The NAm(ONSTRUCTOR GSIMPSON, M-I-N-A I THE Naval Constructor: A Vade Mecum OP SHIP DESIGN FOR STUDENTS, NAVAL ARCHI- TECTS, SHIPBUILDERS AND OWNERS, MARINE SUPERINTENDENTS, ENGI- NEERS AND DRAUGHTSMEN. GEORGE SIMPSON, Member op the Institution op Naval Architects, Assoc. Member American Society of Naval. Engineers. Third Edition, Revised and Enlarged, NEW YORK. D. VAN NOSTRAND COMPANY. LONDON. KEGAN PAUL, TRENCH, TRUBNER, & CO., LTD. h Broadway House, 68-74 Carter Lane, E.C. 1914. A^ Copyright, 1904, BV D. VAN NOSTRAND COMPANY. Copyright, 1914, BY D. VAN NOSTRAND COMPANY. Stanbopc press r. H. QILSON COMPANY BOSTON. U.S. A, PREFACE TO FIRST EDITION. This handbook has been prepared with the object of supplying a ready reference for those engaged in the design, construction, or maintenance of ships, — such a work as should give simply and concisely, information on most of the points usually dealt with in the theory and practice of marine architecture, and in addition much that is new and original. Under the latter head- ing should be included the chapter on Design and many of the tables of standardized fitting details, etc. The Freeboard tables have been explained and their application simplified by working out examples embrac- ing the various types to which freeboards are assigned, including the modern shelter decker, for which rules have recently been issued. While it would have been possible to enlarge greatly on what the author has attempted, it has been deemed prudent at present to restrict somewhat the scope of the book, although at that, it will be found much more comprehensive in its character than existing works on naval architecture. It has been the author's aim to eliminate all obsolete matter and antiquated data, and to bring the book right in line with present day requirements. How nearly he has come to this ideal will be shown by the reception accorded by the profession. His thanks are especially due to Ernest H. Eigg, A. M. I. N. A., for valuable assistance in the prepara- tion of the chapter on Freeboard, to Jas. A. Thomson, M. I. N". A., for aid in the reading of proofs, and to the publishers for their hearty co-operation. GEORGE SIMPSON. 647 Richmond Terrace, Mariner Harbor, New York City, May, 1904. 3431'53 PREFACE TO THIRD EDITION. The preceding editions of this handbook were received so favorably that it was decided to enlarge the third edition by the addition of further "unified" details such as made the earlier editions noteworthy. There has also been included much new matter dealing with ventilation and other subjects, while other portions of the book have been revised and brought up-to-date. It is hoped that in its enlarged form " The Naval Constructor " will continue to occupy its present position as a daily book of reference for those engaged in the design, construction and maintenance of ships. GEORGE SIMPSON. 17 Battery Place, New York City, 1st Mat, 1914. CONTENTS. Section I. — Ship Calculations. Symbols — Algebraical Signs — Displacement — Simpson's First Rule — Multipliers for Subdivided Intervals — Proof of Simp- son's Rule — Displacement Sections! — Bottom Half -breadth — Dis- placement Table — Area of Water Plane — Tons per Inch Immersion — Coefficient — Immersion Passing from Salt to Fresh Water — Area of Midship Section — Coefficient £ — Prismatic Coefficient — Centre of Buoyancy — Approximate Rule for Cen- tre of Buoyancy — Centre of Buoyancy Longitudinally — Trans- verse Metacentre — B. M. — Moment of Inertia of Water Plane — Longitudinal Metacentre — Centre of Flotation — Approximate Rule for L.B.M. — Moment to Change Trim — Change of Trim — Moment to Alter Trim One Inch — Approximate Rule for M. — Alteration in Trim through shipping a small weight — Tchiby- scheff's Sections for " Lucania ' ' — Displacement Sheet by Tchiby- scheff's Rule — Centre of Buoyancy by Tchibyscheff's Rule — L.M.C. and Centre of Flotation by Tchibyscheff's Rule — Trans- verse Metacentres by Tchibyscheff's Rule — Effect of Form of Water Line on Position of Longitudinal Metacentre — Effect of Form of Water Line on Position of Transverse Metacentres — Ex- planation of Tables on Position of Metacentres — Stability Calcu- lation by Tchibyscheff's Rule — Tchibyscheff's Sections for Sta- bility Levers — Calculation of G.Z. by Tchibyscheff's Rule — Cross Curves of Stability — Stability Curves — Design — Block Coefficient — Relation Coefficient e — Mid Area Coefficient fi — Prismatic Coefficient — Area of L.W.L. Coefficient a — Inertia Coefficient "i" — Centre of Gravity Coefficient "g" — Bilge Diagonal Coefficient — Element Coefficient — Relation of the Co- efficients to one another — Element Coefficients for various Types — Coefficients for Centre of Gravity — Moment of Inertia of Waterline Coefficient — Sheer — Contour of Stern — Figureheads and Lacing Pieces — Rail Half-breadths — Load Line Half-breadths — Diagram of Bilge Diagonals — Diagram of L.W.L. Half-breadths — Body Plan of "Oceanic" — Designing the Bossing — Fairing the Bossing — Fairing the Oxter — Elements of Marine Engines — Engine Room Lengths — The Preparation of Specifications — Specification Headings — Freeboard — Length — Breadth — vi Contents Depth of Hold — Coefficient of Fineness — Moulded Depth — Freeboard — Vessels oi Extreme Proportions — Breadth and Depth x — Erections on Deck — Sheer — Round of Beam — Explanatory Notes on Application of Freeboard Tables — Additional Freeboard for Winter North Atlantic for Well-deck Vessels — Rules for Depth of Loading of Turret-deck Vessels — Rules for Shelter- deck Vessels — Load Draught Diagrams — Types of Vessels — Freeboard Marks — Freeboard Tables — Freeboards for Freight- ers — Freeboards for Spar Deckers — Freeboards for Awning Deckers — Sailing Vessels — Kirk's Analysis — Analysis Data — Wetted Surface Formula — Launching — Launching Periods — Launching Curves — Camber of Ways — Declivity of Ways — Pressure on Dog Shoes — Length of Ways — Tables of Launch- ing Data — Calculation of Hull Weights — Ditto by Johnson's Method — Johnson's Curves — Complete Tables of Weights of Steel Shapes — The Transport of Cattle — Arrangement of Stalls and Pens - 1 — Dimensions of Stalls and Pens — Board of Agriculture Regulations — Detailed Weights of Cattle Fittings — Rudder Formulae — Spectacle Frames — Proportions of Spectacle Frames — Propeller Struts — Simpson's Formula for Propeller Struts — Proportions of Brackets — Centre of Gravity by Experiment — Centre of Gravity by Calculation — Strength of Ships — Hogging — Sagging — Curve of Weights — Curve of Buoyancy — Curve of Loads — Curve of Shearing Stresses — Curve of Bending Moments — Specimen Calculations for Mo- ments of Inertia — Diagram of Strength Curves — Resistance of Ships — The Admiralty Constant — Table of Constants for various Types — Froude's Investigations — Law of Comparison — Application of Froude's Law — Speed and Power Curve — Standard Curves of Power — I.H.P. by Independent Method — Skin Resistance — Residuary Resistance Power — Form of Least Resistance — Middendorf's Method — Table of Angles of Entrance and Run — Table of Steamers' Data. Section II. — Strength of Materials. Strength of Materials — Ultimate Strength — Working Load — Proof Strength — Stress aud Strain — Tensile Stress — Compres- sive Stress — -Shearing Stress — Bending Stress — Torsional Stress — Resilience — Elasticity — Modulus of Elasticity — Permanent Set — Moment of Inertia — Neutral Surface — Section Modulus — Moment of Resistance — Radius of Gyration — Various Stresses and their Factors — Elements of Sections — Beam Bending Moments — Elements of Circular Sections — Moment of Inertia of Circular Sections — Strength of Columns — Johnson's Formula for Columns — Least Radius of Gyration for various Sections Contents vii — Values for Johnson's Formula — Pipe Pillars — Standard Pipe Elements — Steel Columns — Strength of Metals and Alloys — Physical Properties of Timber — Strength of Timber — Weight and Strength of Wire Rope — Notes on the Use of Wire Rope — Strength of Chain Cables — Proof Load for Chains — Strength of Guard Chains — Weight of Chain Cables — Breaking Strength of Chains — Elements of Angles — Elements of Bulb Angles — Elements of Deck Beams — Elements of Tees — Elements of Z bars — Tees as Struts — Bending Moments of Pins — Strength of Special Shackles — Riveting U. S. Navy — Standard Rivets — Lloyd's Riveting Table — Tables of Strength of Riveting — Ordered Lengths of Rivets — Shearing and Bearing Tables of Rivets. Section III. — Fittings and Details. Structural Details — Keels — Bar Keel — Keel Scarphs — Tack Rivets in Keels — Universal Bar — Flat Plate Keels — Centre Keelson — Keel Doublings — Stems — Stern Frames — Braces — Gudgeons — Pintles — Riveting of Boss — Rudder Post — Body Post — Rudders — Single Plate Rudder — Norman Head — Rud- der Arms — Coupling Palm — Coupling Bolts — Rudder Stock — Cast Steel Rudder — Balanced Rudders — Heel Bearing — Emer- gency Chains — Types of Rudder Carriers — Rudder Trunks — Tail Plates — Propeller Struts — Area of Propeller Brackets — Boss Barrel — Spectacle Frames — Bossing around Shafts — Tube-end Castings — Framing — Resistance of Frames — Cut Frames — Pressed Plate Chocks — Stapled Collars — Frame Doub- lings — Spirketting Plate — Framing of Superstructure — Reverse Frames — Floors — Stresses on Floors — Flanged Floors — Chan- nel Floors — Water-tight Floors — Floor Brackets — End Floors — Inner Bottoms — Water-tight Compartments — Centre Vertical Girder — Side Girders — Margin Plate — Ceiling on Tanks — Bitumastic Cement — Manholes — Tank" Bleeders — Beams — Beam Camber — Welded Beam Knees — Bracket Knees — Stand- ard Beam Knees — Strong Beams — Carlings — Deck Girders — Beam Collars — Hold Pillars — Built Columns — Pipe Pillars — Standard Solid Heads and Heels — Fitting of Pillars — Heels on Inner Bottoms — Staggered Pillars — Hatches — Size of Hatches — Hatch Corner Doublings — Corner Angles — Hatch Fore and Afters — Bridle Beams — Standard Hatch Cleats — Battening Bar — Hatch Wedges — Hatch Ledges — Hatch Lashing Rings — Hatch Covers — Lifting Rings — Web Frames — Keelsons — In- tercostal Plates — Side Stringers — Bulkhead Collars — Longitudi- nals — Ending of Keelsons — Bulkheads — Collision Bulkheads — Bulkhead Liners — Bottom Plaiting Bhd. — Stiffeners — Stresses viii Contents on Bulkheads — Deep Framing — Caulking — Chafing Pieces — Shell Plating — Arrangement of Strakes — Plate Lines — Fairing the Lines on Model — Shift of Butts — Furnaced Plates — Land- ings — Butts of Plating — Garboard Strake — Sheerstrake — Shell Riveting — Stealers — Jogging — Scarphs of Overlaps — Liners at Overlaps — Scarphing of Landing Edges on Stem and Stern Post — Holes through Shell — Doubling Plates — Hood End Plates — Doublings at Breaks — Pitting Details — The Preparation of De- tails — Standardizing Details — Bill of Material — Standard Hatch- ing — Graphic Division of One Inch — Baldt Anchors — Ingle- field Anchors — Hall Anchors — Admiral Anchors — Anchor Cranes — Formulas for Bevel and Mitre Gear Blanks — Naval Anchor Crane — Stress on Auchor Cranes — Dimensions of An- chor Cranes — Ship's Bells — Weight of Bells — Belay Pins — Balanced Armor Hatch — Standard Bollards — Weights of Bol- lards — Wire Rope Snatch Blocks — Diamond Rope Blocks — 25- Ton Block — Standard Iron Blocks — U.S. Standard Bolts and Nuts — Chain Plates — Cast Steel Cleats — Catting Hooks — Crane Hooks — Navy Boat Crane — Boat-handling Arrangement — Rotating Davit — Mallory Davit — Swan-neck Davit — Mine Davit — Board of Trade Rules for Round Davits — Davit Heads — Weights of Boats and Davit Diameters — Standard Hinged W. T. Doors — Standard Sliding W. T. Doors — Details of W. T. Doors — Standard Eyebolts — Standard Fairleads — Weight of Fair- leads — Flanges for Lead Pipes — Standard Pipe Flanges — Stand- ard Flanges for Ventilation — Standard Hand Wheels (Iron) — Standard Hand Wheels (Brass) — Hawse Pipe Proportions — Weights of Hawse Pipes — Hooks — Cargo Hooks — Swivel Hooks — Trip Hooks — Keys and Key ways — Reversible Pad Eye — Lewis Bolt — Accommodation Ladders — Lashing Triangles — Mooring Pipes — Strength of W. I. Pipes — Plug Cock Keys — Standard Pad Eyes — Strength of Rings — Proportions of Rings — Ordered Lengths of Rivets — Diagrams for Rivets — Ring Plates — Dimensions of Wood Screws — Areas of Sea Anchors — Detail of Sea Anchor — Sisterhooks — Slip Shackles — Trade Shackles — Standard Shackles — Standard Worked Eyes — Towing Bitts — Steering Chain Springs — Screw Steering Gears — Deck Seats — Weights of sidelights — Proportions of Chain Slips — Boom Mount- ings — Spider Bands — Torpedo Net Details — Gaff Mountings — Stuffing Boxes and Glands — Thimbles for Wire Rope — Standard Toggle Pins — Admiralty Turnbuckles — Trolley Block — Uni- versal Joints — Low Pressure Valves — Heavy Pressure Valves — Friction Brake for Cranes — Ventilation — Chart for Ventilation Pipes — Terminals for Exhaust Pipes — Adjustable Terminals — Terminals with Dampers — Standard Sizes of Ventilators and Cowls — Weight of Cowls — Elswick Guns — Vickers Guns — Contents ix Schneider Guns — Krupp Guns — Bethlehem Guns — U. S. Naval Ordnance. Section IV— Rigging and Ropes. Standing Rigging — Table of Wire Rope — Splices — Thimbles — Sheaves — Turnbuckles — Running Rigging — Manila — Hemp — Coir — Blocks — Standard Blocks, U. S. N. — Cargo Blocks — Tackles — Power gained by Blocks — Whip — Double Whip — Gun tackle Purchase — Burton — Double Spanish Burton — Luff Tackle — Rigging Derricks. Section V. — Equipment. Anchors and Chains — Lloyd's Equipment — Lloyd's Table — Hawsers and Warps — Tables of Equipment — Weights — Moor- ing Swivel — Blake Stopper — Senhouse Slip — Admiralty Cables — Chain Cable Links — Club Shackle — Chain Swivel — Renter Shackle — Boats — Notes on Construction — Diagram of Propor- tions — Lifeboats^ — Cutters — Dinghies — Gigs — Barges — Galleys — Table of Scantlings for Rowboats — Sail Area — Drawing of Standard Lifeboat in Detail — Lifting Rings and Slings — Board of Trade Requirements — Supervising Inspector's Requirements — Sea Anchors — Axes, Buckets, etc. — Light Screens — Ton- nage — Various Tonnage Rules — Y. R. A. and N. Y. Y. C. Rules — Windlasses — Towing Machines, etc. Section VI. — Miscellaneous. Tables of Weights — Measures — Oil Fuel Data — Weights of Bolts and Nuts — Tank Capacities — Unit Equivalents — Squares, Cubes, and Fourth Powers of Fractions — Powers and Roots — Speed Tables — Foreign Weights and Measures — Stowages of Merchandise — Cold Storage Temperatures — Distances from Colon, Section VII. — Tables. Complete mathematical tables specially arranged. SYMBOLS COMMON IN NAVAL ARCHI- TECTURE USED IN THIS BOOK. A . S.A. C.E. b . . Bm Bx . Bw. 0. • B . C.B. . C.G. H . D . V . D + D- S- t . F Fr g A. P. F.P. X • Area of load water plane. Sail area in square feet. Centre of effort of sail plan. Distance of centre of effort forward of centre of im- mersed lateral plane. ^4 Coefficient of fineness of load water line = Bilge diagonal coefficient. Moulded breadth of ship. Extreme breadth of ship. Water-line breadth of ship. Coefficient of midship section area : LxB XA Bxd . Centre of gravity of displacement (centre of buoyancy). . Centre of gravity of displacement from aft perpen- dicular. . Centre of gravity of ship above base. . Centre of gravity of ship and engines. . Moulded depth to upper deck. . Displacement in tons of salt water (gross). . Displacement in cubic feet (volume). . Displacement in tons at load draught. . Displacement in tons at light. . Displacement of fore body. . Displacement of after body. . Coefficient of fineness of displacement (block coefficient). . Relation coefficient. . Freeboard from statutory deck line. . Freeboard to top of rail amidship. G II Coefficient of centre of gravity = After perpendicular (after side of rudder post). Forward perpendicular (fore side of stem at upper deck). Indicates the half-length between perpendiculars and is the sign of the mid-section or "dead flat." xi The Naval Constructor X-4 . . • Mid-section area. M. C. . . Height of transverse metacentre above base. G.Z. . . . Stability lever. G.M. . . Height of transverse metacentre above centre of gravity. B.M. . . Height of transverse metacentre above centre of buoy- ancy. L.M.C. . Longitudinal metacentre above base. *cT . . . . Centre of gravity below L.W.L. G . . . . Centre of gravity above L.W.L. p . . . . Prismatic coefficient. I.H.P. . Indicated horse power. E.H.P. . Effective horse power. N.P. . . Nominal horse power. B.P. . . . Length of ship between perpendiculars. W.L. . . Length of ship on load water line. wl . . . . Water line. O.A. . . . Length of ship over all. R . . . . Placed before dimensions indicates that these are the registered or tonnage dimensions. I Moment of inertia of load water plane. M . . . . Metacentre and moment. M " ... Moment to alter trim one inch at load line. .... On drawings locates the intersection of projected water line with the elevation. O . . . . Centre of gravity, or moment about centre, (w) ... Centre of gravity of water line. . Centre of gravity of mid-section area. . Centre of gravity of sail plan, or centre of effort. . Ordinates or stations. x Common interval or abscissa between ordinates. W.S. . . Area of wetted surface. « JB .... Eesistance. \ G, or U, Half-girth of midship section (Lloyd's). d -*rd ■e-. P . V . Draught of water moulded (mean). Draught of water forward ^ Draught of water aft > to bottom of keel. Mean draught ; Power. Speed in knots per hour. . i , D§ x T8 Admiralty constant = — l.M.Jr. Per. xii Symbols Common in Naval Architecture t 3fl" . . . Per inch ; also tons per inch of immersion at L.W.L. □ ' . . . . Square foot. □ ". . . . Square inch. f Cubic foot. Algebraical Signs. -(- Plus, addition. Positive. ^ Semicircle. Compression. — Minus, subtraction. Nega- CD Quadrant. tive. Tension. tst Equal to. co Infinity. 4= Unequal to. Pi Arc. > Greater than. ~ Difference. ^j> Not greater than. [] H Vincula - < Less than. c Constant. 4 intei'val between water lines. These divisions of water lines must be drawn across the body plan of ten sections, and the half breadths read off with a scale and tabulated as in table on following page. rV\ ' >A\ I \\S — | \\V tA -. \T~- 4-V i T" v „ — u L.W.L. ZSZ. Fig. 4. It should be stated in connection with the subdivision of the base line that the length taken for displacement is measured by some designers from the after side of body post i.e., ignoring the propeller aperture ; and by others from the fore side of body post to the after side of stem omitting the moulded size of these for- giugs. Both of these methods are inaccurate besides leading to confusion, as, in the first case, the displacement of the propeller with its boss will equal the displacement cut out for aperture not to mention the volume of the rudder, which is rarely, if ever, taken into account. And in the second case the tiny amount of displacement added at the knuckle formed by the bearding line of plating when the length is taken to forward and after sides of stem and stern post respectively, is compensated for by the gud- geons on stern post. Therefore the most correct and also the most convenient length is from after side of rudder post to for- ward side of stem at load water line. Where vessels have a very flat floor line a half water line should be taken be- tween base line and first water plane, and the keel or bottom half-breadth _ « ee | given a value proportioned to the rise of floor line as in Fig. 5. The Naval Constructor Required the half-breadth x at the keel for the displacement sheet, where 10 feet is the actual scaled length L, 6" the rise of floor, 7" the distance from the rise line to first water line at moulded half-breadth of ship and, of course, 13 inches the water line interval, then : — 13": 7":: 10 feet : x. .-. x = 5.38 feet = bottom breadth. Displacement Table. Water lines apart . 1.25' Load draught . . . . 5.00' Ordinates apart .... 10.00' Displacement length, 100.00' as « Keel. W.L. 1. W.L. 2. W.L. 3. W.L. 4. 8 < §3 to a. S GO co 3 co* M to' J CO BS ,1 3 ■a 1 " 3 J o .1 V 1 s a o 02» 3« I u 3« 1 P4 1 5 >-< 1 3* "5 o E £ | .04 .01 .04 .01 .04 .01 .04 .01 .04 .01 i l .03 03 .08 .08 .18 .18 .43 .43 1.41 1.41 1 3 .02 .01 .16 .12 .73 .55 1.78 1.33 3.10 2.32 2 2 .02 .04 .92 1.84 2.35 4.70 3.78 7.56 4.81 9.62 3 1 .02 02 2.13 2.13 4.03 4.03 5.16 5.16 5.50 5.56 4 2 .02 .04 3.20 6.40 4.98 9.96 5.67 11.34 6.96 11.92 5 1 .02 .02 3.54 3.54 5.20 5.20 5.80 5.80 6.00 6.00 6 2 .02 .04 3.00 6.00 4.66 9.32 5.34 10.68 5.58 11.16 7 1 .02 .02 2.00 2.00 3.58 3.58 4.42 4.42 4.87 4.87 8 2 .02 .04 1.25 2.50 2.28 4.56 3.04 6.08 3.57 7.14 9 f .02 .01 .48 .36 1.00 .75 1.50 1.12 1.90 1.42 n 1 .02 .02 .18 .18 .50 .50 .74 .74 .97 .97 10 \ • • • • • • .03 .01 .03 .01 15 15 Sum ,__ of .30 25.16 43.34 54.68 62.41 = 10 Prod- xl.5 Sum of Mul- tiple ucts. j 2(1) 1( t) 2(1 ) \ .15 + 50.32 + 43.34 + 109.36 + 31.20 = 234.37 (f W.L. interval) X (f ordinate interval) x 2 (both sides) _ 35 ( Cub> ft> of s w in a ton) " T ° _ (1.25xf)x(10xf)x2 35 = .315. Area of Water Plane 234.37 x.315 Displacement to W.L. 4 = 73.82 .15 + 50.32 + 43.34 + 54.68 =148.49 x.315 Displacement to W.L. 3_. =46.77 tons. .15 + 50.32 + <^2US> = 72.09 x.315 Displacement to W.L. 2 = 22.70 tons. .15 + 25.16 = 25.31 X.315 Displacement to W.L. 1 = 7.97 tons. The displacement to the load water line being 73.82 tons it is useful to know what relation that weight bears to the vessel if she were of box section, in other words, the amount that has been cut olff the rectangular block formed by the length, breadth, and draught, to fine it to the required form, or the block coefficient or coeffi- cient of displacement represented by the symbol "5". It will be evident that this coefficient may readily be computed by mul- tiplying the length X breadth X draught, and dividing the product, which is the volume of the box in cubic feet, by 35 to get the tons displaced by the rectangular block. The displacement as calcu- lated, divided by this result, will give the block coefficient " 5 ", or, £^5x3=. 432 nearly. The range of this coefficient for various types is given else- where in the Table of Element Coefficients. Area of Water Plane. Keel. W.L. 1. W.L. 2. W.L. 3. W.L. 4. Sum of products . f common interval, Half-areas . . . Areas of water planes . . . .30 25.16 <4 43.34 54.68 6f 62.41 2.00 2 167.73 2 288.93 2 364.53 2 416.07 2 4.00 335.46 577.86 729.06 832.14 The area of any of the water planes in the specimen displace- ment table will simply be the sum of the products of the particular The Naval Constructor water plane required, multiplied by $ the interval between ordinates. This product doubled will be the total area of both sides. Tons per Inch of Immersion (^jJ"). It is useful to know the amount of displacement of the vessel for each inch of immersion at various draughts, as from this data small amounts of cargo taken out or placed on board can be accurately determined without reference to, or scaling from, the regular displacement curve. It will be seen that if A represents the area of water plane, that this surface multiplied by a layer 1 inch in thickness and divided by 12 will equal the volume of water displaced in cubic feet at the particular water plane dealt with, and that this volume divided by 35 will equal the displace- ment in tons for one inch, or in other words, the tons per inch immersion. Or, ^ x To = To CUDic feet » and the weight of water in the layer A 1 A 420 = tons per inch. Tons per inch immersion in salt water, area of water plane • 420 ' Tons per inch immersion in fresh water, area of water plane > (12 X 36) = 432 So that referring to the table we have been working out, we get : — Keel. W.L. l. W.L. 2. W.L. 3. W.L. 4. Area of water plane 12" X 35 = . . . Tons per inch = 4.00 4*5o .01 335.46 4J0 .79 577.86 420 1.37 741.06 4J0 1.76 832.14 420 1.98S.W. It is often necessary to estimate the tons per inch approxi- mately, and for this purpose the coefficient of the load line or "a" is used. The method of arriving at this coefficient is ex- plained in the chapter on design when the displacement is known. Immersion, from Salt to Fresh Water 9 It has a range of about .6 iu fine vessels to .9 in exceptionally full ones. In the above example it is found to be 832.14 832.14 Length x Breadth ~ 1200 Therefore the tons per inch is equal to L x Bx .694 .694. = 1. 420 Its relation to the other element coefficients is 8 Immersion Passing from Salt to Fresh Water. From what has been previously said it will be obvious that the draught of water, or immersion of a vessel, will undergo a change in passing from fresh water into the sea or vice versa, owing to the difference in density of the two liquids. If we take the case of the ship passing from salt water to fresh, the immersed Volume will be in each case as follows : — Immersed volume in salt water = 35 J), Immersed volume in fresh water = 36 D, where D is the displacement in tons, which in the example we have been investigating equals 73.82 tons. Therefore the volume in cubic feet which the vessel has sunk on entering the fresh water is 36 D - 35 D = 2657 - 2584 = 73 cubic feet. Let T= tons per inch immersion in fresh water . • . area of water plane = 432 T and the extent to which the vessel will sink 73 . 4 12 x 73 73 , AO . , feet = in ^ m -. — ; — = ttx-^7 = 1.02 inches. 432 T 432 T inches 36 T Inversely we have the amount that the vessel emerges in passing out of a river into the ocean. Thickness of the layer which vessel has risen in feet _Difference in volume I) Area of the plane and in inches, Difference in Volume D x 12-_ 12 X 73 _ 73 _ _ . Area of water plane ~ 420 T ~ 69.3 — This immersion and emersion is, of course, the mean amount as the vessel will also slightly change her trim due to the altered position of the centre of gravity of water plane, about which the ship's movements are pivotal. 10 The Naval Constructor Area of Midship Section (X -4)- The area of this, or any of the other sections on the displace- ment table, is calculated by taking the half-breadths of the water lines and integrating them as explained for water-line area. The sum of the products thus obtained is multiplied by f the distance of water lines apart, and that result by 2 for both sides. Where the vessel has little rise of floor a half water line should be introduced, and the bottom half-breadth proportioned to the rise line, as pointed out in the displacement calculation. In the example with which we are dealing, however, the vessel has considerable rise, so that this subdivision has been omitted. Ordinate. Keel. W.L. 1. W.L. 2. W. L. 3. W.L. 4. "5" Half- Breadth. Half- Breadth. Half- Breadth. Half- Breadth. Half- Breadth. Simpson's Multipliers .02 i 3.54 2 5.20 1 5.80 2 6.00 1 .01 + 7.08 + 5.20 + 11.60 + 3.00 = 26.89 $ distance between water lines x .83 Half area of midship section to L. W.L. . . . =22.31 For both sides x2 Midship section area =44.62 The coefficient of this area, or /3, is a very important element of the design as explained elsewhere, and is obtained by dividing the midship area by the area of the rectangle formed by the molded breadth and the draught, or Mid. area Breadth x draught 44.62 60 = .743 coefficient of mid. area. Its relation to the midship-section cylinder or prismatic co- efficient "p" is -> and "p" is equal to the volume of dis- placement divided by the length x mid. area, thus : — P = and consequently, L x B x d x 5 L x B x dx p = prismatic coefficient, Centre of Buoyancy 11 Centre of Buoyancy (C.B.). The centre of buoyancy of the displaced water is simply its centre of gravity, and its location below the load-water line is greater or less in accordance with the form of the immersed body. This distance may be found by dividing the under-jvater part into a number of planes parallel to the load line, and multiplying the volumes, lying between these water planes, by their depth below load-water line. These moments divided by the displacement volume will give the location of centre of buoyancy below load- water plane. So that by taking the functions of the products at each water plane on the sheet we have been working and multi- plying them by the number of the water line they represent below L.W.L., and dividing the sum of those products by the sum of the functions referred to, we shall have the number of water-line intervals (or fraction of an interval), which the C.B. is below load-water line. This result, multiplied by the common interval between water lines, will give the required distance in feet. Keel. W.L.I. W.L. 2. W.L. 3. W.L. 4. Functions of products .15 -f 50.32 + 43.34 + 109.36 + 31.20 = 234.37 4 3 2 10 .60 4-150.96 + 86.68 + 109.36 + = 347.60 347.6 4-234.37 = 1.49 x Water lines apart = 1.25 Centre of buoyancy below W.L. 4 = 1.86 ft. The centre of buoyancy may be determined from the displace- ment curve by calculating the area enclosed within the figure formed by the vertical line representing the draught of 5 ft., the horizontal line equal to the tons displacement at this draught and the curve itself. This area divided by the length of the hori- zontal line referred to, will give the depth of C.B. below L.W.L. In the present example we have : area = 138.6 sq. feet, and length of horizontal line (displacement in tons) = 73.82, and 138.6 , «. -, ^ = 1-87 feet, distance of C.B. below L.W.L. A like result may also be obtained by taking the sum of the products of each water line, and dividing them by the sum of Simpson's multipliers. The mean half-breadths of water lines so obtained may be then used to draw a mean section of the 12 The Naval Constructor vessel on stout paper, which on being cut out with a knife and swung in two positions, the points being intersected afterwards, will give the centre of gravity (buoyancy) very accurately. Various approximate methods are in vogue for finding this centre, some of which are fairly accurate. — a )' (2) Approx. C.B. below L. W.L. = H| + Z Y where A is the area of load-water plane. This centre, as will be explained, has an important bearing on the stability of the ship. Centre of Buoyancy Longitudinally (L.C.B.). Ordin- ATES. Areas. Multi- pliers. Func- tions. Inter- vals. Moments. After Moment. .24 \ .06 5 .30 \ 1.91 1 1.91 *l 8.59 1 6.17 | 4.63 4 18.52 2 14.18 2 28:36 3 85.08 3 21.40 1 21.40 2 42.80 4 5 25.71 26.89 2 1 51.42 26.89 1 51.42 206.71 6 24.14 2 48.28 1 48.28 Forward 7 18.86 1 18.86 2 37.72 8 12.65 2 25.30 3 75.90 9 5.92 \ 4.44 4 17.76 n 2.83 1 2.83 H 12.74 10 .08 \ .02 5 .10 192.50 Preponder- "^ ating moment J-= 14.21 Function of disj )lacemen I . . = 234.40 abaft, Ordi- | nate 5. J 14.21 23474 Common Interval = 10 ft. x .06 = .00 Interval C.B. abaft 5. 0.6 ft. C.B. abaft No. 5. The locus of the centre of buoyancy in a fore-and-aft direction is of course the centre of gravity of the displacement, and is the Transverse Metacentre 13 pivotal point or fulcrum for the moments of all weights placed forward or aft of this position. It will be obvious, therefore, that its location is of great value in determining the trim of the vessel, and the various alterations thereof due to rearrangements of weights on board. Its position is calculated by taking the areas of the sections and putting them through the multipliers ; these functions of areas are in turn multiplied by the number of inter- vals, (each one is forward or aft of the inid-ordinate,) and the difference between these forward and after moments divided by the sum of the area functions. The quotient resulting is the number (or fraction) of intervals that the centre of buoyancy is forward or aft of the \ length according as the moment prepon- derates forward or aft respectively. This centre should be calculated for various draughts, as of course it changes with different draughts and alterations of trim, owing to the changing relationship between the fineness of fore and after bodies at different immersions and trims. Transverse Metacentre (M.C.) The position of this element is, in conjunction with the centre of gravity, the most vital in the design of the ship. As its name implies, it is the centre or point beyond which the centre of gravity of the ship may not be raised without producing unstable equilib- rium in the upright position, or, otherwise stated, if the ship be inclined transversely to a small angle of heel, the centre of buoyancy which originally was on the centre line will move out- board to a new position ; but, as it acts vertically upward, it must somewhere intersect the centre line. This point of intersection is known as the metacentre. One of the factors in the determination of its location above the centre of buoyancy has already been calculated, viz : the volume of displacement V ; the other, the moment of inertia of the water plane about the centre line of ship, we shall proceed to compute. The height M above the C.B. or B.M. is found by : — Moment of Inertia of Water Plane I _ Volume of Displacement ' ' V ~ The moment of inertia of the water plane is a geometrical measure of the resistance of that plane to "upsetting," or when taken about the centre line, as in the case of calculating for trans- verse metacentre, to "careening." So that the greater the water- line breadth the higher will be its value ; for we must imagine the water plane as being divided into a great number of small areas, and each of these multiplied by the square of its distance from the 14 The Naval Constructor centre line of ship, when the sum of these products will equal the moment of inertia of half the water plane, about the middle line of vessel as an axis. As both sides of the water plane are sym- metrical, the total i" will be this result multiplied by 2. Applying this principle to W.L. 4 in the example with which we are con- cerned, we get the following tabular arrangement : — Moment of Inertia of "Water Plane (I). Ordi- Half- Cubes op Simpson's Breadths Half- Mul- Products. of W.L. 4. Breadths. tipliers. .04 i \ 1.41 2.74 2.74 1 3.10 29.79 3 22.34 2 4.81 111.28 2 222.56 3 6.56 171.88 1 171.88 4 6.96 211.71 2 423.42 5 6.00 216.00 1 216.00 6 6.58 173.74 2 347.48 7 4.87 115.50 1 115.50 8 3.57 45.50 2 91.00 9 1.90 6.86 3 i 5.14 »i .97 . 10 .03 ¥ 1,618.06 f C.I (US 10,787.07 | Moment of Inertia = 7,191.38 Volume of Displacement, V = 2,583.70 _ _ _ I 7191.38 _ nn . t B - M - = F = ^583T = 2 - 77ft - The calculation for Moment of Inertia and Transverse Meta- centre above C.B. may be more easily remembered if we treat the cubes of water line half-breadths as the ordinates of a curve two- thirds the area of which will equal I, and this, in turn, divided by Twill give B.M. However, when we know a, or the coefficient of water line, we may arrive very accurately at the moment of inertia of the water Longitudinal Metacentre 15 plane, and consequently at the B.M. without the labor of the foregoing calculation by multiplying the Length by the Breadth 3 by a coefficient, which coefficient will be determined by a and selected from the table given on page 48. By referring to this table, we find for a (value .694) that the coefficient "i" (inertia coefficient) is equal to .0414, whence we get I = L x J3 3 X i — 100 X 12 3 x .0414=7154 moment of inertia, which is sufficiently close for all purposes, and : — By transposing and taking the calculated I, we find 7191 100 X 12 3 = .0416. Longitudinal Metacentre (L.M.C.) From the definition given for the transverse metacentre it will be seen that if the ship be inclined longitudinally, instead of, as in the former case, transversely, through a small angle that the point in which the vertical through the altered C.B. intersects the original one will also give a metacentre known as the longitudinal, or L.M.C. Its principal use and value are in the determination of the moment to alter trim and the pitching qualities of the vessel, or longitudinal stability. It will be obvious that the moment of inertia of the water plane must be taken through an axis at right angles to the previous case, viz., at right angles to the centre line through the centre of gravity of water plane, which will be where the original and new water planes cross one another in a longitu- dinal view. t ™ r, v ^ t> A of Water Plane about its C.G. L.M.C. above C.B. = ^rr-. -— — = • Volume of Displacement Therefore, to calculate the M Ji, we must figure the moment of inertia with, say, ordinate 5 (or any other one) as an axis when the moment about a parallel axis through the centre of gravity plus the product of the area of water plane multiplied by the square of the distance between the two axes will equal the moment about ordinate 5. The moment of inertia about the midship ordinate we shall call I, and the distance of the centre of gravity from this station = x. The moment of inertia about the centre of gravity of plane = I x . We then have I = I\ + Ax 2 , or I x = I — Ax 2 . A clearer conception of this will be obtained from the tabulated arrangement. 16 The Naval Constructor Longitudinal Metacentre. (Common Interval 10 Feet.) 00 X 5 H Pro- Pro- a 8 . Products Ordi- NATES. ducts fok Area. W « 3 ducts for Mo- ments. *a Pm Moments OF Inertia. .04 1 I .01 5 .05 5 .25 | 1.41 1.41 4i 6.34 4h 28.53 1 8.10 3 2.32 4 9.28 4 37.12 2 4.81 2 9.62 3 28.86 3 80.58 3 5.5G 1 5.50 2 * 11.12 2 22.24 4 5 6 696 6.00 5.58 2 1 2 11.92 6.00 11.16 1 1 11.92 1 1 11.92 11.16 67.57 11.16 7 4.87 1 4.87 2 9.74 2 19.48 8 3.57 2 7.14 3 21.42 3 64.26 9 1.90 f 1.42 4 5.68 4 22.72 9i- .97 .97 4* 4.36 4* 19.62 10 .03 i .01 5 .05 5 .25 62.41 52.41 324.13 Area of water plane = 62.41 X (f X 10) x 2. = 832.14 square feet. Distance of centre of flotation abaft ordinate 5 (67.57-52.41) 10 62.41 = 2.42 feet. Moment of inertia of water plane about ordinate 5 = 324.13 x (I x 10) x 102 x 2 = 432,172 = I. Moment of inertia of water plane about axis through its centre of flotation. = 432,172 - (832.14 X 2.422) = 427,304 = J v Longitudinal metacentre above C.B. T ~ loWT = 165 feet = Lon s itudinal B - M - Moment to Change Trim 17 An excellent approximate formula for the longitudinal B.M. is given by J. A. Normand in the 1882 transactions of the I.N. A. Taking the symbols we have been using : — L.B.M.=.0 7 35^i. -^ Applying this formula to the vessel with which we are dealing, we find : -•M. = .0 7 35f^|^= 1 0. 12f ee, which is a very close approximation ^° the calculated result of 165 feet. We may also use the apipruximate formula which we applied in the case of the transverse B.M. altered to suit the new axis with a modified coefficient, as : — L.B.M. =L*xBx h. Moment to Change Trim (Mi). As the centre of gravity of the displacement (or centre of buoy- oncy), either in the vertical or the longitudinal direction may be an entirely different locus from the ship's centre of gravity, it is obvious that unless the moment of the weights of the ship and engines, with all equipment weights, balances about the centre of buoyancy we shall have a preponderating moment deflecting the head or stern, as the moment is forward or aft of the C.B., re- spectively, until the vessel shall have reached a trim in which the pivotal point or C.B. is in the same vertical line as the completed ship's centre of gravity. To determine the moment necessary to produce a change of trim (M i) in a given ship, it is necessary to know the vertical position of the centre of gravity of the vessel and the height of the longitudinal metacentre (L.M.C.). The former may be calculated in detail or preferably proportioned from a similar type ship whose centre of gravity has been found by experiment ; although great accuracy in the location of this centre in calculat- ing the moment is not as important as in the case of G.M. for initial stability, as small variations in its position can only affect the final result infinitesimally. To investigate the moment affect- ing the trim, let us move a weight P already on board of the 100- foot steamer whose calculations are being figured. D = Weight of ship including weight P = 73.82 tons. BM = 165 feet. P = 5 Tons. 4 GM = 160 feet. I = 50 feet (distance moved). L — 100 feet (length of vessel). 18 The Naval Constructor In the figure we have the centre of gravity G to G u and the centre of buoyancy from B to B t , due to the shifting of the weight P forward for a distance represented by I, giving a moment Dx GG l = Pxl, and GG X = —^1' Fig. 6. The new water line is at W\L\ and B x Gx are in the same verti- cal and at right angles to it, and the point of intersection of the original and new water line at u O" equal to the centre of gravity (flotation) of water plane, therefore the triangles GMG X , WOWi, and LOLi, are of equal angle, so that GGj _ WWj _ LLx _ WW X + LL X GM ~ WO ~ L0~ WO + LO ' But WWx + LLi is the change of trim, and WO + LO is the length of the vessel = X, then change of trim L~ ~ but we have seen that WW X + LL X . GG 1 = ~ WO+LO GM X change of trim P x I Then Change of trim = P x Ix L Dx GM J) feet. Substituting the values, we get : — P xlx L 5 X 50' x 100' D x GM 73.82 X 100 = 2. 116 feet = 24^ inches. Calling this change of , trim 24 inches, and assuming that the point of intersection u O " is at the centre of the length, we should have Moment to Alter Trim One Inch 19 the stem immersed 12 inches and the stern raised 12 inches from the original water line, the sum of these figures equalling the total change. Moment to Alter Trim One Inch {M"). From the foregoing it will be seen that the total change of trim being known for a given moment, inversely we may get the amount necessary to alter the trim for one inch only, this being a convenient unit with which to calculate changes of trim when a complexity of varying conditions are being dealt with. As we have seen Pxl = M% the moment to change trim, and therefore, Change of trim = D x GM feet ; • , D x GM __ T X 2 foot or one inch = = M ". 12 x L Substituting values we have : — In designing preliminary arrangements of vessels, it is necessary that we should know fairly accurately the moment which it will take to alter the trim one inch (M") to enable us to arrange the principal weights in the ship, and the varying effects on the trim consequent on their alteration in position or removal. For this purpose a close approximation to this moment (M") is desirable and may be calculated from Normand's formula as follows : If" = ^.0001725, or HX8M. Jo x> Where .A 2 = the square of the water plane area, and B — the great- est breadth of water plane. Applying this approximate formula to the foregoing example, we have : — QQO 142 Jf"= ' x .0001725 = 9.95 foot-tons, 12 as against 9.84 foot-tons found by actual calculations, a difference too insignificant to affect noticeably the change in trim. This moment is useful to have for various draughts, and con- sequently should be calculated for light and load conditions, and for one or two intermediate spots and a curve of M" run on the usual sheet of " Curves of Elements." 20 The Naval Constructor Alteration in Trim through Shipping a Small Weight. If it be required to place a weight on board but to retain the same trim, i.e., to float at a draught parallel to the original one, the weight added must be placed vertically above the centre of gravity of the water plane. Should, however, the weight be re- quired in a definite position, then the altered trim will be as under: — Fig. 7. Instead of dealing with the weight at P let us assume firstly that it is placed on board immediately over the C.G. of water plane, when we shall find the parallel immersion to be a layer P equal to the distance between WL and W\Li whose depth is -^ V Let the weight be now moved to its definite position at a distance I forward of C.G., then Change of trim = ^j^ - = V. GM of course will be the amended height due to altered con- dition after the addition of P. Then : — Draught forward Draught aft C_ __P 2 Wt r Of course we assume that the alteration is of like amount for- ward as aft. This is only partly correct, but where small weights are dealt with is sufficiently so for most purposes. Generally the ship is fuller aft on and near the load line than forward, and prob- ably a water plane midway between base and L.W.L. would have its centre of flotation at the half length, so that a curve drawn through the centres of gravity of the water planes would incline aft, and as we have assumed the weight as being placed on board over the C.G. of the original water plane, it is obvious that the TchibyschefFs Rule 21 new line will have its centre of flotation somewhat further aft, and consequently the tangent of the angle W1OW2 will be less than that of L\OL%. With large weights and differences in the two draughts, the disparity would become sufficiently great to require reckoning, in which event the assumed parallel line in the preceding case would give the water line from which to determine the centre of flotation. Thereafter on finding the change of trim, which we shall call 10 inches, the amount of immersion of stem and emersion of stern post would be in proportion to the distance from to stem and O to post relatively to the length of water line. If we call " O " to stem 60 feet and " " to post 40 feet, the water line length being 100 feet, we have : — Immersion forward T W x 10" = 6 inches ) Total change Emersion aft T 4 o ^ X 10 = 4 inches \ 10 inches. TCHIBYSCHEFF'S RULE. In the preceding pages we have treated with the common appli- cation of Simpson's first rule to ship calculations. Another method, equally, if not more simple, which is slowly gaining favor with naval architects is that devised by the Russian Tchi- byscheff. This rule has the great advantage of employing fewer figures in its application ; more especially is this the case in deal- ing with stability calculations, and its usefulness in this respect is seen in the tabular arrangement given here. It has the addi- tional advantage of employing a much less number of ordinates to obtain a slightly more accurate result and the use of a more simple arithmetical operation in its working out, viz. addition. As the ordinates, however, are not equidistant, it has the dis- advantage of being inconvenient when used in conjunction with designing, and for this reason its use is advocated for the finished displacement sheet and calculations for G.Z. The rule is based on a similar assumption to Simpson's, but the ordinates are spaced so that addition mostly is employed to find the area. The number of ordinates which it is proposed to use having been selected, the subjoined Table gives the fractions of the half length of base at which they must be spaced, starting always from the half length. The ordinates are then measured off and summed, the addition being divided by the number of the ordinates, giving a mean ordinate, which multiplied by the length of base produces the area : — Sum of ordinates _ , , s -x — -r. — — - x Length of base = Area. No. of ordinates & 22 The Naval Constructor Tchibyscheff's Ordinate Table. Number Distance of Ordinates from Middle of OR- of Base, ^ , in DINATES. Fractions of Half the Base Lenoth. 2 .5773 3 X, -7071 4 .1876, .7947 5 X, .3745, .8325 6 .2666, .4225, T8662 7 X, -3239, .5297, .8839 9 3£, .1679, .5288, .6010, .9116 10 .0838, -3127, .5000, .6873, .9162 The employment of this rule to find the volume of displace- ment and the other elements usually tabulated on the displace ment sheet is shown on the attached Tables. The number oi stations used is ten, as in the case of Simpson's rule, but for clearness the, after body five are indicated by Roman numerals, and the fore body ones in Arabic. The displacement length is 600 feet, therefore by taking the fractions given in the preceding table for ten ordinates and multiplying them by 300, we shall obtain the distance of the displacement sections apart. These distances from the half-length and the sections are here given as used for the Table, but it will be observed that the water lines are spaced to suit Simpson's first rule for the vertical sections as no advantage would be gained by the use of Tchibyscheff in this direction, owing to the fewer number of water lines generally neces- sary. The various operations in the Table will be clearly under- stood from the headlines of the respective columns. As already pointed out, the great value of this rule is in the cal- culations to obtain cross curves of stability, specimen tables of which are also given. The fewness of the section's necessary, and the fact that the integrator saves the calculator the tedium of add- ing up, tells greatly in favor of the adoption of this rule for these calculations both as a time saver and an eliminator of the chances of error. T. S. S, "Lucania' 23 T. S. S. "LUCANIA" BODY SECTIONS FOR DISPLACEMENT ETC. BY TCHIBYSCHEFF'S RULE (for calculation see table) ORDINATES FROM AMIOSHIPS:- BEFORE ABAFT 1- — & I -- 25.14 2,_.&._.U__ m 93.90 3--.A— 111-- = 150.00 4.__&.__VI__ = 206.10 27.4. { WATER-LINES 3.833' APART 24 The Naval Constructor Displacement Sheet by Stations Water Lines. 1 1 2 3 4 1 1 i 2 1 2 I .60 .15 29.35 29.35 31.20 23.40 32.30 64.60 32.50 32.50 32.50 65.00 1 .60 .15 29.35 29.35 31.20 23.40 32.25 64.50 32.50 32.50 32.50 65.00 II .60 .15 26.25 26.25 28.84 21.63 31.00 62.00 31.30 31.30 31.40 62.80 2 .60 .15 25.00 25.00 27.35 20.51 29.25 58.50 30.00 30.00 30.20 60.40 III .60 .15 16.90 16.90 20.85 15.64 24.60 49.20 26.55 26.55 27.85 55.70 3 .60 .15 17.50 17.50 19.85 14.89 22.15 44.30 23.35 23.35 24.15 48.30 IV .60 .15 7.80 7.80 11.10 8.33 14.80 29.60 17.50 17.50 19.40 38.80 4 .60 .15 7.00 7.00 11.15 8.36 13.20 26.40 14.45 14.45 15.35 30.70 V .60 .15 1.00 1.00 1.50 1.13 2.55 5.10 3.55 3.55 4.65 9.30- 5 .00 .00 .00 .00 .15 .11 2.20 4.40 3.10 3.10 3.65 7.30 Sum of Ordinates 5.40 160.15 183.19 204.30 214.80 221.65 Functions 1.35 160.15 137.38 408.60 214.80 443.30 Levers 7.00 6.50 6 5 4 3 Moments 9.45 1,040.98 824.28 2,043.00 859.20 1,329.90 Multipliers for Areas Areas of Water Lines 648.00 19,218.00 21,983.00 24,516.00 25,776.00 26,598.00 Divisor for Tons Tons per Inch r= D = 1.543 1 45.76 52.36| 58.371 | 61.37 | 63.29 ■rv , . . ,. , 2X600X2X 3.833 Displacement m cubic feet ^ ^ , A . x o X 10 * _. . L . . 1 2 x 600 x 2 x 3.833 Displacement in tons . . 1 3 x 10 x 35 — x 10: A = Distance of Ordinates. number of stations. t 3 =. Simpsons' multiplier. Displacement Tables 25 Tchibyscheff s Rule. Vertical Sections. 5 6 7 Func- tions. Differ- ences. Levers. Mo- ments. 1 2 * 32.50 32 50 32.40 64.80 32.35 16.18 328.48 .13 .0838 .109 32.50 32.50 32.40 64.80 32.30 16.15 328.35 31.45 31.45 31.50 63.00 31.45 15.73 314.31 13.60 .313 4.259 30.25 30.25 30.35 60.70 30.40 15.20 300.71 28.55 28.55 29.10 58.20 29.25 14.63 265.52 29.48 .500 14.740 24.65 24.65 25.10 50.20 25.40 12.70 236.04 21.00 21.00 22.45 44.90 23.70 11.85 179.93 34.24 .687 23.523 16.10 16 10 16.90 33.80 17.45 8.73 145.69 5.75 5.75 6.90 13.80 8.25 4.13 43.91 13.50 .916 12.367 4.10 4.10 4.50 9.00 4.80 2.40 30.41 226.85 231.60 235.35 = 2i 2,173.31 Distance 54.998 226.85 463.20 117.68 Water Lines = 3.833' 2 1 453.70 463.20 7,023.71 of Water I jines : * T ° B - X 2. Centre of Buoyancy. 7,023.71 x 3.833 , _ ( below 2,173.31 ~ 12d9 J W.L.7 54.998 X 600 „ rn/ , -. -, = 7.59 abaft 3£ 2,173.31X2 * 27,222.00 27,792.00 28,242.00 per Inch : 420. 64.814 66.171 67.243 2,173.31 = : 666,445.2 5 2,173.31 = : 19,041.29 X(3x0i+10x0 2 — 3 ) = Moments. S 1 x-6 T o 7 °-X2 = Area of Water Lines. The Naval Constructor Center of Buoyancy and Water Links. Keel W.L.£ W.L. 1 W.L. 1 W.L. 2 W.L. 3 W.L. 3 W.L. 4 W.L. 5 W.L.5 W.L. 6 W.L. 7 /. 5.40 160.15 183.19 183.19 204.80 214.80 214.80 221.65 226.85 226.85 231.60 235.35 Prod- is i.s. 1.35 160.15 45.80 207.31 91.60 408.60 107.40 814.90 107.40 443.30 113.43 1,479.03 113.43 463.20 117.68 !, 173.34 Mo- ments. 80.07 45.80 125.88 91.60 817.20 322.20 1,356.87 322.20 1,773.20 567.15 4,019.46 567.15 2,779.20 823.76 8,189.5/ Formula. 3.833 x 3.833 x 3.833 x 3.833 x 125.87 207.31 1356.87 814.90 4019.46 1479.07 8189.57 2173.38 C.B. \ iw.\ i: Ki:i.i,. 2.328 10.420 14.450 Displacement in Keel to W.L. I, 8 x 600 X ^X 3.833 y ^ W.L. Ito W.L. 2: 2X 7*f 33 x 2,336.50 = Keel to W.L. 3 : 2 X 6 °° * 2 Q X 3 " 833 x 814.90 = W . L . ! t0 w.L. 4 , 3X600X2X3833 ^ ^ „ = o X J U Keel to W.L. 6 , 2X600X2^X3.83.3 x y^ = W.L. 4 to W.L. 6: «00 * * * 3-833 x 1,880.65= o X 1U Tr 1 . lirT , 2x600x2 X3.833 ft „„,, ,, Keel to W.L. 7 : x 2,173.34 = »j x 10 A 2 X (SxO^SxOjj— 0,) = Area by f rule. — x^xOj + IOxO.,— 3 = Moments. Displacement Tables Displacement, by Tchibyscheffs Rule. 27 183.19 204.30 214.80 183.19 204.30 214.80 221.65 221.65 226.85 231.60 Prod- ucts. 915.95 1634.40 -214.80 2335.55 183.25 612.90 644.40 221.65 1662.14 221.65 907.40 231.60 1360.65 549.57 2043.00 -214.80 Mo- ments. 2377.77 183.19 1225.80 1933.20 4228.79 886.60 4537.20 1389.60 6813.40 Formula. 3.833 x 2377.77 2335.55 C.B. of W.L.-W.L.2 : 5.783X89521 63+2.328x63574.52 89521.63+63574.62 3.833 x 4228 - 79 1662.14 9.76X286577.44+2.328X63574.52 280577.44+63574.1 3.833 x 6813.40 1360.65 19.2X208614.86+8.4X350151.96. 208614.86 + 350151.96 C.B. ABOVE Keel. 1.95 3.833 5.783 4.33 9.76 8.40 19.20 12.45 Cubic Feet 63,574.521 89,521.63 286.577.44 208,614.86 = V. Cubic Feet. C.B. Above Keel. 63,574.52 = Keel to W.L. 1. 2.328 153,096.15 = Keel to W.L. 2. 4.33 249,912.80 = Keel to W.L. 3. 6.383 350,151.96 = Keel to W.L. 4. 8.40 453,558.21 = Keel to W.L. 5. 10.420 558,766.82 = Keel to W.L. 6. 12.45 666,445.24 = Keel to W.L. 7. 14.45 Lever =s A 2 (3 X Oj + 10 X 2 - 3 ) _ A (3 X 0, + 10 X 2 -0 3 ) 24 (5X0!+ 8 X0 2 — 3 ) - 2 X (5x0 1 + 8 X0 2 -0 S )' 28 The Naval Constructor Longitudinal Metacenters and Centers Stations. W.L. 7 . . A respective 2 . . . . Lever respec- tive to Lever 2 Moments Moments for I . . . . W.L. 6 . . A respective 2 . . . . Lever respec tive to Lever 2 Moments Moments for I . . . .084 32.30 64.65 .007 .453 W.L.5 . . A respective 2 . . . . Lever respec- tive to Lever 2 Moments Moments for I . . . . W.L. 4 . . A respective 2 . . . . Lever respec- tive to Lever* Moments Moments for I . . . . 32.40 .084 32.50 .084 32.50 Mi 32.40 64.80 .007 .454 32.50 .007 32.50 31.45 1.05 .313 .329 31.50 1.15 .313 .340 31.45 1.20 .313 .376 31.40 .20 .313 .876 30.40 61.85 6.061 III A 30.35 61.85 6.061 30.25 61.70 6.047 61.60 6.037 29.25 3.85 .50 1.925 29.10 4.00 .50 2.00 28.55 3.90 .50 1.95 25.40 54.65 13.600 27.85 3.70 .50 1.85C 25.10 54.20 13.55 23.70 6.25 .687 4.294 24.65 53.20 .25 13.30 24.15 52.00 14.00 22.45 5.55 3.813 17.45 41.15 .472 19.423 21.00 4.90 3.366 19.40 4.05 .687 2.782 16.90 39.35 .472 18.573 V A 8.25 3.45 .916 3.160 16.10 37.10 472 17.510 15.35 34.75 472 16.400 6.90 2.40 .916 2.198 4.80 13.05 10.962 4.50 11.40 .840 9.576 5.75 1.65 .916 1.511 4.<;r> LOO .916 .916 .840 8 :>,o .840 6.972 A = Difference. 2 = Sum. 2 3 = Sum of Moments (Sums x lever 2 ) for I. Displacement Tables 29 of Flotation, by Tchibyscheff s Rule. 2 OF Moments. Center aft3£ ^ L 1 r a o £ « 2 g h ta o / (AXIS = \L BETWEEN P.P.) Deduction Area W.L. X<* 2 . V h V h 2 2 2 3 -(f); 28,242 X12.09 2 4,128,000 666,445 542,772,000 Lon- gitu- dinal B.M. in Ft. 812.93 10 2X2, =10,800,000 2 3 546,900,000 9.708 50.559 9 - 708X 2S-5 12.09 27,792xl0.813 2 3,249,440 558,767 517,461,760 926.07 8.351 48.214 8 - 351 x 2 "So 10.813 520,711,200 27,222x 9.525 2,469,715 453,558 484,945,085 1069.2 7.203 45.131 -3X^ 9.525 487,414,800 26,598x 8.018 2 1,709,932 350,152 167,107,268 1334.0 5.924 43.409 "***£■ 8.018 468,817,200 2 X = Sum of Ordinates on Displacement Table. 2 2 = Sum of Moments (differences x lever) for Centers of Flotation. 30 The Naval Constructor 1 w IN 2 I 1 i 6 a i 5 eo ■a OS 8 5 ?2 u | 6 i § co 55 1 g • § i i 1 1 S 8 A a x ~2 3 i a 1 i 1 ' si 1 i x " t- t- CO co CO ^ M ICO ,_, t- i ^H CN ^( og 8 s 00 CM i 8 wto g 3 £ 8 g jj o * ^ i 3 g = 8 £ © s IT 10 •>* © * S « s w § w 8 CM rH 3 S 8 b a eS io 5 s s K* 00 »-H s * 3 CO w 1 " 1 w 9 o» t- »H CO "* i2 M 2- I CO °°- o eo 8 | S 55 S i 31 l-H Ifi r-< rf rl •* TH CO »-l o* M ' H > S 1 58 5 oi of 2 S §3 o S o3 H s 1 2. g s i s 1 3 ? s s '8 | M « 8 s a" 8 of *} o3 oo CM TjJ" » Explanation of Table 31 EXPLANATION OF TABLE, GIVING EFFECT OF FORM OF WATER LINE ON POSITION OF LONGITUDINAL METACENTER. Longitudinal and Lateral Stability Compared. — The first four lines are exactly the same as those in the other table ; and the last eight lines differ only in having length and breadth interchanged, so as to give pitching instead of rolling. On comparing them with the following table, it will be noticed that, in the algebraic factor, the length and breadth always inter- change ; and that the numerical factor remains unchanged for forms (1), (3), and (A), namely, the square or rectangle, the circle or ellipse, and the wedge. Of the nine forms selected, these are obviously the only ones in which breadth and length are absolutely interchangeable. With respect to the comparison of the different forms, one with another, if we disregard the wave-bow No. (8), the variation of stability follows much the same sequence for longitudinal as for lateral stability, but with a somewhat less absolute value. This result might be expected ci priori, because the extreme breadth ordinate cuts the outline at right angles in all but the wedge form (9) ; while the extreme length ordinate meets the outline more sharply. In forms (2) and (4) this difference is only of the second order ; but, as the figures show, it is quite sufficient to be of practical importance even in these. Differ Chiefly in Wave-Bow. — The wave-bow form (8) falls altogether out of its sequence, and its stability is less than the wedge form (9) as regards pitching. This is due to the sudden falling off of the extreme ordinate length, which meets the curve tangentially, instead of normally, as the extreme breadth ordinate. Fine Bow Affects Pitch More than Rolling. — If we consider rolling on any given axis, it is easily seen from geometri- cal considerations, and also from the algebraic form of the inte- gral, that the instantaneous stability depends, firstly, on the length of the transverse axis, and, secondly, on the slowness of the rate of diminution of that axis, as we pass along that axis of motion. Hence sharp bows have less stability for pitching than bluff bows, while their lateral stability for rolling is not so very different. Caution in Use of Table. — In the table of lateral stability, the element of length only appears as a simple factor ; therefore, as regards lateral stability, we may compound the moments by 32 The Naval Constructor simple addition for a vessel built up in different lengths for the different forms. Thus, the values in lines 1 to 8 of column (2) are simply the means of the corresponding values in columns (1) and (3). We cannot apply this process to the longitudinal stability because here the length element enters as a cubic factor. If we were so to compound the moments of length, what we should really do would be equivalent to screwing together two longitudinal halves of different vessels ; in the case before mentioned, screwing half a box to half a tub ; not introducing a flat midship length between two semicircular ends. Effect of Form of Water Line 33 Explanation of Table Giving Effect of Form of "Water Line on Position of Metacenter. Explanation of Table. — By the preceding table we can at once make an approximate estimate of the value of any proposed form of water line, by selecting that form in the table to which it comes nearest. From this table we gather that the more nearly the water line approaches to a right parallelogram, the more it will contribute to the stability of a ship. No. 9, on the contrary, the straight line wedge form, is the least stable of these water lines, and from the comparison of the successive groups of lines on the table we shall see exactly how this comes about. Areas on Water Lines. — The first and second lines in the table give the measures simply of the areas of those water lines. From lines 3 and 4 we see that, Fig. 1 being taken as the stand- ard of comparison, Fig. 2 only contains 89 per cent of the rectangular area, and this diminution is effected merely by round- ing off the rectangular corners, the length and breadth remaining the same in both. In Fig. 3, when the curvature of the ends extends quite to the middle of the water line, its area is reduced to 69 per cent. In Fig. 6, by forming the water line of parabolic arcs, a favorite form of some builders, the area is reduced to two- thirds of the rectangle. Figs. 7 and 8 are the lines used for a wave stern and a wave bow ; from which it appears at once how much more powerful the stern contributed to the stability of a ship than the bow ; the stern line being 62 per cent, and the bow line only 50 per cent. Metacentric Moments. — Lines 5 and 6 are the actual measure of the stability (by its moments) for small inclinations. For example : in the rectangle, the moment is one-twelfth part of the product of the length by the cube of the breadth, or .08 of that product ; and as we pass along line 6 we find it gradually diminish, until, in the wedge form, it is only .02, showing that a sharp wedge form has only one-fourth part of the power to carry top weight that the rectangular form has, although its power of buoyancy, or power to carry absolute load, is one-half. This is set out more fully in lines 7 and 8 ; so that by carefully comparing together line 4 and line 8, the relative values of all those figures for carrying absolute weight and for carrying top weight may be clearly seen. Metacentric Intervals. — Lines 9 and 10 measure the powers of ships, formed on these water lines only to carry top weight without upsetting. 34 The Naval Constructor Effect of Form of Water Line on From J. Scott Russell, Length of vessel = L.* Breadth on water line 1 Area of plane of flotation . 2 The same, expressed decimally 3 Ratio to same in rectangular | form 4 The same, expressed decimally bjixsdyl 6 The same, expressed decimally 7 Ratio to same in rectangular form 8 The same, expressed decimally 9 Height of longitudinal meta- center ahove center of dis- placement % 10 The same, expressed decimally* 11 Ratio to same in rectangular ) form % ] 12 The same, expressed decimally % « o LB LB L*B L S B dr. & dr. (1) EBB i .00000 1 .00000 o.os:«:5 (-*> (SB 4+w 0.89270 4 + ff 8 0.89270 16 +5tt 512 0.06194 48+lSn- 128 0.74340 16 + 5ir 16(16 + 4tt) 3(16 + 5tQ 4(16 + 4tt) (3) .2 SB) 0.78540 in 0.78540 0.04909 0.58905 A» 0.06250 It 0.75000 * The length L appears simply as a factor. The numerical factor in the table, therefore, remains unchanged if the proportion of L to B be altered, as in passing from the square to the rectangle, or from the, circle to the ellipse. t That is to say, a trochoid twice the length of a cycloid of the same width. Effect of Form of Water Line 35 Position of Longitudinal Metacenter. Nav. Arch., 1865. amidships = B. Draught of water r= dr. Numerical Factor for (4) (5) (6) (7)t (8) (9) Parabola (Axis Athwart- ships). Trochoid 1 : 2 (a Wave Stern). Curve of Sines (a Wave En- trance). 6 be 1 <3 r > <£> <£> <£> 3 4 TT — 2 4(V2 - 1) 2 3 5 8 i 2 2 0.75000 0.68901 0.6667 0.62500 0.50000 0.50000 3 TT — 2 2 5 1 1 4 -KV2-1) 3 8 2 2 0.75000 0.68901 0.66667 0.62500 0.50000 0.50000 12tt 2 _ 35 192 tt 2 3tt — 8 1 30 80ir 2 — 373 1536 TT 2 »r 2 — 6 24 jt 2 1 48 96 V2— 1 0.04403 0.03583 0.03333 0.02748 0.01634 0.02083 12ir 2 — 35 16 TT 2 3tt — 8 8V2-1 2 5 80ir 2 — 373 128 TT 2 ir 2 — 6 1 4 2tt 2 0.52836 0.42996 0.40000 0.32974 0.19604 0.25000 12*r 2 — 35 144 TT 2 3tt — 8 24 (tt — 2) 1 20 80tt 2 — 373 960 TT 2 TT 2 — 6 1 24 12 TT 2 0.05871 0.05200 0.05000 0.04397 0.03267 0.04167 12jt 2 — 35 12 TT 2 3tt — 8 2 (» — 2) 3 5 80tt 2 — 373 80 TT 2 TT 2 — 6 1 2 TT 2 0.70448 0.62403 0.60000 0.52759 0.39207 0.50000 % The entries in these lines assume that the vessel is flat-bottomed, with vertical sides. The other entries hold good whatever may be the shape of the vessel under water. In general, the height of the metacenter may be found by dividing the entry in lines 5 or 6 by the displacement. 36 The Naval Constructor Effect of Form of Water Line From J. Scott Russell, Length of vessel = L.* Breadth on water line 1 Area of plane of flotation % . 2 The same, expressed deci- mally t 3 Ratio to same in rectangular ) form J 4 The same, expressed decimally bJlyMxt 6 The same, expressed decimallyj 7 Ratio to same in rectangular | form j 8 The same, expressed decimally 9 Height of metacenter above ) center of displacement § . ) 10 The same, expressed deci-) mally § J 11 Ratio to same in rectangular \ forms ) 12 The same, expressed decimallyf g «H LB LB LB* LB* (1) %£ -60 © q GOB 1.00000 1 1.00000 12 0.08338 1 1.00000 1 12 1.00000 (2) © c oe . 1+5 8 0.89270 i±2T 8 0.89270 16-f 3tt 384 0.06621 16 + 37T 32 0.79452 16 + 37T 12(16 + 4tt) 0.07417 16 + 37T 16 + 47T 0.89003 (3) fig IK *« 0.78540 *» 0.78540 A» 0.04909 A* 0.58905 0.06250 It 0.75000 * The length Z appears simply as a factor. The numerical factor in the table, therefore, remains unchanged, if the proportion of L to B be altered, as in passing from the square to the rectangle, or from the circle to the ellipse. t That is to say, a trochoid twice the length of the cycloid of the same width. Effect of Form of Water Line 37 on Position of Metacenter. Nav. Arch., 1865. amidships = B. Draught of water = dr. Numerical Factor for (4) < 5 >. (6) (7)t (8) (9) W H O Parabola (Axis Athwart- ships). 2 o . Curve of Sines (a "Wave En- trance). £ be 1 ► ® «£> O © <3> 3 4 it — 2 2 3 5 8 1 2 i 2 4(V2-1) 0.75000 0.68901 0.6667 0.6250 0.50000 0.50000 3 4 ir — 2 2 3 5 8 1 2 1 2 4(V2-1) 0.75000 0.68901 0.6667 0.62500 0.50000 0.50000 35 1 9 77 — 28 4 55 5 1 768 24 20V2— 28 105 1536 192 48 0.04557 0.04021 0.03810 0.03581 0.02608 0.02083 35 1 9tt — 28 . 16 55 5 1 64 2 20V2— 28 35 128 16 4 0.54688 0.48252 0.45714 0.42969 0.31250 0.25000 35 2 11 5 1 576 35 192 96 24 0.06076 0.05836 0.05714 • 0.05729 0.05208 0.04167 35 24 11 5 1 48 35 16 8 2 0.72917 0.70031 0.68571 0.68750 0.62500 0.50000 t These are all areas or moments, and therefore, for compound forms, it is only necessary to add them, or take a mean of them, as may suit the par- ticular case. § The entries in these lines assume that the vessel is flat-bottomed, with vertical sides. The other entries hold good, whatever may be the shape of the vessel under water. In general, the height of the metacenter may be found by dividing the entry in lines 5 or 6 by the displacement. 38 The Naval Constructor Modulus of Fineness. — Lines 11 and 12 enable us to com- pare the different forms; and by running our eye along line 12 we are enabled to trace the effect of the successive changes in the form of water line, in bringing down the metacenter, and re- ducing the stability of the ship, thus giving what has been some- times called the modulus of fineness of water line. STABILITY CALCULATION, USING THE INTEGRATOR AND APPLYING TCHIBYSCHEFF'S RULE. The following tables will show the application of the above rule to the calculation of the stability levers GZ from the body plan reproduced, noting that the integrator used was metrically divided, and the original drawing was to a scale of j to the foot or g>y full size with ten Tchibyscheff ordinates. The center of gravity was assumed at 24 feet above base. The coefficients are therefore as follows, the length of vessel being 600 feet : — 600 962 x 3.2812 TO * 100X35 =1701 - 5 - For displacements (tons), For levers (feet), .06 x 96 X 3.281 = 18.9. and, Displacement in tons = 1701.5 x sum of differences of area readings. T . , 18.9 X sum of differences of moment readings Sum of differences of area readings or, Displacements (D) = 1701.5 x I ) I respective to II taken up Levers (GZ) = 18.9 x II \ *£« corresponding water The angles calculated were 15°, 30°, 45°, 60°, 75°, and 90°, and the results as tabulated used to plot off the Stability Cross Curves shown from which the Stability Curves at various displacements were taken, the correction being calculated for the new locii of the center of gravity where G is the assumed position below S then GZ = SZ + SG sin 0, and when above S then GZ—SZ — SG sin 0. So that taking the ordinates from the cross curves at the displace- ment dealt with SG being now known, we can determine the exact values of GZ for any angle. Stability Calculations 39 Fig. 9. 40 The Naval Constructor Calculation of GZ Levers for Stability Cross Curves, Using the Integrator and Tchibyscheff s Rule. J o W §4« 2 •< © 3f Af . Sp5 a GZ 6097 4869 5 9808 9808 3711 3.711 6,315 5547 5547 +.678 +.678 3.46 4 1684 1684 1876 5.587 9,520 6051 6285 +.504 +1.182 4.00 O 3 3746 2062 7.649 13,000 6637 +.352 +1.534 3.80 o to 3746 6871 2 5976 5976 2230 9.879 16,800 7186 7420 +.315 +1.849 3.50 L.W.L. 8241 8241 2265 12.144 I 20,550 7544 7778 +.124 +1.973 3.07 L.W.L. 0389 12.148 9754 +1.976 Check 0622 1355 5 4832 4832 4210 4.210 7,160 2078 2078 +.723 +.723 3.25 4 6676 6676 1844 6.054 10,300 2448 2920 +.370 +1.093 3.42 o 3 8599 1923 7.977 13,600 3166 +.246 +1.339 3.18 8599 3402 2 0689 0689 2090 10.067 17,130 3503 3740 +.101 +1.440 2.70 L.W.L. 2860 2860 2171 12.238 | 20,800 3890 4137 +.150 +1.590 2.46 L.W.L. 5090 12.230 5737 +1.600 Check 0521 5890 5 5039 5039 4518 4.518 7,690 6332 6332 +.442 +.442 1.85 4 6783 6783 1744 6.262 10,560 6438 6674 +.106 +.548 1.65 o 3 8637 1854 8.116 13,810 6767 +.093 +.641 1.49 % 8637 7004 2 0685 0685 2048 10.164 17,295 7128 7364 +.124 +.765 1.42 L.W.L. 2880 2195 12.359 21,030 7436 +.072 +.837 1.29 2880 I 7672 L.W.L 5242 12.362 . . . 8511 ... +.839 Check 42 The Naval Constructor 133d 8U3A3T JO 31V09 Cross Curves of Stability 43 lOOJ . _ _ | 5 * e 6 * 1 1 1 1. • 1 o / / /// _ / / // I / / -7 / I_ / / // - / / /*/ ' z */ / Af o /,/// : I_o f?y# i 2 '/ '/ '/ tf v7 - O U C5 §/ » - 5/ "/ -. J - -1 ^ / °/ r* v\ f \ / < A / z — o \U I - Y/\ ^ •»- _ A\V 2 / \ \ \\ 3 ~ o \ v \ ~ o » \\\ \ > v\ \ : S\ \^ \ z > \ \ \ r« s X \\ z * ^\ \\ o ^^ \\ ~ .1.33d 9U3A3T 30 31V08 ^^^^ : [Mil |l 1 1 III 1 1 1 | II 1 1 |ll 1 l|l 1 1 III 1 II | 1 1 II 1 1 1 1 l | 1 II 1 o s * e z i 44 The Naval Constructor CHAPTER II. DESIGN. In the foregoing pages we have treated with the various calcula- tions which confront the naval architect, but the relation of these to one another and to the particular qualities that the projected ship shall possess belong to Design. In designing the ship, nothing should be left to chance, or what is the same thing — trial and error. The vessel must first be de- signed with figures. Before a single line is run on paper, the vari- ous element coefficients should be carefully selected and their functions worked out in consonance with the results desiderated in the finished ship. The relation of these coefficients to one another must be firstly mastered for all types of vessels and con- ditions of draught and trade, when with the aid of the tables given an unerring selection will be possible and a definite result attained. When the way is prepared for the drawing part of the design to be taken in hand, it will be found advantageous to have a definite routine in which to prepare the various views comprised under the general term "Lines." Each step should be taken in its proper time and order. Much time will thus be gained, and a clearer conception of the art of designing obtained. To this end we submit the following method as one fulfilling these proposi- tions, dividing the task broadly into two parts,, viz. : — (a) Figures and (b) Lines, the first embracing the moulded dimensions, draught, element coefficients, and their functions, and the latter, the sheer draught, half-breadth, and body plans. The shipowner will specify the trade for which the ship is in- tended and the limit of draught on the particular service proposed. It will generally be found economical to take advantage of the maximum draught permissible. When the dimensions are solved to meet the requirements stipulated, the grade numerals should be worked out, for the Classification Society's Rules in which it is proposed to class the ship, and if it be found that a grade can be saved either in plating, framing or equipment numerals, or the requirements for extreme proportions evaded by a slight alteration or adjustment of the dimensions, this of course should be done. As an example we shall postulate that the shipowner requires a 3-deck freighter with complete shelter deck to carry 10,000 tons dead weight, exclusive of coal for 12 days' steaming, fresh water and stores, on a mean draught of 27 feet with a B.T. Freeboard and a sea speed of 12 knots. The ship to be classed in American Record and to conform to the U.S. Inspection Laws. To these Design 45 demands of the owner the naval architect should add the G.M. when fully loaded with a homogeneous cargo. Let us call this 1.5 ft. The first point to determine is the amount of displacement we shall require to provide for over and above the specified dead weight of 10,000 tons, to allow for weight of finished ship and machinery, coal, fresh water, and stores. At this stage we cannot calculate these items, as we are uninformed as to the dimensions of the ship, so that the remaining method to solve this is to esti- mate a weight embracing all of these items based on a percentage of the dead weight. This percentage of course is determined from vessels of similar type and trade duly worked out and tabulated by the naval architect. We shall take, then, each step in its proper order : (1) Displacement = dead weight x 1.64 = 16,400 tons. (2) Block coefficient " 5 " = a./S.e. = .79. (3) Relation coefficient "e" =— = .945.* a.p s (4) Mid. area coefficient "fl" = — = .97. (5) Prismatic coefficient "p"=- = .814. (6) Area of L.W.L. coefficient "a" = ^=.861. (7) Moment of inertia coefficient " i " (see table) = .0638. i (8) B.M. coefficient "m " = ?- = . 08. (9) Center of gravity coefficient ' g ' ' = ■== = . 559. (See table. ) (10) Depth " H " to upper deck per Freeboard Tables = 33.5 ft. (11) Depth "fli" to shelter deck = H + 7.5 ft. = 41 ft. (12) Center of gravity above base = H X X g = 41 x.559 = 22.90 ft. (13) Metacenter above base = C.G. + G.M. = 22.90 + 1.50 = 24.40 ft. (14) Breadth "£" to give M.C. of 24.4 ft. = (15) Length -£» = ^ x ^ x§ = 460 ft. (16) B.M. = y =y= 10.23 ft. (17) Center of buoyancy above base * May be taken constant .9, as per -table. 4G The Naval Constructor (18) Bilge diagonal coefficient (see diagram) = .82. (19) Dimensions as determined = 400 x 58' 0" x 33' 0". (20) Displacement " D " 460' X 58.5' X 27' _. lfl .„ . = ^ X .79 = 16,400 tons. oo (21) Calculated weights : Hull complete .... 4,670 tons Machinery 730 " (4,000 I. H. P.) Coal 750 " (for 12 days) Fresh water 200 " Stores 50 " 6,400 " Dead weight 10,000 " Displacement = 16,400 tons Should it be found, however, that the weights calculated for the dimensions as worked out are lighter than anticipated when we started with the 64 per cent of the dead weight, the length should be reduced accordingly. On the other hand, if the weights be excessive, the length must be increased. The length is the only dimension that should be adjusted, as it is the one factor which has no vital relationship to the element coefficients, as it will have been noticed that the primary quality aimed at was the G.M. as a measure of the ship's initial stability ; and as the center of gravity varies with the depth, so the metacentric height is dependent on the breadth and draught. For the preliminary design it will be sufficiently close to esti- mate the machinery weights on the I.H.P. required, and for ordinary merchant practice the power may be calculated fairly accurately by the Admiralty constant with the formula : — T.H.P. = -P > *y» * C We then have for the present example, with constant = 267, speed 12 knots, and displacement 16,400, an indicated horse-power =4000. By referring to the table given elsewhere, it will be found that for twin screw freight steamers with this speed that the I.H.P. per ton of engine boilers and water equals about 5.5, so that we get for a total machinery weight ^ = 730 tons. 5.5 The displacement and coefficients should, in all cases of steel steamers, be calculated to the moulded line of frames, the excess water displaced by the shell plating, amounting to about 1%, being retained in hand as a margin against contingencies. In this case its value is 164 tons, representing 3 inches of draught. * See Table of Constants, and chapter on Kesistance. Relation of Coefficients to One Another 41 Relation of the Coefficients to One Another. Relation coefficient, .9, constant = Block coefficient, 5 = a./S.e. Area of water line coefficient, p S a = or . e p.e /? *? Mid. area coefficient, # = -, or — ' r p a.e Prismatic coefficient, p = — • Bilge diagonal coefficient, i, = X2 t0 |§( P= - 6t0 - 82 >- Type of Vessel. € 6 P P b Steam pinnaces, 30 ft. to ( 60 ft ) .9 .36 .666 .600 .600 .652 .9 .36 .666 .616 .600 .652 r .9 .38 .666 .633 .600 .652 .9 .39 .666 .649 .600 .652 Steam yachts, 100 ft. to .9 .40 .666 .666 .600 .652 300 ft. , also destroyers - .9 .41 .670 .680 .603 .653 and torpedo craft . . .9 .42 .671 .695 .604 .653 .9 .43 .671 .712 .604 .653 k .9 .45 .675 .740 .608 .654 .9 .46 .674 .758 .607 .654 .9 .47 .674 .774 .607 .654 .9 .48 .675 .790 .608 .655 Small river propeller J .9 .49 .676 .804 .609 .656 steamers, 50 ft. to 150 .9 .50 .677 .820 .610 .657 ft. ...... . .9 .51 .679 .834 .611 .659 .9 .52 .680 .849 .612 .661 .9 .53 .683 .860 .615 .663 .9 .54 .688 .870 .620 .665 L .9 .55 .694 .880 .625 .670 Sound and river steamer, .9 .56 .700 .890 .630 .676 150 ft. to 400 ft. . . .9 .57 .703 .900 .633 .679 .9 .58 .707 .910 .637 .683 .9 .59 .712 .920 .641 .687 *• .9 .60 .716 .930 .645 .692 48 The Naval Constructor Type of Vessel. e 6 a P b .9 .58 .677 .950 .610 .667 High speed channel steamers, 200 ft. to 300 ft r "S .9 .9 .9 .59 .60 .61 .689 .697 .707 .953 .956 .959 .620 .627 .636 .665 .673 .681 .9 .62 .716 .962 .644 .690 .9 .63 .725 .965 .652 .698 Ocean liners, 400 ft. to \ 750 ft .9 .9 .64 .65 .734 .743 .968 .971 .661 .669 .706 .714 .9 .66 .755 .975 .680 .722 . » .9 .70 .820 .950 .737 .768 .9 .71 .828 .952 .745 .770 Full-rigged ships, 250 ft. ' .9 .72 .838 .954 .754 .777 to 350 ft .9 .73 .847 .957 .762 .785 I .9 .74 .857 .959 .771 .792 .9 .75 .866 .962 .779 .800 .9 .76 .874 .965 .787 .807 .9 .77 .884 .967 .796 .814 Intermediate liners and freighters, 300 ft. to 700 ft .9 .9 .9 .78 .79 .80 .894 .903 .913 .969 .971 .973 .805 .813 .822 .819 .825 .830 .9 .81 .922 .976 .830 .836 ' .9 .82 .933 .978 .840 .843 - .9 .83 .941 .980 .847 .850 Coefficients of Centers of Gravity for Various Vessels. Value OF"0." Small steamers, as harbor tenders, revenue steamers, etc . .65 to .70 Torpedo boats 67 Torpedo boat destroyers 55 to .60 Auxiliary steam yachts 65 Full-power steam yachts 70 Full-rigged sailing ships 69 to. 71 Shelter-deck intermediate liners .... .60 to .65 Swift ocean liners 56 to .58 Shelter-deck freighters 66 to .58 Three-deck freighters, with poop, bridge, and forecastle 54 to .56 Inertia Coefficients 49 Moment of Inertia of Water Line Coefficients. L x B* x i = I. Water Line Inertia Water Line Inertia Coefficient, Coefficient, Coefficient, Coefficient, "a." " i." "a." "*." .50 .02250 .75 .04841 .51 .02316 .76 .04966 .52 .02383 .77 .05100 .53 .02466 .78 .05233 .54 .02540 .79 .05383 .55 .02633 .80 .05500 .56 .02710 .81 .05650 .57 .02800 .82 .05783 .58 .02910 .83 .05930 .59 .03000 .84 .06075 .60 .03100 .85 .06200 .61 .03200 .86 .06341 .62 .03300 .87 .06500 .63 .03400 .88 .06625 .64 .03500 .89 .06766 .65 .03600 .90 .06900 .66. .03733 .91 .07050 .67 .03844 .92 .07200 .68 .03955 .93 .07341 • .69 .04100 .94 .07500 .70 .04200 .95 .07600 .71 .04325 .96 .07833 .72 .04500 .97 .07900 .73 .04600 .98 .08050 .74 .04700 All the elements insuring the qualities that embody a well- shaped boat of the particular type contemplated and at the same time a stable ship having been thus determined, the lines may be commenced with the certainty that no unnecessary alterations will be required. The freeboard will be calculated from the legal tables given and explained herein, but in any case the limiting draught consistent with the block coefficient determined on as the maximum avail- able for the required speed should be taken advantage of. After carefully drawing the center and other construction lines, and marking off the ten or twenty ordinates that it is proposed to 50 The Naval Constructor use, it will be well to have a definite routine or method in which to draw down the various views comprising what are embraced under the general term " lines." To this end the following will prove a good sequence : 1. The " dead fiat" section on body view. 2. Rail sheer line. 3. Contour of stem and stern in profile. 4. Kail half-breadth. 5. Load water line half-breadth. C. Bilge diagonal. • 7. Transfer L.W.L. and B.D. ^-breadths to body plan. 8. Draw freehand the sections to foregoing. 9. Trial displacement by planimeter. 10. Sheer heights from profile to body plan. Taking this routine in order : — 1st. The dead flat or midship section should present no difficul- ties, as the area of this section is pre-determined from the co- efficient /S. This being so, the height of rise of floor construction line is assigned by giving the easiest bilge consistent with the area of section demanded. In no case should the bilge be "squarer" than the demands of this area require, as in full vessels sufficient difficulty is encountered in setting the bilge strake plates and bending the frames without adding further to it. 2d. In most vessels, except yachts and launches, .it will be found advisable to make the lowest part of sheer at the half-length amidships, as otherwise correction would have to be made for freeboard and the classification societies' numerals. It is -best, then, after fixing the height of bulwark or sheer strake above upper deck to underside of moulding, to run a pencil line parallel to L.W.L. from A. P. to F.P., at which points and above this line the sheer forward and aft should be set up. The amount of sheer will of course depend on the type of vessel, i.e. whether intended for sea or river. In the latter case it is evident the same amount of " spring " would not be required as for over-sea voyages. The standard sheer prescribed by the British freeboard tables will be, however, a good guide, and where this is deemed insufficient or where special cases suggest a departure from these, as in passenger steamers and first class ocean liners, a handy rule and one that gives a very symmetrical sheer is to take one-fifth of the vessel's length in feet, calling the quotient inches which will equal the amount of sheer forward. One-third of this will be the sheer aft, as : — _ = Sheer forward in inches, 5 , Sheer forward . _,, ^ . . . and, = Sheer aft in inches. Inertia Coefficients 51 The amount of sheer having been decided upon with the lowest part, say, at the half-length, the quickest and simplest way to run the sheer line, insuring a fair curve, will be to divide the half- length before and abaft the lowest sheer, into four equal parts, and at each of these points set up the perpendicular heights obtained, as under, postulating in this case that the sheer at F.P. is equal to 82 inches, and the sheer at A. P. 30 inches, giving a mean sheer of 56 inches, as per freeboard tables. 82" x 1.000 = 82" sheer at 4th station = P.P. 82" X .562 = 46" sheer at 3rd station forward of lowest 82" X .250 = 20i" sheer at 2d station forward of " 82" X .0625 = 51" sheer at 1st station forward of «« and for the sheer aft : — 30" X 1.000 = 30" sheer at 4th station = A. P. 30" X .562 = 16|" sheer at 3d station abaft lowest 30" X .250 = 7£" sheer at 2d station abaft " 30" X .0625 = If" sheer at 1st station abaft " By pinning the spline to these spots and adjusting the free ends to the eye, an absolutely fair sheer line may be run in, bearing in mind, however, that in ships with a very full rail line forward, compensation must be given on the sheer to adjust the great dis- parity in the length, of the half-breadth rail line and the same line projected on sheer plan; as, if this be not done, the rail line on model, and of course on the actual ship, will appear as "rounding down." 3d. The contour line of the stem will be very much a matter of individual taste, although above water line it is usual to make it straight unless in special cases. By "straight" is meant "apparently" so, as it is customary to give about f-inch round on face of stem from where it leaves the top of the forefoot curve to stem head, an absolutely straight line adjoining a curve appear- ing as slightly hollow. Also, it is not advisable to make the stem plumb, as the illusion in that case is to make it appear as leaning aft. A rake forward of about twice the moulding of the stem head is common. In outlining the stern and counter the same remarks as to taste apply, care being taken that the counter line where it meets the rudder post is carried by an imaginary curve to harmoniously meet the arch of body post. The counter line, from knuckle moulding to stern post, should be perfectly straight — not hollow. A hollow to this line gives the appearance of an overweighted overhang, and a broken sheer, besides making the plating more difficult to set. 52 The Naval Constructor Dimensions of Figureheads and Lacing Pieces. Fig. 12. A Length of B Size c Depth of D Length of Figure Outside of Stem. Vessel, B.S. op LacijTg Piece. Figure- head. Feet. Inches. Inches. Feet. Inches. 450 121 30^ 9 6 400 12 28| 9 350 1U 26| 8 300 10^ 25 8 250 n 231 7 6 200 9 211 7 150 81 19| 6 100 n 18 6 Note. — Angle o f lacing piece, 45°. The length of overhang of course cannot be arbitrarily fixed, but a very fair proportion for ordinary freighters is ■£$ to -fa of the length. The height of deck or rail at taffrail, or " cock-up," will be dependent on the camber of deck at transom frame (No. 0). The midship camber proportioned to the half-breadth at this frame should be set up and the deck line carried through this spot in a fair curve to taffrail. The height so obtained should be then transferred to body plan, and the deck (or rail line) between No. section and taffrail drawn in as a round of beam curve, from Figureheads 53 which may be obtained the intermediate spots for deck at side (or rail) on sheer plan. 4th. The rail half-breadth will depend on the particular type of ship being designed. In freighters it will be parallel to the center line for probably half the length amidships, whereas in yachts and other fine vessels it will "round " all the way. It is convenient to have rail half-breadths at hand for various types of vessels for, say, ten ordinates with half-end ordinates or which- ever number is adopted as the standard. These should be tabu- lated with the half-breadth amidships as unity, when, with the aid of a slide rule, the half-breadths for the design may be very rapidly proportioned. It will be found convenient to have these for liners, freighters, sound and river steamers, yachts, etc., from good examples of their respective classes. The contour of rail line around taffrail will require careful fairing into the A. P. ordinate spot, and also at center line, where in no case should it be per- fectly straight, the effect of such being a hollow. Neither, on tne other hand, should it come to a "peak" or point, but carefully drawn as an arc of a circle. The knuckle mouldings, whether they be one or more, may with advantage be delineated by tracing the rail line just drawn and transferring it forward to its exact location. By so doing it will be seen that the stern between knuckle and rail lines will develop with a pleasing gradation from " " frame to the upper counter line. Table of Rail Half-Breadths for Various Types. Ordi- nates. "0"=A.P. Ocean Liner. H w . < a go Sail- ing Ships. 03 Oce- anic. .630 .444 .756 .756 .603 .603 .655 * .714 .757 .812 .829 .730 .691 .790 1 .786 .889 .854 .872 .810 .772 .845 2 .882 .990 .918 .934 .910 .875 .912 3 .946 1.000 .951 .977 .967 .955 .965 4 .985 1.000 .988 .994 .979 .995 .987 5 = 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .989 1.000 .991 .994 .979 .978 .971 7 .934 1.000 .965 .965 .960 .930 .944 8 .820 .985 .891 .877 .910 .803 .884 9 .594 .856 .727 .619 .740 .532 .666 9J .358 .572 .576 .366 .515 .298 .404 10 Stem Stem .355 Stem Stem Stem Stem 54 The Naval Constructor 6th. The load water line, as already stated, must circumscribe the area calculated with the aid of the coefficient o. The method of obtaining a has been previously explained. To obtain the form of this water line, and at the same time insure the accuracy of the required enclosed area, it will be found advantageous to prepare a diagram similar to the one opposite, or this one may be used with the aid of proportional compasses. Opposite the value of a for the design in hand half-breadths for ten ordinates may be read off and transferred to the half-breadth plan. Should, however, the line delineated after the spline has been fixed not meet with the designer's individual taste, or where greater fullness or fineness is required for special cases, forward or aft, it will be a very simple matter to modify the line, at the same time observing that what- ever area be cut off at any one point be compensated for elsewhere on the water line, as the offsets taken from the diagram will en- close exactly the area required. Of course the designer may make his own diagram for the number of ordinates he prefers to design with. In any case the run of the line for a few feet forward of the post will require special adjusting when the oxter is being faired. In addition to the diagram, the following table is given of actual load water lines of several types with the coefficients of area of same (a). Load Line Half-Breadths Standardized. Ordi- nates. Fast OCEAN Liner. H w H K O s S3 ft S.S. Yacht. H 1 Sail- ing JShip. H 02 Oce- anic. "0"=A.P. a =.726. a =.857. a =.683. a =.717. a =.797. a =.656. a =.771. Post Post Post Post Post Post Post } .289 .448 .148 .382 .407 .275 .333 1 .531 .770 .479 .642 .678 .483 .631 2 .828 .980 .818 .884 .898 .750 .892 8 .945 1.000 .948 .977 .965 .900 .977 4 .988 1.000 .999 1.000 .992 .980 .995 5 = 1.000 1.000 1.000 .987 1.000 1.000 1.000 G .976 1.000 .928 .932 .989 .900 .980 7 .881 1.000 .793 .791 .955 .760 .942 8 .670 .985 .578 .578 .830 .550 .775 9 .357 .781 .328 .308 .537 .303 .440 H .180 .464 .150 .154 .282 .182 .228 10 Stem Stem Stem Stem Stem Stem Stem L.W.L. Half-Breadths 55 6th. The construction line for the bilge diagonal is variously drawn from rise line or base line ; but the latter is the more use- ful, being adaptable to extremes of types and unaffected by rise of floor line ; i.e., the line should be drawn diagonally across the .65 DIAGRAM OF BILGE DIAGONAL OFFSETS FOR VARIOUS VALUES OF **b" (TEN ORDINATES) $ \ 10 *- jL _s -' o 7 s- / 9 & / 2 / y^ / 7' / / / / 8, / y / Yi (•' / / 91 y y 1 / / / f / / i. / 9/ ** / / y >- — " )'■• <- C. L C F 5H P .7 .75 .8 VALUES OF"b T '(COEFF.OFB.D,) Fig. 13. .85 body plan from the intersection of the base with the half moulded breadth line to center line at load water line height. It is evi- dent that the area enclosed by this line must bear a close relation- 56 The Naval Constructor ship to the prismatic coefficient which varies with p and is equal to -— - to -^ where p ranges from .60 to .82, respectively. .His .yy By determining the value of the bilge diagonal coefficient " 0," and referring to the diagram opposite, the offsets for a line enclos- ing an equivalent area may be taken off and run as a half -breadth line. DIAGRAM OF L. W. L. HALF-BREADTHS FOR VARIOUS VALUES OF "oc" (TEN ORDINATES) ioV 5 OR 1' 5 6 3 7^ 4 r • 8 '~ / / o *> y s s / E 7 - o ? / o J V £ e'- / /' A j i- 9 y / < 5 - / / s s / ' _j 1 H / X L s s -j 3 ,, i j C. 1 .0 : s HI P values 0f"a" (coeff. of l.w.l.) Fig. 14. 7th. The load water line and bilge diagonal half-breadths hav- ing been preliminarily faired, may be lifted off on a slip of pa- per and transferred to body plan construction lines, when there should be no difficulty in drawing in freehand the sections, having the "dead flat" section as one extreme guiding curve and the transom frame as the other. 8th. After the preceding sections have been carefully outlined Body Plan of "Oceanic" 57 BODY PLAN OF "OCEANIC LENGTH B.P. 6&5 f -3l*, B.MLD. 68'-2", D.MLD. 4a'-l" SECTIONS 68.537' APT. STATION No.j STATION No, STATION No. 2 STATION NO. 3 STA TION Noi STATION No. 5 STATION No. 9^ STATION No. ft/H, l~~~~~~^ STATIPN iTION No. 8 STATION No. 7 ELEMENT COEFFICIENTS AREA OF MID. SECT. = 393 BLOCK CO-EFF. J = 666 PRISMATIC CO-EFF. . P = 742 AREA OF L.W.I _a 771 BILGE DIAGONAL -_ _b = 723 RELATION CO-EFF. _£ = Ml Fig. 15. to eye with the guide spots mentioned, the planimeter should be used to take a trial displacement, on the result of which will de- pend how near the designer's judgment has determined the true section line. In any case he cannot have got far away, and a very slight alteration (if any) is all that will be required. 9th. The sheer heights may now be taken from profile and spotted on body plan, level lines being struck across at these 58 The Naval Constructor heights on which to set off the rail half-breadths previously run in plan, as described in paragraph 4. This will enable the completed body plan to be drawn in approximately, from which spots may be obtained to fair up. Having got thus far, the final work of fairing will be a compara- tively easy matter. A buttock line half-way out on the counter will prove a very useful line for this purpose, thereafter taking buttock and water line alternately until the whole body is faired. Where great fairness is required, a complete set of diagonal lines should be run ; but ordinarily this is unnecessary, unless in small craft where the sections are intended directly for the floor with- out further fairing. The following will prove a suitable method for designing and fairing the bossed plating enclosing after-end of shafting. Hav- ing determined the outside diameter of the boss of spectacle frame, lay off the distance to outer edge of boss barrel at forward end of same on the half-breadth plan, as at A. Then take another spot at the fore end of the stern tube equal to the siding of the vessel's bulkhead frame plus one inch clear of the stuffing box flange on the stern tube bulkhead at "C." Through these two spots con- tinue a straight line until it intersects the water plane at the shaft center level "D." The angular space formed by the junction of Bhd Fig. 16. the water plane mentioned and the projected line should then be carefully faired into the eye with a spline, when the resulting line will give you half-breadths at the shaft center height. These half- breadths being transferred to the body plan, radii should be struck through them giving the contour of the bossing, which may be continued freehand into the frame sections above and below the boss, observing that the general tone harmonizes with the outline of spectacle frame previously drawn in, in accordance with the form advocated under that heading. Having outlined the form of bossing on body plan, three diago- nal lines should be struck, the lower one intersecting the arcs forming oxter under spectacle frame, the middle one through the Bossing 59 center of shaft, as shown to diagonal 1J, and the other making a like intersection with the curves of the" slope, as shown on the diagram. These diagonals may now be lifted off and run in the DIAGRAM SHOWING METHOD OF DESIGNING BOSSING. Fig. 17. usual way on half-breadth, faired up, and retransf erred to body plan, thus permitting of same being more accurately delineated, as it will be remembered these were originally drawn freehand. 60 The Naval Constructor Elements of Piston Speed. Class of Steam i:k. to k M • O W w - 3 '■ Ft. per Miu. Type of Propeller. Type of Engine. 400 500 600 700 700 Paddle. River paddle steamer .... River paddle steamer .... River paddle steamer . : . . River paddle steamer .... ( Sea paddle steamer, heavier ) } paddle wheels required . . J 13-15 15-17 18-22 18-22 18-22 ( Side wheels ( feathering it M Inclined it 530 530 600 600 Cargo. Ordinary freight, 300 to 450 . . Ordinary freight, 300 to 450 . . Ordinary freight, 300 to 450 . . Ordinary freight, 300 to 450 . . 8-11 11-13 11-13 11-13 Single screw Twin screw Inverted t« 700 750 Cargo and Passenger. Intermediate steamships, 450-600 | Very large intermediate, cargo I ( and passenger, 600 and over . J 13-16 14-16 Single screw Twin screw Inverted 800 800 950 950 950 Ocean Liners. Passengers and mail .... Passengers and mail .... Passengers and mail .... Passengers and mail .... Passengers and mail .... 16-19 16-19 19-23 19-23 19-23 • Single screw Twin screw Inverted it 800-910 Fast channel & sound steamers 19-23 Twin screw Inverted 950 950 950 Battleships & cruisers, 1st class Battleships & cruisers, 1st class Battleships & cruisers, 1st class 23 23 23 Twin screw M U it «( Inverted tt 1,200 | Torpedo-boat destroyers and ) I scouts ) 30 Twin screw Inverted 5,700 6,000 6,200 7,000 10,000 8,000 Turbine-driven Vessels. \ Turbine river steamer and tur- ) ( bine steam yachts . . . » 1 \ Turbine-driven Atlantic liner, i ( passenger and mail . . . \ i Turbine-driven pass, and mail ) | channel and sound steamers J j Turbine-driven torpedo - boat ) I destroyer and scout . . . J I Turbine-driven torpedo - boat 1 | destroyer and scout ... I (Small 44-ton displacement ex-) j perimental vessel, low coalj ( radius ) 16-22 22 25 30 3G 32 \ Multiple { 6crew Hor. Conip. tt ti Hor. Triple * By permission of Elements of Engines Marine Engines.* 61 Machinery Particulars. _ ji o a> £ M O Number of Cylinders in Each Engine. Cylinder Ratios. Type ot Boilers. Boiler Press. Lbs. Boiler Draft. 2-Comp. Side by side M (> 3-Triple Side by side 1 to 3.5 I : 2.16 : 4.82 II II h Cyl. Loco. Cyl. 100 110 120 160 Nat. Forced it 6.50 7.22 11.00 10.00 9.00 3-Triple 11 M 4-Quad. 1 : 2.65 : 7.1 1 : 2.1 : 4.5 : 9.14 Cyl. 175 200 214 Nat. Forced 4.85 6.00 5.85 5.45 3-Triple 4-Quad. 1 : 2.65 : 7.1 1; 2.07: '4.24: 8.82 Cyl. 200 214 Nat. Assist. 5.12 4.37 3 or 4-Triple 4-Triple 6-Quad. 6-8 Quad. 1 : 2.65 : 6.38 1 : 2.07 : 6.37 1 : 2.08 : 4.16 : 8.71 M M II Cyl. 180 M H 220 Nat. Forced Nat. Forced 7.00 6.00 6.16 5.95 6.25 4-Triple 1 : 2.28 : 5.84 Cyl. 180 Forced 8.00- 9.70 4-Triple 1 : 2.26 : 7.00 Cyl. W. Tube 175 250 Nat. Forced Nat. 8.50 10.00 12.00 4-Triple 1 : 2.36 : 5.50 Yarrow W. Tube 250 Forced 41.00 P? T irson's ) urbine ) No Expansions. 125 135 125 150 Cyl. W. Tube 150 180 170 150 Forced Super- heated steam 12.00 16.00 20.00 55.00 70.00 100.00 J. Calder, B.Sc. 62 The Naval Constructor Level lines as shown at Z 2 > h, h, etc., are now drawn from the point of intersection of frame with diagonals 1 and 2, and the half-breadths taken off at these levels and finally faired-up on half-breadth, when it will be found that the resulting horizontal ribband line, besides acting as a check on the fairness of the di- agonals, will show the " wind " of the shell plating wrapping into oxter and body post and insuring a natural ** snye " without any chance of " gather " or unfairness. The oxter underneath the ship's counter may be faired in a similar manner. Engine Room Lengths Engine Room Lengths. 63 £ fc * 3 8' 6" 10 6 12 9 12 3 13 6 14 16 16 6 17 18 18 4 20 20 20 20 21 21 22 22 22 22 Size of Engines. 10"&20" , 10" 22&40 27 17&26 , 20 15&30 , 21 11, 17, 17 11 10, 16, 26 21 23&46 36 13£, 22£, 36 24 19, 30, 50 30 18, 28, 45 30 21J, 31, 34, 34 24 18£,27, 42 18 21, 34, 59 36 17.26J, 40 24 24, 40, 63 42 22, 36, 57 36 1 9, 32, 52 36 23^, 38, 62 36 24, 38, 62 36 Z fc Sn 22' 0' 23 24 24 26 26 26 26 26 26 6 27 27 6 27 6 27 6 28 28 28 28 28 2 28 3 Size of Engines. 19", 31" 54" 27 42" 40, 65 ttfc 36 28, 39, 57 r 30 36 45, 70 28 54 46. 75 22 48 36, 59 25 42 41*. 68 42 23£, 39, 65 22, 42 35, 59 30, 62 50, 80 28, 54 46, 75 25, 48 42£, 72 T 31, 48 52, 83 25, 54 72 28, 48 46, 76 29, 48 45, 74 32, 48 52, 81 30, 54 50, 80 54 19, 28i, 41, 60 n 42 19£ ,28f,30f,30f , 18 32' 7 ' 34 34 35 35 36 39 7 40 40 42 45 47 6 48 48 59 60 62 6 74 77 6 Size of Engines. 24J", 34£", 49£", -()" 36" 32|, 59, 92 42 24, 34, 48, 68 T. 42 32£, 59, 92 54 40, 66, 106 72 32, 52, 60, 60 42 29, 46, 72 48 31, 43, 60, 86 T. 54 33£, 51, 78 48 34f, 53, 63, 63 T. 'J' 48 30, 43, 63, 89 T. 6 60 32, 45£, 66, 66, 6 54 35, 50, 70, 100 T. 77 28J, 28J, 55, 77, 77 60 43, 69, 79 60 40£, 55, 77, 77, 77 60 40£, 55, 77, 77, 77 54 35|, 50£, 73J, 105 69 49£, 73, 95, 95, 95 60 37, 37, 79, 98, 98^ 69 Twin sets noted with " T.' 64 The Naval Constructor CHAPTER III. THE PREPARATION OP SPECEflCATlONS. Too much care cannot be expended in the drafting of the hull specification. Clearness and conciseness should be aimed at consistent with an embodiment of all details of hull, fittings, and outfits supposed to be supplied, and all repetition or ambiguity of phraseology carefully avoided. Hampering restrictions should be left out. Know your requirements and state them distinctly. As in all other ship construction work, it will pay to have a definite routine or system in which to draft the specification. Of course, it is obviously impossible to have a standard specification which shall apply to all ships, as vessels are so diverse in their types, design, construction, and equipment as to make this an impossibility. But by keeping a routine list of headings of paragraphs before one, and taking these in rotation when drafting the clauses, the liability to omit important requirements is reduced to a minimum, besides the saving in time and distraction of thoughts through having to recollect what comes next. For this purpose the following headings have been selected which will apply to ordinary vessels; Of course, for special types these will require modifications and additions which will suggest themselves. Specification Headings. Title giving type of vessel. character of erections, 1. Dimensions, moulded number of masts. Num- length, breadth and ber of passengers, de- depth, depth of hold, load scription of housing of draft and deadweight. passengers, officers, and 2. Classification. The Govern- crew. Nature of cargo ment laws to which the and handling appliances, vessel and her equipment Location of machinery, are to conform, also full and any special features particulars of the class of the vessel, she is to take at the 4. Material of hull and rivets. Classification Society 5. Keel, and centre girder in concerned. double bottom ships. 3. General Description. Type 6. Bilge or side fenders and of stem and stern, mouldings, docking keels, number of decks, laid or 7. Stem, otherwise, length and 8. Stern frame. Specification Headings 65 9. Shaft brackets. 10. Kudder and stock (also trunk and bearing). 11. Shell plating. 12. Inner bottom, including plating, side girders, floors and margin plate. 13. Scantling in machinery space. 14. Peak tanks. 15. Deep tanks. 16. E. W. storage tanks. 17. Steel decks and flats. 18. Transverse bulkheads. 19. Longitudinal bulkheads. 20. Bunkers, oil or coal. 21. Engine and boiler casings. 22. Shaft tunnels. 23. Oil trunks, expansion. 24. Centre keelson J £j£S2S 25. Side keelsons } j^ med 26. Hold and 'tween deck stringers. 27. Panting arrangements. 28. Frames and reverse frames, in double bottom, up sides and at ends. 29. Floors, . throughout in single-bottomed ships, at ends and tail brackets in double bottom ships, also reference to No. 12. 30. Web frames. 31. Deck beams and knee brackets. 32. Stanchions to beams. 33. Strong beams in E. and B. space. 34. Hatchways and coamings, in oil or cargo spaces, covers, fore and afters, bearers, etc. 35. Cargo and coal ports. 36. Grain trimming hatches. 37. Chain lockers. 38. Machinery Foundations; main, auxiliary and deck machinery, also boiler saddles and shaft and thrust bearing seats. 39. Sheet steel bulkheads. 40. Steel deck houses, other than erections. 41. Bridges, navigating or dock- ing. 42. Steel masts. 43. Steel kingposts. 44. Steel derricks, spars, etc. 45. Wood masts, kingposts and spars. 46. Wood decks. 47. Wood deck houses. 48. Ceiling and sparring. 49. Boat stowage. 50. Anchor stowage. 51. Watertight doors and scut- tles. General description of joiner work, including entrances and . stairways : 52. In passengers' quarters. 53. In officers' quarters. 54. In crew's quarters. 55. Pantry accommodations. 56. Galley accommodations. 57. Ice room. 58. Sidelights and decklights; also borrowed lights. 59. Cattle fittings. 60. Hawse pipes. 61. Bollards and fairleads. 62. Hold ladders. 63. Ladders to erections and bridges. 64. Davits, boat and anchor, also provision or coaling davits. 65. Bails, bulwarks, also rail and awning stanchions. 66. Standing and running rig- ging, including cargo boom handling gear. 66 The Naval Constructor 67. Sails, covers, and awnings. 97. Trim and stability. 68. Cement and tiling. 98. Plans to be furnished own- 69. Paint work. ers. 70. Heating system. Capacity and dead- 71. Lighting system. weight. 72. Ventilating. General arrangement. 72a. Refrigerating system. Cabin booking plans. 73. Deck Machinery, including Piping plans. windlass, winches and Stability curves and capstan, also steam and information. exhaust piping. 99. Docking. 74. Fresh and salt water ser- 100. Trial trips. vice. 101. Inspection fees ("class, 75. Fire, pumping and drain- etc). ing system. 102. General clause relating to 75a ;. Cargo oil system. material, workmanship, 76. Scuppers, from all exposed inspection by owners, houses, etc., and from alterations, extras, etc. sanitary quarters. 77. Engine room and docking Flags. telegraphs. National colors. 77a . Steering gear. House flags, and burgee with 78. Anchors, chains, and line name. outfit. International signal code. 79. Boats and outfits. 80. Flags, etc. Boat Outfit. 81. Hose, fire and wash deck, Ash oars, thole pins or rowlocks. also fire buckets. Rudder (lanyard). 82. Oil tanks, for lamps, etc. Tiller (lanyard). 83. Steaming lights. Painter, 5 fathom line. 84. Lamps and lanterns, also Cable, 20 fathom line. rockets, etc. Boat hook. 85. Navigating instruments. Water breakers. 86. Boatswain's stores. Bread tank. 87. Carpenter's stores. Plugs for bung hole ; 2, with 88. Cargo handling gear, slings, chaiil. hooks, etc. One anchor. 89. Cook's or galley outfit. One sea anchor. 90. Cabin outfit. One bailer. 91. Cutlery outfit. One mast yard and sail. 92. Crockery and glass. One compass 4" card in case. 93. Table linen. Four oil lanterns to burn 8 94. Bed linen and bedding. hours. 95. Spare glasses for side-lights Four oil distributers, 1 gallon in passenger ships. each. 96. Galvanizing. Twelve boat hatchets. Specification Headings 67 Boatswain's Stores. Watch tackles. Relieving tackles. Luff tackles. Spare blocks, double and. single, assorted. Spare sheaves, for boat falls. Snatch blocks. Cargo gins. Deck scrubbers. Wood fenders, with lanyards. Cork fenders, with lanyards. Marline spikes. Crowbars. Chain hooks. Chain slings. Hair crate hooks. Screw shackles. Pairs of grip-hooks. Pairs of case-hooks. Coir brooms and handles. Mops. Ballast shovels. Scrapers, triangular. Scrapers, steel file. Set of funnel blocks and boards. Boatswain's chairs, one to each mast. Pilot ladder. Five-inch portable fire engine pump with hose. Bath bricks. Hand spikes. Paint scrubbers. Pairs of handcuffs. Branding iron. Paint brushes, assorted. Paint pots, one-half gallon. Squeegees, large. Scraping box, tin. Sewing palms. Needles. Beam clamps. Whitewash brushes. Carpenter's stores. " Propeller " notice boards. " Smoking " notice boards. ' ' No admittance ' ' notice boards. Pump hook, jointed. Chain punches. Pitch pot, 3 gals, and ladle. Tar bucket. Grindstone and trough, 18" diam. Shifting spanner, large. Ring spanners, to fit bunker plates, etc. Keys for cargo ports. " " sidelights. " " coal ports. " " mushroom ventilators. Rim spanner for sidelights. Spanners for deep tank hatch bolts. Rail straightener, 3' 6" long. Rod sounding rods. Flexible sounding rods, 2' 0" long. Caulking tools. Caulking mallet. Spare hatch wedges. Capstan bars and rack, Monkey wrench. Wheel-house axes, large. Tools in chest, with ship's name on ; chest and tools. One 26" hand saw. One crosscut. One auger \\". One purger \\". One adze. One hammer. Two top mawls. Two screwdrivers. One jack plane. One hand plane. Three chisels, assorted. Three gimlets, assorted. 68 The Naval Constructor J oil. Steaming Lights. Two masthead ^^ ^ Starboard J for electric. do. do. galvanized iron, for oil. Two riding lights One overtaking light Three ruby lights Three black balls. Spare glasses for lamps, 2 for each. Carriers and halliards for mast- head and riding lights. Lamps and lanterns. "Exit" lamps in passengers' quarters. Dark lanterns (3 for large ships). Cargo lanterns (12 for large ships). White lanterns (2 for large ships). Hurricane lights (5 for large ships) with 3 spare glasses. Lamps for saloon and officers' rooms in small ships. Lamp scissors. Oil funnels. Lamp wicks. Rockets, signal cannon, to be supplied as required by U. S. laws, together with owner's night signals, etc. Navigating Instruments. Standard compass and stand. Ten inch spirit compasses in navigating positions. One spare card. Boat's compasses, 4" card. Sounding machine, or deep sea lead (28 lbs.), line and reel. 130 fathoms. Hand lead (16 lbs.), line, and reel, 30 fathoms. Pelorus. Clocks. Aneroid barometers. Telescope. Binoculars, marine. Log slates. Parallel ruler. Pair dividers. Chart weights. Foghorn. Tarpaulins. Usually 3 to each weather deck hatch ; 1 to others. One rubber sheet to hatches on which cattle are carried. Covers to all sails and instru- ments, wheels, etc., in exposed positions ; weather cloths to shelter passenger decks in large passenger ships. Bakery Outfit. Two biscuit tubes. One biscuit forcer. One apple corer. One bread rasp. One galvanized bucket. One buckwheat jug. Six cake hoops. One hundred and twenty corn bread tins. One dough knife. One scraper. One sugar dredger. One flour dredger. Two flour scoops. One tin opener. One casserole mould. Eighteen (quart) jelly moulds. Six pudding moulds with lids. Seventy-two muffin rings. One bread grater. Specification Headings 69 One nutmeg grater. One barm can. One palette knife. Two sets cutlet paste cutters. Six paste brushes. Two rolling pins. to 14 One flour sieve. One spice box complete. Twelve bread tins. Two French roll tins. Twenty-four open tart tins. One hundred and forty-four patty tins. Six rice pudding tins. Six roll tins. Eighteen sandwich bread tins, with lids. Twenty-four sponge cake frames. One water can. Two egg whisks. One set icing pipes. One icing bag. One enameled whisking bowl. One patent egg whisk. One egg basket. One suet machine. One bread knife. Twelve large bread sheets. One bread prover, galvanized iron, 6' 0" x 2' 5" x V 5" with copper steam pipe. Galley Outfit, Braising pans, copper, with wire nets. Water cans. Butcher's choppers. Cook's saws. Tin colanders. Chopping block. Dippers, tin. Aluminum stew pans, with handles and lid. Sauce pans (enameled iron), 1 qt., 3 pt., and 2 qt. Oval fish kettle and lid. Potato masher. Dog baskets, wicker, tin lined. Sieves, hair mesh. Sieves, wire mesh. Sauce ladles, small. Tin opener. Beef press. Pea soup masher, tammy sieve. Copper stew pans, 6"-16" diam., with long handles, and lids with long handles. Stock bucket. Stock pot. Omelette pans, copper. Prying pans, round. Prying pans, oval. Tormentors. Pokers. Shovels. Rakes. Gridirons, double. Gridirons, large. Sets of skewers, assorted sizes. Egg basket. Glaze pot, copper and brush. Pour-inch basket ladle, wire. Frying baskets, round, wire. Cook's forks. Salt box. Plour box. Wire gravy strainer. Grill tins. Two gallon copper kettle. Jelly bag. Knives, French. Knives, butcher's. Knives, mincing. Knives, oyster. Knives, palette. Knives, potato. Bill of fare frame. Pie pans, 12" x 8", enameled. Pie pans, 8" x 6". 70 The Naval Constructor Steak tongs. Store tins. Stove top hooks. Porridge whisks, strong wire. Cutlet bat. Vegetable cutters. Vegetable scoops. Brawn moulds. Tongue press. Pepper dredgers. Hot pot tins. Plate carriers. Bread grater. Flour dredge. Iron ladles. Larding needles. Trussing needles. Potato masher. Egg slicer. Fish slicer. Spoons, iron. Spoons, wood. Steel. Ship's Galley Outfit. Mess kids, large,- small and oval. Square steamers. One square coffee boiler (28 gal.) B. T. Oval boilers (15 gal.) B. T. Roast tins. Saucepans, iron enameled. One round steam boiler (50 gal.) cast iron with large brass tap. Range. Colanders. Shovel. Poker. Buckets, galvanized irov. Rake. Tormentor. Large ladle. Square duff tins. Chopping block. Pantry Outfit. Pair butter spades. Meat choppers. Poultry choppers. One clock. Dish covers, B. M. Egg slicers. Ice pricker. Jugs (enameled), 1 gallon. Two bread knives. Two carving knives. Two French knives. Two ham knives. Pairs knives and forks for poul try. Plate covers, tin. Iron spoons, 18" long. Lemon squeezer. Tin openers. Slop receivers, 20 gallons. Soup ladles. Soup tureens, B. T. Steel. Waiter's Carpathian. Wire whisks 12"-18". Milk cans with lid and spout, 2 gallons. Steam carving table 6' 0" x 2' 6", with tin top, 3 large, 2 medium and 2 small wells. Steam egg boiler. Steam bain-marie, 4 stew pans, brass frame. One coffee boiler, 10 gallons, E.P. One hot water boiler, 15 gal- lons E. P. Whisking bowl. Water cooler. Electroplate and Cutlery. Asparagus tongs. Butter coolers. Cheese scoops. Specification Headings 71 Tea pots, 3 pints. Tea pots, 1| pints. Coffee pots, 2 pints. Coffee pots, 1 pint. Entree dishes, 10" oval. Entree dish covers, with mov- able handles. Vegetable dishes. Vegetable dish covers, with movable handles. Ice tongs. Sauce frames (Worcestershire, etc.). Prs. fish carvers. Fish forks. Fruit forks. Dessert forks. Pickle forks. Butter knives. Fish knives. Dessert spoons. Soup spoons. Sauce ladles. Soup ladles. Finger bowls. Ice pails. Napkin rings, numbered. Prs. nut crackers. Toast racks, large. Toast racks, small. Fruit knives. Mustard spoons. Salt spoons. Tea spoons. Egg spoons. Table spoons. Sugar bowls, large. " bowls, small. " tongs, small. " tongs, large. Sardine tongs. Cream jugs, large. Cream jugs, small. Fine sugar sifters, gilt bowls. Fine sugar bowls. Syrup jugs, hinged lids. Hot water jugs, 1 pint. Tureen and covers for soup, 6 quarts. Tureen and covers for sauce. Fruit dishes, gilt, large 12" long. Fruit dishes, gilt, small, 9\" long. Wine corks. Waiters, 8", 10", 12". Wine funnel. Glass. Celery glasses. Tumblers. Soda glasses. Champagne glasses. Claret glasses. Liqueur glasses. Port and Sherry glasses. Cocktail glasses. Bedroom tumblers. Pickle jars. Glass dishes, small oval. " " large oval. " " large round. " " small round. " " ground glass for ice cream. Water decanters, saloon. Water decanters, bedroom. Salt casters. Pepper casters, E. P. tops. Red pepper casters, E. P. tops. Salad bowls. China. Dessert plates. Tea cups, afternoon. Tea saucers, afternoon. Earthenware. Breakfast cups and saucers. Tea cups and saucers. After-dinner coffee cups and saucers. 72 The Naval Constructor Egg cups, d. e. Towels, bath. Dinner plates. Dusters. Soup plates. Covers for saloon chairs and Cheese plates. settees. Slop basins. Jardinieres, large. General Stores. Jardinieres, small. Chambers, bedroom. Spring balance. Milk jugs. Scales and weights. Linen. Handy billy. Brooms. Two prs. sheets to each berth. Brushes, banister. One pr. blankets to each berth. Dustpans and brushes. One bed-spread to each berth. Shoe brushes. Two pillow cases to each Buckets. pillow. Mops. Two pillows to each berth. Cuspidores and linings. One mattress, over spring mat- Dinner bell. tress. Cork screws. One mattress cover. Knife board. Three sets tablecloths. Table gong. Napkins. Deck chairs. Table covers, baize, red, etc. Wicker chairs. Glass cloths. Blotting pads. Towels, pantry. Bibles, etc. " passenger, four to each. Chess men, etc. 44 officers, four to each. Library books. " lavatories. Printing press. Freeboard 73 CHAPTER IV. FREEBOARD. In the following tables the word Freeboard denotes the height of the side of a ship above the waterline at the middle of her length, measured from the top of the deck at the side, or, in cases where a waterway is fitted, from the curved line of the top of the deck continued through to the side. The freeboards and the corresponding percentages of reserve buoyancy neces- sary for flush-deck steamers not having spar or awning decks and for flush-deck sailing vessels are given in Tables A and D for vessels of these classes and of various dimensions and pro- portions. The freeboards necessary for spar- and awning-deck steamers are given in Tables B and C. The latter are deter- mined by considerations of structural strength, and they de- note the limitations to depth of loading which are thereby imposed upon first-class vessels of these types. The free- boards and percentages of reserve buoyancy thus obtained be- ing in excess of what would otherwise be required, the amount of such percentages are not given in Tables B and C. The exact freeboard required for a given ship of standard proportions belonging to either of the classes comprised in Tables A and D may be calculated by constructing a displace- ment scale to the height of the deck to which the freeboard is measured, so as to give the whole external volume up to the upper surface of that deck. The percentage of the total volume which is given in the tables as the reserve buoyancy for a vessel of given type and dimensions will be the amount of volume that must be left out of the water. If a waterline be drawn up upon the displacement scale aforesaid to cut off the given per- centage of total volume, the height of side above this line will be the freeboard required. In order to simplify and reduce the work that would be in- volved by the above mode of determining the waterline and the consequent freeboard that correspond to a given percentage of reserve buoyancy, an approximate method is adopted in the following tables, which enables the freeboard of a vessel to be calculated with a sufficient degree of accuracy for all ordinary working purposes. The use of this method not" only saves the time and labor that would be involved by making a complete displacement scale for the whole external volume of the ship, but, what is much more important, it makes the tables easily and directly applicable in cases where such a displacement 74 The Naval Constructor scale for a vessel is not at hand, or where the data requisite for constructing one are not procurable. In this approximate method the form of the ship is taken into account by means of proportionate quantities, which are termed coefficients of fineness, instead of by the exact volumes that a displacement scale would give. It is found that the whole internal volume of a ship as measured for register tonnage divided by the product of the length, breadth, and depth, meas- ured as described in the following clauses, 1, 2, and 3, gives a fractional quantity of coefficient which bears a nearly constant relation to the quantity that would be obtained by dividing the whole external volume below the upper surface of the deck by the product of the length, breadth, and depth. This fractional quantity is called the "coefficient of fineness" for freeboard purposes, and it serves the same practical object, when com- bined with the dimensions of the ship in the manner explained in the tables, as the volume itself would do. In applying such an approximate method as the above, it is necessary to connect the coefficients of fineness given in the tables with a standard sheer and round of beam. The standard scales for sheer and round of beam that have been adapted for this purpose are given in Clauses 18 and 19 hereafter. De- scriptions are also there given of the corrections that should be made for deviations from these standard amounts. The freeboards given in the tables are for flush-deck vessels in all cases. Such reductions in freeboard as may be allowed for deck erections of various kinds and sizes in steamers not having spar or awning decks and in sailing vessels are de- scribed in paragraphs 11, 12, 13, 14, 15, 16, and 17. No reduction of freeboard should be allowed on account of deck erections in spar-deck and awning-deck steamers, except in spar-deck vessels in which an allowance may be made for a long bridge house, see pp. 21 and 22. Tables A and D give the minimum freeboards for first-class iron and steel vessels, the strength of which is at least equal to the requirements of the 100a class in Lloyd's Register for three- deck and smaller vessels. The freeboard of all other iron and steel vessels, classed or unclassed, should be regulated by the same standard, the increase of freeboard required in each case being determined by the limit at which the stress per square inch upon the material of the hull amidships shall not exceed that of the standard class, of the same proportions, form, and moulded depth, when loaded to the freeboards required by Tables A and D. Tables B and C give the freeboards for ves- sels built in accordance with, or equal to, the requirements of Lloyd's Register for the spar- and awning-deck classes, and are Freeboard 75 subject to the conditions just stated for any modifications of strength in excess of diminution of the requirements of their respective classes. 