HANDBOOK FOR MECHANICAL ENGINEERS OF THK UNIVERSITY HANDBOOK FOR MECHANICAL ENGINEERS \ 3 A A OF THB UNIVERSITY HENRY ADAMS PROFESSOR OF ENGINEERING AT THE CITY OF LONDON COLLEGE ; MEMB. INST. MECHANICAL ENGINEERS ; MEMB. INST. CIVIL ENGINEERS : PAST PRESIDENT SOCIETY OF ENGINEERS, ETC. FOURTH EDITION REVISED AND FURTHER ENLARGED, WITH COPIOUS INDEX Hoution: E. & F. K SPON, LIMITED, 125 STEAND $*fo gorfc: SPON & CHAMBERLAIN, 12 COETLANDT STREET 1897 All rights reserved PREFACE. THIS Handbook is now so well established in the favour of the rising generation of Mechanical Engineers, that, in responding to the call for a new edition, the author has again revised the whole and added much new matter. In dealing with a subject of such magnitude there must of necessity be many omissions, but it is hoped that the notes will be found to contain all the more important definitions and formulas of which some knowledge is re- quired in examinations and general practice. 60 QUEEN VICTORIA STKEET, LONDON, E.C. January 1897. EXTEACTS FROM FOEMEE PEEFACES. THE present work ... is not intended in any way to supersede the ordinary text-books, but simply to supplement them in the form of a student's own notes, which should represent a summary of his reading and study. The notes are compiled from various sources; in many cases the authority is given, in others the information is original, or has been derived from sources of which no record has been kept. First Edition, 1883. . . . Busy men must have facts and opinions put before them as briefly as possible, and therefore no apology is requisite for giving the information in as condensed a form as is compatible with accuracy. Second Edition, 1890, . . . When various formula are given for the same thing, they are placed as nearly as possible in chronological order (e.g. N.H.P., p. 240), so that generally, but not always, the last will represent the best and most recent practice. In some cases, where there is no recognised standard, the various formulae given are all in actual use, and therefore represent general practice ; the engineer must in these cases make his own selection. Third Edition, 1893. CONTENTS. SECTION PAGE I. FUNDAMENTAL PRINCIPLES . . 1 II. VARIETIES AND PROPERTIES OF MATERIALS . . 33 II F. STRENGTH OF MATERIALS AND STRUCTURES . . 58 IV. PATTERN-MAKING, MOULDING AND FOUNDING . 104 V. FORGING, WELDING AND EIVETING . . .113 VI. WORKSHOP TOOLS AND GENERAL MACHINERY . 120 VII. POWER TRANSMISSION BY BELTS, ROPES, CHAINS AND GEARING 140 VIII. FRICTION AND LUBRICATION . . . .162 IX. THERMODYNAMICS AND STEAM . . * . 169 X. STEAM BOILERS . 192 Vlll HANDBOOK FOR MECHANICAL ENGINEERS. SECTION PAGB XL THE STEAM ENGINE 237 XII. HYDRAULIC MACHINERY ''. ' . . . .276 XIII. ELECTRICAL ENGINEERING . . . . . 308 XIV. SUNDRY NOTES AND TABLES .. . . .318 APPENDICES : I. SYLLABUS OF CITY GUILDS INSTITUTE . . . 341 II. SYLLABUS OP SCIENCE AND AKT DEPARTMENT . 360 III. SYLLABUS OP CITY OF LONDON COLLEGE . . 375 GENERAL INDEX At end of Book NO. OP PAKA. INDEX TO SUBJECTS. SECTION I. FUNDAMENTAL PRINCIPLES. 1 Induction and deduction 1 2 Force, matter and motion .. ., .. .. .. 2 3 Indestructibility of matter or conservation of mass . . . . 2 4 Particles, molecules and atoms 2 5 Chemical elements 3 6 Chemical compounds 3 7 Solids, liquids and gases 4 8 Molar and molecular motion ... 4 9 Attraction of cohesion and adhesion 5 10 Newton's law of universal gravitation . . . . . . . . 5 11 Force of gravity 5 12 Density, mass and weight 6 13 Plumb line .. .. 7 14 Specific gravity 7 15 Units of force 7 16 Work and energy 8 17 Vis viva and inertia .. .. .. .. .. .. 9 18 Convertibility of energy 9 19 Conservation of energy 9 20 Inertia and momentum .. .. .. .. .. .. 10 21 Galileo's law of inertia 10 22 D'Alembert's principle .. .. .. .. .. .. 11 23 Momentum .. .. .. .. .. .. .. .. 11 24 Modern notation in dynamics 12 25 Laws of motion . . . . . . . . . . . . . . 13 26 Equilibrium .. .. 14 27 Centre of gravity .. .. .. .. 14 HANDBOOK FOE MECHANICAL ENGINEEKS. NO. OP PARA. 28 Centroid or centre of gravity of form 15 29 Centre of gravity of regular solids 16 30 Centrobaryc theorem (Tornliiison) 16 31 Centrifugal and centripetal force 16 32 Centrifugal force 17 33 Centre of gyration . . . . . . . . . . . . 17 34 Vibration and oscillation .. .. .. .. .. .. 18 35 Centre of oscillation 18 36 Pendulum 19 37 Centre of percussion 20 38 Centre of spontaneous rotation .. .. .. .. .. 20 39 Transmissibility of force .. 20 40 Parallelogram of forces . . . . . . . . . . . . 20 41 Equilibrium of forces .. .. .. .. .. .. 20 42 Sense of forces 20 43 Triangle of forces 21 44 Polygon of forces .. .. .. 21 45 Force polygon .. .. .. .. .. .. .. 21 46 Link polygon 21 47 Composition and resolution of forces 22 48 Moments 22 49 Moment of a force .. .. 22 50 Principle of the equality of moments 22 51 Principle of least resistance .. .. .. .. .. 23 52 Couples .. .. 23 53 Classification of mechanics . . . . . . . . . . 23 54 Statics and dynamics .. 23 55 Theory of machines 24 56 Mechanical powers . . . . . . . . . . . . 24 57 The lever, wheel and axle, and toothed gearing . . . . 24 58 The pulley.. .. .. .. .. 25 59 Block and tackle, or pulley gear . . . . . . . . . . 25 60 The inclined plane, wedge, and screw . . . . . . . . 26 61 Steelyards and weighing machines .. .. .. .. 27 62 Useful work of men in foot-lbs. per min 28 63 Comparison of animal power 28 64 Formulae for falling bodies . . . . . . . . . . 28 65 Cartesian co-ordinates . , . . . . . . . . . . 30 66 Rolling on inclined planes . . . . ..^ . . . . 30 67 Brachystochrone, or curve of quickest descent . . . . . . 30 68 Velocity of sound .. ., 31 69 Relative velocities 32 70 The fastest mile 32 INDEX TO SUBJECTS. XI SECTION II. VARIETIES AND PROPERTIES OF MATERIALS. 1-AltA. PAGE 71 Varieties of iron .. .. - ... ..- .. .. .. 33 72 To distinguish wrought iron, steel and cast iron . . . . 33 73 Effect of carbon in iron .. 34 74 Common ores of iron . . . . . . . . . . . . 34 75 Scale of hardness of minerals . . . . . . . . . . 35 76 Roasting and smelting .. 35 77 Chemical action of blast furnace 35 78 Pig iron .. ... .. \ ;' 36 79 Analyses of pig irons . . - 36 80 Classification of pig iron . . - . . - - . . - 37 81 Refining .. ..- ..- 37 82 Puddling 38 83 Squeezing, shingling and rolling 39 84 Molecular condition of iron . . . , . . . . . . 39 85 Crude wrought iron . . . . . . . . . . . . 39 86 Qualities of wrought iron .. 40 87 Single and double sheet iron . . . . . . . . . . 40 88 Iron rolling mills 40 89 Defects in wrought iron ... ... . . . . . . . . 41 90 Casehardening ... ... .. .. .. .. .. 41 91 Casting wrought iron. .... .... .. .. 42 92 Definition of steel ... .... ... 42 93 Varieties of steel, No.. 1 .... ' ,' .,. .. .. 43 94 Classification of blister steel .... ... 43 95 Varieties of steel, No. .2 ... 43 96 Varieties of steel, No. 3 44 97 Varieties of steel, No. 4 .. .. 44 98 Varieties of steel, No. 5 .. */. 45 99 Dannemora cast steel 45 100 Eidsfos Stobestal cast steel 46 101 Relative pig iron and steel production of different countries 46 102 Notes on cast iron . .. . ^ . . 47 103 Qualities of cast iron ... .. 47 104 Chilled and malleable cast iron 47 105 Toughened cast iron .. .. .. .. .. .. 48 106 Copper ... . . ... ... 48 107 Aluminium 48 108 Alloys 49 109 Effect of alloying with copper , .. .. 49 Xll HANDBOOK FOB MECHANICAL ENGINEERS. NO. OF PAEA. PAGE 110 Bronze alloys ~ 50 111 Brass alloys 50 112 Antimony alloys .. .. .. .. .. .. .. 51 113 Nickel alloys 51 114 Various alloys . . ..- 52 115 Fusible alloys 52 116 Alloys fusible below 212 F 53 117 Solders .. 53 118 Melting-points of various metals, &c 53 119 Expansion of metals by heat .. .. .. .. .. 54 120 Weight of various metals in pounds .. .. .. .. 55 121 Multipliers to reduce cubic feet to tons . . . . . . . . 55 122 Use of wood in engineering .. .. .. .. .. 55 123 Fir, deal and pine 56 124 Preserving ironwork 56 SECTION III. STRENGTH OF MATERIALS AND STRUCTURES. 125 Classification of strains 58 126 Definitions of strain and stress 58 127 Proof strength .. .. .. 59 128 Factor of safety 59 129 Testing wrought iron . . . . 60 130 Testing cast iron .. .. 60 131 Specification tests of cast iron .. 61 132 Tests of cast iron for pipe making 61 133 Usual allowance for dead load per sq. inch . . . . . . 62 134 Maximum working strength in tons per sq. inch . . . . 62 135 Ultimate strength of various metals and alloys . . . . 63 136 Comparative strength of iron and steel plates . . . . . . 63 137 Tests of iron and steel, physical and chemical . . . . . . 64 138 Ankarsrums (Swedish) cast iron . . . . . . . . . . 64 139 Strength of malleable cast iron 65 140 Shearing strength compared with tensile strength . . . . 65 141 Approximate strength of girders . . . . . . . . 65 142 Bridges and girders 65 143 Specification tests of wrought iron in bridge and girder work 66 144 Allowance in bridges for changes of temperature . . . . 66 145 Specification tests, common wrought iron 67 INDEX TO SUBJECTS. Xlll KO. OP PAEA. PAGB 146 Specification tests of wrought iron and steel in shipbuilding . . 67 147 Steel and iron shipbuilding , . . , . 68 148 Definition of modulus 68 149 Modulus of rigidity 68 150 Limit of elasticity 68 151 Fatigue of wrought iron ., .. .. .. .. . . 69 152 Hooke's law of elasticity 69 153 Modulus of elasticity 69 154 Definitions of modulus of elasticity .. .. .. .. 70 155 Young's modulus 70 156 Formula for elongation by elasticity .. .. .. .. 70 157 Moduli of elasticity 71 158 Modulus of elasticity of bulk 71 159 Moment of inertia 72 160 Bending moment or moment of flexure 72 161 Bending moment 72 162 Neutral axis 72 163 Moment of inertia 73 164 Radius of gyration 73 165 Modulus of section, or strength modulus . . . . . . 73 166 Moment of rupture 74 167 Modulus of rupture for transverse strains .. .. .. 74 168 Moment of resistance .. .. .. .. .. .. 75 169 Working load for given moment of resistance 75 170 Strength of structures 76 171 Safe load on structures 76 172 Safe load on floors 76 173 Weight of men in crowds 76 174 Flat cast-iron floor-plates 77 175 Theorem of three moments 77 176 Load on the supports of continuous girders 78 177 Approximate safe load on columns and piers .. .. .. 78 178 Effect of load not being axial 79 179 Wrought-iron struts 79 180 Notes on iron columns .. .. .. .. .. .. 79 181 Strength of cast-iron columns 80 182 Approximate safe load on posts 80 183 Pillars and struts of wood 81 184 Ultimate strength of wood posts 82 185 Ultimate strength of timber 82 186 Safe load on timber in direct compression 82 187 Formula for strength of timber beams 82 188 Constants for strength of rectangular beams 83 XIV HANDBOOK FOR MECHANICAL ENGINEERS. NO. OP PARA. PAGE 189 .Experiments on rectangular beams of selected pine .. .. 83 190 .Proportions of beams for strength and stiffness . . . . 84 191 .Approximate proportions of beams. 84 192 Strength and stiffness of timber 85 193 Resilience 85 194 Timber trees ... 86 195 .Sizes of fir timber in balk 86 196 Notes on pile driving .. .. .. .. .. .. 87 197 Formulae for pile driving 87 198 Timber roofs .. 88 199 Wind pressures 88 200 Approximate weight of timber roofs .. .. .. .. 89 201 .Galvanised corrugated iron roofing .. .. .. .. 89 202 Weight of materials for estimating 89 203 Sheet copper 90 204 Sheet lead .. 90 205 Sheet zinc .. 90 206 Handy numbers for weight of iron ., .. .. .. 90 207 Market sizes of plates 91 208 Limits of ordinary prices, Staffordshire district .. .. 91 209 Extract from the Cleveland list of limits and extras .. .. 92 210 Deflection and camber 93 211 Deflection 93 212 Radius of curvature 93 213 Deflection of solid beams 93 214 Coefficients for deflection, rectangular beams 94 215 Coefficients of reaction for deflection 94 216 Approximate deflection of wrought-iron flanged girders . . 95 217 Deflection of girders 95 218 Deflection tests 96 219 Load on bridges 96 220 Deflection of beams under impact . . . . . . . . 97 221 Strength of flat carriage springs .. .. ., .. .. 97 222 Notes on torsion and shafting 98 223 Approximate strength of shafting 99 224 Ultimate torsional strength of various metals . . . . . . 99 225 Torsional modulus of elasticity . . . . . . . . . . 99 226 Transmission of power by shafting 99 227 Formula for strength of shafting 100 228 Molesworth's formula for wrought-iron shafting . . . . 100 229 Diameter of coupling bolts in screw shafts .. .. .. 100 230 Proportions of couplings in screw shaft .. .. .. .. 101 231 Transverse strength of shafts ,. 101 INDEX TO SUBJECTS. XV NO. OP PARA. l^GE 232 Proportions of bolts, nuts and washers in carpentry .. .. 101 233 Strength of bolts 102 234 Strength of bolts (Unwin) 102 235 Flange studs of steam cylinders , .. 102 236 To secure check or lock nuts . . 103 237 Check nuts 103 238 Pressure on bearing area in holes .. .. .. 103 SECTION IV. PATTERN-MAKING, MOULDING AND FOUNDING. 239 Pattern-making 104 240 Black varnish for patterns . . . . . . . . 105 241 "Weight of casting from pattern .. .. .. .. ..105 242 Allowance for machining .. .. ,. .. .. .. 105 243 Moulding in foundry .. .. 105 244 Sand for moulding 106 245 Foundry drying stove 106 246 Notes on moulding and casting 107 247 Cleaning castings .. 107 248 . Classification of iron ores 108 249 Charges employed at Dowlais for different kinds of pig iron .. 108 250 Analyses of pig iron 108 251 Foundry pig ... .. 109 252 Mixtures of pig iron 109 253 Melting metal for castings 110 254 Contraction of metals in cooling .. ... .. .. .. 110 255 Contraction of castings .. .. .. .. .. .. 110 256 Expansion of castings .. .. ., .. .. .. Ill 257 Bronze and brass castings .. .. .. .. ..Ill SECTION V. FORGING, WELDING, . RIVETING, ETC. 258 Forging .. %% .. 113 259 Welding 113 260 Tempering 114 XVI HANDBOOK FOR MECHANICAL ENGINEERS. NO. OP PABA. 261 Colours corresponding to temperature 114 262 Tempering steel 115 263 Notes on riveted joints ' 116 264 Pressure to close rivets ..117 265 Machine riveting for boilers .. .. .. .. .. 117 266 Proportion of rivet diameter to thickness of plate .. .. 118 267 Riveting 118 268 Single riveting in boiler or tank work 118 269 Eivets in tie bars and diagonal riveting generally .. .. 119 270 Notes on caulking .. 119 271 Caulking tools 119 SECTION VI. WORKSHOP TOOLS AND GENERAL MACHINERY. 272 Object of machines 120 273 Machinery in motion .. ..121 274 Useful work and efficiency 121 275 Economical working of machines .. .. .. ,. 121 276 Velocity ratio 122 277 Principle of virtual velocities 122 278 Definitions of the principle of virtual velocities .. .. 123 279 "Work, in terms of angular motion .. .. .. ..123 280 Angular velocity .. .... 123 281 Angular measurement of forces .. .. .. .. .. 124 282 Angle of twist 125 283 Workshop tools 125 284 Hammers 125 285 Work of hammer 126 286 Impact of moving bodies 126 287 Notes on workshop tools and fittings 129 288 Holtzapffel's classification of cutting tools 129 289 Angles of tools 129 290 Cutting speed of machine tools 129 291 Average cutting speeds and feeds .. .. .. .. 130 292 Speed of machine tools 130 293 Cutting speeds 131 294 Speed in cutting metals 131 295 Speed of milling cutters 132 296 Resistances in machine tools .. .. 132 INDEX TO SUBJECTS. XV11 297 Power required to drive lathe 133 298 Screw-cutting 134 299 Screw for worm wheel 135 300 Velocity of wood-working machinery 135 301 Speed of polishing and grinding 136 302 Boiling mill speeds 136 303 Shearing and punching 136 304 Steam hammers 137 305 Steel forging presses .. .. .. .. ^. .. 138 306 Observed horse-power to drive shop tools 138 SECTION VII. POWER TRANSMISSION BY BELTS, ROPES, CHAINS AND GEARING. 307 Transmission of motion 139 308 Notes on belt gearing 139 309 Strength of leather belts 140 310 Large double belts ... 140 311 To find length of belt embracing pulleys 141 312 Notes on hemp ropes 142 313 Strength of Manila ropes 145 314 Formulae for strength of hemp ropes .. .. .. .. 145 315 Hide ropes.. .. ' ..>; 146 316 Fly ropes 146 317 Hope driving 146 318 Curve of rope 147 319 Tests of ropes 147 320 Average tensile strength of ropes 148 321 Wire ropes for lifts 148 322 Experiments on wire rope at Forth Bridge 148 323 Lang's patent wire ropes 148 324 K. S. Newall and Co.'s wire ropes 149 325 Strength of chains 149 326 Eemarks on crane chains .. .. .. .. .. ..150 327 Examination of chains at the Docks in London . . . . 150 328 Circular rings for mooring and sling chains .. .. .. 151 329 Toothed gearing 151 330 Notes on toothed gearing 152 331 Strength and weight of toothed gearing 154 332 Formulae for strength of gearing 154 XV111 HANDBOOK FOE MECHANICAL ENGINEERS. KO. OP PARA. 333 Wheel gearing, Manchester pitch. 155 334 Mill gearing .. 155 335 Speed of mill gearing 156 336 Determining the proportions of gearing 156 337 Proportions of wheel teeth 157 338 Ordinary proportions of keys 157 339 Proportions of cotters through bars .. .. .. .. 157 340 Journals for shafts and axles .. 158 341 Power of craneman, &c 158 342 Hand-power crane .. .. .. .. .. .. .. 159 343 Crab winches 159 344 Rope tackle for lifting 160 345 Safe load on shear legs and derrick poles .. .. .. 160 346 Differential pulley calculations 160 SECTION VIII. FRICTION AND LUBRICATION. 347 Laws of friction 162 348 Angle of repose 162 349 Definitions of friction 163 350 Morin's experiments on friction of motion .. .. .. 163 351 Safe working pressure on moving surfaces .. .. .. 164 352 Experiments on friction 164 353 Friction and heat 164 354 Friction of journals .. .. 165 355 Shop shaft bearings 166 356 Mean coefficients of friction 166 357 Lubricants for various cases 167 358 Action of oils on metals 167 359 Boiling friction r ..168 360 Traction or friction on common roads 168 SECTION IX. THERMODYNAMICS, AND STEAM. 361 Imponderables .. .. 169 362 Universal ether 169 363 Eankine's dynamical theory of heat 169 INDEX TO SUBJECTS. XIX NO. OP PARA.. 364 Sources of heat ..... . ........ 170 365 Sensible heat .............. 170 366 Comparison of thermometers .. .. .. .. .. 170 367 Eifect of change of temperature .......... 171 368 Transfer of heat .............. 171 369 Mechanical equivalent of heat .......... 171 370 Calorie or French unit of heat .......... 172 371 Mayer's experiment .. .. .. .. .. .. 172 372 Entropy ................ 173 373 Capacity of bodies for heat .......... 173 374 Specific heat .............. 173 375 Dulong and Petit's law ............ 174 376 Specific heats of various bodies .......... 174 377 Latent and total heat ............ 175 378 Gases and vapours ............ 175 379 Kinetic theory of gases .......... .. 176 380 Laws of gases .............. 177 381 Volume of a gas at given pressure and temperature .. .. 177 382 Pressure and temperature of steam ........ 178 383 Eelation of pressure to temperature of steam ...... 179 384 Pressure and volume of steam by Boyle and Marriotte's law 179 385 Kelative volume of steam .......... 179 386 Saturated steam .............. 180 387 Properties of saturated steam .......... 180 388 Atmospheric pressure .. .. .. .. .. .. 181 389 Expansion curves .. .. .. .. .. .. .. 181 390 Temperature of boiling water an 1 steam ...... 182 391 Heat required for evaporation .. .. .. .. .. 182 392 Solution and evaporation of steam .. .. .. .. 182 393 First law of thermodynamics .......... 182 394 Second law of thermodynamics .. .. .. .. ..183 395 Carnot's law or function (1824) .......... 184 396 Sir W. Thomson's modification of Carnot's law (1851) .. 184 397 Law of efficiency of thermodynamic engines ...... 184 398 Prof. Thomson's formula for a perfect thermodynamic engine 185 399 General view of heat engine .. .. ...... 185 400 Superheated steam .. .. .. .. .. ..185 401 Condensation of steam .. .. ..- .. .. ..185 402 Velocity of fluids flowing from atmosphere into vacuum .. 186 403 Discharge of steam through pipes .. .. .. .. 187 404 Diameter of steam pipes .. .. .. .. .. .. 187 405 Velocity of steam in pipes .. .. .. .. .. 188 406 Thickness of steam pipes ............ 188 b 2 XX HANDBOOK FOE MECHANICAL ENGINEERS. NO. OF PAEA. 407 Expansion of steam pipes 188 408 Loss of heat by pipes 188 409 Comparative transmission of heat .. .. .. ..189 410 Non-conducting dry hair felt .. .. .. .. .. 189 412 Heating by steam .. .. 190 413 ,. 190 SECTION X. STEAM BOILERS. 414 .. 192 415 Production of steam in Cornish and Lancashire boilers .. 193 416 Horse-power of boilers .. 193 417 Horse-power of boilers from dimensions .. 194 418 Cost of boiler power .. 195 419 .. 195 420 Space occupied by coal .. 195 421 .. 196 422 Chemical composition of fuels .. 196 423 Theoretical units of heat per Ib. of fuel .. 196 424 Absolute heating power of fuel .. 197 425 197 426 Heating by contact of gases .. ]97 427 Kate of transmission of heat .. 197 428 Condition of boiler affecting transmission of heat .. 198 429 Loss of strength in copper plates when heated .. 198 430 Loss of strength in iron plates when heated .. 198 431 Comparative value of heating surfaces .. 199 432 Heating surfaces of boilers .. 199 433 Products of combustion .. 200 434 Air required to burn fuel .. 200 435 Heat in flue .. 201 436 Brick chimney shafts .. 201 437 Force of wind .. 202 438 Size of factory chimney for boilers .. 203 439 Velocity of gases in chimney .. 204 440 London County Council rules for furnace chimney shafts .. 205 441 Eate of combustion .. 205 442 .. 206 INDEX TO SUBJECTS. XXI NO. OP PARA. 443 Heat in boiler furnaces . . 206 444 Loss of heat in boilers 207 445 Duty of engines 208 446 Progress of duty of engines 208 447 Duty of engines compared with coal used 209 448 Modern duty 209 449 Evaporative value at different temperatures 209 450 Hand-firing and mechanical stoking 210 451 Experiments on evaporation in boilers 211 452 Effect of supervision of boilers 211 453 Consumption of steam in engines .. .. .. .. 211 454 Feed- water required for boilers 212 455 Advantage of heating feed-water .. .. .. .. 212 456 Fuel economisers .. .. .. .. .. .. .. 213 457 Consumption of fuel 213 458 Possible economy in coal consumption .. .. ,. ., 213 459 Horse-power per ton weight .. .. .. .. .. 214 460 To calculate size of boilers 214 461 Cornish boiler 215 462 Comparison of Cornish boiler with I.H.P. of engine .. .. 216 463 Proportions of boiler 216 464 Lancashire boilers 217 465 Fire-bars 217 466 Boiler seatings 217 467 Size of manholes in boilers ., .. .. .. .. 218 468 Boiler tubes 218 469 Water gauge glass 219 470 Taper of plugs for boiler cocks .. .. .. .. .. 219 471 Blow and scum 219 472 Blowing-off to prevent incrustation .. .. .. .. 219 473 Boiler scale 220 474 Hardness of water 220 475 Incrustation in boilers . . . . . . . . . . . . 221 476 Sea-water 221 477 Boilers fed with salt water 222 478 Causes of priming 222 479 Corrosion of boilers 222 480 Grease in boiler 222 481 Safety valves for boilers 223 482 Board of Trade rules for safety valves 224 483 To calculate safety valve leverage ., .. .. .. 225 484 Notes on spiral springs . . . . . . . . . . . . 225 485 Spiral springs 226 XX11 HANDBOOK FOB MECHANICAL ENGINEERS. NO. OF PARA. PAGE 486 Spiral springs, Kankine's formula 226 487 Spiral springs for safety valves 227 488 Initial compression of springs for safety valves .. .. 227 489 Spring-balance safety valves 228 490 To calculate springs for safety valves . . . . . . . . 228 491 Factor of safety, steam boilers 228 492 Testing boilers 229 493 Kiveting for boilers 229 494 Small screwed stays or water-space stays 230 495 Long stay bolts 230 496 Strength of flat plates supported by stays (Lloyds' rules) . , 230 497 Strength of flat plates .. 231 498 Strength of flat encastre circular wrought-iron plates . . 232 499 Ultimate strength of boiler shell 232 500 Helical joints for boilers 233 501 Collapsing pressure of boiler tubes .. .. .. .. 233 502 Boilers, comparison between bursting and collapsing pressures 234 503 Collapsing pressures of flues 234 504 Fox's corrugated flues 235 505 Locomotive boilers . . . . . . . . . . . . 235 SECTION XL THE STEAM ENGINE. 506 Early engines 237 507 Economy of high pressure steam . . . . . . . . 238 508 Advantage of expanding steam 238 509 Economy of compound engines . . . . . . . . . . 238 510 Progress of compound engines .. .. .. .. .. 238 511 Horse-power 240 512 Nominal horse-power .. .. .. .. .. .. 240 513 Indicated horse-power 241 514 Effective or brake horse-power 242 515 French horse-power .. .. .. .. .. .. 242 516 Modulus of steam engine 242 517 De Pambour's principles 243 518 Steam worked expansively .. .. 243 519 Table of hyperbolic logarithms 244 520 Mean pressure without logarithms or scales . . . , . . 245 INDEX TO SUBJECTS. XX111 NO. OF PARA. 521 Ordinates to hyperbolic expansion curves 245 522 Simpson's rule 246 523 Eesi stance in steam engines .. .. .. .. .. 246 524 Mean effective pressure, compound engine 247 525 Piston constant for indicator diagrams 247 526 Crank and piston notes 247 527 Slide valves, explanation of terms 249 528 Area of steam ports 250 529 Slide valve notes 250 530 Point of cut-off .. 251 531 Number of expansions 251 532 Triple expansion engines . . . . . . . . . . . . 252 533 Cylinder ratios 252 534 Advantage of steam jacketing .. .. .. .. .. 253 535 Link motions 253 536 Radial valve gears 254 537 Watt's governor 254 538 Efficiency of governor . . . . . . . . . . . . 255 539 Fly- wheels, notes and formulae 255 540 Investigation of fly-wheels .. .. .. .. .. 258 541 Strength of crank pin 259 542 Fly-wheel shaft for rolling mill 260 543 Calculation of engine shafts 260 544 Steam engine dimensions.. .. .. .. .. .. 261 545 Condenser and air pump 262 546 Circulating pump .. .. .. .. .. .. .. 262 547 Circulating water for condensation .. .. .. .. 263 548 Comparison of steam engines . . . . . . . . . . 263 549 Marine engines .. .. .. .. .. .. .. 263 550 Definitions relating to screw propellers .. .. .. 264 551 Speed in knots .. .. 264 552 Notes on screw propellers . . . . . . . . . . 265 553 Relative efficiency of large and small screws . . . . . . 265 554 Slip of screw propeller . . . , . . . . . . . . 266 555 Negative slip 266 556 Pitch of screw propeller 267 557 Relation of pitch to diameter 267 558 Formula for pitch of propeller 268 559 Alteration of pitch 268 560 Indicated horse-power required for screw propeller . . . . 268 561 Built-up crank shafts 269 562 Steamships 269 563 Paddle-wheels .. ..269 XXIV HANDBOOK FOR MECHANICAL ENGINEERS. HO. OF PARA. 564: Efficiency of paddle-wheels .......... 270 565 Equilibrium of floating bodies, as ships *. . . . . 270 566 Displacement of ships .. .. .. .. .. ..271 567 Tractive force of locomotive .. .. .. .. .. 271 568 Adhesion of locomotive wheels ., .* . ...... 272 569 Resistance on railways .. .. .. .. .. .. 272 570 Locomotive express engines .. .. ...... 273 571 Effect of speeds and gradients .. .. >. .. .. 273 572 Railway curves ........ , ..... 274 573 Air condensers .......... .. .. 274 574 Gas engines .............. 275 SECTION XII. HYDRAULIC MACHINERY. 575 Summary of hydraulics . . . . . . . . . . . . 276 576 Torricelli's theorem 277 577 Pressure of water -;.. .. 277 578 Floatation power of water .. ':'., '.. . .,' .. 278 579 Hydrostatic paradox .. .. .. .. .. ..278 580 Principle of Archimedes 278 581 Pascal's principle 279 582 Compressibility of water 279 583 Comparison of discharge through various apertures . . . . 279 584 Practical discharge of water 280 585 Weight and bulk of water 280 586 Useful numbers in connection with water . . . . . . 281 587 Velocities of streams .. .. .. .. .. ..281 588 Discharge over weirs .282 589 Discharge over weirs per foot width 282 590 Flow of water through rectangular notch . . . . . . 283 591 Flow of water through triangular notch 283 592 Rivers, sewers, drains, &c. .. 283 593 Natural evaporation of water 284 594 Efficiency of hydraulic water-raising machines .. .. 284 595 Waterwheels 284 596 Turbines 285 597 Hydraulic ram 285 598 Centrifugal pumps 286 599 Discharge through pipes from natural head 287 INDEX TO SUBJECTS. XXV NO. OF PARA. 600 Friction of water in pipes 288 601 Water supply 288 602 Tests of metal for pipes 289 603 Size of Water Companies' mains 289 604 Freezing of water 289 605 Delivery of water in pipes .. .. .. .. .. 290 606 Mechanical value of fluids under pressure .. .. .. 291 607 Mechanical value of water under accumulator pressure .. 291 608 Power required to work hydraulic machinery .. .. .. 292 609 Hydraulic pressure accumulator 292 610 Pressure in pipe mains 293 611 Variation of accumulator pressure due to working of machinery .. .. .. .. .. .. .. 293 612 Friction of accumulators 294 613 Friction of cup leathers .. .. 294 614 Air accumulators .. .'. .. .. .. .. .. 295 615 Speed of pumping .. .. .. .. .. .. .. 295 616 Atmospheric pressure . . . . . . . . . . . . 296 617 Efficiency of pumps and accumulator . . . . . . . . 296 618 Coefficient of steam engines .. . .. .. .. 296 619 Packing for force pumps . . . . . . . . . . . . 297 620 Proportions of hydraulic pipes . . . . . . . . . . 298 621 Thickness of pipes for hydraulic accumulator mains .. ., 298 622 Thickness of pipes for Water Companies' mains . . . . 298 623 General rules for thickness of cast-iron pipes 299 624 Notes on pipes .*'/ 300 625 Dr, Angus Smith's composition for coating pipes . . . . 300 626 Hydraulic press with hand pump 300 627 Hydraulic forging presses * .. .. .. .. 301 628 Hydraulic press cylinders .. 301 629 Effective pressure for hydraulic cranes and hoists .. .. 302 630 Diaphragm regulator for hydraulic machinery .. .. .. 302 631 Power and speed of hydraulic hauling machines .. . 303 632 Speed of lifting with hydraulic power 304 633 Height of lift for cranes 304 634 Coal weighing cranes 304 635 Lifting rams for hydraulic cranes 305 636 Turning rams for hydraulic cranes 305 637 Areas of valves for machinery under accumulator pressure .. 306 638 Areas of ports in slide valves ..,., 306 639 Counterweights for crane chains 307 640 Strain allowed on wrought iron in hydraulic cranes .. .. 307 641 Lock gates 307 XXVI HANDBOOK FOB MECHANICAL ENGINEERS. SECTION XIII. ELECTRICAL ENGINEERING. KO. OP PARA. PAGE 642 The hypothesis of a universal ether 308 643 Comparison of electricity with other powers .. .. .. 308 644 Electric transmission 308 645 Chief systems of electrical transmission 309 616 Board of Trade division of systems 309 647 Comparative cost of transmitting power 309 648 Electrical units 310 649 Galvanic batteries 310 650 Electrical terms 311 651 Measure of electrical work 312 652 Ohm's law .. .. 312 653 Electrical equations 312 654 Electric lighting 313 655 Power required for electric lighting .. .. .. .. 314 656 Useful formulae 314 657 Electric wiring .. .. 315 658 Light testing or photometry .. .. .. .. ..316 659 Coal gas 316 660 Visibility of light at a distance 316 661 Mild steel cylinders for storing high pressure gases . . . . 316 662 Cylinders for compressed gas 317 SECTION XIV. SUNDRY NOTES AND TABLES. 663 Mathematical concepts 318 664 Lineal measure 318 665 Square measure .. 318 666 Cube measure 319 667 Mathematical signs 319 668 Arithmetical terms 319 669 Nomenclature of large numbers . . . . . . . . . . 320 670 Duodecimals 320 671 Multiplication of decimals 320 672 Prime and irrational numbers 321 INDEX TO SUBJECTS. XXV11 NO. OP PARA. 673 Arithmetical and geometrical series .. .. .. .. 321 674 Types of vulgar fractions .. .. .. .. .. .. 321 675 Katio and proportion 322 676 Keduction of fraction to lowest terms 322 677 Powers and roots 322 678 Solving roots by factors ., .. .. .. .. .. 323 679 Logarithms 323 680 Useful numbers 323 681 Epitome of mensuration . . . . . . . . . . . . 324 682 Colours used in architectural and mechanical drawing . . 326 683 Composition of colours for drawings .. .. .. .. 327 684 Section lines in mechanical drawing 327 685 Basis of French measurements 327 686 French measures 327 687 Equivalents of metric system 328 688 Units in metric system 328 689 Units in foot-second-pound system 329 690 Units employed in engineering calculations 329 691 Decimal equivalents to fractions of an inch 330 692 Whitworth standard bolts and nuts 331 693 Whitworth gas threads 331 694 British Association gauge for apparatus screws . . . . 332 695 Birmingham wire gauge . . . . . . . . . . . . 333 696 Standard sheet and hoop-iron gauge . . . . . . . . 334 \/697 Imperial standard wire gauge . . . . . . . . . . 335 698 Areas of circles advancing by eighths . . . . . . . . 336 699 Square roots and cube roots .. .. .. .. ,. 337 700 Decimal approximations for rapid calculations .. .. 338 APPENDIX I. SYLLABUS OP CITY AND GUILDS OP LONDON INSTITUTE. Gas manufacture 341 Iron and steel manufacture . . . . . . , . . . 343 Telegraphy and telephony . . . . . . . . . . 345 Electric lighting and power transmission . . . . . . 347 Metal plate work 352 Mechanical engineering 353 Manual training metal work 356 XXV111 HANDBOOK FOR MECHANICAL. ENGINEERS. APPENDIX II. SYLLABUS OF GOVERNMENT DEPARTMENT OF SCIENCE AND ART. PAGE (II) Machine construction and drawing 360 (VI) Theoretical mechanics .. 365 (VII) Applied mechanics 370 (XXII) Steam 872 APPENDIX III. SYLLABUS OF ENGINEERING DEPARTMENT OF THE CITY OF LONDON COLLEGE .. .. 376 GENERAL INDEX AT END OF BOOK. HANDBOOK FOB MECHANICAL ENGINEEBS SECTION I. FUNDAMENTAL PKINCIPLES. 1. INDUCTION AND DEDUCTION. THE process of induction is a logical system of forming conclusions from ike special to the general, by which we ad- vance from many individual experiences to a general law; deduction, on the other hand, draws a conclusion from the general to the special, from a general law of nature to an individual case. Haeckel. 2. FORCE, MATTER AND MOTION. Motion is change of place. Intensity of motion is called velocity. Velocity is motion considered in relation to time. Force is that which produces or destroys motion, or which tends to produce or destroy it ; or which alters or tends to alter its direction. Matter is that which is the subject of motion or a tendency to motion. It is the element of resistance in the sensible world. 4 HANDBOOK FOE MECHANICAL ENGINEEES. " Force and matter are correlates, inconceivable apart, they necessarily involve acceptance of space and time." Stallo's Concepts. If one force only acts upon a body, motion must ensue. Forces in equilibrium are called pressures or reactions. Pressures and resistances are the active and passive states of force ; in whatever direction they are exerted they may be measured in Ibs,, and when exerted through any given space may be measured in foot-lbs. Force may be measured by the pressure it produces upon some obstacle, and compared with gravity, or by the motion which it produces in a body in a given time. Motion may be uniform or variable : uniform motion is when a body continues to pass over equal spaces in equal times ; variable motion may be uniformly accelerated, uniformly retarded, or irregular. Philosophically, Matter and Force (Substance and Accident) are known as Mass and Motion, and the ultimate inseparables of Mass, Form and Motion together constitute Matter or the Reality of Things. 3. INDESTRUCTIBILITY OF MATTER, OR CONSERVATION OF MASS. Matter is indestructible. The atoms composing it may enter into new combinations, or may be subjected to new conditions, but no variation can be made in the absolute quantity of matter in the universe. 4. PARTICLES, MOLECULES AND ATOMS. Particles are the smallest visible or tangible portions of the mass. Molecules are the smallest physical portions of matter retaining the properties of the bulk. Atoms are the ultimate indivisible portions of matter, probably spherical and less than the one-hundred-millionth of an inch in diameter. Cauchy defined atoms as " material points without extension." FUNDAMENTAL PKINOIPLES. 3 Molecules are the ultimate products of tlie physical division of matter, atoms the ultimate products of its chemical de- composition. Dr. Paul Carus suggests that the world-substance consists of minute units (possessing a continuity which places them in constant relation to each other) and in its simplest form identical with what physicists call ether ; two or more ether monads forming what we call an atom, various combinations of ether-monads forming the various elementary atoms. Polarity is believed to be inherent in every atom of the universe, material or immaterial. 5. CHEMICAL ELEMENTS. Substances which, after subjection to all methods of analysis at present known, are not separable into two or more components, are known as chemical elements. There are at the present time about seventy acknowledged elements, and two or three doubtful ones. 6. CHEMICAL COMPOUNDS. H 2 0, as the chemical symbol for water, means that it consists of two volumes of the gas hydrogen combined with one volume (at the same temperature and pressure) of the gas oxygen. By weight, however, the proportion is 2 of hydrogen to 16 of oxygen, their atomic weights being H = 1, O = 16, or in other words, oxygen weighs sixteen times as much as an equal bulk of hydrogen. In chemically compound substances a molecule must consist of atoms of all the component elements of the sub- stance, in their proper relative proportions. In chemically simple substances the atoms probably exist in combination as molecules, various combinations producing the phenomena of allotropism, isomorphism, isomerism, &c. Allotropic substances are those which exist under more B 2 HANDBOOK FOE MECHANICAL ENGINEERS. than one form ; the most striking example is carbon, which occurs as diamond, graphite, charcoal and lamp-black. Isomeric substances are composed of the same elements in the same proportions, but exhibit different properties. Isomorphous substances are those having the same crystal- line form and analogous chemical composition. Dimorphism, as when a substance crystallises in either of two different orders of crystals, is a form of allotropy. Amorphous substances are those which have an indefinite form, as pitch, &c. 7. SOLIDS, LIQUIDS AND GASES. In solids the molecules are relatively fixed, in liquids they are coherent but not fixed, in gases they are repellent to each other. Hence solids press downwards only, liquids press downwards and sideways, gases press in all directions. The pressures are the effects of gravity only, when the substances are unconfined. 8. MOLAR AND MOLECULAR MOTION. Molar motion is the motion of masses in contradistinction to the motion of molecules. It expresses the motion of a body as a whole. Molecular motion. The molecules of all bodies are in a state of continual agitation. The hotter a body is the more violently are its molecules agitated. In solids the path described by a'given molecule is limited and confined to a very small space. In liquids a molecule is unlimited in its motion and may penetrate to any part of the space occupied by the liquid. In gases the molecules move with great velocity in straight lines, and in all directions. They therefore diffuse rapidly, the lighter gases more so than the heavier. Clerk Maxwell* FUNDAMENTAL PRINCIPLES. 9. ATTRACTION OF COHESION AND ADHESION. Attraction of cohesion is the molecular attraction between the particles of the same body. Attraction of adhesion is the physical attraction of the particles of dissimilar bodies in opposition to the force of cohesion. Capillary attraction is a form of adhesion, and the term capillarity includes all effects depending upon the adhesion or repulsion between fluids and solids. 10. NEWTON'S LAW OF UNIVERSAL GRAVITATION. All bodies whatever attract each other with a force pro- portional directly to their masses and inversely to the squares of the distances between them. " The reason of these properties of gravity," he said, " I have not as yet been able to deduce ; and I frame no hypotheses." By some writers this statement is divided into two laws of gravitation, thus First law. Every body or substance in the universe attracts every other body with a force proportionate to its mass. Second law. Bodies attract each other inversely as the square of the distance between them. 11. FORCE OF GRAVITY. Gravity, or the attraction one body has for another, being proportional to the mass of the body, that of the earth prac- tically overwhelms all others. The direction of attraction is towards the centre of the mass, hence, under the action of gravity, all bodies tend to fall towards the centre of the earth. Accelerating Force of Gravity, or Acceleratrix of Gravity, is 6 HANDBOOK FOE MECHANICAL ENGINEERS. the velocity imparted to bodies falling near the surface of the earth, in lat. 45 = 32-17 feet per second, say 32-2 = g. Paris . . . lat. 48 50' = 32-1819 Greenwich . . 51 29' = 32-1912 12. DENSITY, MASS AND WEIGHT. Density is the quantity of matter, or units of mass, in a unit of volume. Mass is the quantity of matter in a hody of any volume, and is constant at all heights and in all latitudes = density X magnitude. Masses of different substances are equal when the same force acting upon them for the same time produces the same velocity. Weight is the mass x force of gravity, which is only constant at the same level and same latitude, . * . W 2 u 2 = , or W h, since h = - . In calculating the power exerted in moving a load, as a truck on a railway, we have the inertia overcome in reach- ing the velocity attained ( ) added to work done trans- \ ^ 9 ' porting the load through the space passed over (W ^ s). In coming to rest the inertia is given up again as momentum. The value of the momentum is irrespective of the distance in which the velocity was acquired ; its effect depends entirely upon the distance in which it is expended. 21. GALILEO'S LAW OF INERTIA. A material point, when once set in motion, free from the action of an extraneous force and wholly left to itself, con- tinues to move in a straight line so as to describe equal spaces in equal times. This is also Newton's " First Law of Motion.' ' FUNDAMENTAL PRINCIPLES. 11 22. D'ALEMBERT'S PRINCIPLE. " In whatever manner several bodies change their ac'ual motions, if we conceive that the motion which each body would have in the succeeding instant, if it were quite free, is decomposed into two others, of which one is the motion which it really takes in consequence of their mutual actions, the second must be such that if each body were impelled by this force alone (that is, by the force which would produce this second motion), all the bodies would remain in equi- librio." This is evident ; for if these second constituent forces are not such as would put the system in equilibrio, the other constituent motions could not be those which the bodies really take in consequence of their mutual action, but would be changed by the first. Gregory's l Mechanics.'' 23. MOMENTUM. Pressure (/) applied to a body of given mass (m) free to move, and continued for some definite time (), causes motion at a certain velocity (v). ./, /,,., /, = Z-", / = ^, or the effect varies inversely as the time occupied, and directly as the mass or weight moved and the velocity of movement. When the body is already moving with velocity (v) and it is increased to (i^), then ft = mv l mv. 8 = J (v -f- tfj) t. Momentum or Quantity of motion (Descartes, Newton) = mass x velocity, and represents the constant force which acting for one second would stop a moving body = m v. A mass in motion, having momentum = m v, will, after impact with mass m 1 at rest, have a resulting velocity of mv , 1X , or m v = (m + m 1 ) v l . r , 12 HANDBOOK FOE MECHANICAL ENGINEERS. Moving force, or the Moving quantity of a force, is the momentum generated in one second. The term momentum has been applied indifferently to express the quantity of motion existing in a body and its striking force or power of overcoming resistance, but the latter is more properly denoted by vis viva. Momentum varies as the velocity, and is the measure of a given force during a given time of action. Vis viva varies as the square of the velocity, and is the measure of the force acting through a given distance. In its technical (workshop) use the term momentum signifies the same as actual energy or accumulated work, and is independent of time. Energy = -^- = fs. Impulse = mv = ft. mv 2 mv Average force = - = . 2 t In old books on mechanics "the duplicate ratio of the velocity " means v 2 . Two unequal balls with velocities inversely as their masses will have equal momenta, and the same power to overturn an obstacle, but the swifter ball will penetrate a soft body further than the other, or do more work. They will both overcome the same resistance in the same time, but to have equal piercing effects their masses must be inversely as the squares of their velocities, so that their momentum x velocity may be equal. 24. MODERN NOTATION IN DYNAMICS. Velocity is time-rate of displacement. The SECOND is taken as the unit interval [of time] and the FOOT as the unit distance. Velocity is measured in feet displacement per second, the unit of which is a displacement of 1 foot in 1 second, and this unit velocity is called a VELO. Every velocity requires an interval of time in which to produce a finite displacement however small. FUNDAMENTAL PEINCIPLES. 13 When velocity is uniformly increasing, acceleration is measured by the increased velocity in feet-per-second per second, the unit acceleration is an increased velocity of 1 foot per second in 1 second, or 1 velo per second ; this unit is called a CELO. The quantity of matter in any body is called its mass, the unit mass is a pound or 1 Ib. Force applied; to mass produces acceleration in the direction of the force, the unit force is that force, which acting upon 1 Ib. produces 1 celo, and is called a POUNDAL. The force which produces a celos in m Ibs. is m a poundals, and a mass of m Ibs. with a celos has a MASS- ACCELERATION of ma POUND-CELOS. The accelera- tion of any mass due to gravity (#) is 32*2 pound-celos, hence a weight of 1 Ib. = 32 '2 poundals, or a weight of m Ibs. is a force of m g poundals. The MASS- VELOCITY or MOMENTUM of a body is the product of the number of Ibs. in the body by the number of velos it has. A body of 1 Ib. has unit mass- velocity when it has one velo ; it is then said to have a POUND- VELO. A force acting for a definite interval produces mass- velocity and is called an IMPULSE ; the unit impulse is that which acting on 1 Ib. produces in it 1 velo, and is called a PULSE. It has the same effect as 1 poundal acting for 1 second in producing 1 pound-velo. A pulse might be called a poundal-second. In units of work 1 foot-pound = g foot-poundals. 25. LAWS OF MOTION. Generally known as " Newton's Laws of Motion." r I. Change of state is due to external force. Summary J II. Every force produces its own result. ( III. Action and reaction are equal. FIRST LAW OF MOTION (Kepler, also ascribed to Galileo). All motion is naturally rectilinear and uniform. A body at rest will continue at rest, and if in motion will continue 14 HANDBOOK FOE MECHANICAL ENGINEEKS. to move in a straight line with uniform velocity, unless acted upon by some external force. SECOND LAW OF MOTION (Galileo). If a body be acted upon by two or more forces for a given time, the effect will be the same as if the forces acted independently for the same length of time. This is the foundation of the parallelogram of forces. THIRD LAW OF MOTION (Newton). Action and reaction are always equal and contrary in direction. When a body receives motion from another, the second body loses a quantity of motion equal to that which the first receives. When a pressure produces motion, the quantity of motion, or momentum generated in a given time, is proportional to the pressure. 26. EQUILIBRIUM. May be stable, unstable, indifferent, or mixed. When a body is resting on another, in such a position that its centre of gravity is the lowest possible, it is in stable equilibrium : e.g. when vertically under the point upon which it is supported. When the highest possible, it is in unstable equilibrium : e.g. when vertically over point of support. When constant for any position, the equilibrium is indifferent or neutral : e.g. a sphere. When stable with regard to movement in one direction, and unstable or in- different with regard to another direction, it is said to be in a position of mixed equilibrium : e.g. a cylinder lying on its side. 27. CENTRE OF GRAVITY is that point in a body through which the resultant of the gravities (or weights) of its parts passes, in every position the body can assume. The centre of gravity of two weights, or areas, A, B, placed I distance apart, will be x distance from A when B_ = FUNDAMENTAL PEINCIPLES. 15 The centre of gravity # of a number of bodies in a straight line with regard to any point A at one end of line, W being the weight, and y the distance of W from A, Ax W + W x + W 2 + &c. Bodies in same plane but not in same line must be re- ferred to co-ordinate axes. Bodies not in same plane must be referred to co-ordinate planes. The centre of gravity is not necessarily situated in the solid portion of a body, or enclosed by its surfaces, it is simply the mean central point of the mass. 28. CENTROID, OR CENTRE OF GRAVITY OF FORM. Triangle. Bisect two sides, draw to opposite angles, inter- section = e.g. Trapezium. Divide into two triangles, find e.g. of each and join them. Divide into two triangles in the other direction, find e.g. of each and join them. Intersection of e.g. lines = mean e.g. Tapered Girder Web. t = thickness top, b = bottom, h = height. Height of e.g. = J Retaining Wall, vertical back. Height of e.g. = %h(l + - Distance of e.g. from face to foot = . o o (t -j- v) Tee-Iron . a = area lower part. A= upper d = total depth. t thickness. Height of e.g. from lower edge = J ( d + t ~ ). \ A -f- o,/ 16 HANDBOOK FOR MECHANICAL ENGINEERS. 29. CENTRE OF GRAVITY OF REGULAR SOLIDS. Pyramid . . . . = J height from base. Cone . = J Paraboloid . . . = ^ Hemisphere . = f Hemispheroid . = f Semicy Under . . . = 4244 of its radius from axis. Segment of disc or of \ chord 3 > = = distance cylinder . 12 area Sector of do chord x radius = do arc 30. CENTROBARYO THEOREM (TOMLINSON). The volume of a " solid of revolution " is equal to the area of its generating plane X the circumference described by the centroid of this plane during revolution. In other words, a = area of semi-section parallel with axis ; r = radius or distance of e.g. of semi-section from axis ; Then contents = 2 TT r a. This may be used in finding the weight of iron vases, caps and bases of columns, oval counterweights, &c., when great accuracy is desired. 31. CENTRIFUGAL AND CENTRIPETAL FORCE. A body in motion resists any force tending to make it deviate from a straight line. When the body is rotating, the particles are constrained to move in circular paths. The inertia of the mass resists this constraint and produces tension acting outwards from the centre of rotation. The inertia is in this case called centrifugal force, and the tension centripotal force. FUNDAMENTAL PRINCIPLES. 17 32. CENTRIFUGAL FORCE is the amount required to restrain a body, or part of a body, travelling in a circle, from flying off at a tangent, and is perpendicular to the curve or tangent at each point. The centrifugal force varies as the square of the angular velocity into the radius of the centre of gravity of the section on one side of axis. Centrifugal force in absolute units = m v"/r, in gravita- tion units = W v 2 /g r. Centrifugal force from the earth's rotation acts in oppo- sition to gravity at the equator, and diminishes towards the poles, where it is entirely absent. 