area of opening 
 was 7% greater than given in the tables, to compensate for the vena con- 
 tracta. 
 
 In the last experiment, 89.5 sq. in. represents the actual area of the 
 mouth of the blower less a deduction for a narrow strip of wood placed 
 across it for the purpose of holding the pressure-gauge. In calculating the 
 volume of air discharged in the last experiment the value of vena contracta 
 is taken at 0.80. 
 
 Experiments were undertaken for the purpose of showing the results 
 obtained by running the same fan at different speeds with the discharge- 
 opening the same throughout the series. The discharge-pipe was a conical 
 tube 8 1/2 in. inside diam. at the end, having an area of 56.74 sq. in., which 
 is 7% larger than 53 sq. in.; therefore 53 sq. in., equal to 0.368 square feet, 
 is called the area of discharge, as that is the practical area by which the 
 volume of air is computed. 
 
FANS AND BLOWERS. 
 
 631 
 
 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. 
 
 
 m 
 
 c 
 
 
 °S 
 
 k^\ * 
 
 °'\1 
 
 8 b 
 
 ft3 . 
 
 i 
 
 | 
 
 d 
 
 pi 
 
 3 
 
 3^ 
 ® 
 
 
 H ft 
 
 
 H « 
 
 
 o 
 
 w 
 
 
 i 
 
 1* 
 
 -5 Pi 
 
 1 
 o 
 ft 
 
 1 
 
 o 
 
 •'o t *l 
 
 s 2 „ 
 
 +> ft 
 
 «-. PI .1. 
 
 la 
 
 ft 
 >> 
 
 > 
 
 0> 
 
 | 
 
 21 
 
 O h 
 
 • --0 
 
 ■in 
 
 ■s»-5 
 
 in 
 
 2 W 
 
 'o Sri 
 
 ■-2 » 
 g.S ft 
 
 II 
 
 o 
 '3 
 
 Ph 
 
 £ 
 
 > 
 
 w 
 
 ^> 
 
 > 
 
 o 
 
 > 
 
 H 
 
 H 
 
 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 
 
 20Q.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, and 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 wnen each is in good order. 
 
 For a given speed of fan \y diminution in the size of the blast-orifice 
 decreases the consumption ?t power and at the -same time raises the pres- 
 sure of the blast; but r; increases the consumption of power per unit of 
 orifice for a given pressure of blast. When the orifice has been reduced to 
 the normal si^e 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: in 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. 
 
632 
 
 AIR. 
 
 Capacity of Fans and Blowers. — The following 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.) 
 
 
 
 
 
 1/2 oz. pres- 
 
 3/4 oz. pres- 
 
 I oz. pres- 
 
 2 oz. pres- 
 
 
 
 
 
 sure. 
 
 sure. 
 
 sure. 
 
 sure. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 *° J 
 
 a 
 
 !s.s 
 
 
 & 
 
 h 
 
 
 & 
 
 h 
 
 
 3 
 
 i 
 
 
 a> 
 
 £ 
 
 6 
 
 
 ■ 0> 
 
 
 
 a . 
 
 
 
 a . 
 
 
 
 A . 
 
 
 
 ft . 
 
 
 f! 
 
 Ba 
 
 
 a) a- 
 
 as 
 
 - 1 
 
 id 
 
 Pm 
 
 £3 
 11 
 
 
 
 £3 
 
 31 
 
 tl 
 
 Jl 
 
 2 a 
 
 P4 
 
 £"3 
 2 c 
 
 ^ 
 
 (B 2 
 
 S a 
 
 3 
 
 p4 
 
 . a> 
 2 a 
 
 ■S'i 
 
 J Si 
 
 fc 
 
 Q 
 16 
 
 Q 
 10 
 
 985 
 
 O 
 
 pq 
 0.30 
 
 1200 
 
 
 
 0.56 
 
 PI 
 1390 
 
 O 
 
 pq 
 0.85 
 
 PI 
 
 1966 
 
 
 
 n 
 
 25 
 
 61/8 
 
 1,09 
 
 1,345 
 
 1,555 
 
 2,200 
 
 2.40 
 
 30 
 
 19 
 
 vy* 
 
 12 
 
 830 
 
 1,580 
 
 43 
 
 1012 
 
 1,940 
 
 0.80 
 
 1170 
 
 2,240 
 
 1.22 
 
 1655 
 
 3,175 
 
 3.46 
 
 35 
 
 22 
 
 81/8 
 
 14 
 
 715 
 
 2,155 
 
 59 
 
 876 
 
 2,635 
 
 1 08 
 
 1010 
 
 3,040 
 
 1.66 
 
 1430 
 
 4,310 
 
 4.70 
 
 40 
 
 25 
 
 93/8 
 
 16 
 
 630 
 
 2,820 
 
 77 
 
 772 
 
 3,450 
 
 1 41 
 
 1890 
 
 3.980 
 
 2 17 
 
 1260 
 
 5,640 
 
 6.15 
 
 43 
 
 28 
 
 107/s 
 
 18 
 
 563 
 
 3,560 
 
 97 
 
 689 
 
 4,360 
 
 1 78 
 
 1795 
 
 5,030 
 
 2 74 
 
 1125 
 
 7,140 
 
 7.79 
 
 50 
 
 31 
 
 123/ 8 
 
 20 
 
 508 
 
 4,400 
 
 1.20 
 
 622 
 
 5,390 
 
 2 20 
 
 1719 
 
 6,220 
 
 3 39 
 
 1015 
 
 8,820 
 
 9 63 
 
 55 
 
 34 
 
 131/m 
 
 22 
 
 464 
 
 5,330 
 
 1.45 
 
 567 
 
 6,525 
 
 2.66 
 
 1655 
 
 7,530 
 
 4.10 
 
 927 
 
 10,650 
 
 11.60 
 
 60 
 
 38 
 
 141/9 
 
 24 
 
 413 
 
 6,350 
 
 1.73 
 
 309 
 
 7,775 
 
 3 18 
 
 1587 
 
 8,960 
 
 4 89 
 
 830 
 
 12,700 
 
 13 85 
 
 70 
 
 44 
 
 131/8 
 
 27 
 
 373 
 
 7,440 
 
 2.02 
 
 459 
 
 9,120 
 
 3.72 
 
 1530 
 
 10,500 
 
 5.72 
 
 750 
 
 14,875 
 
 16,20 
 
 80 
 
 30 
 
 l61/ 2 
 
 29 
 
 328 
 
 10,050 
 
 2.75 
 
 402 
 
 12,100 
 
 4.94 
 
 1464 
 
 13,980 
 
 7.62 
 
 656 
 
 19,800 
 
 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- 
 
 
 
 -i 
 
 
 sure. 
 
 sure. 
 
 sure. 
 
 
 sure. 
 
 
 
 
 
 
 
 
 
 
 
 "S.9 
 
 _ft 
 
 0) 
 
 l-~ 
 
 
 ft . 
 
 i 
 
 
 a . 
 
 £ 
 
 
 0) 
 
 ft . 
 
 i 
 
 
 ft . 
 
 k 
 
 
 
 u s 
 
 fc'u 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -2"a5 
 
 ^T3 
 
 
 
 J Si 
 
 
 tin 3 
 
 A |R 
 
 
 «£"§ 
 
 -^ m 
 
 
 
 *% 
 
 "S 
 
 2 » 
 
 S3 £ 
 
 £* 
 
 ."2S 
 
 S.I 
 
 3 
 
 3*1 
 
 2 a 
 
 Pm 
 
 fl 
 
 3l 
 
 2 a 
 
 9 
 
 Pm 
 
 3l 
 
 ■36 
 
 S a 
 
 Pm 
 
 2 c 
 
 ■Si 
 
 la 
 
 fc 
 
 Q 
 
 £ 
 
 Q 
 
 K 
 
 O 
 
 « 
 
 rt 
 
 
 
 ffl 
 
 pej 
 
 
 
 pq 
 
 « 
 
 
 
 P3 
 
 1 
 
 8I/9 
 
 7. 
 
 41/9 
 
 1850 
 
 223 
 
 0.06 
 
 2270 
 
 273 
 
 0.11 
 
 2620 
 
 315 
 
 0.17 
 
 3210 
 
 386 
 
 0.32 
 
 ? 
 
 101/1 
 
 23/r 
 
 51/9 
 
 1535 
 
 332 
 
 0.09 
 
 1880 
 
 407 
 
 0.17 
 
 2170 
 
 469 
 
 0.26 
 
 2660 
 
 576 
 
 0.48 
 
 3 
 
 12 
 
 31/4 
 
 6 1/9 
 
 1310 
 
 464 
 
 13 
 
 1600 
 
 569 
 
 0.23 
 
 1830 
 
 656 
 
 0.36 
 
 2273 
 
 805 
 
 0.66 
 
 4 
 
 151/9 
 
 43/9 
 
 8 1/9 
 
 1015 
 
 705 
 
 22 
 
 1240 
 
 975 
 
 0.40 
 
 1433 
 
 1122 
 
 0.61 
 
 1760 
 
 1377 
 
 1.13 
 
 5 
 
 19 
 
 51/8 
 
 103/ 8 
 
 830 
 
 1185 
 
 32 
 
 1013 
 
 1450 
 
 0.59 
 
 1170 
 
 1675 
 
 0.92 
 
 1435 
 
 2055 
 
 1.68 
 
 6 
 
 221/9 
 
 61/. 
 
 17.3/8 
 
 700 
 
 1686 
 
 46 
 
 858 
 
 2065 
 
 0.84 
 
 990 
 
 2385 
 
 1.30 
 
 1213 
 
 2930 
 
 2.40 
 
 7 
 
 7.6 
 
 71/9 
 
 HI/4 
 
 606 
 
 7735 
 
 61 
 
 742 
 
 2740 
 
 1.12 
 
 838 
 
 3160 
 
 1.72 
 
 1030 
 
 3880 
 
 3.18 
 
 8 
 
 291/9 
 
 8I/0 
 
 161/1 
 
 534 
 
 7.910 
 
 79 
 
 654 
 
 3560 
 
 1 45 
 
 753 
 
 4110 
 
 2.24 
 
 928 
 
 5040 
 
 4.13 
 
 9 
 
 33 
 
 91/2 
 
 181/4 
 
 477 
 
 3660 
 
 1.00 
 
 585 
 
 4490 
 
 1.83 
 
 673 
 
 5175 
 
 2.82 
 
 823 
 
 6350 
 
 5.20 
 
 Note: This table also applies to Type V, cast-iron exhaust fans. 
 
FANS AND BLOWERS. 
 
 633 
 
 Steel Pressure Blowers for Cupolas (Average Application). 
 
 (American Blower Co., 1909.) 
 
 ^ 
 
 .15 
 "o 
 
 s 
 
 141/2 
 
 .ft 
 
 ft.S 
 
 -S 
 
 S 
 
 II 
 
 o 
 
 !l 
 
 5 
 
 3 
 O 
 
 < 
 
 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 
 
 6 
 
 H.P. 
 
 const, 
 at 1000 
 cu. ft. 
 
 1.242 
 
 1.86 
 
 2.48 
 
 3.10 
 
 3.73 
 
 4.35 
 
 4.95 
 
 5.58 
 
 1 
 
 13/8 
 
 3.80 
 
 53/4 
 
 0.18 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 1960 
 361 
 0.45 
 
 2400 
 434 
 0.81 
 
 2770 
 500 
 1.24 
 
 3095 
 560 
 1.74 
 
 3390 
 610 
 
 2.28 
 
 3666 
 665 
 2.89 
 
 3915 
 708 
 3.51 
 
 4150 
 752 
 4.20 
 
 2 
 
 17 
 
 15/8 
 
 4.45 
 
 63/ 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 
 
 2895 
 843 
 3.15 
 
 3130 
 916 
 3.99 
 
 3340 
 978 
 4.84 
 
 3540 
 1038 
 5.79, 
 
 3 
 
 191/2 
 
 17/8 
 
 5.11 
 
 73/4 
 
 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 
 
 4 
 
 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 
 6 
 7 
 8 
 9 
 
 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 
 
 27 
 
 27/8 
 33/8 
 
 7.06 
 8.39 
 
 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 
 
 32 
 
 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 
 
 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. CO 
 
 1625 
 4460 
 24.90 
 
 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 
 
 10 
 
 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 
 
 52 
 
 53/8 
 
 13.6 
 
 191/4 
 
 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 
 
 12 
 
 57 
 
 57/8 
 
 14.92 
 
 21 
 
 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 
 
634 
 
 Steel Pressure Blowers for Cupolas (Average Application).— 
 
 Continued. 
 
 
 "a3 
 
 CD 
 
 J3 
 
 
 
 S.S 
 
 3 
 
 Oz. 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 
 
 In. 
 
 17 28 
 
 19,02 
 
 20.75 
 
 22.5 
 
 24.22 
 
 25.95 
 
 27.66 
 
 
 
 P-fl 
 
 d"cu 
 5 ® 
 
 o g_ 
 
 *o£ 
 
 
 
 
 
 
 
 
 
 
 H.P. 
 
 
 
 
 
 
 
 
 6 
 
 <3 
 5 
 
 T3 
 
 5 
 
 
 .g'S 
 
 Q 
 
 
 const, 
 at 1000 
 cu. ft. 
 
 6.20 
 
 6.82 
 
 7.44 
 
 8.07 
 
 8.69 
 
 9.30 
 
 9.92 
 
 
 17 
 
 15/8 
 
 4.45 
 
 63/ 4 
 
 0.2485 
 
 R.P.M. 
 C.F. 
 H.P. 
 
 3740 
 1093 
 6.78 
 
 3920 
 1148 
 7.83 
 
 4090 
 1196 
 8.9 
 
 
 
 
 
 ?. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R.P.M. 
 
 3255 
 
 3415 
 
 3570 
 
 3710 
 
 3955 
 
 3985 
 
 4120 
 
 3 
 
 191/-, 
 
 17/8 
 
 5.11 
 
 73/4 
 
 0.327 
 
 C.F. 
 
 1440 
 
 1510 
 
 1575 
 
 1642 
 
 1700 
 
 1762 
 
 1820 
 
 
 
 
 
 
 
 H.P. 
 
 8.93 
 
 10.3 
 
 11.72 
 
 13.26 
 
 14.75 
 
 16.4 
 
 18.05 
 
 
 
 
 
 
 
 R.P.M. 
 
 2890 
 
 3030 
 
 3163 
 
 3290 
 
 3420 
 
 3535 
 
 3650 
 
 4 
 
 22 
 
 21/8 
 
 5.76 
 
 83/4 
 
 0.4176 
 
 C.F. 
 
 1840 
 
 1930 
 
 2012 
 
 2095 
 
 2175 
 
 2250 
 
 2325 
 
 
 
 
 
 
 
 H.P. 
 
 11.40 
 
 13.16 
 
 14.96 
 
 16.9 
 
 18.9 
 
 20.9 
 
 23.1 
 
 
 
 
 
 
 
 R.P.M. 
 
 2595 
 
 2720 
 
 2845 
 
 2960 
 
 3075 
 
 3180 
 
 3280 
 
 5 
 
 24 V, 
 
 23/ 8 
 
 6.41 
 
 93/ 4 
 
 0.519 
 
 C.F. 
 
 2280 
 
 2395 
 
 2500 
 
 2605 
 
 2700 
 
 2800 
 
 2885 
 
 
 
 
 
 
 
 H.P. 
 
 14.13 
 
 16.33 
 
 18.6 
 
 21.05 
 
 23.45 
 
 26.05 
 
 23.66 
 
 
 
 
 
 
 
 R.P.M. 
 
 2355 
 
 2470 
 
 2580 
 
 2685 
 
 2790 
 
 2885 
 
 2980 
 
 6 
 
 27 
 
 27/8 
 
 7.06 
 
 103/4 
 
 0.63 
 
 C.F. 
 
 2770 
 
 2910 
 
 3033 
 
 3165 
 
 3280 
 
 3395 
 
 3500 
 
 
 
 
 
 
 
 H.P. 
 
 17.18 
 
 19.85 
 
 22.6 
 
 25.55 
 
 28.50 
 
 31.55 
 
 34.7 
 
 
 
 
 
 
 
 R.P.M. 
 
 1983 
 
 2080 
 
 2170 
 
 2260 
 
 2345 
 
 2430 
 
 2510 
 
 7 
 
 32 
 
 33/s 
 
 8.39 
 
 121/^ 
 
 0.852 
 
 C.F. 
 
 3750 
 
 3930 
 
 4110 
 
 4276 
 
 4430 
 
 4590 
 
 4730 
 
 
 
 
 
 
 
 H.P. 
 
 23.25 
 
 26.80 
 
 30.6 
 
 34.5 
 
 38.5 
 
 42.7 
 
 47. 
 
 
 
 
 
 
 
 R.P.M. 
 
 1715 
 
 1800 
 
 1880 
 
 1955 
 
 2030 
 
 2100 
 
 2170 
 
 8 
 
 37 
 
 37/8 
 
 9.70 
 
 14 
 
 1.069 
 
 C.F. 
 
 4700 
 
 4930 
 
 5150 
 
 5360 
 
 5560 
 
 5760 
 
 5940 
 
 
 
 
 
 
 
 H.P. 
 
 29.15 
 
 33.66 
 
 38.33 
 
 43.25 
 
 48.30 
 
 53.55 
 
 59. 
 
 
 
 
 
 
 
 R.P.M. 
 
 1515 
 
 1590 
 
 1660 
 
 1728 
 
 1792 
 
 1855 
 
 1916 
 
 9 
 
 42 
 
 43/ 8 
 
 10.98 
 
 16 
 
 1.396 
 
 C.F. 
 
 6150 
 
 6450 
 
 6730 
 
 7010 
 
 7270 
 
 7525 
 
 7760 
 
 
 
 
 
 
 
 H.P. 
 
 38.15 
 
 44.00 
 
 50.15 
 
 56.60 
 
 63.2 
 
 70. 
 
 77. 
 
 
 
 
 
 
 
 R.P.M. 
 
 1352 
 
 1418 
 
 1480 
 
 1540 
 
 1600 
 
 1655 
 
 1710 
 
 10 
 
 47 
 
 47/ 8 
 
 12.30 
 
 171/9 
 
 1.67 
 
 C.F. 
 
 7350 
 
 7715 
 
 8055 
 
 8390 
 
 8700 
 
 9010 
 
 9300 
 
 
 
 
 
 
 
 H.P. 
 
 45.60 
 
 52.66 
 
 60. 
 
 67.66 
 
 75.6 
 
 83.9 
 
 92.25 
 
 
 
 
 
 
 
 R.P.M. 
 
 1222 
 
 1282 
 
 1340 
 
 1393 
 
 1447 
 
 1498 
 
 1546 
 
 11 
 
 52 
 
 53/8 
 
 13.6 
 
 191/-) 
 
 2.02 
 
 C.F. 
 
 8900 
 
 9330 
 
 9750 
 
 10140 
 
 10520 
 
 10890 
 
 11220 
 
 
 
 
 
 
 
 H.P. 
 
 55.20 
 
 63.6 
 
 72.5 
 
 82. 
 
 91.5 
 
 101.2 
 1363 
 
 111.33 
 
 
 
 
 
 
 
 R.P.M. 
 
 1113 
 
 1168 
 
 1220 
 
 1270 
 
 1318 
 
 1410 
 
 12 
 
 57 
 
 57/ 8 
 
 14 92 
 
 21 
 
 2.405 
 
 C.F. 
 
 10580 
 
 11100 
 
 11600 
 
 12080 
 
 12520 
 
 12960 
 
 13380 
 
 
 
 
 
 
 
 H.P. 
 
 65.5 
 
 75.70 
 
 86.33 
 
 97.5 
 
 109 
 
 120.5 
 
 132.75 
 
 Cai 
 
 ition in Regard to 
 
 Use of Fan and Blower Tables. — Many en- 
 
 gineei 
 their 
 
 s report that some 
 fans and underestima 
 
 manufacturers' tables overrate the capacity of 
 te the horse-power required to drive them. In 
 
 some 
 
 cases the complaints 
 
 may be due to restricted air outlets, long and 
 
 crook 
 
 gd pipes, slipping of 
 
 belts, too small engines, etc. It may also be 
 
 due t 
 
 d the fact that the \ 
 
 olumes are stated without being accompanied 
 
 1 
 
 sy in 
 
 form 
 
 ation 
 
 as t 
 
 o the 
 
 maintai 
 
 tied r 
 
 esista 
 
 nee, a 
 
 nd th 
 
 3 volu 
 
 mes gi 
 
 ven 
 
FANS AND BLOWEKS. 
 
 635 
 
 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-power 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 outlet, 
 
 inches. 
 
 Approx. 
 weight, 
 pounds.* 
 
 000 
 
 1 to 5 
 
 200 to 1000 
 
 13/s 
 
 40 
 
 00 
 
 5 to 25 
 
 375 to 800 
 
 11/2 
 
 80 
 
 
 
 25 to 45 
 
 370 to 800 
 
 21/2 
 
 140 
 
 1 
 
 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 
 
 8,500 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 
 
 Rated H.P. 28 42 57 72 86 100 116 130 144 159 173 187 202 
 
 Total pres- 
 sure, oz 10.2 11.4 11.912.0 11.9 11.410.910.3 9.7 9.1 8.5 7.9 7.2 
 
 Static pres- 
 sure, oz ..10.211.2 11.611.411.0 10.2 9.2 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 
 says : 
 
 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 
 
636 
 
 AIR. 
 
 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 Pitottube 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, and 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.) 
 
 
 © • 
 P-..S 
 
 03 >> 
 
 -T3 
 
 .9 
 
 2g" 
 
 °.S ° 
 
 "£.9 
 
 a 
 
 
 t a 1 
 
 "S«4-l 
 
 03 6* 
 a> 03 
 
 "- 1 i i 1 
 
 3 a- 
 
 
 3£ 
 
 £-2 
 
 3! a 
 
 "o 
 
 6 
 
 i< 
 
 las-? 
 
 ;5T2 
 
 SUO 
 
 gffl 
 
 is 
 
 «3 
 
 gJ« 
 
 "jscs 
 
 
 S 
 
 £"* 
 
 48 
 
 H 
 
 w 
 
 £ 
 
 A 
 
 % 
 
 i 
 
 < 
 
 <~ 
 
 ^ 
 
 6 
 
 3 
 
 56 
 
 11" 
 
 4 
 
 10" 
 
 .23 
 
 .123 
 
 .11 
 
 .12 
 
 3" 
 
 9 
 
 41/2 
 
 48 
 
 127 
 
 V 4" 
 
 6 
 
 v y 
 
 .49 
 
 .349 
 
 .25 
 
 .35 
 
 41/4" 
 
 12 
 
 6 
 
 64 
 
 226 
 
 V 9" 
 
 8 
 
 V 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 
 
 8 1/2" 
 
 21 
 
 101/2 
 
 64 
 
 693 
 
 y a" 
 
 14 
 
 2' 10" 
 
 2.40 
 
 1.87 
 
 1.34 
 
 1.87 
 
 10" 
 
 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 
 
 y 7" 
 
 4.59 
 
 3.11 
 
 2.25 
 
 3.14 
 
 13" 
 
 30 
 
 15 
 
 64 
 
 1413 
 
 4' 7" 
 
 20 
 
 if o" 
 
 5.58 
 
 3.83 
 
 2.78 
 
 3.83 
 
 141/2" 
 
 36 
 
 18 
 
 64 
 
 2036 
 
 5' 6" 
 
 24 
 
 4' 10" 
 
 7.87 
 
 5.50 
 
 4.00 
 
 5.58 
 
 17" 
 
 42 
 
 21 
 
 64 
 
 2770 
 
 6' 5" 
 
 28 
 
 5' 7" 
 
 10.56 
 
 7.47 
 
 5.44 
 
 7.47 
 
 20" 
 
 48 
 
 24 
 
 64 
 
 3617 
 
 T 3" 
 
 32 
 
 6' 5" 
 
 13.6 
 
 9.79 
 
 7.11 
 
 9.85 
 
 23" 
 
 54 
 
 27 
 
 64 
 
 4578 
 
 8' 2" 
 
 36 
 
 T 3" 
 
 17.0 
 
 12.3 
 
 9.00 
 
 12.3 
 
 26" 
 
 60 
 
 30 
 
 64 
 
 5652 
 
 9' 1" 
 
 40 
 
 8' 0" 
 
 20.9 
 
 15.2 
 
 11.11 
 
 15.3 
 
 281/ 2 " 
 
 66 
 
 33 
 
 64 
 
 6839 
 
 9/ ir 
 
 44 
 
 8' 10" 
 
 25.2 
 
 18.4 
 
 13.41 
 
 18.3 
 
 311/2" 
 
 72 
 
 36 
 
 64 
 
 8144 
 
 1C 10" 
 
 43 
 
 9' 7" 
 
 29.8 
 
 22.2 
 
 16.00 
 
 22.3 
 
 341/2" 
 
 Sirocco or Multivane 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. 
 static pressure, deduct 28.8%; for velocity pressure, deduct 71.2%. 
 
 For 
 
 si 
 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 6 
 
 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 
 
 9 
 
 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 
 
 12 
 
 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 
 3,090 
 1,444 
 
 3.65 
 4,450 
 1,204 
 
 5.25 
 6,060 
 1,032 
 
 7.15 
 
 7.900 
 
 904 
 
 9.3 
 
 2,170 
 1,980 
 3.05 
 
 15 
 
 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 
 3,980 
 1,076 
 
 3.75 
 
 3,390 
 
 1,580 
 
 4.8 
 
 18 
 
 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 
 
 4,880 
 
 1,320 
 
 6.9 
 
 21 
 
 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 
 
 6,620 
 
 1,130 
 
 9.4 
 
 24 
 
 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 
 
 8,680 
 990 
 12.2 
 
 27 
 
 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 
 
 30 
 
 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 
 
 36 
 
 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 
 
 42 
 
 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 
 
 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 
 
 48 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 10,000 
 143 
 1.18 
 
 14,150 
 202 
 3.32 
 
 17,350 
 
 248 
 6.10 
 
 20,000 
 286 
 9.40 
 
 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 
 
 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. 
 
 60 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 15,650 
 114 
 1.84 
 
 22,100 
 161 
 5.20 
 
 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 
 
 66 
 
 Cu. ft. 
 R.P.M. 
 B.H.P. 
 
 18,950 
 
 104 
 
 2.23 
 
 26,800 
 
 147 
 
 6.30 
 
 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 
 
 72 
 
 Cu. ft. 
 R.P.M. 
 B.H.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 
 
 78,000 
 330 
 110. 
 
 78 
 
 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. 
 
 84 
 
 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 
 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. 
 
638 
 
 AIR. 
 
 best results. The vanes, measured radially, have a depth 1/ie the fart 
 diameter. Axially, 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 as 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. 8 in. diam., double inlet, direct- 
 coupled to a 3-phase motor. Average of three tests: Revs, per min., 184; 
 peripheral speed, 6,705 ft. per min.; water-gauge in fan drift and in main 
 drift, 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%. 
 
 The Sturtevant Multivane Fan. A modification of the Sirocco fan 
 has been developed by the B. F. Sturtevant Co., in which the blades are 
 made with spoon-shaped serrations along their iength. The advantage 
 claimed for this construction is that the air is discharged more evenly 
 along the length of the blade. The following table shows the sizes, capac- 
 ities and horse-power required by the fan. 
 
 Sizes, Capacities and Horse-power of Multivane Fans. 
 
 (B. F. Sturtevant Co., 1909.) 
 
 Height 
 of Fan 
 
 Resistance, 1/2 In. 
 
 Resistance, 1 In. 
 
 Resist 
 
 ance, 1 1/2 In. 
 
 
 
 
 
 
 
 
 Casing 
 
 
 
 
 
 
 
 
 1 
 
 inches * 
 
 Vol. 
 
 R.P.M. 
 
 H.P. 
 
 Vol. 
 
 R.P.M. 
 
 H.P. 
 
 Vol. 
 
 R.P.M. 
 
 H.P. 
 
 30 
 
 1,800 
 
 695 
 
 0.45 
 
 2,560 
 
 985 
 
 1.2 
 
 3,100 
 
 1,200 
 
 2.3 
 
 35 
 
 2,600 
 
 580 
 
 0.65 
 
 3,700 
 
 820 
 
 1.8 
 
 4,500 
 
 1,000 
 
 3.4 
 
 40 
 
 3,550 
 
 500 
 
 0.90 
 
 5,000 
 
 700 
 
 2.5 
 
 6,200 
 
 860 
 
 4.5 
 
 50 
 
 4,620 
 
 435 
 
 1.15 
 
 6,500 
 
 615 
 
 3.3 
 
 8,000 
 
 750 
 
 6.0 
 
 60 
 
 7,220 
 
 350 
 
 1.8 
 
 10,200 
 
 490 
 
 5.0 
 
 12,500 
 
 600 
 
 9.3 
 
 70 
 
 10,400 
 
 290 
 
 2.6 
 
 14,700 
 
 410 
 
 7.3 
 
 18,000 
 
 500 
 
 13.4 
 
 80 
 
 14,000 
 
 250 
 
 3.5 
 
 20,000 
 
 350 
 
 10 
 
 24,500 
 
 430 
 
 18.0 
 
 100 
 
 23,500 
 
 190 
 
 5.8 
 
 33,300 
 
 275 
 
 16.5 
 
 40,800 
 
 335 
 
 30.0 
 
 120 
 
 35,000 
 
 160 
 
 8.8 
 
 49,700 
 
 225 
 
 25 
 
 61,000 
 
 275 
 
 45.0 
 
 150 
 
 48,800 
 
 135 
 
 12.0 
 
 69,000 
 
 190 
 
 34 
 
 85,000 
 
 233 
 
 63.0 
 
 170 
 
 65,000 
 
 115 
 
 16.0 
 
 92,000 
 
 165 
 
 46 
 
 112,500 
 
 200 
 
 85.0 
 
 * Full housing. Bottom horizontal discharge. 
 
 The above table gives the volumes and horse-powers of Sturtevant 
 multivane fans operating against a continuously maintained resistance, 
 handling air at 65° F. The table is compiled for single-inlet fans, but 
 when used with double inlet the volumes will be considerably increased 
 (about 15-20%), and the power will also be greater (about 25-35%). It 
 is possible to handle any of the volumes given against any stated pressure 
 with quite an appreciable saving in power as compared with the table 
 horse-power by using a larger fan, and by so doing obtaining lower veloci- 
 
FANS AND BLOWERS. 639 
 
 ties through the fan. It is also possible to handle any stated volume 
 against any pressure given in the table with a considerably smaller fan, 
 but when this is done it requires an increase in horse-power due to the 
 greater velocity, which is increased in proportion to the decrease in size 
 and to the lower mechanical efficiency of an overloaded fan. By main- 
 tained resistance is meant a static pressure existing in the air after it 
 leaves the fan outlet, if the fan is applied to a blowing system. With the 
 suction system, maintained resistance is the static suction existing in the 
 duct just outside the fan inlet. If the fan is so placed in the system that 
 there is resistance to the flow of air on both inlet and outlet, the maintained 
 resistance against which the fan operates is the sum of the static suction 
 existing in the air just before entering the inlet and the static pressure in 
 the air just outside the fan outlet. In ordinary draw-through heating 
 systems a maintained suction is encountered in the fan inlet due to the 
 resistance of the heater, and the maintained pressure is created in the fan 
 outlet due to the piping system. The volumes given are computed from 
 tests in which the average velocity over rectangular or circular pipes is 
 taken as 91% of that velocity (not velocity head) which is read at the 
 center of the pipe by means of the Pitot tube. This method of computing 
 velocity is conservative, especially for pipes having large sectional area. 
 
 High-Pressure Centrifugal Fans. (See page 620.) 
 Methods of Testing Fans. 
 
 (Compiled by B. F. Sturtevant Co., 1909.) 
 
 Various methods are used in testing centrifugal fans, some of which, 
 being crude, credit fans with performances somewhat different from the 
 true performance. Some of the formulae used in determining the per- 
 formances of a fan are given below: 
 
 h v — Velocity head, in. of water; h t — Total or Impact head, in. of 
 water; h s = Static head, in. of water; Q = Cu. ft. per min.; v— Velocity, 
 ft. per min.; w = Density of air, lb. per cu. ft.; A = Area of outlet pipe, 
 sq. ft.; A.H.P S . = Air horse-power crediting the fan with the energy due 
 to static pressure only; A.H.Pj. = Air horse-power, crediting the fan with 
 both the energy due to static pressure and the kinetic energy in the dis- 
 charge; B.H,P.= Brake horse-power. 
 
 r^. «?-io»7l/5 : 
 
 A.H.P S . = Q X h s X 0.0001575; A.H.P^. ~QXh t X 0.0001575. 
 
 Mechanical Efficiency = A.H.P.-f-B.H.P. 
 Volumetric Efn'y= Volume per Revolution -f- Cubical Contents of wheel: 
 Anemometer Method. Anemometers are subject to considerable error 
 as they are very delicate and must be handled with care. Should they be 
 placed in a draft where the velocity is much over 1000 ft. per min. they 
 are apt to be damaged by bending the blades. The methods of calibrating 
 these instruments are faulty, and give some chance of error, even though 
 the instrument be in the same condition as when calibrated. Unless it 
 is frequently calibrated, the instrument may not be true to its calibra- 
 tion curve, which is often a source of considerable error. An anemometer 
 is seldom adapted to taking readings at the fan outlet, or within pipes, as 
 the velocity in most cases exceeds the limitations of the instrument. 
 Therefore, readings are usually taken at a point where the velocity is 
 lower, and consequently over areas of various shapes with unknown co- 
 efficients, thus introducing another source of error. Unless the flow of 
 air is constant, faulty readings are obtained, due to the inertia of the 
 instrument, which results in the fan being credited with a volume greater 
 than the true volume. 
 
640 air. 
 
 Water-Gauge Readings at End of Tapered Cone. In this method, 
 cones are placed on the fan outlet, or on the end of a short outlet pipe. 
 The readings at the end of the cone vary widely, due to the large number 
 of variable eddies. The pressure reading at the end of the cone is a total 
 of two components, static pressure and velocity pressure. Unless the 
 static pressure is deducted from the total pressure the true velocity pressure 
 is not obtained. 
 
 Air-tight Room with Sliding Door. This method consists of the fan dis- 
 charging its air into a closed room whose outlet is a sliding door. In this 
 method, the readings generally take into account not only the volumetric 
 performance but also the static pressure in the room, against which the 
 fan delivers air. All tests by this method must be corrected for leakage of 
 air from the room, the leakage factor being much larger than would be sup- 
 posed. A variable coefficient of orifice is encountered, since at no two 
 Sositions of the sliding door is either the area or shape of orifice the same, 
 headings taken at the door, by anemometers, are subject to the errors of 
 these instruments. If water-gauge readings are taken at the door, the 
 results are in error if it is assumed that all pressure at the door is velocity 
 pressure. Static readings should be made at each station and deducted 
 from the total observed pressure in order to get the velocity head. Even 
 then it is difficult to get a true static reading at the door, as the stream 
 lines are not all perpendicular to the plane of the orifice. 
 
 Pitot Tube in Center of Discharge Pipe. This method requires a dis- 
 charge pipe of the same size as the outlet of the fan. In the center of 
 this pipe and at such a distance from the fan outlet that eddies are prac- 
 tically eliminated, is placed a Pitot tube. The discharge pipe is of such 
 length beyond the tube that when restricted at its end, the stream lines in 
 the vicinity of the tube are not materially affected. By this method the 
 static and total pressures are observed with considerable accuracy. The 
 velocity pressure is determined by subtracting the static pressure from 
 the total pressure. By applying a proper coefficient to the readings at 
 the center the average velocity over the full discharge area is obtained. 
 It is possible to make a more complete test by placing several Pitot tubes 
 in the discharge pipe at different points in a cross-section, thereby obtain- 
 ing an average. But it is found that by taking readings at a distance of 
 eight or ten diameters from the fan outlet very good results are obtained 
 with one tube placed in the center of the section of the pipe, whose read- 
 ings are corrected by a proper coefficient. For medium-size pipes it is 
 found that a coefficient of 0.91 applied to the velocity read at the center 
 of the discharge pipe gives good and conservative results. [Other author- 
 ities give 0.87 as the value of this coefficient. See Pitot Tube, under 
 Illuminating Gas.] 
 
 I Experiments with the tapered cone method and the Pitot tube in the 
 center of pipe method show that the former credits a fan with greater 
 volume than the latter, and also show that there is a variable relation 
 between these two methods as regards the volume of air credited to the 
 fan when it is handling a certain volume of air. The difference in volumes 
 credited the fan becomes greater as the size of the discharge pipe increases. 
 In tests on two fans of different sizes, but of symmetrical design, the Pitot 
 tube in the center of the pipe will record symmetrical results under given 
 conditions, while with the tapered cone the results obtained with the 
 larger fan and larger discharge pipe are beyond those which would have 
 been expected from the symmetry of the fan. 
 
 From the above formulas the air horse-power is a function of two vari- 
 ables, volume and pressure. Opinions vary as to the pressure which 
 should be credited to the fan. It is claimed that 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. It is also claimed that the fan should also be credited with the 
 kinetic energy in the air in the discharge pipe or with the difference be- 
 tween the static pressure in the medium from which the fan is drawing air 
 and the total or impact pressure in the discharge pipe. Efficiencies de- 
 termined by crediting the fan with the former pressure may be called 
 static efficiencies, and those determined by crediting the fan with the 
 latter pressure may be called impact efficiencies. 
 
 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 
 
FANS AND BLOWERS. 641 
 
 the fan, for the purpose of determining static efficiency, the fan is often 
 erroneously credited with a pressure equal to the difference between the 
 medium into which the fan is discharging and the negative static pressure 
 in the pipe leading to the fan inlet, whereas it should be credited only with 
 the difference between the static pressure in the discharging medium and 
 the impact pressure in the inlet pipe. The static suction has a greater 
 negative value than the impact pressure at the same point. -which is the 
 result of the reduction of pressure caused by the air entering the system 
 changing from rest, or zero velocity, to a finite velocity which it has at the 
 point of measurement. 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 read- 
 ing 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. 
 
 From the above methods it is seen that volumetric and mechanical 
 efficiencies of wide variety are obtained, and that where a test is of any 
 importance it is essential that it be made on the most correct lines. Using 
 a Pitot tube in the center of the pipe through which air flows, affords the 
 best means of getting the true pressures as a whole and their separate 
 components, and, consequently, is most accurate in determining the 
 
 JE33- 
 
 Fig. 140 
 
 volume flowing. Fig. 140 shows diagrammat cally the method of test 
 where the Pitot tube is used in the center of the discharge pipe. It also 
 shows how readings could be taken by the cone method at the end of a 
 discharge pipe. The details of the Pitot tube in what is considered its 
 best form are also shown. The impact or total pressure is obtained at the 
 end of the horizontal tube nearest the fan, and read by a water gauge 
 connected to the vertical tube communicating with this point. The 
 static pressure is obtained at the slots in the side of the outer horizontal 
 tube which communicates with the second vertical tube, to which a water 
 gauge may be connected. 
 
 Efficiency of Fans. — Much useful information on the theory and 
 practice of fans and blowers, with results of tests of various forms, will be 
 found in Heating and Ventilation, June to Dec. 1897, in papers by Prof. 
 R. C. Carpenter and Mr. W. G. Walker. It is shown by theory that the 
 volume of air delivered is directly proportional to the speed of rotation, 
 that the pressure varies as the square of the speed, and that the horse- 
 power varies as the cube of the speed. For a given volume of air moved 
 the horse-power varies as the square of the speed, showing the great advan- 
 tage of large fans at slow speeds over small fans at high speeds delivering 
 the same volume. The theoretical values are greatly modified by varia- 
 tions in practical conditions. Professor Carpenter found that with three 
 fans running at a speed of 6200 ft. per minute at the tips of the vanes, and 
 
642 
 
 AIR. 
 
 an air-pressure of 2 1/2 in. of water column, the mechanical efficiency, or the 
 horse-power of the air delivered divided by the power required to drive the 
 fan, ranged from 32% to 47%, under different conditions, but with slow 
 speeds it was much less, in some cases being under 20%. Mr. Walker in 
 experiments on disk fans found efficiencies ranging all the way from 7.4% 
 to 43%, the size of the fans and the speed being constant, but the shape and 
 angle of the blades varying. It is evident that there is a wide margin for 
 improvements in the forms of fans and blowers, and a wide field for experi- 
 ment to determine the conditions that will give maximum efficiency. 
 
 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.) 
 
 .si 
 
 
 
 .5 • 
 
 u 
 
 ft 
 
 f 8g 
 
 s 
 
 ftp, 
 
 6" 
 ■a! 
 
 a 
 
 1% -a 
 
 J3 • g 
 
 * a 
 so"! 
 
 ftft 
 
 g! 
 
 £§.S 
 
 u 
 
 
 J2 K .ts 
 
 j ? d c 
 
 OCMO 
 
 ftg 
 
 is « 
 
 o2'g 
 
 
 
 lis 
 
 11 
 
 2 • & 
 
 " M > a 
 
 0+3 ^ 
 
 S2.>* 
 a mo 
 
 ^ . 
 
 is.s 
 
 S2 3 
 
 fc 
 
 Ph 
 
 > 
 
 > 
 
 w . 
 
 M 
 
 fin 
 
 > 
 
 > 
 
 ffl 
 
 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/s 
 
 7.932 
 
 55.08 
 
 0.03568 
 
 0.6476' 
 
 5/8 
 
 1.080 
 
 4,084 
 
 28.36 
 
 0.00483 
 
 0.1703 
 
 Vr/l 
 
 8,136 
 
 56.50 
 
 0.03852 
 
 0.6818 
 
 3/4 
 
 1.296 
 
 4.473 
 
 31.06 
 
 0.00635 
 
 0.2044 
 
 25/s 
 
 8,334 
 
 57.88 
 
 0.04144 
 
 0.7160 
 
 7/8 
 
 1.512 
 
 4.830 
 
 33.54 
 
 0.00800 
 
 0.2385 
 
 23/4 
 
 8.528 
 
 59.22 
 
 0.04442 
 
 0.7500 
 
 1 
 
 1.728 
 
 5.162 
 
 35.85 
 
 0.00978 
 
 0.2728 
 
 27/8 
 
 8,718 
 
 60.54 
 
 0.04747 
 
 0.7841 
 
 U/8 
 
 1.944 
 
 5.473 
 
 38.01 
 
 0.01166 
 
 0.3068 
 
 3 
 
 8,903 
 
 61.83 
 
 0.05058 
 
 0.8180 
 
 1V4 
 
 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 
 
 H/2 
 
 2.59? 
 
 6.315 
 
 43.86 
 
 0.01794 
 
 0.4090 
 
 33/s 
 
 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 
 
 0.06710 
 
 0.9887 
 
 17/8 
 
 3.240 
 
 7,055 
 
 49.00 
 
 0.02505 
 
 0.5112 
 
 33/4 
 37/ 8 
 
 9,938 
 10,100 
 
 69.01 
 70.14 
 
 0.07058 
 0.07412 
 
 1.0227 
 1 .0567 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (1) 
 
 (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. 
 
FANS AND BLOWERS. 
 
 643 
 
 Pipe Lines for Fans and Blowers. — In installing fans 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 
 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.) 
 
 0, 
 
 h 
 a 
 
 '3 
 
 Length of Pipe in Feet. 
 
 c 
 o 
 
 20 1 40 1 
 
 60 1 80 1 100 1 120 1 140 
 
 "8 u 
 
 2 ~ 
 
 43g 
 
 D 
 
 Diameter of Pipe with Drop of 
 
 §1 
 
 1/4 
 
 1/2 
 
 1/4 
 
 1/2 
 
 V4 
 
 1/2 
 
 1/4 
 
 1/2 
 
 1/4 
 
 1/2 
 
 1/4 
 
 1/2 
 
 1/4 
 
 1/2 
 
 H 
 
 a 
 23 
 
 Oz. 
 6 
 
 Oz. 
 5 
 
 Oz. 
 7 
 
 Oz. 
 6 
 
 Oz. 
 7 
 
 Oz. 
 6 
 
 Oz. 
 8 
 
 Oz. 
 7 
 
 Oz. 
 9 
 
 Oz. 
 8 
 
 Oz. 
 9 
 
 Oz. 
 8 
 
 Oz. 
 9 
 
 Oz. 
 
 1 
 
 500 
 
 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 
 
 IS 
 
 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 
 
644 air. 
 
 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 1/2 oz., a 14-in. pipe will be required. If it is 
 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 Murguein " 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 
 formulae 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; 
 
 = 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 V . 
 
 Q = 0.65aV; V = ^Ygh; Q = 0.65a ^ / 2~gh; 
 
 a = . = equivalent orifice of mine; 
 
 0.65 vigft 
 
 or, reducing to water-gauge in inches and quantity in thousands of cubic 
 feet per minute, 
 
 0.403 Q 
 Vw.G. ; 
 
 •-V* 
 
 O 2 
 
 - — — = equivalent orifice of machine. 
 
 65 2 h 2 g 
 
 The theoretical depression which can be produced by any centrifugal 
 ventilator is double that due to its tangential speed. The formula 
 
 77 = Tl _ YL 
 2o 2g' 
 
 in which T is 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 2 -*■ 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* 
 
MINE-VENTILATING FANS. 
 
 645 
 
 half that 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. 
 
 The following table shows a few results, selected from Mr. Norris's paper, 
 giving the range of efficiency which may be expected under different cir- 
 cumstances. Details of these and other fans, with diagrams of the results, 
 are given in the paper. 
 
 Experiments on Mine-Ventilating Fans. 
 
 
 05 
 
 ?9 
 
 i 
 
 05 . 
 
 as 
 
 "3 
 
 *S 45 
 
 3 c 
 
 
 
 °1 
 
 05 05 
 
 u 
 
 "'S.& 
 
 «H 05 . 
 
 
 05 
 
 i05 
 
 E.a 
 
 O M 
 
 4 . 
 
 82 
 
 11 
 
 
 .2«r 
 
 Is 
 
 m O 
 03 > 
 
 
 -J 
 
 
 
 tj'o 
 
 ^ 
 
 a 05* 
 
 05 g 
 
 03 
 
 3 3 
 
 o.a 
 
 ■si 
 
 "a 
 
 3 a 
 
 3 a 
 
 11 
 
 2<S 
 
 -2 a 
 
 3 ft 05 
 
 
 B.t! 
 
 O c3 
 
 3ft 
 
 05 05 
 
 "3 c 
 
 Sfi'Sb 
 
 o-o.X 
 
 u< 
 
 
 Ph 
 
 o 
 
 O 
 
 
 
 
 
 K 
 
 M 
 
 H 
 
 W 
 
 r 
 
 5517 
 
 236,684 
 
 2818 
 
 3040 
 
 4290 
 
 1.80 
 
 67.13 
 
 88.40 
 
 75.9 
 
 ■* 
 
 A 
 
 100 
 
 6282 
 
 336,862 
 
 3369 
 
 3040 
 
 5393 
 
 2.50 
 
 132.7C 
 
 155.43 
 
 85.4 
 
 L« 
 
 
 111 
 
 6973 
 
 347,396 
 
 3130 
 
 3040 
 
 5002 
 
 3.20 
 
 175.17 
 
 209.64 
 
 83.6 
 
 f«" 
 
 1 
 
 123 
 
 7727 
 
 394,100 
 
 3204 
 
 3040 
 
 5100 
 
 3.60 
 
 223.56 
 
 295.21 
 
 75.7 
 
 J« 
 
 B{ 
 
 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 
 
 *{ 
 
 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 
 
 
 *{ 
 
 40 
 
 3140 
 
 49,611 
 
 1240 
 
 3096 
 
 1580 
 
 0.87 
 
 6.80 
 
 13.82 
 
 49.2 
 
 32 
 
 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 
 
 
 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 
 
 V 
 
 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. 
 
 
 I 
 
 80 1 
 
 6280 
 
 222,3201 2779 
 
 3022 
 
 3540 
 
 2.25 
 
 78.80 
 
 152.60 
 
 52. 
 
 
 Type of fan. 
 
 Diam. 
 
 Width. 
 
 No. inlets. 
 
 Diam. 
 inlets. 
 
 A. Guibal, double 
 
 B. Same, only left hand running 
 
 C. Guibal 
 
 20 ft. 
 
 20 
 
 20 
 
 25 
 
 171/2 
 
 12 
 
 25 
 
 6 ft. 
 6 
 6 
 8 
 4 
 10 
 8 
 
 4 
 4 
 2 
 1 
 
 4 
 2 
 1 
 
 8 ft. 10 in. 
 8 10 
 8 10 
 
 D. Guibal 
 
 11 6 
 
 
 8 
 
 F. Capell 
 
 7 
 
 G. Guibal .' 
 
 12 
 
 
 
646 
 
 AIR. 
 
 An examination of the detailed results of each test in Mr. Norris's table 
 shows a mass of contradictions from which it is exceedingly difficult 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: 
 
 Equivalent 
 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 
 2700 to 4800 
 
 1300 
 1600 
 2100 
 2700 
 3500 
 
 60 to 70 
 70 to 80 
 80 to 90 
 90 to 100 
 100 to 114 
 
 3300 to 5100 
 4000 to 4700 
 3000 to 5600 
 
 4000 
 4400 
 4800 
 
 50 to 60 
 
 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- 
 wardly 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. It is 
 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. 
 
DISK FANS. 647 
 
 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. 
 
 In discussion of Mr. Norris's paper, Mr. A. H. Storrs 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 revolution, 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 condensed below. 
 
 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 more economical than higher ones. 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 AR 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 Hp - is mooT ' while < OT the 2 " ft - fan the net H - p is S 
 
 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 
 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 
 , 1-.+ 1 D*(R- 100) 2 A* (#-100) 2 
 
 be approximately 17 Q0Q 0QQ or 1Q 4Q0>000 - 
 
 The 2-ft. fan was noiseless at all speeds. The 3-ft. fan was also noiseless 
 up to over 450 revolutions per minute. 
 
648 
 
 Speed of fan, revolutions per minute . . 
 
 Net H.P. to drive fan and belt 
 
 Cubic feet of air per minute 
 
 Mean velocity of air in 3-ft. flue, feet 
 
 per minute 
 
 Mean velocity of air in flue, same 
 
 diameter as fan 
 
 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 
 
 Propeller, 
 2 ft. diam. 
 
 750 
 0.42 
 4,183 
 
 593 
 
 1,330 
 9,980 
 1.77 
 5.58 
 
 676 
 0.32 
 3,830 
 
 543 
 
 1,220 
 
 11,970 
 
 1.81 
 
 5.66 
 
 577 
 0.227 
 3,410 
 
 1,085 
 15,000 
 
 5.90 
 
 Propeller, 
 3 ft. diam. 
 
 576 
 1.02 
 7,400 
 
 7,250 
 1.82 
 12.8 
 
 459 
 0.575 
 5,800 
 
 10,070 
 1.79 
 12.6 
 
 373 
 0.324 
 4,470 
 
 13,800 
 1.70 
 12.0 
 
 Experiments made with a Blackman 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. 547): 
 
 .s 
 a 
 
 « 
 
 > 
 
 Cu. ft. of Air 
 delivered 
 per min., 
 
 gin 
 
 o 
 
 w 
 
 i.a 
 
 60 
 
 h 
 
 ■si's 
 
 •2 £w 
 
 pi • 
 
 ■s-SB 
 
 & 
 
 8 8 
 
 a^ 
 k Hi 
 
 m 
 
 IS 
 
 !■« 
 
 a*- 
 
 >> 
 
 is 
 
 W 
 
 350 
 
 25,797 
 32,575 
 41,929 
 47,756 
 For 
 
 0.65 
 2.29 
 4.42 
 7.41 
 series 
 
 
 
 
 
 
 
 1 682 
 
 440 
 534 
 612 
 
 
 1.257 
 1.186 
 1.146 
 1.749 
 
 1.262 
 1.287 
 1.139 
 1.851 
 
 3.523 
 1.843 
 1.677 
 11.140 
 
 5.4 
 2.4 
 3.97 
 4. 
 
 
 .9553 
 1.062 
 .9358 
 
 
 
 
 340 
 
 20,372 
 26,660 
 31,649 
 36,543 
 For 
 
 0.76 
 1.99 
 3.86 
 6.47 
 series 
 
 
 
 
 
 
 
 .7110 
 
 453 
 536 
 627 
 
 
 1.332 
 1.183 
 1.167 
 1.761 
 
 1.308 
 1.187 
 1.155 
 1.794 
 
 2.618 
 1.940 
 1.676 
 8.513 
 
 3.55 
 3.86 
 3.59 
 3.63 
 
 
 .6063 
 .5205 
 .4802 
 
 
 
 
 340 
 
 9,983 
 
 13,017 
 
 17,018 
 
 118,649 
 
 For 
 
 1.12 
 3.17 
 6.07 
 8.46 
 series 
 
 0.28 
 0.47 
 0.75 
 0.87 
 
 
 
 
 
 
 .3939 
 
 430 
 534 
 570 
 
 1.265 
 1.242 
 1.068 
 1.676 
 
 1.304 
 1.307 
 1.096 
 1.704 
 
 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 
 
 8,399 
 10,071 
 11,157 
 For 
 
 1.31 
 
 3.27 
 
 6.00 
 
 series 
 
 0.26 
 0.45 
 0.75 
 
 
 
 
 
 
 .2631 
 
 437 
 516 
 
 1.324 
 1.181 
 1.563 
 
 1.199 
 1.108 
 1.329 
 
 3.142 
 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 
 
POSITIVE ROTARY BLOWERS. 649 
 
 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- 
 tion of the third and fourth 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 over 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 lbs. 
 
 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 cupola 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. 
 
650 
 
 AIR. 
 
 A rotary blower of the two-impeller type is not an economical com- 
 pressor, because the impellers are working against the full pressure at all 
 times, while in an ideal blowing engine the theoretical mean effective 
 pressure on the piston, when discharging air at 15 lbs. pressure, is IH/2 lbs. 
 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 lbs. pressure. 
 
 1. A fan is the cheapest in first cost, and if properly applied may be 
 used economically for pressures up to 8 oz. 
 
 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 lbs. 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 lbs., 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 proportional 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, lbs 
 
 Engine, I.H.P 
 
 Displacement, cu.f t 
 Efficiency 
 
 
 19.30 
 
 0.05 
 23.76 
 19,212 
 
 0.5 
 
 52.83 
 18,727 
 68.5 
 
 1.0 
 100.91 
 
 18,508 
 79 
 
 1.5 
 132.67 
 18,344 
 
 2. 
 176.11 
 18,200 
 85.6 
 
 2.5 
 223.20 
 18,028 
 
 3. 
 
 256.87 
 
 17,966 
 
 86 
 
 3.5 
 
 287.56 
 17,863 
 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 lbs. only. Estimated efficiencies for higher 
 pressures from an extension of the plotted curve are: 6 lbs. 84%, 8 lbs. 
 82%, 10 lbs. 79.5%. The theoretical discharge of the blower was 19,250 
 cu. ft. ' 
 
 
 Capacity of Rotary 
 
 Blowers for 
 
 Cupolas 
 
 . 
 
 Cu.ft 
 
 Revs. 
 
 Tons 
 
 Suitable 
 
 Cu. ft. 
 
 Revs. 
 
 Tons 
 
 Suitable 
 
 per 
 
 per 
 
 per 
 
 for cupola 
 
 per 
 
 per 
 
 per 
 
 for cupola 
 
 rev. 
 
 min. 
 
 hour. 
 
 in. diam.* 
 
 rev. 
 
 min. 
 
 hour. 
 
 in. diam. 
 
 1.5 
 
 ( 200 
 
 1 400 
 
 1 
 2 
 
 } 18 to 20 
 
 45 
 
 f 135 
 } 165 
 
 12 
 15 
 
 I 54 to 66 
 
 3.3 
 
 | 175 
 \ 335 
 
 1 
 2 
 
 } 24 to 27 
 
 
 ( 200 
 ( 130 
 
 18 
 15 
 
 ) 
 
 6 
 
 j 185 
 
 \ 275 
 
 2 
 3 
 
 } 28 to 32 
 
 57 
 
 X 155 
 t 185 
 
 18 
 21 
 
 > 60 to 72 
 
 10 
 
 S 200 
 \ 250 
 
 4 
 5 
 
 \ 32 to 38 
 
 65 
 
 ( 140 
 X 160 
 
 18 
 21 
 
 > 66 to 84 
 
 
 ( 150 
 
 4 
 
 ) 
 
 
 ( 185 
 
 24 
 
 13 
 
 X 190 
 
 5 
 
 \ 32 to 40 
 
 
 ( 125 
 
 21 
 
 ) 
 
 
 ( 175 
 
 6 1/ 2 
 
 ) 
 
 84 
 
 X 145 
 
 24 
 
 > 72 to 90 
 
 
 ( 150 
 
 5 
 
 ) 
 
 
 t 160 
 
 27 
 
 ) 
 
 17 
 
 X 205 
 
 6 1/2 
 
 \ 36 to 45 
 
 
 ( 120 
 
 24 
 
 ) 
 
 
 ( 250 
 
 8 1/ 2 
 
 ) 
 
 100 
 
 X 135 
 
 27 
 
 > 84 to 96 
 
 
 ( 166 
 
 8 
 
 ) 
 
 
 I 160 
 
 30 
 
 ) 
 
 24 
 
 X 200 
 
 10 
 
 \ 42 to 54 
 
 
 ( 115 
 
 27 
 
 1 Two 
 
 
 ( 240 
 
 12 
 
 ) 
 
 118 
 
 X 130 
 
 30 
 
 ( cupolas 
 
 
 ( 150 
 
 10 
 
 ) 
 
 
 I 140 
 
 33 
 
 > 60 to 66 
 
 33 
 
 X 180 
 ( 210 
 
 12 
 14 
 
 > 48 to 60 
 
 
 
 
 
 * Inside diam. The capacity in tons per hour is based on 30,000 cu. ft. 
 of air per ton of iron melted. 
 
STEAM-JET BLOWER AND EXHAUSTER. 
 
 651 
 
 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. . . . 2 1/2 2 1/2 3 
 
 Rotary Gas Exhausters. 
 
 Cu. ft. per rev. 
 Rev. per min.. 
 Diam. of pipe open- 
 ing 
 
 Cu. ft. per rev 
 Rev. per min.. 
 Diam. pipe opening 
 
 2/3 
 
 IV? 
 
 3.3 
 
 6 
 
 10 
 
 13 
 
 17 
 
 24 
 
 200 
 
 180 
 
 170 
 
 160 
 
 150 
 
 150 
 
 140 
 
 130 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 12 
 
 16 
 
 16 
 
 45 
 
 57 
 
 65 
 
 . 84 
 
 100 
 
 118 
 
 155 
 
 200 
 
 no 
 
 100 
 
 95 
 
 90 
 
 85 
 
 82 
 
 80 
 
 80 
 
 20 
 
 24 
 
 -24 
 
 30 
 
 30 
 
 30 
 
 36 
 
 36 
 
 33 
 
 120 
 
 20 
 300 
 75 
 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. lb 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 lbs. 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. 
 
 A blower and exhauster is made by L. Schutte & Co., Philadelphia, on 
 the principle of the steam-jet ejector. The following is a table of capa- 
 cities: 
 
 
 Quantity of 
 Air per hr. 
 
 in 
 cubic feet. 
 
 
 
 Size 
 
 No. 
 
 Quantity of 
 Air per hr. 
 
 in 
 cubic feet. 
 
 
 
 Size 
 No. 
 
 Diameter of 
 Pipes in inches. 
 
 Diameter of 
 Pipes in inches. 
 
 Steam. 
 
 Air. 
 
 Steam. 
 
 Air. 
 
 . 000 
 00 
 
 1 
 
 2 
 3 
 4 
 
 1,000 
 2,000 
 4,000 
 6,000 
 12,000 
 18,000 
 24,000 
 
 1/2 
 3/ 4 
 
 11/4 
 U/2 
 2 
 2 
 
 1 
 
 U/2 
 2 
 
 21/2 
 3 
 
 31/2 
 4 
 
 5 
 6 
 7 
 8 
 9 
 10 
 
 30,000 
 36,000 
 42,000 
 48,000 
 54,000 
 60,000 
 
 21/2 
 
 21/2 
 
 3 
 
 3 
 
 31/2 
 
 31/2 
 
 5 
 6 
 6 
 
 7 
 7 
 8 
 
 The admissible vacuum and counter-pressure, for which the apparatus 
 is constructed, is up to a rarefaction of 20 inches of mercury, and a 
 counter-pressure up to one-sixth of the steam-pressure. 
 
 The table of capacities is based on a steam-pressure of about 60 lbs., 
 and a counter-pressure of about 8 lbs. With an increase of steam- 
 pressure or decrease of counter-pressure the capacity will largely increase. 
 
652 
 
 Another steam-jet blower is used for boiler-firing, ventilation, and 
 similar purposes where a low counter-pressure or rarefaction meets the 
 requirements. 
 
 The volumes as given in the following table of capacities are under the 
 supposition of a steam-pressure of 45 lbs. and a counter-pressure of, say, 
 2 inches of water: 
 
 Size 
 No. 
 
 Cubic 
 
 feet of 
 
 Air 
 
 delivered 
 
 per hour. 
 
 Diam. 
 
 of 
 Steam- 
 pipe in 
 inches. 
 
 Dian 
 inche 
 
 Inlet. 
 
 i. in 
 
 SOf— 
 
 Disch 
 
 Size 
 No. 
 
 Cubic 
 feet of Air 
 delivered 
 per hour. 
 
 Diam. 
 
 of 
 Steam- 
 pipe in 
 inches. 
 
 Diam. in 
 inches of— 
 
 Inlet. Disch 
 
 00 
 
 
 
 1 
 
 2 
 
 3 
 
 6,000 
 12,000 
 30,000 
 60,000 
 125,000 
 
 3/8 
 
 V2 
 1/2 
 3/4 
 
 1 
 
 4 
 5 
 8 
 11 
 14 
 
 3 
 4 
 6 
 8 
 10 
 
 4 
 6 
 8 
 10 
 
 250,000 
 
 500,000 
 
 1,000,000 
 
 2,000,000 
 
 1 
 
 U/4 
 H/2 
 2 
 
 17 
 24 
 32 
 42 
 
 14 
 20 
 27 
 36 
 
 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. 
 
 BLOWING-ENGINES. 
 
 Corliss Horizontal Cross-compound Condensing Blowing-engines. 
 
 (Philadelphia Engineering Works.) 
 
 Indicated 
 Horse-power. 
 
 u 
 
 ftfl 
 
 > 8 
 
 Cu. ft. 
 
 Free 
 Air per 
 
 min. 
 
 U 2 <» 
 
 03 w fl 
 
 3 
 
 i i 
 
 •.S3 
 
 i * 
 
 .5 .S 
 
 J -So 
 
 p. 
 
 < 
 
 ..s-sw 
 
 15 Exp. 
 125 lbs. 
 Steam. 
 
 13 Exp. 
 100 lbs. 
 Steam. 
 
 < 
 
 
 1,572 
 2,280 
 1,290 
 2,060 
 
 40 
 60 
 40 
 60 
 
 30,400 
 45,600 
 30,400 
 45,600 
 
 } ,2 
 
 44 
 42 
 
 78 
 72 
 
 (2) 84 
 (2) 84 
 
 60 
 60 
 
 505,000 
 475,000 
 
 605,000 
 550,000 
 
 1,050 
 1,596 
 
 1,340 
 
 1,980 
 
 40 
 60 
 
 40 
 60 
 
 30,400 
 45,600 
 26,800 
 39,600 
 
 } ,0 
 
 32 
 40 
 
 60 
 72 
 
 (2) 84 
 (2) 78 
 
 60 
 60 
 
 355,000 
 445,000 
 
 436,000 
 545,000 
 
 
 1,152 
 1,702 
 
 40 
 60 
 
 26,800 
 39,600 
 
 }« 
 
 38 
 
 70 
 
 (2) 78 
 
 60 
 
 425,000 
 
 491,000 
 
 
 938 
 1,386 
 
 40 
 60 
 
 26,800 
 39,600 
 
 }.. 
 
 36 
 
 66 
 
 (2) 78 
 
 60 
 
 415,000 
 
 450,000 
 
 
 780 
 1,175 
 
 4U 
 60 
 
 15,680 
 23,500 
 
 I" 
 
 34 
 
 60 
 
 (2) 72 
 
 60 
 
 340,000 
 
 430,000 
 
 
 548 
 821 
 
 40 
 60 
 
 15,680 
 23,500 
 
 },0 
 
 28 
 
 50 
 
 (2) 72 
 
 60 
 
 270,000 
 
 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. 
 
HEATING AND VENTILATION. 653 
 
 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. 
 
 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 C0 2 in 10,000, and badly-ventilated quarters 
 as high as 80 parts. 
 
 An ordinary man exhales 0.6 of a cubic foot of C0 2 per hour. New 
 York gas gives out 0.75 of a cubic feet of C0 2 for each cubic foot of gas 
 burnt. An ordinary lamp gives out 1 cu. ft. of C0 2 per hour. An 
 ordinary candle gives out 0.3 cu. ft. per hour. One ordinary gaslight 
 equals in vitiating effect about 51/2 men, an ordinary lamp 12/3 men, and 
 an ordinary candle 1/2 man. 
 
 To determine the quantity of air to be supplied to the inmates of an un- 
 lighted 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 CO2 in each 10,000 cu. ft. of the entering air; 
 R = cubic feet of CO2 which each 10,000 cu. ft. of the air in the room 
 
 may contain for proper health conditions ; 
 n = number of persons in the room; 
 0.6 = cubic feet of CO2 exhaled by one man per hour. 
 
 during one hour. 
 
 This value divided by v and multiplied by 10,000 gives the proportion 
 of CO2 in 10,000 parts of the air in the room, and this should equal R, the 
 standard of purity desired. Therefore 
 
 10 ' 000 [gjfe +( H 
 
 nrtu 6000 n 
 
 or v = — • 
 
 R—r 
 
 If we place r at 4 and R at 6, v = 6000 n -*■ (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 CO2 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= s _ . - w = 1500 n, or 1500 cu. ft. of fresh air per inmate per hour. 
 
654 
 
 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 
 
 parts of C0 2 in 10,000. 
 cubic feet. 
 
 6 7 8 9 10 15 20 
 
 3000 2000 1500 1200 1000 545 375 
 
 If the original air in the room is of purity of external atmosphere (4 parts 
 of carbonic acid in 10,000), the amount or 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 
 
 Proportion of Carbonic Acid in 10,000 Parts of the Air, not to 
 be Exceeded at End of Hour. 
 
 m Space 
 in Room. 
 
 6 7 8 9 10 | 15 | 20 
 
 Individ- 
 ual. 
 
 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 
 
 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 
 
 too 
 
 None 
 
 445 
 345 
 245 
 145 
 
 45 
 None 
 
 275 
 175 
 73 
 
 None 
 
 800 
 
 
 
 900 
 
 
 
 1000 
 
 
 
 1500 
 
 
 
 2000 
 
 
 
 
 2500 
 
 
 
 
 
 
 
 
 
 
 
 
 
 It is exceptional that systematic ventilation supplies the 3000 cubic 
 feet per inmate per hour, which adequate health considerations demand. 
 For large auditoriums in which the cubic space perindi vidual is great, andin 
 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. per 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 yent-duct, rising to the top of the build- 
 
HEATING AND VENTILATION. 
 
 655 
 
 lng 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 di = 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 - d{) -s- d. 
 
 Or, if t = absolute temperature of external air, and h = absolute tem- 
 perature of the air in the vent-duct, then the pressure =/i (ti — t) ■'■*• t. 
 
 The theoretical velocity, in feet per second, with which the air would 
 travel through the vent-duct under this pressure is 
 
 v=y 
 
 2gh(t 1 -t) 
 
 / 
 
 h(h-t) _ 
 
 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 maybe estimated at approximately 50%, and the 
 actual velocity of the air as it flows through the vent-duct is 
 
 v=-i/ 2gh — ^ — , or, approximately, v=4y h~ 
 
 (ti-t) 
 t 
 
 If V = velocity of air in vent-duct, in feet per minute, and the external 
 air be at 32° Fahr., since the absolute temperature on Fahrenheit scale 
 equals thermometric temperature plus 459.4, 
 
 from which has been computed the following table: 
 
 Quantity of Air, in Cubic Feet, Discharged per Minute 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 
 94 
 108 
 121 
 133 
 143 
 153 
 162 
 171 
 
 108 
 133 
 153 
 171 
 188 
 203 
 217 
 230 
 242 
 
 133 
 162 
 
 188 
 210 
 230 
 248 
 265 
 282 
 297 
 
 153 
 
 188 
 217 
 242 
 265 
 286 
 306 
 325 
 342 
 
 171 
 210 
 242 
 271 
 297 
 320 
 342 
 363 
 383 
 
 188 
 230 
 265 
 297 
 325 
 351 
 375 
 398 
 419 
 
 242 
 297 
 342 
 383 
 419 
 453 
 484 
 514 
 541 
 
 342 
 419 
 484 
 541 
 593 
 640 
 683 
 723 
 760 
 
 419 
 
 15 
 
 514 
 
 20 
 
 593 
 
 25 
 
 663 
 
 30 
 
 726 
 
 35 
 
 784 
 
 40 
 
 838 
 
 45 
 
 889 
 
 50 
 
 937 
 
 
 
656 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 Large 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, t = 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— to). 
 
 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 
 659.) 
 
 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 lbs, 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 lbs. 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 1600 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 14X8 feet, outside temperature 0° 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 -*- 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 0° 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. 
 
 657 
 
 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. Tins 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 be at a temperature of about 86° F., viz., 
 
 69° + 
 
 118,413 
 
 400,000 X 0.01785 
 
 , or( 
 
 i + 17 = 
 
 5 F. 
 
 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 1600 = 80,000 
 thermal units per hour; or, say, 50 gaslights, 50X4800 = 240,000 
 thermal units per hour. The presence of 160 people and the gaslighting 
 would diminish considerably the amount of heat required. Practically, 
 it appears that the heat generated by the presence of 160 people, 64,000 
 heat-units, and by 50 electric lights, 80,000 heat-units, a total of 144,000 
 heat-units, more than covers the amount of heat transmitted through 
 walls, etc. Moreover, that 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 temper- 
 ature. 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 conditions, enter ■ ' = 
 
 about 34° less than 86°, or at about 52° Fahr. Furthermore, the addi- 
 tional vitiation due to gaslighting would necessitate a much larger supply 
 of fresh air than when the vitiation of the atmosphere by the people alone 
 is considered, one gaslight vitiating the air as much as five men. 
 
 The following table shows the calculation of heat transmission (some 
 figures changed from the original) : 
 
 1 T3 
 
 Kind of Transmitting 
 Surface. 
 
 3-8.9 
 
 Calculation 
 of Area of 
 Transmit- 
 ting Sur- 
 face. 
 
 U 
 
 02 
 
 3 
 
 
 69° 
 
 
 36" 
 36" 
 24" 
 36" 
 
 63x22-448 
 
 4x 8x 14 
 42x22- 72 
 
 6x12 
 45x22- 72 
 
 6x12 
 17x22- 72 
 
 6x12 
 32x42-336 
 14x24 
 62x42 
 
 938 
 
 448 
 852 
 
 72 
 918 
 
 72 
 302 
 
 72 
 
 1,008 
 
 336 
 
 2,604 
 
 10 
 83 
 4 
 19 
 2 
 5 
 1 
 5 
 10 
 35 
 4 
 
 9,380 
 
 37,186 
 
 3,408 
 
 1,368 
 
 69 
 
 
 K 
 
 
 33 
 
 
 in 
 
 
 1,836 
 
 in 
 
 
 360 
 
 in 
 
 
 302 
 
 in 
 
 
 360 
 
 69 
 
 Roof 
 
 10,080 
 
 m 
 
 
 11,760 
 
 n 
 
 Floor 
 
 10,416 
 
 
 Supplementary allowance, north c 
 Supplementary allowance, north c 
 
 Exposed location and intermitten 
 
 
 
 
 mtside 
 
 wall, 10%.. 
 
 86,454 
 938 
 
 
 
 % 
 
 3,718 
 
 
 day or night use, 
 
 $0% 
 
 
 
 91,110 
 27,333 
 
 
 
 
 
 118,443 
 
 
 
 
658 
 
 HEATING AND VENTILATION. 
 
 STANDARD VALUES FOR USE IN CALCULATION OF HEATING 
 AND VENTILATING PROBLEMS. 
 
 Heating Value of Coal. 
 
 Anthracite.... . . . 
 
 Semi-anthracite . 
 Semi-bituminous 
 
 Bit. eastern 
 
 Bit. western 
 
 Lignite 
 
 Volatile 
 Matter in 
 the Com- 
 bustible, 
 per cent. 
 
 3 to 7.5 
 7.5 to 12.5 
 12.5 to 25 
 25 to 40 
 35 to 50 
 Over 50 
 
 Heating Value 
 
 per lb. 
 
 Combustible, 
 
 B.T.U. 
 
 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 
 
 Air-dried 
 
 Coal, 
 per cent. 
 
 Ash in 
 Air-dried 
 
 Coal, 
 per cent. 
 
 0.5to 1.0 
 0.5tol.O 
 0.5to 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 boilers, 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- 
 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 effi- 
 ciencies 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, we have the follow- 
 ing as the probable maximum values in British Thermal Units, of the 
 heat available for furnishing steam or heating water or air, for the several 
 efficiencies stated: 
 
 Eff'y 0.80 
 
 B.T.U. 10,080 
 
 Semi- An. 
 
 Semi-Bit. 
 
 Bit. East. 
 
 Bit. West. 
 
 Lignite. 
 
 0.77 
 9,933 
 
 0.75 
 10,837 
 
 0.70 
 9,275 
 
 0.65 
 6,760 
 
 0.60 
 
 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. 
 
HEATING AND VENTILATING PROBLEMS. 
 
 659 
 
 Heat Transmission through Walls, Windows, etc., in B.T.U. per 
 sq, ft. per Hour per Degree of Difference of Temperature. 
 
 Brick Walls. 
 
 Thick- 
 ness, 
 In. 
 
 Wolff. 
 
 Hauss. 
 
 Average, 
 B.T.U. * 
 
 Thickness, 
 In. 
 
 Wolff. 
 
 Hauss. 
 
 Average. 
 B.T.U.* 
 
 4 
 
 0.66 
 
 
 0.537 
 
 25 
 
 
 0.18 
 
 0.188 
 
 43/ 4 
 
 
 0.48 
 
 0.508 
 
 28 
 
 0.18 
 
 
 0.172 
 
 8 
 
 0.45 
 
 
 0.397 
 
 30 
 
 
 0.16 
 
 0.163 
 
 10 
 
 
 0.34 
 
 0.351 
 
 32 
 
 0.16 
 
 
 0.154 
 
 12 
 
 0.33 
 
 
 0.313 
 
 35 
 
 
 0.13 
 
 0.143 
 
 15 
 
 
 0.26 
 
 0.272 
 
 36 
 
 0.145 
 
 
 0.140 
 
 16 
 
 0.27 
 
 
 0.260 
 
 40 
 
 0.13 
 
 0.12 
 
 0.128 
 
 20 
 
 0.23 
 
 0.22 
 
 0.222 
 
 45 
 
 
 0.11 
 
 0.116 
 
 24 
 
 0.20 
 
 
 0.194 
 
 
 
 
 
 * The average figure for brick walls was obtained by plotting the 
 reciprocals of Wolff's and Hauss's figures and drawing a straight line 
 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 B = 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.) 
 
 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. 
 
 Wolff. Hauss 
 B.T.U. B.T.U. 
 
 Wolff. Hauss. 
 B.T.U. B.T.U. 
 
 Glass Surfaces. 
 
 Vault light 
 
 Single window 
 
 Double window 
 
 Single skylight 
 
 Double skylight 
 
 Doors. 
 
 Door 
 
 1-in. pine 
 
 2-in. pine 
 
 Partitions. 
 Solid plaster, 
 
 13/ 4 to2l/4in.. 
 
 2 1/2 to 3 1/4 in . . 
 
 Fireproof 
 
 2-in. pine board. . . . 
 
 1.42 
 1.20 
 0.56 
 1.03 
 0.50 
 
 0.40 
 0.28 
 
 0.30 
 0.28 
 
 1.00 
 0.46 
 1.06 
 0.48 
 
 0.60 
 0.48 
 
 Floors . 
 
 Joists with double 
 floor 
 
 Concrete floor 
 
 Fireproof construc- 
 tion, planked over. 
 
 Wooden beam con- 
 struction, planked 
 over 
 
 Concrete floor 
 brick arch 
 
 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 
 
 Arches with air space 
 
 0.10 
 0.31 
 
 0.22 
 0.20 
 0.16 
 
 0.20 
 0.09 
 0.08 
 
 0.10 
 0.14 
 
660 
 
 HEATING AND VENTILATION. 
 
 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; 31/3% where the height of ceiling is more than 13 ft.; 
 6 2 /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] h- 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; N = 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 heat required by ordinary residences, the formula total heat 
 
 /W nC\ 
 
 — (Ti— To) (-T-+ ^ + ^fi7 * s commonly used. Ti = temp, of room, 
 
 To = outside temp., W = exposed wall surface less window surface, 
 G = glass surface, C = cubic contents 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 wC/56 they multiply the remainder of the ex- 
 pression by a factor for exposure, c = 1.1 to 1.3, depending on the direc- 
 tion 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 = 0; G = 1/5 (W + G). 
 
 
 
 
 
 
 $ 
 
 s 
 
 
 
 
 
 
 **! 
 
 Total Wall, 
 
 Q> 
 
 + 
 
 + 
 
 <© 
 
 
 
 a 
 
 Size, ft. 
 
 3 
 
 (W + G) 
 
 
 
 
 "* 
 
 to 
 
 O* 
 
 &5 
 
 CO 
 
 
 
 
 
 
 
 11 
 
 sq. ft. 
 
 O 
 
 II s 
 
 $ 
 g 
 
 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 
 
 20x20x12 
 
 4,800 
 
 40x12= 480 
 
 96 
 
 10 
 
 13,440 
 
 6,000 
 
 2,688 
 
 4,032 
 
 D 
 
 20x40x14 
 
 11,200 
 
 60x14= 840 
 
 168 
 
 171/3 
 
 23,520 
 
 14.000 
 
 4,704 
 
 7,0:6 
 
 E 
 
 40x40x15 
 
 24.000 
 
 80x15=1200 
 
 240 
 
 20 
 
 33.600 
 
 30.000 
 
 6,720 
 
 10.080 
 
 F 
 
 40x80x16 
 
 51,200 
 
 120x16=1920 
 
 384 
 
 262/3 
 
 54,460 
 
 64.000 
 
 10.892 
 
 16.338 
 
 The figures in the column headed H = 70 (W/4 + G) represent the 
 heat transmitted through the walls, those in the column 70 C/56 are the 
 heat required for one change of air per hour; 0.2 H is the heat correspond- 
 ing to an allowance of 20% for 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. 
 
HEATING BY HOT-AIR FURNACES. 661 
 
 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 0° to 70°, and 1, 2 and 4 persons per 
 100 sq. ft. of floor surface, the heat required for the air is as follow.s: 
 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 toff.. 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 
 
 tt W\ nC~\ 
 
 C l^ + T/ + ~~^6>\^ 1 ~' 11 ^' (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. 659) 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 lb. 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 (^ + x)] + 125 A 
 
 = 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 = 2400, C = 16,000, n = 2, T\ = 70°, T = 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 0° 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- T ) + A X 0.01785 X (Ti - T ) 
 
 = 0.01785 A (T 2 - T ). 
 Heat supplied by furnace = heat for conduction + heat for ventilation 
 
 From which we find A = c (g + ^) (Ti - T ) ■*■ 0.01785 (T 2 -Ti) 
 = 75,600 -h 0.01785 (T 2 - 70°). 
 
 For the value of r 2 T 2 = 100 7 7 2 = 120 r 2 = 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 
 
662 
 
 HEATING AND VENTILATION. 
 
 British Thermal Units Absorbed in Heating 1 Cu. Ft. of Air, or given 
 up in cooling it. — (The air is measured at 70° F.) 
 
 10° 20 30 40 50 56 60 70 80 90 100 101 120 126 130 140 
 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 100 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 
 
 5 6 7 8 9 10 
 48 40 34.3 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 air 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. 
 
 
 Area in 
 sq. in. 
 
 Area, 
 sq.ft. 
 
 Velocity, Feet per Second. 
 
 Diam. 
 
 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. 
 
 I. 
 
 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 air 
 of the standard temperature, as in the following table: 
 
HEATING BY HOT-AIR FURNACES. 
 
 663 
 
 
 Volume of 
 
 Air a 
 
 t Different Temperatures. 
 
 
 
 
 (Atmospheric pressure.) 
 
 
 Fahr. 
 Deg. 
 
 Cu. Ft. 
 in 1 lb. 
 
 Compar- 
 ative 
 Volume. 
 
 Fahr. 
 Deg. 
 
 Cu. Ft. 
 in 1 lb. 
 
 Compar- 
 ative 
 Volume. 
 
 Fahr. 
 Deg. 
 
 Cu.Ft. 
 in 1 lb. 
 
 Compar- 
 ative 
 Volume. 
 
 
 
 11.583 
 
 0.867 
 
 90 
 
 13.845 
 
 1.038 
 
 160 
 
 15.603 
 
 1.169 
 
 32 
 
 12.387 
 
 0.928 
 
 100 
 
 14.096 
 
 1.056 
 
 170 
 
 15.854 
 
 1.188 
 
 40 
 
 12.586 
 
 0.943 
 
 110 
 
 14.346 
 
 1.075 
 
 180 
 
 16.106 
 
 1.207 
 
 50 
 
 12.840 
 
 0.962 
 
 120 
 
 14.596 
 
 1.094 
 
 190 
 
 16.357 
 
 1.226 
 
 62 
 
 13.141 
 
 0.985 
 
 130 
 
 14.848 
 
 1.113 
 
 200 
 
 16.608 
 
 1.245 
 
 70 
 
 13.342 
 
 1.000 
 
 140 
 
 15.100 
 
 1.132 
 
 210 
 
 16.860 
 
 1.264 
 
 80 
 
 13.593 
 
 1.019 
 
 150 
 
 15.351 
 
 1.151 
 
 212 
 
 16.910 
 
 1.267 
 
 Sizes of Air Pipes Used in Furnace Heating. (W. G. Snow, Eng. 
 News, April 12, 1900.) 
 
 
 
 
 
 Length of Room, Ft. 
 
 
 
 
 
 W'th. 
 
 of 
 Room 
 
 Ft. 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 Diameter of Pipe, Ins. 
 
 8.... 
 
 8, 7 
 8, 7 
 
 8,7 
 9,8 
 9,8 
 
 9,8 
 9, 8 
 10, 8 
 10,8 
 
 9, 8 
 10, 8 
 10, 8 
 10,9 
 11,9 
 
 
 
 
 
 
 
 
 10.... 
 
 10, 8 
 
 10, 9 
 
 11, 9 
 
 11, 9 
 
 12, 10 
 
 10, 9 
 
 11, 9 
 
 11, 9 
 
 12, 10 
 
 12, 10 
 
 13, 11 
 
 
 
 
 
 
 12.... 
 
 11, 9 
 
 12, 10 
 
 12, 10 
 
 13, 11 
 13, 11 
 
 12, 10 
 
 12, 10 
 
 13, 10 
 13, 11 
 13, 11 
 
 
 
 
 14.... 
 
 
 13, 10 
 13, 10 
 
 13, 11 
 
 14, 12 
 
 13, 10 
 
 13, 11 
 
 14, 12 
 14, 12 
 
 
 16.... 
 
 
 
 13 11 
 
 18.... 
 
 
 
 
 14 12 
 
 20.... 
 
 
 
 
 
 14, 12 
 
 
 
 
 
 
 
 
 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 V20 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 other 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 to 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. 
 
664 
 
 HEATING AND VENTILATION. 
 
 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 
 
 Av. temp, of the warm air 
 
 Air delivered to heater, cu. ft. per hour. . . . 
 
 B.T.U. absorbed by the dry air per hour. . . 
 
 B.T.U. absorbed by the vapor per hour .... 
 
 Avge. no. of pounds of coal burned per hour 
 
 B.T.U. given by the coal per hour 529,200 
 
 Per cent efficiency of the furnace 
 
 Grate Surface and Rate of Burning Coal. 
 
 In steam boilers for power plants, which are constantly attended by 
 firemen, coal is generally burned at between 10 and 30 lbs. per sq. ft. 
 of grate per hour. In small boilers, house heaters and furnaces, which 
 even in the coldest 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 lbs., 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 lbs. per sq. ft. of grate per hour. This figure, 
 4 lbs., 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. 
 
 39° 
 
 58° 
 
 71 
 
 56 
 
 135° 
 
 152° 
 
 250,896 
 
 249,195 
 
 451,872 
 
 421,496 
 
 2,016 
 
 3,102 
 
 36 
 
 33.5 
 
 529,200 
 
 492,450 
 
 85.7 
 
 86.2 
 
 Rated Capacity of Furnaces and Boilers for House Heating. 
 
 
 
 Coal- 
 burning 
 Capacity 
 
 
 Equiv. 
 lbs. 
 
 Equiv. 
 
 Equiv. 
 
 Diam. 
 
 
 Capacity, 
 
 lbs. 
 
 cu. ft. 
 
 of 
 
 Area in — 
 
 B.T.U. 
 
 Steam 
 
 Air per 
 
 Air at 
 
 Round 
 
 per 
 
 Evap. 
 
 Hour 
 
 70° 
 
 Grate. 
 
 
 Hour. 
 
 Hour. 
 
 212° per 
 Hour. 
 
 Heated 
 100°. 
 
 Heated 
 100°. 
 
 ins. 
 
 ^q.in. 
 
 sq.ft. 
 
 lbs. 
 
 (a) 
 
 (b) 
 
 (O 
 
 (d) 
 
 12 
 
 113.1 
 
 .785 
 
 3.142 
 
 31,420 
 
 32.5 
 
 1,320 
 
 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 
 
 1.76'/ 
 
 7.069 
 
 70,690 
 
 73.2 
 
 2,970 
 
 39,620 
 
 20 
 
 314.2 
 
 2.182 
 
 8.728 
 
 87,280 
 
 90.4 
 
 3,667 
 
 43,920 
 
 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 
 
 141,350 
 
 36 
 
 1017.9 
 
 7.069 
 
 28.276 
 
 282,760 
 
 292.8 
 
 11,881 
 
 V58.490 
 
 Figures in column (b) = (a) -s- 965.7. 
 
 Figures in column (c) = (a) -h (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 lbs. 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 the furnace is fed with coal more frequently a 
 
4 
 
 2.775 
 
 40,000 
 
 27,750 
 
 41.25 
 
 28.61 
 
 156.5 
 
 108.7 
 
 STEAM-HEATING. 665 
 
 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 of 
 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 100 sq. in. of Grate Surface, for Steam, 
 Hot-water, or Furnace Heating. 
 
 (Based on burning 4 lbs. of coal per sq. ft. of grate per hour and 10,000 
 B.T.U. available heating value of 1 lb. of coal.) 
 1 sq. ft. 100 sq. ins. 
 
 grate equals grate equals 
 
 lbs. of coal per hour. 
 B.T.U. per hour. 
 
 lbs. of steam evap. from and at 212° per hr. 
 sq. ft. of steam radiating surface = B.T.U. 
 -4- 255.6*. 
 
 261.4 181.5 sq. ft. of hot-water radiating surface = 
 
 B.T.U. -J- 153 t- 
 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 persq. 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 lbs., 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 21 2°, 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 the coal the boilers 
 should be driven at a rate not greatly exceeding 2 lbs. 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, thus obtaining a greater amount 
 of heating-surface. 
 
666 
 
 HEATING AND VENTILATION. 
 
 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 lbs. of water from and at 212° per sq. ft. of heating-surface per hour. 
 These general considerations lead to the following calculations: 
 1 lb. 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 4- 2000 = 
 5 sq. ft. boiler heating-surface. 1 sq. ft. of boiler-surface will supply 
 2000 -h 250 or 40 ■*- 5 = 8 sq. ft. radiating-surface. 
 
 Low 
 Boiler. 
 
 Medi- 
 um. 
 
 High Boiler. 
 
 1 sq. ft. of grate should burn 
 
 1 sq. ft. of grate should develop. 
 
 1 sq. ft. of grate will require 
 
 1 sq. ft. of grate will supply 
 
 Type of boiler, depending on 
 ratio heating- -*- grate-surface, 
 
 3 
 
 30,000 
 15 
 120 
 
 40,000 
 20 
 160 
 
 B. 
 
 5 lb. coal per hour. 
 50,000 B.T.U. per hour. 
 25 sq. ft. heating-surf. 
 200 sq.ft. radiating-sur. 
 
 C. 
 
 
 
 
 
 Table of 
 
 Ratings. 
 
 
 
 
 
 6 
 
 T3 
 
 a 
 
 1 
 
 <2 
 fa ™ 
 
 13 £ 
 3 n 
 
 aJ§ 
 
 > ,- 
 
 H3 
 
 gfa 
 
 6 
 
 03 
 
 o 
 
 fa " 
 
 ^5 
 
 Is 
 
 m fa 
 
 ft 
 >> 
 
 H 
 
 fa 
 
 6 1 
 xn 
 
 go S 
 W 
 
 O <D 
 
 o a 
 
 
 PS 
 
 05 
 
 a 
 H 
 
 fa 
 
 m 
 
 
 5m 
 
 6 ft 
 
 !> a 
 
 73 6* 
 
 A 1... 
 
 1 
 
 15 
 
 3 
 
 30 
 
 120 
 
 B 8 
 
 .. 8 
 
 160 
 
 32 
 
 320 
 
 1,280 
 
 A 2... 
 
 2 
 
 30 
 
 6 
 
 60 
 
 240 
 
 V, 6 
 
 6 
 
 150 
 
 30 
 
 300 
 
 1,200 
 
 A 3... 
 
 3 
 
 45 
 
 9 
 
 90 
 
 360 
 
 (1 7 
 
 7 
 
 175 
 
 35 
 
 350 
 
 1,400 
 
 A A... 
 
 4 
 
 60 
 
 12 
 
 120 
 
 480 
 
 (1 8 
 
 8 
 
 200 
 
 40 
 
 400 
 
 1,600 
 
 A 5... 
 
 5 
 
 75 
 
 15 
 
 150 
 
 600 
 
 10 
 
 .. 10 
 
 250 
 
 50 
 
 500 
 
 2,000 
 
 B 4... 
 
 4 
 
 80 
 
 16 
 
 160 
 
 640 
 
 12 
 
 .. 12 
 
 300 
 
 60 
 
 600 
 
 2,400 
 
 B 5... 
 
 5 
 
 100 
 
 20 
 
 200 
 
 800 
 
 a 14 
 
 .. 14 
 
 350 
 
 70 
 
 700 
 
 2,800 
 
 B 6... 
 
 6 
 
 120 
 
 24 
 
 240 
 
 960 
 
 C 16 
 
 .. 16 
 
 400 
 
 80 
 
 800 
 
 3,200 
 
 B 7... 
 
 7 
 
 140 
 
 28 
 
 280 
 
 1,120 
 
 
 
 
 
 
 
 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 
 
 R 
 
 
 
 
 
 5|* 
 
 per 
 
 
 
 Heat- 
 
 Radiat- 
 
 H 
 
 R 
 
 R 
 
 B.T.U. 
 
 Hour 
 
 Height. 
 
 G 
 
 mg- 
 
 ing-sur- 
 
 — 
 
 — 
 
 ~ 
 
 per Hour 
 
 per 
 
 
 Grate. 
 
 sur- 
 face. 
 
 face. 
 
 G 
 
 G 
 
 H 
 
 = Rx250 
 
 « 
 
 sq.ft. 
 
 Grate 
 
 * 
 
 Low 
 
 I 2.1 
 
 45 
 
 210 
 
 21.5 
 
 100 
 
 4.7 
 
 52,500 
 
 1,167 
 
 2.5 
 
 1 4.7 
 
 90 
 
 600 
 
 19.1 
 
 128 
 
 6.7 
 
 150,000 
 
 1,667 
 
 3.2 
 
 Medium.. 
 
 ( 4.2 
 
 103 
 
 600 
 
 24.5 
 
 143 
 
 5.8 
 
 150,000 
 
 1,456 
 
 3.6 
 
 \ 8.2 
 
 195 
 
 1,500 
 
 23.8 
 
 183 
 
 7.7 
 
 375,000 
 
 1,923 
 
 4.6 
 
 High 
 
 ( 6.7 
 \ 14.7 
 
 210 
 
 1,200 
 
 31.3 
 
 179 
 
 5.7 
 
 300,000 
 
 1,476 
 
 4.5 
 
 420 
 
 3,300 
 
 28.6 
 
 225 
 
 7.9 
 
 825,000 
 
 1,964 
 
 5.6 
 
 Equals B.T.U. per hour -h 10,000 G. 
 
STEAM-HEATING. 667 
 
 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 lbs. per sq. ft. of grate, according to the type A, B, or C, 
 or the ratio of heating- to grate-surface. 
 
 (b) 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 ~ 59-8) X 970 = B.T.U. 
 
 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 lbs. of coal per sq. ft. of grate surface per 
 hour, and are based on the assumptions of 10,000 B.T.U. utilized per 
 lb. of coal and 270 B.T.U. transmitted by each sq. ft. of radiating sur- 
 face per hour. 
 
668 
 
 HEATING AND VENTILATION. 
 
 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." 
 
 Following 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). 
 
 
 "o ttf 
 
 
 +3 a 
 
 bi 
 
 
 "3 oi 
 
 
 -p a 
 
 
 *S £ 
 
 ll^-g 
 
 
 03 03 
 
 M G 
 
 "8 T ; 
 
 11^-t 
 
 
 03 — ■ 
 03 03 
 
 
 £g 
 
 Square f 
 Direct R 
 tion Boi 
 will Sup 
 
 Size of 
 
 03 
 
 O go 
 
 u a 
 
 Square f 
 Direct R 
 tion Boi 
 will Sup 
 
 Size of 
 
 03^ h 
 
 .20£ 
 1^ 
 
 
 Grate. 
 
 8 zsu 
 
 
 
 Grate. 
 
 b 3 -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 lb. 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 lbs. 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 IV2 lbs. 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. K. Allen, Trans. 
 A. S. H. V. E., 1908.) Ts = temp, of steam; 2 7 1 = temp, of room. 
 7/s-7\ = 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-T t = 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 
 
STEAM-HEATING. 669 
 
 B.T.TJ. 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). .. 200 325 450 560 670 780 870 950 1030 
 
 radiator J (6) . . . 300 550 760 950 1130 1300 
 "Whittier" (b)...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; 
 (&) 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. 
 
 Bv 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, H. 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, 
 
670 
 
 HEATING AND VENTILATION. 
 
 merely by multiplying the figures in the tables by the square root of the 
 assigned drop. The formula from which the tables are calculated is the 
 
 well known one. 
 
 i, W = c -v' 
 
 w (pi — gg) d 5 
 
 , in which W = weight of steam 
 
 in lbs. per minute; w = weight of steam in pounds per cubic foot, at 
 the entering pressure, j> x ; p^ the pressure at the end of the pipe; d the 
 actual diameter of standard wrought-iron pipe in inches, and L the length 
 in feet. The coefficients c are derived from Darcy's experiments on flow 
 of water in pipes, and are believed to be as accurate as any that have 
 been derived from the very few recorded experiments on steam. 
 
 Nominal diam. of pipe. 
 
 Value of c — 
 
 Nominal diam. of pipe. 
 Value of c — 
 
 V?, 
 
 3/ 4 
 
 1 
 
 U/4 
 
 IV?, 
 
 2 
 
 21/?, 
 
 3 
 
 it 8 
 
 42 
 
 4i i 
 
 48 
 
 50 
 
 V2 i 
 
 54.8 
 
 56.2 
 
 4 
 
 41/9 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 57.8 
 
 58.3 
 
 58.7 
 
 59.5 
 
 60.2 
 
 60.8 
 
 61.3 
 
 61.7 
 
 31/2 
 
 57.1 
 
 12 
 
 62.1 
 
 Flow of Steam at Low Pressures in Pounds per Hour for a Uni- 
 form Drop at the Rate of One Pound per 1000 Feet 
 Length of Straight Pipe. 
 
 Nominal 
 Diam. 
 
 of 
 Pipe. 
 
 Steam Pressures, by Gauge, at Entrance of Pipe. 
 
 0.3 1.3 2.3 8.3 4.3 5.3 6.3 8.3 10.3 
 
 Flow of Steam, Pounds per Hour. 
 
 1/2 
 
 1 3/4 
 11/4 
 11/2 
 2... 
 21/2 
 
 31/2 
 4... 
 4l/ 2 
 
 7... 
 8... 
 9... 
 10.. 
 12.. 
 
 19 
 
 40 
 
 61 
 
 120 
 
 195 
 
 345 
 
 505 
 
 701 
 
 938 
 
 1252 
 
 2011 
 
 2936 
 
 4082 
 
 5462 
 
 7314 
 
 11550 
 
 2 
 
 4.3 
 
 4.4 
 
 4.6 
 
 4.7 
 
 4.8 
 
 4.9 
 
 5.1 
 
 7 
 
 10.0 
 
 10.3 
 
 10.5 
 
 10.8 
 
 11.0 
 
 11.3 
 
 11.8 
 
 
 
 19.6 
 
 20.2 
 
 20.7 
 
 21.2 
 
 21.7 
 
 22.3 
 
 23.2 
 
 1 
 
 41.3 
 
 42.5 
 
 43.7 
 
 44.8 
 
 45.9 
 
 46.9 
 
 49.0 
 
 4 
 
 63.2 
 
 65.1 
 
 66.8 
 
 68.6 
 
 70.3 
 
 71.9 
 
 75.0 
 
 8 
 
 124.5 
 
 128.2 
 
 131.6 
 
 135.0 
 
 138.3 
 
 141.5 
 
 147.7 
 
 7 
 
 201.8 
 
 207.5 
 
 213.2 
 
 218.7 
 
 224.0 
 
 229.2 
 
 239.2 
 
 5 
 
 356.1 
 
 366.5 
 
 376.4 
 
 386.1 
 
 395.5 
 
 404.7 
 
 422.4 
 
 3 
 
 520.8 
 
 535.9 
 
 550.5 
 
 564.7 
 
 578.5 
 
 591.8 
 
 618.0 
 
 4 
 
 723.0 
 
 744.0 
 
 764.4 
 
 784.2 
 
 803.4 
 
 822.0 
 
 857.4 
 
 7 
 
 967.6 
 
 995.8 
 
 1023. 
 
 1049. 
 
 1075. 
 
 1100. 
 
 1148. 
 
 
 1291. 
 
 1328. 
 
 1364. 
 
 1399. 
 
 1433. 
 
 1467. 
 
 1531. 
 
 
 2074. 
 
 2134. 
 
 2192. 
 
 2248. 
 
 2303. 
 
 2356. 
 
 2459. 
 
 
 3027. 
 
 3115. 
 
 3199. 
 
 3281. 
 
 3362. 
 
 3440. 
 
 3590. 
 
 
 4208. 
 
 4331. 
 
 4448. 
 
 4564. 
 
 4674. 
 
 4783. 
 
 4991. 
 
 
 3630. 
 
 5794. 
 
 5951. 
 
 6102. 
 
 6252. 
 
 6396. 
 
 6678. 
 
 
 7536. 
 
 7758. 
 
 7968. 
 
 8172. 
 
 8370. 
 
 8562. 
 
 8940. 
 
 
 11916. 
 
 12264. 
 
 12594. 
 
 12918. 
 
 13236. 
 
 13542. 
 
 14136. 
 
 5.3 
 12.3 
 24.2 
 50.9 
 78.0 
 153.6 
 248.8 
 439.3 
 642.6 
 891.6 
 1193. 
 1592. 
 2557. 
 3733. 
 5191. 
 6942. 
 9294. 
 14700. 
 
 For any other drop of pressure per 1000 feet length, multiply the fig- 
 ures in the table by the square root of that drop. 
 
 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. 
 
STEAM-HEATING. 
 
 671 
 
 Proportioning Pipes to Radiating Surface. 
 
 Figures Used in Calculation of Radiating Surface. 
 
 P = Pressure by gauge, lbs. per sq. in. 
 0. 0.3 1.3 2.3 3.3 4.3 5.3 6.3 8.3 10.3 
 
 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 
 
 Temperature Fahrenheit, 1\. 
 212. 213. 216.3 219.4 222.4 225.2 227.9 230.5 235.4 240.0 
 Ti= Ti— 70°, difference of temperature. 
 146.3 149.4 152.4 155.2 157.9 160.5 165.4 170.0 
 
 142. 
 
 Hi = 
 
 143. 
 Tt X l.i 
 
 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 
 
 #1-*- L = steam condensed per sq. ft. radiating surface, lbs. per hour. 
 0.2647 0.267 0.274 0.280 0.286 0.292 0.298 0.303 0.314 0.324 
 
 Reciprocal of above = radiating surface per lb. of steam condensed per 
 
 hour. 
 3.78 3.75 3.65 3.57 3.50 3.42 3.36 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 Supplied by Different Sizes of Pipe. 
 
 On basis of steam in pipe at 0.3 and 10.3 lbs. 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 1b. 
 
 10.3 lb. 
 
 In, 
 
 0.3 1b. 
 
 10.3 1b. 
 
 In. 
 
 0.3 1b. 
 
 10.31b. 
 
 V2 
 3/4 
 
 1 
 
 H/4 
 
 H/2 
 
 2 
 
 16 
 36 
 71 
 150 
 230 
 453 
 
 16 
 38 
 75 
 157 
 241 
 475 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 734 
 1,296 
 1,895 
 2,630 
 3,520 
 4,695 
 
 769 
 1,357 
 1,986 
 2,755 
 3,686 
 4,919 
 
 6 
 7 
 8 
 9 
 10 
 12 
 
 7,541 
 11,010 
 15,307 
 20,482 
 27,427 
 43,312 
 
 7,901 
 11,535 
 16,040 
 21,451 
 28,718 
 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. 
 
672 
 
 HEATING AND VENTILATION. 
 
 Sizes of Steam Pipes in Heating Plants. — G. W. Stanton, in Heating 
 and Ventilating Mag., April, 1908, gives tables for proportioning pipes to 
 radiating surface, from which the following table is condensed: 
 
 Sup- 
 ply 
 
 Radiating Surface Sq 
 
 .Ft. 
 
 Returns. 
 
 Drips. 
 
 Connections. 
 
 Pipe. 
 Ins. 
 
 A 
 
 B 
 
 C 
 
 D 
 
 B 
 
 dD 
 
 A 
 
 BidD 
 
 Ai 
 
 AaBA 
 
 B 2 C 2 
 
 1 
 
 11/4 
 
 H/2 
 
 2 
 
 21/2 
 
 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 
 H/2 
 
 2 
 2 
 
 21/2 
 
 21/2 
 
 21/2 
 
 3 
 
 3 
 
 31/2 
 
 4 
 
 1 
 1 
 
 11/4 
 
 U/2 
 
 2 
 
 21/2 
 
 21/2 
 
 3 
 
 3 
 
 31/2 
 
 31/2 
 
 4 
 
 4 
 
 41/2 
 
 5 
 
 6 
 
 7 
 
 8 
 
 3/4 
 
 3/4 
 1 
 
 11/4 
 H/4 
 U/2 
 1 L/2 
 U/2 
 
 3/4 
 
 , 3/4 
 
 1 
 
 11/4 
 
 11/4 
 
 11/4 
 
 11/4 
 
 H/4 
 H/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 1 
 
 U/4 
 U/2 
 2 
 
 1 
 1 
 
 11/4 
 U/2 
 
 3 
 
 
 
 31/2 
 
 
 
 4 
 
 
 
 41/2 
 
 
 
 6 
 7 
 8 
 9 
 10 
 
 Supply mains and risers 
 are of the same size. 
 Riser connections on 
 the two-pipe system to 
 be the same size as the 
 riser. 
 
 12 
 
 
 
 14 
 
 
 
 16 
 
 
 
 
 
 
 
 
 
 
 
 5 lb. pressure. Ai, 
 
 300 400 500 
 
 600 
 
 700 
 
 800 
 
 900 
 
 1000 
 
 . 58 0.5 . 45 
 
 0.41 
 
 0.38 
 
 0.35 
 
 0.33 
 
 0.32 
 
 A. For single-pipe steam-heating system 
 riser connections. Ai, radiator connections. 
 
 B. Two-pipe system to 5 lb. pressure; Bi, Ci, radiator connections, 
 supply; Bi, Ci, radiator connections, return. 
 
 C. D. Two-pipe system 2 and 5 lbs. 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 
 
 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 lb. 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 op Pipe to be Added for Each Fitting. 
 
 Size Pipe. 
 
 1 
 
 U/4 
 
 U/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 
 
STEAM-HEATING. 673 
 
 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. ^IfcL^Uonr! 011 
 
 40 70 70 lbs. 
 
 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 of 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 
 
674 HEATING AND VENTILATION. 
 
 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 - t), 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, and 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 lbs. 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 12 in "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 lb.) 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 1/20 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 
 
HOT-WATER HEATING. 675 
 
 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 main 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 1 1/4-inch or 1-inch pipe, according to the size of 
 the radiator or coil. A 2-inch main will supply three 1 1/4-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 T2 = 140, (61.37 - 60.98) 
 f- 144 = 0.00271 lb. 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 lb. 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 -f- 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. Tins 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: 
 
 20 X^o/x 60 = CU - ft - ° f WateF 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: 
 
676 
 
 HEATING AND VENTILATION. 
 
 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. 
 
 11/ 4 
 
 75 
 
 107 
 
 200 
 
 314 
 
 540 
 
 780 
 
 1,060 
 
 1,860 
 
 2,960 
 
 4,280 
 
 5 ; 850 
 
 45 
 
 65 
 
 121 
 
 190 
 
 328 
 
 474 
 
 645 
 
 1,130 
 
 1,800 
 
 2,700 
 
 3,500 
 
 127 
 
 181 
 
 339 
 
 533 
 
 916 
 
 1,334 
 
 1,800 
 
 3,150 
 
 5,000 
 
 7,200 
 
 9,900 
 
 250 
 335 
 
 667 
 1,060 
 1,800 
 2,600 
 3,350 
 6,200 
 9,800 
 13,900 
 19,500 
 
 48 
 
 11/2... 
 
 69 
 
 2 
 
 129 
 
 21/2 
 
 202 
 
 3. 
 
 348 
 
 31/2 
 
 502 
 
 4 . . 
 
 684 
 
 5 
 
 1,200 
 
 6 
 
 1,910 
 
 7 
 
 2,760 
 
 8 
 
 3,778 
 
 
 
 The figures are for direct radiation except the last column which is for 
 indirect, 12 in. above boiler. 
 
 Capacity of Risebs. 
 
 Expressed in the number of sq. ft. of direct hot-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 
 71 
 100 
 187 
 292 
 500 
 
 46 
 104 
 140 
 262 
 410 
 755 
 
 57 
 124 
 175 
 325 
 492 
 875 
 
 64 
 142 
 200 
 375 
 580 
 1,000 
 
 48 
 
 11/ 4 
 
 112 
 
 11/2 
 
 160 
 
 2 
 
 300 
 
 21/2 
 
 471 
 
 3 . . . . . 
 
 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) -5- (T — t). 
 
 H = exposure loss in B.T.TJ. per hour. 
 
 Heat necessary to raise this air to the entering temperature from 
 0° F., T X C + 55 = H. 
 
HOT-WATER HEATING. 
 
 677 
 
 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 
 Pipe. 
 
 ' 
 
 11/4 
 
 11/2 2 21/2 3 31/2 4 | 5 6 7 
 
 Length of 
 Run. 
 
 Square Feet of Direct Radiating Surface. 
 
 Feet. 
 100 
 
 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 
 
 
 
 
 200 
 
 1,400 
 1,150 
 1,000 
 700 
 850 
 775 
 725 
 650 
 
 
 
 300 
 
 
 
 400 
 
 
 
 1,600 
 1,400 
 1,300 
 1,200 
 '1,150 
 1,000 
 
 
 500 
 
 
 
 
 
 600 
 
 
 
 
 
 700 
 
 
 
 
 
 1,700 
 
 800 
 
 
 
 
 
 
 1,600 
 
 1000 
 
 
 
 
 
 
 1.500 
 
 
 
 
 
 
 
 
 
 Square Feet of Indirect Radiation. 
 
 100 
 200 
 
 15 
 
 30 
 
 20 
 
 50 
 30 
 
 100 
 70 
 
 200 1 300 
 120 200 
 
 400 
 300 
 
 600 
 400 
 
 1,000 
 700 
 
 
 
 
 
 
 
 
 Square Feet of Direct Radiating Surface. 
 
 1st story 
 2d " 
 
 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 
 
 
 
 
 
 
 
 
 
 3d 
 
 
 
 
 
 
 
 4th " 
 
 
 
 
 
 
 
 
 5th " 
 
 
 
 
 
 
 
 
 6th " 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 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. 
 
678 
 
 HEATING AND VENTILATION. 
 
 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.) 
 
 Size 
 of 
 
 Mains. 
 
 11/4 
 
 U/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 6 
 
 7 
 
 8 
 
 9 
 10 
 11 
 12 
 
 In Cellar 
 
 or 
 
 Basement. 
 
 On One 
 
 or More 
 Floors. 
 Average. 
 
 Branches of Mains. 
 
 First Second 
 Floor Floor 
 10'-15\ 15'-25'. 
 
 Third 
 Floor 
 25'-35\ 
 
 Fourth 
 or Fifth 
 Floor 
 35'-45'. 
 
 Square Feet of Radiating Surface. 
 
 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 
 
 50 
 110 
 180 
 290 
 400 
 620 
 820 
 1,050 
 1,325 
 
 40 
 
 45 
 
 75 
 
 80 
 
 120 
 
 135 
 
 195 
 
 210 
 
 320 
 
 350 
 
 490 
 
 525 
 
 650 
 
 690 
 
 870 
 
 920 
 
 1,120 
 
 1,185 
 
 1,400 
 
 1,485 
 
 50 
 85 
 150 
 230 
 370 
 550 
 730 
 970 
 1,250 
 1,560 
 
 Note. — The heights of the several 
 floors are taken as: 
 1st. 10 to 15 ft.; 2d. 15 to 25 ft. 
 3d. 25 to 35 ft.; 4th. 35 to 45 ft. 
 
 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, and from 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 stud : ed as an original problem to 
 be solved by application of the laws of heat transmission and hydraulics. 
 Forced systems using steam ejectors have come into use to some extent 
 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. 
 
 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 of 
 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 
 
THE BLOWER SYSTEM OF HEATING. 
 
 679 
 
 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 bet wee n the average temperature of 
 the air and the steam temperature, = ^4 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: 
 
 (T s -T a )XHX E 
 R = A X V m X W X 60 X 0.2377 ' 
 
 F. rise for each two-row section; T s = tem- 
 T a = temperature of air; H = square feet of sur- 
 face in two-row sect ion; E = B.T.U. per degree difference between air 
 and steam; E = V^ V 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.; 
 W = weight of 1 cu. ft. of air, lbs. 
 
 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. 
 
 In which R == 
 perature of steam 
 
 
 
 
 
 Number of Rows. 
 
 
 < 
 
 8 | 12 | 16 | 20 | 24 
 
 28 
 
 
 Temperature Rise, Degrees. 
 
 Steam, 
 
 80 lbs. 
 
 V^ = 
 
 1,200 
 
 43 
 
 83 
 
 115 
 
 144 
 
 167 
 
 189 
 
 209 
 
 Steam, 
 
 80 lbs. 
 
 V n = 
 
 1,800 
 
 36 
 
 68 
 
 96 
 
 122 
 
 145 
 
 165 
 
 182 
 
 Steam, 
 
 5 lbs. 
 
 V m = 
 
 1,200 
 
 31 
 
 53 
 
 80 
 
 100 
 
 118 
 
 133 
 
 146 
 
 Steam, 
 
 5 lbs. 
 
 Vm = 
 
 1,800 
 
 25 
 
 48 
 
 68 
 
 86 
 
 101 
 
 115 
 
 128 
 
 A formula for the rise in temperature of air in passing through the 
 coils of a hot-blast heater is given by E. F. Child in The Metal Worker, 
 
 Oct. 5, 1907, as. -follows; R^ KDZ m N * ^V, in which #=rise in 
 
680 
 
 HEATING AND VENTILATION. 
 
 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 ) ■*■ 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 V and depending on experiment. 
 
 For practical purposes and within the range of present knowledge on 
 the subject the formula may be written R = 0.85 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 1 40 50 | 60 I 70 1 80 I 90 1 100 1 120 
 
 
 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 
 
 800 
 
 157 
 
 1000 
 
 147 
 
 1200 
 
 140 
 
 2000 
 
 127 
 
 
 
 Burt S. Harrison (Htg. and Ventg. Mag., Oct. and Nov., 1907) gives the 
 following formula, R=- Tr= .(T-t) Ar , in which !F = temp. of steam 
 
 \l Y Pi " ' U.^4 
 
 in coils, £ = 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 Co'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 below. 
 
 Tests of a" Vento " Cast- Iron Heater. 
 
 Velocity, 
 ft. per Min. 
 
 1600 
 1500 
 1400 
 1300 
 1200 
 1100 
 1000 
 900 
 
 Number of sections heater is Number of sections heater ia 
 
 Rise of temperature, K, per de- 
 gree difference between tem- 
 perature of steam and mean 
 temperature of air for differ- 
 ent velocities of air. 
 
 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 
 0.283 
 0.291 
 0.299 
 0.306 
 0.314 
 
 0.761 
 0.769 
 0.776 
 0.784 
 0.791 
 0.799 
 0.807 
 0.814 
 0.822 
 
 1 
 
 3 
 
 5 
 
 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. 
 
 11.94 
 11.91 
 11.70 
 11.50 
 11.11 
 10.72 
 10.23 
 9.59 
 8.90 
 
 12.17 
 11.76 
 11.28 
 10.79 
 10.21 
 9.63 
 8.99 
 8.28 
 7.56 
 
 12.67 
 12.11 
 11.50 
 10.89 
 10.22 
 9.55 
 8.84 
 8.08 
 7.31 
 
 12.67 
 12.06 
 11.41 
 10.75 
 10.05 
 9.34 
 8.61 
 7.85 
 7.08 
 
 12.50 
 11.86 
 11.18 
 10.51 
 9.81 
 9.09 
 8.36 
 7.60 
 6.48 
 
 12.20 
 11.56 
 10.89 
 10.22 
 9.52 
 8.82 
 8.10 
 7.35 
 6.60 
 
THE BLOWER SYSTEM OF HEATING. 
 
 681 
 
 Tests of a "Vento" Cast-iron Heater. — Continued. 
 
 Velocity, 
 ft. per min 
 
 Final 
 
 temperature, 
 
 T, of 
 
 air 
 
 when entering heater at 0° F. 
 
 Temperature of steam in 
 
 heater, 227°. 
 
 26.5 
 
 51.0 
 
 74.9 
 
 94.7 
 
 111.3 
 
 125.2 
 
 28.1 
 
 52.4 
 
 76.3 
 
 95.8 
 
 112.4 
 
 126.0 
 
 29 5 
 
 53 8 
 
 77 2 
 
 96 7 
 
 113 3 
 
 126 8 
 
 31 1 
 
 55 
 
 77 6 
 
 97 9 
 
 114 3 
 
 127 7 
 
 32 4 
 
 56 4 
 
 79 6 
 
 99 
 
 115 3 
 
 128,7 
 
 34 
 
 57 7 
 
 80 5 
 
 100 
 
 116 2 
 
 129.6 
 
 35 6 
 
 59,1 
 
 82 
 
 100 1 
 
 117 2 
 
 130 5 
 
 36.9 
 
 60.1 
 
 83 
 
 102 1 
 
 118 
 
 131 3 
 
 38.5 
 
 61.6 
 
 84.3 
 
 103.1 
 
 119.0 
 
 132.3 
 
 Friction loss in inches of water 
 due to the sections. 
 
 1600. 
 1500 
 1400 
 1300 
 1200 
 1100 
 1000 
 900 
 
 236 
 
 288 
 
 416 
 
 543 
 
 0.672 
 
 207 
 
 253 
 
 366 
 
 477 
 
 0.590 
 
 180 
 
 220 
 
 318 
 
 415 
 
 0.514 
 
 156 
 
 190 
 
 274 
 
 358 
 
 0.443 
 
 133 
 
 162 
 
 234 
 
 306 
 
 0.378 
 
 111 
 
 136 
 
 197 
 
 257 
 
 0.318 
 
 092 
 
 112 
 
 162 
 
 212 
 
 0.262 
 
 074 
 
 091 
 
 132 
 
 172 
 
 0.212 
 
 0.059 
 
 0.072 
 
 0.104 
 
 0.136 
 
 0.167 
 
 0.800 
 0.703 
 0.613 
 0.528 
 0.450 
 0.378 
 0.312 
 0.253 
 0.200 
 
 Formulae. — s = no. of sections; V = velocity, ft. per min., air measured 
 at 70°; k = rise of temp, per degree difference; t = final temperature. 
 / = friction loss in in. of water, t = 454 k + (2 + k). k = s (0.167 - 
 
 0.005 s) - 0.061 ( "gQQ 00 ) - /=(0.8 s+ 0.2) (F/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 
 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 lb. 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 the air at 82° is saturated, or 100% relative humidity, it 
 contains 0.0235 lb. of water vapor, while 1 lb. at 72° contains 0.0167 lb., 
 so that 0.0068 lb. will be condensed in cooling from vapor at 82° to 
 water at 72°. The total heat (above 32°) in 1 lb. vapor at 82° is 1095.6 
 B.T.U. and that in 1 lb. 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 lb. vapor at 72° is 1091.2, 
 
682 
 
 HEATING AND VENTILATION. 
 
 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 T\ = original and Ti the final temperature of the air, 
 a = vapor in 1 lb. saturated air at T\; b = do. at T2, 
 H = relative humidity of the air at fi; ft = desired do. at T2, 
 U = total heat, in B.T.U., in 1 lb. vapor at T\; u = do. at Ti, 
 w = total heat in water at T2. 
 
 Then total heat abstracted in cooling air from T\ to 7 7 2 = (aH — bh) X 
 (17 - w) + bh (U - u) + 0.2375 (Ti - 7 T 2 ), or aHU - bhu - (aH - 
 bh) w + 0.2375 (Ti - Ti), or aH (U - w) - bh (u - w) + 0.2375 (Ti - 
 T2). 
 
 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° F.), being supplied per person per hour, 
 the temperature of the air before cooling being 82°, with relative humid- 
 ity 80%, and after cooling 72°, with humidity 70%. 
 
 1000 X 1500 = 
 
 1,500,000 cu. 
 112,500 lbs. 
 
 ft., at 0.075 lb. per cu. ft. 
 
 For 1 lb. aH (U - w) - bh ( u - w) + 0.2375 (Ti - T2). 
 
 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 lbs. 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.) 
 
 PQ.S 
 "I 
 w. 
 
 <D 
 
 ti. 
 9, 
 
 
 
 % <D 
 
 ef 
 
 <u 
 
 ^ 
 
 Q3 
 
 u ti-ti 
 
 ti 
 
 ti 
 
 .2 
 
 *0 03 
 
 ti a 
 
 0*03 
 
 W <D 
 
 Ft. of Ai 
 ed per Mi 
 an throug 
 eater. 
 
 
 fcti 
 
 ^Q 
 
 3^W 
 
 P 
 
 42 
 
 « 
 
 W 
 
 
 
 360 
 
 21/9 
 
 6,900 
 
 48 
 
 320 
 
 3 
 
 8,500 
 
 54 
 
 280 
 
 4 
 
 10,500 
 
 60 
 
 250 
 
 5 
 
 12,500 
 
 66 
 
 230 
 
 6 
 
 15,800 
 
 72 
 
 210 
 
 8 
 
 19,800 
 
 84 
 
 180 
 
 10 
 
 26,200 
 
 96 
 
 160 
 
 12 
 
 33,000 
 
 108 
 
 140 
 
 15 
 
 41,600 
 
 120 
 
 125 
 
 18 
 
 50,000 
 
 415,200 
 
 510,000 
 
 630,000 
 
 750,000 
 
 948,000 
 
 1,118,000 
 
 1,572,000 
 
 1,980,000 
 
 2,496,000 
 
 3,000,000 
 
 V- 
 
 £ 
 
 a 
 
 
 
 « 
 
 1(35 
 
 ti 
 
 <D 
 
 *$ 
 $& 
 
 tf °0 
 
 <3% 
 
 ^ 
 
 Oj> 
 
 IjN 
 
 2 C 
 
 ."S . ti 
 
 PK£ 
 
 &jfs 
 
 < gj 
 
 ti 0*0 
 0m# 
 
 
 
 oj ft 
 
 
 § ft<1 
 
 -2-^ 8 
 -3^ ft 
 
 gS 
 
 c3 03 01 
 
 a; aft 
 
 w 
 
 > 
 
 h 
 
 W 
 
 1,021,000 
 
 900 
 
 7.7 
 
 1760 
 
 1,255,000 
 
 
 
 9.45 
 
 
 
 1,550,000 
 
 
 
 11.66 
 
 
 
 1,845,000 
 
 
 
 13.9 
 
 
 
 2,335,000 
 
 
 
 17.55 
 
 
 
 2,900,000 
 
 
 
 22. 
 
 
 
 3,870,000 
 
 
 
 29.1 
 
 
 
 4,870,000 
 
 
 
 36.7 
 
 
 
 6,130,000 
 
 
 
 46.3 
 
 
 
 7,375,000 
 
 
 
 55.5 
 
 
 
 
 580 
 714 
 880 
 1050 
 1325 
 1650 
 2200 
 2770 
 3490 
 4140 
 
PERFORMANCE OF HEATING GUARANTEE. 
 
 683 
 
 Capacities of Fans or Blowers for Hot-blast or Plenum Heating — 
 
 Continued. 
 
 
 
 1 
 
 ~£ 
 
 T3 
 
 T3 O) 
 
 
 += ® 
 
 T3 — 
 
 £.3 
 
 fe « (3 
 
 o - n o 
 = faO 
 
 M 
 
 a 
 
 o 
 
 1 
 
 o 
 
 3 
 
 i 
 a 
 O 
 
 o>'3 
 
 fa 03 
 
 73 
 
 a 
 
 o 
 
 °o' 
 
 32 
 
 '3 
 & 
 
 V 
 
 1 
 
 a 
 
 <B 
 02 
 
 '3 
 
 a 1 
 
 '3 3 
 
 W OQ 
 >> • . 
 
 So — 
 O^ || 
 
 t2 • o 
 
 ■-Soq 
 o> — 
 
 6® 
 
 oj § 
 ^ ■ = i 
 
 fa • • 
 
 ■o'c 
 
 go . 
 
 *©"3 
 
 -■IS 
 
 "Hi 
 
 g> 
 °fa 
 °§ . 
 ^,2 s 
 
 £ «fa 
 IJi 
 
 S'33 3 
 ^ fl.2 ^ 
 
 © 03 -^"CS 
 
 w 
 
 J 
 
 fa 
 
 OS 
 
 s 
 
 ffl 
 
 m 
 
 m 
 
 !> 
 
 «l 
 
 £ 
 
 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 
 
 21/2 
 
 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 
 
 4 l.'o 
 
 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 lbs. 
 
 Peripheral 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 1/10 
 for the engine, 5/ 10 for the fan itself, and s/ 10 for efficiency as regards 
 friction, the fan requires an expenditure of heat to drive it of only 1/38 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-machine utilizes 60 per cent of the 
 engine-power. The coal consumption of the engine per I.H.P. is taken 
 at 8 lbs. 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, 
 
684 HEATING AND VENTILATION. 
 
 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 7 1 = 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 walls per hour 
 per degree of difference of temperature, including allow- 
 ance for ventilation. 
 It 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. 
 
 Then aS (T s - T t ) = bW (T t - To). Let ^ = C; then 
 
 Ti==C (J 7 !- To); T t = 
 
 aS 
 T s + CT Q „ T s - T t 
 
 1 + C ' Ti - To 
 If T t = 70, and T = 0, C = -^ — 
 
 Let T s '= 140° 160° 180° 200° 212° 220° 250° 300° 
 
 Then (7= 1 1.286 1.571 1.857 2.029 2.143 2.571 3.286 
 
 and from the formula 7\= (T s + CT ) + (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 = -20 - 10 10 20 30 40° F. 
 
 Inside Temperatures T t . 
 
 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. K. 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 
 7\ = 58 64 70 77.5 83 90 97 
 
 For all values of T between — 10 and 40 these figures are within one 
 degree 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 lbs. of 
 coal burned per hour. This would be equivalent to 1,980,000 ft.-lbs. •+ . 
 
MINE-VENTILATION. 685 
 
 778 = 2545 heat-units, or 1272 heat-units for 1 lb. 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 gang- 
 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 
 
 unimportant, is p = , in which p = loss of pressure in pounds per 
 
 square foot, 5 = 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 _ u _ q_ 
 ~ p u pv ~ pv ~ V ' 
 
 o h = u = gP = 5.2 qw 
 33,000 33,000 33,000* 
 pa _ u _ p _ 5.2 w 
 
 3 
 
 sv 2 sv 3 
 4. I - 
 
 5. o - 
 
 ' kv 2 o 
 pa 
 
 I kvH 
 
 ksv 2 _ u __ _ / "/ u Y ks ksv 3 u 
 
 a q \Vksla q 
 
 ks I v ' 
 
 a u ksv 3 . I pa . lu 
 
 8. q = va = - = — =^ Ts a = ^ rs a. 
 
 7. pa = ksv 2 = I 4 / j— 1 ks = - ; pa 3 = ksq 2 . 
 
 pa _ u_ _ qp_ _ vpa 
 
 ' kv 2 ~ kv 3 ~ kv 3 ~~ kv 3 
 
 : 10. 
 
 10. u = qp = vpa = ^^ = ksv 3 = 5.2 qw = 33,000 h 
 
 a. - = u = g = //it = K Vm = * Im. 
 
 pa a y ks y ks y ks 
 
686 HEATING AND VENTILATION. 
 
 is. «• = | =, m w sg* 
 
 V ksv 2 
 14 - w = K2 = sT5' 
 To find the quantity of air with a given horse-power and efficiency (e) 
 of engine: 
 
 h X 33,000 X e 
 
 q = v ' 
 
 The value of k, 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 .000,000,00497 
 Straight, large section 00104 .000,000,00549 
 Straight, normal section 00122 .000,000,00645 
 
 1 Straight, normal section 00030 .000,000,00158 
 Straight, normal section 00036 .000,000,00190 
 Continuous curve, normal section .00062 .000,000,00328 
 Sinuous, intermediate section 00051 .000,000,00269 
 Sinuous, small section 00055 . 000,000,00291 
 
 t;™KotWI ( Straight, normal section 00168 .000,000,00888 
 
 J ■ ™"f_ r ®° { Straight, normal section 00144 .000,000,00761 
 
 gangways. ( slightly sinuous, small section. . . .00238 .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 v 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 
 
 A = 0_*7J = Q. t Q = A^., „ = 0.1369X(2) ! . 
 V w 2.7 v w ^.67 VA ' 
 
 ± „ . 0.38 Q , x , . . 0.403 Q ~ *,.. . 
 
 * Murgue gives A = — -^, and Norns A = — -—■ • See page 644, ante. 
 
687 
 
 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 5.2 Xw .„ ,, fXM v 
 
 M = D m w trn or t ; p = / X M;w = — e 
 
 T X 459 
 
 / 
 
 5.2 
 
 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; = 
 
 Vt 
 
 A S X 3.1416 
 
 perimeter of square airway. Then D s 
 
 " 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 quantit y of air t hat will pass when the two fans are 
 worked together will be <\/A 3 + B 3 . (For mine-ventilating fans, see 
 page 644.) 
 
 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° 
 
 39.1° 
 
 1.00000 
 
 35° 
 
 95 o 
 
 1.00586 
 
 70° 
 
 158° 
 
 1.02241 
 
 5 
 
 41 
 
 1.00001 
 
 40 
 
 104 
 
 1.00767 
 
 75 
 
 167 
 
 1.02548 
 
 10 
 
 50 
 
 1 .00025 
 
 45 
 
 113 
 
 1.00967 
 
 80 
 
 176 
 
 1.02872 
 
 15 
 
 59 
 
 1.00083 
 
 50 
 
 122 
 
 1.01186 
 
 85 
 
 185 
 
 1.03213 
 
 20 
 
 68 
 
 1.00171 
 
 55 
 
 131 
 
 1.01423 
 
 90 
 
 194 
 
 1.03570 
 
 25 
 
 77 
 
 1.00286 
 
 60 
 
 140 
 
 1.01678 
 
 95 
 
 203 
 
 1.03943 
 
 30 
 
 86 
 
 1.00425 
 
 65 
 
 149 
 
 1.01951 
 
 100 
 
 212 
 
 1.04332 
 
 Weight of 1 cu. ft. at 39.1° F. = 62.4245 lb. h- 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 lbs. 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. 
 
 H'. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 H'. 
 
 Cu. 
 
 F. 
 
 Cu. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 
 Ft. 
 
 480 
 
 Ft. 
 49 7 
 
 550 
 
 Ft. 
 
 200 
 
 60.12 
 
 270 
 
 58.26 
 
 340 
 
 55.94 
 
 410 
 
 53.0 
 
 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 
 
 230 
 
 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 
 
 600 
 
 41.8 
 
 260 
 
 58.55 
 
 330 
 
 56.30 
 
 400 
 
 53.5 
 
 470 
 
 50.2 
 
 540 
 
 46.3 
 
 
 
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 
 for heat units are from Marks and Davis's Steam Tables, 1909. 
 
 .fa 
 
 i.2 
 
 — 'Xi 
 
 "3 
 
 3 
 
 & fa 
 
 £ 2 
 
 '3 
 
 3 
 
 k fa 
 
 .8.2 
 
 M (5 ° 
 
 ! 
 
 | J* 
 
 -Q 2 
 
 '3 
 
 3 
 
 S-s 
 
 
 
 B 3®, 
 
 "5 
 
 CD 
 
 B££ 
 
 
 a 
 
 B 3.2 
 
 "eS 
 a> 
 
 _H 
 
 w 
 
 H 
 
 £ 
 
 w 
 
 H 
 
 w 
 
 H 
 
 £ 
 
 a 
 
 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 s 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 
 
 111 
 
 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 
 
 62.26 
 
 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: 
 
 50 60 70 80 90 
 62.42 62.37 62.30 62.22 62.11 
 110 120 130 140 150 
 
 61.86 61.71 61.55 61.38 (jl. J8 
 170 180 190 200 210 
 60.80 60.50 60.36 60.13 59.88 
 
 Temp. F 
 
 ..40 
 
 Lbs, per cu. ft. 
 
 ..62.43 
 
 Temp. F 
 
 .100 
 
 Lbs. per cu, ft. 
 
 , 62.00 
 
 Temp. F 
 
 .160 
 
 Lbs, per cu. ft, 
 
 . 61.00 
 
689 
 
 Comparison of Heads of Water in Feet with Pressures in Various 
 Units. 
 
 One foot of water at 39.1° Fahr. = 62.425 lbs. on the square foot; 
 
 = . 4335 lbs. on the square inch; 
 
 = 0.0295 atmosphere; 
 
 = 0.8826 inch of mercury at 30°; 
 
 _ 77 o of feet of air at 32° and 
 
 1 atmospheric pressure ; 
 One lb. on the square foot, at 39.1° Fahr.. = 0.01602 foot of water; 
 One lb. on the square inch, at 39.1° Fahr .. = 2.307 feet of water; 
 One atmosphere of 29 . 922 in. of mercury . . = 33 . 9 feet of water; 
 
 One inch of mercury at 32. 1° = 1 . 133 feet of water; 
 
 One foot of air at 32°, and 1 atmosphere. . = 0.001293 feet of water; 
 
 One foot of average sea-water = 1 .026 foot of pure water; 
 
 One foot of water at 62° F = 62 . 355 lbs. per sq. foot ; 
 
 One foot of water at 62° F = . 43302 lb. per sq. inch; 
 
 One inch of water at 62° F. = .5774 ounce = 0.036085 lb. per sq. inch; 
 One lb. of water on the square inch at 62° F= 2. 3094 feet of water. 
 One ounce of water on the square inch at 
 
 62° F = 1 . 732 inches of water. 
 
 Pressure in Pounds per Square Inch for Different Heads of Water. 
 
 At 62° F. 1 foot head = 0.433 lb. per square inch, 0.433 X 144 = 62.352 
 lbs. per cubic foot. 
 
 Head, feet. 
 
 
 
 1 
 
 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 
 
 23.382 
 
 23.815 
 
 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 lb. per square inch = 2.30947 feet head, 1 atmosphere = 14.7 lbs. 
 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 .62103.931106.24 108.55 
 
 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 
 
 147.811150.12152.42 
 
 154.73 
 
 157.04 
 
 159.35 
 
 70 
 
 161.6629 
 
 163.97 
 
 166.28 
 
 168.59 
 
 170.90 1 173.21 1175.52 
 
 177.83 
 
 180.14 
 
 182.45 
 
 80 
 
 184.7576 
 
 187.07 
 
 189.38 
 
 191.69 
 
 194.00196.31 198.61 
 
 200.92 
 
 203.23 
 
 205.54 
 
 90 
 
 207.8523 
 
 210.16 
 
 212.47 
 
 214.78 
 
 217.09 219.40 221 .71 
 
 224.02 
 
 226.33 
 
 228.64 
 
690 
 
 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 lb. per square inch for every foot of head, 
 or 62.355 lbs. 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 lbs. 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 lbs. 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 cohesion of its atoms is greatly increased, so that its temperature 
 may be raised over 50° above the ordinary boiling-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.) 
 
 Freezing-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 lb. 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.) 
 
THE IMPURITIES OF WATER. 
 
 691 
 
 Ice and Snow. (From Clark.) — 1 cubic foot of ice at 32° F. weighs 
 57.50 lbs.; 1 pound of ice at 32° F. has a volume of 0.0174 cu. ft. = 30.067 
 cu. in. 
 
 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 62° F. being 1. 
 
 At high pressures the melting-point of ice is lower than 32° F., being at 
 the rate of 0.0133° F. for each additional atmosphere of pressure. 
 
 The specific heat of ice is 0.504, that of water being 1. 
 
 1 cubic foot of fresh snow, according to humidity of atmosphere: 
 5 lbs. to 12 lbs. 1 cubic foot of snow moistened and compacted by 
 rain: 15 lbs. to 50 lbs. (Trautwine.) 
 
 Specific Heat of Water. (From Davis and Marks's Steam Tables.) 
 
 Deg. Sp. 
 
 Deg. 
 
 Sp. 
 
 Deg. 
 
 Sp. 
 
 Deg. 
 
 Sp. 
 
 Deg. 
 
 k. 
 
 Deg. 
 
 Sp. 
 
 F. Ht. 
 
 F. 
 
 Ht. 
 
 F. 
 
 Ht. 
 
 F. 
 
 Ht. 
 
 F. 
 
 F. 
 
 Ht. 
 
 20 1.0168 
 
 120 
 
 0.9974 
 
 220 
 
 1.007 
 
 320 
 
 1.035 
 
 420 
 
 1.072 
 
 520 
 
 1.123 
 
 30 1.0098 
 
 130 
 
 0.9974 
 
 230 
 
 1.009 
 
 330 
 
 1.038 
 
 430 
 
 1.077 
 
 530 
 
 1.128 
 
 40 1.0045 
 
 140 
 
 0.9986 
 
 240 
 
 1.012 
 
 340 
 
 1.041 
 
 440 
 
 1.082 
 
 540 
 
 1.134 
 
 50 1.0012 
 
 150 
 
 0.9994 
 
 250 
 
 1.015 
 
 350 
 
 1.045 
 
 450 
 
 1.086 
 
 550 
 
 1.140 
 
 60 0.9990 
 
 160 
 
 1.0002 
 
 260 
 
 1.018 
 
 360 
 
 1.048 
 
 460 
 
 1.091 
 
 560 
 
 1.146 
 
 70 0.9977 
 
 170 
 
 1.0010 
 
 270 
 
 1.021 
 
 370 
 
 1.052 
 
 470 
 
 1.096 
 
 570 
 
 1.152 
 
 80 0.9970 
 
 180 
 
 1.0019 
 
 280 
 
 1.023 
 
 380 
 
 1.056 
 
 480 
 
 1.101 
 
 580 
 
 1.158 
 
 90 0.9967 
 
 190 
 
 1.0029 
 
 290 
 
 1.026 
 
 390 
 
 1.060 
 
 490 
 
 1.106 
 
 590 
 
 1.165 
 
 100 0.9967 
 
 200 
 
 1.0039 
 
 300 
 
 1.029 
 
 400 
 
 1.064 
 
 500 
 
 1.112 
 
 600 
 
 1.172 
 
 110 0.9970 
 
 210 
 
 1 .0050 
 
 310 
 
 1.032 
 
 410 
 
 1.068 
 
 510 
 
 1.117 
 
 
 
 These figures are based on the mean value of the heat unit, that is, 
 Vi80 of the heat needed to raise 1 lb. 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 e-ch 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 U. 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 onlv 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 
 
692 WATER. 
 
 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, wich 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 
 slightlv soluble in cold water, less soluble in hot water, insoluble above 
 27Q° 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,} .. f Sc^da^" of 
 
 iroa - J t magnesia, etc. 
 
 quinhatp nf limp " (Addition of carb. soda, 
 
 bulpnate ot lime. { barium hydrate, etc. 
 
 Chloride and sulphate of mag-) r> rtrrnoift „ (Addition of carbonate of 
 
 nesium. \ Corrosion. | godai etc 
 
 Carbonate of soda in large) p ,■•.„ (Addition of barium chlo- 
 
 amounts. ( ^ nmm S- \ ride, etc. 
 
 Acid (in mine waters). Corrosion. Alkali. 
 
 Dissolved carbonle aeid and} Com>sion . j^oMef UrnTa*,^ ffi 
 
 oxygen - m l ternal coating. 
 
 Grease (from condensed water). lf^?5J°B ° r l Different cases require dif- 
 • Primfne ■ ferent remedies. Consult 
 
 Organic matter (sewage). \ corrosion or fjp ecialist on the sub ' 
 
 ( incrustation/ jec1. 
 
 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: 
 
THE IMPURITIES OF WATER. 
 
 693 
 
 
 Analyses of Boiler-scale. (Chandler.) 
 
 
 
 
 Sul- 
 phate 
 
 of 
 Lime. 
 
 Mag- 
 nesia. 
 
 Silica. 
 
 Per- 
 oxide 
 
 of 
 Iron. 
 
 Water. 
 
 Car- 
 bonate 
 
 of 
 Lime. 
 
 N.Y.C.&H.R 
 
 .Ry.,No. 1 
 No. 2 
 No. 3 
 No. 4 
 No. 5 
 No. 6 
 No. 7 
 No. 8 
 No. 9 
 No. 10 
 
 74.07 
 71.37 
 62.86 
 53.05 
 46.83 
 30.80 
 4.95 
 0.88 
 4.81 
 30.07 
 
 9.19 
 "\8.95 
 
 2.61 
 
 2.84 
 
 0.65 
 1.76 
 2.60 
 4.79 
 5.32 
 7.75 
 2.07 
 0.65 
 2.92 
 8.24 
 
 0.08 
 
 1.14 
 
 14.78 
 
 '.! "t 
 
 0.92 
 
 1.28 
 
 12.62 
 
 •I •< i 
 
 
 
 
 :: :•: : 
 
 1.08 
 1.03 
 0.36 
 
 2.44 
 0.63 
 0.15 
 
 26.93 
 86.25 
 93.19 
 
 •i << . 
 
 
 
 
 
 
 
 
 Analyses in parts per 100,000 of Water giving Bad Results in 
 Steam-boilers. (A. E. Hunt.) 
 
 
 ll 
 
 3 3 
 
 03 
 
 fl.S 
 
 s : 
 
 
 
 
 
 
 
 
 i 
 
 
 L"pq 
 
 o e 
 
 1§ 
 
 
 .2 
 
 0> 
 
 3 
 
 
 
 <v 
 
 
 '•73 
 
 O 
 02 
 
 
 is 
 
 a -.. 
 : ■ 
 -"- : 
 
 ®T3 
 
 O! 
 
 c 
 
 < 
 
 
 
 oj 
 
 
 
 
 71 OJ 
 
 - - 
 
 .2 o 
 
 a 
 
 3 
 
 03 
 
 zs 
 
 6 
 
 
 'S 
 
 c3 
 
 O 
 13 
 
 
 
 
 
 
 
 
 
 a 
 
 3 
 
 
 
 .2-3 
 
 53 CD 
 
 o 
 
 o 
 
 3 
 
 
 
 2 
 
 o 
 
 M 
 
 2 
 
 
 W 
 
 w 
 
 H 
 
 H 
 
 02 
 
 u 
 
 1-1 
 
 o 
 
 < 
 
 o 
 
 
 110 
 151 
 
 75 
 
 25 
 
 38 
 89 
 
 119 
 190 
 95 
 
 39 
 48 
 170 
 
 890 
 360 
 110 
 
 590 
 990 
 ?\ 
 
 780 
 
 38 
 75 
 
 30 
 21 
 10 
 
 640 
 30 
 80 
 
 
 Salt-well 
 
 1310 
 
 
 36 
 
 
 no 
 
 ?1 
 
 161 
 
 V> 
 
 710 
 
 18 
 
 70 
 
 
 
 
 
 80 
 32 
 30 
 
 70 
 82 
 50 
 
 94 
 61 
 41 
 
 81 
 104 
 68 
 
 219 
 28 
 890 
 
 210 
 190 
 42 
 
 90 
 
 38 
 23 
 
 
 
 
 • i >< 
 
 
 
 
 
 
 
 
 
 
 
 
 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. 
 
694 
 
 WATER. 
 
 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 CaC03 per million. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOs. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOs. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOs. 
 
 c.c. Soap 
 Sol. 
 
 Pts. 
 CaCOs. 
 
 0.7 
 
 1.0 
 
 2.0 
 
 3.0 
 
 
 
 5 
 
 19 
 
 32 
 
 4.0 
 
 5.0 
 
 6.0 
 
 7.0 
 
 46 
 
 60 
 
 74 
 
 89 
 
 8.0 
 
 9.0. 
 
 10.0 
 
 11.0 
 
 103 
 
 118 
 
 133 
 
 .....148 
 
 12.0 
 
 13.0 
 
 14.0 
 
 15.0 
 
 164 
 
 .....180 
 196 
 
 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. 897.) — 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 
 
PURIFYING WATER 695 
 
 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. Cary 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 (HC0 3 ) + Na 2 C0 3 = CaC0 3 + 2 NaHCOs. 
 Mg (HCO3) + Na 2 C0 3 = MgCOs + 2 NaHCOs. 
 (free) C0 2 + Na 2 C0 3 + H 2 = 2 NaHCOs. 
 
 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 lbs.; magnesium 
 sulphate, 120 lbs.; calcium carbonate, 100 lbs.; magnesium carbonate, 
 84 lbs.; calcium chloride, 111 lbs.; magnesium chloride, 95 lbs. 
 
 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 cover 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 + y. 
 
 Ify = x, ax = ab -s- (c — 2). 
 
 If y = 1/2 x, ax = ab -s- (c — 1.5). 
 
696 
 
 WATER. 
 
 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 C0 2 
 
 10.62 
 4.77 
 4.67 
 0.00 
 
 19.48 
 
 
 
 
 9.03 
 
 
 
 
 
 8.85 
 
 
 
 
 
 
 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. diam., 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. 
 
 Total solid matter, grains per gallon 
 
 Carbonates of lime and magnesia 
 
 Sulphates of lime and magnesia 
 
 Silica and oxides of iron and aluminum. . 
 
 Total incrusting solids 
 
 Alkali chlorides 
 
 Alkali sulphates 
 
 Total non-in crusting solids 
 
 Pounds scale-forming matter in 1000 gals 
 
 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 found, 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. 
 
HYDRAULICS. 
 
 697 
 
 Quantity of Pure Reagents Required to Remove One Pound op 
 Incrusting or Corrosive Matter from the Water. 
 
 Incrusting or Corrosive 
 
 Substance Held in 
 
 Solution. 
 
 Amount of Reagent. (Pure.) 
 
 Foaming Mat- 
 ter Increased. 
 
 Sulphuric acid 
 
 Free carbonic acid 
 
 Calcium carbonate 
 
 Calcium sulphate 
 
 Calcium chloride 
 
 Calcium nitrate 
 
 Magnesium carbonate. . . 
 Magnesium sulphate 
 
 Magnesium chloride 
 
 Magnesium nitrate 
 
 Calcium carbonate 
 
 Magnesium carbonate. . 
 Magnesium sulphate . . . 
 *Calcium sulphate 
 
 0.571b. lime plus 1 .08 lbs. soda ash 
 
 1.27 lbs. lime 
 
 0.56 1b. lime 
 
 0.78 1b. soda ash 
 
 . 96 lb . soda ash 
 
 0.65 lb. soda ash 
 
 1 .33 lbs. lime 
 
 0.47 lb. lime plus 0.881b. soda ash. 
 0.59 lb. lime plus 1.11 lbs. soda ash 
 . 38 lb . lime plus . 72 lb . soda ash . 
 
 1 .71 lbs. barium hydrate. 
 4.05 lbs. barium hydrate. 
 1 .42 lbs. barium hydrate. 
 1 .26 lbs. barium hydrate. 
 
 1.45 lbs. 
 
 None 
 
 None 
 
 1.04 lbs. 
 
 1.05 lbs. 
 1.04 lbs. 
 None 
 1.18 lbs. 
 1.22 lbs. 
 1.15 lbs. 
 
 None 
 None 
 None 
 None 
 
 * In precipitating the calcium sulphate, there would also be precipi- 
 tated 0.74 lb. of calcium carbonate or 0.31 lb. of magnesium carbonate, 
 the 1.26 lbs. of barium hydrate performing the work of 0.41 lb. of lime 
 and 0.78 lb. of soda-ash, or for reacting on either magnesium or calcium 
 sulphate, 1 lb. of barium hydrate performs the work of 0.33 lb. of lime 
 plus 0.62 lb. 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 = CV 3 \ / 2gH XLH (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 =cL 2/3 ^2gX (^Htf - V#jS) ( 3) 
 
 For rectangular vertical weirsj 
 
 Q =c2/ 3 V2gHXLh (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; H b = head measured from bottom of 
 orifice; H t = head measured from top of orifice; h = H, corrected for 
 velocity of approach, V a = H + 1.33 V a 2 /2g for weirs with no end con- 
 traction, and. H + 1.4 V^/2 g for weirs with end contraction; a= area in 
 square feet; L=length in feet. 
 
HYDRAULICS. 
 
 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, = V2 gH. The 
 actual velocity at the smaller section of the vena contracta is substan- 
 tially the sam e 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 to H/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; 
 ¥ovH/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 -h 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 his 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.) 
 
 I'saj 
 
 Square Orifices. Length of the Side of the Square, in feet. 
 
 HI 
 
 .02 
 
 .03 
 
 .04 
 
 .05 
 
 .07 
 
 .10 
 
 .12 
 
 .15 
 
 .20 
 
 .40 
 
 .60 
 
 .80 
 
 1.0 
 
 Woo 
 
 
 
 
 
 "7628 
 .623 
 
 T621 
 
 .617 
 
 .616 
 .613 
 
 T6TT 
 .610 
 
 
 
 
 
 
 0.4 
 
 
 
 .643 
 .636 
 
 .637 
 .630 
 
 
 0.6 
 
 660 
 
 .645 
 
 .605 
 
 .601 
 
 .598 
 
 .596 
 
 
 1.0 
 
 648 
 
 .636 
 
 .628 
 
 .622 
 
 .618 
 
 .613 
 
 ,610 
 
 .608 
 
 .605 
 
 .603 
 
 .601 
 
 .600 
 
 .599 
 
 3.0 
 
 632 
 
 .622 
 
 .616 
 
 .612 
 
 .609 
 
 .607 
 
 606 
 
 .606 
 
 .605 
 
 .605 
 
 .604 
 
 .603 
 
 .603 
 
 6.0 
 
 623 
 
 .616 
 
 .612 
 
 .609 
 
 607 
 
 .605 
 
 605 
 
 .605 
 
 .604 
 
 .604 
 
 .603 
 
 .602 
 
 .602 
 
 10. 
 
 616 
 
 .611 
 
 .608 
 
 .606 
 
 .605 
 
 604 
 
 .604 
 
 .603 
 
 .603 
 
 .603 
 
 .602 
 
 .602 
 
 .601 
 
 20. 
 
 606 
 
 605 
 
 604 
 
 603 
 
 602 
 
 607, 
 
 602 
 
 602 
 
 602 
 
 ,601 
 
 .601 
 
 .601 
 
 .600 
 
 100. (?) 
 
 .599 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 .598 
 
 
 
 
 Circular Orifices. 
 
 Diameters, in feet. 
 
 
 
 
 H. 
 
 .02 
 
 .03 
 
 .04 
 
 .05 
 
 .07 
 
 .10 
 
 .12 
 
 .15 
 
 .20 
 
 .40 
 
 .60 
 
 .80 
 
 1.0 
 
 0.4 
 
 
 
 
 .637 
 ,624 
 
 .628 
 .618 
 
 .618 
 .613 
 
 .612 
 ,609 
 
 .606 
 .605 
 
 
 
 
 
 
 0.6 
 
 655 
 
 .640 
 
 ,630 
 
 .601 
 
 596 
 
 .593 
 
 .590 
 
 
 1.0 
 
 644 
 
 .631 
 
 .623 
 
 .617 
 
 .612 
 
 .608 
 
 .605 
 
 .603 
 
 .600 
 
 .598 
 
 .595 
 
 .593 
 
 .591 
 
 2. 
 
 632 
 
 .621 
 
 .614 
 
 610 
 
 607 
 
 .604 
 
 .601 
 
 ,600 
 
 .599 
 
 .599 
 
 .597 
 
 .596 
 
 .593 
 
 4. 
 
 ,623 
 
 .614 
 
 609 
 
 605 
 
 603 
 
 .602 
 
 .600 
 
 .599 
 
 .599 
 
 .598 
 
 .597 
 
 .597 
 
 .596 
 
 6. 
 
 618 
 
 .611 
 
 607 
 
 604 
 
 602 
 
 600 
 
 .599 
 
 .599 
 
 .598 
 
 .598 
 
 .597 
 
 .396 
 
 .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 
 
HYDRAULIC FORMULA. 699 
 
 HYDRAULIC FORMULAE. — 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 lb. per sq. in. 
 = 2.309 ft. head, or 1 ft. head = 0.433 lb. 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 2 *■ 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 \ X slope, 
 
 in which c is a coefficient determined by experiment. (See pages following.) 
 
 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) 
 
 -5- 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 = fVrVs = f v «; r = mean hydraulic 
 radius, s = slope = head ■*- length, v = velocity in feet per second, all 
 dimensions in feet. 
 
 Quantity of Water Discharged. — If Q = discharge in cubic feet 
 per second and a = area of channel, Q = av = ac VVs. 
 
 a Vr is approximately proportional to the discharge. It is a maxi- 
 mum at 308° of the circumference, corresponding to 19/20 of the diameter, 
 and the flow of a conduit 19/20 full is about 5 per cent greater than that of 
 one completely filled. 
 
 Values of the Coefficient c. (Chiefly condensed from P. J. Flynn 
 on Flow of Water.) — Almost all the old hydraulic formulae for finding the 
 
700 
 
 HYDRAULICS. 
 
 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. Gan- 
 guillet 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 formulae 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 coeffi- 
 cient 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 formulae, 
 are generally accepted as being approximately correct. 
 
 Table giving Fall in Feet per Mile, the Distance on Slope corre- 
 sponding to a Fall of 1 Ft., and also the Values of S and V$ 
 for Use in the Formula V = C Vrs. . 
 
 s = H -h L = sine of angle of slope = fall of water-surface (H), In 
 any distance (L), divided by that distance. 
 
 Fall in 
 
 Slope, 
 
 Sine of 
 
 v7. 
 
 Fall in 
 
 Slope, 
 
 Sine of 
 
 V7. 
 
 Feet 
 
 1 Foot 
 
 Slope, 
 
 Feet 
 
 1 Foot 
 
 Slope, 
 
 per Mi. 
 
 in 
 
 s. 
 
 
 per Mi. 
 
 in 
 
 s. 
 
 
 0.25 
 
 21120 
 
 0.0000473 
 
 0.006881 
 
 17 
 
 310.6 
 
 0.0032197 
 
 0.056742 
 
 .30 
 
 17600 
 
 .0000568 
 
 .007538 
 
 18 
 
 293.3 
 
 .0034091 
 
 .058388 
 
 .40 
 
 13200 
 
 .0000758 
 
 .008704 
 
 19 
 
 277.9 
 
 .0035985 
 
 .059988 
 
 .50 
 
 10560 
 
 .0000947 
 
 .009731 
 
 20 
 
 264 
 
 .0037879 
 
 .061546 
 
 .60 
 
 8800 
 
 .0001136 
 
 .010660 
 
 22 
 
 240 
 
 .0041667 
 
 .064549 
 
 .702 
 
 7520 
 
 .0001330 
 
 .011532 
 
 24 
 
 220 
 
 .0045455 
 
 .067419 
 
 .805 
 
 6560 
 
 .0001524 
 
 .012347 
 
 26 
 
 203.1 
 
 .0049242 
 
 .070173 
 
 .904 
 
 5840 
 
 .0001712 
 
 .013085 
 
 28 
 
 188.6 
 
 .0053030 
 
 .072822 
 
 1 
 
 5280 
 
 .0001894 
 
 .013762 
 
 30 
 
 176 
 
 .0056818 
 
 .075378 
 
 1.25 
 
 4224 
 
 .0002367 
 
 .015386 
 
 35.20 
 
 150 
 
 .0066667 
 
 .081650 
 
 1.5 
 
 3520 
 
 .0002841 
 
 .016854 
 
 40 
 
 132 
 
 .0075758 
 
 .087039 
 
 1.75 
 
 3017 
 
 .0003314 
 
 .018205 
 
 44 
 
 120 
 
 .0083333 
 
 .091287 
 
 2 
 
 2640 
 
 .0003788 
 
 .019463 
 
 48 
 
 110 
 
 .0090909 
 
 .095346 
 
 2.25 
 
 2347 
 
 .0004261 
 
 .020641 
 
 52.8 
 
 100 
 
 .010 
 
 .1 
 
 2.5 
 
 2112 
 
 .0004735 
 
 .021760 
 
 60 
 
 88 
 
 .0113636 
 
 .1066 
 
 2.75 
 
 1920 
 
 .0005208 
 
 .022822 
 
 66 
 
 80 
 
 .0125 
 
 .111803 
 
 3 
 
 1760 
 
 .0005682 
 
 .023837 
 
 70.4 
 
 75 
 
 .0133333 
 
 .115470 
 
 3.25 
 
 1625 
 
 .0006154 
 
 .024807 
 
 80 
 
 66 
 
 .0151515 
 
 .123091 
 
 3.5 
 
 1508 
 
 .0006631 
 
 .025751 
 
 88 
 
 60 
 
 .0166667 
 
 .1291 
 
 3.75 
 
 1408 
 
 .0007102 
 
 .026650 
 
 96 
 
 55 
 
 .0181818 
 
 . 134839 
 
 4 
 
 1320 
 
 .0007576 
 
 .027524 
 
 105.6 
 
 50 
 
 .02 
 
 .141421 
 
 5 
 
 1056 
 
 .0009470 
 
 .030773 
 
 120 
 
 44 
 
 .0227273 
 
 .150756 
 
 6 
 
 880 
 
 .0011364 
 
 .03371 
 
 132 
 
 40 
 
 .025 
 
 .158114 
 
 7 
 
 754.3 
 
 .0013257 
 
 .036416 
 
 160 
 
 33 
 
 .0303030 
 
 .174077 
 
 8 
 
 660 
 
 .0015152 
 
 .038925 
 
 220 
 
 24 
 
 .0416667 
 
 .204124 
 
 9 
 
 586.6 
 
 .0017044 
 
 .041286 
 
 264 
 
 20 
 
 .05 
 
 .223607 
 
 10 
 
 528 
 
 .0018939 
 
 .043519 
 
 330 
 
 16 
 
 .0625 
 
 .25 
 
 11 
 
 443.6 
 
 .0020833 
 
 .045643 
 
 340 
 
 12 
 
 .0833333 
 
 .288675 
 
 12 
 
 440 
 
 .0022727 
 
 .047673 
 
 528 
 
 10 
 
 .1 
 
 .316228 
 
 13 
 
 406.1 
 
 .0024621 
 
 .04962 
 
 660 
 
 8 
 
 .125 
 
 .353553 
 
 14 
 
 377.1 
 
 .0026515 
 
 .051493 
 
 880 
 
 6 
 
 .1666667 
 
 .408248 
 
 15 
 
 352 
 
 .0028409 
 
 .0533 
 
 1056 
 
 5 
 
 .2 
 
 .447214 
 
 16 
 
 330 
 
 .0030303 
 
 .055048 
 
 1320 
 
 4 
 
 .25 
 
 .5 
 
HYDRAULIC FORMULA. 
 
 701 
 
 Values of V r for Circular Pipes, Sewers, and Conduits of Different 
 Diameters. * 
 
 running full or exactly half full. 
 
 Diam., 
 
 v7 
 
 Diam., 
 
 V7 
 
 Diam., 
 
 V7 
 
 Diam., 
 
 V r 
 
 ft. in. 
 
 in Feet. 
 
 ft. in. 
 
 in Feet. 
 
 ft. 
 
 in. 
 
 in Feet. 
 
 ft. in. 
 
 in Feet. 
 
 3/8 
 
 0.088 
 
 2 
 
 0.707 
 
 4 
 
 6 
 
 1.061 
 
 9 
 
 1.500 
 
 1/2 
 
 .102 
 
 2 1 
 
 .722 
 
 4 
 
 7 
 
 1.070 
 
 9 3 
 
 1.521 
 
 3/4 
 
 .125 
 
 2 2 
 
 .736 
 
 4 
 
 8 
 
 1.080 
 
 9 6 
 
 1.541 
 
 1 
 
 .144 
 
 2 3 
 
 .750 
 
 4 
 
 9 
 
 1.089 
 
 9 9 
 
 1.561 
 
 H/4 
 
 .161 
 
 2 4 
 
 .764 
 
 4 
 
 10 
 
 1.099 
 
 10 
 
 1.581 
 
 H/2 
 
 .177 
 
 2 5 
 
 .777 
 
 4 
 
 11 
 
 1.109 
 
 10 3 
 
 1.601 
 
 13/4 
 
 .191 
 
 2 6 
 
 .790 
 
 5 
 
 
 1.118 
 
 10 6 
 
 1.620 
 
 2 
 
 .204 
 
 2 7 
 
 .804 
 
 5 
 
 1 
 
 1.127 
 
 10 9 
 
 1.639 
 
 21/2 
 
 .228 
 
 2 8 
 
 .817 
 
 5 
 
 2 
 
 1.137 
 
 11 
 
 1.658 
 
 3 
 
 .251 
 
 2 9 
 
 .829 
 
 5 
 
 3 
 
 1.146 
 
 11 3 
 
 1.677 
 
 4 
 
 .290 
 
 2 10 
 
 .842 
 
 5 
 
 4 
 
 1.155 
 
 11 6 
 
 1.696 
 
 5 
 
 .323 
 
 2 11 
 
 .854 
 
 5 
 
 5 
 
 1.164 
 
 11 9 
 
 1.714 
 
 6 
 
 .354 
 
 3 
 
 .866 
 
 5 
 
 6 
 
 1.173 
 
 12 
 
 1.732 
 
 7 
 
 .382 
 
 3 1 
 
 .878 
 
 5 
 
 7 
 
 1.181 
 
 12 3 
 
 1.750 
 
 8 
 
 .408 
 
 3 2 
 
 .890 
 
 5 
 
 8 
 
 1.190 
 
 12 6 
 
 1.768 
 
 9 
 
 .433 
 
 3 3 
 
 .901 
 
 5 
 
 9 
 
 1.199 
 
 12 9 
 
 1.785 
 
 10 
 
 .456 
 
 3 4 
 
 .913 
 
 5 
 
 10 
 
 1.208 
 
 13 
 
 1.803 
 
 11 
 
 .479 
 
 3 5 
 
 .924 
 
 5 
 
 11 
 
 1.216 
 
 13 3 
 
 1.820 
 
 1 
 
 .500 
 
 3 6 
 
 .935 
 
 6 
 
 
 1.225 
 
 13 6 
 
 1.837 
 
 1 1 
 
 .520 
 
 3 7 
 
 .946 
 
 6 
 
 3 
 
 1.250 
 
 14 
 
 1.871 
 
 1 2 
 
 .540 
 
 3 8 
 
 .957 
 
 6 
 
 6 
 
 1.275 
 
 14 6 
 
 1.904 
 
 1 3 
 
 .559 
 
 3 9 
 
 .968 
 
 6 
 
 9 
 
 1.299 
 
 15 
 
 1.936 
 
 1 4 
 
 .577 
 
 3 10 
 
 .979 
 
 7 
 
 
 1.323 
 
 15 6 
 
 1.968 
 
 1 5 
 
 .595 
 
 3 11 
 
 .990 
 
 7 
 
 3 
 
 1.346 
 
 16 
 
 2. 
 
 1 6 
 
 .612 
 
 4 
 
 1. 
 
 7 
 
 6 
 
 1.369 
 
 16 6 
 
 2.031 
 
 1 7 
 
 .629 
 
 4 1 
 
 1.010 
 
 7 
 
 9 
 
 1.392 
 
 17 
 
 2.061 
 
 1 8 
 
 .646 
 
 4 2 
 
 1.021 
 
 8 
 
 
 1.414 
 
 17 6 
 
 2.091 
 
 1 9 
 
 .661 
 
 4 3 
 
 1.031 
 
 8 
 
 3 
 
 1.436 
 
 18 
 
 2.121 
 
 1 10 
 
 .677 
 
 4 4 
 
 1.041 
 
 8 
 
 6 
 
 1.458 
 
 19 
 
 2.180 
 
 1 11 
 
 .692 
 
 4 5 
 
 1.051 
 
 8 
 
 9 
 
 1.479 
 
 20 
 
 2.236 
 
 Kutter's Formula for measures in feet is 
 
 0.00281\ s . 
 
 Vr\ 
 
 <V^s\ 
 
 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 (h) 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 ^rs = c X Vp X Vs. 
 
 Values, of « in Kutter's Formula. — The accuracy of Kutter's for- 
 mula depends, in a great measure, on the proper selection of the coefficient 
 
702 HYDRAULICS. 
 
 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 n, 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 of 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; fine 
 gravel, well rammed, 1/3 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 = cX ^r X ^s, and taking 
 n, the coefficient of roughness in the formula, = .011, .012, and .013, and 
 s = .001, we have the following values of the coefficient c of different 
 diameters of conduit. 
 
HYDRAULIC FORMULAE. 
 
 703 
 
 Talues of c in Formula » = cX ^r X v * for Metal Pipes and 
 Moderately Smooth Conduits Generally. 
 
 By Kutter's Formula. (# = .001 or greater.) 
 
 Diameter. 
 
 ti=.011 
 
 w = .012 
 
 n=.013 
 
 Diameter. 
 
 71= .011 
 
 n=.012 
 
 n= .013 
 
 ft. in. 
 1 
 
 c= 
 47.1 
 61.5 
 77.4 
 87.4 
 105.7 
 116.1 
 123.6 
 133.6 
 140.4 
 145.4 
 149.4 
 
 c = 
 
 c = 
 
 ft. 
 7 
 8 
 9 
 10 
 11 
 12 
 14 
 16 
 18 
 20 
 
 c= 
 
 152.7 
 
 155.4 
 
 157.7 
 
 159.7 
 
 161.5 
 
 163 
 
 165.8 
 
 168 
 
 169.9 
 
 171.6 
 
 c= 
 
 139.2 
 
 141.9 
 
 144.1 
 
 146 
 
 147.8 
 
 149.3 
 
 152 
 
 154.2 
 
 156.1 
 
 157.7 
 
 c= 
 127 9 
 
 2 
 
 
 
 130 4 
 
 4 
 
 
 
 132.7 
 
 6 
 1 
 
 1 6 
 2 
 3 
 4 
 5 
 6 
 
 77.5 
 94.6 
 104.3 
 111.3 
 120.8 
 127.4 
 132.3 
 136.1 
 
 69.5 
 85.3 
 94.4 
 101.1 
 110.1 
 116.5 
 121.1 
 124.8 
 
 134.5 
 136.2 
 137.7 
 140.4 
 142.1 
 144.4 
 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; that is, within these 
 limits c is constant. We further find that up to a slope of 1 in 2640 
 the value of c is, for all practical purposes, constant, and even up to a 
 slope of 1 in 5000 the difference in the value of c is very little. This is 
 exemplified in the following: 
 
 Value of c for Different Values of vV and * in Kutter 
 with « = .013. 
 
 's Formula, 
 
 Vr 
 
 Slope. 
 1 in 1000 
 
 Slope. 
 1 in 2500 
 
 Slope. 
 1 in 3333.3 
 
 Slope. 
 1 in 5000 
 
 Slope. 
 ! in 10,000 
 
 0.6 
 1 
 
 2 
 
 93.6 
 116.5 
 142.6 
 
 91.5 
 115.2 
 142.8 
 
 90.4 
 114.4 
 143.0 
 
 88.4 
 113.2 
 143.1 
 
 83.3 
 109.7 
 143.8 
 
 The reliability of the values of the coefficient of Kutter's formula for 
 pipes of less than 6 in. diameter is considered doubtful. (See note under 
 table on page 704.) 
 
 Values of c 
 
 for Earthen Channels, by Kutter's Formula, for Use 
 
 
 
 in Formula 
 
 v = t 
 
 V rs . 
 
 
 
 Coefficient of Roughness, 
 
 Coefficient of Roughness, 
 
 
 
 n=.0225. 
 
 
 
 n=.035. 
 
 
 
 vV in feet. 
 
 
 ^/r in feet. 
 
 
 0.4 
 
 1.0 
 
 1.8 
 
 2.5 
 
 4.0 
 
 0.4 
 
 1.0 
 
 1.8 
 
 2.5 
 
 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 
 
 3,333 
 
 34. 
 
 61.2 
 
 80.3 
 
 90.1 
 
 102.2 
 
 18.8 
 
 36.9 
 
 51.6 
 
 59.9 
 
 71 
 
 5,000 
 
 33. 
 
 60.5 
 
 80.3 
 
 90.7 
 
 103.7 
 
 18.3 
 
 36.4 
 
 51.6 
 
 60.4 
 
 72.2 
 
 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 
 
704 
 
 HYDRAULICS. 
 
 Darcy's Formula for clean iron pipes under pressure is 
 rs \ 1/2 
 
 0.00007726 +- 
 
 Darcy's formula, as given by J. B. Francis, C. E., for old cast-iron pipe, 
 lined with deposit and under pressure, is 
 
 ?-<$. 
 
 .00082 (12rf + l/ 
 
 in which d = diameter in feet. 
 
 For Pipes Less_ than 5 inches in Diameter, coefficients (c) in the 
 formula v = c ^rs, from the formula of Darcy, Kutter, and Fanning. 
 
 Diam. 
 
 in 
 inches. 
 
 Darcy, 
 
 for Clean 
 
 Pipes. 
 
 Kutter, 
 
 for 
 «=.011 
 s=.001 
 
 Fanning, 
 
 for Clean 
 
 Iron 
 
 Pipes. 
 
 Diam. 
 
 in 
 inches. 
 
 Darcy, 
 
 for Clean 
 
 Pipes. 
 
 Kutter, 
 
 for 
 n=.011 
 s= .001 
 
 Fanning, 
 
 for Clean 
 
 Iron 
 
 Pipes. 
 
 t 
 
 59.4 
 65.7 
 
 74.5 
 80.4 
 84.8 
 88.1 
 
 32. 
 
 36.1 
 
 42.6 
 
 47.4 
 
 51.9 
 
 55.4 
 
 
 13/4 
 
 2 
 
 21/2 
 
 4 
 
 5 
 
 90.7 
 92.9 
 96.1 
 98.5 
 101.7 
 103.8 
 
 58.8 
 
 61.5 
 
 66. 
 
 70.1 
 
 77.4 
 
 82.9 
 
 92.5 
 94.8 
 
 , 3/ « 
 
 U/4 
 
 
 
 80.4 
 
 96.6 
 103.4 
 
 11/2 
 
 88. 
 
 
 
 Mr. Flynn, in giving the above table, says that the facts show that the 
 coefficients diminish from a diameter of 5 inches to! smaller diameters, 
 and it is a safer plan to adopt coefficients varying with the diameter than 
 a constant coefficient. No opinion is advanced as to what coefficients 
 should be used with Kutter 's formula for small diameters. 
 
 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 31/2 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= v max -25.4 ^rs; v = v&+ 10.87 vVs. 
 
 .'. vjj = v — 10.87 "^rs, in which v = mean velocity in feet per second, 
 r max = maximum surface velocity in feet per second, 1^= 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, 
 
VELOCITY OF WATER IN OPEN CHANNELS. 
 
 705 
 
 Safe Bottom and Mean Velocities. — Ganguillet & Kutter give the 
 following table of safe bottom and mean velocity in channels, calculated 
 from the formula v = v^+ 10.87 ^rs: 
 
 Material of Channel. 
 
 Safe Bottom Velocity 
 Vf), in feet per second. 
 
 Mean Velocity v, in 
 feet per second. 
 
 
 0.249 
 0.499 
 1.000 
 1.998 
 2.999 
 4.003 
 4.988 
 6.006 
 10.009 
 
 0.328 
 
 
 0.656 
 
 
 1.312 
 
 
 2.625 
 
 Pebbles 
 
 3.938 
 
 
 5.579 
 
 Conglomerate, soft slate. . . . 
 
 6.564 
 8.204 
 
 
 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, Eng 1 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, 
 varies as the square of the velocity of the current. 
 
 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 
 
706 HYDRAULICS. 
 
 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: __ 
 
 9 = 5.67 Vag, 
 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. 
 
 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, = - • 
 
 o d + ou 
 
 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. 
 
 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 entrancejand to curves, it was found that the value 
 of c in the formula v = c vVs was from 88 to 93. (Eng'g Record, April 
 14, 1894.) 
 
 Flow of Water in a 20-inch Pipe 75,000 Feet Long. — A com- 
 parison of experimental data with calculations bv 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 lbs. per sq. in. at pumping-station: 
 
 95 100 105 110 115 120 125 130 
 
 Total effective head in feet: 
 
 55 66 77 89 100 
 
 Discharge in U. S. gallons in 24 hours, 1 = 
 2,848 3,165 3,354 3,566 3,804 
 Theoretical discharge bv Darcy's formula: 
 * 2,743 3,004 3,244 3,488 3,699 
 Actual velocity in main in feet per second: 
 2.00 2.24 2.36 2.52 2.68 
 
 112 
 1000: 
 3,904 
 
 123 
 4,116 
 
 135 
 4,255 
 
 3,915 
 
 4,102 
 
 4,297 
 
 2.76 
 
 2.92 
 
 3.00 
 
FLOW OF WATER. 
 
 707 
 
 Flow of Water in Circular Pipes, Sewers, etc., Flowing Full. 
 Based on Kutter's Formula, with n = .013. 
 
 Discharge in cubic feet per second. 
 
 
 Slope, or Head Divided by Length of Pipe. 
 
 
 Diam- 
 
 
 
 
 
 eter. 
 
 
 
 
 
 
 
 
 
 
 1 in 40 
 
 1 in 70 
 
 I in 100 
 
 1 in 200 
 
 1 in 300 
 
 1 in 400 
 
 1 in 500 
 
 1 in 600 
 
 5 in. 
 
 0.456 
 
 0.344 
 
 0.288 
 
 0.204 
 
 0.166 
 
 0.144 
 
 0.137 
 
 0.118 
 
 6 " 
 
 0.762 
 
 0.576 
 
 0.482 
 
 0.341 
 
 0.278 
 
 0.241 
 
 0.230 
 
 0.197 
 
 7 " 
 
 1.17 
 
 0.889 
 
 0.744 
 
 0.526 
 
 0.430 
 
 0.372 
 
 0.355 
 
 0.304 
 
 8 " 
 
 1.70 
 
 1.29 
 
 1.08 
 
 0.765 
 
 0.624 
 
 0.54 
 
 0.516 
 
 0.441 
 
 9 " 
 
 2.37 
 
 1.79 
 
 1.50 
 
 1.06 
 
 0.868 
 
 0.75 
 
 0.717 
 
 0.613 
 
 s= 
 
 1 in 60 
 
 1 in 80 
 
 1 in 100 
 
 1 in 200 
 
 1 in 300 
 
 1 in 400 
 
 1 in 500 
 
 1 in 600 
 
 10 in. 
 
 2.59 
 
 2.24 
 
 2.01 
 
 1.42 
 
 1.16 
 
 1.00 
 
 0.90 
 
 0.82 
 
 11 " 
 
 3.39 
 
 2.94 
 
 2.63 
 
 1.86 
 
 1.52 
 
 1.31 
 
 1.17 
 
 1.07 
 
 12 " 
 
 4.32 
 
 3.74 
 
 3.35 
 
 2.37 
 
 1.93 
 
 1.67 
 
 1.5 
 
 1.37 
 
 13 " 
 
 5.38 
 
 4.66 
 
 4.16 
 
 2.95 
 
 2.40 
 
 2.08 
 
 1.86 
 
 1.70 
 
 14 " 
 
 6.60 
 
 5.72 
 
 5.15 
 
 3.62 
 
 2.95 
 
 2.57 
 
 2.29 
 
 2.09 
 
 s = 
 
 1 in 100 
 
 1 in 200 
 
 1 in 300 
 
 1 in 400 
 
 1 in 500 
 
 1 in 600 
 
 1 in 700 
 
 1 in 800 
 
 15 in. 
 
 6.18 
 
 4.37 
 
 3.57 
 
 3.09 
 
 2.77 
 
 2.52 
 
 2.34 
 
 2.19 
 
 16 " 
 
 7.38 
 
 5.22 
 
 4.26 
 
 3.69 
 
 3.30 
 
 3.01 
 
 2.79 
 
 2.61 
 
 18 " 
 
 10.21 
 
 7.22 
 
 5.89 
 
 5.10 
 
 4.56 
 
 4.17 
 
 3.86 
 
 3.61 
 
 20 " 
 
 13.65 
 
 9.65 
 
 7.88 
 
 6.82 
 
 6.10 
 
 5.57 
 
 5.16 
 
 4.83 
 
 22 " 
 
 17.71 
 
 12.52 
 
 10.22 
 
 8.85 
 
 7.92 
 
 7.23 
 
 6.69 
 
 6.26 
 
 s = 
 
 1 in 200 
 
 1 in 400 
 
 1 in 600 
 
 1 in 800 
 
 1 in 1000 
 
 1 in 1250 
 
 1 in 1500 
 
 1 in 1800 
 
 2ft. 
 
 15.88 
 
 11.23 
 
 9.17 
 
 7.94 
 
 7.10 
 
 6.35 
 
 5.80 
 
 5.29 
 
 2ft. 2in. 
 
 19.73 
 
 13.96 
 
 11.39 
 
 9.87 
 
 8.82 
 
 7.89 
 
 7.20 
 
 6.58 
 
 2 " 4" 
 
 24.15 
 
 17.07 
 
 13.94 
 
 12.07 
 
 10.80 
 
 9.66 
 
 8.82 
 
 8.05 
 
 2 " 6 " 
 
 29.08 
 
 20.56 
 
 16.79 
 
 14.54 
 
 13.00 
 
 11.63 
 
 10.62 
 
 9 69 
 
 2 " 8 " 
 
 34.71 
 
 24.54 
 
 20.04 
 
 17.35 
 
 15.52 
 
 13.88 
 
 12.67 
 
 11.57 
 
 s = 
 
 1 in 500 
 
 1 in 750 
 
 1 in 1000 
 
 1 in 1250 
 
 lin 1500 
 
 1 in 1750 
 
 1 in 2000 
 
 1 in 2500 
 
 2ft. lOin. 
 
 25.84 
 
 21.10 
 
 18.27 
 
 16.34 
 
 14.92 
 
 13.81 
 
 12.92 
 
 11.55 
 
 3 " 
 
 30.14 
 
 24.61 
 
 21.31 
 
 19.06 
 
 17.40 
 
 16.11 
 
 15.07 
 
 13.48 
 
 3 " 2in. 
 
 34.90 
 
 28.50 
 
 24.68 
 
 22.07 
 
 20.15 
 
 18.66 
 
 17.45 
 
 15.61 
 
 3 " 4 " 
 
 40.08 
 
 32.72 
 
 28.34 
 
 25.35 
 
 23.14 
 
 21.42 
 
 20.04 
 
 17.93 
 
 3 " 6 " 
 
 45.66 
 
 37.28 
 
 32.28 
 
 28.87 
 
 26.36 
 
 24.40 
 
 22.83 
 
 20.41 
 
 s= 
 
 1 in 500 
 
 1 in 750 
 
 lin 1000 
 
 1 in 1250 
 
 lin 1500 
 
 lin 1750 
 
 1 in 2000 
 
 1 in 2500 
 
 3ft. 8in. 
 
 51.74 
 
 42.52 
 
 36.59 
 
 32.72 
 
 29.87 
 
 27.66 
 
 25.87 
 
 23.14 
 
 3 " 10 " 
 
 58.36 
 
 47.65 
 
 41.27 
 
 36.91 
 
 33.69 
 
 31.20 
 
 29.18 
 
 26.10 
 
 4 " 
 
 65.47 
 
 53.46 
 
 46.30 
 
 41.41 
 
 37.80 
 
 34.50 
 
 32.74 
 
 29.28 
 
 4 " 6in. 
 
 89.75 
 
 73.28 
 
 63.47 
 
 56.76 
 
 51.82 
 
 47.97 
 
 44.88 
 
 40.14 
 
 5 " 
 
 118.9 
 
 97.09 
 
 84.08 
 
 75.21 
 
 68.65 
 
 63.56 
 
 59.46 
 
 53.18 
 
 s = 
 
 1 in 750 
 
 1 in 1000 
 
 lin 1500 
 
 1 in 2000 
 
 1 in 2500 
 
 1 in 3000 
 
 1 in 3500 
 
 1 in 4000 
 
 5ft. 6in. 
 
 125.2 
 
 108.4 
 
 88.54 
 
 76.67 
 
 68.58 
 
 62.60 
 
 57.96 
 
 54.21 
 
 6 " 
 
 157.8 
 
 136.7 
 
 ' 111.6 
 
 96.66 
 
 86.45 
 
 78.92 
 
 73.07 
 
 68.35 
 
 6 " 6 " 
 
 195.0 
 
 168.8 
 
 137.9 
 
 119.4 
 
 106.8 
 
 97.49 
 
 90.26 
 
 84.43 
 
 7 " 
 
 237.7 
 
 205.9 
 
 168.1 
 
 145.6 
 
 130.2 
 
 118.8 
 
 110.00 
 
 102.9 
 
 7 " 6 " 
 
 285.3 
 
 247.1 
 
 201.7 
 
 174.7 
 
 156.3 
 
 142.6 
 
 132.1 
 
 123.5 
 
 s= 
 
 1 in 1 500 
 
 1 in 2000 
 
 1 in 2500 
 
 1 in 3000 
 
 1 in 3500 
 
 1 in 4000 
 
 1 in 4500 
 
 1 in 5000 
 
 8 ft. 
 
 239.4 
 
 207.3 
 
 195.4 
 
 169.3 
 
 156.7 
 
 146.6 
 
 138.2 
 
 131.1 
 
 8 " 6in. 
 
 281.1 
 
 243.5 
 
 217.8 
 
 198.8 
 
 184.0 
 
 172.2 
 
 162.3 
 
 154.0 
 
 9 " 
 
 327.0 
 
 283.1 
 
 253.3 
 
 231.2 
 
 214.0 
 
 200.2 
 
 188.7 
 
 179.1 
 
 9 " 6 " 
 
 376.? 
 
 326.4 
 
 291.9 
 
 266.5 
 
 246.7 
 
 230.8 
 
 217.6 
 
 206.4 
 
 10 " 
 
 431.4 
 
 373.6 
 
 334.1 
 
 305.0 
 
 282.4 
 
 264.2 
 
 249.1 
 
 236.3 
 
708 
 
 HYDKAULICS. 
 
 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 
 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 Vr X "^s corre- 
 sponding to different values of the coefficient of roughness, n. (Based on 
 Kutter's formula.) 
 
 
 
 
 Value of ac V r. 
 
 
 
 Diam. 
 
 
 
 
 
 
 
 ft. in. 
 
 
 
 
 
 
 
 
 n=.0l0. 
 
 w= .011. 
 
 n=.012. 
 
 w=.013. 
 
 n=.015. 
 
 n=.0l7. 
 
 6 
 
 6.906 
 
 6.0627 
 
 5.3800 
 
 4.8216 
 
 3.9604 
 
 3.329 
 
 9 
 
 21.25 
 
 18.742 
 
 16.708 
 
 15.029 
 
 12.421 
 
 10.50 
 
 1 
 
 46.93 
 
 41 .487 
 
 37.149 
 
 33.497 
 
 27.803 
 
 23.60 
 
 1 3 
 
 86.05 
 
 76.347 
 
 68.44 
 
 61.867 
 
 51.600 
 
 43.93 
 
 1 6 
 
 141.2 
 
 125.60 
 
 112.79 
 
 102.14 
 
 85.496 
 
 72.99 
 
 1 9 
 
 214.1 
 
 190.79 
 
 171.66 
 
 155.68 
 
 130.58 
 
 III. 8 
 
 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 
 
 8 
 
 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 
 
 33975 
 
 15 
 
 62748 
 
 57103 
 
 52382 
 
 48413 
 
 42040 
 
 37147 
 
 16 
 
 74191 
 
 67557 
 
 62008 
 
 57343 
 
 49823 
 
 44073 
 
 17 
 
 86769 
 
 79050 
 
 72594 
 
 67140 
 
 58387 
 
 51669 
 
 18 
 
 100617 
 
 91711 
 
 84247 
 
 77932 
 
 67839 
 
 60067 
 
 19 
 
 115769 
 
 105570 
 
 96991 
 
 89759 
 
 78201 
 
 69301 
 
 20 
 
 132133 
 
 120570 
 
 110905 
 
 102559 
 
 89423 
 
 79259 
 
FLOW OF WATER IN PIPES. 
 
 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 
 n = 0.013. (Condensed from Flynn on Water Power.) 
 
 Values of a, and also the values of the factors c V r and ac vV for use 
 
 in the formulae Q = av; v = c V r x v's, and Q = ac Vr X v 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 700.) 
 
 
 
 Clean Cast-iron 
 
 Value of 
 
 Old Cast 
 
 -iron Pines 
 
 Size 01 jripe. 
 
 Pipes. 
 
 ac VV by 
 
 Lined with Deposit. 
 
 
 
 
 
 Kutter's 
 
 Formula, 
 
 when 
 
 
 
 d=diam. 
 in 
 
 a = area in 
 square 
 
 For 
 Velocity, 
 
 For Dis- 
 charge, 
 
 For 
 Velocity, 
 
 For 
 Discharge, 
 
 ft. in. 
 
 feet. 
 
 cV r . 
 
 ac v r. 
 
 n=.013. 
 
 c^r. 
 
 ac^7. 
 
 3/8 
 
 .00077 
 
 5.251 
 
 .00403 
 
 
 3.532 
 
 .00272 
 
 1/2 
 
 .00136 
 
 6.702 
 
 .00914 
 
 
 4.507 
 
 .00613 
 
 3/4 
 
 .00307 
 
 , 9.309 
 
 .02855 
 
 
 6.261 
 
 .01922 
 
 1 
 
 .00545 
 
 11.61 
 
 .06334 
 
 
 7.811 
 
 .04257 
 
 H/4 
 
 .00852 
 
 13.68 
 
 .11659 
 
 
 9.255 
 
 .07885 
 
 H/2 
 
 .01227 
 
 15.58 
 
 .19115 
 
 
 10.48 
 
 .12855 
 
 13/ 4 
 
 .01670 
 
 17.32 
 
 .28936 
 
 
 11.65 
 
 .19462 
 
 2 
 
 .02182 
 
 18.96 
 
 .41357 
 
 
 12.75 
 
 .27824 
 
 21/2 
 
 .0341 
 
 21.94 
 
 .74786 
 
 
 14.76 
 
 .50321 
 
 3 
 
 .0491 
 
 24.63 
 
 1.2089 
 
 
 16.56 
 
 .81333 
 
 4 
 
 .0873 
 
 29.37 
 
 2.5630 
 
 
 19.75 
 
 1.7246 
 
 3 
 
 .136 
 
 33.54 
 
 4.5610 
 
 
 22.56 
 
 3.0681 
 
 6 
 
 .196 
 
 37.28 
 
 7.3068 
 
 4.822 
 
 25.07 
 
 4.9147 
 
 7 
 
 .267 
 
 40.65 
 
 10.852 
 
 
 27.34 
 
 7.2995 
 
 8 
 
 .349 
 
 43.75 
 
 15.270 
 
 
 29.43 
 
 10.271 
 
 9 
 
 .442 
 
 46.73 
 
 20.652 
 
 15.03 
 
 31.42 
 
 13.891 
 
 10 
 
 .545 
 
 49.45 
 
 26.952 
 
 
 33.26 
 
 18.129 
 
 11 
 
 .660 
 
 52.16 
 
 34.428 
 
 
 35.09 
 
 23.158 
 
 
 .785 
 
 54.65 
 
 42.918 
 
 33.50 
 
 36.75 
 
 28.867 
 
 1 2 
 
 1.000 
 
 59.34 
 
 63.435 
 
 
 39.91 
 
 42.668 
 
 1 4 
 
 1.396 
 
 63.67 
 
 88.886 
 
 
 42.83 
 
 59.788 
 
 1 6 
 
 1.767 
 
 67.75 
 
 119.72 
 
 102.14 
 
 45.57 
 
 80.531 
 
 1 8 
 
 2.182 
 
 71.71 
 
 156.46 
 
 
 48.34 
 
 105.25 
 
 1 10 
 
 2.640 
 
 75.32 
 
 198.83 
 
 
 50.658 
 
 133.74 
 
 
 3.142 
 
 78.80 
 
 247.57 
 
 224.63 
 
 52.961 
 
 166.41 
 
 2 2 
 
 3.687 
 
 82.15 
 
 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 
 
 
 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 
 
 
 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 
 
 
 19.635 
 
 126.1 
 
 2476.4 
 
 2659 
 
 84.83 
 
 1665.7 
 
 3 3 
 
 21.648 
 
 129.3 
 
 2799.7 
 
 
 86.99 
 
 1883.2 
 
 5 6 
 
 23.758 
 
 132.4 
 
 3146.3 
 
 3429 
 
 89.07 
 
 2116.2 
 
 3 9 
 
 25.967 
 
 135.4 
 
 3516 
 
 
 91.08 
 
 2365 
 
 
 28.274 
 
 138.4 
 
 3912.8 
 
 4322 
 
 93.08 
 
 2631.7 
 
 6 6 
 
 33.183 
 
 144.1 
 
 4782.1 
 
 5339 
 
 96.93 
 
 3216.4 
 
 
 38.485 
 
 149.6 
 
 5757.5 
 
 6510 
 
 100.61 
 
 3872.5 
 
710 
 
 HYDRAULICS. 
 
 Size of Pipe. 
 
 Clean Cast-iron 
 Pipes. 
 
 Value of 
 
 ac Vr by 
 Kutter's 
 
 Old Cast-iron Pipes 
 Lined with Deposit. 
 
 
 
 
 
 
 
 d=diam. 
 
 a = area 
 
 For 
 
 For Dis- 
 
 Formula, 
 
 For 
 
 For 
 
 in 
 
 in 
 
 Velocity, 
 
 charge, 
 
 when 
 
 Velocity, 
 
 Discharge, 
 ac V r. 
 
 ft. in. 
 
 square 
 feet. 
 
 cv;. 
 
 ac^r. 
 
 n=.013 
 
 cV r . 
 
 7 6 
 
 44.179 
 
 154.9 
 
 6841.6 
 
 7814 
 
 104.11 
 
 4601.9 
 
 8 
 
 50.266 
 
 160 
 
 8043 
 
 9272 
 
 107.61 
 
 5409.9 
 
 8 6 
 
 56.745 
 
 165 
 
 9364.7 
 
 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 
 
 8320.6 
 
 10 
 
 78.540 
 
 179.1 
 
 14066 
 
 16709 
 
 120.4 
 
 9460.9 
 
 10 6 
 
 86.590 
 
 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 
 
 165.130 
 
 216.0 
 
 35660 
 
 44322 
 
 145.2 
 
 23986 
 
 15 
 
 176.715 
 
 219.6 
 
 38807 
 
 48413 
 
 147.7 
 
 26103 
 
 -15 6 
 
 188.692 
 
 223.3 
 
 42125 
 
 52753 
 
 150.1 
 
 28335 
 
 16 
 
 201.062 
 
 226.9 
 
 45621 
 
 57343 
 
 152.6 
 
 30686 
 
 16 6 
 
 213.825 
 
 230.4 
 
 49273 
 
 62132 
 
 155 
 
 33144 
 
 17 
 
 226.981 
 
 233.9 
 
 53082 
 
 67140 
 
 157.3 
 
 35704 
 
 17 6 
 
 240.529 
 
 237.3 
 
 57074 
 
 72409 
 
 159.6 
 
 38389 
 
 18 
 
 254.470 
 
 240.7 
 
 61249 
 
 77932 
 
 161.9 
 
 41199 
 
 19 
 
 283.529 
 
 247.4 
 
 70154 
 
 89759 
 
 166.4 
 
 47186 
 
 20 
 
 314.159 
 
 253.8 
 
 79736 
 
 102559 
 
 170.7 
 
 53633 
 
 Flow of Water in Pipes from. 3/ 8 Inch to 12 Inches Diameter for a 
 Uniform Velocity of 100 Ft. per Min. 
 
 Diam. 
 
 Area 
 
 Cu. Ft. 
 
 U. S. 
 Gallons 
 per Min. 
 
 Diam. 
 
 Area 
 
 Cu. Ft. 
 
 U. S. 
 Gallons 
 per Min. 
 
 in In. 
 
 Sq. Ft. 
 
 per. Min. 
 
 in In. 
 
 Sq. Ft. 
 
 per Min. 
 
 3/8 
 
 .00077 
 
 0.077 
 
 .57 
 
 4 
 
 .0873 
 
 8.73 
 
 65.28 
 
 1/2 
 
 .00136 
 
 0.136 
 
 1.02 
 
 5 
 
 .136 
 
 13.6 
 
 102.00 
 
 3/ 4 
 
 .00307 
 
 0.307 
 
 2.30 
 
 6 
 
 .196 
 
 19.6 
 
 146.88 
 
 1 
 
 .00545 
 
 0.545 
 
 4.08 
 
 7 
 
 .267 
 
 26.7 
 
 199.92 
 
 U/4 
 
 .00852 
 
 0.852 
 
 6.38 
 
 8 
 
 .349 
 
 34.9 
 
 261.12 
 
 H/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 
 
 2 
 
 .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 
 
 
 
 
 
 Short Formulae. E. Sherman Gould, Eng. News, Sept. 6, 1900, 
 shows that Darcy's formulae for cast-iron pipes may be reduced to the fol- 
 lowing approximate forms, in which h is loss of head or drop of hydraulic 
 grade line in feet per 1000, d in ft., v in ft. per sec, Q in cu. ft. per sec. 
 
 8 in. to 48 in. diam. 
 
 3 to 6 in. diam. 
 
 (Rough, Q 2 = hd 5 ; 
 (Smooth, Q 2 = 2hd 5 ; v 
 (Rough, Q 2 = 0.785M5 
 (Smooth, Q* = 1.57MS; 
 
 = 1.27 VtfL 
 = 1.80 VdflT 
 
 v = 1.13 Vdh. 
 v = 1.60 *Sdh. 
 
FLOW OF WATER IN PIPES. 
 
 711 
 
 Flow of Water in Circular Pipes from 3/ 8 Inch to 12 Inches 
 Diameter. 
 
 Based on Darcy's formula for clean cast-iron pipes. Q = ac vV Vg. 
 
 Value 
 
 Dia. 
 in. 
 
 Slope, or Head Divided by Length of Pipe. 
 
 of acvr. 
 
 1 in 10 
 
 lin20 
 
 1 in 40 
 
 I in 60 
 
 1 in 80 
 
 1 in 100 
 
 1 in 150 
 
 1 in 200 
 
 
 
 
 Quan 
 
 tity in 
 
 cubic 
 
 feet per 
 
 second. 
 
 
 
 .00403 
 
 3/s 
 
 .00127 
 
 .00090 
 
 .00064 
 
 .00052 
 
 .00045 
 
 .00040 
 
 .00033 
 
 .00028 
 
 .00914 
 
 l/o 
 
 .00289 
 
 .00204 
 
 .00145 
 
 .00118 
 
 .00102 
 
 .00091 
 
 .00075 
 
 .00065 
 
 .02855 
 
 3/1 
 
 .00903 
 
 .00638 
 
 .00451 
 
 .00369 
 
 .00319 
 
 .00286 
 
 .00233 
 
 .00202 
 
 .06334 
 
 1 
 
 .02003 
 
 .01416 
 
 .01001 
 
 .00818 
 
 .00708 
 
 .00633 
 
 .00517 
 
 .00448 
 
 .11659 
 
 11/4 
 
 .03687 
 
 .02607 
 
 .01843 
 
 .01505 
 
 .01303 
 
 .01166 
 
 .00952 
 
 .00824 
 
 .19115 
 
 \lfc 
 
 .06044 
 
 .04274 
 
 .03022 
 
 .02468 
 
 .02137 
 
 .01912 
 
 .01561 
 
 .01352 
 
 .28936 
 
 13/i 
 
 .09140 
 
 .06470 
 
 .04575 
 
 .03736 
 
 .03235 
 
 .02894 
 
 .02363 
 
 .02046 
 
 .41357 
 
 ?, 
 
 .13077 
 
 .09247 
 
 .06539 
 
 .05339 
 
 .04624 
 
 .04136 
 
 .03377 
 
 .02927 
 
 .74786 
 
 2 l/o 
 
 .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 V s = 
 
 0.3162 
 
 0.2236 
 
 0.1581 
 
 0.1291 
 
 0.1118 
 
 0.1 
 
 0.08165 
 
 0.07071 
 
 Value. Dia. ] Jn 250 , in300 , in350 , in 400 , in 450 , in500 
 of acVr. in. 
 
 1 in 550 1 in 600 
 
 .00403 
 .00914 
 .02855 
 .06334 
 .11659 
 .19115 
 .28936 
 .41357 
 .74786 
 1.2089 
 2.5630 
 4.5610 
 7.3068 
 10.852 
 15.270 
 20.652 
 26.952 
 34.428 
 42.918 
 
 1/2 
 
 I 3 ' 4 
 
 11/4 
 
 »l/2 
 
 13/ 4 
 
 2 
 
 21/2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 10 
 11 
 12 
 
 .00025 
 .00058 
 .00181 
 .00400 
 .00737 
 .01209 
 .01830 
 .02615 
 .04730 
 .07645 
 .16208 
 .28843 
 .46208 
 .68628 
 .96567 
 1 3060 
 1.7044 
 2.1772 
 2.7141 
 
 .00023 
 .00053 
 .00165 
 .00366 
 .00673 
 .01104 
 .01671 
 .02388 
 .04318 
 .06980 
 .14799 
 .26335 
 .42189 
 .62660 
 .88158 
 1.1924 
 1.5562 
 1 .9878 
 2.4781 
 
 .00022 
 .00049 
 .00153 
 .00339 
 .00623 
 .01022 
 .01547 
 .02211 
 .03997 
 .06462 
 . 13699 
 .24379 
 .39055 
 .58005 
 .81617 
 1 . 1038 
 1.4405 
 1.8402 
 2.2940 
 
 .00020 
 .00046 
 .00143 
 .00317 
 .00583 
 .00956 
 .01447 
 .02068 
 .03739 
 .06045 
 .12815 
 .22805 
 .36534 
 .54260 
 .76350 
 1.0326 
 1 .3476 
 1.7214 
 2.1459 
 
 .00019 
 .00043 
 .00134 
 .00298 
 .00549 
 .00901 
 .01363 
 .01948 
 .03523 
 .05695 
 .12074 
 .21487 
 .34422 
 .51124 
 .71936 
 .97292 
 1.2697 
 1.6219 
 2.0219 
 
 .00018 
 .00041 
 .00128 
 .00283 
 .00521 
 .00855 
 .01294 
 .01849 
 .03344 
 .05406 
 .11461 
 .20397 
 .32676 
 .48530 
 .68286 
 .92356 
 1.2053 
 1.5396 
 1.9193 
 
 .00017 
 .00039 
 .00122 
 .00270 
 .00497 
 .00815 
 .01234 
 .01763 
 .03189 
 .05155 
 . 10929 
 .19448 
 .31156 
 .46273 
 .65111 
 .88060 
 1.1492 
 1.4680 
 1.8300 
 
 Value of ^S' 
 
 .06324 .05774 .05345 .05 
 
 .04711 
 
 For U. S. gals, per sec, multiply the figures in the table by 7.4805 
 
 " " min., " " " " ... 48.83 
 " " hour, " " " " .. . 26929.8 
 " 24hrs., " " " " ...646315. 
 
 For any other slope the flow is proportional to the square root of the 
 slope; thus, flow in slope of 1 in 100 is double that in slope of 1 in 400. 
 
712 
 
 HYDRAULICS. 
 
 Flow of Water in House-service Pipes. 
 
 Mr. E. Kuichling, C. E., furnished the following table to the Thomson 
 Meter Co.: 
 
 
 . 
 
 Discharge, 
 
 or Quantity capable of being delivered, in 
 
 
 •— 
 
 Cubic Feet pei 
 
 Minute, from the Pipe, under the 
 
 
 •S ft .S 
 
 3 d oj 
 
 £&£ 
 F4 
 
 conditions 
 
 specified in the first column. 
 
 Condition of 
 Discharge. 
 
 Nominal Diameters of Iron or Lead Service-pipe in 
 Inches. 
 
 
 1/2 
 
 5/8 
 
 3/4 
 
 1 
 
 11/2 
 
 2 
 
 3 
 
 4 
 
 6 
 
 
 30 
 
 1.10 
 
 1.92 
 
 3.01 
 
 6.13 
 
 16.58 
 
 33.34 
 
 88.16 
 
 173.85 
 
 444.63 
 
 Through 35 
 
 40 
 
 1.27 
 
 2.22 
 
 3.48 
 
 7.08 
 
 19.14 
 
 38.50 
 
 101.80 
 
 200.75 
 
 513.42 
 
 feet of ser- 
 
 50 
 
 1.42 
 
 2.48 
 
 3.89 
 
 7.92 
 
 21.40 
 
 43.04 
 
 113.82 
 
 224.44 
 
 574.02 
 
 vice-pipe, 
 
 60 
 
 1.56 
 
 2.71 
 
 4.26 
 
 8.67 
 
 23.44 
 
 47.15 
 
 124.68 
 
 245.87 
 
 628.81 
 
 no back 
 
 75 
 
 1.74 
 
 3.03 
 
 4.77 
 
 9.70 
 
 26.21 
 
 52.71 
 
 139.39 
 
 274.89 
 
 703.03 
 
 pressure. 
 
 100 
 
 2.01 
 
 3.50 
 
 5.50 
 
 11.20 
 
 30.27 
 
 60.87 
 
 160.96 
 
 317.41 
 
 811.79 
 
 
 130 
 
 2.29 
 
 3.99 
 
 6.28 
 
 12.77 
 
 34.51 
 
 69.40 
 
 183.52 
 
 361.91 
 
 925.58 
 
 
 30 
 
 0.66 
 
 1.16 
 
 1.84 
 
 3.78 
 
 10.40 
 
 21.30 
 
 58.19 
 
 118.13 
 
 317.23 
 
 Through 100 
 
 40 
 
 0.77 
 
 1.34 
 
 2.12 
 
 4.36 
 
 12.01 
 
 24.59 
 
 67.19 
 
 136.41 
 
 366.30 
 
 feet of ser- 
 
 50 
 
 0.86 
 
 1.50 
 
 2.37 
 
 4.88 
 
 13.43 
 
 27.50 
 
 75.13 
 
 152.51 
 
 409.54 
 
 vice-pipe, 
 
 60 
 
 0.94 
 
 1.65 
 
 2.60 
 
 5.34 
 
 14.71 
 
 30.12 
 
 82.30 
 
 167.06 
 
 448.63 
 
 no back 
 
 75 
 
 1.05 
 
 1.84 
 
 2.91 
 
 5.97 
 
 16.45 
 
 33.68 
 
 92.01 
 
 186.78 
 
 501.58 
 
 pressure. 
 
 100 
 
 1.22 
 
 2.13 
 
 3.36 
 
 6.90 
 
 18.99 
 
 38.89 
 
 106.24 
 
 215.68 
 
 579.18 
 
 
 130 
 
 1.39 
 
 2.42 
 
 3.83 
 
 7.86 
 
 21.66 
 
 44.34 
 
 121.14 
 
 245.91 
 
 660.36 
 
 Through 100 
 feet of ser- 
 
 30 
 
 0.55 
 
 0.96 
 
 1.52 
 
 3.11 
 
 8.57 
 
 17.55 
 
 47.90 
 
 97.17 
 
 260.56 
 
 40 
 
 0.66 
 
 1.15 
 
 1.81 
 
 3.72 
 
 10.24 
 
 20.95 
 
 57.20 
 
 116.01 
 
 311.09 
 
 50 
 
 0.75 
 
 1.31 
 
 2.06 
 
 4.24 
 
 11.67 
 
 23.87 
 
 65.18 
 
 132.20 
 
 354.49 
 
 vice-pipe, 
 and 1 5 feet 
 vertical 
 
 60 
 
 0.83 
 
 1.45 
 
 2.29 
 
 4.70 
 
 12.94 
 
 26.48 
 
 72.28 
 
 146.61 
 
 393.13 
 
 75 
 
 0.94 
 
 1.64 
 
 2.59 
 
 5.32 
 
 14.64 
 
 29.96 
 
 81.79 
 
 165.90 
 
 444.85 
 
 100 
 
 1.10 
 
 1.92 
 
 3.02 
 
 6.21 
 
 17.10 
 
 35.00 
 
 95.55 
 
 193.82 
 
 519.72 
 
 rise. 
 
 130 
 
 1.26 
 
 2.20 
 
 3.48 
 
 7.14 
 
 19.66 
 
 40.23 
 
 109.82 
 
 222.75 
 
 597.31 
 
 
 30 
 
 0.44 
 
 0.77 
 
 1.22 
 
 2.50 
 
 6.80 
 
 14.11 
 
 38.63 
 
 78.54 
 
 211.54 
 
 Through 100 
 
 40 
 
 0.55 
 
 0.97 
 
 1.53 
 
 3.15 
 
 8.68 
 
 17.79 
 
 48.68 
 
 98.98 
 
 266.59 
 
 feet of ser- 
 
 50 
 
 0.65 
 
 1.14 
 
 1.79 
 
 3.69 
 
 10.16 
 
 20.82 
 
 56.98 
 
 115.87 
 
 312.08 
 
 vice-pipe, 
 
 60 
 
 0.73 
 
 1.28 
 
 2.02 
 
 4.15 
 
 11.45 
 
 23.47 
 
 64.22 
 
 130.59 
 
 351.73 
 
 and 30 feet 
 
 75 
 
 0.84 
 
 1.47 
 
 2.32 
 
 4.77 
 
 13.15 
 
 26.95 
 
 73.76 
 
 149.99 
 
 403.98 
 
 vertical 
 
 100 
 
 1.00 
 
 1.74 
 
 2.75 
 
 5.65 
 
 15.58 
 
 31.93 
 
 87.38 
 
 177.67 
 
 478.55 
 
 rise. 
 
 130 
 
 1.15 
 
 2.02 
 
 3.19 
 
 6.55 
 
 18.07 
 
 37.02 
 
 101.33 
 
 206.04 
 
 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. 
 
FLOW OF WATER THROUGH NOZZLES. 
 
 713 
 
 2 
 
 OOfM^OOf 
 O0> — TOO 
 
 "T^OSift0>Nf\00OISO>OVC0-ift00^»0N0>0\ON0*00 
 mrsiM^NONOiriNBiriOiri— ooovnOW — vo — l> — — ts»N>c 
 
 
 TOOCNlNOONCNlONTONTONONONt->inpO|OTNOOOONO>oom — r*> — 
 TTmmmNONOi>Nt-««aooooNO — NtfitiriiosoooN- mm nooo 
 
 
 
 = 
 
 
 rn OOn T — mO«»,NO — inONOOrnNOrnNOinT 
 TOrNlm<NONONOONOOONONOOaoCNlrriNOO 
 
 — ocoiniMfiOO — 
 
 --(v|N(^t^T'\T'<riJMOin«*tsNOOi3vO^O--Nf 
 
 ooor-»moo — Tno 
 
 o 
 
 tsoomOi>c 
 
 mooorNjoNTminmooinNONomoooo — tcs 
 onoono — tisaNifucoo- Motisoo- r~* 
 
 iNCNicninNooinNO 
 
 ^S^SSi 
 
 OfiNOO* — win — moo — am — NfN]iN.Nm 
 
 mrrimrriTTTinininNONOrN.ooooONONO — 
 
 m — oo — mTinm 
 
 
 
 ON 
 
 OMNOOTt 
 
 mtta-fim(Ni(NitnoNtNO>NOvOi'iO>1 , NOl"t«i!<itiri 
 OTN©NONOToooNoom — omtNoo — NMspNitnoNinrNtfi'NT 
 
 l^jngia 
 
 int^ON — minoo — Tt>.ONO — NooinoNNom 
 CSCN|csirr 1 cn<N-vmTTTinmNONOt>.r«.r-.00ON 
 
 OnON(SN-000 
 OO — cn en Tin m 
 
 co 
 
 c^SSS^ 
 
 OONNI-nOOOO^NnOOiMMIOOOvOCON 
 
 ooNOTOinoNO — TinincNTrnomNomo 
 
 — amONSONtsN 
 
 c< °--- 
 
 on — rn>nNOooominrNONToorNjNoo>'NjooT 
 -N(N)N(NlNwt<N.rfiifiWtNj-ioiniri*NOt> 
 
 ONmoovOT — ooin 
 i^mooooono- — cnj 
 
 - 
 
 — iNQOc^irnnoc^rN^"t^o*\0' — ifi — o^^ON>or^O' — m — coin — TmNO 
 OOMfMMn-NOa>-tn , t'VTm'-Ntr|00'--OONOMritN\OmlsNNIsO>00 
 
 i-oo>-m 
 
 lAONOvO-^iTlMOOflMNONinNM'C 
 
 — — — — rNqtsjcsirgrNjcNrnmrnTTTTinin 
 
 NONONOrNOOOOONON 
 
 o 
 
 On OO On — nO 
 in On O no On 
 
 Nt-OtmOv0t0>NN00(N)N01-!N-O000Mflf0\m'OM 
 
 ifio^MOtntmN- — NOinoinooO'ONOintNiNoo^orNO>o 
 — — — oonpnCNndon — NooMfNrwNiriNOinNMnacAN* 
 
 «-> T !>. 00 On 
 
 — rsitnTTint-NOOON — PNlTr^ON — rninoo — 
 — — — — — --NNNNNmmwwt 
 
 •vrr»O>t00N\OO 
 TTTininNONOt-N 
 
 « 
 
 mo> in oao 
 
 T in OO On — 
 T TOO On On 
 
 inr^r^mr^ONOfsrNinoNinONinooTOT — or->fNmmr^TON 
 
 tfl!fiin00lstC0trflI>N9 0>0VN9NOv0 0\f^-0>0>^in-- 
 
 f>T — r^mONONONOONOTr-iooToofNTrNiONONOoinoooNtNTON 
 
 cnj m t m no 
 
 PnOOOnOnOO — Nd^TiAtsCOO — IJtKOOOONtNOmNOeO 
 
 
 
 T 
 
 Oin no O — 
 
 •Nttvo ooun. 
 ooooons 
 
 ONTONTr-NTinOTOOONCSTON — nOnO— m T On ctn. — oot>.o 
 CNiTOmnqoNNONOooNOr>.in — oooNrnr>NorNooinomt^oor«. 
 tono>— NOOONr>inr-ioomt>.0'— mcnf>iorv,CN)r>.inocninNO 
 
 NNt^fl 
 
 Nor>r>eocoo>o>o-NNTinrN><»o>ON'NT 
 
 inMJO — TnOOOO 
 
 
 T 
 
 no — tiN,nfNiu>NmNO'NtotsoomoNO'ONO^ominl - (Ni 
 
 in Csl — 00t0»t«0NNOONBCNlC0tA0\O— OOOOnO — in 
 
 mT — ooor>.NOo 
 
 — CNjfC|W*lT 
 
 ■NTinif\NONONNWCOaO> — NrnttmrNOO 
 
 o-ofxiTNor^ON — 
 
 
 
 en 
 
 c*3Cc>$oo 
 
 OCtOOOvCOMNl-tNOOINhNlNN— ^OINNtS 
 
 r-N — tNOKitomN- inTtNor^mON — — 
 
 — OONinOTr>ON 
 
 <NCn1cO 
 
 tnTTTinininNONOt>.t>.oooNOO — — mT 
 
 inNONOooo — Nm 
 
 « 
 
 o in o no o 
 08™^ — t 
 
 t o T — lANto- r-jooinONOinrviininoo 
 ooinONtsmm — inoooONor-jtviNor-s.inoT — 
 tsONintNONtnNOO-NinMOOWN.OOtfioONO'NT 
 
 — OO^NOIStsN^ 
 
 O — — MfNl 
 
 'Nmmm'N^mTTTiniriNONOr-.rNOOoooNO 
 
 — i — CN m Tin no in. 
 
 N 
 
 -•nTNINOv 
 n©00 <N T t>. 
 
 moooOinTTNOinONOor>.rnNONOON — inooin 
 m^ooTONmONrninNONO<Nm — noo — ONm 
 
 OC — (Nit^tNONN^NOWnts- TOO— nOCN 
 
 inToomrnONrnON 
 rsNNCrNaiSN 
 
 OO 
 
 -NNNrvlNNwmWW , r^>flifMftNO-or> 
 
 NOOCOaOO-N 
 
 tN 
 
 tNltf\ttMf\'O'Nt'<f^-O<0ONOO*(Nlin(NltCO — M3»O\N*iftinO\'O(N|tf\0000 
 
 tAifMNON-Mm^rm*N»o(Nin'rNo(Ni'Nrt>ONrNiNoa.(NHftomoi'Too 
 
 oooo — 
 
 — — — — — — — pNjrNif-NirvjrNimmmmmTT 
 
 tif\in«iC>ONN 
 
 i 
 
 CO— ■"T'TrNlONNOrNloOrnoOOONOTrviONNOOTr^.ONO — — O-in — — Ontj-oO — 
 Cvlc«>,Tu-NNONOt>.OOaOONONO — CN]tni^iriNOOO>OCNl , r*tM>- TnO On — T 
 
 OOOOOOOOOOO — — — NNNN 
 
 CNirslrnrnmrnTT 
 
 - 
 
 oooom — no — — on too — ovoinoo- oo — in mm no o r^ 
 
 Ov^Oitls- T-OOn — tOOMinoONO\N9CNl<OrflOOOONO 
 
 o — — (N]N(^t^tiMn'Nr'NT'NrinininNO\oiN.»(cova>o- 
 
 csmmmNor>oooN 
 
 o 
 
 i 
 
 S 
 
 m -0 no rq CS — pqornaooooONinON — O — tON^JB 
 .O>m00O>r>.r>. — — r-N,OC-40000TinT000NOT — mT — 
 
 OOnOnOOO— OOCNJO 
 
 ^•rstn in m O 
 — CNmTm 
 
 sONIN — nOON1 , -N^nCOOOOOO>nON 
 (PInOnOInNQOOOONOO — NWiTtNOSINO^ — 
 
 soomt-NOOOoo 
 MTmr^orsTin 
 
 N«\OOiNm8>(Nllft»-Nm»>ONOOOOOO-g 
 — f*"N.NOO*cnNOO'mNOONC<"N.ONNOf s JONNOin(NONNOrc,0 — OO 
 
 NnOOOOnOTCNO 
 
 Qh nN t co' p>i r>.' 
 
 .— in'oToo'm — oon^noooo — minNoomr^oTorNT— -oo 
 pNiCNqmmmTinNONorNooorninrvON — NOOTONmtNogooNO 
 
 m o o o o 
 
 . — CNimT 
 
 SS-S§l§?§|Sg§S||||l 
 
 oooooooo 
 soonOPnITnoSo 
 
714 HYDRAULICS. 
 
 LOSS OF HEAD. 
 
 The loss of head due to friction when water, steam, air, or gas of any 
 kind flows through a straight tube is represented by the formula 
 
 , ,42 D 2 . , «/64.4 hd 
 
 h=f i: 2d' whence v= va T' 
 
 in which I = the length and d = the diameter of the tube, both in feet; 
 v = velocity in feet per second, and /is a coefficient to be determined by 
 experiment. According to Weisbach, / == 0.00644, in which case 
 
 4 /64.4 _ n „ _ n Jhd 
 
 \-rj = 50, and v= 50 \ -— , 
 
 which is one of the older formulae for flow of water (Downing's). Prof. 
 Unwin says that the value of / is possibly too small for tubes of small 
 bore, and he would put / =0.006 to 0.01 for 4-inch tubes, and / = 0.0084 
 to 0.012 for 2-inch tubes. Another formula by Weisbach is 
 
 »-(« 
 
 0.0144 + 
 
 0.01716\ I v* 
 
 Rankine gives 
 
 V v ) d 2g 
 
 /_0.005(l +I f 5 ). 
 
 From the general equation for velocity of flow of water v = c Vr Vs 
 
 = for round pipes c J - 4/ - , we havei; 2 = c 2 - -j and h= —£?■, in which 
 
 c is the coefficient c of Darcy's, Bazin's, Kutter's, or other formula 
 as found by experiment. Since this coefficient varies with the condition 
 of the inner surface of the tube, as well as with the velocity, it is to be 
 expected that values of the loss of head given by different writers will 
 vary as much as those of quantity of flow. 
 
 The relation of the value of c in Chezy 's for mula V = c '^ / rs to the 
 
 e of the coefficient of friction /is c = ^ 
 
 / 2 g/f. 
 
 
 /= .0035 
 c = 135.5 
 /= .0070 
 c= 95.8 
 
 .0040 .0045 .0050 
 127.8 119.6 113.4 
 .0075 .0080 .0090 
 92.6 89.7 84.5 
 
 .0055 
 
 108.1 
 
 .010 
 
 80.2 
 
 .0060 .0065 
 
 103.5 99.4 
 
 .011 .012 
 
 76.5 73.2 
 
 60 70 
 .018 .013 
 
 80 90 100 110 
 .010 .008 .0064 .0053 
 
 120 
 .0045 
 
 130 140 - 150 
 .0038 .0033 .0029 
 
 Equations derived from the formulae. (Unwin.) 
 
 Velocity, ft. per sec v= 4.012 >/dh/(Jl)= 1.273 Q/d*= c Vd/4 X ^s. 
 
 Diameter, ft d= 0.0622 f vl/h = 1.128 ^Q /v. 
 
 Quantity, cu. ft. per sec. Q= 3.149 ^hd 5 /fl. 
 Head, ft h = 0.1008 fQH/d 5 . 
 
 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 Vds, v = 40 Vds^_ 
 
 Q = 44 Vd^s. Q = 31.4 *Sd 5 s. 
 
 d = 0.22^QVs. d = 0.252 ^/QVs. 
 
 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. 
 
LOSS OF HEAD. 
 
 715 
 
 "Values of the Coefficient of Friction. Unwin's "Hydraulics" gives 
 values of/, based on Darcy's experiments, as follows: Clean and smooth 
 pipes, / = 0.005 (1 + 1/12 d). Incrusted pipes, / =0.01 (1 + l/i 2 d). 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). 
 
 Kind of pipe. 
 
 Values of a for velocities in ft. per second. 
 
 Values 
 of j3. 
 
 Drawn wrought iron . . 
 Asphalted cast iron . . . 
 Clean cast iron 
 
 1-2 
 .00375 
 . 00492 
 . 00405 
 
 2-3 
 .00322 
 .00455 
 .00395 
 
 3-4 
 .00297 
 .00432 
 .00387 
 
 4-5 
 .00275 
 .00415 
 .00382 
 
 0.37 
 0.20 
 0.28 
 0.26 
 
 Incrusted cast iron at all velocities a = . 00855 
 
 From the experiments of Clemens Herschel, 1892-6, on clean steel 
 
 riveted pipes, Unwin derives the following values of / for different veloci- 
 ties. 
 
 Ft. per sec 1 2 3 4 5 6 
 
 48-in. pipe, av.of 2. .0066 .0060 .0057 .0055 .0055 .0055 
 
 42-in. pipe, av. of 2. .0067 .0058 .0054 .0054 .0054 .0054 
 
 36-in. pipe 0087 .0071 .0060 .0053 .0047 .0042 
 
 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. 
 
 Two portions of the 48-in. main were tested after being four years in 
 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. E., 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 l = (1 +/o) d -j- 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; (Z>) bell- 
 mouthed inlet, 0.02 to 0.05. Values of l /d are for 
 
 A, 53 B, 75 C, 78 D, 115 
 
 26 38 39 53 
 
 /= 0.005 
 0.010 
 
716 
 
 HYDRAULICS. 
 
 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. 
 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 V 
 
 h 
 0.338 
 
 Q 
 
 32 
 
 h 
 
 Q 
 
 h 
 
 Q 
 53 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 2 
 
 0.296 
 
 41.9 
 
 0.264 
 
 0.237 
 
 65.4 
 
 0.216 
 
 79.2 
 
 0.198 
 
 94 2 
 
 3 
 
 0.698 
 
 48 1 
 
 0.611 
 
 62.8 
 
 0.544 
 
 79 5 
 
 0.488 
 
 98.2 
 
 0.444 
 
 119 
 
 0.407 
 
 141 
 
 4 
 
 1.175 
 
 64.1 
 
 1.027 
 
 83.7 
 
 0.913 
 
 106 
 
 0.822 
 
 131 
 
 0.747 
 
 158 
 
 0.685 
 
 188 
 
 5 
 
 1.76 
 
 80.2 
 
 1.54 
 
 105 
 
 1.37 
 
 132 
 
 1.23 
 
 163 
 
 1.122 
 
 198 
 
 1.028 
 
 235 
 
 6 
 
 2.46 
 
 96.2 
 
 2.15 
 
 125 
 
 1.92 
 
 159 
 
 1.71 
 
 196 
 
 1.56 
 
 237 
 
 1.43 
 
 283 
 
 7.0 
 
 3.26 
 
 112.0 
 
 2.85 
 
 146 
 
 2.52 
 
 185 
 
 2.28 
 
 229 
 
 2.07 
 
 277 
 
 1.91 
 
 330 
 
 
 13 in. 
 
 14 in. 
 
 15 in. 
 
 16 in. 
 
 18 in. 
 
 20 in. 
 
 V 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 2 
 
 0.183 
 
 110 
 
 0.169 
 
 128 
 
 0.158 
 
 147 
 
 0.147 
 
 167 
 
 0.132 
 
 212 
 
 0.119 
 
 262 
 
 3 
 
 .375 
 
 166 
 
 .349 
 
 192 
 
 .325 
 
 221 
 
 .306 
 
 251 
 
 .271 
 
 318 
 
 .245 
 
 393 
 
 4 
 
 .632 
 
 221 
 
 .587 
 
 256 
 
 .548 
 
 294 
 
 .513 
 
 335 
 
 .456 
 
 424 
 
 .410 
 
 523 
 
 5 
 
 .949 
 
 276 
 
 .881 
 
 321 
 
 .822 
 
 368 
 
 .770 
 
 419 
 
 .685 
 
 530 
 
 .617 
 
 654 
 
 6.0 
 
 1.325 
 
 332 
 
 1.229 
 
 385 
 
 1.148 
 
 442 
 
 1.076 
 
 502 
 
 .957 
 
 636 
 
 .861 
 
 785 
 
 7.0 
 
 1.75 
 
 387 
 
 1.63 
 
 449 
 
 1.52 
 
 515 
 
 1.43 
 
 586 
 
 1.27 
 
 742 
 
 1.143 
 
 916 
 
 
 22 in. 
 
 24 in. 
 
 26 in. 
 
 28 in. 
 
 30 in. 
 
 36 in. 
 
 V 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 h 
 
 Q 
 
 2 
 
 0.108 
 
 316 
 
 0.098 
 
 377 
 
 0.091 
 
 442 
 
 0.084 
 
 513 
 
 0.079 
 
 589 
 
 0.066 
 
 848 
 
 3 
 
 .222 
 
 475 
 
 .204 
 
 565 
 
 .188 
 
 663 
 
 .174 
 
 770 
 
 .163 
 
 883 
 
 .135 
 
 1273 
 
 4 
 
 .373 
 
 633 
 
 .342 
 
 754 
 
 .315 
 
 885 
 
 .293 
 
 1026 
 
 .273 
 
 1178 
 
 .228 
 
 1697 
 
 5,0 
 
 .561 
 
 792 
 
 .513 
 
 942 
 
 .474 
 
 1106 
 
 .440 
 
 1283 
 
 .411 
 
 1472 
 
 .342 
 
 2121 
 
 6 
 
 .782 
 
 950 
 
 .717 
 
 1131 
 
 .662 
 
 1327 
 
 .615 
 
 1539 
 
 .574 
 
 1767 
 
 .479 
 
 2545 
 
 7.0 
 
 1.040 
 
 1109 
 
 .953 
 
 1319 
 
 .879 
 
 1548 
 
 .817 
 
 1796 
 
 .762 
 
 2061 
 
 .636 
 
 2868 
 
 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 
 
LOSS OF HEAD. 
 
 717 
 
 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. To 
 reduce pounds pressure to feet multiply by 2.309. 
 
 Cox's Formula. — Weisbach's formula for loss of head caused by the 
 friction of water in pipes is as follows: 
 
 17 • +• u a tn^AA , 0.01716\ L .V- 
 
 Friction-head = (0.0144 H 7=—) g ,_ , , 
 
 \ \/y / 5.367 a 
 
 where L = length of pipe in feet ; 
 
 V = velocity of the water in feet per second; 
 d = diameter of pipe in inches. 
 
 William Cox (Amer. Mach., Dec. 28, 1893) gives a simpler formula 
 which gives almost identical results: 
 
 H = friction-head in feet = 
 
 Hd 
 L 
 
 d 
 4F2+57- 
 
 (1) 
 (2) 
 
 He gives a table by means of which the value of 
 once obtained when V is known, and vice versa. 
 4F2+57-2 
 
 4724. 57 _ 2 
 
 V 
 
 0.0 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 1 
 
 .00583 
 
 .00695 
 
 .00813 
 
 .00938 
 
 .01070 
 
 .01208 
 
 .01353 
 
 .01505 
 
 .01663 
 
 .01828 
 
 2 
 
 .02000 
 
 .02178 
 
 .02363 
 
 .02555 
 
 .02753 
 
 .02958 
 
 .03170 
 
 .03388 
 
 .03613 
 
 .03845 
 
 3 
 
 .04083 
 
 .04328 
 
 .04580 
 
 .04838 
 
 .05103 
 
 .05375 
 
 .05653 
 
 .05938 
 
 .06230 
 
 .06528 
 
 4 
 
 .06833 
 
 .07145 
 
 .07463 
 
 .07788 
 
 .08120 
 
 .08458 
 
 .08803 
 
 .09155 
 
 .09513 
 
 .09878 
 
 5 
 
 .10250 
 
 .10628 
 
 .11013 
 
 .11405 
 
 .11803 
 
 .12208 
 
 .12620 
 
 .13038 
 
 .13463 
 
 .13895 
 
 6 
 
 .14333 
 
 .14778 
 
 .15230 
 
 .15688 
 
 .16153 
 
 .16625 
 
 .17103 
 
 .17588 
 
 .18080 
 
 .18578 
 
 7 
 
 .19083 
 
 .19595 
 
 .20113 
 
 .20638 
 
 .21170 
 
 .21708 
 
 .22253 
 
 .22805 
 
 .22363 
 
 .23928 
 
 8 
 
 .24500 
 
 .25078 
 
 .25663 
 
 .26255 
 
 .26853 
 
 .27458 
 
 .28070 
 
 .28688 
 
 .29313 
 
 .29945 
 
 9 
 
 .30583 
 
 .31228 
 
 .31880 
 
 .32538 
 
 .33203 
 
 .33875 
 
 .34553 
 
 .35238 
 
 .35930 
 
 .36628 
 
 10 
 
 .37333 
 
 .38045 
 
 .38763 
 
 .39488 
 
 .40220 
 
 .40958 
 
 .41703 
 
 .42455 
 
 .43213 
 
 .43978 
 
 11 
 
 .44750 
 
 .45528 
 
 .46313 
 
 .47105 
 
 .47903 
 
 .48708 
 
 .49520 
 
 .50338 
 
 .51163 
 
 .51995 
 
 12 
 
 .52833 
 
 .53678 
 
 .54530 
 
 .55388 
 
 .56253 
 
 .57125 
 
 .58003 
 
 .58888 
 
 .59780 
 
 .60678 
 
 13 
 
 .61583 
 
 .62495 
 
 .63413 
 
 .64338 
 
 .65270 
 
 .66208 
 
 .67153 
 
 .68105 
 
 .69063 
 
 .70028 
 
 !4 
 
 .71000 
 
 .71978 
 
 .72963 
 
 .73955 
 
 .74953 
 
 .75958 
 
 .76970 
 
 .77988 
 
 .79013 
 
 .80045 
 
 15 
 
 .81083 
 
 .82128 
 
 .83180 
 
 .84238 
 
 .85303 
 
 .86375 
 
 .87453 
 
 .88538 
 
 .89630 
 
 .90728 
 
 16 
 
 .91833 
 
 .92945 
 
 .94063 
 
 .95188 
 
 .96320 
 
 .97458 
 
 .98603 
 
 .99755 
 
 1 .00913 
 
 1.02078 
 
 17 
 
 1.03250 
 
 1.04428 
 
 1.05613 
 
 1.06805 
 
 1.08003 
 
 1 .09208 
 
 1 . 10420 
 
 1.11638 
 
 1.12863 
 
 1.14095 
 
 18 
 
 1.15333 
 
 1.16578 
 
 1.17830 
 
 1 . 19088 
 
 1.20353 
 
 1.21625 
 
 1 .22903 
 
 1.24188 
 
 1 .25480 
 
 1.26778 
 
 19 
 
 1.28083 
 
 1.29395 
 
 1.30713 
 
 1.32038 
 
 1.33370 
 
 1 .34708 
 
 1 .36053 
 
 1 .37405 
 
 1 .38763 
 
 1.40128 
 
 20 
 
 1.41500 
 
 1.42878 
 
 1.44263 
 
 1 .45655 
 
 1.47053 
 
 1.48458 
 
 1.49870 
 
 1.51288 
 
 1.52713 
 
 1.54145 
 
 21 
 
 1 .55583 
 
 1.57028 
 
 1.58480 
 
 1.59938 
 
 1.61403 
 
 1 .62875 
 
 1.64353 
 
 1.65838 
 
 1.67330 
 
 1 .68828 
 
 The use of the formula and table is illustrated as follows: 
 
 Given a pipe 5 inches diameter and 1000 feet long, with 49 feet head, 
 
 what will the discharge be? 
 
 If the velocity V is known in feet per second, the discharge is 0.32725 d a V 
 
 cubic foot per minute. 
 
718 HYDRAULICS. 
 
 By equation 2 we have 
 
 4F2+5F- 2 = Hd 
 1200 L 
 
 whence, by table, V = real velocity = 8 feet per second. 
 
 The discharge in cubic feet per minute, if V is velocity in feet per 
 second and d diameter in inches, is 0.32725 dW, whence, discharge 
 
 = 0.3275 X 25 X 8 = 65.45 cubic feet per minute. 
 
 The velocity due the head, if there were no friction, is 8.025 V# 
 = 56.175 feet per second, and the discharge at that velocity would be 
 
 0.32725 X 25 X 56.175 = 460 cubic feet per minute. 
 
 Suppose it is required to deliver this amount, 460 cubic feet, at a 
 velocity of 2 feet per second, what diameter of pipe of the same length 
 and under the same head will be required and what will be the loss of 
 head by friction? j 
 
 d = diameter = 
 
 : V rxo^s - V2OT2B - V70S - 26 - 5 inches - 
 
 Having now the diameter, the velocity, and the discharge, the friction- 
 head is calculated by equation 1 and use of the table; thus, 
 
 „ L4V 2 +5V~2 1000 ^ ftno 20 , „ , , 
 H= d 1200— = 2-6T X °-° 2= 2675= °' 75 f ° 0t ' 
 
 thus leaving 49 — 0.75 = say 48 feet effective head applicable to power- 
 producing purposes. 
 
 Problems of the loss of head may be solved rapidly by means of Cox's 
 Pipe Computer, a mechanical device on the principle of the slide-rule, 
 for sale by Keuffel & Esser, New York. 
 
 Exponential Formulae. Williams and Hazen's Tables. — From 
 Chezy's formula, v = c ^rs, 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°' es s 0-54 , 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 0.001-0-04 to the formula, so that the working formula 
 of Hazen and Williams is 
 
 V = cr 0-63 §0-54 0.001- 0-04 . 
 
 Approximate values given for c are: 
 
 140 for the very best cast-iron pipe, laid straight and when new. 
 130 for good, new cast-iron pipe, very smooth; good masonry aqueducts; 
 small brass pipes.* 
 
 1 20 for cast-iron pipe 5 years old ; riveted steel pipe, new. 
 
 110 for cast-iron pipe 10 years old; steel pipe 10 years old; brick sewers. 
 
 100 for cast-iron pipe 17 years old, roueh. 
 
 90 for cast-iron pipe 26 years old, rough. 
 
 80 for cast-iron pipe 37 years old , very rough. 
 
 * 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.) 
 
LOSS OF HEAD. 
 
 719 
 
 Friction Loss in Clean Cast-iron Pipe. 
 
 Compiled from Weston's "Friction of Water in Pipes" as computed from 
 formulas of Henry Darcy. 
 Pounis loss per 1000 feet in pipe of given diameter. (Small lower 
 figures give Velocity in Feet per Second.) 
 
 U. S.Gals per 
 Min. and (Cu. 
 Ft. per Sec.) 
 
 Diameter of Pipe in Inches. 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 20 
 
 24 
 
 0.00 
 0.18 
 0.01 
 0.35 
 0.02 
 0.53 
 0.03 
 0.71 
 
 30 
 
 250 
 
 (0.56) 
 500 
 (111) 
 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 
 
 0.02 
 0.4 
 0.07 
 0.8 
 0.15 
 1.2 
 0.27 
 1.6 
 
 0.01 
 . 26 
 0.02 
 0.51 
 0.05 
 0.77 
 0.09 
 1.0 
 
 o.oo 
 
 0.23 
 
 6 6\ 
 
 0.45 
 
 1,250 
 
 
 
 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 
 
 9.0 
 7.1 
 12.0 
 8.2 
 
 1.80 
 3.6 
 2.60 
 4.3 
 3.60 
 5.0 
 4.70 
 5.7 
 
 0.83 
 
 2. GO 
 1.10 
 3.13 
 1.6 
 3. 65 
 2.14 
 4.17 
 
 0.42 
 2.0 
 0.61 
 2.4 
 0.83 
 2.8 
 1.10 
 3.2 
 
 0.14 
 1.3 
 0.20 
 1.5 
 0.27 
 l.S 
 0.35 
 2.0 
 
 0.06 
 . Ml 
 0.08 
 1.06 
 0.11 
 1.24 
 0.14 
 1.42 
 
 
 (2.79) 
 1,500 
 
 
 
 
 
 
 03 
 
 (3.34) 
 
 
 
 68 
 
 1,750 
 
 
 
 
 (3.90) 
 
 
 
 
 
 2,000 
 
 
 
 
 05 
 
 (4.46) 
 
 
 
 
 
 
 
 
 
 2,500 
 
 
 
 
 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 
 S.34 
 
 1.70 
 4.0 
 2.40 
 4.8 
 4.30 
 6.4 
 6.80 
 S.O 
 
 0.55 
 
 2.6 
 
 0.79 
 
 3.1 
 
 1.40 
 
 4.1 
 
 2.20 
 
 5.1 
 
 0.22 
 1.80 
 0.32 
 2.10 
 0.56 
 2 . 80 
 1.00 
 3.60 
 
 1.30 
 
 4.30 
 1.70 
 
 5.00 
 2.20 
 5.70 
 2.80 
 6.40 
 
 07 
 
 (5.57) 
 
 Pipe 
 
 inTn 
 
 
 
 113 
 
 3,000 
 
 (6.68) 
 
 
 
 
 10 
 
 36 
 
 48 
 
 
 
 
 1 40 
 
 4,000 
 
 
 
 
 18 
 
 (8.91) 
 
 
 
 
 
 
 
 
 1 80 
 
 5,000 
 
 0.11 
 1.6 
 
 0.03 
 0.89 
 
 
 
 
 
 
 79 
 
 (11.14) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6,000 
 
 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 
 
 41 
 
 (13.37) 
 
 
 
 
 
 
 
 
 2 70 
 
 7,000 
 
 
 
 
 
 
 
 
 56 
 
 (15.60) 
 
 
 
 
 
 
 
 
 3 20 
 
 8,000 
 
 
 
 
 
 
 
 
 71 
 
 (17.82) 
 
 
 
 
 
 
 
 
 
 3 60 
 
 9,000 
 
 
 
 
 
 
 
 
 
 9? 
 
 (20.05) 
 
 
 
 
 
 
 
 
 
 4 10 
 
 10,000 
 
 
 
 
 
 
 
 
 
 1 13 
 
 (22.28) 
 
 
 
 
 
 
 
 
 
 
 4.50 
 
 Vel.ft.per sec. 
 Hd.duevel.ft . 
 
 1 
 0.016 
 
 2 
 0.062 
 
 3 
 
 0.14 
 
 4 
 0.25 
 
 5 
 
 0.39 
 
 6 
 
 0.56 
 
 7 
 0.76 
 
 8 
 1.0 
 
 9 
 13 
 
 10 
 1.6 
 
 11 
 
 1.9 
 
 12 
 
 2.2 
 
 Vel.ft.per sec. 
 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 or. 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 rapidly 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. 
 
720 HYDRAULIC FORMULA. 
 
 Approximate Hydraulic Formulae. (The Lombard Governor Co., 
 Boston, Mass.) 
 
 Head (H) in feet. Pressure (P) in lbs. per sq. in. Diameter (D) in 
 feet. Area (A) in sq. ft. Quantity (Q) in cubic ft. per second. Time 
 (T) in seconds. _ 
 
 Spouting velocity = 8.02 V#. 
 
 Time (7\) to acquire spouting velocity in a vertical pipe, or (Tt) in a 
 pipe on an angle (0) from horizontal: 
 
 T 1 = 8.02 Vff +■ 32.17, T 2 = 8.02 ^H h- 32.17 sin 0. 
 
 Head (#) or pressure (P) which will vent any quantity (Q) through a 
 round orifice of any diameter (Z>) or area (A): 
 
 H=Q 2 + 14.1 D<,= Q 2 •+■ 23.75 A 2 ; P= Q* + 34.1 D 4 ,- Q 2 -h 55.3 A*. 
 
 Quantity (Q) discharged through a round orifice of any diameter (Z>) or 
 area (A) under any pressure (P) or under any head (H): 
 
 Q = V > X 55.3 X A 2 = V PX34.1 X D 4 ; 
 
 = V# x 23.75 X A 2 =V#x 14.71 XD*. 
 
 Diameter (D) or area (A) of a round orifice to vent any quantity (Q) 
 under any head (H) or under any pressure (P) : 
 
 Z) = \/QH-3.84^iJ =V<9-!-5.8^P; A = Q + 4.89V# =Q-=-7.35 V>. 
 
 Time (7 1 ) of emptying a vessel of any area (A) through an orifice of any 
 area (a) anywhere in its side: T = 0.416 A Vf? -j- 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. J 7 = 0.416A(V# — \/j£) -s-a. 
 
 Kinetic energy (K) or foot-pounds in water in a round pipe of any 
 diameter (D) when moving at velocity (V): K = 0.76 X D 2 X L X V. 
 
 Area (a) of an orifice to empty a tank of any area (A) in any time (T) 
 from any head (H): a = T -t- 0.409 A V#. 
 
 Area (a) of an orifice to lower water in a tank of area (A) from head (H) 
 to (/*) in time (T): a = T -*- 0.409 X A X (V# - Vh). 
 
 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 = h x + h 2 + h 3 = 0.1008 /Q 2 (l 1 /d 1 ^ + h/d£ + h/d* 6 ). 
 
 (2) Constant velocity in the main, the discharge jdiminishing from sec- 
 tion to section. H = 0.0551 fv 5/ 2(i,/^Qi+ h/^Q*. + h/^Qz). Equiv- 
 alent main of uniform diameter. Length of equivalent main 
 
 I = d* (h/dj + h/d 2 5 + Zs/ds 6 ). 
 
 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: h = 0.0336 
 fQ 2 l/d 5 , 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 fx (Q x + 0.55 qx)/d 5 . 
 
 Delivery by two or more mains, in parallel. Total discharge = Qt + Q 
 
 +Qa = 3.149 */h/f (y df /l x W dtf> /h+^/ dy> /h) . Diameter of an equivalent 
 
 main to discharge the same total quantity, d= (v^s+V^ +^dy>) 2 l^. 
 
 Long Pipe Lines. — (1) Vyrnwy to Liverpool, 68 miles; 40 million gals. 
 (British) per day. Three lines of cast-iron pipe, 42 to 39 in. diam. One 
 of the 42-in. lines after being laid 12 years, with a hydraulic gradient of 
 
LOSS OF HEAD. 721 
 
 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. 
 
 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. 
 
 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 oil 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 to 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 = To. 131 + 1.847 (^) ?/2 ] 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) conclude 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, 
 
 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. 
 
722 HYDRAULICS. 
 
 Air-bound Pipes. — A pipe is said to be air-bound when, in conse- 
 
 Suence of air being entrapped at the high points of vertical curves in the 
 ne, 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, 
 through which the air may be discharged. The valve may be made auto- 
 matic by means of a float. 
 
 Water-hammer. — Prof. I. P. Church gives the following formula for 
 the pressure developed by the instantaneous closing of a valve in a water 
 pipe: 
 
 V = vCy/g, 
 in which p is pressure in lbs. per sq. in., v velocity in inches per second, 
 C velocity of pr essure wave in inches per second, and g = 386.4 ins. The 
 value of C is ^gEEjt/y (tEx + 2 rE), in which E x = modulus of elasticity, 
 30,000,000 for steel, E = bulk modulus of water = 300,000 lbs. per sq. in. 
 at 50° F, y = 0.03604 = lbs. of water in 1 cu. in., t = thickness of pipe, 
 ins., and r = internal radius of pipe, ins. Example, a 16-in. steel pipe 
 with i/4-in. walls, and v = 60 ins. per second, gives a velocity of the pres- 
 sure wave C = 44,285 ins. per second and a pressure per sq. in. of 2478 
 lbs. If the elasticity of the pipe is not considered, the formula reduces 
 top = 5.29 v, which in the example given gives a pressure of 317.4 lbs. 
 per sq. in. 
 
 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 w 0.96 0.9 0.85 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 table on the following page is condensed 
 from one contained in the pamphlet of " Fire-Stream Tables" of the Asso~ 
 ciated Factory Mutual Fire Ins. Cos., based on the experiments of John R. 
 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 
 nozzles require greater pressures. With the same pressures at the base 
 of the play pipe, the discharge of a3/ 4 -in. smooth nozzle is the same as that 
 of a 7/8-in. 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 
 by adding to the nozzle or play-pipe pressure the friction loss in the 
 hose, and also the friction loss of a Chapman 4-way independent gate 
 
FIRE-STREAMS. 
 
 723 
 
 hydrant ranging from 0.86 lb. for 200 gals, per min. flowing to 2.31 lbs. 
 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, 21/2-in. diam., the loss of head due to 
 friction, for a discharge of 2-10 gallons per minute, is 14.1 lbs. per 100 ft. 
 length; in inferior rubber-lined mill hose, 25.5 lbs., and in unlined linen 
 hose, 33.2 lbs. 
 
 Less than' a 1 1/8-in. smooth-nozzle stream with 40 lbs. 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 lbs. per sq. in. is con- 
 sidered the best hydrant pressure for general use; 100 lbs. 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. 
 
 ,Q 
 
 Fire- 
 steam 
 Distance. 
 
 a 
 
 Hydrant Pressure with Different Lengths of 
 
 Hi 
 
 Hose to Maintain Pressure at Base of Play Pipe. 
 
 V 
 
 Vert. 
 
 Hor. 
 
 6 
 
 52 
 
 50 ft. 
 
 100 ft. 
 
 200 ft. 
 
 300 ft. 
 12 
 
 400 ft. 
 
 500 ft. 
 
 600 ft. 
 
 800 ft. 
 
 1000 
 
 ft. 
 
 10 
 
 17 
 
 19 
 
 10 
 
 11 
 
 11 
 
 13 
 
 13 
 
 14 
 
 15 
 
 16 
 
 20 
 
 33 
 
 29 
 
 73 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 28 
 
 30 
 
 32 
 
 30 
 
 48 
 
 37 
 
 90 
 
 31 
 
 32 
 
 34 
 
 36 
 
 38 1 
 
 40 
 
 41 
 
 45 
 
 49 
 
 40 
 
 60 
 
 44 
 
 104 
 
 42 
 
 43 
 
 46 
 
 48 
 
 50 
 
 53 
 
 55 
 
 60 
 
 65 
 
 50 
 
 67 
 
 50 
 
 116 
 
 52 
 
 54 
 
 57 
 
 60 
 
 63 
 
 66 
 
 69 
 
 75 
 
 81 
 
 60 
 
 72 
 
 54 
 
 127 
 
 63 
 
 65 
 
 68 
 
 72 
 
 76 
 
 79 
 
 83 
 
 90 
 
 97 
 
 70 
 
 76 
 
 58 
 
 137 
 
 73 
 
 75 
 
 80 
 
 84 
 
 88 
 
 92 
 
 97 
 
 105 
 
 114 
 
 80 
 
 79 
 
 62 
 
 147 
 
 84 
 
 86 
 
 91 
 
 96 
 
 101 
 
 106 
 
 111 
 
 120 
 
 no 
 
 90 
 
 81 
 
 65 
 
 156 
 
 94 
 
 97 
 
 102 
 
 108 
 
 113 
 
 119 
 
 124 
 
 135 
 
 146 
 
 100 
 
 83 
 
 68 
 
 164 
 
 105 
 
 108 
 
 114 
 
 120 
 
 126 
 
 132 
 
 138 
 
 150 
 
 163 
 
 7/8-inch smooth nozzle. 
 
 10 
 
 18 
 
 21 
 
 71 
 
 11 
 
 11 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 19 
 
 ?.?. 
 
 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 
 
 I-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 
 
 7.63 
 
 97. 
 
 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 
 
 
 
 
 
 
HYDRAULICS. 
 
 Hydrant Pressures Required with Different Sizes and Lengths of 
 Hose. — Continued. 
 
 1 1/8-inch smooth nozzle. 
 
 
 Fire- 
 Steam 
 Distance. 
 
 a 
 
 a 
 
 
 Hydrant Pressure with Different Lens 
 
 f ths of 
 
 
 ► 3 
 
 Hose to Maintain Pressure at Base of Play Pipe. 
 
 I 
 
 Vert. 
 
 Hor. 
 
 $ 
 
 119 
 
 50 ft. 
 
 100ft. 
 
 200 ft. 
 17 
 
 300 ft. 
 
 400 ft. 
 
 500ft. 
 
 600 ft. 
 
 800 ft. 
 
 1000 
 
 ft. 
 
 10 
 
 18 
 
 22 
 
 12 
 
 14 
 
 20 
 
 24 
 
 27 
 
 30 
 
 36 
 
 43 
 
 20 
 
 36 
 
 38 
 
 168 
 
 25 
 
 28 
 
 34 
 
 41 
 
 47 
 
 54 
 
 60 
 
 73 
 
 85 
 
 30 
 
 52 
 
 50 
 
 206 
 
 37 
 
 42 
 
 52 
 
 61 
 
 71 
 
 80 
 
 90 
 
 109 
 
 128 
 
 40 
 
 65 
 
 59 
 
 238 
 
 50 
 
 56 
 
 69 
 
 81 
 
 94 
 
 107 
 
 120 
 
 145 
 
 171 
 
 50 
 
 75 
 
 66 
 
 266 
 
 62 
 
 70 
 
 86 
 
 102 
 
 118 
 
 134 
 
 150 
 
 181 
 
 213 
 
 60 
 
 83 - 
 
 72 
 
 291 
 
 74 
 
 84 
 
 103 
 
 122 
 
 141 
 
 160 
 
 180 
 
 218 
 
 256 
 
 70 
 
 88 
 
 77 
 
 314 
 
 87 
 
 98 
 
 120 
 
 143 
 
 165 
 
 187 
 
 209 
 
 254 
 
 
 80 
 
 92 
 96 
 99 
 
 81 
 85 
 89 
 
 336 
 356 
 376 
 
 99 
 
 112 
 124 
 
 112 
 126 
 140 
 
 138 
 155 
 
 172 
 
 163 
 183 
 
 204 
 
 188 
 212 
 236 
 
 214 
 241 
 
 239 
 
 
 
 90 
 
 
 
 ion 
 
 
 
 
 
 
 
 
 
 1 l/4-mch smooth nozzle. 
 
 10 
 
 19 
 
 22 
 
 148 
 
 14 
 
 16 
 
 21 
 
 26 
 
 31 
 
 36 
 
 41 
 
 51 
 
 61 
 
 20 
 
 37 
 
 40 
 
 209 
 
 27 
 
 32 
 
 42 
 
 52 
 
 62 
 
 72 
 
 82 
 
 101 
 
 121 
 
 30 
 
 53 
 
 54 
 
 256 
 
 41 
 
 49 
 
 63 
 
 78 
 
 93 
 
 108 
 
 123 
 
 152 
 
 182 
 
 40 
 
 67 
 
 63 
 
 296 
 
 55 
 
 65 
 
 84 
 
 104 
 
 124 
 
 144 
 
 164 
 
 203 
 
 243 
 
 50 
 
 77 
 
 70 
 
 331 
 
 68 
 
 81 
 
 106 
 
 130 
 
 155 
 
 180 
 
 204 
 
 254 
 
 
 60 
 
 85 
 91 
 95 
 99 
 101 
 
 76 
 81 
 85 
 90 
 93 
 
 363 
 392 
 419 
 
 444 
 468 
 
 82 
 96 
 110 
 123 
 137 
 
 97 
 113 
 129 
 145 
 
 162 
 
 127 
 148 
 169 
 190 
 211 
 
 156 
 182 
 
 208 
 234 
 261 
 
 186 
 217 
 
 248 
 
 216 
 252 
 
 245 
 
 
 
 70 
 
 
 
 80 
 
 
 
 
 90 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
 
 1 3/8-inch smooth nozzle. 
 
 10 
 
 20 
 30 
 
 40 
 
 20 
 38 
 55 
 69 
 79 
 87 
 92 
 97 
 100 
 103 
 
 23 
 42 
 56 
 66 
 73 
 79 
 84 
 88 
 92 
 96 
 
 182 
 257 
 315 
 363 
 406 
 445 
 480 
 514 
 545 
 574 
 
 16 
 31 
 47 
 62 
 78 
 93 
 109 
 124 
 143 
 156 
 
 ,9 
 39 
 58 
 77 
 96 
 116 
 135 
 154 
 173 
 193 
 
 27 
 53 
 80 
 107 
 134 
 160 
 187 
 214 
 240 
 
 34 
 68 
 103 
 137 
 171 
 205 
 239 
 
 42 
 83 
 125 
 166 
 208 
 250 
 
 49 
 98 
 147 
 196 
 
 245 
 
 56 
 113 
 169 
 226 
 
 71 
 143 
 214 
 
 86 
 173 
 259 
 
 50 
 
 
 
 60 
 
 
 
 
 70 
 
 
 
 
 
 80 
 
 
 
 
 
 
 90 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
FIEE-STREAMS. 
 
 725 
 
 Pump Inspection Table. 
 
 Discharge of nozzles attached to 50 ft. of 21/2-m. best quality rubber- 
 lined hose, inside smooth. (J. R. Freeman.) 
 
 S2 
 
 
 
 Size 
 
 of Smooth Nozzle. 
 
 
 
 Ring Nozzle. 
 
 Kf=4 
 
 13/4 
 
 U/2 
 
 13/8 
 
 11/4 
 
 11/8 
 
 1 
 
 7/8 
 
 3/4 
 
 13/8 
 
 11/4 
 
 11/8 
 
 10 
 
 193 
 
 163 
 
 146 
 
 127 
 
 107 
 
 87 
 
 68 
 
 51 
 
 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 
 
 325 
 
 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 
 
 Friction Loss in Rubber-Lined Cotton Hose with Smoothest Lining. 
 
 g 
 
 Gallons per Minute Flowing. 
 
 ..0 
 
 Velocity 
 
 
 
 £02 
 la 
 
 Head 
 V 2 - 20. 
 
 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 1000 
 
 a 
 
 
 ^£ 
 
 
 
 S 
 
 Friction Loss, Pounds per 100 ft. Length. 
 
 ■Ft. 
 
 Lbs. 
 
 2 
 
 6.836 
 5.170 
 
 27.3 
 70 7 
 
 61.5 
 
 46 5 
 
 109 
 
 8? 7 
 
 171 
 
 1?9 
 
 
 
 
 
 5 
 10 
 
 0.39 
 1.6 
 
 0.17 
 
 21/8 
 
 189 
 
 
 
 
 0.69 
 
 21/4 
 
 3.790 
 
 15 ? 
 
 34 1 
 
 60 6 
 
 94 7 
 
 136 
 
 186 
 
 
 
 15 
 
 3.5 
 
 1.5 
 
 23/s 
 
 2.895 
 
 11 6 
 
 26 1 
 
 46 3 
 
 72.4 
 
 104 
 
 138 
 
 185 
 
 
 20 
 
 6.2 
 
 2.7 
 
 lih 
 
 2.240 
 
 9 
 
 20 2 
 
 35 8 
 
 56.0 
 
 80.6 
 
 110 
 
 143 
 
 224 
 
 25 
 
 9.7 
 
 4.2 
 
 25/8 
 
 1.748 
 
 7,0 
 
 15 7 
 
 28 
 
 43.7 
 
 62.9 
 
 85.7 
 
 112 
 
 175 
 
 30 
 
 14.0 
 
 6.1 
 
 23/4 
 
 1.391 
 
 5 6 
 
 12 5 
 
 7.7. 3 
 
 34 8 
 
 50 1 
 
 68 ,2 
 
 89,0 
 
 139 
 
 35 
 
 19.0 
 
 8.2 
 
 27/a 
 
 1.097 
 
 4 4 
 
 9 9 
 
 17 6 
 
 71 A 
 
 39 5 
 
 53 8 
 
 70.2 
 
 110 
 
 40 
 
 24.8 
 
 10.7 
 
 3 
 
 0.900 
 
 3 6 
 
 8 1 
 
 14 A 
 
 72 5 
 
 32 A 
 
 44 1 
 
 57.6 
 
 90 
 
 45 
 
 31.4 
 
 13.6 
 
 31/2 
 
 0.416 
 
 1 7 
 
 3 7 
 
 6 7 
 
 10 A 
 
 15,0 
 
 20 A 
 
 26.6 
 
 41.6 
 
 50 
 
 38.8 
 
 16.7 
 
 4 
 
 0.214 
 
 0.9 
 
 1.9 
 
 3.4 
 
 5.4 
 
 7.7 
 
 10.5 
 
 13.7 
 
 21.4 
 
 
 
 
 The above table is computed on the basis of 14 lbs. per 100 ft. length 
 of 21/2-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 
 
726 HYDRAULICS. 
 
 THE SIPHOK* 
 
 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 inte nsity of the 
 force which causes the movement of the fluid, and V = A ^ / 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, N. 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 1/2-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 
 350 ft. below the level, and the length 500 ft. 
 
MEASUREMENT OF FLOWING WATER. 727 
 
 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 Is 
 the hydraulic grade-line. 
 
 Pitot Tube 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 Nosh-and'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 [/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 (Tran s. A. S. 
 M. E., 1903), that in the formula for the Pitot tube, V = c ^2 gH, in 
 which V is the velocity of the current in feet per second, H the head in 
 feet of the fluid corresponding to the pressure measured by the tube, 
 and c an experimental coefficient, c = 1 when the plane at the point of 
 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- 
 ity," and for this case H = 2 X V 2 /2 g instead of V 2 /2 g; but as found in 
 White's experiments the maximum pressure at a point on the plate 
 exactly opposite the jet corresponds to h = V 2 /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- 
 taining a column of water almost exactly equal to the height of the 
 source of the falling water. 
 
 Tests by J. A. Knesche (Indust. Eng'g, Nov., 1909), in which a Pitot 
 tube was inserted in a 4-in. water pipe, gave C = about 0.77 for velocities 
 of 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. 
 
 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. 
 
728 HYDRAULICS. 
 
 The Venturi Meter, invented by Clemens Herschel, and described in 
 a pamphlet issued by the Builders' Iron Foundry of Providence, R.L.is 
 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, 4S-inch, and even 
 20-foot tubes can be readily made. 
 
 Measurement by Venturi Tubes. (Trans. A. S. C. E., Nov., 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 onesurrounding and communicating with the entrance 
 or main pipe, the other with the throat. According to experiments made 
 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 se cond 
 is expressed within two per cent by the formula W= 0.98 X AX v/ 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. 
 
 Measurement of Discharge of Pumping-engines by means of 
 Nozzles. (Trans. A. S. M. L., 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. 
 
MEASUREMENT OF FLOWING WATER. 
 
 729 
 
 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 lbs. 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 
 shut-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. 
 
 Flow through Rectangular Orifices. (Approximate. See p. 698.) 
 
 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 "^ h" X a. Q' = cu. ft. per min.; a = area in sq. in. 
 
 
 "S 
 
 
 tj 
 
 
 T3 
 
 
 ,_, 
 
 
 T3 
 
 
 T3 
 
 
 -0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 m M ■ 
 
 
 M • 
 
 
 "S M • 
 
 
 n M • 
 
 
 "S M • 
 
 
 "S M • 
 
 
 m M ' 
 
 3 <n 
 
 8 £ a 
 
 .3 to 
 
 ,« d-5 
 
 .3 m 
 
 Sg.E 
 
 £ b3 
 
 a! £.3 
 
 .3 "■' 
 
 S 3 3 
 
 rt ^ 
 
 a? is. 3 
 
 c „; 
 
 •5-9 
 
 
 ^ J* a 
 
 
 ^-g S 
 
 
 ^| B 
 
 '" £ 
 
 &H^a 
 
 
 fe -g 3 
 
 'r 4 ' 
 
 fe^'g 
 
 "" a; 
 
 feja a 
 
 "^"o 
 
 0^ 
 
 -i 
 
 
 51 
 
 
 "3 O 
 
 2 m t* 
 
 ■:: 
 
 
 -3 
 
 2 M ti 
 
 -3-g 
 
 2^" 
 
 2.s 
 
 '•§5 8. 
 
 $ s 
 
 |qS 
 
 «.s 
 
 |qI 
 
 5.= 
 
 ^fla 
 
 a - 
 
 as . - 
 
 -§3 » 
 
 2.3 
 
 ■§5 ft 
 
 2.3 
 
 ■§«& 
 
 w 
 
 
 
 13 
 
 
 
 23 
 
 ' 
 
 33 
 
 
 
 3 
 43 
 
 
 
 53 
 
 
 
 63 
 
 
 
 3 
 
 1.12 
 
 2.20 
 
 2.90 
 
 3.47 
 
 3.95 
 
 4.39 
 
 4.78 
 
 4 
 
 1.27 
 
 14 
 
 2.28 
 
 24 
 
 2.97 
 
 34 
 
 3.52 
 
 44 
 
 4.00 
 
 54 
 
 4.42 
 
 64 
 
 4.81 
 
 5 
 
 1.40 
 
 15 
 
 2.36 
 
 25 
 
 3.03 
 
 35 
 
 3.57 
 
 45 
 
 4.05 
 
 55 
 
 4.46 
 
 65 
 
 4.85 
 
 6 
 
 1.52 
 
 16 
 
 2.43 
 
 26 
 
 3.08 
 
 36 
 
 3.62 
 
 46 
 
 4.09 
 
 56 
 
 4.52 
 
 66 
 
 4.89 
 
 7 
 
 1.64 
 
 17 
 
 2.51 
 
 27 
 
 3.14 
 
 37 
 
 3.67 
 
 47 
 
 4.12 
 
 57 
 
 4.55 
 
 67 
 
 4.92 
 
 8 
 
 1.75 
 
 18 
 
 2.58 
 
 28 
 
 3.20 
 
 38 
 
 3.72 
 
 43 
 
 4.18 
 
 58 
 
 4.58 
 
 68 
 
 4.97 
 
 9 
 
 1.84 
 
 19 
 
 2.64 
 
 29 
 
 3.25 
 
 39 
 
 3.77 
 
 49 
 
 4.21 
 
 59 
 
 4.63 
 
 69 
 
 5.00 
 
 10 
 
 1.94 
 
 20 
 
 2.71 
 
 30 
 
 3.31 
 
 40 
 
 3.81 
 
 50 
 
 4.27 
 
 60 
 
 4.65 
 
 70 
 
 5.03 
 
 II 
 
 2.03 
 
 21 
 
 2.73 
 
 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. 
 
730 HYDRAULICS. 
 
 Miner's Inch Measurements. (Pelton Water Wheel Co.) 
 
 The cut, Fig. 141, shows the form of measuring-box ordinarily used, ..__ 
 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. 
 
 and 
 
 Fig. 141. 
 
 Length 
 
 of 
 Opening 
 
 Openings 2 Inches High. 
 
 Openings 4 Inches High. 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 Head to 
 
 inches. 
 
 Center, 
 
 Center, 
 
 Center, 
 
 Center, 
 
 Center, 
 
 Center, 
 
 
 5 inches. 
 
 6 inches. 
 
 7 inches. 
 
 5 inches. 
 
 6 inches. 
 
 7 inches. 
 
 
 Cu. ft. 
 
 Cu. ft. 
 
 Cu.ft. 
 
 Cu.ft. 
 
 Cu.ft. 
 
 Cu. ft. 
 
 4 
 
 1.348 
 
 1.473 
 
 1.589 
 
 1.320 
 
 1.450 
 
 1.570 
 
 6 
 
 1.355 
 
 1.480 
 
 1.596 
 
 1.336 
 
 1.470 
 
 1.595 
 
 8 
 
 1.359 
 
 1.484 
 
 1.600 
 
 1.344 
 
 1.481 
 
 1.608 
 
 10 
 
 1.361 
 
 1.485 
 
 1.602 
 
 1.349 
 
 1.487 
 
 1.615 
 
 12 
 
 1.363 
 
 1.487 
 
 1.604 
 
 1.352 
 
 1.491 
 
 1.620 
 
 14 
 
 1.364 
 
 1.488 
 
 1.604 
 
 1.354 
 
 1.494 
 
 1.623 
 
 16 
 
 1.365 
 
 1.489 
 
 1.605 
 
 1.356 
 
 1.496 
 
 1.626 
 
 18 
 
 1.365 
 
 1.489 
 
 1.606 
 
 1.357 
 
 1.498 
 
 1.628 
 
 20 
 
 1.365 
 
 1.490 
 
 1.606 
 
 1.359 
 
 1.499 
 
 1.630 
 
 22 
 
 1.366 
 
 1.490 
 
 1.607 
 
 1.359 
 
 1.500 
 
 1.631 
 
 24 
 
 1.366 
 
 1.490 
 
 1.607 
 
 1.360 
 
 1.501 
 
 1.632 
 
 26 
 
 1.366 
 
 1.490 
 
 1.607 
 
 1.361 
 
 1.502 
 
 1.633 
 
 28 
 
 1.367 
 
 1.491 
 
 1.607 
 
 1.361 
 
 1.503 
 
 1.634 
 
 30 
 
 1.367 
 
 1.491 
 
 1.608 
 
 1.362 
 
 1.503 
 
 1.635 
 
 40 
 
 1.367 
 
 1.492 
 
 1.608 
 
 1.363 
 
 1.505 
 
 1.637 
 
 50 
 
 1.368 
 
 1.493 
 
 1.609 
 
 1.364 
 
 1.507 
 
 1.639 
 
 60 
 
 1.368 
 
 1.493 
 
 1.609 
 
 1.365 
 
 1.508 
 
 1.640 
 
 70 
 
 1.368 
 
 1.493 
 
 1.609 
 
 1.365 
 
 1.508 
 
 1.641 
 
 80 
 
 1.368 
 
 1.493 
 
 1.609 
 
 1.366 
 
 1.509 
 
 1.641 
 
 90 
 
 1.369 
 
 1.493 
 
 1.610 
 
 1.366 
 
 1.509 
 
 1.641 
 
 100 
 
 1.369 
 
 1.494 
 
 1.610 
 
 1.366 
 
 1.509 
 
 1.642 
 
 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, 
 
MEASUREMENT OF FLOWING WATER. 
 
 731 
 
 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 i'or'small 
 quantities and longer for large quantities. The edges of the notch should 
 be beveled toward the intake side, as shown. The overfall below the notch 
 should not be less than twice its depth. Francis savs 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. 142. 
 
 In the pond, about 6 ft. above the dam, drive a stake, and then obstruct 
 the water until if 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. 
 
 As given by 
 Francis. 
 
 As modified by 
 Smith. 
 
 Weirs with both end contrac- 
 tions 
 
 Weirs with one end contrac- 
 tion su; 
 
 r^ed 00 ™™: } Q - 3.33 »% 3.29 (l + |) #> 
 
 Q = 3.33 (I -0.1 h) /i 3/2 3.29 lh 3 ^ 
 
 Weirs with full contraction . Q = 3.33 (1-0.2 h)h 3 h 3.29 (l - A) /i 3 /2- 
 
 The greatest variation of the Francis formulae from the values of c given 
 by Smith amounts to 3 V2%- The modified Francis formulae, says Smith, 
 
732 
 
 HYDRAULICS. 
 
 will give results sufficiently exact, when great accuracy is not required, 
 within the limits of h, from 0.5 ft. to 2 ft., I being not less than 3 h. 
 
 Q = discharge in cubic feet per second, I = length of weir in feet, h = 
 effective head in feet, measured from the level of the crest to the level of 
 still water above the weir. 
 
 If Q' = discharge in cubic feet per minute, and V and h' are taken in 
 inches, the first of the above formulae reduces to Q' = 0.4 l'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. 
 
 Giving Cubic Feet of Water per Minute that will Flow over a Weir 
 One Inch Wide and from i/s to 207/g Inches Deep. 
 
 For other widths multiply by the width in inches. 
 
 Depth. 
 
 
 1/8 in. 
 
 V4 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 
 
 5.51 
 
 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 
 
 It 
 
 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 698. 
 
 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 formulae. (See also Trautwine's Pocket Book, Unwin's Hydrau- 
 lics, and Church's Mechanics of Engineering.) 
 
 Bazin's Experiments. — M. Bazin (Annates des Ponts 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 783/ 4 in., of the 
 height of the crest above the bottom of the channel from 0.79 to 2.46 ft., 
 
MEASUREMENT OF FLOWING WATER. 
 
 733 
 
 and of the head from 1.97 to 23.62 in. From these experiments he deduces 
 the following formula: 
 
 Q = [0.425+ 0.21 (^JLj^LH V^gH, 
 
 in which P is the height in feet of the crest of the weir above the bottom of 
 the channel of approach, L the length of the weir, // 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 ^2 gH, for a 
 Sharp-crested Weir without Lateral Contraction; the Air 
 being Admitted Freely Behind the Falling Sheet. 
 
 
 Height of Crest of Weir Above Bed of Channel. 
 
 Head, H. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Feet... 0.66 
 
 98 
 
 1 31 
 
 1.64 1.97 
 
 2.62 
 
 3.28 
 
 4.92 
 
 6.56 
 
 00 
 
 
 Inches 7.87 
 
 11.81 
 
 15.75 
 
 19.69 23.62 
 
 31.50 
 
 39.38 
 
 59.07 
 
 78.76 
 
 oo 
 
 Ft 
 
 Tn 
 
 ?n 
 
 m 
 
 m 
 
 m m 
 
 m. 
 
 m 
 
 m 
 
 
 m 
 
 0.164 
 
 1 97 
 
 0.458 
 
 0.453 
 
 'J. 451 
 
 0.450;0.449 
 
 0.449 
 
 0.449 
 
 0.448 
 
 0.448 
 
 0.4481 
 
 230 
 
 2 76 
 
 0.455 
 
 0.448 
 
 J. 445 
 
 0.4430.442 
 
 0.441 
 
 0.440 
 
 0.440 
 
 0.439 
 
 0.4391 
 
 0.295 
 
 3.54 
 
 0.457 
 
 44/' 
 
 J 442 
 
 0.440,0.438 
 
 0.436 
 
 0.436 
 
 0.435 
 
 0.434 
 
 0.4340 
 
 0.394 
 
 4 72 
 
 0.462 
 
 443 
 
 J 442 
 
 0.43810.436 
 
 0.433 
 
 0.432 
 
 0.430 
 
 0.430 
 
 0.4291 
 
 525 
 
 6 30 
 
 0.471 
 
 453 
 
 J, 44 
 
 0.438 0435 
 
 0.431 
 
 0.429 
 
 0.427 
 
 0.426 
 
 0.4246 
 
 0.656 
 
 7 87 
 
 0.480 
 
 o m 
 
 J. 447 
 
 0.440 
 
 0.436 
 
 0.431 
 
 0.428 
 
 0.425 
 
 0.423 
 
 0.4215 
 
 787 
 
 9 45 
 
 0.488 
 
 4Si 
 
 ) 452 
 
 0.444 
 
 0.438 
 
 0.432 
 
 0.428 
 
 0.424 
 
 0.422 
 
 0.4194 
 
 0.919 
 
 11.02 
 
 0.496 
 
 472 
 
 J. 457 
 
 0.448 
 
 441 
 
 0.433 
 
 0.429 
 
 0.424 
 
 0.422 
 
 0.4181 
 
 1.050 
 
 12.60 
 14.17 
 15.75 
 17,32 
 
 
 0.478 
 0.483 
 0.489 
 0.494 
 
 J. 452 0.452 
 0.457 0.456 
 
 0.444 
 0.448 
 0.451 
 0.454 
 
 0.436 
 0.438 
 440 
 0.442 
 
 0.430 
 0.432 
 0.433 
 0.435 
 
 0.424 
 0.424 
 0.424 
 0.425 
 
 0.421 
 0.421 
 0.421 
 0.421 
 
 0.4168 
 
 1.181 
 
 
 0.4156 
 
 1.312 
 
 
 0.472 
 0.476 
 
 0.459 
 0.463 
 
 0.4144 
 
 1.444 
 
 
 0.4134 
 
 1.575 
 
 18.90 
 20.47 
 22.05 
 23.62 
 
 
 
 0.480 
 0.483 
 0.487 
 0.490 
 
 0.467 
 0.470 
 0.473 
 0.476 
 
 0.457 
 0.460 
 0.463 
 0.466 
 
 0.444 
 0.446 
 D.448 
 0.451 
 
 0.436 
 0.438 
 0.439 
 0.441 
 
 0.425 
 0.426 
 0.427 
 0.427 
 
 0.421 
 0.421 
 0.421 
 0.421 
 
 0.4122 
 
 1.706 
 
 
 
 0.4112 
 
 1 837 
 
 
 
 0.4101 
 
 1.969 
 
 
 
 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. 
 
 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 
 Lff 3 /2. A. D. Flinn and C. W. D. Dyer (Trans. A. S. C. E., 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%. 
 
734 WATER-POWER. 
 
 WATER-POWER, 
 
 Power of a Fall of Water — Efficiency. — The gross power of a fall 
 pf water is the product of the weight of water discharged in a unit of time 
 Into 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 lbs. at 60° F., H = total head in feet; then 
 
 DQH = gross power in foot-pounds per second, 
 and DQH -i- 550 = 0.1134 QH = gross horse-power. 
 
 Q' If y ft 9 9ft 
 
 If Q' is taken in cubic feet per minute, H.P. = Q o nnn = .00189Q'#. 
 
 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 = ^r^- 
 
 70o 
 
 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. = QHX 62.36 -v- 550 = 0.1134 QH, in which Q is the discharge in 
 cubic feet per second actually impinging on the float or bucket, and H = 
 
 v 2 v 2 
 
 theoretical head due to the velocity of the stream = -— = — — , in which 
 
 2 g 64.4 
 v is the velocitv in feet per second. If Q f 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. 
 
 Bernouilli's Theorem. — Energy of Water Flowing in a Tube. — 
 v 2 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 2 f 
 
 is the sum of these = \-h-\ — - in feet, in which v = velocity in feet per 
 
 2 g w * 
 
 second,/ = pressure in lbs. per sq. ft., w = weight of 1 cu. ft. of water — 
 
WATER-POWER. 735 
 
 62.36 lbs. If p = pressure in lbs. 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 " Bernouilli'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 lbs. per sq. ft.; or it Q = quantity in cubic feet per second, 
 and p = pressure in lbs. per square inch, W = 144 pQ, and the H.P. 
 
 -.:*££?. T 0.2618 pQ. 
 
 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 8 1/2 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 finishc d 
 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 tlu; 
 high-pressure cylinder of a compound engine of the power required to run 
 that mill, the steam to be taken from the receiver. 
 