1. Length. — The length of the vessel is measured on the load line from the fore side of the stem to the aft side of the sternpost in sailing vessels, and to the aft side of the aft post in steamers. 2. Breadth. — The breadth used in obtaining the coefficient of fineness is the extreme breadth measured to the outside of plank or plating as given on the certificate of the Ship's Regis- try. 3. Depth of Hold. — The depth used in obtaining the coefficient of fineness is the depth of hold as given on the Certif- icate of the Ship's Registry. This dimension is subject to modification in determining the coefficient of fineness as ex- plained in Clause 4. 4. Coefficient of Fineness. — The coefficient of fineness in one-, two-, and three-deck and spar-deck vessels is found by dividing 100 times the gross registered tonnage of the vessel below the upper deck by the product of the length, breadth, and depth of hold. In awning-deck vessels the registered depth and tonnage are taken below the main deck. (a) It is of importance in the application of the rules and tables of freeboard that the coefficient of fineness deduced from the under-deck tonnage and the principal dimensions to be a correct index to the vessel's relative fullness of form, and that a change in any of those elements which affect the coefficient, determined in accordance with the rule set forth, should be considered, and the necessary correction, having regard to the special circumstances of the case, introduced. Among the cases that have from time to time come under notice are the following: (b) Vessel Having a Cellular Bottom Throughout, or Floors of Greater Depth than those Usually Fitted. — In such a case the co- efficient as determined from the under-deck tonnage is in most instances slightly greater than it would be if the vessel were framed on the ordinary transverse system with floors of the usual depth. No general rule can be given for guidance, but it is not difficult, if the depth and slope of the top of the cellular bottom or floor be compared on the midship section with the depth and slope of an ordinary floor, to determine very closely the amount of the correction necessary. (c) Vessel Constructed with Floors of the Ordinary Kind, but with a Cellular Bottom for a -part of the Length Amidships Under 76 The Naval Constructor the Engines and Boilers. — In such case the registered under- deck tonnage is smaller than it would be if the vessel were framed with ordinary floors throughout, the difference being the tonnage of the space between the bottom of the cellular bottom in the part amidships and the level of the ordinary floor. The depth of hold is also measured by the customs officials to the top of the cellular bottom, and this depth is in- serted in the register. Under such circumstances, in order to arrive at the coefficient of fineness the vessel would have, if built on the ordinary system throughout and for which the tables are framed, the tonnage of the volume between the top of the cellular bottom and the level of the ordinary floor should be calculated and added to the registered under-deck tonnage. The tonnage so corrected used in conjunction with the depth of hold to the top of the ordinary floor, gives the coefficient to be used in the tables. (d) Vessel Constructed with a Cellular Bottom Throughout the the Fore and After Holds, but wiih Floors of the Ordinary Kind Fitted for a Part of the Length Amidships Under the Engines and Boilers. — In such a case the tonnage of the space between the top of the ordinary floors in the part amidships and the top of the cellular bottom, if made continuous, should be estimated and deducted from the registered under-deck tonnage and the remainder employed in conjunction with the depth of hold to the top of the cellular bottom in determining the coefficient of fineness. (e) Other cases may in practice arise in which the registered under-deck tonnage, or the registered depth of hold, or registered breadth require modification before being used in the determi- nation of the coefficient of fineness, but little difficulty will be experienced in making the necessary correction if it be re- membered that the coefficient sought is the coefficient the vessel would have if framed on the ordinary transverse system. 5. Moulded Depth. — The moulded depth of an iron or steel vessel, as given in the tables, is the perpendicular depth taken from the top of the upper deck beam at side, at the middle of the length of the vessel, to the top of the keel and the bottom of the frame at the middle fine, except in spar- and awning- deck vessels, in which the depth is measured from the top of the main-deck beams. In wooden and composite vessels the moulded depth is taken to be the perpendicular depth from the top of the upper-deck beam at the side of the vessel amidships to the lower edge of the rabbet at the keel. (a) The form at the lower part of the midship transverse sec- tion of many wooden and composite vessels being of a hollow Freeboard 77 character, as in cases where thick garboard strakes are fitted, the moulded depth in such instances should be measured from the point where the line of the flat of the bottom continued cuts the keel. 6. Freeboard. — The moulded depth, taken as above de- scribed, is that used in the tables for ascertaining the amount of reserve buoyancy and corresponding freeboard in vessels having a wood deck, and the freeboard is measured from the top of the wood deck at side, at the middle of the length of the vessel. (a) On the same principle, in flush-deck vessels, other than spar or awning decked, and in vessels fitted with short poop and forecastle, having an iron upper deck, not covered with wood, the usual thickness of a wood deck should be deducted from the moulded depth of the vessel measured as above, and the amount of reserve buoyancy and corresponding freeboard taken from the column in the tables corresponding with this diminished moulded depth : Example. — In a steamer fitted with an iron upper deck, not covered with wood, and having a moulded depth of 19 ft. 10 ins., four inches, or the usual thickness of a wood deck, must be deducted from this, leaving a depth of 19 ft. 6 ins. The freeboard of such a vessel with a coefficient of fine- ness of 0.76, taken from the column under 19 ft. 6 ins., is 3 ft. 8£ ins., which should be measured from the top of the iron upper deck. (6) In spar-deck vessels having iron spar decks and in awning- deck vessels having iron main decks, the freeboard required by the tables should be measured as if those decks were wood covered. Also in vessels where r 7 o, or more, of the main deck is covered by substantial erections, the freeboard found from the tables should be measured amidships from a wood deck, whether the deck be of wood or iron. In applying this principle to vessels having shorter lengths of substantial enclosed erec- tions the reduction in freeboard, in consideration of its being measured from the iron deck, is to be regulated in proportion to the length of the deck covered by such erections. Thus in a vessel having erections covering t 6 q of the length, the reduction is r % of 3h inches, or 2 inches. 7. For vessels which trim very much by the stern, through the engines being fitted aft, the freeboard, as ascertained from the tables, if set off amidships would not cut off the amount of surplus buoyancy deemed necessary, and in such cases the suitable freeboard amidships could only be determined after full information is obtained regarding the vessel's trim. 78 The Naval Constructor 8. The following example will illustrate the general applica- tion of the tables: In a steamer of the following dimensions, viz., length, 204 ft.; breadth extreme, 29 ft.; depth of hold, 16.0 ft.; registered tonnage under deck, 628 tons; and moulded depth, 17.0 ft.; the under deck capacity in cubic feet is 68,200; by dividing this by 94,656, that is, the product of the length, breadth, and depth of hold, the quotient is 0.72, or the coefficient of fineness. If we now refer to Table A at 17.0 ft. moulded depth and trace the line opposite the coefficient 0.72 to the column cor- responding with this depth, it is found that the winter freeboard given for a first-class steam vessel without erections, whose length is twelve times the moulded depth, is 2 ft. 11 ins., cor- responding with a reserve buoyancy of 25 per cent of the total bulk. 9. Vessels of Extreme Proportions. — For vessels whose length is greater or less than that of the vessel of the same moulded depth for which the tables are framed, the freeboard should be increased or diminished as specified in the footnote to the tables. Thus, if the vessel in the example clause 8 were 224 ft. long, the winter freeboard required would be 2 ft. 11 ins. plus 2 ins. or 3 ft. 1 in. For steam vessels coming under para- graphs 11 and 12 with enclosed erections extending over y 6 ^, or more, of the length of the vessel, the correction for length should be one-half that specified in Tables A. 10. Breadth and Depth. — In framing the tables it has been assumed that the relation between the breadth and depth is such as to ensure safety at sea with the freeboard assigned when the vessel is laden with homogeneous cargo; for vessels of less relative breadth the freeboard should be so increased as to provide a sufficient range of stability, or other means adopted to secure the same. 1 1 . Erections on Deck. — For steam vessels with top- gallant forecastles having long poops, or raised quarter-decks connected with bridge-houses, covering in the engine and boiler openings, the latter being entered from the top, and having an efficiently constructed iron bulkhead at the fore end, a deduc- tion may be made from the freeboard given in the tables, ac- cording to the following scale: (a) When the combined length of the poop, or raised quarter- deck, bridge-house, and top-gallant forecastle is: ffi of the length of the vessel, deduct 90 per cent of the difference between freeboards in Tables A (after correction for sheer) and Tables C. Freeboard 79 T 9 o of the length of the vessel, deduct 85 per cent of the differ- ence between freeboards in Tables A (after correction for sheer) and Tables C. T Vn of the length of the vessel, deduct 80 per cent of the difference between freeboards in Tables A (after correction for sheer) and Tables C. T 8 7 of the length of the vessel, deduct 70 per cent of the differ- ence between freeboards in Tables A (after correction for sheer) and Tables C. T 7 o of the length of the vessel, deduct 55 per cent of the differ- ence between freeboards in Tables A (after correction for sheer) and Tables C. T 6 o of the length of the vessel, deduct 40 per cent of the differ- ence between freeboards in Tables A (after correction for sheer) and Tables C. When the engine and boiler openings are protected only by a long raised quarter-deck, a less reduction in freeboard will be allowed. (6) For intermediate lengths of erections the amount of the reduction in freeboard should be ascertained by interpolation. (c) The above scale of allowance is prepared for vessels hav- ing long poops or raised quarter-decks 3 ft. high for vessels having a length of 100 ft., 4 ft. high at a length of 250 ft., and G ft. high at a length of 400 ft. and upwards. Intermediate lengths in proportion. For raised quarter-decks of less height the length allowed is to be in proportion to the standard of height. (d) It is to be understood in the application of this scale of allowance for erections on deck to vessels with long poops or with raised quarter-decks and bridge-houses combined, that the deduction is a maximum deduction, applicable only to vessels of these types in which the erections are of a most sub- stantial character, the deck openings most effectually pro- tected, and the crew are either berthed in the bridge-house, or the arrangements to enable them to get backwards and for- wards from their quarters are of a satisfactory character. For other vessels of the same class the amount of the deduction should be fixed only after a careful survey. Also such vessels when employed in the Atlantic trade will require to have specially provided greater freeboard than that given in the tables. (e) A sufficient number of clearing ports, as large as practi- cable and with shutters properly hung, should be formed in the bulwarks of these vessels, between the forecastle and the bridge-house for the purpose of speedily clearing this part of the deck of water. 80 The Naval Constructor 12. When the erections on a vessel consist of a top-gallant forecastle, a short poop having an efficient bulkhead, and bridge-house disconnected, the latter in steamers covering th€ engine and boiler openings and being efficiently enclosed with an iron bulkhead at each end, a deduction may be made from the freeboard given in the tables according to the following scale: (a) When the combined length of the erection is: xVir of the length of the vessel, deduct 75 per cent of the dif- ference between freeboards in Tables A (after correction foi sheer) and Tables C. f$r of the length of the vessel, deduct 70 per cent of the difference between freeboards in Tables A (after correction foi sheer) and Tables C. T V°(j of the length of the vessel, deduct 60 per cent of the difference between the freeboards in Tables A (after correction for sheer) and Tables C. ■£$$ of the length of the vessel, deduct 50 per cent of the difference between the freeboards in Tables A (after correction for sheer) and Tables C. T %% of the length of the vessel, deduct 40 per cent of the difference between the freeboards in Tables A (after correctior for sheer) and Tables C. yVu of the length of the vessel, deduct 32 per cent of the difference between the freeboards in Tables A (after correctior for sheer and length) and Tables C (after correction for length) 13. When the erections on a vessel consist of a top-gallanl forecastle and bridge-house only, the latter in steamers cover ing the engine and boiler openings and being efficiently encloser with an iron bulkhead at each end, a deduction may be mad( from the freeboard given in the tables according to the follow- ing scale: (a) When the combined length of the erections is: T 5 ^ of the length of the vessel, deduct 30 per cent of th( difference between the freeboards in Tables A (after correctior for sheer and length) and Tables C (after correction for length) T % of the length of the vessel, deduct 24 per cent of the differ ence between the freeboards in Tables A (after correction foi sheer and length) and Tables C (after correction for length). ■fa of the length of the vessel, deduct 10 per cent of the differ ence between the freeboards in Tables A (after correction foi sheer and length) and Tables C (after correction for length). 14. When the erections on a steam vessel consist of a shori poop or raised quarter-deck of a height not less than that laic down in paragraph 11 and top-gallant forecastle only, th< Freeboard 81 former being enclosed at the fore end with an efficient bulk- head, and when the engine and boiler openings are entirely covered either by the poop or raised quarter-deck or by a strong iron or steel deck-house enclosing the machinery casings, a de- duction may be made from the freeboard given in the tables according to the following scale: When the combined length of the erection is: | of the length of the vessel, deduct 32 per cent of the differ- ence between the freeboards in Table A (after correction for length) and Table C (after correction for length). f of the length of the vessel, deduct 24 per cent of the dif- ference between the freeboards in Table A (after correction for length) and Table C (after correction for length). f of the length of the vessel, deduct 16 per cent of the differ- ence between the freeboards in Table A (after correction for length) and Table C (after correction for length). £ of the length of the vessel, deduct 8 per cent of the differ- ence between the freeboards in Table A (after correction for length) and Table C (after correction for length) . For erections which cover less than | of the length of the vessel, the allowance should be in proportion to that for f covered. When, however, the engine and boiler openings are not entirely covered by the poop or quarter-deck or by a strong iron or steel deck-house, the allowance for erections should be xV of that provided by the foregoing scale. 15. When a steam vessel is fitted with a top-gallant forecastle only, the reduction of freeboard is to be in accordance with the preceding paragraph for a poop not covering the engine and boiler openings and a forecastle of the same combined length. When there is a short poop only, or a raised quarter-deck of a height not less than that laid down in paragraph 11, enclosed at the forward end with an efficient bulkhead and covering the engine and boiler openings, the deduction from the freeboard is to be half the allowance that is given for a poop or quarter- deck of the same character and a forecastle having the same combined length. When the poop or raised quarter-deck does not cover the engine and boiler openings T % of the foregoing allowance is to be given. 16. When the erections on a sailing vessel consist of a short poop and top-gallant forecastle only, the former enclosed at the fore-end with an efficient bulkhead, the deduction from the free- board given in the tables should be according to the following scale: When the combined length of the erection is: | of the length of the vessel, deduct 10 per cent of the reserve 82 The Naval Constructor buoyancy, or 12 per cent of the freeboard required for the flush- decked vessel after correction for length; f of the length of the vessel, deduct 8 per cent of the reserve buoyancy, or 10 per cent of the freeboard required for the vessel flush-decked after correction for length; | of the length of the vessel, deduct 6 per cent of the reserve buoyancy, or 8 per cent of the freeboard required for the vessel flush-decked after correction for length; \ of the length of the vessel, deduct 4 per cent of the reserve buoy- ancy, or 6 per cent of the freeboard required for the flush-decked vessel after correction for length. In cases where less than \ of the length of the vessel is covered by erections, the allowance should be in proportion to that given for erections covering \ of the length. 17. When a sailing vessel is fitted with a top-gallant forecastle only, the reduction in reserve buoyancy should be one-half that pre- scribed by the previous paragraph for the case where, in addition to the forecastle, the vessel is fitted with a poop of the same length. When there is a poop only, the allowance is to be half of that which in this paragraph is given for a forecastle only of the same length. 18. Sheer. — The tables are framed for vessels having a mean sheer of deck measured at the side, as shown in the fol- lowing table: Length Over Which Sheer is Measured. 100 150 200 250 300 350 400 Mean Sheer in Inches Over the Length Specified. Flush-deck Vessels. — Sheer to be measured abreast stem and sternpost 20 14 14| 25 18 18| 30 22 23 35 26 27 40 30 31 45 34 35§ 50 38 40 Vessels having short poops and fore- castles. — Sheer to be measured at points distant £ the length of the vessel from each end Vessels having short forecastles only. — Sheer to be measured abreast the sternpost and at a point distant 5 the length from the stem Freeboard 83 (a) In flush-deck vessels and in vessels to which paras. 11 and 12 apply, when the sheer of deck is greater or less than the above and is of a gradual character, divide the difference in inches be- tween it and the mean sheer provided for by 4 and the result in inches is the amount by which the freeboard amidships should be diminished or increased according as the sheer is greater or less. (b) In vessels having short poops and forecastles, and in those having short forecastles only, the freeboard should be corrected in respect of the excess or deficiency in reserve buoyancy due to variations in sheer from the standard amount over the length uncovered by substantial erections, as provided in the above table. One-fourth the difference between the mean sheer speci- fied and that measured as described is approximately the amount by which the freeboard should be modified in respect of sheer. (c) The divisor 4 is to be used when the sheer is of a gradual character, and is not strictly applicable either to those cases in which the sheer is suddenly increased at the bow or stern, or to those in which it does not maintain its normal rate of increase to the ends of the vessel. (d) In all cases the rise in sheer forward and aft is measured with reference to the deck at the middle of the length, and where the lowest point of the sheer is abaft the middle of the length, one-half the difference between the sheer amidships and the lowest point should be added to the freeboard specified in the tables for flush-deck vessels and for vessels having short poops and forecastles only. (e) Where, as in some instances, vessels fitted with long poops or raised quarter-decks connected with bridge-houses have the deck line rising rapidly from amidships to the front of the bridge, and from that point onwards gradually approaching the normal sheer line, the freeboard may be slightly modified in consider- ation of the increase of height of deck in the "well," (J) In flush-deck vessels and in vessels having short poops and forecastles the excess of sheer for which an allowance is made shall not exceed one-half the total standard mean sheer for the size of the ship. (g) No decrease should be made in the freeboard of spar- and awning-deck vessels, in respect of excess of sheer. 19. Round of Beam. — In calculating the reserve of buoy- ancy an allowance has been made of one-quarter of an inch for every foot of the length of the midship beam for the round up. When the round of the beam in flush-decked vessels is greater than given by this rule divide the difference in inches by 2 and diminish or increase the freeboard by this amount. For vessels with erections on deck the amount of the allowance 84 The Naval Constructor should depend on the extent of the main deck uncovered. This rule for round of beam does not apply to spar- or awning-deck vessels. 20. As a general illustration of the way in which the tables should be used in modifying the freeboard on account of erec- tions on deck, extreme proportions and variations in sheer, the following may be taken as an example. A vessel is 234 ft. long, 29 ft. broad, and has a moulded depth of 17.0 ft., the coefficient of fineness being .72. Suppose the vessel to have a poop and bridge-house of the united length of 121 ft., and a forecastle 20 ft. in length, and let the sheer forward, measured at the side, be 4 ft. 6 ins., and aft, 2 ft. 1 in. Freeboard by Tables A if of the normal Ft * In * length, without erections, and with the normal amount of sheer 2 11 The mean sheer by rule is 33.4 ins. or 6 ins. less than that in the vessel, and the re- duction in freeboard is 6 ins. divided by 4 1J; Freeboard of vessel without erections and with 39£ ins. mean sheer 2 9§ Freeboard by Tables C as awning-decked. . 9| Difference 2 0_ The combined length of the erections is \i\ or T % of the length of the vessel, and the allowance for erections under clause 1 1 will be therefore & of 24 ins., or 9£ ins. We have therefore: Deduct. Amount deducted from freeboard for ex- in " cess of sheer 1| Amount deducted from the freeboard for erections 9£ Amount deducted if vessel be fitted with an uncovered iron main deck (clause 6) -■AX 8| _2 13 The length being 30 ft. in excess of that for which the tables are framed, the addition to the freeboard in respect of the same is one-half of f$ of 1.1 in., or _1| 111 That is 11 J ins. to be deducted from 2 ft. 11 ins., leaving a winter freeboard of 1 ft. 11| in. Corresponding summer freeboard, 1 ft. 9 ins. Freeboard 85 21. Vessels loaded in fresh water may have less freeboard than that given in the several tables according to the following scale: Moulded Depth in Feet. 6 and under 8 8 " 1 11 11 " ' 13 13 " ' 16 16 " ' 19 19 " ' 22 22 " ' 25 25 " ' 28 28 " ' 31 31 " ' 34 Reduction in Freeboard. Without Erections on Deck. Ins. H 2 2* 3 3^ 4 5 5* 6 Awning- deck Vesseb. 3* 4 4* 8 5* 6 61 Spar- deck Ins. 4 H 5 5| 6 Si 7 Memo. — The weight of a cubic foot of salt water is taken, in the above table, to be 64 lbs., and that of fresh water 62.5 lbs. 22. The freeboards assigned by the following tables are not intended to apply to vessels when navigating inland waters or rivers, and when a stretch of such water has to be traversed such deeper loading will be permissible as may be due to the weight of fuel required for consumption between the points of departure and the open sea. 23. The freeboards of vessels having ports, scuppers, or other openings in their sides is to be regulated by the following considerations. When the openings are in the nature of water- tight ports for cargo, coals, etc., and are therefore not intended to be opened except in harbor, no modification of the free- board as determined by the foregoing tables will be necessary, provided the covers of the openings are sufficiently strong and are efficiently secured. In the case, however, of vessels having scuppers through the sides from a 'tween deck space below the upper deck or side scuttles or other openings of a similar nature, when the freeboard as determined by the foregoing tables does not provide a sufficient height from the load-line to the sills of the side scuttles, or to the deck which is drained by the scuppers, the freeboard is to be increased; and the amount of the increase, 86 The Naval Constructor if any, is to depend on the nature of such openings and on the means adopted for closing them. In the case of hinged side- scuttles of the usual pattern, when the glass is of sufficient thickness and the scuttles are efficiently secured by metal bolts and nuts, and hinged watertight iron shutters of deadlights are provided on the inside of the glass, the loadline as determined by the centre of the disc or by the Indian summer line, if so marked, is to be not less than 6 inches below the sill of the lowest side-scuttle. 24. The freeboards required by the foregoing tables are to be assigned on the condition that the engine and boiler casings above the upper deck are of sufficient height and strength, with suitable means provided for closing all openings in them in bad weather, and the weather deck hatchways are properly framed with substantial coamings, and strong hatch covers, the latter being efficiently supported by shifting beams and fore-and-afters suitable to the dimensions of the hatchway. When these conditions are not complied with the freeboard may require to be increased, regard being given, however, to the trade in which the vessel is intended to be employed. 25. In no case shall the deepest loadline in salt water, whether indicating the summer or Indian summer line, be assigned at a higher position than the intersection of the top of the upper deck with the vessel's side, at the lowest part of the deck. In the case of shelter-decked vessels the deck next below the shelter deck is to be regarded as the upper deck. Memorandum of Explanatory Notes on the Application of the Tables of Freeboard, Drawn Up with a View to Securing Uniformity of Practice on the Part of Those Entrusted with the Assignment of Freeboard. Deck Line. — In the case of vessels with uncovered iron or steel decks, a width of gutter waterway is to be assumed, and the point so obtained levelled out to the vessel's side. In the case of vessels of 24 feet beam and under, the width of the waterway assumed shoiHd be 12 inches, and in vessels of 42 feet and above, 21 inches. In vessels of between 24 and 42 feet, beam the width of the gutter waterway is to be taken as half an inch for every foot in beam. Where a wood deck maintains a uniform thickness to the sides of a vessel, the same method should be adopted. In cases where an iron deck is partly covered with wood, the deck-line is to correspond with the top of the deck amidships, Notes on the Tables of Freeboard 87 whether the deck at that part be of wood or of iron, and the necessary corrections should be made in accordance with para- graph 6, as also the correction always required to the statutory deck-line. Bridge-house in Spar-decked Ships. — In a spar-decked ship, where an efficient bridge-house is fitted amidships, cover- ing the engine and boiler openings, if it extends over at least two-fifths of the vessel's length and has scantlings not less than the requirements of Lloyd's Rules (1885) for bridge- houses, it is to be taken into consideration in estimating the strength of the vessel for freeboard. If the scantlings of the bridge-house are equal to the require- ments of Lloyd's Rules (1885) the allowance on this account should not exceed that given in the following table: Moulded Depth of Vessel to Main-deck. Allowance. Feet. 16 Inches. 4 3 2 1 20. . . . 24 28 If, however, the scantlings of the bridge-house are in excess of Lloyd's Rules (1885) the freeboard is to be determined on the basis of a comparison between the strength of the actual vessel and the strength of a vessel of the same dimensions, built to the three-decked rule, and of a vessel built to the spar- deck rule, including a bridge-house in each case. Tables of Freeboard. — Additional freeboard will be re- quired in the case of vessels classed 90A and 80A, or in vessels of equivalent strength thereto in accordance with the following scale: Length of vessel: Feet. 150 175 200 225 250 275 200 90A additions 80A " In. l 2 1 In. l 2 1 Ins. I 2 Ins. 3 4 Ins. 4 If Ins. 1 2 Ins. a 2| Wherever in these explanatory notes reference is made to classes of vessels of Lloyd's various types, it is to be under- 88 The Naval Constructor stood that these apply equally to all other vessels of equivalent strength, whether classed by other classifying associations, such, for instance, as the Bureau Veritas or the British Cor- poration, or unclassed. If the frame spacing be increased one-fourth, the thickness of all the shell-plating, excepting garboard and sheer strakes, should be increased by one-twentieth of an inch over the thick- ness required in the standard ship. Other increases in spacing should be dealt with in the same proportion. Para. 1 — Length. — The length of erection is to be measured with reference to the length of the vessel on the load-line, i.e., any portion of the erections forward of the fore side of the stem on the load-line, or abaft the after side of the after post on the load-line, is not to be measured for deductions. Para. 3 — Depth of Hold. — The depth of hold as used in the computation for ascertaining the coefficient of fineness in iron and steel sailing vessels is to be measured to the top of the ceiling, and in steam vessels to the top of the floors. The cases of vessels having either an excess or a deficiency of mean sheer, as compared with the standard sheer, the registered depth to be used for ascertaining the coefficient of fineness is to be increased for excess of sheer, or reduced for the deficiency of sheer, by one-third of the difference between the standard mean sheer and the vessel's actual mean sheer, after being re- duced to the gradual character, if necessary. Para. 4 — Coefficient of Fineness. — No alteration is to be made in the freeboard in consequence of the coefficient of fineness being either smaller or greater than those given on the page of the tables from which the ship's freeboard is taken. Para. 5 — Moulded Depth. — In cases where a wood deck of extra thickness is fitted, or where a wood deck is doubled throughout, the moulded depth should be increased by the ex- cess of thickness. The freeboard should then be set off from the top of the deck of increased thickness at the side of the vessel. Para. 6 — Freeboard. — In case of the freeboard being ascertained by an actual calculation of the reserve buoyancy, the drawing used in such calculation should be verified by actual measurements at the ship, and such drawing and calcu- lations forwarded to the Board of Trade, and, whatever the result of the calculation, the freeboard assigned should not be less than would be obtained by taking from the tables the free- board corresponding to the smallest coefficient for a vessel of the same moulded depth, except in sailing vessels with large rise of floor (see page 26). Notes on the Tables of Freeboard 89 Freeboard as ascertained by these tables is to be measured to the intersection of the deck with the side of the vessel, but in granting certificates of freeboard this must always be corrected so as to state the freeboard amidships when measured to the deck-line, marked in accordance with the statute. Sub-paras. (A) and (B). — For vessels having iron upper- decks not covered with wood, the allowance is to be made under sub-para, (a), when "the erections extend over less than T % of the length; but in all vessels when the erections cover -fa or more of the length, and in spar- and awning-decked vessels the allow- ance is to be made under sub-para (6). Sub-para. (6.) — (6.) — In spar-decked vessels having iron spar decks and in awning-decked vessels having iron main decks, the freeboard by the tables should be calculated, as if those decks were wood-covered, i.e., the ordinary thickness of a wood deck, less the thickness of the stringer plate, should be deducted from the freeboard, also in vessels where T V or more of the main deck is covered by substantial enclosed erections, the freeboard found from the tables should be measured amidships from a wood deck, or, if the deck is of iron, it should be measured from the iron deck, and the ordinary thickness of a wooded deck required for that size of ship, less the thickness of the stringer plate, should in that case" be deducted from the freeboard. In vessels which have T % of the deck covered, T % the thickness of a wood deck, less the thickness of the stringer plate is to be de- ducted from the freeboard. Between T \ and ^ a proportionate quantity; for example, for T %\ covered allow j\ the thickness of the deck, after deducting the thickness of the stringer plate. The remainder of the paragraph should be read as printed. N.B. — When the deductions referred to in this sub-para. (6) are allowed the moulded depth is not to be reduced as per sub- para, (a) para. 6. Para. 9. — In the case of vessels coming under para. 12 and having the deck erections not entirely enclosed, the effective length of the open portions is to be assessed as described in paras. 13, 14 and 15; if the length of the enclosed erections plus the length of the open portions, where assessed as above, is at all under T % of the vessel's length, the entire correction for length is to be applied. Para. 11. — This paragraph does not apply to vessels in which the effective length of the erections is less than T % of the length, except in cases where the effective length of the after erection is at least T % of the length, and the total effective length of the erections is between T % and T % of the length of the vessel. 90 The Naval Constructor In such cases the allowance should be proportioned between that allowed for erections ^ the length under para. 14 and that allowed for erections covering ^ of the length under para. 11, and the corrections for length and sheer should be included in estimating this allowance. In all other cases of vessels with erections covering less than T ^ of the length, para. 14 is to be used. In the case of vessels having erections which are partly open or are less than the standard height the effective length of the erections is to be computed as directed elsewhere. No allowance is to be made for a monkey forecastle which is less in height than the main or top-gallant rail, or 4 feet, which- ever is the least; where this condition is satisfied, or the fore- castle is a sunk one having an efficient bulkhead at its after end, the length to be used in estimating the allowance is to be obtained by multiplying the length of the monkey forecastle by its height and dividing by 6 feet, the minimum height of a top-gallant forecastle. This rule, as well as that relating to the heights of raised quarter-decks, applies to vessels coming under paras. 12, 13, 14, and 15, as well as under para. 11. In case of vessels having no forecastle but in other respects coming un- der this paragraph, the allowance for erections should be esti- mated on the supposition that there is a forecastle of | the length of the vessel, deducting from this twice the allowance which the vessel would have for such a forecastle under para. 15. Sub-para. (a). — The difference will not be affected by cor- rection for length, as the allowance will be practically the same in both tables. Sub-para. (c). — The engine and boiler openings, if pro- tected only by a raised quarter-deck, will require an addition in freeboard varying from 1 inch in vessels of 15 feet moulded depth to 2 inches in vessels of 20 feet moulded depth. In ves- sels having less than 15 feet moulded depth a proportionate addition should be made. If with a small bridge-house in front of, but not covering the openings, an addition of half the above amount. Sub-para, (d ) . — If the crew are not berthed in the bridge- house, and the arrangements to enable them to get backwards and forwards from their quarters are not satisfactory, an ad- dition should be made to the freeboard of 1 per cent of the moulded depth of the ship in the case of vessels 180 feet or more in length and having wells 70 feet or less in length. If the vessel's length does not exceed 150 feet, or if the well is 80 feet or more in length, the foregoing addition will not be re- quired. In the case of vessels between 150 and 180 feet in Notes on the Tables of Freeboard 91 length, or having wells between 70 and 80 feet in length, the addition is to be found by interpolation. Planks secured in position by lashings are not to be regarded as satisfactory arrangements; and a gangway providing access between the bridge-house and forecastle cannot be considered satisfactory, unless the following requirements at least are complied with: The gangway to be not less than 18 inches wide and to be efficiently supported at suitable intervals. The ends to be strongly bolted to lugs riveted to the bulkheads of bridge and forecastle, or to the hatch coamings, or to iron standards bolted to the deck or to be secured in some equally efficient manner. The top of the gangway to be not less than 2 feet 6 inches above the top of the deck at any part. A life-line or rail to be fitted for the entire length of the gangway and to be supported by wrought-iron stanchions suitably spaced and not less than 2 feet 6 inches in height. If the hatchways are at least 2 feet 6 inches in height the gangway may be fitted between the hatchways and beyond them only, provided that a continuous platform of at least the required height is obtained, and the rail or life-line is fitted and efficiently supported by wrought-iron stanchions for the entire distance including the hatchways. The gangway should be fitted as far inboard as practicable. Sub-para. (e). as follows: The minimum freeing port area is to be Length of Bul- Freeing Port Area warks in on Each Side in "Well," in Feet. Square Feet. 5 4.5 10 6.5 15 7.5 20 8.5 25 9. 30 9.5 35 10. 40 10.5 45 11. 50 11.5 55 12. 60 12.5 * 65 and above, 1 square foot to each 5 feet length of bulwark. 92 The Naval Constructor If the freeing port area is less than that stated above, an addition is to be made to the freeboard of 1 per cent of the moulded depth. The scale of allowance for erections on deck to vessels with top-gallant forecastles having long poops or raised quarter- decks connected with bridge-houses is not to be used without modification, unless the strength of the bulkhead at the front of the poop or bridge-house is at least equivalent to the follow- ing requirements: (a) Poop or bridge bulkheads to be of the thickness of their side plating as required below for vessels under 13 depths to length, with coaming plates -h of an inch thicker, and to be stiffened with bulb angle according to the following scale, spaced 30 inches apart, and connected to the coaming plates and to the deck plating, or to an athwartship plate on the beams both below and above, with a bracket plate to each end of the stiffener. Breadth op Ship Size of Stiffener. Breadth op Ship. Size of Stiffener. 24 30 36 42 5X3X& 6X3X& 7x3x 2 § 7X3XH 46 50 54 58 and above 7£X3§XH 8 1 x3 ! x ^f 82 X03 Xjtf 9 X3|XH Intermediate sizes to be found by interpolation. (b) Horizontal brackets or gusset plates of the same thickness as the coamings to be fitted, connecting the poop or bridge bulkheads with the bulwarks on each side of the vessel at about the height of the rail. In the case of vessels having a fore- castle and raised quarter deck only, the break bulkhead should be the same thickness as required for bridge sides and stiffened with angles 30 inches apart and of the size required for the main frames. In order to obtain the allowance for deck erections provided by this paragraph, the openings, if any, in the bulkhead at the front of the long poop or bridge house, must be provided with hinged iron or steel doors, or with some equally permanent means of closing such openings. When the width of the open- ings exceeds 30 inches, special means are to be provided for maintaining the strength of the hinged doors. The standard of thickness of the side plating of long poops and bridge-houses is that required by Section 44 of Lloyd's Rules, as modified by the Table of Thicknesses of Side Plating of Awning-decked Vessels, given in these tables. Notes on the Tables of Freeboard 93 The additional freeboard for North Atlantic winter is to be as follows: ADDITIONAL FREEBOARD FOR WINTER, NORTH ATLANTIC, FOR WELL-DECK VESSELS. Length of Vessels Proportions of Length of Vessel Over Which Erections Extend 60 tV* #v 75 i 8 A Ft. 180 220 260 300 Ins. 4 3* 8| 3 Ins. 3£ 3* 3 3 Ins. 3 3 2h 2h Ins. 2* 2| 2 2 Ins. 2 2 2 Para 12. — For vessels having no forecastle, but with the other deck erections prescribed in this paragraph, estimate the allowance for erections supposing there is a forecastle \ the length of the vessel, and deduct l\ times the allowance that would be made under para. 15 if the vessel were fitted with such a forecastle only. This rule also applies to vessels having no forecastle, but with a bridge-house, as provided for in para. 13. In steam vessels coming under this paragraph, and having closed erections extending over T 6 o or more of the vessel's length, one-half the length correction specified in Table A is to be made, and the freeboard corrected for sheer only in estimating the al- lowance for erections, as the allowance for length will be prac- tically the same in both Tables. For erections which extend over less than T 4 7 the length of the ship, the allowance is to be in proportion. For instance, if T 3 7 are covered, allow f of 25 per cent. In the case of vessels under 15 ft. moulded depth, in which the combined length of enclosed erections exceeds T % of the vessel's length, or in which the combined length of erections enclosed and open is equivalent to more than T % the vessel's length, sub-paras, (d) and (e) of the preceding paragraph are to apply; but the full addition of one per cent of the moulded depth, under each of these sub-paragraphs, is to be made only when the erections cover T % or more of the length; for lengths of erections intermediate between fV and T %, the required ad- dition is to be in proportion; thus, when T % 5 and this is the maximum deduction for this type of vessel. For erections which extend over less than T % of the length of the ship the allowance is to be in proportion. For instance, ^ covered allow § of 19 per cent. In all the rules governing the deductions to be made from the freeboard it is to be understood as follows: When the top- gallant forecastle is not closed by an efficient bulkhead at the after end the length is never to be estimated at a greater full value than f the length of the ship, but any extension beyond this may be estimated at one-half the value. For instance, if a vessel 240 feet long has an open forecastle 80 feet long, its value for deductions is 30 + 25 = 55 feet. When the top-gallant fore- castle has an efficient bulkhead with an elongation abaft that bulkhead not enclosed at the after end, the full value of the closed-in portion is to be estimated either as | the length of the ship, or the entire length of the enclosed portion, whichever may be the greatest. Open-bridge House. — -When the bridge-house extends from side to side of the ship its value for deductions must be considered on its merits, which will depend upon the security of all deck openings, doors, bunker lids or otherwise. Where these are all properly protected and the bridge-house is open at both ends, one-half the length may be estimated as the value for deductions. Where in addition the fore end is enclosed by an efficient bulkhead f the length may be estimated as the value for deductions. If the openings in the bulkhead at the after end of a bridge erection, having its fore end closed, are efficiently protected by weather boards properly fitted to at least half the height of the erection, the full length of the erection may be allowed in esti- mating its value for freeboard. This does not apply, however, to the case of a long erection falling to be dealt with under paragraph 11, as in well-decked vessels having the well aft, Notes on the Tables of Freeboard 95 except in shelter-decked vessels having efficient means pro- vided for temporarily closing the openings in the shelter-deck in bad weather. In the case of steamers coming under paragraphs 12 and 13, when the engine and boiler openings are not covered by an erection extending from side to side, bridge-houses may have an allowance not exceeding that which would be given for half the length of a bridge-house of the same character covering en- gines and boilers. Paras. 14 and 15. — When the poop has no efficient bulk- head, or the bulkhead does not extend across the vessel, one- half its length may be allowed, provided always proper freeing ports are fitted. When the openings in the bulkhead are provided with efficient weather boards or other efficient temporary means of closing, and extending the full height of the openings, then the full length of the poop may be allowed. In no case, however, shall shifting boards or any other tem- porary means of closing the openings in the bulkheads at the after end of a bridge-house, or fore end of a poop be considered satisfactory, unless the means of their attachment, whether by channels, hooks, cleats, or otherwise, are permanently secured to the bulkheads. The standard heights of forecastles and raised quarter-decks, as defined in para. 11, pages 6 and 16, apply also to these paragraphs. Paras. 16 and 17. — In the case of a sailing vessel having a forecastle and raised quarter-deck, or a raised quarter-deck only, the latter of less than 4 feet in height, the length of raised quarter-deck to be allowed should be in proportion to its height as compared with the standard height of 4 feet. The provisions of the preceding paragraphs relating to the height of forecastles, bulkheads at the after end of forecastles and at the fore end of poops, and the means of closing openings in poop bulkheads, are also to be applied to sailing vessels dealt with under paras. 16 and 17. "Para. 18. Sheer. — Sheer of a gradual character is to be defined as follows: — "At £ the length of the vessel from the stem or sternpost the sheer is to be 55 per cent of the sheer at stem or sternpost; at \ the length from stem to sternpost 26 per cent, and at f the length 7 per cent. "In those cases in which the sheer is required to be taken at the stem and sternpost and the sheer is found to be not of the grad- 96 The Naval Constructor ual character, the following method of computing the effective mean sheer is to be used: — "Let S = mean of the actual sheers at stem and sternpost; "Let Si = mean of sheers at £ length from stem and sternpost -*-.55. "If S is greater than Si the effective mean sheer to be used in the computation of freeboard is Si. C i g " If S is less than Si the effective mean sheer to be used is — =—• "In those cases in which the sheer is required to be taken at £ of the vessel's length from stem or from sternpost the sheer as actually measured at the prescribed point may be used in ordi- nary cases without any correction on account of a departure of the sheer line from the gradual character. "When correcting the depth of hold for excess or deficiency of sheer (paragraph 3, page 23), the mean of the sheers at £ of vessel's length from stem and from sternpost divided by .55 should in all cases be taken as the vessel's actual sheer for this purpose. In cases where there is no forecastle the sheer is to be meas- ured at the stem and sternpost, and corrections made for it in all respects as in the case of flush-decked vessels. When the bridge-house is enclosed, the sheer should be taken at the stem and sternpost and the freeboard corrected for sheer in estimating the allowance for erections. When the bridge- house is not enclosed at both ends, the sheer should be measured as if there were no bridge-house, and the freeboard should or should not be corrected for sheer in estimating the allowance for erections, according as the sheer is measured at the stem or at £ length from the stem. Sub-para. (a). — Surveyors should note that paras. 11 and 12 apply either to vessels of the ordinary well-decked type or to vessels having a poop and forecastle with a disconnected bridge- house. Sub-para. (d). — The extent of the depressed part of the sheer covered by deck erections is to be allowed for in applying this rule. Sub-para. (e). — In vessels obtaining an allowance for deck erections under para. 11 and having considerably less than the normal sheer, the freeboard should be modified in consideration of the decrease of height of deck in the "well." Sub-para. (/). — In flush-deck vessels the total standard means the sheer measured at the stem and sternpost. In vessels Notes on the Tables of Freeboard 97 having poops and forecastles, it means the sheer measured at points distant £ of the vessel's length from stem and stern- post. In vessels obtaining an allowance for deck erections under para. 11, where the sheer drops abaft amidships, the height of the raised quarter-deck is to be taken from the level of the top of the midship beam. Para. 19 — Round of Beam. — In flush-deck sailing vessels the excess of round of beam for which an allowance is made 6hall not exceed the standard round of beam; and for sailing vessels having erections on deck the allowance shall be further reduced in proportion to the extent of the main deck uncovered. Table A. The deductions for summer in vessels having deck erections is to be intermediate between those required by Tables A and C in proportion to the length of the ship covered by those erections. Table B. All vessels equal in strength to Lloyd's spar-decked rule, or which, although in excess of that rule, do not come up to Lloyd's requirements for ships of full scantlings to the upper deck, are to be considered as spar-decked ships, the freeboard for which will vary with their strength. When the height between decks is greater or less than 7 feet, the consequent modification in freeboard will vary from i to § the excess or deficiency of height, the exact proportion to de- pend upon the strength of the vessel. In spar-decked vessels where the height between main and spar deck exceeds 7 feet, the numbers for scantlings should be found assuming the height between decks to be 7 feet; if both these, numbers are in the same grades as the actual scantling numbers of the vessel, the correction for height between decks is to be I of the excess of height above 7 feet. If both the scantling numbers so found are in higher grades than those of the actual vessel, § of the excess of height is to be added, and if either one of these scantling numbers is in a higher grade, \ of the excess of height is to be added. The same principle will apply in cases where the height between decks is less than 7 feet. Since the freeboard is measured from the spar deck, it will be increased if the 'tween deck height is more, and decreased if it is less than 7 feet. 98 The Naval Constructor In computing the freeboard of spar-decked vessels having scantlings in excess of Lloyd's requirements, a comparison is to be made between their scantlings, the scantlings of vessels of the same dimensions classed 100 A built to the three-decked rule, and of vessels built to the 100 A spar-decked rule, and the freeboard is to be proportionate between that given in Table A and that given in Table B, after deducting 12 per cent from the former; but in no case must the freeboard so assigned be less than that provided in Table A, for a vessel of the same dimen- sions, sheer, and camber, or round of beam, and deck erec- tions. In the comparison of scantlings and assignment of freeboard to spar-decked vessels having scantlings in excess of Lloyd's re- quirements, the following method is to be adopted: 1. The difference between the freeboard by Table A (less 12 per cent) and that by Table B to be divided by five, f of it be- ing considered with reference to the longitudinal strength, and | of it with reference to the transverse strength, these al- lowances to be the maximum deduction on each account. 2. In the comparison of steel ships, notwithstanding the general reduction of 20 per cent for steel as compared with iron thicknesses, outside plating in the way of the double bottoms is not to be further reduced by ^ unless its thickness is \% or over. No reduction is to be made in any case unless there are floors connected with every frame. 3. In the calculation of strength the following method is to be adopted: (a) Thin iron or steel plating in weather decks and the inner plating of double bottoms are to have their sectional area re- duced for the purpose of the strength calculation as follows: 1. When the deck beams or floors are fitted on every frame of the usual spacing: Thickness in 20ths 5 6 7 8 9 .6 .7 .9 1 1 2. When the deck beams or floors are fitted on alternate frames: Thickness in 20ths 5 6 7 8 9 .4 .5 .6 .7 .8 When the decks are sheathed with wood, with fastenings not more than 24 inches apart, the factors given in (1) are to be used, whether the beams are on every frame or on alternate frames, but if the fastenings are 48 inches apart, then the fac- Notes on the Tables of Freeboard 99 tors in (2) are to be used unless the beams are fitted on every frame. (6) A deduction of \ is to be made for rivet holes in steel, and \ in iron for the parts in tension. (c) Iron or steel decks which cover not less than § of the mid- ship length of the vessel are to be considered in the calculation just as they would be if of the full length. (d) Such portions of wood weather decks as are continuous throughout the midship portion of the ship are to be considered as equivalent to steel of ^V the section area of the wood. (e) For the purpose of comparison of strength the breadth of the hatchways in the standard vessel shall be deemed to be 5 the breadth of the deck, and the tie-plates should be assumed to be fitted at the side of the hatchways. Table C. The standard of strength for awning-decked vessels is that provided by Lloyd's Rules (1885) for 100 A awning-deck class, as modified and extended by the following table showing the thicknesses of topside plating, etc. All vessels equal in strength to the above standard, or which, although in excess of that standard, do not come up to Lloyd's requirements for a spar-decked vessel, are to be considered as awning-decked vessels, the freeboard of which will vary with their strength. No modification is necessary in respect of the height of 'tween decks of awning-decked vessels. In comparing the freeboard for awning-decked vessels having scantlings in excess of the standard requirements, a comparison is to be made between their scantlings, the scantlings of vessels of the same dimensions built to the 100 A spar-decked rule, and of vessels built to the standard awning-decked rule, and the freeboard is to be proportionate between that given in Table B and that given in Table C. In vessels where the superstructure is of less strength than that required for the standard awning-decked vessel, additions are to be made to the freeboard in the same proportion. In the comparison of scantlings and assignment of freeboard to awning-deck vessels having scantlings in excess of the stand- ard awning-decked vessel, the method of procedure to be similar to that stated above for spar-deck vessels having scantlings in excess of those provided by the spar-decked rule. The thickness of the side plating above the main deck of standard awning-decked vessels, for half the vessel's length amidships, is to be in accordance with the following table. 100 The Naval Constructor Ratio -=. Under 13. 13-14 14-15 Plating Number 10,000 and under 13,100 13,100 " " 15,500 15,500 " " 16,600 16,600 " " 18,700 18,700 " " 26,400 26,400 " " 30,900 30,900 " " 35,200 35,200 " " 40,000 5 6 6 7 8 8 9* 9* 5 and 6 6 6 and 7 7 and 8 8 and 9* 9* 10* lot 6 6 7 8 9* 9 and 10* iot iot * The butts of the awning-deck sheer strake to be treble riveted, and the landing edges of the side plating to be double riveted. f The butts of the strake of side plate below the awning-deck sheer strake to be treble riveted in addition. Note. — For iron read sixteenths and for steel read twentieths of an inch. When two thicknesses are given the greater is that of the awning-deck sheer Btrake. The depth and length are to be measured as defined in Lloyd's Register Rules for estimating the scantling numbers. When Section 46 of the above rules (relating to vessel's pro- portions) applies to these vessels, the increased thicknesses re- quired for sheer strakes, stringers, etc., are to be added to those of the main deck. When one steel deck is required, it is to be fitted at the main deck, and when two steel decks are required they are to be fitted at the awning-deck and the main-deck, for the purpose of comparison of strength for determination of freeboard. For vessels having a plating number exceeding 40,000 the scantlings necessary for the standard awning-decked vessel for the Table C freeboard are to be determined so that the stress per square inch upon the material of the hull amidships shall not exceed that of a standard vessel of the same dimensions and form, and having scantlings equal to the requirements of the 100 A class in Lloyd's Register for three-deck vessels when loaded to the freeboard given in Tables A after deducting 12 per cent from the same. In part awning-decked vessels with raised quarter-decks and long superstructures with the extra strength given in Section 44, Lloyd's Rules for 1889 for iron and steel vessels, where the break of the quarter-deck is fo the vessel's length abaft amid- ships, and the continuity of strength is suitably maintained at such break, a reduction may be made from the freeboard re- quired by Table C in accordance with the following scale. Notes on the Tables or* Freeboard 101 When the break of the quarter-deck is not less than T 3 ¥ the length of the vessel abaft amidships, twice the above men- tioned allowance may be made, and for intermediate lengths of erection the allowance is to be obtained by interpolation. Vessels with plating number under 18,000, 2\ inches. Vessels with plating number 18,000 to 21,000, 3 inches. Vessels with plating number 21,000 to 24,000, 3£ inches. Vessels with plating number 24,000 to 27,000, 2>\ inches. In part awning-deck vessels the standard height of the raised quarter-deck is 4 feet; for raised quarter-decks of less height, extending over y% of the length, the allowance for the erections should be diminished as shown in the following table: Height of R. Moulded Depth of Vessel in Feet. Quar. Dk. Ft. In. Ft. In. Ft. In. Ft. In. Ft. In. Ft. In. Ft. In. 10 12 14 16 18 20 22 Ft. Ina. Ins. Ins. Ins. Ins. Ins. Ins. Ins. 3 6 t i 2 l 2 i t 1 4 3 i 2 i 1 1 H lj A 4 2 6 1 if « If 2 n 3 2 H if 2} 2i H 'Si 4± ^2 1 6 2 2j 3 3f 4J 5 6 For shorter or longer lengths of raised quarter-decks a pro- portionate correction should be made. Table D. Sailing vessels classed A (black) in Lloyd's Register are to be regarded as first-class ships in applying the tables. Hard wood ships, i.e., other than fir or pine, classed A (red) in Lloyd's are to have their freeboards by the tables increased by 8 per cent. Hard wood ships classed (E in Lloyd's are to have their free- boards by the tables increased 15 per cent. Hard wood ships without class are to have their freeboard by the tables increased by 20 per cent, unless opened out for survey, when their freeboards will depend upon their condition. Soft wood ships will require to have their coefficient of fine- ness modified in respect of the excess of the registered breadth caused by the extra thickness of side. That for hard wood ships is already provided for in the tables. 102 The Navral Constructor Soft wood ships classed A (red) in Lloyd's are to have their freeboards by the tables increased 10 per cent. Soft wood ships classed (E in Lloyd's are to have their free- boards increased 20 per cent. Soft wood ships without class are to have their freeboards by the tables increased 25 per cent unless opened out for survey when their freeboards will depend upon their condition. Iron and steel sailing vessels having a greater rate of rise of floor than 1| inches per foot of half breadth may have the moulded depth to be used with the tables reduced by half the difference between the total rise of floor at the half breadth and the total rise at the standard rate of 1| inches per foot; 2\ inches per foot of half breadth is to be the maximum rate of rise on which an allowance is to be made. When the reserve buoyancy is calculated, the percentage taken shall be that corresponding to the depth reduced as above, but in no case shall the free- board be less than that given in the top line of Table D for such percentage. Whichever method be adopted the correction for length is to be applied in relation to the reduced moulded depth. RULES TO REGULATE THE DEPTH OP LOADING OF TURRET-DECK VESSELS AND VESSELS OF SIMDLAR TYPES. 1. A turret is a strongly-constructed continuous erection at the middle line of the vessel, forming with the main or harbour deck an integral part of the hull, having a breadth not less than r 5 ff of the greatest breadth of the vessel and a height not less than 25 per cent of the moulded depth. In assigning free- boards to turret-deck vessels, the following rules should be observed: 2. Hatch coamings at least 2 ft. high and casings to engine and boiler openings at least 4 ft. 6 ins. high to be fitted above the " turret" deck. Any scuttles or other openings in the harbour deck are to be closed water-tight by means of iron or steel plates not less in thickness than the harbour deck, suitably stiffened and strongly bolted in place. The following method of computing the free- board is based on the consideration that the turret-deck hatch- ways are provided with permanent means of closing them, as described in clause 8 of the rules for shelter-decked steamers. 3. The volume of the turret to be estimated from a normal beam line drawn through the point where a vertical line at the quarter breadth of vessel cuts the upper surface of the vessel's deck. Where the turret is nearly one-half the breadth of the Rules for Loading of Turret-deck Vessels 103 vessel, and its transverse section is of rounded form at its base, the base line of the turret is to be drawn through the point where the vertical line at the quarter breadth cuts the upper surface continued in the same curve as the normal line of beam. 4. The reserve buoyancy required by the tables to be esti- mated by taking 70 per cent of the volume of the turret. The height of the turret allowed for is not to exceed 25 per cent of the moulded depth. (It is to be understood that no correction is to be made for an unsheathed iron harbour deck in applying the buoyancy method.) 5. The moulded depth of the vessel to be taken to be the depth at side from the beam line, as before defined, to the top of the keel. 6. If a vessel has sheer, to determine the volume of the turret, the turret base line to be drawn at each section as described above. At the extreme fore end of the vessel the base of the turret to be parallel to the turret deck. 7. Where a poop and forecastle or a forecastle only are fitted on the top of a turret, the allowance for them is to be as follows: When the effective length of these erections is equal to \ of the vessel s length, deduct 8 per cent of the difference between the freeboards in Table A (after correction for sheer) and Table C. For erections of greater or less length the allowance is to be in proportion to the length. The allowance for such erections is not to exceed 10 per cent of the difference between the free- boards in Table A (after correction for sheer) and Table C. The effective length of a poop or forecastle is to be obtained by multiplying its actual length by the ratio which its breadth bears to the breadth of the ship at the after end of the fore- castle or fore end of the poop respectively. The provisions of the freeboard tables regarding the height of forecastles, the bulkheads at the after end of forecastles and at the fore end of poops, and the means of closing the openings in poop bulkheads, are to be applied in these cases. 8. The method described above is only applicable when it is possible to obtain a correct drawing of the "lines" of the ves- sel, and it is only to be employed when facilities are given for verifying the drawing by actual measurements at the ship, in accordance with para. 6 of the freeboard tables. When a veri- fied drawing is obtainable, either the foregoing or the following method may be employed at the option of the owner, but if a verified drawing is not obtainable, the following method only is to be employed. 9. The depth of hold to be used in obtaining the coefficient of fineness in vessels having either an excess or deficiency of sheer is to be modified as described in para. 3, and the coeffi- 104 The Naval Constructor cient thus obtained is to be modified when the vessel is of rounded form at the gunwale, the necessary addition in ordinary cases being .01. 10. The length correction under para. 9 of the load-line tables is to be | of that specified in Table A, where the breadth of the turret is T % of the breadth of the vessel, but the table correction is to be halved where the breadth of the turret is A or more of the breadth of the vessel. For turrets having breadths between -^ and -j*v, the length correction is to be in proportion. 11. In making the sheer correction in accordance with para. 18 of the load-fine tables, the sheer is to be measured at the ends of the vessel. 12. The effective length of the turret is to be obtained by multiplying its length by the ratio of the mean breadth of the turret to the breadth of the vessel amidships. 13. The deduction from the freeboard shown in the tables on account of the turret is to be as follows: Where the effective length of the turret is A of the length of vessel deduct 45 per cent of the difference between the free- boards in Table A (after correction for sheer) and Table C. Where the effective length is •&, deduct 55 per cent, and so on in proportion. For intermediate lengths intermediate per- centages are to be taken. 14. In those vessels having unsheathed harbour or main decks, a correction should be made, when employing the linear method of computation, as described in para. 6 (6). 15. The transverse and longitudinal strength of the vessel are to be regulated by that required for a "three-deck" vessel of the same length, breadth, moulded depth, and coefficient of fineness, and the scantlings of the turret are to be determined so that the stress per square inch upon the material of the turret amidships shall not exceed that of a standard vessel of the same dimensions and form, and having scantlings equal to the require- ments of the 100 A class in Lloyd's Register (1885) for three- deck vessels when loaded to the freeboard given in Table A after deducting 12 per cent from the same. 16. Should a vessel be constructed with a turret less than A the breadth of the vessel or less in height than \ of the moulded depth, or should the radius of curvature at the gunwale exceed 20 per cent of the moulded depth, or should the centre line of the disc when ascertained reach a point above the junction of the vertical side with a rounded gunwale, full particulars and calculations with the proposed assignment are to be submitted to the Board of Trade before freeboards are assigned. 17. The freeboards in the certificates issued are to be set off in feet and inches from the line of the turret deck. Rules for Shelter-decked Steamers 105 RULES FOR THE DETERMINATION OF THE FREEBOARD OF SHELTER-DECKED STEAMERS By the term "shelter-decked steamer" is meant, for the purpose of the following instructions, a steam vessel having a complete superstructure of a substantial character extending over the whole length of the vessel, the superstructure deck (hereinafter called the shelter-deck) being continuous and un- broken at the sides of the vessel, but having one or more open- ings at the middle line, which have no permanent means of closing them, but which may not have means for temporarily closing them. All hatchways in the deck immediately below the shelter- deck should be properly framed with substantial coamings, hatch covers, and shifting beams, etc., as described in para- graph 24. The hatchways should have efficient means of battening down as described in clause 7 of these rules and any stairways or similar openings should have efficient means of In assigning freeboards to shelter-decked vessels, the follow- ing rules should be observed: (1) In making the sheer correction in accordance with para. 18 of the load-line tables, the sheer is to be measured at the ends of the vessel, and the freeboard corrected for sheer in esti- mating the allowance for erections. (2). (a) In the case of shelter-decked vessels having only one opening in the shelter-deck, the length correction under para. 9 of the load-line tables is to be one-half that specified in Table A; and the allowance for deck erections is to be deter- mined under para. 11 in the manner specified below, provided that the effective length of the deck erections, when assessed on the assumption that the opening in the deck is an open well, and in accordance with the different regulations contained in the load-line tables affecting poops, bridges, and forecastle, open or closed, is not less than T % of the length of the vessel. (6) In the case of shelter-decked vessels having an opening at each end of the vessel, and also in the case of vessels having more than two openings in the shelter-deck, the allowance for deck erections is to be determined under para. 12 of the tables, the length correction under para. 9 of the load-line tables is to be one-half that specified in Table A, provided that the effective length of the deck erections, when assessed on the assumption that each opening in the deck is an open well, and in accordance with the different regulations contained in the load-line tables 106 The Naval Constructor affecting poops, bridges, and forecastles, open or closed, is not less than T ' c of the length of the vessel. (3) The effective length of the deck erections is to be cal- culated in the following manner, provided the openings in the shelter-deck do not exceed half the vessel s breadth at the mid- dle of the length of the opening. The length to be taken in the first instance as if each opening were an open well, the value of each part being assessed on that assumption in accordance with the different regulations contained in the load-line tables affecting poops, bridge-houses, and forecastles, open or closed, and also in accordance with the regulations regarding bridge- houses not covering the engine and boiler space. The final allowance for erections will depend upon whether or not tem- porary but efficient means are provided for closing the openings in the shelter-deck. (a) If efficient means as specified below are provided for tem- porarily closing the openings in the shelter-deck, the effective length of the deck erections is to be reckoned as the length computed as prescribed above, plus half the difference between that length and the length of the vessel. (6) If efficient means for temporarily closing the openings are not provided, the effective length of the erections is to be computed by adding to the length computed as above one-fourth, instead of one-half, the difference between that length and the length of the vessel. (c) If the openings in the shelter-deck are wider than as specified above, the addition to the assumed length of erections is to be modified in proportion to the relation which the actual opening holds to the specified breadth and to a complete well. 4. Means for temporarily closing the openings in the shelter- deck may be regarded as efficient, if they are at least equivalent to the following in strength and security. The portable planks for closing the openings to be not less in thickness than re- auired by para. 43 of Lloyd's Rules (1885) for the flat of awning- ecks. The planks to be supported by portable beams, fitted either longitudinally or athwartships, spaced not wider than 5 feet apart, and efficiently secured at their ends, and the deck in way of the openings to be efficiently supported by pillars from the deck below. The portable planks to be provided with eye bolts and lashings, or some other equally efficient means of securing them in place. 5. If efficient means are provided for temporarily closing the openings in the shelter-deck in heavy weather, the freeing ports required by para. 11 (e) need not be provided. If, however, efficient means for closing the openings are not provided, whether in vessels with one or more than one opening in the shelter- Rules for Shelter-decked Steamers 107 deck, then freeing ports with shutters properly hung are to be fitted, having a minimum area as follows: Length of Opening Freeing Port Area on in the Shelter-deck, Each Side in Square Feet. Feet. 5 4.5 10 6.5 15 7.5 20 8.5 25 9.0 If the freeing port area is less than that stated above, an addition is to be made to the freeboard of \ per cent of the vessel's moulded depth, provided, however, that in the case of vessels treated under para. 12, the freeboard is not to be increased be- yond that due to deck erections of the same length and character, but with open wells, as determined by the different regulations contained in the load-line tables affecting poops, bridge-houses, and forecastles. 6. The deduction for summer to be intermediate between Tables A and C, in proportion to the effective length of erections finally allowed for freeboard purposes, and the freeboards assigned to those vessels must never be less than would be assigned for a complete awning-decked vessel of the same dimen- sions. 7. For the purpose of the assignment of freeboards, a hatch- way having strong iron or steel coamings, with hatch rest bars of the usual description, and also cleats for battening down bars securely riveted to the coamings, thwartship beams and fore and afters, substantial hatch covers and tarpaulins, shall be con- sidered to have "permanent means of closing." And a deck erection having no openings in it, except so protected, shall be held to be "permanently enclosed." The above reduction in freeboard for summer voyages from European and Mediterranean ports is to be made from April to September inclusive. In other parts of the world the reduced freeboard shall be used during the corresponding or recognised summer months. Double the above reduction to be allowed for voyages in the fine season in the Indian seas, between the limits of Suez and Singapore. An additional freeboard of two inches should be required for all vessels up to and including 330 feet in length when entering the North Atlantic, when sailing to, or from, the Mediterranean, or any British or European port, and which may sail to, or from, or call at, ports in British North America, or eastern ports in the United States, north of Cape Hatteras, from October to March inclusive. 108 The Naval Constructor Load Draught Diagrams. (Based on British Freeboard Tables.) It is often necessary to get an approximation to the load draught in estimating on proposed vessels, when in many cases there is insufficient time to calculate the freeboard in the regular way. For this purpose the adjoining diagrams have been prepared for cargo vessels from the freeboard tables, and from these the mean moulded load draught may be scaled off with accuracy, always observing that the proper allowances for excess of sheer, erec- tions on deck, and uncovered iron deck, strength, etc., must be made afterwards. These diagrams being graphic reproductions of the various tables, will be found to facilitate the estimating of load draughts where a sufficiently close approximation only is re- quired. It should also be borne in mind that fullness of form influences the freeboard to a considerable extent, therefore the diagram will only read correctly for vessels having coefficients of under deck tonnage from .78 to .82, and judgment must be used when dealing with vessels of finer forms, the freeboards of which are less than in the case of fuller vessels. Types of Vessels SKETCHES ILLUSTRATING THE DIFFERENT TYPES OF VESSELS TO WHICH FREEBOARDS ARE ASSIGNED P'Il FLUSH DECK VESSEL. ENGINE^BpnER_CASINGS. MAINJiECKj- 3 VESSELS HAVING MONKEY FORECASTLE, BRIDGE HOUSE, AND HOOD FOR THE PROTECTION Or 8TEERING GEAR. HOOD g.D NO.2 VESSEL HAVING TOP-GALLANT FORECASTLE, BRIDGE HOUSE, AND POOP F ^JO.3 — li em *j ^ _ oca VESSEL HAVING TOP GALLANT FORECASTLE, BRIDGE HOUSE, AND A SHORT RAISED QUARTER DECK. _R.Q.D. B.D MO.4 1 BRIDGE HOUSE — i AMIDSHIPS SHORT RAISED! QUARTER DECK P"™ 40.5 VESSEL HAVING TOP GALLANT FORECASTLE, WITH A LONG POOP AND BRIDGE HOUSE COMBINED. KNOWN AS A " WELL DECKED VESSEL' WELL „ Figs. 18-22. 110 The Naval Constructor VESSEL HAVING TOP-GALLANT FORECASTLE WITH A LONG RAISED TRANVERSE SECTION9. QUARTER DECK AND BRIDGE HOUSE COMBINED ALSO KNOWN AS A WELL LONG RAUEO DECKED VESSEL a r> QUARTER DECK l , - 1 EXTE NDING SHADE DECKED VESSEL THIS TYPE OF VESSEL HAS A CONTINUOUS UPPER- N °- 7 I DECK OF LIGHT CONSTRUCTION AND WITH OPENING8 IN THE SIDES. OPEN ING SHADE DECK T""""" j •AWNING DECKED VEB8EL' THIS TYPE OF VESSEL HAS A CONTINOUS UPPER DECK OFLIGHTCONSTRUCTION AND THE SIDES COMPLETELY CLOSED ABOVE ENGINE^* BPJLER_CA8ING9. AWNINGJ>ECJ< THE MAIN DECK- _AWNING DECK * -t. r.",rl DECK ' AWNING DECK. 'SPAR DECK VESSEL"THIS TYPE OFVESSEL IS CONSTRUCTED WITH THE 6CANTLING8 ABOVE THE MAIN DECK HEAVIER THAN IN AN"AWNING DECKED" VESSEL BUT NOT SO HEAVY AS IN A "THREE DECKED VES8EL" B.D, SPAR DECK . — t 3 L^. TURRET DECK VESSEL ENGINE *_BpiLi?_ _CASINGS. Asm 5 m TRUNK DECK VESSEL B.D. Figs. 23-28. Freeboard Marks for Steamers 111 Statutory allowance above top of wood deck = 2" Centre of disc below statutory deck line = 6' 7 \' Draught of water moulded * = 26' 10|' DIAGRAMofFREEBOARD MARKS forSTEAMERS. (FOR FREEBOARD SEE TABLES) UPPER DECK LINE (NOT TO BE MARKED ON 8HIP,) THE MARKINGS TO BE CUT INTO PLATING WITH CENTRE-PUNCH MARKS AS SHOWN AND PAINTED WHITE METHOD OF MARKING LINES AND LETTERS WITH CENTRE- PUNCH. CENTRE OF DISC TO BE PLACED AT THE MIDDLE OF THE LENGTH OF THE LOAD WATER LINE — *l LINES FOR SMALL LETTER8 Y THICK. THESE DIMENSIONS TO BE TAKEN FROM CR. OF DISC TO TOP EACH LINE ST'B'D. SIDE SHOWN- PORT SIDE SIMILAR Fig. 30. (Fig. 29 in this edition has been omitted.) 112 The Naval Constructor jjvua avon nv coco mcomroCMOJC\i« o \f N\)[ > ^ /•* ^ *iNQV> ,1* 2= 1i\3ffi CPC^ - / * 5 z $E>55 o * o $vx0a - ,86 J y d a o -i u iVA T h^ O uj H -J u, '\K^ . ,88 a. Jh ^ ,, x <" a *\v*- Q gd?" w SpK $& - ,92 Q UJ * x ^ 5 £ s u S $Kl_ _t «^ ^°u1x- Q fiOr /*• O i^ o^'z m k DIAGRAM Gl IN FLUSH Al PROPORTIONS jj IN EACH CASE T LOAD DRAFT TO CENTRE NOTE. -ALLOWANCES FOR EXCE DECK (IN FLUSH DECK S DRAFT FOR A GIVEN DEP DUE TO UNCOVERED IRC FREEBOARD TABLES. \ ^ »V ^ i InN y\ ^ /9l E ^ ,H IN< \ /SI I ^ ,01 1^ ,8 Load Draught Diagrams 113 DIAGRAM SHOWING RELATIVE DEPTHS AND LOAD DRAFTS IN VARIOUS TYPES OF VESSELS. PROPORTIONS^) IN SPAR DECK SHIP TAKEN TO SPAR DECK (7'-o" ABOVE MAIN DECK*) •1 ii ii AWNING " " " " MAIN " '• " "SAILING " " "UPPER " D DEPTH MOULDED TO RESPECTIVE DECK8. ^<^rf" NOTE:--ALLOWANCES FOR EXCESS OF SHEER AND V. -A ^-<^L. £ p. 26' <^^ «J? -%J 24' FOR GIVEN DEPTH. ^ C ^ *& v *v 22' .; «.kv ^ -fe yV n j^ ^" 20 ' S s&k% » ^ _^3 rfkj > 18' ^ *; #y * >> J< >* _l % P ^ ^ M'J 0OLdf ,v: x Ul ^ j^i 1*' n ^ v k ^ 12' 3 ff ^ o 4 ^ 10' z ^ & u P* 8' ui 1*0 6' g CO o eg o CM a MOULDED DEPTH, TO MAIN DECK IN SPAR AND AWNING DECK VESSELS «' «« "UPPER <« «« SAILING SHIPS. Fig. 32. 114 The Naval Constructor Table A. Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Buoyancy (Winter). 20.4 20.6 20.8 21.0 21.2 21.4 21.6 21.8 Corresponding Height of Freeboard Amidships (Winter). Measured from Top of Deck at Sides. Moulded Depth and Length. 6 6 6 7 i a 7 6 8 8 6 9 / // 9 6 72 78 84 90 96 / 102 / 108 114 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 8 8 8J 8} 9 9J 9 9i 9 9 9J 9} 10 10 101 101 > a 10 10 101 101 11 11 111 11* / // 11 11 111 in 1 1 1 01 1 01 1 1 1 01 1 01 1 1 l H 1 U i a 1 1 i u 1 u 1 2 1 2 1 21 1 21 / a 1 2 1 2 1 21 1 21 1 3 1 3 1 31 1 31 1 3 1 3 1 3} 1 31 1 4 1 4 1 41 1 41 Correction in inches for a 1 change of 10' 1 in the length. 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 Deductions in 1 ins. for sum- | mer voyages. J 1 1 • 1 1 • ' Freeboard Tables 115 Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 22. 0~ 22.2 22.4 22.6 22.8 23.0 23.2 23.4 Corresponding Height of Freeboard Amidships (Winter). Coefficient of Measured from Top of Deck at Side. Moulded Depth and Length. 10 10 6 11 11 6 12 12 6 13 13 6 120 / 126 132 138 144 150 156 162 0.68 1 4 1 5 1 6 i n 1 8* 1 9| 1 11 2 0.70 1 4 1 5 1 6 i n 1 8£ 1 9| 1 11 2 0* 0.72 1 4* 1 5* 1 6£ 1 8 1 9 1 10 1 111 2 1 0.74 1 4| 1 5£ 1 6| 1 8 1 9 1 10 1 111 2 1 0.76 1 5 1 6 1 7 1 8* 1 9* 1 10J 2 2 li 0.78 1 5 1 6 1 7 1 8} 1 9* 1 11 2 0£ 2 2 0.80 1 5* 1 6* i n 1 9 1 10 1 11* 2 1 2 2i 0.82 1 5* 1 6£ i n 1 9 1 10 i m 2 1 2 2i Correction in ins. for a 1 change of 10' j 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 in the length. Deductions in j ins. for sum- | 1 1 1 1 1 1 1 li mer voyages. J 116 The Naval Constructor Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Coefficient of Fineness. Pebcentage Reserve Buoyancy (Winter). 23.6 23.8 24.0 24.2 24.5 24.7 Corresponding Height of Freeboard Amidships (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 14 14 6 15 15 6 16 16 6 168 174 180 186 192 198 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 / // 2 1| 2 14 2 2 2 24 2 3 2 3 2 34 2 4 2 3 2 3 2 3} 2 4 2 44 2 4i 2 5 2 54 2 4 2 4J 2 5 2 54 2 6 2 6 2 6i 2 7 2 5i 2 6 2 6i 2 7 2 74 2 74 2 8 2 84 2 7 2 74 2 8 2 84 2 9 2 9 2 94 2 10 2 84 2 9 2 94 2 10 2 104 2 11 2 114 3 Correction in ins. 1 for a change of > 10' in the length.] 1.0 1.0 1.0 1.0 1.0 1.0 Deduction in ins. for summer voyages. J II li li 14 14 2 Freeboard Tables 117 Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Buoyancy (Winter) 25.0 25.2 25.5 25.7 26.0 Corresponding Height of Freeboard Amid- ships (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 17 17 6 18 18 6 19 204 210 216 222 t 228 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 2 10J 2 10 2 11 2 11} 3 3 0i 3 1 3 l\ 2 Hi 3 3 0£ 3 1 3 1| 3 2 3 2J 3 3 3 1 3 I* 3 2 3 2h 3 3 3 4 3 4| 3 5 3 2J 3 3 3 3* 3 4 3 5 3 5* 3 6 3 6i / // 3 4 3 4 3 5* 3 6 3 "6i 3 1\ 3 8 3 8} Correction in ins. for | a change of 10' in [ the length. 1.1 1.1 1.1 1.1 1.1 Deduction in ins. fori summer voyages. 2 2 2 2 2 118 The Naval Constructor Table A.. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Buoyancy (Winter). 26.2 26.5 26.7 27.0 27.3 27.5 Corresponding Height of Freeboard Amidships (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 19 6 20 20 6 21 21 6 22 234 240 246 252 258 264 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 3 5} 3 «i 3 7 3 8 3 8} 3 9J 3 10 3 10i 3 7i 3 8 3 8* 3 9i 3 10 3 11 3 Hi 4 3 9 3 10 3 10i 3 11} 4 4 1 4 1} 4 2 3 Hi 3 Hi 4 4 1 4 li 4 2i 4 3 4 3i 4 0i 4 li 4 2 4 3 4 3i 4 4i 4 5 4 5i 4 2i 4 3i 4 4 4 5 4 5i 4 6i 4 7 4 7i Correction in ins. ) for a change of / lCJin the length. ) 1.1 1.2 1.2 1.2 1.2 1.2 Deduction in ins. ) for summer / voyages. ) 2* 2* Si 2i 2i 2i Freeboard Tables 119 Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 27.8 28.1 28.3 28.6 28.9 29.2 Corresponding Height of Freeboard Amidships (Winter). Coefficient op Fineness. Measured from Top of Deck at Side. Moulded Depth and Length. 22 6 23 23 6 24 24 6 25 270 276 282 288 i 294 300 0.68 4 4* 4 6* 4 8i 4 10* 5 1 5 3J 0.70 4 5* 4 n 4 9* 4 m 5 ti 5 4 0.72 4 6 4 8 4 10 5 5 2* 5 5 0.74 4 7 4 9 4 11 5 1 5 3 5 5i 0.76 4 7* 4 9* 4 m 5 li 5 4 5 6* 0.78 4 8* 4 10* 5 0i 5 2* 5 4} 5 7 0.80 4 9 4 11 5 1 5 3 5 5* 5 8 0.82 4 9* 4 111 5 2 5 4 5 6* 5 9 Correction in ins. ) for a change of > 1.2 1.2 1.3 1.3 1.3 1.3 10' in the length. ) Deduction in ins. ) for summer £ 3 3 3 3 3 3} voyages. ) 120 The Naval Constructor Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 29.5 29.8 30.1 30.4 30.8 31.1 Corresponding Height of Freeboard Amidships coeiticient of Fineness. (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 25 6 26 26 6 / // 27 27 6 28 306 312 318 324 330 336 0.68 5 5i 5 8 5 10 6 0| 6 3 6 5 0.70 5 6 5 8i 5 10* 6 1 6 3| 6 6 0.72 5 7 5 «!J 5 11| 6 2 6 4} 6 7 0.74 5 7J 5 10 6 0} 6 3 6 5J 6 8 0.76 5 8} 5 11 6 1| 6 4 6 6| 6 9 0.78 5 9 5 111 6 2 6 4* 6 7 6 9} 0.80 5 10 6 0} 6 3 6 .V, 6 8 6 10J 0.82 5 11 6 1} 6 4 6 6| 6 9 6 Hi Correction in ins. ) for a change of > 1.3 1.4 1.4 1.4 1.4 1.4 10' in the length. ) Deduction in ins. ) for summer / voyages. ) H 3* 3J 4 4 4 Freeboard Tables 121 Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 31.3 31.5 31.8 32.0 32.3 32.6 Corresponding Height of Freeboard Amidships (Winter). Coefficient of Fineness. Measured from Top of Deck at Side. Moulded Depth and Length. 28 6 29 29 6 30 30 6 31 342 348 354 360 366 372 0.63 6 7 6 9 6 11 7 1| 7 4 7 6* 0.70 6 8 6 10* 7 0* 7 3 7 5£ 7 8 0.72 6 9 6 11) 7 n 7 4 7 6i 7 9 0.74 6 10 7 Q\ 7 2* 7 5 7 7* 7 10 0.76 6 11 i w 7 3* 7 6 7 8* 7 11 0.78 7 7 2\ 7 5 7 lh 7 10 8 0* 0.80 7 1 7 Zh 7 6 7 8h 7 11 8 1* 0.82 7 2 7 4* 7 7 7 91 8 8 2i Correction in ins. ) for a change of ( 1.5 1.5 1.5 1.5 1.5 1.6 10' in the length. ) Deduction in ins. ) for summer / 4 4} 4* 4* 5 5 voyages. ) 122 The Naval Constructor Table A. — {Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron a nd Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 32.8 33.0 33.3 33.5 33.8 34.0 Corresponding: Height of Freeboard Amidships Coefficient of Fineness. (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 31 6 32 32 6 33 33 6 34 378 384 390 396 402 408 0.68 7 9 7 11| 8 1} / // 8 4 8 6* 8 9 0.70 7 10} 8 1 8 3 8 5} 8 8 8 10} 0.72 7 Hi 8 2 • 8 4 8 6} 8 9 8 11} 0.74 8 0} 8 3 8 5} 8 8 8 10} 9 1 0.76 8 1} 8 4 8 6} 8 9 8 11} 9 2 0.78 8 3 8 5J 8 8 8 10* 9 1 9 3} 0.80 8 4 8 6} 8 9 8 11} 9 2 9 4} 0.82 8 5 8 7} 8 10 9 0} 9 3 9 5} Correction in ins. ) for a change of / 1.6 1.6 1.6 1.6 1.7 1.7 10' in the length. ) • Deduction in ins. ) for summer > 5 5 5} 5} 5} 6 voyages. ) Freeboard Tables 123 Table A. — {Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Buoyancy (Winter). 34.2 34.4 34.6 34.7 34.9 35.1 35.3 35.4 Corresponding Height of Freeboard Amidships (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 34 6 35 35 6 36 36 6 37 37 6 / // 38 414 420 426 432 438 444 450 456 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 8 Hi 9 1 9 2 9 3* 9 4* 9 6 9 7 9 8 9 2 9 3 9 4 9 5* 9 7* 9 8 9 9* 9 10* 9 4 9 5 9 6* 9 8 9 9 9 10* 9 n* 10 1 9 6 9 7 9 8* 9 10 9 11 J 10 0i 10 2 10 3J 9 8* 9 9* 9 11 10 0* 10 2 10 3 10 4* 10 6 9 11 10 10 1* 10 3 10 4* 10 5* 10 7 10 8* 10 \\ 10 2* 10 4 10 5* 10 7* 10 8 10 9* 10 11 10 3i 10 5 10 6* 10 8 10 9* 10 10* 11 11 1* Correction in ins. for a 1 change of 10' [ in the length. Deduction in ins. for summer voyages. 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 6 6 6 6* 6* 6* 6J 7 124 The Naval Constructor Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter) 35.4 35.5 35.6 35.6 35.7 35.7 35.8 35.8 Corresponding Height of Freeboard Amidships Coefficient op Fineness. (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 38 6 39 39 6 40 40 6 41 41 6 42 462 468 474 480 486 492 498 504 0.68 10 5£ 10 7J 10 9} io Hi 11 1} 11 3i 11 6 11 8 0.70 10 7 10 9 10 11 n i 11 3 11 5 11 lh 11 9* 0.72 10 Si 10 .10* 11 0* 11 2J 11 4! 11 fij 11 9 11 11 0.74 10 10 11 11 2 11 4 11 6 11 8 11 10* 12 0i 0.76 11 11} 11 u 11 3} 11 5} 11 7| 11 9} 12 12 2 0.78 11 (I 1 . 11 2i 11 4* 11 7 11 9 11 11 12 1J 12 3J 0.80 11 2 11 4 11 6 11 .Si 11 10.'. 12 0} 12 3 12 5 0.82 11 3* 11 5i ii n 11 10 12 12 2} 12 5 12 7 Correction in ins. for a 1 change of 10' f 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 in the length. Deduction in ins. for summer 7 7 7 7} 7| 71 71 8 voyages. Freeboard Tables 125 Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage Reserve Buoyancy (Winter). 35.8 35.8 35.8 35.8 35.8 35.8 35.8 35.8 Corresponding Height of Freeboard Amidships Coefficient of Fineness. (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. 42 6 43 43 6 44 44 6 45 45 6 46 510 516 522 528 534 540 546 552 0.68 11 10i 12 12 2 12 3* 12 5 12 7 12 9 12 10* 0.70 12 12 2 12 4 12 5* 12 7 12 8i 12 10£ 13 0.72 12 fj 12 3J 12 5i 12 7 12 8i 12 10 13 13 2 0.74 12 3 12 5 12 7 12 8} 12 10 13 13 2 13 4 0.76 12 4* 12 6* 12 8i 12 10 13 13 2 13 4 13 6 0.78 12 6 12 8 12 10 13 13 2 13 Si 13 5i 13 7j 0.80 12 7i 12 9£ 12 Hi 13 1} 13 3* 13 5 13 7 13 9 0.82 12 9* 12 Hi 13 1" 13 8| 13 5* 13 7 13 9 13 10* Correction in ins. for a 1 change of 10' | 1.7 1.7 1.7 17 1.7 1.7 1.7 1.7 in the length.] • Deduction in ins. for summer 8 8 8 8| 8} 8i 8| 9 voyages. 126 The Naval Constructor Table A. — (Continued.) Cargo-carrying Steam Vessels Not Having Spar or Awning Decks. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Steam Vessels (in Salt Water). Percentage of Reserve Buoyancy (Winter). 35.8 35.8 35.8 35.8 35.8 35.8 35.8 35.8 Corresponding Height of Freeboard Amidships Coefficient of Fineness. (Winter). Measured from Top of Deck at Side. Moulded Depth and Length. , „ , ,, , „ t n / // i // / a / ,, 46 6 47 47 6 48 48 6 49 49 6 50 558 564 570 576 582 588 594 600 0.68 13 13 1* 13 3 13 5 13 6* 13 8 13 9i 13 11 0.70 13 1J 13 3 13 4J 13 6* 13 8 13 10 13 Hi 14 1 0.72 13 3} 13 5 13 6J 13 .s.J 13 10 13 11* 14 1 14 3 0.74 13 5i 13 7 13 8i 13 10* 14 14 1* 14 3 14 4} 0.76 13 1\ 13 9 13 10* 14 0* 14 2 14 3* 14 5 14 6i 0.78 13 9 13 10£ 14 14 2 14 3* 14 5 14 6} 14 8i 0.80 13 10* 14 14 \\ 14 3* 14 5 14 6i 14 8 14 10 0.82 14 0J 14 2 14 3i 14 5* 14 7 14 8i 14 10 15 Correction in ins. for a 1 change of 10' 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 in the length. " Deduction in ins. for summer 9 9 9 H 9* 9J 9J H voyages. Freeboard Tables 127 Table B. Cargo-carrying Spar Deck Vessels. Table of Freeboard to Spar Deck for First-class Sea-going Spar Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Spar Deck at Side. Moulded Depth (to Main Deck) and Length. 13 13 6 14 14 6 15 15 6 240 246 252 258 264 270 0.68 0.70 0.72 0.74 0.76 0.78 80 0.82 5 5 5 5* 5 6 5 6* 5 7 5 7* 5 8 5 8} 5 6 5 H 5 7 5 7* 5 8 5 8* 5 9 5 9* 5 7 5 7* 5 8 5 8* 5 9 5 9* 5 10 5 10* 5 8 5 8* 5 9 5 9* 5 10 5 10i 5 11 5 Hi 5 9 5 9* 5 10 5 10* 5 11 5 Hi 6 6 0* 5 10 5 10* 5 11 5 11* 6 6 0* 6 1 6 1* Correction in ins. ) for a change of / 10' in the length . ) 0.9 0.9 0.9 0.9 0.9 0.9 Deduction in ins. ) for summer / voyages. ) 2 2 2 2 H 2* 128 The Naval Constructor Table B. — (Continued.) Cargo-carrying Spar Deck Vessels. Table of Freeboard to Spar Deck for First-class Sea-going Spar Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Spar Deck at Side. Moulded Depth (to Main Deck) and Length. 16 16 6 17 17 6 18 18 6 276 282 288 294 300 306 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 5 11 5 ill 6 6 0} 6 1 6 1} 6 2 6 2\ / // 6 6 0i 6 1 6 1| 6 2 6 2\ 6 3 6 3* 6 1J 6 2 6 2J 6 3 6 3h 6 4 6 4§ 6 5 6 2i 6 3i 6 4 6 4i 6 5 6 5h 6 6 6 H 6 4 6 5 6 5J 6 6 6 6* 6 7 6 1\ 6 8 6 5| 6 6* 6 7 6 7} 6 8 6 8} 6 9 6 9£ Correction in ins. ) for a change of / 10' in the length. ) 1.0 1.0 1.0 1.0 1.0 1.0 Deduction in ins. ) for summer > voyages. ) 2J n 3 3 3 3 Freeboard Tables 129 Table B. — (Continued.) Cargo-carrying Spar Deck Vessels. Table of Freeboard to Spar Deck for First-class Sea-going Spar Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Spar Deck at Side. Moulded Depth (to Main Deck) and Length. 19 19 6 20 20 6 21 21 6 312 318 324 330 336 342 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 6 n 6 8* 6 9 6 9* 6 10 6 10* 6 11 6 Hi 6 9 6 10 6 10j 6 11 6 ll| 7 7 0* 7 1 6 11 7 7 0* 7 1 7 H 7 2 7 2* 7 3 7 0J 7 1§ 7 2 7 3 7 3* 7 4 7 4* 7 5 7 2J 7 3i 7 4 7 5 7 5* 7 6 7 6* 7 7 7 4* 7 5* 7 6 7 7 7 7i 7 8 7 8i 7 9 Correction in ins. ) for a change of / 10' in the length. ) 1.1 1.1 1.1 1.1 1.1 1.2 Deduction in ins. ) for summer > voyages. ; 3* 3* 3* 4 4 4 130 The Naval Constructor Table B. — (Continued.) Cargo-carrying Spar Deck Vessels. Table of Freeboard i Spar Deck for First voyages. ) . 54 54 54 6 6 132 The Naval Constructor Table B. — (Continued.) Cargo-carrying Spar Deck Vessels. Table of Freeboard to Spar Deck for First-class Sea-going Spar Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Spar Deck at Side. Moulded Depth (to Main Deck) and Length. 28 28 6 29 29 6 30 420 426 432 438 444 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0,82 10 2 10 3 10 4 10 5 10 6 10 7 10 7i 10 8i 10 5 10 6 10 7 10 8 10 9 10 10 10 10i 10 111 / // 10 81 10 91 10 101 10 111 11 01 11 11 11 2 11 3 10 111 11 01 11 11 11 21 11 31 11 41 11 51 11 61 11 3 11 4 11 5 11 6 11 7 11 8 11 9 11 10 Correction in ins. ) for a change of > 10'in the length. J 1.4 1.5 1.5 1.5 1.5 Deduction in ins. 1 for summer > voyages. ; 6 6 61 61 61 Freeboard Tables 133 Table C. Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 8 8 6 9 9 6 10 10 6 96 102 108 114 120 126 66 68 0.70 72 74 76 0.78 0.80 1 1 1 li 1J li If 2 1 1 1 t| li li li 2 li li li 2 2 2 2 2* li li li 2 2 2i 2i 3 2 2 2 2i 2i 2i 2i 3 2 2 2 2| 2i 3 3 3i Correction in ins. ) for a change of / 10' in the length ) 0.4 0.4 0.4 0.4 0.4 0.5 Deduction in ins. ) for summer > voyages. ) 2 2 2 2 2 2. 134 The Naval Constructor Table C. — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Heioht of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 11 11 6 12 12 6 13 13 6 132 138 / 144 150 / 156 162 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 2i 2i 2J 3 3 3 3 3i 2J o -i\ 2i 3 3 3} 3i 4 3 3 3 3} 3J 4 4 4* 3} 3} 3i 4 4 4J 4} 5 4 4 4 4} 4J 5 5 5} 4} 41 4} 5 5 5J 51 6 Correction in ins. ) for a change of / 10' in the length. ) 0.5 0.5 0.5 0.5 0.5 0.5 Deduction in ina. ) for summer > voyages. ) 2 2 2 2 2 2 Freeboard Tables 135 Table C — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 14 14 6 15 15 6 16 16 6 168 174 180 186 192 198 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 5 5 .0 51 5* 6 6 61 6* 51 5} 6 6 61 61 7 7 6 6 6* 6* 7 7 o n 71 / // 6* 6* 7 7 71 7* 8 8 7 7 71 8 8 8} 9 9 71 7* 8 81 81 9 91 91 Correction in ins. ) for a change of £ 10' in the length. ) 0.5 0.5 0.5 0.5 0.5 0.5 Deduction in ins. ) for summer > voyages. ) 2 2 2 2 2 21 136 The Naval Constructor Table C — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 17 17 6 18 18 6 19 19 6 204 210 216 222 228 234 66 0.68 70 72 0.74 0.76 0.78 80 8} 8§ 9 9i 9i 10 101 10-5 9 9 9i 10 10 10i 11 11 10 10 10| 11 11 iii 1 1 11 11 11} 1 1 1 0} 1 1 1 1 1 1 1 0} 1 1 1 1 1 11 1 2 1 2 1 1ft 1 1J 1 2 1 2i 1 2} 1 3 1 3} 1 3£ Correction in ins. ) for a change of > 10' in the length. ) 5 5 5 0.6 0.6 0.6 Deduction in ins. ) for summer ? voyages. ) 2| 2ft 2ft 3 3 3 Freeboard Tables 137 Table C. — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 20 20 6 21 21 6 22 22 6 240 246 252 258 264 270 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 1 2* 1 2* 1 3 1 3* 1 8} 1 4 1 4* 1 5 1 4 1 4 1 4* 1 5 1 5 1 5* 1 6 1 6} 1 5 1 5 1 bh 1 6 1 6 1 6£ 1 7 1 7* l H 1 6i 1 7 l H i n 1 8 1 Sh 1 9 . 1 n 1 7i 1 8 1 B| 1 8i 1 9 1 9 1 10 1 8i 1 9 1 9* 1 10 1 10 1 10* 1 11 1 111 Correction in ins. ) for a change of / 10' in the length. ) 0.6 0.6 0.6 0.6 0.6 0.6 Deduction in ins. ) for summer / voyages. ) Si H 3* 3* 4 4 138 The Naval Constructor Table C. — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient or Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 23 23 6 24 24 6 25 25 6 276 282 288 294 300 306 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 1 10 1 10* 1 11 i m 1 nj 2 2 0} 2 1 1 11* 2 2 0* 2 1 2 1 2 U 2 2 2 2* 2 1 . 2 U 2 2 2 2* 2 3 2 3* 2 4 2 4* 2 3 2 31 2 4 2 41 2 5 2 51 2 6 2 61 2 41 2 5 2 51 2 6 2 61 2 7 2 71 2 8 2 61 2 7 2 71 2 8 2 81 2 9 2 91 2 10 Correction in ins. ) for a change of / 10' in the length. ) 0.6 0.6 0.6 0.7 7 0.7 Deduction in ins. ) for summer > voyages. ) 4 M 41 41 5 5 Freeboard Tables 139 Table C. — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 26 26 6 27 27 6 28 28 6 312 318 324 330 336 342 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 2 8 2 8| 2 9 2 n 2 10 2 11 2 11| 3 2 10 2 10* 2 11 2 m 3 3 1 3 U 3 2 3 0* 3 1 3 U 3 2 3 2* 3 3* 3 4 3 4* 3 2\ 3 3 3 3* 3 4 3 4* 3 5* 3 6 3 8* 3 4* 3 5 3 5* 3 6 3 6* 3 n 3 8 3 6* 3 6* 3 7 3 7* 3 8 3 8* 3 9* 3 10 3 10* Correction in ins. ) for a change of ? 10' in the length. ) 0.7 0.7 0.7 0.7 0.7 0.7 Deduction in ins. ) for summer / voyages. ) 5 5* 5* 5* 5i 6 140 The Naval Constructor Table C — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Coefficient of Fineness. Height of Freeboard Amidships (Winter). Measured from Top of Main Deck at Side. Moulded Depth (to Main Deck) and Length. 29 29 6 ... 30 30 6 31 31 6 348 354 360 366 372 378 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 3 8} 3 9 3 9} 3 10 3 10| 3 Hi 4 4 0* 3 10| 3 11 3 Hi 4 0£ 4 1 4 2 4 H 4 3 4 0J 4 1| 4 2 4 3 4 3* 4 4J 4 5 4 5i 4 3 4 4 4 4i 4 5* 4 6 4 7 4 7i 4 8 4 5i 4 6§ 4 7 4 8 4 8J 4 9* 4 10 4 10J 4 8 4 9 4 9* 4 10* 4 11 5 5 0J 5 1 Correction in ins. ) for a change of- / 10' in the length. ) 0.7 0.8 0.8 0.8 0.8 0.8 Deduction in ins. ) for summer > voyages. ) 6 6 6 6 6 6* Freeboard Tables 141 Table C. — (Continued.) Cargo-carrying Awning Deck Vessels. Table of Freeboard for First-class Sea-going Awning Deck Steam Vessels (in Salt Water). Height of Freeboard Amidships 3epth from A to C. (Winter). Measured from Top of Main Deck at Side. For Steamers above 34' Moulded '. Deduct the Following Amount the Freeboards Given in Table Obtain the Freeboards for Table Coefficient of Fineness. Moulded Depth (to Main Deck) and Length. 32 32 6 33 33 6 34 384 390 396 402 408 0.66 4 10* 5 1 5 3} 5 6 5 8 3 0.68 4. 11} 5 2 5 4* 5 7 5 9 3 0.70 5 5 2} 5 5 5 7} 5 9} 3 1 0.72 5 1 5 3} 3 6 5 8} 5 10} 3 1 0.74 5 1} 5 4 5 6} 5 9 5 11 3 2 0.76 5 2} 5 5 5 7} 5 10 6 3 2 0.78 5 3 5 5} 5 8 5 10} 6 0} 3 3 0.80 5 3* 5 6 5 8} 5 11 6 1} 3 3 Correction in ins. ) for a change of £ 0.8 0.8 0.8 0.8 0.8 10' in the length. ) Deduction in ins. ) for summer / 6} 6} 6} 6} 6} voyages. ) 142 The Naval Constructor Table D. Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Pebcentage Reserve Buoyancy Coefficient or (Iron Vessels). 21.7 21.9 22.1 22.3 22.5 Fineness. Corresponding Height or Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- Moulded Depth and Length. , „ / // , „ / // , „ posite. 5 6 6 6 6 7 7 6 55 60 65 70 75 0.64 Si 9i 10i Hi 1 Oi 0.64 0.66 8i 9i 10i Hi 1 0i 0.66 0.68 9 10 11 1 1 1 0.64 0.68 0.70 9 10 11 1 1 1 0.66 0.70 0.72 lij 10i o Hi 1 0i 1 li 0.68 0.72 0.74 9i 10i Hi 1 0i l li 0.70 0.74 10 11 1 1 1 1 2 0.72 10 11 1 1 1 1 2 Correctio l in ins. for a ) change of 10' ii i the > 0.8 0.8 0.8 0.8 0.8 length. ) Freeboard Tables 143 Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Percentage Reserve Buoyancy (Iron Vessels). Coefficient of Fineness. 22.7 22.9 23.1 23.3 23 5 Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- posite. Iron. Moulded Depth and Length. 8 / // 8 6 9 9 6 10 80 85 90 95 100 0.64 0.66 0.68 0.70 0.72 0.64 0.66 0.68 0.70 0.72 0.74 0.64 0.66 0.68 0.70 0.72 0.74 l \\ i U 1 2 1 2 1 2\ 1 2* 1 3 1 3 1 2J 1 2i 1 3 1 3 1 Z\ 1 3* 1 4 1 4 1 3* 1 3J 1 4 1 4 1 4J 1 4J 1 5 1 5 1 4J 1 4J 1 5 1 5 1 5} 1 5* 1 6 1 6 1 5* 1 5i 1 6 1 6 1 6J 1 « 1 7 1 7 Correction in ins. for a ) change of 10' in the ? length. ) 0.8 0.9 0.9 0.9 0.9 144 The Naval Constructor Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Percentage Reserve Buoyancy Coefficient of (Iron Vessels). 23.7 23.9 24.2 24.4 24.6 ] Fineness. Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- posite. Iron. Moulded Depth and Length. 10 6 11 11 6 12 12 6 105 110 115 120 125 0.64 1 6* 1 7* 1 9 1 10* 1 11* 0.64 0.66 1 6* i n 1 9 1 10* 2 0.66 0.68 1 7 1 8 1 9* 1 11 2 0* 0.64 0.68 0.70 1 7 1 8* 1 10 1 11* 2 1 0.66 0.70 0.72 i n 1 9 1 10* 2 2 1* 0.68 0.72 0.74 i « 1 9 1 10* 2 2 1* 0.70 0.74 1 8 1 9* 1 11 2 0* 2 2 0.72 1 8* 1 10 1 11* 2 1 2 2* Correctio i in ins. for a ) change of 10' ii i the > 0.9 0.9 1.0 1.0 1.0 length. > Freeboard Tables 145 Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Coefficient of Fineness. Wood. Com- posite. 0.64 0.66 0.64 0.68 0.66 0.70 0.68 0.72 0.70 0.74 0.72 . Iron. 0.64 0.66 0.68 0.70 0.72 0.74 Correction in ina. for a change of 10' in the length. Percentage Reserve Buoyancy (Iron Vessels). 24.9 25.1 25.3 25.5 25.7 Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Moulded Depth and Length. 130 1.0 13 6 14 6 15 150 2 8* 2 9 2 9| 2 10 146 The Naval Constructor Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Percentage Reserve Buoyancy (Iron Vessels). Coefficient of 26.0 26.2 26.4 26.6 26.8 Fineness. Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- Moulded Depth and Length. , „ , „ , „ , ;, posite. 15 6 16 16 6 17 17 6 155 160 165 170 175 64 , „ , „ , „ , „ , „ 0.64 66 0.66 68 2 8 2 81 2 91 2 10 2 11 2 111 3 01 3 1 3 2 3 21 0.64 0.63 0.70 2 9 2 101 3 3 H 3 3 0.66 0.70 0.72 2 91 2 11 3 01 3 2 3 31 0.68 0.72 0.74 2 10 2 11 3 1 3 21 3 4 0.70 0.74 2 101 3 3 11 3 3 3 41 0.72 2 11 3 01 3 2 3 31 3 5 2 llj 3 1 3 21 3 4 .3 51 Correction in ins. for a ) change of 10' ii i the / 1.1 1.1 1.1 1.1 1.1 length '1 Freeboard Tables 147 Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class {in Salt Water). Percentage Reserve Buoyancy (Iron Vessels). Coefficient of Fineness. 27.1 27.3 27.4 27.5 27.6 Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Com- posite. Iron. Moulded Depth and Length. Wood. 18 18 6 19 19 6 20 180 185 190 195 200 0.64 0.66 0.68 0.70 0.72 0.64 0.66 0.68 0.70 0.72 0.74 0.64 0.66 0.68 0.70 0.72 0.74 3 3* 3 4 3 4} 3 5 3 5£ 3 6 3 6£ 3 7 3 5 3 5| 3 6 3 6| 3 7} 3 8 3 8£ 3 9 3 6* 3 7 3 7* 3 8 3 9 3 % 3 10 3 10* 3 8 3 8* 3 9 3 9| 3 10£ 3 11 3 in 4 3 9* 3 10 3 10i 3 11 4 4 0J 4 1 4 li Correction in ins. for a ) change of 10' in the ? length. ) 1.1 1.1 1.2 1.2 1.2 148 The Naval Constructor Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Waief). Percentage Reserve Buoyancy Coefficient of (Iron Vessels). 27.7 27.9 28.0 28.2 28.3 Fineness. Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- posite. Iron. Moulded Depth and Length. 20 6 21 21 6 22 22 6 205 210 215 220 225 0.64 3 11 . 4 0i 4 2 4 3} 4 5 0.64 0.66 3 11} 4 1 4 3 4 4} 4 6 0.66 0.68 4 4 n 4 3} 4 5 4 6} 0.64 0.68 0.70 4 0} 4 2 4 4 4 .li 4 7 0.66 0.70 0.72 4 1* 4 3 4 5 4 6* 4 8 0.68 0.72 0.74 4 2 4 3} 4 5i 4 7 4 8i 0.70 0.74 4 2} 4 4i 4 6 4 8 4 9} 0.72 4 3 4 5 4 7 4 8| 4 10 Correction in ins. for a ) change of 10' ii i the > 1.2 1.2 1.2 1.2 1.2 length. > Freeboard Tables 149 Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Percentage Reserve Buoyancy (Iron Vessels). Coefficient of Fineness. 28.5 28.6 28.8 28.9 29.1 Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Com- posite. Iron. Moulded Depth and Length. Wood. 23 23 6 24 24 6 25 230 235 240 245 250 0.64 0.66 0.68 0.70 0.72 0.64 0.66 0.68 0.70 0.72 0.74 0.64 0.66 0.68 0.70 0.72 0.74 4 6* 4 71 4 8 4 81 4 91 4 10 4 11 5 4 8 4 9 4 91 4 10 4 11 4 111 5 01 5 11 4 10 4 101 4 111 5 5 1 5 11 5 21 5 31 4 111 5 5 1 5 H 5 21 5 3 5 4 5 5 / a 5 11 5 2 5 3 5 31 5 41 5 5 5 6 5 7 Correction in ins. for a ) change of 10' in the £ length. ) 1.3 1.3 1.3 1.3 1.3 150 The Naval Constructor Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels and Composite and Wood Vessels of the Highest Class (in Salt Water). Percentage Reserve Buoyanct Coefficient of (Iron Vessels). 29.2 29.4 29.5 29.7 Fineness. Corresponding: Height of Freeboard Amidships. Measured from Top of Deck at Side. Wood. Com- Moulded Depth and Length. , „ , „ . „ , „ posite. 25 6 26 26 6 27 255 260 265 270 0.64 5 3 5 5 5 61 5 81 0.64 0.66 5 3J 5 51 5 71 5 91 0.66 0.68 5 4J 5 6f 5 81 5 101 0.64 0.68 0.70 5 5 5 7 5 9 5 11 0.66 0.70 0.72 5 6 5 8 5 10 6 0.68 0.72 0.74 5 61 5 81 5 10* 6 01 0.70 0.74 5 71 5 91 5 111 6 U 0.72 5 81 5 101 6 01 6 21 Correctioi l in ins. for a ) change of 10' i n the / 1.3 1.3 1.3 1.4 length. ) Freeboard Tables 151 Table D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Buoyancy. 29.8 30.0 30.2 30.4 Corresponding Height of Freeboard Amidships. Measured from Top of Deck at Side. Iron. Moulded Depth and Length. 27 6 28 28 6 29 275 280 285 290 0.64 0.66 0.68 0.70 0.72 0.74 0.76 5 101 5 111 6 01 6 1 6 21 6 31 6 01 6 11 6 2 6 3 6 41 6 51 6 2 6 3 6 4 6 5 6 6 6 7 6 4 6 5 6 6 6 7 6 8 6 9 Correction in ins. for a ) change of 10' in the / length. ) 1.4 1.4 1.4 1.4 152 The Naval Constructor Table. D. — (Continued.) Sailing Vessels. Table of Reserve Buoyancy and Freeboard for First-class Sea-going Iron and Steel Sailing Vessels (in Salt Water). Coefficient of Fineness. Percentage Reserve Bdoyanct. 30.6 30.8 31.1 31.4 Corresponding Height of Freeboard Amidshdts. Measured from Top of Deck at Side. Iron. Moulded Depth and Length. 29 6 30 30 6 31 295 300 305 310 0.64 0.66 0.68 0.70 0.72 0.74 0.76 6 6 6 7 6 8 6 9 6 9* 6 10 6 11 6 8 6 9 6 10 6 U 6 111 7 7 1 6 10 6 11 7 7 1 7 U 7 2 7 3 / // 7 7 2 7 3 7 31 7 4 7 5 Correction in ins. for a ) change of 10' in the / length. ) 1.4 1.5 1.5 1.5 Kirk's Analysis 153 CHAPTER V. KIRK'S ANALYSIS. {Trans. Inst, of Nav. Arch.) The following was the method adopted, and here I may premise that for ordinary purposes I assumed that the length of entrance and run were equal — in fact I contented myself by finding the mean of the lengths and angles of entrance and run — but the method is equally applicable to finding them separately when greater accuracy is required. I shall now give the process for finding the mean length and angle of entrance and run. Construct a block ship having the same displacement, mean draught, and area of midship section as the ship under considera- tion, but with rectangular sections, parallel middle body (if neces- sary) and straight-sided wedge-shaped ends. Fig. 34 shows by the curved line IBK the midship section of the actual ship, and by the rectangle CLME the midship section of the block ship, both sec- tions being equal in area and depth, having a common water line IK. The depth AB is the mean draught of the ship. Fig. 35 represents the block ship, and ABDG is the half-breadth plan, the sides being vertical, the transverse sections all rectangular, and the keel parallel to the water line. The sides CD and EF which form the middle body, are parallel to the keel (or to the centre line AB), and the half-breadth GC or LTD is equal to AC, Fig. 34, the half-breadth of the equivalent rectangular midship section (which is in fact the midship section of the block ship), EL being also equal to AB. The angles CA G and DBH are equal, and while the length AB is equal to the length of the ship, the length A G or HB of equal wedges which form the ends is such that the area of the figure ACDBFE multiplied by the mean depth AB, is equal to the volume of the displacement of the actual ship. Complete the rectangle COPE as in the dotted lines. It is obvious that the rectangular solid COPELQ is equal in volume to that of the block ship, in fact to the volume of the displacement of the actual ship, and that the length -,-,.- . , Displacement in cubic feet GB in feet = * . -— , Area of midship section in square feet and the mean length of entrance and run An i tu m vi Displacement AG — length of ship — „. , . . » Midship area 154 The Naval Constructor § 5 1 1 B w W - H § gfc H O ft) y OB H H o < wP 3 W M OS 09 o 3 Principal Dimensions. Draught of Water on Trial. Displace- ment. Midship Section. is? .d-d si ft o ■d h E 1 < d 03 n § o H © 00 a * .5 « © C |£ u o a u < .u 00 ~ J. © © 6.5 5*s 1 s.s. 2,811 342 884 29 11 18 6 20 2 19 4 4,500 .658 Sq.' 643 .92 2 s.s. 2,8H 342 380 29 11 18 4 19 9 19 0$ 4,415 .656 630 .916 3 s.s. 2,911 3440 39 29 11 16 20 18 4,235 .647 604 .907 4 s.s. 2,965 348 390 29 11 17 3 19 11 18 7 4,472 .653 626 .91 5 s.s. 974 2300 32 19 7 13 10 1,227 .625 266 .89 6 s.s. 979 230 32 19 14 9 14 11 14 10 2,034 .683 423 .934 7 s.s. 1,158 2400 320 19 11 11 7 13 8 12 7J 1,693 .647 344 .902 8 s.s. 2,014 2850 350 26 6 13 7 15 10 14 8£ 2,710 .685 454 .936 9 s.s. 534 190 256 15 11 7 12 11 12 3 1,115 .694 268 .904 10 T.S. 2800 600 42 6 24 3 25 3 24 9 7,555 .663 1,287 .903 11 p. 2038 26 6 16 10 6 10 6 10 6 885 .581 230 .87 12 T.S. 2250 300 22 6 12 2 13 2 12 8 1,235 .533 285 .79 13 p. 98 18 8 3 4 9 5 3 5 133 .575 785 .87 14 S.S. 2,160 320 400 21 8 to main deck. 8 9 17 4£ 13 Of 2,335 .522 387 .791 Kirk's Analysis 155 H O W 1 E 02 J H A 3 IT. WW £ ^ G Oh' w E F < I 3 d 1 A* CO Q o o 3d hi CO CD CO O I?gc5 swd Wo T3 CD . X CO 08 fc « M02 Sq. Ft. Ft. Ft. Ft. Ft. Ft. o / Sq. Ft. ,431 11.52 19,348 329.5 34.8 18.5 84.6 86.4 11 38 20,847 .928 642 9.18 19,140 329.5 34.6 18.2 84.2 85.9 11 37 20,605 .929 ,429 11.87 18,892 331.5 35.3 17.1 86.1 87.9 11 35 20,123 .938 ,106 12.94 19,506 335.5 35.4 17.7 85.5 87.3 11 42 20,854 .935 528 9.32 8,552 223.2 28.3 9.4 61.8 63.4 12 54 8,824 .969 805 10.33 10,850 223.2 29.8 14.2 54.9 56.9 15 11 11,468 .946 909 11.14 10,216 232.5 28.7 12.0 60.3 62.0 13 23 10,604 .963 ,195 11.57 13,947 277.7 32.4 14.0 68.8 70.7 13 15 14,650 .952 441 8.63 7,300 184.5 22.9 11.7 38.9 40.5 16 24 7,726 .945 24,021 283.0 54.1 23.8 77.5 82.1 19 14 25,026 .96 ,135 13.33 6,700 203.0 23.2 9.9 68.3 69.3 9 38 7,185 .932 ,450 12.66 8,440 220.8 23.7 12.0 69.1 70.1 9 44 8,942 .944 125 8.54 1,935 97.5 15.5 4.6 324 33.3 13 27 1,922 .993 ,252 13.89 13,750 312.0 31.5 12.3 100.8 102.0 8 53 14,387 .955 156 The Naval Constructor also, The breadth CE = Area midship section Mean draught (ex. keel) and the tangent of the mean half- >\ t angle of entrance and run, —- & Thus from the length, breadth, draught, area of midship section, and displacement, the mean length of entrance and run and the mean angle can be got. There are other methods of working this out, which will occur to any one, but the method given is perhaps the simplest. In order to get the length and angle of entrance and run sepa- rately (instead of the mean as stated), it is necessary to have in addition, the displacement in two portions, one forward of the mid- ship section, and one aft, the dis- „ tance of the midship section from « one end of the ship, and the mean I draught of each of these portions ; : treating them, in fact, as two separate ships, one of which has no run and one no entrance. In my earlier attempts I re- tained the actual breadth of the ship as the breadth of the block ship, and varied the depth, but I prefer the plan before given of using for the block ship the mean draught of the actual ship. In ships with extremely raking sterns or stern posts, I take the length at half depth when that can be got (or the mean length) as the length of the block ship. In single screw steamers, I take the length to the forward stern post. The block ship will often be found of use in forming first or / I m Ip \ \ ~ \ 1 / A i / Wetted Surface 157 ipproximate designs, and in this view it may be interesting to joinpare the wetted skin surface of actual ships with that of the squivalent block ships, this being an important element in speed :alculations and otherwise. In the foregoing table I have selected fourteen ships of very liverse types, giving their dimensions, block models, actual vetted surface (exclusive of that of keels or rudder), and wetted lurface of block ship, and the ratio of one to the other. From this it will be seen that in first approximations in compar- ng one ship with another we shall not commit a grievous error n using the surface of the block ship, and also that a very close ipproximation indeed may be made to the actual wetted surface >y multiplying the surface of the block ship by one of the coeffi- ients in the table, according to the type of the ship. In the econd column SS means single screw, TS means twin screw, and ° paddle. In No. 10 I ought to explain, that not only was the udder of exceptional breadth, part of which, to make the com- >arison with the others more even, has been included, but there pas a peculiar overhanging portion under water near the top of he stern post, by which the mean length taken for the block ship xceeds that of the actual ship between perpendiculars. To show more clearly the relation of the block model to that of he actual ship, I have selected No. 4 in the table, as being a fair xample of a merchant mail steamer of considerable speed, and in •Mg. 36 I have given the curve of areas of transverse sections ; and have put it in this form that the ordinates are equal to the half reas of the corresponding transverse sections divided by the .raught of water (less depth of keel) at the several sections. ?his is in fact the curve of form, or fineness of model. Above this I have drawn the half-breadth plan of the block hip, the length, breadth, and area of this being of course equal to hose of the curve, and the length and angle of entrance and run i mean of those of the actual curve of form. Wetted Surface Formula. W.S.=Lx(~+dr)xc. (!+* Vhere W.S. = wetted surface of hull proper in square feet, ex- cluding bossing, rudder, bar keel, etc. L — length on load water line. B = extreme breadth. dr = extreme draught in flat plate keel vessels, and draught corrected to fiat plate keel conditions in bar keel vessels. c = constant from the following table : 158 The Naval Constructor Ratio of # =5.00 dr 3.33 2.50 2.00 1.667 Block Co- efficient. ■\ r alues of "c .40 1.120 1.130 1.158 1.180 1.200 .45 1.167 1.184 1.211 1.240 1.260 .60 1.215 1.238 1.270 1.300 1.320 .55 1.272 1.299 1.330 1.360 1.380 .60 1.330 1.360 1.390 1.420 1.440 .65 1.397 1.427 1.456 1.480 1.500 .70 1.465 1.494 1.522 1.541 1.560 .75 1.542 1.565 1.588 1.604 1.620 .80 1.620 1.637 1.655 1.668 1.680 .85 1.708 1.715 1.724 1.733 1.740 "Wetted Surface (Taylor's Formula). W.S. =c V-Dx^- where W.S. = wetted surface in square feet, excluding rudde bossing, etc.: D = displacement in tons of 35 cubic feet. L = mean immersed length. B = breadth extreme. H = draught of water, extreme in flat plate keel vessel and corrected to flat plate keel conditions in b keel vessels. c = constant found from the following table : Ratio -=• Constant "c." Ratio ■==• H Constant "c." 2.0 15.63 2.8 15.55 2.1 15.58 2.9 15.58 2.2 15.54 3.0 15.62 2.3 15.51 3.1 15.66 2.4 15.50 3.2 15.71 2.5 15.50 3.3 15.77 2.6 15.51 3.4 15.83 2.7 15.53 3.5 15.89 Note. — This formula becomes unreliable when the block coefficient beyond the limits of .45 and .75, or when the ratio of — is outside the limi given in the table. Launchi ing 159 CHAPTER VI. LAUNCHING* The form of ways for ordinary merchant ships is of compara- tively little importance ; but in special cases, such as armored war vessels or long, light river boats, if there is too little water on the way ends, the vessel is liable to tilt as soon as her C.G. gets over the way ends, and being as it were pivoted at this point, a great pressure is put upon the bottom of the vessel, causing undue local strains, which might possibly force in the bottom plating, frames, etc., in those vessels which are not so strongly constructed as ordi- nary merchant vessels, or the ways might collapse here and then 1- COMMENCEMENT OF 1 ST PERIOD 2. CHANGE BETWEEN 1 ST *& 2 N ° PERIODS 3- END OF 2nd pE R | OD 267 250 210 200 Fig. 36. the vessel would be left to slide off the remaining distance on her keel. To guard against this danger, it is desirable to ascertain by calculations and diagrams if the form of the ways is such that the vessel may be launched without fear of tilting. The time that a vessel takes to travel down the ways may be divided into two periods — the first lasts while she rests entirely * Paper by H. G. Gannaway, Trans. E. Coast, Eng., and Shipb'd, 1887. 160 The Naval Constructor on the ways, and the second, when the stern is afloat and the fore end of the ship is bearing on the fore end of the sliding ways. A base line is first drawn, the measurements along which repre- sent distances travelled by the ship down the ways, the total length in this case being 267 feet. The line AA drawn parallel to the base represents the moment of the ship about the fore end of the sliding ways. In this example the ship's weight is 865 tons, which being multiplied by 97.2 feet, the distance of the C.G. of the ship from the fore end of the sliding ways, = 84,121 foot-tons. The buoyancy moments about the same point are rep- resented by curve B. The position of intersection of this curve with the line A A will indicate where the vessel will be when her stern commences to float aft. At this point the first period ends and the second commences, which in the example is when the vessel has travelled 208' 6" down the ways. Although this is the point where the moments of buoyancy and weight about the fore end of sliding ways become equal, the vessel's stern does not actually lift until she has .moved a few feet beyond this, because an additional amount of displacement is required to overcome the vertical component of the ship's momentum. Observations of the dip of the vessel's keel have proved that this additional displacement is so trifling that a complete investi- gation of its amount is unnecessary for ordinary purposes. The displacement of the vessel throughout the first period is shown by curve D 1 , and for the second period by curve JD 2 . Dur- ing the second period, the after end of the vessel being afloat, and the fore end resting on the sliding ways, it is evident that the buoyancy moment about that point will remain the same as the weight moment all throughout this period. The displacement, of course, increases as the vessel moves down the ways, but the gradual lifting of the stern and lowering of the bows brings the C.B. further forward, and so reduces the leverage while the dis- placement is increasing, thus retaining practically a constant mo- ment. The distance that the line CG is above the base, represents the weight of the ship, the weight on the fore end of the sliding ways being proportional to the distance between this line and curve of displacement D 2 . This weight is 225 tons at the begin- ning of the period, and is reduced to 115 tons at the end. It is important, therefore, that the fore end of the cradle should be made sufficiently strong to carry the load which is thus put upon it. It will be seen then that it is desirable to reduce the duration of the second period as much as practicable, for, since the longer it is, the greater the weight will be on the fore end of the sliding ways, which in the case of heavy vessels renders them liable to come down to the ground and damage their fore ends. In considering the subject of tipping, we take the moments Launching 161 rat the end of the standing ways, and as long as the buoyancy ment remains in excess of the weight moment about this point, re is no fear of the vessel tipping ; but if in any position the mer moment falls short of the latter, it is evident that in order restore equilibrium, the stern will drop, and thus increase the placement until both moments are equal. Tipping, if occurring ill, must take place after the C.G. of the ship has passed the 1 of the standing ways, and before the commencement of the ond period. In the example, the C.G. of the ship has passed B FTTON8 E PTTON8 TONS. *\^ A 80,000 16,000 800 V^8 1 E^-"" --^D 10,000 2,000 100 Fig. 37. cjjAT WAYEND8 way ends when she has moved 174 feet. From about that nt to a little beyond the end of the first period, the buoyancy L weight moments about the end of the standing ways are cal- led at several intervals, and at each interval the latter moment, ng deducted from the former, gives the moments against tip- g. These moments are shown by curve E. If this curve at - part were to run below the base line, it would show that the sel will tilt. The point where this curve is nearest to the base ) gives the position of the vessel when she has least longitudi- stability, which in this case is when the vessel has travelled ra the ways 189 feet, the minimum margin against tipping be- 9,700 foot-tons. t is desirable that the margin be not too small for uncertain sels ; where this was the case they actually did tilt slightly, ch shows that a moderate margin is required in calculation to >w for the error introduced by treating, as it is convenient to in practice, those moments statically instead of dynamically, calculating the buoyancy moments no account is taken of the lie, which would only alter the results slightly ; the variations lg on the right side, may be safely ignored. Besides, the after 162 The Naval Constructor Table of INDEX LETTER. A B c D sT.