33. CENTRE OF GYRATION is that point in a revolving body, at which, if the whole mass were collected, the accumulated work per revolution would remain the same. It is also such that the same angular velocity would be generated in the same time by a given force at any place as would be generated by the same force acting similarly on the body itself. It is measured from the centre of revolution and gives the " radius of gyration." Circular wheel, uniform thickness = r J ^ = -7071 r. Rod revolving about its extremity = I tj . centre . = I ]j T V Fly wheel rim . = / R2 + r V 2 Solid sphere = r J f = 6325 r. Wire ring, revolving about a diam. = r *J . Thin circular plate = 5 r. Thin hollow globe . . . = r J f = -8165 r. Solid sphere revolving round an^| external axis at c distance from > = V e 2 + -f r 2 . centre of sphere . . } Cylinder round its axis . . = r *J J. parallel external axis = *J & _j_ i r z c 18 HANDBOOK FOB MECHANICAL ENGINEERS. 34. VIBRATION AND OSCILLATION. The vibration of a pendulum is the movement from one extreme of its position to the other. The angle formed by the extreme positions is called the amplitude of the vibration. The duration of a vibration is the time occupied in passing through this angle. The beat of a pendulum corresponds to one vibration. An oscillation is a completed cycle, or two vibrations, permitting a return to the starting point. Length of a pendulum in London, in inches, to give any required number (w) of vibrations per minute 140,901-48 35. CENTRE OF OSCILLATION is that point in a vibrating body, in which, if the whole mass were collected, the body would continue to vibrate through the same angle ; and such that any force applied there would generate the same angular velocity in a given time as the same force at the centre of gravity, the parts of the body or system revolving in their respective places. The distance from the point of suspension is equal to the length of a simple pendulum vibrating in the same time. The time of vibration of a simple pendulum = v X \/ .. vibration varies as ^/l. Length of London seconds pendulum = 39-1393 inches. r = radius to centre of gravity. B = gyration. K! = oscillation. FUNDAMENTAL PRINCIPLES. 19 The centre of oscillation is interchangeable with the centre or point of suspension, which then becomes the centre of oscillation. 36. PENDULUM. The formula for a clock pendulum is derived from that for a conical or revolving pendulum, as when the amplitude is small the bob will take the same time to make one revolu- tion as to go straight across the circle and back again. The revolving pendulum forms a cone in space, the sloping side being length of pendulum, say Z, the height, say A, and the radius of base r. There will be three forces acting on the bob the weight acting downwards, the centrifugal force acting horizontally, and the tension of the rod in the direc- tion of the slope of cone. These forces will be in proportion to the three sides of the triangle h, r and I ; hence denoting the centrifugal force by C, we get A : r : : W : C. Now the centrifugal force will be x mass, or , where v is the h a r q r 2 velocity in feet per second ; hence = ^- , or h = ^-^ Now suppose the bob makes one revolution in t seconds, then . , . distance in one revolution it goes a distance 2 TT r : then, as : time 9 TT V = velocity, we get v = ; substitute this value of v in I the equation for h, and we get, after cancelling the r's, Ji = ^ ^ , from which t = 2 TT */ - . When the amplitude is small, A and I may be taken as equal, so that for a clock pendulum each double beat will be done in 2 ?r . / - V g seconds. M.I.C.R, Bath. c 2 20 HANDBOOK FOE MECHANICAL ENGINEEKS. 37. CENTRE OF PERCUSSION is that point in a body revolving about an axis, at which, if it struck an immovable obstacle, all its motion would be destroyed, or it would not incline either way : it is that point with which, if the body strike against any obstacle, no shock will be felt at the point of suspension : it is the same point in a body as the centre of oscillation. 38. CENTRE OF SPONTANEOUS ROTATION, or spontaneous gyration, is that point which remains at rest when a body is struck, or about which it begins to revolve. 39. TRANSMISSIBILITY OF FORCE. Any force acting in a plane may be considered as acting at any point in its line of direction. This is called " the prin- ciple of the transmissibility of force." 40. PARALLELOGRAM OF FORCES. If three forces act in a plane upon a free point which remains at rest, they may be represented in direction and magnitude by three lines, two of which form adjacent sides of a parallelogram and the third is equal and opposite to the diagonal. 41. EQUILIBRIUM OF FORCES. Forces acting upon a body at rest, but free to move, are said to be in equilibrium. 42. SENSE OF FORCES. The word sense is used to assist the word direction in deal- ing with forces ; direction may be looked upon as relating to the position of tlie line, and sense as relating to the position of the arrow-head with regard to the line. FUNDAMENTAL PRINCIPLES. 21 43. TRIANGLE OF FORCES. The three lines described under " parallelogram of forces " will also form a triangle, the arrow-heads pointing all the same way round. 44. POLYGON OF FORCES. When more than three forces in one plane acting upon a point are in equilibrium they may be represented in magni- tude and direction by lines forming a closed polygon. More fully denned in next paragraph. 45. FORCE POLYGON. When forces acting upon a point are represented by con- current lines to form a polygon, open or closed, part of which may overlap other parts, it is called the force polygon, and when unclosed requires a closing line, representing a new force, known as the equilibrant, to balance the remainder. The resultant of a number of forces is equal and opposite to their equilibrant. The resultant of any number of forces does not depend upon the order in which they are drawn as the sides of the polygon, provided their senses are concurrent. 46. LINK POLYGON. When forces act together in a system but not through one point, their leverage or turning moment through a point or pole is found by means of the link polygon or funicular polygon of the forces, which gives the position of the resultant force, otherwise unattainable. The link polygon is obtained by drawing the force polygon and selecting any point (internal or external) for a pole, drawing lines from the pole to the junctions of the sides of the force polygon, and constructing a new polygon with sides parallel to these lines, commencing at any point on one of the 22 HANDBOOK FOE MECHANICAL ENGINEERS. force lines in its original position, and each side terminating upon meeting the direction of the next force, at which point the next side will commence. The resultant force passes through the last intersections, the direction, sense and magnitude being taken from the force polygon. 47. COMPOSITION AND RESOLUTION OF FORCES. Composition of forces takes place when a resultant is substi- tuted for two or more component forces. Eesohtion of forces takes place when a single force is replaced by two or more forces equivalent to it, and is the reverse of the former case. 48. MOMENTS. The moment of any physical agency is the numerical measure of its importance. Thomson and Tail. In mechanics, a moment is generally the product of a force into a leverage. 49. MOMENT OF A FORCE. The product of a force and the perpendicular distance of its direction from any given point, is termed the moment of the force about that point. The moment of a resultant about any point is equal to the sum of the moments of the compo- nents about that point. The term pound-feet would be preferable for moments in leverage to avoid confusion with foot-pounds of energy, both being feet X Ibs. but not acting alike. Pound-feet would then belong to statics and foot-pounds to dynamics. 50. PRINCIPLE OF THE EQUALITY OF MOMENTS. When a body is in equilibrium the sum of the moments of any number of forces that tend to turn the body in one FUNDAMENTAL PRINCIPLES. 23 direction is equal to the sum of the moments of any number of forces that tend to turn the body in the opposite direc- tion. 51. PRINCIPLE OF LEAST EESISTANCE. Moseley (1833). "If there be a system of forces in equilibrium, among which are a given number of resistances, then is each of these a minimum, subject to the conditions imposed by the equilibrium of the whole." Used in finding line of resistance in arches, &c. 52. COUPLES. Two equal and opposite forces acting upon a body, parallel but not in the same line, tend to cause rotation, and are called " a couple." The moment of a couple is one of the forces multiplied by the distance between their lines of action, or the two forces X radius to centre on which they would rotate (i.e. half the distance between their lines of action). A couple can only be equilibrated by another couple tending to cause rotation in the opposite direction and having an equal moment. 53. CLASSIFICATION OF MECHANICS. Mechanics of Known as g Y -i ( Statics, Dynamics, Kinematics, t Kinetics. Liquids or non- C Hydrostatics, Hydrodynamics, elastic fluids . { Hydraulics, Hydrokinetics. Gases or elastic ) a ] t .Pneumatics, Aerostatics, fluids . .3 54. STATICS AND DYNAMICS. Statics is the science of forces in equilibrium, or pressures. Dynamics or kinetics is the science of forces not in equi- librium, i.e. those producing motion. 24 HANDBOOK FOR MECHANICAL ENGINEERS, 55. THEORY OF MACHINES, Machines are mechanical arrangements for transmitting force and utilising it in a convenient manner. Power is a constant sum consisting of pressure and movement, or force and velocity, either of which may be increased with a corre- sponding reduction of the other. The common phrase, " what is gained in power is lost in speed," would be less liable to misapprehension if the word pressure were substituted for power. " A machine is an appliance by means of which energy is transferred from one point to another." 56. MECHANICAL POWERS. A Mechanical Power is any simple arrangement by which a small force can overcome a greater, and Mechanical Ad- vantage* is the ratio of the greater force to the less. The Mechanical powers are more properly called Mechanical Elements, or Simple Machines. They are commonly described as seven, but all referable to two of the number, thus : Lever : Wheel and axle "\ Toothed wheels > Modifications of the lever. Pulley . . J Inclined plane : Screw \ Modifications of the inclined plane. 57. THE LEVER, WHEEL AND AXLE, AND TOOTHED GEARING. Three orders; fulcrum, weight and power, alternately between the other two, principle identical. * For definition of Mechanical Efficiency, see par. 274. FUNDAMENTAL PRINCIPLES. 25 or, taking weight of lever into account, p x = Wy + W'y'. In bent levers the length is measured from the fulcrum on a perpendicular to the direction of the force. Wheel and Axle. Same principle, taking radius as leverage. Toothed Gearing. Ditto. 58. THE PULLEY. n = number of cords shortened by raising the weight. = P, or motion of W : motion of P : : P : W. n Pulleys are sometimes divided into three systems as follows : First system. Each cord has one end fixed and the other passed round a running sheave. The last cord passes over a fixed sheave. Second system. Sheaves contained in a pair of blocks, cord passing from strop of upper block round sheave in upper and lower block alternately. Third system. All cords connected at one end to load, the other end of the first passes over a fixed sheave to strop of a running sheave, second cord passes over this running sheave to strop of next, and so on. Last cord passes over running sheave to the hand. Similar to first system, but inverted. 59. BLOCK-AND-TACKLE, OR PULLEY GEAR. A Hock is the frame in which the wheels, pulleys, or sheaves are secured by means of the pivot, axle or sheave pin. The rope or chain passing over the sheaves, or reeved through the blocks, is called a fall. A combination of blocks, sheaves 26 HANDBOOK FOB MECHANICAL ENGINEERS. and fall is called a tackle. A tacWe containing more than one rope is called a Spanish barton. Snatch blocks are blocks containing one sheave and a movable side permitting the bend or bight of a rope to be inserted to change its direction or lead. 60. THE INCLINED PLANE, WEDGE AND SCREW. Inclined Plane. L:H:: W:P .-. P = 5-W. Li Wedge. L : t : : W : P (P being direct pressure without friction). Percussion and friction must be considered in any practical calculation. Screw. E = radius of lever, p = pitch of screw. 27rK :p:: W : P. Differential Screw. 2 TT E : p' - p : : W : P. Hunter's differential screw obtains an extremely slow movement without employing too fine a thread, by means of the difference in pitch between two threads on the same cylinder ; it is used for micrometer screws. Endless Screw or Worm. N = number of teeth in wheel. n = threads in worm. K = radius of handle or power. r = axle or weight. EN: rn:: W : P. FUNDAMENTAL PRINCIPLES. 27 An endless screw is a coarse thread of short length formed upon an axle and geared -tangentially into a toothed wheel called a " worm wheel." When the endless screw consists of one thread, each revolution moves the wheel one tooth, and a double thread moves the wheel two teeth for one revolution . of the screw. 61. STEELYARDS AND WEIGHING MACHINES. Roman Stater a. Lever of first order, balance-weight movable. Common Steelyard. Similar, but with two fulcra on opposite sides of beam, and two corresponding sets of divisions. Danish Balance. Fixed balance- weight at one end, fulcrum movable. Common Balance or Scales. Arms equal, substance counterpoised by equivalent loose weights. Bent Lever Balance. Fulcrum fixed, counterbalance con- stant, virtual length of arms altered by movement due to weight of substance. Spring Balance. Weight indicated by amount of tension or compression upon a spring. Poolers Weighing Machine. System of compound levers on principle of Eoman Statera. Armstrong Crane Steelyard. Lifting chain passing over pulley on short arm of steelyard, small weights hung to end of long arm, fractional weights coupled together with loose joints so that balance is automatically obtained when suflicient number are lifted. Duclcham's Weighing Machine. Weight indicated by increase of pressure upon liquid enclosed in cylinder hung on lifting chain, weight being hung from piston rod. Shapton's Hydrostatic Weighing Machine. Similar in prin- ciple to Duckham's, but pressure induced by lifting chain passing over sheave on piston rod, instead of load being hung direct. 28 HANDBOOK FOE MECHANICAL ENGINEEKS. 62. USEFUL WORK OF MEN IN FOOT-POUNDS PER MINUTE. Working for 10 hours per day. 8 hours per day. 6 hours per day. 4250 3900 Drawing or pushing horizontally . .. 3120 .. vertically . M 2380 .. 2600 4000 Wheeling material on ramp .... 720 .. Throwing earth up 5 feet .... 470 .. .. Raising material with pulley .. .. 1560 hands .. .. 1470 Carrying do. on back, returning empty 1126 63. COMPARISON OF ANIMAL POWER. Horse . Mule = f horse Ass = 1 Man = 22,000 ft.-lbs. per minute. 14,667 4,400 2,200 64. FORMULA FOR FALLING BODIES. h = Height of fall in feet. toughness, &c. . gun barrels, and for tools ] requiring the greatest > degree of toughness . J Percentage Carbon. Prof. Eggertz' method. . 1-55 to 2-00 . 1-45 1-55 . 1-25 1-45 . I'lO 1-25 . 0-90 1-10 0-75 0-90 0-40 0-75 101. RELATIVE PIG-!RON AND STEEL PRODUCTION OF DIFFERENT COUNTRIES. Pig Iron. Steel. tons. tons. Great Britain . 7,750,657 1,988,045 United States . 4,044,526 1,711,920 Germany and Luxembin g 3,751,775 1,200,000 France . 1,628,941 527,048 Austria and Hungary 760,000 225,752 Belgium 714,677 146,189 Russia 498,000 300,000 Sweden 430,504 74,241 Spain 126,269 10,000 Italy 24,778 3,450 All other countries 150,000 30,000 Martineau and Smith. VARIETIES AND PROPERTIES OF MATERIALS. 47 102. NOTES ON CAST IRON. Stronger in compression than wrought iron, but much weaker in tension. Not so safe as wrought iron when subjected to impact or suddenly applied loads. Used for complex parts of machines, because easier to mould in casting than wrought iron in forging. Principally for wheels, bed-plates and framings. If thickness of different parts varies much, the castings will be strained in cooling. All edges should be well rounded and hollows filleted. Expands at moment of solidification in casting, but con- tracts in cooling. Contraction varies with size and thickness of casting, and quality of metal. 103. QUALITIES OF CAST IRON. No. 1. Grey. Soft. Deficient in strength. Used for ordinary castings. Very fluid when melted. 0-6 to 1-5 per cent, carbon chemically combined, 2-9 to 3 * 7 per cent, mechanically combined. No. 2. Mottled. Variable hardness. Stronger than No. 1. Used for larger castings. More carbon chemically combined, and less mechanically. No. 3. White. Hard. Fusible. Strong. Used for con- version into wrought iron. 3 to 5 per cent, of carbon all chemically combined. These varieties are mixed in various proportions for special purposes. -^-Unwin's 'Machine Design.' 104. CHILLED AND MALLEABLE CAST IRON. . Chilled Cast Iron is ordinary cast iron rapidly cooled during solidification, by using a mould of white or hard cast 48 HANDBOOK FOR MECHANICAL ENGINEERS. iron for the part requiring to be chilled, protected by a wash of loam, causing a chemical combination of the molten iron and carbon. Very hard. Fracture silvery. Direction of crystallisation strongly marked. Malleable Cast Iron is made by heating ordinary castings, preferably of white cast iron, from two to forty hours, ac- cording to size, in contact with oxide of iron or powdered red haematite, causing partial conversion into wrought iron by abstraction of carbon. 105. TOUGHENED CAST IRON. Toughened cast iron is produced by adding to the cast iron, and melting amongst it, from one-fourth to one-seventh of its weight of wrought-iron scrap, which removes some of the carbon from the cast iron, and causes an approximation to steel. ' Notes on Building Construction,' iii. 252. 106. COPPER. Very malleable, and hence specially suited for hammering into thin hemispherical pans, rolling into sheets, &c., also ductile to a less degree. Eendered brittle by absorption of carbon, refined and toughened during manufacture, but may be spoilt again by careless manipulation. May be cast. Can be forged cold, or at red heat, but rapidly scales when hot. Addition of 2 to 4 per cent, of phosphorus improves its fluidity and tenacity. Used for fire-boxes, &c., because it is a good conductor of heat, but loses tenacity in proportion to its temperature. Much used in forming alloys. 107. ALUMINIUM. Aluminium, by the Deville-Castner process, is made at a third of its former price, and for many of the lighter parts of VARIETIES AND PROPERTIES OF MATERIALS. 49 mechanism or delicate machinery may shortly become a sub- stitute for the more common metals, as it does not tarnish even when exposed to damp and impure air. 108. ALLOYS. Bronze is a mixture of (say) 10 copper, 1 tin. Brass is a mixture of (say) 2 copper, 1 zinc. The terms " higher " and " lower " applied to brass ex- press the greater or less quantity of zinc in the composition. High brass consists of 2 copper to 1 zinc. Low brass 4 copper to 1 zinc. Gun-Metal is a mixture of copper, tin and zinc in various proportions, according to the hardness or toughness required : say 16 copper, 2 tin, 1 zinc. May be also called bronze. Muntz-Metal is a mixture of 3 copper, 2 zinc, and is there- fore a brass. Alloys generally fuse at a lower temperature than the average of the component metals. 109. EFFECT OF ALLOYING WITH COPPER. Tin increases the hardness, and whitens the colour through various shades of red, yellow and grey. Zinc in small quantity increases fusibility without reduc- ing the hardness, in greater quantity increases malleability when cold, but entirely prevents forging when hot ; 1 to 2 per cent, of zinc enables sounder castings to be made. Lead increases the ductility of brass, and makes alloy more suitable for turning, filing, &c. ; in large quantity causes brittleness. Phosphorus increases the fluidity and tenacity, reduces the effect of the atmosphere, and allows of tempering. It also produces sounder castings. E 50 HANDBOOK FOR MECHANICAL ENGINEERS. 110. BRONZE ALLOYS. Name. Copper Tin. Zinc. 16 1 Mathematical instruments 12 1 \\ Pumps (very tough) 32 3 "l Pump plungers . . . . 14 1 1 Small toothed wheels . . . 10 1 . . Locomotive bearings . ... 64 112 7 13 1 Locomotive straps and glands Admiralty mixture for valves and mount 130 16 I 4 ings 90 10 2i Hard gun-metal for bearings . . 8 1 .. Baily's metal 32 5 2 G.M. for heavy bearings 32 5 1 Maximum hardness for bearings . 5 1 . Hydraulic valve faces .... 4 1 . Tam-tam (Chinese gongs) . 4 1 , Bell metal 4 or 3 1 , Speculum metal . . 2 1 111. BKASS ALLOYS. Name. Copper. Zinc. Tin. Lead. Tough for engine work 100 15 15 For turning and fitting 3 1 . , A Soft for hammering 7 3 M Yellow brass . 2 1 , . Stop-cocks and valves . 88 10 2 ; ( Rolling-stock bearings . v 77 .. 8 15 Flanges for brazing 32 1 .. 1 Brass for soldering 8 3 Brass, various . . 60-92 8-40 J-3 i-3 Muntz-metal sheathing 3 2 Do. locomotive tubes 66 33 . . "i Nails for sheathing 87 4 9 M Statuary bronze . 90 5 2 1 1 Red brass (Tombak) . 8-10 1 M lt Red sheet brass (German) Bronze for lamps . 11 27 2 6 "i 'i VAEIETIES AND PEOPEETIES OF MATERIALS. 51 112. ANTIMONY ALLOYS. Name. Copper. Tin. Lead. Antimony. Bismuth. Babbitt's metal 1 10 1 lining do. 1 24 2 .. Antifriction do., hard 1 50 5 . , soft 81-88 12-19 Expanding alloy . .. 2 1 Pewter . 100 17 Type metal . 3-7 1 .. Stereotype metal . j >- White brass . i' 77 7 15 7 8 Do. . 3 90 7 Alloy contracting when\ heated . . ./ 1 1 2 113. NICKEL ALLOYS. Name. Copper. Zinc. Nickel. Iron. Common German silver . 60 25 15 Better . . 50 25 25 Chinese Packfong. 55 17 23 3 Argentan, for hammering orl rolling / 40'4 25-4 31-5 2-6 Argentan, for plating . 62 19 13 4-5 hard .... 57-4 25 13 9 Electro 2 - . 8 3-5 4 Solder for German silver (coarsely ) powdered) ) 8 7-5 4 E 2 52 HANDBOOK FOE MECHANICAL ENGINEERS. 114. VARIOUS ALLOYS. Name. Copper. Tin. Zinc. Various. Silver-bell metal . 80 10 6 4 lead. Pot or cock metal ..:. V ft , . .. 2 lead. Ship nails . , , 10 tl 8 1 iron. Cowper's metal Aluminium bronze . 90 2 1 bismuth. 10 aluminium. Sterro-metal . . . 60 "2 35 3 wrought iron. Gedge's metal 60 .. 38-2 1-8 Delta metal . 55 3 411 (1 lead, 1 iron, \ f manganese. Phosphor bronze 82 10 i : I7J lead, i iron, i nickel -i- phosphorus. Common pewter . . .. 83 .. 17 lead. British coinage Bronze 95 4 i Silver . ". . . 7| ^ 92^ silver. Gold . , .' ... v--= 91| gold. 115. FUSIBLE ALLOYS. Melting-point. Lead. Tin. Bismuth. Zinc. Corresponding Absolute Steam Pressure.* deg. F. Ibs. 212 1 3 5 . 14-7 246 1 4 5 28 286 M 1 1 , 54 334 2 1 . 110 336 2 3 M ( 112 392 rt 8 1 . 230 . 442 ft 1 ^ , ^ 472 t p 1 , p< 612 1 ip tt ( t> 648 V i' * This column is added to make the table useful for adjusting the composition of fusible safety plugs for boilers. VABIETIES AND PKOPEKTIES OF MATERIALS. 53 116. ALLOYS FUSIBLE BELOW 212F. Melting-point. Lead. Tin. Bismuth. Zinc. Mercury. Cadmium. 212 5 3 8 210 4 3 8 203 31 19 50 , 1 1 200 1 1 4 g 149 28-5 17 45-5 9 138 8 4 15 3 117. SOLDERS. Name. Tin. Lead. Copper. Zinc. Plumbers' fine solder . coarse Tinmen's fine solder coarse . . Spelter hard 1 1 3 2 1 3 1 1 3 2 soft 1 1 118. MELTING-POINTS OF VARIOUS METALS, Platinum '\ Wrought iron Steel . Cast iron Copper . Gun-metal Yellow brass . Aluminium . Antimony Zinc . . , Lead deg. F. . (?) 8500 3250 to 4300 3250 to 4100 2200 to 2750 . 2000 . 1900 . 1850 . 1800 . 810 . '. 750 620 54 HANDBOOK FOR MECHANICAL ENGINEERS, MELTING-POINTS continued. deg. F. Bismuth .... 480 Tin ..... 440 Wax . . . . ,150 Tallow . . . 100 Water 32 Mercury . . . 38 When a substance J ex P ands I i n the act of fusion, the (contracts) solid parts will < ^ i in the liquid. Such substances have I rise I their temperature of fusion < , , > while under pressure. (lowered} Example f^st iron) (. water 3 119. EXPANSION OF METALS BY HEAT. In fractions of each dimension for one degree Fahrenheit. Wrought iron Cast iron > / 00001235 00001127 Steel . Brass , 00001145 00001894 Copper . Lead . 00001717 00002818 Platinum . Glass , 00000884 00000861 Perry. Water expands ^ of its bulk from 32 F. to 212 F. From 32 F. to 572 F. iron expands ^, copper T ^. For a rise of temperature of 10 F. Iron expands about Copper Brass VARIETIES AND PROPERTIES OF MATERIALS. 55 120. WEIGHT OF VARIOUS METALS IN POUNDS. Name. Cubic Inch. Cubic Foot. Gold 70 41 1203 710 Copper 32 31 550 530 Brass 30 29 525 510 Steel 28 490 Wrought iron Tin . Cast iron 28 26 26 480 460 450 Zinc . , . . 25 435 Aluminium 09 160 121. MULTIPLIERS TO REDUCE CUBIC FEET TO TONS. Wrought iron Steel . 5 =; Cast iron 2143 2175 2009 122. USE OF WOOD IN ENGINEERING. Pattern-making. American yellow pine, New Zealand pine, mahogany, alder, sycamore. Bearings. Lignum vitee (end grain). Brake Blocks. Willow, poplar. Pulley Sheaves. Lignum vitas, box. Buffer Beams. Oak. Cylinder Lagging. Teak, mahogany, oak. Floats for Paddle-wheels. Willow, American elm, English elm. Sluice Paddles. Oak, greenheart. Wheel Teeth. Hornbeam, beech, holly, apple, oak if in damp place. Joiners' Tools. Beech, box. 56 HANDBOOK FOR MECHANICAL ENGINEERS. Hammer Shafts. Ash (cleft). Tool Handles. Ash, beech. Shafts and Springs. Ash, hickory, lancewood. Ordinary framing, piling, &c. Yellow deal, Memel, Riga, or Dantzic (creosoted for outdoor work). Carriage-building. -Teak. Fender and Rubbing pieces. American elm. Scaffold Poles. Spruce fir. Earth Waggons and Barrows. Elm. Hough Gangivays. White deals. 123. Fm, DEAL AND PINE. Fir is a general term for wood used in the rough as distinguished from Deal, a general term for wood wrought and used by the joiner. Pine is another general term used for even grained stuff suitable for panels. Also for pitch pine. Yellow deal and red deal are botanically classed as pine. White deal and spruce deal are botanically classed as fir. Deal is not a botanical term. Planks, deals and battens, and narrow battens are trade terms for boards of certain widths, viz. planks 11 inches, deals 9 inches, battens 7 inches, narrow battens 4J inches. 124. PRESERVING IRONWORK. Painting. Red lead paints are on the whole most suitable, with a little white lead in the first two coats to permit of the paint being worked well into the corners; good raw linseed oil only should be used to mix them for use. Iron oxide paints are cheaper than lead. Coal tar may be used for rough ironwork, underground pipes, &c. ; the tar being heated and J Ib. to 1 Ib. finely sifted slaked lime added per gallon of tar, with sufficient naphtha to thin it for laying on. It must be used hot, but not kept on the fire too long. VARIETIES AND PEOPERTIES OF MATERIALS. 57 Bower-Barff Process. This is specially suited io small pieces exposed to the weather, but not to blows, e.g. rain- water gutters, sanitary fittings and pipes. The articles are raised to a red heat (say 1200 F.) and subjected for some hours (say 6 to 12), to the action of superheated steam, which causes the deposit of a coating of black oxide of iron. It will not stand riveting. Dr. Angus Smith's Composition. The original recipe was " 30 gallons coal tar, 30 Ibs. fresh slaked lime, 6 Ibs. tallow, 3 Ibs. lampblack, 1J Ibs. resin, to be well mixed, boiled twenty minutes and put on hot." The present mixture and method of use vary, but the following may be taken as a good average for dipping cast-iron pipes. For say 2000 miscellaneous pieces (pipes, bends, branches, &c., 3, 4 and 5 inch diameter). Take 7 barrels coal tar, 1 barrel coal oil, and 1 barrel pitch, with 12 tons gas coke for heating them. Provide a wr ought-iron tank about 12 feet long so as to take a 9-foot pipe, put in sufficient coal tar to half cover a pipe, upon this sprinkle the proportion of pitch beaten to a powder, and pour the coal oil on the pitch. Clean the pipes thoroughly, make them as hot as the hand can bear, and turn them over in the liquid for two or three minutes, then place them at an angle to drain. For better work use linseed oil instead of coal oil, in- crease the temperature of the pipes to 500 to 700 F., or until plumber's solder will melt when pressed against them, and leave them in the liquid for ten minutes after turning them over. 58 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION III. STRENGTH OF MATEEIALS AND STRUCTURES. 125. CLASSIFICATION OF STRAINS.* Tension , ,-' ,- . Stretching or pulling Compression. , . Crushing or pushing. Transverse Strain . . . Cross strain or bending. Torsion .... Twisting or wrenching. Shearing . \ Cuttin ' r wlien actin g alon S I the grain of timber, detrusion. 126. DEFINITIONS OF STRAIN AND STRESS. Strain. Every load which acts on a structure produces a change of form, which is termed the strain due to the load. The strain may be temporary or permanent, the former disappearing when the load is removed, the latter remaining as permanent set. Stress. The molecular forces, or forces acting within the material of a structure, which are called into play by external forces, and which resist its deformation, are termed stresses. Unwinds * Machine Design.' Thus the strength of a piece in a given position may be such that a load of so many Ibs. produces a stress of so many Ibs. per square inch, the result being a strain, or change of form of a certain amount, whether temporary or permanent, * See the author's ' Strains in Ironwork.' Spon, 5s. STRENGTH OF MATERIALS AND STRUCTURES. 59 and, when large enough, appearing as stretching, shortening, bending, crumpling, or twisting. Intensity of stress is the pressure per unit of surface, or stress per unit of sectional area. 127. PROOF STRENGTH. It was formerly supposed that the proof strength of any material was the utmost strength consistent with perfect elasticity ; that is, the utmost stress which does not produce a permanent set. Mr. Hodgkinson, however, has proved that a set is produced in many cases by a stress perfectly con- sistent with safety. The determination of proof strength by experiment is now, therefore, a matter of some obscurity ; but it may be considered that the best test known is, tlie not producing an increasing set by repeated application. Rankings ' Applied Mechanics' 128. FACTOR OF SAFETY is an amount fixed by practical experience, varying with the material used, and the manner of using. It is the ratio of the greatest safe stress to the ultimate resistance of the material, such as J, y 1 ^, &c. ; and the calculated resistance of any section, multiplied by the factor of safety suitable to the circumstances, will give the safe working load. If structures never deteriorated they might be loaded to one- third of their breaking weight with perfect safety, but to guard against ordinary contingencies one-fourth of the breaking weight is the maximum permanent load allowable under any circumstances. The factor of safety is usually given in its reciprocal form as 4 or 4 to 1, &c., meaning that the ultimate calculated resistance is four times the working load, thus _ Breaking load Factor of safety = T , r . . -. j . Working load 60 HANDBOOK FOE MECHANICAL ENGINEERS. 129. TESTING WROUGHT IRON.* The strength of a bar should be measured by the work done in producing rupture, i.e. the product of the elongation into the mean stress. A convenient approximation to relative toughness is obtained by observing the maximum stress and the elongation in a given length. The length formerly taken was 8 inches, but 6^ inches is now frequently adopted, so that the increase of length in sixteenths of an inch will represent the elongation per cent. The elongation being principally local, the percentage specified for a length of 8 inches X f- or 1 28, will give the proper percentage for a length of 6 inches. 130. TESTING CAST IRON. " The best and most certain test of the quality of a piece of cast iron is to try any of its edges with a hammer ; if the blow of the hammer make a slight impression, denoting some degree of malleability, the iron is of good quality, provided it be uniform ; if fragments fly off and no sensible indentation be made, the iron will be hard and brittle. The utmost care should be employed to render the iron in each casting of an uniform quality, because in iron of different qualities the shrinking is different, which causes an unequal tension among the parts of the metal, impairs its strength, and renders it liable to sudden and unexpected failures. When the texture is not uniform, the surface of the casting is usually uneven where it ought to have been even. This unevenness, or the irregular swells and hollows on the surface of a casting, is caused by the unequal shrinkage of the iron of different qualities." Tredgold. * See leaflet by the author on * The * Behaviour of Materials under Strain/ STRENGTH OF MATERIALS AND STRUCTURES. 61 131. SPECIFICATION TESTS OF CAST IRON. Three bars, each 3 feet 6 inches long, 2 inches deep and 1 inch wide, to be cast on edge in dry mould from each melting at which any of the specified work is cast. These bars to be tested separately as follows : The lower side, or thin edge, of the casting to be placed downwards* upon rigid bearings, with 3 feet clear span, each bar to deflect not less than T 3 Q inch with a load of 25 cwt. in centre having a bearing not more than 1 inch wide upon the bar, to break with a minimum load of 28 cwt. and an average upon the three bars of not less than 30 cwt. Samples prepared in lathe to bear 2J tons per square inch tensile strain before loss of elasticity, and to break with not less than 7 tons per square inch, or an average on three samples of 7^ tons. Test bars are sometimes cast as projections from an important casting and broken off for testing, but this is a bad method, and gives 10 to 20 per cent, lower results. 132. TESTS OF CAST IRON FOR PIPE-MAKING. " A bar of metal 40 inches long, 2 inches deep and 1 inch wide, the weight of which must not exceed 21 Ibs., shall, when supported on edge at points 36 inches apart, sustain a load of 3000 Ibs. supported at the middle of its bearing for one hour, and shall under this load deflect at least -f inch at the middle ; and a bar 8 inches long and 1 inch square in section shall sustain a load of 8 tons tensile stress for one hour." Note. The test bar should deflect -^ inch with 10 cwt., and recover its position when the load is removed. See also par. 602. * Placed the other way up a reduction of 15 to 20 per cent, in the apparent strength may occur. 62 HANDBOOK FOR MECHANICAL ENGINEERS. 133. USUAL ALLOWANCE FOR DEAD LOAD PER SQUARE INCH SECTIONAL AREA.* Breaking S ' rain. Safe Load. WROUGHT IRON tons tons Tension 22 5 Compression . Shearing 18 20 4 4 MILD STEEL Tension . . v 28 7 Compression . 25 5 Rivets in shear . 24: 6 CAST STEEL Tension . j, . 35 8 Compression . 50 12 CAST IRON Tension 7 9 Compression . 42 7* Shearing 14 2* The compression and shearing values assume that the parts are unable to bend. 134. MAXIMUM WORKING STRENGTH IN TONS PER SQUARE INCH. Constant Load. Variable Load. Wrought Iron for Machinery. Tension only 5. Compressn. only 4. Tension only 3. Compressn. only 2. Alternate Tension and Compression la- Mild Steel for Machinery. Tension only 8. Compressn. only 12. Tension only 5. Compressn. only 7J. Alternate Tension and Compression 2*. Cast Iron for Machinery. Tension only H- Compressn. only 6, Tension only Compressn. only 4*. Alternate Tension and Compression t- * See paper by the author on ' Strength of Iron and Steel/ Demy 8vo, 16 pp. and folding plates. Spon, 6rf. STRENGTH OF MATERIALS AND STRUCTURES. 63 135. ULTIMATE STRENGTH OF VAKIOUS METALS AND ALLOYS, Name. Tension. Tons per sq. inch. Compression. Tons per sq. inch. 27 Aluminium bronze . . * 25 50 Phosphor bronze 25 40 Delta metal ...,. 23 20 Malleable cast iron . . .-' 15 45 Copper (wire). . ".. . 25 .. Copper (sheet and bolt) - * 15 40 Copper (cast) . . . . , * 10 Gun metal . . . . , . 12 48 Brass 10 25 Zinc . . . . . . 3 15 Tin ... ... 2 6 Cast lead . . . 11 3 136. COMPARATIVE STRENGTH OF IRON AND STEEL PLATES. Ultimate Tensile Strength in tons per sq. inch. Elongation per cent. Quality. With Grain. Across Grain. With Grain. Across Grain. Mild steel . 30 28 20 18 Best Yorkshire 24 22 12 7 B. B. Staffordshire . 22 19 9 5 B. 20 18 6 2* HANDBOOK FOR MECHANICAL ENGINEERS. 137. TESTS OF IRON AND STEEL. PHYSICAL. Brand. Point of Permanent Set in tons per Tension in tons per square Elongation per cent. square inch. Lowmoor . . . . . - . 25-50 42-15 Staffordshire 16-82 25-57 27-50 Mild steel . . . : : . 17-92 28-86 45-00 Medium steel . . . 20-87 33-25 35-92 Hard steel . . ..'.' 25-60 39-84 30-50 Tool steel . . . . tt 57-68 14-40 Very hard steel . ...;' 68-67 7-00 CHEMICAL. Brand. C. Mn. Si. P. s. Parkhead common iron . 09 trace 020 316 027 Leeds forge best iron . 14 03 110 085 028 Bowling best iron . 11 trace 10 101 trace Farnley best iron . . 11 01 090 096 012 Lowmoor best iron . 10 01 120 142 022 Landore mild steel . 18 64 013 077 074 Mild steel . . 22 399 062 043 042 Medium steel . , "-' 34 536 024 052 019 Tool steel . . . 97 148 074 034 059 138. ANKARSRUMS (SWEDISH) CAST IRON. Guaranteed tensile strength = 17*8 tons per square inch. Average =19 -5 Extension on 4 inches . =0-28 per cent. Westman, 39 Lombard Street. STRENGTH OF MATERIALS AND STRUCTURES. 65 139. STRENGTH OF MALLEABLE CAST IRON. Ultimate tensile strength per sq. inch = 14 tons. Elongation on 4 inches = 1J per cent. Elastic limit = 7 tons. 140. SHEARING STRENGTH COMPARED WITH TENSILE STRENGTH. Is variable, but averages for Wrought iron 85 per cent. Mild steel 81 per cent. Cast iron 40 Hard steel 64 to 70 Platt and Hayward. 141. APPROXIMATE STRENGTH OF GIRDERS. Safe load in tons distributed when supported at both ends and loaded uniformly. For cast iron = Sectional area of bottom flange in square inches. For wrought iron = Gross sectional area of bottom flange plates x 2f . For rolled iron joist = Area one flange x 4 x depth inches -~- span feet. For steel joist = Area one flange X 5 X depth inches -f- span feet. 142. BRIDGES AND GIRDERS.* A = area of one flange in sq. inches at centre. a = at x feet from one end. D = depth in feet at centre. d = at intermediate points. S = span in feet. W = load in tons concentrated in centre. c = constant = stress per sq. inch allowed in flange. * For general designing, see the author's ' Practical Designing of Structural Ironwork.' Demy 8vo, cloth, 200 pp., with 14 folding plates, containing 180 diagrams. (Spon, 8s. 6c7.) F 66 HANDBOOK FOE MECHANICAL ENGINEERS, _ADc iWS To find section required at any given distance from one end = a, _ Aa?(S- a?) ' W. G. A. & Co., ElswicL 143. SPECIFICATION TESTS OF WROUGHT IRON (BRIDGE AND GIRDER WORK). Class. Tensile Strength, tons per square inch. Elongation * per cent, at twenty tons. Contraction per cent, at point of fracture. Kivetiron 25 10 30 Bod and bar iron 24 7| 20 Angle and tee iron . 22 6 15 Plates, with grain . 21 H 10 Plates, across grain. 18 5 In a length of 8 inches. 144* ALLOWANCE IN BRIDGES FOR CHANGES OF TEMPERATURE. Variation of 15 F. alters length of wrought iron as much as strain of 1 ton per square inch. In exposed situations an allowance of ^ of an inch move- ment, per 100 feet length, is necessary for the purpose of eliminating the strains due to change of temperature. Graham Smith. STREHGTH OF MATERIALS AND STRUCTURES. 67 145. SPECIFICATION TESTS COMMON WROUGHT IKON. Class. Tensile Strength, tons per square inch. Contraction per cent, at point of fracture. Rivet iron 22 20 Bods, bars!and angles . Plates 21 20 I2| 10 Timmins. 146. SPECIFICATION TESTS OF WROUGHT IRON AND STEEL (SHIPBUILDING). Class. Tensile Strength, tons per square inch. Elongation* per cent, on fracture. Toughness, f Rivet iron .... 26 25 650 Rod and bar iron . 24 15 360 Angle and tee iron . 22 12* 275 Iron plates, with grain . 20 7J 150 across grain . 19 6 114 Steel plates (both directions) . 28 20 560 bars and angles . 30 25 750 * In a length of 6i inches. f Should the actual elongation in sixteenths of an inch, multiplied by the stress in tons per square inch, upon rupture, be more than 10 per cent, under the amounts given in the last column, the material will be rejected. Wrought Iron. Cold bending in vice J-inch plate 35, 1-inch plate 55, T V-mch plate 63, J-inch plate 70, rivet iron to double close, without cracking* Steel. Steel plates should be capable of bending to an inside radius of 1^ times their thickness when heated to a low cherry red and cooled in water of a temperature of 58 C. = 82 F. For Admiralty tests, see Molesworth,' p. 28. F 2 68 HANDBOOK FOR MECHANICAL ENGINEERS. 147. STEEL AND IRON SHIPBUILDING. Lloyd's Regulations allow a reduction of 20 per cent, in the scantlings of a steel ship as compared with iron, but the total weight of material used is only about 14 per cent. less. The cost is about the same in steel or iron. 148. DEFINITION OF MODULUS. The term " Modulus " simply means a constant, coefficient or multiplier, by means of which one series or system of quantities can be reduced to another similar series or system. 149. MODULUS OF RIGIDITY is the ratio between the shear stress, in Ibs. per square inch, and the shear strain or movement of a particle in inches at one inch from the fixed end. Stress __ Strain "~ The torsional resistance of any material is proportional to the modulus of rigidity. 150. LIMIT OF ELASTICITY. The maximum stress per square inch sectional area, which any material can undergo without receiving a visible permanent set, is called its limit of elasticity, or elastic strength. The average limits of elasticity are Wrought iron, 10 tons. Cast iron, 2 tons. Steel, 15 tons, STRENGTH OF MATERIALS AND STRUCTURES. 69 And the average elongations under a stress of 1 ton per square inch are Wrought iron ^^. Cast iron T3 ^. Steel Anderson, Wrought iron 12000* Cast iron ^oV^. Steel Kennedy. 151. FATIGUE OF WROUGHT IRON. When repeatedly strained beyond its elastic limit, wrought iron takes an increasing permanent set, and ulti- mately breaks with less than its original maximum load; but if periodically annealed before rupture takes place, its elasticity may be renewed. This loss of strength, being recoverable, may be termed fatigue. 152. HOOKE'S LAW OF ELASTICITY. Hooke' law was " Ut tensio sic vis," which may be freely translated, " As the pull so the stretch " ; or in other words, the elongation or compression is proportional to the stress. 153. MODULUS OF ELASTICITY. A bar in tension or compression is elongated or shortened by an amount proportionate to the stress within certain limits. Assuming the elongation, on increasing the stress, to continue in the same ratio, a certain point would be reached where the bar would be increased to twice its original length. The weight in Ibs. per square inch sec- tional area of the bar, to produce this result, is the modulus of elasticity (E). The amount depends upon the kind and quality of the material employed, and may vary 50 per cent. __ stress per unit of section strain per unit of length * 70 HANDBOOK FOR MECHANICAL ENGINEERS. 154. DEFINITIONS OF MODULUS OF ELASTICITY. The modulus of direct elasticity of a material is the ratio of the stress per unit of section of a bar, to the elongation or compression per unit of length, produced by the stress. Unwinds 'Machine Design.' It is the weight in Ibs. that would stretch or compress a bar, having a sectional area of one square inch, by an amount equal to its own length, called Hooke's law. Cargitt's Strains: When expressed in feet the modulus of elasticity gives the height to which a body would have to be piled in order that any small addition to its top, of its own substance, might compress the rest to an extent equal to the bulk of that added quantity. Dr. Young. 155. YOUNG'S MODULUS. Young's modulus of elasticity was originally expressed in feet, and may be obtained from the common table of moduli in Ibs. per sq. inch as follows : E in Ibs per sq in. = B ^ Modulus), wt. of cub. in. in Ibs. X 12 156. FORMULA FOR ELONGATION BY ELASTICITY. E = Modulus of direct elasticity (see table). I = Length in inches. w = Load per sq. inch sectional area in Ibs. e = Elongation in inches. w X I E Approximately : W in tons X Hn ft. . . , /, , . : - = e in inches for wrought iron. sq. ins. area X 1000 STRENGTH OF MATERIALS AND STRUCTURES. 71 157. MODULI OF ELASTICITY, Ibs. per sq. inch. Cast steel, tempered . . . 40,000,000 Steel, ordinary .... 30,000,000 Wrought-iron bar .... 29,000,000 Ditto plate 25,000,000 Cast iron 18,000,000 Copper 16,000,000 Phosphor bronze .... 14,000,000 Zinc 13,000,000 Gun metal 10,000,000 Brass 9,000,000 Tin 5,000,000 Lead ...... 720,000 Timber, say 2,000,000 The above are sometimes improperly called " Young's Modulus." 158. MODULUS OF ELASTICITY OF BULK. The pressure in Ibs. per square inch upon the exterior of any substance, or the external stress, produces a diminution of bulk per cubic inch, called the cubical strain of the substance. The strain is proportional to the stress, and is equal to the stress divided by a certain number called the modulus of elasticity of bulk, and represented by K. K = Water . . . 300,000 Cast iron . . 14,000,000 Wrought iron . 20 , 000 , 000 Steel ... . 24,000,000 Copper . . . 30,000,000 72 HANDBOOK FOR MECHANICAL ENGINEERS. 159. MOMENT OF INERTIA. The moment of inertia of a section is the summation of the areas of all its individual parts, multiplied by the squares of their distances from the neutral axis. Unwin. Moment of inertia is the sum of the moments of resistance in any given section. Hurst. 160. BENDING MOMENT, OR MOMENT OF FLEXURE is the moment of the external forces on one side of a trans- verse section estimated relatively to the section. p T M = expresses the relation between the bending moment and the curvature of a bar under transverse strain. Unwin. 161. BENDING MOMENT. The bending moment M at a section is equal to the stress at one inch from the centre of gravity of the section multi- plied by the moment of inertia I of the section. M = stress at 1 inch from neutral axis. 162. NEUTRAL Axis. That layer or plane of fibres in a beam, the length of which is unaltered when the beam is bent by the action of a load, is called the neutral surface, and the line in which this layer cuts any cross section of the beam is called the neutral axis of the section. STRENGTH OF MATERIALS AND STRUCTURES. 73 163. MOMENT OF INERTIA. In such structures as beams, &c., the moment of inertia is determined by the radius of gyration (see par. 33) measured from the neutral axis. It is equal to the area of the section multiplied by the square of the radius of gyration. If the moment of inertia (I) of any area (A) be given about an axis through the centre of gravity, its value about any parallel axis, such as the neutral axis, at a distance (d) will be = I -f A d 2 . 164. RADIUS OF GYRATION. The moment of inertia (I) divided by the area of the section (A) gives the square of the radius of gyration (r) r=I A* This is used in ascertaining the strength of struts and columns. 165. MODULUS OF SECTION, OR STRENGTH MODULUS is a function of the dimensions proportional to the moment of resistance of the section. It is the moment of inertia divided by the distance from the neutral axis to the furthest part on the extended or compressed side. Modulus of section x max. strain tension or compression bending moment [Moment of Resistance]. M=/z, =/ c z c . Unwin. 74 HANDBOOK FOE MECHANICAL ENGINEERS. 166. MOMENT OF RUPTURE varies according to the position of load and mode of support, e.g. a beam supported at the ends and loaded in the centre. WZ and if load be distributed or T n i -, moment of rupture In a flanged beam = -r-^- - = stress in flange. depth In a beam of any section, the stability depends upon the equation Moment of Rupture = Moment of Resistance, or M = K. Humber. Moment of Load is the load multiplied by its effective leverage at the point required. The moment of a load divided by the depth of beam will give the horizontal strain on the extreme fibres in its upper and lower sides. Hurst. This Moment of Rupture is by other writers called the Bending Moment. 167. MODULUS OF RUPTURE FOR TRANSVERSE STRAINS. The theoretical value of this is the resistance of the material to direct compression or tension, but it is found from experiments on cross breaking that this value is, from various causes, not sufficiently high, and Professor Rankine has adopted a modulus which is 18 times the load required to break a bar of 1 square inch section, supported on two points 1 foot apart, and loaded in the middle between the supports. STRENGTH OF MATERIALS AND STRUCTURES. 75 c = Cast iron . , 40 , 000 Wrought iron . 42,000 Fir . 5,000 to 10,000 Oak . 10,000 to 13,600 Number. The Modulus of Rupture is sometimes called the " Strength Modulus." 168. MOMENT OP RESISTANCE. The moment of resistance of a section is the moment of inertia multiplied by the modulus of rupture and divided by the distance of the neutral axis from the furthest edge of the section. B-*. y Humber. The moment of resistance of a beam at any section is the sum of all the products obtained by multiplying the actual longitudinal stress taken at each square inch of the section by its distance from the neutral axis. The moment of resistance in a flanged girder is the longitudinal strength of the weakest flange multiplied by the mean depth of the girder. Perry. The Moment of Resistance is sometimes called "the Moment of the Section." The moment of resistance in a beam is proportional to the area of the fibres multiplied by the squares of their distances from the neutral axis. Hurst. 169. WORKING LOAD FOR GIVEN MOMENT OF RESISTANCE. / = greatest safe intensity of stress. LetM = = fz, then W = . o I And again, W 7 4- f 9 Let M = ~ = fz, then W = ^y . 76 HANDBOOK FOR MECHANICAL ENGINEERS. 170. STRENGTH OF STRUCTURES. The strength of structures varies as the square of the linear dimensions of similar parts, excluding the effect of weight; but the weight varies as the cube of the linear dimensions. The strength of a structure of any kind is not therefore to be determined by that of its model, which will always be much stronger in proportion to its size. All works, natural and artificial, have limits of magnitude which, while their materials remain the same, they cannot surpass. Lardner. 171. SAFE LOAD ON STRUCTURES. Cast-iron columns Cast-iron girders for tanks = J breaking weight. Wrought-iron structures Cast iron for bridges and floors = ^ Stone and bricks . . . . = -g- Timber . . = T V Do., temporary structures = ^ Molesworth. 172. SAFE LOAD ON FLOORS. Churches and public buildings. lj cwt. per sq. foot. Warehouses . 2J Dwelling houses . . . 1 173. WEIGHT OF MEN IN CROWDS. Mr. Cowper found by experiment that a number of men averaged 140 Ibs. per square foot. Mr. Parsey considers that men packed closely would weigh at least 112 Ibs. per square foot, but that in ordinary crowds 80 Ibs might be taken as sufficient. On the Continent it is not usual to estimate so high. STKENGTH OF MATEKIALS AND STRUCTURES. 