736 WATER-POWER. 
 
 The coal consumption per H.P. per hour for a compound engine is taken 
 at 1 3/4 lbs. 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 lbs. 
 
 75% of the steam is used as in a compound engine at 1.75 lbs.== 1.31 lbs, 
 25% of the steam is used as in a high-pressure engine at 3.00 lbs. = .75 lb. 
 
 2.06 lbs. 
 The running expenses per H. P. per year are as follows: 
 2.06 lbs. coal per hour = 21.115 lbs. for 10 1/4 hours or one day = 
 
 6503.42 lbs. 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 11/2% on s/4 cost, andinsurance at 
 V2% on exposed portion, the total average per cent is about 
 12V2%, or $65 X O.I21/2 = 8.13 
 
 80 
 
 Gross cost of power and low-pressure steam per H. P. $21 
 
 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. $1.30 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/?% 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 . 26 
 
 Labor 1 . 23 
 
 Total $5.43 
 
 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 saving 
 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 
 saving; or if 6% is a fair interest to receive on money thus invested the 
 value would be $26,700 -*- 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 
 the 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 in the same manner as the value of a permanent power has 
 been represented. 
 
TURBINE WHEELS. 737 
 
 "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 deprecia- 
 tion." 
 
 Mr. Samuel Webber, Iron Age, Feb. and March, 1S93, writes a series of 
 articles showing the development of American turbine wheels, and inci- 
 dentally 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 wheel when made of large diameter 
 (wheels as high as 72 ft. diameter have been made) and properly designed 
 have given efficiencies of over 80%, but they have been almost entirely 
 supplanted by turbines, on account of their 'cumbersomeness, 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. Inward, downward, and out- 
 ward flow: The American type of turbine. 
 
 TURBINE WHEELS. 
 
 Proportions of Turbines. — Prof. De Volson Wood discusses at 
 length the theory of turbines in his paper on Hydraulic Reaction Motors, 
 Trans. A. S. M. E. xiv. 266. His principal deductions which have an 
 immediate bearing upon practice are condensed in the following: 
 Notation, 
 
 Q = volume of water passing through the wheel per second, 
 
 hi = head in the supply chamber above the entrance to the buckets, 
 
 fa = head in the tail-race above the exit from the buckets, 
 
 z\ = fall in passing through the buckets, 
 
 H = h\ + zi — hi, the effective head, 
 
 hi = coefficient of resistance along the guides, 
 
 H2 = coefficient of resistance along the buckets, 
 
 n = radius of the initial rim, 
 
 r2 = radius of the terminal rim, 
 
 V = velocity of the water issuing from supply chamber, 
 
 vi = initial velocity of the water in the bucket in reference to the bucket, 
 
 V2 = terminal velocity in the bucket, 
 
 w = angular velocity of the wheel, 
 
 a = terminal angle between the guide and initial rim = CAB, Fig. 143, 
 
 Vi = angle between the initial element of bucket and initial rim = EAD, 
 
 72 = GFl, the angle between the terminal rim and terminal element of 
 the bucket, 
 
 a = eb, Fig. 144 = the arc subtending one gate opening, 
 
738 
 
 WATER-POWER. 
 
 ai = the arc subtending one bucket at entrance. (In practice a\ is 
 larger than a,) 
 
 0-2 = gh, the arc subtending one bucket at exit, 
 
 K = bf, normal section of passage, it being assumed that the passages 
 and buckets are very narrow. 
 
 k\ = bd, initial normal section of bucket, 
 ki = gi, terminal normal section, 
 ion — velocity of initial rim, 
 wr2 = velocity of terminal rim, 
 = HFI, angle between the terminal rim and actual direction of 
 the water at exit, 
 
 Y = depth of K, y, of oi, and yi of K<l, then 
 K = Ya sin a; Ki = 2/iaisinyi; Ki = yiai sin 72. 
 
 wr 2 
 
 Fig. 143. 
 
 Fig. 144. 
 
 Three simple systems are recognized, n < r2, called outward flow; 
 ri > r 2 , called inward flow: n = r2, called parallel flow. The first and 
 second may be combined with the third, making a mixed system. 
 
 Value of 72 {the quitting angle). — The efficiency is increased as 72 
 decreases, and is greatest for 72 = 0. Hence, theoretically, the terminal 
 element of the bucket should be tangent to the quitting" rim for best 
 efficiency. This, however, for the discharge of a finite quantity of 
 water, would require an infinite depth of bucket. In practice, there- 
 fore, this angle must have a finite value. The larger the diameter of 
 the terminal rim the smaller may be this angle for a given depth of wheel 
 and given quantity of water discharged. In practice 72 is from 10° to 20°. 
 
 In a wheel in which all the elements except 72 are fixed, the velocity of 
 the wheel for best effect must increase as the quitting angle of the bucket 
 decreases. 
 
 Values of a + yi must be less than 180°, but the best relation cannot 
 be determined by analysis. However, since the water should be de- 
 flected from its course as much as possible from its entering to its leaving 
 the wheel, the angle a for this reason should be as small as practicable. 
 
 In practice, a cannot be zero, and is made from 20° to 30°. 
 
 The value n = \Ari makes the width of the crown for internal flow 
 about the same as for n = r-i V1/2 for outward flow, being approximately 
 3 of the external radius. 
 
TURBINE WHEELS. 739 
 
 Values of m and in. — The frictional resistances depend upon the con- 
 struction of the wheel as to smoothness of the surfaces, sharpness of the 
 angles, regularity of the curved parts, and also upon the speed it is run. 
 These values cannot be definitely assigned beforehand, but Weisbach 
 gives for good conditions in = m = 0.05 to 0.10. 
 
 They are not necessarily equal, and m may be from 0.05 to 0.075, and m 
 from 0.06 to 0.10 or even larger. 
 
 Values of yi must be less than 180° — a. 
 
 To be on the safe side, vi may be 20 or 30 degrees less than 180° — 2 a, 
 giving 
 
 yi = 180° - 2 a - 25 (say) = 155° - 2 a. 
 
 Then if a = 30°, vi = 95°. Some designers make vi 90°; others more, 
 and still others less, than that amount. Weisbach suggests that it be less, 
 so that the bucket will be shorter and friction less. This reasoning appears 
 to be correct for the inflow wheel, but not for the outflow wheel. In the 
 Tremont turbines, described in the Lowell Hydraulic Experiments, this 
 angle is 90°, the angle a 20°, and V2 10°, which proportions insured a posi- 
 tive pressure in the wheel. Fourneyron made vi = 90°, and a from 30° to 
 33°. which values made the initial pressure in the wheel near zero. 
 
 Form of Bucket. — The form of the bucket cannot be determined analyti- 
 cally. From the initial and terminal directions and the volume of the 
 water flowing through the wheel, the area of the normal sections may be 
 found. 
 
 The normal section of the buckets will be: K == M; ki = — ; &2= — • 
 
 V Vl V2 
 
 The depths of those sections will be: 
 
 , T K ki k? 
 
 Y = — : : ?/i = : ; 7/2 : 
 
 a sin a' " ai sin vi «2 sin V2 
 
 The changes of curvature and section must be gradual, and the general 
 form regular, so that eddies and whirls shall not be formed. For the same 
 reason the wheel must be run with the correct velocity to secure the best 
 effect. In practice the buckets are made of two or three arcs of circles, 
 mutually tangential. 
 
 The Value of w. — So far as analysis indicates, the wheel may run at any 
 speed; but in order that the stream shall flow smoothly from the supply 
 chamber into the bucket, the velocity V should be properly regulated. 
 
 If /(1 == /(2 = o.lO, rs •*- ri = 1.40, a = 25°, vi = 90°, V2 = 12°, the 
 velocity of the initial rim for outward flow will be for m aximu m efficiency 
 0.614 of the velocity due to the head, or w n = .614 "^2 gH. 
 
 The velocity due to the head would be V2 gH = 1.414 "^gH. 
 
 For an inflow wheel for the ca.se in w hich n 2 = 2 r-?, and the other 
 dimensions as given above, wn = 0.682 V«2 gH. 
 
 The highest efficiency of the Tremont turbine, found experimentally, 
 was 0.79375, and the corresponding velocity, 0.62645 of that due to the 
 head, and for all velocities above and below this value the efficiency was 
 less. 
 
 In the Tremont wheel a = 20° instead of 25°, and 72 = 10° instead of 12°. 
 These would make the theoretical efficiency and velocity of the wheel some- 
 what greater. Experiment showed that the velocity might be consider- 
 ably larger or smaller than this amount without much diminution of the 
 efficiency. 
 
 It was found that if the velocity of the initial (or interior) rim was not 
 less than 44% nor more than 75 % of that due to the fall, the efficiency was 
 75% or more. This wheel was allowed to run freely without any brake 
 except its own f riction, and the velocity of the i nitial rim was observed to 
 be 1.335 V2 gH, half of which is 0.6675 ^2 gH, which is not far from the 
 velocity giving maximum effect; that is to say, when the gate is fully 
 raised the coefficient of effect is a maximum when the wheel is moving with 
 about half its maximum velocity. 
 
 Number of Buckets. — Successful wheels have been made in which the 
 distance between the buckets was as small as 0.75 of an inch, and others as 
 much as 2.75 inches. Turbines at the Centennial Exposition had buckets 
 from 41/2 inches to 9 inches from center to center. If too large they will 
 not work properly. Neither should they be too deep. Horizontal parti- 
 
740 WATER-POWER. 
 
 tions are sometimes introduced. These secure more efficient working in 
 case the gates are only partly opened. The form and number of buckets 
 for commercial purposes are chiefly the result of experience. 
 
 Ratio of Radii. — Theory does not limit the dimensions of the wheel. In 
 practice, 
 
 for outward flow, ri -s- n is from 1.25 to 1.5.0; 
 
 for inward flow, r2 -*■ n is from 0.66 to 0.80. 
 
 It appears that the inflow-wheel has a higher efficiency than the outward- 
 flow wheel. The inflow-wheel also runs somewhat slower for best effect. 
 The centrifugal force in the outward-flow wheel tends to force the water 
 outward faster than it would otherwise flow; while in the inward-flow 
 wheel it has the contrary effect, acting as it does in opposition to the 
 velocity in the buckets. 
 
 It also appears that the efficiency of the outward-flow wheel increases 
 slightly as the width of the crown is less and the velocity for maximum 
 efficiency is slower; while for the inflow-wheek the efficiency slightly in- 
 creases for increased width of crown, and the velocity of the outer rim at 
 the same time also increases. 
 
 Efficiency. — The exact value or the efficiency for a particular wheel 
 must be found by experiment. 
 
 It seems hardly possible for the effective efficiency to equal, much less 
 exceed, 86%, and all claims of 90 or more per cent for these motors should 
 be discarded as improbable. A turbine yielding from 75% to 80% is 
 extremely good. Experiments with higher efficiencies have been reported. 
 
 The celebrated Tremont turbine gave 79V4% without the "diffuser," 
 which might have added some 2%. A Jonval turbine (parallel flow) was 
 reported as yielding 0.75 to 0.90, but Morin suggested corrections reducing 
 it to 0.63 to 0.71. Weisbach gives the results of many experiments, in 
 which the efficiency ranged from 50% to 84%. Numerous experiments 
 give E = 0.60 to 0.65. The efficiency, considering only the energy im- 
 parted to the wheel, will exceed by several per cent the efficiency of the 
 wheel, for the latter will include the friction of the support and leakage at 
 the joint between the sluice and wheel, which are not included in the 
 former; also as a plant the resistances and losses in the supply-chamber 
 are to be still further deducted. 
 
 The Crowns. — The crowns may be plane annular disks, or conical, or 
 curved. If the partitions forming the buckets be so thin that they may be 
 discarded, the law of radial flow will be determined by the form of the 
 crowns. If the crowns be plane, the radial flow (or radial component) 
 will diminish, for the outward-flow wheel, as the distance from the axis 
 increases — the buckets being full — for the angular space will be greater. 
 
 Prof. Wood deduces from the formulae in his paper the tables on the 
 next page. 
 
 It appears from these tables: 1. That the terminal angle, a, has 
 frequently been made too large in practice for the best efficiency. 
 
 2. That the terminal angle, a, of the guide should be for the inflow less 
 than 10° for the wheels here considered, but when the initial angle of the 
 bucket is 90°, and the terminal angle of the guide is 5° 28', the gain of 
 efficiency is not 2% greater than when the latter is 25°. 
 
 3. That the initial angle of the bucket should exceed 90° for best effect 
 for out flow-wheels. 
 
 4. That with the initial angle between 60° and 120° for best effect on 
 inflow wheels the efficiency varies scarcely 1%. 
 
 5. In the outflow-wheel, column (9) shows that for the outflow for best 
 effect the direction of the quitting water in reference to the earth should be 
 nearly radial (from 76° to 97°) , but for the inflow wheel the water is thrown 
 forward in quitting. This shows that the velocity of the rim should some- 
 what exceed the relative final velocity backward in the bucket, as shown 
 in columns (4) and (5). . 
 
 6. In these tables the velocities given are in terms of V2 gh, and the 
 coefficients of this expression will be the part of the head which would 
 produce that velocity if the water issued freely. There is only one case, 
 column (5), where the coefficient exceeds unity, and the excess is so small 
 it may be discarded ; and it may be said that in a properly proportioned 
 turbine with the conditions here given none of the velocities will equal 
 that due to the head in the supply-chamber when running at best effect 
 
TURBINE WHEELS. 
 
 741 
 
 V 
 
 = 
 
 0.67 
 0.76 
 0.84 
 1.00 
 
 Head 
 
 Equivalent 
 
 of Energy 
 
 in quitting 
 
 Water. 
 
 2~g 
 
 © 
 
 as us a: a; 
 
 — o _ <s 
 
 © © © o 
 
 Direc- 
 tion of 
 quitting 
 Water. 
 
 
 • 
 
 vo O pq r^ 
 
 Termi- 
 nal 
 Angle of 
 Guide. 
 
 « 
 
 SS2:2 
 
 Velocity of 
 Exit from 
 Supply- 
 Chamber. 
 V 
 
 - 
 
 mil 
 >>>> 
 
 ifi « MS 
 
 o © o o 
 
 Relative 
 Velocity of 
 
 Entrance. 
 
 vO 
 
 o o o o 
 
 Relative 
 
 Velocity of 
 
 Exit. 
 
 - 
 
 caJ CaJ cd «=» 
 
 1 cs 1 tsl cvjl cq 
 >>>> 
 
 © o co r^ 
 — ' o o ©' 
 
 ■ *3 
 
 C t- > 
 gg II 
 
 "* 
 
 >>>> 
 
 © o © © 
 
 if* 
 
 «n 
 
 © ©' © © 
 
 < >> 
 
 N 
 
 f 00 5- - 
 00 oo CO O^ 
 o ©' ©" ©' 
 
 If 
 
 - 
 
 © © © © 
 
 •G O «"-J >n 
 
 Ha 
 > 
 
 1.48 
 1.50 
 1.55 
 1.65 
 
 
 as as a; a; 
 © © ©' © 
 
 «> 
 
 © -o in r^ 
 
 « 
 
 CS "T © 
 
 t^ 
 
 1^1^ 
 !«M!r^loal(N 
 >>>> 
 
 © © ©' ©' 
 
 5 1 
 
 © © © — 
 ©' © ©' o 
 
 s 
 
 1 CC!| Ct3| tCJi £33 
 
 >>>> 
 
 © © © ©' 
 
 
 I&si&siEcji&s 
 >>>> 
 s § 5 I 
 
 ©' © ©' ©' 
 
 
 1 E33 1 CC! f =E3 1 CCS 
 
 >>>> 
 
 r> vo o o 
 ©©'©©' 
 
 K) 
 
 © © C> CO 
 © O © © 
 
 £ 
 
 • • 
 
 © © © © 
 
 « o» N m 
 
742 
 
 WATER-POWER. 
 
 7. The inflow turbine presents the best conditions for construction for 
 
 Eroducinga given effect, the only apparent disadvantage being an increased 
 rst cost due to an increased depth, or an increased diameter for producing 
 a given amount of work. The larger efficiency should, however, more than 
 neutralize the increased first cost. 
 
 Tes^s of Turbines. — Emerson says that in testing turbines it is a 
 rare thing to find two of the same size which can be made to do their best 
 at the same speed. The best speed of one of the leading wheels is in- 
 variably wide from the tabled rate. It was found that a 54-in. Leffel 
 vvheel under 12 ft. head gave much better results at 78 revolutions per 
 minute than at 90. 
 
 Overshot wheels have been known to give 75% efficiency, but the 
 average performance is not over 60%. 
 
 A fair average for a good turbine wheel may be taken at 75%. In tests 
 of 18 wheels made at the Philadelphia Water- works in 1859 and 1860, one 
 wheel gave less than 50% efficiency, two between 50% and 60%, six 
 between 60% and 70%, seven between 71% and 77%, two 82%, and one 
 87.77%. (Emerson.) 
 
 Tests of Turbine Wheels at the Centennial Exhibition, 1876. 
 (From a paper by R. H. Thurston on The Systematic Testing of Turbine 
 Wheels in the United States, Trans. A. S. M. E., viii. 359.) — In 1876 the 
 judges at the International Exhibition conducted a series of trials of 
 turbines. Many of the wheels offered for tests were found to be more or 
 less defective in fitting and workmanship. The following is a statement 
 of the results of all turbines entered which gave an efficiency of over 75%. 
 Seven other wheels were tested, giving results between 65% and 75%. 
 
 Maker's Name, or Name the 
 Wheel is Known by. 
 
 £S 
 
 h . 
 
 "3 i 
 £S 
 
 <d o cr 
 
 ¥ 
 
 <a o »h 
 
 Is 
 
 32 • 
 
 <V o *- 
 
 OS 
 
 3 m 
 
 .25 
 
 ■s"3 
 
 C+-, M 
 W o *- 
 
 Is 
 
 3 A 
 
 11 
 
 rtrv. 
 g c g? 
 
 
 87.68 
 83.79 
 83.30 
 82.13 
 81.21 
 78.70 
 79.59 
 77.57 
 77.43 
 76.94 
 76.16 
 75.70 
 75.15 
 
 
 86.20 
 
 82.41 
 70.79 
 
 
 75.35 
 
 
 
 
 
 
 
 
 
 
 Thos. Tait 
 
 
 
 70.40 
 55.90 
 68.60 
 79.92 
 
 66.35 
 
 
 55.00 
 
 
 '7K66 
 
 71.01 
 8K24 
 
 
 
 51.03 
 67.23 
 
 
 
 Tyler Wheel 
 
 69.59 
 
 
 
 
 
 74.25 
 ' 73J3 
 '74.89 
 
 
 
 62.75 
 
 
 
 E. T. Cope & Sons 
 
 69.92 
 
 
 
 
 
 
 70.87 
 62.06 
 
 71.74 
 
 
 
 67.08 
 71.90 
 
 67.57 
 70.52 
 
 
 W. F. Mosser & Co 
 
 66.04 
 
 
 
 
 The limits of error of the tests, says Prof. Thurston, were very uncertain; 
 they are undoubtedly considerable as compared with the later work done 
 in the permanent flume at Holyoke — possibly as much as 4% or 5%. 
 
 Experiments with "draught-tubes," or "suction-tubes," which were 
 actually "diffusers" in their effect, so far as Prof. Thurston has analyzed 
 them, indicate the loss by friction which should be anticipated in such 
 cases, this loss decreasing as the tube increased in size, and increasing as 
 its diameter approached that of the wheel — the minimum diameter tried. 
 It was sometimes found very difficult to free the tube from air completely, 
 and next to impossible, during the interval, to control the speed with the 
 brake. Several trials were often necessary before the power due to the full 
 head could be obtained. The loss of power by gearing and by belting was 
 variable with the proportions and arrangement of the gears and pulleys, 
 length of belt, etc., but averaged not far from 30% for a single pair of bevel- 
 
TURBINE WHEELS. 743 
 
 gears, uncut and dry, but smooth for such gearing, and but 10% for the 
 same gears, well lubricated, after they had been a short time in operation. 
 The amount of power transmitted was, however, small, and these figures 
 are probably much higher than those representing ordinary practice. 
 Introducing a second pair — spur-gears — the best figures were but little 
 changed, although the difference between the case in which the larger gear 
 was the driver, and the case in which the small wheel was the driver, was 
 perceivable, and was in favor of the former arrangement. A single straight 
 belt gave a loss of but 2% or 3%, a crossed belt 6% to 8%, when transmit- 
 ting 14 horse-power with maximum tightness and transmitting power. A 
 "quarter turn" wasted about 10% as a maximum, and a "quarter twist" 
 about 5%. 
 
 Dimensions of Turbines. — For dimensions, power, etc., of standard 
 makes of turbines consult the catalogues of different manufacturers. 
 The wheels of different makers vary greatly in their proportions for any 
 given capacity. 
 
 Rating and Efficiency of Turbines. — The following notes and tables 
 are condensed from a pamphlet entitled "Turbine Water-wheel Tests 
 and Power Tables," by R. E. Horton. Water-supply and Irrigation 
 Paper No. 180, U. S. Geol. Survey, 1906. 
 
 Theory does not indicate the numbers of guides or buckets most desir- 
 able. 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 -s- velocity due head for 
 maximum efficiency for a 36-inch Hercules turbine is given below: 
 
 Proportional gate opening . . . Full . 806 . 647 . 489 379 
 
 Maximum efficiency 85.6 87.1 86.3 80 73.1 
 
 Periph. vel. -!- vel. due head. . . 677 . 648 . 641 . 603 . 585 
 
 American turbine practice differs from European practice in that water 
 wheels are placed on the market in standard or stock sizes, whereas in 
 Europe, notably on the Continent, each turbine is designed for the special 
 conditions under which it is to operate, the designs being based on mathe- 
 matical theory and following chiefly the Jonval and Fourneyron types. 
 
 Having been developed by experiment after successive Holyoke tests, 
 American stock pattern turbines probably give their best efficiencies at 
 about the head under which those tests are made — i.e., 14 to 17 ft. 
 The shafts, runners, and cases are so constructed as to enable stock sizes 
 of wheels to be used under heads ranging from 6 to 60 ft. For very low 
 heads they are perhaps unnecessarily cumbersome. For heads exceed- 
 ing 60 ft. American builders commonly resort to the use of bronze buckets 
 and "special wheels," not designed along theoretical lines, as in Europe, 
 but representing modifications of the standard patterns. 
 
 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 verti- 
 cal 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 counterbalance 
 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 5| in. deep and \% inch 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. 
 
744 V/ATER-POWER. 
 
 In practice the theoretical power is multiplied by an efficiency factor E 
 to obtain the net power available on the turbine shaft as determinable by 
 dynamometrical 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, and Q — tabled 
 
 discharge (C.F.M.) for any head H. E = j^'°°° Q x'ff = 528 ' 8 U^H ' 
 
 Relations of Power, Speed and Discharge. — Nearly all American turbine 
 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, 
 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 discharge 
 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 /z : fc 3 /2 ; R H :R h : : H 1 ^ : fcV2 ; Q H :Q h :: H 1 ?? : %% 
 
 If H and h are taken at 16 ft. and 1 ft., respectively, the values of the 
 coefficients P, N, and F are: 
 
 P = M 1G /H 3 /2 = M l6 /64 = 0.01562 M t6 
 
 N = _R 16 /#V2= jj lfl /4 = 0.25 R l6 
 
 F = Q 16 /60 #V2= Q 16 /240 = 0.00417 .Q l8 . 
 
 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 formulas: 
 
 M = MtH ^VHj. = PH 3 /2_ 
 
 R = Rt Vg/ffi = N ^H _ 
 
 Q = Qi ^H/Hi = 60 F y/H. 
 Since at a head of 1 ft^ and M lt R u and Q t equal P, N, and 60 F, 
 respectively, H 3 ^ and "^H x each equals 1. Calculations involving i? 3 /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 discharge 
 and horse-power can be prepared. The peripheral speed corresponding 
 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 revo- 
 lutions 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 rating 
 tables are usually fairly accurate. In the matter of efficiency there are 
 undoubtedly much larger discrepancies. 
 
TURBINE WHEELS. 
 
 745 
 
 Table of H / 2 for Calculating Horse-Power of Turbines. 
 
 t3 
 
 0.0 
 
 0.2 
 
 0.4 
 
 0.6 
 
 0.8 
 
 3 ^ 
 
 X^ 
 
 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 
 
 1.65 
 
 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 
 
 392.4- 
 
 394.61 
 
 4 
 
 8.00 
 
 8.61 
 
 9.23 
 
 9.87 
 
 10.52 
 
 54 
 
 396.81 
 
 399.02 
 
 401.23 
 
 403.45 
 
 405.6/ 
 
 5 
 
 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 
 
 7 
 
 18.52 
 
 19.32 
 
 20.13 
 
 20.95 
 
 21.78 
 
 57 
 
 430.34 
 
 432.60 
 
 434.87 
 
 437.13 
 
 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 
 
 32.53 
 
 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 
 
 47.9 
 
 49.05 
 
 50.15 
 
 51.26 
 
 63 
 
 500.04 
 
 502.43 
 
 504.82 
 
 507.20 
 
 509. GO 
 
 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 
 
 613.43 
 
 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 
 
 686.2 3 
 
 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. 13 
 
 712.85 
 
 30 
 
 164.32 
 
 165.96 
 
 167.61 
 
 169.27 
 
 170.93 
 
 80 
 
 715.54 
 
 718.22 
 
 720.92 
 
 723.60 
 
 726.30 
 
 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. 2 J 
 
 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 
 
 226.89 
 
 228.72 
 
 230.56 
 
 232.40 
 
 87 
 
 811.43 
 
 814.27 
 
 817.0/ 
 
 819.88 
 
 822.70 
 
 38 
 
 234.25 
 
 236.10 
 
 237.96 
 
 239.82 
 
 241.68 
 
 88 
 
 825.51 
 
 828.32 
 
 831.15 
 
 833.97 
 
 836.79 
 
 39 
 
 243.56 
 
 245.43 
 
 247.31 
 
 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 
 
 862.37 
 
 865.22 
 
 41 
 
 262.53 
 
 264.45 
 
 266.33 
 
 268.31 
 
 270.25 
 
 91 
 
 868.08 
 
 870.94 
 
 873.81 
 
 876.68 
 
 879.55 
 
 42 
 
 272.19 
 
 274.1 -5 
 
 276.09 
 
 278.03 
 
 280.01 
 
 92 
 
 882.43 
 
 835.30 
 
 888.1? 
 
 891.07 
 
 893.96 
 
 43 
 
 281.97 
 
 283.9 \ 
 
 285.91 
 
 287.89 
 
 289.88 
 
 93 
 
 896.86 
 
 899.75 
 
 902.6" 
 
 905.55 
 
 908.45 
 
 44 
 
 291.86 
 
 293.8 
 
 295.85 
 
 297.85 
 
 299.86 
 
 94 
 
 911.35 
 
 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 
 
 311.97 
 
 314.02 
 
 316.0^ 
 
 318.11 
 
 32-). 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 
 
 336.7? 
 
 338.81 
 
 340.90 
 
 98 
 
 970.14 
 
 973 . 1 1 
 
 976.09 
 
 979.07 
 
 982.05 
 
 49 
 
 343 00 
 
 345. 10 
 
 347.21 
 
 349.3? 
 
 351.43 
 
 99 
 
 985.03 
 
 988.02 
 
 991.01 
 
 994.00 
 
 996.99 
 
 50 
 
 353 55 
 
 355.67 
 
 357.80 
 
 359.93 
 
 362.07 
 
 100 
 
 1000.00 
 
 
 
 
 
 
 
 
 
 
Rating Table for Turbines. 
 
 Leffel Standard (New Type). Pivot Gate. [1900 list.] 
 
 Diameter of 
 
 Manufacturer's Rating for 
 a Head of 16 Ft. 
 
 Coefficients. 
 
 Runner in 
 Inches. 
 
 H.P. 
 
 ( = M). 
 
 Cu. Ft. 
 per rain. 
 
 Revs, 
 per min. 
 
 Power 
 
 ( = P). 
 
 Dis- 
 charge. 
 ( = F). 
 
 Speed 
 
 ( = iV). 
 
 10 
 
 111/2 
 
 3.70 
 4.9 
 6.5 
 8.4 
 11.00 
 14.9 
 19.4 
 25.25 
 33.61 
 44.3 
 58.2 
 67.75 
 84.1 
 142 
 168 
 2C2 
 247 
 
 53 
 
 201 
 
 267 
 
 348 
 
 455 
 
 602 
 
 802 
 
 1,043 
 
 1,390 
 
 1,831 
 
 2,406 
 
 2,800 
 
 3,475 
 
 5,858 
 
 6,950 
 
 8,340 
 
 10,222 
 
 535 
 463 
 404 
 351 
 306 
 268 
 233 
 202 
 176 
 153 
 134 
 122 
 110 
 96 
 87 
 80 
 72 
 
 0.058 
 .076 
 
 .101 
 
 .131 
 
 .172 
 
 .232 
 
 .303 
 
 .393 
 
 .524 
 
 .691 
 
 .908 
 
 1.058 
 
 1.312 
 
 2.215 
 
 2.621 
 
 3.151 
 
 3.853 
 
 0.220 
 
 .838 
 
 1.113 
 
 1.451 
 
 1.897 
 
 2.510 
 
 3.344 
 
 4.339 
 
 5.796 
 
 7.635 
 
 10.033 
 
 11.676 
 
 14.490 
 
 24.428 
 
 28.982 
 
 34.778 
 
 42.623 
 
 133.8 
 115.8 
 
 131/4 
 
 101.0 
 
 151 4 
 
 87.8 
 
 171/2 
 
 20 
 
 23 
 
 261/2 
 
 30 1/2 
 
 76.5 
 67 
 
 58.2 
 50.5 
 
 44 
 
 35 
 
 38.2 
 
 40 
 
 44 
 
 43 
 
 33.5 
 30.5 
 27.5 
 
 56 
 
 24 
 
 61 
 
 21.8 
 
 66 
 
 20 
 
 74 
 
 18 
 
 Leffel Improved Samson. Pivot Gate. [1897 and 1900 lists.] 
 
 20 
 
 51.7 
 68.3 
 87.3 
 
 116 
 
 158 
 
 207 
 
 262 
 
 324 
 
 405 
 
 497 
 
 597 
 
 708 
 
 2,111 
 2,792 
 3,569 
 4,751 
 6,440 
 8,446 
 10,689 
 13,196 
 16,554 
 20,292 
 24,409 
 28,906 
 
 325 
 283 
 250 
 217 
 186 
 163 
 145 
 130 
 116 
 105 
 96 
 88 
 
 0.806 
 1.065 
 1.362 
 1.810 
 2.465 
 3.229 
 4.087 
 5.054 
 6.318 
 7.753 
 9.313 
 11.045 
 
 8.803 
 11.643 
 14.883 
 19.812 
 26.855 
 35.220 
 44.573 
 55.027 
 69.030 
 84.618 
 101.786 
 120.538 
 
 81 3 
 
 23 . . 
 
 70 8 
 
 26.... 
 
 62 5 
 
 30 
 
 54.3 
 
 35 
 
 46 5 
 
 40 ... 
 
 40 8 
 
 45 
 
 36 3 
 
 50 
 
 32.5 
 
 56 . . 
 
 29.0 
 
 62.... 
 
 26 3 
 
 68 ... 
 
 24.0 
 
 74 
 
 22.0 
 
 Victor High Pressure Turbine. Cylinder Gate. [1903 list.] 
 Ratings for 100 Ft. Head. 
 
 14 
 
 37 
 50 
 
 247 
 332 
 
 656 
 
 574 
 
 0.037 
 .050 
 
 0.412 
 .553 
 
 65.6 
 
 16 
 
 57.4 
 
 is : 
 
 66 
 
 442 
 
 510 
 
 .066 
 
 .733 
 
 51.0 
 
 20 
 
 82 
 
 542 
 
 459 
 
 .082 
 
 .903 
 
 45.9 
 
 22 
 
 106 
 128 
 151 
 173 
 191 
 228 
 272 
 303 
 
 707 
 850 
 1,001 
 1,147 
 1,265 
 1,512 
 1,805 
 2,005 
 
 417 
 383 
 353 
 328 
 306 
 278 
 255 
 235 
 
 .106 
 .128 
 .151 
 .173 
 .191 
 .228 
 .272 
 .303 
 
 1.178 
 1.417 
 1.668 
 1.912 
 2.108 
 2.520 
 3.008 
 3.342 
 
 41.7 
 
 24 
 
 38.3 
 
 26 
 
 35.3 
 
 28 
 
 32.8 
 
 30 . . 
 
 30.6 
 
 33 
 
 27.8 
 
 36 . 
 
 25.5 
 
 39 
 
 23.5 
 
 42 
 
 343 
 
 2,277 
 
 219 
 
 .343 
 
 3.795 
 
 21.9 
 
 45 
 
 387 
 
 2,563 
 
 204 
 
 .387 
 
 4.272 
 
 20.4 
 
 43 
 
 426 
 
 2,820 
 
 191 
 
 .426 
 
 4.700 
 
 19.1 
 
 51 
 
 462 
 
 3,063 
 
 180 
 
 .462 
 
 5.105 
 
 18.0 
 
 54 
 
 504 
 
 3,340 
 
 170 
 
 .504 
 
 5.567 
 
 17.0 
 
 57 
 
 544 
 
 3,605 
 
 161 
 
 .544 
 
 6.008 
 
 16.0 
 
 60 
 
 590 
 
 3,907 
 
 153 
 
 .590 
 
 6.512 
 
 15.3 
 
 63 
 
 619 
 680 
 742 
 799 
 
 4,100 
 4,505 
 4,910 
 5,290 
 
 146 
 139 
 133 
 127 
 
 .619 
 .680 
 
 .742 
 .799 
 
 6.833 
 7.508 
 8.183 
 8.817 
 
 14.6 
 
 66 
 
 13.9 
 
 69 
 
 13.3 
 
 72 
 
 12.7 
 
 am 
 
TURBINE WHEELS. 747 
 
 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 an 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 run- 
 ning at maximum efficiency. 
 
 If V = vent in sq. in., Q = discharge in cu. ft. per min. under a head H, 
 F = dis charge in cu. ft. per sec. under a head of 1 foot, then Q = 60 F/144 
 V2gH = 3.344 V^H, and V = 0.3 QI^H; also V= 17.94 F and F = 
 0.0557 V. 
 
 The vent of a turbine should not be confused with the area of the out- 
 let 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 meas- 
 ured in the narrowest section. 
 
 The high-pressure turbine is a recent design (1903), and is tabled for 
 heads of 70 to 675 feet. 
 
 A 10,000 H.P. Turbine at Snoqualmie, Wash. (Arthur Giesler, 
 Eng. News, Mar. 20, 1906.)— The fall is about 270 ft. high. The machin- 
 ery is placed in an underground chamber excavated in the rock about 
 250 ft. below the surface, and 300 ft. up-stream from the crest of the falls. 
 A tail-race tunnel runs to the lower reach of the river. The wheel 'was 
 designed by the Piatt 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. There .was no precedent for a generator approximating 
 10,000 H.P. running at such a speed. The turbine is a horizontal shaft 
 machine, of the Francis type, radial inward flow with central axial dis- 
 charge. The turbine proper has only one bearing, SS/s X 26 in., the gen- 
 erator having three bearings. The draft tube is on the generator (front) 
 side. The shaft-bearing, thrust-bearing and thrust-balancing devices are 
 at the back side. The wheel is 66 in. outside diam. by 9 in. wide through 
 the vanes. It has 34 vanes which extend a short distance beyond the 
 end plate of the wheel on the discharge side. There are 32 guide vanes, 
 of the swivel type, connected to a rotatable ring which is actuated by a 
 Lombard governor. The turbine wheel or runner is an annular steel 
 casting. It is bolted to a disk 46 in. diam., which is an ■enlargement of 
 the 131/2 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 bv 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. diam. The penstock for 
 each wheel is 84 in. diam., reduced gradually to 66 in. at the wheel. 
 (Bulletin No. 1613, A.-C. Co.) 
 
 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 dis- 
 charges. The throat is perforated with a great number of 6-in. holes, 
 through wmich 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: 
 
 The fall-increaser is a form of power-house foundation construction so 
 made that by running through it water, which would otherwise waste 
 over the dam, the fall acting on the turbines is increased, and the output 
 of power is kept at its maximum quantity, in spite of the back-water 
 
748 WATER-POWER. 
 
 which always accompanies an abundance of river flow passing down the 
 river. 
 
 The results show 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 because 
 there is not enough, or only enough, water to supply the plain turbines; 
 but for the other half of the year the fall-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-increasers had 
 not been built. 
 
 An illustrated description of the fall-increaser, with results of tests, is 
 given in the Harvard Eng'Q Journal, June, 1908. See also U. S. Pat. 
 No. 873,435 and Eng. News, June 11, 1908. 
 
 TANGENTIAL OR I31PULSE 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, without 
 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 so-called fric- 
 tional resistance offered to the motion of the water by the wetted surfaces 
 of the buckets, causing also the conversion of a portion of the energy into 
 heat instead of useful work. Third, in the velocity of the water, as it 
 leaves the bucket, representing energy which has not been converted 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. If, for example, a jet strikes a surface at an 
 angle and is sharply deflected, a portion of the water is backed, the 
 smoothness of the stream is disturbed, and there results considerable 
 loss by impact and otherwise. 
 
 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, as the loss by fric- 
 tion will be proportional to this. 
 
 3. The discharge end of the bucket should be as nearly tangential to 
 the wheel periphery as compatible with the clearance of the bucketwhich 
 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 dis- 
 charge 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. 145, 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 considerable 
 velocity, and represents a large loss of energy. The introduction of the 
 wedge in the Pelton bucket (see Fig. 146) is an efficient means of avoiding 
 this loss. 
 
 Fig. 145. Fig. 146. Fig. 147. 
 
 A wheel of the form of the Pelton (Fig. 147) conforms closely in con- 
 struction to each of these requirements. [In wheels as now made (1909) 
 
TANGENTIAL OR IMPULSE WATER-WHEELS. 749 
 
 the sharp corners shown in this bucket are eliminated. See catalogues 
 of the Pelton Water Wheel Co., Joshua Hendy Iron Works, and Abner 
 Doble Co., all of San Francisco.] 
 
 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 the 
 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 the 
 spouting velocity of the jet, but as soon as the wheel commences to de- 
 velop power by driving machinery, etc., its velocity will drop. In a 
 properly designed wheel the velocity of the rim in lineal feet per minute, 
 at full load, will be from 48 to 50% of the spouting velocity of the jet. 
 
 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 condi- 
 tions 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. 
 
 Standard wheels can generally be adapted one size larger or one size 
 smaller to meet conditions of a variation of speed or volume of flow 
 under a given 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 diameter 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 are so 
 arranged that their respective jets impinge on different buckets at differ- 
 ent parts of the periphery. Three-nozzle and five-nozzle wheels have 
 many disadvantages, when governing is required, and should only be 
 adopted for handling a very large volume of water when other designs 
 cannot be used. 
 
 Combined Heads. — When two or more 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 difference 
 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 arranged 
 to cut the water off one wheel and turn it on to the other. 
 
 Horizontal Wheels. — For electric generating stations, when it is de- 
 sired to place the wheels below the floor of the generators, where vertical 
 direct-connected equipments are used, tangential wheels may be mounted 
 horizontally with vertical shafts and step bearings. 
 
 Notes on Hydraulic Power Installations. (Joshua Hendy Iron 
 Works.)— Apertures of screens must be slightly smaller than the diameter 
 of the smallest nozzle used. 
 
750 WATER-POWER. 
 
 When not in use, keep the pipe full by closing the valve at the lower 
 end. There is less liability for trouble from expansion and contraction 
 with a full pipe line. 
 
 Equip the pipe line with air valves, approximately one for every 20 ft. 
 of head. 
 
 When operating under high heads, when no other precaution has been 
 taken to avoid water ram during the process of governing, it is advisable 
 to install relief valves between the lower end of the pipe line and the 
 gates or controllers. 
 
 When operating under even moderately high heads, if no safety device 
 or by-pass has been installed, and a plain valve is to be used, sliding 
 gates and butterfly valves should not be employed, but only screw gates, 
 as the former would be too rapid in their action and might set up a 
 dangerous water ram. 
 
 The size of the nozzle that must be used on a wheel for maximum 
 efficiency must be such as will just keep the pipe line full. If water 
 overflows, put on a larger nozzle. If the pipe remains partly empty, put 
 on a smaller nozzle, as otherwise the effective head is reduced, with con- 
 siderable loss of efficiency. 
 
 The nozzles may be placed either above or below the wheel, depending 
 on the direction of rotation required. 
 
 Control of Tangential Water-Wheels. — The methods of regulating 
 tangential water-wheels may be classified under five 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. 
 
 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 of 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 is a represen- 
 tative of the first type, and the Lombard-Replogle governor of the 
 second. 
 
 The close regulation that can be obtained with the latter is remarkable. 
 Any size will go into operation and make connection at so slight a devia- 
 tion as one-tenth of one per cent from normal, and in installations 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. 
 
TANGENTIAL OR IMPULSE WATER-WHEEL. 751 
 
 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.) 
 
 a. a 
 
 P 
 
 Q 
 R 
 
 12 
 
 Inch. 
 
 18 
 
 Inch. 
 
 24 
 
 Inch. 
 
 36 
 
 Inch. 
 
 48 
 
 Inch. 
 
 60 
 
 Inch. 
 
 72 
 
 Inch. 
 
 8 
 
 Feet. 
 
 10 
 
 Feet. 
 
 12 
 
 Feet. 
 
 20 ( 
 
 2152 | 
 
 .12 
 3.91 
 
 342 
 
 .37 
 11.72 
 
 228 
 
 .66 
 
 20.83 
 
 171 
 
 1.50 
 
 46.93 
 
 114 
 
 2.64 
 
 83.32 
 
 85 
 
 4.18 
 
 130.36 
 
 70 
 
 6.00 
 
 187.72 
 
 57 
 
 10.64 
 
 332.70 
 
 43 
 
 16.48 
 515.04 
 
 34 
 
 23.80 
 
 748.95 
 
 29 
 
 30 ( 
 
 2636 j 
 
 P 
 
 Q 
 
 R 
 
 .23 
 4.79 
 
 418 
 
 .69 
 
 14.36 
 
 279 
 
 1.22 
 
 25.51 
 
 209 
 
 2.76 
 
 57.44 
 
 139 
 
 4.88 
 
 102.04 
 
 104 
 
 7.69 
 
 159.66 
 
 83 
 
 11.04 
 
 229.76 
 
 69 
 
 19.53 
 
 407.03 
 
 52 
 
 30.00 
 
 630.00 
 
 41 
 
 43.80 
 
 916.47 
 
 35 
 
 40 j 
 
 3043 ( 
 
 P 
 Q 
 R 
 
 .35 
 5.53 
 484 
 
 1.05 
 
 16.59 
 
 323 
 
 1.89 
 
 29.46 
 
 242 
 
 4.24 
 
 66.36 
 
 161 
 
 7.58 
 
 107.84 
 
 121 
 
 11.85 
 
 184.36 
 
 96 
 
 16.96 
 
 265.44 
 
 80 
 
 30.08 
 
 470.27 
 62 
 
 46.60 
 
 728.16 
 49 
 
 67.60 
 
 1058.86 
 
 40 
 
 50 ( 
 3403 J 
 
 P 
 
 Q 
 R 
 
 .49 
 6.18 
 541 
 
 1.49 
 
 18.54 
 
 361 
 
 2.65 
 
 32.93 
 
 270 
 
 5.98 
 
 74.17 
 
 180 
 
 10.60 
 
 131.72 
 
 135 
 
 16.63 
 
 206.13 
 
 108 
 
 23.93 
 
 296.70 
 
 90 
 
 42.05 
 
 525.90 
 69 
 
 65.00 
 
 814.32 
 55 
 
 94.50 
 
 1184.15 
 
 46 
 
 60 \ 
 3727 ( 
 
 P 
 Q 
 R 
 
 .65 
 6.77 
 592 
 
 1.96 
 
 20.31 
 
 395 
 
 3.48 
 
 36.08 
 
 296 
 
 7.84 
 
 81.25 
 
 197 
 
 13.94 
 
 144.32 
 
 148 
 
 21.77 
 
 225.80 
 
 118 
 
 31.36 
 
 325.00 
 
 98 
 
 55.20 
 
 576.00 
 
 75 
 
 85.62 
 
 892.00 
 60 
 
 124.50 
 
 1297.00 
 
 50 
 
 70 S 
 
 4026 ( 
 
 P 
 
 .82 
 7.31 
 640 
 
 2.47 
 
 21.94 
 
 427 
 
 4.39 
 
 38.^7 
 
 320 
 
 9.88 
 87.76 
 2.13 
 
 17.58 
 
 155.88 
 160 
 
 27.51 
 
 243.89 
 
 130 
 
 39.52 
 
 351.04 
 
 106 
 
 70.00 
 
 624.00 
 81 
 
 107.80 
 
 966.24 
 
 64 
 
 157.50 
 
 1405.17 
 
 54 
 
 80 S 
 
 4304 ( 
 
 P 
 Q 
 R 
 
 1.00 
 
 7.82 
 684 
 
 3.01 
 
 23.46 
 
 456 
 
 5.36 
 
 41.66 
 
 342 
 
 12.04 
 
 93.84 
 228 
 
 21.44 
 
 166.64 
 
 171 
 
 33.54 
 
 260.73 
 
 137 
 
 48.16 
 
 375.36 
 
 114 
 
 85.76 
 
 666.56 
 
 87 
 
 134.16 
 
 1042.92 
 69 
 
 192.64 
 
 1501.44 
 
 58 
 
 90 j 
 
 4565 ( 
 
 P 
 
 R 
 
 1.20 
 
 8.29 
 726 
 
 3.60 
 
 24.88 
 
 484 
 
 6.39 
 
 44.19 
 
 363 
 
 14.40 
 
 99.52 
 
 242 
 
 25.59 
 
 176.75 
 
 181 
 
 40.04 
 
 276.55 
 145 
 
 57.60 
 
 398.08 
 
 121 
 
 102.36 
 
 707.00 
 93 
 
 160.16 
 
 1106.20 
 
 73 
 
 230.40 
 
 1592.32 
 
 62 
 
 100 i 
 
 4812 ( 
 
 P 
 R 
 
 1.40 
 
 8.74 
 765 
 
 4.21 
 
 26.22 
 
 510 
 
 7.49 
 
 46.58 
 
 382 
 
 16.84 
 
 104.88 
 
 255 
 
 29.93 
 
 186.32 
 
 191 
 
 46.85 
 
 291.51 
 
 152 
 
 67.36 
 
 419.52 
 
 127 
 
 119.72 
 
 745.28 
 96 
 
 187.40 
 1166.04 
 
 77 
 
 269.44 
 
 1678.08 
 
 64 
 
 120 \ 
 
 5271 ( 
 
 P 
 
 Q 
 R 
 
 1.84 
 9.57 
 838 
 
 5.54 
 
 28.72 
 
 559 
 
 9.85 
 
 51.02 
 
 419 
 
 22.18 
 
 114.91 
 
 279 
 
 39.41 
 
 204.10 
 209 
 
 61.66 
 
 319.33 
 
 167 
 
 88.75 
 
 459.64 
 
 139 
 
 157.64 
 
 816.40 
 
 105 
 
 246.64 
 
 1277.32 
 
 83 
 
 355.00 
 
 1838.56 
 
 70 
 
 140 ( 
 
 5694 j 
 
 P 
 
 1 
 
 2.33 
 
 10.34 
 
 906 
 
 6.99 
 
 31.03 
 
 604 
 
 12.41 
 
 55.11 
 
 453 
 
 27.96 
 
 124.12 
 
 302 
 
 49.64 
 
 220.44 
 
 226 
 
 77.71 
 
 344.92 
 
 181 
 
 111.85 
 
 496.43 
 151 
 
 198.56 
 
 881.76 
 114 
 
 310.84 
 
 1379.68 
 
 90 
 
 447.40 
 
 1985.92 
 
 75 
 
 160 ( 
 
 6087 ( 
 
 P 
 Q 
 R 
 
 2.84 
 
 11.05 
 
 969 
 
 8.54 
 
 33.17 
 
 646 
 
 15.17 
 
 58.92 
 484 
 
 34.16 
 
 132.68 
 
 323 
 
 60.68 
 
 235.68 
 
 242 
 
 94.94 
 
 368.73 
 193 
 
 136.65 
 
 530.75 
 
 161 
 
 242.72 
 
 942.72 
 
 121 
 
 377.76 
 
 1474.92 
 
 97 
 
 546.60 
 
 2123.00 
 
 81 
 
 180 ( 
 
 6456 j 
 
 P 
 Q 
 R 
 
 3.39 
 11.72 
 1024 
 
 10.19 
 
 35.18 
 683 
 
 18.10 
 
 62.49 
 
 513 
 
 40.77 
 
 140.74 
 
 342 
 
 72.41 
 
 249.97 
 
 256 
 
 113.30 
 
 391.10 
 206 
 
 163.08 
 
 562.96 
 
 171 
 
 289.64 
 
 999.83 
 
 128 
 
 453.20 
 
 1564.40 
 
 103 
 
 652.32 
 
 2251.84 
 
 86 
 
 200$ 
 
 6805 j 
 
 P 
 Q 
 R 
 
 3.97 
 12.36 
 
 1080 
 
 11.93 
 
 37.08 
 720 
 
 21.20 
 
 65.87 
 
 540 
 
 47.75 
 
 148.35 
 
 360 
 
 84.81 
 
 263.49 
 
 270 
 
 132.70 
 
 412.25 
 
 216 
 
 191.00 
 
 593.40 
 180 
 
 339.24 
 
 1053.96 
 
 135 
 
 530.80 
 
 1649.00 
 
 108 
 
 764.00 
 
 2373.60 
 
 90 
 
 225 ( 
 
 7215 j 
 
 P 
 
 Q 
 R 
 P 
 Q 
 R 
 
 
 
 
 56.99 
 
 157.33 
 
 382 
 
 66.74 
 165.86 
 . 403 
 
 101.20 
 279.44 
 
 287 
 118.54 
 294.59 
 
 302 
 
 158.38 
 437.23 
 
 229 
 185.47 
 460.91 
 
 241 
 
 227.96 
 629.32 
 
 191 
 266.96 
 663.45 
 
 202 
 
 404.80 
 1117.76 
 144 
 474.16 
 1178.36 
 151 
 
 633.52 
 1748.92 
 115 
 741.88 
 1843.64 
 121 
 
 911.84 
 
 
 
 
 2517.28 
 
 
 
 
 96 
 
 250 ( 
 
 7608 j 
 
 5.56 
 
 13.82 
 1209 
 
 16.68 
 
 41.46 
 
 806 
 
 29.63 
 
 73.64 
 
 605 
 
 1067.84 
 
 2653.80 
 
 101 
 
752 
 
 WATER-POWER. 
 
 Tangential Water- Wheel Table.— Continued. 
 
 
 P 
 Q 
 R 
 
 12 
 Inch. 
 
 18 
 Inch. 
 
 24 
 
 Inch. 
 
 36 
 
 Inch. 
 
 48 
 
 Inch. 
 
 60 
 
 Inch. 
 
 72 
 
 Inch. 
 
 8 
 
 Feet. 
 
 10 
 
 Feet. 
 
 12 
 
 Feet. 
 
 275 ( 
 
 7975 j 
 
 
 
 77.00 
 
 173.94 
 
 423 
 
 136.76 
 
 308.92 
 
 317 
 
 214.00 
 
 483.39 
 
 253 
 
 308.00 
 
 695.76 
 
 211 
 
 547.04 
 
 1235.68 
 
 159 
 
 856.00 
 
 1933.56 
 
 127 
 
 1232.00 
 
 2783.04 
 
 106 
 
 
 
 
 
 
 
 300 ( 
 
 8335 | 
 
 P 
 Q 
 R 
 
 7.31 
 15.13 
 1326 
 
 21.93 
 
 45.42 
 884 
 
 38.95 
 
 80.67 
 
 663 
 
 87.73 
 
 181.59 
 
 442 
 
 155.83 
 
 322.71 
 
 331 
 
 243.82 
 
 504.91 
 
 265 
 
 350.94 
 
 726.76 
 
 221 
 
 623.32 
 
 1290.84 
 
 166 
 
 975.28 
 
 2019.64 
 
 133 
 
 1403.76 
 
 2907.04 
 
 111 
 
 325 ( 
 
 8672) 
 
 P 
 Q 
 R 
 P 
 
 R 
 
 
 
 
 98.93 
 189.10 
 
 460 
 110.56 
 196.25 
 
 477 
 
 175.68 
 335.84 
 
 344 
 196.38 
 348.57 
 
 358 
 
 274.94 
 525.50 
 
 276 
 307.25 
 545.36 
 
 275 
 
 395.72 
 756.40 
 
 230 
 442.27 
 785.00 
 
 238 
 
 702.72 
 1343.36 
 172 
 785.52 
 1394.28 
 179 
 
 1099.76 
 2102.00 
 
 138 
 1229.00 
 2181.44 
 
 143 
 
 1582.88 
 
 3025.60 
 
 115 
 
 
 
 
 
 
 
 350 ( 
 
 9002 | 
 
 9.21 
 16.35 
 
 1432 
 
 27.64 
 
 49.06 
 
 955 
 
 49.09 
 
 87.14 
 
 716 
 
 1769.08 
 
 3140.00 
 
 119 
 
 400 j 
 
 9624 j 
 
 P 
 Q 
 
 R 
 
 11.25 
 17.48 
 1531 
 
 33.77 
 52.45 
 1021 
 
 59.98 
 
 93 16 
 
 765 
 
 135.08 
 
 209.80 
 510 
 
 239.94 
 
 372.64 
 
 382 
 
 375.40 
 
 583.02 
 
 306 
 
 540.35 
 
 839.20 
 
 255 
 
 959.76 
 
 1490.56 
 
 101 
 
 1501.60 
 
 2332.08 
 
 153 
 
 2161.40 
 
 3356.80 
 
 128 
 
 450 ( 
 
 10208 j 
 
 P 
 
 Q 
 R 
 
 13.43 
 
 18.54 
 1624 
 
 40.79 
 55.63 
 1083 
 
 71.57 
 
 98.81 
 812 
 
 161.19 
 
 222.52 
 541 
 
 286.31 
 
 395.24 
 
 406 
 
 447.95 
 
 618.38 
 
 324 
 
 644.78 
 
 890.11 
 
 270 
 
 1145.24 
 
 1580.96 
 
 203 
 
 1791.80 
 
 2473.52 
 
 162 
 
 2579.12 
 
 3560.44 
 
 135 
 
 500 ( 
 
 10760 I 
 
 P 
 
 15.73 
 19.54 
 1713 
 
 47.20 
 58.64 
 1142 
 
 83.83 
 
 104.15 
 
 856 
 
 188.80 
 
 234.56 
 
 571 
 
 335.34 
 
 416.62 
 
 428 
 
 524.66 
 
 651.83 
 
 342 
 
 755.20 
 
 938.25 
 
 285 
 
 1341.36 
 
 1666.48 
 
 214 
 
 2098.64 
 
 2607.02 
 
 171 
 
 3020.80 
 
 3753.00 
 
 143 
 
 550 ( 
 
 11279 J 
 
 P 
 
 R 
 P 
 
 R 
 
 
 
 
 217.82 
 246.00 
 
 599 
 248.16 
 256.95 
 
 625 
 
 386.84 
 436.92 
 
 449 
 440.77 
 456.38 
 
 469 
 
 605.31 
 683.62 
 
 359 
 689.63 
 714.05 
 
 375 
 
 871.28 
 984.00 
 
 299 
 992.65 
 1027.80 
 
 312 
 
 1547.36 
 1747.68 
 
 225 
 1763.08 
 1825.52 
 
 235 
 
 2421 .24 
 2734.48 
 
 179 
 2758.52 
 2856.20 
 
 188 
 
 3485 12 
 
 
 
 
 3936 00 
 
 
 
 
 150 
 
 600 ( 
 
 11787) 
 
 24.26 
 
 25.12 
 
 1876 
 
 62.04 
 64.24 
 1251 
 
 110.19 
 
 114 09 
 
 938 
 
 3970.60 
 
 4111.20 
 
 156 
 
 640 ( 
 
 P 
 
 R 
 P 
 Q 
 
 R 
 
 
 
 
 270.97 
 264.63 
 
 644 
 312.73 
 277.54 
 
 675 
 
 484.16 
 466.12 
 
 483 
 555.46 
 492.95 
 
 506 
 
 748.80 
 731.59 
 
 387 
 869.06 
 771.26 
 
 405 
 
 1083.88 
 1058.52 
 
 322 
 1250.92 
 1110.16 
 
 337 
 
 1936.64 
 1864.48 
 
 242 
 2221.84 
 1971.80 
 
 253 
 
 2995.20 
 2926.36 
 
 194 
 3476.24 
 3085.04 
 
 203 
 
 4335 52 
 
 
 
 
 4234 08 
 
 
 
 
 
 161 
 
 700 ( 
 12731 | 
 
 30.57 
 27.13 
 2026 
 
 78.18 
 69.38 
 1351 
 
 138.86 
 
 123.23 
 
 1013 
 
 5003.68 
 
 4440.64 
 
 169 
 
 750 ( 
 
 13178) 
 
 P 
 
 Q 
 R 
 
 33.91 
 
 28.08 
 2098 
 
 86.70 
 71.82 
 1309 
 
 154.00 
 
 127.56 
 
 1049 
 
 346.83 
 
 287.28 
 
 699 
 
 616.03 
 
 510.25 
 
 524 
 
 963.82 
 
 798.33 
 
 419 
 
 1387.34 
 
 1149.13 
 
 349 
 
 2464.12 
 
 2041.00 
 
 262 
 
 3855.28 
 
 3193.32 
 
 210 
 
 5549.36 
 
 4596.52 
 
 175 
 
 800 ( 
 
 13610) 
 
 P 
 
 Q 
 
 R 
 
 37.35 
 29.00 
 2166 
 
 95.52 
 74.17 
 1444 
 
 169.66 
 
 131.74 
 
 1083 
 
 382.09 
 
 296.70 
 
 722 
 
 678.66 
 
 526.99 
 
 542 
 
 1061.81 
 
 824.51 
 
 433 
 
 1528.36 
 
 1186.81 
 
 361 
 
 2714.64 
 
 2107.96 
 
 271 
 
 4247.24 
 
 3298.04 
 
 217 
 
 6113.44 
 
 4747.24 
 
 181 
 
 900 ( 
 
 14436 j 
 
 P 
 
 Q 
 
 R 
 
 44.57 
 30.76 
 2298 
 
 113.98 
 78.67 
 1532 
 
 202.45 
 
 139.74 
 
 1149 
 
 455.94 
 
 314.70 
 
 766 
 
 809.82 
 
 558.96 
 
 574 
 
 1267.02 
 
 874.53 
 
 459 
 
 1823.76 
 
 1258.81 
 
 383 
 
 3239.28 
 
 2235.84 
 
 287 
 
 5068.08 
 
 3498.12 
 
 229 
 
 7295.04 
 
 5035.24 
 
 192 
 
 1000 ( 
 
 15217 J 
 
 P 
 Q 
 R 
 
 52.20 
 32.42 
 2420 
 
 133.50 
 82.93 
 1615 
 
 237.12 
 
 147.30 
 
 1210 
 
 534.01 
 
 331.72 
 
 807 
 
 948.48 
 
 589.19 
 
 605 
 
 1483.97 
 921.83 
 
 484 
 
 2136.04 
 
 1326.91 
 
 403 
 
 3793.92 
 
 2356.76 
 
 303 
 
 5935.88 
 
 3687.32 
 
 242 
 
 8544.16 
 
 5287.64 
 
 202 
 
 The above tables are compiled on the following ba,sis: 
 
 The head (h) is the net effective head at the nozzle. Proper allowance 
 
 must be made for all losses in the pipe line. 
 
 The velocity of efflux (V) is the approximate spout ing velocity of the 
 
 jet in feet per minute as it issues from the nozzle = V2 gh X 60 = 481.2 
 
 VK. 
 
 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. 
 
TANGENTIAL OR IMPULSE WATER-WHEEL. 
 
 753 
 
 The weight of a cubic foot of water is taken at 39.2° Fahr. = 62.425 lbs. 
 
 The theoretical horse-power = Q X 62.425 xft + 33.000 = 0.00189 Qh. 
 
 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 effec- 
 tive diameter, of half the velocity of efflux of the jet, and equals 7t2C, 
 where C = the circumference (in feet) of the effective diameter. 
 
 Small wheels, up to 24-in. diam., are commonly called motors. 
 
 Amount of Water Required to Develop a Given Horse-Power, with 
 a Given Available Effective Head. 
 
 Horse-Power Based on 85% Efficiency of the Water Wheel. 
 
 Flow in Cubic Feet of Water per Minute Required to 
 Develop Power. 
 
 250 
 
 375 
 
 500 
 
 625 
 
 750 
 
 875 
 
 1000 
 
 1125 
 
 208 
 
 312 
 
 416 
 
 520 
 
 624 
 
 726 
 
 830 
 
 934 
 
 177 
 
 266 
 
 355 
 
 444 
 
 532 
 
 621 
 
 709 
 
 798 
 
 155 
 
 232 
 
 311 
 
 388 
 
 466 
 
 544 
 
 622 
 
 699 
 
 140 
 
 210 
 
 280 
 
 350 
 
 420 
 
 490 
 
 560 
 
 630 
 
 125 
 
 186 
 
 248 
 
 312 
 
 372 
 
 435 
 
 498 
 
 558 
 
 118 
 
 176 
 
 234 
 
 293 
 
 350 
 
 410 
 
 467 
 
 525 
 
 104 
 
 156 
 
 208 
 
 260 
 
 312 
 
 364 
 
 415 
 
 467 
 
 96 
 
 143 
 
 192 
 
 240 
 
 287 
 
 335 
 
 385 
 
 430 
 
 89 
 
 133 
 
 178 
 
 222 
 
 266 
 
 310 
 
 355 
 
 400 
 
 83 
 
 125 
 
 166 
 
 208 
 
 250 
 
 292 
 
 332 
 
 375 
 
 78 
 
 117 
 
 155 
 
 195 
 
 233 
 
 272 
 
 312 
 
 350 
 
 73 
 
 110 
 
 146 
 
 183 
 
 220 
 
 256 
 
 293 
 
 330 
 
 69 
 
 104 
 
 138 
 
 172 
 
 207 
 
 242 
 
 276 
 
 310 
 
 65 
 
 98 
 
 132 
 
 164 
 
 198 
 
 230 
 
 262 
 
 295 
 
 62 
 
 93 
 
 124 
 
 155 
 
 186 
 
 218 
 
 248 
 
 280 
 
 59 
 
 89 
 
 118 
 
 148 
 
 177 
 
 206 
 
 236 
 
 266 
 
 57 
 
 85 
 
 113 
 
 141 
 
 169 
 
 198 
 
 225 
 
 255 
 
 54 
 
 81 
 
 108 
 
 135 
 
 162 
 
 190 
 
 216 
 
 243 
 
 52 
 
 78 
 
 104 
 
 130 
 
 155 
 
 181 
 
 207 
 
 233 
 
 50 
 
 75 
 
 100 
 
 125 
 
 149 
 
 174 
 
 199 
 
 224 
 
 48 
 
 72 
 
 96 
 
 120 
 
 144 
 
 167 
 
 191 
 
 215 
 
 46 
 
 69 
 
 92 
 
 115 
 
 138 
 
 161 
 
 184 
 
 207 
 
 45 
 
 67 
 
 89 
 
 111 
 
 133 
 
 156 
 
 178 
 
 200 
 
 43 
 
 65 
 
 86 
 
 107 
 
 129 
 
 150 
 
 172 
 
 193 
 
 42 
 
 62 
 
 83 
 
 104 
 
 124 
 
 145 
 
 166 
 
 187 
 
 41 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 40 
 
 59 
 
 78 
 
 97 
 
 117 
 
 136 
 
 156 
 
 175 
 
 38 
 
 57 
 
 76 
 
 94 
 
 113 
 
 132 
 
 151 
 
 170 
 
 37 
 
 55 
 
 74 
 
 92 
 
 110 
 
 128 
 
 146 
 
 165 
 
 36 
 
 53 
 
 71 
 
 89 
 
 106 
 
 124 
 
 142 
 
 160 
 
 35 
 
 52 
 
 69 
 
 86 
 
 102 
 
 121 
 
 138 
 
 155 
 
 34 
 
 50 
 
 67 
 
 84 
 
 100 
 
 117 
 
 134 
 
 151 
 
 33 
 
 49 
 
 66 
 
 82 
 
 98 
 
 114 
 
 130 
 
 147 
 
 32 
 
 48 
 
 64 
 
 80 
 
 96 
 
 111 
 
 127 
 
 144 
 
 31 
 
 47 
 
 63 
 
 77 
 
 94 
 
 105 
 
 124 
 
 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 
 
 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 
 
200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 0.20 
 
 0.26 
 
 0.27 
 
 0.26 
 
 0.22 
 
 0.14 
 
 0.03 
 
 62 
 
 75 
 
 80 
 
 77 
 
 64 
 
 41 
 
 13 
 
 0.36 
 
 0.45 
 
 0.51 
 
 0.50 
 
 0.42 
 
 0.30 
 
 0.12 
 
 57 
 
 - 75 
 
 85 
 
 85 
 
 71 
 
 50 
 
 19 
 
 0.41 
 
 0.55 
 
 0.63 
 
 0.66 
 
 0.60 
 
 0.41 
 
 0.20 
 
 48 
 
 64 
 
 73 
 
 76 
 
 74 
 
 66 
 
 51 
 
 0.48 
 
 0.62 
 
 0.70 
 
 0.71 
 
 0.64 
 
 0.43 
 
 0.19 
 
 53 
 
 70 
 
 79 
 
 81 
 
 72 
 
 50 
 
 23 
 
 754 WATER-POWER. 
 
 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 approximate figures 
 are taken: 
 
 Speed, Revolutions per Minute. 
 
 Valve open 200 
 
 Two turns {ijg^J 
 Four turns {i^/\\ 
 Six turns {My*%. 
 Eight turns {]^!J; P ^- 
 
 Water-power Plants Operating under High Pressures. — The fol- 
 lowing notes are contributed by the Pelton 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 lbs. 
 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 travelling at a high 
 rate of speed. 
 
 The London Hydraulic Power Co. has a large number of Pelton wheels 
 from 12 to 18 in. diameter running under pressure of about 1000 lbs. per 
 sq. in. from a system of pressure-mains. The 18-in. wheels weighing 
 30 lbs. have a capacity of over 20 H.P. (See Blaine's "Hydraulic Ma- 
 chinery.") 
 
 Hydraulic Power-hoist of Milwaukee Mining Co., Idaho. — One cage 
 travels up as the other descends; the maximum load of 5500 lbs. 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 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 lbs. 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- 
 Pelton wheel on the shaft of a Riedler duplex compressor. It is used 
 a fly-wheel as well, weighing 25,000 lbs., and develops 500 H.P. at 
 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 
 H.P. each under 800 ft. head are driving an electric transmission plant. 
 These wheels weigh less than 500 lbs. 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). —HP = horse-power delivered; .6 = 62.36 lbs. 
 per cu. ft.; E = efficiency of turbine; q = quantity of water, cubic feet 
 per minute; h = feet effective head: d = inches diameter of jet; v = 
 pounds per square inch effective head; c = coefficient of discharge from 
 nozzle, which may be ordinarily taken at 0.9, 
 
 ■ft, 
 as 1 
 75 
 
THE POWER OF OCEAN WAVES. 
 
 755 
 
 SEqh 
 = 33000 
 
 ■-.001S9Eqh = .00436 Eqp = .00496P«/ 2 V/, 3 = .017 4Pcd 2 vV # 
 
 - oft ^PP w „ //P 
 
 </ = 529.2 -=t = 229 -= — = 
 ■Eh Ep 
 
 ■ 2.62 cd? ^h = 3.99 cd 2 Vp 
 
 # = 201.6 
 
 — — = 57.4 — = 0.381 7= — 0.25 — 
 
 THE POWER OF OCEAN WAVES. 
 
 Albert W. Stahl, U. S. N. {Trans. A. S. M. P., xiii. 438), gives the fol- 
 lowing 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 suc- 
 cessive crests, and the height the vertical distance between the crest and 
 
 the trough, is E = 8 LIT 1 (l - 4.935 j^\ foot-pounds. 
 
 The time required for each wave to travel through a distance equal to 
 
 its own length is P = a/ seconds, and the number of waves passing 
 
 any given point in one minute is N = 
 
 ^ 
 
 Hence the total 
 
 energy of an indefinite series of such waves, expressed in horse-power per 
 foot of breadth, is 
 
 EXN 
 33,000 = 
 
 Vl 
 
 (l-4.935f:). 
 
 By substituting various values for H -*- L, within the limits of such 
 values actually occurring in nature, we obtain the following table of 
 
 Total Energy of Deep-sea Waves in Terms of Horse-power per 
 Foot of Breadth. 
 
 Ratio of 
 
 
 
 Len 
 
 ?th of Waves in Feet. 
 
 
 
 Length to 
 
 
 
 
 
 
 
 
 
 Height of 
 
 
 
 
 
 
 
 
 
 Waves . 
 
 25 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 
 
 300 
 
 400 
 
 50 
 
 0.04 
 
 0.23 
 
 0.64 
 
 1.31 
 
 3.62 
 
 7.43 
 
 20.46 
 
 42.01 
 
 40 
 
 0.06 
 
 0.36 
 
 1.00 
 
 2.05 
 
 5.65 
 
 11.59 
 
 31.95 
 
 65.58 
 
 30 
 
 0.12 
 
 0.64 
 
 1.77 
 
 3.64 
 
 10.02 
 
 20.57 
 
 56.70 
 
 116.38 
 
 20 
 
 0.25 
 
 1.44 
 
 3.96 
 
 8.13 
 
 21.79 
 
 45.98 
 
 120.70 
 
 260.08 
 
 15 
 
 0.42 
 
 2.83 
 
 6.97 
 
 14.31 
 
 39.43 
 
 80.94 
 
 223.06 
 
 457.89 
 
 10 
 
 0.98 
 
 5.53 
 
 15.24 
 
 31.29 
 
 86.22 
 
 177.00 
 
 487.75 
 
 1001.25 
 
 5 
 
 3.30 
 
 18.68 
 
 51.48 
 
 105.68 
 
 291.20 
 
 597.78 
 
 1647.31 
 
 3381.60 
 
 The figures are correct for trochoidal deep-sea waves only, but they 
 give a close approximation for any nearly regular series of waves in deep 
 water and a fair approximation for waves in shallow water. 
 
 The question of the practical utilization of the energy which exists in 
 ocean waves divides itself into several parts: 
 
 1. The various motions of the water which may be utilized for power 
 purposes. 
 
756 WATER-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 irregu- 
 lar 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 output 
 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 defined: 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 of 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 designed 
 upon various principles. His conclusion as to their practicability is as 
 follows: "Possibly none of the methods described in this paper may ever 
 prove commercially 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." 
 
 Continuous Utilization of Tidal Power. (P. Decceur, Proc. Inst. 
 C. E. 1890.) — ■ In connection 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 separated 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 hie her 
 one-third of the tidal range, rising, and the lower basin during the lower 
 one-third of the tidal range, falling. If H be the range in feet, the 
 level in the upper basin would never fall below 2/ 3 H measured from low 
 water, and the level in the lower basin would never rise above 1/3 H. 
 The available head varies between 0.53 H and 0.80 H, the mean value 
 being 2/3 H. If $ square feet be the area of the lower basin, and the 
 above conditions are fulfilled, a quantity 1/3 £# cu. ft. of water is deliv- 
 ered through the turbines in the space of 91/4 hours. The mean flow is, 
 therefore, SH -f- 99,900 cu. ft. per sec, and, the mean fall being Z.$H, 
 the available gross horse-power is about 1/30 S'H 2 , where S' is measured 
 in acres. This might be increased by about one-third if a variation of 
 level in the basins amounting to 1/2 H were permitted. But to reach this 
 end the number of turbines would have to be doubled, the mean head 
 being reduced to 1/2 H, and it would be more difficult to transmit a con- 
 stant power from the turbines. The turbine 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 revolutions per minute, the vanes having 13 ft. 
 internal diameter. The speed would be maintained constant by regulat- 
 ing sluices. 
 
PUMPS AND PUMPING ENGINES. 
 
 757 
 
 PUMPS AND PUMPING ENGINES. 
 
 Theoretical Capacity of a Pump. — Let Q'=cu. ft. per min.; 
 
 G' = U. S. gals, per min. = 7.4805 Q 7 ; d — diam. of pump in inches; 
 I = stroke in inches ; N = number of single strokes per min. 
 
 IN 
 
 Capacity in cu. ft. per min. 
 
 Capacity in U. S. gals, per min. 
 Capacity in gals, per hour 
 
 = Q' = ~. • rr7 ' rk = 0.0004545 N<Jl\ 
 
 4 144 12 
 
 Nffl, 
 
 ' 231 ' 
 
 = 0.0034 N&l; 
 = 0.204 NcPl. 
 
 *- 46.9 Vf^^Vm- 
 
 ■ 4.95 
 
 Vf- 
 
 Diameter required for 
 given capacity per min. J " ^"• c/ \Nl A '^" \ Nl 
 
 If v = piston speed in feet per min., d = 13.54 \— 
 If the piston speed is 100 feet per min.: 
 
 Nl = 1200, and d = 1.354 Vq> = 0.495 >/(?'; G' = 4.08 d 2 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 lbs.; P = 
 pressure in lbs. per sq. ft.: p = pressure in lbs. per sq. in.; H = height of 
 lift in ft.; W = 62.355 Q', P = 144 p, p = 0.433 H, H = 2.3094 p, (?'== 
 7.4805 Q'. 
 
 Q'P = Q'H X 144 X 0.433 = Q'H = G'H 
 33,000 33,000 529.23 3958.9 
 
 WH __ Q'X 62.355 X 2.3094 p = Q'p = G'p 
 221 
 
 HP. 
 
 HP. = 
 
 1. 0104 G' H 
 4000 
 
 33,000 33,000 229.17 1714.3 
 
 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 
 from a height of nearly 34 feet, or the height corresponding to a perfect 
 vacuum (14.7 lbs. 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 
 less 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, 
 
 lbs. per 
 sq. in. 
 
 Vacuum 
 
 in 
 Inches of 
 Mercury. 
 
 Max. 
 Depth 
 of 
 Suc- 
 tion, 
 feet. 
 
 Temp. 
 Fahr. 
 
 Absolute 
 Pressure 
 of Vapor, 
 lbs. per 
 sq. in. 
 
 Vacuum 
 
 in 
 Inches of 
 Mercury. 
 
 Max. 
 Depth 
 of 
 Suc- 
 tion, 
 feet. 
 
 102.1 
 126.3 
 141.6 
 153.1 
 162.3 
 170.1 
 176.9 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 
 27.88 
 25.85 
 23.83 
 21.78 
 19.74 
 17.70 
 15.67 
 
 31.6 
 29.3 
 27.0 
 24.7 
 22.3 
 20.0 
 17.7 
 
 182.9 
 188.3 
 193.2 
 197.8 
 202.0 
 205.9 
 209.6 
 
 8 
 
 9 . 
 10 
 11 
 12 
 13 
 14 
 
 13.63 
 11.60 
 9.56 
 7.52 
 5.49 
 3.45 
 1.41 
 
 15.4 
 13.1 
 10.8 
 8.5 
 6.2 
 3.9 
 1.6 
 
758 
 
 PUMPS AND PUMPING ENGINES. 
 
 The Deane Single Boiler-feed or Pressure Pump. — Suitable for 
 pumping clear liquids at a pressure not exceeding 150 lbs. 
 
 
 Sizes. 
 
 
 Capacity 
 per min. 
 
 
 
 Sizes of Pipes. 
 
 
 
 
 
 
 CD 
 
 
 
 
 
 
 
 
 
 
 Speed. 
 
 Xi 
 
 a 
 
 o 
 ,3 
 
 CI 
 
 
 
 
 
 c 
 
 >» 
 
 >> 
 
 
 0) 
 
 ft fl i 
 
 
 
 el 
 
 
 _^ 
 
 
 0) 
 
 1 
 
 3 
 
 3 a> 
 
 P 
 
 02 
 
 
 fj 
 5 
 
 11 
 o 
 
 .07 
 
 
 
 m 
 150 
 
 S 
 
 "Si 
 3 
 
 x\ 
 
 d 
 
 o3 
 
 m 
 
 3 
 o3 
 ,3 
 
 3 
 
 _o 
 
 3 
 GO 
 
 o3 
 -3 
 
 Q 
 
 
 
 3 
 
 2 
 
 10 
 
 291/ ? 
 
 7 
 
 V? 
 
 3/ 4 
 
 U/4 
 
 1 
 
 1 
 
 3V ? 
 
 21/4 
 
 3 
 
 .09 
 
 150 
 
 13 
 
 33 1/? 
 
 •j v? 
 
 Va 
 
 »/4 
 
 H/4 
 
 1 
 
 IV? 
 
 4 
 
 2 3/s 
 
 3 
 
 .10 
 
 150 
 
 15 
 
 331/? 
 
 71/?, 
 
 i/?, 
 
 3/4 
 
 11/4 
 
 1 
 
 2 
 
 4 
 
 2 V?, 
 
 !> 
 
 .11 
 
 150 
 
 16 
 
 331/? 
 
 71/?, 
 
 V? 
 
 3/4 
 
 H/4 
 
 1 
 
 21/?, 
 
 43/ 4 
 
 3 
 
 3 
 
 .13 
 
 150 
 
 22 
 
 34 
 
 81/-> 
 
 V? 
 
 3/ 4 
 
 H/9, 
 
 11/4 
 
 3 
 
 5 
 
 31/4 
 
 •J 
 
 .23 
 
 125 
 
 31 
 
 431/? 
 
 91/4 
 
 3/4 
 
 1 
 
 2 
 
 U/2 
 
 4 
 
 31/? 
 
 3 3/ 4 
 
 7 
 
 .a 
 
 125 
 
 42 
 
 43 1/? 
 
 91/4 
 
 3/4 
 
 1 
 
 2 
 
 11/?, 
 
 4 V? 
 
 7 
 
 41/4 
 
 8 
 
 .49 
 
 120 
 
 58 
 
 3ll/o 
 
 12 
 
 
 IV? 
 
 3 
 
 2 
 
 5 
 
 7 
 
 41/-> 
 
 10 
 
 ,69 
 
 100 
 
 69 
 
 55 
 
 12 
 
 
 U/o 
 
 3 
 
 2 
 
 6 
 
 71/2 
 
 5 
 
 10 
 
 85 
 
 100 
 
 85 
 
 55 
 
 12 
 
 
 ll/o 
 
 3 
 
 2 
 
 61/? 
 
 8 
 
 5 
 
 12 
 
 1.02 
 
 100 
 
 102 
 
 63 
 
 14 
 
 
 IV? 
 
 3 
 
 21/?, 
 
 7 
 
 10 
 
 6 
 
 12 
 
 1 47 
 
 100 
 
 147 
 
 69 
 
 19 
 
 ll/o 
 
 2 
 
 4 
 
 4 
 
 8 
 
 12 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 69 
 
 19 
 
 2 
 
 21/o 
 
 5 
 
 4 
 
 9 
 
 14 
 
 8 
 
 12 
 
 2.6! 
 
 100 
 
 261 
 
 69 
 
 21 
 
 2 
 
 21/? 
 
 5 
 
 5 
 
 The Deane Single Tank 
 
 or Light-service 
 
 Pum 
 
 3. — These pumps 
 le water-cylinders. 
 
 will all stand a constant working pressure of 75 lbs. on t 
 
 
 Sizes. 
 
 
 
 Capacity 
 per min. 
 
 
 
 
 Sizes of Pipes. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Speed. 
 
 3 
 
 -3 
 
 J 
 3 
 
 
 
 
 
 1>> 
 
 ">> 
 
 ° 6 
 
 »u 
 
 
 
 .3 
 
 
 j 
 
 
 a3 
 
 3 a 
 1*3 
 GO 
 
 
 •8* 
 
 3 o 
 
 <D 
 
 3 
 
 X 
 
 ^ 
 
 i 
 
 03 
 
 m 
 
 3 
 
 3 
 O 
 
 03 
 
 *T3 
 
 
 "o3^ 
 O 
 
 O 
 GQ 
 
 O 
 
 "3 
 O 
 
 60 
 
 3 
 
 s 
 
 X 
 
 X 
 
 3 
 
 Q 
 
 4 
 
 4 
 
 5 
 
 .27 
 
 130 
 
 35 
 
 33 
 
 9 l/o 
 
 V? 
 
 3/4 
 
 2 
 
 U/2 
 
 5 
 
 4 
 
 7 
 
 .38 
 
 125 
 
 48 
 
 43 1/? 
 
 15 
 
 3/4 
 
 1 
 
 3 
 
 21/2 
 
 M/? 
 
 31/o 
 
 7 
 
 .72 
 
 125 
 
 90 
 
 431/0 
 
 15 
 
 3/4 
 
 1 
 
 3 
 
 21? 
 
 71/?, 
 
 71/? 
 
 10 
 
 1.91 
 
 110 
 
 210 
 
 58 
 
 17 
 
 I 
 
 IV? 
 
 5 
 
 4 
 
 8 
 
 6 
 
 12 
 
 1.46 
 
 100 
 
 146 
 
 67 
 
 20 1/2 
 
 1 
 
 ll/o 
 
 4 
 
 4 
 
 6 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 66 
 
 17 
 
 3/4 
 
 1 
 
 4 
 
 4 
 
 8 
 
 7 
 
 12 
 
 2.00 
 
 100 
 
 200 
 
 67 
 
 20 l/o 
 
 1 
 
 U/o 
 
 5 
 
 4 
 
 8 
 
 8 
 
 12 
 
 2.61 
 
 100 
 
 261 
 
 68 
 
 30 
 
 1 
 
 ll/o 
 
 5 
 
 5 
 
 10 
 
 8 
 
 12 
 
 2.61 
 
 100 
 
 261 
 
 68I/2 
 
 30 
 
 11? 
 
 2 
 
 5 
 
 5 
 
 8 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 68 • 
 
 201/2 
 
 1 
 
 U/o 
 
 8 
 
 8 
 
 10 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 68I/2 
 
 30 
 
 1 1/2 
 
 2 
 
 8 
 
 8 
 
 12 
 
 10 
 
 12 
 
 4.08 
 
 100 
 
 408 
 
 64 
 
 24 
 
 2 
 
 21/o 
 
 8 
 
 8 
 
 10 
 
 12 
 
 12 
 
 5.87 
 
 100 
 
 587 
 
 68I/2 
 
 30 
 
 U/o 
 
 2 
 
 8 
 
 8 
 
 12 
 
 12 
 
 12 
 
 5.87 
 
 100 
 
 587 
 
 64 
 
 28l/o 
 
 2 
 
 2 l/o 
 
 8 
 
 8 
 
 10 
 
 12 
 
 18 
 
 8.79 
 
 70 
 
 616 
 
 95 
 
 25 
 
 ll/o 
 
 2 
 
 8 
 
 8 
 
 12 
 
 12 
 
 18 
 
 8.79 
 
 70 
 
 616 
 
 95 
 
 28l/o 
 
 2 
 
 21/o 
 
 8 
 
 8 
 
 12 
 
 14 
 
 18 
 
 12.00 
 
 70 
 
 840 
 
 95 
 
 28l/o 
 
 2 
 
 21/o 
 
 8 
 
 8 
 
 14 
 
 16 
 
 18 
 
 15.66 
 
 70 
 
 1096 
 
 95 
 
 34 
 
 2 
 
 21/o 
 
 12 
 
 10 
 
 16 
 
 16 
 
 18 
 
 15.66 
 
 70 
 
 1096 
 
 95 
 
 34 
 
 2 
 
 2l/o 
 
 12 
 
 10 
 
 18 
 
 16 
 
 18 
 
 15.66 
 
 70 
 
 1096 
 
 97 
 
 34 
 
 3 
 
 3 l/o 
 
 12 
 
 10 
 
 16 
 
 18 
 
 24 
 
 26.42 
 
 50 
 
 1321 
 
 115 
 
 40 
 
 2 
 
 21/o 
 
 14 
 
 12 
 
 18 
 
 18 
 
 24 
 
 26.42 
 
 50 
 
 1321 
 
 135 
 
 40 
 
 3 
 
 31/2 
 
 14 
 
 12 
 
 
 
 
 
 
 
 
 
 
 
 
 
PUMPS AND PUMPING ENGINES. 759 
 
 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, lbs. per sq. in. ; p = resistance per sq. in. on pumps; 
 
 II = head = 2.309 p; p = 0.433 H ; 
 
 „ pc . . , . work done in pump-cvlinder 
 
 E = efficiency of the pump = r - 5 c — ~ — , ,. „ • 
 
 work done by the steam-cylinder 
 
 ,'*— y&'«-W-----*- 
 
 p ' EA' 
 
 V _ 
 ' EP EP 
 
 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 feet 
 per minute is exceeded, the loss from friction may be considerable. 
 
 i ,. , , . . , . . __ / gallons per minute 
 
 The diameter of pipe required is 4.95-%/- — - 
 
 if velocity in feet per minute 
 
 For a velocity of 200 feet per minute, diam. = 0.35 X v gallons per min. 
 
 Sizes of Direct-acting Pumps. — The tables on pages 758 and 760 
 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 in 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." 
 
760 
 
 PUMPS AND PUMPING ENGINES. 
 
 The Worthington Duplex Pump. 
 
 Standard Sizes for Ordinary Service. 
 
 
 
 
 u 
 
 'S-S 
 
 £a . 
 
 .a ° ■ 
 
 
 Sizes of Pipe 
 
 3 for 
 
 
 
 
 a 
 
 05 £ . 
 
 i°1 
 
 
 Short Lengths. 
 
 is 
 
 .2 
 
 
 w 
 
 3 £ 
 
 ** 
 
 .SSI 
 
 To be increas 
 
 3d as 
 
 c 
 
 bo 
 
 a 
 
 _2 
 
 
 "3 bD 
 
 B MS 
 *=< >> 05 
 
 .SI! 
 
 sis 
 
 Sag 
 
 
 length 
 
 increases. 
 
 ">> 
 
 
 
 
 
 
 "a 
 
 
 O B 
 
 tn 03 a 
 
 
 
 
 
 
 
 a 
 
 03 
 
 6 
 
 3 
 
 03 > 
 
 a^ 
 
 B 
 
 a^» 
 
 T3 ^ 
 
 SB,, 
 
 
 
 
 
 03 
 
 c3 
 
 ^ 
 
 
 m tToj 
 
 03 to m 
 
 3 — u 
 
 
 
 
 
 "5 
 
 03 
 
 a; 
 
 
 
 bO 
 
 03 tw 
 
 a ° 
 
 r^ b0^ 
 
 gflo 
 £.3 £ 
 
 03 03 "3 
 
 03 03 S 
 
 "S 3+? 
 
 III 
 
 03 
 ft 
 "ft 
 
 £ 
 
 
 
 03 
 
 a 
 'a 
 
 ■ 3 
 
 03 
 _ft 
 "ft 
 
 fl 
 
 O 
 
 a 
 "a 
 
 i 
 bD 
 03 
 
 a 
 
 | 
 
 
 .2CQ 
 
 g'S.a 
 
 80^ 
 
 -2 O 05 
 
 III 
 
 03 
 
 
 
 
 5 
 
 5 
 
 h5 
 
 Q 
 
 (In 
 
 o- 
 
 5 
 
 m 
 
 w 
 
 m 
 
 s 
 
 3 
 
 2 
 
 3 
 
 .04 
 
 100 to 250 
 
 8 to 20 
 
 2 7/ 8 
 
 3/8 
 
 1/2 
 
 11/4 
 
 1 
 
 41/2 
 
 23/4 
 
 4 
 
 .10 
 
 100 to 200 
 
 20 to 40 
 
 4 
 
 1/2 
 
 3/ 4 
 
 2 
 
 11/2 
 
 51/4 
 
 31/2 
 
 5 
 
 .20 
 
 100 to 200 
 
 40 to 80 
 
 5 
 
 34 
 
 U/4 
 
 21/2 
 
 11/2 
 
 6 
 
 4 
 
 6 
 
 .33 
 
 100 to 150 
 
 70 to 100 
 
 5 5/8 
 
 1 
 
 I 1/2 
 
 3 
 
 2 
 
 71/2 
 
 41/2 
 
 6 
 
 .42 
 
 100 to 150 
 
 85 to 125 
 
 63 8 
 
 11/2 
 
 2 
 
 4 
 
 3 
 
 71/2 
 
 5 
 
 6 
 
 .51 
 
 100 to 150 
 
 100 to 150 
 
 7 
 
 11/2 
 
 2 
 
 4 
 
 3 
 
 71,2 
 
 41/2 
 
 10 
 
 .69 
 
 75 to 125 
 
 100 to 170 
 
 6 3/s 
 
 11/2 
 
 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 
 
 9 7/s 
 
 2 
 
 21/2 
 
 6 
 
 5 
 
 12 
 
 7 
 
 10 
 
 1.66 
 
 75 to 125 
 
 245 to 410 
 
 97/s 
 
 21/2 
 
 3 
 
 6 
 
 5 
 
 14 
 
 7 
 
 10 
 
 1.66 
 
 75 to 125 
 
 245 to 410 
 
 9 7/s 
 
 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 to 610 
 
 12 
 
 I ' : 
 
 3 
 
 6 
 
 5 
 
 16 
 
 81/2 
 
 10 
 
 2.45 
 
 75 to 125 
 
 365 to 610 
 
 12 
 
 
 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 
 
 IOI/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 141/4 
 
 21/2 
 
 3 
 
 8 
 
 7 
 
 16 
 
 IOI/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 
 
 IOI/4 
 
 10 
 
 3.57 
 
 75 to 125 
 
 530 to 890 
 
 HI/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 
 
 
 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 
 
 I8I/2 
 
 14 
 
 10 
 
 6.66 
 
 75 to 125 
 
 990 to 1660 
 
 19 3/ 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 
 
 15 
 15 
 
 11.47 
 11.47 
 
 50 to 100 
 50 to 100 
 
 1145 to 2290 
 1145 to 2290 
 
 21 
 21 
 
 
 
 
 
 25 
 
 
 
 
 
 
 
 
 
 
 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. 
 
PUMPS AND PUMPING ENGINES. 
 
 761 
 
 Number of Strokes Required to Attain a Piston Speed from 50 to 
 
 135 Feet per Minute for Pumps Having Strokes 
 
 from 3 to 18 Inches in Length. 
 
 
 Length of Stroke in Inches. 
 
 «1 
 
 3 
 
 < 
 
 5 
 
 • 
 
 7 | . 
 
 10 
 
 12 
 
 '» 
 
 .. 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 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 
 
 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 
 
 m 
 
 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 
 
 Piston Speed of Pumping-engines. — (John Birkinbine, Trans. A. I. 
 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, 
 thev 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. 
 
 The 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 Vioo 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 lbs. of water per sq. ft. of heating-surface per hour, but 
 
762 PUMPS AND PUMPING ENGINES. 
 
 may be driven up to 6 lbs. 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 Pump 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, 18S4), the valves are of rubber, 3/ 4 inch thick, the opening in 
 valve-seat being 131/2 X 4. V2 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 31/2 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 7.76 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 lbs. 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 Foundrv, 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, I8I/2, 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 lbs. gauge; revolutions per 
 min., 17; static head 37 to 43 ft. Suction valves 128; ports, 4 X 16 1/4 in.; 
 total port area 8576 sq. in. Delivery valves, 96; ports, 4 X 163/4 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. 
 
PUMPS AND PUMPING ENGINES. 
 
 763 
 
 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 of Total Annual Cost op 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 
 
 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. 
 Coal, $3 per ton 
 
 4 per ton. ...... 
 
 5 per ton 
 
 50. 
 
 $24,000 
 
 30.00 
 
 27,000 
 
 51,000 
 
 100. 
 
 $48,000 
 60.00 
 13,500 
 61,500 
 
 120. 
 
 $68,000 
 
 85.00 
 
 11,250 
 
 79,250 
 
 150. 
 
 $118,000 
 
 147.50 
 
 9,000 
 
 127,000 
 
 180. 
 
 $148,000 
 
 185.00 
 
 7,500 
 
 155,500 
 
 1,440 
 2,160 
 3,600 
 6,022 
 
 2,880 
 1,080 
 3,960 
 6,022 
 
 4,080 
 
 900 
 
 4,980 
 
 7,655 
 
 7,080 
 
 720 
 
 7,800 
 
 9,307 
 
 8,880 
 
 600 
 
 9,480 
 
 10,220 
 
 17,280 
 23,040 
 28,800 
 
 8,640 
 11,520 
 14,400 
 
 7,200 
 9,600 
 12,400 
 
 5,760 
 7,680 
 9,600 
 
 4,800 
 6,400 
 8,000 
 
 25,920 
 34,560 
 43,200 
 
 12,960 
 17,280 
 21,600 
 
 10,800 
 14,400 
 18,600 
 
 8,640 
 11,520 
 14,400 
 
 7,200 
 9,600 
 12,000 
 
 26,902 
 32,662 
 38,422 
 
 18,622 
 21,502 
 24,382 
 
 19,835 
 22,235 
 25,035 
 
 22,867 
 24,787 
 26,707 
 
 24,500 
 25,100 
 27,700 
 
 35,522 
 44,182 
 52,822 
 
 22,942 
 27,262 
 31,582 
 
 23,435 
 27,035 
 31,235 
 
 25,747 
 28,627 
 31,507 
 
 26,900 
 29,300 
 31,700 
 
 Cost of Electric Current for Pumping 1000 Gallons per Minute 
 
 100 ft. High. (Theoretical H.P. with 100% efficiency = 
 
 100,000 -^ 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 = 
 80%; 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.-lbs. 
 per min. 
 
 Centrifugal, 1.34 X 0.648 = 0.86382 pump H.P.; X 33,000 = 28,654 
 ft.-lbs. per min. 
 
 1000 gallons 100 ft. high = 833,400 ft.-lbs. per min. 
 
 Triplex, 833,400 -s- 31,838 = 26.1763 K.W. X 8760 hours per year 
 X $0.01 = $2293.04. 
 
 Centrifugal, 833,400 + 28,655 = 29.0840 K.W. X 8760 hours per year 
 X $0.01 = $2547.76. 
 
 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. 
 
764 
 
 PUMPS AND PUMPING ENGINES. 
 
 Cost of Fuel per Year 
 
 for Pumping 1,000 Gallons per Minute 
 
 
 
 100 Ft. 
 
 High by Steam 
 
 Pumps. 
 
 
 
 (») 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 
 100% Effy 
 
 . 90% 
 
 
 
 
 
 
 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 lbs. steam, b, 100% effy., c, 90%. 
 
 (3) Duty per 100 lbs. coal, 90% effy., 8 lbs. steam per lb. coal. 
 
 (4) Lbs. coal per min. for 1000 gals., 100 ft. high. 
 
 (5) Tons, 2000 lbs. in 24 hours. 
 
 (6) Tons per year, 365 days. 
 
 (7) Cost of fuel per year at $3.00 per ton. 
 
 Factors for calculation: 6 = 1980 + a; c = & X 0.9; d = c X 0.8; 
 e = 8334 ^ 100 d\ f = 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 fey 
 Gas Engines. 
 
 Assume a gas engine supplied by an anthracite gas producer using 1.5 
 lbs. of coal per brake H.P. hour, coal costing $3.00 per ton of 2000 lbs. 
 
 Efficiency of triplex pump 80%, of centrifugal pump, 72%. 
 
 1000 gals, per min. 100 ft. high = 833,400 ft.-lbs. per min. -h 33,000 
 = 25.2545 H.P. 
 
 Fuel cost per brake H.P. hour 1.5 lbs. X 300 cents +- 2000 = 0.225 
 cent X 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 
 lbs. of coal. 
 
 Cost of Fuel for Electric Current. 
 
 Based on 10 lbs. steam per I.H.P. hour, 8 lbs. steam per lb. coal, or 
 1.25 lbs. coal per I.H.P. per hour. (Electric line loss not included.) 
 
 Efficiency of engine 0.90, of generator 0.90, combined effy. 0.81. 
 
 I.H.P. = 0.746 K.W., 0.746 X 0.81 = 0.6426 K.W. on wire for 10 lbs. 
 steam. Reciprocal = 16.5492 lbs. steam per K.W. hour. 8 lbs. steam 
 per lb. coal = 2.06865 lbs. coal, at $3.00 per ton of 2,000 lbs. = 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 Univ. 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 
 
CENTRIFUGAL PUMPS. 765 
 
 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 -^ 2 g as a limit. 
 As the flow commences each pound of water discharged will possess the 
 kinetic energy V 2 +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 
 extensive use of intricate mathematical formulae 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 suc- 
 cessful operation of the pump. 
 
 Design of a Four-stage Turbine Pump. — C. W. Clifford, in Am. 
 Mack., 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 
 
766 PUMPS AND PUMPING ENGINES. 
 
 is an abstract of the method adopted. The total head was 1000 ffe. 
 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. 
 
 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 -*- 850 v = 20.24 in. Circumfer- 
 ence C = 63.6 in; h = head for eac h im peller, in ft. 
 
 V — peripheral speed = 1.015 *^2gh = 75.05 ft. per sec, 1.015 being 
 an assumed coefficient. The velocity V is divided into two parts by the 
 formula V t =V - V 2 ; V* = 2 gh -*■ 2 V; whence V t = 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 -s- 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 -5- (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. 148, 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. 149, 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. 150 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 
 
 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 as the square of the velocity for 1 ft. 
 
 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 approxj; 
 imately as follows: a, 481 Vfc; b, 554 Vh; c, 610 Vh; d, 780 ^h\e, 394 "^h. 
 a is a straight radial vane, & 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 Vs5, 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 with 
 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.) 
 
CENTRIFUGAL PUMPS. 
 
 767 
 
768 
 
 PUMPS AND PUMPING ENGINES. 
 
 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 given below 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 electiic 
 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/ 32 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 
 sa me result as the weir from the formula Qi= C X Area of Nozzle X 
 v / 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. 
 
 Test of Steam Turbine Centrifugal Pump, Rated at 1700 Gals. 
 per Min., 100 Ft. Head. 
 
 
 Steam 
 
 
 
 Ol 
 
 
 4-< 
 
 
 M 
 
 3 
 
 "o3 
 O 
 
 
 
 Press, at 
 
 a 
 
 3 
 3 
 
 o3 
 i> 
 
 0> 
 
 a 
 
 
 & 
 
 
 °o • 
 
 £ 
 
 -3 • 
 
 s 
 
 
 
 
 & • 
 
 & Ol 
 
 0"3 
 
 a 
 
 s & 
 
 a- £ 
 
 o 
 
 
 
 3 
 
 No. of 
 Test. 
 
 nor Valve. 
 Lbs. per 
 Sq. In. 
 
 C.-2 
 
 .2 3 
 
 11 
 
 > u 
 
 tf a 
 
 af 
 
 c3 O 
 
 :3 o ^ 
 £ ° 
 
 k 
 
 o 
 M 
 
 Oi 
 
 O Ol 
 
 •eg 
 
 C3.0 
 
 73 . 
 
 3 • 
 u ft 
 
 
 
 6 
 > 
 
 
 
 < 
 
 o 
 
 '3 
 
 
 o> 
 ffl 
 
 
 
 « 
 
 
 Qfa 
 
 £ 
 
 o 
 
 £ 
 
 W 
 
 6 
 
 190 
 
 126 
 
 251/4 
 
 1,547 
 
 47.7 
 
 25.45 
 
 37.43 
 
 22.95 
 
 45.97 
 
 1,978 
 
 0.481 
 
 10 
 
 190 
 
 148 
 
 251/9 
 
 1,536 
 
 56.65 
 
 24.42 
 
 50.44 
 
 34.95 
 
 70.75 
 
 1,958 
 
 0.617 
 
 1 
 
 188 
 
 155.2 
 
 25 
 
 1,553 
 
 59.6 
 
 24.06 
 
 61.50 
 
 44.54 
 
 94.9 
 
 1,860 
 
 0.747 
 
 2 
 
 188 
 
 153.5 
 
 251/ 4 
 
 1,547 
 
 58.9 
 
 24.21 
 
 61.86 
 
 44.55 
 
 100.37 
 
 1,759 
 
 0.756 
 
 3 
 
 188 
 
 150.7 
 
 251/4 
 
 1,540 
 
 57.7 
 
 24.33 
 
 61.47 
 
 43.59 
 
 106.94 
 
 1,615 
 
 0.755 
 
 4 
 
 188 
 
 143.5 
 
 251/9 
 
 1,549 
 
 54.8 
 
 24.53 
 
 60.00 
 
 40.72 
 
 115.46 
 
 1,398 
 
 0.743 
 
 5 
 
 188 
 
 161 
 
 253/ 8 
 
 1,540 
 
 47.5 
 
 24.5 
 
 54.47 
 
 31.80 
 
 125.85 
 
 1,001 
 
 0.676 
 
 6A 
 
 189.5 
 
 170 
 
 751/9 
 
 1,565 
 
 24.9 
 
 
 Shut- 
 
 off T. 
 
 142.15 
 
 
 
 \l 
 
 189 
 189 
 189 
 
 169.5 
 
 169 
 
 169.7 
 
 
 1,537 
 1,535 
 1,538 
 
 
 
 45.15 
 45.12 
 44.62 
 
 43.85 
 43.82 
 42.93 
 
 95.14 
 99.05 
 104.42 
 
 1,826 
 1,753 
 1,629 
 
 
 
 
 
 P 
 
 
 
 
 
 
 
 * 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. 
 •f Non-condensing. 
 
CENTRIFUGAL PUMPS. 
 
 769 
 
 Test of Electric Motor Centrifugal Pump. Diam. of Pump Wheel 
 89/32 In. Rated at 1200 Gals. Per Min. — 45 Ft. Head. 
 2000 Revs.' Per Min. 
 
 
 
 
 
 
 
 
 
 u 
 
 0> 
 
 <u 
 
 . 
 
 a 
 
 S 
 
 
 0> 
 
 H 
 
 'o 
 6 
 
 
 O- 
 
 a 
 8 
 < 
 
 
 o> £ 
 
 M o 
 
 gPn 
 
 « £ 
 * o 
 
 w 
 
 1.2 
 
 S> CD 
 
 M ft 
 
 ° 8 
 
 0> L..S 
 
 o 
 Ph 
 
 o 
 
 H 
 
 En 
 
 tS 
 
 o 
 
 a^ 
 
 <^a 
 
 Ph 
 
 'o 
 >> 
 
 a 
 
 & 
 
 1 
 
 
 242.5 
 
 242.3 
 
 55.2 
 
 54.8 
 
 17.94 
 
 17.80 
 
 15.07 
 
 14.94 
 
 2,006 
 1,996 
 
 3.158 
 3.126 
 
 10.25 
 10.67 
 
 28.52 
 30.12 
 
 1,417 
 
 1,403 
 
 0.680 
 
 ?, 
 
 
 0.714 
 
 3 
 
 
 242 
 
 59 
 
 19.14 
 
 16.22 
 
 1,996 
 
 2.885 
 
 11.80 
 
 36.1 
 
 1,295 
 
 0.728 
 
 4 
 
 
 242 
 
 62.4 
 
 20.24 
 
 17.27 
 
 2,005 
 
 2.826 
 
 12.18 
 
 38.05 
 
 1,268 
 
 0.706f 
 
 5 
 
 
 241.8 
 
 •62.9 
 
 20.39 
 
 17.41 
 
 2,000 
 
 2.525 
 
 13.06 
 
 45.66 
 
 1,133 
 
 0.750 
 
 6 
 
 
 240.8 
 
 66 
 
 21.30 
 
 18.28 
 
 2,005 
 
 2.504 
 
 13.40 
 
 47.25 
 
 1,124 
 
 0.733t 
 
 7 
 
 
 241.4 
 
 64 
 
 20.71 
 
 17.71 
 
 2,003 
 
 2.197 
 
 13.12 
 
 52.7 
 
 986 
 
 0.742 
 
 8 
 
 
 239.7 
 240.9 
 
 66.3 
 63.2- 
 
 21.30 
 20.41 
 
 18.28 
 17.43 
 
 1,997 
 2,007 
 
 2.179 
 1.735 
 
 13.15 
 11.42 
 
 53.28 
 58.10 
 
 978 
 779 
 
 720f 
 
 9 
 
 
 0.665f 
 
 in 
 
 
 242 
 
 62 
 
 20.11 
 
 17.14 
 
 2,003 
 
 1.760 
 
 11.71 
 
 58.76 
 
 790 
 
 0.683 
 
 ii 
 
 
 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. 
 
 t Tests marked f 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. 
 
 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 
 
 
 O 
 
 
 
 
 u 
 
 "3 . 
 
 £ 
 
 
 Press, at 
 
 
 a 
 
 ft 
 
 Oi 
 
 
 * 
 
 O.3. 
 
 
 K,3 
 
 the Gover- 
 nor Valve. 
 
 £ .« 
 
 & 
 
 8 
 
 3 ■/ 
 
 c3 >> 
 
 >^2 
 
 o> . 
 
 Ph 
 
 .&£&. 
 
 
 aw 
 
 Lbs. per 
 Sq. In. 
 
 
 a 
 
 1 
 
 Z — 
 
 O 
 
 3 
 
 03 
 
 (3 
 
 O D'S 
 
 O 
 
 3&H 
 
 o 
 H 
 
 
 3* 
 
 03 ft 
 
 5 a 
 
 a3 
 
 
 3^ 
 
 < 
 
 0> 
 
 pq 
 
 
 m 
 
 
 
 
 £ 
 
 £ 
 
 3 
 P 
 
 
 186 
 
 120.7 
 
 28.1 
 
 25.25 
 
 341 
 
 2,104 
 
 0.830 
 
 135.76 
 
 12.83 
 
 373 
 
 18.63 
 
 106.2 
 
 175 
 
 138.3 
 162.3 
 
 27.5 
 27.05 
 
 24.4 
 25.5 
 
 385 
 
 2,092 
 2,074 
 
 0.799 
 0.790 
 
 193.85 
 288 
 
 17.54 
 
 25.78 
 
 359 
 354 
 
 
 
 181 
 
 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 
 
 m 
 
 2,027 
 
 1.750 
 
 420.5 
 
 35.60 
 
 336 
 
 36.00 
 
 54.9 
 
 181 
 
 182 
 
 25.3 
 
 25.25 
 
 V5 
 
 •2,001 
 
 0.731 
 
 494.35 
 
 40.92 
 
 328 
 
 41.55 
 
 47.7 
 
 180 
 
 182 
 188.3 
 
 24.9 
 25.5 
 
 25.35 
 26.3 
 
 331 
 
 1,962 
 2,014 
 
 0.697 
 0.664 
 
 585.06 
 632.6 
 
 46.19 
 47.58 
 
 312 
 
 299 
 
 
 
 186 
 
 47.43 
 
 41.77 
 
 185 
 
 185 
 
 30 
 
 25.3 
 
 331 
 
 2,012 
 
 3.558 
 
 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 
 
770 
 
 PUMPS AND PUMPING ENGINES. 
 
 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 was 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 
 
 500 " 39 56 65 71 75 77 77.6 77 74 70 
 
 600 " 35 50 62 68 71 74 76 77 78 78 76 54 
 Head. 
 
 400 r.p.m. 55 55 53 51 47 42 34 
 
 500 " 63 86 84 82 78 73 67 63 58 51 
 
 600 " 126 127 125 122 118 115 107 104 101 97 87 55 
 
 The following results were obtained under conditions of maximum 
 efficiency: 
 
 400 r.p.m. 77.7% effy. 2296 gals, per min. 43.6 ft. lift 
 500 " 77.6 " 2794 " " 67.4 
 
 600 " 77.97 " 3235 " " 100.7 
 
 A High-Duty Centrifugal Pump. — A 45,000,000 gal. centrifugal pump 
 at the Deer Island sewage pumping station, Boston, Mass., was tested 
 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 moderate 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 moderately high 
 efficiency. 
 
 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 
 
 Disch. cu. ft. per sec. 
 Water horse-power. . . 
 
 I.H.P 
 
 Effy., engine, gearing 
 
 and pumps 
 
 Duty, per 1000 lbs. stea 
 Duty, per million 
 
 BT.U.infuel 
 
 Therm, effy. from stea 
 Kind of engine, and 
 
 pump 
 
 15.5 
 72.6 
 127.5 
 155.6 
 
 16.2 
 157.0 
 287.4 
 671.2 
 
 11.2 
 116.0 
 147.1 
 229.8 
 
 30.2 
 93.2 
 318.0 
 648.0 
 
 9.5 
 71.4 
 76.5 
 137.7 
 
 28.7 
 68.7 
 222.8 
 503.9 
 
 31.7 
 
 85.6 
 306.8 
 452.3 
 
 6.8 
 130.5 
 98.8 
 193.6 
 
 31.6 
 
 152.9 
 547.9 
 657.7 
 
 81.7 
 72.1 
 
 42.9 
 34.3 
 
 64.2 
 40.7 
 
 49.0 
 33.8 
 
 55,6 
 
 44.3 
 33.9 
 
 67.9 
 78.2 
 
 51.0 
 31.4 
 
 83.3 
 75.4 
 
 37.8 
 8.16 
 
 18.3 
 4.23 
 
 20.7 
 4.68 
 
 24.2 
 4.16 
 
 22.1 
 
 17.3 
 4.09 
 
 51.1 
 9.70 
 
 16.7 
 3.93 
 
 50.1 
 9.61 
 
 a,f 
 
 b,g 
 
 b,g 
 
 b,g 
 
 c, g 
 
 b,g 
 
 a, g 
 
 d,g 
 
 a, g 
 
 13.4 
 30.5 
 46.2 
 90.6 
 
 51.0 
 
 a, Tandem compound condensing Corliss; b, Simple condensing Cor- 
 liss; c, Simple non-condensing Corliss; (/.Triple-expansion condensing, 
 vertical; e, Three-cylinder vertical gas-engine, with gas-producer, 0.85 lb. 
 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. 771 
 
 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 100 lbs. 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 
 lbs. 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 -4-965.7 = 10.355 
 lbs. of water from and at 212° 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 also recommends that the work done be determined by 
 plunger displacement, after making a test for leakage, instead of by 
 measurement of flow by weirs or other apparatus, but advises the use of 
 such apparatus when practicable for obtaining additional data. The 
 following extracts are taken from the report. When important tests are 
 to be made the complete report should be consulted. 
 
 The necessary data having been obtained, the duty of an engine, and 
 other quantities relating to its performance, may be computed by the use 
 of the following formulae: 
 
 r> t — Foot-pounds of work done v 
 
 l. Duty - Total number 0( h eat-units consumed X 1 > UUU ' UUU 
 _ A(P± p + s)X LX N . 
 
 H 
 
 X 1,000,000 (foot-pounds). 
 
 C X 144 
 
 2. Percentage of leakage = X 100 (per cent). 
 
 A. X Li X JS 
 
 3. Capacity = number of gallons of water discharged in 24 hours 
 
 iXLXiVX 7.4805 X24 AXLXNX 1.24675 . 
 
 DX 144 
 of tot 
 I.H.P. - - 
 
 - (gallons). 
 
 Percentage of total frictions, 
 
 A (P ± p + s) X L X N ' 
 £> X 60 X 33,000 
 
 I.H.P. 
 
 _ A(P±p+s)XLXN l . 
 
 A s X M.E.P. XL S X N s ] X iUU (peI Cent; ' 
 
 or, in the usual case, where the length of the stroke and number of strokes 
 of the plunger are the same as that of the steam-piston, this last formula 
 becomes : 
 
 Percentage of total frictions = |"l - \^ ^ p"^ 1 x 10 ° (P er cent -) 
 
 In these f ormulae the letters refer to the following quantities : . 
 
 A = Area, in square inches, of pump plunger or piston, corrected for 
 
 area of piston rod or rods; 
 P = Pressure,' in pounds per square inch, indicated by the gauge on the 
 
 force main ; * 
 
 * E. T. Sederholm, chief engineer of Fraser & Chalmers, in a letter to 
 the author, Feb. 20, 1900, shows that the sum P ± p + s may lead to 
 erroneous results unless the two gauges are placed below the levels of the 
 water in the discharge and suction air chambers respectively, and the 
 connecting pipes to the gauges run so they will always be full of water. 
 He prefers to connect these gauges to the air spaces of the two air cham- 
 bers, running the connecting pipes so they will be full of air only, and to 
 add to the sum of the indications of the two gauges the difference in water 
 level of the two chambers. 
 
772 PUMPS AND PUMPING ENGINES. 
 
 p = Pressure, in pounds per square inch, corresponding to indication of 
 the vacuum-gauge on suction-main (or pressure-gauge, if the 
 suction-pipe is under a head). The indication of the vacuum- 
 gauge, in inches of mercury, may be converted into pounds by 
 dividing it by 2.035; 
 * = Pressure, in pounds per square inch, corresponding to distance be- 
 tween the centers of the. two gauges. The computation for this 
 pressure is made by multiplying the distance, expressed in feet, 
 by the weight of one cubic foot of water at the temperature of the 
 pump-well, and dividing the product by 144; 
 L = Average length of stroke of pump-plunger, in feet; 
 N = Total number of single strokes of pump-plunger made during the 
 trial ; 
 
 As = Area of steam-cylinder, in square inches, corrected for area of piston- 
 rod. The quantity As X M.E.P., in an engine having more than 
 one cylinder, is the sum of the various quantities relating to the 
 respective cylinders: 
 
 L s = Average length of stroke of steam-piston, in feet; 
 
 N s = Total number of single strokes of steam-piston during trial; 
 
 M.E.P. = Average mean effective pressure, in pounds per square inch, 
 measured from the indicator-diagrams taken from the steam- 
 cylinder; 
 
 I.H.P. = Indicated horse-power developed by the steam-cylinder; 
 C = Total number of cubic feet of water which leaked by the pump- 
 plunger during the trial, estimated from the results of the leak- 
 age test; 
 D = Duration of trial in hours ; 
 
 H = Total number of heat-units (B.T.U.) consumed by engine = 
 weight of water supplied to boiler by main feed-pump X total 
 heat of steam of boiler pressure reckoned from temperature of 
 main feed-water + weight of water supplied by jacket-pump X 
 total heat of steam of boiler-pressure reckoned from temperature 
 of jacket-water + weight of any other water supplied X total 
 heat of steam reckoned from its temperature of supply. The 
 total heat of the steam is corrected for the moisture or superheat 
 which the steam may contain. No allowance is made for water 
 added to the feed-water, which is derived from any source ex- 
 cept the engine or some accessory of the engine. Heat added to 
 the water by the use of a flue-heater at the boiler is not to be 
 deducted. Should heat be abstracted from the flue by means of 
 a steam reheater connected with the intermediate receiver of the 
 engine, this heat must be included in the total quantity supplied 
 by the boiler. 
 
 Leakage Test of Pump. — The leakage of an inside plunger (the only 
 tvpe 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 
 
DUTY TRIALS OF PUMPING-ENGINES. 773 
 
 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. 
 
 Table of Data and Results. — In order that uniformity may be se- 
 cured, it is suggested that the data and results, worked out in accordance 
 with the standard method, be tabulated in the manner indicated in the 
 following scheme: 
 
 DUTY TRIAL OF ENGINE. 
 
 DIMENSIONS. 
 
 1. Number of steam-cylinders 
 
 2. Diameter of steam-cylinders ins. 
 
 3. Diameter of piston-rods of steam-cylinders ins. 
 
 4. Nominal stroke of steam-pistons . . * ft. 
 
 5. Number of water-plungers 
 
 6. Diameter of plungers ins. 
 
 7. Diameter of piston-rods of water-cylinders ins. 
 
 8. Nominal stroke of plungers ft. 
 
 9. Net area of steam-pistons sq. ins. 
 
 10. Net area of plungers sq. ins. 
 
 11. Average length of stroke of steam-pistons during trial ft. 
 
 12. Average length of stroke of plungers during trial ft. 
 
 (Give also complete description of plant.) 
 
 TEMPERATURES. 
 
 13. Temperature of water in pump-well degs. 
 
 14. Temp, of water supplied to boiler by main feed-pump degs. 
 
 15. Temp, of water supplied to boiler from other sources degs. 
 
 FEED- WATER. 
 
 16. Weight of water supplied to boiler by main feed-pump . . . lbs. 
 
 17. Weight of water supplied to boiler from other sources lbs. 
 
 18. Total weight of feed-water supplied from all sources lbs 
 
 PRESSURES. 
 
 19. Boiler pressure indicated by gauge lbs. 
 
 20. Pressure indicated by gauge on force main , lbs. 
 
 21. Vacuum indicated by gauge on suction main ins. 
 
 22. Pressure corresponding to vacuum given in preceding line lbs. 
 
 23. Vertical distance between the centers; of the two gauges . . ins. 
 
 24. Pressure equivalent to distance between the two gauges . . lbs. 
 
 MISCELLANEOUS DATA. 
 
 25. Duration of trial hrs. 
 
 26. Total number of single strokes during trial 
 
 27. Percentage of moisture in steam supplied to engine, or 
 
 number of degrees of superheating % or deg„ 
 
 28. Total leakage of pump during trial, determined from results 
 
 of leakage test lbs. 
 
 29. Mean effective pressure, measured from diagrams taken 
 
 from steam-cylinders M.E.P. 
 
 PRINCIPAL RESULTS. 
 
 30. Duty ft.-lbs. 
 
 31. Percentage of leakage % 
 
 32. Capacity gals. 
 
 33. Percentage of total friction .« . % 
 
 ADDITIONAL RESULTS 
 
 34. Number of double strokes of steam-piston per minute — 
 
 35. Indicated horse-power developed by the various steam- 
 
 cylinders ! I.H.P. 
 
 36. Feed-water consumed by the plant per hour lbs. 
 
 37. Feed-water consumed by the plant per indicated horse- 
 
 power per hour, corrected for moisture in steam . .,.,., lbs. 
 
774 
 
 PUMPS AND PUMPING ENGINES. 
 
 38. Heat units consumed per I.H.P. per hour B.T.U. 
 
 39. Heat units consumed per I.H.P. per minute B.T.U. 
 
 40. Steam accounted for by indicator at cut-off and release in 
 
 the various steam-cyiinders : . . . . lbs. 
 
 41. Proportion which steam accounted for by indicator bears 
 
 to the feed-water consumption 
 
 42. Number of double strokes of pump per minute 
 
 43. Mean effective pressure, measured from pump diagrams . M.E.P. 
 
 44. Indicated horse-power exerted in pump-cylinders I.H.P. 
 
 45. Work done (or duty) per 100 lbs. of coal ft.-lbs. 
 
 SAMPLE DIAGRAM TAKEN FROM STEAM-CYLINDERS. 
 
 (Also, if possible, full measurement of the diagrams, embracing pres- 
 sures at the initial point, cut-off, release, and compression; also back 
 pressure, and the proportions of the stroke completed at the various 
 points noted.) 
 
 SAMPLE DIAGRAM TAKEN FROM PUMP-CYLINDERS. 
 
 These are not necessary to the main object, but it is desirable to give 
 them. 
 
 DATA AND RESULTS OF BOILER TEST. 
 
 (In accordance with the scheme recommended by the Boiler-test Com- 
 mittee of the Society.) 
 
 Notable High-duty Pumping Engine Records. 
 
 Date of test . 
 Locality 
 
 Capacity, mil. gal., 24 hrs. . . 
 Diam. of steam cylinders, in 
 
 Stroke, in 
 
 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 I.H.P. per min.. 
 
 Duty, B.T.U. basis 
 
 Duty per 1000 lbs. steam . . . 
 Thermal efficiency, % 
 
 (I) 
 
 1899 
 
 Wildwood, 
 
 Pa. 
 
 .19.5, 29,49.5 
 
 57.5x42 
 
 (2) 143/4 
 
 256 
 
 504 
 
 200 
 
 712 
 
 6.95 
 
 93.05 
 
 12.26, 11.4 
 
 186* 
 
 162.9* 147 .5t 
 
 150.2* 
 
 22.81 
 
 (2) 
 1900 
 St. 
 Louis 
 (10). 
 
 (3) 
 1900 
 Boston 
 Chest- 
 nut Hill 
 
 15 
 34, 62,92 
 
 X42 
 (3)29^ 
 
 292 
 
 126 
 
 801 
 
 3.16 
 
 96.84 
 
 10.68 
 
 202 
 
 158.07 
 
 179.45 
 
 21.00 
 
 30 
 30, 56,87 
 X66 
 (3)42 
 195 
 140 
 185 
 801 
 6.71 
 93.29 
 10.34 
 196 
 156 
 
 178.49 
 21.63 
 
 (4) 
 
 1901 
 
 Boston, 
 
 Spot 
 
 Pond. 
 
 (5) 
 
 1906 
 
 St, 
 Louis 
 
 (3), 
 Bissell's 
 Point. 
 
 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 
 
 20 
 34, 62,94 
 
 72 
 (3)337/ 8 
 198 
 238 
 146 
 859 
 2.27 
 97.73 
 
 202.8 
 158.85 
 181.30 
 20.92 
 
 With reheaters. 
 
 t Without reheaters. 
 
 (1) (2). From Eng. News, Sept. 27, 1900. 
 (4) Do. Nov. 4, 1901. (5) Allis-Clmlmers Co., 
 
 (3) Do. Aug. 23, 1900. 
 
 , Bulletin No. 1609. The 
 
 Wildwood engine has double-acting plungers. 
 
 The coal consumption of the. Chestnut Hill engine was 1.062 lbs. per 
 I H.P. per hour, the lowest figure on record at that date, 1901. 
 
 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 bv 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 
 
VACUUM PUMPS. 
 
 775 
 
 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. 
 lbs. per million B.T.U., and it has not yet been exceeded (1909). 
 
 VACUUM PUMPS. 
 
 The Pulsometer. — In the pulsometer the water is raised by 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 3 1/2-inch suction-pipe, stood 
 40 in. high, and weighed 695 lbs. 
 
 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 — lbs. 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 
 
 _ . „ . lbs. water X increase of temp. 
 
 Pounds of steam = H-048't - T ' 
 
 The results for the four tests are given in 
 
 the following table 
 
 
 Data and Results. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 
 71 
 
 114 
 
 19 
 
 270.4 
 
 3.1 
 
 1617 
 404,786 
 
 75.15 
 4.47 
 
 29.90 
 
 12.26 
 
 42.16 
 
 32.8 
 0.777 
 0.012 
 0.0093 
 0.0065 
 
 10,511,400 
 
 60 
 
 110 
 30 
 277 
 
 3.4 
 931 
 
 186,362 
 80.6 
 5.5 
 54.05 
 12.26 
 66.31 
 57.80 
 0.877 
 0.0155 
 0.0136 
 0.0095 
 
 13,391,000 
 
 57 
 
 127 
 
 43.8 
 309.0 
 
 17.4 
 
 1518 
 228,425 
 
 76.3 
 7.49 
 
 54.05 
 
 19.67 
 
 73.72 
 
 66.6 
 0.911 
 0.0126 
 0.0115 
 0.0080 
 
 11,059,000 
 
 64 
 
 Steam pressure in pipe before 
 
 104.3 
 
 Steam pressure after throttling.. 
 Steam temp, after throttling, °F. . 
 
 26.1 
 
 270.1 
 
 1.4 
 
 
 1019.9 
 
 
 248,053 
 
 Water temp, before entering pump 
 
 Water temperature, rise of 
 
 Water head by gauge on lift, ft.. . . 
 Water head by gauge on suction . . 
 Water head by gauge, total (H) . . 
 Water head by measure, total (h) 
 Coeffi. of friction of plant, h/H 
 
 70.25 
 4.55 
 
 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 lb. evaporates 10 lbs. 
 water 
 
 0.0116 
 0.0081 
 
 12,036,300 
 
 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 
 
776 PUMPS AND PUMPING ENGINES. 
 
 the total heads, but are not proportional thereto. No attempt was made 
 to determine what pressure would give the best efficiency for any par- 
 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 lbs. of steam should produce a greater number of 
 strokes and pump over 50% more water than 26.1 lbs., 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 Tequired 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. 
 
 A very high record of test of a pulsometer is given in Eng'g, Nov. 24, 
 1893, 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 lbs.; work done per pound of steam 21,345 foot-pounds, equal to a 
 duty of 21,345,000 foot-pounds per 100 lbs. of coal, if 10 lbs. 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.) 
 
 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 
 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/ 8 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, 
 

 PUMPING BY COMPRESSED AIR. 777 
 
 For a given submersion (h) and lift (//), the ratio of the two being kept 
 within reasonable limits, (//) being not much greater than (/?,), 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 ■*■ h, 
 the higher was the efficiency. 
 
 The pump, as erected, showed the following efficiencies: 
 
 For H 4- h = 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. 
 
 Air-Lifts for Deep Oil-Wells are described by E. M. Ivens, in Trans. 
 A. S. M. E. 1909, p. 341. The following are soma 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, lbs. 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 h- total ft. of vertical pipe, %. . . 23.6 27.6 28 39 
 
 Pumping efficiency, % 9.3 13.4 19.5 10.3 
 
 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 6V2%. 
 Changing the pipes to 21/2 i^- 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 lbs., duty of whole plant, 19,900,000 ft. lbs. per 1000 lbs. of steam used 
 by the compressors. Two-thirds capacity test, delivery, 2,642,900 gals., 
 mean lift, 25.43 ft., air pressure, 26 lbs., duty, 24,207,000. 
 
 An article in The Engineer (Chicago), Aug. 15, 1904, gives the following 
 formula 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 -5- 16.824; C = 8.24 AD h- L 2 . 
 
 Where L exceeds 180 ft. it will be more economical to use two or more 
 air-lifts in series. 
 
778 PUMPS AND PUMPING ENGINES. 
 
 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 
 Eytelwein as the results of his experiments (from Rankine) : 
 
 Let 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 H below the pond; L, the length of the supply-pipe, from the pond 
 to the waste-clack; D, its diameter in feet; then 
 
 = V(1.63Q); L-,^,^^ : 
 
 -0.2^, when | 
 
 1.12 — 0.2 \\ — , when —does not exceed 20; 
 
 '(Q-q)H 
 1-5- (1 + h/10 H) nearly, when h/H does not exceed 12. 
 
 hh) 
 
 = 1.42 
 
 Wi 
 
 40 
 
 100 200 
 
 72 
 
 44 14 
 
 18 
 
 4.4 0.7 
 
 65.9 
 
 41.4 13.4 
 
 QH 
 
 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 26 
 Efficiency per cent. 72 61 52 44 37 31 25 19 14 9 4 
 The efficiency as calculated by the two formulae 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 + h = 20 
 
 Efficiency, D'Aubuisson's formula, % 80 
 
 q w effy. X QH -*- (H + h)= 40 
 
 Efficiency by Rankine's formula, % 662/ 
 D'Aubuisson's formula is that of the machine itself, on the basis that 
 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 
 only that of the water that runs to waste, and that the work done is 
 lifting the quantity q not from the level of the ram but only from that of 
 the supply pond. D'Aubuisson's formula is 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 5 6 
 Efficiency of machine, %. 
 
 Pumping head, ft. 
 
 2.6 
 
 60 
 
 30 
 60 
 
 20 
 45 
 
 15 
 33 
 
 7 
 18 
 
 
 
 12.3 
 
 
 
 23.2 
 
 60 
 
 65 
 
 53 
 
 40 
 
 20 
 
 
 
 43.5 
 
 55 
 
 60 
 
 53 
 
 42 
 
 30 
 
 
 
 63.1 
 
 
 60 
 
 55 
 
 50 
 
 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 Pearsall'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. 
 
HYDRAULIC-PRESSURE TRANSMISSION. 
 
 779 
 
 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 
 
 Q* 
 
 q* 
 
 L 
 
 D 
 
 I 
 
 d 
 
 Effy. 
 
 % 
 
 Ins. 
 3 
 
 Ft. 
 
 4 
 
 5 
 
 12 
 37.6 
 
 Ft. 
 
 28 
 
 45 
 
 36.4 
 144.1 
 
 35 
 100 
 200 
 6.26 
 
 3.5 
 
 8 
 
 50.5 
 
 1.15 
 
 Ft. 
 
 28 
 
 40 
 
 60 
 192.5 
 
 Ins. 
 3 
 
 41/2 
 41/2 
 6 
 
 Ft. 
 
 1008 
 325 
 945 
 
 1785 
 
 Ins. 
 U/2 
 
 "21/2 
 I0f 
 
 58.9 
 
 41/., 
 
 72.0 
 
 6 
 
 76.6 
 
 6 
 
 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 delivered 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 object of the experi- 
 ment was to find that stroke of clack-valve which would give the highest 
 efficiency. 
 
 Length of stroke, per cent 
 
 100 
 
 80 
 
 60 
 
 46 
 
 Number of strokes per minute 
 
 52 
 
 56 
 
 61 
 
 66 
 
 Supply head, feet of water 
 
 5.67 
 
 5.77 
 
 5.58 
 
 5.65 
 
 Delivery head, feet of water 
 
 19.75 
 
 19.75 
 
 19.75 
 
 19.75 
 
 Total water pumped, pounds 
 
 Total water supplied, pounds 
 
 297 
 
 296 
 
 301 
 
 297.5 
 
 1615 
 
 1567 
 
 1518 
 
 1455.5 
 
 
 64.1 
 
 64.7 
 
 70.2 
 
 71.4 
 
 
 
 The highest efficiency realized was obtained when the clack-valve trav- 
 elled 60% of its full stroke, the full travel being l'Vie in. 
 
 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 Water under high pressure (700 to 2000 lbs. 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, 1S56, No. 
 
780 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 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/Z) 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 +r^ I , or for di-' 
 
 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 QX-r, 1 , and the 
 
 ..:•:.. • • ™ 0.6363A£(H.P.) 3 . , . . , 
 
 horse-power wasted in the pipe is W = ^yrr — , 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 1 2 3 45 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 
 
 With large sheaves, small steel pins, and wire rope for multiplying 
 gear 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 (0.84-0.02 m). 
 
 J. E. Tuit (Eng'g, June 15, 1888) describes some experiments on the 
 friction of hydraulic jacks from 3 1/4 to 135/g-inch 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 lbs. 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 316. 
 
HYDRAULIC-PRESSURE TRANSMISSION. 781 
 
 Cast iron should not be used for pressures exceeding 2000 lbs. per 
 square inch. For higher pressures steel castings or forged steel should 
 be used. For working pressures of 750 lbs. per square inch the test 
 pressure should be 2500 lbs. per square inch, and for 1500 lbs. the test 
 pressure should not be less than 3500 lbs. 
 
 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 
 lbs. pressure per square inch flowing into a flanging-machine ram, 20- 
 inch diameter, through a 1/2-inch pipe contracted at one point to 1/4-inch, 
 gave a velocity of 114 feet per second in the pipe, and 456 feet at the 
 reduced section. Through a 1/2-inch pipe reduced to 3/ 8 _inch at one 
 point the velocity was 213 feet per second in the pipe and 381 feet at the 
 reduced section. In a 1/2-inch pipe without contraction the velocity 
 was 355 feet per second. 
 
 For many of the above notes the author is indebted to Mr. John Piatt, 
 consulting engineer, of New York. 
 
 High-pressure Hydraulic Presses in Iron-works are described bv 
 IR. 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 pipe- 
 circuit. 
 
 6. Steam-pump with fly-wheel, without accumulator and without 
 pipe-circuit. 
 
 The disadvantages of accumulators are thus stated: The weighted 
 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 London. — 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 lbs. 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 lbs. 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 lbs. 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. 
 
782 HYDRAULIC-PRESSURE TRANSMISSION. 
 
 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 lbs. 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 of 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 
 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 Rssen. 
 
HYDRAULIC-PRESSURE TRANSMISSION. 783 
 
 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 3V2 inches; diameter of piston-rod 13 3/4 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. The compressors are bored out to 31 V2 inches diameter, and have 
 47 3 '4-inch stroke. Each of the four cylinders requires a power equal to 
 280 horse-power. The compressed aif 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 forsing-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 new forging-press designed by Mr. John Fritz, ior 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 
 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. 
 
784 
 
 FUEL. 
 
 FUEL. 
 
 Theory of Combustion of Solid Fuel. (From Rankine, somewhat 
 altered.) — The ingredients of every kind of fuel commonly used may be I 
 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 CO2), 
 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 j 
 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 1 
 in fine powder, and 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 to be 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 mineral compounds of various kinds, which are also inert, 
 and 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. 
 
 Oxygen and Air Required for the Combustion of Carbon, Hydro- 
 gen, etc. 
 
 
 
 
 
 
 Gase- 
 
 Heat of 
 
 
 
 Lbs. O 
 
 Lbs.N, 
 = 3.32 
 
 Air per 
 
 ous 
 
 Combus- 
 
 Chemical Reaction. 
 
 per lb. 
 
 lb.= 
 
 Prod- 
 
 tion, 
 
 
 
 Fuel. 
 
 4.32 0. 
 
 ucts 
 
 B.T.U. 
 
 
 
 
 
 
 per lb. 
 
 per lb. 
 
 C to CO2 
 
 C+20=C0 2 
 
 21/3 
 
 8.85 
 
 11.52 
 
 12.52 
 
 14,600 
 
 CtoCO 
 
 C + = CO 
 
 11/3 
 
 4.43 
 
 5.76 
 
 6.76 
 
 4,450 
 
 CO to CO2 
 
 CO + O = CO2 
 
 4 /7 
 
 1.90 
 
 2.47 
 
 3.47 
 
 10,150 
 
 H to H2O 
 
 2 H + = H2O 
 
 8 
 
 26.56 
 
 34.56 
 
 35.56 
 
 62,000 
 
 CH 4 to CO2 ) 
 
 CH 4 + 40 
 
 
 
 
 
 
 andH 2 J 
 
 = C0 2 + 2H 2 
 
 4 
 
 13.28 
 
 17.28 
 
 18.28 
 
 23,600 
 
 S to SO2 
 
 S + 20 = S0 2 
 
 1 
 
 3.32 
 
 4.32 
 
 5.32 
 
 4,050 
 
 For heat of combustion of various fuels see Heat, page 533, 
 
785 
 
 The imperfect combustion of carbon, making carbon monoxide, pro- 
 duces less than one-third of the heat which is yielded by the complete 
 combustion, making carbon dioxide. 
 
 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 C, H, and O be the fractions of one pound of the compound, which 
 consists respectively of carbon, hydrogen, and oxygen, the remainder 
 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 + 62,000 (H - l/ 8 O). 
 
 Analyses of Gases of Combustion. — The following are selected 
 from a large number of analyses of gases from locomotive boilers, to s.how 
 the range of composition under different circumstances (P. H. Dudley, 
 Trans. A.I. M. E., iv. 250): 
 
 No smoke visible. 
 
 Old fire, escaping gas white, engine working 
 
 hard. 
 Fresh fire, much black gas, engine working 
 
 hard. 
 Old fire.damper closed, engine standing still. 
 " " smoke white, engine working hard. 
 New fire, engine not working hard. 
 Smoke black, engine not working hard. 
 
 dark, blower on, engine standingstill. 
 " white, engine working hard. 
 
 Test. 
 
 C0 2 
 
 CO 
 
 O 
 
 N 
 
 I 
 
 13.8 
 
 2.5 
 
 2.5 
 
 81.6 
 
 2 
 
 1 1.5 
 
 
 6 
 
 82.5 
 
 3 
 
 8.5 
 
 
 8 
 
 83 
 
 4 
 
 2.3 
 
 
 17.2 
 
 80.5 
 
 5 
 
 5.7 
 
 
 14.7 
 
 79.6 
 
 6 
 
 8.4 
 
 1.2 
 
 8.4 
 
 82 
 
 7 
 
 12 
 
 1 
 
 4.4 
 
 82.6 
 
 8 
 
 3.4 
 
 
 16.8 
 
 76.8 
 
 9 
 
 6 
 
 
 13.5 
 
 81.5 
 
 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 
 combustion of one lb. of fuel by the weight and by the mean 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 537.) The formula will give approximate results, how- 
 ever, and is sufficiently accurate when relative figures only are desired. 
 
 Let C, H, O, and W represent respectively the percentages of carbon, 
 hydrogen, oxygen, and water in a fuel, and /the pounds of dry gas per 
 
786 
 
 pound of fuel, = C0 2 + N + excess air, then the theoretical elevation of 
 
 the temperature of the fire above the temperature of the atmosphere, 
 
 616 C + 2200 H - 327 O - 44 W 
 
 /+0.02 W +0.18// 
 
 Example. — Required the maximum temperature obtainable by burn- 
 ing moist wood of the composition C, 38; H, 5; O, 32; ash, 1; moisture 24; 
 the dry gas being 15 lbs. per pound of wood, and the temperature of the 
 atmosphere 62°. 
 
 616 X 38 + 2220 X 5 - 327 X 32 - 44 X 24 
 15 + 0.02 X 24+ 0.18 X 5 
 
 = 1403, add 62° = 1465°. 
 
 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 only 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 tr-. 
 
 O+N* 
 
 Proportion of Coke or 
 Charcoal yielded by 
 the Dry Pure Fuel. 
 
 Pure cellulose 
 
 Wood (cellulose and encasing matter) . . 
 
 8 
 
 7 
 
 6@ 5 
 
 4@1 
 1 @ 0.75 
 
 0.28 @ 0.30 
 .30 @ .35 
 .35 @ .40 
 
 
 .40@ .50 
 
 Bituminous coals 
 
 Anthracite 
 
 .50® .90 
 .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.) 
 
 Carbon . . . 
 Hydrogen 
 Oxygen . . . 
 
 ^3 
 O 
 O 
 
 o 
 
 1 
 
 
 
 § 2 "3 
 ~ z z 
 
 
 
 
 ^ 
 
 ^ 
 
 3 
 
 hi 
 
 S 
 
 h-! 
 
 < 
 
 rf 
 
 49.1 
 
 18.65 
 
 30.45 
 
 12.35 
 
 18.10 
 
 3.57 
 
 14.53 
 
 1.42 
 
 6.3 
 
 3.25 
 
 3.05 
 
 1.85 
 
 1.20 
 
 0.93 
 
 0.27 
 
 0.14 
 
 44.6 
 
 24.40 
 
 20.20 
 
 18.13 
 
 2.07 
 
 1.32 
 
 0.65 
 
 0.65 
 
 100.0 
 
 46.30 
 
 53.70 
 
 32.33 
 
 21.37 
 
 5.82 
 
 15.45 
 
 2.21 
 
 13.11 
 
 0.13 
 0.00 
 
 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": 
 
CLASSIFICATION OF SOLID FUELS. 
 
 787 
 
 
 Classification 
 
 of Coals. 
 
 
 
 
 
 
 
 
 Relative 
 
 
 
 
 
 Heating 
 
 Value of 
 
 
 
 Fixed 
 
 Volatile 
 
 Value 
 
 Combus- 
 
 
 
 Carbon. 
 
 Matter. 
 
 per lb. of 
 Combustible 
 
 tible 
 
 Semi-bit. 
 
 = 100 
 
 
 97 to 92.5 
 
 92.5 to 87.5 
 
 3 to 7.5 
 7.5 to 12.5 
 
 14600 to 14800 
 14700 to 15500 
 
 93 
 
 Semi-anthracite 
 
 
 96 
 
 
 
 87.5 to 75 
 75 to 60 
 
 12.5 to 25 
 25 to 40 
 
 15500 to 16000 
 14800 to 15500 
 
 100 
 
 Bituminous, Eastern. 
 
 
 96 
 
 Bituminous, Western 
 
 
 65 to 50 
 
 35 to 50 
 
 13500 to 14800 
 
 90 
 
 
 
 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 25 to over 40%, the higheT 
 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. 
 
 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(6) — Bituminous non-coking. Hocking Valley, Ohio. 
 
 Class 5 — Sub-bituminous. Wyoming, black lignite. 
 
 Class 6 — Lignite, Texas, 
 
788 
 
 Composition of Illustrative Coals — Car-Load Samples. 
 Proximate Analysis of " Air-dried " Sample. 
 
 Class 1 2 3 4a 46 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 12.2 1 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 
 
 Oxvgen 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 
 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 
 some ultimate analyses: 
 
 
 C. 
 
 H. 
 
 O+N. 
 
 7.25 
 8.19 
 4.93 
 
 S. 
 
 Ash. 
 
 Combustible. 
 
 
 C. 
 
 H. 
 
 11.24 
 9.14 
 10.99 
 
 O+N. 
 
 Boghead, Scotland 
 
 63.10 
 
 82.67 
 79.34 
 
 8.91 
 9.14 
 10.41 
 
 0.96 
 
 19.78 
 
 79.61 
 
 82.67 
 83.80 
 
 9.15 
 
 8.19 
 
 Tasmanite, Tasmania. . . 
 
 5.32 
 
 
 5.21 
 
 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 OP COALS. 789 
 
 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 lb. 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 lb., 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 lb., 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. 
 
 
 10 
 30 
 50 
 10 
 
 
 
 
 33.33 
 55.56 
 11.11 
 
 37.50 
 
 
 62.50 
 
 Ash 
 
 
 
 
 
 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, 
 or lignite. Coals containing less than 7.5 per cent volatile matter in the 
 combustible, would be classed as anthracite, between 7.5 and 12.5 per 
 cent as semi-anthracite, between 12.5 and 25 per cent as semi-bituminous, 
 between 25 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 
 14,500 and 15,000 B.T.U. in anthracite, and ranges from 15,500 down to 
 
790 
 
 FUEL. 
 
 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. 
 
 Proximate Analyses and Heating Values of American Coals. 
 
 The accompanying table of proximate, analyses and heating values of 
 American coals is condensed from one compiled by the author for the 
 1898 edition of the Babcock & Wilcox Co. 's book, "Steam." The analyses 
 are selected from various sources, and in general are averages of many 
 samples. The heating values per pound of combustible are either ob- 
 tained from direct caforimetric determinations or calculated from ulti- 
 mate analyses, except those marked (?) which are estimated from the 
 heating values of coals of similar composition. 
 
 Table of Heating Value of Coals. 
 
 
 
 
 
 
 
 oP. 
 
 li 
 
 
 
 
 
 <D 
 
 
 
 
 i>H 
 
 -^ o 
 
 ^ ■£ 
 
 
 
 
 ^ 
 
 a 
 o 
 
 o 
 
 
 
 ^W 
 
 .33 
 
 HS53 
 
 
 6 
 
 3 
 
 
 3 
 
 %8 
 
 
 >B 
 
 $8 
 
 leoretical 
 ration frc 
 at 212° p 
 Combusti 
 
 
 *o 
 
 -S 
 
 1 
 
 -3 
 
 3 
 
 01 
 
 53 §3 
 
 1M 
 
 
 § 
 
 > 
 
 fe 
 
 < 
 
 w 
 
 > 
 
 w 
 
 H 
 
 Anthracite. 
 
 
 
 
 
 
 
 
 
 
 Northern Coal Field . . 
 
 3 42 
 
 4 38 
 
 83 27 
 
 8 20 
 
 73 
 
 13160 
 
 5.00 
 
 14900 
 
 15.42 
 
 East Middle Field .... 
 
 3 71 
 
 3.08 
 
 86.40 
 
 6 27. 
 
 58 
 
 13420 
 
 3.44| 14900 
 
 15.42 
 
 West Middle Field.... 
 
 3 16 
 
 3 72 
 
 81 59 
 
 10 65 
 
 50 
 
 12840 
 
 4.36 14900 
 
 15.42 
 
 Southern Coal Field . . 
 
 3.09 
 
 4.28 
 
 83.81 
 
 8.18 
 
 0.64 
 
 13220 
 
 4.85 
 
 14900 
 
 15.42 
 
 Semi-anthracite. 
 
 
 
 
 
 
 
 
 
 
 Loyalsock Field 
 
 1.30 
 
 8.10 
 
 83.34 
 
 6.23 
 
 1.63 
 
 13920 
 
 8.86 
 
 15500 
 
 16.05 
 
 Bernice Basin 
 
 0.6!> 
 
 9.40 
 
 83.69 
 
 3.34 
 
 0.91 
 
 13700 
 
 10.98 
 
 15500 
 
 16.05 
 
 Semi-bituminous. 
 
 
 
 
 
 
 
 
 
 
 Clearfield Co., Pa 
 
 76 
 
 22 52 
 
 71 82 
 
 3 99 
 
 91 
 
 14950 
 
 24.60 
 
 15700 
 
 16.25 
 
 Cambria Co., Pa 
 
 94 
 
 19 20 
 
 71.12 
 
 7 04 
 
 1 70 
 
 14450 
 
 22.71! 15700 
 
 16.25 
 
 Somerset Co., Pa 
 
 1 58 
 
 16 42 
 
 71 51 
 
 8 62 
 
 1 87 
 
 14200 
 
 20.37 
 
 15800 
 
 16.36 
 
 Cumberland, Md 
 
 1 09 
 
 17.30 
 
 73.12 
 
 7.75 
 
 74 
 
 14400 
 
 19.79 
 
 15800 
 
 16.36 
 
 Pocahontas, Va 
 
 1.00 
 
 21.00 
 
 74.39 
 
 3.03 
 
 58 
 
 15070 
 
 22.50 
 
 15700 
 
 16.25 
 
 New River, W. Va 
 
 0.85 
 
 17.88 
 
 77.64 
 
 3.36 
 
 0.27 
 
 15220 
 
 18.95 
 
 15800 
 
 16.36 
 
 Bituminous. 
 
 
 
 
 
 
 
 
 
 
 Connellsville, Pa 
 
 1 26 
 
 30.12 
 
 59.61 
 
 8.23 
 
 78 
 
 14050 
 
 34.03 
 
 15300 
 
 15.84 
 
 Youghiogheny, Pa 
 
 1.03 
 
 36.50 
 
 59.05 
 
 2.61 
 
 81 
 
 14450 
 
 38.73 
 
 15000 
 
 15.53 
 
 Jefferson Co., Pa.. . . 
 
 1 21 
 
 32.53 
 
 60.99 
 
 4.27 
 
 1.00 
 
 14370 
 
 35.47 
 
 152C0 
 
 15.74 
 
 Brier Hill, Ohio 
 
 4 80 
 
 34 60 
 
 56 30 
 
 4 30 
 
 
 13010 
 
 38.20 
 
 14300 
 
 14.80 
 
 Vanderpool, Ky 
 
 Muhlenberg Co., Ky. . 
 
 4 00 
 
 34 10 
 
 54.60 
 
 7 30 
 
 
 12770 
 
 38.50 
 
 14400 
 
 14.91 
 
 4 33 
 
 33.65 
 
 55.50 
 
 4 95 
 
 1 57 
 
 13060 
 
 38.86 
 
 14400(?) 
 
 14.91 
 
 Scott Co., Tenn 
 
 1 26 
 
 35 76 
 
 53 14 
 
 8 02 
 
 1 80 
 
 13700 
 
 34.17 
 
 15100(?) 
 
 15.63 
 
 Jefferson Co., Ala 
 
 1.55 
 
 34.44 
 
 59 77 
 
 2.62 
 
 1.42 
 
 13770 
 
 37.63 
 
 14400(?) 
 
 14.91 
 
 Big Muddy, III 
 
 7.50 
 
 30.70 
 
 53 80 
 
 8.00 
 
 
 12420 
 
 36.30 
 
 14700 
 
 15.22 
 
 Mt. Olive, 111 
 
 11.00 
 
 35.65 
 
 37.10 
 
 13.00 
 
 
 10490 
 
 47.00 
 
 13800 
 
 14.29 
 
 Streator, 111 
 
 12 00 
 
 33.30 
 
 40 70 
 
 14 00 
 
 
 10580 
 
 45.00 
 
 14300 
 
 14.80 
 
 Missouri 
 
 6.44 
 
 37.57 
 
 47.94 
 
 8.05 
 
 
 12230 
 
 43.94 
 
 I4300(?) 
 
 14.80 
 
 The heating values per pound of combustible given in the table, except 
 those marked (?) are probably within 3% of the average actual heating 
 values of the combustible portion of the coals of the several districts. 
 When the percentage of moisture and ash in any given lot of coal is known 
 
ANALYSIS AND HEATING VALUE OF COALS. 791 
 
 the heating value per pound of coal may be found approximately by 
 multiplying the heating value per pound of combustible of the average 
 coal of the district by the difference between 100% and the sum of the 
 percentages of moisture and ash. 
 
 In 1890 the author deduced from Mahler's tests on European coals 
 the following table of the approximate heating value of coals of different 
 composition. 
 
 
 Approximate Heating Values 
 
 of Coals. 
 
 
 Per Cent 
 Fixed Car- 
 bon in 
 Coal Dry 
 and Free 
 from Ash. 
 
 Heating 
 Value, B.T.U. 
 per lb. 
 Combus- 
 tible. 
 
 Equivalent 
 
 Water 
 Evapora- 
 tion from 
 and at 212° 
 
 per lb. 
 Combus- 
 tible. 
 
 Per Cent 
 Fixed Car- 
 bon in 
 Coal Dry 
 and Free 
 from Ash. 
 
 Heating 
 Value, B.T.U. 
 per lb. 
 Combus- 
 tible . 
 
 Equivalent 
 Water 
 Evapora- 
 tion from 
 and at 212° 
 
 per lb. 
 Combus- 
 tible. 
 
 100 
 97 
 94 
 90 
 87 
 80 
 72 
 
 14,580 
 14,940 
 15,210 
 15,480 
 15,660 
 15,840 
 15,660 
 
 15.09 
 15.47 
 15.75 
 16.03 
 16.21 
 16.40 
 16.21 
 
 68 
 63 
 60 
 57 
 55 
 53 
 51 
 
 15,480 
 15,120 
 14,760 
 14,220 
 13,860 
 13,320 
 12,420 
 
 16.03 
 
 15.65 
 
 15.28 
 
 14.72 
 
 14.35 . 
 
 13.79 
 
 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 percent- 
 age 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 combustible 
 within one or two percent, [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 H/ 2 % 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: 
 
 Heating value per lb. = 146 C + 620 
 
 (*-s> 
 
 40 S, 
 
 in which C, H, and O are respectively the percentages of carbon, hydro- 
 gen and oxygen. Its approximate accuracy is proved by both Mahler's 
 and Lord f nd 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. 
 
 Tests of the U. S. Geological Survey, 1904-1906. — Coals were 
 selected at the mines in different parts of the country for the purpose of 
 testing their relative value in developing power through a steam boiler 
 and engine and through a gas producer and gas engine. The full account 
 of these tests will be found in Bulletins 261, 290 and 323, and Profes- 
 sional Paper 48, of the U. S. Geological Survey. The following table 
 shows approximately the range of heating values per pound of combus- 
 tible, as determined by the Mahler calorimeter, and the range of percent- 
 ages of fixed carbon in the combustible (total of fixed carbon and volatile 
 
792 
 
 matter) in the coals from the several states. The extreme figures, 10,200 I 
 and 15,950, fairly represent the whole range of heating values of the com- j 
 bustible of the coals of the United States, but the figures for each state I 
 do not nearly cover the range of values in that state, and in some cases, j 
 as in Indiana and Illinois, the figures are much lower than the average j 
 heating values of the coals of the states. 
 
 
 Fixed C. %. 
 
 B.T.U.perlb. 
 
 
 89 
 80 to 76.5 
 84 to 77 
 
 67 
 67.5 to 55 
 
 60 
 
 55 to 50.5 
 61.5 to 59 
 62 to 53.5 
 
 56 to 5) 
 50.5 to 47 
 59 to 47.5 
 
 57 to 53.5 
 49 
 
 50.5 to 47 
 48 to 41.5 
 
 48.5 
 
 46 
 48.5 to 42.5 
 44.5 to 34 
 
 14,900 
 
 
 15,950 to 15,650 
 
 
 15,250 to 15,500 
 
 
 15,500 
 
 
 15,500 to 15,000 
 
 
 15,000 
 
 
 14,400 to 13,700 
 
 
 14,800 to 14,200 
 
 
 14,800 to 14,100 
 
 
 14,600 to 13,100 
 
 
 14,300 to 12,600 
 
 
 13,700 to 12,400 
 
 
 13,600 to 12,700 
 
 
 13,300 
 
 
 12,500 to 12,300 
 
 
 13,300 to 10,900 
 
 
 12,100 
 11,500 
 
 
 
 10,200 to 11,400 
 
 
 10,900 to 11,000 
 
 
 
 Average Results of Lord and Haas's Tests. - 
 
 Economy," p. 104.) 
 
 - (" Steam Boiler 
 
 
 
 
 
 
 
 
 
 ■g 
 
 d 
 
 3*ri 
 
 • 
 
 Name of Coal. 
 
 C, 
 
 H 
 
 O 
 
 N 
 
 S 
 
 
 "S 
 
 3 
 
 73 
 
 -*"s 
 
 £ 
 
 
 
 
 
 
 
 -C 
 
 o 
 
 
 X 
 
 T^S 
 
 H 
 
 
 
 
 
 
 
 < 
 
 Ui 
 
 !> 
 
 fe 
 
 > 
 
 W 
 
 Pocahontas, Va.. 
 
 84 87 
 
 4 20 
 
 2 84 
 
 85 
 
 59 
 
 5.89 
 
 76 
 
 18 51 
 
 74.84 
 
 19.82 
 
 15766 
 
 Thacker, W. Va. 
 
 78 65 
 
 5 00 
 
 6.01 
 
 1 41 
 
 1 28 
 
 6.27 
 
 1 38 
 
 35.68 
 
 56.67 
 
 38.62 
 
 15237 
 
 Pittsburg, Pa.. . . 
 
 75.24 
 
 5.01 
 
 7.04 
 
 1 51 
 
 1.79 
 
 8.02 
 
 1 37 
 
 36.80 
 
 53.81 
 
 40.61 
 
 14963 
 
 Middle Kittan- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 75.19 
 
 4.91 
 
 7.47 
 
 1.46 
 
 1.98 
 
 7.18 
 
 1.81 
 
 36.32 
 
 54.69 
 
 39.91 
 
 1480 
 
 Upper Freeport, 
 
 
 Pa. and O 
 
 12 65 
 
 4 82 
 
 1 26 
 
 1 iA 
 
 2 89 
 
 9.10 
 
 1 9i 
 
 M 35 
 
 51.63 
 
 41.98 
 
 14/55 
 
 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 lb. 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 31/2 to 5 in. apart; steamboat, over 31/2 in. 
 and out of screen; broken, through 31/2 in., over 23/4 in. ; egg, 23/4 to 2 in.; 
 stove, 2 to 13/ 8 in.; chestnut, 13/ 8 to 3/ 4 in.; pea, 3/ 4 to 1/2 in.; buckwheat, 
 1/2 to 3/g in.; rice, 3/ 8 to 3/ 16 in.; culm, through 3/ 16 in. 
 
ANALYSIS AND HEATING VALUE OF COALS. 793 
 
 When coal is screened into sizes for shipment the purity of the different 
 sizes as regards ash varies greatly. Samples from one mine gave results 
 as follows: 
 
 
 Screened. 
 
 Analyses. 
 
 Name of Coal. 
 
 Through 
 Inches. 
 
 Over 
 Inches. 
 
 Fixed 
 Carbon. 
 
 Ash. 
 
 Egg 
 
 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 
 
 Stove 
 
 Chestnut 
 
 Pea 
 
 10.17 
 12.67 
 14.66 
 
 Buckwheat 
 
 16.62 
 
 Water. 
 
 Vol. H.C. 
 
 Fixed C. 
 
 Ash. 
 
 Sulphur. 
 
 0.96 
 
 3.56 
 
 82.52 
 
 3.27 
 
 0.24 
 
 to 
 
 to 
 
 to 
 
 to 
 
 to 
 
 1.97 
 
 8.56 
 
 89.39 
 
 9.34 
 
 1.04 
 
 Space Occupied by Anthracite Coal. (/. C. I. W., vol. iii.) — The cubic 
 contents of 2240 lbs. of hard Lehigh coal is a little over 36 feet; an aver- 
 age Schuylkill white-ash, 37 to 38 feet; Shamokin, 38 to 39 feet; Lorberry, 
 nearly 41. 
 
 According to measurements made with Wilkesbarre anthracite coal 
 from the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. 
 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 cf coal of 2240 lbs.; 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, and 32.8 cu. ft. of pea, to make one ton 
 of 2000 lbs. 
 
 Bernice Basin, Pa., Coals. 
 
 Bernice Basin, Sullivan 
 
 and Lycoming Cos.; 
 
 range of 8 
 
 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 Carb. 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 affords 
 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. 
 
 Herold Mine 1.26 28.83 60.79 8.44 0.67 0.013 
 
 Kintz Mine 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. 
 
 Beneath the Connellsville or Pittsburgh coal-bed occurs an interval of 
 from 400 to 600 feet of "barren measures," separating it from the lower 
 productive coal-measures of Western Pennsylvania. The following tables 
 show the great similarity in composition in the coals of these upper and 
 lower coal-measures in the same geographical belt or basin. 
 
794 
 
 Analyses from the Upper 
 
 Coal-measures in a Westward Order. 
 
 Localities. 
 
 Moisture. 
 
 Vol. Mat. 
 
 Fixed Carb. 
 
 Ash. 
 
 Sulphur. 
 
 
 1.35 
 0.89 
 1.66 
 
 3.45 
 15.52 
 22.35 
 31.38 
 33.50 
 37.66 
 
 89.06 
 
 74.28 
 68.77 
 60.30 
 61.34 
 54.44 
 
 5.81 
 9.29 
 5.96 
 7.24 
 3.28 
 5.86 
 
 30 
 
 Cumberland, Md 
 
 Salisbury, Pa 
 
 0.71 
 1.24 
 1 09 
 
 Greensburg, Pa 
 
 Irwin's, Pa 
 
 1.02 
 1.41 
 
 0.86 
 0.64 
 
 Analyses from the Lower 
 
 Coal-measures in a 
 
 Westward Order. 
 
 Localities. 
 
 Moisture. 
 
 Vol. Mat. 
 
 Fixed Carb. 
 
 Ash. 
 
 Sulphur. 
 
 
 1.35 
 0.77 
 1.40 
 1.18 
 0.92 
 0.96 
 
 3.45 
 18.18 
 27.23 
 16.54 
 24.36 
 38.20 
 
 89.06 
 73.34 
 61.84 
 74.46 
 62.22 
 52.03 
 
 5.81 
 6.69 
 6.93 
 5.96 
 7.69 
 5.14 
 
 30 
 
 
 1 02 
 
 Bennington 
 
 Johnstown 
 
 2.60 
 1.86 
 4.92 
 
 Armstrong Co 
 
 3.66 
 
 Analyses of Southern Coals. 
 
 Fixed C. Ash 
 
 Sul- 
 phur. 
 
 Virginia and Kentucky. 
 
 Big Stone Gap Field,* 9 an- 
 alyses, range 
 
 Kentucky. 
 
 Pulaski Co., 3 analyses, 
 range 
 
 Muhlenberg Co., 4 analyses, 
 range 
 
 Pike Co., Eastern Ky., 37 an- 
 alyses, range 
 
 Kentucky Cannel Coals, 5 
 
 analyses, range 
 
 Tennessee. 
 
 Scott Co., range of several I. 
 
 Roane Co., Rockwood 
 
 Hamilton Co., Melville 
 
 Marion Co., Etna 
 
 Sewanee Co., Tracy City 
 
 Kelly Co., Whiteside 
 
 Georgia. 
 
 Dade Co 
 
 Alabama. 
 Warren Field: 
 
 Jefferson Co., Birmingham 
 
 Jefferson Co., Black Creek. 
 
 Tuscaloosa Co 
 
 Cahaba Field, ) Helena Vein 
 
 Bibb Co | Coke Vein.. 
 
 [from 0.80 
 I to 2.01 
 
 [from 1.26 
 [ to 1.32 
 [from 3.60 
 ! to 7.06 
 f from 1 
 i to 1.60 
 from 
 . to 
 
 from 0.70 
 to 1.83 
 1.75 
 2.74 
 0.94 
 1.60 
 1.30 
 
 3.01 
 0.12 
 1.59 
 2.00 
 1.78 
 
 31.44 
 36.27 
 
 35.15 
 39.44 
 30.60 
 38.70 
 26.80 
 41.00 
 40.20 f 
 66.30 f 
 
 32.33 
 41.29 
 26.62 
 26.50 
 23.72 
 29.30 
 21.80 
 
 42.76 
 26.11 
 38.33 
 32.90 
 30.60 
 
 54.80 
 63.50 
 
 60.85 
 
 52.48 
 58.80 
 53.70 
 67.60 
 50 -.37 
 59.80 coke 
 33.70 coke 
 
 46.61 
 61.66 
 60.11 
 67.08 
 63.94 
 61.00 
 74.20 
 
 48.30 
 71.64 
 54.64 
 53.08 
 66.58 
 
 1.73 
 
 8.25 
 
 1.23 
 5.52 
 3.40 
 6.50 
 3.80 
 7.80 
 8.81 
 4.80 
 
 16.94 
 1.11 
 
 11.52 
 3.68 
 
 11.40 
 7.80 
 2.70 
 
 3.21 
 2.03 
 5.45 
 11.34 
 1.09 
 
 0.56 
 1.72 
 
 0.40 
 1.00 
 0.79 
 3.16 
 0.97 
 0.03 
 0.96 
 1.32 
 
 3.37 
 0.77 
 1.49 
 0.91 
 1.19 
 
 2.72 
 0.10 
 1.33 
 0.68 
 0.04 
 
 * This field covers about 120 square miles in Virginia, and about 30 
 square miles in Kentucky. 
 
 t Volatile matter including moisture. 
 
 t Single analyses from Morgan, Rhea, Anderson, and Roane counties 
 fall within this range. 
 
ANALYSIS AND HEATING VALUE OF COALS. 795 
 
 Analyses of Southern Coals — 
 
 - Continued. 
 
 
 
 Moisture. 
 
 Vol. 
 
 Mat. 
 
 Fixed C. 
 
 Ash. 
 
 Sul- 
 phur. 
 
 Texas. 
 
 Eagle Mine 
 
 Sabinas Field, Vein I 
 
 " II 
 
 " III 
 
 " IV 
 
 3.54 
 1.91 
 1.37 
 0.84 
 0.45 
 
 30.84 
 20.04 
 16.42 
 29.35 
 21.6 
 
 50.69 
 
 62.71 
 68.18 
 50.18 
 45.75 
 
 14.93 
 15.35 
 13.02 
 19.63 
 29.1 
 
 i! 15 ' 
 
 Indiana Coals. (J. S. Alexander, Trans. A. I. M. E., iv. 100.) — The 
 typical block coal of the Brazil (Indiana) district differs in chemical com- 
 position but little from the coking coals of Western Pennsylvania. 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 agglutination 
 is prevented, and the coal burns away layer by layer, retaining its form 
 until consumed. 
 
 An ultimate analysis of block coal from Sand Creek by E. T. Cox gave: 
 C, 72.94; H, 4.50; O, 11.77; N, 1.79; ash, 4.50; moisture, 4.50. 
 
 Analyses of other Indiana coals are given below. 
 
 
 Moisture. 
 
 Vol. 
 Mat. 
 
 Fixed C. 
 
 Ash. 
 
 Caking Coals. 
 
 4.50 
 2.35 
 7.00 
 3.50 
 
 8.50 
 2.50 
 5.50 
 
 45.50 
 45.25 
 39.70 
 45.00 
 
 31.00 
 44.75 
 36.00 
 
 45.50 
 51.60 
 47.30 
 46.00 
 
 57.50 
 51.25 
 53.50 
 
 4 50 
 
 Sullivan Co 
 
 Clay Co 
 
 0.80 
 6.00 
 
 Spencer Co 
 
 Block Coals. 
 Clay Co 
 
 2.50 
 3 00 
 
 Martin Co 
 
 Daviess Co 
 
 1.50 
 5.00 
 
 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, Macou- 
 pin 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 lbs. of water evapo- 
 rated from and at 212° per lb. of combustible, in the same boiler that had 
 given 9.88 lbs. 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 lb. 
 
 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 
 
796 
 
 The poorest coal of the series had a heating value of only 8645 B.T.U. 
 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.; moisture 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 same 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 intervention of a 
 fault. 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-anthracitic 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. Wins- 
 low's Arkansas report, being 17.655. 
 
 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 411/2% volatile matter, which is also about the percentage in 
 coals of the McAlester and Lehigh districts. 
 
 "Western Lignites. — The ultimate analyses of some lignites from 
 Utah, Wyoming, Oregon and Alaska are reported by R. W. Raymond in 
 Trans. A. I. M. E., vol. ii. 1873. The range of the analyses is as follows: 
 C, 55.79 to 69.84; H, 3.26 to 5.08; O, 9.54 to 21.82; N, 0.42 to 1.93; S, 
 0.63 to 3.92; moisture, 3.08 to 16.52; ash, 1.68 to 9.28. The heating 
 value in B.T.U. per lb. combustible, calculated by Dulong's formula, 
 ranges from 10,090 to 13,970. 
 
 Analyses of Foreign Coals. (Selected from D. L. Barnes's paper on 
 American Locomotive Practice, Trans. A. S. C. E., 1893.) 
 
 Great, Britain: 
 
 South- Wales 
 
 South-Wales 
 
 Lancashire, Eng 
 
 Derbyshire, 
 
 Durham, " * 
 
 • Staffordshire, " 
 
 Scotlandf 
 
 Scotland! 
 
 South America: 
 
 Chili 
 
 JK ^ 
 
 "8 8 
 
 r6 
 
 li 
 
 &s 
 
 < 
 
 8.5 
 
 88.3 
 
 3.2 
 
 6.2 
 
 92.3 
 
 1.5 
 
 17.2 
 
 80.1 
 
 2.7 
 
 17.7 
 
 79.9 
 
 2.4 
 
 15.05 
 
 86.8 
 
 1.1 
 
 20.4 
 
 78.6 
 
 1.0 
 
 17.1 
 
 63.1 
 
 19.8 
 
 17.5 
 
 80.1 
 
 2.4 
 
 21.93 
 
 70.55 
 
 7.52 
 
 South America: 
 Chili, Chiroqui. . 
 
 Brazil 
 Canada: 
 
 Nova Scotia 
 
 Cape Breton 
 
 Australia. 
 
 Lignite 
 
 Sydney, N.S.W. 
 
 Borneo 
 
 Tasmania 
 
 ^ ^ 
 
 n 
 
 
 
 >% 
 
 *£ 
 
 24.11 
 
 38.98 
 
 24.35 
 
 62.25 
 
 40.5 
 
 57.9 
 
 26.8 
 
 60.7 
 
 26.9 
 
 67.6 
 
 15.8 
 
 64.3 
 
 14.98 
 
 82.39 
 
 26.5 
 
 70.3 
 
 6.16 
 
 63.4 
 
 36.91 
 13.4 
 1.6 
 
 12.5 
 5.5 
 
 10.0 
 2.04 
 14.2 
 30.45 
 
 * Semi-bit. coking coal. f Boghead cannel gas coal. 
 
 % Semi-bit. steam-coal. 
 
RELATIVE VALUE OF STEAM COALS. 797 
 
 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 
 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. Forsyth, 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 getting 
 its samples, to take as much as 300 lbs. 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 lbs., 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 of 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 lbs. of water 
 from and at 212° per lb. of coal, and that of the latter 11.44 lbs. 
 
 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 
 coal 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 tem- 
 perature 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 average of 
 
798 FUEL. 
 
 only 47 thermal units less than the calorimetric tests, the 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 lbs. 
 of water evaporated from and at 212° per lb. of combustible, which is 
 79% of 15.47 lbs., 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 lbs., or 76% of the 
 theoretical 16.4 lbs., may be obtained. For Pittsburgh coal, with a 
 fixed carbon ratio of 68%, 11 lbs., or 69% of the theoretical 16.03 lbs., 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, with a fixed carbon ratio of 60%, 10 lbs., or 66% of the the- 
 oretical 15.28 lbs., 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 lb. 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 greater 
 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 pri- 
 marily caused by the imperfection of the ordinary furnace and its unsuit- 
 ability 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 conditions, 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 combustion chambers to obtain an 
 efficiency of 70% with the highly volatile western coals. 
 
 * Mahler gives Dulong's formula with Berthelot's figure for the heat- 
 ing value of carbon, in British thermal units, 
 
 Heating Power = 14,650 C + 62,025 (h - (° + N), - 1 \ 
 
 The formula commonly used in the United States is 14,600 C + 62,000 
 (H — 1/8 O) + 4050 S. For a description of the Mahler calorimeter 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. 
 
RELATIVE VALUE OF STEAM COALS. 
 
 799 
 
 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: 
 
 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 1% 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-bituminous 
 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 as determined by a calorimeter or the percentage of oxygen. 
 The author has proposed the following for Illinois coal: 
 
 The standard is one containing 14,500 B.T.U. per lb. of pure coal 
 (coal free from moisture and ash), not over 6% moisture and 10% ash - 
 in an air-dried sample. For lower heating value per lb. of pure coal, the 
 price shall be reduced proportionately, and for every 1 % increase in ash 
 or moisture above the specified figures, 2% on 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. 
 
 Evaporative Power of Bituminous 
 
 Coals 
 
 
 
 
 (Tests with Babcock & Wilcox Boilers, Trans. A. S. M. E., iv. 
 
 267.) 
 
 
 
 
 
 
 *s 
 
 0*0 
 
 o3 
 
 3 . 
 
 
 
 
 
 
 
 
 
 n c8 
 
 O . 
 
 r£0 
 
 
 
 
 
 £ 
 
 6 1 
 
 6 
 
 6 1 
 
 ® ii 
 
 ^4 
 
 O 03 
 
 
 ^ 
 
 
 a 
 
 
 ^ 
 
 o 1 
 
 of 
 
 *S 
 
 m . 
 
 1*1 
 
 3™ 
 
 Z. 03 
 
 1 
 
 > 
 
 
 
 
 
 w 
 
 
 e3 C S 
 
 Om 
 
 P'S 
 
 
 
 0> 
 
 Name of Coal. 
 
 
 a? 
 
 3 
 
 fefl 
 
 
 O o3 P- 
 
 6™§ 
 
 a^ 
 
 03 
 
 3 S 
 O c3 
 P-g 
 
 & ° 
 a£ 
 
 a 
 
 O 
 
 w 
 
 1 
 
 
 a 
 
 
 '£ 
 
 » 
 
 _£ 
 
 
 ~ * 
 
 ^ 0^ 
 
 sa 
 
 u, a) 
 
 TJ 
 
 6 
 
 
 3 
 
 e3 
 O 
 
 
 fS 
 
 
 
 d£ a 
 
 £ 
 
 ■23 
 
 o3 \£ 
 
 1 
 
 
 W 
 
 1 . Welsh 
 
 13l/ 2 hrs 
 } IOI/4I1 
 
 40 
 60 
 
 1679 
 
 3126 
 
 7.5 
 8.8 
 
 6.3 
 
 17.6 
 
 2.07 
 4.32 
 
 11.53 
 
 11.32 
 
 12.46 
 12.42 
 
 146 
 
 272 
 
 ~ 96 
 
 2. Anthracite scr's 1/5- 
 Semi-bit. 4/5, 
 
 448 
 
 3. Pittsb'gh fine slack 
 
 4 hrs 
 
 33.7 
 
 1679 
 
 12.3 
 
 21.9 
 
 4.47 
 
 8.12 
 
 9.29 
 
 146 
 
 250 
 
 " 3d Pool lump 
 
 10 " 
 
 43.5 
 
 2760 
 
 4.8 
 
 27.5 
 
 4.76 
 
 10.47 
 
 11.00 
 
 240 
 
 419 
 
 4. Castle Shannon, nr. 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 Pittsb'gh, 3/ 8 nut, 
 
 \ 421/4 h 
 
 69.1 
 
 4784 
 
 10.5 
 
 27.9 
 
 4.13 
 
 10.00 
 
 11.17 
 
 416 
 
 570 
 
 5/8 lump, 
 
 J 
 
 
 
 
 
 
 
 
 
 
 5. 111. " run of mine ". 
 
 6 days 
 
 
 1196 
 
 
 
 1.41 
 
 9.49 
 
 
 104 
 
 54 
 
 " Ind. block 
 
 3 days 
 8 hrs. 
 
 48" 
 
 1196 
 3358 
 
 
 
 2.95 
 4.11 
 
 9.47 
 8.93 
 
 "9:88 
 
 104 
 
 292 
 
 111 
 
 6. Jackson, O., nut .... 
 
 ^6 
 
 32J 
 
 460 
 
 " Staunton, 111., nut.. 
 
 8 " ' 
 
 60 
 
 3358 
 
 17.7 
 
 25.1 
 
 2.27 
 
 5.09 
 
 6.19 
 
 292 
 
 246 
 
 7. Renton screenings . . 
 
 5h50m 
 
 21.2 
 
 1564 
 
 13.8 
 
 31.5 
 
 2.95 
 
 6.88 
 
 7.98 
 
 136 
 
 151 
 
 " Wellington scr'gs . . . 
 
 6h30m 
 
 21.2 
 
 1564 
 
 18.3 
 
 27 
 
 2.93 
 
 7.89 
 
 9.66 
 
 136 
 
 150 
 
 " Black Diam. scr'gs.. 
 
 5h58m 
 
 21.2 
 
 1564 
 
 19.3 
 
 36.4 
 
 3.11 
 
 6.29 
 
 7.80 
 
 136 
 
 "160 
 
 " Seattle screenings . . 
 
 6h24m 
 
 21.2 
 
 1564 
 
 13.4 
 
 31.3 
 
 2.91 
 
 6.86 
 
 7.92 
 
 136 
 
 150 
 
 " Wellington lump. . . . 
 
 6hl9m 
 
 21.2 
 
 1564 
 
 13.8 
 
 28.2 
 
 3.52 
 
 9.02 
 
 10.46 
 
 136 
 
 171 
 
 " Cardiff lump. .. . 
 
 6h47m 
 
 21.2 
 
 1564 
 
 11.7 
 
 26.7 
 
 3.69 
 
 10.07 
 
 11.40 
 
 136 
 
 189 
 
 
 7h23m 
 
 21.2 
 
 1564 
 
 19.1 
 
 25.6 
 
 3.35 
 
 9.62 
 
 11.89 
 
 136 
 
 174 
 
 " South Paine lump . . 
 
 6h35m 
 
 21.2 
 
 1564 
 
 13.9 
 
 28.9 
 
 3.53 
 
 8,96 
 
 10.41 
 
 136 
 
 182 
 
 *' Seattle lump 
 
 6h 5m 
 
 21.2 
 
 1564 
 
 9.5 
 
 34.1 
 
 3.57 
 
 7.68 
 
 8.49 
 
 136 
 
 184 
 
800 
 
 Place of Test: 1. London, England; 2. Peacedale, R. I.; 3. Cincinnati; 
 4. Pittsburgh; 5. Chicago; 6. Springfield, O.; 7. San Francisco. 
 
 In all the above tests the furnace was supplied with a fire-brick arch 
 for preventing the radiation of heat from the coal directly to the boiler. 
 
 Weathering of Coal. (I. P. Kimball, Trans. A. I. M. E., viii. 204.) — 
 The effect of the weathering of coal, while sometimes increasing its 
 weight, is to diminish the carbon and disposable hydrogen and to increase 
 the oxygen and indisposable hydrogen. Hence a reduction in the calo- 
 rific 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- 
 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 lbs. 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. 
 
 (b) Outdoor exposure results in a loss of heating 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 weather- 
 ing 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) confirm the above conclusions, except that 
 4 per cent seems to be amply sufficient to cover the losses sustained by 
 Illinois coals under regular storage-conditions, the larger losses indi- 
 cated in the former series being probably due to the small size of the 
 samples exposed. In these latter tests, the losses sustained by the sub- 
 merged coal, though small in amount, are only slightly less than those 
 indicated for the exposed coal. Screenings and 3-in. nut coal from three 
 mines were stored outdoors, under cover and under water. The average 
 loss in heating value at the end of one week was 0.8%, at the end of two 
 months 1.3%, and at the end of six months 2.0%. Pillar coal exposed 
 underground from 22 to 27 years showed less than 3% loss in heating 
 value as compared with fresh face coal from the same mines. 
 
 An extreme case of weathering was found in coal taken from near an 
 outcrop that had been covered with soil and forest. The coal in this 
 case had become so changed as to appear nearly like lignite, and the 
 analysis shows a corresponding resemblance. The dry coal analysis of 
 the outcrop coal, as compared with fresh face coal 300 ft. from the out- 
 crop, is as follows: 
 
 Ash. Vol. Mat. Fixed C. Sulphur. 
 
 Outcrop 16.86 39.27 43.87 0.85 
 
 Fresh coal 16.25 40.72 43.03 3.91 
 
 The moisture in the outcrop coal was 29.81% and in the fresh coal 
 13.86%. The heating value of the ash-, water- and sulphur-free coal 
 from the outcrop was 11,164 B.T.U. and that of the fresh coal 14,618 
 B.T U. 
 
801 
 
 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 of the Am. Ry. Mast. Mechs. Assn. (Eng. News, July 2, 
 1908). A rate of evaporation as high as 19 lbs. per sq. ft. of heating 
 surface per hour was reached. The comparative economy of raw coal 
 and of briquets was as follows: 
 
 Evap. per sq.ft. heat. surf, per hr., lbs 8 10 12 14 16 
 
 Evap. from and at I Lloydell coal . . . . 9.5 8.8 8.0 7.3 6.6 
 212° per lb. of fuel J Briquetted coal. 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 lbs.; with round briquets, 3.65 lbs. 
 
 Experiments on different binders for briquets are discussed by J. E. 
 Mills in Bulletin No. 343 of the U. S. Geological -Survey, 1908. 
 
 The experiments show that, in general, where it can be obtained, the 
 cheapest binder will be the heavy residuum from petroleum, often known 
 to the trade as asphalt. Four per cent of this binder being sufficient, 
 its cost ranges from 45 to 60 cts. per ton of briquets produced. This 
 binder is available in California, Texas, and adjacent territory. 
 
 Second in order of importance comes water-gas tar pitch. Five to 
 six per cent usually proving sufficient, the cost of this binder ranges 
 from 50 to 60 cts. per ton of briquets. As water-gas pitch is also derived 
 from petroleum, it will be available in oil-producing regions. 
 
 Third in order is coal-tar pitch. This binder is very widely available, 
 From 6.5 to 8% will usually be required, and the cost ranges from 65 to 
 90 cts. per ton of briquets. " 
 
 Other substances are also mentioned which may possibly be used for 
 binders, such as asphalts and tars derived from wood distillation; pitch 
 made from producer-gas tar; and magnesia. Starch and the waste sul- 
 phite liquor from paper mills may also be used, but the briquets made 
 with them are not waterproof. 
 
 Briquetting tests made at the St. Louis exhibition, 1904, with descrip- 
 tions of the machines used are reported in Bulletin No. 261 of the U. S. 
 Geological Survey, 1905. See also paper on Coal Briquetting in the 
 U. S., by E. W. Parker, Trans. A. I. M. E„ 1907. 
 
 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. 
 
802 
 
 FUEL. 
 
 Analyses of Coke. 
 
 (From report of John R. Procter, Kentucky Geological Survey.) 
 
 Where Made. 
 
 Fixed 
 Carbon. 
 
 Ash. 
 
 Sul- 
 phur. 
 
 Connellsville, Pa. (Average of 3 samples) 
 
 Chattanooga, Tenn. "4 
 
 Birmingham, Ala. " "4 " 
 
 Pocahontas, Va. "3 " 
 
 New River, W.Va. " "8 " 
 
 Big Stone Gap, Ky. " "7 " 
 
 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 
 
 Experiments in Coking. Connellsville Region. 
 (John Fulton, Amer. Mfr., Feb. 10, 1893.) 
 
 
 
 
 
 
 M 
 
 03 
 
 Per cent of Yield. 
 
 
 
 .a.d 
 
 T3 
 03 
 M 
 
 on 
 
 03 
 
 s 
 
 03 
 
 03 d 
 
 .S 2 
 
 o 
 
 o 
 O . 
 
 
 
 
 
 
 ■ 
 
 03 
 
 IS 
 
 
 a, . 
 , o 
 
 fc 
 
 H 
 
 < 
 
 p*. 
 
 s 
 
 H 
 
 < 
 
 fe 
 
 s 
 
 H 
 
 Pn 
 
 
 h. m. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 
 
 
 
 
 1 
 
 67 00 
 
 12,420 
 
 99 
 
 385 
 
 7,518 
 
 7,903 
 
 00.80 
 
 3.10 
 
 60.53 
 
 63.63 
 
 35.57 
 
 2 
 
 68 00 
 
 11,090 
 
 90 - 
 
 359 
 
 6,580 
 
 6,939 
 
 00.81 
 
 3.24 
 
 59.33 
 
 62.57 
 
 36.62 
 
 3 
 
 45 00 
 
 9,120 
 
 77 
 
 272 
 
 5,418 
 
 5,690 
 
 00.84 
 
 2.98 
 
 59.41 
 
 62.39 
 
 36.77 
 
 4 
 
 45 00 
 
 9,020 
 
 74 
 
 349 
 
 5,334 
 
 5,683 
 
 00.82 
 
 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 oven 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 reduction 
 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; sulphur, 
 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 61/4 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 
 
803 
 
 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 
 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 
 48,000 
 40,500 
 
 1860 
 3000 
 2400 
 
 780 
 
 Upper Silesia 
 
 840 
 
 492 
 
 
 
 An oven which has been introduced lately into Germany in connection 
 with the recovery of by-products is the Semet-Solvay, which works hotter 
 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 therefore 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 excellent 
 series of articles on the manufacture of coke, by John Fulton, of Johns- 
 town, 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 
 lbs.; in Penna., 76 lbs.; in Ala., Colo., Ga., 111., Ohio, Tenn., and W. Va., 
 it is 80 lbs. 
 
 A Bushel of Coke is almost uniformly 40 lbs., but in exceptional 
 cases, when the coal is very light, 38, 36, and 33 lbs. are regarded as a 
 bushel, in others from 42 to 50 lbs. 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 
 
804 FUEL. 
 
 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 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). (W. H. 
 Biauvelt, Trans. A. I. M. E., xx. 625.) 
 
 WOOD AS FUEL. 
 
 Wood, when newly felled, contains a proportion of moisture which 
 varies very much in different kinds and in different specimens, ranging be- 
 tween 30% and 50%, and being on an average about 40%. After 8 or 
 12 months' ordinary drying in the air 4he 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 lb. 
 of fuel suffices to expel about 3 lbs. 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 2V2 lbs. of wood would prob- 
 ably 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 contain 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 lb. carbon being 7272 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) is 
 about as follows: 
 
 lbs. lbs. 
 
 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, and 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 21/4 lbs. of dry wood are equal 
 to 1 lb. 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,OOo(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 lb. 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 lb., 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. 
 
CHAKCOAL. 
 
 805 
 
 Composition of Wood. 
 
 (Analysis of Woods, by M. Eugene Chevandier.) 
 
 Woods. 
 
 Carbon. 
 
 Hydro- 
 gen. 
 
 Oxygen. 
 
 Nitrogen. 
 
 Ash. 
 
 
 49.36% 
 
 49.64 
 
 50.20 
 
 49.37 
 
 49.96 
 
 6.01% 
 
 5.92 
 
 6.20 
 
 6.21 
 
 5.96 
 
 42.69% 
 
 41.16 
 
 41.62 
 
 41.60 
 
 39.56 
 
 0.91% 
 
 1.29 
 
 1.15 
 
 0.96 
 
 0.96 
 
 1.06% 
 1.97 
 
 Oak 
 
 Birch 
 
 0.81 
 
 
 1.86 
 
 Willow 
 
 3.37 
 
 
 
 
 49.70% 
 
 6.06% 
 
 41 .30% 
 
 1 -05% 
 
 1.80% 
 
 
 
 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 
 
 302° Fahr 
 
 347° Fahr 
 
 392° Fahr 
 
 437° 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 
 
 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 = 4 X 4 X 8 = 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 per cent, of solid wood in a cord as determined 
 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 containing 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 37V2% 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 1/2 parts of wood 
 must be burned in the furnace. Hence in this process the whole expendi- 
 ture of wood to produce from 28 to 30 parts of charcoal is II2V2 parts; 
 
806 
 
 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 1/2 -J- 371/2 = 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, Tenn., 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. (J. C. I. W., vol. vi., p. 26.) 
 
 Results from Different Methods of Charcoal-making. 
 
 
 Character of Wood Used. 
 
 Yield. 
 
 i"3 
 
 <» ag 
 
 3 
 
 m 
 
 
 Coaling Methods. 
 
 CD +a 
 
 111 
 
 a, 
 
 .S«« 
 
 3 
 ^pq g 
 
 5*55.1 
 
 Odelstjerna's experiments 
 Mathieu's retorts, fuel ex- 
 
 Birch dried at 230 F 
 
 
 35.9 
 28.3 
 
 24.2 
 27.7 
 25.8 
 24.7 
 
 18.3 
 22.0 
 
 17.1 
 
 
 
 (Air dry, av. good yel- ) 
 \ low pine weighing > 
 ( abt. 28 lbs. per cu. ft. ) 
 
 | Good dry fir and pine, ) 
 \ mixed. 
 
 ( Poor wood, mixed fir ) 
 { and pine. J 
 ( Fir and white-pine ) 
 ] wood, mixed. Av. 25 > 
 ( lbs. per cu. ft. ) 
 ( Av. good yellow, pine ) 
 \ weighing abt. 25 lbs. > 
 ( per cu. ft. ) 
 
 77.0 
 65.8 
 81.0 
 
 70,0 
 
 72.2 
 
 52.5 
 54.7 
 
 42.9 
 
 63.4 
 
 54.2 
 
 66.7 
 
 62.0 
 59.5 
 
 43.9 
 45.0 
 
 35.0 
 
 15.7 
 
 Mathieu's retorts, fuel in- 
 
 15.7 
 
 Swedish ovens, av. results 
 
 Swedish ovens, av. results 
 Swedish meilers excep- 
 
 13.3 
 13.3 
 13.3 
 
 Swedish meilers, av. results 
 Amez-ican kilns, av. results 
 American meilers, av. re- 
 sults 
 
 13.3 
 17.5 
 17.5 
 
 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. 
 
MISCELLANEOUS SOLID FUELS. 
 
 807 
 
 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: 
 
 Volumes. 
 
 Carbonic oxide 9 . 42 
 
 Oxygen 9 . 25 
 
 Nitrogen 6 . 50 
 
 Carburetted hydrogen .... 5 . 00 
 Hydrogen 1.75 
 
 Volumes. 
 
 Ammonia 90 . 00 
 
 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 oxygen can be 
 drawn by a small hand-pump. 
 
 Composition of Charcoal Produced at Various Temperatures. 
 
 (By M. Violette.) 
 
 
 Temperature of Car- 
 bonization. 
 
 Carbon. 
 
 Hydro- 
 gen. 
 
 Oxygen. 
 
 Nitro- 
 gen and 
 Loss. 
 
 Ash. 
 
 1 
 
 150° Cent. 302° Fahr. 
 
 47.51 
 
 6.12 
 
 46.29 
 
 0.08 
 
 47.51 
 
 2 
 
 200 392 
 
 51.82 
 
 3.99 
 
 43.98 
 
 0.23 
 
 39.88 
 
 3 
 
 250 482 
 
 65.59 
 
 4.81 
 
 28.97 
 
 0.63 
 
 32.98 
 
 4 
 
 300 592 
 
 73.24 
 
 4.25 
 
 21.96 
 
 0.57 
 
 24.61 
 
 ■> 
 
 350 662 
 
 76.64 
 
 4.14 
 
 18.44 
 
 0.61 
 
 22.42 
 
 6 
 
 432 810 
 
 81.64 
 
 4.96 
 
 15.24 
 
 1.61 
 
 15.40 
 
 7 
 
 1023 1873 
 
 81.97 
 
 2.30 
 
 14.15 
 
 1.60 
 
 15.30 
 
 The wood experimented on was that of black alder, or alder buck- 
 thorn, which furnishes a charcoal suitable for gunpowder. It was pre- 
 viously dried at 150 deg. C. = 302 deg. F. 
 
 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 
 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 though the medium 
 of a very small proportion of fire-damp in the air of the mine. The ex- 
 plosive violence of the combustion of dust is largely due to the instan- 
 taneous 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 pul- 
 verized 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 construction. 
 In the place of the ordinary boiler fire-box there is a combustion 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 cham- 
 ber, 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- 
 Hnine to a hisrh 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.) 
 
808 FUEL. 
 
 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. 
 An illustrated description is given in the author's Steam Boiler Economy, 
 p. 183. 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. 1873, 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 ordinary 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) gives 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, 7391 heat-units per pound. 
 
 A paper on Peat in the U. S., by M. R. Campbell, will be found in Min- 
 eral 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. The same applies to shavings, 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. Experiments by Prof. R. H. Thurston 
 (Jour. Frank. Inst., 1874) gave with the Crockett furnace, the wet tan 
 containing 59% of water, an evaporation from and at 212° F. of 4.24 lbs. 
 of water per pound of the wet tan, and with the Thompson furnace an 
 evaporation of 3.19 lbs. per pound of wet tan containing 55% of water. 
 The Thompson furnace consisted of six fire-brick ovens, each 9 ft. X 4 ft. 
 4 ins., containing 234 sq. ft. of grate in all, for three boilers with a total 
 heating surface of 2000 sq. ft., a ratio of heating to grate surface of 9 to 1. 
 The tan was fed through holes in the top. The Crockett furnace was an 
 ordinary fire-brick furnace, 6X4 ft., built in front of the boiler, instead of 
 under it, the ratio of heating surface to grate being 14.6 to 1. The con- 
 ditions of success in burning wet fuel are the surrounding of the mass 
 so completely with heated surfaces and with burning fuel that it may 
 be rapidly dried, and then so arranging the apparatus that thorough 
 combustion may be secured, and that the rapidity of combustion be 
 precisely equal to and never exceed the rapidity of desiccation. Where 
 this rapidity of combustion is exceeded the dry portion is consumed 
 completely, leaving an uncovered mass of fuel which refuses to take fire. 
 
 D. M. Myers (Trans. A.S.M.E., 1909) describes some experiments on 
 tan as a boiler fuel. One hundred lbs. of air dried bark fed to the mill will 
 produce 213 lbs. of spent tan containing 65% moisture. Taking 9500 
 B.T.U. as the heating value per lb. of dry tan and 500° F. as the tempera- 
 ture of the chimney gases, the available heat in 1 lb. 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 iurnace, or 1.93 lbs. of water evaporated 
 from and at 212° per lb. of wet tan. 
 
 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. 
 
MISCELLANEOUS SOLID FUELS. 809 
 
 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 com- 
 position, 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 would have the following percentage composi- 
 tion: 
 
 66% bagasse: Woody Fibre, 37; Combustible Salts, 10; Water, 53. 
 
 72% bagasse: " " 45; " " 9; " 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 lbs. 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 lbs., the lost heat will be as follows: In the waste gases, heating air from 
 86° to 450° F., 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 lbs., or nearly 
 24% less than the 72% bagasse, which gives 229,050 units. Accordingly, 
 one ton of cane of 2000 lbs. at 66% mill extraction will produce 680 lbs. 
 bagasse, equal to 1,259,958 available heat-units, while the same cane at 
 72% extraction will produce 560 lbs. bagasse, equal to 1,282,680 units. 
 
 "A similar calculation for the case of Louisiana cane containing 10% 
 woody fibre, 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. 
 
 "This would make such bagasse worth on an average nearly 92 lbs. 
 coal per ton of cane ground. Under fairly good conditions, 1 lb. coal 
 will evaporate 71/2 lbs. water, while the best boiler plants evaporate 10 
 lbs. Therefore the bagasse from 1 ton of cane at 75% mill extraction 
 should evaporate from 689 lbs. to 919 lbs. of water. The juice extracted 
 from such cane would under these conditions contain 1260 lbs. of water. 
 If we assume that the water added during the process of manufacture is 
 10% (by weight) of the juice made, the total water handled is 1410 lbs. 
 From the juice represented in this case, the commercial massecuite would 
 be about 15% of the weight of the original mill juice, or, say, 225 lbs. 
 Said mill juice 1500 lbs., plus 10%, equals 1650 lbs. liquor handled; and 
 1650 lbs., minus 225 lbs., equals 1425 lbs., the quantity of water to be 
 evaporated during the process of manufacture. To effect a 71/2-lb. evap- 
 oration requires 190 lbs. of coal, and 142 1/2 lbs. for a 10-lb. evaporation. 
 
 "To reduce 1650 lbs. of juice to syrup of, say, 27° Baume, requires 
 the evaporation of 1170 lbs. of water, leaving 480 lbs. of syrup. If this 
 work be accomplished in the open air, it will require about 156 lbs. of 
 coal at 71/2 lbs. boiler evaporation, and 117 at 10 lbs. evaporation. 
 
 "With a double effect the fuel required would be from 59 to 78 lbs., 
 and with a triple effect, from 36 to 52 lbs. 
 
 " To reduce the above 480 lbs. of syrup to the consistency of commer- 
 cial massecuite means the further evaporation of 255 lbs. of water, 
 requiring the expenditure of 34 lbs. coal at 71/2 lbs. boiler evaporation, 
 and 251/2 lbs. with a 10-lb. evaporation. Hence, to manufacture one ton 
 of cane into sugar and molasses, it will take from 145 to 190 lbs. addi- 
 tional coal to do the work by the open evaporator process; from 85 to 
 112 lbs. with a double effect, and only 71/2 lbs. evaporation in the boilers, 
 while with 10 lbs. boiler evaporation the bagasse alone is capable of 
 furnishing 8% more heat than is actually required to do the work. With 
 triple-effect evaporation depending on the excellence of the boiler plant, 
 the 1425 lbs. of water to be evaporated from the juice will require between 
 
810 
 
 62 and 86 lbs. of coal. These vaiues show that from 6 to 30 lbs. of coal 
 can be spared from the value of the bagasse to run engines, grind cane, etc. 
 
 "It accordingly appears," says Prof. Becuel, "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 suerar-houses." 
 
 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 21/4 lbs. 
 of steam from and at 212° was obtained from 1 lb. 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 lbs. per sq. ft. 
 of grate per hour. Not more than 1 .5 lbs. 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 coal per 24 
 hours. 
 
 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. ) 
 
 traces. 
 1.5 
 10. 
 2.5 
 2. 
 
 .590 to .625 
 .636 to .657 
 .680 to .700 
 .714 to .718 
 .725 to .737 
 
 
 140 to 158° 
 
 Chymogene. j '" 
 
 Gasoline (petroleum spirit) . . 
 
 Benzine, naphtha C.benzolene 
 
 ( Benzine, naphtha B 
 
 I Benzine, naphtha A 
 
 
 158 to 248° 
 248° 
 
 14 
 
 to 
 347° 
 
 32 
 
 338° and ) 
 upwards. J 
 
 482° 
 
 Kerosene (lamp-oil) 
 
 50. 
 15. 
 2. 
 16. 
 
 .802 to .820 
 .850 to .915 
 
 100 to 122 
 230 
 
 
 Paraffine wax 
 
 
 
 
 
 
 
 
 
 Lima Petroleum, produced at Lima, Ohio, is of a dark green color, 
 very fluid, and marks 48° Bailing at 15° C. (sp. gr., 0.792). 
 
 The distillation in fifty parts, each part representing 2% by volume, 
 gave the following results: 
 
 Per Sp. Per Sp. Per Sp. Per Sp. Per Sp. Per Sp. 
 cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. cent. Gr. 
 
 0.815 
 .815 
 
 2 
 
 0.680 
 
 IS 
 
 0.720 
 
 34 
 
 0.764 
 
 50 
 
 0.802 
 
 68 
 
 0.820 
 
 88 
 
 4 
 
 .683 
 
 20 
 
 .728 
 
 36 
 
 .768 
 
 52^ 
 
 
 70 
 
 .825 
 
 90 
 
 6 
 
 .685 
 
 22 
 
 .730 
 
 38 
 
 .772 
 
 to}- 
 
 .806 
 
 72 
 
 .830 
 
 
 8 
 
 .690 
 
 24 
 
 .735 
 
 40 
 
 .778 
 
 58 J 
 
 
 73 
 
 .830 
 
 92") 
 
 10 
 
 .694 
 
 :>tt 
 
 .740 
 
 42 
 
 .782 
 
 60 
 
 .800 
 
 76 
 
 .810 
 
 to >- 
 
 12 
 
 .698 
 
 28 
 
 .742 
 
 44 
 
 .788 
 
 62 
 
 .804 
 
 7S 
 
 .820 
 
 100J 
 
 14 
 
 .700 
 
 30 
 
 .746 
 
 46 
 
 .792 
 
 64 
 
 .808 
 
 82 
 
 .818 
 
 
 16 
 
 .706 
 
 32 
 
 .760 
 
 48 
 
 .800 
 
 66 
 
 .812 
 
 86 
 
 .816 
 
 
 RETURNS. 
 
 16 per cent naphtha, 70° Baume. 6 per cent paraffine 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, then gases 
 
LIQUID FUEL. 
 
 811 
 
 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. 
 
 Boiling 
 Point. 
 
 Specific 
 Gravity. 
 
 Density at 
 59° F. 
 
 Petroleum ether. 
 
 Gasoline 
 
 Naphtha G- ; 
 
 Naphtha B 
 
 Naphtha A 
 
 Kerosene. 
 
 °F. 
 104-158 
 158-176 
 176-212 
 212-248 
 248-302 
 302-572 
 
 0.650-0.660 
 .660- .670 
 .670- .707 
 .707- .722 
 .722- .737 
 .753- .864 
 
 3 Baume- 
 85-80 
 80-78 
 78-^8 
 68-64 
 64-60 
 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 evapo- 
 rative power of petroleum in comparison with that of coal, as determined 
 by Messrs. Favre and Silbermann: 
 
 Fuel. 
 
 Specific 
 Gravity 
 
 at 
 32° F., 
 Water 
 = 1 .000 
 
 Chem. Comp. 
 
 Heating 
 power, 
 British 
 Thermal 
 Units. 
 
 Theoret. 
 Evap., 
 lbs. 
 Water per 
 lb. Fuel, 
 from and 
 at 212°F. 
 
 
 C. 
 
 H. 
 
 O. 
 
 Penna. heavy crude oil. . . . 
 Caucasian light crude oil . . 
 Caucasian heavy crude oil. 
 
 Petroleum refuse 
 
 Good English Coal, Mean 
 
 0.886 
 0.884 
 0.938 
 0.928 
 
 1.380 
 
 84.9 
 86.3 
 86.6 
 87.1 
 
 80.0 
 
 13.7 
 13.6 
 12.3 
 11.7 
 
 5.0 
 
 1.4 
 0.1 
 1.1 
 1.2 
 
 8.0 
 
 20,736 
 22,027 
 20,138 
 19,832 
 
 14,112 
 
 21.48 
 22.79 
 20.85 
 20.53 
 
 14.61 
 
 
 
 In experiments on Russian railways with petroleum as fuel Mr. Urquhart 
 obtained an actual efficiency equal to 82% of the theoretical heating- 
 value. The petroleum is fed to the furnace by means 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. Neivs, 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 
 Denton gave an efficiency of 78.5%. As high as 82% has been reported 
 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 lbs.) 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.) 
 
812 
 
 FUEL. 
 
 The following table showing the relative values of petroleum and coal 
 was given by the author in Power, Sept., 1902. It is based on the following 
 assumed data: B.T.U. per lb. of oil 20,000; sp. gr., 0.885; =7.37 lbs. per 
 gal.; 1 barrel = 41 gals. = 310 lbs. 
 
 Coal, B.T.U. 
 
 1 lb. coal 
 
 1 barrel oil 
 
 1 ton coal 
 
 per lb. 
 
 = lbs. oil. 
 
 = lbs. coal. 
 
 = barrels oil. 
 
 10,000 
 
 2. 
 
 620 
 
 3.23 
 
 11,000 
 
 1.818 
 
 564 
 
 3.55 
 
 12,000 
 
 1.667 
 
 517 
 
 3.87 
 
 13,000 
 
 1.538 
 
 477 
 
 4.19 
 
 14,000 
 
 1.429 
 
 443 
 
 4.52 
 
 15,000 
 
 1.333 
 
 413 
 
 4.84 
 
 From this table we see that if coal of a heating value of only 10,000 
 B.T.U. per lb. costs $3.23 per ton, and coal of 14,000 B.T.U. per lb. at 
 $4.52 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 $6.26 and the better coal 
 $9.04 per ton, then oil will be the cheaper fuel if it is below $2 per barrel. 
 
 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 depends 
 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 rebound before touch- 
 ing the heating surface of the boiler. Burners using air at high pressure, 
 40 lbs. per sq. in., without steam, have been used with advantage. Lower 
 pressures have been found not sufficient to atomize the oil. 
 
 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 deposit of lampblack or soot. 
 
 Oil vs. Coal as Fuel. {Iron Age, Nov. 2. 1893.) —Test by the Twin 
 City Rapid Transit Company of Minneapolis and St. Paul. This test 
 showed that with the ordinary Lima oil weighing 6.6 pounds per 
 gallon, and costing 2 1/4 cents per gallon, and coal that gave an evapora- 
 tion of 71/2 lbs. of water per pound of coal, the two fuels were equally 
 economical when the price of coal was $3.85 per ton of 2000 lbs. With 
 the same coal at $2.00 per ton, the coal was 37% more economical, and 
 with the coal at $4.85 per ton, the coal was 20% more expensive than 
 the oil. These results include the difference in the cost of handling the 
 coal, ashes, and oil. 
 
 In 1892 there were reported to the Engineers' Club of Philadelphia 
 some comparative figures, from tests undertaken to ascertain the relative 
 value of coal, petroleum, and gas. 
 
 Lbs. Water, from 
 and at 212° F. 
 
 1 lb. anthracite coal evaporated 9. 70 
 
 1 lb. bituminous coal 10.14 
 
 1 lb. fuel oil, 36° gravity 16 . 48 
 
 1 cubic foot gas, 20 C. P 1, 28 
 
 The gas used was that obtained in the distillation of petroleum, having 
 about the same fuel-value as natural or coal-gas of equal candle-power. 
 
 Taking the efficiency of bituminous coal as a basis, the calorific energy 
 of petroleum is more than 60% greater than that of coal; whereas, theo- 
 retically, petroleum exceeds coal only about 45% — the one containing 
 14,500 heat-units, and the other 21,000. 
 
 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. 
 
ALCOHOL AS FUEL. 
 
 813 
 
 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 in 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 6V2 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 gallons 
 per ton of ingots. Under the most favorable circumstances, charging hot 
 ingots and running full capacity, 41/2 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. 
 
 In all of the trials the oil was vaporized in the Archer producer, an 
 apparatus for mixing the oil and superheated steam, and heating the 
 mixture to a high temperature. From 0.5 lb. to 0.75 lb. of pea-coal was 
 used per gallon of oil in the producer itself. 
 
 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 formulas 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 1/2 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 1/2 gal. of 
 approved pyridin (a petroleum product) bases. 
 
 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, C2H5OH. This material is seldom, if ever, obtained 
 pure, it being generally diluted with water and containing other alco- 
 hols when used for engines. 
 
 Specific Gravity of Ethyl Alcohol at 60° F. Compared with 
 Water at 60°. (Smithsonian Tables.) 
 
 
 Per cent Al- 
 
 
 Per cent Al- 
 
 
 Per cent Al- 
 
 
 cohol. 
 
 
 cohol. 
 
 
 cohol. 
 
 Sp. Gr. 
 
 
 Sp.Gr. 
 
 
 Sp. Gr. 
 
 
 
 
 
 
 
 
 
 Weight. 
 
 Vol. 
 
 
 Weight. 
 
 Vol. 
 
 
 Weight. 
 
 Vol. 
 
 0.834 
 
 85.8 
 
 90.0 
 
 0.826 
 
 88.9 
 
 92.3 
 
 0.818 
 
 91.9 
 
 94.5 
 
 .832 
 
 86.6 
 
 90.6 
 
 .824 
 
 89.6 
 
 92.9 
 
 .816 
 
 92.6 
 
 95.0 
 
 .830 
 
 87.4 
 
 91.2 
 
 .822 
 
 90.4 
 
 93.4 
 
 .814 
 
 93.3 
 
 95.5 
 
 .828 
 
 88.1 
 
 91.8 
 
 .820 
 
 91.1 
 
 94.0 
 
 .812 
 
 94.0 
 
 96.0 
 
 Tne heat of combustion of ethyl alcohol, 94% by volume, as deter- 
 mined by the calorimeter, is 11,900 B.T.U. per lb. — a little more than 
 half that of gasoline (Lucke). Favre and Silbermann obtained 12,913 
 B.T.U. for absolute alcohol. 
 
 The products of complete combustion of alcohol are H2O and CO2. 
 Under certain conditions, with an insufficient supply of air, acetic acid is 
 
814 
 
 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 
 lb. of gasoline, or 1.16 lb. 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 Mil- 
 limeters of Mercury. 
 
 (To convert into pounds per sq. in., 
 inches of mercury, 
 
 multiply by 0.01934; to convert into 
 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. 
 
 °C 
 
 5 
 
 10 
 15 
 
 20 
 25 
 30 
 
 F. 
 32 
 41 
 50 
 59 
 68 
 77 
 86 
 
 12 
 
 17 
 24 
 32 
 44 
 59 
 78 
 
 30 
 40 
 54 
 71 
 94 
 123 
 159 
 
 5 
 
 7 
 9 
 13 
 17 
 
 24 
 32 
 
 99 
 115 
 133 
 154 
 179 
 210 
 251 
 
 °C. 
 35 
 
 40 
 45 
 50 
 55 
 60 
 65 
 
 ° F. 
 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 Air with these Vapors. 
 
 
 
 
 
 1 Pound of Air Contains in Saturated 
 
 
 
 
 
 
 
 Vapor Tension, Inches 
 Mercury. 
 
 
 
 Temp, 
 degs. F. 
 
 
 
 
 
 At 28.95 Inches. 
 
 At 26.05 Inches. 
 
 
 Alcohol 
 
 Water 
 
 Alcohol 
 
 Water 
 
 Alcohol 
 
 Water. 
 
 
 Vapor. 
 
 Vapor. 
 
 Vapor. 
 
 Vapor. 
 
 Vapor. 
 
 Vapor. 
 
 50 
 
 0.950 
 
 0.359 
 
 0.055 
 
 0.008 
 
 0.061 
 
 0.009 
 
 59 
 
 1.283 
 
 0.500 
 
 0.075 
 
 0.011 
 
 0.084 
 
 0.013 
 
 68 
 
 1.733 
 
 0.687 
 
 0.104 
 
 0.016 
 
 0.117 
 
 0.018 
 
 77 
 
 2.325 
 
 0.925 
 
 0.144 
 
 0.022 
 
 0.162 
 
 0.025 
 
 86 
 
 3.090 
 
 1.240 
 
 0.200 
 
 0.031 
 
 0.227 
 
 0.036 
 
 104 
 
 5.270 
 
 2.162 
 
 0.390 
 
 0.063 
 
 0.450 
 
 0.072 
 
 122 
 
 8.660 
 
 3.620 
 
 0.827 
 
 0.135 
 
 1.002 
 
 0.164 
 
 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 
 
FUEL GAS. 815 
 
 one out of every four lbs. of carbon with oxygen derived from water- 
 vapor. The thermic reactions in this operation are as follows: 
 
 Heat-units. 
 4 lbs. C burned to CO (3 lbs. gasified with air and 1 lb. with 
 
 water) develop 17,600 
 
 1.5 lbs. of water (which furnish 1.33 lbs. of oxygen to combine 
 
 with 1 lb. of carbon) absorb by dissociation 10,333 
 
 The gas, consisting of 9.333 lbs. CO, 0.167 lb. H, and 13.39 lbs. 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- 
 densed into finely-divided water before entering the fuel, and conse- 
 quently is considered as water in these calculations. 
 
 The 1.5 lbs. of water liberates 0.167 lb. 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 lbs. 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 the 
 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 lbs. carbon assumed to be burned to CO; 5 lbs. carbon burned 
 to CO2; three fourths of the necessary oxygen derived from air, and one 
 fourth from water. 
 
 -Products. - 
 
 Process. Pounds. Cubic Feet. Anal, by Vol. 
 
 80 lbs. C burned to CO 186.66 2529.24 33.4 
 
 5 lbs. C burned to CO2 18.33 157.64 2.0 
 
 5 lbs. vol. HC (distilled) 5.00 116.60 1.6 
 
 120 lbs. oxygen are required, of 
 which 30 lbs. from H 2 liber- 
 ate H :.... 3.75 712.50 9.4 
 
 90 lbs. from air are associated 
 
 with N ..301.05 4064.17 53.6 
 
 514.79 7580.15 
 
 Energy in the above gas obtained from 100 lbs. anthracite: 
 
 186.66 lbs. CO 807,304 heat-units. 
 
 5.00 " CH 4 117,500 
 
 3.75 " H 232,500 
 
 1,157,304 
 
 Total energy in gas per lb 2,248 " 
 
 Total energy in 100 lbs. 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. 
 
816 
 
 Bituminous Gas. — A theoretical gasification of 100 lbs 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 
 assume! that 50 lbs. of C are burned to CO and 5 lbs. 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 condensing, 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: 
 
 / Products. \ 
 
 Process. Pounds. Cubic Feet. Anal, by Vol. 
 
 50 lbs. C burned to CO 116.66 1580.7 27.8 
 
 5 lbs. C burned to CO2 18.33 157.6 2.7 
 
 32 lbs. vol. HC (distilled) 32.00 746.2 13.2 
 
 80 lbs. O are required, of which 20 
 lbs., derived from H2O, liber- 
 ate H 2.5 475.0 8.3 
 
 60 lbs. 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 lbs. CO 504,554 heat-units. 
 
 " 32.00 lbs. vol. HC 640,000 
 
 2.50 lbs.. H 155,000 
 
 1,299,554 
 
 Energy in coal 1,437,500 
 
 Per cent of energy delivered in gas 90.0 
 
 Heat-units in 1 lb. 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 lbs. 
 
 500 cubic feet of CO weigh 36 . 89 " 
 
 Total weight of 1000 cubic feet 39 . 525 lbs. 
 
 Now, as CO is composed of 12 parts C to 16 of O, the weight of C in 
 36.89 lbs. is 15.81 lbs. and of O 21.08 lbs. When this oxygen is derived 
 from water it liberates, as above, 2.635 lbs. 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 lbs. H. absorb in dissociation from water 2.635 X 62,000 = 163,370 
 15.81 lbs. 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 lbs. C to supply 
 this heat, and we could then make 1000 feet of water-gas from 20.64 lbs. 
 
817 
 
 of carbon (equal 24 lbs. 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-up 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. 
 
 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 
 
 Anthra. 
 
 27.0 
 
 12.0 
 
 1.2 
 
 Bitu. 
 27.0 
 
 H 
 
 12.0 
 
 CH t . 
 
 2.5 
 
 
 0.4 
 
 CO2 
 
 N 
 
 O 
 
 4.0 
 2.0 
 0.5 
 1.5 
 45.6 
 322,000 
 
 2.5 
 57.0 
 0.3 
 
 2.5 
 56.2 
 0.3 
 
 
 
 Pounds in 1000 cubic feet 
 
 Heat-units in 1000 cubic feet. . . . 
 
 45.6 
 1,100,000 
 
 65.6 
 137,455 
 
 65.9 
 156,917 
 
 Natural Gas in Ohio and Indiana. 
 
 (Eng. and M. J., April 21, 1894.) 
 
 
 Fos- 
 
 toria, 
 
 O. 
 
 Find- 
 lay, 
 O. 
 
 St. 
 
 Mary's, 
 
 O. 
 
 Muncie, 
 Ind. 
 
 Ander- 
 son, 
 Ind. 
 
 Koko- 
 mo, 
 Ind. 
 
 Mar- 
 ion, 
 Ind. 
 
 
 1.89 
 92.84 
 .20 
 .55 
 .20 
 .35 
 3.82 
 .15 
 
 1.64 
 93.35 
 .35 
 .41 
 .25 
 .39 
 3.41 
 .20 
 
 1.94 
 93.85 
 .20 
 .44 
 .23 
 .35 
 2.98 
 .21 
 
 2.35 
 92.67 
 .25 
 .45 
 .25 
 .35 
 3.53 
 .15 
 
 1.86 
 93.07 
 .47 
 .73 
 .26 
 .42 
 3.02 
 .15 
 
 1.42 
 94.16 
 .30 
 .55 
 .29 
 .30 
 2.80 
 .18 
 
 1.20 
 
 
 93.57 
 
 Olefiant gas 
 
 Carbon monoxide . 
 Carbon dioxide .... 
 
 .15 
 .60 
 .30 
 .55 
 
 
 3.42 
 
 Hydrogen sulphide 
 
 .20 
 
 Natural Gas as a Fuel for Boilers. — J. M. Whitham {Trans. A. S. 
 M. E., 1905) reports the results of several tests of water-tube boilers with 
 natural gas. The following is a condensed statement of the results : 
 
 
 Cook Vertical. 
 
 Heine. 
 
 Cahall Vert. 
 
 
 Rated H.P. of boilers 
 
 1500 
 
 1500 
 
 200 200 200 
 
 300 
 
 300 
 
 H.P. developed 
 
 1642 
 
 1507 
 
 155 218 258 
 
 340 
 
 260 
 
 Temperature at chimney 
 
 521 
 
 494 
 
 386 450 465 
 
 406 
 
 374 
 
 Gas pressure at burners, oz. 
 
 6.9 
 
 6.4 
 
 
 4.8 
 
 7to30 
 
 Cu. ft. of gas per boiler. . 
 
 
 
 
 
 
 H.P.-hour 
 
 44.9* 
 
 41.0* 
 
 46. Of 40. 7f 38. 3f 
 
 42.3 
 
 34 
 
 Boiler efficiency, % 
 
 72.7 
 
 
 65.8 ... 74.9 
 
 
 
 * Reduced to 4 oz. pressure and 62° F. 
 t Reduced to atmos. press, and 32° F. 
 
818 
 
 FUEL. 
 
 Six tests by Daniel Ash worth on 2-flue horizontal boilers gave cu. ft. of 
 gas per boiler H.B. 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 C0 2 ; 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 
 
 Kind of flame 
 
 Boiler H. P. made per 250-H.P. boiler 
 Cu. ft. of gas (at 4 oz. and 60° F.) per 
 
 H.P. hour 
 
 Chimney temperature 
 
 White 
 247 
 
 Blue 
 213 
 
 White 
 297 
 
 41.6 
 478 
 
 Blue 
 271 
 
 37.9 
 511 
 
 White 
 255 
 
 40 
 502 
 
 Blue 
 227 
 
 43.1 
 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 lbs. 
 
 (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 
 lbs., gas should sell for about 10 cents per 1000 cu. ft 
 
 Analyses of Natural Gas. 
 
 Illuminants 0.45 0.15 0.50 1.6 
 
 Carbonic oxide 0.00 0.00 0.15 1.8 
 
 Hydrogen 0.20 0.30 0.25 0.3 
 
 Marsh gas 81.05 83.20 83.40 81.9 
 
 Ethane 17.60 15.55 15.40 13.2 
 
 Carbonic acid . 00 . 20 . 00 0.0 
 
 Oxygen 0.15 0.10 0.00 0.4 
 
 Nitrogen 0.55 0.50 0.30 0.8 
 
 B.T.U. per cu. ft. at 60° F. and 
 
 14.7 lbs. barometer 1030 1020 1026 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 * 
 
 H 
 
 CIL 
 
 C2H4 
 
 CO2. 
 
 N (by difference) 
 
 25.3 
 9.2 
 3.1 
 0.8 
 
 3.4 
 58.2 
 
 33,213.84 
 12,077.76 
 4,069.68 
 1,050.24 
 4,463.52 
 76,404.96 
 
 2451.20 
 63.56 
 174.66 
 77.78 
 519.02 
 5659.63 
 
 1050.51 lbs.C + 1400.7 lbs. O. 
 63.56 " H. 
 174.66 " CH 4 . 
 77.78 " C2H4. 
 141.54 " C + 377. 44 lbs. O. 
 7350.17 " Air. 
 
 
 100~0 
 
 131,280.00 
 
 8945.85 
 
 
FUEL GAS. 819 
 
 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 lb. 
 
 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 lbs. carbon and 
 724.4 lbs. 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: 
 
 First. That a large percentage of the energy of the coal is lost when the 
 gas is made in the ordinary low producer and cooled to the temperature of 
 the air before being used. To prevent these sources of loss, the producer 
 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 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 formulae: 
 
 C2H4 +60 = 2C0 2 + 2H 2 0; 2H+0 = H 2 0; 
 CH 4 +4.0= CO2+2H2O; CO + O = CO2. 
 
 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. 
 
 ; CO2. O. C2H4. 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 24.0 9.8 3.4 62.0 
 
 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: 
 
 CO2. 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 CO2 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 11/4 lbs. of coal per H.P.-hour as a fair average and 10 lbs. of 
 
820 
 
 coal per hour per square 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 lbs. of coal at full load, and at 10 lbs. 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.TJ. per H.P.-hour will use 160 cu. ft. of 125- 
 B.T.TJ. gas per minute. The wet scrubber will therefore be emptied 5 1/3 
 times every minute, and would require about 8 1/3 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. 
 
 
 
 Producers. 
 
 Wet Scrub- 
 bers. 
 
 Dry Scrubbers. 
 
 H.P. 
 
 
 
 
 
 
 
 
 
 
 Inside 
 Diam. 
 
 Out- 
 side 
 Diam. 
 
 Height. 
 
 Diam. 
 
 Height. 
 
 
 Diam. 
 
 Height. 
 
 
 in. 
 
 in. 
 
 ft. in. 
 
 in. 
 
 ft. in. 
 
 
 in. 
 
 ft. in. 
 
 25 
 
 24 
 
 42 
 
 6 6 
 
 18 
 
 9 9 
 
 Single... 
 
 24 
 
 3 
 
 35 
 
 28 
 
 46 
 
 6 10 
 
 21 
 
 10 3 
 
 ...do.... 
 
 28 
 
 3 
 
 50 
 
 34 
 
 52 
 
 7 4 
 
 26 
 
 11 
 
 Double. 
 
 34 
 
 6 
 
 60 
 
 37 
 
 55 
 
 7 7 
 
 28 
 
 11 5 
 
 ...do.... 
 
 37 
 
 6 
 
 75 
 
 42 
 
 60 
 
 8 
 
 32 
 
 12 
 
 ...do.... 
 
 42 
 
 6 
 
 100 
 
 48 
 
 72 
 
 8 6 
 
 36 
 
 12 9 
 
 ...do.... 
 
 48 
 
 7 
 
 125 
 
 54 
 
 78 
 
 9 6 
 
 41 
 
 14 3 
 
 ...do.... 
 
 52 
 
 7 
 
 150 
 
 58 
 
 82 
 
 9 10 
 
 44 
 
 14 9 
 
 ...do.... 
 
 58 
 
 7 6 
 
 175 
 
 63 
 
 87 
 
 10 3 
 
 48 
 
 15 5 
 
 ...do.... 
 
 63 
 
 7 6 
 
 200 
 
 68 
 
 92 
 
 10 8 
 
 51 
 
 16 
 
 ...do.... 
 
 68 
 
 7 6 
 
 The inside diameter of the producers corresponds to the formula 
 H.P. = 6.25d 2 . 
 
GAS PRODUCERS, 821 
 
 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: 
 
 Diana, 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 lbs. of steam is called a 
 standard horse-power, we have therefore to provide about 1 H.P. of steam 
 for every 80 lbs. 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 lbs. per sq. ft. of surface per hour with bituminous coal carry- 
 ng 10% of ash and 1 1/2 % of sulphur. With gas coal, having high volatile 
 percentage and low ash, this rate can be safely increased to 12 lbs. and in 
 some cases to 15 lbs. per sq. ft. At 10 lbs. per sq. ft., the capacity of a 
 gas producer 8 ft. internal diameter is 500 lbs. per hour, which with gas 
 coals may be increased to a maximum of about 700 lbs. 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 lbs. per hour to get the best results. 
 
822 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 Vi6 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 lbs. 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 50%. 
 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 bloving. 
 
 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 bv volumeis as follows : 
 
 CO, 24.5; H, 17.8; CH 4 and C 2 H 4 , 6.8; total combustibles, 49.1%; C0 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 lbs. 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 CO2 
 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 CO2, 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 Survey, 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 C0 2 and charcoal, and 1300° (2372° F.) for the same percen- 
 tage from C0 2 and coke, and from C0 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 
 lbs. 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, 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. 
 
 823 
 
 Volume per cent. 
 
 fc4, 
 
 
 8 c 
 
 AS 
 
 
 .1 
 
 Hi 
 
 «« O 
 
 il 
 
 sa . 
 
 S «> S 
 I °3 S 
 
 
 A . 
 
 O o3 
 
 II 
 
 a 
 
 o a 
 
 s 
 
 co 
 
 Q 
 
 ^ 
 
 m 
 
 O 
 
 24.8 
 
 8.6 
 
 18.73 
 
 20.0 
 
 56.9 
 
 48.0 
 
 2.3 
 
 2.4 
 
 0.31 
 
 
 22.6 
 
 39.5 
 
 nil 
 
 nil 
 
 0.31 
 
 4.0(?) 
 
 3.0 
 
 3.8 
 
 13.2 
 
 24.4 
 
 25.07 
 
 21.0 
 
 8.7 
 
 7.5 
 
 46.8 
 
 59.4 
 
 48.98 
 
 49.5 
 
 5.8 
 
 0.5 
 
 12.9 
 
 5.2 
 
 6.57 
 
 5.0 
 
 3.0 
 
 nil 
 
 100.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 40.3 
 
 35.4 
 
 44.42 
 
 45.0 
 
 91.2 
 
 98.8 
 
 112.4 
 
 101.4 
 
 113.2 
 
 154.0 
 
 410.0 
 
 581.0 
 
 85.9 
 
 74.7 
 
 88.9 
 
 115.3 
 
 284.0 
 
 381.0 
 
 154.6 
 
 134.5 
 
 160.0 
 
 207.5 
 
 511.2 
 
 658.8 
 
 1,374 
 
 1,195 
 
 1,432 
 
 1,845 
 
 4,544 
 
 6,096 
 
 Hydrogen (H) 
 
 Marsh gas (CH 4 ) 
 
 C n H 2n gases 
 
 Carbonic oxide (CO) 
 
 Nitrogen (N) 
 
 Carbonic acid (CO2) 
 
 Total volume 
 
 Total combustible gases 
 
 Theoretical. 
 Air required for combustion . 
 Calorific value per cu. ft., 
 
 in lb. °C. units 
 
 Do.,B.T.U. percu. ft 
 
 Do., per litre, gram ° C. units 
 
 22.0 
 67.0 
 6.0 
 0.6 
 3.0 
 0.6 
 100.0 
 95.6 
 
 806.0 
 
 495.8 
 
 892.4 
 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 of gas made in a Mond producer at the 
 works of the Solvay Process" Co. in Detroit, Mich. (Mineral Industry, vol. 
 viii, 1900): CO2, 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 
 at St. Louis in 1904. (R. H. Fernald, Trans. A. S. M. E., 1905.) 
 
 Sample. 
 
 B.t.u. 
 per 
 lb. 
 com- 
 bus- 
 tible. 
 
 Pounds per elec- 
 trical H.P. hour 
 at switchboard. 
 
 Sample. 
 
 B.t.u. 
 
 per 
 
 lb. 
 com- 
 bus- 
 tible. 
 
 Pounds per elec- 
 trical H.P. hour 
 at switchboard. 
 
 Coal 
 
 as 
 fired. 
 
 Dry 
 coal. 
 
 Com- 
 bus- 
 tible. 
 
 Coal 
 
 as 
 fired. 
 
 Dry 
 coal. 
 
 Com- 
 bus- 
 tible. 
 
 Ala. No. 2.... 
 Colo. No. 3... 
 
 111. No. 3 
 
 111. No. 4 
 
 Ind.No. 1.... 
 Ind.No. 2.... 
 Okla.No. 1... 
 Okla.No. 4... 
 Iowa No. 2. . . 
 Kan. No. 5. . . 
 
 14820 
 13210 
 14560 
 14344 
 14720 
 14500 
 14800 
 13890 
 13950 
 15200 
 
 1.71 
 2.14 
 1.93 
 2.01 
 2.17 
 1.68 
 1.92 
 1.57 
 2.07 
 1.69 
 
 1.64 
 1.71 
 1.79 
 1.76 
 1.93 
 1.55 
 1.83 
 1.43 
 1.73 
 1.62 
 
 1.53 
 1.58 
 1.60 
 1.57 
 1.71 
 1.39 
 1.66 
 1.17 
 1.30 
 1.43 
 
 Ky.No. 3.. 
 
 Mo. No. 2.. 
 Mont. No. 1 
 N.Dak.No.2 
 Texas No. 1 
 Texas No. 2 
 W.Va.No.l 
 W.Va.No.4 
 W.Va.No.7 
 Wyo. No. 2 
 
 14650 
 14280 
 13580 
 12600 
 12945 
 12450 
 15350 
 15600 
 15800 
 13820 
 
 2.05 
 1.94 
 2.54 
 3.80 
 3.34 
 2.58 
 1.60 
 1.32 
 1.53 
 2.28 
 
 1.91 
 1.71 
 2.25 
 2.29 
 2.22 
 1.71 
 1.57 
 1.29 
 1.50 
 2.07 
 
 1.72 
 1.43 
 1.98 
 2.05 
 1.88 
 1.52 
 1.48 
 1.17 
 1.40 
 1.60 
 
 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 
 
824 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 lb. combustible of the coals are as 1 to 0.808; 
 reciprocal, 1 to 1.24; the lbs. combustible per E. H. P. hour as 1 to 1.75, 
 and lbs. 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 : 
 
 CO-2 O CO H CH 4 N Total 
 
 combustible. 
 
 N. Dak 10.16 0.24 15.82 11.16 3.74 58.88 40.06 
 
 W. Va 8.69 0.23 20.90 14.33 4.85 51.02 30.72 
 
 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 lb. of coal, which was 22.7 cu. ft. per lb. of coal as fired, 
 as compared with 70.6 cu. ft. for the W. Va. coal, measured at 62° F. and 
 14.7 lb. absolute pressure. 
 
 Use of Steam in Producers and in Boiler-furnaces. (R. W. Ray- 
 mond, Trans. A. I. M. E., xx, 635.) — No possible use of steam can cause 
 a gain of heat. If steam be introduced into a bed of incandescent carbon 
 it 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 and 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 auotient by the sum of the quotients. 
 
 Gas-fuel for Small Furnaces. — E. P. Reichhelm (Am. Mach., 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 CARBIDE. 
 
 825 
 
 Kind of Gas. 
 
 Natural gas 
 
 Coal-gas, 20 candle-power 
 
 Carburetted water-gas 
 
 Gasolene gas, 20 candle-power 
 
 Water-gas from coke 
 
 Water-gas from bituminous coal. . . . 
 Water-gas and producer-gas mixed . 
 
 Producer-gas 
 
 Naphtha-gas, fuel 2i/ 2 gals, per 1000 ft. 
 
 M.2 3 
 
 0i 
 
 1,000,000 
 675,000 
 646,000 
 690,000 
 313,000 
 377,000 
 185,000 
 150,000 
 306,365 
 
 3 3 CflN 
 
 750,000 
 506,250 
 484,500 
 517,500 
 234,750 
 282,750 
 138,750 
 112,500 
 229,774 
 
 
 $1.25 
 1.00 
 .90 
 .40 
 .45 
 .20 
 .15 
 .15 
 
 Coal, $4 per ton, per 1,000,000 heat-units utilized 
 
 Crude petroleum, 3 cts. per gal., per 1,000,000 heat-units.. 
 
 $2.46 
 
 2.06 
 
 1.73 
 
 1.70 
 
 1.59 
 
 1.44 
 
 1.33 
 
 .65 
 
 .73 
 
 .73 
 
 Mr. Reichhelm gives the following figures from practice in melting 
 brass with coal and with naphtha converted into gas: 1800 lbs. of metal 
 require 1080 lbs. of coal, at $4.65 per ton, equal to $2.51, or, say, 15 cents 
 per 100 lbs. Mr. T.'s report: 2500 lbs. of metal require 47 gals, of naphtha, 
 at 6 cents per gal., equal to $2.82, or. say, 11V4 cents per 100 lbs. 
 
 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 a 
 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 dayi 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., xvii, 50, is, by volume, CO2, 7.08; CO, 27.80; 
 O, 0.10; N, 65.02. The relative proportions of CO2 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. B. Morehead (Am. Gas Light Jour., July 10, 1905): 
 
 Acetylene is a colorless and tasteless gas. When pure it has a sweet, 
 etheral odor, but in the commercial form it carries small percentages of 
 phosphoreted and sulphureted hydrogen which give it a pungent odor. 
 One cu. ft. requires 11.91 cu. ft. of air for its complete combustion. Its 
 
826 
 
 specific gravity is 0.92, air being 1. It is the nearest approach to gaseous 
 carbon, and it possesses a higher candle power than any other known sub- 
 stance, or 240 candles for 5 cu. ft. It is soluble in its own volume of water, 
 and in varying proportions in ether, alcohol, turpentine and acetone. It 
 liquefies under a pressure of 700 lbs. per sq. in. at 70° F. The pressure 
 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 lbs. of calcium carbide combine with 36 lbs. of water and produce 
 26 lbs. of acetylene and 17 lbs. of pure, slacked lime. [The chemical re- 
 action is CaC 2 + 2H 2 = C2H2 + Ca(OH) 2 .] 
 
 Chemically pure calcium carbide will yield at 70° F. and 30 in. mercury, 
 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 cal- 
 cium carbide amounts to sufficient to raise the temperature of 4.1 lbs. 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 contains 1685 B.T.U. per cubic foot 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 manu- 
 facture, this gas will not compete with coal gas or water gas, or with 
 electricity as supplied in our cities. Acetylene may be stored under pres- 
 sure for railway and other portable lighting, and it may be absorbed in 
 acetone and used for the same purpose. 
 
 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 lbs., 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. 
 
 Calcium carbide, CaC 2 , contains 62.5% Ca and'37.5% C. It is insoluble 
 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 calcium 
 oxide or quicklime and carbon in the shape of coke. [3C+ CaO = 
 CaC 2 + CO.] The temperature is calculated to be from 5000 to 8000° F. 
 The furnaces employ from 250 to 350 electric H.P. each and produce about 
 one ton a day. The output is crushed to different sizes and it is sold 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 calcium 
 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, but 
 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 
 
ACETYLENE AND CALCIUM CARBIDE. 827 
 
 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 bevond 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 in 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 lbs. 
 per sq. in. The oxygen is compressed in a tank at about 150 lbs. pressure. 
 The acetylene is conveyed to the burner through a 1-in. pipe with one 
 3/8-in. branch leading to each blowpipe connection. The oxygen is conveyed 
 through 3/g-in. pipe withi/4-in. branches. The blowpipe is of brass, made on 
 the injector principle. As acetylene is so rich in carbon — 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 oxy-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 Vsto 
 1/4 in. distant from the metal to be welded. Too much acetylene produces 
 two cones and a white color; an excess of oxygen is indicated by a violet 
 tint. 
 
 Theoretically, 21/2 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: 
 
 2 C2H2 (4 vol.) + 5 2 (10 vol.) = 4 C0 2 4- 2 H2O, 
 but it is incompletely burned according to the reaction: 
 C2H2 (2 vol.) + O2 (2 vol.) = 2CO + H 2 . 
 
 Making Oxygen for the Blowpipe. — The distinctive feature which has 
 done the most to make the acetylene welding process of wide commercial 
 value is the introduction of a means for producing oxygen. By combining 
 a chemical product, known as "epurite," with water, pure oxygen is easily 
 obtained. Epurite is composed of chloride of lime, sulphate of copper and 
 sulphate of iron. The sulphate of copper is pulverized and mixed dry 
 with the chloride of lime. In making oxygen, 50 lbs. of this dry mixture 
 are dissolved in warm water. To this solution is added a solution of 
 about 7 lbs. of sulphate of iron dissolved in one gallon of water. 
 
 The oxygen-generating apparatus consists of two lead-lined chambers 
 with a scrubber and settling chamber between. One generator is filled 
 with lukewarm water to which one chemical charge is added. While this 
 solution is being stirred with an agitator a solution of iron sulphate is 
 added which acts as a catalyzer. The reaction is: 
 
 6 Fe2S0 4 Aq + 7 CaOCl 2 Aq + CuS0 4 Aq = 2 Fe 2 3 S0 4 Aq + CuS0 4 Aq 
 
 + Fe 2 Cl 6 + 7 CaCl 2 + 3 CaS0 4 + 7 0. 
 
 The oxygen, liberated, passes through a scrubber and a water-sealed trap 
 
 into a gasometer; from which it is compressed to 10 atmospheres, with an 
 
 air compressor, into a pressure storage tank. 
 
 The Theory and Practice of Oxy-Acetylene Welding is described in an 
 illustrated article by J. F. Springer in Indust. Eng'g., Oct., 1909. 
 
 IGNITION TEMPERATURE OF GASES. 
 
 Mayer and Munch (Berichte der deutscher Gesellschaft, xxvi, 2241) give 
 the following: 
 
 Marsh gas, C 2 H 4 , 667° C. 1233° F. 
 
 Ethane, C 2 H 6 , 616 1141 
 
 Propane, C 3 H 8 , 547 1017 
 
 Acetylene, C 2 H 2 , 580 1076 
 
 Propylene, C 3 H 6 , 504 939 
 
828 
 
 ILLUMINATING-GAS. 
 
 ILLUMINATING-GAS. 
 
 Coal-gas is made by distilling bituminous coal in retorts. The retort 
 is usually a long horizontal semi-cylindrical or o shaped chamber, holding 
 from 160 to 300 lbs. of coal. The retorts are set in "benches" erf 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- 
 stones, 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. 
 
 > 
 
 ■s 
 
 < 
 
 Si . 
 
 o 
 
 8° 
 
 Coke per 
 
 ton of 2240 
 
 lbs. 
 
 
 
 lbs. 
 
 bush. 
 
 3 >>S 
 
 
 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 
 
 
 
 
 
 
 Westmoreland, Pa 
 
 Sterling, 
 
 10,642 
 10,528 
 10,765 
 9,800 
 13,200 
 15,000 
 
 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 
 
 Despard, W. Va 
 
 2494 
 2806 
 
 Petonia, W. Va 
 
 4510 
 
 Grahamite, W. Va 
 
 
 The products of the distillation of 100 lbs. 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 lbs.; tar, 6.5 to 7.5 lbs.; ammonia liquor, 10 to 12 lbs.; 
 purified gas, 15 to 12 lbs.; impurities and loss, 4.5% to 3.5%. 
 
 The composition of the gas by volume ranges about as follows: Hydro- 
 gen, 38% to 48%; carbonic oxide, 2% to 14%; marsh-gas (Methane, 
 CH4), 43% to 31%; heavy hydrocarbons (CwH2», 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- 
 
ILLUMINATING-GAS. 829 
 
 carbons (with due regard to their individual character) to the nature of 
 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 = CO + 2 H, or 2 C + 2 H 2 = C + C0 2 + 4 H, followed 
 by a splitting up of the CO2, 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 nas 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 
 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 of 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. 25.4 26.3 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 
 
830 
 
 ILLUMINATING-GAS. 
 
 Analyses of Water-gas and Coal-gas Compared. 
 
 The following analyses are taken from 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- 
 
 
 Wor- 
 cester. 
 
 Lake. 
 
 Wor- 
 cester. 
 
 Lake. 
 
 gas. 
 
 
 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 
 
 Ethylene 
 
 0.05389 
 0.03834 
 
 
 0.07077 
 0.46934 
 0.17928 
 0.04421 
 
 0.11700 
 0.37664 
 0.19133 
 0.04103 
 
 0.07825 
 
 
 0.18758 
 
 
 0.41087 
 
 
 0.06987 
 
 
 
 
 100.00 
 
 100.00 
 
 100.00 
 
 1.00000 
 
 1.00000 
 
 1.00000 
 
 
 0.5825 
 0.5915 
 
 0.6057 
 0.6018 
 
 0.4580 
 
 
 
 
 
 
 
 
 
 
 
 
 
 B.T.U.fromlcu.ft.: 
 
 650.1 
 597.0 
 
 688.7 
 646.6 
 
 642.0 
 577.0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5311.2 
 
 5281.1 
 
 5202.9 
 
 
 
 
 
 
 
 
 
 22.06 
 
 26.31 
 
 
 
 
 
 
 
 
 
 
 The heating-values (B.T.TJ.) of the gases are calculated from the analy- 
 sis by weight, by using the multipliers given below (computed from 
 results of J. Thomsen), and multiplying the 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 1/2-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 lb. 
 Water Water 
 
 Ethylene . 
 Propylene . 
 
 Liquid. 
 . .21,524.4 
 .21,222.0 
 
 Benzole vapor .18,954.0 
 
 Vapor. 
 20,134.8 
 19,834.2 
 17,847.0 
 
 Heat-units from 1 lb. 
 
 Water Water 
 
 Liquid. Vapor. 
 
 Carbonic oxide . 4,395.6 4,395.6 
 
 Marsh-gas 24,021.0 21,592.8 
 
 Hydrogen 61 ,524.0 51 ,804.0 
 
 Efficiency of a Water-gas Plant. — The practical efficiency of an 
 illuminating water-gas setting is discussed in a paper by A. G. Glasgow 
 (Proc. Am. Gartiqht Assn., 1890) from which the following is abridged: 
 
 The results refer to 1000 cu. ft. of unpurified carburetted gas, reduced to 
 60° F. The total anthracite charged per 1000 cu. ft. of gas was 33.4 lbs., 
 
ILLUMINATING-GAS. 
 
 831 
 
 ash and unconsumed coal removed 9.9 lbs., leaving total combustible 
 consumed 23.5 lbs., 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 
 
 per 
 100 cu. 
 
 ft. 
 
 Com- 
 posi- 
 tion by 
 W'ht. 
 
 Specific 
 Heat. 
 
 
 C0 2 + H 2 S. 
 
 C W H 2» 
 
 CO 
 
 3.8 
 14.6 
 28.0 
 17.0 
 35.6 
 
 1.0 
 
 .465842 
 1 . 139968 
 2.1868 
 .75854 
 .1991464 
 .078596 
 
 .09647 
 .23607 
 .45285 
 .15710 
 .04124 
 .01627 
 
 .02088 
 .08720 
 11226 
 
 I. Carburetted Water-gas.. 
 
 CH 4 
 
 H 
 
 .09314 
 .14041 
 
 
 N 
 
 00397 
 
 
 
 
 
 
 100.0 
 
 4.8288924 
 
 1.00000 
 
 .45786 
 
 
 f C0 2 
 
 CO 
 
 3.5 
 43.4 
 51.8 
 
 1.3 
 
 .429065 
 
 3.389540 
 
 .289821 
 
 .102175 
 
 .1019 
 .8051 
 .0688 
 .0242 
 
 .02205 
 .19958 
 
 II. Uncarburetted gas * 
 
 H 
 
 .23424 
 
 N 
 
 .00591 
 
 . 
 
 
 
 
 
 100.0 
 
 4.210601 
 
 1 .0000 
 
 .46178 
 
 
 r co 2 
 
 0. 
 
 17.4 
 3.2 
 
 79.4 
 
 2.133066 
 
 .2856096 
 
 6.2405224 
 
 .2464 
 .0329 
 .7207 
 
 .05342 
 .00718 
 
 8 f 
 
 N 
 
 .17585 
 
 
 
 
 
 
 100.0 
 
 8.6591980 
 
 1.0000 
 
 .23645 
 
 IV. Generator blast-gases.. -, 
 
 r co 2 
 
 CO 
 
 9.7 
 17.8 
 72.5 
 
 1.189123 
 1.390180 
 5.698210 
 
 .1436 
 .1680 
 .6884 
 
 .031075 
 .041647 
 
 N 
 
 .167970 
 
 
 
 
 I 
 
 
 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: 
 
 B, the energy of the CO produced; 
 
 C, the energy absorbed in the decomposition of the steam; 
 
 Z>, the difference between the sensible heat of the escaping illuminating- 
 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, the heat carried away from the shells by convection (air-currents) ; 
 H, the heat rendered latent in the gasification of the oil; 
 
 /, the sensible heat in the ash and unconsumed coal recovered from 
 the generator. 
 
 The heat equation is A=B+C+D+E+F+G+H+ I; A 
 
 280 
 being known. A comparison of the CO in Tables I and II show that -pr- . 
 
 or 64.5% of the volume of carburetted gas, is pure water-gas, distributed 
 thus: CO2, 2.3%; CO, 28.0%; H, 33.4%; N, 0.8%; = 64.5%. 1 lb. of CO 
 at 60° F. = 13,531 cu. ft. CO per 1000 cu. ft. of gas = 280 -* 13.531 
 = 20.694 lbs. Energy of the CO = 20.694 X 4395.6 = 91,043 heat- 
 units == B. 1 lb. of H at 60° F. = 189.2 cu. ft. H per M of gas = 334 
 -4- 189.2 = 1.7653 lbs. Energy of the H per lb. (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 lb. of H, viz., 8.98 lbs. H 2 0, 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 lb. of H. Energy of 
 the H, then, is 1.7653 X 51,285 = 90,533 heat-units = C. The heat 
 
832 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 
 shell of the apparatus gave figures for the amount of heat lost by radia- 
 tion = 12,454 heat-units = F, and by convection = 15,696 heat-units 
 = G. 
 
 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 lbs. 
 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 £>., E, F, G, and /, 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 lbs. of crude petroleum, were fed into the carburetter 
 per 1000 cu. ft. of gas made; deducting 5 lbs. of tar recovered, leaves 
 30 lbs. 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 ga3 is 
 C0 2 38.0 
 
 C 3 H 6 *146.0x. 117220x21222.0=363200 
 CO 280.0 x. 078100 x 4395.6= 96120 
 CH 4 170.0x.044620x24021.0=182210 
 H 356.0 x. 005594x61524.0 = 122520 
 N 10.0 
 
 1000.0 764050 
 
 The heating-power per M. of the 
 uncarburetted gas is 
 C0 2 35.0 
 
 CO 434.0x.078100x 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 
 of C3H6. 
 
ILLUMINATING-GAS. 833 
 
 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 0.625 sp. 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 maldng it is impracticable to enrich the gas to over twenty 
 candle-power without causing too great a tendency to 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 (Schocl 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 vield 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 the lowest figure given 
 
834 
 
 ILLUMINATING-GAS. 
 
 by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, 
 
 equal to coal at $40 per ton of 2000 lbs., 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, as 
 
 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, 
 5 = specific gravity of gas, air 
 being 1, 
 
 Molesworth gives Q = 1000 
 
 ▼ si 
 
 \f 
 
 (1350)2/i 
 CM 
 (1350) 2 d^_ 
 
 Q = 1350d2 V^ = 
 
 Vf- 
 
 J. P. Gill, Am. Gas-light Jour., 1894, gives Q = 1291 \ 
 
 d*h 
 
 s(l + 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 com mon formula for the 
 flow of compressed air or steam in pipes, Q = c ^{Vi — P2) a b /wL, in 
 which Q = cu. ft. per min., Pi — P2 = difference in pressure in lbs. per 
 sq. in; w = density in lbs. 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 ^d^h -*- si, 
 we find C, the coefficient, = 997, which corresponds nearly with the formula 
 given by Molesworth. 
 
 Wm. Cox (Am. Mach., Mar. 20, 1902) gives the following formula for 
 flow of gas in long pi pes. 
 
 q = 3000 sJ d 2^Bl 
 
 -P2 2 ) 
 
 = 41.3 
 
 s/' 
 
 </ 5 X(pi 2 -p^) 
 
 I xu Y L 
 
 Q= discharge in cu. ft. per hour at atmospheric pressure; d = diam. 
 of pipe in ins.; p, = initial and pt = terminal absolute pressure, lbs. per 
 sq. in.; I = length of pipe in feet, L = length in miles. For p x 2 — p 2 2 
 may be substituted (p, + p 2 ) (p, — pi). The specific gravity of the 
 gas is assumed to be 0.65, air being 1. For fluids of any other sp. gr., 
 s, mult ply the coefficients 3000 or 41.3 by Vo.65/s. For air, s = 1, the 
 coefficients become 2419 and 33.3. J. E. Johnson Jr.'s formula for air, 
 page 596, translated into the same notation as Mr. Cox's, makes the coeffi- 
 cients 2449 and 33.5. 
 
 Services for Lamps. (Molesworth.) 
 
 Lamps. 
 
 Ft. from 
 Main. 
 
 Require 
 Pipe-bore. 
 
 Lamps. 
 
 Ft. from 
 Main. 
 
 Require 
 Pipe-bore. 
 
 2 
 
 40 
 40 
 50 
 100 
 
 3 '8 in. 
 
 1/2 in. 
 5/8 in. 
 3/4 in. 
 
 15 
 
 130 
 150 
 180 
 200 
 
 1 in. 
 
 4 
 
 20 
 
 25 
 
 30 
 
 1 1/4 in. 
 
 6 
 
 1 1/2 in. 
 
 10 
 
 13/4 in. 
 
 (In cold climates no service less than 3/ 4 in. should be used.) 
 
FLOW OF GAS IN PIPES. 
 
 835 
 
 Maximum Supply of Gas through Pipes in cu. ft. per Hour, 
 Specific Gravity being taken at 0.45, calculated from the 
 Formula Q = 1000 V a h h -s- si. (Molesworth.) 
 Length of Pipe = 10 Yards. 
 
 Diameter of 
 
 
 Pressure by the Water-gauge in Inches 
 
 
 
 Pipe in 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Inches. 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.4 
 
 C.5 
 
 0.6 
 
 0.7 
 
 0.8 
 
 0.9 
 
 1.0 
 
 3/8 
 
 13 
 
 18 
 
 22 
 
 26 
 
 29 
 
 31 
 
 34 
 
 36 
 
 38 
 
 41 
 
 V2 
 
 26 
 
 37 
 
 46 
 
 53 
 
 59 
 
 64 
 
 70 
 
 74 
 
 79 
 
 83 
 
 3/4 
 
 73 
 
 103 
 
 126 
 
 145 
 
 162 
 
 187 
 
 192 
 
 205 
 
 218 
 
 230 
 
 1 
 
 149 
 
 211 
 
 258 
 
 298 
 
 333 
 
 365 
 
 394 
 
 422 
 
 447 
 
 471 
 
 H/4 
 
 260 
 
 368 
 
 451 
 
 521 
 
 582 
 
 638 
 
 689 
 
 737 
 
 781 
 
 823 
 
 U/2 
 
 411 
 
 581 
 
 711 
 
 821 
 
 918 
 
 1006 
 
 1082 
 
 1162 
 
 1232 
 
 1299 
 
 2 
 
 843 
 
 1192 
 
 1460 
 
 1686 
 
 1886 
 
 2066 
 
 2231 
 
 2385 
 
 2530 
 
 2667 
 
 Length of Pipe = 100 Yards. 
 
 
 
 
 Pressure by the Water-gauge in 
 
 Inches 
 
 
 
 
 0.1 
 
 8 
 
 0.2 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.75 
 
 1.0 
 
 1.25 
 
 1.5 
 
 2 
 
 2.5 
 
 1/2 
 
 12 
 
 14 
 
 17 
 
 19 
 
 23 
 
 26 
 
 29 
 
 32 
 
 36 
 
 42 
 
 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 
 
 11/4 
 
 82 
 
 116 
 
 143 
 
 165 
 
 184 
 
 225 
 
 260 
 
 291 
 
 319 
 
 368 
 
 412 
 
 U/2 
 
 130 
 
 184 
 
 225 
 
 260 
 
 290 
 
 356 
 
 411 
 
 459 
 
 503 
 
 581 
 
 649 
 
 2 
 
 267 
 
 377 
 
 462 
 
 533 
 
 596 
 
 730 
 
 843 
 
 943 
 
 1033 
 
 1193 
 
 1333 
 
 21/2 
 
 466 
 
 659 
 
 807 
 
 932 
 
 1042 
 
 1276 
 
 1473 
 
 1647 
 
 1804 
 
 2083 
 
 2329 
 
 3 
 
 735 
 
 1039 
 
 1270 
 
 1470 
 
 1643 
 
 2012 
 
 2323 
 
 2598 
 
 2846 
 
 3286 
 
 3674 
 
 31/2 
 
 1080 
 
 1528 
 
 1871 
 
 2161 
 
 2416 
 
 2958 
 
 3416 
 
 3820 
 
 4184 
 
 4831 
 
 5402 
 
 4 
 
 1508 
 
 2133 
 
 2613 
 
 3017 
 
 3373 
 
 4131 
 
 4770 
 
 5333 
 
 5842 
 
 6746 
 
 7542 
 
 Length of Pipe = 1000 Yards. 
 
 
 Pressure by the Water-gauge in Inches. 
 
 
 0.5 
 
 0.75 
 
 1.0 
 
 1.5 
 
 2.0 
 
 2.5 
 
 3.0 
 
 1 
 
 33 
 
 41 
 
 47 
 
 58 
 
 67 
 
 75 
 
 82 
 
 U/2 
 
 92 
 
 113 
 
 130 
 
 159 
 
 • 184 
 
 205 
 
 226 
 
 2 
 
 189 
 
 231 
 
 267 
 
 327 
 
 377 
 
 422 
 
 462 
 
 21/2 
 
 329 
 
 403 
 
 466 
 
 571 
 
 659 
 
 737 
 
 807 
 
 3 
 
 520 
 
 636 
 
 735 
 
 900 
 
 1039 
 
 1162 
 
 1273 
 
 4 
 
 1067 
 
 1306 
 
 1508 
 
 1847 
 
 2133 
 
 2385 
 
 2613 
 
 5 
 
 1863 
 
 2282 
 
 2635 
 
 3227 
 
 3727 
 
 4167 
 
 4564 
 
 6 
 
 2939 
 
 3600 
 
 4157 
 
 5091 
 
 5879 
 
 6573 
 
 7200 
 
836 
 
 
 Length of Pipe = 
 
 = 5000 Yabds. 
 
 
 Diameter of 
 Pipe in 
 
 Pressure by the Water-gauge in Inches. 
 
 
 
 
 
 
 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 extremely 
 cold climates this is now often increased to 1 in., even for a single lamp. 
 The best practice in the U. S. now condemns any service less than 3/ 4 in. 
 
 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 lbs. per 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 
 vapor until the temperature of the steam is reduced to that due its pres- 
 sure. 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 condensed, reducing the pres- 
 sure 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 it - 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 temper- 
 ature. 
 
 The total heat in steam (above 32°) includes three elements: 
 
 1st. The heat required to raise the temperature of the water to the tem- 
 perature 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). 
 
STEAM. 
 
 837 
 
 The sum of the last two elements is called the latent heat of steam 
 Heat required to Generate 1 lb. of Steam from water at 32° F. 
 
 Sensible heat, to raise the water from 32° to 212° = 
 
 Latent heat, 1, of the formation of steam at 212° = . 
 
 2, of expansion against the atmospheric 
 
 pressure, 2116.4 lbs. per sq. ft. X 
 
 26.79 cu. ft. =55,786 foot-pounds -*■ 
 
 778 = 
 
 Heat-units. 
 
 180.0 
 . 897 . 6 
 
 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 lb. 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 Vl80 of the heat required to raise 1 lb. of water from 
 32° to 212° F. By Peabody's definition the heat required to raise 1 lb. of 
 water from 32° to 212° is 180.3 instead of 180 units, and the heat of va- 
 porization at 212° 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, Therm., p. 147; Peabody, Therm., 
 p. 93.) 
 
 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. -lbs. Marks and Davis give the 
 value 777.52 standard ft. lbs., based on later experiments, and on the 
 value of g = 980.665 cm. per sec. 2 , = 32.174 ft. per sec. 2 , fixed by inter- 
 national agreement (1901). 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 investigations involving 
 the value of the mechanical equivalent of heat the value of g for the lati- 
 tude in which the experiments are made must be considered. 
 
 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 obtained 
 in 1905 by Knoblauch, Linde and Klebe. From a table in the article 
 giving pressures for each degree from 0° to 200° C, the following values have 
 been transformed into English measurements (Eng. Digest April, 1909). 
 
 Deg. F. 
 
 Lbs. per sq. 
 in. 
 
 Deg. F. 
 
 Lbs. per sq. 
 in. 
 
 Deg. F. 
 
 Lbs. 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 volume of satu- 
 rated steam are computed by Clapyron's equation (Marks and Davis's 
 Tables) which gives results remarkably close to those found in the ex- 
 periments of Knoblauch, Linde and Klebe. 
 
 Volume of Superheated Steam. — Linde's equation (1905), 
 /l 50, 300, 000 
 
 pv = 0.5962 T-p (1 + 0.0014 2 
 
 ^3 
 
 - 0.0833) 
 
 in which p is in lbs. per sq. ft., v is in cu. ft. and T = t + 459.6 is the 
 absolute temperature on the Fahrenheit scale, has been used in the com- 
 putation of Marks and Davis's tables, 
 
838 
 
 STEAM. 
 
 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. ThuSi 
 2.7074pX.622 _ 1.684 p 
 t + 461 t + 461 ' 
 
 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 
 
 092 t 
 that the correct value is 0.6113+ ' _ , • 
 
 Properties of Superheated Steam. — See the table on page 843, con- 
 densed from 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 
 
 1 
 
 2 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 Lbs. per sq. 
 
 
 
 
 
 
 
 
 
 
 
 
 in 
 
 14.2 
 
 28,4 
 
 56 9 
 
 85.3 
 
 113.3 
 
 142.2 
 
 170.6 
 
 199.1 
 
 227.5 
 
 256.0 
 
 284.4 
 
 Temp, sat., 
 
 
 
 
 
 
 
 
 
 
 
 
 °C 
 
 99 
 
 120 
 
 143 
 
 158 
 
 169 
 
 179 
 
 187 
 
 194 
 
 200 
 
 206 
 
 211 
 
 Temp, sat., 
 
 
 
 
 
 
 
 
 
 
 
 
 °F 
 
 210 
 
 248 
 
 289 
 
 316 
 
 336 
 
 350 
 
 368 
 
 381 
 
 392 
 
 403 
 
 412 
 
 °F. 
 
 °C. 
 
 
 
 
 
 
 
 
 
 
 
 
 212 
 
 100 
 150 
 200 
 250 
 
 0.463 
 .462 
 .462 
 .463 
 
 
 
 
 
 
 
 
 
 
 
 302 
 
 .478 
 .475 
 474 
 
 .515 
 
 .502 
 495 
 
 
 
 
 
 
 
 
 
 392 
 
 .530 
 514 
 
 .560 
 .512 
 
 .597 
 .552 
 
 .635 
 .570 
 
 .677 
 .588 
 
 
 
 
 482 
 
 .609 
 
 635 
 
 .664 
 
 572 
 
 300 
 
 .464 
 
 475 
 
 492 
 
 505 
 
 .517 
 
 .530 
 
 .541 
 
 .550 
 
 .561 
 
 572 
 
 .585 
 
 662 
 
 350 
 
 .468 
 
 477 
 
 492 
 
 .503 
 
 .512 
 
 .522 
 
 .529 
 
 .536 
 
 .543 
 
 .550 
 
 .557 
 
 752 
 
 400 
 
 .473 
 
 .481 
 
 .494 
 
 .504 
 
 .512 
 
 .520 
 
 .526 
 
 .531 
 
 .537 
 
 .542 
 
 .547 
 
 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. 
 
 
 Temperature. 
 
 
 
 Pounds per 
 
 
 Pounds in 
 
 
 
 sq. in. 
 
 
 
 sq. in. 
 
 C. ■ 
 
 Fahr. 
 
 
 C. 
 
 Fahr. 
 
 
 230 
 
 446 
 
 406.9 
 
 340 
 
 644 
 
 2156.2 
 
 240 
 
 464 
 
 488.9 
 
 360 
 
 680 
 
 2742.5 
 
 250 
 
 482 
 
 579.9 
 
 380 
 
 716 
 
 3448.1 
 
 260 
 
 500 
 
 691.6 
 
 400 
 
 752 
 
 4300.2 
 
 280 
 
 536 
 
 940.0 
 
 415 
 
 779 
 
 5017.1 
 
 300 
 
 572 
 
 1261.8 
 
 427 
 
 800.6 
 
 5659.9 
 
 320 
 
 608 
 
 1661.9 
 
 
 
 
 These pressures are higher than those obtained by Regnault's formula, 
 which gives for 415° C. only 4067.1 lbs. per square inch. 
 
839 
 
 Properties- of Saturated Steam. 
 
 (Condensed from Marks and Davis's Steam Tables and Diagrams, 1909, 
 by permission of the publishers, Longmans, Green & Co.) 
 
 m 
 
 
 
 Total Heat 
 
 ►44 
 
 ^<~ 
 
 
 03 
 
 a 
 
 to 
 
 1* 
 
 3 1 -! 
 
 - . 
 
 above 32° F . 
 
 S3 
 
 to ° 
 
 ■5 
 
 $! 
 
 
 ? j2 
 
 a; oj 
 
 1 i 
 
 B-4 
 
 ad 
 
 
 'o 
 
 
 < 
 
 
 "B 1 
 
 I i 
 
 
 
 gifr, 
 
 IS 
 
 >, o 
 
 a".n 
 
 > 
 
 H 
 
 a K 
 
 3 ^ 
 
 i-l 
 
 t> 
 
 " 
 
 to 
 
 to 
 
 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 
 
 29.18 
 
 0.3626 
 
 70 
 
 38.06 
 
 1090.3 
 
 1052.3 
 
 871 
 
 0.001148 
 
 0.0745 
 
 1.9868 
 
 29.09 
 
 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 
 
 1.6416 
 
 19.74 
 
 5 
 
 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 
 
 1.5814 
 
 15.67 
 
 7 
 
 176.85 
 
 144.7 
 
 1136.5 
 
 991.8 
 
 53.56 
 
 0.01867 
 
 0.2579 
 
 1.5582 
 
 13.63 
 
 8 
 
 182.86 
 
 150.8 
 
 1139.0 
 
 988.2 
 
 47.27 
 
 0.02115 
 
 0.2673 
 
 1.5380 
 
 11.60 
 
 9 
 
 188.27 
 
 156.2 
 
 1141.1 
 
 985.0 
 
 42.36 
 
 0.02361 
 
 0.2756 
 
 1.5202 
 
 9.56 
 
 10 
 
 193.22 
 
 161.1 
 
 1143.1 
 
 982.0 
 
 38.38 
 
 0.02606 
 
 0.2832 
 
 1.5042 
 
 7.52 
 
 11 
 
 197.75 
 
 165.7 
 
 1144.9 
 
 979.2 
 
 35.10 
 
 0.02849 
 
 0.2902 
 
 1.4895 
 
 5.49 
 
 12 
 
 201.96 
 
 169.9 
 
 1146.5 
 
 976.6 
 
 32.36 
 
 0.03090 
 
 0.2967 
 
 1 .4760 
 
 3.45 
 
 13 
 
 205.87 
 
 173.8 
 
 1148.0 
 
 974.2 
 
 30.03 
 
 0.03330 
 
 "0.3025 
 
 1.4639 
 
 1.42 
 
 lbs. 
 gage. 
 
 14 
 
 209.55 
 
 177.5 
 
 1149.4 
 
 971.9 
 
 28.02 
 
 0.03569 
 
 0.3081 
 
 1.4523 
 
 14.70 
 
 212 
 
 180.0 
 
 1150.4 
 
 970.4 
 
 26.79 
 
 0.03732 
 
 0.3118 
 
 1.4447 
 
 0.3 
 
 15 
 
 213.0 
 
 18.1.0 
 
 1150.7 
 
 969.7 
 
 26.27 
 
 0.03806 
 
 0.3133 
 
 1.4416 
 
 1.3 
 
 16 
 
 216.3 
 
 184.4 
 
 1152.0 
 
 967.6 
 
 24.79 
 
 0.04042 
 
 0.3183 
 
 1.4311 
 
 2.3 
 
 17 
 
 219.4 
 
 187.5 
 
 1153.1 
 
 965.6 
 
 23.38 
 
 0.04277 
 
 0.3229 
 
 1.4215 
 
 3.3 
 
 18 
 
 222.4 
 
 190.5 
 
 1154.2 
 
 963.7 
 
 22.16 
 
 0.04512 
 
 0.3273 
 
 1.4127 
 
 4.3 
 
 19 
 
 225.2 
 
 193.4 
 
 1155.2 
 
 961.8 
 
 21.07 
 
 0.04746 
 
 0.3315 
 
 1.4045 
 
 5.3 
 
 20 
 
 228.0 
 
 196.1 
 
 1156.2 
 
 960.0 
 
 20.08 
 
 0.04980 
 
 0.3355 
 
 1.3965 
 
 6.3 
 
 21 
 
 230.6 
 
 198.8 
 
 1157.1 
 
 958.3 
 
 19.18 
 
 0.05213 
 
 0.3393 
 
 1.3887 
 
 7.3 
 
 22 
 
 233.1 
 
 201 .3 
 
 1158.0 
 
 956.7 
 
 18.37 
 
 0.05445 
 
 0.3430 
 
 1.3811 
 
 8.3 
 
 23 
 
 235.5 
 
 203.8 
 
 1158.8 
 
 955.1 
 
 17.62 
 
 0.05676 
 
 0.3465 
 
 1.3739 
 
 9.3 
 
 24 
 
 237.8 
 
 206.1 
 
 1159.6 
 
 953.5 
 
 16.93 
 
 0.05907 
 
 0.3499 
 
 1 .3670 
 
 10.3 
 
 25 
 
 240.1 
 
 208.4 
 
 1160.4 
 
 952.0 
 
 16.30 
 
 0.0614 
 
 0.3532 
 
 1 .3604 
 
 11.3 
 
 26 
 
 242.2 
 
 210.6 
 
 1161.2 
 
 950.6 
 
 15.72 
 
 0.0636 
 
 0.3564 
 
 1 .3542 
 
 12.3 
 
 27 
 
 244.4 
 
 212.7 
 
 1161.9 
 
 949.2 
 
 15.18 
 
 0.0659 
 
 0.3594 
 
 1.3483 
 
 13.3 
 
 28 
 
 246.4 
 
 214.8 
 
 1162.6 
 
 947.8 
 
 14.67 
 
 0.0682 
 
 0.3623 
 
 1 .3425 
 
 14.3 
 
 29 
 
 248.4 
 
 216.8 
 
 1163.2 
 
 946.4 
 
 14.19 
 
 0.0705 
 
 0.3652 
 
 1.3367 
 
 15.3 
 
 30 
 
 250.3 
 
 218.8 
 
 1163.9 
 
 945.1 
 
 13.74 
 
 0.0728 
 
 0.3680 
 
 1.3311 
 
 16.3 
 
 31 
 
 252.2 
 
 220.7 
 
 1164.5 
 
 943.8 
 
 13.32 
 
 0.0751 
 
 0.3707 
 
 1.3257 
 
 17.3 
 
 32 
 
 254.1 
 
 222.6 
 
 1165.1 
 
 942.5 
 
 12.93 
 
 0.0773 
 
 0.3733 
 
 1 .3205 
 
 18.3 
 
 33 
 
 255.8 
 
 224.4 
 
 1165.7 
 
 941.3 
 
 12.57 
 
 0.0795 
 
 0.3759 
 
 1.3155 
 
 19.3 
 
 34 
 
 257.6 
 
 226.2 
 
 1166.3 
 
 940.1 
 
 12.22 
 
 0.0818 
 
 0.3784 
 
 1.3107 
 
 20.3 
 
 35. 
 
 259.3 
 
 227.9 
 
 1166.8 
 
 938.9 
 
 11.89 
 
 0.0841 
 
 0.3808 
 
 1 .3060 
 
 21.3 
 
 36 
 
 261.0 
 
 229.6 
 
 1167.3 
 
 937.7 
 
 11.58 
 
 0.0863 
 
 0.3832 
 
 1.3014 
 
 22.3 
 
 37 
 
 262.6 
 
 231.3 
 
 1167.8 
 
 936.6 
 
 11.29 
 
 0.0886 
 
 0.3855 
 
 1.2969 
 
 23.3 
 
 38 
 
 264.2 
 
 232.9 
 
 1168.4 
 
 935.5 
 
 11.01 
 
 0.0908 
 
 0.3877 
 
 1.2925 
 
 24.3 
 
 39 
 
 265.8 
 
 234.5 
 
 1168.9 
 
 934.4 
 
 10.74 
 
 0.0931 
 
 0.3899 
 
 1.2882 
 
 25.3 
 
 40 
 
 267.3 
 
 236.1 
 
 1169.4 
 
 933.3 
 
 10.49 
 
 0.0953 
 
 0.3920 
 
 1.2841 
 
 26.3 
 
 41 
 
 268.7 
 
 237.6 
 
 1169.8 
 
 932.2 
 
 10.25 
 
 0.0976 
 
 0.3941 
 
 1 .2800 
 
840 
 
 STEAM. 
 
 
 
 Properties of Saturated Steam. (Continued.) 
 
 
 go 
 
 gfi 
 
 
 Total Heat 
 
 ^ 
 
 
 • • 
 
 03 
 
 a 
 
 3 1- ? 
 
 3 . 
 
 
 above 32° F. 
 
 „ e3 
 
 fe'S 
 
 Of-! 
 