- s23 Description • «x fa 2x 3* of Vessel and Moulded Dimen- £8 CG W a 3 &$ sions in Feet. ^x £>< *x i*x ccb W^ |i oo (iv H" 02 Declivity of keel per foot . . 9 It TJ 8 // TS 8 ft T~5 8 // IS Declivity of standing ways per foot 8 to 18 Iff lo IS A toil 8 f n ll TS l0 TS i'2" AtoH ro" Camber of standing ways . . 2' 3" ro" Length of standing j Inner ways \ Outer 345' 288' |367' 395' 370' Length of sliding ( Inner ways \ Outer 240' 165' I 284' 330' 305' Breadth of sliding ( Inner ways ( Outer V 10" 1'8"' J** 1'9" vv Area of sliding ways in square feet 1,430 904 1,155 1,067 Total fall in length of standing ways 23' 0" 18' 9" 19'7" 18' 6" Water on way ends .... 8' 7" 6'0" 4' 4" 2'6" Draught of ship forward . . 11' 2" 11' 6" 7'0" 8' or Draught of ship aft . . . . 16' 6" 14' 0" 10' 10£ 10' 5" Draught of ship mean . . . 13' 10" 12' 9" 9'0f" vq» Displacement in tons . . . 2,850 2,500 2,157 2,240 Mean pressure per square foot on sliding ways in tons . . 2.00 2.51 1.9 2.09 Length of first period . . . 278.0 283 250.5 279.5 Length of second period . . 67 84 144.5 90.5 Ratio of length of 2d period to length of sliding ways . . 28% 30% 44% 30% mencement of 2d period 520 550 640 630 Weight on sliding ways at end of second period (in tons) . 250 290 300 380 Margin against tipping . . . 10,500 33,250 80,000 35,300 Table of Launching Data 163 Launching Data. E F G H J K ii M coco Is 1* cc$ £* ^x CO$ cox 8 g35 pf • Wo ^ X St Sfe COM *x (So ^>3 co £X go HE co £X CO ccSi HX Si < As £x CO B0 9 // 8 // A" 9 // A" 9 " A" A" A t0 If A to If r io" A to^-f 1' 10" 8 t n 14 TS l ° T6 ro" A toft 10" 10 f n 14 TS uo TS Atoll l'O" A to H 6" 348' 302' 300' 267' 250' 195' 259' 276' 240' 200' 200' 180' 170' 150' 207' 190' r io'' i'8" 1'9" 1'9" 1'9" 1'8" 1'9" 1'9" 880 666 700 630 595 375 725 665 21' 6" 18' 10" 15' 6" 15' 4" 14' 6" 12' 0" 15' 0" 16' 0" 8' 9" 3' 10" 3' 7" 2' 8" 4'5" 2' 9" 1'9" 2'0" 6' 6 J" 6'0" 5' 7" 5' 9" 8' 7" 4'0" 6' 11" 9' 2" 9'5£" 8' 2" 10' 8" 9 , 0" 7'1" 3' 10" 9' 11" 12' 0" r O * < s - in CO H o <° !! uj 3 UJ a. te < -i _i D X Z o < S v : \ : \ \ - \ \ : ; : : : : : : • -OM g \ \ \ \ \ \ \ \ \ k_ \ \ \ - oooe \ \ \ V \ \ L.0005 ;..L_ i'fi ; 1 1 lli Jit llll l"' :i II I lilt nil Iffll IB Ills l 3 c '. 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H» O O O H)» r+* 0+0 J «+0 <+« t> J The Naval Constructor w o fe < o 05 s H 8 H W F W E M H SIS "IJOONNHiOO'j; 00Pj(OHiO»M00 COeOCOeOCOCOCOTtt •^■^Tf^rttTfiTl*^ NfflO>OqCCNN CD T^Tficicidcdcd^ k si a c H iO«« S H ifl OIMNHICOMN eo co co co co co co cococoTj. Tji •*)< id »C »C d d t^l^t^OOQOOOOJOS eoeocococococo coeocoeococococo odoHHNflfi eo SIS WWCOWCOMCCCO cococoeococococo q^N-H^oo«lO OS QOQOooosososdd d C0C0C0COCOC0Tjd cococoeococococo qwqqeoqqeo co eocococococoeoco eo SIS NO»eO«(Off oooioiaoddc NfNNMMMMK NCOJNIOOOHK) fi iH ^H* tN I CO CO cococoeococococo 00l-4TjJlv.^H-^t>.O CO CO^Tf^uJdldd d cococoeococococo eo SIS O»-HCNtNtNt--o6o6o6dd iccxji-jcoqqtNrj' t>. ddddddi-H--< ri CNtNeococococoeo eo SIS 3 h N N 00 M O •■* O>OH©NNn00 niononiono mioooqccioooq COCCCO'*-^-*-^«5 «5iO>0(0 q KJlOiCiOtOCOCtO t~» CNCNWCNCNtNCNCN CM SIS iflCOXOOHMTt >ONffiHTJ<«00C ddoidddd- i-i.-i^ c> 1-5 »h rn ^h 1-! ci tN r-l_i,_I^H^Hd "l« H> H-* r+o H» «*° e*f H 10 cococoeococococo H» .+» **o r^ «*«>**. H» Weight of Steel Tees ffl & T 185 « ft o . 02 H H g H H 02 02 H to « u 3. 818 218 218 518 SIS 818 318 218 SIS 318 218 *iONOOO>ONM •18 rj< CO rl CO (NHOOOSOOI^CO 10N«HN1<(0(X1 NNNcowrimco •18 N O) ffl CO • • • • ©N 0) H : : : : ^ ,_; ^ c4 ON^HMUJN© M'*!O00OJiHCO'* fidfiiNdcocoM H8 ©H (OH ©O • rt n ■* (O n ffi iOO"5©iOO'C© ONwujioooao **• H» 186 T The Naval Constructor X o fc fc h O 02 X H 8 H W H E g r, r, SIS SIS £18 .OMIsh ,H rH i-l r-( SIS aiNtoacoeon r-JiNfNc^eoevjec-* SIS O CO CO Q ! ! ! i © © © 6 coeqcqiQaNio hhhMNNMM SIS * " ' o6o6o6o)0)0)0© (OOINiOOOh^N dd<-i>H^e^cJC4 SIS (ooi w * ! ! ! '. (6 so n n NOWiOOOHTfS NOOOCOCOOOOO) SNiQQOOnoO) OOOOhhhh SIS h i* to as h t o.o O'O'itONSMW c^^t^oc^'tr^O) t>i>t^t^o6o6o6o6 *»iOO!OHNN (N-*t>.p(N»Ct>.0 oifficidoddi-i SIS .q(N.^;t> : G>^H 00000)0)0)0)00 SIS ittOOOOiM'ONO Tt*iON00aONM »qNi;qo)rin I^o6o6o6ooo6o)0) «I8 ON*!OOOq(NM ooo<©-*nooo«o CC^tDOOONMiC iO»OiO"3c6«0?d«0 ^NOOOO^Nrt h.qiHNr)H©ooq eo«dt^t^t>It^t^o6 °°I8 OHWUJN00ON iO»0»0'CiO»C«dcD 00"5NO)* iq N NNWMCCMMM TfNOMiOOOH^i OOOlHNCCTftON ooftHPjWKjqN TfTi<»cid«d«d»d»d •o|8 aOSOHHNMM Mt|*ONOOOSOh ■*^10 0COM»» NM^iOCONOOO) cococccocowccco ©fflOHHNMM 0>-;poTj<»qiot>.oq <*I8 MNOOJNC'JiM rHCCN tosM»oo»aai -IS NCSH^eoOON OtONNNNOOOO •** CM CM 318 : CC X q OS ^ 00 os as CI c CI -c d CI q CI ci X Cl Cl ci Cl CO ci Cl CC* Cl 'O cc* Cl 3 cc Cl cc <* Cl Cl ■0* Cl iO i.O* Cl 05 CC 318 Cl cc co q CD N X 1- 00 io q 00 00 CC OS 09 o e CI d CI X cc Cl Cl Cl CO Cl 3 ci Cl cc ci CN ci Cl CC* Cl IO CO Cl 3 CC Cl CO i CD O -<*' io CM CN W8 ■o* 00 CN iO CD »0 CO at 60 CI i- CO o l^ 00 CO X X c d -t 0) DO d 3 Cl i-O 3 Cl 3 Cl Cl Cl CO ci 3 CN cc ci Cl 1- ci Cl 3 cc Cl CO CO CN CN SIS co O CO iO io CO 1.0 o CO cc SO i> q CD t^ cc I- 1- o X X X 3 OS OS 1- 3 1 8 8 ci Cl 00 ci CN CN CN CN 918 00 M 1 "3 00 10* '0 iO CO 1- cc I- cc 1- 3 X cc X CO X OS X Cl OS 3 3 3 3 Cl 3 Cl i.O 8 X ^H 3 ^ CN CN 318 q cc* CC CD 05 CO 0) CI "** MS 00 pH rj* lO 1- 'O q CC cc 60 "3 •c X CC* N 3 X CC X 3 ad 3 00 Cl 3 iO X os os* SIS N CN cm* o re Cl CC i-O CC 00 rH CO -tf CO CC q CN iO i.O i-0 i.O* 3 d CC' (0 3 3* X CC* N i- 1- 3 CN IO 00 00 218 CC OS IO t>; S3 CN CN ci ^H * 318 d io 00 CO 00 6 6 3 i-O M X uS 00 o r-J CN X Cl CI CI «0 ci i-0 1^ ci X a ci Cl Cl cc iO M X 2 M Cl 3 CC iO -t OS CC -r Cl 3 X -r 3 3 i.O Cl CC i.O* IO OS IO t^ IO IO* 318 3 IO t~- b- OS OS OS oo d os CC d 3 d CN CO oq q cs i-i H i.O X X OS 3 ci 3 CC ci Cl i.O ci cc 1- ci ■<1< 3 ci i.O cc I- CC cc* X i.O cc* 3 1- CC § CN CO CN ■* Tj5 t' «I8 3 00 r- io CO iO 00 00 re 00 09 00 3 q OS OS X !> q 05 OS d CC CC CD '0 i.O i.O 1- cc -r 3 3 cc Cl cc •0 3 3 X X 3 ci X Cl ci 1- ci 3 50 ci iO Tfi X o CN CO «I8 I- I-* .-i 00 q q I> 00 CI 00 CI 00 00 CO CC I- OS c CI — CO X 1- iO OS Cl 8 60 CC 3 X i- OS ~z N x »o H8 X CO CD ^ CO q ^h cn CO N-N ■* N to 1- ^H IO b- oo c q 00 1.0 00 3 CC 00 iO <* X 3 9 X iO 1- X o 3 00 3 OS OS OS CC OS 3 t 3 -t- 3 OS 3 1- 3 3 3 05 CO O CN 6 d «I8 00 X US O r-1 co cd -M 3 CS CC CD CI i.O (0 CO t>; CO CO CC o 1- 1- CI 1^ 1.0 1-* 3 X 1- 3 l~ 3 OO 00 cc 00 00 10 00 CO X X 00 *I8 <* 3 <* 22 ■o io 83 CM •o* CO cc. ■O* .0 X X io q CC. a X s Cl Cl cc CC i.O q i-O X co q 3 3 N X X CM CO «I8 I- 3 M CO ■* O i-> cc c X t~- MS CC CI X q 3 OS X 3 i.O 3 'O IO Cl i-O* cc cc i-O* CN T i-O i.O 3 iO iO 1^ 3 i-O CO 1- »o •* CO x q iO IO »I8 s re t- co O rH CO CO 3 cc CD 01 CO CI cc ■cc os io CO Tj< CO CO cc' X i.O cc -r S3 cc* cc t- cc I- cc CC X cc § cc CO 3 cc* Cl 3 3 3 iO Cl X Cl cc 1-1 t^ «18 Cl o CM 82 CN CN CM 0) CM cc CI ci CN CO CN CN cc ci ci ci ci i.O ci i-0 ci 3 ci 3 01 1- ci ci ci X ci X ci 3 Cl OS OS CN CN -18 q co io q q X c o CI Tt< CO X s CI CI Cl i^ Cl 3 Cl W CC CO i-O cc jo uing tt CD CD CO CO CD 188 T The Naval Constructor * u fe to •4 o ao H W H to H H to 00 33 w to M u s 818 WWWOOCCWMrt 00(N<©0»CO>CO^ re re re re re re re re SIS 26.7 27.1 27.5 27.9 28.3 28.7 29.1 29.5 ood-HrtHiNfi NTOMMMMMW cdcd**-Ot^©h rf ojoc66c^-h' SIS (OooqiN^NaH Tj5 T j5io»didic'ccd t"5^00OON« Miot^qn^qoo tO(Otd(ONNNN ^lONWttOMC! qcjrftoooH. mm OOOCOOOOOCOJOJOJ •18 (N'tfCOOOO'-^COiq OJ00t»t^i©iOrfj*^H aooiHiNioeoco HtcioqajqiNM CO CO 00 CO CO' ^ ^ ^ ■*HOO>OINO(OCC lONOOONtCiCN ■*-*T)iidid»d»dic H8 OOCOOOCOOOCOOOIN dddoOHHH "5i>oqq'-;coTj«cq HHriNeiNPici NOOINWUJCOC (NCNcococdco'cdcc* •IS (DONiflNOMC oocsico-^tot^oo oiooooo©© Xhtj*M3)(Micoo aHNOJ^CNOO OHHHHrJMH •IS »©OHHN05CC t^t^t^t^t^OOOOOO M^iocoNooqq o6oco6ooo6o6o6oi OSOOhhNMW HCj^ioqwooq r. r. r. 3 r. z. ~. ~ «I8 OOOtCHJMINOO qNooqqniNN cq •IS 2 IO «I8 CO -IS •8»i JO'l JO rang H» 4> n(« H» «»» *> >+> oooooooo -+o >+• «sx Hn «*»<+• H» Weight of Steel Tees T 189 w o < o 00 U H H b> H ft 'SI CO 3 H cnIcm 01 X to 38.6 39.0 39.4 OS OS co CO d d -v q q oi T oi X oi CC CO co -r '0 a '0 -r X i.O 01 a -r a — ■q a ■* t^ 00 SIS -f a cc GO CN q CO t£ t> O GO CO -r 00 cc X X CO 01 a c: 50 a CO d Tin d X Q T 01 ■1- q a oi -r •<* oi 00 oi 01 co T so co a '0 t' a co iO r> ih io cd sis q cc OWN KJ (O "i co co co 83 CO d CO a a cc CC i- co q co O *tf X 88 8 01 a CC q a CC a a CC CO a I- a cc i-O — X 01 oi a oi a co "* 00 CO CO 5IS 00 oi cc H UJffl CO CO CO CO CO CO 01 CO OS CO a 3 CO to CO ad co q d cc I- CO CO 1- CO iq CO X CC 01 X CO X CC a c^ co a CO a a cc a a -t a SIS OS a CO CO CO o rH rH CN co co co M oi CO q oi CO q CO CO w CC CO CO q -r CO CO «* CO co q ■0 CC IO CO "5 CO q a CO OQ CC cc' 5 CO cc H t!< 00 -^ oo oo oo a co co co co SIS » O O! o CN ON CN CO -* a re 6 CO q CO CC CO CO c oi CO M oi CO - oi CO a oi CC co CO CC CO CO CC a M OI CC' 10 CC a co CN i.O CO ■o i.O CO 00 ■0 CO a cc Tf 00 co co SIS CO N 01 q a CN l> t^ CO CN CN CN X X 01 q a OI CO a 01 CC a' 01 a a 01 CN lO 00 CO CO co a oi co CO oi co a oi co a oi co. oi co cc i.O co cc X co cc CO CO SIS CN »>. q cn iO CO CO CN CN CN '0 d oi X S3 O) 04 CO I- OI q 01 a 01 CN X 01 X 01 1^ 90 01 o a 01 co a 01 10 a 01 X a 01 a cc a CO a a cc a a CO 01 CO q CO 00 o r4 oi co co SIS CI iq cc t^ CO GO i> q cn CO Tji Tf CN CN CN 'O CI 9) OI '0 q ■a 01 a CO 0) to • 10 01 X i~ CN q OS 01 01 CO OS 01 X • CO 01 CO X d 01 a q 01 K 01 a q 01 ■0 X 1^ 01 X 01 a co X 01 01 a X 01 1- X X 01 co a 01 X Tf co a a a CN CN SIS SO oi N O M GO .-i CO *N CN CN CN CN CN i- 'O oi 01 § oi 01 0? q CO 0) I- OI CO 01 s CC 01 CO 01 1- a CO 01 o 01 01 01 q <* 01 c a -r 01 01 CO 01 a i.O 01 3 iO 01 I- a a 01 co a 01 2 ol i- a 01 O CN CN CN SIS a' "5 t^ GO 05 — 1 CO oido i-H CN CN 09 6 OI 5 X Q OI a oi CO ci 01 - oi 10 q 01 1- X 01 oi OI a 01 oi 01 a iC oi oi 01 1- CN 01 CO a 01 01 co OI 10 CC co 01 1- '0 co Ol X 1- co 01 a a M 01 o 01 si 01 01 -r * 01 CO Tf q oo CN CN •IS 01 X "H O O O CN ^ CO GO GO a X X X a X CO a 8 a d CO CO a 9) 01 a 01 co d 01 a iC a 01 a q d 01 X X a 01 a 01 co OI oi a t oi i.O a oi -t- 00 oi cc a oi 01 CN ^h CN rj< CN CO CN CN •IS Q a q' o. ■* <-! q cn ■* co co cd 38 CO '0 t- OS 01 a to a a CO 01 1^ CO Q -r a X X 01 X 10 X 01 a X a r> X i X CO a a a a a H 00 x a d a HS O iO o h CN rt* o I- X -t' -r "5 CT> OI 10 K3 a 10 iO a X q X a ■CO CC a •IS 8 oi CO CO Oi CN CN CN LO IN oi oi a 9 oi OI o CO •IS "* ..... q :::::: : :::::::: :::::::: : d> '■ '• •is c*!S ::::::: : :::::::: :::::::: : «n|8 ::::::: : :::::::: :::::::: : -IS | ::::::: : :::::::: :::::::: : JO \ 8ubu [jptmg rang N r+0 -+• <*> H" *fr «h# >-+0 (N CN CN CN CN CN CN CO CC CO CC «*t> nt* t+» CO CO CO 3 Hi n- -* ■H * * J The Naval Constructor to to < h O 92 E H k 1 B to U o K H 818 SIS 218 518 SIS SI 8 318 218 SIS SIS SIS °>I8 O OS h- «5 ; ; ; ; ; ; ; ; • • oo -; "3 os '.'.'.'. '.'.'.'. '.'.'.'. '. '. ' '. bl 00 00 00 •la OS CO • • co r~ : : co c6 nh uja q ■* t* © b»' t-' t~* oo HS • ; MS 00 CN rH rH rH rH T* t- q io xj >oc6 6.31 6.60 6.90 7.20 •III CO rH O CN : ; ; ! :«« N N 00 M ■<* t^ © CN co co co rj* OS •* o »c «tf l> © CN ■r)" ■*)* UJ V$ 5.51 5.76 6.02 6.27 •la 2.13 2.34 2.55 2.76 00 OS © rH OS rH rf CO CN CO CO CO* CO Tj* MJ CO 00 © CN Tt< CO •* Tj* Tj5 4.86 4.89 5.10 5.31 i OS CO CO © NrfiH 00 ■*|S OCN-^CO C~ OS rH CN l^« CO CO CO CO Weight of Steel Zee r 1 191 w o < O w H Ed m H H to 05 00 jjj 5 H SIS | • \ \ \ \ \ \ ■; : : • "i ::.:': :'::": SIS SIS 518 SIS CO rH ;. • . • ; ; ; ; ; '.'.'.'. '.'.'.'. '. '. • • ! ! ; ! ; ; ; ; ; ; ; ; ; ; ; ; ; ; d i t> <-H IQ iti ^6 ^6 <£ © CO IQ 00 q ■* oq t^ oo •IS CO IN O 00 CO t» rH T* os os d q CO K> CO rH 00 CN CO © Orinfi OS 00 CO rt< CO t^. rH IQ IN © do © 11.07 11.36 11.66 11.96 CO >Q iQ iQ IN IQ 00 rH IN CN CN d •IS CO 00 rf OS •o t> © i> IQ O CO rH iq 00 O CO t^ t> 00 00 t^ CN 00 CO iq oq q cq 00 00 OS OS OS ■<* O >Q IQ 00 rH CO © © © © 10.61 10.86 11.12 11.37 •rs CO rt< iQ CO W3 N a H d d "5 d 00 OS O rH co iq oq q tS(S(ON CO ■* IQ CO t^ t^ t^ 8.08 8.29 8.50 8.71 CO Tj* IQ CO q rH CO IQ oo'add «IS OS CO CO o ■* to oo q <* ■<* ■* d S^ h 00 rH co »q q ni k> ^i *6 lO N fl) (O oq q rH cq 16 <£ <£i ^ CO o b- ■<* iq n oo q (OtDlOS rH 00 IQ CN N CO 1(5 S t^ t^ t^ t>^ "is O •^ IC CO 00 CO CO CO co CO CO " ' ' «fS -IS j<^ JO urns rt* **« ■+• t^ r~ l> t>- r+« Hn «t« 00 00 00 00 OS OS OS OS *+» .+» <*• o o o o •+• Hf «(* 192 H The Naval Constructor a o fc < h o 9 H H H fe H H 03 0? W M - s SIS 44.20 45.05 45.90 46.75 47.60 48.45 49.30 50.15 SIS 39.08 39.89 40.70 41.51 42.31 43.12 44.93 44.74 45.54 46.35 47.16 47.97 SIS • • S to : : 22 SS 37.33 38.10 38.86 39.63 40.39 41.16 41.92 42.69 "* IN OS h- CO TjJ Tf lO f * * * SIS »H CO I ; cn q ' CO CO 32.66 33.38 34.10 34.82 35.55 36.27 36.99 37.71 38.44 39.16 39.88 40.60 CO tO N. OS WON* ^ CN CN CO SIS 28.29 28.97 29.65 30.33 ^h OS t^ to q ion q H H ci M CO CO CO CO 33.73 34.41 35.09 35.77 36.45 37.13 37.80 38.49 l^ tO CO ^ r-> 00 to CN os os 6 ^ CO CO "^* ^ SIS 26.78 27.41 28.05 28.69 29.33 29.96 30.60 31.24 31.88 32.51 33.15 33.79 34.43 35.06 35.70 36.34 00 «-H U5 OS q q cn oq CO ^ 00 00 CO CO CO CO SIS CO tN - © 6 -5 -*' CO CO CO CO SIS 20.38 20.85 21.32 21.79 22.25 22.72 23.19 23.66 24.12 24.59 25.06 25.53 OS CO CO o Os ^ Os ^ tO CO CO t^ CN IN CN to rH ^ » CN CO CO CO *^ IN CN CN CN •IS M N H H5 IN to q I t>i t>I 18.21 18.50 18.80 19.10 •IS 11.63 11.88 12.14 12.39 IOO*H CO OS h ^t IN CN CO* CO- t^ tN 00 CO *°. °? *1 "*! CO CO -* ■*' 14.69 14.94 15.20 15.45 HONS t>. q cn •* tO to" CO CD •18 00 OS o ^ r-- os in ■* os os 6 d CO ->1< to CO CO 00 O (N 6 6 *H* r^ 11.48 11.69 11.90 12.11 12.33 12.54 12.75 12.96 00 CO '. '. '. «I8 * : : : «is | : : : : : : : : : : : : : : : : : : : : «I8 | : : : : : : : : : : : : : : : : : : : : -HIS jot] jo iipUB }pBajg (N (N IN IN CO CO CO CO ■*Tf T)l^ tO tO tO to .+» .*» nH> CO CO CO CO Weight of Steel Zee H 193 X u y A i— 1 < h o r. = - a H ft p eo H o SIS 88 iO IQ O iO CN CO »o »o c -r io CI d >C o to «5 SB i Q X "3 in CO ■25 a 10 cc s 5! 62.05 62.90 63.75 s CO iC T IQ •c o cc d cc IO © SIS b- 00 t> IO 00 a OS o CO (N © h iO iO 8 ci 00 ci ■c CI CO cc 'C CO •T »o cc Cl i-C iC — q CO iC •o X CO io CO S iO t X i.C t^ x a IN o X os d d IO CO CO a q CC 5 55 ci CO cc cc - IN © SIS rH 00 IO CN CO t^ T)< rH O 00 00 00 >o a -t -f cc 3 o I- X iQ CO q ci >o Q cc i-0 CO -T '-C cc Cj iO a s >c »o co cn a Tf cn. a CNN iO iO IO IO I- X IO Cl i.C Ci iC X Cl 8 IO © © £18 CN ■* CN 05 CO 00 CO CO irj co CC X N i.C i-C 00 CI os o o d 35 Cl I- iO CO ci »o OS X ci iO rH CO IO q co o CO Th iO iO iO iO X IC i.C c IC cd i-C Cl Cl l>i iC 5tf a (^ iO sia a fr- ee IO rH CN IO CO c IC cc ■0 cc <* i-C X IO SIS CO CO iO --< a 6 CO r}< oo ■* 6 rH g CN ci IB CC CC -r s CC a CO Cl 'C 1- s i.C IO cd X 1^ rH io a °°. ■* q N00OJ CC I- a T cc d 85 8 i-C © IO sis CO CN CO CO IN rH X OS ^C 3 6 ci O i- ci 9 OS CI a X X ci X a cc •c CC cl -r -r CO co »o X tP O tj5 io d ■>* ^ -^ i.C co d -r Cl i- -r X CO ■<* X sis O iO In. IN ■* d CO CO © *o X CO Seo 5 s CO w CO -r S3 O X cc X cc Cl ci cc i- co ci cc Cl Cl Q 6 eo cc X CO X X ■* OS h N N •& •>* -hh IC eo a q 1- cc a IO sis CO -r}< CN t>. IN CN CO CO iO CO in r- co co co co b- CN •<* co X 1- -r CC OS CI iC cc o c? CC •c cc Cl X CO cc cc cc 1^ cc 00 CC K3 (O N 00 CO X CO X co^c^ a cc d s Q <* CN a SIS CO o t>. (N a 6 IN CO CO r-t 6 H CO CO Q -. CO i- q ci 'C ci cc q cc cc CC cc -r Cs CC cc -r CC X X «f cc 'J' cc iC cc rH X IO OON N •odd CO CO CO Cl 1- cc 5 cc iO c? (N © X co SIS O CO c 1- ci CI X o CO CC q CC ■c -t; cc X X cc c CC' ci CC CO IO X CN CO CO CO CO CO i cc cc -t -r cc ■c X 1- cc X CN iO eo •18 CO IN CO O <* d CN © cj CO N IN OS B CI cc t~ cc CI o Cl >* Cl 'C 1- Cl Cl q in* Cl cc ifi Cl i.C CN CO Cl io a eo TJ< t^ rH (DION CN CN CN -v 1- Cl X 1- Cl iC X Cl a X IN *-IS O a •* CO OS OS OS OS OS 1 t^ CC CO «MS «I8 | : : : : : : : : : : : : : : : : : : : : «l§ | : : : : : : : : : : : :. : : : : : : : : «I8 I : : : : : : : : : : : : : : : : : : : : -IS •qa joq JO Y\.PUT3 rang b- o Hn nr. b- b- X X X X a ■+» + i*< o Cl -r» H" «r« O © O 3 H 818 68.00 68.85 69.70 70.55 71.40 72.25 73.10 73.95 74.80 75.65 76.50 77.35 78.20 79.05 79.90 80.75 81.60 82.45 83.30 84.15 SIS 64.92 65.73 66.54 67.35 68.15 68.96 69.77 70.58 71.38 72.19 73.00 73.81 74.61 75.42 76.23 77.04 77.84 78.65 79.46 80.27 218 61.81 62.58 63.34 64.11 64.87 65.64 66.40 67.17 67.93 68.70 69.46 70.23 70.99 71.76 72.52 73.29 74.05 74.82 75.58 76.35 5518 58.67 59.39 60.11 60.83 61.56 62.28 63.00 63.72 64.45 65.17 65.89 66.61 67.34 68.06 68.78 69.50 co to r>- os cn q co co d O r4 CN t- b- b- t~ 218 55.49 56.17 56.85 57.53 58.21 58.89 59.57 60.25 60.93 61.61 62.29 62.97 63.65 64.33 65.01 65.69 66.37 67.05 67.73 68.41 SIS 52.28 52.91 53.55 54.19 54.83 55.46 56.10 56.74 57.38 38.01 58.65 59.29 59.93 60.56 61.20 61.84 62.48 63.11 63.75 64.39 SIS 49.03 49.62 50.22 50.81 51.41 52.00 52.60 53.19 53.79 54.38 54.98 55.57 t» CO CO "5 rH t>. co q tO to to tO 58.55 59.14 59.74 60.33 218 45.75 46.30 46.85 47.40 47.96 48.51 49.06 49.61 50.17 50.72 51.27 51.82 X CO X CO CO OS ■* p CN CN CO -* tO to to to 54.59 55.14 55.69 56.24 SIS CO Tt* to CO ^ OS ^ OS IN CN CO CO ^ ^ •of ^* 44.47 44.98 45.49 46.00 rH CN CO 'S' iqqioq CO t^ t^ 00 48.55 49.06 49.57 50.08 50.59 51.10 51.61 52.12 SIS X "5 CN OS os os d © CO CO ''f tJ« »C CN OS CO Oj i t^ oo oo CO CO CO CO O CO tO 00 rH iq q CO Os os os o CO CO CO ^ 40.80 41.23 41.65 42.08 42.50 42.93 43.35 43.78 •IS OONiOM »0 X CN to rH r^ CN CN CO CO CO CO rH tO OS CO q CN to q cn co co co- co CO CO CO 34.27 34.61 34.95 35.29 H8 25.35 25.64 25.94 26.24 •* CO CO CO U5 X i-i "K <6 cd t-I t^ CN CN CN CN CO r>I '. 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CN CN CN 28.07 28.34 28.62 Q os X 01 MOCN O H^jNO OS OS OS O IN CN CN CO 30.28 30.55 30.83 31.11 31.38 31.66 31.93 32.21 218 24.07 24.33 24.58 90 *r ej OS lO O CO d »6 CN CN O CD q oq d 16 CN (N 26.11 26.37 26.62 CO OS •* © r-WtOO N N l> N CN IN IN CN lOrHCOINNCOOO-* h<* CN T^ os d co ia CO 00 d d 20.04 20.23 20.43 ei co d ei 20.81 21.00 21.19 21.38 N(OtOiOr(q n O) d d d o IN "* rH 00 q t>- ion a OS rH CN 1> 00 00 CO t X CO O N ■* CO 00 OS rH 06 06 06 d rHooiocNCscoco© w^eooftHMio OSOSOSOSOSOO© H8 S NO CO 00 CN CO IC d CO 00 io q CO 00 CN 00 q rH io d d ei d IN N IN N ^lONOO d d d d NNH(OH(OHl() © rH CO ■* CO N OS © i>nnni>nno6 «I8. 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N q CO • OS © rH • * 15 «3 O oo »o CO CN CN CO rjJ m io «o »o H 00 «•* ") IO ON »o « lO O H O N ■* 00 00 OS o >o >o »o o NONW rH CN CN eo co o o o 518 CO N N 00 ■* "<*< "* "* OS OS O rH ■* r- t^ OHNN ^ ^ ^ ^ -tf O CO CO CO -*'•>* io ffi IO IN 00 oitOSN Tf* ^ "^ ^ i; H Nrji oo d d d Tj< •<$< TjH »0 q o q os rH rH CN CN >o io >o >o SIS rH N CO OS 00 oo d os- eo CO CO CO IO h to N © rH rH CN ^ ^ ^ "^ 00 ■* O CO CN CO ■* ■* o OO o CO CO CO CO 37.4 37.9 38.3 38.8 SIS 27.20 27.62 28.05 28.47 28.90 29.32 29.75 30.17 30.60 31.02 31.45 31.87 O * oo cn Tji Tj5 T}5 lO eo co eo co «IS oo co ■* eo •* q cn © Tj5 -rj< ic >o CN CD CD CO CD t^ i> r^ t^ 00 00 00 00 -f. r*< MHl os os os os •4* HN «*• o o o o CN CN CN CN 208' The Naval Constructor w Cj 55 M h 00 s H B H 55 H 05 H 55 M o K H SIS >t N h O ri CN CO <* n. r*. t» t»^ x q «5 co ^< tf) (O N t» t» t* t» MOfth X OS OS Q i>- r* r^. X 81.6 82.4 83.3 84.1 85.0 85.8 86.7 87.5 218 67.8 68.6 69.4 70.3 w* q t>. iq rH rH CN CO t» r- r>- t>. 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SIS 57.1 57.8 58.5 59.2 00 "5 cn q iO co CD CD CO CN OS CO CN CO CO Tj< CO CO CD CD 65.3 66.0 66.6 67.3 68.0 68.7 69.4 70.0 SIS 53.5 54.2 54.8 55.5 56.1 56.7 57.4 58.0 q co q q X OS OS o io m * to H rt N M CO CD CD CD 63.7 64.4 65.0 65.7 SIS 50.0 50.6 51.2 51.8 52.4 53.0 53.5 54.1 t- co q »ti tjJ id id d iO iO iO ifi 57.1 57.7 58.3 58.9 59.5 60.1 60.7 61.3 SIS 46.4 47.0 47.5 48.1 CO (N N M co d d d Tt< ■>*< ■* in X th OS "5 Q H H ci >5 io io io 53.0 53.6 54.1 54.7 55.2 55.8 56.4 56.9 SIS X CO OS ■* CN CO CO T(5 •* Tft T* <* OS tJ< OS ^}J «* ■<* ■* * OS ^* OS ^* d t^ t^ oo 49.0 49.5 50.0 50.5 OiOOiO rH fH CN CN «5 "5 iO ifl SIS CO N N N ai ai <6 d CO CO •* ^i H « H IO f-5 rH CN CN T}< Tj< Tf ■* q »q q ^ CO CO CO ^ Tf Tj< T« «* q co oo cq ■* id id d M* ^ ^ ^ t>; CN t^ CN CO N N 00 SIS 35.70 36.12 36.55 36.97 37.40 37.82 38.25 38.67 © CN IO t» f-; iq q q OS OS OS o CO CO CO ■<* 40.80 41.22 41.65 42.07 q a co s CN CN CO CO r* rjt ^ ^ «I8 M H O UJ rH l« 00 CN (N (N CN CO- CO CO CO CO 33.66 34.04 34.42 34.81 35.19 35.57 35.95 36.34 36.72 37.10 37.48 37.87 38.25 38.63 39.01 39.40 »I8 28.56 28.90 29.24 29.58 29.92 30.26 30.60 30.96 31.28 31.62 31.96 32.30 Tf X CN CO q q co q CN CN CO CO CO CO CO CO 34.00 34.34 34.68 35.02 H8 OS OS X X q CN U5 X rj< id id id CN h ^ n q (O tO (O N CN CN CN CN t~- r- co co co q q cn r>^ t^ t>l x CN CN CN CN CD CD «5 X • • oo oo ! I CN CN »I8 cn r^ co x tJ< co OS — i rH ^H ^ CN CN CN CN CN »18 «I8 «I8 «I8 -IS •eaiqwx pin? q»A\. jo urns H* HN «t* CN CN CN CN -T» HN >*» CN CN CN CN CN CN CN CN CO CO CO CO CN CN CN CN -+. H* «r» Tt< Tf T* Tf CN CN CN CN •+» Hn «+» IO K5 ifl K5 CN CN CN CN Weight of Steel I Sections 209 w o H K < b O ao w H H H H to 02 a ?; M o X SIS 88.4 89.2 0.1 a d 95 X 09 CO iO CN CO as as CO OS OI "O a O OS C5 CO •* oo d OS OS CO rH d ^h' o o O oi o X oi O N. q d ■* o o SIS © oq q J ^j d 00 00 00 d x 00 q oo 00 00 00 00 03 d X d 5 CN .-h rJ CN OS OS a oi 09 l> IO d ■>* 09 OS CO pH d d OS OS a d a a IO CO an? ©00 H d © rH t^ X X q 00 01 00 •^ rH CO Tj< 00 00 C3 d 00 I- id X d t^ X X o i I> IO oo d X X co q os os DO a CD oi CO rH d Tji OS OS «8 rH 05 CO iO iO CO t-~ t^ l^ CO o 00 00 IO oo d OI d X 09 q tp r-I CN X X d X X iO d ^ X X w q d d X X d X X rH OS §8 S8 SIS N ^J H O rH CN t— t^ t- oi co rH 00 >o d 01 d oo q d t^ 01 90 a co oo d cn q X X X co oi X O CO d d X X SIS CO 05 CO CO CO N CO CO CO ot X CO X 00 to IO rH d d CO h- X q t- CN CN co d q q d ■* cn q d d iO d I- oo ■* t>^ 00 SIS OS iO rH h n m CO CO CO co CO co -r q tj; tj? id CO CD o d 3 CD d OS CN 00 CO CO X CO O CO a d CD CD CN X d d •^ r- O oi CO CN CN d SIS io q cq r>l oo oo >o >o "J d IO d 10 CN 00 d d CD CD co co a 3 ■* o CN CO CO CO »o d co .-I CO CO CO CN t> d d CD CD co d CD os d 3 l> 00 co co SIS O "3 i-l CO CO ■*' IO IO w CO ■o d ■0 CO -H id d IO >D CO d io '0 q ih l^ 00 iO iO (0 00 'O CN t^ d d iO IO CN £> d d CO CD 01 to I-- CO CN ^ CN CN CD CO SIS ■*? 1 • oo d a o o >o 10 d as q -. IO iO CN CO d d IO IO i •D d iO q q iO iO SIS O CM IO cn q © t(5 tj< d d 5 o CM »o iO t^ 00 CN rH d iO iO •IS 00 CD -# do© 5 d CO os h- CD O i-i CN CO -r oi -r -f 00 • oi CN o CN CD CO CO s d t^ IO CO l> •fS CO O ^ n no id ic id co co co 90 CO 90 co HS •IS •IS *IS «IS :::.": : : : : : : : : : : : : :';■-:-; «IS | : : : : : : : : : : : : : : : : : : : : -IS put? qa^i jo rang CO CD CO (N CM CN CO 01 CM CN CM CM 00 OI X X CN CN •4* OS OS CN CN os os CN CN Q CO CD CO o o CO CO 210 The Naval Constructor w k >-. O » H s p E H £ OS M g 5 H SIS 105.4 106.2 107.1 107.9 00 CO «5 CO §§2S NOOI-. CN CO CO Tji qf|MH >Q ai d> ~ SIS 100.1 100.9 101.7 102.6 •* n qoo cd ^ >d id o o o o q * « o o o o o 00 CO ■* CM d d --5 . t>- t-» CN 00 CO OS d d s s t~» t^ s r- 78.5 79.1 79.7 80.3 80.9 81.5 82.1 82.7 CO OS iq -h cd cd >t id X X X X SIS iq -< cq CN oo d d d CO CO CO r» t>. CO 00 «* O ~* H CN s s s s OS iO O CO CN CO •* rji t- b- t- t- H N CN 00 id id d d i^ t^ h- b- CO OS iO o s ^ x d s t>. i> s SIS CN t>. CO X CO CO tj< Tj< CO cc CO CD 65.3 65.8 66.3 66.8 CO X CO X N N 00 00 CO CO CO CO "^ OS "^ OS <£ d> d> <6 ■^ OS ^t 4 OS rH pH tN CN 1^ t^ S S SIS 58.0 58.4 58.9 59.4 00«00N »66h iO CO CO CO S 1.762 2.245 .5185 it 21.12 26.90 6.2126 i 2.044 2.603 .6013 I 22.07 28.10 6.4918 15 1^> 2.347 2.989 .6903 if 23.04 29.33 6.7771 1 2.670 3.400 .7854 3 24.01 30.60 7.0686 T~5 3.014 3.838 .8866 A 25.04 31.88 7.3662 i 3.379 4.303 .9940 1 26.08 33.20 7.6699 A 3.766 4.795 1.1075 A 27.13 34.55 7.9798 1 4.173 5.312 1.2272 i 28.20 35.91 8.2958 A 4.600 5.857 1.3530 A 29.30 37.31 8.6179 § 5.049 6.428 1.4849 i 30.41 38.73 8.9462 A 5.518 7.026 1.6230 A 31.55 40.18 9.2806 4 6.008 7.650 1.7671 i 32.71 41.65 9.6211 A 6.520 8.301 1.9175 9 33.89 43.15 9.9678 f 7.051 8.978 2.0739 f 35.09 44.68 10.321 H 7.604 9.682 2.2365 tt 36.31 46.24 10.680 f 8.178 10.41 2.4053 i 37.55 47.82 11.045 II 8.773 11.17 2.5802 it 38.81 49.42 11.416 1 9.388 11.95 2.7612 i 40.10 51.05 11.793 it 10.024 12.76 2.9483 H 41.40 52.71 12.177 212 The Naval Constructor STEEL. — ROUND AND SQUARE BARS. Sectional Area in Inches x 3.4 = Weight per Lineal Foot in Pounds. g Weight per M Weight per Lineal Foot in .'. H £ Lineal Foot in w w 2 fi S » Pounds. Area o Pounds. Area OF© IN Sq. Ins. OF (D IN Sq. Ins. Round. o Square. □ Round. o Square. □ 4 42.72 54.39 12.566 6 96.1 122.4 28.274 tV 44.07 56.11 12.962 A 98.1 125.0 28.866 | 45.44 57.85 13.364 i 100.2 127.6 29.465 3 46.83 59.62 13.772 a 102.2 130.2 30.069 | 48.23 61.41 14.186 i 104.3 132.8 30.680 A 49.66 63.23 14.607 A 106.4 135.5 31.296 1 51.11 65.08 15.033 108.5 138.2 31.919 A 62.58 66.95 15.466 A 110.7 140.9 32.548 | 54.07 68.85 15.904 } 1128 143.6 33.183 A 55.59 70.78 16.349 A 115.0 146.5 33.824 t 57.12 72.72 16.800 t 117.2 149.2 34.472 ft 58.67 74.70 17.257 ft 119.4 152.1 35.125 1 60.25 76.71 17.721 i 121.7 154.9 36.786 H 61.84 78.74 18.190 ft 123.9 157.8 36.450 I 63.46 80.80 18.665 I 126.2 160.7 37.122 « 65.10 82.89 19.147 if 128.5 163.6 37.800 5 66.76 85.00 19.635 7 130.9 166.6 38.485 A 68.44 87.14 20.129 A 133.2 169.6 39.175 | 70.13 89.30 20.629 1 135.6 172.6 39.871 ft 71.86 91.49 21.135 A 137.9 175.6 40.574 i 73.60 93.72 21.648 i 140.4 178.7 41.282 A 75.37 95.96 22.166 A 142.8 181.8 41.997 ¥ 77.15 98.22 22.691 A 145.2 184.9 42.718 A 78.95 100.5 23.221 147.7 188.1 43.445 i 80.77 102.8 23.758 } 150.2 191.3 44.179 A 82.62 105.2 24.301 A 152.7 194.4 44.918 1 84.48 107.6 24.850 I 155.2 197.7 45.664 ft 86.38 110.0 25.406 ft 157.8 200.9 46.415 ? 88.29 112.4 25.967 i 160.3 204.2 47.173 8 90.22 114.9 26.535 if 163.0 207.6 47.937 1 92.16 117.4 27.109 i 165.6 210.8 48.707 ft 94.14 119.9 27.688 it 168.2 214.2 49.483 Steel Weights 213 WEIGHTS. — Half-Round, Hollow Half-Round, Edge, and Convex. Feather Siz iT '- Weight Size. Weight DESCRIP- TION. per Lineal Foot. Descrip- tion. per Lineal Foot. Breadth. Thick- ness. Breadth. Thick- ness. 6 3 48.07 %\ 1 7.17 6} 5 4i 2f 40.39 33.38 27.04 if I 6.64 6.11 4 2 21.36 2J it 5.58 8i lj 18.78 21 f 5.05 ft ^. 3i If 16.36 14.11 12.02 2J 2* 1 4.52 3.98 i im%> 2| i| 10.10 2 f 4.30 % ^H 2i if 8.34 2 f 3.45 w 2i 2 « 6.75 5.34 2 A 3.03 If 2 4.09 H 2 i 2.60 ii f 3.00 If f 3.76 if f 2.09 w If 1 3.02 i | 1.34 If A 2.65 4 H 18.36 H l§§ If } 2.28 « .— 8f 8§ l 15.78 13.36 n f 3.25 8* A 8.83 05 \g n i 2.62 j ph fa 3* } 8.01 i* A 2.30 J2 A \L H I 7.35 ii § 1.98 W J ^s, 3 1 | 6.68 t» 2| 5.34 O ii f 2.99 2 I 3.26 O ii ii 2.70 H | 2.25 ii if 1 A 2.41 2.12 2* I 3.73 2* i 2.98 if 1.82 « 2i 2 1 § 2.69 2.39 1.72 W if! 2 A 2.09 n tV 1.46 « §P 2 1 1.79 ij § 1.19 1 If if I i i 1.57 1.34 1.23 i A 1.56 1.32 if B .93 l 1 1.09 i| A .85 214 The Naval Constructor WEIGHT OF SHEET STEEL. 0000 Birmingham Wibk Gauge and Englihh American (B. & S.) New U.S. Stand- Standard Gauge. Wire Gauge. ard Gauge, 1873. Thickness Weight Thickness \v«iuht Thickness WoiRht in Inches. per Sq. Ft. in Inches. per Sq. Ft. in Inches. per Sq. Ft. .454 18.62 .460 18.76 .406 16.58 000 .425 17.34 .410 16.72 .375 15.30 00 .380 15.50 .365 14.88 .344 14.03 .340 13.87 .325 13.26 .313 12.75 1 .300 12.2-4 .289 11.80 .281 11.48 2 .284 11.59 .258 10.52 .266 10.84 3 .259 10.56 .229 9.36 .250 10.20 4 .238 9.71 .204 8.33 .234 9.56 5 .220 8.98 .182 7.42 .219 8.93 6 .203 8.28 .162 6.61 .203 8.29 7 .180 7.34 .144 5.88 .188 7.65 8 .165 6.73 .129 5.24 .172 7.01 9 .148 6.04 .114 4.66 .156 6.38 10 .134 5.47 .102 4.15 .141 5.74 11 .120 4.89 .091 3.70 .125 6.10 12 .109 4.44 .081 3.29 .109 4.46 13 .095 3.87 .072 2.93 .094 3.83 14 .083 3.38 .064 2.61 .078 3.19 15 .072 2.94 .057 2.32 .070 2.87 16 .065 2.65 .051 2.07 .063 2.55 17 .058 2.37 .045 1.84 .056 2.30 18 .049 1.99 .040 1.64 .050 2.04 19 .042 1.71 .036 1.46 .044 1.79 20 .035 1.42 .032 1.30 .038 1.53 21 .032 1.30 .028 1.16 .034 1.40 22 .028 1.14 .025 1.03 .031 1.28 23 .025 1.02 .023 0.921 .028 1.15 24 .022 0.898 .020 0.821 .025 1.02 25 .020 0.816 .018 0.729 .022 0.89 26 .018 0.734 .016 0.651 .019 0.77 27 .016 0.653 .014 0.581 .017 0.70 28 .014 0.571 .013 0.515 .016 0.64 29 .013 0.531 .011 0.459 .014 0.57 30 .012 0.489 .010 0.409 .013 0.51 31 .010 0.408 .009 0.364 .011 0.45 32 .009 0.367 .008 0.324 .010 0.41 33 .008 0.326 .007 0.288 .009 0.38 34 .007 0.286 .006 0.257 .009 0.35 35 .005 0.204 .006 0.228 .008 0.32 36 .004 0.162 .005 0.204 .007 0.29 Weight of Bulb-angle l 215 aia sis 218 518 l-tl • SIS 218 118 518 SI8 b- O) O Tj< N (-• N 00 00 00 .CO-* -f NOffl 00 tO »0 CO i- 1 on m • COO N h i(5 00 ^HiOOCO qcot^.r-4 •iO«D iO CO CO CO CO CO CO N N S S 00 »I8 -<* -^ -# U5 ^ -t 1(5 lO K5 K5 1(5 (O CO lO CO CO ■18 N IN N N !00(OU5 ^ CO 05 « 0)0)0)0 U5 lO ■* n o M (o qncq a t^ o cq cq occcdo) n q m CO ^ ■* tJH tJ?^-*-"* t)5io»0«5 K5 io iO i(j lO CO CO CO CO CO -tf a ooh m CO CO -^ ■* TfT}- • IO rH : ; id d 218 CN h- • • O IO CO rH ; co cn '. '. ■<* id 218 CO b- ; ; ■* os CO "># • • o io I I CN CN 12.11 12.62 13.13 13.64 rH CN co ■«* l> CN t>. CN CN CO CO 'f SIS • -S3 ! ioio 9.74 10.21 10.67 11.14 10.27 10.73 11.20 11.67 11.28 11.75 12.22 12.68 11.84 12.31 12.77 13.24 SIS Tf N OS iH lO OS CO 00 00 00 OS 9.03 9.45 9.88 10.30 9.51 9.94 10.36 10.79 10.44 10.87 11.29 11.72 CO 00 rH CO OS CO 00 CN O rH rH CN cs|S b- IO CO o o> n n IO 00 CN IO t-' t^ 00 00 7.95 8.29 8.63 8.97 th IO OS CO NOCON GO OS OS OS rj< 00 CN CO rH Tjl OC ) rH OS OS OS o HS CO CN CN CN H ■* NO (OOION 00 00 00 N N O M O d t^ t^ t>^ ■^ tJ< CO CO rH ■«* |> © NNNOO 7.81 8.11 8.41 8.71 CN IO 00 © oo oo oo d •IS CO 00 •"*< OS ^ « Ol H 1C id «5 85 QW h to © cn io t>. CO CO CO cO H N N « M iO 00 O <6 <6 <6 t> 6.90 7.16 7.41 7.67 IO O CO rH N IO N O b^ l> b-' 00 «5|S 4.72 4.93 5.14 5.35 O rH CO if CN ■* CO 00 IO «C "5 «5 5.47 5.69 5.90 6.11 00 OS O CN OS rH T* CO iti to ^6 ^6 00 OS rH CN CN ■* t>. OS cd d d d *I8 00 «0 CN OS OS »H CO f CO •<* TP TjJ 00 IO CN OS CO io t>. 00 Tj< ^ ^ ^4 th 00 "5 CN CO i> OS rH tjJ tj5 r(5 IO CO O t- •<* O CN CO IO to id id >d OS CO CO o CN ■* CO 00 id id id "5 •eSu^u HH«N «4* hV **« H N N N «+» rf. r*« th CN CN CN H> *+. •*• CM CN CN CN -t« r*« <#• CN CN CN CN •qaAl co : : : co : : : Nta co : : : •^ : : : r*« ■* : : : Weight of Bulb-angle 217 w o CO tn H a H oa aa W M 3 818 SIS SIS 5;I8 IN CN 818 IN O ; ; © n os n • • 1> •* ! ; -h in tN IN O 00 O hi q »o cn q h « m co IN IN CN CN IN CN N N N 00 CO sis ■* H 00 U5 00 CO N CN CN CO CO -t 13.42 13.89 14.36 14.82 ■*ON^i ■* OS CO 00 ii •* io'io OS CO CO o OS iH* OS HH "4< d d d TjH rH N TJH © io q ■* <6 <6 & i-^ 218 11.88 12.30 12.73 13.15 i-H ■* CO OS ^ 00 IN CO CN CN CO CO i< N9IN MN H * CO CO ■* -^ 13.86 14.28 14.71 15.13 CN tJH i> OS 00 (N CO o •<# *6 *6 <6 «I8 L0.89 L1.27 LI. 65 L2.04 00 CD >0 CO M N h irs i-H tH IN CN MH O N 0 00 IN «0 Hrifin CN CO O ■* co q q co CN CN CO CO H8 r- co co co 00 i-H TjH N 00 OJ OS oi n n n- n IN iO 00 .-J OS OS OS o 9.95 L0.25 L0.54 L0.84 ■*HH CO CO CO CO CO OS IN d>.d d fh rf t« Tf CO © co q q •18 CO X tP OS oo q co »o . N 00 00 00 OS »0 O CO t-H ■* t>. q 00 00 00 00 00 Ttt OS iO N ON U) oo d os os CO 00 ■* OS i-; co q oq OS OS OS OS lO O CO tH N OIN lO dodo *I8 6.78 6.99 7.20 7.41 O H N ■* HMION t> t^ I> N O IN CO tJ< tqooow N N 00 00 i-h (N CO ■* O) H W lO N 00 CO 00 tC IO N CO rf CO 00 O 00 00 00 OS «I8 O l> •* r-l N 00 O N io "i d d 00 lO -* i-H rj< ic i> q <6 <£ <6 <6 OM ON q oo q t-h d d t> n i-h 00 "3 CN t-h in -^ q l> t^ N N •aSuBU « IN N CO *+• Hn «m IN IN IN CO CN IN CO CO CN -HN CN CO CO CO •q^AV. y ; 2 .5 «r« - . . Tj< - - - iO - - ^ lO ' - - •*> - - . IO - - - 218 The Naval Constructor < fa o • W H s i H j* ce tl W E H SIS 218 . SIS 5518 • • CN O : ; io co CN d to to h- OS CN -^ 00 Cj N w lOCffiN cn ^ r- os O M Nh (O N N 00 h- OS CN •<* q co oo cn N 00 00 OS 00 O CO lO q q q co OS OS OS O i-h i—i i— i CN «I8 «o CO -h OS O •* 00 ^h ii t' "* lO ■* CN O OS »o OS CO CO ■*' t)5 iti io Q9 MO q 00 CN q i<5 U5 (O CO MO M N ■* 00 N CO tOlfiNh 17.49 17.88 18.26 18.64 •18 t^ o ■* t^ IN CO CO CO- O ■* 00 CN CN IC 00 CN CO CO CO Tjn 00 CN CO O O "* N H "* ^ ■* »o" CO O "f 00 q co q q Tf< U0 iC "0 O •* 00 CN Os cn q q in d d d H8 CO CO CN CN * NOW t-h ,-5 CN CN ^ CO CO CO 00 --I ■* t^ r4 CN CN CN CO CO CO CN CO OS CN iC CN CN CO CO CO CN CN CN ■* r^ o q co co ■* "*' 00 M 00 N CN q 00 i-j Tj< Tf ■>* IC •18 OS iC O CO O CO CO GO d d d d CO i-t b- CN •* t>» OS CN d d d ^ b- CN 00 CO i-j ■* q q 11.88 12.13 12.39 12.64 12.65 12.90 13.16 13.41 w|8 8.74 8.96 9.17 9.38 b- 00 OS o O CN ■* N OS OS OS OS «I8 agireiji CN CO CO CO CN CO CO CO CN CO CO CO CN CO CO CO CN CO CO CO •q»AV "t* - . - m - - - to - - - <© : : : t*. ' ~ ' ^ : : : Weight of Bulb-angle TJ219 H o to to h 02 H H 9 H to S g 9B s to M o X H SIS •3S . CN ■* • CO o : ti< d C O CO o d oo SIS OS OS >o CO CC ~ X CO d CO CO oa d CO 39.74 40.55 42.16 OI X c -1- 41.62 42.43 44.05 Ol I- oi CO iO CO -r •* lO co os ■* id SIS IO '. iC CO 09 d re -T qb d cc O N l> co CM 1- CO 37.97 38.74 40.26 s d co 39.77 40.53 42.07 co X d 9 5 co os CO 00 CN CO wa o CN CO t^ OS l> ■* CN CO- CO co oi -r" CO IO co CO 1- co OS co CS M9 t id 36.19 36.91 38.35 X CO 37.90 38.62 40.07 5 00 co 9 09 CO CO o co oq d i-J SIS iO d CO CO 1-4 CO CO OS oi co q oi CO IQ l> oi CO co *t co- co -t* CO o co- co 34.38 35.06 36.42 CO CO id CO 36.01 36.69 38.05 00 8 d CO CC s co oo d CO CO SIS 00 00 IN OS CN Tfl i-l d d - id d CN CN «I8 IO 00 00 CO CN CN CO d d s q d CM X X d CC CM G oi CO s 01 q CM 0) d Ol 21.29 21.68 22.44 9 Ol 22.33 22.71 23.48 8 CO CN X CO CO Ol (>• CO t^ lO CO Tji CN CN =°iS CO I> i-i •* 00 IO 00 fc. O X X 10 I- X C5 CC d 01 c oi 19.36 19.70 20.38 1- OS 20.31 20.65 21.33 os s X OJ CM CN O co co »H CN CN CN HS 8 id 00 00 co os id id 00 CN to -t Ol OS io (0 co X SO CO 1- c O O OS ■* t^ CN t^ t^ 00 1- 09 I- 18.27 18.56 19.16 «IS »{S «!S •aSinqj co -+.-+. «*• CO CO CO CO CO -+» H« co CO CO Tj< CO CO CO ■* •q»A\. 00 : : : X : : : 09 : : : 5 : : : o : : : 220 The Naval Constructor K O 'A < h 05 X H H H H H 2 § 6 3 H 818 X X • • CN OS '. ' oo d 50.29 51.14 51.99 53.69 52.32 53.17 54.02 55.72 54.36 55.21 56.06 57.76 56.42 57.27 58.12 59.82 SIS 44.62 45.42 46.23 47.85 48.16 48.96 49.77 51.39 50.10 50.91 51.72 53.33 52.06 52.86 53.67 55.29 CO •<# IO CO q oo q 1* _l T* (O NOC O) rf * t * SIS 36.59 37.23 37.87 39.14 39.45 40.09 40.73 42.00 41.06 41.70 42.33 43.61 N H IO CN q co q cn CN CO CO iO Tj< Tt< Tf Tj< 44.31 44.95 45.58 46.86 SIS 34.54 35.14 35.73 36.92 37.23 37.83 38.42 39.61 >o IO ■* CO oooioin CO CO CO ^ 40.28 40.88 41.47 42.66 CO CO CN th oq ■* q cn i-5 tN co -^5 "* ■* ■* T* SIS 32.48 33.03 33.58 34.69 35.00 35.55 36.10 37.21 CO OS ^ ^ •. t>. CN CO CO TfS CO CO CO CO 34.10 34.61 35.12 36.14 35.46 35.97 36.48 37.50 36.84 37.35 37.86 38.88 SIS 28.30 28.76 29.23 30.17 30.48 30.94 31.41 32.35 T}4 H 00 1-H f~ CN CO CO i-J CN CN CO CO CO CO CO CN X lO OS O i] CD 00 CO CO CO ■* CO CO CO CO 34.31 34.78 35.25 36.18 SIS 26.18 26.61 27.03 27.88 OS IN Tf OS HfflOOO 00 X OS OS . t*. h q •# i-5 ti q in q W CO ^J* ^ (N CO CO CO ■* CO CO "* if CO CO ^ ^ CO CO ^ "^ CO CO ^l ^ •q»A\. 2 = -• ' S : : : "♦'.•» cn : : : cn : ; ; Weight of Bulb-plate 221 w to h o oo a H a h to H GO to 3 o 3 H «IS •H t> 00 T* ' : : : IM CM CO CO .... «I8 00 -H © CO ii'.\ . . si a c^ 8§ ^ ^ .... -18 . . £ 23 c3 t-^ S3 t- CO 00 oo oo' d d 1 S n » 6 d h oi © q q co ci id id t^ SIS 5.58 6.06 6.56 7.06 8SS©; c~ oo oo o> 9.59 10.01 10.44 11.65 iq So © © fi « * t-i © CO q iq 05 ■«*< o d uo d 00 CO S (N d t^ t^ d SSS8 d d o» d 11.39 12.62 13.38 14.65 «>I8 t- 00 . . CO ^ to » t- a •* •<*' d d 6.19 6.59 7.03 7.45 8 8 5 3 hooooo' 10.29 11.43 12.11 13.29 H8 c4 f io «o lO CO lO «> IS \d id id to t- to 00 . •. °°. °i d t> oo • «I8 1.63 1.84 2.07 2.31 2.52 2.75 2.99 3.24 t~ o t> q im_ CO CO CO "^ 3 8 8. 8. •**#<#' d 00 " ' * id ' ' • (•sni) -+* He» «M c* d» c5 c* 00 CO CO CO T* ^? 3? 3? iffl lO to © © t~ t- oo 222 The Naval Constructor o to to h CC H H to H H to 05 t» w to M •18 | m CI ■*> y-> 1 S53!S CO © CI -- 9 ~ S3 S 58.2 61.1 63.2 66.2 CO t l.~. © 8 P S' g 78.7 81.9 84.1 87.3 1 «-i t- t- *< 1 fc 8 $ s in, ci c» o ills 8 8££ 75.9 79.1 81.1 84.2 •ja 35.6 38.2 40.1 42.7 t- co eo © 53.9 56.7 58.6 61.5 <* eo ci ci 8 8 8 P 73.1 76.2 78.1 81.2 "i 8 34.2 36.6 38.5 41.0 o> •* eo o> 51.8 54.5 56.3 59.1 60.9 63.7 65.6 68.5 CO CO »H rl © eo in oo i- t- i- t- H8 32.8 35.1 36.9 39.3 41.1 43.6 45.4 47.9 t- eo © t- 58.5 61.2 63.0 65.7 67.5 70.4 72.2 75.1 SIS 29.86 31.31 32.05J33.58 33.66 35.28 35.95 37.65 37.56 39.35 39.83|41.70 41.44143.40 43.82 45.86 45.4347.56 47.84 50.04 49.4551.74 51.93,54.31 53.55 56.01 56.09 58.64 57.7160.34 60.29 63.01 61.91 64.71 64.60 67.49 66.22 68.19 68.94! 72.00 218 28.42 30.52 32.05 34.25 35.78 37.96 39.49 41.78 43.31 45.63 47.16 49.55 51.08 53.54 55.07 57.57 59.10 61.71 63.24 65.88 JhI® 26.97 28.99 30.43 32.55 33.99 36.09 37.53 39.74 «.,8 43.42 44.86 47.18 48.62 50.99 52.44 54.85 56.30 58.82 60.27 62.82 SIS 25.53 27.46 28.82 30.85 32.21 34.22 35.58 37.70 39.06 41.21 42.57 44.80 46.16 48.45 49.81 52.13 53.49 55.93 57.29 59.76 SIS ScISS S 8 fc 8 30.42 32.35 33.62 35.66 36.93 39.00 40.27 42.42 43.69 45.90 47.17 49.42 50.69 53.04 54.32 56.70 SIS 22.64 24.40 25.59 27.45 28.64 30.48 31.67 33.62 34.81 36.79 37.98 40.04 41.23 43.35 44.54 46.70 47.89 50.16 51.35 53.64 SIS 21.19 22.87 23.97 25.75 26.85 28.61 29.71 31.58 32.68 34.58 35.68 37.66 38.76 40.80 41.90 43.98 45.08 47.27 48.37 50.59 SIS 19.75 21.34 22.36 24.05 25.07 26.74 27.76 29.54 30.54 32.37 33.39 35.28 36.24 38.25 39.27 41.26 42.28 44.38 45.40 47.53 SIS 18.30 19.81 20.74 22.35 23.28 24.87 25.80 27.50 28.43 30.16 31.09 32.90 33.83 35.70 36.63 38.54 $ . . . 8 • • • SIS 16.86 18.28 19.13 20.65 21.50 23.00 23.85 25.46 26.31 27.95 28.80 30.52 31.37 33.15 34.00 •IS 15.41 16.75 17.51 18.95 19.71 21.13 21.89 23.42 24.18 25.74 26.50 28.14 •18 os ci cs ci » a a n 17.93 19.26 19.94 HS 12.52 13.69 14.28 15.55 •18 oo co 2 cl — — •18 *I8 (sui) 00 OS CS o e>4n« CI CO CO •<* "$" in ST © ©" t- i>? oo ~~" 1 Weight of Bulb-tee T 223 sis 518 118 IIS OHHN •18 n h offl oot-ic—i c5oocoo6o6oi 00 00 Ci © OOOJOSO CO t> N 00 HiflOlN CO © "* N 00 00 N 00 00 OS MMNN |M uj iO >0 CO (N i> i> i> n oo iO O (ON 00 © cn t>. 01 -o »o »o »o co 10 »o co co co co co n »I8 «I8 In oo © n eo-^iooo o (O 00 O «3 OtNrt<00 TlJ CO CO -tf Tji ■<* t}H •<# -tf rji CO IO 00 - CO ■* (6 (ON00 H (O H N HtON CO N N CO 9 SIS 13.36 13.87 14.38 15.40 14.20 14.71 15.22 16.24 co •* io r>- qioqq KJ 1C d N io co r^ os 00 CO 00 00 id to to N SIS 11.53 12.00 12.46 13.40 OS CO CO CO NNNH CN * r-l lO 01009 CO CO ^ ^ ■«< 1-1 |> i-l 00 CO N N co ■* ^ in 14.60 15.07 15.54 16.47 SIS CN IO t- CN IO OS CO CN d © i-5 cn 11.23 11.66 12.08 12.93 11.95 12.37 12.80 13.65 12.65 13.07 13.50 14.35 «£2© CO CO •* id «IS 9.53 9.91 10.29 11.06 NBMO H iO 9 N d d d «h* 10.83 11.21 11.59 12.36 11.46 11.84 12.22 12.99 12.09 12.47 12.86 13.62 «I8 iO 00 CN 00 00 00 C5 OS HU39N ^h •* |>. Tj; Os OS Os O O •* 00 CO nomo d © © ^ b- rH l« CO CN CD OS CO ©do*-* 10.84 11.18 11.52 12.20 H8 CO CO CO CN t^ l> 00 00 8.04 8.34 8.64 9.23 b- b- t> CO 1O00H N 00 00 © © 9.08 9.38 9.67 10.27 os os oo oo IO 00 i-t t>- os os d d »I8 6.53 6.78 7.04 7.55 CO t> t>^ 00 7.44 7.70 7.95 8.46 9^0H oq i-j •* q t^ CO 00 00 8.33 8.58 8.84 9.35 *I8 CO ■* CO 00 * N » M CN CO <* N. 9 H CO N i-" •-' •-' ■£ « rfliON W ifl N H (O <0 tO N OHNiO NOSH U5 CO CO N N 7.08 7.29 7.50 7.93 <*I8 CO O t- i-l IO t>; 00 CN rji ■* Tji id 8383 ■** io »o us OS o H 00 1O 9 IO CO 00 -H «j io id to CN OS CO O 00 9 H iO id id d co Csui) •aSuBi^i jo »efce t-+0 *■(& K+0 CN CN CO CO ■£**! -+0 CO CO CO ^t ( •q sni) jda. -^ CO t)< * Ol 24.89 25.57 26.93 CO' 01 ■6 Ol c-. id Ol O lO q q d t^ IN d co N i> CO 00 1^ t^ X O iO 00 00 s d CO 00 18.94 19.45 29.47 OS CO o d i-i CO IN CN O rH* IN IN 19.96 20.47 20.98 22.00 sis o ce X id re M C0 oi X d iO IN d d OS Ol d (0 I- d HN00 O M-t> odd HI d co d lO CD O rH d tA 10.52 10.78 11.03 11.54 »ia os o I- Ol OS CO 00 Q i-H IN rl CO 00 00 iO X co X CO •* CO lO t-; .-J x o6 d co CC 00 X X CD X q tjj d d iO (O N O q .-H q x oo d d d <*IS 00 d iO M d CB co X CO ■q d X iO CO X d d 0) X d TjH ^H lO ON iO I> 1> ^ Ol CS Ol CD O ^ X 1> t> X iC (N CO KiONO t^ 1^ l> 00 (•BUI) CO CO CO *# co CO CO * CO «H- Hm 1* co Ha ■CO Ha «*» c4« H* e+n CO -^ iji rf (•sui) •T^daa; : : : : : : lO : : : iO : : : IO - - - 226 T The Naval Constructor ft u ?; to tu o cc H H to H s H to tr. te K to 818 35.45 36.30 37.15 38.85 37.99 38.84 39.69 41.39 41.01 41.86 42.71 44.41 43.56 44.41 45.26 46.96 46.61 47.46 48.31 50.01 SIS 33.75 34.56 35.36 36.98 36.17 36.97 37.78 39.40 39.05 39.86 40.67 42.28 41.47 42.28 43.13 44.70 44.40 45.21 46.01 47.63 5518 »o -i 00 <-> OM15H * 518 30.35 31.07 31.79 33.24 32.51 33.23 33.96 35.40 35.14 35.87 36.59 38.03 37.31 38.03 38.75 40.20 00 © IN N OS N rf 00 oi d h ci :: — — — SIS 28.65 29.33 30.01 31.37 30.69 31.37 32.05 33.41 33.19 33.87 34.55 35.91 35.23 35.91 36.59 37.95 37.77 38.45 39.13 40.49 218 26.95 27.59 28.22 29.50 28.86 29.49 30.13 31.41 n nhoo N 00 i(5 S H tH CN CO- CO CO CO CO Tf 00 N O) r* t*. rftD CO CO Tji lO CO CO CO CO 35.56 36.20 36.83 38.11 SIS 25.25 25.84 26.44 27.63 27.03 27.63 28.22 29.41 29.28 29.87 30.47 31.66 CO CO lO ^ OCNTf .-I rH CN CO- CO CO CO CO 33.35 33.94 34.54 35.73 218 m o w » CO ■* tJ<" «5 CN Q OS r*. rn q io CO N S 00 (N CN CN (N SIS 18.45 18.87 19.30 20.15 19.72 20.15 20.57 21.42 21.46 21.88 22.31 23.16 CO CO 00 CO f~ l-J lO T}< cirin <* m h O CO t>; •* lO "5 "5 (O NHion © ^ t>. -^ (OICON iC OS CO ^h ic oq in q t-I t^ 06 oo N H ifl M »o os cn q oo oo a oi 20.09 20.43 20.77 21.45 H8 lO if} ■* Tff co q q >o CO CO CO •& ^ CO CO CO * q q ■* rj< tj5 tj! ui NN 00O> (OfllHto lO IO CO © »I8 >fl tO NO OS .-H CO 00 a* <5 o <5 00 OS i-H CO >o t>- q ■* o d -J J 11.68 li.90 12.11 12.53 (N CO "# h- « K3NH CN CN CN CO -IS lO IN OS CO in ■<* io q 00 00 00 00 £8233 co oo d d (•8UJ) •93uBI.i JO Tf Tj< T»< 1C •4* -f «t* -+» Tf Tj< Tj< »C Tj< •<* lO tO ^* IO lO W ifl 1Q lO tO sui) » : : : r+> - . . CO - - - i> : : : r+« . . . r^ - - - oo : : : Weight- of Bulb-Tee T 227 w O 3= H H ft H cc ft H SIS 48.73 49.58 50.43 52.13 PS 10 X CO IN rH CN CO «o iO n X «s x a cd l!0 CO X co q rr id iO IO X co i- IQ r, iO iO q X iO Q OS X 10 s s CN t^ N IO WHOH ai d> ^ n IO CO CO CD SIS H IN M T(< ^m qtq •i s oo oi rj* ^ rj< ^ o d rH CN X CO d d CI ci •o CI iO co -* CN O tN CO iO IO •C 3 CI IO "*' iO cc co id iO -r d 10 iO iO W H Ifl h IO q rH rH d n oo d IO IO iO CO SIS O N M ffl H 00 ©H Tj" •<* lO ^ ■* •* ■* Tj( 00 iO CO CO rH t>" CO CO d X X 00 q r|H d d ■* IO a. iO X ^0 q ci i0 co cd g i CO CN OS O r>. q CN CN cd Tti id t^ iO IO IO iO SIS OOONN N iO N CO rH CO' lO CO N iO q q q q N N M d CO CO CO CO SIS 00 iO CN lO 00 M 00 N N N 00 O) CN CN h/ d d CO CO CO CO SIS NOW N q q ■* cd co cd i^ CN CN q CN CO CN CN CI few re CI cd CI £8 CO ■* CN «x> •*» -*o W5 iO "O CO LO iO iO 2 «Q iO CO to IO S3 OS I* SO H" + * iO CO CO N (•sui) •q^oci 00 - * ^ OS : : : : : : a : : - o - - - 228 T The Naval Constructor I y < h O 00 9 H H B n a is H i u 3 818 62.10 62.95 63.80 66.35 64.65 65.50 66.35 68.05 67.11 67.96 68.81 70.51 68.81 69.66 70.51 72.21 71.29 72.14 72.99 74.69 SIS 59.21 60.02 60.82 63.24 61.63 62.43 63.24 64.85 64.01 64.81 65.62 67.23 65.62 66.42 67.23 68.84 68.03 68.83 69.64 71.25 SIS 56.32 57.08 57.85 60.14 58.61 59.38 60.14 61.67 60.90 61.67 62.43 63.96 62.43 63.20 63.96 65.49 64.75 65.52 66.28 67.81 1518 53.43 54.15 54.87 57.04 55.59 56.31 57.04 58.48 58.80 58.52 59.25 60.69 59.24 59.96 60.69 62.13 61.48 62.20 62.93 64.37 sis 50.54 51.22 51.90 53.94 52.58 53.26 53.94 55.30 54.70 55.38 56.06 57.42 56.06 56.74 57.42 58.78 58.21 58.89 59.57 60.93 SIS 47.65 48.29 48.92 50.84 49.56 50.19 50.83 52.11 51.60 52.23 52.87 54.15 52.87 53.50 54.14 55.42 54.94 55.57 56.21 57.49 218 CO to lO CO t>. co q t>- •ji tfj to N 46.54 47.14 47.73 48.92 48.49 49.09 49.68 50.87 49.68 50.28 50.87 52.06 51.66 52.26 52.85 54.04 SIS NCI NM X ■* OS CO i-5 tN t •* •* HI 43.52 44.07 44.63 45.73 45.39 45.94 46.50 47.60 46.49 47.04 47.60 48.70 48.39 48.94 49.50 50.60 SIS 38.98 39.49 40.00 41.53 rH (N CO lO to q to to O rH rH (N T« -HH Tf T* 42.29 42.80 43.31 44.33 43.29 43.80 44.31 45.33 CN CO ■* CO rH q rH rH lOilifON ^1 *^1 ^1 ^4 SIS 36.09 36.56 37.02 38.43 37.49 37.95 38.42 39.36 39.19 39.65 40.12 41.06 40.12 40.58 41.05 41.99 tO rH X CN OOtCNN r-I IN IN CO ^ "^ ^ ^* SIS O . rH X x oo d d IN N N © rH © © N h q © NCCOOO b- n t^ oo © ^ © © 00 t> lO IN oo © rH co l> 00 00 00 © ■"*! © © iq -<* cn © h ci » ^i 00 00 00 00 SIS ■ CO CN t^ t^ ■* -^ lO © NiO « O co ■<*' »d © i> t^ t^ t^ 00 00 © © CN © oo iq d n N © t- N N. J> 77.90 78.70 79.51 81.12 SIS 66.28 67.05 67.81 69.34 N^ OCC *il«N OOftOH CO CO N N © t>. CO © CN © N CN © © i-i CO N N N t> © CO © CN q ■* ih i> CN CO Tt< »d N N N N 74.19 74.96 75.72 77.25 fcIS IN ■* N i-H q q co oo oo © © © © © iO N O iji © t> iq © © d © i-h © © N t» © IN lO © IO CN © CO d ^ i-l co N I> N N SIS N »C « OS lO N » N d d d o 56.10 56.70 57.29 58.48 58.22 58.82 59.41 60.60 59.41 60.01 60.60 61.79 SIS 49.49 50.04 50.60 51.70 51.47 52.02 52.58 53.68 NO 00 00 »q r-j q n IN CO CO tJH w iO >o >o 54.61 55.16 55.72 56.82 rt © CN CN N CN 00 © >0 d (O N lO lO lO lO SIS ■* iO CO 00 rH © i-H i-H CO ■<* iO N © iq © © oo oo d © ■* ^ ■* >o 48.99 49.50 50.01 51.03 51.00 51.51 52.02 53.04 CN CO ■* © © iO © © CN CN CO Tj5 lO iO lO lO SIS 00 "* rH IO t>- CO CN CO CO -tf ^ ^ ^ ^ © IO * CO id id © t>^ © iO * id id © •IS co ■* co os q >t oq kj CO CO CO CO ooosw N © ■>*< mr« -+• CD CD CO t^ H« -+> <+« -+• © © © t~ r+, Ht. <+. r+t © © © I> H> Hn c*« -+• © © © N -+* He* «H H-« © © © t> (•8UI) « : : : "* : : : P+1 ■* : : : lO - : - • : : : t-H 230' The Naval Constructor to to -< fa 05 s H H H to fa H >5 as cc H to H SIS 84.26 85.11 85.96 87.66 85.96 86.81 87.66 89.36 88.74 89.59 90.44 92.14 89.44 90.29 91.14 92.84 93.25 94.60 94.95 96.65 SIS 80.48 81.28 82.09 83.70 82.10 82.90 83.71 85.32 84.79 85.59 86.40 88.01 86.41 87.21 88.02 89.63 89.13 89.93 90.74 92.35 SIS OS CO ** t- t- t- X 80.88 81.60 82.33 83.77 SIS 69.13 69.81 70.49 71.85 70.49 71.17 71.85 73.21 eo -i os io q q - t^. t» OS h- iG i-h I r>. r^ ^ t- CO ^f CN X *1 "* ■"! ** C9N00O t- t- t» h- SIS 65.36 65.99 66.63 67.91 66.63 67.26 67.90 69.18 68.98 69.61 70.25 71.53 70.26 70.89 71.53 72.81 72.64 73.27 73.91 75.19 SIS l» b- CO >0 «3HNO> H fi N M CO CO CO CO CO CO iO ■* N CO CS rt (•8UI) •itfdaci CO ;. ;. j •4i **S -8 > t^ 3 » - *-'•: Weight of Steel Hollow Pillars 231 Outside Diameter. Thickness. Weight in Lbs. per Lin. Foot. Inches. Millimetres. Parts of an Inch. Decimals of an Inch. Millimetres. U 64 1 0.25 6.34 6.01 24 64 ft 0.3125 7.93 7.30 21 70 1 0.25 6.34 6.68 2} 70 6 IB 0.3125 7.93 8.14 3 77 1 0.25 6.34 7.34 3 77 A 0.28125 7.14 8.17 3 77 r 0.3125 7.93 8.97 3 77 0.375 9.52 10.51 H 83 f 0.28125 7.14 8.93 1 83 0.375 9.52 11.52 89 t 0.28125 7.14 9.68 34 89 0.375 9.52 12.52 3f 95 f 0.28125 7.14 10.43 3| 95 375 9.52 13.52 4 102 A 0.3125 7.93 12.31 4 102 f B 0.4375 11.11 16.65 41 108 ft 0.3125 7.93 13.14 41 108 ft 0.4375 11.11 17.82 44 115 ft 3125 7.93 13.98 44 115 ft 0.4375 11.11 18.98 4f 121 0.3125 7.93 14.01 4| 121 ft 0.4375 11.11 20.15 5 127 ft 0.3125 7.93 15.65 5 127 ft 0.4375 11.11 21.32 5* 140 ft 0.3125 7.93 17.32 54 140 p 0.4375 11.11 23.66 51 146 i 0.375 9.52 21.53 5| 146 4 0.5 12.69 28.04 6 153 1 0.375 9.52 22.53 6 153 f 0.40625 10.31 24.29 6 153 0.5 12.69 29.37 6 153 ft 0.5625 14.28 32.67 61 159 y 0.40625 10.31 25.37 i 159 ft 0.5625 14.28 34.17 166 y 0.40625 10.31 26.46 64 166 a 0.5625 14.28 35.67 6! 171 0.40625 10.31 27.54 61 171 ft 0.5625 14.28 37.18 7 178 4i '0.40625 10.31 28.63 7 178 41 0.46875 11.90 32.72 7 178 32 0.5625 14.28 38.68 7 178 0.625 15.87 .42.56 74 191 0.46875 11.90 35.22 74 191 f 0.625 15.87 45.90 71 197 J 0.46875 11.90 36.47 71 197 0.625 15.87 47.57 8 203 f 0.46875 11.90 37.73 8 203 0.625 15.87 49.23 84 216 1 0.46875 11.90 40.23 84 216 0.5 12.69 42.73 84 216 ! 0.625 15.87 52.57 1 216 I* 0.6875 8.73 57.38 222 0.5 12.69 44.06 81 222 h 0.6875 8.73 59.21 9 229 0.5 12.69 45.40 9 229 ii 0.6875 8.73 1 61.04 232 The Naval Constructor WEIGHT OF STEEL ANGLES Thickness in Deci- Sum of Flanges. .10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 Thickness in Inches. Milli- metres. 2 .78 3.18 3.57 3.97 4.76 5.16 5.56 5.95 6.75 7.14 2 51 ( l .65 0.77 0.89 1.00 1.11 122 1.33 1.44 1.54 1.64 2 54 ( ).6<> 0.82 0.94 1.07 1.19 1.31 1.42 1.54 1.65 1.76 2 57 < J. 73 0.87 1.00 1.14 1.27 1.39 1.52 1.64 1.76 1.88 2 60 < ).77 0.92 1.06 1.20 1.34 1.48 1.61 1.74 1.87 1.99 2 64 ( >.S2 0.97 1.12 1.27 1.42 1.56 1.71 1.84 1.98 2.11 2 67 ( 1.86 1.02 1.18 1.34 1.50 1.65 1.80 1.95 2.09 2.23 2 70 ( 1.90 1.07 1.24 1.41 1.57 1.73 1.89 2.05 2.20 2.35 2 73 1.94 1.12 1.30 1.48 1.65 1.82 1.99 2.15 2.31 2.47 3 77 1.18 1.36 1.54 1.73 1.90 2.08 2.25 2.42 2.59 3i 79 1.23 1.42 1.61 1.80 1.99 2.17 2.35 2.53 2.71 3i 83 1.28 1.48 1.68 1.88 2.07 2.27 2.46 2.64 2.83 3} 86 1.33 1.54 1.75 1.96 2.16 2.36 2.56 2.75 2.95 ti 89 1.38 1.60 1.82 2.03 2.24 2.45 2.66 2.86 3.07 3 92 1.43 1.66 1.88 2.11 2.33 2.55 2.76 2.97 3.18 3} 95 1.48 1.72 1.95 2.18 2.41 2.64 2.86 3.09 3.30 9 98 1.53 1.78 2.02 2.26 2.50 2.73 2.97 3.20 3.43 4 102 1.84 2.09 2.34 2.58 2.83 3.07 3.31 3.54 ft 108 1.96 2.22 2.49 2.75 3.01 3.27 3.53 3.68 4§ 115 2.08 2.36 2.64 2.92 3.20 3.48 3.75 4.02 4} 121 2.19 2.50 2.80 3.09 3.39 3.68 3.97 4.26 5 127 2.31 2.63 2.95 3.26 3.58 3.88 4.19 4.49 .8 133 2.77 3.10 3.43 3.76 4.09 4.41 4.73 140 2.90 3.26 3.60 3.95 4.29 4.63 4.97 5i 146 3.04 3.41 3.77 4.14 4.50 4.85 5.21 6 153 3.56 3.94 4.32 4.70 5.07 5.45 6i 159 3.71 4.11 4.51 4.90 5.30 5.68 a 166 3.87 4.28 4.70 5.11 5.52 5.92 6} 171 4.45 4.88 5.31 5.74 6.16 7 178 4.62 5.07 5.52 5.96 6.40 7i 184 4.79 5.26 5.72 6.18 6.64 a 191 4.96 5.45 5.92 6.40 6.87 7} 197 5.13 5.63 6.13 6.62 7.11 8 203 5.82 6.33 6.84 7.35 8i 209 6.01 6.54 7.06 7.59 l\ 216 6.74 7.28 7.83 222 6.94 7.51 8.06 9 229 7.73 8.30 9* 242 8.17 8.78 10 254 9.25 10i 267 11 280 m 293 12 305 12* 318 Weight of Steel Angles PER FOOT RUN. L 233 MALS OF AN INCH. 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 Millimetres. 7.74 8.14 8.73 9.32 9.72 10.32 10.71 11.31 11.70 12.30 12.70 13.29 1.73 1.83 1.86 1.96 1.99 2.10 2.12 2.24 , 2^35 2.24 2.37 2.50 2.37 2.51 2.64 2^77 2.50 2.64 2.79 2.93 2.63 2.78 2.93 3.08 3 '.22 2.75 2.92 3.07 3.23 3.39 2.88 3.05 3.22 3.38 3.55 3.7i 3.01 3.19 3.36 3.54 3.71 3.88 3.14 3.32 3.51 3.69 3.87 4.05 4^22 3.26 3.46 3.65 3.84 4.03 4.22' 4.40 3.39 3.60 3.80 4.00 4.19 4.39 4.58 4! 76 3.52 3.73 3.94 4.15 4.35 4.56 4.76 4.95 3.65 3.87 4.09 4.30 4.52 4.73 4.93 5.14 5^34 3.77 4.00 4.23 4.46 4.68 4.90 5.11 5.33 5.54 4.03 4.28 4.52 4.76 5.00 5.24 5.47 5.70 5.93 6.i5 4.28 4.55 4.81 5.07 5.32 5.58 5.83 6.07 6.32 6.56 6!80 7!64 4.54 4.82 5.10 5.37 5.65 5.92 6.18 6.45 6.71 6.97 7.23 7.48 4.79 5.09 5.39 5.68 5.97 6.26 6.54 6.82 7.10 7.38 7.65 7.92 5.05 5.36 5.68 5.99 6.20 6.60 6.90 7.20 7.49 7.78 8.08 8.36 5.30 5.64 5.96 6.29 6.62 6.94 7.25 7.57 7.88 8.19 8.50 9.80 5.56 5.91 6.25 6.60 6.94 7.28 7.61 7.94 8.27 8.60 8.93 9.25 5.81 6.18 6.54 6.90 7.26 7.62 7.97 8.32 8.66 9.01 9.35 9.69 6.07 6.45 6.83 7.21 7.58 7.96 8.33 8.69 9.06 9.42 9.78 10.13 6.32 6.72 7.12 7.52 7.91 8.30 8.68 9.07 9.45 9.82 10.20 10.57 6.58 7.00 7.41 7.82 8.23 8.64 9.04 9.44 9.84 10.23 10.63 11.01 6.83 7.27 7.70 8.13 8.55 8.98 9.40 9.81 10.23 10.64 11.05 11.46 7.09 7.54 7.99 8.43 8.88 9.32 9.75 10.19 10.62 11.05 11.48 11.90 7.34 7.81 8.28 8.74 9.20 9.66 10.11 10.59 11.01 11.46 11.90 12.34 7.60 8.08 8.57 9.05 9.52 10.00 10.47 10.94 11.40 11.86 12.33 12.78 7.85 8.36 8.85 9.35 9.85 10.34 10.82 11.31 11.79 12.27 12.75 13.22 8.11 8.63 9.14 9.66 10.17 10.68 11.18 11.68 12.18 12.68 13.18 13.67 8.36 8.90 9.43 9.96 10.49 11.02 11.54 12.06 12.57 13.09 13.60 14.11 8.62 9.17 9.72 10.27 10.81 11.36 11.90 12.43 12.97 13.50 14.03 14.55 8.87 9.44 10.01 10.58 11.14 11.70 12.25 12.81 13.36 13.90 14.45 14.99 9.38 9.99 10.59 11.19 11.78 12.38 12.97 13.55 14.14 14.72 15.30 15.88 9.89 10.53 11.17 11.80 12.43 13.06 13.68 14.30 14.92 15.54 16.15 16.76 10.40 11.08 11.74 12.41 13.08 13.74 14.39 15.05 15.70 16.35 17.00 17 64 11.62 12.32 13.02 13.72 14.42 15.11 15.80 16.48 17.17 17.85 18.53 12.90 13.64 14.37 15.10 15.82 16.55 17.27 17.98 18.70 19.41 14.25 15.01 15.78 16.54 117.29 18.05 18.80 19.55 20.30 15.66 16.46 17.25 18.04 18.83 19.62 20.40 21.18 !>:; I J The Naval Constructor WEIGHT OF STEEL ANGLES Thickness in Deci- Sum of Flanges. 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 Thickness in Inches. Milli- metres. 13.89 14.28 14.88 15.27 15.87 16.2 7 16.86 17.46 17.85 18.45 5 127 8.19 I 133 140 146 8.65 9.11 9.57 9.41 9.88 9^70 10.20 6 153 10.02 10.36 10.69 li".02 | 159 10.48 10.83 11.18 11.53 166 10.94 11.31 11.67 12.04 i2!io \2.' t 5 '.'.'.'. 61 171 11.40 11.79 12.17 12.55 12.92 13. C 10 .... 7 178 11.86 12.26 12.66 13.06 13.45 13. 1 14 14.23 1 184 12.32 12.74 13.15 13.57 13.98 14.; 8 14.79 191 12.78 13.21 13.65 14.08 14.50 14. < 3 15.35 i5i77 i(U8 7J 197 13.24 13.69 14.14 14.59 15.03 15.4 7 15.91 16.35 16.78 8 203 13.70 14.17 14.63 15.10 15.56 16. ( 12 16.47 16.92 17.37 17.82 « 209 14.16 14.64 15.13 15.61 16.08 16. ', 6 17.03 17.50 17.97 18.43 8* 216 14.61 15.12 15.62 16.12 16.61 17.1 17.59 18.08 18.56 19.05 81 222 15.07 16.59 16.11 16.63 17.14 17. ( 5 18.15 18.66 19.16 19.66 9 229 15.53 16.07 16.60 17.14 17.67 18.1 9 18.71 19.24 19.75 20.27 9} 242 16.45 17.02 17.59 18.16 18.72 19.5 8 19.84 20.39 20.94 21.49 10 254 17.37 17.97 18.58 19.18 19.77 20.C 7 20.96 21.55 22.13 22.72 10* 267 18.29 18.93 19.56 20.20 20.83 21.4 6 22.08 22.70 23.32 23.94 11 280 19.20 19.88 20.55 21.22 21.88 22.1 4 23.20 23.86 24.51 25.17 iii 293 20.12 20.83 21.53 22.24 22.94 23. ( >3 24.32 25.02 25.70 26.39 12 305 21.0421.78 22.52 23.26 23.49 24.' 2 25.45 26.17 26.89 27.61 12* 318 21.96 22.73 23.51 24.48 25 04 25. i il 26.57 27.33 28.08 28.84 13 331 22.88 23.69 24.49 25.30 26.10 26. { 27.69 28.48 29.27 30.06 13| 343 23.79124.64 25.48 26.32 27.15 27. < 8 28.81 29.64 30.46 31.29 14 356 24.7125.59 26.46 27.34 28.21 29. ( 7 29.93 30.80 31.65 32.51 14* 369 25.63 26.54 27.45 28.36 29.26 30.1 6 31.06 31.95 32.84 33.73 15 381 26. 55127.49 28.44 29.38 30.31 31.S 5 32.18 33.11 34.03 34.96 15* 394 27.4728.45 29.42 30.40 31.37 32.1 4 33.30 34.26 35.22 36.18 16 407 28.38 29.40 30.41 31.42 32.42 33.4 2 34.42 35.42 36.41 37.41 0.10 0.12 0.14 0.16 0.18 0.2( ) 0.22 0.24 0.26 0.28 13 331 13| 343 14 356 14* 369 15 381 15} 394 16 407 .... ! Weight of Steel Angles PER FOOT RUN. 235 mals or an Inch. 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 Millimetres. 18.85 19.44 19.84 20.43 20.83 21.43 22.02 22.42 23.01 23.41 24.01 24.40 19.52 20.15 20.78 22.04 23.30 24.56 25.81 27.07 28.33 29.59 30.85 32.10 33.36 34.62 35.88 37.14 38.39 20.00 20.65 21.29 22.58 23.88 25.17 26.46 27.75 29.04 30.34 31.63 32.92 34.21 35.51 36.81 38.10 39.38 21.80 23.13 24.45 25.78 27.10 28.43 29.76 31.08 32.41 33.73 35.06 36.39 37.71 39.04 40.36 22.30 23.66 25.02 26.38 27.74 29.10 30.46 31.82 33.18 34.54 35.90 37.26 38.62 39.98 41.34 25.59 26.99 28.38 29.78 31.17 32.56 33.96 35.35 36.75 38.14 39.53 40.93 42.32 29.02 30.44 31.87 33.30 34.73 36.16 37.58 39.01 40.44 41.87 43.30 33.27 34.77 36.26 37.76 39.26 40.75 42.25 43.74 45.24 37.03 38.56 40.09 41.62 43.15 44.68 46.21 40.91 42.48 44.04 45.61 47.17 0.30 0.32 0.34 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 17.14 17.96 18.68 18.79 19.54 20.29 19.61 20.39 21.18 21.96 20.43 21.25 22.06 22.88 23.70 21.25 22.10 22.95 23.80 24.65 25.50 236 The Naval Constructor i z < k O 3 i Q 2 j B § d ggSSSSSfeSssSSSSsggSSSfisS 3S3S88SSSS8SSa8S58§SS33 • d 3 •<• SSSSSSSSSSSSSSSS^SSQSS 2Si532S8S8SS58S3SSS888S35 St d 8 CO" 14.97 15.95 17.02 18.02 19.02 19.25 20.22 20.49 21.39 21.57 22.56 22.78 23.77 24.11 25.00 26.21 27.47 28.84 30.03 31.58 32.80 33.75 a d SSSSSSSSSSSSSSSSSESSSSS sssssssssssaassasggsss d © esi 14.05 14.98 16.00 16.95 17.88 18.12 19.03 19.31 20.14 20.33 21.26 21.48 22.41 22.75 23.59 24.74 25.95 27.25 28.38 29.87 oo d 8 cs r. 99 r. c 1 — -• -r — - 1 r i - 1 c ~ -r > - ~ — ~ cc a S5 CO ■* «o «o t^ r- OO 00 OS OS O O — CO (M ^ uo «o .... rt HrHrHrtTHrtiHrHMININH(plQ^ll5!0 00tO00N *.OSt^OSt>.C5t^Osa50S©SO>0505N t^t>.i>.t^.oob-oot^oot^oor>.oot>-aooooqoooooocoo xxxxxxxxxxxxxxxxxxxxxx t>.oco«o«ooooo^^H^3'«c050siM--i© • • • CM •»* CO t- © --I CM ■»»< CO 00 -i CM CO © U5 OS t~- r-l CM • • • — I CM CM CO ■>* >0 lO CO CO 1^ 00 OS © CM «C •«*< CO 00 OS • • • CM CN CM CM CN CN CN CN CM CN CM CM CO CO CO CO CO CO CO ©' cd t^.oscor^©io©t^--ocmos • -lOCOOO© CM-* uSCOOOOt-iiOiOOOM oo^oocmcn • • OS © t-* CN CO CO •* •* lO CO t- r~ 00 OS -- CM •»* IC t- 00 • • ^H CN CN CM CM CM CM CM CN CM CM CM CM CN CO CO CO CO CO CO CM CO © 00 »d CNOOCOOS— l©»O00«OCO00J^CO— CCO0000©^HCO-*00 00»-l»O©COOseOCO COf~OS©--l.--t>-t>»Osr>»Ost--OSt>-OSt^OSt^OSOSOSOSOSOSOSCM l>-t~t~t^.00I>.O0t^O0t^O0l^O0t^O0O0O000O0O000© xxxxxxxxxxxxxxxxxxxxxx t^ ©CO COCOOOOOi-H-H ■>*-»*< CO CO OS OS CNTft^© CO '«»<'«*< CN-"*Jnn.t>.t^t^OOOOOOOOOSOSOS©©i-lT-icMCM 238 The Naval Constructor H o 25 H < o 3 Q g D o 1 3 i \ § 2 .1 9 u 3 H OS 00 CO &8S88SS§8S{3£J8gS83S;SSSS;:S sas8838383S;83S3S33338$53 M "ft © 8 CO 8S88S£35«SS3&S23S£82§SSg£SS 2SSS5S?S?ScqSS;SSS8Sg5^8^5???S?^5; 8 d SgSSSSSSSSSgaKSgSSSKSSgSS SS8gJ?3§S?3S&!?5SS?5SgS§5g?§??§oJ?S 9 d 8 ■^oo^HC^ajOcvuoe^iocot^^^coeMO-fcsotoSs ^Ne^e^c-< i>-cco«©* O !>• t~- l>- -«1 CO »o OO CO to MrtrtrtrtNrHNNNIN 8 d CO d O^-IM©-*— i© © CO CM CO CM OS 00 OS CO £5£222S°,CM d CO 00 OS © iO.^I o r^ d oo t^ d •••••••••••••••• '• CO d 00 oo© t^.»o ^HOOIMCO 3 •*»*«* • o CO d l^. t»OS r~co t J i 153X 77X 77 153 X 89 X 89 178X 77X 77 178X 89X 89 191X 77X 77 191 X 89X 89 204 X 77 X 77 204X 89X 89 204X102X102 216X 77X 77 216X 89X 89 229 X 89 X 89 229X102X102 242 X 89 X 89 254X 89X 89 254X102X102 267X 89X 89 280X 89X 89 280X102X102 293 X 89 X 89 305 X 89 X 89 305X102X102 381X102X102 i j g s CO CO CO CO CO CO CO CO ->*l M CO CO •* CO CO -*f< CO CO •"*! coco ■**•"*< XXXXXXXXXXXXXXXXXXXXXXX CO CO CO CO CO CO CO CO •**< CO CO CO ■* CO CO •«*< CO CO ■«*< CO CO -"f^ XXXXXXXXXXXXXXXXXXXXXXX tOCOt^^t^.t~-OOOOOOOOOOOSOSOS©©©'^'-<— CMCNiO Weight of Steel Channels 239 a o K < O 2 1 S g i E B y 3 H o 00 d 3 g S i 3 o H d CM ■*noo T-*t>.00 ;;;;;;;;;;;;;;;;! i !' «5 1~~* to TjtrJtlO 00 d 28 d :::: 41.25 43.71 43.00 44.33 46.90 54.86 CD d d 37.92 39.87 39.21 40.50 42.97 42.21 43.51 46.08 53.84 •** d 3 00 34.29 36.67 35.54 37.24 39.19 38.49 39.75 42.22 41.43 42.69 45.27 52.82 CM d 5 00 JO. 19 52.45 53.67 56.06 54.90 56.56 58.51 57.78 59.01 11.47 10.65 11.88 44.45 51.80 o d a 28.07 30.21 32.55 29.61 31.87 33.06 35.45 34.25 35.88 37.83 37.06 38.26 40.72 39.87 41.06 43.64 50.78 8 d CO 26.37 28.07 27.53 29.67 32.01 29.04 21.29 32.45 34.84 33.61 35.20 37.15 36.35 37.51 39.97 39.09 40.25 42.82 49.76 8 d 8 d 0'*!Ottl(JOM(0(DCN'*COtCiNI^'»'COMOMO'* • ■CO-«*<00'OCi'-l"«J<-'<*iOTt0!OOiQOO>(NCC • • CM c©iOiOT>OOCMCCOSCM (MCMCMCMCNCMCMCMCOCMCOCOCOCOCOCOCOCOCOCOCO'*"-* CO d 00 W5 ON'neS'«<-<)(am0CO(0-HQN!0«'-t-P5'*CNp Ma^^XiOOOOCOCOiOCOOCrHrtMINNNOOCCt^ >lNCCO'*l»>15COONOlO«'HMlO'*iCN!Df-0<0 CMCMCMCMCMCMeMcMCOCMCMCOCOCOCOCOCOCOCOCOCO-^-* 8 d CM Ci*-ICO^HCOCO»OOCOCMQO~ C--Ol'-CCOC5CN00eO00CO00 ONNiO'*CBiONO!SOOOO(Nrt(N'*C<5'0'OtOO>U5 CMCMCMCMCMcMCMCMCVICMCNCOCOCOCOCOCOCOCOCOCOCO't" 3. d 8 C5 0COCOCMCM^H»0 05COOOJOOOOO»COOt^COOOt^.Tt*lC©00»Of^OO'-<03'-iCOCNlCOiO'<* , »Of~CO CMCMCMCMCM'MCMCMCMCNCMCMCOCMCOCOCOCOCOCOCOCO'^' do i i i 153X 77X 77 153X 89X 89 178X 77X 77 178X 89X 89 191X 77X 77 191X 89X 89 204 X 77 X 77 204 X 89 X 89 204X102X102 216X 77X 77 216X 89X 89 229 X 89 X 89 229X102X102 242 X 89 X 89 254 X 89 X 89 254X102X102 267 X 89 X 89 280X 89 X 89 280X102X102 293 X 89 X 89 305 X 89 X 89 305X102X102 381X102X102 i 5 a co co cc cococococo-»**• t^ «D C© «5 «5 ■* ■«*< •"*< CO CO CO CO i CN i ococ^o030sodt^t»»<»«50050si^co — oao N(0NiH«OSrH^00C000'*iHTj(0>l(3C]05CD'*INO00Noo^esicO'<4iu3ceooo<-«co>o010 e§88SaSS2KS8SaSS8aSS8aSJ28aSJ28 CC*>niOe!0N0000ffiOOrtClMK5®NXOrt(NMm!0N»O rt^H^Hi-lOI>.t^t^OOOO*0>05 * 5 lOOiMN. ^^8S§feS??^8 NClMCO^^lOiOiOffltONNOOOlOO^NCCClOiflCMXlO!© (N'*(O00OlMTt(t0MONn(!DO'<1<0)CCN'HiO01MN'-i0O!C0» i-li-lT-l«.t>.000000050> aooocor^t^t^t^r~< HXU3MOKOMOI OiO«3 . ► o Oi C; Cb OUJOOHNNSCSt _ j t^ co oo •gi en ■* o >O5O>O5O500000000 «)00'H'«i«5aiOU3NOnu5 00C<5 0>'>t'OmO II Speed in Knots Fig. 51. by the motion of the waves and the drag of dead water eddies, such as are formed at abrupt endings to bossings, the siding of stern posts and in the wake of propeller struts. The skin resistance is proportional to the area of wetted surface, and is re- sponsible for almost the total resistance up to about 8 knots speed. Beyond this speed the total resistance increases rapidly, showing the effect of the residuary resistance. This will be more readily understood, when we recollect that the wave undulations progres- sively increase in height with increases in speed, and that the crests of these waves are accountable for about 95 per cent of the total residuary resistance, the remaining 5 per cent, as already stated, being due to eddies, etc. Referring to the diagram here reproduced, showing curves of residuary and skin resistances, ' ' the graduated undulations in the residuary resistance curve are due to quasi- hydrostatic pressure against the after-body, corresponding with the variations in its position with reference to the phases of the train of waves comprising the wave line profile, there being a com- parative excess of pressure (causing a forward force or diminution Froude's Law of Comparison 265 of resistance) when the after-body is opposite a crest, and the reverse when it is opposite a trough. Their spacing is uniform at a uniform speed, because waves of given speed have always the same length ; it is more open at the higher speeds, because waves are longer the higher their speed; their amplitude is greater at RESISTANCE IN TONS. RESISTANCE IN TON8. o> 00 o I .1 I.I I ,1 1,1 L RESISTANCE IN TONS. Fig. 52. 1 i, i L i I' I ' II O K> * RESISTANCE IN TONS. the higher speeds, because the waves made by the ship are higher ; and their amplitude diminishes with increased length of middle body, because the Wave system by diffusing itself transversely loses its height." 266 The Naval Constructor 1 i .5 15.5 26.5 16.5 27.5 17.5 29.0 19.0 31.0 20.0 33.0 9 14.5 24.0 14.5 25.0 15.5 26.0 16.5 27.5 17.5 29.0 18.5 30.5 10 13.5 22.5 14.0 23.0 14.5 24.0 15.5 25.5 16.5 27.0 17.5 28.5 11 12.5 21.0 13.0 21.5 13.5 22.0 14.5 23.5 15.0 25.0 16.0 26.5 12 11.5 19.5 12.0 20.0 12.5 20.5 13.0 21.5 14.0 23.0 15.0 24.5 13 10.5 18.0 11.0 18.5 11.5 19.0 12.0 20.0 13.0 21.0 13.5 22.5 14 10.0 16.5 10.5 17.0 10.5 17.5 11.0 18.5 12.0 19.5 12.5 21.0 15 9.0 15.5 9.5 16.0 10.0 16.5 10.5 17.0 110 18.0 11.5 19.0 16 8.5 14.5 8.5 14.5 9.0 15.0 9.5 16.0 10.0 16.5 10.5 17.5 17 8.0 13.5 8.0 13.5 8.5 14.0 9.0 14.5 9.0 15.5 9.5 16.5 18 7.5 12.5 7.5 12.5 7.5 13.0 8.0 13.5 8.5 14.5 9.0 15.0 19 7.0 11..". 7.0 12.0 7.0 12.5 7.5 13.0 8.0 13.5 8.5 14.0 20 6.5 11.0 6.5 11.0 7.0 11.5 7.0 12.0 1 7.5 12.5 8.0 13.0 21 6.0 10.5 6.5 11.0 6.5 10.5 7.0 11.5 7.5 12.0 22 6.0 10.5 6.0 10.5 6.5 11.0 7.0 11.5 23 6.0 10.0 6.0 10.5 6.5 10.5 24 6.0 10.0 6.0 10.0 25 26 6.0 9.5 Angles of Entrance and Run 273 for Ships of Various Lengths and Speeds. in Feet. 200 Ft. 260 Ft. 320 Ft. 390 Ft. 460 Ft. 540 Ft. 620 Ft. to TO TO TO to to TO 260 Ft. 320 Ft. 390 Ft. 460 Ft. 540 Ft. 620 Ft. 720 Ft. a and a and /3 a and /3 a and /3 a and /3 a and /3 a and /3 9 o 0~~ o 5 o o o o o ~~ o o 26.0 42.0 27.5 44.5 24.5 23.0 21.5 39.5 37.0 35.0 26.5 24.5 23.0 42.0 39.5 37.0 28.0 26.5 25.0 44.5 42.0 39.5 28.0 26.5 44.5 41.5 28.0 44.0 20.0 32.5 21.5 34.5 23.0 36.5 24.5 39.0 26.5 41.0 28.5 44.0 19.0 30.5 20.0 32.0 21.5 34.0 23.0 36.0 24.5 38.5 26.5 41.0 28.5 44.0 17.5 28.0 18.5 30.0 20.0 32.0 21.5 34.0 23.0 36.0 25.0 38.0 26.5 41.0 16.0 26.0 17.0 27.5 18.5 29.5 20.0 31.5 21.5 33.5 23.0 35.5 25.0 38.0 14.5 24.0 15.5 25.5 17.0 27.5 18.5 29.0 20.0 31.0 21.5 33.0 23.0 35.0 13.5 22.0 14.5 23.5 15.5 25.0 17.0 27.0 18.5 28.5 20.0 30.5 21.0 32.5 12.5 20.0 13.0 21.5 14.5 23.0 15.5 25.0 17.0 26.5 18.0 28.0 19.5 30.0 11.5 19.0 12.0 20.0 13.0 21.5 14.0 23.0 15.5 24.5 16.5 26.0 18.0 27.5 10.5 17.5 11.0 18.5 12.0 19.5 13.0 21.0 14.0 22.5 15.0 23.5 16.5 25.0 9.5 16.0 10.0 17.0 11.0 18.0 12.0 19.5 13.0 20.5 13.5 21.5 15.0 22.5 9.0 14.5 9.5 15.5 10.0 16.5 11.0 17.5 11.5 18.5 12.5 19.5 8.0 13.5 8.5 14.5 9.0 15.0 10.0 16.0 10.5 17.0 11.0 17.5 12.0 18.5 7.5 12.5 8.0 13.0 8.5 13.5 9.0 14.5 9.5 15.0 10.0 16.0 11.0 16.5 7.0 11.5 7.5 12.0 8.0 12.5 8.5 13.0 9.0 13.5 9.5 14.0 9.5 15.0 6.5 11.0 7.0 11.5 7.5 11.5 7.5 12.0 8.0 12.5 8.5 13.0 8.0 13.5 6.0 10.0 6.5 10.5 7.0 10.5 7.0 11.0 7.5 11.0 7.5 11.5 9.0 12.0 6.0 9.0 6.0 10.0 6.0 10.0 6.0 10.0 65 10.5 7.0 10.5 7.0 11.0 6.0 9.0 6.0 9.0 6.0 10.0 6.0 10.0 6.0 10.5 6.5 10.5 7.0 10.5 274 The Nav,al Constructor Form of Least Resistance 275 appended is a table giving the value of these angles for various speeds and lengths of vessels obtained from actual well-known ships of the best form. On the construction lines of the body plan and profile, a mean water line is drawn half way between keel and load line, as shown atf- By referring to the table of angles, a is selected for the length of vessel being designed and the tangent of the same spotted on the half-breadth plan. This will give the outline of the mean water plane. Two diagonals, D and D lf are struck in on the after body plan, the former intersecting the centre line at half the draught, as well as the base line at a distance equal to the half-breadth of the ship, and Di intersecting the load water plane at centre line as well as the half moulded breadth construction line at the mean water line height, as shown in Fig. 55. The angles /3 and 6 are obtained from the table and transferred to the half-breadth plan representing the half planes of D and D\ respectively. 276 The Naval Constructor ELEMENTS OF Moulded i *° ki, km. Name. Description. Dimensions. 1 1 1 C •< A M 3h •3 ~ 'it | 4 i 1 - — q E 2 « 3 a Campania . 1st Class Ocean / / // / // / // Liner, T.S. . . 600 65 41 6 2610 19,336 .644 .667 .976 Manchuria 1st Class Interme- diate Liner, T.S. GOO 650 43 3 33 2 26,514 .715 .762 .942 Normannia 1st Class Ocean Liner, T.S. . . 500 57 3 38 24 11,588 .59 .625 .94 Tantallon 1st Class Cape Castle . Liner .... 440 505 3411 24 6 10,100 .647 .695 .932 Kiev . . . Russian Volunteer Fleet 419 49 6 32 23 11J 10,640 .738 .769 .959 Texan . . 1st Class Ocean Freighter, T.S. . 471 57 35 27 16,236 .784 .820 .958 Nevadan . 1st Class Ocean Freighter, T.S. . 360 46 27 2 23 8,217 .758 .788 .961 M. S. Dol- Ocean Freighter, lar . . . S.S 300 40 26 22 5,960 .79 .801 .986 Victoria . Channel, T.S. . . 220 28 17 10 860 .502 .569 .822 Jupiter . . Sound, P.S. . . . 230 28 9 6 6 n 699 .578 .621 .930 Greyhound Channel, P.S. . . 230 27 10 610* 690 .568 .622 .913' Tynwald* . Channel, T.S. . . 265 344 14 6 10 1,508 .58 .594 .976 Sandy Hook Sound, T.S. . . . 260 37 15 10 2 1,165 .417 .5 .82 Mayflower . Yacht, T.S. . . . 275 36 6 21 15 6 2,414 .535 .612 .874 Giralda. . Yacht, T.S. . . . 275 350 19 13 6 1,862 .505 .498 .904 Ophelie* . Yacht, Auxiliary Composite . . 160 26 6 17 11 6 568 .407 .59 .682 Lady Tor- frida*. . Yacht, Auxiliary Steel 157 27 17 11 6 552 .3968 .6 .664 Zaida* . . Yacht, T.S. . . . 136| 22 6 13 9 8 9 332 .428 .59 .73 Pizzaro . . Guard Boat, S.S. . 155 21 6 11 6 6* 303 .482 .626 .773 Ponce de Leon . . Guard Boat, S.S. . 135 19 10 6 6 6J 202 .439 .594 .74 Sandoval . Guard Boat, S.S. . 110 15 6 8 9 5 100 .407 .610 .667 Fradera* . Guard Boat, S.S. . 74 11 9 7 3 4 41 .412 .662 .622 Scud* . . Speed Launch, S.S. 86 10 7 5 10 2 9 30 .43 .625 .687 Neuquen* . Revenue Steamer, S.S 65 12 7 4 3 41* .437 .585 .757 Princess Customs Launch, Maud* . S.S 55 12 6 8 4 6 37 .435 .56 .776 Designed by the Author. Elements of Typical Steamers 277 TYPICAL STEAMERS. Si? fa fa fafa ft o M fa fa fa o O OB 8 £ W H K fa 3 fa fa o O SI §5S H txj OS H O ft m ; fa GO H — r. ft o .726 7,610 .4702 2,960 .1829 10,570 .6531 4,665 17,878 29,246 79 22.09 252 .826 7,987 .474 1,844 .1092 9,831 .583 2,100 12,000 75 14 .718 4,525 .416 1,677 .154 6,202 .57 2,525 10,535 16,300 94 20.75 263 .777 .837 7,161 9,065 8,379 3,844 79 17.23 227 2,827 .426 1,167 .1758 3,995 .6019 627 98 13.93 306 .875 3,891 .463 637 .0764 4,528 .539 731 8,390 3,535 75 12.8 245 .847 2,125 .472 531 .118 2,656 .59 528 3,000 75 .868 1,210 .388 328 .105 1,538 .493 447 2,522 1,302 88 11.25 207 .667 272 .26 172 .1641 444 .424 203 736 1,400 201 16.5 260 .693 196 .320 98 .1602 394 .48 221 550 2,425 56 18.18 116 .698 195 .314 88.5 .1425 283.5 .4565 195.5 524 2,022 58 18.49 203 .67 446 .338 236 .179 682 .517 590 1,130 5,200 2,800 161 128 18.92 17.0 190 .721 994 .4716 672 .3186 1,666 .7902 484 2,365 4,604 167 16.36 169 .668 700 .3823 347 .1895 1,047 .5718 500 1,661 7,223 218 20.64 172 .692 115 .164 221 .3150 336 .4790 83 532 646 110 11.73 164 .656 200 .2775 140 .1945 340 .4720 85 598 720 134 11.62 155 .683 132 .312 70 .1653 202 .4773 92 353 620 150 12.8 169 .684 91 .248 39 .1073 130 .3555 55 257 504 242 13.4 193 .652 59 .2193 37 .136 96 .3554 38 167 338 270 13.14 203 .666 31 .2088 24 .1618 55 .3706 29 101 229 294 12.09 167 .67 14 .219 8 .125 22 .344 8| 41 180 295 11.5 100 .686 9 .17 4.4 .083 13.4 .253 14.6 31£ 531 430 20.34 155 .695 12 .22 5 .092 17 .312 12.5 39} 97 318 10.1 119 .68 16 .364 4.5 .102 20.5 .466 10.5 37 81 228 9.27 108 Section II. STRENGTH OF MATERIALS. CHAPTER I. STRESSES. It is by the application of the known strengths, as derived by experiment, of the various materials used in shipbuilding to the physical properties possessed by their geometrical sections that we are enabled to calculate with accuracy the loads they will bear with a predetermined margin of safety when subjected to either of the four simple stresses of tension, compression, shearing and torsion. Ultimate Strength is the direct stress producing rupture of the material. "Working Load is the stress applied in practice, and its ratio to the ultimate strength varies with the nature of the stresses applied, viz. : (1) tension with a dead load ; (2) tension with a live load, or (3) a live load working alternately in opposite directions (see Table). ' H Many of the fittings in shipwork come under the third category, as in rudders, derricks, etc. In derricks the inertia of the load has not only to be overcome, but also the jarring and surging. For this reason a very common factor of safety for these details is ten times the ultimate strength. Proof Strength is the test load to which cranes, davits, der- ricks, chains, cables, etc. are subjected, and is usually a multiple of the working load or ultimate strength. Careful measurements should be taken before applying this load, and these checked after the load has been removed, to discover, if any, the amount of permanent set. Stress and Strain. — Stress is the measure of the internal force or resistance in a bar due to the load applied tending to produce 279 280 The Naval Constructor deformation, and strain is the alteration of form due to the stress. So that the relationship between these two terms really is one of cause and effect, although in general the terms are erroneously used synonymously. Stress is measured by weight and strain in inches, or as a per- centage of the length of the bar or member strained. Thus, we say that a 6-foot bar is subjected to a tensile stress of 20 tons, pro- ducing a strain of J inch per foot (elongation being § inch) or 1.04 per cent of the bar's length. Tensile Stress. — If two equal forces acting in opposite direc- tions, away from each other, be applied to a bar, they will tend to stretch it, thus producing a tensile strain. Compressive Stress. — Should, however, the forces act towards one another they will produce a compressive strain. Shearing Stress. — When two forces acting in opposite direc- tions are exerted through the cross section of a pin or rivet con- necting two flat bars, the pin is subjected to single shear. If, however, another similar bar be connected enclosing either of the other bars, then the pin or rivet will be in double shear, and may be reduced by half its original sectional area. Bending or Transverse Stress. — Bending stresses are im- posed on beams when they are loaded or forces exerted on them, although more correctly, tensile, compressive and shearing stresses are at work simultaneously on the top, bottom and abutments respectively. Torsional Stress is encountered mostly in shafting and in the rudder stocks of ships. In the latter case it consists of twisting stresses acting alternately in opposite directions, requiring a much larger margin of «afety than necessary with any of the other stresses named. Resilience. — This term is applied to the amount of work done by compressing or extending a bar and multiplying the length of such compression or extension by the load which produced it. Elasticity is the property which substances possess of return- ing to their original size and shape after straining. In tension materials increase in length and decrease under compressive stresses, and within certain limits this lengthening or shortening is proportional to the stress applied. From this it is evident that this quality is more important than even the strength of the material in tension or compression. Modulus of Elasticity. — The amount of this proportional variation of the weight applied and the alteration in length of the Stresses 281 bar is known as the modulus of elasticity, and may also be expressed as the tensile force, which, when applied, will double the bar's length, and of course may be different in the same material when subjected to tension, compression or shear. Permanent Set. — If a bar be extended or contracted by the application of a load jeyond its elastic limit, it is said to have permanent set. This would take place in mild steel if a load of 17 tons per square inch of section were exceeded. Fig. 56. Distance*. Akea. Moments. Si = 4.40 X 2.04 = 39.49 8 2 = 1.75 X 1.48 = 4.73 6*3 - 2.00 x 1.64 = 6.56 Si = 3.75 X 2.44 = 34.30 Moment of Inertia J = 85.08 Section Modulus Z = -=-=-=■ = 16.5. 5.15 The Moment of Inertia of a section or body is a mathematical quantity used to calculate the strength of materials, and is taken relatively to the neutral axis or centre of gravity of the section. If the section of a bulb tee beam, as shown in Fig. 66, be cen- trally loaded on top, the fibres above the line xy (neutral axis) will be compressed, and those below extended, and consequently the arc formed by the table of the beam will be shorter, and that formed by the bulb longer, than the arc through the line NS t 282 The Naval Constructor which will be exactly the same length as the original dimension of the beam before the application of the load, the lamina through this axis being neither in compression nor tension, and are therefore known as the neutral surface of the beam. Hence, if we take very small areas at known distances from the neutral axis to their centres of gravity and multiply these areas by the square of their distances above or below this line, we shall have by adding the products together the moments of inertia (I) of the section ; and again by dividing this moment by the distance of the most extreme fibre we shall get the quantity known as the section modulus. In the example given the result is fairly accurate, although a more absolute result may be obtained by greater subdivision of the areas. This, however, is not necessary for ordinary calcula- tions. The value of the section modulus depends entirely on the geo- metrical form of the section. The material of which the beam is made and its ultimate strength known and divided by the factor of safety selected, gives us the safe limiting stress. This stress multiplied by the section modulus produces the moment of resis- tance of the beam. In the example given let the beam be of steel of 60,000 lbs. ultimate strength and the factor of safety 5, we then have £&£&a = 12,000 lbs. safe limiting stress, and section modulus = 16.5 X 12,000 lbs. = 198,000 lbs. moment of resistance. Suppose then that this were a 12-foot boat skid beam fixed at both ends and loaded at centre, what weight of steam pinnace would it safely support ? The maximum bending moment on a beam so loaded would be £ WL where W is the weight and L the length between points of support. Equating this bending moment with the moment of resistance, we have SZ _ WL. then W = 11,000 lbs. Where the figure or section is symmetrical about its centre of gravity the / and other elements may be readily Figured from the appended Table of Elements of Usual Sections. Radius of Gyration. — The radius of gyration is that funda- mental property of a section used in determining the strength of pillars and struts, and its square or r 2 about a given axis is equal to the moment of inertia of the surface about the axis divided by the area, therefore the radius of gyration V inertia Stresses 283 -KI1Q aoHj -SOHJ o © o o © © co co^* © © © © © © t^ T-H © © © © © © © CO CO ^ ©© © ©"t-Tof © © © © © © CO 00 ^ I © © © o © © (N CO rfi §8 o o^ co of © © © © © © JO — p* O 8§ © © iQ©*"i© © © © © © © ©_co © cvfco"^ 8§ t~- CO © © © ©"t^co © © © © © © CO © CO •2 I 111 ooo © © © CO -- r— i ^- ■* Z3 0.0491 (I)* -d*) 16 0.1098 r 4 0.7854 6a 3 W 12 12 12 6ft 3 36 Section Modulus. 0.0982 ZH-d* Wi= 0.1098r 8 ir 2 = 0.2587 r 8 0.7854 6a 2 bh* 0.1178 h* 1 i?4-6* 6 B 24 Base FROM C.G. 0.4244 \h \a \-r I; \ DIUS OF Gyration iV^ 2 "^ 2 0.0699 r 2 Least side 3.46 h 3.46 / 7*2+ 62 ]2 The lesser. — or - 4.24 4.9 Figs. 57 to 64. Elements of Sections ELEMENTS OF SECTIONS.— (Continued.) Section. =* m S — b — *\ Moment of Inertia. 662+6661+61 2 36(2& + &i) Ah 2 9.9 ^2 10.4 19 AM 10.9 ^2 6.1 AM 6.73 Section Modulus. 662+6&61+61 2 12(3 6 + 2&i) Ah 6.7 7.4 Ah 9.5 7.6 ft 2 Ah 3.0 -4 ft 3^3 Base from C.G. 1 3H-&1 3 26 + 6^ h_ 3.1 A- 3.5 A 3.3 Figs. 65 to 71. 28G The Naval Constructor BEAM BENDING MOMENTS. ETC. ■W— LOAD. t— LENGTH OF BEAM BETWEEN 8UPPORT8. K — FIBRE STRESS. I— MOMENT OF INERTIA. E — MODULUS OF ELASTICITY. R— -5— SECTION MODULUS. C— DISTANCE OF EXTREME FIBRES FROM NEUTRAL AXIS. HOW LOADED A SUPPORTED STRESS DIAGRAM ORDINATE6 GIVE BENDING MOMENTS Draw Triangle Draw Triangle if M> ^Tifrx. , G | L © Draw ED-Wt & AF=^ Figs. 72 to 83. Beam Bending Moments 287 BEAM BENDING MOMENTS, ETC. W=Load. K = Fibre Stress. L = Length of Beam between Supports. / = Moment of Inertia. R = - = Section Modulus. E = Modulus of Elasticity C = Distance of Extreme Fibres from Neutral Axis. Bending Moment, M. Deflection, /. Reaction AT A AND B. Safe Load JF Elastic Curve Equation. M= Wx ' Mmax = WL W L* J ~ 3 EI B= W w=*¥ WW y ~ 2EI Vx la; 3 ] \_L 3 Z 3 J , f Wx M WL Mmaz — —3 — 4 W L* f ~ 48 EI W = 4™ JFZ 3 y ~~ 16 EI Vx 4 a; 3 "] \L 3 i3j t^ ,n 1/ Wd\X For AD, M=. — =A- Ld For BD,M=^p Wdd \ Mmax=: f — Li A ~ L Jj W=KR~ dd t _ fFd 2 ^ 2 V ~ 6LEI [ x l ,x l x* 1 L d ^rf, ^dj [2^ x t ar x 3-1 L rf t ^d d^d] For AD, M= ft Wx For BD, Mmax=& WL Md=&WL 7 WL* J ~ 768 EI 5 48^7 For A = ft W B=\hW W _UKR 3 L V WL*Yx 5x3] 32 #/ \_L 3 Z 3 J JF X 3 Vl ~ 32 £7 X [la?! 5ar,» 11 a;, 3 ] Ul + 2 L* 3 Z 3 J .. WL (x 1\ ' M =-Y-\l-1) M WL fT Z 3 7 192 £/ w = s K T R - Li JF Z 3 V ~ 16 EI X [a- 2 4 a? 3 "I U 2 3Z 3 J For A and B, TFZ' /> /— 16 EI W A = B = l W=2™ P y=/- p + *J p *- X >+ L (x-\) 2EI P = TT^-^Constant 288 The Naval Constructor BEAM BENDING MOMENTS, ETC. W— LOAD. L— LENGTH OF BEAM BETWEEN SUPPORTS. K— FIBRE 8TRE88. I MOMENT OF INF.BTIA. E — MODULUS OF ELASTICITY. R—-g— SECTION MODULUS. C— DISTANCE OF EXTREME FIBRES FROM NEUTRAL AXIS. HOW LOADED 4 8UPPORTED STRE88 DIAGRAM ORDINATE8 GIVE BENDING MOMENTS Draw Parabola A- Draw Parabola A-^ X >4qq6666 3)QOQQQQ)% b , xrnrrriv^B OO l QO QOQnOQQO Draw A-^ & BC-^ t^fc&.^-J Figs. 84 to 95. Beam Bending Moments 289 BEAM BEND.NG MOMENTS, JF=Load. ETC. — (Continued.) L — Length of Beam between Supports. E = Modulus of Elasticity. R = - = Section Modulus. K = Fibre Stress. 7= Moment of Inertia. C = Distance of Extreme Fibres from Neutral Axis. Bending Moment, AT. Deflec- tion, /. Reaction at A AND B. Safe Load, W. Elastic Cubve Equation. .. Wx* AT WL Mmax = — ^— W L* J ~ 8 El Ll B z=W _ W L* y ' ~ 24 El Mmax r= — s — o 5 WL* J ~ 384, El W = 8^ It W L* V ~ 24 El X __ Wx /3 a;\ 1/== -2-(i-x) *r WL Mmax — — x— o M ^m WL T ~ 192 El Max. deflec- tion, x = 0.4215 L A-iW B =%W W = 8*fi Li v 48 El* WL/l x x*\ J ~Z8AEl TFZ» V ~2AEl Tx* 2x*.x*>-\ ^ = 1-13 Mmax = ^ f ~ 15 El B =W Li y ~~ 12 El rx lar 5 "] IL 5 Z 5 J MK = A(a + ±L) A W(2d + b) A ~ 2L W(2a + b) 290 The Naval Constructor USE OF THE TABLE OF ELEMENTS OF CIRCULAR SECTIONS. In calculating the scantlings of masts, derricks, kingposts, rud- ders, shafting, and details generally, where circular sections are employed, the Table of Elements will be found very convenient and time-saving, as, having determined on a thickness or a diam- eter to which it is decided to work, the appropriate formulae for the various elements may be read off with facility. In the first column is given the ratio of internal to external di- ameter. It is required to find the elements of a hollow section with an outside diameter D = 5 inches and an internal diameter d= .8 D=4 inches, or 5" x \" thick. Column 2 gives the sectional area coefficient of the pipe, viz., .2826 x D 2 —7.065 square inches. Similarly the coefficient for the moment of inertia, I, is found in the third column to be .02899 by the fourth power of the diam- eter D, or .02899 X 625 = 18.118 = 1. By the fourth column we get the coefficient for the square of the least radius of gyration as .1026 D 2 = .1026 X 25 = 2.565, and in the following or fifth column the radius of gyration = .32 D = .32 x 5" = 1.6. For the modulus of resistance of the section, or I/y,the coefficient for the pipe with a ratio of .8 D is .05798 D* = .05798 X 125 = 7.247. The torsional modulus of resistance is .11595 2)3 - J1595 x 125 = 14493. If it be required to select a diameter of hollow or solid circular section for a given moment of inertia, or, having obtained a diam- eter, it is found advisable to amend the same to another diameter giving the same J, then the increase or decrease of thickness may be readily computed with the aid of column 8, and in a like man- ner the sectional area for a constant moment of inertia is calcu- lated by the coefficients in the following column. The last two columns give, similarly, the diameters and areas for a constant moment of resistance. Inversely we may calculate the diameter of a bar or tube equal to a given moment of inertia, or moment of resistance, or radius of gyration, etc. For example, the diameter is required of a tubu- lar section which shall equal a moment of inertia of 12. It is proposed to make the pipe relatively thin ; therefore we select a ratio of d/D = .90 per column one, from which we get an I co- efficient = .01689 ; therefore, V .01689 V .01689 = 5. 14 inches outside diameter x £ inch thick (fully). Moduli of Circular Sections 291 :S : : M :2 : to :S •?* :§ il • 1^ • 00 01 -co ■0 :S • CO :g :£ to :1 :S : s • o M 'O :3 :S .10 :S| • S :S :S 3 to :S .© ; ,co -cm -a> • •<* • ■** -co 10 -jh -i-i -a -) • 06 10 M to *M 02 • • *■» 1 1^ °5 to cr. CO 10 "5 O co 8 CO t^. a> 3 -OCO'*0>tDNrtCO(10rtNN01HO00NM!O®tON00«rHC)ltl"'5>0"5tOtO!0!ONt^NOOOO»»OSO>01000 tococototot^t^t^t^i asiocoTftco-ticouoait^t^oto iOf-OHe<:>ONO>i-iMiOOOO aaotaooooooHHHHM NOK5N00 1O moMON nciOGi MioooeqHHooN^coootONtoiaffiioooooujooosoorf O'JirtaiffiHiOOOOOOOOOlNNOMOOOOO'HXlcCNTj'OO OONNO(ONNQOMOrtO>O«OCO O •<*< t^ t— Oi t-< torouo<^(^^a>uoiot^coiN>cor-oco^eNico»--(coeNi«i«5c»OJ - . CO <-t 00 "5 CN OS t^- Tf CO i-c CN CM oor~t— ioa3^HOt^^HtocNoo«5cO'* 020^C^CO^OI^050(rC "O tO O CM )05t^Tt((Mcoooa>oor^ooeNi'-it^-cor^ioi^tO(Mto I'HMtOO'O'-iOiartiON'-ilNN'^iOaNOS"* T-^t^OCOt^^H - tjioooosi goo t 000000000SS0! '-s-S"?;-* * 292 The Naval Constructor IS M § I i § 1 I 8S88S888 •4* I H H _ « K M . gg&isisiisli 8 8 3 8 8 8 18 8 w* T^iHiHiHi-Hi-i©©©©©© &H - - - .9 ** ' Ss^c ^SS^^^S^s, Trf "* tr S8S§S8S8 qh* q q q q ia ia eo © £ 5 £ I q q q q © CO l~ © I sss 35 8 o*5 r <* . . ^ 2 « w °1 c?w 3 ° > 5 q|S % ^ llllliilil qq_q§|qq|||q 35©©©©©©©©©© = %S^lSlSllli •e|q 8(NiO§t~a6o6C50>d> Moduli of Circular Sections 293 MODULI OF CIRCULAR SECTIONS o INERTIA OP CIRCULAR SECTIONS. TO / = Mom. of Inertia. Z= Section Modulus. M _ irdT nd 3 nd* _ nd 3 r nd* _ wd> D 64 Z =M /> /_ 64~ z =lv D /= 154 Z =-& 1 0.0491 0.0982 34 65,597 3,859 67 989,166 29,527 2 0.7854 0.7854 85 73,662 4,209 68 1,049,556 30,869 3 3.976 2.651 36 82,448 4,580 69 1,112,660 32,251 4 12.57 6.283 37 91,998 4,973 70 1,178,588 33,674 5 30.68 12.27 38 102,354 5,387 71 1,247,393 35,138 6 63.62 21.21 89 113,561 5,824 72 1,319,167 36,644 7 117.9 33.67 40 125,664 6,283 73 1,393,995 38,192 8 201.1 50.27 41 138,709 6.766 74 1,471,963 39,783 9 322.1 71.57 42 152,745 7,274 75 1,553,156 41,417 10 490.9 98.17 43 167,820 7,806 76 1,637,662 43,096 11 718.7 130.7 44 183,984 8,363 77 1,725,571 44,820 12 1,018 169.6 45 201,289 8,946 78 1,816,972 46,589 13 1,402 215.7 46 219,787 9,556 79 1,911,967 48,404 14 1,886 269.4 47 239,531 10,193 80 2,010,619 50,265 15 2,485 331.3 48 260,576 10,857 81 2,113,051 52,174 16 3,217 402.1 4!) 282,979 11,550 82 2,219,347 54,130 17 4,100 482.3 50 306,796 12,272 83 2,329,605 56,135 18 5,153 572.6 r,l 332,086 13,023 84 2,443,920 58,189 19 6,397 673.4 r,2 358,908 13,804 85 2,562,392 60,292 20 7,854 785.4 63 387,323 14,616 86 2,685,120 62,445 21 9,547 909.2 54 417,393 15,459 87 2,812,205 64,648 22 11,499 1,045 55 449,180 16,334 88 2,943,748 66,903 23 13,737 1,194 56 482,750 17,241 89 3,079,853 69,210 24 16,286 1,357 57 518,166 18,181 90 3,220,623 71,569 25 19,175 1,534 58 555,497 19,155 91 3,366,165 73,982 26 22,432 1,726 59 594,810 20,163 92 3,516,586 76,448 27 26,087 1,932 60 636,172 21,206 93 3,671,992 78,968 28 30,172 2,155 61 679,651 22,284 94 3,832,492 81,542 29 34,719 2,394 62 725,332 23,398 95 3,998,198 84,173 30 39,761 2,651 63 773,272 24,548 96 4,169,220 86,859 31 45,333 2,925 (»4 823,550 25,736 97 4,345,671 89,601 32 51,472 3,217 ' 65 876,240 26,961 98 4,527,664 92,401 33 58,214 3,528 66 931,420 28,225 99 100 4,715,315 4,908,738 95,259 98,175 n : 64 = 0.0490874 ; log (ir : 64) = 0.6909699 — 2. it: 32 = 0.0981748 ; log («■ : 32) = 0.9919999 — 2. 294 The Naval Constructor CHAPTER II. STRENGTH OF COLUMNS. Johnson's Formula. The accompanying table of strengths of wrought iron columns is based on the "straight line " formula proposed by Johnson and gen- erally used in America. The value of the constant K is deduced by making the straight line tangent to the curve of Euler's for- mula. r Where, P = Ultimate compressive unit stress. S = Maximum tensile unit stress. k — A constant whose value depends on the condition of the ends, viz., fixed, flat, hinged or round. L = Length of column in feet. r = Least radius of gyration. This formula may be readily memorized for wrought iron col- umns, thus : — Ultimate unit stress P = 52,500 — 2700— , on which basis the r table has been calculated. Example. — It is required to find the safe load with a factor of safety of 5 for a hollow wrought-steel strut or column with a length of 46 feet, mean diameter 20 inches and one-half inch thick. r = 20 x .35 = 7. r 7 P (from table) = 6,900 lbs. Area of column = ci re. x t = 62.8 x .5 = 31.4 D" Safe Load W= 6,900 lbs. x 31.40 □" = 216,660 lbs. Or, if it be required to find the thickness t of the column in the foregoing example, the load being 216,660 lbs. r = 7. - = 6.57. r P = 6,900 lbs. (from table). Strength of Columns 295 216,660 Area = npoT = 31 - 4D * Area 31.4 _ . . t = = n — s = • 5 inch. Circ. 62.8 Values of r for various sections. When t = R, r=.32D. jfN «=i '=- 8132> - r— *— i d Fig. 96. 4 (See Table of Elements of Circular Sections.) n V ^M\ Least radius of gyration = j. Pig. 97. 1 Tl) Rectangle or square r — .289 D, Pig. 98. L r Pig. 99, m Fig. 100. B Pig. 101. Equal sided angle bar r — -v- r = .4 D 296 The Naval Constructor VALUES FOR JOHNSON'S FORMULA. Column Material and How Supported. s. k. Limit of — r" Mild Steel : Flat ends .... 52,500 2,148 16.3 Hinged ends . . . 52,500 2,640 13.3 Bound ends . . . 52,500 3,408 10.3 Wrought Iron : Flat ends .... 42,000 1,536 18.2 Hinged ends . . 42,000 1,884 14.8 Round ends . . . 42,000 2,436 11.5 Cast Iron : Flat ends .... 80,000 5,256 10.2 Hinged ends . . . 80,000 6,444 8.3 Round ends . . . 80,000 8,316 6.4 Oak: Flat ends . . . . 5,400 336 10.7 Strength of Columns 297 STRENGTH OF WROUGHT IRON OR MILD STEEL COLUMNS. By Johnson's Formula. L in Ft. r in In. 52,500 — 2,700- r 13,125 — 675 - r 10,500 — 540- r 8,750 — 450- r L Ultimate Unit Stress. Safe Unit Stress Safe Unit Stress Safe Unit Stress r Factor =1. Factor = 5. Factor = 6. 1.00 49,800 12,450 9,960 8,300 1.25 49,125 12,281 9,825 8,187 1.50 48,450 12,112 9,690 8,075 1.75 47,775 11,944 9,555 7,963 2.00 47,100 11,775 9,420 7,850 2.25 46,425 11,606 9,285 7,737 2.50 45,750 11,437 9,150 7,625 2.75 45,075 11,269 9,015 7,513 3.00 44,400 11,000 8,880 7,400 3.25 43,725 10,931 8,745 7,287 3.50 43,050 10,762 8,610 7,175 3.75 42,375 10,594 8,475 7,063 4.00 41,700 10,425 8,340 6,950 4.25 41,025 10,256 8,205 6,837 4.50 40,350 10,087 8,070 6,725 4.75 39,675 9,919 7,935 6,612 5.00 39,000 9,750 7,800 6,500 5.25 38,325 9,581 7,665 6,387 5.50 37,650 9,412 7,530 6,275 5.75 36,975 9,244 7,395 6,162 6.00 36,300 9,075 7,260 6,050 6.25 35,625 8,906 7,125 5,937 6.50 34,950 8,737 6,990 5,825 6.75 34,275 8,569 6,855 5,712 7.00 33,600 8,400 6,720 5,600 7.25 32,925 8,231 6,585 5,487 7.50 32,250 8,062 6,450 5,375 7.75 31,575 7,894 6,315 5,262 8.00 30,900 7,725 6,180 5,150 8.25 30,225 7,556 6,045 5,037 8.50 29,550 7,387 5,910 4,925 8.75 28,875 7,219 5,775 4,812 9.00 28,200 7,050 5,640 4,700 9.25 27,525 6,881 5,505 4,587 9.50 26,850 6,712 5,370 4,475 9.75 26,175 6,544 5,235 4,362 298 The Naval Constructor STRENGTH OF WROUGHT IRON OR MILD STEEL COLUMNS. — Continued. By Johnson's Formula.' L in Ft. r in In. 52,500-2,700- 13,125-675- r 10,500—540- 8,750-450- r L Ultimate Unit Stress. Safe Unit Stress Safe Unit Stress Safe Unit Stress T Factor = 4. Factor = 5. Factor = 6. 10.00 25,500 6,375 5,100 4,250 10.26 24,825 6,206 4,965 4,137 10.50 24,150 6,037 4,830 4,025 10.75 23,475 5,869 4,695 3,912 11.00 22,800 5,700 4,560 3,800 11.25 22,125 5,531 4,426 3,687 11.50 21,450 5,362 4,290 3,575 11.75 20,775 5,194 4,135 3,462 12.00 20,100 5,025 4,020 3,350 12.25 19,425 4,856 3,885 3,237 12.50 18,750 4,687 3,750 3,125 12.75 18.075 4,519 3,615 ' 3,012 13.00 17,400 4,350 3,480 2,900 13.25 16,725 4,181 3,345 2,787 13.50 16,050 4,012 3,210 2,675 13.75 15,375 3,844 3,075 2,562 14.00 14,700 3,675 2,940 2,450 14.25 14,025 3,506 2,805 2,337 14.50 13,350 3,337 2,670 2,225 14.75 12,675 3,169 2,535 2,112 15.00 12,000 3,000 2,400 2,000 15.25 11,325 2,831 2,265 1,887 15.50 10,650 2,662 2,130 1,775 15.75 9,975 2,494 1,995 1,662 16.00 9,300 2,325 1,860 1,550 16.25 8,625 2,131 1,725 1,437 16.50 7,950 1,987 1,590 1,325 16.75 7,275 1,819 1,455 1,212 17.00 6,600 1,650 1,320 1,100 17.25 5,925 1,481 1,185 987 17.50 5,250 1,312 1,050 875 17.75 4,575 1,144 915 762 18.00 3,900 975 780 650 18.25 3,225 806 645 537 18.50 2,550 638 510 425 18.75 1,875 469 375 312 Pipe Pillars 299 PIPE PILLARS. «3 10 n 12 Radii of Gyration \ ■y/D 2 + d 2 . Thickness in Decimals of an Inch. .1 .67 1.03 1.38 1.73 2.08 2.43 2.79 3.15 3.51 3.86 4.21 .2 .64 .99 1.35 1.70 2.05 2.40 2.76 3.11 3.47 3.82 4.18 .3 .61 .96 1.31 1.66 2.02 2.36 2.72 3.08 3.44 3.79 4.15 A .58 .93 1.28 1.63 1.98 2.33 2.69 3.04 3.40 3.75 4.11 .56 .90 1.25 1.60 1.95 2.30 2.66 3.01 3.37 3.72 4.08 .54 .88 1.22 1.57 1.92 2.27 2.62 2.97 3.33 3.68 4.04 .7 .52 .85 1.19 1.54 1.89 2.24 2.59 2.94 3.30 3.65 4.01 .51 .83 1.16 1.51 1.86 2.21 2.56 2.91 3.27 3.62 3.97 .50 .81 1.14 1.48 1.83 2.18 2.53 2.88 3.23 3.58 3.94 lln. .50 .79 1.12 1.46 1.80 2.15 2.50 2.85 3.20 3.55 3.90 300 The Naval Constructor STANDARD PIPE ELEMENTS. STANDARD STRENGTH PIPES. < . si o -< - - - < fc fc < O J en g i SgES SB Resis- tance, y' Radii of Gyra- tion, R 1 . t- H 2 i .406 .27 .0573 .0717 .001032 .005195 .014808 .241 1 .54 .364 .1041 .1249 .003312 .012267 .026508 .42 i .675 .494 .1917 .1663 .007267 .02153 .043716 .559 i .84 .623 .3048 .2492 .017045 .04058 .068358 .837 1 1.05 .824 .5333 .3327 .037035 .07054 .111342 1.115 i 1.315 1.048 .8626 .4954 .10665 .1622 .1176721 1.668 n 1.66 1.38 1.496 .668 .1947 .2345 .29125 2.244 i* 1.9 1.611 2.038 .797 .3091 .3254 .46283 2.678 2 2.375 2.067 3.356 1.074 .666 .5609 .61957 3.608 2* 2.875 2.468 4.784 1.708 1.532 1.0657 .89729 5.739 3 3.5 3.067 7.388 2.243 3.023 1.7274 1.3535 7.536 3£ 4 3.548 9.887 2.679 4.788 2.394 1.7868 9.001 4 4.5 4.026 12.73 3.174 7.23 3.213 2.2787 10.66 4* 5 4.508 15.96 3.674 10.41 4.164 2.8326 12.34 5 5.563 5.045 19.99 4.316 15.21 5.468 3.5226 14.50 6 6.625 6.065 28.89 5.584 28.17 8.504 5.0422 18.76 7 7.625 7.023 38.74 6.926 46.5 12.197 6.7165 23.27 8 8.625 7.982 50.04 8.386 72.35 16.777 8.6314 28.18 9 9.625 8.937 62.73 10.03 108.2 22.483 10.782 33.70 10 10.75 10.019 78.84 11.92 160.9 29.935 13.496 40.06 11 12 11.25 99.40 . 13.70 231.7 38.617 16.910 45.95 12 12.75 12 113.1 14.58 279 42.765 19.160 48.98 13 14 13.25 137.9 16.05 373 53.286 23.222 53.92 14 15 14.25 159.5 17.23 461 61.467 26.504 57.89 15 16 15.25 182.3 18.41 562 70.25 30.535 61.77 Standard Pipe Elements 301 STANDARD PIPE ELEMENTS . — (Continued.) A 35ft W & . ©j £ i OH Resis- tance, / M PS - <& o K O A i .405 .205 .033 .086 .001234 .00609 .01288 .29 1 .54 .294 .068 .161 .003807 .01410 .02363 .54 1 .675 .425 .139 .219 .008588 .02545 .03977 .74 i .84 .542 .231 .323 .020204 .04811 .06246 1.09 1 1.05 .736 .452 .414 .045261 .08621 .10276 1.39 6 jz; l 1.315 .951 .71 .648 .10665 .16220 .16466 2.17 § U 1.66 1.272 1.271 .893 .2442 .27012 .27329 3 H l* 1.9 1.494 1.753 1.082 .3952 .41631 .36513 3.63 < H X - 2 2.375 1.933 2.935 1.495 .8767 .73827 .58607 5.02 21 2.875 2.315 4.209 2.283 1.9434 1.3522 .85155 7.67 3 3.5 2.892 6.569 3.052 3.932 2.2771 1.2884 10.25 8J 4 3.358 8.856 3.71 6.325 3.1625 1.7048 12.47 4 4.5 3.818 11.449 4.445 9.72 4.3200 2.1767 14.97 5 5.563 4.813 18.19 6.12 20.67 7.4312 3.38 - 20.34 6 6.625 5.75 25.97 8.505 40.93 12.356 4.8096 28.58 1 .84 .244 .047 .507 .024266 .05777 .04782 1.7 1 1.05 .422 .139 .727 .058098 .11066 .08004 2.44 6 § 3 1 1.315 .587 .271 1.087 .14097 .2144 .12961 3.65 n 1.66 .885 .615 1.549 .3426 .4128 .22115 5.2 H «2 ii 1.9 1.088 .93 1.905 * .57092 .6010 .29961 6.4 2 2.375 1.491 1.744 2.686 1.3194 1.1117 .49148 9.02 H H H 2* 2.875 1.755 2.419 4.073 2.8873 2.0085 .70910 13.68 3 3.5 2.284 4.097 5.524 6.030 3.4457 1.0916 18.56 H a p o ft 3| 4 2.716 5.794 6.772 9.895 4.9475 1.4610 22.75 4 4.5 3.136 7.724 8.18 15.38 6.8355 1.8803 27.48 5 5.563 4.063 12.965 11.34 33.63 12.0906 2.9636 38.12 6 6.625 4.875 18.666 15.896 66.87 20.1872 4.2285 53.11 302 The Naval Constructor STEEL COLUMNS. Size of Column. 12 ins. diameter, I" thick, R — 4.03. 10 ins. diameter, i" thick, R = 3.37. 5 ins. diameter, ' thick, = 2.66. 6 ins. r diameter,! |" thick, 1 Vf = 2.00. t 5 ins. diameter, f" thick, R — 1.64. 4 ins. diameter, \" thick, R — 1.33. 3 ins. diameter, A" thick, 7? =1.00. ^ 2 ins. diameter, \" thick, 11 = 0.66. O oo Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round Length in Feet. 10 12 14 16 18 Greatest Safe Load in Pounds per Sq. In. of Section. 23,000 23,000 •23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 20,770 20,770 19,990 18,650 15,450 15,450 14,700 13,530 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 23,000 20,770 20,770 19,990 18,650 17,350 17,350 16,630 15,430 15,490 15,490 14,740 13,590 14,000 14,000 13,1 11,540 11,640 11,640 10,570 8,560 28,000 J3,000 23,000 23,000 22,810 22,810 22,030 20,950 18,600 18,600 17,850 16,480 15,510 15,510 14,760 13,610 14,370 14,370 13,500 12,090 13,550 13,550 12,540 10,820 11,700 11,700 10,650 8,640 8,920 8,650 7,120 5,060 20,920 20,920 20,140 18,760 17,780 17,780 17,040 15,780 15,490 15,490 14,740 13,590 17,050 17,050 16,390 15,260 15,570 15,570 14,830 13,690 15,570 15,570 14,810 13,670 14,500 14,500 13, 12,280 14,250 13,550 14,250 13,550 13,350 12,540 11,910 10,820 14,000 12,870 11,700 14,000 12,870 11,700 13,060 11,880 10,650 11,540 10,040 8,640 13,060 13,060 12,080 10,270 11,690 11,690 10,630 8,610 9,720 9,670 8,190 6,110 6,780 6,150 4,640 2,790 11,600 11,600 10,520 8,500 10,170 10,140 8,760 6,680 8,350 7,850 6,350 4,310 4,810 4,040 2,580 1,510 10,360 10,340 9,000 6,940 8,970 8,710 7, 5,120 6,850 6,250 4,740 2,860 3,230 2,730 1, 14,830 14,030 13,810 12,450 13,870 13,870 12,880 11,340 12,570 12,570 11,560 9,690 10,670 10,660 9,390 7,350 9,280 9,180 7,620 5,550 7,940 7,420 5,920 3,900 5,590 4,790 3,250 1,880 2,290 2,020 1,090 14,0:50 14,030 13,090 11,590 13,260 13,260 12,260 10,470 11,690 11,690 10,630 9,720 9,670 8,190 6,110 8,500 8,070 6,550 4,510 6, 6,220 4,710 2,850 4,280 3,560 2,230 1,270 1,760 1,450 790 450 13,590 13,690 12,680 10,880 12,500 12,500 11,460 9,580 10,900 10,900 9,670 7,650 8,730 7,200 5,140 7,590 7,050 5,550 3,560 5,910 F,120 3,560 2,040 3,300 2,790 1, 910 Steel Columns 303 STEEL COLUMNS. — Continued. Size of Column. u .1.8 Length in Feet. 20 22 24 26 28 30 32 34 36 Greatest Safe Load in Pounds per Sq. In. of Section. 12 ins. f diameter,! §" thick, ) 72 = 4.03. L 10 ins. r diameter,! h" thick, J 72 = 3.37. L 8 ins. r diameter, J A" thick, 1 72 = 2.66. t 6 ins. r diameter,! §" thick, 1 ,8 = 2.00. L 5 ins. C diameter,! f" thick, ] 72=1.64. L 4 ins. ( diameter,! i" thick, 1 72 = 1.33. L 3 ins. f diameter,! rV'thick,"] 72 = 1.00. ^ 2 ins. f diameter,! £" thick, 1 72 = 0.66. L Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed • Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Rouud Fixed Flat Hinged Round Fixed Flat Hinged Round Fixed Flat Hinged Round 12,930 12,930 11,940 10,110 11,770 11,770 10,730 8,720 10,170 10,130 8,760 6,680 8,350 7,850 6,350 4,310 6,730 6,100 4,580 2,750 4,880 4,100 2,620 1,540 2,650 2,280 1,250 720 12,350 12,350 11,310 9,400 11,150 11,150 9,990 7,960 9,460 9,410 7,870 5,790 7,570 7,030 5,530 3,540 5,990 5,200 3,630 2,080 4,000 3,310 2,050 1,150 2,100 1,860 1,000 580 11,750 11,750 10,700 8,690 10,550 10,540 9,230 7,180 8,970 8,710 7,180 5,120 6,850 6,250 4,740 2,860 5,160 4,370 2,860 1,670 3,280 2,760 1,610 910 1,800 1,490 810 460 11,230 11,230 10,080 8,070 9,980 9^50 8,520 6,450 8,490 8,050 6,540 4,500 6,250 5,500 3,940 2,300 4,350 3,630 2,280 1,300 2,790 2,380 1,320 760 10,730 10,710 9,450 7,410 9,430 9,370 7,830 5,750 7,940 7,420 5,920 3,900 5,590 4,790 3,250 1,880 3,720 3,100 1,880 1,050 2,330 2,050 1,110 650 10,240 10,220 8,850 6,770 9,040 8,830 7,300 5,230 7,350 6,810 5,310 3,340 4,910 4,120 2,640 1,550 3,180 2,700 1,550 870 2,010 1,760 940 550 9,770 9,730 8,260 6,180 8,670 8,090 6,770 4,730 6,830 6,220 4,710 2,850 4,280 3,560 2,230 1,270 2,800 2,390 1,320 760 1,790 1,480 800 460 9,340 9,260 7,710 5,630 8,280 7,780 6,270 4,240 6,380 5,660 4,110 2,420 3,760 3,130 1,910 1,060 2,430 2,120 1,160 670 9,020 8,800 7,260 5,200 7,820 7,290 5,790 3,780 5,910 5,120 3,560 2,040 3,300 2,780 1,620 910 2,110 1,870 1,000 590 304 The Naval Constructor STRENGTH OF METALS AND ALLOYS. (Stresses given in Pounds per Square Inch.) 2 *d 2 ■s . m U A Metal. 111 In OS 9 » 892 If I" "■3 ■*" 31 9 o g 3 "83 Aluminium Bronze: 10% Al, 90% Cu (rolled) l}%Al,98}%Cu(cast) Brass and Bronze : 100,000 26,800 60,000 18.0 .282 Copper Tin Zinc 85 15 — . . 35,500 95,000 63,000 20,000 .319 90 10 — . . 33,000 75,000 52,000 . . . 140 .318 95 5 — . . 30,000 52,000 39,000 16,000 13.7 .317 90 — 10 . . 30,000 48,000 24,000 .322 80 — 20 . . 37,000 65,000 30,000 10,000 12.4 .316 70 — 30 . . 43,000 79,000 36,000 9,100 14.0 .310 60 — 40 . . 49,000 75,000 42,000 16,400 12.2 .308 50 — 50 . . 24,000 117,400 48,000 16,900 11.6 .304 86 12 2 {«»»;, 34,500 02,400 12.5 .315 70 10 20 . . 31,760 .... 43,500 14.5 . . . 60 10 30 . . 21,500 30,200 15.8 . . . 55 \ 44§ . . Bronze, Manganese (cast) 68,900 71,200 22,000 17,700 130, 000 • . . . . . " " (rolled) 100,000 47,700 79,400 80,000 21,500 55,400 " Phosphor . . " Tobin (rolled) 175,000 41,900 . • . .296 Copper (cast) . . . " (sheet) . . . • " wire annealed . 24,800 8,000 180 32,600 39,800 25,000 18.0 Iron Cast (average) 17,000 100,000 6,000 15.0 .26 " Wire annealed . 45,000 75,000 50,000 27,000 26.0 ' ' Wrgt. , rolled bars 36,000 30,000 29.0 " " " plates Lead 50,000 2,050 30,000 1,100 29.0 7,350 . . . 0.85 Steel (mild) .... Tin 67,200 3,500 35,000 1,670 29.00 6,400 4.6 Zinc (cast) .... 5,400 4,050 Physical Properties of Timber 305 PHYSICAL PROPERTIES OF TIMBER. The physical properties of timber, given hereafter, are derived largely from the recent experiments of the Forestry Division, United States Department of Agriculture, which form the most complete and systematic series on record. The following general conclusions seem to be demonstrated: 1. That bleeding (the experiments were made on long-leaf yel- low pine) has no material effect on the strength of timber, the flexibility is slightly increased, but the bled timber will probably endure exposure to the weather as well as the other. 2. That moisture reduces the strength of timber, whether that moisture be the sap, or water absorbed after seasoning. In gen- eral, seasoned timber, or with not more than 12 per cent, moisture, is from 75 per cent, to 100 per cent, stronger than green timber. 3. When artificially dried, timber contains a uniform percent- age of moisture throughout, a condition requiring months or even years to attain in air-dried heavy timber. When kiln-dried at usual temperatures, wood shows no loss of strength compared with air-dried timber of the same percentage of moisture. The effect of very high temperatures and pressures (as used in vulcanizing) is lower strengths than when air-dried. 4. Large timbers are equal in strength per square inch of sec- tion, tested every way, to small timbers, provided they are equally sound and contain the same percentage of moisture. 5. The tests seem to indicate that the strength of woods of uniform structure increases with the specific gravity irrespective of species; i.e., in general, the heaviest wood is the strongest. Oak seems not to belong to the list of woods to which this general remark applies. The data on properties of timbers must be used with consider- able judgment and caution. Seasoned wood will gain weight, to the extent of 5 to 15 per cent., if exposed to the weather, and this excess will be reduced if the wood is kept a week in a warm dry place. Some of the individual tests made by the United States Forestry Division varied considerably from the mean values given in the table. In the case of tension tests, which varied most from the average, a few were as low as 25 per cent., while others reached 190 per cent, of the mean. The elastic limit given in connection with the data from the United States Forestry Division is the relative elastic limit suggested by Professor John- son, as there is no definite "elastic limit" in timber similar to that in some metals. This relative elastic limit is taken where the rate of deflection is 50 per cent, more than it is under initial loads. Modulus of ultimate bending is extreme fibre stress on beam at rupture. The modulus of elastic bending is the fibre stress when the rate of deflection is increased 50 per cent. The modulus of elasticity is derived from transverse tests. :;<><; The Naval Constructor STRENGTH Seasoned timber, moisture 12 per cent and Namk of Material Ash (American) .... Birch Box Cedar (White) Cedar (American Red) . . Chestnut Cottonwood (see Poplar) . Douglas Spruce (Oregon Pine) Fir Gum Hemlock Hickory (American) average Lignum Vitae Mahogany (Spanish) . . Maple Oregon Pine (see Douglas Spruce) Oak (Red) Oak (Black or Yellow) . . Oak (White) Oak (Live) Pine (Southern Yellow, long leafed) Pine (Cuban) Pine (Loblolly) .... Pine (White) Poplar Spruce (Northern) . . . Spruce Pine (Pinus glabra of So. States) .... Walnut (Black) .... pi P3 17,000 15,000 20,000 10,800 11,500 13,000 13,000 8,700 19,600 11,800 14,900 11,150 10,250 10,000 13,600 13,000 13,000 13,000 10,000 7,000 11,000 12,000 10,500 .§5 2 Sf ® a>.2 7,200 8,000 10,300 5,200 6,000 5,300 5,700 7,100 5,700 9,500 9,900 8,200 7,150 7,200 7,300 8,500 10,400 8,000 8,700 7,400 5,400 5,000 6,000 7,300 7,500 1,900 700 800 i,4ob 2,700 1,800 2,300 1.800 2,200 1,260 1,200 1,150 700 1,200 2,500 1,100 400 500 1,300 800 400 1,100 500 1,100 1,100 1,000 835 770 800 400 400 800 Weight in Pounds per Cherry 42.0 Cork 15.6 Ebony 76.1 Strength of Timber 307 OF TIMBER. under. Stresses given in pounds per square inch. ll g3 09 >> 9 s li § eS tab ■sii o .2 3 if Ordinary Working Stress. Tens. Comp. Trans. 7,900 1,640,000 1,645,000 10,800 11,700 7,900 2,000 2,000 2,500 1,200 1,400 1,400 1,000 1,000 1,200 600 700 600 1,200 1,200 1,500 800 900 900 39 33 23 41 5,800 910,000 1,140,000 6,300 7,200 8,100 5,800 6,400 ' 7,800 11,200 1,680,000 1,530,000 1,700,000 2,390,000 1,255,000 7,900 6,400 1,400 700 1,000 32 9,500 7,100 16,000 11,700 9,550 10,000 7,800 1,200 900 900 750 1,800 1,500 1,500 37 25 50 83 53 49 11,000 2,000 1,500 1,500 1,200 1,200 1,200 9,200 8,100 9,600 9,040 10,000 11,100 9,200 6,400 8,400 5,700 1,970,000 1,740,000 2,090,000 1,851,500 2,070,000 2,370,000 2,050,000 1,390,000 1,400,000 1,640,000 1,306,000 11,400 10,800 13,100 11,300 12,600 13,600 11,300 7,900 6,500 8,000 10,000 8,000 9,200 8,100 9,600 1,400 1,400 1,700 900 900 1,000 1,200 1,200 1,500 45 45 50 9,500 10,640 9,400 6,400 8,400 1,600 1,000 1,500 38 1,600 1,200 900 1,200 1,200 1,000 900 700 600 700 700 1,000 1,200 900 750 900 900 900 33 24 26 30 38 Cubic Foot of other Woods. Elm 35 Mahogany (Honduras) 35 Sycamore 37 308 The Naval Constructor TABLE OF WEIGHT AND STRENGTH OF WIRE. M GO tf & <-< < . Weight of w H eg . a w 5c 00 Diameter. OS *%° saag* 5«< H 02 100 Yards. Mile. < sse§g In. MM. Sq. In. Lbs. Lbs. Yds. Lbs. 7/0 .500 12.7 .1963 193.4 3,404 68 43,975 6/0 .464 11.8 .1691 166.5 2,930 67 37,854 6/0 .432 11.0 .1466 144.4 2,541 78 32,823 4/0 .400 10.2 .1257 123.8 2,179 91 28,144 3/0 .372 9.4 .1087 107.1 1,885 105 24,354 2/0 .348 8.8 .0951 93.7 1,649 120 21,302 .324 8.2 .0824 81.2 1,429 138 18,464 1 .300 7.8 .0707 69.6 1,225 161 15,831 2 .276 7.0 .0598 58.9 1,037 190 13,398 3 .252 6.4 .0499 49.1 864 228 11,169 4 .232 6.9 .0423 41.6 732 269 9,467 5 .212 6.4 .0353 34.8 612 322 7,904 6 .192 4.9 .0290 28.5 502 393 6,486 7 .176 4.5 .0243 24.0 422 467 5,450 8 .160 4.1 .0201 19.8 348 566 4,503 9 .144 3.7 .0163 16.0 282 700 3,648 10 .128 3.3 .0129 12.7 223 882 2,882 11 .116 3.0 .0106 10.4 183 1,077 2,368 12 .104 2.6 .0085 8.4 148 1,333 1,903 13 .092 2.3 .0066 6.5 114 1,723 1,489 14 .080 2.6 .0050 6.0 88 2,240 1,126 15 .072 1.8 .0041 4.1 70 2,800 912 16 .064 1.6 .0032 3.2 66 3,500 721 17 .056 1.4 .0025 2.4 42 4,667 552 18 .048 1.2 .0018 1.8 32 6,222 406 19 .040 1.0 .0013 1.2 21 9,333 281 20 .036 0.9 .0010 1.0 18 11,200 228 Notes on the Use of Wire Rope 309 NOTES ON THE USE OF WIRE ROPE. 05 o M a o » u & W oa K>< U w J M - J fc M Of Q to O 1-1 »< 1 0.63 57.29 39.08 2 1.26 28.63 78.18 3 1.88 19.09 117.24 4 2.51 14.29 156.26 5 3.15 11.42 195.24 6 3.78 9.51 234.14 7 4.42 8.14 272.98 8 5.06 7.11 311.74 9 5.70 6.31 350.40 10 6.34 5.67 388.97 11 6.99 5.14 427.41 12 7.65 4.70 465.71 13 8.31 4.33 503.88 14 8.97 4.01 541.90 15 9.64 3.73 579.75 16 10.32 3.48 617.43 17 11.00 3.27 654.90 18 11.69 3.07 692.20 19 12.39 2.90 729.27 20 13.10 2.74 766.12 21 13.82 2.60 802.74 22 14.54 2.47 839.12 23 15.27 2.35 875.23 24 16.02 2.24 911.09 25 16.78 2.14 946.66 26 17.56 2.05 981.94 27 18.34 1.96 1,016.93 28 19.14 1.88 1,051.61 29 19.95 1.80 1,085.97 30 20.78 1.73 1,120.00 31 21.62 1.66 1,153.68 32 22.49 1.60 1,187.02 33 23.37 1.54 1,219.99 34 24.28 1.48 1,252.58 35 25.20 1.42 1,284.81 36 26.15 1.37 1,316.62 37 27.12 1.32 1,348.05 38 28.12 1.28 1,379.07 39 29.14 1.23 1,409.67 40 30.21 1.19 1,439.84 For Vertical Winding at high speeds, one-tenth the breaking strain has been adopted as a sate working load ; it may, however, be increased to one-eighth, according to condi- tions of working. The gross weight hanging over the pulley (including rope) being con- sidered the working load. Hauling on Inclined Plane. — The work- ing load is usually taken at one-sixth the breaking strain, and the following formula for ascertaining the load has been found from experience to give satisfactory results : Plane, 800 yds. Load, 20 tons. Maximum inclination 7 degs. or 1 in 8.14. Cwts. Qrs. Lbs. Gravity of load, 20 tons x 272.98 lbs. per ton Friction of load, 20 tons X 20 lbs. per ton = Gravity of rope, 800 yds. at 2.15 lbs., 1720 -f 8.14 = Friction of rope, 1720—20 = 2J Plough steel rope = 49 1(3 = 55 1 12 Uncoiling Wire Rope. — A reel or turn- table should be used to avoid " kinks " or sharp bends. Lubrication of Ropes.— Both winding and hauling ropes should be well oiled to pro- long duration. The winding rope especially ought to have frequent applications of heavy- bodied hydro-carbon oil, which should be well rubbed into the interstices with a swab, as it is important that the inside of the rope should benefit as well as the outside by its application. N. B. — An unlubricated rope stood 16,000 bends before fracture, whilst the same rope lubricated stood 38,700. 310 The Naval Constructor PROOF OR TEST LOAD FOR CHAINS. d = Diameter of Iron in Inches. The Admiralty Rules are : Test Load in Tons = 18rf* for Studded Links. Test Load in Tons = 12rf 2 for Unstudded Links. d. 18rf». I2d». d. IS (P. 12 rf*. d. 18 rf*. 12 d*. 1 .75 1 10.1 6.7 4 40.5 27.0 . . . 1.17 V 11.9 7.9 i& 47.5 31.7 I 1.69 13.8 9.2 if 55.1 36.7 3.46 2.30 ft 15.8 10.5 if 63.3 42.2 A 4.50 3.00 1 18.0 12.0 2 72.0 48.0 5.70 3.80 *1 22.8 15.2 2 f 81.3 54.2 1 7.03 4.69 11 28.1 18.7 H 91.1 60.7 H 8.51 5.67 1| 34.0 22.7 2| 101.5 67 7 The practice at Elswick is to make the test load 10 per cent, higher than the Admiralty test load. STRENGTH OF CHAIN CABLES (AMERICAN). 33 Break- S3 ing Stress Recommended Admiralty Probable Aver- of Iron Proof Load on Proof Load on 5° in Lbs. per So. In. Cable. Cable. Cable. In. Lbs. Tons. Lbs. Tons. Lbs. Tons. 55,596 33,840 15.11 40,320 18.00 71,172 31.77 it 55,073 37,820 16.88 45,517 20.32 79,544 35.51 54,589 42,053 18.77 51,030 22.78 88,445 39.48 J T% 54,138 46,468 20.74 56,857 25.38 97,731 43.63 U 53,715 5t,084 22.81 63,000 28.12 107,440 47.96 it 53,317 55,903 24.96 69,457 31.01 117,577 52.49 52,941 60,920 27.20 76,230 34.03 128,129 57.20 if 52,584 66,138 29.53 83,317 37.20 139,103 62.10 52,245 71,550 31.94 90,720 40.50 150,485 67.18 if 51,922 77,159 34.45 98,437 43.95 162,283 72.45 51,613 82,956 37.03 106,470 47.53 174,475 77.89 i? 51,317 88.947 39.71 114,817 51.26 187,075 83.52 51,033 95,128 42.47 123,480 55.12 200,074 89.32 W 50,760 101,499 45.31 132,457 59.13 213,475 95.30 50,498 108,058 48.24 141,750 63.28 227,271 101.46 W 50,245 114,806 51.25 151,357 67.57 241,463 107.80 2 50,000 121,737 54.35 161,280 72.00 256,040 114.30 Strength of Small Chains 311 STRENGTH OF SMALL CHAINS. THE FOLLOWING RULES ARE BA8ED ON EXPERIMENTS CAR- RIED OUT BY PROF. H.S. HALE SHAW ON SMALL CHAIN8. LESS THANHS \ SINGLE JACK ' W=78S0d 2 Fig. 102. Fig. 103. ORDINARY WELDED W=39,250d 2 Fig. 104. TRIUMPH" WELDLES8 MACHINE MADE W=78,500d* w = breaking load in lbs. d=6ize of chain in inche8. the safe load may be taken a8 one quarter of breaking load. Fig. 105. 312 The Naval Constructor • DIMENSIONS AND WEIGHT OF CHAIN CABLES* Size of Links (Out- Number Weight per Fathom. Diameter side). of Links in One Fathom. of Iron. Length. Width. Studded Links. Open Links. In. In. In. Lbs. U>s. 5{J » 19i 57.8 52.9 it 8$ is| 64.7 60.1 c ! 4 18 77.7 69.7 It fit 4* 17 84.8 77.4 7 *& 16 94.9 86.8 it 7 t \ i 15* 102.9 95.2 7ft 15 115.5 106.2 If 8 5ft 14 121.7 113.C 81 »x 13ft 134.3 124.2 1* 8H $ 13 144.6 134.9 H 9 m 160.0 146.7 \l y 6 12 170.1 157.3 6ft Hi 183.2 168.9 11 10ft 85 n 192.9 179.1 10ft 6| n 215.6 199.1 lil ioi 8i 10£ 225.0 209.2 10$ 71 10 240.8 219.9 St "ft 7f 10 261.4 240.5 12J 7|. 9* 272.1 250.7 2ft 7f 9 279.1 258.8 ULTIMATE OR BREAKING STRENGTH OF CHAINS. The breaking stress of the iron of which chains are made varies with the diameter of the bar, being less the greater the diameter. If /= breaking stress of iron in tons per square inch, and d = diameter of bar in inches, then /= 26.2 - 2.4 d. Breaking load of chain in tons = W= 1.22 d 2 (26.2 — 2 Ad). This formula allows for the bending action, and for the loss of strength due to the weld. The following table gives values of W for various values of d, calculated by the above formula : d w. d. w. d. w. d. W. X 1.95 1 11.8 ! 29.0 H 82.2 * 3.03 I 14.2 H 36.3 H 93.1 4.34 16.7 if 44.2 2 104.4 1 5.87 f 19.5 if 52.8 24 116.2 7.62 22.5 U 62.0 21 128.5 ft 9.59 H 25.7 if 71.8 2» 141.1 * From Report of Committee of Government Board, IT. S. A., 1879. Elements of Angles 313 CHAPTER III. ELEMENTS OF ANGLES. Fig. 106. Size in Inches. Thick- ness. A BE A in Square Inches. Weight peb Foot in Pounds. Moments of Inertia. Axis, AB. Axis, EF. 8x8 i 7.75 26.4 48.47 19.60 8J X8J 1 15.29 52.8 94.14 39.01 6X6 1 4.36 14.8 15.37 6.20 6J X 61 I 10.65 35.9 36.69 15.48 5 X 5 3.61 12.3 8.73 3.54 51 X 51 H 8.77 29.4 20.72 9.09 4 X 4 f . 2.40 8.2 3.69 1.50 41 X41 3£ X 3£ 5.69 18.6 8.71 . 3.82 A 2.09 7.1 2.45 0.99 3f X 3| \ 4.06 13.7 4.G0 1.97 3X3 1.44 4.9 1.25 0.50 8A x SA 2f X 2| 3.51 11.5 3.01 1.32 1 1.31 4.5 0.95 0.39 3 X3 | 2.70 8.6 2.11 0.90 2h X 2£ 3 ? 0.90 3.1 0.54 0.22 2f X2f 2.33 7.8 1.33 0.59 21 X2| i 0.81 2.7 0.39 0.16 2/ 3 X 2ft 1.66 5.4 0.85 0.37 2 X 2 1 0.71 2.5 0.27 0.11 2, 3 B X 2 T % If X if 1.47 4.8 0.61 0.26 0.62 2.1 0.18 0.08 1^1 X H| § 1.28 4.1 0.39 0.18 4 0.36 1.2 0.08 003 l| X if § 1.14 3.5 0.29 0.13 1 1 X 1 J 4 0.30 1.0 0.05 0.02 if x if 1 0.62 2.0 0.10 0.04 1 X 1 ^ 0.23 0.8 0.02 0.01 H x H * 0.49 1.5 0.05 0.02 314 The Naval Constructor ELEMENTS OF ANGLES. Fig. 106. Distance from Radii of Gyj Resistance. Base to Neutral Axis. Axis AB. Axis EF. Axis AB. d. 2.50 1.59 8.34 2.19 2.48 1.60 16.18 2.43 1.88 1.19 3.53 1.64 1.86 1.21 8.43 1.19 1.56 0.99 2.42 1.39 1.54 1.02 5.76 1.65 1.24 0.79 1.28 1.12 1.24 0.82 3.10 1.34 1.08 0.69 0.98 0.99 1.06 0.70 1.84 1.13 0.93 0.59 0.58 0.84 0.93 0.61 1.39 1.02 0.85 0.55 0.48 0.78 0.88 0.58 1.02 0.93 0.77 0.49 0.80 0.70 0.76 0.50 0.75 0.84 0.69 0.44 0.24 0.63 0.72 0.47 0.50 0.75 0.62 0.39 0.19 0.58 0.64 0.42 0.40 0.68 0.54 0.36 0.15 0.51 0.55 0.38 0.30 0.63 0.47 0.28 0.07 0.42 0.50 0.34 0.25 0.57 0.41 0.26 0.06 0.35 0.40 0.25 0.11 0.43 0.29 0.21 0.03 0.30 0.32 0.20 0.07 0.37 Elements of Bulb Angles 315 ELEMENTS OP BULB ANGLES. OB 10 5 M & n * lie Moments of Inertia. Square op Radius of Gyration. Radius of Gyration. Axis AB. Axis CD. Axis EF. Axis AB. Axis CD. Axis EF. Axis AB. Axis CD. Axis EF. 7.70 26.2 94.17 7.11 5.22 12.23 0.92 0.68 3.50 0.96 0.82 10 11.24 38.2 136.41 11.93 9.19 12.14 1.06 0.82 3.48 1.03 0.90 9 6.74 22.9 67.67 6.58 4.68 10 04 0.98 0.69 3.17 0.99 0.83 9 9.56 32.5 95.71 10.61 7.60 10.01 1.11 0.79 3.16 1.05 0.89 8 5.62 19.1 44.69 4.09 3.06 7.95 0.73 0.54 2.82 0.85 0.74 8 7.77 26.4 61.63 6.43 4.83 7.93 0.83 0.62 2.82 0.91 0.79 7 4.79 16.3 29.74 3.73 2.66 6.21 0.78 0.56 2.49 0.88 0.75 7 6.41 21.8 39.67 5.58 3.93 6.19 0.87 0.61 2.49 0.93 0.78 6 391 13.3 18.31 3.24 2.26 4.68 0.83 0.58 2.16 0.91 0.76 6 5.24 17.8 24.35 4.81 3.29 4.65 0.92 0.63 2.16 0.96 079 5 2.97 10.1 9.84 1.76 1.52 3.31 0.59 0.51 1.82 0.77 0.72 5 3.97 13.5 13.07 2.64 1.86 3.29 0.66 0.47 1.81 0.82 0.68 316 The Naval Constructor ELEMENTS OF DECK BEAMS. Pig. as M * 3 w gig ST to K Moments of Inertia. Square of Radius of Gyration. Radius of Gyration. Axis AB. Axis CD. Axis AB. Axis CD. Axis AB. Axis CD. in 9.51 32.2 179.33 6.36 18.86 0.67 4.34 0.82 in 13.41 45.6 224.19 8.14 16.72 0.61 4.09 0.78 10 8.20 28.0 118.55 6.08 14.46 0.74 3.80 0.86 10 11.32 38.6 145.77 7.54 12.88 0.67 3.59 0.82 9 7.35 25.0 84.99 4.85 11.56 0.66 3.40 0.81 9 9. GO 32.6 100.68 5.78 10.49 0.60 3.24 0.77 8 6.17 21.0 57.75 3.58 9.36 0.58 3.06 0.76 8 8.43 28.6 70.19 4.44 8.33 0.53 2.89 0.73 7 5.32 18.0 36.99 2.56 6.95 0.48 2.64 0.69 7 7.29 24.5 45.32 3.26 6.22 0.45 2.49 0.67 6 4.27 14.5 21.83 1.62 5.11 0.38 2.26 0.62 6 5.77 19.6 26.50 2.07 4.59 0.36 2.14 0.60 5 3.39 11.5 11.96 1.01 3.53 0.30 1.88 0.55 6 4.64 15.8 14.64 1.29 3.16 0.28 1.78 0.53 Elements of Deck Beams 317 ELEMENTS OF DECK BEAMS.— (Continued.) § H g 53 03 H H O H t» M CO 1 j «2 • P fe H fc O o 53e« ««! ? Mg to a M o H ^ O ^ * a to 02 « « to%, OB. a 8Z& 2 as to to g O H" Coefficient for Deflection. < o 2 U CO g Distributed Load. Centre Load. 11§ 27.9 0.60 148.7 3.22 .0000089 .0000143 48.6 5.07 m 36.0 0.60 191.9 3.22 .0000071 .0000114 119.4 5.27 10 20.7 0.54 110.5 2.86 .0000135 .0000217 40.8 4.28 10 26.4 0.54 140.8 2.86 .0000107 .0000172 96.4 4.48 9 16.7 0.48 88.9 2.55 .0000188 .0000303 39.0 3.90 9 20.3 0.48 108.3 2.55 .0000159 .0000256 79.0 4.04 8 12.8 0.43 68.1 2.28 .0000277 .0000446 32.4 3.48 8 16.0 0.43 85.5 2.28 .0000228 .0000367 72.2 3.62 7 9.3 0.38 49.8 2.02 .0000432 .0000695 30.2 3.04 7 11.8 0.38 62.9 2.02 .0000352 .0000568 64.6 3.16 6 6.4 0.32 34.3 1.69 .0000733 .0001180 24.0 2.61 6 8.1 0.32 43.0 1.69 .0000604 .0000972 50.2 2.71 5 4.3 0.26 22.9 1.39 .0001337 .0002147 21.4 2.22 5 5.4 0.26 28.9 1.39 .0001093 .0001755 42.8 2.30 318 The Naval Constructor ELEMENTS OF TEES. — Uneven Legs. Fig. 109. Size ITU < < B w u Z M fc » HOO Moments of INEBTIA. Resistance. Radius of Gybation. 1.37 Inches. Axis Axis Axis Axis Axis Axis X6 X3}X| 7.64 25.97 26.16 12.83 4.12 10.3 4.4 4.59 15.61 25.32 9.11 3.11 8.4 2.8 3A x 6A x 3A x A 3f X 61 X3f X i 3$ X 6 X 3i X A 3A X 6A X 3A X f 3* X6i X3f X « 3| X 6 X3|xi 5.39 18.32 29.80 10.95 3.74 9.8 3.3 6.19 21.05 34.36 12.87 4.37 11.2 3.8 6.68 22.71 34.64 12.59 4.37 11.6 3.9 7.46 25.36 38.86 14.42 4.92 12.8 4.4 8.25 28.05 43.18 16-34 5.66 14.1 5.0 8.64 29.37 42.12 15.44 5.61 14.0 4.9 3A X 6A X 3A x H 3| X 61 X3f X f 9.38 31.89 46.13 17.27 6.16 15.2 5.5 10.16 34.54 50.22 19.18 6.85 16.4 6.0 Elements of Z Bars 321 ELEMENTS OF Z BARS. B Fig. 110. Radii of Gyration. Coefficient in Net Tons for Greatest Safe LoadDistance. Coefficient for Deflection about Axis AB. ft . - m J o g H 2h ■< a Axis AB. Axis CD. Least Axis EF. Fibre Stress 16,000 Lbs. Fibre Stress 12,000 Lbs. Distribu- ted. Centre. 1.20 1.16 0.55 10.0 7.5 .0005694 .0009167 11.0 1.20 1.18 0.55 12.3 9.2 .0004545 .0007317 14.4 1.21 1.20 0.56 14.8 11.1 .0003687 .0005937 18.0 1.13 1.14 0.54 14.9 11.2 .0003809 .0006132 20.4 1.14 1.15 0.54 16.0 12.0 .0003524 .0005674 22.2 1.14 1.16 0.55 17.0 12.8 .0003279 .0005279 24.0 1.60 1.22 0.64 15.9 11.9 .0002689 .0004329 13.6 1.61 1.24 0.65 19.7 14.8 .0002128 .0003426 18.2 1.62 1.26 0.66 23.6 17.7 .0001750 .0002817 23.0 1.54 1.24 0.64 25.1 18.8 .0001702 .0002740 26,6 1.55 1.27 0.65 28.7 21.5 .0001465 .0002359 31.2 1.55 1.28 0.66 32.1 24.1 .0001290 .0002077 35.8 1.48 1.26 0.65 32.3 24.2 .0001321 .0002127 39.0 1.48 1.27 0.66 35.5 26.6 .0001183 .0001905 43.6 1.49 1.29 0.67 38.7 29.0 .0001069 .0001218 .0001721 48.6 1.98 1.32 0.74 28.0 21.0 .0001961 21.4 1.98 1.33 0.75 33.6 25.2 .0001005 .0001618 27.0 1.99 1.35 0.76 39.1 29.3 .0000853 .0001373 32.8 1.91 1.30 0.73 40.6 30.5 .0000841 .0001354 37.6 1.91 1.31 0.74 45.6 34.2 .0000739 .0001190 43.2 1.92 1.33 0.75 50.6 38.0 .0000658 .0001059 49.0 1.84 1.28 0.72 50.5 37.9 .0000676 .0001088 53.2 1.85 1.30 0.73 55.1 41.3 .0000612 .0000984 59.0 2.35 1.41 0.82 45.0 33.8 .0000632 .0001017 30.8 2.35 1.43 0.83 52.4 39.3 .0000537 .0000864 37.6 2.36 1.44 0.84 59.8 44.9 .0000466 .0000750 44.6 2.28 1.37 0.81 61.6 46.2 .0000462 .0000744 50.2 2.28 1.39 0.81 68.4 51.3 .0000412 .0000663 57.0 2.29 1.41 0.83 75.2 56.4 .0000370 .0000596 64.0 2.21 1.34 0.81 74.9 56.2 .0000380 .0000612 69.0 2.22 1.36 0.81 81.2 60.9 .0000347 .0000559 76.0 2.22 1.37 0.82 87.5 65.6 .0000319 .0000513 83.0 322 The Naval Constructor ENDING MOMENTS OF PINS. M , Moment = ^ Z>y. Diameter Diam- eter of Area of Pin in Moments in Inch-Pounds fob Strains of Fibre Pin in LNCHE8. Square Inches. 15,000 Lbs. 20,000 Lbs. 22,000 Lbs. 25,000 Lbs. per per per per Sq. Inch. Sq. Inch. Sq. Inch. Sq. Inch. 0.785 1,470 1,960 2,160 2,450 i J 0.994 2,100 2,800 3,080 3,500 ii 1.227 2,880 3,830 4,220 4,790 if 1.485 3,830 5,100 5,620 6,380 lX 1.767 4,970 6,630 7,290 8,280 1| 2.074 6,320 8,430 9,270 10,500 l| 2.405 7,890 10,500 11,570 13,200 l| 2.761 9,710 12,900 14,240 16,200 2 3,142 11,800 15,700 17,280 19,600 21 3.547 14,100 18,800 20,730 23,600 21 3.976 16,800 22,400 24,600 28,000 2f 4.430 19,700 26,300 28,900 32,900 2 I 4.909 23,000 30,700 33,700 38,400 2 ! 