77 Belgians weigh about 140 Ibs. each, Frenchmen 136 Ibs., while Englishmen weigh 150 Ibs. Mr. F. Young states 80 Ibs. per square foot is quite safe in practice. Mr. Thomas Page packed picked men on a weighbridge with a result of 84 Ibs. per foot super. Mr. George Gordon Page says that for troops on march 35|- Ibs. per square foot is sufficient. The usual practice is to assume the live load as 100 Ibs. per square foot. A. T. Walmisley. Ibs. per sq. foot. French practice (quoted by Stoney and Trautwine) ...... 41 Hatfield in Transverse Strains, ' for soldiers ...... 70 Nash, architect of Buckingham Palace (quoted by Tredgold) . . . .120 W. K. Kernot, Working Men's College, Melbourne 126 Prof. W. C. Kernot, Melbourne University. 143 1 B. B. Stoney, .in < Stresses ' . . .147-4 Prof. Kernot. 174. FLAT CAST-IRON FLOOR PLATES. Thickness ins. = ^ load lbs ' B< 1- ft - x len g th ins ' 380 175. THEOREM OF THREE MOMENTS. If A B C be three consecutive supports of a continuous girder of any number of spans, whether equal or unequal, and Zj Z 2 the consecutive spans ; then let p l p 2 = the loads per unit of span on l r 1 2 respectively ; and Mj M 2 M 3 = the bending moments on A B and C respectively. The relation between M x M 2 and M 3 is always expressed by the equation M, I, + 2 M 2 (Z, + y + M 3 I, = 78 HANDBOOK FOR MECHANICAL ENGINEERS. 176. LOAD ON THE SUPPORTS OF CONTINUOUS GIRDERS of equal spans uniformly loaded, the load on each span being unity, and the supports perfectly level and rigid. No. of Spans. Abut- ment. 1st Pier. 2nd Pier. 3rd Pier. 4th Pier. 5th Pier. 6th Pier. 7th Pier. 2 375 1-25 3 4 1-1 ., .. .. . , . , .. 4 393 1-143 93 .. .. .. .. .. 5 394 1-131 989 ... .. .. .. .. Infinite 3943 1-134 9641 1-0096 9974 1-0007 9998 1-00 When the number of spans exceeds five, the loads on the supports are nearly the same as when the number is infinite. 177. APPROXIMATE SAFE LOAD ON COLUMNS AND PIERS. Cast-iron column or stanchion with metal f inch thick or upwards. Up to 10 diameters long 5 tons per sq. inch. 10 to 15 4 15 to 20 3 20 to 25 2 25 to 30 1 J 30 to 35 | If less than f inch thick take ^ ton per sq. inch less for each |- inch less in thickness. Hard York or Portland stone piers 12 tons per foot super. Stock brick in cement, if covered) with stone template . ( Do. without do. 4 STRENGTH OF MATERIALS AND STRUCTURES. 79 178. EFFECT OF LOAD NOT BEING AXIAL. When the centre of pressure, or resultant of the forces acting on a cross section, does not coincide with the centre of gravity of the section the strength is reduced and the maxi- mum stress increased as follows : W = total load tons. d = distance of centre of pressure from neutral axis of section (i.e. line through centre of gravity). A = area of section in sq. feet. s = mean stress in tons per sq. foot. S = maximum D = distance of point of maximum stress from neutral axis. I = moment of inertia of the section. W ^ D s= _, S = s(l + d 179. WROUGHT-!RON STRUTS. Angle, tee, or cross section, ends fixed. I = length, inches. d = least width, inches. / = factor of safety = 5 to 8. Safe load Ibs. per sq. inch, sect, area = 120 - / tons = - -05 j. 180. NOTES ON IRON COLUMNS. When the length is 26*4 times the diameter, pillars, columns, or vertical struts are of equal strength whether of wrought or cast iron ; when shorter, cast iron is stronger ; when longer, wrought iron is stronger. Gordon. 80 HANDBOOK FOR MECHANICAL ENGINEERS. Cast-iron columns under 5 diameters long, fail entirely by crushing ; from 5 to 20 diameters, partly by crushing partly by bending ; over 20 diameters entirely by bending. 181. STRENGTH OF CAST-IRON COLUMNS. Cast-iron hollow columns : d = external diameter inches (^ to ^ length). t = thickness in inches (not to exceed ^ d ). L = length in feet (ends flat and fixed). Safe load tons per sq. inch = (t + 1) . Cast-iron solid columns : W = breaking weight tons per sq. inch. r = ratio of length to least diameter. w= 42 1 + '003 r 2 Planat. d = diameter inches, I = length feet. Safe load tons = . 4d 2 + -18 1 2 Safe load hollow column = difference of solid columns of internal and external diameters. Bourne. 182. APPROXIMATE SAFE LOADS ON POSTS. Fir post, 10 diameters long, T 2 ^ ton per sq. inch. Oalr 3 vd,K. > >J TTF Approximate safe permanent load in tons on square timber posts of fir - 50 - Reuleaux. STRENGTH OF MATERIALS AND STRUCTURES. 81 Another rule for fir posts, flat ends : I Working load Ibs. per sq. inch = 1000 - 10 - . Stanwood. Another rule : Approx. safe load on fir post : I ins. X d ins/60- 250 For oak posts : 6 = breadth of side in inches. L = length in feet. Safe load in Ibs. 6ms> = safe load, tons. 4 o 2 + L 2 Bourne. 183. PILLARS AND STRUTS OF WOOD. d = diameter or width narrowest side, inches. F = crushing force, short specimen, tons per sq. inch. I = length in inches. S = sectional area, sq. inches. W = breaking weight in tons. * 2 \Fir2-5 200 d 2 RanJcine. W = safe load tons total, a = sectional area, sq. inches. d = least diameter or width side, inches. L = length, feet. W - 1 -07 52 a d * or W - J * 45 a f * ak< 752 a j-soi -| . 27 a f or fi r . The lesser of these two values to be taken. If un- seasoned, the safe load will only be one-half above. G 82 HANDBOOK FOR MECHANICAL ENGINEERS. 184. ULTIMATE STEENGTH OF WOOD POSTS. 24 diameters long = ^ crushing load on short specimens. = ^ > j> > '^ > = T5 > > 185. ULTIMATE STKENGTH OF TIMBER. Name. Tension. Per sq. inch. Compression. Per sq. inch. Ash . 7i tons 4 tons Beech . . 5 4 Elm. 6 4 Mem el and Riga fir . 5 ;; ^2 Larch ... " Honduras mahogany ^2 3j )5 English oak . 6 4 Dantzic Quebec . 1: 3j } 3 Teak . 7 5 Pitch pine ... 3 Hornbeam . 4 " 186. MAXIMUM SAFE LOAD ON TIMBER IN DIRECT COMPRESSION. Fir and deal : With the grain = 450 Ibs. per sq. inch. Across = 250 187. FORMULA FOR STRENGTH OF TIMBER BEAMS. s = span feet. 6 = breadth inches, d = depth inches. B.w. = breaking weight cwts. centre, c = constant. bd* B.w. = c. 8 STRENGTH OF MATERIALS AND STRUCTURES. 83 When load is not central, dividing span into x and y sbd* B.w. = c. 4 x y Safe deflection = ^ inch per foot span. In calculating scantling of timber for practical use under tension or transverse stress, 1 inches must be added to each dimension to allow for the contingency of a knot occurring in the piece. When loaded on top and supported at the ends, the soundest side of a square beam should always be placed downwards, and if rectangular then the soundest of the narrow sides should be downwards. 188. CONSTANTS FOR STRENGTH OF EECTANGULAR BEAMS = weight in cwts. in centre required to fracture a bar 1 inch square and 1 foot long. Wrought iron . . 22 Cast iron . . . 18 Brass . . .10 Greenheart . . 8 Teak. ... 6 English oak . . 5 Quebec and Baltic oak .4*5 Memel Dantzic and 1 , Eiga fir j Spruce fir and larch . .3-5 English elm ... 3 189. EXPERIMENTS ON EECTANGULAR BEAMS OF SELECTED PINE. B.w. Ibs. centre = 6080 -=- (all inches) ; or if I in feet then = 506| . If a given rectangular beam be under a given strain by a given load in a given position which divides the span in G 2 84 HANDBOOK FOB MECHANICAL ENGINEEES. the proportions x and y, then to obtain the same strain when the load divides the span in the proportions m and w, the depth d will be altered to d l = d x * / m n . 190. PROPORTIONS OF BEAMS FOR STRENGTH AND STIFFNESS, WITH MINIMUM AMOUNT OF MATERIAL, Strongest d:b: : 2 Stifiest d:b:: Aproximately for strength, d to b as 1 to 7 ; and for stiffness as 1 to 58 ; but 1 to 5 is often used for beams, where the ends can be fixed sideways, because two can be cut out of a square log, and 1 to 33 or three out of a square log when intermediate staying can be applied, as in joists. Out of a round log of diameter d the strongest beam that can be cut is -816 d x *577 d, and the stiffest -866 d x '5 d 191. APPROXIMATE PROPORTIONS OF BEAMS. Strength. Stifihesa. Convenience. inches 12 X8 inches 12 x7 inches - 12 x 9 or 12 X 6 10x7 10 X 6 10 X 5 9x6J 9x51 9x6 or 9 x 4| 8 x 5J . 8x4| 8x6 or 8 X 4 7x5 7x4 7 X 4J or 7 x 2 6x4 6 x 3 6x4 5 X 3 5x3 5x3 4x3 4 x 2J 4x3 or 4 x 2J 3x2 3x If 3x2 STRENGTH OF MATERIALS AND STRUCTURES. 85 192. STRENGTH AND STIFFNESS OF TIMBER. Name. Stiffness. Strength. Resilience. Ash . 89 119 160 Beech 77 103 138 Riga fir 98 80 64 Memel fir 114 80 56 Larch . 79 103 134 Honduras maho English oak 'any 93 100 96 100 99 100 Dantzic 117 107 99 Quebec 114 86 64 Teak . 126 109 94 Pitch pine . 73 82 92 Oak being taken for comparison as = 100. 193. KESILIENCE, Resilience or Spring is the quantity of mechanical work required to produce the proof stress on a given piece of material, and is equal to the product of the proof strain or alteration of figure, into the mean load which acts during the production of that strain : that is to say, in general, very nearly one-half of the proof load. The Resilience or Spring of a Beam is the work performed in bending it to the proof deflection : in other words, the energy of the greatest shock which the beam can bear without injury: such energy being expressed by the pro- duct of a weight into the height from which it must fall to produce the shock in question. This, if the load be con- centrated at or near one point, is the product of half the proof load into the proof deflection. , ItanMne. The resistance of beams to transverse impact, or a suddenly applied load, is termed their resilience. It is simply propor- tional to the mass or weight of the beam, irrespective of the length or the proportion between the depth and breadth. 86 HANDBOOK FOR MECHANICAL ENGINEERS. Thus, if a given beam break with a certain steady load, a similar beam of twice the length will break with half the load applied in the same way ; but if the short beam be deflected or broken by a certain falling load, the long beam will require double the load dropped from the same height or the load dropped from twice the height, to produce the same effect. Anderson's ' Strength of Materials. ' The work done in deforming a bar up to the elastic limit is termed the resilience of the bar. Unwin. 194. TIMBER TREES. Name. Mean Diameter of Trunk. Average Length of Trunk. Ash , . . . inches 23 feet 38 Beech 27 44 Chestnut 37 44 Elm .... 32 44 Kiga fir . 20 75 Larch .... 33 45 Mahogany 72 40 Norway spruce 15 60 Canadian oak . . 34 53 English oak . 32 42 Sycamore ' . > 29 32 Law. 195. SIZES OF FIR TIMBER IN BALK. Stettin Dantzic Memel Riga . 18 to 20 in. square. 14 16 40 to 50 ft. long. 13 12 Swedish and Norwegian 8 12 35 40 STRENGTH OF MATERIALS AND STRUCTURES. 87 196. NOTES ON PILE-DRIVING.* Gauge, guide, or main piles are whole timbers 9 to 15 inches square, driven about 10 feet apart. Waling-pieces, or walings, are horizontal timbers formed of half balks secured to the guide piles in pairs, one pair near the top and another pair near low- water mark. These serve as guides in driving the intermediate piles. Sheet piling is formed of piles 9 inches by 4J inches or 12 inches by 6 inches, the bottom end chisel-shaped and raking so as to be drawn towards the piles already driven. Intermediate piles may be whole timbers or sheet piling according to circumstances. Puddle is well punned clay filled in between the walls of a cofferdam to prevent passage of water. All piles should be shod; if unprotected the wooden points would break and cause the piles to drive out of line. Shoes for main piles weigh from 10 to 15 Ibs. each, and for sheeting piles from 5 to 8 Ibs. each. The heads of all piles should be hooped, ringed or rung to prevent them from splitting under the blows of the ram or monkey. When piles have to be scarfed to obtain sufficient length, the scarfs should break joint at 6 feet intervals in adjacent piles.* 197. FORMULAE FOR PILE-DRIVING. P = ultimate supporting power in tons = W/. W = safe working load in tons. w = weight of ram in Ibs. = not less than H = height of fall in feet. d = set, or distance driven by last blow, in inches. L = length of pile in feet. * See paper on 'Timber Piling in Foundations and other "Works,' 2nd ed., 24 pp. and folded plate (Spon, Is.). 88 HANDBOOK FOE MECHANICAL ENGINEEKS. 8 mean sectional area of pile in square inches, / = factor of safety = say from 2 to 3. x = energy of last blow in foot-tons 125 c = constant = -= 24 Pd P 2 198. TIMBER ROOFS. span in feet = thickness of truss in inches. 3 span in feet + 3 = depth of tie-beam in inches. King or queen post square in middle, width ends = twice thickness. King post truss up to 30 feet span, queen post truss for larger spans. 199. WIND PRESSURES.* 36 Ibs. per sq. foot steady wind pressure, and 56 Ibs. per sq. foot for gusts in exposed situations, is sufficient to provide for in roofs, bridges, &c., for ordinary cases. * See papers by the author on 'Wind Pressure on Roofs,' 2nd ed., demy 8vo, 12 pp., with folded plate (6cZ.)> and The Force of the Wind,' 8 pp. (3d.) STRENGTH OF MATEKIALS AND STRUCTURES. 89 200. APPROXIMATE WEIGHT OF TIMBER ROOFS. King or queen truss, span in feet 2 = Ibs. per truss. Common rafter and purlins . = 7 Ibs. per ft. sup. J-inch slate boarding . . = 2J Slate battens .... = 1 J ,, Roofing felt .... = Slates and nails (general) = 9 Ceiling (complete) = 12 Snow . . ... = 7% Wind (horizontally) . . =56 The combined efiect in vertical load with trusses usual distance apart may be taken at 60 Ibs. per foot super. 201. GALVANISED CORRUGATED IRON ROOFING. Thickness Q . . Q . "Weight per Square. B.W.G. Size of Sheets. cwt. qrs. Ibs. 16 6 feet x 2 feet to 8 feet X 3 feet 3 14 18 216 20 136 To be laid with 6-inch laps and double riveted at joints ; 3 Ibs. of rivets required per square. 202. "WEIGHT OF MATERIALS FOR ESTIMATING. Wrought iron .... 480 Ibs. per cub. ft. Cast iron 450 Gun-metal and brass . . 530 Cast steel 504 Mild steel .... 490 Lead 700 Copper 550 Zinc 450 Greenheart .... 60 Oak. ..... 50 Fir 40 Granite 160 Bramley Fall and Hard York . 140 90 HANDBOOK FOB MECHANICAL ENGINEERS. 203. SHEET COPPER. Sheets 4 feet by 2 feet. B.W.G. 22 = 1-25 Ibs. per ft. sup. 24 = 1-0 26 -75 OQ . C * > J) 204. SHEET LEAD. Cast sheets, 6 feet wide x 16 to 18 feet long. Milled sheets, 7 feet wide X about 25 feet long. Made 3 to 10 Ibs. per foot super. Lbs. per foot x *017 = thickness in decimals of an inch. 1 sq. foot, 1 inch thick, weighs 60 Ibs. 205. SHEET ZINC. Sheets 2 ft. 8 in. and 3 ft. wide, 7 ft. and 8 ft. long. ~ Oz. per ft. Corresponding Thickness Uauge. sup< to old B.W.G. inches. (Z.G.) No. 10 = 111 25 -019 12 = 15| 23 -025 14 = 18f 21 -031 16 = 24f 19 -041 1 sq. foot, 1 inch thick, weighs 37 J Ibs. 206. HANDY NUMBERS FOR WEIGHT OF IRON. Wrought iron : Sectional area, square inches X 3J = Ibs. per foot run. Cubic inches X * 28 = Ibs. Eound iron, d 2 x 2 62 = Ibs. per foot run. Square feet per ^ inch thick x 5 = Ibs. For weight of rivets in plate girders, take 5 per cent, of weight of plates and angle irons, and in lattice or box girders 2J per cent. STRENGTH OF MATERIALS AND STRUCTURES. 91 Cast iron : Sectional area, square inches X 3'2 X length in feet = lbs. Weight of wrought 5 per cent. = weight of cast. 23 cubic inches = 6 Ibs. 40 Ibs. per square foot, 1 inch thick, is sometimes taken to allow for inaccurate casting. Mild Steel : Weight of wrought iron + 2 J per cent, = weight of mild steel. Some designers add ^ an ^ some ^ to weight in wrought iron. 207. MARKET SIZES OF PLATES. In a well-assorted specification for a fair quantity of material, Staffordshire plates may now be obtained at a minimum price up to 10 cwt. each, 30 feet long and 5 feet 6 inches wide, and Cleveland plates up to 15 cwt. each, 30 feet long and 5 feet wide. Walmisley, 1888. For ordinary prices mild steel plates may be obtained in one piece up to 20 cwt., 30 feet long, 6 feet 6 inches wide, 1^ inches thick, or 60 feet super., and to double these limits for a moderate addition to the price. 208. LIMITS OF ORDINARY PRICES, STAFFORDSHIRE DISTRICT. Plates. Weight 8 cwt., length 20 feet, width 4 feet, 6 inches, 40 feet super., shape regular. Angle and Tee Irons. Length 40 feet, size 2J inches by 2^ by up to 8 united inches. Bars. (Eound and square), diameter J inch to 3 inches,, length 25 feet. Bars. (Flat), size 1 inch by i inch up to 6 inches by 1 inch, length 25 feet. Area 92 HANDBOOK FOE MECHANICAL ENGINEERS. 209. EXTRACT FROM THE CLEVELAND LIST OF LIMITS ,AND EXTRAS. Weight, to 10 cwt. Beyond, 10s. per ton for every cwt. or portion thereof. Length, to 20 feet. Beyond, 2s. Qd. per ton per foot or part thereof. Width, 12 inches to 54 inches. For -^ inch and -| inch thick, 12 inches to 48 inches. Beyond or under, 5s. per ton per inch or part thereof. 60 sq. feet for thicknesses from J inch to 1 inch inclusive. 48 T 3 ^ inch thick. 36 -I Beyond (if sellers undertake them at all), Is. per ton per sq. foot. Boiler plates, except B B B boiler, 48 sq. feet. B B B boiler, 36 sq. feet. Beyond (if undertaken), 2s. 6d. per ton per sq. foot. Thickness, J inch to 1 inch. T 3 inch 10s. per ton, and -| inch 30s. per ton extra. Sketches, 20s. per ton. Curved sketches, 40s. per ton. 4 inch taper allowed before counting sketch. Guarantee. In case of serious defect, or error in dimen- sions, a plate will be replaced, and on receipt of the rejected one the amount originally charged will be credited. Dimen- sions will be worked to as nearly as practicable, but absolute exactness must not be expected. No further liability is undertaken by sellers except by special contract. Stoppage of Works. Should the works of the makers or buyers be stopped by a strike, or by accident to machinery or buildings, current contracts to be suspended during such interruption, but not to be thereby cancelled. Fox, Head & Co. STKENGTH OF MATERIALS AND STRUCTURES. 93 210. DEFLECTION AND CAMBER. Deflection is the displacement of any point in a loaded beam from its position when the beam is unloaded. Camber is an upward curvature, similar and equal to the maximum calculated deflection given to a beam or girder or some line in it in order to ensure its horizontality when fully loaded. 211. DEFLECTION. Eadius of curvature of neutral axis of a beam at any section when under transverse stress M ' 212. EADIUS OF CURVATURE is the radius of the circle coinciding most nearly with a curved line or portion of one. Curvature is the reciprocal of this radius. Thus, if radius be 100 feet, curvature is T ^. If radius alters further on to 120 feet, the change of curvature will be T ^- y^ = ^J^. The curvature of a circle is inversely proportional to its radius, and is measured by the fraction 5-= . radius Goodeve. 213. DEFLECTION OF SOLID BEAMS. A = deflection in inches. I = length in feet. b = breadth in inches. d = depth in inches. W = load in cwts. in centre. c = constant = Cast steel . . 650 Wrought iron . 550 Cast iron . . 330 Teak 50 Quebec oak . 40 Fir and deal . 33 Dantzic oak . 27 Pitch pine , 25 94 HANDBOOK FOE MECHANICAL ENGINEERS. Rectangular beam : I 3 W A A = W = ^ I d 3 c I 3 Z 3 W 3 FW , , Z 3 W l* Ac v A6c Ac 'FW 4 /Z 3 W Square beam, side = */ ? 4 /Z 3 W Cylindrical beam, diameter = A/ X 1 * 7. If load be uniformly distributed, deflection = -f A. Cantilever with distributed load = A 6. Cantilever loaded at end = A 16. Safe deflection in timber = ^^ length, or ^ inch per foot span. 214. COEFFICIENTS FOR DEFLECTION RECTANGULAR BEAMS. A = 8 = Fixed one end, loaded the other 128 load distributed 48 Supported ends, load central . 8 ,, load distributed 5 Fixed both ends, load central . 2 load distributed 1 Wrought iron . . -000002 Cast iron . . . -000003 Steel .... -0000016 Oak .... -0000375 Ash Fir .... Deflection = o inches X inches General formula for beams of uniform section, fixed one W Z 3 end, loaded the other, deflection A = =-^ 215. COEFFICIENTS OF REACTION FOR DEFLECTION. Sox. Unwin. Fixed one end, loaded the other . K = 32 16 load distributed . =12 6 Supported both ends, load central . = 1 1 load distributed = f f Fixed both ends, load central . = f load distributed . = STRENGTH OF MATERIALS AND STRUCTURES. 216. APPROXIMATE DEFLECTION OF WROUGHT-!RON FLANGED GIRDERS of uniform strength, supported at both ends, and carrying uniformly distributed load. Stress allowed = 5 tons per sq. inch tension, 4 tons per sq. inch compression. 8 = span in feet. d = mean depth in inches, D = deflection in inches in centre. __ -0144s 2 d If depth = T V span, D = '012*; ^ = -0144s; ^ = 018s. 217. DEFLECTION OF GIRDERS. In girders with parallel flanges of uniform strength, the deflection produces a circular curve, the amount of deflection varies directly as the load x the gum of the areas of both flanges x the cube of the length, and inversely as the area of top flange x area of bottom flange x depth of web squared, or __ W X (a f + a,) X I 3 hJt ^ in s\ C a t x a b X & c = Wrought iron. Cast iron. Load centre . -016 .. -025 Load distributed -01 .. -018 L = span in inches. W = load tons distributed ends supported. I = moment of inertia. E = modulus of elasticity in Ibs. per square inch. S = stress allowed in tons per square inch. S = deflection in inches. For girder of uniform section : , 5WL 3 "384 El' 96 HANDBOOK FOB MECHANICAL ENGINEERS. For girder of uniform strength : SL 2 Common Rule. Girders to be constructed with a camber of J to J inch per 10 feet of span, to allow for deflection when loaded. Feet span x *005 to -0075 = safe deflection in inches under ordinary loads. Feet span x 02 to 03 = safe deflection in inches under special loads. American practice. Feet span x 01 = safe deflection in inches after permanent set. Board of Trade allows f inch per 100 feet span (= T&TV = -0075) for deflection caused by maximum rolling load beyond the deflection due to maximum dead load. 218. DEFLECTION TESTS. Two main girders 60 feet span erected in yard with cross girders and bearing for railway viaduct. Weight complete, one span with temporary timber, 22 tons. Deflection in centre with 30 tons distributed = 32 in. 60 = *685 90 * = 1-085,, 121-5 = 1-53 do. and 10 tons centre = 1-73 loads removed = 47 , 219. LOAD ON BRIDGES. Assuming deflection to vary directly as load, the WORK done by gradually applied load = load Ibs. x deflection feet, but with suddenly applied load = load Ibs. x deflection feet, because it drops through the whole distance, and the deflection being double that due to the same load gradually applied, the WORK will be quadrupled. A rolling load on a girder is not quite a suddenly applied load, but somewhere STRENGTH OF MATERIALS AND STRUCTURES. 97 between that and a dead load. The stress in a given beam varies as the deflection. T , Ratio of Deflection or Maximum Stress. Dead, gradually applied .... 5 Live, rolling on ..... 8 suddenly applied . . . .10 220. DEFLECTION OF BEAMS UNDER IMPACT. P = weight of load falling upon centre of beam. h = vertical height of fall to surface of unstrained beam. d = static deflection due to P. D = actual dynamic deflection due to impact of falling load. W = weight of beam. m = constant depending upon ratio of P to W. 35 P "35P + 17W* D = d In the case of a suddenly applied load, h = and D = 2 d. Merriman's * Mechanics of Materials' 221. STRENGTH OF FLAT CARRIAGE SPRINGS. For spiral springs, see Art. 484 et seq. E = modulus of elasticity for spring steel = 16,000 tons. e = ultimate extension of fibre, say 0025. 5 = ultimate stress, tons per square inch = E e = 40. L = half length of spring from buckle in inches. 6 = breadth of plate in inches. n = number of plates. W = total load on spring in tons. d = length of offset = v = deflection of spring in inches per ton of load. H 98 HANDBOOK FOE MECHANICAL ENGINEERS. V = working deflection = v W. pi j r = radius of curve of camber = - = approx. 200 t. Safe working load of spring in tons = = 3 JLj 4L 3 LW Half span of spring from buckle = V(2 r Y) v. The deflection varies directly as the load. Another rule : d = deflection in sixteenths of an inch per ton of load. 8 = span in inches. 6 = breadth in inches. t = thickness of leaves in sixteenths of an inch. n = number of leaves. a 6 (n . t 3 ) 222. NOTES ON TORSION AND SHAFTING. Torsion is measured by the load acting at 1 foot radius which is required to fracture a specimen 1 inch diameter. d 3 d* Strength varies as , stiffness as -=-. To run smoothly, long shafting must not twist more than 1 in 10 feet under maximum load. Long shafts are not designed in strict accordance with rule, as they would then be tapered from driving end, involving extra assortment of driving pulleys. Every alteration in diameter of a shaft, unless made at a coupling, must be made gradually by means of a curve at the junction of the two diameters, or a long taper. Factor of safety, long shafts less than 4J inches diameter = T \y ; short shafts and all over 4J inches diameter 3= . STRENGTH OF MATERIALS AND STRUCTURES. 99 Distance apart of supports in feet = 5 = 2000 in addition ) 235. FLANGE STUDS OF STEAM CYLINDERS. For small cylinders allow 2700 Ibs. per sq. inch of net section (minimum diameter of bolts f inch). For large cylinders (over 18 inches diameter) allow 3000 Ibs. ditto ditto. STRENGTH OF MATERIALS AND STRUCTURES. 103 236. To SECURE CHECK OR LOCK NUTS. Put on check nut (J diameter of bolt in thickness), screw up as tight against flange or work as an ordinary nut would be screwed under the circumstances, then put on ordinary thick nut (1 diameter thick), screw it up with the same force and hold on to it with the spanner. Then with a thin spanner reverse the check nut against the other as far as it will go with about the same pressure as before. The check nut has then only the screwing up force to resist, while the thick nut has in addition the strain which may be brought upon it by load or vibration. 237. CHECK NUTS. .... This loosening of a nut can be prevented by adding another nut, which must be screwed hard down upon the first to increase the pressure upon the thread. Willis' l Mechanism.' Note. As described here, the second nut would only be equivalent to thickening the first nut, and would be useless as a check, unless tightened up to the limits of abrasion. 238. PRESSURE ON BEARING AREA IN HOLES. The pressure of a pin in an eye, or a bolt in a hole, or a rivet in a plate, resisting a side pull or shearing stress, should be limited to the safe pressure on bearing surface. The maximum pressure (P) per sq. inch, assuming the bearing surface to be Jth of the circumference, will be = P/* 7854 d t, where P = total pressure, d = diameter, t = thickness. Example. 1^-inch pin, load 3 tons, thickness f inch, P = 3/-7S54 x 1 '5 X '75 = 3-4 tons per sq. inch. Or if required to limit pressure on bearing area to say 2 tons per sq. inch, then 1 J-inch pin with 3 tons load will require thick- ness in eye of t = 3/-78S4 xl*5x2 = l-28 inches. 104 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION IV. PATTERN-MAKING, MOULDING^ AND FOUNDING. 239. PATTERN-MAKING. SMALL patterns made of mahogany or New Zealand pine. Larger patterns made of white or yellow pine. Metal patterns used where a great number of similar castings are required. Wood patterns coated with varnish, to prevent distortion from damp sand, black for general body, red for ends of prints or cores, and yellow for machined faces. Some are one colour only. Patterns should have rounded edges, and filleted angles wherever possible. The thickness of metal throughout a casting should be as uniform as possible, sudden changes of direction being avoided. Sharp angles in a casting are always weak ; the crystals while cooling arrange themselves perpendicularly to the surface, and hence at a sharp turn there is an awkward junction, which becomes a source of weakness. Sufficient taper, say -J inch per foot, must be given to draw out of the sand, and allowance made for knocking to loosen in mould. Holes for bolts, &c., may be " cast in," or " cored out " ; when cast in, sufficient taper must be given to draw the pattern, and small side of hole must be large enough for bolt ; when cored out a print must be put on one or both ends to form support for core. Prints should project from % inch to 3 inches, according to weight of core to be carried. Heel cores are made when the print is at any distance from the parting. PATTEKN-MAKING, MOULDING AND FOUNDING. 105 240. BLACK VARNISH FOR PATTERNS. Lampblack 1 part, shellac 5 parts, methylated finish 16 parts, all by weight. First coat rubbed over with glass paper when dry and second coat then laid on. 241. WEIGHT OF CASTING FROM PATTERN. Multiply weight of deal pattern by 17 for cast iron, 18 for brass, 19 for copper, 25 for lead. Hurst. 242. ALLOWANCE FOR MACHINING. Average on iron castings = -J inch, brass -^ inch. Cast- ings likely to twist k in cooling require more, very small castings require less. In small cylinders J inch in the diameter is sufficient, cylinders over 4 feet diameter say f inch. 243. MOULDING IN FOUNDRY. Green-sand Moulding. Used for light iron castings, fire- bars, rough machine castings, (fee. The ordinary damp sand of the foundry is used in iron boxes or " flasks " for receiving impression from " patterns," the hollow parts being formed of baked sand " cores." Long cores are supported by "chaplets," small and complicated cores are made of " loam." Dry-sand Moulding. Used for ornamental ironwork, important machine castings, and for casting in brass. The sand consists of fresh sand mixed with loam which has been used, or of fresh sand only. When finished, the moulds are dried for several hours. " Blackening " prevents sand melting. Loam Moulding. Used for steam cylinders, bent pipes and complicated work. The mould is often built up with- 106 HANDBOOK FOB MECHANICAL ENGINEERS. out patterns, and consists of brickwork coated with loam and " swept " to required shape by a " loam board." Long straight cores are formed of iron pipe with haybands twisted on to hold the loam, and other cores of loam strengthened by bent " core-irons." The loam is common brick-clay mixed with horse-dung, cow -hair, sand, &c. " Kunners " and "gates " are openings in the sand to let the metal into the mould ; " vents " are openings to let the gases out, formed by prick- ing the sand. 244. SAND FOE MOULDING. Moulding Sand consists of 93 to 96 per cent, of sharp sand and 3 to 6 per cent, of clay. Quality varies for different castings ; the smaller the castings, the more clay the sand may contain ; heavy castings require poorer and coarser sand. Coal and coke are used to make the sand more porous ; this makes the castings rougher, but by giving free vent to the gases makes them sounder. Moulding sand after use is " screened " and wetted before being used again. Parting Sand is the burnt sand scraped off castings, and is used to facilitate the division of the upper and lower boxes in moulding. Core Sand consists of 90 per cent, sharp sand and 10 per cent, of clay, and should be used fresh. 245. FOUNDRY DRYING STOVE. Brick chamber of three sides with arched top shut with close iron doors on fourth side. Size about 10 feet X 10 feet x 7 feet high. Fire-place on one side, flue near ground on opposite side to spread the heat and carry off the moisture, fire fed through a door on outside. Iron shelves on walls for drying small cores and boxes. Eails run from crane into drying stove, so that large moulds may be wheeled in. Stoves of various sizes in large foundry, the larger ones only used when required for very large moulds. PATTERN-MAKING, MOULDING AND FOUNDING. 107 246. NOTES ON MOULDING AND CASTING. Keep most important side of casting at the bottom to ensure density in the metal, as tension flange of girder, &c. Make ample provision for escape of gases by pricking the mould, providing vents, &c. Support long cores and stiffen with core irons to prevent displacement by molten metal. Knock pattern slightly before drawing from mould to enable it to be lifted without breaking the sand. Provide sufficient number of gates to ensure the mould being completely filled with metal. Allow ample head on important castings to cut off all " sullage " or porous and honeycombed portion. The molten metal should be stirred through the gates with an iron rod, called a " feeding rod," to agitate it and cause it to fill angles and corners, more metal being added if required. Directly the metal is run into the mould the gases should be fired to prevent explosion. Metal usually run in afternoon, allowing all night for castings to cool. 247. CLEANING CASTINGS. Moulds taken apart and sand removed as soon as cast- ings have set, castings taken out with tongs and left to cool, time varying according to weight and mass. Gates, or " gits," and partings, or " fins," broken off, and heavy or hard cores removed in foundry before casting is cold. Pro- jections removed in cleaning or fettling shop with chisel, sharp hammer, or worn-out file, and casting well brushed with steel wire brush. Grindstones or emery wheels used in some shops instead of chisel and file. Blow-holes stopped with black putty, cement, or lead, and castings painted with black wash. Badly honeycombed castings thrown on the scrap heap. The scrap averages 25 per cent, of the castings, less on large work. 108 HANDBOOK FOE MECHANICAL ENGINEERS. 248. CLASSIFICATION OF IRON ORES. Mr. Truran classifies the ores of Great Britain into four great divisions, thus : A. The argillaceous ores of the coal formations, having clay, but sometimes silica, as the chief impurity. B. The carbonaceous ores of the coal formations, distin- guished by their large percentage of carbon. C. The calcareous or spathic ores, or the sparry carbo- nates of iron, having lime as their chief earthy admixture. D. The siliceous ores, having silica as their predomi- nating earth. This class is subdivided into the red and brown haematites, the ores of the oolitic formation, the white carbonates, and the magnetic oxides. 249. CHAKGES EMPLOYED AT DOWLAIG FOR DIFFERENT KINDS OF PIG IRON. Foundry Pig. White Forge Pig. Common Forge Fig. Calcined " mine " (fresh ore) Red haematite ore . Forge and refinery cinder Limestone Coal .... cwt. 48 17 50 cwt. 28 10 10 14 42 cwt. 16 25 16 36 Weekly make 130 tons 170 tons 190 tons 250. ANALYSES OF PIG IRON. Carbon, partly combined and partly in a graphitic form Silicon Sulphur . Phosphorus Per cent. 2-3 to 5 0-13 5 0-0 7 0-0 0-0 , 1 5 7 6 87 PATTEKN-MAKING, MOULDING AND FOUNDING. 109 251. FOUNDRY PIG. No. 1 Pig is chiefly used in the foundry. Colour dark grey, crystals large and leafy, carbon in form of graphite. Very soft, melts very fluid, but being coarse-grained, will not give a sharp impression. Cools slowly. For fine castings the presence of a little phosphorus is advantageous : the grain is finer, the iron a lighter colour, and the impres- sions sharper. Used for small castings, hollow ware, small machinery, &c. No. 2 Pig, grey and mottled in colour. Carbon partly combined. Used for large castings in dry sand or loam. Melts fluid, is tough, close texture, fills the mould well, more free from impurities than No. 1. Heavy machine castings made from No. 2, or various mixtures of 1, 2 and 3. No. 3 Pig, hard and white, used for mixing. Carbon all chemically combined. 252. MIXTURES OF PIG IRON. Mixture recommended for girders, &c., where rigidity and strength are required : Lowmoor, Yorkshire, No. 3 30 per cent. Blaina or Yorkshire No. 2 25 Shropshire or Derbyshire No. 3 . 25 Good old cast scrap . . . 20 100 Fairbairn. Mixture for steam cylinders, strong and close grained. No. 5 charcoal pig . . . .8 parts. Scotch pig . . . . . 10 Good cast. scrap . ... 10 110 HANDBOOK FOR MECHANICAL ENGINEERS. For the same, where greater hardness is required. No. 5 charcoal pig Scotch pig Good cast scrap 2 parts. 4 30 Piston rings should he of softer metal than the cylinders. Rigg's ' Steam Engine. 3 253. MELTING METAL FOR CASTINGS. Crucibles are sometimes used for melting iron for trinkets and small goods. The hest castings, whether iron, bronze, or other metal, for machine frames, bells, statues, &c., are made from a reverberatory furnace, run directly from the furnace in dry sand ditches to the mould. The cupola has the advantage of melting iron cheaper than any other furnace ; where strength is unimportant, it is the best method. 254. CONTRACTION OF METALS IN COOLING. Metal. Contraction. In Fractions of Linear Dimensions. In Parts of an Inch per Foot of Linear Dimensions. Cast iron Gun metal Yellow brass . Copper . Zinc and tin . V A * I TV 255. CONTRACTION OF CASTINGS. Heavy pipes Girders, beams, &c. _ i inch per foot. in 14 inches. PATTERN-MAKING, MOULDING AND FOUNDING. Ill = 4 Engine beams ) Connecting rods j Large cylinders, say 70 inches diameter X 10 feet stroke, the contrac- tion of diameter Ditto in length . * Small narrow wheels, about Large heavy wheels Thin brass . Thick brass . Gun-metal rods . Zinc . Copper. . Bismuth . Tin and lead, each Pattern-makers commonly allow for iron castings -J- inch per foot, and for brass castings T 3 inch per foot. The ap- parent contraction varies considerably according to the amount of " rapping " the pattern receives in the sand. inch in 16 inches. [ at top. at bottom. in 16 iches. per foot diam, or more in 9 inches, in 10 inches. in 9 inches, inch per foot. 256. EXPANSION OF CASTINGS. Some castings, owing to their form, expand in one direc- tion while contracting in another. This is known to pattern- makers as " compression." It is usually a [contraction of surface area and expansion in thickness, the expansion taking place in the direction in which the heat most readily radiates, and being chiefly noticeable in tram plates and such like forms. 257. BRONZE AND BRASS CASTINGS. Melted in crucibles, wasting prevented by covering surface with mixture of potash, soda and charcoal powder. Copper melted first, then tin, zinc, or antimony, then cover- 112 HANDBOOK FOE MECHANICAL ENGINEERS. ing applied. Zinc is best added in form of brass, calculating the copper contained. Large strong castings require the metal exposed to fire in fluid state 8 or 10 hours, proof taken by small ladle and broken when cool, judged by crystallisa- tion, and copper or tin added as required. Before casting, bronze is well stirred with heated iron rods. Brass made by melting together copper scraps, crude zinc or spelter, and charcoal powder, remelted for casting. About 7 Ibs. per cwt. is allowed for waste. FORGING, WELDING, RIVETING, ETC. 113 SECTION V. FORGING, WELDING, RIVETING, ETC. 258. FORGING. WROUGHT-IRON at a red heat may be hammered into various shapes, called " forging." When a piece is drawn down smaller it is called " swaging" ; if jumped up thicker, it is called " upsetting." Common iron is not suitable for forging, as the scale or slag in it causes cracks. Double and treble best Staffordshire and ordinary Yorkshire are suitable. The best Yorkshire is used for flanging and difficult forgings ; charcoal iron for light and complicated work. Steel may be forged gradually at a low heat. The greater the proportion of carbon contained, the greater the difficulty of forging. All forging should proceed by easy stages, and care be taken not to burn the iron or steel. Large pieces have a rod or " porter " welded to them for convenience in handling by a crane. 259. WELDING is the process of joining two pieces of wrought iron or steel by heating, and hammering them together. To weld iron the pieces must be brought to a white heat, and the scale swept off before they are put together. Steel requires a much lower heat, and the surfaces should be sprinkled with sand, borax, or silicate of soda, to aid the surface fusion. Borate of soda similarly aids the surface fusion of spelter in hard soldering. The welding temperature depends upon the amount of carbon contained : hence the extra difficulty of welding two pieces of different composition. Mild steel ap- 114 HANDBOOK FOE MECHANICAL ENGINEERS. preaches wrought iron in its welding qualities. Steel faces may with care be welded on to iron tools; shear steel is generally used for this purpose. Average loss of strength in weld is 15 to 20 per cent. In electric welding, a current is passed through the abut- ting edges which are pressed together, surface-fusion is almost immediately produced, and the junction commences at the centre, proceeding uniformly to the outside. This weld is said to be of equal strength with the solid material, but the loss probably reaches 10 per cent. 260. TEMPERING. Steel when heated to a cherry red, and suddenly cooled in water or oil, is rendered very hard. Some suppose that the carbon is caused to take the crystalline or diamond form. For tempering the hardened steel a portion is brightened with a piece of broken grindstone, and then reheated until the film of oxide formed on the surface shows the requisite temperature ; it is then quenched in water, and the hardness is found to be " let down " to the " temper " required. Tempering was formerly considered to be the only true test of steel. 261. COLOURS CORRESPONDING TO TEMPERATURE. Deg. F. Lowest red heat visible in the dark . 635 Faint red 960 Dull red ....... 1290 Brilliant red ...... 1-470 Cherry red , , . . . 1950 Bright cherry red 1830 Orange 2010 Bright orange 2190 White heat ..,,,. 2370 Bright white heat . . . . .2550 Dazzling white heat .... 2730 Welding ox scintillating heat . . 2800 Becquerel> Pouillet^ dc. FOEGING, WELDING, EIVETING, ETC. 115 CO CO CO CO -3 H,g 33 SiV b .a I 2 *f|i w ^ ^3 'S b| D a? P.2 S -S3 1 1 a i I s s .1 ^ nS 43 ,, -rt " iS e S oa" *3 "^ -" : I I HI O F^ rrt 'O ^*- ^0 II S ^' 2 o 5 02 i g> 13 2 t Oi T^ <* O O O O o o o o ? I ^ ^ "3 ^ "3 * ^ o 'S ^ CM g S >, ill 11 ft o if II ft B ^ ^ 3 a ft O i 2 116 HANDBOOK FOB MECHANICAL ENGINEEES. From experiments made by Wedgwood, there is reason to believe that all bodies susceptible of the requisite tempera- ture become red hot at exactly the same point. Wood and most liquids are dissipated before their temperature can be sufficiently raised to be luminous. Gases do not become luminous, even at a much higher temperature than suffices for solids. 263. NOTES ON RIVETED JOINTS. Hard wrought iron is weakened from 15 to 30 per cent, by punching. In punched plates the small sides of the holes should come together. Drilled holes should have the edges chamfered. The tension in a rivet may be estimated at 21,000 Ibs. per square inch of its section. Friction due to this tension would be about 7000 Ibs. per square inch of rivet section. The usual diameter of rivets in hand riveting varies from J inch to -| inch. In machine riveting they may be used up to 1J inch diameter. Maximum efficiency of single riveted joint = | strength of plate. Ordinary efficiency = T V Maximum efficiency of double riveted joint = f strength of plate. Ordinary efficiency = f . Pitch of rivets (for equal area of plate and rivet) = Sect, area of rivet x effective No. of rows diam> ^^^ Thickness of plate Chain riveting = * * * * - Zigzag, reeled, or staggered = X x X x X x - To rivet by hand requires a minimum of 1 diameter, and by machine 1^ diameter of rivet to form head. Length of rivet for good head = thickness of plates passed through -j- \\ diameter + T V inch for each joint. Kivets 6 to 8 diameters long often draw off their heads. Rivets are FORGING, WELDING, RIVETING, ETC. 117 usually -j^ inch smaller than hole, generally f-inch iron in -j^f inch hole, but may be ^-inch iron in f-inch hole. Countersunk rivets 60, countersunk |- diameter of rivet. A rivet hole cannot be punched with its edge nearer the edge of the plate than its own diameter without risk of its bursting through. To this it is safe to add -J- inch to J inch on the plate as the size of rivet and thickness of plate increase. The edges of two holes cannot be nearer than 1 to 1 J diameter without risk of the second hole distorting the first, or the two holes punching into one. The efficiency of the bearing surface of rivets = 5 tons per square inch ; thus a f-inch rivet in a f-inch plate = -| X f x 5 = 3 * 3 tons nearly. 18 rivets go to the " yard" for piecework, irrespective of the pitch. 264. PRESSURE TO CLOSE RIVETS. Experiment : Cold riveting, f-inch rivets. At 10,000 Ibs. rivet swelled and filled hole without forming head. At 20,000 Ibs. head formed and plates slightly pinched. At 30,000 Ibs. rivet well made. At 40,000 Ibs. metal in plates round rivet began to stretch. Therefore, approximately, d in ^ths 2 X 2 = tons pressure required for cold riveting per sq. inch of rivet section, and d in ^ths 2 = tons pressure for hot riveting per sq. inch rivet section. 265. MACHINE RIVETING FOR BOILERS. With f-inch rivets the closing pressure in riveting f-inch plates is 38 tons, J-inch plates 40 tons, and steel plates 45 tons. The cup must be left on until the rivet is black. In hydraulic riveting the pressure on the cup head = 12,000 to 16,000 Ibs. per square inch of surface. 118 HANDBOOK FOE MECHANICAL ENGINEERS. 266. PROPORTION OF EIVET DIAMETER TO THICKNESS OF PLATE. In punching, the resistance of steel = 100 k per sq. cm. iron = 30 Punch = 100 x ^j-, plate = 30 -rd X e. . . d > - r = 1 2 e (e = thickness) ; 100^ 4 but d must be < 3 e, or crushing by the pressure of the rivet on edge of plate will occur, hence the usual proportion of d = 2 e. Planat. 267. ElVETING. Heads *66d x I'QQd with radius of -86 d. Length to make this = 1 d (?), N = tension, o> = section, t = tempera- ture of heated rivet when closed, E = coefficient of elasticity, then N _ 7E< "^ ~ 11 x 81,600' N being the tension capable of producing a stretch equal to that by temperature t. The tension is independent of the length, and varies solely as the closing temperature, which should not exceed 212 F. Adhesion due to this temperature = 9*4 k per sq. mm., and at 150 C. = 14 k . Planat. 268. SINGLE EIVETING IN BOILER OR TANK WORK. t = thickness of plates in inches. d = diameter of rivets p = pitch I = lap of plates FORGING, WELDING, RIVETING, ETC. 119 269. EIVETS IN TIE BARS AND DIAGONAL RIVETING GENERALLY. Prof. Kennedy, in his ' Abstract of Kesults of Experiments on Riveted Joints,' as made by the Research Committee of the Inst. Mech. Eng., says, " It has been found that the net metal measured zigzag should be from 30 to 35 per cent, in excess of that measured straight across in order to ensure a straight fracture. This corresponds to a diagonal pitch of f p -f- - , if p = the straight pitch and d the diameter of the o rivet hole." 270. NOTES ON CAULKING. Caulking consists of burring up the inner edge of the plates in a joint by means of a tool like a flat-ended chisel, to prevent leakage in boilers, tanks, &c. Plates with rough sbeared edges should be chipped even, to a slight bevel, before caulking. Joints appearing at all open should be closed by a flogging hammer before caulking. When the caulking is done on one side only, it should be upon the same side as the riveting. In best work the joints are caulked inside and out. When the lap exceeds three times diameter of rivet the caulking is apt to open the joint, unless done very lightly. 271. CAULKING TOOLS. The caulking tool should be flat-ended and slightly bevelled, from ^ inch to T 3 inch thick x 1 inch to 1 J- inch wide, with one edge square, and the other rounded to prevent cutting into the plate. The rounded edge should be held next to the plate the first time of going along the joint, called splitting the lap, and afterwards reversed. The finished caulking should appear like a parallel groove about -^-inch deep X ^-inch wide in a f-inch plate. 120 HANDBOOK FOB MECHANICAL ENGINEERS. SECTION VI. WOEKSHOP TOOLS AND GENEEAL MACHINEEY. 272. OBJECT OF MACHINES. THE object of machines is to change the direction of motion, or to regulate the distribution of power. They transmit energy and modify it in direction, intensity, or velocity, but they can neither create nor increase power. An engine trans- mitting energy from natural forces is called a prime mover, but is otherwise a machine. The POWER of a machine is measured by the WORK which can be done in a given TIME. Machines are used for 1. Accumulating force upon a given point or object. 2. Increasing or decreasing velocity of motion. 3. Prolonging the action of a power. 4. Changing the direction of motion. 5. Eeducing the time of labour. 6. Producing accuracy in work. The parts may be divided into 1. Receivers. 2. Communicators. 3. Operators. Motive Power may be derived from 1. Man and animals. 5. Action of springs. 2. Fall of water. 6. Expansion of elastic fluids. 3. Force of wind. 7. Electricity and magnetism. 4. Descent of weights. 8. Chemical reactions. WORKSHOP TOOLS AND GENEEAL MACHINERY. 121 273. MACHINERY IN MOTION. In engines or machines in motion, when the power exceeds the work the speed will be accelerated, unless pre- vented, until the resistance + the useful work = the power. When the resistance + the useful work exceeds the power, the speed will be retarded until a balance is again obtained. In the former case the inertia of the parts will absorb some of the power, and in the latter this power will be again given out as momentum. Motion may be rectilinear or curvilinear direct or re- ciprocating uniform or variable (uniformly accelerated, uniformly retarded, or irregular). 274. USEFUL WORK AND EFFICIENCY. Useful work of a machine is that performed in producing the effect for which the machine is designed. Lost work is that performed in producing other effects, as overcoming friction, loss by leakage, &c. The power of a machine is the energy exerted, and the effect the useful work performed, in some interval of time of definite length. The efficiency [or mechanical efficiency"] of a machine is a fraction expressing the ratio of the useful work to the whole work performed or energy expended. This ratio is also called the modulus or coefficient of the machine. The counter-efficiency is the reciprocal of the efficiency, and is the ratio in which the energy expended is greater than the useful work. Hankine's ' Applied Mechanics.' 275. ECONOMICAL WORKING OF MACHINES. In every machine a certain rate of work develops the maximum efficiency. A medium load with a fair velocity produces more units of work than a heavier load with a less velocity, or a lighter load with a greater velocity. 122 HANDBOOK FOE MECHANICAL ENGINEERS. 276. VELOCITY RATIO. The velocity ratio in any machine is the proportion between the movement of the power and the movement of the resis- tance, in the same interval of time; for example, in a punching press it may be 100 to 1 = ^y^, and in a hydraulic crane 1 to 8 = -J. These proportions also express the amount of the resistance (including friction), compared with the power or pressure applied. See also the definitions of virtual velocity, art. 278. The term purchase of a machine is applied, either to the motion or pressure of the resistance compared with the power; in above examples, the purchase of the punching press would be 100, that of the hydraulic crane 8, but the term is generally restricted to the gaining of pressure by the sacrifice of speed, as in the first case. By the mechanical advantage of any machine is meant the ratio of the weight (or resistance) to the power, when in equilibrium. Sometimes improperly called the mechanical efficiency. 