 J3 
 
 > 
 
 
 01 CQ 
 
 af-J 
 
 
 
 |W 
 
 A* 
 
 "B 
 
 ^ 
 
 W 
 
 o>0Q 
 
 u ^ 
 
 a « 
 
 a 
 
 33 
 
 oi a 
 
 13 
 
 £1 
 
 Ol S-< 
 
 a "3 
 
 1 1 
 
 c3 £ 
 
 -M 0> 
 
 v a 
 
 u 
 
 ■3.S0Q 
 
 O a, 
 a>fe 
 
 £,01 
 
 II 
 
 ag 
 go 
 
 
 
 J3 
 
 H 
 
 a K 
 
 £ K 
 
 F-l ' 
 
 > 
 
 H 
 
 m 
 
 27.3 
 
 42 
 
 270.2 
 
 239.1 
 
 1170.3 
 
 931.2 
 
 10.02 
 
 0.0998 
 
 0.3962 
 
 1.2759 
 
 28.3 
 
 43 
 
 271.7 
 
 240.5 
 
 1170.7 
 
 930.2 
 
 9.80 
 
 0.1020 
 
 0.3982 
 
 1.2720 
 
 29.3 
 
 44 
 
 273.1 
 
 242.0 
 
 1171.2 
 
 929.2 
 
 9.59 
 
 0.1043 
 
 0.4002 
 
 1.2681 
 
 30.3 
 
 45 
 
 274.5 
 
 243.4 
 
 1171.6 
 
 928.2 
 
 9.39 
 
 0.1065 
 
 0.4021 
 
 1.2644 
 
 31.3 
 
 46 
 
 275.8 
 
 244.8 
 
 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 
 
 1.2571 
 
 33.3 
 
 48 
 
 278.5 
 
 247.5 
 
 1172.8 
 
 925.3 
 
 8.84 
 
 0.1131 
 
 0.4077 
 
 1.2536 
 
 34.3 
 
 49 
 
 279.8 
 
 248.8 
 
 1173.2 
 
 924.4 
 
 8.67 
 
 0.1153 
 
 0.4095 
 
 1.2502 
 
 35.3 
 
 50 
 
 281.0 
 
 250.1 
 
 1173.6 
 
 923.5 
 
 8.51 
 
 0.1175 
 
 0.4113 
 
 1.2468 
 
 36.3 
 
 51 
 
 282.3 
 
 251.4 
 
 1174.0 
 
 922.6 
 
 8.35 
 
 0.1197 
 
 0.4130 
 
 1.2432 
 
 37.3 
 
 52 
 
 283.5 
 
 252.6 
 
 1174.3 
 
 921.7 
 
 8.20 
 
 0.1219 
 
 0.4147 
 
 1.2405 
 
 38.3 
 
 53 
 
 284.7 
 
 253.9 
 
 1174.7 
 
 920.8 
 
 8.05 
 
 0.1241 
 
 0.4164 
 
 1.2370 
 
 39.3 
 
 54 
 
 285.9 
 
 255.1 
 
 1175.0 
 
 919.9 
 
 7.91 
 
 0.1263 
 
 0.4180 
 
 1.2339 
 
 40.3 
 
 55 
 
 287.1 
 
 256.3 
 
 1175.4 
 
 919.0 
 
 7.78 
 
 0.1285 
 
 0.4196 
 
 1.2309 
 
 41.3 
 
 56 
 
 288.2 
 
 257.5 
 
 1175.7 
 
 918.2 
 
 7.65 
 
 0.1307 
 
 0.4212 
 
 1.2278 
 
 42.3 
 
 57 
 
 289.4 
 
 258.7 
 
 1176.0 
 
 917.4 
 
 7.52 
 
 0.1329 
 
 0.4227 
 
 1.2248 
 
 43.3 
 
 58 
 
 290.5 
 
 259.8 
 
 1176.4 
 
 916.5 
 
 7.40 
 
 0.1350 
 
 0.4242 
 
 1.2218 
 
 44.3 
 
 59 
 
 291.6 
 
 261.0 
 
 1176.7 
 
 915.7 
 
 7.28 
 
 0.1372 
 
 0.4257 
 
 1.2189 
 
 45.3 
 
 60 
 
 292.7 
 
 262.1 
 
 1177.0 
 
 914.9 
 
 7.17 
 
 0.1394 
 
 0.4272 
 
 1.2160 
 
 46.3 
 
 61 
 
 293.8 
 
 263.2 
 
 1177.3 
 
 914.1 
 
 7.06 
 
 0.1416 
 
 0.4287 
 
 1.2132 
 
 47.3 
 
 62 
 
 294.9 
 
 264.3 
 
 1177.6 
 
 913.3 
 
 6.95 
 
 0.1438 
 
 0.4302 
 
 1.2104 
 
 48.3 
 
 63 
 
 295.9 
 
 265.4 
 
 1177.9 
 
 912.5 
 
 6.85 
 
 0.1460 
 
 0.4316 
 
 1.2077 
 
 49.3 
 
 64 
 
 297.0 
 
 266.4 
 
 1178.2 
 
 911.8 
 
 6.75 
 
 0.1482 
 
 0.4330 
 
 1.2050 
 
 50.3 
 
 65 
 
 298.0 
 
 267.5 
 
 1178.5 
 
 911.0 
 
 6.65 
 
 0.1503 
 
 0.4344 
 
 1.2024 
 
 51.3 
 
 66 
 
 299.0 
 
 268.5 
 
 1178.8 
 
 910.2 
 
 6.56 
 
 0.1525 
 
 0.4358 
 
 1 1998 
 
 52.3 
 
 67 
 
 300.0 
 
 269.6 
 
 1179.0 
 
 909.5 
 
 6.47 
 
 0.1547 
 
 0.4371 
 
 1.1972 
 
 53.3 
 
 68 
 
 301.0 
 
 270.6 
 
 1179.3 
 
 908.7 
 
 6.38 
 
 0.1569 
 
 0.4385 
 
 1.1946 
 
 54.3 
 
 69 
 
 302.0 
 
 271.6 
 
 1179.6 
 
 908.0 
 
 6.29 
 
 0.1590 
 
 0.4398 
 
 1.1921 
 
 55.3 
 
 70 
 
 302.9 
 
 272.6 
 
 1179.8 
 
 907.2 
 
 6.20 
 
 0.1612 
 
 0.4411 
 
 1.1896 
 
 56.3 
 
 71 
 
 303.9 
 
 273.6 
 
 1180.1 
 
 906.5 
 
 6.12 
 
 0.1634 
 
 0.4424 
 
 1.1872 
 
 57.3 
 
 72 
 
 304.8 
 
 274.5 
 
 1180.4 
 
 905.8 
 
 6.04 
 
 0.1656 
 
 0.4437 
 
 1.1848 
 
 58.3 
 
 73 
 
 305.8 
 
 275.5 
 
 1180.6 
 
 905.1 
 
 5.96 
 
 0.1678 
 
 0.4449 
 
 1.1825 
 
 59.3 
 
 74 
 
 306.7 
 
 276.5 
 
 1180. 9 
 
 904.4 
 
 5.89 
 
 0.1699 
 
 0.4462 
 
 1.1801 
 
 60.3 
 
 75 
 
 307.6 
 
 277.4 
 
 1181.1 
 
 903.7 
 
 5.81 
 
 0.1721 
 
 0.4474 
 
 1.1778 
 
 61.3 
 
 76 
 
 308.5 
 
 278.3 
 
 1181.4 
 
 903.0 
 
 5.74 
 
 0.1743 
 
 0.4487 
 
 1.1755 
 
 62.3 
 
 77 
 
 309.4 
 
 279.3 
 
 1181.6 
 
 902.3 
 
 5.67 
 
 0.1764 
 
 0.4499 
 
 1.1730 
 
 63.3 
 
 78 
 
 310.3 
 
 280.2 
 
 1181.8 
 
 901.7 
 
 5.60 
 
 0.1786 
 
 0.4511 
 
 1.1712 
 
 64.3 
 
 79 
 
 311.2 
 
 281.1 
 
 1182.1 
 
 901.0 
 
 5.54 
 
 0.1808 
 
 0.4523 
 
 1.1687 
 
 65.3 
 
 80 
 
 312.0 
 
 282.0 
 
 1182.3 
 
 900.3 
 
 5.47 
 
 0.1829 
 
 0.4535 
 
 1.1665 
 
 66.3 
 
 81 
 
 312.9 
 
 282.9 
 
 1182.5 
 
 899.7 
 
 5.41 
 
 0.1851 
 
 0.4546 
 
 1.1644 
 
 67.3 
 
 82 
 
 313.8 
 
 283.8 
 
 1182.8 
 
 899.0 
 
 5.34 
 
 0.1873 
 
 0.4557 
 
 1.1623 
 
 68.3 
 
 83 
 
 314.6 
 
 284.6 
 
 1183.0 
 
 898.4 
 
 5.28 
 
 0.1894 
 
 0.4568 
 
 1.1602 
 
 69.3 
 
 84 
 
 315.4 
 
 285.5 
 
 1183.2 
 
 897.7 
 
 5.22 
 
 0.1915 
 
 0.4579 
 
 1.1581 
 
 70.3 
 
 85 
 
 316.3 
 
 286.3 
 
 1183. 4 
 
 897.1 
 
 5.16 
 
 0.1937 
 
 0.4590 
 
 1.1561 
 
 71.3 
 
 86 
 
 317.1 
 
 287.2 
 
 1183.6 
 
 896.4 
 
 5.10 
 
 0.1959 
 
 0.4601 
 
 1.1540 
 
 72.3 
 
 87 
 
 317.9 
 
 288.0 
 
 1183.8 
 
 895.8 
 
 5.05 
 
 0.1980 
 
 0.4612 
 
 1 . 1520 
 
 73.3 
 
 88 
 
 318.7 
 
 288.9 
 
 1184.0 
 
 895.2 
 
 5.00 
 
 0.2001 
 
 0.4623 
 
 1.1500 
 
 74.3 
 
 89 
 
 319.5 
 
 289.7 
 
 1184.2 
 
 894.6 
 
 4.94 
 
 0.2023 
 
 0.4633 
 
 1.1481 
 
 75.3 
 
 90 
 
 320.3 
 
 290.5 
 
 1184.4 
 
 893.9 
 
 4.89 
 
 0.2044 
 
 0.4644 
 
 1.1461 
 
 76.3 
 
 91 
 
 321.1 
 
 291.3 
 
 1184.6 
 
 893.3 
 
 4.84 
 
 0.2065 
 
 0.4654 
 
 1.1442 
 
 77.3 
 
 92 
 
 321.8 
 
 292.1 
 
 1184.8 
 
 892.7 
 
 4.79 
 
 0.2087 
 
 0.4664 
 
 1.1423 
 
 78.3 
 
 93 
 
 322.6 
 
 292.9 
 
 1185.0 
 
 892.1 
 
 4.74 
 
 0.2109 
 
 0.4674 
 
 1.1404 
 
 79.3 
 
 94 
 
 323.4 
 
 293.7 
 
 1185.2 
 
 891.5 
 
 4.69 
 
 0.2130 
 
 0.4684 
 
 1 . 1385 
 
 80.3' 
 
 95 
 
 324.1 
 
 294.5 
 
 1185.4 
 
 890.9 
 
 4.65 
 
 0.2151 
 
 0.4694 
 
 1.1367 
 
841 
 
 Properties of Saturated Steam. (Continued.) 
 
 •d 
 
 g*c 
 
 
 Total Heat 
 
 ^■A 
 
 
 d-Q 
 
 <D 
 
 a 
 
 3M 
 
 d 1- ? 
 
 
 above 32° F. 
 
 - d 
 
 Ph"S 
 
 Ohh 
 
 "S 
 
 > 
 
 
 m C 
 
 0»+a 
 
 
 
 |w 
 
 A* 
 
 ~B 
 
 •H 
 
 H 
 
 CO d 1 
 £02 
 
 S-i £ 
 
 a « 
 
 a 
 
 0) . 
 
 Mm 
 
 3.Q 
 
 © a 
 
 3 XD 
 
 IS 
 
 5Ji 
 
 a.d 
 
 1 1 
 
 <s .13 
 
 ^§ 
 
 ,d a 
 
 
 1 ! 
 
 "8 g 
 
 M+S 
 
 "5 Eh 
 
 ° e3 
 d^ 
 
 d 5 
 
 O 
 
 £1 
 < 
 
 H 
 
 a W 
 
 £ W 
 
 Hi 
 
 > 
 
 £ 
 
 H 
 
 W 
 
 81.3 
 
 96 
 
 324.9 
 
 295.3 
 
 1185.6 
 
 890.3 
 
 4.60 
 
 0.2172 
 
 0.4704 
 
 1.134f 
 
 82.3 
 
 97 
 
 325.6 
 
 296.1 
 
 1185.8 
 
 889.7 
 
 4.56 
 
 0.2193 
 
 0.4714 
 
 1 . 133C 
 
 83.3 
 
 98 
 
 326.4 
 
 296.8 
 
 1186.0 
 
 889.2 
 
 4.51 
 
 0.2215 
 
 0.4724 
 
 1.1312 
 
 84.3 
 
 99 
 
 327.1 
 
 297:6 
 
 1186.2 
 
 888.6 
 
 4.47 
 
 0.2237 
 
 0.4733 
 
 1.129! 
 
 85.3 
 
 100 
 
 327.8 
 
 298 .3 
 
 1186.3 
 
 888.0 
 
 4.429 
 
 0.2258 
 
 0.4743 
 
 1 . 127} 
 
 87.3 
 
 102 
 
 329.3 
 
 299.8 
 
 1186.7 
 
 886.9 
 
 4.347 
 
 0.2300 
 
 0.4762 
 
 1.1241 
 
 89.3 
 
 104 
 
 330.7 
 
 301.3 
 
 1187.0 
 
 885.8 
 
 4.268 
 
 0.2343 
 
 0.4780 
 
 1 . 120* 
 
 91.3 
 
 106 
 
 332.0 
 
 302.7 
 
 1187.4 
 
 884.7 
 
 4.192 
 
 0.2336 
 
 0.4798 
 
 1.1174 
 
 93.3 
 
 108 
 
 333.4 
 
 304.1 
 
 1187.7 
 
 883.6 
 
 4.118 
 
 0.2429 
 
 0.4816 
 
 1.1141 
 
 95.3 
 
 110 
 
 334.8 
 
 305.5 
 
 1188.0 
 
 882.5 
 
 4.047 
 
 0.2472 
 
 0.4834 
 
 1.1 10C 
 
 97.3 
 
 112 
 
 336.1 
 
 306.9 
 
 1188.4 
 
 881.4 
 
 3.978 
 
 0.2514 
 
 0.4852 
 
 1 . 1076 
 
 99.3 
 
 114 
 
 337.4 
 
 308.3 
 
 1188.7 
 
 880.4 
 
 3.912 
 
 0.2556 
 
 0.4869 
 
 1 . 1045 
 
 101.3 
 
 116 
 
 338.7 
 
 309.6 
 
 1189.0 
 
 879.3 
 
 3.848 
 
 0.2599 
 
 0.4886 
 
 1.10H 
 
 103.3 
 
 118 
 
 340.0 
 
 311.0 
 
 1189.3 
 
 878.3 
 
 3.786 
 
 0.2641 
 
 0.4903 
 
 1.0984 
 
 105.3 
 
 120 
 
 341.3 
 
 312.3 
 
 1189.6 
 
 877.2 
 
 3.726 
 
 0.2683 
 
 0.4919 
 
 1.0954 
 
 107.3 
 
 122 
 
 342.5 
 
 313.6 
 
 1189.8 
 
 876.2 
 
 3.668 
 
 0.2726 
 
 0.4935 
 
 1.0924 
 
 109.3 
 
 124 
 
 343.8 
 
 314.9 
 
 1190.1 
 
 875.2 
 
 3.611 
 
 0.2769 
 
 0.4951 
 
 1.0895 
 
 111.3 
 
 126 
 
 345.0 
 
 316.2 
 
 1190.4 
 
 874.2 
 
 3.556 
 
 0.2812 
 
 0.4967 
 
 1.0865 
 
 113.3 
 
 128 
 
 346.2 
 
 317.4 
 
 1190.7 
 
 873.3 
 
 3.504 
 
 0.2854 
 
 0.4982 
 
 1.0837 
 
 115.3 
 
 130 
 
 347.4 
 
 318.6 
 
 1191.0 
 
 872.3 
 
 3.452 
 
 0.2897 
 
 0.4998 
 
 1.0809 
 
 117.3 
 
 132 
 
 348.5 
 
 319.9 
 
 1191.2 
 
 871.3 
 
 3.402 
 
 0.2939 
 
 0.5013 
 
 1.0782 
 
 119.3 
 
 134 
 
 349.7 
 
 321.1 
 
 1191.5 
 
 870.4 
 
 3.354 
 
 0.2981 
 
 0.5028 
 
 1.0755 
 
 121.3 
 
 136 
 
 350.8 
 
 322.3 
 
 1191.7 
 
 869.4 
 
 3.308 
 
 0.3023 
 
 0.5043 
 
 1.0728 
 
 123.3 
 
 138 
 
 352.0 
 
 323.4 
 
 1192.0 
 
 868.5 
 
 3.263 
 
 0.3065 
 
 0.5057 
 
 1.0702 
 
 125.3 
 
 140 
 
 353.1 
 
 324.6 
 
 1192.2 
 
 867.6 
 
 3.219 
 
 0.3107 
 
 0.5072 
 
 1 .0675 
 
 127.3 
 
 142 
 
 354.2 
 
 325.8 
 
 1192.5 
 
 866.7 
 
 3.175 
 
 0.3150 
 
 0.5086 
 
 1.0649 
 
 129.3 
 
 144 
 
 355.3 
 
 326.9 
 
 1192.7 
 
 865.8 
 
 3.133 
 
 0.3192 
 
 0.5100 
 
 1 .0624 
 
 131.3 
 
 146 
 
 356.3 
 
 328.0 
 
 1192.9 
 
 864.9 
 
 3.092 
 
 0.3234 
 
 0.5114 
 
 1.0599 
 
 133.3 
 
 148 
 
 357.4 
 
 329.1 
 
 1193.2 
 
 864.0 
 
 3.052 
 
 0.3276 
 
 0.5128 
 
 1.0574 
 
 135.3 
 
 150 
 
 358.5 
 
 330.2 
 
 1193.4 
 
 863.2 
 
 3.012 
 
 0.3320 
 
 0.5142 
 
 1.0550 
 
 137.3 
 
 152 
 
 359.5 
 
 331.4 
 
 1193.6 
 
 862.3 
 
 2.974 
 
 0.3362 
 
 0.5155 
 
 1.0525 
 
 139.3 
 
 154 
 
 360.5 
 
 332.4 
 
 1193.8 
 
 861.4 
 
 2.938 
 
 0.3404 
 
 0.5169 
 
 1.0501 
 
 141.3 
 
 156 
 
 361.6 
 
 333.5 
 
 1194.1 
 
 860.6 
 
 2.902 
 
 0.3446 
 
 0.5182 
 
 1.0477 
 
 143.3 
 
 158 
 
 362.6 
 
 334.6 
 
 1194.3 
 
 859.7 
 
 2.868 
 
 0.3488 
 
 0.5195 
 
 1 .0454 
 
 145.3 
 
 160 
 
 363.6 
 
 335.6 
 
 1194.5 
 
 858.8 
 
 2.834 
 
 0.3529 
 
 0.5208 
 
 1.0431 
 
 147.3 
 
 162 
 
 364.6 
 
 336.7 
 
 1194.7 
 
 858.0 
 
 2.801 
 
 0.3570 
 
 0.5220 
 
 1 .0409 
 
 149.3 
 
 164 
 
 365.6 
 
 337.7 
 
 1194.9 
 
 857.2 
 
 2.769 
 
 0.3612 
 
 0.5233 
 
 1.0387 
 
 151.3 
 
 166 
 
 366.5 
 
 338.7 
 
 1195.1 
 
 856.4 
 
 2.737 
 
 0.3654 
 
 0.5245 
 
 1.0365 
 
 153.3 
 
 168 
 
 367.5 
 
 339.7 
 
 1195.3 
 
 855.5 
 
 2.706 
 
 0.3696 
 
 0.5257 
 
 1.0343 
 
 155.3 
 
 170 
 
 368.5 
 
 340.7 
 
 1195.4 
 
 854.7 
 
 2.675 
 
 0.3738 
 
 0.5269 
 
 1.0321 
 
 157.3 
 
 172 
 
 369.4 
 
 341.7 
 
 1195.6 
 
 853.9 
 
 2.645 
 
 0.3780 
 
 0.5281 
 
 1.0300 
 
 159.3 
 
 174 
 
 370.4 
 
 342.7 
 
 1195.8 
 
 853.1 
 
 2.616 
 
 0.3822 
 
 0.5293 
 
 1.0278 
 
 161.3 
 
 176 
 
 371.3 
 
 343.7 
 
 1196.0 
 
 852.3 
 
 2.588 
 
 0.3864 
 
 0.5305 
 
 1.0257 
 
 163.3 
 
 178 
 
 372.2 
 
 344.7 
 
 1196.2 
 
 851.5 
 
 2.560 
 
 0.3906 
 
 0.5317 
 
 1.0235 
 
 165.3 
 
 180 
 
 373.1 
 
 345.6 
 
 1196.4 
 
 850.8 
 
 2.533 
 
 0.3948 
 
 0.5328 
 
 1.0215 
 
 167.3 
 
 182 
 
 374.0 
 
 346.6 
 
 1196.6 
 
 850.0 
 
 2.507 
 
 0.3989 
 
 0.5339 
 
 1.0195 
 
 169.3 
 
 184 
 
 374.9 
 
 347.6 
 
 1196.8 
 
 849.2 
 
 2.481 
 
 0.4031 
 
 0.5351 
 
 1.0174 
 
 171.3 
 
 186 
 
 375.8 
 
 348.5 
 
 1196.9 
 
 848.4 
 
 2.455 
 
 0.4073 
 
 0.5362 
 
 1.0154 
 
 173.3 
 
 188 
 
 376.7 
 
 349.4 
 
 1197.1 
 
 847.7 
 
 2.430 
 
 0.4115 
 
 0.5373 
 
 1.0134 
 
 175.3 
 
 190 
 
 377.6 
 
 350.4 
 
 1197.3 
 
 846.9 
 
 2.406 
 
 0.4157 
 
 0.5384 
 
 1.0114 
 
 177.3 
 
 192 
 
 378.5 
 
 351.3 
 
 1197.4 
 
 846.1 
 
 2.381 
 
 0.4199 
 
 0.5395 
 
 1.0095 
 
 179.3 
 
 194 
 
 379.3 
 
 352.2 
 
 1197.6 
 
 845.4 
 
 2.358 
 
 0.4241 
 
 0.5405 
 
 1.0076 
 
 181.3 
 
 196 
 
 380.2 
 
 353.1 
 
 1197.8 
 
 844.7 
 
 2.335 
 
 0.4283 
 
 0.5416 
 
 1 .0056 
 
 183.3 
 
 198 
 
 381.0 
 
 354.0 
 
 1197.9 
 
 843.9 
 
 2.312 
 
 0.4325 
 
 0.5426 
 
 1 .0038 
 
842 
 
 
 
 Properties of Saturated Steam. {Continued.) 
 
 
 aT • 
 
 Sa 
 
 
 Total Heat 
 
 q4. 
 
 
 ■ 
 
 03 
 
 a 
 
 UA 
 
 Id- 
 
 St 
 
 a 
 
 
 above 32° F . 
 
 ► 03 
 
 "JIM 
 
 "T, 
 
 m 
 
 £o 
 
 fs 
 
 "S 
 
 $ 
 
 M 
 
 03 
 
 a 
 
 b'o3 
 
 S § 
 
 03 u 
 
 03 j£ 
 
 d ft 
 
 03 J, 
 
 +* 03 
 
 03^^ 
 
 -U 03 
 
 .03* g 
 
 Id- 
 
 
 'o 
 
 ft03 
 
 c o 
 
 < 
 
 H 
 
 c tn 
 
 a a 
 
 .-I 
 
 > 
 
 H 
 
 H 
 
 185.3 
 
 200 
 
 381.9 
 
 354.9 
 
 1198.1 
 
 843.2 
 
 2.290 
 
 0.437 
 
 0.5437, 
 
 1.0019 
 
 190.3 
 
 205 
 
 384.0 
 
 357.1 
 
 1198.5 
 
 841.4 
 
 2.237 
 
 0.447 
 
 0.5463 
 
 0.9973 
 
 195.3 
 
 210 
 
 386.0 
 
 359.2 
 
 1198.8 
 
 839.6 
 
 2.187 
 
 0.457 
 
 0.5488 
 
 0.9928 
 
 200.3 
 
 215 
 
 388.0 
 
 361.4 
 
 1199.2 
 
 837.9 
 
 2.138 
 
 0.468 
 
 0.5513 
 
 0.9885 
 
 205.3 
 
 220 
 
 389.9 
 
 363.4 
 
 1199.6 
 
 836.2 
 
 2.091 
 
 0.478 
 
 0.5538 
 
 0.9841 
 
 210.3 
 
 225 
 
 391.9 
 
 365.5 
 
 1199.9 
 
 834.4 
 
 2.046 
 
 0.489 
 
 0.5562 
 
 9799 
 
 215.3 
 
 230 
 
 393.8 
 
 367.5 
 
 1200.2 
 
 832.8 
 
 2.004 
 
 0.499 
 
 0.5586 
 
 9758 
 
 220.3 
 
 235 
 
 395.6 
 
 369.4 
 
 1200.6 
 
 831.1 
 
 1.964 
 
 0.509 
 
 0.5610 
 
 0.9717 
 
 225.3 
 
 240 
 
 397.4 
 
 371.4 
 
 1209.9 
 
 829.5 
 
 1.924 
 
 0.520 
 
 0.5633 
 
 0.9676 
 
 230.3 
 
 245 
 
 399.3 
 
 373.3 
 
 1201.2 
 
 827.9 
 
 1.887 
 
 0.530 
 
 0.5655 
 
 0.9638 
 
 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 
 
 0.5719 
 
 0.9525 
 
 255.3 
 
 270 
 
 407.9 
 
 382.5 
 
 1202.6 
 
 820.1 
 
 1.718 
 
 0.582 
 
 0.5760 
 
 0.9454 
 
 265.3 
 
 280 
 
 411.2 
 
 386.0 
 
 1203.1 
 
 817.1 
 
 1.658 
 
 0.603 
 
 0.5800 
 
 0.9385 
 
 275.3 
 
 290 
 
 414.4 
 
 389.4 
 
 1203.6 
 
 814.2 
 
 1.602 
 
 0.624 
 
 0.5840 
 
 0.9316 
 
 285.3 
 
 300 
 
 417.5 
 
 392.7 
 
 1204.1 
 
 811.3 
 
 1.551 
 
 0.645 
 
 0.5878 
 
 0.9251 
 
 295.3 
 
 310 
 
 420.5 
 
 395.9 
 
 1204.5 
 
 808.5 
 
 1.502 
 
 666 
 
 0.5915 
 
 0.9187 
 
 305.3 
 
 320 
 
 423.4 
 
 399.1 
 
 1204.9 
 
 805.8 
 
 1.456 
 
 0.687 
 
 0.5951 
 
 0.9125 
 
 315.3 
 
 330 
 
 426.3 
 
 402.2 
 
 1205.3 
 
 803.1 
 
 1.413 
 
 0.708 
 
 0.5986 
 
 0.9065 
 
 325.3 
 
 340 
 
 429.1 
 
 405.3 
 
 1205.7 
 
 800.4 
 
 1.372 
 
 0.729 
 
 0.6020 
 
 9006 
 
 335.3 
 
 350 
 
 431.9 
 
 408.2 
 
 1206.1 
 
 797.8 
 
 1.334 
 
 0.750 
 
 0.6053 
 
 8949 
 
 345.3 
 
 360 
 
 434.6 
 
 411.2 
 
 1206.4 
 
 795.3 
 
 1.298 
 
 0.770 
 
 0.6085 
 
 8894 
 
 355.3 
 
 370 
 
 437.2 
 
 414.0 
 
 1206.8 
 
 792.8 
 
 1.264 
 
 0.791 
 
 0.6116 
 
 0.8840 
 
 365.3 
 
 380 
 
 439.8 
 
 416.8 
 
 1207.1 
 
 790.3 
 
 1.231 
 
 0.812 
 
 0.6147 
 
 0.8788 
 
 375.3 
 
 390 
 
 442.3 
 
 419.5 
 
 1207.4 
 
 787.9 
 
 1.200 
 
 0.833 
 
 0.6178 
 
 0.8737 
 
 385.3 
 
 400 
 
 444.8 
 
 422 
 
 1208 
 
 786 
 
 1.17 
 
 0.86 
 
 0.621 
 
 0.868 
 
 435.3 
 
 450 
 
 456.5 
 
 435 
 
 1209 
 
 774 
 
 1.04 
 
 0.96 
 
 0.635 
 
 0.844 
 
 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 
 
 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 of 
 steam in B.T.U. when it is expanded adiabatically from" a higher to a 
 lower pressure is: 
 
 U = H - Hi + T CNi - N). 
 
 U = available B.T.U. in 1 lb. of expanding steam; // and Hi total heat 
 in 1 lb. steam at the two pressures; T = absolute temperature at the 
 lower pressure; N — Ni, difference of entropy of 1 lb. of steam at the two 
 pressures. 
 
 Example. — Required the available B.T.U. in 1 lb. steam expanded 
 from 100 lbs. to 14.7 lbs. 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 lowest pressure 
 and temperature, and that the feed-water from which the steam is made 
 is introduced into the system at the same low temperature. 
 
 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 (5"i - Tz) ■*- T ly 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. 
 
843 
 
 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°. 
 
 Jl. 
 
 
 Degrees of Superheat. 
 
 Oh 
 
 
 
 20 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 400 
 
 500 
 
 20 
 
 228.0 
 
 v 20.08 
 
 20.73 
 
 21.69 
 
 23.25 
 
 24.80 
 
 26.33 
 
 27.85 
 
 29.37 
 
 32.39 
 
 35.40 
 
 
 
 h 11562 
 
 1165.7 
 
 1179.9 
 
 1203.5 
 
 1227.1 
 
 1250. t 
 
 1274.1 
 
 1297.6 
 
 1344.8 
 
 1392.2 
 
 
 
 n 1.7320 
 
 1.7456 
 
 1.7652 
 
 1.7961 
 
 1.8251 
 
 1.852* 
 
 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 
 
 1.794C 
 
 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 
 
 1.8081 
 
 1.8511 
 
 1.8908 
 
 80 
 
 312.0 
 
 v5.47 
 
 5.65 
 
 5.92 
 
 6.34 
 
 6.75 
 
 7.17 
 
 7.56 
 
 7.95 
 
 8.72 
 
 9.49 
 
 
 
 h 1182.3 
 
 1193.0 
 
 1208.8 
 
 1234.3 
 
 1259.0 
 
 1283. t 
 
 1307.8 
 
 1331.9 
 
 1379.8 
 
 1427.9 
 
 
 
 n 1.6200 
 
 1.6338 
 
 1.6532 
 
 1.6833 
 
 1.7110 
 
 1.7366 
 
 1.7612 
 
 1 . 7840 
 
 1.8265 
 
 1.8658 
 
 100 
 
 327.8 
 
 v4.43 
 
 4.58 
 
 4.79 
 
 5.14 
 
 5.47 
 
 5.89 
 
 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 
 
 1.6216 
 
 1.6517 
 
 1.6789 
 
 1.7041 
 
 1.7280 
 
 1 . 7505 
 
 1.7924 
 
 1.8311 
 
 140 
 
 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 
 
 1.6561 
 
 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 1.5379 
 
 1.5541 
 
 1.5753 
 
 1.6049 
 
 1.6312 
 
 1.6558 
 
 1 .6787 
 
 1.7005 
 
 1.7415 
 
 1.7792 
 
 240 
 
 397.4 
 
 v 1.92 
 
 1.99 
 
 2.09 
 
 2.26 
 
 2.42 
 
 2.57 
 
 2.71 
 
 2.85 
 
 3.13 
 
 3.40 
 
 
 
 h 1200.9 
 
 1215.4 
 
 1234.3 
 
 1261.9 
 
 1287.6 
 
 1312.8 
 
 1337.6 
 
 1362.3 
 
 1411.5 
 
 1460.5 
 
 
 
 n 1.5309 
 
 1.5476 
 
 1.5690 
 
 1.5985 
 
 1.6246 
 
 1.6492 
 
 1.6720 
 
 1.6937 
 
 1.7344 
 
 1.7721 
 
 260 
 
 404.5 
 
 vl.78 
 
 1.84 
 
 1.94 
 
 2.10 
 
 2.24 
 
 2.39 
 
 2.52 
 
 2.65 
 
 2.91 
 
 3.16 
 
 
 
 h 1202.1 
 
 1217.1 
 
 1236.4 
 
 1264.1 
 
 1289.9 
 
 1315.1 
 
 1340.0 
 
 L64.7 
 
 1414.0 
 
 1463.2 
 
 
 
 n 1.5244 
 
 1.5416 
 
 1.5631 
 
 1.5926 
 
 1.6186 
 
 1.6430 
 
 1.6658 
 
 1.6874 
 
 1 . 7280 
 
 1.7655 
 
 280 
 
 411.2 
 
 v 1.66 
 
 1.72 
 
 1.81 
 
 1.95 
 
 2.09 
 
 2.22 
 
 2.35 
 
 2.48 
 
 2.72 
 
 2.95 
 
 
 
 h 1203.1 
 
 1218.7 
 
 1238.4 
 
 1266.2 
 
 1291.9 
 
 1317.2 
 
 1342.2 
 
 1367.0 
 
 1416.4 
 
 1465.7 
 
 
 
 n 1.5185 
 
 1.5362 
 
 1.5580 
 
 1.5873 
 
 1.6133 
 
 1.6375 
 
 1.6603 
 
 1.6818 
 
 1.7223 
 
 1 7597 
 
 300 
 
 417.5 
 
 vl.55 
 
 1.60 
 
 1.69 
 
 1.83 
 
 1.96 
 
 2.09 
 
 2 21 
 
 2.33 
 
 2.55 
 
 2.77 
 
 
 
 h 1204.1 
 
 1220.2 
 
 1240.3 
 
 1268.2 
 
 1294.0 
 
 1319.3 
 
 1344.3 
 
 1369.2 
 
 1418.6 
 
 1468.0 
 
 
 
 n 1.5129 
 
 1.5310 
 
 .5530 
 
 1.5824 
 
 1.6082 
 
 1.6323 
 
 1.6550 
 
 1.6765 
 
 1.7168 
 
 1.7541 
 
 350 
 
 431.9 
 
 vl.33 
 
 1.38 
 
 .46 
 
 1.58 
 
 1.70 
 
 1.81 
 
 1.92 
 
 ?.02 
 
 2.22 
 
 2.41 
 
 
 
 h 1206.1 
 
 1223.9 
 
 244.6 
 
 1272.7 
 
 1298.7 
 
 1324.1 
 
 1349.3 
 
 1374.3 
 
 1424 
 
 1473.7 
 
 
 
 n 1.5002 
 
 1.5199 
 
 .5423 
 
 1.5715 
 
 1.5971 
 
 1.62f0 
 
 1.6436 
 
 1.6650 
 
 1 . 7052 
 
 1.7422 
 
 400 
 
 444.8 
 
 v 1.17 
 
 1.21 
 
 .28 
 
 1.40 
 
 1.50 
 
 1.60 
 
 1.70 , 
 
 1.79 
 
 1.97 
 
 2.14 
 
 
 
 h 1207.7 
 
 1227.2 
 
 248.6 
 
 1276.9 
 
 1303.0 
 
 1328.6 
 
 353.9 
 
 1379.1 
 
 1429.0 
 
 1478.9 
 
 
 
 n 1.4894 
 
 1.5107 
 
 .5336 
 
 1.5625 
 
 1.5880 
 
 1.6117 
 
 .6342 
 
 1.6554 
 
 1.6955 
 
 1.7323 
 
 450 
 
 456.5 
 
 v 1.04 
 
 1.08 
 
 .14 
 
 1.25 
 
 1.35 
 
 1.44 
 
 .53 
 
 1.61 
 
 1.77 
 
 1.93 
 
 
 
 h 1209 
 
 1231 
 
 252 
 
 1281 
 
 1307 
 
 1333 
 
 -1358 
 
 383 
 
 1434 
 
 1484 
 
 
 
 n 1.479 
 
 1.502 
 
 .526 
 
 1.554 
 
 1.580 
 
 1.603 
 
 1,626 
 
 1.647 
 
 1.687 
 
 1.723 
 
 500 
 
 467.3 
 
 v0.93 
 
 0.97 
 
 .03 
 
 1.13 
 
 1.22 
 
 1.31 
 
 1.39 
 
 .47 
 
 1.62 
 
 .76 
 
 
 
 h 1210 
 
 1233 
 
 256 
 
 1285 
 
 1311 
 
 1337 
 
 1362 
 
 388 
 
 1438 
 
 489 
 
 
 
 n 1.470 
 
 1.496 
 
 .519 
 
 1.548 
 
 1.573 
 
 1.597 
 
 1.619 
 
 .640 
 
 1.679 
 
 .715 
 
844 
 
 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 "^h' 
 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 lbs. per sq. in., is (14.7 X 100/58) 
 = 25.37 lbs. 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 lbs. 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 1065. 
 
 Outflow of Steam into the Atmosphere. — External pressure per 
 square inch, 14.7 lbs. absolute. Ratio of expansion in nozzle, 1.624. 
 
 
 , 
 
 «4H 
 
 tM 
 
 03 • 
 
 
 , 
 
 <*H 
 
 , 
 
 • 
 
 
 
 O 
 
 rt 
 
 
 
 d 
 
 o 
 
 d 
 
 t<oJ 
 
 "* u 
 
 i3i 
 
 £ 
 
 I* ". i 
 
 £ 1 , 03 
 
 O oaSS a 
 
 ik * • 
 
 is$ 
 
 >> 
 
 , °S 
 
 a£~ 
 
 Mi 
 
 3 so rt 
 
 2ii 
 
 ' 3 fe ° 
 
 -3« 55 
 
 "3 A 
 
 > O 03 
 
 cO a 
 
 ftJaS 
 
 oj a 
 
 SB a; a? 
 
 lis 
 
 9 £ 03 
 
 O g g, 
 
 ,Ol-H m 
 
 =4-1 <$ £ 
 
 111 
 
 > O 03 
 
 oO a 
 
 ischarge pei 
 square inch 
 Orifice per 
 ute. 
 
 £0° 
 
 I'o ". £ 
 
 a. cPh_§ 
 
 < 
 
 > 
 
 < 
 
 Q 
 
 w 
 
 < 
 
 > 
 
 < 
 
 P 
 
 w 
 
 lbs. 
 
 feet 
 p. sec. 
 
 feet 
 per sec . 
 
 lbs. 
 
 H.P. 
 
 lbs. 
 
 feet 
 p.sec. 
 
 feet 
 per sec. 
 
 lbs. 
 
 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 
 
 Bateau'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 lbs. per sq. in. In his paper read at the Intl. Eng'g. Congress at 
 Glasgow (Eng. 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, lbs. 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. 845 
 
 which closely correspond with those in the above table, and with results 
 computed by Rateau's formula, as shown below. 
 
 Abs. press., lbs. 
 
 persq. in 25.37 40 60 75 100 135 165 215 
 
 Discharge per min., 
 
 by table, lbs.... 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. — A formula formerly used for velocity of 
 flow of steam in pipes is the same as Downi ng's for the flow of water in 
 smooth cast-iron pipes, viz., V= 50 ^HD/L, in which V= velocity in feet 
 per second, L = length and D = diameter of pipe in feet, H = height in 
 feet of a column of steam, of the pressure of the steam at the entrance, 
 which would produce a pressure equal to the difference of pressures at the 
 two ends of the pipe. (For derivation of the coefficient 50, see Briggs on 
 "Warming Buildings by Steam," Proc. Inst. C. E., 1882.) 
 
 If Q = quantity in cubic feet per minute, d = diameter in inches, L and 
 H being in feet, the formula reduces to 
 
 Q = 4.7233 Jj^dK # = 0.0448^, d = 0.5374 W '^ • 
 
 These formulae are applicable to air and other gases as well as steam. 
 They are not as accurate as later formulae (see below) in which the coeffi- 
 cients vary with the diameter of the pipe. G. H. Babcock, in "Steam," 
 gives the formula 
 
 W = 87 * /- 
 
 w(pi — gg) d 5 
 
 (V+¥)' 
 
 W=weight of steam flowing, in lbs. per minute, ■u? = density in lbs. per 
 cu. ft. of the steam at the entrance to the pipe, Pi = pressure in lbs. per sq. 
 in. at the entrance, p 2 =pressure at the exit, rf = diam. in inches, L=length 
 in feet. This formula is apparently derived from Unwin's formula for flow 
 of fluids in Ency. B rit., vol. xii, pp . 508, 516. Putting the formula in 
 the form W =c ^w (pi — pz) d 5 /L, in which c will vary with the diam- 
 eter of the pipe, we have, 
 
 For diameter, inches. . . 1 2 3 4 6 9 12 
 
 Value of c 40.7 52.1 58.8 63 68.8 73. 7 79.3 
 
 One of t he m ost widely accepted formulae for flow of water is Darcy's, 
 
 in which c has values ranging from 65 for a 1/2-inch pipe 
 
 up to 11 1.5 for 24-inch. Using Darcy's coefficients, and modifying his 
 formula to make it apply to steam, to the form 
 
 Ihd 
 
 V = C VL4' 
 
 Q = c |/ (Pl -P ,)dt ; or W= c y ^<Pi -*>»>* , 
 we obtain, 
 
 For diameter, inches ..1/2I 2 34 5 6 7 8 
 
 Value of c 36.8 45.3 52.7 56.1 57.8 58.4 59.5 60.1 60.7 
 
 For diameter, inches . . 9 10 12 14 16 18 20 22 24 
 
 Value of c 61.2 61.8 62.1 62.3 62.6 62.7 62.9 63.2 63.2 
 
 In the absence of direct experiments these coefficients are probably as 
 accurate as any that may be derived from formulae for flow of water. 
 . .. . Q 2 wL W*L 
 
 Loss of pressure in lbs. per sq. in. = p\— p%= = - 2 • 
 
 For a comparison of different formulae for flow of steam see a paper 
 by G. F. Gebhardt, in Power, June, 1907, 
 
846 
 
 STEAM. 
 
 (-^'" — V0T1 
 
 Pi) d b 
 (1 + 3.6/d)' 
 
 Table of Flow of Steam in Pipes of Different Diameters and 
 Different Drops in Pressure. (E. C. Sickles, Trans. A. S. M. E., xx 
 354.) — The drop is calculated from the f ormula p\ — p 2 = 0.000131 
 
 Pi and p2, initial and final 
 
 pressures, lbs. per sq. in., d = diam. in ins., W = flow in pounds per 
 minute, w = density of steam in lbs. per cu. ft., L = length of pipe in feet. 
 The table is calculated on the basis of L = 1000 ft. For any other length 
 the drop is proportional to the length -f* 1000. 
 
 Example in Use of the Table. — Required the size of pipe to carry 
 2500 lbs. per min. of steam of 150 lbs. absolute pressure. In the first table 
 we find figures above 2500 lbs. per 'min. as follows: 2667, 13-in. pipe, line 
 2; 2736, 14-in. pipe, line 4; 2527, 15-in. pipe, line 8; 2638, 16-in. pipe, line 
 10; 2623, 18-in. pipe, line 14. In the table on the next page, under 150 
 lbs., we find the corresponding drops per 1000 ft. as follows : line 2, 9.60 lbs.; 
 line 4, 6.83 lbs.; line 8, 4.10 lbs.; line 10, 3.19 lbs.; line 14, 1.72 lbs. 
 
 Steam Discharge in Pounds per Minute. 
 
 Corresponding to Drop in Pressure in table on the next page, for Pipe 
 Diameters in Inches in Top Line. 
 
 Line 
 
 No. 
 
 24 
 
 22 
 
 20 
 
 18 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 10 
 
 1 
 
 14000 
 
 11188 
 
 8772 
 
 6678 
 
 4923 
 
 4163 
 
 3481 
 
 2871 
 
 2328 
 
 1853 
 
 1443 
 
 2 
 
 13000 
 
 10392 
 
 8144 
 
 6203 
 
 4573 
 
 3867 
 
 3233 
 
 2667 
 
 2165 
 
 1721 
 
 1341 
 
 3 
 
 12000 
 
 9593 
 
 7517 
 
 5724 
 
 4220 
 
 3569 
 
 2983 
 
 2461 
 
 1996 
 
 1589 
 
 1237 
 
 4 
 
 11000 
 
 8804 
 
 6891 
 
 5247 
 
 3868 
 
 3271 
 
 2736 
 
 2256 
 
 1830 
 
 1456 
 
 1134 
 
 5 
 
 10000 
 
 7992 
 
 6265 
 
 4770 
 
 3517 
 
 2974 
 
 2486 
 
 2051 
 
 1663 
 
 1324 
 
 1031 
 
 6 
 
 9500 
 
 7705 
 
 5947 
 
 4532 
 
 3341 
 
 2825 
 
 2362 
 
 1940 
 
 1580 
 
 1258 
 
 979 
 
 7 
 
 9000 
 
 7205 
 
 5638 
 
 4293 
 
 3165 
 
 2676 
 
 2237 
 
 1846 
 
 1497 
 
 1192 
 
 928 
 
 8 
 
 8500 
 
 6905 
 
 5321 
 
 4054 
 
 2989 
 
 2527 
 
 2113 
 
 1743 
 
 1414 
 
 1125 
 
 876 
 
 9 
 
 8000 
 
 6506 
 
 5012 
 
 3816 
 
 2814 
 
 2379 
 
 1989 
 
 1640 
 
 1331 
 
 1059 
 
 825 
 
 10 
 
 7500 
 
 6106 
 
 4695 
 
 3577 
 
 2638 
 
 2230 
 
 1865 
 
 1538 
 
 1248 
 
 993 
 
 873 
 
 11 
 
 7000 
 
 5707 
 
 4385 
 
 3339 
 
 2462 
 
 2082 
 
 1740 
 
 1435 
 
 1164 
 
 927 
 
 722 
 
 12 
 
 6500 
 
 5307 
 
 4069 
 
 3100 
 
 2286 
 
 1933 
 
 1616 
 
 1333 
 
 1081 
 
 860 
 
 670 
 
 13 
 
 6000 
 
 4908 
 
 j 758 
 
 2862 
 
 2110 
 
 1784 
 
 1492 
 
 1230 
 
 998 
 
 794 
 
 619 
 
 14 
 
 5500 
 
 4508 
 
 3443 
 
 2623 
 
 1934 
 
 1635 
 
 1368 
 
 1128 
 
 915 
 
 728 
 
 567 
 
 15 
 
 5000 
 
 4108 
 
 3132 
 
 2385 
 
 1758 
 
 1487 
 
 1243 
 
 1025 
 
 832 
 
 662 
 
 516 
 
 Steam Discharge for Pipe Diameters in Inches, Continued. 
 
 Line 
 No. 
 
 9 
 
 8 
 
 799 
 
 7 
 
 560 
 
 6 
 
 371 
 
 5 
 
 4 
 
 31/2 
 
 3 
 55.9 
 
 21/2 
 
 2 
 
 H/2 
 
 1 
 
 1093 
 
 227 
 
 123 
 
 71.6 
 
 28.8 
 
 18.1 
 
 6.81 
 
 2 
 
 1015 
 
 747. 
 
 521 
 
 344 
 
 210 
 
 114.6 
 
 68.6 
 
 51.9 
 
 27.6 
 
 16.8 
 
 6.52 
 
 3 
 
 937 
 
 685 
 
 481 
 
 318 
 
 194 
 
 106.0 
 
 65.6 
 
 47.9 
 
 26.4 
 
 15.5 
 
 6.24 
 
 4 
 
 859 
 
 67,8 
 
 441 
 
 292 
 
 178 
 
 97.0 
 
 62.7 
 
 43.9 
 
 25.2 
 
 14.2 
 
 5.95 
 
 5 
 
 781 
 
 571 
 
 401 
 
 265 
 
 162 
 
 88.2 
 
 59.7 
 
 39.9 
 
 24.0 
 
 12.9 
 
 5.67 
 
 6 
 
 742 
 
 547, 
 
 381 
 
 252 
 
 154 
 
 83.8 
 
 56.5 
 
 37.9 
 
 22.8 
 
 12.3 
 
 5.29 
 
 7 
 
 703 
 
 514 
 
 361 
 
 239 
 
 146 
 
 79.4 
 
 53.5 
 
 35.9 
 
 21.6 
 
 11.6 
 
 5.00 
 
 8 
 
 664 
 
 485 
 
 341 
 
 226 
 
 138 
 
 75.0 
 
 50.5 
 
 33.9 
 
 20.4 
 
 10.9 
 
 4.72 
 
 9 
 
 625 
 
 457 
 
 321 
 
 212 
 
 130 
 
 70.6 
 
 47.6 
 
 31.9 
 
 19.2 
 
 10.3 
 
 4.43 
 
 10 
 
 586 
 
 478 
 
 301 
 
 199 
 
 122 
 
 66.2 
 
 44.5 
 
 23.9 
 
 18.0 
 
 9.68 
 
 4.15 
 
 11 
 
 547 
 
 400 
 
 7.81 
 
 186 
 
 113 
 
 61.7 
 
 41.6 
 
 27.9 
 
 16.8 
 
 9.03 
 
 3.86 
 
 12 
 
 508 
 
 371 
 
 7.61 
 
 172 
 
 105 
 
 57.3 
 
 38.6 
 
 25.9 
 
 15.6 
 
 8.38 
 
 3.68 
 
 13 
 
 469 
 
 343 
 
 741 
 
 159 
 
 97.2 
 
 52.9 
 
 35.6 
 
 23.9 
 
 14.4 
 
 7.74 
 
 3.40 
 
 14 
 
 430 
 
 314 
 
 7.21 
 
 146 
 
 89.1 
 
 48.5 
 
 32.6 
 
 21.9 
 
 13.2 
 
 7.10 
 
 3.11 
 
 15 
 
 390 
 
 286 
 
 200 
 
 132 
 
 81.0 
 
 44.1 
 
 29.6 
 
 20.0 
 
 12.0 
 
 6.45 
 
 2.83 
 
 2.52 
 2.34 
 2.16 
 1.98 
 1.80 
 1.71 
 1.62 
 1.53 
 1.44 
 1.35 
 1.26 
 1.17 
 1.08 
 0.99 
 0.90 
 
FLOW OF STEAM 
 
 847 
 
 Drop in Pressure in Pounds per Sq. In., per 1000 Ft. Length. 
 Corresponding to Discharge in above Table. 
 
 Density * 
 
 0.208 
 
 0.230 
 
 0.273 
 
 0.295 
 
 0.316 
 
 0.338 
 
 0.401 
 
 0.443 
 
 0.485 
 
 0.548 
 
 Pressuref 
 
 90 
 
 100 
 
 120 
 
 130 
 
 140 
 
 150 
 
 180 
 
 200 
 
 220 
 
 250 
 
 Line. 1 
 
 18.10 
 
 16.4 
 
 13.8 
 
 12.8 
 
 11.9 
 
 11.1 
 
 9.39 
 
 8.50 
 
 7.76 
 
 6.87 
 
 2 
 
 15.60 
 
 14.1 
 
 11.9 
 
 11.0 
 
 10.3 
 
 9.60 
 
 8.09 
 
 7.33 
 
 6.69 
 
 5.92 
 
 3 
 
 13.3 
 
 12.0 
 
 10.1 
 
 9.38 
 
 8.75 
 
 8.18 
 
 6.90 
 
 6.24 
 
 5.70 
 
 5.05 
 
 4 
 
 11.1 
 
 10.0 
 
 8.46 
 
 7.83 
 
 7.31 
 
 6.83 
 
 5.76 
 
 5.21 
 
 4.76 
 
 4.21 
 
 5 
 
 9.25 
 
 8.36 
 
 7.5 
 
 6.52 
 
 5.87 
 
 6.09 
 
 5.69 
 
 4.80 
 
 4.34 
 
 3.97 
 
 3.51 
 
 6 
 
 8.33 
 
 7.53 
 
 6.35 
 
 5.48 
 
 5.13 
 
 4.32 
 
 3.91 
 
 3.57 
 
 3.16 
 
 7 
 
 7.48 
 
 6.76 
 
 5.70 
 
 5.27 
 
 4.92 
 
 4.60 
 
 3.88 
 
 3.51 
 
 3 21 
 
 2.84 
 
 8 
 
 6.67 
 
 6.03 
 
 5.08 
 
 4.70 
 
 4.39 
 
 4.10 
 
 3.46 
 
 3.13 
 
 2.86 
 
 2.53 
 
 9 
 
 5.91 
 
 5.35 
 
 4.50 
 
 4.17 
 
 3.89 
 
 3.64 
 
 3.07 
 
 2.78 
 
 2.53 
 
 2.24 
 
 10 
 
 5.19 
 
 4.69 
 
 3.95 
 
 3.66 
 
 3.42 
 
 3.19 
 
 2.69 
 
 2.44 
 
 2 ?,3 
 
 1.97 
 
 11 
 
 4.52 
 
 4.09 
 
 3.44 
 
 3.19 
 
 2.98 
 
 2.78 
 
 2.34 
 
 2.12 
 
 1.94 
 
 1.72 
 
 12 
 
 3.90 
 
 3.53 
 
 2.97 
 
 2.75 
 
 2.57 
 
 2.40 
 
 2.02 
 
 1.83 
 
 1.67 
 
 1.48 
 
 13 
 
 3.32 
 
 3.00 
 
 2.53 
 
 2.34 
 
 2.19 
 
 2.04 
 
 1.72 
 
 1.56 
 
 1.42 
 
 1.26 
 
 14 
 
 2.79 
 
 2.52 
 
 2.13 
 
 1.97 
 
 1.84 
 
 1.72 
 
 1.45 
 
 1.31 
 
 1.20 
 
 1.06 
 
 15 
 
 2.31 
 
 2.09 
 
 1.76 
 
 1.63 
 
 1.52 
 
 1.42 
 
 1.20 
 
 1.C8 
 
 0.991 
 
 0.877 
 
 * Density in lbs. per cu. ft. 
 
 t Pressure, absolute, 
 
 For Flow of Steam at low pressures, see Heating and Ventilation, 
 page 670. 
 
 Carrying Capacity of Extra Heavy Steam Pipes. 
 
 (Power Speciality Co.) 
 
 
 . 03 
 
 200 
 
 150 
 
 100 
 
 50 
 
 
 , C3 ■ 
 
 200 
 
 150 
 
 100 . 
 
 50 
 
 a o— 
 
 .5 £,c 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 co— 1 
 
 1.3 & 
 
 — . c3 ■ 
 
 3 (U co 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 
 
 Pounds of steam 
 hour. 
 
 per 
 
 Pounds of steam per 
 hour. 
 
 i 
 
 0.71 
 
 1210 
 
 872 
 
 618 
 
 362 
 
 6 
 
 25.93 
 
 40800 
 
 31600 
 
 22600 
 
 13210 
 
 11 '4 
 
 1.27 
 
 2000 
 
 1555 
 
 1105 
 
 646 
 
 7 
 
 34.47 
 
 54600 
 
 42250 
 
 30000 
 
 17600 
 
 i*'2 
 
 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 
 
 3 
 
 6.56 
 
 10300 
 
 8050 
 
 5720 
 
 3450 
 
 11 
 
 90.76 
 
 142800 
 
 111500 
 
 79200 
 
 46300 
 
 31/2 
 
 8.85 
 
 13900 
 
 10820 
 
 7720 
 
 4520 
 
 12 
 
 1 08.45 
 
 170500 
 
 133000 
 
 94750 
 
 55400 
 
 4 
 
 11.44 
 
 18000 
 
 14000 
 
 10000 
 
 5850 
 
 14 
 
 153.94 
 
 242000 
 
 1 88200 
 
 133900 
 
 78600 
 
 41/2 
 
 14.18 
 
 22300 
 
 17350 
 
 12320 
 
 7230 
 
 16 
 
 176.71 
 
 277500 
 
 216200 
 
 153800 
 
 90500 
 
 5 
 
 18.19 
 
 28610 
 
 22250 
 
 15800 
 
 9300 
 
 18 
 
 226.98 
 
 357000 
 
 278000 
 
 197500 
 
 115700 
 
 The pounds per hour in the above table are figured for the velocities 
 given below: 
 
 Steam superheated degrees F. . . 
 Velocity, ft. per min 8000 
 
 50 
 8500 
 
 100 
 8950 
 
 150" 
 9450 
 
 200 250 
 9900 10450 
 
 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 form ula for flow would be an exponential one. Ledoux gives 
 
 notation being reduced to English meas- 
 ures. (Annates des Mines, 1892; Trans. A. S. M. E., xx., 365; Power, June, 
 1907.) See Johnson's formula for flow of air, page 596. 
 
 4 / W 2 L 
 d = 0.699 y pil . 94 _ p2l . 94 , his 
 
848 STEAM. 
 
 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 2 -4- 2g is expended in giving the velocity of flow; and the head 
 0.505 v 2 -h2# 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 1 1/2 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 mln. (steam assumed to be admitted during 
 Full Stroke.) 
 
 Diam. of pipe, inches 2 21/2 3 31/2 4 41/2 5 6 
 
 Vel. 4000 5.2 6.5 7.7 9.010.311.612.915.5 
 
 Vel. 6000 6.3 7.9 9.511.112.614.215.819.0 
 
 Vel. 8000 7.3 9.110.9 12.8 14.6 16.4 18.3 21.9 
 
 Horse-power, approx 20 31 45 62 80 100 125 180 
 
 Diam. of pipes, inches ... 7 8 9 10 11 12 13 14 
 
 Vel. 4000 18.1 20.7 23.2 25.8 28.4 31.0 33.6 36.1 
 
 Vel. 6000 22.1 25.3 28.5 31.6 34.8 37.9 41.1 44.3 
 
 Vel. 8000 25.6 29.2 32.9 36.5 40.2 43.8 47.5 51 1 
 
 Horse-power, approx 245 320 406 500 606 718 845 981 
 
 _, , „ . Area of cylinder X piston-speed 
 
 Formula. Area of pipe = r^-rr t— - : — —. — • 
 
 mean velocity of steam in pipe 
 
 For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, 
 and 8000 ft. per min., area of pipe = respectively 0.15, 0.10, and 0.075 X 
 area of cylinder. Diam. of pipe = respectively 0.3873, 0.3162, and 0.2739 X 
 diam. of cylinder. Reciprocals of these figures are 2.582, 3.162, and 
 3.651. 
 
 The first line in the above table may be used for proportioning exhaust 
 pipes, in which a velocity not exceeding 4000 ft. per minute is advisable. 
 The last line, approx. H.P. of engine, is based on the velocity of 6000 ft. 
 per min. in the pi pe, using the correspond ing 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-vives 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. 
 
FLOW OF STEAM. 
 
 849 
 
 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 = >/D 2 S -*- 8100 = D Vs -4- 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- 
 
 Diam. of 
 
 Area of 
 
 Diam. of 
 
 Area of 
 
 
 speed, 
 
 Steam-pipe 
 
 Steam-pipe 
 
 Exhaust 
 
 Exhaust 
 
 to Steam 
 
 ft. per min. 
 
 + D. 
 
 -h .4. 
 
 h- D. 
 
 + A. 
 
 h- 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 
 and 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 
 well-covered steam-pipes this loss may be estimated at about 0.3 lb. 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. 558). 
 
 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 
 
850 
 
 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 lbs. 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 lb. of steam, due to the several drops already 
 found, and the corresponding fraction of 1 lb. 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 lbs. of steam carried. Calcu- 
 late the loss in lbs. of steam condensed by radiation in the pipes of the 
 different diameters, per 1000 lbs. 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 lbs. of steam lost per 1000 
 lbs. 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 lbs. of steam per 1000 lbs. carried. This is to be added to 
 the sum of the losses 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 glven pressures and 1 lb. absolute, based on 
 the Carnot Cycle. E = (Ti - T 2 ) -*■ Tu 
 
 
 Maximum Initial Absolute Pressures. 
 
 Initial Pressure 
 less than Maxi- 
 mum. 
 
 100 
 
 125 
 
 150 
 
 175 
 
 200 
 
 225 
 
 250 
 
 275 
 
 300 
 
 
 Maximum Thermal Efficiency. 
 
 lbs. 
 
 
 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 
 
 2 
 
 .359 
 
 5 
 
 .359 
 
 10 
 
 .358 
 
 20 
 
 .356 
 
 
 
 This table shows that if the initial steam pressure is lowered from 
 100 lbs. to 80 lbs., the efficiency of the Carnot cycle is reduced from 
 0.237 to 0.272, or over 5%, but if steam of 300 lbs. is lowered to 280 lbs. 
 the efficiency is reduced only from 0.360 to 0.356 or 1.1%. Witn 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. 
 
 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 lbs. of steam per hour a distance of 1000 feet, 
 with 100 lbs. initial pressure. 
 
STEAM PIPES. 
 
 851 
 
 Diameter of Pipe. 
 
 6 in. 
 
 7 in. 
 
 8 in. 
 
 10 in. 
 
 12 in. 
 
 I. Interest, etc., 12% per annum. . 
 
 $0.39 
 1.51 
 0.86 
 
 $0.46 
 1.76 
 0.38 
 
 $0.53 
 2.01 
 0.19 
 
 $0.66 
 2.51 
 0.06 
 
 $0.84 
 3 02 
 
 
 02 
 
 
 
 Total per day 
 
 $2.76 
 
 $2.60 
 
 $2.73 
 
 $3.23 
 
 $3.88 
 
 STEAM PIPES. 
 
 Bursting-tests of Copper Steam-pipes. (From Report 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/ 8 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 lbs. per sq. in., of bursting-pressure: 
 
 Pipe number 1 2 3 4 4' 
 
 Actual bursting-strength . . 835 785 950 1225 1275 
 
 Calculated " V 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 gi eater 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. 
 
 It would seem that iron castings are unsuitable for both fittings and 
 valves to be used in any superheated steam work. The only adaptable 
 metal seems to be cast steel. Tests by Bach on this metal show that at 
 572° F. the reduction in breaking 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 
 
852 
 
 highly 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 in 
 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 steam 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- 
 
STEAM PIPES. 853 
 
 sation; in a steanvcurrent water will be carried or swept along rapidly 
 by friction. (Illustrated in Modern Mechanism, p. 807. Patented by 
 J. H. Blessing, Feb. 13, 1872, 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 is led 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 lbs. 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 lb. pressure, and a difference in pressure of 10 lbs. 
 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 71/2 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 lb. 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. 558, 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 11/4-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 lbs. 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, which 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 lbs., although the engines 
 are 500 ft. away from the boilers. 
 
 Equation of Pipes. — For determining the number of small sized 
 pipes that are equal in carrying capacity to one of greater size the table 
 given under Flo w of Air, page 597, is commonly used. It is based on the 
 equation N = ^d^-^di 5 , in which N is the number of smaller pipes of 
 diameter di equal in capacity to one pipe of diameter d. A more 
 accu rate equ ation, based on Unwin's formula for flow of fluids, is N = 
 
 - — f 1+ °' 6 ; (d and di in inches). For d= 2 d\, the first formula gives 
 di 3 Vd + 3.6 
 
854 
 
 THE STEAM-BOILER. 
 
 N = 5.7, and the second N = 6.15, an unimportant difference, but for 
 d == 8 c/i, 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- 
 plicity 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. 
 
 Steam, high pressure to engines, boiler 
 
 cross-overs, leaders and headers 
 
 All other steam lines 
 
 Steam, exhaust 
 
 Steam, drips including traps 
 
 Steam trap discharge 
 
 Blow-offs, drips from water columns 
 
 and low-pressure drips 
 
 Drains from crank pits 
 
 Cold water to primary heaters and 
 
 jacket pumps 
 
 Feed-water, pumps to boilers 
 
 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 
 
 Cylinder oil, low pressure 
 
 Engine oil 
 
 Pneumatic system 
 
 
 Bands, Cou- 
 
 Colors of Pipe. 
 
 plings, Valves, 
 
 
 etc. 
 
 Black 
 
 Brass 
 
 Buff 
 
 Black 
 
 Orange 
 
 Red 
 
 Orange 
 
 Black 
 
 Green 
 
 Black 
 
 Slate 
 
 Red 
 
 Dark Brown 
 
 Blue 
 
 Blue 
 
 Red 
 
 Maroon 
 
 Same 
 
 Green 
 
 Red 
 
 Slate 
 
 Black 
 
 Blue 
 
 Black 
 
 Vermilion 
 
 Same 
 
 Brown 
 
 Black 
 
 Brown 
 
 Green 
 
 Brown 
 
 Red 
 
 Black 
 
 Same 
 
 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 lbs. of water of a temperature of 100° F. into 
 steam at 70 lbs. 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 lbs. of water evaporated per hour being con- 
 sidered to be the steam requirement per indicated horse-power of an 
 average engine. 
 
 The second definition of the term horse-power is an approximate measure 
 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 individual 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 
 
STEAM-BOILER PROPORTIONS. 855 
 
 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. S. M. E., vol. vii, p. 226.) 
 
 The Committee of Judges of the Centennial Exhibition, 1876, in report- 
 ing the trials of competing boilers at that exhibition adopted the unit, 
 30 lbs. of water evaporated into dry steam per hour from feed-water at 
 100° F., and under a pressure of 70 lbs. 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 lbs. evaporated per hour from a 
 feed-water temperature of 212° into steam at the same temperature; 
 The committee of 1899 adopted this definition, 34.5 lbs. per hour, from 
 and at 212°, as the unit of commercial horse-power. Using the figures 
 for total heat of steam given in Marks and Davis's steam tables (1909), 
 34V2 lbs. from and at 212°, is equivalent to 33,479 B.T.U. per hour, or to 
 an evaporation of 30.018 lbs. from 100° feed-water temperature into 
 steam at 70 lbs. pressure. 
 
 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 required to raise 1 lb. of 
 water 1° F. between 32° and 212°. 
 
 Measures for Comparing the Duty of Boilers. — The measure of 
 the efficiency of a boiler is the number of pounds of water evaporated per 
 pound of combustible (coal less moisture and ash), the evaporation being 
 reduced to the standard of "from and at 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 oi 341/2 
 lbs. 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-BOELER 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 lbs. of water from and at 212° F. 
 
 Average proportions for maximum economy for land boilers fired with 
 good anthracite coal: 
 
 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 lbs. 
 
 Combustible burned per H.P. per hour 3 
 
 Coal with 1/6 refuse, lbs. per H.P. per hour 3.6 " 
 
 Combustible burned per sq. ft. grate per hour 9 
 
 Coal with i/e refuse, lbs. per sq. ft. grate per hour 10.8 " 
 
 Water evap'd from and at 212° per lb. combustible ... 11.5 " 
 Water evap'd from and at 212° per lb. coal (1/6 refuse) 9.6 " 
 
856 THE STEAM-BOILER. 
 
 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 lbs. 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 flow 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 lbs. 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 lbs. 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 lbs. 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 . f t . heating-surface 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 very 
 great, causing a serious loss of economy. This 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, 
 the external diameter 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- 
 sistance 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 of 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 hozizontal 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 
 
STEAM-BOILER PROPORTIONS. 
 
 857 
 
 by their common length; to the sum of 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 Bating. 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 from the following table: 
 
 
 a!" 
 
 
 Pounds of Coal burned per square 
 
 
 ■** s 
 
 — < P-* 3 
 
 foot of Grate per hour. 
 
 
 
 |«i 
 
 
 
 8 
 
 10 12 1 15 20 25 I 30 | 35 1 40 
 
 
 
 aj 4> ® 
 
 
 1 1 1 1 1 1 1 
 
 
 
 
 A 
 
 y! 
 
 Sq. Ft. Grate per H. P. 
 
 Good coal and 
 
 no 
 
 3.45 
 
 .43 
 
 .35 
 
 .28 
 
 .23 
 
 .17 
 
 .14 
 
 .11 
 
 .10 
 
 .09 
 
 boiler, 
 
 1 9 
 
 3.83 
 
 .48 
 
 .38 
 
 .32 
 
 .25 
 
 .19 
 
 .15 
 
 .13 
 
 .11 
 
 .10 
 
 
 ( 8.61 
 
 4. 
 
 .50 
 
 .40 
 
 .33 
 
 .26 
 
 .20 
 
 .16 
 
 .13 
 
 .12 
 
 .10 
 
 Fair coal or boiler, 
 
 8 
 
 4.31 
 
 .54 
 
 .43 
 
 .36 
 
 .29 
 
 .22 
 
 .17 
 
 .14 
 
 .13 
 
 .11 
 
 
 I 7 
 
 4.93 
 
 .62 
 
 .49 
 
 .4! 
 
 .33 
 
 .24 
 
 .20 
 
 .17 
 
 .14 
 
 .12 
 
 
 ( 6.9 
 
 5. 
 
 .63 
 
 .50 
 
 .42 
 
 .34 
 
 .25 
 
 .20 
 
 .17 
 
 .15 
 
 .13 
 
 Poor coal or boiler, 
 
 6 
 
 5.75 
 
 .72 
 
 .58 
 
 .48 
 
 .38 
 
 .29 
 
 .23 
 
 .19 
 
 .17 
 
 .14 
 
 
 ( 5 
 
 6.9 
 
 .86 
 
 .69 
 
 .58 
 
 .46 
 
 .35 
 
 .28 
 
 .23 
 
 .22 
 
 .17 
 
 Lignite and poor 
 boiler, 
 
 1 345 
 
 10. 
 
 1.25 
 
 1.00 
 
 .83 
 
 .67 
 
 .50 
 
 .40 
 
 .33 
 
 .29 
 
 .25 
 
 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 lbs. per square foot of grate for anthracite, and 15 lbs. 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. 
 
858 THE STEAM-BOILER, 
 
 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 grates-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 lbs. 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 lbs., 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 lbs. 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. 
 
 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, or 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. 
 
 A formula expressing the relation between capacity, rate of driving, or 
 evaporation per square foot of heating-surface, to the economy, or evapo- 
 ration per pound of combustible is given on page 865. 
 
 Selecting the highest results obtained at different rates of driving with 
 anthracite coal in the Centennial tests (see p. 867), 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, 
 
PERFORMANCE OF BOILERS. 859 
 
 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 S 
 
 Lbs. water evaporated from and at 212° per lb. 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 of 
 driving as well as do the three lines of figures given above. 
 
 For semi-bituminous and bituminous coals the relation of economy to 
 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 lbs. per sq. ft. of 
 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 lbs. of water evaporated per square foot of heating-surface per hour 
 differs greatly with different boilers, and with the same boiler it may differ 
 with different settings and with different coal. The arrangement and size 
 of the gas-passages seem to have an important effect upon the relation of 
 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 of 
 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 5 and 
 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 of 
 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 of CO, and therefore imperfect combustion. The latter, if exces- 
 sive, is indicated by low furnace temperature. The analysis for C0 2 should 
 be made both of the gas sampled just beyond the furnace and of the gas 
 sampled at the flue. Diminished CO2 in the latter indicates air-leakage. 
 
 Less than 5% 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 
 
860 THE STEAM-BOILER. 
 
 stated, and should be p. evented by stopping all visible cracks in the brick- 
 work, and by covering it with a coating impervious to air. 
 
 Autographic C0 2 Recorders are used in many large boiler plants for 
 the continuous recording of the percentage of carbon dioxide in the gases. 
 When the percentage of C0 2 is between 12 and 16, it indicates good fur- 
 nace conditions, when below 12 the reverse. 
 
 Efficiency of a Steam-boiler. — The efficiency of a boiler is the 
 percentage of the total heat generated by the comoustion 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 
 -5- 970 = 15.26 lbs. of water. A boiler which when tested with anthra- 
 cite coal shows an evaporation of 12 lbs. of water per lb. of combustible, 
 has an efficiency of 12 -*- 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 have 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 
 
 Hydrogen 4 . 50 
 
 Oxygen 2.70 
 
 Nitrogen 1.08 
 
 Moisture 2.92 
 
 Ash 8.25 
 
 c. 
 
 O. 
 
 C0 2 = 13.6 = 3.71 
 
 9.89 
 
 CO = 0.2 = 0.09 
 
 0.11 
 
 O = 11.2 = 
 
 11.20 
 
 N = 75.0 = 
 
 
 100.00 
 
 21.20 75.00 
 
 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 -h 3.8 = 26.32 lbs. 
 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 7S.55 -s- 100 = 20.67 
 lbs. 
 
 Each pound of coal furnishes to the dry chimney-gases 0.7855 lb. C, 
 
 0.0108 N, and (2.70- ^p) -*■ 100 = 0.0214 lb. O; a total of 0.8177, say 
 
 0.82 lb. This subtracted from 20.67 lbs. leaves 19.85 lbs. 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 requires 
 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% bv weight of 
 oxygen) is 0,333 -s- 0.23 = 1.45 lb., which added to the 19.85 lbs. already 
 
PERFORMANCE OF BOILERS. 861 
 
 found gives 21.30 lbs. 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= 0.151b. for each lb. of coal. Eacli lb. of coal 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 1b. of H 2 0. 
 
 From the analysis of the chimney-gas it appears that 0.09. -f- 3.80 = 
 2.37% of the carbon in the coal was burned to CO instead of to CO2. 
 
 We now have the data for calculating -the various losses of heat, as 
 follows, for each pound of coal burned: 
 
 20.67 lbs. dry gas X (560° - 60°) X sp. heat 0.24 = 
 . 0.15 lb. vapor in air X (560° - 60°) X sp. ht. 0.4S -■ 
 . 029 lb. moist, in coal heated from 60° to 212° = 
 0.0291b. evap. from and at 212°; 0.029 X 966 
 . 029 lb. steam (heated 212° to 560°) X348 X 0.48 = 
 0.405 lb. H2O from H in coal X (152 + 966 + 
 
 348 X 0.48) 
 0.0237 lb. C burned to CO; loss by incomplete 
 
 combustion, 0.0237 X (14544- 4451) 
 0.02 lb. coal lost in ashes: 0.02 X 14544 
 Radiation and unaccounted for, by difference 
 
 Utilized in making steam, equivalent evapora- 
 tion 10.37 lbs. from and at 212° per lb. of coal ■ 
 
 Heat- 
 units. 
 
 Per cent of 
 Heat -value 
 of the Coal. 
 
 2480 . 4 
 36.0 
 
 4.4 
 28.0 
 
 4.8 
 
 17.41 
 0.25 
 0.03 
 0.20 
 0.03 
 
 520.4 
 
 3.65 
 
 239.2 
 290.9 
 624.0 
 
 1.68 
 2.04 
 4.38 
 
 4228.1 
 
 29.69 
 
 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' 
 duration. 
 
 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 4 per cent. 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 
 62,000 heat-units. Another sourceof error, especiall v with bituminous slack 
 coal hi°:h in moisture, is due to the formation of water-gas, CO - 1 - H, by the 
 decomposition of the water, end the consequent absorption of heat, this 
 water-gas ecaping unbumed 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 
 
862 THE STEAM-BOILER. 
 
 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 01 
 combustion: 
 
 Lbs. of air required to burn) _ 3.032 N 
 one pound of carbon J CO2 + CO 
 
 N 
 Ratio of total air to the theoretical requirement =- 
 
 N- 3.782 O 
 
 Lbs. of air per pound ) _ J Lbs. of air per pound \ y I Per cent of carbon 
 of coal J 1 of carbon J I in coal 
 
 TU , , , , , HC0 2 +80 + 7(CO + N) 
 
 Lbs. dry gas produced per pound of carbon = „ ,-„ — , ~' ■ 
 
 6 (OU2 -r OUJ 
 
 Relation of Boiler Efficiency to the Rate of Driving, Air Supply, 
 etc. — ■ In the author's Steam Boiler Economy (p. 205) a formula is 
 developed showing the efficiency that may be expected, when the com- 
 bustion of the coal is complete, under different conditions. The formula is 
 
 E a K - tcf 970 ac*f* W_ 
 
 E p ~ K (1 + RS/W) K (K - tcf) S ' 
 
 K = heating value per lb. of combustible; E a = actual evaporation from 
 and at 212° per lb. of combustible; E p = possible evaporation = K -f- 
 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 lb. 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 
 
 K- tcf 1 . c*P W 
 
 L970 (1 + RS/W) a \ ' {K- tcf) S ' 
 
 On the diagram below (Fig. 148), 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 / 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; t= 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 
 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 efnciencv for maximum performance, 
 according to the curve, is a little less than 82% at 2 lbs. evaporation per 
 sq. ft. of heating-surface per hour, but it decreases very slowly at higher 
 rates, so that it is 80% at 31/2 lbs., and 76% at 53/ 4 lbs. 
 
 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 /. 
 Excessive air supply is thus shown to be a most potent cause of low 
 .economy. 
 
 «=[«- 
 
PERFORMANCE OF BOILERS. 
 
 863 
 
 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. 152, are plotted, together with the curve for /=20, 
 a= 200, £=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 
 
 84 
 
 
 
 
 
 
 
 
 
 '+" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _£_ 
 
 -300 
 
 Jfi-20 
 
 2 
 
 
 
 80 
 
 78 
 76 
 74 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -. 
 
 
 
 
 
 1 
 
 
 
 
 
 
 , 
 
 , 
 
 
 
 
 # 
 
 
 
 
 fT 
 
 
 
 
 
 
 
 ~s~ 
 
 
 
 
 
 - 
 
 --£% 
 
 
 
 
 
 
 
 
 
 
 
 
 *s< 
 
 
 
 
 -i. 
 
 ^-L. 
 
 
 
 '~- 
 
 -^ 
 
 
 s 
 
 
 
 
 
 
 -^ 
 
 
 
 '-c 
 
 
 *y^ 
 
 
 
 
 't 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ... 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 ■> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J 
 
 72 
 70 
 68 
 66 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 "-C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4\ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 **« 
 
 ^ 
 
 
 
 
 M. 
 
 ercjj - ^ 
 
 <f 
 
 
 
 
 64 
 62 
 
 £60 
 
 
 
 
 
 
 
 
 
 N, 
 
 k 
 
 
 
 
 
 
 -> 
 
 Vj 
 
 tog 
 
 ei 
 
 3 &\ 
 
 RJ 
 
 1 ;- 
 
 
 
 ■«S 
 
 ^ 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v ~ 
 
 
 ^ 
 
 ^ 
 
 *o 
 
 *"> 
 
 
 sQ 
 
 
 0o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 «* 
 
 
 
 
 
 
 
 
 ^56 
 
 P.54 
 
 £52 
 
 fl 50 
 
 •§48 
 
 6 46 
 
 W 44 
 
 42 
 
 40 
 
 38 
 
 36 
 
 34 
 
 32 
 
 30 
 
 28 
 
 26 
 
 24 
 
 22 
 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <>■ 
 
 
 
 
 
 ^^> 
 
 fb 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 :j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y ■ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 " 
 
 
 
 
 
 
 
 F 
 
 = 
 
 F 
 
 i - 
 
 iei 
 
 ic 
 
 l 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 L 
 
 == 
 
 Low 
 
 e 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R 
 
 ~ 
 
 lioot 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 B 
 
 = 
 
 Babcoc 
 
 k( 
 
 fcl 
 
 Vi 
 
 co 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 
 
 = 
 
 Smith 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 G( 
 
 
 - Gallon 
 
 "' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 & 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 2 3 4 5 6 '7-8 
 
 Lbs. of Water Evaporated from and at 212° F. per sq. ft. of Heating Surface per Hour 
 
 ' — ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 *-. 
 
 
 £w„- 
 
 
 
 
 
 
 
 
 
 
 
 
 „, " 
 
 
 Jin 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 e^?«< 
 
 ■Or 
 
 
 
 
 
 
 
 
 
 s'' 
 
 
 ^.r 
 
 -<{«* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <iJSj j 
 
 J <°v 
 
 
 
 
 
 
 
 
 **t p c 
 
 
 
 
 
 ■<5r* 
 
 
 
 
 
 
 
 
 
 utG *v 
 
 >-^ 
 
 o-iK 
 
 
 
 
 ,.., 
 
 
 
 
 
 
 
 
 2e s 
 
 ^r*" 1 
 
 "^O 
 
 -^ 
 
 
 ^%e 
 
 -0 
 
 
 
 
 
 
 lornyc 
 
 oftrTe 
 
 
 
 ^ "~~ 
 
 
 ■^-~~c 
 
 &L; 
 
 
 
 
 
 
 
 
 ""v^ 
 
 34 
 
 
 ^r^ter 
 
 
 
 o- 
 
 — oJJ 
 
 abcock & Wi 
 
 coxTc 
 
 sts 
 
 
 ^x 
 
 6 
 
 1 ^ 
 
 
 „ 
 
 
 
 1 1 1 
 
 
 
 
 1 
 
 
 ko' 
 
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 
 
 Lbs. of Water Evaporated from and at 212° F, per sq. ft-, of Heating Surface per Hour 
 
 radiation, and 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 boiler with W/S from 5.18 to 13.67, together with the 
 
864 
 
 THE STEAM-BOILER. 
 
 maximum Centennial tests. The calculated value of a in all these tests 
 except one ranged from 191 to 454, the highest values being those showing 
 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. 
 
 TESTS OF STEAM-BOILERS. 
 
 Boiler-tests at the Centennial Exhibition, Philadelphia, 1876. — 
 
 (See Reports and Awards Group XX, International Exhibition, Phila., 
 1376; also, Clark on the Steam-engine, vol. i, page 253.) 
 
 Competitive tests were made of fourteen boilers, using good anthracite 
 coal, one boiler, the Galloway, being tested with both anthracite and semi- 
 bituminous coal. Two tests were made with each boiler: one called the 
 capacity trial, to determine the economy and capacity at a rapid rate of 
 driving; and the other called the economy trial, to determine the economy 
 when driven at a rate supposed to be near that of maximum economy and 
 rated capacity. The following table gives the principal results obtained 
 in the economy trial, together with the capacity and economy figures of 
 the capacity trial for comparison. 
 
 
 Economy Tests. 
 
 Capacity 
 
 Tests. 
 
 
 3 O 
 
 £ 
 
 03 
 3 
 
 
 Is* 
 
 i 
 
 
 d 
 
 
 
 1 = 
 
 Name of Boiler. 
 
 • - ~ 
 7 ^ 
 
 o 1 
 
 u ^ 
 
 7"f 
 
 (8 
 .3 
 
 -x 
 ft x 
 
 03 • 
 
 Si? « 
 
 m 
 
 s 
 
 .5 
 
 3 
 
 1 
 
 1 
 
 SB 
 
 
 % 
 
 So 
 
 o 
 $1 
 
 
 o3 - 
 
 
 
 > ft 
 
 >~ o3 
 
 
 
 c3 
 
 
 
 > S 
 
 
 - 1 
 
 '" 03 
 
 -. •-„ 
 
 o3 
 
 o 
 
 P4 
 
 
 
 ft 
 
 s 
 
 03 
 
 3 
 
 "o 
 
 03 
 
 ft 
 A 
 
 o 
 
 W 
 
 ft 
 4 
 
 o 
 W 
 
 Sal 
 
 
 
 lbs. 
 
 % 
 
 lbs. 
 
 lbs. 
 
 ,!f>"' 
 
 % 
 
 iles- 
 
 H.P. 
 
 H.P. 
 
 lbs. 
 
 
 H4 6 
 
 9 1 
 
 10 i 
 
 ; ->S 
 
 12.094 
 
 -i'4H 
 
 
 4! 4 
 
 119 8 
 
 
 
 
 64 3 
 
 Y' n 
 
 10 ,1 
 
 1 fifi 
 
 11.988 
 
 415 
 
 
 3? 6 
 
 57 8 
 
 
 11 064 
 
 
 30 6 
 
 6 8 
 
 1 1 3 
 
 1 87 
 
 11.923 
 
 333 
 
 
 9 4 
 
 47 
 
 
 11 163 
 
 Smith 
 
 45.8 
 
 17 1 
 
 11.1 
 
 > 4 ;> 
 
 11.906 
 
 411 
 
 1 3 
 
 
 99 8 
 
 125 
 
 11 925 
 
 Babcock & Wilcox . 
 
 37.7 10.0 
 
 11.0 2.43 
 
 11.822 
 
 296 
 
 2 7 
 
 
 135.6 
 
 186.6 
 
 10.330 
 
 
 n 7 
 
 M 6 
 
 11 1 
 
 =1 63 
 
 1 1 . 583 
 
 '403 
 
 
 1 4 
 
 103 3 
 
 133 8 
 
 11 216 
 
 Do. semi-bit. coal. 
 
 23.7 
 
 7.9 
 
 8 8 
 
 3 20 
 
 12.125 
 
 325 
 
 3 
 
 
 <0.9 
 
 125.1 
 
 11.609 
 
 Andrews 
 
 15 6 
 
 « n 
 
 10 3 
 
 ? 3? 
 
 11.039 
 
 4WI 
 
 
 71 7 
 
 42 6 
 
 58 7 
 
 9.745 
 
 Harrison 
 
 27.3 
 
 12.4 
 
 8 5 
 
 2 75 
 
 10.930 
 
 517 
 
 9 
 
 
 82.4 
 
 108.4 
 
 9.889 
 
 
 30 7 
 
 1? s 
 
 o >i 
 
 3 30 
 
 10 834 
 
 5?4 
 
 
 ^0 5 
 
 147 5 
 
 162 8 
 
 9 145 
 
 Anderson 
 
 17 5 
 
 9 7 
 
 9 3 
 
 ?, 64 
 
 10.618 
 
 417 
 
 
 15 7 
 
 98 
 
 132 8 
 
 9.568 
 
 Kelly 
 
 ?o 9 
 
 10 8 
 
 Q 
 
 3 8? 
 
 10 312 
 
 
 5 6 
 
 
 81 
 
 99 9 
 
 8 397 
 
 Exeter. , 
 
 33 5 
 
 9 3 
 
 11 4 
 
 1 38 
 
 10.041 
 
 430 
 
 4 7 
 
 
 72.1 
 
 108.0 
 
 9.974 
 
 Pierce 
 
 14 o 
 
 8 n 
 
 11 
 
 4 44 
 
 10.021 
 
 374 
 
 5 ? 
 
 
 51.7 
 
 67.8 
 
 9.865 
 
 Rogers & Black. . . . 
 
 19.0 
 
 8.6 
 
 9.9 
 
 3.43 
 
 9.613 
 
 572 
 
 2.1 
 
 
 45.7 
 
 67.2 
 
 9.429 
 
 Averages 
 
 
 
 
 2.77 
 
 11.123 
 
 
 
 
 85.0 
 
 110.8 
 
 10.251 
 
 The comparison of the economy and capacity trials shows that an 
 average increase in capacity of 30 per cent was attended by a decrease in 
 economy of 8 per cent, but the relation of economy to rate of driving 
 varied greatly in the different boilers. In the Kelly boiler an increase in 
 capacity of 22 per cent was attended by a decrease in economy of -over 
 18 per cent, while the Smith boiler with an increase of 25 per cent in capac- 
 ity showed a slight increase in economy. 
 
 One of the most important lessons gained from the above tests is that 
 there is no necessary relation between the type of a boiler and economy, 
 
TESTS OF STEAM-BOILEES. 865 
 
 Of the five boilers that gave the best results, the total range of variation 
 between the highest and lowest of the five being only 2.3%, three were 
 water-tube boilers, one was a horizontal tubular boiler, and the fifth was 
 a combination of the two types. The next boiler on the list, the Gallo- 
 way, was an internally fired boiler, all of the others being externally 
 fired. 
 
 Some High Rates of Evaporation. — Eng'g, May 9, 1884, p. 415. 
 
 Locomotive. Torpedo-boat. 
 
 Water evap. per sq. ft. H.S. per hour 12.57 13.73 12.54 20.74 
 
 Water evap. per lb. fuel from and at 212° 8.22 8.94 8.37 7.04 
 Thermal units transfd 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 priming. 
 
 Economy Effected by Heating the Air Supplied to Boiler-furnaces. 
 
 — An extensive series of experiments was made by J. C. Hoadley (Trans. 
 A. S. M. E., vi, 676) on a "Warm-blast Apparatus," for utilizing the heat 
 of the waste gases in heating the air supplied to the furnace. The appara- 
 tus, as applied to an ordinary horizontal tubular boiler 60 in. diameter, 
 21 ft. long, with 65 3V2-in. tubes, consisted of 240 2-in. tubes, 18 ft. long, 
 through which the hot gases passed while the air circulated around them. 
 The net saving of fuel effected by the warm blast was from 10.7% to 15.5% 
 of the fuel used with cold blast. The comparative temperatures averaged 
 as follows, in degrees F.: 
 
 Cold-blast Warm-blast 
 
 In heat of fire 
 
 At bridge wall 
 
 In smoke box 
 
 Air admitted to furnace . . . 
 Steam and water in boiler . 
 Gases escaping to chimney . 
 External air 
 
 Boiler. 
 
 Boiler. 
 
 Difference. 
 
 2493 
 
 2793 
 
 300 
 
 1340 
 
 1600 
 
 260 
 
 373 
 
 375 
 
 2 
 
 32 
 
 332 
 
 300 
 
 300 
 
 300 
 
 
 
 373 
 
 162 
 
 211 
 
 32 
 
 32 
 
 
 
 With anthracite coal the evaporation from and at 212° per lb. combus- 
 tible was, for the cold-blast boiler, days 10.85 lbs., days and nights 10.51; 
 and for the warm-blast boiler, days 11.83, days and nights 11.03. 
 
 Maximum Boiler Efficiency with Cumberland Coal. — About 12.5 
 lbs. of water per lb. combustible from and at 212° is about the highest 
 evaporation that can be obtained from the best steam fuels in the United 
 States, such as Cumberland, Pocahontas, and Clearfield. In exceptional 
 cases 13 lbs. has been reached, and one test is on record (F. W. Dean, 
 Eng'g News, Feb. 1, 1894) giving 13.23 lbs. The boiler was internally 
 fired, of the Belpaire type, 82 inches diameter, 31 feet long, with 160 3-inch 
 tubes 121/2 feet long. Heating-surface, 1998 square feet; grate-surface, 
 45 square feet, reduced during the test to 30 1/2 square feet. Double fur- 
 nace, with fire-brick arches and a long combustion-chamber. Feed- 
 water heater in smoke-box. The following are the principal results: 
 
 1st Test. 2d Test. 
 Dry coal burned per sq. ft. of grate per hour, lbs.. . . 8.85 16.06 
 Water evap. per sq.ft. of heating-surface per hour, lbs. 1.63 3.00 
 Water evap. from and at 212° per lb. combustible, in- 
 cluding feed-water heater 13.17 13.23 
 
 Water evaporated, excluding feed-water heater 12.88 12.90 
 
 Temperature of gases after leaving heater, F 360° 469° 
 
 BOILERS USING WASTE GASES. 
 
 Water-tube Boilers using Blast-furnace Gases. — D. S. Jacobus 
 (Trans. A. I. 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 lbs. 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 lb. of the gas, 1413 B.T.U., including the effect 
 
866 
 
 THE STEAM-BOILER. 
 
 of its initial temperature, which was 650° F. Amount of air used to bum 
 1 lb. of the gas = 0.9 lb. Chimney draught, 1 V.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: 
 
 
 By Weight. 
 
 By Volume. 
 
 
 At Entrance. 
 
 At Exit. 
 
 At Entrance. 
 
 At Exit. 
 
 co 2 ...... 
 
 10.69 
 .11 
 26.71 
 62.48 
 2.92 
 11.45 
 14.37 
 
 26.37 
 3.05 
 1.78 
 
 68.ro 
 
 7.19 
 0.76 
 7.95 
 
 7.08 
 0.10 
 27.80 
 65.02 
 
 18 64 
 
 o 
 
 2 96 
 
 CO 
 
 1.98 
 
 
 76 42 
 
 CinC0 2 
 
 
 C in CO . „ 
 
 
 
 Total C 
 
 
 
 
 
 
 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, lbs 3358 2159 1812 3055 
 
 Water evap. per sq. ft. H.S. per hr., lbs 3.3 1.8 12.7 2.2 
 
 Water evap. per lb. coal from and at 212° . . . 5.9 6.24 3.76 6.34 
 Water evap. per lb. comb, from and a t 212° 7.20 4.31 8.34 
 
 In No. 2, 1.38 lbs. of iron were puddled per lb. of coal. 
 In No. 3, 1.14 lbs. of iron were puddled per lb. of coal. 
 No. 3 shows that an insufficient amount of heating-surface was provided 
 for the amount of waste heat available. 
 
 RULES FOR CONDUCTING BOILER-TESTS. 
 
 Code of 1899. 
 
 (Reported by the Committee on Boiler Trials, Am. Soc. M. E.*) 
 
 I. Determine at the outset the specific object of the proposed trial, 
 whether it be to ascertain the capacity of the boiler, its efficiency as a 
 steam-generator, its efficiency and its defects under usual working condi- 
 tions, the economy of some particular kind of fuel, or the effect of changes 
 of design, proportion, or operation; and prepare for the trial accordingly. 
 
 II. Examine the boiler, both outside and inside; ascertain the dimensions 
 of grates, heating surfaces, and all important parts; and make a full 
 record, desrribin? the same, and illustrating special features by sketches. 
 
 III. Notice the general condition of the boiier and its equipment, and 
 record such facts in relation thereto as bear upon the objects in view. 
 
 * The code is here slightly abridged. The complete report of the 
 Committee may be obtained in pamphlet form from the Secretary of the 
 American Society of Mechanical Engineers, 29 West 39th St., New York. 
 
RULES FOR CONDUCTING BOILER-TESTS. 867 
 
 If the object of the trial is to ascertain the maximum economy or capac- 
 ity of the boiler as a steam-generator, the boiler and all its appurtenances 
 should be put in first-class condition. Clean the heating surface inside 
 and outside, remove clinkers from the grates and from the sides of the 
 furnace. Remove all dust, soot, and ashes from the chambers, smoke- 
 connections and flues. Close air-leaks in the masonry and poorly fitted 
 cleaning-doors. See that the damper will open wide and close tight. 
 Test for air-leaks by firing a few shovels of smoky fuel and immediately 
 closing the damper, observing the escape of smoke through the crevices; 
 or by passing the flame of a candle over cracks in the brickwork. 
 
 IV. Determine the character of the coal to be used. For tests of the 
 efficiency or capacity of the boiler for comparison with other boilers the 
 coal should, if possible, be of some kind which is commercially regarded 
 as a standard. For New England and that portion of the country east 
 of the Allegheny Mountains, good anthracite egg coal, containing not 
 over 10 per cent of ash, and semi-bituminous Clearfield (Pa.), Cumberland 
 (Md.), and Pocahontas (Va.) coals are thus regarded. West of the Alle- 
 gheny Mountains, Pocahontas (Va.) and New River (W. Va.) semi-bitu- 
 minous, and Youghiogheny or Pittsburg bituminous coals are recognized 
 as standards.* 
 
 For tests made to determine the performance of a boiler with a partic- 
 ular kind of coal, such as may be specified in a contract for the sale of a 
 boiler, the coal used should not be higher in ash and in moisture than that 
 specified, since increase in ash and moisture above a stated amount is 
 apt to cause a falling off of both capacity and economy in greater propor- 
 tion than the proportion of such increase. 
 
 V. Establish the correctness of all apparatus used in the test for weighing 
 and measuring. These are: 
 
 1. Scales for weighing coal, ashes, and water. 
 
 2. Tanks or water-meters for measuring water. Water-meters, as a 
 rule, should only be used as a check on other measurements. For accu- 
 rate work the water should be weighed or measured in a tank. 
 
 3. Thermometers and pyrometers for taking temperatures of air, steam, 
 feed-water, waste gases, etc. 
 
 4. Pressure-gauges, draught-gauges, etc. 
 
 VI. See that the boiler is thoroughly heated before the trial to its usual 
 working temperature. If the boiler is new and of a form provided with a 
 brick setting, it should be in regular use at least a week before the trial, 
 so as to dry and heat the walls. If it has been laid off and become cold, 
 it should be worked before the trial until the walls are well heated. 
 
 VII. The boiler and connections should be proved to be free from leaks 
 before beginning a test, and all water connections, including blow and 
 extra feed-pipes, should be disconnected, stopped with blank flanges, or 
 bled through special openings beyond the valves, except the particular 
 pipe through which water is to be fed to the boiler during the trial. During 
 the test the blow-off and feed pipes should remain exposed to view. 
 
 If an injector is used, it should receive steam directly through a felted 
 pipe from the boiler being tested.! 
 
 If the water is metered after it passes the injector, its temperature 
 should be taken at the point where it leaves the injector. If the quan- 
 tity is determined before it goes to the injector, the temperature should 
 be determined on the suction side of the injector, and if no change of 
 
 * These coals are selected because they are about the only coals which 
 possess the essentials of excellence of quality, adaptability to various 
 kinds of furnaces, grates, boilers, and methods of firing, and wide distribu- 
 tion and general accessibility in the markets. 
 
 t In feeding a boiler undergoing test with an injector taking steam from 
 another boiler, or from the main steam-pipe from several boilers, the evap- 
 orative results may be modified by a difference in the quality of the steam ■ 
 from such source compared with that supplied by the boiler being tested, 
 and in some cases the connection to the injector may act as a drip for the 
 main steam-pipe. If it is known that the steam from the main pipe is of 
 the same pressure and quality as that furnished by the boiler undergoing 
 the test, the steam may be taken from such main pipe. 
 
868 THE STEAM-BOILER. 
 
 temperature occurs other than that due to the injector, the temperature 
 thus determined is properly that of the feed-water. When the temper- 
 ature changes between the injector and the boiler, as by the use of a 
 heater or by radiation, the temperature at which the water enters and 
 leaves the injector and that at which it enters the boiler should all t>^ taken. 
 In that case the weight to be used is tnat of the water leaving theu.jector, 
 computed from the heat units if not directly measured; and the tem- 
 perature, that of the water entering the boiler. 
 
 Let w = weight of water entering the injector; 
 x = weight of steam entering the injector; 
 hi= heat-units per pound of water entering injector; 
 h2= heat-units per pound of steam entering injector; 
 hz = heat-units per pound of water leaving injector. 
 
 Then w + x = weight of water leaving injector; 
 
 _ hi — hi 
 hi — h% 
 
 See that the steam-main is so arranged that water of condensation 
 cannot run back into the boiler. 
 
 VIII. Duration of the Test. — For tests made to ascertain either the 
 maximum economy or the maximum capacity of a boiler, irrespective of 
 the particular class of service for which it is regularly used, the duration 
 should be at least ten hours of continuous running. If the rate of com- 
 bustion exceeds 25 pounds of coal per square foot of grate-surface per 
 hour, it may be stopped when a total of 250 pounds of coal has been 
 burned per square foot of grate. 
 
 IX. Starting and Stopping a Test. — The conditions of the boiler and 
 furnace in all respects should be, as nearly as possible, the same at the end 
 as at the beginning of the test. The steam-pressure should be the 
 same; the water-level the same; the fire upon the grates should be the 
 same in quantity and condition; and the walls, flues, etc., should be of 
 the same temperature. Two methods of obtaining the desired equality 
 of conditions of the fire may be used, viz., those which were called in the 
 Code of 1885 "the standard method" and "the alternate method," the 
 latter being employed where it is inconvenient to make use of the stand- 
 ard method.* 
 
 X. Standard Method of Starting and Stopping a Test. — Steam being 
 raised to the working pressure, remove rapidly all the fire from the grate, 
 close the damper, clean the ash-pit, and as quickly as possible start a new 
 fire with weighed wood and coal, noting the time and the water-level, 
 while the water is in a quiescent state, just before lighting the fire.f 
 
 At the end of the test remove the whole fire, which has been burned low, 
 clean the grates and ash-pit, and note the water-level when the water is 
 in a quiescent state, and record the time of hauling the fire. The water- 
 level should be as nearly as possible the same as at the beginning of the 
 test. If it is not the same, a correction should be made by computation, 
 and not by operating the pump after the test is completed. 
 
 XI. Alternate Method of Starting and Stopping a Test. — The boiler 
 being thoroughly heated by a preliminary run, the fires are to be burned 
 low and well cleaned. Note the amount of coal left on the grate as nearly 
 as it can be estimated; note the pressure of steam and the water-level. 
 Note the time, and record it as the starting-time. Fresh coal which has 
 
 * The Committee concludes that it is best to retain the designations 
 "standard" and "alternate," since they have become widely known and 
 established in the minds of engineers and in the reprints in the Code of 
 1885. Many engineers prefer the "alternate" to the "standard" method 
 on account of its being less liable to error due to cooling of the boiler at the 
 . beginning and end of a test. 
 
 t The gauge-glass should not be blown out within an hour before the 
 water-level is taken at the beginning and end of a test, otherwise an 
 error in the reading of the water-level may be caused by a change in the 
 temperature and density of the water in the pipe leading from the bottom 
 of the glass into the boiler. 
 
RULES FOR CONDUCTING BOILER-TESTS. 869 
 
 been weighed should now be fired. The ash-pits should be thoroughly 
 cleaned at once after starting. Before the end of the test the fires should 
 be burned low, just as before the start, and the fires cleaned in such a 
 manner as to leave a bed of coal on the grates of the same depth, and in 
 the same condition, as at the start. When this stage is reached, note the 
 time and record it as the stopping-time. The water-level and steam- 
 pressures should previously be brought as nearly as possible to the same 
 point as at the start. If the water-level is not the same as at the start, a 
 correction should be made by computation, and not by operating the 
 pump after the test is completed. 
 
 XII. Uniformity of Conditions. — In all trials made to ascertain max- 
 imum economy or capacity the conditions should be maintained uni- 
 formly constant. Arrangements should be made to dispose of the steam 
 so that the rate of evaporation may be kept the same from beginning to 
 end. 
 
 XIII. Keeping the Records. — Take note of every event connected with 
 the progress of the trial, however unimportant it may appear. Record 
 the time of every occurrence and the time of taking every weight and 
 every observation. 
 
 The coal should be weighed and delivered to the fireman in equal propor- 
 tions, each sufficient for not more than one hour's run, and a fresh portion 
 should not be delivered until the previous one has all been fired. The 
 time required to consume each portion should be noted, the time being 
 recorded at the instant of firing the last of each portion. It is desirable 
 that at the same time the amount of water fed into the boiler should be 
 accurately noted and recorded, including the height of the water in the 
 boiler, and the average pressure of steam and temperature of feed during 
 the time. By thus recording the amount of water evaporated by succes- 
 sive portions of coal, the test may be divided into several periods if desired, 
 and the degree of uniformity of combustion, evaporation, and economy 
 analyzed for each period. In addition to these records of the coal and 
 the feed-water, half-hourly observations should be made of the tem- 
 perature of the feed-water, of the flue-gases, of the external air in the 
 boiler-room, of the temperature of the furnace when a furnace-pyrometer 
 is used, also of the pressure of steam, and of the readings of the instru- 
 ments for determining the moisture in the steam. A log should be kept 
 on properly prepared blanks containing columns for record of the various 
 observations. 
 
 XIV. Quality of Steam. — The percentage of moisture in the steam 
 should be determined by the use of either a throttling or a separating 
 steam-calorimeter. The sampling-nozzle should be placed in the vertical 
 steam-pipe rising from the boiler. It should be made of 1/2-inch pipe, 
 and should extend across the diameter of the steam-pipe to within half 
 an inch of the opposite side, being closed at the end and perforated with 
 not less than twenty 1/8-inch holes equally distributed along and aroun-l 
 its cylindrical surface, but none of these holes should be nearer than 1/2 inch 
 to the inner side of the steam-pipe. The calorimeter and the pipe leading 
 to it should be well covered with felting. Whenever the indications of the 
 throttling or separating calorimeter show that the percentage of moisture 
 is irregular, or occasionally in excess of three per cent, the results should 
 be checked by a steam-separator placed in the steam-pipe as close to the' 
 boiler as convenient, with a calorimeter in the steam-pipe just beyond 
 the outlet from the separator. The drip from the separator should be 
 caught and weighed, and the percentage of moisture computed therefrom 
 added to that shown by the calorimeter. 
 
 Superheating should be determined by means of a thermometer placed 
 • in a mercury-weil inserted in the steam-pipe. The degree of superheating 
 should be taken as the difference between the reading of the thermometer 
 for superheated steam and the readings of the same thermometer for 
 saturated steam at the same pressure as determined by a special experi- 
 ment, and not by reference to steam-tables. 
 
 XV. Sampling the Coal and Determining its Moisture. — As each 
 barrow-load or fresh portion of coal is taken from the coal-pile, a repre- 
 sentative shovelful is selected from it and placed in a barrel or box in a 
 cool place and kept until the end of the trial. The samples are then mixed 
 and broken into pieces not exceeding one inch in diameter, and reduced 
 by the process of repeated quartering and crushing until a final sample 
 
870 THE STEAM-BOILER. 
 
 weighing about five pounds is obtained, and the size of the larger pieces 
 is such that they will pass through a sieve with 1/4-inch meshes. From 
 this sample two one-quart, air-tight glass preserving-jars, or other air-tight 
 vessels which will prevent the 'escape of moisture from the sample, are 
 to be promptly filled, and these samples are to be kept for subsequent 
 determinations of moisture and of heating value and for chemical analyses. 
 During the process of quartering, when the sample has been reduced to 
 about 100 pounds, a quarter to a half of it may be taken for an approxi- 
 mate determination of moisture. This may be made by placing it in a 
 shallow iron pan, not over three inches deep, carefully weighing it, and 
 setting the pan in the hottest place that can be found on the brickwork 
 of the boiler-setting or flues, keeping it there for at least 12 hours, and 
 then weighing it. The determination of moisture thus made is believed 
 to be approximately accurate for anthracite and semi-bituminous coals, 
 and also for Pittsburg or Youghiogheny coal; but it cannot be relied upon 
 for coals mined west of Pittsburg, or for other coals containing inherent 
 moisture. For these latter coals it is important that a more accurate 
 method be adopted. The method recommended by the Committee for 
 all accurate tests, whatever the character of the coal, is described 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 
 adjusted so as to produce somewhat coarse grains (less than Vie inch), 
 thoroughly mix the crushed sample, select from it a portion of from 10 to 
 50 grams, weigh it in a balance which will easily show a variation as small 
 as 1 part in 1000, and dry it in an air- or sand-bath at a temperature 
 between 240 and 280 degrees Fahr. for one hour. Weigh it and record 
 the loss, then heat and weigh it again repeatedly, at intervals of an hour 
 or less, until the minimum weight has been reached and the weight begins 
 to increase by oxidation of a portion of the coal. The difference between 
 the original and the minimum weight is taken as the moisture in the air- 
 dried coal. This moisture test should preferably be made on duplicate 
 samples, and the results should agree within 0.3 to 0.4 of one per cent, 
 the mean of the two determinations being taken as the correct result. 
 The sum of the percentage of moisture thus found and the percentage of 
 surface moisture previously determined is the total moisture. 
 
 XVI. Treatment of Ashes and Refuse. — The ashes and refuse are to be 
 weighed in a dry state. If it is found desirable to show the principal 
 characteristics of the ash, a sample should be subjected to a proximate 
 analysis and the actual amount of incombustible material determined. 
 For elaborate trials a complete analysis of the ash and refuse should be 
 made. 
 
 XVII. Calorific Tests and Analysis of Coal. — The quality of the fuel 
 should be determined either by heat test or by analysis, or by both. 
 
 The rational method of determining the total heat of combustion is to 
 burn the sample of coal in an atmosphere of oxygen gas, the coal to be 
 sampled as directed in Article XV of this code. 
 
 The chemical analysis of the coal should be made only by an expert 
 chemist. The total heat of combustion computed from the results of 
 the ultimate analysis may be obtained by the use of Dulong's formula 
 (with constants modified by recent determinations), viz., 
 
 14,600 0+62,000 
 
 (-*)- 
 
 in which C, H, O, and S refer to the proportions of carbon, hydrogen, 
 oxygen, and sulphur respectively, as determined by the ultimate analysis.* 
 It is desirable that a proximate analysis should be made, thereby deter- 
 mining the relative proportions of volatile matter and fixed carbon. 
 These proportions furnish an indication of the leading characteristics of 
 the fuel, and serve to fix the class to which it belongs. 
 
 * Favre and Silbermann give 14,544 BT.TT. per pound carbon; Berthe- 
 lot, 14.647 B.T.U. Favre and Silbermann give 62,032 B.T.U. per pound 
 hydrogen; Thomsen, 61,816 B.T.U. 
 
RULES FOR CONDUCTING BOILER-TESTS. 871 
 
 XVIII. Analysis of Flue-gases. — The analysis of the flue-gases is an 
 especially valuable method of determining the relative value of different 
 methods' of firing or of different kinds of furnaces. In making these 
 analyses great care should be taken to procure average samples, since the 
 composition is apt to vary at different points of the flue. The composition 
 is also apt to vary from minute to minute, and for this reason the drawings 
 of gas should last a considerable period of time. Where complete deter- 
 minations are desired, the analyses should be intrusted to an expert 
 chemist. For approximate determinations the Orsat or the Hempel 
 apparatus may be used by the engineer. 
 
 For the continuous indication of the amount of carbonic acid present 
 in the flue-gases an instrument may be employed which shows the weight 
 of CO2 in the sample of gas passing through it. 
 
 XIX. Smoke Observations. — It is desirable to have a uniform system 
 of determining and recording the quantity of smoke produced where 
 bituminous coal is used. The system commonly employed is to express 
 the degree of smokiness by means of percentages dependent upon the 
 judgment of the observer. The actual measurement of a sample of soot 
 and smoke by some form of meter is to be preferred. 
 
 XX. Miscellaneoiis. — In tests for purposes of scientific research, in 
 which the determination of all the variables entering into the test is 
 desired, certain observations should be made which are in general unneces- 
 sary for ordinary tests. As these determinations are rarely undertaken, 
 it is not deemed advisable to give directions for making them. 
 
 XXI. Calculations of Efficiency. — Two methods of defining and calcu- 
 lating the efficiency of a boiler are recommended. They are: 
 
 - r, ffi • * x, 1, -i Heat absorbed per lb. combustible 
 
 1. Efficiency of the boiler- Calorific value of ! ib , combustibIe - 
 
 n t^ • .,, , ., , Heat absorbed per ib. coal 
 
 2. Efficiency of the boiler and grate- Calorific vaIue f l lb. coal ' 
 
 The first of these is sometimes called the efficiency based on combusti- 
 ble, and the second the efficiency based on coal. The first is recommended 
 as a standard of comparison for all tests, and this is the one which is under- 
 stood to be referred to when the word "efficiency" alone is used without 
 qualification. The second, however, should be included in a report of a 
 test, together with the first, whenever the object of the test is to determine 
 the efficiency of the boiler and furnace together with the grate (or mechan- 
 ical stoker), or to compare different furnaces, grates, fuels, or methods of 
 firing. 
 
 The heat absorbed per pound of combustible (or per pound coal) is to 
 be calculated by multiplying the equivalent evaporation from and at 212 
 degrees per pound combustible (or coal) by 965.7. 
 
 XXII. The Heat Balance. — An approximate "heat balance " may be 
 included in the report of a test when analyses of the fuel and of the chim- 
 ney-gases have been made. It should be reported in the following form: 
 [see next page.] 
 
 XXIII. Report of the Trial. — The data and results should be reported 
 in the manner given in either one of the two following tables [only the 
 "Short Form" of table is given here], omitting lines where the tests have 
 not been made as elaborately as provided for in such tables. Additional 
 lines may be added for data relating to the specific object of the test. 
 The Short Form of Report, Table No. 2, is recommended for commercial 
 tests and as a convenient form of abridging- the longer form for publication 
 when saving of space is desirable. For elaborate trials it is recommended 
 that the full log of the trial be shown graphically, by means of a chart. 
 
872 
 
 THE STEAM-BOILER. 
 
 Heat Balance, or Distribution of the Heating Value op the Com- 
 , bustible. 
 
 Total Heat Value of 1 lb of Combustible B.T.U. 
 
 Per 
 
 Cent. 
 
 1 - Heat absorbed by the boiler = evaporation from and at 
 212 degrees per pound of combustible X 965.7 * 
 
 2. Loss due to moisture in coal = per cent of moisture 
 referred to combustible -h 100 X [(212 - t) + 966 + 
 48 (T — 212)] (t = temperature of air in the boiler- 
 room, T = that of the flue-gases) 
 
 ? Loss due to moisture formed by the burning of hydro- 
 gen = per cent of hydrogen to combustible •*■ 100 x 9 
 X [(212 - t) + 966 + 0.48 (T - 212)] 
 
 4. t Loss due to heat carried away in the dry chimney-gases 
 
 = weight of gas per pound of combustible x 0.24 x 
 (T-t). 
 
 5. % Loss due to incomplete combustion of carbon 
 
 CO per cent C in combustible , n ,__ 
 = COTTCO X_ 100 x 10,150 
 
 6. Loss due to unconsumed hydrogen and hydrocarbons, 
 
 to heating the moisture in the air, to radiation, and 
 unaccounted for. (Some of these losses may be sepa- 
 rately itemized if data are obtained from which they 
 
 may be calculated) 
 
 Totals 
 
 * [The figure 965.7 (or 966) is taken from the old steam tables. If 
 Peabody's new table (1909) is used it should be changed to 969.7, or if 
 Marks & Davis's table is used, to 970.4.] 
 
 t The weight of gas per pound of carbon burned may be calculated 
 from the gas analyses as follows: 
 
 11 C0 2 +80+7(CO+ N) . ■' ■-. ^ A 
 
 Dry gas per pound carbon = _ .„,_ — , „;,. , in which COi, 
 
 o (OU2 + LUJ 
 CO, O, and N are the percentages by volume of the several gases. As the 
 sampling and analyses of the gases in the present state of the art are 
 liable to considerable errors, the result of this calculation is usually only 
 an approximate one. The heat balance itself is also only approximate 
 for this reason, as well as for the fact that it is not possible to determine 
 accurately the percentage of unburned hydrogen or hydrocarbons in the 
 flue-gases. 
 
 The weight of dry gas per pound of combustible is found by multiply- 
 ing the dry gas per pound of carbon by the percentage of carbon in the 
 combustible, and dividing by 100. 
 
 t CO2 and CO are respectively the percentage by volume of carbonic 
 ^cid and carbonic oxide in the flue-gases. The quantity 10,150 = num- 
 oer of heat-units generated by burning to carbonic acid one pound of car- 
 bon contained in carbonic oxide. 
 
RULES FOR CONDUCTING BOILER-TESTS. 
 
 873 
 
 TABLE NO. 2. 
 
 Data and Results of Evaporative Test. 
 
 Arranged in accordance with the Short Form advised by the Boiler Test 
 
 Committee of the American Society of Mechanical Engineers. 
 
 Code of 1899. 
 
 Made by .on boiler, at 
 
 to determine 
 
 Kind of fuel 
 
 Kind of furnace 
 
 Method of starting and stopping the test (" standard ' : 
 
 or " alternate," Arts. X and XI, Code) 
 
 Grate surface 
 
 Water-heating surface 
 
 Superheating surface. 
 
 total quantities. 
 
 1 . Date of trial 
 
 2. Duration of trial 
 
 3. Weight of coal as fired * 
 
 4. Percentage of moisture in coal f •• 
 
 5. Total weight of dry coal consumed 
 
 6. Total ash and refuse 
 
 7. Percentage of ash and refuse in dry coal 
 
 8. Total weight of water fed to the boiler J 
 
 9. Water actually evaporated, corrected for moisture 
 
 or superheat in steam 
 
 9a. Factor of evaporation § 
 
 10. Equivalent water evaporated into dry steam from 
 and at 212 degrees. || (Item 9 x Item 9a.) , 
 
 HOURLY QUANTITIES. 
 
 1 1 . Dry coal consumed per hour 
 
 12. Dry coal per square foot of grate surface per hour 
 
 13. Water evaporated per hour corrected for quality of 
 
 steam 
 
 14. Equivalent evaporation per hour from and at 212 de- 
 
 15. Equivalent evaporation per hour from and at 212 de- 
 grees per square foot of water-heating surface || 
 
 sq.ft. 
 
 hours 
 
 lbs. 
 
 per cent 
 
 lbs. 
 
 per cent 
 lbs. 
 
 * Including equivalent of wood used in lighting the fire, not including 
 unburned coal withdrawn from furnace at times of cleaning and at end of 
 test. One pound of wood is taken to be equal to 0.4 pound of coal, or, in 
 case greater accuracy is desired, as having a heat value equivalent to the 
 evaporation of 6 pounds of water from and at 212 degrees per pound. 
 (6 X 965.7 = 5794 B.T.U.) The term "as fired" means in its actual 
 condition, including moisture. 
 
 t This is the total moisture in the coal as found by drying it artificially, 
 as described in Art. XV of Code. 
 
 X Corrected for inequality of water-level and of steam-pressure at 
 beginning and end of test. 
 
 § Factor of evaporation = .__ ■, in which H and h are respectively 
 yoo.7 
 the total heat in steam of the average observed pressure, and in water of 
 the average observed temperature of the feed. 
 
 H The symbol "U.E.," meaning "units of evaporation," may be con- 
 veniently substituted for the expression "Equivalent water evaporated 
 into dry steam from and at 212 degrees," its definition being given in a 
 foot-note. 
 
874 
 
 THE STEAM-BOILER. 
 
 TABLE NO. 2 — Continued. 
 Data and Results of Evaporative Test. 
 
 AVERAGE PRESSURES, TEMPERATURES, ETC 
 
 16. Steam pressure by gauge 
 
 17. Temperature of feed-water entering boiler 
 
 18. Temperature of escaping gases from boiler 
 
 19. Force of draught between damper and boiler 
 
 20. Percentage of moisture in steam, or number of de- 
 • grees of superheating 
 
 HORSE-POWER. 
 
 2! . Horse-power developed. (Item 14 -s- 341/2.)* 
 
 22. Builders' rated horse-power 
 
 23. Percentage of builders' rated horse-power developed. 
 
 ECONOMIC RESULTS- 
 
 24. Water apparently evaporated under actual condi- 
 
 tions per pound of coal as fired. (Item 8H-Item3.) 
 
 25. Equivalent evaporation from and at 212 degrees per 
 
 pound of coal as fired. || (Item 10 -=- Item 3.) 
 
 26. Equivalent evaporation from and at 212 degrees per 
 
 pound of dry coal.|| (Item 10 -f- Item 5.) 
 
 27. Equivalent evaporation from and at 212 degrees per 
 
 pound of combustible. [Item 10- -r (Item 5 — 
 
 Item 6) .] 
 
 (If Items 25, 26, and 27 are not corrected for quality 
 of steam, the fact should be stated.) 
 
 EFFICIENCY. 
 
 28. Calorific value of the dry coal per pound 
 
 29. Calorific value of the combustible per pound 
 
 30. Efficiency of boiler (based on combustible) f 
 
 31. Efficiency of boiler, including grate (based on dry 
 
 coal) 
 
 COST OF EVAPORATION. 
 
 32. Cost of coal per ton of lbs. delivered in boiler- 
 
 room 
 
 33. Cost of coal required for evaporating 1000 pounds of 
 
 water from and at 212 degrees 
 
 lbs.p.sq.in, 
 deg. 
 
 ins. of water 
 
 % or deg. 
 
 H.P. 
 per cent 
 
 B.T.U. 
 
 per cent 
 
 * Held to be the equivalent of 30 lbs. of water evaporated from 100 
 degrees Fahr. into dry steam at 70 lbs. gauge-pressure. 
 
 t In all cases where the word "combustible" is used, it means the 
 coal without moisture and ash, but including all other constituents. It 
 is the same as what is called in Europe "coal dry and free from ash." 
 
 II See foot-note on the preceding page. ' 
 
 FACTORS OF EVAPORATION. 
 
 The figures in the table on the next four pages are calculated from the 
 formula F =(H — h) h- 970.4, in which H is the total heat above 32° of 
 1 lb. 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 lbs. steam pressure within the ordinary 
 working limits of pressure. Intermediate values correct to the third 
 decimal place may easily be found by interpolation. 
 
FACTORS OF EVAPORATION 
 
 875 
 
 
 Lbs 
 
 
 
 
 
 
 
 
 
 
 Gauge press. . 0.3 
 
 10.3 
 
 20.3 
 
 30.3 
 
 40.3 
 
 50.3 
 
 60.3 
 
 70.3 
 
 80.3 
 
 85.3 
 
 Abs. press. . . .15. 
 
 25. 
 
 35. 
 
 45. 
 
 55. 
 
 65. 
 
 75. 
 
 85. 
 
 95. 
 
 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 
 
 1.03/0 
 
 209 
 
 34 
 
 34 
 
 1.0200 
 
 50 
 
 89 
 
 1.0321 
 
 47 
 
 71 
 
 92 
 
 1.0401 
 
 206 
 
 65 
 
 65 
 
 31 
 
 81 
 
 1.0320 
 
 52 
 
 79 
 
 1.0402 
 
 1.0423 
 
 32 
 
 203 
 
 96 
 
 96 
 
 62 
 
 1.0312 
 
 51 
 
 83 
 
 1.0410 
 
 33 
 
 54 
 
 63 
 
 200 
 
 1.0127 
 
 1.0227 
 
 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 
 
 1.0417 
 
 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 
 
 1.0510 
 
 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 
 
 1.0505 
 
 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 
 
 68 
 
 34 
 
 84 
 
 1.0723 
 
 55 
 
 82 
 
 1 .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 
 
 1 .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 
 
 1.0912 
 
 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 
 
 1.1209 
 
 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 
 
 1.1221 
 
 70 
 
 1 . 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 
 
 1.1522 
 
 46 
 
 66 
 
 76 
 
 92 
 
 40 
 
 40 
 
 1.1406 
 
 55 
 
 94 
 
 1.1526 
 
 53 
 
 77 
 
 97 
 
 1.1607 
 
 89 
 
 71 
 
 71 
 
 37 
 
 86 
 
 1.1525 
 
 57 
 
 84 
 
 1.1608 
 
 1.1628 
 
 37 
 
 86 
 
 1.1301 
 
 1.1401 
 
 67 
 
 1.1518 
 
 56 
 
 88 
 
 1.1615 
 
 38 
 
 59 
 
 68 
 
 83 
 
 32 
 
 32 
 
 98 
 
 48 
 
 87 
 
 1.1619 
 
 46 
 
 69 
 
 90 
 
 99 
 
 80 
 
 63 
 
 63 
 
 1.1529 
 
 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 
 
 1.1822 
 
 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 
 
 1.1906 
 
 1.1915 
 
 59 
 
 79 
 
 79 
 
 45 
 
 94 
 
 33 
 
 65 
 
 92 
 
 1.1916 
 
 37 
 
 46 
 
 56 
 
 1.1610 
 
 1.1710 
 
 76 
 
 1.1825 
 
 64 
 
 96 
 
 1 . 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 
 
 1.2009 
 
 1.2029 
 
 39 
 
 47 
 
 1.1703 
 
 1.1803 
 
 69 
 
 1.1918 
 
 57 
 
 89 
 
 1.2016 
 
 40 
 
 60 
 
 70 
 
 44 
 
 34 
 
 34 
 
 1.1900 
 
 49 
 
 88 
 
 1.2020 
 
 47 
 
 71 
 
 91 
 
 1. 2101 
 
 41 
 
 65 
 
 65 
 
 31 
 
 80 
 
 1.2019 
 
 51 
 
 78 
 
 1.2102 
 
 1.2122 
 
 32 
 
 38 
 
 96 
 
 95 
 
 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. 
 
 95.3 100.3 105.3 110.3 115.3 120.3 125.3 130.3 135.3 140.3 
 110. 115. 120. 125. 130. 135. 140. 145: 150. 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 
 
 '.03 
 
 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 
 
 55 
 
 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 
 
 107 
 
 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 
 
 85 
 
 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. 
 
 877 
 
 150.3 155.3 160.3 165.3 170.3 175.3 
 165. 170. 175. 180. 185. 190. 
 
 180.3 185.3 190.3 195.3 
 195. 200. 205. 210 
 
 Feed 
 water. 
 
 
 
 
 Factors of Evap 
 
 oration. 
 
 
 
 
 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 
 
 1 .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 
 
 8"1 
 
 87 
 
 91 
 
 95 
 
 99 
 
 1 .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 
 
 1.2111 
 
 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 
 
 96 
 
 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 
 
 1.0515 
 
 1.1520 
 
 110 
 
 1.1506 
 
 1.1511 
 
 1.1515 
 
 1.1521 
 
 1.1526 
 
 1.1530 
 
 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 
 
 53 
 
 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 
 
 1.1728 
 
 32 
 
 35 
 
 89 
 
 1.1722 
 
 1.1727 
 
 31 
 
 35 
 
 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 
 
 1.182? 
 
 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 
 
THE STEAM-BOILER. 
 
 
 Lbs. 
 
 
 
 
 
 
 
 
 
 
 
 Gauge press. 2J0.3 
 
 255.3 210,3 215.3 220.3 225.3 230.3 235.: 
 
 240.3 245.: 
 
 250.. 
 
 Abs. press. . .215. 
 
 220. 
 
 225. 
 
 230. 
 
 235. 
 
 240. 
 
 245. 
 
 250. 
 
 255.. 
 
 260. 
 
 265. 
 
 Feed . 
 water. 
 
 Factors of Evaporation. 
 
 212° F. 
 
 1 .0503 
 
 1.0507 
 
 1.051C 
 
 1.0513 
 
 1.0517 
 
 1.052C 
 
 1.0523 
 
 1.0527 
 
 1.0525 
 
 1 . 053 J 
 
 1.053! 
 
 209 
 
 . 34 
 
 3£ 
 
 41 
 
 44 
 
 4£ 
 
 52 
 
 55 
 
 56 
 
 6C 
 
 64 
 
 6i 
 
 206 
 
 65 
 
 69 
 
 72 
 
 75 
 
 79 
 
 83 
 
 86 
 
 89 
 
 91 
 
 95 
 
 9! 
 
 203 
 
 96 
 
 1.0600 
 
 1.0603 
 
 1.0606 
 
 1.061 
 
 1.0614 
 
 1.0617 
 
 1.0620 
 
 1.0622 
 
 1.0626 
 
 1.062* 
 
 200 
 
 1.0627 
 
 31 
 
 34 
 
 37 
 
 42 
 
 45 
 
 48 
 
 51 
 
 53 
 
 57 
 
 6i 
 
 197 
 
 58 
 
 62 
 
 65 
 
 6S 
 
 73 
 
 76 
 
 79 
 
 82 
 
 84 
 
 88 
 
 9 
 
 194 
 
 89 
 
 93 
 
 96 
 
 1.0700 
 
 1.0704 
 
 1.0707 
 
 1.0710 
 
 I .0713 
 
 1.0715 
 
 1.0719 
 
 1.072. 
 
 191 
 
 1.0720 
 
 1.0724 
 
 1 .0727 
 
 31 
 
 35 
 
 33 
 
 41 
 
 44 
 
 46 
 
 50 
 
 5: 
 
 188 
 
 51 
 
 55 
 
 58 
 
 62 
 
 66 
 
 69 
 
 72 
 
 75 
 
 78 
 
 81 
 
 8- 
 
 185 
 
 82 
 
 86 
 
 89 
 
 93 
 
 97 
 
 1.0800 
 
 1.0803 
 
 1.0806 
 
 1.0809 
 
 1.0812 
 
 1.081! 
 
 182 
 
 1.0813 
 
 1.0817 
 
 1.0820 
 
 1 .0823 
 
 1.0828 
 
 31 
 
 34 
 
 37 
 
 39 
 
 43 
 
 4( 
 
 179 
 
 44 
 
 48 
 
 51 
 
 54 
 
 59 
 
 62 
 
 65 
 
 68 
 
 70 
 
 74 
 
 7; 
 
 176 
 
 75 
 
 79 
 
 82 
 
 86 
 
 90 
 
 93 
 
 96 
 
 99 
 
 1 .0901 
 
 1 .0905 
 
 I.090> 
 
 173 
 
 1 .0906 
 
 1,0910 
 
 1.0913 
 
 1.0916 
 
 1.0921 
 
 1.0924 
 
 1.0927 
 
 1 .0930 
 
 32 
 
 36 
 
 3< 
 
 170 
 
 37 
 
 41 
 
 44 
 
 47 
 
 51 
 
 55 
 
 58 
 
 61 
 
 63 
 
 67 
 
 6< 
 
 167 
 
 68 
 
 72 
 
 75 
 
 78 
 
 82 
 
 86 
 
 89 
 
 92 
 
 94 
 
 98 
 
 1.1001 
 
 164 
 
 99 
 
 1.1003 
 
 1.1005 
 
 1.1009 
 
 1.1013 
 
 1.1016 
 
 1.1019 
 
 1.1023 
 
 1.1025 
 
 1.1029 
 
 31 
 
 •161 
 
 1.1030 
 
 34 
 
 37 
 
 40 
 
 44 
 
 47 
 
 50 
 
 54 
 
 56 
 
 60 
 
 6: 
 
 158 
 
 61 
 
 65 
 
 68 
 
 71 
 
 75 
 
 78 
 
 81 
 
 85 
 
 87 
 
 91 
 
 91 
 
 155 
 
 92 
 
 96 
 
 99 
 
 1.1102 
 
 1.1106 
 
 1.1109 
 
 1.1112 
 
 1.1115 
 
 1.1118 
 
 1.1122 
 
 1.112' 
 
 152 
 
 1.U23 
 
 1.1127 
 
 1.1130 
 
 33 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 53 
 
 5.' 
 
 149 
 
 54 
 
 58 
 
 6) 
 
 64 
 
 68 
 
 71 
 
 74 
 
 77 
 
 80 
 
 83 
 
 8( 
 
 146 
 
 84 
 
 89 
 
 92 
 
 95 
 
 99 
 
 1.1202 
 
 1.1205 
 
 1.1258 
 
 1.1211 
 
 1.1214 
 
 1.121; 
 
 143 
 
 1.1215 
 
 1.1219 
 
 1.1223 
 
 1.1226 
 
 1 . 1230 
 
 33 
 
 36 
 
 39 
 
 42 
 
 45 
 
 41 
 
 14Q 
 
 46 
 
 50 
 
 53 
 
 56 
 
 61 
 
 64 
 
 67 
 
 70 
 
 72 
 
 76 
 
 7< 
 
 137 
 
 77 
 
 81 
 
 84 
 
 87 
 
 92 
 
 95 
 
 98 
 
 1.1301 
 
 1.1303 
 
 1.1307 
 
 1.1311 
 
 134 
 
 1.1308 
 
 1.1312 
 
 1.1315 
 
 1.1318 
 
 1 . 1322 
 
 1.1326 
 
 1.1329 
 
 32 
 
 34 
 
 38 
 
 4 
 
 131 
 
 39 
 
 43 
 
 46 
 
 49 
 
 53 
 
 56 
 
 59 
 
 62 
 
 65 
 
 69 
 
 71 
 
 128 
 
 70 
 
 74 
 
 77 
 
 80 
 
 84 
 
 87 
 
 90 
 
 93 
 
 96 
 
 1.1400 
 
 1.140; 
 
 125 
 
 1.1400 
 
 1.1405 
 
 1.1408 
 
 1.1411 
 
 1.1415 
 
 1.1418 
 
 1.1421 
 
 1.1424 
 
 1.1427 
 
 30 
 
 3. 
 
 122 
 
 31 
 
 35 
 
 39 
 
 42 
 
 46 
 
 49 
 
 52 
 
 55 
 
 58 
 
 61 
 
 6 
 
 119 
 
 62 
 
 66 
 
 69 
 
 72 
 
 77 
 
 80 
 
 83 
 
 86 
 
 88 
 
 92 
 
 9: 
 
 116 
 
 93 
 
 97 
 
 1.1500 
 
 1.1503 
 
 1.1507 
 
 1.1511 
 
 1.1514 
 
 1.1517 
 
 1.1519 
 
 1.1523 
 
 1.152! 
 
 113 
 
 1.1524 
 
 1.1528 
 
 31 
 
 34 
 
 38 
 
 41 
 
 44 
 
 48 
 
 50 
 
 54 
 
 5( 
 
 110 
 
 55 
 
 59 
 
 62 
 
 65 
 
 69 
 
 72 
 
 75 
 
 76 
 
 81 
 
 85 
 
 8; 
 
 107 
 
 85 
 
 90 
 
 93 
 
 96 
 
 1.1600 
 
 1.1603 
 
 1.1606 
 
 1.1609 
 
 1.1612 
 
 1.1615 
 
 1.1611 
 
 104 
 
 1.1616 
 
 1.1620 
 
 1.1624 
 
 1.1627 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 4« 
 
 101 
 
 47 
 
 51 
 
 54 
 
 57 
 
 61 
 
 65 
 
 68 
 
 71 
 
 73 
 
 77 
 
 8( 
 
 98 
 
 78 
 
 82 
 
 85 
 
 88 
 
 92 
 
 95 
 
 98 
 
 1.1702 
 
 1.1704 
 
 1.1708 
 
 1.1711 
 
 95 
 
 1.1709 
 
 1.1713 
 
 1.1716 
 
 1.1719 
 
 1.1723 
 
 1.1726 
 
 1.1729 
 
 32 
 
 35 
 
 39 
 
 4 
 
 92 
 
 39 
 
 44 
 
 47 
 
 50 
 
 54 
 
 57 
 
 60 
 
 63 
 
 66 
 
 69 
 
 7; 
 
 89 
 
 70 
 
 75 
 
 78 
 
 81 
 
 85 
 
 88 
 
 91 
 
 94 
 
 97 
 
 1.1800 
 
 1.180. 
 
 86 
 
 1.1801 
 
 1.1805 
 
 1.1808 
 
 1.1812 
 
 1.1816 
 
 1.1819 
 
 1.1822 
 
 1.1825 
 
 1.1827 
 
 31 
 
 3. 
 
 83 
 
 32 
 
 36 
 
 39 
 
 42 
 
 46 
 
 50 
 
 53 
 
 56 
 
 58 
 
 62 
 
 6 
 
 80 
 
 63 
 
 67 
 
 70 
 
 73 
 
 77 
 
 80 
 
 83 
 
 87 
 
 89 
 
 93 
 
 9: 
 
 77 
 
 94 
 
 98 
 
 1.1901 
 
 1.1904 
 
 1.1908 
 
 1.1911 
 
 1.1914 
 
 1.1917 
 
 1.1920 
 
 1.1924 
 
 1.192 
 
 74 
 
 1.1924 
 
 1 . 1929 
 
 32 
 
 35 
 
 39 
 
 42 
 
 45 
 
 48 
 
 51 
 
 54 
 
 5 
 
 71 
 
 55 
 
 59 
 
 63 
 
 66 
 
 70 
 
 73 
 
 76 
 
 79 
 
 82 
 
 85 
 
 8 
 
 68 
 
 86 
 
 90 
 
 93 
 
 96 
 
 1.2001 
 
 1.2004 
 
 1.2007 
 
 1.2010 
 
 1.2012 
 
 1.2016 
 
 1.201' 
 
 65 
 
 1.2017 
 
 1.2021 
 
 1.2024 
 
 1.2027 
 
 31 
 
 35 
 
 38 
 
 41 
 
 43 
 
 47 
 
 I 
 
 62 
 
 48 
 
 52 
 
 55 
 
 58 
 
 62 
 
 65 
 
 68 
 
 72 
 
 74 
 
 78 
 
 8 
 
 59 
 
 79 
 
 83 
 
 86 
 
 89 
 
 93 
 
 96 
 
 99 
 
 1.2102 
 
 1.2105 
 
 1.2109 
 
 1.211 
 
 56 
 
 1.2110 
 
 1.2114 
 
 1.2117 
 
 1.2120 
 
 1.2124 
 
 1.2127 
 
 1.2130 
 
 33 
 
 36 
 
 40 
 
 4 
 
 53 
 
 41 
 
 45 
 
 48 
 
 51 
 
 55 
 
 58 
 
 61 
 
 64 
 
 67 
 
 70 
 
 7 
 
 50 
 
 71 
 
 76 
 
 79 
 
 82 
 
 86 
 
 89 
 
 92 
 
 95 
 
 98 
 
 1.2201 
 
 1.220 
 
 47 
 
 1.2202 
 
 1.2207 
 
 1.2210 
 
 1.2213 
 
 1.2217 
 
 1.2220 
 
 1.2223 
 
 1.2226 
 
 1.2229 
 
 32 
 
 3 
 
 44 
 
 34 
 
 38 
 
 41 
 
 44 
 
 48 
 
 51 
 
 54 
 
 57 
 
 60 
 
 63 
 
 6 
 
 41 
 
 65 
 
 69 
 
 72 
 
 75 
 
 79 
 
 82 
 
 85 
 
 88 
 
 91 
 
 94 
 
 9 
 
 38 
 
 96 
 
 1.2300 
 
 1.2303 
 
 1.2306 
 
 1.2310 
 
 1.2313 
 
 1.2316 
 
 1.2319 
 
 1.2322 
 
 1.2325 
 
 1.232 
 
 35 
 
 1.2327 
 
 31 
 
 34 
 
 37 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 57 
 
 5 
 
 32 
 
 58 
 
 62 
 
 65 
 
 68 
 
 72 /5 
 
 78 
 
 82 
 
 84 
 
 88 
 
 9< 
 
STRENGTH OF STEAM-BOILERS. 870 
 
 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 places, as in Philadelphia, the construc- 
 tion of boilers is governed by local laws; but generally there are no laws 
 upon the subject, and boilers are constructed according to the idea of 
 individual engineers and boiler-makers. In Europe the construction is 
 generally regulated by stringent inspection laws. The rules of the U. S. 
 Supervising Inspectors of Steam-vessels, the British Lloyd's and Board of 
 Trade, the French Bureau Veritas, and the German Lloyd's are ably 
 reviewed in a paper by Nelson Foley, M. Inst. Naval Architects, etc., 
 read at the Chicago Engineering Congress, 1893, Division of Marine and 
 Naval Engineering. From this paper the following notes are taken, 
 chiefly with reference to the U. S. and British rules: 
 
 (Abbreviations. — T. S., for tensile strength; el., elongation; contr., 
 contraction of area.) 
 
 Hydraulic Tests. — Board of Trade, Lloyd's, and Bureau Veritas. — 
 Twice the working pressure. 
 
 United States Statutes. ■ — One. and a half times the working pressure. 
 
 Mr. Foley proposes that the proof pressure should be 11/2 times the 
 working pressure + one atmosphere. 
 
 Established Nominal Factors of Safety. — Board of Trade, — 4.5 for 
 a boiler of moderate length and of the best construction and workman- 
 ship. 
 
 Lloyd's. — Not very apparent, but appears to lie between 4 and 5. 
 
 United States Statutes. — Indefinite, because the strength of the joint 
 is not considered, except by the broad distinction between single and 
 double riveting. 
 
 Bureau Veritas: 4.4. 
 
 German Lloyd's: 5 to 4.65, according to the thickness of the plates. 
 
 Material for Riveting. — Board of Trade. — Tensile strength of rivet 
 bars between 26 and 30 tons, el. in 10 in. not less than 25%, and contr. of 
 area not less than 50%. (Tons of 2240 lbs.) 
 
 Lloyd's. — T. S., 26 to 30 tons; el. not less than 20% in 8 in. The mate- 
 rial must stand bending to a curve, the inner radius of which is not greater 
 than H 2 times the thickness of the plate, after having been uniformly 
 heated to a low cherry-red, and quenched in water at 82° F. 
 
 United States Statutes. — • No special provision. 
 
 Rules Connected with Riveting. — Board of Trade. — 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 8 1/2". 
 The thickness of double butt-straps (each) not to be less than 5/8 the thick- 
 ness of the plate; single butt-straps not less than 9/s. 
 
 Distance from center of rivet to edge of plate = diam. of rivet X IV2. 
 
 Distance between rows of rivets 
 
 = 2 X diam. of rivet or = [(diam. X 4) + 1] -5- 2, if chain, and 
 
 _ v'Kpitch X 11) + (diam . X 4) ] X (pitch + diam. X 4) ., . ' ow 
 — — 11 zigzag. 
 
 Diagonal pitch= (pitch X 6+ diam. X4)* 10. 
 
 Lloyd's. — 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 
 
 * For specifications for steel for boilers, see p. 483. For riveted joints, 
 see page 401. 
 
880 THE STEAM-BOILER. 
 
 shown by experiment to be greater than given by the formula, the actual 
 strength may be taken in the calculation. 
 
 United Stales Statutes. — No rules. [The rules in 1909 give formulas 
 equivalent to those of the British Board of Trade and tables taken from 
 T. W. Traill's "Boilers, Marine and Land."] 
 
 Material for Cylindrical Shells Subject to Internal Pressure. — 
 Board of Trade. — T. S. between 27 and 32 tons. In the normal condition, 
 el. not less than 18% in 10 in., but should be about 25%; if annealed, not 
 less than 20%. Strips 2 in. wide should stand bending until the sides are 
 parallel at a distance from each other of not more than three times the 
 plate's thickness. 
 
 Lloyd's. — T. S. between the limits of 26 and 30 tons per square inch. 
 El. not less than 20% in 8 in. Test strips heated to a low cherry-red and 
 plunged into water at 82° F. must stand bending to a curve, the inner 
 radius of which is not greater than 11/2 times the plate's thickness. 
 
 U. S. Statutes. — Plates 1/2 in. thick and under shall show a contr. of 
 not less than 50%; when over 1/2 in. and up to3/ 4 m. f not less than 45%; 
 when over 3/ 4 in., not less than 40%. 
 
 Mr. Foley's comments: The Board of Trade rules seem to indicate a 
 steel of too high T. S. when a lower and more ductile one can be got: the 
 lower tensile limit should be reduced, and the bending test might with 
 advantage be made after tempering, and made to a smaller radius. 
 Lloyd's rule for quality seems more satisfactory, but the temper test is 
 not severe. The United States Statutes are not sufficiently stringent to 
 insure an entirely satisfactory material. 
 
 Mr. Foley suggests a material which would meet the following; 25 tons 
 lower limit in tension; 25% in 8 in. minimum elongation; radius for bend- 
 ing test after tempering = the plate's thickness. 
 
 Shell-plate Formulae. — Board of Trade: P = TX J?** X2 - 
 
 U X r 
 D = diameter of boiler in inches; 
 P = working-pressure in lbs. per square inch; 
 t = thickness in inches; 
 
 B = percentage of strength of joint compared to solid plate; 
 T = tensile strength allowed for the material in lbs. per square inch; 
 F = a factor of safety, being 4.5, with certain additions depending on 
 method of construction. 
 
 t = thickness of plate in sixteenths; B and D as before; C — a constant 
 depending on the kind of joint. 
 
 When longitudinal seams have double butt-straps, C = 20. When 
 longitudinal seams have double butt-straps of unequal width, only 
 covering on one side the reduced section of plate at the outer line of rivets, 
 C = 19.5. 
 
 When the longitudinal seams are lap-jointed, C = 18.5. 
 
 U. S. Statutes. — Using same notation as for Board of Trade, 
 
 P= D " „ ■ for single-riveting; add 20% for double-riveting; 
 
 where T is the lowest T.S. stamped on any plate. 
 
 Mr. Foley criticises the rule of the United States Statutes as follows: 
 The rule ignores the riveting, except that it distinguishes between single 
 and double, giving the latter 20% advantage; the circumferential riveting 
 or class of seam is altogether ignored. The rule takes no account of 
 workmanship or method adopted of constructing the joints. The factor, 
 one sixth, simply covers the actual nominal factor of safety as well as 
 the loss of strength at the joint, no matter what its percentage; we may 
 therefore dismiss it as unsatisfactory. 
 
 Rules for Flat Plates. — Board of Trade: P = C( c f + i )2 - 
 
 O — D 
 
 P = working-pressure in lbs. per square inch; 
 S = surface supported in square inches; 
 t = thickness in sixteenths of an inch; 
 C = a constant as per following table: 
 
STRENGTH OF STEAM-BOILERS. 881 
 
 C = 125 for plates not exposed to heat or flame, the stays fitted with nuts 
 
 and washers, the latter at least three times the diameter of the 
 
 stay and 2/3 the thickness of the plate; 
 C = 1S7.5 for the same condition, but the washers 2/3 the pitch of stays 
 
 in diameter, and thickness not less than plate; 
 C = 200 for the same condition, but doubling plates in place of washers, 
 
 the width of which is 2/3 the pitch and thickness the same as the 
 
 plate; 
 C = 112.5 for the same condition, but the stays with nuts only; 
 C == 75 when exposed to impact of heat or flame and steam in contact 
 
 with the plates, and the stays fitted with nuts and washers three 
 
 times the diameter of the stay and 2/3 the plate's thickness; 
 C = 67.5 for the same condition, but stays fitted with nuts only; 
 C == 100 when exposed to heat or flame, and water in contact with the 
 
 plates, and stays screwed into the plates and fitted with nuts; 
 C = 66 for the same condition, but stays with riveted heads. 
 U. S. Statutes. — Using same notation as for Board of Trade. 
 
 C x t 2 
 P= — , where p= greatest pitch in inches, P and t as above; 
 
 C = 112 to 200 according to various specified conditions. [Rules of 1909.] 
 Certain experiments were carried out by the Board of Trade which 
 showed that the resistance to bulging does not vary as the square of the 
 plate's thickness. There seems also good reason to believe that it is not 
 inversely as the square of the greatest pitch. Bearing in mind, says Mr. 
 Foley, that mathematicians have signally failed to give us true theoretical 
 foundations for calculating the resistance of bodies subject to the simplest 
 forms of stresses, we therefore cannot expect much from their assistance 
 in the matter of flat plates. 
 
 The Board of Trade rules for flat surfaces, being based on actual experi- 
 ment, are especially worthy of respect; sound judgment appears also to 
 have been used in framing them. 
 
 Furnace Formulae. — Board of Trade. — Long Furnaces. — 
 CXi 2 
 P = , T .. n , but not where L is shorter than (11.5 t — 1), at which 
 
 length the rule for short furnaces comes into play. 
 
 P = working-pressure in pounds per square inch; t = thickness in 
 
 inches; 
 D = outside diameter in inches ; L = length of furnace in feet up to 10 ft. ; 
 C = a constant, as per following table, for drilled holes: 
 
 C = 99,000 for welded or butt-jointed with single straps, double- 
 riveted ; 
 
 C = 88,000 for butts with single straps, single-riveted; 
 
 C = 99,000 for butts with double straps, single-riveted. 
 
 Provided always that the pressure so found does not exceed that given 
 by the following formulae, which apply also to short furnaces: 
 
 C X t 
 
 " for all the patent furnaces named; 
 
 kdV^ erHa) when ™ th Adamson rin ^ s - 
 
 C= 8,800 for plain furnaces; 
 
 C— 14,000 for Fox; minimum thickness 5/ 16 in., greatest 5/sin.; plain 
 
 part not to exceed 6 in. in length; 
 C= 13,500 for Morison; minimum thickness s/jein., greatest 5/ 8 in.; 
 
 plain part not to exceed 6 in. in length; 
 C= 14,000 for Puryes-Brown; limits of thickness 7/ 16 in. and5/gin., 
 
 plain part 9 in. in length; 
 Cj= 8,800 for Adamson rings; radius of flange next fire 1 1/2 in. 
 U. S. Statutes. — Long Furnaces. — Same notation. 
 
 89 600 X £ 2 
 P= — T n , but L not to exceed 8 ft. [New rules are given in 
 
 1909; see page 884.] 
 
882 THE STEAM-BOILER. 
 
 Mr. Foley comments on the rules for long furnaces as follows: The 
 Board of Trade general formula, where the length is a factor, has a very 
 limited range indeed, viz., 10 ft. as the extreme length, and 135 thicknesses 
 
 C X t 2 
 — 12 in., as the short limit. The original formula, P= _ , is that of 
 
 Sir W. Fairbairn, and was, I believe, never intended by him to apply to 
 short furnaces. On the very face of it, it js apparent, on the other hand, 
 that if it is true for moderately long furnaces, it cannot be so for very long 
 ones. We are therefore driven to the conclusion that any formula which 
 includes simple L as a factor must be founded on a wrong basis. 
 
 With Mr. Traill's form of the formula, namely, substituting (L + 1) 
 for L, the results appear sufficiently satisfactory for practical purposes, 
 and indeed, as far as can be judged, tally with the results obtained from 
 experiment as nearly as could be expected. The experiments to which 
 I refer were six in number, and" of great variety of length to diameter; 
 the actual factors of safety ranged from 4.4 to 6.2, the mean being 4.78, 
 or practically 5. It seems to me, therefore, that, within the limits pre- 
 scribed, the Board of Trade formula may be accepted as suitable for our 
 requirements. 
 
 Material for Stays. — The qualities of material prescribed are as 
 follows: 
 
 Board of Trade. — The tensile strength to lie between the limits of 27 and 
 32 tons per sq. in., and to have an elongation of not less than 20% in 
 10 in. Steel stays which have been welded or worked in the fire should 
 not be used. [Tons of 2240 lbs.] 
 
 Lloyd's. — 26 to 30 ton steel, with elongation not less than 20% in 8 in. 
 
 U . S. Statutes. — The only condition is that the reduction of area must 
 not be less than 40% if the test bar is over 3/ 4 in. diameter. 
 
 Loads allowed on Stays. — Board of Trade. — 9000 lbs. per square 
 inch is allowed on the net section, provided the tensile strength ranges from 
 27 to 32 tons. Steel stays are not to be welded or worked in the fire. 
 
 Lloyd's. — For screwed and other stays, not exceeding 1 1/2 in. diameter 
 effective, 8000 lbs. per square inch is allowed; for stays above IV2 in., 
 9000 lbs. No stays are to be welded. 
 
 U. S. Statutes. — Braces and stays shall not be subjected to a greater 
 stress than 6000 lbs. per sq. in. [As high as 9000 lbs. is allowed in some 
 cases in the rules of 1909.] 
 
 [Rankine, S. E., p. 459, says: "The iron of the stays ought not to be 
 exposed to a greater working tension than 3000 lbs. on the square inch, 
 in order to provide against their being weakened by corrosion. This 
 amounts to making the factor of safety for the working pressure about 
 20." It is evident, however, that an allowance in the factor of safety 
 for corrosion may reasonably be decreased with increase of diameter. 
 W.K.] 
 
 A discussion of various rules and formulae for stay bolts, braces and 
 flat surfaces will be found in a paper bv R. S. Hale, Trans. A. S. M. E., 
 1904. 
 
 C Xd 2 X t 
 Girders. — Board of Trade. P = _ — • P = working pressure 
 
 in lbs. per sq. in.; W = width of flame-box; L = length of girder; p = 
 pitch of bolts; D = distance between girders from center to center; d = 
 depth of girder; t = thickness of sum -of same; C = a constant = 6600 for 
 1 bolt, 9900 for 2 or 3 bolts, and 11,220 for 4 bolts. All dimensions in 
 inches. 
 
 Lloyd's. — The same formula and constants, except that C = 11,000 
 for 4 or 5 bolts, 11,550 for 6 or 7, and 11,880 for 8 or more. 
 
 U. S. Statutes. — [The rules in 1909 are the same as Lloyd's.] 
 
 Tube-Plates. — Board of Trade. P= l (D ~J \ x 20 ' 0Q0 . jy = least 
 
 W X D 
 horizontal distance between centers of tubes in inches ; d = inside diameter 
 of ordinary tubes; t = thickness of tube-plate in inches; W = extreme 
 width of combustion-box in inches from front tube-plate to back of fire- 
 box, or distance between combustion-box tube-plates when the boiler is 
 double-ended and the box common to both ends. 
 
 The crushing stress on tube-plates caused by the pressure on the flame- 
 box top is to be limited to 10,000 lbs. per square inch, 
 
STRENGTH OF STEAM-BOILERS. 883 
 
 Material for Tubes. — Mr. Foley proposes the following: If iron, the 
 quality to be such as to give at least 22 tons per square inch as the mini- 
 mum tensile strength, with an elongation of not less than 15% in 8 ins. 
 If steel, the elongation to be not less than 26% in ins. for the material 
 before being rolled into strips; and after tempering, the test bar to 
 stand completely closing together. Provided the steel welds well, there 
 does not seem to be any object in providing tensile limits. The ends should 
 be annealed after manufacture, and stay-tube ends should be annealed 
 before screwing. 
 
 Holding-power of Boiler-tubes. (See also page 342.) — In Messrs. 
 Yarrow's experiments on iron and steel tubes of 2 in. to 2i'4in. diameter 
 the first 5 tubes gave way on an average of 23,740 lbs., which would ap- 
 pear to be about 2/3 the ultimate strength of the tubes themselves. In all 
 these cases the hole through the tube-plate was parallel with a sharp edge 
 to it. and a ferrule was driven into the tube. 
 
 Tests of the next 5 tubes were made under the same conditions as the 
 first 5, with the exception that in this case the ferrule was omitted, the 
 tubes being simply expanded into the plates. The mean pull required 
 was 15,270 lbs., or considerably less than half the ultimate strength of the 
 tubes. 
 
 Effect of beading the tubes, the holes through the plate being parallel and 
 ferrules omitted. The mean of the first 3, which are tubes of the same 
 kind, gives 26,876 lbs. as their holding-power, under these conditions, as 
 compared with 23,740 lbs. for the tubes fitted with ferrules only. This 
 high figure is, however, mainly due to an exceptional case where the 
 holding-power is greater than the average strength of the tubes them- 
 selves. 
 
 It is disadvantageous to cone the hole through the tube-plate unless its 
 sharp edge is removed, as the results are much worse than those obtained 
 with parallel holes, the mean pull being but 16.031 lbs., the experiments 
 being made with tubes expanded and ferruled but not beaded over. 
 
 In experiments on tubes expanded into tapered holes, beaded over and 
 fitted with ferrules, the net result is that the holding-power is, for the 
 size experimented on, about 3/ 4 of the tensile strength of the tube, the 
 mean pull being 28,797 lbs. With tubes expanded into tapered holes 
 and simply beaded over, better results were obtained than with ferrules; 
 in these cases, however, the sharp edge of the hole was rounded off, which 
 appears in general to have a good effect. 
 
 In one particular the experiments are incomplete, as it is impossible to 
 reproduce on a machine the racking the tubes get by the expansion of a 
 boiler as it is heated up and cooled down again, and it is quite possible, 
 therefore, that the fastening giving the best results on the testing-machine 
 may not prove so efficient in practice. 
 
 N.B. — It should be noted that the experiments were all made under 
 the cold condition, so that reference should be made with caution, the 
 circumstances in practice being very different, especially when there is 
 scale on the tube-plates, or when the tube-plates are thick and subject 
 to intense heat. 
 
 Iron versus Steel Boiler-tubes. (Foley.) — Mr. Blechynden prefers 
 iron tubes to those of steel, but how far he would go in attributing the 
 leaky-tube defect to the use of steel tubes we are not aware. It appears, 
 however, that the results of his experiments would warrant him in going 
 a considerable distance in this direction. The test consisted of heating 
 and cooling two tubes, one of wrought iron and the other of steel. Both 
 tubes were 23/4 in. in diameter and 0.16 in. thickness of metal. The tubes 
 were put in the same furnace, made red-hot, and then dipped in water. 
 The length was gauged at a temperature of 46° F. 
 
 This operation was twice repeated, with results as follows: 
 
 Steel. Iron: 
 
 Original length 55 . 495 in. 55.495 in. 
 
 Heated to 186° F.; increase 0.052 in. 0.048 in. 
 
 Coefficient of expansion per degree F 0000067 .0000062 
 
 Heated red-hot and dipped in water; decrease .007 in. .003 in. 
 
 Second heating and cooling, decrease .031 in. .004 in. 
 
 Third heating and cooling, decrease .017 in. .006 in. 
 
 Total contraction .055 in. .013 in. 
 
884 THE STEAM-BOILER. 
 
 Mr. A. C. Kirk writes: That overheating of tube ends is the cause of the 
 leakage of the tubes in boilers is proved by the fact that the ferrules at 
 present used by the Admiralty prevent it. These act by shielding the tube 
 ends from the action of the fiame, and consequently reducing evaporation, 
 and so allowing free access of the water to keep them cool. 
 
 Although many causes contribute, there seems no doubt that thick 
 tube-plates must bear a share of causing the mischief. 
 
 Rules for Construction of Boilers in Merchant Vessels in the 
 United States. 
 
 (Extracts from General Rules and Regulations of the Board of Supervis- 
 ing Inspectors, Steamboat Inspection Service (as amended Jan., 1909).) 
 
 Tensile Strength of Plate. — From each plate as rolled there shall 
 be taken two test pieces, one for tensile test and one for bending test. 
 The piece for tensile test shall be taken from the side of the plate at 
 about one-third of its length from the top of the plate, and the piece for 
 bending test shall be taken transversely from the top of the plate near the 
 center. 
 
 All the pieces shall be prepared so that the skin shall not be removed, 
 the edges only planed or shaped. 
 
 In no case shall test pieces be prepared by annealing or reduced in size 
 by hammering. 
 
 Tensile-test pieces shall be at least 16 ins. in length, from l J /2 to 31/2 
 ins. in width at the ends, which ends shall join by an easy fillet, a straight 
 part in the center of at least 9 ins. in length and 11/2 ins. in width, . . . 
 marked with light prick punch marks at distances 1 inch apart, spaced 
 so as to give 8 inches in length. 
 
 Only steel plates manufactured by what is known as the basic or acid 
 open-hearth processes will be allowed to be used in the construction or 
 repairs of boilers for marine purposes. 
 
 No plate made by the acid process shall contain more than 0.06 % of 
 phosphorus and 0.04% of sulphur, and no plate made by the basic process 
 shall contain more than 0.04% of phosphorus and 0.04% of sulphur. 
 
 For steel plates the sample must show, when tested, a tensile strength 
 not lower than 50,000 lbs. and not higher than 75,000 lbs. per sq. in. of 
 section, and no such plate shall be stamped with a higher tensile strength 
 than 70,000 lbs.: Provided, however, that for steel plates exceeding a 
 thickness of 0.3125 in. intended for use in externally fired boilers, the 
 sample must show, when tested, a tensile strength not lower than 54,000 
 lbs. and not higher than 67,000 lbs. per sq. in. of section, and no plate 
 exceeding a thickness of 0.3125 in. intended for use in externally fired 
 boilers shall be stamped with a higher tensile strength than 62,000 lbs. 
 Such sample must also show an elongation of at least 25% in a length of 
 2 ins. for thickness up to 1/4 in., inclusive; in a length of 4 ins. for over 
 1'4 to 7/ 16 in., inclusive; in a length of 6 ins. for all plates over 7/ 16 in. The 
 sample must also show a reduction of sectional area as follows: 
 
 At least 50% for thickness up to 1/2 in., inclusive; 45% for thickness 
 over 1/2 to 3/4 in., inclusive, and 40% for thickness over 3/ 4 in. 
 
 Quenching and bending test. — Quenching and bending test pieces shall 
 be at least 12 ins. in length and from 1 to 31/2 ins. in width. The side 
 where sheared or planed must not be rounded, but the edges may have 
 the sharpness taken off with a fine file. The test piece shall be heated 
 to a cherry red (as seen in a dark place) and then plunged into wafer at a 
 temperature of about 82° F. Thus prepared, the sample shall be bent to a 
 curve, the inner radius of which is not greater than 11 '2 times the thick- 
 ness of the sample, without cracks or flaws. The ends must be parallel 
 after bending. 
 
 Cylindrical Shells. — The working steam pressure allowable on 
 cylindrical shells of boilers constructed of plates inspected as required 
 by these rules, when single riveted, shall not produce a strain to exceed 
 one-sixth of the tensile strength of the iron or steel plates of which such 
 boilers are constructed ; but where the longitudinal laps of the cvlindrical 
 parts of such boilers are double riveted, and the rivet holes' for such 
 boilers have been fairly drilled, an addition of 20 per cent to the working 
 pressure provided for single riveting will be allowed. >. 
 
STRENGTH OF STEAM-BOILERS. 885 
 
 The pressure for any dimension of boilers must be ascertained by the 
 following rule, viz.: 
 
 Multiply one-sixth of the lowest tensile strength found stamped on the 
 plates in the cylindrical shell by the thickness — expressed in inches or 
 part of an inch — and divide by the radius or half diameter — also 
 expressed in inches — and the result will be the pressure allowable per 
 square inch of surface for single riveting, to which add 20% for double 
 riveting, when all the rivet boles in the shell of such boiler have been 
 "fairly drilled ' and no part of such holes has been punched. The 
 pressure allowed shall be based on the plate whose tensile strength multi- 
 plied by its thickness gives the lowest product. 
 
 Cylindrical Shells of Water-tube or Coil Boilers. — The working 
 pressure allowable, when such shells have a row or rows of pipes or tubes 
 inserted therein, shall be determined by the formula: 
 
 P = (D - d)X TXS + (DX R), 
 
 where P= working pressure allowable in pounds; D= distance in inches 
 between the tube or pipe centers in a line from head to head; d= dia- 
 meter of hole in inches; T= thickness of plate in inches; S= one-sixth 
 of the tensile strength of the plate; R = radius of shell in inches. 
 
 Convex Heads. — Plates used as heads, when new and made to 
 practically true circles, shall be allowed a steam pressure in accordance 
 with the formula: P = T X S -h R, where P = steam pressure allowable 
 in lbs. per sq. in. ; 7" = thickness of plate in ins.; S = one-sixth of the tensile 
 strength; R = one-half of the radius to which the head is bumped. 
 
 Add 20% when the head is double riveted to the shell and the holes 
 are fairly drilled. 
 
 Bumped heads may contain a manhole opening flanged inwardly, 
 when such flange is turned to a depth of three times the thickness of 
 material in the head. 
 
 Concave Heads. — For concave heads the pressure allowable will be 
 0.6 times the pressure allowable for convex heads. 
 
 Flat Heads. — Where flat heads do not exceed 20 ins. diameter they 
 may be used without being stayed, and the steam pressure allowable 
 shall be determined by the formula: P= CX T 2 -t- A, where P= steam 
 pressure allowable in pounds; T— thickness of material in sixteenths of 
 an inch; A = one-half the area of head in inches; C = 112 for plates 7/jg in. 
 and under; C = 120 for plates over 7/ 16 in. Provided, the flanges are made 
 to an inside radius of at least 1 1/2 inches. 
 
 Flat Surfaces. — The maximum stress allowable on flat plates sup- 
 ported by stays shall be determined by the following formula: 
 
 All stayed surfaces formed to a curve the radius of which is over 21 ins. 
 excepting surfaces otherwise provided for, shall be deemed flat surfaces. 
 
 Working pressure = C X T* -s- P 2 , 
 
 where T = thickness of plates in 16ths of an inch; P = greatest pitch 
 of stays in ins.; C = 112 for screw stays with riveted heads, plates 
 7/i6 thick and under; C= 120 for screw stays with riveted heads, plates 
 above 7/ 16 in. thick; C = 120 for screw stays with nuts, plates 7/ 16 in. 
 thick and under; C = 125 for screw stays with nuts, plates above 
 7/ 16 in. thick and under 9/ 16 in.; C — 135 for screw stays with nuts, 
 plates 9/i6 in. thick and above; C = 175 for stays with double nuts 
 having one nut on the inside and one nut on the outside of plate, without 
 washers or doubling plates; C = 160 for stays fitted with washers or 
 doubling strips which have a thickness of at least 0.5 of the thickness of 
 the plate and a diameter of at least 0.5 of the greatest pitch of the stay, 
 riveted to the outside of the plates, and stays having one nut inside of 
 the plate, and one nut outside of the washer or doubling strip. For T 
 take 72% of the combined thickness of the plate and washer or plate and 
 doubling strip. C = 200 for stays fitted with doubling strips which 
 have a thickness equal to at least 0.5 of the thickness of the plate reen- 
 forced, and covering the full area braced (up to the curvature of the 
 flange, if any), riveted to either the inside or outside of the plate, and 
 stays having one nut outside and one inside of the plates. Washers 
 or doubling plates to be substantially riveted. For T take 72% of the 
 combined thickness of the two plates. C = 200 for stays with plates 
 
886 THE STEAM-BOILER. 
 
 stiffened with tees or angle bars having a thickness of at least 2/ 3 the 
 thickness of plate and depth of webs at least 1/4 of the greatest pitch of 
 the stays, and substantially riveted on the inside of the plates, and stays 
 having one nut inside, bearing on washers fitted to the edges of the webs 
 that are at right angles to the plate. For T take 72% of the combined 
 thickness of web and plate. 
 
 No such flat plates or surfaces shall be unsupported a greater distance 
 than 18 inches. 
 
 Stays. — The maximum stress in pounds allowable per square inch 
 of cross-sectional area for stays used in the construction of marine boilers, 
 when they are accurately fitted and properly secured, shall be ascertained 
 by the following formula: 
 
 P=iXC + a, where P = working pressure in lbs. per sq. in.; A = least 
 cross-sectional area of stay in inches; a = area of surface supported by one 
 stay, in inches; C = 9000 for tested steel stays exceeding 2V2 ins. diam.; 
 C = 8000 for tested steel stays 11/4 ins. and not exceeding 21/2 ins. diam., 
 when such stays are not forged or welded. The ends, however, may be 
 upset to a sufficient diameter to allow for the depth of the thread. The 
 diameter shall be taken at the bottom of the thread, provided it is the 
 least diameter of the stay. All such stays after being upset shall be 
 thoroughly annealed. C = 8000 for a tested Huston or similar type of 
 brace, the cross-sectional area of which exceeds 5 sq. ins.; C = 7000 for 
 such tested braces when the cross-sectional area is not less than 1.227 and 
 not more than 5 sq. ins., provided such braces are prepared at one heat 
 from a solid piece of plate without welds; C = 6000 for all stays not other- 
 wise provided for. 
 
 Flues subjected to External Pressure only. — Plain lap-welded steel 
 flues 7 to 13 ins. diameter. D = outside diam., ins.; T = thickness, ins.; 
 P = working pressure, lbs. per sq. in.; F = factor of safety. 
 
 T = [(F X ^Lt^ 1386] D . This formula is applicable to lengths 
 86670 
 greater than six diameters of flue, to working pressures greater than 100 
 lbs. per sq. in., and to temperatures less than 650° F. 
 
 Riveted flues, made in sections riveted together, 6 to 9 ins. diam., 
 maximum length of sections 60 ins.; over 9 and not over 13 ins. diam., 
 maximum length 42 ins.: P = 8100 X T -4- D. 
 
 Riveted or lap-welded flues, over 13 and not over 28 ins. diam., lengths 
 not to exceed 31/2 times the diam.: 
 
 P = ^~ [(18.75 X T) - (L X 1.03)]. 
 
 (L = length of flue in inches; T = thickness in 16ths of an inch.) 
 
 Furnaces. — The tensile strength of steel used in the construction of 
 corrugated or ribbed furnaces shall not exceed 87,000, and be not less 
 than 54,000 lbs.; and in all other furnaces the minimum tensile strength 
 shall not be less than 58,000, and the maximum not more than 67,000 
 lbs. The minimum elongation in 8 inches shall be 20%. 
 
 All corrugated furnaces having plain parts at the ends not exceeding 
 9 inches in 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 -4- D. 
 
 P = pressure in lbs. 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/ 16 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/iein. 
 
 Purves type, rib projections C = 14,000, T not less than 7/ 16 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/ 16 in. 
 
 Limiting dimensions from center to center of the corrugations or pro- 
 jecting ribs, and of their depth, are given for each furnace. 
 
 Tubes. — Lap-welded tubes are allowed a working pressure of 225 lbs. 
 per sq. in., if of the thicknesses given below, " provided they are deemed 
 safe bv the inspectors." 
 
 1 and 11/4 ins. diam., 0.072 in. thick; 1 1/2 ins., 0.083; 13/ 4 , 2 and 21/4 ins., 
 0.095; 21/2, 23/4 and 3 ins., 0.109; 31/4, 31/2 and 33/4ins., 0.120; 4 and 41/2 
 ins., 0.134; 5 ins., 0.148; 6 ins., 0.165. 
 
STRENGTH OF STEAM-BOILERS. 
 
 887 
 
 Safe Working Pressure in Cylindrical Shells. — The author desires 
 to express his condemnation of the rule of the U. S. Statutes, as giving 
 too low a factor of safety. (See also criticism by Mr. Foley, page 880, ante.) 
 
 If Pb = bursting-pressure, t = thickness, T = tensile strength, c = 
 coefficient of strength of riveted joint, that is, ratio of strength of the 
 joint to that of the solid plate, d = diameter, Pb = 2tTc + d, or if c be taken 
 for double-riveting at 0.7, then P b = lAtT + d. 
 
 By the U. S. rule the allowable pressure P a = ~^ X 1.20 = ^^ ; 
 
 whence Pb = 3.5P a ; that is, the factor of safety is only 3.5, provided the 
 " tensile strength found stamped in the plate " is the real tensile strength 
 of the material. 
 
 The author's formula for safe working-pressure of externally fired 
 
 14,000 1 Pd 
 
 boilers with longitudinal seams double-riveted, is P 
 
 d ' 14,000' 
 thickness and d = diam. in 
 
 P = gauge-pressure in lbs. per sq. in.; t = 
 inches. 
 
 2tTc 
 This is derived from the formula P= —t-t- , taking c at 0.7 and /= 5 
 
 for steel of 50,000 lbs. T.S., or 6 for 60,000 lbs. T.S.; the factor of safety 
 being increased in the ratio of the T.S., since with the higher T.S. there 
 is greater danger of cracking at the rivet-holes from the effect of punching 
 and riveting and of expansion and contraction caused by variations of 
 temperature. For external shells of internally fired boilers, these shells 
 not being exposed to the fire, with rivet-holes drilled or reamed after 
 punching, a lower factor of safety and steel of a higher T.S. may be allow- 
 able. 
 
 If the T.S. is 60,000, a working pressure P = 16,000 t -^- d would give a 
 factor of safety of 5.25. 
 
 The following table gives safe working pressures for different diameters 
 of shell and thicknesses of plate calculated from the author's formula. 
 
 Safe Working Pressures in Cylindrical Shells of Boilers, Tanks, 
 Pipes, etc., in Pounds per Square Inch. 
 
 Longitudinal seams double-riveted. 
 (Calculated from formula P = 14,000 X thickness ■ 
 
 diameter.) 
 
 CD mA 
 
 
 
 Diameter in Inches 
 
 
 
 
 S^c 
 
 
 
 
 
 
 
 
 
 
 24 
 
 30 
 
 36 
 
 38 
 
 40 
 
 42 
 
 44 
 
 46 
 
 48 
 
 50 
 
 52 
 
 1 
 
 36.5 
 
 29.2 
 
 24.3 
 
 23.0 
 
 21.9 
 
 20.8 
 
 19.9 
 
 19.0 
 
 18.2 
 
 17.5 
 
 16.8 
 
 2 
 
 72.9 
 
 58.3 
 
 48.6 
 
 46.1 
 
 43.8 
 
 41.7 
 
 39.8 
 
 38.0 
 
 36.5 
 
 35.0 
 
 33.7 
 
 3 
 
 109.4 
 
 87.5 
 
 72.9 
 
 69.1 
 
 65.6 
 
 62.5 
 
 59.7 
 
 57.1 
 
 54.7 
 
 52.5 
 
 50.5 
 
 4 
 
 145.8 
 
 116.7 
 
 97.2 
 
 92.1 
 
 87.5 
 
 83.3 
 
 79.5 
 
 76.1 
 
 72.9 
 
 70.0 
 
 67.3 
 
 5 
 
 182.3 
 
 145.8 
 
 121.5 
 
 115.1 
 
 109.4 
 
 104.2 
 
 99.4 
 
 95.1 
 
 91.1 
 
 87.5 
 
 84.1 
 
 6 
 
 218.7 
 
 175.0 
 
 145.8 
 
 138.2 
 
 131.3 
 
 125.0 
 
 119.3 
 
 114.1 
 
 109.4 
 
 105.0 
 
 101.0 
 
 7 
 
 255.2 
 
 204.1 
 
 170.1 
 
 161.2 
 
 153.1 
 
 145.9 
 
 139.2 
 
 133.2 
 
 127.6 
 
 122.5 
 
 117.8 
 
 8 
 
 291.7 
 
 233.3 
 
 194.4 
 
 184.2 
 
 175.0 
 
 166.7 
 
 159.1 
 
 152.2 
 
 145.8 
 
 140.0 
 
 134.6 
 
 9 
 
 328.1 
 
 262.5 
 
 218.8 
 
 207.2 
 
 196.9 
 
 187.5 
 
 179.0 
 
 171.2 
 
 164.1 
 
 157.5 
 
 151.4 
 
 10 
 
 364.6 
 
 291.7 
 
 243.1 
 
 230.3 
 
 218.8 
 
 208.3 
 
 198.9 
 
 190.2 
 
 182.3 
 
 175.0 
 
 168.3 
 
 11 
 
 401.0 
 
 320.8 
 
 267.4 
 
 253.3 
 
 240.6 
 
 229.2 
 
 218.7 
 
 209.2 
 
 200.5 
 
 192.5 
 
 185.1 
 
 12 
 
 437.5 
 
 350.0 
 
 291.7 
 
 276.3 
 
 262.5 
 
 250.0 
 
 238.6 
 
 228.3 
 
 218.7 
 
 210.0 
 
 201.9 
 
 13 
 
 473.9 
 
 379.2 
 
 316.0 
 
 299.3 
 
 284.4 
 
 270.9 
 
 258.5 
 
 247.3 
 
 337.0 
 
 227.5 
 
 218.8 
 
 14 
 
 410.4 
 
 408.3 
 
 340.3 
 
 322.4 
 
 306.3 
 
 291.7 
 
 278.4 
 
 266.3 
 
 255.2 
 
 245.0 
 
 235.6 
 
 15 
 
 546.9 
 
 437.5 
 
 364.6 
 
 345.4 
 
 328.1 
 
 312.5 
 
 298.3 
 
 285.3 
 
 273.4 
 
 266.5 
 
 252.4 
 
 16 
 
 583.3 
 
 466.7 
 
 388.9 
 
 368.4 
 
 350.0 
 
 333.3 
 
 318.2 
 
 304.4 
 
 291.7 
 
 280.0 
 
 269.2 
 
888 
 
 THE STEAM-BOILER. 
 
 
 Safe Working Pressures in Cylindrical Shells - 
 
 — Continued 
 
 
 §"2 a 
 
 , Diameter in Inches. 
 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 84 
 
 90 
 
 96 
 
 102 
 
 108 
 
 114 
 
 120 
 
 1 
 
 16.2 
 
 14.6 
 
 13.3 
 
 12.2 
 
 11.2 
 
 10.4 
 
 9.7 
 
 9.1 
 
 8.6 
 
 8.1 
 
 7.7 
 
 7.3 
 
 2 
 
 32.4 
 
 29.2 
 
 25.5 
 
 24.3 
 
 22.4 
 
 20.8 
 
 19.4 
 
 18.2 
 
 17.2 
 
 16.2 
 
 15.4 
 
 14.6 
 
 3 
 
 48 6 
 
 43 7 
 
 39 8 
 
 36,5 
 
 33 7 
 
 31,3 
 
 29.2 
 
 27.3 
 
 25.7 
 
 24.3 
 
 23.0 
 
 21.9 
 
 4 
 
 64 8 
 
 58 3 
 
 53,0 
 
 48,6 
 
 44 9 
 
 41,7 
 
 38.9 
 
 36.5 
 
 34.3 
 
 32.4 
 
 30.7 
 
 29.2 
 
 5 
 
 81 
 
 72 9 
 
 66 3 
 
 60,8 
 
 56 1 
 
 52 1 
 
 48.6 
 
 45.6 
 
 42.9 
 
 40.5 
 
 3d.4 
 
 36.5 
 
 6 
 
 97 2 
 
 87 5 
 
 79 5 
 
 72 9 
 
 67,3 
 
 62 5 
 
 58.3 
 
 54.7 
 
 51.5 
 
 48.6 
 
 46.1 
 
 43.8 
 
 7 
 
 113 4 
 
 102 1 
 
 92,8 
 
 85.1 
 
 78,5 
 
 72 9 
 
 68.1 
 
 63.8 
 
 60.0 
 
 56.7 
 
 53.7 
 
 51.0 
 
 8 
 
 17.9 6 
 
 116 7 
 
 106.1 
 
 97.2 
 
 89.7 
 
 83 3 
 
 77.8 
 
 72.9 
 
 68.6 
 
 64.8 
 
 61.4 
 
 58.3 
 
 9 
 
 145 8 
 
 131 2 
 
 119.3 
 
 109,4 
 
 101.0 
 
 93.8 
 
 87.5 
 
 82.0 
 
 77.2 
 
 72.9 
 
 69.1 
 
 65.6 
 
 10 
 
 167, 
 
 145 8 
 
 132 6 
 
 121.5 
 
 112.3 
 
 104,2 
 
 97.2 
 
 91.1 
 
 85.8 
 
 81.0 
 
 76.8 
 
 72.9 
 
 11 
 
 178 2 
 
 160 4 
 
 145 8 
 
 133.7 
 
 123.4 
 
 114.6 
 
 106.9 
 
 100.3 
 
 94.4 
 
 89.1 
 
 84.4 
 
 80.2 
 
 12 
 
 194 4 
 
 175 
 
 159 1 
 
 145,8 
 
 134.6 
 
 125.0 
 
 116.7 
 
 109.4 
 
 102.9 
 
 97.2 
 
 92.1 
 
 87.5 
 
 13 
 
 210 7 
 
 189 6 
 
 172 4 
 
 158,0 
 
 145.8 
 
 135.4 
 
 126.4 
 
 118.5 
 
 111.5 
 
 105.3 
 
 99.8 
 
 94.8 
 
 14 
 
 226 9 
 
 204 2 
 
 185 6 
 
 170.1 
 
 157.1 
 
 145,8 
 
 136.1 
 
 127.6 
 
 120.1 
 
 113.4 
 
 107.5 
 
 102.1 
 
 15 
 
 243 1 
 
 218 7 
 
 198 9 
 
 182.3 
 
 168.3 
 
 156.3 
 
 145.8 
 
 136.7 
 
 128.7 
 
 121.5 
 
 115.1 
 
 109.4 
 
 16 
 
 259.3 
 
 233.3 
 
 212.1 
 
 194.4 
 
 179.5 
 
 166.7 
 
 155.6 
 
 145.8 
 
 137.3 
 
 129.6 
 
 122.8 
 
 116.7 
 
 Flat Stayed Surfaces in Steam-boilers. — Clark, in his treatise on the 
 Steam-engine, also in his Pocket-hook, gives the following formula: p = 
 407 ts -s- d, in which p is the internal pressure in pounds per square inch 
 that will strain the plates to their elastic limit, t is the thickness of the 
 plate in inches, d is the distance between two rows of stay-bolts in the 
 clear, and s is the tensile stress in the plate, in tons of 2240 lbs., per 
 square inch, at the elastic limit. Substituting values of s for iron, steel, 
 and copper, 12, 14, and 8 tons respectively, we have the following: 
 
 Formulae fob Ultimate Elastic Strength of Flat Stayed Surfaces. 
 
 
 Iron. 
 
 ■ Steel. 
 
 Copper. 
 
 
 p = 5000J 
 pxd 
 5000 
 5000 1 
 
 V 
 
 p = 5700 3 
 
 d 
 
 pxd 
 
 1 ~ 5700 
 
 ,5700 t 
 
 V 
 
 p = 3300J 
 pxd 
 
 1 3300 
 3300 f 
 
 Thickness of plate 
 
 
 V 
 
 For Diameter of the Stay-bolts, Clark gives d' = 0.0024 \ — — , 
 
 in which d' = diameter of screwed bolt at bottom of thread, P = longitudi- 
 nal and P' transverse pitch of stay-bolts between centers, p = internal 
 pressure in lbs. per sq. in. that will strain the plate to its elastic limit, s = 
 elastic strength of the stay-bolts, in lbs. per sq. in. Taking s = 12, 14, 
 and 8 tons, respectively, for iron, steel, and copper, we have 
 
 For iron, d' = 0.00069 ^ PP'p , or if P = P' , d' = 0.00069 P vj- 
 For steel, d' = 0.00064 y /pP'p , or it P = P' ', d' = 0.00064 P v^ ; 
 For copper, d' = 0.00084 VpP'p, or if P = P', d' = 0.00084 P \/p. 
 
 In using formulae for stays a large factor of safety should be taken to 
 allow for reduction of size by corrosion. Thurston's Manual of Steam- 
 boilers, p. 144, recommends that the factor be as large as 15 or 20. The 
 Hartford Steam Boiler Insp. & Ins. Co. recommends not less than 10. 
 
 Strength of Stays. — A. F. Yarrow (Engr., March 20, 1891) gives the 
 following results of experiments to ascertain the strength of water-space , 
 stays; 
 
IMPROVED METHODS OF FEEDING COAL. 
 
 Description. 
 
 Hollow stays screwed into f 
 plates and hole expanded! 
 
 Solid stays screwed into/ 
 plates and riveted over. \ 
 
 Length 
 between 
 Plates. 
 
 4.75 in. 
 4.64 in. 
 4.80 in. 
 4.80 in. 
 
 Diameter of Stay over 
 Threads. 
 
 I in. (hole7/i6in. and 5/ 16 in.) 
 1 in. (hole 9, 16 in. and 7/ie in.) 
 
 7/8 in. 
 
 7/8 in. 
 
 Ulti- 
 mate 
 
 Stress. 
 
 lbs. 
 25,457 
 20,992 
 22,008 
 22,070 
 
 The above are taken as a fair average of numerous tests. 
 
 Fusible plugs. — Fusible plugs should be put in that portion of the 
 heating-surface which first becomes exposed from lack of water. The 
 rules of the U. S. Supervising Inspectors specify Banca tin for the purpose. 
 Its melting-point is about 445° F. The rule says: Every boiler, other than 
 boilers of the water-tube type, shall have at least one fusible plug made 
 of a bronze casing filled with good Banca tin from end to end. Fusible 
 plugs, except as otherwise provided for, shall have an external diameter 
 of not less than 3/4 in. pipe tap, and the Banca tin shall be at least 1/2 in. 
 in diameter at the smallest end and shall have a larger diameter at the 
 center or at the opposite end of the plug; smaller plugs are allowed for 
 pressures above 150 lbs., also for upright boilers. Cylinder-boilers with 
 flues shall have one plug inserted in one flue of each boiler; and also one 
 plug inserted in the shell of each boiler from the inside, immediately 
 below the fire line and not less than 4 ft. from the front end. Other shell 
 boilers shall have one plug inserted in the crown of the back connection. 
 Upright tubular boilers shall have a fusible plug inserted in one of the 
 tubes at a point at least 2 in. below the lowest gauge-cock, but in boilers 
 having a cone top it shall be inserted in the upper tube sheet. All tubes 
 are to be inserted so that the small end of the tin shall be exposed to the 
 fire. 
 
 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. 
 
 Height of Furnace. — Recent practice in the United States makes 
 the height of furnace much greater than it was formerly. With large sizes 
 of anthracite there is no serious objection to having the furnace as low as 
 18 in., measured from the surface of the grate to the nearest portion of 
 the heating surface of the boiler, but with coal containing much volatile 
 matter and moisture a much greater distance is desirable. With very 
 volatile coals the distance may be as great as 5 ft. or even 10 ft. Rankine 
 (S. E., p. 457) says: The clear height of the "crown" or roof of the furnace 
 above the grate-bars is seldom less than about 18 in., and often con- 
 siderably more. In the fire-boxes of locomotives it is on an average 
 about 4 ft. -The height of 18 in. is suitable where the crown of the fur- 
 nace is a brick arch. Where the crown of the furnace, on the other hand, 
 forms part of the heating-surface of the boiler, a greater height is desirable 
 in every case in which it can be obtained; for the temperature of the 
 boiler-plates, being much lower than that of the flame, tends to check the 
 combustion of the inflammable gases which rise from the fuel. As a 
 general principle a high furnace is favorable to complete combustion. 
 
 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. 
 
 The Jukes stoker consisted of longitudinal fire-bars, connected by 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 moving 
 
890 THE STEAM-BOILER. 
 
 from front to rear, gradually advanced the fuel into the furnace and dis- 
 charged 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 receptacle 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 coming 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 
 "pusher" 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 com- 
 bustion 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. lbs. 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. 
 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 distilled 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, made by the Amer. Ship Windlass Co., 
 Providence, R. I., 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. 
 
 SMOKE PREVENTION. 
 
 The following article was contributed by the author to a " Report on 
 Smoke Abatement," presented by a Committee to the Syracuse Chamber 
 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 burning 
 or splitting up of hydrocarbon gases, the hydrogen burning and the 
 
SMOKE PREVENTION. 891 
 
 carbon being 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 way 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 same 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 have 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 burnea. 
 The essential conditions for preventing smoke in boiler fires may be 
 enumerated as follows: 
 
 1. The gases must be distilled from the coal 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 
 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: 
 (1) That the coal be delivered into the furnace in small quantities at a 
 time. (2) That the draught be sufficient to carrv enough air into the 
 furnace to burn the gases as fast as they are distilled. (3) That the air 
 
892 THE STEAM-BOILER. 
 
 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 particle of carbon 
 in the gas meets, before it escapes from the furnace, its necessary supply 
 of air. (5) That the name 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 obtain 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- 
 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. 
 
SMOKE PREVENTION. 893 
 
 No. 6. Babcock & Wilcox. Roney stoker. Horizontal tile-roof baf- 
 fling. Can be run without smoke at capacities of 50 to 100% of rating. 
 
 Nos. 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 lbs. 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 and more 
 than ordinary care in firing. 
 
894 THE STEAM-BOILER. 
 
 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 being 
 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 of 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 pressure 
 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 conven- 
 iently 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 oi fire-grate with fire-bars from 
 5 to 51/2 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. 
 
 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 saving of fuel that may be made by an economizer varies 
 greatly according to the conditions of operation. With a given quan- 
 tity of "chimney gases to be passed through it, its economy will be greater 
 
FUEL ECONOMIZERS. 
 
 895 
 
 (1) the higher the temperature of these gases; (2) the lower the tem- 
 perature 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 heating 
 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 costs 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 lb. 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 bciler and entering the 
 economizer is directly proportional to (100-% of boiler efficiency), and 
 the combined efficiency of boiler and economizer is (2500 - 300) -*- 2500 
 = 88%, which corresponds to an evaporation of (15,000 -*- 970) X 0.88 = 
 13.608 lbs. from and at 212° per lb. of combustible; or assuming the feed- 
 water enters the economizer at 100° F. and the boiler makes steam of 
 150 lbs. absolute pressure, to an evaporation of 11.729 lbs. under these 
 conditions. Dividing this figure into the number of heat units utilized 
 by the economizer per lb. 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, %. 
 
 60 
 
 65 
 
 70 
 
 9000 
 
 9750 
 
 10500 
 
 6000 
 
 5250 
 
 4500 
 
 1000° 
 
 875° 
 
 750° 
 
 300° 
 
 300° 
 
 300° 
 
 4200 
 
 3450 
 
 2700 
 
 28 
 
 23 
 
 18 
 
 9.278 
 
 10.051 
 
 10.824 
 
 4.330 
 
 3.557 
 
 2.884 
 
 448° 
 
 389° 
 
 327° 
 
 70 
 
 65.7 
 
 60 
 
 B.T.U. absorbed by boiler per lb. combustible. . . 
 
 B.T.U. in chimney gases leaving boiler 
 
 Estimated temp, of gases leaving boiler 
 
 Estimated temp, of gases leaving economizer.:.. 
 
 B.T.U. saved by economizer 
 
 Efficiency gained by economizer, % 
 
 Equivalent water evap. per lb. comb, in boiler. . . 
 B.T.U. saved by econ. equivalent to evap. of lbs 
 
 Temp, of water leaving economizer 
 
 Efficiency of the economizer, % 
 
 11250 
 
 3750 
 
 625° 
 
 300° 
 
 1950 
 
 13 
 
 ! 1.598 
 
 2.010 
 
 265° 
 
 52 
 
 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 1/2 lbs. 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 41/2 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. 
 
THE STEAM-BOILER. 
 
 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) 
 -s- (Hi — h), in which h is the total heat above 32° of 1 lb. of water enter- 
 ing, Hi the total heat of 1 lb. of water leaving the economizer, and Hi the 
 total heat above 32° of 1 lb. of steam at the boiler pressure. If h = 100, 
 Hi = 210, Hi = 1200, then the saving according to the formula 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 beat 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 Hi — h 
 heat units per lb. instead of Hi — 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 1S97, using Missouri 
 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 lbs. from 
 and at 212° per lb. 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 combined 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) ■*- 6.27 = 
 11.5%, or as calculated by Mr. Gasche from the formula (Hi — h) -*- 
 (Hi - h), (172.1 - 39.3) -h (1181.8 -h 39.3) = 11.6%. 
 
 The maximum saving of fuel which may be made by the use of an econo- 
 mizer when attached to boilers that are working with reasonable economy 
 is about 15%. Take the case of a condensing engine using steam of 125 
 lbs. gauge pressure, and with a hot-well or feed-water temperature of 
 100° F. The economizer may be expected under the best conditions to 
 raise this temperature about 170°, or to 270°. Then h = 68, Hi = 239, 
 Hi - 1190. (Hi - h) -4- (Hi - h) = 171 -J- 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/i6 in. external diam.; total heating surface 6760 sq. 
 ft., or 3.25 sq. ft. per rated H.P. of the boilers. Draught area through 
 econ., 3 sq. in. per H.P. The stack for each 16 boilers and four econo- 
 mizers 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 econ. 96° (93.5°); leaving 200° (203.8°); rise 104 (110.3). 
 
 Gases entering econ. 548° (603°); leaving 295 (325); drop 253 (278). 
 
 Steam, gauge pressure, 166 (165). Total B.T.U. per lb. from feed 
 temp. 1132 (1134). 
 
 Saving of heat by economizer, %, 9.17 (9.73). 
 
 Reduction of draught in passing through econ., in. of water, 0.16 (0.23). 
 
 Results from Seven Tests of Sturtevant Economizers (Catalogue of 
 B. F. Sturtevant Co.) 
 
 Plants 
 Tested. 
 
 Gases En- 
 
 Gases 
 
 Water En- 
 
 Water 
 
 Increase in 
 
 tering. 
 
 Leaving. 
 
 tering. 
 
 Leaving. 
 
 Tempera- 
 
 Deg. F. 
 
 Deg. F. 
 
 Deg. F. 
 
 Deg. F. 
 
 ture. 
 
 1 
 
 650 
 
 275 
 
 180 
 
 340 
 
 160 
 
 2 
 
 575 
 
 290 
 
 160 
 
 320 
 
 160 
 
 3 
 
 470 
 
 230 
 
 130 
 
 260 
 
 130 
 
 4 
 
 500 
 
 240 
 
 110 
 
 230 
 
 120 
 
 5 
 
 460 
 
 200 
 
 90 
 
 230 
 
 140 
 
 6 
 
 440 
 
 220 
 
 120 
 
 236 
 
 116 
 
 7 
 
 525 
 
 225 
 
 180 
 
 320 
 
 140 
 
INCRUSTATION AND CORROSION. 897 
 
 THERMAL STORAGE. 
 
 In Druitt Halpin's steam storage system (Industries and Iron, Mar. 22, 
 1895) he employs only sufficient boilers to supply tile 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 which 
 it may be drawn at will during heavy load. He proposes that the boilers 
 and tanks shall work under a pressure of 265 lbs. per square inch when 
 fully charged, which corresponds to a temperature of 406° F., and that 
 the engines be worked at 130 lbs. 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 14V4 lbs. of 
 water from 407° to 347° will yield 1 lb. of steam. To allow for radia- 
 tion of loss and imperfect working, this may be taken at 16 lbs. of water 
 per pound of steam. The steam consumption per effective H.P. maybe 
 taken at 18 lbs. per hour in condensing and 25 lbs. 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) ■*■ 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 steam 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. 691, 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 spft 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, and it 
 should be introduced regularly with the feed. 
 
 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 
 CaS0 4 Na 2 C0 3 Na 2 S0 4 CaC0 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 
 
THE STEAM-BOILER. 
 
 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 heating 
 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 action 
 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 lbs. of water per hour, the water containing different 
 amounts of impurity in solution, provided that no water is blown off: 
 
 Grams 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 lbs. per cu. ft.; 0.02 X 1200 X 156 X V12 = 312 lbs. 
 
 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. 
 
 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 i/so of an inch thick requires the 
 burning of 5 per cent of additional fuel; scale 1/25 of an inch thick 
 
 * A committee of the Am. Ry. 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 i'i6 in. thick requires the expenditure of 
 15% more fuel. As the scale thickens the ratio increases; thus when it 
 is 1/4 in. thick, 60% more is required." 
 
INCRUSTATION AND CORROSION. 899 
 
 requires 10 per cent more fuel; i,'i6 of an inch of scale requires 15 per 
 cent additional fuel; Vs of an inch. 30 per cent., and 1/4 of an inch, 66 per 
 cent." 
 
 The absurdity of the last statement may be shown by a simple calcu- 
 lation. Suppose a clean boiler is giving 75% efficiency with a furnace 
 temperature of 2400° F. above the atmospheric temperature, Neglecting 
 the radiation and assuming a constant specific heat for the gases, the 
 temperature of the chimney gases will be 600°. A certain amount of 
 fuel and air supply will furnish 100 lbs. of gas. In the boiler with 1/4 in. 
 scale 66% more fuel will make 66 lbs. more gas. As the extra fuel does 
 no work in evaporating water, its heat must all go into the chimney 
 gas. We have then in the chimney gases 
 
 100 lbs. at 600° F., product 60,000 
 66 lbs. at 2400° F., product 158,400 nio , nn 
 21o,4UU 
 
 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 Vi6 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 1/8, then 3/ 16 in. will reduce it 9/ 8 , 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 of 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, and 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 boiler, 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. 
 
 Kerosene and other Petroleum Oils; Foaming. — Kerosene has 
 been recommended as a scale preventive. See paper by L. F. Lyne 
 (Trans. 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 
 
900 TOE STEAM-BOILER. 
 
 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 
 5 ft. in diam. 3 qts. per week. The water used in the boilers has the fol- 
 lowing analysis: CaC0 3 , 206 parts in a million; MgCCh, 78 parts; F62C03, 
 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 cils 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. Tins 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 
 zinc slabs suspended in the water and «team 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 
 on 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 
 it is renewed. Second, the boilers are filled with sea or fresh water, 
 having added soda to it in the proportion of 1 lb. to every 100 or 120 lbs. 
 of water. The sufficiency of the saturation can be tested by introducing 
 a piece of clean new iron and leaving it in the boiler for ten or twelve 
 hours: if it shows signs of rusting, more soda 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 
 
INCRUSTATION AND CORROSION. 901 
 
 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 ins. wide, and 1/2 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/g 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 bene- 
 ficial 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 being now 
 obtained from another stream supposed to be free from lime and to con- 
 tain only organic matter. Two or three months- after its introduction 
 the tubes and shell were found to be coated with an obstinate 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 con- 
 sumption of coal per I.H.P. per hour goes on gradually increasing until it 
 reaches one and a half times its original amount, and sometimes more. 
 
 Dangerous Steam-boilers discovered by Inspection. — The Hart- 
 ford Steam-boiler Inspection and Insurance Co. reports that its inspec- . 
 tors during 1908 examined 317,537 boilers, inspected 124,990 boilers, both 
 internally and externally, subjected 10,449 to hydrostatic pressure, and 
 found 572 unsafe for further use. The whole number of defects reported 
 was 151,359, of which 15,578 were considered dangerous. A summary 
 is given below. {The Locomotive, Jan., 1909.) 
 
902 
 
 THE STEAM-BOILER. 
 
 Summary, by Defects, for the Year 1893. 
 
 Whole Dan- 
 No. gerous. 
 ' 2,136 
 
 Nature of Defects. 
 
 Defective tubes 8,026 
 
 Tubes too light 1,636 '432 
 
 Leakage at joints 4,845 392 
 
 Water-gauges defective. 2,411 585 
 
 Blow-offs defective 3,818 1,125 
 
 Deficiency of water 391 147 
 
 Safety-valves overloaded 1,216 379 
 
 Safety-valves defective. 1,068 359 
 
 Pressure-gauges def'tive 7,120 531 
 
 Without pressure-gauges. . 322 322 
 
 Unclassified defects 7 3 
 
 Total 151,359 15,878 
 
 Whole Dan- 
 Nature of Defects. No. gerous. 
 
 Deposit of sediment 18,879 1 ,242 
 
 Incrustation and scale.. .37,924 1,193 
 
 Internal grooving 2,649 249 
 
 Internal corrosion 13,053 555 
 
 External corrosion 9,400 698 
 
 Def'tive braces and stays 1,993 503 
 
 Settings defective 5,341 642 
 
 Furnaces out of shape. . . 6,981 380 
 
 Fractured plates 3,119 482 
 
 Burned plates 4,605 440 
 
 Laminated plates 666 44 
 
 Defective riveting 3,395 713 
 
 Defective heads 1,565 223 
 
 Leakage around tubes. .. 10,929 2, 103 
 
 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 injuring 
 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. P. 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 the 
 form and dimensions adopted as a standard by the Hartford Steam-boiler 
 Insurance Co., he says: It is 60 ins. in diameter, containing 66 3-in. 
 tubes, and is 15 ft. long. It has 850 sq. ft. of heating and 30 sq. ft. of 
 grate surface is rated at 60 H.P., but is oftener driven up to 75; weighs 
 9500 lbs., and contains nearly its own weight of water, but only 21 lbs. 
 of steam when under a pressure of 75 lbs. 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 fulcrum 
 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. ins.; P = pressure of steam, in lbs. per sq. in., 
 at which valve will open. 
 
 Then PAXl = WXL+wXg + VXl; 
 whence P = (WL + wg + VI) ■*- Al; W = (PAl - wg - VI) + L; L = 
 (PAl - wg - VI) -^ W. 
 
 Example. — Diameter of valve, 4 ins.; distance from fulcrum to center 
 of ball, 36 ins.; to center of valve, 4 ins.; to center of gravity of lever, 
 151/2 ins.; weight of valve and spindle, 3 lbs.; weight of lever, 7 lbs.; re- 
 quired the weight of ball to make the blowing-off pressure 80 lbs. per sq. 
 in.; area of 4-in. valve = 12.566 sq. ins. Then 
 
 W- 
 
 PAl - wg-Vl _ 80 X 12.566 X 4-7 X 15l/ 2 - 3X4 
 L 36 
 
 = 108.41 
 
 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. 
 
SAFETY-VALVES. 903 
 
 Rules for Area of Safety-valves. 
 
 (Rule of U. S. Supervising Inspectors of Steam-vessels (as amended 1909).) 
 
 The areas of all safety-valves on boilers contracted for or the con- 
 struction of which commenced on or after June 1, 1904, shall be deter- 
 mined in accordance with the following formula: a = 0.2074 X W/P, 
 where a = area of safety-valve, in sq. in., per sq. ft. of grate surface; W = 
 pounds of water evaporated per sq. ft. of grate surface per hour; P — abso- 
 lute pressure per sq. in. = working gauge pressure + 15. 
 
 The value of a multiplied by the square feet of grate surface gives the 
 area of safety valve or valves required. When this calculation results 
 in an odd size of safety-valve use the next larger standard size. 
 
 Example. — Boiler-pressure = 215 lbs. gauge, = 230 absolute, = P. 
 Grate surface = 110 sq. ft. Water evaporated per pound coal = 10 lbs. 
 Coal burned per sq. ft. grate per hour = 30 lbs. Evaporation per sq. ft. 
 grate per hour = 300 lbs. = W. a = 0.2074 X 300 -s- 230 = 0.270. 
 Therefore area of safety-valve = 110 X 0.270 = 29.7 sq. ins., which is 
 too large for one valve. Use two, 14.85 sq. ins. each. Diameter = 43/ 8 
 ins. Each spring-loaded valve shall be supplied with a lever that Will 
 raise the valve from its seat a distance of not less than that equal to 
 one-eighth of the diameter of the valve opening. 
 
 The valves shall be so arranged that each boiler shall have at least one 
 separate safety-valve, unless the arrangement is such as to preclude the 
 possibility of shutting off the communication of any boiler with the 
 safety valve or valves employed. 
 
 Two safety-valves may be allowed on any boiler, provided their com- 
 bined area is equal to that required by rule for one valve. Whenever 
 the area of a safety-valve, as found by the rule, will be greater than that 
 corresponding to 6 inches in diameter, two or more safety-valves, whose 
 combined area shall be equal at least to the area required, must be used. 
 
 The seats of all safety-valves shall have an angle of inclination of 45 
 degrees to the center lines of their axes. 
 
 Comparison of Various Rules for Area of Lever Safety-valves. 
 (Condensed from an article by the author in American Machinist, May 24, 
 1894, with some alterations.)' — Assume the case of a boiler rated at 100 
 horse-power; 40 sq. ft. grate; 1200 sq. ft. heating-surface; using 400 lbs. 
 of coal per hour, or 10 lbs. per sq. ft. of grate per hour, and evaporating 
 3600 lbs. of water, or 3 lbs. per sq. ft. of heating-surface per hour; steam- 
 pressure by gauge, 100 lbs. What size of safety-valve, of the lever type, 
 should be required? 
 
 A compilation of various rules for finding the area of the safety-valve 
 disk, from The Locomotive of July, 1892, is given in abridged form below, 
 together with the area calculated by each rule for the above example. 
 
 Disk Area 
 in sq. in. 
 
 U. S. Supervisors, heating-surface in sq. ft. -s- 25 (old rule) 48 
 
 English Board of Trade, grate-surface in sq. ft. -s- 2 20 
 
 Molesworth, four-fifths of grate-surface in sq. ft 32 
 
 Thurston, 4 times coal burned per hour X (gauge pressure + 10) ... 14.5 
 
 Thurston, 2.5 X heating-surface h- gauge pressure + 10 27.3 
 
 Rankine, 0.006 X water evaporated per hour 21 . 6 
 
 Committee of U. S. Supervisors, 0.005 X water evaporated per hr.. 18 
 
 Suppose that, other data remaining the same, the draught were in- 
 creased so as to burn 13 1/3 lbs. coal per sq. ft. of grate per hour, and the 
 grate-surface cut down to 30 sq. ft. to correspond, making the coal burned 
 per hour 400 lbs., and the water evaporated 3600 lbs., the same as before; 
 then the English Board of Trade rule and Molesworth's rule would give 
 an area of disk of only 15 and 24 sq.in., respectively, showing the absurdity 
 of making the area of grate the basis of the calculation of disk area. 
 
 Other rules give for the area of safety-valve of the same 100-horse- 
 power boiler results ranging all the way from 5.25 to 57.6 sq. ins. 
 
 All of the rules quoted give the area of the disk of the valve as the 
 thing to be ascertained, and it is this area which is supposed to bear 
 6ome direct ratio to the grate-surface, to the heating-surface, to the 
 
904 THE STEAM-BOILER. 
 
 water evaporated, etc. It is difficult to see why this area has been con- 
 sidered even approximately proportional to these quantities, for with 
 small lifts the area of actual opening bears a direct ratio, not to the area 
 of disk, but to the circumference. 
 Thus for various diameters of valve: 
 
 Diameter, ins. 1 2 3 4 5 6 7 
 
 Area, sq. ins 0.785 3.14 7.07 12.57 19.64 28.27 38.48 
 
 Circumference 3.14 6.28 9.42 12.57 15.71 18.85 21.99 
 
 Circum.Xliftof O.lin. 0.31 0.63 0.94 1.26 1.57 1.89 2.20 
 
 Ratio to area 0.4 0.2 0.13 0.1 0.08 0.067 0.057 
 
 A correct rule for size of safety-valves should make the product of the 
 diameter and the lift proportional to the weight of steam to be discharged. 
 
 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 lbs. per second = absolute pressure -s- 70, or in lbs. 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 
 lbs. 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. 
 31/2-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 = lbs. of water evaporated per sq. ft. of grate surface per 
 hour; P = boiler pressure, absolute, lbs. 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 = lbs. 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 Ride. — A = 22.5 G + (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 winch 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 
 
SAFETY-VALVES. 
 
 905 
 
 reality with a given design the lifts are more nearly the same in the differ- 
 ent 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 conclusion is that 
 existing rules and statutes are not safe to follow. Some of these rules in 
 use were formulated before, and have not been modified since, spring 
 safety-valves were invented, and at a time when 120 lbs. was considered 
 high pressure. None of these rules take account of the different lifts 
 which exist in the different makes of valves of the same nominal size, and 
 they thus rate exactly alike valves which actually vary in lift and relieving 
 capacity over 300%. It would therefore seem the duty of all who are 
 responsible for steam installation and operation to no longer leave the 
 determination of safety-valve size and selection to such statutes as may 
 happen to exist in their territory, but to investigate for themselves. 
 
 Formulae for Spring-loaded Safety- Valves. — Let L = lift of valve 
 in.; D = diam. in.; E = discharge, lbs. per hour; P = abs. pressure; 
 A = area of opening; 6 = angle of seat with horizontal. By Napier's 
 formula E = AP X 3600 -5- 70 = 51.43 AP. A = nDL cos (approx- 
 imately). If = 45°, cos 6 = 0.707, whence E = 114.2 LDP. Experi- 
 ments with six different valves, 3, 31/2 and 4 in. stationary, and 11/2. 3 
 and 31/2 in. locomotive, gave an average flow equal to 92.5% of that 
 calculated by the above formula, which is therefore modified by Mr. 
 Darling to the forms E = 105 LDP, and D = 0.0095 E + LP. ... (1) 
 
 To obtain formulae for safety valves in terms of the heating-surface 
 of the boiler Mr. Darling takes for stationary boilers an average evapora- 
 tion of 31/2 lbs. per sq. ft. of heating-surface per hour, with an overload 
 capacity of 100%; for marine boilers, water-tube or Scotch, an overload 
 or maximum evaporation of 10 lbs. per sq. ft. of heating-surface per hour. 
 If H = total boiler heating-surface in sq. ft., these assumptions give for 
 stationary boilers D = 0.068 H ■*- LP, ... (2) and for marine boilers 
 D = 0.095 H -3- LP . . . (3). For locomotive boilers the proper con- 
 stant in the formula was deduced from numerous experiments to be 
 0.055 . . . (4). 
 
 For flat valves the constants in the last four formulae are: (1) 0.0067; 
 (2) 0.065; (3) 0.090; (4) 0.052. 
 
 The following table is calculated from Napier's formula, on the assump- 
 tion of a lift of 0.1 in. and a 45° valve-seat. For any other lift than 0.1 
 in., the discharge is proportional to the lift. The figures should be multi- 
 plied by a coefficient expressing the relation of the discharge of actual 
 valves to the discharge through a plain round orifice (Napier's). In 
 the Consolidated SafetyValve Co.'s experiments the average value of this 
 coefficient was found to be 0.925. 
 
 Steam Discharged in Lbs. per Hour by a Valve Lifting 0.10 in. 
 
 £o5 
 
 Valve diameters, inches. 
 
 03 
 
 1 
 
 H/2 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 5 
 
 51/2 
 
 6 
 
 25 
 
 460 
 
 690 
 
 920 
 
 1150 
 
 1380 
 
 1610 
 
 1840 
 
 2080 
 
 2300 
 
 2540 
 
 2770 
 
 50 
 
 750 
 
 1130 
 
 1500 
 
 1880 
 
 2250 
 
 2630 
 
 3000 
 
 3380 
 
 3760 
 
 4130 
 
 4500 
 
 75 
 
 1040 
 
 1560 
 
 2080 
 
 2600 
 
 3120 
 
 3640 
 
 4160 
 
 4680 
 
 5200 
 
 5720 
 
 6240 
 
 100 
 
 1330 
 
 2000 
 
 2660 
 
 3330 
 
 4000 
 
 4660 
 
 5320 
 
 6000 
 
 6650 
 
 7320 
 
 8000 
 
 125 
 
 1620 
 
 2440 
 
 3250 
 
 4060 
 
 4860 
 
 5670 
 
 6480 
 
 7300 
 
 8100 
 
 8920 
 
 9730 
 
 150 
 
 1910 
 
 2870 
 
 3830 
 
 4790 
 
 5740 
 
 6700 
 
 7650 
 
 8610 
 
 9560 
 
 10520 
 
 11470 
 
 175 
 
 2200 
 
 3300 
 
 4400 
 
 5500 
 
 6600 
 
 7700 
 
 8800 
 
 9900 
 
 11000 
 
 12100 
 
 13200 
 
 200 
 
 2500 
 
 3740 
 
 5000 
 
 6240 
 
 7480 
 
 8730 
 
 9970 
 
 11200 
 
 12460 
 
 13700 
 
 14950 
 
 225 
 
 2780 
 
 4180 
 
 5570 
 
 6960 
 
 8340 
 
 9730 
 
 11120 
 
 12500 
 
 13900 
 
 15300 
 
 16700 
 
 250 
 
 3070 
 
 4610 
 
 6140 
 
 7680 
 
 9200 
 
 10740 
 
 12300 
 
 13800 
 
 15360 
 
 16900 
 
 18450 
 
 275 
 
 3360 
 
 5050 
 
 6720 
 
 8400 
 
 10100 
 
 11760 
 
 13450 
 
 15150 
 
 16800 
 
 18500 
 
 20200 
 
 300 
 
 3650 
 
 5480 
 
 7310 
 
 9150 
 
 10960 
 
 12800 
 
 14600 
 
 16470 
 
 18300 
 
 20100 
 
 22000 
 
906 
 
 THE STEAM-BOILER. 
 
 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 41/2 ins. If greater relieving capacity be required 
 it is the best practice to use duplex valves or additional single valves. 
 
 Relieving Capacities, Consolidated Pop Safety Valves, Stationary 
 Type. (Pounds of Steam per hour.) 
 
 > 
 
 Is 
 
 Gauge Pressures, (lbs. per sq. in.) 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 220 
 
 240 
 
 260 
 
 280 
 
 300 
 
 2 
 
 1890 
 
 2400 
 
 2900 
 
 3400 
 
 3900 
 
 4410 
 
 4910 
 
 5420 
 
 5920 
 
 6430 
 
 6930 
 
 7430 
 
 7940 
 
 21/9 
 
 2360 
 
 3000 
 
 3620. 
 
 4250 
 
 4880 
 
 5500 
 
 6140 
 
 6760 
 
 7400 
 
 8030 
 
 8650 
 
 9300 
 
 9900 
 
 3 
 
 3070 
 
 3890 
 
 4700 
 
 5530 
 
 6350 
 
 7170 
 
 8000 
 
 8800 
 
 9620 
 
 10400 
 
 11200 
 
 12100 
 
 12900 
 
 31/o 
 
 3860 
 
 4880 
 
 5910 
 
 6950 
 
 7960 
 
 9020 
 
 10000 
 
 11100 
 
 12100 
 
 13100 
 
 14200 
 
 15200 
 
 16300 
 
 4 
 
 4410 
 
 5580 
 
 6770 
 
 7950 
 
 9120 
 
 10300 
 
 11500 
 
 12600 
 
 13800 
 
 15000 
 
 16200 
 
 17300 
 
 18500 
 
 41/o 
 
 5310 
 
 6730 
 
 8150 
 
 9570 
 
 11000 
 
 12400 
 
 13800 
 
 15200 
 
 16700 
 
 18100 
 
 19500 
 
 20900 
 
 22400 
 
 5 
 
 6300 
 
 7970 
 
 9650 
 
 11330 
 
 13000 
 
 14700 
 
 16400 
 
 18100 
 
 19700 
 
 21400 
 
 23100 
 
 24800 
 
 26500 
 
 For an extended discussion on safety-valves, see Trans. A. S. M. E., 
 1909. 
 
 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 n the height in feet the water is lifted to the injector; 
 fi the temperature of the water before it enters the injector; 
 ti the temperature of the water after leaving the injector; 
 H the total heat above 32° F. in one pound of steam in the boiler, 
 
 in heat-units; 
 L the work in friction and the equivalent lost work due to radiation 
 
 and lost heat; 
 778 the mechanical equivalent of heat. 
 Then 
 
 S[ H-(U-S2^W(t 2 -t 1 ) + ^ W + S)h+Who + L 
 
 An equivalent formula, neglecting Wh 
 W[(jti-ti) d + 0.1851 p] 
 
 778 
 
 L as small, is 
 1 
 
 44.-] 1 
 
 78j H-(h-32°)' 
 
 orS = 
 
 [J/-(t2- 32°)] d -0.1851 p' 
 
 in which d = weight of 1 cu. ft. of water at temperature h; p — absolute 
 pressure of steam, lbs. 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 ^pressure 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 INJECTOR. 
 
 907 
 
 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. 
 
 . Si 
 
 ill 
 
 H.g 
 
 Kg 
 
 73 
 
 H. 
 
 P. 
 
 M. 
 
 
 H. 
 
 P. 
 
 M. 
 
 S. 
 
 10 
 
 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 
 
 J42°' 
 
 132 
 
 126 
 
 120 
 
 114 
 
 .109 
 
 105 
 
 99 
 
 95 
 
 87 
 
 77 
 
 
 
 
 
 H?° 
 
 20 
 30 
 
 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 
 
 173° 
 162 
 156 
 150 
 143 
 139 
 134 
 129 
 125 
 117 
 107 
 
 135° 
 
 120° 
 
 130° 
 
 134 
 134 
 
 40 
 50 
 60 
 70 
 80 
 90 
 
 140 
 
 141* 
 141* 
 
 113 
 f 15 
 
 118' 
 
 125 
 
 123' 
 123 
 122 
 
 132 
 131 
 130 
 130 
 131 
 137* 
 
 100 
 
 
 
 
 
 
 
 13?* 
 
 
 
 
 
 
 
 
 134* 
 
 
 
 
 
 PI* 
 
 
 
 
 
 
 
 
 * Temperature of delivery above 212°. Waste-valve closed. 
 H, Hancock inspirator; P, Park injector; M, Metropolitan injector; 
 S, Sellers 1876 injector. 
 
 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 under 
 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. Mach., 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 lbs. water delivered to boiler per lb. of steam; 
 temperature of water, 64°; steam pressure, 65 lbs. 
 
 Schaeffer & Budenberg — 1 gal. water delivered to boiler for 0.4 to 
 0.8 lb. 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 lbs. 60 to 90 lbs. 90 to 120 lbs. 120 to 150 lbs. 
 
22 
 
 22 
 
 11 
 
 54.1 
 
 95.5 
 
 75.4 
 
 35.4° 
 
 47.3° 
 
 53.2 
 
 117.4° 
 
 173.7° 
 
 131. r 
 
 13.67 
 
 8.18 
 
 13.3 
 
 908 THE STEAM-BOILER. 
 
 If the water is not over 80° F., the injector will force against a pressure 
 75 lbs. higher than that of the steam. 
 
 Hancock Inspirator Co.: 
 
 Lift in .feet 22 
 
 Boiler pressure, absolute, lbs 75 . 8 
 
 Temperature of suction 34.9° 
 
 Temperature of delivery 134° 
 
 Water fed per lb. of steam, lbs 11.02 
 
 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 boiler 
 and engine is such that half a cubic foot, say 32 lbs. of water, is needed 
 per horse-power, and the boiler-pressure is 100 lbs. per sq. in., then the 
 work of feeding the quantitv of water is 100 lbs. X 144 sq. in. X Vi ft— 
 lb. per hour = 120 ft.-lbs. per min. = 120/33,000 = .0036 H.P., or less 
 than 4/ 10 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 i/io 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 efficiency 
 of steam and power pumps and injector, with and without heater, as used 
 upon a boiler with 80 lbs. gauge-pressure, the pump having a duty of 
 10,000,000 ft.-lbs. per 100 lbs. 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 1.000 
 
 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° . 938 
 
 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. 
 
 909 
 
 FEED-WATER HEATERS. 
 
 Percentage of Saving for Each Degree of Increase in Temperature 
 of Feed-water Heated by Waste Steam. 
 
 Initial 
 
 Steam Pressure in Boiler, lbs. per sq.in.above^Atmosphere. 
 
 
 Temp. 
 
 of 
 Feed. 
 
 
 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 
 
 80 
 
 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 
 
 
 
 
 
 
 
 
 
 .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 lbs. 
 gauge; total heat in steam above 32° = 1185B.T.U. Feed-water, original 
 temperature 60°, final temperature 209° F. Increase in heat-units, 150. 
 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 lb. of steam at the 
 boiler-pressure = H; total heat of 1 lb. of feed-water before entering the 
 heater = hi, and after passing through the heater = hr, 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 firmlv held at the ends and that the modulus 
 of elasticitv is 29,000,000, would require a force of 37,700 lbs. per sq. in. 
 Of course this amount of strain cannot actually take place, since the strip 
 is not firmlv held at the ends, but is allowed to contract to some extent 
 by the elasticitv of the surrounding metal. But, says The Locomotive, 
 we may feel prettv confident that in the case considered a longitudinal 
 strain of somewhere in the neighborhood of 8000 or 10,000 lbs. per sq. in. 
 may be produced by the feed-water striking directlv 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 
 
910 
 
 THE STEAM-BOILER. 
 
 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: 
 
 15° F 67 B.T.U. ) Transmitted in one 
 
 6° " 79 " hour by each sq. ft. 
 
 8° " 89 " I of surface for each 
 
 11°" 114 " [ degree of average 
 
 15°" 129 " difference in temper- 
 
 18° " 139 " J 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 lbs. of water per hour. If the figures given in the 
 table above are accepted as substantially correct, a heater which is to 
 raise 3000 lbs. 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 = lbs. of water per hour; A = area of 
 surface in sq. ft.; T s = temperature of the steam; / = initial tempera- 
 ture of the water; F = final temperature of the water; S = lbs. of steam 
 per hour; H = B.T.U. above 32° F. in 1 lb. of steam; N = B.T.U. in 
 1 lb. of condensed steam; U = B.T.U. transmitted per sq. ft. per hour 
 per degree of mean difference of temperature between the steam and the 
 water. 
 
 Then AU = W log e ' ~ , for heaters. 
 Is — * 
 
 A U ~ S F - T * l0ge T - F ' f ° r condensers - 
 
 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 lbs. 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 
 
 $ 
 
 F 
 
 S 
 
 194 
 
 11.11 
 
 204 
 
 15.34 
 
 90 
 
 2.38 
 
 115 
 
 6.78 
 
 196 
 
 11.73 
 
 206 
 
 . 16.85 
 
 95 
 
 3.03 
 
 120 
 
 8.60 
 
 198 
 
 12.44 
 
 208 
 
 18.93 
 
 100 
 
 3.76 
 
 125 
 
 11.15 
 
 200 
 
 13.20 
 
 210 
 
 22.52 
 
 105 
 
 4.62 
 
 130 
 
 16.25 
 
 202 
 
 14.17 
 
 212 
 
 Infinite 
 
 110 
 
 5.65 
 
 133 
 
 Infinite 
 
 F = final temperature of feed -water- S = sq. ft. of surface. From this 
 table it is seen that if 30 lbs. of water per hour is taken to equal 1 H.P. 
 
STEAM SEPARATORS. 911 
 
 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 if 
 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 561 to 565. 
 
 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 -*- 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 lbs. 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 customary 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. 
 
 If moist steam flowing: at a high velocity in a pipe has its direction sud- 
 denly changed, the particles of water are by their momentum projected in 
 their original direction against the bend in the pipe or wall of the chamber 
 in which the chansre of direction takes place. By making proper provi- 
 sion for drawing off the water thus separated the steam may be dried to a 
 greater or less extent. 
 
 For long steam-pipes a Targe drum should be provided near the engine 
 for trapping the water condensed in the pipe. A drum 3 feet diameter, 
 15 feet hierh, has srivpn good results in separating the water of condensa- 
 tion of a steam-oine 10 inches diameter and 800 feet long. 
 
 Efficiency of Steam Separators. — Prof. R. C. Carpenter, in 1891, 
 made a series of tests of six steam separators, furnishing them with steam 
 containine different Dercentages 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. 
 
912 
 
 THE STEAM-BOILER. 
 
 o 
 
 Test with Steam of about 10% 
 of Moisture. 
 
 Tests with Varying Moisture. 
 
 o £ 
 
 1^ 
 
 Quality 
 of Steam 
 before. 
 
 Quality 
 
 of Steam 
 
 after. 
 
 Efficiency, 
 per cent. 
 
 Quality of 
 Steam be- 
 fore. 
 
 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 lbs. 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; 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 lbs. pressure containing 10% 
 water, the efficiencies, taken approximately 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 
 
 IN STEAM — STEAM 
 
 DETERMINATION OF THE MOISTURE 
 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 
 
DETERMINATION OP THE MOISTURE IN STEAM. 913 
 
 the condensing water, and taking its temperature as it enters and 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 1/2-inch pipe into and 
 through the main pipe near the boiler, and led by a hose, thoroughly 
 felted, to a barrel, holding preferably 400 lbs. 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: 
 
 .. 1 ri- 
 ff - Tlw 
 
 E {hl _ h) _ iT _ hl q 
 
 Q = quality of the steam, dry saturated steam being unity. 
 H = total heat of 1 lb. of steam at the observed pressure. 
 T = total heat of 1 lb. of water at the temperature of steam of the 
 
 observed pressure. 
 h = total heat of 1 lb. of condensing water, original. 
 hi = total heat of 1 lb. 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. Jacobua {Tranc<. 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 and 
 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 the 
 condensed steam read at short intervals of time. 
 
 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 1/2-inch pipe is throttled by an orifice Vi6 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. 
 
914 
 
 THE STEAM-BOILER. 
 
 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 J ^- = — ^^ — — , 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, = 1146.6 at atmospheric pressure; K= specific 
 heat of superheated steam; T = temperature of the throttled and super- 
 heated steam in the calorimeter; t = temperature due to the pressure in 
 the calorimeter, = 212° at atmospheric pressure. 
 
 Taking K at 0.4S and the pressure in the discharge side of the calo- 
 rimeter as atmospheric pressure, the formula becomes 
 
 100 X 
 
 H 
 
 1146.6 - 0.48 (T - 212°) 
 
 From this formula the following table is calculated: 
 Moisture in Steam — Determinations by Throttling Calorimeter 
 
 
 Gauge-pressu 
 
 res. 
 
 Degree of 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Super- 
 
 5 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 JO 
 
 yi> 
 
 80 
 
 85 
 
 90 
 
 heating 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Per Cent of Moisture 
 
 in Steam. 
 
 0° 
 
 0.51 
 
 0.90 
 
 1.54 
 
 2.06 
 
 2 50 
 
 2 90 
 
 3 24 
 
 3.56 
 
 3.71 
 
 3.86 
 
 3 99 
 
 4.13 
 
 10° 
 
 0.01 
 
 0.39 
 
 1.02 
 
 1.54 
 
 1 97 
 
 2 36 
 
 2.71 
 
 3.02 
 
 3.17 
 
 3.32 
 
 3 45 
 
 3 58 
 
 20° 
 
 
 
 0.51 
 0.00 
 
 1.02 
 0.50 
 
 1.45 
 0.92 
 0.39 
 
 1.83 
 1.30 
 0.77 
 0.24 
 
 2.17 
 1.64 
 1.10 
 0.57 
 0.03 
 
 2.48 
 1.94 
 1.40 
 0.87 
 0.33 
 
 2.63 
 2.09 
 1.55 
 1.01 
 0.47 
 
 2.77 
 2.23 
 1.69 
 1.15 
 0.60 
 0.06 
 
 2.90 
 2.35 
 1.80 
 1.26 
 0.72 
 0.17 
 
 3.03 
 
 30° 
 
 
 
 2.49 
 
 40° 
 
 
 
 1.94 
 
 50° 
 
 
 
 
 
 1 40 
 
 60° 
 
 
 
 
 
 
 0.85 
 
 70° 
 
 
 
 
 
 
 
 31 
 
 
 
 
 
 
 
 
 
 
 
 
 Dif.p.deg. 
 
 .0503 
 
 .0507 
 
 .0515 
 
 .0521 
 
 .0526 
 
 .0531 
 
 .0535 
 
 .0539 
 
 .0541 
 
 .0542 
 
 .0544 
 
 .0546 
 
 
 Gauge-pressu 
 
 res. 
 
 Degree of 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Super- 
 
 100 
 
 1 10 
 
 17,0 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 
 
 190 
 
 ZOO 
 
 250 
 
 heating 
 T -212°. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Per Cent of Moistur 
 
 e in Steam. 
 
 0° 
 
 4 39 
 
 4.63 
 
 4.85 
 
 5.08 
 
 5.29 
 
 5.49 
 
 5.68 
 
 5.87 
 
 6.05 
 
 6.22 
 
 6 39 
 
 7.16 
 
 10° 
 
 3.84 
 
 4 08 
 
 4 29 
 
 4 52 
 
 4 73 
 
 4 93 
 
 5 12 
 
 5 30 
 
 5 48 
 
 5 65 
 
 5 82 
 
 6.58 
 
 20° 
 
 3 29 
 
 3 52 
 
 3,74 
 
 3.96 
 
 4 17 
 
 4 37 
 
 4 56 
 
 4.74 
 
 4 91 
 
 5 08 
 
 5 25 
 
 6.00 
 
 30° 
 
 7 74 
 
 2 97 
 
 3 18 
 
 3.41 
 
 3.61 
 
 3 80 
 
 3 99 
 
 4,17 
 
 4 34 
 
 4 51 
 
 4 67 
 
 5.41 
 
 40° 
 
 2 19 
 
 2 42 
 
 2.6.3 
 
 2.85 
 
 3.05 
 
 3 24 
 
 3 43 
 
 3 61 
 
 3 78 
 
 3.94 
 
 4 10 
 
 4.83 
 
 50° 
 
 1.64 
 
 1.87 
 
 2.08 
 
 2.29 
 
 2.49 
 
 ?, 68 
 
 ?. 87 
 
 3.04 
 
 3 21 
 
 3 37 
 
 3.53 
 
 4.25 
 
 60° 
 
 1.09 
 
 1.32 
 
 1.52 
 
 1 74 
 
 1 93 
 
 ?, U 
 
 2 30 
 
 2 48 
 
 ?, 64 
 
 ?, 80 
 
 2.96 
 
 3.67 
 
 70° 
 
 0.55 
 
 o.yy 
 
 97 
 
 1 18 
 
 1 38 
 
 1 56 
 
 1 74 
 
 1 91 
 
 7 07 
 
 ? ?,3 
 
 7. 38 
 
 3.09 
 
 80° 
 
 0.00 
 
 0.22 
 
 0.42 
 
 0.63 
 
 82 
 
 1 00 
 
 1 IS 
 
 1.34 
 
 1 50 
 
 1.66 
 
 1 81 
 
 2.51 
 
 90° 
 
 
 
 
 0.07 
 
 0.26 
 
 0.44 
 
 0.61 
 0.05 
 
 78 
 0.21 
 
 0.94 
 0.37 
 
 1.09 
 0.52 
 
 1.24 
 0.67 
 0.10 
 
 1.93 
 
 100° 
 
 
 
 
 1.34 
 
 110° 
 
 
 
 
 
 
 
 0.76 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Dif.p.deg. 
 
 .0549 
 
 .0551 
 
 .0554 
 
 .0556 
 
 .0559 
 
 .0561 
 
 .0564 
 
 .0566 
 
 .0568 
 
 .0570 
 
 .0572 
 
 .0581 
 
 Separating Calorimeters. — For percentages of moisture beyond the 
 range of the throttling calorimeter the separating calorimeter is used,. 
 
CHIMNEYS. 915 
 
 which is simply a steam separator on a small scale. An improved form 
 of this calorimeter is described by Prof. Carpenter in Poiver, 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., 
 vols, x, xi, xif, 18S9 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 brass 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 plated 
 further away from the latter than 4 feet, and then only when the inter- 
 mediate reservoir or pipe is well covered. 
 
 Usual Amount of 3Ioisture 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 
 
 2g\ 
 
 2gV 
 
 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 
 
 -°f 0.0807^ , . 
 
 ^ { H-H= (0.96 T -i-lW; 
 
 ^(u.084 ) V r 2 / 
 
 in which H = the height of the chimney in feet ; 
 
 t = 493° F., absolute (temperature of melting ice); 
 T!= absolute temperature of the gases in the chimney; 
 t 2 = absolute temperature of the external air. 
 
916 
 
 CHIMNEYS. 
 
 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 lbs. of coal per 
 square foot of grate per hour, for the several temperatures of the chimney 
 gases given. 
 
 
 Chimney Gas. 
 
 Coal per sq. ft. of grate per hour, lbs. 
 
 Outside Air. 
 
 
 
 24 
 
 20 
 
 16 
 
 T2- 
 
 Absolute. 
 
 Temp. 
 Fahr. 
 
 
 
 
 
 Height H, feet. 
 
 520° 
 
 700 
 
 239 
 
 250.9 
 
 157.6 
 
 67.8 
 
 absolute or 
 
 800 
 
 339 
 
 172.4 
 
 115.8 
 
 55.7 
 
 59° F. 
 
 1000 
 
 539 
 
 149.1 
 
 100.0 
 
 48.7 
 
 
 1100 
 
 639 
 
 148.8 
 
 98.9 
 
 48.2 
 
 
 1200 
 
 739 
 
 152.0 
 
 100.9 
 
 49.1 
 
 
 1400 
 
 939 
 
 159.9 
 
 105.7 
 
 51.2 
 
 
 1600 
 
 1139 
 
 168.8 
 
 111.0 
 
 53.5 
 
 
 2000 
 
 1539 
 
 206.5 
 
 132.2 
 
 63.0 
 
 Rankine's formula gives a maximum draught when t = 21/12 t 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 lbs. per cubic foot, h the height of the chimney in feet, and 0.192 the 
 
 factor for converting pressure in lbs. 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 h (D - d). 
 
 The density varies with the absolute temperature (see Rankine). 
 
 -0.084; D =0.0807 
 
 to 
 
 where t is the absolute temperature at 32° F., = 493, t x the absolute 
 temperature of the chimney gases and t 2 that of the external air. Sub- 
 stituting these values the formula for force of draught becomes 
 
 F _0.192 k (™™ - iliiW* P-™ - ™ 5 ). 
 
 * 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, 
 
CHIMNEYS. 
 
 917 
 
 To find the maximum intensity of draught for any given chimney, the 
 heated column being 600° F., and 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 
 100 Feet High. (The Locomotive, 1884.) 
 
 .s >> 
 
 age 
 H 6 
 
 Temperature of the External Air — Barometer, 14.7 lbs 
 
 per sq. in. 
 
 0° 
 0.453 
 
 10° 
 0.419 
 
 20° 
 
 30° 
 
 40° 
 
 50° 
 
 60° 
 0.263 
 
 70° 
 
 80° 
 
 90° 
 
 100° 
 
 200 
 
 0.384 
 
 0.353 
 
 0.321 
 
 0.292 
 
 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. 
 
 «4-, G 
 
 m 
 
 Theoretical Velocity 
 
 _ a 
 
 <o 
 
 Theoretical Velocity 
 
 Z* • 
 
 M.S ■£ 
 
 PI'S 
 
 P4 
 
 in feet per second. 
 
 |1| 
 
 PI'S 
 
 in feet per 
 
 second. 
 
 
 Cold Air 
 
 Hot Air 
 
 Cold Air 
 
 Hot Air 
 
 trj.3 
 
 Entering. 
 
 at Exit. 
 
 
 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 
 
918 
 
 CHIMNEYS. 
 
 Rate 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. 
 
 
 Lbs. of 
 
 
 Lbs. of 
 
 
 Lbs. of 
 
 
 Lbs. of 
 
 Height, 
 
 Coal per 
 
 Height, 
 
 Coal per 
 
 Height, 
 
 Coal per 
 
 Height, 
 
 Coal per 
 
 feet. 
 
 Sq. Ft. of 
 
 feet. 
 
 Sq. Ft. of 
 Grate. 
 
 feet. 
 
 Sq. Ft. of 
 
 feet. 
 
 Sq. Ft. of 
 
 
 Grate. 
 
 
 
 Grate. 
 
 
 Grate. 
 
 20 
 
 7.5 
 
 45 
 
 12.4 
 
 70 
 
 15.8 
 
 95 
 
 18.5 
 
 25 
 
 8.5 
 
 50 
 
 13.1 
 
 75 
 
 16.4 
 
 100 
 
 19.0 
 
 30 
 
 9.5 
 
 55 
 
 13.8 
 
 80 
 
 16.9 
 
 105 
 
 19.5 
 
 35 
 
 10.5 
 
 60 
 
 14.5 
 
 85 
 
 17.4 
 
 110 
 
 20.0 
 
 40 
 
 11.6 
 
 65 
 
 15.1 
 
 90 
 
 18.0 
 
 
 
 
 
 
 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 . 45 
 
 Lbs. coal per sq. ft. grate per hour 10 15 
 
 0.7 
 20 
 
 1.0 
 25 
 
 Thurston's rule for rate of combustion effected by a given 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 V7i — 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 
 2^-1 = 13.14 14.49 15.73 16.89 17.97 19 19.97 21.36 23.49 25.45 27.28 
 
 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 -ineh water-column at the boiler 
 nearest the chimney, and only 1/4-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 
 43.3 
 38.2 
 31.7 
 
 The temperature of the gases in this chimney was assumed to be 552° F., 
 and that of the atmosphere 62°. 
 
SIZE OP CHIMNEYS. 919 
 
 High Chimneys not Necessary. — Chimneys above 150 ft. in height 
 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 
 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 tahle correspond to a coal consumption of 5 lbs. 
 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 
 bevond 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 lbs. 
 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 lbs. per hour, the chimnev 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 of 
 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 of 
 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* - -^- = A - ■= v A. 
 
 For round chimneys, E = ^ (d* - ^\ = A - 0.591 ^A. 
 
920 CHIMNEYS. 
 
 For simplifying calculations, the coefficient of ^ A 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 lbs. of fuel 
 per rated horse-power of boiler per hour. 
 
 5. The power of the chimney varying directly as the effective area, E, 
 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 Viy, 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 ^A) Vjf. 
 
 If the horse-power of boiler is given, to find the size of chimney, the 
 height being assumed, 
 
 E = 0.3 H.P. -*- Vtf; = A - 0.6 VI. 
 
 For round chimneys, diameter of chimney = diam. of E + 4". 
 
 For square chimneys, side of chimney = V ' e + 4". 
 
 If effective area E is taken in square feet, the diameter in inches is d = 
 13.54_V.Z2 + 4", and the side of a square chimney in inches is s = 
 1 2 V_? + 4". 
 
 /0 3 H P \ 2 
 
 If horse-power is given and area assumed, the height H = I — — tt^^ ) ■ 
 
 An approximate formula for chimneys above 1000 H.P. is H.P. = 
 2.5 D 2 Vi_\ 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 918 and 919. No formula for 
 height can be given which will be satisfactory for different classes of coal, 
 kinds and amounts o" ash, styles of grate-bars, etc. A formula in " Ingeni- 
 eurs Taschenbuch," translated into English measures, is/i = 0.216.R 2 + 6d. 
 h= height in ft; R = lbs. 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 3/ 4 in. by Vs in. 
 thick, weighing 6 ozs. per ft. If iron is used it should weigh not less than 
 2V4 lbs. 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 Vi6 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 be 
 avoided. No bend in it should be over 30°. 
 
SIZE OP CHIMNEYS. 
 
 921 
 
 
 .p 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 0> ^^w » 5 
 
 
 
 
 
 
 
 
 -2 53 2 ° !2 ^ 
 
 
 
 
 
 
 
 
 g-co^coGCiEsq 
 w ° > 
 
 vOC^Nt r^orsjir 
 
 >> OOmoOT »tOin OvO — \0 — r^.r^tri 
 
 
 --NN <S cc» t<"> «"> ifiT^tf 
 
 1 u-i\Or»rN 000000 OO-N 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^tS^lO 00^-<Nm tsmfift 
 o 3" — © — in — o- os <v) tj- in 
 <NTr-»© n>oo^ t~s eg — — 
 
 (4 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — — — <M NNKMA rnTmsO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 <D 
 
 ft 
 TJ 
 CD 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 • T NOiftO \OfiOffl O in v© 00 
 
 ■ oo oc-imoo — ^;i^o -Sroovovo 
 — — — — <n cs cs t<^ rcitntin 
 
 *; 
 
 
 
 
 
 
 
 
 
 
 inoo © m in sO oDeoaoN OOtsi^ — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ o o o ro oominm 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \© oo O (N "3" r- or-i 
 
 
 £i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - NNNf 
 
 4 t^c^^-ir! 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 £5 
 
 
 £ 
 
 
 
 
 
 
 
 
 
 
 ^2a 
 
 00 OO O m OvOinf- 
 
 -1-NO 
 
 Hi 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 — CSCSCs 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Nomoo oomo- 
 
 or^oe* 
 
 OvOOs — 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ITS 
 
 
 
 
 
 
 
 
 
 m^rmN c --- ■ 
 
 ^ IsOfMA O^NO^In 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -NNN NlAmt 
 
 £5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 43 
 
 
 
 
 
 
 
 
 v©nO — <\ 
 
 O m Csl OO OsvOOO in \0 !*>. C^l 
 
 
 
 "3 
 
 
 
 
 
 
 
 s£ 
 
 
 
 mrsmoN oo oo m m 
 
 
 
 o 
 
 
 
 
 
 
 
 <N 
 
 <^ -"T rnsC 
 
 COONt \© 00 — «"* -O O- vO m 
 
 
 >> 
 
 
 
 
 
 
 
 
 
 
 
 — — «S«N 
 
 
 
 
 — 
 
 £ 
 
 
 
 
 
 
 
 
 
 
 
 4 Ph - 
 
 43 
 
 
 
 
 
 
 Tin 
 
 CAO>t^N 
 
 vCTt^^T ^ N ^ C 
 
 
 
 
 
 
 
 o 
 
 a 
 i 
 
 
 
 
 
 
 o^- 
 
 00 00 O cr- 
 
 Nc^OO 
 
 O — T& 
 
 
 
 
 
 d M 
 « so 
 
 IS 
 
 o 
 
 P4 
 
 
 
 
 
 
 <NCN 
 
 N«MTk>C 
 
 PnO — <N tlNO\C 
 
 
 
 
 
 "S 
 
 43 
 
 
 
 
 
 
 vO — & 
 
 
 00 \D OO ^t" 
 
 
 
 
 
 
 
 
 w .2 
 
 
 © 
 
 
 
 W 
 
 .5 
 
 
 
 
 
 £2H 
 
 t->. v© r>. o> 
 
 IN00ON 
 
 
 
 
 
 
 
 
 h a 
 
 1 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 3 
 
 p 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 K 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 &'5 
 
 o 
 
 
 
 
 
 — •<»• ao — 
 
 in t T vO 
 vN«*>-<rin 
 
 OMn 
 
 
 
 
 
 
 
 
 
 
 
 © 
 
 
 
 
 
 cs 
 
 O 00 
 
 
 
 
 
 
 
 
 
 
 Ol 
 
 
 o 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 vOCO 
 
 S5SS 
 
 mor-,v© 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 sh 
 
 
 «s 
 
 
 ^1'N^ 
 
 sE?^ 
 
 __ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s> 
 
 
 0O 
 
 ; 
 
 S-^-OOO 
 
 Js^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 02 O 
 
 
 
 
 -, — OOOO 
 
 ©<QSoo 
 
 vO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 — 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 _^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -NOO-rtM 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 
 
 
 
 OS--TJ- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 
 *© 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 II 
 
 
 
 
 ^ IPl O^ in 
 
 "f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ah" 
 
 
 m 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 W 
 
 
 
 
 
 
 
 
 
 e8 
 
 3 
 
 > • 'h 
 
 
 
 
 
 
 
 
 
 M i 
 
 ?T©t^ 
 
 oooor^r^ 
 
 vo-r — oo 
 
 SoRtS 
 
 — O(N0C 
 
 SH2S 
 
 S 
 
 d 1 c 
 
 3 — c>i cn 
 
 <*i-<rm\o 
 
 is.'o?22 
 
 (N(N(nS 
 
 ?*HS 
 
 lAt^O^vO 
 
 o 
 
 H ^° 
 
 
 
 
 
 
 
 ~~ 
 
 fa 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s-tOO 
 
 — gr i^o 
 
 SkSS 
 
 nO t>»00 00 
 
 ^oor^tnrvi 
 
 qo^O 
 
 o 
 
 
 
 
 
 
 
 
 
 
 " M ^^ 
 
 ■<r m r>! oo 
 
 o> n its 2; 
 
 f^vNr^cr 
 
 JTS«S 
 
 sss; 
 
 2 
 
 
 ll 
 
 
 — Tt-s 
 
 om>oo> 
 
 ssss 
 
 ■orgoo'T 
 
 VO 0tl~>00 
 
 oooo 
 
 =sa 
 
 ? 
 
 
 
 
 
 
 
 
 
 
 
 p. a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
922 
 
 CHIMNEYS. 
 
 Some Tall Brick Chimneys (1895). 
 
 Outside 
 Diameter. 
 
 Capacity by the 
 Author's 
 Formula. 
 
 Pounds 
 Coal 
 
 1. Hallsbriickner Hiitte, 
 
 Saxony 
 
 2. Townsend's, Glasgow ... 
 
 3. Tennant's, Glasgow 
 
 4. Dobson & Barlow, Bol- 
 
 ton, Eng 
 
 5. Fall River Iron Co., Bos- 
 
 ton 
 
 6. Clark Thread Co., New- 
 
 ark, N.J 
 
 7. Merrimac Mills, Lowell, 
 
 Mass 
 
 8. Washington Mills, Law- 
 
 rence, Mass 
 
 9. Amoskeag Mills, Man- 
 
 chester, N. H 
 
 10. Narragansett E. L. Co., 
 
 Providence, R.I 
 
 1 1 . Lower Pacific Mills, Law- 
 
 rence, Mass 
 
 12. Passaic Print Works, 
 
 Passaic, N. J 
 
 13. Edison Station Brooklyn, 
 
 Two each 
 
 460 
 
 454 
 435 
 
 3671/2 
 
 350 
 
 335 
 
 282' 9" 
 
 250 
 
 250 
 
 238 
 
 214 
 
 200 
 
 150 
 
 15.7' 
 
 'ii'6''" 
 
 13' 2" 
 
 11 
 
 11 
 
 12 
 
 10 
 
 10 
 
 14 
 
 8 
 
 9 
 
 50" x 120" 
 
 32 
 40 
 
 33' 10" 
 
 30 
 28' 6 
 
 13,221 
 
 9,795 
 8,245 
 5,558 
 5,435 
 5,980 
 3,839 
 3,839 
 7,515 
 2,248 
 2,771 
 1,541 
 
 66,105 
 "48,975" 
 41,225 
 27,790 
 27,175 
 29,900 
 19,195 
 19,195 
 37,575 
 11,240 
 13,855 
 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 brick 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 and spaced 
 
SIZE OF CHIMNEYS. 923 
 
 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 19/ieins. 
 
 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 lbs. 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. 101/4 in., 
 bottom 27 ft. 6 1/2 in. Outside taper 5.2 in 100. Outer shell 7 1/8 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 31/2 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 
 69 ft. to solid rock, and covering an area 45 ft. square. Total cost $32,000. 
 The standard Custodis radial brick is 41/2 in. thick and 6V2 in. wide; 
 radial lengths are 4, 51/2. 7V8, 85/8 and lOVsins. The smallest size has 
 six vertical perforations, 1 in. square, and the largest fifteen. 
 
 Eastman Kodak Co., Pa>chester, 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., 8X 350 ft.; Rochester, N. Y., 9X 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. 
 
 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 lbs. per sq. ft. of projected area; bearing pressure limited to 21 lbs. 
 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 18 1/8 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 78 1/2 ft. at the base, 
 53 ft. 9 in. at the base of the cap; the inside diameters range from 66 1/2 ft. 
 
924 CHIMNEYS. 
 
 at the foundation line to 50 ft. at the top. The chimney is lined with 4-in. 
 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. 
 
 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 or 
 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 Vie 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. If 
 the inside diameter exceeds 5 feet, the top length should be 11/2 bricks; 
 and if under 3 feet, it may be 1/2 brick for ten feet. 
 
 (From The Locomotive, 1884 and 1886.) For chimneys of four feet in 
 diameter and one hundred feet high, and upwards, the best form is cir- 
 cular with a straight batter on the 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 horizontal steps, so that there shall be 
 no tendency to slide after the structure is finished. 
 
 All boiler-chimneys of any considerable 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 contract 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 and 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 the 
 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 top 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 
 oftter wall 200 ft. high and assuming a cubic foot of brickwork to weigh 
 130 lbs;, 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 
 
SIZE OF CHIMNEYS. 925 
 
 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 on that side, and the 
 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 lbs.) 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 lbs. per 
 sq. ft. of a plane surface, directly facing the wind, or 27 1/2 lbs. 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, lbs. per sq. in. The general formula for moment 
 of resistance of a hollow cylinder is M = 1/32 w (D i — Z>i 4 ) S/D. When 
 the thickness is a small fraction of the diameter this becomes approxi- 
 mately M = 0.7854 D 2 TS. 
 
 With steel plate of 60.000 lbs. 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 2 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 lbs. per sq. ft., we get 
 
 Total wind pressure = 50 X V12 D X 1/2 X 6/7 H = 25 DH /IA. 
 
926 
 
 CHIMNEYS. 
 
 The distance of the center of pressure above the top of the bell portion, 
 •= 3/ 7 H, multiplied by the total wind pressure, gives us the bending mo- 
 ment due to the wind, 
 
 inch pounds, 25 DH/\ 4 X 8/7 H X 12 = 9.184 DH 2 . 
 
 Equating the bending and the resisting moment we have T = 0.0013 
 H 2 /D. 
 
 With this formula the maximum thickness of plates was calculated for 
 different sizes of chimneys, as given in the table below. 
 
 In the 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 compression 
 on the leeward side of the stack. A column of steel 150 ft. high would 
 exert a pressure of approximately 500 lbs. per sq. in., which, with steel 
 of 60,000 lbs. 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 Vs in. In designing a stack of such extreme proportions 
 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 of Base-ring Plates of Self-supporting Steel Stacks. 
 
 For normal wind pressure of 50 lbs. per sq. ft. on half the diametral plane. 
 
 Diameter of Stack in feet. 
 
 
 3.5 
 
 4 
 
 .133 
 
 .182 
 .219 
 .271 
 328 
 .390 
 .458 
 .531 
 .609 
 .693 
 
 5 
 
 .106 
 .139 
 .175 
 .217 
 .262 
 .312 
 .366 
 .425 
 .437 
 .555 
 676 
 
 6 
 
 7 
 
 8 
 
 8.5 
 
 9 
 
 9.5 
 
 10 
 
 11 
 
 12 
 
 70 
 
 0.152 
 0.198 
 0.224 
 0.310 
 0.375 
 0.446 
 0.523 
 0.607 
 0.696 
 
 
 
 
 
 
 
 
 
 
 80 
 
 .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 
 
 
 
 
 
 
 
 
 90 
 
 .111 
 .135 
 .164 
 .195 
 .228 
 .265 
 .305 
 .346 
 .391 
 .439 
 .489 
 .542 
 .596 
 .655 
 .717 
 
 
 
 
 
 
 
 100 
 
 .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 
 
 
 
 
 
 110 
 120 
 130 
 140 
 150 
 160 
 170 
 
 .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 
 
 .iJ9 
 .142 
 .166 
 .193 
 .222 
 .252 
 .285 
 .319 
 .356 
 .394 
 .434 
 .476 
 521 
 .567 
 .615 
 
 ",'\30 
 .153 
 .180 
 .203 
 .231 
 .261 
 
 180 
 
 
 
 .702 
 
 .293 
 
 1Q0 
 
 
 
 .326 
 
 ?00 
 
 
 
 
 .361 
 
 7.10 
 
 
 
 
 
 .398 
 
 7?0 
 
 
 
 
 
 437 
 
 ?10 
 
 
 
 
 
 
 477 
 
 740 
 
 
 
 
 
 
 .520 
 
 7.50 
 
 
 
 
 
 
 
 .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 = 1/2 D X H X 50 = 25 DH; lever-arm =V 2 H; 
 hence, turning moment = 12.5 DH 2 . 
 
 Let d = diameter and h = height of foundation. For average con- 
 ditions h = 0.4 d, then volume of foundation = 0.7854 d 2 h,' and for 
 concrete at 150 lbs. per cu. ft., weight of foundation = W = 0.7854 d 2 h 
 X 150 = 47.124 <P. 
 
 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 2 1/2, which is indicated by 
 
SIZE OF CHIMNEYS. 927 
 
 current practice, gives safe stability = 9.4 25 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 be 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 axis 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 add 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 >7 8 
 the diameter of the bolt circle from the axis of turning, which is the tan- 
 gent to the bolt circle. 
 
 Let b = diameter of bolt in inches, n = number of bolts, diameter 
 of bolt circle = 2/ 3 d. Take safe working stress at 8000 pounds per sq. 
 inch. Then resistance to overturning = 0.7854 b 2 X 8000 X 2 fad X 3/gX 
 N = 6283 b 2 Nd/4. Equa ting this to the turning mom ent, 12.5 DH 2 , 
 gives b = 0.0257H.V D/d for 12 bolts, 0.0222 H ^D/d for 18 bolts, 
 and 0.0182 H VD/d for 24 bolts. 
 
 The Babcock & Wilcox Co.'s book "Steam" illustrates a steel chimney 
 at the works of the Maryland Steel Co., Sparrow's Point, Md. It is 
 225 ft. in height above the base, with internal brick lining 13' 9" uniform 
 inside diameter. The shell is 25 ft. diam. at the base, tapering in a curve 
 to 17 ft. 25 ft. above the base, thence tapering almost imperceptibly to 
 14' 8" at the top. The upper 40 feet is of 1/4-inch plates, the next four 
 sections of 40 ft. each are respectively 8/32, 5 /i6, xl /32, and 3/ 8 inch. 
 
 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 reinforcement 
 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 re'enforcement 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. 
 
 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 in#. 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 ringrs bent to 
 the desired circle. The work of erection is done from the inside of the 
 chimney: no outside scaffolding is needed. 
 
 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, 
 
928 
 
 CHIMNEYS. 
 
 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., 220X9 ft.; 
 Atlanta, Ga., 225 X 8 ft.; Chicago, 175 X 7 ft.; Rockville, Conn., 175 X 
 6 ft.; Seymour, Ind., 150 X 5 ft.; Iola, 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 3 4 5 6 7 9 11 
 
 Height, feet 100 100 150 150 150 150 150 
 
 Least diam. foundation.. 15'9" 16' 4" 20'4" 21'10" 22'7" 23'8" 24'8" 
 
 Least depth foundation.. 6' 6' 9' 8' 9' 10' 10' 
 
 Height, feet 125 200 200 250 275 300 
 
 Least diam. foundation 18'5" 23'8" 25' 29'8" 33'6" 26' 
 
 Least depth foundation 7' 10' 10' 12' 12' 14' 
 
 Weight of Sheet-iron Smoke-stacks per Foot. 
 
 (Porter Mfg. Co.) 
 
 Diam. 
 
 Thick- 
 
 Weight 
 
 Diam. 
 
 Thick- 
 
 Weight 
 
 Diam. 
 
 Thick- 
 
 Weight 
 
 inches. 
 
 W. G. 
 
 per ft. 
 
 inches. 
 
 W. G. 
 
 per ft. 
 
 inches. 
 
 W. G. 
 
 per ft. 
 
 10 
 
 No. 16 
 
 7.20 
 
 26 
 
 No. 16 
 
 17.50 
 
 20 
 
 No. 14 
 
 18.33 
 
 12 
 
 
 8.66 
 
 28 
 
 
 18.75 
 
 22 
 
 
 20.00 
 
 14 
 
 
 9.58 
 
 30 
 
 
 20.00 
 
 24 
 
 
 21.66 
 
 16 
 
 
 11.68 
 
 10 
 
 No. 14 
 
 9.40 
 
 26 
 
 
 23.33 
 
 20 
 
 
 13.75 
 
 12 
 
 
 11.11 
 
 28 
 
 
 25.00 
 
 22 
 
 " 
 
 15.00 
 
 14 
 
 
 13.69 
 
 30 
 
 " 
 
 26.66 
 
 24 
 
 " 
 
 16.25 
 
 16 
 
 
 15.00 
 
 
 
 
 
 
 
 
 
 Sheet-iron Chimneys. 
 
 (Columbus Machine Co.) 
 
 
 Diameter 
 
 Chimney, 
 
 inches. 
 
 Length 
 
 Chimney, 
 
 feet. 
 
 Thick- 
 ness 
 Iron, 
 B. W. G. 
 
 Weight 
 lbs. 
 
 Diameter 
 
 Chimney, 
 
 inches. 
 
 Length 
 
 Chimney, 
 
 feet. 
 
 Thick- 
 ness 
 Iron, 
 B.W.G. 
 
 Weight 
 lbs. 
 
 10 
 
 20 
 
 No. 16 
 
 160 
 
 30 
 
 40 
 
 No. 15 
 
 960 
 
 15 
 
 20 
 
 " 16 
 
 240 
 
 32 
 
 40 
 
 " 15 
 
 1020 
 
 20 
 
 20 
 
 " 16 
 
 320 
 
 34 
 
 40 
 
 " 14 
 
 1170 
 
 22 
 
 20 
 
 " 16 
 
 350 
 
 36 
 
 40 
 
 " 14 
 
 1240 
 
 24 
 
 40 
 
 " 16 
 
 760 
 
 38 
 
 40 
 
 " 12 
 
 1800 
 
 26 
 
 40 
 
 " 16 
 
 826 
 
 40 
 
 40 
 
 " 12 
 
 1890 
 
 28 
 
 40 
 
 " 15 
 
 900 
 
 
 
 
 
THE STEAM-ENGINE. 
 
 929 
 
 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 & l/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 lbs., p <* 1/vB, or p cc-jris or pvi* = 
 p V i-0625 = a 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 <* l/v V, 
 or p ocy _1 s ' or pv 1 ' 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., 
 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.£.ilf.£ , .,h\ 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 = 
 
 Pivv, values calculated from formula ■ — = -^ (1 + hyp log R), in which 
 R = V2 -5- vi, pi = absolute initial pressure, P m = absolute mean pressure, 
 vi = initial volume of steam in cylinder at pressure pi, vt = final volume 
 
 of steam at final pressure. Adiabatic law: pv$ = pivys ; values calcu- 
 
 p 
 lated from formula — = 10 R^-QR' 1 ^- 
 
 Ratio 
 of Ex- 
 pansion 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 Ratio 
 of Ex- 
 pansion 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 Ratio 
 of Ex- 
 pansion 
 
 Ratio of Mean 
 to Initial 
 Pressure. 
 
 
 
 
 
 
 R. 
 
 Mar. 
 
 Adiab. 
 
 R. 
 
 Mar. 
 
 Adiab. 
 
 R. 
 
 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 
 
 1.75 
 
 .891 
 
 .881 
 
 4. 
 
 .597 
 
 .571 • 
 
 6.75 
 
 .431 
 
 .403 
 
 2. 
 
 .847 
 
 .834 
 
 4.1 
 
 .588 
 
 .562 
 
 7. 
 
 .421 
 
 .393 
 
 2.2 
 
 .813 
 
 .798 
 
 4.2 
 
 .580 
 
 .554 
 
 7.25 
 
 .411 
 
 .383 
 
 2.4 
 
 .781 
 
 .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 
 
 5.0 
 
 .522 
 
 .495 
 
 9.25 
 
 .349 
 
 .321 
 
 3.4 
 
 .654 
 
 .630 
 
 5.25 
 
 .506 
 
 .479 
 
 9.5 
 
 .342 
 
 .315 
 
 3.5 
 
 .644 
 
 .620 
 
 5.5 
 
 .492 
 
 .464 
 
 9.75 
 
 .336 
 
 .309 
 
 . 3.6 
 
 .634 
 
 .610 
 
 5.75 
 
 .478 
 
 450 
 
 10. 
 
 .330 
 
 .303 
 
930 
 
 THE STEAM-ENGINE. 
 
 Mean Pressure of Expanded Steam. — For calculations of engines 
 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 
 
 =Pi- 
 
 1 4- hyp log R 
 R 
 
 or P m =P;(l + hyplog#), 
 
 in which P m is the absolute mean pressure, pi 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. £ 
 
 Pi!+p , lhyplog _ ____£. p ^ 1+hyplogB 
 
 -P™= - 
 
 -; and if R = 
 
 L ' """ " " I \~ m "* R 
 
 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 ptxv~i%. These latter values are calculated from the formula 
 
 17-16 R-tb 
 
 Pi 
 
 R ib may be found by extracting the square root 
 
 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 
 0.038 
 0.042 
 0.045 
 0.050 
 0.055 
 0.062 
 0.066 
 0.071 
 0.075 
 0.077 
 0.083 
 0.091 
 0.100 
 0.111 
 0.125 
 0.143 
 0.150 
 0.166 
 0.175 
 0.200 
 0.225 
 0.250 
 0.275 
 0.300 
 0.333 
 0.350 
 0.375 
 0.400 
 0.450 
 0.500 
 0.550 
 0.600 
 0.625 
 0.650 
 0.675 
 
 0.1467 
 0.1547 
 0.1638 
 0.1741 
 0.1860 
 0.1998 
 0.2161 
 0.2358 
 0.2472 
 0.2599 
 0.2690 
 0.2742 
 0.2904 
 0.3089 
 0.3303 
 0.3552 
 0.3849 
 0.4210 
 0.4347 
 0.4653 
 4807 
 0.5218 
 0.5608 
 0.5965 
 0.6308 
 0.6615 
 0.6995 
 0.7171 
 0.7440 
 0.7664 
 0.8095 
 0.8465 
 0,8786 
 0.9066 
 0.9187 
 0.9292 
 0.9405 
 
 4.40 
 
 4.33 
 
 4.26 
 
 4.18 
 
 4.09 
 
 4.00 
 
 3.89 
 
 3.77 
 
 3.71 
 
 3.64 
 
 3.59 
 
 3.56 
 
 3.48 . 
 
 3.40 
 
 3.30 
 
 3.20 
 
 3.08 
 
 2.95 
 
 2.90 
 
 2.79 
 
 2.74 
 
 2.61 
 
 2.50 
 
 2.39 
 
 2.29 
 
 2.20 
 
 2.10 
 
 2.05 
 
 1.98 
 
 1.91 
 
 1.80 
 
 1.69 
 
 1.60 
 
 1.5.1 
 
 1.47 
 
 1.43 
 
 1.39 
 
 0.227 
 0.231 
 0.235 
 0.239 
 0.244 
 0.250 
 0.256 
 0.265 
 0.269 
 0.275 
 0.279 
 0.280 
 0.287 
 0.294 
 0.303 
 0.312 
 0.321 
 0.339 
 0.345 
 0.360 
 0.364 
 0.383 
 0.400 
 0.419 
 0.437 
 0.454 
 0.476 
 0.488 
 0.505 
 0.523 
 0.556 
 0.591 
 0.626 
 0.662 
 0.680 
 0.699 
 0.718 
 
 6.82 
 6.46 
 6.11 
 5.75 
 5.38 
 5.00 
 4.63 
 4.24 
 4.05 
 3.85 
 3.72 
 3.65 
 3.44 
 3.24 
 3.03 
 2.81 
 2.60 ' 
 2.37 
 2.30 
 2.15 
 2.08 
 1.92 
 1.78 
 1.68 
 • 1.58 
 1.51 
 1.43 
 1.39 
 1.34 
 1.31 
 1.24 
 1.18 
 1.14 
 1.10 
 1.09 
 1.07 
 1.06 
 
 0.136 
 
 26 
 
 
 24 
 
 
 22 
 
 
 20 
 18 
 
 0.186 
 
 16 
 
 
 15 
 
 
 14 
 
 
 13.33 
 13 
 
 0.254 
 
 12 
 
 
 11 
 
 
 10 
 9 
 
 0.314 
 
 8 
 7 
 
 0.370 
 
 6.66 
 6.00 
 
 0.417 
 
 5.71 
 
 
 5.00 
 4.44 
 
 0.506 
 
 4.00 
 3.63 
 
 0.582 
 
 3.33 
 
 3.00 
 
 0.6'8 
 
 2.86 
 2.66 
 
 0.707 
 
 2.50 
 2.22 
 2.00 
 1.82 
 1.66 
 1.60 
 
 0.756 
 0.800 
 0.840 
 0.874 
 0.900 
 
 1.54 
 1.48 
 
 0.926 
 
THE STEAM-ENGINE. 
 
 931 
 
 Calculation of Mean Effective Pressure, Clearance and Com- 
 pression Considered. — In the above tables no account is taken of 
 
 clearance, which in actual 
 \ ei L — £, — $ 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, pb = 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 ^ fa (1+ c) (l + hyp log l A ; 
 B = pb(L-x); 
 
 C = p c c (l + hyp log ^-jp) =Pb (x+c) (l + hyp log ^r~/ : 
 D = (pi-p c ) c = pic-pb (x + c). 
 Area of A = ABCD - (8 + C + D) 
 
 = Pi(Z+c)(l + hyplogy^) 
 
 - \pb (L-x) + Pb (x + c) (l + hyp log ^~j^)+ Pic-Ph (x 4-c)J 
 
 = Pi(Z+c)(l+hyplog|^) 
 
 I X + c~\ 
 
 - pb I (L - x) + (x + c) hyp log — — I -pic. 
 
 _ „ area of A 
 Mean effective pressure = y 
 
 Example. — Let L = l, 1 = 0.25, z = 0.25, c = 0.1, pi=6Q lbs., Pb = 2 lbs. 
 
 1.1 > 
 
 Area A = 60 (0.25 + 0.1) (l + hyp log ^) 
 
 ■■[ 
 
 (1-0.25) +0.35 hyp log - 
 
 -60X0.1. 
 
 = 21 (1 + 1.145) - 2 [0.75 + 35 X 1.253] - 6 
 
 = 45.045 -2.377- 6 = 36. 668 = mean effective pressure. 
 
 The actual indicator-diagram generally shows a mean pressure con- 
 siderablv 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 chieflv 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, and 
 pipes. 
 
932 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 Scaton. 
 
 Particulars of Engine. Factor. 
 
 Expansive engine, special valve-gear, or with a sepa- 
 rate cut-off valve, cylinder jacketed . 94 
 
 Expansive engine having large ports, etc., and good 
 
 ordinary valves, cylinders jacketed . 9 to . 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 . 92 
 
 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 0.7 to 0.8 
 
 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 lbs. per sq. in.; 
 
 p = average total pressure during stroke in lbs. 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) 
 
 = P(l + hyploga) 
 p R 
 
 To find average pressure p, taking account of clearance, 
 = P(l + c) + P(l + c) hyp log R-Pc 
 
 whence pL + Pc = P(l + c) (1 + hyp log R) ; 
 
 . . _ pL + Pc , P +C „ ,„. 
 
 hyplogi^L-^-^-^-l. ... (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 = — =-^ — c, obtained from formula 
 
 (1), 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 in 
 formula (3) as before, and continue by this method of trial and error till 
 the required values of R and Z are obtained. 
 
 (2) 
 
THE STEAM-ENGINE. 
 
 933 
 
 Example. — P = 70, p = 42.78, L= 60 in., c = 3 in., to find I. Assume 
 I - 21 in. 
 
 P L + C ^- 8 X60 + 3 
 
 hyplogfl^ t+e -1= 21 + 3 1 = 1.653-1 = 0.653; 
 
 hyp log R = 0.653, whence R = 1.92. 
 
 <-*£-'—:&-»-»* 
 
 which is greater than the assumed value, 21 inches. 
 Now assume i = 15 inches: 
 
 42 78 
 ^X60+3 
 
 hyp log R = 15 + 3 1 = 1.204, whence R= 3.5; 
 
 I = — 5 c= o-g— 3 = 18-3 = 15 inches, the value assumed. 
 
 Therefore # = 3.5, and 1 = 15 inches. 
 
 Period of Admission Required for a Given Actual Ratio of Expansion: 
 1= — = c, in inches (4) 
 
 T . . . , T 100 + p. ct. clearance . , 
 
 In percentage of stroke, I =■ — „ p. ct. clearance . (5) 
 
 P (1 + c) P 
 Terminal pressure = — ■ = — (6) 
 
 Pressure at any other Point of the Expansion. — Let Li = length of 
 stroke up to the given point. 
 
 Pressure at the given point = — — (7) 
 
 Mechanical Energy of Steam Expanded Adiabatically to Various 
 Pressures. — The figures in the following table are taken from a chart 
 constructed by R. M. Neilson in Power, Mar. 16, 1909. The pressures 
 are absolute, lbs per sq. in. 
 
 [3 g 
 
 15 
 
 20 
 
 25 
 
 40 
 
 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 170 
 
 200 
 
 250 
 
 "3 s 
 a ® 
 
 Mechanical Energy, Thousands of Foot-Pounds per Lb. of Steam. 
 
 faC4 
 
 
 1^ 
 
 
 
 17 
 
 29.5 
 
 55.5 
 
 77.5 
 
 94.5 
 
 107 
 
 116.5 121 
 
 136.5 
 
 146 
 
 160 
 
 ]?. 
 
 12 
 
 29 
 
 41 
 
 66.5 
 
 88 
 
 104 
 
 116 
 
 126 
 
 135 
 
 145 
 
 154.5 
 
 168.5 
 
 in 
 
 22 
 
 39 
 
 50.5 
 
 75.5 
 
 97 
 
 113 
 
 125 
 
 135.5 
 
 144 
 
 154 
 
 163.5 
 
 176 
 
 8 
 
 34 
 
 50 
 
 62 
 
 86.5 
 
 109 
 
 124 
 
 136 
 
 147 
 
 155 
 
 165.5 
 
 174.5 
 
 186 
 
 6 
 
 49 
 
 64 
 
 76 
 
 101 
 
 123 
 
 138 
 
 150 
 
 160 
 
 168.5 
 
 179.5 
 
 188 
 
 199 
 
 4 
 
 68 
 
 85 
 
 95.5 
 
 120 
 
 142 
 
 157 
 
 168 
 
 177.5 
 
 186 
 
 196 
 
 204.5 
 
 216 
 
 2 
 
 100 
 
 116 
 
 128 
 
 151 
 
 171 
 
 186.5 
 
 197.5 
 
 207 
 
 215 
 
 224 
 
 232.5 
 
 244 
 
 1 
 
 131 
 
 147 
 
 157.5 
 
 181.5 
 
 200.5 
 
 215 
 
 225 
 
 234.5 
 
 243 
 
 250.5 
 
 260.5 
 
 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 lb. 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 engine uses steam 
 and not coal, and it Is independent of the economy of the boiler. 
 
934 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 lb. of coal per H.P. per 
 hour would be equal to 1,980,000 ft.-lbs. per lb. of fuel; 2 lbs. per H.P. 
 per hour equals 990,000 ft.-lbs. per lb. of fuel, etc. 
 
 The duty of pumping-engines is expressed by the number of foot- 
 pounds of work done per 100 lbs. of coal, per 1000 lbs. of steam, or per 
 million heat units. 
 
 When the duty of a pumping-engine is given, in ft.-lbs. per 100 lbs. 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 lbs. 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., 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 lbs. gauge, and vacuum 28 in., uses 13 lbs. of water per I. H.P. per hour, 
 and a high-speed non-condensing engine, with steam at 100 lbs. gauge, 
 uses 30 lbs. 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. <*- 778 = 42.4164 thermal units per minute 
 per indicated horse-power. This figure, 42.4164, 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, 42.4164 divided by 244.3 and by 503.4 gives 
 17.33% and 8.42% efficiency, respectively. 
 
ACTUAL EXPANSIONS. 
 
 935 
 
 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 
 
 .03 
 
 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 
 
 2.75 
 
 .40 
 
 2.50 
 
 2.46 
 
 2.43 
 
 2.40 
 
 2.36 
 
 2.33 
 
 2.30 
 
 2.28 
 
 2.25 
 
 2.22 
 
 2.20 
 
 .50 
 
 2.00 
 
 1.98 
 
 1.96 
 
 1.94 
 
 1.92 
 
 1.90 
 
 1.89 
 
 1.88 
 
 1.86 
 
 1.85 
 
 1.83 
 
 .60 
 
 1.67 
 
 1.66 
 
 1.65 
 
 1.64 
 
 1.63 
 
 1.615 
 
 1.606 
 
 1.597 
 
 1.588 
 
 1.580 
 
 1.571 
 
 .70 
 
 1.43 
 
 1.42 
 
 1.42 
 
 1.41 
 
 1.41 
 
 1.400 
 
 1.395 
 
 1.390 
 
 1.385 
 
 1.380 
 
 1.375 
 
 .80 
 
 1.25 
 
 1.25 
 
 1.244 
 
 1.241 
 
 1.238 
 
 1.235 
 
 1.233 
 
 1.230 
 
 1.227 
 
 1.224 
 
 1.222 
 
 .90 
 
 1.111 
 
 1.11 
 
 1.109 
 
 1.108 
 
 1.106 
 
 1.105 
 
 1.104 
 
 1.103 
 
 1.102 
 
 1.101 
 
 1.100 
 
 1.00 
 
 1.00 
 
 1.00 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 1.000 
 
 Relative Efficiency of 1 lb. of Steam with and without Clearance; 
 
 back pressure and compression not considered. 
 
 = p d + c ) + P d + c) hyp log R - Pc 
 
 L 
 25; c = 7. 
 
 Mean total pressure — 
 Let P = 1 ; L = 100 ; I 
 
 32 + 32 hyp log ^ - 7 
 
 32+ 32 X 1.209 
 
 - = 0.637. 
 
 v 100 100 
 
 If the clearance be added to the stroke, so that clearance becomes zero, 
 the same quantity of steam being used, admission I being then = I + c = 
 32, and stroke L + c = 107, 
 
 32 + 32 hyp log ^ - 
 
 32 
 
 32 + 32 X 1.209 
 
 = 0.707. 
 
 ^ 107 107 
 
 That is, if the clearance be reduced to 0, the amount of the clearance 7 
 being added to both the admission and the stroke, the same quantity 
 of steam will do more work than when the clearance is 7 in the ratio 
 707:637, or 11% more. 
 
 BackPressure Considered. — If back pressure = 0.10 of P, this amount 
 has to be subtracted from p and pi giving p = 0.537, pi = 0.607, the 
 work of a given quantity of steam used without clearance being greater 
 than when clearance is 7 per cent in the ratio of 607: 537, or 13% 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 pressure is uniform through- 
 out the exhaust-stroke, and if compression begins at such point that the 
 
936 
 
 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 Low- 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.) 
 
 IK 
 
 85 ° ""S 
 
 Per cent of Feed-water ac- 
 counted for by the Indicator. 
 
 Per cent of Feed-water due 
 to Cylinder-condensation. 
 
 g8|o 
 
 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 
 
 58 
 66 
 71 
 74 
 
 78 
 82 
 86 
 
 
 
 42 
 34 
 29 
 26 
 22 
 18 
 14 
 
 
 
 10 
 
 74 
 76 
 
 78 
 82 
 85 
 88 
 
 
 26 
 24 
 22 
 18 
 15 
 12 
 
 
 15 
 20 
 30 
 
 40 
 50 
 
 78 
 80 
 84 
 87 
 90 
 
 22 
 20 
 16 
 13 
 10 
 
CYLINDER CONDENSATION. 
 
 937 
 
 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 lbs. 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. 
 
 
 Mean 
 
 Total 
 
 Indicated 
 
 Assurr" 1 *^ 
 
 
 Cut-off 
 
 Effective 
 
 Terminal 
 
 Rate, lbs. 
 
 
 
 Product 
 
 Part of 
 Stroke. 
 
 Pressure, 
 lbs. pet 
 sq. in. 
 
 Pressure, 
 lbs. per 
 sq. in. 
 
 Water per 
 
 I.H.P. per 
 
 hour. 
 
 
 
 of Cols. 
 1 and 6. 
 
 Act'lRate. 
 
 % Loss. 
 
 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 lbs. M.E.P., and a 
 terminal 3 or 4 lbs. 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 lbs. M.E.P. and 30 lbs. 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 = C-^ — . where T denotes the mean admission temper- 
 
 L ^J N 2 
 
 ature, t the mean exhaust temperature, S clearance-surface (square feet)> 
 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 
 
938 
 
 THE STEAM-ENGINE. 
 
 non-condensing engine, 4-ft. stroke, 24 in. diam., 60 revs, per min., initial 
 pressure 90 lbs. gauge, exhaust pressure 2 lbs., we have T — t = 112°, 
 N = 1, L = 880, S = 7 sq. ft.; and, taking C = 0.112 and TP= lbs. 
 
 112V 112 Y7 
 
 water condensed per minute, W = 1X880 = ° -09 lb- per 
 
 minute, or 5.4 lbs. per hour. If the steam used per I.H.P. per hour 
 according to the diagram is 20 lbs., the actual water consumption is 
 25.4 lbs., 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 
 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 p, The Line of Boiler- 
 „ . „„ 'pressure, JK, is 
 
 Fig. 154. 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 
 
INDICATOR-DIAGRAMS. 
 
 939 
 
 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 hnd the area by a planimeter, 
 or other means (see Mensuration, p. 57), 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 
 side. By superposing these cards the pressure or tension on the piston 
 rod may be determined. The pressure or pull on the crank pin at any 
 instant is the pressure or tension in the rod modified by the angle of the 
 connecting rod and by the effect of the inertia of the reciprocating parts. 
 For discussion of this subject see Klein's "High-speed Steam Engine," 
 also papers by S. A. Moss, Trans. A. S. M. E., 1904, and by F. W. Holl- 
 mann, 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 
 proper testing apparatus and allowed for. But after making this correc- 
 tion, even with the best work, the results are liable to variable errors 
 which may amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., 
 v, 310; Denton, Trans. A. S. M. E., xi, 329; David Smith, U. S. N., Proc. 
 Eng'g Congress, 1893, Marine Division. 
 
 Other 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 C E 
 
 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 
 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 
 
 Fig. 155. 
 
940 THE 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. = i^-^rx » 
 
 in which P = mean effective pressure in lbs. 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. 
 
 I.H.P. = ■ -„ n - . in which S = piston speed in feet per minute. 
 
 PLd 2 n Pd?S 
 I.H.P.^ fg"" = 42Qi 7 = 0.0000238 PLd 2 n = 0.0000238 Pd 2 S, 
 
 in which d = diam. of cyl. in inches. (The figures 238 are exact, since 
 7854 -4- 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. — 
 
 Diameter = 205 \ - HJ 
 
 PLn ^la-iuoMsi ~vu y ps 
 
 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. lbs. 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. = 100; 
 B.H.P. = 90; E.H.P. at generator 81, at end of line 76.95. H.P. delivered 
 by motor 69.26. 
 
INDICATED HOKSE-POWER OF ENGINES. 
 
 941 
 
 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 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 lbs., 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. = V2d 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. _ 
 
 "3 » oi 
 
 "3 i 
 
 "rid r 
 .S"o g 
 
 1 Ratio Mean 
 Total to 
 Initial 
 Pressure. 
 
 II 
 
 d w ™; 
 
 W gj d 
 Eh 
 
 a> © 2 
 
 0>-*> CO 
 
 IS 
 
 i. o> 
 
 d q. 
 o . 
 