5.412 26,600 35,500 39,000 44,400 2f 5.940 30,600 40,800 44,900 51,000 2| 6.492 35,000 46,700 51,300 58,300 3 7.069 39,800 53,000 58,300 66,300 <*i 7.670 44,900 59,900 65,900 74,900 31 8.296 50,600 67,400 74,100 84,300 3| 8.946 56,600 75,500 83,000 94,400 3y, 9.621 63,100 84,200 92,600 105,200 3| 10.321 70,100 93,500 102,900 116,900 3§ 11.045 77,700 103,500 113,900 129,400 33 11.793 85,700 114,200 125,600 142,800 4 12.566 94,200 125,700 138,200 157,100 41 13.364 103,400 137,800 151,600 172,300 41 14.186 113,000 150,700 165,800 188,400 4f 15.033 123,300 164,400 180,800 205,500 4? 15.904 134,200 178,900 196,800 223,700 4| 16.800 145,700 194,300 213,700 242,800 4f 17.721 157,800 210,400 231,500 263,000 ? 18.665 170,600 227,500 250,200 284,400 5 19.635 184,100 245,400 270,000 306,800 51 20.629 198,200 264,300 290,700 330,400 51 21.648 213,100 284,100 312,500 355,200 5f 22.691 228,700 304,900 335,400 381,100 5j 23.758 245,000 326,700 359,300 408,300 5 f 24.850 262,100 349,500 384,400 436,800 5f 25.967 280,000 373,300 410,600 466,600 . H 27.109 298,600 398,200 438,000 497,700 Bending Moments of Pins 323 BENDING MOMENTS OF PINS. — (Continued.) Moment = ^ D 8 /. 3 IW) Diameter = . / \f) * 32 DIAM- ETER OP Pin in Inches. Area of Pin in Square Inches. Moments in Inch-Pounds for Fibre Strains of 15,000 Lbs. 20,000 Lbs. 22,000 Lbs. 25,000 Lbs. per per per per Sq. Inch. Sq. Inch. Sq. Inch. Sq. Inch. 6 28.274 318,100 424,100 466,500 530,200 n 29.465 338,400 451,200 496,300 564,000 30.680 359,500 479,400 527,300 599,200 6| 31.919 381,500 508,700 559,600 635,900 1 33.183 404,400 539,200 593,100 674,000 34.472 428,200 570,900 628,000 713,700 35.785 452,900 603,900 664,200 754,800 6$ 37.122 478,500 638,000 701,800 797,500 7 38.485 505,100 673,500 740,800 841,900 71 39.871 532,700 710,200 781,200 887,800 a 41.282 561,200 748,200 823,000 935,300 7§ 42.718 590,700 787,600 866,300 984,500 7£ 44.179 621,300 828,400 911,200 1,035,400 7f 45.664 652,900 870,500 957,500 1,088,100 7f 47.173 685,500 914,000 1,005,300 1,142,500 ?1 48.707 719,200 958,900 1,054,800 1,198,700 8 50.265 754,000 1,005,300 1,105,800 1,256,600 8i 51.849 789,900 1,053,200 1,158,500 1,316,500 8$ 53.456 826,900 1,102,500 1,212,800 1,378,200 8| 55.088 865,100 1,153,400 1,268,800 1,441,800 3 56.745 904,400 1,205,800 1,326,400 1,507,300 8f 58.426 944,900 1,259,800 1,385,800 1,574,800 8f 60.132 986,500 1,315,400 1,446,900 1,644,200 H 61.862 1,029,400 1,372,500 1,509,800 1,715,700 9 63.617 1,073,500 1,431,400 1,574,500 1,789,200 94 65.397 1,118,900 1,491,900 1,641,100 1,864,800 1 67.201 1,165,500 1,554,000 1,709,400 1,942,500 69.029 1,213,400 1,617,900 1,779,600 2,022,300 H 70.882 1,262,600 1,683,400 1,851,800 2,104,300 9f 72.760 1,313,100 1,750,800 1,925,900 2,188,500 9| 74.662 1,364,900 1,819,900 2,001,900 2,274,900 91 76.590 1,418,100 1,890,800 2,079.900 2,363,500 10 78.54 1,472,600 1,963,500 2,159,900 2,454,400 101 82.52 1,585,900 2,114,500 2,325,900 2,643,100 10£ 86.59 1,704,700 2,273,000 2,500,200 2,841,200 lOf 90.76 1,829,400 2,439,300 2,683,200 3,049,100 11 95.03 1,960,100 2,613,400 2,874,800 3,266,800 53 99.40 2,096,800 2,795,700 3,075,400 3,494,800 103.87 2,239,700 2,986,300 3,284,800 3,732,800 12 113.10 2,544,700 3,392,900 3,732,200 4,241,200 / 324 The Naval Constructor TEES AS STRUTS. r = least radius of gyration. Size of Tee in Inches. Length in Feet. 2 4 6 8 10 12 14 16 18 20 Greatest Safe Load in Pounds per Square Inch of Section. 4 X 4) r =.85 \ 3}x 31 ) r =.73 ] 3 X 3) r=.62 } r = 54 \ 2ix2H r =.48 f 2 X 2) r =.41 f lixU } r =.36 J HxU? r = .32 \ Ux n i r =.30 ( 1 x 11 r =.26 \ 16,280 14,680 13,670 13,010 12,600 11,870 11,130 10,400 10,000 9,060 12,110 11,200 10,210 9,310 8,500 7,330 6,310 5,330 4,780 3,540 9,640 8,600 7,390 6,310 5,330 3,970 2,960 2,340 2,070 1,510 7,610 6,420 5,060 3,860 2,960 2,170 1,660 1,200 5,840 4,550 3,190 2,400 1,910 1,290 4,280 3,060 2,210 1,660 1,200 3,040 2,250 1,690 2,330 1,710 1,840 1,250 1,430 Special Shackles 325 SHACKLES. For most purposes in ship details where shackles are used, it is ommou practice to order the shackles given in Table of trade hackles, suiting the size to the chain, wire or inanila rope that L — J i SPECIAL SHACKLES Fig. 111. they are linked with. Where, however, special cases arise in deal- ing with exceptional loads the size of the shackle and pin should be accurately calculated, taking care that the widths between jaws and across the bow are no greater than necessary to take the con- 326 The Naval Constructor nections, as these dimensions are considered as the beams support- ing the load as in the diagram. The dimensions are required of a shackle to take a working load of 10 tons (22,400 lbs.), with a factor of safety of 6 equal to a unit stress of 10,000 lbs. It is assumed that the pin is shipped in a pad-eye, bearing along its entire length, i.e., the load is dis- tributed. We thus have the case of a beam supported at the ends Wl and uniformly loaded, the maximum bending moment M being---- 8 The length I (3") will have previously been determined by the bearing value given in designing the pad-eye. Then, Wl 22,400X3 .„. . . __ -_- = = 8,400 inch-pounds = M. The moment of resistance of a circular section (the pin) is equal to Hs -D 8 } therefore the diameter D which will equal this bending moment (M) just figured with a fibre stress of 10,000 lbs. must be, 7)_ 3 /~ M"~_ 4 3 / 8,400 f V Y~f ~ V :0982 X 10,000 = 204 inches - 32 X/ The diameter of the wire forming the bow at B is calculated in a similar way, noting that the load this time is central, but the ends of the beam being now fixed, we have the same formula for WU the maximum bending moment, viz., — - — Assuming that it has 8 been necessary to bow the shackle, " l\ " has now been increased to 4 inches, so that Wh 22,400x4 110AA . . . „ -g- = — — g = 11,200 inch-pounds = M, and applying the formula for a circular section as in the pin, we have ?/ 11,200 V .0982X 10,000 = 2 * mCheS dlameter at K From the diameter B the wire may be tapered to A, where the sectional area need only be such as will resist tension, but it is usual in practice to increase this amount by 25%, owing to the load at times becoming eccentric, thus throwing a greater stress on one leg. W 22,400 lbs. atgA . nrnl m n T = io!ooo lbs. = 2 - 24 sq - ln - + 25 % = 28 s ^ m - = 1.4 sq. in. per leg. = 1| in. diameter at A. The sectional Special Shackles 327 ie sectional area and dimension C are computed by consider- ing h the length of beam which is now fixed at both ends and uniformly loaded when M is equal to ~^~- The dimensions are lis calculated as in the foregoing, observing that the resistance is now for a rectangle, and the bending moment will consequently equal AC 2 s 328 The Naval Constructor CHAPTER IV. STANDARD RIVETING, U. S. NAVY. 1. All rivet holes through material 1 inch or more in thickness should be drilled, or if punched should afterwards be reamed to fin- ished size. 2. In cases where rivets connect plates of different thickness the size of rivet indicated for the greater thickness with corre- sponding spacing will be used where strength is required, and that indicated for the lesser thickness where water tightness is a special consideration, always provided the greater thickness is not more than double the lesser. 3. Where tap-rivets must be used they should be J inch larger than the corresponding ordinary rivets for the same thickness, except taps into heavy castings and forgings such as stem and stern posts, which should be £ inch larger. Where strength is required, taps should not penetrate less than one diameter, and should penetrate 1£ diameters when the thickness of metal will allow it. 4. Where the spacing given in Table No. 3 cannot be followed exactly, as will generally be the case, make the spacing a trifle closer (as necessary with heavier plating) and a trifle further apart (as necessary with lighter plating), the division between " heavier" and " lighter" plating coming at 7^-pound plates for single rivet- ing ; at 15-pound plates for double riveting and at 25-pound plates for treble riveting. 5. Where the above distinctions are considered too complicated for yard work, the general rule will be to space a trifle closer in all cases, as necessary for equal spacing. 6. Where strength is required in laps and butted connections of plating, with the spacing indicated, single riveting is suitable only for plating under 12£ pounds, and double riveting for plating under 25 pounds. For maximum strength in connections of plat- ing above 30 pounds it will generally be found that quadruple riveting is required. Single Straps. 7. Single butt straps and edge strips, when single or double riveted, should be the same thickness as the plates connected, and where the plates connected are of different thickness, the straps or strips should be of the same thickness as the lighter plate. Single butt straps when treble riveted should be 1^ times the thickness of the plates they connect. Standard Riveting, U.S. Navy 329 Double Butt Straps. 8. Double butt straps should not be used for water-tight work, owing to the difficulty in caulking. They may be used to advan- tage in conditions requiring great strength but not water-tightness. The thickness of each strap should be \ the thickness of plates connected for double riveted straps, and § the thickness for treble riveted straps. The spacing of rivets in rows should be calculated. Size of rivets for double butt straps as follows : For plates from 15 to 20 pounds, exclusive, § inch rivets. •« " " 20 to 25 M inclusive, f " " 44 " above 25 pounds, see Table No. 1. Distance between Rows. 9. Centres of rivets should be placed not less than If times the diameter from the edges of plates connected. In double and treble riveting for laps and singl entraps, the distance from centre to centre of rows should not be less than 2£ diameters; in butt laps and double butt straps the distance between centres of rows should be not less than 3 diameters. (Butt laps should be at least double riveted.) For zigzag riveting the distance between centres of rows should not be less than If diameters for rivets spaced 4 diameters apart in rows. 330 The Naval Constructor TABLE L — Diameter of Rivets. Weight of Plates. oS ■I H fa £ M 00 > 58* a* - M 9 H Qi W a <. as P ft *H O M a i s p o B * s? sff 3 3.0 JSH2'**»1S-»« o P hw 2h'* b Tj*i0«0 00 05 xJliOCNMOtN^CDCDO i— I i-h t— ( i— I i— I ON'*>0 (M (M M M •* iC ® t- 00 OJ O (NNMMtHOCNOOOO MBHW HNNNM^iiio^t-eo rHi-tfNtNOOCO^OCOr-t- r+fHUMHi HN Hn Hn r-li-li-.0 o-CHci-rm- HHHHNINNMM'* r-HHHNcqcOMM HHHHNNIMW rH r-( r-l »-H i-t £ *1 -I Pounds 00 per •^o*-S In. In. In. In. In. In. In. In. Tn. In. In. Sq. Foot, Up to 3 Ex. Up to 2 1 9 32 H iA n 2tV 1A 2A 11 21 4J 3-6 « 2-5 i ft iA 2J M *A 2A »A 2A *A «A 6-8 " 5-7 i 9 if 2i 2J 4 1 3J 4| 31 of 81 8-13 " 7-11 1 u 2A 3f 3* &A 3}| oil *A 7A ioa 13-20 " 11-15 i it 2A *A 3| «A 4i «tt 41 8f 12 | 20-30 " 15-24 i 11 5 4| 7A n 8A 5| ioa 14A 30-40 " 24-32 i 1A 5| 5 H 6i 9i 6i Hi 16 J 40-51 " 32-41 il 1A •j 7 10 | 7A 12H ISA 61 & over 41 &» over 1 H 1 1 1 10A H! 11 9 lx T* B| 14 | 20 f Lloyd's Countersinks 335 FORM OF RIVET TO BE U8E3 IN OUTSIDE 5 S THE TAPERED NECK OF RIVET TO BE OF 8UITABLE LENGTH IN RELATION TO THE THICKNESS OF PLATE IN WHICH IT 18 INTENDED TO Bf USED. Fig. 117. 336 The Naval Constructor LLOYD'S RIVETING Showing Diamett n and Spacing of J U rets and Thickness of plates Diameter of rivets Breadth of treble riveted straps in inches . . , " " double riveted straps in inches . . . " " quadruple riveted butt laps in inches " " treble riveted butt laps in inches . , •» " double riveted butt laps in inches . , " " treble riveted edge laps in inches . , M *« double riveted edge laps in inches . 44 " single riveted edge laps in inches . In f butts of outside pitting, and of upper, spar and middle deck irs of D " '3* dia. c. to c. 4 dia. c. toe. 4£dia. c. to c. 5 dia. c. to c. 7 dia. c. to c. ngt-n gtb. of the vessel amidships (except quadruple riveted butt laps), buttsof deck plating, margin plat In quadruple riveted butt laps girders, lower deck and bold stringers, tie plai stringer plates >n other deck erections ; also butts and edge floor plates, and margin plate angles, edges and butts of bulkhead plating. In flat keel angles, bulkhead frames where caulked, butts and edges of mast plates, and deck plating to beams where single flange beams are fitted to alternate frames. In * frames, reversed frames, floors, keelsons, beam angles, deck and hold stringer angles, face angles on web frames and side stringers, bulkhead stiffen ens, longitudinal angles on continuous girders, verti- cal angles connecting floors and girders and deck plating to beams except where single flange beams are fitted to alternate frames, II 4-1 t In butts connected by single butt straps alternate rivets may be omitted in the back row of treble riveting when the plating number is 20,000 and un- der ; when above this number, the rivets in the back row are not to be more than 5 to 5J diameters apart from centre to centre. All overlapped butts are to have complete rows of rivets. * When the rule frame spacing is 26 inches or above, the rivets in the edges of outside plating (forward and aft) are not to exceed 4 diameters apart from centre to centre, and the rivets attaching the outside plating to frames are to be spaced not more than 6 diameters apart from centre to centre. In deep water ballast tanks above the level of inner bottom, and in fore and after peak water ballast tanks, the rivets through frames and outside plating are to be spaced not more than 6 diameters apart from centre to centre. Before the three-fifths length of a steamer having a tonnage coefficient of .78, or having a full form at the fore part, the rivets in the landing edges of the strakes of plating forming the flat of the bottom to be spaced not more than 4 diameters apart from centre to centre. The rivets in the plating and frames in way of the same to be spaced not more than 5J diameters apart from centre to centre. Rivets to be \ of an inch larger in diameter in the stem, stern frame, and keel, but in no case need these exceed 11" in diameter, and to be spaced 5 diameters apart from centre to centre. In single screw steamers above 350 feet in length, the after lengths of shell plating are to be connected to the portion of the stern frame below the boss with 3 rows of rivets. Rivets in side plate rudders to be of not less size than those required for the upper edge of garboard strake amidships, and to be spaced not more than Lloyd's Riveting Table 337 TABLE, 1903. Breadths of Straps, Butt Laps, and Edge Laps. // >' // // - // // // if // // // // " " - // t 9| 5" 1 3 3f 3| 51 f 5 i 2| 3 SI 3i 51 f % 5 2f 3 3f 5} &&*8 1 "» 5 "4" 2| 3 H 3| 5i f a 12 9 6 3 3* 3* 4 4f 6i t HI 12 9 6 5i 3 3J 3i 4 4| 4, n.l 1-2 !) (i 3 3i 3J 4 4| 61 k 12 :» 6 3 3* 3* 4 19 14 ' 10* "«§ 6 . 3£ 4 4* 5 7 u 1 1!) 14 '4 6 3* 4 4* 5 7 H 1 1!) 14 10} 8ft 6 4 41 5 M 1 19 14 lo.V «i 3i 4 5 7 £5 1 It) 1V 10 i '4 6 3J 4 5 7 21£ 16 ' 12 6| 4 41 6| 1 16 12 4 4J 21} M 12 Si 4 4i 5g 1 16 12 •i 6| 4 4J 5f 5 diameters from centre to centre. The rudder plates are to be countersunk and the rivets are to have full heads and points. Rivets in single plate rudders are to be of not less size than required for attaching the outside plating to the stern frame, and spaced not more than 5 diameters apart from centre to centre. The rivet holes are to he counter- sunk both in rudder plates and the arms, and the rivets are to have full heads and points. Rivets in the edges of deck plating are to be spaced not more than 4 to 4J diameters apart from centre to centre. In single riveted seams one frame rivet is to bo fitted through the landing edges at each frame. In double riveted seams one frame rivet is to be fitted through the landing edges at each frame,, except where the frames or tbe edges of the outside plating are joggled when two rivets are to be fitted. In treble riveted seams two frame rivets (the upper and lower) are to be fitted through the landing edges at each frame. Where the fore and aft flange of the frame does not exceed 3 inches, the rivets attaching the outside plating thereto should not exceed g inch in diameter, and where it is 3£ inches wide, they should not exceed 1 inch in diameter. There are to be at least four rivets in each flange of the angle bars be- tween the frames which connect the stringer plates and intercostal plates to the outside plating. Where the frames are spaced less than 29 inches apart, and where the spacing is 29 inches and not more than 32 inches there are to be five rivets in each flange. The rivets in the beam knees are to be in number and size as required. The rivets in the vertical angles connecting floors and outside brackets to margin plates are to be in number and size as required. The rivets in the connecting g traps for web frames and side stringers are to be in number and size as required. :;:;s The Naval Constructor STANDARD RIVETS. (See Table Opposite.) OOUNTeRBINK OR PLUG HEADS BUTTON MEAD CLASS A , CLASS B , CLASS A CLASS B CLASS A CLA88 B fy^ff^, Figs. 11&-129. Standard Rivets 339 CCod <+, H « ^ H fc * fc >-} 3h ao •SI3AIH dVX S 1 = |S 5 HS: 883888 •g ssvio >; * 3 "*»; -*«3 j 3 S? 5 " ^: ::«::: : ioSioiaS^weowS *"|hH«»]2 < * i " 0|i,i hh •SX3AIH JVX «S^»E •g SSYTO •saraH asmsaaxKiioo <**nj;»p2S'*o!iI2 •savaH Mxasaaxsnoo * «g»BH3-w">t5*> n |n B |2 rt t* , * oa> &*' •SIKIOJ aaaawKVH •avail aaaKii aiioo : :-+"°s ; ;^»S«»» t .»Hts 9 >]2-*o : : :<£ -5"K< SXKIOJ h2|53S *-E"*°32 "K->S-*.«*o^ «B-h«P3J«H5 •sxaAiy; ny 5 r4*«]2«l<»t-]2' ; i C "* D H-fKlxHci'OtJonMt+o Har-w •saiOH aoaaxaivrvia - •gng^'*"'? »K^-H»SSH3S32 rt S t -w-M •xaAia ^o azis v H*io2«*ot-|i5-*w*» •aaawiiij aaaao i**HHS^>: sxvoa oaaaaox HaoAV ^ihs 340 The Naval Constructor m i I a o w OS p > (3 h o H H 5 | S * | : * | * 'isisoeeot> a 1 ss * 1 : ; • ; ;bio(oco CD CO CO t- I- t- 00 d 5g - •«5ioiaoco«ot-t-t-ec 4 *o - ; o ia io co co co t- t- 1- oo c MO y-> | ' ITS IO »a co co so t> t- t- 00 a 1 ; io ia so so t- t» t- oo oo ; * a 1 a 1 - j»oiococoi-t-»>oooo " " a I a 1 •" 1 LO 13 lO CD CD * * J 1 " I ' a 1 a | ~ | to to io «e a b I s i e 1 <: t i "« c J ^t^^iii^ i J:::::::::::: l w jys:.::::::: Riveting Table 341 ■fe* He» Hf»«Hi-Hh»'"H''-*NiolaoHNHN H* Hon He <«**«-» r-^ o ION *-> ^ i H*f e** nt»c**«I^H>(OMfflM j i-+*t**H«He« «H< coH* -torHaeHriiHe* o . 4 hct C500CO»OC0T}' 5 *t? of © o * lOUJ^C0NM(NHHHHHHHH(MM £2 O V »o rH 1 Hi j H-* Mh*He>«Hi Hnhog Hoo^ooH^H* HN 22 He o H* ' "MWHINHrlH rH i-H rl i-l rH 0£ — ' 03 d ••** ^ So • . 4i -P . .J . -^ .00 SHW ^) jo 9 9 &c2 9 bO s ^il i! ft ft ft • -S 8goo«go.Sog33 £ c £ c £ c £ J o c a o CO g 8 i a 3 H 5 i o'S'S'S'S'S'S'S'S'S.s c.g a c d a 55-S5555655 top w> bp bp bp bp bp TJ T5 t2 Tl n3 T3 ^3 Ti T3 t3 .5 .5 .5 .9 .9 .9 .s 03O)Q3a3Q3a3a3a3f»Q3e303c«C3e3eeeJ :U-2 The Naval Constructor o A > && ,0 & a> > ei 1^ §>§§■ ao ©xiovas ~ 2 " u o •ea.iV I* rj uorjo^s A •Haxawvia o •axY'ijao a. . re t~ d 55 l«-jc5oo;ooooooooi>i^i^i-«o«o»iaio3 Hi iSiSiSs fl:: UN'S 2 «-»»2 2 S^-s-s-g-g-s; Strength of Riveting in Ships 343 oiq»JX sdB-ns aiqnoa •AVOU T[Z>VQ fg sjaAia -p 8 » 8A ra »iqnoa pirn aiqeix s;8ai>i d^i pa;8Ata 'epiiupim?) p^aAia ©iq^JX .COrJH^r^OOCOO CO ■* O CD CD CO CS CO -tf O CO t^ •^.iTjdy sv\a f8 * A JH NCOOWN •pa«iuio avoh 5ioea UI S^Artf 9}13UJ8?IV •^.tedy •s'bto: fg 8?3AI>I dBUS JO dt?i paVoAtH aiqnoa •s^ai>i 9UIt?J,i JO ABA\. «I '»^1OOM >o5H(»^'*>o»(X)qrHO^ CqcO*COCOCOCOCO'^COTlH'*»0^ to . fe i-i 05 o w *** •£ §; "ononH-- hoc- :;: H :;; ^f 3 ©HIX , '83H0XI XI rnj do ssaxHaiHX S „(OjO teO|Ort|ON|Oc«|oM<|O«5|O<0|Ol-IO00|O0>IO ^l^ X> |WrHJNr-.|«-H|MrticlrH^r- 1 |««|Mrt| <& None 2H-2i- <& Alter .93 150 A 21 J .812 5.25 3 X3 > 1.50 natelj r. 200 A 22 u « " 4JX3 > <&4 X3 X &3.06 3£x3 X& 3 X2*X& 4.30 250 *8 23 i .937 6.25 5 X3 > <>&5 X3 X &2.83 4ix3 X& 3 X3 Xja 4.10 300 H 24 " " «« 6 X3i> <& 5jx3ix A 3.30 5ix3jx& 4 X3JXA 4.60 350 *3 24 li " ii 6 X3JXA 6 X3JXA 4.80 400 L 3 25 " " " Qhxtyxhi GhXtyXhi 4.80 450 ht 26 1 1.062 7.00 7hX3hXhi 7 X3jxig 4.00 500 hi 27 " " 6.50 , . . . 550 hi 28 (( " ii 600 hi 29 " M 6.00 650 hi 30 11 1.187 6.75 700 hi 31 " " " Strength of Riveting in Ships 347 RIVETING IN SHIPS. Frame Riveting. Three Tiers of Beams. Four Tiers of Beams. Five Tiers of Beams. Frame. Reverse Frame. u a . 00 A C in oo 3 |w a? Frame. Reverse Frame. u a §0 00 a 1 OS Frame. 8® h 0) !l a s oo O* Inches. Inches. Inches. Inches. Inches. ' *y$ X *>2 X 20 6 X3 2 x 2 g 7 X3£xjg 4 X3 2 X& ax^xig 4£X4 X 2 g 6.90 6.70 5.55 8X3JX32X2S 8X3 S X32X2E 8X4 X4 X48 None. 4X4XM Alter- nately. 5.90 5.55 6.62 •' 9x4x4x 2 8 9X4X4X 2 § None 6.15 6.00 348 The Naval Constructor SHEARING AND BEARING All Dimensions Diameter t>F Rivet (In.). Area in Sq. In. Single Shear at «,0UULhs. Bearing Value for i A 1 A Fnu'tioii. Decimal. f 1 1 I i 1 .375 .500 .625 .750 .875 1.000 .1104 .1963 .3068 .4418 .6013 .7854 660 1,180 1,840 2,650 3,610 4,710 1,130 1,500 1,880 1,410 1,690 2,630 1,880 2,340 2,810 2,250 2,810 3,380 3,940 3,280 3,940 4,590 5,250 2,250 2,630 3,000 3,280 3,750 4,500 Diameter of Rivet (In.). Area in Sq. In. Single Shear at 7,500 Lbs. Bearing Value for i A f A Fraction. Decimal. I 1 f ! 1 i .375 .500 .625 .750 .875 1.000 .1104 .1963 .3068 .4418 .6013 .7854 830 1,470 2,300 3,310 4,510 5,890 1,410 1,880 2,340 1,760 2,110 3,280 2,340 2,930 3,520 2,810 3,520 4,220 4,920 4,100 4,920 5,740 6,560 2,810 3,280 3,750 4,100 4,690 5,620 Diameter of Rivet (In.). Area in Sq. In. Single Shear at 10,000 Lbs. Bearing Value for * A i A Fraction Decimal, i i f i I i .375 .500 .625 .750 .875 1.000 .1104 .1963 .3068 .4418 .6013 .7854 1,100 1,960 3,070 4,420 6,010 7.850 1,880 2,500 3,130 2,340 2,810 4,380 3,130 3,910 4,690 3,750 4,690 5,630 6,570 5,470 6,560 7,660 8,750 3,750 4,380 5,000 5,470 6,250 7,500 Diameter of Rivet (In.). Area in Sq. In. Single Shear at 12,000 Lbs. Bearing Value for J A 1 A Fraction. Decimal. i 1 I ! i l .375 .500 .625 .750 .875 1.000 .1104 .1963 .3068 .4418 .6013 .7854 1,320 2,360 3,680 5,300 7,220 9,430 2,350 3,130 3,910 2,930 3,520 5,470 3,910 4,880 5,860 4,690 5,860 7,030 8,210 6,840 8,210 9,580 10,940 4,690 5,470 6,250 6,840 7,820 9,380 In above tables all bearing values above or to right of upper zigzag lines ar© greater than double shear. Values between upper and lower zigzag Shearing and Bearing Value of Rivets 349 VALUE OF RIVETS. in Inches. Different Thicknesses of Plate in In. at 12,000 Lbs. per Sq. In. } A t ii I 1 g 1 H 1 3,000 3,750 4,220 4,690 5,630 6,190 6,750 7,880 8,530 9,750 9,190 10,500 9,840 11,250 12,000 4,500 5,250 6,000 5,160 5,910 6,750 6,560 7,500 7,220 8,250 9,000 Different Thicknesses of Plate in In. at 15,000 Lbs. per Sq. In. i 9 f tt i if 1 H 1 3,750 4,690 5,280 5,860 7,030 7,720 9,030 8,440 9,850 5,630 6,560 7,500 6,330 7,380 8,440 10,670 12,190 11,480 13,130 12,300 14,060 15,000 8,200 9,380 10,310 11,250 Different Thicknesses of Plate in In. at 20,000 Lbs. per Sq. In. \ rs" i tt I ] s 1 if 1 5,000 6,250 7,030 7,810 9,380 10,310 12,030 11,250 13,130 7,500 8,750 10,000 8,440 9,840 11,250 14,220 16,250 15,310 17,500 16,410 18,750 20,000 10,940 12,500 13,750 15,000 Different Thicknesses of Plate in In. at 25,000 Lbs. per Sq. In. 1 A 1 H i 1 3 I if 1 6,250 7,810 8,790 9,770 11,720 12,890 15,040 14,060 16,410 9,380 10,940 12,500 10,550 12,310 14,060 17,770 20,320 19,140 21,880 20,510 23,440 25,000 13,670 15,630 17.190 1.8,750 lines are less than double and greater than single shear. Values below and to left of lower zigzag lines are less than single shear. Section III. DETAILS, STRUCTURAL. KEELS. In steel ships the keel is invariably one of the three forms of bar, flat plate or side bar, the first and third being almost entirely su- perseded by the flat plate type which is on all points a much better method of construction than the others, besides having the great advantage of saving from 6 to 12 inches of draft, there- by increasing the dead weight carrying capacity from about 15 FlG to 1,500 tons respectively on a given immersion. Bar keels should have no place in modern ship construction, unless when required for rubbing purposes only. Bar Keels. These should be made of rolled steel universal bar in preference to the old-fashioned scrap iron forgings and scarphed together in long lengths by right and left-handed scarphs. The scarphs are mostly made nine times the thickness of the bar in length, and the jog, or check, and point should be one fourth the thickness. Scarphs of keel should be close fitting and for that reason must be machined, the connection holes for rivets are drilled, and in addi- tion a few holes, about one third the number of regular ones, should -\ a o j» o ■J o o oj I O O •! o T TACK RIVETS FlO. 133. be drilled of smaller diameter, but countersunk on both sides, for tacking the various lengths together before erecting and riveting the garboard strakes. Care should be taken that these scarphs are shifted well clear of the garboard strake and centre keelson butts and that the joints of scarphs are caulked watertight. 351 352 The Naval Constructor The diameter of the rivets should be in accordance with the re- quirements of the riveting tables given on p. 200, and staggered as shown. The vertical spacing requires special care in keeping clear of the radius of garboard plate and also the caulking edge of same at bottom, which is raised about half an inch from lower edge of bar. For this reason it is advisable to set off the bar full size, drawing in the flanges of garboards before fixing on centres of rivet holes. Flat Plate Keels. Keels of this type are made of a thick plate forming the bottom member of a girder of which the centre keelson is the web. The forms mostly in use are shown by the Figs. 134 and 135. Fig. 136 Fig. 134 shows a very efficient and economical form of flat plate keel and centre keelson devised by the author and designed with a struc- tural /section for small and moderate sized vessels with ordinary floor construction. Where a suitable I section is not obtainable the same construction may be retained with advantage with built- up section. The flat plate keel should always be arranged as an inside strake, as by so doing the keel and its sister member may be laid on the Fig. 135. keel blocks right away without anticipating linering in addition to making a more solid job and saving a small amount of draught. It is a fallacy to place it outside with the intention of disturbing Stems 353 only one plate in the event of damage — a remote contingency which should not be allowed to interfere with good construction. Where a doubling is required by the classification societies' rules it will be found advantageous, where practicable, to increase the plate keel to a sectional area equivalent to that of the keel and doubling, and if double buttstrap be re- quired, the inside one may be fitted in two pieces. Scantlings and riveting will be as specified or to rule requirements. At the forward and after ends the keel plate must efficiently incorporate with the stem and stern frame Respectively, a short ^breeches" plate being usually worked for this FlG 136 purpose. In small con- struction a "spoon" plate is welded to the bottom of stem bar in lieu of the short plate referred to, and a similar plate of " gutter " form welded to stern frame. STEMS. The remarks on bar keels apply equally as regards details to atems. The classification societies' rules allow a reduction in MID. ]S L BREADTH OF FL AT OF KEEL / S TEM OF UNIVERSAL B AB Fig. 137. 354 The Naval Constructor sectional area at stem heads, but as the practice is now to make the stem from universal rolled bar, it will prove no economy to taper it. The usual method of connecting lower part of stem to keel plate are shown by Fig. 137. In straight stems the profile line should be cambered about §" to \" from where it joins the fore- foot curve to stem head, to guard against the illusion of the contour line appearing hollow. STERN FRAME. These frames are mostly forged or cast in steel in one piece for small and moderate sized steamers, and in two or more parts for the larger vessels. As in the case of stems, bar keels, etc., the scantlings are determined from the corresponding numeral of the societies' rules to which the ship is being constructed. The two posts comprising the stern frame, viz., rudder and body posts with the joining arch, are of similar scantlings, but the keel piece con- necting the posts at bottom while of the same sectional area as tlffl| posts, is flattened out to allow of the keel line being curvecT upwards to the clump for keel pintle bearing of rudder for pro- tection to the latter in the event of grounding. Gudgeons are forged on the rudder post of frame from 4 to b\ feet apart to take the pintles ; one, or two in large vessels, being so shaped as to engage the rudder stop at hard-over. This post is connected to the main structure on a deep transom plate clipped to its fore side, and in vessels of over about 300 feet in length the forward or body post must also be carried up and secured in a similar manner. The body post is swelled around the stern tube, having a sectional area through the eye equal to the frame and meeting the post above and below in a fair curve ; the spur or keel part of frame must not be too long to facilitate handling, the general rule being about 2\ frame spaces before the body post, where it incorporates with, or scarphs into, the keel as already described. In steamers over 350 feet length where these frames are of considerable weight, the riveting connecting body post to hood ends of shell plating should be treble below boss and of increased diameter and an addition made to the plating thickness. As in the keels, these holes must be carefully drilled and where scarphs are introduced as in the case of frames of two or more pieces the riveted connection should be developed to equal the bar. It is common to make the contour of body post curvilinear, thus effect- ing an appreciable saving in weight over the straight line, besides giving a more graceful form. In small steamers the after or rudder post may be dispensed with, a spur being carried aft from body post to support heel pintle. Rudders 355 For single screw steamers classed to Lloyds the weight of stern frame may be very closely approximated by taking the first numeral to upper deck and multiplying it by 240 for vessels over 300 feet in length, or by 155 for those under this dimension, as first number x 240 = weight in pounds. RUDDERS. Some of the more common forms of rudders are shown in Figs. 138 to 143. The stresses to which they are subjected and the method of determining the diameter of stock has already been fully described. The single plate rudder, Fig. 138, is the type most commonly adopted in merchant steamers, and is usually built in three parts, viz. : the frame, norman head and plate. The frame may be either cast or forged, bolted i having arms or stays projecting from the stock on alternate sides of centre line spaced opposite each of the gudgeons, which are from 4' to 5' 6" apart. The norman head or stock should be forged in iron or steel with a coupling palm at lower end to connect with a similar palm on head of frame. Allowance should be made on this forging for machining a key to lock the norman head to the frame, and in addition turned coupling bolts are fitted with nuts on under side, threads turned off to a thimble point and split pins fitted. These bolts are from one to three inches in diameter in practice. Their size, however, is not important, as the shearing stresses are all taken on the key. The stock need only be turned in wake of the rudder quadrant where it is sometimes increased in diameter to compensate for cutting the key way. The single plate forming the rudder blade is fitted between, and riveted to, the supporting arms, besides engaging a groove cut down the back of rudder stock. Its thickness ranges from about |" in small steamers to 1J inches in liners. Braces are formed at the ends of supporting arms which are turned out to take fitted pintles. One (two in large rudders) of these braces must be shaped to act as a stopper when the rud- der is put hard-over. The pintles should preferably be fitted Fig. 138. 356 The Naval Constructor separately and of the cone type shown in the detail. It is bad practice to forge pintles on the frame, as besides the difficulty of turning them in a lathe they have the disadvantage of not being readily renewable. The best manner of bushing the pintles is a matter of opinion, the simplest and probably the one most favored being to make the bushes of hard steel with a flange to take the tap screws securing them around the eye of the braces. The weight of the rudder in small vessels is taken on a hard steel disc placed in the heel step bearing with a hole through the heel step BOLTED COUPLING RIVETED JOINT RIVETED JOINT Fig. 139. Fig. 140. for backing it out. In large steamers, however, where the weight of rudder is many tons, the weight should always be taken by a carrier seated inside the counter. Various types of these are shown by engravings 144 to 146. Provision must be made on the back of rudder well clear of water line to fit a Jew's harp shackle for securing the emergency chains, which are from thence carried up the counter, being stopped with ratline stuff to tapped eyes spaced about thirty inches apart. Next in favor to the single plate is the cast steel rudder, Fig. 139, although where only one is being made its cost is against it. For the largest sizes its difficulty of successful manufacture is also to Rudders 357 its disadvantage, although this is got over by casting it in two or more pieces, see Fig. 140, keying these together and riveting them through coupling flanges. When rudders are designed to be cast in one piece, the ribs which are cast on the blade to act as stays should be of easy section, so as not to interfere more than neces- sary with the contraction of the casting in cooling. The oldest method of making the rudder for steel ships is the built type, Fig. 142, which consists of a forged frame having stock, stays, and back piece in one, with two side plates riveted to same Fig. 141. Pig. 142. Fig. 143. after having the inside filled in with fir coated with tar. Its great objection is the cost of forging, especially for large rudders. It has gone completely out of favor unless for yachts, where its appear- ance commands its use, and in light craft of the torpedo boat kind where sufficient stiffness would not be obtainable in a single plate without going into a thickness which would make the weight pro- hibitive. It is also often used with the frame cast in gun metal and the side plates of 16 gauge brass sheet, for wood speed launches, vedettes, pinnaces, etc., although for these craft a cheaper and lighter rudder may be obtained by casting it complete in gun metal or bronze. 358 The Naval Constructor RUDDERICARRIER Fig. 144, Rudders 359 RUDDER CARRIER. Fig. 145. 360 The Naval Constructor WOOD FITTED AFTER RUDDER 18 HUNG 4 THICKNESS MADE ACCORCINGLV Fig. 146. Rudders 361 ELEVATION OF COUPLING FlG. 147. 362 The Naval Constructor Where the rudder stock enters the vessel, watertightness must be ensured by fitting a trunk having a stuffing box and gland at its top. This latter, however, may be dispensed with where a carrier is arranged for, this being an additional element in favor of the adoption of these supports. Before fixing on the counter dimension of the rudder trunk, care should be taken that ample clearness is given to ship and unship the rudder. It will be seen, therefore, that the hole through the counter is much in excess of the diameter of stock, and if not filled in would be unsightly, be- sides allowing a considerable volume of water continually at play inside. It is covered in with a tail plate fitted in halves and secured with hexagon head taps to the counter plating, so as to be easily removable to permit of unshipping the rudder. Good proportions for such details as pintles, gudgeons, braces, couplings, etc. , to meet most requirements are shown in Fig. 147. PROPELLER STRUTS. These brackets for supporting the outer end of tail shaft are gen- erally of pear-shaped section as being the form of least resistance. It is usual to cast them in steel, although they are also sometimes built up. In selecting a suitable area of arm shipbuilders are guided mostly by experience, hence the divergent results seen in practice. The author has therefore devised the formula given on p. 109, in which he has attempted to secure a uniform relationship between the size of these struts and the power transmitted through them. Where possible the centre of the propeller bracket should be placed on a frame to obtain the maximum of stiffness, and the palms of upper and lower arms may be cast on or connected with angle clips. A web spur is sometimes cast or worked on keel length of stern post to take the palm of lower arm instead of flang- ing the latter and riveting it through the keel to it, securing inde- pendent connection for each strut. In wake of the upper palm additional stiffening must be worked by fitting a short local doubling on shell and a stringer inside. The number and diameter of palm fastenings should be developed ac>- cording to the sectional area of the arm, these being in most cases overdone. The sectional area of arms must not be tapered towards the boss, as, although theoretically considered as a cantilever, this would be rational, it must not be lost sight of that the greatest stresses are borne by the ends of the arms adjoining the boss, and are, be- sides, alternating ones inducing fatigue. The engineer will determine the length of boss barrel suitable for bearing and also the finished diameter of the hole, but ample Casting at Stern Tube 363 allowance should be made for boring out to this dimension and also adjusting to centre line of shaft ; this is most important when dealing with cast steel, as it provides the opportunity to detect hidden blow holes. A mass of metal should be avoided where the arm swells to meet the boss either by reducing the fillet to a mini- mum or coring out the metal inside the boss, as otherwise internal stresses will be set up in cooling or dangerous blow holes developed. In high speed vessels it is important to make the pattern "wind" conforming to the run of the water line, thus obviating the arms being dragged across the stream lines and creating eddies. It is surprising the amount of power absorbed by this resistance when brackets are badly set or not set at all. SPECTACLE FRAMES. Spectacle frames have nearly superseded the open A brackets for large merchant vessels. They are enveloped in the hull of the ship, the plating being webbed out and bossed around the shaft for this purpose, as fully explained in the chapter on Design, which see. Where the plating ends on the arms of these frames a good riveted connection must be made, usually double and increased to treble tap rivets around the boss. Local strengthening must also be fitted in wake of spectacle frames by increasing the deep floors in thickness and doubling the ship's frames in their vicinity. CASTING AT STERN TUBE. The outboard end of stern tube in vessels fitted with A brackets is supported by and connected to a steel casting or forging. Its func- tion is similar to the boss on body post of a single screw steamer. STEEL CAST ING COMPOSN. BUSHING RABBET FOR FAIRWATER^y HORIZONTAL SECTION. Fig. 148. 364 The Naval Constructor In large steamers it is usual to extend this casting over two frames in length to give additional support, as shown in Fig. 148, but in small vessels the tube end support need only be from 2 to 4 inches thick, and shaped like Fig. 149. Usually a watertight bulkhead is fitted at the forward and after ends of the stern-tube, the former one being bossed and spectacled at the wings in the manner depicted in the detail given. The inboard palm of the tube end forging is securely riveted to DEEP FLOOR, OR BULKHEAD Fig. 149. wing plate of bulkhead, which must be increased in thickness for the heavier riveting necessarily employed for this purpose. FRAMING. In ships having ordinary floors the frames are invariably run in one piece from centre line to gunwale, and where channel bars or bulb angles are employed with this construction, the floor plates may be reduced in consideration of the excess strength given in their wake. Vessels having a double bottom on the cellular system need only have angle frames on the deep floors with flanges sufficient to take the size of riveting required. Forward in the flat of bottom in full vessels these should be doubled inside tank and in addition local fore and aft stiffening fitted to reenforce against "pounding." Where vessels are classed, as they mostly are, the scantlings of the frames are obtained from the rules of the classification bureau. The angle bars of which they are made is always one with unequal legs, the larger flange standing vertically to the shell plating to obtain the greatest section modulus in the direction of the pressure. Framing 365 Where frames are cut at margin plates of inner bottoms or at water tight fiats, efficient bracket plates of such dimen- sions as will permit of riveting to develop the strength of frame bars should be fitted. See Fig. 153 and 159. In wake of flats where bracket knees are objected to on account of the broken stowage created, or their interference with cabin arrange- ments, the framing may be continuous and smithed angle collars or pressed plate chocks fitted around them to ensure water tightness as in Fig. 150. For simplicity in forming collars, frame and reverse bar or channel section, the reverse bar, or flange, may be cut off and the frame bar doubled for a short distance above and below the flat as compensation as in Fig. 151. Where main frames are stopped at weather deck when the bridge house or superstructure requires a bar of smaller section, the connection between weather deck stringer and frame may be com- pleted with a spirketting plate in lieu of ; the ordinary bracket knee F — ' RESERVE FR. I o i H s o < o s W. T. DECK f. ? ^ ~ o 1 o £ 1 o i -j -! IP hrst ?■- t- S a. CO B w e*= where the Fig. 150. Fig. 151. latter would encroach on the berth- ing space, as shown at Figs. 152 and 153. The inboard member of a ship's framing, called the re- verse bar, whose functions are to provide a flange where- on to fasten the ceiling, or I lining, and to give the neces- ! sary section modulus by ad- ' ding area at a point subjected to corrosion and rough treat- ment, is commonly made of angle section or by the em- ployment of channel bar for the framing. In steamers, however, under about 100 feet it will be found economical 300 The Naval Constructor besides being good construction to omit the reverse bar altogether and increase the sided flange of frame angle to give an equivalent Fig. 152. Fig. 153. REVERSE FRAME Fig. 154. I. A saving in material, riveting and bending will thus be effected. In light vessels where weight must be cut down with- out encroaching on the strength, the maximum section modulus may be obtained for a given depth of web by employing two bars of such dimension of leg as will just give the requisite size of lap to take the proper riveting, as in Fig. 164. The practice in vogue for many years of plac- ing the frame and reverse bars back to back has given place to that of fitting them bosom to bosom where deep framing is adopted, as by this method the beam knees can be fitted without linering in wake of reverse frames. FLOORS. The deep plates riveted to the bottom framing of ships and known as the floors, are placed there to resist the transverse stresses to which the bottom plating is subjected, due to the great water pres- sure externally applied, and the inside forces created by the weight of the structure and cargo. Ordinarily in ships without an inner bottom these are of a size based upon the breadth and depth of the vessel and carried in a fair line up the bilge to a height equal to twice the centre line di- mension as in Fig. 155. It will be seen that this contour at the bilge necessitates furnacing the tail ends to bend them to the re- quired curve, a costly and therefore an objectionable feature. For this reason ordinary floors should be increased in their sided areas and carried straight across, striking the bilge at a point somewhat lower down than with the curved floor. This method permits of the floor being flanged across top in lieu of fitting a reverse bar, Floors 367 although some of the classification bureau penalize flanging plates to the extent of adding one-twentieth to their thickness ; this need not, however, be made unless where specifically required and for that reason cheaper, lighter, and equally efficient construction will be obtained. In small freight steamers and barges a strong and inexpensive floor is obtained by using structural channel section thus elimi- nating the riveting to frame and reverse bar altogether. Floors in inner bottoms are almost entirely fitted as deep solid plates in one piece from centre vertical keel to margin plate, light- ened with large manholes to cut out superfluous material and pro- vide access to the various compartments into which the bottom is sub-divided by the floors and intercostal girders. Deep floors should be lapped to the bottom frames just sufficient to take the riveting. In wake of watertight bulkheads or at ends of ballast Fig. 155. Fig. 156. tanks where the floors are watertight, no holes whatever must be cut in them. The margin plate of inner bottom being continuous, is connected to the main frame by a large bracket plate or tail piece, and by double angles having a specified number of rivets and a gusset plate at top, or in the largest vessels a continuous stringer. The connection to the siding flange of main frame is by lap of sufficient width to take the riveting. See Figs. 157 and 158. At the ends of the vessel where the waterline at top of floor would necessarily be comparatively narrow, increased depth must be given to provide compensatory area and also ensure sufficient width to clip the centre keelson to floors. In the fore peak this additional depth is required to resist buckling and panting, and gen- erally to give local stiffening at a part subjected to unusual stresses. It is also necessary to increase the floors considerably in depth in after-peak, owing to the severe stresses encountered when the propeller " races " and the stern is in air. 3G8 The Naval Constructor INNER BOTTOM. Double bottoms are fitted in vessels to enable them to safely make voyages "in ballast" without incurring heavy expenses by loading and discharging dry ballast. For this purpose the floors are plated over, forming an inner bottom enclosing with the ship's plating a pontoon in which to carry sea water as ballast, an expe- ditious, inexpensive and clean method of doing so. Two or three methods of fitting water bottoms are met with in practice, but as these have given way to the cellular system, it is unnecessary to describe them. This method consists in the subdivision of the space formed by the pontoon referred to, into a great number of small compartments or cells bounded by the floors in a fore and aft direction and transversely by intercostal girder plates, making these cells approximately two feet by four feet, respectively, by the depth of water bot- tom. The water pas- ses freely between these cells as the floors and intercostals are pierced with access holes unless where mentioned here- after. The cells are arranged in separate groups or compartments enclosed by the centre vertical girder, water- tight floors and the margin plate, this larger Fig. 157. subdivision being neces- sary for trimming and filling purposes, as otherwise a large surface of free water would be highly dangerous in certain conditions. As mentioned, the centre vertical plate is continuous fore and aft, fitted usually watertight and connected top and bottom to in- ner plating and plate keel with suitable angle bars. No holes what- ever should therefore be cut through vertical keel plate, and al- though it is not necessary to caulk it in way of ballast tanks, the riveting should be of watertight pitch. Of course where fresh water is carried this longitudinal girder must be properly caulked. At the ends of the vessel where fore and aft subdivision is unnec- essary the centre plate may have access manholes as in the floors. The butt connections are preferably formed with double butt straps, each of about two-thirds the thickness of plate. Through Inner Bottom 369 Fig. 158. butts should not be used here, as besides interfering with the passage of the fore and aft angles they only give single shear value to the riveted con- nection. The outboard side of the inner bottom, or margin plate, is fitted to shell by means of a continuous an- gle bar, the main frames of the ship being cut for that purpose. At the top this plate is flanged in board to take the inner bottom plat- ing as shown in Fig. 157. The butts of margin plate are covered with single strap fitted on the inside of tank. This plate may also be fitted with advantage as shown in Fig. 158 devised by the author, which consists in flanging the plate out- board, a shape that the plate will take more naturally where there is curvature in a fore and aft direction. This out- board flange will also permit of machine riveting and con- necting to the reverse flange or bar on the floor bracket, thus forming a continuous stringer ; or, angle section may be sub- stituted for the flange where facilities for bending are not obtainable. Another method of fitting the margin is illustrated by Fig. 159, where the top plat- ing is carried right out to the shell and flanged upwards to take staggered riveting. Flan- ging is preferable to fitting an angle bar, as in the latter case difficulty would be experienced in putting in the rivets on the horizontal flange of the bar. It is, however, a cheap method of construction, its principal objection being the broken stowage caused by the brackets connecting frame to inner bottom. The inner bottom plating will be of such thickness as the classification societies stipulate where the vessel is classed, when it will be found that increased scantling is required under engines and boilers, and of course the centre strake and margin plate will also be thicker than the rest of the plating, owing to the former being the rider plate member of the girder formed by the centre Fig. 159. 370 The Naval Constructor vertical keel and keel plate, and the latter being an important factor in the longitudinal strength of the ship. For this reasom when arranging the access manholes, these must always be kept clear of the centre strake. A good shift of butts must be arranged for the plating, and these shifted clear of the butts of shell, margin plate and longitudinals. Where the strakes of inner bottom plating are arranged u in and out," the packing liners to outside strakes should be fitted short, the unfilled spaces acting as air holes. The practice of fitting wood ceiling on tank tops is giving way to coating the plating, with tar or bitumastic cement, as this pre- vents the deterioration that goes on under the wood, besides adding to the stowage capacity . Where, however, wood ceiling is required, it must be laid on fore and aft bearers and screwed to same and not fastened through tank top. For this reason, i.e., guarding against leakage the heels of the hold pillars are riveted to vertical flange of tee or angle lugs which are first riveted through in- ner bottom. In arranging the manholes care should be exercised that they are located in accessible parts of holds and clear of cargo hatches. In holds of ordinary length one each side at each end about quar- ter the beam outboard will be sufficient, and in long holds an additional one about the middle of the length. In no case as previously pointed out should they go through the centre strake. The best location aft will of course be in tunnel alleyways, and in machinery spaces they should be fixed by the engineers. This arrangement will contribute to the best circulation of air when the covers are taken off for ventilating purposes. Ample room must be allowed for rim of manhole to clear landings, butts, longitudinal clips, etc. The shell plating forming the bottom of tanks may be reduced Fig. 160. Beams 371 in thickness in consideration of the extra strength added by this construction, and the broad liners fitted to outside strakes in wake of watertight bulkheads may be replaced by narrow liners at watertight floors in tanks. To drain the various compartments of the double bottom when the ship is in dry dock, screw plugs of composition are fitted in the garboard strake and a compensating plate riveted around the hole. A detail of such a fitting is shown by Fig. 160. It is usual to fit similar plugs in the trimming tanks at fore and after peaks. BEAMS. Beams are fitted at various levels, or decks, to tie the ship to- gether and afford supports whereon to lay the decks to take car- goes. The strength of these will depend therefore on the load as well as the span or breadth of beam, as it will be seen that a weather deck beam need not be as strong as the one under it, and so on — each successive tier taking the accumulated load super- imposed. It is common practice to give all decks a round-up or camber, an expensive practice that is unnecessary unless on the weather deck, and only necessary there in a modified sense to obtain the statutory freeboard or to conform to classification requirements. It is a fallacy to imagine that strength is gained by cambering the beams thus supposedly constructing an arch, as you cannot have a compressed beam without abutments, which the sides of the ship are not. To meet the requirements mentioned above, the weather deck should have the standard camber of one-quarter inch to the foot of length, thus a beam 40 feet long will have a round-up at cen- tre line of ten inches. This curve may be set off very quickly with the aid of a common slide rule by setting the courser to the required Fig. 161. £l round-up on the first or top scale and to the half beam on the third scale, when the camber at any desired distance in board of ship's side may be found by moving the courser to the dimension required and read- ing off on top scale. The reading subtracted from the total camber will give the required round-up. This may also be figured as shown in Fig. 161. The beams are connected to the main 372 The Naval Constructor Figs. 162-167. Beams 373 THICKNESS OF BRACKETS DEPENDS ON WEIGHT OF BEAM PER FOOT. (See Figs. 162-1G4.) a . a h a H M 9* o 8* 1 ^ e a > s od 55 & a fa g^5° < a II H "ft 1 to II mo II s X II + II 9 II X II o^ a A. B. c. D. #. F. Rivet Dia. #• Number of Rivets. 5"Z 6"Z Bar. Bar. =S a. 5" 15" 4" 5" 8f" 6" 1\" 1" w 5" 6" 18" 4" 5" 10V 7" 3" r H" 6" 7" 21" 4" 5" 12}" 8" «y r U" 7" 8" 24" 4" 5" 14" 9" 4" f" if 8" 9" 27" 4" 5" 15f" 10" 4J" f" i}" 9" 10" 30" 4" 5" \1\" 11" 5" r if 10" (See Figs. ia>-i67 ) a . P Opq lu < II a . Fw fa u 33 « fa" < X MO * II "S3 to ■*! & + II a w M & CO CO OB a H X II 5 .a W 1 o £ffl fa W fc ^ c& II H 5 « oW^fa O^ * o A. B. c. D. £. /-'. i/. Rivet Bia. 9- N umber of Rivets. 5"Z 6"Z Bar. Bar. a 5" 10" 4" 5" 12V' 4" 14" 21" 5." 1,V" 5" 0" 12" 4" 5" 15" 4*" 16J" 3" r if 6" 7" 14" 4" 5" 17*" 5|" 19*" 3" r 7" 8" 16" 4" 5" 20" 6f 21f" 3" r i" 8" 9" 18" 4" 5" 22}" 6*" 24f" 3" r 9" 10" 20" 4" 5" 25" 7" 27" 3" 1" i\» 10" 374 The Naval Constructor TO FIT CARNEGIE'S 1897 PATTERNS. HJ-H-jf 4 n- Pg* 1" j H? -e- ^ ii Figs. 168 to 170. Beam Depth. A 5. a Z). .e. if" 1" 1 " 1 A". Style. 5" 3 " 3£" tV r r I 6" Si" 4 " I" i" H" 2" 1 ?' H" if I 7" 4J" 4f" 1" r i" If" H" II 8" 5J" 5£" 1" i„ I" li" ii" M n III • 9" 6 " 5»" I" i" 1" U" li" if i| III 10" «i" 6 » 1" i" *" w w 2 1A III Beams 375 frames by welded knees or bracket-plates, the latter being much the cheaper and, where appearance is not important, the better method. The depth of these knees is commonly 2£ times the depth of beam if of channel or bulb tee section, and three times the depth if angle bar be used. The thickness should be the same as the beam unless where welded knees are fitted, when it is good practice to increase the plate one-sixteenth to allow for loss in smithing. When dealing with beams conforming to Lloyd's Rules, it should be noted that the bracket knees are regulated in depth and thickness by the size of the bulb plate required by the table, irrespective of the dimensions of the substituted equivalent sec- tion of channel, bulb angle, or bulb tee. For example, if the rules require a built beam of bulb plate and angles, the former being 10 1" x W't and it was decided to fit the equivalent channel bar of 11" X 81" x y", then the bracket knee would be 26^" x \tf'\ Standard beain knees as used in Navy practice are shown by Figs. 162 to 167. In arranging the riveting in plate knees, the re- quired number is usually specified for classed vessels, and as these are invariably staggered, it is well to locate the first rivet hole as far outboard on the beam, and down on the frame, as practicable. Those in the corner may be treated as common to both arms in counting the number required. Where unsheathed steel decks less than ^V' thick are fitted, beams must be fitted on every frame, with stronger beams at ends of cargo hatchways. Where the thickness is ^ or over, the beams may be fitted on alternate frames with half beams on every frame abreast of hatches. When this spacing is adopted, most societies require closer spacing of rivets through deck plating, viz., 5 diameters apart as against 7 to 8 diameters with the closer spaced beams, so that it is doubtful economy at a sacrifice of efficiency to space them on alternate frames. In the machinery spaces of steamers it is necessary to fit beams of extra strength wherever these can be worked without interfer- ing with the arrangement of engines and boilers. These through beams compensate for the loss in transverse strength through the severance of the regular deck beams at the large machinery open- ings, and serve to tie the ship together and prevent panting of the sides at a part where a considerable weight is permanently carried. In large steamers the machinery arrangement often permits of tw6 adjoining through beams being tied together by cover plates, thus forming an exceptionally strong beam of box sec- tion. Where strong beams cannot be fitted in one piece, owing to interference with the shipping of parts, they should be efficiently bracketed to the casing coamings, care being taken that the con- nection develops the strength of beam. When practicable the pil- lars in machinery spaces should be fitted on these through beams. 376 The Naval Constructor ANGLE BEAM COLLAR The term half beam is applied to those deck beams which are severed in wake of hatch openings. Their inboard ends abut on the hatch side coaming plates, which are in consequence made thicker than the end ones, and the connection is commonly by a single angle clip (taking a specified number of rivets) if a continu- ous fore aud aft angle is fitted at bottom of plate to support the beam ends, or the coaming plate is flanged under the beams for a like purpose. It will be thus seen that this rest will take a great deal of the shear off the rivet connection, besides adding to the strength of the girder formed by the coaming. In wake of small deck openings the inboard beam end may be supported by a carling, or fore and after, of similar section to the beam, except where bulb tee is used with the heel of the carling abutting on beam end and connected to same with, preferably, double clips so as to get double shear value from the rivets. Where heavy local weights or deck machinery are secured, the beams in wake of same should be increased in sec- tion, aud special pillaring or deck girders fitted. It is like- Ji ±__ Fig. 171. wise necessary to increase the strength of the beams at the ends of hatchways by adding to their sectional area — but not to their depth if avoidable. The beams supporting bridge or shade decks fitted over houses and extending to ship's side are frequently carried thwartship in one bar, the casings being scored out and watertight collars fitted, in preference to cutting the beams and fitting bracket plates. These collars are shown by Fig. 171, and may be smithed, stamped, or cast in steel or malleable cast iron. Hold Pillars HOLD PILLARS. 377 Support is given the beams on the various decks by stanchions. Various sections are employed for this purpose, as round bar, pipe, I section and columns built of channel or plate and angle bar. For vessels carrying general cargoes, the pipe section, being circu- lar and light, is probably the best. The I section makes a very H_x sJ/| 6 x« 7 /iexi^ao a HAND HOlI 8'/aX3>j X^ SlNOLE Fig. 172. cheap and efficient column, as forged ends are done away with ; and in vessels requiring large, clear, stowage spaces in holds, built columns should be fitted connected to strong deck girders. A very efficient type of built column is shown by Fig. 172, passed by Lloyd's Register for a span of 80 feet. 378 The Naval Constructor DETAILS OF HEADS AND HEELS FOR PB?E STANCHIONS. SOLID HEADS AND HEELS FOR PIPE STANCHION8 t-T\** "?191'/2LB8. (.-v-HX---^ H-7" «j JL,J_ \ / 31s F& S3 (3 i-A-,742 LBS. (*_9t^_»i 5^-t iw K-12- 11-- -j le- W 1.±lU_: -*-.68VJ Lesr flap u r - -10 9 >4— «j —eiy S3 [0 yqr 1 I [j 49LB8 - Or r— iov£-h ILOtGS REQUIRE IHESi TO B£ FOD&EB AND WEEDED INTO P.IPE WITH A SUITABLE HAMMER TKEY MAY BC OlE'ORBED FuA SHIPS NOT CLASSED AT LLOYDS A STEEL CASTING. WILL BC MORE ECONOMICAL AND CO.UAILT fjff ItltNT.. 5? n NOTE: FOR STANDARD PIPE ELEMENTS. SET TABLE* Figs. 173 to 186. Hatches 379 Where pipe pillars are adopted, the accompanying diagram giving types of solid heads and feet will be found useful. It will be obvious that the hold pillars must be stronger than those in the lower 'tween decks, the sizes being gradually reduced as we approach the upper works, owing to the reduction in the load which the successive tiers of pillars support. As pillars are intended to take compressive stresses their relative strength with a given section is entirely in the end connections, and as the strongest of these is a fixed closely fitted flat end, this form should be adopted wherever possible. Where, however, it cannot be fitted, as on tank tops and with beams of section other than channel where no ridge bars are worked, care should be taken to fit closely the heads and heels on their supports, so that the load shall be taken on the column and not as a shearing stress on their fastenings, which should be relieved wherever possible of doing work. In larger vessels, ridge bars of channel section are fitted under the beams to distribute the load taken by the pillars over all the beams and also to prevent the beams from tripping. In wake of hatchways where pillars are omitted or are fewer in number, inter- costal plates are fitted between the beams and riveted to deck as compensation, thus forming a deck girder. When hold pillars are stepped on inner bottom plating, a short piece of tee bar must first be riveted to tank top and caulked, and the heel of pillar afterwards riveted to the vertical stem of tee bar. A similar arrangement is adopted on expansion trunk tops of oil steamers for heels of gangway stanchions. Where grain or other cargoes liable to shift are carried occasion- ally, the hold pillars may be staggered, the heads taking alternate flanges of the centre line ridge bar, thus providing an intervening space in which to fit the shifting boards. BATCHES. It will be seen that a serious loss in transverse strength is sus- tained by cutting the beams and decks to form hatchways, and it has been explained under the caption beams how this loss is com- pensated for in the deck framing and by increasing the sectional area of the side coaming plates. Hatchways should be no larger than the demands of the par- ticular trade call for, and the corners of these openings, at least on the strength deck, should be round. While it is cheaper to make them square, it will be found false economy. In addition to making them round on the strength deck the corners must be re- enforced with doubling plates extending about 2 frame spaces each way and carried 18 inches or so around the corners. The coam- 380 The Naval Constructor ing angle bar must be welded ; or a much better method is to run this bar to within nearly four feet of the corners around which another section Is fitted having a much broader flange on deck ; this will permit of staggering the rivets and so allow more space for sufficient riveting at the junction of this bar with the deck beam. No bosom piece need be fitted to cover the butt of the corner piece with the straight length of coaming an- gle, Fig. 187. End coaming plates should have "pitch" in preference to camber, as they are more easily made and allow of better fitting the wood hatch covers. The height of coamings on weather deck must be from 2 feet to 2 feet 6 inches, and on other decks from 9 to 12 inches, care being taken that sufficient height is given to permit of the hatch batten- I ^ STANDARD It j-2y"a---*| HATCH CLEAT DRILL FOR % DlA. CSK. RIVET Fig. 188. ing cleats being fitted. At butts of coaming plates the covering strap should be fitted on the outside and the rivets countersunk on both sides. A typical battening cleat is shown by Fig. 188. These may be either die forged or cast in steel and spaced not greater than 2 feet apart along the coaming plate, beginning about nine or ten Web Frames 381 inches from the corners and sufficiently far down to give an easy- fit for tarpaulin. The battening bar is of galvanized flat iron about 2£ x §", and the butts of same must not be at corners, the bar being bent round these to allow of fitting the canvas snugly. The tarpaulin is then secured by elm or oak wedges. The ledges on top of coamings are mostly made of a special rolled section as shown, although where this is not obtainable a zee bar will answer equally well. These ledges should be mitred at the corners and of sufficient depth to house the hatch covers. In addition to the support afforded these by the ledge bar, fore and afters must be fitted, as well as bridle beams, to tie the hatchway, in number and scantling as required by the classification societies. The fore and afters are supported by rests riveted inside the end coamings and the hatch beams by socket slides on the sides. The only other mountings re- quired on cargo hatches are a couple of lashing rings on each side fitted about four feet from the ends ; these may be riveted on coaming plate or deck at discretion. The wood covers should not exceed 24 inches in width, as other- wise they are too heavy, and are usually made of three pine deals, tie bolted with three g" diam. blind bolts. On the- right hand sides of top a lifting bar of iron through-fastened with two clench bolts is fitted, one at each end, and the wood drilled out about 5 inches in diameter to form a receptacle for the hand. These covers must have properly cut-in marks to facilitate replacing them. WEB FRAMES. Web, or, as they are sometimes called, belt, frames are commonly formed by fitting a plate from 15" to 30" deep to the ordinary ship's frame, and riveting an angle bar on the inner edge to stif- fen and add to the resistance of the web. They may be also built with double channel frames with a covering plate on face — an ad- vantageous method where increased room or stowage capacity is desired. Still another method is to fit frames and reverse bars of similar section of angles, webbing them as far apart as possible consistent with the requirements of the riveted overlap. These various methods of constructing web frames have all the same ob- ject in view, viz. : to give the equivalent compensatory transverse strength lost by omitting hold beams where large spaces are re- quired for the stowage of certain freights or in machinery spaces where hold beams cannot be fitted. It will be seen that these beams really perforin the function of struts tending to resist the 382 The Naval Constructor water pressures oif the ship's sides and the hold cargo ; and for this reason, as well as those already given, should have no camber which it is conceivable tends to weaken them. If the hold beams then be left out, the necessary resistance may be given by increas- ing the section modulus of the side framing, and this is obtained by adding webbed frames at stated intervals along the sides, and by the more uniform subdivision in a vertical direction of the areas enclosed, by side stringers fitted intercostally between webs having a covering plate at their intersection, of diamond or half- diamond shape. The side stringers should stand squarely to the ship's frame, thereby insuring the maximum moment of resistance from the material used, as well as avoiding much bevelling of angle bars. In addition to the foregoing, web frames are fitted wherever local losses in transverse strength take place, as at the sides of cargo doors and similar openings and over abrupt terminations of transverse strength, such as take place where a watertight bulk- head stops short of the strength deck. They are also necessary where exceptional local stresses of the nature indicated are applied. KEELSONS. The value of keelsons lies in their contribution to the lon- gitudinal strength of the structure, and, where they are fitted in conjunction with intercostal plates having a shell connec- tion, to the additional assistance given to the hull plating. In general practice it would seem that too much prominence is given to their strength as individual members rather than treating them as component members of the main structure, or ship itself viewed as a girder ; this is seen in the deep centre line keelsons fitted on top of ordinary floors; where continuous centre vertical plates are also fitted, the necessary efficiency and strength required locally may be obtained by thickening the lower parts of the member, as shown in Fig. 135, and at the same time increasing the moment of inertia of the ship's section as a whole about the neutral axis. nSide stringers should be treated similarly, as illustrated by the adjoining sketch, the web instead of one flange of the channel being fitted against the reverse frame, permitting of a better connection thereto, at the same time distributing the resistance to fluid pressures over a greater surface and adding appreciably to the stow- age capacity of the vessel. Where the plates forming side stringers are 18 inches (or over) wide, bracket plates must be fitted underneath to support and keep them standing to their work, except ' ' where webs are 8 feet apart. These brackets should be fitted midway between the web frames. Bulkheads 383 The practice of piercing watertight bulkheads with keelsons and stringers, and fitting angle collars around them to insure water- tightness, should be discouraged, as a much stronger member is ob- tained by cutting the keelson or stringer and connecting same by- bracket plates to the bulkhead. This method, besides, gives a more reliably watertight connection. In arranging keelsons or bottom longitudinals, these where pos- sible should be incorporated with engine foundation girders, or if this be impracticable, an efficient scarph should be made by con- tinuing them past one another for about three frame spaces before terminating. In ships of full form or where the flat of floor is carried well forward, additional intermediate longitudinals must be fitted locally, about half the depth of centre girder and connected to bottom plating to re-enforce the shell against " pounding." Keelsons, longitudinals, or side stringers should never terminate abruptly, but wherever practicable should be ended on and brack- eted to such supports as bulkheads, web frames, deep floors, etc. Care should also be taken to arrange the butts of these members clear of shell butts as well as " shifted " with one another. The rivets in the strap pieces should be developed to equal the strength of the member, and double shear value obtained in these connec- tions wherever possible. BULKHEADS. The steel divisional partitions, built in ships, called "bulkheads," were primarily fitted to isolate the living and machinery spaces from the cargo holds proper, but were soon recognized as having a more important mission in subdividing the ship into watertight compartments besides adding considerably to transverse strength. So that in later years it has become a canon in ship design that a vessel's bulkheads shall be in number and arrangement sufficient to keep the ship afloat with any two compartments open to the sea. Watertight bulkheads must always be carried to the deck above the load waterline, and in the case of the collision or fore- most one, to the weather deck, as the forepeak is the most liable to damage and flooding, producing a great alteration in trim. They may be plated either vertically or horizontally, and efficiently stiffened in accordance with the requirements of the classification societies' rules, observing in arranging stiffeners that these are placed on the reverse to the caulking side. In most yards the practice is to fit watertight bulkheads continuous from tank top to deck level, but it is considered better construction to fit the steel decks continuous and the bulkheads intercostally. As these steel partitions are connected to the ship's side by single 384 The Naval Constructor or double angle frames with closely spaced rivets in the sided flange, it will be seen that this line of perforations around the shell is a source of weakness. To compensate as far as possible for this, it is necessary to fit doubling plates, or "liners, 1 ' where practicable, i.e., in wake of the outside strakes of shell plating. These liners may extend from frame to frame, or, as is more often done, for a sufficient distance on each side of bulkhead, to take an- other row of rivets, observing that these holes need only be spaced for watertight riveting on the caulking side of bulkhead. Owing to the water pressures being greatest on the bottom, the plating is graded in thickness towards the top, and of course the section of stiffening bars is likewise reduced. The lower stiffeners require bracketing to tank top ; and in detailing the riveting of these brackets, it should be borne in mind that one arm takes tensile and the other shearing stresses. Watertight spacing is required for all riveting except stiffeners and their connections. Where web frames or deep framing is substituted for hold beams, additional horizontal stiffening must be given the bulkheads at the level at which the lower deck would ordinarily support the bulkhead, and in addition a deep centre line web fitted. Generally it will be found convenient to arrange for the caulk- ing side of bulkhead to be that side on which the open bevel frame shows, that is, the after side in fore-body bulkheads, and the forward side in after-body bulkheads. There are exceptions, however, to this rule which will suggest themselves in considering deep tank and peak water tests. As, of course, it is only necessary to caulk one side of the bulkhead, the stiffening bars should be arranged on the opposite side. Where stiffening bars, especially angles, are exposed in cargo holds or between deck spaces, their sharp edges must be protected by fitting wood chafing pieces projecting about an inch and a half beyond the toe of bar and bolted to the stiffening flange. SHELL PLATING. The skin of the ship when constructed of steel is almost invari- ably arranged in fore and aft strakes " in " and " out " alternately. For the reasons given when treating on keels, the flat plate should be fitted as an " in " strake, so also should the sheerstrake except in large steamers where a doubling is required. For fitting and shoring purposes, it is an advantage to fit the bilge strake " inside," as well as strakes adjoining longitudinals. In laying off the widths of strake on the midship section, it will facilitate interchangeability of individual plates if all strakes of the same thickness are made similar in width. It will also be found advantageous to work the bilge strake narrower than the Shell Platini 385 others where an odd size is unavoidable. In moderate sized Vessels the outside strakes are usually from 40 to 46 inches wide, and the inside ones 48 to 54 inches, but in the largest ships it will be good practice to increase these widths, although by so doing increased riveting of butts will be necessary. On the other hand, when dealing with small vessels or light scantling craft narrower plates should be worked. The widths having been arranged satisfactorily on the midship section, should now be transferred to a body plan and run in to the PLATE LINES Fig. 191. eye as shown by Fig. 191, observing that in the fore body above the waterline the widths are kept parallel, which necessitates working stealers in the under- water body at the fore end. Kun- ning these plate widths parallel gives a straight, sharp appearance to the sight edges, a very important point when lining off a very full ship, as otherwise the rounding up lines developed would ssr, The Naval Constructor Fig. 192. Shell Plating 387 accentuate and exaggerate the bluff lines. In addition it enables us to work the narrow plates where the form is most difficult to work. In the after body different conditions exist, the most important plate line being that which ends at the oxter, so that it is only necessary to divide the space intervening between that point and the sheer strake into the number of strakes obtaining amidships. The ending of a plate-line in the oxter is advisable to obtain all the furnacing and difficult work on one plate only. Having run the plate lines on body plan to fulfil the foregoing conditions, these may then be taken off and faired up on the model. If it be found that one of the landings crosses the continuous angle of tank margin plate or watertight flat, the line must be stopped abruptly near the point of intersection and "jogged" across for a sufficient distance before resuming its flight. Before any butts whatever are laid off, either for stringers or shell plating, a small diagram should be drawn giving the general scheme for the shift of butts which will enable the various structu- ral plans to proceed simultaneously and independently. No butts on adjacent strakes should be placed nearer one another than two frame spaces, or one frame space where a strake intervenes. The ideal shift of butts, however, is that which shall have not more than one shell butt in any one frame space from keel to gunwale. After the shell plate butts have been arranged, those of stringers, longitudinals, keelsons, etc., may be set off in the best positions in relation to shell. Such plates as require furnacing should be arranged as short as possible, the most difficult of these being the "hip " plate on the quarters, oxter plate, boss plate, the "breeches " plate taking stern frame and plate keel, and the similar plate of spoon form forward adjoining the stem. In some forms of vessels it is also advisable to make a short plate of those having double set at fore and after ends of bilge where the latter begins to curve into the entrance and run of vessel respectively. A scheme of butts such as the one suggested is shown by the accompanying diagram, Fig. 192. The "landings," as the edge overlaps of the in and out strakes of plating are called, should be of the width necessary to take the required size of rivets, which must be spaced for watertight work, i.e., 4 to 4^ diameters apart, observing that where double riveting is employed a single rivet only should be inserted at the closing, or caulking edge, in wake of all frames. In yacht construction where a perfectly smooth topside is desired, the plating is often arranged edge-butt fashion with an inside continuous seam-strap — a more expensive and less efficient method than the other, and adopted solely for appearance. In small moderate sized vessels the garboard and sheerstrake 388 The Naval Constructor landings only are double riveted, but in large vessels all of the landings should be provided with two rows; and where exceptional local loads are carried, as in deep tanks, or in vessels above 480 feet in length, M the lauding edges should be treble riveted for one fourth of the vessel's length in the fore and after bodies for a depth of one third the vessel's depth." Vessels slightly under this dimension may have double riveted landings with an additional rivet added in each frame space within the zone mentioned. Where a change is made from a treble to a double, or from double to single riveted landings, the taper must of course be made on the inside or hidden edge, and should extend over a frame space. Individual plates of strakes should be fitted in as long lengths as the steel makers' limits allow, or the facilities of the particular yard permit, consistent always with good practice. The old method of fitting these with edge-butts having an inside covering strap has been almost entirely superseded by overlapping the plates, a stronger and more enduring method. There are some strakes and special cases, however, where it is still advisable to retain the- edge-butt connection, as in flat plate keels, sheerstrakes and the strake in wake of bilge keels, as by this means we get a closer fit- ting for keel angles, stringer bars and mouldings and bilge bars, elim- inating unsightly work, trouble and the expense of fitting liners. Where the overlapped landing of an outside strake crosses the buttlap of the adjacent inside strake, it will readily be seen that a small wedge-shaped space is formed. To close this up and so ob- tain the necessary watertightness, it is customary to scarph the corner of the overlap, allowing it to be drawn home. In wake of the outside strake overlaps, where they adjoin the inside landing edge, planing is impracticable, and, as a similar wedge-shaped aperture interferes here also with watertightness, this is secured by fitting a tapered liner long enough to take three rivets. A similar tapering away of the outside landing edge is performed where the strakes end on stem and stern post, thus giving the ap- pearance of one flush thickness at these parts. Wherever the shell plating is cut to form cargo doors, coal chutes, sea connections, sidelights, etc., compensation must be given for the loss in strength sustained. More especially is this imperative where these openings occur amidships through the sheerstrake, as it is then obvious that the strength is reduced to a maximum, being at the extreme fibres and where the greatest bending moments are produced. To avoid abrupt discontinuities as much as possible, the corners of all such holes where not circu- lar should have a bold radius, and in addition kept well clear of butts. In addition, doubling plates must be fitted, observing that these should be over the openings and encircling the upper stresses acting on the upper corners, as the stresses acting on the upper Detail Fittings 389 works which need resisting most are tensile. Where sidelights are cut through the sheerstrake, compensation may be given by slightly increasing this strake in thickness or by fitting compensat- ing angle-bars over the openings. The shell plating, as will be seen, really forms, in conjunction with the strength deck, the sides and bottom and top members re- spectively of the ship viewed as a box girder. For this reason the parts taking the greatest stresses are those at the greatest distance from the neutral axis ; and as a ship is not always in the upright position in a seaway, it will be evident that these parts are the sheerstrake, bottom and bilges. Thus the classification societies stipulate for thicker plating at these parts. As the greatest bend- ing moments are exerted amidships, diminishing towards the ends, they require that the maximum thickness shall be retained for a quarter of the vessel's length before and abaft the dead flat frame. There are, however, certain localities beyond these limits where the midship thickness must be maintained if not increased where abnormal local conditions demand it. Conditions such as are re- ferred to exist at the ends of plates adjoining the stern frame, where, besides making the connection to a heavy forging requir- ing very large rivets, excessive vibration of a fatiguing nature is encountered ; and at the bossed plating, oxter and hip plates re- quiring furnacing and much consequent hammering, where a se- rious reduction in the original thickness takes place in addition to the distress to the plate consequent on the treatment to which it is subjected. Also doubling or increased thickness must be pro- vided at abrupt breaks in the longitudinal strength, as at ends of poops or bridge deck superstructures, in wake of hawse pipes, etc., and at other points which present themselves and will be evident to the observant. DETAILS. FITTINGS. Only next in importance to the structural details are the deck and other fittings, on which the convenient and safe handling of the ship depends. These in many cases do not receive that consid- eration which their importance merits. Instead of being calcu- lated on a rational basis and designed accordingly, ship fittings are too often left to the guesswork of the technically untrained, with the result that we often find in these fittings a wide variation in the scantlings employed for a given duty even amongst like fittings on the same ship where different sizes are used. With the object, then, of proportioning these fittings from a rational unit and standardizing them, the following tables of fit- ting details have been prepared or collected. The basis on which the unit is founded is in many cases given, enabling the expe- 390 The Naval Constructor Bill of Material 391 rienced to determine for themselves what variation may safely be made where fittings are being designed for special work. In the preparation of details it will be found to contribute much to their elucidation if a " fitting list " or "bill of material" be added alongside the detail delineated, and each and every part of the fitting given a special " piece number." The number plan of the general arrangement on which the details are assembled should likewise be given, and of course these piece numbers in- dicated on this assembly drawing for identification. The piece numbers will also prove helpful as reference numbers in discus- sions or correspondence relating to the particular fitting. The adjoining specimen plate, with its accompanying bill of mate- rial, has been prepared to illustrate the method advocated. BILL OF MATERIAL FOR ONE BOAT. 9 1 .g i H U % 6 So Name. 44 ft. 6 Pat. 79 Socket M.C.I. 86-370 12 7 Die 670 Rail stanchion .... W.I. «< 70 8 " 673 " " W.I. " 26 yd. 12 Safety chain Red metal 1 I " 12 23 Pat. 103 Thumb screw .... Comp. N. " 43 42 Screw eye Brass ^ £ M 56 as Die 685 Eye bolt W.I. " 28 94 1" W. I. gas pipe sleeve, W.I. *s « 58 96 \" split pin W.I. (galv'd.) ^ X M 74 96 Die 691 Eye in end of rail . . . W.I. e (t 810 ft. 97 \\" rod (top rail) . . . W.I. - 2,365 " 98 1" rod (middle and lower) W.I. » 88 170 l£" tap bolt W.I. " 86 171 Die 675 Rail stanchion .... W.I. " 44 172 " 676 it <« W.I. " 392 The Naval Constructor STANDARD HATCHING FOR VARIOUS MATERIALS. CELLULOSE GLA88 ^J%jJ ^^^^ «^ RED GREEN & WHITE U.S. *mm **&Z6 YELLOW, BROWN 4 GREEN Figs. 194-211. Graphic Division of One Inch 393 GRAPHIC DIVISION OF ONE INCH. 1 INCH DIVIDED INTO STEEL PLATE* LBS. PER SQ. FT. 16™§ 2QIH8 32 NDS. 4QTHS MILLIMETERS. IRON PLATES LBS. PER SQ. FT. 40.80 16 20 32 40 40 38/76 - - — — — 25 — 24 t 38 38 1 14 18 36.72 36 36 - 28 - -" 22 34.68 - 34 34 | ~" * 16 32.64 32 " 20 32 12 — — - 30.60 - 24 - 30 30 - 14 — — 28.56 28 18 28 26 52 26 10 — 20 — ~ 16 24.48 12 _ _ 24 24 L - " 14 22.44 22 22 8 10 — -L 20.40 - 16 - 20 20 O - — — - 12 z 18.36 - 14 - 18 18 8 16.32 6 — 16 — 10 16 - 12 - 14.28 — — 1 14 14 6 - 10 - — 8 12.24 12 12 4 — — - 10.20 — 8 — 10 ' 6 10 — — - 8.16 4 — 6 — 8 8 2 - - 6.12 6 4 6 - 4 " — 4.08 2 — — 4 4 1 ~~ 1 2 2.04 2 1 2 1.02 - - 1 " 1 1 — — — V 394 The Naval Constructor BALDT ANCHOR. Fig. 212. Dimensions of Baldt Stockless Anchors 395 DIMENSIONS OF BALDT STOCKLESS ANCHORS. (Cast Steel.) Weight in Pounds. Lbs. 5,600 5,400 4,760 2,940 1,820 1,680 840 A n 23 23 21J 20 171 I64 14 B 16 16 m 14 10 J 101 9 C 10 10 10 »i 6 6 4f D w H 81 8£ 7* n 51 E n n «i 6| JH 41f 5ft F 9 9 9 9 8 8 4i G 60 60 56J 504 44 4 41 331 H 35 35 334 30J 25 | 251 20 I 53 63 51f 45f 37 J 37 f 30 | J 161 16| m 13J 10 | 10 f 8| K 12 12 llf 8f 7 7 6 L 5| 5f H 5 81 8f 3 M 7 7 H 6 44 44 3& N 23| 23J 21i 20 15 4 15 4 121 2| n 3 24 24 If If P iei 16| 16J 151 114 114 91 Q 6 6 H 5 *J 44 3 B 72 72 72 66 54 54 40 s 8| 8! 8| n n 61 4 T V T 10 10 9| H 6« 6f 54 IT 5 5 5 4 3 3 2| V 6 6 51 4| 31 8| 3 W 18 18 17 16 12 12 »4 X 9 9 8f 8 61 61 5 Y 6f n n 6| 61 51 34 Z CWT. 8 8 n 7 n 51 4§ 50 48| m 26J 161 15 74 396 The Naval Constructor HALL ANCHOR. Dimensions of Hall Anchors 39' DIMENSIONS- OF HALL ANCHORS. °^ . Hog life II 1 ii H ii ii II II i % II S II li 165 3.07 1.93 4.92 1.26 2.64 29.53 14.76 3.62 7.36 10.47 4.06 2.20 220 3.39 2.09 5.43 1.38 2.91 32.52 16.26 3.98 8.11 11.54 4.49 2.44 330 3.86 2.36 6.18 1.57 3.31 37.05 18.54 4.53 9.25 13.15 5.12 2.80 440 4.25 2.64 6.81 1.73 3.66 40.00 20.43 5.00 10.20 14.49 5.63 3.07 550 4.61 2.87 7.36 1.89 3.94 40.28 22.13 5.43 11.06 15.71 6.10 3.31 660 4.88 3.03 7.80 2.00 4.17 46.90 23.47 5.75 11.73 16.65 6.46 3.50 880 5.35 3.35 8.54 2.20 4.61 51.42 25.71 6.30 12.87 18.27 7.09 3.86 1,100 5.79 3.58 9.25 2.40 4.96 55.63 27.80 6.81 13.90 19.72 7.68 4.17 1,320 6.14 3.82 9.80 2.52 5.28 59.02 29.40 7.24 14.76 20.95 8.11 4.41 1,540 6.46 4.02 10.32 2.68 5.55 62.02 30.91 7.60 15.51 22.00 8.54 4.65 1,765 6.77 4.21 10.83 2.80 5.79 65.04 32.52 7.95 16.26 23.11 8.98 4.88 1,985 7.05 4.37 11.26 2.91 6.02 67.68 33.86 8.27 16.93 24.06 9.33 5.12 2,200 7.28 4.53 11.65 2.99" 6.26 69.96 35.00 8.58 17.48 24.88 9.65 5.28 2,760 7.83 4.88 12.56 3.23 6.73 75.28 37.64 9.21 18.82 26.73 10.35 5.67 3,310 8.35 5.20 13.35 3.43 7.17 80.16 40.42 9.80 20.04 28.54 11.02 6.02 3,860 8.78 5.47 14.06 3.62 7.52 84.33 42.50 10.35 21.06 29.96 11.61 6.34 4,410 9.17 5.71 14.69 3.78 7.87 88.47 44.39 10.79 22.00 31.30 12.13 6.65 4,960 9.53 5.95 15.24 3.94 8.15 91.54 46.09 11.22 22.87 32.52 12.60 6.89 5,510 9.88 6.14 15.79 4.06 8.46 94.92 47.82 11.61 23.74 33.70 13.07 7.13 6,610 10.51 6.54 16.81 4.33 9.02 100.99 50.81 12.36 25.24 35.87 13.90 7.60 7,720 11.06 6.89 17.68 4.57 9.49 106.26 53.49 13.03 26.58 37.76 14.65 7.95 8,820 11.58 7.20 18.50 4.76 9.92 111.30 55.93 13.62 27.80 39.83 15.32 8.35 9,920 12.00 7.48 19.21 4.96 10.28 115.36 58.02 14.13 28.82 41.32 15.91 8.66 11,020 12.44 7.76 19.88 5.12 10.67 120.28 60.06 14.65 29.88 42.78 16.46 8.98 13,230 13.23 8.23 21.14 5.43 11.34 127.09 63.88 15.55 31.77 45.46 17.52 9.57 398 The Naval Constructor ADMIRAL ANCHOR. Admiral Anchor ADMIRAL ANCHOR. 399 9,240 7,840 3,080 1,340 6,104 5,180 1,792 910 / // / /' / // / // / n / // / // / // A 8 59 4 6 3 6J 5 5 4 11 3 64 3 1 B 2 9 27 1 11 1 8 2 5 2 14 1 8. 1 6. C 2 4 22 1 6 1 3 2 1 84 1 3 1 1 D 1 10 1 8 1 2$ l 14 1 54 1 4 Hi m F 1 4 13 OlOf 8J 1 1 114 O84 74 G 1 2 1 1 9 7J 1 10J 74 64 H 4 8 44 3 2i 2 6i 3 llj 3 6J 2 6i 2 3 I 1 8 16 i i'i Oil 1 44 1 3 11 94 J 12 8J 117$ 8 6 4 9 8 9 6 7 4i 5 6 K 48 45 3 4 2 7| 4 1 3 8J 2 7J 2 34 L 22 20 1 6 1 2i 1 94 1 9 124 1 i M 07 00 4J 31 54 51 04 3J N 13 1 1 9 74 11 OlOf 73 6§ 08 7J 5J 41 64 6 44 3J P 4i 04 3 0' 24 3| 34 2f 2 Q 10 2 96 8 84 5 3f 8 3 8 64 4 6J R 8i 7i 6 41 7 64 05 41 S 7J 6^ 5 41 6 61 44 3| 400 The Naval Constructor INGLEFIELD ANCHOR. Unit A" = .5693 yj W, where W= weight in lbs. ^^& — k ^§^ r A = unit in inches. 5 = 9.5 A, (7=2.5 A. J) =1.25 A. E=z .6 A. F= .37 A. O = 2.24 A. H= .624 A. / = .773 A. K= .70 A. L= .50 ^4. Jf= .85 A. Fig. 215. Number of Deck Bolts 401 3 - a % 1 \ ^_, £ M 3 \ fe 8 ^S8S8^S CO rti ^ iO iO «D ' S- M o g 5*3 (N^iOCOOONNCOHOO HMTjtiOHHCONIMN NHHH(DiONOiOO - lO 0>0(N ooonoow; i S©iO©"*OOOOC5© (MtJHiOOOI^i-iCOOQO rHCO00»OO>CONO5CON 8£2: (NOiiOCOt^.^T-(OOOiCO C<1 i-l t-I i-l T-H HCOINiOOHOH^N NOfOWHOOJOONCi Compression on the jib: — QXf + QiXh Cm If arrangement cf blocks as shown, then Qi = Q In calculating the dimensions of the crane post the load on the hoisting rope = Qi applied at the foot block, usually fitted to a wrought iron ring around the post, has to be taken into account. Note that this block should be placed as low as pos- sible to reduce the stresses on the post. The shearing stresses at A : The shearing stresses at B: Pi = QXf + QrXb P 2 = QXf + Qi(a+b) Anchor Crane Stresses 403 Now that the forces in all the points A, B, C, D and E are known the bending moment in way of each one has to be figured out. As for T and C, bending stresses will be produced only from the horizontal components T x = T X cos a. and C\ = C X cos /?, while of the vertical com- ponents Ti and C 2 equal to T X sin a and C X cos respec- tively. T 2 will subject the post to tension on the part DE, while C 2 — T 2 will act as a compres- sive load between A and D. As the forces keep the crane in equilibrium, it will be seen that: Pi + Qi + T x must equal P 2 + C x . Bending moment at A, M a = 0. Bending moment at B, Mp = Pi X a. Bending moment at C, M c = Pi = Pi (a + b) — P 2 X b. Bending moment at D, Ma - Pi (a + b + c) - P 2 (b + c) + Qi X C, or also M d = Ti X d. Diagram of Bending Moments. — Along the vertical lines at B, C and D set off at any scale the bending moments as found above, and join the points as shown on sketch. From this dia- gram the moment Mx at any intermediate point may be scaled. Graphic Method to Determine T and S. — The on the different members of the crane may be conveniently found j by graphic construction, and in most cases the result thus obtained is suf- ficiently accurate for practical pur- Take at any scale the vertical line ab to represent the load Qi draw be parallel to the direction of the hoisting rope and equal to Qi. The dotted line will therefore represent their re- sultant, and drawing ad and cd par- allel respectively to DF and EF, these lines will represent the stresses on jib and tierods. From d and c draw horizontally the lines de and cf, and from d vertically the line df. Then we get de = Ti = TX cos a, Fig. 218. 404 The Naval Constructor and cf m Ci «= CX cos a. Further ae = T t = T X sin a and d/= d = C X sin a, the difference between these equal to fg repre- senting the compression on the lower part of the post. For getting out the shearing stress Pi draw on a sketch of the crane a vertical line through F meeting the horizontal line from B at U, then draw AG and make AH at any scale equal to Q. Then HK will represent the shearing at A produced by Q x . Draw Ah horizontally and equal to BC and make AM equal to Qi. If then from M a line is drawn parallel to BL the total shearing stress at A will be represented by HK -\-AN. LNA Calculation of Strength. — In figuring the dimensions of the different members in the anchor crane it is advisable not to use Fia. 219. a factor of safety less than 6, which for ordi- nary wrought steel means a stress of material = 10,000 pounds per square inch, especially if the weight of the crane itself is omitted in the calculation. Based upon a factor of safety = 6, the following formulae are derived : — For the tierods, d = 0.08 VT where d = diameter in inches and T = tension on tierods, two. of which are supposed to be fitted. For the jib, if solid circular section is being used, d = 0.026 v'CZ 2 where d = diameter in inches, C = compression on jib and I = length of jib. For the cranepost, if solid circular section is being used, d = 0.1 ^/M where d = diameter in inches, and M, = bending moment in inch-pounds. In this latter formula the stress of material is assumed equal to 9500 pounds as against 10,000 pounds in the former ones to compensate for the stress produced by the compressive load (Cj — T2) which is not included in the calculation. Mitre and Bevel Gears 405 FORMULAS FOR LAYING OUT BEVEL AND MITRE GEAR BLANKS. Bevel Geara. Planed or Cast Mitre Geara. . Planed or Cast | /f. Fig. 220. Formulas for Bevel Gears. Y = No. of teeth in pinion. YP D = — = 0.318 YP. IT Y D Tan£ = ^- = g>. B = D + (0.636 P cos S). 0.318 P K _ 2 cos^ H H Y 0.368P ^L 2.314 cosy H H Y = S + E. A=S-R. M = ~- (0.318 P sin £). iV = itf -FcosO. P = circular pitch. Y' = no. of teeth in gear. D' = — = o.3i8 yp; y = 90° - y IT B' = D' + (0.636 P cosy). Tan# TanP M' -FcosO'. D 2 cosy' 406 The Naval Constructor K = 0.318 P; L = 0.368 P. 0' = S' + E; A =S -R. When to be cast K = 0.3 P. L = 0.4 P. M'=^ - (0.318 P sin 5'). Formulas for Mitre Gears. P = circular pitch. N = number of teeth. ATP D = 0.318 iVP = —- IT B = D + (0.636 P sin 45°) = D + 0.449 P. A = 45° - S. TWQ „ ' ^ . 0368P lMfl I ; DX 0.707 £ = 45° + C. . TanC = £ 0318P # D X 0.707 M = | - (sin 45° X 0.318 P) = ^ - 0.224 P, = M- (FcosE). H = D x 0.707. L = 0.368 P; K = 0.318 P (when cast L = 0.4P; X = 0.3P). NAVAL ANCHOR CRANE. Fibre Stresses. Crane Post at Forecastle Deck. — Bending moment Wl = 3,260,000 in.-lbs. Diameter D = 16§ ins. Fibre stress = /. — D* 64 7T Moment of resistance = / — jr— =f — D 3 , Naval Anchor Crane 407 WIV = 3,260^00X32 _ ^ ^ sq fe tD 3 7r X 16.5 3 At A: Wl - 2,405,000 in.-lbs., D = 16| ins. ,_ ^2 . 2^5,000X32 = 54601bs . pers , in . AtB: Wl = 1,577,000 in.-lbs., Z) = 13.25 ins. ; W132 1,577,000X32 „ mnlu * = "ST " y XlS.25» = 691 ° lb8 ' PCT Sq - m - AtC: WZ = 1,150,000 in.-lbs., D = 11.6 ins. AtD: WZ = 725,000 in.-lbs., D = 9.95 ins. . W7 32 725,000 X 32 -_ nn .. * = ^ST = xX 9.953 =7500 lbs. per sq. m. At#: W = 300,000 in.-lbs., D = 8.25 ins. ' WIZ2 300,000X32 - AKtlfU / = -T= r x 8.253 = 545 ° lbs ' per Sq - m - Jib. — Total compression on jib - P = 80,000 lbs. + 3500 lbs. = 83,500 lbs. 8-inch extra strong pipe, outside diameter D = 8.625 ins., inside diameter d = 7.625 ins. Modulus of elasticity E = 25,000,000. Moment of inertia / = ^ (D 4 -d 4 ) = ^ (8.625 4 - 7.625) 4 = 106. Length I = 189 ins. Coefficient of safety = n. e! EI > = * 2E ' l = 2 x 25 >ooo>ooo x 106 = o P " n ' I 2 ' n P-l 2 83,500 X 189 2 = 408' The Naval Constructor DIAGRAM OF STRESSES AND BENDING MOMENTS ON ANCHOR CRANE. img foments on Vertical Bending Moments onSpreai 1-IOQOOOinLbs. WOO* Bending Momenta „ onPost C-lOO00OOinLbs MainDech. / Fig. 221. Anchor Crane Stresses 409 Area of section = 12.7 sq. ins. Fibre stress - ^^ = 6580 lbs. per sq. in. Tie Rods. — Diameter = 2\ ins., tension on one tie rod - 24,250 ins. 24,250 fiCQft « Fibre stress = 2125 2 Xt = 6830 lbs ' Spreader. — Section at hub of spreader. Moment of inertia for axis x-x\ = l x = 2267, Z£= ?267 =252. C x 9 Bending moment for axis x - x: = 507,000 in.-lbs. Fibre stress/, = ^~ = 2010 lbs. per sq. in. Moment of inertia for axis y - y: ~ h = 1 86 > h = i?| = 41.3. X „.. Cy 4.5 ^ ,^_ Bending moment for axis y - y = 200,000 -,-r | in.-lbs. Y-H^ . 200,000 Fibre stress f v = 41 3 \<--l&'- A = 4830 lbs. per sq. in. Fjq m Area of section = 49.5 sq. ins. Compression, 18,800 lbs. Fibre stress f c = i^5 = 380 lbs. per sq. in. Total fibre stress /»+/»+/*- 2010 + 4830 + 380 - 7220 lbs. per sq. in. Section 18 ins. from hub. I x 701_ 112 A. 410 The Naval Constructor Bending moment for axisz — x = 267,000 in.-lbs x _.. 267,000 Fibre stress/* 112 = 2380 lbs. per sq. in., ■**t!P^j*CjH"f* Bending moment for axis y —y = 91,000 in.-lbs. /«_"*_„.,. Fia. 223. Fibre stress f v = q =4150 lbs. per sq. in. Area of section 33.8 sq. ins. Compression, 18,800 lbs. 18 800 Fibre stress f c = ' = 560 lbs. per sq. in. 00.8 Total fibre stress = f x +f y +/ c = 2390 + 4150 + 560 = 7100 lbs. per sq. in. Tie Rod Heel Pin. — Pin considered as beam uniformly loaded and fixed at ends. 8 ; 32 Tension on one tie rod P = 24,250 lbs. r*#a /- PI 32 24,250 X 5.5 X 32 8ttZ) 3 8XttX2.875 3 = 7150 lbs. per sq. in. VJ4i -O-l y Fia. 224. ^fe£ * I 1 -U *1H ¥ J/pJedef 2PT3 Fig. 225. Tie Rod Eye Pin. — Figured as tie rod hub pin. 8 J 32 ' PZ 32 45,800 X 7.5 X 32 J 8irD* 8XttX4 s = 7240 lbs. per sq. in. Dimensions of Anchor Cranes DIMENSIONS OF ANCHOR CRANES. 411 « s a One Two H One Two 2|?g * X Tie Tie Jib. 2*?V H H g Tie Tie Jib. H.2 Jift 02 P3 Rod. Rods. EC * Rod. Rods. Foot- cwts. Dia. Dia. Dia. each. Dia. mid- dle. Foot- cwts. Dia. Dia. Dia. each. Dia. mid- dle. 180 6 If hy 3 540 8f 2§ If fl 200 9k " 550 220 6j If If 31 560 " " " 225 585 9 2 k 1« It 240 6f M " " 600 »• 250 " " « 605 " " i< 260 ♦' " M M 630 91 " ii 270 7 2 l i 3 t t 650 " " 275 " " 660 M " " 280 " " " M 675 9* n 2 4* 295 71 " " H 700 u 300 M " 11 715 M " «• 325 M " M " 720 it <( '« 330 n v\ Ij[b 3J 750 9| " " 350 " 770 «« " 360 »< " " " 780 » u •« 375 7f m " M 825 10 2f If* 5 385 " M " 840 " it 390 " " " M 900 10i " « 400 u «« " " 1,000 10J n 2* 51 405 8 % \t 4 1,100 10| 420 u M 1,200 ioa " " 440 " " . " " 1,300 11 3 n 5 i 450 81 " u " 1,400 11* 455 " " " 1,500 ni " " 480 " " " M 1,600 n| H 2| 5f 490 " " " " 1,700 nf 495 8* 21 ij 41 1,800 iif H 2 i 9 500 " 1,900 n| 525 2,000 12 3| 6 412 The Naval Constructor NOTES ON ANCHOR CRANES. The most suitable radius of crane to efficiently fish the anchor having been determined, this dimension in feet multiplied by the weight of anchor including stock, will give the moment in foot- cwts. , to which reference must be made for the corresponding sizes of parts. N.B. — These cranes are in accordance with Lloyd's require- ments per Table 12, but for convenience the moment is given, which will be found much easier of application, and the table has been extended to deal with the heaviest anchors. Of course where the ship is not classed to Lloyd's, the crane should be figured out with a factor of safety of eight, when it will be_ found that the sizes in this table, being empirical, may be con- siderably reduced. The heavier sizes of cranes may with economy be built up with structural sections, or the post and jib may be formed with angle sections having lattice bracing. It will also be found more economical to step the crane post or anchor deck in preference to housing it and making it revolve with the jib. Bronze Ship's Bell 413 BRONZE SHIP'S BELL. Copper 13, Tin 4 parts. Directions for Laying Out. — Divide diameter of bell into 24 parts. \ i \ \\ SHIP'S BELL. Fig. 226. Then AD — 6 parts. 6 — A =11 parts. DB - 14 " A-4 = 4. " B-S=U " P~Q= T Vdiam. B-R=U " Rad. K= 3 J parts. C-c = \ " ^4-8=8 m c — 6 = 5f " Thickness at 8 = 1 part. 6-s = 11 " Arc ^4 — (t, drawn with rad. of 3£ parts from K, wherever that may fall, the rest of curve laid in by hand. Rad. of crown 17 parts may be 16£ to 19; thickness of bell at B, | parts = waist, sound bow = -^ diam. = QP. Part of bell above bis. laid in as a cylinder. 41i The Naval Constructor WEIGHT OF BRONZE SHIPS BELLS. Diameter of Mouth in Inches. W'lKiHT IN Poinds. Diameter of Mouth in Inches. Weight i\ POUM.s. 3 7 8 9 10 11 12 13 14 6 8 10 15 18 22 26 38 55 15 16 17 18 19 20 • 21 22 65 75 100 125 . 156 178 204 231 Note. — Weights given are exclusive of hangers or belfry. BELAY PINS. Fig. 227. Size of A. R. C. 7). z:. .P. rp. Pin. n n n // // n a a \ 4 5 I ItV ft \\ 1 1 4* 6 H J* tt n 1 * 5 7 l If H ifV H I H 8 *A *l *$ ItV H 1 6 9 n Hi lS n if n m 10 i* H ifV H 2 if 3 11 jA 2 ItV if 21 i* 8 12 If 2* ItV i* «] i| 8i 13 H 2| IfV 1H 2| Balanced Armor Hatch 415 Scale of Diagram Iff. Scale of zlnche* , Of 2-5 4 5 6 7 S 9 K> II aftaaKKWfl BALANCED ARMOR HATCH. Fig. 228. 416 The Naval Constructor BALANCED ARMORED HATCH. Determination of Counterweight. — Weight of hatch and fittings complete Wi = 540 lbs. Center of gravity of hatch from hinge pin 20 ins. Lift applied on handle to start: L = 30 lbs. Moment of hatch about hinge pin Wi X 20 = 540 X 20 = 10,800 in.-lbs. Deduct: applied lifting moment L X 36*" = 30 X 36*" = 1,095 in.-lbs. Resulting moment about hinge = 9,705 in.-lbs. 9705 Pressure on roller Pi = sr" = 373 lbs. Jo Moments about centre of upper gear segment: — 373 X 24.8 = P 2 X 5.375 ins. *=;^ 8 -»■» + 15 per cent for friction in teeth and bearings 258 lbs. Total load on teeth = 1980 lbs. Moments about centre of lower gear segment: — 1980 X 5.75" = W 2 X 33.5", ^ 2 = oT^~ — = 340 lbs. = weight of counterweight. oo.o Strength of Teeth for Gear Segments. — Lewis formula: — W = s. p. f. y., p = pitch, W - load on teeth = 1980 lbs., / = face = 2 p, s = 8000 lbs. per sq. in. (man- y = coefficient = 0.1, ganese bronze), 1980 = 8000 X p X 2 p X 0.1, V = 1.13", say H" pitch, 2\" face. 8000 X 2 X 0.1 Strength of Upper Shaft. — Distance between bearings ab0Ut 8 "' 1730 X 8 Maximum bending moment Mb = 5 = 1730 in.-lbs. o Maximum twisting moment M t = 1730 X 5.375 = 9300 in.-lbs. Equivalent bending moment M = 0.35 Mb + 0.65 M t = 0.35 X 1730 + 0.65 X 9300 = 6650 in.-lbs. M = ^d*Xf; /= 10,000 lbs. per sq. in., .. 1 n nfm = 1.9", make 2" to allow for keyways, etc. n"X 1U.UUU ■7 Ship's Bollards 417 SHIPS BOLLARDS (STANDARD). Bollards are invariably made of cast iron of good quality, and should be fairly smooth castings. In small yacht and high class work they are sometimes made of gunmetal, and in battleships of steel. The bolt holes should not be cored but drilled and counter- sunk afterwards, the bolts being of BB iron or steel with full countersunk heads. The diameter B of the barrel should be in accordance with the sizes given in the table, opposite the corresponding length of vessel, and with this dimension as a unit the proportionate sizes of the various parts calculated from the appended proportion table and diagram : Diameter of bollard B=\. Centres C = 2.83 Height H=1.77 Length £ = 5.22 Width of base W=1.50 Ends #=1.20 Diameter of top D=1.16 Depth of ridge R= .33 Thickness of base T= .17 Thickness of side S = . 12 Moulding at top M= .1(5 418 The Naval Constructor STANDARD BOLLARDS 3 C r^ 1 i 1 i r c J i- ! f — UNIT V X 1 1 ) ■\ : 1 — ^_ } K 1 Pig. 229. *i TABLE OF BOLLARDS (Cast Iron). Length OF Ship. Dimen- sion B. Approxi- mate Weight. Length of Ship. Dimen- sion B. Appboxi- M a I !•: Weight. Ft. Ins. Lbs. Ft. Jus. Lbs. 60 3 40 420 13V 1,710 80 3§ 50 440 14 1,900 100 4 60 460 141 2,100 110 H 72 480 15 2,310 120 5 85 500 151 2,525 140 5} 110 520 16 2,750 160 6 145 540 161 3,000 170 6} 185 560 17 3,250 180 7 235 580 171 3,540 190 n 295 600 38 3,850 200 8 360 620 18} 4,140 210 8| 430 640 19 4,440 220 9 • 510 660 19V 4,810 240 n 605 680 20 5,160 280 10 700 700 20J 5,560 300 10J 815 720 21 5,960 320 11 935 740 211 6,390 340 11* 1,070 760 22 6,780 360 12 1,210 780 221 7,240 380 12* 1,375 800 23 7,660 400 13 1,530 850 24 8,560 N.B. —The extra heavy bollards on forecastle head and quarters should be J larger than given in table for the corresponding length of ship. Wire Rope Snatch Blocks 419 Fig. 230. Size of Block. Sheave. Hinge . . Hook.. Block.. Outside diameter . Diameter bottom of groove Thickness Pin Wire Short strap Long strap Diameter Opening Length over all . . Width Thickness Weight 10 INS. 10 8* H l H 2Xi 2X* If 2 24 10i 4 12 10 ii H H 2iXi 2*X* n 27 12f 34 70 lbs. 14 INS. 14 u* H H 2*Xi 2*X* 1J 2* 30 15 3* 104 lbs 16 INS. 16 13* 1! 4 1 3*X* 3*X* 2 n 39 17 4 140 lbs 18 INS. 18 16} « li 1 3iXi 3*X* 2i 3 46 19 44 175 lbs. 420 The Naval Constructor DIAMOND ROPE BLOCKS. ,\1 I rs T <-H-> _L ii ) V , s ■J u / „ -^ Ny t' ,*' N S <-F-> \ $ > ! \ \ / S.---N, •L - .*-, \n V -- □ > I F-> Fig. 231. Diamond Wire Rope Blocks 421 1 pq 1 Swoo (MOO N M OO 81 O H O0 CO CO o •* o CO •* K5 H IN CO Hl§ ~ CM «S t^" CO CO 00 r m» rtiw ms? srw* CM CM CM CN CM CM 4 02 mo r*0 r>W> 5 XXX N N N XX XXX ?r ?r ?r XX H« -«. H« XXX CM CM .♦. — i n ^ 4i •• H-* H* -hW H« «l« -*• Hn hk -h •*« «*• oM «(■« «!•* rti* B. Diam. Bottom Groove. ; OO 00 00 o o O SSS 522 ic >o >o • ; • O O O CM © a 3*2 3* $1 ^ © fl ox a" Q fl © ^ ©*" v 6* I 6 o 2 J** 3 < •< < ^ ft < S ft 269 336 471 368 491 202 269 No. 14 454 568 795 575 767 341 454 " 14 678 848 1,187 828 1,104 509 678 " 13 933 1,166 1,633 1,127 1,503 700 933 " 13 1,257 1,571 2,200 1,472 1,963 943 257 " 12 1,621 2,026 2,837 1,864 2,485 1,216 1,621 " 12 2,018 2,523 3,532 2,301 3,068 1,514 2,018 " 11 3,020 3,775 5,285 3,314 4,418 2,265 3,020 " 10 4,193 5,241 7,338 4,510 6,013 3,145 4,193 " 9 5,510 6,888 9,643 5,891 7,854 4,133 5,510 " 8 6,931 8,664 12,129 7,455 9,940 5,198 6,931 " 7 8,899 11,124 15,573 9,204 12,272 6,674 8,899 " 6 10,541 13,176 18,447 11,137 14,849 7,906 10,541 " 5 12,938 16,173 22,642 13,253 17,671 9,704 12,938 " 4 15,149 18,936 26,511 15,554 20,739 11,362 15,149 " 3 17,441 21,801 30,522 18,040 24,053 13,081 17,441 " 2 20,490 25,613 35,858 20,709 27,612 15,368 20,490 " 1 23,001 28,751 40,252 23,562 31,416 17,251 23,001 " 1 30,213 37,766 52,873 29,821 38,761 22,660 30,213 h" 37,163 46,454 65,035 36,815 49,087 27,872 37,163 6 // a 46,196 57,745 80,843 44,547 59,396 34,647 46,196 54,277 67,846 94,985 53,015 70,686 40,708 54,277 i- 65,092 81,365 113,911 62,219 82,958 48,819 65,092 75,491 94,364 132,109 72,158 96,211 56,618 75,491 h" 86,412 108,015 151,221 82,835 110,447 64,809 86,412 h" 99,929 124,911 174,876 94,248 125,664 74,947 99,929 t 113,302 141,628 198,279 106,397 141,863 84,977 113,302 127,405 159,256 222,959 119,282 159,043 95,554 127,405 16 142,205 177,756 248,859 132,904 177,205 106,654 142,205 X" 157,659 197,074 275,903 147,263 196,350 118,244 157,659 f" 175,745 219,681 307,554 162,356 216,475 131,809 175,745 r 192,678 240,848 337,187 178,187 237,583 144,509 192,678 IS 212,620 265,775 372,085 194,754 '259,672 159,465 212,620 w 230,947 288,684 404,157 212,057 282,743 173,210 230,947 r Corners of jgj nuts = 1.414 flats. Thickness of nuts = diameter of bolt. Thickness of heads = flats of heads and nuts — 2. Sizes of " Sellers " or Franklin Institute finished heads and nuts are (flats and thickness of U.S. rough and finished nuts) — ,0625 //P . Rough heads, same thickness as U.S. nuts. 428 The Naval Constructor CHAIN PLATES. - -A J Fig. 238. Size or Wire. A B c Z) £ F H j x Z, // „ „ // II a // a a ,i // n H 3f * U 1 1* i i n 1 1 H « I 2 1 if f 7 8 n If i 2* 6* 3 | 2i 1 ll f H 2f if I s 7 4* i 2* H If * 1A 2f If 1 »i 74 4* ft 3 It lj I if 2f if I 3* 7* 5i J 'A H if 1 if 2f if i 4* 8* 5* * 2\ if n 1 if 2f 2f i 5 8* 6i i 2| H 2 1 ii 2§ 2| u Proportions of Crane Hooks 429 TABLE OF DIMENSIONS. fXAXz z + AXa' f=W (i+z. A = Area of section, z= Section modulus, a= C r of hook to C. G. of section. A = J5a/W~ Fig. 239. Working A — B — c= D — # = ^= DIA. AT "A" ~ V4 VW. Fig. 240. Navy Boat Crane 431 LIST OF GEARS. Hoisting. Kind. Spur pinion (motor) . , Spur gear , Worm , Worm gear (drum). Face. In. H Pitch Teeth. Pitch. Dia. In. In. 14 H C.P. 7.799 40 1J C.P. 22.282 Triple 3 pitch I 10 R.H. thrd. 9 lead \ 34 3 C.P. 32.468 Rev. per Min. 400 140 140 12.35 Mean dia. of coil of rope on drum = 31" 8.12 X 12.35 A four part hoist = 12' circum. 25.07' per min. hoist. Turning. Kind. Spur pinion (motor) . Spur gear Worm Worm gear . . . Spur pinion. . Circular rack. Face. Teeth. Pitch. Pitch Dia. In. In. 15 11 C.P. 8.356 43 If C.P. 23.953 Single 4 pitch ) 4 lead ) 10 R.H. thrd. 20 4 C.P. 25.465 15 4 C.P. 19.099 96 4 C.P. 122.231 Rev. per Min. 365 127.3 127.3 6.366 6.366 0.S The Naval Constructor NAVY BOAT CRANE. Fiq. 241. Boat Handling Arrangement 433 BOAT HANDLING ARRANGEMENT. lie laws of the principal maritime nations require that not only shall a stated number and kind of boats, lifeboat and work- ing, be installed on board ship, varying of course with the par- ticular requirements of the vessel itself and the trade in which it is employed, but also that these boats shall be efficiently in- stalled on board ship and conveniently arranged with proper boat handling appliances.* To comply with these enactments various arrangements are adopted suited to the special conditions which obtain in the particular vessel, ranging from the simple single davit handling a 10-foot dinghy slung on a single span, usual in harbor tugs and similar craft, to the row of lifeboats on a modern liner handled by steam or electric hoisters, while on the larger war vessels nests of boats are stowed and operated by special electric driven boat cranes or large derrick booms,. Before an arrangement of boat handling appliances can be laid out the special requirements governing the particular case as to number and type of boats must be considered and also the kind of davit decided upon. As already stated the rules and regulations of the hailing country and the trade will deter- mine the former. The kind of davit suitable if the vessel be in the ocean passenger trade is restricted to two or three varieties as shown by the arrangements in the figures, these consisting of the ordinary rotating davit, the Mallory type or the Welin quadrant davit, the latter being an excellent davit but of course slightly more costly than the others, the cheapest and most convenient where there is room to install being that known as the Mallory davit. Rotating Davits. — This is the most common type of davit used on shipboard. The davit and method of installing are shown by Fig. 242, but, of course the heelstep and bearing are suscepti- ble of many variations to suit individual cases or local conditions. The required diameter suitable for a given weight of boat may be calculated by the equation W X a = ^r D 3 f; by transpos- ed ing we get diameter, D * For these requirements see " Inspectors of Steam Vessels, U. S.," " Board of Trade Rules and Regulations." 434 The Naval Constructor ROTATING DAVIT. Fia. 242. Boat Handling Arrangement 435 the lever a, or outreach of davit, being measured with the ship inclined 10 degrees. Where the ship is intended for Lloyd's classification the formula used as required by their Rules is practically similar to the foregoing, but is differently expressed to make it more convenient of application where actual weights of boats are not at hand and to ensure uniformity of requirements. Lloyd's formula is: V LXBXD(H + 4S) C where L, B and D are the length, breadth and depth respectively of the boat, H is the height of the davit above its uppermost point of support, and S is the spread of the davit; each of these dimensions being in feet. The value of the constant term C is to be as follows: — 1. When the davit is to be of wrought iron and of sufficient strength to carry the boat, its equipment and a sufficient number of men to launch it, the value of C is to be 144. 2. When the davit referred to in (1) is to be of wrought ingot steel of from 28 to 32 tons per square inch tensile strength, the value of C is to be 174. 3. When the davit is to be of wrought iron and of sufficient strength to safely lower the boat fully equipped and carrying the maximum number of persons for which it is intended, the value of C is to be 82. 4. When the davit referred to in (3) is to be of wrought ingot steel of from 28 to 32 tons per square inch tensile strength, the value of C is to be 99. The mountings on these davits comprise belay cleat, fairlead sheave, spectacles for span and guys, the span being clipped with sister hooks at one end and shackle on the other, and the guys shackled to spectacle and set up on deck with either lanyard or turnbuckle. On lifeboat davits, it is also obligatory to secure to davit head, lifelines of say 2-inch manila, long enough to reach to waterline and also a rope ladder from span. Where the davits operate the emergency boat (slung outboard at sea), a pudding boom should be lashed to davits suitably padded in wake of chafe to which the boat gripes are secured. Suitable tackling for falls are readily determined from the weight of boat.* In first class practice the cast-steel bearing is bushed with composition either gun metal or babbit and a conical disc of hard steel is inserted in the heelstep, these additions reducing the friction with a consequent acquisition to the ease of operation. * For tackles see Knight's " Seamanship" or " The Naval Constructor." 436 The Naval Constructor MALLORY DAVIT. Fig. 243. Boat Handling Arrangement 437 In the larger classes of war vessels, as battleships and cruisers, a variation of this davit is adopted having a pivoting bearing and a hinged clamp at heelstep to permit of turning down the davits when clearing the deck for action. The -details of this type are various, observing that the bearing is cast in steel and bronze bushed, the swivel pin of wrot steel, and the step bearing of cast steel. A forged operating lever about four feet long is furnished for turning down the davit. Mallory Davits. — These davits are not as common in practice as their many advantages would seem to warrant. They are not proprietory as the name might imply, the designat- ing title being derived from the line of vessels in which they are most often fitted. A reference to Fig. 243 will show that they may be formed very simply from ordinary rectangular universal roll steel of a section at bearing step derived from the equation bh 2 W x a = —^ /, as in the case of the swan-neck davits described on this page, the head and heel dimension being approximately two-thirds of the resulting b and h. Where boats are stowed overhead on skid beams adjoining deck houses Mullory davits are adaptable,, take, up very little room, and cost much less to install than the more common rotating davit, in addition to which they are much more quickly and conveniently operated. It will be seen that they hinge on a heel pin and move outboard between guides one of which may also be utilized as the skid beams and a positive stop inserted between them to limit the outboard range of the davit. The boat, of course, is handled by the usual falls, but the davits are operated by tackles, the maximum pull on which will W be — :— , and the load on the handling part will equal this pull divided by the number of parts in the purchase. Swan-neck Davits. — These davits, illustrated by Fig. 244, are mostly adopted for torpedo boat destroyers and similar craft on account of their lightness and their adaptability to the re- stricted deck area associated with this class of vessel as well as on account of their speed and ease of operation. It will be noted that the boat when stowed in these davits is entirely within the ship's deck line and that no actual deck space is occupied as the boat is carried overhead and securely griped to the davits and no part of the handling gear obtrudes itself beyond the side of ship. A reference to the figure will show that a comparatively small overhang is necessary to lower the boat overboard. • 438 The Naval Constructor SWAN-NECK DAVIT. Tig. 244. Boat Handling Arrangement 439 Davits of this type are usually made from universal roll rec- tangular steel bar although where extreme lightness is essential they may be worked from structural I section. We shall assume, then, that the davits required are intended to handle a 23-foot whaleboat commonly carried on torpedo boat destroyers, and that the weight of boat plus two men is 1300 pounds + 300 pounds equal to a total load of 1600 pounds or 800 pounds per davit. It is sometimes erroneously assumed that one davit may be subjected to the entire load and the fibre stress increased to 15,000 pounds accordingly which of course is just the same as the more correct assumption of dividing the load between the davits and assuming a fibre stress of 7500 per square inch as we have done in the calculation. To determine the section of the davit we have to take the bending moment at A, where the greatest stress comes, with the ship, say 15 degrees, heeled over. Let us assume b = 2\ inches. To find h we have bh 2 WXa=PXc=f°-^> where W = ~9 = 800 pounds, a = 66 inches, c = 27 inches, b = 2 j inches. In this case we will set the fibre stress at a low figure, say 7500 pounds per square inch, allowing a high factor of safety. 440 The Naval Constructor MINE DAVIT. 4" isiyd/j'rong Tapped for {Bolt '* 8 Fig. 246. Boat Handling Arrangement 441 Then: and ^X 66 = 7500^, , t / 800 X 66 X 6 a . A = V 7500X2.25 = 4>33 ~ 4 ° mcheS - For P we have: FXa = PXc, or 800 X 66 = P X 27, where D 800X66 in _. , P = — 27 = 1956 pounds. To determine the diameter at bottom of operating screw threads it would seem reasonable to derive this from the pull P with a fibre stress of 7500 pounds per square inch, or, p - f wd2 where P = 1956 pounds, / = 7500 pounds, where d 2 1950 . nQ — = 1 = 0.26. 