277. PRINCIPLE OF VIRTUAL VELOCITIES. If any machine without friction be in equilibrium and the whole be put in motion, the initial pressure P will be to the final pressure p as the final velocity V is to the initial velocity v, or P : p : : V : v, or p V = P v. Instead of velocity (V and v) we may take " space moved over " (S and *). In practice, as all machines have friction, p will depend upon the friction, but V will be in accordance with the calculation of the leverage or gearing. Let e = the final pressure by experiment, then p e = friction, and the coefficient -or modulus of machine P WOKKSHOP TOOLS AND GENEEAL MACHINERY. 123 278. DEFINITIONS OF THE PRINCIPLE OF VIRTUAL VELOCITIES. Rankine's. The effort and resistance are to each other inversely as the velocities, along their lines of action, of the points where they are applied. Twisden's. If a system of pressures, in equilibrium, act on any machine which receives any small displacement, consistent with the connection of the parts of the machine, the algebraical sum of the virtual moments of the pressure will equal zero. 279. WORK, IN TERMS OF ANGULAR MOTION. r = radius = leverage. 2 TT r = circumference. p = pressure at circumference. rp = moment of pressure. n = number of revolutions. 2 TT n = angular motion. rp X 2 TT n = foot-lbs. work performed, rate of work = work performed in a unit of time as 1 second or 1 min. Hankine. 280. ANGULAR VELOCITY. The angular velocity of a wheel is the speed of a point in the circumference of an imaginary wheel with unity as radius, and making the same number of revolutions per minute as the given wheel. Velocity is taken in feet per second. Revolutions are taken at per minute. ~. ,, ,. T ,., 2irrn irrn Circumferential velocity = = = 10472 r n. oO oO Angular velocity = v ^ H = ^ = -10472 . uU oO Velocity of any point in wheel radius of ditto in feet = an ular velocity. 124 HANDBOOK FOR MECHANICAL ENGINEERS. 281. ANGULAR MEASUREMENT OF FORCES. A radian, or unit of angular rotation, is an arc of a 180 length equal to radius; it contains 57*2958 degrees = 7T A right angle therefore contains 1-5708 radians, two right angles 3-1416 radians, and four right angles 6-2832 radians ; or one revolution = 2 ?r radians, and n revolutions per minute = radians per second. Degrees in an angle 57-2958 - = No. of radians. Radius x No. of radians = length of arc. The angular velocity of a wheel may be measured in radians per second. A round is the angular space traversed in one revolution. A round contains 6 2832 radians. The linear velocity of a point in a wheel is equal to the angular velocity X the distance in feet of the point from the axis. All points in a revolving wheel have the same angular velocity. A torque (Jas. Thomson) is a system of forces, not meeting in one point, which, acting upon a body, may be parallel to and proportional to the sides of a closed polygon, but whose turning moments do not balance about any axis. It is equivalent to a " couple." In machinery it means turning moment or turning force X distance from centre of shaft. In Ayr ton and Perry's dynamometer coupling, or trans- mission dynamometer, the total amount of the forces of the springs in pound-feet, or the " torque," X angular velocity per minute -J- 33,000 = the horse-power, thus : torque x angular v. per minute ' ' = 33,000 WORKSHOP TOOLS AND GENERAL MACHINERY. 125 282. ANGLE OF TWIST. A straight line drawn along a shaft not transmitting power, becomes a spiral while power is being transmitted. The angle between the spiral line at any point and the original direction divided by the radius of the shaft is called the angle of twist. Perry. 283. WORKSHOP TOOLS are divided into two classes, hand tools and machine tools. In the former are included hammers, chisels, files, ratchet braces, spanners, &c. ; and in the latter, lathes, planing, shaping, drilling and slotting machines, &c., in the fitting shop ; and punching and shearing machines, bending rolls, steam hammers, &c., in the smiths' shop. The machine tools are now mostly driven by steam power through shafting connected by belts. A workshop should be so arranged that the raw material coming in at one end would be received at the various tools in the order of the work to be done upon it, and be removed in a finished state at the other end. 284. HAMMERS. Name. Weight. Length of Shaft. Ibs. inches Sledge . 28, 24, 18 and 14 40 Flogging Riveting 7 and 5 4 and 3 30 24 Hand . 2 20 Fitting . If 16 Bench . ii 14 i 12 126 HANDBOOK FOR MECHANICAL ENGINEERS. 285. WORK OF HAMMER. Hammer 2 Ibs., velocity 20 feet per second, drives nail J inch into hard wood ; required the equivalent dead pres- sure. (v. after striking = 20 to 0, mean = 10; therefore t in driving J inch = ^^ of a second.) See art. 64. by P = , -- X = 298 Ibs. gt 3Z A ^ = 298 Ibs. as before ; but this will only be the mean pressure. From experiments it appears that the maximum pressure required is about Ij times mean pressure, so that the actual dead pressure required to force same nail same depth would be 298 X 1 '75 = 521 * 5 Ibs., and the force required to extract it, being about | of pressure to insert it, would be 521-5 x f = 417 Ibs. Where the resistance varies simply as the depth driven, the maximum pressure is double the mean. The same principles apply to pile driving. See papers by the author on * The Force of Hammers ; or, Percussion v. Pressure,* and * Timber Piling in Foundations and other Works.' 286. IMPACT OF MOVING BODIES. In these formula3 mass may be substituted for weight without affecting the result. W = weight of body A giving blow. V = velocity A V 1 = A after impact. w = weight B receiving blow. v = velocity B WORKSHOP TOOLS AND GENERAL MACHINERY. 127 BODIES PERFECTLY ELASTIC. (1) Both moving in same direction. V 1 = 2 W .J + B +. Or, putting R = mutual action between two bodies moving in opposite directions, V 1 = W WV-R W V 1 = w WV -2R For intermediate condition of matter, between perfectly soft and perfectly elastic, use coefficient e R. 128 HANDBOOK FOB MECHANICAL ENGINEERS. Example of Case 2. Body A weighing W = 10 Ibs., moving at velocity V = 20 feet per second, strikes body B weighing w = 30 Ibs. W V 10 X 20 at rest. When perfectly soft or inelastic = - = - --- = 5 feet per second as the resulting velocity of A and B moving together. But, by formula for kinetic energy, if the units of work existing in A remain in the combined masses W V 2 (W + w} V 2 after striking, = v - - '- , the resulting velocity & 9 * 9 would appear to be = 20 loTso = 10 feet per seoond - The explanation is that the total momentum is always the same, but the energy is only constant when the bodies are perfectly elastic, i.e. when the restitution is complete. When the elasticity is imperfect, part of the work is used in com- pressing the particles, and the lost velocity is transformed into heat. If the same bodies were perfectly elastic the resulting velocity of A would be i.e. it would rebound at half the striking velocity, and the resulting velocity of B would be W' ~V /10 x 20\ v 1 = 2 - = 2 ( j = 10 feet per second in forward direction. The energy before and after would be WY 2 _ WY t 2 v>v* ~^g~ 2g ' 2g ' 10 x 20 2 = (10 X - 10 2 ) + (30 x 10 2 ), or 4000 = 1000 + 3000. Q.E.D. WOKKSHOP TOOLS AND GENERAL MACHINERY. 129 287. NOTES ON WORKSHOP TOOLS AND FITTINGS. Top of vice jaws from floor = 40 inches to 44 inches, say average of 42 inches, or level with the elbow. 288. HOLTZAPFFEL'S CLASSIFICATION OF CUTTING TOOLS. Shearing tools act by dividing the material operated on into two parts, which separate from each other by sliding at the surface of separation. Paring tools cut a thin layer or strip called a shaving from the surface of the work, and thus produce a new surface. Scraping tools scrape away small particles from the sur- face of the work, thus correcting the small irregularities which may have been left by the paring tool. 289. ANGLES OF TOOLS. Angle of Tool. For wood J> .~ * . . 30 to 40 wrought iron . . * : 60 cast iron : . V . ' . . 70 brass .... 80 Angle of relief for all tools, 3 to 10 290. CUTTING SPEED OF MACHINE TOOLS. Ft. per Min. Cast steel . . 10 to 12 Mild * . . 12 15 Cast iron . . 15 20 Wrought iron . . 15 25 Gun metal . . 20 40 Yellow brass . . V 40 60 Wood . . .500 2000 when material revolves. .; . .3000 5000 when tool revolves. Grindstone . . 800 Milling wrought iron 80 100 cast steel 25 , 30 K 130 HANDBOOK FOE MECHANICAL ENGINEEES. Average for wrought or cast iron in lathe, shaping, slotting, &o., 20 feet per minute. Generally the cutting speed should be as fast as possible without the tool overheating and losing its temper. 291. AVERAGE CUTTING SPEEDS AND FEEDS. Roughing. Finishing. Speed. Feed. Speed. Feed. Wrought iron . . . ft. per rain. 25 cuts per in. 20 ft. per min. 25 cuts per in. 25 Steel . . . . 18 25 15 30 Cast iron . . . 25 16 25 6 292. SPEED OF MACHINE TOOLS. [ Wrought iron, 20 feet per minute. Speed of cut j Cast 16 I Cuts per inch, 16 to 80. For flat work : Speed in inches per second x 5 = speed in feet per minute. For small diameters : Diameter in inches X revolutions in 16 seconds = speed in feet per minute. For large diameters : Diam. in inches X 16 = d in feet min _ Seconds lor 1 revolution Cutting speed in feet per min. X 5 = ft< tooled per Cuts per inch ' Engineering.' WOKKSHOP TOOLS AND GENERAL MACHINERY, 131 293. CUTTING SPEEDS. Shearing and punching . , 2 ijeet per minute. Turning malleable cast iron 3 Screwing . ..' 6 Turning steel . . . .10 cast iron . . . 16 wrought iron . * 21 bronze * * . < 30 ' English Mechanic.' 294. SPEED IN CUTTING METALS. Turning chilled rolls . . . . 3 to 4 ft. per min. Screw-cutting steel in lathe . ' 7J Turning and planing steel . . 10 Boring cast-iron cylinders . 12 Turning, planing and shaping cast iron 15 to 20 Do. do. wrought iron and very soft cast iron . . . . . 20 40 Do. do. steel . . . . . 24 30 Do. do. brass 36 100 Screw-cutting gun-metal ... 30 Turning copper . *~ . ^ 30 Band-saws for hot iron and steel . 200 300 Circular saws for do. do. . 12,000 to 27,600 Keerayeff. Circular saw, consisting of soft iron disc running at circumferential speed of 12,000 feet per minute, is used for cutting ends of steel rails, with jet of water playing on circumference of saw. E 2 132 HANDBOOK FOE MECHANICAL ENGINEEKS. 295. SPEED OF MILLING CUTTERS. For brass cast iron **. ;'. wrought iron , steel Ft. per min. . 120 : GO ." 48 36 Feed In. per min. , 2-66 , 1-66 , 1-00 0-50 Angle of teeth 70, clearance angle 10. 4 inches diameter = 35 teeth, 6 inches diameter = 43 teeth, 8 inches diameter = 51 teeth. Addy. 296. EESI STANCES IN MACHINE TOOLS. TWIST DRILL. Pressure on head of twist drill in Ibs. requisite to pro- duce proper cut = diameter of drill in inches and decimals X 1500. LATHE. Material. Width of Cut. Depth of Cut. Speed of Cut. Resistance to Traverse of Tool. Sted . ,,. Jj V inches ife inches * ft. per min. 5 Ibs. 600 Wrought iron . * A 10 700 Cast iron & TV 15 325 PLANING MACHINE. Cast iron, width of cut T V inch, speed of cut 11 feet per minute. With depth of cut = ^ inch pressure against tool varied from 356 to 396 Ibs., averaging 373 Ibs., or 4065 ft.-lbs. work per minute. With depth = -^ inch, pressure varied from 340 to 559 Ibs., averaging 458 Ibs., or 5000 foot-lbs. work per minute. WORKSHOP TOOLS AND GENERAL MACHINERY. 133 MILLING CUTTERS MADE FROM "BOHLER" STEEL. Diameter of cutter . . . 36 mm. Revolutions per minute . , . 110 Travel per minute 32 mm. Teed , V ."'j f: ' m " 3 Plates . . . ", ". :;: r> ! V' 4 to 6J- Rails, angles and tees . f *.' J .' " 5^ Rods and bars . . T ' '** 6 to 8 Fly-wheels for mill . * V '~~ . ~ 80 to 100 Wire-drawing rollers . . . 1 to 3J Cold rolling . - r ' . 3- Plate bending .... -^ Keerayejf. 303. SHEARING AND PUNCHING. Resistance to shearing of wrought iron averages 50,000 Ibs. per square inch area of surface cut. This will be the pressure required on the material at the commencement of the stroke. The mechanical work in punching or shearing is estimated by Weisbach as this pressure exerted through one-sixth the thickness of the plate, and the coefficient or modulus of the machine as 66, the friction being taken at 33 per cent, of the gross pressure. For rectangular bars the pressure may be taken as exerted through one-fourth the thickness, and for round bars one-third the diameter. WORKSHOP TOOLS AND GENERAL MACHINERY. 137 Formula for calculating power required : t = Thickness of plate or bar. I = Length or circumference of cut. / = Eesistance of material to shearing. M = Modulus of machine, say 66. P = Gross pressure in Ibs. M Pressure required to punch wrought-iron plates (from experiments). d t PC To punch -J- hole in -J- plate requires 2J tons = 144 i > * 6* 104 f f 13 ,, 92 4 i 22 88 I I ,, 33^ 86 f i 47J 84 f ,, I ,, 62| 82 II 80 80 P = d X t X c. Approximately diameter x thickness X 88 = pressure in tons ; or, area of cut surface x 28 = pressure in tons. Diameter of die = diameter of punch x lyV Point of punch coned 5 with hollow curve. Shearing: falling blade bevelled 3 to 8 in elevation, and 15 in section; fixed blade horizontal and square. 304. STEAM HAMMERS. Weight of hammer in Ibs. for shaft forging = 80 X diameter shaft inches 2 . Weight of anvil = 10 times weight of hammer. 138 HANDBOOK FOR MECHANICAL ENGINEERS. 305. STEEL FORGING PRESSES. Pressure required = 16,000 Ibs. per square inch on the die. 306. OBSERVED H.P. REQUIRED TO DRIVE SHOP TOOLS. Small screw-cutting lathe, 12-inch swing . 0'33 Screw-cutting lathe, 20-inch swing . . 0*47 Large facing lathe, 68-inch swing . . 0*91 Small shaper, 9 J-inch stroke . . . 0-24 Shaper, 15-inch stroke . . . . 0*63 Large shaper, 2 9 -inch stroke . . . 1 14 Planer, 36 inches X 36 inches X 11 feet . 0*84 Large planer, 76 inches X 76 inches X 57 feet 1-47 Small drill press 0-62 Large drill press . . . . . 1 * 24 Radial drill, 6-foot swing . . . .0-53 Small slotter, 8-inch stroke . . . . 28 Medium slotter, 9 J-inch stroke . . . 44 Large slotter, 15-inch stroke . " . . 0'95 Universal milling machine . . . . 0*28 Milling machine, 13-inch cutter head, 12 cutters 0-66 Small punch and shear combined, 7J inches X li inches 0-79 Large plate shears, knives 28 inches X 3-inch stroke 7*12 Large punch press, 3-inch stroke through 1J inches thick . . . . . 4*41 Plate bending rolls, 9J feet X 13 inches . 2-70 "Wood planer, 28-inch rotary knives . . 5*00 Circular saw for wood, 23 inches . 3*23 Circular saw for wood, 35 inches . . 5*64 Band-saw for wood, 34-inch wheel . . 0-96 Tenon and mortising machine , . . 2 73 WOKKSHOP TOOLS AND GENEEAL MACHINEKY. 139 Wood moulding machine, 7J inches x 2J inches. ...... 2-45 Grindstone for tools, 31 inches X 6 inches, 680 feet per minute , ... . 1 * 55 Grindstone for stock, 42 inches X 12 inches, 1680 feet per minute . . . .3-11 Emery wheel saw-grinder, 11 J inches x V. 0-56 Flathers. 140 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION VII. POWER TRANSMISSION BY BELTS, ROPES, CHAINS AND GEARING-. 307. TRANSMISSION OF MOTION. BY rolling contact, as spur wheels and pinions, crown wheel and pinion, face wheel and lantern, bevel wheels, cones, rack and pinion, &c. By sliding contact, as inclined plane, wedge, cams, swash plate, crown wheel escapement, screw, &c. By wrapping contact, as cords and pulleys, belts and pulleys or riggers, speed pulleys, capstan, fusee of watch, &c. By link work, as levers, cranks, treadle of lathe, &c. Tomkins' 'Machine Construction.' 308. NOTES ON BELT GEARING. Coefficient of friction between ordinary leather belting and cast-iron pulleys or drums = *423. Ultimate strength of ordinary leather belting = 3086 Ibs. per square inch. Belts vary from T 3 ^ inch to J inch thick, average -fa inch. The strongest part is one-third of the thickness on the flesh side. Breaking Strain. Safe Working Strain. Through solid part . 675 Ibs. . 225 Ibs. per inch wide. Through riveting . 382 Ibs. . 127 Through lacing . V 210 Ibs. . 70 The working strength of the belt must be taken as that of its weakest part, which is the lacing. POWER TRANSMISSION BY BELTS, ROPES, ETC. 141 The tension of the driving side, which must not exceed the safe working strength of the belt = force transmitted + mean normal tension. The force transmitted = the difference between the tension of the driving side and the tension of the following side. Welch's * Designing Belt Gearing.'' When the arc of contact = 180, the force able to be transmitted may be taken as 50 Ibs. per inch wide. If more or less than half circumference be embraced by belt, the force transmitted may be increased or reduced by about 2-8 Ibs. for every 10 difference from 180. The sum of the tensions, or cross strain on shafting, may be taken as 90 Ibs. per inch wide. The lower side of a belt should be made the driving side when possible, so that the arc of contact may be increased by the sagging of the following side. To increase the capability for transmission of power, the diameters of the pulleys may be increased, retaining the same ratio, the increase of power being obtained by the increased velocity alone. Wide belts are less effective per unit of sectional area than narrow belts. Where a belt would exceed 18 inches wide it is better to use two belts. Long belts are more effective than short belts. All belts should hang slack when not in use. The velocity of lathe belts should be from 25 to 50 feet per second = 1500 to 3000 feet per minute. Convexity of pulleys to receive belt = J inch per foot wide, turned with a broad tool and coarse feed to give a non- slipping surface. Width of pulley = J more than belt. The proportion between the diameters of two pulleys working together should not exceed 6 to 1. Ordinary shop shafting 100 revolutions per minute: belt- ing say 1000 to 1500 feet per minute. The revolutions per minute of two pulleys embraced by the same belt will be inversely proportional to their diameters. 142 HANDBOOK FOR MECHANICAL ENGINEERS. Pulleys from 2 to 3 feet diameter transmit approximately 1 H.P. per inch width of belt at ordinary velocities; or square inches belt in contact with pulley x velocity feet per minute 4- 72,000 = H.P. 309. STRENGTH OF LEATHER BELTS. H.P. = Effective H.P. transmitted. v = velocity of belt in feet per minute. to = width in inches of single belt. ... ..55J5E. ; For double belts multiply H.P. X 1 ' 5 or w x |. Bagshaw & Sons, Batley. Another rule : K = revolutions per minute. D = diameter pulley feet. c = 25 for single belts. 17 for double belts. d = diameter shaft inches, but if overhung, increase by J d. Another rule (A. Towler) : d = diameter smaller pulley inches. a = ratio of arc covered by belt to circumference. Single Double H.P. = do. x 1*75. 310. LARGE DOUBLE BELTS. to = width of double belt in inches. v = velocity feet per second. 3IT1 ___ POWER TRANSMISSION BY BELTS, ROPES, ETC. 14& I = length, inches of arc of contact on lesser pulley. H.P. = horse-power transmitted. __ 66000 x H.P. I X v Evan Leigh. Double belts should not be used over pulleys less than 3 feet 6 inches diameter. Leather link belting is the most suitable for transmitting great power and running at a high velocity. 311. To FIND LENGTH OF BELT EMBRACING PULLEYS. E = radius of larger pulley to centre of belt. r = smaller E = equal pulleys. d = distance between centres of pulleys. n = number of degrees between radii from tangent points. t = length of each of the tangent portions. C = length of part embracing circumference of larger pulley. c = length of part embracing circumference of smaller pulley. L = total length exclusive of laps. t= d* - (R - r) 2 . n = tabular degrees corresponding to cosine having value of -= 360 - 2 n 144 HANDBOOK FOE MECHANICAL ENGINEERS. 312. NOTES ON HEMP EOPES. Italian hemp ropes are stronger than Eussian hemp. New white ropes are stronger and more pliable than tarred ropes, but the latter retain their strength for a longer period, owing to the protection afforded against atmospheric influences. The quantity of tar found most suitable is about 15 per cent, of the weight of the rope. Tarred ropes are stiffer than white by about one-sixth, and in cold weather somewhat more. Eopes which have been some time in use are more flexible than new ones ; the stiffness of ropes increases after a little rest. Wet ropes, if small, are a little more flexible than dry ; if large, a little less flexible. Eopes shorten and swell when wetted. A wet rope, or one saturated with grease, loses half its strength. There is considerable loss of strength from strain, and exposure after use, although a rope may appear perfectly sound. A "plain-laid" rope consists of three twisted strands twisted together. A "hawser-laid" rope is made by twist- ing three plain-laid ropes together, so that a section would show nine strands. Eopes are usually measured by their circumference : hence a 6-inch rope is one 6 inches in circumference, or about If inch diameter. All ropes should be kept dry and free from lime. Eound ropes are better than flat for all purposes. Ultimate strength of new white ropes is about 6000 Ibs. per square inch sectional area, but good ropes may stand 10,000 Ibs. per square inch. Small ropes are slightly stronger, in proportion to their sectional area, than large ones. Double rope slings are not twice the strength of single rope, owing to inequality of strain ; but in a rope fall with sheaves in good order, each fold of the rope may be counted for the strength. POWEE TRANSMISSION BY BELTS, EOPES, ETC. 145 The work absorbed in bending a rope fall over a sheave varies with the quality of the rope, directly as the tension, as the diameter 2 , and inversely as diameter of sheave, and is irrespective of velocity. Include weight of running block in calculating load on fall, and both blocks together with the rope, in weight on strop. Snatch block makes practically no difference in lift- ing power, if it has a good lead. In rope tackle it is usual to allow for the friction in bend- ing round sheaves, &c. = J of the load to be lifted. 313. STRENGTH OF MANILA EOPES. Manila rope varies from 10,000 Ibs. per sq. inch net section ultimate strength for a 2 -inch diameter rope to 12,000 Ibs. per sq. inch for a J-inch diameter rope. Net sectional area = 0*81 of area of circumscribing circle. d = diameter inches circumscribing circle, S = breaking weight in Ibs. S = 100 d 2 (83 - 10 d). Prof. J. J. Flather. 314. FORMULA FOR STRENGTH OF HEMP EOPES. Breaking^ weight new rope, cwts. = circumference 2 X 5. Safe load on = wt. Ibs. per fath. x 3. B.W. new stretched rope = (diameter in ^ths) 2 . Safe load = wt. Ibs. per fath. x 4. on new rope fall = circumference 2 . good = sound old = i , Weight of clean dry rope per) __ A fathom, in Ibs. . . . J ~~ * Minimum diameter of sheave in) . r . n . . , > = circf. rope -f 2 in. inches . } Flat ropes, width about 4 times thickness. wt. Ibs. per fath. approx. = circf. x 2. . B.W. tons = wt. Ibs. per fathom. L 146 HANDBOOK FOE MECHANICAL ENGINEERS. 315. HIDE HOPES- Made by G. Pitts & Sons, Kirkdale, Liverpool, for hand-power delivery cranes, at Is. Wd. per IK Dipped in Stockholm tar to prevent destruction by rats. Circumference* 316. FLY EOPES. When power is transmitted over considerable distances by an endless rope running at a high velocity, the rope is called a fly rope. Much used in engineering shops for driving travelling cranes, carrying heavy pieces of machinery. A three-ply manila rope, or cotton rope, with beeswax well rubbed in together with a little blacklead, is best. Eun 3000 to 5000 feet per minute in cast-iron pulleys with V-grooves, angle 30 to 45, latter for dry rope, former if lubricated* Working strain transmitted about 50 Ibs. per circular inch area. Eope tightened by jockey pulley giving 250 to 300 Ibs., per circular inch stress. Total stress must not exceed one-twentieth ultimate strength. Supported every 10 or 12 feet by flat plates of chilled cast iron. Friction of pulleys is inversely as their diameter, they should not be less than 30 times diameter of rope^ By experiment, a new rope one- quarter inch diameter stretched 1 inch per foot per cwt. Breaking weight in Ibs, averages 720 X circumference 2 , but ropes above 1 inch diameter are comparatively weaker, and below that size stronger. Mechanical efficiency of fly ropes = '6. 317. EOPE DRIVING. a = sectional area of rope in square inches. s = speed in feet per minute. n = number of ropes.. JI.P. = effective horse-power transmitted. c = constant = hemp 100. H p cans . _ 33,000 H J>. = 33,0.00 ; ens J. Bagshaw <& Sons, Bailey. POWER TRANSMISSION BY BELTS, ROPES, ETC. 147 Leather rope, 8 narrow strips secured together and pro- perly jointed, forming 1 J inch square, running in V-groove, angle 90, weighs 1 Ib. per foot run and will transmit 320 Ibs. per square inch of section. Cotton rope, If inch circumference, weighing 1 Ib. per foot run, will transmit 50 I.H.P. at velocity of 5000 feet per minute (600 Ibs. less 60 for tension = 540 Ibs. working strain). Steel rope, ^ inch diameter, weighing J Ib. per foot run, will bear working stress of 405 Ibs. Hemp ropes, although stronger than cotton, do not stand so well. Approximate H.P. of hemp rope = circumference in inches x diameter of driving pulley in feet X revolutions per minute -f- 200. Another rule : H.P. = circumference 2 X velocity in feet per minute X one less than number of ropes -f- 5000. 318. CURVE OF EOPE, A rope or chain when deflected by its own weight hangs in a catenary curve. It approximates to a parabola and is indistinguishable from one when the deflection is- not more than one-tenth of the span. 319. TESTS OF ROPES. Ultimate Tension. Elongation. White hemp . tons per sq. in. 4*75 per cent. 18 Tarred hemp . 3-5 16 White manila . 4-5 15 White aloes . 2^5 Esparto and cocoa fibre 1-0 , . Flat ropes,, hemp or manila\ O.K K tarred . . . -, f Round ropes, with moderate attention, may be worked at a stress equal to one-third breaking stress,, and flat ropes at one-fourth* L 2 148 HANDBOOK FOR MECHANICAL ENGINEERS. 320. AVERAGE TENSILE STRENGTH OF KOPES. Specimens 13 feet long, ends wound on grooved pulleys. Ibs. per sq. inch. White hemp . . . 10,500 to 11,200 Tarred hemp . . . 7,700 8,400 White manila . . . 9,800 10,600 White aloes . . . 5,600 7,000 Flat, tarred hemp, or manila 7,800 8,400 Unannealed wire rope . 55,000 (elongation 6 to 8 per cent.) Annealed wire rope . . 45,000 (elongation 12 to 15 per cent.) Factor of safety 3 to 4. A. Duboul 321. WIRE ROPES FOR LIFTS. Diameter of pulley in inches = circumference of rope (Lang's lay) in sixteenths of an inch. 322. EXPERIMENTS ON WIRE ROPE AT FORTH BRIDGE. Crucible cast steel wire rope was used. With a diameter of sheave = 6 times circumference of rope, rope bent over sheave 5000 times before failure commenced, 15,000 before final destruction. With a diameter = 8 times circumference, 10,000 times and 36,000 respectively. 323. LANG'S PATENT WIRE ROPES. Bessemer Crucible Patent Plough o, -i r -, . x Steel. Steel. Steel. Steel. Strength of material in 1 5 tons per square inch . f Round rope, 6 strands of] 4 in ' cir ? f ' 3 *n. 3* in. 4 in. 6 wires each up to 1 ^ wires ln each strand above these I sizes. Approx. B.W. in tons . =c 2 xl'5 2 2-5 3'5 \\orking load . . = T ^ breaking weight. Weight of round wire ropes in Ibs. per fathom = circf. 2 X -f. J. Bagshaw d Sons, Bailey. POWEK TRANSMISSION BY BELTS, ROPES, ETC. 149 324. K. S. NEWALL & Co.'s IRON WIRE ROPES. Eound Weight in Ibs. per fathom = C 2 X |. B.W. tons = weight in Ibs. per fathom x 2. Safe load cwts. = X 6. Flat- Width = 4J to 5J times thickness. Sectional area X 10 = weight in Ibs. per fathom. Weight inlbs.perfath. X f = B.W. tons. B.W. tons x * = safe working load cwts. Drum for wire rope = 2 feet 6 inches diameter for every $ inch diameter of rope, speed 30 to 50 miles per hour. For slow speeds drum 80 times diameter of rope. 325. STRENGTH OF CHAINS. d Diameter of iron in |ths of an inch. Example | Chain. tons cwts. B.W. in tons, B.B. short-link crane chain . = zd 2 18 ordinary chain .... f^ 2 14 8 (Anderson) . = |cZ 2 13 10 Elswick test in tons, 10 per cent, above Admiralty) 33 d 2 S 1 proof . ./ Admiralty proof strain in tons .... Safe load in tons (Mclesworth, llth ed.) = T * 6 15 4 10 at 5 tons per square inch sectional area , . 4 8J in tons (Molesworth, 21st ed.) = d 2 4 in tons, common rule .... = L d 2 3 12 Maximum temporary load on good annealed "1 9t1 2 319 chain in cwts / (* A^S Safe load, ordinary chain (Anderson), in tons = - 3 -d 2 3 7% for ordinary cranes, in cwts. * . .- = ik 2 14 at 3 tons per sq. inch sectional area 2 13 coal cranes, in cwts = Ijd 2 2 5 old chain, quality and condition) unknown, in cwts / d 2 1 16 Weight in Ibs. per fathom, short link crane chain d 2 36 ordinary = -88d 2 8I| 150 HANDBOOK FOB MECHANICAL ENGINEEKS. Safe load (5 ton cranes and upwards) in tons = Id 2 when made of good iron, but large chains are frequently of common quality. Size of links for crane chains = 3^d X 4fcZ. Admiralty proof strain on rings, in tons = d in -iths 2 -r- 16. stud chain = d in |ths 2 X '281. Common chain cables, B.W. Ibs. = 1,000,000 (|d) 2 . 326. KEMARKS ON CKANE CHAINS.* T 9 inch B.B. tested short link crane chain (Crown S.C.) should break with a load of 13 tons, if the iron bar from which it is made break with 26 tons per square inch ultimate stress ; but a test-piece of the chain 4 feet long breaks usually with a load of 9 to 10 tons, generally opening at the welds. Each chain is tested before use with a maximum load of 4J tons, examined link by link, and used on hydraulic coal cranes to lift maximum gross load of 1 J tons, examined again at frequent intervals and annealed; any links reduced by wear to J an inch at ends are condemned as worn out ; worn links cut out and remainder used down to same limit. A good chain, properly looked after, will make from 100,000 to 150,000 lifts before it is entirely worn out. These chains occasionally fail in use, although the factor of safety adopted allows so great a margin. 327. EXAMINATION OF CHAINS AT THE DOCKS IN LONDON. All chains are taken down, annealed and examined as follows, viz. : Hydraulic crane, lead, lift, &c., chains, every six months. Hand and steam crane, traveller, dockgate and chain gear, every twelve months. The chain gear comprises chain runners, chain necklaces, sweeping and guy chains, chain slings, cattle slings, shackles, dogs and lead hooks. * See paper on Use and Care of Chains for Lifting and Hauling,' read by the author before the Civil and Mechanical Engineers' Society, 1887. POWER TRANSMISSION BY BELTS, ROPES, ETC. 151 328. CIRCULAR EINGS FOR MOORING, AND SLING CHAINS. Circular rings in connection with mooring chains are made of a diameter proportionate to the size of chain, fixed by each maker, but generally four to six times the diameter of the iron. The Admiralty test for rings depends upon the diameter of the iron alone, and is independent of the diameter of the ring. It is Test load cwts. = l (d in -|ths) 2 . To find proper diameter of circular ring in mooring and sling chains : d = diameter of iron of chain in inches suitable for lifting given load. D = diameter of iron of ring in inches. K = mean radius of ring in inches. D = 329. TOOTHED GEARING. A spur wheel has the teeth projecting radially on the circumference. A pinion is the name given to the smaller of two wheels working in gear together. Hence spur wheel and spur pinion, bevel wheel and bevel pinion. A bevel wheel has the teeth projecting on a rim which is inclined to the plane of the circumference at an angle usually between 30 and 60. Mitre wheels are bevel wheels of equal size, geared together at an angle of 90. A crown wheel has the teeth projecting at right angles to the plane of the circumference. A lantern wheel has round pins to act as teeth, fixed between two discs, near the circumference. 152 HANDBOOK FOR MECHANICAL ENGINEERS. A hunting-cog is an additional tooth on a wheel making the teeth of the wheel and pinion prime to each other and equalising the wear. Prime numbers are those which have no divisor in common. A mortice wheel, or shell wheel, is a cast-iron wheel from ordinary patterns, but with hard wood teeth secured in mortices cast in the rim. A rag wheel is a wheel with strong projections upon it which enter the spaces of a special chain called a pitched chain, or link chain, for transmitting power. An intermediate wheel, or idle wheel, on a screw-cutting lathe is used to connect two wheels on different spindles without altering their velocity ratio. A Marlborough wheel is one of double breadth, gearing at the same side into two wheels on different shafts, whose axes are so nearly in the same line as to prevent the use of ordinary spur gear. In effect it is the same as an intermediate wheel. A Geneva stop consists of a disc provided with one tooth, and another disc with five or more spaces, all the parts between the spaces (except one) being hollowed to fit the first disc, so that at each revolution of the first disc the tooth carries the second one through a portion of a revolution, until further rotation is prevented by the part which is not hollowed out coming into contact with the shoulder at side of single tooth. It is a device to prevent overwinding. A fusee is a conical drum upon which a chain is wound to equalise the effect of a coiled spring, by giving a varying leverage, as in a watch, clock, or other mechanism. 330. NOTES ON TOOTHED GEARING. Pinions, wheels and racks are made of cast iron, cast steel, and malleable cast iron ; the latter is strong, but liable to twist or warp. Pinions are sometimes made of wrought iron ; small gearing is frequently made of gun-metal. POWEK TRANSMISSION BY BELTS, ROPES, ETC. 153 If moulded from patterns wheels should be geared so that the taper ends of teeth are on opposite sides. Gearing is increased in strength by shrouding or flanging up to pitch line. The pitch line or pitch circle is the mean circumference of the teeth, or the circumference of a plain wheel without teeth, which would produce the same velocity-ratio if slipping were prevented. The teeth are only to prevent slipping. The pitch of the teeth is the distance from a point on one tooth to a similar point on an adjacent tooth measured along the arc of the pitch circle. The comparative wear of gearing is inversely proportional to the number of teeth ; hence, pinions wear quicker than wheels. Two teeth on a pinion or wheel is the minimum number in gear at one time, each bearing half the total load. The power capable of being transmitted by gearing depends, within reasonable limits, entirely upon the speed; the pressure (at pitch line) depends upon the pitch. The speed should not exceed 1800 feet per minute circum- ferential velocity for ordinary cast-iron wheels, or 2400 for mortise wheels. The velocities of geared wheels are in the inverse ratio of their diameters, The transmission of the power strains the teeth as canti- levers, or s = = c, c for cast iron safe load = 600. The working load should not exceed -^ of the breaking weight. The dimensions of the teeth are proportional to the pitch ; hence, in ordinary proportions the strength is represented by p 2 c, c for cast iron being 1000 as a maximum. The breadth of tooth on face beyond a certain amount, say twice the pitch, cannot be reckoned upon for strength, owing to irregularities in the teeth, and probability of unequal bearing. 154 HANDBOOK FOR MECHANICAL ENGINEERS. 331. STRENGTH AND WEIGHT OF TOOTHED GEARING. Safe pressure in Ibs. at pitch, line on wheel teeth of average proportions : Cast iron, little shock = 625 X pitch 2 . moderate shock = 400 X pitch 2 . excessive shock = 277 x pitch 2 . The latter case also applies to the iron teeth of mortise wheels, which are made thinner than ordinary teeth of same pitch. J. B. Francis' rule for pitch = -044 Jlloa. pressure. Breadth of teeth = 2 to 2 J times pitch. The weight of toothed gearing in Ibs. approximately, is for spur wheels *38 nbp 2 , bevel wheels '325 nbp 2 , where w is number of teeth, b breadth on face, and p pitch. 332. FORMUL/E FOR STRENGTH OF GEARING. s = strain in Ibs. to be transmitted, calculated at pitch circle. p = pitch in inches. c = constant, when teeth of ordinary proportion = Material. Plain. Shrouded. Cast steel . . . 4000 6000 Wrought iron . . 3000 4500 Malleable cast iron . 2000 3000 Gun metal . ... 1500 2000 Cast iron . . . 1000 1500 For slow speeds and uniform pressure c may be increased one-fourth. POWER TRANSMISSION BY BELTS, ROPES, ETC. 155 333. WHEEL GEARING, MANCHESTER PITCH. Diametral pitch (Manchester pitch) No. of teeth diameter of pitch circle in inches Circular pitch = j-. - 7 i mr > diametral pitch or (tooth -f- space) in inches. No. of teeth in wheel = diameter x diametral pitch. No. of teeth Diameter of wheel = -^ , JT-T diametral pitch Addition to diameter for increased No. of teeth _ No. to be added diametral pitch" Outside diameter of wheel = diametral pitch + diameter P itch circle - For example : A 10-pitch wheel (Manchester or diametral pitch) 7*5 inches diameter will have 10 X 7*5 = 75 teeth; another in the same set 4 inches in diameter would have 10 x 4 = 40 teeth, and their true pitch would be 3-1416 x 7-5 3-1416 X 4 75 40 or generally, with w-pitch wheels, true pitch = - inches. 334. MILL GEARING. H = H.P. actual. b = breadth on face inches. D = diameter in feet. p = pitch inches. R = revolutions per minute. n = No. of teeth. 180 D = p cosec - 306 H p = 306 D p = cosec 180 156 HANDBOOK FOR MECHANICAL ENGINEERS. Another formula : N.H.P. = \/(DR) x p 2 & X Gudgeons (Tredgold) : 05 wood 043 cast iron 15 cast steel J w Ibs. X / inches Diameter inches = - - - y 335. SPEED OF MILL GEARING. Maximum safe speeds under favourable conditions for toothed gearing : Ordinary cast-iron wheels . . . 1800 ft. per min. Helical 2400 Mortice 2400 Ordinary cast-steel wheels . . . 2600 Helical 3000 Special cast-iron machine-cut wheels . 3000 A. Towler. 336. DETERMINING THE PROPORTIONS OF GEARING. In toothed gearing exact ratios should be sacrificed to obtain numbers prime to each other. When the wheels are to be equal, one of them should have an additional tooth called a " hunting-cog " ; then each tooth of the one will encounter each tooth of the other, equally often, and equalise the wear. Numbers are prime to each other when they have no common measure, i.e. cannot both be divided without re- mainder by any number except 1 . For wheels to gear properly the number of teeth in each must be proportionate to their diameters in other words, their pitch must be equal. POWER TRANSMISSION BY BELTS, ROPES, ETC. 157 337. PROPORTIONS OF WHEEL TEETH. Parts. Per Cent. Other Authorities. Pitch . Whole length of tooth Pitch line to point to root Thickness at pitch line Width of space at ditto Curve . Breadth of to Thickness of rim . Projecting ribs inside ditto . Thickness of arms . * . Breadth of arms at rim of taper increasing to boss Thickness of rib on arms . metal in boss . . . 15 or 100 100 100 100 tooth . 12 80 60 75 75 it . 51 36-6 25 33 35 . 6i 43-3 35 42 40 h line . 7 46-6 48 48J 45 t ditto v. 8 53-3 52 51J 55 . , radius = pitch, or cycloidal. on face . 250 per cent. . } 44 to 50 175 ^ inch per foot 25 75 to 80 338. ORDINARY PROPORTIONS OF KEYS. !J diam. of shaft up to 4 inches, -i 4 inches to 8 inches. * 8 12 Key square at thick end. Taper J inch per foot. One-third of thickness let in shaft, remainder in wheel. 339. PROPORTIONS OF COTTERS THROUGH BARS. Z> = Breadth of cotter. t = Thickness of cotter. d = Diameter of bar. Through round bars, I = 1-4635 d. t = - Through square bars, b = 1 5 side of bar. t = side of bar 158 HANDBOOK FOR MECHANICAL ENGINEERS. 340. JOURNALS FOR SHAFTS AND AXLES. Length of brass = 0-9 to 1*0 length of journal. Less liable to score in wearing, if slight end play can be given. Thickness and projection of collar and radius of curves d 1 . d 1 . 341. POWER OF CRANEMAN, &c. Eadius of handle . . . . 1 ft. 3 in. to 1 ft. 6 in. Height to centre of axle . . . 2 6 3 Height from ground to path of handle 1 6 1 9 Revolutions of handle per minute . . . * 28 to 23 Speed at circumference of handle for continuous work while lifting . 220 feet per minute Do. do., when lifting and lowering . 330 Force of ordinary labourer on handle 12 Ibs. + friction craneman 15 Maximum ditto, for short time, say 5 minutes, at 440 feet per minute 30 At 8 hours per day, on long lifts, the effective work averages 2380 to 2420 foot-lbs. per minute per man. One man can raise 1 ton with a multiplying power of 150, the friction being about 6J Ibs., and the effective pressure 15 Ibs., making the gross pressure on the handle 21 Ibs., or coefficient = ?. Speed of lifting with hand-power crane = 2 feet per second. In raising weights with a pulley a man can maintain a downward pull of 40 Ibs^ permanently, and equal to his own weight temporarily. POWER TRANSMISSION BY BELTS, ROPES, ETC. 159 342. HAND POWER CRANE. W = load in Ibs. P = power required in Ibs. to overcome load. F = friction of gearing of crane without load. / = friction of gearing due to load. M = multiplying power of gearing. E = efficiency of crane under various loads. By experiment with 10 cwt. crane M = 40, F = 4-21 Ibs., /=-0179W. B. S. Ball 1 ton crane, 4 men at handles, 25 Ibs. each man, multi- plying power 24 to 1. Delivery cranes, short lift, lowering by brake, allow 25 Ibs. for each man, handle 16-inch radius, 30 revolutions per minute, coefficient * 75. Landing cranes, long lift, allow 15 Ibs for each man. 343. CRAB WINCHES. R = radius of handle. r = radius of barrel to centre of rope. A = radius, diameter, or number of teeth in pinion. B = wheel. W = load lifted in Ibs. P = power applied in Ibs* M = modulus of efficiency, or coefficient, say 75. Single purchase crab, W = Px5 x | X M. Double-purchase crab, 160 HANDBOOK FOR MECHANICAL ENGINEERS. 344. ROPE TACKLE FOR LIFTING. Diameter of sheave in inches 3 8| 4 4 5 6 Circumference of rope in) inches .] 1 li 2 Si 3 4 Average strain on rope in ) cwts. for full load . . 1 1 2| 3| 6 8 15 Number of men required for\ full load ....,/ 1 3 6 10 crab crab Maximum power in cwts 2 and 1 sheave 2J 4* 9 , . 2 2 3 7 12 .. 3 2 8| 15 25 35 60 3 3 .. 10* wi 30 42 72 4 3 20 35 49 84 With equal sheaves the fast end must be on top block ; unequal on bottom. Snatch block makes practically no difference if the rope has a good lead. Larger blocks than 6 inches should have chain fall. Blocks 4 inches to 6 inches may have rope or chain. 345. SAFE LOAD ON SHEAR LEGS AND DERRICK POLES. D = inches diameter at bottom. d = top. L = length in feet. E = rake or overhang in feet. W = safe load in tons per pole. Q -pv J Approximate W = = Jj -f- -K 346. DIFFERENTIAL PULLEY CALCULATIONS. D = diameter of larger pulley, d = diameter of smaller pulley. 2D POWER TRANSMISSION BY BELTS, ROPES, ETC. 161 M = modulus or efficiency of machine, then W X M = actual load lifted. Load will not lower by itself when M is less than *5. By experiment with various differential pulleys Load. Multiplying Power. Coefficient. 5 cwt. 16tol -4 10 30 1 -33 30 53 1 -25 162 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION VIII. FKICTION AND LUBRICATION. 347. LAWS OF FRICTION. THE friction between two surfaces, dry or only slightly greasy, is in direct proportion to the force with which they are pressed together (within the limits of abrasion), and is independent of the area of the surfaces in contact. With ample lubrication the friction is reduced, but the heavier the pressure per unit of surface the greater must be the consistency of the lubricant, to prevent it from being squeezed out. The friction between two surfaces at rest is slightly greater than when they are in motion, but when in motion the friction is independent of the velocity so long as the surfaces are kept cool. Friction is not a force ; being passive, it can only act as a resistance. The laws of friction are sometimes stated as follows : First Law of Friction. The friction is proportional to the pressure when the surfaces are the same. Second Law of Friction. Friction is independent of the area of the surfaces in contact. 348. ANGLE OF REPOSE is the angle () made by a flat surface with the hori- zontal when a weight just ceases to move down it by gravity. The corresponding coefficient of friction (tan ) is the FRICTION AND LUBRICATION. 163 fraction of the weight required as pressure just insufficient to produce motion on a horizontal plane. Angle. Coeff. Angle. Coeff. Angle. Coeff. 1| = -03 13 = -23 194 = -35 2 = -04 134 = -24 20 = -36 3 = -05 14 = -25 26 = -50 4 = -07 144 = -26 28 = -53 44 = -08 15 = -27 294 = -57 84 = -15 164 = '30 31 = -60 114 = -20 184 = * 33 35 = * 70 349. DEFINITIONS OF FRICTION. The Limiting Angle of Resistance ( is the angle through which any surface requires to be lifted from the horizontal to cause a body to be on the point of sliding (friction of rest) or to continue sliding (friction of motion). Its magni- tude is fixed by the physical nature of the surfaces in contact. It is also the angle from the vertical made by the resultant of the force or forces acting upon a body when sliding is just about to take place or is taking place. The Coefficient of Friction ^ is the ratio of the pressure P required to overcome the friction of a body on any given horizontal surface, to the whole load W of and on the body ( \ p = ^). Trigonometrically it is equal to the tangent of the limiting angle of resistance (/x, = tan <). It has been proposed to call the " friction of rest " stiction, to distinguish it from the " friction of motion," which would be called friction. The common term for the " friction of rest " is statical friction. 350. MORIN'S EXPERIMENTS ON FRICTION OF MOTION. Dry: Wrought iron on brass 172 Brass on wrought iron 161 Cast . -147 cast -217 M 2 164 HANDBOOK FOB MECHANICAL ENGINEERS Greasy : Wrought iron on brass *160 Brass on wrought iron -166 Cast " -132 cast -107 Lubricated with olive oil : Wrought -078 wrought '072 Cast -078 cast -077 Oak upon elm dry = -f of friction of elm upon oak dry. Note. These results reduced from General Morin's experiments appear to be very questionable, and indicate the necessity for further investigation. 351. SAFE WORKING PRESSURE ON MOVING SURFACES. v = velocity feet per second. p = pressure Ibs. per square inch. but p must not in any case exceed 1200. Rankine. 352. EXPERIMENTS ON FRICTION. Pine upon pine, grain crossed, slide 9 inches X 9 inches, load 14 to 112 Ibs. in motion. ^ W = 1-44 + -252 W. Prof. Ball. In an experiment with a hand brake on the tender of a locomotive on the Northern Eailway of France, it was found that 82 -3 per cent, of the whole power applied was absorbed by friction before reaching the brake block. 353. FRICTION AND HEAT. Friction of any kind, however produced, results in the conversion of mechanical work into heat. One horse-power or 33,000 foot-lbs. of work per minute expended in friction 33 000 produces ! - = 43 British thermal units per minute. FRICTION AND LUBRICATION. 165 354. FRICTION OF JOURNALS. Coefficient of friction (/*), average -08; but under favourable conditions may be as low as *01. Work expended in friction in foot-lbs. per minute = ^W dE= -02lWdI?. Heat units to be dissipated per minute = ( J = 772). J Length of journal depends upon the load and speed, length being increased for high speeds. , W (50 + velocity in feet per minute) / p ina \ i, ^^ - , - . ...., \JjOwt JIG } + 70,000 d. or WE "~ 250,000, to 300,000 s or I.H.R 1= -4 to -33 rad. crank inches Increasing diameter increases friction, because the rubbing surface has further to travel in one revolution. Increasing length reduces the friction per square inch, but does not affect the total friction, because for a given space passed through, with a constant load, the friction is independent of surfaces in contact. The " bearing area " is taken to be the length x diameter. When an overhanging journal is increased in length the diameter must also be increased slightly, to give same 3 /L strength as before, D = d /-j. Pressure on bearings in Ibs. per square inch longitudinal section may be = '70,000 50 + velocity in feet per minute' 166 HANDBOOK FOE MECHANICAL ENGINEERS. but must never exceed 1000, maximum say 800 in slow- running engines, down to 400 Ibs. in quick speed engines. 355. SHOP SHAFT BEARINGS. Allowing 1 square inch per thermal unit per minute. P = load in Ibs. fi = frictional coefficient (say 02). S = surface speed feet per minute. J = Joule's equivalent = 772. T = thermal units evolved per minute. d = diameter of shaft in inches. I = length of bearing in inches. PCJ T^ /X io JL Prof. Goodman, 356. MEAN COEFFICIENTS OF FRICTION. Wood on wood or metal dry, *4 to *6; greasy, '2 to '4; lubricated, ! to *2. Metal on metal wet, *3; dry, '2; greasy, -15; lubri- cated, * 1 standing, or 08 moving. Leather on metal wet, 25 ; dry, 5. Friction of motion = friction of repose X ' 7. Friction varies with the nature of the surfaces, the lubricant, and the temperature. Unguents should be thick for heavy pressures, that they may resist being forced out ; and thin for light pressures, that their viscidity may not add to the resistance. Hankine. In estimating the power to overcome friction, the friction of rest must be taken ; but in estimating the effect of friction as a power to resist motion, say a brake strap, the friction of motion must be taken. FRICTION AND LUBKICATION. 167 357. LUBRICANTS FOR VARIOUS CASES. Under very great pressure with slow speed : Graphite, soapstone, tallow and other greases. Under heavy pressure and high speed: Sperm oil, castor oil and heavy mineral oils. Under light pressures and high speed: Sperm oil, refined petroleum, olive, rape and cotton-seed oil. Ordinary machines : Lard oil, heavy mineral and other vegetable oils. Steam cylinders : Heavy mineral oils. Ballings. 358. ACTION OF OILS ON METALS. The results of twelve months' experiments, by Prof. Red- wood, show that Iron is least affected by seal oil, very little by rape oil, and most by tallow oil. Brass is not affected by rape oil, least by seal oil, and most by olive oil. Tin is not affected by rape oil or whale oil, least by olive oil, and most by cotton-seed oil. Lead is least affected by olive oil, and most by whale oil ; but whale, lard and sperm oils all act to very nearly the same extent on lead. Zinc is not acted on by mineral lubricating oil, least by lard oil, and most by sperm oil. Copper is not affected by mineral lubricating oil, least by sperm oil, and most by tallow oil. Mineral Lubricating Oil has no action on zinc and copper, acts least on brass, and most on lead. Olive Oil acts least on tin and most on copper. Rape Oil has no action on brass and tin, acts least on iron, and most on copper. Tallow Oil acts least on tin and most on copper. Lard Oil acts least on zinc and most on copper. Cotton-seed Oil acts least on lead and most on tin. 168 HANDBOOK FOR MECHANICAL ENGINEERS. Sperm Oil acts least on brass and most on zinc. Whale Oil has no action on tin, acts least on brass, and most on lead. Seal Oil acts least on brass and most on copper. From the foregoing results it will be seen that mineral lubricating oil has, on the whole, the least action on the metals experimented with, and sperm oil the most. For lubricating the journals of heavy machinery, either rape or sperm oil is the best oil to use in admixture with mineral oil, as they have the least effect on brass and iron, which two metals generally constitute the bearing surfaces of an engine. Tallow oil should be used as little as possible, as it has considerable action on iron. 359. EOLLING FRICTION is directly as the pressure, and inversely as the diameter of the rolling bodies. 