 A.<5 
 
 Non-condensing. 
 
 Single Cylinder . 
 
 Compound 
 
 Triple 
 
 Quadruple 
 
 100 
 
 5. 
 
 20 
 
 0.522 
 
 52.2 
 
 15.5 
 
 120 
 
 7.5 
 
 16 
 
 .402 
 
 48.2 
 
 15.5 
 
 160 
 
 10. 
 
 16 
 
 .330 
 
 52.8 
 
 15.5 
 
 200 
 
 12.5 
 
 16 
 
 .282 
 
 56.4 
 
 15.5 
 
 36.7 i 
 32.7 
 37.3 
 40.9 I 
 
 0.524 
 467 
 533 
 584 
 
 
 
 Condensing Engines. 
 
 
 
 
 
 Single Cylinder . . 
 
 Compound 
 
 Triple 
 
 Quadruple 
 
 100 
 120 
 160 
 200 
 
 10. 
 15. 
 
 20. 
 25. 
 
 10 
 8 
 8 
 8 
 
 0.330 
 .247 
 .200 
 .169 
 
 33.0 
 29.6 
 32.0 
 33.8 
 
 2 
 2 
 2 
 2 
 
 31.0 
 27.6 
 30.0 
 31.8 
 
 600 
 
 0.443 
 .390 
 .429 
 .454 
 
 For any other piston-speed than 600 ft. per min., multiply the figures 
 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 -*- 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 943. 
 
 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. 
 
THE STEAM-ENGINE. 
 
 Engine Constants, 
 
 Constant X Piston Speed X M.E.P. = H.P. 
 
 Diam. of 
 Cylinder. 
 
 Even 
 Inches. 
 
 + 1/8 
 
 + V4 
 
 + 3/8 
 
 + 1/2 
 
 + 5/ 8 
 
 + 3/4 
 
 + 7/8 
 
 1 
 
 .0000238 
 
 .0000301 
 
 .0000372 
 
 .0000450 
 
 .0000535 
 
 .0000628 
 
 . 0000729 
 
 .0000837 
 
 2 
 
 .0000952 
 
 .0001074 
 
 .0001205 
 
 .0001342 
 
 .0u01487 
 
 .0001640 
 
 .0001800 
 
 .0001967 
 
 3 
 
 .0002142 
 
 .0002324 
 
 .0002514 
 
 .000/711 
 
 .0u02915 
 
 .0003127 
 
 . 0003347 
 
 .0003574 
 
 4 
 
 .0003808 
 
 .0004050 
 
 .0004299 
 
 .0004554 
 
 .0004819 
 
 .0005091 
 
 . 000537C 
 
 .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 
 
 .002262! 
 
 .0023209 
 
 10 
 
 .0023800 
 
 .0024398 
 
 .0025004 
 
 .0025618 
 
 . 0026239 
 
 . 0026867 
 
 .0027502 
 
 .0028147 
 
 11 
 
 .0028798 
 
 .0029456 
 
 .0030121 
 
 . 0030794 
 
 .0031475 
 
 .0032163 
 
 .003285? 
 
 .0033561 
 
 12 
 
 .0034272 
 
 .0034990 
 
 .0035714 
 
 . 0036447 
 
 . 0037187 
 
 .0037934 
 
 .003869C 
 
 .0039452 
 
 13 
 
 .0040222 
 
 .0040999 
 
 .0041783 
 
 . 0042576 
 
 . 0043375 
 
 .0044182 
 
 .004499; 
 
 .0045819 
 
 14 
 
 .0046648 
 
 .0047484 
 
 .0048328 
 
 . 0049181 
 
 . 005003? 
 
 .0050906 
 
 C05178C 
 
 .0052661 
 
 15 
 
 .0053550 
 
 .0054446 
 
 .0055349 
 
 . 0056261 
 
 .005717? 
 
 .0058105 
 
 .005903? 
 
 .0059979 
 
 16 
 
 .0060928 
 
 .0061884 
 
 .0062847 
 
 .0063817 
 
 . 0064795 
 
 .0065780 
 
 .0066774 
 
 .0067774 
 
 17 
 
 .0068782 
 
 .0069797 
 
 .0070819 
 
 . 0071850 
 
 . 007288} 
 
 .0073932 
 
 .0074985 
 
 .0076044 
 
 18 
 
 .0077112 
 
 .0078187 
 
 .0079268 
 
 . 0080360 
 
 .0081452 
 
 .0082560 
 
 .0083672 
 
 .0084791 
 
 19 
 
 .0085918 
 
 .0087052 
 
 .0088193 
 
 . 0089343 
 
 . C09049C 
 
 .0091663 
 
 .0092835 
 
 .0094013 
 
 20 
 
 .0095200 
 
 .0096393 
 
 .0097594 
 
 . 0098803 
 
 .010001* 
 
 .0101243 
 
 .0102474 
 
 .0103712 
 
 21 
 
 .0104958 
 
 .0106211 
 
 .0107472 
 
 . 0108739 
 
 .011001! 
 
 .0111299 
 
 .0112589 
 
 .0113886 
 
 22 
 
 .0115192 
 
 .0116505 
 
 .0117825 
 
 .0119152 
 
 .012048} 
 
 .0121830 
 
 .0123179 
 
 .0124537 
 
 23 
 
 .0125902 
 
 .0127274 
 
 .0128654 
 
 .0130040 
 
 .013143! 
 
 .0132837 
 
 .0134247 
 
 .0135664 
 
 24 
 
 .0137088 
 
 .0138519 
 
 .0139959 
 
 .0141405 
 
 .014285 C 
 
 .0144321 
 
 .0145789 
 
 .0147266 
 
 25 
 
 .0148750 
 
 .0150241 
 
 .0151739 
 
 .0153246 
 
 .015475 c 
 
 .0156280 
 
 .0157809 
 
 .0159345 
 
 26 
 
 .0160888 
 
 .0162439 
 
 .0163997 
 
 .0165563 
 
 .016713! 
 
 .0168716 
 
 .0170304 
 
 .0171899 
 
 27 
 
 .0173502 
 
 .0175112 
 
 .0176729 
 
 .0178355 
 
 .017998* 
 
 .0181627 
 
 .0183275 
 
 .0184929 
 
 28 
 
 .0186592 
 
 .0188262 
 
 .0189939 
 
 .0191624 
 
 .01933ie 
 
 .0195015 
 
 .0196722 
 
 .0198436 
 
 29 
 
 .0200158 
 
 .0201887 
 
 .0203634 
 
 . 0205368 
 
 .020711? 
 
 .0208879 
 
 .0210645 
 
 .0212418 
 
 30 
 
 .0214200 
 
 .0215988 
 
 .0217785 
 
 .0219588 
 
 .022139? 
 
 .0223218 
 
 .0225044 
 
 .0226877 
 
 31 
 
 .0228718 
 
 .0230566 
 
 .0232422 
 
 . 0234285 
 
 .023615! 
 
 .0238033 
 
 .0239919 
 
 .0241812 
 
 32 
 
 .0243712 
 
 .0245619 
 
 .0247535 
 
 . 0249457 
 
 .025138/ 
 
 .0253325 
 
 .0255269 
 
 .0257222 
 
 33 
 
 .0259182 
 
 .0261149 
 
 .0263124 
 
 .0265106 
 
 .026709! 
 
 .0269092 
 
 .0271097 
 
 .0273109 
 
 34 
 
 .0275128 
 
 .0277155 
 
 .0279189 
 
 .0281231 
 
 .028327? 
 
 .0285336 
 
 .0287399 
 
 .0289471 
 
 35 
 
 .0291550 
 
 .0293636 
 
 .0295729 
 
 .0297831 
 
 .029993? 
 
 .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 
 
 .037133? 
 
 .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 
 
 .(542655 
 
 .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. 
 
 943 
 
 Horse-power per Pound Mean Effective Pressure. 
 
 Formula, Area in sq. in. X piston-speed -*- 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 
 
 51/2 
 
 .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 
 
 1.0496 
 
 71/2 
 
 .1339 
 
 .2678 
 
 .4016 
 
 .5355 
 
 .6694 
 
 .8033 
 
 .9371 
 
 1.0710 
 
 1.2049 
 
 8 
 
 .1523 
 
 .3046 
 
 .4570 
 
 .6093 
 
 .7616 
 
 .9139 
 
 1 .0662 
 
 1.2186 
 
 1 .3709 
 
 81/2 
 
 .1720 
 
 .3439 
 
 .5159 
 
 .6878 
 
 .8598 
 
 1.0317 
 
 1.2037 
 
 1 .3756 
 
 1.5476 
 
 9 
 
 .1928 
 
 .3856 
 
 .5783 
 
 .7711 
 
 .9639 
 
 1.1567 
 
 1.3495 
 
 1.5422 
 
 1.7350 
 
 91/2 
 
 .2148 
 
 .4296 
 
 .6444 
 
 .8592 
 
 1.0740 
 
 1.2888 
 
 1.5036 
 
 1.7184 
 
 1.9532 
 
 10 
 
 .2380 
 
 .4760 
 
 .7140 
 
 .9520 
 
 1.1900 
 
 1.4280 
 
 1.6660 
 
 1 .9040 
 
 2.1420 
 
 11 
 
 .2880 
 
 .5760 
 
 .8639 
 
 1.1519 
 
 1.4399 
 
 1.7279 
 
 2.0159 
 
 2.3038 
 
 2.5818 
 
 12 
 
 .3427 
 
 .6854 
 
 1.0282 
 
 1.3709 
 
 1.7136 
 
 2.0563 
 
 2.3990 
 
 2.7418 
 
 3.0845 
 
 13 
 
 .4022 
 
 .8044 
 
 1.2067 
 
 1.6089 
 
 2.0111 
 
 2.4133 
 
 2.8155 
 
 3.2178 
 
 3.6200 
 
 14 
 
 .4665 
 
 .9330 
 
 1 .3994 
 
 1.8659 
 
 2.3324 
 
 2.7989 
 
 3.2654 
 
 3.7318 
 
 4.1983 
 
 15 
 
 .5355 
 
 1.0710 
 
 1.6065 
 
 2.1420 
 
 2.6775 
 
 3.2130 
 
 3.7485 
 
 4.2840 
 
 4.8195 
 
 16 
 
 .6093 
 
 1.2186 
 
 1.8278 
 
 2.4371 
 
 3.0464 
 
 3.6557 
 
 4.2650 
 
 4.8742 
 
 5.4835 
 
 17 
 
 .6878 
 
 1.3756 
 
 2.0635 
 
 2.7513 
 
 3.4391 
 
 4.1269 
 
 4.8147 
 
 5.5026 
 
 6.1904 
 
 18 
 
 .7711 
 
 1.5422 
 
 2.3134 
 
 3.0845 
 
 3.8556 
 
 4.6267 
 
 5.3978 
 
 6.1690 
 
 6.9401 
 
 19 
 
 .8592 
 
 1.7184 
 
 2.5775 
 
 3.4367 
 
 4.2959 
 
 5.1551 
 
 6.0143 
 
 6.8734 
 
 7.7326 
 
 20 
 
 .9520 
 
 1.9040 
 
 2.8560 
 
 3.8080 
 
 4.7600 
 
 5.7120 
 
 6.6640 
 
 7.6160 
 
 8.5680 
 
 21 
 
 1 .0496 
 
 2.0992 
 
 3.1488 
 
 4.1983 
 
 5.2479 
 
 6.2975 
 
 7.3471 
 
 8.3966 
 
 9.4462 
 
 22 
 
 1.1519 
 
 2.3038 
 
 3.4558 
 
 4.6077 
 
 5.7596 
 
 6.9115 
 
 8.0634 
 
 9.2154 
 
 10.367 
 
 23 
 
 1.2590 
 
 2.5180 
 
 3.7771 
 
 5.0361 
 
 6.2951 
 
 7.5541 
 
 8.8131 
 
 10.072 
 
 11.331 
 
 24 
 
 1 .3709 
 
 2.7418 
 
 4.1126 
 
 5.4835 
 
 6.8544 
 
 8.2253 
 
 9.5962 
 
 10.967 
 
 12.338 
 
 25 
 
 1.4875 
 
 2.9750 
 
 4.4625 
 
 5.9500 
 
 7.4375 
 
 8.9250 
 
 10.413 
 
 11.900 
 
 13.388 
 
 26 
 
 1 .6089 
 
 3.2178 
 
 4.8266 
 
 6.4355 
 
 8.0444 
 
 9.6534 
 
 11.262 
 
 12.871 
 
 14.480 
 
 27 
 
 1.7350 
 
 3.4700 
 
 5.2051 
 
 6.9401 
 
 8.6751 
 
 10.410 
 
 12.145 
 
 13.880 
 
 15.615 
 
 28 
 
 1.8659 
 
 3.7318 
 
 5.5978 
 
 7.4637 
 
 9.3296 
 
 11.196 
 
 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 
 
 21.720 
 
 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 
 
 41.469 
 
 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 
 
 5.9500 
 
 11.900 
 
 17.850 
 
 23.800 
 
 29.750 
 
 35.700 
 
 41.650 
 
 47.600 
 
 53.550 
 
 51 
 
 6.1904 
 
 12.381 
 
 18.571 
 
 24.762 
 
 30.952 
 
 37.142 
 
 43.333 
 
 49.523 
 
 55.713 
 
 52 
 
 6.4355 
 
 12.871 
 
 19.307 
 
 25.742 
 
 32.178 
 
 38.613 
 
 45.049 
 
 51.484 
 
 57.920 
 
 53 
 
 6.6854 
 
 13.371 
 
 20.056 
 
 26.742 
 
 33.427 
 
 40.113 
 
 46.798 
 
 53.483 
 
 60.169 
 
 54 
 
 6.9401 
 
 13.880 
 
 20.820 
 
 27.760 
 
 34.700 
 
 41.640 
 
 48.581 
 
 55.521 
 
 62.461 
 
 55 
 
 7.1995 
 
 14.399 
 
 21.599 
 
 28.798 
 
 35.998 
 
 43.197 
 
 50.397 
 
 57.596 
 
 64.796 
 
 56 
 
 7.4637 
 
 14.927 
 
 22.391 
 
 29.855 
 
 37.318 
 
 44.782 
 
 52.246 
 
 59.709 
 
 67.173 
 
 57 
 
 7.7326 
 
 15.465 
 
 23.198 
 
 30.930 
 
 38.663 
 
 46.396 
 
 54.128 
 
 61.861 
 
 69.597 
 
 58 
 
 8.0063 
 
 16.013 
 
 24.019 
 
 32.025 
 
 40.032 
 
 48.038 
 
 56.044 
 
 64.051 
 
 72.054 
 
 59 
 
 8.2848 
 
 16.570 
 
 24.854 
 
 33.139 
 
 41.424 
 
 49.709 
 
 57.993 
 
 66.278 
 
 74.563 
 
 60 
 
 8.5680 
 
 17.136 
 
 25.704 
 
 34.272 
 
 42.840 
 
 51.408 159.976 
 
 68.544 
 
 77.112 
 
944 
 
 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 lbs. 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 
 single 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, chad, across the compression 
 
 Fig. 156. 
 curve first having drawn OX parallel to the atmospheric line and 14.7 
 lbs. 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 gf 
 to intersect the line XO. This will give the point O, 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 I 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 / 
 draw a diagonal to K, the latter 
 point being the intersection of the 
 vacuum and clearance lines; from Z 
 draw IL parallel with the atmos- 
 pheric line. From L, the point of 
 
 J 3 2 1 M 
 
 E 
 
 l^MT" 
 
 r. 
 
 C_ Lj^oo/ 
 
 
 ^^i. 
 
 Fig. 157. 
 
 intersection of the diagonal JK and the horizontal line IL, draw the verti- 
 
WATER CONSUMPTION OF ENGINES. 945 
 
 c&l 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 -s- 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 of 
 compression. 
 
 Number of cubic feet per stroke = 1 (v^tt! ttt* 
 \ 100 / 144 
 
 Corresponding weight of steam per stroke in lbs. =1 ( .. . J - 
 
 Volume of clearance — . 
 
 14,400 
 
 Weight of steam in clearance = 
 
 144 
 lea 
 
 14,400 
 
 Total weight of I , ( b + c \ wa _ leaw' la Uh ,. 9n M „« 
 
 steam per stroke / \ 100 / 144 14,400 14,400 u T ; w ~ cw J ' 
 
 Total weight of steam ) = 60 nla 
 from diagram per hour) 14,400 L 
 
 - c) w — cw']. 
 
 The indicated horse-power is plan + 33,000. Hence the steam-con- 
 sumption per hour per indicated horse-power is 
 
 60 nla _., , . ., 
 
 14400 [(& + C)W - CW] 137.50 r ^ , 
 
 JU^ — 7T-[(6 + »-«•]. 
 
 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 
 137 5 
 
 the formula becomes — (bw). 
 
 V 
 
 In case of no compression, w' becomes zero, and the water-rate = 
 
 137.5 .„ , . , 
 — — [(b + c) w]. 
 
 * For compound or triple-expansion engines read: divided by the equiv- 
 alent mean effective pressure, on the supposition that all work is done 
 in one cylinder. 
 
946 
 
 THE STEAM-ENGINE. 
 
 Prof. Denton {Trans. A. S. M. E., xiv, 1363) gives the following table 
 of theoretical water-consumption for a perfect Mariotte expansion with 
 steam at 150 lbs. above atmosphere, and 2 lbs. absolute back pressure; 
 
 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 sufficient to determine the fact with regard to the 
 exhaust-valves. 
 
 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 expansion 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 trree 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 Campania and Lucania, with three cranks at 
 120°, there are 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 are 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 avoid excessive pressures and consequent friction. The diminished 
 
COMPOUND ENGINES. 
 
 947 
 
 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 no work; 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 lbs. gauge-pressure ex- 
 panded 20 times, in one, two, and three cylinders, is shown in the 
 following table, by W. H. Weightman, Am. Mach., July 28, 1892: 
 
 Diameter of cylinders, in. . 
 
 Area ratios 
 
 Expansions 
 
 Initial steam-pressures — 
 
 absolute — pounds 
 
 Mean pressures, pounds. . . 
 Mean effective pressures, 
 
 pounds 
 
 Steam temperatures into 
 
 cylinders , 
 
 Steam temperatures out 
 
 of the cylinders 
 
 Difference in temperatures 
 
 Single 
 Cyl- 
 inder. 
 
 165 
 32.96 
 
 28.96 
 366° 
 
 184.2° 
 181.8 
 
 Compound 
 Cylinders. 
 
 33 
 1 
 5 
 
 165 
 86.11 
 
 53.11 
 
 366° 
 
 259.9° 
 106.1 
 
 61 
 3.416 
 
 33 
 19.68 
 
 15.68 
 259.9° 
 
 184.2° 
 75.7 
 
 Triple-expansion 
 Cylinders. 
 
 165 
 
 121.44 
 
 60.64 
 366° 
 
 293.5° 
 72.5 
 
 46 
 2.70 
 2.714 
 
 60.8 
 44.75 
 
 22.35 
 
 293.5° 
 
 234.1° 
 59.4 
 
 61 
 
 4.740 
 2.714 
 
 22.4 
 16.49 
 
 12.49 
 
 234.1° 
 
 184.2° 
 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. 158, 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- 
 stroke 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. 
 
948 
 
 THE STEAM-ENGINE. 
 
 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 
 r n . contained in the first cylinder into the 
 Mbs - second. 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 
 Fig. 158. - Woolf Engine, Ideal j deal receiver-engine the pistons of the 
 Indicator-diagrams. two cylinders are connected to cranks 
 
 at right angles to each other on 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 eaual 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. 159, cd is the line of admission and hg the exhaust-line for the 
 first cylinder; and dg is the expansion-curve and pq the atmospheric line. 
 
 & G ^ do 
 
 fj 
 
 
 y 
 
 I 
 
 
 
 ^y 
 
 
 p 
 
 
 
 2 
 
 1 
 
 3 
 
 ^60 lbs 
 
 
 
 
 r 
 
 
 
 
 
 
 rd* 
 
 
 -40 
 
 i — 
 
 —%- 
 
 
 -W--» 
 
 
 -20 
 
 
 
 i 
 / 
 
 / 
 
 h 
 
 
 - P 
 
 k 
 -o 7 
 
 — ^ 
 
 
 1 
 
 Fig. 159. — Receiver-engine, 
 Ideal Indicator-diagram. 
 
 Fig. 160. —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. 160. 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. 
 
 949 
 
 tional length of the first diagram as applied to the second. Produce oh up- 
 wards, and set off oc equal to the total height of the first diagram above the 
 vacuum-line; and, upon the shortened base/a, 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 calcu- 
 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 
 between the first and second cylinders, which is the cause of an interme- 
 diate fall of pressure, should be reduced to the lowest practicable amount. 
 
 Supposing that there is no loss of steam in passing through the engine, 
 by 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 volume 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 cylindersj 
 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. 161. 
 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 161 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 
 
950 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 low pressure 
 cylinders v and V. _ Thus Grashof gives V -f- v = 0.85 Vr; Hrabak, 
 0.90 Vr; Werner, Vr; 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 the 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 
 than 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; p t 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-i- p n \ therefore, cut-off in high-pressure cylinder — R X p n -5- p\. 
 
 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 lbs., the ratio of the low-pressure 
 to the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 lbs., 
 3.75; for 90 lbs., 4.0; for 100 lbs., 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 lbs. 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 lbs. 
 absolute 4.5 is better, and for 100 lbs. 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 lbs. absolute, 3.4 for 95 lbs., 3.7 for 105 lbs., and 4.0 for 115 lbs. 
 
 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-pressure, a very small receiver will do. The pressure in the receiver 
 should never exceed half the boiler-pressure. (Seaton.) 
 
COMPOUND ENGINES. 951 
 
 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; 
 a' = area of the second cylinder in square inches; 
 r = ratio of the capacity of the second Cylinder to that of the first; 
 L = length of stroke in feet, supposed to be the same for both cylinders 
 I = period of admission to the first cylinder in feet, excluding clearance 
 c = clearance at each end of the cylinders, in parts of the stroke, in ft. 
 U = length of the stroke plus the clearance, in feet; 
 V = period of admission plus the clearance, in feet; 
 5 = length of a given part of the stroke of the second cylinder, in feet; 
 P = total initial pressure in the first cylinder, in lbs. per square inch, 
 
 supposed to be uniform during admission; 
 P' = total pressure at the end of the given part of the stroke s; 
 p .= average total pressure for the whole stroke; 
 R «s= nominal ratio of expansion in the first cylinder, or L -*- I; 
 W — actual ratio of expansion in the first cylinder, of L' -i- V ; 
 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 ./Vis thereby practically reduced below the ratio here stated. 
 
 w = whole net work in one stroke, in foot-pounds. 
 Ratio of expansion in the second cylinder: 
 
 Hit* 
 
 Iti the Woolf engine, 
 In the receiver-engine 
 
 1+ N 
 (n-l)r 
 
 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 p 4- N\; 
 In the receiver-engine, r -p-t of rR f . 
 
 Wofk done in the two cylinders for one stroke, with a givert cut-off 
 and a given combined actual ratio of expansion : 
 
 Woolf engine, w = aP [V(l 4- hyp log R") — c\; 
 Receiver engine, w^aP ft' (1 + hyp log R") -c ( i + ^p- ) 1 1 
 when there is no intermediate fall of pressure. 
 
952 THE STEAM-ENGINE. 
 
 "When there is an intermediate fall, when the pressure falls to S/ 4 2/3 
 1/2 of the final pressure in the 1st cylinder, the reduction of work is 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 = 1 sq. in., P = 63 lbs., U = 2.42 ft., n = 4, R" =a 
 5.969, c = 0.42 ft., r = 3, B' = 2.653; 
 
 w = l X 63 [2.42 (5/ 4 hyp log 5.969) -.42 (l + ^ ^ * ^ 1 =421.55 ft .-lbs. 
 
 Calculation of Diameters of Cylinders of a compound condensing 
 engine of 2000 H.P. at a speed of 700 feet per minute, with 100 lbs. boiler- 
 pressure. 
 
 100 lbs. gauge-pressure = 115 absolute, less drop of 5 lbs. between 
 boiler and cylinder = 110 lbs. initial absolute pressure. Assuming 
 terminal pressure in l.p. cylinder = 6 lbs., the total expansion of steam 
 in both cylinders == 110 -f- 6 = 18.33. Hyp log 18.33 = 2.909. Back 
 pressure in l.p. cylinder, 3 lbs. absolute. 
 
 The following formulae are used in the calculation of each cylinder: 
 
 *. ". - .. . H.P. X 33,000 
 
 (1) Area of cylinder = „ „, ^, - — r— -r- 
 
 ' J 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 
 lbs. 
 
 From (2), mean effective pressure = 23.454 - 3 = 20.454 lbs. 
 2000 X 33 000 
 
 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 lbs., and the mean total pressure 
 10.227 + 3 = 13.227 lbs. 
 
 From (3), 1 4- hyp log R = 13.227 -h 6 = 2.2045. 
 
 Hyp log R = 1.2045, whence R in l.p. cyl. = 3.335. 
 
 From (4), 3.335 X 6 = 20.01 lbs. initial pressure in l.p. cyl. and ter- 
 minal pressure in h.p. cyl., assuming no drop between cvlinders. 
 
 110 -h 20.01 = 18.33 -h 3.335 = 5.497, R in h.p. cyl. 
 
 From (3), mean total pres. in h.p. cyl. = 20.01 X (1 + hyp log 5.497) 
 = 54.11. 
 
 From (2), 54.11 - 20.01 = 34.10, M.E.P. in h.p. cyl. 
 
 /-.x t u i 1000X33,000 100rt . ._. ,. 
 
 From (1), area of h.p. cyl. = ■ — =1382 sq. ins. = 42 ins. diam. 
 
 Cylinder ratio = 4610 h- 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 
 -4- 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. 932. 
 
 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 
 
TRIPLE-EXPANSION ENGINES. 953 
 
 one, but there appears to be an increasing tendency in favor of large 
 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.- 
 xxi, 1002. 
 
 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 lbs. 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 lbs. 
 
 The theoretical M.E.P. with an absolute initial pressure of 150 + 14.7 = 
 164.7 lbs. initial at 16 expansions is 
 
 P(! 4- hyp log 16) _ 164 7 x 3^6 _ ^ 
 
 less 2 lbs. 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 lbs. 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 foot- 
 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 -h 3 = 8.59 lbs. 
 
 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 sq. 
 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 lbs. 
 
 If the intermediate cylinder is 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 ro ot of the ratio of l.p. to h.p. cylinder, 
 which in this case is 1440 -*- (1.1 V9.6) = 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 lbs. 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 932, 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 
 
954 
 
 THE STEAM-ENGINE. 
 
 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 cylin- 
 ders equals the area found by the formulae. 
 
 Notation. 
 
 pi = Initial pressure in the high-pressure cylinder. 
 
 p t = terminal pressure in the low-pressure cylinder. 
 Pb = back pressure in the low-pressure cylinder. 
 
 pt = term press, in h.p. cyl. and initial press, in intermediate cyl. 
 
 P2 = term, press, in int. cyl. and initial press, in l.p. cyl. 
 
 Pi, Ri, Ra. ratio of exp in h.p. int. and l.p. cyls. 
 
 R = total ratio of exp. = Ri X Ri X Rz. 
 
 P = mean effec. press, of the combined ideal diagram, referred to the 
 l.p. cyl. 
 
 Pi, P2, P% = M.E.P. in the h.p., int., and l.p. cyls. 
 HP = horse-power of the engine = PLA3N ■+ 33,000. 
 
 L = length of stroke in feet: N = number of single strokes per min. 
 
 Ai, At, A3, areas (sq. ins.) of h.p. int. and l.p. cyls. (ideal). 
 
 W = work done in one cylinder per foot of stroke. 
 
 ri = ratio of Ai to A\\ rz = ratio of A3 to Ai. 
 
 F\, Fi, F3, diagram factors of h.p. int. and 1 p. cyl. 
 
 ai, ai, a,3, areas (actual) of h.p. int. and l.p. cyl. 
 
 Formula. 
 
 (1) R = Pi -*■ p t . 
 
 (2) P = p t (1 + hyp log R) - p h . 
 
 (3) Ps = 1/3 P. 
 
 (4) Hyp log R 3 = (P3 - Vt + Vb> + Pt- 
 R1R2 = R -*- R3; Ri = Ri = ^RiRi. 
 
 (5) 
 
 (6) p 3 - V t X R3. 
 
 (7) Pi = P3 X Ri. 
 
 (8) m = Pi X Ru 
 
 (9) P 2 = Ps (hyp log 7Z 2 ) = P3R3. 
 
 (10) Pi = Pi (hyp log fli) = P2R2. 
 
 (11) T7 = 11,000 HP -h LiV. 
 
 (12) Ai = W -h Pi; ^2 = W + Pi; A 3 = W -4- P 3 . 
 
 (13) n = A2 -f- Ai = Pi -h P 2 = Ri or P 2 ; r 3 = A3 ■*■ Ai = Pi +■ P 3 . 
 
 (14) ai = Ai *- Pi; a 2 = Ai -4- F 2 ; as = A3 -*■ F z . 
 
 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 lbs. Terminal pressure, 8 lbs. (absolute). 
 
 Pi- 
 
 ,R. 
 
 P. 
 
 Pi, 
 
 P 3 - 
 
 orr2- 
 
 P3- 
 
 P2- 
 
 Pi- 
 
 Pi. 
 
 ri- 
 
 120 
 
 15 
 
 26.66 
 
 8.89 
 
 1.626 
 
 3.037 
 
 13.01 
 
 39.51 
 
 14.45 
 
 43.89 
 
 4.939 
 
 140 
 
 17.5 
 
 27.90 
 
 9.30 
 
 1.712 
 
 3.197 
 
 13.70 
 
 43.79 
 
 15.92 
 
 50.89 
 
 5.472 
 
 160 
 
 20 
 
 28.97 
 
 9.66 
 
 1.790 
 
 3.343 
 
 14.32 
 
 47.86 
 
 17.29 
 
 57.76 
 
 5.980 
 
 180 
 
 22.5 
 
 29.91 
 
 9.97 
 
 1.861 
 
 3.477 
 
 14.89 
 
 51.77 
 
 18.55 
 
 64.52 
 
 6.471 
 
 200 
 
 25 
 
 30.75 
 
 10.25 
 
 1.928 
 
 3.601 
 
 15.42 
 
 55.54 
 
 19.76 
 
 71.16 
 
 6.942 
 
 220 
 
 27.5 
 
 31.51 
 
 10.50 
 
 1.990 
 
 3.718 
 
 15.91 
 
 59.16 
 
 20.90 
 
 77.69 
 
 7.397 
 
 240 
 
 30 
 
 32.21 
 
 10.74 
 
 2.049 
 
 3.826 
 
 16.39 
 
 62.72 
 
 22.00 
 
 84.16 
 
 7.839 
 
TRIPLE-EXPANSION ENGINES. 
 
 955 
 
 Theoretical Mean Effective Pressures, Cylinder Ratios, Etc., 
 of Triple Expansion Engines. 
 
 
 Back pressure, 3 lbs. Terminal pressure, 
 
 10 lbs. (absolute). 
 
 
 pi- 
 
 R. 
 
 P. 
 
 P 3 - 
 
 R 3 . 
 
 ffi, R2, 
 
 or ro- 
 
 P3- 
 
 V-z- 
 
 Pa. 
 
 Pi. 
 
 r%. 
 
 rn 
 
 12 
 
 31.85 
 
 10.62 
 
 1.436 
 
 2.890 
 
 14.36 
 
 41.50 
 
 15.24 
 
 44.04 
 
 4.148 
 
 140 
 
 14 
 
 33.39 
 
 11.13 
 
 1.511 
 
 3.044 
 
 15.11 
 
 45.99 
 
 16.82 
 
 51.20 
 
 4.600 
 
 160 
 
 16 
 
 34.73 
 
 11.58 
 
 1.580 
 
 3.182 
 
 15.80 
 
 50.28 
 
 18.29 
 
 58.20 
 
 5.027 
 
 180 
 
 18 
 
 35.90 
 
 11.97 
 
 1.643 
 
 3.310 
 
 16.43 
 
 54.38 
 
 19.66 
 
 65.09 
 
 5.439 
 
 200 
 
 20 
 
 36.96 
 
 12.32 
 
 1.702 
 
 3.428 
 
 17.02 
 
 58.34 
 
 20.97 
 
 71.88 
 
 5.834 
 
 220 
 
 22 
 
 37.91 
 
 12.64 
 
 1.757 
 
 3.538 
 
 17.57 
 
 62.15 
 
 22.20 
 
 78.54 
 
 6.215 
 
 240 
 
 24 
 
 38.78 
 
 12.93 
 
 1.809 
 
 3.642 
 
 18.09 
 
 65.88 
 
 23.38 
 
 85.15 
 
 6.587 
 
 Given the required H.P. of an engine, its speed and length of stroke, 
 and the assumed diagram factors Fi, Fz, Fs for the three cylinders, the 
 areas of the cylinders may be found by using formulae (11), (12), and 
 (14), and the values of Pi, P2, and Pz 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 the high to the low being the product of the two 
 ratios, that is, the square of the cube root of the number of expansions. 
 Applying this rule to the pressures above given, assuming a terminal 
 pressure (absolute) of 10 lbs. and 8 lbs. respectively, we have, for triple- 
 expansion engines: 
 
 
 Terminal Pressure, 10 lbs. 
 
 Terminal Pressure, 8 lbs. 
 
 pressure 
 (Absolute) . 
 
 No. of Ex- 
 pansions. 
 
 Cylinder Ratios, 
 areas. 
 
 No. 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 
 
 I6I/4 
 171/2 
 183/4 
 20 
 
 1 to 2.53 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 lbs. 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 lbs. absolute; when 135 lbs., 5.4; when 
 145 lbs., 5.8; when 155 lbs., 6.2; when 165 lbs., 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 lbs. 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. 
 
956 THE STEAM-ENGINE. 
 
 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 lbs. 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 1/2 or 1 to 
 9; whilst in a war-ship a terminal pressure would be required of 12 to 13 
 lbs. 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 
 120 deg. 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 
 191/2 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 
 221/2 lbs. 
 
 Velocity of Steam through 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 . Mach., 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 
 lbs.; main shaft 22 in. diameter at the swell; main journals 19 X 38 in.; 
 crank-pins 91/2 X 10 in.; distance between center lines of two engines 
 24 ft. 71/2 in.; Corliss valves, with separate eccentrics for the exhaust- 
 valves 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 lbs. 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: 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 957 
 
 Gauge- 
 
 Absolute 
 
 Terminal 
 
 Ratio of 
 
 Ratios of Areas 
 
 pressures. 
 
 Pressures. 
 
 Pressures. 
 
 Expansion. 
 
 of Cylinders. 
 
 
 
 (12 
 
 14.6 
 
 1 : 1.95 : 3.81 
 
 7.43 
 
 160 
 
 175 
 
 10 
 
 17.5 
 
 1 : 2.05 : 4.18 
 
 8.55 
 
 
 
 ( 8 
 
 21.9 
 
 1 : 2.16: 4.68 
 
 10.12 
 
 
 
 (12 
 
 16.2 
 
 1 : 2.01 : 4.02 
 
 8.07 
 
 180 
 
 195 
 
 10 
 
 19.5 
 
 1 : 2.10: 4.42 
 
 9.28 
 
 
 
 I 8 
 
 24.4 
 
 1 : 2.22: 4.94 
 
 10.98 
 
 
 
 (12 
 
 17.9 
 
 1 : 2.06: 4.23 
 
 8.70 
 
 200 
 
 215 
 
 10 
 
 21.5 
 
 1 : 2.15 : 4.64 
 
 9.98 
 
 
 
 ( 8 
 
 26.9 
 
 1 : 2.28: 5.19 
 
 11.81 
 
 
 
 (12 
 
 19.6 
 
 1 : 2.10: 4.43 
 
 9.31 
 
 220 
 
 235 
 
 10 
 
 23.5 
 
 1 : 2.20: 4.85 
 
 10.67 
 
 
 
 8 
 
 29.4 
 
 1 : 2.33 : 5.42 
 
 12.62 
 
 Seaton says: When the pressure of steam employed exceeds 190 lbs. 
 absolute, four cylinders should be employed, with the steam expanding 
 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 lbs. boiler-pressure, 
 unjacketed cylinders, and separate steam and exhaust valves. 
 
 ECONOMIC PERFOR3IANCE 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 lbs.; net maximum 
 pressure in cylinders 80 lbs. 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, lbs 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 Hirn, 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 lbs., were 15.63 and 15.69 lbs. of water per I. H.P. per 
 hour. 
 
 3. Single Cylinders of Small Size, 8 or 9 in. Diam., Jacketed, 
 Non-condensing. — The best results are obtained at a cut-off of 20 
 per cent, with 75 lbs. maximum pressure in the cylinder; about 25 lbs. 
 of water per I. H.P. per hour. 
 
 4. 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 lbs.: steam per I. H.P. hour, 19.58 lbs. Other engines, with lower 
 steam pressures, gave a steam consumption as high as 26.7 lbs. 
 
 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 
 
958 
 
 THE STEAM-ENGINE. 
 
 computation from nearly perfect indicator diagrams, with allowance 
 for 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 lbs. above zero, and in the condensing table at 3 lbs. 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 lbs. 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 lb. 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 lbs. for 10% cut-off; 4.75 lbs. for 20% 
 cut-off; and 5 lbs. for 30% cut-off. The steam accounted for 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. The 
 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. 
 
 TABLE No. 1. 
 
 Feed-water Consumption, Simple Engines. 
 
 r-condensing engines. condensing engines. 
 
 
 i 
 
 
 Feed-water Re- 
 
 
 h 
 
 
 Feed-water Re- 
 
 
 O 
 | 
 
 £ 
 
 quired per I.H.P. 
 
 
 o 
 
 m 
 
 quired per I.H.P. 
 
 
 
 per Hour. 
 
 
 2 
 
 J2 
 
 per Hour. 
 
 
 <i 
 
 
 
 
 
 <j 
 
 
 
 
 
 > 
 o 
 
 3 
 
 e3J*f 
 58 
 
 Z-, v 3 • 
 
 
 > 
 O 
 
 3 
 
 
 
 to 
 
 S3 
 
 PM 
 
 
 
 to 
 
 03 
 
 £ 
 
 s^ 
 
 
 o 
 
 
 > 
 
 WK! * 
 
 o 
 
 3 
 
 "3 ® 
 
 a> 
 
 M§ 
 
 w<! o> 
 
 3 
 
 c 
 
 4> 
 
 13 ® 
 
 o 
 
 to 
 
 a 
 
 
 espondin 
 [Results 
 Practice, 
 Slight Li 
 
 3 
 
 u 
 
 3 
 
 0J 
 
 > 
 
 to 
 a 
 d 
 
 C 
 
 o & »; 
 |S~1 
 
 espondin 
 1 Results 
 Practice, 
 Slight I 
 
 £ 
 
 "3 ft 
 
 
 H a v 
 
 gas? 
 
 o 
 
 £ 
 
 Oft 
 
 a; 
 
 3 t. hfi 
 
 t 2 M 
 
 ( 
 
 80 
 
 16.07 
 
 27.61 
 
 29.88 
 
 ( 
 
 80 
 
 29.72 
 
 17.30 
 
 18.89 
 
 10 
 
 90 
 
 19.76 
 
 25.43 
 
 27.43 
 
 10 
 
 90 
 
 33.41 
 
 17.15 
 
 18.70 
 
 ( 
 
 100 
 
 23.45 
 
 23.90 
 
 25.73 
 
 i 
 
 100 
 
 37.10 
 
 17.02 
 
 18.56 
 
 ( 
 
 80 
 
 32.02 
 
 21.04 
 
 25.68 
 
 ( 
 
 80 
 
 38.28 
 
 17.60 
 
 19.09 
 
 20 | 
 
 90 
 
 37.47 
 
 23.00 
 
 24.57 
 
 15 
 
 90 
 
 42.92 
 
 17.45 
 
 18.91 
 
 ( 
 
 100 
 
 42.92 
 
 22.25 
 
 23.77 
 
 I 
 
 100 
 
 47.56 
 
 17.32 
 
 18.74 
 
 ( 
 
 80 
 
 43.97 
 
 24.71 
 
 26.29 
 
 { 
 
 80 
 
 45.63 
 
 18.27 
 
 19.69 
 
 30 
 
 90 
 
 50.73 
 
 23.91 
 
 25.38 
 
 20 \ 
 
 90 
 
 51.08 
 
 18.14 
 
 19.51 
 
 ( 
 
 100 
 
 57.49 
 
 23.27 
 
 24.68 
 
 I 
 
 100 
 
 56.53 
 
 18.02 
 
 19.36 
 
 ( 
 
 80 
 
 53.25 
 
 25.76 
 
 27.17 
 
 ( 
 
 80 
 
 57.57 
 
 19.91 
 
 21.25 
 
 40{ 
 
 90 
 
 61.01 
 
 25.03 
 
 26.35 
 
 30 
 
 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 
 
 50 
 
 90 
 
 68.96 
 
 26.32 
 
 27.62 
 
 40 
 
 90 
 
 74.60 
 
 21.24 
 
 22.41 
 
 ( 
 
 100 
 
 77.48 
 
 25.78 
 
 26.99 
 
 
 100 
 
 82.36 
 
 21.13 
 
 22.24 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 959 
 
 The data upon which table No. 3 is calculated are not given, but the 
 feed-water consumption is somewhat lower than has yet been reached 
 (1894), the lowest steam consumption of a triple-expansion engine yet 
 recorded being 11.7 lbs. 
 
 TABLE No. 2. 
 Feed-water Consumption for Compound Condensing Engines. 
 
 Cut-off 
 
 Initial Pressure above 
 Atmosphere. 
 
 Mean Effective Press. 
 
 Feed-water 
 Required 
 
 
 H.P. Cyl., 
 lbs. 
 
 L.P.Cyl., 
 
 lbs. 
 
 H.P. Cyl., 
 lbs. 
 
 L.P.Cyl., 
 
 lbs. 
 
 Hour, lbs. 
 
 ■ 1 
 
 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 
 
 20 j 
 
 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 
 
 30 j 
 
 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 
 
 TABLE No. 3. 
 Feed-Water Consumption for Triple-expansion Condensing Engines. 
 
 Cut-off, 
 
 Initial Pressure above 
 Atmosphere. 
 
 Mean Effective Pressure. 
 
 Feed-water 
 Required 
 per I.H.P. 
 
 cent. 
 
 H.P. 
 Cyl., lb. 
 
 I. Cyl., 
 lbs. 
 
 L.P.Cyl., 
 lbs. 
 
 H.P. Cyl., 
 lbs. 
 
 I. Cyl., 
 
 lbs. 
 
 L.P.Cyl., 
 lbs. 
 
 per Hour, 
 lbs. 
 
 -:■! 
 
 40 j 
 
 120 
 140 
 160 
 
 120 
 140 
 160 
 
 120 
 140 
 160 
 
 37.8 
 43.8 
 49.3 
 
 38.8 
 45.8 
 51.3 
 
 39.8 
 46.8 
 52.8 
 
 1.3 
 2.8 
 3.8 
 
 2.8 
 3.9 
 5.3 
 
 3.7 
 4.8 
 6.3 
 
 38.5 
 46.5 
 55.0 
 
 51.5 
 59.5 
 70.0 
 
 60.5 
 70.5 
 82.5 
 
 17.1 
 18.6 
 20.0 
 
 22.8 
 23.7 
 25.5 
 
 26.7 
 28.0 
 30.0 
 
 6.5 
 7.1 
 8.0 
 
 8.6 
 9.1 
 10.0 
 
 10.1 
 10.8 
 11.8 
 
 12.05 
 11.4 
 10.75 
 
 11.65 
 11.4 
 10.85 
 
 12.2 
 11.6 
 11.15 
 
 Sizes and Calculated Performances of Vertical High-speed 
 Engines^ — The 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. 
 
960 
 
 THE STEAM-ENGINE. 
 
 
 
 
 Simple Engines — 
 
 - Non-condensing. 
 
 
 
 
 
 05 
 
 
 H.P. when 
 
 H.P. when 
 
 H.P. when 
 
 Dimen- 
 sions of 
 
 Wheels. 
 
 dia. face 
 
 
 
 uli 
 
 a 
 
 u 
 
 cutting off 
 
 cutting off 
 
 cutting off 
 
 a, 
 
 
 *°'Z' 
 
 O 
 
 
 at 1/5 stroke. 
 
 at 1/4 stroke. 
 
 at 1/3 stroke 
 
 a 
 S 
 
 «3 02 
 
 3 . 
 
 tj. 
 
 70 
 
 80 
 
 90 
 
 70 
 
 80 
 
 90 
 
 70 
 
 80 
 
 90 
 
 Ft. 
 
 
 "* * 
 
 Q' J 
 
 W 
 
 "370 
 
 lbs. 
 
 "~20 
 
 lbs. 
 "~25 
 
 lbs. 
 
 ~lso 
 
 lbs. 
 ~~ 26 
 
 lbs. 
 
 lbs. 
 ~~36 
 
 lbs. 
 
 ~32 
 
 lbs. 
 ~~37 
 
 lbs. 
 
 ~~ 43 
 
 In. 
 
 ~2V^ 
 
 pqa 
 
 71/9 
 
 10 
 
 4 
 
 3 
 
 »V? 
 
 12 
 
 318 
 
 27 
 
 32 
 
 39 
 
 34 
 
 41 
 
 47 
 
 41 
 
 48 
 
 56 
 
 41/o 
 
 5 
 
 23/ \ 
 
 31/2 
 
 10 V?, 
 
 14 
 
 277 
 
 41 
 
 49 
 
 60 
 
 52 
 
 62 
 
 71 
 
 63 
 
 74 
 
 85 
 
 5'9" 
 
 6 l/o 
 
 31/o 
 
 4 
 
 12 
 
 16 
 
 245 
 
 53 
 
 64 
 
 11 
 
 67 
 
 81 
 
 93 
 
 82 
 
 96 
 
 111 
 
 6' 8" 
 
 9 
 
 4 
 
 41/9 
 
 131/, 
 
 18 
 
 222 
 
 66 
 
 80 
 
 96 
 
 84 
 
 100 
 
 116 
 
 102 
 
 120 
 
 138 
 
 71/9 
 
 !1 
 
 4 
 
 5'" 
 
 16 
 
 20 
 
 181 
 
 95 
 
 115 
 
 138 
 
 120 
 
 144 
 
 166 
 
 146 
 
 177 
 
 198 
 
 8'4" 
 
 15 
 
 41/9 
 
 6 
 
 18 
 
 24 
 
 b8 
 
 119 
 
 144 
 
 173 
 
 151 
 
 181 
 
 208 
 
 183 
 
 215 
 
 748 
 
 10 
 
 19 
 
 5 " 
 
 7 
 
 22 
 
 28 
 
 138 
 
 179 
 
 216 
 
 261 
 
 227 
 
 272 
 
 313 
 
 276 
 
 324 
 
 373 
 
 1 1'8" 
 
 28 
 
 6 
 
 8 
 
 24l/ ? , 
 
 32 
 
 120 
 
 221 
 
 267 
 
 322 
 
 281 
 
 336 
 
 386 
 
 340 
 
 400 
 
 460 
 
 13' 4" 
 
 34 
 
 7 
 
 9 
 
 27 
 
 34 
 
 112 
 
 269 
 
 ^25 
 
 392 
 
 342 
 
 409 
 
 470 
 
 414 
 
 487 
 
 560 
 
 14' 2" 
 
 41 
 
 8 
 
 10 
 
 M.E.P., lbs 
 
 
 24 
 
 29 
 
 35 
 
 30.5 
 
 36.5 
 
 42 
 
 37 
 
 43.5 
 
 50 
 
 Note. — Th ? 
 
 
 
 
 
 nominal-power 
 
 
 ess. 
 
 
 
 
 rating of the en- 
 
 Term'l pr 
 
 
 
 
 
 
 
 
 
 
 gines is at 80 lbs. 
 
 (about), It 
 
 s. . 
 
 17.9 
 
 20 
 
 22.3 
 
 22.4 
 
 25 
 
 27.6 
 
 29.8 
 
 ii.i 
 
 36.8 
 
 gauge Dressure, 
 
 Cyl. cond'n 
 
 % 
 
 26 
 
 26 
 
 26 
 
 24 
 
 24 
 
 24 
 
 21 
 
 21 
 
 21 
 
 steam cut-off at 
 
 Steam perl, 
 hour, lbs. . 
 
 H.P. 
 
 
 
 
 
 
 
 
 
 
 1/4 stroke. 
 
 
 32.9 
 
 30 
 
 27.4 
 
 31.2 
 
 29.0 27.9 
 
 32 
 
 31.4 
 
 30 
 
 
 Compound Engines 
 
 — Non-condensing - 
 
 -High- 
 
 pressure Cylinder 
 
 and Receiver Jacketed. 
 
 
 
 
 H.P., cutting off 
 
 H.P., cutting off 
 
 H.P., cutting off 
 
 Diam. 
 Cylinder, 
 
 
 5 
 
 at 1/4 Stroke 
 
 at 1/3 Stroke 
 
 at 1/2 Stroke 
 
 
 a 
 
 a 
 
 
 in h.p. Cylinder. 
 
 in h.p. Cylinder. 
 
 in h.p. Cylinder. 
 
 inches. 
 
 Cyls. 
 
 Cyls. 
 
 Cyls. 
 
 Cyls. 
 
 Cyls. 
 
 Cyls. 
 
 
 
 
 
 31/3: 1. 
 
 41/2: 1. 
 
 31/3: 1- 
 
 41/2: 1. 
 
 31/3: 1. 
 
 41/2: 1. 
 
 h 
 
 P4 
 
 P4 
 
 80 
 
 90 
 
 130 
 
 150 
 
 80 
 
 90 
 
 130 
 
 150 
 
 80 
 
 90 
 
 130 
 
 150 
 
 H 
 
 W 
 
 A 
 
 J2 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 53/4 
 
 61/9 
 
 U 
 
 10 
 
 370 
 
 7 
 
 15 
 
 19 
 
 32 
 
 23 
 
 31 
 
 35 
 
 46 
 
 44 
 
 55 
 
 64 
 
 79 
 
 63/ 8 
 
 71/9 
 
 131/9 
 
 17. 
 
 318 
 
 9 
 
 19 
 
 24 
 
 40 
 
 29 
 
 39 
 
 45 
 
 59 
 
 % 
 
 70 
 
 81 
 
 101 
 
 ;a/ 4 
 
 9 
 
 16 1/9 
 
 14 
 
 7,77 
 
 14 
 
 28 
 
 36 
 
 60 
 
 43 
 
 58 
 
 67 
 
 87 
 
 83 
 
 104 
 
 121 
 
 159 
 
 9 
 
 IOI/9 
 
 19 
 
 16 
 
 7,46 
 
 18 
 
 37 
 
 47 
 
 78 
 
 57 
 
 76 
 
 87 
 
 114 
 
 109 
 
 136 
 
 158 
 
 196 
 
 101/9, 
 
 12 
 
 221/9 
 
 18 
 
 777 
 
 26 
 
 53 
 
 68 
 
 112 
 
 81 
 
 109 
 
 175 
 
 164 
 
 156 
 
 195 
 
 226 
 
 281 
 
 12 
 
 131/, 
 
 7.5 
 
 70 
 
 185 
 
 32 
 
 65 
 
 84 
 
 139 
 
 100 
 
 135 
 
 154 
 
 202 
 
 192 
 
 241 
 
 279 
 
 34« 
 
 131/9, 
 
 151/9 
 
 281/9 
 
 24 
 
 158 
 
 43 
 
 88 
 
 112 
 
 186 
 
 135 
 
 181 
 
 706 
 
 271 
 
 258 
 
 323 
 
 374 
 
 464 
 
 16 
 
 181/9 
 
 331/9 
 
 28 
 
 138 
 
 57 
 
 118 
 
 151 
 
 7.49 
 
 180 
 
 242 
 
 277 
 
 363 
 
 346 
 
 433 
 
 502 
 
 623 
 
 18 
 
 201/9 
 
 38 
 
 32 
 
 170 
 
 74 
 
 152 
 
 194 
 
 321 
 
 7.32 
 
 312 
 
 357 
 
 468 
 
 446 
 
 558 
 
 647 
 
 803. 
 
 20 
 
 221/9 
 
 43 
 
 34 
 
 117 
 
 94 
 
 194 
 
 249 
 
 417. 
 
 297 
 
 400 
 
 457 
 
 601 
 
 572 
 
 715 
 
 829 
 
 103C 
 
 241/9, 
 
 281/9 
 
 52 
 
 42 
 
 93 
 
 138 
 
 285 
 
 365 
 
 603 
 
 436 
 
 587 
 
 670 
 
 880 
 
 838 
 
 1048 
 
 1215 
 
 150« 
 
 281/ 2 
 
 33 
 
 60 
 
 48 
 
 80 
 
 180 
 
 374 
 
 477 
 
 789 
 
 570 
 
 767 
 
 877 
 
 1151 
 
 1096 
 
 1370 
 
 1589 
 
 1973 
 
 Mean eff. pressure, lbs.. 
 
 3.3 
 
 6.8 
 
 8.7 
 
 14.4 
 
 10.4 
 
 14.0 
 
 16 
 
 21 
 
 20 
 
 25 
 
 29 
 
 36 
 
 Ratio of expansion 
 
 131/2 
 
 181/4 
 
 IOI/4 
 
 133/ 4 
 
 63/ 4 
 
 91/4 
 
 Cyl. condensation, %.. 
 
 14 
 
 14 
 
 16 
 
 16 
 
 12 
 
 12 
 
 13 
 
 13 
 
 10 
 
 10 
 
 11 
 
 11 
 
 Ter. pres. (abt.), lbs. . . 
 
 7.3 
 
 7.7 
 
 7.9 
 
 9 
 
 9,2 
 
 10,4 
 
 10 5 
 
 12 
 
 14 
 
 15 5 
 
 14 6 
 
 17, fi 
 
 Loss from expanding 
 
 
 
 
 
 
 
 
 
 
 
 
 
 below atmosphere, % 
 
 34 
 
 15 
 
 17 
 
 3 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 St.perl.H.P.hour.lbs. 55 
 
 42 
 
 47 
 
 29 
 
 33.3 
 
 77.7 
 
 28.7 
 
 25.4 
 
 30 
 
 26.2 
 
 21 
 
 20 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 961 
 
 
 Compound Engines - 
 
 - Condensing — 
 
 Steam-jacketed 
 
 
 
 
 
 H.P. when 
 
 H.P. when 
 
 H.P. when 
 
 
 
 
 cutting off at 
 
 cutting off at 
 
 cutting off at 
 
 Diam 
 
 
 u 
 
 1/4 Stroke 
 
 1/3 Stroke 
 
 1/2 Stroke 
 
 Cylinder, 
 inches. 
 
 s 
 
 a 
 
 in h. p. Cylinder. 
 
 in h.p. Cylinder. 
 
 in h.p. Cylinder. 
 
 
 
 
 
 
 
 c 
 
 
 Ratio, 
 
 Ratio, 
 
 Ratio, 
 
 Ratio, 
 
 Ratio, 
 
 Ratio, 
 
 
 J* 
 
 s 
 
 33 
 
 US 
 
 31/3: 1. 
 
 4: 1. 
 
 31/3: 1. 
 
 4: 1. 
 
 31/3: 1. 
 
 4: I. 
 
 pi 
 
 Pi 
 
 Pi 
 
 80 
 
 110 
 
 115 
 
 125 
 
 80 
 
 110 
 
 115 
 
 125 
 
 80 
 
 110 
 
 115 
 
 125 
 
 W 
 
 W 
 
 J 
 
 m 
 
 rt 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 6 
 
 61/9 
 
 12 
 
 10 
 
 370 
 
 44 
 
 59 
 
 53 
 
 62 
 
 55 
 
 70 
 
 68 
 
 75 
 
 70 
 
 97 
 
 95 
 
 106 
 
 ftV? 
 
 71/o 
 
 131/9 
 
 12 
 
 318 
 
 56 
 
 76 
 
 67 
 
 78 
 
 70 
 
 90 
 
 87 
 
 95 
 
 90 
 
 123 
 
 120 
 
 134 
 
 8Vl 
 
 9 
 
 161/o 
 
 14 
 
 27^ 
 
 83 
 
 112 
 
 100 
 
 116 
 
 104 
 
 133 
 
 129 
 
 141 
 
 133 
 
 183 
 
 179 
 
 200 
 
 9V"> 
 
 101/9 
 
 19 
 
 16 
 
 246 
 
 109 
 
 147 
 
 131 
 
 152 
 
 136 
 
 174 
 
 169 
 
 185 
 
 174 
 
 239 
 
 234 
 
 261 
 
 II 
 
 12 
 
 221/9 
 
 18 
 
 222 
 
 156 
 
 210 
 
 187 
 
 218 
 
 195 
 
 250 
 
 242 
 
 265 
 
 250 
 
 343 
 
 335 
 
 374 
 
 l?V? 
 
 131/-> 
 
 25 
 
 20 
 
 18!) 
 
 192 
 
 260 
 
 231 
 
 26^ 
 
 241 
 
 308 
 
 298 
 
 Ml 
 
 308 
 
 423 
 
 414 
 
 462 
 
 14 
 
 151/-, 
 
 281/o 
 
 24 
 
 158 
 
 7.58 
 
 348 
 
 310 
 
 361 
 
 .323 
 
 413 
 
 400 
 
 439 
 
 413 
 
 568 
 
 555 
 
 619 
 
 17 
 
 18l/o 
 
 331/o 
 
 28 
 
 138 
 
 346 
 
 467 
 
 415 
 
 484 
 
 433 
 
 554 
 
 536 
 
 588 
 
 554 
 
 761 
 
 744 
 
 830 
 
 19 
 
 201/o 
 
 38 
 
 32 
 
 120 
 
 446 
 
 602 
 
 535 
 
 624 
 
 558 
 
 714 
 
 691 
 
 758 
 
 714 
 
 981 
 
 959 
 
 1070 
 
 21 
 
 22l/o 
 
 43 
 
 34 
 
 112 
 
 572 
 
 772 
 
 686 
 
 801 
 
 715 
 
 915 
 
 887 
 
 972 
 
 915 
 
 1258 
 
 1230 
 
 1373 
 
 26 
 
 281/o 
 
 52 
 
 42 
 
 93 
 
 838 
 
 1131 
 
 1006 
 
 1174 
 
 1048 
 
 1341 
 
 1299 
 
 1425 
 
 1341 
 
 1844 
 
 1801 
 
 2012 
 
 30 
 
 33 
 
 60 
 
 48 
 
 80 
 
 1096 
 
 1480 
 
 1316 
 
 1534 
 
 1370 
 
 1757 
 
 1699 
 
 1863 
 
 1757 
 
 2411 
 
 2356 
 
 2632 
 
 Mean eff. press., lbs 
 
 %... 
 
 20 
 
 27 
 
 24 
 
 28 
 
 25 
 
 32 
 
 31 
 
 34 
 
 32 
 
 44 
 
 43 
 
 48 
 
 Ratio of expansion 
 
 131/2 
 
 I6I/4 
 
 10 
 
 121/4 
 
 63/4 
 
 81/ 4 
 
 
 18 | 18 
 
 20 1 20 
 
 15 1 15 
 
 18 1 18 
 
 12 1 12 
 
 14 1 14 
 
 St. per I.H.P. hour 
 
 lbs. 17. 3| 16.6 
 
 16.6|15.2 
 
 17.0|16.4 
 
 16.3|15.8 
 
 17.5|17.0 
 
 16.8|16.0 
 
 Triple-expansion Engines, 
 
 Non-condensing — Receiver 
 
 only 
 
 
 Jacketed 
 
 
 
 
 
 
 u 
 
 Horse-power 
 
 Horse-power 
 
 Horse 
 
 -power 
 
 Diameter 
 
 if) 
 
 a 
 
 when cutting 
 
 when cutting 
 
 when 
 
 jutting 
 
 Cylinders, 
 
 A 
 
 a 
 
 off at 42% of 
 
 off at 50% of 
 
 off at 67% of 
 
 inches. 
 
 
 Stroke in First 
 
 Stroke in First 
 
 Stroke 
 
 in First 
 
 
 p 
 10 
 
 ■43 © 
 
 n 
 
 Cylinder. 
 
 Cylinder. 
 
 Cylinder. 
 
 H.P. 
 
 LP. 
 
 L.P. 
 
 180 lbs. 
 
 200 lbs. 
 
 180 lbs. 
 
 200 lbs. 
 
 180 lbs. 
 
 200 lbs. 
 
 43/4 
 
 71/9 
 
 12 
 
 370 
 
 55 
 
 64 
 
 70 
 
 84 
 
 95 
 
 108 
 
 51/2 
 
 81/9 
 
 131/9 
 
 12 
 
 318 
 
 70 
 
 81 
 
 90 
 
 106 
 
 120 
 
 137 
 
 6 1/2 
 
 IOI/9 
 
 16 1/9 
 
 14 
 
 277 
 
 104 
 
 121 
 
 133 
 
 158 
 
 179 
 
 204 
 
 71/2 
 
 12 
 
 19 
 
 16 
 
 246 
 
 136 
 
 158 
 
 174 
 
 207 
 
 234 
 
 267 
 
 9 
 
 141/9 
 
 221/9 
 
 18 
 
 222 
 
 195 
 
 226 
 
 250 
 
 296 
 
 335 
 
 382 
 
 10 
 
 16 
 
 25 
 
 70 
 
 185 
 
 241 
 
 279 
 
 308 
 
 366 
 
 414 
 
 471 
 
 1U/? 
 
 18 
 
 281/ ?1 
 
 24 
 
 158 
 
 323 
 
 374 
 
 413 
 
 490 
 
 555 
 
 632 
 
 13 
 
 22 
 
 331/9 
 
 28 
 
 138 
 
 433 
 
 502 
 
 554 
 
 657 
 
 744 
 
 848 
 
 15 
 
 241/9 
 
 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., lbs 
 
 25 
 
 29 
 
 32 
 
 38 
 
 43 
 
 49 
 
 No. of expansions. 
 Cyl. condensation, 
 
 
 16 
 
 14 
 
 13 
 12 
 
 1 
 1 
 
 
 
 %.... 
 
 
 
 Steam p. I.H.P.p.hr., lbs. 
 
 20.76 1 19.36 
 
 19.25 1 17.00 
 
 17.89 
 
 17.20 
 
 Lbs. coal at 81b. evap., lbs. 
 
 2.59 1 2.39 
 
 2.40 | 2.12 
 
 2.23 
 
 2.15 
 
962 
 
 THE STEAM-ENGINE. 
 
 
 Triple-expansion Engines — 
 
 Condensing - 
 
 — Steam-ja 
 
 cket 
 
 ed. 
 
 
 
 
 u 
 
 Horse- 
 
 Horse- 
 
 Horse- 
 
 Horse- 
 
 Diameter 
 
 a> 
 
 a 
 
 power when 
 
 power when 
 
 power when 
 
 power when 
 
 Cylinders, 
 
 .d 
 
 a 
 
 cutting off 
 
 cutting off 
 
 cutting off 
 
 cutting off 
 
 inches. 
 
 G 
 
 c rp 
 
 at 1/4 Stroke 
 
 at 1/3 Stroke 
 
 at 1/2 Stroke 
 
 at 3/4 Stroke 
 
 
 2 
 
 3 3 
 
 "o.S 
 
 in First Cyl. 
 
 in First Cyl. 
 
 in First Cyl. 
 
 in First Cyl. 
 
 pi 
 
 Ph 
 
 P* 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 120 
 
 140 
 
 160 
 
 w 
 
 
 Hi 
 
 03 
 
 « 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 Lbs. 
 
 lbs. 
 
 lbs. 
 
 43/4 
 
 71/9 
 
 12 
 
 10 
 
 370 
 
 35 
 
 42 
 
 48 
 
 44 
 
 53 
 
 59 
 
 57 
 
 72 
 
 84 
 
 81 
 
 97 
 
 110 
 
 51/9 
 
 81/9 
 
 131/9 
 
 12 
 
 318 
 
 45 
 
 53 
 
 62 
 
 56 
 
 67 
 
 76 
 
 73 
 
 92 
 
 107 
 
 104 
 
 123 
 
 140 
 
 6 V? 
 
 J 01/9 
 
 161/9 
 
 14 
 
 277 
 
 67 
 
 79 
 
 92 
 
 83 
 
 100 
 
 112 
 
 108 
 
 137 
 
 159 
 
 154 
 
 183 
 
 208 
 
 71/9 
 
 12 
 
 19 
 
 16 
 
 246 
 
 87 
 
 103 
 
 120 
 
 109 
 
 131 
 
 147 
 
 141 
 
 ItO 
 
 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 
 
 231 
 
 260 
 
 250 
 
 317 
 
 368 
 
 356 
 
 423 
 
 481 
 
 mi-* 
 
 18 
 
 281/9 
 
 24 
 
 158 
 
 206 
 
 245 
 
 284 
 
 258 
 
 310 
 
 348 
 
 335 
 
 426 
 
 494 
 
 477 
 
 D68 
 
 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 
 
 17 
 
 27 
 
 43 
 
 34 
 
 112 
 
 458 
 
 543 
 
 629 
 
 572 
 
 686 
 
 772 
 
 744 
 
 944 
 
 1095 
 
 1058 
 
 1258 
 
 1430 
 
 20 
 
 33 
 
 52 
 
 42 
 
 93 
 
 670 
 
 796 
 
 922 
 
 838 
 
 1006 
 
 1131 
 
 1089 
 
 1383 
 
 1605 
 
 1551 
 
 1844 
 
 2096 
 
 23l/ 2 
 
 38 
 
 60 
 
 48 
 
 80 
 
 877 
 
 1041 
 
 1206 
 
 1096 
 
 1316 
 
 1480 
 
 1424 
 
 1808 
 
 2099 
 
 2028 
 
 2411 
 
 2740 
 
 Mean eff. press., lbs 
 
 16 
 
 19 
 
 22 
 
 20 
 
 24 
 
 27 
 
 26 
 
 33 
 
 38.3 
 
 37 
 
 44 
 
 50 
 
 
 
 
 
 
 
 
 
 Cyl. condensation, % . . • 
 
 19 
 
 19 
 
 19 
 
 16 
 
 16 
 
 16 
 
 12 
 
 12 
 
 12 
 
 8 
 
 8 1 8 
 
 St. p. I.H.P.p. hr., lbs- 
 Coal at 8 lbs. evap., lbs- 
 
 14 1 
 
 13 9 
 
 15 i 
 
 14 3 
 
 1* 9 
 
 13 2 
 
 14 3 
 
 13.6 
 
 13 
 
 15.7 14.9114.7 
 
 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 + 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 lbs. and the total feed 6314 lbs. 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 = I 
 
 Condens. and leakage, % = p. . 
 c = IX P -*■ (100 - p) = 
 
 5 
 60 
 
 7.5 
 
 10 
 43 
 7.5 
 
 15 20 25 30 35 42 
 35 29 24 20 17 15 
 
 .8 8.2 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 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 963 
 
 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 are 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, 1S92.) — 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 1 1/2 lbs. 
 of coal per I.H.P. for a condensing engine, and 13/4 lbs. for a non-conden- 
 sing engine, corresponding to about 13/4 lbs. to 2Vs lbs. 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 lbs. per effective H.P. hour, in the ordinary daily working of the station 
 used 7 1/2 lbs. in 1886, which was reduced to 4.3 lbs. in 1890 and 3.8 lbs. in 
 1891 . . Probably in very few cases were the engines at electric-light stations 
 working under a consumption of 41/2 lbs. 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-power trials this was 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 . 79 . 74 . 63 . 48 
 
 Non-condensing, mechanical efficiency. . 86 0.83 0.78 0.67 0.52 
 
 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 lbs. per hour in a 5-horse-power engine to 22 
 lbs. in a 134-H.P. Harris-Corliss engine. In non-condensing compound 
 engines, the only type tested was the Willans, which ranged from 27 lbs. 
 in a 10-H.P. slow-speed engine, 122 ft. per minute, with steam-pressure 
 of 84 lbs., to 19.2 lbs. in a 40-H.P. engine, 401 ft. per minute, with steam- 
 pressure 165 lbs. A Willans triple-expansion non-condensing engine, 
 39 H.F., 172 lbs. pressure, and 400 ft. piston speed per minute, gave a 
 consumption of 18.5 lbs. In condensing engines, nine tests of simple 
 engines gave results ranging only from 18.4 to 22 lbs. In compound- 
 condensing engines over 100 H.P., in 13 tests the range is from 13.9 to 
 20 lbs. In three triple-expansion engines the figures are 11.7, 12.2, and 
 12.45 lbs., 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 consumption of 21.2 and 21.7 lbs.; and the Meteor and Tartar 
 triple-expansion engines gave 15.0 and 19.8 lbs. 
 
 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: 
 
 l bs. Per I.H.P. hour . Per Effective H.P. h r. 
 Kind of Engine. ^ ^®w," C^I, Steam,' 
 
 Non-condensing 1.80 16.5 2.00 18.0 
 
 Condensing 1.50 13.5 1.75 15.8 
 
964 
 
 THE STEAM-ENGINE. 
 
 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, _ 
 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, lbs. 
 
 i Magazine, 1894. Small engines 
 
 2.96 7.37 8.2 
 
 23.64 19.08 20.08 
 
 36.0 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. 
 neering, June 27, 1890. 
 
 Engi- 
 
 Rated 
 H.P. 
 
 Com- 
 pound or 
 Simple. 
 
 Diam. of 
 Cylinders. 
 
 Stroke, 
 ins. 
 
 Max. 
 Steam- 
 pressure. 
 
 Per Brake H.P. 
 
 per hour. 
 
 u ~ • 
 
 h.p. 
 
 l.p. 
 
 Coal. 
 
 Water. 
 
 
 5 
 
 3 
 2 
 
 simple 
 
 compound 
 
 simple 
 
 7 
 3 
 
 41/2 
 
 "6" 
 
 10 
 6 
 
 71/2 
 
 75 
 110 
 75 
 
 12.12 
 4.8-> 
 11.77 
 
 78.1 lbs. 
 42.03 " 
 89.9 " 
 
 6.11b. 
 8.72" 
 7.64" 
 
 24 
 
 32 
 
 40 
 
 48 
 
 56 
 
 72 
 
 88 
 
 9.3 
 
 29 
 
 28.7 
 
 28.5 
 
 28.3 
 
 28 
 
 27.7 
 
 29 
 
 28.4 
 
 28 
 
 27.5 
 
 27.1 
 
 26.3 
 
 25.6 
 
 32 
 
 30.8 
 
 29.8 
 
 29.2 
 
 28.8 
 
 28.7 
 
 
 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.. 8 12 16 20 
 
 1/8 cut-off, lbs. . . 39 35 32 30 
 
 l/ 4 cut-off, lbs... 39 34 31 29.5 
 
 1/2 cut-off, lbs. . . 39 36 34 33 
 
 Steam-consumption of same engine ; fixed speed, 60 revs, per minute. 
 Varying cut-off compared with throttling-engine for same horse-power 
 and boiler-pressures: 
 Cut-off, fraction 
 
 of stroke 0.1 
 
 Steam, 90 lbs... 29 
 Steam, 60 lbs.. . 39 
 
 0.15 0.2 0.25 0.3 0.4 
 27.5 27 27 27.2 27.8 
 34.2 32.2 31.5 31.4 31.6 
 
 0.5 0.6 0.7 0.8 
 
 28.5 . 
 
 32.2 34.1 36.5 39 
 
 Throttling-engine, 7/ 8 cut-off, for corresponding horse-powers. 
 
 Steam, 90 lbs. . . 42 37 33.8 31.5 29.8 
 
 Steam, 60 lbs 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, Vs. and 1/4 cut-off at 90 lbs. pressure. The loss in economy for 
 about 1/4 cut-off is at the rate of 1/12 lb. 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/g lb. of water below 26 revolutions. Also, at all speeds the 1/4 
 cut-off is more economical than either the 1/2 or Vs cut-off. 
 
 2. At 90 lbs. boiler-pressure and above 1/3 cut-off, to 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 lbs. boiler-pressure, to obtain, by 
 throttling, the same mean effective pressure at 7/ 8 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.) — The tests were made by Dexter Brackett for the Board 
 of Fire Commissioners. Boston. Mass. 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 965 
 
 No. of 
 engine. 
 
 60 
 « . 
 
 PQ 
 
 8°* 
 
 Water evap. 
 per lb. coal, 
 from and at 
 212°. 
 
 II 
 
 
 
 v 
 
 1 
 
 101.0 
 
 lbs. 
 191.0 
 184.0 
 191.0 
 141.6 
 138.4 
 163.7 
 103.3 
 181.6 
 117.3 
 MIA 
 142.5 
 91.1 
 151.4 
 148.4 
 
 lbs. 
 2.26 
 
 lbs. 
 90.2 
 92.3 
 78.4 
 75.7 
 71.5 
 
 102.7 
 72.1 
 92.7 
 68.8 
 
 101.3 
 76.5 
 59.0 
 87.8 
 74.7 
 
 lbs. 
 
 143.2 
 
 124.0 
 
 123.3 
 
 113.8 
 
 136.4 
 
 121.2 
 
 119.6 
 
 143.0 
 
 119.2 
 
 112.8 
 
 111.5 
 
 102.1 
 
 126.8 
 
 128.1 
 
 7,619,800 
 9,632,700 
 5,900,000 
 5,882,000 
 8,112,900 
 8,736,300 
 
 14,026,000 
 9,678,400 
 
 10,201,600 
 7,758,300 
 7,187,400 
 6,482,100 
 7,993,400 
 7,265,000 
 
 galls. 
 549 
 
 1 
 
 499 
 
 2 
 
 3 
 
 4 
 
 85.0 
 74.0 
 86.5 
 86.0 
 
 2.66 
 3.57 
 
 2.88 
 
 535 
 
 482 
 459 
 
 5 
 
 449 
 
 5 
 
 5.87 
 3.45 
 4.94 
 3.51 
 4.49 
 4.22 
 4.10 
 3.76 
 
 545 
 
 6 
 
 7 
 
 86.0 
 112.0 
 140.5 
 174.0 
 225.0 
 
 536 
 596 
 
 8 
 
 910 
 
 9 
 
 482 
 
 10 
 
 419 
 
 10 
 
 564 
 
 11 
 
 229.0 
 
 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.) — Some 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, permin 
 
 1 
 
 15 X H 
 
 15,216 
 
 240 
 
 lflat 
 
 100 
 
 37.2,t 36.2* 
 
 60.2, 58.4 
 
 2 
 16X15 
 20,000 
 
 240 
 
 1 flat 
 
 2-50 
 
 36.7.f 35.8 
 
 61.0 59.7 
 
 3 
 14X12 
 28,644 
 
 300 
 
 1 flat 
 
 2-40 
 
 31. 7, t 32.0 
 
 57.1, 57.4 
 
 4 
 
 16X 14 
 
 719 
 
 270 
 
 4 flat 
 
 Generator, K.W 
 
 Steam per I .H .P .-hr. 
 Steam per K.W.-hr . . 
 
 125 
 37.5,* 36.7 
 54.9, 54.7 
 
 No. of Test. 
 
 Size of engine, ins 
 
 Hours in service 
 
 5 
 
 18 X 18 
 
 32,000 
 
 220 
 
 1 piston 
 
 150 
 
 39.8,f34.7,* 29.5J 
 
 61.8, 51.8, 43.4 
 
 6 
 
 15 X 16 
 5,600 
 250 
 
 1 piston 
 
 100 
 
 36.3,* 33.6 
 
 55.2, 49.4 
 
 7 
 
 12X 18 
 
 10,800 
 
 190 
 
 
 f 2 flat inlet 
 ) 2 Corliss exh. 
 
 75 
 44.0, f 36.7, 34.1 § 
 79.3, 60.5, 53.7 
 
 Generator, K.W 
 
 Steam per I .H . P.-hr . . . 
 Steam per K.W.-hr 
 
 * 3/ 4 load ; f 1/2 load ; t 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 
 
966 THE STEAM-ENGINE. 
 
 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 
 flat valve engine, No. 3, surpassed No. 5 in economy. The flat valve 
 engines give a flatter load cu.ve than the piston valve engines. Compar- 
 ing the lesults of the flat valve engines, the most economical results v. ere 
 obtained from engine No. 3, which had a valve which automatically takes 
 up wear, and if it does not cut, must maintain itself tigiit 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 lbs. per I.H.P. per hour. 1 o "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 lbs. at full load, 
 61.8 and 63.9 I.H.P., and 28.87 and 29.54 lbs. 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 221/2 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., ha.s 
 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 01 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 the amount of waste r-oom 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, 
 8% 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: 
 
 I.H.P. 50 100 200 500 
 
 Revs, per min . 
 
 600-700 550-600 500 350-375. 
 Piston speed, ft. per min. 
 
 600 650 675 750 
 
 Rapid strides have been made during the last few years, despite the 
 
 750 1000 
 
 1500 
 
 2000 
 
 325 250 
 
 200 
 
 160-18(1 
 
 775 800 
 
 900 
 
 1000 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 967 
 
 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 lbs., vacuum 26 ins., superheat 100° F., 
 gave results as shown below, [figures taken from curves in the original]. 
 
 Fraction of full 
 
 load 
 
 Lbs. steam per 
 
 I.H.P. hour.. 12.7 11.85 11.4 11.1 
 Lbs. steam per 
 
 B.H.P. hour.. 16.0 14.8 13.7 12.9 
 
 0.2 0.3 0.4 0.5 0.6 0.7 
 
 10.9 10.8 10.75 10.75 10.8 11.0 
 12.4 12.05 11.85 11.8 11.8 11.8 
 
 Owing to the forced 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 0° 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 theo- 
 retical advantage due to the use of low back pressures or high vacua is 
 shown by the following table, in which the efficiencies are those of the 
 Carnot cycle, E = (Ti - T 2 ) + Ti. With 100 lbs. absolute initial 
 pressure the efficiency is increased from 0.270 to 0.353, or 30.7%, by rais- 
 ing the vacuum from 27.02 to 29.56 ins. of mercury, and with 200 lbs. it 
 is increased from 0.317 to 0.394, or 24.3%, with the same change in 
 the vacuum. 
 
 Abs. Initial Pressure. 
 
 100 
 
 125 
 
 150 
 
 175 
 
 200 
 
 225 
 
 250 
 
 275 
 
 300 
 
 Temp. 
 
 d F- 
 
 Vacuum, 
 
 In. of 
 Mercury. 
 
 Lbs. per 
 Sq. In. 
 
 Carnot Efficiencies. 
 
 115 
 
 27.02 
 
 1.47 
 
 7.70 
 
 285 
 
 298 
 
 308 
 
 317 
 
 325 
 
 332 
 
 339 
 
 345 
 
 108 
 
 27.48 
 
 1.20 
 
 279 
 
 293 
 
 306 
 
 316 
 
 325 
 
 333 
 
 341 
 
 .347 
 
 353 
 
 100 
 
 28.00 
 
 0.95 
 
 289 
 
 .303 
 
 .316 
 
 325 
 
 335 
 
 .343 
 
 350 
 
 .356 
 
 .362 
 
 90 
 
 28.50 
 
 0.70 
 
 302 
 
 .316 
 
 328 
 
 .338 
 
 .347 
 
 .355 
 
 .361 
 
 .368 
 
 .373 
 
 70 
 
 29.18 
 
 0.74 
 
 37.7 
 
 341 
 
 353 
 
 362 
 
 371 
 
 378 
 
 38'? 
 
 391 
 
 .396 
 
 50 
 
 29.56 
 
 0.36 
 
 0.353 
 
 .366 
 
 .377 
 
 .386 
 
 .394 
 
 .402 
 
 .408 
 
 .414 
 
 .419 
 
 The same table shows the advantage of high initial pressure. Thus 
 with a vacuum 27.02 ins. the efficiency is increased from 0.270 to 0.317, 
 or 17.4%, by raising the initial absolute-pressure from 100 to 200 lbs., and 
 with a vacuum of 28.5 ins. the efficiency is increased from 0.302 to 0.347, 
 or 14.9%, by the same rise of pressure. In practice the efficiencies given 
 in the table for the given pressures and temperatures cannot be reached 
 on account of imperfections of the steam-engine, and the fact that the 
 engine does not work on the ideal Carnot cycle. The relative advantages, 
 however, are probably proportional to those indicated by the table, pro- 
 vided the expansion is divided into two or more stages at pressures above 
 
968 THE STEAM-ENGINE. 
 
 100 lbs. The possibility of obtaining very high vacua is limited by he 
 temperature of the condensing 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. 
 
 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 ta 
 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 30V8 X 30 ins. The 
 steam used per I.H.P. hour was: single 20.35 lbs., compound 13.73 lbs. 
 
 Both of the engines are steam-jacketed, practically on the barrels only, 
 with steam at full boiler-pressure, viz., single 106.3 lbs., compound 127.5 lbs. 
 
 The steam-pressure in the case of the compound engine is 127 lbs., or 
 21 lbs. 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 lbs. 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 13/32 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 lbs. 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 lbs., average 12.91. All three cylinders used, two tests 12.67 
 and 12.90 lbs., 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 
 lbs. 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, Trans. A. S. M. E., 
 1903.) — A Rice & Sargent engine, 20 and 40 X 42 ins., was tested with 
 steam about 149 lbs., vacuum 27.3 to 28.8 ins. or 0.82 to 1.16 lbs. abso- 
 lute, r.p.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- 
 erated 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 piston-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, 14 1/2 and 243/ 4 by 271/2 in., 
 gave results as follows: 
 
 Saturated steam, 170 lbs., vacuum 26 in., I.H.P. 366, steam per I.H.P. 
 per hour 12.3 lbs. Steam 170 lbs. superheated 150° F., vac. 26 in., I.H.P. 
 366, steam per I.H.P. per hour, 10.4 lbs. Revs, per 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. 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 969 
 
 Steam Consumption of Sulzer Compound and Triple-expansion 
 Engines with Superheated Steam. 
 
 The figures in the table below were furnished to the author (Aug., 1902) 
 by Sulzer Bros., Winterthur, Switzerland. They are the results of official 
 tests by Prof. Schroter of Munich, Prof. Weber of Zurich, and other 
 eminent engineers. 
 
 COMPOUND ENGINES- 
 
 fs 
 
 o 
 
 PL, 
 
 
 
 3 
 
 a 
 
 
 
 &u 
 
 Dimensions of 
 
 G-2 
 
 I 
 
 W 
 
 
 
 w 3 
 
 
 Cylinders, 
 
 "43 a 
 
 
 ft • 
 
 a M 
 
 a\S 
 
 3 M 
 
 
 
 Inches. 
 
 n 
 
 
 i" 
 
 
 &* 
 
 flPn 
 
 gR 
 
 > 
 
 sr* 
 
 1500 
 
 30.5 and 
 
 85 
 
 130 
 
 356 
 
 2d. A 
 
 850 
 
 13.30 
 
 to 
 
 49.2 x 59.1 
 
 
 132 
 
 428 
 
 26.4 
 
 842 
 
 12.05 
 
 1800 
 
 
 
 122 
 
 482 
 
 26.6 
 
 1719 
 
 12.42 
 
 800 
 
 24 and 
 
 83 
 
 136 
 
 357 
 
 28 
 
 481 
 
 13.00 
 
 to 
 
 40.4 X 51.2 
 
 
 134 
 
 356 
 
 28 
 
 750 
 
 13.10 
 
 1000 
 
 
 
 135 
 
 356 
 
 27.6 
 
 1078 
 
 14.10 
 
 
 
 
 135 
 
 547 
 
 28 
 
 515 
 
 11.32 
 
 
 
 
 132 
 
 533 
 
 27.8 
 
 788 
 
 11.52 
 
 
 
 
 134 
 
 545 
 
 27.2 
 
 1100 
 
 11.88 
 
 950 
 
 26 and 
 
 86 
 
 130 
 
 358 
 
 28.2 
 
 1076 
 
 14.10 
 
 to 
 
 42.3 X51.2 
 
 
 129 
 
 358 
 
 28 
 
 1316 
 
 14.50 
 
 1150 
 
 
 
 . 132 
 
 496 
 
 28.3 
 
 1071 
 
 11.73 
 
 
 do., non-cond'g 
 
 
 136 
 
 527 
 
 
 1021 
 
 15.37 
 
 400 
 
 17.7 and 
 
 110 
 
 135 
 
 577 
 
 26.4 
 
 519 
 
 10.80* 
 
 to 
 
 30.5 X35.4 
 
 
 135 
 
 554 
 
 26.4 
 
 347 
 
 10.35* 
 
 500 
 
 
 
 
 
 
 
 
 1000 
 
 26.9 and 
 
 65 
 
 127 
 
 655 
 
 27.2 
 
 788 
 
 9.91* 
 
 to 
 
 47.2 X 66.9 
 
 
 127 
 
 664 
 
 27.2 
 
 797 
 
 9.68* 
 
 1200 
 
 
 
 128 
 
 572 
 
 27.1 
 
 788 
 
 10.70* 
 
 TRIPLE-EXPANSION ENGINES. 
 
 3000 
 
 321/4,471/4,58x59 
 
 85 
 
 188 
 190 
 
 606 
 397 
 
 28 
 271/4 
 
 2860 
 2880 
 
 8.97 
 11.28 
 
 3000 
 
 34, 49, 61 X 51 
 
 83.5 
 
 189 
 196 
 
 613 
 
 381 
 
 27 
 
 261/4 
 
 2908 
 3040 
 
 9.41 
 11.57 
 
 * With intermediate superheating. 
 to l.p. cylinder, 307 to 349° F. 
 
 Temperature of steam at entrance 
 
 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 lbs. pressure, are reported in Power, June, 1909, as 
 follows: 
 
 Load 
 
 Steam per I.H.P. hour 
 
 1/4 
 
 1/2 
 
 3/4 
 
 Full 
 
 H/4 
 
 50.7 
 
 24.4 
 
 23.2 
 
 23.8 
 
 25.4 
 
 The best result obtained at 130 lbs. pressure was 21.6 lbs., at 115 lbs. 
 pressure 22.6 lbs., and at 85 lbs. pressure 24.3 lbs. Maintained economy 
 
970 THE STEAM-ENGINE. 
 
 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, lbs. per sq. in. 
 
 400 300 250 200 150 100 75 50 
 Ideal Engine 
 
 (Rankine cycle) 6.95 7.5 7.9 8.45 9.20 10.50 11.40 12.9 
 Quadruple Exp. 
 
 Wastes 20% 8.75 9.15 9.75 10.50 11.60 13.0 14.0 15.6 
 
 Triple Exp. 
 
 Wastes 25% 9.25 9.95 10.50 11.15 12.30 14.0 15.1 16.7 
 
 Compound. 
 
 Wastes 33% 10.50 11.25 11.80 12.70 13.90 15.6 16.9 18.9 
 
 Simple Engine. 
 
 Wastes 50% 14.00 15.00 15.80 16.80 18.40 20.4 22.7 25.2 
 
 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 lbs., 
 in the second 115, and in the third 117 lbs. 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 Comp. 3 to 1 
 
 Indicated Horse-Power 112.7 130.0 67.7 
 
 Steam per I.H.P. hour 13.68 15.8 18.03 
 
 A test of a 7500-H.P. engine, at the 59th St. Station of the Interborough 
 Rapid Transit Co., New York, is reported in Pmtrer, Feb., 1906. It is a 
 double cross compound enerine. with horizontal h.p. and vertical l.p. 
 cylinders. With steam at 175 lbs. eauere 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 lbs.; per I.H.P. 
 hour, 11.96 lbs. 
 
 A test of a Fleminer 4-valve eneine. 15 and 40.5 in. diam., 27-in. stroke, 
 positive-driven Corliss valves, flv-wbeel governor, is reported bv 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 V8 7 Ao 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 
 
170 
 
 140 
 
 115 
 
 100 
 
 80 
 
 50 
 
 21.9 
 
 22.2 
 
 22.2 
 
 22.4 
 
 24.6 
 
 28.8 
 
 18.1 
 
 18.2 
 
 18.2 
 
 18.3 
 
 18.3 
 
 20.4 
 
 ECONOMIC PERFORMANCE OF STEAM-ENGINES. 971 
 
 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 
 
 Non-condensing 22 . 6 
 
 Condensing 18.4 
 
 Efficiency of Non-eOndensing 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 
 romewhat 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 the same ratio to that of the high-pressure 
 cvlinder 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 tandem 
 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. 
 of brass pipes per rated H.P. (600). The guarantees were: compound 
 engine, not to exceed 19 lbs. of steam per I. H.P. per hour, with 130 lbs. 
 steam pressure and 1 lb. back pressure in the exhaust pipe, and the 
 simple engine not to exceed 23 lbs. 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 lbs. 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 lbs. per 
 I.H.P, per hour; friction 3.6% of 300 H.P. 
 
972 
 
 THE STEAM-ENGINE. 
 
 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 lbs. gauge, all the other tests 80 lbs. 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., xv, 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, 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 lbs., 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 pi to p s , is 
 
 K = 0.85 (6.95 - 0.92 log p 2 ) /(log Pi - logp 2 ), 
 
 K being in kilograms and pi and P2 in kgs. per sq. meter. From this 
 formula the following table is calculated, the values being transformed 
 into British units. 
 
 Lbs. per 
 
 Lbs. Steam 
 
 at 50% 
 Vacuum . 
 
 Reduction of Steam Consumption (%) by 
 using a Vacuum of 
 
 sq. m. 
 
 60% 
 
 70% 
 
 80% 
 
 90% 
 
 95% 
 
 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 
 30.8 
 33.3 
 
 34.6 
 36.4 
 38.5 
 40.6 
 
 From the entropy diagram it is seen that in expanding from pressures 
 in excess of 100 lbs. per sq. in. down to 1.42 lbs. 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; 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 973 
 
 Increasing 
 
 the 
 
 Vacuum from 
 
 Decreases Steitn 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 lbs. gauge. R.p.m. 100, 
 vacuum 26.5 ins. 
 
 Test No 1 2 3 4 5 6 
 
 Indicated H.P 481 461 347 145 333 258 
 
 Superheat of steam 
 
 entering h.p.cyl... 253° F. 242° 221° 202° 232° 210° 
 B.T.U. supplied per 
 
 I.H.P. per min. ... 198.2 201.7 197.6 192.1 194.0 194.0 
 B.T.U. theoretically 
 
 required. Rankine 
 
 cycle.... 142.4 142.5 130.2 128.0 126.0 128.5 
 
 Efficiency ratio 0.72 0.71 0.66 0.67 0.65 0.66 
 
 Thermal efficiency % 21.39 21.02 21.46 22.07 21.86 21.86 
 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., 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, Oct. 13, 1900.) 
 
 Tests Using Steam. 
 
 Highly Superheated. 
 
 
 Mod- 
 
 
 erately 
 
 
 Super- 
 
 
 heated 
 
 188.4 
 
 190.3 
 
 614 
 
 531 
 
 868 
 
 2,850 
 
 9.56 
 
 10.29 
 
 479 
 
 447 
 
 Initial pressure in h.p. cyl. 
 
 (absolute), lbs 
 
 Temp, of steam in valve 
 
 chest, deg. F 
 
 Total I.H.P 
 
 Lbs. Steam per I.H.P. hour 
 Watt hours per lb. of coal. 
 
 187.3 
 
 195.5 
 
 582 
 2,900 
 9.64 
 477 
 
 585 
 2,779 
 9.67 
 482 
 
 194.6 
 
 381 
 2,951 
 11.77 
 438 
 
 195.9 
 
 381 
 2,999 
 11.75 
 435 
 
 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 341/4 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 
 
974 THE STEAM-ENGINE. 
 
 pressure at drier, 136.5 lbs. (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, lbs., 9.62 (9.60). 
 
 The saving due to the use of superheated steam is reported in numerous 
 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 lbs. per I.H.P. hour, and 10.98 lbs. per B.H.P. 
 hour. The steam pressure in the boiler was 172.6 lbs., 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 test of a Rice & Sargent cross-compound horizontal engine 16 and 
 28 X 42 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 lbs. 
 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 clear- 
 ances were respectively 6, 5.7, 4.4 and 3.5%. R.p.m. 57. Steam pressure, 
 gauge, near throttle, 242.8 lbs., in 1st. receiver 120.7 lbs., in 2d, 30. S lbs., 
 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°. Mr. Hood gives a dia- 
 gram showing graphically the transfer of heat through the several parts 
 of the apparatus, from which the following is taken. The figures are in 
 B.T.U. transferred per minute. 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 975 
 
 
 Received 
 
 from 
 Boiler or 
 Receiv'rs. 
 
 Received 
 
 from 
 Jackets. 
 
 Convert- 
 ed into 
 Work. 
 
 Delivered 
 
 to 
 
 Heater. 
 
 Delivered 
 
 to 
 Jackets. 
 
 
 194,183 
 187,348 
 174,872 
 165,973 
 160,083 
 149,538 
 148,683 
 128,835 
 125,885 
 120,285 
 
 862 
 6,624 
 2,000 
 8,060 
 1,150 
 5,185 
 
 940 
 
 7,697 
 
 
 
 
 17,100 
 
 2,000 
 
 No. 2 Cylinder 
 
 10,899 
 
 
 
 12,800 
 
 1,150 
 
 
 11,695 
 
 
 
 5,100 
 9,100 
 2,350 
 5,690 
 
 940 
 
 
 ii,688 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 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 
 hour assuming 10,000 B.T.U. imparted to the boiler per pound coal, per 
 I.H.P., 1.016 lbs. ; per B.H.P., 1.138 lbs. Dry steam per hour per I.H.P., 
 11.23 lbs.; per B.H.P., 12.58 lbs. 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% saving down to zero, or even in some cases showing 
 an actualloss. 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 resume of facts and opinions on the steam- 
 jacket is given by Prof. Thurston in Trans. A. S. M. E., xiv, 462. See 
 
976 
 
 THE STEAM-ENGINE. 
 
 also Trans. A. S. M. E., 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. 
 
 Sennett asserts that "it has been abundantly proved that steam-jackets 
 are not only advisable but absolutely necessary, in order that high rates of 
 expansion may be efficiently carried out and the greatest possible economy 
 of heat attaned." 
 
 Isherwood finds the gain by its use, under the conditions of ordinary 
 practice, as a general average, to be about 20% on small and 8% or 9% on 
 large engines, varying through intermediate values with intermediate 
 sizes, it being understood that the jacket has an effective circulation, and 
 that both heads and sides are jacketed. 
 
 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. 
 
 Mr. E. D. Leavitt has expressed the opinion that, in his practice, steam- 
 jackets produce an increase of efficiency of from 15% to 20%. 
 
 In the Pawtucket pumping-engine, 15 and 30VsX 30 in., 50 revs, per 
 min., steam-pressure 125 lbs. gauge, cut-off 1/4 in 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 Schrboter from his work on the triple-expansion engines at 
 Augsburg, and Mm 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 
 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.) -7- 
 Cylinders 9 and 16 in. X 14 in. stroke; 112 lbs. 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 H.P 
 
 30 
 22.6 
 
 40 
 
 21.4 
 
 50 
 20.3 
 
 60 
 
 19.6 
 22 
 10.9 
 
 70 
 
 19 
 
 20.5 
 7.3 
 
 80. 
 
 18.7 
 19.6 
 4.6 
 
 90 
 
 18.6 
 19 2 
 3.1 
 
 100 
 
 18.9 
 19.1 
 1.0 
 
 110 
 
 19.5 
 
 19.3 
 
 -1.0 
 
 120 
 
 20.4 
 20.1 
 -1.5 
 
 ]?•> 
 
 Steam per I. H.P. per hr. 
 With jackets, lbs 
 
 21.0 
 
 
 
 
 
 
 
 
 
 
 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 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 977 
 
 particular engine it appears that when running at its most economical 
 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 advantage 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 Inter- 
 national 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 lbs. saturated steam, 28.6 ins. vacuum, 
 and 33 expansions, 12.1 lbs. 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 lbs. saturated steam, 27.6 ins. of vacuum, and 32 ex- 
 pansions, 11.98 lbs. 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 
 of 5400 H.P., 185 lbs. steam pressure, 27.3 ins. vacuum, and 29 expan- 
 sions, 11.93 lbs. of water per I. H.P. per hour, with an initial condensation 
 of about 32%. 
 
 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 the essential condition is the use of a ratio of expansion 
 of about 30, above which the cylinder-condensation loss is liabie 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 
 of the current cylinder and clearance ratios, and with any existing system 
 of jackets and reheaters, or without them, a water consumption of 12.4 lbs. 
 per horse-power is possible, and that a variation of 0.4 lb. below or above 
 this figure may occur by the accidental favorable, or unfavorable, jacket 
 and cylinder-wall expenses which are beyond the exact 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- 
 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 lbs. 
 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 engines 
 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: 
 
978 THE STEAM-ENGINE. 
 
 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 lbs. steam 
 and 28 ins. vacuum required 13.08 lbs. of saturated steam per B.H.P. 
 hour, a gain of 4% over the 600-H. P. turbine. The engine with 18.5 lbs. 
 boiler pressure gave 12.5 lbs. 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 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 lbs. of saturated steam per I.H.P., with 175 lbs. 
 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 laterthe Allis pump, 
 with 85 lbs. steam pressure, has lowered the record to 10.33 lbs. of satu- 
 rated steam per I.H.P., with 196 B.T.U. per H.P. rrinute. 
 
 Gain from Superheating. — In the Belgian compound engine above de- 
 scribed, with steam at 130 lbs., vacuum 27.6 ins., the average consumption 
 of saturated steam, between 45 and 125% of load, was 12.45 lbs. 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 lbs. per 
 I.H.F. hour, computed to be equivalent to 209 B.T.U. per H.P. rrinute, 
 a gain due to superheating of 7%. With steam superheated 307° and 
 the load about 80% of rating the water consun ption was 8.99 lbs. per 
 I.H.P. hour, equivalent to 192 B.T.U. per H.P. ninute. 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- 
 bine is that of Brown & Boveri Parsons Frankfort 4000-H.P. nachine, 
 which, with 183 lbs. gauge pressure and 190° F. superheat, afforded 10.28 
 lbs. per B.H.P. hour, assuming a generator efficiency of 0.95. Beckoning 
 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-power as 
 the turbine, so that its friction load would be onlv 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 
 
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 979 
 
 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 lbs. pressure against a nest of tubes containing sulphur 
 dioxide which is thereby boiled to a vapor at about 170 lbs. 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 be 
 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 6 7 8 
 
 Armature bore, side-crank engines .. . 41/2 51/2 6V2 71/2 8 1/2 10 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 0.002 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- 
 Comp. 
 
 Double, 
 2hor. 
 
 2 vert. 
 Cyis. 
 
 Vert. 
 Cross- 
 Comp. 
 
 Double, 
 2 hor. 
 2 vert. 
 Cyls. 
 
 3 Cyl. Vert. 
 
 Rated H.P 
 
 Cylinders, all 60-in. 
 
 4500 
 
 46,86 
 9, 10 
 14 X 14 
 14 X 14 
 27 ft. 4 in. 
 37 in. 
 34X60 
 
 8000 
 
 44,88 
 
 8 
 18 x 18 
 12X 12 
 25 ft. 3 in. 
 37 in. 
 34X60 
 
 4500 
 
 46, 86 
 9, 10 
 
 14 X 14 
 
 14 X 14 
 27 ft. 
 39 in. 
 
 34X60 
 
 8900 
 
 42, 86 
 
 8, 10 
 
 20 X 18 
 
 12X 12 
 
 25 ft. 3 in. 
 
 37 in. 
 34X60 
 
 5200 
 
 431/2,2-751/2 
 
 9 
 22 & 16 X 14 
 
 Piston rods, diam. in., 
 
 
 14 X 14 
 
 Shaft length 
 
 35 ft 
 
 max. diam 
 
 bearings 
 
 293/ 8 in. 
 26X60 
 
 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 attached 
 to two connecting rods, side by side, hor. and vert., each rod having a 
 bearing 9 in. long on the pin. The crank pins of the Edison engine are 
 16 in. diam. for the side-cranks, and 22 in. for the center-crank. 
 
980 
 
 THE STEAM-ENGINE. 
 
 Some Large Rolling-Mill Engines. 
 
 
 
 P, 
 
 
 J 
 
 Fly-wheel. 
 
 
 
 
 Cylinders. 
 
 Ph 
 
 Type. 
 
 g^ 
 
 
 Location. 
 
 Builders. 
 
 
 
 
 o 
 
 
 rt 
 
 
 Ph~ 
 
 Diam. 
 
 Wt. 
 
 
 
 
 
 
 
 
 ft. 
 
 lbs. 
 
 
 
 1 
 
 44 & 82x60 
 
 65 
 
 Cross-C. 
 
 140 
 
 24 
 
 150,000 
 
 Republic I. &S 
 Co., Youngs- 
 town, Ohio. 
 
 Filer & 
 Stowell. 
 
 2 
 
 46 & 80x60 
 
 80 
 
 Tandem. 
 
 150 
 
 24 
 
 110,000 
 
 Carnegie S. Co., 
 Donora, Pa. 
 
 Wiscon- 
 sin Eng. 
 
 Co. 
 Wm. Tod 
 
 3 
 
 52 & 90x60 
 
 
 
 
 25 
 
 250,000 
 
 
 
 
 
 
 
 
 
 Youngstown, 
 
 Co. 
 
 
 
 
 
 
 
 Ohio. 
 
 
 4 
 
 2 each 
 
 
 Double 
 
 150 
 
 none 
 
 Carnegie S. Co., 
 
 Allis 
 
 
 42& 70x54 
 
 
 Tandem. 
 
 
 
 S. Sharon, Pa. 
 
 Carnegie S. 
 Co.,Du- 
 quesne, Pa. 
 
 Chal- 
 mers Co. 
 
 Mackin- 
 tosh, 
 
 b 
 
 2 each 
 
 60 
 
 Double 
 
 150 
 
 none 
 
 Jones & 
 
 Hemp- 
 
 
 44 & 70X60 
 
 
 Tandem 
 
 
 
 Laughlin 
 Steel Co., 
 
 hill & 
 
 
 
 
 
 
 
 Co. 
 
 
 
 
 
 
 
 Alequippa, 
 
 
 
 
 
 
 
 
 I Pa. J 
 
 
 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 = W2r/p (1) 
 
 in which Wi denotes the weight of the balance weight and p the radius to 
 its center of gravity, Wi 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 (W 2 + Wz) r/p to 3/ 4 (Wo + Wz) r/p, 
 
 . • (2) 
 
 in which W3 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. E., 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 
 layer of felt 5 inches thick was then placed on the foundations and run 
 up 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- 
 
COMMERCIAL ECONOMY — COSTS OF POWER. 981 
 
 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. We thus increase the cost 
 of the engine, etc., as we increase the ^ate of expansion, while at the same 
 time we decrease the fuel consumption, the cost of boiler, etc. So that 
 there is in every engine some point of cut-off, determinable by calculation 
 and graphical construction, which will secure the greatest efficiency for 
 a given expenditure of money, taking into consideration the cost of fuel, 
 wages of engineer and firemen, interest on cost, depreciation of value, 
 repairs to and insurance of boiler and engine, and oil, waste, etc., used 
 for engine. In case of freight-carrying vessels, the value of the room 
 occupied by fuel should be considered in estimating the cost of fuel. 
 
 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 to 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 lbs. 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. 
 
982 THE STEAM-ENGINE* 
 
 Cost of Steam-power. (Chas. T. Main, Trans. A. S. M. E„ X.* 48;)— 
 Estimated costs in New England in 1888, per horse-power* based on engines 
 of 1000 H.P. 
 
 Compound Condens* Non^con- 
 
 Engine. ing Engine, densing 
 
 Engine. 
 
 1. Cost engine and piping, complete. .. .$25.00 $20.00 $17.50 
 
 2. Engine-house 8.00 7.50 7.50 
 
 3. Engine foundations 7.00 5.50 4.50 
 
 4. Total engine plant 40.00 33.00 29.50 
 
 5. Depreciation, 4% on total cost. ..... 1.60 1-32 1.18 
 
 6. Repairs, 2% on total cost 0.80 0.66 0.59 
 
 7. Interest, 5% on total cost 2.00 1.65 1.475 
 
 8. Taxation, 1.5% on 3/ 4 cost 0.45 0.371 0.332 
 
 9. Insurance on engine and house. .... . 0.165 0.138 0.125 
 
 10. Total of lines 5, 6, 7, 8, 9 5.015 4.139 3.702 
 
 11. Cost boilers, feed-pumps, etc 9.33 13.33 16.00 
 
 12. Boiler-house 2.92 4.17 5.00 
 
 13. Chimney and flues 6.11 7.30 8.00 
 
 14. Total boiler-plant 18.36 24.80 29.00 
 
 15. Depreciation, 5% on total cost 0.918 1.240 1.450 
 
 16. Repairs, 2% on total cost 0.367 0.496 0.580 
 
 17. Interest, 5% on total cost 0.918 1.240 1.450 
 
 18. Taxation, 1.5% on 3/ 4 cost 0.207 0.279 0.326 
 
 19. Insurance, 0.5% on total cost. 0.092 0.124 0.145 
 
 20. Total of lines 15 to 19 ...... . 2.502 3.379 3.951 
 
 21. Coal used per I.H.P. per hour, lbs. . . 1.75 2.50 3.00 
 
 22. Cost of coal per I.H.P. per day of 10 1/4 cts. cts. cts. 
 
 hours at $5.00 per ton of 2240 lbs 4.00 5.72 6.86 
 
 23. Attendance of engine per day 0.60 0.40 0.35 
 
 24. Attendance of boilers per day. ..... . 0.53 0.75 0.90 
 
 25. Oil, waste, and supplies, per day .... 0.25 0.22 0.20 
 
 26. Total daily expense 5.38 7.09 8.31 
 
 27. Yearly running expense, 308 days, per 
 
 I.H.P $16,570 $21,837 $25,595 
 
 28. Total yearly expense, lines 10, 20, 
 
 and 27 24.087 29,355 33.248 
 
 29. Total yearly expense per I.H.P. for 
 
 power if 50% of exhaust-steam is 
 
 used for heating 12.597 14.90? 16,663 
 
 30. Total if all exhaust-steam is used for 
 
 heating 8.624 7.916 7.700 
 
 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. I. E. E., vol. x, 
 Mar., 1893. 
 
 Decourcey May (Trans. A. S. M.E., 1894) gives the following estimates 
 
COMMERCIAL ECONOMY — COSTS OF POWER. 983 
 
 of the annual cost of power with different types of engine. He figures 
 interest and depreciation each at 5%, insurance at 1%, and taxes at 11/2% 
 of the cost of the plant. No cost of water is charged. 
 
 Cost of coal per 2240 lbs . 
 
 Cost of 1 I.H.P. per year. 
 
 365 days of 24 hours. 
 
 308 days of 10 1/4 hours. 
 
 Triple-expansion pumping, 
 20 revs 
 
 Triple-expansion without 
 pumps, 50 revs 
 
 Compound mill, best engine 
 
 Compound mill, average.. . 
 
 Compound elec. light, av. . 
 
 Compound trolley 
 
 Triple-expansion trolley. . . 
 
 Condensing mill 
 
 Non-cond., 50 to 200 H.P.. . 
 
 55 
 
 61 
 
 33 
 
 39 
 
 36 
 
 44 
 
 46 
 
 52 
 
 139 
 
 157 
 
 58 
 
 68 
 
 54 
 
 64 
 
 52 
 
 61 
 
 76 
 
 81 
 
 33 
 
 35 
 
 18 
 
 20 
 
 19 
 
 21 
 
 25 
 
 28 
 
 84 
 
 90 
 
 32 
 
 36 
 
 29 
 
 33 
 
 29 
 
 33 
 
 53 
 
 57 
 
 Cost 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 lbs. of coal being used per 
 hour per horse-power. It is useful, among other tilings , 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 lbs., a saving of $9000 per year in fuel may be made by replacing a 
 steam plant of 1000 H.P., requiring 4 lbs. of coal per hour per horse-power, 
 with one requiring only 2 lbs. 
 
 
 Coal Consumption, at 4 lbs. 
 
 
 
 
 
 
 
 
 per H.P. hour; 10 hours a 
 
 
 
 
 
 
 
 
 day; 300 days per Year. 
 
 $2 per 
 Short 
 Ton. 
 
 $3 per 
 Short 
 Ton. 
 
 $ 
 S 
 
 4 per 
 hort 
 
 % 
 
 
 
 1 
 
 Lbs. 
 
 Long Tons. 
 
 Short 
 Tons. 
 
 ron. 
 
 
 
 
 
 
 Cost in 
 
 Cost in 
 
 Cost in 
 
 
 
 Per 
 Day. 
 
 Per 
 Day. 
 
 Per 
 
 Year. 
 
 Per 
 Dav. 
 
 Per 
 Yr. 
 
 Dollars. 
 
 Dollars. 
 
 Dollars. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Day. 
 
 Yr. 
 
 Day. 
 
 Yr. 
 
 Day. 
 
 Yr. 
 
 1 
 
 40 
 
 0.0179 
 
 53.57 
 
 0.02 
 
 6 
 
 0.04 
 
 12 
 
 0.06 
 
 18 
 
 08 
 
 24 
 
 10 
 
 400 
 
 0.1786 
 
 53.57 
 
 0.20 
 
 60 
 
 0.40 
 
 120 
 
 0.60 
 
 180 
 
 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 
 
 17 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 
 
 7.1 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 
 
 9.600 
 
 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 
 
 7.4 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 (Ml 
 
 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 
 
984 
 
 THE STEAM-ENGINE. 
 
 It is usual to consider that a factory working 10 hours a day requires 
 10 1/2 hours coal consumption on account of the coal used in banking or 
 in starting the fires, and that there are 306 working 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 lbs. 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 75 
 20 171/2 
 
 150 
 141/2 
 
 200 
 131/2 
 
 300 
 123/ 4 
 
 500 600 700 800 
 12.8 131/4 14 15 
 
 Relative Commercial Economy of Best Modern Types of Com- 
 pound and Triple-expansion Engines. (J. E. Denton, American 
 Machinist, Dec. 17, 1891.) — The following table and deductions show 
 the relative commercial economy of the compound and triple types for 
 the best stationary practice in steam plants of 500 indicated horse-power. 
 The table is based on the tests of Prof. Schroter, of Munich, of engines 
 built at Augsburg, and those of Geo. H. Barrus on the best plants of 
 America, and of detailed estimates of cost obtained from several first- 
 class builders. 
 
 Trip motion, or Corliss engines 
 of the twin-compound-re- 
 ceiver condensing type, ex- 
 panding 16 times. Boiler 
 pressure 120 lbs. 
 
 Trip motion, or Corliss engines 
 of the triple-expansion four- 
 cylinder-receiver condensing 
 type, expanding 22 times. 
 Boiler pressure 150 lbs. 
 
 The figures in the first column represent the best recorded performance 
 (1891), and those in the second column the probable reliable performance. 
 
 The following table shows the total annual cost of operation, with coal 
 at $4.00 per ton, the plant running 300 days in the year, for 10 hours and 
 for 24 hours per day. 
 
 f Lbs. water per hour per ) , Q A 1 a n 
 
 H.P., by measurement, j ld, ° 14,u 
 Lbs. coal per hour per j 
 
 H.P., assuming 8.5 lbs. J 1 . 60 1 . 65 
 
 actual evaporation. ) 
 Lbs. water per hour per I 1Q , R ,„ on 
 
 H.P., by measurement. J lzOD l^.ou 
 Lbs. coal per hour per ) 
 
 H. P., assuming 8.5 lbs. J 1.48 1.50 
 
 actual evaporation. ) 
 
 
 10 
 
 24 
 
 
 
 
 PerH.P. 
 $9.90 
 9.00 
 0.90 
 
 Per H.P. 
 
 $28.50 
 
 
 25.92 
 
 
 2.60 
 
 
 
 
 $0.23 
 0.23 
 
 0.15 
 
 0.06 
 
 $0.23 
 
 
 0.23 
 
 Annual extra cost of oil, 1 gallon per 24-hour day, 
 at $0.50, or 15% of extra fuel cost 
 
 0.36 
 
 Annual extra cost of repairs at 3% on $4.50 per 24 
 
 0.14 
 
 
 
 
 $0.67 
 
 $0.96 
 
 
 $0.23 
 
 $1.64 
 
 
 
 Increased cost of triple-expansion plant per horse-power, including 
 boilers, chimney, heaters, foundations, piping and erection $4.50 
 
 Taking the total cost of plants at $36.50 and $41 per horse- power re- 
 spectively, the figures in the table imply that for coal at $4 per ton a 
 
COMMERCIAL ECONOMY — COSTS OF POWER. 985 
 
 triple expansion 500 H.P. plant costs $20,500, and saves about $114 per 
 year in 10-hour service, or $826 in 24-hour service, over a compound 
 plant, thereby saving its extra cost in 10-hour service in about 193/4 years, 
 or in 24-hour service in about 23/4 years. 
 
 Power Plant Economics. (H. G. Stott, Trans. A. I. E. E., 1906.) — 
 The following table gives an analysis of the heat losses found in a year's 
 operation of one of the most efficient plants in existence. 
 
 AVERAGE LOSSES IN THE CONVERSION OF 1 LB. OF COAL INTO ELECTRICITY. 
 
 B.T.U. % B.T.U. % 
 
 1. B.T.U. per lb. of coal supplied 14,150 100.0 
 
 2. Loss in ashes 340 2.4 
 
 3. Loss to stack 3,212 22.7 
 
 4. Loss in boiler radiation and air leakage 1,131 8.0 
 
 5. Returned by feed-water heater 441 3.1 
 
 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 pump 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 Ill 0.8 
 
 14. Electrical losses 36 0.3 
 
 15. Engine radiation losses 28 0.2 
 
 16. Rejected to condenser 8,524 60.1 
 
 17. To house auxiliaries 29 0.2 
 
 14,099 99.6 
 
 Delivered to bus bar 1,452 10.3 
 
 The following notes concerning power-plant economy are condensed 
 from Mr. Stott's paper. 
 
 Item 1. B.T.U. per lb. of coal. The coal is bought and paid for on the 
 basis of the B.T.U. found by a bomb calorimeter. 
 
 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 ttie 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 lbs. gauge and 28 ins. vacuum is 
 
 (Ti - r 2 ) h- Ti = (837 - 560) -h 837 = 33%. 
 
 The actual best efficiency of this engine is 17 lbs. 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- 
 
986 THE STEAM-ENGINE. 
 
 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 of cut-off in the low- 
 pressure cylinder, might save 5 or 6%. 
 
 The present type of 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° superheat reduces its 
 steam consumption 13.5%. The shape of the economy curve is much 
 flatter [from 3300 to 8000 K. W. the range of steam consumption is between 
 14.6 and 15.0 lbs. 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: 
 
 Brake-load, per Gas-engine, cu. ft. Petroleum Eng., Petroleum Eng., 
 cent of full of Gas per Brake Lbs. of Oil per 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 following table 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. 
 
COMMERCIAL ECONOMY — COSTS OF POWER. 987 
 
 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. Boiler room or pro- 
 
 ducer room 
 
 3. Coal- and ash-han- 
 
 dling apparatus . . . 
 
 4. Electrical apparatus 
 
 Operation. 
 
 5. Coal- and ash-han- 
 
 dling labor 
 
 6. Removal of ashes .... 
 
 7. Dock rental 
 
 8. Boiler-room labor. . . . 
 
 9. Boiler-room oil, waste, 
 
 etc 
 
 10. Coal 
 
 11. Water 
 
 12. Engine-room me- 
 
 chanical labor 
 
 13. Lubrication 
 
 14. Waste, etc 
 
 15. Electrical labor 
 
 Relative cost of mainte- 
 nance and operation . . 
 
 Relative investment in 
 per cent 
 
 2.57 
 4.61 
 
 0.58 
 1.12 
 
 2.26 
 1.06 
 0.74 
 7.15 
 
 0.17 
 61.30 
 
 7.14 
 
 6.71 
 1.77 
 0.30 
 2.52 
 
 0.51 
 4.30 
 
 0.54 
 1.12 
 
 2.11 
 0.94 
 0.74 
 
 6.68 
 
 0.17 
 57.30 
 0.71 
 
 1.35 
 0.35 
 0.30 
 2.52 
 
 1.54 
 3.52 
 
 0.44 
 1.12 
 
 1.74 
 0.80 
 0.74 
 5.46 
 
 0.17 
 46.87 
 5.46 
 
 4.03 
 1.01 
 0.30 
 
 2.52 
 
 2.57 
 1.15 
 
 0.29 
 1.12 
 
 1.13 
 0.53 
 0.74 
 1.79 
 
 0.17 
 26.31 
 3.57 
 
 6.71 
 1.77 
 0.30 
 
 2.52 
 
 1.54 
 1.95 
 
 0.29 
 1.12 
 
 1.13 
 0.53 
 0.74 
 3.03 
 
 0.17 
 25.77 
 2.14 
 
 4.03 
 1.06 
 0.30 
 2.52 
 
 Storing Heat in Hot Water. — (See also p. 897.) 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 lbs. 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 lbs. 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 lbs. pressure. A reservoir 8 ft. in diameter and 30 ft. 
 long, containing 84,000 lbs. of heated water at 250 lbs. pressure, would 
 supply 5250 lbs. of steam at 130 lbs. pressure. As the steam consump- 
 tion of a condensing electric-light engine is about 18 lbs. 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 lbs. 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 
 
THE STEAM-ENGINE. 
 
 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 
 lbs. 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 lbs. 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 lbs. of steam, or a steam rate of 22.5 lbs. per H.P. hour for the 
 combination. 
 
 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 oh 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 Vi6 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 STEAM-ENGINE TESTS. 
 
 A committee of the Am. Soc. M. E. in 1902 made a report on Engine 
 Tests, which is printed in the Transactions for that year, and also in a 
 pamphlet of 78 pages. A greatly condensed abstract only can be given 
 here. Engineers making tests of engines should have the complete report. 
 In the introduction to the report the Committee says: 
 The heat consumption of a steam-engine plant is ascertained by meas- 
 uring the quantity of steam consumed by the plant, calculating the total 
 heat of the entire quantity, and crediting this total with that portion of 
 the heat rejected by the plant which is utilized and returned to the boiler. 
 The term "engine plant" as here used should include the entire equip- 
 ment of the steam plant which is concerned in the production of the power, 
 embracing the main cylinder or cylinders: the jackets and reheaters: the 
 air, circulating, and boiler-feed pumps, if steam driven; and any other 
 
RULES FOR CONDUCTING STEAM-ENGINE TESTS. 989 
 
 steam-driven mechanism or auxiliaries necessary to the working of the 
 engine. It is obligatory to thus charge the engine with the steam used 
 by necessary auxiliaries in determining the plant economy, for the reason 
 that it is itself finally benefited, or should be so benefited, by the heat 
 which they return; it being generally agreed that exhaust steam from 
 such auxiliaries should be passed through a feed-water heater, and the 
 heat thereby carried back to the boiler and saved. 
 
 In that large class of steam engines which are required to run at a cer- 
 tain limited and constant speed, there should be a considerable reserve of 
 capacity beyond the rated power. It is our recommendation that when a 
 steam engine is operating at its rated power at a given pressure there 
 should be a sufficient reserve to allow a drop of at least 15 per cent in the 
 gauge pressure without sensible reduction in the working speed of the 
 engine, and to allow an overload at the stated pressure amounting to at 
 least 25 per cent. 
 
 Rules for Conducting Steam-engine Tests. Code of 1902. 
 
 I. Object of Test. — Ascertain at the outset the specific object of the test, 
 whether it be to determine the fulfillment of a contract guarantee, to 
 ascertain the highest economy obtainable, to find the working economy 
 and defects under conditions as they exist, to ascertain the performance 
 under special conditions, to determine the effect of changes in the condi- 
 tions, or to find the performance of the entire boiler and engine plant, 
 and prepare for the test accordingly. 
 
 II. General Condition of the Plant. — Examine the engine and the 
 entire plant concerned in the test ; note its general condition. and any points 
 of design, construction, or operation which bear on the objects in view. 
 Make a special examination of the valves and pistons for leakage by apply- 
 ing the working pressures with the engine at rest, and observe the quantity 
 of steam, if any, blowing through per hour. 
 
 III. Dimensions, etc. — Measure or check the dimensions of the cylin- 
 ders when they are hot. If they are much worn, the average diameter 
 should be determined. Measure also the clearance. If the clearance 
 cannot be measured directly, it can be determined approximately from 
 the working drawings of the cylinder. 
 
 IV. Coal. — When the trial involves the complete plant, embracing 
 boilers as well as engine, determine the character of coal to be used. The 
 class, name of the mine, size, moisture, and quality of the coal should be 
 stated in the report. It is desirable, for purposes of comparison, that the 
 coal should be of some recognized standard quality for the locality where 
 the plant is situated. 
 
 V. Calibration of Instruments. — All instruments and apparatus should 
 be calibrated and their reliability and accuracy verified by comparison 
 with recognized standards. 
 
 VI. Leakages of Steam, Water, etc. — In all tests except those of a com- 
 plete plant made under conditions as they exist/the boiler and its con- 
 nections, both steam and feed, as also the steam piping leading to the 
 engine and its connections, should, so far as possible, be made tight. 
 All connections should, so far as possible, be visible and be blanked off, 
 and where this cannot be done, satisfactory assurance should be obtained 
 that there is no leakage either in or out. 
 
 VII. Duration of Test. — The duration of a test should depend largely 
 upon its character and the objects in view. The standard heat test of 
 an engine, and, likewise, a test for the simple determination of the feed- 
 water consumption, should be continued for at least five hours, unless the 
 class of service precludes a continuous run of so long duration. It is 
 desirable to prolong the test the number of hours stated to obtain a num- 
 ber of consecutive hourly records as a guide in analyzing the reliability 
 of the whole. 
 
 The commercial test of a complete plant, embracing boilers as well as 
 engine, should continue at least one full dav of twenty-four hours, whether 
 the engine is in motion during the entire time or not. A continuous coal 
 test of a boiler and engine should be of at least ten hours' duration, or the 
 nearest multiple of the interval between times of cleaning fires. 
 
 VIII. Starting and Stopping a Test. — (a) Standard Heat Test and 
 Feed- Water Test of Engine: The engine having been brought to the normal 
 
990 THE STEAM-ENGINE. 
 
 condition of running, and operated a sufficient length of time to be thor- 
 oughly heated in all its parts, and the measuring apparatus having been 
 adjusted and set to work, the height of water in the gauge glasses of the 
 boilers is observed, the depth of water in the reservoir from which the 
 feed water is supplied is noted, the exact time of day is observed, and 
 the test held to commence. Thereafter the measurements determined upon 
 for the test are begun and carried forward until its close. When the time 
 for the close of the test arrives, the water should, if possible, be brought 
 to the same height in the glasses and to the same depth in the feed-water 
 reservoir as at the beginning, delaying the conclusion of the test if neces- 
 sary to bring about this similarity of conditions. If differences occur, 
 the proper corrections must be made. 
 
 (&) Complete Engine and Boiler Test: For a continuous running test 
 of combined engine or engines, and boiler or boilers, the same directions 
 > apply for beginning and ending the feed-water measurements as those just 
 referred to. The time of beginning and ending such a test should be the 
 regular time of cleaning the fires, and the exact time of beginning and 
 ending should be the time when the fires are fully cleaned, just preparatory 
 to putting on fresh coal. 
 
 For a commercial test of a combined engine and boiler, whether the 
 engine runs continuously for the full twenty-four hours of the day, or only 
 a portion of the time, the fires in the boilers being banked during the time 
 when the engine is not in motion, the beginning and ending of the test 
 should occur at the regular time of cleaning the fires, the method followed 
 being that already given. In cases where the engine is not in continuous 
 motion, as, for example, in textile mills, where the working time is ten or 
 eleven hours out of the twenty-four, and the fires are cleaned and banked 
 at the close of the day's work, the best time for starting and stopping a 
 test is the time just before banking, when the fires are well burned down 
 and the thickness and condition can be most satisfactorily judged. 
 
 IX. Measurement of Heat Units Consumed by the Engine. — The meas- 
 urement of the heat consumption requires the measurement of each 
 supply of feed water to the boiler — that is, the water supplied by the 
 main feed pump, that supplied by auxiliary pumps, such as jacket water, 
 water from separators, drips, etc., and water supplied by gravity or other 
 means; also the determination of the temperature of the water supplied 
 from each source, together with the pressure and quality of the steam. 
 The temperatures at the various points should be those applying to the 
 working conditions. 
 
 The heat to be determined is that used by the entire engine equipment, 
 embracing the main cylinders and all auxiliary cylinders and mechanism 
 concerned in the operation of the engine, including the air pump, circu- 
 lating pump, and feed pumps, also the jacket and reheater when these 
 are used. 
 
 The steam pressure and the quality of the steam are to be taken at 
 some point conveniently near the throttle valve. The quantity of steam 
 used by the calorimeter must be determined and properly allowed for. 
 
 X. Measurement of Feed Water or Steam Consumption of Engine, etc. — 
 The method of determining the steam consumption applicable to all plants 
 is to measure all the feed water supplied to the boilers, and deduct there- 
 from the water discharged by separators and drips, as also tne water and 
 steam which escapes on account of leakage of the boiler and its pipe con- 
 nections and leakage of the steam main and branches connecting the boiler 
 and the engine. In plants where the engine exhausts into a surface con- 
 
 . denser the steam consumption can be measured by determining the quan- 
 tity of water discharged by the air pump, corrected for any leakage of the 
 condenser, and adding thereto the steam used by jackets, reheaters, and 
 auxiliaries as determined independently. 
 
 The corrections or deductions to be made for leakage above referred to 
 should be applied only to the standard heat-unit test and tests for deter- 
 mining simply the steam or feed-water consumption, and not to coal tests 
 of combined engine and boiler equipment. In the latter, no corrections 
 should be made except for leakage of valves connecting to other engines 
 and boilers, or for steam used for purposes other than the operation of the 
 plant under test. Losses of heat due to imperfections of the plant should 
 be charged to the plant, and only such losses as are concerned in the work- 
 ing of the engine alone should be charged to the engine. 
 
KULES FOR CONDUCTING STEAM-ENGINE TESTS. 991 
 
 XI. Measurement of Steam used by Auxiliaries. — It is highly desirable 
 that the quantity of steam used by the auxiliaries, and in many cases that 
 used by each auxiliary, should be determined exactly, so that the net con- 
 sumption of the main engine cylinders may be ascertained and a complete 
 analysis made of the entire work of the engine plant. 
 
 XII. Coal Measurement. — The coal consumption should be deter- 
 mined for the entire time of the test. If the engine runs but a part of the 
 time, and during the remaining portion the fires are banked, the measure- 
 ment of coal should include that used for banking. 
 
 XIII. Indicated Horse-power. — The indicated horse-power should be 
 determined from the average mean effective pressure of diagrams taken 
 at intervals of twenty minutes, and at more frequent intervals if the 
 nature of the test makes this necessary, for each end of each cylinder. 
 With variable loads, such as those of engines driving generators for elec- 
 tric railroad work, and of rubber-grinding and rolling-mill engines, the 
 diagrams cannot be taken too often. 
 
 The most satisfactory driving rig for indicating seems to be some form 
 of well-made pantograph, with driving cord of fine annealed wire leading 
 to the indicator. The reducing motion, whatever it may be, and the 
 connections to the indicator, should be so perfect as to produce diagrams 
 of equal lengths when the same indicator is attached to either end of the 
 cylinder, and produce a proportionate reduction of the motion of the 
 piston at every point of the stroke, as proved by test. 
 
 The use of a three-way cock and a single indicator connected to the 
 two ends of the cylinder is not advised, except in cases where it is imprac- 
 ticable to use an indicator close to each end. If a three-way cock is used, 
 the error produced should be determined and allowed for. 
 
 XIV. Testing Indicator Springs. — To make a perfectly satisfactory 
 comparison of indicator springs with standards, the calibration should be 
 made, if this were practical, under the same conditions as those pertaining 
 to their ordinary use. 
 
 XV. Brake Horse-power. — This term applies to the power delivered 
 from the flywheel shaft of the engine. It is the power absorbed by a fric- 
 tion brake applied to the rim of the wheel, or to the shaft. A form of 
 brake is preferred that is self-adjusting to a certain extent, so that it will, 
 of itself, tend to maintain a constant resistance at the rim of the wheel. 
 One of the simplest brakes for comparatively small engines, which may be 
 made to embody this principle, consists of a cotton or hemp rope, or a 
 number of ropes, encircling the wheel, arranged with weighing scales. 
 or other means for showing the strain. An ordinary band brake may also 
 be constructed so as to embody the principle. The wheel should be pro- 
 vided with interior flanges for holding water used for keeping the rim cool. 
 
 XVI. Quality of Steam. — When ordinary saturated steam is used, its 
 quality should be obtained by the use of a throttling calorimeter attached 
 to the main steam pipe near the throttle valve. When the steam is super- 
 heated, the amount of superheating should be found by the use of a ther- 
 mometer placed in a thermometer-well filled with mercury, inserted in 
 the pipe. The sampling pipe for the calorimeter should, if possible, be 
 attached to a section of the main pipe having a vertical direction, with 
 the steam preferably passing upward, and the sampling nozzle should be 
 made of a half-inch pipe, having at least 20 Vs-in. holes in its perforated 
 surface. 
 
 XVII. Speed. — There are several reliable methods of ascertaining 
 the speed, or the number of revolutions of the engine crank-shaft per 
 minute. The most reliable method is the use of a continuous recording 
 engine register or counter, taking the total reading each time that the 
 general test data are recorded, and computing the revolutions per minute 
 corresponding to the difference in the readings of the instrument. When 
 the speed is above 250 revolutions per minute, it is almost impossible to 
 make a satisfactory counting of the revolutions without the use of some 
 form of mechanical counter. 
 
 XVIII. Recording the Data. — Take note of every event connected with 
 the progress of the trial whether it seems at the time to be important or 
 unimportant. Record the time of every event, and time of taking every 
 weight, and every observation. Observe the pressures, temperatures, 
 water heights, speeds, etc., every twenty or thirty minutes when the con- 
 
992 THE STEAM-ENGINE. 
 
 ditions are practically uniform, and at much more frequent intervals ir 
 the conditions vary. 
 
 XIX. Uniformity of Conditions. — In a test having for an object the 
 determination of the maximum economy obtainable from an engine, or 
 where it is desired to ascertain with special accuracy the effect of pre- 
 determined conditions of operation, it is important that all the condi- 
 tions under which the engine is operated should be maintained uniformly 
 constant. 
 
 XX. Analysis of Indicator Diagrams. — (a) Steam Accounted for by 
 the Indicator: The simplest method of computing the steam accounted 
 for by the indicator is the use of the formula, 
 
 M.E.P. ' 
 
 which gives the weight in pounds per indicated horse-power per hour. 
 In this formula the symbol " M.E.P. " refers to the mean effective pressure. 
 In multiple-expansion engines, this is the combined mean effective pres- 
 sure referred to the cylinder in question. C is the proportion of the stroke 
 completed at points on the expansion line of the diagram near the actual 
 cut-off or release; H the proportion of compression; and E the proportion 
 of clearance; all of which are determined from the indicator diagram. 
 Wc is the weight of one cubic foot of steam at the cut-off or release pressure; 
 and Wh the weight of one cubic foot of steam, at the compression pressure; 
 these weights being taken from steam tables. 
 
 Should the point in the compression curve be at the same height as the 
 point in the expansion curve, then Wc = Wh, and the formula becomes 
 
 (13,750 + M.E.P.) X (C - H) X Wc, 
 
 in which (C — H) represents the distance between the two points divided 
 by the length of the diagram. 
 
 When the load and all other conditions are substantially uniform, it is 
 unnecessary to work -up the steam accounted for by the indicator from all 
 the diagrams taken. Five or more sample diagrams may be selected and 
 the computations based on the samples instead of on the whole. 
 
 (6) Sample Indicator Diagrams: In order that the report of a test may 
 afford complete information regarding the conditions of the test, sample 
 indicator diagrams should be selected from those taken and copies ap- 
 pended to the tables of results. In cases where the engine is of the 
 multiple-expansion type these sample diagrams may also be arranged in 
 the form of a "combined" diagram. 
 
 (c) The Point of Cut-off: The term " cut-off" as applied to steam engines, 
 although somewhat indefinite, is usually considered to be at an earlier 
 point in the stroke than the beginning of the real expansion line. That 
 the cut-off point may be defined in exact terms for commercial purposes 
 as used in steam-engine specifications and contracts, the Committee 
 recommends that, unless otherwise specified, the commercial cut-off, which 
 seems to be an appropriate expression for this term, be ascertained as 
 follows: Through a point showing the maximum pressure during admis- 
 sion, draw a line parallel to the atmospheric line. Through the point on 
 the expansion line near the actual cut-off, referred to in Section XX (a), 
 draw a hyperbolic curve. The point where these two lines intersect is 
 to be considered the commercial cut-off point. The percentage is then 
 found by dividing the length of the diagram measured to this point, by 
 the total length of the diagram, and multiplying the result by 100. 
 
 The commercial cut-off, as thus determined, is situated at an earlier 
 point of the stroke than the actual cut-off used in computing the "steam 
 accounted for" bv the indicator and referred to in Section XX (a). 
 
 (d) Ratio of Expansion: The "commercial" ratio of expansion is the 
 auotient obtained bv dividing 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 volumes are those pertaining to the low-pressure cylinder and high- 
 pressure cvlinder, respectively. 
 
 The "ideal" ratio of expansion is the quotient obtained by dividing 
 the volume of the piston displacement by the volume of the steam at the 
 
RULES FOR CONDUCTING STEAM-ENGINE TESTS. 993 
 
 cut-off (the latter being referred to the throttle-valve pressure), less the 
 volume equivalent to that retained at compression. In a multiple-ex- 
 pansion engine, the volumes to be used are those pertaining to the low- 
 pressure cylinder and high-pressure cylinder, respectively. 
 | (e) Diagram Factor: The diagram factor is the proportion borne by 
 the actual mean effective pressure measured from the indicator diagram 
 [ to that of a diagram in which the various operations of admission, expan- 
 sion, release and compression are carried on under assumed conditions. 
 The factor recommended refers to an ideal diagram which represents the 
 maximum power obtainable from the steam accounted for by the indicator 
 t diagrams at the point of cut-off, assuming first that the engine has no 
 I clearance; second, that there are no losses through wire-drawing the 
 steam during either the admission or the release; third, that the expansion 
 line is a hyperbolic curve; and fourth, that the initial pressure is that of 
 the boiler and the back pressure that of the atmosphere for a non-con- 
 i densing engine, and of the condenser for a condensing engine. 
 
 In cases where there is a considerable loss of pressure between the boiler 
 1 and the engine, as where steam is transmitted from a central plant to a 
 i number of consumers, the pressure of the steam in the supply main should 
 j be used in place of the boiler pressure in constructing the diagrams. 
 
 XXI. Standards of Economy and Efficiency. — The hourly consumption 
 of heat, determined by employing the actual temperature of the feed 
 water to the boiler, as pointed out in Article IX of the Code, divided by 
 the indicated and brake horse-power, that is, the number of heat units 
 consumed per indicated and per brake horse-power per hour, are the stand- 
 ards of engine efficiency recommended by the Committee. The consump- 
 tion per hour is chosen rather than the consumption per minute, so as to 
 conform with the designation of time applied to the more familiar units 
 of coal and water measurement, which have heretofore been used. The 
 British standard, where the temperature of the feed water is taken as 
 that corresponding to the temperature of the back-pressure steam, allow- 
 ance being made for any drips from jackets or reheaters, is also included 
 in the tables. 
 
 It is useful in this connection to express the efficiency in its more scien- 
 tific form, or what is called the "thermal efficiency ratio." The thermal 
 efficiency ratio is the proportion which the heat equivalent of the power 
 developed bears to the total amount of heat actually consumed, as deter- 
 mined by test. The heat converted into work represented by one horse- 
 power is 1,980,000 foot-pounds per hour, and this divided by 778 equals 
 2545 British thermal units. Consequently, the thermal efficiency ratio 
 is expressed by the fraction 
 
 2545 -h B.T.U. per H.P. per hour. 
 
 XXII. Heat Analysis. — For certain scientific investigations, it is 
 useful to make a heat analysis of the diagram, to show the interchange of 
 heat from steam to cylinder walls, etc., which is going on within the cylin- 
 der. This is unnecessary for commercial tests. 
 
 XXIII. . Temperature- Entropy Diagram. — The study of the heat anal- 
 ysis is facilitated by the use of the temperature-entropy diagram in which 
 areas represent quantities of heat, the coordinates being the absolute 
 temperature and entropy. 
 
 XXIV. Ratio of Economy of an Engine to that of an Ideal Engine. — 
 The ideal engine recommended for obtaining this ratio is that which was 
 adopted by the Committee appointed by the Civil Engineers, of London, 
 to consider and report a standard thermal efficiency for steam engines. 
 This engine is one which follows the Rankine cycle, where steam at a con- 
 stant pressure is admitted into the cvlinder with no clearance, and after 
 the point of cut-off, is expanded adiabatically to the back pressure. In 
 obtaining the economy of this engine the feed water is assumed to be 
 returned to the boiler at the exhaust temperature. 
 
 The ratio of the economy of an engine to that of the ideal engine is 
 obtained by dividing the heat consumption per indicated horse-power per 
 minute for the ideal engine bv that of the actual engine. 
 
 XXV. Miscellaneous. — In the case of tests of combined engines and 
 boiler plants, where the full data of the boiler performance are to be deter- 
 mined, reference should be made to the directions given by the Boiler 
 Test Committee of the Society, Code of 1899. (See Vol. XXI, p. 34.) 
 
994 THE STEAM-ENGINE. 
 
 In testing steam pumping engines and locomotives in accordance with 
 the standard methods of conducting such tests, recommended by the 
 committees of the Society, reference should be made to the reports of those 
 committees in the Transactions, Volume XII, p. 530, and in Volume XIV, 
 p. 1312. 
 
 XXVI. Report of Test. — The data and results of the test should be 
 reported in tne manner and in the order outlined in one of the following 
 tables, the first of which gives a summary of all the data and results as 
 applied not only to the standard heat-unit test, but also to tests of com- 
 bined engine and boiler for determining all questions of performance, 
 whatever the class of service; the second refers to a short form of report 
 giving the necessary data and results for the standard heat test; and the 
 third to a short form of report for a feed-water test. 
 
 It is recommended that any report be supplemented by a chart in which 
 the data of the test are graphically presented. [Of the three forms of 
 report mentioned above, the second is given below.] 
 
 Data and Results of Standard Heat Test of Steam Engine. 
 
 Arranged according to the Short Form advised by the Engine Test Com- 
 mittee of the American Society of Mechanical Engineers. Code of 1902. 
 
 1. Made by of 
 
 on engine located at 
 
 to determine 
 
 
 2. Date of trial 
 
 3. Type and class of engine; also of condenser. . 
 
 Dimensions of main engine 
 
 (a) Diameter of cylinder in. 
 
 (b) Stroke of piston it. 
 
 (c) Diameter of piston rod in. 
 
 (d) Average clearance p.c. 
 
 (e) Ratio of volume of cylinder to 
 
 high-pressure cylinder 
 
 (/) Horse-power constant for one 
 pound mean effective pressure 
 and one revolution per minute 
 Dimensions and type of auxiliaries. . . . 
 
 1st Cyl. 2d Cyl. 3d Cyl. 
 
 Total Quantities, Time, etc. 
 
 6. Duration of test . hours 
 
 7. Total water fed to boilers from main source of supply lbs. 
 
 8. Total water fed from auxiliary supplies: 
 
 (a) 
 
 (6) 
 
 (c) 
 
 9. Total water fed to boilers from all sources. . 
 
 10. Moisture in steam or superheating near throttle p. c. or deg. 
 
 11. Factor of correction for quality of steam 
 
 T2. Total dry steam consumed for all purposes lbs. 
 
 Hourly Quantities. 
 
 13. Water fed from main source of supply lbs. 
 
 14. Water fed from auxiliary supplies: 
 
 (a) 
 
 (6) ■ 
 
 (c) 
 
 15. Total water fed to boilers per hour 
 
 1 6. Total dry steam consumed per hour 
 
 17. Loss of steam and water per hour due to drips from 
 
 main steam pipes and to leakage of plant 
 
 18. Net dry steam consumed per hour by engine and aux- 
 
 iliaries 
 
RULES FOR CONDUCTING STEAM-ENGINE TESTS. 995 
 
 Pressures and Temperatures (Corrected). 
 
 19. Pressure in steam pipe near throttle by gauge lbs. per sq. in. 
 
 20. Barometric pressure of atmosphere in ins. of mercury ins. 
 
 21. Pressure in receivers by gauge lbs. per sq. in. 
 
 22. Vacuum in condenser in inches of mercury ins. 
 
 23. Pressure in jackets and reheaters by gauge lbs. per sq. in. 
 
 24. Temperature of main supply of feed water deg. Fahr. 
 
 25. Temperature of auxiliary supplies of feed water: 
 
 (a) 
 
 (6) 
 
 (c) 
 
 26. Ideal feed-water temperature corresponding to pres- 
 
 sure of steam in the exhaust pipe, allowance being 
 
 made for heat derived from jacket or reheater drips . " 
 
 Data Relating to Heat Measurement. 
 
 27. Heat units per pound of feed water, main supply B.T.U. 
 
 28. Heat units per pound of feed water, auxiliary supplies: 
 
 (a) 
 
 (b) 
 
 (c) 
 
 29. Heat units consumed per hour, main supply 
 
 30. Heat units consumed per hour, auxiliary supplies: 
 
 (a) 
 
 (6) 
 
 (c) • . 
 
 31. Total heat units consumed per hour for all purposes. 
 
 32. Loss of heat per hour due to leakage of plant, drips, 
 
 etc " 
 
 33. Net heat units consumed per hour: 
 
 (a) By engine alone " 
 
 (6) By auxiliaries 
 
 34. Heat units consumed per hour by engine alone, reck- 
 
 oned from temperature given in line 26 
 
 Indicator Diagrams. 
 
 35. Commercial cut-off in per cent of stroke [Separate 
 
 36. Initial pressure, lbs. persq. in. above atmosphere . .. Columns 
 
 37. Back pressure at mid-stroke, above or below atmos- for each 
 
 phere, in lbs. per sq. in Cylinder.] 
 
 38. Mean effective pressure in lbs. per sq. in 
 
 39. Equivalent M.E.P. in lbs. per sq. in.: 
 
 (a) Referred to first cylinder 
 
 (6) Referred to second cylinder 
 
 (c) Referred to third cylinder • 
 
 40. Pressure above zero in lbs. per sq. in.: 
 
 (a) Near cut-off 
 
 (b) Near release 
 
 (c) Near beginning of compression 
 
 Percentage of stroke at points where pressures are 
 
 measured: 
 
 (a) Near cut-off 
 
 (&) Near release 
 
 (c) Near beginning of compression 
 
 41. Steam accounted for by indicator in (pounds per 
 
 I.H.P. per hour: (a) Near cut-off; (b) Near release. 
 
 42. Ratio of expansion: (a) Commercial; (6) Ideal 
 
 Speed. 
 
 43. Revolutions per minute rev. 
 
 Power. 
 
 44. Indicated horse-power developed by main-engine cylinders: 
 
 First cylinder H.P. 
 
 Second cylinder 
 
 Third cylinder 
 
 Total 
 
 45. Brake horse-power developed by engine 
 
996 THE STEAM-ENGINE. 
 
 Standard Efficiency and other Results * 
 
 46. Heat units consumed by engine and auxiliaries per hour: 
 
 (a) per indicated horse-power B.T.U. 
 
 (b) per brake horse-power 
 
 47. Equivalent standard coal in lbs. per hour: 
 
 (a) per indicated horse-power. .• lbs. 
 
 (b) per brake horse-power 
 
 48. Heat units consumed by main engine per hour corre- 
 
 sponding to ideal maximum temperature of feed 
 
 water given in line 26: 
 
 (a) per indicated horse-power B.T.U. 
 
 (6) per brake horse-power 
 
 40. Dry steam consumed per indicated horse-power per hour: 
 
 (a) Main cylinders including jackets lbs. 
 
 (b) Auxiliary cylinders • 
 
 (c) Engine and auxiliaries 
 
 50. Dry steam consumed per brake horse-power per hour: 
 
 (a) Main cylinders including jackets 
 
 (b) Auxiliary cylinders 
 
 (c) Engine and auxiliaries 
 
 51. Percentage of steam used by main-engine cylinders 
 
 accounted for by indicator diagrams, near cut-off 
 
 of high-pressure cylinder per cent. 
 
 Additional Data. 
 
 Add any additional data bearing on the particular objects of the test 
 or relating to the special class of service for which the engine is used. 
 Also give copies of indicator diagrams nearest the mean, and the corre- 
 sponding scales. 
 
 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 formulae 
 based partly upon theory and partly upon practice. The practice of 
 builders shows an exceeding diversity of opinion as to correct dimensions. 
 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 addi- 
 tional matter. In order to make a comparison of many of the formulae 
 they have been applied to the assumed cases of six engines of different 
 sizes, and in some cases this comparison has led to the construction of new 
 formulae. 
 
 [Note, 1909. Since the first edition of this book was published, in 
 1895, no satisfactory treatise on this entire subject has appeared, and 
 therefore the matter on pages 997 to 1020 has been left, in the revision 
 for the 8th edition, in practically its original shape. Two notable papers 
 on the subject, however, have appeared: 1, Current 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 ab- 
 stracted on pages 1021 and 1022.] 
 
 Cylinder. (Whitham.) — Length of bore = stroke + breadth of piston- 
 ring — 1/8 to 1/2 in.; length between heads = stroke + thickness of piston 
 + sum of clearances at both ends; thickness of piston = breadth of ring + 
 thickness of flange on one side to carry the ring 4- thickness of follower- 
 plate. 
 
 Thickness of flange or follower 3/ 8 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 Vs to 3/ 8 in. for roughness of castings and 1/1 6 to 
 1/8 in. for each working joint. Naval and other very fast-running engines 
 
 * The horse-power referred to above items 46-50 is that of the main 
 engine, exclusive of auxiliaries. 
 
DIMENSIONS OF PARTS OF ENGINES. 997 
 
 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. (Thurston.) — For engines of the older 
 types and under moderate steam-pressures, some builders have for many 
 years restricted the stress to about 2550 lbs. per sq. in. 
 
 t = apiD+ b (1) 
 
 is a common proportion; t, D, and b being thickness, diam., and a con- 
 stant added quantity varying from to 1/2, all in inches; pi is the initial un- 
 balanced steam-pressure, lbs. per sq. in. In this expression b is made 
 larger for horizontal than for vertical cylinders, as, for example, in large 
 engines 0.5 in the one case and 0.2 in the other, the one requiring reboring 
 more than the other. The constant a is from 0.0004 to 0.0005; the first 
 value for vertical cylinders, or short strokes; the second for horizontal 
 engines, or for long strokes. 
 
 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 lbs. per sq. in.; /, a constant multiplier, = thickness of 
 barrel + 0.25 in. 
 
 Thickness of metal of cylinder barrel or liner, not to be less than p X D 
 
 -*- 3000 when of cast iron * (2) 
 
 Thickness of cylinder-barrel = p X D -4- 5000 + 0.6 in (3) 
 
 Thickness of liner = 1.1 X/ (4) 
 
 Thickness of liner when of steel = p X D -*• 6000 + 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 Xf, if single 
 
 = 0.6 X/, if double 
 cylinder flange =1.4 X /. 
 
 " -cover-flange =1.3 X /. 
 
 " " valve-box flange = 1 . X /. 
 
 door-flange =0.9 X /. 
 
 " " face over ports =1.2 Xf. 
 
 " " " =1.0 X /, when there is a false- 
 
 face. 
 " false-face =0.8 Xf, when cast iron. 
 
 " " " =0.6 Xf, when steel or bronze. 
 
 Whitham gives the following from different authorities: 
 
 VanBuien:i t - - 0001 / ^2 +0 - 15v ^; • ■ ■ < 5 > 
 1 t= 0.03 VDp . . (6) 
 
 Tredgold: t = (D + 2.5) p-4-1900 (7) 
 
 Weisbach: t= 0.8 + 0.00033 pD (8) 
 
 Seaton: t= 0.5 + 0.0004 pD (9) 
 
 TTa «wp11 • ft=0. 0004 pD + i/ 8 (vertical) ; . . .(10) 
 
 nasweu. }£= 0.0005 pZ>+ i/ 8 (horizontal) . .(11) 
 
 Whitham recommends (6) where provision is made for the reboring, 
 and where ample strength and rigidity are secured, for horizontal or 
 vertical cylinders of large or small diameter; (9) for large cylinders using 
 steam under 100 lbs. gauge-pressure, and 
 
 t = 0.003 D Vp for small cylinders (12) 
 
 The following table gives the calculated thickness of cylinders of 
 engines of 10, 30, and 50 in. diam., assuming p the maximum unbalanced 
 pressure on the piston = 100 lbs. per sq. in. As the same engines will 
 be used for calculations of other dimensions, other particulars concerning 
 them are here given for reference. . 
 
 * When made of exceedingly good material, at least twice melted, 
 the thickness may be 0.8 of that given by the above rules. 
 
THE STEAM-ENGINE, 
 
 Dimensions, etc., of Engines. 
 
 Engine, No 1 and 2. 
 
 5 and 6. 
 
 Indicated horse-power I.H.P, 
 
 Diam. of cyl., in D 
 
 Stroke, feet L 
 
 Revs, per min r 
 
 Piston speed, ft. per min 5 
 
 Area of piston, sq. in a 
 
 Mean effective pressure M.E.P 
 
 Max. total unbalanced pressure P 
 
 Max. total pressure per sq. in p 
 
 50 
 
 10 
 
 1 ... 
 
 250 ... 
 
 500 
 
 78.54 
 
 42 
 
 7854 
 
 100 
 
 450 
 30 
 21/2 ... 
 130 
 650 
 706.86 
 32.3 
 70,686 
 100 
 
 1250 
 
 50 
 
 4 ... 8 
 
 90 ... 45 
 
 700 
 
 1963.5 
 
 30 . 
 
 196,350 
 
 100 
 
 The thickness of the cylinders of these engines, according to the first 
 eleven formuhe above quoted, ranges for engines 1 and 2 from 0.33 to 
 1.13 ins., for 3 and 4 from 0.99 to 2.00 ins., and for 5 and 6 from 1.56 to 
 3.00 ins. The averages of the 11 are, for 1 and 2, 0.76 in.; for 3 and 4, 
 1.48 ins.; for 5 and 6, 2.26 ins. 
 
 The average corresponds nearly to the formula t = 0.00037 Dp + 0.4 in. 
 A convenient approximation is t = 0.0004 Dp + 0.3 in., which gives for 
 
 Diameters 10 20 30 40 50 60 in. 
 
 Thicknesses 0.70 1.10 1.50 1.90 2.30 2.70in. 
 
 The last formula corresponds to a tensile strength of cast iron of 12,500 
 lbs., with a factor of safety of 10 and an allowance of 0.3 in. for reboring. 
 
 Cylinder-heads. — Thurston says: Cylinder-heads may be given a 
 thickness, at the edges and in the flanges, exceeding somewhat that of 
 the cylinder. An excess of not less than 25% is usual. It may be 
 thinner in the middle. Where made, as is usual in large, engines, of two 
 disks with intermediate radiating, connecting ribs or webs, that section 
 which is safe against shearing is probably ample. An examination of the 
 designs of experienced builders, by Professor Thurston, gave 
 
 t = Dp h- 3000 +1/4 inch, (1) 
 
 D being the diameter of that circle in which the thickness is taken. 
 
 Thurston also gives t = 0.005 D_Vp + 0.25 (2) 
 
 Marks gives t = 0.003 Vp (3) 
 
 He also says a good practical rule for pressures under 100 lbs. per sq. 
 in. is to make the thickness of the cylinder-heads 1 1/4 times that of the 
 walls; and applying- this factor to his formula for thickness of walls, or 
 0.00028 pD, we have 
 
 £ = 0. 00035 pD (4) 
 
 Whitham quotes from Seaton, 
 t = (pD + 500) -*• 2000, which is equal to 0.0005 pD + 0.25 inch . . (5) 
 
 Beaton's formula for cylinder bottoms, quoted above, is 
 t = 0.1/, in which /= 0.0002 pD + 0.85 in., or £ = 0.00022 pD +0.93 . (6) 
 
 Applying the above formulae to the engines of 10, 30, and 50 inches 
 diameter, with maximum unbalanced steam-pressure of 100 lbs. 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 
 the web is one of tension, and if there should be a nick or 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 
 
DIMENSIONS OF PARTS OF ENGINES. 999 
 
 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 lbs. 
 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 inches apart (Whitham). 
 
 Marks gives for number of bolts 6 = 0. 7854 D 2 p ■*- 5000 c, in which 
 c = area of a single bolt, p = boiler-pressure in lbs. per sq. in.; 5000 lbs. 
 is taken as the safe strain per sq. in. on the nominal area of the bolt. 
 
 Seaton says: Cylinder-cover studs and bolts, when made of steel, should 
 be of such a size that the strain in them does not exceed 5000 lbs. per 
 sq. in. When of less than 7/ 8 inch diameter it should not exceed 4500 lbs. 
 per sq. in. When of iron the strain should be 20% less. 
 
 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 lbs. 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 lbs. be 
 allowed per sq. in. of actual area at the root of the thread, 0.7854 D 2 p = 
 3927 6^; whence &s 2 = 0.0002 D 2 p; 
 
 b =0.0002 -~; s = 0.01414 D y £• For the three engines we have: 
 
 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. -5- 6_j 7 18 30 
 
 Diam. of bolts, s = 0.01414Dy/| 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 = (Dh-50)X^P + 1. 
 
 The thickness of front of piston near the boss =0.2 X x. 
 
 " rim = 0.17 X x. 
 
 back " = 0.18 X x. 
 
 boss around the rod =0.3 Xi. 
 
 flange inside packing-ring = . 23 X x. 
 
 '-' at edge =0.25 X x. 
 
 packing-ring =0.15 X x. 
 
 junk-ring at edge = . 23 Xx. 
 
 inside packing-ring =0.21 Xx. 
 
 at bolt-holes = . 35 Xx. 
 
 „, " metal around piston edge = . 25 Xx. 
 
 The breadth of packing-ring = . 63 X x. 
 
 depth of piston at center =1.4 Xx. 
 
 ' lap of junk-ring on the piston =0.45 Xx. 
 
 SDace between piston bodv and packing-ring =0.3 X x. 
 
 " diameter of junk-ring bolts =0.1 X x + 0.25 In. 
 
 " pitch of junk-ring bolts = 10 diameters. 
 
 " number of webs in the piston = (D 4- 20) -*■ 12. 
 
 " thickness of webs in the piston =0.18 X x. 
 
1000 
 
 THE STEAM-ENGINE. 
 
 Marks gives the approximate rule: Thickness of piston-head = \JlD, 
 in 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 eaual to 0.7 the diameter of the cylinder 
 X breadth of ring-face, should never exceed 200 lbs. 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, \JlD; long stroke 3.31 5.48 7.00 
 
 Marks, -\/lb; short stroke 3.94 6.51 8.32 
 
 Seaton, depth at center = 1.4a; 4.20 9.80 15.40 
 
 Seaton, breadth of ring = 0.63 x 1.89 4.41 6.93 
 
 Whitham, breadth of ring = 0.15 D 1.50 4.50 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 cylinders 
 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 Engines 
 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. + Vs inch, and the width = thickness + l/g inch. 
 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 
 made about 3/igin. 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. Unwin's formula makes the width of a 20 in. 
 ring W = 20 X 0.014+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. diam- 
 eter 3/ 4 in. is a popular and practical width, and 1/2 in. for cylinders of 
 that size and under. 
 
 E. R. McGahey, Machy., Feb., 1906, gives the following tables for sizes 
 of piston rings for cylinders 6 to 20 in., diameter. A = (outside diam. of 
 ring — bore of cylinder); B= thickness (radial) of equal section ring, or 
 least, thickness of eccentric ring; C = width of ring (axial); D = amount 
 cut out or lap; E = greatest thickness of eccentric ring. 
 
 Equal Section Rings. 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 A 
 
 5 /32 
 
 •V32 
 
 3/16 
 
 3/16 
 
 7/32 
 
 1/4 
 
 V4 
 
 9/32 
 
 9/3 > 
 
 5/16 
 
 H/32 
 
 H/32 
 
 3/8 
 
 13/32 
 
 13/32 
 
 B 
 
 1/4 
 
 9/3? 
 
 5/16 
 
 3/8 
 
 13/32 
 
 7/16 
 
 15/32 
 
 1/2 
 
 9 /l6 
 
 19/ 3 , 
 
 5/8 
 
 11/16 
 
 •74 
 
 3/4 
 
 1?/16 
 
 C 
 
 5/16 
 
 3/8 
 
 3/8 
 
 7/16 
 
 7/16 
 
 1/2 
 
 1/2 
 
 9 /l6 
 
 9/16 
 
 H/16 
 
 11/16 
 
 3/4 
 
 3/4 
 
 13/16 
 
 13/16 
 
 D 
 
 3V64 
 
 39/64 
 
 21/32 
 
 23/32 
 
 25/3, 
 
 27/32 
 
 7/8 
 
 15/16 
 
 1 
 
 H/16 
 
 11/8 
 
 13/16 
 
 11/4 
 
 '9/32 
 
 1 11/32 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1001 
 
 
 
 
 
 
 
 Eccentric Rings. 
 
 
 
 
 
 
 1 
 
 .2 
 Q 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 A 
 
 5/32 
 
 5 /32 
 
 3/16 
 
 3/16 
 
 7/32 
 
 1/4 
 
 1/4 
 
 9/32 
 
 9/32 
 
 5/16 
 
 H/32 
 
 U/32 
 
 3/8 
 
 13/32 
 
 13/32 
 
 B 
 
 3/16 
 
 7/32 
 
 V4 
 
 9/32 
 
 9 /32 
 
 5/16 
 
 H/32 
 
 3/8 
 
 13/32 
 
 7/16 
 
 15/32 
 
 15/32 
 
 1/2 
 
 17/32 
 
 9/16 
 
 C 
 
 5/16 
 
 3/8 
 
 3/8 
 
 Vl6 
 
 7/16 
 
 V2 
 
 1/2 
 
 9/16 
 
 9/16 
 
 H/16 
 
 11/16 
 
 3/4 
 
 3/4 
 
 13/16 
 
 13/16 
 
 D 
 
 35/64 
 
 39/64 
 
 21/32 
 
 23/32 
 
 25/32 
 
 27/32 
 
 7/8 
 
 15/16 
 
 I 
 
 U/16 
 
 U/8 
 
 13/16 
 
 H/4 
 
 19/32 
 
 1 H/32 
 
 E 
 
 9/32 
 
 5/16 
 
 H/32 
 
 3/8 
 
 13/32 
 
 7/16 
 
 15/32 
 
 1/2 
 
 9/16 
 
 5/8 
 
 H/16 
 
 H/16 
 
 3/4 
 
 13/16 
 
 7/8 
 
 Fit of Piston-rod into Piston. (Seaton.) — The most convenient 
 and reliable practice is to turn the piston-rod end with a shoulder of Vie 
 inch for small engines, and Vs 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/s in. between it and the shqulder for large pistons 
 and Vie 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 lbs. per sq. in. for iron, 7000 lbs., 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. — Unwin gives 
 
 d"=bD Vp, ......... (1) 
 
 in which D is the cylinder diameter in inches, p is the maximum unbal- 
 anced pressure in lbs. per sq. in., and the constant b = 0.0167 for iron, 
 and b = 0.0144 for steel. Thurston, from an examination of a con- 
 siderable number of rods in use, gives 
 
 -•-V^S-r* ' • •:• • • • < 2 > 
 
 (L in feet, D and d in inches), in which a = 10,000 and upward in the 
 various types of engines, the marine screw engines or ordinary fast engines 
 on shore are given the lowest values, while "low-speed engines" being 
 less liable to accident from shock are given a = 15,000, often. 
 
 Connections of the piston-rod to the piston and to the cross-head should 
 have a factor of safety of at least 8 or 10. Marks gives 
 
 d" = 0.0179 D y/ Pt for iron; for steel d" =0 r 0105 D^p; . . (3) 
 and d" = . 03901 $ ' DWp, for iron; for steel d"=0 , 03525 ^D 2 l 2 p, . (4) 
 in which I is the length of stroke, all dimensions in inches. Deduce the 
 diameter of piston-rod by (3), and if this diameter is less than 1/12 1, then 
 use (4). 
 
 _ . . t-.. „ . . , Diameter of cvlinder ._ 
 Seaton gives: Diameter of piston-rod = =, — -v/p 
 
 The following are the values of F: 
 
 Naval engines, direct-acting F = 60 
 
 return connecting-rod, 2 rods -.-... F — 80 
 
 Mercantile ordinary stroke, direct-acting ...... F = 50 
 
 long " " F = 48 
 
 very long " •" F = 45 
 
 '* medium stroke, oscillating F = 45 
 
 Note. — Long and very long, as compared with the stroke usual for 
 the power of engine or size of cylinder. 
 
1002 
 
 THE STEAM-ENGINE. 
 
 In considering an expansive engine, p, the effective pressure, should be 
 taken as the absolute working pressure, or 15 lbs. 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 lbs., 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 lbs., or the maximum absolute pressure 
 which can be got in the receiver, or about 25 lbs. It is an advantage to 
 make all the rods of a compound engine alike, and this is now the rule. 
 
 Applying the above formulae to the engines of 10, 30, and 50 in. diam- 
 eter, both short and long stroke, we have: 
 
 Diameter of Piston-rods. 
 
 
 
 
 
 10 
 
 30 
 
 50 
 
 
 
 
 12 
 
 1.67 
 1.44 
 
 1.13 
 
 24 
 1.67 
 1.44 
 
 1.40 
 1.91 
 1.73 
 
 2.22 
 
 30 
 5.01 
 4.32 
 
 3.12 
 
 5.37 
 3.70 
 (3.15) 
 3.34 
 5.01 
 
 60 
 5.01 
 4.32 
 
 3.88 
 5.37 
 5.13 
 
 4.72 
 6.67 
 
 48 
 8.35 
 7.20 
 
 5.10 
 
 8.95 
 6.04 
 
 (5.25) 
 5.46 
 8.35 
 
 96 
 
 Unwin, iron, .0167 D Vp 
 
 8.35 
 
 Unwin, steel, 0.0144 D "^p 
 
 7 20 
 
 Thurston y'^g + l (Lin feet).... 
 
 6 35 
 
 Marks iron 0179 D ^p 
 
 1.79 
 1.35 
 (1.05) 
 1.22 
 1.67 
 
 8.95 
 
 Marks, iron 03901 -\j D-Pp 
 
 8.54 
 
 Marks, steel, 0.0105 D ^p 
 
 
 Marks, steel, 0.03525 ^J D 2 l 2 p 
 
 7 72 
 
 
 
 60 
 
 11.11 
 
 
 
 
 
 1.49 
 
 1.82 
 
 4.30 
 
 5.26 
 
 7.11 
 
 8 74 
 
 
 
 The figures in parentheses opposite Marks's third formula would be re- 
 jected since they are-less than i/s of the stroke, and the figures derived 
 by his fourth formula would be taken instead. The figure 1.79 opposite 
 his first formula would be rejected for the engine of 24-inch stroke. 
 
 An empirical formula which gives results approximatin g th e above 
 averages is d" = 0.0145 "^ Dip for short stroke and 0.013 *^Dlp for long 
 stroke engines. 
 
 The calculated results for this formula, for the six engines, are, re- 
 spectively, 1.58, 2.02,4.35, 5.52, 7.10, 9.01. 
 
 Piston-rod Guides. — The thrust on the guide, when the connecting- 
 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, 0, 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 . 258 . 204 . 169 
 
 Secant of the angle 1 . 0327 1 . 0206 1 . 014 
 
 Seaton says: The area of the guide-block or slipper surface on which the 
 thrust is taken should in no case be less than will admit of a pressure of 
 400 lbs., on the square inch; and for good working those surfaces which 
 take the thrust when going ahead should be sufficiently large to prevent 
 
DIMENSIONS OF PARTS OF ENGINES 1003 
 
 the maximum pressure exceeding 100 lbs. per sq. in. When the surfaces 
 are kept well lubricated this allowance may be exceeded. 
 
 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 intensity 
 of pressure on the guide in lbs. per sq. in., p V < 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 -*- V. According to Rankine, for loco- 
 
 44 goo 
 motives, p = ' , where p is the pressure in lbs. 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 lbs. per square 
 inch. 
 
 For a mean velocity of 600 feet per minute, Prof. Thurston's formulas 
 give, p < 100, p > 66.7; Rankine's gives p = 72.2 lbs. per sq. in. 
 Whitham gives, 
 
 --,.-. • , P 0.7854 d 2 p\ 
 
 A = area of slides in square inches = - — == . 
 
 Po^n 2 - 1 po^n 2 - 1 
 
 in which P = total unbalanced pressure, p\ = pressure per square inch 
 on piston, d = diameter of cylinder, p = pressure allowable per square 
 inch on slides, and n = length of connecting-rod -s- length of crank. 
 This is equivalent to the formula, A = P tan -r- p . For n = 5, pi = 
 100 and p = 80, A = . 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 lbs. 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 lbs. 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 lbs. per sq. in. of slide, on account of the inaccessi- 
 bility of the slide, dirt, cinder, etc. 
 
 There is perfect agreement among the authorities as to the formula for 
 area of the slides, A = P tan 9 -f- p p ; but the value given to p , the allow- 
 able pressure per square inch, ranges all the way from 35 lbs. to 500 lbs. 
 
 The Connecting-rod. Ratio of length of connecting -rod to length of 
 stroke. — Experience has led generally to the ratio of 2 or 21/2 to 1, the 
 latter giving a long and easy-workinsr rod, the former a rather short, but 
 yet a manageable one (Thurston). Whitham gives the ratio of from 2 to 
 41/2, and Marks from 2 to 4. 
 
 Dimensions of the Connecting-rod. — The calculation of the diameter 
 of a connecting-rod on a theoretical basis, considering it as a strut subject 
 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. Empiri- 
 cal formulas are as follows: For circular rods, largest at the middle, Z> = 
 diam. of cylinder, I = length of connecting-rod in inches, p = maximum 
 steam-pressure, lbs. per sq. in. 
 
 (1) Whitham, diam. at middle, d" = 0.0272 ^ Dl ^p. 
 
 (2) Whitham, diam. at necks, d" =1.0 to_l.l X diam. of piston-rod. 
 
 (3) Sennett, diam. at middle, d" = D Vp-J-55. 
 
 (4) Sennett, diam. at necks, d" == D Vp-r-60. 
 
 (5) Marks, diam., d"=0.0179 D "S p, if dia m. is greater than 1/24 length. 
 
 (6) Marks, diam., d" = 0.02758 ^ Dl ^p, if diam. found by (5) is less 
 than 1/24 length. 
 
 (7) Thurston, diam., at middle, d" = a A vDL A ^ / p+ C, D in inches, 
 L in feet, a = 0.15 and C = 1/2 inch for fast engines, a = 0.08 and C = 3/ 4 
 inch for moderate speed. 
 
 (8) Seaton says: The rod may be considered as a strut free at both 
 ends, and, calculating its diameter accordingly, 
 
 diameter at middle = V/2 (1 + 4 ar 2 ) -=- 48.5, 
 
1004 
 
 THE STEAM-ENGINE. 
 
 where R = the total load on piston P multiplied by the secant of the 
 maximum angle of obliquity of the connecting-rod. 
 
 For wrought iron and mild steel a is taken at 1/3000. The following are 
 the values of r in practice: 
 
 Naval engines — Direct-acting r = 9 to 11; 
 
 Return connecting-rod r = 10 to 13, old; 
 Return connecting-rod r = 8 to 9, modern; 
 Trunk r = 11.5 to 13. 
 
 Mercantile " Direct-acting, ordinary r = 12. 
 
 Mercantile " Direct-acting, long stroke r = 13 to 16. 
 
 (9) The following empirical formula is given by Seaton as agreeing 
 closely with good modern practice: 
 
 Diameter of connecting- rod at middle = ^IK h- 4, I = le ngth of rod 
 in inches, and K = 0.03 v effective load on piston in pounds. 
 The diam. at the ends may be 0.875 of the diam. at the middle. 
 Seaton's empirical formula when translated into terms of D and p 
 
 is the same as the second one by Marks, viz., d" = 0.02758 vDJ Vp. 
 Whitham's (1) is also practically the same. 
 
 (10) Taking Seaton's more complex formula, with length of connecting- 
 rod = 2.5 X length of stroke, and r_= 12 and 16, respectively, it reduces 
 to: Diam. at middle = 0.02294 Vp and 0.0241iv / p for short and long 
 stroke engines, respectively. 
 
 Applying the above formulas to the engines of our list, we have 
 
 Diameter of Connecting-rods. 
 
 
 
 
 
 10 
 
 30 
 
 50 
 
 
 
 
 12 
 30 
 
 1.82 
 
 1.79 
 
 24 
 60 
 
 1.82 
 
 2.14 
 
 2.54 
 2.67 
 2.14 
 
 30 
 75 
 
 5.46 
 
 5.37 
 
 7.00 
 
 7.97 
 6.09 
 
 60 
 150 
 
 5.46 
 
 5.85 
 
 5.65 
 7.97 
 6.41 
 
 48 
 120 
 
 9.09 
 
 8.95 
 
 11.11 
 
 13.29 
 10.16 
 
 96 
 
 
 240 
 
 (3) d"=^v / p = 0.0182 D^p 
 
 9.09 
 
 (5) d"-0 0179£) Vp~ 
 
 
 (6) d"~ 02758 \/ Dl ^p 
 
 9.51 
 
 (7) d"- 0.15 ^DL ~fp+ 1/2 
 
 2.87 
 
 
 (7) d"-0.08'V / DL'V / p+3/4........... 
 
 8.75 
 
 (9) d"~ 0.03 Vp 
 
 2.67 
 2.03 
 
 13 29 
 
 (10) d" = 0.02294 Vp ; 0.02411 Vp 
 
 10.68 
 
 
 2.24 
 
 2.26 
 
 6.38 
 
 6.27 
 
 10.52 
 
 10.26 
 
 
 
 Formulae 5 and 6 (Marks), and also formula 10 (Seaton), give the 
 larger diameters for the long-stroke engine; formulae 7 give the larger 
 diameters for the short-stroke engines. 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 same, yet in an engine generally the shorter 
 the connecting-rod the greater the number of revolutions, and conse- 
 quently 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 "^v. 
 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 = . 7854 D 2 p, the formula is equivalent to d" = . 0237 \ZP. 
 
DIMENSIONS OF PARTS OF ENGINES. 1005 
 
 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 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 calculation 
 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 pull 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. Between 
 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 crosshead end to the crank-pin end. According to Grashof, the 
 bending action on the rod due to its inertia is greatest at 6/ 10 the length 
 from the crosshead 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 furnishes the author with the following rule for 
 tapered connecting-rod of rectangular section: Take the section as com- 
 puted by the formula d" = 0.1 V DL V/? + 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, mu ltiplyin g L by 4/ 3 , and changing it to I 
 
 in inches, it becomes d = 1/30 '^Dl ^p 4- 3/ 4 in. Taking a rectangular 
 section of the same area as the round section whose diameter is d, 
 and making the depth of the section h = twice the thickness t, we have 
 
 0.7854 d* = ht = 2 P, whence t = 0.627, d = 0.0209 ^ Dl Vp + 0.47 in., 
 which is the formula for the thickness or distance between the parallel 
 sides of the rod. Making the depth at the crosshead 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 
 12 
 30 
 
 1.61 
 2.42 
 3.62 
 
 30 
 30 
 75 
 
 3.60 
 5.41 
 8.11 
 
 50 
 
 48 
 
 
 120 
 
 Thickness,* - 0209 V Dl V^ + 0.47= 
 
 5.59 
 
 
 8.39 
 
 
 12.58 
 
 
 
 The thicknesses t, found by the formula t = 0.0209 V Dl Vp + 0.47, 
 
 aerree 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 
 inches. 
 
 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 the effectiveness of 
 
1006 THE STEAM-ENGINE. 
 
 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 gives I = . 0000247 fpND* = 1.038/ (I.H.P.) + L . (1) 
 Whitham gives I = 0.9075/. (I.H.P.) -=- L (2) 
 
 in which I = length of crank-pin journal in inches,/ == coefficient of fric- 
 tion, which may be taken at 0.03 to 0.05 for perfect lubrication, and 
 0.08 to 0.10 for imperfect; p = mean pressure in the cylinder in pounds 
 per square inch; D = diameter of cylinder in inches; N = number of single 
 strokes per minute; I.H.P. = indicated horse-power; L = length of stroke 
 in feet. These formulae are independent of the diameter of the pin, and 
 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. Both of the above formulae are deduced 
 empirically from dimensions of crank-pins of existing marine engines. 
 Marks says that about one-fourth the length required for crank-pins of 
 propeller engines will serve for the pins of side-wheel engines, and one- 
 tenth for locomotive engines, making the formula for locomotive crank- 
 pins I = 0.00000247 fpND*, or if p = 150, / = 0.06, and N == 600, I = 
 O.013D 2 . 
 
 Whitham recommends for pressure per square inch of projected area, 
 for naval engines 500 pounds, for merchant engines 400 pounds, for 
 paddle-wheel engines 800 to 900 pounds. 
 
 Thurston says the pressure should, in the steam-engine, never exceed 
 500 or 600 pounds per square inch for wrought-iron pins, or about twice 
 that figure for steel. He gives the formula for length of a steel pin, in 
 inches, 
 
 I = PR -s- 600,000, (3) 
 
 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. Where iron is used this figure should be reduced to 
 300,000 and 250,000 for the two cases taken. Pins so proportioned, if 
 well made and well lubricated, 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. 
 
 Thurston also says: The size of crank-pins required to prevent heating 
 of the journals may be determined with a fair degree of precision by 
 either of the formulae given below: 
 
 I = P(V + 20) -*- 44,800 d (Rankine, 1865); ... (4) 
 
 I = PV -5- 60,000 d (Thurston, 1862); (5) 
 
 I = PN - 350,000 (Van Buren, 1866) (6) 
 
 The first two formulae give what are considered by their authors fair 
 working proportions, and the last gives minimum length for iron pins. 
 (V = velocity of rubbing surface in feet per minute.) 
 
 Formula (1) was obtained by observing locomotive practice in which 
 great liability exists of annoyance by dust, and great risk occurs from 
 inaccessibility while running, and (2) by observation of crank-pins of 
 naval screw-engines. The first formula is therefore not well suited for 
 marine practice. 
 
 Steel can usually be worked at nearly double the pressure admissible 
 with iron running at similar speed. 
 
 Since the length of the crank-pin will be directly as the power expended 
 upon it and inversely as the pressure, we may take it as 
 
 I = a (I.H.P.) -r L (7) 
 
 in which a is a constant, and L the stroke of piston, in feet. The values 
 of the constant, as obtained by Mr. Skeel, are about as follows: a = 0.04 
 where water can be constantly used; a = 0.045 where water is not gen- 
 erally used; a = 0.05 where water is seldom used; a = 0.06 where water 
 is never needed, Unwin gives 
 
 I = a (I.H.P.) -*- r (8) 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1007 
 
 in which r = crank radius in inches, a = 0.3 to a == 0.4 for iron and for 
 marine engines, and a = . 066 to a = . 1 for the case of the best steel 
 and for locomotive work, where it is often necessary to shorten up out- 
 side pins as much as possible. 
 
 J. B. Stanwood {Eng'g, June 12, 1891), in a table of dimensions of 
 parts of American Corliss engines from 10 to 30 inches diameter of cylin- 
 der, gives sizes of crank-pins which approximate closely to the formula 
 
 I = 0.275 D"+ 0.5 in.; d = 0.25D" (9) 
 
 By calculating lengths of iron crank-pins for the engines 10, 30, and 
 50 inches diameter, long and short stroke, by the several formulae above 
 given, 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. 
 Nos. (4), (5), and (6) give lengths much greater than the others. Marks 
 (1), Whitham (2), Thurston (7), I = 0.06 I.H.P. -^ L, and Unwin (8), 
 I = 0.4 I.H.P.-*- r, give results which agree more closely. 
 
 The calculated lengths of iron crank-pins for the several cases by 
 formulae (1), (2), (7), and (8) are as follows: 
 
 Length of Crank-pins. 
 
 Diameter of cylinder D 
 
 Stroke L (ft.) 
 
 Revolutions per minute R 
 
 Horse-power I.H.P. 
 
 Maximum pressure lbs. 
 
 Mean pressure per cent of max 
 
 Mean pressure P. 
 
 Length, of crank-pin: 
 
 (1) Whitham, 1 = 0.9075 x. 05 I.H.P. -5- L 
 
 (2) Marks, i= 1 .038 x .05 I.H.P. h-L 
 
 (7) Thurston, 1=0. 06 I.H.P. + L.. 
 
 (8) Unwin, 1 = 0.4 I.H.P. s-r. . . 
 (8) Unwin, 1=0.3 I.H.P. -*-r.,. 
 
 Average 2 . 72 
 
 10 
 
 10 
 
 30 
 
 30 
 
 50 
 
 1 
 
 2 
 
 21/-, 
 
 5 
 
 4 
 
 250 
 
 \ti 
 
 130 
 
 65 
 
 90 
 
 50 
 
 50 
 
 450 
 
 450 
 
 1,250 
 
 7,854 
 
 7,854 
 
 70,686 
 
 70,686 
 
 196,350 
 
 42 
 
 42 
 
 32.3 
 
 32.3 
 
 30 
 
 3,299 
 
 3,299 
 
 22,832 
 
 22,832 
 
 58,905 
 
 2 18 
 
 1.09 
 
 8.17 
 
 4.08 
 
 14.18 
 
 2 59 
 
 1.30 
 
 9.34 
 
 4.67 
 
 16.22 
 
 3.00 
 
 1.50 
 
 10.80 
 
 5.40 
 
 18.75 
 
 3.33 
 
 1.67 
 
 12.0 
 
 6.0 
 
 20.83 
 
 2.50 
 
 1.25 
 
 9.0 
 
 4.5 
 
 15.62 
 
 2.72 
 
 1.36 
 
 9.86 
 
 4.93 
 
 17.12 
 
 50 
 8 
 
 45 
 
 1,250 
 196,350 
 
 30 
 58,905 
 
 7.09 
 8.11 
 9.38 
 10.42 
 7.81 
 
 (8) Unwin, best steel, 1=0.] I.H.P. + 
 (3) Thurston, steel, 1= PR -h 600,000 . 
 
 83 0.42 3.0 1.5 5.21 
 • 1.37 0.69 4.95 2.47 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 its extremity, and, equating its moment with that of the resistance 
 of the pin, 
 
 V2Pl=V32tnd\ and d = V/^y^> 
 
 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 lbs. For steel the diameters found by 
 this formula may be reduced 10%. (Thurston.) 
 Unwin gives the same formula in another form, viz.: 
 
 r^Sf^K-VrV' 
 
 the last form to be used when the ratio of length to diameter is assumed. 
 For wrought iron, t = 6000 to 9000 lbs. per sq. in., 
 
 yb.l/t= 0.0947 to 0.0827; ^5.1/t = 0.0291 to 0.0238. 
 For steel, t = 9000 to 13,000 lbs. per sq. in., 
 
 ^5jjt = 0.0827 to 0.0723; ^5.1/t = 0.0238 to 0.0194. 
 
1008 
 
 THE STEAM-ENGINE. 
 
 Whitham gives d = 0.0327 f/Pl = 2.1058 fy X I.H.P. + LR for 
 strength, and d = 0.0405 *\JPl 3 for rigidity, and recommends that the 
 diameter be calculated by both formulae, and the largest result taken. 
 The first is the same as Unwin's formula, with t taken at 9000 lbs. per sq. 
 in. The second is based upon an arbitrary assumption of a deflection of 
 V300 in. at the center of pressure (one-third of the length from the free 
 end). 
 
 Marks, calculating the diameter for rigidity, gives 
 
 d = 0.066 \ft 
 
 2 = 0.945 <^(H.P.)Z» + 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 the average lengths of the crank-pins already found, we have 
 the following for our six engines: 
 
 Diameter of Crank-pins. 
 
 Diameter of cylinder. . . 
 
 Stroke, ft 
 
 Length of crank-pin. . . . 
 
 Unwin, d = u — '— — . . . 
 Marks, d= 0.066 $pl a D< 
 
 10 
 
 1 
 
 2.72 
 
 10 
 
 2 
 1.36 
 
 30 
 
 21/2 
 9.86 
 
 30 
 5 
 
 4.93 
 
 50 
 
 4 
 
 17.12 
 
 2.29 
 
 1.82 
 
 7.34 
 
 5.82 
 
 12.40 
 
 1.39 
 
 0.85 
 
 6.44 
 
 3.78 
 
 12.41 
 
 50 
 
 8 
 
 8.56 
 
 9.84 
 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: 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 
 10 
 1 
 
 3,299 
 6.23 
 3.78 
 530 
 
 873 
 
 10 
 
 2 
 3,299 
 2.36 
 1.16 
 
 1,398 
 
 2,845 
 
 30 
 
 21/2 
 22,832 
 72.4 
 63.5 
 315 
 360 
 
 30 
 5 
 22,832 
 28.7 
 18.6 
 796 
 1,228 
 
 50 
 4 
 58,905 
 212.3 
 212.5 
 277 
 277 
 
 50 
 
 
 8 
 
 
 58,905 
 
 
 84.2 
 
 
 63.3 
 
 Pressure per square inch, Unwin 
 
 Pressure per square inch, Marks 
 
 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 
 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: 
 
DIMENSIONS OF PARTS OF ENGINES. 1009 
 
 Engine No 12 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. — Whitham says the bearing surface 
 for the wrist-pin is found by the formula for crank-pin design. Seaton 
 says the diameter at the middle must, of course, be sufficient to withstand 
 the bending action, and generally from this cause ample surface is provided 
 for good working; but in any case the area, calculated by multiplying the 
 diameter of the journal by its length, should be such that the pressure 
 does not exceed 1200 lbs. per sq. in., taking the maximum load on the 
 piston as the total pressure on it. 
 
 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 lbs. 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 lbs. per sq. in. and making the 
 length of the crosshead-pin = 4/3 of its diameter, we have d= Vp-f- 40, Z = 
 Vp-8- 30, in which P = maximum total load on piston in lbs., d = diam. 
 and 1= length of pin in inches. For the engines of our example we have: 
 
 Diameter of piston, inches 10 30 50 
 
 Maximum load on piston, lbs 7854 70,686 196,350 
 
 Diameter of crosshead-pin, inches 2 . 22 6 . 65 1 1 . 08 
 
 Length of crosshead-pin, inches 2.96 8.86 14.77 
 
 Stanwood's rule gives diameter, ins 1 . 8 to 2 5 . 4 to 6 9 . 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., lbs 1309 1329 1309 
 
 Which 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, 
 
 D fab* , aX& 2 T 67 , 4 /6T 
 
 If a crank-arm were constructed so that b varied as Vx (as given by 
 the above rule) it would be of such a curved form as to be inconvenient 
 to manufacture, and consequently it is customary in practice to find the 
 maximum value of b and draw tangent lines to the curve at the points; 
 these lines are generally, for the same reason, tangential to the boss of 
 the crank-arm at the shaft. 
 
 The shearing strain is the same throughout the crank-arm; and, con- 
 sequently, is large compared with the bending strain close to the crank- 
 in; and so it is not sufficient to provide there only for bending strains, 
 'he section at this point should be such that, in addition to what is given 
 by the calculation from the bending moment, there is an extra square 
 inch for every 8000 lbs. of thrust on the connecting-rod (Seaton). 
 
 The length of the boss h into which the shaft is fitted is from 0.75 to 
 1.0 of the diameter of the shaft D, and its thickness e must be calculated 
 from the twisting strain PL. (L = length of crank.) 
 
 For different values of length of boss h, the following values of thick- 
 ness of boss e are given by Seaton: 
 
 When h = D, then e = . 35 D ; if steel, . 3. 
 h = 0.9 D, thene = 0.38 D; if steel, 0.32. 
 h = 0.8 D, then e = 0.40 D; if steel, 0.33. 
 h = 0.7 D, then e = 0.41 D; if steel, 0.34. 
 
 Pi 
 T 
 
1010 
 
 THE STEAM-ENGINE. 
 
 The crank-eye or boss into which the pin is fitted should bear the same 
 relation to the pin that the boss does to the shaft. 
 
 The diameter of the shaft-end onto which the crank is fitted should be 
 1.1 X diameter of shaft. 
 
 Thurston says: The empirical proportions adopted by builders will 
 commonly be found to fall well within the calculated safe margin. These 
 proportions are, from the practice of successful designers, about as follows: 
 
 For the wrought-iron crank, the hub is 1.75 to l.S times the least 
 diameter of that part of the shaft carrying full load; the eye is 2.0 to 2.25 
 the diameter of the inserted portion of the pin, and their depths are, 
 for the hub, 1.0 to 1.2 the diameter of shaft, and for the eye, 1.25 to 1.5 
 the diameter of pin. The web is made 0.7 to 0.75 the width of adjacent 
 hub or eye, and is given a depth of 0.5 to 0.6 that of adjacent hub or 
 eye. 
 
 For the cast-iron crank the hub and eye are a little larger, ranging in 
 diameter respectively from 1.8 to 2 and from 2 to 2.2 times the diameters 
 of shaft and pin. The flanges are made at either end of nearly the full 
 depth of hub or eye. Cast iron has, however, fallen very generally into 
 disuse. 
 
 The 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 diam- 
 eter of 0.2% will usually suffice; and a common rule of practice gives an 
 allowance of but one-half of this, or 0.1%. 
 
 The 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 
 
 Stroke S, ins 
 
 Max. pressure on pin P 
 
 (approx.) , lbs 
 
 Diam. crank-pin d 
 
 Dia. shaft, a y -^ — '-, D 
 (a = 4.69, 5.09 and 5.22)... 
 
 Length of boss, 0.8 D 
 
 Thickness of boss, 0.4 D. . . 
 
 Diam. of boss, I.8D 
 
 Length crank-pin eye, 0.8 d 
 Thickness of crank-pin eye, 
 
 0.4d 
 
 Max. mom. T at distance 
 
 V2S— 1/2 D from center of 
 
 pin, inch-lbs 
 
 Thickness of crank-arm a = 
 
 0.75 D 
 
 Greatest b readth, 
 
 b= \/6 T + 9000 a 
 Min. mom. T at distance 
 
 dfrom center of pin= Pd 
 Least breadth, 
 
 &! = V6 T - 9000 a 
 
 10 
 
 12 
 
 10 
 
 24 
 
 30 
 30 
 
 30 
 60 
 
 50 
 
 48 
 
 7854 
 2.10 
 
 7854 
 2.10 
 
 70,686 
 7.34 
 
 70,686 
 5.58 
 
 196,350 
 12.40 
 
 k.74 
 
 3.46 
 
 7.70 
 
 9.70 
 
 12.55 
 
 J 
 2.19 
 1.10 
 4.93 
 1.76 
 
 2.77 
 1.39 
 6.23 
 1.76 
 
 6.16 
 3.08 
 13.86 
 5.87 
 
 7.76 
 3.88 
 17.46 
 4.46 
 
 10.04 
 5.02 
 
 22.59 
 9.92 
 
 0.88 
 
 0.88 
 
 2.94 
 
 2.23 
 
 4.46 
 
 37,149 
 
 80,661 
 
 788,149 
 
 1,848,439 
 
 3,479,322 
 
 2.05 
 
 2.60 
 
 5.78 
 
 7.28 
 
 9.41 
 
 3.48 
 
 4.55 
 
 9.54 
 
 13.0 
 
 15.7 
 
 16,493 
 
 16,493 
 
 528,835 
 
 394,428 
 
 2,434,740 
 
 2.32 
 
 2.06 
 
 7.81 
 
 6.01 
 
 13.13 
 
 50 
 96 
 
 196,350 
 8.87 
 
 12.65 
 6.32 
 
 28.47 
 7.10 
 
 3.55 
 
 7,871,671 
 11.87 
 21.0 
 
 1,741,625 
 9.89 
 
 The Shaft. — Twisting Resistance. — From the general formula 
 for torsion, we have: T = ^d s S = 0.19635 d s S, whence d = t/^4p' 
 
 16 
 
 in which T = torsional moment in inch-pounds, d = diameter in inches, 
 and S = the shearing resistance of the material in pounds per square 
 inch, 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1011 
 
 If a constant force P were applied to the crank-pin tangentially to its 
 path, the work done per minute would be 
 
 PXLX2tz + 12XR = 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 = I.H.P. ■*■ R X 63,025. Therefore 
 
 d = yj 5 . 1 T -*- S = ^321,427 I.H.P. -5- US. 
 
 This may take the form 
 
 d = ^I.H.P. X FIR, or d = a \/l.H.P. -s- R, 
 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 5 6 810 
 
 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 lbs., 
 steel 13,500 lbs., and cast iron 4500 lbs., 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 lbs., and when the shafts are more than 10 inches diameter, 
 8000 lbs. Steel, when made from the ingot and of good materials, will 
 admit of a stress of 12,000 lbs. for small shafts, and 10,000 lbs. 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 hamm ering failing to affect it. 
 
 The formula d = a -\/l.H.P. -f- 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: 
 
 Description of Engine. 
 
 Steam Cut-off 
 at 
 
 Max. 
 
 Twist 
 
 Divided 
 
 by 
 
 Mean 
 
 Twist. 
 Moment. 
 
 Cube 
 Root 
 of the 
 Ratio. 
 
 
 0.2 
 0.4 
 0.6 
 0.8 
 0.2 
 0.3 
 0.4 
 0.5 
 0.6 
 0.7 
 0.8 
 h.p. 0.5, l.p.0.66 
 
 2.625 
 2.125 
 1.835 
 1.698 
 1.616 
 1.415 
 1.298 
 1.256 
 1.270 
 1.329 
 1.357 
 1.40 
 
 1.26 
 
 1.38 
 
 
 1.29 
 
 «i (i 
 
 1.22 
 
 « a 
 
 1.20 
 
 Two-cylinder expansive, cranks at 90° 
 
 Three-cylinder compound, cranks 120° 
 
 Three-cylinder compound, l.p. cranks op- ) 
 posite one another, and h.p. midway j 
 
 1.17 
 1.12 
 1.09 
 1.08 
 1.08 
 1.10 
 1.11 
 1.12 
 
 1.08 
 
1012 THE STEAM-ENGINE. 
 
 Seaton also gives the following rules for ordinary practice for ordinary 
 
 two-cylinder marine engines: 
 
 Diameter of the tunnel-shafts = -^I.H.P. X F/2?,ora ^I.H.P. + R. 
 Compound engines, cranks at right angles: 
 
 Boiler pressure 70 lbs., rate of expansion 6 to 7, F = 70, a = 4.12. 
 
 Boiler pressure 80 lbs., rate of expansion 7 to 8, F = 72, a = 4.16. 
 
 Boiler pressure 90 lbs., rate of expansion 8 to 9, F = 75, a = 4.22. 
 
 Triple compound, three cranks at 120 degrees: 
 
 Boiler pressure 150 lbs., rate of expansion 10 to 12, F = 62, a = 3.96, 
 Boiler pressure 160 lbs., rate of expansion 11 to 13, F = 64, a = 4. 
 Boiler pressure 170 lbs., rate of expansion 12 to 15, F = 67, a = 4.06. 
 
 Expansive engines, cranks at right angles, and the rate of expansion 5, 
 boiler-pressure 60 lbs., F = 90, a = 4.48. 
 
 Single-crank compound engines, pressure 80 lbs., F = 96, a = 4.587 
 
 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 t/^ = 1.34, CI ^p%= 1 • 45, and C/^ = 1.49 
 
 for the 10, 30, and 50-in. engines, respectively. Taking a = 3.5, which 
 corresponds to a shearing strength of 60,000 and a factor of safety of 8 for 
 steel, or to 45,000 and a factor of 6 for iron, we have for the new coeffi- 
 cient a t in the formula d t = a t ^/i.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 = 2.74 3.46 7.67 9.70 12.55 15.82 
 
 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 = ~ X /; and d = <Uj X 10. 2; 
 
 32 ' 
 
 / 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 o n a sect ion 
 of a shaft, then the equivalent twisting moment T\ = B + ^B 2 + T 2 . 
 
 Seaton says: Crank-shafts are subject always to twisting, bending, and 
 shearing strains; the latter are so small compared with the former that 
 they are usually neglected directly, but allowed for indirectly by means 
 of the factor f. 
 
 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- 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1013 
 
 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 + 1/2 length of shaft- 
 bearing 4- 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 
 
 Revs, per min 
 
 Max. press, on pis.P 
 Leverage,* Lin... . 
 Bd.mo.PL= J Bin.-lb 
 Twist, mom. T .... 
 Equiv. twist mom. 
 
 10 
 50 
 250 
 7,854 
 6.32 
 49,637 
 47,124 
 
 118,000 
 
 10 
 50 
 125 
 
 7,854 
 7.94 
 62,361 
 94,248 
 
 175,000 
 
 30 
 450 
 130 
 
 70,686 
 
 22.20 
 
 1,569,222 
 
 1,060,290 
 
 3,463,000 
 
 30 
 
 450 
 
 65 
 
 70,686 
 
 26.00 
 
 1,837,836 
 
 2,120,580 
 
 4,647,000 
 
 50 
 
 1250 
 
 90 
 
 196,350 
 
 36.80 
 
 7,225,680 
 
 4,712,400 
 
 15,840,000 
 
 50 
 
 1250 
 
 45 
 
 196,350 
 
 42.25 
 
 8,295,788 
 
 9,424,800 
 
 (approx.) 
 
 20,850,000 
 
 * Leverage = distance between centers of crank-pin and shaft bearing 
 = l/ 2 2 + 2.25 d. 
 
 Having already found the diameters, on the assumption that the shafts 
 were subjected to a twisting moment T only, we may find the diameter 
 for resisting combined bending and twisting by multiplying the diameters 
 already found by the cube roots of the ratio T\ -5- T, or 
 
 1.40 1.27 1.46 1.34 1.64 1.36 
 Giving corrected diameters di = 3.84 4.39 11.35 12.99 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 4i5/i6to 14i5/i6, 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 
 
1014 
 
 THE ^STEAM-ENGINE. 
 
 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 
 
 i d 2 s 
 obtained from the formula W= 785,400 j^™ (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, lbs 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 
 be nding a nd twisting resistance, T\ = 0.196 d 3 S, in which Ti = B + 
 v / B 2 + T 2 ; T being the maximum, not the mean twisting moment; and 
 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 
 
 3 to 5 or less 
 
 I to 1 or less 
 
 B greater than T . . 
 
 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 
 
 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 
 
DIMENSIONS OF PARTS OF ENGINES. 1015 
 
 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 56 1/2 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 lbs., which, multiplied by 56 1/2 in., gives 
 4,945,445 i n.-lbs. b ending moment at the fillet. Applying the formula 
 T\ = £+ v'.B 2 + T 2 , gives for equivalent twisting moment 9,971,045 in.- 
 lbs. Substituting this value in the formula T\ = 0.196 Sa 3 gives for S 
 the shearing strain 15,070 lbs. per sq. in., or if the metal had a shearing 
 strength of 45,000 lbs., a factor of safety of only 3. Mr. Coffey considers 
 that 6000 lbs. 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 S = 1100, we obtain d s = 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 formulae 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 pressures 
 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, how- 
 ever, 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. 
 
 For shafts resisting torsion only, Marks gives for length of bearing I = 
 0. 0000247 fpND 2 , in which /is the coefficient of friction, p the mean 
 pressure in pounds per square inch on the piston, N the number of 
 single strokes per minute, and D the diameter of the piston. For shafts 
 under the combined stress due to pressure on the crank-pin, weight of 
 fly-wheel, etc., he gives the following: Let Q = reaction at bearing due 
 to weight, S = stress due steam pressure on p iston, a nd Ri = the 
 resultant force; for horizontal engines, Ri = *v / Q 2 +S 2 , for vertical 
 engines Ri = Q + S, when the pressure on the crank is in the same 
 direction as the pressure of the shaft on its bearings, and Ri = Q — S 
 when the steam pressure tends to lift the shaft from its bearings. Using 
 empirical values for the work of friction per square inch of projected area, 
 taken from dimensions of crank-pins in marine vessels, he finds the 
 formula for length of shaft-journals I = 0.0000325/^1 N, and recom- 
 mends that to cover the defects of workmanship, neglect of oiling, and the 
 introduction of dust, / be taken at 0. 16 or even greater. He says that 
 500 lbs. per sq. in. of projected area may be allowed for steel or wrought- 
 iron shafts in brass bearings with good results if a less pressure is not 
 attainable without inconvenience. Marks says that the use of empirical 
 rules that do not take account of the number of turns per minute has 
 resulted in bearings much too long for slow-speed engines and too short 
 for high-speed engines. 
 
 Whitham gives the same formula, with the coefficient 0.00002575. 
 
 Thurston says that the maximum allowable mean intensity of pressure 
 may be, for all cases, computed bv his formula for journals, I = PV ■*■ 
 60,000 d, or by Rankine's, I = P (V + 20) -*- 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 
 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-pin, in proportion to the work falling upon each, i.e., to their 
 
1016 
 
 THE STEAM-ENGINE. 
 
 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 wrought-iron journals: 
 
 Revs, per mi n. = 50 100 150 200 250 500 1000 l/d = 0.004 R+l. 
 Length -h diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0. 
 
 Cast-iron journals may have Z-e-d = 9/i , and steel journals l-^-d = l^Ii, 
 of the above values. 
 
 Unwin gives the following, calculated from the formula !=0.4H.P.+ 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. 
 
 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, 
 
 0.4 
 0.8 
 1.6 
 2. 
 
 12. 
 
 16. 
 20. 
 
 0.8 
 
 1.6 
 
 3.2 
 
 4. 
 
 8. 
 
 12. 
 
 16. 
 
 24. 
 
 32. 
 
 1.2 
 2.4 
 4.8 
 6. 
 
 12. 
 
 18. 
 
 24. 
 
 36. 
 
 2. 
 
 4. 
 
 8. 
 10. 
 20. 
 30. 
 40. 
 
 16. 
 
 20. 
 40. 
 
 Applying these different formulae to our six engines, we have: 
 
 Engine No 
 
 Diam. cyl 
 
 Horse-power 
 
 Revs, per min 
 
 Mean pressure on crank-pin = S 
 
 Half wt. of fly-wheel and shaft = Q. . . . 
 Resultant pressure on bearing 
 
 Diam. of shaft journal 
 
 Length of shaft journal: 
 Marks, 1 = 0. 0000325 /P,7V(/=0. 10) 
 Whitham, Z = 0.00005 15 fRiRif =0.10) 
 
 Thurston, Z = PF-^ (60,000 d) 
 
 Rankine, l = P (V+20) -~ (44,800d).. . 
 
 Unwin, 1= (0.004 R+ 1) d 
 
 Unwin, Z=<MH.P.-^r 
 
 Average 
 
 10 
 
 50 
 250 
 3,299 
 268 
 
 3,310 
 
 3.84 
 
 5.38 
 
 4.27 
 3.61 
 5.22 
 7.68 
 3.33 
 
 4.92 
 
 30 
 450 
 130 
 
 23,185 
 5,968 
 
 23,924 
 11.35 
 
 20.87 
 16.53 
 14.00 
 21.70 
 17.25 
 12.00 
 
 17.05 
 
 30 
 450 
 
 65 
 23,185 
 11,936 
 
 26,194 
 12.99 
 
 11.07 
 
 8.77 
 7.43 
 10.85 
 16.36 
 6.00 
 
 10.00 
 
 50 
 
 1,250 
 
 90 
 
 58,905 
 26,470 
 
 64,580 
 20.58 
 
 37.78 
 29.95 
 25.36 
 35.16 
 27.99 
 20.83 
 
 29.54 
 
 50 
 
 1,250 
 
 45 
 58,905 
 52,940 
 
 79,200 
 21.52 
 
 23. .17 
 18.35 
 15.55 
 22.47 
 25.39 
 10.42 
 
 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 
 
DIMENSIONS OF PARTS OF ENGINES. 
 
 1017 
 
 j for each journal given above, we obtain the pressure per square inch upon 
 (the bearing, as follows: 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 Press, per sq. in., shortest journal 
 
 Longest journal 
 
 259 
 112 
 175 
 
 455 
 115 
 254 
 173 
 
 176 
 97 
 124 
 
 336 
 123 
 202 
 155 
 
 151 
 83 
 106 
 
 353 
 145 
 191 
 
 
 175 
 
 
 
 
 I Many of the formulae give for the long-stroke engines a length of journal 
 j 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 
 i 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 14ij/i6 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 
 i power of journals in actual use, the coefficient varying from 0.10 (or 
 1 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 
 
 PV 
 j formula, I = gTTT^Tr^' reduces to the form I = 0.000004363 PR, in which 
 
 P = mean total load on journal, and R = revolutions per minute. This • 
 lis of the same form as Marks's and Whitham's formulae, in which, if/, the 
 j 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 shaf t, fly-wh eel, 
 
 etc., as calculated by the formula already given, viz., Ri = ^Q 2 + S 2 for 
 horizontal engines, and Ri = Q + 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 3 4 5 6 
 
 Length of journal 4.39 4.39 16.48 12.99 30.80 21.52 
 
 Pressure per square inch 
 
 on journal 196 173 128 155 102 171 
 
 Crank-shafts with Center-crank and Double-crank Arms. — In 
 
 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 
 
1018 
 
 THE STEAM-ENGINE. 
 
 twisting moment, T\ = B + ^B 2 + T 2 , in which Ti is the equivalent 
 twisting moment, B the bending moment, and T the twis ting mo ment. 
 
 This value of T\ is to be used in the formula diameter = "^5.1 T/S. The 
 bending moment is taken as the maximum load on piston multiplied by I 
 one-fourth of the length of the crank-shaft between middle points of the 
 two journal bearings, if the center is midway between the bearings, or I 
 by one-half the distance measured parallel to the shaft from the middle J 
 of the crank-pin to the middle of the after bearing. This supposes the J 
 crank-shaft to be a beam loaded at its middle and supported at the ends, i 
 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- i 
 ward journ al, which is subjected to bending moment only, diameter of ' 
 
 shaft = *\/l0.2 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: 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 Length of shaft, 
 
 
 
 
 
 
 
 assumed, in., L. . 
 
 20 
 
 24 
 
 48 
 
 60 
 
 76 
 
 96 
 
 Max. press, on 
 
 
 
 
 
 
 
 crank-pin, P 
 
 7,854 
 
 7,854 
 
 70,686 
 
 70,686 
 
 196,350 
 
 196,350 
 
 Max. bending mo- 
 
 
 
 
 
 
 
 ment, 5 = V4PL, 
 
 39,270 
 
 49,637 
 
 848,232 
 
 1,060,290 
 
 3,729,750 
 
 4,712,400 
 
 Twisting mom., T 
 
 47,124 
 
 94,248 
 
 1,060,290 
 
 2,120,580 
 
 4,712,400 
 
 9,424,800 
 
 Equiv. twist, mom. 
 
 
 
 
 
 
 
 B + V52 + T 2 ... 
 
 101,000 
 
 156,000 
 
 2,208,000 
 
 3,430,000 
 
 9,740,000 
 
 15,240,000 
 
 Diam. of after jour. 
 
 
 
 
 
 
 
 A iV 5 - 1 Tl 
 
 V 800 ° "" 
 
 3.98 
 
 4.60 
 
 11.15 
 
 13.00 
 
 18.25 
 
 21.20 
 
 Diam. of forw. jour. , 
 
 
 
 
 
 
 
 t 7l0.2 B 
 
 dl ~ V"8000~--" 
 
 3.68 
 
 3.99 
 
 10.28 
 
 11.16 
 
 16.82 
 
 18.18 
 
 The lengths of the journals would be calculated in the same manner as 
 in the case of overhung cranks, by the formula I = 0.000053 fPR, in 
 which P is the resultant of the mean pressure due to pressure of steam on 
 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 two 
 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 case 
 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 
 
DIMENSIONS OF PARTS OF ENGINES. 1019 
 
 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 T\, 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 va lue in the formula for diam eter to resist sim ple 
 
 torsion, viz., d = -^5.1 T + S, we have d = ^5.1 X 1.414 T +■ S, or 
 d = 1.932 \j T jS, 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 t = 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 Ti = maximum twisting 
 moment on after journal of after crank, due to pressure on the after 
 piston. 
 
 Then equivale nt twisting moment on after journal of forward crank =?= 
 B\ + ^Bi 2 + TV. 
 
 On forward journal of after crank = B<i 4- v / .g 2 2 + TV. 
 
 On after journal of after crank = Bi + V# 2 2 + (Ti + T 2 ) 2 . 
 
 These values of equivalent twisting moment are to be used in the 
 
 formula for diameter of journals d = \/5.1 T IS. For the forward 
 
 journal of the forward crank-shaft d = -^10.2 Bi IS. 
 
 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. 
 t(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 adooted 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 
 
 jo urnal = Bz 4- Vff 3 2 T (Ti + T^, and on the after journal = B s + 
 
 VBz\+ (7 7 i+ T 2 + T 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 cvlinder. 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 mav become unbalanced bv thp joint lpaking) and when 
 it is imperfectiv 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 
 coefficient and the load is the force necessary to move the valve, which 
 
1020 THE STEAM-ENGINE. 
 
 equals the maximum thrust on the valve-rod. From this force the diam- 
 eter of the valve-rod may be calculated by the usual formula for 
 co lumns . An empirical formula given by Seaton is: Diam. of rod= d = 
 "vWp/F, in which I = length, and b = breadth of valve, in inches; 
 p = maximum absolute pressure on the valve in lbs. per sq. in., and 
 F a coefficient 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 = 3/3fl| 
 diam. of cyl. = 1/3 diam. of piston-rod. 
 
 Size of Slot-link. (Seaton.) — Let D be the diam. of the valve-rod 
 
 D^^lbp h- 12,000; 
 
 then Diameter of block-pin when overhung = D. 
 
 secured at both ends = 0.75 X Z>. 
 
 eccentric-rod pins =0.7 X D. 
 
 suspension-rod pins = 0.55X D. 
 
 " pin when overhung =0.75XD. 
 
 Breadth of link = . 8 to . 9 X D. 
 
 Length of block = 1 . 8 to 1 . 6 X D. 
 
 Thickness of bars of link at middle = . 7 X D. 
 
 If a single suspension rod of round section, its diameter =0.7 X D. 
 If two suspension rods of round section, their diameter = 0.55 X D. 
 
 Size of Double-bar Links. — When the distance between centers of 
 eccentric pins = 6 to 8 times throw of eccentrics (throw = eccentricity = 
 half-travel of valve at full gear) D as before: 
 
 Depth of bars = 1 . 25 X D + 3/ 4 in. 
 
 Thickness of bars = . 5 X D + 1/4 in. 
 
 Length of sliding-block = 2.5 to 3 X D. 
 
 Diameter of eccentric-rod pins = . 8 X D + 1/4 in. 
 center of sliding-block = 1.3 X D. 
 
 When the distance between eccentric-rod pins= 5 to 51/2 times throw 
 of eccentrics: 
 
 Depth of bars = 1 . 25 XD + 1/2 in. 
 
 Thickness of bars = . 5 X D + 1/4 in. 
 
 Length of sliding-block = 2.5 to 3 X D. 
 
 Diameter of eccentric-rod pins = 0.75 X D. 
 
 Diameter of eccentric bolts (top end) at bottom of thread = . 42 X D 
 when of iron, and 0.38 X D when of steel. 
 
 The Eccentric. — Diam. of eccentric-sheave = 2.4 X throw of eccen- 
 tric + 1 . 2 X diam. of shaft. D as before 
 
 Breadth of the sheave at the shaft ...... = 1 . 15 X D + . 65 in. 
 
 Breadth of the sheave at the strap = D + . 6 in. 
 
 Thickness of metal around the shaft .... =0.7 X D + . 5 in. 
 
 Thickness of metal at circumference .... ^=0.6 X D + . 4 in. 
 
 Breadth of key. =0.7 XD+0.5in. 
 
 Thickness of key = . 25 X D + . 5 in. 
 
 Diameter of bolts connecting parts of strap =0.6 XD+0.1in. 
 
 Thickness of Eccentric-strap. 
 
 When of bronze or malleable cast iron: 
 
 Thickness of eccentric-strap at the middle =0.4XZ>+0.6in. 
 
 Thickness of eccentric-strap at the sides =0.3XD+0.5in. 
 
 When of wrought iron or cast steel: 
 Thickness of eccentric-strap at the middle. ... = . 4 X D + . 5 in. 
 Thickness of eccentric-strap at the sides = . 27 X D + . 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 
 
DIMENSIONS OF PARTS OF ENGINES. 1021 
 
 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 
 
 61, and p t being length, breadth, and maximum steam-pressure on 
 valve of the second cylinder; and for an expansive engine 
 
 W = 2X 
 
 &(**"*)■■«§> «*>**>■ 
 
 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; and the size may be found from 
 :the ordinary rules of construction for any of the parts of the gear. (Sea- 
 ton.) 
 
 Current Practice in Engine Proportions, 1897. (Compare pages 996 
 to 1020.) — 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 
 or other long-stroke engines usually making not more than 100 or 125 revs. 
 per min. Those classed as high speed (H. S.) have a stroke generally of 
 1 to H/2 diameters and a speed of 200 to 300 revs, per min. The results 
 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 
 
 . ; B = . 3 in. ; C varies from . 04 to . 06, mean = . 05. 
 
 Flanges and Cylinder-heads.^ 1 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 = 0.7 D. 
 Average diam. = D/40 + 1/2 in. 
 
 Ports and Pipes. — a = area of port (or pipe) in sq. in.: A = area of 
 piston, sq. in.; V = mean piston-speed, ft. per min.; a = AV /C, in which 
 C = mean velocity of steam through the port or pipe in ft. per min. 
 
 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. 
 
 Steam-ports, L. S. — C = 5000 to 9000, mean 6800; K = 0.08 to 0.10, 
 mean 0.09. 
 
 Exhaust-ports, L. S. — C = 4000 to 7000, mean 5500; K = 0.10 to 0.125, 
 mean 0.11. 
 
 Steam-pipes, H. S. — C = 5800 to 7000, mean 6500. If d = diam. of 
 pipe and D = diam. of piston, d = . 29 D to . 32 D, mean . 30 D. 
 
 Steam-vipes, L. S. — C = 5000 to 8000, mean 6000; d = . 27 to . 35 Z>; 
 mean 0.32 D. 
 
 Exhaust-pipes, H. S. — C = 2500 to 5500, mean 4400; d = 0.33 to 
 0.50 D, mean 0.37 D. 
 
 Exhaust-vipes, L. S. — C = 2800 to 4700, mean 3800; d = 0.35 to 
 . 45 D, mean . 40 D 
 
 Face of Pistons. — F = face; D = diameter. F = CD. H. S.: C = 
 0.30 to 0.60, mean 0.46. L. S.: C = 0.25 to 0.45, mean 0.32. 
 
 Piston-rods. — - d = diam. of rod: D = diam. of piston; L = stroke, in.; 
 d= C V DL . H s . c= 12 t0 175 mean 145 L g . c= 10 to 
 0.13, mean 0.11. 
 
 Connecting-rods. — H. S. (generallv 6 cranks loner, rectangular section): 
 = breadth; h = height of section; Li = length of connecting-rod; 
 D = diam. of piston; b = C ^DLi; C = 0.045 to 0.07. mean 0.057; 
 h = Kb: K = 2.2 to 4, mean 2.7. L. S. (generallv 5 cranks long, cir- 
 cular sections only): C = 0.082 to 0.105, mean 0.092. 
 
1022 THE STEAM-ENGINE. 
 
 Cross-head Slides. — Maximum pressure in lbs. 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 = 0.054to0.10, mean0.07; 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 a^H.P.-j- TV; d= diam.; Z = length; 
 N = revs, per min.; projected area = MA; A = area of piston. H. S.: 
 C — 6.5 to 8.5, mean 7.3; l = Kd; i£ = 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 h- LN 2 ; D = diam. of piston; 
 L = length of stroke, in.; N = revs, per min. H. S. only: C = 1,200,000 
 to 2,300,000, mean 1,860,000. 
 
 Belt-surface per I.H.P. — 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 = C X H.P., C = 30 to 42, mean = 35. 
 
 Fly-wheel (H. S. only). — Weight of rim in lbs.: W = C x XH.P.r 
 Z>i 2 A 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 lbs., including fly-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 
 proportioning 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 formulas may be considered as partly rational and partly em- 
 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. 
 p = unit steam pressure, taken as 125 lbs. per sq. in. above exhaUst as 
 a standard pressure. H.P. = rated horse-power. N = revs, per min. 
 C and K, constants, and d = 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. 
 
 Piston Eod.—d = C^ r DL. H. S.: C = 0.15 (min., 0.125; max., 
 0.187); L. S.: C - 0.114 (min., 0.1; max., 0.156). 
 
 Cylinder. — 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 en sines. 
 
 Stud Bolts. — Number = . 72 D for H. S. (0 . 65 D for Corliss.) Diam. 
 in ins. = 0.04 D + 0.375. 
 
 Ratio (C) of Stroke to Cylinder Diameter (L ID). — For TV > 900, 
 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) ID = 1.63 
 (min., 1.15; max.. 2.4). 
 
 Piston. — Width of face in ins. = CD + 1. Mean value of C = 0.32 
 
DIMENSIONS OF PARTS OF ENGINES. 1023 
 
 ! or H. S. (0.26 for Corliss). Thickness of shell = thickness of cylinder 
 vail X 0.6 (0.7 for Corliss). 
 
 Piston Speeds. — H. S., 605 ft. per min. (min. 320; max., 920); Corliss, 
 >92 ft. per min. (min., 400; max., 800). 
 
 Cross-head. — Area of shoes in sq. ins. =0.53 A (min., 0.37; max., 
 ).72). 
 
 Cross-head Pin. — Diameter = 0.25 D (min., 0.17; max., 0.28). 
 Length for H. S. = diam. X 1.25 (min., 1; max., 1.5); for Corliss == 
 liam. X 1.43 (min., 1; max., 1.9). 
 
 Connecting-rods. — Breadth for H. S. =0.073 ^L C D (min., 0.55; max., 
 ).094). Height = breadth X 2. 28 (min., 1.85; max., 3). For L. S., diam. 
 )f circular rod = . 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 = 0. 4 D (min., 
 
 28; max., 0.526). Diam. for side-crank Corliss = 0.27 D (min., 
 ).21; max., 0.32). Length for H. S. = diam. X 0.87 (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 yTLP ./A (min., 5.4; max., 8.2). For Corliss, diameter = 7.2 
 [^/(H. P./ A) -0.3] (min., 6.4; max., 8). 
 
 Fly-xoheels. — Total weight in pounds for H. S. up to 175 H.P. 
 = 1,300,000,000,000 H.P. /Di 2 A 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 3 ) + 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. /DJN^-K, where C = 890,000,000,000 (min., 625,- 
 000,000,000; max., 1,330,000,000,000), and #=4000 (min., 2,800; max., 
 16000). Diam. in ins.= 4.4X length of stroke. 
 
 Belt Surface per I.H.P. ■ — Square feet of belt surface per minute (S) 
 ifor H. S. = H.P. x 26.5 (min., 10; max., 55). For Corliss engines, 
 \S = 1000 4- (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 lbs. W = (D 2 1 LA 2 ) X 2,000,000 (min., 
 1,370,000; max., 3,400,000). Balance weight opposite crank-pin = 
 0.75 W. 
 
 Weight of engine per I.H.P. — Lbs. per I.H.P. for belt-connected H. S. 
 engines = H.P. X 82 (min., 52; max., 120). Do., for Corliss = H.P. 
 X 132 (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 nothins? external to the bearings, — considerable deflection can be 
 tolerated. When bearings are rigid, or defection 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 
 lensrth has caused much trouble from hot bearings. I have proportioned 
 such shafts so that the deflection will not exceed one-half this extent. 
 
 Tn some shafts, especially those having an oscillating movement, 
 torsional elasticity is a prime' consideration, and the limits can be known 
 onlv by experience. Reuleauv 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. Thave adopted the following as a gen- 
 eral sruide: Permissible twist per foot of length =0.10 degree for easy 
 service, without severe fluctuation of load: 0.075 degree for fluctuating 
 loads suddenly applied: 0.050 degree for loads suddenly reversed. 
 
 Sufficiency of wearing surface and the limitation of pressure per unit 
 
1024 THE STEAM-ENGINE. 
 
 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 lbs., 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 sunaee. 
 Tnis product varies in good practice under various conditions lrom: 
 50,000 to 500,000 ft.-lbs. per mm. For instance, good practice, in later 
 years, has largely increased the. area of crosshead slide surfaces, For 
 crossneads 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 shaits, 
 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 good example of 
 journals severely tested are the recent 110,000-pound freight cars, which 
 bear a pressure of 400 lbs. 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-pin will stand four times the unit pressure that the fly-wheel journal 
 will. 
 
 The amount of pressure that commercial oils will endure at low speeds 
 without breaking down varies from 500 to 1000 lbs. 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 + K) (1). p = allowable pressure in lbs. per 
 sq. in. of projected area, D = diam. of the bearing in ins., N = revs. 
 per min., and P and K depend upon the kind of oil, manner of lubrica- 
 tion, 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- 
 pins is 2000. 
 
 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 
 
DIMENSIONS OF PARTS OF ENGINES. 1025 
 
 Lork where the rapid circulation of the air cools the journals. Higher 
 Ulues 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 
 n feet per second. There are a few cases where a unit pressure sufficient 
 ;o 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 means of the 
 
 nation: i - lW + PKi X& + *0> (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 lfgyN. 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 IV2 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 _ 
 
 L = 20 W ^SN + PK (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 1007.] The length is 
 then recomputed from formula No. 2, taking this new value if it does 
 not differ materially from the one first assumed. 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 
 20-in cylinder, running at 80 r.p.m., and having a maximum unbalanced 
 steam pressure of 100 lbs. 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 v'io)-*- (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 
 
 Z) = 0.09 \JWL Z , 
 
 which limits the deflection to . 003 in. This gives D = 3 . 85 or say 37/ 8 
 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 51/4 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 X6 1/2 
 inches, and this will bring the ratio of the length to the diameter nearer 
 
 to 1/8 "^N 
 
 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., 
 
1026 THE STEAM-ENGINE. 
 
 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 block, 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 lbs. 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 lbs., and a 32-in. 
 engine which has been running for many years shows 667 lbs. 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 lbs., which-figure should be increased for larger bores up to 500 
 lbs. 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. Rankine 
 AE 
 2E Q 
 
 steadiness, in which E is the mean actual energy, and AE 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 
 AE to the whole energy exerted in one period or revolution General 
 Morin found to be from 1/6 to 1/4 for single-cylinder engines using expan- 
 sion; the shorter the cut-off the 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., AE is nearly equal to the 
 whole work performed at each operation. 
 
 AE 
 
 A fly-wheel reduces the coefficient — ^- to a certain fixed amount, being 
 
 about 1/32 for ordinary machinery, and 1/50 or 1/6O for machinery for fine 
 purposes. 
 
 If m be the reciprocal of the intended value of the coefficient of fluc- 
 tuation of speed, AE the fluctuation of energy, / the moment of inertia 
 
 of the fly-wheel alone, and a its mean angular velocity, / = — ^ — As 
 
 the rim of a fly-wheel is usually heavy in comparison with the arms, 
 / may be taken to equal Wr 2 , in which W = weight of rim in pounds, and 
 
 tyiqAE tnoAE 
 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 
 
 - m Jy 2 , in which A = area of piston in square inches, S = stroke in feet, 
 
 j) = mean steam-pressure in lbs. 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 ' W = 1227)2' in wnicn a ran £ es from 10,000,000 to 15,000,000, averaging 
 12,000,000. For gas-engines, in which the charge is fired with everv 
 revolution, the American Machinist gives this latter formula, with a 
 
FLY-WHEELS. 1027 
 
 doubled, or 24,000,000. Presumably, if the charge is fired every other 
 revolution, a should be again doubled. 
 
 Ranirine ("Useful Rules and Tables," p. 247) gives W = 475,000 
 
 • i , in which 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. Inst. 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 = 2V2 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 = ■ — R ' ' ' , and weight of rim per horse-power 
 
 ■= -557^, 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 
 Mv 2 = _W_ (3.14) 2 D 2 fl 2 = CX H.P. (3.14) 2 D 2 R 2 = 850,000 H.P . F1 
 
 2 "64.4 3600 ^£,2 x 64-4 x 360 R 
 
 wheel energy per H.P. = 850,000 -4- 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 formulae 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 ciosely to the formula 
 
 W = 700,000 d 2 s -h D 2 R 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 dutv, 350,000; same, electric lighting, 700.000; 
 for automatic high-speed engines, 1.000,000; for Corliss engines, ordinary 
 dutv 700,000, electric lighting 1,000.000. 
 
 Thurston's formula above given, W = aAS ■*- R*D 2 with a = 12,000,000, 
 when reduced to terms of d and s in inches, becomes W = 785,400 d 2 s -«- 
 
 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 lbs., 
 we obtain W = 5.000.000.000 I.H.P. h- RW 2 . If mean effective pressure 
 - 30 lbs., then W = 6,666,000.000 I.H.P. -^ R S D 2 . 
 
 Emil Theiss (Am. Moch., 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 
 
 Pumoing and shearing machinery d = 20 to 30 
 
 Weaving and paper-making machinery d = 40 
 
 Milling machinery ^=50 
 
 Spinning machinery a = 50 to 100 
 
 Ordinarv 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 =t'X y 2 y^ n ' 
 
 where d is the coefficient of steadiness, V the mean velocity of the fly- 
 wheel rim in feet per second, n the number of revolutions per minute, 
 
1028 
 
 THE STEAM-ENGINE. 
 
 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 com- 
 pression." 
 
 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, l/ 2 . 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 
 
 200 
 400 
 600 
 
 272,690 
 240,810 
 194,670 
 158,200 
 
 218,580 
 187,430 
 145,400 
 108,690 
 
 242,010 
 208,200 
 168,590 
 162,070 
 
 209,170 
 179,460 
 136,460 
 135,260 
 
 220,760 
 188,510 
 165,210 
 
 201,920 
 170,040 
 146,610 
 
 193,340 
 174,630 
 
 182,840 
 167,860 
 
 800 
 
 
 
 
 
 
 
 
 
 
 Single-cylinder 
 
 Condensing 
 
 Engines. 
 
 
 
 $-6 & 
 
 Cut-off, i/ 8 . 
 
 Cut-off, 1/6- 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, 1/2. 
 
 *u 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 O 
 
 Comp. 
 V 
 
 
 
 200 
 
 400 
 
 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 
 
 600 
 
 
 
 
 
 
 
 
 
 
 
 
 Two-cylinder Engines, Cranks at 90°. 
 
 Piston- 
 speed, ft. 
 per min . 
 
 Cut-off, 1/6- 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, 1/2. 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 
 
 200 
 400 
 600 
 800 
 
 71,980 
 70,160 
 70,040 
 70,040 
 
 1 Mean 
 f 60,140 
 
 59,A2Q 
 57,000 
 57,480 
 60,140 
 
 1 Mean 
 [ 54,340 
 
 49,272 
 49,150 
 49,220 
 
 1 Mean 
 [ 50,000 
 
 37,920 
 35,000 
 
 \ Mean 
 f 36,950 
 
 Three-cylinder Engines, Cranks at 120°. 
 
 Piston- 
 
 Cut-off, 1/6- 
 
 Cut-off, 1/4. 
 
 Cut-off, 1/3. 
 
 Cut-off, l/ 2 . 
 
 speed, ft. 
 per min. 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 
 
 Comp. 
 V 
 
 
 
 Comp. 
 
 v - 
 
 
 
 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. 
 
 Weight of Fly-wheels for Alternating-current Units. (J. Begtrup. 
 Am. Mach., July 10, 1902.) — 
 
 WD* + WJ>t - 14 -~ W . 
 
FLY-WHEELS. 1029 
 
 in which W= weight of rim of fly-wheel in pounds, D = mean diameter 
 of rim in feet, Wi = weight of armature in pounds, Di= mean diameter 
 of armature in feet, H = 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-red, 
 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: 
 
 p = 387,700,000 HZ 
 
 N*(WD*+ WiDi 2 )' 
 in winch 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. S. 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 -4- 60. 
 
 W,i2 a Wn 2 Rr 2 
 
 Centrifugal force of whole rim = F = ^- = '" =0. 000341 WRr 2 . 
 
 gR 3600 g 
 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 
 
 2 
 half the radial forces taken at right angles to the diameter is 1 -s- 1/21- — - 
 
 of the sum of these forces; hence the total force F is to be divided by 
 2 X 2 X 1 .5708 = 6.2832 to obtain the tensile strain on the cross-section 
 of the rim, or, total strain on the cross-section = 5 = 0.00005427 WRr 2 . 
 The weight W\ of a rim of cast iron 1 inch square in section is 2 nR x 
 3.125 = 19.635 72 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 V 2 , 
 in which D = diameter of wheel in feet, and V is velocitv of rim in feet 
 per minute. 5i = . 0972 v 2 , if v is taken in feet per second. 
 For wrought iron: 
 
 Si = 0.0011366 R 2 r* = 0.0002842 D 2 r 2 = 0.0000288 V 2 . 
 For steel: 
 
 Si = 0.0011593 R 2 r 2 = 0.0002901 D 2 r 2 = 0.0000294 V 2 . 
 For wood: 
 
 Si = 0.0000888 R 2 r 2 = 0.0000222 D 2 r 2 = 0.00000225 V 2 . 
 
 The specific gravity of the wood being taken at . 6 = 37 . 5 lbs. 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 lbs. 
 
 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 lbs. 
 
 In cast-iron fly-wheel rims, on account of their thickness, there is . 
 difficulty in securing soundness, and a tensile strength of 10.000 lbs. 
 per sq. in, is as much as can be assumed with safety. Using a factor of 
 
1030 THE STEAM-ENGINE. 
 
 safety of 10 gives a maximum allowable strain in the rim of 1000 lbs. 
 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. May., 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 + -*R = 1910 -h R. 
 
 W. H. Boehm, Supt. of the Fly-wheel Dept. of the Fidelity and Casu- 
 alty Co. (Eng. News, Oct. 2, 1902), sa.s: 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: 
 
 7 = 1.6 VsJW, 
 
 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 lbs. per sq. 
 in. as the strength of small test bars, and 10,000 lbs. per s q. in. in lar ge 
 castings, and applying a factor of safety of 10, V = 1.6 Viooo/0.26 <= 
 100 ft. per second for the safe speed. For cast steel of 60,000 lbs. per 
 sq. in., V = 1.6 ^6000 + 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 lbs. per sq. in., 
 and weighing 0.0283 lb. per cu. in., we have, using a factor of safety of 
 20, and remembering that the strength is reduced one-ha lf because the 
 wheel is built up of segments, F = 1.6 V262.5 -*- 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. 
 
 1031 
 
 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. 
 
 
 
 
 
 Diam. 
 
 
 
 
 
 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 
 
 15 
 
 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. Mach., 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 disk# 
 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 few 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 d -*- A 72 
 
 Vf 2 10/ 
 
 in which .£= 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 6000 lbs. per sq. in. 
 
1032 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 
 24 
 48 
 108 
 108 
 
 50 
 88 
 88 
 
 184. 
 
 184 
 
 3,000 
 5,280 
 5,280 
 11,040 
 11,040 
 
 6 
 6 
 6 
 16 
 36 
 
 2/10 
 15/32 
 15/16 
 21/2 
 1/2 
 
 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 lbs., the formula becomes 
 
 t = . 475 d ■*■ . 67 iV 2 = . 7 d + A 2 . 
 
 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% 
 
 (F 1 \ 
 greater. Then the formula becomes t = 0.712 dn- A 2 !-™ — —J, or for a 
 
 fixed maximum rim velocity of 88 ft. per second and F = 6000 lbs., t = 
 1.05 d -s- A 2 . In segmental wheels it is preferable to 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 17:6 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 formula?. The arms, hub, lugs, etc., 
 usually form from one-quarter to one-third the entire weight of the wheel. 
 If b represents the face of a wheel in inches, the weight of the rim (con- 
 sidered as a simple annular ring) will bew = . 82 dtb lbs. If the limit 
 of speed is 88 ft. per second, then for solid wheels t = 0.7 d ■*- A 2 . For 
 sectional wheels (joint between arms) t = 1 . 05 d -*- A 2 . Weight of rim 
 for solid wheels, w = 0.57 d 2 b ■*- A 2 , in pounds. Weight of rim in sec- 
 tional wheels with joints between arms, w = . 86 d 2 b ■*- A 2 , in pounds. 
 Total weight of wheel: for solid wheel, W = 0.76 d 2 b h- A 72 to 0.86 d 2 b h- 
 A 2 , in pounds. For segmental wheels with joint between arms, W = 
 1 . 05 d 2 b -^ A 2 to 1 . 3 d 2 & -r- A 2 , 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. Mach., 
 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 cP. 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. 1033 
 
 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 should be about 28/100 the 
 cross-section of the pulley at that point. (Torrey.) 
 
 Unwin gives d = 0.6337 ^/ BD/n for single belts; 
 
 d = . 798 ^JBDIn for double belts ; 
 
 D being the diameter of the pulley, and B the breadth of the rim, both in 
 inches. These formulae are based on an elliptical section of arm in which 
 b = 0.4 d or d = 2.5b on a width of belt = 4/ 5 the width of the pulley 
 rim, a maximum driving force transmitted by the belt of 56 lbs. per inch 
 of width for a single belt and 112 lbs. for a double belt, and a safe working 
 stress of cast iron of 2250 lbs. per square inch. 
 
 If in Torrey's formula we make & = . 4 d, it reduces to 
 
 WL 
 
 7 WL , 3 /WL 
 
 6= Vi87T5 ;(Z= v/i2 
 
 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, 
 
 ci = 0.6337 ^JBD/n = 0.633^/36X120/8 = 5.16 for single belt, 6 = 2.06; 
 
 d = 0.798 $BD/n = 0.798 ^36 X 120/8 = 6.50 for double belt, & = 2.60. 
 
 According to Torrey, if we take the formula b = WL -■ 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 lbs. 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 lbs. 
 
 Weight of 24 arms (foundry 45,020) 40,349 
 
 Weight of 2 hubs (foundry 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 Linen 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 
 
1034 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 bolts 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 A T ews, 
 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 lbs. 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 4- 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 1/16 in., exhaust-lap 1/8 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 
 2 ec + cd from h to i; then Oi is the crank-angle for cut-off, and fk 4- fh 
 is the fraction of stroke completed at cut-off. Set off Ol = exhaust- 
 
THE SLIDE-VALVE. 
 
 1035 
 
 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 -h fh is the fraction 
 of stroke completed at release, and hq -5- 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. 
 
 ^Cut-off 
 
 Fig. 162. 
 
 If a valve has neither lap nor lead, the line joining the center of the 
 eccentric disk and the center of the snaft 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 
 
 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 + 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 amde, which is 
 the angle through which the eccentric rotates from its middle position 
 
1036 
 
 THE STEAM-ENGINE. 
 
 while the exhaust edge of the valve uncovers its lap. R.elease 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 + 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 iFig. 163): Draw a circle 
 whose diameter equals travel of valve. Draw diameter BA and con' 
 tinue to A 1 , so that the length AA X bears the same ratio to XA as the 
 
 
 
 
 
 
 ^ M 1 
 
 B f 
 
 aNt/ 
 
 \ x y 
 
 
 B l 
 
 """—-^ 
 
 
 ILMm 
 
 )cy c n / 
 
 Fig. 163. — 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 = A A 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) for finding the lap, lead, 
 etc., of a slide-valve when the points of admission, cut-off, and release 
 
THE SLIDE-VALVE. 
 
 1037 
 
 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. 164, to represent on any scale the travel 
 of the valve, and on it draw a circle, with the center O, 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, 
 
 K 
 
 /I ' ^^ 
 
 X ^<^o/ 
 
 \ 
 
 / i Center of^ 
 \ / | Eccentric \ 
 
 i 
 
 // 1 ^ 
 
 / \ I ^ 
 
 M \|E F 
 
 ?/ \ \ 
 
 7 \ N 
 
 P' N*, 
 
 1 iH i KeleaseV- 
 
 /■/ L-J^^ ' \ 
 
 U^^H] \R' X 1 
 
 A 
 
 B 
 
 VAdmissiXDa 
 
 \ L^ — "^L^/7 ^\ -W \ 
 
 j / ^^i^__ClrcVe^< 
 
 -Saofr 
 
 Circle 
 
 Fig. 164. — 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, 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 GFH, called the steam-lap circle, or, for 
 short, the lap circle. 
 
1038 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 the 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' 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 Oh. On OD r 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 JX, 
 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', 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. A F then will be the maximum port-opening. Draw the 
 perpendiculars OK and ED. DOK is the angular advance. 
 
 Draw the diameter DOD', 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 Zeunefs Diagram. — In problems solved by 
 means 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 
 
 OF FW OR' 
 
 ratios -j-=> -r-^< and -j-^- > each multiplied by the maximum port-opening. 
 
THE SLIDE-VALVE. 
 
 1039 
 
 0.017 .033 .05 .067 .083 .1 .107 .133 .15 .167 .2 
 
 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 tne same scale; or the maximum 
 port-opening = 1/2 valve travel minus trie lap. Also in this problem 
 AA' represents tne 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^of^piston, J 10Q 200 3QQ AQQ 5QQ 60Q 7QQ SQQ 9QQ 10QQ 12Q0 
 
 Port area = piston ) 
 area X 
 
 For a velocity of 6000 ft. per min., 
 
 Port area = sq. of diam. of cyl.X piston speed -h 7639. 
 
 The length of the port-opening may be equal to or something less than 
 the diameter of the cylinder, and the width = area of port-opening -s- 
 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 1/16 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 0° to 8°. 
 
 Inside Lead. — Welsbach (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 longer 
 
 Incr. 
 T. 
 
 begins sooner, 
 continues longer 
 
 begins later, 
 ceases sooner 
 
 begins later, 
 ceases later 
 
 begins later, 
 ends sooner 
 
 Incr. 
 AA. 
 
 begins earlier, 
 period unaltered 
 
 begins sooner, 
 per. the same 
 
 begins earlier, 
 per. unchanged 
 
 begins earlier, 
 per. the same 
 
1040 
 
 THE STEAM-ENGINE. 
 
 Zeuner gives the following relations (Weisbach-Dubois, vol.ii, p. 307): 
 US — travel of valve, p = maximum port opening; 
 
 L = steam-lap, I = exhaust-lap; 
 
 R = ratio of steam-lap to half travel = n K g , L = — X S; 
 
 r = ratio of exhaust-lap to half travel = 
 
 0.5 S' 
 I 
 
 l = 2p+2L=2p+RXS;S = 
 
 1-R 
 
 If a = angle BOC between positions of crank at admission and at 
 cut-off, and = angle LOP between positions of crank at release and at 
 
 .. „ 1; sin (180° -a) sin (180° -j8) 
 compression, then R = 1/2 = — 77 ; r = 1/2 
 
 sin 1/2 
 
 sin 1/2 /3 
 
 Crank-angles for Connecting-rods of Different Lengths. 
 
 Forward and Return Strokes. 
 
 "•5 <D fl 
 
 O,^ CD 
 
 
 Ratio of Length of Connecting-rod to Length of Stroke. 
 
 
 2 
 
 21/2 
 
 3 
 
 31/2 
 
 4 
 
 5 
 
 Infi- 
 nite 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For. 
 
 CO 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 For. 
 
 Ret. 
 
 or 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 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. ¥ 
 
 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 
 
 111.2 
 
 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 
 
 123.4 
 
 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 1041, giving the ratio of lap to travel of valve and ratio of travel 
 to port-opening, is abridged from one given by Buel in Weisbach-Dubois, 
 
THE SLIDE-VALVE. 
 
 1041 
 
 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 1040 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 = 21/2 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 > =180°— 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 + .25 - 2.2 = .55 in. 
 
 
 
 Lap and Travel of 
 
 Valve 
 
 
 
 
 §"3*6 h 
 
 "3 
 
 33 A 
 
 » ? O 
 
 *o 
 
 > g 
 
 3*8 ia £i 
 
 *o 
 
 j> g 
 
 •— 
 
 "c3 a 
 
 % 
 
 "d ft 
 
 m ? § 
 
 *a3 
 
 "a a 
 
 •Sfl=° 
 
 > 
 
 >o 
 
 : 1«3° 
 
 > 
 
 >o 
 
 •s-S=° 
 
 > 
 
 > ? 
 
 o-SOts 
 
 2? 
 
 13 Ph 
 
 o'SO-d 
 
 
 
 O'SOtj 
 
 
 
 een P 
 at P< 
 ti and 
 se an 
 
 H 
 
 een P 
 at P 
 n and 
 se an 
 
 
 
 *P Ph 
 
 een P 
 at P« 
 nand 
 se an 
 
 
 
 
 
 ft 
 
 03 O 
 
 ft 
 
 £ ° 
 
 ft 
 
 >«*- 
 
 ^•2 gd 
 
 03 
 l_3 
 
 eh£ 
 
 B^-2 % a 
 
 oj 
 h3 
 
 H£ 
 
 £^•2 S3 d 
 
 3 
 
 H-5 
 
 ngle be 
 of Crai 
 Admiss 
 or Rel 
 pressio 
 
 
 .2^bi 
 ■g-S.9 
 
 ngle be 
 of Crai 
 Admiss 
 or Rel 
 pressio 
 
 II 
 
 ~*3> 
 
 ■gg 
 
 ngle be 
 of Cra: 
 Admisi 
 or Rel 
 pressio 
 
 11 
 
 03 !> 
 
 25 i 
 
 < 
 
 tf 
 
 « 
 
 < 
 
 S 
 
 p? 
 
 < 
 
 tf 
 
 & 
 
 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 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1042 
 
 THE STEAM-ENGINE. 
 
 Relative Motions of Crosshead and Crank. — L = length of con- 
 necting-rod, R = length of crank, 9 = angle of crank with center line of 
 engine, D = displacement of crosshead from the beginning of its stroke, 
 V = velocity of crank- pin, V x = velocity of piston. 
 
 For R = l, D = ver sin 9± (L- ^ L 2 - sin 2 9) , 
 V 1 ~Vsin9/l±- COS& 
 
 ^L 2 -sin 2 9) 
 
 From these formulae Mr. A. F. Nagle computes the following: 
 Piston Displacement and Piston Velocity for eace 10° op Motion 
 
 of Crank. Length of crank = 1. Length of connecting-rod = 5. 
 
 Piston velocity V\ for vel. of crank-pin = 1. 
 
 Angle 
 
 Displacement. 
 
 Veloc 
 
 ty. 
 
 Angle 
 
 of 
 Cr'nk 
 
 Displacement. 
 
 Velocity. 
 
 of 
 Cr'nk 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 For- 
 ward. 
 
 Back. 
 
 10° 
 20° 
 30° 
 40° 
 50° 
 
 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 
 
 "6.899 
 
 0.954 
 1.005 
 1.019 
 1.011 
 1.000 
 
 0.778 
 0.875 
 0.950 
 
 "\.obb 
 
 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 1/8 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 $/iq in. for travels of from 15/ 8 in. to 6 in., 
 and laps of from 1/2 in. to 1 1/2 in., as 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-oflf, for Given Travels and 
 Laps of Slide-valves. 
 
 
 
 
 Periods of Admission, or 
 
 Points of Cut-off, fc 
 
 r the 
 
 
 "3 6 
 
 T3 
 
 
 
 following L 
 
 aps of Valves in inches. 
 
 
 
 H > 
 
 2 
 
 13/ 4 
 
 H/2 
 
 11/4 
 
 % 
 
 1 
 
 7/8 
 
 3/ 4 
 
 5/8 
 
 1/2 
 
 3/8 
 
 in. 
 
 in 
 
 % 
 
 % 
 
 % 
 
 % 
 
 % 
 
 % 
 
 % 
 
 % 
 
 % 
 
 12 
 
 1/4 
 
 88 
 
 90 
 
 93 
 
 95 
 
 96 
 
 97 
 
 98 
 
 98 
 
 99 
 
 99 
 
 10 
 
 1/4 
 
 82 
 
 87 
 
 89 
 
 92 
 
 95 
 
 96 
 
 97 
 
 98 
 
 98 
 
 99 
 
 8 
 
 1/4 
 
 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 
 
 5 
 
 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 
 
 3 
 
 1/8 
 1/8 
 
 
 
 
 23 
 
 50 
 27 
 
 61 
 
 43 
 
 71 
 
 57 
 
 79 
 70 
 
 86 
 80 
 
 91 
 
 21/2 
 
 
 
 
 88 
 
 2 
 
 1/8 
 
 
 
 
 
 
 
 33 
 
 52 
 
 70 
 
 81 
 
 
 
 
 
 
 
 
 
THE SLIDE-VALVE. 
 
 1043 
 
 Periods of Admission, or Points of Cut-off, for given Travels and 
 Laps of Slide-valves. 
 
 Constant lead, 5/ 16 . 
 
 Travel. 
 
 
 
 
 Lap. 
 
 
 
 
 
 Inches. 
 
 1/2 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 H/8 
 
 11/4 
 
 13/8 
 
 U-2 
 
 1 ; V8 
 
 19 
 
 
 
 
 
 
 
 
 
 13/4 
 
 39 
 
 
 
 
 
 
 
 
 
 17/8 
 
 47 
 
 17 
 
 
 
 
 
 
 
 
 2 
 
 55 
 61 
 
 34 
 42 
 
 
 
 
 
 
 
 
 21/8 
 
 14 
 
 
 
 
 
 
 
 21/4 
 
 65 
 
 50 
 
 30 
 
 
 
 
 
 
 
 23/8 
 
 68 
 71 
 74 
 76 
 78 
 80 
 8! 
 83 
 84 
 
 55 
 59 
 63 
 67 
 70 
 73 
 74 
 76 
 78 
 
 38 
 45 
 49 
 56 
 59 
 62 
 65 
 68 
 71 
 
 13 
 27 
 36 
 43 
 47 
 50 
 55 
 59 
 62 
 
 
 
 
 
 
 21/2 
 
 
 
 
 
 
 25/ 8 
 
 12 
 26 
 32 
 38 
 44 
 48 
 51 
 
 
 
 
 
 23/ 4 
 
 
 
 
 
 27/8 
 
 11 
 23 
 30 
 34 
 40 
 
 
 
 
 3 
 
 
 
 
 31/8 
 
 10 
 22 
 29 
 
 
 
 31/4 
 
 
 
 33/ 8 
 
 9 
 
 
 31/2 
 
 85 
 
 80 
 
 73 
 
 64 
 
 53 
 
 45 
 
 34 
 
 20 
 
 
 35/g 
 
 86 
 
 81 
 
 75 
 
 66 
 
 57 
 
 49 
 
 38 
 
 26 
 
 9 
 
 33/4 
 
 87 
 
 82 
 
 76 
 
 68 
 
 60 
 
 52 
 
 42 
 
 32 
 
 19 
 
 37/s 
 
 87 
 
 83 
 
 78 
 
 70 
 
 63 
 
 55 
 
 46 
 
 36 
 
 25 
 
 4 
 
 88 
 
 84 
 
 79 
 
 72 
 
 66 
 
 58 
 
 49 
 
 40 
 
 29 
 
 41/4 
 
 89 
 
 86 
 
 81 
 
 76 
 
 70 
 
 63 
 
 56 
 
 47 
 
 37 
 
 41/2 
 
 90 
 
 87 
 
 83 
 
 79 
 
 73 
 
 67 
 
 61 
 
 54 
 
 45 
 
 43/ 4 
 
 92 
 
 89 
 
 85 
 
 81 
 
 76 
 
 70 
 
 65 
 
 58 
 
 51 
 
 5 
 
 93 
 
 90 
 
 87 
 
 83 
 
 78 
 
 73 
 
 67 
 
 62 
 
 56 
 
 51/2 
 
 94 
 
 92 
 
 89 
 
 86 
 
 82 
 
 78 
 
 73 
 
 68 
 
 63 
 
 6 
 
 95 
 
 93 
 
 91 
 
 88 
 
 85 
 
 82 
 
 78 
 
 74 
 
 69 
 
 Piston- 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 about 
 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 pullev 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 
 
1044 THE STEAM-ENGINE. 
 
 the error that may arise from the looseness of crank-pin and wrist-Din 
 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 bv 
 varying the travel of the valve. The Stephenson link-motion is a com- 
 bination of two eccentrics, called forward and back eccentrics with a link 
 connecting the extremities of the eccentric-rods ; so that bv 'varying the 
 position of the link the valve-rod may be put in direct connection with 
 either eccentric, or may be given a movement controlled in part bv one 
 and in part by the other eccentric. When the link is moved by the revers- 
 ing 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. 
 
 , j 11 VVL ordi , nal 7 shifting-link with open rods, that is, not crossed, the 
 lead ot 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 of lead 
 is equalized for the front and back strokes by curving the link to the radius 
 ot 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, equals 
 180 less twice the angular advance. 
 
 Buel, in Appleton's Cyclopedia of Mechanics, vol. ii, p. 316, 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 exhaust 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 describes 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 in its center, the curves that 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 corre- 
 sponding 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. 
 
 1045 
 
 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 1095.) 
 
 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. 165, drawn through the center 
 of the slot; this radius is generally made equal to the distance from the 
 
 \ 
 
 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 ei 62 should not be less than 21/2 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 slot 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, B 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 
 
 Breadth of the link = 72X16 . 
 
 Thickness T of the bar = RX 0.8 
 
 Length of sliding-block = RX 2.5 
 
 Diameter of eccentric-rod pins = (R X . 7) + 1/4 in. 
 
 Diameter of suspension-rod pin = (R X . 6) + 1/4 in. 
 
 Diameter of suspension-rod pin when overhung. . . = (R X . 8) + 1/4 in. 
 
 Diameter of block-pin when overhung = RXVa 
 
 Diameter of block-pin when secured at both ends . = (R X . 8) + 1/4 in. 
 
1046 THE STEAM-ENGINE. 
 
 The length of the link, that is, the distance from a to 6, measured on a 
 straight line joining the ends of the link-arc in the slot, should be such 
 as to allow tne 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 21/2 to 23/4 times 
 the throw of eccentrics can be found as follows: 
 
 Depth of bars = (R X 1 . 25) + l/2in. 
 
 Thickness of bars = (R X . 5 ) + 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 0.5 ) + 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. 1095.) 
 
 The Walschaert Valve-gear. Fig. 166. — 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 
 
 Fig. 166. — The Walschaert Valve-gear. 
 
 lowered in the link by the reversing rod I, operating through the bell- 
 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 crosshead R. Constant lead is secured by this gear. 
 
GOVERNORS. . 1047 
 
 Other Forms of Valve-gear, as the Joy, Marshall, Hackworth, 
 Bremrae, Walschaert, Corliss, etc., are described in Clark's Steam-engine 
 vol. ii. Power, May 11, 1909, illustrates the Stephenson, Gooch, Allen' 
 Polenceau, Marshall, Joy, Waldegg, Walschaert, 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 Re versing- 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 wtf 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 = 2irrT = or, 
 in which a = the angular velocity, or 2 nT, and 
 
 . gr 2 g . 0.8146. . 9.775. , 
 
 h = tfT = 4^2- 0r h = ~W~ feet = ~W mcheS ' 
 g — 32.16. If N = revs, per minute, h = 35,190 -h iV 2 . 
 
 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 _ 
 
 N ,Jp*L , 18 7.6./-L_ = 187.6 JL 
 
 V I COS a T I COS a T h 
 
 The simple governor is not isochronous; that is, it does not revolve 
 at a uniform speed in all 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 Z = the length of the arm from the point 
 of suspension to the center of gravitv 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 ttT, T being the number of 
 
 ^ .u . /32-.16A , 2hQ\ . 32.16 /, , 2l t Q\ 
 
 revolutions per second ; then a = 4/ — j- — ^1 + —r- ^ J ; n = — -^— \± + -j- g 1 
 
 in feet, or h = 3 ^° /l + — |) in inches, N being the number of revo- 
 lutions per minute. 
 
1048 THE STEAM-ENGINE. 
 
 (1 S7 7\2 7? 4- 1 TV 
 ' \ - , 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-baii 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 Mcintosh & 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; xv, 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. 
 
 More 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. Inst. 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 r% = the maximum and minimum radial distances of the 
 center of the balls or of the centers of gravity of the weights; 
 
GOVERNORS. 1049 
 
 li 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 n ; 
 
 mi and m 2 = the corresponding leverages of the springs; 
 
 Ci and C'i = the centrifugal forces, for 100 revolutions per minute, 
 at radii n and r 2 ; 
 
 Pi and Pi = the corresponding pressures on the spring; 
 
 (It is convenient to calculate these and note them down for refer- 
 ence.) 
 
 Cz and C 4 = maximum and minimum centrifugal forces; 
 
 S = mean speed (revolutions per minute); 
 
 Si and Si = the maximum and minimum number of revolutions 
 per minute; 
 
 Pz and P4, = the pressures on the spring at the limiting number 
 of revolutions (Si and £2); 
 
 P 4 — P3 = 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. 
 Then 
 
 „ sv. 
 
 
 s '= s + Wo ; 
 
 Ci = 0.28XnX W; 
 
 
 C 2 =0.28Xr 2 XTF; 
 
 **>&&• 
 
 
 p 2 =c 2 x— ; 
 
 mi 
 
 *=M#o) !; 
 
 
 *<-™<m-' 
 
 D 
 
 v= 1 ,u- 
 
 = Pz 
 
 V 
 
 p t 
 
 » w = — 
 
 V 
 
 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 formulae for strength and extension of springs, and 
 the least length of the spring as compressed be determined. 
 
 The governor-power = 5 — X j- 9 - 
 
 With a straight centripetal line, the governor-power 
 _ C3+C4 v [ ri-n \ 
 ~ 2 X \ 12 )' 
 
 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 P G = P 5 + D, _ _ 
 
 s 5 =iooy/|2. s fl -iooy|*. 
 
 The speed at which the governor would be isochronous would be 
 
 Vf 
 
 Suppose the pressure on the spring with a speed of 100 revolutions, at 
 the maximum and minimum radii, was 200 lbs, and 100 lbs,, respectively, 
 
1050 
 
 THE STEAM-ENGINE. 
 
 then the pressure of the spring to suit a variation from 95 to 105 revolu- 
 tions will be 100 X (^)'= 90 .2 and 200x(j^) 2 = 220.5 That is, the 
 
 increase of resistance from the minimum to the maximum radius must be 
 220-90 = 130 lbs. 
 
 The extreme speeds due to such a spring, screwed up to different 
 pressures, are shown in the following table: 
 
 Revolutions per minute, balls shut 
 
 Pressure on springs, balls shut 
 
 Increase of pressure when balls open fully 
 
 Pressure on springs, balls open fully 
 
 Revolutions per minute, balls open fully . . 
 Variation, per cent of mean speed 
 
 80 
 
 90 
 
 95 
 
 100 
 
 110 
 
 64 
 
 81 
 
 90 
 
 100 
 
 121 
 
 130 
 
 130 
 
 130 
 
 130 
 
 130 
 
 194 
 
 211 
 
 220 
 
 230 
 
 251 
 
 98 
 
 102 
 
 105 
 
 107 
 
 112 
 
 10 
 
 6 
 
 5 
 
 3 
 
 1 
 
 130 
 274 
 117 
 -1 
 
 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 spring 
 whose stiffness is 50 lbs. per inch acts best when the engine runs at 95, 90 
 
 /90\ 2 
 being its proper speed, then 50 X \qz) =45 lbs. 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. 
 
 Another formula is: Q 
 
 WH 
 
 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; Ti = temperature of the water after condensa- 
 tion, or of the hot-well; Q = pounds of the cooling-water per lb. of steam 
 condensed; then 
 
 1114° + 0.3 T1-T2 
 Q T2-T0 
 
 in which W is the weight of steam con- 
 densed, H the units of heat given up by 1 lb. 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. 
 
 1051 
 
 Pounds of Circulating Water per Pound 
 
 of Steam Condensed. 
 
 Vac- 
 
 Drop. 
 
 Deg. 
 
 F. 
 
 
 
 Inject 
 
 on Water Temperature, Deg. F. 
 
 Ins. 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 85 
 
 90 
 
 29.0 
 
 6 
 
 12 
 18 
 
 37.5 
 
 47.8 
 65.7 
 
 45.7 
 61.8 
 95.5 
 
 58.3 
 87.5 
 
 80.8 
 
 
 
 
 
 
 
 28.5 
 
 6 
 12 
 18 
 
 25.6 
 30.0 
 36.2 
 
 29.2 
 35.0 
 
 43.8 
 
 33.9 
 42.0 
 55.3 
 
 40.3 
 52.5 
 75.0 
 
 50.0 
 70.0 
 
 65.7 
 
 95.5 
 
 
 
 
 28.0 
 
 6 
 12 
 
 18 
 
 21.5 
 
 24.4 
 28.4 
 
 23.9 
 27.7 
 32.8 
 
 26.9 
 31.8 
 38.9 
 
 30.9 
 37.5 
 47.8 
 
 36.3 
 45.7 
 61.8 
 
 43.8 
 58.3 
 87.5 
 
 55.3 
 80.8 
 
 75.0 
 
 
 
 27.0 
 
 6 
 
 12 
 18 
 
 16.4 
 18.1 
 20.2 
 
 17.8 
 19.8 
 22.4 
 
 19.5 
 21.9 
 25.0 
 
 21.5 
 24.4 
 28.4 
 
 23.9 
 27.7 
 32.8 
 
 27.0 
 31.8 
 38.9 
 
 30.9 
 37.5 
 47.8 
 
 36.2 
 
 45.7 
 61.8 
 
 43.8 
 58.3 
 87.5 
 
 55.3 
 80.8 
 
 26.0 
 
 6 
 12 
 18 
 
 14.0 
 15.2 
 16.8 
 
 15.0 
 16.4 
 18.1 
 
 16.2 
 17.8 
 19.8 
 
 17.5 
 19.5 
 21.9 
 
 19.1 
 21.5 
 24.4 
 
 21.0 
 23.9 
 27.7 
 
 23.4 
 26.9 
 31.8 
 
 26.3 
 30.9 
 37.5 
 
 30.0 
 36.3 
 45.7 
 
 35.0 
 43.8 
 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 lbs. 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., lbs., abs. . 30 20 15 12l/ 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, 431 ) 
 
 gives the following: S= , ,„ ,. , in which S = condensing-surface in 
 
 sq. ft.; T\ = 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 Tv, 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 Isherwood's experiments); 
 c = fraction denoting the efficiency of the condensing-surface; W = 
 
1052^ THE STEAM-ENGINE. 
 
 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 
 
 WL 
 the equation S = 18Q (7W) - 
 
 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 T\ at 135° F., and L = 1020, corresponding to 25 in. vacuum, 
 
 a ** . * + ^ C o 1020 TF 17 W 
 
 and t for summer temperatures at 75°, we have: £= ■)= „„ ■• 
 
 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 Tranference 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 561 to 563.) 
 
 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 
 
 1/U = 1/Ai+ d/L + I/A2, 
 in which 1/Ai is the resistance to transmission from steam to metal, I/A2 
 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 I/A2 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 V?, 
 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: 
 1/U = 1/3900 + 1/18,430 + 1/653 = 1/445, 
 
 and U = 445. 
 
 If A 1 be increased to twice its value IT 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 
 
 tg — to 
 
 Surface = S - g log e j^f* 
 
CONDENSERS, AIR-PUMPS, ETC. 1053 
 
 where t s is the saturation temperature and i e 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 steam 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 lb. of air was delivered per hour when 6600 lbs. 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 
 11/2 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 lb. of steam 32 to 37 
 lbs. 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 0.85 
 
 % 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 
 
1054 
 
 THE STEAM-ENGINE. 
 
 that of the vacuum gauge, or preferably to give the absolute pressure in 
 lbs. per sq. in. above a perfect vacuum. 
 
 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 Air with Accompanying Vapor. 
 
 
 Is 
 
 Vacuum, ins. of Mercury, and lbs. 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° 
 
 0.17 
 0.23 
 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 
 
 1.79 
 1.71 
 1.60 
 1.46 
 1.27 
 1.02 
 0.70 
 0.28 
 
 V 
 
 !05 
 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 
 (6) 
 
 P 
 
 0.57 
 0.49 
 0.38 
 0.24 
 0.05 
 
 V 
 
 336 
 393 
 520 
 832 
 (c) 
 
 P 
 
 0.42 
 0.34 
 0.2.3 
 0.09 
 
 V 
 450 
 566 
 852 
 id) 
 
 P 
 
 0.32 
 0.24 
 0.13 
 
 V 
 592 
 800 
 1536 
 
 90° 
 
 
 
 100° 
 
 
 
 
 
 110° 
 
 
 
 
 
 
 
 120° 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 P = partial pressure of air, lbs. per sq. in. V = volume of 1 lb. 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 
 
 Air, 0.25. 
 
 Air, 0.5. 
 
 Air, 0.75. 
 
 Air, 1. 
 
 Steam. 
 
 Steam, 1 . 
 
 Steam, 1 . 
 
 Steam, 1 . 
 
 Steam, I. 
 
 29 
 
 79.5°F. 
 
 75 
 
 71 
 
 67.5 
 
 64.5 
 
 28 
 
 101.5 
 
 96.5 
 
 92.4 
 
 88.8 
 
 85.3 
 
 27 
 
 115 
 
 110 
 
 105.6 
 
 101.7 
 
 98.6 
 
 26 
 
 126 
 
 120.2 
 
 115.5 
 
 111.5 
 
 108.3 
 
 25 
 
 134 
 
 128.4 
 
 123.5 
 
 119.2 
 
 116.2 
 
 24 
 
 141 
 
 135.2 
 
 130.3 
 
 125.8 
 
 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 cu. 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 lbs. 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 s/ 8 in. diam., and 19 
 
CONDENSERS, AIR-PUMPS, ETC. 
 
 1055 
 
 B.W.G. The smaller the tubes, the larger is the surface which can be got 
 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. 
 
 Bimetallic Condenser Tubes. (E. K. Davis, Eng. News, Sept. 2, 
 1909.) —Condenser tubes are usually made of a brass containing about 
 40% zinc. When this alloy is found to be short-lived, due to the presence 
 of corrosive substances in the cooling-water, recourse is had to bronze 
 tubing of "admiralty mixture " (87% copper, 8% tin, 5% zinc) or to pure 
 copper. Sometimes also the tubes for further protection are tinned on the 
 inside or on both sides. 
 
 A condenser tube should not split, should be comparatively free from 
 localized corrosion or pit holes, and should not become brittle under the 
 combined action of steam and cooling-water. 
 
 A bimetallic tube, composed of a copper envelope over an aluminum 
 lining (or vice versa) is unlikely to split, owing to its being composed of 
 two layers of metal. It is slow to corrode with the aluminum surface 
 exposed to the cooling-water, and there is no tendency shown toward 
 becoming brittle. Aluminum, being electro-positive to copper, protects 
 it from corrosion in somewhat the same way that even porous galvanizing 
 protects iron. No corrosion of the copper will take place until the alumi- 
 num has been entirely eaten away for a considerable distance around the 
 perforation, thus leaving a sound tube for a much longer time than is the 
 case when brass or copper is used alone. The usual proportions of metal 
 are, .022 in. thickness of copper and .043 in. of aluminum, making a 
 total of .065 in., or No. 16 Stubs gauge. 
 
 Tube-plates are usually made of brass. Rolled-brass tube-plates 
 should 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/s to 1 in. thick with glands and tape-packings, and 1 to 1 1/4 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 
 H/16 
 
 H/8 
 
 172 
 150 
 137 
 
 15/32 
 13/ie 
 17/32 
 
 128 
 121 
 116 
 
 11/4 
 19/32 
 15/16 
 
 110 
 106 
 99 
 
 Air-pump. — ■ The air-pump in all condensers abstracts the water 
 condensed 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 
 condensation and the air which it contained. The size of the pump is cal- 
 culated from these conditions, making allowance for efficiency of the pump. 
 
 In surface condensation allowance must be made for the water occasion- 
 ally admitted to the boilers to make up for waste, and the air contained 
 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 .5 and that of a double-acting pump at M. When the tem- 
 
1056 
 
 THE STEAM-ENGINE. 
 
 perature of the sea is 60°, and that of the (jet) condenser is 120°, Q being 
 the volume of the cooiing-water and q the volume of the condensed water 
 in cubic feet, and n the number of strokes per minute. 
 
 The volume of the single-acting pump = 2.74 (Q + q) -s- n. 
 
 The volume of the double-acting pump = 4 (Q + q) -h 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 
 he gives .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 lbs. of 
 steam per hour from a surface condenser, which is equivalent to .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 veloc- 
 ity not exceeding 400 ft. per minute. In practice the area is generally in 
 excess of this. (Seaton.) 
 
 Area through foot-valves = D 2 X S <- 1000 square inches. 
 Area through head-valves = D 2 X S -*- 800 square inches. 
 Diameter of discharge-pipe = Z> X v o ■*- 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- 
 pumps used with jet-condensers: Volume of single-acting air-pump driven 
 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 -J- 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 
 
 r/p 2 \0-29 -i 
 
 is P — 3 .46 V\ I ( ) - 1 • where p = absolute pressure of the vacuum 
 
 and P2 the terminal, or atmospheric, pressure, = 14 .7 lbs. 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 -4- 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 
 
 V2 
 
 Theo- 
 retic. 
 
 Theo- 
 retic. 
 
 Vac. in 
 Ins. of 
 Mer- 
 
 Abs. 
 Press., 
 Ins. of 
 
 P2 
 
 Theo- 
 retic. 
 
 Theo- 
 retic. 
 
 Mer- 
 
 Pi 
 
 M.E.P. 
 
 H.P. 
 
 Mer- 
 
 Pi 
 
 M.E.P. 
 
 H.P. 
 
 cury. 
 
 cury. 
 
 
 
 
 cury. 
 
 cury. 
 
 
 
 
 29 
 
 1 
 
 30.00 
 
 2.86 
 
 0.0124 
 
 18 
 
 12 
 
 2.50 
 
 6.21 
 
 0.0271 
 
 28 
 
 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 
 
 1.87 
 
 5.42 
 
 0.0236 
 
 26 
 
 4 
 
 7.50 
 
 5.40 
 
 0.0235 
 
 12 
 
 18 
 
 1.67 
 
 4.88 
 
 0.0212 
 
 25 
 
 5 
 
 6.00 
 
 5.78 
 
 0.0252 
 
 10 
 
 20 
 
 1.50 
 
 4.23 
 
 0.0184 
 
 24 
 
 6 
 
 5.00 
 
 6.05 
 
 0.0264 
 
 8 
 
 22 
 
 1.36 
 
 3.52 
 
 0.0153 
 
 23 
 
 7 
 
 4.28 
 
 6.23 
 
 0.0271 
 
 6 
 
 24 
 
 1.25 
 
 2.73 
 
 0.0119 
 
 22 
 
 8 
 
 3.75 
 
 6.33 
 
 0.0276 
 
 4 
 
 26 
 
 1.15 
 
 1.88 
 
 0.0082 
 
 21 
 
 9 
 
 3.33 
 
 6 37 
 
 0.0278 
 
 2 
 
 28 
 
 1.97 
 
 0.96 
 
 0.0042 
 
 20 
 
 10 
 
 3.00 
 
 6.36 
 
 0.0277 
 
 1 
 
 29 
 
 1.03 
 
 0.49 
 
 0021 
 
CONDENSERS, AIR-PUMPS, ETC. 1057 
 
 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 c ubic fee t. 
 
 Diameter of circulating-pump = 13.55 ^Q-i-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 its 
 periphery 450 to 500 ft. per min. 
 
 The Leblanc Condenser (made by the Westinghouse Machine Co.) 
 accomplishes the separate removal of water and air by means of a pair of 
 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-pump 
 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 the water in the boiler is to 
 that of sea- water, then the gross feed-water =nQ-^ (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 = Vs. 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 
 
1058 
 
 THE STEAM-ENGINE. 
 
 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 lbs. steam per 
 hour and give a vacuum of 22 in., with a terminal pressure in the cylinder 
 of 20 lbs. 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. 
 
 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 
 
 40 30 "24 20 17 
 
 Per Cent ot Power Gained by Vacuum 
 
 Fig. 166. 
 
 be approximated by considering it to be equivalent to a net gain of 12 lbs. 
 mean effective pressure per sq. in. of piston area. If A = area of piston 
 
CONDENSERS, AIR-PUMPS, ETC. 1059 
 
 in sq. ins., S = piston speed in ft. per min., then 12 AS -s- 33,000 = 
 AS -4- 2750 = H.P. made available by the vacuum. If the vacuum = 
 13.2 lbs. per sq. in. = 27.9 in. of mercury, then H.P. = AS h- 2500. 
 
 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 lbs. 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 
 give the percentage of saving. 
 
 The diagram on page 1058 (from 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 lbs. per sq. 
 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 lbs. gauge (= 105 lbs. 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 V4 
 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 lbs. From this 
 subtract the mean absolute back pressure (say 3 lbs. for a condensing 
 engine and 15 lbs. 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 lbs. 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 lbs. in the upper row, in this case 25%. 
 As the diagram does not take into consideration clearance or compression, 
 the results are only approximate. 
 
 Advantage of High Vacuum in Reciprocating Engines. (R. D. 
 Tomlinson, 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 in 
 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 mingles 
 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 
 
1060 THE STEAM-ENGINE. 
 
 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 again. (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. 
 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 so., 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 lb. of steam per hour when supplied with circulating waler 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 
 
CONDENSERS, AIR-PUMPS, ETC. 
 
 1061 
 
 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 lb. 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 heat to be absorbed through the evaporation 
 of the water. The two things to be sought after in cooling-tower 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. 
 
 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 lbs. 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. 
 
 Temperature atmosphere 
 
 Temp, condenser discharge 
 
 Temp, water from tower 
 
 Heat extracted by tower 
 
 Speed of fans, r.p.m 
 
 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 
 
 Max. 
 103 
 128 
 98 
 32 
 160 
 26 
 
 Min- 
 
 83 
 106 
 
 91 
 
 21 
 140 
 
 26 
 
 
 
 The quantity of steam condensed or of water circulated is not stated, 
 but 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- 
 pressure valve-chest, so that there is no loss of energy, and the water con- 
 densed 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. 
 
1062 THE STEAM-ENGINE. 
 
 ROTARY STEAM-ENGINES — STEAM TURBINES. 
 
 Rotary Stea n-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 wbeel, 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 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 
 
ROTARY STEAM-ENGINBS — STEAM TURBINES. 1063 
 
 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. 
 
 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 t — Ei) ■*- E x , in 
 which E t is the kinetic energy of the steam jet impinging on the wheel 
 and Ei 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 
 
1064 
 
 THE STEAM-ENGINE. 
 
 f 
 
 d D/ 
 
 bA 
 
 T2 /, 
 
 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 dis- 
 charge it into the atmosphere, or into the 
 condenser, at the lowest pressure and largest 
 volume possible, and with the lowest pos- 
 sible absolute velocity, or velocity with ref- 
 erence 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 or fric- 
 tional 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 steam containing a certain 
 quantity of heat, H x , transform as great a 
 part of this heat as possible into work, and 
 discharge the remaining part, Hi, into the condenser. The thermal effi- 
 ciency of the operation is (H t — Hi) -*■ Hi, and the theoretical limit of 
 this efficiency is (7\ — Ti) -s- !T2,in which 7\is the initial and Ti the final 
 absolute temperature. 
 
 Referring to temperature entropy diagram, Fig. 167, the total heat 
 above 32° F. of 1 lb. of steam at the temperature 7\ is represented by 
 the area OACDG and its entropy is fa. Expanding adiabatically to Ti 
 part of its heat energy is converted into work, represented by the area 
 BCDF, while OABFG represents the heat discharged into the condenser. 
 The total heat of 1 lb. of dry saturated steam at T 2 is greater than this by 
 the area EFGH, the fraction FE -f- BE representing moisture in the 1 lb. 
 of wet steam discharged. If H t = heat units in 1 lb. of dry steam at 
 the state-point D, and Hi = heat units in 1 lb. of dry steam at the state- 
 point E, at the temperature Ti, then the energy converted into work = 
 BCDF = Hi - Hi + (fa - fa) Ti. This quantity is called the avail- 
 able energy E a , of 1 lb. of steam between the temperatures T x and Ti. 
 
 If the steam is initially wet, as represented by the state-point d and 
 entropy <j> x , then the work done in adiabatic expansion is BCdfB, 
 which is equal to E a = H x - Hi + (fa - fa) Ti -{fa - <j> x )(T x - Ti). 
 The quantity fa — <j> x = {L/T\) (1 — x), in which L = latent heat of 
 evaporation at the temperature T lt and x = the moisture in 1 lb. of 
 steam. The values of H lt Hi, fa, fa, 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 fa, 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 Ti and T s . The increase of entropy above fa 
 
 H 
 
 Fig. 167. 
 
KOTARY STEAM-ENGINES — STEAM TURBINES. 1065 
 
 is & - $1 = Clog e (T s /Tt). The energy converted into work is # = 
 H t - Hz + (& - ft) ^2 + [1/2 (T s + Ti) - T 2 ] (<f> 3 - 4>x). 
 
 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 W is the weight (in this case 1 lb.). V is the velocity in feet per 
 second, and g = 32.2. As the energy E a is in heat units, it is multi- 
 plied by 778 to convert it into foot-pounds, and we have 
 
 V =^778 X 2gE a = 223.8 ^E~ 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 Rateau's formula, see page 847, or from Gras- 
 hof's formula as given by Moyer, F = A Pi ' 9 ' ■*■ 60, or A = 60 F ■*■ 
 . P J - 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 lbs. per sec, 
 and P is the absolute pressure, lbs. per sq. in. This formula is applicable 
 in all cases where the final pressure P2 does not exceed 58% of the initial 
 pressure. For wet steam the formula becomes F = A Pi ' 97 h- 60 Va;, 
 A = 60 F "^x •*- Pi 0-97 , in which x is the dryness quality of the inflow- 
 ing steam, 1 — x being the moisture. 
 