4 7500 ' and d = 0.58 inch. This, however, ignores the possibility of the screw being sub- jected to a bending stress or a combination of bending and com- pressive stresses caused by the movement of the vessel swaying the load. As the intensity of these is problematical we can only take care of it by using good judgment in selecting a suitable diameter. In the present case 1^-inch diameter over the threads should provide an ample margin. » The thrust R on pin at B is more easily determined graphi- cally as indicated in Fig. 1. In our case we get R = 3786 pounds. • The section of the davit should be gradually tapered down from A towards B and C. It is good practice to make the section near head C about two-thirds of the section at A. For larger davits it is desirable to figure the strength at different sections along the davit in order to make it as light as possible. Pins at A, B, and D should always be figured for bending to 442 The Naval Constructor insure proper strength. In many cases, especially in smaller davits of this kind as illustrated here, it will be found that the diameter of pin thus figured is too small to be practicable and should, therefore, be increased properly. Besides the athwartship screw-arm stay, an additional fore and aft stay is fitted to each davit to steady it and also to pro- vide support against collapsing through the minor axis (espe- cially for davits of rectangular section) ; this latter eventuality, however, is not likely to occur with davits of such small sizes as generally fabricated in this type. Where occasion suggests it, it may be well to check for com- pression by Euler's formula: P _ 2 EI where P = W = load in pounds, E = modulus of elasticity, I = moment of inertia of section, I = vertical (projected on the load line) length of davit in inches. / should in every case provide a sufficiently large factor of safety. As the illustration shows, the davits are tied longitudinally by wire rope span and stay to the deck, a turnbuckle being fitted to set up. Screw Gear. — With d = 1| inches. For square threads the following proportions are generally adopted: — /i = - , say in this case h= T&'> *** say 32'- To find the power P necessary to turn the hand- Fig. 247. wheel, we have: PXr = QX^, where r = radius of handwheel, in this case = 7", d l = 1^~ = 1.34375". Boat Handling Arrangement 443 WELIN DAVIT. Fig. 248. 444 The Naval Constructor To find Q we have : where W = 1956 pounds (see above), h = A-inch = 0.3125, ^ = 0.671875 inch, n = friction — coefficient, in this case = abt. 0.1. Then: and n in _ 0.3125 + 6.28X0.672X0.1 OAO , Q = 1956 6.28X0.672-0.3125X0.1 " 343 P ° Unds p = ^1 = 343 X 0.672 = 33 pQunds< As handwheels usually are operated by both hands each hand would exert -q- = 16£ pounds. Mountings. — The mountings or fittings on these davits comprise the span and stays previously mentioned of l^-inch circ. galvanized steel or iron wire rope with turnbuckle and eye- bolts through the neutral axis of davit section for securing, and lashing pad eyes, say T Vmch wire by lj-i n °h to take setting up lanyards. One pair of blocks per davit either wood or iron suited to the size of falls rove in this case 6-inch iron blocks with phosphor bronze sheaves for 2j-inch circ. manila and a 3|-inch fairlead sheave of gun metal bolted through davit where shown. A combined belay pin and slip to release the sword matting gripe which is secured at top part to an eye in davit head and a chafing pad stuffed with oakum and covered with leather to pro- tect the whaleboat. Board of Trade Rules for Davits 445 BOARD OF TRADE RULES FOR ROUND DAVITS — SOLID AND HOLLOW. In many cases the regulations require the davits to be of sufficient strength to safely lower the boats into the water, fully equipped and carrying the maximum number of persons for which they measure. It will frequently happen that the same set of davits will be used for launching both open and decked lifeboats, and the diameter of the davits should be governed by the weight of the boat which imposes the greatest load on them when loaded with the maximum number of persons for which it measures. The weights of the various types of boat should, therefore, be ascertained from time to time; and, in estimating the weight of the persons carried, an average of 1£ cwts. (140 lbs.) should be allowed for each person. The load on the davits includes the weight of the boat, equip- ments as specified in General Rules 8 and 9, maximum number of persons for which the boat measures by the rule, and blocks and falls. As the blocks are frequently made of metal and fitted with metal pulleys, their weight is considerable. A wooden boat of section A, about 28 feet long, complete with equipments and gear as mentioned above and carrying 50 persons, is taken as imposing a load of 100 cwts. on the davits, or 2 cwts. per person for which the boat measures. This may be stated as follows: — W where W = total load on davits in cwts. : N = maximum number of persons for which the boat measures; w = load on davits in cwts. per per- son carried. If the davits proposed are found to be equal in diameter to the dimensions obtained by the following rule (2), no objection need be raised, provided that, (a) the relative strength along the tapered parts is fully maintained, and (6) the total weight of the boat, equip- fig. 249. ments, maximum number of persons for which it measures, and blocks and falls does not exceed 2 cwts. per per- son, as ascertained by rule (1). 446 The Naval Constructor \ X D(H + 4S) m d (2) Where L = length of boat, in feet; B = breadth of boat, in feet; D = depth of boat, in feet; H = height of davit, in feet, above upper support; S = span of davit, in feet; C m constant, to be taken as 86 for iron davits, and 104 for solid ingot steel davits of from 27 to 32 tons tensile strength, and for hollow welded davits of from 26 to 30 tons tensile strength; d = diameter, in inches, of solid davit. In dealing with hollow davits the equivalent sections may be found by the usual formula after the cube of the required diam- eter of solid davit has been ascertained by rule (2), as follows: — (3) or . 3 ////3 v mi\ (4) \ II v — ± I Where d = diameter, in inches, of solid davit; Dh = outside diameter, in inches, of hollow davit; dh = inside diameter, in inches, of hollow davit; m = the ratio -j- • dh Boats vary considerably in weight, small ones being relatively heavier than large ones, and weldless steel ones heavier than wooden ones, and a modification of the constant C, rule (2), will sometimes be required. This can easily be made when the maximum weight to be imposed on the davits is known and the quantity w has been found by rule (1). In the case of weldless steel boats w may be about 2.1 cwts., in which case the modi- fication of the constant C in rule (2) will be: — C X 2 — J-: — ■" modified constant. D h < - D h * D h x 3 / 1 d* X m 4 \ Board of Trade Rules for Davits 447 In the case of solid iron davits, the constant, modified as above, will be: — 86X2 82, and for steel davits 2.1 104X2 2.1 Formula (2) applies to boats of sections A, B, or D, in which the entire cubic capacity is measured for the persons carried, the constant C being reduced or increased as w is shown to be greater or less than 2 cwts. It also applies to boats of section C when the weight of the boat, equipments, and persons allowed, ivv— — — = = — t K K C *S 35 70 A -s V- ° An 5 • t£ bU h ~50 A 1 \ "fcW ~T c- 30 Y -20 j £m t o 3 10 20 30 40 50 60 70 80 90 100 Dia, of Core or Hole in Percentage of Rod.Dia. Fig. 250. does not exceed that of an ordinary wooden boat of similar size of Section A, B, or D. In the case of davits which are only required to be strong enough to carry the boat and equipments and a sufficient num- ber of men to launch it, no objection need be raised if the diam- eter is not less than that found by formula (2), but using a constant, C, of 144 for davits of untested material. The constants given for steel davits are on the understanding that the material is tested and found to be within the limits given. 448 The Naval Constructor DAVIT HEADS. HQ|«-!H Tons. A B c D g F G // j X L m N 0.9 1.2 1.5 1.7 1.9 2.3 2.8 3.3 a If 2 2i 21 2f 3 3J 8| 2* 2* 2| 3| 3t 3f 4 4f 7 8 1 H if H lj H if 1 1 11 if If ll If If f A i 2 9 1 f 1 1 H if if if if if 2 2i t» 8 1 1A ft if 11 2^ If 3| 3 r 5 31 4i 4f s- A y A A tf 1 i 1 i 7 f f If 1 H li 1 l A ! 1 1 f f 1 8 f f f 2 A f 1* if Tons. P Q R 5 r U if 2 21 2f 2* 2f 3 H it ±2 If it* 2 2i V I J il f 17 1 f £ H l X Y a I \i H if 11 z 1 f i 1 if A 1 a 2f 3 3i 3* 31 31 41 4f Bl A | 1 1 i A 0.9 1.2 1.5 1.7 1.9 2.3 2.8 3.3 1 4 7 ¥ tt if H if 1 1 H lj if lj U if f f f il H H U H 1 H if if if if if if i 1 1 i s Weights of Boats and Davit Diameters 449 WEIGHTS OP BOATS AND DAVIT DIAMETERS. Diameter Dimensions *a h of Boats. 5Sx Build Ss3 3g MS BE of Boat. Desckiption. L. B. D. fi« 10 4 3 1 7 670 3 2 £ Wood clench Dinghy. 12 4 6 1 9 900 3 4 2| " 14 4 8 1 11 1,120 3 6 3 " 16 4 10 2 1,350 38 11 " 18 5 2 0£ 1,550 3 9 Cutter. 20 5 4 2 2 1,800 40 4 M 20 5 10 2 4 2,000 4 4 4J " carvel Yacht's launch. 22 5 10 2 4 2,240 4 4 4£ " clench Cutter. 22 6 2 4 2,450 4 6 4.1 " carvel Yacht's launch. 24 7 3 3 2,450 5 5 4! " clench Lifeboat. 24 6- 2 9 2,800 4 6 4| " carvel Yacht's launch. 26 7 6 3 3 2,700 5 7 .6§ M clench Lifeboat. 27 5 9 3 5,600 4 4 3 " diagonal Steam pinnace. 28 8 6 3 8 2,900 6 4 " clench Lifeboat. 30 8 6 3 8 3,000 64 6 II u Lifeboat. 30 7 3 10 7,600 5 3 7 I " diagonal Steam navy pinnace. 32 7 4 4 7,850 5 6 7f M II II 36 8 4 3 13,500 60 9 II II M 40 8 6 4 9 18,500 6 4 8 (3) M II 14 42 8 2 4 6 14,000 6 2 71(3) 8|(3) Royal barge. 45 8 6 4 6 21,300 6 4 Steam navy pinnace. 47 9 4 6 22,400 69 9 (3) " M " 50 9 3 5 8 23,500 7 Crane II II II 56 9 9 4 10 27,500 7 4 Crane II U II 60 9 6 410 28,500 7 2 Crane These davit diameters are figured for the moment exerted with the shii inclined, and are taken for a fibre stress of 12,000 lbs. per square inch, witl one davit taking the entire load. 450 The Naval Constructor NAVY STANDARD. Hinged Watertight Doors. Size of Opening in the Clear. Dimensions over Door Frame. Breadth of Frame. 5 6x30 i ii in 6 lj x 3 7 5 6x22 5 0x3 6 lg x 2 9 5 7J X 3 7 3$ inches each side and end with 5 0x20 4 0x20 5 7j X 2 7 4 1\ x 2 7 I inch extra on one side for hinge pads. 3 6x20 4 lg x 2 7 2 6x16 3 If x 2:1 Sliding Watertight Doors. / // / // in i ii 4 9x20 5 6J x 2 8 4" V.S.W.T.D. 3 3x20 4 0J x 2 8 4" V.S.W.T.D. Sliding Watertight Doors SLIDING WATERTIGHT DOOR. 451 CAST IRON DOOR O WROT.IRON FACING BAR8 "ITT JUL 4 The Naval Constructor STANDARD EYEBOLTS Fig. 256. A. 5. c. D. E. i^. o. Breae AT Tons * A II H A H A If 1 A 1A i A H i H A H H *A if H A 3 J i M 1A A i A 5 1 H if M i ItV I 6 i A i-H i§ A u A 8 i i n HI II 1A i 22 H H »l 2 H ift A 27 n 1 2f 2| J il ft 33 u ItV 3J *A A 2A H 40 If 1t 3 5 Sf 2f f 2i f 47 2 11 M •n 1 2£ if 50 Table of Fairleads 455 TABLE OF FAIRLEADS (Cast Iron). Single Eoller. Fig. 257. Length of Ship (Ft.). Unit Dimen- sion IN Inches. d. Approxi- mate "Weight in Pounds. Length of Ship (Ft.). Unit Di- mension in Inches. d. Approxi- mate Weight in Pounds. 100 3 34 470 11 1,670 110 " H 54 490 11$ 1,907 120 4 80 520 12 2,167 150 H 115 550 m 2,450 170 5 156 570 13 2,750 190 H 208 600 13* 3,085 200 6 271 620 14 3,435 215 H 345 650 U\ 3,820 240 7 430 680 15 4,230 280 n 530 710 15£ 4,670 300 8 644 740 16 5,140 330 8* 770 760 16£ 5,635 360 9 915 780 17 6,165 390 n 1,073 800 17* 6,720 410 10 1,253 850 18 7,315 440 10£ 1,452 .... Weight without roller = d s X .6 = lba. Weight with one roller = d 3 X 125. Weight with two rollers = d 3 X 1.5. 456 The Naval Constructor STANDARD FLANGES FOR LEAD PIPES. k- -L- »| Bolt Holes Drilled note: no finish on ca8t iron flanges Fig. 258. Fbom to 100 Pounds Pressure. N s A. £. c. -D. G. H. L. R. s. r. 2 * . © g a <2 o3 o e N 55 2 n «i 41 2| i n 8 1 1 1 6 4 f n 8 7 51 31 I 101 8J f i 1 8 5 f 3 31 71 5f 3f 1 11 01 I * J 8 5 I 31 4 8* n 41 1 llf 0| 3 1 I 8 6 5 S 4 4f 9 7 4| 1J 13 11 I f A 8 6 a T H «* ©I 7| 61 1J 13J HJ i A A 8 6 I 5 6| 101 81 6i 11 141 121 i 1 A 8 6 1 6* «l lOf 8| «i 11 14f 12J i 1 A 10 7 1 6 6f 111 0* 7 1| 15£ 13£ i 1 A 10 7 1 Standard Pipe Flanges PIPE FLANGES, STANDARD. 457 Fig. 259. J From to 100 Pounds Pressure per Square Inch. 1H &£ 3 P © ■83 a ^ M © sf II .2 Q © ss -343 ©O S -u hi 5 CO Is i« s 0D ® © be c s H ,a 00 Sffl S • Is 8* s © a °° 11 i 1 CO O 00 © a .i 3 ff O u © a a y*. B. C. ^. G. zr. 0. // // II 11 // * II it a a a | * .840 Sf 21 H ■h * .109 14 * 3 I i 1.050 4 2| H \ * .113 14 * 3 1 1 1.315 Ji 8| If \ i .134 11) 1 3 H H 1.660 6* »| 2* \ 1 .140 1U f 3 H H 1.900 5* 8? 2* t\ 1 .145 1H f 4 2 2 2.375 3 4* 3 f J .154 in I 4 2* »i 2.875 7 6| 8| * 1 .204 8 1 5 3 8 3.50 n 5f 4J J 1 .217 8 | 5 8* »4 4.00 H 6| 4f it A .226 8 f 6 4 4 4.50 9 7 &* 1 1 .237 8 I 6 4* 4* 5.00 9f 7| 6 1 * .246 8 f 6 5 5 5.563 10} 8| 6* § .259 8 I 6 6 6 6.625 111 »l u 1 1 .280 8 i 7 r>s The Naval Constructor STANDARD FLANGES FOR VENTILATION. ft— -Vi — * T" .to r i - I* B ^ m;^ ^ L Figs. 260 to 262. Inside Diameter OF Pipe. Flange. Bolts. No. Size Inside Diameter or Pipe. 8* 9 9* 10 10* 11 Hi 12 12* 13 13* 14 14* 15 15* 16 Flange. Bolts. No. Size, a Inside Diameter of Pipe. 16* 17 17* 18 18* 19 19* 20 20* 21 21* 22 22* 23 23* 24 Flange. Bolts. No. Size. Hand Wheels 459 HAND WHEELS (Iron). Fig. 263. Diameter. No. A. B. a x>. E. F. G. H. . JC Arms. 2 " i 1 A \ A \ II A 4 n a 1 A \ f A 1 4 3 J 1 1 A 1 A 4 H I 1 i A i A i 4 4 ft U A 1 A A 1 5 ±h 1 if • A A 1 * A 5 5 it JA I A 1 1 | 1 5 6 1 if I J f A 6 7 l n A, I i f 1 6 8 ItV Hi A I ^t B it 6 9 H m \ A 1 I 1 6 10 1A u \ f }A it it 6 12 1A n A ;a 7 I 1A 6 14 n 2A f I it 1 IA 6 16 if 2| tt it }A H if 6 18 n 3| t 7 5 1A l| 1} 6 21 lit *l H 1 if H if 6 24 *t 4 1 *A if n n 6 460 The Naval Constructor HAND WHEELS (Brass). Fig. 2<&. DlAM., A. B. a 2). • J?. A 1» Hi 2* l H L| 13.3 Trip Hooks 467 TRIP HOOKS. Fig. 274. A B c D E f G H j A' L M N p fi s 1 2 2| 1 2 1 2 H 5 8 1 H 8 1 I 8 5 8 1 2 & 8 * 5 8 31 2 9 ft if 4 tt H 10 U 3 4 3 4 5 8 ti 5 4 4 2^ 5 t 6 8 2| 7 8 if 1* 12 U 1 7 8 i +t 1 t 1 1 5^ 3* 7 8 1 2* H if 2* 16 2 l| if i ItV 5 8 1 H 6* 4 if 1* 3| 1 1 2J 3 20 24 lj l| H If i H H 8 4| U 1| 4i 1 4 2f 3* 24 3 U If If If l l* 468 The Naval Constructor 00 ■a 3 S886&38gsS88!g$5S353558&S!988$ HrlrifINn B a o « Eg - as w S 2 oo to 1 v , , . . , •*> .•*» .«*> . .*• .^ .-*» 5 :::::::::- :~:~ :-:*:*:*:: v Hn .«*» .*** .«-»» . .H» .*+# ,H» .... v • • «>|5'-i5-*«*° • «*» • «*• • • -*m* • hm i "K«h*h-*«* m ** ; r *° i^ ;h» ;-m ;,*, :;:;::: ; ^ •xaAia jo naxawvia fl s "r1rtCS t -!s»M-* D -* e n!s=**'-»» «Sh««2-w :::::".:::: «t»t-J^a]2«^^^5 c ^^ r * M+0 r«^H4-*l-« S ; <^^T^^%^%^$$^% n -£l$®« Bo H 5 i-i*-(NM7j<>0©t-00Ci©NTj<©ai0©iffl©in©iQO 2<4 ©©©©©©©©©o©©©©©©©©©©©©©© Standard Pad-Eyes 469 STANDARD PAD-EYES. FO.R 2 RIVETS. STANDARD PAD-EYES. FOR 4 OR MORE RIVETS. r~\ i L "1 Fig. 275. 3S.i. Fig. 276. 470 The Naval Constructor REVERSIBLE PAD-EYE. 5U.S.S.ThnperInch -:;7"--^ ^FT~?* — = ^ = ^ — ** / ^ t--t--r--— ---r--J-f 4 —6 Did. -JjD^uT-l Fig. 277. Lewis Bolt 471 LEWIS BOLT. ->*- 3f--->, f w~** 1 >i j C- %ts , J — Note. Cover to be Carefully .*-,/■., IT Fitted toSocket Fig. 278. 472 The Naval Constructor : L o — • 1 - T s! CI 5:2 CO ^ X i 4 X a 1 ■« 8 3 -2 a CO ■* m ? * 00 .. eo *.X CO c> X CO h 8^ 5 HI is *2 ™H -*• V CO *■ CO •2 if 2? ** « L fc V 5? V > ; 5 ? ? X :*x CI X h ; <*>< 5><2hxh. 00 CO CO CO i-l «9 ^ 2 V 5 -5 5 X^,XE„ « x ; e> CO c* ™ ? CO ■OM <* CO ^O 1»« t^ CO . 5 J ; t ; Y ?>? ^.x Hi ,x -** l»Tx h*h.s x 3><^Xh- «5 C* ; J c» ~g " H» (M S7 ■* CO ? H ^-x «R i»x j i.T; . l)«Hil A S AI X hm H« 0) o» ; s C • .. C* HjX 1 < • X -+« s «R ; s . 6 «2 .^HjX Sx^Xh. ' 1 •J « 2 © © © t i '. "3 : >• * °3 : S ■s « ja q O PJ > I •2 Lashing Triangles LASHING TRIANGLES. f j — -*j 473 f® J --> 10 V.T- D 01 <- ©J '^. for Bolts Fig. 279. Fob Wire. A 5i 5f 6f 8 9 n 5 6J 6 c i i 2 i 8 3 4 I D 5 8 4 i 8 1 H I l If if if F a \ 1 4 7 8 1 H it m 2| 1 U H if H j 2f 3 4^ 5i 2| 3 3f 4i 5i L 7 8 1 H if lj M t 3 8 3 8 I f ■N 5 8 5. 8 ! 7 8 H 7 ¥ 7 8 I H if p i ? s 8 3 4 I 8 1 8 Q ! 3 4 2 3 3* 8 474 The Naval Constructor S 2 _§»» H » N P5 M ^TH.-ieMeseoi<'<»<«o3t^o»©(Nco J 1 g -c «**»* ■*< T^lO Slffl 5? «? S? ?? oo 00 00 ft* Ha ■•« Hn IO 00 O « (i) t*NoooH(ijT((eNo>o-n* .~i^H»-<^Hc^ C N tt a Oh(NM*i9»N»«OhM«* 1 E .3 5 £ • B io H" ■*.!*• ■HiMHaHa .4m.toM.li.ltu < I in w Oh M M « o ^^«iO00 C'*miMOO)OON®!DiO'>|i COeOCOCOCOC •-< t— ■"«< «-i stotoinin^mMNrtHOOOoiosi gggggggggggggggggg tooooortinooio'* ^'* * ' H ."5: i: i , ' , . M . f i llj o"lO «5 ffl l", -h CO UJ M O ggggggggggggggggggg i>T im" oo «3 ra c >n •■« i-^" ■* 2; oo to •>** eg <-H'-cOOO050»050000t--t>«0tO«0>CiO»C'5 gggggggggggggggggggg .-TrCco © r^"^^^^ t-Tt^ ■-«DO»iC>C>C-^c*->tl'^''^COt^mcOCO-^Ot^lf5i— I t-h (M O0 t^ t>- CI OincC50Nt^0000050>0 478 The Naval Constructor 3UIM JO U3X3WVIQ Proportions of Rings 479 TABLE II. — Proportions of Rings for Standard Short-link Chains. ! 5 B " Chain. !" Chain. IB Chain. \" Chain. P.L. 1* Tons. P.L. | Tons. P.L. 2\ Tons. P.L. 3 Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. T6 1 A i\ 5 8 1 3 - H 1A 4 1ft 5 8 z-k 44 2 f If ft 2A H 3 3 4 2} }t 24 5 3A f 4A if 3| 8 3A 4 4*4 If 5& 7 8 4H 44 4& &4 8 61 fl 5M 1 64 1 7A IA 6A 14 71 iV Chain. 1" Chain. H" Chain. \"K 2hain. P.L. 3| Tons. P.L. < If Tons. P.L. 5| Tons. P.L. 3f Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. H U 1 8 W it i! IA 2i I 2^ 1* 2| 1 2& 14 2H H 3^ 1 3A IA m 1A 3A l 4 IA 3H 1* 3| 14 4| 1A 4^ 14 4f IA 4& 1A 4f« }4 5f| IA 5& 14 64 H 5H iA 74 H 6f IA 6& 1A 6f i| »A IA 7M if 74 14 7| if 9| IA 8f 1A 9 li 9| • if 10i 480 The Naval Constructor TABLE II. — (Con tinued.) \i" Chain. i" Chain. H" Chain. 1" Chain. P.L. 7ft Tons. P.L. 9J Tons. P.L. 10§ Tons. P.L. 12 Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 1* i H 21 lft 2H 1* 2f lft If 3& If 31 lft 3& H a| 3tf lft 31 n 3| 1ft 4 lft 4H 1* 4 lft 4ft it 4f 14 5A lft 51 if 5 1ft 5& lft gj 1 5 Is 6 IH 5} 1| 6^ ll 7& IH 61 If 6* lft 71 If 8& If 7\ Iff 7A If 8* 91 if* 8f U 8f l» 9H 1*1 10| 9tf iff 2 9f 10ft 1A" Dhain. H" Chain. i&" Chain. 1J" Chain. P.L. K } Tons. P.L. 15* Tons. P.L. 1 3/(, Tons. P.L. 181 Tons. M.S. M.I.D. M.S. M.I.D. 3& M.S. M.I.D. M.S. M.I.D. H 3& lft If 3^ If 3A lft m If m IH 3& IH 41 11 4A 1« U If 41 H 4ft lh 4M If 41 ih 4tt i+f 6ft 1! 51 ill 5& u 5f 2 6 Iff 6A u 6A ill 6^ 2V* 6^ u 7& W 7^ 2 6H 21 7A in 81 2 7ii 2tV 7& 2^ 8 2 9 2^ 88 2| 8| 21 91 2^ 10 2| 9f 2A 9A 2ft 10 2* m 2ft 10H 21 101 2f 11 21 HI 2A HI 2^ 12 2f 12f 24 13ft Proportions of Rings 481 TABLE II. — (Continued.) 1 T V' Chain. If" Chain. 1 T 7 B " Chain. li" Chain. P.L. 20| Tons. P.L. 22f Tons. P.L. 24f Tons. P.L. 27 Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 11 1*1 2 2^ 2| 2& 2j 2^ 2f 2A 2} 2A 2| 4& 4| 5| 5| 6& 8« 9f 10tt HI 12H 13f lit 2 2& 2| 2^ 2J 2| 2^ 2£ 2& 2f 2H 2| 4& 4f 5^ 5| 6| 7| m 9^ 10A 111 12} 13A 14| 2 2A 2| 2^ 2| 2A 2| 2A 2* 2& 2| 2ft 2i 2H 21 4& 4& 6* 5| 6f m 7f 8& 9& 10J 11 12« 13*1 15* 2 2A 2J 2A 2| 2^ 2£ 2& 2| 2ft 2! 24i 21 2ft 3 H 4& e* 61 7* 81 9^ 91 ioU in 12ft 13£ MA 15| M.S. = Minimum size of iron in ring. M.I.D. = Maximum internal diameter of ring. (P P.L. - Proof load - 18.7 ^ , d = dia. of iron in ring, where and D m mean dia. of ring. Safe load = One half the proof load. 482 The Naval Constructor TABLE III. — Proportions of Rings for Double-leg Sling-Chains. ft" Chain. |" Chain. /a" Chain. 1" Chain. P.L. 21 Tons. P.L. 31 Tons. P.L. 4J Tons. P.L. 6 Tons M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 5 8 U 4 If* $ Iff 1 24 1* 2 H 2J H n 1* 2*4 2f i 3 l 3A ll 3& tt 3* ft 3J| 1* 3$ 1* 4^ i 4ft l 4| 14 4|i 5| If 41 $ m 1* j>4f 1* Iff 5! i 7« 1* 7A H 61 If 6| 1* 8« 1* 8^ 1* 8& 1* 7A l* 10| if 10 if 9 T 7 s ll 9 1* 10| 1* 10f / B " Chain. f " Chain. U" Chain. I" Chain. P.L. 7J Tons. P.L. 91 Tons. P.L. Hi Tons. P.L. 131 Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 1* JA i'i f 11 2*f 11 3& 1* 3 l* 1* 3i 1* m H 3f if 3| 11 4i If 4 *■ 1* 4* i* 4& 1* 4H 1*4 4# 11 6| i* 5& 14 51 if 6f 1* 5« l* 6& m 6* m 6^ ll erf it 7A if 7| if 7H l* 7^ m 8 ill 8^ i*f 84 If 9& if 9& ii 9^ 2 9 1 10* m 10* i« 10| 2tV 10 U* ii 11* 2 n! 2f 114 2^ 12| 2A 124 Proportions of Rings TABLE III. — (Continued.) 483 ijj" Chain. J" Chain. tt" Chain. • 1" Chain. P.L. 15$ Toi 18. D. P.L. 18i Tons. P.L. 21 Tons. P.L. 24 Tons. M.S. M.I. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. n aft n 3! If 4 2 4 i« 4 in a ltf 4£ 2ft a i| 4ft i* 4| 2 51 2| 5| ifc 5ft m 5| 2ft 5f 2ft 6 n 51 2 6| 2* 6ft 2| 6| m 8 2ft Sff 2ft 7f 2}| 7ft 2 7ft 2£ 7H % 71 2* 8ft 2ft 8ft 2ft 8| 2ft 8H 2ft 8| 2* 9ft 2J 91 2| 9ft 2* 9H 2ft 10ft 2ft 10ft 2ft 10ft 2ft 10ft 2i lift 2* lift 2* lift 2| HI 2A 12ft 2ft 12ft •2ft 12ft 13| 2H 12ft n 13ft 2* 13± 2| 2! 13| 2H 14ft 2il 14ft W»"C HAIN. li" Chain. P.L. 27 Tons. P.L. 30J Tons. M.S. M.I.D. M.S. M.I.D. 2i 4£ 2i 4^ 1 * 5 2^ r 5| 5f 2* 5^ I 2ft 6ft 2^ 2i 6t V 2* 6| 7t * 2ft n 2t* T 7^ 4 81 n 8| 2ft 9ft 2f r 9, % 4 9| 2f idj 24* 1QH 2f 1 11 2f HI n llj 2H 12ft 2f i m 1 2f 13J 3 m 2^ 14ft 3^ 14| 3 15f 3i 15i 1 484 The Naval Constructor TABLE IV. — Proportions of Rings for Three-leg Sling-Chains. A" Chain. I" Chain. / B " Chain. P.L. 3| Tons. P.L. 4J Tons. P.L. 6f Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. It 1ft 3f 4 # 5& 6f 8& if 1ft If 1ft a 7f 8f m }ft If If |ft If i| 4M i 7| 9 10* 111 13f i" Chain. T V' Chain. f " Chain. P.L. 9 Tons. P.L. 11 J Tons. P.L. 13J Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. a 1* 1ft If ltt If 1« lit 6| 6f 7& 8& 91 10ft Hi 13ft 11* iji if lit 2 2^ 2f 2& 6i n 8^ 9& 10* Hi m 13« 15ft If 1.U 2 2^ 2f 2^ 21 Jft 2f 7^ 7| 8tf 9H ioi| n« 13* 14f 15f Proportions of Rings TABLE IV. — (Continued.) 485 \l" Chain. J" Chain. J|" Chain. P.L. 161 Tons. P.L. 20J Tons. P.L. 23/s Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 2& 7& 2* 81 2^ 9 21 8£ 2ft 8*f 24 m 2ft 9^ 2f 9M 2& ioi 2} 10f 2^ io|§ 2| ntt 2ft lift 2* m 2tt 12| 2f 12| 2& 13 2| 13H 2^ 13f 2f 14 2M ii| 2| 14H 2H ISA 21 151 2& 16* 21 16| 2« 17ft 2f 17ft 2H 17f 3 3ft 18ft 19tt J" Chain. H"c HAIN. P.L. 27| Tons. P.L. 31 i Tons. M.S. M.I.D. M.S. M.I.D. 21 9H 2*§ 10f 2H 101 21 m 2! Hf m 12ft 2M 12ft 3 13 21 13i 3A 14 2H l4 31 15 3 15f 3& 16 3A 16ft H 171 31 171 3A 181 3& 181 3f 19ft si 20| 3A 20H 486 The Naval Constructor TABLE V. - Proportions of Rings for Four-leg Sling-Chains. A" Chain. I" Chain. X V' Chain. P.L. 4| Tons. P.L. 6J Tons. P.L. 9 Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 1* n \t 61 8& 1ft If 1ft If 1ft 71 8| 9ft 1ft U m H 5* 6f 7ft 8ft 9f 10ft HI i" Chain. A" Chain. f " Chain. P.L. 12 Tons. P.L. 15 Tons. P.L. 18* Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. U lji if 2 21 6* 7ft Si 9f 10ft lift 12^ l4 If 2 2| 2A 2§ 2A 2f 5ft gA 7ft 8 81 9f ion HI 13ft 14i 2 2ft 21 2A 2i 2ft 21 2ft 2i 2ft 2f 2H 6ft m h\ 8§ 9i 10^ HI 12A 13i 14ft 15H 16M Lengths of Countersink Point Rivets 487 TABLE V.— (Continued.) W Chain. J" Chain. il" Chain. P.L. 22* Tons. P.L. 27 Tons. P.L. 31 f Tons. M.S. M.I.D. M.S. M.I.D. M.S. M.I.D. 2t 3 s 21 2A 2f 2^ 2* 2A 2| 2H 2f 2tt 2| 2M 6* 7il 8f 9& 10A Hf 12f 13ft 14J 15| 161 ISA 2^ 2£ 2& 2f 2& 2f 2H 2| 2*| 3 3A 3| 3A 3| 7h 81 9A 9£ io« Hi 12ft 13} 14ft 15f 16ff 18 19i 20ft 2f 2H 2| 2tf 2* 2M 3 3^ 3| s 3tI 31 3ft 3| 3^ 3* 8| 9f 10$ . 1U 12^ 13 14 15 16 TO 181 19^ 20H 22 THE ORDERED LENGTHS OF COUNTERSINK POINT RIVETS. 1. The following curves for ordering countersink point rivets are based on the U. S. Navy standard rivets and countersink. Curves should be read to the longest "ordered length." 2. Where more than two thicknesses are connected, add \" to each extra thickness. 3. Length of snap point rivets use the rule: total thickness of plates + one diam. -+- }"j except for excessive thickness, add \" . 4. For hydraulic riveting add 1" to the length required for hand or machine work. 5. The curves for f" to f" rivets are computed -fa", and f" to 1" rivets, \" longer than required to theoretically fill the hole. 6. The type of head has no bearing on the ordered length. 488 The Naval Constructor N N ^i 1^ sz % *£ fe •V <53 c V . N. N v> ^^ "7 •f -V V- m|*2 -K ro|«£ ^ 1^ M v> -C •S! sa #5 s _1 feS ,^v o V s •i N Ordered Lengths of Rivets 489 HeO ">i s feH- c (I) ^ ^ W ^ V o> Join- ts u O i M b^ in]oO "V •V -Irs. £■ K> 00 in 'S -1 «4- KD <£ CO C * I r saipui'-sjutQja.funoo .joL^ctefl 490 The Naval Constructor Voc > *^ +* ^s CD — c e _i 2'* H ^ ^ ^ ,v -> u O \ $ ^ 4- (1) > bC I F 9 Q £ -|r, H2 to|oO irvjiS -H ssijoux'^uisja+uno^ p m-dafl Ordered Lengths of Rivets 491 f>|S2 -In i»I« k>1|i 492 The Naval Constructor •*> ^> •A ^ •*> **< ^ ^ */ H<*> 5 tol* =|iS injco o|i H;« i-i F 1* «5 rlrtnntm o8 a B ® .2* C ' "■3 > '3 SI c8 u fig fi •-EHSHS^'+.ag-K^ -OK •'S'>_«l<*^«J 0,,:B, UH"liNOM»Q»©»NlOaNlOMH^li-lt-ei5©»i i I- X 05 t- CI CC l* CO I- « C rn »n. i~ tr x — CI -* t- Q CI 1 • iO"*«2oi'-i©e»oot- .too . ■* co >~© : 8 | , 5 *3.B fiB > C^TcO cS"cD CO CO CO CO CO CD . ® II OHNeo<*io«t-»ojOHN«*iawsooo 8S888 , Areas of Sea Anchors 49( 2o + IS 3 xjO - o EL 00 n o H 00 O H m 3 H as ce H ► 9 p i n n ■j 3 ji^j I t-^nirjgiCot-^iOCscot-r-iiocJcot-T-i CGpH J ?3 co co co co co co co c^ co co w e$ com c8 co p i t-*t~* tA- t-"t>*t^*i> co*cc*c©~c©"cc*cc*co*a6"cc" cc*h cs co t- rH uo ©-co t-Higont-iHiflaw ci co co -t -t -r i.o i- © sct-t-woooo« cmo»oioioioio5oiojoioio:io«oioioioi i 8|S|S|88388|8||§8 in ia io io io © co* to" co co co co*©"co*co* t-Tt-T to Eh siiSSsllssaligg^l Eh 1 co co^TjrTjr^r^r^^TjTTjrTirio ia»oio'io • • 1 CO t~ y^ \a © CO t~.i— c lO©C0t>T-lia©COl> 00fC| 'l rl r- rl rl rl rl rl rl rl rl rH i-H rH r-l 8 o H of of of of of of of of of CO*" CO CO CO CO* co" CO CO* ft? LO©COt~r-iin©COt»r-iiQ©COt-r-iiO© oloicoco-^T^^iaiccocoot-t-cococo 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1.700 1,800 1,900 2,000 32 M H M CO 03 5 • OWOiOOiOOioOiOOOOiOOO .. © of co oi © © ci co oi © © oi © of © ©" w*iot>©T-ccoir:coT-=?i-©-toBo1 r-lt-lr-lr-IOIOIOlCOCOCO**! *-* 27.56 39.06 52.56 68.06 85.56 105.06 126.56 150.06 175.56 203.06 232.56 264.06 297.56 333.06 370.56 410.06 © | 8S3Ss|s3||g|||s| 'apiS l£>©t>CO©©"^OICO'*CO©© 496 The Naval Constructor :2 1 /»Dia. Thimble "T i 3 Manila Rope Heavy f t I , Brass Eyelet. } Lashing Rope ■1 Dia. Rod $ Long Link 4 , Short Link Chain Long Link Swivel 2 7' FIG. 290. Standard Shackles 497 STANDARD SHACKLES (As Manufactured). Anchor Shackles. Fig. 291. Size of Shackle, A. Size of Pin, Opening at Eye, C. Depth under Pin Inside, D. Width of Swell Inside, J5. n // /> H // i A } n if A 1 f n 1 1 tV e ij H A I t if if 1 A I 2J -if 9 i i H if f 1 n H 2 I 1 }i 3 21 1 ji 3i 21 i| if 3| 2f H if n 4 21 if if 2 41 31 if if 2J 4f 31 n if n 6 31 i| if H 6* 4* it ii 3 7 M ii 2 s 71 5 2 *i 3| 7! 51 498 The Naval Constructor SISTERHOOKS. "« "« «o to II e "<3 II •a OS © U 13 © II o II 13 US i » d 5 // „ „ „ „ // „ „ f 2h 2 4 A 1 4 A 1 8 ft 600 10 1 3ft 1 ft i i 4 } 4 1065 12 s 8 4* H ft § A 5 8 ft 1660 12 i m li ft a { 3 4 l* 2390 14 i H l! ft 5 8 ^ I 1ft 3260 16 i 6f 2 ft 3 4 1 2 1 lj 4260 18 ii 7^ 2i l I ft If 1ft 5390 20 ij 8* 2| H ft 5 8 i! if 6650 20 Slip Shackles 499 500 The Naval Constructor SLIP SHACKLES. W. Load (Fac. of Safety 5). A. B. 10 c. 10 4 21 F. 2* G. 21 6 11 K. 65 tons . . . 4 100 tons . . . 4f 9 8 3* 2* 2f 4| 5 If 5 150 tons . . . H 9 8 « 21 3 a 5* If 5 200 tons.. . 6i 10 8f 4* n 3* 2* 6 2 5* W. Load (Fac. of L. M. N. 0. P. Q. R. 8. T. r/. V. Safety 5). 10f 3i 5h 3 9 11 If 4 3 4 3! 21 65 tons. 100 tons. 8i 3| 5 2f 8 li if 3 I •3| 2} 150 tons. 10 3f 5 2f 8 11 If 3* 7 '8 4 2* 200 tons. 11* 4 5* 3 9 11 If 4 2 8 41 2f W. Load (Fac. of w. X. Y. z. Al. #1. 01. J>1. jn. Fl. 0L Safety 5). lh 1A 11 2f 4 21 2i 2 3* 5 8 3 8 65 tons. 100 tons. l\ H 11 2| 4| 2f a 21 3* I J 150 tons. if if li 3i 4! 2| 2* 21 31 ! i 200 tons. i| li If 3| 51 31 2| 2| 41 I 1 Standard Shackles 501 STANDARD SHACKLES (As Manufactured). (Continued.) Chain Shackles. m$) T Fig. 294. Size of Shackle, A. Size of Pin, Opening at Eye, C. Depth under Pin Inside, D. n i, ip „ \ A A J i } A 1 1 ifV J A f H A I it 11 t t ItV 2 I 1 n 2f I n 2A i* if 3 n H if 3J n if if 4i n n ii 41 i| it 2 5i it if 2£ M n ii 2i 6 ii 2 2 J •1 2 2i 2f 7 502 The Naval Constructor STANDARD SHACKLES. Fig. 295. Shackles. Bow Iron Iron Iron Iron Dia. Jaws 8£ Bkeaking in at at at at of in lw ►.35 Load Clear. Sides. Bow. Sides. Bow. Pin. Clear. w-ga in Pounds. £° a. d. d v c. c x . D. e. /• 9- 9,000 9,000- 11,000 it k % \ J 1 f 1 ii 11 1 lA 11,000- 15,500 f A 1 H § 1A 15,500- 20,000 20,000- 24,000 If ? a | IA I il 24,000- 31,000 m it B { if 31,000- 37,500 it \\ if t I l 2A 37,500- 44,000 ij 1? it is 2 A 44,000- 53,000 lit « ia n 2 4 53,000- 62,000 62,000- 70,500 2 2A It it If ; It i? kh 70,500- 79,500 It l-h it J l IA n 211 79,500- 88,000 If if ll 6 5 It I* l 3 88,000- 99,000 w 1 T 7 S 1A 1A IS 1 s 3* 99,000-110,000 *A It in iH il 3 A 110,000-121,000 H* 4 m 11 IJ iH i» 5A 121,000-132,500 4 5? i¥ If lif 11 1 3ft 132,500-143,500 2J 1 lil 1 3 I 143,500-154,500 2i 9 5 1 u lil 1A lit 11 ,** 21 154,500-165,500 8? $ 1* 1 8 I? 2 i 33 165,500-176,500 2| 2 lil 2fV m IA 4 176,500-187,500 2H m 2 If 11 2A 2 1A It *A 187,500-198,500 M if 2A 2 A 2 a 198,500-210,000 It 2 4 2A 210,000-221,000 ft hi 111 2 4 it 1A 4ft 221,000-245,000 2 18 2A i* 2* ii *A WORKED EYES. Worked Eyes. Breaking Load in Pounds. Wire. Clear. h. A;. TO. n. 0. P> ?• a a II a a a a 9,000 A 1 A fV 1 tV tV 9,000- 11,000 Tf n f tV H f * 11,000- 15,500 f i| 6 f H f j 15,500- 20,000 H if i H U if tV 20,000- 24,000 a 4 HV ft 1 if I f 24,000- 31,000 it if i If if ItV f 31,000- 37,500 i HV i I if 1* ii 37,500- 44,000 it H HV l iff ItV f 44,000- 53,000 w* if li ItV HI li it 53,000- 62,000 HV if HV n 2tV ItV I 62,000- 70,500 1* if n ItV 2tV ItV if 70,500- 79,500 Mr Hf *A H 21 1J l 79,000- 88,000 U 11 ItV ItV 2i ItV HV 88,000- 99,000 iA 2 U ItV 2f l*i if 99,000-110,000 if 2 ItV li 2f if li 110,000-121,000 HV 2 T V 1« ItV 2| HI HV 121,000-132,500 if 2* HI iff 3 tV if ii 132,500-143,500 }A 2 T V il itf 3f HI HV 143,500-154,500 it 2 T V m If 3i 2iV HV 154,500-165,500 Hi 2i 2 T V if 3f 2* HV 165,500-176,500 l« 2A 2 T V H 3£ 2 T V ItV 176,500-187,500 if 2A 2 T V 2 3f 2i 1J 187,500-198,500 IB 2f 2 T V 2 3f 2f HV 198,500-210,000 l| 2f 2i 2 T V 3| 2 T V if 210,000-221,000 11 2 T V 2f 2 t V w n IB 221.000-245,000 2 2J 2 J 2i 4 2 T V if 504 The Naval Constructor TOWING BITTS. (Cast Iron.) Fig. 298. Diameter. Weight of Casting. Weight of Fastenings and Chock. Total, Wek;ht. In. Lbs. Lbs. Lbs. 12 2,040 145 2,185 15 3,975 280 4,255 18 6,875 480 7,355 21 10,900 765 11,665 24 16,500 1,140 17,640 Steering Chain Springs 505 506 The Naval Constructor 6 § | s 1 s z I Q 1 & w ll.K).\\|,l.| u t •m8u»q - ; 0«HMNM«M'*'»"Oifll010N apie^no -o 1 »nn«^'*^*'0>oifle« H* **« Mt« frl ; ooOHHHeqpiwwM^^ioe CO ; NB^^iDiOIOONOOMOOON ft) S ^^H-H-^^^^^^^^-W.-h.M. o> v ^^^usioiseeeNNNoooooi ft, ; *H «» "H «M rt< •+• fH ■">! Ha W H .+« «w> f*> «*» o ; ^sJ^ssss^HS^^^^^ps fe! ; ***»********H.* h ^ MS n ">-( -*» hM ""S c*o .*» h«i e 5 «** M«> &3 ; w^^H-H-H-^i-^^^^-WHJi^-H., S 5 H- '^"H^^'-S-W-W.-W-HiH- *..*. fit, HrtrtiHi-lrtHrtrHrHCIM "«" .. ->c-H.i.4--*.-t-1-«H.«Hi-Ni«W«HiH-H-H« Q - HrtHH«NNNNMNNNWW o » i-H» H» rH m Hi< Hn «• BK Ha -w H< •*• 0Q * o« *. tW n» BH ^< «(» m. «, « BW h„ b, ^, ^ I 0>050>OSOOOO-h-Ht-ImhC' «H •+« UK "H "H B fl^H--,-^^^ 3 Lg h~ "P -*. -•- 25 3S - O '^«(-»H0 , ^H«H«H«' S M-*.«*.hS^S*.3S3Sh- - d ^."h "" "K h* .*. : : : : : : 1 \ \ \ i 5 < t» a : ">£ "S .*. .*. .*> *>« "V *> He, He. He. °S •" W d 1-1 He, •£#-**. -B «S -B «. h. *. a . Hi d n(» s |H'VlHB^-*i* 8 H 8 V<*«»*'* O T3 6 d *^* - i a rW r*> «M OW MW H *> K d H< ^« "2 *H ** W> l*» #0 "-h ""h ••* HO H11 s d *>. He, r* "*» •*• "H M"0 r> H« r, > «*» H H»HHHHHNINN«NN 3 w a S •< H O - , d ,H,H,H*_,^ T -,,_,^ l ,_r_;^f_ M »n d SSSKh-SS^^-S-;-^^^^^ ... a* di» m m w w _*e Ml* «H« «H «K HH «H -»1 -K H» H«> n |H - a* •** 3" h» •* (w 25 hc ^* »* o> a rtHHHHHHHHNNININ ">% | q l0 »*«(iii(i l >< h H4iH" 6 ><'>'i»**«l<«Wi« « d "K « Hn Ha H« «o *>! Ha 4t aK *>" cet^t»t^ooooo»oooo-H^ • d *1010U5(B01 Gaff Mountings GAFI* MOUNTINGS. 521 Fig. 311. 522 The Naval Constructor GAFF MOUNTINGS. Fig. 312. Stuffing Boxes and Glands 523 Fig. 313. Ws 5,3 5,3 5.3 t( <§ H .2 * is us .5 cS ■— ' cs'r* K*r* w"7" o^o^o^o^ HrtHHHH-HC^CIlMIMIN^nMMnMCO'J' rtrtHNWNIN * •* 5 tJ< iO lOiO ^^H2^H rt t f HeMciHn»^«]2o)|>WwH'nMHx>i1xit+ortj) i-Hr-i-H»H(M^s^ci(MCicococoeo-*"#Tr"#m»aio ^ lo j2 10 S ,0 H' e H K ^ rw * ::>e * DW ' oot *M N !2 t ' ssuag ^ t ~H l "w O " 0> H 0> M S! irt 0> i-i®H a l- uo.ii t ^^^^^^"S^^E" «- M '- M f -H'" l v, t -W a] w®M 0i l-i«,w«' SS8.I.I I v avot r INMWNHN 1^ l H r r " ,, """- ,, ~"- |r ""-"~'fr ,• " 1X1 AXA 1XA AX1 ixA AX! ixA 11 if if lit 21 21 2f p 8 2 1 2 5 8 f 3 4 1 11 if U 2 21 2f 11 1A if li 2 21 11 if if 21 2| 21 3 I 8 11 li If u 2 2 3 8 1 2 5 8 5 8 3 4 4 7 8 A 1 4 1 4 A A 1 i 8 A A i 4 1 4 A 1 2- 5 8 3 4 1 8 1 H lj 3 8 1 2 1 2 f 4 3 4 7 8 A A 5 8 3 4 7 8 1 1 530 The Naval Constructor LOW PRESSURE > S I A B A l Si C D Di D, Ih E F / y x L M TV 1 ! 6 3 1 1 15 it 7 34 3} 41 74 84 81 101 'if 21 24 2J is 4 2] 8 2 A A u 15 15 H Ik 2 H if n 44 5 A it> 4| 51 3} 4 i] 21 25 2? A 1 4 54 i .v. U "n A A 24 114 3| 5} u 61 42 2; 35 \ A A n 11 2 A A 3 124 3} 61 21 7} 6] S| 4 i 1 i 3 « A 14 U 2 A Si 13 4} 64 2A 7} 05 32 41 i 1 A _r. 12 If 25 A 4 13| 4} 6} m 81 n H 5.1 i 1 A 1 12 15 25 1 *i 15 51 74 3 91 8 5 5] 6 u 1 i A 1U 11 14 21 1 A 5 16 5} 8 3} 9f a ff| Sj S| n 1 5 % 2 U M 21 5 A 54 16f 6} 8} 34 101 H a SJ 7 u 1 IS A 2 2 1| 25 5 A 6 18 6} 9 3} 11 10} Si 75 71 u 1 1 2 2 i;5 25 A * A 6J 18} 71 9| 41 HI n 7,1 8 81 if 1 lA 1 21 15 22 A 7 20 8 9f 4f 13} HI 72 S| 9 u 1 H i 21 1! 22 A 71 214 8f 10 4f 134 125 ■SI % 91 n 1 n I 25 H 3 A 8 22} 91 10f 5 14} m 9 K 10 15 1 i A i 25 12 3 1 A 84 24 9! 10} 5} 141 141 94 io| 105 l] 1 l A 1 21 12 31 1 A 9 254 101 Hi 54 15f 15 10 n ill 1] 1 15 N 21 U 31 * A n 26} 10} Hf 55 16 15] 10) ill iij 1] 1 lA H 22 2 3} 4 A A A A A 10 28 HI 12 61 16| 16} 11 12 12J 2 1 i-l H 22 2 32 5 10* 29} 11} 124 6! 174 17} 111 121 121 2 1 il H 21 2 35 1 11 304 121 13 6f 17} is 12 13 13.1 2 1 H 21 21 3} 5 114 31} 12f 13} 61 19 18} 121 135 m 21 1 15 3 21 4 5 A 12 33 13 13f 71 19} 191 13 J 141 145 21 1 15 3 21 4 H $ 12* 344 13} 14} n 20} 20} 135 14? ill 21 1 15 31 21 41 H 2 13 36 13} 14} 7} 20| 21 141 151 155 21 1 U 35 22 45 ii A A 134 374 141 15} 8 21} 21] 14 5 16] 155 21 1 H 31 22 41 2 14 39 144 15} 8} 21} 22 J 151 16| 1«5 21 I U 31 3 42 2 144 404 15 16} 8| 22| 23J 15] 161 171 21 i n 35 3 45 2 A 15 42 154 16} 9 22} 24 101 - 175 171 21 1 i] 31 3 4 5 1 A Low Pressure Valves 531 VALVES. p Q ft S T 7 A A A I 3 B x 3 , ft 3 it I i i I A ft ft ft 3 8 I f 1G A A 1 A A I I u X w 3 o Pi 6 B u Eh « £ o g 8 6 a 3 (5 « > o O g CO d g to 1 • B B H i d> 3D H is a b c d i / li « n if H if if u 11 2 2 2f 21 2| 2| 21 21 3 3 31 Si 31 3f 31 3* N 41 M 5j 52 « 7 1 71 81 81 9 91 101 11 111 12 121 13 1.31 14 141 15 15i 16 3ft 4 4ft 6 61 7| 8f 9f 10| HI 12J 13J 14f 15* 16f 17f 18f 21 22 23 24 25 26* 28 28* 29 31 32 33 A A A ft £ A ft ft h 1 2 \ h 1 1 1- 1 1- 1 1 i I 1 i 2 1 1 1 1 i{ H li 11 M 1* 11 n 21 21 2.1 22 22 22 n 2! 22 2f 21 22 2\ n 2! t 1 A {, A 1 1 1 2 A 5 - f 1 1,1 J 1 HI 13 1 I 1 I 1 1 1 I 1 I 21 31 31 4f 41 5! 61 61 7i 8 8f 9* 101 HI 111 121 131 13f 141 141 15f 16 17 17f 181 18| 191 191 20| 20f 6 6 6 6 6 6 6 6 8 8 10 10 12 12 12 14 14 16 16 18 18 18 18 20 20 20 20 20 22 ! 1 1 1 f f i t f 4 8 5 1 1 1 1 \ \ \ \ \ f f 1 I 1 1 1 1 1 1 1 1 1 11 11 11 U u 11- 1-2 n n n li u ii M 11 H if H 11 i! H if ft ft A h \ 1 1 1 1 1 1 \ \ ! I ! I 4 I i 1 1 1 1 A A A A A A l l l l l h 1 i i 1 1 * 1 1 1 i 1 1 i \ 1 I I f 1 1 1 1 1 i 1 21 2ft 2ft 2J 21 2 8 21 3 3 31 31 N 3', 3i 31 4i H 42 n M H 45 51 51 51 52 51 If U ii 2 2 21 21 21 21 21 21 21 21 21 21 31 31 31 31 31 3| 31 3} 31 31 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ft A ft I f ! 1 1 1 1 1 1 1 1 1 1 I f 1 I ! ! i 4 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 i i i t i 1 I 1 1 1 1 1 i f 4 8 1 I 1 ! I 1 532 The Naval Constructor mil Low Pressure Valves 533 534 The Naval Constructor LOW PRESSURE 5 •< > O I 1 i 1 14 14 2 24 3 31 4 41 5 51 6 64 7 74 8 84 9 94 10 101 11 111 12 121 13 131 14 141 15 -4 1 4 i A A A A 1 U ii 1A IS LI U 11 lH II U ii£ 2 22 2i 8] h H 1 J 2 J 1 N 3] £ 4 i 1 1 i 1 I l| il L| 11 11 i| il i| i| 2 2 2 2 21 2 J Si 21 H c A A A 1 4 4 4 4 1 1 1 i 1 1 1 4 4 1 4 1 4 4 4 4 1 4 1 D il 1A H 14 2 24 34 3f 44 4J 51 51 6| 61 74 84 81 94 10 101 11 HI 12 121 13 131 141 14! 151 15! 164 161 E F G // l J K L M N P Q R T U 16 if! 16 14 It 14 14 14 12 12 12 12 12 12 12 12 12 12 12 12 12 1(1 10 10 10 10 10 10 10 2 I 1 1 U H U 2 2 2 i 3 , ; i 3 , 4 4 A 4 1 4 1 1 1 2 A A A 1 3 B 4 41 5 51 6 61 7 74 8 8| B H 10 101 111 12 121 13 131 14 HI 15 ii I il il li L] 12 U 1:2 US H 2 2 A 2A 21 22 2' 22 3 3 31 3:2 31 32 8| 32 42 41 42 41 1 A 4 A a i i i i i A A 1 4 A A i il 11 1 i 4 ii il il 1 1 1 ii 41 24 22 21 2| 2\ 3 3 32 H N 8| 4 4 44 4| 4 U 41 5 5 51 51 52 52 8* H n U H u 2] 21 2 H 2| 22 22 3 J 3 J 8| 3-1 32 32 a i ii 4 4 41 41 42 42 ft* 4J 14 LA If 12 12 2 2 2A 2A 2x0 2A 21 2] ■'It 2[* H 3! 31 8j N 31 31 31 3| 31 81 31 i i i i i i i i n ii ii 14 ii U n If 1] ii H 12 14 II II * i 4 A 4 1 4 5 S 1 ii 1 il tl \l I I 1 J 1 t 2 1 A A A A A 4 •1 1 4 A A 1 1 ii ii if, ii 1 u u 1} u 12 14 H n 1! i! 12 11 2 2 2i 22 24 I I 2 A A A 4 4 4 A IB ii 1 4 1 | f Low Pressure Valves 535 VALVES. V W X Y 1 1 Z Si d fc £° 9 8 a b ! d e / a h « k I I, m n P i 5 A r 2 3 H "\ 1 A 7 A i' ' ' i ii' i i' if" t li' ii ii' A 3 11 2 5 A 7 A i . . 1 2 l 2 12 1 U 12 H 1 4 1A 1 1 1 6 A A . A 2A 11 A 11 2 12 n H 1 4 H 1 lA f f 6 A r, . A 22 ti 21 A If 1 12 H l A 2 5 U 1 H 1 4 6 1 1 • . A 21 12 21 A 12 1 12 12 U 11 6 H U 1 1 6 i 1 I A • A • A 22 H 31 A 12 8 U 12 12 11 6 H 1 U 1 1 5 1 2 3 U 31 1 U i 4 21 U If 2 7 H If 1 1 5 i 1 • 9 • 18 3] if 41 1 if 1 22 U H i 8 l! 2 If 11 1 5 I 1 • 11 31 n 41 1 2 1 22 2 if 2 8 if 1 If 11 i s 5 3 1 1 • • 11 3 A 15 51 A 2 H 21 21 If 15 9 li 1 If u 2 4 1 1 3 4 32 2 H A A 21 U S 21 U 1 10 U 1 If li I 4 1 1 1 • • I 4 2 6 § A 21 U 31 21 12 1 10 2 1 H li 3 4 2 I - 12 ■U 22 6i 2 1 22 H 32 21 2 1A 11 2 1 H n 4 .4 \ 1 • • if 42 22 61 | 5 8 21 12 31 22 2 H 12 21 1 u u 1 4 1 1 • • 11 a 2, 72 i 2 21 if 41 22 21 H 12 21 11 2 u 3 4 4 1 1 i • 1b ■i! 21 72 i f 21 2 41 21 21 1A 14 2f U 2 if 1 4 1 A. kl 1) 21 81 i 22 21 42 21 21 U% 14 2! H 2 if I 4 1 A 3 . 1 H 21 81 i I 22 21 41 21 21 lA 14 21 1! 21 « J 4 1 9 10 3 ki 51 3 91 i ! 3 22 51 22 22 l A 16 21 I! 21 n I 4 2 A 3 si 51 3 91 i 3 21 51 22 22 l A 16 2i H 2i n 4 1 1 i J s 1A 5? 31 10 i 2 31 22 52 22 22 1A 16 2| ii 21 If 4 1 1 I UA 5! 31 10J i 2 31 22 52 3 3 i! 18 21 11 21 2 4 1 1 1 UA 51 32 101 t 2 31 3 61 31 81 12 18 21 11 2f 2 4 1 1 i j b 1A 6 32 11? 5 S i 31 31 6i 31 31 12 18 31 if 2f 2J u 4 1 2 i Uf 8A 32 112 f • 4 32 31 62 31 31 U 21 31 il 21 21 4 1 1 < Uf 61 32 211 5 8 2 41 31 61 32 32 If 21 31 H 22 22 4 1 53 r Ul H 32 122 1 2 *1 32 71 4 4 M 21 31 U 3 21 4 1 IS X Ul 61 81 131 8 2 41 4 71 41 41 H 21 31 11 3 21 4 1 2 13 1 Ul 62 4 131 2 2 41 4 7? 41 41 11 21 31 H 3 21 4 I 12 1 111 6| 4 14 1 3 4 41 4 72 41 41 2A 24 536 The Naval Constructor HEAVY PRESSURE > > H 1 1 i 1 u H 2 21 3 31 4 41 5 Si 6 61 7 71 8 81 9 91 10 101 11 111 12 121 13 131 14 141 15 A 6 7 71 81 a m m 13 w 15 16 16 1 18 w 20 21} 22J 24 251 26J 28 29 J 3(1} 811 33 31} 36 37} 89 40} 42 U 1} 11 21 2} a *i 33 41 43 BJ 53 63 63 72 8 8:5 91 91 101 103 in 113 121 12| 13 13| 133 141 14} u 10} 3 8* 33 41 42 Bl 53 61 6} 6? 71 8 82 9 02 02 10 10J 103 11} 111 12 121 13 13i 181 141 143 16] 153 161 163 B, l 11 U 1} If H 2} 21 21 3 1 N 33 41 4} 43 5 51 5} 53 6 6} 6} 63 7 71 7} 73 8 81 81 82 c 33 42 45 51 H 63 73 82 82 9) 10} 111 12 12} 131 14 14} 151 16 16} 17} 18 183 19} 20 20} 21} 221 23 233 241 243 D '23 3 3} 4 43 5} 62 7i 8 83 9} 101 11 112 122 13} 141 15 153 16} 171 18 183 19] 201 21 213 22} 231 24 1 li 12 13 21 22 32 33 4} 5 5} 6 6} 72 73 81 9 9i 10 10} 11 11} 12 12} 131 132 141 142 151 153 161 D 2 D t E F G H / A A A A A A A A A A A A A A A A A A A A A A A A A J i i i i i i 12 1J 12 12 12 H U 1! H 12 12 11 12 12 12 1} 1} 1} 1} 1} K H H i} i} 13 12 2 21 23 22 2} 23 2! 3 31 32 31 32 31 32 4 42 42 4} 42 42 13 5 52 L U 12 1} 12 13 12 2 21 21 21 21 23 3 3 3 31 32 3} 3} 33 33 33 4 4 4 41 41 .1/ 22 22 22 23 22 31 31 32 33 32 4 42 4} 42 42 51 51 61 5} 52 6 62 61 62 62 62 7 N A i 2 f n n l l H H 1 2 h IS 1 l 1A 1A 1A U u 1A 1A l A U A A A A A A A A A A A A 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 P if" n 13 12 2 2} 21 22 22 23 22 32 32 32 3} 32 32 32 4 41 42 4} 42 43 42 51 51 Q 4 4f 51 5f 61 71 7f 8 81 91 10 101 101 Hi 12 121 12f 131 141 14} 15f 151 161 17} 18 181 19 A A A A A A A A A A "i i i ia 12 U 1A 1A 12 l A i} i} i} if if if 13 13 13 13 13 4* 51 53 61 62 72 81 82 03 102 102 112 112 12} 13 132 142 142 15} 16 162 172 172 181 193 192 203 5! 61 62 73 8 82 92 9-2 lo- ll 11} 12 12} 13 132 141 143 151 153 163 161 172 23 32 4 4} 51 6 62 7 7} 81 9 01 10 I0| 111 113 121 122 131 133 142 142 152 152 162 171 17} i i I 1 1 12 U U U U 1} 1} U 11 11 U 2 2 2 2i 22 22 21 21 21 21 21 Heavy Pressure Valves 537 VALVES. R 1 ?! S T J7 V w X H O 9 g g 5 P £ d g eg 1 Q g a 6 g 10 1 • 00 « 05 > w o s o 3 H « 55 00 H a I ) c d e / 3& . 4 . 4A . 6 i 61 \ 71 - 8f - 9f 101 1 Hi i 12! 1 13! i 14| I 15* I 16f 1 171 : 18f 1 20 i 21 | 22 . 24 . 25 . 261 . 28 . 28-| . 29 . 31 32 . 33 . \ li \ If ' If ill H 2i 2| 2f 2f 2f 2! 21 \ 31 i 31 t 31 .31 .3! • 3f .41 • 41 .41 • 4f .4! . 4! . 5 . 5 i 1- 1 A 1 1 ft h i 1 A 1 i H H i ! I li! 52 I 1 1§ l lA iA li 11 If u li H i! U li 21 2 J 21 21 21 21 21 21 21 2! 2? 25 25 25 21 i 8 1 1 1 4 I 1 H ii U « 11 K H 12 I 4 11 li 2 21 21 21 21 2^ 21 2} 21 3 32 35 31 41 « H H 51 51 61 05 71 71 75 9 91 10 10 ioi n ill m 121 13 I 1 1 ! I 3. 4 5 8 1 1 i 1 1 1 1 1 U li u ii lA lA lA il M « H li 51 6 6! 71 71 81 91 10 101 ill 12 121 13! 13! 141 15! 161 17 17! 18! 18| 19! 201 21 21! 22 6 8 8 8 10 10 10 10 10 12 12 12 12 14 14 14 16 16 18 18 18 18 i i i 1 i 1. 1 1 1 1 H U u li it 1 H H H U ii U if If li H ii H U li H 1*1 15 1 15 1 15 1 15 1 HI 1*1 1*1 2 1 2 1 8 i 1 A 1 A f 1 ! 1 I 1 f i f ! 1 1 1 i 1 1 1 1 fl 1,1 11 M U H H 1* ±8 U 1! H ft 1 1 1 1 1 1 1 | 1 I I 1 1 1 1 1 1 2 A 21 2i 3 8i 31 35 41 42 4 4| M 51 52 ,c 55 5± 6 62 02 62 0! 61 71 71 li 2 2! 21 24 21 2! 2! 3 3! 31 31 3! 3! 4 41 41 41 4! 41 5 5! 51 5! 5! 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 i I 1 a 8 f ! 1 1 i ! 5 8 ! I I 1 1 4 ! 1 1 I 2 4 | 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 i 1 1 1 1 1 i 1 1 1 1 I ! 1 4 ! 3. ! Naval Constructor fl/UO 3AIOA SSOJl UO LjJUOACj %)14± ; Heavy Pressure Valves 539 540 The Naval Constructor HEAVY PRESSURE ! 1 k O i a to 1 * 1 11 H 2 2* 3 31 4 4* 5 6 61 7 71 8 ft 9 H 10 10J 11 111 12 12* 13 13i 14 14* 15 .1 i i 1 ft ft 1 ft I A U U H ii ii n u u 2 2; 21 2] 21 21 2i 2| 2| 2] 3 N 3| 81 3 2 B C D li! LA H U 2 21 81 32 4.t M 51 51 N N 71 •Si 8] »i to 10 1 11 111 12 12 j 1:5 181 141 14; 152 16 lO 1 , 17 E f H H u ii 21 22 2f 22 81 32 81 .4 •li 4| 4? « 51 H 51 51 6i • 16 4 15 f 3f 25 U 1 15 51 25 U 1A. u 25 | 15 15 1 12 a i 2l 4 15 f 318 2f U •'1 f H 51 2f 15 H • n 25 I 2 if 1 12 ,1 4 1ft f 4A 21 11 1 if 5i 3 u il • U 2:1 l 21 15 1 14 i 1 B lA 4 l* 1 4 A 25 15 1 if 55 35 11 1A . U n 1 21 2 1 14 t 1 HI 4 if I 4A 3 n A 2 61 31 If 1A. if 35 1 25 25 15 14 1 1 H! 4 lH l « 31 15 A 2 A 6f 35 u lA . 1A 3i H 2i 21 15 16 1 1 HI 4 IH 1 5 31 15 A 2 A 71 4 H 1A. 1A 35 15 25 25 H 16 li 1 wll 4 2A 1 61 3:1 If A 25 71 45 11 1A. U 3' H 2f 21 U 16 if 1 Hi 4 2 A U 51 35 11 1 7 A 71 41 if 1A. 111 35 U 25 25 11 18 1 . ,U 4 2 A U 55 4 15 1 2 A 81 45 if if • Mb 35 U 3 25 H 18 1 * Ml 4 21 il « 4 2 i 2f 9 45 15 if 2 I'll" 4 if 3 25 11 18 1 5 M| 4 21 if 6 41 21 f 211 9 5 2 if 2 Mil H 15 35 25 if 21 H J I 1 * 4 21 if 61 45 21 1 21S H 55 2 U 2 [HI 45 H 31 3 if 21 1 J l* 4 2!i! 15 6^ 45 21 1 35 10 55 21 11 2 Mi 41 u 35 31 if 21 1 ! *2 4 21;! 15 65 4f 25 ! 35 10 55 21 U 2 21 45 u 35 31 if 21 1 3 S 2 4 21;; 15 H 45 2^ f 35 101 6 21 U 2 121 45 H 35 31 if 21 1 i ?2 4 31 u 71 5 2f 5 31 u 6 21 If 3 2| 4j u 35 31 2 24 U s 5 2i 4 31 If 71 55 21 1 31 m 65 21 2A3 2f 45 15 35 31 2 24 11 * 9 21 4 35 If 71 51 2f 1 31 m H 21 2A3 2f S If 35 3f 2 24 U 3 *2* 4 31 2 71 55 3 l 31 121 61 n 2A3 b 2f 5.1 11 41 3| 2 i 24 H i 5 2i 4 31 2 8 H 3 1 31 13 71 2f 2A3 b 21 542 The Naval Constructor FRICTION BRAKE FOR CRANES. The crane brake is solely for the purpose of preventing the load from falling when there is no other sustaining force and preventing the load from falling faster than desired when lower- ing. Incorrect disposition of the friction of a brake in relation to the load and power makes its purpose unattainable, and an improper proportion of friction to load makes its operation doubt- ful and unsatisfactory, causing it to either slip or stall the motor when trying to lower. The general features of brake friction brakes are as follows: A cam in some part of the transmission mechanism is so designed that the downward pressure of the load causes an axial pull in the shaft which presses friction Fia. 323,— Cone Brake " Naval " Boat Crane Full Load Torque = 7880 In- Lbs. surfaces together. The outer casing or barrel is allowed to rotate with the other parts when hoisting, but prevented from rotating when lowering by ratchet and pawls or band brake. Lowering, then, is always accompanied by relative motion between the friction discs or cones and whatever friction is developed between these tends to prevent the load from lowering and must necessarily be overcome or relieved. The proper arrangement of friction brakes is obtained by dividing the friction between the power and load ends of brake, half being on the motor side and half on the load side of the cam. Examples of this type are shown in the cone brake for a gantry crane and in the Seller's type of disc friction brake supplied for naval boat cranes. The reasons for this arrangement will be developed in the follow- ing discussion. . Friction Brake for Cranes 543 Fig. 324. Case I. — Two friction brakes designed with all the friction on the load side of cam as shown on accompanying sketches, Figs. 323 and 325, one taken from the automatic brake for boat crane of battleship and the other being the brake supplied by the builders of the gantry crane. This arrangement of friction is entirely erroneous, as the motor must always keep some force on the cam to prevent the friction surfaces from separating, and allowing the load to slip. Suppose AO, Fig. 324, to represent the force required to overcome the load, applied at mean radius on the cam, OB represents the axis of the shaft. If in a given design we assume that an axial pull of OC is required to cause sufficient friction to overcome the load, GG will represent the slope of a cam which will just supply the requisite pull. OD is its normal pressure, and AD = OC is the axial component. With cam GG the friction of the brake just balances the load supported by AO. When this brake is lowering and the motor withdraws its pressure against the cam, the load will drop until it overtakes the power side of the cam and causes a normal pressure with an axial component sufficient to again set up the frictions. This same normal pressure always tends to drive the motor downward and it will thus be seen that even when the load is being lowered the motor must exercise a force against the cam in the direction tending to lift the load. Thus, with the above cam GG and axial component OC, we find by drawing the balance diagonal AC, that in lowering at constant speed, one-half of the load is overcome by the friction of the brake, see AL, and the other half has to be overcome by an upward pressure of the motor, see OL. Suppose we represent by R the ratio of the axial pull in the shaft due to hoisting full load to the axial pull required to just balance the load. In the case above, R = 1. Suppose R = 2, the axial component being AE = 2 OC, we find that when lowering at constant speed the friction of the brake overcomes AM = f of the load, and the motor has to supply OM = f of the load in the direction tending to lift the load. Again, if R = 3, the axial component = AF = 3 OC, and the motor lowers with \ load supported by the motor, ON, and f load supported by the friction of the brake, AN. Thus, if R = n, the lowering will take place with — — : of the load overcome by friction in the brake and — t-^c supported n + 1 r,4i The Naval Constructor by a raising pressure on the motor side of the cam. In a brake, with all of the friction on the load side of the cam it is obvi- ously impossible to check the tendency of the load to drop without maintaining an upward pressure on the motor side of the cam so as to keep the friction set. The main object of an automatic brake is therefore impossible to obtain with this arrangement, and the motor is run backward against the force which it has to apply on the cam in order to keep the friction surfaces operative. The best that can be done with this arrange- ment is to make the value of R as large as possible, by using say 8 to 10 degrees angle of cones and as small a lead of cam as the shaft will stand, thereby reducing the value — — -. to be supported by the motor. A magnetic clutch on the motor, or great friction of bearings is necessary to hold the cam in such an arrangement when power is cut off from motor. Calculation of Cone Brake for Gantry Crane. The full-load force on 25,^-inch pitch diameter gear is 2400 25 l pounds. The torque then is 2400 X -=* = 30,400 inch-pounds. m fleshts with Motor Pinion Load 1400 Lbs ZO'Slopt Fig. 325. —Cone Brake for Gantry Crane Full Load Torque = 30,400 In-Lbs. Taking the mean radius of the brake cones as 9^ inches, the force of friction required at this radius is • ' _ = 3200 pounds. Then if we assume a coefficient of friction of 0.1 between the friction surfaces, the normal pressure required on the cones will Friction Brake for Cranes 545 be 32,000 pounds. This has to be obtained by a suitable angle of cam in combination with the slope of the friction cones. Tak- ing the mean radius of the cam as 3 inches we get — '-x — = 10,133 o pounds tangential pressure. Referring to diagram, Fig. 327, OB represents the axis of brake shaft. Laying down this cam pressure to the scale of 10,000 pounds = 1 inch we obtain OA normal to OB. If we use 12-inch pitch for the cam its slope is represented by CD, and we find from the normal OE that the axial pull will be ON, friction not considered. Allowing for 0.15 coefficient of friction on the cam we lay off FOE an angle whose tangent is 0.15 and obtain OM as the axial pull. Extend MF and intersect same by OG the required normal pressure 32,000 pounds to scale. Perpendicular Fig. 326. —Original Disc Brake on Gantry Crane. to this we get the slope of the cones OH, which will obtain the above normal pressure with the given axial pull. By measure- ment BOH is found to be 21 j degrees. If we use a cone angle of 20 degrees and return through the construction from H-G-F- E-CD we find that the necessary axial pull will be given by a cam whose lead is 12| inches. The use of 12-inch lead on cam with 20-degree cones will, therefore, furnish a friction slightly in excess of that required under the conditions mentioned. Prob- ably the friction between the cones will never reach a lower coefficient than the 0.1 assumed, but in case this should occur the first motion will produce vibration destroying the friction on the cam surface and produce additional axial pull approaching ON. The construction of point K shows that brake will operate on a coefficient of 0.08 or less when cam friction is destroyed. The width of the cones is determined by the pressure desired. Using 50 pounds per square inch we need — -^ — = 640 square inches area and of each cone. 640 9.5 X 2ir 50 lOf inches width, say b\ inches width 546 The Naval Constructor The oiling system is designed to pick up oil outside of cones and deposit same between cones when lowering, so that the oil must pass continually from small to large ends of both cones. There are, as seen by the above, and by reference to Fig. 324, three quantities inter-related in brakes of the class just designed for the gantry crane. The normal pressure required on the friction surfaces, the angle of the cones, and, the lead of the cam. With given materials the pressure per square inch can be decided upon and the diameter and breadth of cones chosen to take the total pressure which is the frictional torque needed divided by the mean radius of cones and by the coefficient of friction. This quantity arranged, we can assume a value for one of the other variables and determine the remaining quan- tity, a couple of trials being needed to obtain a suitable set of values. If, instead of 50 pounds per square inch, we had used materials allowing 200 pounds per square inch as in Fig. 324, the brake, Fig. 327, could have been much smaller, and a design with 6-inch mean radius of cones would have 15-degree cones each 3| inches wide with a 10-inch lead on cam of 3-inch radius. The axial pull is least affected by friction on the cam when the lead is such as to give a cam angle of about 40 degrees, and angles between 25 and 40 degrees are therefore prefer- able. Lubrication of the cam should be arranged or the operator instructed to keep cam well greased. Pawls should be designed carefully, as light as possible and nearly- balanced; and their friction levers should be long enough to posi- tively operate the pawls. Wood friction pieces slip when wet and metal pieces when oily so corks are used since they have 0.30 to 0.36 coefficient of friction under varying conditions and, with relatively smaller pressure, have 3 to 6 times the life of wood for friction blocks. Fig. 327. Case II. — Taking the second case, where all of the friction is gathered on the motor side of the cam, we get a brake the re- verse of the above arrangement in which all of the purposes are obtainable but liable to be unsatisfactory if for any reason, Friction Brake Cranes 547 such as lack of attention to lubrication, the coefficients of friction on the working surfaces should vary greatly from those expected. Let OA, Fig. 324, again represent the lifting force of the motor on the cam, GG the slope of the cam and OC the axial compo- nent required to just balance the load. If all power be turned off the motor or even if the motor pinion or couplings be removed, the lowering tendency of the load will cause the normal pressure OD whose axial component OC locks the fric- tions and prevents dropping. Now suppose this brake to be designed for 0.1 coefficient of friction, the friction on the cam not being considered. If for some reason this coefficient of friction should drop to 0.08 or the friction between the sliding Fig. 328. — Sellers Type Disc Friction Brake for Boat Crane Full Load Torque = 21,900 In. Lbs. surfaces of the cam should become apparent, this normal pres- sure OD will be insufficient to lock the load. We must then design for the worst conditions allowing, say, 0.15 coefficient of friction on the cam. If this brake were allowed to run dry and the co- efficient of friction between the working surfaces rose to, say 0.15, and the friction between the cam surfaces was overcome by the vibration of the machinery, then the pressure of the load on the cam would cause an axial component supplying more than twice the necessary friction, and the motor to lower must exert more than its normal power, i.e., run overloaded to force the load down. Case III. — This state of affairs can be overcome by the arrangement of brakes shown in Figs. 325 and 328, in which the friction is divided between the motor and load ends. In these 548 The Naval Constructor brakes the cones or discs will have the same total area as in the foregoing case, but with a marked difference in operation. Take the case when R = 1, the axial component OC, Fig. 324, will cause just enough friction to balance the load when starting to lower. The motor must overcome the difference between the resistance of the friction on its side of the cam and the turning effect of the load pressure against the cam. As soon as this is overcome the pressure betweeen the cam surfaces drops to \ of its hoisting value, that is, \ of load AL will be overcome by friction on load side and other half Oh by friction on the motor side, so that in lowering this brake the motor must give downward direction,' but no power is required to lower unless R exceeds 1. This brake must be designed also for minimum conditions expected, say coefficient of friction = 0.1 on sliding surfaces and = 0.15 on cam surfaces. It locks to an equal extent as the brake just discussed with friction entirely on the power side of cam, but instead of using full power or overload on the motor when lower- ing under adverse conditions, on this brake it would only require a large force to overcome the first frictional set of the brake when starting to lower and would lower thereafter with never more than one-half of the motor's normal load, as can be seen by the discussion of Fig. 324. Even if this brake were designed well on the safe side, say R = \\, to provide a margin when locking the load and should double its coefficient of friction the force of \\ normal load which would stall the motor in Case II could be easily furnished for the instant necessary in starting by a series wound motor, and the brake thereafter would lower easily with some small downward force exerted by the motor. This last arrangement with frictions divided between motor and load ends, in addition to being effectively self-locking and unapt to stall, has the further advantage of being the least complicated of all cases as can be seen by comparison of Figs. 325 and 328. VENTILATION. The accompanying sketch shows a complete system of ventila- tion designed and calculated according to results of experiments relative to deliveries of ventilation systems on board ship made by D. W. Taylor, Naval Constructor, U. S. N., at the Experi- mental Model Basin, Navy Yard, Washington, D. C. The first point to be determined in laying out any system of ship ventilation is the amount of air that is required in each compartment to be ventilated, assuming that the number of cubic feet of air to be delivered per minute as marked on sketch at each terminal is the amount required at that special point for the efficient ventilation of any compartment or com- Ventilation System 549 VENTILATION SYSTEM. 6{'0la: \i'D/a.-Ye/'/50Z IS'Dia.-V&>- C' ' ptrrvn. '<-Steel Plate Electric Fan ^^£&s-. Capacity 1500 Cub- Ft "% r * perMinAtMaxe.Speed Fia. 329. 550 The Naval Constructor partments, such as engine rooms, water closets, cabin spaces, storerooms, magazines, etc.; the fan is then placed in the most convenient location for economy in piping. The next step is the head of the main or mains which should be as straight as possible with the number of bends reduced to a minimum. Then make the standard conditions at the first outlet 5 pounds pres- sure, and about 2000 feet per minute velocity. "This pressure of 5 pounds per square foot is for standard conditions of air, density corresponding to a barometric height of 30 inches, a temperature of 70 degrees Fahrenheit and a relative humidity of 70 per cent. Under these standard conditions a cubic foot of air weighs 0.07465 pound. The pressure of 5 pounds is equiva- lent to a pressure head of 67 feet of standard density air. A velocity of 2000 feet per minute corresponds to a velocity head of 17.27 feet. The total head then against which air is delivered to the supply main is 84.27 feet." As the branches lead off do not change the size of the main until sufficient air has been removed to reduce the velocity to a value between 1200 and 1500 feet per minute. Then contract the mains with a taper of 1£ inches to the foot until the area is so reduced that the velocity again becomes about 2000 feet per minute. Repeat the contraction wherever necessary, but do not reduce the final diameter of the main to less than twice the diameter of the last branch. A 15j-inch diameter pipe is selected for the first section of the main, on account of giving the nearest velocity to 2000 feet per minute. After branches A, B, and C have been taken off the velocity is reduced to 1458 feet per minute. Being below 1500 feet per minute the main is reduced in size with a taper of 1^ inches to the foot to 13-inch diameter which increases the velocity to 2007 feet per minute. At the beginning of the 13-inch diameter or B.B. section of the main, the direction is changed 90 degrees which should be done with an elbow having a radius of throat not less than diameter of pipe. When branches D and E have been taken off the velocity becomes 1302 feet per minute; the main is again reduced in size with a taper 1 \ inches to the foot to 10§-inch diameter increasing the velocity to 1995, and again branches F and G reduce the velocity to 1247 feet per minute, which necessitates changing the size of the main to 8j-inch diameter, bringing the velocity up to 2020 feet per min- ute. Branches H and / again reduce it to 1212 feet per minute as the main should never be reduced to less than twice the diameter of the last branch but it can now only be reduced to about 7-inch diameter to be settled definitely later when sizes of branches are determined. Chart for Ventilation Pipes 551 84nuiu j ad -4 j -no uisaoiniOA ■U|UJpd493j OOOIA+POPA S3qOU]UrS|k3U|LUJ31 40 3ZJ9 JCy.3|0O£ \^mS^SMI^%V»nMlMWHV« , :V'! "oO v> OJ Yu LJ £«l hjM CVI *CVI OJ CJ CVI «!j To To M Q CM OJ & = rO To' V ~M- J tfj lc to lo To U k> 2 CVI to OJ >0 V tn to t© to to CD © OJ V OJ > OJ o to °o i£> "o 'in o V to *°P *o < "o OJ In CO cu V CVJ "cm to o to to o V Weight of Standard Ventilator Cowls 559 WEIGHT OP STANDARD VENTDLATOR COWLS. Diameter of Ventilator Trunk. In. 10 12 14 16 18 20 22 24 26 28 30 33 36 42 48 Length of Parallel Neck below Centre of Throat Radius. Area in Square Feet Plus Laps. Weight of Cowl in Pounds, Exclusive of Fittings. In. Sq. Ft. Lbs. *\ 5.5 11.25 3 7.5 15.50 3$ 10.5 21.50 4 13.75 28.00 *l 17.50 35.75 5 22.00 45.00 H 27.00 55.00 6 32.50 66.25 H 39.00 79.50 7 45.50 93.00 n 53.75 172.00 8i 64.50 205.00 9 77.50 247.00 101 105.00 335.00 12 135.00 430.00 Thickness in U.S. Gauge. No. 18 U.S. G. No 14 560 The Naval Constructor ELS WICK Diam. of bore, ins Diam. of bore, mm Len. of bore, cals Wt. of gun 1.46 37 25 Lbs. 79 Oz. 1.125 1540 18 1.9 1.46 37 45 Lbs. 268 1.5 Oz. 4.5 2300 55 4.3 25 1.85 47 40 Lbs. 506 3.3 Oz. 7.94 2132 104 5.2 25 1.85 47 50 Lbs. 1067 3.3 Lbs.oz. 1 4f 1 6 2800 179 7.8 25 1.85 47 50 Lbs. 852 3.3 Oz. 15.0 2700 166 7.4 25 1.85 47 46 Lbs. 560 3.3 Oz. 10.0 2300 121 5.7 25 2.24 57 40 Lbs. 840 6 Oz. 9.2 1968 161 5.6 25 Wt. of proj., lbs Wt. of Cord., ch Wt. ofM.D., ch Muz. vel. f. a Muz. ener. f. t Pen. at muz., ins Rds. per min How- itzer. How- itzer. How- itzer. Diam. of bore, ins Diam. of bore, mm Len. of bore, cals Wt. of gun 4 102 8.75 Lbs. 220 20 Oz. n 950 125 4 102 40 Cwt. 26 31 Lbs. 5* 2300 1137 12 4 102 50 Cwt. 42 31 Lbs. 11 3000 1934 16.0 12 4.3 109.2 12.5 Cwt. 7 40 Oz. 15.75 980 266 4.7 120 12 Cwt. 8 35 Lbs.oz. 1 4* 1150 321 4.7 120 40 Cwt. 42 45 Lbs.oz 5 5 2200 1510 11.6 12 4.7 120 45 Cwt. 53 45 Lbs. oz 8 2J 9 4 2570 2061 15.2 12 Wt. of proj., lbs.... Wt. of Cord., ch Wt. of M.D.,ch.... Muz. vel. f. a Muz. ener. f. t Pen. at muz., ins Elswick Guns 561 GUNS. Jointed Gun. Field. House Artil- lery. Field. 2.24 2.953 3 3 3 3 3 3.3 57 75 76 76 76 76 76 84 50 14.13 40 50 19.2 28 23 28 Cwt. Lbs. Cwt. Cwt. Cwt. Cwt. Cwt. Cwt. 10| 210 12 18* 4 n 6 9 6 11.75 w 12.5 12.5 14.3 12.5 18.5 Oz. Lbs. oz. Lbs. oz. Lbs. oz. 71 1 10 3 4 1 3| Lbs. oz. Oz. Oz. Lbs. oz. 1 3 2 4 131 1204 1 4 1 8 2400 1100 2210 2800 1458 1755 1700 1635 240 98 423 680 185 305 250 336 8.0 8.8 11.6 25 20 20 20 15 15 20 20 4.7 5 5 6 6 6 6 7.5 120 127 127 152 152 152 152 190 50 32 8.4 12.2 40 45 50 45 Cwt. Tons. Cwt. Cwt. Tons. Tons. Tons. Tons. 66 2 9 20 6.6 7.35 8.75 13.8 45 60 50 100 100 100 100 200 Lbs. Oz. Lbs. Lbs. Lbs. 8.5 11.5 18.3 26 36 Lbs. oz. Lbs. oz. Lbs. 15 3000 9 8 2115 782 3 5 1000 22 31 34 75 2500 2800 2930 2850 2808 1861 212 693 4334 5436 5952 11,264 19.4 13.0 - 19.5 23.1 24.8 30.4 12 10 9 9 9 6 562 The Naval Constructor ELS WICK GUNS. — (Continued.) I )ia in . of bore, ins. . Diam. of bore, mm. Len. of bore, cals Wt. of gun Wt. of proj., lbs. Wt. of Cord., ch. Wt.ofM.D., ch.. Muz. vel. f. a Muz. ener. f . t Pen. at muz., ins. Rds. per min 7.5 190 50 Tons. 15 200 Lbs. 77,5 2,950 12,068 32.0 6 45 Tons. 18.0 250 Lbs. 80 2,800 10,872 32.2 5 203 50 Tons. 21 250 Lbs. 85 2,950 12,069 34.8 5 210 44 Tons. 18.1 308.6 Lbs. 47 Lbs. 52 2,300 11,320 27.0 5 Jointed Gun 9.2 234 45 Tons. 26.75 380 Lbs. 122 2,750 19,926 35.9 4 Field 9.2 234 50 Tons. 28 Lbs. 136 3,000 23,712 39.8 4 Diam. of bore, ins. . Diam. of bore, mm. Len. of bore, cals. . . . Wt. of gun Wt. of proj., lbs. Wt. of Cord., ch. Wt. ofM.D., ch. Muz. vel. f. a. . . . Muz. ener. f . t Pen. at muz., ins. Rds. per min. . . . Field. How- itzer. How- itzer. 10 10 12 12 12 254 254 305 305 305 45 50 40 40 45 Tons. Tons. Tons. Tons. Tons. 36.25 36 48.5 51 59.3 500 500 850 Lbs. 141 850 850 Lbs. Lbs. Lbs. Lbs. 167 180 155 260 286 2,800 2,900 2,400 2,650 2,800 27,181 29,157 33,949 41,386 46,208 40.9 42.95 38.4 44.6 48.5 3 3 2 2 2 38 rds. in 1 min. 45 sec. from 4 guns; 35 rds. in 1 min. 45 sec. from min. from 10 guns. 7.5" gun 4 guns. 6" gun — 74 rds. in 1 min. from 10 guns; 78 rds. in 4.7" gun — 79 rds. in 1 min. from 8 guns. 4" gun — 59 rds. in 45 sec. from 8 guns. 12 pr. gun — 10 rds. in 31 sec. from 1 gun. Some results actually obtained under service conditions at a target. 12" gun — 8 rds. in 2 min. 10 sec. from 1 turret (pr. of guns); 16 rds. in 2 min. 45 sec. from 2 turrets (4 guns). 9.2" gun — 57 rds. in 2 min. from 6 guns; 44 rds. in 2 min. from 6 guns; 13 rds. in 2 min. from 2 guns. Vickers Guns and Mountings 563 VICKERS GUNS AND MOUNTINGS. Wt. of mounting com plete with shield Theory of shield, ins. . . Wt. of shield Angle of elevation Angle of depression Wt. of mounting com plete with shield Theory of shield, ins Wt. of shield Angle of elevation Angle of depression Wt. of mounting compl. with shield Theory of shield, ins. . . Wt. of shield Angle of elevation , Angle of depression 37 MM. 30 Cal. c. q. 1. 4 1 10 0.1875 q. 1. 3 11 16° 25° 37 MM. 42.5 Cal. c. q. 1. 4 3 20 0.16 q. 1. 1 22 15° 20° 3-PDR. 50 Cal. c. q. 1. 11 3 0.25 c. q. 1. 1 20° 20° 6-PDR. 50 Cal. c. q. 1. 14 2 no shield 20° 10° Moun- tain 3 Ins. 12* Ph. 14.3 Cal. c. q. 1. 7 3 0.1 q. 1. 1 17 25° 15° Weight of Carb. WITHOUT Limber. 11 3 0.125 q. 1. 2 16° 6° Weight of Carr. and Limber with 24 Rounds. t. c. q. 1 5 1 0.144 c. q. 1. 1 15 16° 10° 3 In. Semi-Aut. 50 Cal. t. c. q. 1. 10 2 no shield 20° 10° 4 Ins. 50 Cal. t. c. q. 1 2 4 2 no shield 15° 10° Weight of Carr. without Limber. 4.7 Ins. 45 Cal. c. q, 1. 17 3 no shield 50° 5° t. c. q. 1. 3 13 3 2 and 0.313 c. q. 1. (17 (110 20° 7° 4.7 Ins. 48.4 Cal. Weight of Carr. WITHOUT Limber. t. c. q. 1. 5 9 2 3 t. c. q. 1. 1 12 2 20° 10° t. c. q. 1. 2 14 3 0.23 c. q. 3 3 50° 0° 564 The Naval Constructor VICKERS, SONS AND MAXIMS 3 Pdr. 50 Cal. 6 Pdr. 50 Cal. 3 Ins. 12* Pr. 14.3 C. 37 mm. 30 Cal. 37 MM. 49.5 Cal. Diam. of bore, ins 1.457 43.5 73.75 13 0.0782 c. q. 1. 3 2 24 1800 22.5 1.9 1.5 1.457 62 94 14 0.1875 1.25 c. q. 1. 5 1 19 2300 45.85 3.3 2.6 300 1.85 92.5 98.9 17 1.066 3.3 c. q. 1. 5 2 4 2800 79.4 6.7 5.1 30 2.244 112.2 118.6 16 . 1.55 6 c. q. 1. 9 1 5 2600 281 7.5 5.4 28 3 42.94 47.23 12 0.5 12.5 c. q. 1. 2 12 3 1150 115 20 Max. pr. in chamber, Wt. of charge, lbs Wt. of proj., lbs Wt. of gun Muz. vel. f. s Pen. of W. I. pi. at muz. Gavre form., ins Pen. of M. st. pi. at muz. Gavre form., ins. Pen. of hard st. pi. at 3000 yds. Gavre form., Rds. per minute 300 6 In. Howit. 6 Ins. 45 Cal. 6 Ins. 50 Cal. 7.5 Ins. 45 Cal. 7.5 Ins. 50 Cal. Diam. of bore, ins 6 94.5 102.8 9.85 5.3 90.3 c. q. 18 3 1285 1035 6 269.5 279.2 17.75 35.25 100 t. c. q. 7 8 2 3012 6290 23.65 18.4 6.3 10 6 300 310.07 18 43 100 t. c. q. 7 16 3190 7056 25.8 20 7.2 10 7.5 337.5 349.2 18 78.25 200 t. c. q. 14 2 2,875 11,465 28.75 22.25 7.5 375 386.7 17.5 80.03 200 t. c. q. 16 3,007 12,540 30.75 23.7 Max. pr. in chamber, Wt. of charge, lbs Wt. of gun Muz. vel. f. s Pen. of W. I. pi. at muz. Gavre form., ins Pen. of M. st. pi. at muz. Gavre form., ins Pen. of hard st. pi. at 3000 yds. Gavre form., 8.9 8 9.35 8 Rds. per min Vickers Guns and Mountings 565 GUNS AND MOUNTINGS. Field. 3 In. S. Aut. 50 Cal. 4 Ins. 50 Cal. 4.33 In. Howit. 13.5 C. 4.7 Ins. 45 Cal. 4.7 Ins. 48.4 Cal. Lt. 3 Ins. 22 Cal. Hvy 2.95 Ins. 30 Cal. 3 64.96 69.3 2.95 99.46 103.8 3 150 159.995 4 201 . 15 208.45 4.33 58.45 63.55 4.724 212.6 220 4.724 228.45 236.2 16 1 12.5 16.0 1.032 14.33 17 3.625 12.5 18 11.25 31 12.5 1.0 35.27 17 19 45 18 17 45.14 c. q. 1. 4 2 1600 220 c. q. 1. 7 2 6 1660 274 c. q. 1. 19 2700 632 t. c. q. 2 1 3 3030 1975 c. q. 7 1 1045 267 t. c. q. 3 3 3 2925 2670 t. c. q. 3 2 3050 2910 9.65 16.0 16.65 17.8 7.5 12.4 12.9 13.8 25 20 25 15 12 12 8 Ins. 48.5 Cal. 9.2 Ins. 47 Cal. 9.2 Ins. 50 Cal. 10 Ins. 45 Cal. 10 Ins. 48.6 Cal. 12 Ins. 45 Cal. 12 Ins. 50 Cal. 8 388.75 400 9.2 429.3 442.35 9.2 460 473 10 450 464.6 10 486 500 12 540 557.55 12 600 617.7 18 90 216.7 t. c. q. 14 3 3,090 14,350 18 170.5 380 t. c. q. 28 1 3,025 24,110 18 184 380 t. c. q. 27 16 1 3,070 24,835 18 190.5 478.4 t. c. q. 34 17 18 172 496.6 t. c. q. 27 17 18 356 850 t. c. q. 57 14 18.5 344 850 t. c. q. 65 17 2,850 26,945 2,863 28,225 2,950 51,290 3,010 53,400 31.5 39.25 39.95 38.9 40.2 50.65 52.1 24.4 30.45 31.0 30.1 31.15 39.25 40.4 9.8 6 13.35 4 13.75 4 13.8 3 14.65 3 19.5 2 20.0 2 566 The Naval Constructor SCHNEIDER 305 274.4 240 12.0 45 52.9 826 2,952 50,007 38.3 29.3 12.0 50 57.3 826 3,116 55,717 41.6 31.9 10.9 45 38.5 606 2,952 36,670 34.6 25.5 10.9 50 41.7 606 3,116 40,859 37.4 27.8 9.4 45 25.8 407 2,952 24,667 30.1 21.2 9.4 50 27.9 407 3,116 27,487 32.3 23.1 Wt. of A.P. proj., lbs Wt. of charge* Muz. vel., ft. see Muz. energy, ft. tons Perf .of steel at muz. (ins.) Perf . of steel at 3000 yds. 120 100 75 4.7 45 3.2 48 2952 2932 13.9 6.4 4.7 50 3.5 48 3116 3268 15.0 6.9 3.3 45 1.9 28.6 2952 1734 11.6 4.6 3.9 50 2.0 28.6 3116 1931 12.5 4.9 2.9 50 0.85 14.3 2871 820 9.3 2.9 60 1.2 14.3 3035 917 10.0 Wt. of A.P. proj., lbs Wt. of charge * Muz. vel., ft. sec Muz. energy, ft. tons Perf . of steel at muz. (ins.) Perf. of steel at 3000 yds. Not Schneider Guns 567 GUNS 210 200 175 150 8.3 8.3 7.9 7.9 6.9 6.9 5.9 5.9 45 50 45 50 45 50 45 50 17.3 18.6 14.9 16.2 10.0 10.8 6.3 6.8 275 2,952 275 3,116 231 2,952 231 3,116 165 2,952 165 9 9 99 3116 3,116 2952 16,667 18,572 14,002 15,601 10,000 11,143 6001 6886 26.2 28.3 24.3 26.3 22.1 23.9 18.2 20.1 17.5 19.2 16.1 17.3 13.8 15.2 10.2 11.8 65 57 47 37 2.5 2.5 2.21 2.21 1 .8 1.4 50 60 50 60 60 60 0.5 5 0.76 0.45 0.55 .30 0.17 8.8 8.8 6 6 3 .3 1.76 2952 3116 2952 3116 3 116 3116 533 594 362 400 223 119 7.9 9.1 7.1 7.5 5 .9 5.0 stated. 568 The Naval Constructor 03 24.44 76.78 3,558 6.03 90.39 12.4 39.47 3196 2858 6389 18.98 26.84 5.66 a c W ^H »■* 1 » 22.00 47.49 2.015 5.34 90.39 12.4 34.40 3008 2697 5680 17.41 24.52 5.29 W5U co. -h -i § 828 © O © ^ (D © it § § S2S*8S8 aKi8 S S "*' CI <-i *-« Ciirsir»M00r- 14 « NNH^MiQlONCClOM CO US § WKJiONIO««CIN OO CO ^H t- T* »0 rt rt 1-1 (NOOiieoaocooseq^Hco t- NOOHlHllOlOtOOlNOOi t^ US •N • • • rt » H . .. ">." o^ » < US 5.5 4.21 4189 1.86 0.86 9.68 2.57 3022 2661 1952 1.92 7.24 i-i t- eo c.WS i HnrtOH^ecNN i-» t-< • 3 ■* f gun re, ins , lbs.. , tons proj. i in lbs in ft.-i ;y tot steel i iron, p St., w " 5 2 h3 len. c of bo of gun of gun of St. of ch. .vel. . eneri thru. thro, rmula Krup •< < S oc H Krupp Guns 569 o _, OS OO OS CC J^oo50oimo«oi>-_oo lOO «5 ■^ ^< OM «* in us n ■*' h h eo w N ?S ^ -* o o •* t~ oo os ■"* co lO ^ t- OS * N O 00 CO « N O •* •>*< Hi •* S 3 8 § d 3 S ^* N " 3 25 t* l^ OS CN to CO t-. M "O 115 co o o os io o co co co (~- o § « Mfl N N » » « » * t| ^rt »COO) too "* eo Hi lO •* N s a t- 00 ■**< Hi Woo£:"totsodoM N t:N eoooCi-H-^Oi-i '-'cm f~ OS CO io OS Hi t- •& O) N O OSi-HOOOCO lOtMCMOOi-ltOlOOt^tOi-l »o to 9 dt>-J2' , *- i-H T* Nlfl'geo'oioONWN^rt (MO^^HiJ'OOO ^ > H .s a tn .J c 1 *■ E s o CO 3 o len. of gun of bore, ins of gun, lbs. . of gun, tons of st. proj. i of ch. in lbs . vel. in ft.-s . energy tot CO a §• 5 £ S 5 aw 3£ & $Hii i-ii'S'l tJ O b «® **" «® 570 The Naval Constructor BETHLEHEM ORDNANCE. Cal. Len. or Bore in Cal. Cal. Wt. OF Gun. Wt. OF Proj. At Muzzle. Per. of W.I. Gavre Form- ula. At 3000 Yds . Range. Veloc- ity. En- ergy. Dan- gerous Space for Tar- get 25' High. En- ergy. Ft.- tons. Per. of B. Hard-faced Arm. Pierc. Proj. with Normal Impact. Ins. 1.457 Cals. 50 Cms. 3.7 Lbs. 120 Lbs. Ft.-lb. sec. 2150 Ft.- tons. 37 Ins. Yds. Ins. 1.831 50 4.7 550 3 2400 119 2.244 50 5.7 960 6 2400 240 3 50 7.62 1900 Tons. 13 2800 707 4 45 10.16 2.3 33 2600 1545 9.8 240 755 4 50 10.16 2.6 33 3000 2060 12.1 315 1,000 5 45 12.7 3.4 60 2600 2810 12.8 255 1,575 5 50 12.7 4.75 60 3000 3745 15.8 340 2,035 6 45 15.24 7.2 105 2600 4965 16.9 275 2,970 6.9 6 50 15.24 8.4 105 3000 6550 20.0 365 3,950 8.3 7 45 17.78 12.7 165 2800 8965 23.2 330 5,790 9.5 7 50 17.78 14.5 165 3000 10,300 25.5 385 6,640 10.4 8 35 20.32 15.2 316 2250 10,500 28.3 235 8,240 11.0 8 45 20.32 18.6 260 2800 14,230 29.1 350 9,860 12.3 8 50 20.32 22.3 260 3000 16,220 32.2 405 11,350 13.4 10 35 25.4 30.0 604 2250 21,200 38.6 245 16,580 14.8 10 45 25.4 35.4 515 2800 27,990 40.8 370 21,080 17.2 10 50 25.4 43.9 515 3000 32,110 44.7 430 24,070 18.7 12 35 30.48 52.0 1046 2250 36,700 50.1 250 29,880 19.1 12 45 30.48 53.8 870 2800 47,290 51.7 380 36,790 21.7 12 50 30.48 66 870 3000 54,280 57.1 435 42,350 23.7 14 35 35.56 57.4 1660 2150 53,190 50.4 230 44,660 22.3 14 45 35.56 70.3 1350 2450 56,170 52.4 295 45,090 22.4 18 30 45.72 60.0 2075 2150 66,490 49.2 225 52,750 21.1 Guns less than 3" cals. are chambered for fixed ammunition with the powder and projectiles in brass cartridge cases. Guns from 3" cals. upwards, and includ- ing the 6" L 45 gun, can be chambered to use either fixed ammunition, or loose ammunition with the powder in cartridge bags and the projectile separate from the powder. Guns above 6" cal. and including the 6" L 45 gun are chambered for loose ammunition. The breech mechanisms of all guns up to 10" are operated by Bethlehem Steel Company STEEL COMPANY. 571 ORDNANCE. At 8000 Yds. Range. Limiting Ranges beyond Cal. Dangerous Space for Target 25' high. Energy. Perf. of B. Hard-faced Arm. by Capped Arm. Pierc. Proj. with Norm. Impact. Proj. will not perforate Krupp Hard-faced Arm. of 12" and 7" thickness. 12" plate. 7" plate. Yds. Ft.-tons Ins. Yds. Yds. Ins. 1.457 1.851 2.244 3 4 55 1,307 4 1 2,870 4 5 5 6 75 1,749 4 9 4,500 6 70 2,285 6.1 6,350 7 85 3,267 6.7 7,310 7 60 5 060 8 1 10,230 8 85 5,457 8.6 3,240 10,420 8 95 6,235 9.0 4,420 11,610 8 65 11,120 11.5 7,300 Max. range 10 95 13,160 12.8 9,075 " " 10 115 15,150 13.9 10,560 " " 10 70 21,700 15.6 14,180 " " 12 105 24,615 16.9 14,560 " " 12 120 28,135 18.3 16,330 " " 12 70 33,650 18.7 Max. range " " 14 85 32,030 18.1 " " " " 14 65 36,360 16.7 15,100 18 the single motion of a hand-lever. Those of the larger guns are operated by the revolution (3 to 5 turns) of a crank. The 8", Wand 12" L 50 guns, and the 14" L 45 gun are for use in turrets, and are of great weight at the breech in order to balance the long muzzles, so that a com- paratively small barbette may be used. 572 The Naval Constructor UNITED STATES Gun. Mark. 6 2 A H Tot. Len. Cap. of Cham- ber in Ins. Travel of Proj. in Ins. Wt. of Cl N. Wt. OF Proj. © « o S H Ins. Tons. Lbs. Lbs. 3" R.F.G. II, III 50 154 219 128.3 0.9 13 3.85 3" S.A. V, VI 50 159 219 128.3 1.0 13 3.85 4" R.F.G. III, IV, V, VI •40 164 331 134.5 1.5 33 4.85 4" VII 50 205 652 168.3 2.6 33 9.0 4 » VIII 50 205 652 168.3 2.9 33 12.3 5" II, III, IV 40 206 656 167.8 3.1 50 10.0 5" B.L.R. V, VI 50 256 1,200 215.6 4.6 60 19.2 5" VI 50 256 1,200 215.6 4.6 50 20.5 5" R.F.G. VII 51 261 1,165 215.6 5.0 50 23.8 6" R.F.G. II, III 30 196 1,318 145.4 4.8 105 18.8 6" IV, VII 40 256 1,320 205.8 6.0 105 18.8 6" IX 45 270 1,320 221.7 7.0 105 18.8 6" B.L.R. VI 50 300 2,101 247.5 8.3 105 30.0 6" VIII 50 300 2,101 247.5 8.6 105 37.0 7" B.L.R. II 45 323 3,643 259.8 12.7 165 58.0 8" B.L.R. III, IV 35 305 3,170 245.8 13.1 260 43.8 8" V 40 343 5,243 273.1 18.1 260 78.0 8" VI 45 369 5,243 299.1 18.7 260 98.5 10" I, II 30 329 6,779 251.1 25.1 510 90.0 10" III 40 413 7,222 327.0 34.6 510 207.5 12" I, II 35 441 11,991 345.2 45.3 870 160.0 12" III, IV 40 493 17,096 392.2 52.1 870 237.5 12" III, IV 40 493 17,096 392.2 52.1 870 305.0 12" V 45 553 16,974 452.0 52.9 870 305.0 12" VI 45 553 14,970 452.0 53.6 870 340.0 12" VII 50 607 14,296 506.3 56.1 870 340.0 13" 1,11 35 479 15,068 374.9 61.4 1130 180.0 14" II 45 642 63.1 1400 365.0 United States Naval Ordnance 573 NAVAL ORDNANCE. Muz. Vbl. Muz. Energy Pen. at Muz. Krupp Arm. Using Capped Proj. At 3000 Yds. At 6000 Yds. At 9000 Yds. Remain- ing Vel. Pene- tration. Remain- ing Vel. Pene- tration. Remain- .Vef. Pene- tration. Ft.-sec. Ft.-tons. Ins. Ft.-sec. Ins. Ft.-sec. Ins. Ft.-sec. Ins. 2700 658 3.3 1230 1.2 848 0.8 2700 658 3.3 1230 1.2 848 0.8 2000 915 3.4 1156 1.7 897 1.2 2500 1,430 4.6 1432 2.2 979 1.4 853 1.2 2800 1,794 5.3 1627 2.6 1033 1.5 878 1.2 2300 1,834 5.3 1286 2.6 934 1.7 829 1.4 2700 3,032 6.2 1692 3.5 1102 2.0 928 1.6 3000 3,122 6.4 1732 3.2 1057 1.7 877 1.4 3150 3,439 6.8 1835 3.5 1091 1.8 895 1.4 1950 2,768 5.3 1305 3.2 1009 2.3 909 2.0 2150 3,365 6.0 1440 3.6 1058 2.4 934 2.1 2250 3,685 6.3 1511 3.8 1086 2.5 948 2.1 2600 4,920 7.6 1770 4.7 1207 2.9 996 2.2 2800 5,707 8.3 1923 5.2 1297 3.2 1026 2.3 2700 8,338 9.6 1948 6.4 1382 4.2 1083 3.0 2100 7,948 8.6 1576 6.0 1206 4.2 1040 3.6 2500 11,264 10.6 1898 7.5 1428 5.3 1141 4.0 2750 13,360 12.0 2106 8.6 1589 6.1 1227 4.4 2000 14,141 10.7 1590 8.0 1274 6.1 1103 5.0 2700 25,772 15.6 2184 11.9 1747 9.0 1406 6.9 2100 26,596 14.2 1733 11.2 1433 8.8 1219 7.2 2400 34,738 16.8 1994 13.3 1649 10.5 1396 8.3 2600 40,768 18.5 2171 14.8 1801 11.7 1500 9.3 2700 43,964 19.4 2259 15.5 1877 12.3 1561 9.8 2850 48,984 20.8 2393 16.6 1991 13.3 1553 10.6 2950 52,483 21.7 2483 17.5 2071 13.9 1719 11.0 2000 31,333 15.0 1679 12.0 1413 9.7 1221 8.1 2600 65,606 28.3* 23.4* Section IY. RIGGING AND ROPES. CHAPTER I. The rigging and ropes of a modern steamship still constitute a very important part of the vessel's equipment, notwithstanding the almost total abolition of sail area, and its extinction as a propelling agent in the present day steamer. Generally too little attention is devoted to what are considered the minor details of a steamship's rigging, by those best qualified to determine the sizes of ropes and blocks, and the arrangement of tackles on a mechanical basis. The array of derricks around the masts and kingposts of a freighter, with their varying loads of from 2 \ to 50 tons, exemplify the necessity for a closer acquaintance with the staying, guying and tackling of these appliances, to en- sure that the whole of the system shall be designed throughout on an uniform basis. RIGGING. By the term " rigging" is generally denoted the standing rigging, or that part whose function is to stay or support the masts, spars and funnels, and comprises the shrouds, guys, pendants, bowsprit shrouds, jib-boom guys, stays and backstays. These supports are now invariably made of galvanized wire rope, either iron or mild steel, the latter being employed where strength and lightness are desired, or where heavy working derricks are fitted. A special quality called plough steel, is sometimes used when exceptionally great loads have to be lifted. Indeed, it will often be found cheaper to employ plough steel in these cases, as the number of shrouds or stays may thereby be reduced, thus effecting a greater saving in the quantity required than the extra cost in quality has involved. Wire Rope. — As its name implies, wire rope is manufactured from small steel or iron wires, twisted into strands, six of which (usually) are laid up around a tarred hemp centre, the strands having a wire heart where strength is more important than flexi- 575 576 The Naval Constructor bility, otherwise where used as running gear and flexibility is a necessity they also have a hempen centre. The number of wires constituting a strand varies with the degree of flexibility required, 19 wires to a strand being ordinary flexible rope, and 37 wires extra flexible, such as would be used for derrick topping lifts. Steel wire rope for ship rigging should always be galvanized, otherwise it deteriorates rapidly, and where it is used for running gear, it should be soaked in boiling tallow and linseed oil, a process which will add much to its life. Great care must be used at all times in handling it so as to avoid sharp nips or kinks, either of which is fatal. For this reason when used as hawsers, wire rope must be stowed on a reel having a core of suitable diameter, and in the case of running rigging, the proper diameter of sheave for a given size of wire is important. An undersized sheave shortens the life of the best rope, and by distorting the fibres, weakens its strength. Approximate diameters of sheaves for extra flexible steel wire rope, are given in the table on page 381. Splices. — Splices in wire rope, such as are necessary around thimbles and elsewhere, weaken its strength from 10 to 15 per cent. It is necessary, therefore, to take account of this in fixing on the safe working load. Likewise in ordering the lengths of rope, allowance must be made on net sizes for the number of splices worked. Thimbles. — In working eyes in the ends of wire rope, it is necessary that the fibres forming the inside of eye should be protected from the destructive effect of a link or shackle pin bearing on same. To guard against this, the splice is worked around heart shaped eyes or thimbles. These, like the sheaves, must be of a suitable size for a given circumference of rope. Sheaves and Splices 577 SHEAVES FOR EXTRA FLEXIBLE V/IRE ROPE. STEEL For Steering Leads, Topping Lifts and Purchases. Circum- Diameter Weight Circum- Diameter Weight ference of in ference of in of Rope. Sheave. • Brass.* of Rope. Sheave. Brass.* In. In. Lbs. In. In. Lbs. 1 4* 2* 8* 16 46 H 6 5* H 17 54 if 7 8* 4 18 66 if 8 11 H 19 78 2 9 15 H 20£ 107 H 10| 20 4f 2H 120 *t 12 26 5 23 138 H 13 29 S| 25 163 3 14 34 6 27 190 H 14* 37 H 30 235 * Weight in cast iron = Brass X LENGTH OF WIRE ROPE REQUIRED FOR SPLICES. Circum- Allowance Allowance ference OF for Iron Wire for Steel Wire Manila. Rope. Rope. Rope. In. In. In. 1 9 12 li 12 18 2 15 21 2i 18 24 An average 3 20 30 allowance of 15 n 22 33 inches is made 4 24 36 for Manila. 4* 27 39 5 30 42 6 35 48 7 40 54 578 The Naval Constructor GALVANIZED IRON AND STEEL WIRE RIGGING ROPES. To Admiralty or Li .oyp's Requirements. Sizes. Breaking Stress. Weight per Best Best (ialvan- ('.alv.uiiy.fd - Circum. Diameter. Fathom. Galvanized ized Mild Patent Iron. Steel. Steel. Inches. Inches. Lbs. Tons. Tons. Tons. 1 .318 0.96 1.2 1.75 2.8 11 .397 1.2 1.5 2.25 3.6 If .397 1.5 1.87 3 4.5 If .437 1.8 2.25 3.25 5.4 n .477 2.1 2.62 4 6.3 if .517 2.5 3.12 5 7.5 if .557 2.9 3.62 6.5 8.7 if .596 3.3 4.12 6 9.9 2 .636 3.8 4.7 7 11.4 2* .676 4.3 5.3 8 12.9 *§ .716 4.8 6.0 9 14.4 n .755 5.3 6.6 10 15.9 H .795 5.9 7.3 11 17.7 2f .835 6.6 8.2 12 19.8 n .875 7.1 8.8 13 21.3 n .915 7.8 9.7 14.5 23.4 3 .954 8.5 10.6 16 25.5 81 .994 9.2 11.5 17.5 27.6 8f 1.03 9.9 12.3 19 29.7 a 1.07 10.7 13.3 20.5 32.1 3* 1.11 11.5 14.3 22 34.5 3f 1.15 12.3 15.3 24 36.9 8f 1.19 13.2 16.5 26 39.6 8| 1.23 14.1 17.6 28 42.3 4 1.27 15.0 18.7 30 45.0 if 1.31 16.0 20.0 32 48.0 4* 1.35 17.0 21.2 34 51.0 4| 1.39 18.0 22.5 36 54.0 4§ 1.43 19.0 23.7 38 57.0 *f 1.47 20.1 25.1 40 63.3 if 1.51 21.2 26.5 42 63.6 4| 1.55 22.4 28.0 44 67.2 5 1.59 23.5 29.3 48 70.5 5f 1.67 26.0 32.5 53 78.0 6] 1.75 28.5 35.6 58 85.5 6 1.9 1 34.0 42.5 68 102.0 Standard Hoisting Rope 579 STANDARD HOISTING ROPE. — SWEDISH IRON. (Roebling.) Composed of 6 Strands and a Hemp Center, 19 Wires to the Strand. Approx. Proper Diameter Approx. Approx. Strength Working of Drum Diameter ClRCUM. IN Weight per in Tons Load in or Sheave in Inches. Inches. Foot. of 2000 Tons op in Feet Lbs. 2000 Lbs. Advised. 2f 8f 11.95 Ill 22.2 17 21 7| 9.85 92 18.4 15 21 71 8.0 72 14.4 14 2 61 6.30 55 11.0 12 H H 5.55 50 10.0 12 H 51 4.85 44 8.8 11 H 5 4.15 38 7.6 10 1} 4J 3.55 33 6.6 9 H 41 3.00 28 5.6 81 U 4 2.45 22.8 4.56 71 H 31 2.00 ' 18.6 3.72 7 3 1.58 14.5 2.90 6 i 2f 1.20 11.8 2.36 51 • f 21 0.89 8.5 1.70 41 I 2 0.62 6.0 1.20 4 A U 0.50 4.7 0.94 31 1 H 0.39 3.9 0.78 3 A H 0.30 2.9 0.58 21 ! H 0.22 2.4 0.48 21 A 1 0.15 1.5 0.30 2 1 1 0.10 1.1 0.22 H Cast Steel. 21 8f 11.95 211 42.2 11 21 n 9.85 170 34.0 10 21 71 8.00 133 26.6 9 2 61 6.30 106 21.2 8 U H 5.55 96 19.0 8 if 51 4.85 85 17.0 7 H 5 4.15 72 14.4 61 l* 4f 3.55 64 12.8 6 if 41 3.00 56 11.2 51 H 4 2.45 47 9.4 5 11 31 2.00 38 7.6 41 l 3 1.58 30 6.0 4 J H 1.20 23 4.6 31 i 21 0.89 17.5 3.5 3 f 2 0.62 12.5 2.5 21 A U 0.50 10.0 2.0 21 1 U 0.39 8.4 1.68 2 A H 0.30 6.5 1.30 If I H 0.22 4.8 0.96 H A 1 0.15 3.1 0.62 H 1 ! 0.10 2.2 0.44 1 :,so The Naval Constructor jo t?KI ^lONOJOOON^tOiO^aHONiJitiCOOM hi rtHriHHHrtHH(N(N(NN(N gU5 000N'00'-;iO?|iN©(N(N(30CO(N'<}d OS r* OS Tin © CD CN OS* <* © £ HHH(NiMNMW^iOOCD50XO B j05^qt»«0©OOHOOO^NNMiON'* *OH(N(NM^o6x05H(NTli©Q66(NN'N r^ HHHHrH(N!N t- co ® 10 10 •* HOJt^OMHOJN»OWHONiOMHCSiO cocoTtiiocot-i^cocoHHMwniOiONai o> S Jr fci — 3 m cc •uioq; -Btf J9d 9AB9qs JO "Kid •uih pq'~ce •xnoqi s 5 ® qco l CONCOOHMT)(iO^COO(NCO^CCNar-i'* HHHHHHHCSNIN(NN(N(NCO« NCOiOCJ^r>M05>0'f COt^-^t^QO^rJlCOkOCO O d 00 CN id OS CO t^ CN t^ CN CO O fcH Hr1HHNNOCCCOT)(^lOCDl> 5 s £13 00 . I— © CO 05 CO © >0 t-~"t*CN?-HrHCNCO>OOSCNt~COCS»OTtH MW*i0Ot^NC00iOHH(NC0T)ii0i0N05 Mild Steel Open Thimbles 581 TABLE OF MILD STEEL OPEN THIMBLES. For Steel Wire Rope or Hawsers. (British Admiralty.) Circum- ference of Rope or Hawser. Score. Size in Clear. Weight Each. Width. Depth. Width. Length. In. In. In. In. In. Lbs. 1 .4 .2 .87 1.50 i n&n .6 .3 1.31 2.25 ft If & 2 .8 .4 1.75 3.00 4 2i &2J 1.0 .5 2.18 3.75 2A 2f &3 1.2 .6 2.62 4.50 3 T f • 3J 1.4 .7 3.06 5.25 6 4 1.6 .8 3.50 6.00 9 41 1.8 .9 3.93 6.75 HI 5 2.0 1.0 4.37 7.50 16 1 51 2.2 1.1 4.81 8.25 231 6 2.4 1.2 5.25 9.00 26 i 61 2.6 1.3 5.68 9.75 37 1 7 2.8 1.4 6.12 10.50 44 1 8 3.2 1.6 7.00 12.00 661 582 The Naval Constructor q o M | § s* ** < < J* H * * Hoo Hoo H» H» ^ **£ •K «M> HS H* K5f» £ •Hoo hi *HS H« *S 0*» HW &5 **$ < e** ^o H* P*0 •m» «■** t^» Ol 5 HS X H» f j HS •mx •oK0 Hoo H* K take 5 H5 H* i-Hi to * coioo ? eoh* Hoc ^ r+N lOJCO ■oto Hoo H* <^ i r+4 ml* J* „to HS J* co|o co 1 I CO 1 Ml-* CO up MM 584 The Naval Constructor WIRE ROPE END-FITTINGS. TyiMBLLftNpHOM. Figs. 337-344. Rope Fittings 585 Rope End Fittings. — Another method of forming an eye on the end of wire rope, is to work an open eye with groove-shaped ends, to enclose the rope, and through which they are riveted as shown in the plate. This " shoe," however, is rarely resorted to unless on the bowsprit shrouds, and similar rigging on yachts, where small close-fitting eyes are desired for neat appearance. Some of the more common forms of wire rope end fittings are illustrated on the preceding page. Their various uses will suggest themselves to the observant. Parcelling and Serving. — In ordinary merchant work, the lower ends of shrouds and stays for 6 or 7 feet are wormed and parcelled with two overlapping layers of cotton sheeting, painted and thereafter served. Where stays are subjected to much chafing, they should be doubly served and covered with leather in the collars. , No serving must be fitted on stays which carry sails, as it would only be cut to pieces by the chafe of the hanks. Turnbuckles. — Standing rigging is invariably set up with turnbuckles, or rigging screws to enable the wire to be tautened, as quite an appreciable amount of "stretch" takes place, more particularly in new rope. These screws are proportioned to the breaking strength of the wire, which should be spliced around a solid heart-shaped core for the heavier sizes, or an open thimble in the case of light wire. Where used for shrouds, the lower end must be arranged to swivel freely, and the pad-eye riveted to sheerstrake, the connection developing the same strength as the screw. Where, however, they are set up fore and aft on stays, the pad should have a shackle-eye for pin, as 'thwartship movement is not then desirable, and the shackle-eye will permit of a smaller diameter pin being used. In proportioning screws under one inch in diameter, an allow- ance of about 20 per cent must be added to the area of metal at root of thread, as compensation for the loss of strength sustained in cutting the screw. Screws should be smeared with tallow and coated with a canvas cover. Sheerpoles. — It is usual to fit a rod to the heads of turn- buckles to shrouds connecting and supporting the heads in their relative position, and preventing the screws from slacking back. In small vessels it may be from g" to § " diameter, seized to each head with seizing wire. Where heavy rigging is dealt with, the sheerpole is bolted through the heart of turnbuckle, and bosses jumped on to form receptacles tor belay pins. Ratlines — Are commonly made of hemp or wire rope, seized at outer shrouds and passing around the others in a clove hitch, 586 The Naval Constructor and spaced about 24 inches apart. Rope, however, is being fast displaced by iron rod ratlines, seized with wire to shrouds. ROPES. Manila and hemp, tarred and white, are the materials from which most ship's ropes are made. As its name indicates, "Manila" hails from the Philippines, and is made from the fibre of the wild banana. Hemp rope is made from the fibre of the hemp plant, the Russian variety being most generally used. Tow lines are sometimes made of coir, which is manufactured from the tough fibrous husk of the cocoanut. In referring to ropes, the circumference always denotes the size. Manila. — All running ropes and those used for sundry work on shipboard are made of Manila, as hemp, though stronger when white, is not pliable enough. It is usual to make it of 3 strands, although 4-stranded or shroud-laid rope is also made ; and for yacht work, 4-strand Manila is best, as it is smaller in diameter for a given strength, besides being neater. Manila is of greater strength than tarred hemp, and stands the weather much better than the untarred or white hemp, although not so strong as the latter. The following tables give strengths and weights of Manila, hemp, and coir ropes : — Manila Rope 587 MANILA ROPE. go? 5£§ Diam- eter OF Rope. Wt. per Foot. Break- ing Stress. i w a £ * O Diame- ter of Rope. Wt. PER Foot. Break- ing Stress. Lbs. Lbs. Lbs. Lbs. i A .035 405 H 11 .640 16,200 I i .045 585 5 If .720 20,000 1 A .055 700 H If .835 23,650 n 1 .065 900 6 11 1.05 27,000 n A .075 1,170 61 2 1.15 29,250 H i .085 1,800 6| n 1.25 31,690 n A .110 2,295 7 21 1.42 33,800 2 1 .140 3,200 ?! 21 1.70 36,750 21 I ..170 3,750 8 2A 2.00 39,200 2* if .200 4,050 B* 2| 2.30 50,000 2| I .240 6,050 9 21 2.65 54,190 3 i .275 7,200 n 3 3.00 57,800 31 *A .325 7,875 10 »A 3.40 75,000 3| M .360 9,800 11 pi 4.00 96,000 Si 1A .410 10,500 12 81 4.70 101,000 4 n .460 11,250 13 41 5.65 117,000 *i if .510 13,500 14 41 6 50 ' 158,300 4 iA .585 14,450 15 M 7.50 172,500 :>ss The Naval Constructor HEMP CORDAGE. .5 fa a g * H £2^ WO w Mb fc 05 » W Kind. In. Lbs. Lbs. Lbs. Lbs. | 6 .018 336 .015 476 1 12 .037 672 .031 1,008 40 Thread 1 15 .047 896 .039 1,344 Yarn Hemp. H 21 .062 1,120 .052 1,680 i| 33 .098 1,680 .083 2,352 Tarred is l| 42 .125 2,240 .105 3,136 Riga. 2 54 .161 3,024 .134 4,144 2* 66 .196 3,808 .160 5,162 White is 2J 84 .250 4,480 .208 6,496 Italian. 2} 102 .302 5,600 .240 7,800 3 120 .355 6,720 .296 9,408 3i 105 .414 7,840 .331 11,000 30 Thread H 123 .485 8,512 .403 12,544 " Yarn Hemp. 4 159 .626 11,200 .522 16,240 . Tarred is *i 201 .791 14,448 .661 20,720 Riga. 5 249 .995 17,696 .816 25,760 White is 6 360 1.40 25,760 1.18 36,960 J Italian. 6* 351 1.66 28,672 1.40 43,200 25 Thread 7 408 1.92 33,152 1.61 47,000 Yarn Hemp. n 468 2.07 38,000 1.85 51,520 Tarred is St. 8 534 2.52 43,456 2.11 58,240 Petersburg. 9 675 3.18 53,760 2.66 73,920 White is 12 1,200 5.65 96,500 4.72 131,040 Italian. Hemp. — Hemp rope deteriorates rapidly when exposed to wind and weather, and for this reason, when practicable, it is tarred, although doing so weakens it. Hemp should only be used for warps and bolt ropes of sails, as it is much too hard for other purposes, more especially when wet. The following rules give the equivalent circumference of tarred and white hemp rope for a working load in tons of one third the breaking stress : — *sfl X load = circumference of white rope. V9 x load = circumference of tarred rope. Length of Reel 589 Other Rope. — A variety of small stuff is used in ship work for sundry purposes, the principal kinds of which, and their purposes, follow : — Cotton Rope is only used for halliards and sheets in small craft, being much softer than Manila. Houseline is used for lacing sails, etc. Marline is a small kind of tarred hemp, used for serving ropes and splices. Serving twine (tarred or waxed) is used for whipping the ends of ropes and other small jobs. COIR ROPE. fa tf a fa ri 3 tf ft a I fa 3 « ft % H H g 8* 24 20 34 6 24 59 22 8* 30 13 55 6 6 30 43 25 4 24 25 30 6$ 24 63 19 4 30 16 49 6i 30 46 27 ** 24 35 25 7 24 70 18 H 30 20 43 7 30 50 26 5 24 43 23 a 24 75 18 5 30 27 38 4 n 30 53 26 &! 24 51 22 6 8 24 80 17 9 5* 30 35 31 6 8 30 55 27 590 The Naval Constructor CHAPTER II. BLOCKS. Blocks are divided broadly into two varieties, wood and iron, the former being used when reeving falls or tackles of Manila, and the latter for wire rope. Wood blocks are either " made " or " mortised," and may have metal or lignum-vitae sheaves. The space in the block between the wood and the sheave is called the " swallow, 1 ' the opposite end of the block being named the " breech," and the sides the " cheeks." The frame of the block may be strapped with iron or rope, a score being cut to form a housing for same. All good blocks should be fitted with patent roller sheaves, especially for halliards and sheets, or for any heavy work. For topsail, sheet, throat and peak halliard purchases, etc., ash blocks, rope stopped, should be used. For derricks on freighters, where wire rope is used for heavy loads, iron blocks are best ; where Manila falls and topping lifts are fitted, wood blocks are most suitable. It will be evident that a good deal of power can be wasted by friction of the sheave on pin, and also by the rope chafing, through insufficient "swallow." To minimize the loss due to friction through the former cause, the pins should be bushed. Various bushings are employed for this purpose, probably the most efficient being a gunmetal or bronze sheave with spotted graphite next the pin. The loss due to friction is 10 per cent for each sheave. Blocks are designated "single," "double," or "treble," in accordance with the number of sheaves fitted, and are variously named to denote either a particular shape or as indicating the purpose for which they are intended. Some of the more common ones are : — Snatch Blocks are used to divert the lead on the hauling part of a fall or tackle, having for this purpose a hinged part on one of the cheeks, to permit of placing the rope in, which would other- wise require reeving — a tedious and often impracticable process. They are usually fitted at heels of derricks, and on deck, to take warping and other leads, and are mostly made of iron, the old- fashioned wood snatch block being clumsy and cumbersome. Fiddle Blocks take the name from their resemblance to the instrument, being constructed with two sheaves placed tandem, to permit of reeving separate halliards leading in opposite directions. Blocks 591 They are to be found on peak-halliards, at preventer stay tackles, etc., and are made in wood where Manila is rove, and in iron for wire rope. Gin Blocks are used on derrick heads and spans in conjunc- tion with a whip for handling cargo, and comprise a skeleton frame and sheave of iron. Cat and Fish Blocks are fitted to the anchor davit, or crane, and consist of a pair of blocks with double or treble sheaves, hav- ing a large swallow. The fish (or lower) block has a large hook, sometimes made to trip, for fishing the anchor by the gravity band on the stock. These blocks are made in both wood and iron, the latter being often fitted with Manila falls. Clump Blocks are made short and thick, as their name im- plies. They are used for tacks and sheets, and for this reason are extra large in the swallow. Made iu wood and iron. Wrecking Blocks are large, extra heavy iron strapped blocks, with lashing shackles, and are used for rigging up special derricks for temporary use with heavy loads. Cheek-Blocks have only one side, the other cheek being formed by fitting against a spar. The size of a block is designated by the length of the shell, and this is determined from the circumference of the rope which it reeves, as a unit. For most purposes three times the size of rope gives a suitable block, but in a few cases, where the minimum of friction and extra ease is desired in the swallow, as with blocks for boat davit tackles, three and one half times should be taken, e.g., a block for ordinary purposes to reeve three-inch Manila would be 9 inches, but if required for davit falls, the size would be increased to 10 inches. The diameter of sheave is usually about two thirds of the size of block, a 12-inch block having an 8-inch diameter sheave. In ordering blocks it is necessary to prepare a list, giving a concise but full and exact description of each individual block, embracing the following points : — Sheaves. — The number of sheaves to be indicated by "S," " D," or " T," and whether of lignum-vitse, brass, or iron sheaves, bushed or patent roller bushed. Name. — The purpose for which the block is intended should be given, as, "jib-sheets," " derrick falls, " etc. Shackles should be very clearly specified where they are for special fittings. Ordinarily the shackle is fitted with its pin at right angles to the axis of the sheave, this being the most natural 592 The Naval Constructor way to engage the strap of block, therefore when the word M shackle," without further description, is used, it is always fitted in this manner. Where, however, it is essential to have it with the shackle pin running parallel with sheave pin (as is often necessary to get the falls of a tackle to lead in line with hauling part) the words "reverse shackle " must be used. If the shackle be required with its jaw uppermost, "reverse upset shackle" should be specified. It often happens that a block is required with an eye to engage a shackle, which the blockmaker is not required to furnish. In such cases it is well to state whether the eye should be " worked " or a " shackle-eye " wanted. A " worked eye," of course, is one having its edge worked round like a ring, the " shackle-eye" being drilled straight through, so that the inserted pin bears along its entire length. For a given diameter of pin, that in a shackle-eye would be twice as strong as the one bearing on a worked eye, so that where other considerations do not count, it is economy to fit a shackle eye. Beckets are small eyes fastened at the breech end of blocks to take the thimble on the standing part of a tackle. They are useful to have on all spare tackle blocks. Strops. — When blocks are intended for brace or guy pen- dants, they should be specified as having a score cut to receive the rope strop. Hooks should not be used on blocks where heavy loads are dealt with. For loads under ten tons they are equally reliable with shackles, besides being handier. They should be specified as "loose," " stiff front," "side," or " swivel " hook, as required, and the working load given in all cases, as many of the hooks on low grade blocks are considerably inferior in strength to the other parts of the fitting. Sister, or Match Hooks are used for a variety of purposes, and consist of two hooks on a common eye, arranged to open, and when closed, to form a seemingly solid eye. Lashing Shackles are especially large in the bow, and wider at the jaws, than ordinary shackles, being fitted to the heavier classes of double and treble blocks, to permit of their taking a Manila or wire rope lashing. Swivel Jaws are sometimes fitted to the upper block in davit tackles. Appended is a table giving actual weights of blocks, fitted with shackles and beckets complete, which will be of use in estimating rigging and outfit weights. Sheaves for Iron Blocks 593 STRENGTH AND "WEIGHT OF RIGGING CHAIN. (B B B Quality.) * Working Load t Breaking Weight Size. F. S. 4 Stress per Foot in in Pounds. in Pounds. Pounds. A 675 2,700 .5 1 1,260 5,040 .75 A 1,876 7,504 1.08 i 2,660 10,640 1.50 3,640 14,560 2.00 ft 4,620 18,480 2.67 A 5,740 22,960 3.33 1 6,860 27,440 4.17 M 8,120 32,480 5.17 t 9,800 39,200 6.18 a 11,200 44,800 7.00 i 12,460 49,840 8.00 H 14,280 57,120 8.85 i 15,960 63,840 10.00 ItV 17,640 70,560 12.00 li 19,320 77,280 15.00 1'i 23,940 95,760 17.50 i| 32,200 128,800 20.00 if 44,520 178,080 26.70 2 58,520 234,080 36.70 * B B quality = 20% less than table, t B quality = 30% less than table. SIZE OF SHEAVES FOR IRON BLOCKS. Sow A W cc m g Sow a w cc oq°k o S o a ft a cc M O « g n // a II a a II II II 2* 1 7 n I 13 2A H H h . . . 8 H A 14 2| I 4 ( 9 if * 15 3 tt 4* I t\ 10 2 A 16 81 I 5 I i 11 *i 1 17 »i H 6 l 5 12 H T6 18 8| l 594 The Naval Constructor WEIGHT Kind of Blocks. a §8 02 o3 M S 9Q s 00 2 A ft H H H g s X 09 hi H' H 2 w 30 CO I ft H w 2 H 7. 00 « g H W 2 M 02 00 2 H W 2 W Wood .... Wood .... Wood .... Wood .... Wood .... Wood .... Wood .... Wood .... Wood .... Cargo block Gin Gin Iron block } Wire rope J Iron block j Wire rope | Iron block i Wire rope ) Wood snatch Iron snatch . Rope w. iron Rope w. iron Rope w. iron 8 D T S D T S D T S D T S D T '/ 4 4 4 4 4 4 i H H if 2i 31 5 5 5 5 6 5 i] 2J 3| 5| 8 6 i; (3 8 8 6 6 6 21 4 4* 41 6 92 7 ia 14 7 7 7 7 7 7 7 7 7 7 7 7 3 B| 6! 61 91 12f 71 10 14 9 13 19 8 8 8 8 8 8 8 8 8 8 8 8 8 41 71 10 81 13 18 91 141 201 12 10 181 28 B D B 9 9 i) 9 9 9 51 9 HI 10§ 16 231 HI 19 27 10 10 10 10 10 10 10 10 10 10 10 sheave 10 sheave 10 sheave 10 10 10 10 10 10 6 HI 15 14 251 35 161 29 39 19 21 40 60 100 22 261 22 38 51 Weight of Blocks 595 OF BLOCKS. s CO i - H S * as s O M N 5 "Weight ik Lbs. Size. a a w M I* ■■1 BO GO P5 H X o H s 00 a * 00 to n w jjj EB CO HI W II 11 21 11 3 11 4 11 2. 11 3. 11 4' 12 12 12 3J 12 L 12 J 12 J 12 ) 12 r 12 12 12 12 slieave 12 sheave 12 sheave 12 12 12 r2 12 12 111 .. 20^ .. 28| .. 22 13 33 13 45 13 25 13 38 13 50 13 26 . . 23 . . 25i .. 67 .'. 109 . . 145 . . 33 .. 41 . . 31 . . 58 . . 81 . . a 14 14 14 30 14 44 14 62 14 33 14 47 14 65 14 14 14 slieave 14 sheave 14 sheave 14 14 14 14 14 14 20J 35 49 39 64 89 49 73 105 35 28 89 150 210 46 56 54 100 134 16 ir> 15 15 15 15 15 15 15 15 44 69 100 51 77 112 35 60 96 150 18 16 it; 16 16 16 16 16 16 10 16 16 16 71 120 168 70 62 68 68 80 166 .'10 18 18 18 18 18 18 18 18 188 83 100 90 105 150 201 20 20 20 130 140 147 596 The Naval Constructor ssM «eo^eow«wcc»^<3r«oo^o»oojcc5«o^j2S * (ONlOOM'O'OOCINrtO^I 3 I w M o £ a I B * NNMMCOCO"*'*li5lf5>fl«5.0000®OSO>O>e<5'*'<(l'O ■£\ - i -Too c?c "Vh • -*r • *+« • •*• • H-* ."5-SU... .-wu~*«. 1 in i°3 r 'r;'n?¥«flOoi'-r^ X - - ^~T~"~ "— 'co^ o ~J7?~s."*?'~~ ci ci O h 9 z o 3 5 « ■^t ^ iS'Jo «* r>. t^ oo oo OJ o» o o 'H -h o S Z £ ^<^iiQiQ«tONNooooo>a>oO'' <^h>*J Vug U-2-H ? °« K>, ' S W-^^3*. ^ff h iff? I rfHWf Hfk'f--^ Figs. ,345, 346. 598 The Naval Constructor CHAPTER III. TACKLES. 00 LBS. PLUS POWER 50 LBS. J TO BALANCE SINGLEWHIP When ropes are reeved through blocks to multiply the power it is proposed to apply, the combined gear constitutes what is known as a tackle. The principle of the block and tackle is the distribu- tion of weight in various points of support, the mechanical advantage derived depend- ing entirely upon flexibility and tension of the rope, and the number of sheaves in the moving block, hence by tackles the power applied to raise is to the weight as the number of parts attached to the moving block, therefore (1) divide the weight to be raised by the number of parts leading "to," "from," or "made fast" to the moving block, and the quotient is the power re- quired to produce equi- librium — omitting friction. (2) Divide the weight to be raised by the power proposed, and the quo- tient is the number of sheaves in, or parts at- tached to, the moving block. It should be noted that the upper block of a tackle has to bear the weight to be raised, and the power applied to lift it. No power is gained by increasing the diameter of the sheaves, but by doing so you decrease friction. In arranging the blocks for a purchase, note that the hauling part, -where possible, should lead from the moving block, as by so arrang- ing, the power is increased. Tackles are named variously, sometimes as threefold, fourfold, etc., referring to the number of ropes rove ; and as guy-tackles, sheet-tackles, etc., or by a distinctive name, whose derivation in most cases is obscure, like Spanish burton, etc. A single "whip and whip-upon-whip are shown by Figs. 272 and 273 and their mechanical advantage indicated. WHIP UPON WHIP Fig. 347. Fig. 348. Tackles 599 Strictly the single whip is not really a tackle, as no mechanical advantage is gained. If we reverse the arrangement, and instead of fixing the block, we make one end of the rope fast and haul on the other after it is rove through the block, which is now movable, we have a tackle with the power applied doubled. The next simplest form to the foregoing is the gun-tackle purchase, shown by Fig. 274, which consists of two single blocks, one movable and the other fixed. In the dia- gram, the power is shown as being applied to the fixed pulley, which results in doubling the power only. If, however, the order be reversed, and the rope becketed to the lower lbs block, from which the hauling end would now lead, we should increase the power gained so that 150 lbs. could be sustained in equilibrium by the application of 50 lbs. In all tackles the hauled- on block has not only to tackle support the load pendant purchase on it, but also the power^^g required to lift the load. The luff-tackle pur- chase shown in Fig. 275, Fig. 349. j s a j so known as a watch- tackle, and has exactly the same mechanical advantages, although consisting of a double and single block, as the gun-tackle with the hauling part taken from the movable block, that is to say, the power applied equals one third of the weight to be raised. The case, however, is different if the hauling rope of the luff-tackle 8INGLE be taken from the movable block, when the ratio of power to weight is increased to one quarter. A twof old purchase consists of two double blocks, and has a ratio of power to weight of one quarter, when hauled on from the fixed block, and of one fifth when from the moving block. A threefold purchase comprises a pair of treble blocks with a mechanical advantage of one sixth leading from the fixed block, and one seventh when hauled on from the moving block. Fig. 276 shows a single Spanish burton, which is composed of two single blocks with the tackle reeved as shown. This LUFF TACKLE PURCHAS 000 The Naval Constructor purchase has the same power as the luff tackle, but less friction. It is a handy and powerful purchase, used for doing odd jobs. The double Spanish burton is made up of a luff-tackle and a whip, with the standing parts toggled on together to the becket of the lower single block. It has the same power, but with much less friction, as a threefold pur- chase hauled on from the moving block. Relieving tackles are usually two or three-fold purchases, having the fixed block shackled on end of spare tiller, and the hauling block made fast on the quarter. These tackles are used for steering, in case of break-down, and need only to be figured for the steamer going at slightly over half speed. A tackle may be attached to the hauling part of another tackle, and so multiply the powers of which they are comprised. In arranging purchases the minimum number of sheaves for the power required should be used, and all superfluous fair- leads dispensed with, as each additional sheave fitted for that purpose absorbs power. As an example of the application of the fore- going notes on purchases to the finding of a suitable tackle for a given load, let us take the case of relieving tackles on tiller. The twisting moment on the rud- der head is first calculated by the rule given on page 106, which we shall assume to be 150,000 inch-lbs. With a spare tiller 50 inches long from centre of stock to shackle burton pin, we should have a net load of 3,000 lbs. to move, and it is proposed to use a four- fold purchase (i.e., 2 double blocks) for the purpose, which will increase the load by four tenths (4 sheaves by one tenth of the load Pig. 352. eac h f or friction), making the actual load to be operated 3,000 + 1,200 = 4,200 lbs. The moving block being on the tiller head, it is not practicable to haul from it, therefore we have only 4 parts at this block. Dividing the total load by four ropes, we get 1,050 lbs. (.47 ton) tension on each fall. With SINGLE SPANISH BURTON Fig. 351. Tackles 601 a factor of safety of 4|, using the best Manila rope, we get the equivalent circumference from the formula Vtension X 10 = V^7xTo = 2|", say 2\", as the manufactured sizes grade by quarters. The size of the double blocks to take the rope would be 7 inches, obtained by the rule on p. 394, and it would require four men to handle the hauling part. It is desired to lift a weight of 12 tons with a ship's derrick, and the maximum load on the winch must not exceed 5 tons; required the purchase, size of steel wire rope falls and blocks ? Owing to the heavy load dealt with in this case, the factor of safety need not exceed 5. The hauling part of falls to be led through a lead- ing block at heel of derrick. Load to be raised 12 tons Friction of 5 sheaves 6 " Derrick gear A " Total load to overcome 18.4 As the load on the winch may not exceed 5 tons, the purchase should be -^ = four parts in the falls — a twofold purchase. 4.o A factor of safety of 5 having previously been decided upon, we get for the breaking stress 4.6 X 5= 23 tons, and the equivalent cir- cumference of special flexible steel wire rope, per table = 3 inches circ, which will require two double blocks with sheaves 13$ inches in diameter. It should be noted that the maximum tension comes on the hauling part in hoisting, but on the standing part in lowering. The stress on topping lift, allowing for friction of one sheave, and power applied is equal to 9 4 tons, requiring special flexible steel wire rope of 3^" circumference. A fourfold purchase rove with Manila 4" circ. having two 12" double blocks, with wide mortise and the hauling part taken from the moving block, will be suitable for the load of 9.4 tons minus the power applied, i.e., 8\ tons. The following tables give the strength of tackles and the break- ing stress from actual test of hooks and shackles, fitted by the makers to the various sizes of blocks. The proper workingload for new Manila ropes is $ of the breaking stress. Of course, first grade Manila will develop a greater strength than what is shown by the accompanying tables of tackles, which are based on the strength of new rope adopted by the manufac- turers, and consequently should be worked to when figuring the safe working load. The Naval Constructor Rule to iind the equivalent circumference of Manila rope tor a given working load or tension (in tons) on one part of a fall, based on a factor of safety of 8 ; — Circumference = V^O * tension which is very easily memorized. Inversely, the safe working load for a given circumference of Manila will be Circ. 10 = safe load. STRENGTH OF TACKLES Ordinary Blocks. - o M s 5 83 Two Single Blocks. Two Double Blocks. Two Treble Blocks. Breaking Stress of Hooks in Lbs. Breaking Stress of Rope in Lbs. Breaking Stress ot Hooks in Lbs. Breaking Stress of Hope in Lbs. Breaking Stress of Hooks in Lbs. Breaking Stress ot Kope in Lbs. 3 1 1,143 1,400 1,492 2,800 2,219 4,200 3* H 1,492 1,800 2,218 3,600 2,985 5,400 4 n 2,218 3,600 2,985 7,200 3,987 10,800 5 2 2,985 6,400 3,987 12,800 5,410 18,200 6 2i 3,987 8,100 5,410 16,200 6,360 24,300 7 2f 6,410 12,100 6,360 24,200 9,356 36,300 8 3 6,360 14,400 9,356 28,800 13,720 43,200 9 3 9,356 14,400 13,720 28,800 16,030 43,200 10 3J 13,720 19,600 16,030 39,200 18,722 58,800 12 4 16,030 22,500 18,722 45,000 20,375 67,500 14 4J 18,722 28,900 20,375 57,800 28,300 86,700 16 5 20,375 40,000 Twofold 28,300 80,000 Fourfold 35,680 120,000 Sixfold Strength of Tackles 603 STRENGTH OF TACKLES. Wide Mortise and Heavy Tackle. Size of Two Single Blocks. Two Double Blocks. Two Treble Blocks. Break- Break- Break- Break- Break- ing Stress of Hooks in Lbs. Break- Block. S r O O ing Stress of Hooks in Lbs. ing Stress of Kope in Lbs. ing Stress of Hooks in Lbs. ing Stress of Kope in Lbs. ing Stress of Kope in Lbs. 7 3 6,360 14,400 9,350 28,800 13,720 43,200 8 H 9,356 19,600 13,720 39,200 16,030 58,800 9 3J 13,720 19,600 16,030 39,200 18,722 58,800 10 4 16,080 22,500 19,050 45,000 19,050 67,500 12 4f 19,050 32,400 20,375 64,800 28,300 97,200 14 6J 28,300 43,300 35,680 86,600 35,680 129,900 16 6i 35,680 48,400 Twofold. 72,100 96,800 Fourfold. 72,100 145,200 Sixfold. Wrecking Blocks and Lashing Shackles. Size of Block. * w fc 8 u 3 m En O O Two Single Blocks. Two Double Blocks. Two Treble Blocks. Break- ing Stress of Shackles in Lbs. Break- ing Stress of Rope in Lbs. Break- ing Stress of Shackles in Lbs. Break- ing Stress of Kope in Lbs. Break- ing Stress of Shackles in Lbs. Break- ing Stress of Rope in Lbs. 18 20 22 24 7 8 ii 116,300 132,532 155,542 172,400 67,600 78,400 115,600 192,000 Twofold. 132,532 155,542 172,400 235,620 135,200 156,800 231,200 384,000 Fourfold. 155,542 172,400 235,620 265,995 202,800 235,200 346,800 576,000 Sixfold. 604 The Naval Constructor DERRICK CAPACITY Item. 2£ Tons. 5 TOXS. Falls J 130' of 2f" G.S.W.R., single whip, 170 lbs. 65' of 3" G.S.W.R., single whip, 110 lbs. 60' of 2J" G.I.W.R., 60 lbs. 8' 0" of f p " crane chain, 25 lbs. 30 fathoms of 4" Ma- nila, 90 lbs. 60 fathoms of 3" Ma- nila, 96 lbs. 2 @ 50 lbs. = 100 lbs. 1 @ 60 lbs. = 60 lbs. 6 @ 40 lbs. = 240 lbs. 100 lbs. l^ of 3" G.S.W.R., single whip, 220 lbs. 65' of 3£" G.S.W.R., single whip, 135 lbs. 60' of 21" G.I.W.R., 60 lbs. 8' 0" of W' crane chain, 55 lbs. 40 fathoms of 4" Ma- nila, 120 lbs. 60 fathoms of 3" Ma- nila, 96 lbs. 2 @ 60 lbs. = 120 lbs-. 1 @ 70 lbs. = 70 lbs. 6 @ 40 lbs. = 240 lbs. 150 lbs. Topping Lift | Guys { Chain { Topping Lift Purchase . . j Guy Purchase j Fall Blocks Topping Lift Blocks . . . Shackles, etc Total weight of gear for one boom, excluding wire rope- reels, forgings to mast or boom, gooseneck, etc. 1,051 lbs. 1,266 lbs. Derrick Rigging 605 RIGGING. OF DERRICK. 10 Tons. 20 Tons. 50 Tons. 260' of 3" G.S.W.R., gun tackle, 435 lbs. 120'of3£"G.S.W.R., gun tackle, 250 lbs. &y of 2|" G.I.W.R., 80 lbs. 300' of 4" G.S.W.R., luff tackle, 765 lbs. 300' of 3^" G.S.W.R., tackle rove, 630 lbs. 60' of 3" G.I.W.R., 100 lbs. 710' of 3" G.P.S.W.R. (plough steel), Mech. adv. of tackle 7= 1,200 lbs. 540' of 3" G.P.S.W.R., Mech. adv. 6 = 910 lbs. 100' @ 3£" G.I.W.R., 210 lbs. Shackles used. 40 fathoms of 4" Ma- nila, 120 lbs. 60 fathoms of 3" Ma- nila, 96 lbs. 3 @ 60 lbs. = 180 lbs. 2 @ 60 lbs. = 120 lbs. 6 @ 40 lbs. = 240 lbs. 200 lbs. 40 fathoms of 4" Ma- nila, 120 lbs. 60 fathoms of 3£" Ma- nila, 130 lbs. l@1001bs. t_2o 0lb 2@ eoibs.j-^ 20108 - 2@ 100lbs. = 2001bs. 6 @ 40 lbs. = 240 lbs. 300 lbs. Direct to winch. 100 fathoms of 3£" Manila, 220 lbs. 1 @ 150 lbs. ) 1 @ 100 lbs. \ — 370 lbs. 2@60 lbs.) 1 @ 50 lbs. ) 2 @ 100 lbs. [ = 310 lbs. 1@60 lbs.) 4 @ 40 lbs. = 160 lbs. 800 lbs. 1,721 lbs. 2,705 lbs. 4,180 lbs. Section V. CHAPTER I. EQUIPMENT. In a modern steamship the Equipment, as understood by the classification societies, comprises that part of a vessel's outfit which relates to the handling of the ship and the safety of her complement, and in Lloyd's Register is represented by the nu- meral " 1 " after the character. Under this heading are included, anchors, chains, hawsers, boats, steering gear, windlass, and the requirements of the Board of Trade Regulations or the United States Inspection Laws. Lloyd's Equipment. The equipment as regards anchors, chains, hawsers, warps, etc. is regulated by the number produced by the sum of the measure- ments in feet arising from the addition of the half-moulded breadth of the vessel at the middle of the length, the depth from the upper part of the keel to the top of the upper deck beams (with the normal camber), and the girth of the half midship frame section of the vessel, measured from the centre line at the top of the keel to the upper deck stringer plate, multiplied by the length of the vessel for a one, two, and three decked vessel and for a spar decked vessel. For a vessel having a complete awning deck, or a continuous shade deck, the equipment number is to be increased one-eighth beyond that given by the measurements defined above to the main deck. For a steam vessel with a partial awning deck, poop, top gal- lant forecastle, bridge house or a raised quarter deck the equip- ment number is to be increased beyond that for a flush or spar-decked vessel by that proportion of the addition made for a complete awning deck (i.e., one-eighth) which the combined length of the erection bears to the length of the vessel. Where erections are fitted upon erections, the equipment number is to be corre- spondingly increased in the same proportion. (Sect. 39 of Lloyd's Rules. ) 607 The Naval Constructor Em J us^< r H r H_i_i,H.**H~HC>4CNC4<-4*4 aissssgssssSSSSS SSSSaSSiSSSS888888 ^S8§SSii8g O N N l» O © © © © CM © © t~ © N 00 » O H M (B OS M M M N N N N IO H CO M ooSooot^-t^-^cS CO lO $8 io © o cm © © co r» r^ oo © © IN (N fl U5 "O 00 O O CM U5 M CO 00 •♦ 6 6 CM N W lO IO rt CO lO lO 5 a i CM CM CO 00 O0 © iC5 lO 'O (M CM CM CO CO 13 O CM CM CM O O CM -H CO © §8 8 3 CO CO CO •><»< ■* T* ■<* CMcoeo-^eocoeMiM H H H H IN M o o CO CM CO ■»* © © U5 t~ oo co r^ oo •# m co t- O N « © © © 88888SS -h t~ r» t^ 8 8 « H H CO N - >♦ *-T i-^ ** cm cm" 00 00 © CM © © © ' 8 3 U5 — t* CO ^ O N * 5| US N M •^ 00 00 CM tH CO W N « » * ^' ^ lO ") tt) i« 5.S OOSOOONCONNOOOOONOOOlOieC McecOHH»p'iO«e>ddNH*^l«NNN (NaiOlOlOlNMCONNNMCOOlCCCOiOiacOCO N CO 00 o o_ N CO C» N « O ID O N N N oo oo ■** ^^^rt^e^cMCM*cM"eoeo-^a5or©*">jI'iOo6*© 8 2 8 £§ "O 00 rt « M M ^ * lllif OQ c» a — a* cm00c©©00cm©cmcm©00co©©©©©©©cm nmioocOlC50)ll5 !N*ON«oiaocot>oo J3hNCO , C«>0>OCBCOXS)0 8 8 CM ■>* © © © t -r. c-i >o CO oo fill 88S888SS8S888S8888SS «©co©co©cocoeO©coco i00t-OO>NHNNNt»N rj © i-H ■* « O) OJ OO QO 00 ■* ■>*< »o to to CM CM CM O © © CO CO CO 00 00 00 8 8 s a •ra -IOi 00 O0 O O i-< CM CM ■>* ■>*< 00 O0 CO CO CO CO CO © O ^H 00 00 t» t- 00 00 >o ■*llJCOCOO>Oirtrt CMCMCMCMCMCMCOCO 3 CWOOOOOOO -*©©©©©©© ooooooooo o ooooooooo o ©coto-<* co CO O to ^ O CM O rt M I* if) N CM CM CM CM CM CM Oi © CM CO to cococococoeococococococococococococococo CO CO CO CO O © © © © o o 3 o o CO N CN 00_ CB n cos* cq •* n CM CM CO CO CO SoooooooooSooooo ©Q £a cMOOqcOCOCOCOOOOCM_rJ^oqcM^oqcOCOC»g^g »" (8 00* rt t" N O" » N O CO* CC g « N rt So" §, Tf^^KMffliOCOCOCONNNMOOOOO Olg^j 610 The Naval Constructor As an example of the method of applying the foregoing rule, let ns take the case of a 3-deck vessel, having a complete shelter- deck, and a bridge superstructure with houses erected on it. This type will clearly exemplify all of the requirements of the rule, as we shall calculate the numeral firstly for a 3-deck vessel, to which we will then add one eighth for the complete shelter- deck, afterwards increasing it by the proportion that the length of bridge superstructure bears to the length of ship (or how much of another eighth we shall take), and finally resolving the area of the deck erections or superstructure into an equivalent length of vessel enclosing the same area, and adding its propor- tionate value. Example : — Required the equipment numeral for a three- decked vessel having a complete shelter-deck on which is built a superstructure having deck houses on top : — Dimensions : 550' X 65' X 41' to shelter deck 33.5' to upper deck Length of superstructure . . 250' Size of deck houses . . . . 100' x 40' = 4,000 sq. ft. = 4oo&= 61.5' equivalent length Half-breadth 32.50' Depth (to U.DK+16i" camber), 34.85' Half girth 63.00' 130.35' Length X 550' 71,692.5 Add £ for complete shelter deck 8,961.5 Add proportion of £ repre- sented by 250' of super- structure 4,073.1 Add proportion of •£ repre- sented by 61.5' equiva- lent length of houses . 1,001.8 Equipment number . . . 