360. TRACTION, OR FRICTION ON ROADS. Cart on common road = ^ load. Carriage on plank road = T ^y on railroad ,= ^ 169 SECTION IX. THEKMOJDYNAMICS, AND STEAM. 361. IMPONDERABLES. LIGHT, heat, electricity and magnetism were formerly sup- posed to be material substances without weight, and were known as " imponderables " ; they are now considered as modes of motion. 362. UNIVERSAL ETHER. Sound waves require air for their transmission through space ; heat and light are independent of air in their passage, and may be transmitted across a vacuum. It is therefore supposed that there is a medium, more rarefied than air, per- vading all space, which transmits waves of heat and light as air does sound. 363. KANKINE'S DYNAMICAL THEORY OF HEAT. Each atom of matter consists of a nucleus or central physical point enveloped in an elastic atmosphere, which is retained in its position by forces attractive towards the nucleus or centre. The elasticity due to heat arises from the centrifugal force of revolutions or oscillations among the particles of the atomic atmospheres ; so that quantity of heat is the vis viva of those revolutions or oscillations. The medium which transmits light and radiant heat consists of the nuclei of the atoms vibrating independently, or almost independently, of their atmospheres. So that the absorption of light and radiant heat is the transference of 170 HANDBOOK FOE MECHANICAL ENGINEERS. motion from the nuclei to their atmospheres, and the emission of light and radiant heat the transference of motion from the atmospheres to their nuclei. 364. SOURCES OF HEAT. Friction, Percussion, Mechanical stress, Chemical action, Electrical action. 365. SENSIBLE HEAT. The Temperature of a body is its thermal state considered with reference to its power of communicating heat to other bodies. Cleric Maxwell. This is commonly called its sensible heat. For purposes of measurement some definite effect produced by heat must be selected, e.g. the alteration in length or volume of a substance which expands and contracts uniformly when heated or cooled. At all ordinary temperatures the ratio of increment in volume to increment in absolute temperature is practically constant in the case of mercury; it is, moreover, a liquid at such temperatures, and easily measured ; hence the Mercurial Thermometer is that most commonly used for determining the temperature of a body. 366. COMPARISON OF THERMOMETERS. No. of Degrees between Freezing and Boiling Point of Absolute Zero of Tem- perature.* Freezing Point of Water. Point of Maximum Density of Water. Boiling Point of Water. Water. Great Britain and America : Fahrenheit = F. . 180 -461 -2f 32 39-1 212 Sweden, France, &c. : Centigrade or Celsius = C. 100 -274 4 100 Russia and Spain : Re'aumur = R. 80 -219-2 3-2 80 * Or point of absolute negation of heat. f Box 458*4, Goodeve 459' 13. .-. 9F. = 5 C. = 4E. THERMODYNAMICS, AND STEAM. 171 To convert from one scale to another : F = f C + 32, C = f (F - 32), K = f (F - 32), F = -|E + 32, C = B, R = | C. 367. EFFECT OF CHANGE OF TEMPERATURE. All bodies expand by heat and contract by cold, i.e. ex- pand by addition of heat and contract by loss of heat ; more precisely change of temperature alters the relation between the attractive and repulsive forces of the atoms of a solid body, and therefore alters the distance at which they would remain in equilibrium, neither attracting nor repelling each other. In the case of gases, the atoms repel each other at all temperatures, and the effect of a change of temperature is to alter the amount of the repulsive force and pressure upon the containing vessel, increasing them with increase of tempera- ture, and vice versa. 368. TRANSFER OF HEAT. Radiation of heat is the transfer which takes place between bodies at all distances apart, in the same manner and accord- ing to the same laws as the radiation of light. The intensity of radiant heat diminishes as the square of the distance from the radiating body. Conduction is the transfer of heat between two bodies, or parts of a body, which touch each other. Convection, or carrying of heat, means the transfer and diffusion of the state of heat in a fluid mass by means of the motion of the particles of that mass. 369. MECHANICAL EQUIVALENT OF HEAT. British Thermal Unit, or unit of heat, is the quantity of heat required to raise 1 Ib. of pure water, at its point of maximum density ( = 39-1 F.), through 1 F. Joule's Equivalent (J) is the mechanical effect resident in one thermal unit = 772 foot-lbs. By Micalesco's experi- ments, with modern appliances, a closer value would seem to be 772 -3 foot-lbs. 172 HANDBOOK FOR MECHANICAL ENGINEERS. By Chase's value of y (= the ratio of specific heats of gases = 1-405,285), Prof. Thurston makes J = 778-12 foot-lbs., or 427 kilogrammetres per calorie. When the centigrade scale is used, the point of maximum density of water will be 4 C., the thermal unit the quantity of heat required to raise 1 Ib. water through 1 C., and its mechanical equivalent 1390 foot-lbs. The Quantity of Heat involved in any operation may be expressed directly by its mechanical equivalent in foot-lbs. 370. CALORIE OR FRENCH UNIT OF HEAT. A calorie represents the heat required to raise 1 kilo- gramme of pure water 1 C. from its point of maximum density 4 C. A calorie is equal to nearly four British heat units = C. British thermal units p ^ ^ ^ unitg> 3-96832 French thermal units = Briti8h thermal units . 0-251996 By other writers, especially on elasticity, a calorie is said to be the amount of heat required to raise 1 gramme, &c. = foot-lbs. This is made = c. 371. MAYER'S EXPERIMENT. Dr. Mayer of Heilbronn found that 1 cubic foot of air at 32 F., 14-7 Ibs. pressure, heated to 525-2 F., expansion being prevented, requires 6*73 units of heat. Heated to same temperature with expansion under constant pressure requires 6*73 + 2-746= 9-476 units, and volume will be doubled (as the temperature is raised from 32 + 461*2 = 493-2 to 525*2 + 461*2 =986*4 and 986-4 -=-493 -2 = 2). The pressure of 1 atmosphere or 2116*3 Ibs. on square foot is moved through 1 foot, or 2116-3 foot-lbs. of work has been done, and 2116-3 being divided by 2-746, the units of heat which have disappeared, we obtain 770-7 foot-lbs. as the THERMODYNAMICS, AND STEAM. 173 mechanical equivalent of 1 unit of heat. Although the 2 '746 units of heat cease to exist as sensible heat, they cannot be called latent as they are transformed into work. 372. ENTROPY. Entropy (Clausius, 1848) Thermodynamic Function (Eankine) is such a quantity as, multiplied by absolute temperature, will give the capacity which heat has theoretically of per- forming mechanical work. Mechanical work, electricity, and heat are different forms of energy. Mechanical work is measured by foot-lbs., being the product of ihe force in Ibs. into the space in feet through which it acts. Electrical energy is measured by the watt, being the product of the intensity of current in volts into the quantity of current in amperes. The same requirement applies to heat energy ; the intensity is measured by tempera- ture and the quantity by entropy. Entropy has been described by Prof. Dwelshauver-Dery as a heat scale which varies with the absolute temperature, as gravity varies on the surface of the earth with the distance from the centre. 373. CAPACITY OF BODIES FOR HEAT. Capacity for Jieat (Irvine) of a body is the number of units of heat required to raise one pound weight of the body one degree in temperature. 374. SPECIFIC HEAT. The Specific Heat (Gadolin) of a body is its capacity fur heat compared with that of an equal weight of water. It is the quantity of heat requisite to change its temperature any stated number of degrees ( = a) compared with that which would produce the same effect on water at 60 F. and 30 inch barometer (= 6), and it is therefore expressed by the frac- tion , which may be made referable to weight or volume. 174 HANDBOOK FOR MECHANICAL ENGINEERS. If a unit mass of a substance absorbs a quantity of heat q in passing from a temperature T, to a temperature T + ' then the ratio q / 1 is termed the mean specific heat for t from the temperature T. The limit of the ratio q / /, as t is diminished, is termed the true specific heat at the temperature T. The specific heat of all bodies (except gases) increases slightly with the temperature. The specific heat of a gas at constant pressure under which it expands, is greater than at constant volume. 375. DULONG AND PETIT's LAW. Dulong and Petit' 8 Law (1819). The specific heats of the chemical elements are inversely proportional to their atomic weights, so that their product is in all cases constant. It is generally expressed as, " the atoms of all elementary bodies have the same specific heat." Neumann, Regnault and Kopp have shown that this law applies to compounds as well as elements, the specific heat of a compound being the sum of the specific heats of its component elements. 376. SPECIFIC HEATS OF VARIOUS BODIES. Specific heat of water at 39 1 F. . =1 iron . . . . = '114 air at constant pressure = '238 air at constant volume = *169 steam gas at constant pressure . . . = *475 steam gas at constant volume . . . = *37 The specific heat of saturated steam (= -305) is the quantity by which the total heat of steam is increased for each degree of temperature. Thermal units required to raise any body t in tempera- ture = weight x specific heat X t. THERMODYNAMICS, AND STEAM. 175 377. LATENT AND TOTAL, HEAT. Latent heat (Black 1757) is the heat absorbed or disengaged by a body without alteration of temperature, upon a change of state or alteration in the aggregation of its molecules. Approximately the latent heat of steam = 1115 '7 times sensible heat F. Ice in melting absorbs as much heat as would raise the same weight of water at 32 F. to 174-65 F. Water in evaporating from 212 F. absorbs as much heat as would raise 966 times the quantity 1 F., or six times the quantity from 51 F. to 212 F. Total heat. Dr. Black's theory of the latent and sensible heat of steam was that the sum of the two was constant at all temperatures. Eegnault's experiments showed that the total heat was not constant, but increased slowly with increase of tempera- ture, and was equal in F. to {(Sensible temperature in F. - 32) x '305} + 1123-7. Approximately the total heat of steam = 1115 + -3 times sensible heat F. 378. GASES AND VAPOURS. Permanent gases are constant elastic fluids which cannot be liquefied. The temperature being constant, the volume of a gas is inversely as its pressure. The product of the volume and pressure of any gas is proportional to the absolute temperature. v = volume of a perfect gas t = absolute temperature = constant. p = pressure In raising the temperature of a gas under constant pres- sure, mechanical work is done in providing the necessary space for its expansion. 176 HANDBOOK FOE MECHANICAL ENGINEERS. When a gas is heated, the expansion is about ^-^ of its volume at C. for each degree C. increase of temperature, or permanent gases expand 00202 of volume for each F. increase of temperature from 32 F. under a constant pressure. Ordinary gases are those which do not liquefy at ordinary temperatures or pressures, and the farther they are removed from their point of liquefaction the nearer they approach the character of permanent gases. Vapours are gases near their point of liquefaction. Ordi- nary high or low pressure steam is a vapour, superheated steam is a gas. Vapour of water is absorbed by the air at all temperatures, the higher the temperature of the air the more water it is capable of holding in solution. 379. KINETIC THEORY OF GASES. A gaseous body consists of a swarm of innumerable solid particles incessantly moving about with different velocities in rectilinear paths of all conceivable directions, the velocities and directions being changed by mutual encounters at inter- vals which are short in comparison with ordinary standards of duration, but indefinitely long as compared with the duration of the encounters. " Gases consist of atoms which behave like solid, perfectly elastic spheres moving with definite velocities in void space." Kroenig. A gas consists of a number of molecules, flying in straight lines, and impinging like little projectiles not only on one another, but also on the sides of the vessel holding the gas. Gases of every kind will diffuse into each other. It is thought that the velocity of a molecule of hydrogen at 32 F. and at the atmospheric pressure is 6097 feet per second. Goodeve. THEKMODYNAMICS, AND STEAM. 177 380. LAWS OF GASES. Boyle s Law (1662), also enunciated by Marriotte (1676) The volume of a gas varies inversely as the pressure. It may also be stated thus : the pressure of a gas is propor- tional to its density. The law is most nearly fulfilled when the temperature of the gas is farthest removed from its point of condensation. Charles' Law (1787). All gases expand equally, and the volume varies directly as the absolute temperature. Dalton (1801). A gas at any temperature increases in volume for a rise of 1 by a constant fraction of its volume at that temperature. Gay-Lussac (1802). The augmentation of volume which a gas receives when the temperature increases 1 is a certain fixed proportion of its initial volume at C. Under a constant pressure all gases expand uniformly with equal additions of heat, and with a constant volume all gases increase equally in pressure for equal increments of heat. Avogadros Law (1811), also attributed to Ampere and Gay-Lussac. Equal volumes of all substances, when in the gaseous state and under like conditions of pressure and temperature, contain the same number of molecules. Boyle's is sometimes called the first law of gases, and Charles' the second law. 381. VOLUME OF A GAS AT GIVEN PRESSURE AND TEMPERATURE. V = volume of gas at T and P Ibs. v = t p Ibs. T _ 458-44- t P = V X 458T+T X Box, on Heat.' 178 HANDBOOK FOR MECHANICAL ENGINEERS. v = volume of elastic fluid given weight and pressure at 32 F. V = volume it will occupy at same pressure at t F. V = v+ - 00202 v(t- 32). Gay Lussac. The volume of a gas under constant pressure expands 1 3665 times when raised from 32 to 212 F. 382. PRESSURE AND TEMPERATURE OF STEAM. p = Ibs. per square inch. t = temperature F. 1 to 24 atmospheres : 2697+ 006 7 */p - 39- Arago and Dulong. p = (-2697+ 006803 t) 5 . t = 147 * - 39-644. 1 to 4 atmospheres : 201-18 t = 201-18^- 103. Up to 90 Ibs. per sq inch : 177 t = 177 (-y 2^) - 100. Tredgold. I to 4 atmospheres : _ /98-8 + er sq. foot. g = force of gravity = 32-2. v = velocity in feet per second. W Usually p = 2116-4, then 2 x 32-2 x 2116-4 = 136,296 16, and .approximately 136,300 or for water v = 46-5, and air = 1338. In all cases allowance must be made for friction, say 100,000 approx. v = Velocity from one medium to another of given pressures P and p. v -"' w THERMODYNAMICS, AND STEAM. 187 Steam of all pressures will rush into a perfect vacuum with a velocity of about 2000^feet per second, no allowance being made for friction. Steam of 60 Ibs. pressure will rush into atmosphere about 1800 feet per second. 403. DISCHARGE OF STEAM THROUGH PIPES. The velocity of discharge in pipes is in all cases pro- portional to the sectional area divided by the circumference ; in round pipes this equals one-fourth of the diameter, thus: 4 _ d TT d 4 and quantity discharged therefore varies as the diameter 3 . The pressure lost in discharging a fixed volume of steam varies inversely as the 4th power of the diameter of the orifice. The steam pipe for an engine must be calculated as if constantly passing steam of the maximum velocity required to supply any part of the stroke. With single cylinder engines maximum velocity may be taken as 1 57 times the mean velocity ; and with double cylinder engine, cranks at right angles, maximum = I'll times mean. Single cylinder : Max. = TT s R. _ .. , TT ,, .*. Max. exceeds mean by - = 1 *57. Mean = 2 s R. J 2 Box. 404. DIAMETER OF STEAM PIPES. A = area of piston in sq. inches. S = piston speed feet per minute. . , AS Area steam pipe sq. inches = Another rule (approximate) : Diameter steam pipe in inches = 188 HANDBOOK FOR MECHANICAL ENGINEEES. 405. VELOCITY OF STEAM IN PIPES 100 feet per second. Unwin. Through main steam pipe . .130 feet per second. stop and throttle valves 90 steam ports . . . 80 f Practical Engineer.' 406. THICKNESS OF STEAM PIPES. Cast-iron steam pressure pipes between 2 inches and 12 inches diameter, and up to 70 Ibs. boiler pressure. d + 4 = t in -^ths of an inch. For exhaust steam, suction and ordinary low-pressure pipes of cast iron, d + 10 = t in ^nds of an inch. Large copper steam pipes (length = 5 diameters). d = inside diameter inches. t = thickness inches. p = working pressure (factor of safety 6). By experiments^-- 407. EXPANSION OF STEAM PIPES. Steam pipes expand and contract about 1 inch in 50 feet, or -02 inches per foot; hence the necessity for inserting expansion pipes between each rigid connection. 408. Loss OF HEAT BY PIPES. A 4-inch steam pipe covered in hair felt and canvas loses about 120 units of heat per foot run per hour at 60 Ibs. per sq. inch pressure ; bright copper pipe 350 units, rough black pipe 700 units. Sox. THEKMODYNAMICS, AND STEAM. 189 409. COMPARATIVE TRANSMISSION OF HEAT. 1. Through various materials in mass. Poultry feathers ... . . 6*2 Hair felt. ...'.. 11 '4 Cork powder . , . .13*6 Sawdust. . . . . ^ . 14*2 Plaster of Paris . . ' . 36-2 Asbestos powder . . . 47*9 Fossil meal . . . . 52 1 Fine sand ... . .56-3 2. Through various materials prepared as non-conducting coverings. Slag wool, hair and clay paste . 10*0 Fossil meal and hair paste . 10*4 Paper pulp alone . . . .14-7 Asbestos fibre wrapped tightly . 17*9 Fossil meal and asbestos powder . 26-3 Coal ashes and clay paste, wrapped with straw 29-9 Clay, dung and vegetable fibre paste 39-6 Paper pulp, clay and vegetable fibre 40 6 Note. Other considerations, such as cost and durability, niubt receive attention in any practical application. 410. NON-CONDUCTING DRY HAIR FELT. Maker's Number. 1 2 Approx. Weight per sheet 31" x 20". Approx. Thickness uncompressed. oz. inches 12 T%. to J 16 * to f 24 i 32 I to f 40 I tof 48 1 190 HANDBOOK FOR MECHANICAL ENGINEERS. 411. COMPARATIVE EADIATION. Approximate units of heat emitted per square foot per hour by pipes per 1 F. difference of temperature by radiation and air contact combined. Dull tinned or galvanised surface . 62 + 005 Diff. in F. Black iron . . . . . -9 + -005 Eusted iron, wrought or cast . 1 04 -f- 005 Or, say for any system of pipes 2 to 4 inches diameter 1 5 units, and for f-inch thin brass pipes 2-25 units, per 1 F. difference of temperature. 412. HEATING BY STEAM. When the external temperature is 10 F. below freezing point, in order to maintain a temperature of 60 F. there will be required with steam at 212 F. (a) One square foot of pipe surface for each 6 square feet of window glass. (6) One square foot of ditto for each 6 cubic feet per minute of air escaping for ventilation. (c) One square foot of ditto for each 100 square feet of roof, wall, or ceiling. (c?) One square foot of ditto for each 80 cubic feet of space. Approximately 1 cubic foot boiler space is sufficient for 2000 cubic feet space in rooms. Each foot-run of 4-inch pipe will heat 200 cubic feet air 1 F. per minute. Each H.P. of boiler will warm 40,000 cubic feet of space. 413. HEATING BY HOT WATER. Grate surface, 50 square inches per 100 feet run of 4-inch pipe. Boiler surface exposed to fire, 2 square feet per 100 feet oi 4-inch pipe. THERMODYNAMICS, AND STEAM. 191 Fuel required, 2J to 5 Ibs. per hour per 100 feet run of 4-inch pipe. For factories, 5 to 6 feet run of 4-inch pipe per 100 cubic feet. For waiting-rooms, &c., 7 to 8 feet of 4-inch pipe per 100 cubic feet. For greenhouses and hot-houses, required temperature F. 20 = feet run of 4-inch pipe per 100 cubic feet. Pipes to be laid on rollers to allow for expansion and contraction, which equals 1J inches in 100 feet. Air-cocks to be provided at highest points of pipe and wherever air is likely to lodge. Stop-cocks may be half size of pipe, say 4-inch pipe = 2-inch cock. Supply cistern = $ contents of boiler and pipes, and connected to return pipe. Kust joint cement, 1 Ib. sal-ammoniac, 1 Ib. flour of sulphur, 1 cwt. cast-iron borings, made to a paste with water and caulked into sockets. Special joints with india-rubber rings are now generally used for cast-iron hot-water pipes. 192 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION X. STEAM BOILERS. 414. VARIETIES OF BOILERS. Early Forms. Spherical and cry lind re-spherical, of cast iron, afterwards all wrought iron. Haystack or Balloon Boiler. Used formerly in Stafford- shire : conical sides, dome top, small flat or hollow bottom. Wagon Boiler. Used formerly in Lancashire: flat ends, cylindrical top, bollow curved sides and bottom, held by stays. Egg-ended Boiler or cylindro-spherical, set horizontally, with "flash" flues, afterwards made with internal flue, furnace always external. Eastrick Boiler. Same as last, but set vertically, one or more horizontal flues leading to main flue through boiler. Cornish Boiler (Trevithick). Cylindrical, flat ended, with one flue tube containing furnace. London form shorter than original Cornish. Lancashire Boiler (Fair bairn, 1844). Similar to last, but with two flue tubes side by side containing furnaces. Breeches-flued Boiler. Similar to last, but with flue tubes uniting into one at back of bridges. Butterley Boiler. Similar to Cornish, but with flue tube enlarged at front end, and made elliptical to take wide furnace. Galloway Boiler of Cornish or Lancashire type, but with taper water tubes placed diagonally across flue tubes. French, or Elephant Boiler. Formed of three horizontal cylindrical parts connected to each other by necks, two of these (heaters or bouilleurs) surrounded by brick flues. STEAM BOILERS. 193 Fairbairn Boiler. Same type as last, but with flue tube through each heater. Marine Boilers. Formerly made flat-sided, or any shape to fit ship, stayed where required. Now made cylindrical, short, large diameter, one, two, or three furnace tubes, com- bustion chamber at back end in one or more divisions. 50 to 250 small tubes from combustion chamber to smoke box at front end. Locomotive Boilers. Square furnace box at one end, water jacketed, connected with cylindrical boiler shell containing 200 to 300 small tubes for passage of gases to chimney. Field Boiler. Vertical cylindrical, with furnace contained in inner cylinder, top of latter below water line and holding suspended in flame 50 to 60 small double tubes for circulation of water. Bdbcock and Wilcox Boiler. Sectional water-tube boiler with inclined wrought- iron tubes expanded front and back into vertical sinuous headers which are connected by vertical tubes to cross-boxes on a horizontal steam and water drum. No stayed surfaces, and all joints metal to metal. All parts being of small diameter, the boiler is exceptionally safe from disastrous explosions. 415. PRODUCTION OF STEAM IN CORNISH AND LANCASHIRE BOILERS. Approximately, 1 sq. foot of grate surface, 1 sq. yard of heating surface, 1 cubic yard of boiler space, will evaporate 1 cubic foot of water in 1 hour, producing 1 N.H.P., each cubic inch of water forming 1 cubic foot of steam at atmospheric pressure. 416. HORSE-POWER OF BOILERS. Nominal H.P. of Boiler = cubic feet of water evaporated from 60 F. at any pressure in one hour = say 70,000 heat units. Heat H.P. of Boiler is the amount of heat expressed in foot-lbs. transferred from the products of combustion into the water and steam per minute 4- 33,000. Mechanical H.P. of Boiler is the mechanical work done o 194 HANDBOOK FOR MECHANICAL ENGINEERS. per minute by the water as it evaporates and expands into steam -f- 33,000. If P be absolute steam pressure in Ibs. per sq. foot, V = No. of cubic feet of steam produced per minute. P V Then = mechanical horse-power of boiler. oo,UOO In America a commonly accepted unit of horse-power for steam boilers is the evaporation of 30 Ibs. water per hour from and at 212 F. The actual horse-power developed by the steam from a boiler depends upon the engine in which it is utilised. In an average modern engine 1 cubic foot of water evaporated per hour will develop 4 horse-power. 417. HORSE-POWER OF BOILERS FROM DIMENSIONS. S = heating surface in sq. yards. g = grate surface in sq. feet. !1 for ordinary coal, f for good steam coal. J for best coal only. R* Armstrong. a = area in sq. feet of water surface in boiler -f- horizontal sectional area of furnace tube in Cornish or Lancashire boiler. H. P.= Plain cylindrical boiler a "6" .. .. vs- 9 a 6 to 8 ** T b a 4-5 9 1. /Q Multitubular boiler .... 5 to -8 | to |S o v isgr Marine boiler (I.H.P. = 5 N.H.P.) . - * 7 iv^S gf STEAM BOILERS. 195 Another rule : Norn. H.P. = ^ length boiler in feet X diameter in feet. The average number of cubic feet water evaporated per hour from cold feed with ordinary firing and good steam coal, is generally taken as the nominal horse-power of boiler, but two-thirds of a cubic foot is sufficient to develop 1 indi- cated horse-power in most steam engines. 418. COST OF BOILER POWER. Total cost of boiler power per horse-power per annum, including interest on capital, fuel, attendance and renewals, say 51. 10s. for Lancashire and Cornish boilers, and 8Z. for locomotive type. 419. EFFICIENCY OF BOILERS. The Efficiency, Evaporative efficiency, or Economic efficiency of a steam boiler is measured by the proportional quantity of the whole heat of combustion of a given fuel, which is absorbed into the boiler and applied to the conversion of water into steam, and is expressed by the weight of water evaporated from and at 212 F. by 1 Ib. of the fuel. The Evaporative power of a boiler is expressed by the total quantity of water evaporated per hour, or per square foot of grate area per hour, or per sq. foot or sq. yard of heating surface per hour. D. K. Clark. 420. SPACE OCCUPIED BY COAL. Solid coal, say 40 cubic feet per ton. Coal stores contain 45 cubic feet per ton. Navy allowance for bunkers, 48 cubic feet per ton. Coals will run down shoot at slope of 6 inches in 1 foot, or 26 ; and down screen bars at 36. o 2 196 HANDBOOK FOR MECHANICAL ENGINEERS. 421. CALORIFIC VALUE OF FUELS. Coals of lowest calorific capacity are those which burn with a long flame, their heat of combustion varying from 7840 to 8570 calories per kilogramme ; after which come the gas coals, varying from 8400 to 8770 calories. The most advantageous coals appear to be generally the bituminous and semi-bituminous varieties, which show from 8570 to 8870 calories. Some anthracitous coals possess considerable calorific value, while the true anthracites approach, by their heat of combustion, the ordinary flaming coals, giving 8700 to 8100 calories. Petroleum gives 11,000 calories. Mahler. Calories per kilog. x 1 8 = British heat units per Ib. fuel. 422. CHEMICAL COMPOSITION OF FUELS. Coal (mean 97 kinds). Coke. Wood (ord. state). Peat (ord. state). Carbon . 8040 850 408 464 Hydrogen 0519 .. 042 048 Oxygen . Nitrogen and sulphur Water . 0787 0246 334 200 248 200 Ashes . 0408 150 016 040 Totals 1-0000 423. THEORETICAL UNITS OF HEAT PER LB. OF FUEL. A Coal (mean of 97) ' . . 13,006 294 Coke 10,970 269 Wood (dry) .... 6,582 161 (ordinary) . . . 5,265 129 Charcoal 12,000 294 Peat (dried) . . . 8,736 202 Column A gives cubic feet of air at 62 F. required per Ib. of fuel. Box on ' Heat.' STEAM BOILERS. 197 424. ABSOLUTE HEATING POWER OP FUEL. p = absolute heating power of fuel in " calories." C = percentage of carbon in fuel. H = percentage of hydrogen in fuel. W = of chemically combined or hygro- scopic water. p = 80-8 -f 296-3H - 6-4W. ' Industries.' The Calorific Power (Dr. Percy) of a substance is the number of units of heat produced by the combustion of a unit of weight of the substance. 425. UNITS OF HEAT PER LB. OF FUEL (BY EXPERIMENT). Hydrogen burning to water . 50,000 Carbon carbonic oxide . . 3,500 carbonic acid . . 14,000 Carbonic oxide ? , . 4,000 Welsh coal . 8,500 Newcastle coal . 8,000 Lancashire coal . 7,500 Derbyshire coal . 7,000 Wood (ordinary state) . 5,000 426. HEATING BY CONTACT OF GASES. When difference of temperature is doubled, the rate of transmission is increased 2 35 times. 427. BATE OF TRANSMISSION OF HEAT. In locomotive boilers the rate of transmission per square foot of heating surface is 11 tnermal units per hour per degree Fahrenheit of difference in temperature. J. A. Longridge. In the boiler of s.s. Meteor, tested by Prof. Kennedy, 4769 thermal units per sq. foot heating surface per hour 198 HANDBOOK FOE MECHANICAL ENGINEERS. were transmitted, or only 3 thermal units per hour per degree Fahrenheit of difference in temperature. D. Halpin. The average number of units of heat transmitted through boiler plates per sq. foot of surface per hour and per degree difference of temperature varies from 5 to 6 B.T.U. (British thermal units). 428. CONDITION OF BOILER AFFECTING TRANSMISSION OF HEAT. Heat units absorbed per sq. foot per hour per degree Fahrenheit of difference in temperature. Condition of Boiler. 1 sq. ft. Heating Surface per Ib. Coal Burned per hour. 4 sq. ft. Heating Surface per Ib. Coal Burned per hour. Very clean boiler 6-5 4-6 Fairly 6-0 4-3 Bather dirty ... 5-5 4-1 M. Longridge. 429. Loss OF STRENGTH IN COPPER PLATES WHEN HEATED. At boiling point, 60 Ibs. pressure, 307 '5 F. = 10 per cent. At 500 F 50 At faint red heat, 1000 F 75 At dull red heat, 1300 F 100 430. Loss OF STRENGTH IN IRON PLATES WHEN HEATED. At boiling point, 60 Ibs. pressure, 307-5 F. = nil If anything, the strength increases up to 320 F. At about 550 F. decrease begins to be perceptible. At faint red heat, say 1000 F. . . 25 per cent. At duU red heat, say 1300 F. . .50 STEAM BOILERS. 199 431. COMPARATIVE VALUE OF HEATING SURFACES. Area of shell exposed to flame . . = 1 Horizontal area above flame . . . = 1 Surface inclined towards flame , = Vertical surface , . . . = ^ Surface inclined from flame , . = Horizontal surface below flame . = Internal cylindrical flues = ^ circumference. Small tubes . = Shell of Cornish or Lancashire boiler =f to f of lower half. 432. HEATING SURFACE OF BOILERS. Class. Proportion of Heating Surface to Grate Surface. Heating Surface to evaporate 1 cubic foot per hour. Plain cylindrical . . Cornish and Lancashire . Multitubular .... 10-16 to 1 15-25 to 1 30-40 to 1 60-80 to 1 J 8 sq. feet 1* 9 6 Vertical 10-16 In portable boilers tried by Bramwell for the Koyal Agricultural Society, with a heating surface varying from 16 to 37 sq. feet per cubic foot evaporated per hour, the total heat effect varied from 651 to 776, and the temperature of escaping gases from 775 F. to 500 F. He recommended in the ordinary way 12 to 15 sq. feet heating surface per cubic foot evaporated per hour, and a grate surface of -^ to $ of this. Babcock and Wilcox water-tube boiler, 11 J sq. feet heating surface to each N.H.P. A Lancashire boiler will evaporate 5 Ibs. water per sq. foot total heating surface per hour, or 2 cubic feet per sq. foot fire-grate surface per hour, without pushing. 200 HANDBOOK FOR MECHANICAL ENGINEERS. 100 Ibs. coal 433. PRODUCTS OF COMBUSTION. 80 Ibs. carbon.. 5 Ibs hydrogen . . 15 Ibs. sundry . . . 1; 960 Ibs. [ 746 Jibs, nitrogen air 21 3 J Ibs. oxygen . .. l801bs.( 140lbs - nitr S en V 40 Ibs. oxygen . air (293J Ibs. carbonic acid gas, I say 2520 cub. ft. {45 Ibs. water, say 946 cub. ft. steam. . .15 Ibs. ash. I886J Ibs. nitrogen, [ say 12,000 cub. ft. These figures assume perfect combustion and no losses. 434. AIR REQUIRED TO BURN FUEL. For the complete combustion of 1 Ib. of fuel, the Ibs. air theoretically necessary = -117 times the percentage of carbon 4- " 35 times the percentage of free hydrogen, e. g. carbon, 70 per cent. ; hydrogen, 3 per cent. 117 x 70 -f -35 x 3 = 9-24 Ibs. air per Ib. fuel. ' Industries.' Good Lancashire coal requires theoretically 10 Ibs. weight of air per Ib. of coal for perfect combustion, but should be allowed 15 to 16 Ibs. in practice. M. Longridge. Practically, we may say, 13 cubic feet of air at 60 F., 30" bar., weigh 1 Ib., and 12 Ibs. air are required to combine with constituents of 1 Ib. coal for perfect combustion, but to allow for working conditions, 24 Ibs. is necessary; or 312 cubic feet = 700,000 cubic feet of air per ton of coal. 100 cubic inches atmospheric air at 60 F. and 30" bar. = 31 grains; .*. 1 cubic foot = *093 Ibs.; 12 cubic feet oxygen weigh 1 Ib., and to obtain 1 Ib. oxygen, 5 Ibs. air must pass through fire = 60 cubic feet. STEAM BOILERS. 201 2 to 3 Ibs. oxygen required to burn 1 Ib. of coal, or, assuming only two-thirds effective, 180 to 270 cubic feet will be required. In general, the quantity of air provided should be double the minimum theoretical quantity. Air and smoke together equal about 2000 cubic feet per cubic foot of water evaporated, temperature say 800 F. Maximum 'economical draught for boilers = pressure due to ^ inch head of water, causing consumption of 36 Ibs. coal per hour per sq. foot fire-grate, and requiring 24 Ibs. air per Ib. coal. Air spaces in fire door = 3 sq. inches per sq. foot of fire- grate. 435. HEAT IN FLUE. With Cornish boiler, temperature of escaping gases at base of flue may be as low as 500 F. With short multitubular boiler, as high as 1200 F. A pyrometer indicating up to 1000 F. was placed in the flue at end of a multitubular boiler of locomotive type, con- taining tubes 7 feet x 2| inches, when the pointer went beyond the range of the instrument = say 1100 F. The temperature is generally ascertained by hanging strips of metal foil, on an iron wire, across the flue, and noting which are melted by the heat, viz. : copper 2000, aluminium 1800, zinc 750, lead 630, tin 440. Temperature of boiler furnace, say 2400 F. 436. BRICK CHIMNEY-SHAFTS. The bond usually adopted is one course of headers to four of stretchers. Up to 120 feet high the top length is generally one brick thick ; above that height, top length 1^ brick thick. Height of any length of uniform section should not exceed 30 feet, and should be less in thin sections. 202 HANDBOOK FOB MECHANICAL ENGINEERS. 45 feet is an ordinary total height for two steam boilers, but in some towns, as Manchester and Leeds, the minimum height allowed is 90 feet. A minimum wind pressure of 55 Ibs. per sq. foot must be allowed for in calculating stability. Bound chimneys should not exceed 25 times internal diameter in height. 437. FORCE OF WIND. Miles per hour X 88 = feet per minute. 22 , X ^r = second. _ i> 2 ft. per sec. 500 Button. p = 144 velocity miles per hour. Crosby. p = pressure in Ibs. per sq. foot against a plane surface normal to direction of wind. a = area of maximum section in sq. feet perpendicular to direction of wind. 6 = angle of exposed surface with plane of section. c = coefficient according to shape of surface presented. P = total resistance of surface in direction of wind. P = c . a . p. Coefficients, c = Disc or rectangular plane . . = 1 Cylinder . . . . = Sphere ,. ;; . . = g- Wedge . . . . . = sin sin 6 Cone or pyramid . . . y- A square chimney presents the same resistance either square or diagonally placed. STEAM BOILERS. 203 A roof may be taken as equal to a wedge whose base is twice the rise of roof; sin 6 would then be measured from vertical. An inclined plane of area a will at small angles present a resistance approximately varying as sin 2 6 ap, and at large angles as sin 6 a p. A formula agreeing closely with Hutton's experiments is P = ap sin 0i-84 cos e f a being full area of surface. In Hutton's experiments a = 32 sq. inches. 438. SIZE OF FACTORY CHIMNEY FOR BOILERS. W = weight of coal burnt in Ibs. per hour. A = area of chimney in sq. feet at top. H = height of chimney in feet. c = cubic feet evaporated per hour. A = i w or, A = Chimney for single boiler, area = | fire-grate. Do. under 150 feet highl l for more than one) " = TTr " Do. over 150 feet high do. = ^ , . Ibs. coal per hour X 12 Area of chimney in sq. inches = - V height feet Bourne. Area of chimney usually ^ area of fire-grate and 40 feet high. Scott Russell. 20 square inches area per N.H.P. of engine. Height of about 20 times internal diameter. Flues area of fire-grate, diminishing to T V at chimney. 204 HANDBOOK FOB MECHANICAL ENGINEERS. Height of chimney = 45 feet. area fire-grate , . , Area of chimney = /.-..-, KQ * Elswick. *J height x 1*58 Do. = 1 J sq. ins. per Ib. of coal per hour. Murray. 120 x grate surface sq. ft. Area chimney sq. ins. = - Vheight fee T. T. Henthorn. A- boiler H.P. + 10 -> Area sq. feet = ,, . ,. f \ Berg. V height feet Boiler horse-power of chimney = 3^ (area sq. feet 0*6 Varea) ^/height feet. W. Kent. Effective area of chimney = 2 inches less all round than actual area. d inches 3 Approximate horse-power of round chimney = -r Funnel for marine engine = 3 to 5 sq. inches per indi- cated horse-power. 439. VELOCITY OF GASES IN CHIMNEY. Velocity of gases = 8 V motive height = 8 ^/h ^ , T ) / *"" Do. practically = 6 i T - t V 500 Tredgold. Ordinary velocity of gases in chimney shaft = 2-4 J H. Most economical temperature of escaping gases = 600 Fahr. At this temperature the volume of air entering furnace is doubled on exit. A cubic foot of water requires 10 Ibs. coal to evaporate it ; 10 Ibs. coal require 210 Ibs. air for complete combustion, = say 2750 cubic feet. STEAM BOILERS. 205 The force of the draught in a chimney stack is the deficiency of weight of the column of rarefied air in the chimney compared with a similar column of the external air. A factory chimney erected by Boulton and Watt, 80 feet high, 400 sq. inches area, coal consumption 300 Ibs. per hour, had a suction in chimney = 1 inch of water. 440. LONDON COUNTY COUNCIL EULES FOR FURNACE CHIMNEY SHAFTS. The width of a shaft at the base, if square on plan, must be at least one-tenth, and if circular on plan at least one- twelfth of the total height. A shaft must have a batter of 2 inches in every 10 feet of height. The brickwork must be at least 8J inches thick at the top of the shaft and for 20 feet below, and must be increased 4J inches in thickness for every 20 feet of additional height, measured downwards. No portion of the enclosures of a shaft is permitted to be constructed of fire-brick, and any fire-brick lining to be used must be in addition to the thickness of, and independent of, the brickwork. No cornice or other projection is allowed to project more than the thickness of the brickwork at the top of the shaft. 441. RATE OF COMBUSTION. In Ibs. of coal burnt per sq. foot of fire-grate per hour. Cornish boilers ..... 3J Old land boilers 10 Eecent land boilers .... 13-14 Modern marine boilers . . . 16-24 Locomotive boilers . . . 80-120 206 HANDBOOK FOB MECHANICAL ENGINEEES. Another account : lba Cornish boilers for pumping engines . . 4-10 and others for factory uses. 10-15 Marine boilers, ordinary rates . . . 15-20 Boilers with strong chimney draught . 20-30 Locomotives . . . . . . 60-120 A boiler may be made to do 70 per cent, more work if the consumption of fuel can be doubled, but the life of the boiler will be considerably shortened. 442. BOILER FURNACES. With bituminous fuel the layer in the furnace should be about 4 to 6 inches thick, and should never exceed 12 inches. Thin firing is more economical, but requires more careful stoking. Fresh fuel should be put in front of the fire and the red-hot fuel pushed back, or should be spread thinly over the surface after the hollows are filled up. With coke or hard coal the fire may be thicker, especially if a blast be used. For locomotive boilers the fire may be 18 inches thick. For land boilers with hand firing, fuel should be added about every half hour, and more air admitted for the next ten minutes. Small coal, or slack, has about half the evaporative power of coal or coke. 443. HEAT IN BOILER FURNACES. 1. Temperature of furnace, say about 2500 F. 2. escaping gases, say 600 to 1200 F. 3. steam and water in boiler, say 300 F. 4. water in condenser, say 100 F. Difference between (1) and (2) is absorbed by the water in raising its temperature, by the steam as latent heat, and STEAM BOILERS. 207 by the air entering furnace in excess of quantity required for combustion. Difference between (2) and (3) is utilised in creating draught ; 600 is the most economical temperature of escap- ing gases, as it allows sufficient difference of temperature for rapid passage of heat to water, and the density is sufficiently reduced to give rapid ascending current in chimney shaft. Difference between (3) and (4) is utilised in the engine. The difference of temperature or quantity of sensible heat does not by itself represent the comparative efficiency. 444. Loss OF HEAT IN BOILERS. Assuming that it requires 10 Ibs. of coal to evaporate 1 cubic foot of water from 60 into steam at 60 Ibs. per square inch gauge pressure, the loss of heat may be shown, as follows, to be nearly 50 per cent. : Total heat of combustion in 1 Ib. of coal in British thermal units = say 13,000. 13,000 units per Ib. x 10 Ibs. coal . . = 130,000 Steam at 60 Ibs. pressure has a total heat of 1207 units. 1207 - 60 temperature of feed- water = 1147 units per Ib. of water. 1 cub. ft. water = 62-5lbs. 62-5 x 1147 = 71,687 Loss in chimney, 24 Ibs. air, required to burn 1 Ib. coal. 24 x 10 = 240 Ibs. to burn 10 Ibs. coal. Specific heat of air = -2374. Temperature of escaping gases = 600. 240 x -2374 x 600 . . . . = 34,185 Loss in hot ashes, fuel dropped through, &c., say 7 per cent, of total heat . . . = 9,100 Loss by radiation and conduction, say 7 per cent .... . = 9,100 Loss by imperfect combustion, say 4J per cent. = 5,850 129,922 In ordinary cases large boilers utilise about 8000 units of heat per Ib. of coal. 208 HANDBOOK FOE MECHANICAL ENGINEERS. 445. DUTY OF ENGINES. "Duty" dates from Lean's ' Reporter,' published in 1811. s = standard of comparison in Ibs. = Cwt. any coal . . . 112 Ibs. Bushel Welsh coal . . 94 Newcastle coal . 84 w = Ibs. weight coal burnt per I.H.P. per hour. n = No. of cwts. or bushels burnt per hour. I.H.P. X 33,000 X 60 Duty m ft. -Ibs. per standard = - _ 33,000 X 60 x 8 ~~ OO1 7 A Duty in million ft.-lbs. per cwt. = - w Cornish duty (prior to 1855) : g = gallons of water pumped per hour. / = feet lift of water pumped. n = bushels of 94 Ibs. coal. Since 1855 Cornish duty has been reckoned upon the cwt. of 112 Ibs. 446. PROGRESS IN DUTY OF ENGINES. A.D. 1700 Savery ... 5 million ft.-lbs. per 100 Ibs. fuel 1770 Newcomen . . 12 1780 Watt ... 27 1830 Cornish engine . 87 1890 Multiple cylinder .120 But even in the last case less than one-eighth of the theoretical value of the fuel is obtained. Prof. Thuraton. STEAM BOILERS. 209 447. DUTY OF ENGINES COMPABED WITH COAL USED. C = consumption of coal per I.H.P. in Ibs. D = duty in million Ibs. raised 1 foot high by 1 cwt. of coals. 0. D. 1 . . 221-760 1-5 . . 147-840 2 . . 110-880 2-5 . . 88-704 3 * . . 73-920 4 55-440 C. D. 5 . . 44-352 6 . . 36-960 7 . . 31-680 8 , _ . 27-720 9 , . 24-640 10 22-176 448. MODERN DUTY. The duty of a steam engine alone is measured by the amount of steam used per hour per I.H.P. The duty of an engine and boiler combined is measured by the coal consumed per hour per I.H.P. The E.H.P. or Brake H,P. ought, however, to be taken in preference to the I.H.P. 449. EVAPORATIVE VALUE AT DIFFERENT TEMPERATURES. In stating the evaporative power of a boiler, it is usual to express it in terms of feed-water evaporated from 212. t = actual temperature of feed- water. T = total heat of steam under given pressure. c = cubic feet of water evaporated from t. C = from 212 by same quantity of heat. T t - heat imparted* T- t 210 HANDBOOK FOR MECHANICAL ENGINEERS. 450. HAND-FIRING AND MECHANICAL STOKING. Summary of trials of Vicars' mechanical stokers at the City of London Electric Lighting Station, Bankside, S.E., against hand-firing. Babcock and Wilcox Boilers. Hand-Firing. Vicars' Patent System. Date of trial . . . . 26th April, 1894 4th June, 1894 Duration of trial . . . 9 hours 6 hours Description of fuel used . * Nixon's Navigation ( Bituminous rough, \ small Price of fuel used . 16. per ton 10s. per ton Fuel consumed 13, 664 Ibs. 9184 Ibs. Ashes and cliuker . 532 Ibs. 1022 Ibs. Weight of combustible . 13,1321bs. 8162 Ibs. Per cent, of ash . 3*9 per cent. 11*1 per cent. Draught in flue (av.) 48" water 55" water Temperature in flue (av.) 210-8 C. 453 F. Water evaporated . 118,535 Ibs. 82, 100 Ibs. Temperature of feed water 54-3Fahr. 62 F. Average steam pressure . 145 -9 Ibs. 157 -5 Ibs. Water evaporated per hour 13, 170 Ibs. 13, 683 Ibs. Water evaporated per Ib. ofl fuel under actual conditions / 8 -67 Ibs. 8 -94 Ibs. Water evaporated per Ib. of) combustible . . . .f 9 -02 Ibs. 10 -05 Ibs. Water evaporated per Ib. ofl fuel from and at 212 F. ./ 10 -50 Ibs. 10-78 Ibs. Water evaporated per Ib. of! combustible from and at} 212 F. .) 10 -93 Ibs. 12 -12 Ibs. Cost of evaporating 500 gallons 40 -8d. 24 -8d. STEAM BOILERS. 211 451. EXPERIMENTS ON EVAPORATION IN BOILERS. Class. Size. Lbs,. Water per Ib. Coal. Lbs. Coal per cubic foot Water. Cornish . , 20 H.P. 6-764: 9-212 Lancashire 25 7'547 8-256 Galloway . 35 9-5 6-579 Field . 10-9 5-734 In a case where an engine was allowed to get into bad condition, with considerable leakage past valves and pistons, it appeared as if 3 Ibs. of water were evaporated by 1 Ib. of coal, or 21 Ibs. of coal were required to evaporate 1 cubic foot of water. This was on the assumption that the engine required only the normal amount of steam. 452. EFFECT OF SUPERVISION OF BOILERS. Men being aware the work was measured : 100 hours, evaporation (average from and at 212 F.) =9*7 Ibs. water per Ib. fuel. Men not being aware the work was measured : 220 hours, evaporation (average from and at 220 F.) = 9*3 Ibs. water per Ib. fuel. Difference = 4J per cent, in favour of supervision. E. Bennis. 453. CONSUMPTION OF STEAM IN ENGINES. Non-condensing . . 30 Ibs. steam per I.H.P. per hour. Compound condensing 20 Triple compound .15 ,, p 2 212 HANDBOOK FOE MECHANICAL ENGINEERS. 454. FEED- WATER REQUIRED FOR BOILERS. Gallons feed-water required per lieur = say nom. H.P. of boiler x 10 to allow for losses, or I.H.P. of engine x 5 for ordinary work, or x 6 for maximum work. Boilers supplying engines pumping water against ac- cumulator pressure and working intermittently require about 2 \ gallons per working hour per effective H.P. on the average of the year. 455. ADVANTAGE OF HEATING FEED- WATER. 1 Ib. water requires 160 units of heat to raise it from 52 F. to 212 F., and 1000 units of heat to evaporate it from and at 212 F. If, therefore, the feed-water be raised to 212 F. by means of exhaust steam, the 160 units will be saved, and the resulting economy will be 160 x 100 = 13*8 per cent. gain. 1000 -f 160 Or, putting it another way, the percentage of gain at any pressure by increasing the temperature of feed-water may be found by the following formula : H = total heat of steam at boiler pressure. T = temperature of feed after heating. t = before 100 (T - I) Gain per cent. = v _ , * Example ; A boiler working at 100 Ibs. pressure is sup- plied with water at 100 F. from a condensing engine. When passed through a Green's economiser, the temperature of the feed is raised to 250 F. What is the gain per cent. ? H = 1216-5. T = 250. 2 = 100. Then STEAM BOILERS. 213 456. FUEL ECONOMISERS. Those by Green and Son, Limited, of Manchester and Wakefield, are best known. They act by heating the feed- water and removing lime, and consist of a series of 4-inch cast-iron pipes, about 9 feet long, in four or more rows, placed vertically in main flue and connected by top and bottom boxes. The feed- water passes through these on its way to the boiler, and the products of combustion pass on the outside in the opposite direction. An economiser receiv- ing the gases at 650 F., and reducing their temperature to 350 F., may raise the feed-water from 100 F. to 250 or 300 F., and produce an economy of from 10 to 15 per cent, in the fuel consumption. The number of economiser pipes per boiler is four pipes per ton of coal consumed per week, or say, one pipe to every 3 I.H.P. 457. CONSUMPTION OF FUEL. The consumption of coal per I.H.P. depends upon the boiler as well as the engine, say Non-condensing engine 3 Ibs. coal per I.H.P. per hour. Simple condensing 2 Compound 1*75 Triple compound 1 5 Quadruple 1-25 458. POSSIBLE ECONOMY IN COAL CONSUMPTION. Total units heat (B.T.U.) in 1 Ib. coal say 12,000, repre- senting 12,000 X 772 foot-lbs. = 9,264,000 foot-lbs., or if all 33,000 X 60 utilised a consumption of ... = '213 Ibs. coal per y ,^o4, ooo H.P. per hour, while the average consumption is actually about ten times that amount. But *213 Ibs. is less than a perfect engine would consume owing to the unavoidable loss 214 HANDBOOK FOR MECHANICAL ENGINEERS. in the condenser, e.g. let 1 lb. coal supply steam without any loss, at 300 Ibs. pressure = 417 F., the condenser being 100 F., then 417 "" 10Q = -36 which is the ratio of the 417 -f- 460 . 21 3 available units to the total units of heat, and = 6 Ibs. 36 coal per H.P. per hour as the maximum possible efficiency with a perfect engine under the conditions stated, or from ^ to J of what is now usually obtained. 459. H.P. PER TON WEIGHT. Maximum I.H.P. of engines per ton of boiler weight, including fittings, mountings and water. Torpedo boats, Thorney croft boiler . . 77*8 Locomotive engines . . . . . 55 '4 Small high-pressure marine . . . 12-0 Do. compound . . . . 16 '0 Do. triple compound , . . 20*0 In Maxim's flying machine the total weight of engines and boiler complete = 8 Ibs. per E.H.P. = 280 H.P. per ton. 460. To CALCULATE SIZE OF BOILER. Say Cornish boiler for high-pressure engine : d = diameter of cylinder in feet. s = stroke in feet. H = revolutions per minute. r = ratio of cut-off. p = boiler pressure, Ibs. per sq. inch by gauge. n = number of cylinders. S = cubic feet steam required per hour, allowing 25 per cent, for contingencies. S = 1-25 d 2 STEAM BOILERS. 215 v = relative volume of steam at p pressure. W = weight of water to be evaporated in Ibs. per hour. W= 62-5S V c = combustion of coal in Ibs. per sq. foot fire-grate per hour, say for Cornish boiler = 12 Ibs. e = evaporation in Ibs. of water from 60 F. per Ib. of coal, say for Cornish boiler = 7 Ibs. c x e = Ibs. water evaporated per sq. foot fire-grate per hour. A = area of fire-grate in sq. feet. ce I = length of fire-grate in feet, say 4* 5 to 5 5, but must not exceed twice the width. w = width of fire-grate in feet. to =-7-+ '166. D = diameter of boiler shell = 1 75 w. L = length of = 4D. When w exceeds 3 25, make two Cornish boilers or one Lancashire. For latter, D = 2 J w (w being width of one furnace). 