 For superheated steam F = A P 1 °' m (l+ 0.00065 D) -f- 60; A = 60P + 
 PjO-9/ (i + 0.00065 D), D being the superheat in degrees F. 
 
 When the final pressure Pi is greater than 0.58 Pi, 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 P1/P2, are approximately as follows: 
 P 2 -hPi= 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 
 c= 1. 0.995 0.985 0.975 0.965 0.955 0.945 0.93 0.910.88 0.85 
 Pi + P t = 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 
 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, X2, is found from the 
 formula x 2 = {x x Lr/T x + X - 2 ) T2/L2, (8) 
 
 in which 0i and 02 are the entropies of the liquid, Li and L2 the latent 
 heats of evaporation, and x 1 and X2 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 Davis'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 A 1 /A Q =V /V 1 X v^/Vq X Xt/x b , in which A is in the area in 
 sq. ins., V the velocity in ft. per sec, v the volume of 1 lb. 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/A for the largest cross section of a properly designed nozzle is nearly 
 proportional to the ratio of the initial to the final pressure. Moyer 
 gives it as At/A = 0.172 P^/Pt + 0.70, and for Pi/P2 greater than 25, 
 Ai/A Q = 0.175 (P 1 /P 2 )°- 94 + 0.70. 
 
 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. 
 Moyer gives an empirical formula for the length between the throat and 
 the mouth, L = Vl5 Aq 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%. 
 
1066 
 
 THE STEAM-ENGINE. 
 
 Speed of the Blades. — If V b = peripheral velocity of the blade, 
 V x = 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 V x 
 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^/Vl 
 
 For Vi = 3000 ft. per sec, the efficiency for different blade speeds is 
 about as follows: 
 
 V b = 200 400 600 800 1000 1200 1400 1600 1800 2000 
 
 Efficiency % 23 44 60 72 81 87 89 87 80 71 
 
 The highest efficiency is obtained when V b = about 1/2 V2. It is 
 difficult, for mechanical reasons, to use speeds much greater than 500 ft. 
 per sec, therefore the highest efficiencies are often sacrificed in commer- 
 cial 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 moving 
 
 4JVF 6/ NV b . 
 blades in a single pressure stage, efficiency = — ^ — (cos a — J • 
 
 Referring to Fig. 168, if Vi is the absolute direction and velocity of the 
 entering jet, V b the direction and velocity of the blade, the resultant, 
 V r , is the velocity and direction of the jet rela- 
 tively to the blade, and the edge of the blade 
 is made tangent to this direction. Also V x , the 
 resultant of V b and V r at the other edge of the 
 blade, is the absolute velocity and direction of 
 the steam escaping from the wheel. If /? is the 
 angle between F r and V b , the maximum energy 
 is abstracted from the steam when the angle 
 between V z and V b = 90 - 1/2 /?, and the effi- 
 ciency is cos /? -*- cos 2 1/2 0. 
 
 For details of design of blades, and of turbines 
 in general, see Moyer, Foster, Thomas, Stodola 
 and other works on Steam Turbines, also Pea- 
 body'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. 
 
 1. Few stages. 
 
 2. Expansion in nozzles. 
 
 3. Large drop in pressure in a 
 
 stage. 
 
 4. Initial steam velocities 1000 to 
 
 4000 ft. per sec. 
 
 5. Blade velocities 400 to 1200 ft. 
 
 per sec 
 
 6. Best efficiency when the blade 
 
 velocity is nearly half the ini- 
 tial velocity of steam. 
 
 Reaction. 
 
 Many stages. 
 
 No nozzles. 
 
 Small drop in pressure in a 
 
 stage. 
 All steam velocities low, 300 to 
 
 600 ft. per sec. 
 Blade velocities 150 to 400 ft. 
 
 per sec. 
 Best efficiency when the blade 
 
 velocity is nearly equal to 
 
 the highest velocity of the 
 
 steam. 
 
 Loss 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 b , in horse-power: 
 
 F w = 0.08 d 2 (m/100) 2 - s w + (1 + 0.00065 D) 2 , 
 F b = 0.3 d 7.i- c (m/100)2- 8 w-h (1 + 0.00065 D) 2 , 
 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 lbs. per cu. ft., and D = super- 
 heat in degrees F. The sum of F w and F b is the friction of the di^k and 
 blades. For moist steam the term 1 + 0.00065 D is to be omitted, and 
 the expression multiplied by a coefficient c, whose value is approxi- 
 mately as follows: 
 
ROTARY STEAM-ENGINES STEAM TURBINES. 1067 
 
 Per cent mois- 
 ture in steam 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. 167 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 designs and to 50% 
 or more in small sizes or poor designs. 
 
 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 lbs. gauge, 28.5 ins. vacuum, and 100° F. superheat. 
 
 7500-K.W. 
 
 Westing- 
 
 house- 
 Parsons. 
 
 Correc- 
 tions, 
 per cent. 
 
 9000-K.W. 
 
 Curtis, 
 
 Correc- 
 tions, 
 per cent. 
 
 Average steam pressure 
 
 Average vacuum, ins., referred 
 
 to 30-in. barometer 
 
 Average superheat, deg. F 
 
 Average load on generator,K.W. 
 Steam cons., lbs.. per K.W.-hr. . 
 
 Net correction, per cent 
 
 Corr. st. cons., lbs. per K.W.-hr. 
 
 177.5 
 
 27.3 
 
 95.7 
 
 9830.5 
 
 15.15 
 
 -3.36 
 -0.29 
 
 179 
 
 29.55 
 116 
 8070 
 13.0 
 
 h 12.39 
 h 1.28 
 
 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% fo r 
 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 
 
1068 
 
 THE STEAM-ENGINE. 
 
 are equivalent respectively to 9.58 and 9.72 lbs. per I.H.P.-hour, assum- 
 ing 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. 
 
 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 
 Westinghouse-Parsons, per cent gain per 
 
 5.1 
 5.0 
 
 3.14 
 5.2 
 
 4.8 
 4.0 
 
 3.05 
 4.4 
 
 4.6 
 3.5 
 
 2.95 
 3.7 
 
 4.2 
 3.0 
 
 2.87 
 
 Theoretical per cent gain per inch of vac. 
 
 3.0 
 
 The following results of tests of turbines of different makes are selected 
 from a series of tables in Moyer's "Steam Turbines". 
 
 lis 
 
 1^ 
 
 MS 
 
 
 a 
 
 0) 1 
 
 $£ 
 
 
 £ 
 
 MS 
 3 £ 
 
 
 i ■ 
 
 ji 
 
 
 s* 
 
 8* 
 
 o^ 
 
 £*-* 
 
 o3 "' 
 
 !> 
 
 &* 
 
 XT 
 
 <§« 
 
 O^ 
 
 £*-* 
 
 g«* 
 
 2000 ( 
 
 c. | 
 
 555 
 
 155 
 
 204 
 
 28.5 
 
 18.09 
 
 300 ( 
 W.-P.j 
 
 233 
 
 145 
 
 4.1 
 
 28.0 
 
 15.99 
 
 1067 
 
 170 
 
 120 
 
 28.4 
 
 16.31 
 
 461 
 
 145 
 
 4.8 
 
 28.0 
 
 13.99 
 
 2024 
 
 166 
 
 207 
 
 28.5 
 
 15.02 
 
 688 
 
 140 
 
 7.0 
 
 27.2 
 
 15.73 
 
 1 
 
 5374 
 
 182 
 
 133 
 
 29.4 
 
 13.15 
 
 ( 
 
 383 
 
 153 
 
 2 
 
 28.2 
 
 14.15 
 
 9000 1 
 
 8070 
 
 179 
 
 116 
 
 29.4 
 
 13.00 
 
 1 
 
 756 
 
 149 
 
 1 
 
 27.8 
 
 13.28 
 
 C, ) 
 
 10186 
 
 176 
 
 147 
 
 29.5 
 
 12.90 
 
 500 J 
 
 1122 
 
 149 
 
 5 
 
 26.5 
 
 14.32 
 
 1 
 
 13900 
 
 198 
 
 140 
 
 29.3 
 
 13.60 
 
 w.-p.i 
 
 386 
 
 148 
 
 3 
 
 0.8 
 
 24.94 
 
 1500 ( 
 
 530 
 1071 
 
 145 
 131 
 
 110 
 124 
 
 28.9 
 
 28.3 
 
 21.58 
 18.24 
 
 I 
 
 767 
 1144 
 
 14; 
 
 126 
 
 3 
 11 
 
 0.8 
 0.8 
 
 22.10 
 24.36 
 
 1585 
 
 128 
 
 125 
 
 27.5 
 
 17.60 
 
 1000 ( 
 W.-P.J 
 
 752 
 
 151 
 
 
 
 27.5 
 
 14.77 
 
 300/ 
 P. i 
 
 303 
 297 
 
 158 
 161 
 
 
 
 
 26.6 
 
 
 23.15 
 34.20 
 
 1503 
 2253 
 
 147 
 145 
 
 
 
 
 27.0 
 25.2 
 
 13.61 
 15.29 
 
 f 
 
 194 
 
 171 
 
 47 
 
 27 7 
 
 31 97 
 
 3000 t 
 
 2295 
 
 152 
 
 102 
 
 26.2 
 
 12.36 
 
 1000 I 
 
 425 
 
 144 
 
 21 
 
 27.6 
 
 24.91 
 
 W.-P.I 
 
 4410 
 
 144 
 
 87 
 
 26.2 
 
 11.85 
 
 R. ) 
 
 871 
 
 166 
 
 11 
 
 23.6 
 
 24.61 
 
 300 ( 
 
 D I 
 
 196 
 
 198 
 
 16 
 
 27.4 
 
 15.62 
 
 
 1024 
 
 164 
 
 10 
 
 25.0 
 
 21.98 
 
 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., De Laval. Note that the figures of steam consumption in the first 
 half of the table are in lbs. per K.W.-hour ; in second half, in lbs. per Brake 
 H.P.-hour. 
 
 A test of a Westinghouse double-flow turbine at the Williamsburg 
 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 lbs.; 
 Superheat, 80.1° F.; Vacuum, 28.6 ins.; Load, 13,384 K.W.; Steam per 
 K.W.-hour, 14.4 lbs.; Efficiency of generator, 98%; Windage, 2.0%; 
 Equivalent B.H.P., 18,620; Steam per B. H.P.-hour, 10.3 lbs. 
 
 The Largest Steam Turbine, 1909. (Eng. News, Dec. 30.) — A 
 Westinghouse combination double-flow turbine is about to be tested 
 which is capable of developing 22,000 H.P. with 1.75 lbs. steam pressure 
 and 28 ins. vacuum, and it is estimated that the steam consumption will 
 be about 10 lbs. per B. H.P.-hour. The principal dimensions are: length 
 over all. 19 ft. 8 ins.; height, 9 ft.; width, 9 ft.; weight, 110,000 lbs.; weight 
 per H.P. developed, 5 lbs.; speed, 1800 r.p.m. 
 
ROTARY STEAM-ENGINES — STEAM TURBINES. 1069 
 
 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 lbs. per B.H.P.-hour of different makes of impulse turbines. 
 
 Type. 
 
 Rated H.P 
 Water f1 '" 
 
 lated H.F 
 
 %1&SS:::: 
 
 ™ te i Full load.. 
 at 11 1/4 load. . . 
 
 Sturte- 
 vant. 
 
 20 
 72 
 65 
 61 
 58 
 
 Terry. 
 
 50 
 59 
 
 46 
 44 
 
 100 
 58 
 48 
 43 
 40 
 
 200 
 55 
 47 
 42 
 39 
 
 150 
 52 
 44 
 41 
 39 
 
 50 
 44 
 36 
 33 
 31 
 
 200 
 32 
 30 
 29 
 28 
 
 Dry steam, 150 lbs. 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. 
 
 permin 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 lbs. 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 lbs. abso- 
 lute, the initial steam pressure in the engine being 200 lbs. absolute and 
 the vacuum 28 ins. 
 
 Back pressure of engines, lbs. abs 
 
 Initial pressure, turbine, lbs. abs 
 
 Theoretical B.T.U. ( £ Jjgg? • — 
 
 utilized per lb of steam \ ^1 
 
 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 28 1/2 ins. 
 Inches vacuum at admission 
 
 valve 4 8 12 16 20 24 
 
 Per 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, 
 
 16 
 
 13V2 8 
 
 15 
 
 121/2 7 
 
 178 
 
 189 218 
 
 142 
 
 131 100 
 
 320 
 
 320 318 
 
1070 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 897 and 987.) 
 
 The following results of tests of a Westinghouse low-pressure turbine 
 are reported by Francis Hodgkinson. 
 
 Steam press., 
 
 lb. 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., 
 
 lbs 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, lbs. 
 
 abs 4.1 5.1 6.1 7.2 8.3 9.4 11.0 13.5 
 
 Steam per ) 2 7i/ 2 in vac. 75 47.5 38 33 30 28 26.5 24.5 
 
 hour lbs ) 28 in - vac - 62 42 33 29 27 25.5 24.5 22.5 
 
 The total steam consumption per hour followed the Willans law, 
 being directly proportional to the power after adding a constant for 
 load, viz.: for 271/2-in. vacuum the total steam consumption per hour 
 was 12,000 lbs. + 18 X H.P., and for 28-in. vacuum, 9000 lbs. + 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 lbs. absolute and the vacuum 281/2 ins. 
 
 K.W. output 1500 2000 3000 4000 5000 6000 7000 
 
 Steam per K.W.-hr., lb.. .. 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 lbs. absolute, and 
 the turbines from 16 lbs. to 0.75 lb., the vacuum being 28.5 ins. with 
 the barometer at 30 ins. 
 
 Engine. Turbine. 
 
 Theoretical steam per K.W.-hour, lbs 18 17.8 
 
 Steam per K.W.-hr. at switchboard, lbs 27 . 7 26 . 6 
 
 Combined efficiency of engine and dynamo, per cent ... 65 67 
 
 Steam per K.W.-hour for combined plant = 1 -^ (1/27.7 + 1/26.6) = 
 
 13.6 lbs. 
 
 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 lbs. below atmosphere to 15 or 
 20 lbs. 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 lbs. of steam per hour. Allowing 8% for moisture in the 
 exhaust, 29,440 lbs. of dry steam will be available for the turbine, which 
 at 33 lbs. per K.W.-hour will develop 893 K.W., making a total output of 
 1893 K.W. for 32,000 lbs. steam, or 16.9 lbs. per K.W.-hour. The engine 
 alone as a condensing engine will develop 1320 K.W. at 24.2 lbs. 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., and 
 condensing, 1470 K.W., and of the combined unit 2500 K.W. 
 
INTERNAL-COMBUSTION ENGINES. 1071 
 
 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 774.] 
 
 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. McAlpine 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 been tested, 
 giving an efficiency of 98.5% (Eng'g, Sept. 17; Eng. News, Oct. 21 and Dec. 
 30, 1909). 
 
 NAPHTHA ENGINES. —HOT-AIR ENGINES. 
 
 Naphtha engines are in use to some extent in small yachts and 
 launches. The naphtha is vaporized in a boiler, and the vapor is used ex- 
 pansively in the engine cylinder, as steam is used ; it is then condensed and 
 returned to the boiler. A portion of the naphtha vapor is used for fuel un- 
 der the boiler. According to the circular of the builders, the Gas Engine 
 and Power Co. of New York, a 2-H.P. engine requires from 3 to 4 quarts! of 
 naphtha per hour, and a 4-H.P. engine from 4 to 6 quarts. The chief 
 advantages of the naphtha-engine and boiler for launches are the saving 
 of weight and the quickness of operation. A 2-H.P. engine weighs 200 lbs., 
 a 4-H.P. 300 lbs. It takes only about two minutes to get under headway. 
 (Modern Mechanism, p. 270.) 
 
 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's 
 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 lbs. per brake H.P. per hour. Mean 
 pressure on pistons 15.37 lbs. per square inch, and in pumps 15.9 lbs., the 
 area of working cylinders being twice that of the pumps. The hot air 
 supplied was about 1160° F. and that 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. lxix; 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; " In- 
 ternal Combustion Engines," by Carpenter and Diederichs; "Gas Engine 
 Design," by C. E. Lucke: " Gas and Petroleum Engines," by W. Robin- 
 son; "The Modern Gas Engine and the Gas Producer," by A. M. Levin. 
 For practical operation of gas and oil engines, see "The Gas Engine," 
 by F. R. Jones, and "The Gas Engine Handbook," by E. W. Roberts. 
 
1072 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.S.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, diiving it forward. ( Rotary gas-engines or gas turbines, are still, 
 1910, 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; (b) 
 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. 169 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, .BC 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 
 line of expulsion of the burned gases, the 
 = — ■ £ ' pressure being slightly above the atmos- 
 A t?^„ i<;q B phere on account of the resistance of the 
 
 * IG - lby - 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. 169 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 of 
 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. 169, 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 Z>, when the gases of combustion are at their 
 highest temperature; P e the pressure at E, when the exhaust valve begins 
 to open. For the hypothetical case of a cylinder with walls incapable of 
 absorbing or conducting heat, and of perfect and instantaneous combustion 
 
INTERNAL COMBUSTION ENGINES. 1073 
 
 or explosion of the fuel, an 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 lbs. per sq. in. absolute, and the 
 temperature say 62° F., or 522° absolute. The pressure at C, or P c , would 
 depend on the ratio V x -h F 2 , V x being the original volume of the mixture 
 in the cylinder before compression, or the piston displacement plus the 
 volume of the clearance space, and 7 2 the volume after compression, or 
 1 the clearance volume, and its value would be P c = P s ( VJ V2) . The 
 1 absolute temperature at the end of compression would be T c = 522 X 
 j ( Vi/Vt) 1 ]^, or it may be found from the formula P S V S + T s = P c V p + T c , 
 I the subscripts 5 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. ine 
 j work done in compressing the mixture would be calculated by the formula 
 ! for compressed air (see page 607). The theoretical rise of tempera- 
 j ture at the end of the explosion, T x , above the temperature at the end of 
 I the compression T c may be found from the formula (T x - T c ) C v = H, 
 \ in which U is the amount of heat in British thermal units generated by 
 \ the combustion of the fuel in 1 lb. 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- 
 ing pressure P x may be found from the formula P x = P C X (T x /T£ 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 worn; 
 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 91 
 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 diagra m - ^ 
 power is found by the usual formula for steam-engines, H.P. = f^j.i; 
 33,000, in which P is the mean effective pressure in lbs. per sq. in., L trie 
 length of stroke in feet, A the area of the piston in square inches, and J\ 
 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 or 
 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 
 
1074 
 
 INTERNAL-COMBUSTION 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 
 
 Kerosene, injected on a hot bulb, may be as low a, 
 Casoline, used in carburetor requiring a vacuum. 
 
 Gasoline, with but little initial vacuum 
 
 Producer gas 
 
 Coal gas 
 
 Blast-furnace gas 
 
 Natural gas 
 
 Lb. 
 45-75 
 
 80-130 
 100-160 
 Av. 80 
 130-180 
 
 90-140 
 
 30-40 
 20 
 
 25-40 
 50-30 
 56-40 
 Av. 45 
 48-30 
 52-40 
 
 Factors for two-cycle engines are about 0.8 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/V 2 from 3 to 8, on absolute pressures in the cylinder 
 before compression from 13 to 16 lbs., 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 lbs. per sq. in., 
 and absolute temperatures at the end of the explosion of 1800° to 3000° F. 
 Compression Pressures. 
 
 * ,£ 
 
 n = 1.3. 
 
 m *? 
 
 n=1.34. 
 
 * 5 o 
 
 
 
 
 
 
 
 
 S' B « 
 
 
 
 
 
 
 B m 03 
 
 
 
 
 
 
 6 * 
 
 P s =13 
 
 13.5 
 
 14 
 
 15 
 
 16 
 
 o p3 
 
 o 
 
 P s =13 
 
 13.5 
 
 14 
 
 15 
 
 16 
 
 3.00 
 
 54.2 
 
 56.3 
 
 58.4 
 
 62.6 
 
 66.7 
 
 3.00 
 
 56.7 
 
 58.9 
 
 61 
 
 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 
 
 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. 
 
 A w 
 
 
 
 n=1.3 
 
 
 
 s ,? 
 
 
 
 n = 1.34. 
 
 
 kg.S 
 
 8 & 
 
 
 
 
 
 
 a§.2 
 
 1 a 
 
 
 
 
 
 620° 
 
 660° 
 
 700° 
 
 740° 
 
 780° 
 
 620° 
 
 660° 
 
 700° 
 
 740° 
 
 780° 
 
 3.00 
 
 862 
 
 918 
 
 973 
 
 1029 
 
 1084 
 
 3.00 
 
 901 
 
 959 
 
 1017 
 
 1075 
 
 1132 
 
 4.00 
 
 940 
 
 1000 
 
 1061 
 
 1122 
 
 1182 
 
 4.00 
 
 993 
 
 1057 
 
 1122 
 
 1186 
 
 1750 
 
 5.00 
 
 1C05 
 
 1070 
 
 1134 
 
 1199 
 
 1264 
 
 5.00 
 
 1072 
 
 1141 
 
 1210 
 
 1279 
 
 1348 
 
 6.00 
 
 1061 
 
 1130 
 
 1198 
 
 1267 
 
 1335 
 
 6.00 
 
 1140 
 
 1214 
 
 1287 
 
 1361 
 
 1434 
 
 7.00 
 
 1112 
 
 1183 
 
 1255 
 
 1327 
 
 1398 
 
 7.00 
 
 1201 
 
 1279 
 
 1357 
 
 1434 
 
 1512 
 
 8.00 
 
 1157 
 
 1232 
 
 1306 
 
 1381 
 
 1456 , 
 
 8.00 
 
 1257 
 
 1338 
 
 1420 
 
 1501 
 
 1582 
 
INTERNAL-COMBUSTION ENGINES. 
 
 1075 
 
 Absolute Pressures per Square Inch at Release. 
 Corresponding to Explosion Pressures commonly obtained. 
 Note: — The expansion ratios in the left-hand column are based on 
 the volume behind the piston when the exhaust valve begins to open. 
 
 « . 
 O » 
 
 "to *- 
 
 n e =1.29. 
 
 a 
 o k 
 
 n e =1.32. 
 
 
 
 
 
 G O 
 
 
 
 
 ft a 
 
 
 Value of P x 
 
 
 «3-£ 
 
 
 Value of P x 
 
 
 fl« 
 
 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. 
 
 a 
 
 .2 « 
 
 n e =1.29. 
 
 a 
 S.2 
 
 n e =1.32. 
 
 is 
 
 
 Value of T x 
 
 
 
 Value of T x 
 
 
 1800 
 
 2100 2400 2700 
 
 3000 
 
 1800 
 
 2100 2400 2700 
 
 3000 
 
 3.00 
 
 1309 
 
 1527 
 
 1745 
 
 1963 
 
 2182 
 
 3.00 
 
 1266 
 
 1478 
 
 1689 
 
 1900 
 
 2111 
 
 4.00 
 
 1204 
 
 1405 
 
 1606 
 
 1806 
 
 2007 
 
 4.00 
 
 1155 
 
 1348 
 
 1540 
 
 1733 
 
 1925 
 
 5.00 
 
 1129 
 
 1317 
 
 1505 
 
 1693 
 
 1881 
 
 5.00 
 
 1075 
 
 1255 
 
 1434 
 
 1613 
 
 1792 
 
 6.00 
 
 1070 
 
 1249 
 
 1427 
 
 1606 
 
 1784 
 
 6.00 
 
 1015 
 
 1184 
 
 1353 
 
 1522 
 
 1691 
 
 7.00 
 
 1024 
 
 1194 
 
 1365 
 
 1536 
 
 1706 
 
 7.00 
 
 966 
 
 1127 
 
 1288 
 
 1449 
 
 1610 
 
 8.00 
 
 985 
 
 1149 
 
 1313 
 
 1477 
 
 1641 
 
 8.00 
 
 925 
 
 1079 
 
 1234 
 
 1388 
 
 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 lbs. per 
 sq. in. absolute; these are high figures, however, the more usual figures 
 being about 2300° and 250 lbs. 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. 
 
 .2 
 
 * 
 
 
 
 w 6 
 
 * 
 
 ^5 
 
 _d 
 
 OP 
 
 .2 
 
 g P 
 
 Oj 
 
 ft 
 
 B 
 
 So 
 
 6 
 a 
 
 o 
 
 8 
 
 d 
 
 a 
 
 OH 
 
 03 
 
 ft 
 ft 
 
 T30 
 
 03 
 ft 
 
 s 
 
 r 3 §H 
 
 § 2 
 
 o 
 
 
 03 
 
 
 
 ^2 
 
 
 
 
 O 
 
 K 
 
 o 
 
 M 
 
 o 
 
 £ 
 
 o 
 
 PM 
 
 o 
 
 3 
 
 4.0 
 
 146 
 
 195 
 
 168 
 
 5.0 
 
 192 
 
 6.0 
 
 225 
 
 7.0 
 
 211 
 
 4.2 
 
 156 
 
 208 
 
 179 
 
 5.2 
 
 202 
 
 6.2 
 
 234 
 
 7.2 
 
 218 
 
 4.4 
 
 166 
 
 221 
 
 190 
 
 5.4 
 
 211 
 
 6.4 
 
 243 
 
 7.4 
 
 225 
 
 4.6 
 
 175 
 
 234 
 
 202 
 
 5.6 
 
 221 
 
 6.6 
 
 252 
 
 7.6 
 
 232 
 
 4.8 
 
 185 
 
 247 
 
 213 
 
 5.8 
 
 230 
 
 6.8 
 
 261 
 
 7.8 
 
 239 
 
 5.0 
 
 195 
 
 260 
 
 224 
 
 6.0 
 
 240 
 
 7.0 
 
 270 
 
 8.0 
 
 246 
 
 * Per cubic foot measured at 32° F. 
 The following figures are given by Poole as a rough approximate 
 guide to the mean effective pressures in lbs. per sq. in. obtained with 
 
1076 
 
 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 lbs. 
 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 
 H.P. 
 
 Compression Pressure, 
 abs. lbs. per sq. in. 
 
 Engine 
 H.P. 
 
 Compression Pressure. 
 
 
 100 
 
 115 
 
 130 
 
 145 
 
 160 
 
 100 
 
 115 
 
 130 
 
 145 
 65 
 
 160 
 
 10 
 
 55 
 
 60 
 
 65 
 
 
 
 10 
 
 
 65 
 
 65 
 
 
 25 
 
 60 
 
 65 
 
 70 
 
 75 
 
 
 25 
 
 60 
 
 65 
 
 65 
 
 70 
 
 75 
 
 50 
 
 65 
 
 70 
 
 75 
 
 80 
 
 80 
 
 50 
 
 65 
 
 70 
 
 70 
 
 75 
 
 80 
 
 100 
 
 70 
 
 75 
 
 80 
 
 85 
 
 85 
 
 100 
 
 65 
 
 70 
 
 75 
 
 80 
 
 85 
 
 250 
 
 75 
 
 80 
 
 85 
 
 90 
 
 90 
 
 250 
 
 70 
 
 75 
 
 80 
 
 85 
 
 90 
 
 500 
 
 80 
 
 85 
 
 90 
 
 90 
 
 90 
 
 500 
 
 75 
 
 80 
 
 85 
 
 90 
 
 90 
 
 Natural and Illuminating Gases. 
 
 Engine 
 H.P. 
 
 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 
 
 M5 
 
 65 
 
 75 
 
 85 
 
 100 
 
 
 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 
 
 70 
 75 
 80 
 85 
 
 75 
 80 
 85 
 90 
 
 80 
 85 
 90 
 95 
 
 85 
 90 
 90 
 95 
 
 
 Sizes of Large Gas Engines. — From a table of sizes of the Nurnberg 
 
 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 18 20 21 22 24 24 26 28 30 32 
 
 Stroke cyl., ins 24 24 30 30 30 36 36 36 42 42 
 
 Revs, per min 150 150 125 125 125 115 115 115 100 100 
 
 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 of C 0.8 0.8 0.84 0.84 0.85 0.95 0.93 0.94 0.95 0.96 
 
 Diam., ins 34 36 38 40 42 44 46 48 50 52 
 
 Stroke, ins 42 48 48 48 54 54 54 60 60 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 of C 0.96 1 1.01 1.02 1.06 1.07 1.08 1.07 1.09 1.09 
 
INTERNAL-COMBUSTION ENGINES. 
 
 1077 
 
 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- 
 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 lbs. 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, sinele 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 2V2 
 
 Bore, mm 64 
 
 H. P., 1 cylinder... . 2 1/2 
 H.P., 2 cylinders. . . 5 
 H.P., 4 " ... 10 
 H.P., 6 " ... 15 
 
 Approximate Estimate of the Horse-power of a Gas Engine. — 
 From the formula I.H.P. = PLAN -J- 33,000, in which P= mean effective 
 pressure in lbs. per sq. in., L = length of stroke in ft., A = area of piston 
 in sq. ins., iV = No. of explosion strokes per min., we have I.H.P. = Pd 2 S + 
 42,017, in which d = 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 2 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: 
 
 3 
 
 31/2 
 
 4 
 
 41/2 
 
 5 
 
 5V2 
 
 6 
 
 76 
 
 89 
 
 102 
 
 114 
 
 127 
 
 140 
 
 154 
 
 3.6 
 
 4.9 
 
 6.4 
 
 8.1 
 
 10 
 
 12.1 
 
 14.4 
 
 7.2 
 
 9.8 
 
 12.8 
 
 16.2 
 
 20 
 
 24.2 
 
 28.8 
 
 14.4 
 
 19.6 
 
 25.6 
 
 32.4 
 
 40 
 
 48.4 
 
 57.6 
 
 21.6 
 
 29.4 
 
 38.4 
 
 48.6 
 
 60 
 
 72.6 
 
 86.4 
 
 
 Piston speed, ft. per minute. 
 
 M.E.P. 
 
 
 
 lbs. per 
 sq. in. 
 
 500 600 700 800 900 
 
 1000 
 
 
 
 
 Value of C for two explosions per revolution 
 
 
 50 
 
 0.50 
 
 0.60 
 
 0.70 
 
 0.80 
 
 0.90 
 
 1.00 
 
 60 
 
 0.60 
 
 0.72 
 
 0.84 
 
 0.96 
 
 1.08 
 
 1.20 
 
 70 
 
 0.70 
 
 0.84 
 
 0.98 
 
 1.12 
 
 1 .26 
 
 1.40 
 
 80 
 
 0.80 
 
 0.96 
 
 1.12 
 
 1.28 
 
 1.44 
 
 1.60 
 
 90 
 
 0.90 
 
 1.08 
 
 1.26 
 
 1.44 
 
 1.62 
 
 1.80 
 
 100 
 
 1.00 
 
 1.20 
 
 1.40 
 
 1.60 
 
 1.80 
 
 2.00 
 
 110 
 
 1.10 
 
 1.32 
 
 1.54 
 
 1.76 
 
 1.98 
 
 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, 
 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 
 
1078 INTERNAL-COMBUSTION ENGINES. 
 
 provide some method of atomizing and vaporizing the oil at a high tem- 
 perature, such as injecting it into a hot vaporizing chamber at the end 
 of the cylinder, or into a chamber heated by the exhaust gases. In the 
 Diesel oil engine the oil is ignited by the heat of the highly compressed 
 air in the cylinder. 
 
 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., 
 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 lbs. per sq. in., the charge of oil is injected, by a jet of air-at about 
 600 lbs. 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 lb. with Solar fuel oil, and 0.484 lb. 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 lb., 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 lb., or 
 115,800 B.T.U. per gallon. 
 
 A gasolene engine having a compression pressure of 70 lbs. 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 lbs. is about 30% greater than that of a gasolene engine 
 of the same size and speed having a compression pressure of 70 lbs. 
 
 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 
 
INTEKNAL-COMBUSTION ENGINES. 1079 
 
 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 Diederichs, 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 lbs. of water per pound of 
 hydrogen contained in the gas. See page 533. 
 
1080 
 
 INTERNAL-COMBUSTION ENGINES. 
 
 tion 30° in advance of the dead center, while the efficiency with ignitioi? 
 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 lest 
 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. 
 
 lbs. 
 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- 
 
 bausto 
 
 2.67 
 2.67 
 4.32 
 4.32 
 
 187 
 247 
 187 
 247 
 
 54.3 
 51.5 
 69.3 
 65.2 
 
 7.11 
 7.35 
 7.43 
 7.40 
 
 18.5 
 17.4 
 17.0 
 16.8 
 
 140 
 141 
 190 
 184 
 
 1022 
 1137 
 867 
 992 
 
 18.0 
 18.1 
 
 24.4 
 23.7 
 
 51.2 
 45.6 
 53.8 
 49.5 
 
 30.8 
 36.3 
 21.8 
 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 lb. coal per I.H.P. hour, as compared with 1.06 lbs. 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 lb. 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 lbs. of West 
 Virginia coal per B.H.P. hour, and the poorest result 3.23 lbs. 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 lb. 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. 1081 
 
 100-H.P. Otto gas engine showed a consumption of 0.97 lb. 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 lb., with 
 a Tangye engine and a suction gas producer, using Welsh anthracite coal. 
 Other tests show figures ranging from 0.74 lb. to 1,95, the last with a 
 Westinghouse 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%; Mond gas, 1 test, 23.7%; blast-furnace gas, 3 tests, 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 lb., 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 lb. 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 lb. 
 
 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*. CODE OF 1903. 
 
 (From the report of the committee of the A. S. M. E. on Engine Tests.) 
 [Only a brief abstract is here given. The items, 1, Objects of the Tests; 
 2, General Conditions of the Engine; 3, Dimensions; 5, Calibration of 
 Instruments, are practically the same as in the report on Steam Engine 
 Tests.] 
 
 IV. Fuel. — Decide upon the gas or oil to be used, and if the trial is 
 to be made for maximum efficiency, the fuel should be the best of its 
 class that can readily be obtained, or one that shows the highest calorific 
 power. 
 
 VI. Duration of Test. — The duration of a test should depend largely 
 upon the objects in view, and in any case the test should be continued until 
 the successive readings of the rates at which oil or gas is consumed, 
 taken at say half-hourly intervals, become uniform and thus verify each 
 other. If the object is to determine the working economy, and the period 
 of time during which the engine is usually in motion is some part of 
 twenty-four hours, the duration of the test should be fixed for this number 
 of hours. If the engine is one using coal for generating gas, the test 
 should be of at least twenty-four hours' duration. 
 
 VII. Storting a Test. — In a test for determining the maximum econ- 
 omy of an engine, it should first be run a sufficient time to bring all 
 the conditions to a normal and constant state. 
 
 If a test is made to determine the performance under working condi- 
 tions, the test should bej?in as soon as the regular preparations have 
 been made for starting the engine in practical work, and the measurements 
 should then commence and be continued until the close of the period 
 covered by the day's work. 
 
 VIII. Measurement of Fuel. — If the fuel used is coal furnished to a gas 
 
 * Hot-air engines are not included in this code, those in the market 
 being of comparatively small size, and seldom tested. 
 
1082 INTERNAI^COMBUSTION ENGINES. 
 
 producer, the same methods apply for determining the consumption as 
 are usea in steam-boiler tests. 
 
 If the fuel used be gas, the only practical method of measurement is 
 the use of a meter through which the gas is passed. The temperature 
 and pressure of the gas should be measured, and the quantity of gas 
 should be determined by reference to the calibration of the meter, taking 
 into account the temperature and pressure of the gas. 
 
 If the fuel is oil, this can be drawn from a tank which is filled to the 
 original level at the end of the test, the amount of oil required for so 
 doing being weighed ; or, for a small engine, the oil may be drawn from a 
 calibrated vertical pipe. 
 
 IX. Measurement of Heat- Units Consumed by the Engine. — The num- 
 ber of heat-units used is found by multiplying the number of pounds of 
 coal or oil or the cubic feet of gas consumed, by the total heat of combus- 
 tion of the fuel as determined by a calorimeter test. In determining the 
 total heat of combustion no deduction is made for the iatent heat of the 
 water vapor in the products of combustion. 
 
 It is sometimes desirable, also, to have a complete chemical analysis 
 of the oil or gas. The total heat of combustion may be computed, if 
 desired, from the results of the analysis, and should agree well with the 
 calorimeter values. 
 
 X. Measurement of Jacket Water. — The jacket water mny be meas- 
 ured by passing it through a water meter or allowing it to flow from a 
 measuring tank before entering the jacket, or by collecting it in tanks 
 on its discharge. 
 
 XI. Indicated Horse-power. — The directions given for determining 
 the indicated horse-power for steam engines apply in all respects to inter- 
 nal combustion engines. 
 
 XII. Brake Horse-power. — The determination of the brake horse- 
 power is the same for internal combustion as for steam engines. 
 
 XIII. Speed. — The same directions apply to internal combustion 
 engines as to steam engines for the determination of speed. 
 
 In an engine which is governed by varying the number of explosions 
 or working cycles, a record should be kept of the number of explosions 
 per minute; or if the engine is running at nearly maximum load, by 
 counting the number of times the governor causes a miss in the ex- 
 plosions. 
 
 XIV. Recording the Data. — The pressures, temperatures, meter 
 readings, speeds, and other measurements should be observed every 20 
 or 30 minutes when the conditions are practically uniform, and at more 
 frequent intervals if they are variable. Observations of the gas or oil 
 measurements should be taken with special care at the expiration of each 
 hour, so as to divide the test into hourly periods, and reveal the uniform- 
 ity, or otherwise, of the conditions and results as the test goes forward. 
 
 XV. Uniformity of Conditions. — When the object of the test is to 
 determine the maximum economy, all the conditions relating to the 
 operation of the engine should be maintained as constant as possible 
 during the trial. 
 
 XVI. Indicator Diagrams. — Sample diagrams nearest to the mean 
 should be selected from those taken during the trial and appended to the 
 tables of the results. If there are separate compression or feed cylinders, 
 the indicator diagrams from these should be taken and the power deducted 
 from that, of the main cylinder. 
 
 XVII. Standards of Economy and Efficiency. — The hourly consump- 
 tion of heat, divided by the indicated or the brake horse-power, is the 
 standard expression of engine economy recommended. 
 
 In making comparisons between the standard for internal combustion 
 engines and that for steam engines, it must be borne in mind that the 
 steam engine standard does not cover the losses due to combustion, while 
 the internal combustion engine standard, in cases where a crude fuel 
 such as oil is burned in the cylinder, does cover these losess. 
 
 The thermal efficiency ratio per indicated horse-power or per brake 
 horse-power for internal combustion engines is expressed by the fraction 
 2545 -*- B.T.U. per H.P. per hour. 
 
 XVIII. Heat Balance. — For purposes of scientific research, a heat 
 balance should be drawn which shows the manner in which the total 
 
TESTS OF GAS AND OIL ENGINES. 1083 
 
 heat of combustion is expended in the various processes concerned in 
 the working of the engine. It may be divided into three parts: first, 
 the heat which is converted into the indicated or brake work; second, the 
 heat rejected in the cooling water of the jackets; and third, the heat 
 rejected in the exhaust gases, together with that lost through incomplete 
 combustion and radiation. 
 
 To determine the first item, the number of foot-pounds of work per-* 
 formed by, say, one pound or one cubic foot of the fuel, divided by 778, 
 gives the number of heat-units desired. The second item is determined 
 by measuring the amount of cooling water passed through the jackets, 
 equivalent to one pound or one cubic foot of fuel consumed, and multi- 
 plying this quantity by the difference in the sensible heat of the water 
 leaving the jacket and that entering. The third item is obtained by 
 subtracting the sum of the first two items from the total heat supplied. 
 The third item can be subdivided by computing the heat rejected in the 
 exhaust gases as a separate quantity. The data for this computation 
 are found by analyzing the fuel and the exhaust gases, or by measuring 
 the quantity of air admitted to the cylinder in addition to that of the gas 
 or oil. 
 
 XIX. Report of Test. — The data and results of a test should be re- 
 ported in the manner outlined in one of the following tables, the first of 
 which gives a complete summary when all the data are determined, and 
 the second is a shorter form of report in which some of the minor items 
 are omitted. [The short form is given below.] 
 
 Data and Results of Standard Heat Test of Gas or Oil Engine. 
 
 Arranged according to the Short Form advised by the Engine Test 
 Committee, American Society of Mechanical Engineers. Code of 
 1902. 
 
 1 Made by. . of 
 
 on engine located at 
 
 to determine 
 
 2. Date of trial 
 
 3. Type and class of engine . 
 
 4. Kind of fuel used 
 
 (a) Specific gravity deg Fahr. 
 
 (b) Burning point 
 
 (c) Flashing point 
 
 5. Dimensions of engine: 
 
 1st Cyl. 2d Cyl. 
 (a) Class of cylinder (working or for com- 
 pressing the charge) 
 
 (&) Single or double acting 
 
 (c) Cylinder dimensions: 
 
 Bore in. 
 
 Stroke ft. 
 
 Diameter piston rod in. 
 
 (d) Average compression space, or clear- 
 
 ance, in per cent 
 
 (e) Horse-power constant for one lb. M.E.P. 
 
 and one revolution per minute 
 
 Total Quantities. 
 
 6. Duration of test hours 
 
 7. Gas or oil consumed cu. ft. ( pr lbs. 
 
 8. Cooling water supplied to jackets 
 
 9. Calorific value of fuel by calorimeter test, determined 
 
 by calorimeter B.T.U. 
 
 Pressures and Temperatures. 
 
 10. Pressure at meter (for gas engine) in inches of water . . . ins. 
 
 11. Barometric pressure of atmosphere: 
 
 (a) Reading of barometer 
 
 (b) Reading corrected to 32 degs. Fahr 
 
1084 LOCOMOTIVES. 
 
 12. Temperature of cooling water: 
 
 (a) Inlet deg. Fahr. 
 
 (6) Outlet 
 
 13. Temperature of gas at meter (for gas engine) " 
 
 14. Temperature of atmosphere: 
 
 (a) Dry bulb thermometer •• 
 
 (b) Wet bulb thermometer ♦' 
 
 (c) Degree of humidity " 
 
 15. Temperature of exhaust gases " 
 
 Data Relating to Heat Measurement. 
 
 16. Heat units consumed per hour (pounds of oil or cubic 
 
 feet of gas per hour multiplied by the total heat of 
 combustion) , B.T.U. 
 
 17. Heat rejected in cooling water per hour 
 
 Speed, etc. 
 
 18. Revolutions per minute rev. 
 
 19. Average number of explosions per minute 
 
 Indicator Diagrams. 
 
 20. Pressure in lbs. per sq. in. above atmosphere: 
 
 1st Cyl. 2d Cyl. 
 
 (a) Maximum pressure 
 
 (6) Pressure just before ignition 
 
 (c) Pressure at end of expansion 
 
 (d) Exhaust pressure 
 
 (e) Mean effective pressure 
 
 Power. 
 
 21. Indicated horse-power: 
 
 First cylinder H.P. 
 
 Second cylinder 
 
 Total 
 
 22. Brake horse-power 
 
 23. Friction horse-power by friction diagrams 
 
 24. Percentage of indicated horse-power lost in friction. . per cent. 
 
 Standard Efficiency, and Other Results. 
 
 25. Heat units consumed by the engine per hour: 
 
 (a) Per indicated horse-power B.T.U. 
 
 (6) Per brake horse-power 
 
 26. Pounds of oil or cubic feet of gas consumed per hour: 
 
 (a) Per indicated horse-power lbs. or cu. ft. 
 
 (6) Per brake horse-power 
 
 Additional Data. 
 Add any additional data bearing on the particular objects of the test 
 or relating to the special class of service for which the engine is to be 
 used. Also give copies of indicator diagrams nearest the mean, and the 
 corresponding scales. 
 
 LOCOMOTIVES. 
 
 Resistance of Trains. — Resistance due to Speed. — Various formula 
 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 lbs. per ton of 2000 lbs. = ViV + 4. 
 
 Speed 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 
 
 Resistance. 31/4 4.5 53/ 4 7 8 1/4 9.5 103/ 4 12 13V* 14.5 17 19.5 22 24.5 27 
 
LOCOMOTIVES. 1085 
 
 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 lbs. per ton, dropping to 4 or 5 lbs. at 5 miles 
 an hour. 
 
 By Baldwin Locomotive Works: 
 
 Resistance in lbs. per ton of 2000 lbs. = 3 + v h- 6. 
 
 Speed 5 10 15 20 25 30 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 ihat 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 lbs. per ton on smooth 80-lb. 51/s-in. rails. The resist- 
 ance of an 80-car freight train, 60,000 lbs. per car, as given by indicator 
 cards, at speeds between 15 and 25 miles per hour, is represented by the 
 formula R = 1 + l/s F, in which R = resistance in lbs. 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 Formulae for Resistance. — 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 for 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 lbs. per ton (of 2000 lbs.) for 72-ton cars (including 
 weight of empty car) to 6 to 8 lbs. 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 lbs. per ton, or 1.11% of the weight on drivers, (b) 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 to the tender, the same per ton as that 
 due to the cars, (d) Grade resistance = 20 lbs. 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 lbs. 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 the 
 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 .5.50 
 
 P 60.4 69.177.2 83.7 89.0 93.5 96.8 98.7 99.7 100 100 
 
 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 99 97.8 96.8 95.7 94.7 93.5 
 
 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, lbs. per ton 
 
 13.10 7.84 6.62 5.78 4.66 3.94 3.44 3.06 3.00 
 
1086 LOCOMOTIVES. 
 
 From plotted curves of resistances of trains of empty and loaded cars 
 the following figures are derived. R — resistance in lbs. per ton. 
 
 Wt. loaded, tons 75 70 65 60 55 50 
 
 Wt. empty, tons 21 20.3 19.5 18.6 17.6 16.5 
 
 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 
 
 Per cent 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 «.45 9.05 9.60 10.3 
 
 The resistance of passenger cars is derived from the formula R = 5.4 + 
 0.002(F - 15) 2 + 100 ■*- (V + 2) 3 . V in miles per hour, R = resistance 
 in lbs. per ton (2000 lbs.) 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 
 
 V = 40 45 50 60 70 80 90 
 
 R = 6.65 7.20 7.85 9.45 11.45 13.85 16.65 
 
 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. 
 
 R = 6 + 0.11 V + ^~ [1 + 0.1 (n - 1)]. 
 
 (B) For standard interurban electric cars, 25 tons to 40 tons; maximum 
 speed, 60 m.p.h.; cross section, 100 sq. ft. 
 
 22 = 5+ 0.13 V+ 0.3V*/T[1 + 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 V*/T [1 + 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 +• . 13 V + 0.385 V 2 /T [1 + 0.1 (n - 1)]. 
 
 R = resistance in lbs. per ton of 2000 lbs., F= speed in miles per hour 
 T == Weight of train in tons, n — number of ears 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 lbs., 2000 X 1/5280 = 0.3788 lb. per ton, or if 
 R g = resistance in lbs. 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 lbs. per ton for each per cent of grade. 
 
 Resistance due to Curves. — Mr. G. P. Henderson in his book entitled 
 "Locomotive Operation" gives the resistance due to curvature at 0.7 
 lb. per ton of 2000 lbs. per degree of the curve. (For definition of 
 degrees of a railroad curve see p. 55.) For locomotives, this factor is 
 sometimes doubled, making the resistance in lbs. 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 lb. per ton per degree of curva- 
 ture for the resistance of cars on curves. 
 
LOCOMOTIVES. 1087 
 
 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 504), 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 
 
 F 2 V Vi 2 — Vi* 
 P = 70 -s- =95.6 -. =70 ■ ^ , where P = the accelerating force in 
 
 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. Vi and V2 = the smaller and greater velocities, respectively, 
 in miles per hour, for a change of speed. 
 
 Total Resistance. — The total resistance in lbs. per ton of 2000 lbs. 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 lbs. 
 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 lbs. 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 the 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 + r, 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 S/D,iu. pounds 
 at the circumference of the drivers. 
 
 Concerning the effect of increasing speed on tractive force, Mr. Hender- 
 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 
 
 8 Pd 2 s 
 in the equation Actual tractive force = - 1 — j? — 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 = . 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., 1900, p. 140) gives an account of some dynamometer 
 tests 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 tho 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 
 1/4 to 1/5 of the load on the drivers. 
 
1088 
 
 LOCOMOTIVES. 
 
 Tractive Force of a Locomotive. — Single Expansion. 
 Let F = indicated tractive force in lbs. 
 
 p = average effective pressure in cylinder in lbs. per sq. in. 
 
 S = stroke of piston in inches. 
 d = diameter of cylinders in inches. 
 D = diameter of driving-wheels in inches. Then 
 4 xd*pS = (1 2 pS 
 
 4:7lD 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). 
 
 1/8 
 
 0.1 
 .125 
 .15 
 .175 
 .2 
 
 .25 = 1/4 
 .3 
 
 0.15 
 .2 
 .24 
 .28 
 .32 
 .4 
 .46 
 
 0.333 = 1/3 
 .375 = 3/ 8 
 .4 
 .45 
 
 J5 =lh 
 
 0.5 = 
 .55 
 .57 
 .62 
 .67 
 .72 
 
 0.625 = 5/ 8 
 .666 = 2/3 
 .7 
 
 • 75 =3/ 4 
 .8 
 .875 = 7/ 8 
 
 0.79 
 .82 
 .85 
 .89 
 .93 
 
 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 fairiy 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, al'ow for wire drawing to the steam chest and drop in 
 pressure due to expansion, and internal friction by writing the formula: 
 
 Actual Tractive Force = — — =r , d, S, and D being a.3 before and P 
 
 representing boiler pressure in lbs. 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 lbs. C= diam. of high-pressure cylinder in Ins. 
 c= diam. of low-pressure cylinder in ins. P= boiler-pressure in lbs. 
 <S= stroke of piston in ins. D= 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 
 
 : c*sxyaP 
 
 T= ■ 
 
 T= - 
 
 D 
 
 The above formulae are for speeds of from 5 to 10 miles an hour, or 
 less; above that the capacity of 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 for 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. 
 
 1089 
 
 W=4:P= - 
 
 Let W = weight on drivers in lbs.; P = tractive force in lbs., = say 
 0.25 W; pi = boiler-pressure in lbs. per sq. in.; p = mean effective 
 pressure, = 0.85 pv, d = diam. of cylinder, S = length of stroke, and 
 D = diam. of driving-wheels, all in inches. Then 
 
 4 d*pS _ 4:d 2 X0.85piS 
 D D 
 
 Whence d = 0.5 "\|^J= 0.542 \^J • 
 
 Von Borries's rule for the diameter of the low-pressure cylinder of a 
 compound locomotive is d- = 2ZD -5- 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: 
 
 Ratio of Cylinder p in percent of p for Boiler-pres- 
 Volumes. Boiler-pressure, sure of 176 lbs. 
 
 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-power 
 is H.P. = pLaN ■*- 33,000, in which p = mean" effective pressure, L = 
 stroke in feet, a = area of cylinder = 1/4 xd 2 , N = number of single 
 strokes per minute, LN = piston speed, ft. per min. Let M = speed of 
 train in miles per hour, 5 = length of stroke in inches, and D = diam- 
 eter of driving-wheel in inches. Then LN = M X88 X 2 S -*• nD. 
 Whence for the two cylinders the horse-power is 
 
 2XpXV4^X176gXM pd 2 SM 
 nD X 33,000 375 D ' 
 
 Class of Engine. 
 
 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 
 
 60 in. 
 
 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 Dull 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 
 a locomotive boiler cannot be made too large. In other words, boilers for 
 
1090 
 
 LOCOMOTIVES. 
 
 locomotives should always 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 lbs. of water from and at 212°. 
 
 Ordinary rate of combustion, 65 lbs. per sq. ft. of grate per hour. 
 
 Ratio of grate to heating surface, 1 : 60 to 90. 
 
 Heating surface per lb. 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) ........ 21/3 square feet. 
 
 Simple Locomotives (cut-off 1/2 to 3/ 4 stroke) 22/3 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 
 
 Bituminous slack and free burning. . 
 
 40 to 45 
 
 Low grade bituminous, lignite and 
 
 30 to 40 
 
 
 
 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 lbs, of fuel per mile, or 
 34V4 lfr s » P er sq. ft- °f g rate P er hour. 
 
LOCOMOTIVES. 
 
 1091 
 
 Grate-surface, Smoke-stacks, and Exhaust-nozzles for Locomo- 
 motives. — A. E. Mitchell, Supt. of Motive Power of the Erie R. R., says 
 (1895) that some roads use the same size of stack, 13 1/2 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 1/430 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 
 
 Grate-area 
 for Anthra- 
 cite Coal, in 
 
 Grate-area 
 for Bitumin- 
 ous Coal, in 
 
 Diameter 
 of Stacks, 
 in inches. 
 
 Nozzles. 
 
 Nozzles. 
 
 Cylinders, 
 in inches. 
 
 Diam. of 
 
 Diam. of 
 
 
 sq. in. 
 
 sq. in. 
 
 
 Orifices, in 
 inches. 
 
 Orifices, in 
 inches. 
 
 12x20 
 
 1591 
 
 1217 
 
 91/2 
 
 2 
 
 213/ie 
 
 13x20 
 
 1873 
 
 1432 
 
 IOI/2 
 
 21/8 
 
 3 
 
 14x20 
 
 2179 
 
 1666 
 
 111/4 
 
 25/16 
 
 31/4 
 
 15x22 
 
 2742 
 
 2097 
 
 121/2 
 
 29/i 6 
 
 3*1/16 
 
 16x24 
 
 3415 
 
 2611 
 
 14 
 
 27/8 
 
 41/16 
 
 17x24 
 
 3856 
 
 2948 
 
 15 
 
 31/16 
 
 4->A6 
 
 18x24 
 
 4321 
 
 3304 
 
 153/ 4 
 
 31/4 
 
 4"V8 
 
 19x24 
 
 4810 
 
 3678 
 
 161/2 
 
 37/16 
 
 413/16 
 
 20x24 
 
 5337 
 
 4081 
 
 171/2 
 
 35/ 8 
 
 31/16 
 
 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 connction with extension 
 front, 
 
o 
 
 o 
 
 O 
 
 Ob 
 
 O'OO Oc 
 
 o 
 
 o 
 
 o o 
 
 1092 LOCOMOTIVES. 
 
 Arches now (1909) are 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, lbs. per sq. in. 120 140 160 180 200 220 210 
 Steam per 1 H.P. hour, lbs. 29.1 27.7- 26.6 26. 25.5 25.1 24.7 
 Coal per 1 H.P. hour, lbs. 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 = lbs. evaporated from and 
 at 212" per lb. 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 r 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. 
 
 n O O o O e 
 
 OOP OF 
 
 P P P o n o 
 P DOC) o h 
 
 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, " 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 
 third the trailers. Other types are the "Pacific," 4-6-2; the "Prairie," 2-6-2; 
 
LOCOMOTIVES. 
 
 1093 
 
 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 -v- 2 P. WT h- 2 R = S. 
 
 O 
 
 o o 
 
 o 
 
 o 
 
 R = radius of min. curve in feet. W — rigid wheel-base. 
 
 P = play of driving-wheels in T = total wheel-base. 
 
 decimals of 1 ft. R = radius of curve. 
 
 W = rigid wheel-base in feet. 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 HP. was required to 
 work unbalanced valves at 40 miles per hour, for the balanced valves 
 2.2 HP. only was necessary. 
 
 [Later tests were reported by the Master Mechanics' Committee in 1896. 
 Unbalanced valves required from 3/ 4 to 21/2 per cent of the LHP. for 
 their motion, balanced valves from 1/3 to 1/2 as much, and piston valves 
 about 1/5 or i/e. Generally in balanced valves, the area of balance = 
 area of exhaust port + area of two bridges + 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 53 54 57 60 66 
 
 Speed, revolutions 224 248 248 258 263 277 292 321 
 
 Average pressure per sq. in.: 
 
 Actual 51.5 44.0 47.3 43.0 41.3 42.5 37.3 36.3 
 
 Calculated 46.5 46.5 44.7 43.8 41.6 39.5 35.9 
 
 The "average pressure calculated" was figured on the assumption that 
 the mean effective pressure would 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 lbs. 
 per sq. in. is the greatest that can be realized in the cylinders of a given 
 engine at 40 miles an hour, 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 capacity for speed of any locomotive 
 its power must be increased, and at least by as much as the speed is to 
 t>e increased, One way to accomplish this is to increase the boiler-» 
 
1094 LOCOMOTIVES. 
 
 Eressure. That this is generally realized, is shown by the increase in 
 oiler-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 lbs.; 4, 165 lbs.; 2, 170 lbs.; 13 180 lbs.; 
 1, 190 lbs. 
 
 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 61/2-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 17V4-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 181/2-in. 
 cylinder at a cost of 23.5 lbs. of water per I. H.P. per hour. The 171/4 
 in. port, 424 H.P., at the rate of 22.9 lbs. 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. 
 
 1095 
 
 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 Camden 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 
 lbs.; coaches, each, 59,200 lbs.; Pullman car, 85,500 lbs. 
 
 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, 113 7/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 lbs. per sq. in.; total weight of engine and tender, 227,000 lbs.; 
 weight on drivers (about), 78,600 lbs. 
 
 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 about 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 location 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 
 angula*r 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 & 
 
 Vl6 pos. 
 
 
 1/32 pos. 
 1/16 neg. 
 
 
 3 /l6 neg. 
 
 V4 neg. 
 1/4 neg. 
 
 1/4 pos. 
 
 
 
 
 abt 3/ 16 
 
 
 9/64 neg. 
 
 
 
 Chicago Great Western 
 
 Chicago & Northwestern 
 
 3 /l6 to 9/ie 
 1/4 pos. 
 
 
1096 
 
 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 dimensions 
 are from Engineering News, June, 1893. The first, or Decapod engine, 
 has ten-coupled driving-wheels. - It is one of the heaviest and most power- 
 ful engines built up to that date for freight service. The second is a sim- 
 ple 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 Loco- 
 motive 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 compound cylinders. 
 
 Dimensions of Some American Locomotives. 
 
 (Baldwin Loco. Wks., 1904-8.) 
 
 
 
 Boilers. 
 
 Tubes. 
 
 Heating 
 Surface. 
 
 Driving 
 Wheels 
 
 Diam., 
 
 Weight, lbs. 
 
 S 03 
 
 it 
 
 firn 
 
 a?*S 
 
 No. 
 
 Ln 
 
 
 
 
 on 
 
 Total 
 
 "8?; 
 
 <u 
 
 o3 c 
 
 
 .2 c 
 
 a 
 
 <D . 
 
 -Srr 
 
 ins. 
 
 Drivers 
 
 Engine 
 
 rt 
 
 GO 
 
 w 
 
 O m 
 
 
 .-1 
 
 fe m 
 
 H M 
 
 
 
 
 
 
 
 
 
 
 ft. in. 
 
 
 
 
 
 i 
 
 150 
 
 47 
 
 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 
 
 700 
 
 60 
 
 7.5 9 
 
 287 
 
 2 
 
 11 7 
 
 133 
 
 1733 
 
 69 
 
 83,680 
 
 124,420 
 
 4 
 
 700 
 
 67. 
 
 30 
 
 272 
 
 2 
 
 16 1 
 
 136 
 
 2279 
 
 68 
 
 112,000 
 
 159,000 
 
 5 
 
 700 
 
 76 
 
 37.2 
 
 298 
 
 21/4 
 
 13 10 
 
 200 
 
 2414 
 
 51 
 
 164,000 
 
 179,500 
 
 6 
 
 700 
 
 68 
 
 35 
 
 306 
 
 21/4 
 
 14 6 
 
 195 
 
 2593 
 
 56 
 
 166,000 
 
 186,000 
 
 7 
 
 700 
 
 66 
 
 49.5 
 
 273 
 
 21/4 
 
 18 10 
 
 190 
 
 3015 
 
 79 
 
 101,420 
 
 193,760 
 
 8 
 
 700 
 
 70 
 
 53.5 
 
 318 
 
 21/4 
 
 19 
 
 195 
 
 3543 
 
 79 
 
 144,600 
 
 209,210 
 
 9 
 
 7,10 
 
 70 
 
 55 
 
 303 
 
 21/4 
 
 21 
 
 190 
 
 3772 
 
 74 
 
 151,290 
 
 230,940 
 
 10 
 
 7.7.5 
 
 78 
 
 58.5 
 
 463 
 
 21/ 4 
 
 19 
 
 210 
 
 5155 
 
 57 
 
 237,800 
 
 267,800 
 
 11 
 
 200 
 
 84 
 
 68.4 
 
 401 
 
 21/4 
 
 21 
 
 232 
 
 4941 
 
 57 
 
 394,150 
 
 475,900 
 
 Type and cylinder size: 1 Mogul, 13X18; 2, Mogul, 16X20; 3, American, 
 18X24; 4, 10-wheel balanced compound, 16X26 and 26X28; 5. Consoli- 
 dation, 22 X28; 6, Consolidation, 23 and 35X32; 7, Atlantic, 15 and 25 X 
 26; 8, Prairie, 17 and 28X28; 9, Pacific, 22X28; 10, Decapod, 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 under 
 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 connected to ana 
 operated with a common reversing rigging. By this means the tractive 
 power can be doubled over that of the ordinary engine for a given weipnt 
 of rail with a substantial saving in fuel. (See paper by C. J. Melhn, 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-gauge 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 class 
 
LARGE AMERICAN LOCOMOTIVES 
 
 1097 
 
 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- 
 Wheel-base : 
 
 Driving 
 
 Total engine 
 
 " tender 
 
 eng. and tender. . 
 Wt. in working-order: 
 
 On drivers 
 
 On truck-wheels 
 
 Engine, total 
 
 Tender " 
 
 Eng. and tend., loaded 
 Cylinders: 
 
 h.p.(2) - 
 
 1-P- (2) ....... 
 
 Piston-rod, diam 
 
 Connecting-rod, l'gth. . 
 
 Steam-ports 
 
 Exhaust-ports 
 
 Valves, out. lap, h.p. . . 
 Out. lap, l.p. . . . 
 
 " in. lap, h.p 
 
 " in. lap, l.p 
 
 max. travel . . . 
 
 lead, h.p 
 
 " lead, l.p 
 
 Boiler.— Type 
 
 Diam. barrel inside .... 
 Thickness of plates . . . 
 Height from rail to 
 
 center line 
 
 Length of smoke-box . . 
 
 Working pressure 
 
 Firebox.— type 
 
 Length inside 
 
 Width " 
 
 Depth at front 
 
 Thickness side plates. . 
 back plate . . 
 crown-sheet, 
 tube sheet.. . 
 
 Grate-area 
 
 Stay-bolts, U/8 in 
 
 Tubes — iron.. 
 
 Pitch 
 
 Diam., outside 
 
 Length 
 
 Heating-surface : 
 
 Tubes, exterior 
 
 Fire-box. 
 
 Miscellaneous: 
 
 Exhaust-nozzle, diam . 
 
 Stack, smal'st diam. . . 
 
 height from 
 
 rail to top 
 
 50 in. 
 
 30 " 
 9 XlOin. 
 5 X10" 
 41/ 2 X 9 " 
 
 18 ft. 10 in. 
 
 27 " 3 " 
 
 16 " 8 " 
 
 53 " 4 " 
 
 170,000 lbs. 
 29,500 " 
 192,500 " 
 117,500 " 
 310,000 " 
 
 16X28 in. 
 27X28 " 
 
 4 in. 
 9' 87/ 16 " 
 
 281/2X2 in. 
 
 281/2X8 " 
 
 7/s in. 
 
 5 /8 " 
 
 86 in. 
 40 " 
 
 9 X 121/2 in 
 6I/4XIO " 
 41/sX 8 " 
 
 8 ft. 6 in. 
 23" 11 " 
 15 "21/2 ' 
 47 " 81/ 8 " 
 
 84,000 lbs. 
 
 40,000 " 
 124,000 " 
 
 80,000 " 
 204,000 " 
 
 19X24 in. 
 
 33/s in. 
 8 ft. IV2 in. 
 
 U/ 2 Xl8in. 
 
 23/4X18 " 
 
 1 in. 
 
 6 in. 
 
 Vl6in. 
 
 5/16 " 
 
 Straight 
 
 6 ft. 21/2 in. 
 
 3/4 in. 
 
 8 ft. in. 
 5 " 77/8 " 
 
 180 lbs. 
 
 Wootten 
 
 10' 1 1 9/ie" 
 
 8 ft. 21/8 in. 
 
 4 " 6 " 
 
 5 /l6 in. 
 
 5/16 " 
 
 3/8" 
 
 V2" 
 
 89.6 sq. ft. 
 
 pitch, 41/4 in. 
 
 354 
 
 23/4 in. 
 
 2 
 
 lift. 11 in. 
 
 2,208.8 ft. 
 234.3 " 
 
 5 in. 
 1 ft. 6 in. 
 
 15ft.61/ 2 in. 
 
 VlO in. 
 "51/2 in'-' 
 
 Wagon top 
 
 4ft. 9in. 
 
 9/16 in. 
 
 7 ft. 11 1/2 in. 
 4 " 8 
 
 190 lbs. 
 
 Buchanan 
 
 9 ft. 63/ 8 in. 
 
 3 " 47/8 " 
 
 6 " II/4 " 
 
 5/16 in. 
 
 5/!6 " 
 
 3/8" 
 
 V2 " 
 
 30.7 sq.ft. 
 
 4 in. 
 
 268 
 
 57 in. 
 29 1/4 & 40" 
 1 1 X 12" 
 
 6V2XIO" 
 71/2X12"' 
 
 19 ft. 9 in. 
 35 " II " 
 
 234,580 It 
 52,660 
 287,240 
 
 19X32 in. 
 
 32X32 " 
 
 293/4X15/8' 
 
 and 13/ 4 " 
 
 293/4X63/4" 
 
 7/8 in. 
 
 3/4 " 
 neg. 1/4 in. 
 neg. 3/ 8 " 
 
 6 in. 
 
 " 
 
 Vs " 
 Wagon to 
 
 783/4 in. 
 7/8 & 1 Vie" 
 
 225 lbs. 
 
 108 in. 
 78 " 
 80 1/4 in. 
 781/4 " 
 3/8 " 
 
 2 in. 
 12 ft. in. 
 
 1,697 g 
 233 
 
 31/2 in. 
 1 ft. 3 1/4 in. 
 
 14 ft. 10 in. 
 
 21/4 in. 
 20 ft. 
 
 4,586 sq. ft. 
 210 " 
 
 * Back truck journals. 
 
1098 
 
 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, i3/i6 and 27/ 32 ins.; work- 
 ing pressure, 200 lbs. 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, 11 X 12 ins., other journals, 10 X 12 ins.; 
 truck (4), 30 1/2 ins. dia., journals, 6 X 10 ins.; tender (8),33ty2 ins. dia., 
 journals, 6X11 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, 
 93 ft. 6V2 ins.; weight: on drivers, 394,150 lbs., on front truck, 14,500 lbs., 
 on back truck, 17,250 lbs., total engine 425,900 lbs., total engine and 
 tender 596,000 lbs.; 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 lbs. 
 18.9 lbs. 
 19.7 lbs. 
 21.4 lbs. 
 
 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 
 single 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 20 30 40 50 
 
 Lbs. water per I.H.P. hour — simple. . 26 23 22 22 23 
 
 Lbs. water per I.H.P. hour — compound .. .. 18 18 18 
 
 Cut-off per cent of stroke . . . 
 Lbs. water per I.H.P. hour - 
 Lbs. water per I H.P. hour - 
 
 60 
 
 - simple ... 24 
 ■compound 18 1/2 
 
 70 
 26 
 
 191/2 
 
 80 90 100 
 
 29 33 38 
 
 201/2 221/2 25 
 
 Indicator-tests of a Locomotive at High Speed. (Locomotive 
 Eng'g, June, 1893.) — Cards were taken by Mr. Angus Sinclair on the 
 locomotive drawing the Empire State Express. 
 

 
 Results 
 
 op Indicator-diagrams. 
 
 
 Card No. 
 
 Revs 
 
 Miles 
 per hour. 
 
 I.H.P. 
 
 Card No. 
 
 Revs. 
 
 Miles 
 per hour 
 
 1 
 
 160 
 
 37.1 
 
 648 
 
 7 
 
 304 
 
 70.5 
 
 2 
 
 260 
 
 60.8 
 
 728 
 
 8 
 
 296 
 
 68.6 
 
 3 
 
 190 
 
 44 
 
 551 
 
 9 
 
 300 
 
 69.6 
 
 4 
 
 250 
 
 58 
 
 891 
 
 10 
 
 304 
 
 70.5 
 
 5 
 
 260 
 
 60 
 
 960 
 
 11 
 
 340 
 
 78.9 
 
 6 
 
 298 
 
 69 
 
 983 
 
 12 
 
 310 
 
 71.9 
 
 LOCOMOTIVES. 1099 
 
 I.H.P. 
 
 977 
 972 
 1,045 
 1,059 
 1,120 
 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, 18 X 23/4 in. Valve-travel, 51/2 in. Out- 
 side lap, 1 in.; inside lap, V64 in. Journals: driving-axle, 8I/2X 10i/2in.; 
 truck-axle, 6 X 10 in. 
 
 The train consisted of four coaches, weighing, with estimated load, 
 340,000 lbs. The locomotive and tender weighed in working order 200,000 
 lbs., 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 lbs. According to 
 this, the power exerted on the rails to move the train is 6553 lbs., or 24 
 lbs. per ton. The speed is 37 miles an hour. When a speed of nearly 
 60 miles an hour was reached the average cylinder-pressure is 40.7 lbs., 
 representing a total traction force of 4520 lbs., without making deduc- 
 tions for internal friction. If we deduct 10% for friction, it leaves 15 lbs. 
 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 lbs. Deducting 
 10% again for friction, this leaves 17.6 lbs. per ton as the power exerted 
 in keeping the train up to a velocity of 70 miles. Throughout the trip 
 7 lbs. of water were evaporated per lb. of coal. The work of pulling 
 the train from New York to Albany was done on a coal consumption of 
 about 31/8 lbs. 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. K., 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 Conducting 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. R. 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, lbs. 
 
 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 lb. 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 12 14 
 
 Equiv. evap. per lb. 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 
 
1100 
 
 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 8 1/2 to more than 16 lbs. 
 of 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, 1622, 1641 
 
 
 Kind of Locomotive. 
 
 
 Simple 
 Freight. 
 
 Com- 
 pound 
 Freight. 
 
 Com- 
 pound 
 Passen- 
 ger. 
 
 
 23.67 
 23.83 
 28.95 
 
 20.26 
 22.03 
 25.31 
 
 18.86 
 
 Water per I.H.P. hr. at maximum load 
 
 Water per I.H.P. hr. at max. consumption. .. 
 
 21.39 
 24.41 
 
 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 lbs. per I.H.P. hour; compound locomotives between 
 18.6 and 27 lbs.; and with superheating the minimum steam consumption 
 was reduced to 16.6 lbs. 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 snowed 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 lbs. is required to overcome the friction of each coupled axle, 
 while with grease the required force is from 800 to 1100 lbs. 
 
 The lowest figures for dry coal consumed per dynamometer H.P. hour 
 were approximately as follows: 
 Revs, per min. 40 80 160 240 
 
 Compound freight engine, {§?h°P? 500° fof 80C? "ll 
 Compound passenger engine, {^jj ^ 1 /;;; |q| j^ ^5% 
 
 A complete report of the St. Louis locomotive tests is contained in a 
 book 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., 
 xxvii, 610. 
 
 Weights and Prices of Locomotives, 1885 and 1905. 
 (Baldwin Loco. Wks.) 
 
 Type. 
 
 W'gt 
 
 Price 
 
 Price 
 per 
 lb. 
 
 $ 0828 
 .0912 
 .0892 
 .0854 
 
 2 
 
 American. . . . 
 
 Mogul 
 
 Ten wheel . . . 
 Consolidation 
 
 80,857 
 72,800 
 85,000 
 92,400 
 
 $6,695 
 6,662 
 7.583 
 7,888 
 
 Type. 
 
 American 
 
 Atlantic 
 
 Pacific 
 
 Ten wheel 
 Consolidation 
 
 Price 
 W'ght Price per 
 
 102,000 
 187,200 
 227,000 
 156,000 
 192,460 
 
 $9,410 
 15,750 
 15,830 
 13,690 
 14,500 
 
 $.092 
 083 
 070 
 
 " 
 
LOCOMOTIVES. 
 
 1101 
 
 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; 
 forthe 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 lbs. 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 Trac- 
 
 on tive Passenger, 1905. 
 
 Driver. Force. 
 
 Weight Trac- 
 
 on tive 
 
 Driver. Force. 
 
 American, single-ex. 
 American, comp .... 
 American, single-ex.. 
 American, comp 
 Ten-wheel type, com 
 
 Average 
 
 75,210 
 83,860 
 64,560 
 78,480 
 93,850 
 
 17,270 
 12,900 
 15,550 
 14,050 
 16,480 
 
 15,250 
 
 Atlantic, comp. .. . 
 Atlantic, single-ex.. 
 Pacific, single-ex. . 
 Pacific, single-ex. . 
 Atlantic, single-ex. 
 
 101,420 
 103,600 
 141,290 
 114,890 
 80,930 
 
 22,180 
 23,800 
 29,910 
 25,610 
 21,740 
 
 Freight, 1893. 
 
 Freight, 1905. 
 
 24,648 
 
 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. 
 Consol., 2-cyl. comp.. 
 
 Consol , 
 Consol., s 
 Consol., s 
 
 ngle-ex.. 
 ngle-ex.. 
 ngle-ex. . 
 
 234,580 
 166,000 
 151,490 
 171,560 
 165,770 
 
 Average . , 
 
 62,740 
 40,200 
 40,150 
 44,080 
 45,170 
 
 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. 
 Per cent efficiency of boiler 
 
 12 
 
 40 
 
 80 
 
 120 
 
 160 
 
 200 
 
 80 
 
 75 
 
 67 
 
 59 
 
 51 
 
 43 
 
 A rate of 12 lbs. is given as representing stationary-boiler practice, 40 
 lbs. English locomotive practice, 120 lbs. average American, and 200 
 lbs. maximum American, locomotive practice. 
 
 Pages 473 and 475 of Henderson's " Locomotive Operation" give 
 diagrams of evaporation per lb. 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 Railwav Master Mechanics' Association on Compound Loco- 
 motives (Am. Mach., 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- 
 ing possibilities of further improvement in pressure and in fuel and water 
 economy. (&) It has lessened the amount of water (dead weight) to be 
 
1102 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, or 
 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 course, 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. (&) These advantages 
 and 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 every locomotive 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; 5 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 
 a 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 Gazette, 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 1 2 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 lbs. when a superheater is used, and to have cylinders of larger dimen- 
 sions than when ordinary steam of 200 lbs. 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. S. M. E„ vol. xvi, 305; and Trans. Am. Ry. Master Mechanics* Assn., 
 
LOCOMOTIVES. 1103 
 
 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 (Pror. 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 16i/4in. diameter, the wheel-base 
 2 ft. 9 in.; the frame 7 ft. 41/4 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, 26V2 gallons; working- 
 pressure, 170 lbs. per sq. in. tractive power, say, 1412 lbs., or 9.22 lbs. per 
 lb. 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., and 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 reducticn 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 lbs. of water from and at 212° F., 
 or to 17.1 lbs. at 8 1/2 atmospheres, or 125 lbs. per sq. in., effective pres- 
 sure. The highest evaporative duty was 14 lbs. of water under 8V2 
 atmospheres per lb. 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. 
 
 Fireless 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 thus 
 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 5 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 
 is 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., 
 corresponding to 225 lbs. per sq. in. The steam from the reservoir is 
 
1104 
 
 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 lbs. to 67 lbs., 530 
 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 lbs. 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 35 tons are on 
 the coupled wheels. The speed varies from 15 miles to 25 miles per hour. 
 The trains 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 lbs. working pressure; but sometimes seamless steel cylinders 
 of small diameter, designed for a working pressure of 2000 lbs. or upwards, 
 are used. The customary maximum pressure in the locomotive tank is 
 800 lbs. gauge, and the working pressure in the cylinders is from 130 to 
 140 lbs. The following table is condensed from one in a circular of the 
 Baldwin Locomotive Works, No. 45, 1GG1. 
 See account of the Mekarski compressed-air locomotives, page 624 ante. 
 
 Dimensions and Tractive Power of Four Coupled Compressed- Air 
 Locomotives Having Two Storage Tanks. 
 
 Class 
 
 Cylinders, inches 
 
 Diam. of drivers 
 
 Wheel base 
 
 Approx. weight, lbs.. 
 
 Inside dia. of tanks. . 
 
 Aggregate tank vol., 
 cu. ft 
 
 App. height , 
 
 App. width over 
 tanks 
 
 App. width over cyl- 
 inders 
 
 App. length over 
 bumpers 
 
 g h Full stroke...... 
 
 •43 I 3/4 Stroke cut-off 
 
 rt o V2 Stroke cut-off 
 
 £Ph 1/4 Stroke cut-off 
 
 4-4-C 
 
 4-6-C 
 
 4-8-C 
 
 4-10-C 
 
 4-1 2-C 
 
 4-16-C 
 
 4-18-C 
 
 5X10 
 22" 
 4 r 0" 
 10,000 
 26" 
 
 6X10 
 
 24" 
 4' 3" 
 14,000 
 
 28" 
 
 7X12 
 24" 
 4' 6" 
 18,000 
 30" 
 
 8X14 
 
 26" 
 
 5' 3" 
 
 23,000 
 
 32" 
 
 9X14 
 28" 
 5' 5" 
 27,000 
 34" 
 
 11X14 
 
 28" 
 
 5' 6" 
 
 37,000 
 
 38" 
 
 12X16 
 30" 
 6' 0" 
 
 44,000 
 40" 
 
 75 
 
 4' 5" 
 
 100 
 4' 10" 
 
 130 
 
 5' 0" 
 
 170 
 
 5' 4" 
 
 200 
 5' 8" 
 
 280 
 6' 0" 
 
 320 
 
 6' 4" 
 
 if 10" 
 
 Gauge 
 + 24" 
 
 5' 2" 
 Gauge 
 + 26" 
 
 5' 6" 
 Gauge 
 + 27" 
 
 5' 10" 
 
 Gauge 
 + 28" 
 
 6' 3" 
 Gauge 
 +30" 
 
 7 0" 
 Gauge 
 + 32" 
 
 7' 4" 
 Gauge 
 +33" 
 
 12' 0" 
 1350 
 1290 
 940 
 510 
 
 14' 0" 
 1785 
 1700 
 1240 
 670 
 
 15' 0" 
 2915 
 2780 
 2025 
 1100 
 
 17' 0" 
 
 4100 
 3900 
 2840 
 1540 
 
 18' 0" 
 4820 
 4580 
 3345 
 1815 
 
 20' 0" 
 7200 
 6860 
 4995 
 2710 
 
 2W 6" 
 9140 
 8705 
 6340 
 3440 
 
 Draw-bar pull on any grade = tractive power - (.0075 + % of grade) 
 X weight of engine. 
 
 Working pressure in cylinders 140 lbs.; tank storage pressure, 800 lbs. 
 
 Other sizes of engines are 51/2 X 10 in., 6X12 in., and 8 X12in„ 24-in. 
 diam. of drivers; 9 X14 in., 26-in. drivers, and 10 X 14 in., 28-in. drivers. 
 
COMPRESSED-AIR LOCOMOTIVES. 
 
 
 1105 
 
 Cubic Feet of Air, 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 
 
 
 600 
 
 700 
 
 800 
 
 
 600 
 
 700 
 
 800 
 
 600 
 
 700 
 
 800 
 
 Cylinder working 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 130 
 
 135 
 
 140 
 
 
 130 
 
 135 
 
 140 
 
 
 130 
 
 135 
 
 140 
 
 
 
 
 
 Grade. 
 
 R 
 
 V 
 
 V 
 
 V 
 
 R 
 
 V 
 
 V 
 
 V 
 
 R 
 
 V 
 
 V 
 
 V 
 
 Level 
 
 20.0 
 
 1.16 
 
 0.99 
 
 87 
 
 30.0 
 
 1 74 
 
 1 50 
 
 1 31 
 
 40.0 
 
 2 33 
 
 1 99 
 
 1 74 
 
 V2% 
 
 31.2 
 
 1.81 
 
 1.56 
 
 1.36 
 
 41.2 
 
 2 40 
 
 2 05 
 
 1 79 
 
 51.2 
 
 2.98 
 
 2 56 
 
 2 23 
 
 1% 
 
 42.4 
 
 2 47 
 
 2 12 
 
 1 85 
 
 52.4 
 
 i 05 
 
 2 61 
 
 2 28 
 
 62.4 
 
 3.643.11 
 
 2 73 
 
 2% 
 
 64.8 
 
 3,78 
 
 3 24 
 
 2 83 
 
 74.8 
 
 4 35 
 
 3 73 
 
 3 26 
 
 84.8 
 
 4 94 
 
 4 24 
 
 3 70 
 
 3% 
 
 87.2 
 
 5.08 
 
 4 35 
 
 3 81 
 
 97.2 
 
 5 67 
 
 4 86 
 
 4 25 
 
 107.2 
 
 6 25 
 
 5 35 
 
 4 69 
 
 US:::::::::::::: 
 
 109.6 
 
 6.39 
 
 5.48 
 
 4.79 
 
 119.6 
 
 6 97 
 
 5 97 
 
 5 22 
 
 129.6 
 
 7 56 
 
 6 47 
 
 5 67 
 
 132.0 
 
 7.69 
 
 6.60 
 
 5.77 
 
 142.0 
 
 8.27 
 
 7.09 
 
 6.20 
 
 152.0 
 
 8.86 
 
 7.60 
 
 6.64 
 
 R= resistance per ton of 2240 lbs. in pounds. V = cubic feet of air. 
 
 Air Locomotives with Compound Cylinders and Atmospheric Interheaters 
 are built by H. K. Porter Co. The air enters the high-pressure cylinder 
 at 250 lbs. gauge pressure and is expanded down to 50 lbs., 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 lbs. 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 lbs. down to atmos- 
 phere without unmanageable refrigeration. 
 
 The following calculation shows the relative economy of a single- cylinder 
 locomotive using air at 150 lbs. and of a compound using air at 250 lbs. 
 in the high-pressure and 50 lbs. in the low-pressure cylinder, non-expan- 
 sive working being assumed in both cases. 
 
 11.2 cu. ft. of free air at 150 lbs. 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. lbs. of energy. 
 
 11.2 cu. ft. of free air at 250 lbs. gauge if used in a cylinder 0.623 sq. ft. 
 area and 1 ft. stroke would develop 0.623 X 144 X 250= 22,425 ft lbs. 
 
 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. lbs., if 
 the heat is restored between the two cylinders. Gain by compounding 
 with interheating, over simple cylinders with 150 lbs. 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. lbs.; with compound 
 cylinders and atmospheric interheater, 35,880 ■*- 11.2 = 3205 ft. lbs. 
 
 The above calculations have been practically confirmed by actual 
 tests, which show 1900 ft. lbs. of work per cubic foot of free air with the 
 simple locomotive and 3000 ft. lbs. 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 
 800 and 1000 lbs. per sq. in. into the storage reservoir, and it requires an 
 average of about 12,000 ft. lbs. per cubic foot of free air to compress and 
 deliver it at these pressures. The efficiency of the two systems then is: 
 1900 + 12000 = 16% for the simple locomotive, and 3000 + 12000 = 
 25% for the compound with atmospheric interheater. 
 
1106 
 
 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 lbs. applied on a lever arm at a distance =~ a ins. from 
 the axis, <S = shearing resistance at the outer fiber, in lbs. per sq. in., then 
 
 If R = revolutions per minute, then the horse-power transmitted = 
 
 H p = Pa2 *R = *&S X2nR = RSd 3 . 
 33,000X12 16X33,000X12 321,000' 
 
 7321,000 H. P. .VCXH.P. 
 
 d= V RS = V ~R 
 
 In practice, empirical values are given to S and to the coefficients 
 K = 5.1/5 and C = 321,000/S, 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 lbs. respectively, whence 
 
 for head shafts d = 
 
 \/W 
 
 V80H.P. , .. . .. . ,753 EU 
 
 a/ — r> — ; for line shafts d= 4/ — ^- 
 
 Jones & Laughlin Steel Co. gives the following for steel shafts: 
 
 Turned. Cold-rolled. 
 
 For simply transmitting power ) 
 
 and short countershafts, bear- \ H.P. = d s R ■+■ 50 H.P = d 3 R * 40 
 ings not more than 8 ft. apart ) 
 
 A teSg s Tfr&art' neSha ' tS :} Hp -' is ' J - 9 ° H.P.-« + 70 
 
 As prime movers or head shafts! 
 
 carrying main driving pulley I H p = wsp ^ 105 H P = d*R ■* 100 
 or gear, well supported by( nr - an ' vzo atr - aK ' 1UU 
 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 sha ft D to carry load at center of bays from 2 to 12 ft. 
 
 D '\/i<"- 
 
 span, D = %/ - d\ in which d is the diameter derived from the formula 
 
 for head shafts, Ci= length of bay in inches, and Ci = distance in inches 
 between centers of bearings in accordance with the formula for horse- 
 
1107 
 
 power of head shafts. (Jones & Laughlin Steel Co.) Values of Ci for 
 different diameters d are as follows: 
 
 d c x 
 
 d c x 
 
 d c x 
 
 d 
 
 Cl 
 
 d Cx 
 
 d c x 
 
 1 to 13/ 8 15 
 
 213/ie 25 
 
 315/ie & 4 37 
 
 5 1/4 & 5 3/ 8 
 
 55 
 
 63/ 8 71 
 
 73/8 88 
 
 Hl/16 & l 3 /4 16 
 
 27/8 to 3 26 
 
 43/ie 40 
 
 51/2 
 
 5/ 
 
 61/2 73 
 
 71/2 91 
 
 U3/16 & 17/8 17 
 
 3 1/8 to 3 1/4 28 
 
 41/4 41 
 
 55/8 
 
 59 
 
 65/8 75 
 
 75/8 93 
 
 U5/16 to 21/8 18 
 
 33/8 30 
 
 47/ie & 41/2 44 
 
 53/4 
 
 61 
 
 63/ 4 77 
 
 73/4 96 
 
 23/ie & 21/ 4 19 
 
 3 7/i6 & 3 1/2 31 
 
 43/4 47 
 
 57/8 
 
 63 
 
 67/8 79 
 
 77/8 99 
 
 2-3/16 to 27/ie 20 
 
 39/16 & 35/ 8 33 
 
 413/i 6 49 
 
 6 
 
 65 
 
 7 81 
 
 8 101 
 
 21/2 to 25/8 24 
 
 3 H/16 & 3 3/4 34 
 
 5 51 
 
 61/8 
 
 6/ 
 
 71/8 84 
 
 8I/2 112 
 
 211/16 & 23/4 22 
 
 3 7/8 36 
 
 51/ 8 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 = ^319,586 X Z> 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 lbs. 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 100 ft. 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 \J d 2 , for shaft without pulleys; 
 L = 5 ^d 2 , for shaft carrying pulleys. (L in ft., d in ins.) 
 
 Deflection of Shafting. (Pencoyd Iron Works.) — For continuous 
 line-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 lbs. 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 
 lbs., we derive from authoritative formulae the following: 
 
 L = -\/873 d 2 , d = ^1,3/873, for bare shafting; 
 
 L = ^/l75d 2 , d = VL3/175, f or 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 §0 proportioned as to deflect not more than 
 
1108 
 
 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. -f- R, L = ^720 d 2 , for bare shafts; 
 
 d = ZJ70 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. ... 2345 6-789 
 
 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. = d*R + 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. G 
 
 215/16 
 
 25 
 
 51 
 
 76 
 
 101 
 
 127 
 
 15/8 
 
 4.3 
 
 8.6 
 
 12.8 
 
 17.1 
 
 21 
 
 3 
 
 27 
 
 54 
 
 81 
 
 108 
 
 135 
 
 1 n /l6 
 
 4.8 
 
 9.6 
 
 14.4 
 
 19.2 
 
 24 
 
 31/8 
 
 31 
 
 61 
 
 91 
 
 122 
 
 152 
 
 13/4 
 
 5.4 
 
 10.7 
 
 16.1 
 
 21 
 
 27 
 
 33/16 
 
 32 
 
 65 
 
 97 
 
 129 
 
 162 
 
 1 !3/l6 
 
 5.9 
 
 11.9 
 
 17.8 
 
 24 
 
 30 
 
 31/4 
 
 34 
 
 69 
 
 103 
 
 137 
 
 172 
 
 t7/ 8 
 
 6.6 
 
 13.1 
 
 19.7 
 
 26 
 
 33 
 
 33/8 
 
 38 
 
 77 
 
 115 
 
 154 
 
 192 
 
 I 15/16 
 
 7.3 
 
 14.5 
 
 22 
 
 29 
 
 36 
 
 37/16 
 
 41 
 
 81 
 
 122 
 
 162 
 
 203 
 
 2 
 
 8.0 
 
 16.0 
 
 24 
 
 32 
 
 40 
 
 31/, 
 
 43 
 
 86 
 
 128 
 
 171 
 
 214 
 
 21/16 
 
 8.8 
 
 17.6 
 
 26 
 
 35 
 
 44 
 
 39/16 
 
 45 
 
 90 
 
 136 
 
 180 
 
 226 
 
 21/8 
 
 9.6 
 
 19.2 
 
 29 
 
 38 
 
 48 
 
 35/ 8 
 
 48 
 
 95 
 
 143 
 
 190 
 
 238 
 
 23/ie 
 
 10.5 
 
 21 
 
 31 
 
 42 
 
 52 
 
 3H/16 
 
 50 
 
 100 
 
 150 
 
 200 
 
 251 
 
 21/4 
 
 11.4 
 
 23 
 
 34 
 
 45 
 
 57 
 
 33/4 
 
 55 
 
 105 
 
 158 
 
 211 
 
 264 
 
 2">/l6 
 
 12.4 
 
 25 
 
 37 
 
 49 
 
 62 
 
 37/ 8 
 
 58 
 
 116 
 
 174 
 
 233 
 
 291 
 
 23/s 
 
 13.4 
 
 27 
 
 40 
 
 54 
 
 67 
 
 315/ie 
 
 61 
 
 122 
 
 183 
 
 244 
 
 305 
 
 27/ie 
 
 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 
 
 2H/16 
 
 19.4 
 
 39 
 
 58 
 
 77 
 
 97 
 
 41/2 
 
 91 
 
 182 
 
 273 
 
 365 
 
 456 
 
 23/4 
 
 21 
 
 41 
 
 62 
 
 •83 
 
 104 
 
 43/4 
 
 107 
 
 214 
 
 322 
 
 429 
 
 537 
 
 213/is 
 
 22 
 
 44 
 
 67 
 
 89 
 
 111 
 
 5 
 
 125 
 
 250 
 
 375 
 
 500 
 
 625 
 
 For H.P. transmitted by turned steel shafts, as prime movers, etc., 
 multiply the figures by 0.8. 
 
 For shafts, as second movers or line shafts, i 
 bearings 8 ft. apart, multiply by ] 
 
 For simply transmitting power, short counter- 
 shafts, etc., bearings not over 8 ft. apart, multi- 
 ply by 
 
 Cold-rolled Turned 
 1.43 1.11 
 
1109 
 
 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 their 
 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, 
 radius of bolt circle, in inches, n = number of bolts, S = allowab le shear - 
 ing stress per sq. in., then ^rd 3 5-f-16 = i/4 nd 2 rS, whence d= 0.5 ^D 3 /(nr)- 
 Kimball and Barr give n = 3 +D/2, but this number may be modified for 
 convenience in spacing, etc. 
 
 Effect of Cold Rolling. — Experiments by Prof. R. H. Thurston in 
 jl902 on hot-rolled and cold-rolled steel bars (Catalogue of Jones & 
 (Laughlin Steel Co.) showed that the cold-rolled steel in tension had its 
 lelastic 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 lbs. per sq. in., and that of the 
 smallest bar 73,600 lbs. In the hot-rolled steel bars the maximum 
 strength of the full-sized bar was 62,900 lbs. and that of the smallest bar 
 58,600 lbs. 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 = * ~ — - • 
 
 «i 
 A 10-inch hollow 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 opposite 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. Mach. Jan. 28, 
 1897. — D, diam. of collar; T, thickness; d, diam. of set screw; I, length. 
 All in inches. 
 
 
 
 
 
 
 
 
 Loose Collars. 
 
 
 
 
 
 
 
 Shaft 
 
 D 
 13/4 
 
 17/8 
 
 21/4 
 25/8 
 
 23/ 4 
 3 
 
 T 
 
 3/4 
 
 13/16 
 
 15/16 
 
 1 
 
 11/16 
 
 H/8 
 
 d 
 
 7/16 
 
 7/16 
 7/16 
 7/16 
 1/2 
 5/8 
 
 I 
 5/16 
 3/8 
 7/16 
 7/16 
 9/16 
 9/16 
 
 Shaft 
 
 D 
 
 33/8 
 
 3 3/4 
 
 4 
 
 41/2 
 
 47/s 
 
 53/ie 
 
 T 
 
 13/16 
 H/4 
 15/16 
 17/16 
 15/8 
 13/4 
 
 d 
 
 ~5/8 
 5/8 
 ■>/8 
 5/8 
 3/4 
 3 /4 
 
 I 
 
 5/8 
 H/16 
 H/16 
 13/16 
 13/16 
 15/16 
 
 Shaft 
 
 D 
 
 t 
 
 17/8 
 
 17/8 
 
 17/8 
 
 2 
 
 2 
 
 d 
 
 3/4 
 3/4 
 3/4 
 3/4 
 3/4 
 
 I 
 
 1 
 
 H/4 
 
 U/2 
 
 15/8 
 
 13/ 4 
 
 2 
 
 21/4 
 
 21/2 
 
 23/4 
 
 3 
 
 31/4 
 
 31/2 
 
 4 
 
 41/2 
 5 
 
 51/2 
 6 
 
 513/16 
 
 67/16 
 
 615/ie 
 
 71/2 
 
 8 
 
 1 
 1 
 1 
 1 
 
 1 
 
 Fast Collars. 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 Shaft 
 
 D 
 
 T 
 
 U/2 
 13/4 
 2 
 
 21/4 
 
 2 
 
 21/4 
 25/8 
 3 
 
 1/2 
 1/2 
 1/2 
 9/16 
 
 21/2 
 23/4 
 3 
 31/4 
 
 31/4 
 35/8 
 4 
 
 41/4 
 
 9/16 
 5/8 
 H/16 
 11/16 
 
 31/2 
 4 
 
 41/2 
 
 45/8 
 53/8 
 6 
 7 
 
 7/8 
 
 15/16 
 1 
 H/8 
 
 51/2 
 6 
 
 61/2 
 7 
 
 75/8 
 81/4 
 9 
 93/ 4 
 
 13 
 
 13 
 H 
 
 16 
 
 4 
 8 
 2 
 
1110 
 
 SHAFTING, 
 
 
 'aa^euiBtQ 
 
 CA ^T IPl IT* \© tXi Is 
 
 
 ^j^» » -. s 
 
 
 •satput 
 'q^Bubq; 
 
 ifnOIMWao-Nm^vOoOO^-mmoOoo 
 
 •sm 'xog jo 'Sui 
 -j^ag jo q^Sdaq; 
 
 \Ot>»0»0'-Nm'*>Ci»0 
 
 N^ vCaOON 
 
 
 
 00 
 
 C 
 cj 
 
 bfl 
 £ 
 
 CO 
 
 oi 
 c 
 
 *a 
 
 a 
 
 o 
 
 1 
 
 m 
 *S 
 
 O 
 M 
 
 m 
 
 'o, 
 
 6 
 
 a 
 
 o 
 
 a 
 J 
 
 5 
 
 8 a «-l -isj 
 
 •d«" g^H- 
 
 ,£ B J= 13 3 *• 
 "| &! ^ « 
 
 1 n . u g £^ 
 
 "6 2 S+^-o 
 
 CO m B 
 
 ^ p 
 
 ^ 
 
 c*-* 
 
 - 
 
 lis 
 
 \C 
 
 »0-N 
 
 o 
 
 jogjog 
 
 ^ 
 
 ^r5«N*^rn 
 
 
 <s r>i ™ rs rs rs r^ 
 
 T 
 
 NNNNNNNN 
 
 n- 
 
 00 £ © £j rq JT JO £j w 
 
 ^ 
 
 
 Sr 
 
 m^oiNoo-— * J3<Q 
 
 & 
 
 jn^-ot^oo^^-jQ 
 
 r>l 
 
 ^ *T in IT\ ^O PS 00 
 
 ^S 
 
 
 
 rq 
 
 r^^'T^inS^S 
 
 B «j ^~ ~ "S 
 
 M 
 
 rq(V!r^n^T-«3-irivO 
 
 
 '$ 
 
 — NNKMAtin 
 
 
 S 
 
 S-O — — M 
 
 S 2 
 
 »0*0 
 
 
 ■S °| • 
 
 SnUQB 
 
 i.^.(sjfqc^^fi^fAt<> 1 Tr , <riiMn , ovor>.t>.oo 
 
 u 
 
 lb 
 
 bfljS-o oi r 
 
 £r!«!lf 
 
 
 
 
 
PULLEYS. 1111 
 
 PULLEYS. 
 
 Proportions of Pulleys. (See also Fly-wheels, page 1031.) — Let 
 = number of arms, D = diameter of pulley, S = thickness of belt, 
 it = 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, ei = thickness of arm at rim, c = 
 amount of crowning; dimensions in inches. 
 
 Unwin. Reuleaux. 
 
 B = width of rim 9/ 8 (# + o .4) 9/s /? to 5/ 4 /? 
 
 t = thickness at edge of rim 0.75+0 .005 D j ( $ffc to */!?? 1 '* 
 
 T = thickness at middle of rim ... 2t+ c 
 
 I For single . BD 
 
 belts = 0.6337V IT K n 
 
 h = breadth of arm at hub < ' . — i/. in + £ + _±L 
 
 For double . * BD /iU1 ' ^ 4 r 20 n 
 [belts = 0.798 V ~£ 
 
 hi = breadth of arm at rim 2/ 3 h .8 h 
 
 e = thickness of arm at hub 0.4 h .5 h 
 
 e\ = thickness of arm at rim .4 h x .5 hi 
 
 n = number of arms, for a single set 3 + j=~ 1/2 ( 5 + ^-^ | 
 
 IB for sin.-arm 
 pulleys. 
 2 B for double- 
 arm pulleys. 
 
 M = thickness of metal in hub hto^/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 ei 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., €i = .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 its taken as 
 elliptical. 
 
 The following solution for breadth of arm is proposed by the author: 
 Assume a belt pull of 45 lbs. 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 2 -r-l, 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 lbs., 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 b = e = OAh 
 
 the thickness. We then have/P - 10 X -^A; = 900 - = 3535X0.4ft» t 
 
 n ■*- 2 n 1/2 D 
 
 3/ qr»rj nn ^/rD 
 
 whence h = 4 / - — = 0.6331/ , which is practically the same as 
 
 the value reached by Unwin from a different set of assumptions. 
 
1112 
 
 Convexity of Pulleys. — Authorities differ. Morin gives a rise equal 
 to 1/10 of the face; Molesworth, 1/24; others from i/s to 1/96. 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. 
 
 CONE OR STEP PUIXEYS. 
 
 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 
 
 - 2 L cos / 
 
 ? = angle whose sine is 
 
 D+ d 
 2L 
 
 LCos / 
 
 V"-m- 
 
 The length of the belt is constant when D + d is constant; that is, in ai 
 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 ._, .'. , 
 ro = ~2-t T28T' (Rankxne.) 
 
 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 
 
 D + d , (D - d) 2 
 the axes, D = 
 
 - r, be assumed, then 
 
 12.566 L 
 If a series of differences of radii of the steps, R ■ 
 R + t (R — r) 2 
 
 for each pair of steps — - — = r — ' R ' , and the radii of each may 
 
 be computed from their half sum and half difference, as follows: 
 R+ r , R - r R + r R - r 
 
 *=— + -2T- ; r = —2 2— 
 
 A. J. Frith (Trans. A. 8. 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 
 
 Ratio. 
 
 Trial Diams. 
 
 Values of 
 
 {D-dY- 
 
 D 
 
 d 
 
 D+ d 
 
 12.56 L 
 
 50 
 50 
 50 
 50 
 
 4 
 3 
 2 
 1 
 
 40 
 
 37.5 
 33.333 
 25 
 
 10 
 
 12.5 
 16.666 
 25 
 
 0.7165 
 
 .4975 
 .2212 
 .0000 
 
 Amount 
 to be 
 Added. 
 
 1 
 
 0.0000 
 .2190 
 .4953 
 .7165 
 
 Corrected Values. 
 
 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 
 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 edi- 
 tions of this Pocket-book, but are now replaced by the more recent graphi- 
 cal solution by Burmester, given below, and by algebraic formulae deduced 
 
CONE OR STEP PULLEYS 
 
 1113 
 
 from it by the author, which give results far more accurate than are required 
 in practice. 
 
 In all cases 0.8 of the thicknessof the belt should be subtracted from the 
 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.) 
 
 Burmester's Method, Dr. R. Burmester, in his " Lehrbuch der 
 Kinematik" (Machinery's Reference Series, No. 14, 1908), gives a graphi- 
 cal solution of the cone-pulley problem, which while not theoretically 
 exact is much more accurate than practice requires. 
 
 From A on a horizontal line AB, Fig. 170, draw a 45° line, AC. Lay off 
 AS on AC equal, on any convenient scale, the larger the better, to the 
 distance between centers of the" 
 shafts, and from S draw ST per- 
 pendicular to AC. Make SK = 
 1/2 AS, and with radius AK draw 
 an arc of a circle, XY. From a 
 convenient point D on AC draw 
 a vertical line FDE, and make 
 DE equal the given radius of a 
 step on one cone, and EF equal 
 the given radius of the corre- 
 sponding step on the other cone. 
 Draw FG and EH parallel to AC. 
 From the point G on the arc drop 
 a vertical line cutting EH in H. 
 Through H draw a horizontal 
 line MO, touching AC at M. 
 Then if horizontal distances are 
 measured from M, as Ma, MH, 
 MP, to equal the radii of the 
 pulleys or steps on one cone, the 
 corresponding vertical distances 
 ab, HG and PN will be the radii 
 of the corresponding steps on the 
 other cone. 
 
 If the radii of the two steps of any pair are to bear a certain ratio, as 
 ab -s- Ma, from M draw a line at an angle with MO whose tangent equals 
 that ratio, and from the point where it cuts the arc, as b, drop a vertical, 
 ba. Ma and ba will be the radii required. 
 
 Using Burmester's diagram the author has devised an algebraic solution 
 of the problem (Indust. Eng., June, 1910) which leads to the following 
 equations: 
 
 Let L— distance between the centers, = AS on the diagram. 
 
 r = radius of the steps of equal diameter on the two cones, = MP 
 = PN. 
 n, r 2 = Ma, ab, radii of any pair of steps. 
 
 a = co-ordinates of M, referred to A, = 0.79057 L - r . 
 
 Fig. 170. 
 
 If r t is given, r 2 = Vi.25 L 2 - (0.79057 L - 
 If the ratio r 2 -=- r x is given, let r 2 /r x = c: r 2 : 
 
 r + n) 2 - 
 
 = CTx. 
 
 0.79057 L + r . 
 
 We then have a + cr-i = v'.fi! 2 — (a + ri) 2 , which reduces to 
 
 (1 + c 2 ) r x 2 + 2 a (1 + c) n = 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 + c 2 )rx2+ (1.58114 L - 2 r ) (1+ c)r x = 3.16228 Lr - 2r 2 , 
 in which L, r and c are given and r x is to be found. 
 
 Let L = 100, c = 4, r = 12.858 as in Mr. Frith's example, page 1112. 
 
 Then 17ri 2 + 10ar x , = 12,500 -8764.62, from which n =5.001, r? = 20.004. 
 
 If c = 3, r x = 6.304, r 2 = 18.912. If c = 2, r t = 8.496, r 2 = 16.992. 
 
 Checking the results by the approximate formula for length of belt, 
 page 1125, viz, Length = 2L + !t(r 1 +r 2 )+ (r 2 - n) 2 -h d, we have 
 for C = 1, 200 + 80.79 +0 = 280.79 
 
 2, 200 + 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. 
 
1114 
 
 J. J. Clark (Indust. Eng., Aug., 1910) gives the following solution: 
 Using the same notation as above, 
 
 (c 2 1)2 y,i2+?r(c+1)ri=27rro (1) 
 
 «(c+l)r 1 + Lx(^£)=2«r (2) 
 
 x = (r 2 -rtf + L* (3 ) 
 
 The quadratic equation (1) gives the value of r\ 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 x , 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, «2, so, s n = speeds of the driven shaft, 
 D u Di, D3, D n = diameters of the pulleys on the driving cone, 
 
 di, rf?, d 3 , d ft = diams. of corresponding pulleys on the driven cone, 
 £Di = Mi; SDz =s 2 d2, etc. 
 s 1 /S^Dx/d 1 = rn s n /S = D n /d n , = r n . 
 
 The speed of the driving shaft being constant, the several speeds of 
 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-f 
 sion, thenr 2 /ri = rz/r 2 = r n /r n _ 1 = c, a constant. 
 
 r n ■* r i = c n_1 ; c = n ~ 1 vV n - r x 
 
 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 n=5? 
 
 Log 2.197 = 0.341830 
 
 Log 0.76923 = 1.886056 
 
 0.455774 
 
 Divide by n- 1,= 4, 0.113943 = log of 1.30. 
 
 If Di/di = 1, then AM = 1 -> 1.3 = 0.769; D 3 d 3 = 1.30; DJdv 
 1.69; ZVds = 2.197. 
 
1115 
 
 BELTING. 
 
 Theory of Belts and Bands. — A pulley is driven by a belt by means 
 of the friction between the surfaces in contact. Let Tx be the tension on 
 the driving side of the belt, Ti the tension on the loose side; then S, = Tx 
 — Ti, 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 formulas are derived by calculus (Rankine's 
 Mach'y and Millwork, p. 351; Carpenter's Exper. Eng'g, p. 173): 
 
 fi=e/<> ; r 2 =-%; Tx-T 2 =Tx-^ = Tx(l-e-f e ). 
 Tx-T 2 = Tx (1 - e~f e ) = Tx (1 - \^~f Qm ) = Tx (1 -10~°- 00758 »; 
 
 Tx = 10 0.00758 >; Ti = To _ x 10 0.00758 >;:r2 = Tx . 
 
 If the arc of contact between the band and the pulley expressed in 
 turns and fractions of a turn == n, 6 = 2im; ef e = io 2 - 7288 -/"; that is, ef d 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 belts on iron pulleys, Morin 
 found f = .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 
 winch 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: 
 
 Let i 
 
 2 S = 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 order 
 to acquire the velocity of the band. (See Cooper on Belting, p. 101.) 
 If T c = centrifugal tension; 
 
 V= velocity in feet per second; 
 <7= 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 lbs. per cubic foot gives W = 56 -5- 144 = .388. 
 T c = WV 2 +• g = 0.388 F 2 -^- 32.2 = .012F 2 . 
 
 /= 0.15 
 
 0.25 
 
 
 0.42 
 
 0.56 
 
 2.7288/= 0.41 
 
 0.68 
 
 
 1.15 
 
 1.53 
 
 7r and n = 1/2, then 
 
 
 
 
 
 Ti + T 2 = 1.603 
 
 2.188 
 
 
 3.758 
 
 5.821 
 
 Ti -f- 5 = 2.66 
 
 1.84 
 
 
 1.36 
 
 1.21 
 
 1 + T2 + 25= 2.16 
 
 1.34 
 
 
 0.86 
 
 0.71 
 
 ary practice it is usual to 
 
 assume 
 
 To 
 
 = S; Tx -- 
 
 = 2S; Tx + T 2 
 
1116 BELTING. 
 
 Belting Practice. Handy Formulae for Belting. — Since in the 
 practical application of the above formulae the value ot the coefficient of 
 friction must be assumed, its actual value varying within wide limits 
 (15% to 135%), and since the values of T\ and Ti also are fixed arbi- 
 trarily, it is customary in practice to substitute for these theoretical 
 formulae more simple empirical formulae and rules, some of which are 
 given below. 
 
 Let d = diam. of pulley in inches; 7rd = circumference; 
 
 V = velocity of belt in ft. per second; v = vel. in ft. per minute; 
 a = angle of the arc of contact: 
 
 I/ = length of arc of contact in feet = nda -4- (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 -s- t; 
 r.p.m.=revs. per minute; r.p.s. = revs, per second = r.p.m. -f- 60. 
 
 F ^ X , p ,..g x ^ =0 .004363 d X,p. m .= ^^ ; 
 
 ird 
 v= jTj X r.p.m.; = .2618 d X r.p.m. 
 
 „ TT _, Svw SVw SwdX r.p.m. 
 
 Horse-power, H.P. = 33^- = -^ = 126Q5Q • 
 
 If F = working tendon per square inch = 275 lbs., and t = 7/ 32 inch, 
 S = 60 lbs. nearly, then 
 
 H.P. = ||=0 .109 Vw = .000476 wd X r.p.m. = wd **£ m ' ■ (1) 
 
 If F = 180 lbs. per square inch, and t = Ve inch, S = 30 lbs., then 
 
 H.P.= ^ = 0.055 Vw = 0. 000238 wdX r.p.m. = wd ^o™' ' (2) 
 
 If the working strain is 60 lbs. 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 lbs. 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. = I. H.P. 
 
 H.P. = ^ =0.06 Vw = .000262 wd X r.p.m. = wd ^g' 1 "' • (3) 
 
 This corresponds to a working strain of 33 lbs. per inch of width. 
 
 Many writers give as safe practice for single belts in good condition a 
 working tension of 45 lbs. per inch of width. This gives 
 
 H.P.= ^ = .0818 Vw = .000357 wd X r.p.m. = Wd i5 r '*?' m ' • (4) 
 
 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 
 
 = 0.1169 Fw = 0.00051 wtfXr.p.m. = wd *J']? — 
 \ 19ou 
 
 (■ r >) 
 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 h- 12. The above formulae translated into this 
 form give: 
 
 (1) For S = 60 lbs. per inch wide; H.P. = 46 sq. ft. per minute. 
 
 (2) " S = 30 " " " H.P. = 92 
 
 (3) " S = 33 " " " H.P. = 83 
 
 (4) " S = 45 " " " H.P. = 61 
 
 (5) " S = 64.3" " " H.P. = 43 " " (double belt). 
 
1117 
 
 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 
 t nda ' TT _ Svw Sw w nd w w a 
 
 feet. Since L = -^^ and H.P. = ^q = 33^ X - X r.p.m. X ^ 
 
 we obtain by substitution H.P. = _--„ XLX r.p.m., and the five for- 
 
 lboUU 
 mul£e then take the following form for the several values of S: 
 
 H.P.= wLX 27 r f m - (l) 
 
 H.P. (double belt) 
 
 wL X r.p.m. wL X r.p.m . wL X r.p.m 
 
 550 Uj: 500 W; 367 { ); 
 
 _ wL X r.p.m. 
 
 ~ 257 
 
 (5). 
 
 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 (5-0 .012 7 2 ) -h 550. 
 
 For/ = .40, a = 180°, C = .715, w = I. 
 
 Laced Belts, S = 275. 
 
 Riveted Belts, S = 400. 
 
 0) 
 
 Thickness in inches = t. 
 
 CD 
 
 ~ .-- 
 >^ 
 
 15 
 
 Thickness in inches = t. 
 
 
 1/7 
 51 
 
 1/6 
 0.59 
 
 3/16 
 
 63 
 
 7/32 
 
 0.73 
 
 1/4 
 
 84 
 
 Vie 
 
 1.05 
 
 1/3 
 
 1.18 
 
 7/32 
 1 69 
 
 V4 
 
 1 94 
 
 5/16 
 
 Vs 
 
 3/8 
 
 7/16 
 3 39 
 
 1/2 
 
 10 
 
 2.42 
 
 2 58 
 
 2 91 
 
 3.87 
 
 15 
 
 75 
 
 0,88 
 
 1.00 
 
 1.16 
 
 1.32 
 
 1.66 
 
 i.yy 
 
 20 
 
 2 24 
 
 ?. 57 
 
 3.21 
 
 3 42 
 
 3 85 
 
 4,49 
 
 5.13 
 
 20 
 
 1.00 
 
 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 
 
 75 
 
 1 23 
 
 1 43 
 
 1 61 
 
 1 88 
 
 2 16 
 
 2 69 
 
 2 86 
 
 SO 
 
 i 31 
 
 3 79 
 
 4 74 
 
 5 05 
 
 5 67 
 
 6.62 
 
 7.58 
 
 30 
 
 1 47 
 
 1 72 
 
 1 93 
 
 2 25 
 
 2 58 
 
 y U 
 
 3 44 
 
 35 
 
 3 82 
 
 4 37 
 
 5 46 
 
 5 83 
 
 6 56 
 
 7 65 
 
 8 75 
 
 35 
 
 1 69 
 
 1 97 
 
 2 22 
 
 2 59 
 
 2 96 
 
 3 70 
 
 3 94 
 
 40 
 
 4 33 
 
 4 95 
 
 6 19 
 
 6.60 
 
 7 47. 
 
 8.66 
 
 9.90 
 
 40 
 
 1 90 
 
 2 22 
 
 2 49 
 
 2,90 
 
 y 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 
 
 3.6/ 
 
 4,58 
 
 4 89 
 
 50 
 
 5 26 
 
 6 01 
 
 7 51 
 
 8 02 
 
 9 07 
 
 10 57. 
 
 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 7.8 
 
 10 43 
 
 17. 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 
 
 5.13 
 
 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, = 5245 ft. p. min. 
 
 105.4 ft. per sec. = 6324 ft. per min. 
 
 In the above table the angle of subtension, 
 
 Should it be 
 
 Multiply above 
 
 values by J .65| 
 
 A. F. Nagle's Formula (Trans. A. S. M. E., vol 
 Tables published in 1882). 
 
 is taken at 180°. 
 
 200° 
 
 1100° 
 
 110° 
 
 120° 
 
 130° 
 
 140° 
 
 150° 
 
 160° 
 
 170° 
 
 180°. 
 
 1 .70 
 
 .75 
 
 .79 
 
 .83 
 
 .87 
 
 '.91 
 
 .94 
 
 .97 
 
 1 1 
 
 1.05 
 1881, p. 91. 
 
 H.P.= CVtw 
 
 C = 1 - 10 -0-00758 fa; 
 
 a = degrees of belt contact; 
 / = coefficient of friction; 
 w = width in inches ; 
 
 - .012 F 2 \ 
 
 < 550 J' 
 
 t= thickness in inches; 
 v= velocity in feet per second; 
 S== stress upon belt per square inch. 
 
1118 
 
 BELTING. 
 
 Taking S at 275 lbs. per sq. in. for laced belts and 400 lbs. per so. in, 
 for lapped and riveted belts, the formula becomes 
 
 H.P.= CVtw (0 .50 - .0000218 V*) for laced belts; 
 H.P. = CVtw (0 .727 - .00002J8 F 2 ) for riveted belts. 
 Values ofC= 1- 10-o.oo758/ a . (Nagle.) 
 
 
 Degrees of contact = a. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 90° 
 
 100" 
 
 II0 U 
 
 120° 
 
 130° 
 
 I40 u 
 
 150° 
 
 160° 
 
 170° 
 
 180° 
 
 200° 
 
 0.15 
 
 0.210 
 
 0.230 
 
 0.250 
 
 0.270 
 
 0.288 
 
 0.307 
 
 0.325 
 
 342 
 
 359 
 
 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 
 
 .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. 
 
 
 
 .9 w 
 
 •3d 
 
 «m fl 
 
 Form. 1 
 
 Form .2 
 
 Form. 3 
 
 P\)rm. 4 
 
 Form. 5 
 double 
 
 Nagle's 
 
 Form. 
 
 In, 
 
 o * 
 
 . S 
 
 H.P. = 
 
 wv 
 
 H.P. = 
 wv 
 
 H.P. = 
 
 wv 
 
 H.P. = 
 
 wv 
 
 belt 
 H.P.= 
 
 7 /32-in. single 
 belt. 
 
 
 
 *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 
 
 20 
 
 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 
 7200 
 
 550 
 600 
 
 
 
 
 
 
 4.05 
 3.49 
 
 7.97 
 
 120 
 
 
 
 
 
 
 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 
 formulae for horse-power so as to give the value of w. Thus: 
 
 . „ x 550 H.P. 9.17 H.P. 2101 H.P. 275 H.P. 
 
 From formula (1), w = 
 
 From formula (2), w = 
 
 From formula (3), w = 
 
 From formula (4), w = 
 
 From formula (5),* w = 
 
 * For double belts. 
 
 v V (IX r.p.m. 
 1100 H.P. 18. 33 H.P. 4202 H.P. 
 
 L Xr.p.m." 
 530 H.P. 
 
 v V d X r.p.m. 
 1000 H.P. 16.67 H.P. 3820 H.P. 
 
 L Xr.p.m. 
 500 H.P. 
 
 v V d X r.p.m. 
 733 H.P. 12.22 H.P. 2800 H.P. 
 
 L X r.p.m. 
 360 H.P. 
 
 v V dXr.p.Tn. 
 513 H.P. 8.56 H.P. 1960 H.P. 
 
 L Xr.p.m.' 
 257 H.P. 
 
 v V dX r.p.m. 
 
 L Xr.p.m." 
 
BELTING. 
 
 1119 
 
 Many authorities use formula (1) for double belts and formula (2) or 
 (3) for single belts. 
 
 To obtain the width by Nagle's formula, Wm ' ny t fo_ Q qi' 2 vzy or 
 
 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, 
 sip, 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 thck- 
 ness, in a piece of leather one foot square, so that 
 
 
 Lbs. 
 
 per Sq. 
 
 Ft. 
 
 Approx. 
 Thick- 
 ness. 
 
 Actual 
 Thick- 
 ness. 
 
 Vel. per 
 Inch for 
 1 H.P. 
 
 Safe Strain 
 per Inch 
 Width. 
 
 
 16 oz. 
 24 " 
 28 " 
 33 " 
 45 " 
 
 V6in. 
 
 V4" 
 5/16 " 
 
 1/3 " 
 9/16 " 
 
 0.16 in. 
 0.24 " 
 0.28 " 
 0.33 " 
 0.45 " 
 
 625 ft. 
 417 " 
 357 " 
 303 " 
 222 " 
 
 52.8 lbs. 
 
 
 78.1 " 
 
 
 92.5 " 
 
 
 109 '• 
 
 3-ply 
 
 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 I Inch 
 Width. 
 
 Velocity per Inch for 
 for 1 H.P. 
 
 3-ply 
 
 4 " 
 
 5 " 
 
 6 " 
 
 7 •« 
 
 8 " 
 
 0.18 in. 
 0.24 " 
 0.30 " 
 0.35 " 
 0.40 " 
 0.45 " 
 
 45 pounds 
 
 65 " 
 
 85 " 
 105 " 
 125 " 
 145 " 
 
 735 ft. per min. 
 508 " " " 
 388 " " " 
 314" " " 
 264 " " " 
 218 " " " 
 
 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, in which F is an empirical factor, are based on the following 
 assumptions: A belt of single thickness will stand a stress on the tight 
 side, 2\, of 60 lbs. per inch of width, a double belt 105 lbs., and a 
 triple belt 150 lbs., and have a fairly long life, requiring only occasional 
 taking up; the ratio of tensions T/T 2 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 the pulley due to the elasticity of the belt 
 and not to slip) should not exceed 1% — this requires that the differ- 
 
1120 
 
 ence in tensions T t — To should not be greater than 40 lbs. per inch of 
 width for single, 70 for double and 100 for triple belts. 
 
 Pulley diam, 
 
 Under 
 8 in. 
 
 8 to 
 36 in. 
 
 Over 
 3 ft. 
 
 Under 
 14 in. 
 
 14 to 
 60 in. 
 
 Over 
 
 5 ft. 
 
 Under 
 21 in. 
 
 21 to 
 
 84 in. 
 
 Over 
 7 ft. 
 
 Belt thick- 
 ness. 
 
 Single. 
 
 S'gle. 
 
 S'gle. 
 
 Dbl. 
 
 Dbl. 
 
 Dbl. 
 
 Triple. 
 
 Triple. 
 
 Triple. 
 
 Factor 
 
 T x - T 2 
 
 Creep, %.... 
 
 T t + T 2 
 
 T t 
 
 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 was 
 tightened. 
 
 The tension under which each belt was spliced was carefully figured so 
 as to place it under an initial strain — while the belt was at rest immedi- 
 ately after tightening — of 71 lbs. per inch of width of double belts. This 
 is equivalent, in the case of 
 
 Oak tanned and fulled belts, to 192 lbs. 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- 
 clusions, 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 width 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 
 
 35 lbs. 
 
 80 sq. f to 
 
 950 ft. 
 30 H.P. 
 
 30 lbs. 
 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- 
 
 1100 ft. 
 
 Or: A double belt 6 in. wide, running 4000 to 
 5000 ft. per min., will transmit 
 
 25 H.P. 
 
 The terms "initial tension," "effective pull," etc., are thus explained 
 by Mr, Taylor: When pulleys upon which belts are tightened are at rest, 
 
BELTING. 1121 
 
 both strands of the belt (the upper and lower) are under 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 side 
 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, 749) 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 lbs. per in. of width, or 240 lbs. per sq. in. 
 section. They will not maintain this tension for any length of time, 
 however. 
 
 Belt-clamps having spring-balances between the two pairs of clamps 
 should be used for weighing the tension of the belt accurately 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 lbs. per inch of 
 width, corresponding to an effective pull of 65 lbs. per inch of width, and 
 
 (B) according to a more economical rule of a total load of 54 lbs., corre- 
 sponding to an effective pull of 26 lbs. 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. 
 
1122 BELTING. 
 
 The stretch during the first six months of the life of belts is 36% of 
 their entire stretch (A); 15% (B). 
 
 A double 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 running 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 ana out of use. 
 
 The best form of belt-shifter for wide belts is a pair of rollers twice the 
 width of belt, either of wnicn 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., xv, 
 242.) — The most notable feature in Mr. Taylor's paper is the great dif- 
 ference between Ms 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 
 problem which Mr. Taylor undertakes to solve is quite a different one 
 from that which is solved by the ordinary rules with their variations. Tho 
 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- 
 
 f)ower may be transmitted with the minimum cost for belt repairs, the 
 ongest 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 1-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 yule, "but that such a pro- 
 portion involved undue strain from overtightening to prevent slipping, 
 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 due 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 and wide belts, such 
 as engine "fly-wheel belts. 
 
MISCELLANEOUS NOTES ON BELTING . 1123 
 
 Earth's Studies on Beltingo (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 A — 140 -^-(500 + V), in which A is the sum of the tension on 
 the tight side and one-half the tension on the slack side of the belt, and 
 V is the velocity in feet per minute. 
 
 Taking Mr. Taylor's data as a starting point, Mr Barth 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 lbs. 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 lbs. Further, the maximum initial 
 tension, that is, the initial tension 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 lbs. 
 for a machine belt, and 240 lbs. 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 ^n tight side + 1/2 tension in slack side 
 = 240 lbs. 
 Velocity, ft. per min... 500 1000 2000 3000 4000 5000 6000 
 
 Initial tension, t 124 120 121 128 136 144 152 
 
 Centrifugal tension t c . 0+ 3 13 31 56 86 124 
 
 Difference, t - t c 123 117 108 ,97 80 58 28 
 
 Tensionontightside.il 210 212 211 207 198 187 173 
 Tension on slack side, fa 60 54 57 68 84 107 134 
 Effective pull. t± - fa . . 150 158 154 139 114 80 39 
 Sum of tensions fa + fa 270 268 269 274 282 294 307 
 H.P. per sq. in. of sec- 
 tion 2.27 4.79 9.33 12.64 13.82 12.12 7.09 
 
 H.P. per in. width, 5/ie 
 
 in. thick 0.71 1.50 2.82 3.95 4.32 3.71 2.22 
 
 Belts driving countershafts, fa + V2 fa = 160 lbs. 
 
 Velocity of belt, ft. per min 500 1000 2000 3000 4000 5000 
 
 Initial tension, to 82 81 83 89 96 102 
 
 Tension on tight side, fa 140 141 140 134 125 114 
 
 . Tension on slack side, tt 40 38 41 53 69 92 
 
 Effective pull, fa - fa 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, 5/ 16 in. thick 3.47 0.97 1.87 2.30 2.12 1.04 
 
 MISCELLANEOUS NOTES ON BELTING. 
 
 Formulae 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 
 small pulleys, however, when a double belt is used, there is not such per- 
 
 i 
 
1124 BELTING. 
 
 feet contact between the pulley-face and the belt, due to the rigidity of 
 the latter, and more work is necessary to bend the belt-fibers than when a 
 tninner and more pliable belt is used. The centrifugal force tending to 
 throw the belt from the pulley also increases with the thickness, ana 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 of 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 in 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 i/io 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 8-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/ 8 in. from the ends of the belt. The second row 
 should be at least l°/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 pullev, and then set that point on the driven 
 Dulley 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 
 eanh other. 
 
 In quarter-twist belts, in order that the belt may remain on the pulleys, 
 
MISCELLANEOUS NOTES ON BELTING. 1125 
 
 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 And 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) -s- 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 
 product add 3.1416, and multiply the sum by the radius of the pulley. 
 Or length of belt in contact with the pulley 
 
 = radius X U + .0349 a) = radius X *(1 + a/90). 
 For the smaller pulley, length=radius X Or— .0349 a) 
 = radius X f(l — a) -*-90. 
 
 The above rules refer to Open Belts. The accurate formula for length 
 of an open belt is, 
 
 Length = ttR(1 + a/90) + nr(l -a/90) + 2 L cos a. 
 
 = R (tt+ 0.0349 a) + r (tt-O .0349 a) + 2 Z, 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) h- L; cos a = ^U - (R - r) 2 -*- L. 
 An approximate formula is 
 Length = 2 L + n (R + r) + (R - r) 2 /L 
 
 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 = ir R(l 4-/3/90) + nr (1 + j8/90) + 2 L cos /S 
 = (R + r) X (tt + 0.0349 J3) + 2 L cos j8, 
 
 in which /3 = angle whose sine is (R + r) -f- L\ cos )3 = "^L 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 eve in inches, X the number of turns made 
 by the belt and by 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. 
 
 Relations of the Size and Speeds of Driving and Driven Pulleys. 
 — The driving pulley is called the driver, D, and the driven pulley 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 = dr -^ R; 
 
 Diam. of driver = diam. of driven X revs, of driven -*- revs, of driver. 
 d = DR -h r; 
 
 Diam. of driven = diam. of driver X revs, of driver -4- revs, of driven. 
 
1126 
 
 BELTING . 
 
 R = dr -*• 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 ■+■ diam. of driven. 
 
 Evils of Tight Belts. (Jones and Laughlins.) — Clamps with power- 
 ful screws are often used to put on belts with extreme tigntness, and with 
 most injurious strain upon tne 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 some figures showing the power it takes, in 
 average modern mills with first-class shafting, to drive the shafting 
 alone: 
 
 Mill 
 
 Whole 
 Load, 
 H.P. 
 
 Shaftin 
 
 I Alone. 
 
 Mill 
 No. 
 
 Whole 
 Load, 
 H.P. 
 
 Shafting Alone. 
 
 Wo. 
 
 Horse- 
 power. 
 
 Per cent 
 of whole. 
 
 Horse- 
 power. 
 
 Per cent 
 of whole. 
 
 1 
 2 
 3 
 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 Jhave 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 
 purpose 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 
 
MISCELLANEOUS NOTES ON BELTING. 1127 
 
 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 
 motion shall be from the top of the driving to the top of the driven pulley, 
 when the sag will inc p ease 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 and not against 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- 
 
 E roofing leather, though a positive water-proofing material has not yet 
 een 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 110° of heat. 
 
 Strength of Belting. — The ultimate tensile strength of belting does 
 not generally enter as a factor in calculations of power transmission. 
 
 The strength of the solid leather in belts is from 2000 to 5000 lbs. 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 lbs. per sq. in., averaging 273 lbs. 
 
 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 faces 
 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, 
 lest 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 
 
1128 
 
 heavy double-leather belts 40 inches wide each, and one 24 inches wide. 
 The engine indicated 1950 H.P., of which probably 1850 H.P. was trans- 
 mitted by the belts. The belts were considered to be heavily loaded, but 
 not overtaxed. (30 X 3.14 X 104 X 61) + 1850 = 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. 
 
 Belt Dressings. — We advise that no belt dressing should be used 
 except when the belt becomes dry and husky, and in such instances we 
 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. Our expe- 
 rience convinces us that resin should never be used on leather belting. 
 (Fayerweather & Ladew.) 
 
 Belts should not be soaked in water before oiling, and penetrating ods 
 should but seldom be used, except occasionally when a belt gets very 
 dry and husky from neglect. It may then be moistened a little, and 
 have neat's-foot 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 lbs. tension per inch of 
 width to 100% increase with 20 lbs. tension. 
 
 Cement for Cloth or Leather. (Molesworth.) — 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 ^ery durable, 
 and has great tensile strength, and when adjusted for service it has the 
 most perfect hold on the pulleys, hence is less liable to slip than leather. 
 
 Never use animal oil or grease on rubber belts, as it will greatly injure and 
 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 
 side next the pulley with boiled linseed-oil. (From circulars of manufac- 
 turers.) 
 
 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-ply rubber belt = (length of arc of contact on smaller pulley 
 in ft. X width of belt in ins. X revs, per min.) -4- 325. For a 5-ply belt 
 multiplv bv It's, for a 6-plv by 12/ 3 , for a 7-ply by 2, for an 8-pIv by 21 '3. 
 When the proper weight of duck is used a 3- or 4-ply rubber belt is equal 
 to a single leather belt and a 5- or 6-ply rubber to a double leather belt. 
 
ROLLER CHAIN AND SPROCKET DRIVES. 
 
 1129 
 
 When the arc of contact is 180°, H.P. of a 4-ply belt = width in ins. X 
 velocity in ft. per min. -s- 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 
 two 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 pulley 3 ft. diam., 
 30 ft. apart at 200 r.p.m. 
 
 
 Rope 
 Drive. 
 
 Leather 
 Belt. 
 
 Steel Belt. 
 
 
 2200 
 530 
 
 $335 
 13 
 
 1120 
 240 
 
 $425 
 6 
 
 460 
 
 
 30 
 
 
 $250 
 
 
 0.5 
 
 
 
 ROLLER CHAIN ANI> SPROCKET DRIVES. 
 
 The following is abstracted from an article by A. E. Michel, in Machy, 
 Feb., 1905. 
 
 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 2,000 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 1 ll/ 4 11/2 13/4 2 
 
 Tens, strength, lbs. 1,200 1,200 4,000 6,000 9,000 12,000 19,000 25,000 
 Block chain linch, 1,200 to 2,500; li/2inch, 5,000. 
 
 The safe working load of a chain is dependent on the amount of rivet 
 bearing surface, and varies from 1/5 to 1/40 of the tensile strength, accord- 
 ing to the speed, 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 twice the rivet bearing surface and half again as much 
 tensile strength as the similar single one. 
 
 The length of chain for a given drive may be found by the following 
 formula: 
 
1130 • BELTING. 
 
 All dimensions in inches. D = Distance between centers of shafts. 
 A = 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 a. 
 
 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 multiples 
 of twice the pitch, as a union of the ends can be effected only with an out- 
 side and an inside link. 
 
 Wherever possible, the distance between centers of shafts should permit 
 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 conoition 
 is destructive. If a fixed center distance must be used, and roults 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. 
 
 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 efficiency 
 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°/ N. Tan /?= sin a -?■ (B/A + cos a). 
 Pitch diameter = A/Sin 0. 
 
 Bottom diam.=pitch diam.— &. Outside diam.=pitch diam. + 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. 4- D - E. 
 
 8 to 12 
 Teeth. 
 
 13 to 16 
 Teeth. 
 
 1/2 in. to 3/ 4 in. 
 1 in. to 2 ins... . 
 
 0.062 in. 
 0.125 in. 
 
 0.031 in. 
 0.062 in. 
 
 Sprocket diameters should be very accurate, particularly the base ; 
 diameter, which should not vary more than 0.002 in. from the calculated i 
 values. Sprockets should be gauged to discover thick teeth and inaccurate I 
 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 
 
ROLLER CHAIN AND SPROCKET DRIVES. 1131 
 
 results. Fewer may De 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 of the chain between the links, 
 
 A = 1/2 W = width of tooth at top. B = uniform width below pitch line. 
 B = W — V64 in. when W = 1/4 in. or less. 
 
 = W— 1/32 in. when W = 5/ 16 to 5/ 8 in. inclusive. 
 
 = w— 1/16 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 beyond 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 
 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- 
 ance. Accordingly, chain makers now advise the following pitch line 
 clearance for standard rollers: 
 
 Pitch, in., 
 
 1/2 
 
 3/4 
 
 1 
 
 1V4 
 
 1V2 
 
 13/4 
 
 2 
 
 Clearance, in., 
 
 V32 
 
 Vie 
 
 3 /32 
 
 3/16 
 
 7/32 
 
 V8 
 
 5 /32 
 
 Cutters may be obtained from Brown & Sharpe Mfg. Co. with this 
 clearance. 
 
1132 BELTING. 
 
 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 generally made of 
 malleable iron. For conveyers for clean substances, flour, wheat and 
 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, noise- 
 lessly, 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 transmission 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-adjusting forms of teeth have 
 been invented, of which the Renold silent-chain gear is one of the best. 
 
 The makers of the Morse rocker chain, also an excellent chain, recom- 
 mend it for use under the following conditions: (1) Where room is lack- 
 ing for the proper sized 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 maximum power per inch of width is 
 desired. 
 
 The Renold silent chain and the Morse rocker chain find springs 
 necessary in the sprocket wheel. This springiness the belt naturally 
 possesses, and where maximum power is not necessary at a low speed 
 under service conditions of moisture and dirt, as in automobile trans- 
 mission, the belt will be cheaper to install, cheaper to maintain, cheaper 
 to repair in case of breakdown, and more efficient than any chain. A 
 leather belt will run on very short centers and transmit very high powers, 
 but it should be run at higher speed than a long belt. 
 
 For slow service, for positive transmission, for rough service, gears 
 are rivals of chain .transmission. For fast service, for springy transmis- 
 sion, for clean, dry work, leather belts are still the best. — Harrington 
 Emerson, Am. Mach., April 6, 1909. 
 
 It is to be regretted that there is no standard among chain manufac- 
 turers for the correct outline of sprocket cutters and amount of clearance 
 for various sizes of chain. If it is clearly understood that the high quality 
 roller and block chains now on the market require correctly cut sprockets 
 properly proportioned for the particular conditions of service they are 
 to work under, there will be a large increase in their use for power trans- 
 mission, and the troubles now incident to incorrect installations could be 
 wholly obviated. — C. C. Myers, Am. Mach., Aug. 5, 1909. 
 
 A 350-H.P. Silent Chain Drive has been built by the Link Belt Co. 
 The gears are 12 ft. apart, centers. The drive consists of two strands, 
 each 12 ins. wide, of Renold silent chain of 2-in. pitch. The pinion is 
 of forged steel, about 16 1/2 in. diameter, 27-in. face, 26 teeth, bore 29 in. 
 ■ long 10 in. diameter. The main gear is made of two cast-iron wheels, 
 side by side, each 76i/2-in. diameter, 131/2-in. face, 120 teeth. Each 
 wheel is provided with steel flanges and a special hub containing a series 
 of stiff coiled springs in compression through which the driving force is 
 transmitted from the hub to the wheel. The object of this device is to 
 provide an equalizing factor between the power shaft and the teeth of 
 the wheel, so that any unevenness in the rotation and consequent shock 
 will be absorbed by the device. The pinion is mounted on the armature 
 of a motor running' 300 r.p.m., and the speed of the driven gear is 65 r.p.m. 
 The speed of the chain belt is 780 ft. per minute. Three of these drives 
 have been constructed to transmit power for wire' drawing. — (Power, 
 Dec. 28, 1909.) 
 
TOOTHED- WHEEL GEARING. 
 
 1133 
 
 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 
 number of teeth and to the diameter. Thus the wheel that has twice as 
 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 
 oarts — 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, 
 
 eS Referring 1 1? Fig 6 17i, 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. „ ■'■*■. i„ 
 
 No of teeth 3.1416 
 
 Diametral pitch ■■ 
 
 Fig, 171. 
 
 Circular pitch 
 
 = diam. of pitch-circle in inches circular pitch 
 diam.X 3.1416 3.1416 
 
 No. of teeth diametral pitch' 
 
 diam. 
 
 Some writers use the term diametral pitch to mean No of teet h = 
 
 circular pitch ^ but tfae first definit i on j s the more common and the more 
 3.1416 
 
1134 
 
 GEARING. 
 
 convenient. A wheel of 12 in. diam. at the pitch-circle, with 48 teeth, is 
 48 /i2 = 4 diametral pitch, or simply 4 pitch. The circular pitch of the 
 same wheel is 12 X 3.1416-5- 48= 0.7854, or 3.1416-s- 4= 0.7854 in. 
 
 
 Relation of Diametral to Circular Pitch. 
 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Cir- 
 cular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 Circular 
 Pitch. 
 
 Diame- 
 tral 
 Pitch. 
 
 1 
 
 3. 142 in. 
 
 11 
 
 0.286 in. 
 
 3 
 
 1.047 
 
 15/16 
 
 3.351 
 
 U/2 
 
 2.094 
 
 12 
 
 .262 
 
 21/2 
 
 1.257 
 
 7/8 
 
 3.590 
 
 2 
 
 1. 571 
 
 14 
 
 .224 
 
 2 
 
 1.571 
 
 13/16 
 
 3.867 
 
 21/4 
 
 1.396 
 
 16 
 
 .196 
 
 17/8 
 
 1.676 
 
 3/4 
 
 4.189 
 
 21/2 
 
 1.257 
 
 18 
 
 .175 
 
 13/ 4 
 
 1.795 
 
 11/16 
 
 4.570 
 
 23,4 
 
 1.142 
 
 20 
 
 .157 
 
 l 5 /8 
 
 1.933 
 
 5/8 
 
 5.027 
 
 3 
 
 1.047 
 
 22 
 
 .143 
 
 H/2 
 
 2.094 
 
 9 /l6 
 
 5.585 
 
 31/2 
 
 .898 
 
 24 
 
 .131 
 
 17/16 
 
 2.185 
 
 1/2 
 
 6.283 
 
 4 
 
 .785 
 
 26 
 
 .121 
 
 13/8 
 
 2.285 
 
 7/16 
 
 7.181 
 
 5 
 
 .628 
 
 28 
 
 .112 
 
 15/16 
 
 2.394 
 
 3/8 
 
 8.378 
 
 6 
 
 .524 
 
 30 
 
 .105 
 
 11/4 
 
 2.513 
 
 5/16 
 
 10.053 
 
 7 
 
 .449 
 
 32 
 
 .098 
 
 13/16 
 
 2.646 
 
 1/4 
 
 12.566 
 
 8 
 
 .393 
 
 36 
 
 .087 
 
 U/8 
 
 2.793 
 
 3/16 
 
 16.755 
 
 9 
 
 .349 
 
 40 
 
 .079 
 
 H/16 
 
 -2.957 
 
 1/8 
 
 25.133 
 
 10 
 
 .314 
 
 48 
 
 .055 
 
 1 
 
 3.142 
 
 Vl6 
 
 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 
 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. 
 
 
 
 .-d 
 
 c3.£ 
 
 .A 
 £1 
 
 i.s 
 
 $ 
 
 S2j 
 
 is 
 
 .A 
 £1 
 
 i.s 
 
 
 l.s 
 
 .A 
 
 Z a) 
 
 is 
 
 H 
 
 Q 
 
 H 
 
 5 
 
 H 
 
 Q 
 
 H 
 
 Q 
 
 H 
 
 Q 
 
 H 
 
 5 
 
 to 
 
 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 
 
 24.878 
 
 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 
 
 87, 
 
 26.101 
 
 97 
 
 30.876 
 
 ??. 
 
 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 
 
 74 
 
 7.639 
 
 40 
 
 12.732 
 
 55 
 
 17.507 
 
 70 
 
 22.282 
 
 85 
 
 27.056 
 
 100 
 
 31.831 
 
 75 
 
 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. 
 
TOOTHED-WHEEL GEARING. 
 
 1135 
 
 Proportions of Teeth 
 
 Circular 
 
 Pitch 
 
 = 1. 
 
 
 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 Depth of tooth above pitch-line 
 
 Depth of tooth below pitch-line 
 
 0.35 
 .40 
 .70 
 .75 
 .05 
 .45 
 .54 
 .09 
 
 0.30 
 .40 
 .60 
 .70 
 .10 
 .45 
 .55 
 .10 
 
 0.37 
 .43 
 .73 
 .80 
 .07 
 .47 
 .53 
 .06 
 .47 
 
 0.33 
 
 'M 
 .75 
 
 0.30 
 
 .40 
 
 0.30 
 .35 
 
 
 .70 
 
 .65 
 
 
 
 
 .45 
 .55 
 .10 
 
 .45 
 
 .475 
 .525 
 .05 
 .70 
 
 485 
 
 
 515 
 
 
 03 
 
 
 .65 
 
 
 
 
 
 7. 
 
 8. 
 
 9. 
 
 10.* 
 
 Depth of tooth above pitch- 
 
 0.25 to 0.33 
 .35 to .42 
 
 0.30 
 .35+. 08" 
 
 0.318 
 
 .369 
 
 .637 
 
 .687 
 
 .04 to .05 
 
 .48 to .5 { 
 
 .52 to .5 { 
 .0 to .04 
 
 1+ P 
 
 Depth of tooth below pitch- 
 line 
 
 1.157 + P 
 2-P 
 
 Total depth of tooth 
 
 .6 to .75 
 
 .65 +.08" 
 
 2.157-P 
 0.I57+P 
 
 Thickness of tooth 
 
 Width of space 
 
 Backlash 
 
 .48 to .485 
 
 .52 to .515 
 .04 to .03 
 
 .48 -.03" 
 
 .52 +.03" 
 .04+. 06" 
 
 1.51 -s-Pto 
 1.57 +P 
 1.57 -hPto 
 1.63 + P 
 
 .Oto .06-rP 
 
 * 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 
 adjacent teeth. The term is now but little used, except in connection 
 with chain and sprocket gearing. 
 
 Chordal pitch = diam. of pitch-circle X sine of = j— — -r- Chordal 
 
 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. Chordal 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 14V2 , C. H. Logue uses a 20° involute with the following proportions: 
 Addendum 0.25P' = 0.7854 -e-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 pitch. 
 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. 
 
1136 
 
 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; 
 
 D' '— diameter of iDitch-circle.. 
 
 D = whole diameter 
 
 N = number of teeth 
 
 V = velocity 
 
 d' = diameter of pitch-circle. . 
 
 d = whole diameter. 
 
 n = number of teeth 
 
 u = velocity 
 
 Larger 
 Wheel. 
 
 Smaller 
 Wheel. 
 
 These 
 wheels run 
 together. 
 
 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; 
 
 ir = 3.1416. 
 
 P' = circular pitch, or the distance from the center of one tooth to the 
 center of the next measured on the pitch-circle. 
 
 Formulae 
 
 for a single w 
 
 heel: 
 
 
 N+2 
 D ' 
 
 "-£& 
 
 D"=|=2s 
 
 s=~= ^ = 0.3183 P'; 
 
 N 
 D''' 
 
 »-§>• 
 
 N = PD-2; 
 N = PD'\ 
 
 D' D 
 
 S N N+2' 
 
 IT 
 
 D=»p; 
 
 J 10' 
 
 S + ^W + 2^)= & - 
 
 7T 
 
 D = D> +| 
 
 ' l P 
 
 1/2 P*. 
 
 Formulas for a pair of wheels: 
 
 
 
 b = 2aP; 
 
 PD'V 
 
 v ' 
 
 D 2a{N+2)_ 
 b ' 
 
 
 
 PD'V 
 
 rl 2 a (n+2) 
 a b 
 
 
 _ NV m 
 
 v ' 
 
 n ' 
 
 b 
 
 fl= 2P ; 
 
 
 iV v + V 
 
 N' 
 
 D'+d' 
 a= -2—' 
 
 
 bV 
 
 v + V 
 
 u v + V 
 
 „ 2aV 
 
 d== 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.. 3 4 6 8 12 16 
 
 Face, inches 3 and 4 2i/ 2 13/ 4 and 2 1 1/4 and H/2 3/ 4 and 1 1/2 and 5/ 8 
 
 The Walker Company gives: 
 Ci r cular pitch, in. . 1/2 5 /8 
 
 3/4 7/ 8 1 
 13/4 2 21/2 
 
 H/2 
 41/2 
 
 2 21/2 3 4 5 6 
 6 71/2 9 12 16 20 
 
TOOTHED-WHEEL GEARING. 
 
 1137 
 
 The following proportions of gear-wheels are recommended by Prof. 
 Coleman Sellers. (Stevens Indicator, April, 1892.) 
 
 
 Proportions 
 
 of Gear-wheels. 
 
 
 
 
 Circular 
 
 Pitch. 
 
 P 
 
 Outside of 
 Pitch-line. 
 P X 0.3. 
 
 Inside of Pitch-line. 
 
 Width of Space. 
 
 Diametral 
 Pitch. 
 
 For Cast 
 
 or Cut 
 Bevels or 
 
 For Cut 
 Spurs. 
 P X 0.35 
 
 For Cast 
 Spurs or 
 
 For Cut 
 Bevels or 
 
 
 
 for Cast 
 
 Bevels. 
 
 Spurs. 
 
 
 
 
 Spurs. 
 
 P x 0.525. 
 
 PX0.5I. 
 
 
 
 
 P x 0.4. 
 
 
 
 
 
 1/4 
 
 0.075 
 
 0.100 
 
 0.088 
 
 0.131 
 
 0.128 
 
 12 
 
 0.2618 
 
 .079 
 
 .105 
 
 .092 
 
 .137 
 
 .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 
 
 
 1/2 
 
 .15 
 
 .20 
 
 .175 
 
 .263 
 
 .255 
 
 6 
 
 0.5236 
 
 .157 
 
 .209 
 
 .183 
 
 .275 
 
 .267 
 
 
 9/16 
 
 .169 
 
 .225 
 
 .197 
 
 .295 
 
 .287 
 
 
 5/8 
 
 .188 
 
 .25 
 
 .219 
 
 .328 
 
 .319 
 
 5 
 
 0.62832 
 
 .188 
 
 .251 
 
 .22 
 
 .33 
 
 .32 
 
 
 3/4 
 
 .225 
 
 .3 
 
 .263 
 
 .394 
 
 .383 
 
 4 
 
 0.7854 
 
 .236 
 
 .314 
 
 .275 
 
 .412 
 
 .401 
 
 
 7/8 
 
 .263 
 
 .35 
 
 .307 
 
 .459 
 
 .446 
 
 
 1 
 
 .3 
 
 .4 
 
 .35 
 
 .525 
 
 .51 
 
 3 
 
 1.0472 
 
 .314 
 
 .419 
 
 .364 
 
 .55 
 
 .534 
 
 
 U/8 
 
 .338 
 
 .45 
 
 .394 
 
 .591 
 
 .574 
 
 2S/4 
 
 1.1424 
 
 .343 
 
 .457 
 
 .40 
 
 .6 
 
 .583 
 
 
 H/4 
 
 .375 
 
 .5 
 
 .438 
 
 .656 
 
 .638 
 
 21/2 
 
 1.25664 
 
 .377 
 
 .503 
 
 .44 
 
 .66 
 
 .641 
 
 
 13/8 
 
 .413 
 
 .55 
 
 .481 
 
 .722 
 
 .701 
 
 
 H/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 
 
 1.05 
 
 1.02 
 
 BV2 
 
 2.0944 
 
 .628 
 
 .838 
 
 .733 
 
 1.1 
 
 1.068 
 
 
 21/4 
 
 .675 
 
 .9 
 
 .788 
 
 1.181 
 
 1.148 
 
 
 21/2 
 
 .75 
 
 1.0 
 
 .875 
 
 1.313 
 
 1.275 
 
 
 23/4 
 
 .825 
 
 1.1 
 
 .963 
 
 1.444 
 
 1.403 
 
 
 3 
 
 .9 
 
 1.2 
 
 1.05 
 
 1.575 
 
 1.53 
 
 1 
 
 3.1416 
 
 .942 
 
 1.257 
 
 1.1 
 
 1.649 
 
 1.602 
 
 
 31/4 
 
 .975 
 
 1.3 
 
 1.138 
 
 1.706 
 
 1.657 
 
 
 31/2 
 
 1.05 
 
 1.4 
 
 1.225 
 
 1.838 
 
 1.785 
 
 Thickness of rim below root = depth of tooth. 
 
 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 required. In calculating for pulleys, multiply or divide by their 
 diameter in inches. 
 
 If D = diam. of driving wheel, d = diam. of driven, R = revolutions 
 per minute of driver, r = revs, per min. of driven, RD = rd; 
 R = rd + D; r = RD + d; D = dr + R; d = DR + r. 
 
 It N = No. of teeth of driver and n = No. of teeth of driven, NR = nr; 
 N = nr + R; n = NR + r; R = rn + AT; 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 
 
1138 GEARING. 
 
 diameter of 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 pistons 4, 4, and 3 in. diameter. The 
 large wheels are the drivers, and the first makes 36 revs, per min. 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.? 
 
 36X3X4X4 , ■ 
 
 12X12X12 = lr -P- m ° Ans - 
 
 Milling Cutters for Interchangeable Gears. — The Pratt & 
 Whitney 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. 
 
 Will cut from..... 135 
 to Rack 
 
 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. 172 let PL and pi be the pitch- 
 circles of two gear-wheels; GC and gc are two equal generating-circles, 
 whose radii should be taken as not greater than one-half of the radius 
 of the smaller pitch-circle. If the circle gc be rolled to the left on the 
 larger pitch-circle PL, the point will describe an epicycloid, Oefgh. If 
 the other eenerating-eircle GC be rolled to the right on PL, the point 
 will describe a hvpocycloid Oabcd. These two curves, which are tanerent 
 at 0, form the two parts of a tooth curve for a gear whose pitch-circle is 
 PL. The uoper part Oh is called the face and the lower part Od is called 
 the flank. If the same circles be rolled on the other pitch-circle vl, they 
 will describe the curve for a tooth of the gear pi, which will work properly 
 with the tooth on PL. 
 
 The cycloidal curves may be drawn without actually rolling the gen- 
 erating-circle, as follows: Oh the line PL, from 0, step off and mark eauar 
 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 
 
 2 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 55 
 
 35 
 
 26 
 
 21 
 
 17 
 
 14 
 
 12 
 
 134 
 
 54 
 
 34 
 
 25 
 
 20 
 
 16 
 
 13 
 
FORMS OF THE TEETH. 
 
 1139 
 
 center, but beyond PL. With the radius of the generating-circle, and 
 with 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 to one of the 
 equal divisions, as 01, step off on the generating circle go the points a', V, 
 c', d', then take suceessivelv the chordal distances 0a, Ob', Oe , 0a, 
 and lay them off on the several arcs 6e, If, 8g, 9h, and la, 2b, 3c, 4d; 
 through the points efgh and abed draw the tooth curves. 
 
 Fig. 172. 
 
 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 lt 
 and that of the flank OH by the root curve R or R t . R and r represent 
 the root and addendum curves for a large number of small teeth, and R^r 
 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. (Some erear-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 
 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. 
 
1140 
 
 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 hanks 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. 173. 
 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. 173. 
 
 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 line pO, with radii successively equal to the chord 
 distances a, Ob, c, Od, Oe, 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 P0, and t 0Z/, with the same 
 radii, the tangent arcs H and K may be drawn, which will give the tooth 
 for the gear whose pitch-circle is PL. 
 
 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 tooth 
 would have been radial. 
 
 The Involute Tooth. — In drawing the involute-tooth curve, Fig. 174, 
 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 6, 
 the line of obliquity AB is drawn through O normal to a common tangent 
 
FORMS OF THE TEETH. 
 
 1141 
 
 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°. From 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 i/io 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. 174. 
 
 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. 
 
 In the involute system the customary standard form of tooth is one 
 having an angle of obliquity of 15° (Brown and Sharpe use 141/2°) an 
 addendum of about one-third the circular pitch, and a clearance of about 
 one-eighth of the addendum. In this system the smallest gear of 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 of 
 30° with each other. 
 
 To draw the teeth of a rack which is to gear with an involute wheel (Fig. 
 175). — Let AB be the pitch-line of the rack and AI = 77' = the pitch. 
 Through the pitch-point / draw EF at the given angle of obliquity. 
 
 Fig. 175. 
 
 Draw AE and I'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 l/g 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 contrarv direction. The outer half of the 
 working, face AE may be slightly curved, Mr. Grant makes it a circular 
 
1142 GEARING. 
 
 arc drawn from a center on the pitch-line with a radius = 2.1 inches 
 divided by the diametral pitch, or .67 in. X circular pitch. 
 
 To Draw an Angle of 15° without using a Protractor. — From C, on the 
 line AC, 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. 176. 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 221/2° 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 
 root of the curve is connected to the clearance by a fillet, which should 
 be as lar^e as possible to give increased strength to the tooth, provided 
 it is not large enough to cause interference. 
 
 Molesworth gives the following method of construction by circular! 
 arcs: 
 
 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 in thick lines. Circles drawn through centers thus^ 
 
FORMS OF THE TEETH. 
 
 1143 
 
 found will give the lines in which the remaining centers will be. The 
 radius DA for striking the root AB is the pitch 4- the thickness of the 
 tooth. The radius CE for striking the point of the tooth EF = the pitch. 
 
 one slightly in advance of 
 
 Fig. 177. 
 
 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. 
 
 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 ; 
 great as h\ a •: J -" n * 1 ' ~" r,T - which will incree«» U 
 strength 
 
 Twist ' 
 gears w< e | togeth< 
 
 the othe 
 tinuing 
 separate 
 
 instead ol being _ steps take form ot a spiral oi 
 
 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. 178. 
 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. 178). 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 Machy's Reference Series No. 20. 
 
 Worm- gearing. — 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 will not drive the worm. 
 
1144 
 
 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. 179 ab is the 
 diam. of the pitch-circle, 
 cd is the diam. at the 
 throat. 
 
 Example. — Pitch of 
 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 . 
 
 The Hindley Worm. — In the Hind ley 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 Hindley worm see Am. Mach., April 1, 1897 and 
 Mad*, 1., 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 ppex 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. 180, 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 ., 
 OI draw AIA', cutting the axes in B« 
 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 p IG i§0 
 
 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'l; 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 
 
FORMS OF THE TEETH. 1145 
 
 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 llankine'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 dtsciib- 
 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 
 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 to the device 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 teeih 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 
 train 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. 
 
 Differential bevel-gears have been used with advantage in mowing- 
 machines. A description of their construction and operation is given by 
 Mr. Balch in the article from which the above extracts are taken. 
 
1146 
 
 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. 
 
 Spur pinion. . . 
 Spiral pinion. 
 
 Spiral pinion or worm. , 
 
 45° 
 30 
 20 
 15 
 10 
 
 7 
 
 5 
 
 Velocity at pitch-line in feet per min. 
 
 3 
 
 0.90 
 .81 
 .75 
 .67 
 .61 
 .51 
 .43 
 ,34 
 
 10 
 
 40 
 
 100 
 
 0.935 
 
 0.97 
 
 0.98 
 
 .87 
 
 .93 
 
 .955 
 
 .815 
 
 .89 
 
 .93 
 
 .75 
 
 .845 
 
 .90 
 
 .70 
 
 .805 
 
 .87 
 
 .615 
 
 .74 
 
 .82 
 
 .53 
 
 .72 
 
 .765 
 
 .43 
 
 .60 
 
 .70 
 
 200 
 
 0.985 
 .965 
 .945 
 .92 
 .90 
 .86 
 .815 
 .765 
 
 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 
 pressure, the temperature, and the condition of the surfaces. The excess- 
 ive friction of worm and spiral gearing is largely due to the end thrust on 
 the collars of the shaft. This 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 1 
 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 j 
 greater the less the radius of the worm. Generally the radius of the j 
 worm = 1 .5 to 3 times the pitch of the thread of the worm or the circular j 
 pitch of the worm-wheel. For a one-threaded worm the efficiency is j 
 only 2/ 5 to 1/4: for a two-threaded worm, 4/7 to 2/5; for a three-threaded j 
 worm, 2/3 to 1/2. Since so much work is wasted in friction it is not sur- j 
 prising that the wear is excessive. The following table gives the calcu- I 
 lated 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, assuming a coefficient of 
 friction of .15: 
 
 No. of 
 
 Radius of Worm ■*■ Pitch. 
 
 Threads. 
 
 1 
 
 11/4 
 
 U/ 2 
 
 13/4 
 
 2 
 
 21/2 
 
 3 
 
 4 
 
 6 
 
 1 
 
 0.50 
 
 0.44 
 
 0.40 
 
 0.36 
 
 0.33 
 
 0.28 
 
 0.25 
 
 0.20 
 
 0.14 
 
 2 
 
 .67 
 
 .62 
 
 .57 
 
 .53 
 
 .50 
 
 .44 
 
 .40 
 
 .33 
 
 .25 
 
 3 
 
 .75 
 
 .70 
 
 .67 
 
 .63 
 
 .60 
 
 .55 
 
 .50 
 
 .43 
 
 .33 
 
 4 
 
 .80 
 
 .76 
 
 .73 
 
 .70 
 
 .67 
 
 .62 
 
 .57 
 
 .50 
 
 .40 
 
EFFICIENCY OF GEARING. 
 
 1147 
 
 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: 
 
 t ana' (1 -/tana;) 
 tan a + / ' 
 
 In which E = efficiency; 
 
 • (1) E = 
 
 tana (1 — /tan a) 
 
 approx., 
 
 (2) 
 
 tan a+ 2/ 
 
 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 ra dius o f the 
 two is equal. Eq. (1) gives a maximum for E wh en tan a = v'l +/ 2 — / 
 ... (3) and eq. (2) a maximum when tan a = V2 + 4/ 2 — 2/ . . . . (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 between Thread-angle Speed and Efficiency of Worm 
 Gears. 
 
 
 
 
 
 
 
 Velocity of 
 
 
 
 
 
 
 Pitch-line, 
 feet per 
 
 5 
 
 ,0 
 
 20 1 30 
 
 40 
 
 « 
 
 minute. 
 
 
 
 Efficiency. 
 
 
 
 3 
 
 35 
 
 52 
 
 66 
 
 73 
 
 76 
 
 77 
 
 5 
 
 40 
 
 56 
 
 69 
 
 76 
 
 79 
 
 80 
 
 10 
 
 47 
 
 62 
 
 74 
 
 79 
 
 82 
 
 82 
 
 20 
 
 52 
 
 67 
 
 78 
 
 83 
 
 85 
 
 86 
 
 40 
 
 60 
 
 74 
 
 83 
 
 87 
 
 88 
 
 88 
 
 100 
 
 70 
 
 82 
 
 88 
 
 91 
 
 91 
 
 91 
 
 200 
 
 76 
 
 85 
 
 91 
 
 92 
 
 92 
 
 92 
 
 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. 
 
 
 Single-thread 
 Worm 1 " Pitch, 
 21 Pitch Diam. 
 
 Double- 
 thread 
 Worm 2" 
 Pitch, 2\ 
 Pitch Diam. 
 
 Double- 
 thread 
 Worm 2\" 
 
 Pitch, 4£ 
 Pitch Diam. 
 
 Revolutions per minute 
 
 Velocity at pitch-line, feet per 
 
 128 
 
 96 
 1700 
 
 201 
 
 150 
 1300 
 
 272 
 
 205 
 1100 
 
 425 
 
 320 
 700 
 
 128 
 
 96 
 1100 
 
 201 
 
 150 
 1100 
 
 272 
 
 205 
 1100 
 
 201 
 
 235 
 1100 
 
 272 
 
 319 
 
 700 
 
 425 
 
 498 
 
 Limiting pressure, pounds 
 
 400 
 
1148 
 
 GEARING . 
 
 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: 
 
 
 
 2 
 
 1 4 
 
 1 6 
 
 1 8 
 
 1 10 
 
 1 14 
 
 1 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 
 
 93 
 
 96.3 
 
 97 
 
 97 
 
 Second speed, ratio 1 . 76 to 1 ... 
 
 800 
 
 87 
 
 92.5 
 
 94 
 
 93 
 
 94 
 
 93 
 
 
 Second speed, ratio 1 . 76 to 1 ... 
 
 1,500 
 
 79 
 
 88 
 
 92.5 
 
 94 
 
 95 
 
 93 
 
 94 
 
 First speed, ratio 3.36 to 1 
 
 800 
 
 75 
 
 87.5 
 
 93 
 
 94 
 
 94 
 
 93.5 
 
 92.5 
 
 First speed, ratio 3.36 to 1 
 
 1,500 
 
 70 
 
 84 . 
 
 89 
 
 92 
 
 93 
 
 92 
 
 
 Reverse speed, ratio 4.32 to 1.. . 
 
 800 
 
 73 
 
 84 
 
 67 
 
 87 
 
 86 
 
 82.5 
 
 Reverse speed, ratio 4.32 to I... 
 
 1,500 
 
 
 70 
 
 B 
 
 83 
 
 86 
 
 87 
 
 85 
 
 Worm-gear axle, ratio 6.83 to 1.. 
 
 400 
 
 85 
 
 8/ 
 
 86.5 
 
 83.3 
 
 84 
 
 80 
 
 Jb 
 
 Worm-gear axle, ratio 6.83 to I.. 
 
 800 
 
 83 
 
 87 
 
 88.5 
 
 89 
 
 89 
 
 88 
 
 87 
 
 Worm-gear axle, ratio 6.83 to 1 .. 
 
 1,500 
 
 80 
 
 85 
 
 87.5 
 
 88.3 
 
 89 
 
 89 
 
 89 
 
 Two bevel-wheel axles were tested, one a floating type, ratio 15 to 32, 
 14V2° 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.rn., 
 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 
 were 7/i6 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- 
 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., 1886), from an examination of the bibliography of the 
 subject, beginning in 1796, found that according to the constants and 
 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 
 formula? on the subject might be expressed in one of three forms, viz.s 
 Horse-power = CVpf, or CVp 2 , or CVp*/; 
 
 in which C is a coefficient, V = velocity of pitch-line in feet per second. 
 V = pitch in inches, and / = face of tooth in inches. 
 
STRENGTH OF GEAR-TEETH. 
 
 1149 
 
 From an examination of precedents he proposed the following formula 
 for cast-iron wheels: 
 
 0.910 Vpf 
 
 H.P. = 
 
 Vl + 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, as 
 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 t ive 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 lbs. 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 following table: 
 
 No. of 
 
 Factor for Strength, y. 
 
 No. of 
 
 Factor for Strength, y. 
 
 
 
 
 
 
 
 Teeth. 
 
 Involute 
 20° Ob- 
 liquity. 
 
 Involute 
 
 15° and 
 
 Cycloidal 
 
 Radial 
 Flanks. 
 
 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. 
 
 100 or 
 less. 
 
 200 
 
 300 
 
 600 
 
 900 
 
 1200 
 
 1800 
 
 2400 
 
 
 8000 
 20000 
 
 6000 
 15000 
 
 4800 
 12000 
 
 4000 
 10000 
 
 3000 
 7500 
 
 2400 
 6000 
 
 2000 
 5000 
 
 1700 
 
 Steel........ 
 
 4300 
 
 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. 
 
1150 GEARING. 
 
 Mr. Lewis gives the following example to illustrate the use of the tables: 
 Let it be required to find the working strength of a 12-toothed pinion of 
 1-inch pitch, 21/2-inch 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 = .078; and multiply- 
 7 ing these values together, we have \v =1560 pounds. For 
 [ the wheel we have y = .134 and J/ = 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, refer- 
 ring to Fig. 181: 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 
 ; y = factor depending upon shape of teeth and formative 
 number N; W = working load on teeth. 
 
 D 3 — d 3 d 
 
 W = spfy 3 D2 , D _ d y or, more simply, W = spfy ^ , 
 
 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 formulas 
 for the working strength of the three systems of gearing, which agree 
 very closely with those obtained by use of the table: 
 
 (0 912\ 
 0.154 ^— J; 
 
 For involute 15°, and cycloidal, W = spf (o.l24 - ~^) '• 
 
 (0 276 \ 
 0.075 '- — ■ J; 
 
 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 - 000HP - , may take the form H.P. = *ffi^ , in which 
 
 V 06, (JUL) 
 
 v = velocity in feet per minute; or since v = dn X r.p.m. -s- 12 = 
 .2618 d X r.p.m., in which d = diameter in inches, 
 
 "• - 3^0 - spfv iz;r- = - ~™ r* >< **^ 
 
 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. 
 
 Comparison of the Harkness and Lewis Formulas. — Take an 
 average case in which the safe working strength of the material, s = 6000, 
 v = 200 ft. per min.. and y = .100, the value in Mr. Lewis's table for an 
 involute tooth of 15° obliquity, or a cycloidal tooth, the number of teeth 
 in the wheel being 27. 
 
 "-^- M00 g- 100 -t- 1 ^^ 
 
 if V is taken in feet per second. 
 
 Prof. Harkness gives H.P. = °- 910 y ^/ _ . If the y in t he denominator 
 Vi + 0.65 V 
 be taken at 200 -4- 60 = 31/3 ft. per sec, H.P. = 0.571 pfV, or about 
 52% of the result given by Mr. Lewis's formula. This is probably as 
 close an agreement as can be expected, since Prof. Harkness derived his 
 formula from an investigation of andent precedents and rule-of-thumb 
 practice, largely with common cast gears, while Mr. Lewis's formula was 
 
STRENGTH OF GEAR-TEETH. 
 
 1151 
 
 derived from considerations . of modern practice with 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 expressio n to the sam e reduction by means of the denominator of 
 his formula, Vl + O-Go 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 s, for cast-iron 8000, and for steel 20,000 lbs. at speeds of 100 ft. 
 per minute and less: 
 
 v = speed of teeth, ft. per min.. 
 V = speed of teeth, ft. per sec. 
 
 Safe stress s, cast iron, Lewis . . 
 
 Relati ve do., a ± 8000 
 
 1 h- V\ +0.65 V 
 
 Relative val. c + 0.693 
 
 Sl = 8000 X (c +0.693).. 
 
 Mean of s and s lt cast-iron = S2. 
 Mean of s and s lt for steel = S3.. 
 Safe stress for steel, Lewis 
 
 8000 
 1 
 
 6930 
 
 1 
 8000 
 8000 
 20000 
 20000 
 
 31/3 
 
 6000 
 0.75 
 5621 
 
 6200 
 15500 
 15003 
 
 4800 
 0.6 
 
 4850 
 0.700 
 
 5600 
 
 5200 
 13000 
 12000 
 
 4000 
 0.5 
 
 3650 
 0.526 
 4208 
 4100 
 10300 
 10000 
 
 900 1200 
 15 20 
 
 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 
 
 2400 
 40 
 
 1700 
 0.2125 
 .1924 - 
 0.277 
 
 2216 
 
 2000 
 
 4900 
 
 4300 
 
 In Am. Mach., Jan. 30, 1902, Mr. Lewis says that 8,000 lbs. was given 
 as safe for cast-iron t.eeth, either cut or cast, and that 20,000 lbs. was 
 intended for any steel suitable for 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. = 1 -f- Vi + o.65 VX .910 Vpf= 1 .053 pf, 
 
 Lewis- HP = spfyv = spfyV = 800Q X 1 2 /3 Pfv 
 550 
 
 33,000 
 
 550 
 
 24.24 pfy, 
 
 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 = 1.260pf; 
 
 For 20° inv., 19 teeth, or 15° inv., 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 
 tooth, according to Mr. Lewis, will transmit more than double the horse- 
 power given by Prof. Harkness's formula. 
 
 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 pf, 
 X = breaking load of tooth in pounds, p = pitch, / = face. If a factor 
 of safety of 10 be taken, this would give for safe working load W =200 pf. 
 
 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, savs: "The strength and dura- 
 bility of cast-iron teeth require that they shall transmit a force of 80 lbs. 
 
1152 GEARING. 
 
 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. -h 850. 
 
 Jones & Laughlins give H.P. = pfd X r.p.m. •*- 550. 
 
 These formulae transformed give W = 128 pf 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 = .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 th e pres- 
 sure is distributed along the edge of the tooth: p = K x "^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 K x this reduces to W = 200 pf and W = 139 pf, 
 respectively. 
 
 Box, in his Treatise on Mill Gearing, gives H.P. = 12 p 2 f v'dn ■*■ 1000, 
 in which n = number of revolutions per minute. This formula differs 
 from the more modern formulae in making the H.P. vary as p 2 f, instead 
 of as pf, and in this respect itjs no doubt incorrect. 
 
 Making the H.P. vary as v ' dn or as "^v, instead of directly as v, makes 
 the velocity a factor of the working strength as in the Harkness and 
 Lewis formulae, the relative strength varying as l/^v, which for different 
 velocities is as follows : 
 
 Speed of teeth in £t. per J j 0Q 2QQ 30Q 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 formulae they may in general 
 be reduced to either of the following forms: 
 
 .P. = Cpfv, H.P. = dpfd X 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. -h 126,050; 
 w 33,000 H.P . 126,050 H.P. 00 nnA ^ - , H.P. H.P. W 
 
 W ~ v = dX r.p.m. =33 - 000 W; g/ — cT- ftdXr.p.m. -T 
 
 C, = 0.2618 C; c = 33,000 C; C = 3.82 '&, 
 
 In the Lewis formula C varies with the form of the tooth and with the 
 speed, and is equal to sy -e- 33,000, in which y and s are the values taken 
 from the table, and c = sy. 
 
 In the Harkness formula C varies with .the speed and is equal to 
 
 910 / ■ 
 
 - (F being in feet per second), = 0.01517 -*- vi + 0.011 v. 
 
 Vl + 0.65 V 
 
 In the Box for mula C vari es with the pitch and also with the velocity; 
 
 and equals 12 p ^f * r - p " m - = .02345 '-*- , c - 33,000 C = 774 *~ 
 
 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, Ci, and c are constants. Reducing 
 the several formulae to the form W = cpf, we have the following; 
 
STRENGTH OF GEAR-TEETH. 1153 
 
 Compaeison or Different Formula for Strength of Gear-teeth. 
 
 Safe working pressure per inch pitch and per inch of face, or value of 
 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 shoot 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 p/is equivalent to H.P. = p/cZ X r.p.m. -i-630 = pfv 
 h-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. tt- 850, or pfd X 
 r.p.m. -f- 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, 1889, 
 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. The 
 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. 
 per min. 
 
 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, 9 ft. 
 2 ins.; weight of hub, 15 tons; and total weight of gear, 663/ 4 tons. The 
 
1154 GEARING. 
 
 rim 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 lbs. 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 
 30°. 
 
 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., 
 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 lbs., requiring, if 
 the angle is 40° and the coefficient of friction 0.18, a pressure of 7524 lbs. 
 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 were 
 tested in peripheral contact with driving wheels of iron, aluminum and 
 type metal. All the wheels were 16 in. diam.; the face of the driving 
 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 lbs. 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 
 of 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 lbs. per sq. in. 
 
STRENGTH OF GEAR-TEETH. 
 
 1155 
 
 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 lbs.; leather fiber, 1,200 lbs.: tarred fiber, 1,200 lbs.; leather, 750 lbs.; 
 sulphite fiber, 700 lbs. 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 lbs. 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 frictional contact with iron, aluminum and type metal. 
 
 „, , ,'*■"'». . nTJ rf u WPN X 0.6/ 
 
 The formula for horse-power is H.P. = — n X — 
 
 = KdWN, in 
 = safe work- 
 
 12 33000 
 
 which d = diam. in inches, W = width of face in inches, P - „. 
 ing pressure in lbs. 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 
 
 
 0.255 
 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 
 
 0.00022 
 
 Leather fiber 
 
 Tarred fiber 
 
 Sulphite fiber 
 
 0.00035 
 0.00031 
 0.00034 
 0.00029 
 
 
 
 Horse-power = K x dWN. 
 
 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 exceedingly 
 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. 
 
 For cone clutches, Reuleaux states that the angle of the cone should 
 not be less than 10°, in 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. 
 
1156 
 
 Horse- 
 power. 
 
 Block 
 Area. 
 
 Diam. at 
 Block, Ins. 
 
 Circumferen- 
 tial Pull at 
 Block Center. 
 
 Total 
 Pressure. 
 
 Total Pres- 
 sure per 
 sq. in. 
 
 25 
 32 
 50 
 98 
 
 Ins. 
 120 
 141 
 208 
 280 
 
 16 
 18 
 
 21.5 
 27.5 
 
 Lbs. 
 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 4Vi6 ins; 
 area of do., 36V2 sq. ins.; axial pressure, 1000 to 1200 lbs.; 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 -h 63,000 sin. 6, 
 
 in which P = assumed pressure of engaging spring in lbs., / = coeff. of 
 friction, which in ordinary practice is about 0.25; r = mean radius of 
 the cone, ins.; R = v.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 theV'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 P/Q=e? ia where P = pull at fixed 
 end of coil; Q=pull at free end of coil; e= base of natural iogarithms = 
 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 = 
 (12 X 33,000) = 0.00000793 DNP. 
 
 revs., per min., then H.P. =nDNP-* 
 
HOISTING AND CONVEYING. 
 
 1157 
 
 HOISTING AND CONVEYING. 
 
 Strength of Ropes and Chains. — For the weight and strength of rope 
 for hoisting see notes and tables on pages 386 to 391. For strength of 
 chains see page 251. 
 
 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 
 
 H/8 
 4000 
 8000 
 12000 
 
 14 
 
 
 9 /l6 
 150 
 250 
 400 
 
 3/ 4 
 250 
 400 
 650 
 
 7/8 
 700 
 1200 
 1900 
 
 1 
 
 2000 
 4000 
 6000 
 
 M/4 
 7000 
 
 
 
 12000 
 
 
 19000 
 
 
 
 LOADS IN TONS. 
 
 
 Wide Mortise with 
 Loose Hooks. 
 
 Extra Heavy with 
 
 Shackles. 
 
 Size, inches 
 
 Rope, diam., in . 
 
 8 
 1 
 1/2 
 
 1 
 2 
 
 10 
 
 11/4 
 2 
 3 
 4 
 
 12 
 15/16 
 
 4 
 
 6 
 
 8 
 
 14 
 
 8 
 10 
 
 16 
 
 13/4 
 
 10 
 
 12 
 
 14 
 
 18 
 
 2 
 
 20 
 
 21/ 4 
 
 22 
 
 21/2 
 
 24 
 3 
 
 2 double blocks. . . . 
 2 triple 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 
 
 Two 
 
 Two 
 
 Two 
 
 Two 
 
 Two 
 
 Singles. 
 
 Doubles. 
 
 Triples. 
 
 Singles. 
 
 Doubles. 
 
 Triples. 
 
 8 
 
 3 
 
 4 
 
 5 
 
 4 
 
 5 
 
 6 
 
 10 
 
 4 
 
 5 
 
 6 
 
 6 
 
 8 
 
 10 
 
 12 
 
 5 
 
 6 
 
 7 
 
 8 
 
 10 
 
 12 
 
 14 
 
 6 
 
 7 
 
 8 
 
 10 
 
 12 
 
 15 
 
 16 
 
 7 
 
 8 
 
 10 
 
 12 
 
 15 
 
 20 
 
 18 
 
 8 
 
 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 
 is 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 
 
1158 
 
 HOISTING AND CONVEYING. 
 
 Chain Block Hoisting Speeds. 
 
 (Yale & Towne Mfg. Co., 1908.) 
 
 
 Pull 
 in Pounds re- 
 quired on 
 Hand-Chain 
 
 to Lift 
 Full Loads. 
 
 Feet of Hand- 
 
 Hoisting Speeds. Feet per Minute 
 Attainable and No. of Men re- 
 
 
 Chain to be 
 
 
 Pullea by 
 
 quired for Hoisting Full Loads 
 
 a 
 
 Operator to 
 
 Lift Load 
 
 One Foot 
 
 High. 
 
 without Pulling over 80 Lb. 
 
 ^03 
 
 Triplex. 
 
 Duplex. 
 
 Differ- 
 ential. 
 
 ftH 
 
 
 
 
 
 
 i i 
 
 
 
 73 
 
 
 T3 
 
 
 o 
 
 CD 
 
 X 
 
 <d_; 
 
 X 
 
 CD 
 
 X 
 
 CD 
 
 S 
 
 
 
 h3 
 
 ia^ 
 
 CD~ 
 
 o . 
 
 Hi 
 
 *s . 
 
 h-5 
 
 °fl 
 
 
 ft 
 
 a 
 
 3 
 
 <d-2 
 
 a 
 
 a 
 
 3 
 
 JC~ 
 
 3 
 
 ^ 
 
 2^ 
 
 £§ 
 
 "3 
 
 O CD 
 
 3 
 
 £S 
 
 
 H 
 
 Q 
 
 2 
 
 H 
 
 a 
 
 a 
 
 l*i 
 
 
 Of 
 
 *■ 
 
 ta 
 
 
 6~ 
 6 
 
 h— 
 
 V4 
 V2 
 
 
 
 72 
 122 
 
 
 
 18 
 24 
 
 
 
 
 
 1 
 
 62 
 
 68 
 
 21 
 
 40 
 
 8. 
 
 16. 
 
 24. 
 
 1 
 
 4. 
 
 1 
 
 2 
 
 1 
 
 82 
 
 87 
 
 216 
 
 31 
 
 59 
 
 30 
 
 4. 
 
 8. 
 
 12. 
 
 1 
 
 2. 
 
 1 
 
 3 70 
 
 3 
 
 H/2 
 
 110 
 
 94 
 
 246 
 
 35 
 
 80 
 
 36 
 
 4.8 
 
 9.6 
 
 14.4 
 
 2 
 
 2.40 
 
 2 
 
 2 50 
 
 3 
 
 2 
 
 12a 
 
 115 
 
 308 
 
 42 
 
 93 
 
 42 
 
 3.6 
 
 7.2 
 
 10.8 
 
 2 
 
 1.80 
 
 2 
 
 2 30 
 
 4 
 
 3 
 
 114 
 
 132 
 
 557 
 
 69 
 
 126 
 
 38 
 
 2 3 
 
 4,6 
 
 6 9 
 
 2 
 
 1 10 
 
 ?. 
 
 2 30 
 
 7 
 
 4 
 
 124 
 110 
 130 
 135 
 140 
 130* 
 135* 
 143* 
 
 142 
 145 
 145 
 160 
 160 
 
 
 84 
 125 
 126 
 168 
 210 
 125* 
 168* 
 210* 
 
 155 
 195 
 252 
 310 
 390 
 
 
 1.7 
 1.3 
 
 1.1 
 
 0.8 
 0.6 
 1.1 
 0.8 
 0.6 
 
 3.3 
 
 2.6 
 2.2 
 1.6 
 1.2 
 
 2.2 
 1.6 
 1.2 
 
 5.2 
 3.9 
 3.3 
 2.4 
 1.8 
 3.3 
 2.4 
 1.8 
 
 2 
 2 
 2 
 2 
 2 
 4 
 4 
 4 
 
 0.80 
 0.65 
 0.50 
 0.35 
 0.30 
 
 2 
 2 
 2 
 2 
 2 
 
 
 
 5 
 
 
 
 6 
 
 
 
 8 
 
 
 
 10 
 
 
 
 12 
 
 
 
 16 
 
 
 
 
 
 
 
 
 
 20 
 
 
 
 
 
 
 
 
 
 * On each of the two hand-chains. 
 
 t The number of men is based on each man pulling not over 80 lb. 
 One man pulling 160 lb. or less, as given in the first two columns, can lift 
 the full capacity of any Triplex or 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 513.) The relative efficiency and durability of the three types 
 are as follows: 
 
 
 Differen- 
 tial. 
 
 Duplex. 
 
 Triplex. 
 
 
 35 
 
 20 
 40 
 
 50 
 80 
 80 
 
 100 
 
 
 100 
 
 
 too 
 
 
 
 Efficiency of Hoisting 
 
 11, 1903. 
 
 Tackle. — (S. L. Wonson, Eng. News, June 
 
 1 1/4 to 2-in. Manila rope. 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 
 
 
 1.91 
 96 
 
 2.64 
 
 88 
 
 3.30 
 
 83 
 
 3.84 
 77 
 
 4.33 
 
 72 
 
 4.72 
 67 
 
 5 08 
 
 5 37 
 
 
 
 Efficiency, per cent 
 
 64 
 
 60 
 
 
 
 3/4-in. Wire rope. 
 
 Parts of line. 
 
 3 
 
 4 1 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 7.08 
 59 
 
 13 
 
 Ratio load to pull 
 
 Efficiency, per cent 
 
 2.73 
 91 
 
 3.474.11 
 87 1 82 
 
 4.70 
 78 
 
 5.20 5.68 
 
 74 1 71 
 
 6.08 
 68 
 
 6.46 
 65 
 
 6.78 
 62 
 
 7.34 
 56 
 
HOISTING AND CONVEYING. 
 
 1159 
 
 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 investiga- 
 tion. They apply to hooks of capaci- 
 ties from 250 lb. to 20,000 lb. Each 
 size of hook is made from some com- 
 mercial size of round iron. The basis in 
 each case is, therefore, 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 di- 
 mensions, 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 re- 
 sistance to spreading and to ultimate 
 rupture, which the amount of material 
 in the original bar admits of. The 
 symbol A is used to indicate the nom- 
 inal capacitv of the hook in tons of 
 2000 lb. The formulae which deter- 
 mine the lines of the other parts of the 
 hooks of the several sizes are as follows, 
 the measurements being all express'ed 
 in inches: 
 
 Fig. 182. 
 
 H = 1.08 A; L = 1.05.4; 
 ; / = 1.33 A; M = 0.50 4; 
 ; J = 1.20 A; N = 0.85 5 - 
 
 0.16; 
 
 Z) = 0.5A +1.25; G = 0.75 D ; 
 
 E = 0.64 A + 1.60 ; O = 0.363 A + 0.6 
 
 F = 0.33 A + 0.85 ; Q = 0.64 A +1.60 '; 
 
 K = 1.13-4; U = 0.866 4. 
 
 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 following: 
 Capacity of hook: 
 
 V8 V4 1/2 1 H/2 2 3 4 5 6 8 10 tons. 
 Dimension A: 
 
 5/8 "/IB 3/4 H/16 H/4 1 3/g 13/4 2 21/4 21/ 2 27/ 8 31/4 In. 
 
 Experiment has shown that hooks made according to the above formu- 
 lae 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 overlooked, and 
 which must proceed to a considerable length before rupture will occur 
 and the load be dropped. 
 
 Iron versus Steel Hooks. — F. A. Waldron, for over fifteen years con- 
 nected with the manufacturing of hooks, in the works of the Yale & Towne 
 Mfg. Co., after careful observation of hooks made of different materials and 
 in different forms, says that the only proper material from which hooks 
 can be made and be perfectly reliable is a high-grade puddled iron. 
 While a steel hook, properly made, may stand from 25 to 50% greater 
 load than a wrought-iron hook, it does not follow that the steel hook is 
 better and more reliable than the iron hook. 
 
 Iron hooks, made in accordance with the Towne formula, having serious 
 surface defects, have been tested to destruction, and none of them, in. 
 spite of these defects, have broken at less than 2 1/2 times the working load, 
 while several steel hooks broke at the working load, without a moment's 
 warning. (Trans. A. S. M. E., 1903.) 
 
 Heavy Crane Hooks. — A. E. Holcomb, vice-pres. of the Earth Moving 
 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 common 
 use. As a result certain values which gave the best results were sub- 
 stituted in "Gordon's" formula and a formula was thereby obtained which 
 was srood for hooks of any size desired, provided the proper allowable fiber 
 stress per square inch was made use of when designing. From this 
 
1160 
 
 HOISTING AND CONVEYING. 
 
 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, 
 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 
 conditions: 
 
 A hook was made of hammered steel having an elastic limit or yield 
 point at approximately 36,000 lbs. per sq. in. fiber stress and having the 
 following important dimensions: d = 75/gin.; r = 4l/2in.; D = 207/igin. 
 
 When the applied load reached 150,000 lbs. 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 
 hook held the load. Upon increasing the load still further, the hook 
 opened still more. From the dimensions of the hook as originally formed, 
 we find from the formula or table that the fiber stress with a load of 
 150,000 lbs.' was 37,900 lbs. 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 lbs., 
 or under the yield point. 
 
 The designer must use his own judgment as to the selection of a proper 
 allowable fiber stress, being governed therein by the nature of the material 
 to be used and the probability of the hook being 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 
 lbs. 
 
 5,000 to 
 15,000 
 lbs. 
 
 15,000 
 . to 
 30,000 
 lbs. 
 
 30,000 
 
 to 
 60,000 
 lbs. 
 
 60,000 
 
 to 
 100,000 
 
 lbs. 
 
 100,000 
 
 lbs. 
 and up. 
 
 
 .2,000 
 6,000 
 12,000 
 
 2,500 
 8,000 
 16,000 
 
 
 
 
 
 
 10,666 
 
 20,000 
 
 11,250 
 22,500 
 
 12,500 
 25,000 
 
 
 Hammered steel 
 
 27,500 
 
 Mr. Holcomb's formula and his table in condensed form are given 
 below: 
 
 DiKECTioNS. — 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 2 = square of the radius 
 of gyration. / = allowable fiber stress in lbs. per sq. in., 20,000 lbs. for 
 hammered steel. For other letters see Fig. 183. 
 
 P S 
 
 f 
 
 1 + 
 
 2/02/1 
 R 2 
 
 General formula. 
 
 (1) 
 
 Vx = - 
 
 d 2 (b 2 + 4 be + c 2 ) 
 ~~ 18(b 2 + 2 be + c 2 ) ' 
 b+ 2 c w d 
 
 . (2) 
 . (3) 
 
 r**l 
 
 Fig. 183. 
 
 (b + 2 c „ d\ 
 yo = KTTe- X 3) + r - 
 Assuming b = 0.66 d; 1 
 
 _i \__ we have: 
 
 P_ d* 
 
 f _ 7.44d+ 12.393 r = 
 
 di = 0.5 d. 
 
 D = 2r+ 1.5d. 
 
 . . (4) 
 = 0.22d, 
 
 K. (5) 
 
 
HOISTING AND CONVEYING. 
 Values of K. 
 
 1161 
 
 d. 
 
 r. 
 
 0.50 
 
 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 
 
 0.75 
 
 0.331 
 
 .437 
 
 .559 
 
 .697 
 
 .852 
 
 1.039 
 
 1.226 
 
 1.429 
 
 1.649 
 
 1.886 
 
 2.138 
 
 2.408 
 
 2.694 
 
 3.008 
 
 3.315 
 
 3.651 
 
 4.003 
 
 4.757 
 
 5.578 
 
 1.00 
 
 1.50 
 
 2.00 
 
 2.50 
 
 3.00 
 
 3.50 
 
 4.00 
 
 5.00 
 
 6.00 
 
 2.00 
 
 0.292 
 
 .391 
 
 .504 
 
 .632 
 
 .776 
 
 .953 
 
 1.129 
 
 1.321 
 
 1.530 
 
 1.754 
 
 1.995 
 
 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 
 
 1.148 
 
 1.336 
 
 1.544 
 
 1.760 
 
 1.996 
 
 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 
 
 1.067 
 
 1.239 
 
 1.426 
 
 1.627 
 
 1.843 
 
 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 
 
 1.129 
 
 1.321 
 
 1.490 
 
 1.691 
 
 1.913 
 
 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 
 
 
 
 
 
 2.25 
 
 
 
 
 
 2.50 
 
 
 
 
 
 2.75 
 
 
 
 
 
 3.00 
 
 0.411 
 
 .508 
 
 .617 
 
 .738 
 
 .873 
 
 1.038 
 
 1.214 
 
 1.374 
 
 1.563 
 
 1.770 
 
 1.983 
 
 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 
 
 21.846 
 
 23.535 
 
 25.388 
 
 
 
 
 3.25 
 
 
 
 
 3.50 
 
 
 
 
 3.75 
 
 
 
 
 4.00 
 
 0.805 
 
 0.943 
 
 1.124 
 
 1.275 
 
 1.453 
 
 1.647 
 
 1.849 
 
 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 
 
 21.023 
 
 22.658 
 
 24.358 
 
 
 
 4.25 
 
 
 
 4.50 
 
 
 
 4.75 
 
 
 
 5.00 
 
 
 
 5 25 
 
 
 
 5.50 
 5.75 
 6.00 
 6.50 
 7.00 
 7.50 
 
 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 
 
 '2/246 
 2.719 
 3.244 
 
 8 00 
 
 
 
 3.825 
 
 8.50 
 
 
 
 4,460 
 
 9.00 
 
 
 
 5.152 
 
 9.50 
 
 
 
 5.901 
 
 10.00 
 
 
 
 
 6.708 
 
 10 50 
 
 
 
 
 7.573 
 
 11.00 
 
 
 
 
 8.498 
 
 11.50 
 
 
 
 
 9.482 
 
 12.00 
 
 
 
 
 10.697 
 
 U2.50 
 
 
 
 
 11.802 
 
 13.00 
 
 
 
 
 12.967 
 
 13.50 
 
 
 
 
 
 14.195 
 
 14 00 
 
 
 
 
 
 15.484 
 
 14 50 
 
 
 
 
 
 16.835 
 
 15 00 
 
 
 
 
 
 18.248 
 
 15.50 
 
 
 
 
 
 19.724 
 
 16.00 
 
 
 
 
 
 21.262 
 
 
 1 
 
 
 
 
 
 For values of K and r intermediate to those given in the table 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) \ _ 
 
 (3.985-3.338)/ X (7 -° " 6>5) ~ 6 - 78 ' 
 
 Tabular values, 
 
 d = 6.50 
 d = 7.00 
 
 Vhence: d= 6.5 + 
 
 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 below. 
 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. 
 
1162 HOISTING AND CONVEYING. 
 
 Strength of Hooks and Shackles. 
 
 Hooks.* 
 
 Shackles. 
 
 Hooks.* 
 
 Shackles. 
 
 
 £ 
 
 j,- 
 
 
 
 J3 
 
 J=J - 
 
 
 
 
 
 
 
 
 
 
 
 M 
 
 M 
 
 
 
 M 
 
 M 
 
 
 
 R • 
 
 
 
 
 C . 
 
 C • 
 
 
 8 
 
 
 £"3 
 
 Description of 
 
 
 CD 02 
 
 OQ S 
 
 Description of 
 
 o 
 
 £3 
 
 <D Q 
 
 «i 3 
 
 Fracture. 
 
 
 WJ 3 
 
 0>„° 
 
 Fracture. 
 
 
 :§fc 
 
 T^ 
 
 
 
 ~Ph 
 
 rS^ 
 
 
 <D 
 
 s 
 
 § 
 
 
 a> 
 
 O 
 
 § 
 
 
 co 
 
 H 
 
 H 
 
 
 CO 
 
 H 
 
 EH 
 
 
 V-> 
 
 1,890 
 
 
 
 13/8 
 
 17310 
 
 103,750 
 
 
 9 /lB 
 
 2.560 
 
 
 
 20,940 
 
 1 19,800 
 
 Eye of shackle. 
 
 5/8 
 
 3,020 
 
 
 
 mi* 
 
 23,670 
 
 125,900 
 
 Eye of shackle. 
 
 3/ 4 
 
 4,470 
 
 20,700 
 
 Eye of shackle. 
 
 13/4 
 
 27,420 
 
 146,804 
 
 Sheared shackle 
 
 V* 
 
 6,280 
 
 38,100 
 
 Eye of shackle. 
 
 
 
 
 pin. 
 
 1 
 
 12,600 
 
 51,900 
 
 Eye of shackle. 
 
 17/8 
 
 36,120 
 
 162,700 
 
 Eye of shackle. 
 
 •1/8 
 
 13,520 
 
 62,900 
 
 Sheared shackle 
 pin. 
 
 2 
 
 38,100 
 
 196,600 
 
 Shackle at neck 
 of eye. 
 
 H/4 
 
 16,800 
 
 75,200 
 
 Eye of shackle. 
 
 2l/ 2 
 
 55.380 
 
 210,400 
 
 Eye of shackle. 
 
 * All the hooks failed by straightening the hook. 
 Horse-power Required to Raise a Load at a Given Speed. — H.P. = 
 
 Gy ° SS 33^00 t mlb X Speed in ft- Per min ' T ° thiS add 25% t0 5 ° % f ° r 
 friction,' contingencies, etc. The gross weight includes the weight of 
 cage, rope, etc. In a shaft with two cages balancing each other use the 
 net load 4- 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 lb. per sq. in.; S = stroke 
 of cylinder, inches; C = circumference of hoisting-drum, inches; L = 
 load lifted by hoisting-rope, lb.; F = friction, expressed as a diminution 
 
 of the load. Then L = A X ^ X 2S - F. 
 
 An example in Coll'y Engr., July, 1891, is a pair of hoisting-engines 
 24" X 40", drum 12 ft. diam., average steam-pressure in cylinder = 
 59.5 lb.; A = 904.8; P = 59.5; S = 40; C = 452.4. Theoretical load, 
 not allowing for friction, AXPX2S + C = 9589 lb. The actual load 
 that could just be lifted on trial was 7988 lb., making friction loss F = 
 1601 lb., 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 lb. due to inertia; W = weight of load in lb.; V = maximum 
 velocity in ft. per second; T = time in seconds taken to acquire the 
 velocity V; g = 32.16. 
 
 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 lb.: the strain when the 
 load was lifted gently was 11,525 lb.; with 3 in. of slack chain it was 
 19,025 lb.; with 6 in. slack 25,750 lb., and with 9 in. slack 27,950 lb. 
 
 Limit of Depth for Hoisting. — Taking the weight of a cast-steel 
 hoisting-rope of li/sin. diameter at 2 lb. per running foot, and its break- 
 
HOISTING AND CONVEYING. 1163 
 
 ing strength at 84,000 lb., it should, theoretically, sustain itself until 
 42,000 feet long before breaking from its own weight. But taking the 
 usual factor of safety of 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 -4- 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, Trails. 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 509 
 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 feet, and all coal came from one opening. 
 The engines were fast motion, 22 X 48 inches, conical drums 4 feet 1 inch 
 long, 7 feet diameter at small end and 9 feet at large end. (Eng'g News, 
 Nov., 1891.) 
 
 The 31ost Powerful Hoisting Engines ever built are said to be two 
 32 X 72 duplex double-drum units built in 1906 for the Boston and 
 Montana Co., at Butte, Mont. Each is designed to lift a dead load, 
 unbalanced, of 17 tons out of a 3,500-ft. vertical shaft, at the rate of 
 2,500 ft. per minute. Each hoist has two drums, 12 ft. diameter and 5 ft. 
 6 ins. face, mounted on the same shaft and driven by 12-ft. diameter flat- 
 disk reversible friction clutches. 
 
 Pneumatic Hoisting. (H. A. Wheeler, Trails. 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 the air from above the 
 piston, the lower side being open to the atmosphere. Its use was dis- 
 continued on account of the failure of the mine. Mr. Wheeler gives a 
 description of the system, but criticises 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 
 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 31ine-Hoists. — An important paper on this subject, by 
 D. B. Rushmore and K. A. Paulv, will be found in Trans. A. 1. M. E., 1910. 
 
 Counterbalancing of Winding-engines. (H. W. Hughes, Columbia 
 Coll. Qly.) — Engines running unbalanced are subject to enormous 
 variations in the load; for let W = weight of cage and empty tubs, say 
 6270 lb.: c = weight of coal, say 4480 lb.; r = weight of hoisting rope, 
 sav 6000 lb.; r' = weight of counterbalance rope hanging down pit, say 
 6000 lb. The weight to be lifted will be: 
 
 If weight of rope is unbalanced. If weight of rope is balanced. 
 At beginning of lift: -\ 
 
 W+c+r-W or 10,480 lb. W + c + r - (W + r'), 
 
 At middle of lift: f I or 
 
 W+c+^- (iF 4-^) or 4480 lb. W + c 4- | 4- ^- (w + | + ^V M480 
 
 At end of lift: " f 
 
 W + c - (IP 4- r) or minus 1520 lb. W + c + r' - (W + r), J 
 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. 
 
1164 HOISTING AND CONVEYING. 
 
 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; 
 
 C = 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 for 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, 
 
 (Wv* 
 
 A ■ 
 
 KITH^)}* 
 
 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 
 
 hi = reduced length of rope in t attached to ascending cage; 
 h 2 = increased length of rope in t attached to descending cage; 
 w = weight of rope per foot in pounds. Then 
 
 V(Wv 2 \ , < ( T vt\ hiw + h,2iv)l _ 
 
 PNSC 
 
 Applying the 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 Rove. — At the initial stage the tapering rope enables us 
 to wind from greater depths than is possible with ropes of uniform section. 
 The thickness of such a rojpat any point should only be such as to safely 
 bear the load on it at thfiJmmmi:^^ 
 
 With tapering ropes \ve Qfrfain a smaller difference between the initial 
 and final load, but the difterence is still considerable, and for perfect 
 equalization of the load we^w&ust 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 consists 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, 
 
 
CRANES. 1165 
 
 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, very 
 expensive, and the lateral displacement of the winding rope from the 
 center line of pulley becomes very great, owing to their necessary large 
 width. 
 
 (g) 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 arrange- 
 ment may be likened to an endless rope, the two cages being simply 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. 
 
 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: 
 
 Rotary 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. 
 
trolle 
 
 1166 HOISTING AND CONVEYING. 
 
 (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 rotating 
 the crane, and of hoisting and lowering the load. 
 
 Rectilinear Cranes. 
 
 (9) Bridge-cranes. — Having a fixed bridge spanning an opening, and a 
 olley 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. 515, 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 4- 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 heavv cranes geared for high speeds. 
 Cranes of over 15 tons capacity usuallv'have an auxiliary hoist of 1/5 the 
 capacity of the main hoist, and usually operated by the same 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, especiallv 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 Reouirod 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 th-; 
 power required to move the dead load. On hoist motions 331/3% is 
 allowed for friction of the moving parts, thus giving a motor of 1/3 greate- 
 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 331/3% 
 of the horse-power required to drive the crane and load plus the trac h wheel 
 
CRANES. 
 
 1167 
 
 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 tne greatest starting torque. 
 
 Walter G. Stephan says {Iron 'iraae Rev,, Jan. 7, 1909) that the bridge 
 girders should be made of two plates latticed, or box girders, their depth 
 varying from Vio 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.). 
 
 Distance Run- 
 way Rail to 
 Highest Point. 
 
 Ft. 
 6 
 6 
 7 
 
 Distance 
 
 Center of 
 
 Rail to Ends 
 
 of Crane. 
 
 In. 
 
 Wheel Base of 
 End Truck. 
 
 Ft. 
 9 
 10 
 II 
 12 
 12 
 
 Maximum 
 Load per 
 Wheel; Trol- 
 ley at End of 
 Bridge. 
 
 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 
 to 40 tons. 
 
 Standard Hoisting and Traveling Speeds of Electric Cranes. 
 
 (Pawling & Harnischfeger, 1908.) 
 
 Capacity, 
 
 Hoisting 
 
 Bridge Travel 
 
 Capacity 
 
 Speed Aux. 
 
 Tons (2000 
 
 Speed, Ft. per 
 
 Speed, Ft. per 
 
 Aux. Hoist, 
 
 Hoist, Ft. per 
 
 Lb.). 
 
 Min. 
 
 Min. 
 
 Tons. 
 
 Min. 
 
 5 
 
 10 
 
 25-100 
 20-75 
 
 300-450 
 300-450 
 
 
 
 3 
 
 30-75 
 
 25 
 
 10-40 
 
 250-350 
 
 f.J 
 
 50-125 ) 
 25-60 ( 
 
 40 
 
 9-30 
 
 250-350 
 
 \i 
 
 40-100 1 
 25-60 \ 
 
 50 
 
 8-30 
 
 200-300 
 
 u 
 
 40-100 ) 
 25-60 j 
 
 75 
 
 6-25 
 
 200-250 
 
 15 
 
 20-50 
 
 125 
 
 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. 
 
1168 
 
 HOISTING AND CONVEYING. 
 
 Notable Crane Installations. (1909.) 
 
 ^ 
 
 
 
 A 
 
 H.P.of 
 
 >> 
 
 S. 
 
 l'« 
 
 L 
 
 , 
 
 a 
 
 
 
 § 
 
 
 1 
 
 
 Hoist 
 
 jv 
 
 M 
 
 3 
 
 1.9 
 
 gifi 
 
 !§ 
 
 
 
 £ 
 
 a 
 
 "o 
 H 
 o 
 
 6 
 
 Motor. 
 
 
 "3 o 
 
 as 
 .S ft 
 
 02^ 
 as a 
 
 
 ^2 
 
 ^3 
 
 
 "S 
 
 a 
 
 
 6 oj 
 
 03 
 
 o 
 
 m 
 
 £ 
 
 O " 
 
 3 
 
 <1S 
 
 w 
 
 w 
 
 w 
 
 PQ 
 
 H 
 
 Q 
 
 ^ 
 
 a 
 
 
 Ft. In. 
 
 
 
 
 
 
 
 
 
 
 Ft.In. 
 
 
 
 150 
 
 65 
 
 1 
 
 25 
 
 75f 
 
 s 
 
 30 
 
 75 
 
 8-24 
 
 150-200 
 
 100-150 
 
 7 
 
 4 
 
 i 
 
 150 
 
 55 
 
 1 
 
 30 
 
 120 
 
 35 
 
 50 
 
 8 
 
 150-200 
 
 75-100 
 
 
 5 
 
 3 
 
 150 
 
 65 
 
 2 
 
 15 
 
 75f 
 
 30t 
 
 18f 
 
 75 
 
 10-25 
 
 150-200 
 
 100-150 
 
 7 "6" 
 
 4 
 
 1 
 
 125* 
 
 
 2 
 
 
 110 
 
 J50| 
 130J 
 
 63 
 
 100| 
 
 10 
 
 200 
 
 f 801 
 1125/ 
 100-150 
 
 5 10 
 
 6 
 
 2 
 
 1 
 
 120 
 
 56 7 
 
 2 
 
 10 
 
 50f 
 
 18 
 
 iot 
 
 52+ 
 
 10-25 
 
 150-300 
 
 5 5 
 
 7 
 
 
 100 
 
 65 
 
 2 
 
 10 
 
 sot 
 
 18 
 
 iot 
 
 50 
 
 10-25 
 
 200-250 
 
 100-150 
 
 5 5 
 
 8 
 
 J 
 
 80 
 
 74 
 
 2 
 
 10 
 
 40f 
 
 18f 
 
 iot 
 
 40 
 
 10-25 
 
 200-250 
 
 100-150 
 
 5 101/2 
 
 9 
 
 ' 
 
 50 
 
 129 III/4 
 
 1 
 
 15 
 
 50 
 
 25 
 
 71/ 2 
 
 50 
 
 10 
 
 100-150 
 
 80-100 
 
 8 6 
 
 10 
 
 3 
 
 50 
 
 125 10 
 
 1 
 
 15 
 
 50 
 
 25 
 
 71/2 
 
 50 
 
 10 
 
 100-150 
 
 80-100 
 
 8 6 
 
 11 
 
 3 
 
 50 
 
 121 2 
 
 1 
 
 5 
 
 75 
 
 15 
 
 15 
 
 75 
 
 111/2 
 
 225 
 
 125 
 
 8 4 
 
 12 
 
 2 
 
 * Four-girder ladle crane, t On each trolley. 
 
 % Divided equally between 2 motors for series-parallel control. 
 
 1. Pawling & Harnischfeger; 2. Alliance Mach. Co.; 3. Morgan En>- 
 gineering 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. djam. 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. 
 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 779, ante. ] 
 
 Electric versus Hydraulic Cranes for Docks. — A paper by V. L. j 
 Raven, in Trans. A. S. M. E., 1904, describes some tests of capacity and ; 
 
CRANES. 1169 
 
 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 lbs. of coal burned in the power station, and the second with 
 an electric crane in 51/4 hours, with 2912 lbs. 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 formulae 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, Pi = journal friction 
 of wheels or axles, P3 = inertia of trolley and load. P = sum of these 
 
 resistances = Pi + Pi+P 3 = (T+L) ( fr~yv*^ '+ rr|^) in which r = weight 
 
 of trolley, L = load, f t = coeff. of rolling frictionrabout 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 lb. 
 per sq. in.; f/ 2 is more apt to be 0.05 unless the lubrication is perfect. See 
 Friction and Lubrication, W. K.l 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. -J- 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 = F /Fh. The actual work to raise 
 the load per minute = Fhv = Lc = F v -s- 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 magnet 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 
 voltage, due to the inductive kick when the circuit is opened. The wear- 
 ing plate, which takes the shocks incident to picking up the load, is usualljr 
 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- 
 iriven locomotive cranes, and when so used are usually supplied with 
 Current from a small steam-driven generator set mounted on the crane, 
 ;team being drawn from the boiler of the crane. Nos. 5 and 6 are adapted 
 "or use with overhead electric traveling cranes in cases wheje large lifts 
 ;ind high speed of handling are essential. 
 
1170 
 
 HOISTING AND CONVEYING. 
 
 zes and Capacities of the Electric Controller & Mfg. Co. 'a 
 Type S-A Lifting Magnets. (1909). 
 
 Weight. 
 
 Lb. 
 2,100 
 3,200 
 4,800 
 6,600 
 
 Average 
 current at 
 220 volts. 
 
 Amp. 
 11 
 27 
 35 
 45 
 
 Lifts in machine cast pig 
 iron. 
 
 Maximum 
 lift. 
 
 Average 
 lift. 
 
 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. 
 
 10 
 35 
 50 
 
 Weight 
 lb. 
 
 75 
 1,650 
 5,000 
 
 Maximum* 
 
 Lifting 
 
 Capacity, 
 
 lb. 
 
 800 
 5,000 
 20,000 
 
 Average 
 
 Lifting 
 
 Capacity, 
 
 lb. 
 
 100-300 
 
 500-1,000 
 
 1,000-2,000 
 
 Current 
 
 Required 
 
 at 220 volts, 
 
 amperes. 
 
 1 
 15-18 
 30-35 
 
 Head room- 
 required , 
 ft. 
 
 ♦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 
 De considered in calculating the capacity of a given magnet under given 
 conditions The following results have been selected from a great num- 
 be? 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 sa y w .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 ^e tean^j. wghjj 
 consequent heavv decrease in the size of the load. The average lilt is 
 therefore less than the maximum lift in handling a given lot of material. 
 
 mS?^tSftom 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: 
 
 Skull P cracker balls up to 20,000; ingot (or if ground man places 
 magnet two) each, 6,000; billet slabs, 900-6,000 . A 
 
 The above weights depend on dimensions and whether in pile or 
 stacked evenly. , . . ., 1 _„ 
 
 Machine cast pig iron, 1,250; sand cast pig iron, 1,150. . 
 
 These are values obtained in unloading railway cars, including lean 
 
 1 Machine cast pfg 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 
 shan's 1250- boiler plate scrap, 1,100; farmers' scrap (harvesting 
 mafhfnery parts, plow Joints, etc..), 900; small risers from steel castings 
 1 600- fine wire scrap, scrap tubing not over 3 ft. long, loose even or 
 laminati?? Jcrap, 500; bundled scrap, 1,200; miscellaneous junk deal- 
 ers' scrap, 4.00-80>'\ 
 
TELPHERAGE. 
 
 1171 
 
 Commercial Results with a 52-inch, 5,000 pound Magnet. 
 (Electric Controller & Mfg. Co., 1908.) 
 
 * 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 unloaded from car to stock pile. 5. Boiler plate 
 scrap handled from stock pile to charging boxes. 6. Farmers' scrap, com- 
 prising knotters and butters from threshing and binding machines, sections 
 of cutter bars from mowers, broken steel teeth from hay rakes, plow points, 
 etc., 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. Pensylvania 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 1/2-inch X 10 inches X 6 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 lbs. 
 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 lbs. and gives substantially the same average lift. 
 
 TELPHERAGE. 
 
 Telpherage is a name given to a system of transporting materials in 
 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 C. M. Clark, in Trans. A. I. E. E., 
 (1902. A series of circulars of the United Telpherage Co., New York, 
 ishow 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 machin- 
 ery consists of the telpher or the conveying power, with accompanying 
 trailers; the portable electric hoist or the vertical elevating power, and 
 ihe carriers containing the load. Among the accessories are brakes, 
 Switches and controlling devices of many kinds. 
 
1172 HOISTING AND CONVEYING. 
 
 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 1.76 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, 
 with the buckets attached thereto at intervals. They are used to handle 
 the smaller sizes of coal in small quantities. They run at high speeds, 
 usually 34 to 40 revolutions of the head wheel per minute, and have a 
 capacity up to 40 tons per hour. 
 
 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, 
 
COAL-HANDLING MACHINERY. 1173 
 
 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 to 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 crots-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 higher 
 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. 
 
 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; 
 <S = speed in feet per minute; A and B constants depending on angle of 
 incline from horizontal. See example below. 
 
1174 
 
 HOISTING AND CONVEYING. 
 
 Values of A and B. 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 Angle, 
 Deg. 
 
 A 
 
 B 
 
 
 
 0.343 
 
 0.01 
 
 10 
 
 0.50 
 
 0.01 
 
 30 
 
 0.79 
 
 0.009 
 
 2 
 
 0.378 
 
 0.01 
 
 14 
 
 0.57 
 
 0.01 
 
 34 
 
 0.84 
 
 0.008 
 
 4 
 
 0.40 
 
 0.01 
 
 18 
 
 0.63 
 
 0.009 
 
 38 
 
 0.88 
 
 0.008 
 
 6 
 
 0.44 
 
 0.01 
 
 22 
 
 0.69 
 
 0.009 
 
 42 
 
 0.92 
 
 0.007 
 
 8 
 
 0.47 
 
 0.01 
 
 26 
 
 0.74 
 
 0.009 
 
 46 
 
 0.95 
 
 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 
 
 ~2T4 
 2.8 
 3.1 
 4.6 
 4.9 
 5.6 
 6.3 
 8.1 
 8.9 
 
 18 
 
 2.3 
 2.7 
 2.8 
 4.4 
 4.7 
 5.2 
 6.0 
 7.7 
 8.4 
 
 24 
 
 2.26 
 2.6 
 2.7 
 4.3 
 4.4 
 4.9 
 5.9 
 7.4 
 8.2 
 
 36 
 
 ~~2l 
 
 2.5 
 2.6 
 4.2 
 
 4.1 
 4.7 
 5.7 
 7.2 
 7.9 
 
 12 
 
 18 
 
 24 
 T6 
 
 4.9 
 
 '9.6 
 
 14.7 
 
 36 
 
 ~X5 
 2.8 
 5.5 
 
 ib'j' 
 
 "\\'.8 
 
 48 
 
 54 
 
 72 
 
 78 
 
 612 
 618 
 818 
 824 
 1018 
 1024 
 1224 
 1236 
 1424 
 
 
 88 
 
 3 
 
 5 
 
 .0 
 .7 
 
 
 2.7 
 5.3 
 
 
 85 
 
 
 
 103 
 
 4.7 
 
 4.6 
 
 108 
 
 
 11 
 
 .5 
 
 10.4 
 
 110 
 
 9.07 
 14.04 
 
 8.8 
 13.8 
 11.34 
 19.4 
 
 114 
 
 
 
 
 
 122 
 
 
 
 
 
 124 
 
 
 
 
 20.5 
 
 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 fig- 
 ures denote the pitch in inches. 
 
 Pin Chains. 
 
 Roller Chains. 
 
 No. 
 
 Pitch of Flights, 
 Inches. 
 
 
 No. 
 
 Pitch of Flights, Inches. 
 
 
 12 
 
 18 
 
 24 
 
 3 
 
 12 
 
 18 
 
 24 
 
 36 
 
 
 
 — 
 
 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 
 
 7.7 
 9.5 
 10.5 
 
 6.9 
 8.8 
 9.5 
 
 6.2 
 8.0 
 9.0 
 
 5.7 
 7.5 
 7.8 
 
 
 
 Weight of Flights with Wearing-shoes and Bolts. 
 
 Size, Inches. 
 
 ' Steel. 
 
 Malleable Iron. 
 
 Suspended Flights. 
 
 Size. 
 
 Y 
 
 height, Lb. 
 
 4x10 
 4x12 
 5x10 
 5x12 
 5x15 
 6x18 
 8x18 
 8x20 
 8x24 
 10x24 
 
 3.5 
 3.9 
 4.1 
 4.6 
 5.8 
 8.1 
 10.1 
 11.0 
 12.6 
 15.2 
 
 4.3 
 4.7 
 5.2 
 5.7 
 5.9 
 9.2 
 12.7 
 13.4 
 14.4 
 17.4 
 
 6x14 
 8x19 
 10x24 
 10x30 
 10x36 
 10x42 
 
 12.37 
 15.55 
 25.57 
 29.37 
 33.17 
 34.97 
 
COAL-HANDLING MACHINERY. 
 
 1175 
 
 Example. — Required the H.P. for a rnonobaf 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 8X19 suspended 
 flights, spaced 18 inches apart. 
 
 0.5 X 100 X 200 + 0.008 (400 X 5.7 + 267 X 15.55) X 100 . 
 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. 
 
 H.P. 
 
 = 15.15. 
 
 
 Horizontal Conveyors. 
 
 Inclined Conveyors. 
 
 Size of 
 Flight. 
 
 Flight 
 
 Every 
 
 16". 
 
 Flight 
 
 Every 
 
 18". 
 
 Flight 
 
 Every 
 24". 
 
 Pounds 
 Coal per 
 Flight. 
 
 10° 
 
 Flights 
 Every 
 
 24". 
 
 20° 
 
 Flights 
 
 Every 
 
 24". 
 
 30° 
 
 Flights 
 
 Every 
 
 24". 
 
 6x14 
 8x19 
 
 Tons. 
 69.75 
 
 Tons. 
 62 
 130 
 
 Tons. 
 46.5 
 97.5 
 
 172.5 
 
 220 
 
 268 
 
 315 
 
 31 
 65 
 115 
 147 
 179 
 210 
 
 Tons. 
 
 40.5 
 
 78 
 150 
 184 
 225 
 264 
 
 Tons. 
 
 31.5 
 
 62 
 120 
 146 
 177 
 210 
 
 Tons. 
 22.5 
 52 
 
 10x24 
 
 
 90 
 
 10x30 
 
 
 
 116 
 
 10x36 
 
 
 
 142 
 
 !0x42 
 
 
 
 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 flights 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 conveyors are run at any speed from 200 to 800 feet per minute, 
 and are made in widths varying from 12 inches to 60 inches. 
 
 Capacity of Belt Conveyors in Tons of Coal per Hour. 
 
 Width 
 of 
 
 Velocity, Feet per 
 Minute. 
 
 Width 
 
 of 
 Belt, 
 ins. 
 
 Velocity, Feet per Minute. 
 
 Belt, 
 Ins. 
 
 300 
 
 350 
 
 400 
 
 300 
 
 35G 
 
 400 
 
 450 
 
 500 
 
 12 
 14 
 16 
 
 18 
 
 34 
 
 47 
 62 
 78 
 
 72 
 91 
 
 82 
 104 
 
 20 
 24 
 30 
 36 
 
 96 
 139 
 218 
 315 
 
 112 
 162 
 254 
 368 
 
 128 
 186 
 290 
 420 
 
 210 
 326 
 
 472 
 
 520 
 
1176 
 
 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. 
 
 
 0.86 
 1.76 
 1.26 
 0.60 
 
 Earth 
 
 Sand 
 
 Stone (crushed) 
 
 1.4 
 
 
 1.8 
 
 Clay 
 
 2.0 
 
 Coke 
 
 
 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 
 Spacing, ft. 
 
 12-16 in. 
 41/2-5 
 
 18-22 in. 
 4-41/2 
 
 24-30 in. 
 31/2-4 
 
 32-36 in. 
 3-31/2 
 
 The stress in the belt should not exceed 18 to 20 lb. 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 stiff- 
 ness of the belt fixes the number of plies. The minimum number of plies 
 is as follows: 
 
 Belt width, in. 
 Minimum plies 
 
 12-14 
 3 
 
 16-20 
 4 
 
 22-28 
 5 
 
 30-36 
 6 
 
 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 
 18 
 
 In. 
 
 16-18 
 
 16-18 
 
 20-24 
 
 20-24 
 
 20-24 
 
 In. 
 
 22 
 24 
 26 
 28 
 30 
 
 In. 
 
 20-30 
 
 24-30 
 
 24-30 
 
 24-30 
 
 30-36 
 
 In. 
 32 
 34 
 36 
 
 In. 
 30-36 
 30-42 
 30-48 
 
 20 
 
 
 
 Horse-power to Drive Belt Conveyors. (C. K. Baldwin, Tra^s. 
 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. If it 
 should be necessary to increase the speed, the load should be increased 
 in proportion and the power figured accordingly. 
 
 For level conveyors 
 
 HP. = CX TX L + 1000. 
 For inclined conveyors 
 
 H.P. = (C X T X L -5- 1000) + (TX H -*■ 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, i 
 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 for- i 
 mulse above do not include gear friction, should the conveyor be gear- ! 
 driven. 
 
WIRE-ROPE HAULAGE. 
 
 1177 
 
 Constants for Formulae Above. 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 Width of 
 Belt. 
 
 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 125 Lb. 
 per Cu. Ft. 
 
 H.P. Re- 
 quired for 
 Each Mov- 
 able or 
 Fixed 
 Tripper. 
 
 Minimum 
 
 Plies of 
 
 Belt. 
 
 Maximum 
 Plies of 
 Belt. 
 
 In. 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 26 
 28 
 30 
 32 
 34 
 36 
 
 0.234 
 0.226 
 0.220 
 0.209 
 0.205 
 0.199 
 0.195 
 0.187 
 0.175 
 0.167 
 0.163 
 0.161 
 0.157 
 
 0.147 
 0.143 
 0.140 
 0.138 
 0.136 
 0.133 
 0.131 
 0.127 
 0.121 
 0.117 
 0.115 
 0.114 
 0.112 
 
 1/2 
 1/2 
 3/ 4 
 I 
 
 11/4 
 U/2 
 13/4 
 2 
 
 21/4 
 21/2 
 23/ 4 
 3 
 31/4 
 
 3 
 3 
 4 
 4 
 4 
 5 
 5 
 5 
 5 
 6 
 6 
 6 
 6 
 
 4 
 4 
 5 
 5 
 6 
 6 
 7 
 7 
 8 
 8 
 9 
 10 
 10 
 
 When horse-power and speed are known the stress in the belt in pounds 
 per inch of width is 
 
 Stress - H - P - X 33,000 
 
 Stress g^^ 
 
 From this the number of plies can be found, using 20 lb. 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. h\, 1908.) —Different materials used in the construction 
 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 
 cableways. 
 
 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 Enefine-plane. 
 
 III. The Tail-rope System. 
 
 IV. The Endless-rope Svstem. 
 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-actins: inclined plane is gravity: consequently this mode of transport- 
 ins: 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. 
 
1178 HOISTING AND CONVEYING. 
 
 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 track 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 
 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 of 
 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 lb. 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 of 
 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 13/4 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 on 
 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 
 
WIRE-ROPE HAULAGE. 
 
 1179 
 
 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 
 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 run 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.) 
 
 ^ 
 
 
 
 
 
 
 .j 
 
 
 
 fa 
 
 ■J. 
 
 A® 
 
 £_• 
 
 ■J. 
 
 A§ 
 
 fa . 
 
 ■J; 
 
 J*g 
 
 2T5 
 Si 
 
 c • 
 »-H a 
 
 u o 
 0'£ 
 
 J2 
 
 t* o 
 
 e>V3 
 
 •-a e 
 
 © c 
 ~~ o 
 
 "3 
 
 
 ftN 
 
 a 
 < 
 
 02 t-,° 
 £ 5 § 
 
 
 c 
 < 
 
 ||1 
 
 
 1 
 
 < 
 
 III 
 
 CO 
 
 Ft. 
 
 
 
 Ft. 
 
 
 
 Ft. 
 
 
 
 5 
 
 2° 52' 
 
 140 
 
 55 
 
 28° 49' 
 
 1003 
 
 no 
 
 47° 44' 
 
 1516 
 
 10 
 
 5° 43' 
 
 240 
 
 60 
 
 30° 58' 
 
 1067 
 
 120 
 
 50° 12' 
 
 1573 
 
 15 
 
 8° 32' 
 
 336 
 
 65 
 
 33° 02' 
 
 1128 
 
 130 
 
 52° 26' 
 
 1620 
 
 20 
 
 11° 10' 
 
 432 
 
 70 
 
 35° 00' 
 
 1185 
 
 140 
 
 54° 28' 
 
 1663 
 
 25 
 
 14° 03' 
 
 527 
 
 75 
 
 36° 53' 
 
 1238 
 
 150 
 
 56° 19 7 
 
 1699 
 
 30 
 
 16° 42' 
 
 613 
 
 80 
 
 38° 40' 
 
 1287 
 
 160 
 
 58° 00' 
 
 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 o 32 / 
 
 1415 
 
 190 
 
 62° 15' 
 
 1804 
 
 50 
 
 26° 34' 
 
 933 
 
 100 
 
 45° 00' 
 
 1450 
 
 200 
 
 63° 27' 
 
 1822 
 
 The above table is based on an allowance of 40 lb. 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: 
 
1180 HOISTING AND CONVEYING. 
 
 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 
 The second method is used for long distances, divided into short spans 
 and is only applicable for light loads which are to be 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 lb. 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 lb. 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 alO-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 of 
 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 lbs. 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 lbs. in some sections. 
 
 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 span AB; 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 z; all measures being in feet and pounds. 
 
WIEE-ROPE HAULAGE. 1181 
 
 h\ 
 
 Fig. 184. 
 For deflection due to rope alone, 
 
 . mnw , ws 2 . . . 
 
 ft = . at x, or -~- at center of span. 
 
 For deflection due to load alone, 
 
 h = —~ at x, or — . at center of span. 
 
 If V = V2 s, ft = —, at .r, or j- at center of span. 
 
 ^at:r,orf fi 
 ts ' 4t 
 
 If // = ?», ft = —7 — at a*, or —. at center of span. 
 
 For total deflection, 
 
 , wmns + 2 gny , ws 2 + 4 gy . , . 
 
 ft = —, — - — at x, or - — —7 — - at center of span. 
 
 T , , . , wmn + gn , ws 2 + 2 gs . . 
 
 If y = V2 s, ft = —, — - at x, or ^-7 at center of span. 
 
 _. . wmns + 2 gmn . ids 2 + 2 gs , . . 
 
 If y = m, ft = —: — - — at x, or — -, at center of span. 
 
 2 is St 
 
 If the tension is required for a given deflection, transpose t and ft in 
 above formulae. 
 
 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 
 carriage 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 
 to distinguish them from the latter, which are termed " inclined " hoist- 
 conveyors. 
 
 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 
 
1182 
 
 HOISTING AND CONVEYING. 
 
 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 t( 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 moved 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 21/2 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 dam. 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 1 , 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: 
 
 : St/ nn , W = T+ S, and R -- 
 
 from which we obtain W ■■ 
 
 efnn_ 
 
 -R, 
 
 in which e = 2.71828, the base of the Naperian system of logarithms. 
 The following are some of the values of /: 
 
 Dry. Wet. 
 Wire-rope on a grooved iron drum. ... 0. 120 0.085 
 
 Wire-rope on wood-filled sheaves 0. 235 0. 170 
 
 Wire-rope on rubber and leather filling 0.495 0.400 
 The importance of keeping the rope dry is evident from these figures. 
 e fnrr j j 
 
 The values of the coefficient — : . corresponding to the above values 
 
 e fnn_ t 
 
 off, for one up to six half-laps of the rope on the driving-drum or sheaves, 
 are as follows: 
 
 Greasy. 
 0.070 
 0.140 
 0.205 
 
 / 
 
 n - Number of Half-laps on Driving-wheel. 
 
 \ 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 0.070 
 
 9.130 
 
 4.623 
 
 3.141 
 
 2.418 
 
 1.999 
 
 1.729 
 
 0.085 
 
 7.536 
 
 3.833 
 
 2.629 
 
 2.047 
 
 1.714 
 
 1.505 
 
 0.120 
 
 5.345 
 
 2. 777 
 
 1.953 
 
 1.570 
 
 1.358 
 
 1.232 
 
 0.140 
 
 4.623 
 
 2.418 
 
 1.729 
 
 1.416 
 
 1.249 
 
 1.154 
 
 0.170 
 
 3.833 
 
 2.047 
 
 1.505 
 
 1.268 
 
 1.149 
 
 1.085 
 
 0.205 
 
 3.212 
 
 1.762 
 
 1.338 
 
 1.165 
 
 1.083 
 
 1.043 
 
 0.235 
 
 2.831 
 
 1.592 
 
 1.245 
 
 1.110 
 
 1.051 
 
 1.024 
 
 0.400 
 
 1.795 
 
 1.176 
 
 1.047 
 
 1.013 
 
 1.004 
 
 1.001 
 
 
 1.538 
 
 1.093 
 
 1.019 
 
 1.004 
 
 r .001 
 
 
 
 
TRANSMISSION OF POWER BY WIRE ROPE. 1183 
 
 r 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. 
 
 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 resist- 
 ance, is about as follows: 
 
 n= 12 3 4 5 6 
 
 Increase in tension in endless rope, 
 compared with direct stress % 40 9 21/3 2/3 1/5 1/ 10 
 
 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 syste.n. 
 
 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 lb. per sq. in. of the rope, 
 core included, and a factor of safety of 10: log G = i^-^3680 -f 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 lb. per sq. in., and then G is obtained bv 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 John 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 table 
 on page 1185. 
 
 The approximate strength of iron-wire rope composed of wires hav- 
 ing a tensile strength of 75,000 to 90,000 lbs. per sq. in. is half that of 
 cast-steel rope composed of wires of a tensile strength of 150,000 to 
 190,000 lbs. 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 lbs. 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 
 material upon which the rope tracks. 
 
 For ordinary purposes the maximum safe stress should be about one- 
 third the ultimate, and for shafts and elevators about one-fourth the ulti- 
 mate. In estimating the stress due to the load for 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 1/2 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. 
 
1184 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 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. 
 
 Approximate Breaking Strength of Steel-Wire Ropes. 
 
 6 strands of 19 
 
 wires each. 
 
 
 6 strands of 7 
 
 wires each. 
 
 a 
 
 o 
 
 ni • 
 
 
 Approximate breaking 
 
 fi? 
 
 
 Approximate breaking 
 
 Wt. 
 
 
 stress, lbs 
 
 
 O 
 
 r 
 
 s 
 
 Wt. 
 
 stress, lbs. 
 
 . a 
 
 
 
 
 
 
 
 
 
 ft., 
 
 lbs. 
 
 Cast 
 steel. 
 
 Extra 
 strong 
 steel. 
 
 Plow 
 steel. 
 
 ft., 
 
 lbs. 
 
 Cast 
 steel. 
 
 Extra 
 strong 
 steel. 
 
 Plow 
 steel. 
 
 21/4 
 
 8.00 
 
 312,000 
 
 364,000 
 
 416,000 
 
 H/9 
 
 3.55 
 
 136,000 
 
 158,000 
 
 182,000 
 
 2 
 
 6.30 
 
 248,000 
 
 288,000 
 
 330,000 
 
 1 3/8 
 
 3.00 
 
 116,000 
 
 136,000 
 
 156,000 
 
 N/ 4 
 
 4.85 
 
 192,000 
 
 224,000 
 
 256,000 
 
 U/4 
 
 2.45 
 
 96,000 
 
 112,000 
 
 128,000 
 
 l>/8 
 
 4.15 
 
 168,000 
 
 194,000 
 
 222,000 
 
 U/8 
 
 2.00 
 
 80,000 
 
 92,000 
 
 106,000 
 
 IV? 
 
 3.55 
 
 144,000 
 
 168,000 
 
 192,000 
 
 1 
 
 1.58 
 
 64,000 
 
 74,000 
 
 84,000 
 
 N/8 
 
 3.00 
 
 124,000 
 
 144,000 
 
 164,000 
 
 Vh 
 
 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 
 
 iVs 
 
 2.00 
 
 84,000 
 
 98,000 
 
 112,0 i 
 
 U/18 
 
 0.75 
 
 31,600 
 
 36,800 
 
 42,000 
 
 l 
 
 1.58 
 
 68,000 
 
 78,000 
 
 88,000 
 
 5/8 
 
 0.62 
 
 26,400 
 
 30,200 
 
 34,000 
 
 V/8 
 
 1.20 
 
 52,000 
 
 60,000 
 
 68,000 
 
 »/lfl 
 
 0.50 
 
 21,200 
 
 24,600 
 
 28,000 
 
 V4 
 
 0.89 
 
 38,800 
 
 44,000 
 
 50,000 
 
 l/o 
 
 0.39 
 
 16,800 
 
 19,400 
 
 22,000 
 
 W8 
 
 0.62 
 
 27,200 
 
 31,600 
 
 36,000 
 
 7/1 ft 
 
 0.30 
 
 13,200 
 
 15,000 
 
 17,100 
 
 »/l« 
 
 0.50 
 
 22,000 
 
 25,400 
 
 29,000 
 
 3/8 
 
 0.22 
 
 9,600 
 
 11,160 
 
 12,700 
 
 V2 
 7/6 
 3/8 
 
 39 
 
 17,600 
 13,600 
 
 20,200 
 15,600 
 
 22,800 
 17,700 
 13,100 
 
 5/16 
 9 /32 
 
 15 
 
 6,800 
 5,600 
 
 7,760 
 6,440 
 
 
 0.30 
 
 125 
 
 
 0.22 
 
 10,000 
 
 11,500 
 
 
 
 ■Vifi 
 
 0.15 
 
 6,800 
 
 8,100 
 
 
 
 
 
 
 
 V4 
 
 0.10 
 
 4,800 
 
 5,400 
 
 
 
 
 
 
 
 The sheaves (Fig. 185) are usually of cast iron, and are made as light 
 as possible consistent with the requisite strength. Various materials 
 
 + sfit'-^-o nave been used for fillm g tne bottom of the 
 
 't \ I a Section groove, such as tarred oakum, jute yarn, 
 
 J a ! a ofRim hard wood, India-rubber, and leather. The 
 
 filling which gives the best satisfaction, how- 
 ^ ever, in ordinary transmissions consists of 
 m J|a segments of leather and blocks of India- 
 jr j§^3§L of Arm 111 rubber soaked in tar and packed alternately 
 
 T i f Mm M ' W in tne g roove - Where the working tension 
 
 v is very great, however, the wood filling is 
 to be preferred, as in the case of long-dis- 
 tance 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 
 
 *- Ea 
 
 Fig. 185. 
 
 ' 2.06 (R -s- d)+ C 
 
 k = bending stress in lbs.; E = modulus of elasticity = 28,500,000: 
 =» aggregate area of wires, sq. ins.; R = radius of bend; d = diam, of 
 /ires, ins. 
 
 For 7-wire rope d=i/9 diam. of rope; C = 9.27. 
 
 " 19-wire " d = Vi5 " " " ; C = 15.45. 
 
 " the Seale cabled = 1/12 " " " ; C = 12.36. 
 From this formula the tables below have been calculated. 
 
TRANSMISSION OF POWER BY WIRE ROPE. 
 
 1185 
 
 Bending Stresses, 7-wire Rope. 
 
 Diam. bend. 
 
 24 
 
 36 
 
 48 
 
 60 
 
 72 
 
 84 
 
 96 
 
 108 
 
 120 
 
 132 
 
 Diam. Rope. 
 
 
 
 
 
 
 
 
 
 
 
 Hi 
 
 826 
 
 553 
 
 412 
 
 333 
 
 277 
 
 238 
 
 208 
 
 185 
 
 166 
 
 151 
 
 9 /32 
 
 1,120 
 
 750 
 
 563 
 
 451 
 
 376 
 
 323 
 
 282 
 
 251 
 
 226 
 
 206 
 
 5/16 
 
 1,609 
 
 1,078 
 
 810 
 
 649 
 
 541 
 
 464 
 
 406 
 
 361 
 
 325 
 
 296 
 
 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 
 
 V2 
 
 6,200 
 
 4,161 
 
 3,131 
 
 2,510 
 
 2,095 
 
 1,797 
 
 1,574 
 
 1,400 
 
 1,260 
 
 1,146 
 
 9 /l6 
 
 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 
 
 U /l6 
 
 
 10,922 
 
 8,230 
 
 6,603 
 
 5,513 
 
 4,731 
 
 4,144 
 
 3,687 
 
 3,320 
 
 3,020 
 
 3/4 
 
 
 14,202 
 
 10,706 
 
 8,591 
 
 7,174 
 
 6,158 
 
 5,394 
 
 4,799 
 
 4,322 
 
 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 
 
 14 686 
 
 12 869 
 
 11 452 
 
 10 317 
 
 9,386 
 
 'Vs 
 
 
 
 36,289 
 
 29,165 
 
 24,416 
 
 20,942 
 
 18,355 
 
 16 336 
 
 14 718 
 
 13,391 
 
 11/ 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 
 
 U/ 2 
 
 
 
 
 
 57,835 
 
 49,718 
 
 43,599 
 
 38,821 
 
 34,987 
 
 31,842 
 
 
 
 
 
 
 
 Bending Stresses, 19-wire Rope. 
 
 Diam. Bend. 
 
 12 
 
 24 
 
 36 
 
 48 
 
 60 
 
 72 
 
 84 
 
 96 
 
 108 
 
 120 
 
 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 
 
 9 /l6 
 
 
 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 
 
 U/8 
 
 11/4 
 
 
 
 28,153 
 
 21,276 
 
 17,099 
 
 14,293 
 
 12,278 
 
 10,761 
 
 9,578 
 
 8,689 
 
 
 
 38,034 
 
 28,766 
 
 23,130 
 
 19,340 
 
 16,618 
 
 14,567 
 
 12,967 
 
 11,(83 
 
 J 3/8 
 
 
 
 51,609 
 
 39,067 
 
 31,430 
 
 26,290 
 
 22,594 
 
 19,811 
 
 17,637 
 
 15,893 
 
 M/2 
 15/8 
 13/4 
 17/8 
 2 
 
 
 
 66,065 
 
 50,049 
 
 40,284 
 
 33,707 
 
 28,976 
 
 25,410 
 
 22,625 
 
 20,390 
 
 
 
 
 62,895 
 
 50,647 
 
 42,391 
 
 36,450 
 
 31,969 
 
 28,470 
 
 25,661 
 
 
 
 
 79,749 
 
 64,252 
 
 53,798 
 
 46,270 
 
 40,590 
 
 36,152 
 
 32,589 
 
 
 
 
 97,018 
 
 78,202 
 
 65,500 
 
 56,347 
 
 49,438 
 
 44,039 
 
 39,701 
 
 
 
 
 
 94,016 
 
 78,769 
 
 67,778 
 
 59,478 
 
 52,989 
 
 47,777 
 
 21/4 
 
 
 
 
 
 134,319 
 
 112,611 
 
 96,943 
 
 85,103 
 
 75,F40 
 
 68,396 
 
 2V2 
 
 
 
 
 
 
 154,870 
 
 133,386 
 
 117,137 
 
 104,417 
 
 94,189 
 
 
 
 
 
 
 
 
 Horse-Power Transmitted. — The general formula for the amount 
 of power capable of being transmitted is as follows: 
 
 H.P. = [cd 2 - 0.000006 (w+ g t + g 2 )]v; 
 
 in which d = diameter of the rope in inches, v = velocity of the rope in 
 feet per second, w = weight of the rope, <7i = weight of the terminal 
 sheaves and shafts, gi = weight of the intermediate sheaves and shafts 
 (all in lbs.), 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: 
 
1186 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 
 Number of laps about sheaves or drums. 
 
 c = for steel rope on 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 5.61 
 6.70 
 9.29 
 
 8.81 
 9.93 
 11.95 
 
 10.62 
 11.51 
 
 12.70 
 
 11.65 
 12.26 
 12.91 
 
 12.16 
 12.66 
 12.97 
 
 12 56 
 
 Wood 
 
 12 83 
 
 Rubber and leather.. 
 
 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 series 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, 
 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 
 Maximum Safe Working Tension. 
 
 Diameter 
 
 
 Steel. 
 
 
 
 Iron. 
 
 
 of Rope, 
 
 
 
 
 
 
 
 In. 
 
 7-Wire. 
 
 12-Wire. 
 
 I9-Wlre. 
 
 7-Wire. 
 
 12-Wire. 
 
 19-Wire. 
 
 -V4 
 
 20 
 
 15 
 
 12 
 
 40 
 
 30 
 
 24 
 
 ¥*6 
 
 25 
 
 19 
 
 15 
 
 50 
 
 38 
 
 30 
 
 3/8 
 
 30 
 
 22 
 
 18 
 
 60 
 
 45 
 
 36 
 
 7 /l6 
 
 35 
 
 26 
 
 21 
 
 70 
 
 53 
 
 42 
 
 V2 
 
 40 
 
 30 
 
 24 
 
 80 
 
 60 
 
 48 
 
 »/l6 
 
 45 
 
 33 
 
 27 
 
 90 
 
 68 
 
 54 
 
 5/8 
 
 50 
 
 37 
 
 30 
 
 100 
 
 75 
 
 60 
 
 U/16 
 
 55 
 
 41 
 
 32 
 
 110 
 
 83 
 
 66 
 
 3/ 4 
 
 60 
 
 44 
 
 35 
 
 120 
 
 90 
 
 72 
 
 7/8 
 
 70 
 
 52 
 
 41 
 
 140 
 
 105 
 
 84 
 
 t 
 
 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 on the next page. 
 
 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." 
 
TRANSMISSION OF POWER BY WIRE ROPE. 1187 
 Horse-power Transmitted by a Steel Rope on Wood-filled Sheaves. 
 
 
 
 
 Veloci 
 
 ty of Rope in Feet 
 
 per Second 
 
 
 
 of Rope, 
 
 
 
 
 
 
 
 
 
 
 
 In. 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 Vi 
 
 4 
 
 8 
 
 13 
 
 17 
 
 21 
 
 25 
 
 28 
 
 32 
 
 37 
 
 40 
 
 5 /l6 
 
 7 
 
 13 
 
 20 
 
 26 
 
 33 
 
 40 
 
 44 
 
 51 
 
 57 
 
 62 
 
 3/8 
 
 10 
 
 19 
 
 28 
 
 38 
 
 47 
 
 56 
 
 64 
 
 73 
 
 80 
 
 89 
 
 7/16 
 
 13 
 
 26 
 
 38 
 
 51 
 
 63 
 
 75 
 
 88 
 
 99 
 
 109 
 
 121 
 
 V 3 
 
 17 
 
 34 
 
 51 
 
 67 
 
 83 
 
 99 
 
 115 
 
 130 
 
 144 
 
 159 
 
 9 /l6 
 
 22 
 
 43 
 
 65 
 
 86 
 
 106 
 
 128 
 
 147 
 
 167 
 
 184 
 
 203 
 
 5 /8 
 
 27 
 
 53 
 
 79 
 
 104 
 
 130 
 
 155 
 
 179 
 
 203 
 
 225 
 
 247 
 
 %6 
 
 32 
 38 
 52 
 68 
 
 63 
 76 
 104 
 ,35 
 
 95 
 103 
 156 
 202 
 
 126 
 150 
 206 
 
 157 
 186 
 
 186 
 223 
 
 217 
 
 245 
 
 
 
 3/4 
 
 
 
 7 /8 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 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 of the span, and the deflec- 
 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 2 h = .00008 S 2 
 driving " M " ...hi =. 000025 S* h t = .00005 S 2 
 
 slack " " "...//•> = .0000875 ,S 2 h% = .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 oe greater in proportion to the increased surface. 
 
1188 TRANSMISSION OF POWER BY WIRE ROPE. 
 
 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. 1186), 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 
 hold good in this case, so that for very 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 on the next page, 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 actual tension 
 in pounds, gives the radius of curvature assumed by the rope in cases 
 where 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 " 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 
 
ROPE-DRIVING. 
 
 1189 
 
 cases will be governed by the table headed " Diameters of Minimum 
 Sheaves Corresponding to a Maximum Safe Working Tension " on page 
 1186. 
 
 Radius of Curvature of Wire Ropes in Inches for 1-lb. Tension. 
 
 Formula: R= Ed^n -s- 5.25 t cos 1/2 <?; in which R = radius of curvature; 
 E = modulus of elasticity = 28,500,000; <J = diameter of wires; n = no. 
 of wires; = angle of bend; t = working stress (lbs. and ins.). 
 Divide by stress in pounds to obtain radius in inches. 
 
 Diam. 
 
 
 
 
 
 
 
 
 of 
 
 160° 
 
 165° 
 
 170° 
 
 172° 
 
 174° 
 
 176° 
 
 178° 
 
 Wire. 
 
 
 
 
 
 
 
 
 a; f 1/2 
 
 4,226 
 
 5,623 
 
 8,421 
 
 10,949 
 
 14,593 
 
 21,884 
 
 43,762 
 
 & 5 /8 
 
 11,090 
 
 14,753 
 
 22,095 
 
 26,731 
 
 35,628 
 
 53,429 
 
 106,841 
 
 «| 3 /4 
 
 22,274 
 
 29,633 
 
 45,412 
 
 54,417 
 
 72,530 
 
 108,767 
 
 217,500 
 
 ©1 7/ 8 
 
 43,184 
 
 57,451 
 
 86,040 
 
 102,688 
 
 136,869 
 
 205,251 
 
 410,440 
 
 £ ' 
 
 71,816 
 
 95,541 
 
 143,085 
 
 175,182 
 
 233,492 
 
 350,150 
 
 700,193 
 
 £ 1 Vs 
 
 112,763 
 
 150,016 
 
 224,667 
 
 280,607 
 
 374 010 
 
 560,872 
 
 1,121,574 
 
 0U11/4 
 
 169,135 
 
 225,012 
 
 336,982 
 
 427,689 
 
 570,050 
 
 854,858 
 
 1,709,459 
 
 of V2 
 
 12,914 
 
 17,179 
 
 25,727 
 
 31,125 
 
 41,485 
 
 62,212 
 
 124,405 
 
 ft 5 /8 
 
 29,762 
 
 39,594 
 
 59,297 
 
 75,988 
 
 101,282 
 
 151,884 
 
 303,723 
 
 7 /8 
 
 62,313 
 
 82,899 
 
 124,151 
 
 157,570 
 
 210,018 
 
 314,948 
 
 629,800 
 
 116,239 
 
 154,641 
 
 231,593 
 
 291,917 
 
 389,085 
 
 583,479 
 
 1 164,099 
 
 .a I' 
 
 199,323 
 
 265,173 
 
 397,129 
 
 497,998 
 
 663,767 
 
 995,390 
 
 1 ,990,478 
 
 £ 1 1/8 
 
 320,556 
 
 426,459 
 
 638,674 
 
 797,697 
 
 1,063,217 
 
 1,594,422 
 
 3,188,359' 
 
 £ln/ 4 
 
 504,402 
 
 671,041 
 
 1,004,965 
 
 1,215,817 
 
 1,620,513 
 
 2,430,151 
 
 4,859,561 
 
 ROPE-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 lbs. 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 inches; H = horse-power; 
 
 F = centrifugal force in pounds; L = distancebetweenpulleys.it.; 
 
 P = pounds per foot of rope; w = working strain in pounds; 
 
 R = force in pounds doing useful work; 
 S = strain in pounds on the rope 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 lbs. 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 
 
1190 
 
 ROPE-DRIVING. 
 
 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 -e- 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, 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 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 38 
 36 
 34 
 32 
 30 
 28 
 26 
 24 
 
 40 
 38 
 36 
 34 
 32 
 30 
 28 
 H 26 
 | 24 
 
 cS 28 
 
 o20 
 
 2 18 
 
 ffiW 
 
 H 
 
 ROPE DRIVING 
 
 Horse Power of manila 
 rope at various speeds 
 
 
 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 tf 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d$> 
 
 
 
 
 
 
 
 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 „ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 l*p 
 
 o 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 20 
 18 
 16 
 14 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^~ 
 
 
 
 
 
 
 
 ^s 
 
 
 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 f/ 
 
 
 | 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 \ 
 
 
 
 12 
 10 
 8 
 
 z 
 
 
 
 
 ■$, 
 
 -' 
 
 
 ■V 
 
 w 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 12 
 
 10 
 
 8 
 6 
 4 
 2 
 
 
 
 Q 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 \ 
 
 1 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 \ 
 
 \ 
 
 
 
 // 
 
 / 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 £ 
 
 / 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 vo 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .. 100 110 120 1.30 140. 
 Velocity of Driving Rope in feet per second 
 Fig. 186. 
 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 1/3 (T — F). 
 
 Hence t = (T - F)/Z + F (1) 
 
 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. 
 
ROPE-DRIVING. 
 
 1191 
 
 With these assumptions of allowable strains the horse-power will be 
 
 H= 2v (r-F)-i-(3X 550) 
 
 (2) 
 
 Transmission ropes are usually from 1 to 2 inches in diameter. A 
 computation of the horse-power for four sizes at various speeds and 
 under ordinary conditions, based on a maximum strain equivalent to 
 200 lbs. for a rope one inch in diameter, is given in Fig. 186. 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 
 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 = ~-=- + 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. 
 
 Horse-power of Transmission Rope at Various Speeds. 
 
 Computed from formula (2) given above. 
 
 
 Speed of the Rope in feet per minute. 
 
 
 
 
 
 
 
 
 
 
 
 
 l«d 
 
 & 
 
 1500 
 
 2000 
 
 2500 
 
 3000 
 
 3500 
 
 4000 
 
 4500 
 
 5000 
 
 6000 
 
 7000 
 
 8000 
 
 
 l/o 
 
 1.45 
 
 1.9 
 
 2.3 
 
 2,7 
 
 3 
 
 3.2 
 
 3.4 
 
 3.4 
 
 3.1 
 
 2.2 
 
 
 
 20 
 
 5/8 
 
 2.3 
 
 3.2 
 
 3.6 
 
 4.2 
 
 4.6 
 
 5.0 
 
 5.3 
 
 5.3 
 
 4.9 
 
 3.4 
 
 
 
 24 
 
 3/J 
 
 3.3 
 
 4.3 
 
 5 2 
 
 5.8 
 
 6.7 
 
 7 2 
 
 7,7 
 
 7 7 
 
 7.1 
 
 4.9 
 
 
 
 30 
 
 7/S 
 
 4.5 
 
 5.9 
 
 7.0 
 
 8.2 
 
 9.1 
 
 9 8 
 
 10.8 
 
 10,8 
 
 9.3 
 
 6.9 
 
 
 
 36 
 
 1 ™ 
 
 5.8 
 
 7.7 
 
 9.2 
 
 10.7 
 
 11.9 
 
 12,8 
 
 13.6 
 
 13.7 
 
 12.5 
 
 8.8 
 
 
 
 42 
 
 niA 
 
 9.2 
 
 12.1 
 
 14.3 
 
 16.8 
 
 18.6 
 
 20,0 
 
 21.2 
 
 21.4 
 
 19.5 
 
 13.8 
 
 
 
 54 
 
 i# 
 
 13.1 
 
 17.4 
 
 20.7 
 
 23.1 
 
 26.8 
 
 28.8 
 
 30.6 
 
 30.8 
 
 28.2 
 
 19.8 
 
 
 
 60 
 
 13/ 4 
 
 18 
 
 23.7 
 
 28.2 
 
 32.8 
 
 36.4 
 
 39 2 
 
 41,5 
 
 41 8 
 
 37.4 
 
 27,6 
 
 
 
 72 
 
 2 
 
 23.2 
 
 30.8 
 
 36.8 
 
 42.8 
 
 47.6 
 
 51.2 
 
 54.4 
 
 54.8 
 
 50 
 
 35.2 
 
 
 
 84 
 
 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. 
 
1192 
 
 ROPE-DRIVING. 
 
 Sag op the Rope Between Pulleys. 
 
 Distance 
 between 
 
 Driving Side. 
 
 
 Slack Side of Rope. 
 
 Pulleys 
 in feet. 
 
 All Speeds. 
 
 80 ft. per sec. 
 
 60 ft. per sec. 
 
 40 ft. per sec. 
 
 40 
 60 
 80 
 100 
 120 
 140 
 160 
 
 feet 4 inches 
 
 " 10 
 
 , .... 5 .. 
 
 2 " " 
 
 2 " 11 " 
 
 3 " 10 " 
 5 " 1 
 
 feet 7 inches 
 
 1 " 5 " 
 
 2 " 4 " 
 
 3 " 8 " 
 5 " 3 " 
 7 " 2 " 
 9 " 3 " 
 
 feet 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 applies 
 also to the idle and tension pulleys as well as to the main driving-pulley. 
 
 The angle of the sides of the grooves in which the rope runs varies, 
 with different engineers, from 45° to 60°. 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. 
 
 Tension on the Slack Part of the Rope. 
 
 Speed of 
 Rope, in feet 
 
 Diameter of the Rope and Pounds Tension on the Slack Rope. 
 
 
 
 
 
 
 
 
 per second. 
 
 V2 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 U/4 
 
 M/2 
 
 l3/ 4 
 
 2 
 
 20 
 
 10 
 
 27 
 
 40 
 
 54 
 
 71 
 
 110 
 
 162 
 
 216 
 
 283 
 
 30 
 
 14 
 
 29 
 
 42 
 
 56 
 
 74 
 
 115 
 
 170 
 
 226 
 
 296 
 
 40 
 
 15 
 
 31 
 
 45 
 
 60 
 
 79 
 
 123 
 
 181 
 
 240 
 
 315 
 
 50 
 
 16 
 
 33 
 
 49 
 
 65 
 
 85 
 
 132 
 
 195 
 
 259 
 
 339 
 
 60 
 
 18 
 
 36 53 
 
 71 
 
 93 
 
 145 
 
 214 
 
 285 
 
 373 
 
 70 
 
 19 
 
 39 59 
 
 78 
 
 101 
 
 158 
 
 236 
 
 310 
 
 406 
 
 80 
 
 21 
 
 43 64 
 
 85 
 
 111 
 
 173 
 
 255 
 
 340 
 
 445 
 
 90 
 
 24 
 
 48 70 
 
 93 
 
 122 
 
 190 
 
 279 
 
 372 
 
 487 
 
 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 
 
 Smallest Diameter 
 
 Length of Rope to 
 
 Approximate 
 
 Rope, 
 
 of Pulleys, in 
 
 allow for Splicing, 
 
 Weight, in lbs. per 
 
 in inches. 
 
 inches. 
 
 in feet. 
 
 foot of rope. 
 
 V2 
 
 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 
 
 11/4 
 
 54 
 
 10 
 
 0.60 
 
 U/2 
 
 60 
 
 12 
 
 0.83 
 
 13/4 
 
 72 
 
 13 
 
 1 .10 
 
 2 
 
 84 
 
 14 
 
 1.40 
 
ROPE-DRIVING. 
 
 1193 
 
 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 of 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. 
 
 Data of Manila Transmission Rope. 
 
 From the " Blue Book " of The American Mfg. Co., New York. 
 
 
 
 
 
 
 Length of 
 
 
 
 
 
 
 
 
 Splice, ft. 
 
 
 ft 
 
 ill 
 
 9— 
 
 ft 
 o 
 
 "3 
 
 a 
 
 Q 
 
 S <B 
 
 IS 
 
 g* 
 
 .9 M 
 
 a 
 
 H 
 
 |l 
 
 9& 
 
 a 
 
 a 
 
 
 is 
 
 a 
 5 
 
 3 
 
 & 
 
 in 
 
 < 
 
 
 
 m 
 
 ffi 
 
 02 
 
 1*™ 
 
 0-8 
 
 02 
 
 ■RP5."9 
 
 3/ 4 
 
 0.5625 
 
 0.20 
 
 3,950 
 
 112 
 
 6 
 
 8 
 
 
 28 
 
 760 
 
 7/8 
 
 0.7656 
 
 0.26 
 
 5,400 
 
 153 
 
 6 
 
 8 
 
 
 32 
 
 650 
 
 1 
 
 1. 
 
 0.34 
 
 7,000 
 
 200 
 
 7 
 
 10 
 
 Ya 
 
 36 
 
 570 
 
 H/8 
 
 1.2656 
 
 0.43 
 
 8,900 
 
 253 
 
 7 
 
 10 
 
 16 
 
 40 
 
 510 
 
 M/4 
 
 1 . 5625 
 
 0.53 
 
 10,900 
 
 312 
 
 7 
 
 10 
 
 16 
 
 46 
 
 460 
 
 13/8 
 
 1.8906 
 
 0.65 
 
 13,200 
 
 378 
 
 8 
 
 12 
 
 15 
 
 50 
 
 415 
 
 1V2 
 
 2.25 
 
 0.77 
 
 15.700 
 
 450 
 
 8 
 
 12 
 
 18 
 
 54 
 
 380 
 
 15/8 
 
 2. 6406 
 
 0.90 
 
 18,500 
 
 528 
 
 8 
 
 12 
 
 18 
 
 60 
 
 344 
 
 13/ 4 
 
 3.0625 
 
 1.04 
 
 21,400 
 
 612 
 
 8 
 
 12 
 
 18 
 
 64 
 
 330 
 
 2 
 
 4. 
 
 1.36 
 
 28,000 
 
 800 
 
 9 
 
 14 
 
 20 
 
 72 
 
 290 
 
 21/4 
 
 5.0625 
 
 1.73 
 
 35,400 
 
 1,012 
 
 9 
 
 14 
 
 20 
 
 82 
 
 255 
 
 21/2 
 
 6.25 
 
 2.13 
 
 43,700 
 
 1,250 
 
 10 
 
 16 
 
 22 
 
 90 
 
 230 
 
 Weight of transmission rope = 0.34 X diam. 2 
 
 Breaking strength = 7,000 X diam. 2 
 
 Maximum allowable tension = 200 X diam. 2 
 Diam. smallest practicable 
 
 sheave, = 36 X diam. 
 
 Velocity of rope (assumed) = 5,400 ft. per min. 
 
 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 formlu33 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 occu~ 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. 
 
1194 FRICTION AND LUBRICATION. 
 
 Mr. Miller refers to a 250-H.P. drive which has been running ten years, 
 the large pulley being grooved 60° and the smaller 45°. This drive was 
 designed to use a li/4-in. manila rope, but the grooves were made deep 
 enough so that a 7/ 8 -in. rope would not bottom. In order to determine the 
 value of the drive a common 7/g-in. rope was put in at first, and lasted six 
 years, working under a factor of safety of only 14. 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 13/ 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 of cords on the 
 smaller machine appliances; the fiber, being softer and more flexible 
 than manila hemp, 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 fope 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. Inst. 
 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 
 enhanced power-transmitting value, its immunity from frequent atten- 
 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. 
 
 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 d, and the coefficient by /. / = tan 0. 
 
 Friction of Rest 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: 
 
FRICTION AND LUBRlCATiON. 
 
 1195 
 
 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. 
 
 
 Values of /. 
 
 
 
 
 
 per square 
 
 Wrought iron on 
 
 Wrought on 
 
 Steel on 
 
 Brass on 
 
 inch. 
 
 Wrought Iron. 
 
 Cast Iron. 
 
 Cast Iron. 
 
 Cast IrOn. 
 
 187 
 
 0.25 
 
 0.28 
 
 0.30 
 
 0.23 
 
 224 
 
 .27 
 
 .29 
 
 .33 
 
 .22 
 
 336 
 
 .31 
 
 .33 
 
 .35 
 
 .21 
 
 448 
 
 .38 
 
 .37 
 
 .35 
 
 .21 
 
 560 
 
 .41 
 
 .37 
 
 .36 
 
 .23 
 
 672 
 
 Abraded 
 
 .38 
 
 .40 
 
 .23 
 
 784 
 
 
 Abraded 
 
 Abraded 
 
 .23 
 
 Law of TJnlnbricated 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 + , 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 .080 .051 .047 .040 
 
 Adhesion, lbs. per gioss 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.) 
 
 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 + r. f 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 0.02. 
 
 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 
 
1196 
 
 FRICTION AND LUBRICATION. 
 
 Thurston gives the value of / for ordinary railroads, 0.003; well-laid 
 railroad track, 0.002; best possible railroad track, 0.001. 
 
 The few experiments that have been made upon the coefficients of 
 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 1 
 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 to that of solid fric- 
 tion as the journal is run dry, and to 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.) 
 
 /=ta: 
 
 Dry masonry and brickwork. . . 
 Masonry and brickwork with 
 
 damp mortar 
 
 Timber on stone 
 
 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 on earth, damp clay 
 
 Earth on earth, wet clay 
 
 Earth on earth, shingle and 
 
 gravel 
 
 31° to 35° 
 
 361/2° 
 
 22° 
 
 35° to I62/3 
 
 26 1/ 2 ° to 11 1/ 3 ° 
 
 31° to III/3 
 
 14° to 81/ 2 ° 
 
 27° 
 
 181/4° 
 
 14° to 45° 
 
 21° to 37° 
 45° 
 17° 
 
 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 
 
 1.67 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 
 
 Coefficients of Friction of Journals. (Morin.) 
 
 Material. 
 
 Unguent. 
 
 Lubrication. 
 
 Intermittent 
 
 Continuous. 
 
 Cast iron on cast iron j 
 
 Cast iron on bronze j 
 
 Cast iron on lignum vitse . . . 
 Wrought iron on cast iron . ) 
 Wrought iron on bronze. . J 
 Iron on lignum vitse j 
 
 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 
 
 0.07 to 0.08 
 0.11 
 0.19 
 0.10 
 0.09 
 
 
 Prof. Thurston says con 
 results are probably obtains 
 Those here given are so grea 
 and temperature, that they c 
 
 ^erning the above 
 d in good practice 
 tly modified by va 
 annot be taken as c 
 
 figures that 
 with ordinar 
 riations of sp< 
 orrect for gent 
 
 much better 
 y machinery, 
 ed, pressure, 
 ,ral purposes. 
 
FRICTION AND LUBRICATION. 
 
 1197 
 
 Friction of Motion. — The following is a table of the angle of repose 
 0, the coefficient of friction / = tan 0, and its reciprocal, 1 -J- /, for the 
 materials of mechanism — condensed from the tables of General Morin 
 (1831) and other sources, as given by Rankine: 
 
 No. 
 
 Surfaces. 
 
 Wood on wood, dry 
 
 " " " soa] 
 
 Metals on oak, dry 
 
 " " wet 
 
 " " soapy 
 
 " elm, dry 
 
 Hemp on oak, dry 
 
 " " " wet 
 
 Leather on oak 
 
 " metals, dry 
 
 metals, wet 
 
 greasy . . 
 
 oily 
 
 Metals on metals, dry 
 
 " " " wet 
 
 Smooth surfaces, occasion- 
 ally greased 
 
 Smooth surfaces, continu- 
 ously greased 
 
 Smooth surfaces, best results 
 Bronze on lignum vitse, con- 
 stantly wet 
 
 14° to 261/2° 
 1 1 1/ 2 ° to 2° 
 261/2° to 31° 
 131/2° to 14° 
 
 1 1 1/2° 
 
 111/2° to 14° 
 
 28° 
 
 181/2° 
 
 15° to 191/2° 
 
 291/ 2 ° 
 
 20° 
 
 13° 
 
 81/2° 
 81/ 2 ° to 11° 
 
 161/2° 
 
 4° to 4 1/ 2 ° 
 
 1 3/ 4 ° to 2° 
 3°? 
 
 0.25 to 0.5 
 0.2 to 0.04 
 0.5 to 0.6 
 0.24 to 0.26 
 
 0.2 
 0.2 to 0.25 
 
 0.53 
 
 0.33 
 0.27 to 0.38 
 
 0.56 
 
 0.36 
 
 0.23 
 
 n 15 
 0.15 to 0.2 
 
 0.05 
 0.03 to 0.036 
 
 >-/• 
 
 4 to 2 
 
 5 to 25 
 2 to 1.67 
 
 4.17 to 3.85 
 
 5 
 
 5 to 4 
 
 1.89 
 
 3 
 
 3.7 to 2.86 
 
 1.79 
 
 2.78 
 
 4.35 
 
 6.67 
 
 6.67 to 5 
 
 3.33 
 
 14.3 to 12.5 
 
 20 
 
 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. 
 
 Oils. 
 
 8 
 
 16 
 
 32 
 
 48 
 
 Sperm, lard, neat's-f t., etc. . 
 Olive, cotton-seed, rape, etc. 
 
 .159 to .250 
 .160 to .283 
 .248 to .278 
 .154 to .261 
 
 .138 to .192 
 .107 to .245 
 .124 to .167 
 .145 to .233 
 
 .086 to .141 
 .101 to .168 
 .097 to .102 
 .086 to .178 
 
 .077 to .144 
 .079 to .131 
 .081 to 122 
 
 Mineral lubri eating-oils 
 
 .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 lbs. per square inch pressure was 
 0.0034; with 200 lbs., 0.0051; with 300 lbs., 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, lbs. per sq. in. 1 2 3 4 5 
 
 Coefficient 0.38 0.27 0.22 0.18 0.17 
 
 These high coefficients, however, and the great decrease in the coefficient 
 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 viscosity 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. In$t. M. E. 
 Nov., 1883) show that the absolute friction, that is, the absolute tan- 
 
1198 FRICTION AND LUBRICATION. 
 
 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- 
 crease in direct proportion to the load, as it should do according to the 
 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 lbs. per sq. in., and with mineral oil 625 lbs. 
 
 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 lbs. 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 lbs. 
 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 lbs. per sq. in. 
 
 With an oil-pad under the journal feeding rape-oil, the bearing fairly 
 carried 551 lbs. 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 1/1500 
 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- 
 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 speed of 
 rubbing of 150 feet per minute, with lard and with sperm oil, gave the 
 following: 
 
 Press, per sq. in., lbs. 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 0.0137 0.0085 0.0053 0066 0.125 
 
 The coefficients at starting were: 
 
 With sperm 0.07 0.135 0.14 0.15 0.185 0.18 
 
 Withlard 0.07 0.11 0.U 0.10 0.12 0-12 
 
FRICTION AND LUBRICATION. 
 
 1199 
 
 The Coefficient at a speed of 150 feet per minute decreases with increase 
 Of pressure until 500 lbs. per sq. in. is reached; above this it increases. 
 The coefficient at rest or at starting increases with the pressure through- 
 out the range of the tests. 
 
 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. 
 
 
 Nominal Load, in lbs. per sq. in. 
 
 Lubricant in Bath. 
 
 625 
 
 520 
 
 415 
 
 310 
 
 205 
 
 153 
 
 100 
 
 
 Coefficient of Friction. 
 
 
 
 .0009 
 .0017 
 .0014 
 .0022 
 seiz'd 
 
 .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 
 .0077 
 
 .0105 
 .0078 
 
 .0027 
 .0052 
 .0038 
 .0083 
 .0019 
 .0037 
 
 .002 
 .004 
 
 .0042 
 
 " "471 " " 
 
 
 .009 
 
 Mineral crease: 157 ft. per min.. . . 
 471 " " .... 
 
 .001 
 .002 
 
 .0076 
 .0151 
 
 .003 
 
 " "* 47i "" " ' :;::::; 
 
 
 0064 
 
 
 (5731b. 
 .001 
 
 .001 
 .0015 
 .0012 
 .0018 
 
 004 
 
 " " 471 " " 
 
 .007 
 
 Mineral-oil: 157 ft. per min 
 
 "471 " " 
 
 ,0013 
 
 .004 
 .007 
 
 Rape-oil fed by 
 
 
 0125 
 
 siphon lubricator: j ^. V<^ .. 
 Rape-oil, pad 
 
 
 
 
 0068 
 
 .0152 
 
 
 
 
 0099 
 
 .0099 
 
 under journal: j^ 7.^ «« 
 
 
 
 
 0099 
 
 .0133 
 
 
 
 
 
 
 
 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 wear, 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 
 
1200 FRICTION AND LUBRICATION. 
 
 cast-iron slide-valve will wear longer of itself and cause less wear to 
 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., 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 
 for all pressures. 
 
 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, 1S88, 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 winch 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 lbs. per ton instead of the 3 to 6 lbs. 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 relationsbetween 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 I 
 ' 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 j 
 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-j 
 
FRICTION AND LUBRICATION. 1201 
 
 dance of lubricant, such 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 
 tram 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. 
 
 In American Machinist, Oct. 23, 1890, Prof. Denton 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 is 
 from i/e 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 
 
 0.00139 
 0.0098 
 0.0090 
 
 1.00 
 
 
 7.06 
 
 
 6.48 
 
 
 
 With a load of 293 lbs. per sq. in. and a journal speed of 314 ft. per 
 nin. Mr. Tower found the coefficient of friction to be .0016 with an oil- 
 Dath, 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 
 i'ound that the frictional resistance per square inch under varying loads 
 
 nearly constant, as below: 
 
1202 
 
 FRICTION AND LUBRICATION. 
 
 Load in lbs. per sq. in. 529 468 415 363 310 258 205 153 100 
 F sq U in nal IeS1St ' Per } 0-416 0.514 0.498 0.472 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 frictional resistance then varies directly as the load, as shown 
 by Mr. Tower in Table VIII of his report (Proc. Inst. M. E., 1883). 
 
 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 
 faction was then very great, and nearly constant under varying condi- 
 tions of the lubrication, load, and temperature. But as the speed in- 
 creased 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 minute, the friction was reduced 70%; 
 in another case the friction was reduced 67% when the velocity was 
 increased from 1 to 100 ft. per minute; 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 
 
 0.001C 
 .0013 
 .0014 
 
 0.0012 
 .0014 
 .0015 
 
 0.0013 
 .0015 
 .0017 
 
 0.0014 
 .0017 
 .0019 
 
 0.0015 
 .0018 
 .0021 
 
 0.0017 
 .002 
 .0024 
 
 520 lbs. 
 468 lbs. 
 415 lbs. 
 
 The variation of 
 inverse ratio, Law 4. 
 per minute: 
 
 friction with temperature is approximately in the 
 Take, for example, Mr. Tower's results, at 262 ft. 
 
 Temp. F. 
 
 110° 
 
 100° 
 
 90° 
 
 80° 
 
 70° 60° 
 
 
 0.0044 
 0.00451 
 
 0.0051 
 
 006 
 
 0.0073 
 00733 
 
 0.0092 
 00964 
 
 0.0119 
 
 0.01252 
 
 
 0.005181 00608 
 
 
 
 
 
 
 
 
 
 
 
 
 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 tem- 
 perature 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° 
 
 125° 
 
 130° 
 
 135° 
 
 140° 
 
 145° 
 
 
 
 
 0.022 
 
 0.0180 
 0.0040 
 
 0.0160 
 0.0020 
 
 0.0140 
 0.0020 
 
 0.0125 
 0.0015 
 
 0.01150 0110 
 
 0.0106 
 0.0004 
 
 0.0102 
 
 Decrease of coeff . . 
 
 0.0010 
 
 0.0005 
 
 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; 
 
FRICTION AND LUBRICATION. 1203 
 
 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. Inst. M. E., 
 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 holding 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 lbs. per sq. in. of bearing- 
 surface was as much as it would bear safely at the highest speed without 
 seizing, although it carried 90 lbs. 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 lbs. per sq. in., diminishing to 
 1/30 at 75 lbs. 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, 
 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 lbs. 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 lbs. per sq. in. was reached with impunity; 
 and if the 600 lbs. 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 lbs. 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 
 lbs. per sq. in., but the speed of rubbing in tins 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. 
 
 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, giving 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 the 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 lbs. per sq. in. 
 
 Prof. Thurston (Friction end Lost Work, p. 240) says 7000 to 9000 lbs. 
 pressure per square inch is reached on the slow-working and rarely 
 moved pivots of swing bridges. 
 
 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- 
 
1204 FRICTION AND LUBRICATION. 
 
 stant load on an ordinary journal it is difficult and almost impossible 
 to have more than 200 lbs. 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 IDs. 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. 
 
 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 lbs. 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 lbs. 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 lbs. 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, lbs. 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 lbs. per sq. in. without any signs of 
 heating or seizing. 
 
 Friction of Car- journal Brasses. (J. E. Denton, Trans. A. S. M. E., 
 xii, 405.) — A new brass dressed with an emery-wheel, loaded with 5000 
 lbs., may have an actual bearing-surface on the journal, as shown by the 
 polish of a portion of the surface, of only 1 square inch. With this pressure 
 of 5000 lbs. 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 
 
FRICTION AND LUBRICATION. 1205 
 
 on the viscosity of the oil. With a pressure of 1000 lbs. per sq. in., revo- 
 lutions from 170 to 320 per min., and temperatures of 75° to 113° F., witli 
 botn sperm and paraffine oils, a coefficient of as low as 0.11% has been 
 obtained, the oil being fed continuously by a pad. 
 
 Experiments on Overheating of Bearings. — Hot Boxes. (Denton.) 
 — Tests witn car brasses loaded from 1100 to 4500 lbs. per sq. in. gave 
 7 cases of overlieating out of 32 trials. The tests show how purefy a 
 matter of chance is tne overheating, as a brass which ran hot at 5000 lbs. 
 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 tne 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 
 friction. 
 
 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: 
 
 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 by Fric- 
 inch-lbs. tioninft.-lbs. 
 
 per min. 
 
 Flat surfaces fWS 
 
 Shafts and journals 1/2 fWd 0.2618 fWdn 
 
 Flat pivots 2/3/TFr 0.349 fWrn 
 
 Collar-bearing 2 /3/TT r2 ?~ ri ? 0.349 fWn r ''~ ri ' 
 
 r 2 z-ri 2 r 2 2 -r 1 2 
 
 Conical pivot 2 /3fWr cosec a 0.349 fWrn cosec a 
 
 Conical journal 2 /sfWr sec a 0.349 fWrn sec a 
 
 Truncated-cone pivot 2/3 fw T2 ~ Tl 0.349 fW r2 ~ n 
 
 r 2 sin a r 2 sin a 
 
 Hemispherical pivot fWr 0.5236 fWrn 
 
 Tractrix, 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; 
 r 2 = 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. 
 
i206 FRICTION AND LUBRICATION, 
 
 To obtain the horse-power, divide the quantities in the last column 
 by 33,000. Horse-power absorbed by friction of a shaft = <£.— "- 
 
 126,050 
 
 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, 
 
 tT 2firr TT7 . , j 0.2618 fWdn . . lfc 
 
 U = . Wn inch-pounds = — — . foot-lbs. 
 