85,728.9 The preceding "Table 22 " of Lloyd's Rules shows the require- ments of that Society for steam vessels based on the above rule. American Ship Windlasses 611 AMERICAN SHIP WINDLASSES. Steam Steam Pump Lloyd's Size Capstan Brake Equipment of Chain Engines. Windlasses Windlasses Numbers. Cable. Weight in Lbs. Weight in Lbs. " // // // Lbs. Lbs. 6,150- 7,490 i| and 1 4X6 7,000 5,000 7,490- 9,770 Mr ' ' 1* 4x 6 8,500 6,800 9,770-11,740 Mr ' ' H 5x 7 9,000 7,300 11,740-13,450 Mr * ' if 6x 8 12,000 9,000 13,450-16,720 ItV ' 4 l* 7x 8 13,000 12,250 16,720-19,780 M ' 1 H 8x 8 17,000 16,250 19,780-24,220 Iff ' ' if 9x 8 17,850 17,100 24,220-30,020 Iff ' • n 9X9 19,500 18,750 30,020-35,450 4* ' ' 2 10x10 27,000 24,000 35,450-43,600 Mr ' ' 2* 10 x 10 23,000 31,000 43,600-51,000 Mr ' 1 2 * 12 x 12 31,000 33,000 51,000-59,000 2f ' 12 x 12 33,000 35,000 THE SHAW AND SPIEGLE PATENT AUTOMATIC STEAM TOWING MACHINE. & fc h & i . o . •J. O H O H o , w o « « H pj K v & «Km (S * m tfWft £2© 6 3 3 • PJ g2P4 b3* w ]<-w>4< J<— -«r — *cy 614 The Naval Constructor rflhW u) Admiralty Cable Requirements 615 ADMIRALTY CABLE REQUIREMENTS. Samples shall be taken by the Overseer indiscriminately for testing from every description of iron included in any one in- voice, provided the number of bars, etc., so included does not exceed 50, and if above that number, one for every 50 or portion of 50 of each description. The samples may be tested to show the fibre, strength, ductility, and other qualities of the iron, and if not found satisfactory, the lot from which they are taken may be rejected. In cases where the quantity of each size is small, and the total quantity of bars of all sizes does not exceed 50 No., one sample only need be tested, provided that all the bars represented thereby are supplied by one maker, and that the Overseer is satisfied as to the quality of the iron; the sample for testing shall be selected by him, and the acceptance or rejection of the batch shall depend upon the result of the tests. The samples of every description of iron shall have an ulti- mate tensile strength respectively: — Of not less than 23 tons to the square inch of section, for sizes under 2\ inches; Of not less than 22^ tons to the square inch of section, for sizes from 2\ to 2^ inches, both sizes inclusive; and Of not less than 22 tons to the square inch of section, for sizes above 2^ inches; with an elongation of 20 per cent, in a length of 8 inches, for all sizes of iron. Tensile tests, if not made on the premises of the Iron Manu- facturer, shall be applied at a public testing house at the Con- tractors' expense, and in the presence of the Overseer. Forge Test, Cold. Every bar of 1-inch diameter and above shall admit of bending cold to the same radius as ^ — , the end of the link for which \C~ it is to be used, thus: Z"" 3 Bars under 1 inch to admit of bending cold, thus: A sample shall be notched and bent, thus: to show the fibre and quality of the iron, which is to be entirely satisfactory to the Overseer. Forge Test, Hot. Bars shall be punched with a punch one-third the diameter of the bar, at a distance of one and one-half diameters from the 616 The Naval Constructor end of the bar. The hole may then be drifted out to one and one-quarter times the diameter of the bar. The side of the hole may then be split ; and the ends must ad- mit of turning back without fracture, thus: -The whole of the articles, including the annealed crucible cast steel or forged steel stud pins of the cables, and the tinned steel pins, etc., shall be made only of material approved by the Overseer. The iron for the articles enumerated in Schedules II and III shall be also well hammered and rolled, and of quality approved by the Overseer. Anchor shackle bolts shall be made of blooms at least twice worked, and not of bar iron. The square links and shackles, to- gether with the swivels and bolts, shall be worked or drawn out under hammers oT sufficient weight, and the welds or shuts shall be made in the most perfect and solid manner. No iron shall be used in which the brand-mark is so deeply cut as to unduly weaken the section, or is so situated as to make unsatisfactory work in form- ing the link, and the Contractors shall make arrangements for stor- ing the Admiralty cable iron separately from all other cable iron. All the stud pins of the chain cable shall be marked on one side with the name or initials of the Contractors, and on the other side with the date of the year of delivery into store. The several lengths of each chain cable, and mooring, pendant or bridle chain, and the joining shackles and large shackles to be connected therewith, shall be marked as follows, viz. : — The end links of the lengths of the cable with a distinguishing num- ber, and the broad arrow; the joining shackles and anchor shackles with the same distinguishing number, the broad arrow, and the initials of the Contractors* the mooring and other swivels and splicing shackles, on their largest part, with a dis- tinguishing number, the broad arrow, and the initials of the Contractors; and the splicing shackles and swivels with the date of the year of delivery into store, in addition. Cables and all cable gear will be received for the first four months of each year with the last year's date on the stud pins. Tests. — The whole of the articles enumerated in Schedules I, II and III, shall be subjected, before delivery, to the proof strains prescribed in the Specification and Tables herewith, and to the following breaking test, which shall be first applied. Chain Cables, Bridle and Pendant. — A sample of three links taken from each length of chain cable, or each bridle and pendant chain, shall be subject to tensile strain until it breaks. The links shall be cut out at the public testing machine in the presence of the Overseer, when practicable. Should it break under a less strain than 50 per cent in excess of the proof strain, the entire length of which that portion is a sample shall be rejected. Dimensions for Chain Cables 617 Cables and gear which pass the proving and breaking tests shall be minutely examined by the Overseer, and any flaws or defects which he may point out shall be remedied to his satis- faction before the cables and gear are forwarded to the yards. The cables, etc., shall be cleaned sufficiently to permit of the Overseer guaranteeing the absence of flaws or defects. TABLES OF DIMENSIONS, TESTS, ETC., FOR ADMIRALTY CHAIN CABLES. 41 a " « B « z Og s &< a 3 si! n St £Q3 Dimensions of Com- mon Links Subject to the Latitude Stated in Clause 4 of the Specification. 9 h IBs S < « w oH *2 Weight of 100 Fathoms of Cable, with the Nec- essary Joining Shack- les, ETC., SUBJECT TO THE Latitude Stated in 6 E m w • w 5 « i O o g g 3 <-» 83 . < E o B a E w S o o j 2 2 1 L d »f B o 3 1 H J* o n a o 1 I 18 III Mi T3 o3 » £33 1 £ £ Ins. Ins. Ins. Ozs. Cwts. Qrs. Lbs. Lbs. Lbs. Lbs. Lbs. Tons. 3* 21 12.6 150.0 588 359 182.25 171.5 134 176.4 3i 19* 11.7 119.8 507 287.5 145.9 137 107.25 161.6 3 18 10.8 94.5 432 226.1 114.75 108 84.38 145.8 2J 16i 9.9 72.8 363 174 88.38 83 65 129.3 i 15| 9.2 58.9 315 21 140 71.5 66.3 52.6 118.2 15 9.0 54.7 300 130 66.4 62.5 48.8 112* 14i 8.5 47.5 270 3 112 56.9 53.5 41.9 101* 91* 2i 13* 8.1 40 243 95 48.4 45.5 35.6 2* 12* 7.6 33.6 216 3 80 40.75 38.3 30 8U 2 12 7.2 28. 192 67 34 32 25 72 11 nj 6.7 23 168 3 55.25 28 26.33 20.6 63i 55i n 10* 6.3 18.8 147 44.9 22.78 21.5 16.75 i 9| 5.8 15 126 3 36 18.25 17.2 13.4 47i 9 5.4 11.8 108 28 14.34 13.5 10.5 40* it 8* 4.9 9 90 3 21.75 11 10.37 8.2 34 » 7* 4.5 6.9 75 16.31 8.32 7.75 6.1 28* 22J i| 6i 4.0 5.0 63 3 4 11.87 6.10 5.7 4.5 6 3.6 3.5 52 3 6 8.37 4.25 4 3.2 18 j 3 3.1 2.4 40 1 20 5.61 2.84 2.66 2.2 13* i 2.7 1.5 29 2 2 3.53 1.79 1.68 1.4 10* i 4* 2.5 1.14 24 3 23 2.72 1.37 1.29 1.1 8* 3f 2.2 0.86 20 2 14 2.04 1.03 1.03 0.8 7 i 3f 2.0 0.62 16 2 23 1.49 0.75 0.702 0.58 i 3 1.8 0.44 13 22 1.04 0.53 0.47 0.41 i 21 1.6 0.30 10 12 0.7 0.34 0.33 0.28 3* 21 1.35 0.184 7 1 20 0.44 0.22 0.21 0.18 m The breaking strain of the several sizes of cables shall not fall short of the above proof strains, with 50 per cent added. Note. — The above proof strains are equivalent to the following strains per circular * inch of iron, viz., 3* inch, 504 lbs.; 3* inch, 536.5 lbs.; 3 inch, 567 lbs.; 2f inch, 598.5 lbs.; 2 T 9 8 inch and under, 630 lbs. The table can be used for calcu- lating the weight of cable in lengths less than 12* fathoms. 618 The Naval Constructor ADMIRALTY CHAIN CABLES. Common Links, A. Second End Links, Ii. Extreme End Links, C. Size of Iron, Length Ex- treme, Width Ex- treme, Size of Iron, Length Ex- treme, Width Ex- treme, Size of Iron, Length Ex- treme, Width Ex- treme, F. 0. //. J. /. K. L. M. N. Ins. Ins. Ins. Ins. Ins. Ins. Ins. Ins. Ins. 3} 19| Hi 31 21 13 31 22 13 3ft 191 ill 3ft 20| 12i 318 211 12} 31 18} lit 31 201 121 3} 21 121 3ft 184 in 3ft 191 12i IN 20} 12} 3 18 101 3i 191 12 3} 20} 12 218 171 10} 3ft 191 HI 31 19} 11J 2} 17i 101 31 181 HI 3} 19} 111 IH 161 101 3ft 18i Hi 3ft 19 Hi 2} 16* 91 3 171 11 3} 181 11 ill 161 911 218 171 10} 3ft 18} 10} 2i 15} 91 21 17 101 31 17} 104 2ft 151 9i 218 161 101 3ft 17} 10} 24 15 9 2i 161 10 3 16} 10 2ft 14f 8i m 151 9} 218 16ft 9} 21 m 8ft 21 15ft 91 21 16 94 2ft 13} 8ft 2ft 15 9} 2} 15} 9} 2} 131 81 21 141 9 m 15ft 9 2ft 131 71 21 14 ft 8} 21 14} 8} H 12} 711 2ft 13i 81 2ft 14} 81 2ft 12| 7ft 2ft 131 81 21 134 8} 2 12 7ft 21 13 8 2ft 134 8 HI in 7 2ft 12 ft 7} 2ft 13 7} n in 6i 2 121 71 21 1211 74 H8 101 61 US III 71 2ft 12ft 7} U 101 6ft ii 11} 7 21 1118 7 IH 101 6ft ill toil 6} 2 11} 6} if • 9} 5} 11 101 61 118 11 64 lft 91 51 liJ 101 6} H 101 6} H 9 5ft i| 9} 6 118 101 6 lft 8f 5ft lft 9ft 5} lH 9} 5} ii 81 411 H 81 51 H 9} 54 lft 71 4i lft 81 51 H 813 5} U 71 41 if 81 5 lft 8ft 5 lft 71 41 lft 711 4} 11 8 4} U 6} 4ft H 71 41 lft 7} 44 lft 61 3}g I la 6} 4} 11 7} 4} l 6 3f H 61 4 lft 6} 4 II 51 31 6ft 3} U 6} 3} J 5} 31 18 5} 31 lft 5} 34 U 41 218 1 51 3} l 5ft 3} i 41 211 13 41 3 18 5 3 11 41 21 i 44 2} H 4} 2} f 3} 21 11 4 21 i 4ft 24 ft 31 2ft 1 31 2} fi 318 2} * 3 113 ft 3} 2 * 3} 2 ft 21 lft 1 218 1} ft 218 1} Details of Links and Shackles 619 CHAIN CABLE LINKS. Fig. 356. PROPORTIONS AND DETAILS OF LINKS SHACKLES. h AND Q85' * ^ Fig. 357. 620 The Naval Constructor ADMIRALTY CHAIN ' CABLES.— [Continued.) Shackles, D. Shackle Pins, E. Size of Length Width Iron, Extreme, Extreme, R S T U V w 0. P. Q. Ins. Ins. Ins. Ins. Ins. Ins. Ins. Ins. Feet Ins. 41 23 13 2H 51 31 31 i 6 2ft 4ft 22J 121 21 51 3ft 313 i 6 on 41 22 121 2ft 5 31 3i f 5 HA 4 21| 121 21 41 3ft 313 i 5 9} 31 211 12 2ft m 3 3! t 5 8! m 20} lt| 21 4ft 213 3ft t 5 7! 3f 201 ni 2ft 4ft 21 31 t 5 51 3! 20 Hi 21 41 213 3i 4 5 4i 3ft 191 n 2ft 4ft 21 3ft 4 5 213 34 191 101 21 4ft 2H 3ft 1 5 lft 31 18f 101 2ft 41 21 31 4 1113 3ft 181 101 2 41 2ft 3ft 1 1013 3J 17J 10 2 4 21 3 4 91 3ft 17ft 9i m 31 2ft 213 1 713 3ft 161 91 3H 21 21 4 61 3 16ft 91 3& 2ft 2! ft 5 HI 16 9 m 31 21 2H ft 34 2} 151 8} 31 2ft 2| ft 2 H 15 81 it« 3i 21 2ft ft Oft 2H 141 ' 81 3ft 2ft 21 ft 3 Hi 2f 14ft 8 3ft 2 2ft i 3 n 9ft 13H 71 ift 31 1H 2ft i 3 81 2ft 131 71 3 H 21 i 3 613 n 12} 71 ift 2} H3 2ft i 3 5ft 2i 12ft 7 213 H 21 i 3 41 2ft nil 61 2& m 2 ft 3 2U 21 111 61 ift 2f H 113 ft 3 lft 2ft 11 61 21 ift « ft 2 lift til lOf 6 ift 2f H 113 ft 2 10! 1} 101 51 2ft ift itt ft 2 813 li 9* 51 ift 2ft ii if 1 2 74 H3 9ft 51 ift 2} ift lft 1 2 6ft 1ft 8} 5 2 11 H 1 2 413 li 8ft 41 li n ift ift 1 2 31 1ft 711 41 iig H ift 1 2 113 H 71 41 11 m lft U ft 2 01 lft 71 4 13 if 1 lft ft 101 1ft 6f 3i ii 11 11 ft 9ft lft 6ft 31 U H \ lft ft 713 1 5i 31 ift 13 l A 6ft 13 5ft 3 ift i 13 413 1 41 21 ft H H 13 3i H 4ft 21 ift f i 2ft J 4 21 ft is ft H 01 H 3ft 2 ft \i 4 i m ft 51 li H ft ft 91 Club Shackle 621 CLUB SHACKLE. Fig. 358. 622 The Naval Constructor CHAIN SWIVEL. p — 7069 - >j K--2 .---*| Yi^^ms-MAo^ Section A.B : f<--2./59->| • -Al4Ss\*- Section G.H.1 Fig. 359. Kenter Shackle 623 KENTER SHACKLE. laij Dimensions of Kenter Shackles. M/M Approx. ins... Inches Inches Inches Inches Weight in lbs M/M Approx. ins. . Inches Inches Inches Inches Weight in lbs M/M Approx. ins. . Inches Inches Inches Inches Weight in lbs D 20 22 i 8 24 if 26 1 28 30 33 IA D ff « IA R H H 5 8 u f H i 8 L 4 if 5* 6J 6f 7* 71 W 3f 3| 41 if 5 5* T H IfV IA IA m m 2 2.2 3.3 4.4 6.6 7.75 8.8 11 30 1 3 - 2A 13.3 Z> 39 42 45 48 51 54 57 60 63 u 91 2i 18.8 66 2f 15f 10| 3H 92.5 H lj 10 7 24.2 2f m 16| lit 99 u 1A 10f n 2B 30 72 2H it 17 HI 4A 121 H if Hf 71 2|f 35 75 211 ill 17| 12| 41 135 2 If 12 8| 31 42 78 3 2A 18* 121 4| 150 2 \ 12f 81 31 52 81 3A 21 191 13| 41; 21 If 13| 91 3| 60 84 2 T 3 e 191 131 5 ^8 1A 141 91 3A 7.25 87 3A 21 20| 14| 5A 21 Hi 141 10f 3| 81.5 90 JA 2| 21| 15 5A 624 The Naval Constructor MUSHROOM MOORING ANCHORS. Weight in Lbs. A. B. a i>. £7. P. G. IT. J. a:. 6,000 5 6 / // 6 9 6* / // 5 9£ / // 3 10J 13f 61 41 4 12 3,600 5 5 6 5 5 3 6 HJ 6* 4 31 12 1,850 4 4 4 4 3 10 2 8| 9| 4* 31 21 9 1,200 3 3 3 8 8* 3 1 2 2 8 8* 3 H 81 Weight in Lbs. L. M. jr. O. P. » tl OS n CO B 3 B ; ° v CN CO -8 •* © co cn *n 10 os «o T* CN ■<* 00 © CN © coo TfWIO 00 © CN — 1 05 03 « H H H P t O v © CO >o 3 5 5 © oo OS © 00 © CO © i-irH 00 * © ^ 00 CO 5 © 1 © CN OS rH 00 HIO CN OS -H © 00 H 00 OS -8 © ; © CO © © ■* © n i-l OS CO © CN t- ft *H OS© CO CO 5 © .35 CO © rH t- © © rH ■»* •* rH r}< t- OS CN © CN t © O © 5 © .8 IO © © t> OS t- H CO iJHCMJO OOOIM — CO -8 © 5 © © ft 113 OOiJtOO oo i* co © oo rH cn cn t* 5 © -85 co 5 © -8 CO0S00 00CO00 © CN ij< Tl< tO ft n CN IN** 5 © os t- t- 00 5 ° rt ft N COOO ©, °° •* irO 00 © CO CN CN lO 5 © -8 © © cs os as SO o 5 © ^8 .rH © CN ft rH 00 rH 1ft CN 05 rH coooh ooos i © -a co cn 5 © -a oo © co oo io if oo eoiieo t< ft ci cjh i - SB 05 © a si CD -1 ii'H l1) ** liiili^s£iS|3|i-i O O O H HHH H © CD I*- • h • «S .<2 . a .a . © 2 a .* • 1 '1 " s 1 ' CD . fl . cmIo^. CO OO 630 The Naval Constructor DIMENSIONS AND Length Extreme . . Breadth Depth R . ., ( Sided . . . Keel ) Moulded . . Stem and stern post, sided Transom, thick . . f Sided . . Floors J Moulded . floors < Grownto t shape . « f Sided .... •3 ( Lower § MouMed !,-£ fc I I end Gunwales) TM& Breasthooks . . m ( Fixed . . . j* < Portable . . H (^ Gun platform Mast thwarts { J™*; Other thwarts { ™S* f Knees to thwarts, i sided ) Thickness of plank » when finished . . J Strakes, No., about, j No. of oars, provision j to be made for . . j 34 8 10 2 1U 31" r," No. 4 li' No. 2 If' 94" 7" H" \" No. 16 14 32 8 6 2 10 3" 4:1" 2J" % 3" No. 4 30 8 1 28* 3" 4|" 1 If" % 7" H" i" No. 15 IS 28 7 2 6* If" I 7" H" i" Nu. 15 10 27 7 264. 3" 4) No. 4 1*" 1" 2" 24" No. 2 5 !!" U" 7" U" *" No. 15 Id 26 7 2 5* 1 iy W' 1" U" A" No. 10 10 25 7 3 2 5* 23 611 2 4* 2f" I" n- 2" No. 2 4 23 5 6 2 2 2|" 4" 2* •No. 2 1" Dimensions and Scantlings of Row Boats 631 SCANTLINGS OF ROW BOATS. SO CO M M H H O s M h H O W w jjjj ft < M SO li < 33 6 J 6 W 6 B 6 6 5 2 20 5 6 2 2 18 6 2 2 2J" 4" 16 5 7 2 1 21- 4" 14 5 2 2 2 21" 3*" 12 5 2 1 32 5 6 2 2 24" 3§" 30 5 6 2 2 24" 3f" 28 5 6 2 2 2J" 3f" 27 5 6 2 2 24" 3g" 26 5 6 2 2 24" 3§" 25 5 6 2 2 24" 3f" 24 5 6 2 2 24" 3|" 23 5 6 2 2 24" 3|" 22 5 6 2 2 24" 3|" 200 5 6 2 2 24" 3f" / // 18 5 2 2 24" 3§" 2&" 21" 2|" 24" 2J" li" li" H" li" li" li" li" 1|" l" f" No. 4 1" 1" 1" I" No. 4 1" li" No. 2 1" If" 1" No. 2 1" 11" 1" No. 2 ir i" No. 2 1" ii" i" No. 2 r 1" 1" No. 4 1" 1" 1" 1" No. 4 1" 1" 1" No. 4 1" 1" 1" No. 4 1" 1" I" No. 4 1" 1" J" Jso. 4 1" 1" 1" 1" No. 4 1" 1" No. 4 1" r i" 1" No. 4 1" |" t" I" t" t" 1" 1" |" 1" 1" 1" 1" 1" t" 1" 1" No. 1 7 if" No. 1 7 No. 1 7 H" No. 2 6 H" 14" No. 1 6 i" 1|» No. 2 5 No. 1 5 No. 2 5 No. 1 5 14" No. 1 4 h" $> No. 1 4 No. 4 No. 2 3 I" No. 3 11" No. 1 2 If- No. 1 2 1 1 1 1 14" 7" W 8" ii" 7" 4" 8" 4" 7" H" 7" H" 7" 1" 7" 1" 7" 1" 7" 1" 7" 7" 1" 7" 1" 7" 1" 7" 1" 7" 1" 7" 1" 7" i" 14" 1" r i" r i" 3" i" r i" i" '*" i" i" 1" h" tV iV i" f" i" 1" 1" ¥' i" I" I" 1" 1" 1" I" No. 14 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 No. 13 4 6 6 6 6 6 6 6 5 5 5 4 4 4 4 4 632 The Naval Constructor YACHTS' LAUNCHES. Length. Beam. Depth. Draft Aft. Weight Com- plete. Speed in Knots. Class of Machin- ery.* 16 4 3 1 10 1 4 Cwts. 8* 5 H.P. 5 18 4 6 2 1 6 10 6 5 20 5 2 2 1 6 12 6 5 22 5 3 2 6 1 8 16 7 10 23 6 5 4 2 8 2 18 7* 15 25 5 6 2 10 2 19 8 15 27 6 2 10 2 4 25 10 25 30 6 3 3 2 4 30 10 25 35 6 6 3 2 2 10 45 12 35 45 7 6 4 3 90 12 50 55 8 6 5 3 3 10 140 12 80 * Compound engines with water tube boilers. Standard Ship's Life-Boat 63; 634 The Naval Constructor CHAPTER III. BRITISH RULES FOR STEAMSHIPS CARRYING PASSENGERS, BOATS AND LIFE-SAVING APPLIANCES. (a) Ships of Division A, Class 1, shall carry boats placed under davits, lit and ready for use, and having proper appliances for getting them into the water, in number and capacity as pre- scribed by the table in the appendix to these Rules (see page 433) ; such boats shall be equipped in the manner required by, and. shall be of the description defined in, the General Rules appended hereto. (6) Masters or owners of ships of this class claiming to carry fewer boats under davits than are given in the table must declare before the collector or other officers of customs, at the time of clearance, that the boats actually placed under davits are suf- ficient to accommodate all persons on board, allowing 10 (ten) cubic feet of boat capacity for each adult person, or "statute adult." (c) Not less than half the number of boats placed under davits, having at least half the cubic capacity required by the tables, shall be boats of Section A or Section B. The remaining boats may also be of such description, or may, in the option of the ship- owner, conform to Section C, or Section D, provided that not more than two boats shall be of Section D. (d) If the boats placed under davits in accordance with the table do not furnish sufficient accommodation for all persons on board, then additional wood, metal, collapsible or other boats of approved description (whether placed under davits or otherwise), or approved life-rafts, shall be carried. One of these boats may be a steam launch; but in that case the space occupied by the engines and boilers is not to be included in the estimated cubic capacity of the boat. Subject to the provisions contained in paragraph (/) of these rules, such additional boats or rafts shall be of at least such carrying capacity that they and the boats required to be placed under davits by the table provide together in the aggregate, in vessels of 5,000 tons gross and upwards, three fourths, and in vessels of less than 5,000 tons gross, one half, more than the minimum cubic contents required by column 3 of the table. For this purpose 3 cubic feet of air-case in the life-raft is to be esti- mated as 10 cubic feet of internal capacity. Provided always that the rafts will accommodate all the persons for which they are to British Rules for Steamships 635 be certified under the Eules, and also have 3 cubic feet of air-case for each person. All such additional boats or rafts shall be placed as conveniently for being available as the ship's arrangements admit of, having regard to the avoidance of undue encumbrance of the ship's deck, and to the safety of the ship fov her voyage. (e) In addition to the life-saving appliances before mentioned, ships of this class shall carry not less than one approved life-buoy for every boat placed under davits. They shall also carry ap- proved life-belts, or other similar approved articles of equal buoy- ancy suitable for being worn on the person, so that there may be at least one for each person on board the ship. (/) Provided, nevertheless, that no ship of this class shall be re- quired to carry more boats or rafts than will furnish sufficient accommodation for all persons on board. ' General Rules. Boats. — All boats shall be constructed and properly equipped as provided by these Rules, and all boats and other life-saving appliances are to be kept ready for use to the satisfaction of the Board of Trade. Internal buoyancy apparatus may be con- structed of wood, or of copper or yellow metal, of not less than 18 ounces to the superficial foot or of other durable material. Section A. A boat of this section shall be a life-boat, of whale- boat form, properly constructed of wood or metal, having for every 10 cubic feet of her capacity, computed as in Rule 2, at least one cubic foot of strong and serviceable enclosed air-tight compartments, so constructed that water cannot find its way into them. In the case of metal boats, an addition will have to be made to the cubic capacity of the air-tight compartments, so as to give them buoyancy equal to that of the wooden boat. Section B. A boat of this section shall be a life-boat, of whale- boat form, properly constructed of wood or metal, having inside and outside buoyancy apparatus together equal in efficiency to the buoyancy apparatus provided for a boat of Section A. At least one-half of the buoyancy apparatus must be attached to the outside of the boat. Section C. A boat of this section shall be a life-boat, properly constructed of wood or metal, having some buoyancy apparatus attached to the inside and (or) outside of the boat equal in ef- ficiency to one-half of the buoyancy apparatus provided for a boat of Section A or Section B. At least one-half of the buoy- ancy apparatus must be attached to the outside of the boat. Section D. A boat of this section shall be a properly con- structed boat of wood or metal. 636 The Naval Constructor Section E. A boat of this section shall be a boat of approved construction, form and material, and may be collapsible. Cubic Capacity. — The cubic capacity of a boat shall be deemed to be her cubic capacity, ascertained (as in measuring ships for tonnage capacity) by Simpson's rule ; but as the appli- cation of that rule entails much labor, the following simple plan, which is approximately accurate, may be adopted for general purposes, and when no question requiring absolute correct ad- justment is raised : — Measure the length and breadth outside and the depth inside. Multiply them together and by .6 ; the product is the capacity of the boat in cubic feet. Thus, a boat 28 feet long, 8 feet 6 inches broad, and 3 feet 6 inches deep, will be regarded as having a ca- pacity of 28 x 8.5 x 8.5 = 499.8, or 500 cubic feet. If the oars are pulled in rowlocks, the bottom of the gunwale of the row- lock is to be considered the gunwale of the boat for ascertaining her depth. Number of Persons for Boats. — The number of persons a boat of Section A shall be deemed fit to carry shall be the num- ber of cubic feet, ascertained as above, divided by 10. The number of persons a boat of Section B, Section C, Sec- tion D, or Section E shall be deemed fit to carry, shall be the number of cubic feet, ascertained as per rule, divided by 8. The space in the boat shall be sufficient for the seating of the persons carried in it, and for proper use of the oars. Appliances for Lowering Boats. — Appliances for getting a boat into the water must fulfil the following conditions : — Means are to be provided for speedily, but not necessarily simultaneously or automatically, detaching the boats from the lower blocks of the davit tackles ; the boats placed under davits are to be attached to the davit tackles and kept ready for service ; the davits are to be strong enough and so spaced that the boats can be swung out with facility ; the points of attachment of the boats to the davits are to be sufficiently away from the ends of the boats to insure their being easily swung clear of the davits ; the boat's chocks are to be such as can be expeditiously removed ; the davits, falls, blocks, eyebolts, rings, and the whole of the tackling are to be of sufficient strength ; the boat's falls are to be long enough to lower the boat into the water with safety when the vessel is light. The life-lines shall be fitted to the davits, and be long enough to reach the water when the vessel is light ; and hooks are not to be attached to the lower tackle blocks. Equipments for Collapsible or other Boats, and for Life-Rafts. — In order to be properly equipped, each boat shall be provided as follows : — Number of Persons for Life-Rafts 637 (a) With the full single-banked complement of oars, and two spare oars. (b) With two plugs for each plug-hole, attached with lanyards or chains, and one set and a half of thole pins or crutches, attached to the boat by sound lanyards. (c) With a sea-anchor, a baler, a rudder and a tiller, or yoke lines, a painter of sufficient length, and a boat-hook. The rudder and the baler to be attached to the boat by sufficiently long lan- yards, and kept ready for use. In boats where there may be a difficulty in fitting a rudder, a steering oar may be provided instead. (d) A vessel to be kept filled with fresh water shall be provided for each boat. (e) Life-rafts shall be fully provided with a suitable approved equipment. Additional Equipments for Boats of Section A and Section B. — In order to be properly equipped, each boat of Sections A and B, in addition to being provided with all the requisites laid down in Kule, shall be equipped as follows, but not more than four boats in any one ship require to have this outfit, and where boats of Sections A or B are carried in lieu of boats of Sections C or D, this additional outfit need not be insisted on : — (a) With two hatchets or tomahawks, one to be kept in each end of the boat, and to be attached to the boat by a lanyard. (6) With mast or masts, and with at least one good sail, and proper gear for each. (c) With a line becketted round the outside of the boat and securely made fast. {d) With an efficient compass. (e) With one gallon of vegetable or animal oil, and a vessel of an approved pattern, for distributing it in the water in rough weather. (/) With a lantern trimmed, with oil in its receiver sufficient to burn eight hours. Number of Persons for Life-Rafts. — The number of persons that any approved life-raft for use at sea shall be deemed to be capable of carrying, shall be determined with reference to each separate pattern approved by the Board of Trade ; provided always, that for every person so carried there shall be at least three cubic feet of strong and serviceable enclosed air-tight com- partments, constructed so that water cannot find its way into them. Any approved life-raft of other construction may be used, provided that it has equivalent buoyancy to that hereinbefore 638 The Naval Constructor described. Every such approved life-raft shall be marked in such a way as to plainly indicate the number of adult persons it can carry. Buoyant Apparatus. — Approved buoyant apparatus shall be deemed sufficient, so far as buoyancy is concerned, for a number of persons, to be ascertained by dividing the number of pounds of iron which it is capable of supporting in fresh water by 32. Such buoyant apparatus shall not require to be inflated before use, shall be of approved construction, and marked in such a way as plainly to indicate the number of persons for whom it is sufficient. Life-Belts. — An approved life-belt shall mean a belt which does not require to be inflated before use, and which is capable at least of floating in the water for 24 hours with 15 pounds of iron suspended from it. Life-belts are to be cut out 2 inches under the arm-pits, and fitted so as to remain securely in their place when put on. Lif e-Buoys. — An approved life-buoy shall mean either : (a) A life-buoy built of solid cork, capable of floating in water for at least 24 hours with 32 pounds of iron suspended from it ; or (6) A strong life-buoy of any other approved pattern or material, provided that it is capable of floating in water for at least 24 hours with 32 pounds of iron suspended from it, and provided also that it is not stuffed with rushes, cork shavings, or other shavings, or loose granulated cork or other loose material, and does not require inflation before use. All life-buoys shall be fitted with beckets securely seized, and not less than two of them shall be fitted with life-lines 15 fathoms in length. Position of Life-Buoys and Life-Belts. Water-tight Compartments. — All life-buoys and lif e-belts shall be so placed as to be readily accessible to all persons on board, and so that their position may be known to those for whom they are intended. When ships of any class are divided into efficient water-tight compartments to the satisfaction of the Board of Trade, they shall only be required to carry additional boats, rafts and buoy- ant apparatus of one-half the capacity required by these Kules, but the exemption shall not extend to life-jackets or similar approved articles of equal buoyancy suitable to be worn on the person. The table referred to in the foregoing Rules, showing the mini- mum number of boats to be placed under davits and their mini- mum cubic contents, follows : — Number and Capacity of Boats 639 BOAT CAPACITY FOR STEAMERS. (British Law.) Gross Tonnage. 10,000 9,000 8,500 8,000 7,750 7,500 7,250 7,000 6,750 6,500 6,250 6,000 5,750 5,500 5,250 5,000 4,750 4,500 4,250 4,000 3,750 3,500 3,250 3,000 2,750 2,500 2,250 2,000 1,750 1,500 1,250 1,000 900 800 700 500 400 300 200 100 and upwards . and upwards . and under 9,000 8,500 8,000 7,750 7,500 7,250 7,000 6,750 6,500 6,250 6,000 5,750 5,500 5,250 5,000 4,750 4,500 4,250 4,000 3,750 3,500 3,250 3,000 2,750 2,500 2,250 2,000 1,750 1,500 1,250 1,000 900 800 700 500 400 300 200 Minimum Num BEB OF Boats to be Placed under Davits. Total Minimum Cubic Contents of Boats to be Placed under Davits LxfixDx.6 5,500 5,250 5,100 5,000 4,700 4,600 4,500 4,400 4,300 4,200 4,100 4,000 3,700 3,600 3,500 3,400 3,300 2,900 2,900 2,800 2,700 2,600 2,500 2,400 2,100 2,050 2,000 1,900 1,800 1,700 1,500 1,200 1,000 900 800 700 600 400 350 640 The Naval Constructor Note. — Where in ships already fitted the required cubic con- tents of boats placed under davits is provided, although by a smaller number of boats than the minimum required by this table, such ships shall be regarded as complying with the rules as to boats to be carried under davits. In case of vessels under 200 tons gross tonnage, the capacity of any boat to be supplied should not be less than 125 feet. If, how- ever, in any case this rule be found impracticable, a discretion may then be exercised by the Board of Trade. In cases where a small vessel is unable to cany more than one boat, a discretion may be exercised by the Board of Trade ; but whenever one boat only is carried, there must be proper provision to enable it to be placed readily in the water on either side of the ship. Capacity and Form of Life-Boats. — As regards the boats of Sections A, B, C, and D, Rule 1, the surveyors will see that the requirements of the Rules are observed, and that the capacity of the boats, and the number of persons they are fit to carry, are ascertained by Rules 2 and 3 (page 430). In measuring boats the length and breadth are to be regarded as the extreme dimen- sions measured to the outside of the plank. The number of per- sons for which a boat is to be passed is, however, subject to the further condition that the space in the boat shall be sufficient for the seating of them all, and the proper use of the oars. That this requirement is fulfilled must be ascertained by' practical experi- ment in all cases before a declaration is granted, unless one or more boats in a ship are of the same pattern, when only one of such boats need be tested. Life-boats (except those of Section C) should be built whale-boat fashion, both ends alike. In ships which have been fitted with boats previous to the Rules coming into force, square-sterned boats need not be condemned if fitted with the required amount of buoyancy, but all life-boats of Sections A and B subsequently supplied, or supplied to new ships, must be built whale-boat fashion. All collapsible boats, and all boats whether collapsible or not, if constructed of any material other than wood or metal, must be in accordance with a pattern approved by the Board of Trade before they are passed as a portion of the life-saving appliances required by the Rules. Stowage of Boats. — All boats required by the Rules to be placed under davits are to be kept fit and ready for use ; and when they are swung inboard and resting on the chocks, the chocks are to be so constructed that the boat can be at once swung outboard without requiring to be lifted by the tackles — i.e., it shall not be necessary to take more than the weight of the boat. The manner in which the additional boats, not requiring to be Lifeboat Buoyancy 641 placed under davits, are to be stowed, will vary in different ships, but they must be stowed to the satisfaction of the surveyors, so as to be as readily available for use as is practicable, having due con- sideration to the circumstances mentioned in the Rules. In all cases where boats are stowed on skids, a batten and space platform of about 2J" planks should be fitted from skid to skid, under and alongside the boat, when being launched forward or aft, and as a platform for the men. Equipments. — The equipments for all boats are provided for in the Rules, and surveyors are to see that the requirements are carefully complied with. The painters for boats are not to be less than 20 fathoms in length. When the Rules require a life-boat of Section C to be carried, and owners choose to provide a boat of Section A or J5, the addi- tional equipments required by General Rule 6 for boats of Section A and Section B need not be insisted on. Rudder. — In some of the collapsible boats it is difficult to fit a rudder ; in this case a steering oar properly fitted may be passed instead. Buoyancy. — The buoyancy of life-boats of Section B must be partly inside and partly outside the boat, and a boat in which it is wholly inside or wholly outside shall not be passed as a boat of Section B. In the case of life-boats of Section C, one-half the buoyancy must be outside the boat ; the remainder may be either inside or outside, or partly inside and partly outside. The inside buoyancy for boats of Sections A, B, and C, must consist of strong and serviceable enclosed air-tight compartments, such that water cannot find its way into them. The outside buoyancy for boats of Section B must consist of solid cork covered with canvas, and painted and attached to the outer skin of the boat to the satisfaction of the surveyors, both as regards its position and also as regards its attachment. No other material is to be used unless expressly sanctioned by the Board of Trade. The outside buoyancy must be equal to at least half the buoyancy required for boats of Section A, and the inside and out- side buoyancy together must equal in efficiency the buoyancy re- quired for a boat of Section A. To effect this 1.25 cubic feet of cork is to be considered as equivalent to 1 cubic foot of air-case. The foregoing remarks apply to outside buoyancy for boats of Section C, excepting that the total buoyancy is only required to be half that of boats of Section A or Section B. When the solid cork is not permanently attached to the side of the boat in such a 642 The Naval Constructor manner that moisture cannot collect between the two surfaces, it wiil require to be removed every time a declaration is granted to ascertain (1) whether the cork is becoming sodden ; (2) whether moisture is collecting between the cork and the skin of the boat, and in that way rotting the wood. The consideration (2) will not apply to metal boats. Air-Cases, Material and Construction. — Air-cases are re quired by the Rules to be constructed of wood, or of copper or yellow metal of not less than 18 ounces to the superficial foot, or of other durable material. The average weight of 18 ounce copper air-cases is about 5 pounds per cubic foot, and if air-cases of other material exceed this weight, the cubic capacity of the air-cases must be correspondingly increased. As yellow metal in time becomes extremely brittle, copper is far preferable. Zinc is not durable material, and should not be passed ; neither should galvanized iron or steel cases be passed for new boats. A note should be made in each district of all ships whose boats are already tilled with galvanized iron or steel air-cases, with a view to their being frequently inspected. Steel or iron air-cases previously passed of less thickness than 21 ounces are not to be rejected so long as they continue in good condition. Copper and yellow metal air-cases are to be made with proper hook joints not less than three-eighths of an inch in width, ham- mered well down and soldered, and no other joint is to be passed unless specially approved by the Board of Trade. The cases are not to exceed four feet in length ; they are to he substantially enclosed with wood, which is to be close-jointed so as to cover any exposed part of the air-case, and the wood form- ing the top is not to be less than one inch in thickness. The coverings in the boats over the air-cases should be secured with brass screws, so as to enable the cases to be removed with- out difficulty for examination, and no air-case which is not en- closed from the outer shell of the boat should be passed. Spaces filled with or containing any material are not to be deemed air-spaces unless specially approved by the Board of Trade. Copper or yellow metal air-cases must not be carried in con- tact with the skin of the metal boats. Where boats not required by the Rules to be fitted with air- cases are so fitted, as, for instance, in some of the collapsible or semi-collapsible boats, these provisions as to air-cases need not be insisted upon. Steam Launches, etc., Carried by Steamships. — In the cases of launches er other boats propelled by steam power, which Life-Rafts, Buoyant Apparatus 643 31 e carried as part of the additional boat equipment required by the Rules made under the provisions of the Merchant Shipping- Act, an inspection of the boat, machinery, and boilers, and of the mounting and fitting thereof, should be made. Steam launches must not be passed as a part of the boat equipment required to be under davits. In case of any vessel provided with a steam launch or boat in addition to the boat capacity required under the Rules, the sur- veyors need not interfere unless they have reason to believe that there is some defect in the boat, machinery, or boiler, or in the fittings or arrangement thereof, which might be dangerous to life. Boats Already Supplied. — In carrying these instructions into effect, surveyors are to be careful not to interfere unnecessa- rily with boats supplied before November, 1890, but in the case of new boats coming under survey for the first time, as well as in all cases in which the fittings of the boats require renewal, the Rules contained in these instructions are to be strictly adhered to. Appliances for Lowering Boats. — These appliances must be in accordance with Rule 4, of the General Rules, and must, in the surveyor's opinion, be such as not to endanger human life. They should be tested at each survey for renewal of a passenger certificate. The question of determining whether the requirements of the Rules respecting appliances for lowering boats are complied with in the case of any particular kind of gear coming under the sur- veyor's notice, shall be left to the principal officers of the districts. In order to insure uniformity of practice, each principal officer, who may pass any particular disengaging gear, should request the maker to supply 50 copies of the plans and specifications for distribution among the surveyors in the several districts. These copies should be sent to the Board of Trade by the Principal Officer, together with his report upon the gear. No certificates of approval for disengaging gear will be issued. The Principal Officer should also report to the Board of Trade when any particular disengaging gear has been inspected and deemed unsatisfactory or unsafe, and should explain fully in such report the details which, in his opinion, render it undesirable. No formal certificate of approval will, however, be granted by the Board of Trade or their officers for any special kind of gear. Life-Rafts, Buoyant Apparatus. — No part of the gear which is intended to bear the weight of the boat must be made of cast iron, and life-rafts are to be approved by the Board of Trade ; they are to be supplied with a suitable equipment to the satisfac- 644 The Naval Constructor tion of the surveyors, and this must include a sea-anchor, not less than 20 fathoms of hawser, and oars in proportion to the size of the raft. The number of persons that any approved life-raft for use at sea is to be deemed capable of carrying is the number that the raft is able to seat safely, provided always that for every person so carried there are at least three cubic feet of strong and service- able enclosed air-tight compartments. Approved buoyant apparatus is to be deemed sufficient for a number of persons to be ascertained by dividing the number of pounds of iron which it is capable of supporting in fresh water by 32, provided also that the sides and ends of the apparatus shall afford a space of one horizontal foot for each person for whom it is certified, and that a line for the people to cling to is properly becketted all round it. Such buoyant apparatus shall not re- quire to be inflated before use, and shall be of approved con- struction. Marking. — Surveyors will note that rafts and buoyant ap- paratus shall be marked in such a way as to plainly indicate the number of adult persons for which they are deemed sufficient. Plates will be supplied by the Board of Trade to be screwed on to the woodwork of both rafts and buoyant apparatus, indicating this number ; and forms of demand (surveys 116 for rafts and 116a for buoyant apparatus) for plates, to be filled up and returned to the Board of Trade, will be issued for the use of the Principal Officer. No raft or buoyant apparatus is to be regarded as finally approved until the marking-plate has been affixed. Air-Cases of Rafts, etc. — The instructions in the case of life- boats apply equally to life-rafts and buoyant apparatus, so far as the length, weight and enclosure of the air-cases are concerned, excepting that as life-rafts and buoyant apparatus are only in- tended to be used in cases of extreme need, and are consequently not exposed to the same wear and tear as the life-boats, a mini- mum weight of 16 ounces, copper or yellow metal, may be passed. Life-Belts. — No life-belt is to be passed that is not capable of floating in fresh water for 24 hours with 15 pounds of iron sus- pended from it. It should be cut out 2 inches under the arm- pits, and fitted so as to remain securely in its place when put on. When any other material than solid cork is used for buoyancy, it must be specially approved by the Board of Trade. All new life- belts should be fitted with adjustable shoulder-straps. It is desirable that notices should be posted indicating the place of stowage of any belts which are not plainly visible to pas- sengers. Life- Buoys 645 Life-Buoys. — No life-buoy stuffed with rushes or with cork shavings or other shavings, or granulated cork, or any loose material, is to be passed. All cork life-buoys are to be built of solid cork, and fitted with lines becketted and securely seized to the life-buoy, and none are to be passed that will not float for 24 hours in fresh water with 32 pounds of iron suspended from them. If life-buoys are not made of solid cork, the pattern and material must be approved by the Board of Trade. No contrivance is to be passed as a life-buoy that requires inflation before use. Life- buoys are to be secured by a toggle and becket, or any other similar method, so that they can be quickly released ; they must not be lashed or seized to the rail or any part of the vessel, but must be kept so as to be ready for use at a moment's notice in case of an emergency. Not less than two of the life-buoys, one on each side of the ship, are to be fitted with life-lines 15 fathoms in length. Oil-distributing Apparatus. — Vessels for distributing oil are to be to the satisfaction of the surveyors, and are to be so con- structed as to distribute the oil evenly and gradually on the sur- face of the water. 646 The Naval Constructor CHAPTER IV. UNITED STATES NAVIGATION LAWS RELAT- ING TO BOATS AND LIFE-SAVING APPLIANCES. The British requirements as to the build of boats, number of oars, life-lines, and the rule for calculating the capacities of life- boats, are similar to the American regulations, excepting that for river steamers the capacity is divided by 7 to give the number of persons carried. Boat Ladders. — Where ladders or steps are necessary to en- able passengers on board to escape conveniently to the life-boats, such steps shall be provided and placed on each side of the steamer, with manropes of suitable size and of sufficient length to reach the water ; and one of the means of escape from one deck to another shall be near the stern of the vessel. Relieving Tackle. — Extra steering apparatus for all steamers carrying passengers, consisting of relieving tackles or tiller, must be provided. Metal Life-Boats must be constructed of good iron or other suitable metal not less in thickness than 18 B.W.G. Davits. — All life-boats must, if possible, be carried on cranes or davits ; but if impossible so to carry all the life^boats required, the remainder must be stowed near at hand, so as to be easily and readily launched when required. River Steamers. — Steamers navigating rivers only (except ferry-boats, canal-boats, and towing-boats, of less than 50 tons) must have one good substantial boat. The cubic capacity of such boat as found by the rule given on p. 444 divided by 7 will deter- mine the number of persons to be carried. Freight, Canal, and Towing Steamers. — Freight, canal, and towing steamers of less than 50 tons must be equipped with boats or rafts, as, in the opinion of the inspectors, may be neces- sary, in case of disaster, to secure the safety of all persons on board. Excursions by Permit. — Steamers making an excursion under a permit must have at least one life-boat, and shall be equipped with other life-boats, or their equivalents, as, in the Life-Boats for Ocean Steamers 647 judgment of the inspectors, will best secure the safety of all per- sons on board in case of disaster. Automatic Plug. — All metal life-boats hereafter built shall be furnished with an automatic plug. River Passenger Steamers. — Passenger steamers navigat- ing rivers (excepting steamers of 100 gross tons and under, here- inafter provided for) must be supplied, in addition to the boat required in the paragraph "River Steamers," with life-boats in proportion to their tonnage, as follows : Steamers over 100 and not over 300 gross tons . 1 boat. Steamers over 300 and not over 600 gross tons . 2 boats. Steamers over 600 and not over 900 gross tons . 3 boats. Steamers over 900 and not over 1,200 gross tons . 4 boats. Steamers over 1,200 gross tons 5 boats. Aggregate Capacity. — The aggregate capacity of life-boats on steamers navigating the Red River of the North and rivers whose waters flow into the Gulf of Mexico and their tributaries, shall not be less than 120 cubic feet to each boat for the number of boats as given in the table ; and for life-boats on steamers navi- gating other rivers than those named, the aggregate capacity shall not be less than 180 cubic feet to each boat as given in the table ; and where smaller life-boats are employed for either class of river steamers, their aggregate capacity shall not be less than the aggregate capacity of the larger boats ; provided, however, that river steamers required, under the table, to carry more than two boats, may, where the owners prefer to do so, supply the boat capacity above that number with a good, substantial life-raft or rafts, such raft or rafts to be of an aggregate carrying capacity not less than that of the boats so omitted. Capacity may Equal Complement. — No steamer embraced in the foregoing section shall be required to have more life-boats, or of a greater capacity, than sufficient to carry the passengers allowed by the certificate of inspection (including the crew). One of the life-boats, unless exempted by the supervising inspector, must be made of metal. Life-Boats for Ocean Steamers. — The total capacity of life- boats, or of life-boats and life-rafts, on steamers navigating the ocean (except steamers of 100 gross tons and under, hereinafter provided for), shall not be less than the capacity given, according to tonnage, in the following table : 648 The Naval Constructor BOAT CAPACITY FOR OCEAN STEAMERS. (American Law.) Gross Tonnage. Total Capacity of Boats in Cubic Feet. Steamers over : 100 and not over 200 200 300 300 ' " 400 400 ' 500 500 « 1,000 1,000 « 1,500 1,500 ' " 2,000 2,000 ' 2,500 2,500 ' « 3,000 3,000 ' 3,500 3,500 « 4,000 4,000 « 5,000 5,000 5,500 5,500 ' 6,000 6,000 ' " 6,500 6,500 ' ' »• 7,000 7,000 • 7,500 7,500 • 8,000 8,000 « 8,500 8,500 ' 9,000 9,000 « 9,500 9,500 ' 10,000 10,000 « 10,500 10,500 « 11,000 11,000 ' ' " 11,500 11,500 « 12,000 12,000 ' i m 12,500 12,500 « 13,000 13,000 « 13,500 13,500 « " 14,000 14,000 ' 14,500 14,500 15,000 15,000 . 540 720 1,080 1,260 1,620 1,800 2,160 2,340 2,700 2,880 3,240 3,420 3,870 4,320 4,770 5,220 5,670 6,120 6,570 7,020 7,470 7,920 8,145 8,370 8,595 8,820 9,045 9,270 9,495 9,720 9,945 10,170 10,395 Note. — Not more than one-third of the boat capacity required on ocean steamers may be substituted by its equivalent in approved life rafts or approved collapsible (folding) life-boats. These boats must be of suitable dimensions, and each not less than 180 cubic feet capacity. (For good proportions of boats, see diagram on p. 421.) Life-boats of Lake, Bay, and Sound Steamers 649 LIFE-BOATS FOR STEAMERS NAVIGATING NORTHWESTERN LAKES, BAYS, AND SOUNDS. Gross Tonnage. No. OF Boats. Capacity of Boats. Steamers over : 100 and not over 200 . . . 200 " " 300 300 " " 400 400 " " 500 500 " " 1,000 1,000 " " 1,500 1,500 " " 2,000 2,000 " " 2,500 2,500 " " 3,000 3,000 " " 3,500 3,500 " " 4,000. .... 4,000 " " 4,500 4,500 " " 5,000 5,000 m " 5,500 ..... 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Cu. Ft. 360 540 720 900 1,080 1,260 1,440 1,620 1,800 1,980 2,160 2,340 2,835 3,330 Note on Table. — Steamers above 5,500 gross tons shall be furnished with an additional boat of hot less than 495 cubic feet capacity for each additional 500 tons burden, or fraction thereof ; or if the owners or agents prefer, two boats may be used ; pro- vided, the aggregate capacity shall be the same as the one boat described. These boats shall be substantially built with reference to the trade in which the steamer is engaged, and shall not be of less dimensions than 20 ft. x 5 ft. x 3 ft.,* unless, where smaller life- boats are employed, their aggregate capacity shall equal the aggre- gate capacity of the larger boats ; provided, however, that no steamer shall be required to have more life-boats than sufficient to carry the passengers she is allowed by the certificate of inspection, together with her officers and crew. Not more than one third of the boat capacity required on lake, bay, and sound steamers may be substituted by its equivalent in approved life-rafts or approved collapsible (folding) life-boats. * For good proportions, see diagram on page 421. 650 The Naval Constructor Marking of Boats. — All wood boats required on steam-ves- sels shall have branded or cut on the stem thereof the net cubic feet contents of such boats, figured as follows : Multiply the outside length, outside width, and inside depth together and the product by .6, and divide the product by 10 for ocean, lake, bay, or sound steamers ; and for river steamers, di- vide the product by 7 ; the quotient will be the number of persons such a boat is allowed to carry. Example. — The carrying capacity of a boat 20 feet in length, 6 feet 6 inches in breadth, and 2 feet 3 inches deep, will be deter- mined as under : For ocean, lake, bay, or sound steamers, 20 x 5.5 x 2.25 X .6 148.5 „_ -10- - = -^0-= 15 persons. For river steamers, same boat, — ^— = 21 persons. Metal boats shall have net cubic feet measurement painted on stem in black letters and figures not less than £ inch high on a white ground. Every life-raft shall have stencilled on it in a conspicuous place (the number of persons it can carry, as determined by) the net cubic feet contents as per ratio in the following paragraph : Life-Raft Capacity. — All life-rafts and floats shall have an actual buoyancy of 187£ lbs. upon oceans for every person al- lowed, and 150 lbs. upon lakes, bays, sounds, and rivers for every person allowed. Such life-rafts and floats must be suitably equipped with life-lines and oars. All rubber and canvas rafts shall be kept inflated at all times. Life-Floats. — When wooden life-floats are required on steam- vessels, in compliance with law they shall be at least of the follow- ing dimensions, or other proper dimensions of equal cubical capac- ity, viz., 4 feet in length, 14 inches in breadth, and 2 inches in thickness. These floats shall be made of white pine wood, or any other wood not exceeding white pine * in weight per cubic foot. Drags, or Floating Anchors. — Drags, or floating anchors, shall be constructed so as to be capable of being compactly stowed near the head of the ship. (For a detail of these anchors, see p. 363.) Steamers navigating the ocean must be provided with at least one drag, of area as follows : — For steamers of 400 gross tons and * What is known as white pine in the States is called yellow pine in the British Isles. Drags or Floating Anchors 651 under, not less than 25 superficial feet ; for steamers of over 400 gross tons, the area of drag shall not be less than that deter- mined by adding to 25 square feet one square foot for each addi- tional 25 gross tons above 400 tons. Example. — The area of a drag on a vessel of 1,000 tons will equal : — or , 1,000-400 . n . 4 2 ^ H ^"H — 49 square feet. 25 Steamers of over 5,000 tons gross may be equipped with two or more drags, provided the total area is not less than that required by this rule. Steamers whose routes do not extend off anchor- age are not required to have drags, or floating anchors, on board. (A table giving areas for sea-anchors based on the above rule is given on p. 362.) Every life-preserver adjustable to the body of a person shall be made of good, sound cork blocks or other suitable material, with belts and shoulder straps properly attached, and shall be con- structed so as to place the cork underneath the shoulders and around the body of the person wearing it, the shoulder straps to be sewed on at least eight inches apart on the back of the preserver, and sewed together at an angle where they cross the body, and must also have a strap across the breast from one shoulder strap to the other, sewed fast at one end and with a buttonhole at the other, with a button on shoulder strap to which the cross piece can be buttoned, and all belt life-preservers shall be not less than 54 inches in length, measurement from end to end around the body. And it shall be the duty of the inspectors to see by actual examination that every such life-preserver contains at least six pounds of good cork, which shall have a buoyancy of at least four pounds to each pound of cork. Inspectors are further re- quired to see such life-preservers are distributed throughout the cabins, staterooms, berths, and other places convenient for passengers on such steamer ; and there shall be a printed notice posted in every cabin and stateroom, and in conspicuous places about the decks, informing passengers of the location of life- preservers and other life-saving appliances, and of the mode of applying or adjusting the same. Cork cushions, when constructed of good, sound cork blocks or other suitable material, with belts and shoulder straps properly attached, said cushions to contain not less than six pounds of cork, when passed by local inspectors, may be used in lieu of life-preservers on small pleasure steamers. Barges towed by steamers and carrying passengers on regular "night routes" shall have a life-preserver for each passenger; and, in addition thereto, shall be supplied with a yawl boat, ten buckets and three axes. 652 The Naval Constructor Every sea-going steamer and every steamer navigating the great Northern and Northwestern lakes carrying passengers shall have not less than three water-tight cross bulkheads. Such bulkheads shall reach to the main deck in single -decked vessels, otherwise to the deck next below the main deck. For wooden hulls they shall be fastened to suitable framework, which framework must be securely attached to the hull and caulked. For iron hulls they shall be well secured to the framework of the hulls and strengthened by stanchions of angle iron placed not more than two feet from centre to centre. One of the bulkheads must be placed forward and one abaft of the engines and boilers. The third or collision bulkhead must be placed not nearer than five feet from the stem of the vessel. Iron bulkheads must be made not less than one-quarter of an inch in thickness, and wooden bulkheads must be of equal strength and covered with iron plates not less than one-sixteenth of an inch in thickness. Steam ferry-boats of 50 tons burden and over must be supplied with life-boats as in the judgment of the inspector will best pro- mote the security of life on board of such vessels in case of disas- ter, according to the average number of passengers carried per trip. Table of dimensions of boats for passenger steamers of 100 gross tons and under, navigating lakes, bays, sounds, and rivers, other than the Red River of the North and rivers whose waters flow into the Gulf of Mexico. Boats of other dimensions of equivalent cubical capacity may be used i — Number of Tons (Gross). as <

3 2^ P 1| P o « *& 2 J u 1 ©fa ■a o g3 0> 1 o 1 « oq Ph « Ph « Ph M Ph Ph Ph , 1 19.35 19.35 20.2 20.2 20.4 20.4 20.2 20.2 2 4 18.85 75.4 20.4 81.6 20.5 82.0 20.35 81.4 3 2 16.65 33.3 20.15 40.3 20.25 40.5 20.0 40.0 4 4 11.85 47.4 19.6 78.4 19.85 79.4 17.8 71.2 5 1 1.85 1.85 3.0 3.0 6.35 6.35 6.35 6.35 177.3 223.5 228.65 219.15 *i of Com- mon In- 1.05* 8865 1.03 6705 .99 .95 109575 205785 terval 17730 22350 205785 197235 Breadths. 186.165 230.205 226.363 208.192 Area 1. Area 2. Area 3. Area 4. Area 5. Schedule for Tonnage Calculations 669 TONNAGE CALCULATIONS. Cubic Content and Register Tonnage Tonnage of Poop ok Other Closed-in Space. Break of Deck. Mean Length, 32.15 Ft. Common Interval between Breadths, 16.075 Ft. Area C. Feet. 10.9 - i. 2= 19.10 18.65 14.95 8.75 1.0 09 ja r3% "5 Hi 0) o ?>fc PM w 19.1 74.6 29.9 .35.0 1.0 159.6 .91 145.236 Area 6. Area 7. Feet. O 8 .2 3 ^ OCG g n l 4 186.17 2 230.21 4 226.36 2 208.19 4 145.24 1 ^3 - o 744.68 460.42 905.44 416.38 580.96 5 i. 3 a 11 2^ « i 20.0 4 18.6 1 17.15 20.0 74.4 17.15 111.55 £ of com. inter, betw. breadths. ht. of break Cu. ft. 1,195.82 -f 100 = 11.96 reg. T 3107.88 6.26 f i of common interval i between areas. 621576 1864728 Area 7. 19455.32 -f 100 = 194.55 reg. T. under deck. 11.96 break of deck as above 206.51 gross tonnage. 670 The Naval Constructor Length for Tonnage. — The length at the tonnage deck in all cases of the usual sheer is to be taken on the upper surface of the deck to the inside of the stringer angle bar at stem and stern, the length so obtained being subdivided into an equal number of parts as under : — Subdivision of Tonnage Length per British Law. Class I. Length of 50 feet and under, 4 equal parts. Class II. Length above 50 feet to 120 feet, into 6 equal parts. Class III. Length above 120 feet to 180 feet, into 8 equal parts. Class IV. Length above 180 feet to 225 feet, into 10 equal parts. Class V. Length above 225 feet and upwards, into 12 equal parts. Subdivision of Tonnage Length per American Law. Class I. Length of 50 feet and under, into 6 equal parts. Class II. Length above 50 feet to 100 feet, into 8 equal parts. Class III. Length above 100 feet to 150 feet, into 10 equal parts. Class IV. Length above 150 feet to 200 feet, into 12 equal parts. Class V. Length above 200 feet to 250 feet, into 14 equal parts. Class VI. Length above 250 feet, into 16 equal parts. The stations at these subdivisions are the points at which the areas are calculated, and are numbered from forward aft, the foremost being numbered one, making the last ordinate in each case an odd number. Depths. — The depths are taken at each point of division as above, from the under side of tonnage deck to the ceiling at inner edge of limber strake, deducting therefrom one-third of the beam- camber ; the depths so taken are to be divided into four equal parts if the midship depth does not exceed 16 feet, otherwise into six equal parts. (See Fig. 287.) Breadths. — These are measured off at each point of the verti- cal division of the depth as described, to the inner edge of the Marking of Ship 671 side ceiling. In the case of vessels having no ceiling or sparring, the breadths must be taken to the inner edge of frame-bars. The lower breadth, when the vessel has no horizontal flat or floor, is limited to the distance between the two limber strakes, and in flat-floored vessels to the extent of the horizontal flatness. Where the ceiling varies in thickness on the sides, as in crossing a keelson or stringer, or at dumping pads, the average thickness should be taken. (See Fig. 287.) Sections for Areas. — When the sections have been prepared in accordance with the foregoing, the' half -breadths may be meas- ured off and tabulated in the manner shown in the accompanying table, and integrated by means of Simpson's first rule to deter- mine the under-deck tonnage. The erections, hatches, and shelter-deck, 'tween decks (if any), may now be calculated in detail, and added to the under-deck tonnage to obtain the gross. Engine Room Deduction. — The actual space enclosed by the engine room must be calculated, and the percentage it bears to the gross tonnage determined to enable the allowance conceded by law to be made. Should this percentage be over thirteen and under twenty, an allowance of thirty-two per cent may be de- ducted from the gross tonnage in computing the net register, or the tonnage on which a ship's dues are usually paid. Should, however, the actual engine room not exceed thirteen per cent of the gross tonnage, the allowance would then be the actual space plus § of same. It should be noted that the gross tonnage is the same whether the vessel is a steamer or a sailing ship. Tonnage Deductions. — All spaces which have been meas- ured and deducted from the gross tonnage, as officers' rooms, crew's forecastle, chain-locker, chart-house, etc., mustbe properly marked over the door by having the certification cut in, and also inside, on a beam or other conspicuous place. MARKING OP SHIP. Name. — The vessel's name must be marked on each bow, and the name and port of registry on the stern, on a dark ground, in white or yellow letters, or on a light ground in black letters. The letters should preferably be black, and not less than 4 inches long. In addition, ships of American registry must have their name cut in large name boards fitted on each side of top of pilot .house, with letters not less than 6 inches high. 672 The Naval Constructor Official Number and Tonnage. — The official number and the net registered tonnage must be cut in on the main beam or the 'thwartship coaming of main hatch. Draught Marks. — A scale of feet denoting the draught of water must be cut in on each side of the stem and stern-post from one foot below light line to about two feet above deep load draught. These should be in Roman letters or figures, 6 inches long, the lower line of such letters or figures to coincide with the draught line indicated. The figures, after being cut in, should be painted white or yellow on a dark ground. Space for Seamen. — In arranging crew's quarters, care must be taken that a minimum capacity of 72 cubic feet is allowed for each seaman, and a clear floor space of not less than twelve square feet. NEW YORK YACHT CLUB RACING RULES. Rating Formula. — Yachts shall be rated for classification and time allowance according to the following formula : — . f Length multiplied by square Rating measurement = ^-^ J «** of sail area divided by 5 -\/D 1 placement. The result is the measurement for classification and time allow- ance. Length. — The mean of the length over all, exclusive of bul- warks and rail, and of the length on the load water plane, both measurements to be taken parallel to the middle vertical plane, and at a distance from it equal to one-quarter (^) of the greatest beam at the load water line. In case the width of the stern on deck exceeds one-half (£) the greatest beam at the load water line, the measurement for the length over all shall be taken to a point abaft the stern, where the continuation of the fair line of the top edge of the plank- sheer would intersect the quarter beam line. Sail Area. — Sail area to be obtained as follows, and the square root of this area to be the yJSA in formula : — Mainsail. — A. Measured from the top of the boom (under the pin for outhaul shackle on traveller, or clew slide, when hauled chock out) to the gaff under the pin of the sheave of the topsail sheet, provided the peak cringle of the mainsail does not extend beyond the pin ; in the case of the yacht having no top- Measurement of Sails 673 sail, or of the peak cringle extending beyond the pin of the topsail-sheet sheave, the measurement to be taken to the peak lacing-hole. B. Perpendicular to A, measured to underside of gaff close in to the mast. C. Measured from top of boom over the pin of the sheave or outhaul or end of clew slide to underside of gaff close in to the mast. Fig. 366. D. Perpendicular to C, measured in to the mast, in a line with the top of the boom, or to tack cringle of mainsail, if below top of boom. Club Topsail. — E. Measured from upper side of gaff close in to the mast to pin of sheave for topsail sheet, or to lacing-hole in club. F. Perpendicular to E, measured to lower lacing-hole in sprit. G. From lacing-hole to lacing-hole in sprit. H. Perpendicular to (?, measured to pin of sheave for topsail sheet in gaff ; or to upper lacing-hole in club. Jib Header. — K. Measured from top of gaff close in to mast to pin of halyard sheave in topmast. L. Perpendicular to K, measured to pin of topsail sheet sheave in gaff j or to upper lacing-hole in club. 674 The Naval Constructor Lugs ail — To be measured as mainsail, except as follows : — A. Upper end measured to peak lacing-hole in yard. B and C. Forward end measured to lower lacing-hole in yard. D. Lower end measured to tack cringle of mainsail, if below top of boom, or forward of mast. Headsails. — I. The perpendicular I to be measured from the deck, at the foreside of the mast to where the line of the luff of the foremost headsail, or of the spinnaker halyard, as the case may be, when extended, cuts such perpendicular. In the case of a schooner the perpendicular I shall be measured upon the fore- mast, unless she has a main spinnaker, the height of which exceeds the perpendicular upon the foremast, in which case the excess shall be added to the perpendicular I. J. The base J to be measured from the foreside of the mast to where the line of the luff of the foremost headsail, when extended, cuts the bowsprit, other spar, hull, etc., as the case may be. In all cases, if the distance from the centre fore-and-aft line of the mast to the outer end of the spinnaker boom exceeds the distance from the foreside of the mast to the bowsprit end (where cut by the line of the luff of the foremost headsail) the excess shall be added to the base of the fore triangle. In the case of a schooner, the base J shall be measured from the foremast, but if the main or longest spinnaker boom exceeds the before-mentioned distance, the excess shall be added to the base J. In the case of a yacht having no headsail, but carrying a spin- naker, the area for headsail shall be computed from the length of spinnaker boom, and the height from deck to where the line of the halyard of the spinnaker when extended cuts the mast. A spinnaker may have a headstick, or board, not longer than one-twentieth the length of the spinnaker boom, but not a foot- yard, or more than one sheet, or any other contrivance for extend- ing the sail to other than a triangular shape. In the case of a yacht carrying a square sail, or square topsail, or raffee (together or separately), the actual area of the same shall be computed ; and if such area exceed the area of the fore trian- gle, the excess shall be used in the total area for determining the rating. Foresail of Schooners. — To be measured as mainsail, except that the lower end of A is to be taken at foreside of mainmast, in a line with main boom gooseneck. Directions for Measuring Sails. — The measurer shall take measurements I and J for fore triangle, G and E for club topsail, and the length of spinnaker boom. If the other measurements Calculation of Sail Areas 675 are supplied by the sailmaker, the measurer shall check them by measuring the following : — Boom, — from lower end of A to lower end of D. Gaff or lug yard, — from upper end of A to forward end of B. Club Topsail, — sheet to outer lacing-hole. •In cases where it is necessary for the official measurer to meas- ure the sails, he shall do so in the following manner : Take the length of boom from mast to pin of sheave for outhaul, and length of gaff from mast to pin of topsail sheet sheave or lacing-hole, as the case may require ; then hoist the sail with the tack fast and set the peak and luff up taut, and let go the topping lifts so that the weight of the boom coines on the leach of the sail. With a line and tape, measure the leach and luff and the diagonal C. For the beadsail measure the height I and the distance J, as provided for in the section dealing with headsail. For topsail the sail should be hoisted and marked in a line with the gaff ; then low- ered and the other dimensions taken. From the measurements so taken a sail plan should be made and the other above-specified measurements obtained therefrom. CALCULATION OP SAIL AREAS. Mainsail. — Multiply A by B and C by D, and add the two products together and divide by 2. Yard Topsail. — Multiply E by F and G by H, and add the two products together and divide by 2. Jib Header. — Multiply K by L and divide by 2. Headsails. — Multiply I by J" and divide by 2. Lugsails and Headsails. — No deduction is to be made from headsail area on the score of any portion of the lugsail area ahead of the mast. Sails Bounded by Curved Edges. — Any increase in the area of sails due to curved edges, extended by battens, or other- wise, beyond the line between the points for measurement, shall be computed as follows : Multiply the base E by two-thirds of the perpendicular P. Displacement. — Z>. Displacement to be obtained as follows : At points dividing the length of the load water line into five equal parts, find areas of immersed cross sections in square feet ; from the areas in square feet obtained and load water line length, find approximate displacement in cubic feet, which will be the L in formula. 676 The Naval Constructor Limit of L.W.L. — One half (£) of any excess of L.W.L. over one hundred and fifteen per cent (115%) of L shall be added to the rating measurement. The L.W.L. shall be the distance in a straight line between the points farthest forward and farthest aft, where the hull, exclusive of the rudder post, is intersected by the surface of the water when the yacht is afloat, in racing trim. Limit of Draught. — Limit of draught in feet =.133 (rating measurement) + 2.66. Any excess of draught, exclusive of centre-board, as per above formula, shall be multiplied by five (5) and added to the rating measurement. The draught of any vessel, exclusive of centre-board, shall not exceed eighteen (18) feet. Limit of Sail Area. — Any excess of the square root of sail area over one hundred and thirty-five per cent (135%) of I shall be added to the rating measurement. All measurements of hull shall be taken with only such persons on board as shall be required by the measurer. All measurements specified may be certified to by the designer, in a certificate to be filed with the measurer of the club, but such certificate must be accompanied by drawings, showing the meas- urements taken, and the true line of flotation of the vessel when measured in racing trim, which measurement and line of flotation must be verified by the measurer, before any certificate of meas- urement shall be accepted by the secretary. If from any peculiarity in the build of a yacht, or other cause, the measurer shall be of opinion that the rule will not rate the yacht fairly, or that in any respect she does not comply with the requirements of these rules, he shall report the circumstances to the Regatta Committee, who, with the measurer, after due inquiry, shall award such a certificate of rating as they may consider equitable, and the measurement shall be deemed incom- plete until this has been done. CLASSIFICATION. Schooners. — Class A. All over 100 feet, rating measurement. Class B. Not over 100 feet and over 80 feet, rating measure- ment. Class C. Not over 80 feet and over 64 feet, rating measure- ment. Class D. Not over 64 feet and over 51 feet, rating measurement. Class E. Not over 51 feet, rating measurement. Ballast, etc. ^1 Single-masted Vessels and Yawls. — Class F. All over 100 feet, rating measurement. Class G. Not over 100 feet and over 80 feet, rating measurement. Class H. Not over 80 feet and over 64 feet, rating measure- ment. Class I. Not over 64 feet and over 51 feet, rating measure- ment. Class J. Not over 51 feet and over 40 feet, rating measure- ment. Class K. 40 feet and under, rating measurement. Sails. — Yachts in races may carry the following sails : — Schooners. — Mainsail, foresail, fore staysail, jib, flying-jib, jib-topsail, fore and main gaff topsail, maintopmast staysail, and spinnaker. Sloops and Cutters. — Mainsail, fore staysail, jib, flying- jib, jib-topsail, gaff topsail, and spinnaker. Yawls. — Same as sloops and cutters, with mizen and mizen- staysail. Balloon Sails. — Yachts may set light sails over working sails. Boats and Life-Buoys. — All yachts shall carry at least two serviceable life-buoys on deck ready for use. Classes A and B of schooners, and F and G of single-masted vessels and yawls, shall carry on deck a serviceable round-bottom boat, not less than 14 feet in length ; and classes C and D of schooners, and JET and I of single-masted vessels and yawls, a boat as above, not less than 12 feet in length; and in classes E of schooners, and J and K of single-masted vessels and yawls, a boat as above, not less than 10 feet in length. All boats to have oars and rowlocks or tholepins lashed in. Bulkheads, Ballast, etc. — Floors must be left down and bulkheads and doors left standing ; water-tanks kept in place, and at least one bower anchor and cable kept on board. All yachts, except in classes A of schooners and G of single-masted vessels and yawls, shall keep their galley fixtures and fittings on board and in their proper places. Trimming by dead-weight shall not be allowed after the preparatory signal. Neither ballast nor water shall be taken in or discharged after 9 p.m. of the day before a race, but the above restriction may be waived as to water, only by permission. Crew. — The number of men permitted on a yacht during a race shall not exceed that given by the following table : — 678 The Naval Constructor Classes A and F. One man for every 250 square feet of sail area, or fraction thereof. Classes B, C, Z), E, G, H, I, J, and K. One man for every 300 square feet of sail area, or fraction thereof. BUILDERS' OLD MEASUREMENT TONNAGE This tonnage, commonly called B. O. M., is still much in vogue with yacht builders, but obsolete otherwise. B.O.M.=< L -^ BX ^, 94 where L is the length of vessel measured along top of keel from after side of stern post, to the intersection of a perpendicu- lar with the' fore part of stem under the bowsprit, and B is the extreme breadth to outside of planking, exclusive of doublings. THAMES MEASUREMENT TONNAGE. This rule was formulated by the Royal Thames Yacht Club, and is much used for the measurement of yachts. TM ~ 94 ' where L is the length measured in a straight line at the deck from the fore part of stem to the after part of stern post, and B is the extreme breadth to outside of planking. Section VI. WEIGHT OF A CUBIC FOOT OF SUBSTANCES. Name of Substances. Pounds A. Acacia 44.4 Alder 34.6 Aluminum, cast 160 Aluminum, sheet 168 Aluminum, bronze 478 Alum 107 Antimony .... 417 Anthracite coal, broken, cubic foot averages 54 A ton, loose, occupies 40-43 cubic feet. Apple wood 49.5 Air . .' 0.08 Ash (American) 39 Asphalte 156 Asbestos Board |" thick, per square foot 65 B. Barley 38 Basalt 170 Babbit, white brass 456 Beech 43.8 Bell, metal 502.5 Birch 33 Bismuth 608 Bitumastic solution per gallon 9 Bituminous coal, broken, cubic foot averages .... 49 A ton, loose, occupies 43-48 cubic feet. Box wood 62.5 Brick, best pressed 150 Brick, common hard 125 Brick, soft inferior 100 Brickwork, pressed brick 140 Brickwork, ordinary 112 Brass, common 525-530 Brass, wire 533 Bronze 544 679 680 The Naval Constructor Name of Substances. Pounds. C. Camphor 62 Cedar, American red 30.8 Cedar, white 23 Cement, hydraulic, ground, loose, American 56 Cement, hydraulic, ground, loose, English, Portland . . 90 Cement and sand (3 to 1) 130 Cement, hydraulic, Louisville, hushel = 62 Cement, hydraulic, Portland, bushel = 96 Cement, Roman 100 Charcoal 183 Cherry 42 Chalk 183 Chestnut 41 Clay 119 Clay, in lump, loose 63 Coral 168 Cork 15.0 Copper . 554 Coal, bituminous, solid 84 Coal, bituminous, broken, loose 49 Coal, bituminous, heaped bushel, loose 74 Coke, loose, of good coal 62 Coke, loose, heaped bushel 40 Cypress 41 D. Deals, Riga 43 E. Earth, common loam, dry, loose 76 Earth, common loam, dry, moderately rammed .... 95 Ebony 79.4 Elder 43.4 Elm, English 35 Emery 251 Elm, Canada 45 F. Felspar 168 Fir (see Red Pine, etc.) 31-41 Flagging 168 Flint 164 Freestone 153 Weight of a Cubic Foot of Substances 681 Name of Substances. Pounds. G Granite .'....' 164 Graphite 137 Glass, flint 192 Glass, crown 157 Glass, plate • . . . 172 Gold, pure cast 1,200 Gold, standard 1,106 Gneiss 168 Greenheart 62.5 Gunmetal 534 Gum wood 37 Gypsum 143 Gypsum, ground, bushel = 70 H. Hay (compact, old) 8 Hawthorn 56.8 Hazel 53.7 Hemlock 25 Hornbeam 47.4 I. Ice 58.7 India-rubber 58 Iron, cast (average) 450 Iron, wrought, purest 485 Iron, wrought, average . 480 Ironwood 71 Ivory 114 J. Jackwood 42 L. Laburnum 67.4 Larch 31.0 Lancewood 42.1 Lead, cast 708.5 Lead, sheet 711.5 Lignum-vitse 83.2 Lime, quick, ground, loose, or in small lumps .... 53 Lime, quick, ground, loose, thoroughly shaken .... 75 Lime, quick, ground, loose, struck bushel 66 Limestones . 168 682 The Naval Constructor Name of Substances. Pounds Limestones, loose, in irregular fragments 96 Lime, loose, bushel = 70 Lime, well shaken, bushel = 80 Lime wood . . 35 Linoleum, \" thick (incl. cement) per sq. ft 1.5 M. Mahogany, Spanish 53 Mahogany, Honduras 35 Marble 170 Maple 49 Masonry, of granite or limestone, well dressed .... 165 Masonry, of dry rubble, well scabbled 138 Masonry, of sandstone, well dressed 144 Mercury, fluid 849 Mercury, solid 977 Mica 183 Mortar, hardened 103 Muntz metal 511 N. Nickel (hammered) 541 Nickel (cast) 516 Nitric Acid 79.4 O. Oak, British 58 Oak, Riga 43 Oak (American, red, black or yellow) 45 Oak (American, white) 50 Oil (linseed) 58 Oil (olive) 57 Oil (petroleum) 48-58 Oil (whale) 58 Ore (red iron) .327 Ore (brown) 245 Ore (Clydesdale) 191 Oregon Pine (Douglas Spruce) 32 P. Paper (building) per roll of 400 sq. ft 52 Petroleum, standard refined . ........ 57.75 Petroleum, Texas 58. Phosphor Bronze 537 Pitch 69 Weight of a Cubic Foot of Substances 683 Name of Substances. Pounds. Pitch pine (U. S. yellow pine) 41 Pine (long leafed Georgia yellow pine) 38 Platinum 1,414 Plumbago 140 Poplar 32 Pewter 703 Q. Quartz 163-169 S. Salt, coarse 45 Sand, of pure quartz, dry, loose ... .... 90-106 Sand, well shaken 99-117 Sand, perfectly wet 120-140 Sandstones (fit for building) 151 Satinwood 60 Snow, freshly fallen 5-12 Snow, moistened and compacted by rain 15-50 Shingle . . 88 Silver (standard) 644 Slate , 178 Spruce, Northern 26 Spruce, Southern 30 Steel . . 490 Steel, cast 493 Sycamore 36.8 T. Tallow 59 Tar 63 Talc . . . 168 Teak Burmese 46 Tile, common 113 Tiling, inlaid rubber, per sq. ft 2 Tiling, vitrified brick, 1^ thick, per sq. ft 9 Tiling, white, ^ in. thick, per sq. ft 5 Tin 462 Type metal 653 Trap 170 W. Walnut, black , 38 Water, pure rain or distilled, at 60° F 62£ 684 The Naval Constructor Name of Substances. Pounds. Water, salt «64 Wheat 48 Willow 25.3 White Pine (called yellow pine in England) 24 White metal, Babbitt 456 Y. Yew o . . . 50.3 Z. Zinc, rolled 449 Zinc, cast 437 WEIGHT OF SAIL CANVAS. Canvas, No. 1 2 3 4 5 6 7 8 Lbs. per Sq. Ft. .205 .197 .184 .171 .154 .141 .128 .113 .104 Oil Fuel Chart 685 OIL FUEL CHART. Xk?a-i3d(qT0irZZ)suoi uox usd (|*3-Zfr)?pjji?g Fiq. 367. 686 The Naval Constructor DATA FOR FUEL OIL. Specific Gravity. °Bb. Weight in Lbs. per Gal. Weight in Lbs. per Bbl. Weight in Lbs. per Cv. Ft. Cu. Ft. per Ton. Gallons per Ton. Barrels per Ton. 1.0000 10 8.33 349.86 62.355 35.9 268.9 6.43 0.9929 11 8.27 347.34 61.912 36.1 270.8 6.46 0.9859 12 8.21 344.82 61.475 36.5 272.8 6.50 0.9722 13 8.16 342.72 61.045 36.7 274.6 6.54 0.9790 14 8.10 340.20 60.621 36.9 276.6 6.59 0.9655 15 8.04 337.68 60.202 37.2 278.6 6.65 0.9589 16 7.99 335.58 59.792 37.5 280.3 6.69 0.9523 17 7.93 333.06 59.380 37.7 282.4 6.73 0.9459 18 7.88 330.96 58.981 38.1 284.2 6.77 0.9395 19 7.83 328.86 58.582 38 3 286.0 6.82 0.9333 20 7.78 326.76 58.195 38.5 287.9 6.86 0.9271 21 7.72 324.24 57.809 38.8 290.0 6.91 0.9210 22 7.67 322.14 57.428 39.0 292.0 6.96 0.9150 23 7.62 320.04 57.053 39.2 293.9 7.01 0.9090 24 7.57 317.94 56.680 39.5 295.7 7.06 0.9032 25 7.53 316.26 56.319 39.8 297.4 7.09 0.8974 26 7.48 314.16 55.957 40.1 299.4 7.14 0.8917 27 7.43 312.06 55.601 40.3 301.4 7.18 0.8860 28 7.38 309.96 55.149 40.6 303.5 7.24 0.8805 29 7.34 308.28 54.903 40.8 305.2 7.28 0.8750 30 7.29 306.18 54.560 41.1 307.2 7.32 0.8484 35 7.07 296.94 52.991 42.4 316.8 7.55 0.8235 40 6.86 288.12 51.349 43.7 326.3 7.78 140 The above table is based on the formula 130 + For each 10° F. above 60° F. add 0.7° Be. For each 10° F. below 60° F. subtract 0.7° Be. 42 gals. = 1 bbl. 1 ton = 2240 lbs. He. = Sp. Gr. Weight and Stowage of Oil 687 -WEIGHT AND STOWAGE OP OIL. (Petroleum.) Weight ix Pounds per Gallon. Pounds per Cubic Foot. Cubic Feet per Ton. Gallons per Ton. 6.50 48.63 46.06 344.6 6.55 49.05 45.67 342.0 6.60 49.38 45.36 339.4 6.65 49.75 45.02 336.8 6.70 50.13 44.68 334.3 6.75 50.50 44.36 331.9 6.80 50.88 44.03 329.4 6.85 51.25 43.71 327.0 6.90 51.62 43.39 324.6 6.95 52.00 43.07 322.3 7.00 52.36 42.78 320.0 7.05 52.75 42.46 317.8 7.10 53.12 42.17 315.5 7.15 53.50 41.87 313.2 7.20 63.86 41.59 311.1 7.25 54.24 41.30 309.0 7.30 54.61 41.01 306.9 7.35 54.99 40.73 304.8 7.40 55.37 40.46 302.7 7.45 55.74 40.19 300.7 7.50 56.11 39.92 298.6 7.55 56.48 39.66 296.6 7.60 56.85 39.40 294.7 7.65 57.23 39.14 292.8 7.70 57.61 38.88 290.9 7.75 57.99 38.63 289.0 7.80 58.36 38.39 287.2 7.85 58.73 38.14 285.3 7.90 59.10 37.90 283.5 7.95 59.47 37.66 281.7 8.00 59.85 37.42 280.0 688 The Naval Constructor WHITWORTH STANDARD BOLTS AND NUTS. (Dimensions are Given to the Nearest ^ Inch.) £h Bolt Head and Nuts. §« Size £3 2 w of DlAMETEB w ,2 5° Width across Flats. Width across Corners. Height of Bolt Head. -- Split- pins L.S.G. of Tap- ping Hole. " a 11 a 11 NO. a A A \ a^ A f and A 24 15 J and A i i and A A " A a :: a 20 14 A A A " A H \ " A 18 14 i § if '« A II A " A 16 13 i " A A if " A if " A 1 14 13 A " A i J "A }A A 12 12 f " A A " A A 1 " A 1 1 " A A " A 12 12 I ; •• a J \ " A \ " A A " A 11 11 i " A ft 1A " A H " A 11 11 A " A i i* " A if f " A 10 10 1 if if " A iA " A if M A 10 10 if 1 JA " A 1 rf " A \ " A 9 9 if " A if JA " A 1 ! " A if 9 9 * " A ; i m a 1 rf " A 1 8 8 if " A H Hf " A 2i " A if " A 7 7 if " A 1} 2 » A 2A " A ;a " a 7 6 iA if 2* " * n " a iA " A 6 5 H "A 1* 21 "" ^ 2f " A iA 6 4 ii " A if 2* * 2if " A if " A 5 3 if if 2| 8A 1 * "A 5 2 I'J 1* 2* »A " A 1 1 " A 4£ 1 iA " A 2 2* * ff if 4 1 iff " A 21 3| " A fA " A m " a 4 A 4f 2} ? * A 1ft » S 2A 4 A 2A 2f » 2 f " A 81 f 2| " A 3 1* " a *A " A 2f 8| f 2f " A 3* fif " A *A u A m " a 3i f 2if " A ft jH " A «r* " A 3A gi A 3f 3J H " A «t " A 3* " A 3 A 3A " A 4 5ff M A 6 1 84 3 1 3A " A *i 2) 7A " A 3U " A H i 3f " A 4£ 6if M A n m 8| 4 " A 41 l\ u 2* 4* " A 2| A 4i " A 5 7 ! "A 9 " A M *f I 4* " A 5* 8if " ^ 10A " A *H 2f if 5 M A 6 10 11 i " A n 2| | &A " A Weight of Bolts and Nuts 689 ,0 00 C<1 8 g g °. 00 t~ ta e^ «' ei fl « • * ©. ^ 2 ? § n S! S S ^rH-*cocoJj©i>jeo© ^THOt» ^Aosoot-tort-^it-:© ^©©o©©©©©© t- m P. P. a ,3 M a IS a i2 o a o W o pq « 690 The Naval Constructor CAPACITIES OP TANKS PER FOOT Width of Tank. Length 2" 2' 6" 3' 3' 6" 4' 4' 6" 5' 5' 6" 6' 6' 6" 2ft. . . 2 ft. 6 in. 3 ft. . . Gal. 29.9 Gal. 37.4 46.75 Gal. 44.88 56.1 67.32 Gal. 52.36 65.45 78.54 91.63 Gal. 59.84 74.80 89.76 104.72 119.68 Gal. 67.32 84.15 101. 117.81 134.64 151.47 Gal. 74.8 93.5 112.2 130.9 149.6 168.30 187. Gal. 82.28 102.85 123.42 144. 164.56 185.13 205.7 226.27 Gal. 89.76 112.20 134.64 157.08 179.52 202. 224.4 246.84 269.28 Gal. 97.24 121.55 145.86 170.17 194.48 218.79 243.1 267.41 291.72 316.03 3 ft. 6 in. 4 ft 4 ft. 6 in. 5 ft. . . 5 ft. 6 in. 6 ft. . . 6 ft. 6 in. 7 ft. . . 7 ft. 6 in. 8 ft. . 8 ft. 6 in. 9 ft. . . 9 ft. 6 in. 10 ft. . . Note. — To convert to British gallons, multiply by Capacities of Tanks 691 OP DEPTH (Rectangular) of Tank. 7' 7' 6" 8' 8' 6" 9' 9' 6" 10' 10' 6" 11' 11' 6" 13' Gal. Gal. Gal. Gal. Gal. Gal. Gal. Gal. Gal. Gal. Gal. 104.72 112.20 119.68 127.16 134.64 142.12 149.6 157. 164.56 172. 179.52 130.9 140.25 149.6 158.95 168.3 177.65 187. 196.35 205.7 215.05 224.4 157. 168.3 179.52 190.74 202. 213.18 224.4 235.62 246.84 258.06 269.28 183.26 196.35 209.44 222.53 235.62 248.71 261.8 274.89 288. 301.07 314.16 209.44 224.4 239.36 254.32 269.28 299.2 314.16 329.12 344.08 359. 374. 235.62 252.45 269.28 286.11 303. 319.77 336.6 353.43 370.26 387.09 404. 261.8 280.5 299.2 317.9 336.6 355.3 374. 392.7 411.4 430.1 448.8 288. 308.55 329.12 349.7 370.26 390.83 411.4 332. 452.54 473.11 493.68 314.16 336.6 359.04 381.48 403.92 426.36 448.80 471.24 493.68 516.12 538.56 340.34 364.65 388.96 413.27 437.58 461 .89 486.2 510.51 534.82 559.13 583.44 366.52 392.70 418.88 445.06 471.24 497.42 523.6 549.78 575.96 602.14 628.32 420.75 448.8 476.85 405.9 532.95 561. 589.05 G17.1 645.15 673.2 478.72 508.64 538.56 568.48 598.4 628.32 658.24 688.16 718.08 540.43 572.22 604.01 635.80 667.59 699.38 731.17 762.96 605.88 639.54 673.2 706.86 740.52 774.18 807.84 675.07 710.6 746.13 781.66 817.19 852.72 748. 7MK 4 822.8 860.2 897.6 Weight of a U.S. gallon = 8£ lbs. Weight of a Britifi gallon, F. W. = 10 lbs. 692 The Naval Constructor CONTENTS OF TANKS PER FOOT OF DEPTH (Cylindrical). DlAM. U.S. Gallons. DlAM. U.S. Gallons. DlAM. U.S. Gallons. Ft. In. 1 Foot in Depth. Ft. In. 1 Foot in Depth. Ft. In. 1 Foot in Depth. 1 5.87 11 710.69 21 2,590.22 1 3 9.17 11 3 743.36 21 3 2,652.25 1 6 13.21 11 6 776.77 21 6 2,715.04 1 9 17.98 11 9 810.91 21 9 2,778.54 2 • 23.49 12 848.18 22 2,842.79 2 3 29.73 12 3 881.39 22 3 2,907.76 2 6 36.70 12 6 917.73 22 6 2,973.48 2 9 44.41 12 9 954.81 22 9 3,039.92 3 52.86 13 992.62 23 3,107.10 3 3 62.03 13 3 1,031.17 23 3 3,175.01 3 6 73.15 13 6 1,070.45 23 6 3,243.65 3 9 82.59 13 9 1,108.06 23 9 3,313.04 4 93.97 14 1,151.21 24 3,383.15 4 3 103.03 14 3 1,192.69 24 3 3,454.00 4 6 118.93 14 6 1,234.91 24 6 3,525.59 4 9 132.52 14 9 1,277.86 24 9 3,597.90 5 146.83 15 1,321.54 25 3,670.95 5 3 161.88 15 3 1,365.96 25 3 3,744.74 5 6 117.67 15 6 1,407.51 25 6 3,819.26 5 9 194.19 15 9 1,457.00 25 9 3,894.52 6 211.44 16 1,503.62 26 3,970.50 6 3 229.43 16 3 1,550.97 26 3 4,047.23 6 6 248.15 16 6 1,599.06 26 6 4,124.68 6 9 267.61 16 9 1,647.89 26 9 4,202.96 7 287.80 17 1,697.45 27 4,281.80 7 3 308.72 17 3 1,747.74 27 3 4,361.46 7 6 330.38 17 6 1,798.76 27 6 4,441.86 7 9 352.76 17 9 1,850.53 27 9 4,522.98 8 375.90 18 1,903.02 28 4,604.85 8 3 399.76 18 3 1,956.25 28 3 4,686.48 8 6 424.36 18 6 2,010.21 28 6 4,770.77 8 9 449.21 18 9 2,064.91 28 9 4,854.84 9 475.75 19 2,120.34 29 4,939.64 9 3 502.55 19 3 2,176.51 29 3 5,025.17 9 6 530.08 19 6 2,233.29 29 6 5,111.44 9 9 558.35 19 9 2,291.04 29 9 5,198.44 10 587.35 | 617.08 J 647.55 f 20 2,349.41 30 5,286.18 10 3 20 3 2,408.51 30 3 5,374.65 10 6 20 6 2,468.35 30 6 5,463.85 10 9 678.27 20 9 2,528.92 30 9 5,553.79 Note. — To clnvert to British gallons, x .8 Pressure of Water at Various Heads 693 PRESSURE OF WATER AT VARIOUS HEADS. Formula : P = H' X -4334 = Pounds. P — H'X .0304 = Kilos. Pressure, «. * Pressure, » "i Pressure, P, IN P, IN P, IN S>8 fill Pounds Kilos Pounds Kilos Pounds Kilos per per per per per per Sq. In. Sq. Cm. Sq. In. Sq. Cm. Sq. In. Sq. Cm. lin. .03608 .002537 27 ft. 11.691 .82196 64 ft. 27.712 1.94836 2 .07216 .005074 28 12.124 .85240 65 28.145 1.97880 3 .10824 .007611 29 12.557 .88284 66 28.578 2.00925 4 .14432 .010148 30 12.990 .91329 67 29.011 2.03969 5 .18040 .012685 31 13.423 .94373 68 29.444 2.07013 6 .21648 .015222 32 13.856 .97417 69 29.877 2.10057 7 .25256 .017759 33 14.289 1.00462 70 30.310 2.13102 8 .28864 .020296 34 14.722 1.03406 71 30.743 2.16146 9 .32472 .022833 35 15.155 1.06450 72 31.176 2.19190 10 .36080 .025370 36 15.588 1.09495 73 31.609 2.22235 11 .39688 .027907 37 16.021 1.12539 74 32.042 2.25279 1ft. .433 .030443 38 16.454 1.15583 75 32.475 2.28323 2 .866 .060886 39 16.887 1.18627 76 32.908 2.31368 3 1.299 .091329 40 17.320 1.21773 77 33.341 2.34412 4 1.732 .121773 41 17.753 1.24817 78 33.774 2.37456 5 2.165 .152216 42 18.186 1.27861 79 34.207 2.40500 6 2.598 .182659 43 18.619 1.30906 80 34.640 2.43545 7 3.031 .213102 44 19.052 1.33950 81 35.073 2.46589 8 3.464 .243545 45 19.485 1.36994 82 35.506 2.49633 9 3.897 .273989 46 19.918 1.40039 83 35.939 2.52678 10 ' 4.330 .30443 47 20.351 1.43083 84 36.372 2.55722 11 4.763 .33487 48 20.784 1.46127 85 36.805 2.58766 12 5.196 ,36531 49 21.217 1.49171 86 37.238 2.61811 13 5.629 .39576 50 21.650 1.52216 87 37.671 2.64855 14 6.062 .42620 51 22.083 1.55260 88 38.104 2.67899 15 6.495 .45664 52 22.516 1.58304 89 38.537 2.70943 16 6.928 .48709 53 22.949 1.61349 90 38.970 2.73989 17 7.361 .51753 54 23.382 1.64393 91 39.403 2.77033 18 7.794 .54797 55 23.815 1.67437 92 39.836 2.80077 19 8.227 .57841 56 24.248 1.70482 93 40.269 2.83122 20 8.660 .60886 57 24.681 1.73526 94 40.702 2.86166 21 9.093 .63930 58 25.114 1.76570 95 41.135 2.89210 22 9.526 .66974 59 25.557 1.79614 96 41.568 2.92255 23 9.959 .70019 60 25.980 1.82659 97 42.001 2.95299 24 10.392 .73063 61 26.413 1.85703 98 42.434 2.98343 25 10.825 .76107 62 26.846 1.88747 99 42.867 3.01387 26 11.258 .79152 63 27.279 1.91792 100 43.300 3.04432 The above table is calculated for f resb water at a temperature of 62° F. 694 The Naval Constructor UNIT EQUIVALENTS. * HEAT, ELECTRICAL AND MECHANICAL. Unit. Equivalents. 1 K.W. hour= 1,000 watt hours. 1 . 34 horse-power hours. 2,654,200 ft.-Ibs. 3,600,000 joules. 3,412 heat units. 367,000 kilogram metres. 0.235 lb. carbon oxidized with perfect efficiency. 3 . 53 lbs. water evaporated from and at 212 degrees F. 22 . 75 lbs. of water raised from 62 degrees to 212 degrees F. 1 H.P. hour= 0.746 K.W. hour. 1,980,000 ft.-lbs. 2,545 heat-units. 273,740 k.g.m. 0.175 lb. carbon oxidized with perfect efficiency. 2.64 lbs. water evaporated from and at 212 degrees F. 17.0 lbs. water raised from 62 degrees to 212 degrees F. 1 kilowatt = • 1,000 watts. 1 . 34 horse-power. 2,654,200 ft.-lbs. per hour. 44,240 ft.-lbs. per minute. 737.3 ft.-lbs. per second. 3,412 heat-units per hour. 56.9 heat-units per minute. 0.948 heat-unit per second. 0.2275 lb. carbon oxidized per hour. 3.53 lbs. water evaporated per hour from and at 212 degrees F. 1H.P.= 746 watts. 0.746 K.W. 33,000 ft.-lbs. per minute. 550 ft.-lbs. per second. 2,455 heat-units per hour. 42.4 heat-units per minute. 0. 707 heat-unit per second. 0.175 lb. carbon oxidized per hour. 2.64 lbs. water evaporated per hour from and at 212 degrees F. Unit Equivalents 695 UNIT EQUIVALENTS.— (Continued.) HEAT, ELECTRICAL AND MECHANICAL. Unit. Equivalents. 1 Joule = 1 watt second. 0.000000278 K.W. hour. 0.102k.g.m. 0.0009477 heat-unit. 0.7373 ft.-lbs. 1 f t.-lb. = • 1.356 joules. 0.1383 k.g.m. 0.000000377 K.W. hour. 0.001285 heat-unit. 0.0000005 H.P. hour. 1 watt= 1 joule per second. 0.00134 H.P. 3.412 heat-units per hour. 0.7373 ft.-lb. per second. 0.0035 lb. water evaporated per hour. 44.24 ft.-lbs. per minute. 1 watt per J sq. in.= 8.19 heat-units per square foot per minute. 6371 ft.-lbs. per square foot per minute. 0. 193 H.P. per square foot. 1 heat unit = 1,055 watt seconds. 778 ft.-lbs. 107.6 kilogram metres. 0.000293 K.W. hour. 0.000393 H.P. hour. 0.0000688 lb. carbon oxidized. 0.001036 lb. water evaporated from and at 212 degrees F. 1 heat unit 1 per sq. ft. per < min. = | 0. 122 watt per square inch. 0.0176 K.W. per square foot. 0.0236 H.P. per square foot. 1 kilogram metre = 7.233 ft.-lbs. 0.00000365 H.P. hour. 0.00000272 K.W. hour. 0.0093 heat-unit. 696 The Naval Constructor UNIT EQUIVALENTS.— (Continued.) HEAT, ELECTRICAL AND MECHANICAL. Unit. Equivalents. 1 lb. carbon oxidized with perfect effi- ciency = 14,544 heat-units. 1.11 lbs. anthracite coal oxidized. 2.5 lbs. dry wood oxidized. 21 cubic feet illuminating-gas. 4.26 K.W. hours. 5.71 H.P. hours. 11,315,000 ft.-lbs. 15 lbs. of water evaporated from and at 212 degrees F. 1 lb. water evaporated from and at 212 degs. F. 0.283 K.W. hour. 0.379 H.P. hour. 965.7 heat-units. 103,900 k.g.m. 1,019,000 joules. 61,300 ft.-lbs. 0.0664 lb. of carbon oxidized. Water Notes 697 WATER NOTES. 1 United States gallon : 1 United States gallon = 1 United States gallon : 1 United States gallon = 1 British gallon 1 British gallon : 1 British gallon : 1 British gallon : 1 cubic foot of sea water = 1 cubic inch of sea water : 1 cubic foot of fresh water : 1 cubic inch of fresh water : 1 ton of sea water 1 ton of fresh water : Weight of fresh water : 1 cubic foot of fresh water 1 cubic foot of fresh water = 1 cubic foot of fresh water 1 litre of fresh water 1 litre of fresh water = 1 litre of fresh water 1 litre of fresh water Head of water in feet X .4334 : Head of water in feet x .0304 231 cubic inches. .83 British gallon. 3.8 litres. 8^ pounds fresh water. 277.274 cubic inches. 1.205 United States gallons. 4.543 litres. 10 pounds fresh water. 64.05 pounds = .0286 ton. .037,035 pounds. 62.39 pounds = .0279 ton. .0361 pound. 34.973 cubic feet. 35.905 cubic feet. weight of salt water x .974. 7.476 United States gallons. 6.232 British gallons. 28.375 litres. .264 United States gallon. .22 British gallon. ! 61.0 cubic inches. .0353 cubic foot. ; Pressure in lbs. per sq. in. : Pressure in kilos per sq. cm. AREAS OF CIRCLES. Diam- Area. Circum- Diam- Area. Circum- eter. ference. eter. ference. 4 .000767 .09817 ii .22166 1.6690 15 .003068 .19635 ft .24850 1.7671 t .006903 .012271 .29452 y .27688 1.8653 .39270 t .30680 1.9635 A .019175 .49087 §4 .33824 2.0617 3 TB .027612 .58905 H .37122 2.1598 7 .037583 .68722 M .40574 2.2580 .049087 .78540 i .44179 2.3562 ft .062126 .88357 if .47937 2.4544 ft .076699 .98175 11 .51849 2.5525 §4 .092806 1.0799 H .55914 2.6507 1 .11045 1.1781 i .60132 2.7489 13 3~S .12962 1.2763 .64504 2.8471 h .15033 1.3744 .69029 9.9452 ¥ .17257 1.4726 H .73708 3.0434 .19635 1.5708 l .78540 3.1416 698 The Naval Constructor AREAS OF CIRCLES And Lengths of the Sides of Squares of the Same Area. Diam. x .8862 = Side of Square. . < < .< g U 30 ■** ^ « OH. M ^ 2 o w . a u 5 5£m ft. <» ■< u A o w . © H«5 $ 3 t o » a & Qccg o S3 00 _ - ■/. 1 .785 .89 21 346.36 18.61 41 1,320.26 36.34 1* 1.767 1.33 21* 363.05 19.05 41* 1,352.66 36.78 2 3.142 1.77 22 380.13 19.50 42 1,385.45 37.22 2* 4.909 2.22 22* 397.61 19.94 42* 1,418.63 37.66 3 7.069 2.66 23 415.48 20.38 43 1,452.20 38.11* 3* 9.621 3.10 23* 433.74 20.83 43* 1,486.17 38.55 4 12.566 3.54 24 452.39 21.27 44 1,520.53 38.99 4* 15.904 3.99 24* 471.44 21.71 44* 1,555.29 39.44 5 19.635 4.43 25 490.88 22.16 45 1,590.43 39.88 5* 23.758 4.87 25* 510.71 22.60 45* 1,625.97 40.32 G 28.274 5.32 26 530.93 23.04 46 1,661.91 40.77 6* 33.183 5.76 26* 551.55 23.49 46* 1,698.23 41.21 7 38.485 6.20 27 572.56 23.93 47 1,734.95 41.65 7* 44.179 6.65 27* 593.96 24.37 47* 1,772.06 42.10 8 50.266 7.09 28 615.75 24.81 48 1,809.56 42.58 8* 56.745 7.53 28* 637.94 25.26 48* 1,847.46 42.98 9 63.617 7.98 29 660.52 25.70 49 1,885.75 43.43 9* 70.882 8.42 29* 683.49 26.14 49* 1,924.43 43.87 10 78.540 8.86 30 706.86 26.59 50 1,963.50 44.31 10* 86.590 9.30 30* 730.62 27.03 50* 2,002.97 44.75 11 95.03 9.75 31 754.77 27.47 51 2,042.83 45.20 11* 103.87 10.19 31* 779.31 27.92 51* 2,083.08 45.64 12 113.10 10.63 32 804.25 28.36 52 2,123.72 46.08 12* 122.72 11.08 32* 829.58 '28.80 52* 2,164.76 46.53 13 132.73 11.52 33 855.30 29.25 53 2,206.19 46.97 13* 143.14 11.96 33* 881.41 29.69 53* 2,248.01 47.41 14 153.94 12.41 34 907.92 30.13 54 2,290.23 47.86 14* 165.13 12.85 34* 934.82 30.57 54*« 2,332.83 48.30 15 176.72 13.29 35 962.11 31.02 55 2,375.83 48.74 15* 188.69 13.74 35* 989.80 31.46 55* 2,419.23 49.19 16 201.06 14.18 36 1,017.88 31.90 56 2,463.01 49.63 16* 213.83 14.62 36* 1,046.35 32.35 56* 2,507.19 50.07 17 226.98 15.07 37 1,075.21 32.79 57 2,551.76 50.51 17* 240.53 15.51 37* 1,104.47 33.23 57* 2,596.73 50.96 18 254.47 15.95 38 1,134.12 33.68 58 2,642.09 51.40 18* 268.80 16.40 38* 1,164.16 34.12 58* 2,687.84 51.84 19 283.53 16.84 39 1,194.59 34.56 59 2,733.98 52.29 19* 298.65 17.28 39* 1,225.42 35.01 59* 2,780.51 52.73 20 314.16 17.72 40 1,256.64 35.45 60 2,827.74 53.17 20* 330.06 18.17 40* 1,288.25 35.89 60* 2,874.76 53.62 Squares, Cubes, etc., of Fractions 699 SQUARES, CUBES, AND FOURTH POWERS OP FRACTIONS. No. Square. Cube. Fourth Power. No. Square. Cube. Fourth Power. A 0.0002441 0.000003815 0.00000005961 fi 0.4104 0.2629 0.1684 A 0.0009766 0.00003052 0.0000009537 14 0.4307 0.2826 0.1855 ^¥ 0.002197 0.0001030 0.000001922 II 0.4514 0.3033 0.2038 A 0.003906 0.0002441 0.00001526 ft 0.4727 0.3250 0.2234 A 0.006104 0.0004768 0.00003725 n 0.4944 0.3476 2444 3 32 0.008789 0.0008240 0.00007725 ti 0.5166 0.3713 0.2669 A 0.01196 0.001308 0.0001431 u 0.5393 0.3961 0.2909 1 8 0.01563 0.001953 0.0002441 I 0.5625 0.4219 0.3164 A 0.01978 0.002781 0.0003911 n 0.5862 0.4488 0.3436 5 32 0.02441 0.003815 0.0005961 H 0.6104 0.4768 0.3725 H 0.02954 0.005077 0.0008727 fi 0.6350 0.5060 0.4032 A 0.03516 0.006592 0.001236 H ff 0.6602 0.5364 0.4358 1 3 6 4 0.04126 0.008381 0.001702 0.6858 0.5679 0.4703 A 0.04785 0.01047 0.002290 H 0.7119 0.6007 0.5068 U 0.05493 0.01287 0.003018 55 6¥ 0.7385 0.6347 0.5454 i 4 0.06250 0.01563 0.003906 I 8 0.7656 0.6699 0.5862 H 0.07056 0.01874 0.004978 fl 0.7932 0.7065 0.6290 A 0.07910 0.02225 0.006257 fj 0.8213 0.7443 0.6745 H 0.08813 0.02617 0.007768 fi 0.8499 0.7835 0.7223 5 0.09766 0.03052 0.009537 « 0.8789 0.8240 0.7725 u 0.1077 0.03533 0.01159 fi 0.9084 0.8659 0.8253 u 0.1182 0.04062 0.01396 fi 0.9385 0.9091 0.8807 8 0.1292 0.04641 0.01668 If 0.9690 0.9539 0.9390 0.1406 0.05273 0.01978 l 1.000 1.000 1.000 If 0.1526 0.05960 0.02328 1A 1.031 1.048 1.064 13 0.1650 0.06705 0.02724 i l 1.063 1.097 1.131 0.1780 0.07508 0.03168 h\ 1.096 1.147 1.201 A 0.1914 0.08374 0.03664 1A 1.129 1.199 1.274 It 0.2053 0.09304 0.04216 1A 1.162 1.253 1.351 if 0.2197 0.1030 0.04828 lj2 1.196 1.308 1.431 fi 0.2346 0.1136 0.05505 1A 1.231 1.365 1.515 2 0.2500 0.1250 0.06250 a 1.266 1.424 1.602 6? 0.2659 0.1371 0.07069 1A 1.301 1.484 1.693 if 0.2822 0.1499 0.07965 1 5 i 32" Hi 1.337 1.546 1.787 M 0.2991 0.1636 0.08944 1.373 1.609 1.996 9 0.3164 0.1780 0.1001 1A 1.410 1.675 1.989 H 0.3342 0.1932 0.1117 Hi 1.448 1.742 2.095 19 32 0.3526 0.2093 0.1243 1A 1.485 1.810 2.206 II 0.3713 0.2263 0.1379 m 1.524 1.881 2.322 5 8 0.3906 0.2441 0.1526 n 1.563 1.953 2.441 700 The Naval Constructor SQUARES, CUBES, AND FOURTH POWERS OF FRACTIONS — (Continued.) No. "IS Square. Cube. Fourth Power. No. Square. Cube. Fourth Power. 1.602 2.027 2.566 Iff 2.692 4.416 7.245 1 n 1.642 2.103 2.695 ill 2.743 4.543 7.525 HI 1.682 2.181 2.829 Iff 2.795 4.673 7.813 if\ 1.723 2.261 2.968 iff 2.848 4.805 8.109 lf| 1.764 2.343 3.111 L« 2.901 4.940 8.414 l|I 1.806 2.426 3.260 2.954 5.077 8.727 in 1.848 2.512 3.415 ill 3.008 5.217 9.048 it 1.891 2.600 3.575 l! 3.063 5.359 9.379 it! 1.934 2.689 3.740 Iff 3.117 5.504 9.718 iff 1.978 2.781 3.911 125 *8? 3.173 5.652 10.07 in 2.022 2.875 4.087 Iff 3.229 5.802 10.43 if* 2.066 2.970 4.270 iff 3.285 5.954 10.79 iff 2.112 3.068 4.459 HI 3.342 6.110 11.17 Hi 2.157 3.168 4.654 1« 3.399 6.268 11.56 Hi 2.203 3.271 4.855 HI 3.457 6.428 11.95 If 2.250 3.375 5.063 H 3.516 6.592 12.36 Iff 2.297 3.482 5.277 Iff 3.574 6.758 12.78 iff iff 2.345 3.590 5.498 H! 3.634 6.927 13.20 2.393 3.701 5.726 iff 3.694 7.099 13.64 lft 2.441 3.815 5.961 iff 3.754 7.273 14.09 H£ 2.490 3.930 6.203 Iff 3.815 7.451 14.55 Hi 2.540 4.048 6.452 1« 3.876 7.631 15.02 ill 2.590 4.168 6.709 HI 3.938 7.814 15.51 if 2.641 4.291 6.973 2 4.000 8.000 16.00 POWERS AND ROOTS OF USEFUL FACTORS. n 1 n n* n* Vn l 0.564 . Kil2. Kil2. Kil-!. Kil-'. KIP. Kil2. Kil2. Kil2. Kil2. 0.0000 2.5899 5.1798 7.7697 10.359 12.929 15.539 18.129 20.718 23.309 10 25.899 28.490 31.079 33.669 36.259 38.829 41.439 44.029 46.619 49.209 20 51.798 54.388 56.978 59.56S 62.158 64.728 67.338 69.928 72.518 75.108 30 77.697 80.287 82.877 85.467 88.057 90.627 93.238 96.828 98.417 101.01 40 103.59 106.18 108.77 111.36 113.95 116.52 119.13 121.72 124.31 126.90 50 129.29 131.88 134.47 137.06 139.65 142.22 144.83 147.42 150.01 152.50 60 155.39 157.98 160.57 163.16 165.75 168.32 170.93 173.52 176.11 178.70 70 181.29 183.88 186.47 188.06 191.65 194.22 196.83 199.42 202.01 204.60 80 207.19 209.77 212.36 214.95 217.55 220.11 222.73 225.31 227.91 230.50 90 233.09 235.68 238.27 240.86 243.45 246.02 248.63 251.22 253.81 256.40 100 258.99 261.58 264.17 266.76 269.35 271.92 274.53 277.12 279.71 282.20 Conversion of Square Kilometres into Square Miles. Sq. kllom. 1 2 3 4 5 6 7 8 9 Sq. m. Sq. m. Sq. m. Sq. m. Sq. m. Sq. m. Sq. m. Sq. m Sq. m. Sq. m. 0.0000 0.3861 0.7722 1.1583 1.5445 1.9304 2.3166 2.7028 3.0890 3.4749 10 3.8612 4.2471 4.6334 5.0195 5.4057 5.7916 6.1778 6.5640 6.9502 7.3362 20 7.7224 8.1081 8.4946 8.8807 9.2669 9.6528 10.039 10.425 10.811 11.197 30 11.583 11.969 12.355 12.741 13.127 13.513 13.899 14.286 14.672 15.058 40 15.445 15.830 16.217 16.603 16.989 17.375 17.761 18.146 18.534 18.920 50 19.304 19.691 20.076 20.462 20.848 21.234 21.620 22.007 22.393 22.779 60 23.166 23.552 23.938 24.324 24.710 25.096 25.482 25.869 26.245 26.641 70 27.028 27.413 27.800 28.186 28.572 28.958 29.344 29.731 30.117 30.503 80 30.890 31.274 31.662 32.048 32.434 32.820 33.206 33.593 33.979 34.365 90 34.749 35.135 35.521 35.907 36.293 36.679 37.065 37.452 37.838 38.224 100 38.612 38.996 39.384 39.770 40.156 40.542 40.928 41.315 41.701 42.087 732 The Metric System. Conversion of Cubic Feet into Cubic Decimetres. Cubic feet. 1 2 3 4 5 6 7 8 9 Dm3. Dm 8 . Dm3. Dm2. Dms. Dm3. Dm8. Dm3. Dm3. Dm 8 . 0.0000 28.316 56.632 84.948 113.26 141.58 169.90 198.21 226.53 254.84 10 283.16 311.47 3:59.79 268.11 396.42 424.74 453.06 481.37 509.69 538.00 20 566.32 594.64 622.96 651.27 679.58 707.90 736.22 764.53 792.85 821.16 30 849.48 877.80 906.11 934.43 962.74 991.06 1019.4 1047.7 1076.0 1104.3 40 1132.6 1160.8 1189.2 1217.5 1245.9 1274.2 1302.5 1330.8 1359.1 1387.4 60 1415.8 1444.0 1472.4 1500.7 1529.1 1557.4 1688.7 1614.0 1642.3 1670.6 60 1698.9 1727.2 1755.5 1783.8 1812.2 1840.5 1868.8 1897.1 1925.4 1953.7 70 1982.1 2010.3 2038.7 2067.0 2095.4 2123.7 2152.0 2180.3 2208.6 2236.9 80 2265.3 2293.5 2321.9 2350.2 2378.6 2406.9 2435.2 2463.5 2491.8 2520.1 90 2548.4 2576.6 2605.0 2633.3 2661.6 2690.0 2718.3 2746.6 2774.9 2803.2 100 2831.6 2859.8 2888.2 2916.5 2944.9 2973.2 3001.5 3029.8 3058.1 3086.4 Conversion of Cubic Decimetres into Cubic Feet. Cubic dm. 1 2 3 4 5 6 7 8 9 Fts. Fts. Ft 8 . Ft3. Ff. FR Fts. Ft -5 . Fts. Ft3. 0.0000 0.0353 0.0706 0.1059 0.1413 0.1766 0.2119 0.2472 0.2825 0.3178 10 0.3531 0.3884 0.4237 0.4590 0.4944 0.5297 0.5540 0.6003 0.6356 0.6709 20 0.7063 0.7416 0.7766 0.8122 0.8476 0.8829 0.9182 0.9535 0.9888 1.0241 30 1.0594 1.0947 1.1300 1.1653 1.2007 1.2360 1.2713 1.3066 1.3419 1.3772 40 1.4126 1.4479 1.4832 1.5185 1.5539 1.5892 1.6245 1.6608 1.6951 1.7304 50 1.7658 1.8011 1.8364 1.8717 1.9071 1.9424 1.9777 2.0130 2.0483 2.0836 60 2.1189 2.1542 2.1895 2.2248 2.2602 2.2955 2.3308 2.3661 2.4014 2.4367 70 2.4721 2.5074 2.5427 2.5780 2.6134 2.6487 2.6840 2.7193 2.7546 2.7899 80 2.8252 2.8605 2.8958 2.9311 2.9665 3.0018 3.0371 3.0724 3.1077 3.1430 90 3.1784 3.2137 3.2490 3.2S43 3.3197 3.3550 3.3903 3.4256 3.4609 3.4962 100 3.5315 3.5668 3.6021 3.6374 3.6728 3.7081 3.7434 3.7787 3.8140 3.8493 Pounds per Square Foot into Kilogrammes per Square Metre. LbS. pr fts. 1 2 3 4 5 6 7 8 9 K.m2. K.m2. K.m2. K.m2. K.m2. K.m2. K.m2. K.m2. K.m2. K.m2. 0.0000 4.8825 9.7650 14.647 19.530 24.413 29.295 34.177 39.006 43.943 10 48.825 53.707 58.590 63.472 68.355 73.238 78.120 83.002 87.831 92.768 20 97.650 102.53 107.41 112.30 117.18 122.06 126.94 131.83 136.66 141.59 30 146.47 151.35 156.23 161.12 165.90 170.88 175.76 180.65 185.47 190.41 40 195.30 200.13 205.06 209.95 214.83 219.71 224.59 229.48 234.30 239.24 50 244.13 249.01 253.89 258.78 263.66 268.54 273.42 278.31 283.13 288.08 60 292.95 297.83 302.71 307.60 312.48 317.36 322.24 327.13 331.95 336.89 70 341.77 346.65 351.53 356.42 361.20 366.18 371.06 375.95 880.77 385.71 80 390.06 394.94 399.82 404.71 409.59 414.47 419.35 424.24 429.06 434.00 90 439.43 444.31 449.19 454.08 458.96 463.34 468.72 473.61 478.43 483.37 100 488.25 493.13 498.01 502.90 507.78 512.66 517.54 522.43 527.25 532.19 Kilogra mmes per Square Metre into Pounds per Square Foot. K. per m*. i 2 3 4 5 6 7 8 9 Lb. ft2 Lb. ft* Lb. ft 2 Lb.ft2Lb.ft2 Lb. ft 2 Lb. ft 2 Lb. W Lb. ft2 Lb. ft* 0.0000 0.2048 0.4096 0.6144 0.8192 1.0240 1.2289 1.4337 1.6385 1.8433 10 2.0481 2.2529 2.4577 2.6625 2.8673 3.0721 3.2770 3.4818 3.6866 3.8914 20 4.0962 4.3010 4.5058 4.7106 4.9154 5.1202 5.3251 5.5299 5.7347 5.9395 30 6.1444 6.3492 6.5540 6.7588 6.9636 7.1684 7.3733 7.5781 7.7829 7.9877 40 8.1925 8.3973 8.6021 8.8069 9.0117 9.2165 9.4214 9.6262 9.8310 10.036 50 10.240 10.445 10.649 10.854 11.059 11.264 11.469 11.674 11.878 12.083 60 12.289 12.494 12.698 12.903 13.108 13.313 13.518 13.723 13.927 14.132 70 14.337 14.542 14.746 14.951 15.156 15.361 15.566 15.771 15.975 16.180 80 16.385 16.590 16.794 16.999 17.204 17.409 17.614 17.819 18.023 18.228 90 18.433 18.638 18.842 19.047 19.252 19.457 19.662 19.867 20.071 20.276 100 20.481 20.686 20.890 21.095 21.300 21.505 21.710 21.915 22.119 22.324 The Metric System. 733 Pounds per Square Inch into Atmospheric Press ure. Lbs. pr in 2 . At. 1 2 3 4 5 6 7 8 9 At. At. At. At. At. At. At. At. At. 0.0000 0.0680 0.1361 0.2041 0.2722 0.3402 0.4082 0.4763 0.5443 0.6124 10 0.6804 0.7484 0.8165 0.8845 0.9526 1.0206 1.0886 1.1567 1.2247 1.2928 20 1.3608 1.4288 1.4969 1.5649 1.6330 1.7010 1.7690 1.8371 1.9051 1.9732 30 2.0413 2.1093 2.1774 2.2454 2.3135 2.3814 2.4495 2.5176 2.5856 2.6537 40 2.7217 2.7897 2.8578 2.9258 2.9939 3.0619 3.1299 3.1980 3.2660 3.3341 50 3.4021 3.4701 3.5382 3.6062 3.6743 3.7423 3.8103 3.8784 3.9464 4.0145 60 4.0825 4.1505 4.2186 4.2866 4.3547 4.4227 4.4907 4.5588 4.6268 4.6949 70 4.7630 4.8310 4.8991 4.9671 5.0352 5.1031 5.1712 5.2393 5.3073 5.3754 80 5.4434 5.5114 5.5795 5.6475 5.7156 5.7836 5.8516 5.9197 5.9877 6.0558 90 6.1238 6.1918 6.2599 6.3279 6.3960 6.4640 6.5320 6.6001 6.6681 6.7362 100 6.8042 6 8722 6.9403 7.0083 7.0764 7.1444 7.2124 7.2805 7.3485 7.4166 Atmospheric Pressure into Pounds per Square Inch. Atm. pres. 1 2 3 4 5 6 7 8 9 Lb. in 2 Lb. in 2 Lb. in 2 Lb. in 2 Lb. in 2 Lb.in 2 Lb.in 2 Lb.in* Lb.in 2 Lb.in« 0.0000 14.697 29.393 44.090 58.787 73.483 88.180 102.87 117.57 132.27 10 146.97 161.67 176.36 191.06 205.76 220.45 235.15 249.84 264.54 279.24 20 293.93 308.63 323.32 338.02 352.72 367.41 382.11 396.80 411.50 426.20 30 440.90 455.60 470.29 484.99 499.69 514.38 529.08 543.77 558.47 573.17 40 587.87 602.57 617.26 631.96 646.66 661.35 676.05 690.74 705.44 720.14 50 734.83 749.53 764.22 778.92 793.62 808.31 823.01 837.70 852.40 867.10 60 881.80 896.50 911.19 925.89 940.59 955.28 969.98 984.67 999.37 1014.1 70 1028.7 1043.4 1058.1 1072.8 1087.5 1102.2 1116.9 1131.6 1146.3 1161.0 80 1175.7 1190.4 1205.1 1219.8 1234.5 1249.2 1263.9 1278.6 1293.3 1308.0 90 1322.7 1337.4 1352.1 1366.8 1381.5 1396.2 1410.9 1425.6 1439.3 1455.0 100 1469.7 1484.4 1499.1 1513.8 1528.5 1543.2 1557.9 1572.6 1586.3 1602.0 Pounds per Square Inch into Kilogrammes per Square Centimetre. Lbs. prin 2 . o * 2 3 4 5 6 7 8 9 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm 2 K.cm* 0.0000 0.0703 0.1406 0.2109 0.2812 0.3515 0.4218 0.4921 0.5625 0.6328 10 0.7031 0.7734 0.8437 0.9140 0.9843 1.0546 1.1249 1.1952 1.2655 1.3358 20 1.4062 1.4765 1.5468 1.6171 1.6874 1.7577 1.8280 1.8983 1.9686 2.0389 30 2.1092 2.1795 2.2498 2.3202 2.3905 2.4608 2.5311 2.6014 2.6717 2.7420 40 2.8123 2.8826 2.9529 3.0232 3.0935 3.1639 3.2342 3.3045 3.3748 3.4451 50 3.5154 3.5857 3.6560 3.7263 3.7966 3.8669 3.9372 4.0075 4.0779 4.1482 60 4.2185 4.2888 4.3591 4.4294 4.4997 4.5700 4.6403 4.7106 4.7809 4.8512 70 4.9216 4.9919 5.0622 5.1325 5.2028 5.2731 5.3434 5.4137 5.4840 5.5543 80 5.6246 5.6949 5.7652 5.8356 5.9059 5.9762 6.0465 6.1168 6.1871 6.2574 90 6.3277 6.3980 6.4683 6.5386 6.6089 6.6793 6.7496 6.8199 6.8902 6.9605 100 7.0308 7.1011 7.1714 7.2417 7.3120 7.3823 7.4526 7.5229 7.5933 7.6636 Kilogrammes per Square Centimetre into Pounds per Square Inch. K. per cm 2 . 1 2 3 4 5 6 7 8 9 Lb.in 2 Lb.in 2 Lb.in 2 Lb.in 2 Lb.in 2 Lb.in'- Lb.in 2 Lb.in 2 Lb.in 2 Lb.in» 0.0000 14.223 28.446 42.670 56.893 71.116 85.339 99.562 113.78 128.01 10 142.23 156.45 170.68 184.90 199.12 213.35 227.57 241.79 256.02 270.24 20 284.46 298.69 312.91 327.13 341.36 355.58 369.80 384.03 398.25 412.47 30 426.70 440.92 455.14 469.36 483.59 497.81 512.03 526.26 540.48 554.70 40 568.93 583.15 597.37 611.60 625.82 640.04 654.27 668.49 682.71 696.94 50 711.16 725.38 739.61 753.83 768.05 782.28 796.50 810.72 824.94 839.17 60 853.39 867.61 881.84 896.06 910.28 924.51 938.73 952.95 967.18 981.40 70 995.62 1009.8 1024.1 1038.3 1052.5 1066.7 1081.0 1095.2 1109.4 1123.6 80 1137.8 1152.1 1166.3 1180.5 1194.7 1209.0 1223.2 1237.4 1251.6 1265.9 90 1280.1 1294.3 1308.5 1322.7 1337.0 1351.2 1365.4 1379.6 1393.9 1408.1 100 1422.3 1436.5 1450.8 1465.0 1479.2 1493.4 1507.7 1521.9 1536.1 1550.3 7: J The Metis ic System. Conversion of English Pounds into Kilogrammes. £ug. lbs. 1 2 3 4 5 6 7 8 9 Kilo. Kilo. Kilo. Kilo. Kilo. Kilo. Kilo. Kilo. Kilo. Kilo. 0.000 0.453 0.907 1.361 1.814 2.268 2.722 3.175 3.629 4.082 10 4.536 4.989 5.443 5.897 6.350 6.804 7.258 7.711 8.165 8.618 20 9.072 9.525 9.979 10.43 10.89 11.34 11.79 12.25 12.70 13.15 30 13.61 14.06 14.52 14.97 1542 15.88 16.33 16.78 17.24 17.09 40 18.14 18.59 19.05 19.50 19.95 20.41 20.86 21.31 21.77 22.22 50 22.68 23.13 23.59 24.04 24.49 24.95 25.40 25.85 26.31 26.76 60 27.22 27.67 28.13 28.58 29.03 29.49 29.94 30.39 30.85 31.30 70 31.75 32.20 32.66 33.11 38.56 34.02 34.47 34.92 35.38 80 36.29 36.74 37.20 37.65 38.10 38.56 39.01 39.46 39.92 40.87 90 40.82 41.27 41.73 42.18 42.63 43.09 43.54 43.99 44.45 44.90 100 45.36 45.81 46.27 46.72 47.17 47.63 48.08 48.53 48.99 49. 1 1 Conversion < »f Kilogrammes into English Pounds. Fr. kilo. 1 2 3 4 5 6 7 8 9 Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. 0.000 2.205 4.410 6.615 8.820 11.02 13.23 15.43 17.64 19.84 10 22.05 24.25 26.46 28.67 30.87 33.07 35.28 37.48 39.69 41.89 20 44.10 46.30 48.51 50.72 52.92 55.12 57.33 59.53 61.74 63.94 30 66.15 68.35 70.56 72.77 74.97 77.17 79.38 81.58 83.79 85.99 40 88.20 90.40 92.61 94.82 97.02 99.22 101.4 103.6 105.8 108.0 50 110.2 112.5 114.6 116.8 119.0 121.2 123.4 125.6 127.8 130.0 60 132.3 134.5 136.7 138.9 141.1 143.3 145.5 147.7 149.9 152.1 70 154.3 156.5 158.7 160.9 163.1 165.3 167.5 169.7 171.9 174.1 80 176.4 178.6 180.8 183.0 185.2 187.4 189.6 191.8 194.0 196.2 90 198.4 200.6 202.8 205.0 207.2 209.4 211.6 213.8 216.0 218.2 100 220.5 222.7 224.9 227.1 229.3 231.5 233.7 235.9 238.1 240.3 Conversion of English Tons into Metric Tons. Eng. tons. | . 2 | 3 4 S 6 7 8- 9 M. ton M. ton M. ton M. ton M.ton M.ton M.ton M.ton M.ton M.ton 0.000 1.016 2.032 3.048 4.064 5.080 6.096 7.112 8.128 9.144 10 10.16 11.18 12.19 13.21 14.12 15.24 16.26 17.27 18.29 19.30 20 20.32 21.34 22.35 23.37 24.38 25.40 26.42 27.43 28.45 29.46 50 30.48 31.50 32.51 33.53 34.54 35.56 36.58 37.59 38.61 39.62 40 40.64 41.66 42.67 43.69 44.70 45.74 46.74 47.75 48.77 49.78 50 50.80 51.82 52.83 53.85 64.86 55.88 56.90 57.90 58.93 59.94 60 60.96 61.97 62.99 64.01 65.02 66.04 67.06 68.07 69.09 70.10 70 71.12 72.14 73.15 74.17 75.18 76.20 77.22 78.23 79.25 80.26 80 81.28 82.29 83.31 84.33 85.34 86.36 87.38 88.39 89.41 90.42 90 91.44 92.46 93.47 94.49 95.50 96.52 97.54 98.55 99.57 100.6 100 101.6 102.6 103.6 104.6 105.7 106.7 107.7 108.7 109.7 110.7 Conversion of Metric Tons Into English Tons . Fr. m. ton. 1 2 3 4 5 6 t 8 9 E. ton E. ton E. ton E. ton E. ton E. ton E. ton'E. ton E. ton E. ton 0.000 0.984 1.969 2.953 3.937 4.921 5.906 6.890 7.874 8.858 10 9.843 10.83 11.81 12.79 13.78 14.76 15.75 16.73 17.72 18.70 20 19.69 20.67 21.66 22.64 23.63 24.61 25.60 26.58 27.56 28.55 30 29.53 30.51 31.50 32.48 33.47 34.45 35.44 36.42 37.40 38.39 40 39.37 40.35 41.34 42.32 43.31 44.29 45.28 46.26 47.24 48.23 50 49.21 50.19 51.18 52.16 53.15 54.13 55.12 56.10 57.08 58.07 60 59.06 60.04 61.03 62.01 63.00 63.98 64.97 65.95 66.93 67.92 70 68.90 69.88 70.87 71.85 72.84 73.82 74.81 75.79 76.77 77.76 80 78.74 79.72 80.71 81.69 82.68 83.66 84.65 85.63 86.61 87.60 90 88.58 89.56 90.55 91.53 92.52 93.50 94.49 95.47 96.45 97.44 100 98.43 99.41 100.4 101.4 102.4 103.3 104.3 105.3 106.3 107.3 The Metric System. 735 Conversion of English Ounces Avoirdupois into French Grammes. Eng. ozs. 1 | 2 | 3 4 | . | 6 ' 8 | 9 Grams Grams, Grams Grams Grams Grams Grams Grams Grams Grams 0.0000 28.348 56.697 j 85.046 113.39 141.74 170.09 198.44 226.79 255.14 10 283.48 311.83 340.18 368.52 396.87 425.22 453.57 481.92 510.27 538.62 20 566.97 595.32 623.67 652.01 680.36 708.71 737.06 765.41 793.76 822.11 30 850.46 878.81 907.16 935.50 963.85 992.20 1020.5 1048.9 1077.2 1105.6 40 1133.9 1162.2 1190.6 1218.9 1247.3 1275.6 1304.0 1332.3 1360.7 1389.0 50 1417.4 1445.7 1474.1 1502.4 1530.8 1559.1 1587.5 1615.8 1644.2 1672.5 60 1700.9 1729.2 1756.6 1785.9 1814.3 1842.9 1871.0 1899.3 1927.7 1956.0 70 1984.4 2012.7 2041.1 2079.4 2097.8 2126.1 2154.5 2182.8 2211.2 2239.5 80 2267.9 2296.2 2324.6 2352.9 2381.3 2409.6 2438.0 2466.3 2494.7 2523.0 90 2551.4 2579.7 2608.1 2636.4 2664.8 2693.1 2721.5 2739.8 2778.2 2806.5 100 2834.8 2863.1 2891.5) 2919.8 2948.2 2976.5 3004.9 3033.2 3061.6 3089.9 Conversion of French Grammes into English Ounces Avoirdupois. Fr. grams. 1 2 3 4 5 6 7 8 9 Ozs. Ozs. Ozs. Ozs. Ozs. Ozs. Ozs. Ozs. Ozs. Ozs. 0.0000 0.0353 0.0705 0.1058 0.1411 0.1768 0.2116 0.2469 0.2822 0.3175 10 0.3527J 0.3880 0.4232 0.4585 0.4938 0.5295 0.5643 0.5996 0.6349 0.6702 20 0.7055 0.7408 0.7760 0.8113 0.8466 0.8823 0.9171 0.9524 0.9877 1.0230 30 1.0582, 1.0935 1.1287 1.1640 1.1993 1.2350 1.2698 1.3051 1.3404 1.3757 40 1.4110 1.4463 1.4815 1.5168 1.5521 1.5878 1.6226 1.6579 1.6932 1.7285 50 1.7687 1.8040 1.8392 1.8745 1.9098 1.9455 1.9803 2.01-56 2.0509 2.0862 60 2.1165 2.1518 2.1870 2.2223 2.2576 2.2933 2.3281 2.3634 2.3987 2.4340 70 2.4692 2.5045 2.5397 2.5750 2.6103 2.6460 2.6808 2.7161 2.7514 2.7867 80 2.8220 2.8573 2.8925 2.9278 2.9631 2.9988 3.0336 3.0689 3.1042 3.1395 90 3.1747 3.2100 3.2452 3.2805 3.3158 3.3515 3.3863 3.4216 3.4569 3.4922 100 3.5275 3.5628 3.5980 3.6333 3.6686 3.7043 3.7391 3.7744 3.8097 3.8450 Conversion of English Grains Troy into French Grammes. Eng. grains 12 3 4 5 6 7 8 9 Grams Grams Grams Grams Grams Grams Grams Grams Grams Grams 0.0000! 0.0648 0.1296 0.1944 0.2592 0.3240 0.3888 0.4535 0.5183 0.5831 10 0.6479| 0.7127 0.7775 0.84231 0.9071 0.9719 1.0367 1.1014 1.1662 1.2310 20 1.2959i 1.3607 1.4255 1.4903 1.5551 1.6199 1.6847 1.7494 1.8142 1.8890 30 1.9438: 2.0086 2.0734 2.1382 2.2030 2.2678 2.3326 2.3973 2.4621 2.5269 40 2.5918! 2.6566 2.7214 2.7862 2.8510 2.9158 2.9806 3.0453 3.1101 3.1749 50 3.2398 3.3046 3.3694 3.4342 3.4990 3.5638 3.6286 3.6933 3.7581 3.8229 60 3.8877 1 3.9525 4.0173 4.0821 4.1469 4.2117 4.2765 4.3412 4.4060 4.4708 70 4.5357! 4.6005 4.6653 4.7301 4.7949 4.8597 4.9245 4.9892 5.0540 5.1188 80 5.18301 5.2484 5.3132 5.3780 5.4428 5.5076 5.5724 5.6371 5.7019 5.7667 90 5.8316 ' 5.8964 5.9612 6.0260 6.0908 6.1556 6.2204 6.2851 6.3499 6.4147 100 6.4795 6.5443 6.6091 6.6739 6.7387 6.8035 6.8683 6.9330 6.9978 7.0626 Conversion of French Grammes into English Grains Troy. Fr. grams. 1 2 3 4 5 6 7 8 9 Grs. Grs. Grs. Grs. Grs. Grs. j Grs. Grs. Grs. Grs. 0.0000 15.433 30.866 46.299 61.732 f 7.165 912.599 108.03 123.46 138.90 10 154.33 169.76 185J9 200.63 216.06 231.49! 246.93 262.36 277.79 293.23 20 308.66 324.09 339.52 354.96 370.39 385.82 401.26 416.69 432.12 447.56 30 462.99 478.42 493.86 509.29 524.72 540.15 555.59 571.02 586.45 601.89 40 617.65 632.75 648.18 663.95! 679.38 694.81 709.92 725.35 740.78 756.22 50 771.65 787.08 802.52 817.95 833.38 848.82 864.25 879.68 895.11 910.55 60 925.99 941.42 956.85 972.29 987.72 1003.1 1018.6 1034.0 1049.4 1064.9 70 1080.3 1095.7 1111.2 1126.6 1142.0J 1157.5 1172.9 1188.3 1203.7 1219.2 80 1234.6 1250.0 1265.5 1280.1 1296.311311.8 1327.2 1342.6 1358.1 1373.5 90 1389.0 1404.4 1419.8 1435.3 1450.7| 1466.1 1481.6 1497.0 1512.4 1527.9 100 1543.3 1558.7 1574.1 1589.6 1605.0 1620.4 1635.9 1651.3 1666.7 1682.2 736 The Metric System. Horse-power into ChevaUvapeur H.-power. 1 2 3 4 5 6 7 8 9 C.-v. C.-T. C.-v. C.-v. C.-v. C.-v. C.-v. C.-v. C.-v. C.-v. 0.0000 1.0136 2.0272 3.0408 4.0544 5.0680 6.0816 7.0952 8.1088 9.1224 10 10.136 11.150 12.163 13.176 14.190 15.204 16.218 17.231 18.245 19.258 20 20.272 21.308 22.299 23.313 24.326 25.240 26.354 27.367 28.381 29.394 80 30.408 31.422 32.435 33.449 34.462 35.476 36.490 37.503 38.517 39.530 40 40.544 41.557 42.571 43.585 44.598 45.612 46.626 47.639 48.653 49.666 50 50.680 51.693 52.707 53.721 54.734 55.748 56.762 57.775 58.789 59.802 60 60.816 61.829 62.843 63.857 64.870 65.884 66.898 67.911 68.925 69.938 70 70.952 71.965 72.979 73.993 75.006 76.020 77.034 78.047 79.061 80.074 80 81.088 82.102 83.115 84.129 85.142 86.156 87.170 88.183 89.197 90.210 90 91.224 92.338 93.251 94.265 95.278 96.292 97.306 98.319 99.333 100.34 100 101.36 102.37 103.30 104.40 105.41 106.43 107.44 108.45 109.47 110.48 ChevaUvapeur into Horse-power Chev.-vap. 1 2 3 4 5 6 7 8 9 H.-p. H.-p. H.-p. H.-p. H.-p. H.-p. H.-p. H.-p. H.-p. H.-p. 0.0000 0.9863 1.9726 2.9589 3.9452 4.9315 5.9178 6.9041 7.8904 8.8767 10 9.8630 10.849 11.835 12.822 13.808 14.794 15.781 16.767 17.753 18.739 20 19.726 20.712 21.698 22.685 23.671 24.657 25.644 26.630 27.616 28.602 30 29.589 30.575 31.561 32.548 33.534 34.520 35.507 36.493 37.479 38.465 40 39.452 40.438 41.424 42.411 43.397 44.383 45.370 46.356 47.342 48.328 50 49.315 50.301 51.287 52.274 53.260 54.246 55.233 56.219 57.205 58.191 60 59.178 60.164 61.150 62.137 63.123 64.109 65.096 66.082 67.068 68.054 70 69.041 70.027 71.013 71.990 72.986 73.972 74.959 75.945 76.941 77.917 80 78.904 79.890 80.876 81.863 82.849 83.835 84.822 85.808 86.794 87.780 90 88.767 89.753 90.739 91.726 92.712 93.698 94.785 95.671 96.657 97.643 100 98.630 99.616 100.60 101.59 102.57 103.56 104.55 105.53 106.52 107.50 Foot-pounds into Kilogrammetres. Foot-lba. 1 | 2 3 4 I 5 6 7 8 9 Kgm. Kgm. 1 Kgm. Kgm. Kgm. Kgm. Kgm. Kgm. Kgm. Kgm. 0.0000 0.13820.2764 0.4146 0.5528 0.6910 0.8292 0.9674 1.1056 1.2438 10 1.3820 1.5202 1.6584 1.7966 1.9348 2.0731 2.2112 2.3494 2.4876 2.6259 20 2.7640 2.9022 3.0404 3.1786 3.3168 3.4552 3.5933 3.7315 3.8696 4.0078 30 4.1400 4.2842 4.4224 4.5606 4.6988 4.8370 4.9751 5.1134 5.2517 5.3897 40 5.5280 5.6666 5.8044 5.9426 6.0808 6.2191 6.3572 6.4954 6.6336 6.7718 50 6.9100 7.0482 7.1864 7.3246 7.4628 7.6010 7.7393 7.8775 8.0155 8.1538 60 8.2920 8.4303 8.5684 8.7066 8.8448 8.9830 9.1212 9.2594 9.3976 9.5359 70 9.6740 9.8122 9.9504 10.088 10.227 10.365 10.503 10.641 10.779 10.918 80 11.056 11.194 11.322 11.570 11.609 11.747 11.885 12.023 12.161 12.300 90 12.438 12.576 12.714 12.855 12.991 13.129 13.267 13.405 13.544 13.682 100 13.820 13.958 14.096 14.235 14.373 14.511 14.649 14.787 14.925 14.064 Kilogrammetres into Poot-pounds Kgm. 1 2 3 4 5 6 7 8 9 Ft. -lb. Ft.-lb. Ft.-lb. Ft.-lb. Ft. -lb. Ft. -lb. Ft.-lb. Ft.-lb. Ft. -lb. Ft.-lb. 0.0000 7.2334 14.467 21.700 28.934 36.166 43.400 50.734 57.868 65.100 10 72.334 79.567 87.101 94.034 101.27 108.50 115.74 123.07 130.20 137.43 20 144.67 151.90 158.43 166.37 173.60 180.84 188.08 195.40 202.54 209.77 30 217.00 224.23 231.77 238.70 245.93 253.17 260.41 267.73 274.87 282.10 40 289.34 2%. 57 304.11 311.04 318.27 325.50 332.75 340.07 347.21 354.44 50 361.66 368.89 376.43 383.36 390.59 397.82 405.07 412.39 419.53 426.76 60 434.00 441.23 448.77 455.70 462.93 470.17 477.41 484.73 491.87 499.10 70 507.34 514.57 522.11 529.04 536.27 543.50 550.75 558.07 565.21 572.44 80 578.68 585.91 593.45 599.38 607.61 614.85 622.09 629.41 636.55 643.78 90 651.00 658.23 665.77 672.70 679.93 687.17 694.41 701.73 708.87 716.10 100 723.34 730.57 738.11 745.04 752.27 759.51 76675 774.07 781.21 788.44 The Metric System. 737 Conversion of Foot-tons into Tonnes- metres Foot-tons. 1 2 3 4 5 6 7 8 9 T.-m. T.-m. T.-m. T.-m. T.-m. T.-m. T.-m. T.-m. T.-m. T.-m. 0.0000 0.3097 0.6194 0.9291 1.2382 1.5484 1.8581 2.1678 2.4775 2.7872 10 3.0969 3.3166 3.7163 4.0260 4.3356 4.6453 4.9550 5.2667 5.5744 5.8841 20 6.1938 6.4135 6.8132 7.1229 7.4325 7.7422 8.0519 8.3636 8.6713 8.9810 30 9.2906 9.6003 9.9100 10.219 10.529 10.839 11.149 11.460 11.768 12.078 40 12.387 12.697 13.006 13.316 13.626 13.935 14.245 14.557 14.864 15.174 50 15.484 15.794 16.103 16.413 16.723 17.032 17.342 17.654 17.961 18.271 60 18.581 18.891 19.200 19.510 19.820 20.129 20.439 20.751 21.058 21.368 70 21.678 21.988 22.297 22 607 22.917 23.226 23.536 23.848 24.155 24.465 80 24.775 25.085 25.394 25.704 26.014 26.323 26.633 26.945 27.252 27.562 90 27.872 28.182 28.491 28.801 29.111 29.420 29.730 30.042 30.349 30.659 100 30.969 31.279 31.588 31.898 32.208 32.517 32.827 33.139 33.446 33.756 Conversion of Tonnes -metres into Foot-tons T.