461. CORNISH BOILER. Approximate heating surface in sq. yards of unit value, space occupied by seatings. Total capacity in cubic feet = L ^ (D 2 - d 2 ) = - 8 L (D 2 - 216 HANDBOOK FOR MECHANICAL ENGINEERS. Approximate space for steam, remainder water, -= -13 LD 2 . Minimum steam space = quantity required for 10 revo- lutions of engine. Water space 5 to 10 cubic feet per N.H.P,, and 5 feet super, water surface per N.H.P. 462. COMPARISON OF CORNISH BOILER WITH I.H.P. OF ENGINE. I.H.P. of engine = effective heating surface of boiler in sq. yards of unit value. J I.H.P. of engine = cubic yards total capacity of boiler, of which I = steam, f = water. f I.H.P. of engine = area of fire-grate in sq. feet. Steam receiver may be attached to boiler, maximum size equal in diameter to flue tube, length = twice diameter. Steam dome to allow supply pipe to take dry steam, may equal f diameter of flue tube, with height = diameter of flue. 463. PROPORTIONS OF BOILERS. Cornish boilers (one flue). N.H.P. Length. Diam. Furnace. Flue Diam. Diam. Length. 15 20 30 ft. in. 16 6 21 6 26 ft. in. 4 9 5 5 9 ft. in. 2 9 3 3 3 ft. in. 4 5 6 6 ft. in. 2 9 2 6 2 6 Lancashire boilers (2 flues). ft. ft. in. ft. in. ft. in. ft. in. 20 20 6 2 4 1 9 25 25 6 2 4 6 1 9 30 28 6 6 2 3 5 2 35 30 7 2 6 5 6 2 3 For more than 35 H.P. two or more boilers are required. STEAM BOILERS. 217 464. LANCASHIRE BOILERS. Goodeve's proportions : d = diameter of one tube. Shell = 2J d. Space between tubes = -15 d. Space between tubes and shell = '12 d. Width bottom flue = 1 d. 465. FIRE-BARS. Ordinary furnaces should not exceed 6 feet in length for Welsh coal, the bars being in two lengths ; for Newcastle or other flaming coal, say 4 feet 6 inches long, with bars in one length. Dead-plate should be 9 to 15 inches wide. Fire- bars say 3 feet long, 3 inches deep in middle, f inch thick at top, tapered to f inch thick at bottom ; bevelled one end to rest on dead-plate, to allow for expansion, and notched at other to rest on wrought-iron bearer : if notched both ends, there should be not less than 1 inch play. Chipping faces or distance pieces on bars should be made at both ends and middle. Air spaces between bars f- inch to f inch, usually J inch. The fire-grate should incline downwards towards the back, inch to 1 inch per foot. Passage above bridge = one-sixth area of grate. Perforations in furnace door, f inch to ^ inch diameter ; total area, from 2 to 5 sq. inches per sq. foot fire-grate. 466. BOILER SEATINGS. With old form of wheel draught the boiler was set on a mid-feather : this is a bad arrangement. Should be set on fireclay blocks forming side walls, the resting surfaces not wider than one-twentieth diameter of boiler, or J inch per foot diameter. Flues should be large enough for a man to pass entirely 218 HANDBOOK FOE MECHANICAL ENGINEEKS. round, area should be kept as uniform as possible, corners rounded, and angles filled up. Plain cylindrical boilers should be hung by wrought-iron brackets at intervals, riveted on, and supported on stone but not bolted down, and should be set with flash flues, i.e. the gases pass directly from furnace, over the bridge, and along bottom of boiler, to chimney. Boilers should be set with a fall of about 1 in 200, or ^ inch per foot, towards front. 467. SIZE OF MANHOLES IN BOILERS. 12 x 8 inch can be entered by small boy. 13 X 9 lad. 14 x 10 average man. 15 X 12 stout man. 468. BOILER TUBES. Class of Boiler. Ratio, Length to Diameter. Ratio, Tube Area to Grate Area. Multitubular boilers, wit i chimney) 24tol Ito7 Locomotive boilers 120 to 1 1 to4 Small marine boilers, with sure engines high pres-"k 33tol 1 to6 Large marine boilers, with engines condensing j 20tol 1 to 3 1 sq. foot of fire-box is equal to 3 sq. feet tube surface ; J diameter should be left between the tubes for circulation and escape of steam. Heating surface of small tubes = of circumference, of furnace tubes = ^ circumference. In multitubular boilers the stay- tubes should be spaced so as to support the whole plate, irrespective of support from other tubes. STEAM BOILEES. 219 469. WATER-GAUGE GLASS. Lowest sight-level of water-gauge glass should be 3 to 4 inches above furnace crown or highest point of boiler exposed to flame. Water heated from its point of maximum density (39 F.) to boiling-point (212 F.) expands about one twenty-third of its volume. 470. TAPER OF PLUGS FOR BOILER-COCKS. For pressures up to 30 Ibs. per sq. inch, a taper of 1 in 8 on each side is found to work well ; but for pressures of about 100 Ibs., a taper of 1 in 12 is necessary to insure tightness; say 1 in 10 minimum for pressure of 60 Ibs. 471. BLOW AND SCUM. The sediment in a boiler, and the floating impurities, should be blown out after a short period of rest, say during meal times. When laying off for cleaning, the water should not be all blown out, or the scale will harden excessively and be more difficult to remove. 472. BLO WING-OFF TO PREVENT INCRUSTATION. A 20 H.P. boiler working at a pressure of 70 Ibs. per sq.'inch (316 F.) will blow off 120 cubic feet of water in a day of 12 hours. To replace the water thus blown off, 120 cubic feet of cold water at 60 have to be introduced ; and to bring it to 316, 1,904,640 heat units, otherwise 272 Ibs. of coal, are required. The remedy for this is to soften and heat the feed-water before its introduction to the boiler. 220 HANDBOOK FOB MECHANICAL ENGINEERS. 473. BOILER SCALE. Increased quantity of fuel required to evaporate water : Scale ^ inch thick = 15 per cent. i = 60 i i, = 150 Prof. J. G. Eogers. Order of deposition of impurities as water becomes con- centrated : 1. Carbonate of lime. 2. Sulphate of lime. 3. Salts of iron, as bases or oxides, and some of these of magnesia. 4. The silica or alumina, usually with more or less of organic matter. 5. Common salt. M. Couste. Soda (carbonate) is the best natural de-incrustant. 474. HARDNESS OF WATER. When a water contains in solution one part by weight of lime, or other equivalent hardening salt, in 100,000 parts of water, it is said to possess 1 of hardness. Water of less than 6 of hardness softens lead to an extent dangerous to health if used for domestic purposes. Parts carbonate lime per 100,000 water X yV = grains per imperial gallon, or degrees of hardness on Clark's scale. Carbonate of lime produces temporary hardness in water, sulphate of lime produces permanent hardness. Water is said to be hard when it contains more than 7 grains of dissolved mineral matter per gallon. The water of London holds about 16 grains, that of Kent 24 grains. All well waters are more or less hard. STEAM BOILERS. 221 475. INCRUSTATION IN BOILERS. If water contains 20 grains of mineral impurities per gallon, J cwt. of scale is precipitated and left by the water boiled away in a week of 60 hours, at the rate of 350 gallons evaporated per hour. If allowed to accumulate, this gives a coating of T %- inch in 3 months over 250 sq. feet of plate. If the feed-water contains 30 grains of solid matter per gallon, a 20 H.P. boiler will deposit half a pound per hour. 476. SEA-WATER. Proportion of salt in water of open sea Red Sea . Mediterranean British Channel Arctic Ocean Black Sea . Baltic Parts per 1000. . 32 to 38 43 38 35-5 28-5 21 6-6 Ure. Average specific gravity of sea- water at 60 F., pure distilled water being 1 : Faraday Mallett 1-027 1-0278 Marcett Fitzroy Salts contained in sea-water : Chloride of sodium . Muriate of magnesia Sulphate of magnesia Sulphate of lime .... Others . ' 7 Total I . . Weight of 1 cubic foot about 64-14 Ibs. 1-0277 1-027 Parts per 1000. . 25 3 2 1 1 . 32 Faraday. 222 HANDBOOK FOE MECHANICAL ENGINEEES. 477. BOILERS FED WITH SALT WATER. E = evaporation in cubic feet per hour. D = density allowed in boiler, normal sea- water being 1-000. d = density of feed-water. C = cubic feet of brine to be blown out per hour. ~ D-d To find D when J feed blown off: 478. CAUSES OF PRIMING. Changes in density of feed-water, as fresh to salt, or vice versa. Eapid extraction of steam after perfect rest ; sometimes sudden starting of engines. Feeding with muddy water, or water contaminated with sewage. Steam-space too limited. Defective circulation in boiler. Hard firing. 479. CORROSION OF BOILERS. When rivet heads between high and low water line are attacked, the corrosion has been reduced in land boilers by painting the inside of boiler between those levels with a mixture of " drippings from shafts, boiled oil and blacklead " every time the boilers are cleaned out. This was adopted at Woolwich Arsenal. 480. GREASE IN BOILER, when carried over with the steam, is very detrimental to life and efficiency of boiler. The thin coating of grease deposited only during a ship's trial trips has been found to reduce the efficiency of the tubes as heating surfaces from 8 to 15 per cent., the mean result of many experiments being 11 per cent. ' A/ OK THK STEAM BOILERS. 481. SAFETY VALVES FOR BOILERS should always be in duplicate. Area in sq. inches for each = -004 to *006 area of fire- grate surface, usually -025 sq. inches per sq. foot heating surface, or 5 sq. inches per sq. foot grate surface, irrespective of working pressure. Actual lift of valve = -- or , but freedom must be p oo allowed for a lift of J d. The lift required is less for large valves and heavy pressures than for small valves and light pressures. Valves should be flat faced to prevent sticking, face J- inch to ^ inch wide. In estimating the blow-off" pressure, add T ^ inch to the actual diameter inside face of seat. When diameter would exceed 4 inches, two or more valves must be provided. A = effective area of heating surface, sq. feet. H = boiler H.P. (1 cub. ft. per hour evap. from 60). G = grate surface, sq. feet. A c/TTioK/m r H-j-2*5,y/H A A = 8(H + 2-5 VH), G = , G = & ID Diam. of safety valve, ins. = * / Box. -r,. f f , i /grate surface, sq. ft Diam. of safety valve, ins. = A /^ -* ' V gauge pressure, Ibs. TredgM. Twin safety valves, each ., grate surface, sq. ft. Area = 18 - ' ^ . ; abs. press., Ibs. sq. in. 0*6 heating surface, sq. ft. or area = - rr ? abs. press., IDS. sq. in. 224 HANDBOOK FOR MECHANICAL ENGINEERS. Or one as above fitted as an easing Talve, and one as follows loaded to 1 Ib. per sq. inch less . grate surface, sq. ft. Area = 4 -^ rr p- + area of guides of valve ; abs. t)ress.. IDS. SQ. in. abs. press., Ibs. sq. in. 0*133 heating surface, sq. ft. or area = r & .. -^-* abs. press., Ibs. sq. in. + ditto. If the heating surface exceeds 30 sq. feet per square foot of fire-grate, safety valve must be determined from heating surface. Inst. Eng. Scot. Heating surface in sq. feet 4- 25 = area valve disc sq. inches. U.S. Board of Supervisors. 005 x Ibs. water evaporated per hour = area valve disc sq. inches. Committee of U.S. Board of Supervising Inspectors. Area sq. inches = grate area sq. feet. Molesworfh. Orifice of safety valve (flat faced) = circf. x lift. (mitred) = circf. x lift -f- 1*414. Somerscales. a = effective area of opening. d = diameter, I = lift. Flat-faced, a = Id IT. Mitred, a = 2J ld-\- 1 I 482. BOARD OF TRADE RULES FOR SAFETY VALVES. Boiler Pressure. Area per sq. ft. of Fire-Grate. Boiler Pressure. Area per sq. ft. of Fire-Grate. 15 1-25 70 441 30 '833 80 394 40 681 90 357 50 576 100 326 60 500 120 277 STEAM BOILERS. 225 483. To CALCULATE SAFETY-VALVE LEVERAGE. a = area of valve in sq. inches. p gauge pressure in Ibs. per sq. inch. "W = weight on end of lever in Ibs. w = weight of lever in Ibs. w' = weight of valve and stud in Ibs. L = distance between weight and fulcrum in inches. g = centre of gravity of lever and do. I = valve centre and do. L - wg + WL. , - ~ P= p The lever safety valve was invented by Papin. 484. NOTES ON SPIRAL SPRINGS. Effective number of coils = generally two less than apparent number, owing to flattening at ends for bases. Stroke = effective number of coils X compression or ex- tension of each coil. Minimum pitch of spiral = diameter of steel in inches + twice compression of one coil under full load, but coils may lie close when spring is for tension only. Diameter of coil = say 8 times diameter of steel. Working load may stretch each coil = J diameter of steel composing spring. To increase stroke, add to the number of coils. Spring in tension is more accurate for exact work than one in compression. Best form of section is circular, but square form is stronger, as 10 to 7. Two or more springs may be used, one within the other. 226 HANDBOOK FOR MECHANICAL ENGINEERS. 485. SPIRAL SPRINGS. Formula for strength and deflection. E = Compression or extension of one coil in inches. D = Diameter of coil in inches from centre to centre. d = Diameter or side of square of steel composing spring in y^ths of an inch. W = Weight applied in Ibs. c = a constant found by experiment, which may be taken as 22 for round steel and 30 for square steel. D'W '-' 486. SPIRAL SPRINGS, KANKINE'S FORMULA. d = diameter of wire in inches. c = coefficient of transverse elasticity of wire, say 10,500,000 to 12,000,000 for charcoal iron wire and steel. r = radius to centre of wire in coil. n = effective number of coils. / = greatest safe shearing stress, say 30,000. W = any load not exceeding greatest safe load. v = corresponding extension or compression. W = greatest safe steady load. v = greatest safe steady extension or compression. W = greatest safe sudden load. W cd* 64nr 3 r cd >e ascertained by direct experimei Rankines ' Machinery and Mill work.' W should be ascertained by direct experiment. v STEAM BOILEKS. 227 In two series of experiments analysed by the author, the ratio W to v was greater by 12 and 30 per cent, respectively than given by the formula, the former in tension, the latter in compression. 487. SPIRAL SPRINGS FOR SAFETY VALVES. a = area of valve in sq. inches. c = 11,000 for square steel = 8000 for round steel. D = diameter of spring, inches centre to centre of coil. E = compression or extension of one coil, inches. p = pressure Ibs. per sq. inch on valve. d = diameter of steel or side of square in inches. d l = in sixteenths. d = Let then Wap E = ; for square steel ; oO d/i for round steel. * Practical Engineer.' 488. INITIAL COMPRESSION OF SPRINGS FOR SAFETY VALVES may be 40 times the lift of the valve, and assuming the lift of all sizes to be T ^ inch, the initial compression will then be 4 inches. Or may be I'll diameter of valve in inches. Or, by another rule : 80 x d of valve ios. Initial compression = ^ lbs , sq . in . If lever is used, then movement of lever must be taken in calculating spring, instead of lift of valve. Q 2 228 HANDBOOK FOK MECHANICAL ENGINEEES. 489. SPRING-BALANCE SAFETY VALVES. The levers are generally proportioned so that 1 Ib. pressure per sq. inch on the valve gives 1 Ib. pull on the spring, but the spring is tightened up to the blowing-off pressure, so that the actual indication is only shown when the blowing-off pressure is exceeded. The length of lever from centre of valve to fulcrum is made equal to diameter of valve, and the length from fulcrum to centre of attach- ment of spring is made equal to the diameter of valve multiplied by its area, all inches. The total length may be increased if the same proportion of its subdivisions be retained. 490. To CALCULATE SPRINGS FOR SAFETY VALVES. Given boiler pressure and grate surface, find 1. Diameter of valve. 2. Load required. 3. Lift of valve. 4. Initial compression of spring. 5. Assume diameter of coils. 6. Find diameter of steel. 7. Compression of each coil. 8. Effective number of coils. 9. Pitch of spiral. 10. Effective length of spring. 11. Total length. 491. FACTOR OF SAFETY, STEAM BOILERS. Test pressure = | ultimate strength. Working pressure, if under periodical inspection, = ^ do. Working pressure, if not under independent inspection, = i do. In estimating ultimate strength, ample allowance to be made for defects in design or workmanship. STEAM BOILERS. 229 492. TESTING BOILERS. Government Yards. New boilers to be tested by hydraulic pressure to three times their working pressure. Boilers in use not to be worked more than 300 hours without being laid off for examination. To be tested periodically to twice their working pressure. Best Private Practice. New boilers to be tested to twice their working pressure. Boilers in use not to be worked more than 1000 hours without being laid off for examina- tion. To be tested after repairs to 1J times their working pressure. If working with impure water, to be examined after 500 hours. Locomotive Boilers. Usually tested by hydraulic pressure to not more than 10 per cent, above working pressure, say 160 Ibs. working pressure =175 Ibs. test pressure. 493. RIVETING FOR BOILERS. In iron : Ring seams to be single riveted, longitudinal seams double riveted. For equal area of plate and rivet, the linear pitch in single riveted joints and diagonal pitch in double riveted joints should be sectional area of one rivet . = ii-!-i c r~i T diameter ot rivet. thickness of plate For same conditions, the linear pitch in double riveted joints should be 2 sectional area of one rivet thickness of plate + diameter of nvet, but is generally made about one-sixth less than this, to avoid straining in caulking. Double riveting should always be zigzag. For rivets in double shear, take 1 75 times above areas. Fairbairn estimated strength of solid plate at 50,000 Ibs. 230 HANDBOOK FOR MECHANICAL ENGINEEKS. per sq. inch, double riveted joint as worth 70 per cent., and single riveted joint 56 per cent. He recommended double riveted longitudinal joints 2J inches linear pitch, 2 inches diagonal pitch [say for f inch rivets and f inch plates]. 494. SMALL SCREWED STAYS OK WATER-SPACE STAYS. p = working pressure in Ibs. per sq. inch. P = pitch of stays in inches. a = net sectional area of sta} 7 . s = safe stress in Ibs. per sq. inch = 4000 copper, 5000 wrought iron, 6000 steel. a s say 4 to 4J inches pitch for locomotive work, 6 to 8 inches for marine work. Diameter | to 1 inch, generally double the thickness of plates. 495. LONG STAY BOLTS should be strong enough to support the area assigned to them, with a factor of safety of , assuming no support from the thickness of plate. 496. STRENGTH OF FLAT PLATES SUPPORTED BY STAYS (LLOYD'S RULES). p = working pressure Ibs. per sq. inch. P = greatest pitch of stays in inches. t = thickness of plate in sixteenths of an inch. c = constant = 90 for plates up to ^ inch thick held by screw stays with riveted heads. 100 for plates above T 7 ^ inch do. do. 110 for plates up to T 7 ^ inch thick held by screw stays and nuts. STEAM BOILERS. 231 120 for plates above T 7 inch do. do. 140 for plates held by plain stays with double nuts. 160 for do. do. and washers at least half thickness of plates and diameter of f pitch, riveted to the plates, In the case of front plates of boilers in steam space and exposed to direct action of heat, reduce these numbers by 20 per cent. ct 2 497. STRENGTH OF FLAT PLATES. t = thickness in inches. r = radius if circular. I = length if rectangular. 6 = breadth ,, p = pressure in Ibs. per sq. inch. / = maximum stress on material per sq. inch. a = distance centre to centre of stays in inches. s = side of square plate in inches. Circular plate supported at edge, /=.'_.,,. J 6 t 2 Circular plate encastre, j Square plate stayed, /*,3 *-.* y 3 J 2 /-?.;^ 9 t 2 Square plate encastre, Rectangular plate encastre, / _ . . p. Unwin. 232 HANDBOOK FOR MECHANICAL ENGINEEES. 498. STRENGTH OF FLAT ENCASTR^ CIRCULAR WROUGHT-!RON PLATES. p = working pressure Ibs. per sq. inch. P = test P = ultimate P = bulging to elastic limit. t = thickness in inches. T = in sixteenths of an inch. d = diameter of plate in inches. r = radius / = maximum stress on material in Ibs. per sq. inch. _ 440 (T + I) 2 d 2 - 12 Pract. Eng. Pocket-Book. P = 60,000 ^ (safe load = J test pressure). H. Cherry. P = 1000 -r (12 tons elastic strength per sq. inch of material ; J = safe load). D. K. Clark. P = f^ (/= 44,800 Ibs.; I P = safe load). Unwin. P = /I 2 (safe load i). r 2 v Eankine. 499. ULTIMATE STRENGTH OF BOILER-SHELL. Longitudinal strength : 2tc pd -- < = STEAM BOILERS. 233 Transverse strength: p d -^ = ir(t + d)tc 9 divide by TT d, then but - will rarely exceed -01, and may therefore be omitted. d 4tc pd ... p . = tC9 P=-^, = j- or the transverse strength is double the longitudinal. 500. HELICAL JOINTS FOR BOILERS. Katio of strength to longitudinal joint = 2 " V (3 cos 2 + !)' = angle of inclination from longitudinal direction. 501. COLLAPSING PRESSURE OF BOILER TUBES. Length not exceeding 15 diameters. Cylindrical : (100 fc) 2 ' 19 p = 33-6i x l /-; L d Fairbairn or log_p = 1-5265 + 2- 19 log 100 k -logLd; or, approximately, 800,000 f 2 234 HANDBOOK FOB MECHANICAL ENGINEERS. Elliptical : 800,000* 2 p = T /0 . j r = radius of flatter curve, L(2r) _ 800,000 < 2 2D 2 D d are the two diameters in inches, L the length in feet. 502. BOILERS. COMPARISON BETWEEN BURSTING AND COLLAPSING PRESSURES. P = internal or bursting pressure in Ibs. per square inch. p = external or collapsing c = ultimate strength of single riveted joint = say 30,000 Ibs. I = length of unsupported cylindrical tube in feet. D = diameter of boiler in inches. d = tube T = thickness of shell plate in inches. t = tube plate R = ratio of tube diameter to shell diameter = =- 2Tc 60,000 T 800,000 1 2 P 60,000 Tld _ TIE p ~~ 800,000 * 2 D ~ 13-3 < 2 ' 1 Q . q /2 .-. WhenP=p, thenZ = ^i. 503. COLLAPSING PRESSURES OF FLUES. L' x D" r A* 1 1" TV r 400 97 158 235 329 441 Ibs. per sq. in. 500 77 126 188 263 353 > 600 65 105 157 219 294 700 55 90 134 188 252 j> 800 48 79 117 164 229 H 900 43 70 104 146 196 H 1000 38 63 94 131 176 55 Munro. STEAM BOILERS. 235 Length 7 diameters or over. t = thickness in sixteenths of an inch. I) = diameter in feet. 16 t 2 * = -&' Where length is less than 7 diameters the strength is inversely as the length, or the collapsing pressure 7D = *T- W. I. Ellis. 504. Fox's CORRUGATED FLUES. t = thickness in inches. D = mean diameter inches. p = working pressure in Ibs. per sq. inch. 14, 000 t P= -D ' Board of Trade. t = thickness in sixteenths. D = maximum diameter inches. = 1234 (* ~ 2 ) Lloyd's Registry. 505. LOCOMOTIVE BOILER. Pressure 130 to 150 Ibs. per sq. inch. Feet of heating surface = inches diameter piston 2 X 4. Heating surface of firebox = y 1 ^- to T V of total. Sq. feet area fire-grate = inches diameter piston 1. Tubes 10 to 12 feet long, If inch to 1| inch internal diameter, 11 to 13 W.G., f inch clearance between. Shell plates f inch to inch, t = - when t = thickness sixteenths, p = pressure Ibs. sq. inch, d = diameter inches. 236 HANDBOOK FOE MECHANICAL ENGINEERS. Diameter of shell = diameter piston X 3. Smoke-box tube plate = 1J t. Side plates, outer casing, fire-box = t -f- T T inch. Throat plate and back plate = t -f- i inch. Firedoor = 18 inches X 12 inches. Inner casing of fire- box, copper. Inner tube plate, upper part = J inch thicker than lower part. Holes in tube plates = |- inch smaller at fire-box end and | larger at smoke-box end than mean outside diameter of tubes. Stay bolts, 4 inch pitch, J inch over thread with f inch plate, I inch with ^ inch plate, ff inch with f inch plate. Girder stays (8) in two plates 5 inches X f inch to 6 inches X f inch, 2 inches clearance above crown, secured by stay bolts same size as in sides of fire-box. Steam dome = ^ diameter of barrel, height = diameter, thickness same as shell plates, top f inch to J inch thick, and 7^ inches high. Manholes, 16 inches diameter. Twin safety valves, each with clear passage of area = -rsinnr f heating surface . . diameter in inches = *08 Cheating surface, sq. feet. Conical seats, bearing T 1 F inch wide. Chimney, 13 feet 3 inches from rail level to top, smallest diameter in inches = 4 ^/grate area, sq. feet. Steam pipe = T ^- area of piston. Air space through bars = ^ of grate area. Fire-bars, centre depth = length ; thickness, top = length; thickness, bottom = j-J^ length; end depth = f middle depth. * Hallway Press.' 237 SECTION XI. THE STEAM ENGINE. 506. EARLY ENGINES. Savery's Engine. A receiver was filled with steam from a boiler, the communication closed and water applied exter- nally ; condensation allowed water to rise through a bottom clack ; steam again admitted above drove the water up to a higher level through an upper clack. Newcomen's Engine. Open-topped cylinder had a loosely fitting piston attached by rod and chain to one end of a beam, the beam pivoted at its centre and attached by chain to pump rods at other end. Steam admitted under piston at atmo- spheric pressure allowing weight of pump rods to lift piston and force water up from the pump. Jet of water admitted into the cylinder then caused condensation, and pressure of atmosphere forced piston down while lifting pump rods. Waifs First Engine was a Newcomen engine with the cylinder closed on top and steam admitted instead of air, and with a separate condenser. In the old atmospheric engine increased power required increased diameter and stroke of piston ; in Watt's engine increased power was obtainable by increasing the steam pressure only. The general proportions of beam engines were : Depth of beam = diameter of cylinder. Stroke of piston = twice dia- meter. Length of beam = three times the stroke. Area of beam flanges at centre = 3 sq. inches per 2000 Ibs. on piston. Indoor stroke when piston going into cylinder, outdoor stroke reverse. 238 HANDBOOK FOE MECHANICAL ENGINEERS. 507. ECONOMY OF HIGH-PRESSURE STEAM. The pressure of steam increases in a greater ratio than its density, whence it follows that the higher the pressure to which the steam is raised, the less proportionate quantity of water it contains, and therefore the less fuel is consumed, since a given quantity of fuel will evaporate nearly the same weight of water at all temperatures. Pole. The expenditure of heat, to produce a given weight of steam at a pressure of 10 atmospheres, is only 4 per cent, more than that required at a pressure of 1 atmosphere. Doubling the pressure in the boiler, with one-third more coal, doubles the power obtained from the engine. Thus the power] obtained is greater in proportion than the extra amount of coal used to increase the pressure of steam in the boiler. 508. ADVANTAGE OF EXPANDING STEAM. When steam is cut off at f of the stroke, the power of an engine is only diminished by 7 per cent., while the consump- tion of steam is diminished by 33 per cent. Cut off at half stroke the power is reduced 16 per cent., and the consumption of steam 50 per cent. 609. ECONOMY OF COMPOUND ENGINES. The economy of compound engines consists mainly in the higher pressure of steam employed permitting greater expan- sion, and in the subdivision of the work over two or more cylinders, limiting the range of temperature in each, and therefore the loss from condensation. 510. PROGRESS OF COMPOUND ENGINES. 1781. Hornblower patented the use of two cylinders where the steam first operated in one and then by expansion THE STEAM ENGINE. 239 in the other also, and applied them to a single-acting pump- ing engine. 1782. Watt patented cutting off steam before end of stroke, but had previously adopted it. 1804. Woolf patented small and large cylinders of same stroke, pistons moving in same direction and parallel. Steam used first in small cylinder, then in large. Applied to double-acting engines with separate condenser. 1805. Earle patented the use of large and small cylinders superposed, with two pistons mounted on the same rod* 1820. Aitken and Steel built engines with three cylinders, two small and one large. 1834. Wolff patented a compound engine with two cylin- ders and intermediate reservoir to regulate the pressures. Also the conversion of simple engines to compound by the addition of a high or low-pressure cylinder to a low or high- pressure engine. 1839. Whitman patented the trunk piston, the steam first acting in the annular space of the cylinder, then expanding into the other end. 1841. Sims patented Earle's arrangment, with the excep- tion that the bottom of the smaller piston was in constant communication with the top of the larger and with the condenser. 1842. Zander patented the use of a small cylinder to receive the steam, passing after slight expansion into two larger cylinders all connected with same crank shaft. The low-pressure cylinders were steam jacketed. 1844. Smith patented high and low-pressure oscillating cylindei s working same crank. Perkins adopted very high pressures. 1845. McNaught patented addition of a high-pressure cylinder between the main centre and crank of beam engine. 1854. First successful application of compound cylinders to marine engines by Randolph, Elder & Co. 240 HANDBOOK FOE MECHANICAL ENGINEERS. 511. HORSE-POWEE. Actual H.P = 33,000 foot-lbs. per minute in all calcula- tions, but the actual work of a horse is about 22,000 foot-lbs. per minute. One H.P of 33,000 foot-lbs. per minute = approximately, 15 foot-tons per minute. 512. NOMINAL HORSE-POWER. Waffs nominal H.P. for low-pressure engine (pressure 7 Ibs. per sq. inch* above atmosphere) = area sq. inches X 7 x 128 x ^ stroke feet 4- 33,000 = d in inches 2 X >J stroke feet -4- 47. Boulton and Watt's N.H.P. for high-pressure engines, = d 2 ^ 14 (. . 11 sq. in. piston per N.H.P.) Do. do. for condensing engines, = d 2 -4- 28 (. . 22 sq. inches piston per N.H.P.) Bourne's N.H.P. three times that of Watt, viz. for a pressure of 21 Ibs. above atmosphere. 'Royal Agricultural Society's old rule was 10 circular inches of piston area and 50 Ibs. pressure represent a nominal horse- power. At the present time N.H.P. is a useless commercial term, generally depending upon size of cylinder, and irrespective of pressure or speed. Sometimes N.H.P. for non-condensing engines wasd 2 x $ stroke feet -4- 20 ; for simple condensing engines d 2 -f 30 ; and for compound engines (D 2 -f d 2 ) ~ 33 or 30. * In all machinery actuated by fluid pressure, the square inch, which is the standard unit, introduces a needless complication. James Watt lost a good opportunity in not establishing the circular inch as the standard. Circ. inches x 7854 = sq. inches. Sq. inches x 1 27324 = circ. inches. THE STEAM ENGINE. 241 Admiralty N.H.P. was formerly used in classifying the power of marine engines, = area sq. in. x speed ft. per min. X 7 -f- 33,000. = d in. x speed ft. per min. -f- 6000. = about one-sixth of the indicated H.P. Section's estimated H.P. = D 2 l.p. cylr. X Vp X revns. per min. x stroke ft. 4- 8500. Lloyd's Committee N.H.P. (1872) D 2 X stroke ft. 630 where F = total width fire-grate inches. N.E.C. Inst. Eng. and Shp. (1877) Normal I.H.P. = for screw engines -^ (D 2 x I/ stroke ft. + 3 B) $ p. = for paddle engines T^- (D 2 x I/ stroke ft. + 5 B) fy p. where B = the heating surface of the boilers in sq. ft., and if there are two low press, cylrs. D 2 = sum of sqs. of diams. 513. INDICATED HORSE-POWER. Indicated H.P. = mean p Ibs. sq. in. from indicator dia- gram x area of piston ( + same for other pistons) x speed feet per minute -j- 33,000, or p.l.a.n 33,000 ' p being mean pressure, Z length of stroke, a area of piston, n number of strokes per minute. Rough estimate of I.H.P. of engine = (-^?r~ Y, which is correct for a mean effective pressure of 42 Ibs. per sq. inch and piston velocity of 500 feet per minute. 242 HANDBOOK FOR MECHANICAL ENGINEERS. 514. EFFECTIVE OR BRAKE HORSE-POWER. Effective H.P. = actual H.P. of work done, or useful effect given out from engine, either estimated, or found by friction brake, or by measurement of work performed. It is the net work done by the engine after deducting friction and loss. The effective H.P. of any engine, compared with the steam used, is the measure of its efficiency or economy. Brake H.P. = the power given off from the crank shaft, through the fly-wheel, or a pulley, to an absorption or transmission dynamometer. To ascertain Brake H.P. W = weight Ibs., L = leverage feet, B = revolutions per minute. B.H.P. = 33,000 515. FRENCH HORSE-POWER. French H.P. (Force de cheval or Cheval-vapeur). 1 kilogrammetre = 1 kilogramme (2 '205 Ibs.) raised 1 metre (3-281 feet) = 7-2346 foot-lbs. 1 kilogrammetre per second = 434 foot-lbs. per minute. 75 kilogrammetres per second, or 4500 kilogrammetres per minute = 32,550 foot-lbs. per minute, or about y 1 ^ less than a British H.P., hence " Chevaux de 75 kilogs" French H.P. x *9863 = British H.P. British H.P. X 1 '014 = French H.P. French I.H.P. = Cheval indique. 516. MODULUS OF STEAM ENGINE. The modulus of a steam engine, or coefficient of mecha- nical efficiency, is found by dividing the effective or brake H.P. by the indicated H.P. THE STEAM ENGINE. 243 517. DE PAMBOUR'S PRINCIPLES. 1. When the engine has attained a uniform motion, the work done by the steam in the cylinder is equal to the work which is due to the total resistance. 2. The steam which is generated in the boiler is equal to that expended in the cylinder. 518. STEAM WORKED EXPANSIVELY. p = absolute initial pressure. s = stroke. m = mean pressure. n = ratio of whole stroke to stroke before cut-off. When cut off at any part of stroke, as - ; then its Efficiency = 1 + hyp. log n. Mean pressure = - p (1 -f hyp. log n). Initial pressure = mn . 1 + hyp. log n Pressure at any point in the expansion curve at x 1 ~ s distance from commencement of stroke = p. Advantage of working expansively = 1 + hyp. log n to 1, or 100 X hyp. log ft per cent. gain. Distance travelled to attain maximum velocity p s s - * or m n 1 -f hyp. log n Cut-off for maximum efficiency (Pole) P 24,250 ^ ^ = -|- 65 useless resistances P * Terminal pressure = - > or -th of p. R 2 244: HANDBOOK FOR MECHANICAL ENGINEERS. Units of work per sq. inch of piston in one stroke All pressures are measured from perfect vacuum, the atmospheric line is a variable element. Above formulae assume theoretically perfect indicator diagrams and expansion according to Boyle and Marriotte's law. In ordinary land engines the mean pressure found above must be multiplied by 8 to give the mean pressure from an indicator diagram. Clearance spaces each end = ^ to -^ cylinder capacity. 519. TABLE OF HYPERBOLIC LOGARITHMS. Cut-off. No. Hyp. Log. I 1-2 1823215 I 1-25 2231435 & 4 1-33' 2851788 1 1-5 4054652 1 1-66' 5068176 * 2-0 6931472 | 2-5 9162907 1 2-66' 9783260 3-0 1-0986124 JL 4 4-0 1-3862943 5-0 1-6094379 i 6-0 1-7917595 i. 7-0 1-9459100 i 8-0 2-0794414 i 9-0 2-1972245 TV 10-0 2-3025851 Com. log X 2-3025851 = Hyp. log. Hyp. log X -434294819 = Com. log. THE STEAM ENGINE. 245 520. MEAN PRESSURE WITHOUT LOGARITHMS OR SCALES. To find mean pressure of theoretical indicator diagram (say at Exam.) without logarithms or scales. Example : Cut-off at -$ of stroke, then intermediate pressures will be as follows : By Inside By Outside Rectangles. Rectangles. At 1st tenth ^ - 1- < - 1- 2nd . * 1- -.-. . 1- 3rd . r ' 1- ...... 1- 4th , 1- . '- 1- 5th -* V 1- - . 1- 6th - . 1- . . 1- 7th = f . . '857 . . 1- 8th = f . . -75 . . -857 9th = f . . '667 . . -75 10th = T V '6 -667 8-874 9-274 8-874 9-274 2)18-148 . . mean = *9074 of boiler pressure. 9074 Checking this by hyp. log the multiplier = '9041, so that the error is less than J of 1 per cent. 521. ORDINATES TO HYPERBOLIC EXPANSION CURVES. Initial pressure = p. Cut-off at T %, then ordinate at T %- = f p. > A = P- rV = fp, and so on. 246 HANDBOOK FOR MECHANICAL ENGINEERS. Cut-off at J ( = ^Q), then ordinate at ^ ( = ^) = TIT v == 2~o/ ~ and so on. 522. SIMPSON'S RULE. For area of any irregular figure. Divide area into any even number of parts by odd number of lines or ordinates. Take the sum of the extreme ordinates, four times the sum of the even ordinates, and twice the sum of the odd ordinates (omitting the first and the last ordinates) multiply the total by one-third of the distance betwen ordi- nates, this equals the area. For indicator diagram, divide length into ten equal parts by eleven lines, measure effective length of each, and number them. Then (1st 4- llth) + 4 (2nd + 4th + 6th + 8th + 10th) + 2 (3rd 4- 5th 4- 7th 4- 9th) -r 30 = mean pressure, 523. RESISTANCE IN STEAM ENGINES. 1. The load or useful work. 2. The friction of the unloaded engine = 1 to 3 Ibs. per sq. inch. 3. Additional friction due to the load = say | of mean pressure. 4. Back pressure = 4 to 5 ibs. absolute i.e. above perfect vacuum for condensing engines, or 15 to 18 Ibs. absolute for non-condensing engines. The coefficient or modulus will then be 6 to 75. Generally the friction maybe taken as 10 per cent, of the H.P. in a non-condensing engine, and 18 per cent, of the H.P. in a condensing engine. The average friction of a stationary engine with shafting is considered to be = 3 Ibs. per sq. inch of the boiler pressure ; and of a marine engine, 1 \ Ibs. per sq. inch. THE STEAM ENGINE. 247 524. MEAN EFFECTIVE PRESSURE, COMPOUND ENGINE. m = mean effective pressure, supposing all work done in low pressure cylinder. p = boiler pressure by gauge. * = V 6jp. J. Macfarlane Gray. 525. PISTON CONSTANT FOR INDICATOR DIAGRAMS. When several are to be worked out the " piston constant " will be found useful, thus : area sq. ins. X ft. stroke, piston constant = - qo QQQ - multiplied by 2 if same diagram is to answer for both ends of stroke, and by 2 again if to answer for 2 cylinders. Then, I.H.P. = const, x mean press. Ibs, per sq. in. X rev. per min. In finding the effective pressure on the piston at any part of stroke, take steam pressure x area one side back pressure X area other side. In an ordinary indicator diagram from one end of cylinder, the steam line and exhaust line belong to the same side of piston, and would therefore only give the effective pressure approximately. 526. CRANK AND PISTON NOTES. a = Length of connecting rod. b = Length of crank. x = Distance of piston from end of stroke furthest from crank, when point of maximum leverage is reached. 0;' = Distance as before, when crank has made quarter revolution from dead centre. x = (a + b) - V a 2 + & 2 - a/ = (a + 6) - V a 2 - b\ These values divided respectively by 2 b will give the pro- portion of stroke where these points occur. 248 HANDBOOK FOE MECHANICAL ENGINEEKS. All the distances are measured from tlie end of stroke furthest from crank. p = pressure on piston (total). p l = thrust in connecting rod. 6 = angle of connecting rod with horizontal. p 2 = pressure on guide bar. p s = turning effort on crank. = angle of crank with horizontal, then * sin d> = sin =- 6 sin 6 = sin $ - a Pi= p X cosec p 2 = p x tan Between tangential points in 1 st and 4 th quadrants, p z = p x cos 6 X sin (< -f- 6). Beyond do. do. through 2 nd and 3 rd quadrants, p 3 = p x cosec X sin (< 0). d = distance as before for any angle of crank = 6 + a (6 cos < + V a 2 6 2 sin 2 0. sn Velocity of piston _ sin Velocity of crank pin cos * For a simple introduction to Trigonometry, see the author's ' Prac- tical Trigonometry ' (Whittaker & Co., 2s. Qd. net). THE STEAM ENGINE. 249 Approximately the maximum pressure on guide bar may be found thus : Length con. rod : length crank : : press, on piston : press, on guide bar. Pressure on guide bar should be limited to from 100 to 400 Ibs per sq. inch. Piston speed = twice stroke feet x revolutions per minute. 527. SLIDE VALVES, EXPLANATION OF TERMS. Travel of slide valve is twice throw of eccentric where connected direct, and should not be less than 2 (outside lap ~f- steam port). Lap, outside lap, steam lap, or cover is the distance the slide reaches beyond outer edge of steam port when in centre of travel. Inside lap, or exhaust lap, is the distance from inside edge of steam port to edge of slide port, or space in slide, when in centre of its travel. Negative, or minus, inside lap occurs when both steam ports are open to the exhaust in the central position, sometimes found in quick-running engines. Lead is the amount of opening of steam port by slide when piston is at commencement of stroke, due to eccentric being set in advance of crank. Generally equal each end and vary- ing from ^ inch to inch. Inverted engines usually set with more lead at bottom than top, to allow for dropping of slide due to wear, and to equalise the diagrams. Angular advance of eccentric is lap + lead, set off from centre, along centre line of crank, and transferred perpendi- cularly on to circumference of throw circle. Width of face of slide valve = width of steam port -J- steam lap + exhaust lap. Amount of opening of port, steam or exhaust, = half travel -lap. 250 HANDBOOK FOR MECHANICAL ENGINEERS. 528. AREA OF STEAM PORTS. A = area of piston. a = area of steam port. b = area of exhaust port. v = velocity of piston feet per minute. v A ~ 4800 ' v A ~ 6000 " Baker (Weale's Series, ' Steam Engine,' p. 71): Watt's condensing engines, a = 1 sq. inch per N.H.P. Bourne (' Hbk. Steam Engine,' p. 313) : a = 1 sq. inch per N.H.P. or J K A. Also a = diam. cylr. 2 x v X '032 4- 140. Burgh (' Slide Valve,' p. 10) : high press, engine, a H.P. X *6 or -5. Low press, engine, a = H.P. x 1 * to -75. Eankine (' Steam Engine,' p. 414) :a = ^A. for v 200 to 240. Sir W. G. A. & Co. : a = -^ A, b = 2 a, v = 200. Adams, a = -^ to -^ A, b = If a, v = 350 to 500. Shapton, a = diam. cylr. 2 x '038. Bigg, a = A x v -r- 6000. Thickness of bar between ports = 5 steam port, mini- mum 1 inch, or = thickness of metal in cylinder. Length of steam port should be in proportion to dia- meter of cylinder, say 6 to *8 cylinder diameter. To shorten travel, increase length of port. Locomotives and other fast running engines should have the lap a little over J of the travel, and lead -fa travel. Bourne. Ordinary engines with simple D slide, lap = J travel and cut-off at stroke. 529. SLIDE YALVE NOTES. r = ratio of cut-off in cylinder. T = travel of slide. L = lap I = lead w = width of steam port. THE STEAM ENGINE. 251 T = 2 (w + L). L = (J T 1 -r) - 2L + I Effect of obliquity of connecting rod is to make cut-off later on the outdoor stroke and earlier on the indoor stroke, or, in other words, to draw all points of an indicator diagram nearer the crank or stuffing-box end of a cylinder. 530. POINT OF CUT-OFF when slide is set with equal lead A = distance travelled by piston before cut-off. B = remainder of stroke. C = distance centre crosshead to centre crank shaft at point of cut-off = a -f- b A. Cut-off on outdoor stroke = A. A x B Do. indoor = A ^ O To equalise cut-off, shift slide. 531. NUMBER OF EXPANSIONS. The steam is usually expanded in Simple condensing engines from 3 to 5 times. Two cylinder compounds 7 9 Triple compounds 12 15 Quadruple compounds 16 18 The total expansion is found by dividing the capacity (d 2 I) of the low-pressure cylinder up to point of release by the capacity (d? I) of high pressure cylinder up to point of cut-off. Intermediate cylinders do not affect the ratio. 252 HANDBOOK FOR MECHANICAL ENGINEERS. 532. TRIPLE EXPANSION ENGINES. Theoretical terminal pressure should be about 12 J Ibs. absolute. Cut-off in H.P. (high pressure) cylinder should be about half stroke. T ~P Ratio of capacity =^ = abs. br. press, x * 04 = say 6J. Do LJ- = sa y2i. T "P Do. ~ ~ n Approximately, in a triple expansion engine 13 Ibs. water converted into steam of 175 to 200 Ibs. pressure will give 1 horse-power. 533. CYLINDER KATIOS. Two-cylinder compounds. p = initial pressure in cylinder, say 5 Ibs. less than boiler. n = number of tenths up to cut-off in high-pressure cylinder. r== 105* Triple compounds. p = gauge pressure, from say 125 to 175. r for small = 1 intermediate = *015j? + *3 large = 075 p 4*75. THE STEAM ENGINE. 253 534. ADVANTAGE OF STEAM JACKETING. Triple expansion engine indicating 175 H.P.at55 revolu- tions per minute with 120 Ibs. boiler pressure. High-pressure jacket alone gave 1J per cent. gain. Intermediate 2 Low-pressure 6J Best result with boiler steam in all three jackets was 14*1 Ibs. steam per I.H.P. per hour (including jacket steam) with 146 Ibs. boiler pressure and 61 revolutions per minute. B. Donkiu. Steam jacketing prevents much of the condensation in the cylinder, which takes place in the jacket instead. Its usefulness is greater as the expansion is greater, owing to the increased range of temperature. 535. LINK MOTIONS. StepJienson's. Link curved, concave side towards eccen- trics, shifted to vary position of motion block, block moving in direct line with slide rod, lead increasing towards midgear with open rods and decreasing with crossed rods. Length of link three times travel of valve. Gooch's. Link curved, concave side towards spindle, maintained in central position by rod swinging on a stud, motion block shifted in link by radius rod connected to valve spindle, lead constant. Allan's. Link straight, link and motion block moved in opposite directions by rocking shaft, lead increasing towards mid-gear with open rods, and decreasing with crossed rods. Joy's. Link curved, moving on a fixed pivot, concave side towards valve, no eccentrics ; pendulum rod attached to centre of connecting rod at one end and to radius bar at other end ; another bar pivoted on motion block, one end 254 HANDBOOK FOE MECHANICAL ENGINEERS. connected to valve rod and other end to pendulum rod ; link moved on centre to alter valve ; distribution of steam symmetrical. 536. EADIAL VALVE GEARS. A radial valve gear has been denned as one in which the motion is taken from some point of a vibrating link, a second point of which moves in a closed curve, while a third point moves in a straight line or open curve, but the characteristic feature is rather in the mode of reversing. The link motions reverse by moving the free end of the valve radius rod, with its sliding piece, to one side or the other of the centre of an oscillating link. The radial gears reverse by altering the path of the fulcrum point in the valve lever or vibrating link. 537. WATT'S GOVERNOR, commonly called a pendulum governor, usually makes 30 revolutions per minute ; then h = 39 1 inches = length of London seconds pendulum. Whole arm 3, upper portion 2, link 2, variation of velocity 10 per cent. Weight of ball = 3*174 x resistance of throttle valve connections. Gene- rally : w = weight required to open throttle valve in Ibs. W = weight of one ball of governor in Ibs. L = whole length centre of suspension to centre of ball in inches. I = length from centre of suspension to centre of attachment of link in inches. h = height from centre line of balls when rotating at given speed to centre of suspension in inches. E = revolutions per minute of governor. 35225 ^ _ WOlw p _ 187-68 ~BT* ~TOL~' ~7~F ^3 Weight of cast-iron ball = ^707. Diam.= ^ 7-27 W. Hann. THE STEAM ENGINE. 255 Note. In the Watt governor, the virtual point of sus- pension does not coincide with the actual points, owing to the pendulum arms being pivoted to projecting lugs at top of spindle. For accurate work the measurements should be taken to the virtual point of suspension, which is found by producing the centre line of pendulum rods to intersect with vertical axis. 533. EFFICIENCY OF GOVERNOR. The height of a Watt governor is measured from the plane of rotation of the balls to the intersection of the direc- tion of the arms, and therefore, in the ordinary construction, it reduces as the balls fly out, whence the efficiency also reduces. In Head's governor the arms are continued through the spindle and pivoted beyond, so that as the balls fly out the height is slightly increased and also the efficiency. 539. FLY-WHEELS, NOTES AND FORMULA. F = total centrifugal force in Ibs. radially = ^! = . 00034 rWR 2 rg = total tension in arms to be divided by number of arms for tension in each. d = mean diameter and r = mean radius of rim in feet. W = weight of rim in Ibs. R = revolutions per minute. Tension at any cross section of rim in Ibs. per sq. inch F = (safe limit = 2500 Ibs.) ; 2 TT 1 fl 2 j (where v = linear velocity ft. per sec. ; = approx. 256 HANDBOOK FOE MECHANICAL ENGINEERS. M = foot-lbs. momentum at 1 revolution per minute. U = units of work (foot-lbs.) accumulated in fly-wheel at any velocity. U = MR 2 . E = excess of demand or supply in any given time in foot-lbs. R max. R min. = greatest variation allowed in speed, i.e. revolutions per minute. M = ? R 2 max. R 2 min. The diameters of fly-wheels will be as 5 J M, the dimen- sions of rim being proportional to diameter. Perry. n = number of revolutions per second. r = effective radius of gyration in feet. U = units of work stored in wheel. Variation from mean velocity not to exceed , usually m A- to A- a = area of section of rim in sq. inches. H.P. X 1803 X m r 3 x R 3 H.P. x 2275 X m Weight in tons = 2 y R 3 * Mean radius = X Morin. THE STEAM ENGINE. 257 E = revolutions per minute. A = sectional area rim sq. feet. r = radius feet to inside of rim. H = I.H.P. of engine. n = ratio of mean velocity to difference between mean and either extreme (say 10 for a difference of 10 per cent.). __ 12 /H r - E" X V "A"' 0. Byrne. Ultimate velocity at centre of gravity of rim to produce bursting = 19,235 feet per minute; .'. safe velocity, say 5000 feet per minute. C. E. Emery. U foot-lbs. energy required to be given out in t seconds or revolutions, when 8 seconds or revolutions can be used to restore it, will require an average of E foot-lbs. in fly-wheel. E = s + t And if the variation of velocity must not exceed c per cent, on either side of v, mean velocity in feet per second when running at n revolutions per minute, 2 Trr n ~60~' v (100 + c) _ v (100 - c) and the necessary weight W of fly-wheel rim will be ITT -^20 ^* = ~~2 ~2 * Allen. Fly-wheels may be designed for an accumulated energy equal to the foot-lbs. given out by the engine in three revolutions. Hendry. 258 HANDBOOK FOB MECHANICAL ENGINEERS. P = total average pressure on piston in Ibs. S = stroke in feet. D = mean diameter of rim in feet. W = weight of rim in cwts. A = sectional area of rim in sq. inches. PS 1-42 W -45D' T5^ Multiply by 1*5 when cut off earlier than \ stroke. Diameter usually 3J to 4 times stroke of engine. Maximum safe circumferential velocity 80 feet per second. ' Practical Engineer Pocket Boole' 540. INVESTIGATION OF FLY-WHEELS. "W v 2 = mass (m), - = height (h), kinetic energy = J m v 2 , Cl 2i (3 W v 2 potential energy = W A, accumulated work = , then Wv 2 but or W r 2 * c _ _11_L_ M 3600 X 64-4 5871 " Wr 2 .*. Energy of fly-wheel = X R 2 . Energy stored up in any rotating body = JIa 2 , where I = moment of inertia about the axis = ^my 2 , a = any velocity in radians per second. THE STEAM ENGINE. 259 '27rK\ 2 T 7T 2 E 2 T 2 . . M of fly-wheel = ~S = - 00548 1. 1800 But M of fly-wheel = |^. ... -005481= g and Wr 2 Wr 2 "" 5871 X '00548 ~~ 32-17' 541. STRENGTH OF CRANK PIN. p = uniformly distributed load in Ibs. I = length of journal in inches. d = diameter of journal in inches. / = greatest safe stress per sq. inch. Say, wrought iron . ^ . 6000 to 9000 steel . . ... . 9000 to 13500 cast iron . ." . , . 3000 to 4500 ^ = greatest bending moment at fixed end of journal. a M = & = -0982d 3 = modulus of circular sec. = . = M = cZ 3 x = ^= -0491 d* = moment of 2. Oa . O4 inertia of circular section. V Pi 3 /&-l ~ V ^1964? ~V ~ / 260 HANDBOOK FOR MECHANICAL ENGINEERS. 542. FLY-WHEEL SHAFT FOR ROLLING MILL. d = diameter steel shaft, inches. W = weight fly-wheel, tons. S = span between bearings in feet. 543. CALCULATION OF ENGINE SHAFTS. By law of virtual velocities, mean pressure on crank pin , TT 2s d^m am .*-X.X-- -5-^351 but the force being irregular, the maximum must be taken for the crank and fly-wheel shaft ; say full pressure on piston acting at radius of crank, d 2 7rp J s = ~ at radius -. 4 2 Beyond the fly-wheel may be substituted for as the strain will there be practically uniform. p = maximum boiler pressure, Ibs. per sq. inch. m = mean pressure in cylinder s = stroke of piston in feet. d = diameter inches. a = area sq. inches. / = factor of safety. Steam Hyde. eng. and engine. steam winches. Wrought iron and steel . J ^ Cast iron T J F ^ THE STEAM ENGINE. 