 V1+/2 V1+/2 
 
 For perfectly fitted journals U = 2.54 fnrWn 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 = fir 2 rWn inch-lbs. = 0A112fWdn ft.-lbs. 
 
 Resistance of railway trains and wagons due to friction of trains: 
 
 Pull on draw-bar — /X 2240 4= 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 8 with the vertical radius the normal pressure is 
 proportional to cos 8. If p = normal pressure on a unit of surface, 
 w = total ioad on a unit of length of the journal, and r = radius of journal, 
 w cos 8 = 1.57 rp, p = w Cos 8 -4 s 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 
 
 Load per sq. in.* 
 
 83 83 83 83 83 
 
 Speed, r.p.m. 
 
 309 506 180 179 301 
 Speed, ft. per min.* 
 1215 1990 708 704 1180 
 Friction H.P.f 
 
 12.6 21.7 6.43 5.12 10.1 16 17.9 41.9 47.8 52.3 
 
 Cceff. 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 3V2 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 bv from 0.002 in. for a 1/2-m. 
 journal to 0.009 for 6 in., for 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. Fof 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 paper 
 read before the Manchester Assoc, of Engrs. (Am. Mach., Jan. 16, 1908, 
 
 33.6 
 
 42.3 
 
 47 
 
 47 
 
 50.5 
 
 112 
 
 141 
 
 157 
 
 157 
 
 168 
 
 454 
 
 480 
 
 946 
 
 1243 
 
 1286 
 
 1785 
 
 1890 
 
 3720 
 
 4900 
 
 5050 
 
FRICTION AND LUBRICATION. 1207 
 
 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 lbs. at 100 r.p.m. and 189 lbs. at 500 r.p.m., and 
 for a 5-in. journal 189 lbs. at 100 and 283 lbs. 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 D^^/N 1 ^ 
 " horizontal " ..p= 660 dVw/N 1 /* 
 " single-acting four-cycle gas en- : , 
 
 gines p = 1350 #Vi3/jvV4 
 
 For crank pins of. vert, and hor. double-acting engines, p = 1560 dV^/N 1 /* 
 " " " " single-acting four-cycle gas engines, p = 3000 D^^/N 1 /* 
 
 For dead loads with ordinary lubrication p = 400 iV -1 /.5 
 
 " forced " p = 1600 jV _1 /4 
 
 p = allowable pressure in lbs. per sq. in. of projected area; D = diam. 
 in ins.; N = revs. per. min. 
 
 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 lbs. 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. 
 
 Archbutt and Deeley's "Lubrication and Lubricants" gives the follow- 
 ing table of allowable pressures in lbs. per sq. in. of projected area of 
 different bearings: 
 
 Crank-pin of shearing and punching machine, hard steel, inter- 
 mittent load bearing 3000 
 
 Bronze crosshead neck journals 1200 
 
 Crank pins, large slow engine 800-900 
 
 Crank pins, marine engines 400-500 
 
 Main crankshaft bearing, fast marine 400" 
 
 Same, slow marine 600 
 
 Railway coach journals 3Q0-400 
 
 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. (Oberlin 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 lbs. per sq. in. of projected area. Upon the eccentric the pressure 
 against the pitman driving the ram is. some 7000 lbs. 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 
 
1208 FRICTION AND LUBRICATION. 
 
 toggle-pins, running in cast iron or bronze bearings, 3 in. in diam. by nearly 
 14 in. long. These run habitually, for maximum work, under a load of 
 20,000 lbs. 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 the largest 
 portion or driving whorl being perhaps not 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 
 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. 
 
 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 2 *™ 3 x 6080° = ^li^ X 217 " 1 ' in 
 
 which S = speed of ship in knots per hour, P = total thrust in lbs. 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, lbs,.. . 112,700 89,000 33,600 154,000 
 
 Pressure per sq. in. of surface, lbs 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. M. E., 
 1905.) — Bearing areas for locomotive journals are determined chiefly 
 by the possibilities of lubrication. On driving journals the -following 
 figures of pressure in lbs. per sq. in. of projected area give good service: 
 passenger, 190; freight, 200; switching, 220 lbs. Crank pins may be 
 loaded from 1500 to 1700 lbs.; wrist pins to 4000 lbs. per sq. in. Car and 
 tender bearings are usually loaded from 300 to 325 lbs. 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. in. of projected area for all shafts is 140 lbs. 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 
 
 !:; 
 
PIVOT-BEARINGS. 1209 
 
 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-BEARING S . 
 
 The Schiele Curve. — W. H. Harrison (Am. Mach., 1891) says t"ie 
 Schiele curve is not as good a form for a bearing as the segment of % 
 sphere. He says: A mill-stone weighing a ton frequently bears its whc 3 
 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 lbs. 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 
 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 frictionl 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 lbs., 
 and on another occasion with 300 lbs. per sq. in. The white-metal bear- 
 ing under similar conditions heated and seized with a load of 240 lbs. 
 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-hath Pivot. — A nearlv 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'a, July 14, 1893. p. 41: 
 
 The optical apparatus, weighing; about 1 ton. rests on a circular cast- 
 iron table, which is supported bv 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 supDort, 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 riridly 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 lbs.), while the horizontal clearance at the bottom is 0.4 in. 
 
1210 
 
 FRICTION AND LUBRICATION. 
 
 BALL-BEARINGS, ROLLER-BEARINGS, 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. d\am., the 
 friction in starting from rest was 1/4 the friction of an ordinary 31/2-in. 
 bearing, but at a car speed of 10 miles per hour it was 1/2 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 Roller 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 
 
 Hyatt Bearing. 
 
 McKeel Bearing. 
 
 Babbitt Bearing. 
 
 of 
 Journal. 
 
 Max. 
 
 Min. 
 
 Ave. 
 
 Max. 
 
 Min. 
 
 Ave. 
 
 Max. 
 
 Min. 
 
 Ave. 
 
 1 15/16 
 23/16 
 
 .032 
 .019 
 .042 
 .029 
 
 .012 
 .011 
 .025 
 .022 
 
 .018 
 .014 
 .032 
 .025 
 
 .033 
 
 .017 
 
 .022 
 
 .074 
 .088 
 .114 
 .125 
 
 .029 
 .078 
 .083 
 .089 
 
 .043 
 082 
 
 27/ie 
 215/16 ' 
 
 .028 
 .039 
 
 .015 
 .019 
 
 .02J 
 .027 
 
 .096 
 .107 
 
 The friction of the roller bearing is from one-fifth to one-third that of a 
 
 J)lain bearing at moderate loads and speeds. It is noticeable that as the 
 oad 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 
 bore on a cast-iron sleeve and in the Hyatt on a soft-steel one. If roller 
 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 lbs. The rolls 
 are enclosed in a bronze supporting cage. (Trans. A. S. M. E., 1905.) 
 
 D 
 
 d 
 
 N 
 
 P 
 
 D 
 
 d 
 
 N 
 
 P 
 
 D 
 
 d 
 
 N 
 
 P 
 
 2 
 21/2 
 
 4 
 5 
 
 1/4 
 
 5/16 
 3/8 
 
 7/16 
 9 /l6 
 
 20 
 
 22 
 22 
 24 
 24 
 
 3,500 
 
 7,000 
 13,000 
 24,000 
 37,000 
 
 6 
 7 
 8 
 9 
 12 
 
 H/16 
 
 13/16 
 7/8 
 1 
 11/4 
 
 24 
 
 22 
 22 
 24 
 26 
 
 50,000 
 70, COO 
 90,000 
 115,000 
 175,000 
 
 15 
 18 
 20 
 
 24 
 
 13/8 
 13/8 
 
 11/2 
 11/2 
 
 28 
 32 
 34 
 38 
 
 255,000 
 325,000 
 400,000 
 576,000 
 
 
 
 
 
 
BALL-BEARINGS, ROLLER-BEARINGS,' ETC. 1211 
 
 Surface speed of journal to 50 ft. per min. Length of journal 11/2 
 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 
 3 1/16-3 1/4 
 4 l/i 6 -4 1/4 
 5 1/16-5 1/4 
 6 1/16-6 1/2 
 8I/16-8V2 
 9 1/16-9 1/2 
 
 59/16 
 
 8 
 
 105/i 6 
 123/ 8 
 147/s 
 183/ 4 
 201/2 
 
 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 
 
 9,500 
 
 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." 
 
 Size of 
 
 Bearing. 
 
 ins. 
 
 Number and 
 Size of Rollers, 
 ins. 
 
 R.p.m. 
 
 Weight 
 
 on 
 Bear- 
 ings, lbs. 
 
 Lineal 
 inches. 
 
 Weight 
 per lin. 
 in., lbs. 
 
 Weight 
 on each 
 
 roll, 
 
 lbs. 
 
 43/4X 6H/i 6 
 
 43/4 X 71/4 
 51/2X 8 1/2 
 
 7 X 103/8 
 71/2X1 15/ 16 
 
 8 x 151/2 
 
 36 5/ 8 x5/ 16 
 32 3/ 4 x5/8 
 54 3/4X5/8 
 48 1 xl/2 
 54 1 x 1/2 
 70 H/4X5/8 
 
 500 
 470 
 420 
 370 
 325 
 300 
 
 6,000 
 10,000 
 15,000 
 20,000 
 25,000 
 60,000 
 
 111/4 
 
 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., 
 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 
 of the Hvatt bearing in comparison with other bearings: 
 
 A shaft 152 ft. long, 2i5/i6 in. diam. supported by 20 bearings, belt- 
 driven from one end, gave a friction load of 2.28 H.P. with babbitted 
 bearings, and 0.80 H.P. with Hyatt bearings. With 88 countershafts 
 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. 
 
1212 FRICTION AND LUBRICATION. 
 
 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 
 flat 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 
 3/4 in. diam., 10 ins. long. The Hyatt rollers were made of 1/2 X 1/8 in. 
 steel strip. With 2000 lbs. load and plain rollers it took 26 lbs. to move 
 the plate, and with the Hyatt rollers 9 lbs. With 3000 lbs. load and 
 plain rollers the resistance was 34 lbs., with Hyatt rollers 17 lbs. 
 
 In tests 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 0S)362 down to 0.0196, the loads increasing from 
 64 to 264 lbs.; 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 IV2 ins. and loads 
 from 1900 to 8300 lbs., 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 lbs., and at 410 
 r.p.m. with 5900 lbs. The bronze bearing seized at 130 r.p.m. with 3500 lbs., 
 at 320 r.p.m. with 5100 lbs., and at 582 r.p.m. with 2700 lbs. 
 
 The makers have found that the advantages of roller bearings of the 
 type described are especially great with either high speeds or heavy loads. 
 Generally, the best results are obtained for line-shaft work up to speeds of 
 600 rev. per min., when a load of 30 lbs. 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 lbs. 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 
 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 excentrically 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. 
 
BALL-BEARINGS, ROLLEIt-BEARINGS, ETC. 1213 
 
 It may be written as: 
 
 L = Knd 2 , in which L = load capacity in pounds; n = number of 
 bails; 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 sh-H 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/i6 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 for 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. 
 
 1 1 . Thrust B earing s : 
 
 With the thrust type, consisting of one flat plate and one seat plate 
 with grooved ball races, the load capacity decreases with speed or 
 
 L _ K 1 nd? 
 
 </R ' 
 
 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. 
 
 K x = 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 0.0001 
 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. 
 
 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 dif- 
 ferent 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, of ball circle (the circle passing through 
 
1214 
 
 FRICTION AND LUBRICATION. 
 
 the centers of the balls) ; d = diam. of balls; n= number of balls; s = aver- 
 age clearance space between the balls. Then D = (d + s) -s- sin (180°/n); 
 d = D sin (1807ft) - s; s = D sin (180°/ft) - d: n = 180° -*■ angle whose 
 sine is (d + s) -s- D. The clearance s should be about 0.003 in. 
 
 
 
 Values of 
 
 1807ft 
 
 AND OF SIN 1807ft. 
 
 
 
 
 
 8 
 
 
 
 8 
 
 
 
 ,8 
 
 
 
 £ 
 
 n. 
 
 .8 
 
 o 
 2 
 
 n. 
 
 4 
 
 1 
 
 n. 
 
 8* 
 
 1 
 
 n. 
 
 8* 
 
 I 
 
 
 1 
 
 _c 
 
 
 1 
 
 a 
 
 
 1 
 
 ,a 
 
 
 1 
 
 # c 
 
 
 "~ 
 
 CO 
 
 
 "" 
 
 <a 
 
 
 "" 
 
 CQ 
 
 
 """ 
 
 Hi 
 
 3 
 
 60 
 
 0.86603 
 
 15 
 
 12 
 
 0.20791 
 
 27 
 
 6.667 
 
 0.11609 
 
 39 
 
 4.615 
 
 0.08047 
 
 4 
 
 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 
 
 .1Q453 
 
 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. Eveland, Trans. A. S. M. E., 
 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 {Tram. 
 A. S. M. E., 1909) describes a series of tests made by Dodge and Day on a 
 2!5/i6 in. line shaft 72 ft. long, alternately equipped with plain ring-oiling 
 babbitted boxes and with Hess-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 lbs. 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- 
 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 "<7," 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 
 
FRICTION OF STEAM-ENGINES. 1215 
 
 pivot beyond the solid support is practically worthless. A high-grade uni- 
 form 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 machinery and most 
 testing machinery 5000 lbs. per inch of length is ample. Loads of 10,000 
 lbs. 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 lbs. per inch of length. For 
 greater loads the sharp edge is rubbed with an oilstone, so that a smooth- 
 ness 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 STEA3I-ENGINES. 
 Distribution of the Friction of Engines. — Prof. Thurston, in his 
 " Friction and Lost Work," gives the following: 
 
 Main bearings 
 
 Piston and rod 
 
 Crank-pin 
 
 Cross-head and wrist-pin 
 
 Valve and rod 
 
 Eccentric strap 
 
 Link and eccentric 
 
 1. s 
 
 2. 
 
 3. 
 
 47.0 
 
 35.4 
 
 35.0 
 
 32.9 
 
 25.0 
 
 21.0 
 
 6.8 
 5.4 
 
 5.1) 
 4.1} 
 
 13.0 
 
 2.5 
 
 26.4) 
 
 22.0 
 
 5.3 
 
 4.0) 
 
 
 
 9.0 
 
 100.0 
 
 100.0 
 
 100.0 
 
 Total 
 
 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 
 lbs., and then becomes constant. The friction generally increases with 
 increase of speed, but there arc exceptions to this rule. 
 
 Prof. Denton (Stevens Indicator, July, 1890), comparing the calculated 
 friction of a number of engines with the friction as determined by measure- 
 ment, finds that in one case, a 75-ton ammonia ice-machine, the friction of 
 the compressor, 17 1/2 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- Per cent 
 
 power, of whole. 
 
 Crank-pins and effect of piston-thrust on main shaft .71 11 .4 
 
 Weight of fly-wheel and main shaft 1 .95 32 .4 
 
 Steam-valves .23 3.7 
 
 Eccentric 0.07 1.2 
 
 Pistons 0.43 7.2 
 
 Stuffing-boxes, six altogether .72 11.3 
 
 Air-pump. . 2 .10 32 .8 
 
 Total friction of engine with load 6 .21 100 .0 
 
 Total friction per cent of indicated power. 4.27 
 
1216 FRICTION AND LUBRICATION. 
 
 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 pump-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 
 wheei 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 1196, but if the pressure is great enough 
 to force out the lubricant, then the coefficient becomes much greater 
 and the surface or surfaces will cut and wear, with a rapid rise of tempera- 
 ture. 
 
 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 1115. 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 
 E. R. Douglas, Am. Mach., Dec. 26, 1901, and R. B. Brown, Mach'y, 
 April, 1909. For friction brake dynamometers see Dynamometers. 
 
 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 blocks of various forms. The work done by a 
 clutch while the surfaces are in sliding contact, and before thev 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 that 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, 
 
FRICTION OF HYDRAULIC PLUNGER PACKING. 
 
 1217 
 
 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 lbs., and wooden surfaces should 
 not be loaded beyond 20 to 25 lbs. 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 direction 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 of 
 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., Oct. 8, 1908.) — 
 In the practice of the Browning Engineering Co., Cleveland, O., in 
 regard to the design of band brakes the equations are: 
 
 T= PX, t= T -P,S = p^ F , *= S X D X 0.262 X revolutions per 
 
 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 
 
 N 
 from the accompanying table, X = „__ in which log. N = 10 2-7288 /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, 
 # = 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 lbs. acting on a diameter of 20 ins. 
 
 Then 
 
 P= 3000 X 20-^30 = 2000 pounds, X = 1.68 (from table), T = 2000 X 
 1.68 = 3360 pounds, t = 3360 - 2000 = 1360 pounds, S = 2X3360-^ 
 (30 X4) = 56 (within the limit), & = 56 X30 X0.62 X100 = 44,000 (within 
 the limit). 
 
 
 Values of X. 
 
 
 Values of X. 
 
 Degrees. 
 
 
 
 Degrees. 
 
 
 
 
 
 
 
 
 7=0.2. 
 
 /=0.3. 
 
 7=0.4. 
 
 
 f=0.2. 
 
 /=0.3. 
 
 /=0.4. 
 
 180 
 
 2.14 
 
 1.64 
 
 1.40 
 
 260 
 
 1.68 
 
 1.35 
 
 1.19 
 
 195 
 
 2.03 
 
 1.56 
 
 1.35 
 
 270 
 
 1.64 
 
 1.32 
 
 1.18 
 
 210 
 
 1.93 
 
 1.50 
 
 1.30 
 
 280 
 
 1.60 
 
 1.30 
 
 1.17 
 
 240 
 
 1.76 
 
 1.40 
 
 1.23 
 
 290 
 
 1.57 
 
 1.28 
 
 1.15 
 
 250 
 
 1.72 
 
 1.37 
 
 1.21 
 
 300 
 
 1.54 
 
 1.26 
 
 1.14 
 
 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 
 
1218 FRICTION AND LUBRICATION. 
 
 ju, which is constant for 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., i£ = 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., i£ = as 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 V47rd 2 p, the ratio of the loss of 
 pressure to the total pressure is Kpd^- x UTzd?p, or, using the extreme values 
 of K, 0.0312 and 0.299, the ratio ranges from 0.04 n-d to 0.38 + d, or from 
 4 to 38 per cent divided by the diameter in inches. 
 
 Walter Ferris {Am. Mach., Feb. 3, 1898) derives from the formula 
 given above the following formula for the pressure produced by a hemp- 
 packed hydraulic intensifier made with two plungers of different diameters: 
 A-KD 
 
 in which P2 = pressure per sq. in. produced by the intensifier, pi= initial 
 pressure, A=area and £> = diam. of the larger plunger, a==area and rf = 
 diam. 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 17 3 /4 ins., either one of which could 
 be used as desired. 
 
 Diam. of large plunger, in. 14V4 14V4 173/4 173/4 
 
 Initial pressure, lbs. per sq. in. 285 475 335 350 
 
 Intensified pressure, lbs. 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. — (X 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 
 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 
 
 ♦Assuming K = 0.2. The efficiency calculated by the formula in each 
 case was 0.953. 
 
LUBRICATION. 1219 
 
 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. 
 
 Relative Value of Lubricants. (J. E. Denton, Am. Mack., 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 all materials liable to produce oxidation or "gum- 
 ming." 
 
 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 safetv 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. 
 
 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 made 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. 
 
1220 
 
 FRICTION AND LUBRICATION. 
 
 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. R. R. 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 0° 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. 
 
 Paraffine 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 V? 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. 
 
 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 
 J material can be seen. 
 
 500° Fire-test Oil. — This grade of oil will not be accepted if sample 
 flashes below 494° F.; (2) shows precipitation with 
 
 from shipment (1) 
 
 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. R. Specifications for Lubricating Oils (1894). (In 
 force in 1902.) 
 
 Constituent Oils. 
 
 Parts by volume. 
 
 
 
 
 
 1 
 
 
 
 
 1 
 
 
 
 
 1 
 I 
 4 
 
 i i 
 
 1 2 
 
 2 1 
 
 1 
 1 
 
 I 
 
 1 
 
 1 
 
 2 
 
 
 500° fire-test oil 
 
 
 1 
 
 4 
 
 
 
 
 Well oil . . . 
 
 1 
 
 
 4 
 
 2 
 
 1 
 
 
 
 
 
 
 
 Used for 
 
 A 
 
 B 
 
 Ci 1 c 2 1 c 3 
 
 Dt 
 
 Do 
 
 D s 
 
 E 
 
LUBRICATION. 
 
 1221 
 
 A, freight cars; 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.; Ci, 
 Z>2, in March, April, May, Sept., Oct., and Nov.; C3, Dz, in June, July, 
 and August. Weights per gallon, A, 7.4 lbs.; B, C, D, E, 7.5 lbs. 
 
 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 
 
 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 
 020 
 
 431.0 
 
 
 
 0.019 
 
 
 
 
 
 Testing Oil for Steam Turbines. (Robert Job, Trans. Am. Soc. for 
 Testing Matls., 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 of 
 by prescribing that when one ounce of the oil is placed in a 4-oz. bottle 
 with two ounces of boiling water, the bottle corked and shaken hard for 
 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 inquirv 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 
 
1222 FRICTION AND LUBRICATION. 
 
 run readily on less than 8 drops of 600 W oil per minute. If 3000 drops 
 are figured to the quart, ana 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: 
 
 Torli^ rnmnmind pnHnP \ 20 and 33 X 48 = 83 reVS - P er min - ; X dr0 P of 
 
 Corliss compound engine, j oil per min to 1 drop in two minutes , 
 
 * triple exp. " 20, 33, and 46 x 48; 1 drop every 2 minutes. 
 
 f 20 and 36 x 36; 143 revs, per min.; 2 drops 
 Porter-Allen " ] of oil per min., reduced afterwards to 1 drop 
 
 ( per min. 
 R ,. .. (15 and 25 x 16; 240 revs, per min.; 1 drop 
 
 I 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 cylinders 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 pints per 1,000 sq. ins. 
 
 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 
 may be due to smoothness of cylinder surface, kind and pressure of piston 
 rings, quality of oil, method of introducing 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 
 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. 
 
SOLID LUBRICANTS. 1223 
 
 Soda Mixture for Machine Tools. (Penna. R. R. 1894.) — Dissolve 
 5 lbs. 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., 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 1 1 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 shalt 
 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 "oildag." 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 
 soapstone, 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. 
 
1224 
 
 THE FOUNDRY. 
 
 THE FOUNDRY. 
 
 (See also Cast-iron, pp. 414 to 429, and Fans and Blowers, pp. 626 to 643.) 
 
 Cupola Practice. 
 
 The following table and the notes accompanying it are condensed from 
 an article by Simpson Bolland in Am. Mach., June 30, 1892: 
 
 84 
 16 
 3000 
 9000 
 1310 
 11,790 
 26 
 31 
 
 Diam. of lining, in 
 
 Height to char'g door, ft 
 
 Fuel used in bed, lbs 
 
 First charge of iron, lbs. 
 Other fuel charges, lbs... 
 Other iron charges, lbs.. 
 
 Diam. blast pipe, in 
 
 No. of 6-in. round tuyeres. . 
 
 Equiv. No. flat tuyeres 
 
 Width of flat tuyeres, in... 
 Height of flat tuyeres, in. . 
 
 Blast pressure, oz 
 
 Size of Root blower, No... . 
 
 Revs, per min 
 
 Engine for blower, H.P — 
 
 Sturtevant blower, No 
 
 Engine for blower, H.P.. . . 
 Melting cap., lbs. per hr. . . 
 
 36 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 12 
 
 13 
 
 14 
 
 15 
 
 15 
 
 16 
 
 840 
 
 1380 
 
 1650 
 
 1920 
 
 2190 
 
 2460 
 
 2520 
 
 4140 
 
 4950 
 
 5760 
 
 6570 
 
 7380 
 
 302 
 
 554 
 
 680 
 
 806 
 
 932 
 
 1058 
 
 2718 
 
 4986 
 
 6120 
 
 7254 
 
 8388 
 
 9522 
 
 14 
 
 18 
 
 20 
 
 22 
 
 22 
 
 24 
 
 3.7 
 
 6.8 
 
 10.7 
 
 13.7 
 
 15.4 
 
 19 
 
 4 
 
 6 
 
 8 
 
 8 
 
 8 
 
 10 
 
 2 
 
 2.5 
 
 2.5 
 
 3 
 
 3 
 
 3 
 
 13.5 
 
 13.5 
 
 15.5 
 
 16.5 
 
 18.5 
 
 18.5 
 
 8 
 
 12 
 
 14 
 
 14 
 
 14 
 
 16 
 
 2 
 
 4 
 
 4 
 
 5 
 
 5 
 
 6 
 
 241 
 
 212 
 
 277 
 
 192 
 
 240 
 
 163 
 
 2.5 
 
 10 
 
 14 
 
 18 V, 
 
 23 
 
 33 
 
 4 
 
 6 
 
 7 
 
 8 
 
 8 
 
 9 
 
 3 
 
 93/4 
 
 16 
 
 22 
 
 22 
 
 35 
 
 4820 
 
 10,760 
 
 13,850 
 
 16,940 
 
 21,200 
 
 26,070 
 
 16 
 3.5 
 
 16 
 
 16 
 
 7 
 
 160 
 
 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 exception. 
 
 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. 
 
THE FOUNDRY. 1225 
 
 [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 4 1/2, showing a loss of over two-thirds of the heat by 
 imperfect combustion. [Combustion 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 purpose 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,' 1 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. 
 
 31elting 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 10.2 12.4 14.8 13.8 13.0 
 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 9.5 12 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 tons 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 lbs. of 
 coke on bottom bed; a 36-in. cupola, 700 to 800 lbs.; a 48-in. cupola, 
 1500 lbs.; and a 60-in. cupola should have one ton of fuel on bottom bed. 
 
1226 
 
 THE FOUNDRY. 
 
 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 Col well 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 Molder'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., 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 Sturtevant blower, the maximum melting rate, from iron 
 down to blast off, 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 coke, 2000 iron; 300 coke, 2000 iron; and thereafter all 
 charges were 200 coke, 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 
 11 1/4 in. high and of a total area of 1/9.02 of the area of the 54-in. circle. 
 
 No. of Test. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Total tons. . . 
 
 22.7 
 
 24. 
 
 22.15 
 
 24.25 
 
 24.25 
 
 22.65 
 
 24. 
 
 20.30 
 
 23.85 
 
 22.35 
 
 Tons per hr.. 
 
 9.45 
 
 8.88 
 
 8.86 
 
 9.15 
 
 9.66 
 
 10.24 
 
 10.43 
 
 10.91 
 
 11.35 
 
 11.17 
 
 Lbs. per min* 
 
 19.81 
 
 18.61 
 
 18.55 
 
 19.17 
 
 20.25 
 
 21.44 
 
 21.82 
 
 22.95 
 
 23.77 
 
 23 39 
 
 Iron -r- cokef 
 
 7.54 
 
 7.40 
 
 7.28 
 
 8.58 
 
 8.94 
 
 8.71 
 
 9.02 
 
 9.02 
 
 10.02 
 
 9.49 
 
 Blast, oz 
 
 11.60 
 
 10.63 
 
 10.00 
 
 9.47 
 
 9.80 
 
 9.86 
 
 10.00 
 
 10.13 
 
 10.55 
 
 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 lbs. to 2000 lbs. 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 of 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. 
 
THE FOUNDRY. 
 
 1227 
 
 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: 
 
 lbs. 
 
 A— Bed of fuel, coke 1 ,500 
 
 First charge of iron 5,000 
 
 All other charges of iron 1 ,000 
 
 First and second charges of 
 coke, each 200 
 
 Four next charges of coke, 
 
 each 
 
 Six next charges of coke, each 
 
 Nineteen next charges of coke, 
 
 each 
 
 lbs 
 
 Thus for a melt of 18 tons there would be 5120 lbs. 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 . 
 
 lbs. 
 
 B— Bed of fuel, coke 1 ,600 
 
 First charge of iron 1,800 
 
 First charge of fuel 150 
 
 All other charges of iron, 
 
 each 1.00C 
 
 For an 18-ton melt 5060 lbs. of coke would be necessary, giving a ratio 
 of 7.1 lbs. of iron to 1 pound of coke, 
 lbs. 
 
 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 lbs. of coke would be used, or a ratio of 8.5 to 1. 
 lbs. 1 lbs. 
 
 D— Bed of fuel, coke 1,800 All charges of coke, each 200 
 
 First charge of iron 5,600 | All other charges of iron 2,900 
 
 In a melt of 18 tons, 3900 lbs. of fuel would be used, giving a ratio of 
 9.4 pounds of iron to 1 of coke. Very high, indeed, for stove-plate. 
 
 lbs. lbs. 
 
 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 lbs. of coal would be used, giving a ratio of 
 7.7 lbs. of iron to 1 lb. 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., 
 1907.) — The v elocity 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 o f 14.69 lbs, or 235 oun ces, = 0.77884 lb., the formula reduces 
 to V = Vi ,746,700 p/(235 + 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. 
 
 lbs- 
 Second and third charges of 
 
 fuel 130 
 
 All other charges of fuel, 
 
 each 100 
 
 lbs. 
 
 All other charges of iron 2,000 
 
 All other charges of coke 150 
 
 All other charges of iron, each 2,000 
 All other charges of coal, each 175 
 
 P 1 Q 
 
 H.P. 
 
 P 
 
 Q 
 
 H.P. 
 
 V 
 
 Q 
 
 H.P. 
 
 ]> 
 
 Q 
 
 H.P. 
 
 1 35.85 
 
 0.00978 
 
 6 
 
 86.89 
 
 0.1422 
 
 11 
 
 116.45 
 
 0.3493 
 
 16 
 
 139.03 
 
 0.6067 
 
 2 
 
 50.59 
 
 0.02759 
 
 7 
 
 93.66 
 
 0.1788 
 
 12 
 
 121.38 
 
 0.3972 
 
 17 
 
 143.03 
 
 0.6631 
 
 3 
 
 61.83 
 
 0.05058 
 
 8 
 
 99.92 
 
 0.2180 
 
 13 
 
 126.06 
 
 0.4470 
 
 18 
 
 146.88 
 
 0.7211 
 
 4 
 
 71.24 
 
 0.07771 
 
 9 
 
 105.76 
 
 0.2596 
 
 14 
 
 130.57 
 
 0.4986 
 
 19 
 
 150.61 
 
 0.7804 
 
 5 
 
 79.48 
 
 0.1084 
 
 10 
 
 111.25 
 
 0.3034 
 
 15 
 
 134.89 
 
 0.5518 
 
 20 
 
 154.22 
 
 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 
 DW/3, D = diam. of wheel in ins., W = width of wheel at circumference, 
 
1228 
 
 THE FOUNDRY. 
 
 in inches. For the ordinary type of fan at constant speed maximum 
 efficiency and power are secured at or near the capacity area; the power 
 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 and 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. 
 
 as 
 5£ 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 r.p.m. 
 cu. ft. 
 h.p. 
 
 h.p. 
 
 r.p.m 
 cu. ft 
 h.p. 
 
 r.p.m 
 cu. ft 
 h.p. 
 
 Total Pressure in Ounces per Square Inch. 
 
 2660.0 
 
 520.0 
 
 1.7 
 
 2000.0 
 
 700.0 
 
 2.3 
 
 1590.0 
 
 870.0 
 
 2. 
 
 1330.0 
 1040.0 
 
 3.4 
 
 1140.0 
 
 1220.0 
 
 3.9 
 
 2860.0 
 
 560.0 
 
 2.1 
 
 2150.0 
 
 750.0 
 
 2.9 
 
 1720.0 
 
 940.0 
 
 3.6 
 
 1430.0 
 
 1120.0 
 
 4.3 
 
 1230.0 
 
 1310.0 
 
 5.0 
 
 3050.0 
 
 600.0 
 
 2.6 
 
 2290.0 
 
 800.0 
 
 3.5 
 
 1830.0 
 1000.0 
 
 4.4 
 
 1530.0 
 
 1200.0 
 
 5.2 
 
 1310.0 
 
 1400.0 
 
 6.1 
 
 3230.0 
 
 640.0 
 
 3.1 
 
 2420.0 
 
 850.0 
 
 4.2 
 
 1940.0 
 
 1060.0 
 
 5.2 
 
 1620.0 
 1270.0 
 
 1380.0 
 
 1480.0 
 
 7.3 
 
 10 11 12 13 14 15 16 
 
 3400.0 
 
 670.0 
 
 3.6 
 
 2550.0 
 
 890.0 
 
 4.9 
 
 2040.0 
 1110.0 
 
 1700.0 
 
 1340.0 
 
 7.3 
 
 1460.0 
 1560.0 
 5 
 
 r.p.m. 1000.0 1070.0 1150.0 1210.0 1270.0 1330.Q 1390.0 1450.0 1500.0 1550.0 1590.0 
 
 48 \ cu. ft. 1390.0 1500.0 1600.0 1690.0 1780.0 1860.0 1940.0 2020.0 2090.0 2160.0 2230.0 
 
 h.p. 4.5 5.7 7.0 8.3 9.7 11.2 12.7 14.3 15.9 17.7 21.0 
 
 3560.0 
 
 700.0 
 
 4.2 
 
 2670.0 
 
 930.0 
 
 5.6 
 
 2140.0 
 
 1160.0 
 
 7.0 
 
 1780.0 
 1400.0 
 
 1530.0 
 
 1630.0 
 
 9.8 
 
 3710.0 
 
 730.0 
 
 4.8 
 
 2780.0 
 
 970.0 
 
 6.4 
 
 2230.0 
 
 1210.0 
 
 7.9 
 
 1850.0 
 
 1460.0 
 
 9.5 
 
 1590.0 
 
 1700.0 
 
 11.1 
 
 3850.0 
 
 760.0 
 
 5.4 
 
 2890.0 
 
 1010.0 
 
 7.1 
 
 2310.0 
 1260.0 
 
 1930.0 
 
 1510.0 
 
 10.7 
 
 1650.0 
 
 1770.0 
 
 12.5 
 
 3990.0 
 780.0 
 
 2990.0 
 
 1040.0 
 
 8.0 
 
 2390.0 
 
 1310.0 
 
 10.0 
 
 2000.0 
 
 1570.0 
 
 11.9 
 
 1710.0 
 
 1830.0 
 
 13.9 
 
 4120.0 
 
 810.0 
 
 6.6 
 
 3090.0 
 1080.0 
 
 2470.0 
 
 1350.0 
 
 11.0 
 
 2060.0 
 
 1620.0 
 
 13.2 
 
 1770.0 
 
 1890.0 
 
 15.4 
 
 4250.0 
 
 830.0 
 
 7.3 
 
 3190.0 
 
 1110.0 
 
 9.7 
 
 2550.0 
 
 1390.0 
 
 12.1 
 
 2120.0 
 
 1670.0 
 
 14.5 
 
 1820.0 
 
 1950.0 
 
 17.0 
 
 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 lb. coke 6 '! 7 8 9 10 
 
 Cu. ft. air per ton of iron 33,000 31,000 29,000 27,000 25,000 
 
 It is customary to provide blower capacity on a basis of 30,000 cu. ft., 
 which corresponds 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 
 I2V2 and 14V8 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 
 
THE FOUNDRY. 
 
 1229 
 
 were melted in 3.77 hours, or 7.65 tons per hour, while with the rotary 
 blower 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,Vp. or^ITR 
 
 v* m 
 
 Poo V 2 __ 
 
 H.P. oc M3 or Vp3 
 
 D 2 
 
 Foe 1 ■ 
 Poc d 
 H.P. oc P or 1 h- D i 
 E oc M , P, or 1 -h D* 
 
 M oc D 
 For a given cupola 
 E oc M 2 , or P 
 Duration of beat 
 oc l -- 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 power 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. 
 
 Pressure 
 per sq. 
 in., oz. 
 
 
 Diameter inside 
 Lining, in. 
 
 Capacity per 
 Hour, tons. 
 
 18 
 
 0.25- 0.5 
 
 24 
 
 1.00- 1.5 
 
 30 
 
 2.00- 3.5 
 
 36 
 
 4.00- 5.0 
 
 42 
 
 5.00- 7.0 
 
 48 
 
 8.00-10.0 
 
 54 
 
 9.00-12.0 
 
 60 
 
 12.00-15.0 
 
 66 
 
 14.00-18.0 
 
 72 
 
 17.00-21.0 
 
 78 
 
 19.00-24.0 
 
 84 
 
 21.00-27.0 
 
 Volume of Air 
 permin., cu. ft. 
 
 5- 7 
 7- 9 
 8-11 
 8-12 
 8-13 
 8-13 
 9-14 
 9-14 
 9-15 
 10-15 
 10-16 
 10-16 
 
 150- 300 
 600- 900 
 1,200- 2,000 
 2,200- 2,800 
 2,700- 3,700 
 4,000- 5,000 
 4,500- 6,000 
 6,000- 7,500 
 7,000- 9,000 
 8,500-10,500 
 9,500-12,000 
 10,500-13,500 
 
 Horse- 
 power. 
 
 0.5- 1.5 
 2.0- 6.0 
 5.0- 15.0 
 10.0-23.0 
 12.0- 32.0 
 18.0- 45.0 
 22.0- 60.0 
 30.0- 75.0 
 35.0- 90.0 
 45.0-110.0 
 52.0-130.0 
 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 lbs.; 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 lb. fuel, 9V2; per cent weight of good 
 castings, 75; one week, 13V4 tons per hour, 10.3 lbs. iron per lb. fuel; 
 per cent weight of good castings, 75.3. The increase was made by putting 
 in an additional row of tuyeres and using stronger blast, 14 ounces. Coke 
 was used as fuel. (W. O. Webber, Trans. A. S. M. E. t xii, 1045.) 
 
1230 
 
 THE FOUNDRY. 
 
 Power Required for a Cupola Fan. (Thos. D. West, The Foundry, 
 April, 1904.) — -The power required when a fan is connected with a cupoia 
 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 lbs. of iron per lb. 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. Mach., 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 lbs. 
 
 New scrap 3,005 " 
 
 Millings 200 " 
 
 Loss of metal 1 ,481 " 
 
 Amount melted 26,000 lbs. 
 
 Loss of metal, 5.69%. Ratio of loss, 1 to 17.55. 
 
 Use 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 character 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 415 and 422.) 
 
 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- 
 raony 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 
 
THE FOUNDRY. 
 
 1231 
 
 the designer, especially in the cooling and shrinking of the various parts 
 ot a large casting after being poured. 
 
 Castings are often designed with a useless multiplicity of 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 7\ 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 tne 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 lbs. 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, 1/8 inch per foot. For zinc, 5/ 16 inch per foot. 
 
 " brass, 3/ 16 " " " " tin, V12 " 
 
 " steel, 1/4 " " " " aluminum, 3/ 16 " " " 
 
 " mal. iron, Vs " " " " britannia, 1/32 " 
 
 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 423.) 
 
 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 1/8 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 1/2-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 425.) 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. 
 Foundrymen'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. 
 
1232 
 
 THE FOUNDRY. 
 
 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 
 a casting. 
 
 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. Ail of 
 these alloys may be made of purer quality in the electric furnace. 
 
 
 Ferro- 
 
 Spiegel- 
 
 Silicon 
 
 Ferro- 
 
 Ferro- 
 
 Ferro- 
 
 
 Mn. 
 
 eisen. 
 
 Spiegel. 
 
 sil. 
 
 phos. 
 
 Chrome. 
 
 Mn 
 
 41.5- 87.9 
 
 9.25-29.75 
 
 17.50-20.87 
 
 1.17- 2.20 
 
 3.00- 5.90 
 
 1.55- 2.30 
 
 Si 
 
 0.10- 0.63 
 
 0.42- 0.95 
 
 9.45-14.23 
 
 8.10-17.00 
 
 0.50- 0.84 
 
 0.13-0.36 
 
 P 
 
 0.09- 0.20 
 
 0.06- 0.09 
 
 0.07- 0.10 
 
 0.06- 0.08 
 
 15.71-20.50 
 
 0.04- 0.07 
 
 C 
 
 5.62- 7.00 
 
 3.94- 5.20 
 
 1.05- 1.89 
 
 0.90- 1.75 
 
 0.27- 0.30 
 
 5.34- 7.12 
 
 S 
 
 nil 
 
 nil-trace 
 
 nil 
 
 0.02- 0.05 
 
 0.16- 0.33 
 
 Cr, 13.50-41.39 
 
 The following are typical analyses of other alloys made in the electric 
 furnace: 
 
 
 Si 
 
 Fe 
 
 Mn 
 
 Al 
 
 Ca 
 
 Mg 
 
 C 
 
 S 
 
 P 
 
 Ti 
 
 
 1.21 
 45.65 
 69.80 
 
 
 
 0.30 
 9.45 
 2.55 
 
 
 
 3.28 
 0.55 
 1.14 
 
 0.03 
 0.01 
 0.01 
 
 0.02 
 0.03 
 0.04 
 
 53 
 
 Ferro-aluminum-silicide 
 
 Ferro-calcium-silicide 
 
 44.15 
 11.15 
 
 tr. 
 
 0.22 
 
 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 hvdro- 
 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 
 m 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 molds are used, no provision is made 
 against shrinkage, and the casting is removed from the mold as soon as 
 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 
 
THE FOUNDRY. 
 
 1233 
 
 failure. The mold should be so heavy that it will not become highly 
 heated in use. Casting a 4-in. pipe weighing 65 lbs. every seven min- 
 utes in a mold weighing 6500 lbs. 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 also possesses some of the properties of high-carbon 
 steel. A piece of 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 furnace 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 the 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: 
 CO, 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; CO, 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. 
 
 
 lbs. 
 10.7 
 12.9 
 8.5 
 12.5 
 16.7 
 14.1 
 
 lbs. 
 10.4 
 12.7 
 8.2 
 12.1 
 16.1 
 13.6 
 
 lbs. 
 12.8 
 15.3 
 10.1 
 14.9 
 19.8 
 16.7 
 
 lbs. 
 12.2 
 14.6 
 9.7 
 14.2 
 19.0 
 16.0 
 
 lbs. 
 12.5 
 
 Honduras 
 
 Spanish 
 
 15. 
 9.9 
 
 
 14.6 
 
 " ' white 
 
 19.5 
 
 
 16.5 
 
 
 
 Molding Sand. (Walter Bagshaw, Proc. Inst. 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 
 oxide of iron. Sand containing much of the metallic oxides, and especially 
 
1234 
 
 THE FOUNDRY. 
 
 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 for 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 2V4 in. of overhang. 
 
 in the centrifugal machine .. . " " 2 " 21/4 " " 
 
 through a riddle " " 13/ 4 " 21/8 " " 
 
 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 Piles (Castings, July, 1908) 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 lbs. 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. 
 
 
 in 
 
 in. 
 
 
 in. 
 
 in. 
 
 
 in. 
 
 in. 
 
 16 tons 
 
 54 
 
 56 
 
 3 tons 
 
 31 
 
 32 
 
 300 lbs. 
 
 f Hi/2 
 
 1U/2 
 
 14 " 
 
 52 
 
 53 
 
 2 " 
 
 27 
 
 28 
 
 250 " 
 
 103/ 4 
 
 11 
 
 12 " 
 
 49 
 
 50 
 
 1 Va" 
 
 241/2 
 
 25 
 
 200 " 
 
 10 
 
 IOV2 
 
 10 " 
 
 46 
 
 48 
 
 1 ton 
 
 22 
 
 22 
 
 150 " 
 
 9 
 
 91/ 2 
 
 8 " 
 
 43 
 
 44 
 
 3/4" 
 
 20 
 
 20 
 
 100 " 
 
 8 
 
 81/2 
 
 6 " 
 
 39 
 
 40 
 
 V2" 
 
 17 
 
 17 
 
 75 " 
 
 7 
 
 71/2 
 
 4 " 
 
 34 
 
 35 
 
 V4" 
 
 131/2 
 
 131/2 
 
 50 *' 
 
 6V2 
 
 6V2 
 
THE MACHINE-SHOP. 
 
 1235 
 
 THE MACHINE-SHOP. 
 
 SPEED OF CUTTING-TOOLS IN LATHES, MILLING 
 3IACHINES, ETC. 
 
 Relation of diameter of rotating tool or piece, number of revolutions 
 and cutting-speed: 
 
 Let d = diam. of rotating piece in inches, n = No. of revs, per min.; 
 S = speed of circumference in feet per minute; 
 c ndn n „ fi ,oj S 3.82 5 . 3.82 5 
 
 S = IT =0-2«18dn; n- ^-^ = -j- ; d .- ^-- 
 
 Approximate rule: Number of revolutions per minute = 4 X speed in 
 feet per minute -e- diameter in inches. 
 
 
 
 
 Table of 
 
 Cutting-speeds. 
 
 
 
 
 In 
 
 c3 G 
 
 Feet per minute. 
 
 > 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 s"" 
 
 Revolutions per minute. 
 
 ■ V4 
 
 76.4 
 
 152.8 
 
 229.2 
 
 305.6 
 
 382.0 
 
 458.4 
 
 534.8 
 
 611.2 
 
 687.6 
 
 764.0 
 
 3 /8 
 
 50 9 
 
 101.9 
 
 152.8 
 
 203.7 
 
 254.6 
 
 305.6 
 
 356.5 
 
 407.4 
 
 458.3 
 
 509.3 
 
 i/ 2 
 
 38.2 
 
 76.4 
 
 114.6 
 
 152.8 
 
 191.0 
 
 229.2 
 
 267.4 
 
 305.6 
 
 343.8 
 
 382.0 
 
 5/8 
 
 30.6 
 
 61.1 
 
 91.7 
 
 122.2 
 
 152.8 
 
 183.4 
 
 213.9 
 
 244.5 
 
 275.0 
 
 305.6 
 
 3/4 
 
 25.5 
 
 50.9 
 
 76.4 
 
 101.8 
 
 127.3 
 
 152.8 
 
 178.2 
 
 203.7 
 
 229.1 
 
 254.6 
 
 7/8 
 
 21.8 
 
 43.7 
 
 65.5 
 
 87.3 
 
 109.1 
 
 130.9 
 
 152.8 
 
 174.6 
 
 196.4 
 
 218.3 
 
 1 
 
 19.1 
 
 38.2 
 
 57.3 
 
 76.4 
 
 95.5 
 
 114.6 
 
 133.7 
 
 152.8 
 
 171.9 
 
 191.0 
 
 U/8 
 
 17.0 
 
 34.0 
 
 50.9 
 
 67.9 
 
 84.9 
 
 101.8 
 
 118.8 
 
 135.8 
 
 152.8 
 
 169.7 
 
 H/4 
 
 15.3 
 
 30.6 
 
 45.8 
 
 61.1 
 
 76.4 
 
 91.7 
 
 106.9 
 
 122.2 
 
 137.5 
 
 152.8 
 
 13/8 
 
 13.9 
 
 27.8 
 
 41.7 
 
 55.6 
 
 69.5 
 
 83.3 
 
 97.2 
 
 111.1 
 
 125.0 
 
 138.9 
 
 H/2 
 
 12.7 
 
 25.5 
 
 38.2 
 
 50.9 
 
 63.6 
 
 76.4 
 
 89.1 
 
 101.8 
 
 114.5 
 
 127.2 
 
 13/4 
 
 10.9 
 
 21.8 
 
 32.7 
 
 43.7 
 
 54.6 
 
 65.5 
 
 76.4 
 
 87.3 
 
 98.2 
 
 109.2 
 
 2 
 
 9.6 
 
 19.1 
 
 28.7 
 
 38.2 
 
 47.8 
 
 57.3 
 
 66.9 
 
 76.4 
 
 86.0 
 
 95.5 
 
 21/4 
 
 8.5 
 
 17.0 
 
 25.5 
 
 34.0 
 
 42.5 
 
 50.9 
 
 59.4 
 
 67.9 
 
 76.4 
 
 84.9 
 
 21/2 
 
 7.6 
 
 15.3 
 
 22.9 
 
 30.6 
 
 38.2 
 
 45.8 
 
 53.5 
 
 61.1 
 
 68.8 
 
 76.4 
 
 23/4 
 
 6.9 
 
 13.9 
 
 20.8 
 
 27.8 
 
 34.7 
 
 41.7 
 
 48.6 
 
 55.6 
 
 62.5 
 
 69.5 
 
 3 
 
 6.4 
 
 12.7 
 
 19.1 
 
 25.5 
 
 31.8 
 
 38.2 
 
 44.6 
 
 50.9 
 
 57.3 
 
 63.7 
 
 31/2 
 
 5.5 
 
 10.9 
 
 16.4 
 
 21.8 
 
 27.3 
 
 32.7 
 
 38.2 
 
 43.7 
 
 49.1 
 
 54.6 
 
 4 
 
 4.8 
 
 9.6 
 
 14.3 
 
 19.1 
 
 23.9 
 
 28.7 
 
 33.4 
 
 38.2 
 
 43.0 
 
 47.8 
 
 41/2 
 
 4.2 
 
 8.5 
 
 12.7 
 
 17.0 
 
 21.2 
 
 25.5 
 
 29.7 
 
 34.0 
 
 38.2 
 
 42 5 
 
 5 
 
 3.8 
 
 7.6 
 
 11.5 
 
 15.3 
 
 19.1 
 
 22.9 
 
 26.7 
 
 30.6 
 
 34.4 
 
 38.1 
 
 51/2 
 
 3.5 
 
 6.9 
 
 10.4 
 
 13.9 
 
 17.4 
 
 20.8 
 
 24.3 
 
 27.8 
 
 31.2 
 
 34.7 
 
 6 
 
 3.2 
 
 6.4 
 
 9.5 
 
 12.7 
 
 15.9 
 
 19.1 
 
 22.3 
 
 25.5 
 
 28.6 
 
 31.8 
 
 7 
 
 2.7 
 
 5.5 
 
 8.2 
 
 10.9 
 
 13.6 
 
 16.4 
 
 19.1 
 
 21.8 
 
 24.6 
 
 27.3 
 
 8 
 
 2.4 
 
 4.8 
 
 7.2 
 
 9.6 
 
 11.9 
 
 14.3 
 
 16.7 
 
 19.1 
 
 21.5 
 
 23.9 
 
 9 
 
 2.1 
 
 4.2 
 
 6.4 
 
 8.5 
 
 10.6 
 
 12.7 
 
 14.8 
 
 17.0 
 
 19.1 
 
 21.2 
 
 10 
 
 1.9 
 
 3.8 
 
 5.7 
 
 7.6 
 
 9.6 
 
 11.5 
 
 13.3 
 
 15.3 
 
 17.2 
 
 19.1 
 
 11 
 
 1.7 
 
 3.5 
 
 5.2 
 
 6.9 
 
 8.7 
 
 10.4 
 
 12.2 
 
 13.9 
 
 15.6 
 
 17.4 
 
 12 
 
 1.6 
 
 3.2 
 
 4.8 
 
 6.4 
 
 8.0 
 
 9.5 
 
 11.1 
 
 12.7 
 
 14.3 
 
 15.9 
 
 13 
 
 1.5 
 
 2.9 
 
 4.4 
 
 5.9 
 
 7.3 
 
 8.8 
 
 10.3 
 
 11.8 
 
 13.2 
 
 14.7 
 
 14 
 
 1.4 
 
 2.7 
 
 4.1 
 
 5.5 
 
 6.8 
 
 8.2 
 
 9.5 
 
 10.9 
 
 12.3 
 
 13.6 
 
 15 
 
 1.3 
 
 2.5 
 
 3.8 
 
 5.1 
 
 6.4 
 
 7.6 
 
 8.9 
 
 10.2 
 
 11.5 
 
 12.7 
 
 16 
 
 1.2 
 
 2.4 
 
 3.6 
 
 4.8 
 
 6.0 
 
 7.2 
 
 8.4 
 
 9.5 
 
 10.7 
 
 11.9 
 
 18 
 
 1.1 
 
 2.1 
 
 3.2 
 
 4.2 
 
 5.3 
 
 6.4 
 
 7.4 
 
 8.5 
 
 9.5 
 
 106 
 
 20 
 
 1.0 
 
 1.9 
 
 2.9 
 
 3.8 
 
 4.8 
 
 5.7 
 
 6.7 
 
 7.6 
 
 8.6 
 
 9.6 
 
 22 
 
 .9 
 
 \.7 
 
 2.6 
 
 3.5 
 
 4.3 
 
 5.2 
 
 6.1 
 
 6.9 
 
 7.8 
 
 8.7 
 
 24 
 
 .8 
 
 1.6 
 
 2.4 
 
 3.2 
 
 4.0 
 
 4.8 
 
 5.6 
 
 6.4 
 
 7.2 
 
 8.0 
 
 26 
 
 .7 
 
 1.5 
 
 2.2 
 
 2.9 
 
 3.7 
 
 4.4 
 
 5.1 
 
 5.9 
 
 6.6 
 
 7.3 
 
 28 
 
 .7 
 
 1.4 
 
 2.0 
 
 2.7 
 
 3.4 
 
 4.1 
 
 4.8 
 
 5.5 
 
 6.1 
 
 6.8 
 
 30 
 
 .6 
 
 1.3 
 
 1.9 
 
 2.5 
 
 3.2 
 
 3.8 
 
 4.5 
 
 5.1 
 
 5.7 
 
 6.4 
 
 36 
 
 .5 
 
 1.1 
 
 1.6 
 
 2.1 
 
 2.7 
 
 3.2 
 
 3.7 
 
 4.2 
 
 4.8 
 
 5.3 
 
 42 
 
 .5 
 
 .9 
 
 1.4 
 
 1.8 
 
 2.3 
 
 2.7 
 
 3.2 
 
 3.6 
 
 4.1 
 
 4.5 
 
 48 
 
 .4 
 
 .8 
 
 1.2 
 
 1.6 
 
 2.0 
 
 2.4 
 
 2.8 
 
 3.2 
 
 3.6 
 
 4.0 
 
 54 
 
 .4 
 
 .7 
 
 1.1 
 
 1.4 
 
 1.8 
 
 2.1 
 
 2.5 
 
 2.8 
 
 3.2 
 
 3.5 
 
 60 
 
 .3 
 
 .6 
 
 1.0 
 
 1.3 
 
 1.6 
 
 1.9 
 
 2.2 
 
 2.5 
 
 2.9 
 
 3.2 
 
1236 
 
 THE MACHINE-SHOP. 
 
 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 tine 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 11 3^ 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 11 K 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 3^ 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 have twice as many threads per inch as it actually has, and then ignore 
 
GEARING OF LATHES. 
 
 123' 
 
 the compounding entirely. Some lathes arc so constructed that the stud 
 on which the first driver is placed revolves only half as fast 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 -irich 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/ 32i 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 i/ 2 threads per inch, then its pitch being 4/ 10 
 inch, we have the fractions 4/ 10 and 25/ 32i 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. 
 
 
 
 
 fcs 
 
 
 
 
 
 Whole Threads. 
 
 ZQ 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 110 
 
 120 
 
 130 
 
 
 20 
 
 
 8 
 
 6 
 
 4 4/5 
 
 4 
 
 3 3/ 7 
 
 2 2/ii 
 
 2 
 
 1 11/13 
 
 2 
 
 11 
 
 22 
 
 44 
 
 30 
 
 18 
 
 
 9 
 
 7 1/5 
 
 6 
 
 5 1/7 
 
 3 3/n 
 
 3 
 
 2 IO/13 
 
 3 
 
 12 
 
 24 
 
 48 
 
 40 
 
 24 
 
 16 
 
 12 
 
 9 3/5 
 
 8 
 
 6 6/ 7 
 
 4 4/n 
 
 4 
 
 3 9/13 
 
 4 
 
 13 
 
 26 
 
 52 
 
 50 
 
 30 
 
 20 
 
 l!> 
 
 
 10 
 
 8 4/7 
 
 5 5/11 
 
 5 
 
 4 8/13 
 
 5 
 
 14 
 
 28 
 
 66 
 
 60 
 
 36 
 
 24 
 
 18 
 
 14 2/5 
 
 
 IO2/7 
 
 6 6/n 
 
 6 
 
 5 7/i3 
 
 6 
 
 15 
 
 30 
 
 72 
 
 yo 
 
 42 
 
 28 
 
 21 
 
 16 4/s 
 
 14 
 
 
 7 7/ii 
 
 7 
 
 68/13 
 
 7 
 
 16 
 
 33 
 
 78 
 
 no 
 
 66 
 
 44 
 
 33 
 
 26 2/5 
 
 22 
 
 18 6/7 
 
 
 II 
 
 102/ 13 
 
 8 
 
 18 
 
 36 
 
 
 120 
 
 il 
 
 48 
 
 36 
 
 28 4/5 
 
 24 
 
 20 4/7 
 
 13 1/u 
 
 
 1 1 VIS 
 
 9 
 
 20 
 
 39 
 
 
 130 
 
 76 
 
 bl 
 
 39 
 
 31 1/5 
 
 26 
 
 22 3/7 
 
 142/n 
 
 13 
 
 
 10 
 
 21 
 
 42 
 
 
 Ten gears are sufficient to cut all the usual threads, with the exception 
 of perhaps IIV2, 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 
 
 gitch 6 or any other desirable pitch, and establishing the proper ratio 
 etween 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 of 
 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 
 
THE MACHINE-SHOP. 
 
 and "quick change" gear train. The threads per inch usually available 
 range from 2 to 46 in a 12-inch lathe to 1 to 24 in a 30-inch 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 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. 
 
 Metr'c 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.) — No rule 
 can be given which will produce exact results, owing to the fact 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, 
 
 2 — 1 3 
 
 — s — Xt= 1^ inches. 
 
 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 of high 
 speed steel and to heavy work requiring tools not less than 1/2 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. 187 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. 188. The 
 actual dimensions of a 1-inch roughing tool are shown in Fig. 189. 
 Let R = radius of point of tool, A = width of tool, L = length of shank, 
 and H = height of shank, all in inches. Then L = 14 A + 4; H = 1.5 A; 
 R = 0.5 A — 0.3125 for cutting hard steel and cast iron; R = 0.5 A — 
 0.1875 for soft steel. The meaning of the terms back slope, etc., is shown 
 in Fig. 187. 
 
 Angles for Tools. 
 
 * Material cut. 
 
 a = clearance. 
 
 b = back slope. 
 
 c = side slope. 
 
 Cast iron; Hard steel. 
 
 6 degrees. 
 
 8 degrees. 
 
 14 degrees. 
 
 Medium steel; 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 divides metals to 
 be cut into general classes: (a) cast iron and hard steel, steel of 0.45-0.50 
 percent 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 ar-4 cast iron should be 68 degrees; 
 
1240 
 
 THE MACHINE-SHOP. 
 
 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, 
 
 h If" — +tf'l3S — i 
 
 Fig. 189. 
 
 and it is also easier to feed. The nose of the tool should be set to one 
 side, as in Fig. 189 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. 
 
TAYLORS EXPERIMENTS. 1241 
 
 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 D. 
 
 Use of Water on Tool. — With the best high speed steel tools, a 
 gain of 16 per cent in cutting speed can be made in cutting cast iron, 
 steel or wrought iron by throwing a heavy stream of water directly on 
 the chip at the point where it is being removed from the forging by the 
 tool. Not less than three gallons a minute should be used for a 2 X 21/2- 
 inch 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 + 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. 1/2 X3/ 4 5/ 8 xl 3/ 4 X 1 l/ 8 7/ 8 X I % lXl 1/2 
 
 Hours. 1.25 1.25 1.25 1.5 1.5 
 
 Size of tool. 
 
 Inches. 1 V4X 1 7/ 8 U/2X2 1/4 13/4X2 3/4 2x3 
 
 Hours. 1.75 2.0 2.5 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 1244 and 1245. 
 
 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 arid high speed. With a_given depth of cut, a 
 cutting speed of S, and a feed of F, S varies as l/^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. 
 
1242 THE MACHINE-SHOP. 
 
 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 lb. 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 rirst 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.; 
 
 (6) rapidly from that temperature to just below the melting-point. 
 
 (c) cooling fast to below the breaking-down point, i.e., 1550°F. 
 
 (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. 
 
taylor's experiments. 1243 
 
 Cooling the tool by plunging it in on or water, renders it liable to fire 
 cracks and to brittfeness 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 tool. 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. 189, 
 and of the chemical composition and heat treatment given in the pre- 
 ceding paragraphs, should be run at the cutting speeds given in the tables 
 on pages 1244 and 1245 in order to last one hour and 30 minutes without 
 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, find the proper value for the size of tool in the tables below and 
 divide by 2.7. The economical speed for a thread tool is similarly found 
 by dividing by 4. The thickness of chip in the latter case is the advance 
 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- 
 ness and to the area of the chip and to the cube of the cutting speed. 
 Or if U= thickness or feed, d = depth of cut, a x = area of the cut and 
 «i= cutting speed, for any given set of working conditions, and ticiai and 
 S2 values for another set of conditions, then the durability of the tool 
 
1244 
 
 THE MACHINE-SHOP. 
 
 
 1 
 
 1 
 
 •2 
 
 64.2 
 49.4 
 35.7 
 29.1 
 25.2 
 20.5 
 
 58.9 
 45 4 
 328 
 26.8 
 232 
 18.8 
 
 52.0 
 40.1 
 29 
 23 7 
 20.5 
 166 
 
 47.7 
 36.7 
 26.5 
 21 6 
 187 
 15.2 
 
 23.4 
 
 16 5 
 134 
 
 JgSg-'j 
 
 Ui 
 
 *J 
 
 o^-am^ 
 
 552553 
 
 »eoo>em"od 
 
 £53533 
 
 £•35 
 
 ssiSs ; 
 
 ■3 
 
 a 
 
 «J 
 
 0008»- 
 
 © o' r>i <> %d © 
 
 jg|S2S 
 
 qoto-e 
 foj^'g — oo 
 
 mm 
 
 OOOm*«) 
 
 llSSi j 
 
 e 
 1 
 
 3 
 
 
 n 
 
 1 
 
 1 
 
 Irs* 
 
 ES52-2 : 
 
 ov^auj : 
 
 i*U j ; 
 
 15S 
 
 52 
 
 
 |||l y 
 
 © © •© 0> * . 
 
 ©©.©■«© 
 
 SS3S j ■ 
 
 ©C4 — - 
 
 11 
 
 s 
 
 iill i i 
 
 ooooo 
 
 s*a««jj : 
 
 3S2 — — • 
 
 ooooo 
 
 5552 : 
 
 111;:; 
 
 °°- : : : : 
 
 1 
 
 j 
 
 I 
 
 J 
 
 
 I^rS55 
 
 JJ5g5§ 
 
 »mmqis.r« 
 
 iSSagi 
 
 5555^3 
 
 SSgg&i 
 
 o 
 
 o 
 
 <S 
 
 H 
 
 
 
 *J 
 
 i&ss 
 
 liSi53 
 
 SS^^S® 
 
 SSSSREi" 
 
 SSSSSw 
 
 2-5-;-- 
 
 1 
 
 OOOOBN 
 
 
 555555; 
 
 00»*'0if| 
 
 55*555 
 
 S 
 
 \ 
 
 o 
 
 J 
 QQ 
 
 1 
 
 X 
 
 55^5 : : 
 
 KISS •' 
 
 sis'SIS 
 
 -£5£5 : 
 
 £*5i<3 | ; 
 
 SiSSsi ^ 
 
 4 
 
 Opqir, . . 
 
 HISS : 
 
 555555 
 
 mm \ 
 
 sas j : 
 
 -§R ■ • 
 
 i 
 
 to 
 
 iii 1 1 
 
 5S5.5.5 
 
 qooooo 1 ooooo - 
 
 llii • ; 
 
 555 
 
 1 
 
 1 
 
 
 S£*m°S 
 
 5SSSSS 
 
 OvOr- 
 
 
 
 
 * 
 
 55 
 
 ?.S2S;;2: 
 
 s&rsse: 
 
 *SSS23 
 
 OONOiOm 
 
 © 
 
 3 
 
 1 
 
 fa 
 
 a 
 a 
 I 
 
 *l 
 
 mm 
 
 ONOT.^t 
 
 
 -NO;>qm* 
 
 SS3SSS 
 
 ssSSS'S 
 
 1 
 
 oooooo 
 
 OOOO'tB 
 
 igSEi 
 
 1II3SS 
 
 oo-o;eio 
 
 55 5 52 2 
 
 l 
 
 
 SmS* I \ 
 
 55S-S : 
 
 ssaaa 
 
 jA-'jOOjtn'o 
 
 §3253 : 
 
 3255 : : 
 
 
 §5SS •' : 
 
 52522 "" 
 
 ||S2ss 
 
 5S552S 4 
 
 RSSR* j 
 
 oo>om^ : 
 
 a 
 
 1 
 
 I 
 
 S;I;Q8 ' ■ 
 
 ooooo '. 
 
 S— SSIri • 
 
 ©ooooo 
 ©' ©' e\ » <?>' g 
 
 ooooo* 
 
 52553 : 
 
 o«g*'g< ; ; 
 
 H 
 
 6 
 
 "3 
 
 'C 
 
 1 
 
 1-s 
 
 .3 8.3 8.2 
 
 S8SS ff S 
 
 s s a 8 » 3 
 
 S S3 8.« 3 
 
 .3 8 3.8 » 2 
 
 *ISf& 
 
 
 
 3 
 
 * 
 
 ff 
 
 1 
 
 * 
 
 •" 
 
 =? 
 
taylor's experiments. 
 
 1245 
 
 4 
 
 a 
 
 I 
 1 
 
 es 
 
 a 
 
 60.O 
 42.8 
 28.5 
 22.2 
 18.7 
 
 OO'ls'j; 
 
 IN • 
 
 piv— vq . . 
 
 <*■! r>» «■* on •' ' 
 ■A<r\N— ; ; 
 
 0«n<r\ - • 
 
 1 
 
 
 
 
 ©•".cop — - 1 omift-» • 
 
 qq-ts • • j mop • • 
 
 
 
 
 O 1 o^rar>\D : 
 
 9 9 ""."". 9 • 1 oo-^. • • 
 
 999 _■ : 
 
 
 v : 
 
 
 1 
 
 CO 
 
 3 
 
 S2?S j i 
 
 Boasq 
 
 • I* 1 * 
 
 
 p 
 
 
 1 
 
 
 
 
 OOlst • • | poo 
 
 M TcOMO . . ONQ 
 
 ; : 1 9°. 
 
 
 p 
 
 
 
 
 
 1 
 
 pppp • • 
 
 pop 
 
 
 po 
 
 ill 
 
 o 
 6 
 
 
 
 
 
 a 
 4 
 
 I 
 3 
 
 "2 
 
 
 p-rfpcq • | — "o»««q • 
 
 1 <rcqo> 
 
 
 
 OOONts . I ©©OOPICO • 
 
 eoo'irlf'f*; • 0'>t— ■ — •* ; 
 © eo >n *r <*\ ; orsmtm * 
 
 vqvtprsN . 
 
 INN»,N • • 
 
 cosS-*S : 
 
 j cocoa 
 
 
 1 
 
 SOOtt • 
 — *o~cot>. ; 
 
 OOO'O'O • 
 
 8333$ ; 
 
 OOO 'T to • 
 COrnOM^sO 1 
 
 pOoq'T . • 
 
 ©Or>. 
 •6 -6 »' 
 
 1A— t^ 
 
 
 1 
 
 03 
 
 S3 1 — 
 
 aso-rm : : 
 
 rsico.evi • • • 
 
 co«r\«"> : : : 
 
 '*•« .'11! 
 
 1 9 ; • 
 
 S : : 
 
 
 
 ppoo • • 
 
 ©Otnoo • • 
 
 SSSS : ; 
 
 99*. • • • 
 
 oo • • ■ ■ 
 ■*» > > 1 '. ■'. '. 
 £2 • ■ • 
 
 9 •• 
 
 
 1 
 
 pppp • • 
 
 pppp • • 
 
 999 • ■ • 
 
 pp . . . . 
 
 © • • 
 
 oo . : 
 
 
 a 
 
 2 
 
 fci ) in a T CO T a 
 
 co\qp»moo 
 
 OOiASSt-scO 
 
 op nO >o •■ CO 
 
 j 00 — >q - ; • • 
 
 tmN- : : 
 
 
 Of^C0«TM»»(S I ©MOT— T I •0<As>OI>.— . 1 «N*mif\ . 
 
 — ^a'co'— ' t*\ t4<6v\vfo6ei o'op'oo'v>«Xt»" ] m'mu-iso'— ' ; 
 -emttn ©t>.ir\*rc*\m ao^-mmfs i a0>O^-<*\««v : 
 
 iri«'o"<s ; ; 
 
 1 
 
 OOOOt'T 1 OOO.0N'O| I OOIsOmN 1 OOfflrsCs • 
 cs^OMtroovO lorn — cor** I eo «n &• t-s >0 >ri >©<scPt^>o ; 
 
 ©p©«A . • 
 
 55 
 
 •2 
 
 OTmq • • 
 
 -mNNO • 
 
 ■*«p>-q«>. • • 
 
 —■■*>o'oo" : 
 
 r^ccr^ • • • 
 
 S'*» : : : 
 
 ts,© • 
 
 39 ; 
 
 
 
 pppoq • • 
 
 <N — — . t 
 
 ooNme • | qqmts 
 — *rat>-o . t^tMsoNO ; ; 
 
 oo© • • • 
 
 ©"i"»<s : : : 
 
 ooi>i ; ; . 
 
 ©T -. 
 
 eo'gj : 
 
 
 "3 
 
 CO 
 
 pppp ; • 
 
 ooopp • 1 pppp • • 
 tn^rO'-oo '. e'd-'is I ; 
 
 OO© • • • 
 
 ©in-* r ; '. 
 
 99 : 
 
 
 1 
 
 i 
 
 s 
 
 i- 
 
 3828,2 
 
 3S28«2 
 
 3 S 2^ . 2 
 
 ^8 2 8^ 2 
 
 £ft£g^3 
 
 jjs 
 
 y 
 
 * 
 
 
 
 
 5 
 
 1 
 
 «~ 
 
 
1246 
 
 THE MACHINE-SHOP. 
 
 will be the same when tid 1 s 1 s = hats??, or for constant durability S2 — 
 
 «l-y/(*r%l + (WCz). 
 
 New 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. 
 
 Material Cut. 
 
 Diam. Depth. Feed £ p *f d Length of 
 cutin. in. f *;.P ei ' Cut. 
 
 H/4 
 11/4 
 U/4 
 
 7/8 
 7/8 
 7/8 
 11/4 
 U/2 
 U/4 
 1x2 
 1x2 
 U/4 
 U/4 
 
 Steel, 2.00 C 
 
 Steel, 0.70 C 
 
 Steel, 0.70 C... 
 
 Steel, 0.40C 
 
 Steel, 0.40 C 
 
 Cast iron 
 
 Cast iron 
 
 Cast iron 
 
 Steel, 0.40 C 
 
 Steel 
 
 Nickel steel 
 
 Steel casting, 0.45 C. 
 Steel, 0.60 C 
 
 4 
 
 4 
 5 ft. 
 5 ft. 
 5 ft. 
 53/ 8 in. 
 93/ 4 in. 
 31/2 in. 
 20 in. 
 71/2 in. 
 
 V4 
 3/16 
 1/8 
 1/8 
 V8to3/ 16 
 
 5 /l6 
 
 1/8 
 V8 
 3 /8 
 1/2 
 
 m 
 
 9 /64 
 
 Vl6 
 
 Vl6 
 Vl6 
 Vl6 
 1/32 
 VlO 
 V32 
 1/8 ■ 
 
 Vio 
 
 1/8 
 0.072 
 1/8 
 1/26 
 
 43/ 4 in.* 
 13 in.t 
 
 87/ 8 in. 
 28 ins., t 
 28 ins., § 
 
 41/2 ins. 
 
 6 ins. 
 
 8 ins. 
 54 ins. 
 72 ins. 
 124 ins. 
 15 to 20 min.|| 
 18 in. 
 
 * Then 1 3/4 in. at 50 ft. per min. t Then 1 1/8 in. at 65 ft. per min. 
 t 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 Vs in. feed. 
 
 The following results were obtained in drilling: 
 
 Drill 
 size. 
 
 Material. 
 
 Rev. 
 per 
 min. 
 
 Feed 
 
 per 
 
 rev. 
 
 Speed 
 per 
 min. 
 
 Drilled without Re- 
 grinding. 
 
 3/4 in. 
 3/4 
 3/4 
 13/16 
 
 Close cast iron 
 
 Steel, 0.25 C 
 
 466 
 
 247 
 526 
 400 
 
 0.018 
 0.011 
 
 8 1/2 in. 
 
 6 in. 
 
 31/2 
 
 70 holes, 3 ins. deep. 
 60 holes, 23/4 ins. deep. 
 12 holes, 21/2 ins. deep. 
 14 in. at one operation. 
 
 
 Steel 
 
 
 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. 
 
 Use of a Magnet to Determine the Hardening Temperature. 
 (Catalogue of Firth-Sterling Steel Co.) — At the proper hardening heat a 
 piece of regular tool steel loses its power to attract a magnet. By touch- 
 ing a magnet against the tool as it heats up in the furnace, the magnet 
 will take hold until the proper heat for quenching is reached, and then it 
 will not take hold at any point. This determines the lowest heat at which 
 it can be hardened. 
 
 By heating slowly, trying with a magnet frequently, and dipping the 
 tool when the magnet will not take hold, an extremely hard tool will be 
 secured and one which will do excellent work. The magnet should not 
 be allowed to become heated. In order to guard against the loss of 
 magnetism in a horseshoe magnet an electro-magnet may be made by 
 passing an electric current through a coil of wire wound on an iron rod. 
 
 CASE-HARDENING, 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 
 
MILLING CUTTERS. 1247 
 
 the metal, converting it into high carbon steel. The depth of penetra- 
 tion and the percentage of carbon absorbed increase with the temperature 
 and with the length of time allowed for the process. In the old cementa- 
 tion 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 for a considerable time, 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 V64 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 cooled 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/g 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. The distortion 
 is more important than the increase in bulk. 
 
 MILLING CUTTERS. 
 
 George Addy (Proc. Inst. M. E., Oct., 1890, p. 537) gives the following: 
 Analyses of Steel. — The following are analyses of milling cutter 
 blanks, made from best quality crucible cast steel and from self-harden- 
 ing "Ivanhoe" steel: 
 
 C Si P 
 
 Crucible Steel, 1.2 0.112 0.018 
 Ivanhoe Steel, 1.67 0.252 0.051 
 
 The first analysis is of a cutter 14 in. diam., 1 in. wide, which gave 
 very good service at a cutting-speed of 60 ft. per min. Large milling 
 cutters are sometimes built up, the cutting-edges only being of tool steel. 
 A cutter 22 in. diam. by 5 1/2 in. wide has been made in this way, the teeth 
 being clamped between two cast-iron flanges. Mr. Addy recommends 
 for this form of tooth one with a cutting-angle of 70°, the face of the 
 tooth being set 10° back of a radial line on the cutter, the clearance-angle 
 being thus 10°. At the Clarence Iron Works, Leeds, the face of the tooth 
 is set 10° back of the radial line for cutting wrought iron and 20° for steel. 
 
 Pitch of Teeth. — For obtaining a suitable pitch of teeth for 
 milling-cutters of various diameters there exists no standard rule, the 
 pitch being usually decided in an arbitrary manner according to individual 
 taste. For estimating the pitch of teeth in a cutter of any diameter from 
 4 in. to 15 in., Mr. Addy has worked out the following rule, which he has 
 found capable of givin g good results in pra ctice: 
 
 Pitch in inches = \/(diam. in inches X 8) X 0.0625 = 0.177 Vdiam. 
 
 J. M. Gray gives a rule for pitch as follows: The number of teeth in a 
 milling cutter ought to be 100 times the pitch in inches; that is, if there 
 were 27 teeth, the pitch ought to be 0.27 in. The rules are practically 
 
 Mn S Tungsten c 
 
 iron, D] 
 ifferenc 
 
 0.36 0.02 
 
 2.56 0.01 4.65 
 
 98.29 
 90.81 
 
1248 
 
 THE MACHINE-SHOP. 
 
 the same, for if d ■ 
 f erence, c = pn; d ■ 
 
 diam., 
 pn _ 
 
 n = no. of teeth, p = pitch, c = circum- 
 ^^ = 31.83p 2 ; p=Vo.0314d = 0.177 Vd; 
 
 No. of teeth, n. = 3.14d ^- p. 
 
 Teeth of Plain or Spiral Milling Cutters. (Mach'y, April, 1907.) — 
 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. 
 No. of teeth = 5X diam ' + 24 ; Length of Spiral = 9 X diam. + 4. 
 
 Diameter of cutter, 
 
 2 21/4-21/2 23/4 3 3V 3 4 41/2 5 ,51/ 2 6 61/ 2 7 7l/ 2 8 
 Number of teeth, 
 
 16 18 18 18 20 20 22 24 24 26 26 28 30 30 32 
 Length oT one turn of spiral, inches, 
 
 22 241/4 261/2 283/ 4 31 35i/ 2 40 441/2 49 53l/ 2 58 62l/ 2 67 71 1/ 2 76. 
 
 A cutter with an 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°. 
 
 Nicked Cutters. — -Cutters for milling broad surfaces, whether of the 
 spiral or straight type, usually have nicks cut in the teeth, the nicks 
 being staggered in consecutive teeth. These afford relief from jam- 
 ming the teeth with chips. 
 
 Side Milling Cutters. (Mach'y, April, 1907.) — 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. 
 Diam. of cutter, 
 
 2 21/4 21/2 23/4 3 3V 2 4 4i/ 2 5 5i/ 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 
 
 Milling Cutters with Inserted Teeth. — When it is required to use 
 milling cutters of a greater diameter than about 8 in., 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 hardening them, but also on account 
 of the difficulty in obtaining a uniform degree of hardness or temper. 
 
 Keyways in 31illing Cutters. — A number of manufacturers have 
 adopted the keyways shown below, as standards. The dimensions in 
 inches are given in the tables. 
 
 Fig. 190.— Square Key way. 
 
 Diam. 
 Hole, 
 
 3/8-9/16 
 
 5/8-7/8 
 
 15/16-1 1/8 
 
 13/16-13/s 
 
 1 7/16-1 3/4 
 
 1 13/16-2 
 
 2 V16-2 1/2 
 
 29/16-3 
 
 Width 
 W 
 
 3 /32 
 
 1/8 
 
 5/32 
 
 3/16 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/16 
 
 Depth, 
 D 
 
 3/64 
 
 1/16 
 
 5/64 
 
 3/32 
 
 1/8 
 
 5/32 
 
 3/16 
 
 3 /l6 
 
 Radius, 
 R 
 
 0.020 
 
 0.030 
 
 0.035 
 
 0.040 
 
 0.050 
 
 0.060 
 
 0.060 
 
 0.060 
 
MILLING CUTTERS 
 
 1249 
 
 
 
 Fig. 191. — Half-round Keyway 
 
 
 
 Diam. 
 Hole, H 
 
 3/8-5/8 
 
 H/16-13/16 
 
 7/8-1 3/16 
 
 1 1/4-1 7/ 16 
 
 1 1/2-2 
 
 21/l6-2 7/i 6 
 
 2 1/2-3 
 
 Width 
 W 
 
 1/8 
 
 3/16 
 
 1/4 
 
 5 /l6 
 
 3/8 
 
 7/16 
 
 1/2 
 
 Depth, 
 D 
 
 Vie 
 
 3/32 
 
 1/8 
 
 5 /32 
 
 3/16 
 
 7/32 
 
 1/4 
 
 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, arid 
 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. 
 
 *s 
 
 Feed. 
 
 u . 
 
 
 
 
 
 
 a 
 
 
 
 
 
 
 73 
 
 
 T3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0) 
 
 
 O <d' 
 
 A 
 
 J3 
 
 3 
 
 CD 
 
 '3 ^ 
 
 <3 o> 
 
 c 
 
 3 
 C 
 
 fi 
 
 la 
 
 a 
 6 
 
 3 
 
 o 
 
 
 a . 
 cu 2 
 
 gP-4 
 
 erg 
 
 fSfM 
 
 §0 
 
 § 
 
 3 
 
 a 
 
 -a 
 
 o 
 
 "Shh 
 
 o a ' 
 
 £ 
 
 Oh 
 
 £ 
 
 o 
 
 Q 
 
 $ 
 
 w 
 
 § 
 
 w 
 
 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 
 
 Extreme Results with Milling Machines. — Horace L. Arnold (Am. 
 Mach., Dec. 28, 1893) gives the following results in flat-surface milling, 
 obtained in a Pratt & Whitney milling machine: The mills for the flat 
 cut were 5 in. diam., 12 teeth, r 40 to 50 r.p.m. and 47/g in. feed per min. 
 One single cut was run over this piece at a feed of 9 in. per min., but 
 the mills showed plainly at the end that this rate was greater than they 
 could endure. At 50 r.p.m. for these mills the figures are as follows, with 
 47/ 8 in. feed: Surface speed, 64 ft., nearly; feed per tooth, 0.00812 in.; 
 cuts per in., 123. And with 9-in. feed per min.: Surface speed, 64 ft. 
 per min.; feed per tooth, 0.015 in.; cuts per in., 662/3. 
 
1250 THE MACHINE-SHOP. 
 
 At a feed of 47/g in. per min., the mills stood up well in this job of 
 cast-iron surfacing, while with a 9-in. feed they required grinding after 
 surfacing one piece; in other words, it did not damage the mill-teeth to 
 do this job with 123 cuts per in. of surface finished, but they would not 
 endure 662/3 cuts per in. In this cast-iron milling the surface speed 
 of the mills does not seem to be the factor of mill destruction; it is 
 the increase of feed per tooth that prohibits increased production of 
 finished surface. This is precisely the reverse of the action of single- 
 pointed lathe and planer tools in general; with such tools there is a sur- 
 face-speed limit which cannot be economically exceeded for dry cuts, 
 and so long as this surface-speed limit is not reached, the cut per tooth 
 or feed can be made anything up to the limit of the driving power of the 
 lathe or planer, or to the safe strain on the work itself, which can in many 
 cases be easily broken by a too great feed. 
 
 In wrought metal extreme figures were obtained in one experiment 
 made in cutting keyways 5/ 16 in. wide by Vs in. deep in a bank of 
 8 shafts 1 1/4 in. diam. at once, on a Pratt & Whitney, No. 3 column 
 milling machine. The 8 mills were successfully operated with 45-ft. 
 surface speed and 19 1/2 in. per min. feed; the cutters were 5-in. diam., 
 with 28 teeth, giving the following figures, in steel: Surface speed, 45 
 ft. per minute; feed per tooth, 0.02024 in.; cuts per inch, 50, nearly. 
 Fed with the revolution of mill. Flooded with oil, that is, a large 
 stream of oil running constantly over each mill. Face of tooth radial. 
 The resulting keyway was described as having a heavy wave or cutter- 
 mark in the bottom, and it was said to have shown no signs of 
 being heavy work on the cutters or on the machine. As a result of the 
 experiment it was decided for economical steady work to run at 17 r.p.m., 
 with a feed of 4 in. per min., flooded cut, work fed with mill revolution, 
 giving the following figures: Surface speed, 221/4 ft. per min.; feed per 
 tooth, 0.0084 in.; cuts per in., 119. 
 
 The Cincinnati Milling Machine Co. (1906) gives the following exam- 
 ples of rapid milling machine work: Gray iron castings 10 1/4 in. wide, 
 14 in. long X l 3 /4 in. thick, finished all over, and a slot 5/ 8 x 1 in. cut 
 from the solid. A gang of five cutters was used, two of 8 in., two of 
 31/2 in. and one of 53/ 4 in. diameter, respectively. These took a cut 
 3/is in. deep across the top and two edges, and milled the slot in one 
 operation. The table travel was 4.2 in. per minute. The average time, 
 including chucking, was 15.6 minutes. 
 
 Gray iron castings 3 in. and 6V2 in. wide X 251/4 in. long, 11/4 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 1/2-in. part. 
 The total time for finishing, including chucking, was seven minutes. The 
 planer required 23 minutes for the same operation. In finishing the 
 opposite side of these castings, two castings are milled at one setting, 
 s/16 in. of stock being removed all over and two slots 5/ 8 x 5 /s 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 revolutions per minute 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 milling 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, Vs 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 inches and the time required ■ 
 6 1/2 minutes. 
 
 The following table summarizes a number of typical jobs of milling: 
 
MILLING CUTTERS 
 
 1251 
 
 Typieal Milling Jobs. 
 
 (Cincinnati Milling Mach. Co.; Brown & Sharpe Mfg. Co., 1907.) 
 
 
 
 Cut, 
 Inches . 
 
 Cutter. 
 
 fl - 
 
 83 
 
 a 
 
 a 
 
 s "»? 
 
 3 
 
 O 
 
 3 
 
 
 
 > 
 
 U 
 
 13 
 > 
 
 83 fl 
 
 -S-2 
 
 o 
 "o 
 
 
 
 _fl 
 
 fl 
 
 ^fl 
 
 0,1 
 
 w. u 
 
 I* 
 
 a> a; 
 «■§ 
 — fl 
 
 3 
 
 
 ft 
 
 6 
 
 g 
 
 
 
 t3 
 
 
 eSrs 
 
 1 
 
 
 Q 
 
 -a 
 
 | 
 
 Q 
 
 > 
 
 
 83 
 83 
 
 3*8 
 
 
 Spline (R) . . . 
 
 Steel .... 
 
 5 /32 
 
 3 /l6 
 
 21/2 
 
 166 
 
 108 
 
 0.05 
 
 8.3 
 
 0.243 
 
 Keyseat (R) . . 
 
 Gray iron . . 
 
 3 /ie 
 
 3 / 8 
 
 2 1/2 
 
 166 
 
 108 
 
 0.108 
 
 17.9 
 
 1.04 
 
 Keyseat (R) . . 
 
 Lumen metal 
 
 1/8 
 
 •Vl« 
 
 2 
 
 211 
 
 110 
 
 0.15 
 
 31.6 
 
 0.74 
 
 Surfacing (F) . 
 
 Brass .... 
 
 0.01 
 
 2 l/o 
 
 31 
 
 100 
 
 78 
 
 0.25 
 
 25.0 
 
 0.675 
 
 Surfacing (F) . 
 
 Tool steel . . 
 
 Vl6 
 
 21/o 
 
 31 
 
 37 
 
 29 
 
 0.05 
 
 1.85 
 
 0.289 
 
 Face Milling (F) 
 
 Gray iron . . 
 
 0.015 
 
 8 
 
 10 
 
 47 
 
 123 
 
 0.30 
 
 \4.\ 
 
 1.692 
 
 Face Milling (R) 
 
 Gray iron . . 
 
 V8 
 
 6 
 
 8 
 
 26 
 
 54 
 
 0.168 
 
 4.36 
 
 3.27 
 
 Surfacing (R) . 
 
 Gray iron . . 
 
 1/8 
 
 21/2 
 
 32 
 
 100 
 
 78 
 
 0.30 
 
 30.0 
 
 9.375 
 
 Surfacing (F) . 
 
 Bronze casting 
 
 1/64 
 
 3 
 
 32 
 
 166 
 
 130 
 
 0.05 
 
 8.3 
 
 0.389 
 
 T-slotting . . . 
 
 Gray iron . . 
 
 See Note 3 
 
 11/16 
 
 252 
 
 75 
 
 0.05 
 
 12.6 
 
 6.693 
 
 Surfacing . . . 
 
 Gray iron . . 
 
 0.10 112 
 
 4.5 4 
 
 45 
 
 52 
 
 0.266 
 
 12. 
 
 14.4 
 
 Surfacing . . . 
 
 Gray iron . . 
 
 1/8 12 
 
 3.5* 
 
 53 
 
 55 
 
 0.226 
 
 12. 
 
 18.0 
 
 Surfacing . . . 
 
 Gray iron . . 
 
 0.20 12 
 
 4 4 
 
 61 
 
 65 
 
 0.148 
 
 9.02 
 
 21.6 
 
 (F) Finishing cut; (R) Roughing cut. 
 
 1 End mill; 2 spiral mill with nicked teeth; work done by peripheral 
 teeth. 3 Both sides of cutter engaged, making slot width equal to 
 cutter diameter; slot Vie* 1/2 inch. * Carbon steel nicked spiral cutter. 
 
 Tests with a Helical Milling Cutter, 3 in. diam., 6 in. long; 8 teeth; 
 pitch of helix, 183/ 4 in.; notched teeth; on cast iron and on mild steel, 
 are reported by P. V. Vernon in Am. Mach., June 3, 1909. The cutter 
 was run at a constant speed, 84 turns per minute, cutting speed 66 ft. 
 per min. In the tests on cast iron the depth of cut was varied from 
 0.14 to 1.10 in., and the feed per min. from 109/ie in. to 127/ 32 in. The 
 material removed per minute ranged from 7.39 to 15.23 cu. in., and the 
 cu. in. per min. per net machine horse-power from 1.06 to 1.52, averaging 
 about 1.30. 
 
 In the tests on steel the depth of cut was 0.10 to 1.10 in. and the feed 
 103/g to 05/g in. per min. ; the material removed per min. from 2.88 to 6.27 
 cu. in. per min. ; and the cu. in. per min. per net H.P. from 0.47 to 0.71, aver- 
 aging about 0.57. No regular relation appears between the rate of feed 
 and the metal removed per min., but the maximum output on cast iron 
 was obtained with a cut 5/ 8 in. deep and a feed of 4"/s in. per min.; and 
 on mild steel with a cut 0.12 in. deep and a feed of 91/2 in. per min. 
 
 Milling "with" or "against" the Feed. — Tests made with the 
 Brown & Sharpe No. 5 milling-machine (described by H. L. Arnold, 
 in Am. Mach. x 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 41/2 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 41/2-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 
 
1252 THE MACHINE-SHOP. 
 
 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 H/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 milling 
 cutters was much greater when they were run in the "old" way. The 
 Brown & Sharpe 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 sidewise and make a crooked slot. 
 
 Modern Milling Practice. (Cincinnati Milling Machine Co., 1907.) — 
 The limit of milling operations is determined by the strength and dura- 
 bility 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 experience, 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 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. 
 The clearance angle should be kept low; about 3 degrees for steel, and not 
 more than 5 degrees for gray iron. 
 
 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 40 20 60 
 
 High speed steel cutters. 
 
 80 80 40 120 
 
 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 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. Keyseating and similar work can be best done with a 
 plain cutter rather than a side mill. 
 
 In general small cutters are preferable to large ones, and the hole 
 should be as small as the strength of the arbor will permit. It is 
 advisable in surface milling to have the cutter wider than the work. 
 
 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 lb. sal soda, 1/2 pint 
 lard oil, 1/2 pint soft soap and water enough to make 10 quarts. 
 
 Milling Machine versus Planer. — For comparative data of work 
 done by each see paper by J. J. Grant, Trans. A. S. M. E., ix, 259. 
 He says: The advantages of the milling machine over the planer are 
 many, among which are the following: Exact duplication of work; 
 rapidity of production — the cutting being continuous; lower cost of 
 
 Eroduction, as several machines can be operated by one workman, and 
 e not a skilled mechanic; and lower cost of tools for producing a given 
 amount of work. 
 
DRILLS. 
 
 1253 
 
 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 -f- (size of drill X 3.1416). 
 Number of revolutions = Constant X speed in feet. 
 Speed in feet = Number of revolutions ■*■ constant. 
 
 Size 
 
 Con- 
 
 Size 
 
 Con- 
 
 Size 
 
 Con- 
 
 Size 
 
 Con- 
 
 Size 
 
 Con- 
 
 Drill. 
 
 stant. 
 
 Drill. 
 
 stant. 
 
 Drill. 
 
 stant. 
 
 Drill. 
 
 stant. 
 
 Drill. 
 
 stant. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 V8 
 
 30.55 
 
 3/4 
 
 5.09 
 
 13/s 
 
 2.78 
 
 2 
 
 1.91 
 
 25/ 8 
 
 1.45 
 
 a /l« 
 
 20.38 
 
 13/lfi 
 
 4.70 
 
 17/16 
 
 2.66 
 
 21/16 
 
 1.85 
 
 2H/16 
 
 1.42 
 
 V4 
 
 15.28 
 
 V* 
 
 4.36 
 
 H/7 
 
 2.55 
 
 21/8 
 
 1.80 
 
 23/4 
 
 1.39 
 
 Wi« 
 
 12.22 
 
 15/16 
 
 4.07 
 
 19/16 
 
 2.44 
 
 23/16 
 
 1.75 
 
 213/ie 
 
 1.36 
 
 3/8 
 
 10.19 
 
 1 
 
 3.82 
 
 15/8 
 
 2.35 
 
 21/4 
 
 1 70 
 
 27/g 
 
 1.33 
 
 7/16 
 
 8.73 
 
 H/1R 
 
 3.59 
 
 1 H/16 
 
 2.26 
 
 25/tfi 
 
 1.65 
 
 215/16 
 
 1.30 
 
 V? 
 
 7.64 
 
 I 1/8 
 
 3.39 
 
 13/ 4 
 
 2.18 
 
 23/ 8 
 
 1.61 
 
 3 
 
 1.27 
 
 9/16 
 
 6.79 
 
 13/1R 
 
 3.22 
 
 1 13/16 
 
 2.11 
 
 27/ie 
 
 1.57 
 
 31/16 
 
 1.25 
 
 5/8 
 
 6.11 
 
 1 1/4 
 
 3.06 
 
 IV/8 
 
 2.04 
 
 21/, 
 
 1.53 
 
 31/8 
 
 1.22 
 
 U/16 
 
 5.56 
 
 10/16 
 
 2.91 
 
 1 15/16 
 
 1.97 
 
 29/16 
 
 1.49 
 
 31/4 
 
 1.18 
 
 Speed of Drills. — The Cleveland Twist Drill Co. (1907) gives the 
 following speeds in r.p.m. for drilling wrought iron, machinery steel or 
 soft tool steel, with high speed and carbon steel drills. 
 
 1, 
 
 
 ■ai 
 
 a 
 
 
 T3 
 
 £ 
 
 h 
 
 frl 
 
 £ 
 
 o • 
 
 
 S3 
 
 o3 ® 
 002 
 
 grc 
 
 S3 
 
 O02 
 
 ftm 
 
 S3 
 
 OM 
 
 Mm 
 
 S3 
 
 OOl 
 
 aft 
 
 1/16 
 
 1834 
 
 3057 
 
 13/16 
 
 141 
 
 235 
 
 19/16 
 
 73.4 
 
 122 
 
 2 5/! 6 
 
 49.5 
 
 82.7 
 
 VS 
 
 917 
 
 1528 
 
 7/8 
 
 131 
 
 218 
 
 I 5/ 8 
 
 70.5 
 
 117 
 
 23/s 
 
 48.2 
 
 80.5 
 
 3/16 
 
 611 
 
 1020 
 
 15/16 
 
 122 
 
 204 
 
 Hl/16 
 
 67.9 
 
 113 
 
 27/ib 
 
 47.0 
 
 78.5 
 
 1/4 
 
 458 
 
 765 
 
 I 
 
 115 
 
 191 
 
 I 3/4 
 
 65.5 
 
 109 
 
 2V ? 
 
 45.8 
 
 76.5 
 
 5/16 
 
 367 
 
 612 
 
 H/16 
 
 108 
 
 180 
 
 U3/16 
 
 63.2 
 
 105.3 
 
 2 9/! fi 
 
 44.7 
 
 74.6 
 
 3/8 
 
 306 
 
 510 
 
 I 1/8 
 
 102 
 
 170 
 
 I 7/8 
 
 61.1 
 
 102 
 
 25/ 8 
 
 43.7 
 
 72.8 
 
 7/16 
 
 262 
 
 437 
 
 13/iR 
 
 96.5 
 
 160 
 
 U5/16 
 
 59.2 
 
 98.7 
 
 2U/16 
 
 42.6 
 
 71.1 
 
 lh 
 
 229 
 
 382 
 
 H/4 
 
 91.8 
 
 153 
 
 2 
 
 57.3 
 
 95.6 
 
 23/4 
 
 41.7 
 
 69.5 
 
 9/16 
 
 204 
 
 340 
 
 15/16 
 
 87.3 
 
 145 
 
 21/16 
 
 55.6 
 
 92.7 
 
 213/i 6 
 
 40.7 
 
 68.0 
 
 5/8 
 
 184 
 
 306 
 
 13/8 
 
 83.3 
 
 139 
 
 21/8 
 
 54.0 
 
 90.0 
 
 27/s 
 
 39.8 
 
 66.5 
 
 H/16 
 
 167 
 
 277 
 
 17/16 
 
 79.8 
 
 133 
 
 23/lfi 
 
 52.4 
 
 87.4 
 
 2 15/ t 6 
 
 39.0 
 
 65.1 
 
 3/4 
 
 153 
 
 255 
 
 H/2 
 
 76.3 
 
 127 
 
 21/4 
 
 51.0 
 
 85.0 
 
 3 
 
 38.2 
 
 63.6 
 
 The feed per revolution recommended for drills smaller than 1/2-in. 
 is from 0.004 to 0.007 in.; and from 0.005 to 0.01 in. for drills larger 
 than 1/2-in. 
 
 High Speed Steel Drills. — The Cleveland Twist Drill Co. says 
 that a high speed steel drill should be started with a peripheral 
 speed between 50 and 60 ft. per minute, and a feed of 0.005 to 0.010 • 
 in. per revolution for drills over 1/2-in. 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. When used in steel or wrought 
 iron, the drill should be flooded with a good lubricant. For brass, paraffine 
 oil is recommended, and for cast iron, an air blast. 
 
 Power Required to Drive High Speed Steel Drills. — The American 
 Tool Works Co. (1907) obtained some remarkable results with drills of 
 high-speed steel as shown in the tables below. The machine used was 
 a triple-geared radial, and the drill was of the " Celfors " type, a flat bar of 
 steel, twisted, affording ease of lubrication, and a free escape for the chips. 
 
1254 
 
 THE MACHINE-SHOP. 
 
 Power Required to Drill Steel with High Speed Steel Drills. 
 
 Size of 
 Drill. 
 
 R.P.M. 
 
 Cutting 
 Speed, 
 
 Feeds. 
 
 H.P. Re- 
 
 
 
 quired. 
 
 Inches. 
 
 
 Ft. per Min- 
 
 In. per Rev. 
 
 In. per Min. 
 
 9/16 
 
 356 
 
 52.3 
 
 .012 
 
 4.27 
 
 4.2 
 
 3/ 4 
 
 313 
 
 61.5 
 
 .012 
 
 3.75 
 
 10.8 
 
 U/32 
 
 188 
 
 50.9 
 
 .024 
 
 4.51 
 
 9.0 
 
 15/32 
 
 188 
 
 56.9 
 
 .024 
 
 4.51 
 
 9.3 
 
 1 23/3 2 
 
 128 
 
 57.6 
 
 .024 
 
 3.07 
 
 8.4 
 
 1 31/32 
 
 167 
 
 86.2 
 
 .012 
 
 2.00 
 
 7.8 
 
 Power Required to Drill Cast Iron 3 in. thick with High Speed 
 Steel Drill. 
 
 Size of 
 
 
 Cutting 
 
 Feeds. 
 
 
 Drill, 
 
 R.P.M. 
 
 Speed, 
 
 
 
 H.P. 
 
 
 
 Inches. 
 
 
 Ft. per Mm. 
 
 In. per Rev. 
 
 In. per Min. 
 
 
 1 1/32 
 
 313 
 
 84.5 
 
 .046 
 
 14.4 
 
 13.2 
 
 17/32 
 
 313 
 
 99.8 
 
 .046 
 
 14.4 
 
 15.3 
 
 1 15/32 
 
 216 
 
 83.1 
 
 .033 
 
 7.1 
 
 12.6 
 
 1 23/3 2 
 
 216 
 
 97.0 
 
 .033 
 
 7.1 
 
 16.8 
 
 1 31/32 
 
 128 
 
 66.0 
 
 .033 
 
 4.22 
 
 15.6 
 
 31/2 
 
 60 
 
 55.0 
 
 .024 
 
 1.44 
 
 10.2 
 
 Extreme Results with Radial Drills. (F. E. Bocorselski, Am. 
 Mach., Mar. 17, 1910.) — Three different radial drilling machines, de- 
 signed to drive high-speed steel drills of the twisted type to the limit 
 of their endurance, were tested by drilling steel billets of about 0.70 
 carbon at speeds and feeds which caused the drills to break after drill- 
 ing holes from 2 to 1 1 ins. deep. The following are a few of the results 
 obtained with different sizes of drill. 
 
 Drill 
 
 Revs, 
 per 
 min. 
 
 Cutting 
 speed, 
 ft. per 
 min. 
 
 Feed. 
 
 Metal removed. 
 
 Max. 
 H.P. 
 
 H.P. 
 
 per lb. 
 
 per 
 
 min. 
 
 size, 
 ins. 
 
 Per rev. 
 in. 
 
 Ins. per 
 min. 
 
 Cu. ins. 
 per min. 
 
 Lbs. per 
 min. 
 
 11/2 
 
 H/2 
 U/4 
 H/8 
 H/16 
 
 290 
 312 
 330 
 208 
 330 
 
 113 
 123 
 107 
 61.3 
 91 
 
 0.0207 
 0.0323 
 0.0207 
 0.022 
 0.0207 
 
 6 
 
 10.08 
 6.83 
 4.58 
 6.83 
 
 10.56 
 17.23 
 8.33 
 4.54 
 6. 
 
 2.95 
 4.97 
 2.33 J 
 1.27 
 1.68 
 
 25 
 
 56.0 
 
 24.8 
 
 22.6 
 
 24.8 
 
 8.48 
 11.4 
 10.6 
 17.8 
 14.8 
 
 The H.P. of one of the machines running light at full speed was 4.4; 
 running light at slow speed 2 H.P. 
 
 It was concluded from these tests, which were destructive to the 
 drills, that for maximum production and considering the life of the drills, 
 it is best to run a 1-in. drill at about 300 r.p.m. with a feed of 0.015 in. 
 per rev., and a 11/2-in. drill 225 r.p.m. with a feed of 0.02 in. per revolu- 
 tion, 
 
 Some Data on High-Speed Drilling are given by G. E. Hallenbeck 
 in Iron Tr. Rev., April 29, 1909. A Baker high-speed drilling machine 
 was used. Holes lVsin. diam. were drilled through 41/4-in. blocks of 
 cast iron in 82/3 seconds per hole, or at the rate of 29 in. per min. Holes 
 15/ie in- diam. were drilled through 3/ 4 in. steel plate in 31/2 seconds. 
 
 Experiments on Twist Drills. — An extensive series of experiments 
 on the forces acting on twist drills of high-speed steel when operating 
 
DRILLS. 
 
 1255 
 
 on cast-iron and steel is reported by Dempster Smith and A. Poliakoff, in 
 Proc. Inst. M. E., 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, / =(1800 1 + 9)d 2 , for medium cast-iron; 
 T = (3200 4 + 20) J 2 , for medium steel. End thrust, lbs., P = 115,000 
 t — 200, for medium cast-iron; P = 160,000(d - 0.5)4 +• 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 11/2 in., 
 P = 25,500 4 +; 3/4 in. to ll/ 2 in., P = 30,000 4 + 200. 
 
 A second series of experiments, with soft cast-iron of C.C., 0.2; G.C., 
 2.9; Si, 1.41; Mn, 0.68; S, 0.035; P, 1.48, and medium steel of C, 0.31; 
 Si, 0.07; Mn, 0.50; S, 0.018; P, 0.033: tensile strength, 72,600 lbs. per 
 sq. in., gave results from which were derived the following approximate, 
 equations: 
 
 Torque, lbs.-ft./ T = 740 d^t ' 7 , or Wd 2 + 100 4(14 d 2 + 3) for cast-iron, 
 T = 1640 di*8fo.7 f or 28 d 2 (l + 100 4) for medium steel, 
 
 End thrust, lbs. P = 35,500 d°-7 4°- 75 , or 200 d+ 10,000 t for cast iron, 
 P = 35,500 d°-U°- 6 , or 750 d + 1000 4(75 d + 50) for 
 medium steel, 
 
 and for different sizes of drill the following equations: 
 
 Drill. 
 
 3/ 4 
 
 1 
 
 M/2 
 
 
 5+ 1,100* 
 125 + 82,000 * 
 7.5+3,350* 
 550+ 109,000 * 
 
 10+1,750* 
 200 + 89,000* 
 17.5 + 4,400* 
 750+131,000* 
 
 25+3,700 * 
 350+103,000* 
 
 
 Steel T = 
 
 40 + 9,000 * 
 
 Steel P = 
 
 1,250+162,000* 
 
 
 
 
 Drill. 
 
 2 
 
 21/2 
 
 3 
 
 
 40+ 580 * 
 
 500+110,000* 
 
 75+12,500* 
 
 1,500+181,250* 
 
 60 + 8,800* 
 600+126,000* 
 112.5+19,050* 
 1,725 + 224,375* 
 
 90+12,900* 
 
 Cast ironP = 
 
 850+140,000* 
 
 Steel T - 
 
 175 + 26,250* 
 
 Steel P = 
 
 2,350+280,000* 
 
 
 
 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 feed. The horse- 
 power varies as t ' 7 and as d°- 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 d 0-2 4 ' 3 , 
 and is independent of the revolutions. 
 
 While the chisel point of the drill scarcely affects the torque it is account- 
 able 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. 
 
 Taking the average recommended speed of 48 ft. per minute for cast 
 iron and 60 ft. for mild steel, and the results obtained in these tests, the 
 figures given in the following table are derived. 
 
1256 
 
 THE MACHINE-SHOP. 
 
 Revolutions per Minute, Feed per Revolution, Cubic Inches Re- 
 moved per Minute, and Horse-power when Drilling Soft 
 Cast-iron and Medium Hard Steel. 
 
 Soft Cast Iron. 
 
 Medium Hard Steel. 
 
 
 
 u '£ 
 
 &.S 
 
 0> 
 
 
 . 
 
 ^ftl 
 
 u 
 
 & a 
 
 
 fiici 
 
 T3 
 
 goo X 
 
 Cl o>-- 
 
 •S.2 ^ 
 
 .S3 « 
 
 if 5 
 
 .2 > 
 
 ■° 2 
 
 o 
 
 o 
 
 il 
 
 -5 
 
 •H.3 ii 
 
 2 a °°- 
 
 .S-d - 
 
 .2 > 
 
 -° 2 
 
 O 
 ft 
 h 
 
 o 
 A 
 
 o 
 H 
 
 ° ce- o> 
 (-,-£ ft 
 
 ftS is 
 
 Vi 
 
 735 
 
 0.0075 
 
 0.27 
 
 0.295 
 
 1.092 
 
 l /4 
 
 920 
 
 0.0063 
 
 0.284 
 
 0.721 
 
 2.54 
 
 3/8 
 
 490 
 
 0.0086 
 
 0.462 
 
 0.4405 
 
 0.954 
 
 2/8 
 
 614 
 
 0.0072 
 
 0.485 
 
 1.078 
 
 2.22 
 
 V2 
 
 368 
 
 0.0094 
 
 0.682 
 
 0.586 
 
 0.862 
 
 1/2 
 
 460 
 
 0.00795 
 
 0.716 
 
 1.426 
 
 1.99 
 
 ••5/4 
 
 245 
 
 0.0109 
 
 1.17 
 
 0.8766 
 
 0.748 
 
 3 /4 
 
 306 
 
 0.0091 
 
 1.23 
 
 2.152 
 
 1.75 
 
 1 
 
 184 
 
 0.0119 
 
 1.715 
 
 1.167 
 
 0.681 
 
 1 
 
 230 
 
 0.01 
 
 1.8 
 
 2.863 
 
 1.59 
 
 H/4 
 
 147 
 
 0.0129 
 
 2.32 
 
 1.457 
 
 0.628 
 
 M/ 
 
 184 
 
 0.0108 
 
 2.44 
 
 3.574 
 
 1.47 
 
 n/2 
 
 122 
 
 0.0136 
 
 2.92 
 
 1.748 
 
 0.598 
 
 I 1 / 
 
 153 
 
 0.0114 
 
 3.08 
 
 4.285 
 
 1.39 
 
 1 3/4 
 
 105 
 
 0.0144 
 
 3.63 
 
 2.038 
 
 0.563 
 
 13/ 
 
 131 
 
 0.0121 
 
 3.81 
 
 5.005 
 
 1.31 
 
 2 
 
 92 
 
 0.015 
 
 4.32 
 
 2.328 
 
 0.539 
 
 2 
 
 115 
 
 0.0126 
 
 4.54 
 
 5.715 
 
 1.26 
 
 21/4 
 
 81.7 
 
 0.0156 
 
 5.05 
 
 2.619 
 
 0.519 
 
 21/4 
 
 102 
 
 0.0131 
 
 5.3 
 
 6.436 
 
 1.21 
 
 2i/ 2 
 
 73.5 
 
 0.0162 
 
 5.82 
 
 2.909 
 
 0.500 
 
 21/2 
 
 92 
 
 0.0136 
 
 6.12 
 
 7.136 
 
 1.165 
 
 23/4 
 
 66.75 
 
 0.0167 
 
 6.6 
 
 3.199 
 
 0.486 
 
 23/4 
 
 83.5 
 
 0.014 
 
 6.92 
 
 7.857 
 
 1.135 
 
 3 
 
 61.3 
 
 0.0172 
 
 7.4 
 
 3.489 
 
 0.472 
 
 3 
 
 76.5 
 
 0.0144 
 
 7.76 
 
 8.567 
 
 1.105 
 
 31/4 
 
 56.5 
 
 0.0176 
 
 8.22 
 
 3.78 
 
 0.46 
 
 31/ 4 
 
 70.5 
 
 0.0148 
 
 8.66 
 
 9.267 
 
 1.07 
 
 3l/ 2 
 
 52.5 
 
 0.0181 
 
 9.05 
 
 4.07 
 
 0.45 
 
 31/2 
 
 65.6 
 
 0.0151 
 
 9.5 
 
 9.998 
 
 1.05 
 
 33/4 
 
 49 
 
 0.0185 
 
 10.0 
 
 4.36 
 
 0.436 
 
 33/4 
 
 61.25 
 
 0.0155 
 
 10.48 
 
 10.718 
 
 1.024 
 
 4 
 
 46 
 
 0.019 
 
 10.8 
 
 4.65 
 
 0.431 
 
 4 
 
 57.5 
 
 0.0158 
 
 11.4 
 
 11.42 
 
 1.0 
 
 POWER REQUIRED FOR MACHINE TOOLS. 
 
 Resistance Overcome in Cutting Metal. (Trans. A. S. M. E., 
 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 the sharpness of the tool used. If the cut is 
 nearly square in section, the power required is a minimum; if wide and 
 thin, ia maximum. The dullness of a tool affects but little the power 
 required for a heavy cut. 
 
 Heavy Work on a Planer. — Wm. Sellers & Co. write as follows 
 to the American Machinist: The 120-inch planer table is geared to run 
 18 feet per minute under cut, and 72 feet per minute on the return, 
 which is equivalent, without allowance for time lost in reversing, to con- 
 tinuous cut of 14.4 feet per minute. Assuming the work to be 28 feet 
 long, we may take 14 feet as the continuous cutting speed per minute, 
 the 0.8 of a foot being much more than sufficient to cover time loss in 
 reversing and feeding. The machine carries four tools. At Vs inch feed 
 per tool, the surface planed per hour would be 35 square feet. The sec- 
 tion of metal cut at 3/ 4 inch depth would be 0.75 inch X 0.125 inches X 4 = 
 0.375 square inch, which would require approximately 30,000 pounds 
 pressure to remove it. The weight of metal removed per hour would be 
 14X12X0.375X0.26 X 60 = 1082.8 lb. Our earlier form of 36 in. planer 
 has removed with one tool on 3/ 4 in. cut on work 200 lb. of metal Der hour, 
 and. the 120 in. machine has more than five times its capacity. The total 
 pulling power of the planer is 45,000 lb. 
 
 Horse-power Required to Run Eathes. — The power required 
 to 4o useful work varies with the depth and breadth of chip, with the 
 
POWER REQUIRED FOR MACHINE TOOLS. 1257 
 
 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. 
 
 Hartig's investigations show that it requires less total power to turn 
 off a given weight of metal in a given time than it does to plane off the 
 same amount; and also that the power is less for large than for small 
 diameters. (J. J. Flather, Am. Mach., April 23, 1891.) 
 
 Horse-power Required to Remove Metal in Lathes. 
 
 (Lodge & Shipley Mach. Tool Co., 1906.) 
 20-Inch Cone-Head Lathe. 
 
 
 Cutting 
 Speed, 
 ft. per 
 
 Cut, In. 
 
 Diam. 
 
 Cu. in. 
 
 Lb. 
 
 H.P. used 
 by Lathe. 
 
 Cu.in. 
 
 
 
 of 
 work, 
 
 remov- 
 ed per 
 
 remov- 
 ed per 
 
 
 
 
 Cut. 
 
 
 
 
 
 ed per 
 
 
 nun. 
 
 Depth. 
 
 Feed. 
 
 in. 
 
 nun. 
 
 hour. 
 
 Idle. 
 
 With 
 Cut. 
 
 H.P. 
 
 Crucible 
 
 C 35 
 
 0.109 
 
 1/8 
 
 227/3 2 
 
 5.74 
 
 96 
 
 0.48 
 
 3.90 
 
 1.471 
 
 Steel 
 
 ) 65 
 
 0.055 
 
 1/8 
 
 35/ 8 
 
 5.33 
 
 90 
 
 0.74 
 
 4.60 
 
 1.158 
 
 0.60 
 
 ) 62.5 
 
 0.109 
 
 Vlfi 
 
 3 5/ie 
 
 5.125 
 
 86 
 
 0.49 
 
 4.65 
 
 1.102 
 
 Carbon 
 
 ( 32.5 
 
 0.094 
 
 VlO 
 
 35/ie 
 
 3.656 
 
 62 
 
 0.49 
 
 2.64 
 
 1.384 
 
 
 ( 62.5 
 
 0.273 
 
 Vn 
 
 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 
 
 
 C 115 
 
 0.086 
 
 1/12 
 
 155/64 
 
 9.88 
 
 153 
 
 0.21 
 
 2.54 
 
 3.889 
 
 Open- 
 hearth 
 Steel 
 0.30 
 
 Carbon 
 
 ( 50 
 
 0.109 
 
 1/8 
 
 223/32 
 
 8.2 
 
 138 
 
 0.69 
 
 5.34 
 
 1.535 
 
 ) 45 
 
 0.117 
 
 1/8 
 
 21/2 
 
 7.91 
 
 134 
 
 0.53 
 
 5.11 
 
 1.547 
 
 ) 45 
 
 0.217 
 
 Vl9 
 
 217/64 
 
 6.439 
 
 109 
 
 0.69 
 
 4.10 
 
 1.570 
 
 t 32.5 
 
 0.109 
 
 1/8 
 
 223/64 
 
 5.33 
 
 90 
 
 0.36 
 
 4.04 
 
 1.319 
 
 Average H.P. running idle 0.53; average H.P. with cut 4.25. 
 20-Inch Geared-Head Lathe, 
 
 
 
 
 
 
 
 H.P. used 
 
 
 
 Cutting 
 
 Cut, in. 
 
 Diam. 
 
 Cu. in. 
 
 Lb. 
 
 by Lathe. 
 
 Cu. in. 
 
 
 Speed, 
 ft. per 
 
 
 of 
 work 
 
 remov- 
 ed per 
 
 remov- 
 ed per 
 
 
 
 Cut. 
 
 
 
 
 
 ed per 
 H.P. 
 
 
 min. 
 
 Depth. 
 
 Reed. 
 
 in. 
 
 mm. 
 
 hour. 
 
 Idle. 
 
 With 
 Cut. 
 
 0.50 
 
 ( 40 
 
 0.266 
 
 VlO 
 
 227/32 
 
 12.75 
 
 215 
 
 2.11 
 
 11.1 
 
 1.142 
 
 Carbon 
 
 \ 50 
 
 0.281 
 
 1/15 
 
 227/32 
 
 11.25 
 
 190 
 
 1.58 
 
 8.35 
 
 1.347 
 
 Crucible 
 
 ) 75 
 
 0.281 
 
 1/15 
 
 227/32 
 
 16.87 
 
 285 
 
 1.58 
 
 12.69 
 
 1.329 
 
 Steel. 
 
 ( 85 
 
 0.109 
 
 Vl5 
 
 2 1/4 
 
 7.43 
 
 126 
 
 1.28 
 
 8.98 
 
 0.827 
 
 
 ( 45 
 
 0.609 
 
 Vl6 
 
 721/32 
 
 20 57 
 
 320 
 
 1.34 
 
 694 
 
 2.963 
 
 Cast 
 
 ) 62.5 
 
 0.609 
 
 Vl6 
 
 721/32 
 
 28.56 
 
 445 
 
 1.35 
 
 9.50 
 
 3.006 
 
 Iron 
 
 ) 85 
 
 0.641 
 
 1/16 
 
 721/32 
 
 40.82 
 
 636 
 
 1.64 
 
 12.69 
 
 3.216 
 
 
 ( 80 
 
 0.281 
 
 1/8 
 
 3 3/ 3 2 
 
 33.75 
 
 526 
 
 1.18 
 
 10.49 
 
 3.217 
 
 Open- 
 hearth 
 Steel 
 0.15 
 
 Carbon 
 
 ( 125 
 
 0.250 
 
 V->8 
 
 421/32 
 
 13.4 
 
 226 
 
 1.62 
 
 10.60 
 
 1.265 
 
 ) 105 
 
 0.188 
 
 Vl2 
 
 4 5/32 
 
 19.68 
 
 33? 
 
 0.94 
 
 11.56 
 
 1.702 
 
 ) 40 
 
 0.172 
 
 1/6 
 
 327/32 
 
 13.75 
 
 232 
 
 1.75 
 
 12.49 
 
 1.100 
 
 ( 180 
 
 0.094 
 
 1/16 
 
 3 Vie 
 
 12.65 
 
 213 
 
 2.15 
 
 11.20 
 
 1.129 
 
 Average H.P. running idle 1.543; average H.P. with cut 10.55. 
 
1258 
 
 THE MACHINE-SHOP. 
 
 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 (1907) 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 Lodge & Shipley Co. (1906) made an exhaustive series of 
 tests to determine the power required to remove metal, using both the 
 cone-head lathe and the more modern geared-head lathe. The table on 
 page 1257 shows the results obtained with 20-in. lathes of each type. 
 
 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 required. 
 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. 
 
 
 0.035 
 0.067 
 
 0.032 
 
 0.030 
 
 0.14 
 
 
 
 
 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, exclu- 
 sive of friction losses, H.F. = Kw, K being a constant and w the pounds 
 of metal removed per minute. For hard steel K = 2.5; for soft steel 
 K = 1.8; for wrought iron, K = 2.0; for cast iron, if = 1.4. This formula 
 gives results about 50 % lower than Prof. Benjamin's. 
 
 The Westinghouse Elec. and Mfg. Co. (1906) gives a set of formulae 
 based on the dimensions of the machine. 
 
 For Engine Lathes using one cutting tool of water-hardened steel, cutting 
 20 ft. per minute, H.P. = 0.15 S — l?for heavy engine lathes, as forge 
 lathes, H.P. = 0.234 S - 2, S being the swing of the lathe, inches. 
 
 For Boring Mills using one cutting tool of water-hardened steel, cutting 
 20 ft. per min., H.P. = 0.25 S — 4. S = swing of mill, inches. 
 
 For Milling Machines using water-hardened steel cutters at 20 ft. per 
 minute, H.P. =0.3 W. W= distance between housings, inches. 
 
 For Drill Presses using water-hardened steel drills, running at a periph- 
 eral cutting speed of 20 feet per minute, H.P. = 0.06 8. 
 
 For Heavy Radial Drill Presses, H.P. = 0.1 S. 
 
 S = swing of drill, inches, in both cases. 
 
 In general, in all the above Westinghouse formulae, if high-speed steel 
 tools are used, running at higher cutting speeds than above, the increase 
 in horse-power is proportional to the increase in speed. 
 
 Planers. For planers, in which the length of bed in feet is approximately 
 two-tenths of the width between housings in inches, using- water-hardened 
 steel tools, cutting at 15 to 20 ft. per minute, H.P. = 3 W. 
 
 For Heavy Forge Planers, H.P. = 4.92 W. 
 W = width between housings, feet. 
 
 These formulae are for planers having a ratio of return to cutting speeds 
 of about 3:1, and are for planers with two tools in operation. If more 
 than two tools are operated, or if the ratio of cutting and return speeds 
 is increased, or if the length of bed is greater than given above, the horse- 
 power given by the above formulae should be increased. The horse- 
 power required by motor-driven planers is principally determined by the 
 current inrush at the instant of quick reverse, rather than by that actually 
 required to cut the metal. Motors for operating planers should have 
 greater overload capacity than for any other tool. 
 
POWER REQUIRED FOR MACHINE TOOLS. 1259 
 
 
 Horse 
 
 -power 
 
 to Drive Machine Tools. 
 
 
 
 
 Cut, 
 
 Inches. 
 
 C 
 
 
 H.P.Re 
 quired. 
 
 
 
 
 
 
 fg 
 
 
 
 
 
 Is 
 
 
 
 
 1* 
 
 
 J 
 
 £ 
 
 
 ■j 
 
 -6 
 
 ji 
 
 ts& 
 
 £ a 
 
 ] 
 
 - 
 
 
 
 1 
 
 
 
 
 
 -J^ 
 
 
 
 
 o 
 H 
 
 eS 
 8 
 
 4) 
 
 fa 
 
 Q 
 
 Qfa 
 CQ 
 
 £" 
 
 < 
 
 
 
 fa 
 
 1 
 
 72-in. wheel 
 
 Hard steel 
 
 Vl2 
 
 3/16 & 1/4 
 
 13.7 
 
 1.69 
 
 4.5 
 
 4.2 
 
 25 H.P. shunt 
 
 lathe 
 
 
 1/8 
 
 3/16&V4 
 
 11.6 
 
 2.15 
 
 6.4 
 
 5.4 
 
 wound vari- 
 
 
 
 3/16 
 
 /l6& 3 /8 
 
 13.2 
 
 5.55 
 
 8.4 
 
 13.9 
 
 able speed. 
 
 
 
 3/16 
 
 3/8 &3/ 8 
 
 13.2 
 
 6.3 
 
 12.0 
 
 15.7 
 
 
 90-in. whee] 
 
 Hard steel 
 
 3/16 
 
 3/l6& 3 /l6 
 
 13.0 
 
 3.1 
 
 12.0 
 
 7.7 
 
 25 H.P. shunt 
 
 lathe 
 
 
 3/16 
 
 5 /l6& 5 /l6 
 
 8.8 
 
 3.5 
 
 8.1 
 
 8.7 
 
 wound vari- 
 
 
 
 1/5 
 
 1/4 &V4 
 
 15.5 
 
 5.3 
 2.33 
 
 9.0 
 
 13.2 
 
 able speed. 
 
 42-in. lathe 
 
 Soft steel 
 
 Vl6 
 
 1/4 
 
 44 
 
 3.8 
 
 4.2 
 
 15 H.P. shunt 
 
 
 
 Vl6 
 
 1/8 
 
 44 
 
 1.17 
 
 1.7 
 
 1.9 
 
 wound vari- 
 
 
 " " 
 
 Vl6 
 
 1/8 
 
 44 
 
 1.17 
 
 2.6 
 
 1.9 
 
 able speed. 
 
 
 Cast iron 
 
 1/16 
 
 1/8 
 
 108 
 
 2.63 
 
 5.8 
 
 3.7 
 
 
 
 " " 
 
 Vl6 
 
 3/16 
 
 46 
 
 1.74 
 
 2.9 
 
 2.5 
 
 
 
 
 1/16 
 
 3/16 
 
 58 
 
 2.12 
 
 2.2 
 
 3.0 
 
 
 30-in. lathe 
 
 Wro't iron 
 
 1/8 
 
 3/16 
 
 54. 
 
 4.2 
 
 6.6 
 
 8.4 
 
 10 H.P. shunt 
 
 
 
 1/8 
 
 3/16 
 
 42 
 
 3.2 
 
 4.0 
 
 6.4 
 
 wound vari- 
 
 
 Cast iron 
 
 3/32 
 
 5 /32 
 
 42 
 
 1.92 
 
 3.0 
 
 2.7 
 
 able speed. 
 
 
 
 3/32 
 
 Vl6 
 
 61 
 
 1.12 
 
 1.5 
 
 1.6 
 
 
 
 
 1/64 
 
 1/4 
 
 47 
 
 2.30 
 
 2.0 
 
 3.2 
 
 
 Axle lathe 
 
 Soft steel 
 
 3 /l6 
 
 1/4 
 
 27 
 
 4.3 
 
 5.9 
 
 7.7 
 
 35 H.P. sh. w'd 
 
 
 
 1/16 
 
 1/4 
 
 51 
 
 2.7 
 
 5.0 
 
 4.9 
 
 var. speed. 
 
 72-in. boring 
 
 Soft steel 
 
 1/8 
 
 1/16&V32 
 
 44 
 
 1.76 
 
 2.9 
 
 3.2 
 
 25 H.P. shunt 
 
 mill . . 
 
 
 3/16 
 
 I/32&V16 
 
 40 
 
 2.38 
 
 2.6 
 
 4.3 
 
 wound vari- 
 
 
 " " 
 
 1/8 
 
 1/8 &V8 
 
 51 
 
 5.41 
 
 9.6 
 
 9.7 
 
 able speed. 
 
 
 " " 
 
 1/8 
 
 3/16 
 
 47 
 
 3.75 
 
 7.2 
 
 6.8 
 
 
 
 Cast iron 
 
 Vl6 
 
 3/8 
 
 28 
 
 2.05 
 
 2.6 
 
 2.9 
 
 
 
 
 1/16 
 
 1/4 
 
 39 
 
 1.90 
 
 2.7 
 
 2.7 
 
 
 24-in. drill 
 
 Wro't iron 
 
 1/64 
 
 1 l/ 4 to3* 
 
 25.1 
 
 0.81 
 
 2.3 
 
 1.6 
 
 
 press 
 
 " " 
 
 1/64 
 
 1 l/ 4 to 3* 
 
 29.7 
 
 0.96 
 
 2.7 
 
 1.9 
 
 
 
 " " 
 
 1/64 
 
 U/4to3* 
 
 25.9 
 
 0.83 
 
 1.3 
 
 1.7 
 
 
 
 •+ << 
 
 1/64 
 
 11/ 4 drill 
 
 74.5 
 
 0.52 
 
 3.5 
 
 1.0 
 
 
 
 " " 
 
 1/64 
 
 11/4 drill 
 
 20.9 
 
 0.54 
 
 1.2 
 
 1.1 
 
 
 60-in. planer 
 
 Soft steel 
 
 1/6 
 
 1/4 
 
 25.5 
 
 3.62 
 
 5.9 
 
 6.5 
 
 20 H.P. com- 
 
 
 " " 
 
 1/6 
 
 1/4 
 
 25.7 
 
 3.65 
 
 6.5 
 
 6.6 
 
 pound 
 
 
 Wro't iron 
 
 3 /l6 
 
 5/l6& 5 /l6 
 
 23 
 
 8.95 
 
 21.0 
 
 17.9 
 
 wound vari- 
 
 
 
 1/2 
 
 1/32 & 1/32 
 
 17.5 
 
 1.82 
 
 2.7 
 
 3.6 
 
 able speed. 
 
 
 Cast iron 
 
 1/8 
 
 1/8 &Vl6 
 
 22.2 
 
 1.72 
 
 6.5 
 
 3.4 
 
 
 
 
 i/s & Vie 
 
 1/4 &5/16 
 
 30 
 
 4.74 
 
 9.3 
 
 6.6 
 
 
 
 
 1/7 
 
 1/4 &V4 
 
 22.6 
 
 5.03 
 
 7.6 
 
 7.1 
 
 
 
 
 1/4 
 
 7/l6&3/ 8 
 
 28.9 
 
 18.3 
 
 23.2 
 
 25.6 
 
 
 42-in. planer 
 
 Soft steel 
 
 5 /32 
 
 Vs 
 
 24.3 
 
 4.73 
 
 12.1 
 
 9.5 
 
 15 H.P. com- 
 
 
 
 1/8 
 
 Vs 
 
 36 
 
 3.7 
 
 7.8 
 
 11.4 
 
 pound 
 
 
 Cast iron 
 
 3/l6 
 
 3/16 
 
 37 
 
 4.06 
 
 4.7 
 
 5.7 
 
 wound vari- 
 
 
 
 3/16 
 
 L /8 
 
 37 
 
 2.71 
 
 4.1 
 
 3.8 
 
 able speed. 
 
 19-in. slotter 
 
 Hard steel 
 
 V32 
 
 L/4 
 
 30.0 
 
 0.8 
 
 2.0 
 
 2.0 
 
 13 H.P. comp. 
 
 
 Soft steel 
 
 1/32 
 
 V8 
 
 23.3 
 
 0.93 
 
 1.3 1.7 
 
 w'd var. speed. 
 
 * Enlarging hole from smaller dimensions to larger. 
 
1260 
 
 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 in driv- 
 ing under the conditions given in the table on page 1259. The results 
 obtained are compared with those computed by Campbell's formula 
 above. 
 
 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. 
 
 Size of Motors for Machine Tools. (Elec. World, May 27, 1905.) — 
 The average size of motor usually fitted to machine tools is shown by the 
 table below, being compiled by the Electro- Dynamic Co. from published 
 data. In special cases the power required may be several times the 
 value here given. v 
 
 Boring Mills. 
 
 34 and 36 in. . . 
 42, 48 and 50 in. 
 
 H.P. 
 . 5 
 
 . 71/2 
 
 H.P. 
 60 in.. ..... 10 
 
 6 ft. and 7 ft. . . 15 
 
 8 ft 
 
 10 ft 
 
 H.P. 
 . . 20 
 . . 25 
 
 Engine Lathes. 
 
 12 and 14 in. . . 
 
 16 in 
 
 20 to 25 in. . . . 
 
 H.P. 
 . 1 
 
 . H/2 
 . 2 
 
 H.P. 
 20 and 30 in. ... 3 
 36 in 4 
 
 42 and 48 in. ... 5 
 
 54 in 
 
 60 in 
 
 72 in 
 
 H.P. 
 . . 6 
 
 • • 71/2 
 . . 10 
 
 Drill Presses. 
 
 21 to 32 in. . . 
 
 H.P 
 . 2 
 
 1 H.P. 
 1 36 to 48 in. . . . 3 
 
 50 to 60 in. . 
 
 H.P. 
 . . 5 
 
 Planers. 
 
 
 
 H.P. 
 
 
 
 H.P. 
 
 17 X 17in. 
 
 X 3 to 6 ft. . 
 
 . 4 
 
 42 X 42 in. 
 
 X 10 to 12 ft. . 
 
 10 
 
 22 X 24 in. 
 
 X 4 to 10 ft. . 
 
 . 5 
 
 48 X 48 in 
 
 X 12 to 14ft. . 
 
 15 
 
 26 X 26 in 
 
 X 6 to 12 ft. . 
 
 6 
 
 50 X 60 in. 
 
 X 14 to 18 ft. . 
 
 20 
 
 30 X 30 in. 
 
 X 6 to 1 4 ft. . 
 
 . 7i/ 3 
 
 60 X 60 in. 
 
 X 20 to 22 ft. . 
 
 25 
 
 36 X 36 in. 
 
 X 8 to 16 ft. . 
 
 . 71/2 
 
 72 X 72 in. 
 
 X 20 to 24 ft. . 
 
 30 
 
 H.P. I 
 . 5 I 16 and 18 in. 
 
 H.P. I 
 71/21 26 to 36 in. 
 
 H.P. 
 10 
 
 
 
 Shapers. 
 
 
 
 
 12 to 16 in. . 
 18 to 20 in. . 
 
 H.P. 
 . . 2 
 . . 3 
 
 24 to 26 in. . . 
 28 to 30 in. . . 
 
 H.P. 
 . 5 
 . 6 
 
 36 in. . . . 
 
 H.P 
 ... 8 
 
 The values given above for engine lathes are less than those used by 
 the R. K. LeBlond Mach. Tool Co., which recommends (1907) the fol- 
 lowing size motors for use with its lathes. 
 
 Swing of lathe. 
 
 Horse-power of Motor. 
 
 Speed 
 ratio. 
 
 Maximum speed 
 
 in. 
 
 Medium duty. 
 
 Heavy duty. 
 
 range R.P.M. 
 
 12 and 14 
 
 16 
 
 18, 20, 22 
 
 24, 27, 30 
 
 32, 36 
 
 24* 
 
 "l 
 
 3 
 
 5 
 
 71/2 
 15 
 
 2 
 3 
 
 5 
 
 71/2 
 10 
 25 
 
 3 to 1 
 3 to 1 
 3 to 1 
 3 to 1 
 3 to 1 
 2 to 1 
 
 1500 
 1500 
 1500 
 1500 
 1500 
 750-1500 
 
 High Speed Roughing Lathe. 
 
POWER REQUIRED FOR MACHINE TOOLS. 1261 
 
 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 2 i/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%. 
 
 Horse-power consumed in Machine-shops. — How much power 
 is required to drive ordinary machine tools? and how many men 
 can be employed per horse-power? are questions which it is impos- 
 sible to answer by any fixed rule. The power varies greatly according 
 to the conditions in each shop. The following table given by J. J. Flather 
 in his work on Dynamometers gives an idea of the variation in several 
 large works. The percentage of the total power required to drive the 
 shafting varies from 15 to 80, and the number of men employed per total 
 H.P. varies from 0.62 to 6.04. 
 
 Horse- 
 
 power; Friction 
 
 ; Men Employed. 
 
 
 
 
 
 Horse-power. 
 
 
 "3 
 o 
 
 
 
 
 
 CD 
 > 
 
 > 
 
 > 
 
 
 
 Name of Firm. 
 
 Kind 
 
 of 
 Work. 
 
 
 ■a 
 Q 
 
 2bi 
 
 •a 
 
 §6 
 
 ■a 
 
 Q 
 
 3 
 
 a 
 
 
 4> 
 
 a 
 
 
 
 1 
 
 o 
 
 
 '3 § 
 
 a 
 
 <hcX! 
 
 a 
 
 3 
 
 
 0+ 3 
 
 
 
 H 
 
 ti 
 
 « 
 
 PM 
 
 fc 
 
 & 
 
 fc 
 
 Lane & Bodley . . 
 
 E. & W. W. 
 
 58 
 
 
 
 
 132 
 
 2.27 
 
 
 J. A. Fay & Co. . . 
 
 W. W. 
 
 100 
 
 15 
 
 85 
 
 15 
 
 300 
 
 3.00 
 
 3.53 
 
 Union Iron Works . 
 
 E..M.M. 
 
 400 
 
 95 
 
 305 
 
 23 
 
 1600 
 
 4.00 
 
 5.24 
 
 Frontier Iron & Brass 
 
 
 
 
 
 
 
 
 
 Works 
 
 M. E., etc. 
 
 25 
 
 8 
 
 17 
 
 32 
 
 150 
 
 6.00 
 
 8.82 
 
 Taylor Mfg. Co. . . 
 Baldwin Loco. Works 
 
 E. 
 
 95 
 
 
 
 
 230 
 
 2.42 
 
 
 L. 
 
 2500 
 
 2000 
 
 500 
 
 80 
 
 4100 
 
 1.64 
 
 8.20 
 
 W. Sellers & Co. (one 
 
 
 
 
 
 
 
 
 
 department) . . . 
 Pond Mach. Tool Co. 
 
 H.M. 
 
 102 
 
 41 
 
 61 
 
 40 
 
 300 
 
 2.93 
 
 4.87 
 
 M.T. 
 
 180 
 
 75 
 
 105 
 
 41 
 
 432 
 
 2.40 
 
 4.11 
 
 Pratt & Whitney Co. 
 
 
 120 
 
 
 
 
 725 
 
 6.04 
 
 
 Brown & Sharpe Co. 
 
 
 230 
 
 
 
 
 900 
 
 3.91 
 
 
 Yale & Towne Co. . 
 
 C. &L. 
 
 135 
 
 67 
 
 68 
 
 49 
 
 700 
 
 5.11 
 
 10.25 
 
 Ferracute Mach. Co. 
 
 P. &D. 
 
 35 
 
 11 
 
 24 
 
 31 
 
 90 
 
 2.57 
 
 3.75 
 
 T. B. Wood's Sons . 
 
 P. &S. 
 
 12 
 
 
 
 
 30 
 
 2.50 
 
 
 Bridgeport Forge Co. 
 
 H. F. 
 
 150 
 
 75 
 
 75 
 
 50 
 
 130 
 
 0.86 
 
 1.73 
 
 Singer Mfg. Co. . . 
 
 S.M. 
 
 1300 
 
 
 
 
 3500 
 
 2.69 
 
 
 Howe Mfg. Co. . . . 
 
 
 350 
 
 
 
 
 1500 
 
 4.28 
 
 
 Worcester Machine 
 
 
 
 
 
 
 
 
 
 Screw Co 
 
 M.S. 
 
 40 
 
 
 
 
 80 
 
 2.00 
 
 
 Hartford Mach. Screw 
 
 
 
 
 
 
 
 
 
 Company .... 
 
 M.S. 
 
 400 
 
 100 
 
 300 
 
 25 
 
 250 
 
 0.62 
 
 0.83 
 
 Nicholson File Co. . 
 
 F. 
 
 350 
 
 
 
 
 400 
 
 1.14 
 
 
 Averages . . . 
 
 346.4 
 
 
 
 38.6 
 
 818.3 
 
 2.96 
 
 5.13 
 
 
 
 
 Abbreviations: E., engine; W. W., wood-working machinery; M. M., 
 mining machinery; M. E., marine engines: L., locomotives; H. M., heavy 
 machinery; M. T., machine tools; C. & L., cranes and locks; P. & D., 
 presses and dies; P. & S., pulleys and shafting; H. F., heavy forgings; 
 S. M., sewing-machines; M. S., machine-screws: F., files. 
 
 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 
 
1262 THE MACHINE-SHOP. 
 
 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 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. 
 This presupposes that under the head of shafting are included elevators, 
 fans and blowers. 
 
 Power Required to Drive Machines in Groups. — L. P. Alford 
 (Am. Mach., 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 portion with its machines by an 
 electric motor, readings of the power required being taken every 5 min- 
 utes. The average power required for the entire factory was consider- 
 ably less than the sum of the power required for the individual 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 individ- 
 ual case. 
 
 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., 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/ 16 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. 
 
 Rfese'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 of 
 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 aisk will cut 
 either cast iron, wrought iron, or steel. It will cut a bar of steel 13/s 
 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 iatter 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- 
 
EMERY WHEELS AND GRINDSTONES 1263 
 
 paint, (See description in App. Cyc. Mech.; also U. S. 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 applied 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 
 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 lbs. 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. 
 
 EMERY WHEELS AND GRINDSTONES. 
 
 References: " Precision Grinding," by Darbyshire; " Emery Wheels, 
 their Selection and Use," published by Brown & Sharpe Mfg. Co.; " Points 
 on Grinding," C. H. Norton; " Versuche ueber die Leistung von Schmirgel 
 und Karborundum Scheiben bei Wasserzufuehrung," G. Schlesinger; 
 " Die Festigkeit der kuenstlichen Schmirgel und Karborundum Scheiben, 
 ihre Arbeitsleistung und ihre Wirthshaftlichkeit im Werkstattbetriebe," 
 G. Schlesinger. 
 
 Selection of Grinding Wheels. (Contributed by Norton Co., 1908.) — 
 The essential features of a modern grinding wheel which should be thor- 
 oughly understood by the user are: the definition of grain and grade, and 
 the particular conditions of grinding which cause them to vary. 
 
 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, and 200; when finer than 200, the grits are termed 
 flours, being designated as F, FF, FFF and SF; F being the coarsest and 
 SF the finest. Grits from 12 to 30 are generally used on all heavy work, 
 such as snagging; 36 to 80 cover nearly all tool-grinding, saw-gumming, 
 and nearly all operations where precision in measurement is sought; 90 
 and finer are used for special work, such as grinding steel balls and fine 
 edge work; over 200 is used mostly for oil and hand rubbing stones. 
 
 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 breaking 
 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 
 
1264 THE MACHINE-SHOP. 
 
 must use a very strongly bonded wheel, on account of the leverage exerted 
 on its grain, which tends to tear out the cutting particles before they have 
 done their work. If the contact is a broad one, as in like grinding a hole, 
 or where the work brings a large part of 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 10,000 feet , corresponding to a stress of 250 lbs. per square inch. 
 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. 
 
 Grades of Emery. — The numbers representing the grades of emery 
 run from 8 to 120, and the degree of smoothness of surface they leave may 
 be compared to that left by files as follows: 
 
 8 and 10 represent the cut of a wood rasp. 
 
 " a coarse-rough file. 
 " " an ordinary rough file. 
 " " a bastard file. 
 " " a second-cut file. 
 " " a smooth 
 " " a superfine " 
 " " a dead-smooth file. 
 
 Speed of Polishing-wheels. 
 
 Wood covered with leather, about 7000 ft. per minute. 
 
 Wood covered with a hair brush, about 2500 revs, for largest. 
 
 Wood covered IV2" to 8" diam., hair 1" to 11/4" long, 
 
 ab 4500 revs, for smallest. 
 
 Walrus-hide wheels, about 8000 ft. per minute. 
 
 Rag-wheels, 4 to 8 in. diameter about , .7000 ft. per minute. 
 
 Safe Speeds for Grindstones and Emery-wheels. — G. D. Hiscox 
 (Iron Age, April 7, 1892), by an application of the formula for centrifugal 
 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 
 formulas are: 
 
 Stress per sq. in. of section of a grindstone = (0.7071D X A) 2 X 0.0000795 
 Stress per sq. in. of section of an emery-wheel= (0.7071D X A) 2 X 0.00010226 
 
 D = diameter in feet, A = revolutions per minute. 
 
 He takes the weight of sandstone at 0.078 lb. per cubic inch, and that 
 of an emery-wheel at 0.1 lb. per cubic inch; Ohio stone weighs about 0.081 
 lb. and Huron stone about 0.089 lb. 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 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 remaining 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 
 
 16 
 
 20 
 
 24 
 
 30 
 
 36 
 
 40 
 
 46 
 
 60 
 
 70 
 
 80 
 
 90 
 
 " 100 
 
 L20 
 
 F and FF 
 
EMERY WHEELS AND GRINDSTONES. 
 
 12G5 
 
 Revolutions per 31inute 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 
 
 1000 
 
 1 2000 
 
 3000 
 
 1 4000 1 5000 1 6000 1 7000 1 8000 
 
 9000 
 
 10000 
 
 1 
 
 Stress per Square Inch, Pounds. 
 
 3 
 
 12 1 27 
 
 48 | 75 1 108 1 147 1 192 
 
 243 
 
 300 
 
 5 
 
 Revolutions per Minute. 
 
 1 
 
 3820 
 
 7639 
 
 11459 
 
 15279 
 
 19099 
 
 22918 
 
 26738 
 
 30558 
 
 34377 
 
 38197 
 
 7 
 
 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 
 
 ?.?. 
 
 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 Wb 
 
 eels. 
 
 
 
 
 
 (Circumferences in Feet, Diameters in Inches.) 
 
 
 
 ^ 
 
 
 _^ 
 
 
 +3 
 
 
 ^ 
 
 
 ^ 
 
 
 
 
 fa 
 
 
 fa 
 
 
 fa 
 
 
 fa 
 
 
 fa ■ 
 
 
 fa 
 
 a 
 
 
 fl 
 
 
 a 
 
 
 a 
 
 
 a 
 
 
 a 
 
 
 M 
 
 «H 
 
 
 •H 
 
 1-1 
 
 y 
 
 1-1 
 
 1 
 
 M 
 
 •a 
 
 M 
 
 1 
 
 3 
 
 1 
 
 1 
 
 i 
 
 | 
 
 
 i 
 
 I 
 
 1 
 
 1 
 
 1 
 
 fa 
 
 o 
 
 3 
 
 13 
 
 o 
 
 25 
 
 o 
 
 (A 
 37 
 
 O 
 
 fa 
 49 
 
 o 
 
 fa 
 
 Q 
 
 1 
 
 .262 
 
 3.403 
 
 6.546 
 
 9.687 
 
 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 
 
 72 
 
 5.760 
 
 34 
 
 8.901 
 
 46 
 
 12.043 
 
 58 
 
 15.184 
 
 70 
 
 18.326 
 
 11 
 
 2.880 
 
 7.3 
 
 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 and divide the 
 product by 3.14 times the diam. of the wheel in inches. 
 
1266 
 
 THE MACHINE-SHOP. 
 
 of 80 lb. per sq. in. A section of the same stone dry, broke at 146 lb. per 
 sq. in. A better quality stone broke at stresses of 186 and 116 lb. per sq. 
 in. when dry and wet respectively. 
 
 Selection of Emery Wheels. — The Norton Co. (1907) publishes the 
 following 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 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. 
 
 Table for Selection of Grades. 
 
 Class of Work. 
 
 Large cast iron and steel castings . 
 
 Small cast iron and steel castings . 
 
 Large malleable iron castings . . . 
 
 Small malleable iron castings . . . 
 
 Chilled iron castings 
 
 Wrought iron 
 
 Brass castings 
 
 Bronze castings 
 
 Rough work in general 
 
 General machine-shop use .... 
 
 Lathe and planer tools 
 
 Small tools 
 
 Wood-working tools 
 
 Twist drills (hand grinding) . . . 
 
 Twist drills (special machines) . . 
 
 Reamers, taps, milling cutters, etc 
 (hand grinding) 
 
 Reamers, taps, milling cutters, etc 
 (special machines) 
 
 Edging and joining agricultural im- 
 plements . . 
 
 Grinding plow points 
 
 Surfacing plow bodies 
 
 Stove mounting 
 
 Finishing edges of stoves 
 
 Drop forgings 
 
 Gumming and sharpening saws . . 
 
 Planing-mill and paper-cutting knives 
 
 Car- wheel grinding 
 
 No. of 
 Grain or 
 Degree of 
 Coarse- 
 ness usu- 
 ally Fur- 
 nished. 
 
 12 to 20 
 20 " 30 
 20 
 
 30 
 20 
 30 
 30 
 30 
 30 
 
 46 
 100 
 60 
 60 
 60 
 
 100 
 
 60 
 
 Grade 
 Letters 
 or De- 
 grees of 
 Hardness 
 usually 
 
 Fur- 
 nished. 
 
 Q to R 
 P " Q 
 Q " R 
 P " Q 
 Q " R 
 ' Q 
 P 
 
 P 
 
 O 
 P 
 
 1 N 
 N 
 M 
 
 Grade Letters or 
 Degrees of Hard- 
 ness. Furnished 
 in Exceptional 
 
 Some- 
 
 Some- 
 
 times 
 
 times 
 
 Soft as 
 
 Hard as 
 
 P 
 
 U 
 
 
 
 R 
 
 P 
 
 W 
 
 
 
 U 
 
 p 
 
 u 
 
 
 
 R 
 
 N 
 
 Q 
 
 
 R 
 
 
 
 R 
 
 M 
 
 P 
 
 L 
 
 
 H 
 
 O 
 
 
 * w 
 
 
 u 
 
 M 
 
 Q 
 
 L 
 
 o 
 
 I 
 
 M 
 
 N 
 
 R 
 
 EXPLANATION OF GRADE LETTERS. 
 
 Extremely 
 
 Soft. 
 
 Soft 
 
 
 A 
 
 E 
 
 B 
 
 F 
 
 C 
 
 G 
 
 D 
 
 . H 
 
 Medium 
 
 Medium. 
 
 Medium 
 
 Hard. 
 
 Extremely 
 
 Soft. 
 
 
 Hard. 
 
 
 Hard. 
 
 I 
 
 M 
 
 Q 
 
 U 
 
 Y 
 
 J 
 
 N 
 
 R 
 
 V 
 
 Z 
 
 K 
 
 O 
 
 S 
 
 w 
 
 
 L 
 
 P 
 
 T 
 
 X 
 
 
 The intermediate letters between those designated as soft, medium 
 soft, etc., indicate so many degrees harder or softer; e.g., L is one grade 
 or degree softer than medium; O, 2 degrees harder than medium but not 
 quite medium hard. 
 
EMERY WHEELS AND GRINDSTONES. 
 
 1267 
 
 For 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. 
 
 Special Wheels. — Rim wheels and iron-center wheels are specialties 
 that require the maker's guarantee and assignment of speed. 
 
 Strains in Grindstones. 
 
 Limit of Velocity and Approximate Actual Strain per Square 
 
 Inch of Sectional Area for Grindstones of 
 
 Medium Tensile Strength. 
 
 Diam- 
 
 Revolutions per Minute. 
 
 eter. 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 350 
 
 400 
 
 feet. 
 
 lbs. 
 
 lbs. 
 3.57 
 5.57 
 8.04 
 10.93 
 14.30 
 18.08 
 22.34 
 32.17 
 
 lbs. 
 6.35 
 9.88 
 14.28 
 19.44 
 27.37 
 32.16 
 
 lbs. 
 
 9.93 
 15.49 
 22.34 
 30.38 
 
 lbs. 
 14.30 
 22.29 
 32.16 
 
 lbs. 
 18.36 
 28.64 
 
 lbs. 
 
 21/2 
 3 
 
 2.47 
 3.57 
 4.86 
 6.35 
 8.04 
 9.93 
 14.30 
 19.44 
 
 39.75 
 
 3V2 
 
 
 
 
 
 
 ft 
 
 6 
 
 7 
 
 
 
 Approximate breaking strain ten 
 times the strain for size opposite the 
 
 
 
 
 
 
 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 ruie 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." 
 
 Diamft 8 71/ 2 7 6l/ 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 
 
 The following table, from the Mechanical World, is for the diameter of 
 stones and the number of revolutions they should run per minute (not to 
 be exceeded), with the diameter of change of shift-pulleys required, vary- 
 ing each shift or change 2i/ 2 inches, 21/4 inches, or 2 inches in diameter 
 for each reduction of 6 inches in the diameter of the stone. 
 
 Diameter of 
 
 Revolutions 
 per Minute. 
 
 Shift of Pulleys, in inches. 
 
 Stone. 
 
 21/ 2 
 
 21/4 
 
 2 
 
 ft. in. 
 
 
 
 
 
 8 
 
 135 
 
 40 
 
 36 
 
 32 
 
 7 6 
 
 144 
 
 37i/ 2 
 
 333/4 
 
 30 
 
 7 
 
 154 
 
 35 
 
 311/2 
 
 28 
 
 6 6 
 
 166 
 
 32l/ 2 
 
 291/ 4 
 
 26 
 
 6 
 
 180 
 
 30 
 
 27 
 
 24 
 
 5 6 
 
 196 
 
 271/2 
 
 24i3/ 4 
 
 22 
 
 5 
 
 216 
 
 25 
 
 221/2 
 
 20 
 
 4 6 
 
 240 
 
 221/2 
 
 2OI/4 
 
 18 
 
 4 
 
 270 
 
 20 
 
 18 
 
 16 
 
 3 6 
 
 308 
 
 171/2 
 
 153/4 
 
 14 
 
 3 
 
 360 
 
 15 
 
 131/2 
 
 12 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
1268 
 
 THE MACHINE-SHOP. 
 
 Columns 3, 4, and 5 are given to show that if we start an 8-foot stone 
 with, say, a countershaft pulley driving a 40-inch pulley on the grind- 
 stone spindle, and the stone makes the right number (135) of revolutions 
 per minute, the reduction in the diameter of the pulley on the grinding- 
 stone spindle, when the stone has been reduced 6 inches in diameter, will 
 require to be also reduced 21/2 inches in diameter, or to shift from 40 
 inches to 371/2 inches, and so on similarly for columns 4 and 5. Any 
 other suitable dimensions of pulley may be used for the stone when eight 
 feet in diameter, but the number of inches in each shift named, in order 
 to be correct, will have to be proportional to the numbers of revolutions 
 the stone should run, as given in column 2 of the table. 
 
 Varieties of Grindstones. 
 
 (Joshua Rose.) 
 
 For Grinding Machinists' Tools. 
 
 Name of Stone. 
 
 Nova Scotia, ] 
 
 Bay Chaleur (New ) 
 
 Brunswick), J 
 
 Liverpool or Melling 
 
 Kind of Grit. 
 
 All kinds, from 
 finest to coarsest 
 Medium to finest 
 Medium to fine 
 
 Texture of Stone. Color of Stone. 
 
 All kinds, from 
 hardest to softes 
 Soft and sharp 
 
 Soft, with sharp 
 grit 
 
 Blue or yellowish 
 
 gray. 
 Uniformly light 
 
 blue 
 Reddish 
 
 For Woodworking Tools. 
 
 Wickersley . . . 
 
 Liverpool or Melling 
 
 Bay Chaleur (New ) 
 
 Brunswick), J 
 
 Huron, Michigan . 
 
 Medium to fine 
 Medium to fine j 
 
 Medium to finest 
 Fine 
 
 Very soft 
 
 Soft, with sharp 
 
 grit 
 Soft and sharp 
 Soft and sharp 
 
 Grayish yellow 
 Reddish 
 
 Uniform light blue 
 Uniform light blue 
 
 For Grinding Broad Surfaces, as Saws or Iron Plates. 
 
 Newcastle . . 
 Independence 
 Massillon . . . 
 
 Coarse to med'm 
 
 Coarse 
 
 Coarse 
 
 The hard ones 
 Hard to medium 
 Hard to medium 
 
 Yellow 
 
 Gravish white 
 Yellowish white 
 
 SCREWS, SCREW-THREADS, ETC. 
 
 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 
 1 + / cotan a' 
 
 in which f 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 = 
 
 - fp/c , 
 
 1 + fc/p 
 

 
 si 
 
 SCREWS, SCREW-THREADS, ETC. 
 
 1269 
 
 
 SSgS ; 
 
 
 
 
 oo S3 S 8 „ 8 si? oo^ S-§? c § S-S? *>!><-?? «.!?<-§? «-§ *-§? 
 
 : a • • • s 
 
 :.o •& . : :«g :. :^ :::::::.:::... . 
 
 j ; g oo*'"S"""S""* 
 
 • • • • *CQ ■ • •§§" • • • • -^ • ■ -$T • • '^~ ■ • • 
 
 * * " ' SO tH ' ° CD CO ' ' CO SO ' ' ' 
 
 ^ : :^ : :s^ : :p- : :$-§- ::::::::: . 
 
 jojo co_S.?i 2? Jo .»£?■ CO^^.N CYJ,CO.CO 00 CO [ ".-4? -5?! '.'.'.'.'.'• 
 
 OO ■ -coco • -f* • -<NcN • -<n<vj 
 
 (SCS • •— — • • — — ■ . — — . • — — 
 
 oo oo ao oo vo o ^o \C m ^ -<i- tJ- — — oq«N — — • •©© • • 
 
 vO^O'0*1 , ^ , ^ , tMNNNOO--OOOOo > >»0>0»(l 
 
 4S 
 
 Q 
 
 
 ^2 to 
 
 3^ 
 
 °& 
 
 f3 ° 
 •3 2 
 
 o o> 
 
 «3 OJO 
 
 o 
 O . 
 
 CD 1> 
 CO 
 
 
 
 . 
 
 
 
 ,fi CI 
 
 '>, 
 
 C 
 
 cm 
 
 H 
 
 s 
 
 - 
 
 r w 
 
 -d 
 
 T>' 
 
 
 
 
 § 
 
 £ : 
 
 
 ^ 
 
 ■" 
 
 £ 
 
 H 
 
 i 
 
 ^ 
 
 
 jj 
 
 O 
 
 
 53 H3 
 
1270 THE MACHINE-SHOP. 
 
 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 H/ 2 21/2 31/2 41/2 
 
 Mean circumference of thread, in.. , . 3.927 7.069 10.21 13.35 
 
 Cotangent a = c + p =7.854 14.14 20.42 26.70 
 
 Tangent a = p -i- c =0.1273 .0707 .0490 .0375 
 
 Efficiency if/ = 0.10 =55.3% 41.2% 32.7% 27.2% 
 
 Efficiency if f= 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 .15, 
 p== P + d F y 
 
 3d ' v + d 
 
 For bolts of the dimensions given above, 1/2-inch pitch, and outside 
 diameters H/2, 21/2, 31/2, 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. " 
 
 Trautwine says: "In practice the friction of the screw (which under 
 heavy loads becomes very great) make the theoretical calculations of 
 but little value." 
 
 Weisbach says: "The efficiency is from 19 per cent to 30 per cent." 
 
 Efficiency of a Differential Screw. — A correspondent of the 
 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 ^ V21 inch. 
 Experiments were made to determine the force required to punch an 
 11/16-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 2tt 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 /i6 X t X V4 = 27,000 pounds, and the efficiency of the punch would 
 be 27,000 -4- 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 -e- 73,800 = 36.7 per cent. The screws were of tool- 
 steel, well fitted, and lubricated with lard-oil and plumbago. 
 
 TAPER BOLTS, PINS, REAMERS, ETC. 
 
 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 Vs-inch taper per 1 inch. Standard 
 bolt taper V16 inch per foot. 
 
 Taper Reamers. — The Pratt & Whitney Co. makes standard taper 
 reamers for locomotive work taper 1/16 inch per foot from 1/4 inch diameter; 
 
TAPER BOLTS, PINS, REAMERS, ETC.. 
 
 1271 
 
 4 inch length of flute to 2 inch diameter; IS 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 17/ 16 inches to 14 inches. 
 
 
 
 
 
 31orse Tapers. 
 
 
 
 
 
 
 
 
 
 bf2 
 G'fi 
 
 
 faO 
 
 9 
 
 0>GG 
 
 w 
 
 a 
 Q 
 
 CO £, 
 
 m 
 
 ■£$ 
 
 M 
 
 a 
 
 0) 
 
 fa 
 
 & . 
 
 ' 5 
 ^§ 
 
 3 
 
 -; 
 
 O . 
 35 3 
 
 3 c 
 So 
 
 s 
 
 "o . 
 
 s s 
 
 H 
 
 0) 
 
 — 9 
 
 ~ 
 
 Ha « 
 
 w W 
 
 9 1= 
 
 0. 
 Oi 
 
 Q 
 a 
 
 Si 
 
 .9 
 
 m 
 
 
 
 
 
 4) 
 
 a 
 H 
 
 e 
 
 D 
 
 252 
 
 A 
 356 
 
 P 
 
 2 
 
 B 
 
 H 
 
 K 
 
 L 
 
 IF 
 
 T 
 
 d 
 
 « 
 
 72 
 
 a 
 
 S 
 
 
 
 211/32 
 
 21/32 
 
 U5/16 
 
 9/16 
 
 .160 
 
 1/4 
 
 .24 
 
 5/32 
 
 5/32 
 
 .04 
 
 27/32 
 
 .625 
 
 
 
 .369 
 
 .475 
 
 21/8 
 
 29/16 
 
 23/16 
 
 21/16 
 
 3/4 
 
 .213 
 
 1/5 
 
 .35 
 
 13/64 
 
 3/16 
 
 .05 
 
 23/8 
 
 .600 
 
 1 
 
 , .572 
 
 .700 
 
 29/16 
 
 31/16 
 
 25/s 
 
 21/2 
 
 7/8 
 
 26 
 
 3/8 
 
 17/32 
 
 1/4 
 
 1/4 
 
 .06 
 
 27/s 
 
 .602 
 
 2 
 
 .778 
 
 .938 
 
 33/16 
 
 33/ 4 
 
 31/4 
 
 31/16 
 
 H/16 
 
 .322 
 
 7/16 
 
 3/ 4 
 
 5/16 
 
 9/32 
 
 .08 
 
 39/16 
 
 .602 
 
 3 
 
 1.020 
 
 1.231 
 
 41/16 
 
 43/ 4 
 
 41/8 
 
 3 7 8 
 
 11/4 
 
 .478 
 
 1/2 
 
 31/32 
 
 15/32 
 
 5/16 
 
 .10 
 
 41/2 
 
 .623 
 
 4 
 
 1.475 
 
 1.748 
 
 53/16 
 
 6 
 
 51/4 
 
 415/i 6 
 
 11/2 
 
 .635 
 
 •V8 
 
 113/32 
 
 5/8 
 
 3/8 
 
 .12 
 
 53/ 4 
 
 .630 
 
 5 
 
 2.116 
 
 2.494 
 
 71/4 
 
 85/i 6 
 
 7 3/8 
 
 7 
 
 13/4 
 
 .76 
 
 7/8 
 
 2 
 
 3/4 
 
 1/2 
 
 .15 
 
 8 
 
 .626 
 
 6 
 
 2.75 
 
 3.27 
 
 10 
 
 115/ 8 
 
 101/8 
 
 91/2 
 
 25/s 
 
 1.135 
 
 13/8 
 
 2H/16 
 
 11/8 
 
 3/4 
 
 .18 
 
 111/4 
 
 .625 
 
 7 
 
 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. 
 
 ^f^fa ^ 
 
 Fig. 192. — Morse Tapers. See table above. 
 
 The Jarno 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. 
 
1272 THE MACHINE-SHOP. 
 
 Thus, No. 3 Jarno taper is 1 1/2 inches long, 0.3 inch diameter at the small 
 end and 3/ 8 inch diameter at the large end. 
 
 Standard Steel Taper-pins. — The following sizes are made by The 
 Pratt & Whitney Co.: Taper 1/4 inch to the foot. 
 Number: 
 
 123 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: 
 
 5/32 H/64 3 /l6 7/32 Vi 19 /64 U/32 l 3 /32 V2 19 /32 23/32 
 
 Lengths from 
 
 3/4 3/ 4 3/ 4 3/4 3/ 4 3/ 4 3/ 4 1 H/ 4 H/ 2 U/ 2 
 
 To* 
 
 1 H/4 H/2 l 3 /4 2 21/4 31/4 33/4 41/2 51/4 6 
 
 Diameter small end of standard taper-pin reamer :f 
 0.135 0.146 0.162 0.183 0.208 0.240 0.279 0.331 0.398 0.482 0.581 
 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. 
 
 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 + 0.2t, 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 
 the die accurately. For punching nuts, the punch fits in the die. (Am. 
 Mach.) 
 
 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/ 8 -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 worked 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 
 w eight. Th e third method is by computation, and the formula is x=> 
 v d 2 + 4dh for a sharp-cornered cup, where x = diameter of blank, 
 d = diameter of cup, h = height of cup. For a round-cornered cup 
 
 * Lengths vary by 1/4 inch each size. 
 
 t Taken 1/2 inch from extreme end. Each size overlaps smaller one 
 about 1/2 inch. 
 
FORCE AND SHRINK FITS. 1273 
 
 where the corner is sm all, say radi us of corner less than 1/4 height of cup, 
 the formula is x = (V(d 2 + 4 dh) — r, about; r 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 
 done with 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. 
 
 _, , , , , Weight of drop X fall X efficiency 
 
 Formula: Mean pressure in pounds = : -• 
 
 compression 
 
 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. 
 
 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 li/ie 
 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. 
 
 F.ORCING, 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. Wheji 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.) 
 
 Shrinkage Fits. — In 1886 the American Railway Master Mechanics' 
 Association recommended the following shrinkage allowances for tires of 
 standard locomotives. The tires are uniformly heated by gas-flames, 
 slipped over the cast-iron centers, and allowed to cool. The centers are 
 turned to the standard sizes given below, and the tires are bored smaller 
 by the amount of the shrinkage designated for each: 
 
 Diameter of center, in 38 44 50 56 62 66 
 
 Shrinkage allowance, in 040 .047 .053 .060 .066 .070 
 
 This shrinkage allowance is approximately Vso inch per foot, or 1/960- 
 A common allowance is V1000. Taking the modulus of elasticity of steel at 
 30,000,000, the strain caused by shrinkage would be 30,000 lb. per sq. in., 
 less an uncertain amount due to compression of the center. 
 
 Amer. Machinist published at a later date a table of " M. M. allowances 
 for shrink fits" which correspond to the following: Allowance = 0.001 
 (d+ 1) .for d = 20 to 40 in.: 0.001 (d + 2) for d = 41 to 60 in.; 0.001 
 (d+ 3) for d =61 to 83 in.; 0.088 for d = 84 in. d = diam. of wheel center. 
 For running force fits, Am. Mach. gives the following allowances: d=diam. 
 of bearing or hole, a = allowance. 
 
 d = 
 
 1 » 
 
 * 
 
 3 
 
 4 
 
 5 1 6 
 
 7 
 
 8 1 9 1 10 
 
 Running, a =... 
 
 ... —0.001 
 .1+0.001 
 
 .002 
 .003 
 
 .003 
 .005 
 
 .0035 
 006 
 
 .0037 .004 
 .007 (.008 
 
 .0042 
 0085 
 
 .0042 .0043 .0044 
 .009 |.01 |.0105 
 
 
 
 
 
 
1274 
 
 THE MACHINE-SHOP. 
 
 d = 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 | 18 
 
 19 
 
 20 
 
 Running, a= 
 
 -0.0045 
 + 011 
 
 .0046 
 .0115 
 
 .0047 
 .012 
 
 .0048 
 .013 
 
 .0049 
 014 
 
 .005 
 .0145 
 
 .0051 .0052 
 .015 I .0155 
 
 .0053 
 .016 
 
 .0055 
 .017 
 
 
 
 Allowances for drive fits are one-half those for force fits. 
 
 Limits of Diameters for Fits. C. W. Hunt Co. (Am. Mach., 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 0.003 
 
 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 0.005 in. 
 for press fit, from 0.0005 d+ 0.001 in. for 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 1/16 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. — In use by General 
 Electric Co. (John Riddell, Trans. A.S.M. E., xxiv, 1174). 
 
 l.s 
 S 
 
 2 
 
 4 
 
 8 
 
 12 
 
 16 
 
 20 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 A, B 
 
 0.0005 
 
 .00075 
 
 .001 
 
 .001 
 
 .0012 
 
 .0012 
 
 .0015 
 
 .0015 
 
 .0017 
 
 .0017 
 
 .002 
 
 .0o2 
 
 0023 
 
 C 
 
 0.0005 
 
 .00075 
 
 .0015 
 
 .0017 
 
 .0020 
 
 .0023 
 
 .0025 
 
 .0028 
 
 .003 
 
 .0033 
 
 .0035 
 
 .0038 
 
 004 
 
 D 
 
 0.0005 
 
 .00075 
 
 .0017 
 
 .0025 
 
 .0033 
 
 .004 
 
 .0045 
 
 .005 
 
 .0058 
 
 .0063 
 
 .0068 
 
 .0073 
 
 .008 
 
 E 
 
 0.0015 
 
 .0027 
 
 .0045 
 
 .0057 
 
 .007 
 
 .008 
 
 .0093 
 
 .0115 
 
 .0125 
 
 .0128 
 
 .0138 
 
 .015 
 
 .016 
 
 A, minus allowance for sliding fit. B, plus allowance for commuta- 
 tors and split hubs. C, press fit for armature spiders, so^'d steel. D, 
 do., solid cast iron. E, press fit for couplings, and shrink fit. 
 
 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 11/2 to 21/4 in. diam.; 0.003 to 0.006 for 2i/ 2 ins.; 0.004 to 0.006 for 
 23/4 to 31/2 ins.; 0.005 to 0.007 in. for 4 and 41/2 ins.; 0.006 to 0.008 in. 
 for 5 ins.; 0.009 to 0.011 in. for 6 ins. Dodge Mfg. Co. allows from 1/64 
 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 1/54 in. on a 21/2-in. hole. 
 
 Watt Mining Car Wheel Co. allows Vie in. for all sizes of wheels, and 
 i/ie in. end play. A large fan-blower concern allows 0.005 to 0.01 in. 
 on fan journals from 9/i6 to 27/ie ins. 
 
 Pressure Required for Press Fits. (Am. Mach., March 7, 1907.) — 
 The following approximate formulae give the pressures required for press 
 fits of cranks and crank-pins, as used by an engine-building firm. jP = total 
 pressure on ram, tons; D = diameter inches. 
 
 Crank fits up to D =10. 
 Crank fits D = 12 to 24. 
 Straight crank-pins. 
 Taper crank-pins. 
 
 p = 
 
 9.9 D 
 
 - 14. 
 
 p = 
 
 5 D + 40. 
 
 p = 
 
 13 D. 
 
 
 p = 
 
 14 D ■ 
 
 - 7. 
 
 
FORCE AND SHRINK FITS. 
 
 1275 
 
 The allowance for cranks and straight pins is 0.0025 inch per inch of 
 diameter. Taper cranks, taper Vi6 inch per inch, are fitted on the 
 lathe to within l/s inch of shoulder and then forced home. 
 
 Stresses due to Force and Shrink Fits. — S. H. Moore, Trans. 
 A. S. M. E., vol. xxiv, gives the following allowances for different fits 
 
 For shrinkage fits, d =(i7/ie D + 0.5) h- 1000. For forced fits d = 
 (2 D + 0.5) -*- 1000. For driven fits, d = (i/ 2 D + 0.5) -r- 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 Lamg'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. 
 
 S hl = 15,000,000 d + (fc + 0.6); S hi = i 5 ,000,000 d * (1 + 0.6//;); for a 
 
 cast-iron ring on a steel shaft. 
 S hl = 30,000,000 d -*- (1 + fc); S h2 = 30,000,000 d -*- (1 + 1/K); for a 
 
 steel ring on a steel shaft. 
 5^= radial unit pressure between the surfaces; S^ 2 = 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 -f- 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., 1 1/4 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 lbs.: 
 
 Force Fits, 
 Tension. 
 
 Force Fits, 
 Torsion. 
 
 Shrink Fits, 
 Tension. 
 
 Shrink Fits, 
 Torsion. 
 
 D 
 
 F.lbs. 
 
 Per 
 
 sq.in. 
 
 D 
 
 F.lbs. 
 
 Per 
 
 sq. in. 
 
 D 
 
 F.lbs. 
 
 Per 
 
 sq. in. 
 
 D 
 
 F,lbs. 
 
 Per 
 sq. in. 
 
 1.001 
 1.0015 
 1.002 
 1.0025 
 
 1000 
 2150 
 2570 
 4000 
 
 318 
 685 
 818 
 1272 
 
 1.0015 
 1.0015 
 1.002 
 1 .0025 
 
 2200 
 2800 
 4200 
 4600 
 
 700 
 
 892 
 1335 
 1465 
 
 1.001 
 
 1.001 
 
 1.002 
 
 1.002 
 
 1.0025 
 
 1.0025 
 
 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 
 
 700 
 2290 
 3118 
 4395 
 5410 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1276 THE MACHINE-SHOP. 
 
 PROPORTIONING PARTS OP MACHINES IN A SERIES 
 OF SIZES. 
 
 The following method was used by Coleman Sellers (Stevens Indicator, 
 April, 1892) to get the proportions of the parts of machines, based upon 
 the size obtained in building a large machine and a small one to any series 
 of machines. This formula is used in getting up the proportion-book and 
 arranging the set of proportions from which any machine can be con- 
 structed of intermediate size between the largest and smallest of the series. 
 
 Rule to Establish Construction Formulae." — Take difference be- 
 tween-the nominal sizes of the largest and the smallest machines that have 
 been designed of the same construction. Take also the difference between 
 the sizes of similar parts on the largest and, small est machines selected. 
 Divide the latter by the former, and the result obtained will be a 
 " factor, " which, multiplied by the nominal "capacity of the intermediate 
 machine, and increased or diminished by a constant "increment," will 
 give the size of the part required. To find the "increment:" Multiply 
 the nominal capacity of some known size by the factor obtained, and sub- 
 tract the result from the size of the part belonging to the machine of 
 nominal capacity selected. 
 
 Example. — Suppose the size of a part of a 72-inch machine is 3 inches, 
 and the corresponding part of a 42-inch machine is l'7/ 8 , or 1.875 inches: 
 then 72 - 42 = 30, and 3 inches - 17/ 8 inches = Us inches = 1.125. 
 1.125-H30 = 0.0375 = the " factor, " and .0375X42 = 1.575. Then 1.875- 
 1.575 = .3 = the "increment" to be added. Let D = nominal capacity; 
 then the formula will read: x = D X .0375 + .3. 
 
 Proof: 42 X .0375 + .3 = 1.875, or 17/ 8 , the size of one of the selected 
 parts. 
 
 Some prefer the formula: aD + c = x, in which D = nominal capacity 
 in inches or in pounds, c is a constant increment, a is the factor, and 
 x = the part to be found. 
 
 KEYS. 
 
 Sises of Keys for Mill-gearing. (Trans. A. S. M. E., xiii, 229.)— 
 E. G. Parkhurst's rule: Width of key= Vs diameter of shaft, depth = 
 1/9 diameter of shaft; taper Vs inch to the foot. 
 
 Custom in Michigan saw-mills: Keys of square section, side = 1/4 
 diameter of shaft, or as nearly as may be in even sixteenths of an inch. 
 
 J. T. Hawkins's rule: Width = 1/3 diameter of hole; depth of side abut- 
 ment in shaft = 1/8 diameter of hole. 
 
 W. S. Huson's rule: 1/4-inch key for 1 to 11/4-in. shafts, 5/i6-in. key for 
 11/4 to 11/2-inch shafts, 3/ 8 -inch key for 1 1/2 to 13/ 4 -inch shafts and so on. 
 Taper i/s inch to the foot. Total thickness at large end of splrce, 4/5 
 width of key. 
 
 Unwin (Elements of Machine Design) gives: Width = 1/4 d + 1/ 8 inch. 
 Thickness = Vs d 4- i/s inch, in which d = diameter of shaft in inches. 
 When wheels or pulleys transmitting only a small amount of power are 
 keyed oh large shafts, he says, these dimensions are -excessive. In that 
 case, if H.P. = horse-power transmitted by the wheel or pulley, N = 
 r.p.m., P = force acting at the circumference, in pounds, and R = radius 
 of pulley in inches, take 
 
 r= J/ 100 H.P MM 
 
 V jV or T 630 
 
 Prof. Coleman Sellers (Stevens Indicator, April, 1892) gives the follow- 
 ing- The size of keys, both for shafting and for machine tools, are the 
 proportions adopted bv William Sellers & Co., and rigidly adhered to 
 during a period of nearly forty years. Their practice in making keys and 
 fitting them is, that the keys shall always bind tight sidewise, but not top 
 and bottom ; that is, not necessarily touch either at the bottom of the key- 
 seat in the shaft or touch the top of the slot cut in the gear-wheel that is 
 
1277 
 
 fastened to the shaft; but in practice keys used in this manner depend 
 upon the fit of the wheel upon the shaft being a forcing fit, or a fit that is 
 so tight as to require screw-pressure to put the wheel in place upon the 
 shaft. 
 
 Size of Keys for Shafting. 
 
 Diameter of Shaft, in. Size of Key, in. 
 
 H/4 17/16 HI/16 5/l6X3/ 8 
 
 H5/16 23/i6 7/16XV2 
 
 27/16 9/ie X 5/ 8 
 
 211/16 215/i6 33/i6 3.7/i 6 U/ 16 X 3/ 4 
 
 315/16 47/ie 415/ie 13/ 16 X 7/ 8 
 
 57/i6 515/i 6 67/ie 15/ 16 X 1 
 
 615/ie 77/i6 715/ie 87/is 815/i 6 H/ttXU/s 
 
 Length of key-seat for coupling == U/2X nominal diameter of shaft. 
 
 Size of Keys for Machine Tools. 
 
 Diam. of Shaft, in. 
 
 i5/i6 and under . 
 
 1 to 13/ie . . 
 
 H/4 to 17/ie . . 
 
 1 1/ 2 to 1 U/16 . . 
 13/4 to 23/ie . . 
 21/4 to 2U/16 
 
 Size of Key, 
 in. sq. 
 
 ... 1/8 
 
 . • • 3/16 
 ... 1/4 
 • • . 5/16 
 . . . 7/ 16 
 9/16 
 
 23/4 tO 315/16 U/16 
 
 Diam. of Shaft, in, 
 4 to 57/ie 
 51/2 to 615/ie 
 7 to 815/ie 
 9 tO 1015/16 
 11 to 1215/ie 
 13 to 1415/16 
 
 Size of Key, 
 in. sq. 
 . . 13/ie 
 
 • • 15/16 
 
 • • H/16 
 . . 13/16 
 
 • • 15/16 
 
 • • 17/ie 
 
 John Richards, in an article in Cassier's Magazine, writes as follows: 
 There are two kinds or systems of keys, both proper and necessary, but 
 widely different in nature. 1. The common 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 taken 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 evi- 
 dence 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 accu- 
 rate work of any kind, indeed, cannot be, because of the wedging strain, 
 and also the difficulty of inspecting completed work. 
 
1278 THE MACHINE-SHOP. 
 
 I. Dimensions of Flat Keys, in Inches. 
 
 Diam. of shaft . . 
 
 1 
 
 11/4 
 
 U/, 
 
 I3/ 4 
 
 2 
 
 2 V, 
 
 3 
 
 31/ ? 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 Breadth of keys 
 
 1/4 
 
 5/16 
 
 3/8 
 
 7/1 fi 
 
 V?, 
 
 5/8 
 
 3/4 
 
 7/8 
 
 1 
 
 H/8 
 
 13/8 
 
 H/2 
 
 13/4 
 
 Depth of keys . . 
 
 5 /32 
 
 3/l6 
 
 1/4 
 
 ^32 
 
 5/16 
 
 3/8 
 
 V/16 
 
 1/2 
 
 •V8 
 
 H/16 
 
 13/16 
 
 '/8 
 
 1 
 
 II. Dimensions of Square Keys, in Inches. 
 
 Diameter of shaft . . 
 
 Breadth of keys 
 
 Depth of keys . 
 
 13/4 
 H/32 
 3/8 
 
 2 
 13/32 
 7/16 
 
 21/2 
 15/32 
 
 1/2 
 
 3 
 17/32 
 9/16 
 
 31/2 
 
 9/16 
 5/8 
 
 4 
 11/16 
 3/4 
 
 III. Dimensions of Sliding Feather-keys, in Inches. 
 
 Diameter of shaft . 
 Breadth of keys . . . 
 Depth of keys 
 
 11/4 
 
 U/» 
 
 13/4 
 
 2 
 
 21/4 
 
 21/?, 
 
 3 
 
 31/2 
 
 4 
 
 1/4 
 
 1/4 
 
 V16 
 
 5/16 
 
 3/8 
 
 3/8 
 
 1/2 
 
 9/16 
 
 9/16 
 
 3/8 
 
 3/8 
 
 7/16 
 
 7/16 
 
 1/2 
 
 1/2 
 
 5/8 
 
 3/4 
 
 »/4 
 
 41/2 
 
 5/8 
 7/8 
 
 P. Pryibil furnishes the following table of dimensions to the Am. 
 Machinist. He says: "On special heavy work and very short hubs we 
 put in two keys in one shaft 90 degrees apart. With special long hubs, 
 where we cannot use keys with noses, the keys should be thicker than 
 the standard. 
 
 Diameter of 
 Shafts, Inches. 
 
 Width, 
 Inches. 
 
 Thick- 
 ness, In. 
 
 Diameter of 
 Shafts, Inches. 
 
 Width, 
 Inches. 
 
 Thick- 
 ness, In. 
 
 3/4 to 1 Vie 
 
 1 1/8 to 1 5/ 16 
 1 7/ie to 1 H/16 
 115/ 16 to23/ 16 
 27/ 16 to 211/ie 
 215/ 16 to33/ 16 
 
 3/16 
 5/16 
 
 3/8 
 
 1/2 
 5/8 
 3/4 
 
 3/16 
 1/4 
 5/16 
 3/8 
 1/2 
 9/16 
 
 37/i 6 to 311/i 6 
 315/ 16 to43/ 16 
 47/ 16 to 4H/ 16 
 47/ 8 to 53/ 8 
 57/ 8 to 63/ 8 
 67/s to 73/ 8 
 
 :$ 
 
 11/2 
 13/ 4 
 
 5/8 
 11/16 
 
 3/4 
 15/16 
 1 
 U/8 
 
 Keys longer than 10 inches, say 14 to 16 inches, l/i6inch thicker; keys 
 longer than 10 indie's, say 18 to 20 inches, l/s inch thicker; and so on. 
 Special short hubs to have two keys. 
 
 For description of the Woodruff system of keying, see circular of the 
 Pratt & Whitney Co.; also Modern Mechanism, page 455. 
 
 For keyways in milling cutters see page 1248. 
 
 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 
 
HOLDING-POWER OF KEYS AND SET-SCREWS. 1279 
 
 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 lbs.; average 2064. 
 
 B, radius of rounded ends about 1/2-in. 2747 to 3079 lbs.; average 2912. 
 
 C, radius of rounded ends about 1/4-in. 1902 to 3079 lbs.; average 2573. 
 
 D, ends cup-shaped and case-hardened 1962 to 2958 lbs.; 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. 
 
 C. The ends were found, after the first two trials, to be flattened, as 
 in B. 
 
 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 way 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, and 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 1/4" X 15/32*, 40,184 to 47,760 lbs. ; average, 42,726 
 
 B, refined iron, 2" X 1/4" X 15/32", 36,482 to 39,254 lbs. ; average, 38,059 
 
 C, tool steel, 1" X V4" X 15/32", 91,344 & 100,056 lbs. ; 
 
 D, mach'y steel, 2" X 1/4" X 15/32" 64,630 to 70,186 lbs. ; average, 66,875 
 
 E, Norway iron, 1 1/3" X W X 7/ie" 36,850 to 37,222 lbs. ; average, 37,036 
 
 F, cast-iron, 2" X 1/4" X 15/32", 30,278 to 36,944 lbs. ; average, 33,034 
 
 G, cast-iron, 1 1/3" X W X 7/l6", 37,222 & 38,700. 
 H, cast-iron, 1" X V2" X 7/i 6 ", 29,814 & 38,978. 
 
 In A and B some crushing took place before shearing. In E, the 
 keys, being only 7/ 16 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. 
 
M 
 
 1280 THE MACHINE-SHOP. 
 
 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 extension 
 
 of the spring measuring the 
 amount of the pulling force; and 
 (2) a paper-covered drum, rotated 
 either at a uniform speed by clock- 
 work, or at a speed proportional 
 to the speed of the traction, 
 through gearing, on which the 
 extension of the spring is regis- 
 tered by a pencil. From the 
 average height of the diagram 
 drawn by the pencil above the 
 Fig. 193. 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. 193, from Flather on Dynamometers.) 
 
 Primarily this consists of a lever connected to a revolving shaft or pulley 
 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 and screw up 
 on bolts b,b, until the friction induced balances the weights and the lever 
 is maintained in its horizontal position while the revolutions 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. 107 : the friction 
 may be weighed on a platform-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 = 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. 
 
DYNAMOMETERS. 
 
 1281 
 
 Then will W = PV =2 nLNP. 
 
 Since H.P. = PV -5- 33,000, we have H.P. = 2 nLNP -*- 33,000. 
 
 If L = 33 + 2 ?r, we obtain H.P. = NP -5- 1000. 33-^-2 « 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 lbs. 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 31/2%. : 
 
 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 circum. of wheel in feet per minute; K = coefficient; then 
 K= WV + H.P. 
 
 Prof. Flather obtains the values of K given in the last column of the 
 subjoined table: ? 
 
 
 Brake- 
 pulley. 
 
 Design of Brake. 
 
 150 
 148.5 
 146 
 180 
 150 
 150 
 142 
 100 
 76.2 
 290\ 
 250 f 
 3221 
 290/ 
 
 33 
 
 33.38 
 32.19 
 32 
 
 32 
 
 38.31 
 126.1 
 191 
 
 273/4 
 
 Royal Ag. Soc, compensating. . . . 
 
 McLaren, compensating. 
 
 McLaren, water-cooled arid comp 
 Garrett, water-cooled and comp . 
 Garrett, water-cooled and comp . 
 
 Schoenheyder, water-cooled 
 
 Balk 
 
 Gately & Kletsch, water-cooled . . 
 Webber, water-cooled 
 
 Westinghouse, water-cooled 
 
 Westinghouse, water-cooled . 
 
 802 
 741 
 749 
 282 
 
 1385 
 209 
 
 84.7 
 465 
 
 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. 
 
1282 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 Instead of assuming an average coefficient, Prof. Flather proposes the 
 following: 
 
 Water-cooled brake, non-compensating, K = 400; W= 400 H.P. -*■ V. 
 
 Water-cooled brake, compensating, If = 750; W = 75Q H.P. -r- V. 
 
 Non-cooling brake, with or without compensating device, K = 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. 
 
 A6000H.P. Hydraulic Absorption Dynamometer, built by the West- 
 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 McAlpine turbine reduction gear (seepage 1071). 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 
 6i 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 ceiled 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- 
 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 forms 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 elaborate discussion of the thermodynamic theory 
 of the action of the various fluids used in the production of cold was 
 published by M. Ledoux in the Annates 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 Denton, Jacobus, and Riesen- 
 berger, 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 matter given below 
 is taken. Other references are Wood's Thermodynamics, Chap. V, and 
 numerous papers bv Professors Wood, Denton, jacobus, and Linde in 
 Trans. A. S. M. E., vols, x to xiv Johnson's Cyclopaedia, article on 
 Refrigeratins'-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; Re- 
 
ICE-MAKING OR REFRIGERATING MACHINES. 1283 
 
 frigeration, by J. Wemyss Anderson, and Refrigeration, Cold Storage and 
 Ice-making, by A. J. Wallis-Taylor. For properties of Ammonia and Sul- 
 phur 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 Tee 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 vapors. 
 
 The maximum pressure is determined by the temperature of the con- 
 denser and the nature of the volatile liquid; this pressure is often very 
 high. 
 
 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-machines 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 superheated 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 
 temperature of water from considerable depth below the surface, to 
 about -95° F., the temperature of surface-water in hot climates. The 
 volatile liquid emploved 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 
 
1284 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 single stroke of the piston shall be sufficient to 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 different temperatures between — 22° and 
 + 104°. 
 
 Pressures 
 
 and Boiling-points of Liquids available for Use 
 
 
 
 in Refrigerating-machines. 
 
 
 
 Temp. 
 
 
 
 
 
 
 
 
 of 
 Ebulli- 
 
 
 Tension of Vapor, in lbs. per s 
 
 q. in., above Zero. 
 
 
 tion. 
 
 
 
 
 
 
 
 
 Deg. 
 
 Sul- 
 phuric 
 Ether. 
 
 Sulphur 
 
 Ammonia. 
 
 Methylic 
 
 Carbonic 
 
 Pictet 
 
 Ethyl 
 Chloride. 
 
 Fahr. 
 
 Dioxide. 
 
 Ether. 
 
 Acid. 
 
 Fluid. 
 
 — 40 
 
 
 
 10.22 
 13.23 
 16.95 
 21.51 
 27.04 
 
 
 
 
 
 31 
 
 
 
 
 
 
 
 — 22 
 
 "YM" 
 
 5.56 
 7.23 
 9.27 
 
 11.15 
 
 13.85 
 17.06 
 
 
 
 2. 13 
 
 -13 
 
 251.6 
 292.9 
 
 
 2.80 
 
 - 4 
 
 13.5 
 
 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 
 17.59 
 
 77.64 
 90.32 
 
 197.83 
 227.76 
 
 
 1207.9 
 1338.2 
 
 73.2 
 82.9 
 
 31.78 
 
 104 
 
 
 37.12 
 
 
 
 
 The table shows that the use of ether does not readily lead to the pro- 
 duction of low temperatures, because its pressure becomes then very 
 feeble. 
 
 Ammonia, on the contrary, is well adapted to the production of low 
 temperatures. 
 
 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° lower 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, C>H 5 C1. 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. 
 
SULPHUR DIOXIDE AND AMMONIA GAS. 
 
 1285 
 
 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. 
 
 PROPERTIES 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 u 
 
 s 
 
 is 
 
 *s 
 
 a 
 
 
 
 ^ 
 
 11^ 
 
 
 o 
 
 03-3 
 
 1-2 
 
 3 fe s 
 
 J- 
 
 Increase of 
 Volume dur- 
 ing Evapo- 
 ration. 
 u 
 
 Density of Va- 
 por or Weigh 
 of 1 cu.ft. 
 1 + V 
 
 
 Absolut* 
 sure in 
 sq. in. 
 
 P -s- 
 
 Total H 
 reckom 
 32° F. 
 A 
 
 
 +3 O *» 
 
 5« 
 
 HeatEq 
 of Ext< 
 Work. 
 AP 
 
 15* 
 
 c -2 
 
 Deg. F. 
 
 Lbs. 
 
 B.T.U. 
 
 B.T.U. 
 
 B.T.U. 
 
 B.T.U. 
 
 B.T.U. 
 
 Cu.ft. 
 
 Lbs. 
 
 -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 SO2 at various temperatures, the results agreeing closely with 
 those of Regnault up to the highest figure of the latter, 149° F., 178 lbs. 
 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. lbs. per sq. in. 
 
 104.4 120.1 137.5 156.7 179.5 203.8 230.7 260.5 331.1 371.8 418. 
 
 Density of Liquid Ammonia. (D'Andreff, Trans. A.S.M. E., x, 641. 
 
 At temperature C -10 -5 5 10 15 20 
 
 At temperature F .... +14 23 32 41 50 59 68 
 
 Density .6492 .6429 .6364 .6298 .6230 .6160 .6086 
 
 These may be expressed very nearly by 
 
 8 = 0.6364 - 0.0014£° Centigrade; 
 8 = 0.6502 - 0.0007777 10 Fahr. 
 
 Latent Heat of Evaporation of Ammonia. (Wood, Trans. A. S. 
 M. E„ x, 641.) 
 
 h e = 555.5 - 0.613 T - 0.000219T 2 (in B.T.U. ,° F); 
 
 Ledoux found h e = 583.33 - 0.5499 T - 0.0001 173 T 72 . 
 
 For experimental values at different temperatures determined by Prof. 
 Denton, see Trans. A. S. M, E„ xii, 356. For calculated values, see 
 vol. x, 646, 
 
ICE-MAKING OR REFRIGERATING MACHINES. 
 
 Properties of the Saturated Vapor of Ammonia. 
 
 (Wood's Thermodynamics.) 
 
 Temperature. 
 
 Pressure, 
 Absolute. 
 
 Heat of 
 Vapori- 
 zation, 
 thermal 
 
 Volume 
 of Vapor 
 
 Volume 
 of Liquid 
 
 per lb., 
 
 cu.ft. 
 
 Weight 
 
 of a cu. 
 
 ft. of 
 
 Vapor. 
 
 Degs. 
 
 Abso- 
 
 Lbs. per 
 
 Lbs. per 
 
 per lb., 
 cu. ft. 
 
 F. 
 
 lute, F. 
 
 sq.ft. 
 
 sq. in. 
 
 units. 
 
 lbs. 
 
 - 40 
 
 420.66 
 
 1540.7 
 
 10.69 
 
 579.67 
 
 24.372 
 
 0.0234 
 
 0.0410 
 
 - 35 
 
 425.66 
 
 1773.6 
 
 12.31 
 
 576.69 
 
 21.319 
 
 .0236 
 
 .0468 
 
 - 30 
 
 430.66 
 
 2035.8 
 
 14.13 
 
 573.69 
 
 18.697 
 
 .0237 
 
 .0535 
 
 - 25 
 
 435.66 
 
 2329.5 
 
 16.17 
 
 570.68 
 
 16.445 
 
 .0238 
 
 .0608 
 
 - 20 
 
 440.66 
 
 2657.5 
 
 18.45 
 
 567.67 
 
 14.507 
 
 .0240 
 
 .0689 
 
 - 15 
 
 445.66 
 
 3022.5 
 
 20.99 
 
 564.64 
 
 12.834 
 
 .0242 
 
 .0779 
 
 -, 10 
 
 450.66 
 
 3428.0 
 
 23.80 
 
 561.61 
 
 11.384 
 
 .0243 
 
 .0878 
 
 - 5 
 
 455.66 
 
 3877.2 
 
 26.93 
 
 558.56 
 
 10.125 
 
 .0244 
 
 0988 
 
 
 
 460.66 
 
 4373.5 
 
 30.37 
 
 555.50 
 
 9.027 
 
 .0246 
 
 .1108 
 
 5 
 
 465.66 
 
 4920.5 
 
 34.17 
 
 552.43 
 
 8.069 
 
 .0247 
 
 1239 
 
 10 
 
 470.66 
 
 5522.2 
 
 38.34 
 
 549.35 
 
 7.229 
 
 .0249 
 
 1383 
 
 15 
 
 475.66 
 
 6182.4 
 
 42.93 
 
 546.26 
 
 6.492 
 
 .0250 
 
 '1544 
 
 20 
 
 480.66 
 
 6905.3 
 
 47.95 
 
 543.15 
 
 5.842 
 
 .0252 
 
 1712 
 
 25 
 
 485.66 
 
 7695.2 
 
 53.43 
 
 540.03 
 
 5.269 
 
 .0253 
 
 1898 
 
 30 
 
 490.66 
 
 8556.6 
 
 59.41 
 
 536.92 
 
 4.763 
 
 .0254 
 
 .2100 
 
 35 
 
 495.66 
 
 9493.9 
 
 65.93 
 
 533.78 
 
 4.313 
 
 .0256 
 
 2319 
 
 40 
 
 5o0.66 
 
 10512 
 
 73.00 
 
 530.63 
 
 3.914 
 
 .0257 
 
 2555 
 
 45 
 
 505.66 
 
 11616 
 
 80.66 
 
 527.47 
 
 3.559 
 
 .0259 
 
 '2809 
 
 50 
 
 510.66 
 
 12811 
 
 88.96 
 
 524. 30 
 
 3.242 
 
 .0261 
 
 ..3085 
 
 55 
 
 515.66 
 
 14102 
 
 97.93 
 
 521.12 
 
 2.958 
 
 .0263 
 
 3381 
 
 60 
 
 520.66 
 
 15494 
 
 107.60 
 
 517.93 
 
 2.704 
 
 .0265 
 
 .3698 
 
 65 
 
 525.66 
 
 16993 
 
 118.03 
 
 514.73 
 
 2.476 
 
 .0266 
 
 .4039 
 
 70 
 
 530.66 
 
 18605 
 
 129.21 
 
 511.52 
 
 2.271 
 
 .0268 
 
 .4403 
 
 75 
 
 535.66 
 
 20336 
 
 141.25 
 
 508.29 
 
 2.087 
 
 .0270 
 
 .4793 
 
 80 
 
 540.66 
 
 22192 
 
 154.11 
 
 505.05 
 
 I 920 
 
 .0272 
 
 .5208 
 
 85 
 
 545.66 
 
 24178 
 
 167.86 
 
 501.81 
 
 1.770 
 
 .0273 
 
 .5650 
 
 90 
 
 550.66 
 
 26300 
 
 182.8 
 
 498.11 
 
 1.632 
 
 .0274 
 
 6128 
 
 95 
 
 555.66 
 
 28565 
 
 198.37 
 
 495.29 
 
 1.510 
 
 .0277 
 
 .6623 
 
 100 
 
 560.66 
 
 30980 
 
 215.14 
 
 492.01 
 
 1.398 
 
 .0279 
 
 .7153 
 
 105 
 
 565.66 
 
 33550 
 
 232.98 
 
 488.72 
 
 1.296 
 
 .0281 
 
 .7716 
 
 110 
 
 570.66 
 
 36284 
 
 251.97 
 
 485.42 
 
 1.203 
 
 .0283 
 
 .8312 
 
 115 
 
 575.66 
 
 39188 
 
 272.14 
 
 482.41 
 
 1.119 
 
 .0285 
 
 8937 
 
 120 
 
 580.66 
 
 42267 
 
 293.49 
 
 478.79 
 
 1.045 
 
 .0287 
 
 9569 
 
 125 
 
 585.66 
 
 45528 
 
 .316.16 
 
 475.45 
 
 0.970 
 
 .0289 
 
 1 0309 
 
 130 
 
 590.66 
 
 48978 
 
 340.42 
 
 472.11 
 
 0.905 
 
 .0291 
 
 1 1049 
 
 135 
 
 595.66 
 
 52626 
 
 365.16 
 
 468.75 
 
 0.845 
 
 .0293 
 
 1.1834 
 
 140 
 
 600.66 
 
 56483 
 
 392.22 
 
 465.39 
 
 0.791 
 
 .0295 
 
 1.2642 
 
 145 
 
 605.66 
 
 60550 
 
 420.49 
 
 462.01 
 
 0.741 
 
 .0297 
 
 1.3495 
 
 150 
 
 610.66 
 
 64833 
 
 450.20 
 
 458.62 
 
 0.695 
 
 .0299 
 
 1 4388 
 
 155 
 
 615.66 
 
 69341 
 
 481.54 
 
 455.22 
 
 0.652 
 
 .0302 
 
 1.5337 
 
 160 
 
 620.66 
 
 74086 
 
 514.40 
 
 451.81 
 
 0.613 
 
 .0304 
 
 1.6343 
 
 165 
 
 625.66 
 
 79071 
 
 549.04 
 
 448.39 
 
 0.577 
 
 .0306 
 
 1.7333 
 
 Density of Ammonia Gas. — Theoretical, 0.5894; experimental, 
 0.596. Regnault (Trans. A. S. M. E., x, 633). 
 
 Specific Heat of Liquid Ammonia. (Wood, Trans. A. S. M. E., 
 x, 645.) — The specific heat is nearly constant at different temperatures, 
 and about equal to that of water, or unity. From 0° to 100° F., it is 
 c = 1.096 - 0.00127 1 , nearly. 
 
 In a later paper by Prof. Wood (Trans. A. S. M. E., xii, 136) he gives 
 a higher value, viz., c= 1.12136 + 0.000438 T. 
 
 L. A. Elleau and Wm. D. Ennis (Jour. Franklin Inst., April, 1898) 
 give the results of nine determinations, made between 0° and 20° C, 
 which range from 0.983 to 1.056, averaging 1.0206. Von Strombeck 
 
PROPERTIES OF AMMONIA. 
 
 1287 
 
 {Jour. Franklin Inst., Dec, 1890) found the specific heat between 62° and 
 31° C. to be 1.22876. Ludeking and Starr {Am. Jour. Science, iii, 45, 200) 
 obtained 0.886. Prof. Wood deduced from thermodynamic equations 
 c = 1.093 at —34° F. or —38° C., and Ledoux in like manner finds 
 c = 1.0058+ 0.003658 t° C. Elleau and Ennis give Ledoux's equation 
 with a new constant derived from their experiments, thus c = 0.9834 + 
 0.003658 £° C. 
 
 50° F. 
 8 10 12 14 16 18 
 
 .966 .960 .953 .945 .938 .931 
 26 28 30 32 34 36 
 .907 .902 .897 .892 .888 .884 
 Specific Heat of Ammonia Vapor at the Saturation Point. (Wood, 
 Trans. A. S. M. E., x, 644.) — For the range of temperatures ordinarily 
 used in engineering practice, the specific heat of saturated ammonia is 
 negative, and the saturated vapor will condense with adiabatic expansion. 
 The liquid will evaporate with the compression of the vapor, and when all 
 is vaporized will superheat. 
 
 Regnault (Rel. des. Exp., ii, 162) gives for specific heat of ammonia-gas 
 0.50836. (Wood, Trans. A. S. M. E., xii, 133.) 
 
 Weight of Superheated Ammonia Vapor at 15.67 lbs. Gauge Pressure 
 ( = 30.67 lbs. abs.) (C. E. Lucke, Ice and Refrigeration, Mar., 1908.) 
 Weight at 0° F. 0.1107 lbs. 
 
 Strength of Aqua Ammonia at ( 
 
 % NH 3 by wt. 2 4 6 
 
 Sp.gr. 0.986 .979 .972 
 
 % NH 3 20 22 24 
 
 Sp.gr. 0.925 .919 .913 
 
 Temp. 
 
 Lb. per 
 
 Temp. 
 
 Lb. per 
 
 Temp. 
 
 Lb. per 
 
 Temp. 
 
 Lb. per 
 
 °F. 
 
 cu. ft. 
 
 °F. 
 
 cu.ft. 
 
 °F. 
 
 cu. ft. 
 
 °F. 
 
 cu. ft. 
 
 5 
 
 0.1095 
 
 25 
 
 0.1050 
 
 125 
 
 0.08706 
 
 225 
 
 0.07438 
 
 10 
 
 0.1085 
 
 50 
 
 0.09986 
 
 150 
 
 0.08351 
 
 250 
 
 0.07176 
 
 15 
 
 0.1072 
 
 75 
 
 0.0952 
 
 175 
 
 0.08033 
 
 275 
 
 0.06932 
 
 20 
 
 0.1061 
 
 100 
 
 0.09096 
 
 200 
 
 0.07713 
 
 300 
 
 0.06703 
 
 Specif 
 
 ic Heat 
 
 and Available Lat 
 
 jnt Hea 
 
 t of Hot 
 
 Liquid Ammonia 
 
 at 15.67 
 
 bs. gauge 
 
 ; pressure. (Lucke 
 
 ) Latent 
 
 heat at 1 
 
 5.67 lbs. 
 
 and 0° F. 
 
 = 550.5 
 
 B.T.U. 
 
 Specific heat = 1.0 
 
 96 - 0.0 
 
 012 T°. 
 
 
 
 Temp. 
 
 of 
 Liquid 
 Supply. 
 
 Specific 
 Heat. 
 
 Correc- 
 tion for 
 Cooling. 
 
 Available 
 
 Latent 
 
 Heat for 
 
 Saturated 
 
 Vapor. 
 
 Temp. 
 
 of 
 Liquid 
 Supply. 
 
 Specific 
 Heat. 
 
 Correc- 
 tion for 
 Cooling. 
 
 Available 
 Latent 
 Heat for 
 Satu- 
 rated 
 Vapor. 
 
 5 
 
 1.090 
 
 5.45 
 
 550.05 
 
 55 
 
 1.030 
 
 56.65 
 
 498.85 
 
 10 
 
 1.084 
 
 10.84 
 
 544.66 
 
 60 
 
 1.024 
 
 61.44 
 
 494.06 
 
 15 
 
 1.078 
 
 16.17 
 
 539.33 
 
 65 
 
 1.018 
 
 66.17 
 
 489.33 
 
 20 
 
 1.072 
 
 21.44 
 
 534.06 
 
 70 
 
 1.012 
 
 70.84 
 
 484.66 
 
 25 
 
 1.066 
 
 26.65 
 
 528.85 
 
 75 
 
 1.006 
 
 -75.45 
 
 480.05 
 
 30 
 
 1.060 
 
 31.80 
 
 523.70 
 
 80 
 
 1.000 
 
 80.00 
 
 475.50 
 
 35 
 
 1.054 
 
 36.89 
 
 518.61 
 
 85 
 
 0.994 
 
 84.49 
 
 471.01 
 
 40 
 
 1.048 
 
 41.92 
 
 513.68 
 
 90 
 
 0.988 
 
 88.92 
 
 466.58 
 
 45 
 
 1.042 
 
 46.89 
 
 508.61 
 
 95 
 
 0.982 
 
 93.29 
 
 462.21 
 
 50 
 
 1.036 
 
 51.80 
 
 503.70 
 
 100 
 
 0.976 
 
 97.60 
 
 457.90 
 
 The latent heat for saturated vapor is subject to three corrections in 
 determining the available latent heat. First, for the temperature of the 
 liquid which must be cooled from its supply temperature to the tem- 
 perature corresponding to the back pressure, as in the table above; 
 second, for wetness of vapor, a deduction of 5.555 B.T.U. for each 1% of 
 moisture; third, for superheat of vapor in case it leaves the expansion 
 coils or cooler hotter than the temperature corresponding to the pressure, 
 an addition of the number of degrees superheat multiplied by the specific 
 heat, taken as 0.508. 
 
1288 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 "Solubility of Ammonia. (Siebel.) — One pound of water will dis- 
 solve the following weights of ammonia at the pressures and temperatures 
 F° stated. 
 
 Abs. 
 
 
 
 
 Abs. 
 
 
 
 
 Abs. 
 
 
 
 
 Press. 
 
 32° 
 
 68° 
 
 104° 
 
 Press. 
 
 32° 
 
 68° 
 
 104° 
 
 Press. 
 
 32° 
 
 68° 
 
 104° 
 
 per 
 
 
 
 
 per 
 
 
 
 
 per 
 
 
 
 
 sq.in. 
 
 
 
 
 sq.m. 
 
 
 
 Tb~ 
 
 sq. m. 
 
 ~Tb7 
 
 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 lb. 
 
 14.67 
 
 0.899 
 
 0.518 
 
 0.338 
 
 21.23 
 
 1.236 
 
 0.651 
 
 0.425 
 
 27.99 
 
 1.603 
 
 0.780 
 
 0.486 
 
 15.44 
 
 0.937 
 
 0.635 
 
 0.349 
 
 22.19 
 
 1.283 
 
 0.669 
 
 0.434 
 
 28.95 
 
 1.656 
 
 0.801 
 
 0.493 
 
 16.41 
 
 0.980 
 
 0.556 
 
 0.363 
 
 23.16 
 
 1.330 
 
 0.685 
 
 0.445 
 
 30.88 
 
 1.758 
 
 0.842 
 
 0.511 
 
 17.37 
 
 1.029 
 
 4). 574 
 
 0.378 
 
 24.13 
 
 1.388 
 
 0.704 
 
 0.454 
 
 32.81 
 
 1.861 
 
 0.881 
 
 0.530 
 
 18.34 
 
 1.077 
 
 0.594 
 
 0.391 
 
 25.09 
 
 1.442 
 
 0.722 
 
 0.463 
 
 34.74 
 
 1.966 
 
 0.919 
 
 0.547 
 
 19.30 
 
 1.126 
 
 0.613 
 
 0.404 
 
 26.06 
 
 1.496 
 
 0.741 
 
 0.472 
 
 36.67 
 
 2.070 
 
 0.955 
 
 0.565 
 
 20.27 
 
 1.177 
 
 0.632 
 
 0.414 
 
 27.02 
 
 1.549 
 
 0.761 
 
 0.479 
 
 38.60 
 
 
 0.992 
 
 0.579 
 
 Properties of Saturated Vapors . — The figures in the following table 
 are given by Lorenz, on the authority of Mollier and of Zeuner. 
 
 
 Heat of 
 Vaporization, 
 
 Heat of Liquid, 
 B.T.U. per lb. 
 
 Absolute 
 Pressure, 
 
 Volume of 
 lib., 
 
 c F 
 
 B.T.U. per lb. 
 
 lbs. per sq. in. 
 
 cubic feet. 
 
 
 NH 3 
 
 C0 2 
 
 S0 2 
 
 NH 3 
 
 C0 2 
 
 S0 2 
 
 NH 3 
 27.1 
 
 C0 2 
 
 S0 2 
 
 NH 3 
 10 33 
 
 C0 2 
 312 
 
 S0 2 
 
 - 4° 
 
 589 
 
 117 6 
 
 171 
 
 -31.21 
 
 -17.19 
 
 -11.16 
 
 288.7 
 
 9 27 
 
 8 06 
 
 + 14° 
 
 580 
 
 110 7 
 
 168 2 
 
 -15.89 
 
 - 9.00 
 
 - 5.69 
 
 41.5 
 
 385.4 
 
 14 75 
 
 6 92 
 
 729 
 
 5 27 
 
 32° 
 
 569 
 
 99 8 
 
 164 2 
 
 
 
 
 
 
 
 61.9 
 
 503.5 
 
 22 53 
 
 4 77 
 
 167 
 
 3 59 
 
 50° 
 
 555 5 
 
 86 
 
 158 9 
 
 16.51 
 
 10.28 
 
 5.90 
 
 89.1 
 
 650.1 
 
 33.26 
 
 3 38 
 
 170 
 
 2 44 
 
 68° 
 
 539 9 
 
 66 5 
 
 152 5 
 
 33.58 
 
 23.08 
 
 12.03 
 
 125.0 
 
 826.4 
 
 47.61 
 
 2,47 
 
 083 
 
 1 71 
 
 86° 
 
 521 4 
 
 27.1 
 
 144 8 
 
 51.28 
 
 45.45 
 
 18.34 
 
 170.8 
 
 1040. 
 
 66.36 
 
 1.83 
 
 048 
 
 1 ?.?, 
 
 104° 
 
 500.4 
 
 
 135.9 
 
 69.58 
 
 
 24.88 
 
 227.7 
 
 
 90.30 
 
 1.39 
 
 
 0.88 
 
 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. (Bert helot, from 
 Siebel.) — Heat developed when a solution of 1 lb. NH 3 in n lbs. water 
 is diluted with a great amount of water = Q = 142/w B.T.U. Assuming 
 925 B.T.U. to be developed when 1 lb. NH 3 is absorbed by a great deal 
 (say 200 lbs.) of water, the heat developed in making solutions of different 
 strengths (1 lb. NH 3 to n lbs. water) = Q t = 925 - 142/rc, B.T.U. Heat 
 developed when b lbs. NH 3 is added to a solution of 1 lb. NH 3 + n lbs. 
 water = Q 3 = 925 - 142 (2 b + W)/n B.T.U. 
 
 Let the weak liquor enter the absorber with a strength of 10%,= 1 lb. 
 NH 3 + 9 lbs. water, and the strong liquor leave the absorber with a 
 strength of 25%, = 3 lbs. NH 3 + 9 lbs. water, b = 2, n = 9; Q 3 = 925 X 
 2 — 142 (4+ 4)/9 = 1724 B.T.U. Hence by dissolving 2 lbs. of ammonia 
 gas or vapor in a solution of 1 lb. ammonia in 9 lbs. water we obtain 
 12 lbs. 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 lbs. 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, , 
 
COMPARISON OF DIFFERENT COOLING AGENTS. 1289 
 
 Cooling Effect, Compressor Volume, and Power Required, with 
 Different Cooling Agents. (Lorenz.) 
 
 Cooling Agent. 
 
 1 . Temp, in front of regulating 
 
 valve 
 
 2. Vaporizer pressure, lbs. per 
 
 sq. in 
 
 3. Condenser pressure, lbs. per 
 
 sq. in 
 
 4. Heat of evaporation, B.T.U. 
 
 per lb 
 
 5. Heat imparted to the liquid 
 
 6. Cold produced per lb. B.T.U 
 
 7. Cooling agent circulated for 
 
 yield of 100,000 B.T.U. per 
 hour, lbs 
 
 8. Stroke volume for 100,000 
 
 B.T.U. per hour, cu. ft 
 
 9. Minimum H.P. per 100,000 
 
 B.T.U. per hour 
 
 10. Ratio Heat of evap. -f- cold 
 
 produced 
 
 11. Ratio total work to minimum 
 
 12. Total I.H.P. per 100,000 
 
 B.T.U. per hour 
 
 13. Cooling effect per I.H.P. hr.. 
 
 NH 3 
 
 68 
 
 41.5 
 
 125.0 
 
 580.2 
 49.47 
 530.73 
 
 188.4 
 
 1,300 
 
 4.98 
 
 1.093 
 1.175 
 
 5.85 
 17,100 
 
 C0 2 
 
 68 
 
 385.4 
 
 826.4 
 
 110.7 
 32.08 
 78.62 
 
 1272. 
 
 292 
 
 4.98 
 
 1.40J 
 1.513 
 
 7.53 
 13,300 
 
 so 2 
 
 68 
 
 14.75 
 
 47.61 
 
 168.2 
 17.72 
 150.48 
 
 664.3 
 
 3,507 
 
 4.98 
 
 1.118 
 1.202 
 
 5.99 
 16,700 
 
 NH 3 
 
 50 
 
 41.5 
 
 125.0 
 
 580.2 
 32.4 
 547.8 
 
 182.5 
 1,264 
 
 4.98 
 
 1.059 
 1.138 
 
 5.67 
 17,600 
 
 ( r> 2 
 
 50 
 
 385.4 
 
 826.4 
 
 110.7 
 19.28 
 91.42 
 
 1094. 
 
 242 
 
 4.98 
 
 1.211 
 1.302 
 
 6.48 
 15,400 
 
 S0 2 
 
 50 
 
 14.75 
 
 47.61 
 
 168.2 
 11.59 
 156.61 
 
 638.5 
 
 3,365 
 
 4.98 
 
 1.074 
 1.155 
 
 5.75 
 17,400 
 
 Ratios of Condenser Pressure, C. P., and Mean Effective Pres- 
 
 
 
 SURE, M. P., TO 
 
 Vaporizer Pressure, 
 
 V. P. 
 
 
 
 Ph 
 > 
 
 ~Ph 
 
 > 
 
 Ph 
 
 > 
 
 Ph 
 > 
 •1- 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 > 
 
 Ph 
 
 Ph 
 
 Pi 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 Ph 
 
 o 
 
 £ 
 
 o 
 
 S 
 
 O 
 
 S 
 
 O 
 
 £ 
 
 O 
 
 § 
 
 O 
 
 S 
 
 1.0 
 
 0. 
 
 2.0 
 
 0.752 
 
 3.0 
 
 1.249 
 
 4.0 
 
 1.684 
 
 5.0 
 
 1.947 
 
 6.0 
 
 2.216 
 
 1.2 
 
 0.186 
 
 2,2 
 
 0.865 
 
 3 2 
 
 1.344 
 
 4 2 
 
 1.711 
 
 5.2 
 
 2.006 
 
 7 
 
 2.454 
 
 1.4 
 
 0.350 
 
 2.4 
 
 0.970 
 
 3 4 
 
 1.414 
 
 4.4 
 
 1.766 
 
 5.4 
 
 2.062 
 
 8,0 
 
 2.666 
 
 1.6 
 
 0.487 
 
 2 6 
 
 1.070 
 
 3 6 
 
 1.491 
 
 4 6 
 
 1.829 
 
 5 6 
 
 2.116 
 
 9 
 
 2.858 
 
 1.8 
 
 0.630 
 
 2.8 
 
 1.163 
 
 3.8 
 
 1.564 
 
 4.8 
 
 1.891 
 
 5.8 
 
 2.168 
 
 10.0 
 
 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 -5- 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, \0.15. 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 NH3 and SO2 
 machines 10% and for CO2 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 SO2 machines 79,125 
 B.T.U. and for CO2 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 to other condenser and evaporator temperatures. 
 Each change of condition requires a separate calculation. The final 
 
1290 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 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 Brine Used to Absorb Refrigerating Effect of 
 Ammonia. (J. E. Denton, 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 lbs., 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 are as follows (Lehr- und Handbuch der Thermochemie, 
 1882): 
 
 Specific heat 0.791 0.805* 0.863 0.895 0.931 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 23 
 
 Deg. Salinometer 60° F 4 20 40 60 80 100 
 
 Sp. gravity 60° F 1.007 1.037 1.073 1.115 1.150 1.191 
 
 Per cent of salt, by wt 1 5 10 15 20 25 
 
 Wt. of 1.. gallon, lbs 8.40 8.65 8.95 9.30 9.60 9 94 
 
 Wt. of 1 cu. ft., lbs 62.8 64.7 66.95 69.57 71.76 74.26 
 
 Freezing point ° F 31.8 25.4 18. 6 12.2 6.86 1.00 
 
 Specific heat 0.992 0.960 0.892 0.855 0.829 0.783 
 
 Chloride of Calcium solution is commonly used instead of brine. 
 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 4 (- 5° to + 15°) 
 
 1.14 0.773 + 0.00064 4 (- 10° to + 20°) 
 
 1.20 0.710 + 0.00064 t (- 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. 
 
 N£ 
 
 , 
 
 
 
 <£ 
 
 . 
 
 
 
 vj 
 
 . 
 
 
 
 a 
 
 > 
 
 
 
 a 
 
 > 
 
 
 
 
 > 
 
 
 
 3 
 
 
 
 o5 • 
 mfa 
 a> . 
 
 3 
 
 Wfa 
 
 Ofe 
 
 
 *fa 
 
 05 . 
 
 fQfa 
 
 Ofe 
 
 id 
 s-.a 
 
 e5 • 
 
 o?fa 
 
 % D S 
 
 Z* 
 
 '~C 
 
 £Q 
 
 <N& 
 
 a^ 
 
 fc<3 
 
 £Q 
 
 aw 
 
 ^ 
 
 £Q 
 
 Q 
 
 m 
 
 fa 
 
 fa 
 
 Q 
 
 02 
 
 fa 
 
 fa 
 
 Q 
 
 Xfl 
 
 Ph 
 
 fa 
 
 1. 
 
 1.007 
 
 1 
 
 +31.10 
 
 21 
 
 1.169 
 
 19 
 
 + 1.76 
 
 32 
 
 1.283 
 
 30 
 
 -54.40 
 
 5.5 
 
 1.041 
 
 5 
 
 27.68 
 
 22 
 
 1.179 
 
 20 
 
 - 1.48 
 
 35 
 
 1.316 
 
 33 
 
 -25.24 
 
 11 
 
 1.085 
 
 10 
 
 22.38 
 
 23 
 
 1.189 
 
 21 
 
 - 4.90 
 
 35.5 
 
 1.327 
 
 34 
 
 - 9.76 
 
 17 
 
 1.131 
 
 15 
 
 12.20 
 
 26 
 
 1.219 
 
 24 
 
 -17.14 
 
 36.5 
 
 1.338 
 
 35 
 
 + 2.84 
 
 20 
 
 1.159 
 
 18 
 
 4.64 
 
 29 
 
 1.250 
 
 27 
 
 -32.62 
 
 37.5 
 
 1.349 
 
 36 
 
 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 
 
 * Interpolated. 
 
MACHINES USING DIFFERENT COOLING AGENTS. 1291 
 
 Boiling points of calcium chloride solutions: 
 
 Sp. Gr. at 59° F 1.104 1.185 1.268 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. at boiling point 1.085 1.119 1.209 1.308 1.365 1.452 1.526 1.619 
 
 "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 1-14 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 equiva- 
 lent to the effect of the melting of ice at 32° to water of the same tempera- 
 ture. 
 
 In making artificial ice the 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 is 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 reboiling, and using steam expansively in a compound 
 engine. 
 
 Ether-machines, used in India, are said to have produced about 6 lbs. 
 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 lbs. pressure is compressed to 210 or 240 lbs. 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 lbs., 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 
 
1292 ICE-MAKING OR REFRIGERATING! MACHINES. 
 
 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 CO2 plants on 
 shipboard. He describes a large duplex C0 2 compressor built by the 
 Brown-Cochrane Co., Lorain, O. Tests of C0 2 machines by a committee of 
 the Danish Agricultural Society were reported in 1899, in "Ice and Gold 
 Storage," of London. Carbon-diosride machines are built also by Kroeschel 
 Bros., Chicago. . 
 
 Methyl-Chloride machines are made by Railway and Stationary Refrig- 
 erating Co., New York City. The compressor is a rotary pump. When 
 driven by an electric motor the complete apparatus is very compact, 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 lbs., and per pound of coal ranging 
 from 44.7 to 21.1 lbs., as the temperature corresponding to the pressure of 
 the vapor in the condenser rises from 59° to 104° F. The theoretical 
 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%. There are other losses due to superheating the gas at the brine- 
 tank, and in the pipe leading from the brine-tank to the compressor,, so 
 that in actual practice a sulphur-dioxide machine, working under the 
 conditions of an absolute pressure in the condenser of 56 lbs. per sq.in. 
 and the corresponding temperature of 77° F., will give about 22 lbs. of iQe- 
 melting capacity per pound of coal, which is about 60% of the theoretical 
 amount neglecting friction, or 70% including friction. 
 
 Sulphur-dioxide machines are not now used in the United States (1910). 
 
 Refrigerating-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 freezing- 
 point of water. The water vapor is compressed from, say, a pressure of 
 0.1 lb. per sq. in. to IV2 lbs. and discharged into a condenser. It is then 
 condensed and removed by means of an ordinary air-pump. The prin- 
 ciple 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 11/2 lbs. per sq. in., and a coal 
 consumption of 3 lbs. per I.H.P. per hour, gives an ice-melting effect of 
 34.5 lbs. per pound of coal, neglecting friction. Ammonia for ice-making 
 conditions gives 40.9 lbs. 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 condenser- 
 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§% more pipe surface than a wet compression system, 
 
AMMONIA MACHINES. 1293 
 
 in which the ammonia leaves the coils containing sufficient entrained 
 liquid to maintain a wet compression condition in the compressor. 
 
 The flooded system is one 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 
 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 System, 
 a small size compressor, a small size evaporating system, a large amount 
 of ammonia. 
 
 A Wet Compression plant will need, with a Wet Compression Evapo- 
 rating System, a large size compressor, a medium size evaporating system, 
 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 com- 
 munication 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 with 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 refriger- 
 ating 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 bv 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 the vapor therefrom, still under considerable pressure, is admitted to 
 
1294 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 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 
 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 liquor 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 of 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 lbs. suction and 170 lbs. 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, owing 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. 
 
 Belative 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 lb. of coal imparts 10,000 B.T.TJ. to the boiler. The condensed steam 
 from the generator of the absorption-machine is assumed to be returned 
 
 Condenser. 
 
 Refrigerat- 
 ing Coils. 
 
 fe 
 
 Pounds of Ice-melting Effect 
 per lb. of Coal. 
 
 %&i 
 
 
 u 
 
 
 u 
 
 Compress. 
 
 Absorption- 
 
 2^1 
 
 
 ft 
 
 g 
 
 3 
 
 
 ft 
 3 
 
 0> 
 0> 
 
 Machine. 
 
 Machine.* 
 
 1 
 
 ft 
 
 8Ph 
 
 "3 . 
 
 8^ 
 
 achine in 
 ammonia 
 
 ump ex- 
 the gen- 
 
 le amm. 
 
 exhausts 
 
 mosphere 
 
 heater, 
 
 temp, to 
 ;r. 
 
 ill 
 
 b£ 
 V 
 
 a 
 
 d 
 
 a 
 
 ft 
 0> 
 
 3, a 
 
 3* 
 
 T3 
 ft 
 
 a 
 
 0) 
 
 H 
 
 O) 
 
 ft 
 
 < 
 ft 
 
 a 
 
 01 
 
 ■eg 
 
 ■as 
 
 ~ o 
 
 Absorption-m 
 which the 
 circulating-p 
 hausts into 
 erator. 
 
 In which t 
 circ. pump 
 into the at 
 through a 
 yielding 212° 
 the f eed-wat« 
 
 iil 
 
 G &«* 
 a ti o 
 
 ^5^2 — 
 
 e« 8 ** 
 go ft 
 
 61.2 
 
 110.6 
 
 5 
 
 33.7 
 
 61.2 
 
 38.1 
 
 71.4 
 
 38.1 
 
 33.5 
 
 969 
 
 59.0 
 
 106.0 
 
 5 
 
 33.7 
 
 59.0 
 
 39.8 
 
 74.6 
 
 38.3 
 
 33.9 
 
 967 
 
 59.0 
 
 106.0 
 
 5 
 
 33.7 
 
 130.0 
 
 39.8 
 
 74.6 
 
 39.8 
 
 35.1 
 
 931 
 
 59.0 
 
 106.0 
 
 -22 
 
 16.9 
 
 59.0 
 
 23.4 
 
 43.9 
 
 36.3 
 
 31.5 
 
 1000 
 
 86.0 
 
 170.8 
 
 5 
 
 33.7 
 
 86.0 
 
 25.0 
 
 46.9 
 
 35.4 
 
 28.6 
 
 988 
 
 86.0 
 
 170.8 
 
 5 
 
 33.7 
 
 130.0 
 
 25.0 
 
 46.9 
 
 36.2 
 
 29.2 
 
 966 
 
 86.0 
 
 170.8 
 
 -22 
 
 16.9 
 
 86.0 
 
 16.5 
 
 30.8 
 
 33.3 
 
 26.5 
 
 1025 
 
 86.0 
 
 170.8 
 
 -22 
 
 16.9 
 
 130.0 
 
 16.5 
 
 30.8 
 
 34.1 
 
 27.0 
 
 1002 
 
 104.0 
 
 227.7 
 
 5 
 
 33.7 
 
 104.0 
 
 19.6 
 
 36.8 
 
 33.4 
 
 25.1 
 
 1002 
 
 104.0 
 
 227.7 
 
 -22 
 
 16.9 
 
 104.0 
 
 13.5 
 
 25.3 
 
 31.4 
 
 23.4 
 
 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. 
 
EFFICIENCY OF REFRIGERATING MACHINES. 1295 
 
 to the boiler at the temperature of the steam entering 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 26 1/4 lbs. 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 absorption system, see Ledoux's 
 work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus, 
 Trans. A. S. M. E., xiv, 1416, 1436; and papers by Denton and Jacobus, 
 Trans. A. S. M. E., x, 792, xiii, 507. 
 
 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 1311) 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 -h 
 778 = 2786 B.T.U. Then 14,776 h- 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 colder 
 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 -s- (T t - T ), in which Tt 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 
 
 / PO TsDed r fich'^x e ra 1 Se r l- ° f brine or other 
 ice-melting capacity) _ 1 p X f gera'Ture "" ge J circulating fluid 
 per pound of fuel J 144 x pounds of fuel used per hour 
 
 The Ice-melting capacity is expressed as follows: 
 
 / 24 v SSHflS hP«t 1 of brine circulated per 
 Tons (of 2000 lbs.) •> 1 v r?n« ?«f % 1 hour 
 
 ice-melting ca- 1 = ± x ran g e of tem P- } 
 
 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 difference 
 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 -f- heat received from boiler. 
 The efficiency of the refrigerating-machine = heat received from the brine- 
 tank or cold-room •*- 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 •*- heat re- 
 ceived from the boiler. 
 
1296 ICE-M4KING OR REFRIGERATING MACHINES. 
 
 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, condenser 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, lb 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, lb., 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, lb. . 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 cooled. For average practice back pres- 
 sures for the production of required temperatures should be approxi- 
 mately as follows: 
 
 Temperature of room, ° F 10 15 20 28 32 36 40 50 60 
 
 Back pressure, gage, lb 10 12 15 22 25 27 30 35 40 
 
 Temperature of ammonia, ° F... -10-5 8 12 14 17 2226 
 
 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. 
 
 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 — 
 (t t — £o)/1330, in which ti = the theoretical temperature of gas after 
 compression and £ = temperature of gas delivered to the compressor. The 
 temperature ti, = T\ — 460, is calculated from the formula for adiabatic 
 compression, T x = T (Pi/P ) ' 24 , in which T t and T are absolute tem- 
 peratures and Pi and P absolute pressures. In eight tests by Prof. 
 Denton the volumetric efficiency ranged from 73.5% to 84%, and they 
 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 vapor 
 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 gauge pressures of suction and condenser. 
 
 Suction pressures 
 
 Cond. press. 140 
 
 Cond. press. 170 — 
 Cond. press. 200 
 
 tt E F 
 
 323° 0.76 10.35 
 
 221° 0.83 4.57 
 
 167° 0.87 2.96 
 
 15 
 
 Ti E F 
 
 358° 0.73 11.02 
 254° 0.81 4.78 
 192° 0.86 3.07 
 
 30 
 
 ~t E \ F 
 
 388° 0.71 11.57 
 
 280° 0.79 5.03 
 
 216° 0.84 3.21 
 
AMMONIA MACHINES. 
 
 1297 
 
 Pounds of Ammonia per Minute to Produce 1 Ton of Refrigeration, 
 and Percentage of Liquid Evaporated at the Expansion Valve. 
 
 Condenser, Pressure and 
 Temperature. 
 
 Refrigerator, pressure and 
 temperature lbs.,— 29°. . 
 
 Refrigerator pressure and 
 
 , temperature 15 lbs., — 0°... 
 
 Refrigerator pressure and 
 temperature, 30 lbs., -17°. 
 
 140 lbs., 80°. 
 
 170 lbs., 90°. 
 
 200 lbs., 100°. 
 
 0.431 lb., 19% 
 0:4201b., 14.4% 
 0.415 1b., 11.6% 
 
 0.441 lb., 20.8% 
 0.4301b., 16.2% 
 0.4251b., 13.4% 
 
 0.451 lb., 22.5% 
 0.4401b., 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) - 231 ~U, 
 Po = suction and p t condenser pressure, abs. lbs. per sq. in. The maxi- 
 mum M.E.P. occurs when p = p x -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 331/3% 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 Tiorse-power (C) and the engine horse-power (E) are given 
 below for the conditions named . 
 
 Suction 
 pressure. 
 
 Cond. press., 140. 
 Cond. press., 170. 
 Cond. press., 200. 
 
 (M) 
 46.5 
 50.5 
 55.0 
 
 (C) 
 2.10 
 
 2.42 
 2.78 
 
 (E) 
 2.80 
 3.23 
 3.71 
 
 67.0 
 74.5 
 
 (C) 
 1.19 
 1.40 
 1.64 
 
 (E) 
 1.59 
 1.87 
 2.19 
 
 as 
 
 75.0 
 85.0 
 
 (C 
 0.83 
 1.00 
 1.19 
 
 (E) 
 1.11 
 1.33 
 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 lbs., 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, lbs. per sq. in: L = length of stroke in 
 ft.; a = area of piston in sq. ins.; n= no. of compressions per minute: 
 E c = apparent volumetric efficiency, the ratio of the volume of ammonia 
 apparently taken in per stroke to the full displacement of the piston; 
 w c = weight of 1 cu. ft. of ammonia vapor at the back pressure, as it exists 
 in the cylinder when compression begins; L c = 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 
 
 T 
 
 LaE c nw c X L c X 60 X 24 
 144 X 288,000 
 
 W C L C * E c 
 
 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 
 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 
 
1298 ICE-MAKING OK REFRIGERATING MACHINES. 
 
 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 lbs. per minute is calculated 
 from the formula P = (144 X 2000) -5- [1440 1 - (fit - ho)] in which 
 I is the latent heat of evaporation at the back pressure in the cooler, and 
 hi and h 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 lbs. in 24 hours = 288,000 
 B.T.U. 
 
 B = 
 C = 
 
 Pounds of ammonia evaporated per minute. 
 
 Cubic feet of gas to be handled per minute by the compressor. 
 
 I. 
 
 
 Head or Condenser Gauge Pressure and Corresponding 
 Temperature. 
 
 w. 
 B.P. 
 
 100 
 
 lb. 
 63.5° 
 
 110 
 
 lb. 
 68° 
 
 120 
 
 lb. 
 72.6° 
 
 130 
 
 lb. 
 77.4° 
 
 140 
 
 lb. 
 80.3° 
 
 150 
 
 lb.. 
 
 83.8° 
 
 160 
 
 lb. 
 87.4° 
 
 170 
 
 lb. 
 90.8° 
 
 180 
 
 lb. 
 93.8° 
 
 190 
 
 lb. 
 96.9° 
 
 200 
 
 lb. 
 100° 
 
 572.78 ) 
 .0556 \ 
 ) 
 
 B 
 
 C 
 
 .4159 
 7.482 
 
 .4199 
 7.551 
 
 .4240 
 7.626 
 
 .4284 
 7.703 
 
 .4310 
 7.761 
 
 .4343 
 7.812 
 
 .4376 
 7.870 
 
 .4408 
 7.929 
 
 .4440 
 7.986 
 
 .4470 
 8.041 
 
 .4501 
 8.095 
 
 566.14 ) 
 .0,33 j 
 
 B 
 
 C 
 
 .4122 
 5.636 
 
 .4160 
 5.675 
 
 .4202 
 5.732 
 
 .4243 
 5.790 
 
 .4271 
 5.826 
 
 .4308 
 5.878 
 
 .4335 
 5.914 
 
 .4366 
 5.970 
 
 .4397 
 5.999 
 
 .4437 
 6.039 
 
 .4458 
 6.081 
 
 560.69 ) 
 .0910} 
 10 ) 
 
 B 
 C 
 
 .4093 
 4.502 
 
 .4130 
 4.543 
 
 .4171 
 4.587 
 
 .4204 
 4.625 
 
 .4237 
 4.662 
 
 .4271 
 4.698 
 
 .4302 
 4.733 
 
 .4332 
 4.766 
 
 .4363 
 4.799 
 
 .4392 
 4.833 
 
 .4423 
 4.865 
 
 556.11 ) 
 .1083 | 
 15 ) 
 
 B 
 C 
 
 .4068 
 3.756 
 
 .4106 
 3.791 
 
 .4145 
 3.827 
 
 .4186 
 3.866 
 
 .4211 
 
 3.889 
 
 .4244 
 3.918 
 
 .4276 
 3.948 
 
 .4288 
 3.975 
 
 .4336 
 4.003 
 
 .4365 
 4.030 
 
 .4394 
 4.058 
 
 552,83 ) 
 .1258 \ 
 20 ) 
 
 B 
 C 
 
 .4040 
 3.211 
 
 .4077 
 3.241 
 
 .4116 
 
 3.272 
 
 .4158 
 3.305 
 
 .4182 
 3,324 
 
 .4214 
 3.350 
 
 .4245 
 3.375 
 
 .4275 
 3.398 
 
 .4304 
 3.422 
 
 .4333 
 3.444 
 
 .4362 
 3.467 
 
 548.40 ) 
 .1429 ) 
 25 ) 
 
 B 
 C 
 
 .4025 
 2.819 
 
 .4062 
 2.843 
 
 .4102 
 2.870 
 
 .4140 
 2.898 
 
 .4167 
 2.916 
 
 .4198 
 2.938 
 
 .4229 
 2.959 
 
 .4258 
 2.980 
 
 .4287 
 3.000 
 
 .4316 
 3.020 
 
 .4345 
 3.040 
 
 545.13) 
 .1600 [ 
 30 ) 
 
 B 
 C 
 
 .4013 
 2.507 
 
 .4049 
 2.530 
 
 .4088 
 2.555 
 
 .4128 
 2.580 
 
 .4152 
 2.600 
 
 .4184 
 2.615 
 
 .4213 
 2.633 
 
 .4243 
 2.653 
 
 .4273 
 2.671 
 
 .4300 
 2.687 
 
 .4329 
 2.706 
 
 542.80 ) 
 .1766 £ 
 35 ) 
 
 B 
 
 C 
 
 .3991 
 2.260 
 
 .4028 
 2.280 
 
 .4066 
 2.302 
 
 .4105 
 2.925 
 
 .4130 
 
 2.338 
 
 .4161 
 2.356 
 
 .4188 
 2.373 
 
 .4220 
 2.390 
 
 .4249 
 2.406 
 
 .4277 
 2.422 
 
 .4305 
 2.443 
 
 539.35 ) 
 .1941 \ 
 40 ) 
 
 B 
 C 
 
 .3984 
 2.052 
 
 .4020 
 2.071 
 
 .4058 
 2.090 
 
 .4098 
 2.111 
 
 .4122 
 2.123 
 
 .4153 
 2.139 
 
 .4183 
 2.155 
 
 .4211 
 2.175 
 
 .4240 
 2.185 
 
 .4269 
 2.200 
 
 .4296 
 2.214 
 
 I, Latent heat of volatilization, w, weight of vapor per cubic foot, 
 back pressure or suction gauge pressure. 
 
 10 
 
 8.5° 
 
 15 
 
 -1° 5.66 c 
 
 25 
 
 11.5* 
 
 35 
 
 21.7° 
 
 40 
 
 26.1 
 
 Back Pressures 5 
 
 Temperatures —28.5° —17.5° 
 
 Mr. Matthews defines a standard ton of refrigeration as the equivalent 
 of 27 lbs. of anhydrous ammonia evaporated per hour from liquid at 
 90° F. into saturated vapor at 15.67 lbs. 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 lb. of ammonia 
 from a temperature of — 28.5° F. into saturated vapor at atmospheric 
 pressure. 
 
CAPACITY OF MACHINES. 
 
 1299 
 
 Size and Capacities of Ammonia Refrigerating Machines. — ■ 
 
 York Mfg. Co. Based on 15.67 lbs. back-pressure, 185 lbs. condensing 
 pressure, and condensing water at 60° F. 
 
 Si* 
 
 Comp 
 
 gle-Acting Compressors. 
 
 Double-Acting Compressors. 
 
 ™essors. 
 
 Engine. 
 
 Capacity 
 
 Tons 
 Refrig- 
 eration . 
 
 Compressors. 
 
 Engine. 
 
 Capacity 
 Tons 
 
 Bore. 
 
 Stroke. 
 
 Bore. 
 
 Stroke. 
 
 Bore. 
 
 Stroke. 
 
 Bore. 
 
 Stroke. 
 
 Refrig- 
 eration. 
 
 71/2 
 
 10 
 
 111/9 
 
 10 
 
 10 
 
 9 
 
 15 
 
 131/9 
 
 12 
 
 20 
 
 9 
 
 12 
 
 131/9 
 
 12 
 
 20 
 
 11 
 
 18 
 
 16 
 
 15 
 
 30 
 
 11 
 
 15' 
 
 16 
 
 15 
 
 30 
 
 121/2 
 
 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 
 
 281/9 
 
 32 
 
 175 
 
 21 
 
 32 
 
 281/9 
 
 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 compound engines. 
 
 Displacement and Horse-Power per Ton of Refrigeration. 
 Dry Compression. S. A., Single-acting; D. A., double-acting. 
 
 
 Suction Gauge Pressure and Corresponding Temp. 
 
 
 51b.= 
 
 101b. = 
 
 15.671b. 
 
 20 lb. = 
 
 25 1b.= 
 
 
 - 17.5° F. 
 
 -8.5°F. 
 
 = 0°F. 
 
 5.7° F. 
 
 11.5° F. 
 
 Condenser Gauge 
 Pressure and Corresp. 
 
 
 
 
 
 
 
 c 
 
 
 a 
 
 
 
 
 
 
 
 Temp, of Liquid at 
 
 * 
 
 o 
 H 
 
 
 o 
 
 
 o 
 
 
 o 
 
 
 o 
 
 Expansion valve. 
 
 ft 
 
 ft 
 
 
 ft 
 
 
 a 
 
 EH 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fi 
 
 a 
 
 Q 
 
 ft 
 
 H 
 
 ft 
 
 W 
 
 ft 
 
 O 
 
 ft 
 
 
 c 
 
 fk 
 
 a 
 
 ru 
 
 z 
 
 K 
 
 a 
 
 fk 
 
 g 
 
 Ph 
 
 
 j3 
 
 K 
 
 3 
 
 w 
 
 6 
 
 W 
 
 6 
 
 m 
 
 D 
 
 W 
 
 
 o 
 
 1-1 
 
 o 
 
 1-1 
 
 u 
 
 1-1 
 
 u 
 
 '- , 
 
 y 
 
 *-! 
 
 145 lb. 82° F., S.A 
 
 12,608 
 
 1,654 
 
 9,811 
 
 1.4 
 
 7829 
 
 1.195 
 
 6765 
 
 1.065 
 
 5836 
 
 0.943 
 
 145 1b. 82° F.,D.A 
 
 14,645 
 
 1.921 
 
 11,300 
 
 1.612 
 
 8901 
 
 1.358 
 
 7625 
 
 1.2 
 
 6522 
 
 1.054 
 
 165 1b.89°F.,SA 
 
 13,045 
 
 1 834 
 
 10,148 
 
 1 56 
 
 8092 
 
 1.341 
 
 6990 
 
 1.201 6027 
 
 1.071 
 
 165ib.89°F.,D.A 
 
 15,203 
 
 2 137 
 
 11,720 
 
 1.802 
 
 9224 
 
 1.529 
 
 7898 
 
 1.357 6751 
 
 1.2 
 
 185 lb. 95.5° F., S.A. ... 
 
 13,491 
 
 ?. on 
 
 10,487 
 
 1 72 
 
 8362 
 
 1.4865 
 
 7219 
 
 1 .336 6223 
 
 1.197 
 
 185 lb. 95. 5° F., DA.... 
 
 15,774 
 
 2 354 
 
 12,150 
 
 1.993 
 
 9555 
 
 1.7 
 
 8176 
 
 1.513 
 
 6985 
 
 1.344 
 
 2051b. 101.4° F., S.A... . 
 
 13,947 
 
 2 192 
 
 10,834 
 
 1.879 
 
 8630 
 
 1.631 
 
 7450 
 
 1.47 
 
 6420 
 
 1,323 
 
 205 1b.101.4°F.,D.A.... 
 
 16,362 
 
 2.571 
 
 12,590 
 
 2.184 
 
 9890 
 
 1.87 
 
 8459 
 
 1.67 
 
 7222 
 
 1.488 
 
 * 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. 
 
1300 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 Small Sizes of Refrigerating Machines. 
 
 Capacity, tons , 
 
 Compressor, diam., in. 
 Compressor, stroke, in 
 
 Engine, diam., in 
 
 Engine, stroke, in 
 
 Single-acting, 
 Vertical. 
 
 1 1/4 
 
 41/2 
 5 
 5 
 
 2-6 
 6 
 8 
 6 
 
 Double-acting, 
 Horizontal. 
 
 21/2 
 
 51/2 
 
 10 
 
 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 lbs. gauge, corresponding to 
 0° F. temperature of saturated ammonia vapor, and a condensing pressure 
 of 185 lbs. 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. 
 
 
 Suction Gauge Pressure and Corresponding Temp. 
 
 
 51b = 
 
 -17.5°. 
 
 10 lb = 
 
 -8.5°F. 
 
 15.671b. 
 = 0°F. 
 
 20 lb. = 
 5.7° F. 
 
 25 lb. = 
 11.5° F. 
 
 30 lb. = 
 16.8° F. 
 
 Temp. 
 
 o 
 
 P-l 
 
 w 
 
 c 
 
 
 
 Ph 
 
 X 
 
 a 
 
 O 
 
 H 
 
 
 o 
 
 Ph 
 W 
 
 a 
 
 o 
 H 
 
 P^ 
 
 w 
 
 a 
 
 o 
 
 P4 
 
 145 1b. = 82° 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 
 
 63 4 
 
 165 1b. = 89° F 
 
 185 1b. = 95.5° F 
 
 205 1b. = 101.4° F 
 
 70.1 
 76.5 
 86.2 
 
 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: 
 
 Tons 
 
 R.P.M 
 
 Piston speeds. . 
 
 20 
 
 30 
 
 40 
 
 50 60 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 240 
 
 300 
 
 400 
 
 90 
 
 78 
 
 73 
 
 68 64 
 
 60 
 
 581/-, 
 
 57 
 
 56 
 
 55 
 
 54 
 
 53 
 
 52 
 
 51 
 
 481/9 
 
 200 
 
 215 
 
 228 
 
 240 250 
 
 270 
 
 280 
 
 286 
 
 290 
 
 293 
 
 296 
 
 300 
 
 315 
 
 340 
 
 378 
 
 500 
 
 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 11/4-in. 
 pipe, is used, but this necessitates higher condenser pressures. If F = 
 sq. ft. of cooling surface, h = heat of evaporation of 1 lb. ammonia at 
 the condenser temperature, K = lbs. of ammonia circulated per minute, 
 m ~ B.T.U. 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 - U), For t = 80 and ti == 70, ni 
 
CONDENSERS AND COOLING TOWERS. 
 
 1301 
 
 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, 1 i/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°. 
 
 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 
 1 l/ 4 -in. 
 pipe. 
 Ft. per 
 min. 
 
 Total 
 
 gallons 
 
 used 
 
 per 
 
 min. 
 
 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 
 
 1.16 
 
 1.165 
 1.165 
 1.18 
 1.24 
 1.30 
 
 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 
 
 1.71 
 1.71 
 1.71 
 1.71 
 1.71 
 1.71 
 
 0.0016 
 
 0.004 
 
 0.007 
 
 0.011 
 
 0.016 
 
 0.030 
 
 1.7116 
 
 1.714 
 
 1.717 
 
 1.721 
 
 1.726 
 
 1.74 
 
 Capacity Constant. 
 
 100 
 
 7.77 
 
 0.777 
 
 2.28 
 
 10. 
 
 225 
 
 2.04 
 
 0.001 
 
 2.041 
 
 150 
 
 11.65 
 
 1.165 
 
 5.75 
 
 10. 
 
 185 
 
 1.71 
 
 0.004 
 
 1.714 
 
 200 
 
 15.54 
 
 1.554 
 
 9.98 
 
 10. 
 
 165 
 
 1.54 
 
 0.009 
 
 1.549 
 
 250 
 
 19.42 
 
 1.942 
 
 15. 
 
 10. 
 
 155 
 
 1.46 
 
 0.018 
 
 1.478 
 
 300 
 
 23.31 
 
 2.331 
 
 21.6 
 
 10. 
 
 148 
 
 1.40 
 
 0.030 
 
 1.43 
 
 400 
 
 31.08 
 
 3.108 
 
 37.8 
 
 10. 
 
 140 
 
 1.33 
 
 0.071 
 
 1.401 
 
 The horse-power per ton is for single-acting compressor with 15.67 lbs. 
 suction pressure. 
 
 The friction in water pump and connections should be added to water 
 horse-power and to total horse-power. 
 
 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 148 109 58 
 
 Temperature of the atmosphere 78° 78.5° 78° 
 
 Relative humidity, % 47 49 97 
 
 Initial temperature 85.5° 85° 86° 
 
 Final temperature 78° 76° 75° 
 
 Range 7.5° 9° 11° 
 
1302 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 The final temperatures which may be obtained when the initial tem- 
 perature does not exceed 100° are as follows: 
 
 Atmosphere temp. 
 
 95° I 90° 1 85° 80° 1 75° 1 70° 
 
 
 Final temperature of water leaving tower. 
 
 (90 
 
 100 
 
 95 
 
 90 
 
 85 
 
 80 
 
 75 
 
 80 
 
 98 
 
 92 
 
 88 
 
 83 
 
 78 
 
 73 
 
 Humidity, % J J} 
 
 95 
 92 
 
 90 
 
 88 
 
 86 
 83 
 
 80 
 78 
 
 76 
 
 74 
 
 71 
 69 
 
 50 
 
 89 
 
 84 
 
 79 
 
 75 
 
 70 
 
 66 
 
 140 
 
 85 
 
 80 
 
 76 
 
 71 
 
 67 
 
 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 Refrigerating-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°. 
 
 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-cylinder 9.9-in. 
 bore and 16.5-in. stroke, and also in tests by Prof. Denton 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 lb. of Coal, 
 
 assuming 3 lbs. per hour per 
 
 Horse-power. 
 
 Test. 
 
 Condenser. 
 
 Suction. 
 
 Theoretical 
 Friction* 
 included. 
 
 Actual. 
 
 Per cent of 
 
 Loss Due to 
 
 Cylinder 
 
 Superheating. 
 
 1(24 
 
 fl^26 
 £i25 
 
 72.3 
 70.5 
 69.2 
 68.5 
 
 84.2 
 82.7 
 84.6 
 
 26.6 
 
 14.3 
 
 0.5 
 
 -11.8 
 
 15.0 
 - 3.2 
 -10.8 
 
 50.4 
 37.6 
 29.4 
 22.8 
 
 27.4 
 21.6 
 18.8 
 
 40.6 
 30.0 
 22.0 
 16.1 
 
 24.2 
 17.5 
 14.5 
 
 19.4 
 20.2 
 25.2 
 29.4 
 
 11.7 
 19.0 
 
 22.9 
 
 * Friction taken at figures observed in the tesjs, 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 refrigerative 
 effect and the heat (or mechanical work) consumed, also the cooling 
 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) 
 •*- T: in which T e = 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. (Continued on page 1305.) 
 
TEST-TRIALS OP REFRIGERATING MACHINES. 1303 
 
 £ a 
 
 .s- ^ 
 
 3 £3 
 
 2 3 w a. 
 
 
 •am^'Bjad 
 -ui9£ jo aStnjy; -j O of 3urams 
 -s-b '^;iobcJb3 Supjaui-ao'i jo 
 uo X Ja, d •aa^'BAi' -SuisuapuoQ 
 
 "3 
 
 |22 
 
 
 •uorjoijjj miM. "Japuipto 
 -un3a;g jo '• j-jj J9d anotj iad 
 {T30Q jo -sqj f SuiuinssB 'JBOQ JO 
 qi aad /C-;iO'Bd'BQ Suppui-aoj 
 
 
 e> >r\ — 
 
 
 •^uauiao'B|d 
 -siq uo^sij jo (jooj oiqnQ 
 jad XjpudTJQ 2upiaui-aoj_ 
 
 
 ill 
 
 ooo 
 ooo 
 
 
 03^3-2 
 
 S H- S 
 
 •jaAvod 
 -asjojj jad jnoq aaj 
 
 
 ooo 
 
 
 •uoi;ouj q^JA\. 
 •uoissajduioQ jo O 1 
 spo^' jo -qi-^JJaj 
 
 1-1 
 
 
 ooi? t 
 o o o 
 
 
 a 
 s 
 
 • 
 03 
 
 "3. 
 
 3 
 
 a 
 o 
 
 & 
 
 'o 
 o 
 
 
 
 ft 
 
 q 
 ft 
 
 
 •jaAvod ^ 
 -urea^g pa^oipuj io 
 jo *uoi-jou j %L\Y ^ 
 
 ft 
 
 ooo 
 
 
 •uoj^ouj ^noq^t^ ^ 
 
 ft 
 
 OOO 
 
 o-o 
 
 
 •padojaA 
 -9q s^iuq psuuaqx ^ 
 aAi^'BSa^ jo jaqranfj 
 
 H 
 
 on <n pq 
 
 
 •jasuapuog „ 
 ^-b pa^OBJ^sqy ^ajj O 1 
 
 
 E"S 
 
 
 •passaad g 
 -uioq BT3Q jo ;qSta^ 5 
 
 
 ONvOOv 
 
 o' o o 
 
 
 •uoissaiduioo jo ^ 
 
 pug ^13 SBQ JO 8Jn^BJ3dUI9 J^ "" 
 
 ft 
 
 bi 
 
 Q 
 
 CO o — ' 
 
 — — ^j 
 
 
 •snoo-3ui}^ja3uj <-i 
 -ay; ui ajrissajjj' a^rqosqy + 
 
 3 . 
 na 
 
 Isl 
 
 
 JOCl 
 
 ~pu 
 
 •SJI03 
 
 3 A> 
 odsaj 
 
 -Sup-BjaSujay; ut 
 ajtissajj o^ Sui ,2 
 ioq ajn^ujadmaj, 
 
 
 ft 
 
 ooo 
 
 OO =5. 
 
 7 
 
 3 v G+* g 
 
1304 ICE-MAKING OE REFRIGERATING MACHINES. 
 
 I g| 
 
 -as 
 
 
 o 5 
 
 ^9 
 
 CO s 
 
 n» a 
 
 a s« . 
 
 « o » w 
 
 * H O h 
 c8 S 55 S 
 
 * m -H Q 
 
 S .BO 
 A ° H 
 
 3 2-5 
 S.-o2 
 
 |Bg 
 S oS 
 
 o g w 
 
 05 
 
 sjnoq ^s at X^io-bcJ 
 -■bq Sui^aui-aoj jo 
 uoj, .lad a;nmj\[ aaj 
 
 • A^iO'Bd'BQ Sulcata 
 -ao'j jo uoj, jaj 
 
 •duia^jo 
 aSu'B'jjQOf SuiuinssB 
 '^uauiaoBidsiQ uo^ 
 
 -91 J JO ■%} ho J8J 
 
 •^uaux 
 -ao-BjdstQ uo? 
 -sij joHj'no jaj 
 
 uorjou^uii^ 
 
 •uoic> 
 
 •uopouj q^JAi 
 
 •uor> 
 -vug %r\omis& 
 
 •uopoijj 
 aad ' jnojj aaj 
 
 •uot^oij^j Sui 
 -pnpui 'papuadxg; 
 5 T J °iWJ°'qi-^ J9 d 
 
 •uopoij^ ^no 
 -tjiim 'papuadxg 
 
 nOOOOOOO 
 
 -8§§§gS 
 
 00 fNOO« 
 
 ■noo "T o r> ««ii 1 no 
 - m 00 cry 00 in eg 
 
 -"* r^ fi Cn] (N CnI 
 
 jaMod-uiBa^g pa^-eo 
 
 -ipuj JO 'UOI^OUJ U^IM. 
 
 iioissaadiuoQ 10 >[-io^y 
 
 •uopouj ^noq^iAi 
 uoissajdraoQ 10 i[j6^ 
 
 •papuad 
 -xg ^an 01 loajjg; 
 
 ui ^oajjg; Sui^BJQSup'a; 
 
 •jasuapuoQ 
 moij An/we pauj'BO ^ajj 
 
 •uoissajdraog 
 jo pug %v ajh^'BJadraaj, 
 
 •jasuapuoQ 
 ui amssajj a^njosqv 
 
 ,Q 01—. 
 
 jasuapuoQ ui jod'B^ I 
 jo -ssajjj o? ariQ -draax I 
 
 3-No"' T r'rNfo'"oN"oo" 
 
 sooooo 
 
 "f hN — On -O nO 
 _W fNq__rrOO 
 
 £^0 00000 
 © 00000 
 
 = S|? 
 
 000000 
 
 ^i£irnOOOin (N 
 ^'N0'fs'~00'"ON"o'"'- " 
 
 -OOnOO(NnO 
 
 ^-<r f^ — on r>. -<r 
 
 ^fn pnj — on 00 r>' 
 
 ^00 o <n T no r>s 
 
 n p> o m in oc 
 
 
 m I 
 
 < W 
 
 5 S 3 fe 
 2 S 
 
 SO « 
 
 fe IS s§ 
 
 00 h 
 
 O p 
 
 On ON On O OO O 
 
 ^O OOOOO 
 
 — tn ^ ^ in in in 
 
 (17) 
 0.1611 
 .1620 
 .1628 
 .1636 
 .1643 
 .1649 
 
 (16) 
 .000116 
 .000114 
 .000111 
 .000109 
 .000107 
 .000105 
 
 (15) 
 23.4 
 20.6 
 18.4 
 16.5 
 14.9 
 13.5 
 
 (14) 
 26.9 
 23.7 
 21.1 
 18.9 
 17.1 
 15.5 
 
 (13) 
 70.2 
 61.8 
 55.1 
 49.4 
 44.7 
 40.6 
 
 i~Ntv. m eo -«r no 
 
 (11) 
 
 9,980 
 
 8,790 
 
 7,840 
 
 7,030 
 
 6,360 
 
 5,780 
 
 (10) 
 .00504 
 .00444 
 .00396 
 .00355 
 .00321 
 .00292 
 
 (9) 
 .00580 
 .00510 
 .00455 
 .00408 
 .00369 
 .00335 
 
 (8) 
 6,530 
 7,280 
 8,000 
 8,750 
 9,480 
 10,200 
 
 (7) 
 
 5,680 
 
 6,330 
 
 6,960 
 
 7,610 
 
 8,240 
 
 8,870 
 
 (6) 
 4.48 
 3.95 
 3.52 
 3.15 
 2.85 
 2.59 
 
 (5) 
 32.93 
 32.31 
 31.69 
 31.05 
 30.41 
 29.75 
 
 (4) 
 40.28 
 40.50 
 40.70 
 40.90 
 41.07 
 41.23 
 
 (3) 
 224.1 
 252.2 
 280.2 
 308.3 
 336.2 
 364.0 
 
 O — NO 00 00 
 
 £Tg £j ~4- S on 1 
 
 ^0- 00 p> no in t 
 
TEST-TRIALS OF REFRIGERATING MACHINES. 1305 
 
 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 cooling 
 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 indis- 
 pensable; no less important is the precaution of using at each spot simul- 
 taneously 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. 
 
 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 
 refrigerating-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. 
 
 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 (particularlv for compression-machines) it will be possible to obtain 
 for the heat received and rejected a balance exhibiting small discrepancies 
 only. 
 
1306 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 Report of Test. — Reports intended to be used for comparison with 
 the figures found for other machines will therefore have to embrace at 
 least the following observations: 
 Refrigerator: 
 
 Quantity of brine circulated per hour 
 
 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 
 
 Compression-machine. 
 Compressor: 
 
 Indicated work L t 
 
 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 ± Qz. 
 
 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 Q2 
 
 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 ± Qs 
 
 Heat Balance: 
 
 Qe + Q'e = <?i + Q* ± Os. 
 For the calculation of efficiency and for comparison of various tests, 
 the actual efficiencies must be compared with the theoretical maximum 
 of efficiency Q -i- (AL) max. ^ T + (T e - T) corresponding to»the tem- 
 perature range. 
 
 Temperature Range. — For the temperatures (T and T c ) 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 - (AL) = T +(T C - T), 
 in which Q = quantity of heat abstracted (cold produced) ; 
 
 AL --= thermal equivalent of the mechanical work expended; 
 L = the mechanical work, and A = 1 ~ 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 -^ Q' = u, and Q' IQ = (T c - T) * (uT), 
 
PERFORMANCES OF ICE-MAKING MACHINES, 1307 
 
 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. Denton. (Trans. A. S. M. E., xii, 326.) 
 
 ACTUAL PERFORMANCES OF ICE-MAKING MACHINES. 
 
 The table given on page 1308 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 
 
 B. Pictet fluid dry-compression 
 
 Schroter. 
 
 ( Renwick & 
 \ Jacobus. 
 Denton. 
 
 9.9 
 11.3 
 28.0 
 
 10.0 
 12.0 
 
 16.5 
 24.4 
 23.8 
 
 
 18.0 
 
 E. Ammonia dry-compression 
 
 30.0 
 
 
 
 
 
 
 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 to 16.14 lbs. of ice per pound of coal, according as 
 the suction pressure varies from about 45 to 8 lbs. 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- 
 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 24.16 lbs. 
 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 lbs. 
 
 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 lbs. 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. 
 
1308 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 For brewery refrigerating conditions, line 17, we have 26.24 lbs. "ice- 
 melting capacity," and for ice-making conditions, line 13, the "ice- 
 melting capacity " is 17.47 lbs. 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. 
 
 — Actual Performance of Ice-making Machines. 
 
 
 02 ^ 
 
 
 £a . 
 
 
 Ph «2 -3 
 
 
 u a * 
 
 
 
 
 
 
 3— S 
 
 
 1 £ § 
 
 
 ^so 1 
 
 
 <3^ M 
 
 
 
 H 
 
 
 
 
 
 
 
 a> 
 
 
 <S 
 
 c 
 
 a 
 
 a 
 
 T3 
 
 
 3 
 
 
 
 fc 
 
 CJ 
 
 w 
 
 1 
 
 135 
 
 55 
 
 2 
 
 131 
 
 42 
 
 3 
 
 128 
 
 30 
 
 4 
 
 126 
 
 22 
 
 5 
 
 20U 
 
 42 
 
 6 
 
 136 
 
 60 
 
 7 
 
 131 
 
 45 
 
 8 
 
 126 
 
 24 
 
 9 
 
 117 
 
 41 
 
 10 
 
 130 
 
 60 
 
 11 
 
 57 
 
 21 
 
 12 
 
 56 
 
 15 
 
 13 
 
 55 
 
 10 
 
 14 
 
 60 
 
 7 
 
 15 
 
 91 
 
 15 
 
 16 
 
 61 
 
 22 
 
 17 
 
 59 
 
 16 
 
 18 
 
 59 
 
 7 
 
 19 
 
 54 
 
 22 
 
 20 
 
 89 
 
 16 
 
 21 
 
 62 
 
 6 
 
 22 
 
 59 
 
 15 
 
 23 
 
 175 
 
 54 
 
 24 
 
 166 
 
 43 
 
 25 
 
 167 
 
 23 
 
 26 
 
 162 
 
 28 
 
 27 
 
 176 
 
 42 
 
 28 
 
 152 
 
 40 
 
 3 
 
 3 
 C 
 
 
 i 
 
 
 
 a 
 
 
 r , 
 
 y 
 
 a 
 
 s 
 
 w 
 
 % 
 
 3 
 
 £ 
 
 
 
 pq 
 
 05 
 
 95 
 72 
 71 
 68 
 64 
 70 
 77 
 76 
 75 
 8) 
 
 104 
 81 
 80 
 79 
 75 
 
 103 
 82 
 65* 
 81* 
 84 
 85 
 83 
 88 
 79 
 
 30 
 18 
 
 - 9 
 13 
 31 
 28 
 14 
 
 - 2 
 -16 
 
 14 
 
 31 
 
 16 
 
 -16 
 
 31 
 
 16 
 
 -17 
 
 -53* 
 
 -40* 
 
 15 
 
 13 
 
 16 
 
 44.9 
 45.1 
 
 45.1 
 
 44.8 
 
 45.0 
 
 45.2 
 
 45.1 
 
 44.7 
 
 45.0 
 
 31.7 
 
 57.0 
 
 56.8 
 
 57.1 
 
 57.6 
 
 59.3 
 
 57.3 
 
 57.5 
 
 57. 
 
 35.3 
 
 42.9 
 
 34. 
 
 63.2 
 
 93.4 
 
 58.1 
 
 57.7 
 
 57.9 
 
 58.9 
 
 14.4 
 16.7 
 
 16.0 
 
 19.5 
 
 10.5 
 
 10.7 
 
 12.1 
 
 18.0 
 
 13.5 
 
 14.8 
 
 22.9 
 
 22.9 
 
 24.0 
 
 25.7 
 
 16.9 
 
 14.0 
 
 12.8 
 
 21 
 
 22.3 
 
 14.7 
 
 24.3 
 
 21.9 
 
 32.1 
 
 22.7 
 
 18.6 
 
 19.3 
 
 19.7 
 
 
 
 M 
 
 , 
 
 
 p 
 
 
 -i.S 
 
 "+3 
 
 
 
 
 "S "J^ 
 
 
 
 a 
 
 a 
 
 o 
 
 I! 
 
 >> 
 
 
 
 
 03 
 
 21 
 
 £2 
 
 i 
 
 
 ■5 "3 
 
 £0 ^ 
 
 cfe 
 
 ®= 
 
 
 gofl 
 
 t- J3 
 
 
 a 
 
 O 
 
 
 Sec 
 
 >> - 
 
 * ° 2 
 
 •y' = 
 
 "43 05 
 
 .E '■'- 
 
 CL z 
 7~ 
 
 ;£ 
 
 03 a 
 
 
 
 
 l^> 
 
 £ a 
 
 «H.g 
 
 is 
 
 03 03 
 
 
 
 Q 
 
 w 
 
 S 
 
 26.2 
 
 40.63 
 
 30.8 
 
 19.1 
 
 54.8 
 
 19.5 
 
 30.01 
 
 33.5 
 
 20.2 
 
 53.4 
 
 13.3 
 
 22.03 
 
 37.1 
 
 25.2 
 
 50.3 
 
 9.0 
 
 16.14 
 
 42.9 
 
 29.1 
 
 44.7 
 
 16.5 
 
 19.07 
 
 36.0 
 
 28.5 
 
 77.0 
 
 29.8 
 
 46.29 
 
 28.5 
 
 19.9 
 
 56.8 
 
 21.6 
 
 33.23 
 
 31.3 
 
 21.9 
 
 56.4 
 
 9.9 
 
 17.55 
 
 41.1 
 
 28.3 
 
 46.1 
 
 20.0 
 
 33.77 
 
 33.1 
 
 22.9 
 
 50.6 
 
 19.5 
 
 45.01 
 
 35.2 
 
 23.8 
 
 52.0 
 
 25.6 
 
 33.07 
 
 39.9 
 
 22.2 
 
 24.1 
 
 17.9 
 
 24.11 
 
 41.3 
 
 24.0 
 
 23.1 
 
 11.6 
 
 17.47 
 
 42.2 
 
 25.2 
 
 20.4 
 
 5.7 
 
 10.14 
 
 54.5 
 
 38.5 
 
 16.8 
 
 15.7 
 
 16.05 
 
 36.2 
 
 23.1 
 
 31.5 
 
 28.1 
 
 36.19 
 
 33.4 
 
 22.5 
 
 26.8 
 
 19.3 
 
 26.24 
 
 34.6 
 
 25.0 
 
 25.6 
 
 6.8 
 
 11.93 
 
 47.5 
 
 33.4 
 
 18.0 
 
 17.0 
 
 38.04 
 
 39.5 
 
 22.6 
 
 22.6 
 
 11.9 
 
 16.68 
 
 37.7 
 
 27.0 
 
 32.7 
 
 3.5 
 
 9.86 
 
 54.2 
 
 39.5 
 
 17.7 
 
 10.3 
 
 3.42 
 
 71.7 
 
 56.9 
 
 26.6 
 
 4.9 
 
 3.0 
 
 80.0 
 
 63.0 
 
 89.2 
 
 73.9 
 
 24.16 
 
 32.8 
 
 11.7 
 
 65 9 
 
 37.9 
 
 14.52 
 
 37.4 
 
 22.7 
 
 57.6 
 
 46.5 
 
 17.55 
 
 34.9 
 
 18.6 
 
 59.9 
 
 74.4 
 
 23.31 
 
 30.5 
 
 13.5 
 
 70.5 
 
 42.2 
 
 20.1 
 
 47.8 
 
 
 
 
 
 * Temperature of air at entrance and exit of expansion-cylinder. 
 
 t On a basis of 3 lbs. of coal per hour per H.P. of steam-cylinder of 
 compression-machine and an evaporation of 11.1 lbs. of water per pound 
 of combustible from and at 212° F. in the absorption-machine. 
 
 % 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. 
 
 || Actual, including resistance due to inlet and exit valves. 
 
PERFORMANCES OP ICE-MAKING MACHINES. 
 
 1309 
 
 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 manufacturers 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 in eight trials are as follows: 
 
 H 
 
 Ammonia 
 Pressures, 
 lbs. above 
 Atmosphere. 
 
 Brine 
 Tempera- 
 tures, 
 Degrees F. 
 
 Capacity Tons 
 Refrigerating 
 . Effect per 24 
 hours. 
 
 Efficiency ibs. of 
 Ice per lb. of 
 Coal at 3 lbs. 
 Coal per hour 
 perH.P. 
 
 Water-consump- 
 tion, gals, of 
 Water per min. 
 per ton of Ca- 
 pacity. 
 
 Ratio of Actual 
 Weights of Am- 
 monia circu- 
 lated. 
 
 o8 
 
 a 
 
 d 
 
 
 
 d 
 
 Con- 
 densing 
 
 Suc- 
 tion. 
 
 Inlet. 
 
 Outlet. 
 
 I 1 
 
 I 
 
 8 
 7 
 4 
 6 
 2 
 
 151 
 161 
 147 
 152 
 . !05 
 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 
 
 1.0 
 1.0 
 1.70 
 1.93 
 1.91 
 2.59 
 
 1.0 
 1.0 
 1.60 
 1.92 
 1.88 
 2.57 
 
 The principal results in four tests are given in the table on page 1311. 
 The fuel economy under different conditions of operation is shown in 
 the following table: 
 
 
 3 
 03 
 
 a <» 
 _o 
 
 QD 
 
 Pounds of Ice-melting Effect with 
 Engines — 
 
 B.T.U.per lb.of Steam 
 with Engines — 
 
 Ah 
 
 wija 
 
 Non-con- 
 densing. 
 
 Non-com- 
 pound Con- 
 densing. 
 
 Compound 
 Con- 
 densing. 
 
 a 
 
 5 M 
 
 8.S 
 
 o 
 Sz; 
 
 M 
 
 a 
 a 
 
 C 
 
 o 
 O 
 
 ■si 
 
 •S3 
 
 a 
 
 o 
 
 p 
 
 03 O 
 
 ho 
 
 2B 
 
 u & 
 
 J2 . 
 03 O 
 
 a£ 
 
 u <3 
 
 £ . 
 03 O 
 
 ai 
 
 03 03 
 
 u 
 
 B a 
 o o 
 
 150 
 150 
 105 
 105 
 
 28 
 7 
 
 28 
 7 
 
 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 
 
 The non-condensing engine is assumed to require 25 lbs. of steam per 
 I.H.P. per hour, the non-compound condensing 20 lbs., and the compound 
 condensing 16 lbs., and the boiler efficiency is assumed at 8.3 lbs. of water 
 per lb. 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 lbs. above the atmosphere, with which a 
 temperature of 0° F. can be produced, to 28 lbs. above the atmosphere, 
 with which the temperatures of refrigeration are confined to about 28° F. 
 At the lower pressure only abant 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 lbs. 
 
1310 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 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 lbs. back 
 
 Eressure. For example, a difference of 100% in the rate of circulation of 
 rine, while producing a proportional difference in the range of tempera- 
 ture of the latter, made no practical difference in capacity. 
 
 The brine-tank was 10 1/2 X 13 X 102/3 ft., and contained 8000 lineal 
 feet of 1-in. pipe as cooling-surface. The condensing-tank was 12 X 10 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 lbs. suction-pressure and about 150 lbs. condensing- 
 pressure.' Under these conditions, for a non-condensing steam-engine 
 consuming coal at the rate of 3 lbs. per hour per I.H.P. of steam-cylinders, 
 24 lbs. of ice-refrigerating effect are obtained per lb. of coal consumed. 
 For the same condensing-pressure, and with 7 lbs. suction-pressure, which 
 affords temperatures of 0° F., the possible economy falls to about 14 lbs. of 
 refrigerating effect per lb. 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 lbs. 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 lbs. The work of compression is thereby increased about 
 20%, and the resulting "economy" is reduced to about 18 lbs. of "ice 
 effect" per lb. of coal at 28 lbs. suction-pressure and 11.5 at 7 lbs. If, on 
 the other hand, the supply of water is made 3 gallons per minute, the 
 condensing-pressure may be confined to about 105 lbs. 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 lbs. of 
 "ice effect" per lb. of coal for 150 lbs. condensing-pressure and 28 lbs. 
 suction-pressure 30.0, and for 7 lbs. 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 lbs., and the economy of the refrigerating-machine becomes, for 
 28 lbs. back pressure, 43.0 lbs. of " ice-effect " per lb. of coal, or for 7 lbs. 
 back pressure 27.5 lbs. of ice effect per lb. of coal. If a compound con- 
 densing-engine can be used with a steam-consumption per hour per 
 horse-power of 16 lbs. of water, the economy of the refrigerating-machine 
 may be 25% higher than the figures last named, making for 28 lbs. back 
 pressure a refrigerating-effect of 54.0 lbs. per lb. of coal, and for 7 lbs. 
 back pressure a refrigerating effect of 34.0 lbs. per lb. of coal. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1311 
 
 Performance of a 75-ton Refrigerating-machine. 
 
 (Denton.) 
 