-metre8. 1 2 3 4 5 6 7 8 9 F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. F.-tn. 0.0000 3.2290 6.4581 9.6871 12.916 16.145 19.374 22.603 25.832 29.061 10 32.290 35.519 38.758 41.977 45.206 48.435 51.664 54.893 58.122 61.351 20 64.581 67.810 71.049 74.268 77.497 80.726 83.955 87.184 90.413 93.642 30 96.871 100.10 103.34 106.56 109.79 113.01 116.24 119.47 122.70 125.93 40 129.16 133.39 135.63 138.85 142.07 145.30 148.53 151.76 154.99 158.22 50 161.45 164.68 167.92 171.14 174.36 177.59 180.82 184.05 187.28 190.51 60 193.74 196.97 200.21 203.43 206.65 209.88 213.11 216.34 219.57 222.80 70 226.03 229.26 232.50 235.72 238.94 242.17 245.40 248.63 251.86 255.09 80 258.32 261.55 264.79 268.01 271.23 274.46 277.69 280.92 284.15 287.38 90 290.61 293.84 297.08 300.30 303.52 306.75 309.98 313.21 316.44 319.67 100 322.90 326.13 329.37 332.59 335.81 339.04 342.27 345.50 348.73 351.96 British Thermal Units into French Calories. B. T. U. 1 2 3 4 5 6 7 8 9 Cal. Cal. Cal. Cal. Cal. Cal. Cal. Cal. Cal. Cal. 0.0000 0.2520 0.5040 0.7560 1.0080 1.2600 1.5120 1.7640 2.0160 2.26SO 10 2 5200 2.7720 3.0240 3.2760 3.5280 3.7800 4.0320 4.2840 4.5360 4.7880 20 5.0399 5.2919 5.5439 5.7959 6.0478 6.2699 6.5419 6.8039 7.0559 7.3079 30 7.5600 7.8120 8.0640 8.3160 8.5680 8.8200 9.0720 9.3340 9.5760 9.8280 40 10.080 10.332 10.584 10.836 11.088 11.340 11.512 11.844 12.096 12.348 50 12.600 12.852 13.104 13.356 13.608 13.860 14.112 14.364 14.616 14.868 60 15.120 15.372 15.624 15.876 16.128 16.380 16.632 16.884 17.136 17.388 70 17.640 17.892 18.144 18.396 18.648 18.900 19.152 19.404 19.656 19.908 80 20.160 20.412 20.664 20.916 21.168 21.420 21.672 21.924 22.176 22.428 90 22.680 22.932 23.184 23.436 23.688 23.940 24.192 24.444 24.696 24.948 100 25.200 25.452 25.704 25.956 26.208 26.460 26.712 26.964 27.216 27.468 French Calories Into British Thermal Units. Calories. 1 2 3 4 5 6 7 8 9 T. U. T. U. T. U. T. U. T. U. T. U. T. U. T. U. T. U. T. U. 0.0000 3.9683 7.9366 11.905 15.873 19.842 23.810 27.778 31.746 35.715 10 39.683 43.651 47.620 51.598 55.520 59.525 63.493 67.461 71.429 75.398 20 79.366 83.334 87.303 91.271 95.203 99.208 103.17 107.14 111.11 115 08 30 119.05 123.02 126.98 130.95 134.89 138.89 142.86 146.83 150.80 154.7? 40 158.73 162.70 166.66 170.62 174.57 178.57 182.54 186.51 190.48 194.45 50 198.42 202.39 206.35 210.39 214.26 218.26 222.23 226.20 230.16 234.14 60 238.10 242.07 246.03 250.00 253.94 258.94 261.91 265.88 269.85 273.82 70 277.78 281.75 285.72 289.68 293.62 297.62 301.59! 305.56 309.53 313.50 80 317.46 321.43 325.40 329.36 33S.29 337.30 341.271 345.24 349.20 353.18 90 357.15 361.12 365.09 369.05 372.98 376.99 380.96 384.93 388.90 392.87 100 396.83 400.80 404.77 408.73 412.67 416.67 420.64 424.61 428.58 432.55 738 Natural Trigonometrical Functions 6 j ft K S Sine. VER8. Cos. Cose- cant. Tang. Co- tang. Se- cant. Vers. Sin. Co- sine. 9 6 K ft ~~0 .00000 1.0000 Infin. .00000 Inlin. 1.0000 .00000 1.0000 10 .00291 .99709 343.77 .00291 343.77 1.0000 .00000 .99999 50 90 20 .00582 .99418 171.89 .00582 171.88 1.0000 .00002 .99998 40 30 .00873 .99127 114.59 .00873 1 14.59 1.0000 .00004 .99996 30 40 .01103 .98836 85.946 .01164 85.940 1.0001 .00007 .99993 20 50 .01454 .98546 68.757 .01454 68.750 1.0001 .00010 .99989 10 1 .01745 .98255 57.299 .01745 57.290 1.0001 .00015 .99985 89 10 .02036 .97964 49.114 .02036 49.104 1.0002 .00021 .99979 50 20 .02327 .97673 42.976 .02327 42.964 1.0003 .00027 .99973 40 30 .02618 .97382 38.201 .02618 38.188 1.0003 .00034 .99966 30 40 .02908 .97091 34.382 .02910 34.368 1.0004 .00042 .99958 20 50 .03199 .96801 31.257 .03201 31.241 1.0005 .00051 .99949 10 2 .03490 .96510 28.654 .03492 28.636 1.0006 .00061 .99939 88 10 .03781 .96219 26.450 .03783 26.432 1.0007 .00071 .99928 50 20 .04071 .95929 24.562 .04075 24.542 1.0008 .00083 .99917 40 30 .04362 .95638 22.925 .04366 22.904 1.0009 .00095 .99905 30 40 .04652 .95347 21.494 .04657 21.470 1.0011 .00108 .99892 20 50 .04943 .95057 20.230 .04949 20.205 1.0012 .00122 .99878 10 3 .05234 .94766 19.107 .05241 19.081 1.0014 .00137 .99863 87 10 .05524 .94476 18.103 .05532 18.075 1.0015 .00153 .99847 50 20 .05814 .94185 17.198 .05824 17.169 1.0017 .00169 .99831 40 30 .06105 .93895 16.380 .06116 16.350 1.0019 .00186 .99813 30 40 .06395 .93605 15.637 .06408 15.605 1.0020 .00205 .99795 20 50 .06685 .93314 14.958 .06700 14.924 1.0022 .00224 .99776 10 4 .06976 .93024 14.335 .06993 14.301 1.0024 .00243 .99756 86 10 .07266 .92734 13.763 .07285 13.727 1.0026 .00264 .99736 50 20 .07556 .92444 13.235 .07577 13.197 1.0029 .00286 .99714 40 30 .07846 .92154 12.745 .07870 12.706 1.0031 .00308 .99692 30 40 .08136 .91864 12.291 .08163 12.250 1.0033 .00331 .99668 20 50 .08426 .91574 11.868 .08456 11.826 1.0036 .00356 .99644 10 5 .08715 .91284 11.474 .08749 11.430 1.0038 .00380 .99619 85 10 .09005 .90995 11.104 .09042 11.059 1.0041 .00406 .99594 50 20 .09295 .90705 10.758 .09335 10.712 1.0043 .00433 .99567 40 30 .09584 .90415 10.433 .09629 10.385 1.0046 .00460 .99540 30 40 .09874 .90126 10.127 .09922 10.078 10049 .00489 .99511 20 50 .10163 .89836 9.8391 .10216 9.7882 1.0052 .00518 .99482 10 6 .10453 .89547 9.5668 .10510 9.5144 1.0055 .00548 .99452 84 10 .10742 .89258 9.3092 .10805 9.2553 1.0058 .00579 .99421 50 20 .11031 .88969 9.0651 .11099 9.0098 1.0061 .00110 .99390 40 30 .11320 .88680 8.8337 .11393 8.7769 1.0065 .00643 .99357 30 40 .11609 .88391 8.6138 .11688 8.5555 1.0068 .00676 .99324 20 50 .11898 .88102 8.4046 .11983 8.3449 1.0071 .00710 .99290 10 7 .12187 .87813 8.2055 .12278 8.1443 1.0075 .00745 .99255 83 10 .12476 .87524 8.0156 .12574 7.9530 1.0079 .00781 .99219 50 20 .12764 .87236 7.8344 .12869 7.7703 1.0082 .00818 .99182 40 30 .13053 .86947 7.6613 .13165 7.5957 1.0086 .00855 .99144 30 40 .13341 .86659 7.4957 .13461 7.4287 1.0090 .00894 .99106 20 50 .13629 .86371 7.3372 .13757 7.2687 1.0094 .00933 .99067 10 8 .13917 .86083 7.1853 .14054 7.1154 1.0098 .00973 .99027 82 10 .14205 .85795 7.0396 .14351 6 9682 1.0102 .01014 .98986 50 20 .14493 .85507 6.8998 .14648 6.8269 1.0107 .01056 .98944 40 30 .14781 .85219 6.7655 .14945 6.6911 1.0111 .01098 .98901 30 40 .15068 .84931 6.6363 .15243 6.5605 1.0115 .01142 .98858 20 50 .15356 .84644 6.5121 .15540 6.4348 1.0120 .01186 .98814 10 9 .15643 .84356 6.3924 .15838 6.3137 1.0125 .01231 .98769 81 Co- Vers. Se- Co- Tan- Cose- Vers Sine. Sine. Sin. cant tang. gent. cant. Cos. Natural Trigonometrical Functions. 739 6 w Q g s Sine. Vers. Cos. Cose- cant. Tang. Co- TANG. Se- cant. 1.0125 Vers. Sin. Co- sine. 'a 6 ~9~ .15643 .84356 6.3924 .15838 6.3137 .01231 .98769 81 10 .15931 .84069 6.2772 .16137 6.1970 1.0129 .01277 .98723 50 20 .16218 .83782 6.1661 .16435 6.0844 1.0134 .01324 .98676 40 30 .16505 .83495 6.0588 .16734 5.9758 1.0139 .01371 .98628 30 40 .16791 .83208 5.9554 .17033 5.8708 1.0144 .01420 .98580 20 50 .17078 .82922 5.8554 .17333 5.7694 1.0149 .01469 .98531 10 10 .17365 .82635 5.7588 .17633 5.6713 1.0154 .01519 .98481 80 10 .17651 .82349 5.6653 .17933 5.5764 1.0159 .01570 .98430 50 20 .17937 .82062 5.5749 .18233 5.4845 1.0165 .01622 .98378 40 30 .18223 .81776 5.4874 .18534 5.3955 1.0170 .01674 .98325 30 40 .18509 .81490 5.4026 .18835 5.3093 1.0176 .01728 .98272 20 50 .18795 .81205 5.3205 .19136 5.2257 1.0181 .01782 .98218 10 11 .19081 .80919 5.2408 .19438 5.1445 1.0187 .01837 .98163 79 10 .19366 .80634 5.1636 .19740 5.0658 1.0193 .01893 .98107 50 20 .19652 .80348 5.0886 .20042 4.9894 1.0199 .01950 .98050 40 30 .19937 .80063 5.0158 .20345 4.9151 1.0205 .02007 .97992 30 40 .20222 .79778 4.9452 .20648 4.8430 1.0211 .02066 .97934 20 50 .20506 .79493 4.8765 .20952 4.7728 1.0217 .02125 .97875 10 12 .20791 .79209 4.8097 .21256 4.7046 1.0223 .02185 .97815 78 10 .21076 .78924 4.7448 .21560 4.6382 1.0230 .02246 .97754 50 20 .21360 .78640 4.6817 .21864 4.5736 1.0236 .02308 .97692 40 30 .21644 .78356 4.6202 .22169 4.5107 1.0243 .02370 .97630 30 40 .21928 .78072 4.5604 .22475 4.4494 1.0249 .02434 .97566 20 50 .22211 .77788 4.5021 .22781 4.3897 1.0256 .02498 .97502 10 13 .22495 .77505 4.4454 .23087 4.3315 1.0263 .02563 .97437 77 10 .22778 .77221 4.3901 .23393 4.2747 1.0270 .02629 .97371 50 20 .23061 .76938 4.3362 .23700 4.2193 1.0277 .02695 .97304 40 30 .23344 .76655 4.2836 .24008 4.1653 1.0284 .02763 .97237 30 40 .23627 .76373 4.2324 .24316 4.1127 1.0291 .02831 .97169 20 50 .23910 .76090 4.1824 .24624 4.0611 1.0299 .02900 .97099 10 14 .24192 .75808 4.1336 .24933 4.0108 1.0306 .02970 .97029 76 10 .24474 .75526 4.0859 .25242 3.9616 1.0314 .03041 .96959 50 20 .24756 .75244 4.0394 .25552 3.9136 1.0321 .03113 .96887 40 30 .25038 .74962 3.9939 .25862 3.8667 1.0329 .03185 .96815 30 40 .25319 .74680 3.9495 .26172 3.8208 1.0337 .03258 .96741 20 50 .25601 .74399 3.9061 .26483 3.7759 1.0345 .03332 .96667 10 15 .25882 .74118 3.8637 .26795 3.7320 1.0353 .03407 .96592 75 10 .26163 .73837 3.8222 .27107 3.6891 1.0361 .03483 .96517 50 20 .26443 .73556 3.7816 .27419 3.6470 1.0369 .03560 .96440 40 30 .26724 .73276 3.7420 .27732 3.6059 1.0377 .03637 .96363 30 40 .27004 .72996 3.7031 .28046 3.5656 1.0386 .03715 .96285 20 50 .27281 .72716 3.6651 *. 28360 3.5261 1.0394 .03794 .96206 10 16 .27564 .72436 3.6279 .28674 3.4874 1.0403 .03874 .96126 74 10 ,27843 .72157 3.5915 .28990 3.4495 1.0412 .03954 .96045 50 20 .28122 .71877 3.5559 .29305 3.4124 1.0420 .04036 .95964 40 30 .28401 .71608 3.5209 .29621 3.3759 1.0429 .04118 .95882 30 40 .28680 .71320 3.4867 .29938 3.3402 1.0438 .04201 .95799 20 50 .28959 .71041 3.4532 .30255 3.3052 1.0448 .04285 .95715 10 17 .29237 .70763 3.4203 .30573 3.2708 1.0457 .04369 .95630 73 10 .29515 .70485 3.3881 .30891 3.2371 1.0466 .04455 .95545 50 20 .29793 .70207 3.3565 .31210 3.2041 1.0476 .04541 .95459 40 30 .30070 .69929 3.3255 .31530 3.1716 1.0485 .04628 .95372 30 40 .30348 .69652 3.2951 .31850 3.1397 1.0495 .04716 .95284 20 50 .30625 .69375 3.2653 .32171 3.1084 1.0505 .04805 .95195 10 18 .30902 .69098 3.2361 .32492 3.0777 1.0515 .04894 .95106 72 Co- Vers. SE- Co- Tan- Cose- Vers. Sine. sine. Sin. cant. TANG. gent. cant. Cos. 740 Natural Trigonometrical Functions. 6 $ kj Sine. .30902 Vers. Cos. "(KKMW Cose- cant Tang Co- TANG Se- cant V i i:s Sin. Co- sine. .05106 v. W ft 18 3.2361 .32492 3.0777 1.0515 .04894 72 10 .31178 .68822 3.2074 .32814 3.0475 1.0525 .04985 .95015 M 20 .31454 .68545 3.1792 .33136 3.0178 1.0535 .05076 .94924 40 30 .31730 .68269 3.1515 .33459 2.9887 1.0545 .05168 .94832 80 40 .32006 .67994 3.1244 .33783 2.9600 1.0555 .05260 .94740 20 50 .32282 .67718 3.0977 .34108 2.9319 1.0566 .05354 .94646 to 19 .32557 .67443 3.0715 .34433 2.9042 1.0576 .05448 .94552 71 10 .32832 .67168 3.0458 .34758 2.8770 1.0587 .05543 .94457 50 20 .33106 .66894 3.0206 .35085 2.8502 1.0598 .05639 .94361 to 30 .33381 .66619 2.9957 .35412 2.8239 1.0608 .05736 .94264 80 40 .33655 .66345 2.9713 .35739 2.7980 1.0619 .05833 .94167 20 50 .33928 .66071 2.9474 .36068 2.7725 1.0630 .05932 .94068 10 20 .34202 .65798 2.9238 .36397 2.7475 1.0642 .06031 .93969 70 10 .34475 .65525 2.9006 .36727 2.7228 1.0653 .06131 .93869 50 20 .34748 .65252 2.8778 .37057 2.6985 1.0664 .06231 .93769 40 30 .35021 .64979 2.8554 .37388 2.6746 1.0676 .06333 .93667 30 40 .35293 .64707 2.8334 .37720 2.6511 1.0688 .06435 .93565 20 50 .35565 .64435 2.8117 .38053 2.6279 1.0699 .06538 .93462 10 21 .35837 .64163 2.7904 .38386 2.6051 1.0711 .06642 .93358 69 10 .36108 .63892 2.7694 .38720 2.5826 1.0723 .06747 .93253 60 20 .36379 .63621 2.7488 .39055 2.5605 1.0736 .06852 .93148 40 30 .36650 .63350 2.7285 .39391 2.5386 1.0748 .06958 .93042 80 40 .36921 .63079 2.7085 .39727 2.5171 1.0760 .07065 .92935 20 50 .37191 .62809 2.6888 .40065 2.4960 1.0773 .07173 .92827 10 22 .37461 .62539 2.6695 .40403 2.4751 1.0785 .07282 .92718 68 10 .37730 .62270 2.6504 .40741 2.4545 1.0798 .07391 .92609 50 20 .37999 .62000 2.6316 .41081 2.4342 1.0811 .07501 .92499 40 30 .38268 .61732 2.6131 .41421 2.4142 1.0824 .07612 .92388 80 40 .38537 .61463 2.5949 .41762 2.3945 1.0837 .07724 .92276 20 50 •38805 .61195 2.5770 .42105 2.3750 1.0850 .07836 .92164 10 23 .39073 .60927 2.5593 .42447 2.3558 1.0864 .07949 .92050 67 10 .39341 .60659 2.5419 .42791 2.3369 1.0877 .08063 .91936 50 20 .39608 .60392 2.5247 .43136 2.3183 1.0891 .08178 .91822 40 30 .39875 .60125 2.5078 .43481 2.2998 1.0904 .08294 .91706 30 40 .40141 .59858 2.4912 .43827 2.2817 1.0918 .08410 .91590 20 50 .40408 .59592 2.4748 .44175 2.2637 1.0932 .08527 .91472 10 24 .40674 .59326 2.4586 .44523 2.2460 1.0946 .08645 .91354 66 10 .40939 .59061 2.4426 .44872 2.2286 1.0961 .08764 .91236 50 20 .41204 .58795 2.4269 .45222 2.2113 1.0975 .08884 .91116 40 30 .41469 .58531 2.4114 .45573 2.1943 1.0989 .09004 .90996 80 40 .41734 .58266 2.3961 .45924 2.1775 1.1004 .09125 .90875 20 50 .41998 .58002 2.3811 .46277 2.1609 1.1019 .09247 .90753 10 25 .42262 .57738 2.3662 .46631 2.1445 1.1034 .09369 .90631 65 10 .42525 .57475 2.3515 .46985 2.1283 1.1049 .09492 .90507 BO 20 .42788 .57212 2.3371 .47341 2.1123 1.1064 .09617 .90383 40 30 .43051 .56949 2.3228 .47697 2.0965 1.1079 .09741 .90258 30 40 .43313 .56686 2.3087 .48055 2.0809 1.1095 .09867 .90133 20 50 .43575 •56424 2.2949 .48414 2.0655 1.1110 .09993 .90006 10 26 .43837 .56163 2.2812 .48773 2.0503 1.1126 .10121 .89879 64 10 .44098 .55902 2.2676 .49134 2.0352 1.1142 .10248 .89751 50 20 .44359 .55641 2.2543 .49495 2.0204 1.1158 .10377 .89623 40 30 .44620 .55380 2.2411 .49858 2.0057 1.1174 .10506 .89493 80 40 .44880 .55120 2.2282 .50222 1.9912 1.1190 .10637 .89363 20 50 .45140 .54860 2.2153 .50587 1.9768 1.1207 .10768 .89232 10 27 .45399 .54601 2.2027 .50952 1.9626 1.1223 .10899 .89101 63 Co- Vers. Se- Co- Tan. Cose- Vers. Sine. sine. Sin. cant. TANG. GENT. cant. Cos. Natural Trigonometrical Functions 741 6 pa fc £ Sine. Vers. Cos. Cose- cant. Tang. Co. TANG. Se- cant. Vers. Sin. Co- sine. g S 6 27 .45399 .54601 2.2027 .50952 1.9626 1.1223 .10899 .89101 63 10 .45658 .54:542 2.1902 .51319 1.9486 1.1240 .11032 .88968 50 20 .45917 .54083 2.1778 .51687 1.9347 1.1257 .11165 .88835 40 30 .46175 .53825 2.1657 .52057 1.9210 1.1274 .11299 .88701 30 40 .46433 .53567 2.1536 .52427 1.9074 1.1291 .11434 .88566 20 50 .46690 .53310 2.1418 .52798 1.8940 1.1308 .11569 .88431 10 28 .46947 .53053 2.1300 .53171 1.8807 1.1326 .11705 .88295 62 10 .47204 .52796 2.1185 .53545 1.8676 1.1343 .11842 .88158 50 20 .47460 .52540 2.1070 .53919 1.8546 1.1361 .11980 .88020 40 30 .47716 .52284 2.0957 .54295 1.8418 1.1379 .12118 .87882 30 40 .47971 .52029 2.0846 .54673 1.8291 1.1397 .12257 .87742 20 50 .48226 .51774 2.0735 .55051 1.8165 1.1415 .12397 .87603 10 29 .48481 .51519 2.0627 .55431 1.8040 1.1433 .12538 .87462 61 10 .48735 .51265 2.0519 .55812 1.7917 1.1452 .12679 .87320 50 20 .48989 .51011 2.0413 .56194 1.7795 1.1471 .12821 .87178 40 30 .49242 .50758 2.0308 .56577 1.7675 1.1489 .12964 .87035 30 40 .49495 .50505 2.0204 .56962 1.7555 1.1508 .13108 .86892 20 50 .49748 .50252 2.0101 .57348 1.7437 1.1528 .13252 .86748 10 30 .50000 .50000 2.0000 .57735 1.7320 1.1547 .13397 .86602 60 10 .50252 .49748 1.9900 .58123 1.7205 1.1566 .13543 .86457 50 20 .50503 .49497 1.9801 .58513 1.7090 1.1586 .13690 .86310 40 30 .50754 .49246 1.9703 .58904 1.6977 1.1606 .13837 .86163 30 40 .51004 .48996 1.9606 .59297 1.6864 1.1626 .13985 .86015 20 50 .51254 .48746 1.9510 .59691 1.6753 1.1646 .14134 .85866 10 31 .51504 .48496 1.9416 .60086 1.6643 1.1666 .14283 .85717 59 10 .51753 .48247 1.9322 .60483 1.6534 1.1687 .14433 .85566 50 20 .52002 .47998 1.9230 .60881 1.6425 1.1707 .14584 .85416 40 30 .52250 .47750 1.9139 .61280 1.6318 1.1728 .14736 .85264 30 40 .52498 .47502 1.9048 .61681 1.6212 1.1749 .14888 .85112 20 50 •52745 .47255, 1.8959 .62083 1.6107 J. 1770 .15041 .84959 10 32 .52992 .47008 1.8871 .62487 1.6003 1.1792 .15195 .84805 58 10 .53238 .46762 1.8783 .62892 1.5900 1.1813 .15350 .84650 50 20 .53484 .46516 1.8697 .63299 1.5798 1.1835 .15505 .84495 40 30 .53730 .46270 1.8611 .63707 1.5697 1.1857 .15661 .84339 30 40 .53975 .46025 1.8527 .64117 1.5596 1.1879 .15817 .84182 20 50 .54220 .45780 1.8443 .64528 1.5497 1.1901 .15975 .84025 10 33 .54464 .45536 1.8361 .64941 1.5399 1.1924 .16133 .83867 57 10 .54708 .45292 1.8279 .65355 1.5301 1.1946 .16292 .83708 50 20 .54951 .45049 1.8198 .65771 1.5204 1.1969 .16451 .83549 40 30 .55194 .44806 1.8118 .66188 1.5108 1.1992 .16611 .83388 30 40 .55436 .44564 1.8039 .66608 1.5013 1.2015 .16772 .83228 20 50 .55678 •44322 1.7960 .67028 1.4919 1.2039 .16934 .83066 10 34 .55919 .44081 1.7883 .67451 1.4826 1.2062 .17096 .82904 56 10 .56160 .43840 1.7806 .67875 1.4733 1.2086 .17259 .82741 50 20 .56401 .43599 1.7730 .68301 1.4641 1.2110 .17423 .82577 40 30 .56641 .43359 1.7655 .68728 1.4550 1.2134 .17587 .82413 30 40 .56880 .43120 1.7581 .69157 1.4460 1.2158 .17752 .82247 20 50 .57119 .42881 1.7507 .69588 1.4370 1.2183 .17918 .82082 10 35 .57358 .42642 1.7434 .70021 1.4281 1.2208 .18085 .81915 55 10 .57596 .42404 1.7362 .70455 1.4193 1.2233 .18252 .81748 50 20 .57833 .42167 1.7291 .70891 1.4106 1.2258 .18420 .81580 40 30 .58070 .41930 1.7220 .71329 1.4019 1.2283 .18588 .81411 30 40 .58307 .41693 1.7151 .71769 1.3933 1.2309 .18758 .81242 20 50 .58543 .41457 1.7081 .72211 1.3848 1.2335 .18928 .81072 10 36 .58778 .41221 1.7013 .72654 1.3764 1.2361 .19098 .80902 54 Co- Vers. Se- CO- Tan- Cose- Vers. Sine. sine. Sin. cant TANG. gent. cant. Cos. 742 Natural Trigonom etrical Functions. o" w ft i Sine. Vers. Cos. Cose- cant. Tang. Co- tang. Se- cant. Vers. Sin. Co- sine. 9 6 w 5 ~36 .58778 .41221 1.7013 .72654 1.3764 1.2361 .19098 .sosKrj 54 10 .59014 .40986 1.6945 .73100 1.3680 1.2387 .19270 .80730 50 20 .59248 .40752 1.6878 .73547 1.3597 1.2413 .19442 .80658 40 30 .59482 .59716 .40518 1.6812 .73996 1.3514 1.2440 .19614 .80386 30 40 .40284 1.6746 .74447 1.3432 1.2467 .19788 .80212 20 50 .59949 .40051 1.6681 .74900 1.3351 1.2494 .19962 .80038 10 37 .60181 .39818 1.6616 .75355 1.3270 1.2521 .20136 .79863 53 10 .60413 .39586 1.6552 .75812 1.3190 1.2549 .20312 .79688 50 20 .60645 .39355 1.6489 .76271 1.3111 1.2577 .20488 .79512 40 30 .60876 .39124 1.6427 .76733 1.3032 1.2605 .20665 .79335 SO 40 .61107 .38893 1.6365 .77196 1.2954 1.2633 .20842 .79158 20 50 .61337 .38663 1.6303 .77661 1.2876 1.2661 .21020 .78980 10 38 .61566 .38434 1.6243 .78128 1.2799 1.2690 .21199 .78801 52 10 .61795 .38205 1.6182 .78598 1.2723 1.2719 .21378 .78622 50 20 .62023 .37976 1.6123 .79070 1.2647 1.2748 .21558 .78441 40 30 .62251 .37748 1.6064 .79543 1.2572 1.2778 .21739 .78261 30 40 .62479 .37521 1.6005 .80020 1.2497 1.2807 .21921 .78079 20 50 .62706 .37294 1.5947 .80498 1.2423 1.2837 .22103 .77897 10 39 .62932 .37068 1.5890 .80978 1.2349 1.2867 .22285 .77715 51 10 .63158 .36842 1.5833 .81461 1.2276 1.2898 .22469 .77531 50 20 .63383 .36617 1.5777 .81946 1.2203 1.2929 .22653 .77347 40 30 .63608 .36392 1.5721 .82434 1.2131 1.2960 .22837 .77162 30 40 .63832 .36168 , 1.5666 .82923 1.2059 1.2991 .23023 .76977 20 50 .64056 .35944 1.5611 .83415 1.1988 1.3022 .23209 .76791 10 40 .64279 .35721 1.5557 .83910 1.1917 1.3054 .23395 .76604 50 10 .64501 .35499 1.5503 .84407 1.1847 1.3086 .23583 .76417 50 20 .64723 .35277 1.5450 .84906 1.1778 1.3118 .23771 .76229 40 30 .64945 .35055 1.5398 .85408 1.1708 1.3151 .23959 .76041 30 40 .65166 .34834 1.5345 .85912 1.1640 1.3184 .24149 .75851 20 50 .65386 .34614 1.5294 .86419 1.1571 1.3217 .24338 .75661 10 41 .65606 .34394 1.5242 .86929 1.1504 1.3250 .24529 .75471 49 10 .65825 .34175 1.5192 .87441 1.1436 1.3284 .24720 .75280 50 20 .66044 .33956 1.5141 .87955 1.1369 1.3318 .24912 .75088 40 30 .66262 .33738 1.5092 .88472 1.1303 1.3352 .25104 .74895 30 40 .66479 .33520 1.5042 .88992 1.1237 1.3386 .25297 .74702 20 50 .66697 .33303 1.4993 .89515 1.1171 1.3421 .25491 .74509 10 42 .66913 .33087 1.4945 .90040 1.1106 1.3456 .25685 .74314 48 10 .67129 .32871 1.4897 .90568 1.1041 1.3492 .25880 .74119 50 20 .67344 .32656 1.4849 .91099 1.0977 ' 1.3527 .26076 .73924 40 30 .67559 .32441 1.4802 .91633 1.0913 1.3563 .26272 .73728 30 40 .67773 .32227 1.4755 .92170 1.0849 1.3600 .26469 .73531 20 50 .67987 .32013 1.4709 .92709 1.0786 1.3636 .26666 .73333 10 43 .68200 .31800 1.4663 .93251 1.0724 1.3673 .26865 .73135 47 10 .68412 .31588 1.4617 .93797 1.0661 1.3710 .27063 .72937 50 20 .68624 .31376 1.4572 .94345 1.0599 1.3748 .27263 .72737 40 30 .68835 .31164 1.4527 .94896 1.0538 1.3786 .27462 .72537 30 40 .69046 .30954 1.4483 .95451 1.0476 1.3824 .27663 .72337 20 50 .69256 .30744 1.4439 .96008 1.0416 1.3863 .27864 .72136 10 44 .69466 .30534 1.4395 .96569 1.0355 1.3902 .28066 .71934 46 10 .69675 .30325 1.4352 .97133 1.0295 1.3941 .28268 .71732 50 20 .69883 .30117 1.4310 .97699 1.0235 1.3980 .28471 .71529 40 30 .70091 .29909 1.4267 .98270 1.0176 1.4020 .28675 .71325 30 40 .70298 .29702 1.4225 .98843 1.0117 1.4060 .28879 .71121 20 50 .70505 .29495 1.4183 .99420 1.0058 1.4101 .29084 .70916 10 45 .70711 .29289 1.4142 1.0000 1.0000 1.4142 .29289 .70711 45 Co- Vers. Se- Co- Tan- Cose- Vers. Sine. sine. Sin. cant. TANG. gent. cant. Cos. CIRCUMFERENCE AND AREA OF CIRCLES. The Circle. Notation. d = diameter of the circle. r = radius of the circle. p = periphery or circumference. a = area of a circle or part thereof. b = length of a circle-arc. c = chord of a segment, length of. h = height of a segment. s = side of a regular polygon. v = centre angle. w = polygon angle. All measures must be expressed in terms of the same unit. Formulas for the Circle. Periphery or Circumfer- ence. P = TTd = 3.14d. Diameter and Radius. it . 3.14 yirea o/ Me ft'rcte. a = — = 0.7854d2. 4 p = 2tjt = 6.28r. 2ir 6.28 ' a = »rr 2 = 3.14r2. p = li^a = 3.54» / aT d = 2-%fc = 1.128^ 4tt 12.56 2a 4a r = , ^Sfc^ Diam- /— >v >^^S eter. o IP eter. o (J) eter. o (J 1 3.1416 0.7854 51 160.22 2042.8 101 317.30 8011.9 2 6.2832 3.1416 52 163.36 2123.7 102 320.44 8171.3 S 9.4248 7.0686 53 166.50 2206.2 103 323.58 8332.3 4 12.566 12.5664 54 169.65 2290.2 104 326.73 8494.9 5 15.708 19.6350 55 172.79 2375.8 105 329.87 8659.0 6 18.850 28.2743 56 175.93 2463.0 106 333.01 8824.7 7 21.991 38.4845 57 179.07 2551.8 107 336.15 8992.0 8 25.133 50.2655 58 182.21 2642.1 108 339.29 9160.9 9 28.274 63.6173 59 185.35 2734.0 109 342.43 9331.3 10 31.416 78.54 60 188.50 2827.4 110 345.58 9503.3 11 34.558 95.03 61 191.64 2922.5 111 348.72 9676.9 12 37.699 113.10 62 194.78 3019.1 112 351.86 9852.0 13 40.841 132.73 63 197.92 3117.2 113 355.00 10028.8 14 43.982 153.94 64 201.06 3217.0 114 358.14 10207.0 15 47.124 176.71 65 204.20 3318.3 115 361.28 10386.9 16 50.265 201.06 66 207.35 3421.2 116 364.42 10568.3 17 53.407 226.98 67 210.49 3525.7 117 367.57 10751.3 18 56.549 254.47 68 213.63 3631.7 118 370.71 10935.9 19 59.690 283.53 69 216.77 3739.3 119 373.85 11122.0 20 62.832 314.16 70 219.91 3818.5 120 376.99 11310 21 65.973 346.36 71 223.05 3959.2 121 380.13 11499 22 69.115 380.13 72 226.19 4071.5 122 383.27 11690 23 72.257 415.48 73 229.34 4185.4 123 386.42 11882 24 75.398 452.39 74 232.48 4300.8 124 389.56 12076 25 78.540 490.87 75 235.62 4417.9 125 392.70 12272 26 81.681 530.93 76 238.76 4536.5 126 395.84 12469 27 84.823 572.56 77 241.90 4656.6 127 398.98 12668 28 87.965 615.75 78 245.04 4778.4 128 402.12 12868 29 91.106 660.52 79 248.19 4901.7 129 405.27 13070 30 94.248 706.86 80 251.33 5026.6 130 408.41 13273 31 97.389 754.77 81 254.47 5153.0 131 411.55 13478 32 100.53 804.25 82 257.61 5281.0 132 414.69 13685 33 103.67 855.30 83 260.75 5410.6 133 417.83 13893 34 106.81 907.92 84 263.89 6541.8 134 420.97 14103 35 109.96 962.11 85 267.04 5674.5 135 424.12 14314 36 113.10 1017.88 86 270.18 5808.8 136 427.26 14527 37 116.24 1075.21 87 273.32 5944.7 137 430.40 14741 38 119.38 1134.11 88 276.46 6082.1 138 433.54 14957 39 122.52 1194.59 89 279.60 6221.1 139 436.68 15175 40 125.66 1256.63 90 282.74 6361.7 140 439.82 15394 41 128.81 1320.25 91 285.88 6503.9 141 442.96 15615 42 131.95 1385.44 92 289.03 6647.6 142 446.11 15837 43 135.09 1452.20 93 292.17 6792.9 143 449.25 16061 44 138.23 1520.52 94 295.31 6939.8 144 452.39 16286 45 141.37 1590.43 95 298.45 7088.2 145 455.53 16513 46 144.51 1661.90 96 301.59 7238.2 146 458.67 16742 47 147.65 1734.94 97 304.73 7389.8 147 461.81 16972 48 150.80 1809.55 98 307.88 7543.0 148 464.96 17203 49 153.94 1885.74 99 311.02 7697.7 149 468.10 17437 50 157.08 1963.50 100 314.16 7854.0 150 471.24 17671 Circumference and Area of Circles. 745 Circum. Area. Circum. Area. Circum. Area. Diam- • — \ if*m^ Diam- >~\ /^Hl\ Diam- /^\ ^m^ eter. o fP eter. O fp eter. o IP 151 474.38 17908 201 631.46 31731 251 788.54 49481 152 477.52 18146 202 634.60 32047 252 791.68 49876 153 480.66 18385 203 637.74 32365 253 794.82 50273 154 483.81 18627 204 640.89 32685 254 797.96 50671 155 486.95 18869 205 644.03 33006 255 801.11 51071 156 490.09 19113 206 647.17 33329 256 804.25 51472 157 493.23 19359 207 650.31 33654 257 807.39 51875 158 496.37 19607 208 653.45 33979 258 810.53 52279 159 499.51 19856 209 656.59 34307 259 813.67 52685 160 502.65 20106 210 659.73 34636 260 816.81 53093 161 505.80 20358 211 662.88 34967 261 819.96 53502 162 508.94 20612 212 666.02 35299 262 823.10 53913 163 512.08 20867 213 669.16 35633 263 826.24 54325 164 515.22 21124 214 672.30 35968 264 829.38 54739 165 518.36 21382 215 675.44 36305 265 832.52 55155 166 521.50 21642 216 678.58 36644 266 835.66 55572 167 524.65 21904 217 681.73 36984 267 838.81 55990 168 527.79 22167 218 684.87 37325 268 841.95 56410 169 530.93 22432 219 688.01 37668 269 845.09 56832 170 534.07 22698 220 691.15 38013 270 848.23 57256 171 537.21 22966 221 694.29 38360 271 851.37 57680 172 540.35 23235 222 697.43 38708 272 854.51 58107 173 543.50 23506 223 700.58 39057 273 857.66 58535 174 546.64 23779 224 703.72 39408 274 860.80 58965 175 549.78 24053 225 706.86 39761 275 863.94 59396 176 552.92 24328 226 710.00 40115 276 867.08 59828 177 556.06 24606 227 713.14 40471 277 870.22 60263 178 559.20 24885 228 716.28 40828 278 873.36 60699 179 562.35 25165 229 719.42 41187 279 876.50 61136 180 565.49 25447 230 722.57 41548 280 879.65 61575 181 568.63 25730 231 725.71 41910 281 882.79 62016 182 571.77 26016 232 728.85 42273 282 885.93 62458 183 574.91 26302 233 731.99 42638 283 889.07 62902 184 578.05 26590 234 735.13 43005 284 892.21 63347 185 581.19 26880 235 738.27 43374 285 895.35 63794 186 584.34 27172 236 741.42 43744 286 898.50 64242 187 587.48 27465 237 744.56 44115 287 901.64 64692 188 590.62 27759 238 747.70 44488 288 904.78 65144 189 593.76 28055 239 750.84 44863 289 907.92 65597 190 596.90 28353 240 753.98 45239 290 911.06 66052 191 600.04 28652 241 757.12 45617 291 914.20 66508 192 603.19 28953 242 760.27 45996 292 917.35 66966 193 606.33 29255 243 763.41 46377 293 920.49 67426 194 609.47 29559 244 766.55 46759 294 923.63 67887 195 612.61 29865 245 769.69 47144 295 926.77 68349 196 615.75 30172 246 772.83 47529 296 929.91 68813 197 618.89 30481 247 775.97 47916 297 933.05 69279 198 622.04 30791 248 779.12 48305 298 936.19 69747 199 625.18 31103 249 782.26 48695 299. 939.34 70215 200 628.32 31416 250 785.40 49087 300 942.48 70686 746 Circumference and Area op Circles. Circum Area. Circum Area. Circum. Area. Diam- S^\ s— V Diam- /*->. >«ss^ Diam- y^V /""""N eter. o tp eter. o w eter. 401 o o 801 945.62 71158 351 1102.70 96 762 1259.78 126 293 302 948.76 71631 352 1105.84 97 314 402 1262.92 126 923 303 951.90 72107 353 1108.98 97 868 403 1266.06 127 556 304 955.04 72583 354 1112.12 98 423 404 1269.20 128190 305 958.19 73062 355 1115.27 98 980 405 1272.35 128 825 306 961.33 73542 356 1118.41 99 538 406 1275.49 129 462 307 964.47 74023 357 1121.55 100 098 407 1278.63 130100 308 967.61 74506 358 1124.69 100 660 408 1281.77 130 741 309 970.75 74991 359 1127.83 101223 409 1284.91 131382 310 973.89 75477 360 1130.97 101788 410 1288.05 132 025 311 977.04 75964 361 1134.11 102 354 411 1291.19 132 670 312 980.18 76454 362 1137.26 102 922 412 1294.34 133 317 313 983.32 76945 363 1140.40 103 491 413 1297.48 133 965 314 986.46 77437 364 1143.54 104 062 414 1300.62 134 614 315 989.60 77931 365 1146.68 104 635 415 1303.76 135 265 316 992.74 78427 366 1149.82 105 209 416 1306.90 135 918 317 995.88 78924 367 1152.96 105 785 417 1310.04 136 572 318 999.03 79423 368 1156.11 106 362 418 1313.19 137 228 319 1002.17 79923 369 1159.25 106 941 419 1316.33 137 885 320 1005.31 80425 370 1162.39 107 521 420 1319.47 138 544 321 1008.45 80928 371 1165.53 108 103 421 1322.61 139 205 322 1011.59 81433 372 1168.67 108 687 422 1325.75 139 867 323 1014.73 81940 373 1171.81 109 272 423 1328.89 140 531 324 1017.88 82448 374 1174.96 109 858 424 1332.04 141196 325 1021.02 82958 375 1178.10* 110 447 425 1335.18 141863 326 1024.16 83469 376 1181.24 111036 426 1338.32 142 531 327 1027.30 83982 377 1184.38 111628 427 1341.46 143 201 328 1030.44 84496 378 1187.52 112 221 428 1344.60 143 872 329 1033.58 85012 379 1190.66 112 815 429 1347.74 144 545 330 1036.73 85530 380 1193.81 113 411 430 1350.88 145 220 331 1039.87 86049 381 1196.95 114 009 431 1354.03 145 896 332 1043.01 86570 382 1200.09 114 608 432 1357.17 146 574 333 1046.15 87092 383 1203.23 115 209 433 1360.31 147 254 334 1049.29 87616 384 1206.37 115 812 434 1363.45 147 934 335 1052.43 88141 385 1209.51 116 416 435 1366.59 148 617 336 1055.58 88668 386 1212.65 117 021 436 1369.73 149 301 337 1058.72 89197 387 1215.80 117 628 437 1372.88 149 987 338 1061.86 89727 388 1218.94 118 237 438 1376.02 150 674 339 1065.00 90259 389 1222.08 118 847 439 1379.16 151 363 340 1068.14 90792 390 1225.22 119 459 440 1382.30 152 053 341 1071.28 91327 391 1228.36 120 072 441 1385.44 152 745 342 1074.42 91863 392 1231.50 120 687 442 1388.58 153 439 343 1077.57 92401 393 1234.65 121304 443 1391.73 154134 344 1080.71 92941 394 1237.79 121922 444 1394.87 154 830 345 1083.85 93482 395 1240.93 122 542 445 1398.01 155 528 346 1086.99 94025 396 1244.07 123163 446 1401.15 156 228 347 1090.13 94569 397 1247.21 123 786 447 1404.29 156 930 348 1093.27 95115 398 1250.35 124 410 448 1407.43 157 633 349 1096.42 95662 399 1253.50 125 036 449 1410.58 158 337 350 1099.56 96211 400 1256.64 125 664 450 1413.72 1 159 043 Circumference and Area of Circles. 747 Circum. Area. Circum. Area. Circum. Area. Diam- /"->v /^^. Diam- /TS y^SS^ Diam- /~\ /^H^v eter. o w eter. o w eter. o IP 451 1416.86 159 751 501 1573.94 197 136 551 1731.02 238 448 452 1420.00 160 460 502 1577.08 197 923 552 1734.16 239 314 453 1423.14 161 171 503 1580.22 198 713 553 1737.40 240 182 454 1426.28 161 883 504 1583.36 199 504 554 1740.44 241 051 455 1429.42 162 597 505 1586.50 200 296 555 1743.58 241 922 456 1432.57 163 313 506 1589.65 201 090 556 1746.73 242 795 457 1435.71 164 030 507 1592.79 201886 557 1749.87 243 669 458 1438.85 164 748 508 1595.93 202 683 558 1753.01 244 545 459 1441.99 165 468 509 1599.07 203 482 559 1756.15 245 422 460 1445.13 166190 510 1602.21 204 282 560 1759.29 246 301 461 1448.27 166 914 511 1605.35 205 084 561 1762.43 247 181 462 1451.42 167 639 512 1608.50 205 887 562 1765.58 248 063 463 1454.56 168 365 513 1611.64 206 692 563 1768.72 248 947 464 1457.70 169 093 514 1614.78 207 499 564 1771.86 249 832 465 1460.84 169 823 515 1617.92 208 307 565 1775.00 250 719 466 1463.98 170 554 516 1621.06 209 117 566 1778.14 251607 467 1467.12 171287 517 1624.20 209 928 567 1781.28 252 497 468 1470.27 172 021 518 1627.35 210 741 568 1784.42 253 388 469 1473.41 172 757 519 1630.49 211 556 569 1787.57 254 281 470 1476.55 173 494 520 1633.63 212 372 570 1790.71 255176 471 1479.69 174 234 521 1636.77 213 189 571 1793.85 256 072 472 1482.83 174 974 522 1639.91 214 008 572 1796.99 256 970 473 1485.97 175 716 523 1643.05 214 829 573 1800.13 257 869 474 1489.11 176 460 524 1646.20 215 651 571 1803.27 258 770 475 1492.26 177 205 525 1649.34 216 475 575 1806.42 259 672 476 1495.40 177 952 526 1652.48 217 301 576 1S09.56 260 576 477 1498.54 178 701 527 1655.62 218128 577 1812.70 261 482 478 1501.68 179 451 528 1658.76 218 956 578 1815.84 262 389 479 1504.82 180 203 529 1661.90 219 787 579 1818.98 263 298 480 1507.96 180 956 530 1665.04 220 618 580 1822.12 264 208 481 1511.11 181 711 531 1668.19 221452 581 1825.27 265120 482 1514.25 182 467 532 1671.33 222 287 582 1828.41 266 033 483 1517.39 183 225 533 1674.47 223 123 583 1831.55 266 948 484 1520.53 183 984 534 1677.61 223 961 584 1834.69 267 865 485 1523.67 184 745 535 1680.75 224 801 585 1837.83 268 783 486 1526.81 185 508 536 1683.89 225 642 586 1840.97 269 702 487 1529.96 186 272 537 1687.04 226 484 587 1844.11 270 624 488 1533.10 187 038 538 1690.18 227 329 588 1847.26 271547 489 1536.24 187 805 539 1693.32 228175 589 1850.40 272 471 490 1539.38 188 574 540 1696.46 229 022 590 1853.54 273 397 491 1542.52 189 345 541 1699.60 229 871 591 1856.68 274 325 492 1545.66 190 117 542 1702.74 230 722 592 1859.82 275 254 493 1548.81 190 890 543 1705.88 231 574 593 1862.96 276 184 494 1551.95 191 665 544 1709.03 232 428 594 1866.11 277 117 495 1555.09 192 442 •545 1712.17 233 283 595 1869.25 278 051 496 1558.23 193 221 546 1715.31 234 140 596 1872.39 278 986 497 1561.37 194 000 547 1718.45 234 998 597 1875.53 279 923 498 1564.51 194 782 548 1721.59 235 858 598 1878.67 280 862 499 1567.65 195 565 549 1724.73 236 720 599 1881.81 281802 500 1570.80 196 350 550 1727.88 237 583 600 1884.% 282 743 748 Circumference and Area of Circles. Circum. Area. Circum. Area. Circum. Area. Diam- /"—N /SH^. Diam- /^\ ,<^^V Diam- s~*\ _,»— V eter. o w eter. o IP eter. o o 601 1888.10 283 687 651 2045.18 332 853 701 2202.26 385 945 602 1891.24 284 631 652 2048.32 333 876 702 2205.40 387 047 603 1894.38 285 578 653 2051.46 334 901 703 2208.54 888 151 604 1897.52 286 526 654 2054.60 335 927 704 2211.68 389 256 605 1900.66 287 475 655 2057.74 336 955 705 2214.82 390 363 606 1903.81 288 426 656 2060.88 337 985 706 2217.96 391 471 607 1906.95 289 379 657 2064.03 339 016 707 2221.11 392 580 608 1910.09 290 333 658 2067.17 340 049 708 2224.25 393 692 609 1913.23 291289 659 2070.31 341083 709 2227.39 394 805 610 1916.37 292 247 660 2073.45 342 119 710 2230.53 395 919 611 1919.51 293 206 661 2076.59 343 157 711 2233.67 397 035 612 1922.65 294166 662 2079.73 344 1% 712 2236.81 398 153 613 1925.80 295128 663 2082.&S 345 237 713 2239.96 399 272 614 1928.94 296 092 664 2086.02 346 279 714 2243.10 400 393 615 1932.08 297 057 665 2089.16 347 323 715 2246.24 401 515 616 1935.22 298 024 666 2092.30 348 368 716 2249.38 402 639 617 1938.36 298 992 667 2095.44 349 415 717 2252.52 403 765 618 1941.50 299 962 668 2098.58 350 464 718 2255.66 404 892 619 1944.65 300 934 669 2101.73 351 514 719 2258.81 406 020 620 1947.79 301907 670 2104.87 352 565 720 2261.95 407150 621 1950.93 302 882 671 2108.01 353 618 721 2265.09 408 282 622 1954.07 303 858 672 2111.15 354 673 722 2268.23 409 416 623 1957.21 304 836 673 2114.29 355 730 723 2271.37 410 550 624 1960.35 305 815 674 2117.43 356 788 724 2274.51 411687 625 1963.50 306 796 675 2120.58 357 847 725 2277.65 412 825 626 1966.64 307 779 676 2123.72 358 908 726 2280.80 413 965 627 1969.78 308 763 677 2126.86 359 971 727 2283.94 415 106 628 1972.92 309 748 678 2130.00 361035 728 2287.08 416 248 629 1976.06 310 736 679 2133.14 362 101 729 2290.22 417 393 630 1979.20 311725 680 2136.28 363 168 730 2293.36 418 539 631 1982.35 312 715 681 2139.42 364 237 731 2296.50 419 686 632 1985.49 313 707 682 2142.57 365 308 732 2299.65 420 835 633 1988.63 314 700 683 2145.71 366 380 733 2302.79 421986 634 1991.77 315 696 684 2148.85 367 453 734 2305.93 423139 635 1994.91 316 692 685 2151.99 368 528 735 2309.07 424 292 636 1998.05 317 690 686 2155.13 369 605 736 2312.21 425 447 637 2001.19 318 690 687 2158.27 370 684 737 2315.35 426 604 638 2004.34 319 692 688 2161.42 371 764 738 2318.50 427 762 639 2007.48 320 695 689 2164.56 372 845 739 2321.64 428 922 640 2010.62 321699 690 2167.70 373 928 740 2324.78 430 084 641 2013.67 322 705 691 2170.84 375 013 741 2327.92 431247 642 2016.90 323 713 692 2173.98 376 099 742 2331.06 432 412 643 2020.04 324 722 693 2177.12 377 187 743 2334.30 433 578 644 2023.19 325 733 694 2180.27 378 276 744 2337.34 434 746 645 2026.33 326 745 695 2183.41 379 367 745 2340.49 435 916 646 2029.47 327 759 696 2186.55 380 459 746 2343.63 437 087 647 2032.61 328 775 697 2189.69 381554 747 2346.77 438 259 648 2035.75 329 792 698 2192.83 382 649 748 2349.91 439 433 649 2038.89 330 810 699 2195.97 383 746 749 2353.05 440 609 650 2042.04 331831 700 2199.11 384 845 750 2356.19 441786 Circumference and Area op Circles. 749 Circum. Area. Circum. Area. Circum. Area. Diam- S~\ /*ssv Diam- /"~\ >*s^S Diam- /" — \ /^i^ eter. o IP eter. o w eter. o IP 751 2359.34 442 965 801 2516.42 503 912 851 2673.50 568 786 752 2362.48 444 146 802 2519.56 505171 852 2676.61 570 124 753 2365.62 445 328 803 2522.70 506 432 853 2679.78 571 463 754 2368.76 416 511 804 2525.84 507 694 854 2682.92 572 803 755 2371.90 447 697 805 2528.98 508 958 855 2686.06 574 146 756 2375.04 448 883 806 2532.12 510 223 856 2689.20 575 490 757 2378.19 450 072 807 2535.27 511490 857 2692.34 576 835 758 2381.33 451 262 808 2538.41 512 758 858 2695.49 578 182 759 2384.47 452 453 809 2541.55 514 028 859 2698.63 579 530 760 2387.61 453 646 810 2544.69 515 300 860 2701.77 580 880 761 2390.75 454 841 811 2547.83 516 573 861 2704.91 582 232 762 2393.89 456 037 812 2550.97 517 848 862 2708.05 583 585 763 2397.04 457 234 813 2554.11 519 124 863 2711.19 584 940 764 2400.18 458 434 814 2557.26 520 402 864 2714.34 586 297 765 2403.32 459 635 815 2560.40 521681 865 2717.48 587 655 766 2406.46 460 837 816 2563.54 522 962 866 2720.62 589 014 767 2409.60 462 041 817 2566.68 524 245 867 2723.76 590 375 768 2412.74 463 247 818 2569.82 525 529 868 2726.90 591738 769 2415.88 464 454 819 2572.96 526 814 869 2730.04 593102 770 2419.03 465 663 820 2576.11 528102 870 2733.19 594 468 771 2422.17 466 873 821 2579.25 529 391 871 2736.33 595 835 772 2425.31 468 085 822 2582.31 530 681 872 2739.47 597 204 773 2428.45 469 298 823 2585.53 531 973 873 2742.61 598 575 774 2431.59 470 513 824 2588.67 533 267 874 2745.75 599 947 775 2434.73 471 730 825 2591.81 534 562 875 2748.89 601320 776 2437.88 472 948 826 2594.96 535 858 876 2752.04 602 696 777 2441.02 474168 827 2598.10 537 157 877 2755.18 604 073 778 2444.16 475 389 828 2601.24 538 456 878 2758.32 605 451 779 2447.30 476 612 829 2604.38 539 758 879 2761.46 606 831 780 2450.44 477 836 830 2607.52 541061 880 2764.60 608 212 781 2453.58 479 062 831 2610.66 542 365 881 2767.74 609 595 782 2456.73 480 290 832 2613.81 543 671 882 2770.88 611 PC'/ 783 2459.87 481 519 833 2616.95 544 979 883 2774.03 61z 366 784 2463.01 482 750 834 2620.09 546 288 884 2777.17 613 754 785 2466.15 483 982 835 2623.23 547 599 885 2780.«1 615 143 786 2469.29 485 216 836 2626.37 548 912 886 2783.45 616 534 787 2472.43 486 451 837 2629.51 550 226 887 2786.59 617 927 788 2475.58 487 688 838 2632.65 551541 888 2789.73 619 321 789 2478.72 488 927 839 2635.80 552 858 889 2792.88 620 717 790 2481.86 490 167 840 2638.94 554177 890 2796.02 622 114 791 2485.00 491 409 841 2642.08 555 497 891 2799.16 623 513 792 2488.14 492 652 842 2645.22 556 819 892 2802.30 624 913 793 2491.28 493 897 843 2648.36 558142 893 2805.44 626 315 794 2494.42 495 143 844 2651.50 559 467 894 2808.58 627 718 795 2497.57 4% 391 845 2654.65 560 794 895 2811.73 629124 796 2500.71 497 641 846 2657.79 562 122 896 2814.87 630 530 797 2503.85 498 892 847 2660.93 563 452 897 2818.01 631938 798 2506.99 500 145 848 2664.07 564 783 898 2821.15 633 348 799 2510.13 501399 849 2667.21 566 116 899 2824.29 634 760 800 2513.27 502 655 850 2670.35 567 450 900 I 2827.43 636 173 750 <'li:< IMFERENCH and Area op Circles. Circum. Area. Cirrnm. Area. Ciivuffl, Area. Diam- /^\ /" — N Diam- /*"V /" — N I>i:mi- /■ — V /-— V eter. o IP eter. o w eter. 967 o o 901 2830.58 637 587 934 2934.25 685147 3037.92 734 417 902 2833.72 639 003 935 2937.39 686 615 968 3041.06 735 937 903 2836.86 640 421 936 2940.53 688 084 969 3044.20 737 458 904 2840.00 641840 937 2943.67 689 555 970 3047.34 738 981 905 2843.14 643 261 938 2946.81 691028 971 3050.49 740 506 906 2846.28 644 683 939 • 2949.96 692 502 972 3053.63 742 032 907 2849.42 G46107 940 2953.10 693 978 973 3056.77 743 559 908 2852.57 647 533 941 2956.24 695 455 974 3059.91 745 088 909 2855.71 648 960 942 2959.38 696 934 975 3063.05 746 619 910 2858.85 650 388 943 2962.52 698 415 976 3066.19 748 151 911 2861.99 651 818 944 2965.66 699 897 977 3069.34 749 685 912 2865.13 653 250 945 2968.81 701380 978 3072.48 751221 913 2868.27 654 684 946 2971.95 702 865 979 3075.62 752 758 914 2871.42 656118 947 2975.09 704 352 980 3078.76 754 2% 915 2874.56 657 555 948 2978.23 705 840 981 3081.90 755 837 916 2877.70 658 993 949 2981.37 707 330 982 3085.04 757 378 917 2880.84 660 433 950 2984.51 708 822 983 3088.19 758 922 918 2883.98 661874 951 2987.65 710 315 984 3091.33 760 466 919 2887.12 663 317 952 2990.80 711 809 985 3094.47 762 013 920 2890.27 664 761 953 2993.94 713 307 986 3097.61 763 561 921 2893.41 666 207 954 2997.08 714 803 987 3100.75 765111 922 2896.55 667 654 955 3000.22 716 303 988 3103.89 766 662 923 2899.69 669 103 956 3003.36 717 804 989 3107.04 768 215 924 2902.83 670 554 957 3006.50 719 306 990 3110.18 769 769 925 2905.97 672 006 958 3009.65 720 810 991 3113.32 771325 926 2909.11 673 460 959 3012.79 722 316 992 3116.46 772 882 927 2912.26 674 915 960 3015.93 723 823 993 3119.60 774 441 928 2915.40 676 372 961 3019.07 725 332 994 3122.74 776 002 929 2918.54 677 831 962 3022.21 726 842 995 3125.88 777 564 930 2921.68 679 291 963 3025.35 728 354 996 3129.03 779128 931 2924.82 680 752 964 3028.50 729 867 997 3132.17 780 693 932 2927.96 682 216 965 3031.64 731382 998 3135.31 782 260 933 2931.11 683 680 966 3034.78 732 899 999 31138.45 783 828 Note.— When it is desired to find the circumference corresponding to any diameter not in the table, point off as many places in the circumfer- ence as have been pointed off in the diameter, and point off twice as many places in this area as have been pointed off in the diameter. Thus : Xameters. Circumferences. Areas 9.16 28.777 65.8 91.6 287.77 6 589.9 916. 2877.7 658 993. 9160. 28777. 65 899 321. When it is desired to find the circumference or area for any diameter consisting of a whole number and a decimal, it may be done by taking the difference between the tabular figures for the diameters between which the given diameter lies and multiplying this difference by the decimal and adding the result to the tabular value corresponding to the next lower diameter. POWERS AND ROOTS. Number. Squares. Cubes. V Roots. f Boots. Reciprocals. 1 1 1 1.000 0000 1.000 0000 1.000 000 000 2 4 8 1.414 2136 1.259 9210 .500 000 000 3 9 27 1.732 0508 1.442 2496 .333 333 333 4 16 64 2.000 0000 1.587 4011 .250 000 000 5 25 125 2.236 0680 1.709 9759 .200 000 000 6 36 216 2.449 4897 1.817 1206 .166 666 667 7 49 343 2.645 7513 1.912 9312 .142 857 143 8 64 512 2.828 4271 2.000 0000 .125 000 000 9 81 729 3.000 0000 2.080 0837 .111 111 111 10 100 1000 3.162 2777 2.154 4347 .100 000 000 11 121 1331 3.316 6248 2.223 9801 .090 909 091 12 144 1728 3.464 1016 2.289 4286 .083333 333 13 169 2197 3.605 5513 2.351 3347 .076 923 077 14 196 2 744 3.741 6574 2.410 1422 .071 428 571 15 225 3 375 3.872 9833 2.466 2121 .066 666 667 16 256 4 096 4.000 0000 2.519 8421 .062 500 000 17 289 4 913 4.123 1056 2.571 2816 .058 823 529 18 324 5 832 4.242 6407 2.620 7414 .055 555 556 19 361 6 859 4.358 8989 2.668 4016 .052 631 579 20 400 8000 4.472 1360 2.714 4177 .050 000 000 21 441 9 261 4.582 5757 2.758 9243 .047 619 048 22 484 10 648 4.690 4158 2.802 0393 .045 454 545 23 529 12167 4.795 8315 2.843 8670 .043 478 261 24 576 13 824 4.898 9795 2.884 4991 .041 666 667 25 625 15 625 5.000 0000 2.924 0177 .040 000 000 26 676 17 576 5.099 0195 2.962 4960 .038 461 538 27 729 19 683 5.196 1524 3.000 0000 .037 037 037 28 784 21952 5.291 5026 3.036 5889 .035 714 286 29 841 24 389 5.385 1648 3.072 3168 .034 482 759 30 900 27 000 5.477 2256 3.107 2325 .033 333 333 31 961 29 791 5.567 7644 3.141 3806 .032 258 065 32 1024 32 768 5.656 8542 3.174 8021 .031 250 000 33 1089 35 937 5.744 5626 3.207 5343 .030 303 030 34 1156 39 304 5.830 9519 3.239 6118 .029 411 765 35 1225 42 875 5.916 0798 3.271 0663 .028 571 429 36 1296 46 656 6.000 0000 3.301 9272 .027 777 778 37 1369 50 653 6.082 7625 3.332 2218 .027 027 027 38 1444 54 872 6.164 4140 3.361 9754 .026 315 789 39 1521 59 319 6.244 9980 3.391 2114 .025 641 026 40 1600 64 000 6.324 5553 3.419 9519 .025 000 000 41 1681 68 921 6.403 1242 3.448 2172 .024 390 244 42 1764 74 088 6.480 7407 3.476 0266 .023 809 524 43 1849 79 507 6.557 4385 3.503 3981 .023 255 814 44 1936 85184 6.633 2496 3.530 3483 .022 727 273 45 2 025 91125 6.708 2039 3.556 8933 .022 222 222 46 2 116 97 336 6.782 3300 3.583 0479 .021 739 130 47 2 209 103 823 6.855 6546 3.608 8261 .021 276 600 48 2 304 110 592 6.928 2032 3.634 2411 .020 833 333 49 2 401 117 649 7.000 0000 3.659 3057 .020 408 163 50 2500 125 000 7.071 0678 3.684 0314 .020 000 000 51 2 601 132 651 7.141 4284 3.708 4298 .019 607 843 52 2 704 140 608 7.211 1026 3.732 5111 .019 230 769 752 Powers and Roots Number. Squares. Cubes. l' Roots. f Boots. Reciprocals. 53 2809 148 877 7.2801099 3.756 2858 .018 867 925 54 2 916 157 464 7.348 4692 3.779 7631 .018 518 519 55 3025 166 375 7.416 1985 3.802 9525 .018 181 818 56 3136 175 616 7.483 3148 3.825 8624 .017 857 143 57 3 249 185 193 7.549 8344 3.848 5011 .017 543 860 58 3364 195 112 7.615 7731 3.870 8766 .017 241 379 59 3 481 205 379 7.681 1457 3.892 9965 .016 949 153 60 3600 216 000 7.745 9667 3.914 8676 .016 666 667 61 3 721 226 981 7.810 2497 3.930 4972 .016 393 443 62 3 844 238 328 7.874 0079 3.957 8915 .016 129 032 63 3 969 250 047 7.937 2539 3.979 0571 .015 873 016 64 4096 262144 8.000 0000 4.000 0000 .015 625 000 65 4225 274 625 8.062 2577 4.020 7256 .015 384 615 66 4356 287 496 8.124 0384 4.041 2401 .015 151 515 67 4 489 300 763 8.185 3528 4.061 5480 .014 925 373 68 4 624 314 432 8.246 2113 4.081 6551 .014 705 882 69 4 761 328 509 8.306 6239 4.101 5661 .014 492 754 70 4900 343 000 8.366 6003 4.121 2853 .014 285 714 71 5 041 357 911 8.426 1498 4.140 8178 .014 084 517 72 5184 373 248 8.485 2814 4.160 1676 .013 888 889 73 5 329 389 017 8.544 0037 4.179 3390 .013 698 630 74 5 476 405 224 8.602 3253 4.198 3364 .013 513 514 75 5 625 421 875 8.660 2540 4.217 1633 .013 333 333 76 5 776 438 976 8.717 7979 4.235 8236 .013 157 895 77 5929 456 533 8.774 9644 4.254 3210 .012 987 013 78 6 084 474 552 8.831 7609 4.272 6586 .012 820 513 79 6 241 493 039 8.8881944 4.290 8404 .012 658 228 80 6 400 512 000 8.944 2719 4.308 8695 .012 500 000 81 6 561 531441 9.000 0000 4.326 7487 .012 345 679 82 6 724 551368 9.055 3851 4.344 4815 .012 195 122 83 6 889 571 787 9.110 4336 4.362 0707 .012 048 193 84 7 056 592 704 9.165 1514 4.379 5191 .011 904 762 85 7225 614125 9.219 5445 4.396 8296 .011 764 706 86 7 396 636 056 9.273 6185 4.414 0049 .011 627 907 87 7 569 658 503 9.327 3791 4.431 0476 .011 494 253 88 7 744 681472 9.380 8315 4.447 9692 .011 363 636 89 7 921 704 969 9.433 9811 4.464 7451 .011 235 955 90 8100 729 000 9.486 8330 4.481 4047 .011 111 111 91 8 281 753 571 9.539 3920 4.497 9414 .010 989 011 92 8 464 778 688 9.591 6630 4.514 3574 .010 869 565 93 8 649 804 357 9.643 6508 4.530 6549 .010 752 688 94 8836 830 584 9.695 3597 4.546 8359 .010 638 298 95 9 025 857 375 9.746 7943 4.562 9026 .010 526 316 96 9 216 884 736 9.797 9590 4.578 8570 .010 416 667 97 9 409 912 673 9.848 8578 4.594 7009 .010 309 278 98 9604 941192 9.899 4949 4.610 4363 .010 204 082 99 9 801 970 299 9.949 8744 4.626 0650 .010 101 010 100 10 000 1000 000 10.000 0000 4.6415888 .010 000 000 101 10 201 1 030 301 10.049 8756 4.657 0095 .009 900 990 102 10 404 1061208 10.099 5049 4.672 3287 .009 803 922 103 10 609 1 092 727 10.148 8916 4.687 5482 .009 708 738 104 10 816 1 124 864 10.198 0390 4.702 6694 .009 615 385 Powers and Roots 753 Number. Squares. Cubes. V Roots. f Roots. Reciprocals. 105 11025 1 157 625 10.246 9508 4.717 6940 .009 523 810 106 11236 1 191 016 10.295 6301 4.732 6235 .009 433 962 107 11449 1225 043 10.344 0804 4.747 4594 .009 345 794 108 11664 1259 712 10.392 3048 4.762 2032 .009 259 259 109 11881 1295 029 10.440 3065 4.776 8562 .009 174 312 110 12100 1331000 10.488 0885 4.791 4199 .009 090 909 111 12 321 1 367 631 10.535 6538 4.805 8995 .009 009 009 112 12 544 1404 928 10.583 0052 4.820 2845 .008 928 571 113 12 769 1 442 897 10.630 1458 4.834 5881 .008 849 558 114 12 996 1481544 10.677 0783 4.848 8076 .008 771 930 115 13 225 1 520 875 10.723 8053 4.862 9442 .008 695 652 116 13 456 1560 896 10.770 3296 4.876 9990 .008 620 690 117 13 689 1 601 613 10.816 6538 4.890 9732 .008 547 009 118 13 924 1 643 032 10.862 7805 4.904 8681 .008 474 576 119 14 161 1 685 159 10.908 7121 4.918 6847 .008 403 361 120 14 400 1728 000 10.954 4512 4.932 4242 .008 333 333 121 14 641 1 771 561 11.000 0000 4.946 0874 .008 264 463 122 14 884 1 815 848 11.045 3610 4.959 6757 .008 196 721 123 15129 1 860 867 11.090 5365 4.973 1898 .008 130 081 124 15 376 1 906 624 11.135 5287 4.986 6310 .008 064 516 125 15 625 1 953 125 11.180 3399 5.000 0000 .008 000 000 126 15 876 2 000 376 11.224 9722 5.013 2979 .007 936 508 127 16129 2 048 383 11.269 4277 5.026 5257 .007 874 016 128 16 384 2 097 152 11.313 7085 5.039 6842 .007 812 500 129 16 641 2 146 689 11.357 8167 5.052 7743 .007 751 938 130 16 900 2197 000 11.401 7543 5.065 7970 .007 692 308 131 17161 2 248 091 11.445 5231 5.078 7531 .007 633 588 132 17 424 2 299 968 11.489 1253 5.091 6434 .007 575 758 133 17 689 2 352 637 11.532 5626 5.104 4687 .007 518 797 134 17 956 2 406 104 11.575 8369 5.117 2299 .007 462 687 135 18 225 2 460 375 11.618 9500 5.129 9278 .007 407 407 136 18 496 2 515 456 11.661 9038 5.142 5632 .007 352 941 137 18 769 2 571 353 11.704 6999 5.155 1367 .007 299 270 138 19 044 2 628 072 11.747 3401 5.167 6493 .007 246 377 139 19 321 2 685 619 11.789 8261 5.180 1015 .007 194 245 140 19 600 2 744 000 11.832 1596 5.192 4941 .007142 857 141 19 881 2 803 221 11.874 3421 5.204 8279 .007 092 199 142 20164 2 863 288 11.916 3753 5.217 1034 .007 042 254 143 20 449 2 924 207 11.958 2607 5.229 3215 .006 993 007 144 20 736 2 985 984 12.000 0000 5.241 4828 .006 944 444 145 21025 3 048 625 12.041 5946 5.253 5879 .006 896 552 146 21316 3 112 136 12.083 0460 5.265 6374 .006 849 315 147 21609 3 176 523 12.124 3557 5.277 6321 .006 802 721 148 21904 3 241 792 12.165 5251 5.289 5725 .006 756 757 149 22 201 3 307 949 12.206 5556 5.301 4592 .006 711 409 150 22 500 3 375 000 12.247 4487 5.313 2928 .006 666 667 151 22 801 3 442 951 12.288 2057 5.325 0740 .006 622 517 152 23104 3 511 008 12.328 8280 5.336 8033 .006 578 947 153 23 409 3 581 577 12.369 3169 5.348 4812 .006 535 948 154 23 716 3 652 264 12.409 6736 5.360 1084 .006 493 506 155 24 025 3 723 875 12.449 8996 5.371 6854 .006 451 613 156 24 336 3 796 416 12.489 9960 5.383 2126 .006 410 256 754 Powers and Roots Number. Squares. Cubes. V Roots. fBoota. Reciprocals. 157 24 649 3 869 893 12.529 9641 5.394 6907 .006 369 427 158 24 964 3 944 312 12.569 8051 5.406 1202 .006 329 114 159 25 281 4 019 679 12.609 5202 5.417 5015 .006 289 308 160 25 600 4096 000 12.649 1106 5.428 8352 .006 250 000 161 25 921 4 173 281 12.688 5775 5.440 1218 .006 211 180 162 26 244 4 251528 12.727 9221 5.451 3618 .006 172 840 163 26 569 4 330 747 12.767 1453 5.462 5556 .006 134 969 164 26 896 4 410 944 12.806 2485 5.473 7037 .006 097 561 165 27 225 4 492 125 12.845 2326 5.484 8066 .006 060 606 166 27 556 4 574 296 12.884 0987 5.495 8647 .006 024 096 167 27 889 4 657 463 12.922 8480 5.506 8784 .005 988 024 168 28 224 4 741 632 12.961 4814 5.517 8484 .005 952 381 169 28 561 4 826 809 13.000 0000 5.528 7748 .005 917 160 170 28 900 4 913 000 13.038 4048 5.539 6583 .005 882 353 171 29 241 5 000 211 13.076 6968 5.550 4991 .005 847 953 172 29 584 5 088 448 13.114 8770 5.561 2978 .005 813 953 173 29 929 5 177 717 13.152 9464 5.572 0546 .005 780 347 174 30 276 5 268 024 13.190 9060 5.582 7702 .005 717 126 175 30 625 5 359 375 13.228 7566 5.593 4447 .005 714 286 176 30 976 5 451 776 13.266 4992 5.604 0787 .005 6S1 818 177 31329 5 545 233 13.304 1347 5.614 6724 .005 649 718 178 31684 5 639 752 13.341 6641 5.625 2263 .005 617 978 179 32 041 5 735 339 13.379 0882 5.635 7408 .005 586 592 180 32 400 5 832 000 13.416 4079 5.646 2162 .005 555 556 181 32 761 5 929 741 13.453 6240 5.656 6528 .005 524 862 182 33124 6 028 568 13.490 7376 5.667 0511 .005 494 505 183 33 489 6 128 487 13.527 7493 5.677 4114 .005 464 481 184 33 856 6229 504 13.564 6600 5.687 7340 .005 434 783 185 34 225 6 331 625 13.601 4705 5.698 0192 .005 405 405 186 34 596 6 434 856 13.638 1817 5.708 2675 .005 376 344 187 34 969 6 539 203 13.674 7943 5.718 4791 .005 347 594 188 35 344 6 644 672 13.711 3092 5.728 6543 .005 319149 189 35 721 6 751 269 13.747 7271 5.738 7936 .005 291 005 190 36100 6 859 000 13.784 0488 5.748 8971 .005 263 158 191 36 481 6 967 871 13.820 2750 5.758 9652 .005 235 602 192 36 864 7 077 888 13.856 4065 5.768 9982 .005 208 333 193 37 249 7 189 517 13.892 4400 5.778 9966 .005 181 347 194 37 636 7 301 384 13.928 3883 5.788 9604 .005 154 639 195 38 025 7 414 875 13:964 2400 5.798 8900 .005 128 205 196 38 416 7 529 536 14.000 0000 5.808 7857 .005 102 041 197 38 809 7 645 373 14.035 6688 5.818 6479 .005 076 142 198 39 204 7 762 392 14.071 2473 5.828 4867 .005 050 505 199 39 601 7 880 599 14.106 7360 5.838 2725 .005 025 126 200 40 000 8000 000 14.142 1356 5.848 0355 .005 000 000 201 40 401 8120 601 14.177 4469 5.857 7660 .004 975 124 202 40 804 8 242 408 14.212 6704 5.867 4673 .004 950 495 203 41209 8 365 427 14.247 8068 5.877 1307 .004 926 108 204 41 616 8 489 664 14.282 8569 5.886 7653 .004 901 961 205 42 025 8 615 125 14.317 8211 5.896 3685 .004 878 049 206 42 436 8 741 816 14.352 7001 5.905 9406 .004 854 369 207 42 849 8 869 743 14.387 4946 5.915 4817 .004 830 918 208 43 264 8 998 912 14.422 2051 5.924 9921 .004 807 692 Powers and Roots 755 Number. Squares. CubeB. V Roots. f Roots. Reciprocals. 209 43 681 9 129 329 14.456 8323 5.934 4721 .004 784 689 210 44100 9 261000 14.491 3767 5.943 9220 .004 761 905 211 44 521 9 393 931 14.525 8390 5.953 3418 .004 739 336 212 44 944 9 528128 14.560 2198 5.962 7320 .004 716 981 213 45 369 9 663 597 14.594 5195 5.972 0926 .004 694 836 214 45 796 9 800 341 14.628 7388 5.981 4240 .004 672 897 215 46 225 9 938 375 14.662 8783 5.990 7264 .004 651 163 21G 46 656 10 077 696 14.696 9385 6.000 0000 .004 629 630 217 47 089 10 218 313 14.730 9199 6.009 2450 .004 608 295 218 47 524 10 360 232 14.764 8231 6.018 4617 .004 587 156 219 47 961 10 503 459 14.798 6486 6.027 6502 .004 566 210 220 48 400 10 648 000 14.832 3970 6.036 8107 .004 545 455 221 48 841 10 793 861 14.866 0687 6.045 9435 .004 524 887 222 49 284 10 941 048 14.899 6644 6.055 0489 .004 504 505 223 49 729 11 089 567 14.933 1845 6.064 1270 .004 484 305 224 50176 11 239 424 14.966 6295 6.073 1779 .004 464 286 225 50 625 11 390 625 15.000 0000 6.082 4020 .004 444 444 226 51076 11 543 176 15.033 2964 6.099 1994 .004 424 779 227 51529 11 697 083 15.066 5192 6.100 1702 .004 405 286 228 51984 11 852 352 15.099 6689 6-109 1147 .004 385 965 229 52 441 12 008 989 15.132 7460 6.118 0332 .004 366 812 230 52 900 12 167 000 15.165 7509 6.126 9257 .004 347 826 231 53 361 12 326 391 15.198 6842 6.135 7924 .004 329 004 232 53 824 12 487 168 15.231 5462 6.144 6337 .004 310 345 233 54 289 12 649 337 15.264 3375 6.153 4495 .004 291 845 234 54 756 12 812 904 15.297 0585 6.162 2401 .004 273 504 235 55 225 12 977 875 15.329 7097 6.171 0058 .004 255 319 236 55 6% 13 144 256 15.362 2915 6.179 7466 .004 237 288 237 56169 13 312 053 15.394 8043 6.188 4628 .004 219 409 238 56 644 13 481 272 15.427 2486 6.197 1544 .004 201 681 239 57 121 13 651 919 15.459 6248 6.205 8218 .004 184 100 240 57 600 13 824 000 15.491 9334 6.214 4650 .004 166 667 241 58 081 13 997 521 15.524 1747 6.223 0843 .004 149 378 242 58 564 14 172 488 15.556 3492 6.231 6797 .004 132 231 243 59 049 14 348 907 15.588 4573 6.240 2515 .004 115 226 244 59 536 14 526 784 15.620 4994 6.248 7998 .004 098 361 245 60 025 14 706 125 15.652 4758 6.257 3248 .004 081 633 246 60 516 14 886 936 15.684 3871 6.265 8266 .004 065 041 247 61009 15 069 223 15.716 2336 6.274 3054 .004 048 583 248 61504 15 252 992 15.748 0157 6.282 7613 .004 032 258 249 62 001 15 438 249 15.779 7338 6.291 1946 .004 016 064 250 62 500 15 625 000 15.811 3883 6.299 6053 .004 000 000 251 63 001 15 813 251 15.842 9795 6.307 9935 .003 984 064 252 63 504 16 003 008 15.874 5079 6.316 3596 .003 968 254 253 64 009 16 194 277 15.905 9737 6.324 7035 .003 952 569 254 64 516 16 387 064 15.937 3775 6.333 0256 .003 937 008 255 65 025 16 581 375 15.968 7194 6.341 3257 .003 921 569 256 65 536 16 777 216 16.000 0000 6.349 6042 .003 906 250 257 66 049 16 974 593 16.031 2195 6.357 8611 .003 891 051 258 66 564 17 173 512 16.062 3784 6.366 0968 .003 875 969 259 67 081 17 373 979 16.093 4769 6.374 3111 .003 861 004 260 67 600 17 576 000 16.124 5155 6.382 5043 .003 846 154 756 Powers and Roots . Number. Squares. Cubes. J 7 Hoots. f Hoots. Reciprocals. 261 68121 17 779 581 16.155 4944 6.390 6765 .003 831 418 262 68 644 17 984 728 16.186 4141 6.398 8279 .003 816 794 263 69169 18 191 447 16.217 2747 6.406 9585 .003 802 281 264 69 696 18 399 744 16.248 0768 6.415 0687 .003 787 879 265 70 225 18 609 625 16.278 8206 6.423 1583 .003 773 585 266 70 756 18 821 096 16.309 5064 6.431 2276 .003 759 398 267 71289 19 034 163 16.340 1346 6.439 2767 .003 745 318 268 71 824 . 19 248 832 16.370 7055 6.447 3057 .003 731 343 269 72 361 19 465 109 16.401 2195 6.455 3148 .003 717 472 270 72 900 19 683 000 16.431 6767 6.463 3041 .003 703 704 271 73 441 19 902 511 16.462 0776 6.471 2736 .003 690 037 272 73 984 20 123 643 16.492 4225 6.479 2236 .003 676 471 273 74 529 20 346 417 ■16.522 7116 6.487 1541 .003 663 004 274 75 076 20 570 824 16.552 9454 6.495 0653 .003 649 635 275 75 625 20 796 875 16.583 1240 6.502 9572 .003 636 364 276 76176 21 024 576 16.613 2477 6.510 8300 .003 623 188 277 76 729 21 253 933 16.643 3170 6.518 6839 .003 610 108 278 77 284 21 484 952 16.673 3320 6.526 5189 .003 597 122 279 77 841 21 717 639 16.703 2931 6.534 3351 .003 584 229 280 78 400 21 952 000 16.733 2005 6.542 1326 .003 571 429 281 78 961 22 188 041 16.763 0546 6.549 9116 .003 558 719 282 79 524 22 425 768 16.792 8556 6.557 6722 .003 546 099 283 80 089 22 665 187 16.822 6038 6.565 4144 .003 533 569 284 80 656 22 906 304 16.8522995 6.573 1385 .003 521 127 285 81225 23 149 125 16.881 9430 6.580 8443 .003 508 772 286 81796 23 393 656 16.911 5345 6.588 5323 .003 496 503 287 82 369 23 639 903 16.941 0743 6.596 2023 .003 484 321 288 82 944 23 887 872 16.970 5627 6.603 8545 .003 472 222 289 83 521 24 137 569 17.000 0000 6.611 4890 .003 460 208 290 84100 24 389 000 17.029 3864 6.619 1060 .003 448 276 291 84 681 24 642 171 17.058 7221 6.626 7054 .003 436 426 292 85 264 24 897 088 17.088 0075 6.634 2874 .003 424 658 293 85 849 25 153 757 17.117 2428 6.641 8522 .003 412 969 294 86 436 25 412 184 17.146 4282 6.649 3998 .003 401 361 295 87 025 25 672 375 17.175 5640 6.656 9302 .003 389 831 2% 87 616 25 934 836 17.204 6505 6.664 4437 .003 378 378 297 88 209 26 198 073 17.233 6879 6.671 9403 .003 367 003 298 88 804 26 463 592 17.262 6765 6.679 4200 .003 355 705 299 89 401 26 730 899 17.291 6165 6.686 8831 .003 344 482 300 90 000 27 000 000 17.320 5081 6.694 3295 .003 333 333 301 90 601 27 270 901 17.349 3516 6.701 7593 .003 322 259 302 91204 27 513 608 17.378 1472 6.709 1729 .003 311 258 303 91809 27 818 127 17.406 8952 6.716 5700 .003 301 330 304 92 416 28 094 464 17.435 5958 6.723 9508 .003 289 474 305 93 025 28 372 625 17.464 2492 6.731 3155 .003 278 689 306 93 636 28 652 616 17.492 8557 6.738 6641 .003 267 974 307 94 249 28 934 443 17.521 4155 6.745 9967 .003 257 329 308 94 864 29 218 112 17.549 9288 6.753 3134 .003 246 753 309 95 481 29 503 609 17.578 3958 6.760 6143 .003 236 246 310 96100 29 791 000 17.606 8169 6.767 8995 .003 225 806 311 96 721 30 080 231 17.635 1921 6.775 1690 .003 215 434 312 97 344 30 371 328 17.663 5217 6.782 4229 .003 205 128 Powers and Roots 757 Number. Squares. Cubes. V Roots. f Roots. Reciprocals. 313 97 969 30 664 297 17.691 8060 6.789 6613 .003 194 888 314 98 596 30 959 144 17.720 0451 6.796 8844 .003 184 713 315 99 225 31 255 875 17.748 2393 6.804 0921 .003 174 603 316 99 856 31 554 496 17.776 3888 6.811 2847 .003 164 557 317 100 489 31 855 013 17.804 4938 6.818 4620 .003 154 574 318 101124 32 157 432 17.832 5545 6.825 6242 .003 144 654 319 101 761 32 461 759 17.860 5711 6.832 7714 .003134 796 320 102 400 32 768 000 17.888 5438 6.839 9037 .003 125 000 321 103 041 83 076 161 17.916 4729 6.847 0213 .003 115 265 322 103 684 33 386 248 17.944 3584 6.854 1240 .003 105 590 323 104 329 33 698 267 17.972 2008 6.861 2120 .003 095 975 324 104 976 34 012 224 18.000 0000 6.868 2855 .003 086 420 325 105 625 34 328 125 18.027 7564 6.875 3433 .003 076 923 326 106 276 34 645 976 18.055 4701 6.882 3888 .003 067 485 327 106 929 34 965 783 18.083 1413 6.889 4188 .003 048 104 328 107 584 35 287 552 18.110 7703 6.896 4345 .003 048 780 329 108 241 35 611 289 18.138 3571 6.903 4359 .003 039 514 330 108 900 35 937 000 18.165 9021 6.910 4232 .003 030 303 331 109 561 36 264 691 18.193 4054 6.917 3964 .003 021 148 332 110 224 36 594 368 18.220 8672 6.924 3556 .003 012 048 333 110 889 36 926 037 18.248 2876 6.931 3088 .003 003 003 334 111 556 37 259 704 18.275 6669 6.938 2321 .002 994 012 335 112 225 37 595 375 18.303 0052 6.945 1496 .002 985 075 336 112 896 37 933 056 18.330 3028 6.952 0533 .002 976 190 337 113 569 38 272 753 18.357 5598 6.958 9434 .002 967 359 338 114 244 38 614 472 18.384 7763 6.965 8198 .002 958 580 339 114 921 38 958 219 18.411 9526 6.972 6826 .002 949 853 340 115 600 39 304 000 18.439 0889 6.979 5321 .002 941 176 341 116 281 39 651 821 18.466 1853 6.986 3681 .002 932 551 342 116 964 40 001 688 18.493 2420 6.993 1906 .002 923 977 343 117 649 40 353 607 18.520 2592 7.000 0000 .002 915 452 344 118 336 40 707 584 18.547 2370 7.006 7962 .002 906 977 345 119 025 41 063 625 18.574 1756 7.013 5791 .002 898 551 346 119 716 41 421 736 18.601 0752 7.020 3490 .002 890 173 347 120 409 41 781 923 18.627 9360 7.027 1058 .002 881 844 348 121 104 42 144 192 18.654 7581 7.033 8497 .002 873 563 349 121 801 42 508 549 18.681 5417 7.040 5860 .002 865 330 350 122 500 42 875 000 18.708 2869 7.047 2987 .002 857 143 351 123 201 43 243 551 18.734 9940 7.054 0041 .002 849 003 352 123 904 43 614 208 18.761 6630 7.060 6967 .002 840 909 353 124 609 43 986 977 18.788 2942 7.067 3767 .002 832 861 354 125 316 44 361 864 18.814 8877 7.074 0440 .002 824 859 355 126 025 44 738 875 18.841 4437 7.080 6988 .002 816 901 356 126 736 45 118 016 18.867 9623 7.087 3411 .002 808 989 357 127 449 45 499 293 18.894 4436 7.093 9709 .002 801 120 358 128164 45 882 712 18.920 8879 7.100 5885 .002 793 296 359 128 881 46 268 279 18.947 2953 7.107 1937 .002 785 515 360 129 600 46 656 000 18.973 6660 7.113 7866 .002 777 778 361 130 321 47 045 831 19.000 0000 7.120 3674 .002 770 083 362 131 044 47 437 928 19.026 2976 7.126 9360 .002 762 431 363 131 769 47 832 147 19.052 5589 7.133 4925 .002 754 821 364 132 496 48 228 544 19.078 7840 7.140 0370 .002 747 253 758 Powers AND HOOTS Number. Squares. Cubes. /EootaT f Boom. Reciprocals. 365 133 225 48 627 125 19.104 9732 7.146 5695 .002 739 726 366 133 956 49 027 896 19.131 1265 7.153 0901 .002 732 240 367 134 689 49 430 863 19.157 2441 7.159 5988 .002 724 796 368 135 424 49 836 032 19.183 3261 7.166 0957 .002 717 391 369 136161 50 243 409 19.209 3727 7.172 5809 .002 710 027 370 136 900 50 653 000 19.235 3841 7.179 0544 .002 702 703 371 137 641 51 064 811 19.261 3603 7.185 5162 .002 695 418 372 138 384 51 478 848 19.287 3015 7.191 9663 .002 688 172 373 139 129 51 895 117 19.313 2079 7.198 4050 .002 680 965 374 139 876 52 313 624 19.339 0796 7.204 8322 .002 673 797 375 140 625 52 734 375 19.364 9167 7.211 2479 .002 666 667 376 141 376 53 157 376 19.390 7194 7.217 6522 .002 659 574 377 142129 53 582 633 19.416 4878 7.224 0450 .002 652 520 378 142 884 54 010 152 19.442 2221 7.230 4268 .002 645 503 379 143 641 54 439 939 19.467 9223 7.236 7972 .002 638 521 380 144 400 54 872 000 19.493 5887 7.243 1565 .002 631 579 381 145161 55 306 341 19.519 2213 7.249 5045 .002 624 672 382 145 924 55 742 968 19.544 8203 7.255 8415 .002 617 801 383 146 689 56 181 887 19.570 3858 7.262 1675 .002 610 966 384 . 147 456 56 623104 19.595 9179 7.268 4824 .002 604 167 385 148 225 57 066 625 19.621 4169 7.274 7864 .002 597 403 386 148 996 57 512 456 19.646 8827 7.281 0794 .002 590 674 387 149 769 57 960 603 19.672 3156 7.287 3617 .002 583 979 388 150 544 58 411 072 19.697 7156 7.293 6330 .002 577 320 389 151 321 58 863 869 19.723 0829 7.299 8936 .002 570 694 390 152100 59 319 000 19.748 4177 7.306 1436 .002 564 103 391 152 881 59 776 471 19.773 7199 7.312 3828 .002 557 545 392 153 664 60 236 288 19.798 9899 7.318 6114 .002 551 020 393 154 449 60 698 457 19.824 2276 . 7.324 8295 .002 544 529 394 155 236 61 162 984 19.849 4332 7.331 0369 .002 538 071 395 156 025 61 629 875 19.874 6069 7.337 2339 .002 531 646 896 156 816 62 099 136 19.899 7487 7.343 4205 .002 525 253 397 157 609 62 570 773 19.924 8588 7.349 5966 .002 518 892 898 158 404 63 044 792 19.949 9373 7.355 7624 .002 512 563 399 159 201 63 521 199 19.974 9844 7.361 9178 .002 506 266 400 160 000 64 000 000 20.000 0000 7.368 0630 .002 500 000 401 160 801 64 481 201 20.024 9844 7.374 1979 .002 493 766 402 161604 64 964 808 20.049 9377 7.380 3227 .002 487 562 403 162 409 65 450 827 20.074 8599 7.386 4373 .002 481 390 404 163 216 65 939 264 20.099 7512 7.392 5418 .002 475 248 405 164 025 66 430 125 20.124 6118 7.398 6363 .002 469 136 406 164 836 66 923 416 20.149 4417 7.404 7206 .002 463 054 407 165 649 67 419 143 20.174 2410 7.410 7950 .002 457 002 408 166 464 67 917 312 20.199 0099 7.416 8595 .002 450 980 409 167 281 68 417 929 20.223 7484 7.422 9142 .002 444 988 410 168100 68 921000 20.248 4567 7.428 9589 .002 439 024 411 168 921 69 426 531 20.273 1349 7.434 9938 .002 433 090 412 169 744 69 934 528 20.297 7831 7.441 0189 .002 427 184 413 170 569 70 444 997 20.322 4014 7.447 0343 .002 421 308 414 171396 70 957 944 20.346 9899 7.453 0399 .002 415 459 415 172 225 71 473 375 20.371 5488 7.459 0359 .002 409 639 Powers and Roots 759 Number. Squares. Cubes. ^Roots. f Roots. Reciprocals. 417 173 889 72 511 713 20.420 5779 7.470 9991 .002 398 082 418 174 724 73 034 632 20.445 0483 7.476 9664 .002 392 344 419 175 561 73 560 059 20.469 4895 7.482 9242 .002 386 635 420 176 400 74 088 000 20.493 9015 7.488 8724 .002 380 952 421 177 241 71 618 461 20.518 2845 7.494 8113 .002 375 297 422 178 084 75 151 448 20.542 6386 7.500 7406 .002 369 668 423 178 929 75 686 967 20.566 9638 7.506 6607 .002 364 066 424 179 776 76 225 02 1 20.591 2603 7.512 5715 .002 358 491 425 180 625 76 765 625 20.615 5281 7.518 4730 .002 352 941 426 181 476 77 308 776 20.639 7674 7.524 3652 .002 347 418 . 427 182 329 77 854 483 20.663 9783 7.530 2482 .002 341 920 428 183 184 78 402 752 20.688 1609 7.536 1221 .002 336 449 429 184 041 78 953 589 20.712 3152 7.541 9867 .002 331 002 430 184 900 79 507 000 20.736 4414 7.547 8423 .002 325 581 431 185 761 80 062 991 20.760 5395 7.553 6888 .002 320 186 432 186 624 80 621 568 20.784 6097 7.559 5263 .002 31^815 433 187 489 81 182 737 20.808 6520 7.565 3548 .002 309 469 434 188 356 81 746 504 20.832 6667 7.571 1743 .002 304 147 435 189 225 82 312 875 20.856 6536 7.576 9849 .002 298 851 436 190 096 82 881 856 20.880 6130 7.582 7865 .002 293 578 437 190 969 83 453 453 20.904 5450 7.588 5793 .002 288 330 438 191844 84 027 672 20.928 4495 7.594 3633 .002 283 105 439 192 721 84 604 519 20.952 3268 7.600 1385 .002 277 904 440 193 600 85 184 000 20.976 1770 7.605 9049 .002 272 727- 441 194 481 85 766 121 21.000 0000 7.611 6626 .002 267 574 442 195 364 86 350 888 21.023 7960 7.617 4116 .002 262 443 443 196 249 86 938 307 21.047 5652 7.623 1519 .002 257 336 444 197 136 87 528 384 21.071 3075 7.628 8837 .002 252 252 445 198 025 88 121 125 21.095 0231 7.634 6067 .002 247 191 446 198 916 88 716 536 21.118 7121 7.640 3213 .002 242 152 447 199 809 89 314 623 21.142 3745 7.646 0272 .002 237 136 448 200 704 89 915 392 21.166 0105 7.651 7247 .002 232 143 449 201 601 90 518 849 21.189 6201 7.657 4138 .002 227 171 450 202 500 91 125 000 21.213 2034 7.663 0943 .002 222 222 451 203 401 91 733 851 21.236 7606 7.668 7665 .002 217 295 452 204 304 92 345 408 21.260 2916 7.674 4303 .002 212 389 453 205 209 92 959 677 21.283 7967 7.680 0857 .002 207 506 454 206 116 93 576 664 21.307 2758 7.685 7328 .002 202 643 455 207 025 94 196 375 21.330 7290 7.691 3717 .002 197 802 456 207 936 94 818 816 21.354 1565 7.697 0023 .002 192 982 457 208 849 95 443 993 21.377 5583 7.702 6246 .002 188 184 458 209 764 96 071 912 21.400 9346 7.708 2388 .002 183 406 459 210 681 96 702 579 21.424 2853 7.718 8448 .002 178 649 460 211600 97 336 000 21.447 6106 7.719 4426 .002 173 913 461 212 521 97 972 181 21.470 9106 7.725 0325 .002 169 197 462 213 444 98 611 128 21.494 1853 7.730 6141 .002 164 502 463 214 369 99 252 847 21.517 4348 7.736 1877 .002 159 827 464 215 296 99 897 344 21.540 6592 7.741 7532 ,002 155 172 465 216 225 100 544 625 21.563 8587 7.747 3109 .002150 538 466 217 156 101 194 696 21.587 0331 7.752 8606 .002 145 923 467 218 089 101 847 563 21.610 1828 7.758 4023 .002 141 328 468 219 024 102 503 232 21.633 3077 7.763 9361 .002 136 752 760 Towers and Roots . Number. Squares. Cubes. ^Boots. f Roots. Reciprocals. 469 219 961 103 161 709 21.656 4078 7.769 4620 .002 132 196 470 220 900 103 823 000 21.679 4834 7.774 9801 .002 127 660 471 221841 104 487 111 21.702 5344 7.780 4904 .002 123 142 472 222 784 105 154 048 21.725 5610 7.785 9928 .002 118 644 473 223 729 105 828 817 21.748 5632 7.791 4875 .002 114 165 474 224 676 106 496 424 21.771 5411 7.796 9745 .002 109 705 475 225 625 107 171 875 21.794 4947 7.802 4538 .002 105 263 476 226 576 107 850 176 21.817 4242 7.807 9254 .002 100 840 477 227 529 108 531333 21.840 3297 7.813 3892 .002 0% 436 478 228 484 109 215 352 21.863 2111 7.818 8456 .002 092 050 479 229 441 109 902 239 21.886 0686 7.824 2942 .002 087 683 480 230 400 110 592 000 21.908 9023 7.829 7353 .002 083 333 481 231361 111 284 641 21.931 7122 7.8351688 .002 079 002 482 232 324 111 980 168 21.954 4984 7.840 5949 .002 074 689 483 233 289 112 678 587 21.977 2610 7.846 0134 .002 070 393 484 234 256 113 379 904 22.000 0000 7.851 4244 .002 066 116 485 235 225 114 084 125 22.022 7155 7.856 8281 .002 061 856 486 236196 114 791 256 22.045 4077 7.862 2242 .002 057 613 487 237 169 115 501 303 22.068 0765 7.867 6130 .002 053 388 488. 238144 116 214 272 22.090 7220 7.872 9944 .002 049 180 489 239121 116 930169, 22.113 3444 7.878 3684 .002 044 990 490 240100 117 649 000 22.135 9436 7.883 7352 .002 040 816 491 241081 118 370 771 22.158 5198 7.889 0946 .002 036 660 492 242 064 119 095 488 22.181 0730 7.894 4468 .002 032 520 493 243 049 119 823 157 22.203 6033 7.899 7917 .002 028 398 494 244 036 120 553 784 22.226 1108 7.905 1294 .002 024 291 495 245 025 121 287 375 22.248 5955 7.910 4599 .002 020 202 496 246 016 122 023 936 22.271 0575 7.915 7832 .002 016 129 497 247 009 122 763 473 22.293 4968 7.921 0994 .002 012 072 498 248 004 123 505 992 22.315 9136 7.926 4085 .002 008 032 499 249 001 124 251 499 22.338 3079 7.931 7104 .002 004 008 500 250 000 125 000 000 22.360 6798" 7.937 0053 .002 000 000 501 251001 125 751 501 22.383 0293 7.942 2931 .001 996 008 502 252 004 126 506 008 22.405 3565 7.947 5739 .001 992 032 503 253 009 127 263 527 22.427 6615 7.952 8477 .001 988 072 504 254 016 128 024 064 22.449 9443 7.958 1144 .001 984 127 505 255 025 128 787 625 22.472 2051 7.963 3743 .001 980 198 506 256 036 129 554 216 22.494 4438 7.968 6271 .001 976 285 507 257 049 130 323 843 22.516 6605 7.973 8731 .001 972 387 508 258 064 131 096 512 22.538 8553 7.979 1122 .001 968 504 509 259 081 131872 229 22.561 0283 7.984 3444 .001 964 637 510 260100 132 651 000 22.583 1796 7.989 5697 .001 960 784 511 261121 133 432 831 22.605 3091 7.994 7883 .001 956 947 512 262 144 134 217 728 22.627 4170 8.000 0000 .001 953 125 513 263169 135 005 697 22.649 5033 8.005 2049 .001 949 318 514 264 1% 135 796 744 22.671 5681 8.010 4032 .001 945 525 515 265 225 136 590 875 22.693 6114 8.015 5946 .001 941 748 516 266 256 137 388 096 22.715 6334 8.020 7794 .001 937 984 517 267 289 138 188 413 22.737 6341 8.025 9574 .001 934 236 518 268 324 138 991 832 22.759 6134 8.031 1287 .001930 502 519 269 361 139 798 359 22.781 5715 8.036 2935 .001 926 782 520 270 400 140 608 000 22.803 5085 8.041 4515 .001 923 077 Powers and Roots 761 Number. Squares. Cubes. ^Roots. f Boots. Reciprocals. 521 271 441 141 420 761 22.825 4244 8.046 6030 .001 919 386 522 272 484 142 236 648 22.847 3193 8.051 7479 .001 915 709 523 273 529 143 055 667 22.869 1933 8.056 8862 .001912 046 524 274 576 143 877 824 22.891 0463 8.062 0180 .001 908 397 525 275 625 144 703 125 22.912 8785 8.067 1432 .001 904 762 526 276 676 145 531 576 22.934 6899 8.072 2620 .001 901 141 527 277 729 146 363 183 22.956 4806 8.077 3743 .001 897 533 528 278 784 147 197 952 22.978 2506 8.082 4800 .001 893 939 529 279 841 148 035 889 23.000 0000 8.087 5794 .001 890 359 530 280 900 148 877 001 23.021 7289 8.092 6723 .001 886 792 531 281961 149 721 291 23.043 4372 8.097 7589 .001 883 239 532 283 024 150 568 768 23.065 1252 8.102 8390 .001 879 699 533 284 089 151 419 437 23.086 7928 8.107 9128 .001 876 173 534 285156 152 273 304 23.108 4400 8.112 9803 .001 872 659 535 286 225 153 130 375 23.130 0670 8.118 0414 • .001 869 159 536 287 296 153 990 656 23.151 6738 8.123 0962 .001 865 672 537 288 369 154 854 153 23.173 2605 8.128 1447 .001 862 197 538 289 444 155 720 872 23.194 8270 8.133 1870 .001 858 736 539 290 521 156 590 819 23.216 3735 8.138 2230 .001 855 288 540 291600 157 464 000 23.237 9001 8.143 2529 .001 851 852 541 292 681 158 340 421 23.259 4067 8.148 2765 .001 848 429 542 293 764 159 220 088 23.280 8935 8.153 2939 .001 845 018 543 294 849 160 103 007 23.302 3604 8.158 3051 .001 841 621 544 295 936 160 989 184 23.323 8076 8.163 3102 .001 838 235 545 297 025 161878 625 23.345 2351 8.168 3092 .001 834 862 546 298 116 162 771 336 23.366 6429 8.173 3020 .001 831 502 547 299 209 163 667 323 23.388 0311 8.178 2888 .001828154 548 300 304 164 566 592 23.409 3998 8.183 2695 .001 824 818 549 301 401 165 469 149 23.430 7490 8.188 2441 .001 821 494 550 302 500 166 375 000 23.452 0788 8.193 2127 .001 818 182 551 303 601 167 284 151 23.473 3892 8.198 1753 .001 814 882 552 304 704 168 196 608 23.494 6802 8.203 1319 .001811594 653 305 809 169 112 377 23.515 9520 8.208 0825 .001 808 318 554 306 916 170 031 464 23.537 2046 8.213 0271 .001 805 054 555 308 025 170 953 875 23.558 4380 8.217 9657 .001 801 802 556 309 136 171 879 616 23.579 6522 8.222 8985 .001 798 561 557 310 249 172 808 693 23.600 8474 8.227 8254 .001 795 332 558 311 364 173 741 112 23.622 0236 8.232 7463 .001 792 115 559 312 481 174 676 879 23.643 1808 8.237 6614 .001 788 909 560 313 600 175 616 000 23.664 3191 8.242 5706 .001 785 714 561 . 314 721 176 558 481 23.685 4386 8.247 4740 .001 782 531 562 315 844 177 504 328 23.706 5392 8.252 3715 .001 779 359 563 316 969 178 453 547 23.727 6210 8.257 2635 .001 776 199 564 318 096 179 406 144 23.748 6842 8.262 1492 .001 773 050 565 319 225 180 362 125 23.769 7286 8.267 0294 .001 769 912 566 320 356 181 321 496 23.790 7545 8.271 9039 .001 766 784 567 321 489 182 284 263 23.811 7618 8.276 7726 .001 763 668 568 322 624 183 250 432 23.832 7506 8.281 6255 .001 760 563 569 323 761 184 220 009 23.853 7209 8.286 4928 .001 757 469 570 324 900 185 193 000 23.874 6728 8.291 3444 .001754 386 571 326 041 186 169 411 23.895 6063 8.296 1903 .001 751 313 572 327 184 187 149 248 23.916 5215 8.301 0304 .001748 252 762 Powers and Roots . Number. Squares. Cubes. V' Roots. f Boots. Reciprocals. 573 328 329 188 132 517 23.937 4184 8.305 8651 .001 745 201 574 329 476 189 119 224 23.958 2971 8.310 6941 .001 742 160 575 330 625 190 109 375 23.979 1576 8.315 5175 .001 739 130 576 331776 191 102 976 24.000 0000 8.320 3353 .001 736 111 577 332 927 192 100 033 24.020 8243 8.325 1475 .001 733 102 578 334 084 193 100 552 24.041 6306 8.329 9542 .001 730 104 579 335 241 194 104 539 24.062 4188 8.334 7553 .001 727 116 580 336 400 195 112 000 24.083 1891 8.339 5509 .001 724 138 581 337 561 196 122 941 24.103 9416 8.344 3410 .001 721 170 582 338 724 197 137 368 24.124 6762 8.349 1256 .001 718 213 583 339 889 198 155 287 24.145 3929 8.353 9047 .001 715 266 584 341056 199 176 704 24.166 0919 8.358 6784 .001 712 329 585 342 225 200 201 625 24.186 7732 8.363 4466 .001 709 402 586 343 396 201 230 056 24.207 4369 8.368 2095 .001 706 485 587 344 569 202 262 003 24.228 0829 8.372 9668 .001 703 578 588 345 744 203 297 472 24.248 7113 8.377 7188 .001 700 680 589 346 921 204 336 469 24.269 3222 8.382 4653 .001 697 793 590 348100 205 379 000 24.289 9156 8.387 2065 .001 694 915 591 349 281 206 425 071 24.310 4996 8.391 9428 .001692 047 592 350 464 207 474 688 24.331 0501 8.396 6729 .001 689 189 593 351649 208 527 857 24.351 5913 8.401 3981 .001 686 341 594 352 836 209 584 584 24.372 1152 8.406 1180 .001 683 502 595 354 025 210 644 875 24.392 6218 8.410 8326 .001 680 672 696 355 216 211 708 736 24.413 1112 8.415 5419 .001 677 852 597 356 409 212 776 173 24.433 5834 8.420 2460 .001 675 042 598 357 604 213 847 192 24.454 0385 8.424 9448 .001 672 241 599 358 801 214 921 799 24.474 4765 8.429 6383 .001 669 449 600 360 000 216 000 000 24.494 8974 8.434 3267 .001 666 667 601 361201 217 081 801 24.515 3013 8.439 0098 .001 663 894 602 362 404 218 167 208 24.535 6883 8.443 6877 .001 661 130 603 363 609 219 256 227 24.556 0583 8.448 3605 .001 658 375 604 364 816 220 348 864 24.576 4115 8.453 0281 .001 655 629 605 366 025 221 445 125 24.596 7478 8.457 6906 .001 652 893 606 367 236 222 545 016 24.617 0673 8.462 3479 .001 650 165 607 368 449 223 648 543 24.637 3700 8.467 0001 .001 647 446 608 369 664 224 755 712 24.657 6560 8.471 6471 .001 644 737 609 370 881 225 866 529 24.677 9254 8.476 2892 .001 642 036 610 372 100 226 981 000 24.698 1781 8.480 9261 .001 639 344 611 873 321 228 099 131 24.718 4142 8.485 5579 .001 636 661 612 374 544 229 220 928 24.738 6338 8.490 1848 .001 633 987 613 375 769 230 346 397 24.758 8368 8.494 8065 .001 631 321 614 376 996 231 475 544 24.779 0234 8.499 4233 .001 628 664 615 378 225 232 608 375 24.799 1935 8.504 0350 .001 626 016 616 379 456 233 744 896 24.819 3473 8.508 6417 .001 623 377 617 380 689 234 885 113 24.839 4847 8.513 2435 ' .001 620 746 618 381924 236 029 032 24.859 6058 8.517 8403 .001 618 123 619 383161 237 176 659 24.879 7106 8.522 4331 .001 615 509 620 384 400 238 328 000 24.899 7992 8.527 0189 .001 612 903 621 385 641 239 483 061 24.919 8716 8.531 6009 .001 610 306 622 386 884 240 641 848 24 939 9278 8.536 1780 .001 607 717 623 388129 241 804 367 24.959 9679 8.540 7501 .001 605 136 624 389 376 242 970 624 24.979 9920 8.545 3173 .001 602 564 Powers and Roots 763 Number. Squares. Cubes. ^Roots. f Roots. Reciprocals. 625 390 625 244 140 625 25.000 0000 8.549 8797 .001 600 000 626 391 876 245 134 376 25.019 9920 8.554 4372 .001 597 444 627 393 129 246 491 883 25.039 9681 8.558 9899 .001 594 896 628 394 384 247 673 152 25.059 9282 8.563 5377 .001 592 357 629 395 641 248 858 189 25.079 8724 8.568 0807 .001 589 825 630 396 900 250 047 000 25.099 8008 8.572 6189 .001 587 302 631 398 161 251 239 591 25.119 7134 8.577 1523 .001 584 786 632 399 424 252 435 968 25.139 6102 8.581 6809 .001 582 278 633 400 689 253 636 137 25.159 4913 8.586 2247 .001 579 779 634 401 956 254 840 104 25.179 3566 8.590 7238 .001 577 287 635 403 225 256 047 875 25.199 2063 8.595 2380 .001 574 803 636 404 496 257 259 456 25.219 0404 8.599 7476 .001 572 327 637 405 769 258 474 853 25.238 8589 8.604 2525 .001 569 859 638 407 044 259 694 072 25.258 6619 8.608 7526 .001 567 398 639 408 321 260 917 119 25.278 4493 8.613 2480 .001 564 945 640 409 600 262 144 000 25.298 2213 8.617 7388 .001 562 500 641 410 881 263 374 721 25.317 9778 8.622 2248 .001 560 062 642 412 164 264 609 288 25.337 7189 8.626 7063 .001 557 632 643 413 449 265 847 707 25.357 4447 8.631 1830 .001 555 210 644 414 736 267 089 984 25.377 1551 8.635 6551 .001 552 795 645 416 025 268 336 125 25.396 8502 8.640 1226 .001 550 388 646 417 316 269 585 136 25.416 5302 8.644 5855 .001 547 988 647 418 609 270 840 023 25.436 1947 8.649 0437 .001 545 595 648 419 904 272 097 792 25.455 8441 8.653 4974 .001 543 210 649 421201 273 359 449 25.475 4784 8.657 9465 .001 540 832 650 422 500 274 625 000 25.495 0976 8.662 3911 .001 538 462 651 423 801 275 894 451 25.514 7013 8.666 8310 .001 536 098 652 425 104 277 167 808 25.534 2907 8.671 2665 .001 533 742 653 426 409 278 445 077 25.553 8647 8.675 6974 .001 531 394 654 427 716 279 726 264 25.573 4237 8.680 1237 .001 529 052 655 429 025 281 Oil 375 25.592 9678 8.684 5456 .001 526 718 656 430 336 282 300 416 25.612 4969 8.688 9630 .001 524 390 657 431649 283 593 393 25.632 0112 8.693 3759 .001 522 070 658 432 964 284 890 312 25.651 5107 8.697 7843 .001 519 757 659 434 281 286 191 179 25.670 9953 8.702 1882 .001 517 451 660 435 600 287 496 000 25.690 4652 8.706 5877 .001 515 152 661 436 921 288 804 781 25.709 9203 8.710 9827 .001 512 859 662 438 244 290 117 528 25.729 3607 8.715 3734 .001 510 574 663 439 569 291 434 247 25.748 7864 8.719 7596 .001 508 296 664 440 896 292 754 944 25.768 1975 8.724 1414 .001506 024 665 442 225 294 079 625 25.787 5939 8.728 5187 .001 503 759 666 443 556 295 408 296 25.806 9758 8.732 8918 .001 501 502 667 444 889 296 740 963 25.826 3431 8.737 2604 .001 499 250 668 446 224 298 077 632 25.845 6960 8.741 6246 .001 497 006 669 447 561 299 418 309 25.865 0343 8.745 9846 .001 494 768 670 448 900 300 763 000 25.884 3582 8.750 3401 .001 492 537 671 450 241 302 111 711 25.903 6677 8.754 6913 .001 490 313 672 451 584 303 464 448 25.922 9628 8.759 0383 .001 488 095 673 452 929 304 821 217 25.942 2435 8.763 3809 .001 485 884 674 454 276 306 182 024 25.961 5100 8.767 7192 .001 483 680 675 455 625 307 546 875 25.980 7621 8.772 0532 .001 481 481- 676 456 976 308 915 776 26.000 0000 8.776 3830 .001 479 290 7G4 Powers and Roots Number. Squares. Cubes. V Roots, f Boots. Reciprocals. 677 458 329 310 288 733 26.019 2237 8.780 7084 .001 477 105 678 459 684 311 665 752 26.038 4331 8.785 0296 .001 474 926 679 461041 313 046 839 26.057 6284 8.789 3466 .001472 754 680 462 400 314 432 000 26.076 8096 8.793 6593 .001 470 588 681 463 761 315 821 241 26.095 9767 8.797 9679 .001 468 429 682 465124 317 214 568 26.115 1297 8.802 2721 .001 466 276 683 466 489 318 611 987 26.134 2687 8.806 5722 .001 464 129 684 467 856 320 013 504 26.153 3937 8.810 8681 .001 461 988 685 469 225 321 419 125 26.172 5047 8.815 1598 .001 459 854 686 470 596 322 828 856 26.191 6017 8.819 4474 .001 457 726 687 471969 324 242 703 26.210 6848 8.823 7307 .001 455 604 688 473 344 325 660 672 26.229 7541 8.828 0099 .001 453 488 689 474 721 327 082 769 26.248 8095 8.832 2850 .001 451 379 690 476100 328 509 000 26.267 8511 8.836 5559 .001 449 275 691 477 481 329 939 371 26.286 8789 8.840 8227 .001 447 178 692 478 864 331 373 888 26.305 8929 8.845 0854 .001 445 087 693 480 249 332 812 557 26.324 8932 8.849 3440 .001 443 001 694 481 636 334 255 384 26.343 8797 8.853 5985 .001 440 922 695 483 025 335 702 375 26.362 8527 8.857 8489 .001 438 849 696 484 416 337 153 536 26.381 8119 8.862 0952 .001 436 782 697 485 809 338 608 873 26.400 7576 8.866 3375 .001 434 720 698 487 204 340 068 392 26.419 6896 8.870 5757 .001 432 665 699 488 601 341 532 099 26.438 6081 8.874 8099 .001 430 615 700 490 000 343 000 000 26.457 5131 8.879 0400 .001 428 571 701 491 401 344 472 101 26.476 4046 8.883 2661 .001 426 534 702 492 804 345 948 408 26.495 2826 8.887 4882 .001 424 501 703 494 209 347 428 927 26.514 1472 8.891 7063 .001 422 475 704 495 616 348 913 664 26.532 9983 8.895 9204 .001 420 455 705 497 025 350 402 625 26.551 8361 8.900 1304 .001 418 440 706 498 436 351 895 816 26.570 6605 8.904 3366 .001 416 431 707 499 849 353 393 243 26.589 4716 8.908 5387 .001 414 427 708 501264 354 894 912 26.608 2694 8.912 7369 .001 412 429 709 502 681 356 400 829 26.627 0539 8.916 9311 .001 410 437 710 504 100 357 911 000 26.645 8252 8.921 1214 .001 408 451 711 505 521 359 425 431 26.664 5833 8.925 3078 .001 406 470 712 506 944 360 944 128 26.683 3281 8.929 4902 .001 404 494 713 508 369 362 467 097 26.702 0598 8.933 6687 .001 402 525 714 509 796 363 994 344 26.720 7784 8.937 8433 .001 400 560 715 511225 365 525 875 26.739 4839 8.942 0140 .001 398 601 716 612 656 367 061 696 26.758 1763 8.946 1809 .001 396 648 717 514 089 368 601 813 26.776 8557 8.950 3438 .001 394 700 718 515 524 370 146 232 26.795 5220 8.954 5029 .001 392 758 719 516 961 371 694 959 26.814 1754 8.958 6581 .001 390 821 720 518 400 373 248 000 26.832 8157 8.962 8095 .001 388 889 721 519 841 374 805 361 26.851 4432 8.966 9570 .001 386 963 722 521284 376 367 048 26.870 0577 8.971 1007 .001 385 042 723 522 729 377 933 067 26.888 6593 8.975 2406 .001 383 126 724 524 176 379 503 424 26.907 2481 8.979 3766 .001 381 215 725 525 625 381 078 125 26.925 8240 8.983 5089 .001 379 310 726 527 076 382 657 176 26.944 3872 8.987 6373 .001 377 410 727 528 529 384 240 583 26.962 9375 8.991 7620 .001 375 516 728 529 981 385 828 352 26.981 4751 ! 8.995 8899 .001 373 626 Powers and Roots. 765 Number. Squares. Cubes. } Roots. f Roots. Reciprocals. 729 531 441 387 420 489 27.000 0000 9.000 0000 .001 371 742 730 532 900 389 017 000 27.018 5122 9.004 1134 .001 369 863 731 534 361 390 617 891 27.037 0117 9.008 2229 .001 367 989 • 732 535 824 392 223 168 27.055 4985 9.012 3288 .001 366 120 733 537 289 393 832 837 27.073 9727 9.016 4309 .001 364 256 734 538 756 395 446 904 27.092 4344 9.020 5293 .001 362 398 735 540 225 397 065 375 27.110 8834 9.024 6239 .001 360 544 736 541696 398 688 256 27.129 3199 9.028 7149 .001 358 696 737 543169 400 315 553 27.147 7149 9.032 8021 .001 356 8j2 738 544 644 401 947 272 27.166 1554 9.036 8857 .001 355 014 739 546121 403 583 419 27.184 5544 9.040 9655 .001 353 180 740 547 600 405 224 000 27.202 9140 9.045 0419 .001 351 351 741 549 081 406 869 021 27.221 3152 9.0491142 .001 349 528 742 550 564 408 518 488 27.239 6769 9.053 1831 .001 347 709 743 552 049 410 172 407 27.258 0263 9.057 2482 .001 345 895 744 553 536 411 830 784 27.276 3634 9.061 3098 .001 344 086 745 555 025 413 493 625 27.294 6881 9.065 3677 .001 342 282 746 556 516 415 160 936 27.313 0006 9.069 4220 .001 340 483 747 558 009 416 832 723 27.331 3007 9.073 4726 .001 338 688 748 559 504 418 508 992 27.349 5887 9.077 5197 .001 336 898 749 561001 420 189 749 27.367 8644 9.081 5631 .001 335 113 750 562 500 421 875 000 27.386 1279 9.085 6030 .001 333 333 751 564 001 423 564 751 27.404 3792 9.089 6352 .001 331 558 752 565 504 425 259 008 27.422 6184 9.093 6719 .001 329 787 753 567 009 426 957 777 27.440 8455 9.097 7010 .001 328 021 754 568 516 428 661 064 27.459 0604 9.101 7265 .001 326 260 755 570 025 430 368 875 27.477 2633 9.105 7485 .001 324 503 756 571 536 432 081 216 27.495 4542 9.109 7669 .001 322 751 757 573 049 433 798 093 27.513 6330 9.113 7818 .001 321 004 758 574 564 435 519 512 27.531 7998 9.117 7931 .001 319 261 759 576 081 437 245 479 27.549 9546 9.121 8010 .001 317 523 760 577 600 438 976 000 27.568 0975 9.125 8053 .001 315 789 761 579 121 440 711 081 27.586 2284 9.129 8061 .001 314 060 762 580 644 442 450 728 27.604 3475 9.133 8034 .001 312 336 763 582169 444 194 947 27.622 4546 9.137 7971 .001 310 616 764 583 696 445 943 744 27.640 5499 9.141 7874 Ml 308 901 765 585 225 447 697 125 27.658 6334 9.145 7742 .001 307 190 766 586 756 449 455 096 27.676 7050 9.149 7576 .001 305 483 767 588 289 451217 663 27.694 7648 9.153 7375 .001 303 781 768 589 824 452 984 832 27.712 8129 9.157 7139 .001 302 083 769 591 361 454 756 609 27.730 8492 9.161 6869 .001 300 390 770 592 900 456 533 000 27.748 8739 9.165 6565 .001 298 701 771 594 441 458 314 Oil 27.766 8868 9.169 6225 .001 297 017 772 595 984 460 099 648 27.784 8880 9.173 5852 .001 295 337 773 597 529 461 889 917 27.802 8775 9.177 5445 .001 293 661 774 599 076 463 684 824 27.820 8555 9.181 5003 .001 291 990 775 600 625 465 484 375 27.838 8218 9.185 4527 .001 290 323 776 602 176 467 288 576 27.856 7766 9.189 4018 .001 288 660 777 603 729 469 097 433 27.874 7197 9.193 3474 .001 287 001 778 605 284 470 910 952 27.892 6514 9.197 2897 .001 285 347 779 606 841 472 729 139 27.910 5715 9.201 2286 .001 283 697 780 608 400 474 552 000 27.928 4801 «.205 1641 .001 282 051 766 Powers and Roots Number. Squares. Cubes. Kfiftote f RootH. Reciprocate, 781 609 961 476 379 541 27.946 3772 9.209 0962 .001 280 410 782 611524 478 211 768 27.964 2629 9.213 0250 .001 278 772 783 613 089 480 048 687 27.982 1372 9.216 9505 .001 277 139 784 614 656 481 890 304 28.000 0000 9.220 8726 .001 275 510 785 616 225 483 736 625 28.017 8515 9.224 7914 .001 273 885 786 617 7% 485 587 656 28.035 6915 9.228 7068 .001 272 265 787 619 369 487 443 403 28.053 5203 9.232 6189 .001 270 648 788 620 944 489 303 872 28.071 3377 9.236 5277 .001 269 036 789 622 521 491 169 069 28.089 1438 9.240 4333 .001 267 427 790 624100 493 039 000 28.106 9386 9.244 3355 .001 265 823 791 625 681 494 913 671 28.124 7222 9.248 2344 .001 264 223 792 627 264 496 793 088 28.142 4946 9.252 1300 .001 262 626 793 628 849 498 677 257 28.160 2557 9.256 0224 .001 261 034 794 630 436 500 566 184 28.178 0056 9.259 9114 .001 259 446 795 632 025 502 459 875 28.195 7444 9.263 7973 .001 257 862 796 633 616 504 358 336 28.213 4720 9.267 6798 .001 256 281 797 635 209 506 261 573 28.231 1884 9.271 5592 .001 254 705 798 636 804 508 169 592 28.248 8938 9.275 4352 .001 253 133 799 638 401 510 082 399 28.266 5881 9.279 3081 .001 251 564 800 640 000 512 000 000 28.284 2712 9.283 1777 .001250 000 801 641601 513 922 401 28.301 9434 9.287 0444 .001 248 439 802 643 204 515 849 608 28.319 6045 9.290 9072 .001 246 883 803 644 809 517 781 627 28.337 2546 9.294 7671 .001 245 330 801 646 416 519 718 464 28.354 8938 9.298 6239 .001 243 781 805 648 025 521 660 125 28.372 5219 9.302 4775 .001 242 236 806 649 636 523 606 616 28.390 1391 9.306 3278 .001 240 695 807 651249 525 557 943 28.407 7454 9.310 1750 .001 239 157 808 652 864 527 514 112 28.425 3408 9.314 0190 .001 237 624 809 654 481 529 475129 28.442 9253 9.317 8599 .001 236 094 810 656100 531 441 000 28.460 4989 9.321 6975 .001 234 568 811 657 721 533 411 731 28.478 0617 9.325 5320 .001 233 046 812 659 844 535 387 328 28.495 6137 9.329 3634 .001 231 527 813 660 969 537 367 797 28.513 1549 9.333 1916 .001 230 012 814 662 596 539 353 144 28.530 6852 9.337 0167 .001 228 501 815 664 225 541343 375 28.548 2048 9.340 8386 .001 226 994 816 665 856 543 338 496 28.565 7137 9.344 6575 .001 225 499 817 667 489 545 338 513 28.583 2119 9.348 4731 .001 223 990 818 669124 547 343 432 28.600 6993 9.352 2857 .001 222 494 819 670 761 549 353 259 28.618 1760 9.356 0952 .001 221 001 820 672 400 551368 000 28.635 6421 9.359 9016 .001 219 512 821 674 041 553 387 661 28.653 0976 9.363 7049 .001 218 027 822 675 684 555 412 248 28.670 5424 9.367 5051 .001 216 545 823 677 329 557 441 767 28.687 9716 9.371 3022 .001215 067 824 678 976 559 476 224 28.705 4002 9.375 0963 .001 213 592 825 680 625 561 515 625 28.722 8132 9.378 8873 .001 212 121 826 682 276 563 559 976 28.740 2157 9.382 6752 .001 210 654 827 683 929 565 609 283 28.757 6077 9.386 4600 .001 209 190 828 685 584 567 663 552 28.774 9891 9.390 2419 .001 207 729 829 687 241 569 722 789 28.792 3601 9.394 0206 .001 206 273 830 688 900 571 787 000 28.809 7206 9.397 7964 .001 204 819 831 690 561 573 856 191 28.827 0706 9.401 5691 .001 203 369 832 692 224 .575 930 368 28.844 4102 9.405 3387 .001 201 923 Powers and Roots 767 Number. Squares. Cubes. V Roots. f Roots. Reciprocals. 833 693 889 578 009 537 28.861 7394 9.409 1054 .001 200 480 834 695 556 580 093 704 28.879 0582 9.412 8690 .001 199 041 835 697 225 582 182 875 28.896 3666 9.416 6297 .001 197 605 836 698 896 584 277 056 28.913 6646 9.420 3873 .001 196 172 837 700 569 586 376 253 28.930 9523 9.424 1420 .001 194 743 838 702 244 588 480 472 28.948 2297 9.427 8936 .001 193 317 839 703 921 590 589 719 28.965 4967 9.431 6423 .001 191 895 840 705 600 592 704 000 28.982 7535 9.435 3800 .001 190 476 841 707 281 594 823 321 29.000 0000 9.439 1307 .001 189 061 842 708 964 596 947 688 29.017 2363 9.442 8704 .001 187 648 843 710 649 599 077 107 29.034 4623 9.446 6072 .001 186 240 844 712 336 601 211 584 29.051 6781 9.450 3410 .001 184 834 845 714 025 603 351 125 29.068 8837 9.454 0719 .001 183 432 846 715 716 605 495 736 29.086 0791 9.457 7999 .001 182 033 847 717 409 607 645 423 29.103 2644 9.461 5249 .001 180 638 848 719 104 609 800 192 29.120 4396 9.465 2470 .001 179 245 849 720 801 611 960 049 29.137 6046 9.468 9661 .001 177 856 850 722 500 614 125 000 29.154 7595 9.472 6824 .001 176 471 851 724 201 616 295 051 29.171 9043 9.476 3957 .001 175 088 852 725 904 618 470 208 29.189 0390 9.480 1061 .001 173 709 853 727 609 620 650 477 29.206 1637 9.483 8136 .001 172 333 854 729 316 622 835 864 29.223 2784 9.487 5182 .001 170 960 855 731 025 625 026 375 29.240 3830 9.491 2200 .001 169 591 856 732 736 627 222 016 29.257 4777 9.494 9188 .001 168 224 857 734 449 629 422 793 29.274 5623 9.498 6147 .001 166 861 858 736 164 631 628 712 29.291 6370 9.502 3078 .001 165 501 859 737 881 633 839 779 29.308 7018 9.505 9980 .001 164 144 860 739 600 636 056 000 29.325 7566 9.509 6854 .001 162 791 861 741 321 638 277 381 29.342 8015 9.513 3699 .001 161 440 862 743 044 640 503 928 29.359 8365 9.517 0515 .001 160 093 863 744 769 642 735 647 29.376 8616 9.520 7303 .001 158 749 864 746 496 644 972 544 29.393 8769 9.524 4063 .001 157 407 865 748 225 647 214 625 29.410 8823 9.528 0794 .001 156 069 866 749 956 649 461 896 29.427 8779 9.531 7497 .001 154 734 867 751 689 651 714 363 29.444 8637 9.535 4172 .001 153 403 868 753 424 653 972 032 29.4618397 9.539 0818 .001 152 074 869 755 161 656 234 909 29.478 8059 9.542 7437 .001 150 748 870 756 900 658 503 000 29.495 7624 9.546 4027 .001 149 425 871 758 641 660 776 311 29.512 7091 9.550 0589 .001 148 106 872 760 384 663 054 848 29.529 6461 9.553 7123 .001 146 789 873 762 129 665 338 617 29.546 5734 9.557 3630 .001 145 475 874 763 876 667 627 624 29.563 4910 9.561 0108 .001 144 165 875 765 625 669 921 875 29.580 3989 9.564 6559 .001 142 857 876 767 376 672 221 376 29.597 2972 9.568 2782 .001 141 553 877 769129 674 526 133 29.614 1858 9.571 9377 .001 140 251 878 770 884 676 836 152 29.631 0648 9.575 5745 .001 138 952 879 . 772 641 679 151 439 29.647 9342 9.579 2085 .001 137 656 880 774 400 681 472 000 29.664 7939 9.582 8397 .001 136 364 881 776 161 683 797 841 29.681 6442 9.586 4682 .001135 074 882 777 924 686 128 968 29.698 4848 9.590 0937 .001 133 787 883 779 689 688 465 387 29.715 3159 9.593 7169 .001 132 503 884 781 456 690 807 104 29.732 1375 9.597 3373 .001 131 222 768 Powers and Roots Number. Squares. Cubes. t'Rooti f Roots. Reciprocals. 885 783 225 693 154 125 29.748 9496 9.600 9548 .001 129 944 886 784 996 695 506 456 29.765 7521 9.604 5696 .001 128 668 887 786 769 697 864 103 29.782 5452 9.608 1817 .001 127 396 888 788 544 700 227 072 29.799 3289 9.611 7911 .001 126 126 889 790 321 702 595 369 29.816 1030 9.615 3977 .001 124 859 890 792100 704 969 000 29.832 8678 9.619 0017 .001 123 596 891 793 881 707 347 971 29.849 6231 9.622 6030 .001 122 334 892 795 664 707 932 288 29.866 3690 9.626 2016 .001 121 076 893 797 449 712 121 957 29.883 1056 9.629 7975 .001 119 821 894 799 236 714 516 984 29.899 8328 9.633 3907 .001 118 568 895 801025 716 917 375 29.916 5506 9.636 9812 .001 117 818 896 802 816 719 323 136 29.933 2591 9.640 5690 .001 116 071 897 804 609 721734 273 29.949 9583 9.644 1542 .001 114 827 898 806 404 724 150 792 29.966 6481 9.647 7367 .001 113 586 899 808 201 726 572 699 29.983 3287 9.651 3166 .001 112 347 900 810 000 729 000 000 30.000 0000 9.654 8938 .001 111 111 901 811801 731 432 701 30.016 6621 9.658 4684 .001 109 878 902 813 604 733 870 808 30.033 3148 9.662 0403 .001 108 647 903 815 409 736 314 327 30.049 9584 9.665 60% .001 107 420 904 817 216 738 763 264 30.066 5928 9.669 1762 .001 106 195 905 819 025 741 217 625 30.083 2179 9.672 7403 .001 104 972 906 820 836 743 677 416 30.099 8339 9.676 3017 .001 103 753 907 822 649 746 142 643 30.116 4407 9.679 8604 .001 102 536 908 824 464 748 613 312 30.133 0383 9.683 4166 .001 101 322 909 826 281 751 089 429 30.149 6269 9.686 9701 .001 100 110 910 828100 753 571 000 30.166 2063 9.690 5211 .001 098 901 911 829 921 756 058 031 30.182 7765 9.694 0694 .001 097 695 912 831744 758 550 828 30.199 3377 9.697 6151 .001 096 491 913 833 569 761 048 497 30.215 8899 9.701 1583 .001 095 290 914 835 396 763 551 944 30.232 4329 9.704 6989 .001 094 092 915 837 225 766 060 875 30.248 9669 9.708 2369 .001 092 896 916 839 056 768 575 296 30.265 4919 9.711 7723 .001 091 703 917 840 889 771 095 213 30.282 0079 9.715 3051 .001 090 513 918 842 724 773 620 632 30.298 5148 9.718 8354 .001 089 325 919 844 561 776 151 559 30.315 0128 9.722 3631 .001 088 139 920 846 400 778 688 000 30.331 5018 9.725 8883 .001 086 957 921 848 241 781229 961 30.347 9818 9.729 4109 .001 085 776 922 850 084 783 777 448 30.364 4529 9.732 9309 .001 084 599 923 851929 786 330 467 30.380 9151 9.736 4484 .001 083 423 924 853 776 788 889 024 30.397 3683 9.739 9634 .001 082 251 925 855 625 791 453 125 30.413 8127 9.743 4758 .001 081 081 926 857 476 794 022 776 30.430 2481 9.746 9857 .001 079 914 927 859 329 796 597 983 30.446 6747 9.750 4930 .001 078 749 928 861184 799 178 752 30.463 0924 9.753 9979 .001 077 586 929 863 041 801 765 089 30.479 5013 9.757 5002 .001 076 426 930 864 900 804 357 000 30.495 9014 9.761 0001 .001 075 269 931 866 761 806 954 491 30.512 2926 9.764 4974 .001 074 114 932 868 624 809 557 568 30.528 6750 9.767 9922 .001 072 961 933 870 489 812 166 237 30.545 0487 9.771 4845 .001 071 811 934 872 356 814 780 504 30.561 4136 9.774 9743 .001070 664 935 874 225 817 400 375 30.577 7697 9.778 4616 .001 069 519 936 876 096 820 025 856 30.594 1171 9.781 9466 .001 068 376 Powers and Roots 769 Number. Squares. Cubes. V Roots, f Roots. Reciprocals. 937 877 969 822 656 953 30.610.4557 9.785 4288 .001 067 236 938 879 844 825 293 672 30.626 7857 9.788*9087 .001 066 098 939 881721 827 936 019 30.643 1069 9.792 3861 .001 064 963 940 883 600 830 584 000 30.659 4194 9.795 8611 .001 063 830 941 885 481 833 237 621 30.675 7233 9.799 3336 .001 062 699 942 887 364 835 896 888 30.692 0185 9.802 8036 .001 061 571 943 889 249 838 561 807 30.708 3051 9.806 2711 .001 060 445 944 891 136 841 232 384 30.724 5830 9.809 7362 .001 059 322 945 893 025 843 908 625 30.740 8523 9.813 1989 .001 058 201 946 894 916 846 590 536 30.757 1130 9.816 6591 .001 057 082 947 896 809 849 278 123 30.773 3651 9.820 1169 .001 055 966 948 898 704 851 971 392 30.789 6086 9.823 5723 .001 054 852 949 900 601 854 670 349 30.805 8436 9.827 0252 .001 053 741 950 902 500 857 375 000 30.822 0700 9.830 4757 .001 052 632 951 904 401 860 085 351 30.838 2879 9.833 9238 .001 051 525 952 906 304 862 801 408 30.854 4972 9.837 3695 .001 050 420 953 908 209 865 523 177 30.870 6981 9.840 8127 .001 049 318 954 910 116 868 250 664 80.886 8904 9.844 2536 .001 048 218 955 912 025 870 983 875 30.903 0743 9.847 6920 .001 047 120 956 913 936 873 722 816 30.919 2477 9.851 1280 .001 046 025 957 915 849 876 467 493 30.935 4166 9.854 5617 .001 044 932 958 917 764 879 217 912 30.951 5751 9.857 9929 .001 043 841 959 919 681 881 974 079 30.967 7251 9.861 4218 .001 042 753 960 921600 884 736 000 30.983 8668 9.864 8483 .001 041 667 961 923 521 887 503 681 31.000 0000 9.868 2724 .001 040 583 962 925 444 890 277 128 31.016 1248 9.871 6941 .001 039 501 963 927 369 893 056 347 31.032 2413 9.8751135 .001 038 422 •964 929 296 895 841 344 31.048 3494 9.878 5305 .001 037 344 965 931225 898 632 125 31.064 4491 9.881 9451 .001 036 269 966 933156 901 428 696 31.080 5405 9.885 3574 .001 035 197 967 935 089 904 231 063 31.096 6236 9.888 7673 .001 034 126 968 937 024 907 039 232 31.112 6984 9.892 1749 .001 033 058 969 938 961 909 853 209 31.128 7648 9.895 5801 .001 031 992 • 970 940 900 912 673 000 31.144 8230 9.898 9830 .001 030 928 971 942 841 915 498 611 31.160 8729 9.902 3835 .001 029 866 972 944 784 918 330 048 31.176 9145 9.905 7817 .001 028 807 973 946 729 921 167 317 31.192 9479 9.909 1776 .001 027 749 974 948 676 924 010 424 31.208 9731 9.912 5712 .001 026 694 975 950 625 926 859 375 31.224 9900 9.915 9624 .001 025 641 976 952 576 929 714 176 31.240 9987 9.919 3513 .001 024 590 977 954 529 932 574 833 31.256 9992 9.922 7379 .001 023 541 978 956 484 935 441 352 31.272 9915 9.926 1222 .001 022 495 979 958*441 938 313 739 31.288 9757 9.929 5042 .001 021 450 980 960 400 941 192 000 31.304 9517 9.932 8839 .001 020 408 981 962 361 944 076 141 31.320 9195 9.936 2613 .001 019 168 982 964 324 946 966 168 31.336 8792 9.939 6363 .001 018 330 983 966 289 949 862 087 31.352 8308 9.943 0092 .001 017 294 984 968 256 952 763 904 31.368 7743 9.946 3797 .001 016 260 985 970 225 955 671 625 31.384 7097 9.949 7479 .001 015 228 986 972 196 958 585 256 31.400 6369 9.953 1138 .001 014 199 987 974 169 961 504 803 31.416 5561 9.956 4775 .001 013 171 988 976 144 964 430 272 31.432 4673 9.959 8389 .001 012 146 770 Powers and Roots Number. Squares. Cubes. I 7 Roots. f Roots. Reciprocals. asy 978 121 967 361 669 31.448 3704 9.963 1981 .001 011 122 990 980100* 970 299 000 BL4M98M 9.966 5549 .001 010 101 991 982 081 973 242 271 31.480 1525 9.969 9055 .001 009 082 992 984 064 976 191 488 31.496 0315 9.973 2619 .001008 065 993 986 049 979 146 657 31.511 9025 9.976 6120 .001 007 049 994 988 036 982 107 784 31.527 7655 9.979 9599 .001 006 036 995 990 025 985 074 875 31.543 6206 9.983 3055 .001 005 025 996 992 016 988 047 936 31.559 4677 9.986 6488 .001 004 016 997 994 009 991 026 973 31.575 3068 9.989 9900 .001 003 009 998 996 004 994 Oil 992 31.591 1380 9.993 3289 .001002 004 999 998 001 997 002 999 31.606 9613 9.996 6656 .001 001 001 1000 1000 000 1000 000 000 31.622 7766 10.000 0000 .001000 000 1001 1002 001 1 003 003 001 31.638 5840 10.003 3222 .000 999 0010 1002 1004 004 1 006 012 008 31.654 3866 10.006 6622 .000 998 0040 1003 1006 009 "1 009 027 027 31.670 1752 10.009 9899 .000 997 0090 1004 1 008 016 1 012 048 064 31.685 9590 10.013 3155 .000 996 0159 1005 1 010 025 1 015 075 125 31.701 7349 10.016 6389 .000 995 0249 1006 1 012 036 1 018 108 216 31.717 5030 10.019 9601 .000 994 0358 1007 1 014 049 1 021 147 343 31.733 2633 10.023 2791 .000 993 0487 1008 1016 064 1 024 192 512 31.749 0157 10.026 5958 .000 992 0635 1009 1 018 081 1 027 243 729 31.764 7603 10.029 9104 .000 991 0803 1010 1020100 1 030 301 000 31.780 4972 10.033 2228 .000 990 0990 1011 1 022 121 1 033 364 331 31.796 2262 10.036 5330 .000 989 1197 1012 1 024 144 1 036 433 728 31.811 9474 10.039 8410 .000 988 1423 1013 1 026 169 1 039 509 197 31.827 6609 10.043 1469 .000 987 1668 1014 1028196 1 042 590 744 31.843 3666 10.046 4506 .000 986 1933 1015 1030 225 1 045 678 375 31.859 0646 10.049 7521 .000 985 2217 1016 1032 256 1 048 772 096 31.874 7549 10.053 0514 .000 984 2520 1017 1 034 289 1 051 871 913 31.890 4374 10.056 3485 .000 983 2842 1018 1 036 324 1 054 977 832 31.906 1123 10.059 6435 .000 982 3183 1019 1 038 361 1 058 089 859 31.921 7794 10.062 9364 .000 981 3543 1020 1040 400 1 061 208 000 31.937 4388 10.066 2271 .000 980 3922 1021 1 042 441 1 064 332 261 31.953 0906 10.069 5156 .000 979 4319 1022 1044 484 1 067 462 648 31.968 7347 10.072 8020 .000 978 4736 1023 1 046 529 1 070 599 167 31.984 3712 10.076 0863 .000 977 5171 1024 1 048 576 1 073 741 824 32.000 0000 10.079 3684 .000 976 5625 1025 1 050 625 1 076 890 625 32.015 6212 10.082 6484 .000 975 6098 1026 1 052 676 1 080 045 576 32.031 2348 10.085 9262 .000 974 6589 1027 1054 729 1 083 206 683 32.046 8407 10.089 2019 .000 973 7098 1028 1056 784 1 086 373 952 32.062 4391 10.092 4755 .000 972 7626 1029 1058 841 1 089 547 389 32.078 0298 10.095 7469 .000 971 8173 1030 1060 900 1 092 727 000 32.093 6131 10.099 0163 .000 970 8738 1031 1062 961 1 095 912 791 32.109 1887 10.102 2835 .000 969 9321 1032 1065 024 1 099 104 768 32.124 7568 10.105 5487 .000 968 9922 1033 1067 089 1 102 302 937 32.140 3173 10.108 8117 .000 968 0542 1034 1069156 1 105 507 304 32.155 8704 10.112 0726 .000 967 1180 1035 1071225" 1 108 717 875 32.171 4159 10.115 3314 .000 966 1836 1036 1 073 2% 1 111 934 656 32.186 9539 10.118 5882 .000 965 2510 1037 1075 369 1 115 157 653 32.202 4844 10.1218428 .000 964 3202 1038 1 077 444 1 118 386 872 32.218 0074 10.125 0953 .000 963 3911 1039 1 079 521 1 121 622 319 32.233 5229 10.128 3457 .000 962 4639 1040 1081600 1 124 864 000 32.249 0310 10.131 5941 .000 961 5385 Powers and Roots. 771 Squares. 1 083 681 1 085 764 1 087 849 1 089 936 1 092 025 1 094 116 1 096 209 1 098 304 1 100 401 1 102 500 1 104 601 1 106 704 1 108 809 1 110 916 1 113 025 1 115 136 1 117 249 1 119 364 1 121 481 1 123 600 1 125 721 1 127 844 1 129 969 1 132 096 1134 225 1 136 356 1 138 489 1 140 624 1 142 761 1144 900 1 147 041 1 149 184 1 151 329 1 153 476 1 155 625 1 157 776 1 159 929 1 162 084 1 164 241 1 166 400 1 168 561 1 170 724 1 172 889 1 175 056 1177 225 1 179 396 1 181 569 1 183 744 1 185 921 1188100 1 190 281 1 192 464 Cubes. v' Roots, f Roots 1 128 111 921 1 131 366 088 1 134 626 507 1 137 893 184 1 141 166 125 1 144 445 336 1 147 730 823 1 151 022 592 1 154 320 649 1 157 625 000 1 160 935 651 1 164 252 608 1 167 575 877 1 170 905 464 1 174 241 375 1 177 583 616 1 180 932 193 1 184 287 112 1 187 648 379 1 191 016 000 1 194 389 981 1 197 770 328 1 201 157 047 1 204 550 144 1 207 949 625 1 211 355 496 1 214 767 763 1 218 186 432 1 221 611 509 1 225 043 000 1 228 480 911 1 231 925 248 1 235 376 017 1 238 833 224 1 242 296 875 1 245 766 976 1 249 243 533 1 252 726 552 1 256 216 039 1 259 712 000 1 263 214 441 1 266 723 368 1 270 238 787 1 273 760 704 1 277 289 125 1 280 824 056 1 284 365 503 1 287 913 472 1 291 467 969 1 295 029 000 1 298 596 571 1 302 170 688 32.264.5316 32.280 0248 32.295 5105 32.310 9888 32.326 4598 32.341 9233 32.357 3794 32.372 8281 32.388 2695 32.403 7035 32.419 1301 32.434 5495 32.449 9615 32.465 3662 32.480 7635 32.496 1536 32.511 5364 32.526 9119 32.542 2802 32.557 6412 32.572 9949 32.588 3415 32.603 5807 32.619 0129 32.634 3377 32.649 6554 32.664 9659 32.680 2693 32.695 5654 32.710 8544 32.726 1363 32.741 4111 32.756 6787 32.771 9392 32.787 1926 32.802 4398 32.817 6782 32.832 9103 32.848 1354 32.863 3535 32.878 5644 32.893 7684 32.908 9653 32.924 1553 32.939 3382 32.954 5141 32.969 6830 32.984 8450 33.000 0000 33.015 1480 33.030 2891 33.045 4233 10.134 8403 10.138 0845 10.141 3266 10.144 5667 10.147 8047 10.151 0406 10.154 2744 10.157 5062 10.160 7359 10.163 9636 10.167 1893 10.170 4129 10.173 6344 10.176 8539 10.180 0714 10.183 2868 10.186 5002 10.189 7116 10.192 9209 10.196 1283 10.199 3336 10.202 5369 10.205 7382 10.208 9375 10.212 1347 10.215 3300 10.218 5233 10.221 7146 10.224 9039 10.228 0912 10.231 2766 10.234 4599 10.237 6413 10.240 8207 10.243 9981 10.247 1735 10.250 3470 10.253 5186 10.256 6881 10.259 8557 10.263 0213 10.266 1850 10.269 3467 10.272 5065 10.275 6644 10.278 8203 10.281 9743 10.285 1264 10.288 2765 10.291 4247 10.294 5709 10.297 7153 Reciprocals. .000 960 6148 .000 959 6929 .000 958 7728 .000 957 8544 .000 956 9378 .000 956 0229 .000 955 1098 .000 954 1985 .000 953 2888 .000 952 3810 .000 951 4748 .000 950 5703 .000 949 6676 .000 948 7666 .000 947 8673 .000 946 9697 .000 946 0738 .000 945 1796 .000 944 2871 .000 943 3962 .000 942 5071 .000 941 6196 .000 940 7338 .000 939 8496 .000 938 9671 .000 938 0863 .000 937 2071 .000 936 3296 .000 935 4537 .000 934 5794 .000 933 7068 .000 932 8358 .000 931 9664 .000 931 0987 .000 930 2326 .000 929 3680 .000 928 5051 .000 927 6438 .000 926 7841 .000 925 9259 .000 925 0694 .000 924 2144 .000 923 3610 .000 922 5092 .000 921 6590 .000 920 8103 .000 919 9632 .000 919 1176 .000 918 2736 .000 917 4312 .000 916 5903 .000 915 7509 772 Powers and Roots Number. Squares. Cubes. ^Roote! f Boots. Reciprocals. 1093 1 194 649 1 305 751 357 33.060 5505 10.300 8577 .000 914 9131 1094 1196 836 1309 338 584 33.075 6708 10.303 9982 .000 914 0768 1095 1199 025 1312 932 375 33.090 7842 10.307 1368 .000 913 2420 10% 1 201 216 1 316 532 736 33.105 8907 10.310 2735 .000 912 4008 1097 1203 409 1 320 139 673 33.120 9903 10.313 4083 .000 911 5770 1098 1205 604 1 323 753 192 83.136 0830 10.316 5411 .000 910 7468 1099 1 207 801 1 327 373 299 33.151 1689 10.319 6721 .000 909 9181 1100 1210 000 1 331 000 000 33.166 2479 10.322 8012 .000 909 0909 1101 1 212 201 1 334 633 301 33.181 3200 10.325 9284 .000 908 2652 1102 1 214 404 1 338 273 208 33.196 3853 10.329 0537 .000 907 4410 1103 1 216 609 1 341 919 727 33.211 4438 10.332 1770 .000 906 6183 1104 1 218 816 1 345 572 864 33.226 6955 10.335 2985 .000 905 7971 1105 1221025 1 349 232 625 33.241 5403 10.338 4181 .000 904 9774 1106 1 223 236 1 352 899 016 33.256 5783 10.341 5358 .000 904 1591 1107 1 225 449 1 356 572 043 33.271 6095 10.344 6517 .000 903 3424 1108 1227 664 1 360 251 712 33.286 6339 10.347 7657 .000 902 5271 1109 1 229 881 1 363 938 029 33.301 6516 10.350 8778 .000 901 7133 1110 1232100 1 367 631 000 33.316 6625 10.353 9880 .000 900 9009 1111 1 234 321 1 371 330 631 33.331 6666 10.357 0964 .000 900 0900 1112 1 236 541 1 375 036 928 33.346 6640 10.360 2029 .000 899 2806 1113 1238 769 1 378 749 897 33.361 6546 10.363 3076 .000 898 4726 1114 1 240 996 1382 469 544 33.376 6385 10.366 4103 .000 897 6661 1115 1 243 225 1 386 195 875 33.391 6157 10.369 5113 .000 896 8610 1116 1 245 456 1 389 928 896 33.406 5862 10.372 6103 .000 896 0753 1117 1247 689 1 393 668 613 33.421 5499 10.375 7076 .000 895 2551 1118 1 249 924 1 397 415 032 33.436 5070 10.378 8030 .000 894 4544 1119 1 252 161 1 401 168 159 33.451 4573 10.381 8965 .000 893 6550 1120 1254 400 1 404 928 000 33.466 4011 10.384 9882 .000 892 8571 1121 1256 641 1 408 694 561 33.481 3381 10.388 0781 .000 896 0607 1122 1258 884 1 412 467 848 33.496 2684 10.391 1661 .000 892 2656 1123 1 261 129 1 416 247 867 33.511 1921 10.394 2527 .000 890 4720 1124 1 263 376 1 420 034 624 33.526 1092 10.397 3366 .000 889 6797 1125 1265 625 1 423 828 125 33.541 0196 10.400 4192 .000 888 8889 1126 1 267 876 1 427 628 376 33.555 9234 10.403 4999 .000 888 0995 1127 1 270 129 1 431 435 383 33.570 8206 10.406 5787 .000 887 3114 1128 1272 384 1 435 249 152 33.585 7112 10.409 6557 .000 886 5248 1129 1 274 641 1 439 069 689 33.600 5952 10.412 7310 .000 885 7396 1130 1276 900 1 442 897 000 33.615 4726 10.415 8044 .000 884 9558 1131 1 279 161 1 446 731 091 33.630 3434 10.418 8760 .000 884 1733 1132 1 281 424 1 450 571 968 33.645 2077 10.421 9158 .000 883 3922 1133 1 283 689 1 454 419 637 33.660 0653 10.425 0138 .000 882 6125 1134 1285 956 1 458 274 104 33.674 9165 10.428 0800 .000 881 8342 1135 1288 225 1 462 135 375 33.689 7610 10.431 1443 .000 881 0573 1136 1 290 496 1 466 003 456 33.704 5991 10.434 2069 .000 880 2817 1137 1292 769 1 469 878 353 33.717 4306 10.437 2677 .000 879 5075 1138 1295 044 1 473 760 072 33.734 0556 10.440 3677 .000 878 7346 1139 1 297 321 1 477 648 619 33.749 0741 10.443 3839 .000 877 9631 1140 1299 600 1 481 544 000 33.763 8860 10.446 4393 .000 877 1930 1141 1 301 881 1 485 446 221 33.778 6915 10.449 4929 .000 876 4242 1142 1304 164 1 489 355 288 33.793 4905 10.452 5448 .000 875 6567 1143 1 306 449 1 493 271 C07 33.808 2830 10.455 5948 .000 874 8906 1144 1308 736 1 497 193 984 33.823 0691 10.458 6431 .000 874 1259 Powers and Roots 773 Number. Squares. Cubes. V Roots. f Roots. Reciprocals. 1145 1311025 1 501 123 625 33.837 8486 10.461 6896 .000 873 3624 1146 1 313 316 1 505 060 136 33.852 6218 10.464 7343 .000 872 6003 1147 1 315 609 1 509 003 523 33.867 3884 10.467 7773 .000 871 8396 1148 1 317 904 1 512 953 792 33.882 1487 10.470 8158 .000 871 0801 1149 1 320 201 1 516 910 949 33.896 9025 10.473 8579 .000 870 3220 1150 1 322 500 1 520 875 000 33.911 6499 10.476 8955 .000 869 5652 1151 1 324 801 1 524 845 951 33.926 3909 10.479 9314 .000 868 8097 1152 1 327 104 1 528 823 808 33.941 1255 10.482 9656 .000 868 0556 1153 1 329 409 1 532 808 577 33.955 8537 10.485 9980 .000 867 3027 1154 1 331 716 1 536 800 264 33.970 5755 10.489 0286 .000 866 5511 1155 1 334 025 1 540 798 875 33.985 2910 10.492 0575 .000 865 8009 1156 1 336 336 1 544 804 416 34.000 0000 10.495 0847 .000 865 0519 1157 1 338 649 1 548 816 893 34.014 7027 10.498 1101 .000 864 3042 1158 1 340 964 1 552 836 312 34.029 3990 10.501 1337 .000 863 5579 1159 1 343 281 1 556 862 679 34.044 0890 10.504 1556 .000 862 8128 1160 1345 600 1 560 896 000 34.058 7727 10.507 1757 .000 862 0690 1161 1 347 921 1 564 936 281 34.073 4501 10.510 1942 .000 861 3264 1162 1350 244 1 568 983 528 34.088 1211 10.513 2109 .000 860 5852 1163 1 352 569 1 573 037 747 34.012 7858 10.516 2259 .000 859 8452 1164 1 354 896 1 577 098 944 34.117 4442 10.519 2391 .000 859 1065 1165 1 357 225 1 581 167 125 34.132 0963 10.522 2506 .000 858 3691 1166 1 359 556 1 585 242 296 34.146 7422 10.525 2604 .000 857 6329 1167 1 361 889 1 589 324 463 34.161 3817 10.528 2685 .000 856 8980 1168 1 364 224 1593 413 632 34.176 0150 10.531 2749 .000 856 1644 1169 1 366 561 1597 509 809 34.190 6420 10.534 2795 .000 855 4320 1170 1368 900 1 601 613 000 34.205 2627 10.537 2825 .000 854 7009 1171 1 371 241 1 605 723 211 34.219 8773 10.540 2837 .000 853 9710 1172 1 373 584 1 609 840 448 34.234 4855 10.543 2832 .000 853 2423 1173 1 375 929 1 613 964 717 34.249 0875 10.546 2810 .000 852 5149 1174 1 378 276 1 618 096 024 34.263 6834 10.549 2771 .000 851 7888 1175 1 380 625 1 622 234 375 34.278 2730 10.552 2715 .000 851 0638 1176 1 382 976 1 626 379 776 34.292 8564 10.555 2642 .000 850 3401 1177 1 385 329 1 630 532 233 34.307 4336 10.558 2552 .000 849 6177 1178 1 387 684 1 634 691 752 34.322 0046 10.561 2445 .000 848 8964 1179 1 390 041 1 638 858 339 34.336 5694 10.564 2322 .000 848 1764 1180 1 392 400 1 643 032 000 34.351 1281 10.567 2181 .000 847 1576 1181 1 394 761 1 647 212 741 34.365 6805 10.570 2024 .000 846 7401 1182 1 397 124 1 651 400 568 34.380 2268 10.573 1849 .000 846 0237 1183 1 399 489 1 655 595 487 34.394 7670 10.576 1658 .000 845 3085 1184 1 401 856 1 659 797 504 34.409 3011 10.579 1449 .000 844 5946 1185 1 404 225 1 664 006 625 34.423 8289 10.582 1225 .000 843 8819 1186 1 406 596 1 668 222 856 34.438 3507 10.585 0983 .000 843 1703 1187 1 408 969 1 672 446 203 34.452 8663 10.588 0725 .000 842 4600 1188 1 411 344 1 676 676 672 34.467 3759 10.591 0450 .000 841 7508 1189 1 413 721 1 680 914 629 34.481 8793 10.594 0158 .000 841 0429 1190 1 416 100 1 685 159 000 34.496 3766 10.596 9850 .000 840 3361 1191 1 418 481 1 689 410 871 34.510 8678 10.599 9525 .000 839 6306 1192 1 420 864 1 693 669 888 34.525 3530 10.602 9184 .000 838 9262 1193 1 423 249 1 697 936 057 34.539 8321 10.605 8826 .000 838 2320 1194 1 425 636 1 702 209 384 34.554 3051 10.608 8451 .000 837 5209 1195 1 428 025 1 706 489 875 34.568 7720 10.611 8060 .000 836 8201 1196 1 430 416 1 710 777 536 34.583 2329 10.614 7652 .000 836 1204 774 Powers and Roots Number. Squares. Cubes. V Roots. fftoota Reciprocals. 1197 1432 809 1 715 072 373 34.597 6879 10.617 7228 .000 835 4219 1198 1435 204 1 719 374 392 34.612 1366 10.620 6788 .000 834 7245 1199 1 437 601 1 723 683 599 34.626 5794 10.623 6331 .000 834 0284 1200 1440 000 1728 000 000 34.641 0162 10.626 5857 .000 833 3333 1201 1 442 401 1 732 323 601 34.655 4469 10.629 5367 .000 832 6395 1202 1444 804 1 736 654 408 34.669 8716 10.632 4860 .000 831 9468 1203 1447 209 1 740 992 427 34.684 2904 10.635 4338 .000 831 2552 1204 1 449 616 1 745 337 664 34.698 7031 10.638 3799 .000 830 5648 1205 1 452 025 1 749 690 125 34.713 1099 10.641 3244 .000 829 8755 1206 1454 436 1 754 049 816 34.727 5107 10.644 2672 .000 829 1874 1207 1 456 849 1 758 416 743 34.741 9055 10.647 2085 .000 828 5004 1208 1 459 264 1 762 790 912 34.756 2944 10.650 1480 .000 827 8146 1209 1 461 681 1 767 172 329 34.770 6773 10.653 0860 .000 827 1299 1210 1464 100 1 771 561 000 34.785 0543 10.656 0223 .000 826 4463 1211 1 466 521 1 775 956 931 34.799 4253 10.658 9570 .000 825 7638 1212 1468 944 1 780 360 128 34.813 7904 10.661 8902 .000 825 0825 1213 1 471 369 1 784 770 597 34.828 1495 10.664 8217 .000 824 4023 1214 1 473 796 1 789 188 344 34.842 5028 10.667 7516 .000 823 7232 1215 1 476 225 1 793 613 375 34.856 8501 10.670 6799 .000 823 0453 1216 1 478 656 1 798 045 696 34.871 1915 10.673 6066 .000 822 3684 .1217 1 481 089 1 802 485 313 34.885 5271 10.676 5317 .000 821 6927 1218 1 483 524 1 806 932 232 34.899 8567 10.679 4552 .000 821 0181 1219 1485 961 1 811 386 459 34.914 1805 10.682 3771 .000 820 3445 1220 1488 400 1 815 848 000 34.928 4984 10.685 2973 .000 819 6721 1221 1 490 841 1 820 316 861 34.942 8104 10.688 2160 .000 819 0008 1222 1 493 284 1 824 793 048 34.957 1166 10.691 1331 .000 818 3306 1223 1 495 729 1 829 276 567 34.971 4169 10.694 0486 .000 817 6615 1224 1 498 176 1 833 764 247 34.985 7114 10.696 9625 .000 816 9935 1225 1500 625 1 838 265 625 35.000 0000 10.699 8748 .000 816 3265 1226 1 503 276 1 842 771 176 35.014 2828 10.702 7855 .000 815 6607 1227 1 505 529 1 847 284 083 35.028 5598 10.705 6947 000 814 9959 1228 1507 984 1 851 804 352 35.042 8309 10.708 6023 .000 814 3322 1229 1 510 441 1 856 331 989 35.057 0963 10.711 5083 .000 813 6696 1230 1512 900 1 860 867 000 35.071 3558 10.714 4127 .000 813 0081 1231 1 515 361 1 865 409 391 35.085 6096 10.717 3155 .000 812 3477 1232 1 517 824 1 869 959 168 35.099 8575 10.720 2168 .000 811 6883 1233 1520 289 1 874 516 337 35.114 0997 10.723 1165 .000 811 0300 1234 1522 756 1 879 080 904 35.128 3361 10.726 0146 .000 810 3728 1235 1 525 225 1 883 652 875 35.142 5668 10.728 9112 .000 809 7166 1236 1 527 696 1 888 232 256 35.156 7917 10.731 8062 .000 809 0615 1237 1530169 1892 819053 35.171 0108 10.734 6997 .000 808 4074 1238 1 532 644 1 897 413 272 35.185 2242 10.737 5916 .000 807 7544 1239 1535121 1 902 014 919 35.199 4318 10.740 4819 .000 807 1025 1240 1537 600 1 906 624 000 35.213 6337 10.743 3707 .000 806 4516 1241 1 540 081 1 911 240 521 35.227 8299 10.746 2579 .000 805 8018 1242 1542 564 1 915 864 488 35.242 0204 10.749 1436 .000 805 1530 1243 1 545 049 1 920 495 907 35.256 2051 10.752 0277 .000 804 5052 1244 1 547 536 1 925 134 784 35.270 3842 10.754 9103 .000 803 8585 1245 1550 025 1 929 781 125 35.284 5575 10.757 7913 .000 803 2129 1246 1 552 516 1 934 434 936 35.298 7252 10.760 6708 .000 802 5682 1247 1555 009 1 939 096 223 35.312 8872 10.763 5488 .000 801 9246 1248 1557 504 1 943 764 992 35.327 0435 10.766 4252 .000 801 2821 Powers and Roots. 775 Number. Squares. Cubes. I 7 Roots. f Roots. Reciprocals. 1249 1560 001 1 948 441 249 35.341 1941 10.769 3001 .000 800 6405 1250 1 562 500 1 953 125 000 35.355 3391 10.772 1735 .000 800 0000 1251 1565 001 1 957 816 251 35.369 4784 10.775 0453 .000 799 3605 1252 1 567 504 1 962 515 008 35.383 6120 10.777 9156 .000 798 7220 1253 1 570 009 1 967 221 277 35.397 7400 10.780 7843 .000 798 0846 1254 1 572 516 1 971 935 064 35.411 8624 10.783 6516 .000 797 4482 1255 1 575 025 1 976 656 375 35.425 9792 10.786 5173 .000 796 8127 1256 1 577 536 1 981 385 216 35.440 0903 10.789 3815 .000 796 1783 1257 1 580 049 1 986 121 593 35.454 1958 10.792 2441 .000 795 5449 1258 1582 564 1 990 865 512 35.468 2957 10.795 1053 .000 794 9126 1259 1585 081 1 995 616 979 35.482 3900 10.797 9649 .000 794 2812 1260 1587 600 2 000 376 000 35.496 4787 10.800 8230 .000 793 6508 1261 1590121 2 005 142 581 35.510 5618 10.803 6797 .000 793 0214 1262 1 592 644 2 009 916 728 35.524 6393 10.806 5348 .000 792 3930 1263 1 595 169 2 014 698 447 35.538 7113 10.809 3884 .000 791 7656 1264 1 597 696 2 019 487 744 35.552 7777 10.812 2404 .000 791 1392 1265 1 600 225 2 024 284 625 35.566 8385 10.815 0909 .000 790 5138 1266 1 602 756 2 029 089 096 35.580 8937 10.817 9400 .000 789 8894 1267 1 605 289 2 033 901 163 35.594 9434 10.820 7876 .000 789 2660 1268 1 607 824 2 038 720 832 35.608 9876 10.823 6336 .000 788 6435 1269 1 610 361 2 043 548 109 35.623 0262 10.826 4782 .000 788 0221 1270 1612 900 2 048 383 000 35.637 0593 10.829 3213 .000 787 4016 1271 1 615 441 2 053 225 511 35.651 0869 10.832 1629 .000 786 7821 1272 1 617 984 2 058 075 648 35.665 1090 10.835 0030 .000 786 1635 1273 1 620 529 2 062 933 417 35.679 1255 10.837 8416 .000 785 5460 1274 1 623 076 2 067 798 824 35.693 1366 10.840 6788 .000 784 9294 1275 1 625 625 2 072 671 875 35.707 1421 10.843 5144 .000 784 3137 1276 1 628 176 2 077 552 576 35.721 1422 10.846 3485 .000 783 6991 1277 1 630 729 2 082 440 933 35.735 1367 10.849 1812 .000 783 0854 1278 1 633 284 2 087 336 952 35.749 1258 10.852 0125 .000 782 4726 1279 1 635 841 2 092 240 639 35.763 1095 10.854 8422 .000 781 8608 1280 1 638 400 2 097 152 000 35.777 0876 10.857 6704 .000 781 2500 1281 1 640 961 2 102 071 841 35.791 0603 10.860 4972 .000 780 6401 1282 1 643 524 2 106 997 768 35.805 0276 10.863 3225 .000 780 0312 1283 1 646 089 2 111 932 187 35.818 9894 10.866 1454 .000 779 4232 1284 1 648 656 2 116 874 304 35.832 9457 10.868 9687 .000 778 8162 1285 1 651 225 2 121 824 125 35.846 8966 10.871 7897 .000 778 2101 1286 1 653 796 2 126 781 656 35.860 8421 10.874 6091 .000 777 6050 1287 1 656 369 2 131 746 903 35.874 7822 10.877 4271 .000 777 0008 1288 1 658 944 2 136 719 872 35.888 7169 10.880 2436 .000 776 3975 1289 1 6G1 521 2 141 700 569 35.902 6461 10.883 0587 .000 775 7952 1290 1 664 100 2 146 689 000 35.916 5699 10.885 8723 .000 775 1938 1291 1 666 681 2 151 685 171 35.930 4884 10.888 6845 .000 774 5933 1292 1 669 264 2 156 689 088 35.944 4015 10.891 4952 .000 773 9938 1293 1 671 849 2 161 700 757 35.958 3092 10.894 3044 .000 773 3952 1294 1 674 436 2 166 720 184 35.972 2115 10.897 1123 .000 772 7975 1295 1 677 025 2 171 747 375 35.986 1084 10.899 9186 .000 772 2008 1296 1 679 616 2 176 782 336 36.000 0000 10.902 7235 .000 771 6049 1297 1 682 209 2 181 825 073 36.013 8862 10.905 5269 .000 771 0100 1298 1 684 804 2 186 875 592 36.027 7671 10.908 3290 .000 770 4160 1299 1 687 401 2 191 933 899 36.041 6426 10.911 1296 .000 769 8229 1300 1690 000 2 197 000 000 36.055 5128 10.913 9287 .000 769 2308 776 Powers and Roots. Number. Squares. Cubes. I 7 Boots. f Roots. 