261 k = ultimate strength, 1-inch bar, 1 foot radius. Cast Mild Wrought Cast steel. steel, iron. iron. 1250 1000 750 600 c = constant or safe load = fk. Steam engine . 200 175 125 60 Hydraulic engine &c. 125 100 75 40 D = diameter of shaft in inches. For crank shaft : 3 /d* X 7T X p X 8 " V 4x 2 x/X & V 2-5c* And beyond the fly-wheel : 3 / d 2 x m X s = \f v 9, v f v fc For two cylinders, let diameter = D + *15D. For three cylinders = D + 3 D. 544. STEAM ENGINE DIMENSIONS. t thickness in inches. d = diameter p = boiler pressure, Ibs. per sq. inch. A = area of piston in sq. inches. S = length of stroke in inches. D = diameter of piston Cylinder walls, t = +-5. covers, t = ^ inch thicker than cylinder, and stiffened as required. Cover studs, d = maximum stress on net section, 2000 Ibs. per sq. inch, minimum dia- meter = f inch. Cylinder flange, t = diameter studs X 1 J. 262 HANDBOOK FOE MECHANICAL ENGINEERS. Pitch of studs, (T being thickness of cover in sixteenths). Piston rod, d = -0167 D Jp if iron, = 0144DVP if steel Crank shaft, if well supported, d = 3600 Connecting rod, length = 3 S. Crosshead pin, diameter = d piston rod X 1 ' 25 length = do. X 1'4. 3 /A 7 Crank pin, diameter = V-~Q (/=lgth. = ljdiam.) Pressure on bearing surfaces = 400 Ibs. per sq. inch. A practical rule for thickness of steam cylinder for small engines = J d + thickness for re-boring, with a minimum of | in. 545. CONDENSER AND AIR PUMP. In the old jet or spray condenser, the air pump had to remove at each stroke the water used by the engine as steam and also the condensing water. In the surface condenser only the former has to be removed by the air pump, the circulating pump dealing with the water producing conden- sation. In the multitubular surface condensers, the water producing condensation passes through the tubes while the steam is in contact with the outside, or vice versa. 546. CIRCULATING PUMP. The quantity of water provided by the circulating pump must be such that its velocity through the condenser tubes is sufficient to abstract the heat from the steam and convert it to water in the hot-well at a suitable temperature for re- transfer to the boiler by the air pump. The heat gained by the circulating water is equal to the heat lost by the steam. THE STEAM ENGINE. 263 In order to obtain rapid condensation, the quantity of injection water supplied is usually about thirty times the weight of steain to be condensed. 547. CIRCULATING WATER FOR CONDENSATION. The ordinary surface condenser requires 30 Ibs. circulating water to condense 1 Ib. steam. The Korting self-acting condenser without regulation requires 25 Ibs. water, and with regulation 18 Ibs. water, to condense 1 Ib. steam. 548. COMPARISON OF STEAM ENGINES. Engines same type. Boiler pressure same. Cut-off same. Multiplier for proportionate linear dimensions equals / required H.P. V oriinal H.P. = * r ' original H.P. and the revolutions per minute will be original revolutions without allowing for difference in proportion of friction. Friction varies approximately as $/ r. 549. MARINE ENGINES. Marine engineers' rule for engines of varying power, but same type : Required cylinder diameter = /reqd. H.P. orig. pist. speed /orig. cylr.V \r orig. H.P. * reqd. pist. speed \ diam. / 264 HANDBOOK FOB MECHANICAL ENGINEERS, Examples. I.H.P., 6000. Cylinder 43, cut-off 8J / 10. 62 8i/10. 96 8/10. Piston rods same size. Stroke, 4 feet 3 inches. Boiler pressure, 135. Eevolutions, 95. Piston speed, 807-5. I.H.P., 2750. Cylinder 30, cut-off 8J / 10. 44 8J/10. 68 8/10. Stroke, 3 feet. Boiler pressure, 135. Eevolutions, 130. Piston speed, 780. 550. DEFINITIONS RELATING TO SCREW PROPELLERS. Length - A 1 B 1 measured along the axis of the shaft. Angle = P O H, which is a plane triangle when developed. Pitch = the distance traversed on A 1 B 1 for one complete revolution of A 1 P. Slip = the difference between the theoretical forward motion, calculated from the pitch of the screw, and the actual progress of the ship. Area = A 1 P O B, surface of blade in sq. feet. Thread or Helix = Outer edge of blade, O P. Diameter = Diameter of cylinder circumscribing the thread of screw. A 1 P = radius. 551. SPEED IN KNOTS. Speed in knots X 1 15 = miles per hour. 6080 feet = 1 knot. 5280 = 1 mile. Feet per minute -4- 88 = miles per hour. 4- 101J = knots THE STEAM ENGINE. 265 Speed of ship in knots (per hour) __ 3 / I.H.P. x sectional coeff. of performance, say 600 ~ \/ area immersed midship section, sq. feet or _ 3 / I.H.P. x displacement coeff. of performance, say 240 ~~ \/ cube root of sq. of displacement in tons 552. NOTES ON SCREW PROPELLERS. In the common form of propeller the screw surface is generated by a line perpendicular to the axis of the shaft revolving round the shaft and progressing uniformly along it. Screw surfaces are also generated by a line at right angles to a conical surface ; in some cases the vertex of the cone points aft, and in others forward. In some the surface is traced out by a line perpendicular to a sphere ; the object in such cases being to diminish, if possible, centrifugal action of the water. Screws of same pitch have different angles if their diameters differ ; angle reducing as diameter increases. The screws are either right or left-handed, and may have two, three, or four blades. 553. EELATIVE EFFICIENCY OF LARGE AND SMALL SCREW. " As regarded the relative efficiency of large and small screws, if consideration were confined to the propellers alone, apart from the vessels they were designed to propel and the ser- vices they were intended to perform, efficiency was indepen- dent, within certain limits, of the absolute size of the screw, According to Mr. Froude, the screw for a vessel of 500 I.H.P., and 10 knots speed per hour, might be 10 feet in diameter, 0*8 pitch-ratio, and run at 138 revolutions per minute ; or it might be 15 J feet in diameter, 2'5 pitch-ratio, and run at 33 J revolutions. Both screws would be credited with an 266 HANDBOOK FOE MECHANICAL ENGINEERS. efficiency of 69 per cent. ; but the large screw was at a disadvantage when placed in a following stream, on account of the greater difference in the velocity of wake currents which it experienced, and also because of its greater liability to emerge from the water. To maintain a high speed against head winds and sea, a relatively large screw was desir- able ; the case was analogous to that of a tug. For such a purpose increased diameter should not be associated with increased pitch-ratio. " 554. SLIP OF SCREW PROPELLER. Slip is less when pitch is small and speed great, but more danger from heated bearings. When pitch is small, the propeller is less liable to break from a blow. The slip is diminished, cseteris paribus, by 1. Decreasing the angle of the screw. 2. Increasing the diameter of the screw. 3. Increasing the length of the screw. But the friction increases rapidly with the surface of the blade. The indicated horse-power varies as the square of the speed of the ship x number of revolutions of screw X pitch. The most economical speed is when the vessel steams half as fast again as the opposing current, or half as fast again as a vessel it desires to overtake. 555. NEGATIVE SLIP. Negative slip in screw propellers is caused either by the skin friction of the ship giving a forward velocity to the water in which the screw works, depending upon the lines of the ship, and the position and size of screw; or it is caused by an increase of pitch due to the straining of a weak propeller by the pressure of the water ; or it is due to the pitch of the propeller being incorrectly estimated. THE STEAM ENGINE. 267 556. PITCH OF SCREW PROPELLER. Ordinary propellers have the pitch uniform throughout each blade, the angle varying with the distance from the axis, originally known as Smith's propeller. Screws of increasing pitch are sometimes used, and known as Woodcroft's propeller. Propellers with two blades are common in large ships, but those with three or four blades are better when the draught is small or in a rough sea. Feathering-screws have the blades pivoted so that the angle, and thereby the pitch, may be altered. The pitch of a screw varies with the ratio of the circle described by the screw to the immersed midship section. 557. EELATION OF PITCH TO DIAMETER. There does not appear to be any advantage in adhering to a fixed relation of pitch to diameter. Dimensions rather than form regulate the efficiency. In Thorneycroft's experi- ments it was found that 1. The disc-area was proportional to the I.H.P. and inversely proportional to the cube of the speed. 2. The revolutions per minute were proportional to the speed, and inversely proportional to the diameter. 3. The constants were of the form V 3 C A = disc area X ^ ki.r. C B = revolutions x TT when V = speed of screw through the water D = diameter of screw in feet. H.P. = effective H.P. in screw shaft. 268 HANDBOOK FOB MECHANICAL ENGINEERS. 558. FORMULA FOR PITCH OF PROPELLER. C = constant. = 737 ordinary mercantile marine. = 600 cargo ships with full run. B = revolutions per minute. D = diameter propeller in feet. Pitch in feet The pitch should never exceed 2J times diameter. Another rule : Blade surface = 35 per cent, of disc area. Breadth of blade = -| pitch. Eatio pitch to diameter, average 1^ to 1. Coarse pitch requires more surface than fine pitch. 'Mechanical World.' 559. ALTERATION OF PITCH. With same mean pressure on piston, for small alterations of pitch pitch X knots 2 = constant. and pitch 3 X revolutions 2 = constant. . . increasing pitch reduces revolutions and speed. Somerscales. 560. INDICATED H.P. REQUIRED FOR SCREW PROPELLER. E = revolutions per minute. D = diameter of propeller in feet. L = length P = pitch 8 = slip in fraction of unity (as J). = angle of blade at periphery. O p T> Knots (per hour) = -- (1 - s). THE STEAM ENGINE. 269 561. BUILT-UP CRANK SHAFTS. City of Rome s.s., Whitworth compressed steel. Dif- ference in diameter of fitting parts allowed for shrinkage diameter. 562. STEAM SHIPS. Scott Russell's rules. Greatest speed in knots = V 2J times length of after body. At moderate speeds, resistance in Ibs. = speed knots 2 (-^displacement tons) 2 X "8 to 1'5. Effective H.P. = resistance Ibs. x speed knots ^ 326 T T . T TT T resistance Ibs. X speed knots Indicated H.P. average = 200 m . T . sinecle screw Twin screws, dimensions = - >-- revolutions = single screw X V 2. 563. PADDLE WHEELS. k = speed of vessel in knots. N = revolutions of engine per minute. r = radius of rolling circle in feet, or circle with circum- ferential velocity equal to ship's motion. 6080 k 16 fc r = K = radius outside wheel in feet. b = breadth radially of float-board or paddle in feet. m = mean radius, to centre of gyration, of float-boards. -r + bY 270 HANDBOOK FOR MECHANICAL ENGINEERS. v = circumferential velocity of centre of pressure of float- boards in feet per second. a = area of float-boards in sq. feet. p = pressure in Ibs. on vertical float-board. 62-5 a 6080 n = number of paddle wheels. Effective H.P. required = Hann and Gener. 564. EFFICIENCY OF PADDLE WHEELS. Common, light draught . . . . = 666 deep . . . . = '553 Feathering (Morgan's patent) all depths = 666 565. EQUILIBRIUM OF FLOATING BODIES, AS SHIPS. When a floating body is in equilibrium, the centre of gravity of the body and the e.g. of the displaced fluid are in the same vertical line. When the floating body is moved through a small angle, the intersection of the originally vertical line through e.g. of body, with vertical line through e.g. of now displaced fluid, is called the metacentre (Bouguer). The floating body will return to its original position so long as the metacentre remains above the e.g. of body. The equilibrium is stable, unstable, or indifferent, respectively, as the metacentre falls above, below, or coincides with the e.g. of the body. When a body floats on a fluid it displaces a quantity equal in weight to itself, and when it sinks it displaces a quantity equal in bulk. THE STEAM ENGINE. 271 566. DISPLACEMENT OF SHIPS. Length X "breadth x draught x coefficient of fineness = displacement, e.g. H.M. Blake. 375 x 65 X 25-75 X '502 = 9000 tons. Admiralty displacement formula, D^V 3 c = , is not correct, it should be 1)0-6 y log c = log __ + a V. _ E Mamel 567. TRACTIVE FORCE OF LOCOMOTIVES. d = diameter of piston in inches. a = area of piston in sq. inches. I = length of stroke in feet. n number of cylinders. D = diameter driving wheel in feet. Then the tractive force at circumference of driving wheels for each Ib. per sq. inch mean effective pressure on piston _ 2anl . d 2 1 T5"' = U* Also let //, = adhesion of wheels to rails (say 2) W = weight on driving wheels, then W /* = maximum possible tractive force. The greatest mean effective pressure on piston is com- monly assumed to be 85 per cent, of boiler pressure, but this will be different for each design of valve gear, other things being equal. The ordinary mean effective pressure on piston would probably not exceed 50 per cent, of boiler pressure. The tractive power of a locomotive decreases as the speed increases. T = traction in Ibs. for two cylinders. p = boiler pressure Ibs. per sq. inch. d diameter of piston in inches. 272 HANDBOOK FOR MECHANICAL ENGINEERS. I = stroke in inches. D = diameter driving wheel in inches. K = coefficient = 65 for cut-off at ths. T K* dn r-K-g-. De Pambour. H.P. of locomotive = tractive force Ibs. X V miles per hour 5280 88 T V X 60 x 33,000 33,000' 568. ADHESION OF LOCOMOTIVE WHEELS. Locomotive driving wheels will commence to slip if the force at circumference equals about - of the load . > =448 Ibs. per ton. Westinghouse and Galton . = 246 4 Poiree . . . * =465-9 Pennsylvania Railroad . = 550 Northern Pacific Eailroad . = 670 Eng. Week. Adhesion depends principally upon the state of the weather, and varies from a maximum of \ load to a minimum of y 1 ^ load, average say \ load. 569. RESISTANCE ON RAILWAYS. Straight and level railway, in good condition, resistance (R) in Ibs. per ton of total load (W). _ v miles per hour 2 ~T71~ Do. on incline of 1 in m = R + ( - W X 2240 ) \m / On Prussian railways, R is taken at T ^ W = 22-4 Ibs. per ton. By experiment in railway goods stations, R = 30 Ibs. per ton moving slowly. THE STEAM ENGINE. 273 A train of 300 tons total can be hauled 40 miles per hour on a level with 600 I.H.P. (F. W. Dean). This gives a resis- tance of 18-75 Ibs. per ton, assuming E.H.P. = I.H.P. 570. LOCOMOTIVE EXPRESS ENGINES. Inside cylinder engine, 17 inches diameter, 24 inches stroke, firegrate 15 sq. feet area, heating surface, firebox 89 sq. feet, tubes 1013 sq. feet. Load on axles, 9*45 tons leading, 11 tons driving, 8 '75 tons trailing. Total wheel base 15 feet 8 inches. Can draw 293 tons on a level, at 45 miles per hour, with 120 Ibs. per sq. inch. Leading wheels 3 feet 1\ inches diameter, driving and trailing coupled 6 feet 7J inches diameter. Coal 26-3 Ibs. per mile, with 10 coaches. L. & N. W. Railway. 571. EFFECT OF SPEEDS AND GRADIENTS. An engine of uniform power will pull 40 vehicles at 20 miles per hour. 30 30 21 40 15 50 11 60 and running at 15 miles per hour will pull 42 vehicles on a level 34 up 1 in 600 27 300 20 150 15 100 12 75 9 50 Du Bosquet. T 274 HANDBOOK FOR MECHANICAL ENGINEERS. 572. RAILWAY CURVES. W = maximum rigid wheel base of rolling stock in feet. G = gauge of railway, i.e. inside measurement between rails in feet. E = minimum radius of curve in feet. E = 9WG. Examples : Coal wagon, wheel base 8 feet 6 inches, gauge 4 feet 8J inches, wheels 3 feet diameter, radius of curve = 360 feet = 5 chains radius. Four-wheel-coupled tank locomotive, wheel base 3 feet 6 inches, gauge 2 feet, wheels 1 foot 6 inches diameter, radius of curve = say 60 feet radius. 573. Am CONDENSERS. Steam passed through thin brass tubes, air circulated by fan outside. With J inch inside diameter of tubes, 5-feet run = 1 sq. foot cooling surface. Weight of condenser, say 1 ton per 800 sq. feet cooling surface. Difference of tem- perature of air at entrance and exit say 80 P. May be used for producing blast after leaving condenser. Loss of heat by f -inch pipe for air contact only = 2-25 units of heat per sq. foot per hour per 1 F. difference of inside and outside. At 212 F. 1 Ib. of steam contains 966 units of latent heat which are given up on condensation. Example .-Steam 212, air mean 100, difference 112, 112 X 2-25 = 252 units passing per sq. foot per hour. 252 - = -26, say J Ib. steam may be condensed per sq. foot per 9ob hour. Experiments on single pipes give much higher effi- ciency, but this is probably on account of radiation playing a more important part. By an article in ' Engineering ' (1869) Ib. may be taken. THE STEAM ENGINE. 275 At a consumption of 30 Ibs. steam per H.P. per hour, and an estimate of ^ Ib. condensed per sq. foot per hour, cooling surface = 120 sq. feet per H.P. And for 80 F. difference of air temperatures we have weight of air required per Ib. of steam = Units of heat to be absorbed by air Diff. of entrance and ) I specific heat of air at exit, F it constant pressure U 966 (T- 0-238 8 50 X 30 ibs. steam per H.P. = 1500 Ibs. air per H.P. At T V Ib. as the weight of a cubic foot of air we require 1500 X 10 = 15,000 cubic feet air per H.P. per hour. If boiler evaporates 5 Ibs. per sq. foot heating surface per hour, then cooling surface must equal 20 times heating surface. When temperature of air = 59 F., copper will condense about 0*28 and cast iron 0-36 Ibs. steam per sq. foot per hour. 574. GAS ENGINES. The Otto cycle of working : First revolution jOutstroke draws in air and gas. llnstroke compresses charge. Second revolution JOutstroke caused by the explosion llnstroke discharges burnt products. T 2 276 HANDBOOK FOR MECHANICAL ENGINEERS. SECTION XII. HYDEAULIC MACHINERY.* 575. SUMMARY OF HYDRAULICS. THE quantities discharged from different apertures of similar character, vary directly as the areas, and as \/ altitudes. On account of friction, a small orifice discharges propor- tionally less water ; and of several orifices having the same area, that with the smallest perimeter discharges most : hence a circular orifice is most advantageous. Water issuing from a sharp-edged circular aperture is contracted at distance of A- diameter from ossu orifice, from 1 to. . . . I 6 " 1 . >631 Eytelwein 64 in area, called " vena contracta." Vein contracts more with greater head, therefore discharge slightly diminished below theoretical discharge due to altitude. When the orifice is not sharp-edged, the contraction is partially suppressed and the flow increased. Water flowing from pipe of sectional area A into one of less sectional area a, will have a coefficient of contraction 1 = V / ( 2 ' 618 " 1 ' 618 S Rarikine. = *618 when A is infinite, say a large tank. * See lecture by the author 'on ' Hydraulic Machinery, Past and Pre- sent/ read before the Railway Officials' Association in 1880. Demy 8vo, 42 pp., and folding plate of illustrations (Spon, Is.). HYDRAULIC MACHINERY. 277 The discharge through a tube of diameter = length is the same as through simple orifice of equal diameter. The discharge increases up to a length of 4 diameters. The discharges through horizontal conduit pipes are directly as the altitudes and inversely as A/ length. To have perceptible and continuous discharge, head must not be less than -7- Vertical bends discharge less water than hori- loOO zontal, and horizontal bends less than straight pipes. Eight angle bends 1 foot radius, with a flow of 32 feet per second, lose approximately 1 foot head, or for any other flow, say '001 v 2 . The discharge through pipes varies approximately as diameter 2 . In prismatic vessels twice as much is discharged from the same orifice if the vessel be kept full, during the time it would take to empty itself. 576. TORRICELLI'S THEOREM. Particles of fluid escaping from an orifice possess the same velocity as if they had fallen freely in vacuo from a height equal to that of the fluid surface above the centre of the orifice. 577. PRESSURE OF WATER. "Water transmits pressure equally in all directions (Pascal), and its own weight acts as additional pressure in proportion, to the depth from surface. Pressure is perpendicular to containing surface. Water is only compressible to a very small extent. Pressure per unit of area is affected solely by depth, and is entirely independent of extent of surface. Area of any portion of containing surface in sq. feet x distance of its centre of gravity in feet from surface of liquid x weight of liquid per cubic foot = pressure upon that por- tion of containing surface. The " centre of pressure " on a plane surface, or point 278 HANDBOOK FOR MECHANICAL ENGINEERS. where pressures would be balanced by a resistance, is J height, or f down from surface. The pressure of the air is not able to sustain a column of water more than 34 feet high, hence water cannot by any possibility be raised by direct suction from a greater depth the exact amount varies with the barometric pressure and the method employed. If pressure be applied to a liquid entirely filling a closed vessel, that pressure will be transmitted equally to all parts of the liquid. 578. FLOATATION POWER OF WATER. When a solid body floats on a liquid, the weight of the liquid displaced is equal to the weight of the body. When a heavy body is immersed in water, it displaces an equal bulk, and loses weight equal to the weight of water displaced. . weight of body in air Specific gravity = we i g h t o f equal bulk of water' or weight of body in air weight in air weight in water * Solid cast iron loses 14 J per cent, of its weight when immersed in water. 579. HYDROSTATIC PARADOX. " Any quantity of fluid, however small, may be made to balance and support any quantity or weight, however great." Thus the water in a 3-inch pipe from a tank on the top of a building may support a load of many cwts. in the cradle of a hoist. 580. PRINCIPLE OF ARCHIMEDES. When a body is immersed in water it loses weight, and the loss of weight is equal to the weight of the water dis- placed by the body. HYDRAULIC MACHINERY. 279 581. PASCAL'S PRINCIPLE. "If a vessel full of water, closed on all sides, has two openings, the one a hundred times as large as the other, and if each be supplied with a piston which fits exactly, a man pushing the small piston will exert a force which will equilibrate that of a hundred men pushing the piston which is a hundred times as large, and will overcome that of ninety-nine. And whatever may be the proportion of these openings, if the forces applied to the pistons are to each other as the openings, they will be in equilibrium." Blaise Pascal's ' Equilibrium of Liquids* 582. COMPRESSIBILITY OF WATER. Water is popularly supposed to be incompressible, but " If the water of the ocean were to suddenly cease being compressible, the result would be that 4 per cent, of the habitable land on the globe would be submerged, because the mean depth of water would be raised by 116 feet." Prof. Tail. 583. COMPARISON OF DISCHARGE THROUGH VARIOUS APERTURES. Theoretical velocity in feet per second = V head in feet x 2 g. Theoretical discharge being 1, Short tube projecting into reservoir = 5. Orifice in thin plate, 1 in. diameter = 62. Tube 2 diameters long = 82. Conical tube approaching form of contracted vein = 92. edges rounded off = 98. 280 HANDBOOK FOB MECHANICAL ENGINEERS. Or, say theoretical velocity ft. per second = 8 04 J head ft. Effective velocity through orifices of the\ form of vena contracta, well- 1 placed sluices, large bridge [ = 7 ' 5 * ** openings, &c. . . . ,J large vertical pipes and narrow > bridge openings . . . f = 3<75 V*- sluices without side walls, dock 1 gates, and mill stream sluices } ** * 584. PRACTICAL DISCHARGE OF WATER. h = head in feet. c = discharge in cubic feet per minute. a = area in square feet. !450 for bridges, &c. 400 pipes, &c. 300 ordinary sluices. Beardmore. When the outlet is "drowned" the head will be the difference in level between water over inlet and outlet. 585. WEIGHT AND BULK OF WATER. A standard or imperial gallon of water was formerly 277-274 cubic inches, is now 10 Ibs. avoirdupois at 62 F. and 30" bar. = 277-123 cubic inches, or -160372 cubic feet. Capt. E. M. Shaw. A cubic foot of pure water at its point of maximum density, 39 F. [39-1 F., or 4 C.], weighs 998-8 ounces = 62-425 Ibs. Twisden. Standard weight of water = 62-321 Ibs. per cubic foot. Sale of Gas Act, 1859. HYDRAULIC MACHINERY. 281 The experiments of the Standards Office of the Board of Trade show that a cubic inch of water weighs 252-286 grains instead of 252-458 grains, of which 5760 go to the pound Troy, and 7000 to the pound Avoirdupois, therefore a gallon of water now equals 277-463 cubic inches. < The Engineer,' 1889. U.S. standard gallon weighs 8J Ibs., and contains 231 cubic inches. A cubic foot of average sea water weighs 64 Ibs. A cubic foot of ice at 32 F. is 5 Ibs. lighter than a cubic foot of water at same temperature. Water in freezing expands ^ of its bulk. Weight per Cubic Foot. Ibs. Ice . 58-078 Water, maximum density 39i- F. . 62-4491 60 F. . 62-39 212 F. . 59-745 average, say . . . .62-4 Span's Dictionary. 586. USEFUL NUMBERS IN CONNECTION WITH WATER. Cubic feet x 6-232, say 6J = gallons. Cubic feet per minute X 9000 = gallons per 24 hours. Head in feet x ' 434 = Ibs. per sq. inch. Lbs. per sq. inch x 2 3 = feet-head. Tons x 224 = gallons. Diameter inches 2 -4- 10 = gallons per yard. Weight of sea water = 1 '027 weight of fresh water. 168 gallons = 21 bushels = 27 cubic feet = 1 cubic yard. 587. VELOCITIES OF STREAMS. s = surface velocity centre of stream. b = bottom m = mean velocity of whole stream. 6 = (Vs-l) 2 , w=-8?-~^, or m= 'S (s - Js+ -5). DuBuat. 232 HANDBOOK FOE MECHANICAL ENGINEEKS. m = 705 s + * 001 s 2 . von Wagner. w = s + 2 5 V 5 s. Beardmore. m = -835 8. Neville. m = f 8. Adams. m = 653 s. Baumgarten. ( + 7-783) . s + 10-345 Prony. Velocities may be feet per minute, or inches per second, &c. Inches per second X 5 = feet per minute. 588. DISCHARGE OVER WEIRS. h = true head from sill to still surface in feet. c = discharge in cubic feet per minute per foot width. c = 214 //F. When the water passes the point where the constant head begins to deflect, with an appreciable initial velocity = v feet per second, c = 214 */h 3 + -035t> 2 /i 2 . For small weirs : I = length of weir or notch in inches. g = gallons discharged per minute. d = depth of head in inches. g = 2 I */&. 589. DISCHARGE OVER WEIRS PER FOOT WIDTH. h = height of flow on edge of rule over square notch or edge of horizontal weir. c = cubic feet per minute. h = 1 inch, then c = 5-10 li 7-14 11 9-23 If 11'78 2 14-43 Hawksley. HYDRAULIC MACHINERY. 283 590. FLOW OF WATER THROUGH KECTANGULAR NOTCH. Q = cubic feet per second. b = breadth of notch. h = height of surface of still water above bottom of notch. c = a coefficient of discharge. B = breadth of weir. Q = f c . b Ji . tjlgh = 5 35 c b h VT. If b = l width of weir (the minimum advisable), c = 595 whole width of weir c = 667 For any intermediate proportions c = ' 57 + j^g CotteriWa App. MecL 591. FLOW OF WATER THROUGH TRIANGULAR NOTCH. When b = 2 A, c = -595, Q = 2-54 A*. fc = 4A, c=-620, Q = 5-3A* f Cotterill's App. Mech. 592. KIVERS, SEWERS, DRAINS, &c. D = hydraulic mean depth in feet sectional area of streams or pipes partly iull = = : 7 > wetted perimeter diameter of pipes running full or half full only = / = fall in feet per mile. M = mean velocity in feet per minute. d = diameter of pipe in feet. 284 HANDBOOK FOR MECHANICAL ENGINEERS. I = length in feet. Ti = head or fall in feet. c = cubic feet per minute. I = mean hydraulic inclination = - M= X 2/x 55, c = M = 6000 V D ~7l~ _ 2356 \fd 5 ~~ M = 92-26 Beardmore. Leslie. Eytelwein. 593. NATURAL EVAPORATION OF WATER. Mean evaporation of water from open surface in London, large body of water 21 inches per annum, small body 50 inches ; rainfall during same period 25 inches. 594. EFFICIENCY OF HYDRAULIC WATER-RAISING MACHINES. Hydraulic ram . . . Turbines and pumps . . Overshot water wheel and pumps Poncelet Breast Undershot 595. WATERWHEELS. . 75 . 60 . . '55 . -45 . -44 . -28 G. H. Hughes. Undershot Wheel. Float boards radial, or inclined 20 towards current when not used in tidal stream. Breadth may equal or exceed diameter. Maximum efficiency when velocity of wheel equals half velocity of stream. HYDKATJLIC MACHINERY. 285 Breast Wheel. Floats shrouded or covered at the sides and curved to form buckets. Breastwork of masonry built up round wheel as high as centre line. Stream led down a masonry slope to act on wheel by momentum and gravity. Suited for moderate supply of water and fall of 6 or 8 feet. Overshot Wheel. Floats formed into buckets. Water led in trough to top of wheel. Eatio of width to diameter usually small. Kequires less water to drive it than the other forms, and is more than twice the power of an undershot wheel of same size. Fall must not be less than diameter of wheel. Smeaton found that in ordinary wheels the velocity of cir- cumference should not exceed 3 feet per second. Poncelet Water wheel. Undershot, floats curved to meet stream, maximum effect when velocity of stream equals 2 J times velocity of wheel. Modulus = 7. 596. TURBINES. Fourneyrons (1827). Water admitted in centre of wheel, passing along curved guides, and discharged at circumference against guides curved in opposite direction. Thompson's Vortex Wheel. Water admitted at circum- ference and discharged at centre, can be fixed above tail- race up to 30 feet, power being obtained by suction. Fontaine's and Jonval's Parallel I'low Wheels. Water ad- mitted above through fixed inclined vanes and discharged below, axis vertical, inclined vanes on wheel with angle reversed. 597. HYDRAULIC KAM. Where a fall of water of not less than 2 feet can be obtained through an inclined supply pipe, the hydraulic ram may be used for raising water to a considerable height, say 150 feet, without the intervention of other machinery. The action is as follows : The water passing through the drive 286 HANDBOOK FOB MECHANICAL ENGINEEES. pipe (supply or injection pipe) gradually increases in velocity until it suddenly closes the pulse valve through which it is escaping, when a small quantity is forced by the momentum of the bulk through the delivery valve into the air vessel, and thence into the delivery pipe or rising main. The escape valve being then relieved, the supply water again flows through until its velocity is sufficient to close the valve. This alternate motion is repeated as long as the condi- tions remain unaltered. The pulsations vary from 30 to 100 per minute, according to the fall of water. Average proportions and results are : D = diameter of fall pipe in inches. / = fall in feet. d = diameter of rising main in inches. h = head of ditto in feet. G = gallons per minute to work ram. g = gallons raised in 24 hours. 7i does not generally exceed 50 /. d = JD. G = 3 D 2 . g = 3000 D 2 598. CENTRIFUGAL PUMPS. Power required to drive them varies as the 1 5 power of the lift. a = gallons lifted per minute. H = lift in feet. T TT P - 10axH1 ' 6 2 x 33,000* Speed at periphery = 8 V H = feet per second. A. Hanssen. Note.K 1 ' 5 = Hi = V H" 3 . HYDRAULIC MACHINERY. 287 599. DISCHARGE THROUGH PIPES FROM NATURAL HEAD. d. c. d. c. H = head of water in feet .... L = length of pipe in feet .... d = diameter of pipe in inches . c = constant (see table) .... W = cubic feet discharged per minute w c 1 1| 2* 1 4 5 6 4-71 8-48 13-02 26-69 46-67 73-50 151-02 263-87 416-54 7 8 9 10 12 15 18 24 30 612-32 854-99 1147-61 1493-47 2356-00 4115-93 6493-14 13328-0 23282-0 /L VH' /&W J W = 4-71 \/-=-, - area of steam piston, and ram 3*6 inches diameter = ^ area of pump. Boiler pressure 60 Ibs. per sq. inch by gauge. Cut-off f stroke. Mean pressure by calculation = 56 Ibs. per sq. inch, by indicator diagram 45 Ibs. per sq. inch. 16 inches diameter = 201*06 sq. inches area, 5-1 inches diameter = 20 43 sq. inches area, 3 6 inches diameter = 10- 18 sq. inches area. HYDEAULIC MACHINERY. 297 Power = 201-06x48x^x120x1* = log . 67 IHp Effect = 20-48X700X2X60X1} _ 6% logs = 82 . 33 E . H . R 33 , 000 QO . OO Coefficient = I ^=- 75, or 75 per cent, on the indicated horse-power. In connection with the above engine the following par- ticulars may be useful: Fly-wheel 9 feet diameter; two wrought-iron Lancashire boilers, 6 feet diameter X 20 feet long ; two flues, each 28 inches diameter, with five Galloway tubes. Double-acting lift pump. Tank, 1500 gallons, for return water. 18-inch accumulator, 23 feet stroke. In another case the coefficient was found to be as high as 82, but *75 is more usual. 619. PACKING FOR FORCE PUMPS. Cup-leathers (invented by Bramah) may be single, double, or treble. If single, the open end should be turned towards the delivery end of the pump. If double, they may be back to back, or both turned towards delivery end of pump. If treble, two should be back to back, and the third put as a duplicate to the one turned towards delivery end. In all cases the back of the leather should be closely supported by a washer curved to the shape of the leather. Double leathers back to back are generally used, and last from two days to four months, average say one month. Only the middle of the back of best oil-dressed hide is used. Spun-yarn is sometimes used, the same as for glands of hydraulic machinery generally. It is plaited and formed into rings by splicing, soaked in tallow, and screwed up in a mould to form solid rings of exact size to fit pump. Eope is sometimes used in the same way, being selected of the exact diameter required. The two latter methods are said to last from four to six months, but there is probably more leakage than with leathers. 298 HANDBOOK FOR MECHANICAL ENGINEERS. 620. PROPORTIONS OF HYDRAULIC PIPES. For accumulator pressure of 700 Ibs. per sq. inch : inside diameter (d) in inches -f- 2 = thickness of metal in ^ths. Filling pipes made by local firms, ^ inch thicker. Flanges oval, 2*85 d x I'55d and J d thick, with two square- necked bolts each ^ d in diameter for 5-inch pipes and upwards, or d -{- 5 = diameter in ^ths for 5-inch pipes and under. Another rule for bolts is 2 (d -+ 2) = diameter in 621. THICKNESS OF PIPES FOR HYDRAULIC ACCUMULATOR MAINS. For 700 Ibs. per sq. inch : Armstrong . . . . t = h '25 8 d Brown . . . . t = 6 622. THICKNESS OF PIPES FOR WATER Co.'s MAINS. H = head of water in feet. d = diameter of pipe in inches. t = thickness of metal in inches. x = 0*37 for pipes less than 12 inches diameter. 0*5 from 12 to 30 0-6 30 to 50 p = working pressure in Ibs. per sq. inch. r = inside radius of pipe in inches. c = working strength of metal in Ibs. per sq. inch. = 3360 for cast iron, 500 for lead. For 200 feet head : Hawksley . t = -18 Jd. Unwin . . t = -11 ]j d + -1. HYDRAULIC MACHINERY. 299 J " " 10 125 Molesworth . t = 000054 H d + a;, or say = 0108 d -j- ^ Burnell . . t = B. Latham n , . H d fd Rankme . t = -^^^ or ^ -, whichever is greater, with a minimiim of f inch. Trail twine gives as the usual American practice, d (IP . o\ , {\ P v = K^" 7 " i r^ 5 ' l\ / J but suggests as an improvement, f/JL4r2w'irjr x f+-* =< m Im 2 l\"8 / J T where w = cohesion of metal in Ibs. per sq. inch, say 16,800. / = factor of safety, say 6. p = internal pressure in Ibs. per sq. inch. 623. GENERAL RULES FOR THICKNESS OF CAST-IRON PIPES. Unwin. . *='^(\/l 7 7 7 7 l+ P -l\ Barlow . t = ^. AAA X 5 for safety. IbUUU j_ Adams - ' ' = 6o^ + To5 + TF(+- 125for steam >' Cam p in '= + ' 66 - 300 HANDBOOK FOR MECHANICAL ENGINEERS. 624. NOTES ON PIPES. Iron, composition, and lead pipes are measured by their inside diameter, brass and copper pipes by their outside diameter. Wrought-iron pipes are bent by filling with sand and making red-hot, keeping the joint on the side of the bend. 625. DR. ANGUS SMITH'S COMPOSITION FOR COATING PIPES. Original recipe was 30 gallons coal tar, 30 Ibs. fresh slaked lime, 6 Ibs. tallow, 3 Ibs. lampblack, 1 J Ib. resin ; to be well mixed, boiled 20 minutes and put on hot. The modern practice varies, but a good mixture is 3J barrels coal tar, J barrel coal oil, J barrel pitch, with 6 tons gas coke for heating pipes. Made and used as follows : Into a wrought-iron tank long enough to take a 9- feet pipe, sufficient coal tar to half cover a pipe is put, then pitch beaten to a powder, and sprinkled on the tar, and coal oil poured on the pitch. The pipes heated to 180 to 200, or as hot as the hand can bear, are put into the liquid separately and turned over and over for 2 or 3 minutes, then placed at an angle to drain, with the lower end clear of the liquid. The above quantities will do about 1000 pieces, bends, branches and straight pipes, or say f barrel coal tar to 100 9-feet lengths of 4-inch pipes. This method avoids risk from the liquid catching fire. 626. HYDRAULIC PRESS WITH HAND-PUMP. P = pressure in Ibs. on handle of pump. d = diameter of pump in inches. power leverage I = effective leverage = =r-r , - resistance leverage D = diameter of press in inches. M = modulus or coefficient of press, say = '8. W = total load in Ibs., or maximum effort of press. D 2 HYDRAULIC MACHINERY. 301 Moseley (' Illustrations of Mechanics,' p. 197) says, * The discovery of it [the hydraulic press] is usually attributed to Pascal ; it belongs, however, to the celebrated Stevin, mathematician to the Prince of Nassau, the inventor of decimals." 627. HYDRAULIC FORGING PRESSES. Hydraulic forging presses capable of exerting a pressure of 1000 to 10,000 tons are used in large works for converting steel ingots into large forgings, &c. They are actuated by a pressure of between 2 and 3 tons per sq. inch to keep down the size of the rams. Smaller presses, exerting say from 25 to 250 tons, are worked at a pressure of 100 atmospheres, or 1500 Ibs. per sq. inch. Ordinary presses are worked from the accumulator pres- sure of 700 Ibs. per sq. inch sometimes with the addition of an intensifier to give the final squeeze. 628. HYDRAULIC PRESS CYLINDERS. d = diameter of ram in inches. c = clearance between ram and cylinder. t = thickness of cylinder in inches. p = pressure in Ibs. or tons per sq. inch. T = maximum tensile strength per sq. inch of material in same units. t-**2. c-- T 12 Bottom hemispherical inside and out, except flat part outside to stand on, = J d in diameter, and joined with easy radius. Another rule : P =. bursting pressure in tons per sq. inch. D = outside diameter in inches. d = inside T = tensile strength tons per sq. inch of material. 302 HANDBOOK FOE MECHANICAL ENGINEERS. Another rule : p = internal bursting pressure, Ibs. per sq. inch. r = inside radius of cylinder in inches. s = ultimate tensile strength of metal per sq. inch. say cast iron 18,000 Ibs. gun-metal 36,000 Ibs. t = thickness of metal in inches. r + t s-p t P. Barlow. Common rule : Thickness of cylinder = radius of bore. This is supposed to be safe at 3 tons per sq. inch working pressure, but is really not safe at more than 2 tons per sq. inch. Permanent safe working pressure = ^ bursting pressure. Maximum working pressure allowable = J bursting pressure. N.B. A press worked occasionally up to of its bursting pressure, burst after 4J years' use. 629. EFFECTIVE PRESSURE FOR HYDRAULIC CRANES AND HOISTS. p = accumulator pressure in Ibs. per sq. inch. m = ratio of multiplying power. E = effective pressure in Ibs. per sq. inch, including all allowances for friction, but not for weight of moving parts. E = p(-84 - -02m). 630. DIAPHRAGM EEGULATOR FOR HYDRAULIC MACHINERY. When a hydraulic crane or hoist works too quickly, and it is desired to reduce the speed to a safe limit, it is usual to partially close the stop valve ; but when there is a risk of this being interfered with, a brass diaphragm, -|th diameter HYDRAULIC MACHINEEY. 303 thick and about ^-inch at edge, is placed in a pipe joint near the working valves. The hole in the diaphragm should be tapered, the small side being next to the machine. To find size : A = area of lifting ram, sq. inches. m = ratio of multiplying power. s = speed of lifting with full load, feet per second. p = accumulator pressure, Ibs. per sq. inch. a = area of small side of hole (large side = twice dia- meter of small side). ~ - -046m For direct-acting passenger lifts a diaphragm is always required next to the cylinder. Urnney's rule : For 700 Ibs. per sq. inch, D = diameter of lifting ram in inches. d = diameter of hole in inches. " 220 m For other pressures, D 2 * 631. POWER AND SPEED OF HYDRAULIC HAULING MACHINES. Strain on Hauling Speed, Hope. ft. per rnin. -D ., j 2000 Ibs, 180 Radway capstans . . Barge , . 1J tons 120 Ship - . 2J to 5 tons 80 Railway traversers . . 75 Ibs. per ton of load. Lock gate marines . 1 375 Ibs. per foot width of entrance. 304 HANDBOOK FOB MECHANICAL ENGINEERS. 632. SPEED OF LIFTING WITH HYDRAULIC POWER. Warehouse cranes and jiggers 6 feet per second. Platform cranes and small luggage lifts, 4 feet per second. Passenger and waggon hoists, 2 feet per second. Large passenger hoists, over 50 feet lift, first and last 10 feet average 4 feet per second, intermediate height 8 feet per second. At the Blackpool Tower the hoists were designed to lift 325 feet in rather less than 1 minute, say average 5^ feet per second. Maximum speed under any circumstances, 10 feet per second. General formula for warehouse cranes : W = load in tons. h = height of lift in feet. v = velocity in feet per second. v = W + 10 633. HEIGHT OF LIFT FOR CRANES. Wool warehouse cranes. Height of lift = net height bottom floor to top floor -\- 6 feet. Underside of jib head sheave 10 feet 6 inches above level of top floor. Coal cranes. Minimum height of lift on floating wharf = 40 feet. Height of lift at fixed jetty 50 to 60 feet. Height of lift to riverside hoppers 60 to 80 feet. 634. COAL- WEIGHING CRANES. To find maximum section of weigh-beam, rectangular bar, single or double. T = Ibs. diagonal thrust on sheave-pin per cwt. of load. L = effective leverage of thrust in inches, measured perpendicularly to main knife edge. HYDRAULIC MACHINERY. 305 C = cwts. maximum gross load. 6 = breadth, or combined breadth, of weigh-beam in inches. d = depth of weigh-beam in inches at centre of motion. TLC for a statical factor of safety of 1\ to 1. 635. LIFTING RAMS FOR HYDRAULIC CRANES. W = load to be lifted in Ibs. w = weight of ram, crosshead, sheaves and chain. Z = height of lift in feet. m = multiplying power. c = coefficient of effect = 84 - 02 w. a = area of ram in sq. inches. s = stroke of ram in inches. p = accumulator pressure in Ibs. per sq. inch. C = capacity of cylinder in cubic feet. For horizontal cylinders : Ww WZ a = C = pc 144 pc For vertical cylinders : Wl + O, = pc For inverted cylinders : ^ WZ- -. pc 144 pc 636. TURNING EAMS FOR HYDRAULIC CRANES. W = load in tons. R = rake in feet. I = length between bearings in feet. d = diameter of turning drum in feet. 306 HANDBOOK FOR MECHANICAL ENGINEERS. p = accumulator pressure, Ibs. per sq. inch. m multiplying power of turning cylinder (usually 2 to 1). a = area of turning ram in sq. inches. Alternative formulae : 120 WE 2 TO 3000 WE m a = - 5 - - a = - r-= -- lap lap ' Idp 637. AREAS OF VALVES FOR MACHINERY UNDER ACCUMULATOR PRESSURE. A = area of lifting ram. m = ratio of multiplying power. v = velocity of load in feet per second. V = velocity of water through, valve, feet per second. W = weight of ram, crosshead, sheaves, chain, &c., in Ibs. a = area of lifting valve (mitred spindle). a : = area of lowering valve (mitred spindle). Av Av a = == i = - ===== mV * / W W When cylinder is horizontal, then = area of returning 700 ram. 638. AREAS OF PORTS IN SLIDE VALVES. v = velocity of load in feet per second. m = ratio of multiplying power. A = area of ram in sq. inches. Area of pressure port = (opening side, V-shaped), yy m 1*5 Av Area ol exhaust port = 98 TO The dimensions of the slide should be such that the unbalanced pressure does not exceed 1000 Ibs. per sq. inch on the net working surface of metal. HYDRAULIC MACHINERY. 307 639. COUNTERWEIGHTS FOR CRANE CHAINS. The overhauling weights should be oval, i.e. egg-shaped, with small end on top to avoid catching under beams, &c. Hole for chain should be -J- inch larger than cross section of links, and interior should be cored out to J inch clear all round. The approximate weight of counterbalance required is th of the load. 640. STRESS ALLOWED ON WROUGHT IRON IN HYDRAULIC CRANES. Tons per sq. inch. Tension. Compression. Ballast and coaling cranes . . 2^ 1 Warehouse and other cranes lifting from 1 to 5 tons .... 3 2 Cranes lifting more than 5 tons . 3^ 3 641. LOCK GATES. The span of a pair of gates should form the diagonal of a square, the curve of the centre line of gates being struck from the opposite corner of the square, radius = length of side = '707 span, giving angle of 136, or rise of ^ span. The pressure of water per sq. foot varies at different depths, being 62 5 x difference of head on the two sides at the point considered. The hauling strain on gate chains averages 336 Ibs, per foot width of entrance, but in practice hydraulic and other machines are calculated for an effective strain on the chain of 375 Ibs. per foot width of entrance. The total weight of a pair of gates averages 2J tons per foot width of entrance. x 2 308 HANDBOOK FOK MECHANICAL ENGINEEKS. SECTION XIII. ELECTKICAL ENGINEEBING. 642. THE HYPOTHESIS OP A UNIVERSAL ETHER. ALL space, interatomic as well as interstellar, is filled with a continuous, elastic, perfectly fluid, vibrating medium, in which are propagated light, radiant heat and electricity, as sound is in air. This fluid cannot, however, consist of ordi- nary matter, as it possesses some of the properties of a solid. 643. COMPARISON OF ELECTRICITY WITH OTHER POWERS. Electricity should not be compared to steam or gas, both of which generate and exert a force or power of themselves ; but it would be proper to compare electricity with hydraulic, or belt, or rope transmission of power. Sandwell. 644. ELECTRIC TRANSMISSION. Electric transmission by continuous current may be illus- trated by its analogy to hydraulics. The dynamo is essen- tially a rotary pump, pumping electricity instead of water. In the following sentences the analogous electrical terms are bracketed. The pump (dynamo) forces the water (current) at a certain number of pounds pressure (volts), as indicated by a pressure gauge (volt-meter) to overcome the friction (resist- ance) of the pipes (wire) in order that the water (current) may flow at the rate of so many gallons (amperes) per minute, as recorded by the water meter (ammeter). The larger the pipe (wire) the more water (current) can be carried, and the less will be the friction (resistance). Manifestly the pipe ELECTRICAL ENGINEERING. 309 (wire) might be so small that the friction (resistance) would absorb a very large proportion of the power of the pump (dynamo), leaving but little remaining for useful effect. If the pipe (wire) be too large, it will cost too much ; if it be too small, the loss will be too great. The pipes (wire) require valves (switches) to regulate and direct the water (current), with fittings (contacts) sufficient to convey the water (current) without leak (drop), and safety relief valves (fusible strips) must be provided to prevent damage from over-pressure (over-voltage). 645. CHIEF SYSTEMS OF ELECTRICAL TRANSMISSION. 1. Alternating current where the current flows in dif- ferent directions or the high tension system. 2. The continuous current, or low pressure, or storage system. 3. Pulsating current, continuous in direction, but varying in strength, usually of high tension. 646. BOARD OF TRADE DIVISION OF SYSTEMS. Low Tension System, if working below 300 volts with con- tinuous currents, or 150 volts with alternating currents. High Tension System, if working above these limits. 647. COMPARATIVE COST OF TRANSMITTING POWER. TVfpfhnH 1093 Yards. 5465 Yards. 10 E.H.P. 50 E.H.P. 10 E.H.P. 50 E.H.P. By cables 1-77 1-35 4-69 2-65 electricity 2-21 1-87 2-64 2-37 hydraulics 2-90 2-07 5-29 3-02 compressed air . 2-98 2-29 4-66 2-99 * Revue Universelle des Mines.' 310 HANDBOOK FOB MECHANICAL ENGINEEKS. 648. ELECTRICAL UNITS. The VOLT is the practical unit of electromotive force, or difference of potential or electrical pressure. The OHM is the practical unit of resistance, which varies directly as the length and inversely as the area of section- of a conductor. The AMPERE, formerly called the Weber, is the practical unit of strength of current, or velocity. The COULOMB is the practical unit of quantity, and repre- sents the amount of electricity given by one ampere in one second. (The term " coulomb " is becoming obsolete.) The FARAD is the unit of capacity of an electrical receiver ; one-millionth of this, or the MICROFARAD, is taken as the practical unit. The WATT is the practical unit of work, and is the amount of work required to force one ampere through one ohm during one second. The JOULE is the unit of heating, and represents the heat- ing effect caused by one ampere of current passing through a resistance of one ohm for one second. The volt may be understood as a measure of pressure, the ampere of quantity, the watt of power ; thus a current of 10 amperes at 10 volts = 100 watts. 649. GALVANIC BATTERIES will produce an electric current sufficient for telegraphic or telephonic purposes and electric bells, but not sufficient for lighting. When coupled up in series i.e. copper of first cell to zinc of second, and so on the electromotive force or " pressure " is increased in proportion to the number of cells. When coupled up parallel i.e. all the coppers to one wire and all the zincs to another the E.M.P. is the same as from one cell, but the strength of current or " volume " is greater ELECTRICAL ENGINEERING. 311 because the internal resistance is reduced. Coupling up in series gives intensity, and parallel gives quantity. Common forms are the Leclanche, Grove's, Bunsen's, DanielPs and the Bichromate Batteries. 650. ELECTRICAL TERMS. An electric current flows in a battery from the Positive (or +) plate to the Negative (or ) plate, and outside the battery from the Positive pole (connected to the plate) through a conductor to the Negative pole (connected to the + plate). If the Electromotive force, E.M.F. or Potential difference = 1 Volt, and the resistance through which the current flows = 1 Ohm, the strength of the current = I Ampere, the quantity of electricity flowing per second = 1 Coulomb, and the work per second = 1 Joule. If it requires 1 coulomb of electricity to charge a condenser to a potential of I volt, the capacity of the condensed = 1 Farad. If the mean force of attraction between two opposite charges of electricity = 1 dyne, the work done per centimetre displacement = 1 Erg. If electricity flows through any measuring instrument, the terminals at which it enters and leaves are electrodes ; that at which the current enters = anode, that at which it leaves = cathode. A fluid decomposable by electricity is an elec- trolyte, the products of the decomposition are ions. A volt is about 7 per cent, less than E.M.F. of Standard Daniell cell. An ohm is the resistance of a column of mer- cury 106*2 cm. long x 1 sq. mm. section, at C. It is about the resistance of a pure copper wire -^ inch diameter and 250 feet long. The legal ohm = '998 true ohm; B.A. ohm = '9889 legal ohm = -987 true ohm. One ampere deposits 1 '118 milligrammes of silver per second. The capacity of a knot (6080 feet) of submarine cable is about ^ of a microfarad. The prefix meg multiplies the unit by one million, micro divides it by one million, milli divides it by one thousand. The Board of Trade Commercial Unit = 1000 Watt-hours = 1 34 H.P. working for an hour. C. E. Grove. 