 
 T3 <a 
 
 T3 o^ 
 
 TJ $24 
 
 "O 09 
 
 
 
 o £ ° 
 
 a 2 « 
 
 Sa 
 
 
 >>~ 
 
 >>NPQ 
 
 >>in 
 
 
 
 
 
 
 
 w 
 
 
 83 a s 
 
 
 U I 
 
 O ^ 
 
 ° <* 
 
 O S 
 
 
 3§Ph 
 
 .5 «rifl 
 
 S3 >> H 6 
 a S3 W S 
 
 SSf-i 
 
 S § 2 1 
 
 S3 CM 
 
 
 
 Maxi 
 Eco 
 Brir 
 Pre! 
 
 * 8"c£ 
 
 S«eJ 
 
 Av. high ammonia press, above atmos 
 
 151 lbs. 
 
 152 lbs. 
 
 147 lbs. 
 
 161 lba. 
 
 Av. back ammonia press, above atmos 
 
 28 " 
 
 8.2 " 
 
 13 " 
 
 27.5 " 
 
 Av. temperature brine inlet 
 
 36.76° 
 
 6.27° 
 
 14.29° 
 
 
 Av. temperature brine outlet 
 
 28.86° 
 
 2.03° 
 
 2.29° 
 
 28 45° 
 
 A v. range of temperature 
 
 7.9° 
 
 4.24° 
 
 12 00° 
 
 7.91° 
 
 Lbs. of brine circulated per minute 
 
 2281 
 
 2173 
 
 943 
 
 2374 
 
 Av. temp, condensing-water at inlet 
 
 44.65° 
 
 56.65° 
 
 46.9° 
 
 54.00° 
 
 Av. temp, condensing-water at outlet 
 
 83.66° 
 
 85.4° 
 
 85.46° 
 
 82.86° 
 
 Av. range of temperature 
 
 39 01° 
 
 28 75° 
 
 38 56° 
 
 28 80° 
 
 Lbs. water circulated p. min. thro' cond'ser 
 
 442 
 
 315' 
 
 257 
 
 60K5 
 
 Lbs. water per min. through jackets 
 
 25 
 
 44 
 
 40 
 
 14 
 
 Range of temperature in jackets 
 
 24 0° 
 
 16 2° 
 
 16 4° 
 
 29 1° 
 
 Lbs. ammonia circulated per min 
 
 *28.17 
 
 14^68 
 
 16.67 
 
 28 J2 
 
 Probable temperature of liquid ammonia, 
 
 
 
 
 
 entrance to brine-tank 
 
 *71.3° 
 
 + 14° 
 
 *68° 
 
 -8° 
 
 *63.7° 
 
 -5° 
 
 76 7° 
 
 Temp, of amm. corresp. to av. back press. 
 
 14° 
 
 Av. temperature of gas leaving brine-tanks 
 
 34.2° 
 
 14.7° 
 
 3.0° 
 
 29.2° 
 
 Temperature of gas entering compressor — 
 
 *39o 
 
 25° 
 
 10.13° 
 
 34° 
 
 Av. temperature of gas leaving compressor 
 
 Av. temp, of gas entering condenser 
 
 Temperature due to condensing pressure. . . 
 
 213° 
 
 263° 
 
 239° 
 
 221° 
 
 200° 
 
 218° 
 
 209° 
 
 168° 
 
 84.5° 
 
 84.0° 
 
 82.5° 
 
 88.0° 
 
 Heat given ammonia: 
 
 
 
 
 
 By brine, B.T.U. per minute 
 
 14776 
 
 7186 
 
 8824 
 
 14647 
 
 By compressor, B.T.U. per minute 
 
 2786 
 
 2320 
 
 2518 
 
 3020 
 
 By atmosphere, B.T.U. per minute 
 
 140 
 
 147 
 
 167 
 
 141 
 
 Total heat rec. by amm., B.T.U. per min.. . . 
 
 17702 
 
 9653 
 
 11409 
 
 17708 
 
 Heat taken from ammonia: 
 
 
 
 
 
 By condenser, B.T.U. per min 
 
 17242 
 
 9056 
 
 9910 
 
 17359 
 
 By jackets, B.T.U. per min 
 
 608 
 
 712 
 
 656 
 
 406 
 
 By atmosphere, B.T.U. per min 
 
 182 
 
 338 
 
 250 
 
 252 
 
 Total heat rej. by amm., B.T.U. per min — 
 
 18032 
 
 10106 
 
 10816 
 
 18017 
 
 Dif. of heat rec'd and rej., B.T.U. per min... 
 
 330 
 
 453 
 
 407 
 
 309 
 
 % work of compression removed by jackets 
 
 22% 
 
 31% 
 
 26% 
 
 13% 
 
 Av. revolutions per min 
 
 58.09 
 32.5 
 
 57.7 
 27.17 
 
 57.88 
 27.83 
 
 58 89 
 
 Mean eff. press, steam-cyl., lbs. per sq. in.. . 
 
 32.97 
 
 Mean eff. press, amm.-cyl., lbs. per sq. in. . . 
 
 65.9 
 
 53.3 
 
 59.86 
 
 70.54 
 
 Av. H.P. steam-cylinder 
 
 85.0 
 65.7 
 23.0 
 
 71.7 
 54.7 
 24.0 
 
 73.6 
 59.37 
 20.0 
 
 88.63 
 
 Av. H.P. ammonia-cylinder 
 
 71.20 
 
 Friction in per Cent of steam H.P 
 
 19.67 
 
 Total cooling water, gallons per min. per 
 
 
 ton per 24 hours 
 
 0.75 
 74.8 
 
 1.185 
 36.43 
 
 0.797 
 
 44 64 
 
 0.990 
 
 Tons ice-melting capacity per 24 hours 
 
 74.56 
 
 Lbs. ice-refrigerating eff. per lb. coal at 3 
 
 
 
 
 
 lbs. per H.P. per hour 
 
 24.1 
 
 14.1 
 
 17.27 
 
 23.37 
 
 Cost coal per ton of ice-refrigerating effect 
 
 
 at $4 per ton 
 
 $0,166 
 
 $0,283 
 
 $0,231 
 
 $0,170 
 
 Cost water per ton of ice-refrigerating effect 
 
 
 at$1 per 1000 cu. ft 
 
 $0,128 
 $0,294 
 
 $0,200 
 $0,483 
 
 $0,136 
 $0,467 
 
 $0,169 
 
 Total cost of 1 ton of ice-refrigerating eff. . . 
 
 $0,339 
 
 Figures marked thus (*) are obtained by calculation; all other figures 
 Obtained from experimental data; temperatures in Fahrenheit are degrees. 
 
1312 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 
 
 2 
 
 3 
 
 4 
 
 5 
 
 
 
 Temp, of refrig- ) Inlet, deg. F 
 
 erated brine ) Outlet, deg. F... 
 
 43.194 
 
 28.344 
 
 13.952 
 
 -0.279 
 
 28.251 
 
 37.054 
 
 22.885 
 
 8.771 
 
 -5.879 
 
 23.072 
 
 
 0.861 
 1,039.38 
 
 0.851 
 908.84 
 
 0.843 
 633.89 
 
 0.837 
 414.98 
 
 0.851 
 
 Brine circ. per hour, cu. ft 
 
 800.93 
 
 Cold produced, B.T.U. per hour. . . 
 
 342,909 
 
 263,950 
 
 172,776 
 
 121,474 
 
 220,284 
 
 Cooling water per hour, cu. ft 
 
 338.76 
 
 260.83 
 
 187.506 
 
 139.99 
 
 97.76 
 
 I.H.P. in steam-engine cylinder. . . 
 
 15.80 
 
 16.47 
 
 15.28 
 
 14.24 
 
 21.61 
 
 Cold pro- ) Per I.H.P. in comp.-cyl 
 
 24,813 
 
 18,471 
 
 12,770 
 
 10,140 
 
 11,151 
 
 
 21,703 
 
 16,026 
 
 11,307 
 
 8,530 
 
 10,194 
 
 h., B.T.U. ) Per lb. of steam 
 
 1,100.8 
 
 785.6 
 
 564.9 
 
 435.82 
 
 512.12 
 
 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 lbs. 
 per lb. of coal on a basis of boiler economy equivalent to 3 lbs. of steam 
 per I.H.P. in a good non-condensing steam-engine. The ammonia was 
 worked between 138 and 23 lbs. 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 refrig- 
 eration". Following are the principal average results (Bulletin of York 
 Mfg. Co.): 
 
 Date of test, 1908 Mar. 6. Mar. 7 Mar. 
 
 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 
 
 Temp, brine, outlet 
 
 Revs, per min 
 
 Lbs. liquid NH3 per min. . 
 Sue. press, at mach. lb. . . 
 
 Condenser pressure 
 
 Indicated H.P 
 
 Tons Refrig. Capy, 24 hrs. 
 I.H.P. per ton capacity . . 
 
 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 
 
 18.13 
 186.8 
 105.11 
 
 66.65 
 1.439 
 
 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 
 
 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 lbs. dry steam, 38 lbs. gauge pressure condensed, 
 evaporates 32.2% strong liquor to 22.3% weak liquor. 
 
 Exchanger. — 3.01 lbs. weak liquor at 264° cools to 111°. 
 
 Absorber. — Adds 0.43 lbs. vapor from the brine cooler, making 3.44 
 lbs, strong liquor at 111° to go to the pump. 
 
PERFORMANCES OF ICE-MAKING MACHINES. 1313 
 
 Exchanger. — 3.44 lbs. 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 lb., goes 
 to the rectifier. 
 
 Rectifier. — Cools the gas to 110° separating water vapor as 0.0682 lb. 
 drip liquor which returns through a trap to the generator. 
 
 Condenser. — 0.43 lb. NH3 gas at 110° cooled and condensed to liquid 
 at 90° by 2 gals, of water per rain, heated from 73° to 86°. 
 
 Expansion Valve and Cooler. — Reduces liquid to 0° 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: 
 
 Condenser Pressures. 
 
 
 140 170 
 
 
 200 
 
 
 
 Suction Pressures. 
 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 
 
 15 
 
 30 
 
 
 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 
 
 Wl per cent 
 
 SG, pounds.. 
 
 SL, pounds 
 
 26.9 
 27.9 
 2.2 
 
 SI, strong liquor; Wl, weak liquor; SG, lbs. of .steam per hour per ton 
 of refrigeration for the generator, SL, do. for the liquor pump. Pressures 
 are in lbs. per sq. in., gauge. 
 
 The following table gives the steam consumption in lbs. 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 
 
 CC 
 
 23.9 
 
 A 
 
 30.1 
 
 
 
 The economy of the absorption machine is much better for all conditions 
 than that of a simple non-condensing engine-driven compressor. At 
 suction gauge pressures above 8 to 10 lbs. the economy of the compound 
 condensing engine-driven compressor exceeds that of the absorption 
 machine, the absorption machine giving the superior economy at suction 
 pressures below 8 to 10 lbs. 
 
1314 ICE-MAKING OR REFRIGERATING MACHINES. 
 
 Means for Applying the Cold. (M. C. Bannister, Liverpool Eng'g 
 Soc'y, 1890.) — The most useful means for applying the cold to various 
 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 conveying 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 
 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 lbs. above the 
 atmosphere and 15 lbs. suction-pressure. 
 
 In a compression type of machine the useful circulation of ammonia, 
 allowing for the effect of cylinder-heating, is about 13 lbs. per hour per 
 indicated horse-power of the steam-cylinder. This weight. of ammonia 
 produces about 32 lbs. 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 lbs. About 7.0 lbs. 
 of this covers the steam-consumption of the steam-engines driving the 
 brine circulating-pumps, the several cold-water pumps, and leakage, 
 drips, etc. Consequently, the main steam-engine must consume 36 lbs. of 
 steam per hour per I.H.P., or else live steam must .be condensed to supply 
 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 lbs. of feed- 
 water may then be evaporated, on the average, per lb. of coal. 
 
 The ice made per pound of coal will then be 32 ■* (43.0 -h 8.5) = 6.0 
 lbs. 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 power 
 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 lbs. of 
 net ice, may be 14 lbs. per hour. The other motors at 50 lbs. of steam 
 per horse-power will use 7.5 lbs. per hour, making the total consumption 
 per steam horse-power of the compressor 21.5 lbs. Taking the evapora- 
 
ARTIFICIAL ICE-MANUFACTURE. 1315 
 
 tion at 8 lbs., the feed-water temperature being limited to about 110°, the 
 coal per horse-power is 2.7 lbs. per hour. The net ice per lb. of coal is 
 then about 32 h- 2.7 =11.8 lbs. The best results with "plate-system" 
 plants, using a compound steam-engine, have thus far afforded about 10V2 
 lbs. of ice per lb. 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 lbs. 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 
 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 directlv 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 lee-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 97 
 
 Av. pressure of ammonia-gas at condenser, lbs. per sq. in. above 
 
 atmos. . . 135 .2 
 
 Average back pressure of amm.-gas, lbs. per sq. in. aboveatmos. 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 lee-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 lbs. pressure enters an evaporator, distilling off steam at 70 !bs., 
 which operates the pumps and auxiliary machinery. These exhaust 
 into the ice machine generator under 10 lbs. 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 of 
 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 lbs. water per pound of coal 
 the economy of the plant will be 10 1/2 lbs. ice per pound of coal, a result 
 which cannot be obtained even with compound condensing engines and 
 compression machines. 
 
1316 
 
 MARINE ENGINEERING. 
 
 Heat-exchanging 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 being 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 lbs. pressur3, using 6V3 K.W., or 8 1/2 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: 
 
 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, compound 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 
 25 
 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. 
 
 MARINE ENGINEERING. 
 
 Rules for Measuring Dimensions and Obtaining Tonnage of 
 "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 vessel. 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 
 
MARINE ENGINEERING. 1317 
 
 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 
 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. LX B X D X 0.75^ 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 lbs.) 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 lbs. 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 tins volume, we have V = LX BX D. 
 
 The volume of displacement may then be expressed as a percentage 
 of the volume V, known as the " block coefficient. " This percentage varies 
 for 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 -^ (L X B X W); 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 = DX 35-*- (area of immersed water sectionXL). 
 Seaton gives the following values: 
 
 Coefficient Coefficient of 
 of Fineness. Water-lines 
 
 Finely-shaped ships .55 .63 
 
 Fairly-shaped ships .61 .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 water 
 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 v essels is 
 Resistance = speed 2 X -^/displacement 2 X a constant, or R = £ 2 D* X C. 
 
 If D = displacement in pounds, S = speed in feet per minute, R 
 resistance in foot-pounds per minute, R = CS 2 D%. The work done in 
 overcoming the resistance through a distance equal to Sis RX S = CS S D*; 
 and if E is the efficiency of the propeller and machinery combined, the 
 indicated horse-power I. H.P.= CS 3 D%-i- (EX 33,000). 
 
 If S = speed in knots, D — displacement in tons, and C a constant 
 
1318 
 
 MARINE ENGINEERING. 
 
 which includes all the constants for form of vessel, efficiency of mechanism, 
 etc., I.H.P. - SW^-i-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 
 displacement is D and wetted surface W. Then D = L 8 or L =^D, 
 and W = 5X L 2 = 5 X ( V- ) 2 - Tnat is > w varie s as D$. 
 
 Another approximate formula is 
 
 I.H.P. = area of immersed midship section X S* ■+■ 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, 
 
 Value 
 
 Value 
 
 knots. 
 
 of C. 
 
 of K. 
 
 15 to 17 
 
 240 
 
 620 
 
 15 " 17 
 
 190 
 
 500 
 
 13 " 15 
 
 240 
 
 650 
 
 11 " 13 
 
 260 
 
 700 
 
 11 " 13 
 
 240 
 
 650 
 
 9 " 11 
 
 260 
 
 700 
 
 13 " 15 
 
 200 
 
 580 
 
 11 " 13 
 
 240 
 
 660 
 
 9 " 11 
 
 260 
 
 700 
 
 11 " 13 
 
 220 
 
 620 
 
 9 " 11 
 
 250 
 
 680 
 
 11 " 12 
 
 220 
 
 600 
 
 9 " 11 
 
 240 
 
 640 
 
 9 " 11 
 
 220 
 
 620 
 
 11 " 12 
 
 200 
 
 550 
 
 10 " 11 
 
 210 
 
 580 
 
 9 " 10 
 
 230 
 
 620 
 
 9 " 10 
 
 200 
 
 600 
 
 Ships over 400 feet long, finely shaped,. 
 .. 300 
 
 Ships over 300 feet long, fairly shaped . 
 Ships over 250 feet long, finely shaped . 
 
 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 
 
 Ships under 200 feet long, fairly shaped 
 
 Coe fficient of Perfo rmance of Vessels. — The quotient 
 
 ^1 (displacement) 2 X (speed in knots) 3 -4- 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., 
 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. Mansel'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 steamers at ordinary 
 
 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. 
 
MARINE ENGINEERING. 1319 
 
 Rank'ine's Formula for total resistance of vessels of the "wave-line" 
 type is: 
 
 R =ALBV* (1 + 4 sin* 6 + sin 4 6), 
 
 in which equation 6 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 
 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 oi 
 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 
 important. 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 6, 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 proDer 
 constant coefficient selected from the following: 
 
 For clean painted vessels, iron hulls A = .01 
 
 For clean coppered vessels A =0 .009 to .008 
 
 For moderately rough iron vessels A = .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 ease 200 to 260. 
 
 The form of the vessel, even when designed by skillful and experienced 
 naval architects, will often 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. = SV Z + 20,000, in which S is the "augmented 
 surface." The expression SV S -5- 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 D%V 3 •*• H.P. has been called the locomotive performance. 
 (See Rankine's Treatise on Shipbuilding, 1864; Thurston's Manual of the 
 Steam-engine, part ii, p. 16; also paper by F. T. Bowles, U. S. N., Proc. 
 U. S. Naval Institute, 1883.) 
 
 Rankine's method 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. 
 
 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 
 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. 
 
1320 
 
 MARINE ENGINEERING. 
 
 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 tine 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 
 
 &+® 
 
 XH; 
 
 Tangent of half angle of entrance = y 2 B/F = 5/(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° 0.3 to .36 
 
 12 to 14 knots 21° to 18° 0.26 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 parallelo- 
 piped, and fore-body and after-body, prisms having isosceles triangles for 
 bases, as shown in Fig. 194. 
 
 
 D 
 
 E 
 
 t 
 
 5: 
 
 G 
 
 K 
 
 
 L 
 
 Fig. 194. 
 
 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 -4- KL=B. Volume of block = {F+M) X 
 BX H; midship section = BX H; displacement in tons = volume in 
 cubic ft. ■*- 35. 
 
 AH = AG+ GH = F+ M = displacement X 35 + (B X H). 
 
 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 10 knots 
 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 = (15/10)3 X 5 = 16.875. 
 Then I.H.P. required = 16.875 X 162 = 2734. 
 
 When the shin is exceptionally well-proportioned, the bottom quite 
 clean, and the efficiency or the machinery high, as low a rate as 4 I.H.P. 
 per 100 feet of wetted skin of block model mov 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 
 measure of the resistance of the ship, and can only be relied on as a means 
 of deciding the size of engines for speed, so long as the efficiency of the 
 engine and propeller is known definitely, or so long as similar engines and 
 
MARINE ENGINEERING. 
 
 1321 
 
 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-bladed 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 horse-power 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.) 
 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 FfPoc 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 2 ' 8 
 
 0/69 
 
 239 
 
 535 
 
 1. 
 
 1.666 
 
 2,565 
 
 3 729 
 
 5 185 
 
 6.964 
 
 9.095 
 
 11.60 
 
 14.52 
 
 17,87 
 
 21 67 
 
 S 2,9 
 
 0701 
 
 227 
 
 524 
 
 1 
 
 1 697 
 
 2.653 
 
 3.908 
 
 5 499 
 
 7 464 
 
 9,841 
 
 12.67 
 
 15.97 
 
 19 80 
 
 24 19 
 
 S3 
 
 0640 
 
 216 
 
 512 
 
 1. 
 
 1.728 
 
 2 744 
 
 4.096 
 
 5 832 
 
 8. 
 
 10,65 
 
 13 82 
 
 17,58 
 
 21 95 
 
 77 
 
 ,S3.1 
 
 0584 
 
 205 
 
 501 
 
 1. 
 
 1 760 
 
 2.838 
 
 4 293 
 
 6 185 
 
 8 574 
 
 11.52 
 
 15 09 
 
 19.34 
 
 24 33 
 
 30 14 
 
 S3* 2 
 
 0533 
 
 195 
 
 490 
 
 1. 
 
 1.792 
 
 2.935 
 
 4.500 
 
 6,559 
 
 9.189 
 
 12.47 
 
 16.47 
 
 21.28 
 
 26.97 
 
 33.63 
 
 S3-3 
 
 0486 
 
 185 
 
 479 
 
 1. 
 
 1.825 
 
 3.036 
 
 4.716 
 
 6 957 
 
 9.849 
 
 13 49 
 
 17,98 
 
 23.41 
 
 29 90 
 
 37,54 
 
 S3'4 
 
 0444 
 
 176 
 
 468 
 
 1. 
 
 1 859 
 
 3.139 
 
 4.943 
 
 7,378 
 
 10,56 
 
 14 60 
 
 19.62 
 
 25 76 
 
 33 14 
 
 41 90 
 
 S3-5 
 
 .0405 
 
 .167 
 
 .458 
 
 1. 
 
 1.893 
 
 3.247 
 
 5.181 
 
 7.824 
 
 11.31 
 
 15.79 
 
 21.42 
 
 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 with increase of 
 speed remaining constant? The first step is to find the rate of increase, 
 thus: 14^ : 16# :: 587 : 900. 
 
 x log 16 - x log 14 = log 900 - log 587; 
 x (0.204120 - 0.146128) = 2.954243 - 2.768638, 
 whence x (the exponent of £ in formula H.P. =c S x ) = 3.2. 
 
 From the table, for S^ 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 -s- 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 lbs. 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 = 101 1/3 ft. per min., 33,000 -4- 101 1/3 = 
 325.658 lbs. per horse-power; and for any other speed 325.658 lbs. divided 
 by the speed in knots; or for 
 
 1 knot 325.66 lbs. 8 knots 40.71 lbs. 
 
 2 knots 162.83 " 9 " 36.18 " 
 
 3 " 108.55 " 10 " 32.57 " 
 
 4 *' 81.41 " 11 " 29.61 " 
 
 5 " 65.13 " 12 " 27.14 .*' 
 
 6 " 54.28 " 13 " 25.05 " 
 
 7 " 48.52 " 14 " 23.26 " 
 
 More accurate methods than those above given for estimating the horse- 
 power required for anv proposed ship are: 1. Estimations calculated 
 rom the results of trials of "similar" vessels driven at "corresponding' 
 
 15 knots 21.71 lbs. 
 
 16 ' 
 
 ' 20.35 
 
 17 ' 
 
 ' 19.16 
 
 18 ' 
 
 ' 18.09 
 
 19 * 
 
 ' 17.14 
 
 20 ' 
 
 ' 16.28 
 
1322 
 
 MARINE ENGINEERING. 
 
 _., "similar" vessels being those that have the same ratio of length 
 to breadth and to draught, and the same coefficient of fineness, and 
 "corresponding" speeds those which are proportional to the square roots 
 of the lengths of the respective vessels. Froude 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. =£ 3 Z)3 -*■ 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 di ameters of screw in the 9th column are from formu la D = 3.31 
 ^J/l.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 -4- 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. 1321. 
 
 F. E. Cardullo, Mach'y, April, 1907.. gives the following formula as 
 closely approximating the speed of modern types of hulls: S = 6.35 
 3 / IH p 
 1/ ' 2/ ,* ' m wn i c h & = speed in knots, D = displacement in tons. If 
 
 we take S = 10 knots, then I.H.P. -j- D 2 /3 = 3.906. Let D = 10,000, and 
 S = 10, then H.P. = 1813. The table on page 1323 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 j 
 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 j 
 in tons. 
 
 Block Coefficient. 
 
 0.25 
 
 0.3 
 
 0.35 
 
 0.4 
 
 L 
 
 D 
 
 L 
 
 D 
 
 L 
 
 D 
 
 L 
 
 D 
 
 78 
 
 105 
 
 75 
 
 100 
 
 72 
 
 95 
 
 69 
 
 90 
 
 71 
 
 81 
 
 69 
 
 77 
 
 66 
 
 73 
 
 63 
 
 70 
 
 65 
 
 62 
 
 63 
 
 60 
 
 60 
 
 58 
 
 57 
 
 55 
 
 59 
 
 47 
 
 57 
 
 45 
 
 54 
 
 44 
 
 5?. 
 
 42 
 
 54 
 
 36 
 
 52 
 
 35 
 
 50 
 
 34 
 
 48 
 
 32 
 
 50 
 
 28 
 
 48 
 
 27 
 
 46 
 
 26 
 
 44 
 
 25 
 
 46 
 
 22 
 
 44 
 
 21 
 
 42 
 
 20 
 
 40 
 
 19 
 
 41 
 
 17 
 
 40 
 
 16 
 
 38 
 
 15 
 
 37 
 
 14 
 
 J« 
 
 13 
 
 37 
 
 12 
 
 35 
 
 1U/9 
 
 34 
 
 1.1 
 
 35 
 
 9 
 
 34 
 
 81/D! 
 
 32 
 
 8 
 
 31 
 
 71/9, 
 
 32 
 
 6 V? 
 
 31 
 
 6 
 
 30 
 
 5V-> 
 
 29 
 
 5 
 
 30 
 
 4 V? 
 
 29 
 
 41/ 4 
 
 28 
 
 33/4 
 
 21 
 
 31/9, 
 
 28 
 
 3V4 
 
 27 
 
 3 
 
 26 
 
 23/4 
 
 25 
 
 21/2 
 
 
 Speed 
 
 in Knots 
 
 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Brake Horse-power. 
 
 20 
 17 
 
 15 
 
 21/2 
 
 30 
 25 
 
 22 
 19 
 16 
 13 
 12 
 11 
 
 9 
 
 7 
 
 51/2 
 
 5 
 
 41/2 
 
 43 
 37 
 32 
 27 
 24 
 20 
 17 
 15 
 13 
 11 
 
 9 
 
 7 
 
 61/2 
 
MARINE ENGINEERING. 
 
 1323 
 
 Estin: 
 
 late 
 
 I Displacement, Horse-power, etc., 
 
 of Steam-vessels of 
 
 
 
 
 Various Sizes. 
 
 
 
 
 M - 
 
 
 Si 
 A 3 
 
 J* I 
 
 Displacement. 
 
 LBDX C 
 
 35 
 
 Wetted Surface 
 
 LQ..1D+BQ 
 
 sq. ft. 
 
 Estimated Horse- 
 power at 10 knots. 
 
 Diam. of S 
 revs, pe 
 
 crew for 10, 
 (1 and 100 
 
 ||. 
 
 Calc. 
 from Dis- 
 
 Calc. from 
 Wetted 
 
 
 If Pitch = 
 
 If Pitch = 
 
 
 
 
 
 tons. 
 
 
 placem't. 
 
 Surface. 
 
 Diam. 
 
 1.4 Diam. 
 
 12 
 
 3 
 
 1.5 
 
 0.55 
 
 0.85 
 
 48 
 
 4.3 
 
 2.4 
 
 4.4 
 
 3.6 
 
 <«{ 
 
 3 
 
 1.5 
 
 .55 
 
 1.13 
 
 64 
 
 5.2 
 
 3.2 
 
 4.6 
 
 3.8 
 
 4 
 
 2 
 
 .65 
 
 2.38 
 
 96 
 
 8.9 
 
 4.8 
 
 5.1 
 
 4.2 
 
 20 | 
 
 3 
 
 1.5 
 
 .55 
 
 1.41 
 
 80 
 
 6.0 
 
 4.0 
 
 4.7 
 
 3.9 
 
 4 
 
 2 
 
 .65 
 
 2.97 
 
 120 
 
 10.3 
 
 6.0 
 
 5.3 
 
 4.3 
 
 24 { 
 
 3.5 
 
 1.5 
 
 .55 
 
 1.98 
 
 104 
 
 7.5 
 
 5.2 
 
 5 
 
 4.1 
 
 4.5 
 
 2 
 
 .65 
 
 4.01 
 
 152 
 
 12.6 
 
 7.6 
 
 5.5 
 
 4.5 
 
 30 { 
 
 4 
 
 2 
 
 .55 
 
 3.77 
 
 168 
 
 11.5 
 
 8.4 
 
 5.4 
 
 4.4 
 
 5 
 
 2.5 
 
 .65 
 
 6.96 
 
 224 
 
 18.2 
 
 11.2 
 
 5.9 
 
 4.8 
 
 40{ 
 
 4.5 
 
 2 
 
 .55 
 
 5.66 
 
 235 
 
 15.1 
 
 11.8 
 
 5.7 
 
 4.7 
 
 6 
 
 2.5 
 
 .65 
 
 11.1 
 
 326 
 
 24.9 
 
 16.3 
 
 6.3 
 
 5.2 
 
 50 { 
 
 6 
 
 3 
 
 .55 
 
 14.1 
 
 420 
 
 27.8 
 
 21.0 
 
 6.4 
 
 5.4 
 
 8 
 
 3.5 
 
 .65 
 
 26 
 
 558 
 
 43.9 
 
 27.9 
 
 7.1 
 
 1 5.8 
 
 60 { 
 
 8 
 
 3.5 
 
 .55 
 
 26.4 
 
 621 
 
 42.2 
 
 31.1 
 
 7.0 
 
 5.7 
 
 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 
 
 12 
 
 4.5 
 
 .65 
 
 70.2 
 
 1082 
 
 85.1 
 
 54.1 
 
 8.1 
 
 6.6 
 
 80 { 
 
 12 
 
 4.5 
 
 .55 
 
 67.9 
 
 1140 
 
 79.2 
 
 57.0 
 
 7.9 
 
 6.5 
 
 14 
 
 5 
 
 .65 
 
 104.0 
 
 1408 
 
 111 
 
 70.4 
 
 8.5 
 
 7.0 
 
 90 •{. 
 
 13 
 
 5 
 
 .55 
 
 91.9 
 
 1408 
 
 97 
 
 70.4 
 
 8.3 
 
 6.8 
 
 16 
 
 6 
 
 .65 
 
 160 
 
 1854 
 
 147 
 
 92.7 
 
 9 
 
 7.3 
 
 f 
 
 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 
 
 120 \ 
 
 16 
 
 6 
 
 .65 
 
 214 
 
 2472 
 
 179 
 
 124 
 
 9.4 
 
 7.6 
 
 i 
 
 18 
 
 6.5 
 
 .75 
 
 30? 
 
 2946 
 
 250 
 
 147 
 
 10 
 
 8.2 
 
 l 
 
 16 
 
 6 
 
 .55 
 
 211 
 
 2660 
 
 169 
 
 133 
 
 9.2 
 
 7.4 
 
 140 { 
 
 18 
 
 6.5 
 
 .65 
 
 306 
 
 3185 
 
 227 
 
 159 
 
 9.8 
 
 8.0 
 
 ( 
 
 20 
 
 7 
 
 .75 
 
 420 
 
 3766 
 
 312 
 
 188 
 
 10.5 
 
 8.5 
 
 
 17 
 
 6.5 
 
 .55 
 
 278 
 
 3264 
 
 203 
 
 163 
 
 9.6 
 
 7.8 
 
 160 ] 
 
 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 
 
 74\ 
 
 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 
 
 I 
 
 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 ! 
 
 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 
 
 ( 
 
 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 
 
 I 
 
 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 
 
 jm 
 
 11157 
 
 34875 
 
 2171 
 
 1744 
 
 15.4 
 
 12.6 
 
 500 j 
 
 52 
 
 18 
 
 .55 
 
 7354 
 
 29600 
 
 1454 
 
 1480 
 
 14.2 
 
 11.6 
 
 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 
 
 I 
 
 64 
 
 24 
 
 .75 
 
 18103 
 
 49665 
 
 2998 
 
 2483 
 
 16.4 
 
 13.4 
 
 ( 
 
 60 
 
 22 
 
 .55 
 
 12446 
 
 42900 
 
 2065 
 
 2145 
 
 15.2 
 
 12.5 
 
 600 \ 
 
 64 
 
 24 
 
 .65 
 
 17115 
 
 50220 
 
 2656 
 
 2511 
 
 15.4 
 
 13.1 
 
 
 68 
 
 26 
 
 .75 
 
 22731 
 
 58020 
 
 3489 
 
 2901 
 
 16.9 
 
 13.8 
 
1324 MARINE ENGINEERING. 
 
 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 lbs., and the force of gravity at 32, we have from the common for- 
 
 Vi IV Vi *W 
 
 mula for force of acceleration, viz.: F= M-r = — -r- , or i* 1 =* — vi, when 
 
 i second. 
 
 64 A V 
 Thrust of screw in pounds = — ^r— (V — v) — 2 AV (V — v). 
 
 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 t 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 savs: 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 = ^qqq 3 ,!^ - in which- S = speed in 
 
THE SCREW-PROPELLER. 
 
 1325 
 
 knots, R = revolutions per minute, and x = percentage of apparent slip. 
 For a slip of 10%, pitch = 112.6 S -s- R. 
 
 D = diameter of propeller = K 
 
 I I-H.P. K 
 
 being a coefficient given 
 
 = 20,0 00^ I .H.P. -i-(PXR) 3 . 
 
 t C Vl.H.P. +■ R, in which C is a coeffi- 
 
 in the table below. If K = 20, D = 
 
 Total developed area of blades = 
 cient to be taken from the table. 
 
 Anoth er form ula for pitch, given in Seaton's Marine Engineering, is 
 
 C v 3 / 1 H P 
 P— p 4/ * ' ' , in which C= 737 for ordinary vessels, and 660 for slow- 
 speed cargo vessels with full lines. 
 
 Thickness of blade at root 
 
 V nb 
 
 X k, 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 -V 0.4 in.; cast steel 0.03 D + 
 0.4 in.; gun-metal 0.03 D + 0.2 in.; high-class bronze 0.02 D +0.3 in., 
 where D = diameter of propeller in feet. 
 
 Propeller Coefficients. 
 
 Descriptiou of Vessel. 
 
 gig 
 
 J 
 
 hi 
 
 Bluff cargo boats 
 
 Cargo, moderate lines 
 
 Pass, and mail, fine lines. . 
 
 " very fine.. 
 Naval vessels, " " . 
 Torpedo-boats, •.' ..." . 
 
 8-10 
 10-13 
 13-17 
 13-17 
 17-22 
 17-22 
 16-22 
 16-22 
 20-26 
 
 Twin 
 One 
 
 Twin 
 
 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.LorS. 
 G.M.orB 
 
 C. I., cast iron; G. M., gun-metal; B., bronze; S. 
 
 From the formulae D = 20,000 
 
 Vcpx 
 
 x rv 
 
 and P 
 
 steel; F.S., forged steel. 
 7371. H. P. 
 
 v/- 
 
 R D 2 
 
 if 
 
 P = D and R = 100, we obtain D = -^ 400 X I.H.P. = 3.31 ^/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 1323 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 approximately 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: 
 
 _4 5_ 6 7 8 9 11 12 13 14 15 16 
 
 $(S - 10)3 
 
 = 0.577 0.660 0.736 0.807 0.875 0.939 1.059 1.116 1.170 1.224 1.275 1.327 
 
1326 
 
 MARINE ENGINEERING. 
 
 Speed: 
 17 18 
 
 19 
 
 20 
 
 21 22 23 24 25 26 27 
 
 yos-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 by Seaton, quoted above, should be used. 
 
 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, 
 R — Ws -s- g; Rv = Wsv 4- g. 
 
 This impelling action must, to secure maximum efficiency 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+6)] + 2 = v+ 8/2; 
 and the work performed would be 
 
 R (v+ 8/2) = Wvs ■*■ g+ Ws 2 -J- 2 fit, 
 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 dis- 
 charged with maximum backward velocity, the screw must have an 
 axially increasing pitch. 
 
 The true screw is by far the more usual form of propeller, in all steamers, 
 both merchant and naval. (Thurston, Manual of the Steam-engine, 
 part ii, 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. h- 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 
 
 15.55 
 
 1.4 
 
 19.5 
 
 2.0 
 
 22.9 
 
 0.9 
 
 16.22 
 
 1.5 
 
 20.1 
 
 2.1 
 
 23.5 
 
 1.0 
 
 16.88 
 
 1.6 
 
 20.7 
 
 2.2 
 
 24 
 
 1.1 
 
 17.55 
 
 1.7 
 
 21.3 
 
 2.3 
 
 24.5 
 
 1.2 
 
 18.2 
 
 1.8 
 
 21.8 
 
 2.4 
 
 25.0 
 
 1.3 
 
 18.8 
 
 1.9 
 
 22.4 
 
 2.5 
 
 25.4 
 
 (&) 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. 
 
THE SCREW-PROPELLER. 
 
 1327 
 
 (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. 
 
 (g) 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. 
 
 (k) An efficient form of blade is an ellipse having a minor axis equal 
 to four-tenths the major axis. 
 
 (t) The pitch of wide-bladed screws should increase from forward to 
 aft, but a uniform pitch gives satisfactory results when the blades are 
 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 vibiation, 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., 18S7: S. W. Barnaby, Proc. Inst. 
 C. E„ 1890, vol. cii, and D. W. Taylor's " Resistance of Ships and Screw 
 Propulsion." Also Mr. Taylor's paper in Proc. Soc. Nav. Arch. & Marine 
 Engrs., 1904. Mr. Taylor found the highest efficiencies, exceeding 70%, 
 in propellers with pitch ratios from 1.0 to 1.5 ratio of width of blade to 
 diameter of 1/8 to 1/5, 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. 
 Another important feature is that, although these experiments are not 
 a direct guide to the selection of the most efficient propeller for a particu- 
 lar ship, they supply the means of analyzing the performances of screws 
 fitted to vessels, and of thus indirectly determining what are likely to be 
 the best dimensions of screw for a vessel of a class whose results are 
 known. Thus a great advance has been made on the old method of trial 
 upon the ship itself, which was the origin of almost every conceivable 
 erroneous view respecting the screw-propeller. {Proc. Inst. 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 sq. ft. X 7 3 /H.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 D 2 = Cj X I.H.P./P*. Revs, 
 per min. = Cr X V/D. The constants Ca and Cr assume a standard 
 value of the speed of the wake, equal to 10% of the speed of the ship. 
 In a very full shi£ 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, %. 
 
 63 
 
 67 
 
 68 
 
 69 
 
 68 
 
 66 
 
 63 
 
 Pitch ratio. 
 
 Ca 
 
 Cr 
 
 C A 
 
 CR 
 
 C A 
 
 Cr 
 
 C A 
 
 CR 
 
 C A 
 
 Cr 
 
 C A 
 
 Cr 
 
 C A 
 
 Cr 
 
 0.80 
 
 468 
 
 122 
 
 304 
 
 128 
 
 215 
 
 134 
 
 157 
 
 142 
 
 115 
 
 150 
 
 86 
 
 160 
 
 65 
 
 171 
 
 1.00 
 
 546 
 
 99 
 
 355 
 
 104 
 
 251 
 
 109 
 
 184 
 
 115 
 
 135 
 
 123 
 
 100 
 
 131 
 
 76 
 
 140 
 
 1.20 
 
 625 
 
 83 
 
 405 
 
 87 
 
 288 
 
 92 
 
 210 
 
 97 
 
 154 
 
 104 
 
 115 
 
 111 
 
 87 
 
 119 
 
 1.40 
 
 704 
 
 72 
 
 456 
 
 76 
 
 325 
 
 80 
 
 236 
 
 85 
 
 173 
 
 90 
 
 129 
 
 97 
 
 98 
 
 104 
 
 1.60 
 
 780 
 
 63 
 
 507 
 
 67 
 
 360 
 
 71 
 
 263 
 
 75 
 
 193 
 
 80 
 
 144 
 
 87 
 
 109 
 
 93 
 
 1.80 
 
 
 
 558 
 
 60 
 
 396 
 
 64 
 
 290 
 
 68 
 
 212 
 
 73 
 
 159 
 
 78 
 
 17.0 
 
 84 
 
 2.QQ 
 2.20 
 2.40 
 
 
 
 609 
 660 
 710 
 
 55 
 50 
 47 
 
 432 
 469 
 505 
 
 58 
 54 
 50 
 
 315 
 342 
 369 
 
 62 
 57 
 53 
 
 231 
 250 
 270 
 
 67 
 62 
 57 
 
 173 
 
 187 
 202 
 
 72 
 67 
 62 
 
 131 
 142 
 153 
 
 77 
 
 
 
 7? 
 
 
 
 67 
 
 
 
 
1328 
 
 MARINE ENGINEERING. 
 
 vjj-bs 
 
 lj-bs 'aoBjiug 
 
 SUL}139JJ 
 
 •SJOtTSJ 'IT3UX 
 
 uo paadg 
 
 <IH pa^oipui 
 
 
 
 4.'^u9tuaot|dsiQ 
 
 *»J 'n^ia 
 
 •%j 'q+ddQ 
 
 •^j 'q^pTOjy 
 
 *■%} *q;Su8T[ 
 
 •a^d 
 
 ^■«■^ON-^0'CO^--- 
 
 OO -"I" — ^tNOOOOOvOTiO 
 
 a^ oo" ao" ©" o" c^f t" "^■"•cTe;* °o" 
 
 )*OONNNNOO»q;Nr«- ■ 
 )>Ot>tslNtsI>>OvOvO»CNtsl>, • 
 
 8n 
 
 ^-O^T 
 
 - . . • . -sO 04 
 
 rq m •* ■* os • • 
 
 O sO © — if\CM>NN\ON £ 
 
 t»OM>0000»0 — — NNOtf 
 
 OOOOOOOOOOQOOOOO 
 U-\000000(NOOOOOOOO 
 
 -o iT> co mmoMfiifio in o o o o o o 
 r-drrso*©*©"— "r<"\"T"©"o»"©"©"r>."so" 00*00" 
 
 OOOOOOOOOOmcJCC^Oini^ 
 
 • O* • Cvl its its Os irt s© 
 
 •Os ■ — O © c^ M oo O COtrwt 
 
 l~>.fArsJfr>itsqf<|rOfMrA<S«>00tNO'Osr^! 
 
 irsrsirs)c-q{virsirsirsirgrsi(NrsicorsiNfo 
 
 © m^r 
 
 (AvCNOo'cOpQ-N.-tjaSf 
 
 "V sQ ITS sQ sQ sQ s£ 
 
 • a • '■ 
 
 : o : : 
 
 :« : j 
 So g-c 
 
 
 CfO^^^aop^HoMcQWJ 
 
 I Jjj! »o m 2 •» r 
 
 Ilf|2|fgs 
 
 *— <- -•- • Con 
 
 ^^_- - bet-" _=,-, 
 
 .ceo c •- c° ^S 
 
 
 
 
 • rap-si h§i 
 
 (- . .oS ^ sU >-i c M cd 
 
 lis "ilii jl 
 
 I 1*1 of If || 
 
 ■^N.iUCB 
 
 
 
 
MARINE PRACTICE 
 
 1329 
 
 Marine Practice, 1901. — The following tables and "summary of 
 results" are taken from a paper on "Review of Marine Engineering in 
 the Last Ten Years," by Jas. McKechnie, Proc. Inst. M. E., 1901: Eng. 
 News, Aug. 29, 1901. 
 
 Particulars of Cargo Steamers for North Atlantic Trade, to illustrate 
 Fuel Economy of Large-Capacity Ships. (All are three-decked vessels, 
 with shelter deck, to Class 100 Al at Lloyd's. Speed of all at sea, 13 
 knots.) 
 
 
 Draft, 
 ft. ins. 
 
 Dis- 
 place- 
 ment, 
 
 
 Dead- 
 w'ght, 
 tons. 
 
 
 
 Immersed . 
 
 C to 
 
 Dimensions. 
 
 Area, 
 
 Girth 
 
 S*- 
 — ^ 
 
 
 
 
 
 
 
 fT ° 
 
 sq.ft. 
 
 ft. 
 
 £ 
 
 
 
 
 
 
 
 
 Q ° 
 
 
 
 " 
 
 390'x45'9"x29'6". .. 
 
 24 6l/ 2 
 
 8,640 
 
 0.69 
 
 5,000 
 
 3.475 
 
 266 
 
 1,092 
 
 87.8 
 
 8.0 
 
 415'x4&'9"x31'0". .. 
 
 25 6 
 
 10,240 
 
 0.696 
 
 6,000 
 
 3,725 
 
 277 
 
 1,209 
 
 92.46 
 
 7.1 
 
 438'x51'5"x32'8". .. 
 
 26 31/2 
 
 11,870 
 
 0.702 
 
 7,000 
 
 3,970 
 
 287 
 
 1,314 
 
 96.46 
 
 6.5 
 
 458'x53'9"x34'0". .. 
 
 27 OI/2 
 
 13,500 
 
 0.71 
 
 8,000 
 
 4,225 
 
 295 
 
 1,412 
 
 100.0 
 
 6.05 
 
 475'x55'9"x35'5". .. 
 
 27 11 
 
 15,100 
 
 0.715 
 
 9,000 
 
 4,475 
 
 300 
 
 1,513 
 
 103.64 
 
 5.7 
 
 493'x58'0"x36 / 7". .. 
 
 28 7 
 
 16,750 
 
 72 
 
 10,000 
 
 4,725 
 
 305 
 
 1,610 
 
 107.0 
 
 5 42 
 
 521' X6I' 2"x38' 9". .. 
 
 30 
 
 19,850 
 
 0.728 
 
 12,000 
 
 5,200 
 
 311 
 
 1,780 
 
 112.8 
 
 4.97 
 
 535' x 62' 9"x39'9". .. 
 
 30 7 
 
 21,47(1 
 
 O.Jil 
 
 13,000 
 
 5,430 
 
 313 
 
 1,862 
 
 115.4 
 
 4.8 
 
 548' x 64' 1"X4C9". .. 
 
 31 3 
 
 23,070 
 
 0.736 
 
 14,000 
 
 5,675 
 
 314 
 
 1,946 
 
 118.0 
 
 4 66 
 
 570' X 66' 9" X 42' 4". .. 
 
 32 41/2 
 
 26,150 
 
 0.742 
 
 16,000 
 
 6,130 
 
 316 
 
 2,097 
 
 122.5 
 
 4.4 
 
 * The rate of coal consumption is assumed in all cases at 1.5 lbs. per 
 I.H.P. per hour. 
 
 Comparison of Marine Engines for the Years 1872, 1881, 1891, 1901. 
 
 Boilers, Engines and Coal. 
 
 Boiler press., lbs. per sq. in 
 
 Heating surface, per sq. ft. grate 
 
 Heat'g surf., per I.H.P., sq. ft 
 
 Coal, per sq. ft. of grate, lbs. per hr.. 
 
 Revolutions per minute 
 
 Piston speed, ft. per min 
 
 Coal per I.H.P. per hr., lbs 
 
 Av. consumption, long voyage 
 
 Average Results. 
 
 52.4 
 "aA\ 
 
 55.67 
 376 
 2.11 
 
 77.4 
 30.4 
 
 3.917 
 13.8 
 59.76 
 
 467 
 
 1.83 
 
 2.0 
 
 158.5 
 31.0 
 3.275 
 15.0 
 63.75 
 529 
 1.52 
 1.75 
 
 197 
 38 & 43* 
 
 3.0 
 18&28* 
 87 
 654 
 1.48 
 1.55 
 
 * Natural and forced draft respectively. 
 
 Summary of Results. — Steam pressures have been increased in the 
 merchant marine from 158 lbs. to 197 lbs. per sq. in., the maximum 
 attained being 267 lbs. per sq. in., and 300 lbs. 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. per ton of machinery. The net result 
 in respect of speed is that 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 of those of ten years ago; the maximum speed attained by 
 any craft was 25 knots, as compared with 36.581 knots now. while the 
 number of ships of over 20 knots was 8 in 1891, and is 58 now [1901]. 
 
1330 
 
 MARINE ENGINEERING. 
 
 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: 
 
 
 Diameter 
 
 of Rotor, 
 
 ins. 
 
 Length of Blades, ins. 
 
 Turbines. 
 
 In First 
 Expansion. 
 
 In Last 
 Expansion. 
 
 H.P 
 
 96 
 140 
 104 
 
 23/ 4 
 21/ 4 
 
 123/ 8 
 22 
 
 L.P 
 
 
 8 
 
 
 
 Total cooling surface, main condensers, 82,800 sq. ft; area of exhaust 
 inlet, 158 sq. ft; bore of circulating discharge pipes, 32 ins. 
 
 Boilers. — Working pressure, 195 lbs. 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, 158,352 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, together 
 witli 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 B 
 Jour 
 
 Diameter. 
 
 earing 
 rials. 
 
 Effective 
 Length. 
 
 Pressure 
 Per Sq. In. 
 of Bearing 
 Surface. 
 
 At 190 Revs. 
 
 Surface Speed 
 
 of Journal . 
 
 H.P. rotor 
 
 27 1/ 8 in. 
 331/s in. 
 24 1/ 8 in. 
 
 443/4 in. 
 561/2 in. 
 343/ 4 in 
 
 80 lbs. 
 72 lbs. 
 83 lbs. 
 
 
 
 
 
 1200 ft. per min. 
 
 
 
 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 18 21 23 25.4 
 
 Shaft horse-power 13,400 20,500 33,000 48,000 68,850 
 
 Steam cons, per shaft, H.P. hr. 
 
 of turbines, lbs 21.23 17.24 14.91 13.92 12.77 
 
 of auxiliaries, lbs 5.3 3.72 2.6 2.01 1.69 
 
 totallbs 26.53 20.96 17.51 15.93 14.46 
 
 Temperature of feed water, 
 
 °F 200 200 199 179 165 
 
 Coal cons. lbs. per shaft . . 
 
 H.P. hr 2.52 2.01 1.68 1.56 1.43 
 
 Estimated steam and coal consumption under service conditions, at 
 
 same speeds: 
 Steam cons, of auxiliaries, 
 
 per shaft H.P. hr., lbs.. 6.97 4.92 3.41 2.65 2.17 
 Steam cons, of total per 
 
 shaft H.P. hr., lbs 28.20 22.16 18.32 16.57 14.94 
 
 Coal cons., lbs. 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 
 Queenstown to Sandy Hook, 2781 nautical miles, Nov. 3-8, 1908, 4 days, 
 18 hrs. 40 m.: Averages: Steam pressure at boilers, 168 lbs.; temperature 
 hot-well, 74.5°; feed water, 197°; vacuum, 28.1 in.; speed, 24.25 knots; 
 
THE PADDLE-WHEEL. 1331 
 
 speed, best day, 24.8 knots; revolutions, 181.1; slip, 15.9%. Total coal, 
 4976 tons. Steam consumption: main turbines, 851,500 lbs., = 13.1 lbs. 
 per shaft H.P. hr. (on a basis of 65,000 shaft H.P.); auxiliary machinery, 
 114,000 lbs., = 1.75 per H.P. hr.; evaporating plant and healing, 32,500 Lbs., 
 = 0.5 lb. per H.P. hr. Total, 998,000 lbs., = 15.35 lbs. per shaft H.P. 
 hour. Average coal burned, 43 1/2 tons per hour. Water evaporated 
 per lb., coal 10.2 lbs. from feed at 196°, = 10.9 lbs. from and at 212°. 
 Coal for all purposes per shaft H.P. hour, 1.5 lbs. Coal per sq. ft. of 
 grate per hour, 24.1 lbs. The coal was half Yorkshire and 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. 
 
 Relation of Horse-Power to Speed. — If &i and S2 are two successive 
 speeds and P1P2 the corresponding horse-powers, then to find the value 
 of the exponent x in the equation H.P. a> S x , we have 
 
 x = (log Pi - log PO h- (log S 2 - log £,). 
 Applying this formula to the horse-powers and speeds of the " Lusitania" 
 we find that between 15.77 and 18 knots x = 3.21; between 18 and 21 
 knots x = 3.09; between 21 and 23 knots x = 4.12; between 23 and 
 25.4 knots x = 3.63. 
 
 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 lbs. 
 absolute, and then passes to the turbine. For manoeuvering 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 lbs. and a water consumption of 
 11 lbs. 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/s, 
 49V4, 747/8 and 1121/4 ins., by 6 ft. stroke. Steam, 230 lbs., delivered 
 from 19 cylindrical boilers, through four 17-in. steampipes. Coal used 
 I in 24 hours, 764 tons, in 124 furnaces; 1.4 lbs. 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 =CX I.H.P. -h D. 
 D is 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 1/8 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. 
 
1332 MARINE ENGINEERING. 
 
 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) -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. 
 
 When a ship is working always in smooth water the immersion of the 
 top edge should not exceed i/s 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 (D +2). 
 The breadth of the float = 0.35 X the length. 
 The thickness of floats = V12 the breadth. 
 Diameter of gudgeons = thickness of float. 
 Seaton and Rounthwaite's Pocket-book gives: _ 
 Number of floats =60-5- Vi?, 
 where R is number of revolutions per minute. 
 
 . fl ■■. r , +N I.H.P. X 33,000 X K 
 Area of one float (in square feet) = — at y (n Y R^ ' 
 
 where 2V = 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 efHciencv. (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/s-mch 
 diameter, and with a pressure of 2500 lbs. 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 
 
FOUNDATIONS. 1333 
 
 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) 2 . 
 „, ffi . . 2AV(V-v)v 2v 
 
 The efficiency is . „ . T . r^ — ; — . „ , T . rr = ■=-— ■ This expression 
 
 2 AV (V - v) v + AV (V -v) 2 V+v 
 equals unity when V = v, that, is, when the velocity of the jet with refer- 
 ence to the earth, or V — v, = ; but then the thrust of the propeller is 
 also 0. The greater the value of V as compared with v, the less the 
 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. 
 
 The whole theory of propulsion may be summed up in Rankine's 
 words: "That propeller is the best, other tilings being equal, which drives 
 astern the largest body of water at the lowest velocity." 
 
 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 oroof , see 
 account of trials by C. J. Everett, Jr., given by Prof. J. Burkitt Webb, 
 Trans. A. S. M. E., xii, 904. 
 
 CONSTRUCTION OP BUILDINGS.* 
 
 FOUNDATIONS. 
 
 Bearing Power of Soils. — Ira O. Baker, "Treatise on Masonry 
 Construction." 
 
 Kind of Material. 
 
 Rock — the hardest — in thick layers, in native bed. 
 
 Rock equal to best ashlar masonry 
 
 Rock equal to best brick masonry 
 
 Rock equal to poor brick masonry 
 
 Clay on thick beds, always dry 
 
 Clay on thick beds, moderately dry 
 
 Clay, soft 
 
 Gravel and coarse sand, well cemented 
 
 Sand, compact, and well cemented 
 
 Sand, clean, dry 
 
 Quicksand, alluvial soils, etc 
 
 Bearing Power in 
 Tons per Square Foot. 
 
 Minimum. 
 
 Maximum. 
 
 200 
 
 25 
 
 
 30 
 
 15 
 
 20 
 
 5 
 
 10 
 
 4 
 
 6 
 
 2 
 
 4 
 
 1 
 
 2 
 
 8 
 
 10 
 
 4 
 
 6 
 
 2 
 
 4 
 
 0.5 
 
 1 
 
 * The limitations of space forbid any extended treatment of this subject. 
 Much valuable information upon it will be found in Traut wine's 'Civil 
 Engineers' Pocket-book," and in Kidder's " Architects and Builders 
 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 TM Clark (J. R. 
 Oseood & Co.. Boston); " The American House Carpenter, and The Theory 
 of Transverse Strains," both bv 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. 
 
1334 
 
 CONSTRUCTION OF BUILDINGS. 
 
 The building code of Greater New York specifies the following as the 
 maximum permissible loads for different soils: 
 
 " 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." 
 
 Bearing Power 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, 8 = penetration under last blow, or the average under 
 last five blows. 
 
 Safe Strength of Brick Piers, exceeding six diameters in height. 
 (Kidder.) 
 
 Piers laid with rich lime mortar, tons 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. 
 
 
 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 
 
 
 
 MASONRY. 
 
 Allowable Pressures on Masonry in Tons per Square Foot. 
 
 (Kidder.) 
 
 Different Cities.* 
 
 (l) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 
 60 
 40 
 30 
 
 
 72-172 
 
 50-165 
 
 28-115 
 
 18 
 
 15 
 
 n Vs 
 
 8 
 
 
 
 
 40 
 
 
 
 
 
 
 
 
 
 12 
 
 
 121/2 
 9 
 
 '61/2 
 
 15 
 
 i i 1/2 
 u 
 
 
 Hard-burned brick in natural cement 
 
 Hard-burned brick in cement and lime . . . 
 Hard-burned brick in lime mortar 
 
 15 
 12 
 8 
 
 9 
 
 "6' 
 
 12 
 9 
 5 
 
 6 
 
 4 
 
 15 
 12 
 8 
 
 9 
 *8' 
 
 
 
 
 
 
 
 12 
 12 
 
 30 
 10 
 4 
 
 
 
 8 
 
 is"" 
 
 8 
 
 5-7 
 
 "a 
 
 
 10 
 
 In foundations: 
 
 
 
 
 
 15 
 
 
 
 
 
 
 
 
 
 * From building laws, (1) Boston, 1 
 York, 1899; (4) Chicago, 1S93; (5) St 
 1899; (7) Denver, 1898. 
 
 Crushing Strength of 12-in. Cu 
 
 Pounds per square foot. The concret 
 cement, 2 parts sand, with average cone 
 
 S97; 
 . Lc 
 
 l>es 
 
 3 W3 
 
 rete 
 
 (2) 
 uis, 
 
 of 
 
 s in 
 ston 
 
 Buffa 
 1897; 
 
 Concr 
 
 ade o 
 e and 
 
 lo, 1 
 
 (6) 
 
 ete. 
 
 f 1 I 
 grav< 
 
 S97; 
 Phila 
 
 (Kic 
 )art ] 
 jI, as 
 
 delp 
 
 der 
 Port 
 belo 
 
 Vew 
 hia, 
 
 and 
 
 W. 
 
BEAMS AND GIRDERS. 
 
 1335 
 
 
 10 days. 
 
 45 days. 
 
 3 mos. 
 
 6 mos. 
 
 1 year. 
 
 
 130,750 
 136,750 
 
 172,325 
 266,962 
 
 324,875 
 
 361,600 
 298,037 
 
 440,040 
 
 
 396,200 
 
 
 
 408,300 
 
 6 parts (3/4 stone, V4 grano- 
 lithic) 
 
 
 
 
 
 388,700 
 
 
 99,900 
 
 234,475 
 
 385,612 
 234,475 
 
 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: 
 Extreme fiber stress in compression in con- 
 crete 500 lbs. 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: 
 Safe load in lbs. 
 
 Breadth in inches = 
 
 2 X breadth X square of depth X A 
 span in feet 
 span in feet X load 
 2 X square of depth X A 
 
 The depth is taken in inches. The coefficient A, is Vi8 the maximum 
 fiber stress for safe loads, and is the safe load for a beam 1 in. square, 1 ft. 
 span. The following 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 11 
 
 Slate 50 
 
 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 lbs. per square inch; for lintels, 
 brackets, or corbels, compression 13,500 lbs. per square inch, and tension 
 3000 lbs. per square inch. For girders, beams, corbels, brackets, and 
 trusses, 16,000 lbs. per square inch for steel and 12,000 lbs. for iron. 
 
 For plate girders: 
 
 Flange area = maximum bending moment in ft .-lbs. -i-(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 = 10,000 for steel; 6,000 for iron. 
 
1336 
 
 CONSTRUCTION OF BUILDINGS. 
 
 For rivets in single shear per square inch of rivet area: 
 
 If shop-driven, steel, 9000 lbs., iron, 7500 lbs.; if field-driven, steel, 
 
 7500 lbs., iron, 6000 lbs. 
 
 For timber girders: S = cbd 2 -s- 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. 
 
 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- 
 tp i TT7 _ 4 PBD 2 stress = 1000 lbs. per square inch, for white 
 
 oak; B, breadth in inches; D, depth in inches; 
 L, distance between supports in inches. 
 
 3L 
 
 • SI 
 
 Distance between Supports in Feet. 
 
 10 11 12 14 I 15 16 17 18 i 19 21 I 23 i 25 i 26 
 
 Safe Load in Tons of 2000 Pounds. 
 
 2x6 
 2x8 
 2x10 
 2x12 
 3X6 
 3x8 
 3x10 
 3x12 
 3x14 
 3x16 
 4x10 
 4x12 
 4x14 
 4x16 
 4x18 
 
 0.67 
 1.19 
 1.85 
 2.67 
 1.00 
 1.78 
 2.78 
 4.00 
 5.45 
 7.11 
 3.70 
 5.33 
 7.26 
 9.48 
 12.00 
 
 0.50 
 
 0.89 
 
 1.39 
 
 2.00 
 
 0.75 
 
 1.33 
 
 2 
 
 3.00 
 
 4.08 
 
 5.33 
 
 2.78 
 
 4.00 
 
 5.44 
 
 7 
 
 9.00 
 
 0.29 
 0.51 
 0.79 
 1.14 
 0.43 
 0.76 
 1.19 
 1.71 
 2.37 
 3.05 
 1.59 
 2.2.9 
 3.11 
 4.06 
 5.14 
 
 0.22 
 0.40 
 0.62 
 0.39 
 0.33 
 0.59 
 0.93 
 I .33 
 1.82 
 2.37 
 1 .23 
 1.78 
 2.42 
 
 4.00 
 
 26 
 72 
 25 
 17 
 68 
 29 
 3.1613.00 
 79 
 
 0.34 
 0.53 
 0.76 
 0.29 
 0.51 
 0.79 
 1.14 
 1.56 
 2.03 
 1.06 
 1.52 
 2.07 
 2.71 
 3.43 
 
 0.28 
 0.43 
 0.64 
 
 0.43 
 0.62 
 
 0.41 
 0.64 
 0.92 
 1.25 
 1.64 
 0.85 
 1.23 
 1.68 
 2.19 
 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 
 safe stress per square inch on beams of different kinds of wood according 
 to the building laws of the cities named) and divide by 1000. 
 
 
 Hem- 
 lock. 
 
 S P™- Ptae' 6 
 
 Oak. 
 
 Yellow 
 Pine. 
 
 
 800 
 
 900 900 
 
 750 750 
 
 900 
 
 1100 
 TOOOf 
 
 1080 
 
 1100* 
 1250 
 1440 
 
 
 
 
 
 
 
 * Georgia pine. t White oak. 
 
 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 materia 
 make only the two upper stories 16 ins. thick, the next three 20 ins., anc 
 so on down. 
 
 In buildings less than five stories in height the top story may be IS 
 ins. in thickness. 
 
WALLS. 
 
 1337 
 
 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 
 High. 
 
 Stories. 
 
 1st. 2d. 3d. 4th. 5th. 6th. 7th. 8th. 9th- 10th 11th 12th 
 
 12-18 
 13-20 
 16-22 
 18-22 
 20-26 
 20-28 
 22-32 
 24-32 
 24-36 
 28-36 
 28-40 
 
 12-13 
 
 12-1 
 
 16-18 
 
 16-22 
 
 18-22 
 
 20-26 
 
 20-28 
 
 24-32 
 
 24-32 
 
 28-36 
 
 28-36 
 
 12-16 
 12-18 
 16-20 
 16-22 
 18-24 
 20-26 
 20-28 
 24-32 
 24-32 
 28-36 
 
 12-16 
 12-20 
 16-20 
 16-22 
 18-24 
 20-26 
 20-28 
 24-30 
 24-32 
 
 12-16 
 13-20 
 16-20 
 16-22 
 20-24 
 20-26 
 24-28 
 24-32 
 
 12-16 
 13-20 
 16-20 
 16-22 
 20-24 
 20-26 
 24-28 
 
 12-17 
 13-20 
 10-20 
 16-22 
 20-24 
 20-26 
 
 12-17 
 16-20 
 16-20 
 20-22 
 20-24 
 
 12-17 
 16-20 
 16-20 
 20-22 
 
 13-17 
 16-20 
 
 (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; 
 
 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 12 1/2 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 lbs. 
 
 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 " 
 
 Every floor 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 formula, 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 formula?, namely: Cast iron, 80,000; 
 wrought or rolled iron, 40,000: rolled steel. 4S,000: white pine and spruce, 
 3500: pitch or Georgia pine, 5000: American oak, 6000. T^e 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. 
 
1338 CONSTRUCTION OF BUILDINGS. 
 
 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 compressive 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 lbs. Sandstone, 
 white marble, granite, and other kinds of building-stone shall be deemed 
 to weigh 160 lbs. 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, 11V2 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 smooth at 
 both ends, and shall rest on iron or 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 
 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 21/2 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 have 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 not 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 
 
FLOORS. 1339 
 
 a wall or floor or both, shall be so proportioned that the loads which may 
 come upon them shall not produce strains in tension or compression upon 
 the flanges of more than 12,000 lbs. for iron, nor more than 15,000 lbs. 
 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 lbs. 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/g 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 lbs. 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 the 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 of 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. (Etig'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: 
 
 Authorities. Weight of Crowd, 
 
 lbs. 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 ^43 1 
 
 Experiments by Mr. B. B. Stoney ("On Stresses," p. 617) 147.4 
 
 Experiments by Prof. L. J. Johnson, Eng. News, April 14, ( 134.2 
 
 1904 Uo 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.) Pounds per square 
 foot. 
 
 For dwellings, sleeping and lodging rooms 40 lbs. 
 
 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, light storage, and light manufactur- 
 ing 120* *« 
 
 * Also to sustain a concentrated load at any point of 4000 lbs. 
 
 STRENGTH OF FLOORS. 
 
 (From circular of the Boston Manufacturers' Mutual Insurance Co.) 
 The following tables were prepared by C. J. H. Woodbury, for determin- 
 ing safe loads on floors. Care should be observed to select the figure 
 giving the greatest possible amount and concentration of load as the one 
 
1340 CONSTRUCTION OF BUILDINGS. 
 
 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 specified, unless a 
 lower factor of safety is warranted under the advice of a competent 
 engineer. 
 
 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 center 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 lbs. per cubic foot, and 
 that of Southern pine at 48 lbs. per cubic foot. 
 
 Table I was computed upon a working modulus of rupture of Southern 
 pine of 2160 lbs., 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 are 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. 
 
 These tables are computed for beams one inch in width, because the 
 strength of beams increase directly as the width when the beams are 
 broad enough not to cripple. 
 
 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. 
 span, will sustain 118 lbs. per foot of span; and for a beam 10 ins. wide 
 the load would be 1180 lbs. per foot of span, or 1471/2 lbs. per sq. ft. of 
 floor for Southern-pine beams. From this should be deducted the weight 
 of the floor, 17 1/2 lbs. per sq. ft., leaving 130 lbs. per sq. ft. as a safe load. 
 If the beams are of spruce, multiply 1471/2 by 0.78, reducing the load to 
 115 lbs. Deducting the weight of the floor, 16 lbs., leaves the safe net 
 load as 90 lbs. 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 dis- 
 tortion 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 lbs. for Southern pine; the same table can be applied to spruce, 
 whose modulus of elasticity is taken as 1,200,000 lbs., if six tenths of 
 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 21/2 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 f the load 
 on the plank is sustained by the beam at each end of the plank, and 10/15 
 by the beam under the middle of the plank; so that for a completed floor 
 3/g 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 
 
STRENGTH OF FLOORS. 
 
 1341 
 
 it were not so, 3/ 8 of the whole load upon the floor would be sustained by 
 every other beam, and 5/ 8 of the load by the corresponding 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 lbs. per foot of span, or 75 lbs. 
 per sq. ft. of floor, for Southern-pine beams. Deducting the weight of 
 the floor, 17 1/2 lbs. per sq. ft., leaves 57 lbs. per sq. ft. as the advisable 
 load. 
 
 If the beams are of spruce, the result of 75 lbs. should be multiplied 
 by 0.6, reducing the load to 45 lbs. The weight of the floor, in this 
 instance amounting to 16 lbs., would leave the net load as 29 lbs. 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 the limit of safe load as found 
 by Table I, as would be the case under the conditions of this problem. 
 
 Mill Columns. ■ — Timber posts offer more resistance to fire than iron 
 pillars, and have generally displaced them in millwork. Experiments 
 at the U. S. Arsenal at Watertown, Mass., show that sound timber posts 
 of the proportions customarily used in millwork yield by direct crushing, 
 the strength being directly as the area at the smallest part. The columns 
 yielded at about 4500 lbs. per sq. in., confirming the general practice of 
 allowing 600 lbs. per sq. in. as a safe load. Square columns are one 
 fourth stronger than round ones of the same diameter. 
 
 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.) 
 
 flj 
 
 Depth of Beam in inches. 
 
 a 
 
 2 
 
 * 
 
 * 
 
 5 
 
 *6 | 7 | 8 | 9 | 10 1 11 1 12 | 13 
 
 14 
 
 u 
 
 16 
 
 
 Load in pounds per foot of Span. 
 
 38 
 27 
 20 
 15 
 
 86 
 60 
 
 44 
 34 
 27 
 22 
 
 154 
 
 107 
 
 78 
 60 
 47 
 38 
 32 
 27 
 
 240 
 167 
 122 
 94 
 74 
 60 
 50 
 42 
 36 
 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 
 
 m 
 
 540 
 397 
 304 
 240 
 194 
 161 
 135 
 115 
 99 
 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 
 
1342 
 
 CONSTRUCTION OP BUILDINGS. 
 
 II. Distributed Loads upon Southern-pine Beams Sufficient to 
 Produce Standard Limit of Deflection. 
 
 "5 
 «£ 
 
 a 
 a 
 
 Depth of Beam, in inches. 
 
 a" 
 
 ■I»l« 
 
 .|« 
 
 7 | 8 
 
 9 
 
 10|ll 
 
 - 
 
 M 
 
 14 
 
 |W 
 
 | 16 
 
 
 
 Loac 
 
 in pounds per foot of Span 
 
 
 
 
 
 5 
 6 
 7 
 8 
 9 
 
 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 
 16! 
 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 
 
 in 
 
 
 
 .1200 
 
 ii 
 
 
 
 .1452 
 
 i?, 
 
 
 
 
 .1728 
 
 H 
 
 
 
 
 
 .2028 
 
 14 
 
 
 
 
 
 .2352 
 
 15 
 
 
 
 
 
 
 .2700 
 
 16 
 
 
 
 
 
 
 .3072 
 
 17 
 
 
 
 
 
 
 
 .3468 
 
 18 
 
 
 
 
 
 
 
 3888 
 
 19 
 
 
 
 
 
 
 
 
 .4332 
 
 ?n 
 
 
 
 
 
 
 
 
 .4800 
 
 71 
 
 
 
 
 
 
 
 
 
 .5292 
 
 ?? 
 
 
 
 
 
 
 
 
 
 .5808 
 
 ?3 
 
 
 
 
 
 
 
 
 
 
 .6348 
 
 74 
 
 
 
 
 
 
 
 
 
 
 .6912 
 
 75 
 
 
 
 
 
 
 
 
 
 
 
 .7500 
 
 
 
 
 
 
 
 
 
 
 Maximum Spans for 1, 2 and 3 Inch Plank. (Am. Mach., Feb. 11, 
 1904.) — Let w = load per sq. ft.; I = length in ins.; W = wl/12; S =• 
 safe fiber stress, using a factor of safety of 10; b = width of plank; d = 
 thickness: p = deflection, E = coefficient of elasticity, / = moment of 
 inertia = V12 bd 3 . 
 
 Then Wl/S = Sbd 2 /6; s = 5 Wl 3 h- 384 EI. Taking S at 1200 lbs., E 
 at 850,000 and s = I -*■ 360 for long-leaf yellow pine, the following figures 
 for maximum span, in inches, are obtained: 
 
 Uniform load, lbs. per sq. ft. . 40 
 
 1 in nlank i For strength . . 75 
 1-m. plank | For deflection . 37 
 
 9 in n i an vf For strength.. 151 
 2-111 • plank \ For deflection . 75 
 
 q in nla nk I For Strength . . 227 
 d-in. piank j For deflection . 113 
 
 For white oak S mav be taken at 1000 and E at 550,000; for Canadian 
 spruce, S = 800, E = 600,000; for hemlock, S = 600, E = 450,000. 
 
 60 
 
 80 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 61 
 33 
 
 53 
 30 
 
 48 
 
 28 
 
 39 
 
 24 
 
 33 
 22 
 
 
 
 123 
 66 
 
 107 
 60 
 
 96 
 55 
 
 78 
 48 
 
 67 
 
 44 
 
 60 
 41 
 
 55 
 38 
 
 185 
 99 
 
 161 
 90 
 
 144 
 83 
 
 117 
 73 
 
 101 
 66 
 
 91 
 61 
 
 83 
 
 58 
 
 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 lbs. 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. 
 
MILL BUILDINGS. 
 
 1343 
 
 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. 
 
 $1.90 
 
 $1.66 
 
 $1.58 
 
 $1.54 
 
 $1.51 
 
 $1.49 
 
 $1.48 
 
 $1.47 
 
 $1.46 
 
 50 
 
 1.52 
 
 1.29 
 
 1.21 
 
 1.18 
 
 1.16 
 
 1.15 
 
 1.14 
 
 1.13 
 
 1.13 
 
 75 
 
 1.41 
 
 1.21 
 
 1.12 
 
 1.08 
 
 1.06 
 
 1.04 
 
 1.03 
 
 1.02 
 
 1.02 
 
 125 
 
 1.32 
 
 1.09 
 
 1.02 
 
 0.98 
 
 0.96 
 
 0.94 
 
 0.94 
 
 0.93 
 
 0.92 
 
 25 
 
 2.00 
 
 1.62 
 
 1.52 
 
 1.47 
 
 1.44 
 
 1.41 
 
 1.39 
 
 1.38 
 
 1.36 
 
 50 
 
 1.50 
 
 1.21 
 
 1.13 
 
 1.09 
 
 1.06 
 
 1.05 
 
 1.04 
 
 1.03 
 
 1.02 
 
 75 
 
 1.34 
 
 1.08 
 
 1.01 
 
 0.97 
 
 0.94 
 
 0.92 
 
 0.92 
 
 0.91 
 
 0.90 
 
 125 
 
 1.22 
 
 0.97 
 
 0.90 
 
 0.86 
 
 0.84 
 
 0.82 
 
 0.81 
 
 0.80 
 
 0.86 
 
 Three Stories. 
 
 25 
 
 1.98 
 
 1.57 
 
 1 47 
 
 1.42 
 
 1.39 
 
 1.38 
 
 1.36 
 
 1.35 
 
 1.34 
 
 50 
 
 1.47 
 
 1.17 
 
 1.07 
 
 1.03 
 
 1.01 
 
 1.00 
 
 0.98 
 
 0.98 
 
 0.98 
 
 75 
 
 1.30 
 
 1.05 
 
 0.98 
 
 0.94 
 
 0.91 
 
 0.89 
 
 0.88 
 
 0.87 
 
 0.86 
 
 125 
 
 1.18 
 
 0.93 
 
 0.86 
 
 0.82 
 
 0.80 
 
 0.78 
 
 0.77 
 
 0.76 
 
 0.76 
 
 Four Stories. 
 
 25 
 
 2.00 
 
 1.61 
 
 1.50 
 
 1.45 
 
 1.42 
 
 1.40 
 
 1.38 
 
 1.37 
 
 1.36 
 
 50 
 
 1.38 
 
 1.17 
 
 1.10 
 
 1.05 
 
 1.02 
 
 1.00 
 
 LOO 
 
 0.99 
 
 0.98 
 
 75 
 
 1.32 
 
 1.08 
 
 97 
 
 0.93 
 
 0.90 
 
 0.88 
 
 0.88 
 
 0.87 
 
 0.87 
 
 125 
 
 1.20 
 
 0.93 
 
 0.85 
 
 0.81 
 
 0.78 
 
 0.77 
 
 0.76 
 
 0.75 
 
 0.74 
 
 25 
 
 2.10 
 
 1 7?. 
 
 1.57 
 
 1.51 
 
 1.48 
 
 1.46 
 
 1.44 
 
 1.43 
 
 1.42 
 
 50 
 
 1.53 
 
 1.21 
 
 1.12 
 
 1.08 
 
 1.05 
 
 1.04 
 
 1.03 
 
 1.02 
 
 1.02 
 
 75 
 
 1.35 
 
 1.08 
 
 0.98 
 
 0.94 
 
 0.92 
 
 0.90 
 
 0.89 
 
 0.88 
 
 0.86 
 
 125 
 
 1.22 
 
 0.96 
 
 0.86 
 
 0.82 
 
 0.79 
 
 0.78 
 
 0.77 
 
 0.76 
 
 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- ) o, lt< ,: j_ wa u„ 
 
 Brick walls, cost per ) Outside walls. . 
 sq. ft. of surface. . . J Inside walls 
 
 $2.00 
 1.75 
 
 0.40 
 0.40 
 
 $2.90 
 2.25 
 
 0.44 
 0.40 
 
 $3.80 
 2.80 
 
 0.47 
 0.40 
 
 $4.70 
 3.40 
 
 0.50 
 0.43 
 
 $5.60 
 3.90 
 
 0.53 
 0.45 
 
 $6.50 
 4.50 
 
 0.57 
 0.47 
 
 Columns, including piers and castings, cost each $15. 
 
 Assumed Height of Stories. — From ground to first floor, 3 ft. Buildings 
 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. 
 
1344 ELECTRICAL ENGINEERING. 
 
 In buildings over two stories, plumbing $75 for each fixture including 
 piping and partitions. Two fixtures on each floor up to 5000 sq. ft. of 
 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 
 fair 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 lbs. 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 lbs. 
 per sq. ft. or less will cost about 25% more than the slow-burning type 
 of mill construction. 
 
 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, s.; 
 
 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, at Paris, = 9S1 centimeters in 1 second; 
 
 Unit of force = 1 dyne = ^- gramme = -°Qg046 lb. = 0.000002247 lb. 
 
 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 32.185 feet per 
 second at Paris, and the meter = 39.37 inches, we have 
 
 1 gramme = 32.185 X 12 ~ 0.3937 = 981.00 dynes. 
 Unit of work = 1 erg =1 dyne-centimeter = 0.00000007373 ft.-lb.; 
 Unit of power = 1 watt = 10 million ergs per second, 
 
 = 0.7373 foot-pound per second, 
 
 = 0^73 = _L of 1 horse-power =0.00134 H.P. 
 550 746 * 
 
 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 cutting 
 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 conductor) by 1 centimeter of 
 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. 
 
STANDARDS OF MEASUREMENT. 1345 
 
 The C.G.S. unit of 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 how, 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'. 
 
 Watt (ampere- volt, or volt-ampere), the unit of power, P. 
 
 Joule (volt-coulomb), the unit of energy or work, W. 
 
 Farad, the unit of 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, C=§. 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 -r- R will give 
 the number of amperes current strength in that circuit. 
 
 The above six formulae can be combined by substitution or elimination, 
 so as to give the relations between any of the quantities. The most 
 important of these are the following: 
 
 EI E 2 
 
 <?=§*, C = j;t, W=IEt=^t=PRt=Pt, 
 
 H-IB. V-f. P=f=/ 2 tf=f=<f. 
 
 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 for 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 poles or electrodes of a Clark's cell at a tem- 
 perature of 15° C, and prepared in the manner described in the standard 
 specifications. 
 
 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 in 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 
 
1346 ELECTRICAL ENGINEERING. 
 
 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 B.A. unit = 0.9889 legal ohm; 
 
 1 international ohm = 1.0136 B.A. units, IB. A. unit = 0.9866 int. ohm; 
 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 = tyiooo of an ampere; 
 1 micro-farad = 1 millionth of a farad. 
 
 Relations of Various Units. 
 
 1 ampere =1 coulomb per second ; 
 
 1 volt-ampere =1 watt = 1 volt-coulomb per sec. ; 
 
 r = 0.7373 foot-pound per second, 
 1 watt \ = 0.0009477 heat-unit per sec. (Fahr.), 
 
 I = V746 of one horse-power; 
 
 r = 0.7373 foot-pound, 
 1 joule < = work done by one watt in one sec, 
 
 1 = 0.0009477 heat-unit; 
 
 1 British thermal unit = 1055.2 joules; 
 
 1 kilowatt, or 1000 watts = 1000/746 or 1.3405 horse-powers; 
 
 1 kilowatt-hour, r = 1.3405 horse-power hours, 
 
 1000 volt-ampere hours, \ = 2,654,200 foot-pounds, 
 
 1 British Board of Trade unit, (. = 3412 heat-units; 
 
 1 hm-^P nowpr J = 746 watts = 746 volt-amperes, 
 
 1 horse-power { = 33000 foot-pounds per minute. 
 
 The ohm, ampere, and volt are defined 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 a current of one ampere to flow through a resistance of 
 one ohm. 
 
 For Methods of making Electrical Measurements, Testing, etc., 
 see Munroe & Jamieson's Pocket-Book of Electrical Rules, Tables, and 
 Data; S. P. Thompson's Dynamo-Electric Machinery; Carhart & Patter-: 
 son's Electrical Measurements; and works on Electrical Engineering. 
 
 Equivalent Electrical and 3fechanical 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 1347 is taken, with some modifications. 
 
 Units of the Magnetic Circuit. 
 
 Unit magnetic pple 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 centi- 
 meter 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 conductor 
 when its velocity across the field is 1 centimeter per second. A field of 
 
EQUIVALENT ELECTRICAL AND MECHANICAL UNITS. 1347 
 
 
 5"3o ! 
 
 0<~ w 
 2 u £ 
 
 oS»a 
 
 — o© 
 
 
 v O.S 3 K s. 
 _c< — m §(Nr^£;£ 
 
 
 
 
 
 «8' 
 2" 
 
 5 a a 'S 
 
 
 , N © O 
 
 
 
 — ©©©©> 
 
 ^s 
 
 atl! g -ij: 
 
 2 .£&' 
 a S 3..J 
 
 a£ cw 
 
 £'*a a 
 
 •a S g+? P ! o p 
 • ag . S o5 d • < 
 o -i w£ "a £ is -a „ 
 
 5 d^,r, j a — £ 
 
 -^5 
 
 a a '3 »-^> Sjn 
 
 f? a o o . o3 
 
 o'oijgd «N t-.' 
 
 as iS 
 
 o e t* X 
 
 3 93 Q,° 
 
 5 a +> O 
 
 
1348 ELECTRICAL ENGINEERING. 
 
 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, <f>. 
 
 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, n. 
 
 Gilbert = unit of magnetomotive force, is the amount of M.M.F. that 
 would be produced by a coil of 10 -h 4?r 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; it is the reluctance of a cubic centi- 
 meter of an air-pump vacumm. Symbol, R. 
 
 Reluctance is that quantity in a magnetic circuit which limits the flux 
 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 symbol is n. 
 
 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 bv a coefficient, n., 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 -v- 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 
 
 The permeability of a number of materials may be determined by means 
 of the table on page 1384. 
 
 ANALOGIES BETWEEN THE FLOW OF WATER AND 
 ELECTRICITY. 
 
 Water. Electricity. 
 
 Head, difference of level, in feet. \ Volts; electro-motive force; differ- 
 
 Difference of pressure, lbs. per sq. in. J ence of potential ; E. or E.M.F. 
 
 Resistance of pines, apertures, etc., 1 Ohms, resistance, R. Increases di- 
 increases with length of pipe, with rectly as the length of the conduc- 
 contractions, roughness, etc.: de- \ tor or wire and inversely as its sec- 
 creases with increase of sectional tional area, R <» I -f- ,s. It varies 
 area. I with the nature of the conductor. 
 
 Rate of flow, as cubic ft. per second, 1 Amperes: current; current strength; 
 gallons per min., etc., or volume intensity of current; rate of flow; 
 divided by the time. In the min- [ 1 ampere = 1 coulomb per second, 
 ing regions sometimes expressed Amr>pr^— volts • r— — • Tf — TJ? 
 in " miners' inches. " J Am P eres ~ ohms - l ~ R • *-■"*• 
 
ELECTRICAL RESISTANCE. 
 
 1349 
 
 ANALOGIES BETWEEN THE FLOW OF WATER AND 
 ELECTRICITY — Continued. 
 
 Water. 
 Quantity, usually measured in cubic 
 ft. or gallons, but is also equiva- 
 lent to rate of flow X time, as cu. 
 ft. per second for so many hours. 
 
 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 lbs. 
 per square foot against which the 
 water is pumped. 
 
 Power, rate of work. Horse-power = 
 ft.-lbs. of work in 1 min. ~ 33,000. 
 In water flowing in pipes, rate of 
 flow in cu. ft. per second X resist- 
 ance to the flow in lbs. per sq. ft. 
 -r- 550. 
 
 Electricity? 
 
 Coulomb, unit of quantity, Q, — 
 rate of flow X time, as ampere- 
 seconds. 1 ampere-hour = 3600 
 coulombs. 
 ,Joule, volt-coulomb, W, the unit of 
 work, = product of quantity by 
 the electro-motive force = volt- 
 ampere-second. 1 joule = 0.7373 
 foot-pound. 
 
 If C (amperes) = rate of flow, and 
 E (volts) = difference of pressure 
 between two points in a circuit, 
 energy expended = IEt, = PRt. 
 
 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. 
 = 1746 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 oo l h- s. 
 
 If r = the resistance of a conductor 1 unit in length and 1 square unit 
 in sectional area, R = rl -=- s. The common unit of length for electrical 
 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 -r- 8 = 10 X 1000 -4- 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. 
 
 Relative Conductivities of Different Metals at 0° and 100° C. 
 
 (Matthiessen.) 
 
 
 Conductivities. 
 
 Metals. 
 
 Conductivities. 
 
 Metals. 
 
 At 0°C. 
 At32°F. 
 
 At 100° C. 
 At 212° F. 
 
 At 0°C. 
 At 32° F. 
 
 At 100° C. 
 At 212° F. 
 
 
 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 
 1.245 
 
 8 67 
 
 Copper, hard .... 
 
 Gold, hard. 
 
 Zinc, pressed .... 
 
 
 5 86 
 
 Arsenic 
 
 Antimony 
 
 Mercury, pure. . 
 Bismuth 
 
 3.33 
 3.26 
 
 
 0.878 
 
 
 
 
 
 
 
 Resistance of Various Metals and Alloys. — Condensed from a 
 table compiled by H. F. Parshall and H. M. Hobart from different authori- 
 ties. R = resistance in ohms per mil foot = resistance per centimeter 
 cube x 6.015. C=«= percent increase of resistance per degree C. 
 
1350 
 
 ELECTRICAL ENGINEERING. 
 
 Aluminum, 99% pure 
 
 Aluminum, 94; copper, 6.. 
 Al. bronze, Al 10; Cu, 90.. 
 Antimony, compressed. . . 
 
 Bismuth, compressed 
 
 Cadmium, 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;A1, 6.5 
 
 Copper, 65; nickel, 25 
 
 Cu, 70; manganese, 30 
 
 German silver 
 
 Cu, 60; Zn, 25; Ni, 15.... 
 
 Gold, 99.9% pure 
 
 Gold, 67; silver, 33 
 
 Iron, very pure. 
 
 R 
 
 C 
 
 15.4 
 
 0.423 
 
 17.4 
 
 .381 
 
 75.5 
 
 .105 
 
 211 
 
 .389 
 
 780 
 
 .354 
 
 60 
 
 .419 
 
 9.35 
 
 .428 
 
 9.54 
 
 .388 
 
 17.7 
 
 
 37.8 
 
 .158 
 
 31.7 
 
 
 53.0 
 
 .090 
 
 89.5 
 
 .065 
 
 205 
 
 .019 
 
 605 
 
 .004 
 
 180 
 
 .036 
 
 13.2 
 
 .377 
 
 61.8 
 
 .065 
 
 54.5 
 
 .625 
 
 White cast iron 
 
 Gray cast iron 
 
 Wrought iron , 
 
 Soft steel, C, 0.045 
 
 Manganese steel, Mn, 12. 
 
 Nickel steel, Ni, 4.35 
 
 Lead, pure 
 
 Manganin, 
 
 Cu, 84; Mn, 12;Ni, 4 
 
 Cu, 80.5;Mn,3;Ni, 16.5 
 Cu, 79.5 ;Mn, 19.7; Fe,0.{ 
 
 Mercury , 
 
 Nickel 
 
 Palladium, pure 
 
 Platinum, annealed 
 
 Platinum, 67; silver, 33 . . . 
 
 Phosphor bronze 
 
 Silver, pure , 
 
 Tin, pure , 
 
 Zinc, pure 
 
 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 
 .62 
 .354 
 .247 
 .133 
 .394 
 .400 
 .440 
 .406 
 
 (D) Dewarand Fleming; (M) Matthiessen. 
 
 Conductivity of Aluminum. — J. W. Richards (Jour. Frank.. Inst, 
 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 C. Weston, how- 
 ever (Proc. Electrical Congress, 1893, p. 179), has found copper-nickel- 
 zinc alloys (German silver) which had a resistance of nearly 28 times 
 that of copper, and a temperature coefficient of about one-half that given 
 by Matthiessen. 
 
 Conductors and Insulators in Order of their Value. 
 
 (non-conductors). 
 Ebonite 
 Gutta-percha 
 India-rubber 
 Silk 
 
 Dry paper 
 Parchment 
 Dry leather 
 Porcelain 
 Oils 
 
 According to Culley, the resistance of distilled water is 6754 million 
 times as great as that of copper. Impurities in water decrease its resist- 
 ance. 
 
 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 of 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 substances 
 used for various electrical purposes by which 1 ohm is increased by a 
 rise of temperature of 1° C. 
 
 I Gold, silver 0.00065 
 
 Cast iron , 0.00080 
 
 I Copper 0.00400 
 
 CONDUCTORS. 
 
 INSULATORS 
 
 All metals 
 
 Dry air 
 
 Well-burned charcoal 
 
 Shellac 
 
 Plumbago 
 
 Paraffin 
 
 Acid solutions 
 
 Amber 
 
 Saline solutions 
 
 Resins 
 
 Metallic ores 
 
 Sulphur 
 
 Animal fluids 
 
 Wax 
 
 Living vegetable substances 
 
 Jet 
 
 Moist earth 
 
 Glass 
 
 Water 
 
 Mica 
 
 Platinoid 0.00021 
 
 Platinum silver 0.00031 
 
 German silver (see above).. 0.00044 I 
 
DIRECT ELECTRIC CURRENTS. 1351 
 
 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. Temo. C. Hard. Annealed. R,atio. 
 
 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 of Resistance of Copper Wire. (Trans. A. I. E. E., 
 Sept. and Nov., 1890.) — Matthiessen's standard is: A hard-drawn copper 
 wire 1 meter long,, weighing 1 gramme, has a resistance of 0.1469 B.A. 
 unit at 0° C. Relative conducting power (Matthiessen): silver, 100; 
 hard or unannealed copper, 99.95; soft or annealed copper, 102.21. Con- 
 ductivity of copper at other temperatures than 0° C, C t =C (1 — 0.00387 t 
 + 0.000009009 t 2 ). 
 
 The resistance is the reciprocal of the conductivity, and is 
 R t = R d (1 + 0.00387 t + 0.00000597 t 2 ). 
 
 The shorter formula R t = R Q (1 + 0.00406 is commonly used. , 
 
 A committee of the Am. Inst. Electrical Engineers recommend the 
 
 following as the most correct form of the Matthiessen standard, taking 
 
 8.89 as the sp. gr. of pure cooper: 
 
 A soft copper wire 1 meter long and 1 mm. diam. has an electrical 
 
 resistance of 0.02057 B.A. unit at 0° C. From this the resistance of a soft 
 
 copper wire 1 foot long and 0.001 in. diam. (mil-foot) is 9.720 B.A. units 
 
 at 0.° C. \ 
 
 Standard Resistance at 0° C. B.A. Units. Legal Ohms. Internat. 
 
 Ohms. 
 Meter-millimeter, soft copper 0.02057 0.02034 0.02029 
 
 Cubic centimeter " 0.000001616 0.000001598 0.000001593 
 
 Mil-foot " 9.720 9.612 9.590 
 
 1 mil -ft. of soft copper at 10°. 22 Cor 50°. 4 F. 10. 9.977 
 
 " " " " r ' " 15°.5 " 59°. 9 F. 10.20 10.175 
 
 " " " " " " 23°.9 " 75° F. 10.53 10.505 
 
 Hard-drawing and annealing are found to produce proportional changes 
 in the conductivity and the temperature coefficient. The range of con- 
 ductivity of numerous samples representative of the copper now in com- 
 mon use for electrical purposes is from 94.5% to 101.8% (on the basis of 
 100% corresponding to 1.7213 micro-ohms per centimeter-cube, at 20°C. 
 
 Using this result, a measurement of the conductivity of a sample gives 
 also its temperature coefficient. Thus. 020 (in the formula, R^ — R20 [1 + 
 a w (t - 20)] for a sample of copper is given by multiplying 0.00393 by the 
 percentage conductivitv. The value assumed by the Am. Inst. El. En., 
 Oq = 0.0042, or ao = 0.00387, is the true temperature coefficient for 
 copper of 98.6% conductivity. (J. H. Dellinger, Elec. Rev., May 7, 1910.) 
 
 For tables of the resistance of copper wire, see pages 1357 and 1358, 
 also page 240. 
 
 Taking Matthiessen's standard of pure copper as 100%, some refined 
 metal has exhibited an electrical conductivity equivalent to 103%. 
 Matthiessen found that impurities in copper sufficient to decrease its 
 density from 8.94 to 8.90 produced a marked increase of electrical resist- 
 ance. 
 
 DIRECT ELECTRIC CURRENTS. 
 
 Ohm's Law. — This law expresses the relation between the three 
 fundamental units of resistance, electrical pressure, and current. It is: 
 _, L electrical pressure , E , „ ,„ A E 
 
 Current ^ resistance ; 7= R : whence * = /«. and B - r 
 
1352 ELECTRICAL ENGINEERING. 
 
 In terms of the units of the three quantities, 
 
 . volts .■ ; volts 
 
 Amperes = —r ; volts = amperes X ohms; ohms = — • 
 
 ohms amperes 
 
 Examples: Simple Circuits. — 1. If the source has an effective electrical 
 pressure of 100 volts, and the resistance is two ohms, what is the current? 
 
 E 
 = R ~~ 
 
 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 -s- 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. 195, be a source of current, 
 such as a battery or generator, producing a difference of potential or 
 E.M.F. of 120 volts, measured across ab, and let the circuit contain four 
 conductors whose resistances, n, ri, r%, r 4 , are 1 ohm each, and three 
 
 a ri /-\ r» s-\ other resistances, Ri, R2, R3, each 2 ohms. The 
 
 1 -* — ( ) — — ( h total resistance is 10 ohms, and by Ohm's law 
 
 S: R Ro tne current I = E + R = 120 + 10 = 12 ana- 
 
 's- A - 1 2 r 3 p ereS- This current is constant throughout the 
 
 I ^- ^ circuit, and a series circuit is therefore one of 
 
 i: if. \_) constant current. The drop of potential in the 
 
 * R whole circuit from a around to b is 120 volts, 
 
 F IG 195 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, R2, #3 is 2 X 12 = 24 volts. 
 
 Parallel, Divided, or Multiple Circuits. — Let B, Fig. 196, 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 Sg 
 Ri, R2, R3, of 2 ohms each. Consider 
 that the resistance of the wires is so small 
 that it may be neglected. Let the con- 
 ductances of the four paths be repre- 
 sented by C s . Ci, C 2> Cs. The total Fig. 196. 
 conductance is C s + C t + Ci + Cs = C and the total resistance R =• 
 1 -*■ 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. 
 
 *=H6VH4)= i+3 - 5=0 - 286ohm - 
 
 The current I = E -*■ R = 770 amperes. 
 
 Conductors in Series and Parallel. — Let the resistances in parallel 
 be the same as in Fig. 196, 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, 
 efgh and eg. Find the resistance and the conductance of each and the 
 total resistance (the reciprocal of the joint conductance) of the parallel 
 
DIRECT ELECTRIC CURRENTS. 1353 
 
 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 + 2 + 0.1 = 2.2 0.4545 
 
 R b of eR 2 g = 2 0.5 
 
 Joint R c = 1.048 0.9545 
 
 R d oice+ dg+ R c =1.248 0.8013 
 
 R e of cRid «= 2 0.5 
 
 Joint R/ = 0.7687 1.3013 
 
 R g of ac+bd+ Rf = 0.9687 1.0332 
 
 Rh of s = 0.5 2 
 
 Joint R a + R h = 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. 
 "c.Rid = 227.3 X 0.5 -f- 1.3013 = 87.34 amp. 
 
 e = 227.3 X 0.8013 -f- 1.3013 = 139.96 " 
 " eR?g = 139.96 X 0.5 h- 0.9545 = 73.31 " 
 " fRz = 139.96 X 0.4545 -H 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 - 2X 22.7 = 174.6 volts; across eg, 174.6- 2 
 X 14.0 = 146.6, and across fh 146.6 - 2 X 667 = 133.3 volts. Taking 
 these voltages and the resistances R\, R2, R3, each 2 ohms, we find from 
 J - E -*- 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 R 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 / = 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 
 / = E -i- R, watts = E 2 -r- R = electro-motive force 2 4- resistance. 
 
 Example. — What H.P. is required to supply 100 lamps of 40 ohms 
 resistance each, requiring an electro-motive force of 60 volts? 
 
 E 2 60 2 
 The number of volt-amperes for each lamp is -=- = — , 1 volt-ampere 
 
 60 2 
 -0.00134 H.P.; therefore — 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 ei is the efficiency of the 
 dynamo, B.H.P. = E.H.P. -f- e\. If e<> is the mechanical efficiency of the 
 engine, the indicated horse-power, I. H.P. = brake H.P. ~ ei = E.H.P. -~- 
 
 (61 X 62). 
 
1354 ELECTRICAL ENGINEERING. 
 
 If ex and e% 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 = PRt. Since I = E + R, 
 
 PRt = ^IRt = EIt = E^t = ~- 
 
 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 difference 
 in potential between the ends of the conductor. 
 
 The electrical unit of heat, or "joule" = 10 7 ergs = heat generated in 
 one second by a current of 1 ampere flowing through a resistance of one 
 ohm = 0.239 gramme of water raised 1° C. H = PRt X 0.239 gramme 
 calories = PRt 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, while 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 : Vio, and therefore the ten 
 thin wires can dissipate more than t-hree 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 formula are given by 
 Kennelly: 
 
 T= ■*, X 90,000 +t; 
 
 T = temperature of the wire and t that of the air, in Fahrenheit degrees; 
 / — current in amperes, d = diameter of the wire in mils. 
 
 If we take T - t = 90° F., ^90 - 4.48, then 
 
 d = 10 ^JP and I = ^d 3 + 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. 
 
DIRECT ELECTRIC CURRENTS. 
 
 1355 
 
 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 I PR 
 
 t being the temperature rise in degrees Fahr.; S, 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 copper 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 = aS, 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. 
 
 Allowable Carrying Capacity of Copper "Wires. 
 
 (For inside wiring, National Board of Fire Underwriters' Rules.) 
 
 B.&S. 
 
 Circular 
 
 Amperes. 
 
 Circular 
 
 Amperes. 
 
 
 
 
 
 Gauge. 
 
 Mils. 
 
 Rubber 
 
 Other In- 
 
 Mils. 
 
 Rubber 
 
 Other In- 
 
 
 
 Covered . 
 
 sulation. 
 
 
 Covered. 
 
 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 
 
 1,000,000 
 
 650 
 
 1,000 
 
 3 
 
 52,630 
 
 76 
 
 110 
 
 1,100,000 
 
 690 
 
 1,080 
 
 2 
 
 66,370 
 
 90 
 
 131 
 
 1,200,000 
 
 730 
 
 1,150 
 
 1 
 
 83,690 
 
 107 
 
 156 
 
 1,300,000 
 
 770 
 
 1,220 
 
 
 
 105,500 
 
 127 
 
 185 
 
 1,400,000 
 
 810 
 
 1,290 
 
 00 
 
 133,100 
 
 150 
 
 220 
 
 1 ,600,000 
 
 890 
 
 1,430 
 
 000 
 
 167,800 
 
 177 
 
 262 
 
 1,800,000 
 
 970 
 
 1,550 
 
 0000 
 
 211,600 . 
 
 210 
 
 312 
 
 2,000,000 
 
 1,050 
 
 1,670 
 
 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 insulation, 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 insidation is required to be at least 
 V32 inch thick for all sizes from No. 14 B. & S. gauge to 500,000 mils and 
 L/8 inch thick for larger sizes. 
 
1356 
 
 ELECTRICAL ENGINEERING. 
 
 Drop of Voltage of Wires with Currents Allowed by Underwriters* 
 Rules, as in the above Table. 
 
 
 Volts 
 
 Volts drop per 
 
 
 Volts 
 
 Volts d 
 
 rop per 
 
 B.&S. 
 
 drop per 
 1000 
 
 1000 ft. 
 
 Circular 
 Mils. 
 
 drop per 
 1000 
 
 1000 ft. 
 
 Gauge. 
 
 Rubber 
 
 Weather 
 
 Rubber 
 
 Weather 
 
 
 feet. 
 
 Covered . 
 
 proof. 
 
 
 feet. 
 
 Covered. 
 
 proof. 
 
 14 
 
 2.56 
 
 30.0 
 
 39.7 
 
 200,000 
 
 0.052 
 
 10.5 
 
 15.7 
 
 12 
 
 1.6 
 
 26.5 
 
 35.7 
 
 300,000 
 
 .035 
 
 9.5 
 
 14. 
 
 10 
 
 1.05 
 
 23.5 
 
 31.4 
 
 400,000 
 
 .026 
 
 8.7 
 
 13.8 
 
 8 
 
 .685 
 
 20.6 
 
 28.6 
 
 500,000 
 
 .021 
 
 8.2 
 
 12.4 
 
 6 
 
 .400 
 
 17.6 
 
 25.0 
 
 600,000 
 
 .018 
 
 7.9 
 
 11.7 
 
 5 , 
 
 .316 
 
 16.6 
 
 23.6 
 
 700,000 
 
 .015 
 
 7.5 
 
 11.4 
 
 4 
 
 .252 
 
 15.8 
 
 22.5 
 
 800,000 
 
 .013 
 
 7.2 
 
 11.0 
 
 3 
 
 .200 
 
 14.8 
 
 21.4 
 
 900,000 
 
 .0118 
 
 7.0 
 
 13.8 
 
 2 
 
 .158 
 
 13.7 
 
 20. 
 
 1,000,000 
 
 .0105 
 
 6.8 
 
 10.5 
 
 1 
 
 .126 
 
 13.0 
 
 18.9 
 
 1,100,000 
 
 .0095 
 
 6.6 
 
 10.3 
 
 
 
 .100 
 
 12.7 
 
 17.7 
 
 1,200,000 
 
 .00875 
 
 6.3 
 
 9.9 
 
 00 
 
 .079 
 
 11.4 
 
 16.7 
 
 1,300,000 
 
 .00808 
 
 6.2 
 
 9.8 
 
 000 
 
 .063 
 
 10.8 
 
 16. 
 
 1,400,000 
 
 .0075 
 
 6.1 
 
 9.7 
 
 0000 
 
 .049 
 
 10.1 
 
 15. 
 
 1,600,000 
 
 .00655 
 
 5.84 
 
 9.4 
 
 
 
 
 
 1,800,000 
 
 .00582 
 
 5.65 
 
 9.1 
 
 
 
 
 
 2,000,000 
 
 .00524 
 
 5.5 
 
 8.8 
 
 Copper- wire Table. — The table on pages 1357 and 1358 is abridged from 
 one computed by the Committee on Units and Standards of the Ameri- 
 can Institute of Electrical Engineers {Trans., Oct., 1893). 
 
 Wiring Table for Motor Service. 
 
 Carrying Capacity in Amperes is Figured at 25% increased Capacity, as 
 Required by the Underwriters. 
 
 Safe Carrying Capacity in 
 Amperes 
 
 9.6|13.6 
 
 20. 
 
 26. 
 
 36. 
 
 42.4 
 
 50.4 
 
 60. 
 3 
 
 70.4 
 2 
 
 80. 
 1 
 
 100 
 
 
 120 
 
 Wire Gauge No. B. 
 
 and S . . . 
 
 14 
 
 12 
 
 10 
 
 8 
 
 6 
 
 5 
 
 4 
 
 00 
 
 Horse-power. 
 
 Distance in Feet that the Differe 
 Horse-powers 
 can be Transmitted with a Loss of Oi 
 
 
 At Volts. 
 
 At 
 amperes 
 
 e Volt. 
 
 115 
 
 230 
 
 500 
 
 
 
 1/2 
 1 
 
 "l" 
 ■-•■ 
 
 4 
 
 "71/2 
 10 
 
 ...... 
 
 26" 
 
 25 " 
 
 1.0 
 2.0 
 2.3 
 4.0 
 4.5 
 6.0 
 7.5 
 9.0 
 12.5 
 16.5 
 18.0 
 21.1 
 25.0 
 28.2 
 33.1 
 37.6 
 42.0 
 56.5 
 75.3 
 113.0 
 
 192 
 96 
 83 
 48 
 43 
 32 
 25 
 21 
 15 
 
 308 
 154 
 135 
 
 77 
 68 
 51 
 40 
 34 
 24 
 18 
 
 490 
 245 
 213 
 122 
 108 
 81 
 65 
 54 
 40 
 29 
 27 
 23 
 20 
 
 778 
 389 
 348 
 194 
 173 
 127 
 104 
 86 
 61 
 47 
 43 
 37 
 30 
 27 
 23 
 
 1232 
 616 
 535 
 308 
 273 
 205 
 164 
 137 
 100 
 76 
 68 
 58 
 50 
 43 
 37 
 32 
 29 
 
 
 
 
 
 
 
 
 
 
 780 
 680 
 390 
 346 
 260 
 208 
 173 
 125 
 96 
 86 
 77 
 62 
 55 
 47 
 41 
 38 
 
 960 
 834 
 480 
 426 
 320 
 258 
 213 
 153 
 118 
 106 
 91 
 76 
 68 
 58 
 51 
 45 
 34 
 
 
 
 
 
 
 
 1/2 
 
 
 
 
 
 
 
 608 
 540 
 405 
 328 
 270 
 194 
 147 
 135 
 115 
 97 
 86 
 76 
 64 
 58 
 43 
 32 
 
 780 
 700 
 520 
 416 
 347 
 250 
 189 
 173 
 146 
 125 
 110 
 94 
 83 
 73 
 55 
 41 
 
 985 
 875 
 656 
 525 
 438 
 315 
 239 
 219 
 186 
 157 
 140 
 119 
 104 
 93 
 70 
 52 
 
 1232 
 1095 
 821 
 657 
 547 
 394 
 298 
 273 
 233 
 197 
 174 
 148 
 131 
 116 
 87 
 65 
 43 
 
 
 V2 
 
 1 
 
 1395 
 1045 
 
 
 
 836 
 
 1 
 
 2 
 3 
 
 697 
 501 
 
 380 
 
 2 
 
 4 
 5 
 
 348 
 297 
 750 
 
 
 71/2 
 
 io" 
 ...... 
 
 20 
 30 
 
 ?,?,?, 
 
 4 
 
 
 
 
 189 
 
 
 
 
 
 164 
 
 5 
 
 
 
 
 
 143 
 
 71/2 
 
 
 
 
 
 111 
 
 10 
 
 
 
 
 
 
 
 82 
 
 15 
 
 
 
 
 
 
 
 
 55 
 
 
 
 
 
 
 
 
 
 
 
 
 
DIRECT ELECTRIC CURRENTS. 1357 
 
 ^rsle^^r^.^^^.l^^'^f^^<> — P>if«MAOi 
 
 ^ISS??^2^£ 
 
 OOOOSOOOOQOOOOOOOOOOOOOSOOOO 2^i^S!r^^^,^-,o 
 
 o § § § 8 o o S o o o o S o o S.o © S © © © o © o o o o o o © o o § © o o S o o o S 
 
 IslS 
 
 =i o cd o o o cr . :.■ o S o o o o e 
 ooooooooooooooSoooooc 
 
 -orsv^poOfNO'Q^covO'A^iN^vo-oa: 
 
 ■OQ? — ^^NOrsNOOirvQvO>piAO'^ , TNaO^«Ac>N 
 
 IN«ONOC>iAONOONOrs3r^OO-N«r.-ONC>-«f>Oin^^C>'^rsN 
 
 OQOOoSoOOOQOQOOOOOOOOOO ■ N^TinrNSNNO-OON- 
 
 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO---- — r^i^r^in 
 
 ooooooooooooooooooooooooooooooobooooooooo 
 
 OOOOOOOON^OC>'0-n , iA-QN^»tA«-t»A-»r>N^-tfMAOOOtCNOt^^- 
 
 -•^O'lJ'OOMooo- r** >o »r» r-» cvj o ^o 
 
 
 
 OOC0N>ONIS , Oc0a0N'O00C0O*tC>->0OO>0-pv0^C>OO--^a^NN 
 
 "Bf*X&S!£i3§ 
 
 
 
 >o oo o>o<«go-ogT o^oo-oooo»5ou;o 3 oo- o £. o«oc~ ©©.©©£© 
 
 O^lft0-O , TO , TO^^O'S«»O7^-O<A(sS'r'T00O^(y-»nO^ON-iATC0rNO^ 
 
 S?,iCj9S-5^<<i5Sa3S^^SSoocc2££2_!mj2z2£ ' ' 00 ° or ^'^" 00 ' r " rs oo 
 
 p t 
 
 
 I I § 
 
1358 
 
 ELECTRICAL ENGINEERING. 
 
 * 2; 
 
 i 
 
 6 
 
 d 
 
 § 
 
 1 
 
 1 
 
 rfc. 
 
 a" 
 
 006259 
 007267 
 007892 
 009952 
 01047 
 01252 
 01255 
 01583 
 01635 
 0.01996 
 02051 
 0.02516 
 02649 
 0317,3 
 03205 
 03957 
 0.04001 
 05008 
 05045 
 06362 
 0.06541 
 07586 
 08022 
 08903 
 0.1012 
 1276 
 0^1282 
 1583 
 0.1608 
 0.2003 
 0.2028 
 0.2558 
 0.2616 
 0.3225 
 0.4067 
 0.5129 
 0.6466 
 0.8011 
 
 8154 
 1.028 
 
 1 296 
 
 o- 
 
 0-005648 
 006558 
 007122 
 008980 
 009443 
 01130 
 01132 
 01428 
 01475 
 0.01801 
 01851 
 02271 
 02390 
 02863 
 02892 
 03570 
 03610 
 04519 
 04552 
 05740 
 05902 
 0.06845 
 0.07239 
 08033 
 0.09128 
 0.1151 
 0.1157 
 0.1428 
 1451 
 0.1807 
 0.1830 
 
 2308 i 
 0.2361 
 0.2910 
 3669 
 4627 
 5835 
 7230 
 7357 
 9277 
 1.170 
 
 II 
 
 005055 
 •0 005870 
 006374 
 008038 
 008452 
 01011 
 01014 
 01278 
 01321 
 01612 
 01657 
 02032 
 02139 
 02563 
 02588 
 03196 
 03231 
 04045 
 04075 
 05138 
 0.05283 
 06127 
 06479 
 07190 
 0.08170 
 1030 
 0.1035 
 1278 
 1299 
 1618 
 1638 
 2066 
 0.2113 
 
 0.2605 1 
 0.3284 
 0.4142 
 0.5222 
 0.6471 
 0.6585 
 8304 
 1.047 
 
 ■ft 
 
 Is 
 
 8153 
 J 099 
 
 1 296 
 
 2 061 
 
 2 279 
 3.262 
 
 3 278 
 5 212 
 5 565 
 8 287 
 8 756 
 
 13 18 
 
 14 60 
 
 20 95 
 
 21 38 
 
 32 58 
 
 33 32 
 52 19 
 52 97 
 84 23 
 89 04 
 
 119 8 
 133 9 
 165 
 213 
 338 6 
 342 
 521 3 
 538 4 
 835 1 
 856 2 
 1,361 } 
 1.425 
 
 2,165 ! 
 3,441 
 5,473 
 8.702 
 
 13,360 i 
 13,870 ' 
 22,000 
 34,980 
 
 j 
 
 
 197 8 
 170.4 
 156 9 
 124 4 
 118 3 
 98 90 
 98 66 
 78 24 
 75 72 
 62 05 
 60 36 
 49 21 
 46 75 
 . 39 02 
 38 63 
 31 29 
 30 95 
 24 73 
 24 54 
 19 46 
 18 93 
 16 32 
 15 43 
 13 91 
 12 24 
 9 707 
 9 658 
 7 823 
 7 698 
 6 181 
 6 105 
 4 841 
 4 733 
 3.839 
 3 045 
 2 414 
 1.915 
 1 545 
 1.519 
 1.204 
 0.9550 
 
 1 
 
 161 3 
 
 187 3 
 203 4 
 256 5 
 269 7 
 
 322 6 
 
 323 4 
 407 8 
 421 4 
 514 2 
 528.6 
 648.4 
 682 6 
 817 6 
 825 9 
 
 1,020 
 
 1.031 
 
 1.290 
 
 1.300 
 
 1.639 
 
 1,685 
 
 1,955 
 
 2.067 
 
 2,294 
 
 2,607 
 
 3,287 
 
 3.304 
 
 4.078 
 
 4.145 
 
 5,162 
 
 5.227 
 
 6,591 
 
 6,742 
 
 8,311 
 10,480 
 13.210 
 16,660 
 20;650 
 21.010 
 26,500 
 33.410 
 
 i 
 1 
 
 
 1 226 
 9097 
 7713 
 4851 
 4387 
 3066 
 3051 
 1919 
 1797 
 1207 
 1142 
 07589 
 06849 
 04773 
 04678 
 03069 
 03002 
 01916 
 01888 
 001187 
 01123 
 008350 
 007466 
 006062 
 004696 
 002953 
 082924 
 0001918 
 001857 
 0001197 
 001168 
 0007346 
 0007019 
 0004620 
 0002905 
 0001827 
 0001149 
 000007484 
 00007210 
 00004545 
 00002858 
 
 oi 
 
 ■fiU, 
 
 006200 
 005340 
 004917 
 003899 
 003708 
 003100 
 003092 
 002452 
 002373 
 001945 
 001892 
 001 542 
 001465 
 001223 
 001211 
 0009808 
 0009699 
 0007749 
 0007692 
 0.0006100 
 0005933 
 0005116 
 0004837 
 0.0004359 
 0.0003836 
 0003042 
 0003027 
 0002452 
 0002413 
 0.0001937 
 0.0001913 
 000(517 
 0.0001483 
 0,0001203 
 00009543 
 00007568 
 00006001 
 00004843 
 00004759- 
 00003774 
 00002993 
 
 
 Il3§a§§53§§§iif5§a5^ 
 
 
 04526 
 04200 
 04030 
 03589 
 03500 
 03200 
 03196 
 02846 
 02800 
 02535 
 0250 
 02257 
 0.0220 
 0.02010 
 0200 
 0180 
 01790 
 0.0160 
 01594 
 0142 
 0.0140 
 0.0130 
 0.01264 
 0120 
 0.01126 
 01003 
 0.0100 
 0090 
 0.008928 
 0.0080 
 0.007950 
 007080 
 0.0070 
 006305 
 0056 15 
 0.0050 
 004453 
 0.0040 
 0.003965 
 003531 
 0.003145 
 
 i 
 
 6 
 
 CQtJQ 
 
 — ^fS N N N <M<S <s| J^P* «"* «**\ «* *\ *\ €** 
 
 CJai 
 
 °" *->*'«- "« ««?««•«• 
 
ELECTRIC TRANSMISSION, DIRECT CURRENTS 1359 
 
 ELECTRIC TRANSMISSION, DIRECT CURRENTS. 
 
 Cross-section of Wire Required for 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; 
 / = current, in amperes; 
 A = sectional area of wire, in circular mils; 
 
 then /= ^ ; R = 7 ; R = r ~r ; whence A = 
 
 R I A e 
 
 The value of r for soft copper wire at 75° F. is 10.505 international ohms. 
 For ordinary drawn copper wire the value of 10.8 is commonly taken, cor- 
 responding to a conductivity of 97.2 per cent. 
 
 For a circuit, going and return, the total length is 2L, and the formula 
 becomes A = 21.6 IL -5- e, L here being the distance from the point of 
 supply to the point of delivery. 
 
 If E is the voltage at the generator and a the per cent of drop in the line, 
 
 then e = Ea + 100, and A = 2160IL . 
 aE 
 
 P 91 fiO PT 
 
 If P = the power in watts, = EI, then / = ~, and A = " • 
 
 tL aE 1 
 
 If P k = the power in kilowatts, A = 2,160,000 P^L -*- aE 2 . 
 If L m = the distance in miles and A c the area in circular inches, then 
 A c = 6405 Pj c L m -*- aE 2 . If A s = area in square inches, A s = 5030 Pj c L 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 Allowable Capac- 
 ity 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. See Appendix to Vol. II of " Crocker's Electric 
 Lighting." 
 
 Weight of Copper for a Given Power. — Taking the weight of 
 a mil-foot of copper at 0.0000030271b., the weight of copper in a circuit of 
 length 2 Land cross-section A, in circ. mils, is 0.000006054 LA lbs., = W. 
 Substituting for A its value 2 160 PL -4- aE 2 we have 
 W = 0.0130766 PL 2 -f- aE 2 ; P in watts, L in ft. 
 
 W = 13.0766 P k L 2 -4- aE 2 ; P k in kilowatts, L in ft. 
 
 17 = 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 
 
 145,822 
 
 36,456 
 
 9,114 
 
 1,458 
 
 365 
 
 91 
 
 3,645,560 
 
 911,390 
 
 227,848 
 
 36,456 
 
 9,114 
 
 2,278 
 
 570 
 
 
 
 
 
 1,000 
 2,000 
 5,000 
 10,000 
 20,000 
 40,000 
 60,000 
 
 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. 
 
1360 
 
 ELECTRICAL ENGINEERING. 
 
 Short-circuiting. — From the law 7 = E/R it is seen that with any pres- 
 sure E, the current 7 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. — Lord Kelvin's rule for the 
 most economical section of conductor for a given voltage is that for which 
 the annual interest on capital outlay is equal to the annual cost of energy 
 wasted. 
 
 Tables have been compiled by Professor Forbes and others in accordance 
 with modifications of this rule. For a given entering horse-power the ques- 
 tion is merely one as to what current density, or how many amperes per 
 square inch of conductor, should be employed. Kelvin's rule gives about 
 393 amperes per square inch, and Professor Forbes's tables give a current 
 density of about 380 amperes per square inch as most economical 
 
 Bell (" Electric Transmission of Power") shows that while Kelvin's rule 
 correctly indicates the condition of minimum cost in transmission for a 
 given current and line, it omits many practical considerations and is inappli- 
 cable to most power transmission work. Each plant has to be considered 
 on its merits and very various conditions are likely to determine the line 
 loss in different cases. Several cases are cited by Bell to show that neither 
 Kelvin's law nor any modification of it is a safe guide in determining the 
 proper allowance for loss of energy in the line. 
 
 Wire Tables. — The tables on this and 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) -*- A ■= Drop in volts. 
 7 = 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 7 and 
 L are combined in the table, in the compound factor " ampere feet." 
 
 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 on next page. 
 
 Table I. — 110-volt and 220-volt Two-wire Circuits. 
 
 Wire 
 
 Sizes; 
 
 Line Loss in Percentage of the Rated Voltage; and Power 
 
 B. & S. Gauge. 
 
 Loss in Percentage of the Delivered Power. 
 
 110 V. 
 
 220 V. 
 
 1 
 
 U/2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 1 8 
 
 10 
 
 
 0000 
 
 21,550 
 
 32,325 
 
 43,100 
 
 64,650 
 
 86,200 
 
 107,750 
 
 129,300 
 
 172,400 
 
 215,500 
 
 
 000 
 
 17,080 
 
 25,620 
 
 34,160 
 
 51,240 
 
 68,320 
 
 85,400 
 
 102,480 
 
 136,640 
 
 170,800 
 
 
 00 
 
 13,550 
 
 20,325 
 
 27,100 
 
 40,650 
 
 54,200 
 
 67,750 
 
 81,300 
 
 108,400 
 
 135,500 
 
 0000 
 
 
 
 10,750 
 
 16,125 
 
 21,500 
 
 32,250 
 
 43,000 
 
 53,750 
 
 64,500 
 
 86,000 
 
 107,500 
 
 000 
 
 1 
 
 8,520 
 
 12,780 
 
 17,040 
 
 25,560 
 
 34,080 
 
 42,600 
 
 51,120 
 
 68,160 
 
 85,200 
 
 00 
 
 2 
 
 6,750 
 
 10,140 
 
 13,520 
 
 20,280 
 
 27,040 
 
 33,800 
 
 40,560 
 
 54,080 
 
 67,600 
 
 
 
 3 
 
 5,360 
 
 8,040 
 
 10,720 
 
 16,080 
 
 21,440 
 
 26,800 
 
 32,160 
 
 42,880 
 
 53,600 
 
 1 
 
 4 
 
 4,250 
 
 6,375 
 
 8,500 
 
 12,750 
 
 17,000 
 
 21,250 
 
 25,500 
 
 34,000 
 
 42,500 
 
 2 
 
 5 
 
 3,370 
 
 5,055 
 
 6,740 
 
 10,110 
 
 13,480 
 
 16,850 
 
 20,220 
 
 26,960 
 
 33,700 
 
 3 
 
 6 
 
 2,670 
 
 4,005 
 
 5,340 
 
 8,010 
 
 10,680 
 
 13,350 
 
 16,020 
 
 21,360 
 
 26,700 
 
 4 
 
 7 
 
 2,120 
 
 3,180 
 
 4,240 
 
 6,360 
 
 8,480 
 
 10,600 
 
 12,720 
 
 16,960 
 
 21,200 
 
 5 
 
 8 
 
 1,680 
 
 2,520 
 
 3,360 
 
 5,040 
 
 6,720 
 
 8,400 
 
 10,800 
 
 13,440 
 
 16,800 
 
 6 
 
 9 
 
 1,330 
 
 1,995 
 
 2,660 
 
 3,990 
 
 5,320 
 
 6,650 
 
 7,980 
 
 10,640 
 
 13,300 
 
 7 
 
 10 
 
 1,055 
 
 1,582 
 
 2,110 
 
 3,165 
 
 4,220 
 
 5,275 
 
 6,330 
 
 8,440 
 
 10,550 
 
 8 
 
 11 
 
 838 
 
 1,257 
 
 1,675 
 
 2,514 
 
 3,350 
 
 4,190 
 
 5,028 
 
 6,700 
 
 8,380 
 
 9 
 
 12 
 
 665 
 
 997 
 
 1,330 
 
 1,995 
 
 2,660 
 
 3,320 
 
 3,990 
 
 5,320 
 
 6,650 
 
 10 
 
 13 
 
 527 
 
 790 
 
 1,054 
 
 1,580 
 
 2,108 
 
 2,635 
 
 3,160 
 
 4,215 
 
 5,270 
 
 11 
 
 .14 
 
 418 
 
 627 
 
 836 
 
 1,254 
 
 1,672 
 
 2,090 
 
 2,508 
 
 3,344 
 
 4,180 
 
 12 
 
 
 332 
 
 498 
 
 665 
 
 997 
 
 1,330 
 
 1,660 
 
 1,995 
 
 2,660 
 
 3,325 
 
 14 
 
 
 209 
 
 313 
 
 418 
 
 627 
 
 836 
 
 1,045 
 
 1,354 
 
 1,672 
 
 2,090 
 
ELECTRIC TRANSMISSION, DIRECT CURRENTS. 1361 
 
 
 Table II. — 500, 1000, and 2000 Volt Circui 
 
 ts. 
 
 
 Wire Sizes; 
 B. & S. Gauge. 
 
 Line Loss in Percentage of the Rated Voltage; and 
 Power Loss in Percentage of the Delivered Power. 
 
 500 V. 
 
 1000 V. 
 
 2000 V. 
 
 1 
 
 M/2 
 
 2 
 
 2V2 
 
 3 
 
 4 
 
 5 
 
 0000 
 000 
 
 00 
 
 1 
 2 
 3 
 
 4 
 5 
 6 
 
 7 
 8 
 
 9 
 10 
 11 
 12 
 
 0000 
 
 000 
 
 00 
 
 
 
 1 
 
 2 
 3 
 4 
 5 
 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 
 
 14 
 
 
 
 4 750 
 
 
 
 
 
 Examples in the Use of the Wire Tables. — 1. Required the maxi- 
 mum load in amperes at 220 volts that can be carried 95 feet by No. 6 
 wire without exceeding \\% drop. 
 
 Find No. 6 in the 220-volt column of Table I; opposite this in the \\% 
 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 circuit 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 dynamo or motor varies with its load and with 
 the size of machine, ranging about as follows for dynamos at full load: 
 
 Kilowatts 30 50 100 200 500 1000 
 
 Efficiency % 90 91 92 93 94 95 
 
 For motors at full load the efficiences run about as follows: 
 
 H.P. 1 2 5 10 20 50 75 100 
 
 Effy. % 75 80 85 88.5 90 91 91.5 91.6 
 
 The efficiency of both generators and motors decreases, at first very 
 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. The following is a rough approximation for 
 direct-current machines: Decrease of efficiency at half-load, 3%; 1/4 load, 
 10% ; Vs load, 20 % ; Vi6 load, 50%. The loss in transmission, due to fall in 
 
1362 
 
 ELECTRICAL ENGINEERING. 
 
 Resistances of Pure Aluminum Wire.* 
 
 Conductivity 62 in the Matthiesen Standard Scale. Pure aluminum weighs 
 167.111 pounds per cubic foot. 
 
 of o 
 
 Resistances at 70° F. 
 
 « 6 
 
 Resistances at 7C 
 
 °F. 
 
 gfc 
 
 
 
 
 'i z 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 !« 
 
 Ohms 
 per 1000 
 Feet. 
 
 Ohms 
 .per 
 Mile. 
 
 Feet 
 per 
 Ohm. 
 
 Ohms per 
 Pound. 
 
 
 Ohms 
 per 1000 
 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 re- 
 sistance of a pure soft copper wire 1 meter long, having a weight of 1 
 gram = 0. 141729 International Ohm at 0° C. 
 
 (From Aluminum for Electrical Conductors; Pittsburgh Reduction Co.) 
 
 electrical pressure or " drop " 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%. 
 
 The methods for long-distance transmission may be divided into three 
 general classes: (1) continuous current; (2) alternating current; and (3) 
 rotary-conventer or " motor-dynamo " systems. There are many factors 
 which govern the selection of a system. For each problem considered 
 there will be found certain fixed and certain unfixed conditions. In 
 general the fixed factors are: (1) capacity of source of power; (2) cost of 
 power at source; (3) cost of power by other means at point of delivery; 
 (4) danger considerations at motors; (5) operating conditions; (6) con- 
 struction conditions (length of line, character of country, etc.). The 
 partly fixed conditions are: (7) power which must be delivered, i.e., the 
 efficiency of the system; (8) size and number of delivery units. The 
 variable conditions are: (9) initial voltage; (10) pounds of copper on line; 
 (11) original cost of all apparatus and construction; (12) expenses, operat- 
 ing (fixed charges, interest, depreciation, taxes, insurance, etc.); (13) 
 liability of trouble and stoppages; (14) danger at station and on line; (15) 
 convenience in operating, making changes, extensions, etc. 
 
ELECTRIC TRANSMISSION. DIRECT CURRENTS. 1363 
 
 Systems of Electrical Distribution in Common Use. 
 
 I. Direct Current. 
 
 A. Constant Potential. 
 
 110 to 125 and 220 to 250 Volts.— Distances less than, say, 
 1500 feet. 
 
 For incandescent lamps. 
 
 For arc-lamps, usually 2 in series. 
 
 For motors of moderate sizes. 
 200 to 250 and 440 Volts, 3-wire. — Distances less than, sav 
 5000 feet. 
 
 For incandescent lamps. 
 
 For arc-lamps, usually 2 in series on each branch. 
 
 For motors 110 or 220 volts, usually 220 volts. 
 500 Volts. — Distances less than, say, 20,000 feet. 
 
 Incidentally for arc-lamps, usually 10 in series. 
 
 For motors, stationary and street-car. 
 
 B. Constant Current. 
 
 Usually 5, 6V2, or 9V2 amperes, the volts increasing to several 
 thousand, as demanded, for series arc-lamps. 
 
 II. Alternating Current. 
 
 A. Constant Potential. 
 
 For incandescent lamps, arc-lamps, and motors. 
 Polyphase Systems. 
 
 For arc and incandescent lamps, motors, and rotary con- 
 verters for giving direct current. 
 Polyphase — 2- and 3-phase — high tension (25,000 volts and 
 
 over), for long-distance transmission; transformed by 
 
 step-up and step-down transformers. 
 
 B. Constant Current. 
 
 Usually 5 to 6.6 amperes. For arc-lamps. 
 The Relative Advantages of Different Systems vary with each par- 
 ticular transmission problem, but in a general way may be tabulated as 
 below: 
 
 
 System. 
 
 Advantages. 
 
 Disadvantages. 
 
 
 ( Low voltage. 
 
 Safety, simplicity. 
 
 Expense for copper. 
 
 3 
 
 
 ( High voltage. 
 
 Economy, simplicity. 
 
 Danger; difficulty of 
 building machines. 
 
 .5 
 
 
 
 8 
 
 3-wire. 
 
 Low voltage on machines 
 and saving in copper. 
 
 Not saving enough in 
 copper for long dis- 
 tances. Necessity for 
 " balanced " system. 
 
 Multiple-wire. 
 
 Low voltage at machines 
 and saving in copper. 
 
 
 Single phase. 
 
 Economy of copper. 
 
 Cannot start under load. 
 Low efficiency. 
 
 a 
 
 Multiphase. 
 
 Economy of copper, syn- 
 chronous speed unnec- 
 essary; applicable to 
 very long distances. 
 
 Requires more than two 
 wires. 
 
 < 
 
 Motor-dynamo. 
 
 High- voltage A.C. trans- 
 mission. Low- voltage 
 D.C. delivery. 
 
 Expensive. 
 Low efficiency. 
 
1364 
 
 ELECTRICAL ENGINEERING 
 
 TABLE OF ELECTRICAL HORSE-POWERS. 
 
 Volts X Amperes _ 
 
 H.P., or 1 volt ampere = .00 13405 H.P. 
 
 
 
 Read amperes at top and volts at side 
 
 or vice versa. 
 
 
 
 
 
 
 
 Volts or Amperes. 
 
 Is 
 
 
 
 
 
 1 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 110 
 
 120 
 
 1 
 
 .00134 
 
 .0134 
 
 .0268 
 
 .0402 
 
 .0536 
 
 .0670 
 
 .0804 
 
 .0938 
 
 .1072 
 
 .1206 
 
 .1341 
 
 .1475 
 
 .1609 
 
 2 
 
 .00268 
 
 .0268 
 
 .0536 
 
 .0804 
 
 .1072 
 
 .1341 
 
 .1609 
 
 .1877 
 
 .2145 
 
 .2413 
 
 .2681 
 
 .2949 
 
 .3217 
 
 3 
 
 .00402 
 
 .0402 
 
 .0804 
 
 .1206 
 
 .1609 
 
 .2011 
 
 .2413 
 
 .2815 
 
 .3217 
 
 .3619 
 
 .4022 
 
 .4424 
 
 .4826 
 
 4 
 
 .00536 
 
 .0536 
 
 .1072 
 
 .1609 
 
 .2145 
 
 .2681 
 
 .3217 
 
 3753 
 
 .4290 
 
 4826 
 
 .5362 
 
 .5898 
 
 .6434 
 
 5 
 
 .00670 
 
 .0670 
 
 .1341 
 
 .2011 
 
 .2681 
 
 .3351 
 
 .4022 
 
 .4692 
 
 .5362 
 
 .6032 
 
 .6703 
 
 .7373 
 
 •8043 
 
 6 
 
 .00804 
 
 .0804 
 
 .1609 
 
 .2413 
 
 .3217 
 
 .4022 
 
 .4826 
 
 .5630 
 
 .6434 
 
 .7239 
 
 .8043 
 
 .8847 
 
 .9652 
 
 7 
 
 .00938 
 
 .0938 
 
 .1877 
 
 .2815 
 
 .3753 
 
 .4692 
 
 .5630 
 
 .6568 
 
 .7507 
 
 .8445 
 
 .9384 
 
 1.032 
 
 1.126 
 
 8 
 
 .01072 
 
 .1072 
 
 .2145 
 
 .3217 
 
 .4290 
 
 .5362 
 
 .6434 
 
 .7507 
 
 .8579 
 
 .9652 
 
 1.072 
 
 1.180 
 
 1 287 
 
 9 
 
 .01206 
 
 .1206 
 
 .2413 
 
 .3619 
 
 .4826 
 
 .6032 
 
 .7239 
 
 .8445 
 
 .9652 
 
 1.086 
 
 1.206 
 
 1.327 
 
 1.448 
 
 10 
 
 .01341 
 
 .1341 
 
 .2681 
 
 .4022 
 
 .5362 
 
 .6703 
 
 .8043 
 
 .9383 
 
 1.072 
 
 1.206 
 
 1.341 
 
 1.475 
 
 1.609 
 
 11 
 
 .01475 
 
 .1475 
 
 .2949 
 
 .4424 
 
 .5898 
 
 .7373 
 
 .8847 
 
 1.032 
 
 1.180 
 
 1.327 
 
 1.475 
 
 1.622 
 
 1.769 
 
 12 
 
 .01609 
 
 .1609 
 
 .3217 
 
 .4826 
 
 .6434 
 
 .8043 
 
 .9652 
 
 1.126 
 
 1.287 
 
 1.448 
 
 1.609 
 
 1.769 
 
 1.930 
 
 13 
 
 .01743 
 
 .1743 
 
 .3485 
 
 .5228 
 
 .6970 
 
 .8713 
 
 1.046 
 
 1.220 
 
 1.394 
 
 1.568 
 
 1.743 
 
 1.917 
 
 2.091 
 
 14 
 
 .01877 
 
 .1877 
 
 .3753 
 
 .5630 
 
 .7507 
 
 .9384 
 
 1.126 
 
 1.314 
 
 1.501 
 
 1.689 
 
 1.877 
 
 2.064 
 
 2.252 
 
 15 
 
 .02011 
 
 .2011 
 
 .4022 
 
 .6032 
 
 .8043 
 
 1.005 
 
 1.206 
 
 1.408 
 
 1.609 
 
 1.810 
 
 2.011 
 
 2.212 
 
 2.413 
 
 16 
 
 .02145 
 
 .2145 
 
 .4290 
 
 .6434 
 
 .8579 
 
 1.072 
 
 1.287 
 
 1.501 
 
 1.716 
 
 1.930 
 
 2.145 
 
 2.359 
 
 2.574 
 
 17 
 
 .02279 
 
 .2279 
 
 .4558 
 
 .6837 
 
 .9115 
 
 1.139 
 
 1.367 
 
 1.595 
 
 1.823 
 
 2.051 
 
 2.279 
 
 2.507 
 
 2.735 
 
 18 
 
 .02413 
 
 .2413 
 
 .4826 
 
 .7239 
 
 .9652 
 
 1.206 
 
 1.448 
 
 1.689 
 
 1.930 
 
 2.172 
 
 2.413 
 
 2.654 
 
 2.895 
 
 19 
 
 .02547 
 
 .2547 
 
 .5094 
 
 .7641 
 
 1.019 
 
 1.273 
 
 1.528 
 
 1.783 
 
 2.037 
 
 ::".■: 
 
 2.547 
 
 2.801 
 
 3.056 
 
 20 
 
 .02681 
 
 .2681 
 
 .5362 
 
 .8043 
 
 1.072 
 
 1.340 
 
 1.609 
 
 1.877 
 
 2.145 
 
 2.413 
 
 2.681 
 
 2.949 
 
 3.217 
 
 21 
 
 .02815 
 
 .2815 
 
 .5630 
 
 .8445 
 
 1.126 
 
 1.408 
 
 1.689 
 
 1.971 
 
 2.252 
 
 2.533 
 
 2.815 
 
 3.097 
 
 3.378 
 
 22 
 
 .02949 
 
 .2949 
 
 .5898 
 
 .8847 
 
 1.180 
 
 1.475 
 
 1.769 
 
 2.064 
 
 2.359 
 
 2.654 
 
 2.949 
 
 3.244 
 
 3.539 
 
 23 
 
 .03083 
 
 .3083 
 
 .6166 
 
 .9249 
 
 1.233 
 
 1.542 
 
 1.850 
 
 2.158 
 
 2.467 
 
 2.775 
 
 3.083 
 
 3.391 
 
 3.700 
 
 24 
 
 .03217 
 
 .3217 
 
 .6434 
 
 .9652 
 
 1.287 
 
 1.609 
 
 1.930 
 
 : !.)■■ 
 
 2.574 
 
 2.895 
 
 3.217 
 
 3.539 
 
 3.861 
 
 25 
 
 .03351 
 
 .3351 
 
 .6703 
 
 1.005 
 
 1.341 
 
 1.676 
 
 2.011 
 
 2.346 
 
 2.681 
 
 3.016 
 
 3.351 
 
 3.686 
 
 4.022 
 
 26 
 
 .03485 
 
 .3485 
 
 .6971 
 
 1.046 
 
 1.394 
 
 1.743 
 
 2.091 
 
 2.440 
 
 2.788 
 
 3.137 
 
 3.485 
 
 3.834 
 
 4.182 
 
 27 
 
 .03619 
 
 .3619 
 
 .7239 
 
 1.086 
 
 1.448 
 
 1.810 
 
 2.172 
 
 2.534 
 
 2.895 
 
 3.257 
 
 3.619 
 
 3.981 
 
 4.343 
 
 28 
 
 .03753 
 
 .3753 
 
 .7507 
 
 1.126 
 
 1.501 
 
 1.877 
 
 2.252 
 
 2.627 
 
 3.003 
 
 3.378 
 
 3.753 
 
 4.129 
 
 4.504 
 
 29 
 
 .03887 
 
 .3887 
 
 .7775 
 
 1.166 
 
 1.555 
 
 1.944 
 
 2.332 
 
 2.721 
 
 3.110 
 
 3.499 
 
 3.887 
 
 4.276 
 
 4.665 
 
 30 
 
 .04022 
 
 .4022 
 
 .8043 
 
 1.206 
 
 1.609 
 
 2.011 
 
 2.413 
 
 2.815 
 
 3.217 
 
 3.619 
 
 4.022 
 
 4.424 
 
 4.826 
 
 31 
 
 .04156 
 
 .4156 
 
 .8311 
 
 1.247 
 
 1.662 
 
 2.078 
 
 2.493 
 
 2.909 
 
 3.324 
 
 3.740 
 
 4.156 
 
 4.571 
 
 4.987 
 
 32 
 
 .04290 
 
 .4290 
 
 .8579 
 
 1.287 
 
 1.716 
 
 2.145 
 
 2.574 
 
 3.003 
 
 3.432 
 
 3.861 
 
 4.290 
 
 4.719 
 
 5.148 
 
 33 
 
 .04424 
 
 .4424 
 
 .8847 
 
 1.327 
 
 1.769 
 
 2.212 
 
 2.654 
 
 3.097 
 
 3.539 
 
 3.986 
 
 4.424 
 
 4.866 
 
 5.308 
 
 34 
 
 .04558 
 
 .4558 
 
 .9115 
 
 1.367 
 
 1.823 
 
 2.279 
 
 2.735 
 
 3.190 
 
 3.646 
 
 4.102 
 
 4.558 
 
 5.013 
 
 5.469 
 
 35 
 
 .04692 
 
 .4692 
 
 .9384 
 
 1.408 
 
 1.877 
 
 2.346 
 
 2.815 
 
 3.284 
 
 3.753 
 
 : ■; 
 
 4.692 
 
 5.161 
 
 5.630 
 
 40 
 
 .05362 
 
 .5362 
 
 1.072 
 
 1.609 
 
 2.145 
 
 2.681 
 
 3.217 
 
 3.753 
 
 4 290 
 
 4.826 
 
 
 5.898 
 
 6.434 
 
 45 
 
 .06032 
 
 .6032 
 
 1.206 
 
 1.810 
 
 2.413 
 
 3.016 
 
 3.619 
 
 4.223 
 
 4.826 
 
 5.439 
 
 6.032 
 
 6.635 
 
 7.239 
 
 50 
 
 .06703 
 
 .6703 
 
 1.341 
 
 2.011 
 
 2.681 
 
 3.351 
 
 4.022 
 
 
 5.362 
 
 6.032 
 
 6.703 
 
 7.373 
 
 8.043 
 
 55 
 
 .07373 
 
 .7373 
 
 1.475 
 
 2.212 
 
 2.949 
 
 3.686 
 
 4.424 
 
 5.161 
 
 
 6.635 
 
 7.373 
 
 8.110 
 
 8.847 
 
 60 
 
 .08043 
 
 .8043 
 
 1.609 
 
 2.413 
 
 3.217 
 
 4.022 
 
 4.826 
 
 5.630 
 
 6^434 
 
 7.239 
 
 8.043 
 
 8.047 
 
 9.652 
 
 65 
 
 .08713 
 
 .8713 
 
 1.743 
 
 2.614 
 
 3.485 
 
 4.357 
 
 5.228 
 
 6.099 
 
 6.970 
 
 7.842 
 
 8.713 
 
 9.584 
 
 10.46 
 
 70 
 
 .09384 
 
 .9384 
 
 1.877 
 
 2.815 
 
 3.753 
 
 4.692 
 
 5.630 
 
 6.568 
 
 7.507 
 
 8.445 
 
 9.384 
 
 10.32 
 
 11.26 
 
 75 
 
 .10054 
 
 1.005 
 
 2.011 
 
 3.016 
 
 4.021 
 
 5.027 
 
 6.032 
 
 7.037 
 
 8.043 
 
 9.048 
 
 10.05 
 
 11.06 
 
 12.06 
 
 80 
 
 .10724 
 
 1.072 
 
 2.145 
 
 3.217 
 
 4.290 
 
 5.362 
 
 6.434 
 
 7.507 
 
 8- 579 
 
 9.652 
 
 10.72 
 
 11.80 
 
 12.87 
 
 85 
 
 .11394 
 
 1.139 
 
 2.279 
 
 3.418 
 
 4.558 
 
 5.697 
 
 6.836 
 
 7.976 
 
 9.115 
 
 10.26 
 
 11.39 
 
 12.53 
 
 13.67 
 
 90 
 
 .12065 
 
 1.206 
 
 2.413 
 
 3.619 
 
 4.826 
 
 6.032 
 
 7.239 
 
 8.445 
 
 9.652 
 
 10.86 
 
 12.06 
 
 13.27 
 
 14.48 
 
 95 
 
 .12735 
 
 1.273 
 
 2.547 
 
 3.820 
 
 5.094 
 
 6.367 
 
 7.641 
 
 8.914 
 
 10.18 
 
 11.46 
 
 12.73 
 
 14.01 
 
 15.28 
 
 100 
 
 .13405 
 
 1.341 
 
 2.681 
 
 4.022 
 
 5.362 
 
 6.703 
 
 8.043 
 
 9.384 
 
 10.72 
 
 12.06 
 
 13.41 
 
 14.75 
 
 16.09 
 
 200 
 
 .26810 
 
 2.681 
 
 5.362 
 
 8.043 
 
 10.72 
 
 13.41 
 
 16.09 
 
 18.77 
 
 21.45 
 
 24.13 
 
 26.81 
 
 29.49 
 
 32.17 
 
 300 
 
 .40215 
 
 4.022 
 
 8.043 
 
 12.06 
 
 16.09 
 
 20.11 
 
 21.13 
 
 28.15 
 
 32.17 
 
 36.19 
 
 40.22 
 
 44.24 
 
 48.26 
 
 400 
 
 .53620 
 
 5.362 
 
 10.72 
 
 16.09 
 
 21.45 
 
 26.81 
 
 32.17 
 
 37.53 
 
 42.90 
 
 48.26 
 
 53.62 
 
 58.98 
 
 64.34 
 
 500 
 
 .67025 
 
 6.703 
 
 13.41 
 
 20.11 
 
 26.81 
 
 33.51 
 
 40.22 
 
 46.92 
 
 53.62 
 
 60.32 
 
 67.03 
 
 73.73 
 
 80.43 
 
 600 
 
 .80430 
 
 8.043 
 
 16.09 
 
 24.13 
 
 32.17 
 
 40.22 
 
 48.26 
 
 56.30 
 
 64.34 
 
 72.39 
 
 80.43 
 
 88.47 
 
 96.52 
 
 700 
 
 .93835 
 
 9.384 
 
 18.77 
 
 28.15 
 
 37.53 
 
 46.92 
 
 56.30 
 
 65.68 
 
 75.07 
 
 84.45 
 
 93.84 
 
 103.2 
 
 112.6 
 
 800 
 
 1.0724 
 
 10.72 
 
 21.45 
 
 32.17 
 
 42.90 
 
 53.62 
 
 64.34 
 
 75.07 
 
 85.79 
 
 96.52 
 
 107.2 
 
 118.0 
 
 128.7 
 
 900 
 
 1.2065 
 
 12.06 
 
 24.13 
 
 36.19 
 
 48.26 
 
 60.32 
 
 72.39 
 
 84.45 
 
 96.52 
 
 108.6 
 
 120.6 
 
 132.7 
 
 144.8 
 
 1.000 
 
 1.3405 
 
 13.41 
 
 26.81 
 
 40.22 
 
 53.62 
 
 67.03 
 
 80.43 
 
 93.84 
 
 107.2 
 
 120.6 
 
 134.1 
 
 147.5 
 
 160.9 
 
 2,000 
 
 2.6810 
 
 26.81 
 
 53.62 
 
 80.43 
 
 107.2 
 
 134.1 
 
 160.9 
 
 187.7 
 
 214.5 
 
 241.3 
 
 268.1 
 
 294.9 
 
 321.7 
 
 3,000 
 
 4.0215 
 
 40.22 
 
 80.43 
 
 120.6 
 
 160.9 
 
 201.1 
 
 241.3 
 
 281.5 
 
 321.7 
 
 361.-9- 
 
 402.2 
 
 442.4 
 
 482.6 
 
 4,000 
 
 5.3620 
 
 53.62 
 
 107.2 
 
 160.9 
 
 214.5 
 
 268.1 
 
 321.7 
 
 375.3 
 
 429.0 
 
 482.6, 
 
 536.2 
 
 589.8 
 
 643.4 
 
 5,000 
 
 6.7025 
 
 67.03 
 
 134.1 
 
 201.1 
 
 268 1 
 
 335 1 
 
 402.2 
 
 469.2 
 
 536.2 
 
 603.2 
 
 670.3 
 
 737.3 
 
 804.2 
 
 6,000 
 
 8.0430 
 
 80.43 
 
 160.9 
 
 241.3 
 
 321.7 
 
 402.2 
 
 482.6 
 
 563.0 
 
 643.4 
 
 723.9 
 
 804.3 
 
 884.7 
 
 965.2 
 
 7,000 
 
 9.3835 
 
 93.84 
 
 187.7 
 
 281.5 
 
 375.3 
 
 469.2 
 
 5(i3.0 
 
 656.8 
 
 750.7 
 
 844.5 
 
 938.4 
 
 1032 
 
 1126 
 
 8.000 10.724 
 
 107.2 
 
 214.5 
 
 321.7 
 
 429.0 
 
 536.2 
 
 613.4 
 
 750.7 
 
 857.9 
 
 1IH5.2 
 
 1072 
 
 1180 
 
 1287 
 
 9,000 12.065 
 
 120.6 
 
 241.3 
 
 361.9 
 
 482.6 
 
 603.2 
 
 723.9 
 
 844.5 
 
 965.2 
 
 1086 
 
 1206 
 
 1327 
 
 1448 
 
 10,000 13.405 
 
 134.1 
 
 268.1 
 
 402.2 
 
 536.2 
 
 670.3 
 
 804.3 
 
 938.3 
 
 1072 
 
 1206 
 
 1341 
 
 1475 
 
 1609 
 
ELECTRIC TRANSMISSION, DIRECT CURRENTS. 1365 
 
 Cost of Copper for Long-distance Transmission. 
 
 (Westinghouse El. and Mfg. Co.) 
 
 Cost of Copper Required for the Delivery of One Mechanical 
 horse-power at motor shaft with various voltages at motor 
 Terminals, or at Terminals of Lowering Transformers. 
 Loss of energy in conductors (drop) equals 20%. Motor efficiency, 90%. 
 Length of conductor per mile of single distance, 11,000 ft., to allow for 
 sag. Cost of copper taken at 16 cents per pound. 
 
 Miles. 
 
 1000 v. 
 
 2000 v. 
 
 3000 v. 
 
 4000 v. 
 
 5000 v. 
 
 10,000 v. 
 
 1 
 
 $2.08 
 
 $0.52 
 
 $ 0.23 
 
 $0.13 
 
 $0.08 
 
 $0.<52 
 
 2 
 
 8.33 
 
 2.08 
 
 0.93 
 
 0.52 
 
 0.33 
 
 0.08 
 
 3 
 
 18.70 
 
 4.68 
 
 2.08 
 
 1.17 
 
 0.75 
 
 0.19 
 
 4 
 
 33.30 
 
 8.32 
 
 3.70 
 
 2.08 
 
 1.33 
 
 0.33 
 
 5 
 
 52.05 
 
 13.00 
 
 5.78 
 
 3.25 
 
 2.08 
 
 52 
 
 6 
 
 74.90 
 
 18.70 
 
 8.32 
 
 4.68 
 
 3.00 
 
 0.75 
 
 7 
 
 102.00 
 
 25.50 
 
 11.30 
 
 6.37 
 
 4.08 
 
 1 02 
 
 8 
 
 133.25 
 
 33.30 
 
 14.80 
 
 8.32 
 
 5.33 
 
 1.33 
 
 9 
 
 168.60 
 
 42.20 
 
 18.75 
 
 10.50 
 
 6.74 
 
 1.69 
 
 10 
 
 208.19 
 
 52.05 
 
 23.14 
 
 13.01 
 
 8.33 
 
 2.08 
 
 11 
 
 251 .90 
 
 63.00 
 
 28.00 
 
 15.75 
 
 10.08 
 
 2.52 
 
 12 
 
 299.80 
 
 75.00 
 
 33.30 
 
 18.70 
 
 12.00 
 
 3.00 
 
 13 
 
 352.00 
 
 88.00 
 
 39.00 
 
 22.00 
 
 14.08 
 
 3.52 
 
 14 
 
 408.00 
 
 102.00 
 
 45.30 
 
 25.50 
 
 16.32 
 
 4.08 
 
 15 
 
 468.00 
 
 117.00 
 
 52.00 
 
 29.25 
 
 18.72 
 
 4.68 
 
 16 
 
 533.00 
 
 133.00 
 
 59.00 
 
 33.30 
 
 21.32 
 
 5.33 
 
 17 
 
 600.00 
 
 150.00 
 
 67.00 
 
 37.60 
 
 24.00 
 
 6.00 
 
 18 
 
 675.00 
 
 169.00 
 
 75.00 
 
 42.20 
 
 27.00 
 
 6.75 
 
 19 
 
 750.00 
 
 188.00 
 
 83.50 
 
 47.00 
 
 30.00 
 
 7.50 
 
 20 
 
 833.00 
 
 208.00 
 
 92.60 
 
 52.00 
 
 33.32 
 
 8.33 
 
 Cost of Copper required to deliver One Mechanical Horse-power 
 at Motor-shaft with varying Percentages of Loss in Conductors, 
 upon the assumption that the potential at motor terminals is 
 in Each Case 3000 Volts. 
 
 Motor efficiency, 90%. Cost of copper equals 16 cents per pound. 
 Length of conductor per mile of single distance, 11,000 ft. 
 
 Miles. 
 
 10% 
 
 15% 
 
 20% 
 
 25% 
 
 30% 
 
 1 
 
 $0.52 
 
 $0.33 
 
 $0.23 
 
 $0.17 
 
 $0.13 
 
 2 
 
 2.08 
 
 1.31 
 
 0.93 
 
 0.69 
 
 0.54 
 
 3 
 
 4.68 
 
 2.95 
 
 2.08 
 
 1.55 
 
 1.21 
 
 4 
 
 8.32 
 
 5.25 
 
 3.70 
 
 2.77 
 
 2.15 
 
 5 
 
 13.00 
 
 8.20 
 
 5.78 
 
 4.33 
 
 3.37 
 
 6 
 
 18.70 
 
 11.75 
 
 8.32 
 
 6.23 
 
 4.85 
 
 7 
 
 25.50 
 
 16.00 
 
 11.30 
 
 8.45 
 
 6.60 
 
 8 
 
 33.30 
 
 21.00 
 
 14.80 
 
 11.00 
 
 8.60 
 
 9 
 
 42.20 
 
 26.60 
 
 18.75 
 
 14.00 
 
 10.90 
 
 10 
 
 52.05 
 
 32.78 
 
 23.14 
 
 17.31 
 
 13.50 
 
 11 
 
 63.00 
 
 39.75 
 
 28.00 
 
 21.00 
 
 16.30 
 
 12 
 
 75.00 
 
 47.20 
 
 33.30 
 
 24.90 
 
 19.40 
 
 13 
 
 88.00 
 
 55.30 
 
 39.00 
 
 29.20 
 
 22.80 
 
 14 
 
 102.00 
 
 64.20 
 
 45.30 
 
 33.90 
 
 26.40 
 
 15 
 
 117.00 
 
 73.75 
 
 52.00 
 
 38.90 
 
 30.30 
 
 16 
 
 133.00 
 
 83.80 
 
 59.00 
 
 44.30 
 
 34.50 
 
 17 
 
 150.00 
 
 94.75 
 
 67.00 
 
 50.00 
 
 39.00 
 
 18 
 
 169.00 
 
 106.00 
 
 75.00 
 
 56.20 
 
 43.80 
 
 19 
 
 188.00 
 
 118.00 
 
 83.50 
 
 62.50 
 
 48.70 
 
 20 
 
 208.00 
 
 131.00 
 
 92.60 
 
 69.25 
 
 54.00 
 
1366 ELECTRICAL ENGINEERING. 
 
 ELECTRIC RAILWAYS. 
 
 Space will not admit of a proper treatment of this subject in this work. 
 Consult Crosby and Bell, The Electric Railway in Theory and Practice; 
 Fairchild, Street Railways; Merrill, Reference Book of Tables and Formulae 
 for Street Railway Engineers; Bell, Electric Transmission of Power; 
 Dawson, Engineering and Electric Traction Pocket-book; The Standard 
 Handbook for Electrical Engineers; and Foster's Electrical Engineers' 
 Pocket-book. The last named devotes 240 pages to the subject of electric 
 railways. 
 
 Electric Railway Cars and Motors. (Foster.) — Small cars weighing 
 10 to 12 tons may be fitted with two 35-H.P. motors and be geared for a 
 maximum speed of 25 to 30 miles per hour. Larger cars of the single- 
 truck variety weighing close to 15 tons may be equipped with 40-H.P. 
 motors. Suburban cars weighing 18 to 25 tons and measuring 45 ft. over 
 all may be equipped with four 50-H.P. motors and be geared for a maxi- 
 mum speed of 40 m.p.h. Larger types of suburban cars, 50 ft. over all, 
 seating 52 passengers, weigh 28 to 30 tons and are equipped with four 
 75-H.P. motors geared for a maximum speed of 45 m.p.h. The largest 
 type of suburban car is equipped with four 125-H.P. motors, and is geared 
 for a maximum speed of 60 m.p.h. 
 
 Grades upon city lines may run as high as 13 per cent, and to surmount 
 these it is necessary to have every axle on the car equipped with motors; 
 thus single-truck cars require two, and double-truck cars four motors; 
 and even then the cars will be unable to surmount these grades with very 
 bad conditions of track. The motor capacity per car should be liberal, 
 not so much from the danger of overheating the motors as to prevent 
 undue sparking when surmounting the heavy grades. 
 
 A 4000-H.P. Electric Locomotive, built by the Westinghouse El. 
 & Mfg. Co., for the New York terminal and tunnel of the Penna. R.R., is 
 described in Eng'g News, Nov. 11, 1909. 
 
 In wheel arrangement, weight distribution, and general character of 
 the running gear it is the practical equivalent of two American-type steam 
 locomotives coupled back to back. The motors are mounted upon the 
 frame and are side-connected through jack shafts to driving wheels by a 
 system of cranks and parallel connecting rods. The connecting rods are 
 all rotating links between rotating elements, and thus can be perfectly 
 counterbalanced for all speeds. The center of gravity is approximately 
 72 ins. above the rails. 
 
 In these electric locomotives the variable pressure of the unbalanced 
 piston of the steam locomotive is replaced by the more constant torque 
 and more constant rotating effort of the drive wheels, so that the pull 
 upon the drawbar is thereby constant and uniform. The engine will 
 start a train of 550 tons trailing load upon grades of approximately 2%. 
 A tractive effort of 60,000 lbs., and a normal speed of 60 miles per hour, 
 with full train load on a level track, are guaranteed. 
 
 The total weight of the locomotive is 332,100 lbs., of which 208,000 lbs. 
 is on the eight drivers. The locomotive is claimed to develop 4000 H.P. 
 for short times, say 20 minutes, without abnormal temperature rise. Each 
 half of the locomotive carries a single motor, four 68-in. drive wheels and 
 one four-wheel, swing-bolster, swivel truck, with 36-in. wheels. Each 
 section has its own steel cab, the two cabs being connected by a vestibule. 
 
 The rigid wheel-bases are 7 ft. 2 in. and the total wheel-base of each 
 half is 23 ft. The motive power consists of two motors of a 600-volt, 
 2000-H.P., commutating-pole type. Each motor weighs complete with- 
 out its crank, 42,000 lbs. The main-field winding is in two sections, both 
 of which are used together at low-speed operation. At high speeds only 
 one-half is needed, and at intermediate control points one is shunted with 
 resistance. These field positions are available for all series and parallel 
 groupings of the motors, so that eight running positions (or speeds) are 
 possible. Bridging connections are used in passing from series to parallel 
 groupings of the motors, so that the main circuits are not opened in the 
 process. 
 
ELECTRIC LIGHTING — ILLUMINATION. 1367 
 
 ELECTRIC LIGHTING. — ILLUMINATION. 
 
 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 candle-foot. Since the 
 illumination varies inversely as the square of the distance, one candle- 
 foot 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, cr 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. 
 
 Luminosity, brightness of surface; flux emitted per unit area of surface. 
 
 Candle-power, the unit of luminous intensity. A spermaceti candle 
 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 dis- 
 placed 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 con- 
 structed 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=l Ameri- 
 can Candle = 1.11 Hefners = 0.1 04 Carcel unit. 1 Hefner = 0.90 Inter- 
 national 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 -4-4*, 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 dimen- 
 sion 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 
 
 If E = the illumination at any point in a surface, / the intensity of light 
 coming from a source, 9 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 h- V*. 
 
 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 respec- 
 tively 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 
 
1368 
 
 ELECTRICAL ENGINEERING. 
 
 arc (red 100), 130, 190. Moore carbon dioxide tube, 120, 520. Wels- 
 bach mantle, 3/ 4 % cerium, 81, 28. Do., 1 1/4% cerium, 69, 14.5. Do., 1 3/ 4 % 
 cerium, 63, 12.3. Tungsten lamp, 1.25 watts per mean horizontal 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 follow- 
 ing summary of the principles of effective vision: 
 
 1. The eye works with approximately normal efficiency upon surfaces 
 possessing an effective luminosity of one lumen per square foot 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 reduced 
 by a diffusing medium when the rays enter the eye at an angle below 60° 
 with the horizontal. 
 
 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. 
 
 Arc Lamps are divided into three classes: 1. Those which produce 
 light by the incandescence of intensely hot refractory electrodes. 2. 
 Those which produce light mainly from the luminescence in the arc of 
 mineral salts vaporized from carbon electrodes. 3. Those which produce 
 light by the luminescence of metallic vapor derived solely from the cathode, 
 the anode being unconsumed. 
 
 The Carbon Arc. — In direct-current open arcs the anodes are consumed 
 at the rate of 1 to 2 inches per hour, and the cathodes, or negatives, at 
 half this rate. In alternating-current open arcs the consumption is equal 
 in both carbons, 1 to 1.5 inches per hour. Enclosed arcs have longer life 
 owing to the restricted oxidation of the carbons, but they are of reduced 
 brilliancy and lower efficiency. Carbons of the ordinary sizes burn Vie 
 to 1/8 in. per hour, giving a life of 100 to 150 hours for direct-current and 
 80 to 100 hours for alternating-current lamps. The enclosing globes 
 absorb from 8 to 40% of the light. 
 
 The Flaming Arc. — The carbons are impregnated with calcium fluoride 
 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, Fe 3 4 , and titanium and chromium oxides. The 
 anode consists of copper or brass. It is well adapted to series operation 
 with low currents. The 4-ampere lamp, using 80 volts per lamp, is highly 
 successful for street illumination. 
 
 Illumination by Arc Lamps at Different Distances. — Several 
 diagrams 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. 
 
 Horizontal Distance from Lamp, Feet. 
 
 20 1 30 1 40 I 50 | 100 1 150 1 200 1 250 
 
 Kind of Lamp. 
 
 Foot-candles, normal illumi- 
 nation. 
 
 A. Open carbon arc, D.C., 6.6 amps. 
 
 B. Enclosed carbon arc, A.C. 6.6 " 
 
 0J0 
 
 0.40 
 .19 
 
 0.29 
 .135 
 
 0.20 
 .10 
 
 1. 10 
 .65 
 .51 
 .21 
 
 .032 
 
 .027 
 
 .31 
 
 .15 
 
 .15 
 
 .07 
 
 .014 
 .013 
 .14 
 .055 
 .075 
 .035 
 
 .006 
 .006 
 .08 
 .03 
 .045 
 .022 
 
 .002 
 .002 
 05 
 
 
 
 
 .85 
 .69 
 .30 
 
 n? 
 
 E. Magnetite arc, 6.6 " 
 
 F. Magnetite arc, 4. " 
 
 ".Al 
 
 1.00 
 .40 
 
 .025 
 .018 
 
ELECTRIC LIGHTING — ILLUMINATION. 
 
 13G9 
 
 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, 1520M.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.G. 6 amp., D.C.series magnetite arc, 79 volts, 510 watts, 1450 M.L.H.C.-P. 
 75 to 100 hours per trim. 
 
 F. 4 amp., D.C. series magnetite arc, 80 volts, 320 watts, 575 M.L.H.C.-P., 
 150 to 200 hours per trim. 
 
 Data of Some Arc Lamps. 
 
 Type of Lamp. 
 
 D.C. series carbon, open 
 
 D.C. series carbon, enclosed. 
 
 A.C. series carbon, enclosed. 
 
 D.C. multiple carbon, en- 
 closed 
 
 A.C. multiple carbon, en- 
 closed 
 
 D.C. flame arcs, open 
 
 Regenerative, semi-enclosed 
 
 A.C. flame arcs, open 
 
 Magnetite, open 
 
 Hours 
 
 per 
 Trim. 
 
 Am- 
 peres. 
 
 Ter- 
 minal 
 Volts. 
 
 Ter- 
 minal 
 Watts. 
 
 9 to 12 
 100 to 150 
 70 to 100 
 
 9.6 
 6.6 
 7.5 
 
 50 
 72 
 75 
 
 480 
 475 
 480 
 
 100 to 150 
 
 5.0 
 
 110 
 
 550 
 
 70 to 100 
 10 to 16 
 
 70 
 10 to 16 
 70 to 100 
 
 6.0 
 10 
 
 5 
 10 
 
 6.6 
 
 110 
 55 
 70 
 55 
 80 
 
 430 
 440 
 350 
 
 467 
 528 
 
 2.25 
 
 2.40 
 0.45 
 0.26 
 0.55 
 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. 
 
 Watts per Square Foot Required for Arc Lighting. — W. D'A. 
 
 Ryan {Am. Elect' n, Feb., 1903) gives the following table, deduced from 
 experience, showing the amount of energy required for good illumination 
 by means of enclosed arcs, based on watts at lamp terminals. 
 
 Building. 
 
 Machine-shops; high roofs, electrically driven machinery, no 
 
 belts 
 
 Machine-shops; low roofs, belts and other obstructions 
 
 Hardware and shoe stores 
 
 Department stores; light material, bric-a-brac, etc 
 
 Department stores ; colored material 
 
 Mill lighting; plain white goods 
 
 Mill lighting; colored goods, high looms 
 
 General office; no incandescents 
 
 Drafting rooms 
 
 Watts per 
 sq. ft. 
 
 0.5 to 1 
 0.75 to 1.25 
 0.5 to 1 
 0.75 to 1.25 
 1 to 1.5 
 0.9 to 1.3 
 1.1 to 1.5 
 1.25 to 1.75 
 1.5 to 2 
 
 The space in sq. yds. properly illuminated by 450-watt enclosed arc 
 lamps is given as follows in the Int. Library of Technology, vol. 13: Out- 
 door areas, 2000-2500 sq. yds.; trainsheds, 1400-1600; foundries (general 
 illumination), 600-800; machine-shops, 200-250; thread and cloth mills, 
 200-230. 
 
 The Mercury Vapor Lamp, invented by Peter Cooper Hewitt, is an 
 arc of luminous mercury vapor contained 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 electric connection with the wires, and a current is passed 
 through it, part of the mercury is vaporized, and on the tube being in- 
 clined so that the liquid mercury remains at one end, an electric arc is 
 
 * M. H. C.-P. = mean horizontal candle-power; M.L.H.C.-P. =mean lower 
 hemispherical candle-power, 
 
1370 
 
 ELECTRICAL ENGINEERING. 
 
 formed in the vapor throughout the tube. The tubes are made about 
 1 in. in diameter and of different lengths, as below. The mercury vapor 
 lamp is very efficient, but the color of the light is unsatisfactory, being 
 deficient in red rays. The spectrum consists of three bands, of yellow, 
 green and violet, respectively. The intrinsic brilliancy of the lamp is 
 very moderate, about 17 candle-power per square inch. Commercial 
 lamps are made of the sizes given below. The lamp is essentially a direct- 
 current lamp, but it may be adapted to alternating-current by use of the 
 principle of the mercury arc rectifier. The tubes have a life ordinarily 
 of about 1000 hours. 
 
 Mercury Arc Lamps. 
 
 Type. 
 
 Kind of 
 Circuit. 
 
 Length, 
 inches. 
 
 Volts. 
 
 Am- 
 peres. 
 
 Watts. 
 
 Hemi- 
 spher. 
 Candle- 
 power. 
 
 Watts 
 
 per 
 Candle 
 
 H 
 K 
 U 
 P 
 F 
 
 d.c. 
 d.c. 
 d.c. 
 d.c. 
 a.c. 
 
 203/4 
 
 45 
 
 78 
 
 50 
 
 50 
 
 52-55 
 100-120 
 206-240 
 100-120 
 100-120 
 
 3.5 
 3.5 
 2.0 
 3.5 
 
 177-193 
 350-420 
 412-480 
 350-420 
 400-520 
 
 300 
 700 
 900 
 800 
 750-900 
 
 0.64 
 0.55 
 0.48 
 0.48 
 0.53-0.58 
 
 
 
 
 Incandescent Lamps. — Candle-power of nominal 16-c.p. 110-volt 
 carbon lamp: 
 
 Mean horizontal 15.7 to 16.6, mean spherical 12.7 to 13.8, mean hemi- 
 spherical 14.0 to 14.6, mean within 30° from tip 7.9 to 10.9. 
 
 Ordinary carbon lamps take from 3 to 4 watts per candle-power. A 16- 
 candle-power lamp using 3.5 watts per candle-power or 56 watts at 110 
 volts takes a current of 56-^110 = 0.51 ampere. For a given efficiency 
 or watts per candle-power the current and the power increase directly as 
 the candle-power. An ordinary lamp taking 56 watts, 13 lamps take 1 
 H.P. of electrical energy, or 18 lamps 1.008 kilowatts. 
 
 Rating of Incandescent Lamps. — Lamps are commonly rated in 
 terms of their mean horizontal candle-power, and their energy consump- 
 tion in terms of watts per mean horizontal candle-power. The mean 
 spherical intensity differs from the horizontal intensity by a factor which 
 varies with different kinds and styles of lamp. In carbon lamps it is 
 usually about 82%, and in tantalum and tungsten lamps about 76 to 78% 
 of the mean horizontal candle-power. 
 
 The new lamp ratings (May, 1910) of the National Electric Lamp 
 Association^ designate all lamps by wattage instead of by candle-power 
 as formerly. 
 
 Lamps are labeled with a three-voltage label and the regular type of 
 16 c.-p. carbon lamp, in general use, will be made on the basis of 3.1 watts 
 per c.-p. at top voltage. 
 
 Carbon Lamps. 
 
 Nom- 
 inal 
 Watts. 
 
 Actual 
 
 Watts. 
 
 Actual 
 Watts 
 
 per 
 Candle. 
 
 Actual 
 Candle- 
 power. 
 
 3<2 
 
 a3 
 
 Nom- 
 inal 
 Watts 
 
 Actual 
 Watts. 
 
 Actual 
 Watts 
 
 per 
 Candle. 
 
 Actual 
 Candle- 
 power. 
 
 3 '* 
 
 10 
 
 
 10 
 
 5.00 
 
 2.0 
 
 2000 
 
 ( 
 
 T. 60.0 
 
 2.97 
 
 20.2 
 
 700 
 
 20 
 
 
 20 
 
 4.15 
 
 4.8 
 
 2000 
 
 60 1 
 
 M. 57.9 
 
 3.18 
 
 18.3 
 
 1000 
 
 ( 
 
 T 
 
 25 
 
 3.10 
 
 8.1 
 
 500 
 
 1 
 
 B. 55.7 
 
 3.39 
 
 16.4 
 
 1500 
 
 25 
 
 M. 
 
 24.1 
 
 3.31 
 
 7.3 
 
 725 
 
 ( 
 
 T. 100.0 
 
 2.97 
 
 33.6 
 
 600 
 
 ( 
 
 R 
 
 ?3 2 
 
 3.52 
 
 6.6 
 
 1050 
 
 100 \ 
 
 M. 96.4 
 
 3.18 
 
 30.5 
 
 850 
 
 ( 
 
 T 
 
 30 
 
 3.23 
 
 9.3 
 
 1050 
 
 1 
 
 B. 92.9 
 
 3.39 
 
 27.4 
 
 1350 
 
 30 
 
 
 28 9 
 
 3.46 
 
 8.4 
 
 1500 
 
 ( 
 
 T. 120.0 
 
 2.97 
 
 40.4 
 
 600 
 
 ( 
 
 R 
 
 7.7 8 
 
 3.69 
 
 7.5 
 
 2100 
 
 120 \ 
 
 M. 115.8 
 
 3.18 
 
 36.6 
 
 850 
 
 ( 
 
 T 
 
 50 
 
 2.97 
 
 16.8 
 
 700 
 
 ) 
 
 B. 111.4 
 
 3.39 
 
 32.8 
 
 1350 
 
 5 o{ 
 
 M. 
 B. 
 
 48.2 
 46.4 
 
 3.18 
 3.39 
 
 15.2 
 13.7 
 
 1000 
 1500 
 
 
 
 
 
 
 T, top; M, middle; B, bottom voltage. 
 
ELECTRIC LIGHTING — ILLUMINATION. 
 
 13T1 
 
 The 50- and 60-watt sizes correspond respectively to the old 16-c -p., 3.1- 
 watt lamp (at top voltage) and the old 16-c-p., 3.5-watt lamp (at bottom 
 voltage). 
 
 The hours life of all of the listed carbon lamps shows the total life and 
 not the useful life or that formerly given as to 80% of initial c.-p. 
 
 The Gem Lamp is an improved type of the carbon lamp, having a carbon 
 filament heated to such a degree in an electric oven that it takes on the 
 properties of metal and hence the name, Gem " Metalized Filament." 
 
 Variation in Candle-Power, Efficiency, and Life. — The follow- 
 ing table shows the variation in candle-power, etc., of standard 100 to 
 125 volt, 3.1 and 3.5 watt carbon lamps, due to variation in voltage sup- 
 plied to them. It will be seen that if a 3.1-watt lamp is run at 10% 
 below its normal voltage, it may have over 9 times as long a life, but it 
 will give only 53% of its normal lighting power, and the light will cost 
 50% more in energy per candle-power. If it is run at 6% above its normal 
 voltage, it will give 37% more light, will take nearly 20% less energy for 
 equal light power, but it will have less than one-third of its normal life. 
 
 Per cent 
 
 Per cent of 
 Normal 
 Candle- 
 power. 
 
 Watts per 
 
 Relative 
 
 Watts per 
 
 Relative 
 
 Normal 
 
 Candle, 3.1 
 
 Life, 3.1 
 
 Candle, 
 
 Life, 
 
 Voltage. 
 
 watt Lamp. 
 
 watt 
 
 3.5 watts. 
 
 3.5 watts. 
 
 90 
 
 53 
 61 
 69.5 
 
 4.65 
 4.24 
 3.90 
 
 9.41 
 
 5.55 
 3.45 
 
 5.36 
 4.85 
 4.44 
 
 
 92 
 
 
 94 
 
 '"im" 
 
 96 
 
 79 
 
 3.60 
 
 2.20 
 
 4.09 
 
 2.47 
 
 98 
 
 89 
 
 3.34 
 
 1.46 
 
 3.78 
 
 1.53 
 
 99 
 
 94.5 
 
 3.22 
 
 1.21 
 
 3.64 
 
 1.26 
 
 100 
 
 100 
 
 3.10 
 
 1.00 
 
 3.50 
 
 1.00 
 
 101 
 
 106 
 
 2.99 
 
 .818 
 
 3.38 
 
 .84 
 
 102 
 
 112 
 
 2.90 
 
 .681 
 
 3.27 
 
 .68 
 
 104 
 
 124 
 
 2.70 
 
 .452 
 
 3.05 
 
 .47 
 
 106 
 
 137 
 
 2.54 
 
 .310 
 
 2.85 
 
 .31 
 
 The candle-power of a lamp falls off with its length of life, so that during 
 the latter half of its life it has only 60 per cent or 70 per cent of its rate 
 candle-power, and the watts per candle-power are increased 60 per cent or 
 70 per cent. After a lamp has burned for 500 or 600 hours it is more eco- 
 nomical to break it and supply a new one if the price of electrical energy 
 is that usually charged by central stations. 
 
 Incandescent Lamp Characteristics. — From a series of curves given 
 in Wickenden's " Illumination and Photometry " the following approxi- 
 mate figures have been derived : 
 
 LIFE, CANDLE-POWER AND WATTS PER CANDLE-POWER. 
 
 Hours 
 
 
 
 50 
 
 100 
 
 Lamps 
 Carbon 
 Tantalum 
 Tungsten 
 
 100 
 100 
 100 
 
 102 
 144 
 104 
 
 96 
 119 
 110 
 
 Carbon 
 
 Tantalum 
 
 Tungsten 
 
 100 
 100 
 100 
 
 99 
 80 
 97 
 
 98 
 90 
 96 
 
 200 300 400 500 600 
 Per cent of candle-power. 
 
 95 91 88 86 83 81 
 
 100 97 95 93 90 88 
 112 110 104 100 98 95 
 
 Per cent Watts per candle. 
 
 103 107 109 111 112 115 
 
 101 104 106 107 109 109 
 97 100 102 103 107 108 
 
 700 800 900 
 
 84 80 
 
 92 90 
 
 119 
 
 110 112 
 
 11Q 111 
 
 RELATION OP CANDLE-POWER TO TERMINAL VOLTS. 
 
 Per cent normal volts 84 88 92 ' 96 100 104 108 112 
 
 Per cent normal candle-power. 
 Carbon .. 46 60 78 100 123 154 
 
 Tantalum 46 56 68 82 100 118 139 161 
 
 Tungsten 54 63 73 86 100 115 134 158 
 
 The above figures show the necessity of close regulation of voltage of 
 lighting circuits. Slight reductions of voltage cause the light to fall far 
 below normal, while excess voltage greatly diminishes the life of the lamps. 
 
1372 
 
 ELECTRICAL ENGINEERING 
 
 RELATION OF ENERGY CONSUMPTION TO TERMINAL VOLTS. 
 
 Per cent normal volts 92 94 96 98 100 102 
 
 104 
 
 106 
 
 108 
 
 Per cent normal watts per candle-power. 
 
 
 
 
 Carbon 124 116 108 100 94 
 Tantalum 126 118 112 106 100 95. 
 Tungsten 120 115 110 105 100 96 
 
 88 
 90 
 92 
 
 82 
 87 
 88 
 
 83 
 85 
 
 Average Performance of Tantalum and Tungsten Lamps. - 
 
 (Winchenden.) 100 to 125 volts. 
 
 
 Tantalum. 
 
 Tungsten. 
 
 Rated horizontal c-p 
 
 Mean spherical c-p 
 
 Rated watts per c-p 
 
 Watts per m. spher. c-p.. . 
 
 12.5 
 8.9 
 2.5 
 2.53 
 
 25. 
 
 900* 
 
 20 
 15.8 
 2.0 
 
 2.53 
 40. 
 900* 
 
 40 
 31.6 
 
 2.0 
 
 2.53 
 
 80 
 800f 
 
 20 
 15.6 
 1.25 
 1.60 
 
 25 
 
 800 
 
 32 
 
 24.0 
 
 1.25 
 
 1.62 
 
 35-45 
 
 800 
 
 48 
 37.6 
 1.25 
 1.59 
 50-70 
 800 
 
 80 
 
 62.9 
 1.25 
 1.58 
 
 85-115 
 800 
 
 200 
 152 
 1.25 
 1.64 
 230-270 
 
 
 800 
 
 
 
 *For direct current; 500 hrs. for 60 cycle alt. current. f500 to 700 hrs. 
 for alt. current. 
 
 Specifications for Lamps. (Crocker.) — The initial candle-power of 
 any lamp at the rated voltage should not be more than 9 per cent above 
 or below the value called for. The average candle-power of a lot should 
 be within 6 per cent of the rated value. The standard efficiencies (of the 
 carbon lamp) are 3.1, 3.5, and 4 watts per candle-power. Each lamp at 
 rated voltage should take within 6 per cent of the watts specified, and the 
 average for the lot should be within 4 per cent. The useful life of a lamp 
 is the time it will burn before falling to a certain candle-power, say 80 
 per cent of its initial candle-power. For 3.1 watt lamps the useful life 
 is about 400 to 450 hours, for 3.5 watt lamps about 800, and 4 watt lamps 
 about 1600 hours. 
 
 Special Lamps. — The ordinary 16 c-p. 110-volt is the old standard 
 for interior lighting. Improved forms of incandescent lamp, such as the 
 tungsten, are now, 1910, rapidly coming into use, so that no one style of 
 lamp can be considered the standard. Thousands of varieties of lamps 
 for different voltages and candle-power are made for special purposes, 
 from the primary lamp, supplied by primary batteries using three volts 
 and about 1 ampere and giving 1/2 c.-p., and the 3/4 c.-p. bicycle lamp, 4 
 volts and 0.5 ampere, lamps of 100 c-p. at 220 volts. Series lamps of 
 1 c.-p. are used in illuminating signs, 2/3 
 ampere and 12.5 to 15 volts, eight lamps 
 being used on a 110-volt circuit. Standard 
 sizes for different voltages, 50, 110, or 220, 
 are 8, 16, 24, 32, 50, and 100 c.-p. 
 
 The Nernst Lamp depends for its oper- 
 ation upon the peculiar property of certain 
 rare earths, such as yttrium, thorium, zir- 
 conium, etc., of becoming electrical con- 
 ductors when heated to a certain tem- 
 perature; when cold, these oxides are 
 non-conductors. The lamp comprises a 
 " glower " composed of rare earths mixed 
 with a binding material and pressed info a 
 small rod; a heater for bringing the glower 
 up to the conducting temperature; an auto- 
 matic cut-out for disconnecting the heater 
 when the glower lights up, and a " ballast " 
 consisting of a small resistance coil of wire 
 having a positive temperature-resistance co- 
 efficient. The ballast is connected in series with the glower; its presence 
 is required to compensate the negative temperature-resistance coefficient of 
 
ELECTRIC LIGHTING — ILLUMINATION. 
 
 the glower; without the ballast, the resistance of the glower would become 
 lower and lower as its temperature rose, until the flow of current through 
 it would destroy it. Fig. 195 shows the elementary circuits of a simple 
 Nernst lamp. The cut-out is an electromagnet connected in series with the 
 glower. When current begins to flow through the glower, the magnet 
 pulls up the armature lying across the contacts of the cut-out, thereby 
 cutting out the heater. Tne heater is a coil of fine wire either located 
 very near the glower or encircling it. The glower is from V32 to Vi6 
 inch in diameter and about 1 inch long. 
 
 In the original Nernst lamp the glowers were adapted only for alternat- 
 ing-current, but direct-current glowers are now made. 
 
 The lamps are made with one glower, or with two, three, or six glowers 
 connected in parallel, and for operation on 100 to 120 and 200 to 240 volt 
 circuits. A 30-glower lamp for 220 volts, rated at 2000 c.-p., is also made. 
 
 Lamps with one glower are rated at 66 watts (110 volt), 88 (220 v.), 
 110 and 132 watts (110 or 220 v.) with a corresponding mean horizontal 
 candle-power of 50, 77, 96 and 114, respectively. The 2- 3- and 4-glower 
 lamps are multiples of the 132 watt (220 v.) single glower lamps, their 
 m.h.c.-p. being respectively 231, 359 and 504. The Nernst lamp is 
 commonly used where units of intermediate size between incandescent 
 and arc lamps are desired. 
 
 Cost of Electric Lighting. A. A. Wohlauer (El. World, July, 1908.) 
 — 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 K.W. hour for electric energy. The life, K, is that of the lamp for 
 incandescent lamps, of the glower for Nernst lamps, of the electrode for 
 arc lamps, and of trie vapor tube for vapor lamps. 
 
 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 = 1000 P/(KL S ). 
 
 C t = (£ s X R) + C t = cost per 1000 candle hours. 
 R = rate in cts. per K.W. hour. 
 
 Amp. Volts. 
 
 Rating. 
 
 
 
 
 Incandescent Lamps. 
 
 
 R=2 
 
 4 
 
 10 
 
 
 0.31 
 0.45 
 2.3 
 1.0 
 0.36 
 0.91 
 
 110 
 110 
 110 
 110 
 110 
 110 
 
 13.2 
 16.5 
 
 82 
 42.5 
 17 
 72 
 
 3.8 
 3.05 
 3.05 
 2.6 
 2.3 
 1.4 
 
 8 
 10 
 35 
 
 32.5 
 25 
 100 
 
 450 
 450 
 450 
 500 
 700 
 800 
 
 1.35 
 1.35 
 0.95 
 1.5 
 2.25 
 1.8 
 
 16 c.p. 
 20 c.p. 
 100 c.p. 
 110 Watt 
 20 c.p. 
 80 c.p. 
 
 10.3 
 
 8.8 
 
 8 
 
 8.2 
 
 9.1 
 
 6.4 
 
 17.9 
 14.8 
 14.1 
 13.4 
 13.7 
 9.2 
 
 40.7 
 
 
 33.2 
 
 
 37, 4 
 
 
 29 
 
 
 77 5 
 
 Tungsten 
 
 17.6 
 
 Direct-Current Arc Lamps. 
 
 Open arc 
 
 Enclosed 
 
 Carbon 
 
 Miniature 
 
 Magnetite 
 
 Flaming 
 
 Blondel 
 
 Inclined flaming. . 
 
 Inclined enclosed 
 
 flaming 
 
 10 
 
 55 
 
 400 
 
 1.3 
 
 4 
 
 10 
 
 1 
 
 10 amp. 
 
 4 6 
 
 7.2 
 
 5.0 
 
 110 
 
 760 
 
 2 1 
 
 4 5 
 
 150 
 
 0.1 
 
 5 
 
 4 4 
 
 8.6 
 
 10 
 
 110 
 
 550 
 
 2 
 
 4 
 
 16 
 
 0.5 
 
 10 
 
 5 
 
 9 
 
 2.5 
 
 110 
 
 150 
 
 1 8 
 
 3 
 
 20 
 
 1. 
 
 2.5 
 
 5 6 
 
 9 ?. 
 
 3.5 
 
 110 
 
 7.25 
 
 1 7 
 
 5 
 
 150 
 
 0.155 
 
 3.5 
 
 3 71 
 
 7 11 
 
 10 
 
 55 
 
 600 
 
 75 
 
 8 5 
 
 10 
 
 1 2 
 
 10 
 
 3 9 
 
 5 4 
 
 5 
 
 55 
 
 550 
 
 5 
 
 17.5 
 
 18 
 
 1.25 
 
 5 
 
 3 5 
 
 4.5 
 
 10 
 
 55 
 
 1100 
 
 0.5 
 
 9 
 
 10 
 
 0.8 
 
 10 
 
 2.6 
 
 3.6 
 
 5.5 
 
 100 
 
 1500 
 
 0.365 
 
 15 
 
 70 
 
 1.55 
 
 5.5 
 
 1.03 
 
 1.76 
 
 15 
 
 21.2 
 
 21 
 
 20 
 
 17.2 
 9.9 
 7.5 
 6.6 
 
1374 
 
 ELECTRICAL ENGINEERING. 
 
 Illuminant. 
 
 Amp, Volts. 
 
 P K C r Rating. 
 
 Ct = (S g X R) 
 
 + C r 
 
 Alternating-Current Arc Lamps. 
 
 
 15 
 7.5 
 10 
 10 
 10 
 
 
 300 
 230 
 425 
 1000 
 715 
 
 1.75 
 2.6 
 0.8 
 0.55 
 0.5 
 
 5 
 
 4.5 
 
 8.5 
 
 9 
 
 12.5 
 
 13 
 
 100 
 7 
 10 
 15 
 
 1.1 
 
 0.2 
 
 2.8 
 
 0.65 
 
 1.15 
 
 15 amp. 
 7.5 
 10 
 10 
 10 
 
 5.7 
 5.6 
 7.2 
 2.9 
 3.3 
 
 9.2 
 10.8 
 8.8 
 4 
 4.3 
 
 19.7 
 
 
 26.4 
 
 Flaming 
 
 Inclined flaming. . 
 Blondel 
 
 13.6 
 7.3 
 37. 
 
 Mercury-Vapor Lamps. 
 
 Cooper Hewitt I 3.5 | 
 
 Quartz 1 4.0 I 
 
 110 I 7701 0.5 I 600 1400010.2 13.5 amp. 1 1.4 I 2.4 I 5.4 
 220 I2740| 0.33| 350 |l000|0. 125|4.2 0.85 1.45 3.25 
 
 ELECTRIC WELDING. 
 
 The apparatus most generally used consists of an alternating-current 
 dynamo, feeding a comparatively high-potential current to the primary 
 coil of an induction-coil or transformer, the secondary of which is made so 
 large in section and so short in length as to supply to the work currents 
 not exceeding two or three volts, and of very large volume or rate of flow. 
 The welding clamps are attached to the secondary terminals. Other 
 forms of apparatus, such as dynamos constructed to yield alternating 
 currents direct from the armature to the welding-clamps, are used. 
 
 The conductivity for heat of the metal to be welded has a decided influ- 
 ence on the heating, and in welding iron its comparatively low heat conduc- 
 tion assists the work materially. (See papers by Sir F. Bramwell, Proc. 
 Inst. C. E., part iv., vol. cii. p. 1; and Elihu Thomson, Trans. A. I. M. E., 
 xix. 877.) 
 
 Fred. P. Royce, Iron Age, Nov. 28, 1892, gives the following figures 
 showing the amount of power required to weld axles and tires: 
 
 AXLE- WELDING. 
 
 Seconds 
 
 1-inch round axle requires 25 H.P. for 45 
 
 1-inch square axle requires 30 H.P. for. 48 
 
 1 1/4-inch round axle requires 35 H.P. for ". . . . 60 
 
 ll/4-inch square axle requires 40 H.P. for 70 
 
 2-inch round axle requires 75 H.P. for 95 
 
 2-inch square axle requires 90 H.P. for 100 
 
 The slightly increased time and power required for welding the square 
 axle is not only due to the extra metal in it, but in part to the care which 
 it is best to use to secure a perfect alignment. 
 
 TIRE- WELDING. 
 
 Seconds. 
 
 1 X 3/i6-inch tire requires 11 H.P. for 15 
 
 1V4 X3/g-inch tire requires 23 H.P. for.. , 25 
 
 IV2 X3/g-inch tire requires 20 H.P. for 30 
 
 IV2 XV2-inch tire requires 23 H.P. for 40 
 
 2 X 1/2-inch tire requires 29 H.P. for 55 
 
 2 X3/4-inch tire requires 42 H.P. for 62 
 
 The time above given for welding is of course that required for the actual 
 application of the current only, and does not include that consumed by 
 placing the axles or tires in the machine, the removal of the upset and 
 other finishing processes. From the data thus submitted, the cost of 
 welding can be readily figured for any locality where the price of fuel and 
 cost of labor are known. 
 
ELECTRIC HEATERS. 1375 
 
 In almost all cases the cost of the fuel used under the boilers for produc- 
 ing power for electric welding is practically the same as the cost of fuel 
 used in forges for the same amount of work, taking into consideration the 
 difference in price of fuel used in either case. 
 
 Prof. A. B. Kennedy found that 21/2-inch iron tubes 1/4-inch thick were 
 welded in 61 seconds, the net horse-power required at this speed being 23.4 
 (say 33 indicated horse-power) per square inch of section. Brass tubing 
 required 21.2 net horse-power. About 60 total indicated horse-power 
 would be required for the welding of angle-irons 3 X3 XV2-inch in from two 
 to three minutes. Copper requires about 80 horse-power per square inch 
 of section, and an inch bar can be welded in 25 seconds. It takes about 
 90 seconds to weld a steel bar 2 inches in diameter. 
 
 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 sub- 
 stance which will permit the conduction and radiation 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 = PRtX 0.24, 
 
 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. 
 
 The Consolidated Car-heating Co.'s electric heater consists of a galvan- 
 ized iron wire wound in a spiral groove upon a porcelain insulator. Each 
 heater is 305/g in. long, 87/g in. high, and 65/s in. wide. Upon it is wound 
 392 ft. of wire. The weight of the whole is 231/2 lbs. 
 
 Each heater is designed to absorb 1000 watts of a 500-volt current. Six 
 heaters are the complement for an ordinary electric car. For ordinary 
 weather the heaters may be combined by the switch in different ways, so' 
 that five different intensities of heating-surface are possible, besides the 
 position in which no heat is generated, the current being turned off. 
 
 For heating an ordinary electric car the Consolidated Co. states that 
 from 2 to 12 amperes on a 500-volt circuit is sufficient. With the outside 
 temperature at 20° to 30°, about 6 amperes will suffice. With zero or 
 lower temperature, the full 12 amperes is required to heat a car effectively. 
 
 Compare these figures with the experience in steam-heating of railway- 
 cars, as follows: 
 
 1 B. T. U. = 0.29084 watt-hours. 
 
 6 amperes on a 500-volt circuit = 3000 watts. 
 
 A current consumption of 6 amperes will generate 3000 *■ 0.29084 = 
 10,315 B.T.U. per hour. 
 
 In steam-car heating, a passenger coach usually requires from 60 lbs. of 
 steam in freezing weather to 100 lbs. in zero weather per hour. Supposing 
 the steam to enter the pipes at 20 lbs. pressure, and to be discharged at 
 200° F., each pound of steam will give up 983 B.T.U. to the car, Then 
 
1376 ELECTRICAL ENGINEERING. 
 
 the equivalent of the thermal units delivered by the electrical-heating 
 system in pounds of steam, is 10,315 -*■ 983 = 10'V2, nearly. 
 
 Thus the Consolidated Co.'s estimates for electric-heating provide the 
 equivalent of IOV2 lbs. of steam per car per hour in freezing weather and 
 21 lbs. in zero weather. 
 
 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. delivered at the fly-wheel with an expenditure of 21/2 lbs. 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.-lbs. energy per 
 hour =2180 heat-units. But since it required 2V2 lbs. 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 2 180 -e- 2 1/2 = 872 H.U. An 
 ordinary steam-heating system utilizes 9652 H.U. per lb. of coal for heat- 
 ing; hence the efficiency of the electric system is to the efficiency of the 
 steam-heating system as 872 to 9652, o>r about 1 to 11. (Eng'g News, 
 Aug. 9, '90; Mar. 30, '92; May 15, '93.) 
 
 Electric Furnaces. (Condensed from an article by J. Wright in 
 Elec. Age, May, 1904. The original contains illustrations of many styles 
 of furnace.) — Electric furnaces may be divided into two main classes, 
 (1) those in which the heating effect is produced by the electric arc estab- 
 lished between two carbon or other electrodes connected with the source 
 of current, commonly known as arc furnaces; and (2) those in which the 
 heating effect is produced by the passage of the current through a resist- 
 ance, which either forms part of the furnace proper, or is constituted, 
 by a suitable conducting train, of the material to be treated in the furnace. 
 Such furnaces are known as resistance furnaces. 
 
 The Moissan arc furnace consists of two chalk blocks, bored out to 
 receive a carbon crucible which encloses the center or hearth of the furnace 
 proper. Into this cavity pass two massive carbon electrodes, through 
 openings provided for them in the walls of the structure, which is held 
 together by clamps. The arc established between the ends of the carbons 
 when the current is turned on plays over the center of the crucible, heat- 
 ing its contents. 
 
 In the Siemens arc furnace a refractory crucible of plumbago, magnesia, 
 lime, or other suitable material is supported at the center of a cylinder 
 or jacket, and packed around with broken charcoal, or other poor con- 
 ductor of heat. The negative electrode consists of a massive carbon rod 
 passing vertically through the lid of the crucible, and free to move 
 vertically therein. The positive electrode, which may be of iron, plati- 
 num or carbon, consists of a rod passing up through the base of the crucible. 
 The furnace was originally designed for the fusion of refractory metals 
 and their ores. Electrical contact is established between the lower 
 electrode and the semi-metallic mass in the crucible, and the arc continues 
 to play between the surface of the mass and the movable carbon rod. 
 As the current through the furnace increases, that through the shunt 
 winding of a solenoid which controls the position of the movable rod 
 diminishes, thereby raising the negative electrode and restoring equilib- 
 rium. 
 
 The Willson furnace is a modification of the Siemens, the solenoid 
 regulation of the upper movable carbon being replaced by a worm and 
 hand wheel, while the furnace is made continuous in operation by the 
 provision of a tapping hole for drawing off the molten products. This 
 type of furnace was employed by Willson in the manufacture of calcium 
 carbide; many other types of arc furnaces have been developed from 
 these earlier forms. (See El. Age, May, 1904, for illustrations.) 
 
 The Borchers furnace is typical of that class in which a core, forming 
 part of the furnace itself, is heated by the passage of the current through 
 it, and imparts its heat to the surrounding mass of material contained in 
 the furnace. It consists of a block of refractory material, im the center of 
 which is an opening forming the crueible, into which is fed the material to 
 
PRIMARY BATTERIES. 
 
 1377 
 
 be treated. This space is bridged by a thin carbon rod which is attached, 
 at its extremities, to two carbon electrodes, passing through the walls of 
 the furnace. The current heats the smaller rod to a very high tempera- 
 ture, and the rod diffuses its heat throughout the mass, from its center 
 outwards. 
 
 H. I. Irvine has brought out a resistance furnace in which the heated 
 column consists of a fused electrolyte, maintained in a state of fusion by 
 the passage of the current, and communicating its heat by radiation and 
 diffusion, to the encircling charge, which is packed around it. 
 
 A novel type of resistance furnace, patented independently, with some 
 slight variation of detail, by Colby, Ferranti, and Kjellin, is worked on 
 the inductive principle, and consists of an annular, or helical, channel in 
 a refractory base, filled with a conducting, or semi-conducting, medium, 
 which constitutes the furnace charge, and has a heavy current induced 
 in it by a surrounding coil of many turns, carrying an alternating current. 
 The device, in fact, acts as the closed-circuit secondary of a step-down 
 transformer. 
 
 The Acheson furnace for the manufacture of carborundum is a rough 
 firebrick structure, through the end walls of which project the electrodes 
 consisting of composite bundles of carbon rods set in metal clamps. The 
 space between the two electrodes is bridged by a conducting path of coke, 
 which constitutes the core of the furnace. This core is packed round 
 with the raw material, consisting of coke, sand, sawdust and common salt. 
 
 A 2 1/2 ton H6roult electric steel furnace has been installed by the Firth- 
 Sterling Steel Co. at Demmler, Pa. In this furnace an arc is formed 
 between the bath of metal and two graphite electrodes which are sus- 
 pended over it. Single-phase, sixty-cycle alternating current is used 
 and is stepped down to 110 volts by transformers from the 11, 000- volt 
 mains. The furnace consumes about 250 kilowatts. It produces steel 
 equal in quality to crucible steel, at a cost little greater than open-hearth 
 steel. (El. Review, May 14, 1910.) 
 
 The Iron Trade Review, 1906, contains a series of illustrated articles 
 on electric furnaces, by J. B. C. Kershaw. See also paper by C. F. Bur- 
 gess, in Trans. Western Socy. of Engrs., 1905, and papers in Trans. Am. 
 Electro Chemical Society, 1902 and later dates. 
 
 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 tem- 
 peratures 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 1,700°, 
 however, the silicon leaves the carbon and combines with the oxygen of 
 the air. Silundum cannot 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 ins., 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. 
 
 Elements. 
 + 
 
 Electrolyte. 
 
 Depolarizer. 
 
 E.M.F. 
 volts. 
 
 
 Cu 
 
 Cu 
 
 Pt 
 
 C 
 
 Cu 
 
 C 
 
 Pt 
 
 Pt 
 
 C 
 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Zn 
 Cd 
 Zn 
 
 Dilute H2SO4 
 
 ZnSC-4 
 Dilute H2SO4 
 Dilute H2SO4 
 Cone. NaOH 
 
 NH4CI 
 
 ZnSC-4 
 
 CdSC-4 
 Various electro 
 
 Concent. CuS0 4 
 Concent. CuSCh 
 HNO3 
 K 2 Cr 2 7 
 CuO 
 Mn0 2 
 Hg 2 S0 4 
 Hg 2 S0 4 
 yte pastes. 
 
 1.07 
 
 
 1. 
 
 
 1.9 
 
 Fuller 
 
 2.1 
 
 Edison- Lalande 
 
 0.7-0.9 
 1.4 
 
 Clark 
 
 Weston 
 
 Dry battery 
 
 1.44 
 1.02 
 
 l-rl.,8 
 
1378 ELECTRICAL ENGINEERING. 
 
 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. 
 
 ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES. 
 
 The original, or Plants, storage battery consistedof two plates of metallic 
 lead immersed in a vessel containing sulphuric acid. An electric current 
 being sent through the cell the surface of the positive plate was converted 
 into peroxide of lead, Pb02. This was called charging the cell. After 
 being thus charged the cell could be used as a source of electric current, 
 or discharged. Plante and other authorities consider that in charging, 
 Pb02 is formed on the positive plate and spongy metallic lead on the 
 negative, both being converted into lead oxide, PbO, by the discharge, 
 but others hold that sulphate of lead is made on both plates by discharg- 
 ing, and that during the charging Pb0 2 is formed on the positive plate and 
 metallic Pb on the other, sulphuric acid being set free. 
 
 The acid being continually abstracted from the electrolyte as the dis- 
 charge proceeds, the density of the solution becomes less. In the charging 
 operation this action is reversed, the acid being reinstated in the liquid 
 and therefore causing an increase in its density. 
 
 The difference of potential developed by lead and lead peroxide im- 
 mersed in dilute H 2 S0 4 is about two volts. A lead-peroxide plate gradu- 
 ally loses its electrical energy by local action, the rate of such loss varying 
 according to the circumstances of its preparation and the condition of the 
 cell. 
 
 In the Faure or pasted cells lead plates are coated with minium or lith- 
 arge made into a paste with acidulated water. When dry these plates 
 are placed in a bath of dilute H 2 S0 4 and subjected to the action of the 
 current, by which the oxide on the positive plate is converted into peroxide 
 and that on the negative plate reduced to finely divided or porous lead. 
 
 The " Chloride Accumulator " made by The Electric Storage Battery 
 Co., of Philadelphia, consists of modified Plante positives and modified 
 Faure negatives. The positive plate, called the Manchester type, con- 
 sists of a hard lead grid into which are pressed " buttons " of corrugated 
 pure lead tape, rolled into spirals. When electrolytically " formed," 
 these buttons become coated with lead peroxide. The negative is the 
 so-called " Box " type, in which the grid is made in two halves which are 
 riveted together after " pasting " with lead oxide, the latter upon charg- 
 ing being reduced to spongy lead. The outside faces are covered with 
 perforated lead sheet, which serves to retain the spongy lead or active 
 material. 
 
 The following tables give the elements of several sizes of " chloride " 
 accumulators. Type G is furnished in cells containing 11-75 plates, and 
 type H from 21 plates to any greater number desired. The voltage of cells 
 of all sizes is slightly above two volts on open circuit, and during discharge 
 
ELECTRICAL ACCUMULATORS. 
 
 1379 
 
 varies from that point at the begining to 1.75 at the end when working 
 at the normal (eight-hour) rate. At higher rates the final voltage is lower. 
 
 Accumulators are largely used in central lighting and power stations, in 
 office buildings and other large isolated plants, for the purpose of absorbing 
 the energy of the generating plant during times of light load, and for giving 
 it out during times of heavy load or when the generating plant is idle. The 
 advantages of their use for such purposes are thus enumerated : 
 
 1. Reduction in coal consumption and general operating expenses, due 
 to the generating machinery being run at the point of greatest economy 
 while in service, and being shut down entirely during hours of light load 
 the battery supplying the whole of the current. 
 
 TYPE. 
 
 Size of Plates. 
 
 "C M 
 43/ 8 x4 in. 
 
 "D" 
 
 6x6m. 
 
 Number of plates 
 
 r>. . • i For'8 hours . . 
 
 Dl lt* T SJ For 5 hours „. 
 
 amperes. .^ For 3 hours , 
 
 Normal charge rate 
 
 Outside dimensions of \ \Vlcif h 
 rubber jar, inches: (Height 
 
 Outside dimensions of \ \yjjf n 
 glass jar, inches: ( Height 
 
 Weight of electrolyte. [ fjgg/*™ 
 
 lbs - : { jar: 
 
 Weight of cell com- { *ggj 
 plete,withacid,lbs.: irl 
 
 ^Height of cell over 
 all, inches: 
 
 . jars 
 glass jars 
 rubber 
 jars. 
 
 8V2 
 
 '43/ 4 
 
 71/4 
 64/ 2 
 
 83/ 4 
 8I/4 
 91/2 
 
 63 
 471/4 
 
 v 2 
 
 * 41/2, 51/2, and 6I/2 ins. 1 8/4, I, and I V4. lbs. X 7l/ 2 , 9l/ 2 and 1 1 1/2 lbs 
 "D "Yacht type, rubber jars, 5, 7, and 9 plates, 2V2 in. higher than standard. 
 
 TYPE'E.'" 
 Size of Plates, 73/ 4 x73/ 4 in. 
 
 TYPE " F.'' 
 Size of Plates, 
 11x101/2 in. 
 
 Number of plates. . . . 
 
 5 
 
 7 
 
 9 
 
 11 
 
 13 
 
 15 
 
 9 
 
 II 
 
 13 
 
 15 
 
 1; 
 
 D* 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 5 
 
 
 i1 
 
 21 
 
 28 
 
 35 
 
 42 
 
 49 
 
 56 
 
 JO 
 
 84 
 
 98 
 
 112 
 
 7 
 
 peres: |Fbr3hrs. 
 
 30 
 
 40 
 
 W , 
 
 60 ' 
 
 70 
 
 80 
 
 100 
 
 120 
 
 140 
 
 160 
 
 10 
 
 iFor 1 hr. 
 
 40 
 
 60 
 
 HO • 
 
 100 
 
 120 
 
 140 
 
 160 
 
 200 
 
 240 
 
 280 
 
 320 
 
 20 
 
 
 10 
 
 15, 
 37/ 8 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 M) 
 
 60 
 
 70 
 
 80 
 
 5 
 
 V5 Length, in. 1 rub- 
 
 27/8 
 
 5 
 
 61/8 
 
 8V« 
 
 8V2 
 
 11. 
 
 U> 
 
 163/4 
 
 1*3/8 
 
 20 
 
 Vh 
 
 4» £ Width, in. >ber 
 
 8 l/o 
 
 8'/? 
 
 8V ? 
 
 81/? 
 
 »!/■> 
 
 81/2 
 
 i*Vs 
 
 15 
 
 15 
 
 15 
 
 
 
 11 
 
 1! 
 
 II 
 
 d-Vs 
 
 II 
 
 II 
 
 
 201/4 
 103/g 
 
 201/4 
 
 201/4 
 
 201/4 
 
 
 
 51/, 
 
 63/ 4 
 
 8 
 
 II 
 
 113/s 
 
 9 
 
 l06/ 8 
 
 12 
 
 
 
 O £ Width, in.} S oi 
 
 91/8 
 
 91/8 
 
 91/8 
 
 ?V8 
 
 91/8 
 
 91/8 
 
 121/2 
 
 12 V? 
 
 123/4 
 
 123/4 
 
 
 
 *3 Height, in.)^""' 
 
 11 3/ 8 
 
 H3/8 
 
 1 r*/» 
 
 it 3/8 
 
 M3/ 8 
 
 II 1/8 
 
 I'l 
 
 M 
 
 1/ 
 
 17 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Weight of 
 
 jars. 
 
 I8I/2 
 
 20 
 
 241/2 
 
 26 
 
 35 
 
 34 
 
 63 
 
 09 
 
 67 
 
 79 . 
 
 
 
 electrolyte: 
 
 ber 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 jars. 
 
 51/2 
 
 8 
 
 101/2 
 
 12 
 
 17 
 
 I8V 2 
 
 
 99 
 
 111 
 
 123 
 
 133 
 
 6 
 
 Weight of 
 tell com- 
 plete, with 
 
 glass 
 jar. 
 rub-. 
 
 49 
 
 60 
 
 74 
 
 86 1/2 
 
 104 
 
 112 
 
 
 
 
 
 
 
 acid: 
 
 jar. 
 
 glass 
 jar. 
 
 rub- 
 jar. 
 
 29V2 
 
 40»/2 
 
 52 
 
 63 
 
 77 
 
 87 
 
 tank 
 
 
 332 
 
 372 
 
 411 
 
 20 
 
 Height of cell 
 over all, in 
 inches: 
 
 20 
 
 121/2 
 
 20 
 121/2 
 
 20 
 
 mf 2 
 
 20 
 12 1/2 
 
 20 
 
 121/2 
 
 20 
 
 nu 2 
 
 273/4 
 £ank 
 
 273/4 
 
 331/4 
 
 273/4 
 
 331/4 
 
 273/4 
 
 331/4 
 
 273/4 
 331/4 
 
 
 *D — addition per plate from 25 to 75 plates 
 sions and weights. 
 
 approximate as to dimen- 
 
1380 
 
 ELECTRICAL ENGINEERING. 
 
 type'"g." 
 
 Size of Plates, I55/ I6 x 1 5 5/ 16 i n . 
 
 TYPE " H." 
 Size of Plates. 
 15 5/16X30 "/to in. 
 
 Number of platea 
 
 II 
 
 13 
 
 15 
 
 17 
 
 25 
 
 75 
 
 D* 
 
 21 
 
 23 
 
 25 
 
 75 
 
 D* 
 
 Discharge |f- f hrs. 
 
 100 
 
 120 
 
 140 
 
 160 
 
 240 
 
 740 
 
 10 
 
 400 
 
 440 
 
 480 
 
 480 
 
 20 
 
 140 
 
 168 
 
 196 
 
 224 
 
 336 
 
 1036 
 
 14 
 
 560 
 
 616 
 
 672 
 
 2072 
 
 28 
 
 nlrpV" |For3hrs. 
 
 200 
 
 240 
 
 280 
 
 320 
 
 480 
 
 1480 
 
 20 
 
 800 
 
 880 
 
 960 
 
 2960 
 
 40 
 
 Peres. ( For , hr 
 
 400 
 
 480 
 
 560 
 
 640 
 
 960 
 
 2960 
 
 40 
 
 1600 
 
 1760 
 
 1920 
 
 5920 
 
 20 
 
 Nornjal charge rate . 
 
 100 
 
 120 
 
 140 
 
 160 
 
 240 
 
 740 
 
 10 
 
 400 
 
 440 
 
 480 
 
 480 
 
 20 
 
 Outside fr,eneth 
 dimensions ) w: .f. 
 of tank. Sc- 
 inches: [Height. 
 
 151/2 
 
 I6I/4 
 
 I8V2 
 
 20 
 
 275/ 8 
 
 697/ 8 
 
 7/8 
 
 25 V 
 
 26 3/4 
 
 283/ 8 
 
 697/ 
 
 Va 
 
 l93/ 4 
 
 193/ 4 
 
 193/4 
 
 193/4 
 
 203/4 
 
 21V, 
 
 
 2U/2 
 
 21 1/ 2 
 
 2ll/ 2 
 
 211/2 
 
 497/2 
 
 
 26 
 
 26 
 
 26 
 
 26 
 
 261/2) 
 
 277/- 
 
 
 487/8 
 
 487/ 8 
 
 487/ 
 
 
 Weight of electrolyte 
 
 
 
 
 
 
 
 
 
 
 
 
 
 in pounds 
 
 188 
 
 210 
 
 231 
 
 253 
 
 338 
 
 876 
 
 10.5 
 
 583 
 
 625 
 
 668 
 
 1741 
 
 21 5 
 
 Weight of cell, com- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 plete, with electro- 
 lyte in lead-lined 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 tank, pounds 
 
 568 
 
 645 
 
 719 
 
 798 
 
 1165 
 
 3300*" 40 
 
 1967 
 
 2121 
 
 2278 
 
 6215 
 
 78 
 
 Height of cell over 
 
 
 
 
 
 
 
 
 
 
 
 
 
 all, inches 
 
 39 
 
 39 
 
 39 
 
 39 
 
 40, 
 
 4U/2 
 
 ■:•' 
 
 62V4 
 
 62.1/4 
 
 621/4 
 
 631/4 
 
 _ *D = addition per plate from 25 to 75 plates; approximate as to dimen- 
 sions and weights. 
 
 2. The possibility of obtaining good regulation in pressure during fluc- 
 tuations in load, especially when the day load consists largely of elevators 
 and similar disturbing elements. 
 
 3. To meet sudden demands which arise unexpectedly, as in the case of 
 darkness caused by storm or thunder-showers; also in case of emergency 
 due to accident or stoppage of generating-plant. 
 
 4. Smaller generating-plant required where the battery takes the peak 
 of the load, which usually only lasts for a few hours, and yet where no 
 battery is used necessitates sufficient generators, etc., being installed to 
 provide for the maximum output, which in many cases is about double 
 the normal output. 
 
 The Working Current, or Energy Efficiency, of a storage-cell 
 is the ratio between the value of the current or energy expended in the 
 charging operation, and that obtained when the cell is discharged at any 
 specified rate. 
 
 In a lead storage-cell, if the surface and quantity of active material be 
 accurately proportioned, and if the discharge be commenced immediately 
 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 regu- 
 lated. Since the current efficiency decreases as the discharge rate in- 
 creases, 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%. 
 
 As the normal average discharging electro-motive force of a lead 
 secondary cell never exceeds 2 volts, and as an average electro-motive 
 force during normal charge of about 2.35 volts is required at its poles 
 to overcome both its opposing electro-motive force and its internal 
 resistance, there is an initial loss of at least 15% between the voltage 
 required to charge it and that at which it discharges. Thus with a cur- 
 rent efficiency of 90% and a volt efficiency of 85% the energy efficiency 
 under the best conditions cannot be much over 75%, while in practice 
 it is nearer 70%. 
 
 Important General Rules. — Storage cells should not be excessively 
 charged, undercharged or allowed to stand when completely discharged. 
 
 In setting up new cells the manufacturer should always be consulted 
 as to the proper purity and specific gravity of the electrolyte (solution) 
 to be used in the cells and also as to the duration of the initial charge. 
 
ELECTROLYSIS. 1381 
 
 Charging should be done at the normal rate (as given by the manu- 
 facturer) or as near to it as possible. At regular periods once each week 
 or two weeks, depending on whether the cells have to be charged daily 
 or not, an overcharge should be given, lasting until the specific gravity 
 of the electrolyte and the cell voltage have risen to a maximum and 
 remained constant for about one hour. The end of charge voltage may 
 vary from 2.40 to 2.70 volts per cell. All other charges termed " regular 
 charges " should cease shortly before the maximum values obtained on 
 the preceding overcharge are reached. If cells are standing idle they 
 should receive an overcharge once every two weeks. 
 
 Discharges should be stopped when the cell voltage has fallen to 1.80 
 volts with current flowing at or about the normal rate. The fall in 
 specific gravity of the electrolyte is also useful as a guide on the discharge 
 and the manufacturer should be consulted as to the proper limits. 
 
 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 such 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. 
 
 ELECTROLYSIS, 
 
 The separation of a chemical compound into its constituents by means 
 of an electric current. Faraday gave the nomenclature relating to elec- 
 trolysis. The compound to be decomposed is the Electrolyte, and the 
 process Electrolysis. The plates or poles of the battery are Electrodes. 
 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 15% 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 equiva- 
 lents 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. 
 
 The table on page 1382 (from " Practical Electrical Engineering ") is 
 calculated upon Lord Rayleigh's determination of the electro-chemical 
 equivalents and Roscoe's atomic weights. 
 
1382 
 
 ELECTRICAL ENGINEERING. 
 
 ELECTRO-CHEMICAL EQUIVALENTS. 
 
 
 
 
 
 H? 
 
 > 
 
 
 
 c 
 
 
 0) 
 
 W 
 
 * 
 
 >> 
 
 £ 
 
 1 , 
 
 
 
 
 a 
 
 a 
 
 s| 
 
 
 
 o> o> 
 
 oj 
 
 
 ^13 
 
 > 
 
 <3 
 
 O ro 
 
 Hi 
 
 1.00 
 
 1.00 
 
 Ki 
 
 39.04 
 
 39.04 
 
 Nai 
 
 22.99 
 
 22.99 
 
 Al 3 
 
 27.3 
 
 9.1 
 
 Ma-., 
 
 23.94 
 
 11.97 
 
 AU3 
 
 196.2 
 
 65.4 
 
 Agi 
 
 107.66 
 
 107.66 
 
 Cu 2 
 
 63.00 
 
 31.5 
 
 C Ul 
 
 63.00 
 
 63.00 
 
 H>, 
 
 199.8 
 
 99.9 
 
 H gl 
 
 199.8 
 
 199.8 
 
 Sm 
 
 117.8 
 
 29.45 
 
 Sn 2 
 
 117.8 
 
 58.9 
 
 Fa, 
 
 55.9 
 
 18.64$ 
 
 Fe 2 
 
 55.9 
 
 27.95 
 
 Ni 2 
 
 58.6 
 
 29.3 
 
 Zn 2 
 
 64.9 
 
 32.45 
 
 Pb 2 
 
 206.4 
 
 103.2 
 
 Oo 
 
 15.96 
 
 7.98 
 
 CMi 
 
 35.37 
 
 35.37 
 
 Ii 
 
 126.53 
 
 126.53 
 
 Br, 
 
 79.75 
 
 79.75 
 
 ^3 
 
 14.01 
 
 4.67 
 
 lil^ 
 
 si 11 
 lit! 
 
 o 03 
 
 Electro-positive. 
 
 Hydrogen 
 
 Potassium 
 
 Sodium 
 
 Aluminum 
 
 Magnesium 
 
 Gold 
 
 Silver 
 
 Copper (cupric) 
 
 (cuprous) 
 
 Mercury (mercuric)., 
 (mercurous) 
 
 Tin (stannic) 
 
 " (stannous) 
 
 Iron (ferric) 
 
 " (ferrous) 
 
 Nickel 
 
 Zinc 
 
 Lead 
 
 Electro-negative. 
 
 Oxygen 
 
 Chlorine 
 
 Iodine 
 
 Bromine 
 
 Nitrogen 
 
 0.010384 
 
 0.40539 
 
 0.23873 
 
 0.09449 
 
 0.12430 
 
 0.67911 
 
 1.11800 
 
 0.32709 
 
 0.65419 
 
 1.03740 
 
 2.07470 
 
 0.30581 
 
 0.61162 
 
 0.19356 
 
 0.29035 
 
 0.30425 
 
 0.33696 
 
 1.07160 
 
 0.08286 
 0.36728 
 1.31300 
 0.82812 
 0.04849 
 
 96293.00 
 2467.50 
 4188.90 
 1058.30 
 
 804.03 
 1473.50 
 
 894.41 
 3058.60 
 1525.30 
 
 963.99 
 
 481.99 
 3270.00 
 1635.00 
 5166.4 
 3445.50 
 3286.80 
 2967.10 
 
 933.26 
 
 0.0373 8 
 1.4595° 
 0.8594^ 
 0.34018 
 0.44747 
 2.4448° 
 4.0250° 
 1.1770° 
 2.35500 
 3.73450 
 7.46900 
 1.10090 
 2.20180 
 0.69681 
 1 .04480 
 1 .09530 
 1 .21330 
 3.85780 
 
 *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. 
 
 JBecquerel'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 -5- valency, 
 as defined 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 hydrogen liberated per second X number of seconds X current 
 strength X 107.7 = 0.00001038 X 10 X 10 X 107.7 = 0.11178 gram. 
 
 Weight of copper deposited in 1 hour by a current of 10 amperes = 
 
 0.00001038X 3600X10X 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 -s- 0.00001038 
 weight of element liberated per second 
 — 0.00001038 Xchemical equivalent of element 
 
THE MAGNETIC CIRCUIT. 1383 
 
 THE MAGNETIC CIRCUIT. 
 
 For units of the magnetic circuit, see page 1346. 
 
 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 4rc square centimeters 
 If <j> = 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 =(f>L-t- 4x. 
 
 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 + <lx. 
 
 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 = ML H =LABH -f- 4tt, 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 = ^ — ' ' , or 7=-^; Amperes = — r — • 
 Resistance R ohms 
 
 Similarly, in the magnetic circuit 
 
 _,. Magnetomotive Force . F _, _, Gilberts 
 
 Flux= ■ — p , — - , or <£= „ • Maxwells = — 
 
 Reluctance ' R Oersteds 
 
 Reluctance is the reciprocal of permeance, and permeance is equal to 
 permeability X path area -f- path length (metric measure); hence 
 <f>= Fjua-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 A t )n6A5a+ 2.54?= 3.192/xaA^H- I. 
 The ampere-turns required to produce a given magnetic flux in a given 
 path will be 
 
 A t *= 4>l+ 3.192 /ia = 0.3133 <j>l+na. 
 Since magnetic flux -f- 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 + p. 
 This formula 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 
 
ia84 
 
 ELECTKICAL ENGINEERING. 
 
 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 of B and H 
 
 
 a 
 
 g 
 
 3 
 
 5*8 
 
 Cast Iron. 
 
 Cast Steel. 
 
 Wrought Iron. 
 
 Sheet Metal. 
 
 H 
 
 <g 
 
 o3 & • 
 
 <D 
 
 e3 a • 
 
 a> 
 
 1 V 
 
 x a . 
 
 $ 
 
 1 O) 
 
 « a . 
 
 
 3*8 
 
 B0 4 | 
 
 
 m i| 
 
 SJ2.S 
 O-r, . 
 
 m il 
 
 ||.S 
 
 m ,1 
 
 a — -5 
 
 
 
 
 g& 
 
 
 g=l 
 
 
 O o3 
 72 OJO 
 
 
 10 
 
 7.95 
 
 20.2 
 
 4.3 
 
 27.7 
 
 11.5 
 
 74.2 
 
 13.0 
 
 83.8 
 
 14.3 
 
 92.2 
 
 20 
 
 15.90 
 
 40.4 
 
 5.7 
 
 36.8 
 
 13.8 
 
 89.0 
 
 14.7 
 
 94.8 
 
 15.6 
 
 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 
 
 13C.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-gaps each Vi6in. 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-turns 
 = 4X40=160. 
 
 The density in the sheet iron = 768,000 -5- 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.= B*a + 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 coil-and-plunger type of electro-magnets 
 
DYNAMO-ELECTRIC MACHINES. 1385 
 
 is discussed in a series of articles by C. R. Underbill, in Elec. World, 
 April 29, May 13, and Oct. 7, 1905. 
 
 Various forms of magnetic chucks are illustrated and described by O. S. 
 Walker, in Am. Mach., Feb. 11, 1909. 
 
 For magnets used in hoisting, see page 1169. 
 
 Determining the Polarity of Electro-magnets. — If a wire is 
 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 as 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. 
 
 There are three classes of dynamo-electric machines, viz.: 
 
 1. Generators, for the conversion of mechanical into electrical energy. 
 
 2. Motors, for the conversion of electrical into mechanical energy. 
 Generators and motors are both subdivided into direct-current and 
 
 alternating-current machines. 
 
 3. Transformers, for the conversion of one character or voltage of cur- 
 rent into another, as direct into alternating or alternating into direct, or 
 from one voltage into a higher or lower voltage. 
 
 Kinds of Dynamo-electric Machines as regards Manner of 
 Winding. 
 
 1. Separately-excited Dynamo. — The field magnet coils have no connec- 
 tion with the armature-coils, but receive their current from a separate 
 machine or source. 
 
 2. Series-wound Dynamo. — The field winding and the external circuit 
 are connected in series with the armature winding, so that the entire arma- 
 ture current must pass through the field-coils. 
 
 Since in a series-wound dynamo the armature-coils, the field, and the ex- 
 ternal circuit are in series, any increase in the resistance of the external 
 circuit will decrease the electromotive force from the decrease in the mag- 
 netizing currents. A decrease in the resistance of the external circuit will, 
 in a like manner, increase the electromotive force from the increase in the 
 magnetizing current. The use of a regulator avoids these changes in the 
 electromotive force. 
 
 3. 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 electromotive force, and a decrease in the resistance 
 of the external circuit decreases the electromotive 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 cir- 
 cuit 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 electromotive 
 force to become greater. If, on the contrary, the resistance of the external 
 circuit decreases, less current passes through the field, and the electro- 
 motive force is proportionately decreased. 
 
 4. Compound-wound Dynamo. — The field magnets are wound with two 
 separate sets of coils, 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. 
 
1386 
 
 ELECTRICAL ENGINEERING. 
 
 Motors. — The above classification in regard to winding applies also to 
 motors. 
 
 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 to itself and at right angles to the lines of the 
 field. The force producing this tendency is P=IBI dynes, in which 
 Z=length of the wire, 7 = the current in C.G.S. units, and B=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-i- 10 = IBIX 10 -1 . 
 
 If Pjff. is taken in kilograms, 
 
 P k = IBI + 9,810,000 = 10.1937 IBIX 10~ 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 
 10 centimeters of the wire = 10.1937 X 10 X 100X5000 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. 
 
 Let / = current in the armature in amperes, £' = the electromotive force 
 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 = 4>Nn -J- 10 8 ; whence 
 
 <j>NI-r- 10 8 = 2xTX1.356; 
 <j>NI <j>NI 
 
 10 8 X 2tt X 1.356 8.52 X 10 8 P ouna - Ieet - 
 
 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 
 
 4> = %ndXlX 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. 
 
 4> = ~- X 20 X 30,000 X y^j = 7,540,000. 
 „ 7,540,000X120X400 , OJ _ , . . 
 
 T = 8.52 X 100,000,000 = 424 " 8 P ound " feet - 
 Total peripheral force = 424.8 -e- 0.5 = 849.6 lbs. 
 Drag per conductor = 849.6 -s- 120 = 7.08 lbs. 
 
 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-power and Revolutions. — T= torque in pound-feet, 
 H.P. = T X Rpm. X 6.2832 -r- 33,000 = IE -J- 746. Whence Torque 
 = 7.0403 EI h- Rpm. or 7 times the watts -*- 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 
 the E.M.F., for IE = H.P. X 746, whence E.M.F. or E = H.P. X 746-=-/. 
 * 1 ft.-lb. per second = 1.356 watts. 
 
DYNAMO-ELECTRIC MACHINES. 1387 
 
 If H.P., as above, = 40.5, and /= „ 
 
 400 
 
 The E.M.F. may also be calculated by the following formulae: 
 I = Total current through armature; 
 e a = E.M.F. in armature in volts; 
 
 N = Number of active conductors counted all around armature; 
 V = Number of pairs of poles (p = 1 in a two-pole machine); 
 n= Speed in revolutions per minute; 
 $ = Total flux in maxwells. 
 
 _,, , . I e n =4>N — 10 -8 for two-pole machines. 
 
 Electromotive J a 60 
 
 force: j = p<f>N j% for multipolar machines with series- 
 
 {. 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 
 square centimeters, 1= length of core in centimeters, n the permeability of 
 the core, and <£= flux in maxwells. Then 
 
 _ Magnetomotive Force _ 1.257 NI 
 
 r Reluctance (£-e-A/i) 
 
 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 L it 
 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 A t , 
 A 2 , A3 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 m, and of 
 the armature nz. The permeability of the air-gaps is taken as unity. Then 
 the total reluctance of the machine will be 
 
 Li L2 , L3 > 
 Aifii A 2 A S fi s 
 
 ™_ « . 1.257 NI 
 
 The flUX, <£ = 77 — — : . , fT — . . , IT -. : . 
 
 (Lj -i- Aifj-i) + (L 2 ■*■ A 2 ) + {Lz -5- A 3^3) 
 
 The ampere-turns necessary to create a given flux in a machine may be 
 
 found by the formula, 
 
 Arr , [(Lt -5- AtMi) + (L 2 -4-A 2 ) + (L 8 -?• Az^s)] 
 NI = * L257 ' 
 
 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. 
 
 *The length of the path in the field magnet cores L t includes that portion 
 of the path which lies in the piece joining the cores of the various field 
 magnets. 
 
1388 ELECTRICAL ENGINEERING. 
 
 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 transformers, 
 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 alternat- 
 ing current rapidly rises from zero to a maximum, falls to zero, reverses 
 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 abscis- 
 sas 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. 172; the best forms of alternators give a curve that is a 
 very close approximation to the sine curve, and all calculations and de- 
 ductions 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 treat- 
 ing of alternating currents, is sometimes spoken of as ohmic resistance. 
 The word resistance, used alone, always means the ohmic resistance. In 
 alternating currents, in addition to the resistance, several other quantities, 
 which affect the flow of current, must be taken into consideration. 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 containing 
 only resistance, the current and e.m.f. are in phase; in a current contain- 
 ing inductance the e.m.f. attains its maximum value before the current, 
 or leads the current. In a circuit containing capacity the current 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 -f- t or 0.637 of the maximum 
 value. 
 
 The value of greatest importance 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 resist- 
 ance of the circuit is the heat lost in the circuit. 
 
 The comparison of the maximum, average, and effective values is as 
 follows: 
 #Effec. =#Max. X 0.707; #Aver. =#Max.X 0.637; #Max. = 1.41 X #Effec. 
 
 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. 172), 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 
 
 *Only a very brief treatment of the subject of alternating currents can 
 be given in this book. The following works are recommended as valuable 
 for reference: Alternating Currents and Alternating Current Machinery, 
 by D. C. and J. P. Jackson; Standard Polyphase Apparatus and Systems, 
 by M. A. Oudin; Polyphase Electric Currents, by S. P. Thompson; Electric 
 Lighting, by F. B. Crocker, 2 vols.; Electric Power Transmission, by Louis 
 Bell; Alternating Currents, by Bedell and Crehore; Alternating-current 
 Phenomena, by Chas. P. Steinmetz. The two last named are highly 
 mathematical. 
 
ALTERNATING CURRENTS 1389 
 
 double the frequency. A current of 120 alternations per second has a 
 period of i/eo 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 adoption of 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 low frequency current cannot be used on lighting circuits, as the lights 
 will flicker 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 low 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 the conductor. If the current 
 be changed in strength or direction, 
 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- Fig. 198. 
 ductor remains constant. The unit of 
 
 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. 198, 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 Wheat- 
 stone bridge by substituting for a standard resistance a standard of induc- 
 tance or a standard 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 valuee shown on the volt and ammeters 
 will not be true simultaneous values. Referring to Fig. 172, 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 
 
1390 
 
 ELECTRICAL ENGINEERING. 
 
 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= IX EX power factor= I XEXcos9, 
 where 6 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 below, in the section on Im- 
 pedance Polygons. 
 
 Reactance, Impedance, Admittance. — In addition to the ohmic 
 resistance of a circuit there are also resistances due to inductive, 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 nfL. 
 
 Condensive reactance = ■ . 
 
 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 s um of the sq uares of the resistance and the reactance. 
 Impedance = Z = v / R 2 + (2tt/L) 2 w hen inductance is present in the circuit. 
 
 Impedance = Z = ^R i + ( - — ^ J when capacity is present in the circuit. 
 
 Admittance is the reciprocal of impedance, = 1 -s- 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 - -^-^ ; Z = \j R* + ( 2 n/L - tt^tptY- 
 
 2 irjC M \ 2 irJC / 
 
 In all cases the tangent of the angle of lag or lead is the reactance divided 
 by the resistance. In the last case 
 
 2nfL--^ 
 tan0 = ^- C . 
 
 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 omhic resistance. 
 With low frequencies and small wires the skin effect is small, but it becomes 
 quite important with high frequencies and large wires. 
 
 The skin effect factor, by which the ohmic resistance is to be multiplied 
 to obtain the virtual resistance, for different sizes of wire and frequencies 
 is as follows: 
 
 Wire No. 
 
 
 
 00 
 
 000 
 
 0000 
 
 1/2 in- 
 
 3/ 4 in. 
 
 1 in. 
 
 
 
 
 
 1.001 
 1.006 
 1.027 
 
 1.002 
 1.008 
 1.039 
 
 1 .UO/ 
 1.040 
 1.156 
 
 1.020 
 
 
 i .66i 
 
 1.008 
 
 1.002 
 1.010 
 
 1.005 
 1.017 
 
 1.111 
 
 130 cycles, factor 
 
 1.397 
 
 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 m 
 
 Impedance Polygons. — 1. Series Circuits. — The impedance of a circuit 
 can be determined graphically as follows. Suppose a circuit to con- 
 tain a resistance R and an inductance L, and to carry a current / of fre- 
 quency/. In Fig. 199 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 tt/L. Join a and c. The line ac represents the impedance of 
 the circuit. The angle d between ab and ac is the angle of lag of the cur- 
 
ALTERNATING CURRENTS. 
 
 1391 
 
 rent behind the e.m.f., and the power factor of the circuit is cosine 6 
 e.m.f. of the circuit is E = IZ. 
 
 Fig. 199. 
 
 Fig. 200. 
 
 If the above circuit contained, instead of the inductance L, a capacity C, 
 then would the polygon be drawn as in Fig. 200. The line be woula be pro- 
 portional to - and would be drawn in a direction opposite to that of 
 
 be in Fig. 199. The impedance would again ba Z, the e.m.f. would be 
 Z XI, 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. 201. 
 The impedance of the circuit would be represented by ad, and the angle of 
 lag by 6. 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. 
 
 1 
 
 27T/JC.. 
 
 Fig. 201. 
 
 Fig. 202. 
 
 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. 202. 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. 203) contains a resistance, R lt of 15 ohms, a 
 capacity, C it of 100 microfarads (0.000100 farad), a resistance, R 2 , of 12 
 
 R.r=15 Kj =.0001 0Q R 2 =12 
 
 Fig. 203. 
 
 ohms, and inductance of L u of 0.05 henry, and a resistance R3, 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 
 iin Dressed 
 The resistance is represented in Fig. 204 by the horizontal line ab, 15 
 
1392 
 
 ELECTRICAL ENGINEERING. 
 
 Ri— 15 
 
 Fig. 204. 
 
 units long. The capacity is represented by the line be, drawn downwards 
 from b and whose length is 
 
 2j7/Ci = 2X3.1416X60X0.0001 = 26>55 - 
 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 L x . Its length is 
 
 2nfLi=2 X3.1416 X60 X 0-05= 18.85. 
 From the point e a horizontal line ef, 20 
 units long, is drawn to represent Rz. The 
 )\fi r=20 / nne adjoining a and / will represent the 
 impedance of the circuit in ohms. The 
 angle 0, between ab and af, 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 n co 
 
 /= -7T = -T~-g = 2.53 amperes. 
 
 The power factor = cos = cos 9° 15' = 0.987, 
 
 The power in the circuit at 120 volts is 
 
 / X E X cos d = 2.53 X 120 X 0.987 = 299.6 watts. 
 
 2. Parallel Circuits. — If two circuits be arranged 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 various branches separate. 
 Consider a circuit, Fig. 205, consisting of two 
 branches. The first branch contains a resist- 
 ance Rt and an inductance Li in series with 
 it. The second branch contains a resistance 
 R 2 in series with an inductance L 2 . The im- 
 pedance of the circuit may be determined by 
 treating each of the two branches as a sepa- 
 rate series circuit, and drawing the impedance 
 polygon for each branch on that assumption. 
 Having found the impedance the current flow- 
 ing 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. 206, consisting of two branches. 
 Branch 1 consists of a resistance R t = 12 ohms, an inductance L x = 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 R 3 = 10 ohms, and an inductance L 3 = 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 
 in the circuit. Construct the impedance polygons for the two branches 
 separately as shown in Fig. 207, a and b. 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 
 
 Ri L a 
 
 r-VVWWfifH 
 
 Fig. 205. 
 
ALTERNATING CURRENTS. 
 
 1393 
 
 the two branches, and drawing them from the point o, in Fig 207 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. 
 
 R! = 12 U=.05 R 2 =4 Ki^.00012 
 
 -A/WWoWtfMA/V— [=> 
 
 £-g 
 
 O- 
 
 E.M.F.=100 
 
 L 2 =.015 R 3 =10 L 3 =.03 
 
 Fig. 206. 
 R 2 -=4 
 
 Ri<=42 
 
 ■^=.0619 
 
 Fig. 207. 
 
 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 ^~\ 10~ 9 . 
 
 L per mile = (80.5 + 740 log ~\ 10 -6 . 
 
 in which L is the inductance in henrys of each wire, A is the interatrial dis- 
 tance between the two wires, and d is the diameter of each, both in inches. 
 If the circuit is of iron wire, the formulas become 
 
 L per foot = (2286 + 140.3 log ~\ 10 -9 . 
 h per mile = (l2070 + 740 log 2A} lO" 8 , 
 
1394 
 
 ELECTRICAL ENGINEERING. 
 
 Inductance, in Millihenrys per Mile, for Each of Two Parallel 
 Copper Wires. 
 
 Interaxial 
 
 
 
 
 American Wire Gauge Number. 
 
 
 
 
 Distance, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ins. 
 
 0000 
 
 000 
 
 00 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 6 
 
 1 130 
 
 1,168 
 
 1 205 
 
 1,242 
 
 1,280 
 
 1,317 
 
 1.354 
 
 1 392 
 
 1,466 
 
 1.540 
 
 1,615 
 
 1 690 
 
 12 
 
 1 353 
 
 1 391 
 
 1 428 
 
 1,465 
 
 1.502 
 
 1.540 
 
 1.577 
 
 1 614 
 
 1.689 
 
 1,764 
 
 1,838 
 
 1 913 
 
 24 
 
 1.576 
 
 1.614 
 
 1.651 
 
 1.688 
 
 1.725 
 
 1.764 
 
 1.800 
 
 1.838 
 
 1.912 
 
 1.986 
 
 2.061 
 
 2,135 
 
 36 
 
 1 707 
 
 1 745 
 
 1 784 
 
 1 818 
 
 1 856 
 
 1.893 1.931 
 
 1 968 
 
 2 043 
 
 2.117 
 
 2 192 
 
 2 7,66 
 
 60 
 
 1 871 
 
 1,909 
 
 1 946 
 
 1 982 
 
 2.023 
 
 2.058 2.095 
 
 2 132 
 
 2 208 
 
 2 282 
 
 2 356 
 
 2.432 
 
 96 
 
 2.023 
 
 2.059 
 
 2.097 
 
 2.134 
 
 2.172 
 
 2.2102.246 
 
 2.283 
 
 2.358 
 
 2.433 
 
 2.507 
 
 2.582 
 
 Capacity of Conductors. — All conductors are included in three 
 classes, viz.: 1. Insulated conductors with metallic protection; 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 formula taken from Crocker's " Electric Lighting." 
 
 -, „ * l 7361 k 10 -15 _ 
 
 Class 1. C per foot = , — (D ^ ,y , C per mile== 
 
 ™ ' ~ , . 7361 X 10 -15 _ ., , 
 
 Class 2. C per foot = log(4ft + d) , C per mile = ^ft 
 
 38. 83 k 10~ 9 
 ,-„ (D * d) * 
 38.83 X 10~ 9 
 
 Class 3 
 
 ,.t 
 
 per foot of each wire : 
 
 3681 X IO-1 5 
 
 log (2A+d) 
 w ., , . . 19.42 X 10-° 
 
 C per mile of each wire = log ( 2 A+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 
 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. 208). 
 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° 
 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 shown in Fig. 209. 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. 
 
 Fig. 208. 
 
ALTERNATING CURRENTS. 
 
 1395 
 
 The four-wire system of distribution is shown in Fig. 210. The two 
 phases are entirely independent, and for lighting purposes may be operated 
 as two single-phase circuits. 
 
 g ^txro ; (S^^QQQQa 
 
 Fig. 209. 
 
 Fig. 210. 
 
 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. 211. 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. 
 
 ^ffiffiffi. 
 
 Fig. 211. 
 
 Fig. 212. 
 
 The Y connection is shown in Fig. 212. 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 composed of lights, they must be equally loaded 
 or the lights will fluctuate. If the three circuits are perfectly balanced, 
 the lights will remain steady. In this form of connection each wire may 
 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 point 
 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. 213. 
 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. 210. 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 operation, the result will be correct. If the circuits are per- 
 fectly balanced, twice the reading of one wattmeter will be the total power. 
 
 Fig. 213. 
 
1396 
 
 ELECTRICAL ENGINEERING. 
 
 The power of two-phase currents distributed by three wires may oe 
 measured by two wattmeters as shown in Fig. 209. 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 e/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. 214 if the system is 
 Y-connected, and as in Fig. 215 if the system is A-connected. The sum of 
 
 Fig. 214. 
 
 Fig. 215. 
 
 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. 216. If the power factor of the system is greater 
 than 0.50, the arithmetical 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 dis- 
 turbing the relative connection of their coarse- and fine-wire coils. If the 
 deflections of the needles are reversed, 
 the difference of the readings is the 
 power. If the needles are deflected in 
 the same direction as at first, the sum of 
 the readings is the power. 
 
 Alternating-current Generators. — 
 These differ little from direct current 
 generators in many respects. Any direct- 
 current generator, if provided with col- 
 lector rings instead of a commutator, 
 could be used as a single-phase alternator. 
 The frequency would in most cases, how- 
 ever, be too low for any practical use. 
 The fields of alternators are always 
 separately excited; the machines are 
 sometimes compounded by shunting some of their own current around the 
 fields through a rectifying device which changes the current to pulsating 
 direct current. In all large machines the armature is stationary and the 
 field magnets Tevolve. 
 
 Fig. 216. 
 
 ALTERNATING-CURRENT CIRCUITS. 
 
 Calculation of Alternating-current Circuits. — The following 
 formulae and tables are issued by the General Electric Co. They afford a 
 convenient method of calculating the sizes of conductors for, and determin- 
 ing 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 
 the conductors are less than 18 inches apart, the loss of voltage is de- 
 creased, and vice versa. 
 
 
ALTERNATING-CURRENT CIRCUITS. 
 
 1397 
 
 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 consumer's 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. 
 
 Area of conductor, circular mils = 
 
 DX WXK. 
 
 PXE* 
 
 Current in main conductors = W X T -s- E 
 Volts lost in lines = PXEXM -f- 100; 
 D*X WX KX A 
 
 Pounds copper = 
 
 P X E* X 1,000,000 
 
 The following tables give values for the various constants: 
 
 
 
 Values 'or M — Wires 18 In. Apart.* 
 
 
 
 
 
 ,-—25 Cycles - 
 
 
 , 40 Cycles * 
 
 , 60 Cycles - 
 
 
 
 125 Cycles — » 
 
 Factors— 
 
 .95 .90 .85 
 
 .80 
 
 95 .90 .85 80 
 
 95 .90 .85 
 
 80 
 
 .95 
 
 .90 .85 80 
 
 
 
 
 
 
 
 
 0000 
 
 1.17 1 16 1.12 
 
 1 (M. 
 
 1.32 1.36 1.36 1 32 
 
 1.53 1/64 1.67 
 
 
 2 21 
 
 2 54 .2.72 2.76 
 2 22.2 34 2:37 
 
 000 
 
 1 12 1.09 1 05 
 
 99 
 
 1.24 1.26- 1.24 1.19 
 
 1 41 1 49 1 ,50 
 
 1 47 
 
 1.97 
 
 00 
 
 108 1.0,4 99 
 
 97 
 
 1 18 1 18 1.14 1.09 
 
 1.32 1 36; 1.35 
 
 1 11 
 
 1 77 
 
 1 96 2.04 2.04 
 
 
 
 1.05 1.00 94 
 
 a? 
 
 1 13 1 II 1.06 1.01 
 
 1.24 1.26 1.24 
 
 1 19 
 
 1.61 
 
 1.74 -180 1.79 
 
 1 
 
 1 .02 .96 .90 
 
 81 
 
 1.09 1 05 1 00 .94 
 
 1.18 1 17 1.14 
 
 1 ,)H 
 
 1 47 
 
 1.57 1 59 1.56 
 
 2 
 
 1.00 .93 .86 
 
 79 
 
 1 .05 1 01 .,95 ,88 
 
 1.12 1.10 1 06 
 
 1 (HI 
 
 1.37 
 
 1 42 1 42 1 39 
 
 3 
 
 98 .91 .84 
 
 M 
 
 1.02 .97 .90 83 
 
 1.08 1.05 .99 
 
 91 
 
 1 27 
 
 1 30 1 28 t 24 
 
 
 .96 ,89 .81 
 
 74 
 
 100 .94 .86 .80 
 
 1.05 1.00- .94 
 
 .87 
 
 1 20 
 
 1 21 1 18 1 13 
 
 5 
 
 .95 .88 .80 
 
 77, 
 
 .98 ;92 .84 .77 
 
 1 .02 .97 .90 
 
 Hi 
 
 1.15 
 
 1.13 1 09 1 03 
 
 * 
 
 ,94 .86 .78 
 
 7(1 
 
 97 .90 .82 .74 
 
 1 00 94 .87 
 
 79 
 
 1.10 
 
 1.07 1.02 .96 
 
 7 
 
 .94 .85 .77 
 
 69 
 
 .95 .88 .80 .72 
 
 98 ..91 .84 
 
 76 
 
 1 06 
 
 1.02 .96 „90 
 
 8 
 
 .93 .85 .76 
 
 AH 
 
 94 .87 .79 ,71 
 
 .97 .89 .82 
 
 74 
 
 1 03 
 
 .98 .92' 85 
 
 <> 
 
 .92 .84 .76 
 
 6/ 
 
 94 .86 .77 .69 
 
 .95 ,88 .801 
 
 7? 
 
 1 01 
 
 .95 .88 81 
 
 10 
 
 .92 .83. .75 
 
 .67 
 
 ,93 .85 .76 .68- 
 
 .94- .86. .79 
 
 .71 
 
 .99 
 
 .92 .85 .78 
 
 
 Wires 36 in. Apart, t 
 
 '■ JT-(.+i*a.«)«*r«. 
 
 
 
 0000 
 
 1.22 1.23 1.20 
 
 \ 15 
 
 
 
 000 
 00 
 
 
 1.16 1.15 111 
 III 1.08 I-.04 
 1.07 1.03 .98 
 
 1.05 
 .97 
 91 
 
 X ■= Reactance. 
 
 ft, = Resistance, ohms per 1 000 ft. at 60° F. (Wire 100% 
 
 Matthiessen's standard.) 
 
 1 
 
 2 
 
 104 .99 .93 
 
 1 02 .95 89 
 
 86 
 .82 
 
 X = 0.000882 [logio 0) + 0.109 J 
 
 
 
 
 t For higher volt- 
 ages. 10.000-200,000. 
 
 / 
 
 = inches between wire 
 = radius of wire.rtnche 
 = cycles per sec. 
 
 Sj 
 
 
 Per cent of 
 
 Value of K. 
 
 Value of T. 
 
 <0 ' 
 
 3-3 
 
 Power Factor. 
 
 100 
 
 95 1 85 
 
 80 
 
 100 
 
 95 
 
 85 
 
 80 
 
 
 System: 
 
 2160 
 1080 
 1080 
 
 2400 
 1200 
 1200 
 
 3000 
 1500 
 1500 
 
 3380 
 1690 
 1690 
 
 1.00 
 0.50 
 0.58 
 
 1.05 
 0.53 
 61 
 
 1.17 
 0.59 
 68 
 
 1.25 
 0.62 
 7? 
 
 6 04 
 
 
 12.08 
 
 Three-phase, 3-wire 
 
 9 06 
 
 
 
 
 
 
 *P should be expressed as a whole number, not as a decimal; thus a 5 
 per cent loss should be written 5 and not .05. 
 
1398 
 
 ELECTRICAL ENGINEERING 
 
 Relative Weight of Copper Required ill 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-wire. 1 . 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 0.750 
 
 " " m 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 alternating 
 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 o£ 
 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 
 lln ® \ 2 miles long, as required by the example. 
 
 , *! *£ ls desired to ascertain the size of wire which will give 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 in- 
 versely as the per cent energy loss 
 
 di3tance9 to which 100 kw. three-phas3 current can be transmitted over dlffer- 
 ent'Sizes of Wires at Deferent Potentiaxs, Assummimg an Enefgt Loss Of 10% 
 and A Power Factor of 85% 
 
 Num- 
 1 ber 
 B.&S. 
 
 Circular 
 Mils. 
 
 Distance of Transmission for Various Potentials 
 
 at Receiving End, in feet 
 
 2.000 
 
 3,000 
 
 4.000 
 
 5.000 
 
 6.000 
 
 8,000 
 
 10.Q00 | 12,000 
 
 15.000 
 
 20,000 
 
 25,000 
 
 30,000 
 
 6 
 9 
 4 
 
 26,250 
 33JOO 
 41.740 
 
 1 32 
 
 1 66 
 2.10 
 
 2.98 
 3.75 
 4.74 
 
 5.28 
 8.40 
 
 8 27 
 10.40 
 13 15 
 
 11 92 
 15.00 
 18.96 
 
 21.12 
 26.56 
 33.60 
 
 33 1 
 
 41.6 
 52.6 
 
 47 68 
 60 00 
 75 84 
 
 74 50 
 93 75 
 118.50 
 
 132 4 
 166.4 
 210.4 
 
 206 75 
 260 00 
 328 75 
 
 298 
 375 
 474 
 
 3 
 
 2 
 1 
 
 52,630 
 66,370 
 83,690 
 
 2.54 
 3 33 
 4.21 
 
 5.96 
 7.51 
 9 48 
 
 10.16 
 13.32 
 16,84 
 
 16.55 
 20.85 
 26 32 
 
 23.84 
 30 04 
 37.92 
 
 40.64 
 53 28 
 67.36 
 
 66.2 
 83.4 
 HJ5.3 
 
 95 36 
 120.16 
 151.6* 
 
 149 00 
 187.75 
 212.00 
 
 254.8 
 333 6 
 421.2 
 
 413 75 
 
 521.25 
 658.00 
 
 596 
 751 
 948 
 
 
 
 00 
 ( 000 
 
 105,500 
 133,100 
 .167,800 
 
 5.29 
 6 71 
 8.45 
 
 11 92 
 15.11 
 19 04, 
 
 21.16 
 26 84 
 33 80 
 
 33 10 
 41 97 
 52 85 
 
 47 68 
 60.44 
 76.16 
 
 84.64 
 
 107 36 
 135.20 
 
 132 4 
 167 9 
 211.4 
 
 191 72 
 241 76 
 304.64 
 
 298 00 
 377 75 
 476.00 
 
 529 6 
 671 6 
 845.6 
 
 827 50 
 1049.25 
 1321 25 
 
 1192 
 1511 
 1904 
 
 ,0000 
 
 211.600 
 250.000 
 500,000 
 
 10 62 23 92 
 12.58 28.33 
 25.17 56 66 
 
 42 48 
 50 32 
 100 68 
 
 66 42 
 78.67 
 157 35 
 
 95.68 
 113 32 
 226 64 
 
 169.92 
 
 201 28 
 402 72 
 
 265 7 
 314 7 
 629 4 
 
 382 72 
 453 28 
 906 56 
 
 598.00 
 708,25 
 I4I6 1 50 
 
 1062 8 
 1258 8 
 2517 6 
 
 1660.50 
 1966 75 
 3933 75 
 
 2392 
 2833 
 5666 
 
 Notes on High-tension Transmission. (General Electric Co., 1909.)- 
 The cross-sectional area and, consequently, weight of conductors varies 
 inversely as the square of the voltage for a given power transmission. 
 The cost of conductors is therefore reduced 75% every time the voltage 
 is doubled. The cost of other apparatus and appliances increases with, 
 increasing voltage. In the longest lines, from about 190 miles up, the 
 saving in copper with the highest practicable voltages is so great that the 
 
ALTERNATING-CURRENT CIRCUITS. 
 
 1399 
 
 other expenses are rendered practically negligible. In the shorter lines, 
 however, from about one mile to 60 or 75 miles, the most suitable voltage 
 must be determined in each individual case. The voltages in the follow- 
 ing table will serve as a guide. 
 
 Voltages Advisable for Various Line Lengths. 
 
 Miles. 
 
 Volts. 
 
 Miles. 
 
 Volts. 
 
 Miles. 
 
 Volts. 
 
 1 
 
 1-2 
 2-3 
 
 500-1000 
 1000-2300 
 2300-6600 
 
 3-10 
 10-15 
 15-20 
 
 6,600-13,200 
 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 higher 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. 
 
 Inches. 
 
 Volts. 
 
 Inches. 
 
 Volts. 
 
 Inches. 
 
 5,000 
 15,000 
 30,000 
 
 28 
 40 
 48 
 
 45,000 
 60,000 
 75,000 
 
 60 
 
 72 
 84 
 
 90,000 
 105,000 
 120,000 
 
 96 
 108 
 120 
 
 Skin Effects. — For the frequencies and sizes of cables used In trans- 
 mission lines, skin effect does not appreciably alter the resistance; for 
 example, the resistance of a solid copper wire 3/ 4 in. diameter at 60 cycles 
 is increased only 21/2%, the resistance of a stranded cable of the same 
 external diameter being increased a still smaller amount. This refers 
 only to non-magnetic materials; with steel cable skin effect cannot be 
 neglected, and a calculation must be made for it. 
 
 Frequency. — So far as the transmission line alone is concerned, the 
 lower frequencies are the more desirable, because they reduce the in- 
 ductance drop and charging current. Oscillations of dangerous magni- 
 tude are less likely with the lower frequencies than with the higher. The 
 A.I.E.E. recognizes two frequencies, viz: 25 and 60, as standard, but 
 frequencies of 15 and in some cases 12.5 are being advocated. 
 
 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 copper, 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. 
 
1400 
 
 ELECTRICAL ENGINEERING. 
 
 «100 VoltT*] k-100 Voft 
 
 100 Turns 
 
 100 Turns 
 
 MJULX 
 
 innywoinri 
 
 86 Turns 
 
 (70 o qOooo" 
 
 100 Tunu 
 
 ^60 Volts- 
 
 U 
 
 -50 Vr- 
 
 -60 Volts- 
 
 Fig. 217. 
 
 TRANSFORMERS, CONVERTERS, ETC. 
 
 Transformers. — A transformer consists essentially of two coils of wire, 
 one coarse and one fine, wound upon an iron core. The function of a trans- 
 former is to convert electrical energy from one potential to another. 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 " trans- 
 former. 
 
 The relation of the primary and secondary vol- 
 tages depends on the number of turns in the two 
 coils. Transformers may also be used to change 
 current of one phase to current of another phase. 
 The windings and the arrangement of the trans- 
 formers must be*adapted to each particular case. 
 In Fig. 217 an arrangement is shown whereby 
 two-phase currents may be converted into three- 
 phase. Two transformers are required, one 
 having its primary and secondary coils in the 
 relation of 100 to 100, and the other having its 
 primary and secondary in the relation of 100 
 to 86. The secondary of the 100-to-100 trans- 
 former is tapped at its middle point and joined to one terminal of the 
 other secondary. Between any pair of the three remaining terminals of 
 the secondaries there will exist a difference of potential of 50. 
 
 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 PR loss due to heat. If It, Ri, be the current and resistance 
 respectively of the primary, and I 2 , R2, the current and resistance respec- 
 tively of the secondary, then the total copper loss is W c =It 2 Rt +/ 2 2 ^2 and 
 
 the percentage of copper loss is — — ^sr~^ — " » wnere 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. 
 
 Transformers are sometimes cooled by means of forced air or water cur- 
 rents or by immersing them in oil, which tends to equalize the temperature 
 in all parts of the transformer. 
 
 Efficiency of Transformers. — 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 consider- 
 ably 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-K.W. 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 = 0.15K.W. 
 
 Copper loss, 1/2 load = 0. 15 X (V2) 2 = 0.0375 K.W. 
 
 Iron loss K. W. hours = 0. 15 X24 = 3.6. 
 
 Copper loss, full load, K. W. hours = 0. 15 X3 = 0.45. 
 
 Copper loss, 1/2 load, K.W. hours = 0.0375 X2= 0.075. 
 
 Output, K.W. hours =H (10 X3) +(5 X2) }-=40. 
 
 Input, K.W. hours = 40+3.6+0.45+0.075 = 44.125. 
 
 All-day efficiency = 40 -5- 44. 125 = 0.907. 
 The transformers heretofore discussed are constant-potential trans- 
 formers 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. 
 
ELECTRIC MOTORS. 1401 
 
 Converters, etc. — In addition to static transformers, various ma- 
 chines arc used for the purpose of changing the voltage of direct currents 
 or the voltage phase or frequency of alternating currents, and also for 
 changing alternating currents to direct or vice versa. These machines are 
 all rotary and are known as rotary converters, motor-dynamos, and 
 dynamotors. 
 
 A rotary converter consists of a field excited by the machine itself, and 
 an armature which is provided with both collector rings and a commuta- 
 tor. It receives direct current and changes it to alternating, working as a 
 direct-current motor, or it changes alternating to direct current working 
 as a synchronous motor. 
 
 A motor-dynamo consists of a motor and a dynamo mounted on the 
 same base and coupled together by a shaft. 
 
 A dynamotor has one field and two armature windings on the same core. 
 One winding performs the functions of a motor armature, and the other 
 those of a dynamo armature. 
 
 A booster is a machine inserted in series in a direct-current circuit to 
 change its voltage. It may be driven either by an electric motor or other- 
 wise. 
 
 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. 
 
 ELECTRIC MOTORS. 
 
 Classification of Motors. — (From the Standardization Rules of 
 the A. I, E. E.) 
 
 a. Constant-speed Motors, in which the speed is either constant or does 
 not materially vary; such as synchronous motors, induction motors with 
 small slip, and ordinary direct-current shunt motors. 
 
 b. Multi-speed Motors (two-speed, three-speed, etc.), which can be op- 
 erated at any one of several distinct speeds, these speeds being practically 
 independent of the load, such as motors with two armature windings. 
 
 c. Adjustable-speed Motors, in which the speed can be varied gradually 
 over a considerable range; but when once adjusted remains practically 
 unaffected by the load, such as shunt motors designed for a considerable 
 range of field variation. 
 
 d. Varying-speed Motors, or motors in which the speed varies with the 
 load, decreasing when the load increases; such as series motors. 
 
 The selection of a motor for a specified service involves, 
 
 a. Mechanical ability to develop the requisite torque and speeds, as 
 given by its speed-torque curve. 
 
 6. Ability to commutate successfully the current demanded. 
 
 c. Ability to operate in service without occasioning a temperature rise 
 in any part which will endanger the life of the insulation. 
 
 The nominal rating, or the horse-power output which a motor can give 
 with a rise of temperature not exceeding 90 degrees at the commutator 
 and 75 degrees at any other part after an hour's run on a test stand is a 
 method of designating motors which is in common usage, though it is 
 not a proper measure of service capacity. 
 
 Motor Classification of the Am. Assn. of Electric Motor Manu- 
 facturers. (Elec. Jour., Aug. 1909.) — Alternating-current motors and 
 direct-current motors can easily be classified under the same speed head- 
 ings, and this has been done as below. 
 
 A. — Constant Speed Motors — in which the speed is either constant 
 or does not vary materially, such as synchronous motors, induction motors 
 with small slip, ordinary direct-current shunt motors, and direct current 
 
1402 
 
 ELECTRICAL ENGINEERING. 
 
 compound-wound motors, the no-load speed of which is not more than 
 20 per cent higher than the full-load speed. 
 
 B. — Multi-Speed Motors — (two-speed, three-speed, etc.) — which can 
 be operated at any one of several distinct speeds, these speeds being 
 practically independent of the load, such as direct-current motors with 
 two armature windings and induction motors with primary windings 
 capable of being grouped so as to form different numbers of poles. 
 
 C. — Adjustable Speed Motors. — - (1) Shunt-wound motors in which 
 the speed can be varied gradually over a considerable range, but when 
 once adjusted remains practically unaffected by the load, such as motors 
 designed for a considerable range of speed by field variation. 
 
 (2) Compound-wound motors in which the speed can be varied 
 gradually over a considerable range, as in (1), and, when once adjusted, 
 varies with the load, similar to compound-wound constant-speed motors 
 or varying-speed motors, depending upon the percentage of compounding. 
 
 D. — ■ Varying Speed Motors, or motors in which the speed varies with 
 the load, decreasing when the load increases, such as series motors and 
 heavily compounded motors. Examples of heavily compounded motors 
 are those designed for bending roll service and mill service, in which 
 shunt-winding is provided only to limit the light-load operating speed. 
 
 Many motor applications can be made more intelligently if, in addition 
 to using the classification given above, the service is described in terms of 
 continuous or intermittent duty, and load constant or varying. In order 
 to make this point clear, the following table has been prepared, giving 
 one example of each of the different classes of service. Practically every 
 motor application can be listed under one or the other of these headings. 
 
 Classification of Motors. 
 
 Constant. 
 Adjustable. 
 Varying. 
 Multi-speed. 
 
 Duty. 
 
 Continuous. 
 
 Intermittent. 
 
 Continuous. 
 
 Intermittent. 
 
 Continuous. 
 
 Intermittent. 
 
 Continuous. 
 
 Intermittent. 
 
 Load. 
 
 {Constant. 
 Varying. 
 {Constant. 
 Varying. 
 ( Constant. 
 \ Varying. 
 | Constant. 
 ( Varying. 
 | Constant. 
 ( Varying. 
 ( Constant. 
 1 Varying. 
 | Constant. 
 I Varying. 
 
 {Constant. 
 Varying. 
 
 Example. 
 
 Fan. 
 
 Line-shaft. 
 Vacuum pump. 
 Paper-cutter. 
 Paper calender. 
 Printing press. 
 Vacuum pump. 
 Lathe. 
 Small fan. 
 Bending press. 
 House pump. 
 Crane. 
 Fan. 
 * 
 
 Fire pump. 
 
 The Auxiliary-pole Type of Motor. (J. M. Hippie, El. Jour., May, 
 1906.) — 
 
 Among the methods of controlling the motor speed, the most satis- 
 factory is the single voltage direct-current system in which the variation 
 of speed is obtained by. shunt-field control. The insertion of resistance 
 in the shunt-field circuit varies the strength of the magnetic field, and as 
 the strength of field is decreased the speed of the motor is increased in 
 direct proportion. 
 
 An ordinary shunt- wound motor operating under the above conditions 
 over a speed range of four to one will spark excessively at the brushes 
 unless the motor is rated considerably under its normal capacity. This 
 sparking is due principally to the weakened magnetic field and to the 
 distortion or shifting of this field due to reaction on it by the field produced 
 by the ampere turns in the armature. 
 
 The use of an auxiliary field by correcting this condition produces 
 
 *Multi-speed motors are at present almost exclusively alternating- 
 current motors. The classes of service in which these motors are used are 
 limited, but a considerable field may develop later. 
 
ELECTRIC MOTORS. 1403 
 
 sparkless commutation and a condition of practical stability of field and 
 consequently of speed in the motor. This auxiliary field is produced by 
 a winding in series with the armature and placed on pole-pieces midway 
 between the main pole-pieces. The distortion at the point of commuta- 
 tion which would occur if there was no auxiliary winding is prevented by 
 the field produced by the auxiliary winding. This field being always 
 proportional to the load the commutation is accomplished sparkle, sly at 
 all loads up to heavy overloads. 
 
 Motors of this type are reversible with no change in setting of brushes 
 or other adjustment. The brushes being fixed in the neutral position it 
 is only necessary to reverse the current in both auxiliary field and arma- 
 ture to secure exactly similar operating conditions in the reverse as in the 
 forward direction. 
 
 Speed of Electric Motors. — Any direct-current motor, no matter 
 what its type of field winding, if supplied with current of constant potential 
 at its terminals, will run at constant speed if its field strength and the load 
 do not change. The speed of a given motor is directly proportional 
 to the net impressed e.m.f. divided by the effective field strength. The 
 net impressed e.m.f. is that part of the supply e.m.f. which must be 
 exactly opposed by the counter e.m.f. of the armature. Thus, if the 
 supply voltage is 250 volts, the lead 50 amperes and the armature circuit 
 resistance 0.2 ohm, the net impressed e.m.f. will be 240 volts, because the 
 armature drop is 0.2 x50= 10 volts. The " effective " field strength Is 
 the actual field flux set up by the fieid winding after overcoming the arma- 
 ture reaction, which always weakens the field slightly. 
 
 In the case of a shunt-wound motor operated on a constant-potential 
 circuit with an adjustable external resistance in series with the armature, 
 no matter at what point the external resistance may be set, so long as it 
 remains at that point, giving unchanging voltage at the motor terminals, 
 the speed will be constant unless the field strength or load be altered, 
 The speed of a series-wound motor increases very rapidly with decreasing 
 load when operated on a constant-potential circuit, becoming so high at 
 no load as to be destructive to the armature. The reason for this is that 
 the armature current passes also through the field winding, so that any 
 decrease in armature current weakens the field and causes the speed to 
 increase far beyond the rate it would attain with a constant field. (C.P. 
 Poole, Power, July, 1907.) 
 
 The speed of a shunt motor is dependent upon the details of its entire 
 design. The following equation shows the relation of the speed to the 
 main elements of the machine: 
 
 (E-I a R a )c 10 8 
 
 W= MpN ' 
 
 where E is the impressed electromotive force, R a the resistance of the 
 armature, I a the current through it, c the number of parallel circuits for 
 the current through the armature, M the magnetic flux (number of lines 
 of force) per pole, p the number of poles, N the number of armature con- 
 ductors, and n the speed in revolutions per second. (El. Review, July 17, 
 1909.) 
 
 The simplest form cf an electric motor is the shunt-wound machine. 
 When connected with an ordinary electric lighting circuit, it. runs at a 
 steady speed, drawing hardly any current until it is required to furnish 
 power, and at that moment it consumes power only in proportion to the 
 work done. If connected to a circuit of lower pressure, it will run equally 
 well, but at lower speed. If required to make extra effort, as in starting 
 machinery, it will furnish up to five times its full power without trouble. 
 
 When running free, if its speed is increased by the application of exter- 
 nal power, as by a belt, it becomes a dynamo and pumps current into the 
 line; this, in turn, throws work upon the machine and tends to slow it 
 down. The machine is, therefore, in itself a factor tending to the pres- 
 ervation of constancy of speed and to the preservation of constancy in 
 the pressure on the circuit, and it is ideal in its simplicity, having abso- 
 lutely no governing or accessory parts. 
 
 The shunt-wound motor runs at practically constant speed under all 
 loads, and if closer uniformity of speed is desired, it can be arranged to 
 run within any desired limits of variation by setting the brushes in a 
 position shifted slightly from their usual place, or by adding to the field 
 
1404 ELECTRICAL ENGINEERING. 
 
 winding a few turns, connected in series with the armature, and reversed 
 in comparison with the main winding. Either of these arrangements 
 causes the motor to speed up under load, and the extent of this action 
 may be adjusted to equal precisely the tendency ordinarily met of slowing 
 down under load. (S. S. Wheeler, Elec. Age, Dec, 1904.) 
 
 Speed Control of Electric Motors. Rheostats. (The Electric Con- 
 troller and Mfg. Co.) — A motor of any size, when its armature is at rest, 
 offers a very low resistance to the flow of current and an excessive and 
 perhaps destructive current would flow through it if it were connected 
 across the supply mains while at rest. Take the case of a motor adapted 
 to a normal full-load current of 100 amperes and having a resistance of 
 0.25 ohm; if this motor were connected across a 250- volt circuit a current 
 of 1,000 amperes would flow through its armature — in other words, it 
 would be overloaded 900% with consequent danger to ils windings and 
 also to the driven machine. In the case of the same motor, with a rheostat 
 having a resistance of 2.25 ohms inserted in the motor circuit, at the time 
 of starting the total resistance to the flow of current would be the resist- 
 ance of the motor (0.25 ohm) plus the resistance of the rheostat (2.25 
 ohms), or a total of 2.5 ohms. Under these conditions exactly full-load 
 current, or 100 amperes, would flow through the motor, and neither the 
 motor nor the driven machine would be overstrained in starting. This 
 shows the necessity of a rheostat for limiting the flow of current in starting 
 the motor from rest. 
 
 An electric motor is simply an inverted generator or dynamo — con- 
 sequently when its armature begins to revolve a voltage is generated within 
 its windings just as a voltage is generated in the windings of a generator 
 when driven by a prime-mover. This voltage generated within the moving 
 armature of a motor opposes the voltage of the circuit from which the 
 motor is supplied, and hence is known as a " counter-electromotive force." 
 The net voltage tending to force current through the armature of a motor 
 when the motor is running is, therefore, the line voltage minus the counter- 
 electromotive force. 
 
 In the case of the motor above cited, when the armature reaches such 
 a speed that a voltage of 125 is generated within its windings, the effective 
 voltage will be 250 minus 125, or 125 volts, and, therefore, the resistance 
 of the rheostat may be reduced to one ohm without exceeding the full- 
 load current of the motor. As the armature further increases its speed 
 the resistance of the rheostat may be further reduced until when the motor 
 has almost reached full speed all of the rheostat may be cut out, and the 
 counter-electromotive force generated by the motor will almost equal 
 the voltage supplied by the line so that an excessive current cannot flow 
 through the armature. 
 
 In practice, a rheostat is provided for starting an electric motor, the 
 resistance conductor being divided into sections, such that the entire 
 length or maximum resistance of the rheostat is in circuit with the motor 
 at the instant of starting and the effective length of the conductor, and 
 hence its resistance may be reduced as the motor comes up to speed. 
 
 In cutting out the resistance of a starting rheostat care must be used 
 not to cut it out too rapidly. If the resistance is cut out more rapidly 
 than the armature can speed up-, a sufficient counter-electromotive force 
 will not be generated to properly oppose the flow of current, and the 
 motor will be overloaded. 
 
 If all the resistance of the starting rheostat is not cut out the motor will 
 operate at reduced voltage, and hence at less than normal speed. A 
 rheostat so arranged that all or a portion of its resistance may be left in 
 a motor circuit to secure reduced speeds is called a " rheostatic controller." 
 Such rheostatic controllers are used for controlling series and compound- 
 wound motors driving cranes, and similar machinery requiring variable 
 speed under the control of an operator. 
 
 In a series- wound motor the speed varies inversely as the load — the 
 lighter the load the higher the speed. A series-wound motor of any size 
 when supplied with full voltage under no load, or a very light load, will 
 " run, away " just as will a steam-engine without a governor when given 
 an open throttle. 
 
 For a given load a series-wound motor draws the same current irrespec- 
 tive of the speed and for a given load the speed varies directly as the volt- 
 age. The speed at a given load may be varied by varying the resistance 
 
ELECTRIC MOTORS. 1405 
 
 in the motor circuit — in the meantime if the load on the motor be con- 
 stant the current drawn from the line will be constant regardless of the 
 
 The above statements relate to the use of a rheostat in series with a 
 series-wound motor. If a resistance or rheostat be placed in parallel 
 with the field of a series- wound motor the speed will be increased instead 
 of decreased at a given load. This is known as shunting the field of the 
 motor. This shunt would never be applied till the motor has been brought 
 up to normal full speed by cutting out the starting resistance. With a 
 " shunted field " a motor is driving a load at a speed higher than normal 
 and therefore requires a correspondingly increased current. 
 
 If a resistance is placed in parallel with the armature of a series motor, 
 the motor will operate at less than normal speed when all of the starting 
 resistance has been cut out. This connection is known as a " shunted 
 armature connection " and is useful where a low speed is desired at light 
 loads and is particularly useful in some cases where the load becomes a 
 negative one, that is, where the load tends to overhaul the motor, as in 
 lowering a heavy weight. 
 
 A shunt-wound motor, unlike a series motor, when supplied with full 
 voltage, maintains practically a constant speed regardless of variations in 
 load within the limits of its capacity. It automatically acts like a steam- 
 engine having a very efficient governor. 
 
 The speed of a shunt-wound motor may be decreased below normal by 
 a rheostatic controller in series with its armature and may be increased 
 above normal by means of a rheostat in series with its field winding. The 
 latter rheostat is known as a " field rheostat," and, to be effective, must 
 have a high resistance owing to the small current which flows through the 
 shunt-field winding. 
 
 A compound-wound motor is a hybrid between a series and shunt- 
 wound motor and its characteristics are likewise of a hybrid nature. 
 
 A compound-wound motor will not " run away " under no load as will 
 a series motor, but its speed decreases as the load increases, though not 
 so rapidly as is the case with a series-wound motor. 
 