1 692 601 1695 204 1697 809 1 700 416 I 703 025 1 705 636 1 708 249 1 710 864 1 713 481 1 716 100 1 718 721 1 721 344 1723 969 1 726 596 1729 225 1731856 1 734 489 1 737 124 1 739 761 1 742 400 1 745 041 1747 684 1 750 329 1 752 976 1 755 625 1 758 276 1760 929 | 1763 584 1 766 241 1768 900 1 771 561 1 774 224 1 776 889 1 779 556 1 782 225 1 784 896 1 787 569 1 790 244 1792 921 1795 600 1 798 281 1800 964 1803 649 1806 336 1809 025 1 811 716 1 814 409 1 817 104 1 819 801 1822 500 1825 201 1 827 904 2 202 073 901 2 207 155 608 2 212 245 127 2 217 342 464 2 222 447 625 2 227 560 616 2 232 681 443 2 237 810 112 2 242 946 629 2 248 091 000 2 253 243 231 2 258 403 328 2 263 571 297 2 268 747 144 2 273 930 875 2 279 122 496 2 284 322 013 2 289 529 432 2 294 744 759 2299 968 000 2 305 199 161 2 310 438 248 2 315 685 267 2 320 940 224 2 326 203 125 2 331 473 976 2 336 752 783 2 342 039 552 2 347 334 289 2 352 637 000 2 357 947 691 2 363 266 368 2 368 593 037 2 373 927 704 2 379 270 375 2 384 621 056 2 389 979 753 2 395 346 472 2 400 721 219 2 406 104 000 2 411 494 821 2 416 893 688 2 422 300 607 2 427 715 584 2 433 138 625 2 438 569 736 2 444 008 923 2 449 456 192 2 454 911 549 2 460 375 000 2 465 846 551 2 471 326 208 36.069 3776 36.083 2371 36.097 0913 36.110 9402 36.124 7837 36.138 6220 36.152 4550 36.166 2826 36.180 1050 36.193 9221 36.207 7340 36.221 5406 36.235 3419 36.249 1379 36.262 6287 36.276 7143 36.290 4246 36.304 2697 36.318 0396 36.331 8042 36.345 5637 36.359 3179 36.373 0670 36.386 8108 36.400 5494 36.414 2829 36.428 0112 36.441 7343 36.455 4523 36.469 1650 36.482 8727 36.496 5752 36.510 2725 36.523 9647 36.537 6518 36.551 3388 36.565 0106 36.578 6823 36.592 3489 36.606 0104 36.619 6668 36.633 3181 36.646 9144 36.660 6056 36.674 2416 36.687 8726 36.701 4986 36.715 1195 36.728 7353 36.742 3461 36.755 9519 36.769 5526 10.916 7265 10.919 5228 10.922 3177 10.925 1111 10.927 9031 10.930 6937 10.933 4829 10.936 2706 10.939 0569 10.941 8418 10.944 6253 10.947 5074 10.950 1880 10.952 9673 10.955 7451 10.958 5215 10.961 2965 10.964 0701 10.966 8423 10.969 6131 10.972 3825 10.975 1505 10.977 9171 10.980 6823 10.983 4462 10.986 2086 10.988 9696 10.991 7293 10.994 4876 10.997 2445 11.000 0000 11.002 7541 11.005 5069 11.008 2583 11.011 0082 11.013 7569 11.016 5041 11.019 2500 11.021 9945 11.024 7377 11.027 4795 11.030 2199 11.032 9590 11.035 6967 11.038 4330 11.041 1680 11.043 9017 11.046 6339 11.049 3649 11.052 0945 11.054 8227 11.057 5497 Powers and Roots 777 Number. Squares. Cubes. V Roots. f Roots. Reciprocals. 1353 1830 609 2 476 813 977 36.783 1483 11.060 2752 .000 739 0983 1354 1 833 316 2 482 309 864 36.796 7390 11.062 9994 .000 738 5524 1355 1836 025 2 487 813 875 36.810 3246 11.065 7222 .000 738 0074 1356 1838 736 2 493 326 016 36.823 9053 11.068 4437 .000 737 4631 1357 1 841 449 2 498 846 293 36.837 4809 11.071 1639 .000 736 9197 1358 1 844 164 2 504 374 712 36.851 0515 11.073 8828 .000 736 3770 1359 1 846 881 2 509 911 279 36.864 6172 11.076 6003 .000 735 8352 1360 1849 600 2 515 456 000 36.878 1778 11.079 3165 .000 735 2941 1361 1 852 321 2 521 008 881 36.891 7335 11.082 0314 .000 734 7539 1362 1 855 044 2 526 569 928 36.905 2842 11.084 7449 .000 734 2144 1363 1 857 769 2 532 139 147 36.918 8299 11.087 4571 .000 733 6757 1364 1 860 496 2 537 716 544 36.932 3706 11.090 1679 .000 733 1378 1365 1 863 225 2 543 302 125 36.945 9064 11.092 8775 .000 732 6007 1366 1 865 956 2 548 895 896 36.959 4372 11.095 5857 .000 732 0644 1367 1 868 689 2 554 497 863 36.972 9631 11.098 2926 .000 731 5289 1368 1 871 424 2 560 108 032 36.986 4840 11.100 9982 .000 730 9942 1369 1 874 161 2 565 726 409 37.000 0000 11.103 7025 .000 730 4602 1370 1876 900 2 571 353 000 37.013 5110 11.106 4054 .000 729 9270 1371 1 879 641 2 576 987 811 37.027 0172 11.109 1070 .000 729 3946 1372 1 882 384 2 582 630 848 37.040 5184 11.111 8073 .000 728 8630 1373 1 885 129 2 588 282 117 37.054 0146 11.114 5064 .000 728 3321 1374 1 887 876 2 593 941 624 37.067 5060 11.117 2041 .000 727 8020 1375 1 890 625 2 599 609 375 37.089 9924 11.119 9004 .000 727 2727 1376 1 893 376 2 605 285 376 37.094 4740 11.122 5955 .000 726 7442 1377 1 896 129 2 610 969 633 37.107 9506 11.125 2893 .000 726 2164 1378 1 898 884 2 616 662 152 37.121 4224 11.127 9817 .000 725 6894 1379 1 901 641 2 622 362 939 37.134 8893 11.130 6729 .000 725 1632 1380 1904 400 2 628 072 000 37.148 3512 11.133 3628 .000 724 6377 1381 1 907 161 2 633 789 341 37.161 8084 11.136 0514 .000 724 1130 1382 1 909 924 2 639 514 968 37.175 2606 11.138 7386 .000 723 5890 1383 1 912 689 2 645 248 887 37.188 7079 11.141 4246 .000 723 0658 1384 1 915 456 2 650 991 104 37.202 1505 11.144 1093 .000 722 5434 1385 1 918 225 2 656 741 625 37.215 5881 11.146 7926 .000 722 0217 1386 1 920 996 2 662 500 456 37.229 0209 11.149 4747 .000 721 5007 1387 1 923 769 2 668 267 603 37.242 4489 11.152 1555 .000 720 9805 1388 1 926 544 2 674 043 072 37.255 8720 11.154 8350 .000 720 4611 1389 1 929 321 2 679 826 869 37.269 2903 11.157 5133 .000 719 9424 1390 1 932 100 2 685 619 000 37.282 7037 11.160 1903 .000 719 4245 1391 1 934 881 2 691 419 471 37.296 1124 11.162 8659 .000 718 9073 1392 1 937 664 2 697 228 288 37.309 5162 11.165 5403 .000 718 3908 1393 1 940 449 2 703 045 457 37.322 9152 11.168 2134 .000 717 8751 1394 1 943 236 2 708 870 984 37.336 3094 11.170 8852 .000 717 3601 1395 1 946 025 2 714 704 875 37.349 6988 11.173 5558 .000 716 8459 1396 1 948 816 2 720 547 136 37.363 0834 11.176 2250 .000 716 3324 1397 1 951 609 2 726 397 773 37.376 4632 11.178 8930 .000 715 8196 1398 1 954 404 2 732 256 792 37.389 8382 11.181 5598 .000 715 3076 1399 1 957 201 2 738 124 199 37.403 2084 11.184 2252 .000 714 7963 1400 1960 000 2 744 000 000 37.416 5738 11.186 8894 .000 714 2857 1401 1 962 801 2 749 884 201 37.429 9345 11.189 5523 .000 713 7759 1402 1 965 604 2 755 776 808 37.443 2904 11.192 2139 .000 713 2668 1403 1 968 409 2 761 677 827 37.456 6416 11.194 8743 .000 712 7584 1404 1 971 216 2 767 587 264 37.469 9880 11.197 5334 .000 712 2507 778 Powers and Roots Number. Squares. Cubes. V' Roots. f Roots. Reciprocals. 1405 1974 025 2 773 505 123 37.483 3296 11.200 1913 .000 711 7438 1406 1 976 836 2 779 431 416 37.496 6665 11.202 8479 .000 711 2376 1407 1 979 649 2 785 366 143 37.509 9987 11.205 5032 .000 710 7321 1408 1 982 464 2 791 309 312 37.523 3261 11.208 1573 .000 710 2273 1409 1985 281 2 797 260 929 37.536 6487 11.210 8101 .000 709 7232 1410 1988100 2803 221000 37.549 9667 11.213 4617 .000 709 2199 1411 1990 921 2 809 189 531 37.563 2799 11.216 1120 .000 708 7172 1412 1 993 744 2 815 166 528 37.576 5885 11.218 7611 .000 708 2153 1413 1996 569 2 821 151 997 37.589 8922 11.221 40S9 .000 707 7141 1414 1999 3% 2 827 145 944 37.603 1913 11.224 0054 .000 707 2136 1415 2002 225 2 833 148 375 37.616 4857 11.226 7007 .000 706 7138 1416 2 005 056 2 839 159 2% 37.629 7754 11.229 3448 .000 706 2147 1417 2 007 889 2 845 178 713 37.643 0604 11.231 9876 .000 705 7163 1418 2 010 724 2 851 206 632 37.656 3407 11.234 6292 .000 705 2186 1419 2 013 561 2 857 243 059 37.669 6164 11.237 2696 .000 704 7216 1420 2 016 400 2863 288 000 37.682 8874 11.239 9087 .000 704 2254 1421 2 019 241 2 869 341 461 37.696 1536 11.242 5465 .000 703 7298 1422 2 022 084 2 875 403 448 37.709 4153 11.245 1831 .000 703 2349 1423 2 024 929 2 881 473 967 37.722 6722 11.247 8185 .000 702 7407 1424 2 027 776 2 887 553 024 37.735 9245 11.250 4527 .000 702 2472 1425 2 030 625 2 893 640 625 37.749 1722 11.253 0856 .000 701 7544 1426 2 033 476 2 899 736 776 37.762 4152 11.255 7173 .000 701 2623 1427 2 036 329 2 905 841 483 37.775 6.535 11.258 3478 .000 700 7708 1428 2 039 184 2 911954 752 37.788 8873 11.260 9770 .000 700 2801 1429 2 042 041 2 918 076 589 37.802 1163 11.263 6050 .000 699 7901 1430 2 044 900 2 924 207 000 37.815 3408 11.266 2318 .000 699 3007 1431 2 047 761 2 930 345 991 37.828 5606 11.268 8573 .000 698 8120 1432 2 050 624 2 936 493 568 37.841 7759 11.271 4816 .000 698 3240 1433 2 053 489 2 942 649 737 37.854 9864 11.274 1047 .000 697 8367 1434 2 056 356 2 948 814 504 37.868 1924 11.276 7266 .000 697 3501 1435 2 059 225 2 954 987 875 37.881 3938 11.279 3472 .000 696 8641 1436 2 062 096 2 961 169 856 37.894 5906 11.281 9666 .000 696 3788 1437 2 064 969 2 967 360 453 37.907 7828 11.284 5849 .000 695 8942 1438 2 067 844 2 973 559 672 37.920 9704 11.287 2019 .000 695 4103 1439 2 070 721 2 979 767 519 37.934 1535 11.289 8177 .000 694 9270 1440 2 073 600 2 985 984 000 37.947 3319 11.292 4323 .000 694 4444 1441 2 076 481 2 992 209 121 37.960 5058 11.295 0457 .000 693 9625 1442 2 079 364 2 998 442 888 37.973 6751 11.297 6579 .000 693 4813 1443 2 082 249 3 004 685 307 37.986 8398 11.300 2688 .000 693 0007 1444 2 085136 3 010 936 384 38.000 0000 11.302 8786 .000 692 5208 1445 2 088 025 3 017 196 125 38.013 1556 11.305 4871 .000 692 0415 1446" 2 090 916 3 023 464 536 38.026 3067 11.308 0945 .000 691 5629 1447 2 093 809 3 029 741 623 38.039 4532 11.310 7006 .000 691 0850 1448 2 096 704 3 036 027 392 38.052 5952 11.313 3056 .000 690 6078 1449 2 099 601 3 042 321 849 38.065 7326 11.315 9094 .000 090 1312 1450 2102 500 3 048 625 000 38.078 8655 11.318 5119 .000 689 6552 1451 2 105 401 3 054 936 851 38.091 9939 11.321 1132 .000 689 1799 1452 2108 304 3 061 257 408 38.105 1178 11.323 7134 .000 688 7052 1453 2111209 3 067 586 777 38.118 2371 11.326 3124 .000 688 2312 1454 2 114 116 3 073 924 664 38.131 3519 11.328 9102 .000 687 7579 1455 2117 025 3 080 271 375 38.144 4622 11.331 5067 .000 687 2852 1456 2 119 936 3 086 626 816 38.157 5681 11.334 1022 .000 686 8132 Powers and Roots. 779 Squares. Cubes. V Boots. f Roots. Reciprocals. 2 122 849 2 125 764 2128 681 2 131 600 2 134 521 2 137 444 2 140 369 2 143 296 2 146 225 2 149 156 2 152 089 2 155 024 2 157 961 2160 900 2 163 841 2 166 784 2 169 729 2 172 676 2 175 625 2178 576 2 181 529 2 184 484 2 187 441 2190 400 2 193 361 2 196 324 2 199 289 2 202 256 2 205 225 2 208 196 2 211 169 2 214 144 2 217 121 2 220100 2 223 081 2 226 064 2 229 049 2 232 036 2 235 025 2 238 016 2 241009 2 244 004 2 247 001 2 250 000 2 253 001 2 256 004 2 259 009 2 262 016 2 265 025 2 268 036 2 271 049 2 274 064 3 092 990 993 3 099 363 912 3 105 745 579 3 112 136 000 3 118 535 181 3 124 943 128 3 131 359 847 3 137 785 344 3 144 219 625 3 150 662 6% 3 157 114 563 3 163 575 232 3 170 044 709 3 176 523 000 3 183 010 111 3 189 506 048 3 196 010 817 3 202 524 424 3 209 046 875 3 215 578 176 3 222 118 333 3 228 667 352 3 235 225 239 3 241 792 000 3 248 367 641 3 254 952 168 3 261 545 587 3 268 147 904 3 274 759 125 3 281 379 256 3 288 008 303 3 294 646 272 3 301 293 169 3 307 949 000 3 314 613 771 3 321 287 488 3 327 970 157 3 334 661 784 3 341 362 375 3 348 071 936 3 354 790 473 3 361 517 992 3 368 254 499 3 375 000 000 3 381 754 501 3 388 518 008 3 395 290 527 3 402 072 064 3 408 862 625 3 415 662 216 3 422 470 843 3 429 288 512 38.170 6693 38.183 7662 38.196 8585 38.209 9463 38.223 0297 38.236 1085 38.249 1829 38.262 2529 38.275 3184 38.288 3794 38.301 4360 38.314 4881 38.327 5358 38.340 5790 38.353 6178 38.366 6522 38.379 6821 38.392 7076 38.405 7287 38.418 7454 38.431 7577 38.444 7656 38.457 7691 38.470 7681 38.483 7627 38.496 7530 38.509 7390 38.522 7206 38.535 6977 38.548 6705 38.561 6389 38.574 6030 38.587 5627 38.600 5181 38.613 4691 38.626 4158 38.639 3582 38.652 2962 38.665 2299 38.678 1593 38.691 0843 38.704 0050 38.716 9214 38.729 8335 38.742 7412 38.755 6447 38.768 5439 38.781 4389 38.794 3294 38.807 2158 38.820 0978 38.832 9757 11.336 6964 11.339 2894 11.341 8813 11.344 4719 11.347 0614 11.349 6497 11.352 2368 11.354 8227 11.357 4075 11.359 9911 11.362 5735 11.365 1547 11.367 7347 11.370 3136 11.372 8914 11.375 4679 11.378 0433 11.380 6175 11.383 1906 11.385 7625 11.388 3332 11.390 9028 11.393 4712 11.396 0384 11.398 6045 11.401 1695 11.403 7332 11.406 2959 11.408 8574 11.411 4177 11.413 9769 11.416 5349 11.419 0918 11.420 6476 11.424 2022 11.426 7556 11.429 3079 11.431 8591 11.434 4092 11.436 9581 11.439 5059 11.442 0525 11.444 5980 11.447 1424 11.449 6857 11.452 2278 11.454 7688 11.457 3087 11.459 8476 11.462 3850 11.464 9215 11.467 4568 .000 686 3412 .000 685 8711 .000 685 4010 .000 684 9315 .000 684 4627 .000 683 9945 .000 683 5270 .000 683 0601 .000 682 5939 .000 682 1282 .000 681 6633 .000 681 1989 .000 680 7352 .000 680 2721 .000 679 8097 .000 679 3478 .000 678 8866 .000 678 4261 .000 677 9661 .000 677 5068 .000 677 0481 .000 676 5900 .000 676 1325 .000 675 6757 .000 675 2194 .000 674 7638 .000 674 3088 .000 673 8544 .000 673 4007 .000 672 9474 .000 672 4950 .000 672 0430 .000 671 5917 .000 671 1409 .000 670 6908 .000 670 2413 .000 669 7924 .000 669 3440 .000 668 8963 .000 668 4492 .000 668 0027 .000 667 5567 .000 667 1114 .000 666 6667 .000 666 2225 .000 665 7790 .000 655 3360 .000 664 8936 .000 664 4518 .000 664 0106 .000 663 5700 .000 663 1300 780 Powers and Roots Number. Squarei. Cubes. ^Eootfc f Roots. Reciprocals. 1509 2 277 081 3 436 115 229 38.845 8491 11.469 9911 .000 062 6905 1510 2 280100 3 442 951 000 38.858 7184 11.47 .000 662 2517 1511 2 283 121 3 449 795 831 38.871 5834 11.175 0562 .000 661 8134 1512 2 286144 3 456 649 728 38.884 4442 11.477 5871 .000 661 :?7.77 1513 2 289 169 3 463 512 697 38.897 3006 11.480 1169 .000 660 9385 1514 2 292196 3 470 384 744 38.910 1529 11.482 6455 .000 660 5020 1515 2 295 225 3 477 265 875 38.923 0009 11.485 1731 .000 660 0660 1516 2 298 256 3 484 156 096 38.935 8447 11.487 6995 .000 659 6306 1517 2 301 289 3 491 055 413 38.948 6841 11.490 2249 .000 659 1958 1518 2 304 324 3 597 963 832 38.961 5194 11.492 7491 .000 658 7615 1519 2 307 361 3 504 881 359 38.974 3505 11.495 2722 .000 658 3278 1520 2 310 400 3 511 808 000 38.987 1774 11.497 7942 .000 657 8947 1521 2 313 441 3 518 743 761 39.000 0000 11.500 3151 .000 657 4622 1522 2 316 484 3 525 688 648 39.012 8184 11.502 8348 .000 657 0302 1523 2 319 529 3 532 642 667 39.025 6326 11.505 3535 .000 656 5988 1524 2 322 576 3 539 605 824 39.038 4426 11.507 8711 .000 656 1680 1525 2 325 625 3 546 578 125 39.051 2483 11.510 3876 .000 655 7377 1526 2 328 676 3 553 559 576 39.064 0499 11.512 9030 .000 655 3080 1527 2 331729 3 560 558 183 39.076 8473 11.515 4173 .000 654 8788 1528 2 334 784 3 567 549 552 39.089 6406 11.517 9305 .000 654 4503 1529 2 337 841 3 574 558 889 39.102 4296 11.520 4425 .000 654 0222 1530 2 340 900 3 581 577 000 39.115 2144 11.522 9535 .000 653 5948 1531 2 343 961 3 588 604 291 39.127 9951 11.525 4634 .000 653 1679 1532 2 347 024 3 595 640 768 39.140 7716 11.527 9722 .000 652 7415 1533 2 350 089 3 602 686 437 39.153 5439 11.530 4799 .000 652 3157 1534 2 353156 3 609 741 304 39.166 3120 11.532 9865 .000 651 8905 1535 2356 225 3 616 805 375 39.179 0760 11.535 4920 .000 651 4658 1536 2 359 296 3 623 878 656 39.191 8359 11.537 9965 .000 651 0417 1537 2 362 369 3 630 961 153 39.204 5915 11.540 4998 .000 650 6181 1538 2 365 444 3 638 052 872 39.217 3431 11.543 0021 .000 6.50 1951 1539 2 368 521 3 645 153 819 39.230 0905 11.545 5033 .000 649 7726 1540 2 371600 3 652 264 000 39.242 8337 11.548 0034 .000 649 3506 1541 2 374 681 3 657 983 421 39.255 5728 11.550 5025 .000 648 9293 1542 2 377 764 3 666 512 088 39.268 3078 11.553 0004 .000 648 5084 1543 2 380 849 3 673 650 007 39.281 0387 11.555 4972 .000 648 0881 1544 2 383 936 3 680 797 184 39.293 7654 11.557 9931 .000 647 6684 1545 2 387 025 3 687 953 625 39.306 4880 11.560 4878 .000 647 2492 1546 2 390 116 3 695 119 336 39.319 2065 11.562 9815 .000 646 8305 1547 2 393 209 3 702 294 323 39.331 9208 11.565 4740 .000 646 4124 1548 2 398 304 3 709 478 592 39.344 6311 11.567 9655 .000 645 9948 1549 2 399 401 3 716 672 149 39.357 3373 11.570 4559 .000 645 5778 1550 2 402 500 3 723 875 000 39.370 0394 11.572 9453 .000 645 1613 1551 2 405 601 3 731 087 151 39.382 7373 11.575 4336 .000 644 7453 1552 2 408 704 3 738 308 608 39.395 4312 11.577 9268 .000 644 3299 1553 2 411 809 3 745 539 377 39.408 1210 11.580 4069 .000 643 9150 1554 2 414 916 3 752 779 464 39.420 8067 11.582 8919 .000 643 5006 1555 2 418 025 3 760 028 875 39.433 4883 11.585 3759 .000 643 0868 1556 2 421 136 3 767 287 616 39.446 1658 11.587 8588 .000 642 6735 1557 2 424 249 3 774 555 693 39.458 8393 11.590 3407 .000 642 2608 1558 2 427 364 3 781 833 112 39.471 5087 11.592 8215 .000 641 8485 1559 2 430 481 3 789 119 879 39.484 1740 11.595 3013 .000 641 4368 1560 2 433 600 3 796 416 000 39.496 8353 11.597 7799 .000 641 0256 Powers and Roots 781 Number. Squares. Cubes. VRoots. f Roots. Reciprocals. 1561 2 436 721 3 803 721 481 39.509 4925 11.600 2576 .000 640 6150 1562 2 439 844 3 811 036 328 39.522 1457 11.602 7342 .000 640 2049 1563 2 442 969 3 818 360 547 39.534 7948 11.605 2097 .000 639 7953 1564 2 446 096 3 825 641 444 39.547 4399 11.607 6841 .000 639 3862 1565 2 449 225 3 833 037 125 39.560 0809 11.610 1575 .000 638 9776 1566 2 452 356 3 840 389 496 39.572 7179 11.612 6299 .000 638 56% 1567 2 455 489 3 847 751 263 39.585 3508 11.615 1012 .000 638 1621 1568 2 458 624 3 855123 432 39.597 9797 11.617 5715 .000 637 7551 1569 2 461 761 3 862 503 009 39.610 6046 11.620 0407 .000 637 3486 1570 2 464 900 3 869 883 000 39.623 2255 11.622 5088 .000 636 9427 1571 2 468 041 3 877 292 411 39.635 8424 11.624 9759 .000 636 5372 1572 2 471 184 3 884 701 248 39.648 4552 11.627 4420 .000 636 1323 1573 2 474 329 3 892 119 157 39.661 0640 11.629 9070 .000 635 7279 1574 2 477 476 3 899 547 224 39.673 6688 11.632 3710 .000 635 3240 1575 2 480 625 3 906 984 375 39.686 2696 11.634 8339 .000 634 92% s 1576 2 483 776 3 914 430 976 39.698 8665 11.637 2957 .000 634 5178 1577 2 486 929 3 921 887 033 39.711 4593 11.639 7566 .000 634 1154 1578 2 490 084 3 929 352 552 39.724 0481 11.642 2164 .000 633 7136 1579 2 493 241 3 936 827 539 39.736 6329 11.644 6751 .000 633 3122 1580 2 496 400 3 944 312 000 39.749 2138 11.647 1329 .000 632 9114 1581 2 499 561 3 951 805 941 39.761 7907 11.649 5895 .000 632 5111 1582 2 502 724 3 959 309 368 39.774 3636 11.652 0452 .000 632 1113 1583 2 505 889 3 966 822 287 39.786 9325 11.654 4998 .000 631 7119 1584 2 509 056 3 974 344 704 39.799 4976 11.656 9534 .000 631 3131 1585 2 512 225 3 981 876 625 39.812 0585 11.659 4059 .000 630 9148 1586 2 515 396 3 989 418 056 39.824 6155 11.661 8574 .000 630 5170 1587 2 518 569 3 996 969 003 39.837 1686 11.664 3079 .000 630 1197 1588 2 521 744 4 004 529 472 39.849 7177 11.666 7574 .000 629 7229 1589 2 524 921 4 012 099 469 39.862 2628 11.669 2058 .000 629 3266 1590 2 528 100 4 014 679 000 39.874 8040 11.671 6532 .000 628 9308 1591 2 531 281 4 027 268 071 39.887 3413 11.674 0996 .000 628 5355 1592 2 534 464 4 034 866 688 39.899 8747 11.676 5449 .000 628 1407 1593 2 537 649 4 042 474 857 39.912 4041 11.678 9892 .000 627 7464 1594 2 540 836 4 050 092 584 39.924 9295 11.681 4325 .000 627 3526 1595 2 544 025 4 057 719 875 39.937 4511 11.683 8748 .000 626 9592 15% 2 547 216 4 065 356 736 39.949 9687 11.686 3161 .000 626 5664 1597 2 550 409 4 073 003 173 39.962 4824 11.688 7563 .000 626 1741 1598 2 553 604 4 080 659 192 39.974 9922 11.691 1955 .000 625 7822 1599 2 556 801 4 088 324 799 39.987 4980 11.693 6337 .000 625 3%9 1600 2 560 000 4 096 000 000 40.000 0000 11.6% 0709 .000 625 0000 The use of the table of powers and roots may be extended far beyond Its apparent limits by the observance of the following rules : Remembering that the extraction of the square root of a number is simply the separating it into two equal factors, we have: to extract the square root of any whole number and decimal, when the whole number is within the limits of the table, simply find the square root of the whole number in the table and divide the given number and decimal by this root. The quotient will be another factor, very nearly equal to the required root. Add the divisor and the quotient together and divide by two, and the result will be the true root to a very close degree of approximation. These tables, together with those of Metric System and Logarithms have been taken by permission from Suplee's " Reference Book." 7v_> Logarithms. LOGARITHMS. There are four fundamental rules for operations with powers : a m t a n = a m + ". That is, the product of any two powers of a number is equal to the num- ber raised to a power whose exponent is the mm of the exponents of the two factors. o"» = a» - *. a» Or, the quotient of two powers is equal to the number raised to a power whose exponent is the difference of the exponents of divisor and dividend. (o n )« = a WB . Or, any power may be raised to a higher power by multiplying the two exponents. V a m =a». Or, any root of any power may be extracted by dividing the exponent by the index of the root. If we take any number, such as 2, and use it as the base of a geometri- cal series, we will see that the exponents form an arithmetical series. Thus, the exponent of 1 = 0, of 2 = 1, of 4 = 2, of 8 = 3, etc. ; or, proceed- ing, we may arrange the following little table : Powers. Exponents. Powers. Exponents. Powers. Exponents. 1 1024 10 1048576 20 2 1 2048 11 2097152 21 4 2 4096 12 4194304 22 8 3 8192 13 8388608 23 16 4 16384 14 16777216 24 32 5 32768 15 64 6 65536 16 128 7 131072 17 256 8 262144 18 512 9 524288 19 Suppose now we wish to multiply 128 by 512, we see that 128 = 2 7 and 512 = 29; hence, 128 x 512 = 2*'-» = 2 16 , and in the table, opposite the exponent 16, we find the power 65536, which is the product of the two factors, obtained by the simple addition of the exponents. Again, 128 T To raise a number to a power, such as 16 to the fifth power, we have 16 = 2* and (2*)& = Z» = 1048576. Again, the seventh root of 2097152 is formed as follows : 2097152 - 22i an d f ~& - 2 V = 23 = 8. In the small table of the powers of 2 given above there are many gaps, because only those powers which have whole exponents are given. For all the numbers between 16 and 32, for example, the exponents will be deci- mals, and will be greater than 4 and less than 5, etc. In practice, the base used is not 2, but 10, and all the intermediate exponents have been com- puted to many decimals, these forming a table of logarithms. Logarithms. 783 Table of Logarithms of Numbers. Pages 82 to 104 give the mantissas, or decimal portions of the logarithms, of all whole numbers from 1 to 10009. The characteristics, or whole num- bers, which, with these decimals, form the complete logarithms, are found as follows : The logarithm of 1 = 0, of 10 = 1, of 100 = 2, of 1000 = 3, etc. ; hence, the logarithm of any number between 100 and 1000 must lie between 2 and 3, and be greater than 2 and less than 3, and so for any number. There- fore we have the rule that the whole portion of a logarithm of any num- ber is one less than there are figures in the number. The decimal portion for any number below 10009 is taken directly from the table. Thus, log. 365 = 2.56229, the decimal portion, 56229, being found directly opposite 365 in the table, and the whole portion being 2, or 1 less than the number of places in 365. In like manner we have log. 36.5 =1.56229, log. 3.65 = 0.56229. The mantissa, or decimal portion, is always positive, but the character- istic is negative when the number is less than unity. Thus, log. 0.365 =1.56229, log. 0.0365 ="2.56229, log. 0.00365=5.56229, the minus being placed over the characteristic to show that it applies to that portion only, and not to the mantissa. If the given number has more than three places, the mantissa is found in the body of the table. Thus, the logarithm of 1873 = 3.27254, the figures 0.27 being found opposite 187, and the 254 on the same horizontal line under 3. If the last three figures of the mantissa are preceded by an asterisk, the first two figures are to be taken from the next line below, in the first column. Thus, log. 3897 = 3.59073, in which, opposite 389, we find 58, and then, passing on under 7, we find *073, the asterisk indicating that we are to go one line below, taking out 59, not 58, for the first two figures of the mantissa, giving us 0.59073, as above. The table, as will be seen, enables the logarithm of any number of four places to be taken out at once. If the number of which the logarithm is required has more than four places, the logarithm can be found from the table, as follows : In the column at the extreme right of each page, under the heading P. P. (Proportional Parts), will be found in the black figures the differences between any logarithm and the next succeeding logarithm for the adjoin- ing portions of the table. The smaller figures in the same column form little multiplication tables, in which these differences are multiplied by 0.1, 0.2, 0.3, etc. The use of these proportional parts and their decimal parts is best shown by actual example. Suppose it is desired to find the logarithm of 18702. Opposite 187 and under in the table we find the mantissa, 0.27184. The proportional part, or difference at this point between one logarithm and the next, is 23, or, in other words, there is a difference of 23 between the last two figures of the logarithm of 1870 ard 1871. For 0.1 difference in the number, the difference in the logarithms would be 2.3 ; for 0.2, it would be 4.6, etc., as shown in the small table under 23 in the column P. P. For 2 points additional, therefore, we simply add 4.6 to the loga- rithm of 1870, and we have the logarithm of 18702. Thus, log. 1870 =0.27184 p. p. for 2 = 4.6 log. 18702 = 4.271886, or 4.27189 784 Logarithms. Again, let it be required to find the logarithm of 36.797. log. 35.79 = 1.65376 p. p. = 12 p. p. for 7 ■• 8.4 log. 35.797 = 1.553844 If the given number has six or more figures the method is the same, except that the proportional part is reduced one-tenth for each additional figure. Thus, the logarithm of 3725.96 is found as follows : log. 3725 = 3.57113 p. p. = 11 p. p. for 9 = 9.9 p. p. for 6 = 0.66 log. 3725.96 = 3.5712356, or 3.57124 The operation of finding the number corresponding to a given loga- rithm is the reverse of the preceding. Thus, the number corresponding to the logarithm 2.73924 is found as follows : In the table the next smaller logarithm is 73918, and its number = 584500 The given log. = 73924 and the difference =6 The nearest difference in the table = 5.6 = corresponding to 7 Subtracting 0.4 corresponding to 5 Hence, the number is 584575 Since the characteristic = 2, there must be one more place before the decimal point ; hence, log. 2.73924 = num. 584.575 Logarithms op Numbers. 785 Num. 100 to 139. Log. 000 to 145. P. P. 00 000 043 087 130 173 432 475 518 561 604 860 903 945 988 *030 01 284 326 368 410 452 703 745 787 828 870 02 119 160 202 243 284 531 572 612 653 694 938 979 *019 *060 *100 03 342 383 423 463 503 743 782 822 862 902 04 139 179 218 258 297 532 571 610 650 689 922 961 999 *038 *077 05 308 346 385 423 461 690 729 767 805 843 06 070 108 145 183 221 446 483 521 558 595 819 856 893 930 967 07 188 225 262 298 335 555 591 628 664 700 918 954 990 *027 *063 08 279 314 350 386 422 636 672 707 743 778 991 *026 *061 *096 *132 09 342 377 412 447 482 691 726 760 795 830 10 037 072 106 140 175 380 415 449 483 517 721 755 789 823 857 11 059 093 126 160 193 394 428 461 494 528 727 760 793 826 860 12 057 090 123 166 189 385 418 450 483 516 710 743 775 808 840 13 033 066 098 130 162 354 386 418 450 481 672 704 735 767 799 988 *019 *051 *082 *114 14 301 333 364 395 426 613 644 675 706 737 217 260 303 346 389 647 689 732 775 817 *072 *115 *157 *199 *242 494 536 578 620 662 912 953 995 *036 *078 325 366 407 449 490 735 776 816 857 898 *141 *181 *222 *262 *302 543 583 623 663 703 941 981 *021 *060 *100 336 376 415 454 493" 727 766 805 844 883 *115 *154 *192 *231 *269 500 538 576 614 652 881 918 956 994 *032 258 296 333 371 408 633 670 707 744 781 *004 *041 *078 *U5 *151 372 408 445 482 518 737 773 809 846 882 *099 *135 *171 *207 *243 458 493 529 565 600 814 849 884 920 955 *167 *202 *237 *272 *307 517 552 587 621 656 864 899 934 968 *003 209 243 278 312 346 551 585 619 653 687 890 924 958 992 *025 227 261 294 327 361 561 594 628 661 694 893 926 959 992 *024 222 254 287 320 352 548 581 613 646 678 872 905 937 969 *001 194 226 258 290 322 513 545 577 609 640 830 862 893 925 956 *145 *176 *208 *239 *270 457 489 520 551 582 768 799 829 860 891 4.4 8.8 13.2 17.6 •22.0 26.4 30.8 35.2 39.6 4.3 8.6 12.9 17.2 21.5 25.8 30.1 34.4 38.7 42 41 4.2 8.4 12.6 16.8 21.0 25.2 29.4 33.6 37.8 40 4.0 8.0 12.0 16.0 20.0 24.0 '28.0 32.0 36.0 38 7.6 11.4 15.2 19.0 22.8 26.6 30.4 34.2 36 1 3.6 2 7.2 3 10.8 4 14.4 6 18.0 6 21.6 7 25.2 8 28.8 y 32.4 4.1 8.2 12.3 16.4 20.5 24.6 28.7 32.8 36.9 39 3.9 7.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 37 3.7 7.4 11.1 14.8 18.5 22.2 25.9 29.6 33.3 35 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 31.5 P. P. ree Logarithms of Numbers. Num . 140 to 179. Log . 146 to 255. N L 1 2 3 4 5 6 7 8 9 P. P. 140 14 613 644 675 706 737 768 799 829 860 891 34 33 141 922 953 983 *014 *045 *076 *106 *137 *168 *198 • 3.3 6.6 142 15 229 259 290 320 351 381 412 442 473 503 1 0.1 6.8 143 534 564 594 625 655 685 715 746 776 806 B 10.2 9.9 144 836 866 897 927 957 987 *017 *047 *077 *107 4 . r > 13.6 17.0 13.2 16 5 145 16 137 167 197 227 256 286 316 346 376 406 6 7 B 20.4 28.8 27.2 19.8 23.1 20.4 146 435 465 495 524 554 584 613 643 673 702 147 732 761 791 820 850 879 909 938 967 997 9 30.6 29.7 148 17 026 056 085 114 143 173 202 231 260 289 32 31 149 319 348 377 406 435 464 493 522 551 580 150 609 638 667 696 725 754 782 811 840 869 1 2 3.2 6.4 3.1 6.2 151 898 926 955 984 *013 *041 *070 *099 *127 *156 8 9.6 9.3 152 18 184 213 241 270 298 327 355 384 412 441 4 6 c. 12.8 16.0 19.2 12.4 15.5 18.6 153 469 498 526 554 583 611 639 667 696 724 154 155 752 19 033 780 061 808 089 837 117 865 145 893 173 921 201 949 977 *005 229 257 285 7 8 9 22.4 25.6 28.8 21.7 24.8 27.9 156 312 340 368 396 424 451 479 507 535 562 30 29 157 590 618 645 673 700 728 756 783 811 838 158 866 893 921 948 976 *003 *030 *058 *085 *112 1 3.0 2.9 159 20 140 167 194 222 249 276 303 330 358 385 2 3 6.0 9.0 5.8 8.7 160 412 439 466 493 520 548 575 602 629 656 4 5 6 12.0 15.0 18.0 11.6 14.5 17.4 161 683 710 737 763 790 817 844 871 898 925 162 952 978 *005 *032 *059 *085 *112 *139 *165 *192 7 21.0 20.3 163 21 219 245 272 299 325 352 378 405 431 458 8 9 24.0 27.0 23.2 26.1 164 484 511 537 564 590 617 643 669 696 722 165 748 775 801 827 854 880 906 932 958 985 28 27 166 22 Oil 037 063 089 115 141 167 194 220 246 1 2.8 2.7 167 272 298 324 350 376 401 427 453 479 505 2 3 4 5.6 8.4 11.2 5.4 8.1 10.8 168 531 557 583 608 634 660 686 712 737 763 169 170 789 23 045 814 070 840 096 866 121 891 147 917 172 943 198 968 994 *019 223 249 274 5 7 14.0 16.8 19.6 13.5 16.2 18.9 171 300 325 350 376 401 426 452 477 502 528 9 22.4 25.2 21.6 24.3 172 553 578 603 629 654 679 704 729 754 779 173 805 830 855 880 905 930 955 980 *005 *030 26 25 174 24 055 080 105 130 155 180 204 229 254 279 1 2.6 2.5 175 304 329 353 378 403 428 452 477 502 527 2 3 4 5.2 7.8 10.4 5.0 7.5 10.0 176 551 576 601 625 650 674 699 724 748 773 177 797 822 846 871 895 920 944 969 993 *018 5 13.0 12.5 178 25 042 066 091 115 139 164 188 212 237 261 6 7 8 15.6 18.2 20.8 15.0 17.5 20.0 179 285 310 334 358 382 406 431 455 479 503 180 527 551 575 600 624 648 672 696 720 744 9 23.4 22.5 N L 1 2 3 4 5 6 7 8 9 P. P . Logarithms of Numbers. 787 Num 180 to 219. Log 255 to 342. N L 1 2 3 4 5 6 7 8 9 P. P. 180 25 527 551 575 600 624 648 672 696 720 744 24 181 768 792 816 840 864 888 912 935 959 983 1 2 2.4 4.8 182 26 007 031 055 079 102 126 150 174 198 221 183 245 269 293 316 340 364 387 411 435 458 3 7.2 184 482 505 529 553 576 600 623 647 670 694 4 5 9.6 12.0 185 717 741 764 788 811 834 858 881 905 928 6 7 8 14.4 16.8 19.2 186 951 975 988 *021 *045 *068 *091 *114 *138 *161 187 27 184 207 231 254 277 300 323 346 370 393 9 21.6 188 416 439 462 485 508 531 554 577 600 623 23 189 046 669 692 715 738 761 784 807 830 852 190 875 898 921 944 967 989 *012 *035 *058 *081 1 2 2.3 4.6 191 28 103 126 149 171 194 217 240 262 285 307 3 6.9 192 330 353 375 398 421 443 466 488 511 533 4 5 6 9.2 11.5 13.8 193 556 578 601 623 646 668 691 713 735 758 194 195 780 29 003 803 026 825 048 847 070 870 092 892 115 914 137 937 959 981 159 181 203 7 8 9 16.1 18.4 20.7 196 226 248 270 292 314 336 358 380 403 425 22 197 447 469 491 513 535 557 579 601 623 645 198 667 688 710 732 754 776 798 820 842 863 1 2.2 199 885 907 929 951 973 994 *016 *038 *060 *081 2 3 4.4 6.6 200 30 103 125 x 146 168 190 211 233 255 276 298 4 5 6 8.8 11.0 13.2 201 320 341 363 384 406 428 449 471 492 514 202 535 557 578 600 621 643 664 685 707 728 7 15.4 203 750 771 792 814 835 856 878 899 920 942 8 9 17.6 19.8 204 963 984 *006 *027 *048 *069 *091 *112 *133 *154 205 31 175 197 218 239 260 281 302 323 345 366 21 206 387 408 429 450 471 492 513 534 555 576 1 2.1 207 597 618 639 660 681 702 723 744 765 785 2 3 4 4.2 6.3 8.4 208 806 827 848 869 890 911 931 952 973 994 209 210 32 015 222 035 243 056 263 077 284 098 305 118 325 139 346 160 181 201 366 387 408 5 6 7 10.5 12.6 14.7 211 428 449 469 490 510 531 552 572 593 613 8 9 16.8 18.9 212 634 654 675 695 715 736 756 777 797 818 213 838 858 879 899 919 940 960 980 *001 *021 19 214 33 041 062 082 102 122 143 163 183 203 224 1 2.0 1.9 215 244 264 284 304 325 345 365 385 405 425 2 3 4 4.0 6.0 8.0 3.8 5.7 7.6 216 445 465 486 506 526 546 566 586 606 626 217 646 666 686 706 726 746 766 786 806 826 5 1 ).0 9.5 218 846 866 885 905 925 945 965 985 *005 *025 6 1 7 1 8 1 2.0 4.0 6.0 11.4 13.3 15.2 219 34 044 064 084 104 124 143 163 183 203 223 220 242 262 282 301 321 341 361 380 400 420 9 1 8.0 17.1 N L 1 2 3 4 5 6 7 8 9 P . P 7ss Logarithms of Numbhbs. Num. 220 to 259. Lo K . 342 to 414. N L t 2 3 4 5 6 7 8 9 P . P. 220 34 242 262 282 301 321 341 361 380 400 420 221 439 459 479 498 518 537 557 577 596 616 20 222 635 655 674 694 713 733 753 772 792 811 1 2.0 223 224 830 35 025 850 044 869 064 889 083 908 102 928 947 967 986 *005 122 141 160 180 199 2 3 i 4.0 6.0 8.0 225 218 238 257 276 295 315 334 353 372 392 5 6 10.0 12.0 14.0 226 411 430 449 468 488 507 526 545 564 583 7 227 603 622 641 660 679 698 717 736 755 774 8 16.0 228 793 813 832 851 870 889 908 927 946 965 9 18.0 229 984 *003 *021 *040 *059 *078 *097 *116 *135 *154 230 36 173 192 211 229 248 267 286 305 324 342 19 231 361 380 399 418 436 455 474 493 511 530 232 549 568 586 605 624 642 661 680 698 717 1 1.9 233 736 754 773 791 810 829 847 866 884 903 2 3 4 3.8 5.7 7.6 234 922 940 959 977 9% *014 *033 *051 *070 *088 235 37 107 125 144 162 181 199 218 236 254 273 5 6 9.5 11.4 236 291 310 328 346 365 38 .401 420 438 457 7 13.3 237 475 493 511 530 548 566 5 603 621 639 8 9 15.2 17.1 238 658 676 694 712 731 749 767 785 803 822 239 840 858 876 894 912 931 949 967 985 *003 240 38 021 039 057 075 093 112 130 148 166 184 241 202 220 238 256 274 292 310 328 346 364 18 242 382 399 417 435 453 471 489 507 525 543 243 561 578 596 614 632 650 668 686 703 721 1 2 3 1.8 244 739 757 775 792 810 828 846 863 881 899 3.6 5.4 245 917 934 952 970 987 *005 *023 *041 *058 *076 4 5 7.2 9.0 246 39 094 111 129 146 164 182 199 217 235 252 6 10.8 247 270 287 305 322 340 358 375 393 410 428 7 8 9 12.6 14.4 1R2 248 445 463 480 498 515 533 550 568 585 602 249 620 637 655 672 690 707 724 742 759 777 250 794 811 829 846 863 881 898 915 933 950 251 967 985 *002 *019 *037 *054 *071 *088 *106 *123 252 40 140 157 175 192 209 226 243 261 278 295 253 312 329 346 364 381 398 415 432 449 466 17 254 483 500 518 535 552 569 586 603 620 637 1 1.7 255 654 671 688 705 722 739 756 773 790 807 2 3 3.4 5.1 256 824 841 858 875 892 909 926 943 960 976 4 6.8 257 993 *010 *027 *044 *061 *078 *095 *111 *128 *145 5 6 7 8.5 10.2 11.9 258 41 162 179 196 212 229 246 263 280 296 313 259 330 347 363 380 397 414 430 447 464 481 8 9 13.6 15.3 260 497 514 531 547 564 581 597 614 631 647 N L 1. 2 3 4 5 6 7 8 9 P . P. Logarithms of Numbers. 789 Num. 260 to 299. Log. 414 to 476. N L 1 2 3 4 5 6 7 8 9 P . P. 260 41 497 514 531 547 564 581 597 614 631 647 261 664 681 697 714 731 747 764 780 797 814 262 830 847 863 880 896 913 929 946 963 979 263 9% *012 *029 *045 *062 *078 *095 *111 *127 144 264 42 160 177 193 210 226 243 259 275 292 308 17 265 325 341 357 374 390 406 423 439 455 472 1 ii 266 488 504 521 537 553 570 586 602 619 635 2 3.4 267 651 667 684 700 716 732 749 765 781 797 3 5.1 268 813 830 846 862 878 894 911 927 943 959 4 5 6 6.8 8.5 10.2 269 975 991 *008 *024 *040 *056 *072 *088 *104 *120 270 43 136 152 169 185 201 217 233 249 265 281 7 8 11.9 13.6 271 297 313 329 345 361 377 393 409 425 441 9 15.3 272 457 473 489 505 521 537 553 569 584 600 273 616 632 648 664 680 696 712 727 743 759 274 775 791 807 823 838 854 870 886 902 917 275 933 949 965 981 996 *012 *028 *044 *059 *075 276 44 091 107 122 138 154 170 185 201 217 232 16 277 248 264 279 295 311 326 342 358 373 389 278 404 420 436 451 467 483 498 514 529 545 1 1.6 279 560 576 592 607 623 638 654 669 685 700 2 3 3.2 4.8 280 716 731 747 762 778 793 809 824 840 855 4 5 6 6.4 8.0 9.6 281 871 886 902 917 932 948 963 979 994 *010 282 45 025 040 056 071 086 102 117 133 148 163 7 11.2 283 179 194 209 225 240 255 271 286 301 317 8 9 12.8 14.4 284 332 347 362 378 393 408 423 439 454 469 285 484 500 515 530 545 561 576 591 606 621 286 637 652 667 682 697 712 728 743 758 773 287 788 803 818 834 849 864 879 894 909 924 288 939 954 969 984 *000 *015 *030 *045 *060 *075 289 46 090 105 120 135 150 165 180 195 210 225 15 290 240 255 270 285 300 315 330 345 359 374 1 1.5 291 389 404 419 434 449 464 479 494 509 523 2 3 4 3.0 4.5 6.0 292 538 553 568 583 598 613 627 642 657 672 293 687 702 716 731 746 761 776 790 805 820 5 7.5 294 835 850 864 879 894 909 923 938 953 967 6 7 9.0 10.5 295 982 997 *012 *026 *041 *056 *070 *085 *100 *114 8 9 12.0 13.5 296 47 129 144 159 173 188 202 217 232 246 261 297 276 290 305 319 334 349 363 378 392 407 298 422 436 451 465 480 494 509 524 538 553 299 567 582 5% 611 625 640 654 669 683 698 300 712 727 741 756 770 784 799 813 828 842 N L 1 2 3 4 5 6 7 8 9 P . P. 790 Logarithms of Numbers. Num. 300 to 339. Log. 477 to 531. N L 1 2 3 4 5 6 7 8 9 P. P. 300 47 712 727 741 756 770 784 799 813 828 842 301 857 871 885 900 mi 929 943 958 972 986 302 48 001 015 029 044 058 073 087 101 116 130 303 144 159 173 187 202 216 230 244 259 273 304 287 302 316 330 344 359 373 387 401 416 14 305 430 444 458 473 487 501 515 530 544 558 1 ' « 306 572 586 601 615 629 643 657 671 686 700 l 2 i.i 2.8 307 714 728 742 756 770 785 799 813 827 841 3 4.2 308 855 869 883 897 911 926 940 954 968 982 4 5 6 5.6 7.0 8.4 309 996 *010 *024 *038 *052 *066 *080 *094 *108 *122 310 49 136 150 164 178 192 206 220 234 248 262 7 8 9.8 11.2 311 276 290 304 318 332 346 360 374 388 402 9 12.6 312 415 429 443 457 471 485 499 513 527 541 313 554 568 582 596 610 624 638 651 665 679 314 693 707 721 734 748 762 776 790 803 817 315 831 845 859 872 886 900 914 927 941 955 316 969 982 996 *010 *024 *037 *051 *065 *079 *092 13 317 50 106 120 133 147 161 174 188 202 215 229 318 243 256 270 284 297 311 325 338 352 365 1 1.3 319 379 393 406 420 433 447 461 474 488 501 2 3 2.6 3.9 320 615 529 542 556 569 583 596 610 623 637 4 5 6 5.2 6.5 7.8 321 651 664 678 691 705 718 732 745 759 772 322 786 799 813 826 840 853 866 880 893 907 7 9.1 323 920 934 947 961 974 987 *001 *014 *028 *041 8 9 10.4 11.7 324 51 055 068 081 095 108 121 135 148 162 175 325 188 202 215 228 242 255 268 282 295 308 326 322 335 348 362 375 388 402 415 428 441 327 455 468 481 495 508 521 534 548 561 574 328 587 601 614 627 640 654 667 680 693 706 329 720 733 746 769 772 786 799 812 825 838 12 330 851 865 878 891 904 917 930 943 957 970 1 1.2 331 983 996 *009 *022 *035 *048 *061 *075 *088 *101 2 3 4 2.4 3.6 4.8 332 52 114 127 140 153 166 179 192 205 218 231 333 244 257 270 284 297 310 323 336 349 362 5 6.0 334 375 388 401 414 427 440 453 466 479 492 6 7 7.2 8.4 335 504 517 530 543 556 569 582 595 608 621 8 9 9.6 10.8 336 634 647 660 673 686 699 711 724 737 750 337 763 776 789 802 815 827 840 853 866 879 338 892 905 917 930 943 956 969 982 994 *007 339 53 020 033 046 058 071 084 097 110 122 135 340 148 161 173 186 199 212 224 237 250 263 N L 1 2 3 4 5 6 7 8 9 P . P. Logarithms of Numbers. 791 Num. 340 to 379. Log. 531 to 579. N L 1 2 3 4 5 6 7 8 9 P. P. 340 53 148 161 173 186 199 212 224 237 250 263 341 275 288 301 314 326 339 352 364 377 390 342 403 415 428 441 453 466 479 491 504 517 343 529 542 555 567 580 593 605 618 631 643 344 656 668 681 694 706 719 732 744 757 769 13 345 782 794 807 820 832 845 857 870 882 895 1 2 1.3 2.6 346 908 920 933 945 958 970 983 995 *008 *020 347 54 033 045 058 070 083 095 108 120 133 145 3 3.9 348 158 170 183 195 208 220 233 245 258 270 4 5 6 5.2 6.5 7.8 349 283 295 307 320 332 345 357 370 382 394 350 407 419 432 444 456 469 481 494 506 518 7 8 9.1 10.4 351 531 543 555 568 580 593 605 617 630 642 9 11.7 352 654 667 679 691 704 716 728 741 753 765 353 777 790 802 814 827 839 851 864 876 888 354 900 913 925 937 949 962 974 986 998 *011 355 £5 023 035 047 060 072 084 096 108 121 133 356 145 157 169 182 194 206 218 230 242 255 12 357 267 279 291 303 315 328 340 352 364 376 358 388 400 413 425 437 449 461 473 485 497 1 1.2 359 509 522 534 546 558 570 582 594 606 618 2 3 2.4 3.6 360 630 642 654 666 678 691 703 715 727 739 4 5 6 4.8 6.0 7.2 • 361 751 763 775 787 799 811 823 835 847 859 362 871 883 895 907 919 931 943 955 967 979 7 8.4 363 991 *003 *015 *027 *038 *050 *062 *074 *086 *098 8 9 9.6 10.8 364 56 110 122 134 146 158 170 182 194 205 217 365 229 241 253 265 277 289 301 312 324 336 366 348 360 372 384 396 407 419 431 443 455 367 467 478 490 502 514 526 538 549 561 573 368 585 597 608 620 632 644 656 667 679 691 369 703 714 726 738 750 761 773 785 797 808 11 370 820 832 844 855 867 879 891 902 914 926 1 1.1 371 937 949 961 972 984 996 *008 *019 *031 *043 2 3 4 2.2 3.3 4.4 372 57 054 066 078 089 101 113 124 136 148 159 373 171 183 194 206 217 229 241 252 264 276 5 5.5 374 287 299 310 322 334 345 357 368 380 392 6 7 6.6 7.7 375 403 415 426 438 449 461 473 484 4% 507 8 9 8.8 9.9 376 519 530 542 553 565 576 588 600 611 623 377 634 646 657 669 680 692 703 715 726 738 378 749 761 772 784 795 807 818 830 841 852 379 864 875 887 898 910 921 933 944 955 967 380 978 990 *001 *013 *024 *035 *047 *058 *070 *081 N L 1 2 3 4 S 6 7 8 9 P . P. 792 Logarithms op Numbers. Num 380 to 419. Log 579 to 623. N L 1 2 3 4 5 6 7 8 9 P. P. 380 57 978 990 *001 *013 *024 *035 *047 »058 *070 *081 381 58 092 104 115 127 138 149 161 172 184 195 882 206 218 229 240 252 263 274 286 297 309 883 320 331 343 354 365 377 388 399 410 422 884 433 444 456 467 478 490 501 512 524 535 11 885 546 557 569 580 591 602 614 625 636 647 386 659 670 681 692 704 715 726 737 749 760 1 2 2.2 887 771 782 794 805 816 827 838 850 861 872 3 3.3 388 883 894 906 917 928 939 950 961 973 984 4 5 6 4.4 5.5 6.6 389 995 *006 *017 *028 *040 *051 *062 *073 *084 *095 390 59 106 118 129 140 151 162 173 184 195 207 7 8 7.7 8.8 891 218 229 240 251 262 273 284 295 306 318 9 9.9 392 329 340 351 362 373 384 395 406 417 428 893 439 450 461 472 483 494 506 517 528 539 894 550 561 572 583 594 605 616 627 638 649 895 660 671 682 693 704 715 726 737 748 759 396 770 780 791 802 813 824 835 846 857 868 10 897 879 890 901 912 923 934 945 956 966 977 898 988 999 *010 *021 *032 *043 *054 *065 *076 *086 1 1.0 899 60 097 108 119 130 141 152 163 173 184 195 2 3 2.0 3.0 400 206 217 228 239 249 260 271 282 293 304 4 5 6 4.0 5.0 6.0 401 314 325 336 347 358 369 379 390 401 412 402 423 433 444 455 466 477 487 498 509 520 7 7.0 403 531 541 552 563 574 584 595 606 617 627 8 9 8.0 9.0 404 638 649 660 670 681 692 703 713 724 735 405 746 756 767 778 788 799 810 821 831 842 406 853 863 874 885 895 906 917 927 938 949 407 959 970 981 991 *002 *013 *023 *034 *045 *055 408 61 066 077 087 098 109 119 130 140 151 162 409 172 183 194 204 215 225 236 247 257 268 410 278 289 300 310 321 331 342 352 363 374 411 384 395 405 416 426 437 448 458 469 479 412 490 500 511 521 532 542 553 563 574 584 413 595 606 616 627 637 648 658 669 679 690 414 700 711 721 731 742 752 763 773 784 794 415 805 815 826 836 847 857 868 878 888 899 416 909 920 930 941 951 962 972 982 993 *003 417 62 014 024 034 045 055 066 076 086 097 107 418 118 128 138 W9 159 170 180 190 201 211 419 221 232 242 252 263 273 284 294 304 315 420 325 335 346 356 366 377 387 397 408 418 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Numbers. 793 Num 420 to 459. Log 623 to 662. N L i 2 3 4 5 6 7 8 9 P. P. 420 62 325 335 346 356 366 377 387 397 408 418 421 428 439 449 459 469 480 490 500 511 521 422 531 542 552 562 572 583 593 603 613 624 423 634 644 655 665 675 685 696 706 716 726 424 737 747 757 767 778 788 798 808 818 829 425 839 849 859 870 880 890 900 910 921 931 426 941 951 961 972 982 992 *002 *012 *022 *033 427 63 043 053 063 073 083 094 104 114 124 134 428 144 155 165 175 185 195 205 215 225 236 10 429 246 256 266 276 286 296 306 317 327 337 430 347 357 367 377 387 397 407 417 428 438 1 2 l.U 2.0 431 448 458 468 478 488 498 508 518 528 538 3 3.0 432 548 558 568 579 589 599 609 619 629 639 4 5 6 4.0 5.0 6.0 433 649 659 669 679 689 699 709 719 729 739 434 749 759 769 779 789 799 809 819 829 839 7 8 9 7.0 8.0 9.0 435 849 859 869 879 889 899 909 919 929 939 436 949 959 969 979 988 998 *008 *018 *028 *038 437 64 048 058 068 078 088 098 108 118 128 137 438 147 157 167 177 187 197 207 217 227 237 439 246 256 266 276 286 296 306 316 326 335 440 345 355 365 375 385 395 404 414 424 434 441 444 454 464 473 483 493 503 513 523 532 442 542 552 562 572 582 591 601 611 621 631 443 640 650 660 670 680 689 699 709 719 729 444 738 748 758 768 777 787 797 807 816 826 445 836 846 856 865 875 885 895 904 914 924 9 446 933 943 953 963 972 982 992 *002 *011 *021 1 0.9 447 65 031 040 050 060 070 079 089 099 108 118 2 3 4 1.8 2.7 3.6 448 128 137 147 157 167 176 186 196 205 215 449 225 234 244 254 263 273 283 292 302 312 5 6 4.5 5.4 450 321 331 341 350 360 369 379 389 398 408 7 6.3 451 418 427 437 447 456 466 475 485 495 504 8 9 7.2 8.1 452 514 523 533 543 552 562 571 581 591 600 453 610 619 629 639 648 658 667 677 686 696 454 706 715 725 734 744 753 763 772 782 792 455 801 811 820 830 839 849 858 868 877 887 456 896 906 916 925 935 944 954 963 973 982 457 992 *001 *011 *020 *030 *039 *049 *058 *068 *077 458 66 087 0% 1% 115 124 134 143 153 162 172 459 181 191 200 210 219 229 238 247 257 266 460 276 285 295 304 314 323 332 342 351 361 N L 1 2 3 4 5 6 7 8 9 P. P. 794 Logarithms op Numbers. Nutn 460 to 499. Log. 662 to 698. N L 1 2 3 4 5 6 7 8 9 P. P. 460 66 276 285 295 304 314 323 332 342 351 361 461 370 380 389 398 408 417 427 436 445 455 462 464 474 483 492 502 511 521 530 539 549 463 558 567 577 586 596 605 614 624 633 642 464 652 661 671 680 689 699 708 717 727 736 465 745 755 764 773 783 792 801 811 820 829 466 839 848 857 867 876 885 894 904 913 922 467 932 941 950 960 969 978 987 997 *006 *015 468 67 025 034 043 052 062 071 080 089 099 108 10 469 117 127 136 145 154 164 173 182 191 201 470 210 219 228 237 247 256 265 274 284 293 1 2 1.0 2.0 471 302 311 321 330 339 348 357 367 376 385 3 3.0 472 394 403 413 422 431 440 449 459 468 477 4 5 6 4.0 5.0 6.0 473 486 495 504 514 523 532 641 550 560 569 474 475 578 669 587 679 5% 688 605 697 614 706 624 715 633 724 642 651 660 733 742 752 7 8 9 7.0 8.0 9.0 476 761 770 779 788 797 806 815 825 834 843 477 852 861 870 879 888 897 906 916 925 934 478 943 952 961 970 979 988 997 *006 *015 *024 479 68 034 043 052 061 070 079 088 097 106 115 480 124 133 142 151 160 169 178 187 196 205 481 215 224 233 242 251 260 269 278 287 296 482 305 314 323 332 341 350 359 368 377 386 483 395 404 413 422 431 440 449 458 467 476 484 485 494 502 511 520 529 538 547 556 565 485 574 583 592 601 610 619 628 637 646 655 9 486 664 673 681 690 699 708 717 726 735 744 1 0.9 487 753 762 771 780 789 797 806 815 824 833 2 3 4 1.8 2.7 3.6 488 842 851 860 869 878 886 895 904 913 922 489 490 931 69 020 940 028 949 037 958 046 966 055 975 064 984 073 993 *002 *011 082 090 099 5 6 7 4.5 5.4 6.3 491 108 117 126 135 144 152 162 170 179 188 8 9 7.2 8.1 492 197 205 214 223 232 241 249 258 267 276 493 285 294 302 311 320 329 338 346 355 364 494 373 381 390 399 408 417 425 434 443 452 495 461 469 478 487 496 504 513 522 531 539 496 548 557 566 574 583 592 601 609 618 627 497 636 644 653 662 671 679 688 697 705 714 498 723 732 740 749 758 767 775 784 793 801 499 810 819 827 836 845 854 862 871 880 888 500 897 906 914 923 932 940 949 958 966 975 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Numbers. 795 Num. 500 to 539. Log. 698 to 732. IN L 1 2 3 4 5 6 7 8 9 P. P. 500 69 897 906 914 922 932 940 949 958 966 975 501 984 992 *001 *010 *018 *027 *036 *044 *053 *062 502 70 070 079 088 096 105 114 122 131 140 148 503 157 165 174 183 191 200 209 217 226 234 504 243- 252 260 269 278 286 295 303 312 321 505 329 338 346 355 364 372 381 389 398 406 506 415 424 432 441 449 458 467 475 484 492 507 501 509 518 526 535 544 552 561 569 578 508 586 595 603 612 621 629 638 646 655 663 9 509 672 680 689 697 706 714 723 731 740 749 510 757 766 774 783 791 800 808 817 825 834 1 2 0.9 1.8 511 842 851 859 868 876 885 893 902 910 919 3 2.7 512 927 935 944 952 961 969 978 986 995 *003 4 5 6 3.6 4.5 5.4 513 71 012 020 029 037 046 054 063 071 079 088 514 515 096 181 105 189 113 198 122 206 130 214 139 223 147 231 155 240 164 172 248 257 7 8 9 6.3 7.2 8.1 516 265 273 282 290 299 307 315 324 332 341 517 349 357 366 374 383 391 399 408 416 425 518 433 441 450 458 466 475 483 492 500 508 519 517 525 533 542 550 559 567 575 584 592 520 600 609 617 625 634 642 650 659 667 675 521 684 692 700 709 717 725 734 742 750 759 522 767 775 784 792 800 809 817 825 834 842 523 850 858 867 875 883 892 900 908 917 925 524 933 941 950 958 966 975 983 991 999 *008 525 72 016 024 032 041 049 057 066 074 082 090 8 526 099 107 115 123 132 140 148 156 165 173 1 0.8 527 181 189 198 206 214 222 230 239 247 255 2 3 4 1.6 2.4 3.2 528 263 272 280 288 296 304 313 321 329 337 529 530 346 428 354 436 362 444 370 452 378 460 387 469 395 477 403 485 411 419 493 501 5 6 7 4.0 4.8 5.6 531 509 518 526 534 542 550 558 567 575 583 8 9 6.4 7.2 532 591 599 607 616 624 632 640 648 656 665 533 673 681 689 697 705 713 722 730 738 746 534 754 762 770 779 787 795 803 811 819 827 535 835 843 852 860 868 876 884 892 900 908 536 916 925 933 941 949 957 965 973 981 989 537 997 *006 *014 *022 *030 *038 *046 *054 062 *070 538 73 078 086 094 102 111 119 127 135 143 151 539 159 167 175 183 191 199 207 215 223 231 540 239 247 255 263 272 280 288 296 304 312 N L 1 2 3 4 5 6 7 8 9 P. P. 796 Logarithms of Numbers. Num. 540 to 579. Log. 732 to 763. 73 239 247 255 263 272 820 828 336 344 352 400 408 416 424 432 480 488 496 504 512 560 568 576 584 592 640 648 656 664 672 719 727 735 743 751 799 807 815 823 830 878 886 894 902 910 957 965 973 981 989 74 036 044 052 060 068 115 123 131 139 147 194 202 210 218 225 273 280 288 296 304 351 359 367 374 382 429 437 445 453 461 507 515 523 531 539 586 593 601 609 617 663 671 679 687 695 741 749 757 764 772 819 827 834 842 850 8% 904 912 920 927 974 981 989 997 *005 75 051 059 066 074 082 128 136 143 151 159 205 213 220 228 236 282 289 297 305 312 358 366 374 381 389 435 442 450 458 465 511 519 526 534 542 587 595 603 610 618 664 671 679 686 694 740 747 755 762 770 815 823 831 838 846 891 899 906 914 921 967 974 982 989 997 76 042 050 057 065 072 118 125 133 140 148 193 200 208 215 223 268 275 283 290 298 343 350 358 365 373 280 288 296 304 312 360 368 376 384 892 440 448 456 464 472 520 528 536 544 552 600 608 616 624 632 679 687 695 703 711 759 767 775 783 791 838 846 854 862 870 918 926 933 941 949 997 *005 *013 *020 *028 076 084 092 099 107 155 162 170 178 186 233 241 249 257 265 312 320 327 335 343 390 398 406 414 421 468 476 484 492 500 547 554 562 570 578 624 632 640 648 656 702 710 718 726 733 780 788 796 803 811 858 865 873 881 889 935 943 950 958 966 *012 *020 *028 *035 *043 089 097 105 113 120 166 174 182 189 197 243 251 259 266 274 320 328 335 343 351 397 404 412 420 427 473 481 488 496 504 549 557 565 572 580 626 633 641 648 656 702 709 717 724 732 778 785 793 800 808 853 861 868 876 884 929 937 944 952 959 *005 *012 *020 *027 *035 080 087 095 103 110 155 163 170 178 185 230 238 245 253 260 305 313 320 328 335 380 388 395 403 410 Logarithms of Numbers. 797 Num 580 to 619. Log. 763 to 792. N L 1 2 3 4 5 6 7 8 9 P. P. 580 76 343 350 358 365 373 380 388 395 403 410 8 581 418 425 433 440 448 455 462 470 477 485 1 2 0.8 1.5 582 492 500 507 515 522 530 537 545 552 559 583 567 574 582 589 597 604 612 619 626 634 3 2.4 584 641 649 656 664 671 678 686 693 701 708 4 5 3.2 4.0 585 716 723 730 738 745 753 760 768 775 782 6 7 8 4.8 5.6 6.4 586 790 797 805 812 819 827 834 842 849 856 587 864 871 879 886 893 901 908 916 923 930 9 7.2 588 938 945 953 960 967 975 982 989 997 *004 589 77 012 019 026 034 041 048 056 063 070 078 590 085 093 100 107 115 122 129 137 144 151 591 159 166 173 181 188 195 203 210 217 225 592 232 240 247 254 262 269 276 283 291 298 593 305 313 320 327 335 342 349 357 364 371 594 379 386 393 401 408 415 422 430 437 444 595 452 459 466 474 481 488 495 503 510 517 596 525 532 539 546 554 561 568 576 583 590 597 597 605 612 619 627 634 641 648 656 663 7 598 670 677 685 692 699 706 714 721 728 735 599 743 750 757 764 772 779 786 793 801 808 1 2 0.7 1.4 600 815 822 830 837 844 851 859 866 873 880 3 4 5 2.1 2.8 3.5 601 887 895 902 909 916 924 931 938 945 952 602 960 967 974 981 988 996 *003 *010 *017 *025 6 4.2 603 78 032 039 046 053 061 068 075 082 089 097 7 8 9 4.9 5.6 6.3 604 104 111 118 125 132 140 147 154 161 168 605 176 183 190 197 204 211 219 226 233 240 606 247 254 262 269 276 283 290 297 305 312 607 319 326 333 340 347 355 362 369 376 383 608 390 398 405 412 419 426 433 440 447 455 609 462 469 476 483 490 497 504 512 519 526 610 533 540 547 554 561 569 576 583 590 597 611 604 611 618 625 633 640 647 654 661 668 612 675 682 689 696 704 711 718 725 732 739 613 746 753 760 767 774 781 789 796 802 810 614 817 824 831 838 845 852 859 866 873 880 615 888 895 902 909 916 923 930 937 944 951 616 958 965 972 979 986 993 *000 *007 *014 *021 617 79 029 036 043 050 057 064 071 078 085 092 618 099 106 113 120 127 134 141 148 155 162 619 169 176 183 190 197 204 211 218 225 232 620 239 246 253 260 267 274 281 288 295 302 N L 1 2 3 4 5 6 7 8 9 P P. 706 Logarithms of Ntjmbbrs. Num. 620 to 659. Log. 792 to 819. N L i 2 3 4 5 6 7 8 9 P. P. 620 79 239 246 253 260 267 274 281 288 295 302 621 309 316 323 330 337 344 351 358 365 372 622 379 386 393 400 407 414 421 428 435 442 623 449 456 463 470 477 484 491 498 505 511 624 518 525 532 539 546 553 560 567 574 581 625 588 595 602 609 616 623 630 637 644 650 626 657 664 671 678 685 692 699 706 713 720 627 727 734 741 748 754 761 768 775 782 789 628 7% 803 810 817 824 831 837 844 851 858 629 865 872 879 886 893 900 906 913 920 927 630 934 941 948 955 962 969 975 982 989 996 631 80 003 010 017 024 030 037 044 051 058 065 632 072 079 085 092 099 106 113 120 127 134 633 140 147 154 161 168 175 182 188 195 202 634 209 216 223 229 236 243 250 257 264 271 635 277 284 291 298 305 312 318 325 332 339 636 346 353 359 366 373 380 387 393 400 407 7 637 414 421 428 434 441 448 455 462 468 475 638 482 489 496 502 509 516 523 530 536 543 1 0.7 639 550 557 564 570 577 584 591 598 604 611 2 3 1.4 2.1 640 618 625 632 638 645 652 659 665 672 679 4 5 6 2.8 3.5 4.2 641 686 693 699 706 713 720 726 733 740 747 642 754 760 767 774 781 787 794 801 808 814 7 4.9 643 821 828 835 841 848 855 862 868 875 882 8 9 5.6 6.3 644 889 895 902 909 916 922 929 936 943 949 645 956 963 969 976 983 990 996 *003 *010 *017 646 81 023 030 037 043 050 057 064 070 077 084 647 090 097 104 111 117 124 131 137 144 151 648 158 164 171 178 184 191 198 204 211 218 649 224 231 238 245 251 258 265 271 278 285 650 291 298 305 311 318 325 331 338 345 351 651 358 365 371 378 385 391 398 405 411 418 652 425 431 438 445 451 458 465 471 478 485 653 491 498 505 511 518 525 531 538 544 551 654 558 564 571 578 584 591 598 604 611 617 655 624 631 637 644 651 657 664 671 677 684 656 690 697 704 710 717 723 730 737 743 750 657 757 763 770 776 783 790 796 803 809 816 658 823 829 836 842 849 856 862 869 875 882 659 889 895 902 908 915 921 928 935 941 948 660 954 961 968 974 981 987 994 *000 *007 *014 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Numbers. 799 Sum . 660 to 699. Log . 819 to 845. N L 1 2 3 4 5 6 7 8 9 P. P. 660 81 954 961 968 974 981 987 994 *000 *007 *014 7 661 82 020 027 033 040 046 053 060 066 073 079 1 I 0.7 1.4 662 086 092 099 105 112 119 125 132 138 145 663 151 158 164 171 178 184 191 197 204 210 2.1 664 217 223 230 236 243 249 256 263 269 276 4 5 2.8 3.5 665 282 289 295 302 308 315 321 328 334 341 6 7 8 4.2 4.9 5.6 666 347 354 360 367 373 380 387 393 400 406 667 413 419 426 432 439 445 452 458 465 471 9 6.3 668 478 484 491 497 504 510 517 523 530 536 669 543 549 556 562 569 575 582 588 595 601 670 607 614 620 627 633 640 646 653 659 666 671 672 679 685 692 698 705 711 718 724 730 672 737 743 750 756 763 769 776 782 789 795 673 802 808 814 821 827 834 840 847 853 860 674 866 872 879 885 892 898 905 911 918 924 675 930 937 943 950 956 963 969 975 982 988 676 995 *001 *008 *014 *020 *027 *033 *040 *046 *052 677 83 059 065 072 078 085 091 097 104 110 117 6 678 123 129 136 142 149 155 161 168 174 181 679 187 193 200 206 213 219 225 232 238 245 1 2 0.6 1.2 480 251 257 264 270 276 283 289 296 302 308 3 4 5 1.8 2.4 3.0 681 315 321 327 334 340 347 353 359 366 372 682 378 385 391 398 404 410 417 423 429 436 6 3.6 683 442 448 455 461 467 474 480 487 493 499 7 8 9 4.2 4.8 5.4 684 506 512 518 525 531 537 544 550 556 563 685 569 575 582 588 594 601 607 613 620 626 686 632 639 645 651 658 664 670 677 683 689 687 696 702 708 715 721 727 734 740 746 753 688 759 765 771 778 784 790 797 803 809 816 689 822 828 835 841 847 853 860 866 872 879 690 885 891 897 904 910 916 923 929 935 942 691 948 954 960 967 973 979 985 992 998 *004 692 84 Oil 017 023 029 036 042 048 055 061 067 693 073 080 086 092 098 105 111 117 123 130 694 136 142 148 155 161 167 173 180 186 192 695 198 205 211 217 223 230 236 242 248 255 696 261 267 273 280 286 292 298 305 311 317 697 323 330 336 342 348 354 361 367 373 379 698 386 392 398 404 410 417 423 429 435 442 699 448 454 460 466 473 479 485 491 497 504 700 510 516 522 528 535 541 547 553 559 566 N L 1 2 3 4 5 6 7 8 9 P. P. MM) Logarithms op Numbers. Num. 700 to 739. Log. 845 to 869. N L 1 2 3 4 5 6 7 8 9 P. P. 700 84 510 516 522 528 535 541 547 553 559 566 701 572 578 584 590 597 603 609 615 621 628 702 634 640 646 652 658 665 671 677 683 689 703 696 702 708 714 720 726 733 739 745 751 704 757 763 770 776 782 788 794 800 807 813 705 819 825 831 837 844 850 856 862 868 874 706 880 887 893 899 905 911 917 924 930 936 707 942 948 954 960 967 973 979 985 991 997 708 85 003 009 016 022 028 034 040 046 052 058 709 065 071 077 083 089 095 101 107 114 120 710 126 132 138 144 150 156 163 169 175 181 711 187 193 199 205 211 217 224 230 236 242 712 248 254 260 266 272 278 285 291 297 303 713 309 315 321 327 333 339 345 352 358 364 714 370 376 382 388 394 400 406 412 418 425 715 431 437 443 449 455 461 467 473 479 485 716 491 497 503 509 516 522 528 534 540 546 717 552 558 564 570 576 582 588 594 600 606 6 718 612 618 625 631 637 643 649 655 661 667 719 673 679 685 691 697 703 709 715 721 727 1 2 u.o 1.2 720 733 739 745 751 757 763 769 775 781 788 3 4 1.8 2.4 721 794 800 806 812 818 824 830 836 842 848 5 3.0 722 854 860 866 872 878 884 890 896 902 908 6 7 8 3.6 4.2 4.8 723 914 920 926 932 938 944 950 956 962 968 724 974 980 986 992 998 *004 *010 *016 *022 *028 9 5.4 725 86 034 040 046 052 058 064 070 076 082 088 726 094 100 106 112 118 124 130 136 141 147 727 153 159 165 171 177 183 189 195 201 207 728 213 219 225 231 237 243 249 255 261 267 729 273 279 285 291 297 303 308 314 320 326 730 332 338 344 350 356 362 368 374 380 386 731 392 398 404 410 415 421 427 433 439 445 732 451 457 463 469 475 481 487 493 499 504 733 510 516 522 528 534 540 546 552 558 564 734 570 576 581 587 593 599 605 611 617 623 735 629 635 641 646 652 658 664 670 676 682 736 688 694 700 705 711 717 723 729 735 741 737 747 753 759 764 770 776 782 788 794 800 738 806 812 817 823 829 835 841 847 853 859 739 864 870 876 882 888 894 900 906 911 917 740 923 929 935 941 947 953 958 964 970 976 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Numbers. 801 Num. 740 to 779. Log. 869 to 892. N L 1 2 3 4 5 6 7 8 9 P. P. 740 86 923 929 935 941 947 953 958 964 970 976 741 982 988 994 999 *005 *011 *017 *023 *029 *035 742 87 040 046 052 058 064 070 075 081 087 093 743 099 105 111 116 122 128 134 140 146 151 744 157 163 169 175 181 186 192 198 204 210 745 216 221 227 233 239 245 251 256 262 268 746 274 280 286 291 297 303 309 315 320 326 747 332 338 344 349 355 361 367 373 379 384 748 390 396 402 408 413 419 425 431 437 442 749 448 454 460 466 471 477 483 489 495 500 750 506 512 518 523 529 535 541 547 552 558 751 564 570 576 581 587 593 599 604 610 616 752 622 628 633 639 645 651 656 662 668 674 753 679 685 691 697 703 708 714 720 726 731 754 737 743 749 754 760 766 772 777 783 789 755 795 800 806 812 818 823 829 835 841 846 756 852 858 864 869 875 881 887 892 898 904 757 910 915 921 927 933 938 944 950 955 961 6 758 967 973 978 984 990 996 *001 *007 *013 *018 759 88 024 030 036 041 047 053 058 064 070 076 1 2 v.o 1.2 760 081 087 093 098 104 110 116 121 127 133 3 4 1.8 2.4 761 138 144 150 156 161 167 173 178 184 190 5 3.0 762 195 201 207 213 218 224 230 235 241 247 6 7 8 3.6 4.2 4.8 763 252 258 264 270 275 281 287 292 298 304 764 309 315 321 326 332 338 343 349 355 360 9 5.4 765 366 372 377 383 389 395 400 406 412 417 766 423 429 434 440 446 451 457 463 468 474 767 480 485 491 497 502 508 513 519 525 530 768 536 542 547 553 559 564 570 576 581 587 769 593 598 604 610 615 621 627 632 638 643 770 649 655 660 666 672 677 683 689 694 700 771 705 711 717 722 728 734 739 745 750 756 772 762 767 773 779 784 790 795 801 807 812 773 818 824 829 835 840 846 852 857 863 868 774 874 880 885 891 897 902 908 913 919 925 775 930 936 941 947 953 958 964 969 975 981 776 986 992 997 *003 *009 *014 *020 *025 *031 *037 777 89 042 048 053 059 064 070 076 081 087 092 778 098 104 109 115 120 126 131 137 143 148 779 154 159 165 170 176 182 187 193 198 204 780 209 215 221 226 232 237 243 248 254 260 N L 1 2 3 4 5 6 7 8 9 P. P. S02 Logarithms op Numbers. Num . 780 to 819. Log 892 to 913. N L o 1 2 3 4 5 6 7 8 9 P. P. 780 89 209 215 221 226 232 237 243 248 254 260 781 265 271 276 282 287 293 298 304 310 315 782 321 326 332 337 343 348 354 360 365 371 783 376 382 387 393 398 404 409 415 421 426 784 432 437 443 448 454 459 465 470 476 481 785 487 492 498 504 509 515 520 526 531 537 786 542 548 553 559 564 570 575 581 586 592 787 597 603 609 614 620 625 631 636 642 647 788 653 658 664 669 675 680 686 691 697 702 789 708 713 719 724 730 735 741 746 752 757 790 763 768 774 779 785 790 796 801 807 812 791 818 823 829 834 840 845 851 856 862 867 792 873 878 883 889 894 900 905 911 916 922 793 927 933 938 944 949 955 960 966 971 977 794 982 988 993 998 *004 *009 *015 *020 *026 *031 795 90 037 042 048 053 059 064 069 075 080 0S5 796 091 097 102 108 113 119 124 129 135 140 797 146 151 157 162 168 173 179 184 189 195 5 798 200 206 211 217 222 227 233 238 244 249 799 255 260 266 271 276 282 287 293 298 304 1 2 v.o 1.0 800 309 314 320 325 331 336 342 347 352 358 3 4 1.5 2.0 801 363 369 374 380 385 390 396 401 407 412 5 2.5 802 417 423 428 434 439 445 450 455 461 466 6 7 8 3.0 3.5 4.0 803 472 477 482 488 493 499 504 509 515 520 804 526 531 536 542 547 553 558 563 569 574 9 4.5 805 580 585 590 596 601 607 612 617 623 628 806 634 639 644 650 655 660 666 671 677 682 807 687 693 698 703 709 714 720 725 730 736 808 741 747 752 757 763 768 773 779 784 789 809 795 800 806 811 816 822 827 832 838 843 810 849 854 859 865 870 875 881 886 891 897 811 902 907 913 918 924 929 934 940 945 950 812 956 961 966 972 977 982 988 993 998 *004 813 91 009 014 020 025 030 036 041 046 052 057 814 062 068 073 078 084 089 094 100 105 110 815 116 121 126 132 137 142 148 153 158 164 816 169 174 180 185 190 196 201 206 212 217 817 222 228 233 238 243 249 254 259 265 270 818 275 281 286 291 297 302 307 312 318 323 819 328 334 339 344 350 355 360 365 371 376 820 381 387 392 397 403 408 413 418 424 429 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms op Numbers. 803 Num. 820 to 859. Log. 913 to 934. 5 6 91 381 387 392 397 403 434 440 445 450 455 487 492 498 503 508 540 545 551 556 561 593 598 603 609 614 645 651 656 661 666 698 703 709 714 719 ' 751 756 761 766 772 803 808 814 819 824 855 861 866 871 876 908 913 918 924 929 960 965 971 976 981 92 012 018 023 028 033 065 070 075 080 085 117 122 127 132 137 169 174 179 184 189 221 226 231 236 241 273 278 283 288 293 324 330 335 340 345 376 381 387 392 397 428 433 438 443 449 480 485 490 495 500 531 536 542 547 552 583 588 593 598 603 634 639 645 650 655 686 691 696 701 706 737 742 747 752 758 788 793 799 804 809 840 845 850 855 860 891 896 901 906 911 942 947 952 957 962 993 998 *003 *008 *013 93 044 049 054 059 064 095 100 105 110 115 146 151 156 161 166 197 202 207 212 217 247 252 258 263 268 298 303 308 313 318 349 354 359 364 369 399 404 409 414 420 4-50 455 460 465 470 408 413 418 424 429 461 466 471 477 482 514 519 524 529 535 566 572 577 582 587 619 624 630 635 640 672 677 682 687 693 724 730 735 740 745 777 782 787 793 798 829 834 840 845 850 882 887 892 897 903 934 939 944 950 955 986 991 997 *002 *007 038 044 049 054 059 091 096 101 106 111 143 148 153 158 163 195 200 205 210 215 247 252 257 262 267 298 304 309 314 319 350 355 361 366 371 402 407 412 418 423 454 .459 464 469 474 505 511 516 521 526 557 562 567 572 578 609 614 619 624 629 660 665 670 675 681 711 716 722 727 732 763 768 773 778 783 814 819 824 829 834 865 870 875 881 886 916 921 927 932 937 967 973 978 983 988 *018 *024 *029 *034 *039 069 075 080 085 090 120 125 131 136 141 171 176 181 186 192 222 227 232 237 242 273 278 283 288 293 323 328 334 339 344 374 379 384 389 394 425 430 435 440 445 475 480 485 490 495 *04 Logarithms of Numbers. Num 860 to 899. Log 934 to 954. N L 1 2 3 4 S 6 7 8 9 P. P. 860 93 450 455 460 465 470 475 480 485 490 495 861 500 505 510 515 520 526 531 536 541 546 862 551 556 561 566 571 576 581 586 591 596 863 601 606 611 616 621 626 631 636 641 646 864 651 656 661 666 671 676 682 687 692 697 865 702 707 712 717 722 727 732 737 742 747 866 752 757 762 767 772 777 782 787 792 797 867 802 807 812 817 822 827 832 837 842 847- 868 852 857 862 867 872 877 882 887 892 897 869 902 907 912 917 922 927 932 937 942 947 870 952 957 962 967 972 977 982 987 992 997 871 94 002 007 012 017 022 027 032 037 042 047 872 052 057 062 067 072 077 082 086 091 0% 873 101 106 111 116 121 126 131 136 141 146 874 151 156 161 166 171 176 181 186 191 196 875 201 206 211 216 221 226 231 236 240 245 876 250 255 260 265 270 275 280 285 290 295 877 300 305 310 315 320 325 330 335 340 345 8 878 349 354 359 364 369 374 379 384 389 394 1 2 0.5 1.0 879 399 404 409 414 419 424 429 433 438 443 880 448 453 458 463 468 473 478 483 488 493 3 4 1.5 2.0 881 498 503 507 512 517 522 527 532 537 642 5 2.5 882 547 552 557 562 567 571 676 581 586 591 6 7 8 3.0 3.5 4.0 883 596 601 606 611 616 621 626 630 635 640 884 645 650 655 660 665 670 675 680 685 689 9 4.5 885 694 699 704 709 714 719 724 729 734 738 886 743 748 753 758 763 768 773 778 783 787 887 792 797 802 807 812 817 822 827 832 836 888 841 846 851 856 861 866 871 876 880 885 889 890 895 900 905 910 915 919 924 929 934 890 939 944 949 954 959 963 968 973 978 983 891 988 993 998 *002 *007 *012 *017 *022 *027 *032 892 95 036 041 046 051 056 061 066 071 075 080 893 085 090 095 100 105 109 114 119 124 129 894 134 139 143 148 153 158 163 168 173 177 895 182 187 192 197 202 207 211 216 221 226 8% 231 236 240 245 250 255 260 265 270 274 897 279 284 289 294 299 303 308 313 318 323 898 328 332 337 342 347 352 357 361 366 371 899 376 381 386 390 395 400 405 410 415 419 900 424 429 434 439 444 448 453 458 463 468 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Numbers. S05 Num. 900 to 939. Log. 954 to 973. 95 424 429 434 439 444 472 477 482 487 492 521 525 530 535 540 569 574 578 583 588 617 622 626 631 636 665 670 674 679 684 713 718 722 727 732 761 766 770 775 780 809 813 818 823 828 856 861 866 871 875 904 909 914 918 923 952 957 961 966 971 999 *004 *009 *014 *019 96 047 052 057 061 066 095 099 104 109 114 142 147 152 156 161 190 194 199 204 209 237 242 246 251 256 284 289 294 298 303 332 336 341 346 350 379 384 388 393 398 426 431 435 440 445 473 478 483 487 492 520 525 530 534 539 567 572 577 581 586 614 619 624 628 633 661 666 670 675 680 708 713 717 722 727 755 759 764 769 774 802 806 811 816 820 848 853 858 862 867 895 900 904 909 914 942 946 951 956 960 988 993 997 *002 *007 97 035 039 044 049 053 081 086 090 095 100 128 132 137 142 146 174 179 183 188 192 220 225 230 234 239 267 271 276 280 285 313 317 322 327 331 448 453 458 463 468 497 501 506 511 516 545 550 554 559 564 593 598 602 607 612 641 646 650 655 660 689 694 698 703 708 737 742 746 751 756 785 789 794 799 804 832 837 842 847 852 880 885 890 895 899 928 933 938 942 947 976 980 985 990 995 *023 *028 *033 *038 *042 071 076 080 085 090 118 123 128 133 137 166 171 175 180 185 213 218 223 227 232 261 265 270 275 280 308 313 317 322 327 355 360 365 369 374 402 407 412 417 421 450 454 459 464 468 497 501 506 511 515 544 548 553 558 562 591 595 600 605 609 638 642 647 652 656 685 689 694 699 703 731 736 741 745 750 778 783 788. 792 797 825 830 834 839 844 872 876 881 886 890 918 923 928 932 937 965 970 974 979 984 *011 *016 *021 *025 *030 058 063 067 072 077 104 109 114 118 123 151 155 160 165 169 197 202 206 211 216 243 248 253 257 262 290 294 299 304 308 336 340 345 350 354 SOU LOGARITHMS OP NUMBERS. Num. 940 to 979. Log. 973 to 991. N L 1 2 3 4 5 6 7 8 9 P. P. 940 97 313 317 322 327 331 336 340 345 350 354 941 359 364 368 373 377 882 387 391 396 400 942 405 410 414 419 424 428 433 437 442 447 943 451 456 460 465 470 474 479 483 488 493 944 497 502 506 511 516 520 525 529 534 539 945 543 548 552 557 562 566 571 575 580 585 946 589 594 598 603 607 612 617 621 626 630 947 635 640 644 649 653 658 663 667 672 676 948 681 685 690 695 699 704 708 713 717 722 949 727 731 736 740 745 749 754 759 763 768 5 950 772 777 782 786 791 795 800 804 809 813 1 0.5 951 818 823 827 832 836 841 845 850 855 859 2 3 4 1.0 1.5 2.0 952 864 868 873 877 882 886 891 8% 900 905 953 909 914 918 923 928 932 937 941 946 950 5 2.5 954 955 959 964 968 973 978 982 987 991 996 6 7 3.0 3.5 955 98 000 005 009 014 019 023 028 032 037 041 8 9 4.0 4.5 956 046 050 055 059 064 068 073 078 082 087 957 091 096 100 105 109 114 118 123 127 132 958 137 141 146 150 155 159 164 168 173 177 959 182 186 191 195 200 204 209 214 218 223 960 227 232 236 241 245 250 254 259 263 268 961 272 277 281 286 290 295 299 304 308 313 962 . 318 322 327 331 336 340 345 349 354 358 963 363 367 372 376 381 385 390 394 399 403 964 408 412 417 421 426 430 435 439 444 448 965 453 457 462 466 471 475 480 484 489 493 4 966 498 502 507 511 516 520 525 529 534 538 1 0.4 967 543 547 552 556 561 565 570 574 579 583 2 0.8 1.2 1.6 2.0 968 588 592 597 601 605 610 614 619 623 628 3 4 5 969 632 637 641 646 650 655 659 664 668 673 970 677 682 686 691 695 700 704 709 713 717 6 7 2.4 2.8 971 722 726 731 735 740 744 749 753 758 762 8 3.2 972 767 771 776 780 784 789 793 798 802 807 9 3.6 973 811 816 820 825 829 834 838 843 847 851 974 856 860 865 869 874 878 883 887 892 8% 975 900 905 909 914 918 923 927 932 936 941 976 945 949 954 958 963 967 972 976 981 985 977 989 994 998 *003 *007 *012 *016 *021 *025 *029 978 99 034 038 043 047 052 056 061 065 069 074 979 078 083 087 092 0% 100 105 109 114 118 980 123 127 131 136 140 145 149 154 158 162 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms op Numbers. 807 Num. 980 to 1000. Log . 991 to 999. N L 1 2 3 4 5 6 7 8 9, P. P. 980 99 123 127 131 136 140 145 149 154 158 162 981 167 171 176 180 185 189 193 198 202 207 982 211 216 220 224 229 233 238 242 247 251 983 255 260 264 269 273 277 282 286 291 295 984 300 304 308 313 317 322 326 330 335 339 985 344 348 352 357 361 366 370 374 379 383 986 388 392 3% 401 405 410 414 419 423 427 987 432 436 441 445 449 454 458 463 467 471 988 476 480 484 489 493 498 502 506 511 515 ' 989 520 524 528 533 537 542 546 550 555 559 4 990 564 568 572 577 581 585 590 594 599 603 1 0.4 991 607 612 616 621 625 629 634 638 642 647 2 3 4 0.8 1.2 1.6 992 651 656 660 664 669 673 677 682 686 691 993 695 699 704 708 712 717 721 726 730 734 5 2.0 994 739 743 747 752 756 760 765 769 774 778 6 7 2.4 2.8 995 782 787 791 795 800 804 808 813 817 822 8 9 3.2 3.6 996 . 826 830 835 839 843 848 852 856 861 865 997 870 874 878 883 887 891 896 900 904 909 998 913 917 922 926 930 935 939 944 948 952 999 957 961 965 970 974 978 983 987 991 996 1000 000 000 043 087 130 174 217 260 304 347 391 N L 1 2 3 4 5 6 7 8 9 P. P. Logarithms of Important Numbers. Number. Logarithm. It = 3.141 593 0.497 150 If = 4.188 790 0.622 089 fr = 0.523 599 1.718 999 l = 0.318 310 "1.502 850 7r2 = 9.869 604 0.994 300 1 = 0.101 321 1.005 700 vz = 1.772 454 0.248 575 1 = 0.564 190 1.751 425 fm = 1.464 592 0.165 717 1 = 0.682 784 1.834 283 - 1.240 701 0.093 667 INDEX. a, 8, 45, 47, 49, 54 Acacia, 679 Accommodation ladders, 472 Acres in hectares, 731 Adjustable terminal, exhaust pipes, 555 556 Admiralty cables, 615-618 " constant, 262 knot, 701 " turnbuckles, 527 Agriculture, dept. of regulations, 171 Air, 679 Alder, 679 Algebraical signs, ix Alleyways, cattle, 172 Allowances for splices, 577 Alteration in trim through shipping a weight, 20 Aluminum, cast, 679 sheet, 679 bronze, 679 Analysis data, Kirk's, 153-157 Anchor gears, 431 Anchors, 394-400 mooring, 624, 625 Angle-steel, weight of, 232-237 Angle-bulb, weight of, 236 Animals, space allotted to, 172 Antimony, 679 Anthracite, 679 Apple wood, 679 Approximate rule for C. of B., 12, 45 rule for L. B. M., 17 " rule for M", 19 Area of circles, 697, 744-750 " of lightening holes, 246 " of L. W. L. and coefficient a, 8, 45, 47, 48, 54 " of midship section and coeffi- cient/3, 10 " of propeller brackets, 169, 170, 362 " of water plane, 7 Armor, weight of, 245 Asbestos board, 679 Ash, 679 Asphalt, 679 Awning decked vessel, 99, 110, 133 Axes, fire, 654 8, 10, 45, 47, 48, 57 Babbit metal, 679 Balanced rudders, 166, 357 Bar keel, 351, 352 Barley, 679 Barrels, 654 Basalt, 679 Battening bar, 381 Beam bending moments, 286, 287 " camber, 51, 371 " collars, 376 " -knees, 372, 373, 375 Beams, 371-376 Beckets, 592 Beech, 679 Belay pins, size of, 414 Bell, metal, 679 Bells, proportions of ship's, 413 " size and weight of, 414 Bending moments of pins, 322, 323 " moments of stress, 280 Bevel gear, formula for, 405 Bilge diagonal coefficient, 45, 47, 48, 55, 57 Bethlehem guns, 570, 571 Birch, 679 Bismuth, 679 Bitts, towing, 504 Bituminous coal, 679 Bitumastic cement, 370 " cement solution, 679 Blake stopper, 613 Block coefficient, 8, 7, 45, 47, 48 Blocks, 590-597 25-ton, 424 " cat and fish, 591 " cargo, 597 " clump, 591 " cheek, 591 " fiddle, 590 gin, 591 snatch, 419, 590 " wrecking, 591 " sheaving for, 591 " shackles for, 591 standard iron, 422, 423 " weight of, 595 u U. S. Navy, 596 Board of Trade Regulations, 634-645 Boat crane, navy, 432 " davits, 432-449 Boats, 626-634 " proportions of, 627 " scantlings of, 628, 630, 631 " rules and regulations, 634-655 " weight of, 449 809 810 Index Body plan of "Oceanic," 57 " poet, 354 Boilers, U. S. law, 655 Bollards, proportions, 417 Bollards, size and weight of, 418 Bolts and nuts, U. S. Standard, 427, 428 " and nuts, Whitworth Standard, 688 " and nuts, weight of, 426, 427, 689 B. M., 13 Boom mountings, 514-516 Boss barrel, 59, 170, 362 Bossing around shafts, 58, 59, 170, 363, 364 " fairing the, 58, 59, 170 Bottom half-breadth, 5 Boxes, stuffing, 523 Boxwood, 679 Braces, 355, 361 Bracket knees, 372, 373, 375 Brackets, area of propeller, 169, 170, 362 Brake, friction, for cranes, 542-548 " cone, for gantry crane, 544 Brass, 679 " sidelights, weight of, 513 " wire, 679 Breaking strength of chains, 3 10, 311 Brick, 679 Brickwork, 679 Bridge house, 87, 110, 376 Bridle beams, 381 British Corporation, rudder formula, 168 British Board of Trade regulations, 634-645 Bronze, 679 Buckets, fire, 654 Builders' old measurement tonnage, 678 Built columns, 377 Bulb angle, weight of, 215-220 " plate, weight of, 221-224, 241 " section, Lloyd's, 247 " tee, weight of, 223-230, 240 Bulkhead collars, 365, 383 " collision, 384 liners, 383 plating, 384 " stiff eners, 384 Bulkheads, 383, 384 Bullivant's thimbles, 524 Burton, Spanish, 599 Butts, plating, 386 " shift of, 386 Buttstraps, Lloyd's table of, 336, 337 " strength of riveted, 343 U. S. Navy, table of, 334 Tables, admiralty, 615-618 Calculation of (i. Z„ 40, 41 Calculations, ship, 1-280 Calories into thermal units, 737 Camber of ways, 162 Camphor, 680 Capacities of circular tanks, 692 of lifeboats, 639, 648, 652 " of rectangular tanks, 690, 691 Carlings, 376 Cast steel rudder, 356 " steel, weight of, 680 Cat and fish blocks, 591 Cattle alleyways, 172 " fittings, weight of, 172 " transport of, 171 Catting hooks, 430 Caulking, 384 Cedar, 680 Ceiling on tanks, 370 Cement, bitumastic, 370 Louisville, 680 Portland, 680 Roman, 680 Centimetres to inches, 726 Centre keelson, 351, 352 " of buoyancy, 11, 17, 26, 27, 45, " of buoyancy by Tchibyscheff 's rule, 26, 27 " of buoyancy longitudinally, 12, 18, 25 " of flotation, 16, 18, 29 " of gravity, 251-253 " of gravity coefficient "g," 45, 48 " vertical girder, 351, 352, 368 Chafing pieces, 384 Chain plates, 428 " slips, proportions, 513 " rigging, 593 " swivel, 622 Chalk, 680 Change of trim, 18 Channel bars, weight of, 238 floors, 367 Characteristic of logarithm, 782 Charcoal, 680 Cheek blocks, 591 Cherry, 680 Chestnut, 680 Cheval-vapeur into horse-power, 736 Circle, formulae for, 743 Circles, circumference and area of, 697, 698 Circumference and area of circles, 744-750 Clay, 680 Cleats, belay, 425 " hatch, 380 Clips, wire rope, 584 Index 811 Club shackle, 621 Clump blocks, 591 Coal, 680 Coefficient a, 8, 45, 47, 48, 54 0, 10, 45, 47, 48, 57 5 (fineness), 7, 45, 47, 48, 75 g (gravity), 48 " i (inertia), 49 Coir rope, 589 Collars, beams, 376 " bulkhead, 365, 383 Collision bulkhead, 383 Columns, built, 377 " strength of, 302-311 Compressive stress, 280 Cone brake for gantry, 544-548 Constants, admiralty, 262, 263 Corner angles, hatch, 380 Correction for variations (freeboard) , 93 Cotton rope, 589 Countersink, Lloyd's, 335 " point rivets, 487 Coupling bolts, 355, 361 " palm (rudder), 355, 356, 361 Covers, hatch, 381 Cowl ventilators, 557-558 Cowls, weight of, 559 Crane hooks, 429 Cranes, dimensions of anchor, 406- 411 " notes on anchor, 412 " stresses on, 402—404 Cross curves of stability, 42 Cubic centimetres into cubic inches, 732 " decimetres into cubic feet, 732 " feet into cubic decimetres, 732 " inches into cubic centimetres, 732 " metres into cubic yards, 730 " yards into cubi« metres, 730 Cut frames, 365 Cypress, 680 S, coefficient, 7, 45, 47, 48, 72 Davit heads, 448 Data, Kirk's analysis, 153-157 " launching, 161, 162 " steamers, 276, 277 Davits, Board of Trade Rules, 445- 447 " diameters of, 449 " mallory, 433, 436, 437 " mine, 440, " rotating, 433 " screw gear, 442 swan-neck, 437, 438 *' Welin, 443 Deck girders, 376 Deck seats, 509-511 " line, 86 Declivity of ways, 162 Deductions for erections (freeboard), 93 Deep framing, 366 Department of agriculture regula- tions, 171 Derrick rigging, 604, 605 Design, 44-63 Designing the bossing, 58, 59 Details of fittings, 389 of standardizing, 389 " of structure, 350 Details, the preparation of, 391 Diagram of bilge diagonals, 55 Diagram of L. W. L. half-breadths, 56 Diamond wire rope blocks, 420, 421 Dimensions for freeboard, 73 " for tonnage, 667 Disc friction brake, 547 Displacement, 1, 6, 24, 25 " sections, 4 sheet by Tchiby- scheff's rule, 24 Displacement table, 6, 24 Distances from colon, 721 Division boards, cattle, 172 Donkey boiler, 655 Doubling plates, 379, 388 Doublings at breaks, 388, 389 " at hatchways, 379 e, relation coefficient, 47, 48 Earth, 680 Ebony, 680 Effect of form of waterline, 34-37 Effective horse-power, 270-271 Elasticity, 280 Elements of angles, 313-314 " of bulb-angles, 315 '* of circular sections, 293 " of coefficients for various types, 44, 47, 48 of deck beams, 316, 317 " of marine engines, 60, 61 of sections, 284, 285 of tee bars, 318, 319 of zee bars, 320, 321 Elm, 680 Elswick guns, 560-562 Emergency chains, 356 Emery, 680 End floors, 367 Engine room lengths, 63 Engines, elements of marine, 60, 61 Equipment, 607-625 Lloyd's, 607, 610 numerals, 608, 609 Explanation of tables of metacentres, 31-33 812 Index Exponent of logarithm, 783 Eyebolts, standard, 454 Eyes, pad, 468 " worked, 603 Factors, useful, powers and roots, 700 " of safety, 282, 283 Fairing the bossing, 58, 59 " the oxter, 62 " plate lines, 384, 385, 387 Fairleads, proportions of, 455 " weight of, 455 Falls, cargo and purchase, 580, 604, 605 Feet to metres, 726 Fiddle blocks, 590 Figureheads and lacing pieces, 52 Fir, 680 Fitting of pillars, 379 Fittings, details of, 389 " weight of cattle, 172 " weight of horse, 173 Fixed terminals, exhaust pipes, 554 Flagging, 680 Flanges, lead pipe, 456 standard pipe, 457 " ventilation, 458 Flanged floors, 368, 369 Flat plate keels, 351, 352 Flexible steel wire ropes, 578-580 Flint, 680 Floor brackets, 369, 370 Floors, 368, 369 " at ends, 369 " channel, 369 " flanged, 368, 369 " in inner bottom, 370 " ordinary, 369 " watertight, 369 Flush deck vessel, 109, 112 Footboards, cattle, 172 Footlocks, cattle, 172 Footpounds into kilogrammetres, 736 Foot tons into tonnes-metres, 737 Foreign weights and measures, 706- 710 Formulae for the circle, 744-750 Fractions, squares, cubes and fourth powers, 699, 700 Frame doublings, 363, 364, 365 " riveting, 347 Framing, 364, 365 " of superstructure, 364, 365 Franklin Institute standard bolts, 427 Freeboard, 73-152 " examples, 77 " marks, 111 " tables, note on, 86 tables, 87, 115 Freeboards for awning deckers, 99, 133 Freeboards for freighters, 114 " for sailing vessels, 101, 142 for shelter deckers, 105 " for spar deckers, 77, 89, 127 " for turret steamers, 102 " for winter North Atlantic, 93 Freeing port area, 91 Freestone, 680 French measures, 725 Friction brake for cranes, 542-548 Froude's Law of Comparisons, 187 Functions, natural trigonometrical, 738-742 Furnaced plates, 387 Gaff mountings, 519-522 Garboard strake, 350, 351 Germanischer Lloyd's, rudder for- mula, 168 Gin blocks, 591 Glands, stuffing boxes and, 523 Glass, 681 Gold, 681 Grains into grammes, 735 Grammes into grains, 735 " into ounces, 735 Granite, 681 Graphite, 681 Greenheart, 681 Gudgeons, 352, 353, 359 Gum, 681 Gun tackle purchase, 599 Guns and mountings, weight of, 560- 573 Gunmetal, 681 Guys, 604, 605 Guy purchase, 604, 605 Gypsum, 681 Hall anchors, 296, 397 Hand wheels, standard, 459, 460 Hatch, balanced armor, 415, 416 cleats, 380 " corner doublings, 380 " covers, 381 edges, 381 " fore and afters, 381 " lashing rings, 381 " wedges, 381 Hatches, 379 Hatching, standard sectional, 392 Hawse pipes, proportions of, 462 " pipes, weight of, 463 Hawthorn, 681 Hay, 681 Hazel, 681 Headboards, cattle, 172 Hectares into acres, 731 Heel bearing of rudders, 356 Index 813 Heels, stanchion, 379 Hemlock, 681 Hemp cordage, 588 " rules for strength of, 588 Hold pillars, 377-379 Holes through shell, 386, 387 Hollow pillars, weight of, 231 Hood end plates, 353, 389 Hooks, various, 464 cargo, 465 swivel, 466 trip, 467 for blocks, 592 for catting, 430 crane, 429 match, 592 sister, 592 Hornbeam, 681 Horse fittings, weight of, 173 " stalls, 172 Horse-power into cheval vapeur, 736 Houseline, 589 I section, weight of, 205-210 Ice, 681 Immersion, passing from salt to fresh water, 9 " tons per inch, 8 Inch, graphic division of the, 393 Inches to centimetres, 726 India rubber, 681 Indicated horse-power, 271, 277. Inertia coefficient, 17, 44 " moment of, 281, 284, 285, 287, 288, 291, 292, 293 " moment of for circular sec- tions, 292, 293 Inglefield anchors, 400 Inner bottoms, 370 Inspection laws, American and British, 634-655 Intercostal plates, 382 Interlocking rubber tiling, 681 International rules, 1897, 656-662 Iron, cast, 681 " wrought, 681 Ironwood, 681 Ivory, 681 Jackwood, 681 Jogging, 387 Johnson's formula for columns, 296 " formula for steel hulls, 176 Keel doublings, 353 " scarphs, 351 Keels, 351, 352 Keelsons, 382, 383 Kenter shackle, 623 Keys and key ways, 461 " plug cock, 476 Kilogrammes into pounds, 734 per sq. cm. into lbs. per sq. inch, 733 Kilogrammetres into foot-pounds, 736 Kilometres into sea miles, 727 " into statute miles, 727 Kirk's analysis, 153-157 Knees, beam, 372, 373, 375 " bracket, 373 Krupp guns, 568, 569 Laburnum, 681 Lacing pieces, 52 Lancewood, 681 Landings, 388 Larch, 681 Lashing rings, 381 Launching, 159, 161 curves, 159, 161 data, 160, 161 " periods, 159 L. W. L. area of, 8, 45, 47, 48, 54 Lead, cast, 681 " sheet, 681 Least radius of gyration of various sections, 284, 285, 295 Ledges, hatch, 381 Lewis bolt, 471 Lifeboats, 633-655 Life-floats, 650 Life-preservers, 644, 645, 651 Life-rafts, 643, 650 Lifting rings, 381 Light screens, 657 Lightening holes, 246 Lignum vitae, 681 Lime, 681 Limestone, 681 Lime wood, 682 Liners, 370 " at overlaps, 388 bulkhead, 384 Linoleum, 682 Litres into U. S. gallons, 729 Lloyd's equipment rule, 607 " riveting table, 336 " rudder formula, 166 L. M. C. by Tchibyscheff's rule, 28, 29 Load draught diagrams, 108, 113 " line diagram, 56 " line half breadths, 53 Logarithms of numbers, 782-807 " of important numbers, 807 Longitudinal metacenter, 16, 17, 28, 29, 31, 34, 45 Longitudinals, 383 Lucania, Tchibyscheff sections for, 23 Luff tackle purchase, 599 814 Index Mahogany, 682 Manholes in inner bottoms, 370 Manila ropes, 586-589 Mantissa of logarithm, 783 Maple, 682 Marble, 682 Margin plate in tanks, 388, 389, 390 Marine engines, elements of, 60, 61 Marline, 589 Mathematical tables, 724-807 Metacentre, longitudinal, 16, 17, 28, 29, 31, 34, 35 transverse, 13, 30, 33, 36, 37. 45 Metres, into feet, 726 into yards, 730 Metric system, 725 " tons into tons, 734 Mica, 682 Middendorf's method, 271 Midship section area, 10 Mid. area coefficient /3, 10, 45, 47, 48 Millimetre, 725 Mitre gear, formula for, 406 Modulus of elasticity, 280 Moment of inertia, 256, 281, 284, 285, 287, 288, 291, 292, 293 " of inertia of circular sec- tions, 292, 293 " of inertia of waterline coeffi- cients, 49 " of inertia of water plane, 14 of resistance, 282, 284, 285, 287, 289, 291, 292 " to alter trim one inch, 19 " to change trim, 17 Monkey forecastle, 109 Mooring anchors, 624, 625 " pipes, 474 " swivel, 612 Mortar, 682 Multipliers for subdivided intervals, 3 for Tchibyscheff's rule, 22 Mushroom mooring anchors, 624, 625 Muntz metal, 682 Natural sines, 738-742 " trigonometrical functions, 738-742 Nautical mile, 701 Neutral surface, 282, 283 New York Yacht Club racing rules, 672-678 Nickel, 682 Nitric acid, 682 Norman head, 354 Notes on wire rope, 308, 309 Numbers, logarithms of, 782-807 " powers and roots of, 751- 782 Nuts, U. S. standard, 426, 427 Oak, 682 "Oceanic" body plan of, 57 Oil fuel chart, 685 " fuel data, 686 " linseed, 682 " olive, 682 " petroleum, 682 " whale, 682 Openings, tonnage, 105 Ordered lengths of rivets, 488-492 Ore, red iron, 682 " brown, 682 " Clydesdale, 682 Oregon pine, 682 Ounces into grammes, 735 Oxter, fairing the, 62 x, 744 Pad eyes, standard, 468, 469 " eyes, reversible, 470 Paper, building, 682 Parcelling and serving, 585 Parson's turbines, 60 Pens, cattle, 171 " sheep, 172 Permanent set, 281 Petroleum, refined, 682 Texas, 682 Pewter, 683 Phosphor bronze, 682 Physical properties of timber, 305 Pillar heads and heels, 378 Pillars, hold, 377-379 " pipe, 299 " weight of tubular, 244 Pins, belay, 414 ' moments on, 322, 323 " standard toggle, 525 Pine, Georgia, 683 Pintles, 353, 355, 360 Pipe, 300-303, 378, 379 Pitch, 682 Pitch pine, 683 Plate lines, 385 Plating, shell, 384-389 Platinum, 683 Plough steel, 575 Plug cock, keys, 476 Plumbago, 683 Poop, 109 Poplar, 683 Pounds per sq. inch into atmospheric pressure, 733 " per sq. inch into kilogrammes per sq. cm., 733 " into kilogrammes, 734 Powers and roots of numbers, 751- 782 Pressed plate chocks, 365 Pressure on dog-shores, 164 Index 815 Pressure of water at various heads, 693 Prismatic coefficient, 10, 45, 47, 48 Proof load for chain, 310 " of Simpson's rule, 3 " of strength, 279 Propeller brackets, area of, 169, 170, 362 struts, 168-170, 362, 363 " struts, Simpson's formula, 168 Proportions of chain slips, 513 of towing bitts, 504 " of ventilating cowls, 558 of ship's bells, 413 Quartz, 683 Radius of gyration, 282 Rail half breadths, 53 Raised quarter deck, 109 Range lights, 658 Ratlines, 585 Reels, length of, 589 Regulations, Board of Trade, 634-645 Dept. of Agriculture, 171 " U. S. Inspection, 646- 655 Relation coefficient, 45, 47, 48 " of the coefficients to one another, 47 Resilience, 280 Resistance of framing, 364 moment of, 282, 284 of ships, 262-275 form of least, 271-275 skin, 264-266, 271 " wave-making, 264-266, 271 Reverse frames, 365-366 Rigging, derrick, 604, 605 " and ropes, 575-605 " standing, 575 " chain, 593 . ropes, 578-581 screws, 526, 527 Ring plates, 493 Rings, proportions of, 479-487 " wrought iron, 478 Riveting of boss, 353 U. S. Navy standard, 328 Lloyd's, 340 strength of, 342-347 Rivets, standard, 338 ordered lengths of, 488-492 Roots and powers of numbers, 751- 782 Rope, coir, 589 " hemp, 586, 588 " manila, 586, 587 " small stuff, 589 Rope, cotton, 589 wire, 575 " end fittings, 584, 585 Ropes, 586-589 rigging and, 575-605 Round bar, weight of, 211 " of beam (freeboard), 97 Rudder, area, 165, 166 arms, 355 balanced, 166, 357 cast steel, 356 coupling bolts, 355, 361 coupling palm, 355, 356, 361 carriers, 358, 359, 360 emergency chains, 356 heel bearing, 356 tail plates, 360 trunks, 360 post, 354 stock, 166, 167, 168, 355 Rule for moment to alter trim, 19 " for moment to change trim, 17, 18 " for ordering rivets, 345 " for pressure on dog shores, 164 " for pressure on rudder, 165 ' for prismatic coefficient, 10, 45 " for propeller struts (Simpson's), 169 " for radius of gyration, 282, 284, 285, 291, 294 " for racing yachts (N. Y. Y. C), 672-678 " for relation coefficient, 45 " for riveting (Lloyd's), 340 " for row boats, 626 ' for rudder area, 165 " for rudder stocks, 165-168 " for sail area, 628 " for sea anchors, 495, 650 " for size of blocks, 591 " for shackles, 325, 326 " for spectacle frames, 170 " for speed and power, 263, 266, 267, 268, 269, 270, 271 " for strength of hemp, 588 " for strength of manila, 587 " for steamships (British), 634- 645 " for steamships (American), 646- 655 " for stresses on anchor'cranes, 411 " for tackles, 602, 603 " Tchibyscheff's, 21, 25, 41 " for tons per inch, 8 " for twisting moments on rud- ders, 166 ' for wetted surface, 157, 158 " for area of water plane, 7 " for B. M., 16, 45 816 Index Rule for bending moments on beams, 287, 289 " for bending moments on pins, 322, 323 ' for bilge diagonal coefficient, 47 " for bollards, 417 " for bottom breadth, 6 " forC. B., 11, 12, 45 " for centre of gravity, 251-253 " for centre of gravity coefficient, 45, 48 " for centre of pressure on rud- ders, 165 ' for chain cable links, 619 ' for catting hooks, 430 " for columns (Johnson's), 302- 311 " for crane hooks, 429 " for davits, 433 " for end links on cables, 619 " for fairleads or chocks, 455 ' for finished steel weight, 175 ' for freeing port area, 76 ' for hawse pipes, 462 ' for inertia coefficient, 17, 45 ' for iron rings, 478 " for Johnson's for steel columns, 302 " for Johnson's for steel weights, 175 " for L. B. M., 17 " for L. C. B., 12 " forL. M. C, 16 " for maximum bending moment on hull, 261 " for mid. area, 10 Sailing vessels, freeboard, 101, 143 Salt, 683 Sand, 683 Sandstone, 683 Satinwood, 683 Scantlings for small boats, 628, 630, 631 Scarphing of landing edges, 388 of keels, 352 Schneider guns, 566-567 Screens, light, 657 Screws, dimensions of wood, 494 rigging, 526, 527 Sea anchors, areas of, 495 " anchors, detail of, 496 " miles into kilometres, 727 Section modulus, 282 Sellers' standard bolts and nuts, 426, 427 Senhouse slip, 614 Serving twine, 589 Shackles for blocks, 591 lashing, 592 special, 325-327 Shackles standard, 497, 501, 502 Shade deck vessel, 1 10 Shearing and bearing values for m rivets, 349 stress, 280 Sheaves, 577 for blocks, 591, 593 Sheep pens, 1 72 Sheer, 50, 82 " for boats, 626 ' for freeboard, 95 " poles, 585 " strake, 384, 386, 388, 389 Shell plating, 386-389 " plate lines, 387 " riveting, 388 Shelter deck vessel, 105, 112 Shift of butts, 386 Shingle, 683 Ship's bells, 413, 414 Shoe for wire rope, 584 Side girders in tanks, 368 " lights, weights of brass framed, 513 " stringers, 382, 386 Signs, algebraical, ix Silver, 683 Simpson's first rule, 1 " formula for struts, 168 Single plate rudders, 354 Sisterhooks, 498 Size of hatches, 379 Slate, 683 Slip shackles, 499, 500 Slips, proportions of chain, 513 Snatch blocks, 419, 590 Snow, 683 Space, crew, 672 Spanish Burton, 599 Spar deck vessel, 97, 110, 127 Spars for small boats, 626 Specification headings, 64-72 Specifications, the preparation of, 64 Spectacle frames, 170, 363 Speed and power, 262, 263 " tables, 701-705 Spider bands, 517 Spirketting plate, 365, 366 Splices, 576 " allowances for, 577 Spruce, 683 Square bar, weight of, 211 " centimetres into square inches, 728 " foot into kilogrammes per sq. metre, 732 " inches into square centi- metres, 728 " kilometres into square miles, 731 Index 817 Square bar, metres into square yards, 730 " metres into pounds per sq. foot, 732 " miles into square kilo- metres, 731 " yards into square metres, 730 Squares, cubes and fourth powers, 699, 700 Square of numbers, 751-782 roots of numbers, 751-782 Stability calculation, 38, 43 " curves, 43 Staggered pillars, 379 Stalls, cattle, 171, 172 " horse, 172 Standard pipe elements, 304, 305 Standard rivets, 328 " shackles, 502 thimbles, 582, 583 " toggle pins, 525 " ventilator cowls, 557, 558 Stapled collars, 365 Statute miles into kilometres, 727 Statutory deck line, 86 Stealers, 385 Steamers data, 276, 277 Steel, weights of, 180-230. plough, 575 " wire rope, 578-580 Steering chain springs, 505, 506 gears, screw, 507, 508 Stem, contour of, 51 " scarph of, 353 Stems, 353, 354 Stern frames, 354, 355 Stowage of merchandise, 711-719 of oil, 687 Strakes, arrangement of, 385 Strength of chain cables, 310 " of columns, 294 " of guard chains, 311-349 of materials, 279-349 " of metals and alloys, 304 " of rings, 477 of special shackles, 325, 326 of tackles, 602, 603 of timber, 305-307 W. I. pipe, 475 Stress and strain, 279 Stresses on floors, 366 Strong beams, 375 Strops for blocks, 592 Structural details, 350 Stuffing boxes and glands, 523 Swivel jaws, 592 Sycamore, 683 Symbols, vii Table of logarithms of numbers, 782- 807 of powers and roots, 751-782 " of strength of rivetting, 342- 347 Tack rivets in keels, 350 Tackle, gun, 599 luff, 599 Tackles, 598-606 relieving, 600 strength of, 602, 603 Tail plates, 362 Talc, 683 Tallow, 683 Tank bleeders, 670, 671 Tanks, circular, 692 rectangular, 690, 691 Tar, 683 Tchibyscheff's rule, 22 sections, 39 sections for "Luca- nia," 23 Teak, Burmese, 683 Tee steel, weight of, 185-189 Tees as struts, 324 Temperatures, cold storage, 720, 721 Tensile stress, 280 Terminals for exhaust pipes, 554-557 Thames measurement tonnage, 678 Thermal units into calories, 737 Thimbles for wire rope, 524, 576, 581- 583 Threefold purchase, 599 Tile, 683 Tiling, 683 Timber, 305 Tin, 683 Toggle pins, 525 Tons into metric tons, 734 Tonnes-metres into foot tons, 737 Tonnage, 667-671 B. O. M., 678 " openings, 105 " Thames measurement, 678 schedule, 668-669 Tons per inch immersion, 8 Topgallant forecastle, 109 Topping lifts, 601, 604, 605 Torpedo net details, 518 Torsional stress, 280 Towing machine, steam, 611 Towing bitts, 504 Transverse metacentre, 13, 30, 33, 36, 37, 45 " metacentre by Tchiby- scheff's rule, 30 Trap, 683 Trial trip tables, 701 Triangles, lashing, 473 Trigonometrical functions, natural, 738-742 SIS Index Trim, alteration to, 20 moment to alter one inch, 19 " moment to change, 17 Trolley block, 528 Trunk deck vessel, 1 10 Tube end castings, 363, 364 Turbines, Parsons marine, 60 Turnbuckles, 585 Admiralty, 527 Turret deck vessel, 110 Twine, serving, 589 Types of rudder carriers, 358, 359, 360 " vessels (freeboard), 109, 110 Ultimate strength, 279 U. S. Dept. of Agriculture, 171 U. S. Inland Rules, 662-666 U. S. gallon into litres, 729 U. S. inspection laws, 646-655 U. S. naval ordnance, 572, 573 U. S. standard bolts and nuts, 426, 427 Unit equivalents, 694, 695, 696 Universal bar, 354 " joints, 529 Values for Johnson's formula, Valves, low pressure, 530-535 " heavy pressure, 536-541 Various stresses and their factors, 283 Ventilation, 548-558 " pipes, 551 Ventilator cowls, 557, 558 Ventilators, cattle, 172 Vickers guns, 563-565 Walnut, 683 Water, 683 notes, 697 plane, area of, 7 Watertight compartments, doors, details of, 453 doors, hinged, 452 " doors, sizes of, 450 " doors, sliding, 451 floors, 367 Ways, length of, 162 Web frames, 381, 382 Weights and measures, foreign, 706- 710 Wedges, hatch, 381 Weight of Acacia, 679 of alder, 679 " of aluminum, 679 of anchors, 624, 625 ** of angle steel, 180-184, 233- 237 " of antimony, 679 \ of anthracite coal, 679 " of armor, 245 Weight of ash, 679 " of asphalt, 679 " of asbestos board, 679 of Babbit metal, 679 of bars, 211-213 of bells, 414 of bitts, 504 " of blocks, 595 of boats, 449 of bollards, 418 of bolts, 426, 427, 689 of brick, 679 of brass, 679 " of bronze, 679 " of bulb-angle, 215-220 of bulb-plate, 221, 222, 241 of bulb tee, 223-230, 240 of cables, 312 " of camphor, 680 " of canvas, 684 " of cement, 680 " of chain, 312 of channel, 195-204, 238, 239 " of coal, 680 " of copper, 680 " of cowl ventilators, 559 of deals, Riga, 680 of elm, 680 of fir, 680 of glass, 681 " of greenheart, 681 " of gunmetal, 681 of hemlock, 681 " of hemp rope, 588 of hollow pillar, 231 " of India rubber, 681 " of I-section, 205-210 of iron, 681 of larch, 681 of lead, 681 " of lignum vitae, 681 of lime, 681 of linoleum, 682 " of mahogany, 682 " of manila rope, 587 of maple, 682 of Muntz metal, 682 of nickel, 682 of oak, 682 of oil, 682, 687 of ore, 682 " of Oregon pine, 682 of paper, 682 " of petroleum, 682 " of phosphor bronze, 682 of pine, 683 of pitch, 683 " of pitch pine, 683 of poplar, 683 " of punchings, 246 of rope, 587, 588 Index 819 Weight of rope wire, 578 of round bar, 211 of sand, 683 of satinwood, 683 of shapes, 180-230 of sheaves, 577 of sheet steel, 214 of sidelights, 513 of spruce, 683 of steel plating, 243 of square bar, 211 of tallow, 683 of tar, 683 of teak, 683 of tee bar, 185-189 of tee bulb, 223-240 of thimbles, 577 of tiling, inlaid rubber, 683 of tiling vitrified brick, 683 of tiling, white, 683 of timber, 305 of tin, 683 of tubular pillars, 244 of walnut, 683 of water, 683 of white pine,. 684 of yew, 684 of zee bars, 190-194, 242 of zinc, 684 Weights and measures, foreign, 706— 710 Welded beam knees, 372, 373, 375 Well decked vessel, 93, 109 Wetted surface formula, 157 Wheat, 684 Whip, 598 " upon-whip, 599 White metal, 684 pine, 684 Whitworth bolts and nuts, 688 Willow, 684 Windlasses, 611 Wire ropes, flexible steel, 578-580 " ropes, end fittings for, 584 " ropes, thimbles for, 581 " rope, notes on, 308, 309 Worked eyes, standard, 503 Working load, 279 Wrecking blocks, 591 Yacht's launches, 632 Yacht racing rules, 672-678 Yards into metres, 730 Yew, 684 Zee bar, weight of, 190-194, 242 Zinc, 684 ISHERWOOD SYSTEM OF SHIP CONSTRUCTION MEANS Increased Strength Increased Capacity for Bale Goods Increased Deadweight Carrying Capacity Improved Ventilation Reduced Cost of Maintenance Reduced Vibration Suitable for all types of vessels Specially advantageous for oil steamers, Passenger and lake steamers For Particulars Apply to J. W. ISHERWOOD 4 LLOYD'S AVENUE, LONDON, E. C. Tel. Add. "Ishercon, London" OR TO S. C. Chambers & Co., 3 King St., Liverpool PARKS PNEUMERCATOR" ^Bt^ 1 OKrT WiWKm "Parks Pneumercator" In Captain's Office of New England Coaf & Cpke Co's steamer "Newton INDICATES AND REGISTERS FORWARD, AFT and MEAN DRAFTS of vessels.alongside Dock, at Anchor or Under-way, in either salt or fresh water. Shows TRIM and LIST of vessel under the same conditions. WEIGHS AND MEASURES BULK CARGOES, such as coal, oil, grain, ore, lumber, molasses etc. BUNKERS, either coal or oil, checking consump- tion of same. MEASURES AND INDICATES DEPTH, HEIGHT and VOLUME of any liquid or semi-liquid in Tanks, Reservoirs, Dry- docks etc. "PARKS PNEUMERCATOR" The Indicating and Registering portion of the instrument can be installed at any dis- tance either above or below the part of the apparatus connected to the source of press- ure. In marine work, this is preferably, The Captain's Office, Chartroom or Pilot House, (see photograph) Operating and control valves are an in- tegral part of the instrument itself and the accuracy of the readings can be instantly checked. Various models are manufactured for Marine, Submarine and Stationary service. Estimates furnished and booklet con- taining full details of the instrument, its op- eration and installation sent on application. Address: GARDNER GORNETT QUIMBY ENGINEERING CO, 118 Liberty St. or Philadelphia New York, N. Y. Pennsylvania, U. S. A. CONSULTING ENGINEERS GEORGE SIMPSON JACOBS & BARRINGER, Ltd. 17 Battery Place 78 Gracechurch St. New York London * 0) C* O £ >- z < o IR SHOPS , ETC. 4 J 3 CO o i Z V V fa S o u < Y D oklyn. AND BOILE CIALTY ITS. DERRICKS a o II B * a M lit D H CO Z o i z 2 m M w OS Q Z < u o Q Jh Q DR imilton, Brc ACHINE ING A SPE TRIC UGH and extens: t, lifting ca] ty 6.000 toi tons, over sill, over sill. u co o o "0 ng, lifting capacity 6.000 feet long, 20 feet draught feet long, 25 feet draught CO > Z O Q Z CO X H D O CO 9 o, CQ c o ±i £ o CO Z 3 o m YARD, DRY DOC1 ks, fully eqi Dock, 560 kNo. 1, 37 , 400 feet lc No. 1. 510 No. 2. 620 < UJ UJ Z >- £ UJ Q_ X u « -* -* -* iniii H CO 2 ~T~ . IS - Q Q Q CO < mm OO Q E § o e J CO QC Five New Secti Pontt Grav Grav UJ UJ 5 UJ REILLY MULTICOIL FEED WATER HEATER REILLY MULTICOIL NAVY TYPE EVAPORATOR G-R MULTISCREEN FEED WATER FILTER REILLY apparatus is standard throughout the world in MARINE work. Our thirty years experience is at your service SPECIALTIES and spares always in stock Write for catalogues CO THE GRISCOM-RUSSELL (Formerly THE JAMES REILLY REPAIR & SUPPLY CO.) ENGINEERS-MANUFACTURERS LAND-MARINE 2119 West St. Bldg. New York ''Watch the Thermometer" ECKLIFF CIRCULATORS FOR SCOTCH MARINE BOILERS , Fully protected b$ U. S. and Foreign Patents Have achieved results — have established records, that most Marine Engineers and Constructors believed impossible of accom- plishment. In every installation, they are creating and maintain- ing perfect circulation, are equalizing temperatures at top and bottom of boilers and eliminating all boiler troubles arising from imperfect circulation. They are guaranteed to do that. Eckliffs are now in use by the U. S. Revenue Cutter Service U. S. Naval Department U. S. War Department and by Many of the largest Steamer* on Salt and Fresh Water. A large Dredging Company recently installed an Eckliff in one of its 12 ft. 6 in. — 3 furnace boilers; 120 pounds steam press- ure was raised in forty five minutes, from cold water — tempera- tures at top and botton of boiler the same — have saved from 1 50 pounds to 1 80 pounds of coal per hour since installation — haven't had to clean boiler since, except to remove previously deposited scale which the action of the Eckliff loosened. No wonder this company is now pushing the installation of seventeen more Eckliffs; it'll mean a saving, in coal alone, of twenty-fine tons a day. This is but one typical instance of Eckliff Service. There are many more. Write or phone our representative. He will satisfy you on every point and refer you to Eckliff users you know. ECKLIFF AUTOMATIC Boiler Circulator Co. DETROIT 47 Shelby St. MICHIGAN New York: Philadelphia: 33 Broadway Bullitt Bldg. LIDGERWOOD MARINE SPECIALTIES The Lidgerwood Mfg. Co. has for 40 years held foremost place in its line of products. (Incorporated 1873, virtual successor to Speedwell Iron Works, founded 1802, where engines of SAVANNAH, first steamer to cross the ocean, were built.) Special attention of ship designers and own= ers is called to the following products for use on vessels and wharves: Steam and Electric Hoists Ships Winches Steering Engines Telemotors Marine Transfer for Bulk Cargo Package Cargo Handling Devices Marine Breeches Buoy for Life Saving at Sea Marine Cableways for Coaling War- ships at Sea Cableways for Transporting Cargo be- tween Ship and Shore For catalogues and full information address: LIDGERWOOD MANUFACTURING CO., 96 LIBERTY STREET, NEW YORK CITY. Wire Rigging Roebling ships' rigging and guy ropes are all treat- ed by double galvanizing process, insuring a tenacious coating of zinc which forms an excellent protection for the wire. We make also galvanized mooring lines, wire tiller ropes, wire ropes for hoisting, galvanized hawsers and high strength wire for defence against attack by torpedo. In addition to the above we make iron, steel and copper wire both bare and insulated, also insulated electrical cables. John A. Roebling's Sons Go. TRENTON, N. J. Branches: Chicago, Philadelphia, Pittsburg, Cleveland, Atlanta. John A. Roebling's Sons Co. of New York 117=119=121 Liberty St., N. Y. John A. Roebling's Sons Co. of California San Francisco Los Angeles Seattle Portland, Oregon "BITUMASTIC" COATINGS f / — n — \ \ Solution / / ^g \ \ Cement REGISTERED Enamel Permanent Protection Against Corrosion Water Ways, Decks, Tanks, Bilges, Tank Tops, Coal Bunkers, Inner Bottom Tanks, Floors, Peaks, Refrigerating Spaces Inquire for full particulars and estimates American Bitumastic Enamels Go. JAMES HERMISTON & SON 322 So. Delaware Ave. 17 Battery PL Philadelphia, Pa. New York WAILES, DOVE & CO., Ltd, 5 St. Nicholas Buildings NEWCASTLE-ON-TYNE Cables" BITUMASTIC" Newcastle-on-Tyne PATENTEES AND MANUFACTURERS OF 'BITUMASTIC" SPECIALTIES FOR PREVENTING CORROSION Patent "BITUMASTIC" Deck Coverings FOR LEVELLING AND FLUSHING UP DECK PLATING ADOPTED BY THE LEADING OWNERS IN LIEU OF WOOD FOR ALL DECKS IN WAY OF ACCOMMODATION PERMANENT PROTECTION FOR STEEL WORK CORTICENE OR RUBBER TILING EASILY LAID ON Patent "BITUROS" Enamel for Protecting fresh water tanks from corrosion Does not taint the water Thousands of tanks coated Send for Particulars De RUSETT'S Patent Hatch Covers ADVANTA6ES No Tarpaulins to get cut. No cor- ners to crack, or bunch. Water cannot lodge on the cover ana soak through. There is nothing to get out of order. Hatch is clear to work directly the cover is lifted. No hatch beams or girders to be removed. No side projection inside the coaming on which cargo can be damaged. . For full particulars apply to CHARLES SKENTELBERY 111 Devonshire St. Boston, Mass., U. S. A. D. C. REID 18 Broadway New York City Broker for the sale of steam- ers of all descriptions Representative of SWAN, HUNTER and WIGHAM RICHARDSON, Ltd. Wallsend-on Tyne, England Ship, Engine, Boiler and Floating Dock Builders and Repairers Inquiries Solicited Cable Address "Huntreid" New York Telephone 2172 Broad HOLZAPFELS INTERNATIONAL Compositions for bottoms of Steel and Iron Vessels Obtainable at all parts of the world and in use by the fastest and most important vessels of the United States and foreign navies. TOTAL TONNAGE PAINTED IN 1912 16.784.906 Gross Tons Manufactured by Holzapfels American Composition Co. John A. Donald, President John Crowe Harland, General Manager 18 BROADWAY NEW YORK, U. S. A. "BITUCOAT" COMPOSITIONS SOLUTION, ENAMEL, COVERING AND CEMENT Are unequalled for Goal Bunkers, Floors, Tanks under Boilers and Engines, Cold Storage Chambers, Peaks, Decks, Inside Holds, Deep Tanks, etc. Specially recommended for pontoon docks SPECIFY CAIL'S "BITUCOAT" COMPOSITION The WILLIAM CAIL BITMO CO. E. McDERMOTT HOWE, Manager 18 Broadway - - New York, U. S. A. STRATFORD OAKUM Quality guaranteed Is standard everywhere. Made in Jersey, City, U. S. A. GEORGE STRATFORD OAKUM CO. MORRIS METALLIC PACKINGS The Standard Packing for Marine use AN our Pack- ings tested, be- fore shipment, to 50% above boiler pressure Records of Six Years' Service Without Attention or Repairs Morris Metallic Packing Co. NEW YORK PHILADELPHIA LONDON NORWAY VON HOVELING'S COMPOSITIONS FOR STEAMERS AND SHIPS Largely used by the different Navies of the World, and by most of the steam and sailing Ship and Yacht owners. Agencies in all the principal ports of the world. SOLE MANUFACTURERS IN THE UNITED STATES The VON HOVELING AMERICAN COMPOSITION CO., Ltd. Office, Whitehall Building, 17 Battery Place, New York. Factory, 41st Street, South Brooklyn, N. Y. Cable Address, "GLISSADE." New York Tel. 41 46-41 47 Rector FOR BITUMINOUS WORK IN BUNKERS, HOLDS, BALLAST TANKS, PEAKS, BILGES, BOILER ROOMS. &c. SPECIFY "BRIGGS" SOLUTION AND ENAMELS Briggs Bituminous Composition Co., Inc. 17 Battery Place, New York, U. S. A. Cable Address "CEMENT, N. Y." Telephone 4146-4147 Rector ROSS SCHOFIELD SYSTEM OF CIRCULATION IN SCOTCH MARINE BOILERS. NOW USED BY THE PRINCIPAL STEAMSHIP LINES of the WORLD. 3,000,000 H. P. NOW IN USE. Ross Schofield Company 17 BATTERY PLACE, NEW YORK. The Parsons Marine Steam Turbine Co., Ltd. TURBINIA WORKS. Wallsend-on-Tyne, England. Total Horsepower afloat and under construction, approximately 10,000,000. 6EARED TURBINE INSTALLATIONS 450,000 S. H. P. OFFICE: 97 Cedar Street, New York. RElPADD BITUMINOUS SOLUTION, ENAMEL, CEMENT For the protection off interior steel surfaces, bunkers, bilges, ballast tanks, double bottoms, etc., etc. RELPACO has been applied to sur- faces off U. S. battleships NEVADA, TEXAS, ARKANSAS; Argentine bat- tleships RIVADAVIA & MORENO; Chinese cruiser FEI-HUNG and many others. RELIANCE COMPOSITIONS (Anti-corrosive & anti-fouling) For bottoms of steel vessels RED LEAD COMPOSITION, HOLD PAINTS, DECK PAINTS, DUTT & RIVET CEMENT. RELIANCE PAINT COMPANY 16 Coenties Slip New York ►» .S JS 175 Pages 4^X7^ Illustrated Cloth, NET $2.00 MARINE ENGINE DESIGN Including the Design of Turning and Reversing Engines By E. M. BRAGG Assistant Professor of Naval Architecture and Marine Engineering, University of Michigan. CONTENTS The Heat Engine. Calculations for Cylinder Diameters and Stroke. Strength of Materials and Factors of Safety. Cylinders. Pistons. Cylinder Covers. Calculations for Cylinders and Pistons. Maximum Load on Reciprocating Parts. Piston Rods. Allowable Pressure on Bearing Surfaces. Crosshead Blocks. Slipper. Calculations for Piston Rod, Crosshead and Slipper. Connecting Rod. Crank Shaft For- mula. Lloyd's Rules for Shafting. Bureau Veritas Rules for Shafting. American Bureau of Shipping Rules for Shafting. Crank Shaft Proportions. Maximum Loads on Main Bear- ing. Engine Bed. Main Bearing Caps. En- gine Frame. Calculations for Crank Shaft and Main Bearings. Steam Speeds and Valve Diagrams. Location of Center Lines of Cyl- inders. Calculations for Steam Speeds, Valves, Receiver Pipes and Distance between Cylinder Centers. Piston Valve, Slide Valves and Valve Gear. Calculations for Drag Rods. Eccentric Rods, Links, Eccentrics, Eccentric Straps and Reverse Shafts. Turning Engine Design. Reversing Engine Design. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 Park Place - - New York 122 Pages 5 Hx 7% Cloth 102 Illustrations NET $1.50 Marine Gas Engines Their Construction and Management BY CARL H. CLARKE, S.B. Naoal Architect and Engineer CONTENTS Types of Engines: — Principles and Operation of Each Type. Advantages of Each Type. Two-Cycle Engines: — General Construction. Description of Some Standard Types. Pumps. Four-Cycle Engines: — General Construction. Description of Standard Types. Vaporizers and Carburetters: — Va- porization of Fuel. Principles of Operation and Description of Standard Types. Ignition Devices: — Principles of Ignition. Mechanisms of Igniters. Timers. Spark Coils. Plugs. Bat- teries. Dynamos. Magnetos. Ignition* Wire: — Diagrams for Wiring. Spark Coils. Distributor. Lubrication: — Meth- ods of Lubricating the Several Parts. Multiple-Cylinder Engines: — Description and Construction of Standard Types. Reversing Mechanisms: — Reversing Propeller. Reversing Gears. Reversing Engines. Propellers: — Definitions. Ef- ficiency. Measuring Propellers. Calculations. Installation: Foundation. Piping. General Considerations and Description. Operation and Care of Engines: — General Instructions. Hints on Finding Troubles. Care of Engine and Outfit. Power of Engines: — Horse Power. Formulas for Power. Methods of Finding Power. Brakes. Selecting an Engine: — Gen- eral Considerations as to Type, Size and Construction. Does not deal with the matter from a theoretical standpoint. The idea is rather to describe the con- struction and principles of operation of the standard types in a plain and simple and well illustrated form. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 Park Place / ."' New York 159 Plates 6%x9 l 4 Inches 565 Pages Cloth, $7.50 Net. Half Morocco, $9.00 Net. MODERN SEAMANSHIP By REAR ADMIRAL AUSTIN M. KNIGHT, U. S. N. Sixth Edition, Rewritten and Enlarged In the present edition about one-half of the material retained from earlier editions has been entirely re- written and a large part of the remainder entirely revised. Three entirely new chapters have been added. All of the chapters in the previous editions dealing with sailing ships have been discarded, but a brief description of such vessels is Included in the appendix. CONTENTS The Hull and Fittings of a Ship. Rope. Knotting and Splicing. Mechanical Appliances on Shipboard. Blocks and Tackles. Handling Heavy Weights. Compass. Log and Lead. Submarine Signals. Boats. Handling Boats in a Surf. Ground Tackle. Carrying Out Anchors. The Steering of Steamers, The Rules of the Road. Manoeuvring to Avoid Collission. Piloting. Handling a Steamer Alongside a Dock. Placing a Ship in Dry Dock. Weather and the Laws of Storms. Handling Steamers in Heavy Weather. The Handling of Torpedo Vessels. Keeping Stations and Manoeuvring in Squadron. Towing. Rescuing the Crew of a Wreck. Man Overboard. Stranding. Hints for Junior Officers Doing Line Duty. Appendix. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 Park Place - - New York FOURTEENTH EDITION, ENLARGED With a New Chapter on Electric Lighting 8vo. Cloth 404 Illustrations 507 Pages NET $2.00 THIRTY-SECOND THOUSAND LESSONS IN PRACTICAL ELECTRICITY PRINCIPLES, ARITHMETICAL PROBLEMS. EXPERIMENTS AN ELEMENTARY TEXT BOOK With Numerous Tables, Formulas, and Two Large Instruction Plates. By C. WALTON SWOOPE Associate Member, American Institute of Electrical Engineers. I«ate Instructor of Applied Electricity at the Spring Garden Institute, Philadelphia. CONTENTS 1. — Magnetism. 2. — Magnetisation. 3. — Magnetic Fields. 4. — Theory of Magnetism. 5. — Magnet Induction. 6. — Mag- netic Circuits. 7. — Earth's Magnetism. 8. — Voltaic Electricity. 9 — Batteries. 1 0. — Electrolysis. 1 1 . — Measurement of Current Strength. 12. — Resistance. 13. — Ohm's Law and Battery Connections. 14. — Circuits and Their Resistance. 1 5. — Electro- magnetism. 16. — Galvanometers. 17. — Electromagnets. 18. Ammeters. 19. — Electrical Work and Power. 20. — Meas- urement of Pressure. 21. — Measurement of Resistance. 22. Electrical Development of Heat. 23. — Electrodynamics. 24. Electromagnetic Induction. 25. — The Induction Coil. 26. Dynamo Electric Machines. 27. — Armatures 28. — Direct Current Dynamos. 29. Direct Current Motors. 30. — Electric Lighting. 31. Alternating Currents. Tables. Formulas. This book combines the principles of electricity upon which the practical applications of to-day depend, with the experimental demonstration of these principles and the elements of the arith- metic of electricity used in making practical electrical measure- ments and calculations. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 Park Place - - New York 275 Pages 5^x8 Illustrated Cloth,, NET $2.00 Cold Storage, Heating and Ventilating on Board Ship By S. F. WALKER CONTENTS COLD STORAGE. The Cold Storage Prob- lem. Methods of Cooling the Cold Chambers. Methods of Cooling the Air. Leading the Cooled Air into the Cold Chambers. How the Low Temperature of the Brine or Refrigerant is Produced. The Condenser. Lubrication and Stuffing Boxes of Compressors. Absorption Machines. Circulating Pumps. How Refrig- erating Apparatus is Measured. Power Required for Refrigerating Apparatus. Cooling Water. Form of Apparatus for Use on Board Ship. Other Applications of Refrigeration on Board Ship. Cooling Magazines and Officers' and Men's Quarters. Faults. HEATING. Special Requirements on Board Ship, Difficulties. Methods of Heating Available. Hot Water, Steam, Air, Combined Air and Steam Radiator. The Thermotank System. The System Applied to the S. S. Lusitania. Heating by Electricity. Regulating Heat Delivered by Electric Heaters. VENTILATING. Ventilation by Heating and Cooling. Ventilation of Laboratories and Cattle Spaces. Fans. Size and Power Re- quired. Testing Air Current. Estimating Heat Required. Apparatus Estimated to be Required for Heating the Different Saloons, State Cabins, etc. Cost of Furnishing Heat Required. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 PARK PLACE NEW YORK SECOND E 312 Pages 5x6^ 124 Illustrations NET $2.00 Handbook for the Care and Operation of NAVAL MACHINERY BY Lieut. H. C. Dinger, U. S. N. {Being an Extended and Enlarged Form of a Series of Articles Published in the "Journal of the Amer. Society of Naval Engrs." CONTENTS Operation of Naval Machinery. Getting Underway. Running Engines Underway. Accidents Underway. Care and Overhaul of Main Plant. General Rules for Overhauling Machinery. Cylinders. Valves and Valve Gear. Engine Adjustments. Oiling Gear, Friction and Lubrication. Condenser and Pumps. Fittings and Auxiliaries. Joints and Packings. Stuff- ing-Boxes. Lagging and Clothing. Feed and Filter Tanks. Feed Water Heaters. Evaporators and Distillers. Heating System. Steam Launches. Re- frigerating Plant. Gauges and Thermometers. Rev- olution Counters, Telegraphs and Revolution Indica- tors. Piping. Valves and Cocks. Cleaning, Painting, and Points in Doing Work. Care and Subdivision of Hull. Special Auliliary Engines. Steam Steering Gear, Air Compressors. Blowers and Blower Engines. Ash Hoists and Ejectors. Workshop Machinery. Spare Parts and Tests. Spare Parts and Outfit of Accessories. Tests of Machinery and Piping. D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 PARK PLACE - - - NEW YORK A Cnliiloft of Teclinical. Industrial Engineering and Scientific Publication* NOSTRAND COMPANY . N.w York This 224 Page Catalog is Free ¥HIS is a complete list of all our tech- nical, industrial, engineering and scientific publications and importations clas- sified by subjects and carefully described. We carry a complete stock of the publications of all other publishers and are especially well fitted to fill your orders for books on marine and naval engineering — All inquiries are given prompt and careful attention D. VAN NOSTRAND COMPANY Publishers and Booksellers 25 Park Place - - New York Practical Mathematics for Young Engineers. F. HOVENDEN 144 Pages B # x 7 h Illustra ted Net $1.00 Hints to Engineers for the Board of Trade Examinations. W. D. MARTIN 141 Pages S x7% Illustrat ed Net $1.00 Marine Engineers' Drawing Book for Board of Trade Examinations. W. C. McGIBBON Seventh Edition 137 Pages \2% x 9% Flexible Cloth 59 Plates Net $2.00 Indicator Diagrams for Marine Engineers. W. C. McGIBBON 196 Pages 1% x 9% 197 Illustra tions Net $3.00 Mechanical and Marine Engineering Science. A. N. SOMERSCALES Fourth Edition 544 Pages £% x 8^ 216 Illustrations Net $5.00 Lessons in Mechanics for Marine Engineers and Engineering Students. A. N. SOMERSCALES 280 Pages 5 x 7 l A 149 Illustra tions Net $1.50 Simple Problems in Marine Engineering Design. J. W. M. SOTHERN and R. M. SOTHERN Third Edition 202 Pages 5^x7^ Flexible Cloth Net $1.00 "Verbal" Notes and Sketches for Marine Engineers. J. W. M. SOTHERN Eighth Edition, Enlarged and Rewritten, 709 Pages 6y 2 x 9'A 545 Illustra tions Net $5.00 Elementary Mathematics for Marine Engineers J W. M. SOTHERN and R. M. SOTHERN 180 Pages 5 ^x7^ Illustra ted Net $1.00 Marine Engineers B. of T. Examinations. JOHN TOD and W. C. McGIBBON 390 Pages 5^x8 288 Illustrations 4 Plates Net $1.50 D. VAN NOSTRAND COMPANY 25 Park Place New York SPECIFY * o * hat' 343153 3 UNIVERSITY OF CALIFORNIA LIBRARY