 The characteristics of a compound-wound motor are particularly valu- 
 able in cases where the load is subject to wide variation. It will give a 
 strong torque in starting and driving heavy loads and at the same time 
 will not race dangerously when the load is suddenly relieved. 
 
 The speed of a compound-wound motor may be reduced below normal 
 by means of a rheostat in the circuit of its armature. The speed may be 
 increased above normal by shunting and even short-circuiting the series 
 field winding, and may be still further increased by means of a field rheostat 
 in series with the shunt-field winding. 
 
 Rheostatic controllers are also employed for the control of alternating 
 current induction motors of the so-called " slip-ring type." Such motors 
 have characteristics in many ways similar to those of direct current shunt- 
 wound motors, and speeds lower than normal may be obtained by insert- 
 ing resistance in series with the windings of the secondary or rotor. 
 
 Selection of Motors for Different Kinds of Service. (F. B. Crocker 
 and M. Arendt, El. World, Nov., 1907.)— The types of direct-current 
 motor are as follows: 
 
 DIRECT-CURRENT MOTORS. 
 
 Type. Operative Characteristics. 
 
 Shunt-wound motors Starting torque usuallv 50 to 100 per cent 
 
 greater than rated running torque, and 
 
 fairly constant speed over wide load 
 
 ranges. 
 Series-wound motors Powerful starting torque, speed varying 
 
 greatly (inversely) with load changes. 
 Compound-wound motors.. . .Compromise between shunt and series 
 
 types. 
 Differently-wound motors ...Starting torque very small, speed can be 
 
 made almost absolutely constant for load 
 
 changes within rated capacity. 
 
 The conditions under which machinery operates, in regard to varying 
 speed and power required of the driving motor, may be divided into four 
 
1406 ELECTRICAL ENGINEERING. 
 
 classes, and certain types of motors are usually best suited to these divi- 
 sions, which are as follows: 
 
 (a) Work which requires the motor to operate automatically at a 
 practically constant speed, regardless of load changes or other conditions. 
 
 (6) Work requiring frequent starting and stopping and wide varia- 
 tions in speed, including sometimes rapid acceleration. 
 
 (c) An approximately steady load or work that varies as some function 
 of the speed should it change. 
 
 (d) Work in which the power varies regardless of the speed, or where 
 speed variations with constant torque may be desired. 
 
 The first case (a) applies to line-shaft equipments with many machines 
 operated by the same motor and where slight speed variations may be 
 allowed; the direct-current shunt or slightly compounded motor or the 
 alternating-current induction motor would answer, depending upon the 
 character of electric current available. A refinement of this problem is 
 encountered in the driving of textile machinery, especially silk looms, with 
 which even a slight speed variation might affect the appearance of the 
 finished product. In such instances the alternating-current. motors, poly- 
 phase induction or polyphase synchronous, are generally employed be- 
 cause the speed of direct r current motors varies considerably with voltage 
 changes and the variation in temperature which occurs after several hours 
 of operation, whereas the speed of the alternating-current motors, unless 
 the voltage varies greatly, is primarily dependent upon the frequency 
 of the supplied current. 
 
 The second class (b) is divided into two parts, the first being electric 
 traction and crane service, in which the motor is frequently started and 
 stopped and rapidly accelerated at starting; or where the speed is to be 
 adjusted automatically to the load, slowing down when heavily loaded 
 or climbing a steep grade. These conditions are well satisfied by the 
 series motor of either the direct or alternating-current types, depending 
 upon the current supplied. Elevator service is of this character as regards 
 frequent starting and stopping, but after rapid acceleration it calls for 
 a speed independent of the load. Hence, to fulfill both requirements, 
 elevator motors when of direct-current type are heavily over-compounded 
 to give the series characteristic at starting; then, when the motor is up 
 to speed, the series field winding is short-circuited and it operates as a 
 shunt machine. Recently, however, two-speed shunt motors have been 
 employed for this service, the field being of maximum strength for start- 
 ing and sparking prevented by use of inter-poles. If only alternating 
 current is available the polyphase induction motor should be employed, 
 but for powerful starting torque either slip-ring or compensator control 
 would be necessary. For the second subdivision of this clr.ss the motor 
 must be started and stopped frequently and not rapidly accelerated, but 
 on the contrary simply " inched " forward at the start, as in the operation 
 of printing presses, gun turrets, etc. These conditions of service are 
 satisfied by a direct-current compound motor provided with double 
 armature and series-parallel control of the machine. 
 
 The third class (c) of work is the operation of pumps, fans or blower 
 equipments and its requirements are satisfied by the series motor, whose 
 speed adjusts itself to the work, and also because it exerts the maximum 
 torque required at starting. It must be, however, either geared or directly 
 connected to the apparatus, because the breaking of the belt or the sudden 
 removal of the load would cause a series motor to race and become injured. 
 The operation of pumps by electric motors is usually effected by gearing, 
 since ordinary plunger pumps do not operate efficiently if driven in excess 
 of fifty strokes per minute, and to accomplish this by direct connection 
 would demand a very low speed and costly motor. Centrifugal pumps 
 operating at high speed may be direct driven. 
 
 The fourth class (d) is found in individual machine-tool service, for 
 which the maximum allowable cutting or turning speed requires the 
 number of revolutions of the work or tool to vary inversely as the diameter 
 of the cut. This condition is satisfied best by the direct-current shunt or 
 slightly compounded motors, as they are readily controlled in speed by 
 variation of the applied voltage, shunt field weakening, etc. 
 
 It is to be noted that (a) and (c) regulate automatically to maintain a 
 constant speed while (6) and (d) are controlled by hand to give variable 
 speeds. Furthermore, (6) is usually under control of the hand all the time, 
 
ELECTRIC MOTORS. 1407 
 
 whereas (d) is set to operate at a desired speed for some time and regulates 
 automatically when so adjusted. 
 
 The Electric Drive in the Machine-Shop. (A. L. De Leeuw, 
 Trans. A.S.M.E., 1909.) — Absence of reliable data is apparent all over 
 the field of this subject, and it will therefore be impossible to say before- 
 hand with any fair degree of certainty how much, if anything, can be 
 gained by the conversion of a shop from a shaft to motor drive. 
 
 Nothing but an exhaustive study of the entire plant in all its aspects 
 will clearly show what may be accomplished. The saving of power is 
 by no means the only nor the most important economy resulting from a 
 conversion to electric drive, and such a conversion may even be highly 
 economical, though there be an actual loss in power consumed. 
 
 The question whether alternating or direct current should be used is 
 especially difficult of solution, and there is a wide difference of opinion 
 among engineers as to which is best. Given a plant covering a large area 
 and using large amounts of current, of which only a small portion is used 
 for variable-speed machinery, and of sufficient size to permit of the use of 
 a separate unit for lighting current, then alternating current would be the 
 logical solution. On the other hand, given a compact plant, using a large 
 portion of the power for variable-speed machinery, direct-driven by mo- 
 tors, and of which the lighting load is small in the daytime, then it would 
 be natural to select direct current. As a rule, however, conditions are not 
 so simple. Of late the problem has been complicated by the fact that 
 many machine tools may be had with single-pulley drive, to which an 
 alternating-current or a direct-current motor is equally applicable. 
 
 The points in favor of the alternating-current motor are: 
 
 a High break-down point; that is, the motor goes on with no material 
 change of speed under very heavy overload. 
 
 b Freedom from commutator trouble. This is especially valuable 
 where fine chips are made, or where compressed air is used in connection 
 with the machine. The better makes of direct-current motors are now 
 equally free from this kind of trouble. 
 
 c Most cities are now lighted by alternating current, so that city cur- 
 rent can be used in smaller plants, provided the machine tools are arranged 
 for this kind of motor. 
 
 The points in favor of the direct-current motor are: 
 
 a Wider air-gap, allowing a greater amount of wear in the bearings 
 before the motor has to be repaired. 
 
 b The possibility of power and lighting-loads on the same circuits with- 
 out the poor regulation due to inductive load. 
 
 c The possibility of using variable-speed motors. This is, perhaps, 
 the greatest argument in favor of the direct-current motor. Though it is 
 possible to run a great many machine tools by a motor, yet one of the 
 greatest advantages of such a drive is not available, unless the motor is of 
 the variable-speed variety. 
 
 The combination of alternating and direct current has its advantages, 
 especially where it is possible to purchase current from some large power 
 company which delivers its product as alternating current. Transformers 
 reduce the voltage at the entrance to the shop, and the low-voltage alter- 
 nating current can be used for all purposes except for driving variable- 
 speed motors, and perhaps some auxiliary apparatus such as magnetic 
 clutches, lifting magnets, etc. 
 
 See also papers on this subject by Chas. Robbins and John Riddell, 
 Trans. A.S.M.E., 1910. 
 
 Choice of Motors for Machine Tools. (Chas. Fair, Proc. A. I.E. E., 
 1910.) — Shunt-wound direct-current, or squirrel-cage rotor, alternating 
 current: For bolt cutter; boring machine; boring mill; boring bar; center- 
 ing machine; chucking machine; boring, milling and drilling machines; 
 drill, radial; drill press; grinder-tool, etc.; keyseater, milling-broach ; lathe; 
 milling machine; pipe-cutter; saw, small circular; screw machine; tapper. 
 
 Compound-wound direct-current, or squirrel-cage rotor: For grinder- 
 castings; reciprocating keyseater; saw, cold bar and I-beam; saw, hot; 
 shaper; slotter; tumbling barrel or mill. 
 
 Compound-wound direct-current or squirrel-cage rotor, or squirrel- 
 cage rotor with high starting torque: For bolt and rivet header; bulldozer; 
 bending machine; corrugating roll; punch press; shear. 
 
 Other machines may be driven as indicated below, (a) shunt, (&> 
 
1408 ELECTRICAL ENGINEERING. 
 
 compound, (c) series, direct-current motors, (d) squirrel-cage rotor, 
 (e) ditto, high starting torque, (/) slip ring induction motor with external 
 rotor resistance. Raising and lowering cross rails oo boring mills and 
 planers, (&), (c), (e). Bending rolls, (6), (c), (/). Gear cutters, (a), (b), 
 (d). Drop hammers, (6), (e). Tire lathes, (/) may be used, as it allows 
 for slowing down when cutting hard spots. Lathe carriages, (c), (e). 
 Heavy slab milling, (a), (&), (d). Planers, (6), (d), (e). Planers, rotary, 
 («), (&), (d). Swaging, (b), (d), (e). Shunt motors are used in the follow- 
 ing cases: when the 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 lineshaft drives, etc. 
 
 Compound-wound motors are used where there are sudden calls for 
 excessive power of short duration, as on planers, punch presses, etc. 
 
 Series motors should be used where speed regulation is not essential 
 and where excessive starting torque and slow starting speeds are required, 
 as for operating cranes. 
 
 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. Series motors, however, should never be 
 used when the motor can run without load, as the speed would accelerate 
 beyond the point of safety. 
 
 The alternating current motor of the squirrel-cage rotor type corresponds | 
 to the constant-speed, shunt, direct-current motor, but with a high-resist- 
 ance rotor it approaches more closely the characteristics of a compound 
 direct-current motor. Variable speed machines, driven by squirrel-cage 
 rotors must 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 would 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 rev. 
 per min., and are made for both constant horse-power and constant 
 torque. These motors would be used where alternating current only was 
 available, or direct current limited; and the speed range of the motor, 
 together with one or two change gears, would give the required speeds. 
 
 ALTERNATING-CURRENT MOTORS. 
 
 Synchronous Motors. — Any alternator may be used as a motor, pro- 
 vided it be brought into synchronism with the generator supplying the cur- 
 rent to it. The operation of the alternating-current motor and generator 
 is similar to the operation of two generators in parallel. It is necessary to 
 supply direct current to the field. The field circuit is left open until the ma- 
 chine is in phase with the generator. If the motor has the same number of 
 poles as the generator, it will run at the same speed; if a different number, 
 the speed will be that of the generator multiplied by the ratio of the number 
 of poles of the motor to that of the generator. Single-phase, synchronous 
 motors are not self-starting. . Polyphase motors may be made self-starting, 
 but it is better to bring the machines to speed by independent means before 
 supplying the current. The machines may be started by a small induc- 
 tion motor, the load on the synchronous motor being thrown off, or the 
 field may be excited by a small direct-current generator belted to the 
 motor, and this generator may be used as a motor to start the machine, 
 current to run it being taken from a storage battery. If the field of a 
 synchronous motor be properly regulated to the load, the motor will 
 exercise no inductive effect on the line, and the power factor will be 1. If 
 the load varies, the current in the motor will either lead or lag behind the 
 e.m.f. and will vary the power factor. If the motor be overloaded so that 
 there is a diminution of speed, the motor will fall out of step with the 
 generator and stop. 
 
ALTERNATING-CURRENT MOTORS. 1409 
 
 Synchronous motors are often put on the same circuit with induction 
 motors. The synchronous motor in this case may, by increasing the field 
 excitation, be made to cause the current to lead, while the induction motor 
 will cause it to lag. The two effects will thus tend to balance each other 
 and cause the power factor of the circuit to approach 1. 
 
 Synchronous motors are best used for large units of power at high volt- 
 ages, where the load is constant and the speed invariable. They are un- 
 satisfactory where the required speed is variable and the load changes. 
 Two great disadvantages of the synchronous motor are its inability to 
 start under load and the necessity of direct-current excitation. 
 
 Induction Motors. — The distinguishing feature of an induction motor 
 is the rotating magnetic field. It is thus explained: In Fig. 218 let ab, cd 
 be two pairs of poles of a motor, a and b being wound from one leg or pair 
 of wires of a two-phase alternating circuit, and c and d from the other 
 leg, the two-phases being 90° apart. At the instant when a and b are 
 receiving maximum current so as to make a a north 
 pole and b a south pole, c and d are demagnetized, and 
 a needle placed between the poles would stand as 
 shown in the cut. During the progress of the cycle of 
 the current the magnetic flux at a decreases and that at 
 c increases, causing the point of resultant maximum 
 intensity to shift, and the needle to move clockwise 
 toward c. A complete rotation of the resultant point 
 is performed during each cycle of the current. An 
 armature placed within the ring is caused to rotate sim- j> IG 218 
 
 ply by the shifting of the magnetic field without the use 
 of a collector ring. The words " rotating magnetic field " refer to an 
 area of magnetic intensity and must be distinguished from the words 
 " revolving field," which refer to the portion of the machine constituting 
 the field magnet. 
 
 The field or " primary " of an induction motor is that portion of the 
 machine to which current is supplied from the outside circuit. 
 
 The armature or " secondary " is that portion of the machine in which 
 currents are induced by the rotating magnetic field. Either the primary 
 or the secondary may revolve. In the more modern machines the second- 
 ary revolves. The revolving part is called the " rotor," the stationary 
 part the " stator." The rotor may be either of the ring or the drum type, 
 the drum type being more common. A common type of armature is the 
 " squirrel-cage." It consists of a number of copper bars placed on the 
 armature-core and insulated from it. A copper ring at each end connects 
 the bars. The field windings are always so arranged that more than one 
 pair of poles are produced. This is necessary in order to bring the speed 
 down to a practical limit. If but one pair of poles were produced, with a 
 frequency of 60, the revolutions per minute would be 3600. 
 
 The revolving part of an induction motor does not rotate as fast as the 
 field, except at no load. When loaded, a slip is necessary, in order that the 
 lines of force may cut the conductors in the rotor and induce currents 
 therein. The current required for starting an induction motor of the squir- 
 rel-cage type under full load is 7 or 8 times as great as the current for 
 runningat full load. A type of induction motor known as " Form L," built 
 by the General Electric Co., will start with the full-load current, provided 
 the starting torque is not greater than the torque when running at full load. 
 
 Induction motors should be run as near their normal primary e.m.f. as 
 possible, as the output and torque are directly proportional to the square 
 of the primary pressure. A machine which will carry an overload of 50 
 per cent at normal e.m.f. will hardly carry its full load at 80 per cent of the 
 normal e.m.f. 
 
 Induction Motor Applications. (A. M. Dudley, Elec. Jour., July, 
 1908.) Squirrel-Cage Motors for Constant Speed Service. — 
 
 Motor-Generator Sets. — Small starting torque is required and good 
 speed regulation, which characteristics are preeminently met by a squirrel- 
 cage motor with very low resistance in the secondary rings. A fair speci- 
 fication on a large set is that it shall start on 30 to 40% of full voltage, 
 and draw current not in excess of IV4 times full-load current. 
 
 Pumps. — With a centrifugal pump decreasing the head pumped against 
 increases the load on the motor. This type of pump will raise considerably 
 more than four-thirds the amount of water 30 feet that it will 40 feet, 
 with the result that the motor is overloaded if it is designed for 40 ft. 
 
1410 
 
 ELECTRICAL ENGINEERING. 
 
 head. In this the centrifugal pump is exactly opposite to the plunger 
 or reciprocating pump, which, being positive in its action, increases its 
 load with increase of head and vice versa. [In some modern types of 
 centrifugal pump the load decreases with decrease of head after reaching 
 the maximum load corresponding to the head for which the pump is 
 designed. See catalogue of the De Laval Steam Turbine Co., 1910. W. K.] 
 
 Induction Motor Applications. 
 
 
 Squirrel Cage. 
 
 Phase- Wound . 
 
 Constant Speed. 
 
 Variable Speed. 
 
 Constant Speed. 
 
 Variable Speed. 
 
 ! —Motor-generator 
 
 1 — Starting mo- 
 
 1 — Flour mills. 
 
 1 — Hoists and 
 
 sets. 
 
 tors. 
 
 2 — Paper ma- 
 
 winches . 
 
 2— Pumps. 
 
 2 — Crane motors 
 
 chinery, pulp 
 
 2 — Cranes. 
 
 3 — Blowers. 
 
 3— Fly-wheel 
 
 grinders, 
 
 3— Elevators. 
 
 4 — Line-shaft drive. 
 
 service. 
 
 beaters. 
 
 4— Fly-wheel mo- 
 
 5 — Cement machin- 
 
 Punches, 
 
 3— Belt convey- 
 
 tor-generator 
 
 ery. 
 
 Shears, etc. 
 
 ors. 
 
 sets. 
 
 6 — Wood-working 
 
 4 — Sugar centri- 
 
 4 — Wood planers. 
 
 5 — Steel mill ma- 
 
 machinery (ex- 
 
 fugals. 
 
 5 — Air compress- 
 
 chinery, charg- 
 
 cept planers). 
 
 5 — Laundry ex- 
 
 ors. 
 
 ing machines, 
 
 7— Cotton-mill ma- 
 
 tractors. 
 
 6 — Line shafting. 
 7 — Driving-wheel 
 
 hoists. 
 
 chinery. 
 
 6 — Brake motors 
 
 6 — Coal and ore 
 
 8 — Paper machin- 
 
 7— Cross-head 
 
 lathes. 
 
 unloaders. 
 
 ery, calenders, 
 
 motors. 
 
 
 7 — Dredging ma- 
 
 Jordan engines. 
 
 8 — Valve motors. 
 
 
 chinery. 
 
 9 — Concrete mixers. 
 
 
 
 8— Shovels. 
 
 9 — Mine haulage. 
 
 Blowers.— Rotary blowers, except positive blowers, have a charac- 
 teristic similar to centrifugal pumps, in that the load varies with the 
 amount of air delivered and becomes less as the pressure against which 
 the blower is working increases. That is to say, the maximum load 
 which could be put on a motor driving a blower of this nature would be to 
 take away all delivery pipes and let the blower exhaust into the open air. 
 
 Line Shafting. — Squirrel-cage motors are used very successfully 
 for driving line-shafting where the idle belts are run on loose pulleys, in 
 this way keeping down the starting torque. 
 
 Cement Mills. — The possibility of entirely covering the bearings and 
 the absence of all moving contacts make the squirrel-cage motor succe?s- 
 • ful where the more complicated construction and moving contact sur- 
 faces of the wound secondary motor or the direct-current machine are 
 damaged by accumulation of dust. In starting up a tube mill it must 
 be rotated through nearly 90% before the charge of pebbles and cement 
 begins to roll. This makes the starting condition severe and a motor 
 should have a starting torque of not less than twice full-load torque to 
 do the work. 
 
 Wood-working Machinery. — On account of high friction and great 
 inertia, the starting torque is sometimes so high and of so long duration 
 (thirty seconds to one minute) that it is better to apply a wound-secondary 
 motor. 
 
 Paper Machinery. — If calenders are driven with a constant speed 
 motor it is necessary to make some provision either by mechanical speed- 
 changing devices or a small auxiliary motor for securing a slow threading 
 speed. 
 
 Squirrel-Cage Variable Speed Motors. — These motors in general have 
 high resistance end rings, high slip and high starting torque. The 
 torque increases automatically as the speed decreases. In these general 
 respects they resemble a direct-current series motor and are in fact fitted 
 for the same class of work, with the added advantage that they have a 
 limiting speed and cannot run away under light load. 
 
 Fly-Wheel Service. — In driving tools which are used with fly-wheels 
 such as punches, shears, straightening rolls and the like, the usefulness 
 
ALTERNATING-CURRENT MOTORS. 1411 
 
 of high slip comes in, as if the fly-wheel is to give up its energy, it is 
 obliged to slow down in speed when the load comes on. A motor with 
 good regulation and low slip would try to run at constant speed, carrying 
 the fly-wheel and load as well, but the motor in question " lies down " 
 and allows the fly-wheel to carry the peak load, speeding up again when 
 the peak has passed. 
 
 Centrifugals. — In sugar centrifugals is an application where the sole 
 purpose of the motor is to accelerate the load to full speed, in say thirty 
 seconds, where it is allowed to run one minute and then shut down to 
 repeat the cycle a minute later. The centrifugal consists of a cylindrical 
 basket with perforated walls and mounted around a vertical shaft as an 
 axis. The same principle is used in laundry extractors where the wet 
 linen is placed in a similarly perforated basket and the water whirled out 
 by centrifugal force. 
 
 Constant-Speed Motors with Phase-wound Secondaries. — There are 
 classes of service which require a heavy starting torque combined with 
 close speed regulation after the motor is up to speed. These require- 
 ments are exactly met by a motor with a phase-wound secondary. 
 The secondary winding itself has a very low resistance, which means a 
 small " slip," high running efficiency and power-factor and good regula- 
 tion when the secondary is short-circuited. The insertion of external 
 resistance enables the motor to develop maximum torque at the start 
 with a moderate starting current. 
 
 Flour-Mills. — The number of line shafts, belts and gears in flour 
 mills makes a very heavy starting condition and the nature of the product 
 and its quality demand absolute speed within a few revolutions per 
 minute. The best solution is the phase-wound rotor. 
 
 Other Examples. — There is another class of machinery which is not 
 so exacting about regulation but which has the same feature of heavy 
 starting and runs continuously after once up to speed. Under this head 
 come most of the applications of this type of motor. They are, paper 
 pulp grinders, which, on account of the inertia of the grindstones, are 
 hard to start; pulp beaters; belt conveyors, which may be required to 
 start when full of coal, rock or cement crushers; air compressors, which 
 have a high starting friction because of the construction and the number 
 of parts; line shafting where the belts run for the most part on the work- 
 ing pulleys and are therefore heavy to start. Under the best possible 
 conditions, if line shafting is employed, the loss of power from this source 
 alone, due to friction, is 25 to 30% and may run up to 40 or 50%. This 
 is a strong argument for individual drive of machines wherever practicable. 
 
 Motors with Phase-wound Secondaries for Variable Speed Service. — 
 The application, which is typical of this class, is found in hoist and 
 crane service. Motors for this work are designed for intermittent oper- 
 ation and given a nominal rating based upon the horse-power which 
 they will develop for one-half hour with a temperature rise of 
 40° C. They never operate for as long a period as thirty minutes 
 continuously and they are called upon at times to develop a torque 
 greatly in excess of their nominal rating. For these reasons motors of 
 this class should never be applied on a horse-power basis, but always on 
 a torque basis. Since torque is the main consideration and the service 
 is intermittent these motors are usually wound for the maximum torque 
 which they will develop and given a nominal rating based upon one-third 
 to one-half of this torque. Double drum hoists, hoisting in balance, and 
 large mine haulage propositions in general require a motor rated on a 
 different basis. For this service the motor should have the necessary 
 maximum torque and be able to develop for about two or three hours, 
 with a safe rise in temperature, a horse-power equivalent to the square 
 root of the mean square requirement of the hoisting cycle. These are 
 only general rules and the most careful consideration should be given in 
 each individual case to secure a motor which will perform the work 
 satisfactorily. 
 
 Coal and Ore Unloading Machinery. — Dredges — Power-Shovels. — 
 Owing to the complication of the cycle of operation there is more diffi- 
 culty in providing a motor for this apparatus than in the case of a plain 
 hoist. Usually the number of cycles per hour given is the maximum 
 which the apparatus can develop and in practice it will not be possible 
 to operate at so high a speed. This in itself is somewhat of a factor of 
 
1412 r ELECTRICAL ENGINEERING. 
 
 safety, though not one which can be relied upon, as the test for accept- 
 ance is ordinarily made at the contract number of operations per hour. 
 
 The most impressive application of motors of this class and perhaps 
 in the operation of any electrical apparatus is the fly-wheel motor-gen- 
 erator set for hoisting or heavy reversing roll service in steel mills. Ser- 
 vice of this nature is extremely fluctuating in its requirements, having 
 very great peaks one instant and almost nothing the next. This is a 
 severe strain on the generating plant from which power is being drawn. 
 
 Alternating-Current Motors for Variable Speed. (W. I. Slichter, 
 Trans. A.S.M.E., 1903.) — 
 
 The speed of an alternating-current motor may be controlled in a 
 number of ways: 
 
 (a) By varying the potential applied to the primary of a motor having 
 a suitable resistance in the secondary. 
 
 (b) By varying the resistance in the secondary circuit. 
 
 (c) By changing the connections of the primary in a manner to change 
 the number of poles. 
 
 (d) By varying the frequency of the applied voltage. 
 
 The changeable pole and variable frequency methods are the most 
 efficient, but do not permit of a variation through a wide range of speed. 
 The rheostatic control is the simplest and easiest of control, giving a range 
 from standstill to full speed, but is not as efficient as the first two, although 
 more efficient than potential control. The last mentioned has the dis- 
 advantages of low efficiency and considerably increased heating in the 
 motor itself, and is also unstable at low speeds, say below one-third speed. 
 That is, a small variation in torque or a smaller variation in voltage will 
 cause a considerable variation in speed. 
 
 Mr. Geo. W. Colles, in a discussion of Mr. Schlichter's paper, says that 
 the variable-speed induction-motor problem has not yet been solved. 
 
 Of the four possible methods given, the first is the simplest, as here it is 
 merely necessary to insert a compensator in circuit with the motor. This, 
 however, is decidedly unsatisfactory, as, owing to the necessity of having 
 a high-resistance secondary, even the full-speed efficiency of the motor is 
 largely reduced, while at quarter-speed it is about 17%, and even at half- 
 speed only 37%. 
 
 All the other solutions given are too complicated, and they cannot be 
 regarded as other than makeshifts. The resistance-in-secondary method 
 is the only one that has been used to any extent. This nullifies the meri- 
 torious natural features of the squirrel-cage motor, whose complete freedom 
 from exposed contacts, commutator and slip-rings made it much simpler, 
 and therefore cheaper, than the direct-current motor; and it now becomes 
 more expensive and delicate, and considerably less efficient. The effi- 
 ciency is now but 65% at 3/ 4 load, 43% at V2 load, and only 22 % at 1/4 
 load. 
 
 SIZES OF ELECTRIC GENERATORS AND MOTORS. 
 (Condensed from Bulletins of the General Electric Co., 1910.) 
 
 Direct-connected Engine-driven Railway Generators. Form S. 
 
 6-pole, Kw 100 150 200 200 200 
 
 Speed, r.p.m 275 200 200 150 120 
 
 8-pole, 300 Kw., 120 and 100 r.p.m.; 400 Kw., 150, 120 and 100 r.p.m.; 
 
 500 Kw., 120 r.p.m. 
 10-pole, 500 Kw., 100 and 90 r.p.m. 14-pole, 800 Kw., 100 and 80 r.p.m. ; 
 14-pole, 1000 Kw., 100 and 80 r.p.m.; 1200-Kw., 80 r.p.m., 16-pole, 1600 
 
 Kw., 100 and 75 r.p.m. 
 20-pole, 2000 Kw., 75 r.p.m.; 24-pole, 2500 Kw., 75 r.p.m.; 26-pole, 2700 
 Kw., 90 r.p.m. 
 
 Slow and Moderate Speed Belt-driven Generators. Type CL. 
 Form B. 
 
 (6 poles, Kw . 
 Speed, 125 and 250 volts 
 Slow 1 Speed, 500 volts 
 Speed j 6-poles, Kw. 
 
 I Speed, 125 and 250 volts 
 LSpeed, 500 volts 
 
 Moderate ( 6 poles, Kw 
 
 Speed 1 Speed, 125, 250 and 500 v. 
 
 16 
 
 22 
 
 22 
 
 
 30 
 
 40 
 
 750 
 
 900 
 
 725 
 
 
 700 
 
 650 
 
 815 
 
 850 
 
 725 
 
 
 700 
 
 650 
 
 55 
 
 75 
 
 100 
 
 
 150 
 
 
 625 
 
 550 
 
 550 
 
 
 550 
 
 
 625 
 
 550 
 
 525 
 
 
 455 
 
 
 25 
 
 35 
 
 45 
 
 60 
 
 75 
 
 90 
 
 1100 
 
 1050 
 
 975 925 
 
 850 
 
 750 
 
ELECTRIC GENERATORS AND MOTORS. 
 
 1413 
 
 40 
 
 25 
 
 25 
 
 35 
 
 50 
 
 785 
 
 675 
 
 650 
 
 600 
 
 730 
 
 635 
 
 610 
 
 560 
 
 800 
 
 675 
 
 650 
 
 600 
 
 90 
 
 125 
 
 185 
 
 
 500 
 
 470 
 
 440 
 
 
 470 
 
 440 
 
 410 
 
 
 500 
 
 500 
 
 430 
 
 
 55 
 
 70 
 
 85 105 
 
 150 
 
 900 
 
 850 
 
 800 700 
 
 
 845 
 
 800 
 
 750 655 
 
 490 
 
 Slow and Moderate Speed Belt-driven Motors. Type CL.. Form B. 
 '6 poles, Kw 20 
 
 125 and 250 volts, speed. 690 
 110 and 220 volts, speed. 650 
 
 Slow j 500 volts, speed 750 
 
 Speed ] 6 poles, Kw. 65 
 
 125 and 250 volts, speed. 575 
 110 and 220 volts, speed. 540 
 
 .500 volts, speed .„. 575 
 
 f 6 poles, Kw 30 
 
 Moderate i 125, 250 and 500 volts, 
 
 Speed j speed 1025 975 
 
 (.110 and 220 volts, speed 965 915 
 
 After a continuous run of 10 hours, at full-rated load, the rise in tem- 
 perature above that of the surrounding air, as measured by the ther- 
 mometer, will not exceed the following: Armature, 35° C. ; Commutator, 
 40° C, Field, 45° C. The motors will operate for two hours at 25% 
 overload, and withstand a momentary overload of 50% without injurious 
 heating. 
 
 Belt-driven Alternators. Form P. Revolving Field. 
 
 Poles 6 
 
 Kw 30 
 
 Speed 1200 
 
 Amperes at ( balanced 3- phase load 7 . 5 
 
 full load j balanced 2-phase load 6.5 
 
 2300 volts (single-phase load 10 
 
 Built with or without direct-connected exciters. Adapted to 2- or 
 3-phase windings without change except in the armature coils. Poten- 
 tials, 3-phase, 240, 480, 600, 1150, 2300; 2-phase, 240, 480, 1150, 2300. 
 When used as synchronous motors these machines have a condenser 
 effect, and in consequence can be used to improve the power factor 
 when used in combination with induction motors. 
 
 The full-load single-phase rating at 100% power factor is 80% of the 
 full-load 3-phase rating at both 100% and 80% power factor. The full- 
 load single-phase rating at any power factor from 100 to 80% is the unity 
 power factor single-phase rating multiplied by the power factor. For 
 instance, for the 8-100-900 machine, which is the full-load 3-phase rating 
 unity and 80% power factor, the single-phase rating for 100% at both 
 power factors is 80 Kw., and for 80% power factor it is 80 X 0.8= 64 Kw. 
 
 Slow and Moderate Speed Machines with Commutating Poles. 
 
 Generators, Type DLC, Form A. 
 
 6 
 
 8 
 
 8 
 
 12 
 
 12 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 
 
 1200 
 
 900 
 
 900 
 
 600 
 
 600 
 
 12.5 
 
 18.8 
 
 25 
 
 37.5 
 
 50 
 
 11 
 
 16.5 
 
 22 
 
 33 
 
 44 
 
 16.5 
 
 24.5 
 
 33 
 
 49 
 
 65 
 
 Slow Speed. 
 
 Moderate Speed. 
 
 
 Poles. 
 
 Kw. 
 
 Speed. 
 
 Kw. 
 
 Speed. 
 
 Frame. 
 
 125 v. 
 250 v. 
 
 500 v. 
 
 575 v. 
 
 125 v. 
 250 v. 
 
 500 v. 
 
 575 v. 
 
 1 
 
 4 
 
 20 
 
 950 
 
 950 
 
 1050 
 
 30 
 
 1300 
 
 1300 
 
 1425 
 
 2 
 
 4 
 
 25 
 
 900 
 
 900 
 
 1000 
 
 40 
 
 1200 
 
 1200 
 
 1325 
 
 3 
 
 4 
 
 35 
 
 850 
 
 850 
 
 950 
 
 50 
 
 1150 
 
 1150 
 
 1250 
 
 4 
 
 6 
 
 45 
 
 775 
 
 775 
 
 850 
 
 65 
 
 1100 
 
 1100 
 
 1200 
 
 5 
 
 6 
 
 60 
 
 750 
 
 750 
 
 825 
 
 80 
 
 1050 
 
 1050 
 
 1150 
 
 6 
 
 6 
 
 75 
 
 700 
 
 700 
 
 775 
 
 100 
 
 1000 
 
 1000 
 
 1000 
 
 7 
 
 6 
 
 100 
 
 675 
 
 675 
 
 750 
 
 125 
 
 950 
 
 950 
 
 1050 
 
 8 
 
 6 
 
 125 
 
 650 
 
 650 
 
 700 
 
 150 
 
 900 
 
 875 
 
 900 
 
 9 
 
 6 
 
 150 
 
 600 
 
 600 
 
 650 
 
 200 
 
 *850 
 
 775 
 
 850 
 
 10 
 
 6 
 
 200 
 
 *500 
 
 500 
 
 550 
 
 300 
 
 *750 
 
 700 
 
 750 
 
 * Not to be made for 125 volts. 
 
1414 
 
 ELECTRICAL ENGINEERING. 
 
 Motors, Type DLC. 
 
 Slow Speed. 
 
 Moderate Speed. 
 
 Frame 
 
 Poles 
 
 H.P 
 
 
 Speed. 
 
 
 125 v. 
 250 v. 
 
 115v. 
 230 v. 
 
 550 v. 
 
 1 
 
 4 
 
 20 
 
 825 
 
 800 
 
 925 
 
 2 
 
 4 
 
 25 
 
 775 
 
 750 
 
 875 
 
 3 
 
 4 
 
 35 
 
 725 
 
 700 
 
 825 
 
 4 
 
 6 
 
 50 
 
 675 
 
 650 
 
 750 
 
 5 
 
 6 
 
 65 
 
 650 
 
 625 
 
 700 
 
 6 
 
 6 
 
 80 
 
 625 
 
 600 
 
 675 
 
 7 
 
 6 
 
 100 
 
 600 
 
 575 
 
 650 
 
 8 
 
 6 
 
 125 
 
 575 
 
 550 
 
 625 
 
 9 
 
 6 
 
 175 
 
 525 
 
 500 
 
 575 
 
 10 
 
 6 
 
 250 
 
 *450 
 
 425 
 
 500 
 
 Speed. 
 
 125 v. 115 v. 
 250 v. 230 v. 
 
 1150 
 1100 
 1050 
 1000 
 950 
 900 
 825 
 775 
 *725 
 *675 
 
 1100 
 1050 
 1000 
 .950 
 900 
 850 
 800 
 750 
 700 
 650 
 
 1250 
 1200 
 1150 
 1100 
 1025 
 975 
 925 
 850 
 750 
 675 
 
 * Not to be made for 125 or 115 volts. 
 
 The first eight sizes are made with enclosed and partly enclosed as 
 well as open casings. For the several types of casings the horse-powers 
 are as below: 
 
 H.P., Slow Speed. 
 
 H.P., Moderate Speed. 
 
 Frame 
 
 Open 
 
 Semi- 
 En- 
 closed. 
 
 En- 
 closed 
 Venti- 
 lated. 
 
 Totally 
 
 En- 
 closed. 
 
 Frame 
 
 Open 
 
 Semi- 
 En- 
 closed. 
 
 En- 
 closed 
 Venti- 
 lated. 
 
 Totally 
 
 En- 
 closed. 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 20 
 25 
 35 
 50 
 65 
 80 
 100 
 125 
 
 20 
 25 
 35 
 50 
 65 
 80 
 100 
 125 
 
 20 
 25 
 35 
 50 
 65 
 80 
 100 
 125 
 
 10 
 
 12V2 
 
 171/2 
 
 25 
 
 30 
 
 40 
 
 50 
 
 60 
 
 1 
 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
 30 
 40 
 55 
 70 
 90 
 125 
 150 
 175 
 
 30 
 40 
 55 
 70 
 90 
 125 
 150 
 175 
 
 30 
 40 
 55 
 70 
 90 
 125 
 150 
 175 
 
 15 
 20 
 27 
 
 Small Moderate Speed Engine-driven Alternators. 
 
 Poles 24 26 28 32 36 
 
 Kw 50 75 105 150 240 
 
 Speed 300 276 257 225 200 
 
 Amperes at ( balanced 3-phase load. 12.6 17.6 26.5 37.6 60 
 
 full load \ balanced 2-phase load. 10.8 15.2 23 33 52 
 
 2300 volts ( single-phase load 15 21 32 45 73 
 
 Potentials, 3-phase, 240, 480, 600, 1150, 2300; 2-phase, 240, 480, 1150, 
 2300. 
 
 Box-Frame Type of Railway Motors. Four Field Coils. 
 H.P., 18, 42, 45, 75, 50, 75, 100, 125, 160, 170, 200, 225. 
 The first two sizes are for 24-in. gauge, the next two for 36-in., and the 
 others for standard gauge. 
 
 Commutating Pole Railway Motors. 
 
 Made in six sizes 50 to 200 H.P. Wound for 600 volts. The two 
 smallest have split frames: the others box frames. 
 
 The commutating poles, located between the main exciting pole pieces, 
 are connected up with their windings in series with one another and with 
 the armature. The magnetic strength of the commutating poles varies 
 
ELECTRIC GENERATORS AND MOTORS. 
 
 1415 
 
 therefore with the current through the armature, and a magnetic field is 
 produced of such intensity as to properly reverse the current in the 
 armature coils short-circuited during commutation. The pole pieces are 
 so proportioned and wound as to compensate for armature reaction, and 
 practically non-flashing and sparkless commutation is insured up to the 
 severest overloads. As the magnetizing current around the commutating 
 poles is reversed with the armature, the poles perform their functions 
 equally well in whichever direction the motors are running. 
 
 Due to the good commutating characteristics of commutating pole 
 railway motors, their overload capacities are considerably increased, and 
 a more rugged form of motor is obtained which is less 'subject to injury 
 through careless handling by motormen than the present standard rail- 
 way motor. 
 
 Small Polyphase Motors. 
 
 60-cycle, 4-pole, 1800 r.p.m., H.P., V 6 , V4, V2, 3 /4, 1, 1 V2, 2, 3, 5, 7V.2, 
 10, 15. 
 
 60-cycle, 4-pole, 1200 r.p.m., H.P., 1/4, 1/2, 3 /4, 1, IV2, 2, 3, 5, 71/2. 
 
 60-cycle, 8-pole, 900 r.p.m., H.P., 1/4, V2, 3 /4, 1, 2, 3, 5. 12-pole, 600 
 r.p.m.,H.P., 1/4, 1/2, 3 /4, 1, 2, 3. 
 
 40-cycle, 4-pole, 1200 r.p.m., H.P., 1/4, 1/2, 1, IV2, 2, 3, 5. 6-pole, 800 
 r.p.m., H.P., 1/4, V2, 1, 2, 3,. 
 
 25-cycle, 2-pole, 1500 r.p.m., H.P., 1/4, V2, 1, 2, 3, 5, 71/2. 
 
 25-cycle, 4-pole, 750 r.p.m., H.P., 1/4, V3, V2, 1, 2, 3, 5. 6-pole, 500 
 r.p.m., H.P., 1/4, ¥2, 1, 2, 3. 
 
 The speeds given are synchronous speeds. Full-load speeds are from 
 93 to 97% of the synchronous. 
 
 Motors below 1 H.P. are adapted for 110 and 220 volts; others for 
 110, 220, 440 and 550 volts. 
 
 Single-phase Motors, 110 and 220 volts. 
 
 60-cycle, 4-pole, 1800 r.p.m., H.P., 1/4, ty& 1, 2, 3, 5, 7 1/2, 10, 15. 
 60-cycle, 6-pole, 1200 r.p.m., H.P., 1/4, V2, 1, 1 V2, 2, 3, 5, 71/2, 10. 
 25-cycle, 2-pole, 1500 r.p.m., H.P., 1/4, ¥2, 3 /4, 2, 3, 5, 71/2, 10. 
 25-cycle, 4-pole, 750 r.p.m., H.P., 1/4, 1/2, 1, IV2, 2, 3, 5. 
 
 Type CQ Motors. Continuous Current. 
 
 No. of 
 Poles 
 
 3 
 3 
 5 
 5 
 
 71/2 
 71/2 
 10 
 
 10 
 
 * Speed (Shunt-Wound Motors). 
 
 110 v. 
 
 115v. 
 
 125 v. 
 
 220 v. 
 
 230 v. 
 
 250 v. 
 
 500 v. 
 
 550 v. 
 
 600 v. 
 
 2200 
 
 2300 
 1850 
 
 2450 
 1950 
 
 2200 
 1800 
 
 2300 
 1850 
 
 2450 
 1950 
 
 
 
 
 1800 
 
 2100 
 
 2250 
 
 2400 
 
 1600 
 
 1650 
 
 1750 
 
 1600 
 
 1650 
 
 1750 
 
 1850 
 
 2000 
 
 2150 
 
 1425 
 
 1475 
 
 1550 
 
 1425 
 
 1475 
 
 1550 
 
 1675 
 
 1800 
 
 1925 
 
 1935 
 
 2000 
 
 2100 
 
 1935 
 
 2000 
 
 2100 
 
 2240 
 
 2400 
 
 2575 
 
 1240 
 
 1275 
 
 1350 
 
 1240 
 
 1275 
 
 1350 
 
 1450 
 
 1575 
 
 1700 
 
 1825 
 
 1900 
 
 2090 
 
 1825 
 
 1900 
 
 2050 
 
 2200 
 
 2350 
 
 2500 
 
 1060 
 
 1100 
 
 1175 
 
 1060 
 
 1100 
 
 1175 
 
 1250 
 
 1350 
 
 1450 
 
 1600 
 
 1650 
 
 1750 
 
 1600 
 
 1650 
 
 1750 
 
 1850 
 
 2000 
 
 2150 
 
 1060 
 
 1100 
 
 1175 
 
 1060 
 
 1100 
 
 1175 
 
 1250 
 
 1350 
 
 1450 
 
 1600 
 
 1650 
 
 1750 
 
 1600 
 
 1650 
 
 1750 
 
 1850 
 
 2000 
 
 2150 
 
 1060 
 
 1100 
 
 1175 
 
 1060 
 
 1100 
 
 1175 
 
 1250 
 
 1350 
 
 1450 
 
 1475 
 
 1525 
 
 1625 
 
 1475 
 
 1525 
 
 1625 
 
 1725 
 
 1850 
 
 1975 
 
 800 
 
 825 
 
 875 
 
 800 
 
 825 
 
 875 
 
 1050 
 
 1125 
 
 1200 
 
 17,7ft 
 
 1250 
 
 1310 
 
 1220 
 
 1250 
 
 1310 
 
 1400 
 
 1500 
 
 1600 
 
 635 
 
 650 
 
 685 
 
 635 
 
 650 
 
 685 
 
 835 
 
 900 
 
 965- 
 
 975 
 
 1000 
 
 1050 
 
 975 
 
 1000 
 
 1050 
 
 1250 
 
 1350 
 
 1450 
 
 610 
 
 625 
 
 660 
 
 610 
 
 625 
 
 660 
 
 775 
 
 835 
 
 890 
 
 900 
 
 925 
 
 975 
 
 900 
 
 925 
 
 975 
 
 1150 
 
 1250 
 
 1350 
 
 * Speed at full load is subject to a maximum variation of 4% above 
 or below standard. 
 
1416 
 
 ELECTRICAL ENGINEERING. 
 
 The standard CQ open motor will deliver its rated horse-power output 
 continuously without a temperature rise in any part exceeding 45° C. 
 by the thermometer above the surrounding air. An overload of 25% 
 may be maintained for one hour continuously without injurious heating 
 or sparking, or a 40% over'oad momentarily. 
 
 Motors developed from the CQl frame and smaller will operate semi 
 or totally enclosed within the same load limits as when open. Owing to 
 the fact that the CQ2 and larger frames have less radiating surface per 
 horse-power than the smaller frames, the ratings attainable with them 
 when enclosed are necessarily reduced to keep the heating within estab- 
 lished limits. 
 
 The voltages for which standard motors are built are 115, 230 and 550. 
 When motors are rated at 115 volts, they may be used on circuits ranging 
 between 110 and 125 volts, and when rated at 230 volts, they may be 
 used on circuits ranging between 220 and 250 volts, and standard heating 
 guarantees will be maintained. 
 
 When motors are rated at 550 volts, they may be used on circuits 
 ranging between 500 and 600 volts, inclusive, and standard heating 
 guarantees will be maintained up to 550 volts, and at 600 volts the heat- 
 ing will not be injurious. 
 
 Se wing-Machine Motors. 
 
 Ratings, H.P., Vao, Vis, Vio, Vs, Ve. 
 
 Speed, r.p.m., 1800, 1800, 1500, 1800, 2300, for direct current ; 
 
 alternating current 1800 r.p.m. for all sizes. 
 
 Wound for 115 and 230 volts, D.C., and 110 and 220 volts, A.C., 60 
 cycles. 
 
 On special order, machines may be furnished for any commercial volt- 
 age between 50 and 250, and for any standard frequency between 25 
 and 145 cycles. 
 
 SYMBOLS USED IN ELECTRICAL DIAGRAMS. 
 
 a o-spst 
 i cb o-spdt 
 a R: dpst 
 
 4l -®- -&- 
 
 _DPDT Galvanometer. Ammeter. Voltmeter. 
 
 "• jvww| — 
 Wattmeter. 
 
 Switches; *S, single; 
 D, double; P, pole; 
 T, throw. 
 
 Non-inductive 
 Resistance. 
 
 Inductive 
 Resistance. 
 
 Capacity 
 or Condenser. 
 
 Lamps. 
 
 i 13 
 
 £= 
 
 Motor Shunt-wound Motor Series-wound 
 or Generator. or Generator. Motor or Generator. 
 
 Two-phase Three-phase Battery. Trans- Compound- Separately 
 Generator. Generator. former, wound Motor excited Motor 
 
 or Generator, or Generator. 
 
INDEX. 
 
 Abbreviations, 1 
 
 Abrasion, resistance to, of manga- 
 nese steel, 471 
 Abrasive processes, 1262-1268 
 Abscissas, 71 
 Absolute temperature, 540 
 
 zero, 540 
 Absorption of gases, 579 
 
 of water by brick, 348 
 
 refrigerating-machines, 1293-1313 
 Accelerated motion, 501 
 Acceleration, definition of, 497 
 
 force of, 501 
 
 work of, 504 
 Accumulators, electric, 1378 
 Acetylene and calcium carbide, 825 
 Acetylene blowpipe, 827 
 
 -flame welding, 464 
 
 generators and burners, 826 
 Acheson's deflocculated graphite, 
 
 1223 
 Acme screw thread, 226 
 Adiabatic compression of air, 604 
 
 curve, 929 
 
 expansion, 575 
 
 expansion of air, 606 
 
 expansion in compressed air- 
 engines, 608 
 
 expansion of steam, 929 
 Adiabatically compressed air, mean 
 
 effective pressures, table, 609 
 Admiralty metal, composition of, 
 
 366 
 Admittance of alternating currents, 
 
 1389 
 Air (see also Atmosphere), 580-653 
 
 and vapor mixture, weight of, 584, 
 586 
 
 -bound pipes, 722 
 
 carbonic acid allowable in, 653 
 
 cooling of, 568, 681 
 
 compressed, 593, 604-626 (see 
 Compressed air) 
 
 compressor, hydraulic, 622 
 
 compressors, centrifugal, 620 
 
 compressors, effect of intake 
 temperatures, 619 
 
 compressors, high altitude, table 
 of, 611 
 
 compressors, intercoolers for, 620 
 
 compressors, tables, 614, 615 
 
 density and pressure, 581, 586 
 
 flow of, in pipes, 591 
 
 flow of, in long pipes, 595 
 
 flow of, in ventilating ducts, 655 
 
 Air, flow of, through orifices, 588 
 
 friction of, in underground pas- 
 sages, 685 
 
 head of, due to temperature 
 differences, 687 
 
 heating of, see also Heating 
 
 heating of, by compression, 604 
 
 horse-power required to com- 
 press, 606 
 
 lift pump, 776 
 
 liquid, 579 
 
 loss of pressure of, in pipes, tables, 
 593-595 
 
 manometer, 581 
 
 properties of, 580 
 
 pump, 1055 
 
 pump for condenser, 1053, 1055 
 
 pump, maximum work of, 1056 
 
 pyrometer, 528 
 
 specific heat of, 537 
 
 thermometer, 530 
 
 velocity of, in pipes, by anemom- 
 eter, 596 
 
 volumes, densities, and pressures, 
 581, 586, 663 
 
 volume transmitted in pipes, 591 
 
 weight and volume of, 28 
 
 weight of (table), 586 
 
 weight of, 173 
 Alcohol as fuel, 813 
 
 denatured, 813 
 
 engines, 1078 
 
 vapor tension of, 814 
 Aiden absorption dynamometer, 
 
 1281 
 Algebra, 34-38 
 Alsrebraic symbols, 1 
 Alligation, 9 
 Alloys, 360-385 
 
 aluminum, 371, 375, 376 
 
 aluminum-antimony, 375 
 
 aluminum-copper, 371 
 
 aluminum-silicon-iron, 374 
 
 aluminum, tests of, 374 
 
 aluminum-tungsten, 375 
 
 aluminum-zinc, 375 
 
 antimony, 381, 383 
 
 bearing metal, 380 
 
 bismuth, 379 
 
 caution as to strength of, 373 
 
 composition of, "n brass foundries, 
 366 
 
 composition by mixture and by 
 analysis, 364 
 
 copper-manganese, 376 
 
 1417 
 
1418 
 
 INDEX. 
 
 Alloys, copper-tin, 360 
 
 copper-tin-lead, 369 
 
 copper-tin-zinc, 363-367 
 
 copper-zinc, 362 
 
 copper-zinc-iron, 369 
 
 ferro-, 1232 
 
 for casting under pressure, 371 
 
 fusible, 380 
 
 Japanese, 368 
 
 liquation of metals in, 364 
 
 magnetic, of non-magnetic met- 
 als, 378 
 
 nickel, 378 
 
 the strongest bronze, 365 
 
 vanadium and copper, 371 
 
 white metal, 382 
 Alloy steels, 470-480 (see Steel) 
 Alternating-current motors, vari- 
 able speed, 1412 
 Alternating currents, 1387 
 
 admittance, 1389 
 
 average, maximum, and effective 
 values, 1388 
 
 calculation of circuits, 1397 
 
 capacity, 1389 
 
 capacity of conductors, 1394 
 
 converters, 1400 
 
 delta connection, 1395 
 
 frequency, 1388 
 
 generators for, 1396 
 
 impedance, 1389 
 
 impedance polygons, 1390 
 
 inductance, 1389 
 
 induction motor, 1409 
 
 measurement of power in poly- 
 phase circuits, 1395 
 
 Ohm's law applied to, 1390 
 
 power factor, 1389 
 
 reactance, 1389 
 
 single and polyphase, 1395 
 
 skin effect, 1390 
 
 synchronous motors, 1409 
 
 transformers, 1400 
 
 Y-connection, 1395 
 Alternators, sizes of, tables, 1413 
 Altitude by barometer, 582 
 Aluminum, 174 
 
 alloys (see Alloys) 
 
 alloys used in automobile con- 
 struction, 376 
 
 alloys, various, 371, 375, 376 
 
 alloys, tests of, 374 
 
 brass, 373 
 
 bronze, 371 
 
 bronze wire, 243 
 
 coating on iron, 449 
 
 conductors, cost compared with 
 copper, 1399 
 
 effect of, on cast iron, 416 
 
 electrical conductivity of, 1350 
 
 properties and uses, 357 
 
 sheets and bars, table, 220 
 
 solder, 359 
 
 steel, 472 
 
 strength of, 358 
 
 thermit process, 372 
 
 wire, 243, 359 
 
 Aluminum wire, electrical resistance 
 
 of, table, 1362 
 Ammonia, carbon dioxide and sul- 
 phur dioxide, cooling effect, 
 and compressor volume, 1289 
 gas, properties of, 1287 
 heat generated by absorption of, 
 
 1288 
 liquid, density of, 1285 
 liquid, specific heat of, 1286 
 liquid, specific heat and available 
 
 latent heat, 1287 
 solubility of, 1288 
 vapor, superheated, weight of, 
 1287 
 Ammonia-absorption refrigerating 
 machine, 1293, 1313 
 test of, 1315 
 Ammonia-compression refrigerating 
 machines, 1292, 1303. 
 tests of, 1307-1311 
 Ampere, definition of, 1345 
 Analyses, asbestos, 257 
 boiler scale, 693 
 boiler water, 693 
 cast iron, 416-419 
 coals, 789-797 
 crucible steel, 466, 469 
 fire-clay, 255 
 gas, 824 
 
 gases of combustion, 785 
 magnesite, 257 
 Analysis of rubber goods, 356 
 Analytical geometry, 71-74 
 Anchor forgings, strength of, 331 
 Anemometer, 596 
 Angle, economical, of framed struc- 
 tures, 522 
 of repose of building material, 
 1196 
 Angles, Carnegie steel, properties of, 
 table, 295-298 
 plotting without protractor, 54 
 problems in, 39, 40 
 steel, table of properties of, 295, 
 
 296 
 steel, table of safe loads, 297, 298 
 steel, tests of, 340 
 trigonometrical properties of, 67 
 Angular velocity, 498 
 Animal power, 507-509 
 Annealing, effect on conductivity, 
 1351 
 effect of, on steel, 454, 455 
 influence of, on magnetic capa- 
 city of steel, 459 
 malleable castings, 431 
 of steel, 460, 468 (see Steel) 
 of steel forgings, 458 
 of structural steel, 460 
 Annuities, 15-17 
 Annular gearing, 1145 
 Anthracite, classification of, 787 
 composition of, 787 
 gas, 815 
 sizes of, 792 
 space occupied by, 793 
 
 
INDEX. 
 
 1419 
 
 Anti-friction curve, 51, 1209 
 
 metals, 1199 
 Anti-logarithm, 135 
 Antimony, in alloys, 383, 336 
 
 properties of, 175 
 Apothecaries' measure and weight, 
 
 18,20 
 Arbitration bar, for cast iron, 418 
 Arc, circular, length of, 59 
 
 circular, relations of, 59 
 
 lamps, see Electric lighting 
 
 lighting of areas, watts per 
 square foot required for, 1369 
 
 lights, electric, 1368 
 Arcs, circular, table, 123, 124 
 Arches, corrugated, 186 
 Area of circles, table, 111-119 
 
 of circles, square feet, diameters 
 feet and inches, 127, 128 
 
 of geometrical plane figures, 
 55-62 
 
 of irregular figures, 57, 58 
 
 of sphere, 63 
 Arithmetic, 2-33 
 Arithmetical progression, 10 
 Armature, torque of, 1385 
 Armature-circuit, e.m.f. of, 1386 
 Armor-plates, heat treatment of, 
 
 458 
 Asbestos, 257 
 
 Asphaltum coating for iron, 447 
 Asses, work of, 509 
 Asymptotes of hyperbola, 74 
 Atmosphere, see also Air 
 
 equivalent pressures of, 27 
 
 moisture in, 583 
 
 pressure of, 581 
 Atomic weights (table), 170 
 Autogenous welding, 464 
 Austenite, 456 
 
 Automatic cut-off engines, 937 
 Automobile engines, rated capacity 
 of, 1077 
 
 gears, efficiency of , 1148 
 
 screws and nuts, table, 222 
 Automobiles, steel used in, 486 
 Avogadro's law of gases, 578 
 Avoirdupois weight, 19 
 Axles, forcing fits of, by hydraulic 
 pressure, 1273 
 
 railroad, effect of cold on, 441 
 
 steel, specifications for, 483, 485 
 
 steel, strength, of, 332 
 
 Babbitt metal, 383, 384 
 
 Babcock & Wilcox boilers, tests 
 
 with various coals, 799 
 Bagasse as fuel, 809 
 Balances, to weigh on incorrect, 20 
 Ball-bearings, 1210 
 
 saving of power by, 1214 
 Balls and rollers, carrying capacity 
 
 of, 317 
 Balls for bearings, grades of, 1214 
 
 hollow copper, 322 
 Band brakes, design of, 1217 
 
 Bands and belts for carrying coal, 
 etc., 1175 
 and belts, theory of, 1115 
 Bank discount, 13 
 Bar iron, see also Wrought iron 
 Bars, eye, tests of, 338 
 
 iron and steel, commercial sizes 
 
 of, 179 
 Lowmoor iron, strength of, 330 
 of various materials, weights of, 
 
 178 
 steel, 461, see Steel 
 twisted, tensile strength of, 264 
 wrought-iron, compression tests 
 of, 337 
 Barometer, leveling with, 582 
 
 to find altitude by, 582 
 Barometric readings for various alti- 
 tudes, 582 
 Barrels, number of, in tanks, 133 
 
 to find volume of, 66 
 Basic Bessemer steel, strength of, 
 
 452 
 Batteries, primary electric, 1377 
 
 storage, 1378 
 Baume's hydrometer, 172 
 Bazin's experiments on weirs, 732 
 Beams and girders, safe loads on, 
 1335 
 formula for flexure of, 282 
 formulae for transverse strength 
 
 of, 282-285 
 of uniform strength, 286 
 special, coefficients for loads on, 
 
 285 
 steel, formulae for safe loads on, 
 
 284 
 wooden, safe loads, by building 
 
 laws, 1336 
 yellow pine, safe loads on, 1336, 
 1340 
 Beardslee's tests on elevation of 
 
 elastic limit, 261 
 Bearing pressure on rivets, 403 
 Bearing pressures with intermittent 
 
 loads, 1207 
 Bearings, allowable pressure on, 
 1203, 1206 
 and journals clearance in, 1206 
 ball, 1210 
 
 calculating dimensions of, 1025 
 cast-iron, 1199 
 conical roller, 1211 
 engine, temperature of, 1209 
 for high rotative speeds, 1208 
 for steam turbines, 1208 
 knife-edge, 1214 
 mercury pivot, 1209 
 of Corliss engines, 1208 
 of locomotives, 1208 
 oil pivot, in Curtis steam turbine, 
 
 1063 
 oil pressure in, 1204 
 overheating of, 1205 
 pivot, 1205, 1209 
 roller, 1210 
 shaft, length of, 1015 
 
1420 
 
 bea-bol 
 
 INDEX. 
 
 Bearings, steam-engine, 1165 
 
 thrust, 1208 
 Bearing-metal alloys, 380-384 
 
 practice, 382 
 Bearing-metals, anti-friction, 1199 
 
 composition of, 367 
 Bed-plates of steam-engine, 1025 
 Bell-metal, composition of , 366 
 Belt conveyors, 1175 
 Belt dressings, 1128 
 
 factors, 1119 
 Belts, arrangement of, 1126 
 
 care of, 1127 
 
 cement for leather or cloth, 1128 
 
 centrifugal tension of, 1115 
 
 endless, 1127 
 
 evil of tight, 1126 
 
 lacing of, 1124 
 
 length of, 1125 
 
 open and crossed, 1112 
 
 quarter twist, 1124 
 
 sag of, 1126 
 
 steel, 1120 
 Belting, 1115-1132 
 
 Barth's studies on, 1123 
 
 formulae, 1116 
 
 friction of, 1115 
 
 horse-power of, 1116-1119 
 
 notes on', 1123 
 
 practice, 1116 
 
 rubber, 1128 
 
 strength of, 335, 1127 
 
 Taylor's rules, 1120-1122 
 
 theory of, 1115 
 
 vs. chain drives, 1132 
 
 width for given horse-power, 
 1118 
 Bends, effects of, on flow of water 
 in pipes, 721 
 
 in pipes, 593 
 
 in pipes, table, 214, 215 
 
 pipe, flexibility of, 215 
 
 valves, etc., resistance to flow in, 
 848 
 Bending curvature of wire rope, 
 1188 
 
 tests of steel, 454 
 Bent lever, 511 
 Bernouilli's theorem, 734 
 Bessemer converter, temperature 
 in, 527 
 
 steel, 451 {see Steel, Bessemer) 
 Bessemerized cast iron, 429 
 Bevel wheels, 1144 
 Billets, steel, specifications for, 483 
 Binomial, any power of, 34 
 
 theorem, 38 
 Bins, coal-storage, 1172 
 Birmingham gauge, 29 
 Bismuth alloys, 379 
 Bismuth, properties of, 175 
 Bituminous coal {see Coal) 
 Black body radiation, 552 
 Blast area of fans, 629 
 
 furnaces, consumption of char- 
 coal in, 806 
 
 furnaces, steam-boilers for, 865 
 
 Blast furnaces, temperatures in, 528 
 
 pipes, see Pipes 
 Blechynden's tests of heat trans- 
 mission, 567 
 Blocks or pulleys, 513 
 
 efficiency of, table, 1158 
 
 strength of, 1157 
 Blooms, steel, weight of, table, 185 
 Blow, force of, 504 
 Blowers, see also Fans. 
 Blowers and fans, 626-652 
 
 and fans, comparative efficiency, 
 631 
 
 blast-pipe diameters for, 643 
 
 capacity of, 632 
 
 experiments with, 629 
 
 for cupolas, 633, 634 
 
 in foundries, 1227 
 
 rotary, 649 
 
 rotary, table of, 650 
 
 steam-jet, 651 
 
 velocity due to pressure, 629 
 Blowing-engines, dimensions of, 
 652 
 
 machines, centrifugal, 622 
 Blue heat, effect on steel, 458 
 Board measure, 20 
 Boats, see Ships 
 Bodies, falling, laws of, 497 
 Boiler compounds, 898 
 
 explosions, 902 
 
 feeders, gravity, 908 
 
 feed-pumps, 761 
 
 furnaces, height of, 889 
 
 furnaces, use of steam in, 824 
 
 heads, 885 
 
 heads, strength of, 314, 316 
 
 heating-surface for steam heat- 
 ing, 664, 667 
 
 plate, strength of, at high tem- 
 peratures, 439 
 
 scale, analyses of, 693 
 
 tubes used as columns, 341 
 
 tubes, expanded, holding power 
 of, 342 
 
 tubes, dimensions of, table, 209 
 
 tube joints, rolled, slipping point 
 of, 342 
 Boilers for house heating, 665 
 
 horse-power of, 854 
 
 incrustation of, 691, 692 
 
 locomotive, 1089 
 
 natural gas as fuel for, 817 
 
 of the "Lusitania" 1330 
 
 for steam-heating, 667 
 
 steam, 854 {see Steam-boilers) 
 Boiling, resistance to, 543 
 Boiling-point of water, 690 
 Boiling-points of substances, 532 
 Bolts and nuts, 221-228 
 
 and pins, taper, 1271 
 
 effect of initial strain in, 325 
 
 holding power of in white pine, 
 324 
 
 square-head, table of weights of, 
 229 
 
INDEX 
 
 bol-can 
 
 1421 
 
 Bolts, strength of, tables, 325, 326 
 
 track, weight of, 230 
 
 variation in size of iron for, 223 
 Boyle's or Mariotte's law, 574, 577 
 Braces, diagonal, stresses in, 516 
 Brackets, cast-iron, strength of, 277 
 Brake horse-power, definition of, 
 991 
 
 Prony, 1280 
 Brakes, band, design of, 1217 
 
 electric, 1217 
 
 friction, 1216 
 
 magnetic, 1217 
 Brass alloys, 366 
 
 and copper tubes, coils and bends, 
 214 
 
 influence of lead on, 369 
 
 plates and bars, weight of, 
 tables, 219, 220 
 
 rolled, composition of, 367 
 
 sheet and bars, table, 220 
 
 tube, seamless, table, 215, 216 
 
 wire, weight of, table, 219 
 Brazing of aluminum bronze, 373 
 
 metal, composition of, 366 
 
 solder, composition of, 366 
 Brick, absorption of water by, 348 
 
 kiln, temperature in, 528 
 
 piers, safe strength of, 1334 
 
 sand-lime, tests of, 349 
 
 specific gravity of, 174 
 
 strength of, 336, 347-350 
 
 weight of, 174, 347 
 Bricks, fire, number required for 
 various circles, table, 254 
 
 fire, sizes and shapes of, 253 
 Bricks, magnesia, 257 
 Brickwork, allowable pressures on, 
 1334 
 
 measure of, 177 
 
 weight of, 177 
 Bridge iron, durability of, 442 
 
 links, steel, strength of, 331 
 
 members, strains allowed in, 272 
 
 trusses, 517-521 
 Brine, boiling of, 543 
 
 properties of, 543, 544 
 Brinell's tests of hardness, 342 
 Briquettes, coal, 801 
 Britannia metal, composition of, 
 
 383 
 British thermal unit (B.T.U.), 
 
 532, 837 
 Brittleness of steel, see Steel 
 Bronze, aluminum, strength of, 372 
 
 ancient, composition of, 364 
 
 deoxidized, composition of, 371 
 
 Gurley's, composition of, 366 
 
 manganese, 377 
 
 navy-yard, strength of, 374 
 
 phosphor, 370 
 
 strength of, 319, 321, 334 
 
 Tobin, 367, 368 
 
 variation in strength of, 362 
 Buildings, construction of, 1333- 
 1344 
 
 fire-proof, 1338 
 
 Buildings, heating and ventilation 
 
 of, 656 
 mill, approximate cost of, 1342 
 
 transmission of heat through 
 
 walls of, 659 
 walls of, 1336 
 Building-laws, New York City, 
 
 1337-1340 
 on columns, New York, Boston, 
 
 and Chicago, 277 
 Building-materials, coefficients of 
 
 friction of, 1196 
 sizes and weights, 174, 17S, 1S6, 
 
 190 
 Bulkheads, plating and framing for, 
 
 table, 316 
 stresses in due to water-pressure, 
 
 315 
 Buoyancy, 690 
 Burmester's method of calculating 
 
 cone pulleys, 1113 
 Burning of steel, 457 
 Burr truss, stresses in, 518 
 Bush-metal, composition of, 366 
 Bushel of coal and of coke, weight 
 
 of, 803 
 Butt-joints, riveted, 405 
 
 C. G. S. system of measurements, 
 
 1344 
 C0 2 , carbon dioxide, carbonic acid 
 C0 2 recorders, autographic, 860 
 C0 2 , temperature required for pro- 
 duction of, 822 
 Cable, formula for deflection of, 
 1180 
 
 traction ropes, 247 
 Cables, chain, proving tests of, 251 
 
 chain, wrought-iron, 251-252 
 
 flexible steel wire, 249 
 
 galvanized steel, 248 
 
 suspension-bridge, 248 
 Cable-ways, suspension, 1181 
 Cadmium, properties of, 175 
 Calcium carbide and acetylene, 825 
 
 chloride in refrigerating-ma- 
 chines, 1290 
 Calculus, 74-83 
 Caloric engines, 1071 
 Calorie, definition of, 532 
 Calorimeter for coal, Mahler bomb, 
 798 
 
 steam, 912-915 
 
 steam, coil, 913 
 
 steam, separating, 914 
 
 steam, throttling, 913 
 Calorimetric tests of coal, 797, 798 
 Cam, 512 
 Campbell's formula for strength of 
 
 steel, 453 
 Canals, irrigation, 704 
 Candle-power and life of lamps, 
 "1370 
 
 definition of, 1367 
 
 of electric lights, 1368-1373 
 
 of gas lights, 830 
 Canvas, strength of, 335 
 
1422 
 
 INDEX. 
 
 Capacity, electrical, 1389 
 
 electrical, of conductors, 1394 
 Cap-screws, table of standard, 225 
 Cars, steel plate for, 483 
 Car-heating by steam, 673 
 Car-journals, friction of, 1204 
 Car-wheels, cast iron for, 426, 427 
 Carbon, burning out of steel, 461 
 dioxide, see C0 2 
 effect of on strength of steel, 452 
 gas, 814 
 Carbonic acid allowable in air, 653 
 Carbonizing see Case-hardening, 
 Carborundum, made in the electric 
 
 furnace, 1377 
 Cargo hoisting by rope, 390 
 Carnegie steel sections, properties 
 
 of, 287-306 
 Carnot cycle, 572, 574 
 
 cycle, efficiencies of, 967 
 cycle, efficiency of steam in, 850 
 Carriages, resistance of, on roads, 
 
 509 
 Carriers, bucket, 1172 
 Case-hardening of iron and steel, 
 
 486, 1246 
 Casks, volume of, 66 
 Cast copper, strength of, 334, 360 
 Cast-iron, 414-429 
 
 addition to, of ferro-silicon, 
 titanium, vanadium and man- 
 ganese, 426 
 analyses of, 416-419 
 and aluminum alloys, 375 
 bad, 429 
 
 bars, tests of, 419 
 beams, strength of, 427 
 Bessemerized, 429 
 chemistry of, 415-419 
 columns, eccentric loading of, 278 
 columns, strength of, 274-278 
 columns, tests of, 275 
 columns, weight of, table, 191 
 combined carbon changed to 
 
 graphitic by heating, 424 
 compressive strength of, 267 
 corrosion of, 441 
 cylinders, bursting strength of, 
 
 427 
 durability of, 442 
 effect of cupola melting, 425 
 expansion in cooling, 423 
 growth of by heating, 1231 
 hard, due to excessive silicon, 
 
 1231 
 influence of length of bar on 
 
 strength, 422 
 influence of phosphorus, sulphur, 
 
 etc., 415 
 journal bearings, 1199 
 malleable, 429 
 manufacture of, 414 
 mixture of, with steel, 429 
 mobility of molecules of, 424 
 permanent expansion of, by heat- 
 ing, 429 
 
 Cast-iron pipe, 191-195 (see Pipe, 
 cast-iron) 
 pipe-fittings, sizes and weights, 
 
 196, 199 
 relation of chemical composition 
 
 to fracture, 421 
 shrinkage of, 415, 423, 1231 
 specifications for, 418 
 specific gravity and strength, 428 
 strength of, 421 
 strength in relation to silicon and 
 
 cross-section, 422 
 strength in relation to size of 
 bar and to chemical constitu- 
 tion, 421 
 tests of, 330, 419, 420 
 theory of relation of strength to 
 
 composition, 421 
 variation of density and tenacity , 
 
 428 
 water pipe, transverse strength 
 
 of, 427 
 white, converted into gray by 
 heating, 424 
 Castings, deformation of, by shrink- 
 age, 423 
 from blast-furnace metal, 425 
 hard, from soft pig, 425 
 hard to drill, due to low Mn., 426 
 iron, analysis of, 417 
 iron, strength of, 330 
 made in permanent cast-iron 
 
 molds, 1232 
 malleable, rules for use of 433 
 shrinkage of, 1231 
 specifications for, 418 
 steel, 464-466 
 
 steel, specifications for, 464, 486 
 steel, strength of, 333 
 weakness of large, 1230 
 weight of, from pattern, 1233 
 Catenary, to plot, 53 
 Cement as a preservative coating, 
 447 
 for leather belts, 1128 
 Portland, strength of, 336 
 Portland, tests of, 351 
 weight and specific gravity of, 
 174 
 Cements, mortar, strength of, 350 
 Cementation or case-hardening, 
 
 486, 1246 
 Cementite, 416, 456 
 Center of gravity, 492 
 of regular figures, 492. 
 of gyration, 494 
 of oscillation, 494 
 of percussion, 494 
 Centigrade Fahrenheit conversion 
 table, 524, 525 
 thermometer scale, 524, 525 
 Centrifugal fans (see Fans, cen- 
 trifugal) 
 fans, high-pressure, 621 
 force, 497 
 force in fly-wheels, 1029 
 
INDEX. 
 
 1423 
 
 Centrifugal pumps (see Pumps, 
 centrifugal), 764-770 
 
 tension of belts, 1115 
 Chains, formulas for safe load on. 
 326 
 
 link belting, 1172 
 
 monobar, 1174 
 
 pin, 1174 
 
 .pitch, breaking and working 
 strains of, 252 
 
 roller, 1174 
 
 sizes, weights and properties, 
 251, 252 
 
 specifications for, 251 
 
 strength of, table, 251, 252 
 
 test of, table, 251, 252 
 Chain-blocks, efficiency of , 1158 
 Chain-cables, proving tests of, 251 
 
 weight and strength of, 251 
 Chain-drives, 1129 
 
 vs. belting, 1132 
 
 silent, 350 H.P., 1132 
 Chain-hoists, 1157 
 Chalk, strength of, 349 
 Change gears for lathes, 1237 
 Channels, Carnegie steel, properties 
 of, table, 292 
 
 open, velocity of water in, 704 
 
 safe loads, table, 293 
 
 strength of, 330 
 Charcoal, 805-807 
 
 absorption of gases and water 
 by, 806 
 
 bushel of, 177 
 
 composition of, 806 
 
 pig iron, 417, 428 
 
 results of different methods of 
 making, 806 
 
 weights per cubic foot, 177 
 Charles's law, 574, 578 
 Chatter in tools, 1241 
 Chemical elements, table, 170 
 
 symbols, 170 
 Chemistry of cast iron, 415 
 Chezy's formula for flow of water, 
 
 699 
 Chilling cast iron, 418 
 Chimneys, 915-928 
 
 draught, power of, 917 
 
 draught, theory, 915 
 
 effect of flues on draught, 918 
 
 for ventilating, 683 
 
 height of, 919 
 
 height of water column due to 
 unbalanced pressure in, 917 
 
 largest in the world, 923 
 
 lightning protection of, 920 
 
 radial brick, 923 
 
 rate of combustion due to, 918 
 
 reinforced concrete, 927 
 
 sheet iron, 928 
 
 size of, 919-928 
 
 size of, table, 921 
 
 stabilitv of, 924 
 
 steel, 925 
 
 steel, design of, 925 
 
 steel, foundation for, 926, 928 
 
 Chimneys, tall brick, 922 
 velocity of air in, 917 
 Chisels, cold, cutting angle of, 1238 
 Chord of circle, 59 
 Chords of trusses, strains in, 519 
 Chrome paints, anti-corrosive, 445 
 
 steel, 471 
 Chromium vanadium steels, 476- 
 
 478 
 Cippoleti weir, 733 
 Circle, 58-61 
 area of, 58 
 diameter of to enclose a number 
 
 of rings, 52 
 equation of, 72 
 
 large, to describe an arc of, 52 
 length of arc of, 59 
 length of arc of, Huyghen's 
 
 approximation, 59 
 length of chord of, 59 
 problems, 40-42 
 properties of, 58, 59 
 relations of arc, chord, etc., of, 59 
 relations of, to equal, inscribed 
 and circumscribed square, 60 
 sectors and segments of, 61 
 area in square feet, diameter in 
 inches (tables of cylinders), 
 127, 128 
 circumference and area of, table, 
 
 111-119 
 circumferences in feet, diameters 
 
 in inches, table, 1265 
 circumferences of, 1 inch to 32 
 feet, 120 
 Circuits, alternating current, see 
 Alternating current 
 electric, see Electric circuits 
 electric, e.m.f. in, 1352 
 electric, polyphase, 1395 (see 
 
 Alternating currents) 
 electric, power of, 1353 
 magnetic, 1383 
 Circular arcs, lengths of, 59 
 lengths of, tables, 123, 124 
 curve, formulas for, 60 
 functions, Calculus, 82 
 inch, 18 
 measure, 20 
 mil, 18, 30, 31 
 mil wire gauge, 31 
 mil wire gauge, table, 30 
 pitch, 1134 
 ring, 61 
 
 segments, areas of, 121, 122 
 Circumference of circles, 1 inch to 
 32 feet, table, 120 
 of circles, table, 111-119 
 Cisterns and tanks, no. of barrels 
 in, 133 
 capacity of, 128 
 Classification of iron and steel, 413 
 Clay, cubic feet per ton, 178 
 fire, analysis, 255 
 melting point of, 529 
 Clearance between journal and 
 bearing, 1206 
 
1424 
 
 cle-com 
 
 INDEX. 
 
 Clearance in steam-engines, 936, 996 
 Clutches, friction, 1155, 1216 
 
 friction coil, 1156 
 Coal, analysis of, 789-797 
 
 analyses of various, table, 794 
 
 and coke, Connellsville, 793 
 
 approximate heating value of, 
 791 
 
 anthracite, sizes of, 792 
 
 bituminous, classification of, 787 
 
 caking and non-caking, 788 
 
 calorimeter, 798 
 
 calorimetric tests of, 797, 798 
 
 cannel, 788 
 
 classification of, 786, 787 
 
 conveyors, 1172 
 
 cost of for steam power, 983 
 
 cubic feet per ton, 177 
 
 Dulong's formula for heating 
 value of, 798 
 
 efficiencies of, in gas-engine tests, 
 823 
 
 evaporative power of, 799 
 
 foreign, analysis of, 796 
 
 furnaces for different, 798 
 
 heating value of, 789-792, 797 
 
 products of distillation of, 803 
 
 proximate analysis and heating 
 value of, table, 790 
 
 purchase of by specification, 799 
 
 Rhode Island graphitic; 788 
 
 sampling of, for analysis, 797 
 
 semi-anthracite, 793 
 
 semi-bituminous, composition of, 
 787-792 
 
 space occupied by anthracite, 
 793 
 
 steam, relative value of, 797 
 
 storage bins, 1172 
 
 tests of, 791 
 
 vs. oil as fuel, 812 
 
 washing, 802 
 
 weathering of, 800 
 
 Welsh, analysis of, 796 
 Coal-gas, composition of, 830 
 
 manufacture, 828 
 Coatings, preservative, 447-450 
 Coefficient of elasticity, 260, 351 
 
 of fineness, 1317 
 
 of friction, definition, 1194 
 
 of friction of journals, 1197 
 
 of friction, rolling, 1195 
 
 of friction, tables, 1195-1197 
 
 of performance of ships, 1318 
 
 of propellers, 1325 
 
 of transverse strength, 282 
 
 of water lines, 1317 
 
 of expansion, 539 (see Expansion 
 by heat) 
 Coils and bends of brass tubes, 214 
 Coils, electric, heating of, 1355 
 Coils, heat radiated from, in 
 
 blower system, 679 
 Coiled pipes, 214 
 Coke, anaiyses of, 802 
 
 by-products of manufacture of, 
 802, 803 
 
 Coke, foundry, quality of, 1232 
 
 weight of, 177 
 Coke-ovens, generation of steam 
 
 from waste heat of, 803 
 Coking, experiments in, 802 
 Cold, effect of, on railroad axles, 
 441 
 effect of on strength of iron and 
 steel 440 
 Cold-chisels, form of, 1238 
 Cold-drawing, effect of, on steel, 
 
 339 
 Cold-drawn steel, tests of, 339 
 Cold-rolled steel, tests of, 339 
 Cold-rolling, effect of, on steel, 455 
 Cold-saw, 1262 
 
 Collapse of corrugated furnaces, 
 318 
 of tubes, tests of, 320 
 resistance of hollow cylinders 
 to, 318-322 
 Collars for shafting, 1109 
 Cologarithm, 136 
 
 Color determination of tempera- 
 ture, 531 
 scale for steel tempering, 469 
 values of various illuminants, 
 1367 
 Columns, Bethlehem shapes, 309, 
 310 
 built, 272 
 Carnegie channel, dimensions 
 
 and safe loads, 305, 306 
 cast-iron, strength of, 274-278 
 cast-iron, tests of, 275 
 cast-iron, weight of, table, 191 
 eccentric, loading of, 278 
 Gordon's formula for, 270 
 Hodgkinson's formula for, 269 
 made of old boiler tubes, tests 
 
 of, 341 
 mill, 1341 
 
 permissible stresses in, 277 
 strength of, 274 
 
 strength of, by New York build- 
 ing laws, 1337 
 wrought-iron, tests of, 338 
 wrought-iron, ultimate strength 
 
 of, table, 271 
 steel, built, 272 
 
 Z-bar, tables of safe loads on, 
 300-304 
 Combination, 10 
 Combined stresses, 312 
 Combustion, analyses of gases of 
 
 heat of, 533 
 
 of fuels, 784 
 
 of gases, rise of temperature 
 in, 786 
 rate of, due to chimneys, 918 
 
 theory of, 784 
 Composition of forces, 489 
 Compound engines (see Steam- 
 engines, compound), 946-953 
 
 interest, 14 
 
 locomotives, 1098, 1101 
 
1425 
 
 Compound numbers, 5 
 proportion, 7 
 
 units of weights and measures, 
 27, 28 
 Compressed-air, 593, 604-626 
 adiabatic and isothermal com- 
 pression, 604 
 adiabatic expansion and com- 
 pression, tables, 609, 610 
 compound compression, 609 
 cranes, 1168 
 diagrams, curve of, 611 
 drills driven by, 616 
 engines, adiabatic expansion in, 
 
 608 
 engines, efficiency, 613 
 flow of, in pipes, 594 
 for motors, effect of heating, 612 
 formulae, 606 
 for street railways, 625 
 heating of, 604 
 hoisting engines, 618 
 horse-power required to com- 
 press air, 606 
 locomotive, 1104 
 losses due to heating, 606 
 . loss of energy in, 604 
 
 machines, air required to run, 
 
 616, 618 
 mean effective pressures, tables, 
 
 609, 610 
 mine pumps, 625 
 moisture in, 584 
 motors, 612 
 motors with return-air circuit, 
 
 620 
 Popp system, 612 
 practical applications of, 619 
 pumping with (see also Air- 
 lift), 617 
 reheating of, 619 
 tramways, 624, 625 
 transmission, 593 
 transmission, efficiencies of, 613 
 volumes, mean pressures per 
 
 stroke, etc., table, 605 
 work of adiabatic compression, 
 607 
 Compressed steel, 464 
 Compressibility of liquids, 172 
 
 of water, 691 
 Compression, adiabatic, formulae 
 for, 606 
 and flexure combined, 312 
 and shear combined, 312. 
 and torsion combined, 312 
 in steam-engines, 935 
 of air, adiabatic, tables, 609, 610 
 Compressive strength, 267-269 
 strength of iron bars, 337 
 strengths of woods, 344, 346 
 tests, specimens for, 268 
 Compressors, air, effect of intake 
 temperature, 619 
 air, tables of, 614-615 
 Concrete, crushing strength of 12- 
 in. cubes, 1334 
 
 Concrete, durability of iron in, 412 
 reinforced, allowable working 
 stresses, 1335 
 Condenser, barometric, 1051 
 
 the Leblanc, 1057 
 Condensers, 1050-1061 
 air-pump for, 1053, 1055 
 calculation of surface of, 910 
 choice of, 1059 
 circulating pump for, 1057 
 cooling towers for, 1060 
 cooling water required, 1050 
 continuous use of cooling water 
 
 in, 1058 
 contraflow, 1053 
 ejector, 1051 
 
 evaporative surface, 1057 
 for refrigerating machines, 1300 
 heat transference in, 1052 
 increase of power due to, 1058 
 jet, 1050 
 surface, 1051 
 tubes and tube plates of, 1054, 
 
 1055 
 tubes, heat transmission in, 563 
 Condensing apparatus, power used 
 
 by, 1053 
 Conduction of heat, 553 
 of heat external, 554 
 of heat internal, 553 
 Conductivity, electric (see Elec- 
 tric conductivity) 
 electrical, of metals, 1349 
 Conductors, electrical, heating of, 
 1354 
 electrical, in series or parallel, 
 resistance of, 1352 
 Conduit, water, efficiency of, 735 
 Cone, measures of, 63 
 
 pulleys, 1112 
 Connecting-rods, steam-engine, 
 1003, 1004 
 tapered, 1005 
 Conic sections, 74 
 Conoid, parabolic, 66 
 Conservation of energy, 506 
 Constantan, copper-nickel alloy, 
 
 379 
 Constants, steam-engine, 941 
 Construction of buildings, 1333- 
 
 1344 
 Controllers, for electric motors, 
 
 1404 
 Convection, loss of heat due to, 
 
 570 
 Convection of heat, 553 
 
 Dulong's law of, table of factors 
 for, 571 
 Conversion tables, metric, 23-27 
 Converter, Bessemer, temperature 
 
 in, 527 
 Converters, electric, 1400 
 Conveying of coal in mines, 1178 
 Conveyors, belt, 1175 
 cable-hoist, 1181 
 coal, 1172 
 horse-power required for, 1173 
 
1426 
 
 Conveyors, screw, 1175 
 
 Cooling agents in refrigeration, 
 
 1289 
 Cooling of air, 568 
 
 for ventilation, 681 
 Cooling-tower practice in refrigerat- 
 ing plants, 1301 
 for condensers, 1060 
 Co-ordinate axes, 71 
 Copper, 175 
 
 Copper and vanadium alloys, 371 
 Copper ball pyrometer, 526 
 balls, hollow, 322 
 cast, strength of, 334, 360 
 drawn, strength of, 334 
 effect of on cast iron, 415 
 manganese alloys, 376 
 nickel alloys, 378 
 plates, strength of, 334 
 rods, weight of, table, 218 
 steels, 475 
 strength of at high temperatures, 
 
 344 
 tubing, bends and coils, 214 
 tubing, weight of, table, 216 
 weight required in different 
 systems of transmission, 1398 
 wire and plates, weight of, table, 
 
 219 
 wire, carrying capacity of, Un- 
 derwriter's table, 1355 
 wire, cost of for long-distance 
 
 transmission, 1363 
 wire, cross section required for a 
 
 given current, 1359 
 wire, electrical resistance, table, 
 
 1357, 1358 
 wire, stranded, 242 
 wire, weight of for electric cir- 
 cuits, 1359 
 tin-aluminum alloys, 375 
 tin alloys, 360 
 
 tin alloys, properties and com- 
 position of, 360 
 tin-zinc alloys, properties and 
 
 composition, 363 
 tin-zinc alloys, law of variation 
 
 of strength of, 364 
 zinc alloys, strength of, 364 
 zinc alloys, table of composition 
 
 and properties, 362 
 zinc-iron alloys, 369 
 Cord of wood, 805 
 Cordage, technical terms relating 
 to, 388 
 weight of, table, 386-391, 1157 
 Cork, properties of, 355 
 Corn, weight of, 178 
 Corrosion by stray electric currents, 
 446 
 due to overstrain, 446 
 electrolytic theory of, 444 
 of iron, 443 
 
 of steam-boilers, 443, 897 
 prevention of, 444 
 
 Corrosion, resistance of aluminum 
 alloys to, 376 
 resistance to of nickel steel, 474 
 Corrosive agents in atmosphere, 
 
 442 
 Corrugated arches, 186 
 furnaces, 319, 881 
 iron, sizes and weights, 186 
 plates, properties of Carnegie 
 steel, table, 289 
 Cosecant of an angle, table, 166-169 
 Cosine of an angle, 67 
 
 table, 166, 169 
 Cost of coal for steam-power, 983 
 of steam-power, 981, 982-984 
 Cotangent of an angle, 67 
 Cotangents of angles, table, 166- 
 
 169 
 Cotton ropes, strength of, 335 
 Coulomb, definition of, 1345 
 Counterbalancing of hoisting-en- 
 gines, 1163 
 of locomotives, 1102 
 of steam-engines, 980 
 Counterpoise system of hoisting, 
 
 1164 
 Couples, 491 
 Couplings, flange, 1109 
 
 hose, standard sizes, 207 
 Coverings for steam-pipe, tests of, 
 
 558-561 
 Coversine of angles, table, 166-169 
 Cox's formula for loss of head, 717 
 Crane chains, 251, 252 
 installations, notable, 1168 
 pillar, 150-ton, 1168 
 Cranes, 1165 
 
 and hoists, power required for, 
 
 1169 
 classification of, 1165 
 compressed-air, 1168 
 electric, 1166-1168 
 electric, loads and speeds of, 
 
 1167 
 guyed, stresses in, 516 
 jib, 1165 
 
 power required for, 1166 
 quay, 1168 
 
 simple, stresses in, 515 
 traveling, 1166-1169 
 Crank angles, steam-engine, table, 
 1040 
 arm, dimensions of, 1009 
 pins, steam-engine, 1005-1009 
 pins, steel, specifications for, 483 
 shaft, steam-engine, torsion and 
 
 flexure of, 1019 
 shafts, steam-engine, 1017-1019 
 Cranks, steam-engine, 1009 
 Critical point in heat treatment of 
 steel, 456 
 temperature and pressure of 
 gases and liquids, 580 
 Cross-head guides, 1002 
 
 pin, 1009 
 Crucible steel, 451, 457, 466-470 
 
 (see Steel, crucible) 
 
 
cru-dri 
 
 1427 
 
 Crushing strength of masonry 
 
 materials, 349 
 Crystallization of iron by fatigue, 
 
 441 
 Cubature of volumes, 78 
 Cube root, 9 
 
 roots, table of, 94-109 
 Cubes of decimals, table, 109 
 Cubes of numbers, table, 94-109 
 Cubic feet and gallons, table, 129 
 
 measure, 18 
 Cupola fan, power required for, 
 1230 
 gases, utilization of, 1230 
 practice, 1224-1230 
 practice, improvement of, 1226 
 results of increased driving, 1229 
 Cupolas, blast-pipes for, 643 
 blast-pressure in, 1224-1228 
 blowers for, 633, 634 
 charges for, 1224-1227 
 charges in stove foundries, 1227 
 dimensions of, 1224 
 loss in melting iron in, 1230 
 rotary blowers for, 650 
 slag in, 1225 
 Current motors, 734 
 Currents, electric (see Electric cur- 
 rents) 
 Curve of PV n construction of, 576 
 Curves in pipe-lines, resistance of, 
 
 721 
 Cutting metal, resistance over- 
 come in, 1256 
 metals by oxyacetylene flame, 
 
 464 
 speeds of machine tools (see also 
 
 Tools, cutting), 1235 
 speeds of tools, economical, 1243 
 stone with wire, 1262 
 Cut-off for various laps and travel 
 
 of slide valves, 1042 
 Cycloid, construction of, 51 
 
 differential equations of, 82, 83 
 integration of, 82 
 measures of, 62 
 Cycloidal gear-teeth, 1138 
 Cylinder-condensation in steam- 
 engines, 936-937 
 lubrication, 1222 
 measures of, 63 
 Cylinders, hollow, resistance of to 
 collapse, 318-322 
 hollow, under tension, 316 
 hooped, 317 
 hydraulic press, thickness of, 317, 
 
 780 
 locomotive, 1088 
 steam-engine (see Steam-en- 
 gines) 
 steam-engine, ratios of, 950, 952, 
 
 956 
 tables of capacities of, 127 
 thick hollow, under tension, 316 
 thin hollow, under tension, 317 
 Cylindrical ring, 65 
 
 tanks, capacities of, table, 128 
 
 Dalton's law of gaseous pressures, 
 
 Dam, stability of, 491 
 
 Darcy's formula, flow of water, 704 
 
 formula, table from, of flow of 
 water in pipes, 709-711 
 Decimal equivalents of fractions, 3 
 
 equivalents of feet and inches, 5 
 
 gauge, 33 
 Decimals, 3 
 
 squares and cubes of, 109 
 Delta connection for alternating 
 currents, 1395 
 
 metal wire, 243, 369 
 Denominate numbers, 5 
 Deoxidized bronze, 371 
 Derrick, stresses in, 516 
 Diagonals, formulae for strains in, 
 
 519 
 Diametral pitch, 1134 
 Diesel oil engine, 1078 
 Differential calculus, 74-83 
 
 coefficient, 76 
 
 coefficient, sign of, 79 
 
 gearing, 1145 
 
 of exponential function, 80, 81 
 
 partial, 76 
 
 pulley, 513 
 
 second, third, etc., 78 
 
 screw, 514 
 
 screw, efficiency of, 1270 
 
 windlass, 514 
 Differentials of algebraic functions, 
 
 75 
 Differentiation, formulas for, 75 
 Discount, 12 
 
 Disk fans (see Fans, disk) 
 Displacement of ships, l3l7, 1322 
 Distillation of coal, 803 
 Distiller for marine work, 1061 
 Distilling apparatus, multiple sys- 
 tem, 543 
 Domed heads of boilers, 316 
 Domes on steam boilers, 889 
 Draught power of chimneys, 916, 
 
 917 
 Draught theory of chimneys, 915 
 Drawing-press, blanks for, 1272 
 Dressings, belt, 1128 
 Driers and drying, 547 
 
 performance of, 549 
 Drift bolts, resistance of in timber, 
 
 323 
 Drill gauge, table, 30 
 Drill pres?, horse-power required by, 
 
 1253, 1256 
 Drills, high-speed steel, 1253 
 
 rock, air required for, 616. 
 
 rock, requirements of air-driven, 
 616 
 
 tap, sizes of, 225, 1269 
 
 twist, experiments with, 1254 
 
 twist, speed of, 1253 
 Drilling, high-speed, data on, 1254 
 
 holes, speed of, 1253 
 
 steel and cast iron, power re- 
 quired for, 1254 
 
1428 
 
 dro-ele 
 
 INDEX. 
 
 Drop in electric circuits, 1352 
 in voltage of wires of different 
 
 sizes, 1356 
 press, pressures obtainable by, 
 1273 
 Dry measure, 19 
 
 Drying and evaporation, 542-547 
 apparatus, design of, 550 
 in a vacuum, 546 
 of different materials, 547 
 Ductility of metals, table, 177 
 Dulong's formula for heating value 
 of coal, 798 
 law of convection, table of factors 
 
 for, 571 
 law of radiation, table of factors 
 for, 570 
 Durability of cutting tools, 1243 
 
 of iron, 441,442 
 Durand's rule for areas, 57 
 Dust explosions, 807 
 
 fuel, 807 
 Duty, measure of, 28 
 of pumping-engine, 771 
 trials of pumping-engines, 771- 
 775 
 Dynamic and static properties of 
 
 steels, 476 
 Dynamics, fundamental equations 
 
 of, 502 
 Dynamo-electric machines, classi- 
 fication of, 1385 
 machines, e.m.f. of armature 
 
 circuit, 1386 
 machines, moving force of, 1385 
 machines, strength of field, 1387 
 machines, tables of, 1412 
 machines, torque of armature, 
 1385 
 Dynamometers, 1280 
 Alden absorption, 1281 
 hydraulic absorption, 6000 H.P., 
 
 1282 
 Prony brake, 1280 
 traction, 1280 
 transmission, 1282 
 Dyne, definition of, 488 
 
 Earth, cubic feet per ton, 178 
 Eccentric loading of columns, 278 
 
 steam-engine, 1020 
 Economical angle of framed struc- 
 tures, 522 
 Economics of power-plants, 984 
 Economizers, fuel, 894 
 Edison wire gauge, 31 
 
 wire-gauge table, 30 
 Efficiency, definition of, 12 
 
 of a machine, 507 
 
 of compressed-air engines, 613 
 
 of compressed-air transmission, 
 613 
 
 of electric transmission, 1361 
 
 of fans, 631 
 
 of fans and chimneys for venti- 
 lation, 683 
 
 of injector, 907 
 
 Efficiency of pumps, 759 
 
 of riveted joints, 405, 407 
 
 of screws, 1270 
 
 of steam-boilers, 860 
 
 of steam-engines, 934 
 Effort, definition of, 503 
 Ejector condensers, 1051 
 Elastic limit, 259-262 
 
 apparent, 260 
 
 Bauschinger's definition of, 261 
 
 elevation of, 261 
 
 relation of, to endurance, 261 
 
 resilience, 260 
 
 resistance to torsion, 311 
 
 Wohler's experiments on, 261 
 Elasticity, coefficient of, 260 
 
 modules of, 260 
 
 module of, of various materials, 
 351 
 Electric brakes, 1217 
 Electric circuits {see Circuits, elec- 
 tric) 
 
 current, cost of fuel for, 764 
 
 current, determining the direc- 
 tion of, 1384 
 
 current required to fuse wires, 
 1355 
 
 currents, alternating, 1387 (se* 
 Alternating currents) 
 
 currents, direct, 1352 
 
 currents, heating due to, 1354 
 
 currents, short-circuiting of, 
 1360 
 
 drive in the machine-shop, 1407 
 
 furnaces, 1376 
 
 generators, usual sizes, tables, 
 1412 
 
 heaters, 684 
 
 light stations, economy of en- 
 gines in, 963 
 
 lighting, 1367 
 
 lighting, cost of, 1373 
 
 lighting, terms used in, 1367 
 
 locomotive, 4000 H.P., 1366 
 
 motors {see also Motors), 1385, 
 1402 
 
 motors, alternating current, va- 
 riable speed, 1412 
 
 motors, auxiliary pole type, 
 1402 
 
 motors, commercial sizes, tables, 
 1412 
 
 motors for machine tools, 1407 
 
 motors, selection of, for different 
 service, 1405 
 
 motors, speed of, 1403 
 
 motors, speed control of, 1404 
 
 motors, types used for various 
 purposes, 1410 
 
 process of treating iron surfaces, 
 449 
 
 railway cars, resistance of, 1086 
 
 railway cars and motors, 1366 
 
 railways, 1366 
 
 storage-batteries, 1378 
 
 transmission, 1359-1364 {see 
 Transmission, electric) 
 
INDEX. 
 
 1429 
 
 Electric transmission, high tension, 
 notes on, 1399 
 transmission lines, spacing for 
 
 high voltages, 1399 
 welding, 1374 
 
 wires (see Wires and Copper 
 wires) 
 Electrical and mechanical units, 
 equivalent values of, 1347 
 conductivity of steel, 453 
 distribution, systems in use, 
 
 1364 
 engineering, 1344-1416 
 heating, 684 
 horse-power, 940, 1353 
 horse-power, table, 1364 
 machinery, alternating current, 
 
 standard voltages of, 1-699 
 machinery, shaft fit, allowances 
 
 for, 1274 
 machines, tables of (see Dyna- 
 mo-electric machines), 1412 
 power, cost of, 985 
 resistance, 1349 
 resistance of different metals 
 
 and alloys, 1350 
 symbols, 1416 
 systems, relative advantages of, 
 
 1363 
 units, relations of, 1346 
 Electricity, analogies to flow of 
 water, 1348 
 standards of measurements, 1344 
 systems of distribution, 1364 
 units used in, 1344 
 Electro-chemical equivalents, 1381 
 Electro-magnets, 1384 
 polarity of, 1384 
 strength of, 1384 
 Electro-magnetic measurements, 
 
 1348 
 Electro-motive force of armature 
 
 circuit, 1386 
 E.M.F. of electric circuits, 1352 
 Electrolysis, 1382 
 Electrolytic theory of corrosion, 
 
 444 
 Elements, chemical, table, 170 
 Elements of machines, 510-515 
 Elevators, coal, 1172 
 gravity discharge, 1172 
 perfect discharge, 1172 
 Ellipse, construction of, 46, 47 
 equations of, 72 
 measures of, 61 
 Ellipsoid, 65 
 
 Elongation, measurement of, 265 
 Emery, grades of, 1263-1266 
 wheels, speed and selection of, 
 
 1263, 1266 
 wheels, strains in, 1264 
 Endless screw, 514 
 Endurance of materials, relation of, 
 
 to elastic limit, 261 
 Energy, available, of expanding 
 steam, 842 
 conservation of, 506 
 
 Energy, definition of, 503 
 
 intrinsic or internal, 574 
 
 measure of, 503 
 
 mechanical, of steam expanded 
 to various pressures, 933 
 
 of recoil of guns, 506 
 
 of water in a pipe, 720 
 
 of water flowing in a tube, 734 
 
 sources of, 506 
 Engines, alcohol, 1078 
 
 automobile, capacity of, 1077 
 
 blowing, 652 
 
 compressed air, efficiency of, 613 
 
 fire, capacities of, 725 
 
 gas, 1071-1084 (see Gas-engines) 
 
 hoisting, 1163 
 
 hot-air or caloric, 1071 
 
 hydraulic, 783 
 
 internal combustion, 1071-1084 
 
 oil and gasoline, 1077 
 
 marine, steam-pipes for, 848 
 
 naphtha, 1071 
 
 petroleum, 1077 
 
 pumping, 771-775 (seePumping- 
 engines) 
 
 solar, 988 
 
 steam, 929 (see Steam-engines) 
 
 winding, 1163 
 Entropy, definition of, 573 
 
 of water and steam, 576 
 
 of water and steam, tables, 839- 
 843 
 
 temperature diagram, 574 
 Epicycloid, 51 
 
 Equalization of pipes, 596, 853 
 Equation of payments, 14 
 
 of pipes, 853 
 Equations, algebraic, 35-37 
 
 of circle, 72 
 
 of ellipse, 72 
 
 of hyperbola, 73 
 
 of parabola, 73 
 
 quadratic, 36 
 
 referred to co-ordinate axes, 7 
 Equilibrium of forces, 492 
 Equivalent orifice, mine ventila- 
 tion, 686 
 Equivalents, electro-chemical, 1381 
 Erosion of soils by water, 705 
 Euler's formula for long columns, 
 
 269 
 Evaporation, 542-547 
 
 by exhaust steam, 545 
 
 by multiple system, 543 
 
 factors of, 874-878 
 
 in a vacuum, 546 
 
 in salt manufacture, 543 
 
 latent heat of, 542 
 
 of sugar solutions, 545 
 
 of water from reservoirs and 
 channels, 543 
 
 total heat of, 542 
 
 unit of, 855 « 
 Evaporator, for marine work, 1061 
 Evolution, 8 
 Exhauster, steam-jet, 651 
 
1430 
 
 INDEX. 
 
 Exhaust-steam, evaporation by, 
 545 
 for heating, 981 
 Expansion, adiabatic, formulae for, 
 606 
 by heat, 538 
 coefficients of, 539 
 of air, adiabatic, tables, 609, 610 
 of cast iron, permanent by heat- 
 ing, 429 
 of gases, construction of curve of, 
 
 576 
 of gases, curve of, 74 
 of iron and steel, 441 
 of liquids, 540 
 of nickel steel, 474 
 of solids by heat, 539 
 of steam, 929 
 
 of steam, actual ratios of, 935 
 of timber, 345 
 of water, 687 
 Explosions, dust, 807 
 Explosive energy of steam-boilers, 
 
 902 
 Exponents, theory of, 37 
 Exponential function, differential 
 
 of, 80, 81 
 Eye bars, tests of, 338 
 
 Factor of safety, 352-355 
 of safety, formulas for, 354 
 of safety in steam-boilers, 879 
 of evaporation, 874-878 
 Factory heating by fan system, 
 
 681 
 Fahrenheit -Centigrade conversion 
 
 table, 524, 525 
 Failures of stand-pipes, 328 
 
 of steel, 462 
 Fairbairn's experiments on riveted 
 
 joints, 401 
 Falling bodies, graphic represen- 
 tation, 498 
 bodies, height and velocity of 
 
 tables, 499, 500 
 bodies, laws of, 497 
 Fans (see also Blowers) 
 and blowers, 626-653 
 and blowers, comparative effi- 
 ciencies, 631 
 best proportions of, 627 
 blast-area of, 629 
 centrifugal, 621, 626 
 centrifugal, high-pressure, 621 
 cupola, power required for, 1230 
 design of, 627 
 disk, 647-649 
 effect of resistance on capacity 
 
 of, 636 
 efficiency of, 631, 641, 648 
 experiments on, 630, 631 
 for cupolas, 633 
 
 high-pressure, capacity of, 635 
 influence of speed on efficiency, 
 
 647 
 influence of spiral casings, 646 
 methods of testing, 639 
 
 Fans, pipe lines for, 643 
 . pressure due to velocity of, 627 
 quantity of air delivered by, 628 
 theory of efficiency of, 641 
 Farad, definition and value of, 
 
 1345 
 Fatigue, effect of, on iron, 441 
 
 resistance of steels, 447 
 Feed and depth of cut, effect of, on 
 
 speed of tools, 1241 
 Feed-pump (see Pumps) 
 Feed water, cold, strains caused 
 by, 909 
 water heaters, 909-911 
 water heaters, transmission of 
 
 heat in, 564 
 water heating, saving due to, 
 
 909 
 water, purification of, 694, 695 
 water to boilers by gravity, 908 
 Feet and inches, decimal equiva- 
 lents of, table, 5 
 Fence wires, corrosion of, 444 
 Ferrite, 416, 456 
 
 Ferro-alloys for foundry use, 1232 
 silicon, addition of, to cast-iron, 
 
 426 
 silicon, dangerous, 1232 
 Field, magnetic, 1346 
 Fifth roots and powers of numbers, 
 
 110 
 Fineness, coefficient of, 1317 
 Finishing temperature, effect of. 
 
 in steel rolling, 454 
 Fink roof truss, 521 
 Fire, temperature of, 785 
 Fire-brick arches in locomotives, 
 
 1091 
 Fire-brick, number required for 
 various circles, table, 254 
 refractoriness of, 255 
 sizes and shapes of, 253 
 weight of, 253 
 Fire-clay, analysis of, 255 
 
 pyrometer, 526, 529 
 Fire-engines, capacities of, 725 
 Fire-proof buildings, 1338 
 Fire-streams, 722-725 
 
 discharge from nozzles at dif- 
 ferent pressures, 723 
 effect of increased hose length, 
 
 723 
 friction loss in hose, 725 
 pressure required for given 
 length of, table, 723 
 Fireless locomotive, 1103 
 Fits, force and shrink, 1273 
 
 force and shrink, pressure re- 
 quired to start, 1275 
 limits of diameter for, 1274 
 press, pressure required for, 
 
 1274 
 running, 1274 
 stresses due to, 1275 
 Fittings (see Pipe-fittings) 
 
 cast-iron pipe, sizes and weights, 
 table, 196-197 
 
INDEX. 
 
 fla-for 
 
 1431 
 
 Flagging, strength of, 550 
 
 Flanges, cast-iron, forms of, 202 
 forged and rolled steel, 200 
 forged steel, for riveted pipe, 
 
 214 
 for riveted pipe, 201 
 pipe, extra heavy, table, 199 
 pipe, standard, table, 198 
 
 Flat plates in steam-boilers, 880, 
 885, 888 
 plates, strength of, 313 
 steel ropes, 248 
 surfaces in steam-boilers, 888 
 
 Flanged fittings, cast-iron, 203 
 fittings, cast-steel, 204 
 
 Flexure of beams, formula for, 282 
 and compression combined, 312 
 and tension combined, 312 
 and torsion combined, 312 
 
 Flight conveyors, 1172 
 
 Flights, sizes and weights of, 1174 
 
 Floors, maximum load on, 1337, 
 1340 
 strength of, 1337-1340 
 
 Flow of air in long pipes, 595 
 of air in pipes, 591 
 of air through orifices, 588, 642 
 of compressed air, 594 
 of gases, 579 
 of gas in pipes, 834-836 
 of gas in pipes, tables, 835 
 of metals, 1273 
 of steam at low pressure, 669 
 of steam, capacities of pipes, 
 
 847 
 of steam in long pipes, 847 
 of steam in pipes, 845 
 of steam, loss of pressure due to 
 
 friction, 845 
 of steam, loss of pressure due to 
 
 radiation, 849 
 of steam, Napier's rule, 844 
 of steam, resistance of bends, 
 
 valves, etc., 848 
 of steam through a nozzle, 844, 
 
 1065 
 of steam through safety valves, 
 
 905 
 of steam, tables of, 669, 846, 847 
 of water, 697 
 of water, approximate formulse, 
 
 720 
 of water, Chezy's formula, 699 
 of water, D'Arcy's formula, 704 
 of water, experiments and tables, 
 
 706-713 
 of water, exponential formula, 
 
 718 
 of water, fall per mile and slope, 
 
 table, 700 
 of water, formulse for, 697-706 
 of water in cast-iron pipe, 706 
 of water in house service pipes, 
 
 table, 712 
 of water in pipes, 699 
 
 Flow of water in pipes at uniform 
 
 velocity, table, 710 
 of water in pipes, table from 
 
 D'Arcy's formula, 709-711 
 of water in pipes, table from 
 
 Kutter's formula, 707, 708 
 of water in 20-in. pipe, 706 
 of water in riveted steel pipes, 
 
 714 
 of water, Kutter's formula, 701 
 of water over weirs, 697, 731 
 of water through nozzles, table, 
 
 713 
 of water through orifices, 697 
 of water through rectangular 
 
 orifices, 72_9 
 of water, VV for pipes and con- 
 duits, table, 701 
 of water, values of c, 703 
 of water, values of coefficient of 
 
 friction, 715 
 Flowing water, horse-power of, 
 
 734 
 water, measurement of, 727- 
 
 733 
 Flues, collapsing pressure of, 318 
 corrugated, British rules, 318, 881 
 corrugated, U. S. rules, 886 
 
 {see also Tubes and Boilers) 
 Flux, magnetic, 1348 
 Fly-wheels, centrifugal force in, 
 
 1029 
 diameters for various speeds, 
 
 1030 
 steam-engine, 1026-1034 {see 
 
 Steam-engines) 
 wire-wound, for extreme speeds, 
 
 1034 
 weight of, for alternating current 
 
 units, 1028 
 Foaming or priming of steam- 
 boilers, 692, 899 
 Foot-pound, unit of work, 503 
 Force, centrifugal, 497 
 definitions of, 488 
 graphic representation of, 489 
 moment of, 490 
 of a blow, 504 
 of acceleration, 501 
 of wind, 597 
 units of, 488 
 Forces, composition of, 489 
 equilibrium of, 492 
 parallel, 491 
 parallelogram of, 489 
 parallelopipedon of, 490 
 polygon of, 489 
 resolution of, 489 
 work, power, etc., 503 
 Forced draught in steam-boilers, 
 
 894 
 Forcing and shrinking fits, 1273 
 
 {see Fits) 
 Forging and grinding of tools, 1240 
 heating of steel for, 468 
 hydraulic. 782 
 of tool steel, 464, 468, 1240 
 
1432 
 
 for-gal 
 
 INDEX. 
 
 Forgings, steel, annealing of, 458 
 
 strength of, 331 
 Forging-press, hydraulic, 782 
 Foundation walls, thickness of, 
 
 1334 
 Foundations of buildings, 1333 
 
 masonry, allowable pressures on, 
 1334 
 Foundry coke, quality of, 1232 
 
 irons (see Pig iron and Cast iron) 
 
 ladles, dimensions of, 1234 
 
 molding-sand, 1233 
 
 practice, 1224-1234 
 
 practice, shrinkage of castings, 
 1231 
 
 practice, use of softeners, 1230 
 
 use of ferro alloys in, 1232 
 Fractions, 2 
 
 product of, in decimals, 4 
 Frames, steam-engine, 1025 
 Framed structures, stresses in, 515- 
 
 522 
 Framing, for tanks with flat sides, 
 
 316 
 Francis's formulae for weirs, 731 
 Freezing point of water, 690 
 French measures and weights, 22- 
 27 
 
 thermal unit, 532 
 Frequency of alternating currents, 
 1387 
 
 standard, in electric currents, 
 1399 
 Friction and lubrication, 1194-1223 
 
 brakes and friction clutches, 1216 
 
 brakes, capacity of, 1281 
 
 clutches, 1155 
 
 coefficient of, definition, 1194 
 
 coefficient of, in water-pipes, 715 
 
 coefficient of, tables, 1195-1197 
 
 drives, power transmitted by, 
 1154 
 
 fluid, laws of, 1196 
 
 laws of, of lubricated journals, 
 1201 
 
 loss of head by, in water-pipes , 
 716 
 
 moment of, 1205 
 
 Morin's laws of, 1200 
 
 of car iournals, 1204 
 
 of hydraulic packing, 780, 1217 
 
 of lubricated journals, 1199-1209 
 
 of air in mine passages, 685 
 
 of metals, under steam pressure, 
 1200 
 
 of motion, 1194, 1197 
 
 of pivot bearings, 1205, 1209 
 
 of rest, 1195 
 
 of solids, 1195 
 
 of steam-engines, 1215 
 
 of steel tires on rails, 1195 
 
 rollers, 1210 
 
 rolling, 1195 
 
 unlubricated, law of, 1195 
 
 work of, 1205 
 Frictional gearing, 1154 
 
 heads, flow of water, 716 
 
 Frustum of cone, 63 
 
 of parabolic conoid, 66 
 
 of pyramid, 63 
 
 of spheroid, 65 
 
 of spindle, 66 
 Fuel, 784-827 
 
 bagasse, 809 
 
 charcoal, 805-807 (see Charcoal) 
 
 coke, 801-804 (see Coke) 
 
 combustion of, 784 
 
 dust, 807 
 
 economizers, 894 
 
 for cupolas, 1225, 1232 
 
 gas, 814 (see Gas) 
 
 gas, for small furnaces, 824 
 
 heat of combustion of, 533,784 
 
 liquid, 810-814 
 
 peat, 808 
 
 pressed, 801 
 
 sawdust, 808 
 
 solid, classification of, 786 
 
 straw, 808 
 
 theory of combustion of, 784 
 
 turf, 808 
 
 weight of, 177 
 
 wet tan bark, 808 
 
 wood, 804, 805 
 Functions, of sun and difference of 
 angles, 69 
 
 of twice an angle, 70 
 
 trigonometric, tables of, 166, 169 
 
 trigonometric, of half an angle, 70 
 Furnace flues, steam-boiler, for- 
 
 mulse for, 881 
 Furnace for melting iron for mallea- 
 ble castings, 430 
 
 heating (see Heating) 
 Furnaces, blast, gases of, 825 
 
 blast, temperature in, 528 
 
 corrugated, 319 
 
 down draught, 890 
 
 electric, 1376 
 
 for different coals, 798 
 
 for house heating, 664 
 
 gas, fuel for, 824 
 
 hot-air, heating of, 661 
 
 industrial, temperatures, in, 527 
 
 open hearth, temperature in, 528 
 
 steam-boiler (see Boiler-furnaces) 
 Fusibility of metals, 175-177 
 Fusible alloys, 380 
 
 plugs in boilers, 379, 889 
 Fusing temperatures of substances, 
 
 527, 532 
 Fusing-disk, 1262 
 Fusion, latent heat of, 541 
 
 of electrical wires, 1355 
 
 g, value of, 498 
 
 Gallon, British and American, 28 
 
 Gallons and cubic feet, table, 129 
 
 per minute, cubic feet per second, 
 129 
 Galvanic action, corrosion by, 443 
 Galvanized wire rope, 247 
 
 wire, test for, 450 
 
INDEX. 
 
 gal-gen 
 
 1433 
 
 Galvanizing by cementation, 450 
 
 iron surfaces, 449, 450 
 Gas (see also Fuel-gas, Water-gas, 
 Producer gas, Illuminating gas) 
 
 ammonia, 1285-1289 
 
 analyses by volume and weight, 
 824 
 
 and oil engines, rules for testing, 
 1081 
 
 and vapor mixtures, laws of, 578 
 
 anthracite, 815 
 
 bituminous, 816 
 
 carbon, 814 
 
 coal, 828 
 
 flow of, in pipes, 834-836 (see 
 Flow of gas) 
 
 flow of, in long pipes, 596 
 
 fuel (see also Water-gas) 
 
 fuel, cost of, 833 
 
 fuel for small furnaces, 824 
 
 illuminating, 828-834 (see Illu- 
 minating-gas) 
 
 natural, 817, 818 
 
 perfect, equations of a, 574 
 
 producer, 818 
 
 producer, combustion of, 819 
 
 producer, from ton of coal, 818 
 
 sulphur-dioxide, 1285 
 
 water, 817, 829-833 (see Water- 
 gas) 
 Gases, absorption of, by liquids, 
 579 
 
 Avogadro's law of, 578 
 
 combustion of, rise of tempera- 
 ture in, 786 
 
 cupola, utilization of, 1230 
 
 densities of, 578 
 
 expansion of, 575, 577 
 
 expansion of by heat, table, 538 
 
 flow of, 579 
 
 heat of combustion of, 533 
 
 law of Charles, 574, 578 
 
 liquefaction of, 579 
 
 Mariotte's law of, 577 
 
 of combustion, analyses of, 785 
 
 physical properties of, 577-580 
 
 specific heats of, 535, 537 
 
 waste, use of, under boilers, 865, 
 866 
 
 weight and specific gravity of, 
 table, 173 
 Gas-engine, economical perform- 
 ance of, 1080 
 
 heat losses in, 1080 
 
 tests with different coals, 823 
 Gas-engines, 1071-1084 
 
 calculation of the power of, 1073 
 
 conditions of maximum effi- 
 ciency, 1079 
 
 efficiency of, 1079 
 
 four-cycle and two-cycle, 1072 
 
 governing, 1079 
 
 horse-power, estimate of, 1077 
 
 ignition, 1078 
 
 mean effective pressure in, 1076 
 
 pressures developed in, 1072 
 
 Gas-engines, sizes of, 1076 
 
 temperatures and pressures in, 
 
 1072, 1074 
 tests of, 1081-1084 
 Gas-exhausters, rotary, 651 
 Gas-producer practice, 821 
 Gas-producers and scrubbers, pro- 
 portions of, 819 
 use of steam in, 824 
 Gasoline engines, 1077 
 
 vapor pressures of, 814 
 Gauge, decimal, 33 
 sheet metal, 29, 31-33 
 Stub's wire, 29, 30 
 wire, 29-31 
 Gauges, limit, for iron for screw 
 
 threads, 223 
 Gauss, definition and value of, 
 
 1346, 1348 
 Gear, reduction, for steam turbines, 
 
 1071 
 reversing, 1020 
 wheels, calculation of speed of. 
 
 1137 
 wheels, formulae for dimensions, 
 
 1135, 1136 
 wheels, milling cutters for, 1138 
 wheels, proportions of, 1137 
 worm, 514 
 Gears, automobile, efficiency of, 
 
 1148 
 lathe, for screw cutting, 1236 
 of lathes, quick change, 1237 
 Gears, spur, machine-cut, 1153 
 
 with short teeth, 1135 
 Gearing, annular, 1145 
 bevel, 1144 
 chordal pitch, 1135 
 comparison of formulae, 1150- 
 
 1153 
 cycloidal teeth, 1138 
 differential, 1145 
 efficiency of, 1146-1148 
 forms of teeth, 1138-1145 
 formulae for dimensions of, 1135, 
 
 1136 
 frictional, 1154 
 involute teeth, 1140 
 pitch, pitch-circle, etc., 1133 
 pitch diameters for 1-inch circu- 
 lar pitch, 1135 
 proportions of teeth, 1135, 1136 
 racks, 1141 
 raw-hide, 1153 
 relation of diametral and circular 
 
 pitch, 1134 
 speed of, 1153 
 spiral, 1143 
 stepped, 1143 
 strength of, 1148-1156 
 toothed-wheel, 514, 1133-1153 
 twisted, 1143 
 worm, 1143 
 
 worm, efficiency of, 1147 
 Generator sets, standard dimensions 
 
 of, 979 
 
1434 
 
 gen-hea 
 
 INDEX. 
 
 Generators, alternating current, 
 1396 (see Dynamo electric 
 machines) 
 electric, 1385, 1412 
 Geometrical problems, 38-54 
 progression, 11 
 propositions, 54 
 Geometry,, analytical, 71 
 German silver, 334, 378 
 conductivity of, 1350 
 Gesner process, treating iron sur- 
 faces, 449 
 Gilbert, unit of magneto-motive 
 
 force, 1348 
 Girders, allowed stresses in plate 
 and lattice, 274 
 and beams, safe load on, 1334 
 building, New York building 
 
 laws, 1338 
 iron-plate, strength of, 331 
 steam-boiler, rules for, 882 
 Warren, stresses in, 520 
 Glass, skylight, sizes and weights, 
 190 
 strength of, 343 
 weight of, 174 
 Gordon's formula for columns, 270 
 Gold, mating temperature of, 527 
 
 properties of, 175 
 Governing of gas-engines, 1079 
 Governor, inertia, 1048 
 Governors, steam-engine, 1047- 
 
 1050 
 Grade line, hydraulic, 721 
 Grain, weight of, 178 
 Granite, strength of, 335, 348 
 Graphite, Acheson's deflocculated, 
 1223 
 lubricant, 1223 
 paint, 447 
 Grate surface, for house heating, 
 boilers and furnaces, 665 
 surface in locomotives, 1091 
 surface of a steam-boiler, 857 
 Gravel, cubic feet per ton, 178 
 Gravity, acceleration due to, 497 
 boiler-feeders, 908 
 center of, 492 
 
 specific (see Specific gravity), 
 170-174 
 Grease lubricants, 1221 
 Greatest common measure or 
 
 divisor, 2 
 Greek letters, 1 
 
 Greenhouses, hot-water, heating 
 of, 674 
 steam-heating of, 673 
 Grinding of tools, 1240, 1241 
 
 wheel for high-speed tools, 1240, 
 
 1267 
 wheels (see Grindstones and 
 
 Emery wheels) 
 wheels, speeds of, 1264 
 Grindstones, speed of, 1267 
 strains in, 1267 
 varieties of, 1268 
 
 Guest's formula for combined 
 
 stresses, 312 
 Gun-bronze, variation in strength 
 
 of, 362 
 Gun-iron, variation in strength of, 
 
 428 
 Gun-metal (bronze), composition 
 
 of, 366 
 Guns, energy of recoil of, 506 
 Gurley's bronze, composition of, 366 
 Guy ropes, wire, 247 
 
 for stand-pipes, 327 
 Guy-wires, table of weights, and 
 
 strength, 249 
 Gyration, center of, 494 
 radius of, 279 
 table of radii of, 495 
 
 H-columns, Bethlehem steel, 309, 
 
 310 
 Halpin heat storage system, 897, 
 
 987 
 Hammering, effect of, on steel, 464 
 Hardening of steel, 455 
 Hardness of copper-tin alloys, 361 
 of metals, Brinell's tests, 342 
 electro-magnetic tests of, 343 
 scleroscope tests, 343 
 of water, 694 
 Harvey process of hardening steel, 
 
 1246 
 Haulage, wire-rope, 1177-1181 
 wire-rope, endless rope system, 
 
 1178 
 wire-rope, engine-plane, 1178 
 wire-rope, inclined-plane, 1177 
 wire-rope, tail-rope system, 1178 
 wire-rope tramway, 1179 
 Hauling capacity of locomotives, 
 
 1087 
 Hawley down-draught furnace, 890 
 Hawsers, flexible steel wire, 249 
 steel, table of sizes and strength, 
 
 249 
 steel, weight of, 249 
 Head, frictional, in cast-iron pipe, 
 table, 719 
 loss of, 714-722 (see Loss of 
 
 head) 
 of air, due to temperature differ- 
 ences, 687 
 of water, 699 
 
 of water, comparison of, with 
 various units, 689 
 Heads of boilers, 885 
 
 of boilers, unbraced, wrought - 
 iron, strength of, 314 
 Heat, 523-577 
 
 conducting power of metals, 553 
 conduction by various substances, 
 
 554-561 
 conduction of, 553 
 convection of, 553 
 effect of on grain of steel, 456 
 expansion due to, 538 
 generated by electric current, 
 1354 
 
INDEX. 
 
 1435 
 
 Heat, latent, 541 (see Latent heat) 
 
 loss by convection, 570 
 
 losses in steam power plants, 985 
 
 mechanical equivalent of, 532, 
 837 
 
 of combustion, 533 
 
 of combustion of fuels, 533, 784 
 
 quantitative measurement of, 
 532 
 
 radiating power of substances, 
 552 
 
 radiation of, 551 (see also Radia- 
 tion) 
 
 reflecting power of substances, 
 552 
 
 resistance, coefficients of, 556 
 
 resistance, reciprocal of con- 
 ductivity, 555 
 
 specific, 534-538 (see Specific 
 heat) 
 
 steam, storing of, 897, 987 
 
 storage, Halpin system, 897, 987 
 
 transmission, Blechynden's tests 
 of, 567 
 
 transmission from flame to water, 
 567 
 
 transmission from gases to water, 
 566 
 
 transmission from steam to water, 
 561, 652 
 
 transmission, in condenser tubes, 
 563 
 
 transmission in feed water heater, 
 564 
 
 transmission in radiators, 669 
 
 transmission, resistance of metals, 
 553 
 
 transmission through building 
 walls, etc., 557, 659 
 
 transmission through plates, 553, 
 567 
 
 transmission through plates from 
 steam or hot water to air, 569 
 
 treatment of steel (see Steel) 
 
 treatment of high speed tool 
 steel, 1242 
 
 unit of, 532, 837 
 
 units per pound of water, 688 
 Heaters and condensers, calcula- 
 tion of surface of, 910 
 
 cast iron, for hot-blast heating, 
 680 
 
 cast iron, tests of, 680 
 
 electric, 1375 
 
 feed-water, 909-911 
 
 feed-water, open type, 911 
 
 feed-water, transmission of heat 
 in, 564 
 Heating a building to 70°, 683 
 Heating and Ventilation, 653-687 
 
 allowance for exposure and leak- 
 age, 660 
 
 blower system, 678-681 
 
 boiler heating surface, 667 
 
 computation of radiating surface, 
 669 
 
 heating surface, indirect, 669 
 
 Heating and Ventilation, heating 
 
 value of radiators, 656, 668 
 
 hot-water heating, 674-678 (see 
 
 Hot-water heating) 
 overhead steam pipes, 673 
 steam-heating, 665-674 (see 
 
 Steam-heating) 
 transmission of heat through 
 building walls, 659 
 Heating air, heat absorbed in, 662 
 Heating, blower system, capacity 
 of fans for, 682 
 by electricity, 684 
 by exhaust steam, 981 
 by hot-air furnaces, 661 
 by hot water, 675 (see Hot-water 
 
 heating) 
 by steam (see Steam-heating) 
 furnace, size of air pipes for, 663 
 furnace, with forced air supply, 
 
 664 
 guarantees, performance of, 683 
 of electrical conductors, 1354 
 of factories by blower system, 681 
 of greenhouses, 673 
 of large buildings, 656 
 of steel for forging, 468 
 of tool steel, 467 
 value of coals, 797, 798 
 value of wood, 804 
 water by steam coils, 565 
 Heating-surface of steam boiler, 
 
 855, 856 
 Heat-insulating materials, tests 
 
 of, 555 
 Height, table of, corresponding to 
 
 a given velocity, 499 
 Helical steel springs, 395 
 Helix, 62 
 
 Hemp rope, table of strength and 
 weight of, 386, 387 
 rope strength of, 335 
 Henry, definition and value of, 
 
 1345 
 High speed tool steel (see Steel, 
 
 and Tools) 
 Hindley worm gear, 1144 
 Hobson's hot-blast pyrometer, 528 
 Hodgkinson's formula for columns, 
 
 269 
 Hoisting by hydraulic pressure, 
 781 
 counterpoise system, 1164 
 cranes, 1165 (see Cranes) 
 effect of slack rope, 1162 
 endless rope system, 1165 
 engines, 1163 
 
 engines, compressed-air, 618 
 engines, counterbalancing of, 
 
 1163 
 horse-power required for, 1162 
 Koepe system, 1165 
 limit of depth for, 1162 
 loaded wagon system, 1164 
 of cargoes, 390 
 pneumatic, 1163 
 
1436 
 
 Hoisting rope, 386 
 
 rope, iron or steel, dimensions, 
 strength, and properties, table, 
 244 
 ropes, sizes and strength of, 390, 
 
 906 
 ropes, stresses in, on inclined 
 
 planes, 1179 
 rope, tension required to pre- 
 vent slipping, 1182 
 suspension cable ways, 1181 
 tapering ropes, 1164 
 Holding power of bolts in white 
 pine, 324 
 power of expanded boiler tubes, 
 
 342 
 power of lag-screws, 324 
 power of nails in wood, 324 
 power of nails, spikes and screws, 
 
 323 
 power of tubes expanded into 
 
 sheets, 342 
 power of wood screws, 324 
 Hollow cylinders, resistance of to 
 coUapse, 318-322 
 shafts, torsional strength of, 311 
 Homogeneity test for fire-box 
 
 steel, 484 
 Hooks and shackles, strength of, 
 1161 
 heavy crane, 1159 
 proportions of, 1159 
 Horse-gin, 509 
 Horse, work of, 508 
 Horse-power, brake, definition of, 
 991 
 computed from torque, 1386 
 constants, of steam-engines, 
 
 941-944 
 cost of, 735 
 definition of, 28, 503 
 electrical, 940, 1353 
 electrical, table of, 1364 
 hours, definition of, 503 
 nominal, definition of, 944 
 of fans, 630 
 of flowing water, 734 
 of marine and locomotive boilers, 
 
 857 
 of steam-boilers, 854 
 of steam-boilers, builders' rat- 
 ing, 857 
 of steam-engines, 940-946 
 Hose couplings, national stand- 
 ard, 207 
 fire, friction losses in, 725 
 hydrant pressures required with 
 
 different lengths of, 723 
 rubber-lined, friction loss in, 725 
 Hot-air engines, 1071 
 Hot-air heating (see Heating) 
 Hot-blast pyrometer, Hobson's, 
 528 
 system of heating, 680 (see Heat- 
 ing) 
 Hot boxes, 1205 
 
 Hot-water heating, 674-678 
 
 heating, arrangement of mains, 
 
 674 
 heating, computation of radiating 
 
 surface, 675, 677 
 heating, indirect, 676 
 heating of greenhouses, 674 
 heating, rules for, 674 
 heating, size of pipes for, 675 
 heating, sizes of flow and return 
 
 pipes, 678 
 heating, velocity of flow, 674 
 heating with forced circulation, 
 678 
 House-heating (see Heating) 
 House-service pipes, flow of water 
 
 in, table, 712 
 Howe truss, stresses in, 520 
 Humidity, relative, table of, 551, 
 
 583 
 Hyatt roller bearings, 1211 
 Hydraesfer process, treating iron 
 
 surfaces, 449 
 Hydrant pressures required with 
 
 different lengths of hose, 723 
 Hydraulic air compressor, 622 
 apparatus, efficiency of, 780 
 cylinders, thickness of, 780 
 engine, 783 
 forging, 782 
 formulae, 697-706 
 formulae, approximate, 720 
 grade-line, 721 
 packing, friction of, 780 
 pipe, table, 212 
 power in London, 781 
 press, thickness of cylinders for, 
 
 317 
 presses in iron works, 781 
 pressure, hoisting by, 781 
 pressure, transmission, 779-783 
 pressure transmission, energy of, 
 
 779, 780 
 pressure transmission, speed of 
 water through pipes and 
 valves, 781 
 ram, 778, 779 
 riveting machines, 782 
 Hydraulics (see Flow of water) 
 Hydrometer, 172 
 
 dry and wet bulb, 583 
 Hyperbola, asymptotes of, 74 
 construction of, 50 
 curve on indicator diagrams, 
 
 944 
 equations of, 73 
 Hyperbolic logarithms, tables of, 
 
 163-165 
 Hypocycloid, 51 
 
 I-beams (see also Beams) 
 
 Carnegie, table of, 288 
 
 safe loads on, 290 
 
 spacing of, for uniform load, 291' 
 Ice, properties of, 691 
 
 strength of, 344 
 
INDEX. 
 
 1437 
 
 Ice-making, absorption evaporator 
 system, 1316 
 
 making machines, 1282-1316 (see 
 Refrigerating machines) 
 
 making plant, test of, 1315 
 
 making, tons of ice per ton of 
 coal, 1316 
 
 making with exhaust steam, 1316 
 
 manufacture, 1314 (see Refrige- 
 erating machines) 
 
 melting effect, 1291 
 Ignition in gas engines, 1078 
 Illuminating-gas, 828-834 
 
 calorific equivalents of constitu- 
 ents, 830 
 
 coal-gas, 828 
 
 fuel value of, 833 
 
 space required for plants, 832 
 
 water-gas, 829 
 Illumination, 1367 
 
 by arc lamps at different dis- 
 tances, 1368 
 
 of buildings, watts per square foot 
 required for, 1369 
 
 relation of, to vision, 1368 
 Illuminants, relative color values 
 
 of, 1367 
 Impact, 505 
 Impedance, 1389 
 
 polygons, 1390 
 Impulse water wheels, 749 (see Wa- 
 ter wheel, tangential) 
 Impurities of water, 691 
 Incandescent lamp, 1370 
 
 lamps (see Lamps) 
 Inches and fractions as decimals 
 
 of a foot, table, 5 
 Inclined-plane, 512 
 
 motion on, 502 
 
 stresses in hoisting ropes on, 1179 
 
 wire-rope haulage, 1177 
 Incrustation and scale, 691, 692 
 India rubber, action under tension, 
 356 
 
 vulcanized, tests of, 356 
 Indicated horse-power, 940-946 
 Indicator diagrams, analysis of, 992 
 
 rig, 939 
 
 tests of locomotives, 1098 
 Indicators, steam-engine, 938-946 
 (see Steam-engines) 
 
 steam-engine, errors- of, 939 
 Indirect heating radiators, 669 
 Inductance, 1389 
 
 of lines and circuits, 1393 
 Induction, magnetic, 1348 
 
 motor applications, 1410 
 
 motors, 1409 
 Inertia, definition of, 488 
 
 moment of, 279, 493 
 Ingots, steel, segregation in, 462 
 Injector, 776 
 
 efficiency of, 907 
 
 equation of, 906 
 Inoxidizable surfaces, production 
 
 of, 448 
 Inspection of steam-boilers, 901 
 
 Insulation, underwriters', 1355 
 Insulators, electrical value of, 1350 
 
 heat, 555 
 Intensity of magnetization, 1346 
 Integrals, 76 ■ 
 
 table of, 81, 82 
 Integration, 77 
 Intercoolers for air compressors, 
 
 620 
 Interest, 12 
 
 compound, 13 
 Interpolation, formula for, 87 
 Invar, iron-nickel alloy, 475, 540 
 Involute, 53 
 gear-teeth, 1140 
 
 gear-teeth, approximation of, 
 1142 
 Involution, 7 
 
 Iron and steel, 175, 413-484 
 and steel, classification of, 413 
 and steel, effect of cold on 
 
 strength of, 440 
 and steel, inoxidizable surface 
 
 for, 448 
 and steel, Pennsylvania Rail- 
 road specification for, 438 
 and steel, preservative coatings 
 
 for, 447-450 
 and steel, relative corrosion of, 
 
 444 
 and steel, rustless coatings for, 
 
 447-450 
 and steel sheets, weight of, 181 
 and steel, specific heat of, 535, 
 
 536 
 and steel, tensile strength at 
 high temperatures, 439 
 Iron bars (see Bars) 
 
 bars, weight of square and round, 
 
 180 
 bridges, durability of, 442 
 cast, 414-429 (see Cast-iron) 
 coefficients of expansion of, 441 
 color of, at various temperatures, 
 
 531 
 copper-zinc alloys, 369 
 corrosion of, 443 
 corrugated, sizes and weights, 
 
 186 
 durability of, 441-442 
 flat-rolled, weight of, 182, 183 
 for bolts, variation in size of, 223 
 for stay-bolts, 438 
 latent heat of fusion of, 541 
 malleable, 429 (see Malleable 
 
 iron) 
 pig (see Pig-iron and Cast-iron) 
 plates, approximating weight of, 
 
 461 
 plate, weight of, table, 184 
 properties of, 175 
 rivets, shearing resistance of, 407 
 rope, flat, table of strength of, 
 
 387 
 lope, table of strength of, 386 
 shearing strength of, 340 
 sheets, weights of, 33, 181 
 
1438 
 
 INDEX. 
 
 Iron tubes, collapsing pressure of, 
 
 silicon-aluminum alloys, 374 
 
 wrought, 435-439 (see Wrought 
 iron) 
 Iridium, properties of, 175 
 Irregular figure, area of, 57, 58 
 
 solid, volume of, 66 
 Irrigation canals, 704 
 Isothermal compression of air, 604 
 
 expansion, 575 
 
 expansion of steam, 929 
 
 Japanese alloys, composition of, 
 
 368 
 Jarno tapers, 1271 
 Jet condensers, 1050 
 
 propulsion of ships, 1333 
 
 reaction of a, 1333 
 Jets, vertical water, 722 
 Joints, riveted, 401-412 (see Riv- 
 eted joints) 
 Joists, contents of, 21 
 Joule, definition and value of, 1345 
 Joule's equivalent, 533 
 Journals (see also Shafts, and Bear- 
 ings) 
 
 coefficients of frictioa of, 1197 
 Journal-bearings, cast-iron, 1199 
 
 friction of, 1199-1209 
 
 of engines, 1015 
 
 Kaolin, melting point of, 529 
 Kelvin's rule for electric trans- 
 mission, 1360 
 Kerosene for scale in boilers, 899 
 Keys, dimensions of, 1276 
 for machine tools, 1277 
 for shafting, sizes of, 1277 
 holding power of, 1278 
 sizes of, for mill-gearing, 1276 
 Keyways for milling cutters, 1248 
 Kinetic energy, 503 
 King-post truss, stresses in, 517 
 Kirkaldy's test on strength of 
 
 materials, 330-336 
 Knife-edge bearings, 1214 
 Knot, or nautical mile, 17 
 Knots, 391-392 
 
 Koepe's system of hoisting, 1165 
 
 Krupp steel tires and axles, 332 
 
 Kutter's formula, flow of water, 701 
 
 formula, table from, of flow of 
 
 water in pipes, 707, 708 
 
 Lacing of belts, 1124 
 
 Ladles, foundry, sizes of, 1234 
 
 Lag screws, 234 
 
 holding power of, 324 
 Lamp, mercury vapor, 1369 
 Lamps, arc, 1368 
 
 arc, data of, 1369 
 
 arc, illumination by, at different 
 distances, 1368 
 
 incandescent, characteristics of, 
 1371 
 
 Lamps, incandescent electric, 1370 
 
 incandescent, rating of, 1370 
 
 incandescent, variation in can- 
 dle-power, efficiency and life, 
 1371 
 
 life of, 1370-1376 
 
 Nernst, 1372 
 
 specifications for, 1372 
 
 tantalum and tungsten, 1372 
 Land measure, 17 
 Lang lay rope, 246 
 Lap and lead in slide valves, 1034- 
 
 1036 
 Lap-joints, riveted, 406 
 Latent heat of ammonia, 1285 
 
 heat of evaporation, 542 
 
 heat of fusion of various sub- 
 stances, 541 
 
 heat of fusion of iron, 541 
 Lathe, change-gears for, 1237 
 
 cutting speed of, 1235 
 
 horse-power to run, 1257-1260 
 
 rules for screw-cutting gears, 
 1236 
 
 setting taper in, 1238 
 
 tools, forms of, 1238 
 Lattice girders, allowed stresses in, 
 
 274 
 Laws of falling bodies, 497 
 
 of motion, 488 
 Lead and tin tubing, 217, 218 
 
 coatings on iron surfaces, 450 
 
 effect of, on copper alloys, 369 
 
 pipe, tin-lined, sizes and weights, 
 table, 217 
 
 pipe, weights and sizes of, table, 
 217 
 
 properties of, 175 
 
 sheet, weight of, 218 
 
 waste-pipe, weights and sizes of, 
 218 
 Lead-lined iron pipe, 218 
 Leakage of steam in engines, 946 
 Least common multiple, 2 
 Leather, strength of, 335 
 Le Chatelier's pyrometer, 526 
 Lentz compound engine, 9"" 
 Leveling by barometer, 582 
 
 by boiling water, 582 
 Lever, 510 
 
 bent, 511 
 Lighting, electric, 1367 
 
 electric, cost of, 1373 
 Lightning protection of chimneys, 
 
 920 
 Lignites, analysis of, 796 
 Lime and cement mortar, strength 
 of, 350 
 
 weight of, 178 
 Limestone, strength of, 349 
 Limit, elastic, 259-262 . 
 
 gages for screw-thread iron, 223 
 Lines of force, 1382 
 Links, steel bridge, strength of, 331 i 
 
 steam-engine, size of, 1020 
 Link-belting, sizes and weights, 
 1174 
 
 _. 
 
INDEX. 
 
 lin-mag 
 
 1439 
 
 Link-motion, locomotive, 1095 
 
 steam-engine, 1044-1046 
 Lintels in buildings, 1338 
 Liquation of metals in alloys, 364 
 Liquefaction of gases, 579 
 Liquid air, 579 
 
 measure, 18 
 Liquids, absorption of gases by, 579 
 
 compressibility of, 172 
 
 expansion of, 540 
 
 specific gravity of, 172 
 
 specific heats of, 535 
 Loading and storing machinery, 
 
 1169 
 Locomotive boilers, size of, 1089 
 
 crank-pin, quantity of oil used 
 on, 1223 
 
 cylinders, 1088 
 
 electric, 4000 H.P., 1366 
 
 engine performance, 1099 
 
 forgings, strength of, 331 
 
 link-motion, 1095 
 
 testing, 1099 
 Locomotives, 1084-1105 
 
 boiler pressure, 1093 
 
 classification of, 1092 
 
 compounding of , 1101 
 
 compressed-air, 1104 
 
 compressed-air, with compound 
 cylinders, 1105 
 
 counterbalancing of, 1102 
 
 dimensions of, 1096-1098 
 
 drivers, sizes of, 1094 
 
 economy of high pressures in, 
 1092 
 
 effect of speed on cylinder pres- 
 sure, 1093 
 
 efficiency of, 1087 
 
 exhaust-nozzles, 1091 
 
 fire-brick arches in, 1091 
 
 fireless, 1103 
 
 fuel efficiency of, 1095 
 
 fuel waste of, 1101 
 
 grate surface of, 1091 
 
 hauling capacity of, 1087 
 
 horse-power of, 1089 
 
 indicator tests of, 1098 
 
 light, 1103 
 
 leading types of, 1092 
 
 Mallet compound, 1096 
 
 narrow gauge, 1103 
 
 performance of high speed, 1094 
 
 petroleum burning, 1103 
 
 smoke-stacks, 1091 
 
 speed of, 1094 
 
 steam distribution of, 1093 
 
 steam-ports, size of, 1094 
 
 superheating in, 1102 
 
 tractive power of, 1088, 1101 
 
 types of, 1092 
 
 valve travel, 1094 
 
 water consumption of, 1098 
 
 weight of, 1100 
 
 Wootten, 1090 
 Logarithmic curve, 74 
 
 ruled paper, 85 
 
 sines, etc., table, 169 
 
 Logarithms, 80 
 
 hyperbolic, tables of, 163-165 
 
 tables of, 136-163 
 
 use of, 134-136 
 Logs, area of water required to 
 store, 254 
 
 weight of, 254 
 Loop, steam, 852 
 Loops of force, 1382 
 Long measure, 17 
 Loss and profit, 12 
 
 of head, 714-722 
 
 of head, Cox's formula, 717 
 
 of head in cast-iron pipe, tables, 
 719 
 
 of head in riveted steel pipes, 714 
 Lowmoor iron bars, strength of, 330 
 Lubricant water as a, 1222 
 Lubricants, examination of, 1219 
 
 grease, 1221 
 
 measurement of durability, 1218 
 
 oil, specifications for, 1219 
 
 qualifications of good, 1219 
 
 relative value of, 1219 
 
 soda mixture, 1223 
 
 solid, 1223 
 
 specifications for petroleum, 1219 
 Lubrication, 1218-1223 
 
 of engines, quantity of oil needed 
 for, 1221 
 
 of steam-engine cylinders, 1222 
 Lumber, weight of, 254 
 Lumen, definition of, 1367 
 "Lusitania," turbines and boilers 
 of, 1330 
 
 performance of, 1330 
 Lux, definition of, 1367 
 
 Machine screws, A.S.M.E. stan- 
 dard, table, 226 
 screws, taps for, 1269 
 shop, 1235-1279 
 shop, electric drive in, 1407 
 shops, horse-power required in, 
 1256-1262 
 Machines, dynamo-electric (see 
 
 Dynamo-electric machines) 
 Machine tools, electric motors for, 
 1260, 1407 
 tools, keys for, 1277 
 tools, power required for, 1256- 
 
 1260 
 tools, proportioning a series of 
 
 sizes of, 1276 
 tools, soda mixture for, 1222 
 tools, speed of, 1235 
 Machines, efficiency of, 507 
 
 elements of, 510-515 
 Machinery, coal-handling, 1172- 
 1177 
 horse-power required to run, 
 1256-1262 
 Maclaurin's theorem, 79 
 Magnalium, magnesium-aluminum 
 
 alloy, 376 
 Magnesia bricks, 257 
 Magnesium, properties of, 176 
 
1440 
 
 mag-met 
 
 INDEX. 
 
 Magnet, use of, to determine har- 
 dening temperature of steel, 
 1246 
 agnets, electro-, 1384 
 lifting, 1169 
 Magnetic alloys of non-magnetic 
 metals, 378 
 balance, 459 
 brakes, 1217 
 
 capacity of iron, effect of anneal- 
 ing on, 459 
 circuit, 1382 
 circuit, units of, 1348 
 fie?d, 1346 
 
 field, strength of, 1387 
 flux, magnetic induction, 1348 
 moment, 1346 
 
 pole, unit of, definition, 1346 
 Magnetization, intensity of, 1346 
 Magneto-motive force, 1348, 1383 
 Magnolia metal, composition of, 
 
 381 
 Mahler's calorimeter, 798 
 Malleability of metals, table, 177 
 Malleable castings, annealing, 431 
 castings, design of, 433 
 castings, pig iron for, 430 
 castings, rules for use of, 433 
 castings, tests of, 435 
 iron, 429 
 iron, composition and strength 
 
 of, 430 
 iron, improvement in quality, 
 
 434 
 iron, physical characteristics, 
 
 432 
 iron, shrinkage of, 431 
 iron, specifications, 433 
 iron, strength of, 430, 434 
 iron test bars, 432 
 Mandrels, standard steel, 1272 
 Manganese bronze, 377 
 -copper alloys, 376 
 effect of, on cast-iron, 415, 426 
 effect of, on steel, 452 
 properties of, 176 
 steel, 470 
 Manila rope, 386 
 
 rope, weight and strength of, 391 
 Manograph, a high-speed engine- 
 indicator, 939 
 Manometer, air, 581 
 Man-wheel, 508 
 Man, work of, tables, 507, 508 
 Marble, strength of, 335 
 Marine engine, internal combus- 
 tion, 1322 
 engineering. 1316-1333 (see 
 
 Ships and Steam-engines) 
 practice, 1329 
 Mariotte's law of gases, 577 
 Martensite, 416, 456 
 Masonry, allowable pressures on, 
 1334 
 crushing strength of, 349 
 materials, weight and specific 
 gravity of, 174 
 
 Mass, definition of, 487, 501 
 
 = weight h- g, 503 
 Materials, 170-257 
 strength of, 258-359 
 strength of, Kirkaldy's tests, 
 
 330—336 
 various, weights of, table, 178 
 Maxima and minima, 79, 80 
 Maxwell, definition and value of, 
 
 1348 
 Measure and weights, compound 
 units, 27, 28 
 and weights, metric system, 22-27 
 Measures, apothecaries, 18, 20 
 board and timber, 20 
 circular, 20 
 dry, 19 
 liquid, 18 
 long, 17 
 nautical, 17 
 
 of work, power and duty. 28 
 old land, 17 
 shipping, 19 
 solid or cubic, 18 
 square, 18 
 surface, 18 
 time, 20 
 Measurement of vessels, 1316 
 of air velocity, 596 
 of elongation, 265 
 of flowing water, 727-733 
 Measurements, miner's inch, 730 
 Mechanics, 487-522 
 Mechanical and electrical units, 
 equivalent values of, 1347 
 equivalent of heat, 532, 837 
 powers, 510 
 stokers, 889 
 Mekarski compressed-air tram- 
 way, 624 
 Melting points of substances, 532 
 
 temperatures, 527 
 Mensuration, 55-67 
 Mercury, properties of, 176 
 
 vapor lamp, 1369 
 Mercury-bath pivot, 1209 
 Mercurial thermometer, 523 
 Mesure and Nouel's pyrometric 
 
 telescope, 529 
 Metacenter, definition of, 690 
 Metals, anti-friction, 1179 
 
 coefficients of expansion of, 539 
 coefficients of friction of; 1196 
 electrical conductivity of, 1349 
 flow of, 1273 
 
 heat-conducting power of, 553 
 life of under shocks, 262 
 properties of, 174-177 
 resistance overcome in cutting 
 
 of, 1256 
 specific gravity of, 171 
 specific heats of, 535, 536 
 table of ductility, infusibility, 
 malleability and tenacity, 177 
 tenacity of at various tempera- 
 tures, 439 
 weight of, i; I 
 
INDEX. 
 
 1441 
 
 Metaline lubricant, 1223 
 
 Metallography, 456 
 
 Meter, Venturi, 728 
 
 Meters, water delivered through, 
 
 722 
 Metric conversion tables, 23-27 
 
 measures and weights, 22-27 
 
 screw-threads, cutting of, 1238 
 Microscopic constituents of cast- 
 iron and steel, 416, 456 
 Mil, circular, 18, 30, 31 
 Mill buildings, approximate cost 
 of, 1342 
 
 columns, 1341 
 
 power, 735 
 Milling cutters, for gear-wheels, 
 1138 
 
 cutters, helical, tests with, 1251 
 
 cutters, inserted teeth, 1248 
 
 cutters, key ways in, 1248 
 
 cutters, lubricant for, 1252 
 
 cutters, number of teeth in, 1248 
 
 cutters, pitch of teeth, 1247 
 
 cutters, side, 1248 
 
 cutters, spiral, 1248 
 
 cutters, steel for, 1247 
 
 machines, cutting speed of, 1249 
 
 machines, feed of, 1249 
 
 machines, high results with, 
 1250 
 
 machines, typical jobs on, 1251 
 
 machines vs. planer, 1252 
 
 power required for, 1249 
 
 practice, modern, 1252 
 Mine fans, experiments on, 645 
 
 ventilation, 685 
 Mines, centrifugal fans for, 644 
 Mine- ventilating fans, 645 
 Miner's inch, 18 
 
 inch measurements, 730 
 Modulus of elasticity, 260 
 
 of elasticity of various materials, 
 351 
 
 of resistance or section modulus, 
 280 
 
 of rupture, 282 
 Moisture in atmosphere, 583 
 
 in steam, determination of, 912- 
 915 
 Molding-sand, 1233 
 Molds, cast-iron, for iron castings, 
 
 analysis of, 1233 
 Moment of a couple, 491 
 
 of a force, 490 
 
 of friction, 1205 
 
 of inertia, 279, 493 
 
 statical, 490 
 Moments, method of, for deter- 
 mining stresses, 519 
 
 of inertia of regular solids, 493 
 
 of inertia of structural shapes, 
 279 
 Momentum, 502 
 Mond gas producer, 822 
 Monel metal, copper-nickel alloy, 
 
 379 
 Monobar, chain conveyor, 1173 
 
 Morin's laws of friction, 1200 
 Morse tapers, 1271 
 Mortar, strength of, 350 
 Motion, accelerated, formulae for, 
 501 
 
 friction of, 1194, 1197 
 
 Newton's laws of, 488 
 
 on inclined planes, 502 
 
 perpetual, 507 
 
 retarded, 497 
 Motor boats, power of engines for, 
 
 1322 
 Motors, alternating-current, 1408 
 
 compressed-air, 612 
 
 electric (see Electric motors) 
 
 electric, classification of, 1401 
 
 for electric railways, 1366 
 
 water current, 734 
 Moving strut, 511 
 Mule, work of, 509 
 Multiphase electric currents, 1395 
 Multiple system of evaporation, 
 
 543 
 Multivane fans, 636 
 Muntz metal, composition of, 366 
 Mushet steel, 472 
 
 Nails, cut, table of sizes and 
 weights, 234 
 cut vs. wire, 324 
 holding power of, 323 
 wire, table of sizes and weights, 
 235, 236 
 Nail-holding power of wood, 324 
 Naphtha engines, 1071 
 Napier's rule for flow of steam, 
 
 844 
 Natural gas, 817, 818 
 Nautical measure, 17 
 
 mile, 17 
 Nernst electric lamps, 1372 
 Newton's laws of motion, 488 
 Nickel-copper alloys, 378 
 Nickel, effect of on properties of 
 steel, 473 
 properties of, 176, 357 
 steel, 472 
 steel, tests of, 472 
 steel, uses of, 474 
 -vanadium steels, 475 
 Niter process, treating iron sur- 
 faces, 449 
 Nordberg feed-water heating sys- 
 tem, 974 
 Nozzles, flow of steam through, 
 844, 1065 
 flow of water in, 713 
 for measuring discharge of pump- 
 ing engines, 728 
 water, efficiency of, 753 
 Nut and bolt heads, thickness of, 
 222 
 
 Oats, weight of, 178 
 Ocean waves, power of, 755 
 Oersted, unit of magnetic reluo 
 tance, 1348 
 
1442 
 
 ohm-pip 
 
 INDEX. 
 
 Ohm, definition and value of, 1345 
 Ohm's law, 1352 
 law applied to alternating cur- 
 rents, 1390 
 law applied to parallel circuits, 
 
 1352 
 law applied to series circuits, 
 1352 
 Oil as fuel, 812 
 fire-test of, 1220 
 for steam turbines, 1221 
 lubricating 1218-1223 (see Lu- 
 bricants) 
 parafflne, 1220 
 pressure in a bearing, 1204 
 quantity needed for engines, 
 
 1221 
 vs. coal as fuel, 812 
 well, 1220 
 -engines, 1077 
 
 tempering of steel forgings, 458 
 Open-hearth furnace, tempera- 
 tures in, 527 
 steel (see Steel, open-hearth), 451 
 Ordinates and abscissas, 71 
 Ores, cubic feet per ton, 178 
 Orifice, equivalent, in mine venti- 
 lation, 686 
 flow of air through, 588 
 flow of water through, 697 
 rectangular, flow of water 
 through, table, 729 
 Oscillation, center of, 494 
 
 radius of, 494 
 Overhead steam-pipe radiators, 673 
 Ox, work of, 509 
 Oxy-acetylene welding, 464 
 Oxygen, effect of on strength of 
 steel, 453 
 
 it, value and relations of, 58 
 Packing, hydraulic, friction of, 
 
 1217 
 Packing-rings of engines, 1000 
 Paddle-wheels, 1331 
 Paint, 447 
 
 qualities of, 448 
 
 quantity of, for a given surface, 
 448 
 Paper, logarithmic, ruled, 85 
 Parabola, area of by calculus, 77 
 
 construction of, 49, 50 
 
 equations of, 73 
 
 path of a projectile, 501 
 Parabolic conoid, 66 
 
 spindle, 66 
 Parallel forces, 491 
 Parallelogram area of, 55 
 
 of forces, 489 
 
 of velocities, 499 
 Parallelopipedon of forces, 490 
 Parentheses in algebra, 35 
 Partial payments, 14 
 Parting and threading tools, speed 
 
 of, 1243 
 Patterns, weight of, for castings, 
 1233 
 
 Payments, equation of, 14 
 Pearlite, 416, 456 
 Peat, 808 
 
 Pelton water-wheel, 748 
 Pendulum, 496 
 conical, 496 
 Percentage, 12 
 Percussion, center of, 494 
 Perforated plates, strength of, 402 
 Permeability, magnetic, 1348, 1383 
 Permeance, magnetic, 1348 
 Permutation, 10 
 Perpetual motion, 507 
 Petroleum as a metallurgical fuel, 
 813 
 cost of as fuel, 812 
 engines, 1077 
 Lima, 810 
 
 products of distillation of, 810 
 products, specifications for, 1219 
 value of as fuel, 811 
 Petroleum-burning locomotives, 
 
 1103 
 Pewter, composition of, 383 
 Phosphor-bronze, composition of, 
 366 
 specifications for, 370 
 springs, 401 
 strength of, 370 
 Phosphorus, influence of, on cast- 
 iron, 415 
 influence of, on steel, 452 
 Piano-wire, strength of, 239 
 Pictet fluid, for refrigerating, 1284 
 Piezometer, 727 
 Pig-iron (see also Cast iron) 
 analysis of, 416 
 charcoal, strength of, 428 
 distribution of silicon in, 424 
 for malleable castings, 430 
 grading of, 414 
 
 influence of silicon, etc., on, 415 
 sampling, 418 
 specifications for, 418 
 tests of, 419 
 Piles, bearing power of, 1334 
 Pillars, strength of, 269 
 Pine, strength of, 344 
 Pins, forcing fits of by hydraulic 
 pressure, 1273 
 taper, 1272 
 Pinions, raw-hide, 1153 
 Pipe bends, flexibility of, 215 
 branches, compound pipes, for- 
 mula for, 720 
 cast-iron, friction loss in, table, 
 
 719 
 cast-iron, specifications for metal 
 
 for, 419 
 coverings, tests of, 559 _, 
 dimensions, Briggs standard, 
 
 202, 207 
 fittings, flanged, 203-206 
 fittings, valves, etc., resistance of, 
 
 672 
 flanges, extra heavy, table, 199 
 flanges, table of standard, 198 
 
INDEX. 
 
 pip-pla 
 
 1443 
 
 Pipe, iron and steel, strength of, 
 
 341 
 iron, tin-lined and lead-lined, 218 
 threading of, force required for, 
 
 341 
 wooden stave, 218 
 Pipes, air, carrying capacity of, 662 
 air, loss of pressure in, tables, 
 
 593-595 
 air-bound, 722 
 and valves for superheated steam, 
 
 851 
 bent and coiled, 214, 215 
 block-tin, weights and sizes of, 
 
 218 
 cast-iron, 191-195 
 cast-iron, formulae for thickness 
 
 of, 193 
 cast-iron, safe pressures for, 
 
 tables, 194, 195 
 cast-iron, thickness of, for vari- 
 ous heads, 192, 193 
 cast-iron, transverse strength of, 
 
 427 
 cast-iron, weight of, 191-195 
 coiled, table of, 214 
 effects of bends in, 593, 727 
 equalization of, table, 597 
 equation of, 853 
 flow of air in, 59 1 
 flow of gas in, 834-836 
 flow of steam in, 845 
 flow of water in, 699 
 for steam heating, 669 
 house-service, flow of water in, 
 
 table, 712 
 iron and steel, corrosion of, 443 
 lead, safe heads for, 217 
 lead, tin-lined, sizes and weights, 
 
 table, 217 
 lead, weights and sizes of, table, 
 
 217 
 lines for fans and blowers, 643 
 lines, long, 721 
 loss of head in, 714-722 (see 
 
 Loss of head) 
 maximum and mean velocities 
 
 in, 727 
 proportioning to radiating sur- 
 face, 671 
 resistance of the inlet, 715 
 rifled, for conveying heavy oils, 
 
 721 
 riveted flanges for, table, 213 
 riveted hydraulic, weights and 
 
 safe heads, table, 212 
 riveted-iron, dimensions of, 
 
 table, 211 
 riveted, safe pressure in, 887 
 riveted steel, loss of head in, 717 
 riveted steel, water, 329 
 sizes of threads on, 207 
 spiral riveted, table of, 213 
 steam (see Steam-pipes) 
 steam, sizes of in steam heating, 
 
 672 
 table of capacities of, 127 
 
 Pipes, volume of air transmitted in 
 table, 591 
 welded, standard, table of di- 
 mensions, 208 
 Pipe-joint, Rockwood, 202 
 Piping, power-house, identification 
 
 of by different colors, 854 
 Piston rings, steam-engine, 1000 
 rods, steam-engine, 1001-1003 
 Piston valves, steam-engine, 1043 
 Pistons, steam-engine, 999 
 Pivot-bearings, 1205, 1209 
 Pivot-bearing, mercury bath, 1209 
 Pitch, diametral, 1134 
 of gearing, 1133 
 of rivets, 404 
 of screw-propeller, 1325 
 Pitot tube gauge, 727 
 
 tube, use in testing fans, 640 
 Plane, inclined, 512 (see Inclined 
 Plane), 
 surfaces, mensuration of, 55 
 Planer, heavy work on, 1256 
 horse-power required to run, 
 
 1258, 1260 
 vs. Milling machine, 1252 
 Planers, cutting speed of, 1256 
 Planished and Russia iron, 449 
 Plank, Wooden, maximum spans 
 
 for, 1332 
 Plates (see also Sheets) 
 
 acid-pickled, heat transmission 
 
 through, 565 
 areas of, in square feet, table, 
 
 130, 131 
 boiler, strength of at high tem- 
 peratures, 439 
 brass, weight of, tables, 219, 220 
 Carnegie trough, properties of, 
 
 table, 289 
 circular, strength of, 3J3 
 copper, strength of, 334 
 copper, weight of, table, 219 
 corrugated steel, properties of, 
 
 table, 289 
 flat, cast-iron, strength of, 313 
 flat, for steam-boilers, rules for, 
 
 880, 885, 888 
 flat, unstayed, strength of, 314 
 for stand-pipes, 327 
 iron and steel, approximating 
 
 weight of, 461 
 iron, weight of, table, 184 
 of different materials, table for 
 
 calculating weights of, 178 
 perforated, strength of, 402 
 punched, loss of strength in, 401 
 staved, strength of, 315 
 steel boiler, specifications for, 
 
 483 
 steel, for cars, specifications for, 
 
 483 
 steel, specifications for, 481 
 steel, tests of, 331, 333 
 transmission of heat through, 
 561 
 
1444 
 
 pla-pum 
 
 Plates, transmission of heat through, 
 from air to water, 566 
 
 transmission of heat through, 
 from steag^to air, 569 
 Plate-girder, strength of, 331 
 Plate-girders, allowed stresses in, 
 
 274 
 Plating for bulkheads, table, 316 
 
 for tanks, table, 316 
 
 steel, stresses in, due to water 
 pressure, 315 
 Platinite, 475, 540 
 Platinum, properties of, 176 
 
 pyrometer, 526 
 
 wire, 243 
 Plenum system of heating, 678 
 Plough-steel rope, 246 
 
 wire, 239 
 Plugs, fusible, in steam boilers, 889 
 Plunger packing, hydraulic, friction 
 
 of, 1217 
 Pneumatic hoisting, 1163 
 
 postal transmission, 624 
 Polarity of electro-magnets, 1384 
 Polishing wheels, speed of, 1264 
 Polyhedron, 64 
 Polygon, area of, 56 
 
 construction of, 43-45 
 Polygons, impedance, 1390 
 
 of" forces, 489 
 
 table of, 46, 56 
 Polyphase circuits, 1395 
 Popp system of compressed-air, 612 
 Population of the United States, 11 
 Portland cement, strength of, 336 
 Port opening in steam-engines, 
 
 1039 
 Postal transmission, pneumatic, 
 
 624 
 Potential energy, 503 
 Pound-calorie, definition of, 532 
 Pounds per square inch, equiva- 
 lents of, 27 
 Power and work, measures of, 28 
 
 animal, 507 
 
 definition of, 503 
 
 electrical cost of, 985 
 
 factor of alternating currents, 
 1389 
 
 hydraulic, in London, 781 
 
 of a waterfall, 734 
 
 of electric circuits, 1353 
 
 of ocean waves, 755 
 
 unit of, 503 
 Powers of numbers, algebraic, 34 
 
 of numbers, tables, 7, 94-110 
 Power-plant economics, 984 
 Pratt truss, stresses in, 518 
 Preservative coatings, 447-450 
 Press fits, pressure required for, 
 1274 
 
 high-speed steam-hydraulic, 783 
 
 hydraulic forging, 782 
 
 hydraulic, thickness of cylinders 
 for, 317 
 Presses, hydraulic, in iron works, 
 781 
 
 Presses, punches, etc., 1272 
 
 Pressed fuel, 801 
 
 Pressure, collapsing of flues, 318 
 
 collapsing of hollow cylinders, 
 318 
 Pressures of adiabatically com- 
 pressed air, 609 
 Priming, or foaming, of steam 
 
 boilers, 692, 899 
 Prism, 63 
 Prismoid, 64 
 
 rectangular, 63 
 Prismoidal formula, 64 
 Problems, geometrical, 38-54 
 
 in circles, 40-42 
 
 in lines and angles, 38-40 
 
 in polygons, 43-46 
 
 in triangles, 42 
 Process, the thermit, 372 
 Producers, gas {see Gas-producers) 
 Producer-gas, 818-825 (see Gas) 
 Producers, gas, use of steam in, 824 
 Profit and loss, 12 
 Progression, arithmetical and geo- 
 metrical, 10, 11 
 Projectile, parabola path of, 501 
 Prony brake, 1280 
 Propeller shafts, strength of, 332 
 
 screw, 1324 (see Screw-propeller) 
 Proportion, 6 
 
 compound, 7 
 Pulleys, 1111-1114 
 
 arms of, 1032 
 
 cone, 1112 
 
 convexity of, 1112 
 
 differential, 513 
 
 for rope-driving, 1192 
 
 or blocks, 513 
 
 proportion of , 1111 
 
 speed of, 1125, 1137 
 Pulsometer, tests of, 775 
 Pumps, air, for condensers, 1053, 
 1055 
 
 air-lift, 776 
 
 and pumping engines, 757-779 
 
 boiler-feed, 761 
 
 boiler-feed, efficiency of, 908 
 
 centrifugal, 764-770 
 
 centrifugal, design of, 765 
 
 centrifugal, multi-stage, 765 
 
 centrifugal, relation of height of 
 lift to velocity, 766 
 
 centrifugal, tests of, 768, 770 
 
 circulating, for condensers, 1057 
 
 depth of suction of, 757 
 
 direct-acting, efficiency of, 759 
 
 direct-acting, proportion of steam 
 cylinder, 759 
 
 feed, for marine engines, 1057 
 
 high-duty, 762 
 
 horse-power of, 757 
 'jet, 776 
 
 leakage, test of, 772 
 
 lift, water raised by, 759 
 
 mine, operated by compressed- 
 air, 625 
 
 piston speed of, 760 
 
INDEX. 
 
 pum-ref 
 
 1445 
 
 Pumps, rotary, 770 
 
 speed of water in passages of, 759 
 
 steam, sizes of, tables, 758, 760 
 
 suction of, with hot water, 757 
 
 theoretical capacity of, 757 
 
 vacuum, 775 
 
 valves, 761, 762 
 Pump-inspection table, 725 
 Pumping by compressed air, 617, 
 777 (see also Air-lift) 
 
 by gas-engines, cost of, 764 
 
 by steam pumps, cost of fuel for, 
 764 
 
 cost of electric current for, 763 
 
 engine, screw, 762 
 
 engine, the d* Auria, 762 
 Pumping-engines, duty trials of, 
 771-775 
 
 economy of, 763 
 
 high-duty records, 774 
 
 table of data for duty trials of, 
 773 
 
 use of nozzles to measure dis- 
 charge of, 728 
 Punches, clearance of, 1272 
 
 spiral, 1272 
 Punched plates, strength of, 402 
 Punching and drilling of steel, 459, 
 
 460 
 Purification of water, 694 
 Pyramid, 63 
 
 frustum of, 63 
 Pyrometer, air, Wiborgh's, 528 
 
 copper-ball, 526 
 
 fire-clay, Seger's, 528 
 
 Hobson's hot-blast, 52S 
 
 LeChatelier's, 526 
 
 principles of, 523 
 
 thermo-electric, 526 
 
 Uehling-Steinbart, 530 
 Pyrometers, graduation of, 527 
 Pyrometric telescope, 529 
 Pyrometry, 523 
 
 Quadratic equations, 36 
 Quadrature of plane figures, 77 
 
 of surfaces of revolution, 78 
 Quadrilateral, area of, 44 
 
 area of, inscribed in circle, 55 
 Quadruple-expansion engines, 956 
 Quantitative measurement of heat, 
 
 532 
 Quarter-twist belt, 1124 
 Quartz, cubic feet per ton, 178 
 Queen-post truss, inverted, stresses 
 in, 518 
 
 truss, stresses in, 517 
 Quenching test for soft steel, 483 
 
 Rack, gearing, 1141 
 Radian, definition of, 499 
 Radiating power of substances, 
 552 
 surface, computation of, for hot- 
 water heating, 675 
 surface, computation of, for 
 steam heating, 669 
 
 Radiating surface, proportioning 
 
 pipes for, 671 
 Radiation, black body, 552 
 of heat, 551 
 
 of various substances, 552, 569 
 Stefan and Boltzman's law, 552 
 table of factors for Dulong's 
 laws of, 570 
 Radiators, experiments with, 668, 
 679 
 indirect, 669 
 
 overhead steam-pipe, 673 
 steam and hot-water, 668 
 steam, removal of air from, 673 
 transmission of heat in, 668 
 Radius of gyration, 279, 494 
 
 of gyration, graphical method 
 
 for finding, 280 
 of gyration of structural shapes, 
 
 279, 280 
 of oscillation, 494 
 Rails, steel, specifications for, 484 
 
 steel, strength of, 331 
 Railroad axles, 441 
 
 track, material required for one 
 
 mile of, 232 
 trains, resistance of, 1084-1087 
 trains, speed of, 1094 
 Railway, street, compressed-air, 
 624, 625 
 track bolts and nuts, 230 
 Railways, electric, 1366 
 
 narrow-gauge, 1103 
 Ram, hydraulic, 778 
 Rankine's formula for columns, 
 
 270 
 Ratio, 6 
 
 Raw-hide pinions, 1153 
 Reactance of alternating currents, 
 
 1389 
 Reamers, taper, 1270 
 Reaumur thermometer-scale, 523 
 Recalescence of steel, 455 
 Receiver-space in engines, 950 
 Reciprocals of numbers, tables of, 
 88-93 
 use of, 93 
 Recorder, continuous, of water or 
 steam consumption, 940 
 carbon dioxide, or C0 2 , 860 
 Rectangle, definition of, 55 
 value of diagonal of, 55 
 Rectangular prismoid, 63 
 Rectifier, in absorption refrigera- 
 ting machine, 1293 
 mercury arc, 1401 
 Red lead as a preservative, 447 
 Reduction, ascending and de- 
 scending, 5 
 Reese's fusing disk, 1262 
 Reflecting power of substances, 
 
 552 
 (Refrigerating (see also Ice-making,) 
 1282 
 direct-expansion method, 1314 
 
1446 
 
 INDEX. 
 
 Refrigerating-machines, actual and 
 theoretical capacity, 1302 
 air-machines, 1291 
 ammonia absorption, 1293, 1313 
 ammonia compression, 1292, 
 
 1303 
 condensers for, 1300 
 cylinder-heating, 1296 
 dry, wet, and flooded systems, 
 
 1292 
 ether-machines, 1291 
 heat-balance, 1305 
 ice-melting effect, 1291 
 liquids for, pressure and boiling- 
 points of , 1284 
 mean effective pressure and 
 
 horse-power, 1297 
 operations of, 1283 
 performance of, 1307 
 performance of a single acting 
 
 compressor, 1312 
 pipe-coils for, 1302 
 pounds of ammonia per minute, 
 
 1297 
 properties of brine, 1290 
 properties of vapor, 1284-1287 
 quantity of ammonia required 
 
 for, 1298 
 rated capacity of, 1300 
 relative efficiency of, 1295 
 relative performance of am- 
 monia-compression and ab- 
 sorption machines, 1294 
 sizes and capacities, 1299 
 speed of, 1300 
 
 sulphur-dioxide machine, 1292 
 test reports of, 1306 
 temperature range, 1306 
 tests of, 1302 
 using water vapor, 1292 
 volumetric efficiency, 1296 
 Voorhees multiple-effect, 1297 
 Refrigerating plants, cooling tower 
 
 practice in, 1301 
 Refrigerating systems, efficiency 
 
 of, 1296 
 Refrigeration, 1282-1316 
 a reversed heat cycle, 574 
 means of applying the cold, 1314 
 Regenerator, heat, 987 
 Regnault's experiments on steam, 
 
 838 
 Reinforced concrete, working 
 
 stresses of, 1335 
 Reluctance, magnetic, 1348, 1383 
 Reluctivity, magnetic, 1348 
 Reservoirs, evaporation of water in. 
 
 543 
 Resilience, elastic, 260 
 
 of materials, 260 
 Resistance, elastic, to torsion, 311 
 electrical (see Electrical resist- 
 ance), 1349 
 electrical, effect of annealing on, 
 
 1351 
 electrical, effect of temperature 
 on, 1350 
 
 Resistance, electrical, in circuits, 
 
 1352 
 electrical, internal, 1353 
 electrical, of copper-wire, 1351, 
 
 1357 
 electrical, of steel, 453 
 electrical, standard of, 1351 
 elevation of ultimate, 261 
 modulus of, or section modulus, 
 
 280 
 of copper wire, rule for, 242 
 of metals to repeated shocks, 262 
 of ships, 1317 
 of trains, 1084 
 work of, of a material, 260 
 Resolution of forces, 489 
 Retarded motion, 497 
 Reversing-gear for steam-engines, 
 
 dimensions of, 1020 
 Rheostats, 1404 
 Rhomboid, definition and area of, 
 
 55 
 Rhombus, definition and area of, 55 
 Rivets, bearing pressure on, 403 
 cone-head, for boilers, 231 
 diameters of, for riveted joints, 
 
 table, 406 
 in steam-boilers, rules for, 879 
 pitch of, 404 
 
 pressure required to drive, 412 
 round head, weight of, 228 
 steel, chemical and physical tests 
 
 of, 412 
 steel, specifications for, 481 
 tinners', table, 232 
 Riveted iron pipe, dimensions of, 
 
 table, 211 
 joints, 333, 401-412 
 joints, British rules for, 410 
 joints, drilled, vs. punched holes, 
 
 401 
 joints, efficiencies of, 405 
 joints, notes on, 402 
 joints of maximum efficiency, 
 
 408 
 joints, proportions of, 405 
 joints, single riveted lap, 404 
 joints, table of proportions, 411 
 joints, tests of double riveted 
 
 lap and butt, 406 
 joints, tests of, table, 337 
 joints, triple and quadruple, 408 
 pipe, flow of water in, 714 
 pipe, weight of iron for, 213 
 Rivet-iron and steel, shearing re- 
 sistance of, 407 
 Riveting, cold, pressure required 
 
 for, 412 
 efficiency of different methods, 
 
 402 
 hand and hydraulic, strength of, 
 
 402 
 machines, hydraulic, 782 
 of structural steel, 459 
 pressure required for, 412 
 Roads, resistance of carriages on, 
 
 509 
 
INDEX. 
 
 1447 
 
 Rock-drills, air required for, 616 
 
 requirements of air-driven, 616 
 Rods of different materials, table 
 for calculating weights of, 178 
 Rollers and balls, steel, carrying 
 
 capacity of, 317 
 Roller bearings, 1210 
 
 chain and sprocket drives, 1129 
 Rolling of steel, effect of finishing 
 
 temperature, 454 
 Roofs, strength of, 1337 
 Roof-truss, stresses in, 521 
 Roofing materials, 186-190 
 
 materials, weight of various, 190 
 Rope for hoisting or transmission, 
 386 
 
 hoisting, iron and steel, 244 
 
 manila, data of, 1189-1193 
 
 manila, hoisting and transmis- 
 sion, life of, 391 
 
 wire (see Wire-rope) 
 Ropes and cables, 386-393 
 
 cable-traction, 247 
 
 cotton and hemp, strength of, 
 335 
 
 flat iron and steel, table of 
 strength of, 248, 387 
 
 hemp, iron and steel, table of 
 strength and weight of, 386 
 
 hoisting (see Hoisting-rope) 
 
 "Lang Lay," 246 
 
 locked-wire, 250 
 
 manila, 386 
 
 manila, weight and strength of, 
 390, 391 
 
 splicing of, 389 
 
 steel flat, table of sizes, weight 
 and strength, 248, 387 
 
 steel-wire hawsers, 249 
 
 table of strength of iron, steel 
 and hemp, 386 
 
 taper, of uniform strength, 1183 
 
 technical terms relating to, 388 
 
 wire (see Wire-rope) 
 Rope-driving, 1191-1194 
 
 English practice, 1194 
 
 pulleys for, 1192 
 
 horse-power of, 1191 
 
 sag of rope, 1191 
 
 tension of rope, 1190 
 
 various speeds of, 1191 
 
 weight of rope, 1193 
 Rope-transmission, 386 
 Rotary blowers, 649 
 
 steam-engines, 1062 
 Rotation, accelerated, work of, 504 
 Rubber belting, 1128 
 
 goods, analysis of, 356 
 
 vulcanized, tests of, 356 
 Rule of three, 6, 7 
 Running fits, 1274 
 Rupture, modulus of, 282 
 Russia and planished iron, 449 
 
 Safety, factor of, 352-355 
 Safety valves for steam-boilers, 
 902-906 
 
 Safety valves, spring-loaded, 904 
 Salt, weight of, 178 
 
 solubility of, 544 
 Salt-brine manufacture, evapo- 
 ration in, 543 
 
 properties of, 543, 544, 1290 
 
 solution, specific heat of, 537 
 Sand, cubic feet per ton, 178 
 
 molding, 1233 
 Sand-blast, 1262 
 Sand-lime brick, tests of, 349 
 Sandstone, strength of, 349 
 Saturation point of vapors, 578 
 Sawing metal, 1262 
 Sawdust as fuel, 808 
 Scale, boiler, 692, 897 
 
 boiler, analyses of, 693 
 
 effect of, on boiler efficiency, 898 
 
 removal of, from steam boilers, 
 900 
 Scales, thermometer, comparison 
 
 of, 524, 525 
 Scantling, table of contents of, 21 
 Schiele pivot bearing, 1209 
 Schiele's anti-friction curve, 51 
 Scleroscope, for testing hardness, 
 
 343 
 Screw, 62 
 
 bolts, efficiency of, 1270 
 
 conveyors, 1175 
 
 differential, 514 
 
 differential, efficiency of, 1270 
 
 efficiency of, 1270 
 
 (elemtjrit of machine), 512 
 
 heads. A.S.M.E. standard, table, 
 223' 
 
 propeller, 1324 
 
 propeller, coefficients of, 1325 
 
 propeller, efficiency of, 1326 
 
 propeller, slip of, 1326 
 Screws and nuts for automobiles, 
 table, 222 
 
 cap, table of standard, 225 
 
 lag, holding power of, 324 
 
 lag, table of, 234 
 
 machine, A.S.M.E. standard, 
 226 
 
 set, table of standard, 225 
 
 wood, dimensions of, 234 
 
 wood, holding power of, 324 
 Screw-thread, Acme, 223 
 Screw-threads, 220-227 
 
 British Association standard, 222 
 
 English or Whit worth standard, 
 table, 220 
 
 International (metric) standard, 
 222 
 
 limit gauges for, 223 
 
 metric, cutting of, 1238 
 
 standard sizes for bolts and taps, 
 224 
 
 U. S. or Sellers standard table of, 
 221 
 Scrubbers for gas producers, 819 
 Sea-water, freezing-point of, 690 
 Secant of an angle, 67 
 Secants of angles, table of, 166-169 
 
1448 
 
 INDEX. 
 
 Section modulus of structural 
 
 shapes, 280, 281 
 Sector of circle, 61 
 Sediment in steam-boilers, 898 
 Seger pyrometer cones, 528 
 Segment of circle, 61 
 Segments, circular, areas of, 121, 
 
 122 
 Segregation in steel ingots, 462 
 Self-inductance of lines and cir- 
 cuits, 1393 
 " Semi-steel," 428 
 Separators, steam, 911 
 Set-screws, holding power of, 1278 
 
 standard table of, 225 
 Sewers, grade of, 706 
 Shackles, strength of, 1161 
 Shaft-bearings, 1015 
 
 bearings, large, tests of, 1206 
 couplings, flange, 1109 
 Shaft fit, allowances for electrical 
 machinery, 1274 
 governors, 1048 
 Shafts and bearings of engines, 
 1023 
 hollow, 1109 
 hollow, torsional strength of, 
 
 311 
 steam-engine, 1010-1019 
 steel propeller, strength of, 
 Shafting, 1106-1110 
 collars for, 1109 
 deflection of, 1107 
 formulae for, 1106 
 horse-power transmitted by, 
 
 1108 
 keys for, 1277 
 laying out, 1109, 1110 
 power required to drive, 1261 
 Shaku-do, Japanese alloy, 368 
 Shapers, power required to run, 
 
 1260 
 Shapes of test specimens, 266 
 structural steel, properties of, 
 287-310 
 Shear and compression combined, 
 312 
 and tension combined, 312 
 poles, stresses in, 516 
 Shearing, effect of on structural 
 steel, 459 
 resistance of rivets, 407 
 strength of iron and steel, 340 
 Shearing strength of woods, table, 
 347 
 strength, relation to tensile 
 strength, 340 
 Sheaves, diameter of, for given 
 tension of wire rope, 1186 
 for wire rope transmission, 1184 
 size of, for manila rope, 390 
 Sheets (see also Plates) 
 Sheet aluminum, weight of, 220 
 brass, weight of, 220 
 copper, weight of, 219 
 metal, strength of, 334 
 
 Sheet metal, weight of, by decimal 
 gauge, 33 
 iron and steel, weight of, 181 
 Shelby cold-drawn tubing, 210 
 Shells for steam-boilers, material 
 for, 880 
 spherical, strength of, 316 
 Shell-plate formulae for steam- 
 boilers, 880 
 Sherardizing, 450 
 Shibu-ichi, Japanese alloy, 368 
 Shingles, weights and areas of, 189 
 Ship " Lusitania," performance of, 
 
 1330 
 Ships, Atlantic steam, perform- 
 ance of, 1328 
 coefficient of fineness of, 1317 
 coefficient of performance, 1318 
 coefficient of water lines, 1317 
 displacement of, 1317, 1322 
 horse-power of, 1321-1323 
 horse-power of, from wetted 
 
 surface, 1323 
 horse-power of internal com- 
 bustion engines for, 1322 
 horse-power for given speeds, 
 
 1321 
 jet propulsion of, 1332 
 relation of horse-power to speed, 
 
 1331 
 resistance of, 1317 
 resistance of, per horse-power, 
 
 1321 
 resistance of, Rankine's formula, 
 
 1319 
 rules for measuring, 1316 
 rules for tonnage, 1317 
 small sizes, engine power re- 
 quired for, 1322 
 wetted surface of, 1320 
 with reciprocating engine, and 
 turbine combined, 1331 
 Shipbuilding, steel for, 483 
 Shipping measure, 19, 1316 
 Shocks, resistance of metals to 
 repeated, 262 
 stresses produced by, 263 
 Short circuits, electric, 1360 
 Shrinkage fits (see Fits, 1273) 
 of cast-iron, 415, 423 
 of alloys, 384 
 of castings, 1231 
 of malleable iron castings, 431 
 strains relieved by uniform cool- 
 ing, 423 
 Sign of differential coefficients, 79 
 of trigonometrical functions, 68 
 Signs, arithmetical, 1 
 Silicon, distribution of, in pig iron, 
 424 
 excessive, making cast-iron hard. 
 
 1231 
 influence of, on cast-iron, 415, 
 
 422 
 influence of, on steel, 452 
 relation of, to strength of cast- 
 iron, 415, 422 
 
sil-sph 
 
 1449 
 
 Silicon-aluminum-iron alloys, 374 
 Silicon-bronze, 371 
 Silicon-bronze^wire, 243, 371 
 Silundum, 1377 
 Silver, melting temperature, 527 
 
 properties of, 176 
 Simpson's rule for areas, 57 
 Sine of an angle, 67 
 Sines of angles, table, 166-169 
 Single-phase circuits, 1395 
 Siphon, 726 
 Sirocco Fans, 633 
 Skin effect in alternating currents, 
 
 1390, 1399 
 Skylight glass, sizes and weights, 
 
 190 
 Slag bricks and slag blocks, 256 
 Slag in cupolas, 1225 
 
 in wrought iron, 436 
 Slate roofing, sizes, areas, and 
 
 weights, 189 
 Slide Rule, 83 
 Slide-valves, steam-engine, (see 
 
 Steam-engines, 1034-1047) 
 Slope, table of, and fall in feet per 
 
 mile, 700 
 Slotters, power required to run, 
 
 1260 
 Smoke-prevention, 890-893 
 Smoke-stacks, sheet-iron, 928 
 
 locomotive, 1091 
 Snow, weight of, 691 
 Soapstone lubricant, 1223 
 
 strength of, 349 
 Soda mixture for machine tools, 
 
 1222 
 Softeners in foundry practice, 
 
 1230 
 Softening of water, 695 
 Soils, bearing power of, 1333 
 
 resistance of, to erosion, 705 
 Solar engines, 988 
 Solder, brazing, composition of, 
 366 
 for aluminum, 359 
 Soldering aluminum bronze, 373 
 Solders, composition of various, 
 
 385 
 Solid bodies, mensuration of, 62- 
 67 
 measure, 18 
 Solid of revolution, 65 
 Solubility of common salt, 544 
 
 of sulphate of lime, 545 
 Sorbite, 456 
 Sources of energy, 506 
 Specific gravity, 170-174 
 
 gravity and Baume's hydrometer 
 
 compared, table, 172 
 gravity and strength of cast iron, 
 
 428 
 gravity of brine, 544 
 gravity of cast-iron, 428 
 gravity of copper-tin alloys, 360 
 gravity of copper-tin-zinc alloys, 
 
 364 
 gravity of gases, 173 
 
 Specific gravity of ice, 691 
 gravity of liquids, table, 172 
 gravity of metals, table, 171 
 gravity of steel, 461 
 gravity of stones, brick, etc., 174 
 Specific heat, 534-538 
 
 heat, determination of, 534 
 heat of ammonia, 1286 
 heat of air, 587 
 heat of gases, 535, 537 
 heat of ice, 691 
 
 heat of iron and steel, 535, 536 
 heat of liquids, 535 
 heat of metals, 536 
 heat of saturated steam, 837 
 heat of solids, 535 
 heat of superheated steam, 838 
 heat of water, 536, 691 
 heat of woods, 536 
 Specifications for boiler-plate, 483 
 for castings, 418 
 for cast iron, 418 
 for chains, 251 
 for elliptical steel springs, 399 
 for foundry pig iron, 418 
 for galvanized wire, 239 
 for helical steel springs, 395 
 for incandescent lamps, 1372 
 for malleable iron, 433 
 for metal for cast-iron pipe, 419 
 for oils, 1219 
 
 for petroleum lubricants, 1219 
 for phosphor-bronze, 370 
 for purchase of coal, 799 
 for spring steel, 483 
 for steel axles, 483, 485 
 for steel billets, 483 
 for steel castings, 464, 486 
 for steel crank-pins, 483 
 for steel for automobiles, 486 
 for steel forgings, 482 
 for steel rails, 484 
 for steel rivets, 481 
 for steel splice-bars, 485 
 for steel tires, 485 
 for structural steel, 480 
 for structural steel for ships, 483 
 for tin and terne-plate, 188 
 for wrought iron, 437-438 
 Speed of cutting, effect of feed and 
 
 depth of cut on, 1241 
 of cutting tools, 1235 
 of vessels, 1321 
 Sphere, measures of, 63 
 Spheres of different materials, table 
 
 for calculating weight of, 178 
 table of volumes and surfaces, 
 
 125, 126 
 Spherical polygon, area of, 64 
 segment, volume of, 65 
 shells and domed boiler heads, 
 
 316 
 shells, strength of, 316 
 shell, thickness of, to resist a 
 
 given pressure, 316 
 triangle, area of, 64 
 zone, area and volume of, 65 
 
1450 
 
 sph-ste 
 
 INDEX. 
 
 Spheroid, 65 
 
 Spikes, holding power of, 323 
 
 wire* 233 
 
 railroad and boat, 233 
 Spindle, surface and volume of, 65, 
 
 66 
 Spiral, 52, 62 
 
 conical, 62 
 
 construction of, 52 
 
 gears, 1143 
 
 plane, 62 
 Spiral-riveted pipe-fittings, table, 
 214 
 
 pipe, table of, 213 
 Splices, railroad track, tables, 233 
 Splice-bars, steel, specifications for, 
 
 485 
 Splicing of ropes, 388 
 
 of wire rope, 393 
 Springs, 394-401 
 
 elliptical, specifications for, 399 
 
 elliptical, sizes of, 399 
 
 for engine-governors, 1048-1050 
 
 helical, 396 
 
 helical, formulae for deflection 
 and strength, 395 
 
 helical, specifications for, 395 
 
 helical, steel, tables of capacity 
 and deflection, 395-400 
 
 laminated steel, 394 
 
 phosphor-bronze, 401 
 
 semi-elliptical, 394 
 
 steel, strength of, 333 
 
 steel, chromium-vanadiun, 401 
 
 to resist torsion, 399 
 Sprocket wheels, 1130 
 Spruce, strength of, 345 
 Square, definition of, 55 
 
 measure, 18 
 
 root, 8 
 
 roots, tables of, 94-109 
 
 value of diagonal of, 55 
 Squares of decimals, table, 109 
 
 of numbers, table, 94-109 
 Stability, 490 . 
 
 of dam, 491 
 Stand-pipe at Yonkers, N. Y., 328 
 Stand-pipes, 327-329 
 
 failures of, 328 
 
 guy-ropes for, 327 
 
 heights of, for various diameters 
 and plates, table, 329 
 
 thickness of plates of table, 329 
 
 thickness of side plates, 327 
 
 wind-strain on, 328 
 Statical moment, 490 
 Static and dynamic properties of 
 
 steel, 476 
 Stays, steam-boiler, loads on, 882 
 
 steam-boiler, material for, 882 
 Stay-bolt iron, 438 
 Stay-bolts in steam-boilers, 888 
 Stayed surfaces, strength of, 315 
 Steam, 836-854 
 
 determining moisture in, 912-915 
 
 dry, definition, 836 
 
 Steam, dry, identification of, 915 
 energy of, expanded to various 
 
 pressures, 933 
 entropy of, tables, 839-843 
 expanding, available energy of, 
 
 842 
 expansion of, 929 
 flow of, 844-851 (see Flow of 
 
 steam) 
 gaseous, 838 
 generation of, from waste heat 
 
 of coke-ovens, 803 
 heat required to generate 1 
 
 pound of, 837 
 latent heat of, 836 
 loop, 852 
 
 loss of pressure in pipes, 849 
 maximum efficiency of, in Carnot 
 
 cycle, 850 
 mean pressure of expanded, 930 
 metal, 368 
 
 power, cost of, 981-984 
 receivers on pipe lines, 853 
 Reghault's experiments on, 838 
 saturated, definition, 836 
 saturated, density, volume and 
 
 latent heat of, 839 
 saturated, properties of, table, 
 
 839-842 
 saturated, specific heat of, 837 
 saturated, temperature and pres- 
 sure of, 837 
 saturated, total heat of, 836 
 separators, 911 
 superheated (see also Superheated 
 
 steam) 
 superheated, definition, 836 
 superheated, economy of steam- 
 engines with, 969 
 superheated, pipes and valves 
 
 for, 851 
 superheated, properties of, 843 
 superheated, specific heat of, 838 
 temperature of, 836 
 vessels (see Ships) 
 weight of, per cubic foot, table, 
 
 839 
 wet, definition, 836 
 Steam-boiler, 854-901 
 compounds, 898 
 efficiency, computation of, 860 
 efficiency, relation of, to rate of 
 
 driving, air-supply, etc., 862 
 furnaces, height of, 889 
 plates, ductility of, 884 
 plates, tensile strength of, 884 
 tests, heat-balance in, 872 
 tests, rules for, 866-874 
 tubes, holding power of, 883 
 tubes, iron and steel, 883 
 tubes, material for, 883 
 Steam-boilers, bumped heads, rules 
 
 for, 885 
 conditions to secure economy of, 
 
 859, 862 
 construction of, 879-889 
 
 i 
 
1451 
 
 Steam-boilers, construction of, 
 United States merchant-vesssl 
 rules, 884 
 
 corrosion of, 443, 897 
 
 curves of performance of, 863 
 
 dangerous, 901 
 
 domes on, 889 
 
 down-draught furnace for, 890 
 
 effect of heating air for furnaces 
 of, 865 
 
 evaporative tests of, 864-868 
 
 explosive energy of, 902 
 
 factors of evaporation, 874-878 
 
 factors of safety of, 879 
 
 feed-pumps for, efficiency of, 908 
 
 feed-water heaters for, 909-911- 
 
 feed-water saving due to heat- 
 ing of, 909 
 
 flat plates in, rules for, 880, 885, 
 888 
 
 flues and gas passages, propor- 
 tions of, 858 
 
 foaming or priming of, 692, 899 
 
 for blast-furnaces, 865 
 
 forced combustion in, 894 
 
 fuel economizers, 894 
 
 furnace formulae, 881 
 
 fusible plugs in, 889 
 
 girders, rules for, 882 
 
 grate-surface, 855, 857 
 
 grate-surface, relation to heating- 
 surface, 857 
 
 gravity feeders, 908 
 
 heating-surface in, 855, 856 
 
 heating-surface, relation of, to 
 grate-surface, 857 
 
 heat losses in, 861 
 
 height of chimney for, 919, 921 
 
 high rates of evaporation, 865 
 
 horse-power of, 854 
 
 hydraulic test of, 879 
 
 incrustation of, 897-902 
 
 injectors on, 906-908 (see In- 
 jectors) 
 
 marine, corrosion of, 900 
 
 maximum efficiency with Cum- 
 berland coal, 865 
 
 measure of duty of, 855 
 
 mechanical stokers for, 889 
 
 performance of, 858 
 
 pressure allowable in, 884-888 
 
 proportions of, 855-858 
 
 proportions of grate and heat- 
 ing-surface for given horse- 
 power, 855, 857 
 
 proportions of grate-spacing, 857 
 
 riveting, rules for, 879 
 
 safety-valves, discharge of steam 
 through, 905 
 
 safety-valves for, 902-906 
 
 safety-valves, formula? for, 902 
 
 safety-valves, spring-loaded, 904 
 
 safe working-pressure, 887 
 
 scale compounds, 898 
 
 scale in, 897-902 
 
 sediment in, 898 
 
 shells, material for, 880 
 
 Steam-boilers, shell-plate, formula? 
 for, 880 
 
 smoke prevention, 890-893 
 
 stay bolts in, 888 
 
 stays, loads on, 882 
 
 stays, material for, 882 
 
 strain caused by cold feed-water, 
 909 
 
 strength of, 879-889 
 
 strength of rivets, 879 
 
 tests of, at Centennial Exposi- 
 tion, 864 
 
 tube-plates, rules for, 882 
 
 use of kerosene in, 899 
 
 use of zinc in, 901 
 
 using waste gases, 865, 866 
 Steam-calorimeters, 912-915 
 Steam-consumption in engines, 
 Willans law, 962 
 
 continuous recorder of, 940 
 Steam-domes on boilers, 889 
 Steam-engines, 929 
 
 advantages of compounding, 946 
 
 advantages of high initial and 
 low back pressure, 967 
 
 and turbine, in 1904, best econ- 
 omy of, 977 
 
 bed-plates, dimensions of, 1025 
 
 bearings, size of, 1015 
 
 clearance in, 936 
 
 compound, 946-953 
 
 compound, best cylinder ratios, 
 952 
 
 compound, calculation of cylin- 
 ders of, 952 
 
 compound, combined indicator 
 diagram, 949 
 
 compound condensing, test of 
 with and without jackets, 976 
 
 compound, economy of, 968 
 
 cylinder condensation, experi- 
 ments on, 937 
 
 cylinder condensation, loss by ,936 
 
 compound, two vs. three cylin- 
 ders, 968 
 
 compound, formulae for expan- 
 sion and work in, 951 
 
 compound, high-speed, perform- 
 ance of, 960, 961 
 
 compound, high-speed, sizes of, 
 960, 961 
 
 compound, non-condensing, effi- 
 ciency of, 971 
 
 compound, receiver, ideal dia- 
 gram, 947 
 
 compound, receiver space in, 950 
 
 compound, receiver type, 947 
 
 compound, steam-jacketed, per- 
 formances of, 960 
 
 compound, steam-jacketed, test 
 of, 976 
 
 compound, Sulzer, water con- 
 sumption of, 969 
 
 compound, velocity of steam in 
 passages of, 956 
 
 compound vs. triple-expansion, 
 
1452 
 
 INDEX. 
 
 Steam-engines, compound, water 
 
 consumption of, 959 
 compound, Wolff, ideal diagram, 
 
 947 
 compression, effect of, 935 
 condensers, 1050-1061 (see Con- 
 densers) 
 connecting-rod ends, 1005 
 connecting-rods, dimensions of, 
 
 1003-1005 
 cost of, 981-984 
 counterbalancing of, 980 
 crank-pins, dimensions of, 1005- 
 
 1009 
 crank-pins, pressure on, 1008 
 crank-pins, strength of, 1007 
 cranks, dimensions of, 1009 
 crank-shafts, dimensions of, 
 
 1017-1019 
 crank-shafts for torsion and 
 
 flexure, 1019 
 crank-shafts for triple-expansion, 
 
 1019 
 crank-shafts, three-throw, 1019 
 cross head and crank, relative 
 
 motion of, 1042 
 cross head-pin, dimensions of, 
 
 1009 
 cut-off, most economical point of, 
 
 981 
 cylinders, dimensions of, 996, 997 
 cylinder-head bolts, size of, 999 
 cvlinder-heads, dimensions of, 
 
 998 
 design, current practice, 1022 
 dimensions of parts of, 979, 996- 
 
 1026 
 eccentric-rods, dimensions of, 
 
 1020 
 eccentrics, dimensions of, 1020 
 effect of moisture in steam, 972 
 economic performance of, 957- 
 
 981 
 economy at various loads and 
 
 speeds, 963, 964 
 economy, effect on, of wet steam, 
 
 972 
 economy of compound vs. triple- 
 expansion, 984 
 economy of, in central stations, 
 
 963 
 economy of, simple and com- 
 pound compared, 968 
 economy under variable loads, 
 
 963 
 economy with superheated steam 
 
 969 
 efficiency in thermal units per 
 
 minute, 934 
 estimating I.H.P. of single cylin- 
 der and compound, 940 
 exhaust steam used for heating, 
 
 981 
 expansions in, table, 935 
 fly-wheels, 1026-1034 
 fly-wheels, arms of, 1032 
 
 Steam-engines, fly-wheels, centrifu- 
 gal force in, 1029 
 fly-wheels, diameters of, 1030 
 fly-wheels, formulae for, 1026, 
 
 1027 
 fly-wheels, speed, variation in, 
 
 1026, 1027 
 fly-wheels, strains in, 1031 
 fly-wheels, thickness of rim of, 
 
 1032 
 fly-wheels, weight of, 1027, 1028 
 fly-wheels, wooden rim, 1033 
 foundations embedded in air, 980 
 frames, dimensions of, 1025 
 friction of, 1215 
 governors, fly-ball, 1047 
 governors, fly-wheel, 1048 
 governors, shaft, 1048 
 governors, springs for, 1048-1050 
 guides, sizes of, 1002 
 highest economy of, 975 
 high piston speed in, 966 
 high-speed, British, 966 
 high-speed Corliss, 966 
 high-speed, economy of, 965 
 high-speed, performance of, 959- 
 
 962 
 high-speed, sizes of, 959-962 
 high-speed throttling, 967 
 horse-power constants, 941-944 
 indicated horse-power of single- 
 cylinder, 940-946 
 indicator diagrams, 938 
 indicator diagram, analysis of, 
 
 992 
 indicator diagrams, to draw 
 
 clearance line on, 944 
 indicator diagrams, to draw ex- 
 pansion curve, 944 
 indicator rigs, 939 
 indicators, effect of leakage, 946 
 indicators, errors of, 939 
 influence of vacuum and super- 
 heat on economy, 972 
 Lentz compound, 968 
 limitations of speed of, 966 
 link motions, 1044-1046 
 links, size of, 1020 
 mean and terminal pressures, 930 
 mean effective pressure, calcu- 
 lations of, 931 
 measures of duty of, 933 
 non-condensing, 958, 960, 961 
 oil required for, 1221 
 pipes for, 848 
 pistons, clearance of, 996 
 pistons, dimensions of, 999 
 piston-rings, size of, 1000 
 piston-rod guides, size of, 1002 
 piston-rods, fit of, 1001 
 piston-rods, size of, 1001 
 piston-valves, 1043 
 prevention of vibration in, 980 
 proportions, current practice, 
 
 1021 
 proportions of, 996-1026 
 quadruple expansion, 956 
 
INDEX. 
 
 1453 
 
 Steam-engines, quadruple, perform- 
 ance of, 974 
 ratio of expansion in, 932 
 reversing gear, dimensions of, 
 
 1020 
 rolling-mill, sizes of, 980 
 rotary, 1062 
 
 setting the valves of, 1043 
 shafts and bearings, 1010-1023 
 shafts, bearings for, 1015 
 shafts, bending resistance of, 
 
 1012 
 shafts, dimensions of, 1010-1017 
 shafts, equivalent twisting mo- 
 ment of, 1012 
 shafts, fly-wheel, 1013 
 shafts, twisting resistance of, 
 
 1010 
 single-cylinder, economy of, 957 
 single-cylinder, high-speed, sizes 
 
 and performance of, 960 
 single-cylinder, water consump- 
 tion of, 957-959 
 slide-valve, definitions, 1034 
 slide-valve diagrams, 1035-1039 
 slide-valve, effect of changing 
 
 lap, lead, etc., 1039 
 slide-valve, effect of lap and lead, 
 
 1034-1036 
 slide-valve, lead, 1039 
 slide-valve, port opening, 1039 
 slide-valve, ratio of lap to travel, 
 
 1040 
 slide-valves, crank-angles, table, 
 
 1040 
 slide-valves, cut-off for various 
 lap and travel, table, 1042, 
 1043 
 slide-valve, setting of, 1043 
 slide-valves, relative motion of 
 
 crosshead and crank, 1042 
 small, coal consumption of, 964 
 small, water consumption of, 963 
 steam consumption of different 
 
 types, 969 
 steam-jackets, influence of, 975 
 steam-turbines and gas-engines 
 
 compared, 986 
 Sulzer compound and triple-ex- 
 pansion, 969 
 superheated steam in, 969 
 to change speed of, 1048 
 to put on center, 1043 
 three-cylinder, 1019 
 rules for tests of, 988 
 triple-expansion, 953-956 
 triple-expansion and compound, 
 
 relative economy, 984 
 triple-expansion, crank-shafts 
 
 for, 1019 
 triple-expansion, cylinder pro- 
 portions 953-955 
 triple-expansion, cylinder ratios, 
 
 956 
 triple-expansion, high-speed, 
 sizes and performances of, 961, 
 962 
 
 Steam - engines, triple - expansion, 
 non-condensing, 961 
 
 triple-expansion, sequence of 
 cranks in, 956 
 
 triple-expansion, steam-jacketed, 
 performance of, 961, 962 
 
 triple-expansion.theoreticalmean 
 effective pressures, 954 
 
 triple-expansion, types of, 956 
 
 triple-expansion, water consump- 
 tion of, 959, 969 
 
 use of reheaters in, 975 
 
 using superheated steam, 972- 
 974 
 
 valve-rods, dimensions of, 1019 
 
 Walschaert valve-gear, 1046 
 
 water consumption from indi- 
 cator-cards, 945 
 
 water consumption of, 937 
 
 with fluctuating loads, wasteful, 
 934 
 
 with sulphur-dioxide addendum, 
 978 
 
 wrist-pin, dimensions of, 1009 
 Steam fire-engines, capacity and 
 
 economy of, 964 
 Steam heating, 665-674 
 
 heating, diameter of supply 
 mains, 671, 673 
 
 heating, indirect, 669 
 
 heating, indirect, size of regis- 
 ters and ducts, 669 
 
 heating of greenhouses, 673 
 
 heating, pipes for, 669 
 
 heating, vacuum systems of, 673 
 
 jackets on engines, 975 
 
 jet blower, 651 
 
 jet exhauster, 651 
 
 jet ventilator, 652 
 
 pipe coverings, tests of, 558-561 
 
 pipes, 851-854 
 
 pipes, copper, tests of, 851 
 
 pipes, copper, strength of, 851 
 
 pipes, failures of, 851 
 
 pipes for engines, 848 
 
 pipes for marine engines, 848 
 
 pipes, proportioning for mini- 
 mum loss by radiation and 
 friction, 849 
 
 pipes, riveted -st eel, 852 
 
 pipes, uncovered, loss from, 853 
 
 pipes, underground, condensa- 
 tion in, 853 
 
 pipes, valves in, 852 
 
 pipes, wire- wound, 851 
 
 turbines, 1062-1071 
 
 turbine, low-pressure, combined 
 with high pressure reciprocating 
 engine, 1331 
 
 turbines, testing oil for, 1221 
 
 turbines and gas-engine, com- 
 bined plant of, 986 
 
 turbine and steam-engine com- 
 pared, 978 
 
 turbines, efficiency of, 1067 
 
 turbines, impulse and reaction, 
 1062, 1066 
 
1454 
 
 Steam turbines, low-pressure, 
 1069 
 turbines, reduction gear for, 1071 
 turbines, speed of the blades, 
 
 1066 
 turbines, steam consumption of, 
 
 1067 
 turbines, theory of, 1063 
 turbines using exhaust, from re- 
 ciprocating engines, 1069, 1331 
 Steamships, Atlantic, performances 
 
 of, 1328 
 Steel, 451-487 
 
 alloy, heat treatment of, 479 
 
 aluminum, 472 
 
 analyses and properties of, 452 
 
 and iron, classification of, 413 
 
 annealing of, 459, 460, 468 
 
 axles, specifications for, 483, 485 
 
 axles, strength of, 332 
 
 bars, effect of nicking, 461 
 
 beams, safe load on, 284 
 
 bending tests of, 454 
 
 Bessemer basic, ultimate strength 
 
 of, 452 
 Bessemer, range of strength of, 
 
 454 
 billets, specifications for, 483 
 blooms, weight of, table, 185 
 bridge-links, strength of, 331 
 brittleness due to heating, 458 
 burning carbon out of, 461 
 burning, overheating, and re- 
 storing, 457 
 castings, 464-466 
 castings, specifications for, 464, 
 
 486 
 castings, strength of, 333 
 cementation or case-hardening 
 
 of, 1246 
 chrome, 471 
 
 chromium- vanadium, 476-478 
 chromium-vanadium spring, 401 
 cold-drawn, tests of, 339 
 cold-rolled, tests of, 339 
 color-scale for tempering, 469 
 comparative tests of large and 
 
 small pieces, 455 
 copper, 475 
 corrosion of, 443, 444 
 crank-pins, specifications for, 483 
 critical point in heat treatment 
 
 of, 456 
 crucible, 466-470 
 crucible, analyses of, 466, 469 
 crucible, effect of heat treatment, 
 
 457, 466 
 crucible, selection of grades of, 
 
 466 
 crucible, specific gravities of, 466 
 effect of annealing, 455 
 effect of annealing on grain of, 454 
 effect of annealing on magnetic 
 
 capacity, 459 
 effect of cold on strength of, 440 
 effect of finishing temperature in 
 
 rolling, 454 
 
 Steel, effect of heating, 457 
 
 effect of heat on grain, 456, 466 
 effect of oxygen on strength of, 
 
 453 
 electrical conductivity of, 453 
 endurance of, under repeated 
 
 stresses, 463. 
 expansion of, by heat, 540 
 eye-bars, test of, 338 
 failures of, 462 
 fatigue resistance of, 477 
 fire-box, homogeneity test for, 
 
 '484 
 fluid-compressed, 464 
 for car-axles, specifications, 483, 
 
 485 
 for different uses, analyses of, 
 
 481-486 
 forgings, annealing of, 458 
 forgings, oil-tempering of, 458 
 forgings, specifications for, 482 
 for rails, specifications, 484 
 hardening of, 455 
 hardening temperature of, use of 
 
 a magnet to determine, 1246 
 harveyizing, 1246 
 heating in a lead bath, 467 
 heating in melted salts by an 
 
 electric current, 467 
 heating of, for forging, 468 
 heat treatment of Cr-Va steel, 
 
 478 
 high-speed tool, 470 
 high-speed tool, emery wheel for 
 
 grinding, 1240, 1267 
 high-speed tool new, tests of, 
 
 1246 
 igh-speed tool, Taylor's ex- 
 periments, 1238 
 high-strength, for shipbuilding, 
 
 483 
 ingots, segregation in, 462 
 life of, under- shock, 263 
 low strength of, 453 
 low strength due to insufficient 
 
 work, 454 
 manganese, 470 
 
 manganese, resistance to abra- 
 sion of, 470-471 
 manufacture of, 451 
 melting, temperature of, 528 
 mixture of, with cast iron, 429 
 Mushet, 472 
 nickel, 472 
 nickel, tests of, 472 
 nickel- vanadium, 475 
 of different carbons, uses of, 469 
 open-hearth, range of strength 
 
 of, 454 
 open-hearth, structural, strength 
 
 of, 454 
 plates (see Plates, steel) 
 rails, specifications for, 484 
 rails, strength of, 331 
 range of strength in, 454 
 recaleseence of, 455 
 
INDEX. 
 
 ste-str 
 
 1455 
 
 Steel, relation between chemical 
 composition and physical char- 
 acter of, 452 
 rivet, shearing resistance of, 407 
 rivets, specifications for, 481 
 rope, flat, table of strength of, 
 
 387 
 rope, table of strength of, 386 
 shearing strength of, 340 
 sheets, weight of, 181 
 soft, quenching test for, 483 
 specifications for, 480-487 
 specific gravity of, 461 
 splice-bars, specifications for, 485 
 spring, strength of, 333 
 springs (see Springs, steel) 
 static and dynamic properties of, 
 
 476 
 strength of, Kirkaldy's tests, 331 
 strength of, variation in, 454 
 structural, annealing of, 460 
 structural, drilling of, 460 
 structural, effect of punching and 
 . shearing, 459 
 
 structural, for bridges, specifica- 
 tions of, 480 
 structural, for buildings, specifi- 
 cations of, 480 
 structural, for ships, specifica- 
 tions of, 483 
 structural, punching of, 460 
 structural, riveting of, 459 
 structural shapes, properties of, 
 
 287-310 
 structural, specifications for, 480 
 structural, treatment of, 459-460 
 structural, upsetting of, 460 
 structural, welding of, 460 
 struts, 271 
 tempering of, 468 
 tensile strength of, at high tem- 
 peratures, 439 
 tensile strength of, pure, 453 
 tires, specifications for, 485 
 tires, strength of, 332 
 tool, composition and heat treat- 
 ment of, 1243 > 
 tool, heating of, 467 
 tungsten, 472 
 used in automobile construction, 
 
 486 
 very pure, low strength of, 453 
 water-pipe, 329 
 welding of, 460, 463 
 wire gauge, tables, 30 
 working of, at blue heat, 458 
 working stresses in bridge mem- 
 bers, 272 
 Stefan and Boltzman law of radia- 
 tion, 552 
 Sterro metal, 369 
 St. Gothard tunnel, loss of pressure 
 
 in air-pipe mains in, 595 
 Stoker, Taylor gravity underfeed, 
 
 890 
 Stokers, mechanical, for steam- 
 boilers, 889 
 
 Stokers, under-feed, 890 
 Stone, strength of, 335, 347 
 
 weight and specific gravity of, 
 table, 174 
 Stone-cutting with wire, 1262 
 Storage of steam heat, 897, 987 
 batteries, 1378 
 batteries, efficiency of, 1380 
 batteries, rules for care of, 1381 
 Storms, pressure of wind in, 599 
 Stoves, for heating compressed-air, 
 efficiency of, 612 
 foundries, cupola charges in, 1227 
 Straight-line formula for columns, 
 
 271 
 Strain and stress, 258 
 Strand, steel wire, for guys, 249 
 Straw as fuel, 808 
 Stream, open, measurement of 
 
 flow, 729 
 Streams, fire, 722-725 (see Fire- 
 streams) 
 running, horse-power of, 734 
 Strength and specific gravity of 
 cast iron, 428 
 compressive, 267-269 
 compressive, of woods, 344, 346 
 loss of, in punched plates, 401 
 of anchor-forgings, 331 
 of aluminum, 358 
 of aluminum-copper alloys, 371 
 of basic Bessemer steel, 452 
 of belting, 335 
 of blocks for hoisting, 1157 
 of boiler-heads, 314, 315 
 of boiler-plate at high tempera- 
 tures, 439 
 of bolts, 325, 326 
 of brick, 336 
 
 of brick and stone, 347, 350 
 of bridge-links, 331 
 of bronze, 334, 360 
 of canvas, 335 
 of castings, 330 
 of cast iron, 421 
 of cast-iron beams, 427 
 of cast-iron columns, 274 
 of cast-iron cylinders, 427 
 of cast-iron flanged fittings, 428 
 of cast iron, relation to size of 
 
 bar, 421 
 of cast-iron water-pipes, 194, 
 
 427 
 of chain cables, table, 251, 252 
 of chains, table, 251, 252 
 of chalk, 349 
 of cement mortar, 350 
 of columns, 269-278, 1337 
 of copper at high temperatures • 
 
 344 
 of copper plates, 334 
 of copper-tin alloys, 361 
 of copper-tin-zinc alloys, graphic 
 
 representation, 364 
 of copper-zinc alloys, 364 
 of cordage, table, 386-391, 1157 
 of crank-pins, 1007 
 
1456 
 
 INDEX. 
 
 Strength of electro-magnet, 1386 
 of nagging, 350 
 of flat plates, 313 
 of floors, 1337-1340 
 of German silver, 334 
 of glass, 343 
 of granite, 335 
 of gun-bronze, 362 
 of hand and hydraulic riveted 
 
 joints, 402 
 of ice, 344 
 of iron and steel, effect of cold 
 
 on, 440 
 of iron and steel pipe, 341 
 of lime-cement mortar, 350 
 of limestone, 349 
 of locomotive forgings, 331 
 of Lowmoor iron bars, 330 
 of malleable iron, 430, 434 
 of marble, 335 
 of masonry, 349 
 of materials, 258-359 
 of materials, Kirkaldy's tests 
 
 330-336 
 of perforated plates, 402 
 of phosphor-bronze, 370 
 of Portland cement, 336 
 of riveted joints, 337, 401-411 
 of roof trusses. 521 
 of rope, 335, 386, 1193 
 of sandstone, 349 
 of sheet metal, 334 
 of silicon-bronze wire, 371 
 of soapstone, 349 
 of spring steel, 333 
 of spruce timber, 345 
 of stayed surfaces, 315 
 of steam-boilers, 879-889 
 of steel axles, 332 
 of steel castings, 333 
 of steel, open-hearth structural 
 
 454 
 of steel propeller-shafts, 332 
 of steel rails, 331 
 of steel tires, 332 
 of structural shapes, 287-310 
 of timber, 344-347 
 of twisted iron, 264 
 of unstayed surfaces, 314 
 of welds, 251, 333 
 of wire, 335, 336 
 of wire and hemp rope, 334, 335 
 of wrought-iron columns, 271 
 of yellow pine, 344 
 range of, in steel, 454 
 shearing, of iron and steel, 340 
 shearing, of woods, table, 347 
 tensile, 265 
 tensile, of iron and steel at high 
 
 temperatures, 439 
 tensile, of pure steel, 453 
 torsional, 311 
 transverse, 282-286 
 Stress and strain, 258 
 
 due to temperature, 312 
 Stresses allowed in bridge members, 
 
 272 
 
 Stresses combined, 312 
 effect of, 258 
 
 in framed structures, 515-522 
 in plating of bulkheads, etc., 
 
 due to water-pressure, 315 
 in steel plating due to water 
 
 pressure, 315 
 produced by shocks, 263 
 Structures, framed, stresses in, 515 
 Structural materials, permissible 
 stresses in, 1335 
 shapes, elements of, 280 
 shapes, moment of inertia of, 
 
 279 
 steel shapes, properties of, 287- 
 
 310 
 shapes, radius of|gyration of, 279 
 shapes, steel (see Steel, struc- 
 tural, also Beams, angles, 
 etc.), 
 steel, rolled sections, proper- 
 ties of, 287-310 
 Strut, moving, 511 
 Struts, steel, formulae for, 271 
 strength of, 269 
 
 wrought-iron, formulas for, 271 
 Suction lift of pumps, 757 
 Sugar manufacture, 809 
 
 solutions, concentration of, 545 
 Sulphate of lime, solubility of, 545 
 Sulphur dioxide addendum to 
 steam-engine, 978 
 dioxide and ammonia-gas, pro- 
 perties of, 1285 
 dioxide refrigerating-machine, 
 
 1292 
 influence of, on cast iron, 415 
 influence of, on steel, 452 
 Sum and difference of angles, 
 
 functions of, 69 
 Sun, heat of, as a source of power, 
 
 988 
 Superheated steam, effect of on 
 steam consumption, 972 
 steam, economy of steam-en- 
 gines with, -969 
 steam, practical application of, 
 973 
 Superheating, economy due to, 
 978 
 in locomotives, 1102 
 Surface condensers, 1051 
 
 of sphere, table, 125, 126 
 Surfaces of geometrical solids, 
 62-67 
 of revolution, quadrature of, 78 
 unstayed flat, 314 
 Suspension cableways, 1181 
 Sweet's slide-valve diagram, 1036 
 Symbols, chemical, 170 
 
 electrical, 1416 
 Synchronous-motor, 1409 
 
 T-shapes, properties of Carnegie 
 
 steel, table, 294 
 Tackle, hoisting, 1158 
 Tackles, rope, efficiency of, 391 
 
1457 
 
 Tail-rope, system of haulage, 1178 
 Tanbark as fuel, 808 
 Tangent of an angle, 67 
 Tangents of angles, table of, 166- 
 
 169 
 Tangential or impulse water- 
 wheels, tables of, 751 
 Tanks andjcisterns, number of bar- 
 rels in, 133 
 capacities of, tables, 128, 132 
 with flat sides, plating and fram- 
 ing for, 316 
 Tantalum electric lamps, 1371 
 Taps, A.S.M.E. standard, 227 
 formulae and table for screw- 
 threads of, 224 
 Tap-drills, tables of, 227, 1269 
 Taper, to set in a lathe, 1238 
 Tapered wire rope, 1183 
 Taper pins, 1272 
 Tapers, Jarno, 1271 
 
 Morse, 1271 
 Taylor's experiments on cutting 
 tools of high-speed steel, 1238 
 Taylor's rules for belting, 1120 
 
 theorem, 79 
 Teeth of gears, forms of, 1138- 
 1145 
 of gears, proportions of, 1135, 
 1136 
 Telegraph-wire, joints in, 239 
 
 tests of, table, 238 
 Telpherage, 1171 
 Temperature, absolute, 540 
 
 determination of by color, 531 
 determinations of melting-points 
 
 effect 'of on strength, 344, 439- 
 
 441 
 of fire, 785 
 rise of, in combustion of gases, 
 
 786 
 stress due to, 312 
 Temperature-entropy diagram, 574 
 -entropy diagram of water and 
 steam, 576 
 Temper carbon, in cast-iron, 416 
 Tempering, effect of, on steel, 468 
 of steel, 468 
 
 oil, of steel forgings, 458 
 Tenacity of different metals, 177 
 of metals at various tempera- 
 tures, 344, 439 
 Tensile strength, 265 
 
 strength, increase of, by twist- 
 ing, 264 
 strength of iron and steel at 
 
 high temperatures, 439 
 strength of pure steel, 453 
 strength (see Strength) 
 tests, precautions in making, 
 
 266 
 tests, shapes of specimens for, 
 266 
 Tension and flexure combined, 312 
 
 and shear, combined, 312 
 Terne-plate, 188 
 Terra cotta, weight of, 186 
 
 Tests, compressive (see Compres- 
 sive strength) 
 of steam-boilers, rules for, 866 
 of steam-engines, rules for, 988 
 of strength of materials (see 
 
 Strength) 
 tensile (see Strength and Ten- 
 sile strength) 
 Test-pieces, comparison of large 
 
 and small, 455 
 Thermal capacity, 534 
 storage, 897, 987 
 units, 532 
 Thermit process, the, 372 
 
 welding process, 463 
 Thermodynamics, 571-577 
 
 laws of, 572 
 Thermometer, air, 530 
 
 centigrade and Fahrenheit com- 
 pared, tables, 524 
 Threads, pipe, 202, 207 
 Threading and parting tools, speed 
 of, 1243 
 pipe, force required for, 341 
 Three-phase transmission, rule for 
 sizes of wires, 1398 
 circuits, 1395 
 Thrust bearings, 1208 
 Tides, utilization of power of, 756 
 Ties, railroad, required per mile 
 
 of track, 232 
 Tiles, weight of, 186 
 Timber (see also wood) 
 
 beams, safe loads, 1335, 1341 
 beams, strength of, 344 
 expansion of, 345 
 measure, 20 
 preservation of, 347 
 strength of, 344-347 
 table of contents in feet, 21 
 Time, measures of, 20 
 Tin, alloys of (see Alloys) 
 lined iron pipe, 218 
 plates, 187 
 properties of, 176 
 plates, 187 
 Tires, locomotive, shrinkage fits, 
 1273 
 steel, friction of on rails, 1195 
 steel, specifications for, 485 
 steel, strength of, 331 
 Titanium, additions to cast-iron, 
 416, 426 
 aluminum alloy, 375 
 Tobin bronze, 368 
 Toggle-joint, 511 
 Tool steel (see also Steel) 
 
 steel high-speed, composition 
 
 and heat-treatment, of, 1242 
 steel, best quality, 1242, 
 steel, high-speed, new (1909), 
 tests of, 1246 
 
 steel, high-speed, Taylor's ex- 
 periments, 1238 
 steel in small shops, best treat- 
 ment of, 1243 
 steel of different qualities, 1243 
 
1458 
 
 INDEX. 
 
 Tools, cutting, durability of, 1243 
 economical cutting speed of, 
 
 1243 
 cutting, effect of feed and depth 
 
 of cut on speed of, 1241 
 cutting, in small shops, best 
 
 method of treatment, 1243 
 cutting, interval between grind- 
 
 ings of, 1241 
 cutting, pressure on, 1241 
 forging and grinding of, 1240 
 cutting, use of water on, 1241 
 machine (see Machine tools) 
 parting and thread, cutting speed 
 of, 1243 
 Toothed-wheel gearing, 514, 1133 
 Tonnage of vessels, 1316 
 Tons per mile, equivalent of, in lbs. 
 
 per yard, 28 
 Torque computed from watts and 
 revolutions, 1386 
 horse-power and revolutions, 
 
 1386 
 of an armature, 1386 
 Torsion and compression com- 
 bined, 312 
 and flexure combined, 312 
 elastic resistance to, 311 
 of shafts, 1010,1106 
 tests of refined iron, 339' 
 Torsional strength, 311 
 Track bolts, 232 
 
 spikes, 233 
 Tractive force of a locomotive, 
 
 1087 
 Tractrix, Schiele's anti-friction 
 
 curve, 51 
 Trains, railroad, resistance of, 1084 
 railroad, speed of, 1094 
 loads, average, 1101 
 Trammels, to describe an ellipse 
 
 with, 46 
 Tramways, compressed-air 624 
 
 wire-rope, 1180 
 Transformers, efficiency of, 1400 
 
 electrical, 1400 
 Transmission, compressed-air (see 
 compressed-air) 
 electric, 1359, 1396 
 electric, area of wires, 1359 
 electric, cost of copper, 1365 
 electric, economy of, 1360 
 electric, efficiency of, 1361 
 electric, systems of, 1363 
 electric, weight of copper for, 1359 
 electric, wire table for, 1360 
 hydraulic-pressure (see Hy- 
 draulic-pressure transmis- 
 sion, 
 of heat (see Heat) 
 of power bv wire-rope (see Wire- 
 rope), 1183-1189 
 pneumatic postal, 624 
 rope, iron and steel, 245 
 rope (see Rope-driving) 
 wire-rope (see Wire-rope) 
 Transporting power of water, 565 
 
 Triple-expansion engine (see 
 
 Steam-engines) 
 Transverse strength, 282-286 
 Trapezium and Trapezoid, 55 
 Triangles, mensuration of, 55 
 
 problems in, 42 
 
 spherical, 64 
 
 solution of, 70 
 Trigonometrical computations by 
 slide rule, 84 
 
 formulae, 69 
 
 functions, table, 166-169 
 
 functions, logarithmic, 169 
 Trigonometry, 67-70 
 Triple effect evaporators, 543 
 Troostite, 456 
 
 Trough plates, properties of, 289 
 Troy weight, 19 
 Trusses, bridge, stresses in, 517 
 
 roof, stresses in, 521 
 Tubes, boiler, table, 209 
 
 boiler, used as columns, 341 
 
 brass, seamless, 216 
 
 collapse of, formulas for, 320 
 
 collapse of, tests of, 320 
 
 collapsing pressure of, table, 321 
 
 copper, 216 
 
 expanded, holding . power of, 
 342, 883 
 
 lead and tin, 217 
 
 of different materials, weight of, 
 178 
 
 seamless aluminum bronze, 372 
 
 steel, cold-drawn, Shelby, 210 
 
 surface per foot of length, 211 
 
 welded, extra strong, 209 
 
 Tube-plates, steam-boiler, rules for, 
 
 882 
 Tungsten and aluminum alloy, 375 
 
 electric lamps, 1371 
 
 steel, 472 
 Turbine wheel, tests of, 742 
 
 wheels, 737-748 
 
 wheels, proportions of , 739 
 
 wheel tables, 751 
 Turbines, fall-increaser for, 747 
 
 of 13,500 H.P., 747 
 
 rating and efficiency of, 743 
 
 steam (see Steam-turbines) 
 Turf or peat, as fuel, 808 
 Turnbuckles, 231 
 Tuyeres for cupolas, 1224 
 Twist drills (see Drills) 
 
 drills, sizes and speeds, 1254 
 Twist-drill gauge, table, 30 
 Twisted steel bars, strength of, 264 
 Two-phase currents, 1394 
 Type-metal, 384 
 
 Uehling and Steinbart pyrometer, 
 
 530 
 Underwriters' rules for electrical 
 
 wiring, 1355 
 Unequal arms on balances, 20 
 Unit o.f evaporation, 855 
 of force, 488 
 of power, 503 
 
INDEX. 
 
 1459 
 
 Unit of heat, 532 
 
 of work, 502 
 Units, electrical and mechanical, 
 equivalent values of, 1347 
 
 electrical, relations of, 1346 
 
 of the magnetic, circuit, 1346 
 United States, population of, 11 
 
 standard sheet metal, gauge, 31 
 Unstayed surfaces, strength of, 314 
 Upsetting of structural steel, 459 
 
 Vacuum at different temperatures, 
 757 
 drying in, 546 
 high advantage of, 1059 
 high, influence of on economy, 
 
 972 
 inches of mercury and absolute 
 
 pressures, 1053 
 pumps, 775 
 
 systems of steam heating, 673 
 Valve-gear, Stephenson, 1044 
 
 Walschaert, 1046 
 Valves and elbows, friction of air 
 in, 593 
 and fittings, loss of pressure due 
 
 to, 721 
 pump, 762 
 in steam pipes, 852 
 straight-way gate, 199 
 Valve-stem or rod, design of, 1019 
 
 (see Steam-engines) 
 Vanadium and copper alloys, 371 
 effect of on cast iron, 416, 426 
 steel spring, 401 
 -chrome steel, 476-478 
 -nickel steels, 475 
 Vapor pressures of various liquids, 
 814 
 water, and air mixture, weight 
 
 of, 584, 586 
 ammonia, carbon dioxide and 
 sulphur dioxide, properties of, 
 1288 
 and gases, mixtures of, 578 
 saturation point of, 578 
 Vaporizer pressures in refrigerating, 
 
 1288 
 Varnishes, 448 
 Velocity, angular, 498 
 
 due to filling a given height, 500 
 parallelogram of, 499 
 table of height corresponding to 
 a given, 499 
 Ventilating ducts, quantity of air 
 carried by, 655 
 fans, 626-648 
 Ventilation (see also Heating and 
 Ventilation) 
 cooling air for, 681 
 of mines (see Mine-Ventilation) 
 by a steam-jet, 652 
 of mines, equivalent orifice, 686 
 Ventilators, centrifugal for mines, 
 
 644 
 Venturi meter, 728 
 
 Versed line of an arc, 68 
 
 sines, table, 166-169 
 Verticals, formulae for strains in, 
 
 519 
 Vessels (see also Ships) 
 Vessels, framing of, table, 316 
 Vibrations in engines, preventing, 
 
 980 
 Vis- viva, 502 
 Volt, definition of, 1345 
 Voltages used in long-distance 
 
 transmission, 1399 
 Volumes of revolution, cubature of, 
 
 78 
 Vulcanized India rubber, 356 
 
 Walls of buildings, thickness of, 
 1336 
 
 of warehouses, factories, etc., 
 1337 
 
 windows, etc., heat loss through, 
 659 
 Walschaert valve-gear, 1046 
 Warren girder, stresses in, 520 
 Washers, wrought and cast, tables 
 
 of, 230 
 Washing of coal 
 Water, 687-697 
 
 amount of to develop a given 
 horse-power, 753 
 
 abrading power of, 705 
 
 analysis of, 693 
 
 as a lubricant, 1222 
 
 boiling point of, 690 
 
 boiling point at various baro- 
 metric pressures, 582 
 
 comparison of head in feet with 
 various units, 689 
 
 compressibility of, 691 
 
 conduits, long, efficiency of, 735 
 
 consumption of locomotives, 1098 
 
 consumption of steam-engines 
 (see Steam-engines) 
 
 current motors, 734 
 
 erosion and abrading by, 705 
 
 flow of (see Flow of water) 
 
 flowing in a tube, power of, 734 
 
 flowing, measurement of, 727 
 
 freezing-point of, 690 
 
 hammer, 722 
 
 hardness of, 694 
 
 head of, 689 
 
 heating of, by steam coils, 565 
 
 heat-units per pound of, 688 
 
 horse-power required to raise, 757 
 
 impurities of, 691 
 
 in pipes, loss of energy in, 780 
 
 jets, vertical, 722 
 
 meters, capacity of, 722 
 
 pipe, cast-iron, transverse 
 strength of, 427 
 
 pipes, compound with branches, 
 720 
 
 power, 734 
 
 power plants, high pressure, 754 
 
 power, value of, 735 
 
 pressures and heads, table, 689 
 
1460 
 
 INDEX. 
 
 Water pressure on vertical surfaces, 
 690 
 pressure per square inch, equiva- 
 lents of, 28, 689 
 prices charged for in cities, 722 
 pumping by compressed air, 776 
 purification of, 694-697 
 quantity of discharged from 
 
 pipes, 707-712 
 specific heat of, 536, 691 
 total heat and entropy of, 839- 
 
 842 
 tower (see Stand-pipe) 
 tower at Yonkers, N. Y., 328 
 transporting power of, 565 
 under pressure, energy of, 734 
 units of pressure and head, 689 
 velocity of, in open channels, 704 
 velocity of, in pipes, 707-712 
 vapor and air mixture weight of, 
 
 584, 586 
 weight at different temperatures, 
 
 687, 688 
 weight of one cubic foot, 28 
 wheels, 737 
 
 wheels, jet, power, of, 755 
 wheels, Pelton, 748 
 wheels, tangential, 750 
 wheels, tangential choice of, 749 
 wheel, tangential table, 751 
 
 Waterfall, power of a, 734 
 
 Water-gas, 829 
 analyses of, 830 
 manufacture of, 830 
 plant, efficiency of, 831 
 plant, space required for, 832 
 
 Waber-softening apparatus, 695 
 
 Waves, ocean, power of, 755 
 
 Weathering of coal, 800 
 
 Webster's formula for strength of 
 steel, 452 
 
 Wedge, 512 
 volume of, 63 
 
 Weighing on an incorrect balance, 20 
 
 Weight, definition of, 487 
 
 and specific gravity of materials 
 171-174 (see also Material in 
 question) 
 measures of, 19 
 
 Weir dam measurement, 731 
 flow of water over, 731 
 trapezoidal, 733 
 
 Welds, strength of, 333 
 
 Welding by oxy-acetylene flame,464 
 electric, 1374 
 of steel, 460, 463 
 process, the thermit, 463 
 
 Welding by oxy-acetylene flame, 
 464 
 electric, 1374 
 of steel, 460, 463 
 process, the thermit, 463 
 
 Wheat, weight of, 178 
 
 Wheel and axle, 514 
 
 Wheels, turbine (see Turbine Wheel) 
 
 Whipple truss, 518 
 
 White-metal alloys, 382, 383 
 
 Whitworth process of compressing 
 
 steel, 464 
 Wiborgh air-pyrometer, 528 
 Wildwood pumping-engine, high 
 
 economy of, 774 
 Willans law of steam consumption, 
 
 962 
 Wind, 597-603 
 force of, 597 
 
 pressure of, in storms, 598 
 strain on stand-pipes, 328 
 Winding engines, 1163 
 Windlass, 514 
 
 differential, 514 
 Windmills, 599-604 
 
 capacity and economy, 601 
 Wire, aluminum, properties of, 
 
 243, 1362 
 aluminum bronze, 243 
 brass, properties of, 243 
 brass, weight of, table, 219 
 copper, hard-drawn, specification 
 
 for, 243 
 copper, stranded, 242 
 copper, rule for resistance of, 242 
 copper, table of size, weight and 
 
 resistance of Edison gauge, 240 
 copper, telegraph and telephone, 
 
 241 
 copper, weight of bare and insu- 
 lated, 241 
 galvanized, for telegraph and 
 
 telephone lines, 238 
 galvanized iron, specifications for, 
 
 239 
 galvanized steel strand, 249 
 gauges, tables, 29 
 insulated copper, 241 
 iron and steel 237-239 
 nails, 235, 236 
 phosphor-bronze, 243 
 piano, strength of, 239 
 platinum, properties of, 243 
 plow steel, 239 
 of different metals, 243 
 silicon-bronze, 243,371 
 steel, properties of, 237 
 stranded feed, table, 242 
 telegraph, joints in, 239 
 telegraph, tests of, 238 
 weight per mile-ohm 238 
 Wires of various metals, strength of 
 
 336 
 Wire-rope, 244-250 
 
 rope, bending curvature of, 1188 
 
 rope, bending stress of, 1184 
 
 rope, breaking strength of, 1184 
 
 rope, flat, 248 
 
 rope, galvanized, 247 
 
 rope haulage (see Haulage) 
 
 rope, horse-power transmitted by 
 
 1185 
 rope, horse-power transmitted 
 
 1185 
 rope, locked, 250 
 rope, notes on use of, 250 
 rope, plow steel, 246 
 
1461 
 
 Wire-rope, radius of curvature of, 
 1189 
 
 rope, sag or deflection of, 1187 
 
 rope, splicing of, 395 
 
 ropes, strength of, 334 
 
 rope, sheaves for, 1184 
 
 rope, tapered, 1183 
 
 rope tramways, 1179 
 
 rope transmission, deflection of 
 rope, 1180, 1187 
 
 rope transmission, inclined, 1188 
 
 rope transmission, limits of span, 
 1187 
 
 rope transmission, long distance, 
 1188 
 
 rope, transmission of power by, 
 1183 
 
 rope transmission, sheaves for 
 1186 
 Wire-wound fly-wheels, 1034 
 Wiring rules, Underwriters' 355, 
 
 table for direct currents, 1360 
 
 table for motor service, 1356 
 
 table for three-phase transmis- 
 sion lines, 1398 
 Wohler's experiments on strength 
 
 of materials, 261 
 Wood (see also Timber) 
 
 as fuel, 804 
 
 composition of, 805 
 
 drying of, 347 
 
 expansion of, by heat, 345 
 
 expansion of, by water, 345 
 
 heating value of, 804 
 
 holding power of bolts in, 323 
 
 nail-holding power of, 323 
 
 screws, dimensions of, 234 
 
 screws, holding power of, 323 
 
 strength of, 344-347 
 
 strength of, Kirkaldy's tests, 336 
 
 weight of, table, 173 
 
 weight and heating values of, 804 
 
 weight per cord, 255 
 
 Woods, American, shearing strength 
 of, 347 
 
 tests of, 346 
 Wooden fly-wheels, 1033 
 
 stave pipe, 218 
 Woolf compound engines, 947 
 Wooten locomotive, 1090 
 Work, definition of, 28, 502 
 
 energy, power, 502 
 
 of adiabatic compression, 607 
 
 of acceleration, 504 
 
 of accelerated rotation, 504 
 
 of a man, horse, etc., 507-509 
 
 of friction, 1205 
 Worm gearing, 514, 1143 
 Wrist-pins, dimensions of, 1009 
 Wrought iron, chemical composi- 
 tion of, 436 
 
 iron, effect of rolling on strength 
 of, 437 
 
 iron, manufacture of, 435 
 
 iron, slag in, 436 
 
 iron, specifications, 437, 438 
 
 strength of, 330, 337, 435-439 
 
 iron, strength of, at high tem- 
 peratures, 439 
 
 iron, strength of, Kirkaldy's tests, 
 331 
 
 Yacht rigging, galvanized steel, 248 
 Yield point, 259 
 
 Z-bar columns, dimensions of, 300- 
 
 304 
 Z-bars, Carnegie, properties of, 299 
 Zero, absolute, 540, 837 
 Zeuner's slide-valve diagram, 1036 
 Zinc alloys (see Alloys) 
 
 properties of, 177 
 
 use of, in steam boilers, 901 
 Zone, spherical, 65 
 
 of spheroid, 65 
 
 of spindle, 65 
 
ALPHABETICAL INDEX TO ADVERTISEMENTS. 
 
 PAGE 
 
 ALPHONS CUSTODIS CHIMNEY CONSTRUCTION COMPANY. . 4 
 
 AMERICAN ENGINE COMPANY 15 
 
 AMERICAN PIPE MANUFACTURING COMPANY 13 
 
 AMERICAN STEEL & WIRE COMPANY 17 
 
 ANSONIA BRASS AND COPPER COMPANY 14 
 
 ATLAS PORTLAND CEMENT COMPANY 16 
 
 BABCOCK & WILCOX COMPANY, THE 4 
 
 BALDWIN LOCOMOTIVE WORKS 2 
 
 BOSTON BELTING COMPANY 15 
 
 BROWN HOISTING MACHINERY COMPANY, THE 17 
 
 CHAPMAN VALVE MANUFACTURING COMPANY 13 
 
 CRESSON & COMPANY, GEORGE V 11 
 
 HUNT, ROBERT W. & COMPANY 19 
 
 INGERSOLL-RAND COMPANY 7 
 
 KEUFFEL & ESSER COMPANY 20 
 
 LESCHEN & SONS ROPE COMPANY, A 10 
 
 LIDGERWOOD MANUFACTURING COMPANY 6 
 
 LODGE & SHIPLEY MACHINE TOOL COMPANY, THE 12 
 
 LUNKENHEIMER COMPANY, THE 5 
 
 MANNING, MAXWELL & MOORE 2 
 
 MAURER & SON, HENRY 16 
 
 MORSE TWIST DRILL AND MACHINE COMPANY 9 
 
 NATIONAL TUBE COMPANY 3 
 
 NEW YORK BELTING & PACKING COMPANY 8 
 
 NORWALK IRON WORKS COMPANY, THE 9 
 
 PENNSYLVANIA WIRE GLASS COMPANY 19 
 
 PITTSBURGH MANUFACTURING COMPANY 12 
 
 RANDOLPH-CLOWES COMPANY 14 
 
 RIDER-ERICSSON ENGINE COMPANY 12 
 
 ROEBLING'S SONS COMPANY, JOHN A 20 
 
 RUGGLES-COLES ENGINEERING COMPANY 6 
 
 SELLERS & COMPANY, WILLIAM, INCORPORATED 11 
 
 SIMMONS COMPANY, JOHN 14 
 
 STANDARD STEEL WORKS COMPANY 2 
 
 UNDER-FEED STOKER COMPANY OF AMERICA, THE 8 
 
 WILEY & SONS, JOHN 18 
 
 YALE & TOWNE MANUFACTURING COMPANY, THE 1 
 
CLASSIFIED INDEX TO ADVERTISEMENTS. 
 
 PAGE 
 
 Aerial Wire Rope Tramways. Leschen & Sons Rope Co., A 10 
 
 Belting and Hose. 
 
 Boston Belting Co 15 
 
 New York Belting & Packing Co 8 
 
 Boiler Tubes. National Tube Co 3 
 
 Boiler Tubes (Brass). Randolph-Clowes Co 14 
 
 Boilers, Steam. Babcock & Wilcox Co., The 4 
 
 Brass Rods, Sheets, Tubes, Wire, etc. 
 
 Ansonia Brass and Copper Co 14 
 
 Randolph-Clowes Co 14 
 
 Bureau op Inspection, Tests and Consultation. 
 
 Robert W. Hunt & Co 19 
 
 Cables. Leschen & Sons Rope Co., A 10 
 
 Cableways (Aerial Wire Rope). Leschen & Sons Rope Co., A 10 
 
 Car Wheels — Solid Forged, Rolled and Steel Tired. 
 
 Standard Steel Works Co 2 
 
 Cement, American Portland. Atlas Portland Cement Co 16 
 
 Chain Blocks — Triplex, Duplex and Differential. 
 
 Blocks. The Yale & Towne Manufacturing Co 1 
 
 Chimneys. Alphons Custodis Chimney Construction Co 4 
 
 Chucks, Milling Cutters, Reamers, Spring Cutters, Taps, etc. 
 
 Morse Twist Drill and Machine Co 9 
 
 Compressors — Air, Gas, etc. 
 
 Norwalk Iron Works Co., The 9 
 
 Concrete Construction (Reinforced). 
 
 Brown Hoisting Machinery Co., The 8 
 
 Alphons Custodis Chimney Construction Co 4 
 
 Concrete Reinforcement — Wire. American Steel & Wire Co 17 
 
 Copper Wires, Cables, Bars, Sheets, Tubes, etc. 
 
 Ansonia Brass and Copper Co , 14 
 
 Crushers — Ore, Rock, Stone. 
 
 Geo. V. Cresson Co 11 
 
 Drills — Compressed and Electric Air. 
 
 Ingersoll-Rand Co 7 
 
 Drills, Power and Hand. 
 
 Norwalk Iron Works Co., The 9 
 
 Drills, Twist. Morse Twist Drill and Machine Co 9 
 
 Dyers— Mineral and Grain. 
 
 Ruggles-Coles Engineering Co 6 
 
 Electric Hoists. The Yale & Towne Manufacturing Co 1 
 
 Engineering Requisites. Lunkenheimer Co., The 5 
 
 Engineers and Contractors. 
 
 Brown Hoisting Machinery Co., The 17 
 
 Engineers — Founders — Machinists. 
 
 Pittsburgh Manufacturing Co 12 
 
 Engines. 
 
 American Engine Co 15 
 
 Rider-Ericsson Engine Co 12 
 
 Engines, Blowing. 
 
 Lidgerwood Mfg. Co 6 
 
 Fire Brick, Tiles, Slabs, Cupola Linings, Clay Retorts, etc. 
 
 Maurer & Son, Henry 1«6 
 
CLASSIFIED INDEX TO ADVERTISEMENTS. 
 
 PAGE 
 
 Fuel-Economizers and Furnaces. 
 
 Under-Feed Stoker Co. of America, The 8 
 
 Hoisting Machinery — Elevators, Conveyors, etc. 
 
 Brown Hoisting Machinery Co., The 17 
 
 Lidgerwood Mfg. Co 6 
 
 Hydrants. 
 
 Chapman Valve Mfg. Co 13 
 
 Pittsburgh Manufacturing Co 12 
 
 Insulated Wires and Cables. 
 
 Ansonia Brass and Copper Co 11 
 
 Locomotives. Baldwin Locomotive Works 2 
 
 Machine Tools. 
 
 Manning, Maxwell & Moore 2 
 
 Mechanical Stokers. Under-Feed Stoker Co. of America, The. ... 8 
 
 Milling Machines, Shapers, Planers, Punches, Rolls, Shears, 
 Lathes, Machine Tools, Bolts, etc. 
 
 Lodge & Shipley Machine Tool Co., The 12 
 
 Sellers & Co., William (Incorporated) 13 
 
 Mining and Quarrying Machinery. 
 
 Brown Hoisting Machinery Co., The 17 
 
 Ingersoll-Rand Co 7 
 
 Norwalk Iron Works Co., The <) 
 
 Packing — Piston, Valve, Joint. 
 
 Boston Belting Co 15 
 
 New York Belting & Packing Co 8 
 
 Pipe, Water and Gas. 
 
 American Pipe Mfg. Co 13 
 
 National Tube Co 3 
 
 Simmons Co., John 14 
 
 Pumping Machinery. 
 
 Rider-Ericsson Engine Co 12 
 
 Railway Supplies. Manning, Maxwell & Moore , 2 
 
 Rivets — -Boiler and Structural. 
 
 Pittsburgh Manufacturing Co 12 
 
 Rope (Wire). 
 
 Leschen & Sons Rope Co., A 10 
 
 Roebling's Sons Co., John A 20 
 
 Rope (Wire and Manila). Leschen & Sons Rope Co., A 10 
 
 Rubber Goods. 
 
 Boston Belting Co 15 
 
 New York Belting & Packing Co 8 
 
 Stokers — Automatic. Under-Feed Stoker Co. of America, The 8 
 
 Surveying Instruments. Keuffel & Esser Co 20 
 
 Telegraph. Telephone and Trolley Wire. 
 
 Roebling's Sons Co., John A 20 
 
 Tramways (Aerial Wire Rope). Leschen & Sons Rope Co., A. . . . 10 
 
 Valves — Gas, Water, and Steam. 
 
 Chapman Valve Mfg. Co 33 
 
 Lunkenheimer Co., The. 5 
 
 Water-Supply. Rider-Ericsson Engine Co 12 
 
 Water-Works, Contractors for. American Pipe Mfg. Co 13 
 
 Wire for Concrete Reinforcement. American Steel & Wire Co.. . 17 
 
 Wire Glass. Pennsylvania Wire Glass Co 19 
 
In 1876 
 
 WE first made the Differential 
 Chain Block; we were the 
 exclusive manufacturers un- 
 der the Weston patents and the exclu- 
 sive Weston licensees. 
 
 We can fairly say that the whole 
 history of the evolution of chain 
 hoists has been written in our shops — 
 thirty-four years of unceasing search 
 for improvement. 
 
 The Triplex Block of today — (the best hand 
 hoist made ; the highest mechanical efficiency) — 
 has cut-steel gears ; bronze bushings ; drop-forged 
 pinions and shaft; welded hand chains; steel 
 gear cover. 
 
 Every part of the Triplex Block is standard- 
 ized and interchangeable. The whole dirt-proof, 
 durable, efficient. 
 
 4 styles: Differential, Duplex, Triplex, Electric. 
 41 sizes: An eighth of a ton to forty tons. 
 300 active stocks: ready for instant call all over 
 the United States. 
 
 The Yale & Towne Mfg, Co, 
 
 Only Makers of Genuine Yale Locks 
 9 Murray Street, - - New York 
 
 Foreign Warehouses : The Fairbanks Co., London and Glasgow. 
 Fenwick Freres & Co., Paris, Brussels, Liege and Turin. 
 Yale & Towne Co., Ltd., Hamburg. F.W. Home, Yokohama. 
 
 Canadian Warehouses : The Canadian Fairbanks Co., Ltd., Mon- 
 treal, Toronto, St. John, N.B., Winnipeg, Calgary, Vancouver. 
 
Baldwin Locomotive Works 
 
 MANUFACTURERS OF 
 
 locomotives 
 
 OF EVERY DESCRIPTION 
 
 PHILADELPHIA, PA., U. S. A. 
 Gable Address : - - - " Baldwin," Philadelphia 
 
 STANDARD STEEL WORKS CO. 
 
 HARRISON BLDG., PHILADELPHIA, PA., U. S. A. 
 
 SOLID FORGED ROLLED AND 
 STEEL TIRED WHEELS 
 
 mounted on axles fitted with Motor Gears for 
 
 Electric Railway Service. 
 
 LOCOMOTIVE TIRES RAILWAY SPRINGS 
 
 FORGINGS CASTINGS 
 
 Manning, Maxwell & Moore 
 
 (INCORPORATED) 
 
 Machine Tools and Railway Supplies 
 
 Owning and Operating 
 
 THE SHAW ELECTRIC CRANE CO. 
 
 Shaw Electric Traveling Cranes 
 Shaw Wrecking Cranes 
 
 THE ASHCROFT MFG. CO. 
 
 Steam Pressure or Vacuum Gauges 
 Tabor Steam Engine Indicators 
 Edson Recording Gauges 
 
 THE CONSOLIDATED SAFETY VALVE CO. 
 
 Consolidated Pop Safety Valves 
 
 THE HANCOCK INSPIRATOR CO. 
 
 Hancock Inspirators 
 Hancock Ejectors 
 Hancock Valves 
 
 THE HAYDEN & DERBY MFG. CO. 
 
 Metropolitan Injectors 
 H-D Ejectors 
 
 85-87-89 LIBERTY STREET, NEW YORK 
 
Thought It Was Steel, but It Wasn't 
 
 7 
 
 9 
 
 The Master Mechanic of a large Eastern Railway System 
 recently received as a " sample " from a competitor of ours, 
 a small section of Boiler Tube tagged — " Spellerized Steel." 
 
 It was a rather worn-looking specimen, as the illustration par- 
 tially indicates. (The holes shown were drilled by the chemist, 
 but otherwise it is in the same condition as received.) 
 
 It was shown to one of our representatives, and on examina- 
 tion he was a little inclined to doubt whether it was " Spellerized 
 i Steel," and sent it to the Mill for examination and analysis. 
 
 A careful analysis indicated that the material was charcoal 
 IRON and NOT STEEL. 
 
 While the circumstances in this case are a little unusual, yet 
 it is typical of the attitude which prevails in many instances. 
 In other words, it is assumed (in many cases) that if a Boiler 
 Tube rusts quickly, it is steel, and if it lasts any considerable 
 length of time, it is iron. There is no basis of fact for such a 
 presumption. 
 
 We formerly manufactured both iron and steel Boiler Tubes ; 
 becoming convinced, however, by the experience of ourselves 
 and many others, that the steel Boiler Tube was the "MODERN 
 BOILER TUBE," and the most economical tube, we abandoned 
 the manufacture of iron tubes and are now confining our atten- 
 tion in the Boiler Tube line to the steel tube. 
 
 This action was not taken lightly nor without due reference to 
 all known circumstances, and our actual knowledge of the goods, 
 based on years of manufacturing experience. 
 
 Many of the largest consumers have reduced their Boiler Tube 
 expense by the use of the "MODERN BOILER TUBE." 
 
 Do you feel that you can profitably afford to ignore their 
 experience? 
 
 NATIONAL TUBE COMPANY 
 
 General Sales Offices, Frick Building, Pittsburgh, Pa. 
 DISTRICT SALES OFFICES 
 
 ATLANTA NEW ORLEANS PITTSBURGH ST. LOUIS 
 
 CHICAGO NEW YORK PORTLAND SALT LAKE CITY 
 
 DENVER PHILADELPHIA SAN FRANCISCO SEATTLE 
 
 Export Representatives: U S. Steel Products Export Co., New York City 
 3 
 
The Babcock & Wilcox Co, 
 
 85 Liberty Street, New York. 
 
 flakers of 
 
 BABCOCK & WILCOX 
 
 Stirling, Rust, 
 
 Water Tube Steam Boilers 
 
 Steam Superheaters, 
 
 Mechanical Stokers. 
 
 Works : 
 Bayonne, New Jersey. Barberton, Ohio* 
 
 Tj 
 
 CHIMNEY CONSTRUCTION COMPANY ll 
 
 \HEWYOBK^ ] ^ BENNETT BLDG^/ 
 
 CHIMNEYS. 
 
 PERFORATED 
 I RADIAL BRICK. 
 
 I REINFORCED j 
 I CONCRETE. I 
 
 Main Office: BENNETT BUILDING, NEW YORK. 
 
 BRANCHES: 
 
 CHICAGO, PHILADELPHIA, BOSTON, ATLANTA, CLEVELAND, 
 
 ST. LOUIS, DETROIT, PITTSBURG, KANSAS. 
 
 Catalogue on application. 
 
 4 
 

 1 
 
 ■ 
 
 
 1 
 
LIDGERWOOD 
 
 HOISTING ENGINES 
 
 STEAM AND ELECTRIC 
 
 MORE THAN 300 STYLES AND SIZES 
 TO SUIT ALL CONDITIONS 
 
 ALL BUILT ON THE 
 DUPLICATE PART 
 
 SYSTEM 
 
 OVER 
 
 32,000 
 
 STEAM AND ELEC- 
 TRIC HOiSTS 
 IN USE 
 
 Send for Catalogs 
 
 We Design and Manufacture 
 
 DRYERS 
 
 STANDARD AND SPECIAL 
 
 FOR ALL KINDS OF 
 
 MINERALS, GRAINS, Etc. 
 
 USING 
 
 DIRECT HEAT, INDIRECT HEAT, OR STEAM HEAT 
 
 RUGGLES-COLES ENGINEERING CO. 
 
 NEW YORK— CHICAGO 
 6 
 
AIR POWER 
 MACHINERY 
 
 For Forty Years the World's Standard 
 of Economy 
 
 AIR AND GAS COMPRESSORS 
 
 ROCK DRILLS 
 
 HAMMER DRILLS 
 
 ELECTRIC-AIR DRILLS 
 
 PLUG DRILLS 
 
 COAL MINING MACHINES 
 
 STONE CHANNELERS 
 
 ELECTRIC-AIR CHANNELERS 
 
 PNEUMATIC PUMPS 
 
 PNEUMATIC TOOLS 
 
 CORE DRILLS 
 
 Descriptive Literature Sent on Request 
 
 INGERSOLL=RAND 
 COMPANY 
 
 NEW YORK LONDON 
 
 OFFICES IN ALL PRINCIPAL CITIES OF THE WORLD 
 
New York Belting and Packing Co. 
 
 LIMITED 
 
 91 AND 93 CHAMBERS STREET, N. Y. 
 
 for more than sixty years manufacturers of high- 
 grade mechanical rubber goods, including 
 
 " 1846 " PARA BELTING 
 
 AIR BRAKE, FIRE, GARDEN, STEAM, AND WATER 
 HOSE, ETC. 
 
 COBB'S PISTON ROD PACKING 
 INDESTRUCTIBLE WHITE SHEET PACKING, ETC. 
 
 ORIGINAL MANUFACTURERS OF 
 
 INTERLOCKING RUBBER TILING 
 
 Moulded Rubber Goods of Every Description 
 
 THE JONES STOKER 
 
 The ONLY system of mechanical stoking 
 in which, the fuel supply and the air supply 
 are automatically proportioned to each other 
 and to varying loads by the steam pressure. 
 THE ADVANTAGES OF SUCH AUTOMATIC 
 REGULATION ARE OBVIOUS. 
 
 THE 
 
 Under=Feed Stoker Co. of America 
 
 MARQUETTE BUILDING, CHICAGO 
 
Morse Twist Drill & Machine Co, 
 
 New Bedford, Mass., U. S. A. 
 
 MAKERS OF MORSE 
 
 Arbors 
 Center Keys 
 
 Chucks 
 
 Counterbores 
 
 Countersinks 
 
 Cutters 
 
 Dies 
 
 Drills 
 
 Gauges 
 
 Lathe Centers 
 
 Machines 
 
 Mandrels 
 
 Metal Slitting Saws 
 
 Mills 
 
 Reamers 
 
 Screw Plates 
 
 Sleeves 
 
 Sockets 
 
 Taps 
 
 Taper Pins 
 
 Threading Tool 
 
 Wrenches 
 
 THE NORWALK AIR COMPRESSOR 
 
 OF STANDARD PATTERN 
 
 ^ is built with Tandem 
 Compound Air Cylind- 
 ers. Corliss Air valves 
 
 on the intake cylinders 
 insure small clearance 
 spaces. The Intercooler 
 between the cylinders 
 saves power by remov- 
 ing the heat of compres- 
 sion before the work is 
 done, not after, and 
 the compressing is all 
 done by a straight pull 
 and push on a continu- 
 ous piston rod. The 
 Compressor is self-con- 
 tained ; the repair bills 
 
 are reduced to a minimum, and the machine is economical and efficient. 
 
 Special machines for high pressures and for liquefying gases. Compound aad 
 
 Triple Steam Ends. 
 
 4 catalog, explaining its many points of superiority, is sent free to 
 business men and engineers who apply to 
 
 THE NORWALK IRON WORKS CO., 
 
 SOUTH NORWALK, CONN. 
 
 9 
 
ESTABLISHED 1857 
 
 L LESGHEN & SONS ROPE GO. 
 
 920-932 NORTH FIRST STREET, ST, LOUIS, MO. 
 
 WIRE ROPE AERIAL WIRE ROPE 
 
 for . TRAMWAYS. 
 
 MIMES, QUARRIES, single and double 
 
 ELEVATORS, ETC. ROPE SYSTEMS. 
 
 BRANCH OFFICES: 
 
 NEW YORK 
 
 10 
 
WM. SELLERS & CO. 
 
 (INCORPORATED) 
 
 PHILADELPHIA, PA. 
 
 LABOR-SAVING MACHINE TOOLS 
 
 Tool Grinders, Drill Grinders 
 
 TRAVELING CRANES, JIB CRANES, SHAFTS 
 
 PULLEYS, HANGERS, COUPLINGS, Etc. 
 For Power Transmission 
 
 HYDRAULIC TESTING MACHINES 
 
 Sellers-Emery System 
 
 IMPROVED INJECTORS FOR BOILERS 
 TURNTABLES FOR LOCOMOTIVES AND CARS 
 
 GEO.V.CRESSONCU, 
 
 Moan Office amd Works, 
 
 Allegheny Ave. west of Seventeenth St., Philadelphia, Pa. 
 
 New York Office: 90 West St. 
 
 Engineers, Founders, and MachinlstSc 
 
 Manufacturers of 
 
 POWER TRANSMITTING MACHINERY, 
 
 CRUSHING ROLLS and JAW CRUSHERS, 
 
 Builders of 
 
 SPECIAL MACHINERY TO ORDER. 
 
 11 
 
Pittsburgh Manufacturing Company 
 
 ENGINEERS— FO UNDERS— MACHINISTS 
 PITTSBURGH, PA. 
 
 MANUFACTURERS 
 
 BOILER AND STRUCTURAL RIVETS 
 
 TIE RODS AND FOUNDATION BOLTS 
 BRIDGE PINS AND FORGINGS COLUMN BASES 
 
 FIRE HYDRANTS AND GATE VALVES SLUICE GATES 
 
 DOMESTIC WATER-SUPPLY 
 
 " REECO " RIDER HOT-AIR 
 PUMPING ENGINES 
 
 " REECO " ERICSSON HOT-AIR 
 PUMPING ENGINES 
 
 "REECO" ELECTRIC PUMPS 
 
 New catalogue on application to nearest 
 store 
 
 RIDER-ERICSSON ENGINE CO. 
 
 35 Warren St., New York 239 & 241 Franklin St., Boston 
 17 W. Kinsie St., Chicago 40 North 7th St., Philadelfhia 
 
 Engine and Turret LATHES 
 
 with 
 
 PATENT OR CONE PULLEY HEADSTOCK 
 
 Sizes 14" to 48" swing 
 
 The Lodge and Shipley Machine Tool Co. 
 
 CINCINNATI, OHIO, U. S. A. 
 12 
 
AMERICAN PIPE AND 
 CONSTRUCTION CO. 
 
 ENGINEERS AND CONTRACTORS 
 
 MANUFACTURERS OF 
 
 PHIPP ? S HYDRAULIC PIPE 
 
 112 NORTH BROAD STREET 
 PHILADELPHIA 
 
 CHAPMAN VALVE MFG. CO., 
 
 WORKS AND MAIN OFFICE: 
 
 INDIAN ORCHARD, MASS. 
 
 BRANCH OFFICES: 
 
 BOSTON, NEW YORK, PHILADELPHIA, BALTIMORE, 
 ALLENTOWN, PA.; CHICAGO, ST. LOUIS, SAN FRAN- 
 CISCO, LONDON, ENGLAND; PARIS, FRANCE; AND 
 JOHANNESBURG, SOUTH AFRICA. 
 
 VALVES 
 
 MADE IN ALL SIZES AND 
 FOR ALL PURPOSES AND 
 PRESSURES. 
 
 CORRESPONDENCE SOLICITED* 
 
 13 
 
TO BIN BRONZE 
 
 Trade Mark, "Registered in U. S. Patent Office " 
 
 MOTOR BOAT SHAFTING ?SS?t. t SSi?te?tSj 
 
 NON-CORROSI VE IN SEA WA TER. Can be forged at Cherry Red Heat. 
 Tensile Strength equal to tliat of machinery steel 
 
 Round, Square and Hexagon Rods for Studs, Bolts, Nuts, etc Rolled 
 Sheets and Plates for Pump Linings, Condensers, Rudders, Center 
 Boards, etc. Hull Plates for Yachts and Launches, Powder Press 
 Plates, Boiler and Condenser Tubes. Pump Piston Rods. 
 
 For tensile, torsional and cruising tests see descriptive pamphlet, 
 furnished on application. 
 THE ANSONIA BRASS AND COPPER CO., 99 John Street, New York, Sole Manufacturers 
 
 Randolph-Clowes Co 
 
 Waterbury, Conn. 
 Brass and Copper Rolling Mills 
 
 AND 
 
 Tube Works. 
 
 SEAMLESS BRASS and COPPER 
 
 TUBES and SHELLS 
 
 Up to 36 Inches Diameter. 
 
BOSTON BELTING- CO. 
 
 MAKERS OF HIGH GRADE 
 
 RUBBER BELTING 
 
 for power transmission and conveying 
 materials 
 
 HOSE 
 
 for water, steam, gas, air, suction, fire 
 protection, etc. 
 
 PACKINGS 
 
 in great variety for rods, flanges and 
 joints 
 
 GASKETS, VALVES, RUBBER-COVERED ROLLERS 
 and MECHANICAL RUBBER GOODS 
 
 that are 
 
 Superior in quality 
 atisfactory in service 
 
 Boston New York 
 
 256-260 Devonshire St. 100-102 Reade St. 
 
 Buffalo 
 90 Pearl St. 
 
 AMERICAN-BALL DUPLEX 
 COMPOUND ENGINE 
 
 AND 
 
 DIRECT-CONNECTED 
 GENERATOR. 
 
 The latest develop- 
 ment in practical 
 steam-engineering. 
 
 The highest econ- 
 omy of steam with 
 the simplest possi- 
 ble construction. 
 
 Complete electric and steam equipments fur" 
 nished of our own manufacture. 
 
 AMERICAN ENGINE CO., 
 ^ew York GfSee-95 Liberty St. Bound Brook, H. J. 
 
PORTLAND 
 
 ILAO CEMENT 
 
 The U. S. government bought 4,500,000 barrels of 
 '"Atlas " for use in the construction of the Panama Canal. 
 
 The ATLAS Portland CEMENT Co. 
 
 30 BROAD STREET, NEW YORK 
 
 Daily productive capacity over 50,000 barrels — the largest in the 
 world 
 
 ESTABLISHED 1856. 
 
 HENRY MAURER & SON, 
 
 MANUFACTURERS OF 
 
 FIBE BRISK T T1LES. SLABS, GOPOLfl LI9IIH&S, 
 
 Of All Shapes and Sizes. 
 
 Office, 420 East 23d Street, 
 
 Works, Maurer, N. J. NFW YflRl^ 
 
 P. O., Telegraph, and R. R. Statiea.) IN d VV I V-/r\r\. 
 
 16 
 
fCTIlff 7T 1 
 
 / V 7" 
 
 i XI- y^ 7 - 
 
 7X7X 
 
 REINFORCED CONCRETE 
 CONSTRUCTION 
 
 using a special corrugated iron ; attached to buildings in 
 
 the ordinary way and plastered with Portland cement, 
 
 making a light, strong, fire-proof construction for roofs, 
 
 walls, floors, etc. 
 
 THE BROWN HOISTING MACHINERY CO., 
 
 Engineers, Designers, and Builders of 
 Hoisting Machinery of Every Description, 
 
 Main Office and Works, CLEVELAND, OHIO. 
 
 Branch Offices, NEW YORK and PITTSBURG 
 17 
 
BOOKS ON GAS TESTING, GAS ANALYSIS 
 AND THE GAS ENGINE 
 
 CLERK. THE GAS, PETROL, AND OIL ENGINE. 
 
 Vol. I. General Principles of the Internal-combustion Engine, 
 together with Historical Sketch. New Edition, Revised and 
 Enlarged. 8vo, vi + 390 pages, 126 figures. Cloth, $4.00 nee. 
 
 GILL. GAS AND FUEL ANALYSIS FOR ENGINEERS. 
 
 A Compend for Those Interested in the Economical Application 
 of Fuel. Fifth Edition, Revised. 12mo, vi+117 pages, 20 
 figures. Cloth, $1.25. 
 
 HUTTON. THE GAS-ENGINE. 
 
 Third Edition, Revised. 8vo, xx+562 pages, 241 figures. 
 Cloth, $5.00. 
 
 JONES. THE GAS-ENGINE. 
 
 8vo, ix + 447 pages, 142 figures. Cloth, $4.00. 
 
 LEVIN. THE MODERN GAS-ENGINE AND THE GAS 
 PRODUCER. 
 
 Svo, xviii + 485 pages, 181 figures. Cloth, $4.00 net. 
 
 MacFARLAND. STANDARD REDUCTION FACTORS 
 FOR GASES. 
 
 A Number of Tables Necessary for the Reduction of the 
 Volume of Any Gas at Any Temperature, Pressure, and Degree 
 of Saturation to its Equivalent Volume under Standard Con- 
 ditions. Together with a Table for the Numerical Solution of 
 Certain Exponential Equations. Svo, xi + 54 pages. Cloth, 
 $1.50. 
 
 MEHRTENS. GAS-ENGINE THEORY AND DESIGN. 
 
 Large 12mo, v + 256 pages, 241 figures. Cloth, $2.50. 
 
 STONE. PRACTICAL TESTING OF GAS AND GAS 
 
 METERS. 
 Svo, x + 337 pages, 51 figures. Cloth, $3.50. 
 
 JOHN WILEY & SONS 
 43 and 45 East 19th Street, New York City 
 
 London, CHAPMAN & HALL, Ltd. Montreal, Can., RENOUF PUB. CO. 
 
 18 
 
Robert W. Hunt, Jno. J. Cone, Jas. C. Hallsted, D. W. McNaugher 
 
 ROBERT W. HUNT & CO., ENGINEERS 
 
 Bureau of Inspection, Tests and Consultation 
 
 NEW YORK, CHICAGO, PITTSBURG, ST. LOUIS, 
 
 90 West St. 1121 The Rookery. Monongahela Bank Bldg. Syndicate Trust Bldg. 
 
 LONDON, SAN FRANCISCO, MONTREAL, MEXICO CITY, 
 
 Cannon St., Norfolk House. 425 Washington St. Canadian Ex. Bldg. 20 San Francisco Bldg. 
 
 CONSULTING, DESIGNING AND SUPERVISING 
 ENGINEERS ON ALL ENGINEERING MATTERS 
 
 Inspection of All Materials of Construction at Points 
 of Manufacture 
 
 RESIDENT INSPECTORS IN ALL INDUSTRIAL CENTERS 
 
 Chemical and Physical Laboratories 
 
 REPORTS ON PROPERTIES AND PROCESSES 
 
 FOR 
 
 TRAIN SHEDS, FERRY HOUSES, PIERS, POWER HOUSES, MOTOR 
 FACTORIES, MACHINE SHOPS, GAS PLANTS AND SIMILAR BUILD- 
 INGS SUBJECT TO EXCEPTIONAL STRAIN AND EXPOSED TO EX- 
 TRAORDINARY STRESSES DUE TO OCCUPANCY AND ENVIRONMENT 
 USE 
 
 SOLIDWIREGLASS 
 
 MADE BY THE CONTINUOUS PROCESS, TO IMMEDIATE AND PERMA- 
 NENT ADVANTAGE 
 
 IT POSSESSES GREATER STRENGTH THAN ANY OTHER MAKE AND 
 WHEN PROPERLY GLAZED, STANDS AGAINST FIRE AND 
 WEATHER. 
 
 ^M MM Pennsylvania Building 
 
 YI f\/ A MIiA Philadelphia 
 
 qI im vr\ii|ir\ 
 
 I RE ML kSSWQ 100 Broadway, New York 
 19 
 
KEUFFEL & ESSER CO. 
 
 127 FULTON ST., N. Y. General Offices and Factories, HOBOKEN, N. J. 
 CHICAGO ST. LOUIS — SAN FRANCISCO — MONTREAL 
 
 DRAWING MATERIALS. MATHEMATICAL AND SURVEYING 
 iNSTRUMENTS. MEASURING TAPES 
 
 Our Paragon Drawing Instruments enjoy 
 an excellent and wide leputation. They are 
 of the most precise workmanship, the finest 
 finish, the most practical design, z/nd are made 
 in the greatest variety. We also h ave Key , 
 Excelsior and other brands of instruments. 
 
 We carry the largest and most complete 
 assortment of Drawing Papers, Tracing Cloths 
 and Papers, Blueprint, Blackprintand Brown- 
 print Papers, Profile Papers. 
 
 K & E Measuring Tapes, Steel, Metallic. Linen. 
 Most accurate. Best quality. Largest assortment. 
 We make the greatest variety of engine-divided 
 Slide Rules, and call especial attention to our Patented 
 Adjustment, which insures permanent, smooth work- 
 ing of the slide. Some of our other well-known cal- 
 culating instruments are the Reckoning Machine, 
 Fuller's Slide Rule,Thacher's Calculating Instrument, 
 Sperry's Pocket Calculator, etc. 
 
 Our complete 
 
 (550 page) catalogue 
 
 on request