312 HANDBOOK FOR MECHANICAL ENGINEERS. 651. MEASURE OF ELECTRICAL WORK. A = strength of current in amperes. V = electromotive force in volts. O = resistance in ohms. C = quantity of electricity in coulombs. t = time in seconds. H.P. = actual horse-power. W = units of work or watts (1 unit = 10 million ergs absolute C.G.S. measurement). = A, HP = ^ " 746 " 746 746 W = AV = A 2 0. 1 watt = y^g- of a H.P. = 1 volt-ampere = 10 7 ergs per sec. 1 kilowatt = 10 10 ergs per sec. 652. OHM'S LAW. The strength of a current (amperes) varies directly as the electromotive force (volts), and inversely as the resistance (ohms). 653. ELECTRICAL EQUATIONS. Amperes x volts = Watts. Joules X time = Watts. Coulombs per second = Amperes. Watts 4- 746 = Effective H.P. Coulombs -4- volts = Farads. 7373 foot-lbs. per second = 1 Joule. Yolts x coulombs = Joules. ELECTRICAL ENGINEERING. 313 654. ELECTKIC LIGHTING. "To make the matter quite clear, let a practical illus- tration be taken. Let it be supposed that a house has to be lighted by a hundred incandescent lamps, each requiring a current of -75 of an ampere urged by an electromotive force of 100 volts. The rate at which energy is expended in each lamp, expressed in volt-amperes or watts, of which 746 are equal to a horse-power, will be -75 X 100, that is 75. The energy expended in the 100 lamps will be at the rate of 7500 watts, which are equal to 10-05 H.P. But this, it must be remembered, is the actual rate at which energy is expended in the lamps. The energy that has to be developed by the engine is greater, for no dynamo-electric machine is perfectly efficient, no dynamo machine gives out as elec- trical energy the exact equivalent of the mechanical energy expended upon it. Let it be supposed that the machine used in ^our installation has a commercial efficiency ' of 80 per cent., that is, that 80 per cent, of the mechanical energy put into the machine reappears in the external or lamp circuit as electrical energy, the balance being wasted in heating the armature coils, and the friction of axles, slipping of belts, and other mechanical sources of loss. Then the rate at which energy is generated by the steam engine must be 10-05 X 1'25, that is 12-55 H.P. This mechanical energy is to be produced by the combustion of coal, and if all the heat liberated in the combustion of coal could be collected and utilised, the supply of coal required to generate energy at the rate of 12*55 H.P. would be very small; but, unfortunately, steam engines even of the best make have but low efficiency, and a horse-power-hour of energy requires in practice somewhere about 4J Ibs. of coal for its production; 12-55 horse-power-hours will therefore require about 56 J Ibs. of coal say, roughly, half a hundredweight, the cost of which is not more than Qd. Assuming that the lamps were required to burn for 1800 hours a year that is, 314 HANDBOOK FOE MECHANICAL ENGINEERS. on an average, nearly 5 hours a day the annual cost for coal would be 451. The prime cost of a suitable dynamo machine and engine (with boiler) would be, say, 300Z., the interest on which at 4 per cent, would be 12Z., and the annual depreciation, at 10 per cent., 30Z. ; the cost of attendance would be about 60Z. ; so that the prime cost would be 300Z., and the total annual cost 147Z., or 1Z. 9s. 5d. per lamp." Probert, 1888. 655. POWER REQUIRED FOR ELECTRIC LIGHTING. Under good conditions the engine power required equals Arc lights . . 1 I.H.P. per 1000 candle-power. Incandescent lights 1 200 1 I.H.P. will supply 16 8-candle incandescent lamps. 656. USEFUL FORMULAE. To convert Mils to millimetres . . multiply by -0253994 Inches . 25-3994 Sq. inches to sq. mm. . 645-137 Cubic inches to cubic mm. 16,386-18 Yards to metres . . -914383 Miles to kilometres . . 1-6093 Pounds to kilogrammes . -45359 Millimetres to mils . 39 3708 Millimetres to inches . -0373708 Sq. millimetres to sq. ins. -00155006 Cubic mm. to cubic inches 000061027 Metres to yards; . . 1-09363 Kilometres to miles . -62138 Kilogrammes to Ibs. . 2-204621 1 kilometre = 1093-6 yards. 1 mile =1-6093 kilometres. 1 kilo =2-2046 Ibs. Pure copper weighs 555 Ibs. per cubic foot. Conrady & Co. ELECTRICAL ENGINEERING. 315 657. ELECTRIC WIKING. Table showing legal standard wire gauge, with the equiva- lent in millimetres. The number of amperes required to fuse it. Safe carrying current in amperes. Number of 100 volt 16-candle-power lamps that it can supply with a drop of 5 per cent, in voltage per 1000 yards. Gauge of tin fuse wire required to protect it. ' S.W.G. Millimetres. Safe Current in Amperes. Amperes that will Fuse it. Number of 100 Volt Lamps 16 C.P. S.W.G. of .Tin Wire for Safety Fuse. 22 0-71 1 45 30 21 0-81 2 50 27 20 0-91 3 60 1 22 19 1-02 4 75 2 20 18 1-22 5 95 4 20 17 1-42 6 125 5 19 16 1-63 8 170 6 18 15 1-83 10 200 8 17 14 2-03 13 250 9 16 13 2-34 15 300 11 15 12 2-64 20 360 13 14 11 2-95 25 430 16 13 10 3-25 30 500 20 12 9 3-66 35 580 26 11 8 4-06 40 670 33 10 7 4-47 45 790 41 9 6 4-87 50 900 50 8 5 5-38 60 1100 60 7 4 5-89 70 1400 75 6 3 6-40 80 1600 90 5 2 7-01 100 2900 110 4 1 7-62 120 3300 140 3 In running wires, wherever a small wire is branched from a larger one, insert a fuse to protect the smaller wire. Fuses should be on porcelain or slate with screwed covers. Conrady & Co. 316 HANDBOOK FOB MECHANICAL ENGINEERS. 658. LIGHT-TESTING, OR PHOTOMETRY. The standard candle is a sperm candle, six to the pound, and burning at the rate of 120 grains of spermaceti per hour. 659. COAL GAS. The distribution of the light in numerous jets increases the convenience but decreases the total quantity of light, e.g.: 5 cub. ft. per hour burnt in 1 jet gives a light = 28 candles 2 jets, each 2 J ft, =21-16 5 jets, each 1 foot, = 15 660. VISIBILITY OF LIGHT AT A DISTANCE. 1 candle-power visible at .1 nautical mile. )> >j . . 2 10 (with opera glass) 4 5> 5> 5 Am. Int. Mar. Cong., 1889. 661. MILD STEEL CYLINDERS FOR STORING HIGH PRESSURE GASES. Standard pressure for gas = 120 atmospheres. Solid Drawn. Lap Welded. Ultimate tensile strength Ibs. per sq. inch sectional area of metal 66,000 54,000 Standard sizes : Thickness. External diameter, 4 inches . -f% inch -^ inch }> 5g F2" 2" '> 7 . ^ not made Bursting pressure per sq. inch . 2J tons 2J tons Limit of elasticity per sq. inch of metal .... 45,000 Ibs. 35,000 Ibs. Actual hydraulic test pressure per sq. inch . . . . 1J tons 1J tons ELECTRICAL ENGINEERING. 317 662. CYLINDERS FOR COMPRESSED GAS. P = internal bursting pressure tons per sq. inch. d = internal diameter of cylinder in inches. t = thickness of sides of cylinder in inches. x = percentage of extension on the material at the stress /(say 20 per cent, on 10 inches). / = maximum stress on the material in tons per sq. inch (say 32 tons). r_ <'+* Prof. Goodman. 318 HANDBOOK FOE MECHANICAL ENGINEERS. SECTION XIV. SUNDKY NOTES AND TABLES. 663. MATHEMATICAL CONCEPTS. In ARITHMETIC we deal with number, and by inference with magnitude or quantity. In GEOMETRY we add the ideas of space and direction. In STATICS we add to the foregoing the idea of pressure, and in DYNAMICS we add force and motion. 664. LINEAL MEASURE. 7 '92 inches . . . . = 1 link. 12 inches . . . . = 1 foot. 3 feet . . . . = 1 yard. 6 feet =1 fathom. 25 links, or 5J yards . . . = 1 rod or pole. 100 links, or 66 feet, or 4 poles . = 1 chain (Gunter's). 40 poles, or 10 chains . = 1 furlong. 320 poles, or 80 chains, or 8 furlongs . . , . = 1 mile. 6080 27 feet . . . . = 1 nautical mile. 6080 feet per hour . , . =1 Admiralty knot. 665. SQUARE MEASURE. 144 sq. inches . . . = 1 sq. foot. 9 sq. feet = 1 sq. yard. 625 sq. links, or 30J sq. yards . = 1 perch. 40 perches, or 2 sq. chains . = 1 rood. 100,000 sq. links, 160 perches, 10 sq. chains, or 4 roods . = 1 acre. SUNDRY NOTES AND TABLES. 319 43,560 sq. feet, or 4840 sq. yards = 1 acre. 640 acres = 1 sq. mile. 666. CUBE MEASURE. 1728 cubic inches . . = 1 cubic foot. 27 cubic feet . . . . = 1 cubic yard. 667. MATHEMATICAL SIGNS. -f- Plus, or add. Minus, or subtract. X Multiply by. -4- Divide by. = Is equal to. < Less than. > Greater than, cc Varies as. oo Infinity. .-. Therefore. . Since. Plus minus, i.e. either plus or minus, according to circumstances. 2 Sigma, the sum, or " summation of the products of." TT Pi, the ratio of circumference to diameter. Theta, angle of incidence. JJL Mu, coefficient of friction. t 1570 3-988 6-28 9 tt 1398 3-551 5-592 10 1 1250 3-175 5- 11 1113 2-827 4-452 12 0991 2-517 3-964 13 ti 0882 2-240 3-528 14 0785 1-994 3-14 15 0699 1-775 2-796 16 yV 0625 1-587 2-50 17 0556 1-412 2-224 18 tt 0495 1-257 1-98 19 M 0440 1-118 1-76 20 it 0392 996 1-568 21 0349 886 1-396 22 'h 03125 794 1-25 23 02782 707 1-1128 24 ft 02476 629 9904 25 02204 560 8816 26 tt 01961 498 -7844 27 tt 01745 4432 698 28 '-h 015625 3969 625 29 0139 3531 556 30 0123 3124 492 31 0110 2794 440 32 0098 2489 392 33 0087 2210 348 34 0077 1956 300 35 0069 1753 276 36 0061 1549 244 37 0054 1371 216 38 0048 1219 192 39 0043 1092 172 40 05386 0980 1544 SUNDRY NOTES AND TABLES. 335 697. IMPERIAL STANDARD WIRE GAUGE. Table of sizes, weights, lengths and breaking strains of iron wire under the Imperial Standard Wire Gauge issued by the Iron and Steel Wire Manufacturers' Association. (In force from March 1st, 1884.) Size on Wire Gauge. Diameter. Sectional Area in sq. inches. Weight of Length of cwt. Breaking Strain. Inch. Milli- metres. 100 yards. Mile. An- nealed. Bright. Ib. Ib. yards Ib. Ib. 7/0 0-500 12-7 0-1963 193-4 3404 58 10470 15700 6/0 0-464 11-8 0-1691 166-5 2930 67 9017 13525 5/0 0-432 11 0-1466 144-4 2541 78 7814 11725 4/0 0-400 10-2 0-1257 123-8 2179 91 6702 10052 3/0 0-372 9-4 0-1087 107-1 1885 105 5796 8694 2/0 0-348 8-8 0-0951 93-7 1649 120 5072 7608 1/0 0-324 8-2 0-0824 81-2 1429 138 4397 6595 1 0-300 7-6 0-0707 69-6 1225 161 3770 5655 2 0-276 7 0-0598 58-9 1037 190 3190 4785 3 0-252 6-4 0-0499 49-1 864 228 2660 3990 4 0-232 5-9 0-0423 41-6 732 269 2254 3381 5 0-212 5-4 0-0365 34-8 612 322 1883 2824 6 0-192 4-9 0-0290 28-5 502 393 1544 2316 7 0-176 4-5 0-0243 24 422 467 1298 1946 . 8 0-160 4-1 0-0201 19-8 348 566 1072 1608 V 9 0-144 3-7 0-0163 16 282 700 869 1303 10 0-128 3-3 0-0129 12-7 223 882 687 1030 11 0-116 3 0-0106 10-4 183 1077 564 845 12 0-104 2-6 0-0085 8-4 148 1333 454 680 13 0-092 2-3 0-0066 6-5 114 1723 355 532 14 0-080 2 0-0050 5 88 2240 268 402 15 0-072 1-8 0-0041 4 70 2800 218 326 16 0-064 1-6 0-0032 3-2 56 3500 172 257 17 0-056 1-4 0-0025 2-4 42 4667 131 197 18 0-048 1-2 0-0018 1-8 32 6222 97 145 19 0-040 1 0-0013 1-2 21 9333 67 100 20 0-036 0-9 o-ooio 1 18 11200 55 82 1 mil = inch. 336 HANDBOOK FOE MECHANICAL ENGINEER?. 698. AREAS OF CIRCLES, ADVANCING BY EIGHTHS. Diam. Areas. o '* 'I 'I '* 'I 'I '* o 0122 0490 1101 1963 3068 44171 -6013 1 7854 9940 1-227 1-485 1-767 2-074 2-405 2-761 2 3-142 3-546 3-976 4-430 4-909 5-412 5-939 6-492 3 7-069 7-670 8-296 8-946 9-621 10-32 11-04 11-79 4 12-57 13-36 14-19 15-03 15-90 16-80 17-72 18-66 5 19-63 20-63 21-65 22-69 23-76 24-85 25-97 27-11 6 28-27 29-46 30-68 31-92 33-18 34-47 3.V78 37-12 7 38-48 39-87 41-28 42-72 44-18 45-66 47-17 48-71 8 50-26 51-85 53-46 55-09 56-74 58-43 60-13 61-86 9 63-62 65-40 67-20 69-03 70-88 72-76 74-66 76-59 10 78-54 80-52 82-52 84-54 86-59 88-66 90-76 92-89 11 95-03 97-21 99-40 101-6 103-9 106-1 108-4 110-8 12 113-1 115-5 117-9 120-3 122-7 125-2 127-7 130-2 13 132-7 135-3 137-9 140-5 143-1 145-8 148-5 151-2 14 153-9 156-7 159-5 162-3 165-1 168-0 170-9 173-8 15 176-7 179-7 182-7 185-7 188-7 191-7 194-8 197-9 16 201-1 204-2 207-4 210-6 213-8 217-1 220-4 223-7 17 227-0 230-3 233-7 237-1 240-5 244-0 247-4 250-9 18 254-5 2f>8-0 261-6 265-2 268-8 272-4 276-1 279-8 19 283-5 287-3 291-0 294-8 298-6 302-5 306-4 310-2 20 314-2 318-1 322-1 326-1 330-1 334-1 338-2 342-3 21 346-4 350-5 354-7 358-8 363-1 367-3 371-5 375-8 22 380-1 384-5 388-8 393-2 397-6 402-0 406-5 411-0 23 415-5 420-0 424-6 429-1 433-7 438-4 443-0 447-7 24 452-4 457-1 461-9 466-6 471-4 476-3 481-1 486-0 25 490-9 495-8 500-7 505-7 510-7 515-7 520-8 525-8 26 530-9 536-0 541-2 546-4 551-5 556-8 562-0 567-3 27 572-6 577-9 583-2 58* -6 594-0 599-4 604-8 610-3 28 615-8 621-3 626-8 632-4 637-9 643-6 649-2 654-8 29 660-5 666-2 672-0 677-7 683-5 689-3 695-1 701-0 30 706-9 712-8 718-7 724-6 730-6 736-6 742-6 748-7 31 754-8 760-9 767-0 773-1 779-3 785-5 791-7 798-0 32 804-2 810-5 816-9 823-2 829-6 836-0 842-4 848-8 33 855-3 861-8 868-3 874-8 881-4 888-0 894-6 901-3 34 907-9 914-6 921-3 928-1 934-8 941-6 948-4 955-3 35 962-1 969-0 975-9 982-8 989-8 996-8 1003-8 1010-8 36 1017-9 1025-0 1032-1 1039-2 1046-4 1053 5 1060-7 1068-0 37 1075-2 1082-5 1089-8 1097-1 1104-5 1111-8 1119-2 1126-7 38 1134-1 1141-6 1149-1 1156-6 1164-2 1171-7 1179-3 1186-9 39 1194-6 1202-3 1210-0 1217-7 1225-4 12H3-2 1241-0 1248-8 40 1256-6 1264-5 1272-4 1280-3 1288-3 1296-2 1304-2 1312-2 SUNDKY NOTES AND TABLES. 337 699. SQUARE BOOTS AND CUBE ROOTS. No. Squnre Hoots. Cube Roots. No. Square Roots. Cube Roots. No. Square Roots. Cube Roots. 1 1-0000 1 0000 41 6-4031 3-4482 81 9-0000 4-3267 2 1-4142 1-2599 42 6-4807 3-4760 82 9-0553 4-3444 3 1-7320 1-4122 43 6-5574 3-5033 83 9-1*104 4-3620 4 2-0000 1-5874 44 6-6332 3 5303 84 9-1651 4-3795 5 2-2360 1-7099 45 6-70S2 3-5568 85 9-2195 4-3968 6 2-4491 1-8171 46 6-7823 3-5830 86 9-2736 4-4140 7 2-6457 1-9129 47 6-8556 3-6088 87 9-3273 4-4310 8 2-8284 2-0000 48 6 ' 9282 3-6342 88 9-3808 4-4479 9 3-0000 2-0800 49 7-0000 3-6593 89 9-4339 4-4647 10 3-1622 2-1544 50 7-0710 3-6840 90 9-4868 4-4814 11 3-3166 2-2239 51 7-1414 3-7084 91 9-5393 4-4979 12 3-4641 2-2894 52 7-2111 3-7325 92 9-5916 4-5143 13 3-60.i5 2-3513 53 7-2801 3-7562 93 9-6436 4-5306 14 3-7416 2-4101 54 7-3484 3-7797 94 9-6953 4-5468 15 3-8729 2-4G62 55 7-4161 3-8029 95 9-7467 4-5629 16 4-0000 2-5198 56 7-4833 3-8258 96 9-7979 4-5788 17 4-1231 2-5712 57 7-5498 3-8485 97 9-8488 4-5947 18 4-242tJ 2-6207 58 7-6157 3-8708 98 9-8994 4-6104 19 4-3588 2-6684 59 7-6811 3-8929 99 9-9498 4-6260 20 4-4721 2-7144 60 7-7459 3-9148 100 10-0000 4-6415 21 4-5825 2-7589 61 7-8102 3-9364 101 10-0498 4-6570 22 4-6904 2-8020 62 7-8740 3-9578 102 10-0995 4-6723 23 4-7958 2-8438 63 7-9372 3-9790 103 10-1488 4-6875 24 4-8989 2-8844 64 8-0000 4-0000 104 10-1980 4-7026 25 5-0000 2-9240 65 8-0622 4-0207 105 10-2469 4-7176 26 5-0990 2-9624 66 8-1240 4-0412 106 10-2956 4-7326 27 5-1961 3-0000 67 8-1853 4-0615 107 10-3440 4-7474 28 5-2915 3-0365 68 8-2462 4-0816 108 10-3923 4-7622 29 5-3851 3-0723 69 8-3066 4-1015 109 10-4403 4-7768 30 5-4772 3-1072 70 8-3666 4-1212 110 10-4880 4-7914 31 5-5677 3-1413 71 8-4261 4-1408 111 10-5356 4-8058 32 5-6568 3-1748 72 8-4852 4-1601 112 10-5830 4-8202 33 5-7445 3 2075 73 8-5440 4-1793 113 10-6301 4-8345 34 5-8309 3-2396 74 8-6023 4-1983 114 10-6770 4-8488 35 5-9160 3-2710 75 8-6602 4-2171 115 10-7238 4-8629 36 6-0000 3-3019 76 8-7177 4-2358 116 10-7703 4-8769 37 6-0827 3-8322 77 8-7749 4-2543 117 10-8166 4-8909 38 6-1644 3-3819 78 8-8317 4-2726 118 10-8627 4-9048 39 6-2449 3-3912 79 8-8881 4-2908 119 10-9087 4-9186 40 6-3245 3-4199 80 8-9442 4-3088 120 10-9544 4-9324 338 HANDBOOK FOR MECHANICAL ENGINEERS. 700. DECIMAL APPROXIMATIONS FOR KAPID CACLULATIONS. Feet . X 00019 = miles. ,, . . . X 1-5 = links. Yards . X 0006 miles. Links . X 22 = yards. ,, ... X 66 = feet. Sq. inches . X 007 = sq. feet. Sq. feet X 111 = sq. yards. Sq. yards X 00021 = acres. Acres . X 4840 = sq. yards. Circular inches X 0055 = sq. feet. j X 7854 = sq. inches. Cylindrical inches X 0005 = cubic feet. > j> X 0028 = gallons. feet . X 0291 = cubic yards. J> 55 X 4-895 = gallons. Cubic inches X 00058 = cubic feet. feet . X 04 = cubic yards. X 6-232 = gallons. J> JS X 779 = bushels. inches X 00045 = 5) J) * X 263 = Ibs. cast iron. X 282 = Ibs. wrought iron. J ) X 283 = Ibs. steel. Bushels X 1-284 cubic feet. Gallons X 1605 )> APPENDICES z 2 341 APPENDIX I. Session 1896-97. SYLLABUS OF CITY AND GUILDS OF LONDON TECHNICAL INSTITUTE IN (11) Gas Manufacture. (12) Iron and Steel Manufacture. (38) Telegraphy and Telephony. (39) Electric Lighting and Power Transmission. (4-1) Metal Plate Work. (46) Mechanical Engineering. (68) Manual Training Metal Work. 11. GAS MANUFACTURE. I. Syllabus. The Examination will include questions founded on such subjects as the following : OKDINARY GRADE. 1. The construction of a retort or oven best adapted for the destructive distillation of coal. 2. The setting of retorts, and construction of retort furnaces. 3. The effects of temperature in modifying the quantity and quality of the gas produced. 4. The description and arrangement of apparatus employed for the conveyance of the gas immediately upon its leaving the retorts. 5. The description of apparatus best adaptedffor cooling the gas. 6. The most suitable condition of the gas for effective purification. 7. A description of the various instruments used in gas-works for ascertaining and recording pressure and exhaust. 8. The laying of mains and service pipes. 9. The construction of gas meters. 10. The fixing of meters and the fitting up of premises for the supply of gas. 11. A description of the various kinds of gas burners in general use. 12. The use of an exhauster. 13. The methods employed for controlling pressure at the works, so as to secure an adequate supply of gas at the various points of consump- tion, with a due regard for economical effect. 14. The simplest methods of ascertaining the purity and illuminating power of gas. 342 HANDBOOK FOE MECHANICAL ENGINEERS. 15. A description of the materials and methods employed for the purification of gas. 16. Influence of temperature and atmospheric pressure upon the volume of gas. 17. A description of the various tests employed for determining the values of ammoniacal liquor and spent oxide. HONOUBS GRADE. In the Honours Examination more difficult questions will be set in the above subjects, and in addition a knowledge will be required of : 1. The characteristic properties of the various kinds of coal, and their value for gas-making purposes. 2. The effects of temperature upon the production of residuals. 3. The chemical composition of coal gas. 4. The chemistry of purification. 5. Gas analysis. 6. The development of illuminating power. 7. The practice of photometry. 8. Labour saving appliances in the retort house, and the working of retorts. 9. The construction of gasholders, purifiers and other gas apparatus. 10. The working up of ammoniacal liquor. 11. The principles of combustion, and their application to the working of retort furnaces. 12. Carburetted water gas. 13. The enrichment of coal gas by means of oil, &c. II. Full Technological Certificate. A Provisional Certificate will be granted on the results of the above Examination. For the full Technological Certificate in the Ordinary Grade, the candidate who is not otherwise qualified (see Rules 40-1) will also be required to have passed the Science and Art Department's Examination in the Elementary Stage at least ; and for the full Certificate in the Honours Grade, in the Advanced Stage at least in two of the following Science subjects : II. Machine Construction and Drawing. VII. Applied Mechanics. VIII. Light and Heat. XI. Organic Chemistry. XII. Geology. XIX. Metallurgy. XXII. Steam. X. Inorganic Chemistry. III. Works of Reference. Treatise on the Science and Practice of the Manufacture and Distribution of Coal Gas (King, 11 Bolt Court, E.C.); Newbigging's Handbook for Gas Engineers and Managers (King) ; Richards on Gas Works (Spon) ; Dibdin's Practical Photometry (King) ; Thorpe's Quantitative Analysis (Longmans) ; Thorpe's Dictionary of Applied Chemistry, article on Gas (Longmans) ; Cripps' The Guide Framing of Gasholders (King) ; (The Chemistry of Gas Manufacture, by W. J. A. Butterfield (Griffin); The Journal of Gaslighting, with special reference to Lecture on Gas Manufacture by C. Hunt, vol. 51, and APPENDIX I. 343 the articles on Coal Gas, its Manufacture, Distribution and Consump- tion, vols. 59,60,61 and 62; Gas Engineers' Laboratory Handbook by G. Hornby ; Gas Manufacture, by J. Hornby (Bell and Sons). Transac- tions of the Incorporated Gas Institute ; Transactions of the Incorporated Institution of Gas Engineers. Articles on Coal Gas, by L. T. Wright, in Thorpe's Dictionary of Applied Chemistry (Longmans). 12. IRON AND STEEL MANUFACTURE.' I. Syllabus. The Ordinary Grade is limited to the portio is of the Syllabus enclosed within brackets thus [ ]. The Honours Grade includes the whole Syllabus. The Examination will include questions founded or. such subjects as the following : 1. [Composition and general characters of the chief iron ores. Pre- paration of raw ores for smelting ; changes in composition thereby produced.] Mechanical preparation of iron ores. Magnetic concentration. 2. [Construction and mode of working of blast furnaces, and subsidiary appliances.] 3. [Nature of fluxes requisite under various conditions. Composition of slags. Utilisation of blast furnace cinder, and of forge and mill cinder in the blast-furnace.] 4. Hot and cold blast ; effects of these and of variations in amount of fuel and flux, and in their nature, on the production and character of the iron made. 5. [Characters of pig iron from various kinds of ore ; effects of foreign elements on these characters.] Characters and methods of preparation of spiegeleisen, ferro-manganese, ferro-chrome, and other alloys of iron. 6. [General chemical and physical distinctions between pig iron, wrought iron and steel.] Modern classification of iron and steel. Phy- sical properties of iron and steel. 7. Methods of casting iron and steel. Foundry appliances and operations. Furnaces, crucibles and moulds, &c., requisite for large steel castings. Malleable iron castings ; chilled castings. 8. [Conversion of pig iron into malleable iron in open hearths ; refin- ing, puddling and boiling ; fettling, and its uses ; hand and machine puddling. Machinery and appliances requisite, such as helves, hammers, squeezers, rolls, &c.] and hydraulic forging machinery, steam hammers, rolling mills, and their respective advantages and disadvantages. Manu- facture of bars, plates, rods, rails, tyres, hoops, wire, cold rolled shafting, &c. 9. [Conversion of malleable iron into steel. Blister, shear and cast steel. The effects of the presence of carbon, silicon, phosphorus, sulphur and manganese.] 10. [Conversion of pig iron into steel. Puddled steel. Acid and basic- Bessemer processes. Acid and basic open hearth processes] and other analogous special processes. 11. [Production of malleable iron or steel direct from the ore. Small blast furnaces. Catalan forge, Wootz, Chenot, Siemens], Husgafvel and other analogous processes. 344 HANDBOOK FOR MECHANICAL ENGINEERS. 12. Machinery and appliances requisite for manufacture of cast steel, Bessemer steel, and other kinds of steel largely used, including steel compressing machinery. 13. The variations occurring in the qualities of different kinds of steel, the causes of these variations, and the methods by which the various sources of imperfection may be best avoided or overcome. 14. [The nature of the physical] and chemical [tests of the qualities of iron and steel, and the effects on these qualities of foreign elements. Comparative strength of iron and steel.] 15. [Hardening and tempering of steel, including the use of oil, water and cold surfaces; precautions to be used in reheating large masses of steel, to avoid fracture ] General principles involved. 16. [Case-hardening.] 17. [Welding of iron and steel. Conditions requisite to produce good welds.] 18. [General nature of the leading chemical and physical changes occurring during the smelting of pig iron, its conversion into malleable iron, and the production of steel of various kinds.] 19. Machinery for cutting, shaping and working wrought iron. 20. Preparation of tin and tern plates, and of galvanised iron sheets, plain and corrugated. 21. Methods of analyses relating to iron and iron ores. II. Full Technological Certificate. A Provisional Certificate will be granted on the results of the above Examination. For the full Technological Certificate in the Ordinary Grade, the candidate who is not otherwise qualified (see Rules 40-1) will also be required to have passed the Science and Art Department's Examination in the Elementary Stage at least; and for the full Certificate in the Honours Grade, in the Advanced Stage at least in two of the following Science subjects : II. Machine Construction and Drawing. VI. Theoretical Mechanics. VII. Applied Mechanics. X. Inorganic Chemistry. XIX. Metallurgy. III. Works of Reference. In addition to the smaller text-books on the metallurgy of iron and steel, students may consult Percy's Iron and Steel ; Sir L. Bell's Principles of the Manufacture of Iron and Steel ; Turner's Metallurgy of Iron ; and Howe's Steel ; also the article Iron in the Encyclopaedia Britannica, and should especially refer to the Journal of the Iron and Steel Institute for accounts of new processes and inventions, and experimental researches and trials, &c., published since the formation of the Institute, whereby much valuable practical informa- tion may be obtained. Much valuable information may also be gained from the Transactions of the Institute of Civil Engineers and the American Institute of Mining Engineers. Students who read German will find the works of Dr. Wedding and Professor Ledebur of great assistance. APPENDIX I. 345 38. TELEGRAPHY AND TELEPHONY. I. Syllabus. The Examination will include questions founded on such subjects as the following : ORDINARY GRADE. 1. The fundamental principles of electricity in their application to the Electrical Engineering industries. 2. Units of Measurement, Standards of resistance, their practical construction and adjustment ; electromotive force and capacity ; effects of temperature variation. 3. Galvanometers principles and manufacture of (a) absolute, (&) sensitive, (c) dead beat, (d) astatic, (e) differential. Shunts, ordinary and constant resistance. 4. Resistance coils construction of ; gauge and kind of wire for; methods of winding and insulating. 5. Condensers construction and testing of. 6. Instruments necessary for the equipment of an electrical testing room (a) for land telegraph lines, (&) for cables ; methods of using the apparatus in the simpler forms of testing ; apparatus required by linemen. 7. Electrical testing as applied to the inspection of apparatus and to the detection and removal of faults. 8. Essential qualities of iron and steel for temporary and permanent magnets respectively; methods of making permanent magnets ; treatment of iron for electro-magnets ; simple calculations as to the effective power of a permanent mngnet or an electro-magnet. 9. The construction of telegraph, and telephone lines, overhead and underground. 10. The construction of submarine cables and the simpler of the phenomena connected therewith. 11. The simpler systems of telegraphy worked by hand, including the double current duplex. 12. Batteries used in telegraphy and telephony ; principles, action and construction ; methods of grouping ; universal battery working ; applica- tion of secondary batteries to universal working. 13. The principles involved in the electrical transmission of sound and speech ; the various systems of telephony and the instruments employed therein, including receivers, transmitters, call bells, and exchange switch- boards. 14. Faults in land and submarine lines ; their nature, and the general principles of localisation. 15. Nature and methods of preventing disturbances and damage by earth currents and lightning. 16. Testing of materials employed in the construction of lines and apparatus. HONOURS GRADE. Candidates for Honours must have previously passed in the Ordinary Grade. 346 HANDBOOK FOB MECHANICAL ENGINEERS. In the Honours Examination, which may be either in I. Telegraphy, or, II. Telephony, more difficult questions will be set in the subjects of the Oidinary Grade, and in addition a knowledge will be required of: SECTION I. TELEGRAPHY. 1. The systems of high speed, quadruplex, multiplex and type-printing telegraphs actually in use in Great Britain. 2. The manufacture, laying, testing, working and repairing of sub- marine cables. 3. Practical methods for the supply of current, other than by primary batteries. 4. The commercial adaptability of the various systems of telegraphy. 5. The Wheatstone bridge, tangent galvanometers and reflecting galvanometer, in theory and practice. 6. Eepeaters principles and construction of; employment and adjust- ment of, for single and double current, simplex and duplex circuits. 7. Causes limiting the speed of automatic telegraph working, and methods of reducing and increasing them. 8. Making of working drawings for simple telegraph apparatus. 9. Daily and other periodic tests in theory and practice. SECTION II. TELEPHONY. 1. Transmitters and Receivers various forms, construction and special features of; adjustment of materials for. 2. Induction coils object of. Translation from single wire to double wire systems by means of. 3. Methods of working telephones and telegraph instruments simultaneously on the same wire ; theory of. 4. Conditions which limit the distance to which telephonic trans- mission is possible ; use of iron and copper wires. 5. Metallic loop system of working advantages of; inductive disturb- ances and methods of overcoming them ; theory of methods. 6. Call bells magnets and battery bells; magneto calls; construc- tion of. 7. Individual calls for several stations on one circuit theory and practical arrangement of. 8. Exchange switchboard systems for single and for double wires. Multiple switches. 9. Switches, intermediate, &c. 10. Automatic call boxes. 11. Hughes' Induction Balance. II. Full Technological Certificate. A Provisional Certificate will be granted on the results of the above Examination. For the full Technological Certificate in the Ordinary Grade, the candidate who is not otherwise qualified (see Rule 38) will also be required to have passed the Science and Art Department's Examination, in the Elementary Stage at APPENDIX I. 347 least ; and for the full Certificate in the Honours Grade, in the Advanced Stage at least, in two of the following Science subjects : V. Mathematics. VI. Theoretical Mechanics. VII. Applied Mechanics. VIII. Sound, Light and Heat. IX. Magnetism and Klectricity. X. Inorganic Chemistry. III. "Works of Reference. Culley's Handbook of Telegraphy (Longmans); S. P. Thompson's Electricity and Magnetism (Macmillan) ; Fleeming Jenkin's Electricity ( Longman sj ; Ayrton's Practical Elec- tricity (Cassell); Stewart and Gee's Practical Physics (Macmillan); Bottone's Electrical Instrument Making (Whittaker) ; Maycock's First Book of Electricity and Magnetism (Whittaker); Noad's Student's Textbook of Electricity (Crosby Lock wood); Preece and Sivew right's Telegraphy (Longmans) ; Preece and Stubbs* The Telephone (Whittaker) ; Sliugo anil Urooker's Electrical Engineering (Longmtns); Kempe's Handbook of Electrical Testing (Spon) ; Munro and Jamieson's Electrical Rules and TaMes (Griffin); Poole's Practical Telephone Handbook (Whittaker) ; Bell's Telegraphist's Guide (Office of Electricity). 39. ELECTKIC LIGHTING AND POWER TRANSMISSION. With the view of encouraging Artisans to take a complete course of instruction in this subject, an Elementary Examination will be held preliminary to that in the Ordinary Grade. No certificates will be given to candidates on the results of the Preliminary Examination only, but their successes will be notified to the centre at which they were examined. Candidates may take the Ordinary Grade without having passed the Preliminary, or both Examinations may be taken in the same year. Those who pass the Preliminary Examination as well as the Examination in the Ordinary Grade (whether in the same or in a previous year) will not be required to produce a Science and Art Department's Certificate in the subject of Electricity and Magnetism before they are eligible for the full Technological Certificate, and only one Science Certificate will be required. In the Preliminary Examination no questions will be set involving calculations beyond the ordinary rules of arithmetic as applied to such matters as Ohm's Law : nor will any questions be asked concerning the chemical applications of electric currents. Wiremen who are candidates for the Certificate in the Wiremen's Examination will, after passing the Preliminary Examination, be eligible to proceed to the Practical Examination for Wiremen to be held later in the summer. The Preliminary Examination will be held on Monday, May 3rd, from 7 to 10. In the Ordinary Grade questions will be set that presuppose an acquaintance with elementary algebra including quadratic equations, and a knowledge of the simple trigonometrical quantities, sine, cosine, &c. The candidate must be able to plot values in the form of curves. He is strongly recommended to learn the use of the slide-rule, and should bring 348 HANDBOOK FOE MECHANICAL ENGINEERS. one to the Examination, or he may use in calculation a table of four-figure logarithms. Greater accuracy in working out examples than can be obtained by the use of the slide-rule is not required. In marking the answers the Examiners will take note not only of the correctness of the results, but also of the methods used. Simple common-sense methods in which the general accuracy of the work can be tested step by step are to be preferred to the use of long and -complicated formulae. Candidates are expected to be able to make simple 'hand-sketches showing sizes of parts. The Examination in the Ordinary Grade will be held on Tuesday, May 4th, from 7 to 10. In the Honours Grade there are three sections corresponding to the three main branches ot the electrical engineering industry. The candidate must elect for himself in which of the three sections he desires to be examined. The examination will be confined solely to the single section he selects, and any questions may be asked on the subjects contained in this section, such es can be answered by a practical eltctrical engineer who has devoted himself specially to these subjects. In the Honours Grade the candidate may, during the examination, use an Eltctiical Engineering Pocket Book; but if he avail himself of this, he must state the title of the book on his answer paper, and in his answers give references to the pages of the book he has consulted. The Examination in the Honours Grade will be held on Tuesday, May 4th, from 7 to 10. I. Syllabus. The Preliminary Examination will include questions founded on the following subjects : 1. General notions about electro-motive force, current, resistance and the principles of electric circuits, simple and branching. The voltage required to produce any required current in a wire of given resistance. Simple descriptive knowledge of battery cells and of accumulators. 2. The construction and action of electric bells ; the arrangements of battery cells and of circuits for bells. Use of relays. 3. General descriptive knowledge of magnets and electro-magnets. Best methods of winding electro magnet coils for various services. 4. Simple principles and use of electric measuring instruments, ampere-meters, volt-meters, delicate mirror galvanometers, resistance coils. 5. The induction of currents by motion of magnets. Notions about magnetic lines of force. Magneto-generators for electric bells. Simple descriptive knowledge of the common sorts of dynamos and alternators. 6. The induction of currents by action of currents in neighbouring circuits. The effect of iron cores. Simple descriptive knowledge of induction coils and of transformers for alternate currents. 7. Simple principles of electric motors and of electro-magnetic mechanism. The magnetic drag on wires carrying currents. 8. Elementary descriptive knowledge about Glow lamps and Arc lamps, and their arrangement in parallel and in series. The necessary parts of Arc lamps, and their action. 9. The relations between mass, weight and force. Distinction between work and power. Relations between heat and work. Relation between the watt, the kilowatt, and the horse-power. Watt-meters. 10. Systems of wiring houses. Methods of jointing. General know- APPENDIX I. 349 ledge about conducting and insulating materials and their mechanical and electrical properties. Wiring rules. Meaning and calculation of drop. PEACTICAL EXAMINATION FOE WIREMEN. The Practical Examination for Wiremen will be held at different centres, where the necessary arrange uiintrf can be made, and as soon as possible after the Preliminary Written Examination, at a date to be subsequently fixed. Notice of what the Candidates are required to bring with them to the Examination will be given at the time of the Written Examination. The extra fee for this Examination is One Shilling. ORDINARY GRADE. In addition to the subjects for the Preliminary Examination, Candidates for the Ordinary Grade Certificate are expected to be acquainted with the following matters, except the parts contained in brackets [ ]. 1. Comparison between the British units of mechanical measure- ment, and the international units based on the centimetre and the gramme. 2. The laws of Ohm and of Faraday respecting steady currents. Laws of Helmholtz and of Maxwell respecting sudden and periodic currents. Simple 'properties of alternate currents. 3. Electric measuring instruments for the workshop. Wheat- stone's bridge. Standards of resistance, electro-motive force and capacity. 4. Practical ampere-meters, volt-meters and watt-meters. Electro- dynamometeis, current balances, electrostatic volt-meters, hot wire instruments. 5. Magnetic properties of materials, magnetising force, induction and permeability. Hysteresis. [Methods to determine these quantities.] 6. The selenoid and its properties. The electromagnet [and its adaptations to electro-mechanical devices.] 7. Mechanical strength and electric properties of materials. Con- ductivity of metals and alloys, and its change with temperature. Mechanical qualities and resistance of insulating materials, and the influence of temperature. [Testing of insulation resistance. Ohm- meters.] 8. Condensers. Work stored in a condenser. [Dielectric strength of insulating materials and its relation to mechanical strength, incombusti- bility and specific inductive capacity.] 9. fundamental points of magneto-electric induction. Self and mutual induction. [Induction balances. Standards of self-induction.] 10. Outline of the theory of continuous-current dynamos and motors. Characteristic curves. Simple cases of transmission of power. 11. The magnetic circuit as applied to dynamo machines. Types of field magnets and armatures, considered magnetically. 12. The winding of field magnets and armatures. 13. The mechanical features of dynamos and motors as regards strength of parts, heating, durability, ease of repair, construction of brushes, commutators, terminals, &c. 350 HANDBOOK FOE MECHANICAL ENGINEERS. 14. Motor generators, fundamental rules as to winding, speed and output. 15. The electrical and mechanical efficiency of dynamos and motors. [Methods of determining efficiency.] 16. The construction and elementary theory of alternators and trans- formers. [Alternate-current motors.] [17. The efficiency of alternate -current apparatus.] [18. The transmission of power by alternate and polyphase currents.] 19. Practical method of arranging lamps and circuits. 20. Glow lamps and arc lamps, watts per candle. [Photometry, illumination of rooms and open spaces.] 21. Secondary batteries, construction, and maintenance. [22. Supply meters. Meter testing.] 23. Distribution of electrical energy from central stations, direct and transformer systems, continuous and alternating currents, two wire and multiple-wire mains. [24. Central Stations. Load Diagrams. Conduits.] HONOURS GRADE. Candidates for Honours must have previonsly passed in the Ordinary Grade. Candidates will be examined in one of the following Sections: SECTION. I. Electrical Instruments and Eegulating Appliances; their construction, use, &c. ; or, SECTION II. Dynamos, Motors, Accumulators and Transformers ; their construction, use, &c. ; or, SECTION III. Light and Power Distribution, Mains and Central Stations. The candidate for the Honours Grade Examination must elect in which of the three sections he desires to be examined. The examination will be confined solely to the single section he selects, and any questions may be asked on the subjects contained in this section, such as can be answered by a practical Electrical Engineer who has devoted himself specially to these subjects. SECTION I. -ELECTRICAL INSTRUMENTS, &C. More difficult questions will be set in subjects 1 to 10 inclusive, including the subjects contained in brackets, and in addition, a know- ledge will be required of: Galvanometers, sensitive, aperiodic, differential, ballistic. Use of shunts. Calibration of instruments. Measurement of very large and very small resistances. Instruments for alternate currents. Switch- boards ; safety devices ; automatic regulators. Portable instruments for electric and magnetic measurements. Photometry. Supply meters ; meter testing. SECTION II. DYNAMOS, &C. More difficult questions will be set in subjects 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, including those in brackets, and in addition a know- ledge will be required of : APPENDIX I. 351 The designing of dynamos for arc and incandescent lighting, of alternators and transformers; armature winding; armature reaction; heating and sparking of machines ; parallel working of alternators ; the construction of motors for special purposes, and gearing of same. Poly- phase machines. SECTION in. ELECTRIC LIGHT AND POWER. More difficult questions will be set in subjects 4, 9, 12, 13, 14, 17, 18, 19, 20, 21, including those in brackets, and in addition a knowledge will be required of: Electric transmission and distribution of power by continuous and alternating currents, electric railways and tramways, private electric light installations, the electrical equipment of central stations, including arrangement of dynamos, batteries, switchboard and regulating appliances ; overhead and underground mains; safety devices, testing devices, fire office rules ; sizes of the feeders and mains in the two and three wire systems ; use of substations. II. Full Technological Certificate. A Provisional Certificate will be granted on the results of the above Examination. For the full Technological Certificate in the Ordinary Grade, the candidate who is not otherwise qualified (see above and Rules 40-1) will also be required to have passed the Science and Art Department's Examination, in the Elementary Stage at least ; and for the full Certificate in the Honours Grade, in the Advanced Stage at least, in two of the following Science subjects : II. Machine Construction and Drawing. V. Mathematics. VI. Theoretical Mechanics. VII. Applied Mechanics. VIII. Sound, Light and Heat. IX. Magnetism and Electricity. III. Works of Reference. Absolute Measurements in Elec- tricity and Magnetism, by A. Gray (Macmillan) ; Practical Electricity, Ayrton (Cassell) ; Dynamo-Electric Machinery, by S. P. Thompson (Spon) ; Alternate Current Transformers, by K. W. Weekes (Biggs) ; Electric Lamps, by J. A. Fleming (Biggs); The Incandescent Lamp, by G. S. Ram (Electrician Office) ; Theory of Alternating Currents, by Bedell and Crehore ; Magnetic Induction, by J. A. Ewing (Electrician Office) ; Electric Transmission of Energy, by Kapp (Whittaker) ; Elec- trical Engineering, by Slingo and Brooker (Longman) ; The Dynamo, by Hawkins and Wallis (Whittaker); Dynamo Machinery, by J. Hopkin- son (Whittaker) : Electric Light and Power, by A. F. Guy (Biggs) ; Photometry, by A. Palaz ; Transformers, by G. Kapp (Whittaker, 1895) ; The Alternate Current Transformer, by J. A. Fleming (Electrician Office); The Electromagnet, by S. P. Thompson (Spon); Electric Light Cables and the Distribution of Electricity, by S. A. Russell (Whittaker) ; The Electric Railway, by Crosby and Bell (Whittaker) ; Electric Traction, by A. Reckenzaun (Biggs); Polyphase Currents, by S. P. Thompson (Spon). The current electrical periodicals. The Journal of the Institution of Electrical Engineers. 352 HANDBOOK FOB MECHANICAL ENGINEERS. 41. METAL PLATE WORK. 1. Syllabus. The Examination will include questions founded on such subjects as the following : ORDINARY GRADE. 1. Calculations for dimensions of vessels to hold given quantities ; sizes of main and branch pipes for stoves and ventilating purposes. Weights, sizes and gauges of sheets, wire, rivets, &c. 2. The setting-out of patterns for elbows formed by circular, oval and oblong pipes meeting at any angle ; T-elbovvs, tapering Y-pieces, bends, &c. Patterns for round, oval, oblong and other simple forms of equal tapering bodies used by boilermakers, copperbmiths, iron, zinc and tin- plate workers. 3. Shape of notches, and allowances for lap, wire, &c., for seams of various kinds. Methods of joining sheet-metal by (a) soldering, (b) riveting, and (c) grooving. 4. Solders and soldering. Composition and uses of hard and soft solders. Theory and practice of soldering, brazing, autogenous soldering, fluxes, useful alloys, &c. 5. Annealing, stretching, raising, planishing and general principles of working up sheet copper, brass, zinc, iron (plain and coated). 6. The various hand and machine tools used in metal plate work. Comparison of hand and machine tools for special work. It is important that candidates should acquire facility in the pro- duction of clear and neat working drawings, and give answers which show their practical connection with some branch of metal plate work. HONOURS GRADE. Candidates for Honours must liave passed in a previous year in the Ordinary Grade. 1. WRITTEN EXAMINATION. In the written Examination more diffi- cult questions will be set in some of the above subjects, and in addition candidates will be required to show a knowledge of : (1) The physical and chemical properties of iron, lead, antimony, aluminium, bismuth, mercury, tin, zinc, copper, nickel and silver. (2) Alloys. The composition and properties of brasses, bronzes, tin- plate, galvanised iron, &c. Tinning processes. (3) Fuel: composition and physical character of various kinds, and the modes of applying them in metal plate work. (4) Patterns and working drawings to scale of a more advanced character will be required. 2. PRACTICAL WORK. Each candidate will also be required to execute in suitable material, in the year preceding the Examination, an original piece of work, and to forward the same to London (carriage paid) a week prior to the date of the Written Examination. The specimen of work must be accompanied by a working drawing, with particulars of the quan- tity and nature of the materials used, and must be of such dimensions APPENDIX I. 353 that it can fit into a box not larger than two cubic feet. A certificate signed by the candidate's employer, or by the class teacher and a member of the School Committee, stating that the work has been executed by the candidate himself, without assistance, must be forwarded with the specimen. The work should be such as will show the candidate's skill in the more important branches of metal work in which he is engaged. II. FULL TECHNOLOGICAL CERTIFICATE. A Provisional Certificate will be granted on the results of the above Examination. For the full Technological Certificate in the Ordinary Grade, the candidate who is not otherwise qualified (see Rules 40-1) will also be required to have passed the Science and Art Department's Examination in the Elementary Stage at least ; and for the full Certificate in the Honours Grade in the Advanced Stage at least, in two of the following Science subjects : I. Practical, Plane and Solid Geometry. II. Machine Construction and Drawing. VI. Theoretical Mechanics. VII. Applied Mechanics. X. Inorganic Chemistry. XIX. Metallurgy. Certificates showing that the candidate has passed the Elementary Examination of the Science and Art Department in Geometrical Drawing, as well as in Freehand or Model Drawing, will be accepted in lieu of one of the above Science subjects for the full Technological Certificate in either grade of the Examination. III. WORKS OF REFERENCE : Byrne, Practical Metal- Worker's Assist- ant (Philadelphia) ; Miller's Chemistry, vol. ii. ; Bloxam and Huntington, Metals (Longman, Green & Co.) ; Davidson, Drawing for Metal Plate Workers (Cassell & Co.); Metal Plate Work, C. T. Millis (Spon). 46. MECHANICAL ENGINEERING. ORDINARY GRADE. The Examination in the Ordinary Grade will consist of two parts, which will be held in the same year. To obtain a Certificate or Prize, the candidate must pass in both parts of the Examination in the same year. The fee for the entire examination is Two Shillings. PART I. The Examination in Part I. will be held on Monday, May 3rd, 1897, from 7 till 10. Candidates will be examined in two only of the following three divisions :-. (.4) The modification of velocity and effort by mechanism. Kine- matic chain and elementary machine. Transmission of motion by link- work, belts, toothed gearing and hydraulic connection. Mechanisms derived from the simplest kinematic chains. Velocity and effort curves. Relation of velocity and acceleration curves. 2 A 354 HANDBOOK FOE MECHANICAL ENGINEERS. (B) Elementary relations of stress and strain. The strength of materials to resist tension, compression, shearing, torsion and bending. Application of the rules of the strength of materials to the design of the simpler machine elements. Considerations which determine factors of safety. (C) The theory of the action of the steam engine and boilers so far as it can be dealt with without thermodynamics. Indicator diagrams ; flywheels ; governors ; the simplest forms of steam valves and valve gears. PART II. The Examination in Part II. will be held on Tuesday, May 4th, from 7 till 10. Candidates will be examined in one only of the following four divisions : (A) Machine drawing and designing. In this examination the candidate will be allowed the use of any one pocket book or treatise on machine designing he may choose to bring with him. Exercises will be given in drawing simple machine details and in designing them to suit given conditions. (jB) Pattern making, moulding, founding and brass founding. Timbers used by pattern makers. Wood-working tools. Building up patterns. Core prints and core boxes. Moulding sand and loam. Moulding tools. Systems of moulding, Parting surfaces. Gates, vents and ladles. Foundry mixtures. Cupolas and crucible furnaces. Brass and gun-metal mixtures. (0) Chipping, filing, turning, drilling, shaping and milling. The grinding and tempering of tools. Cutting speeds. Calculation of change wheels and pulley sizes. Use of measuring instruments, gauges and scribing blocks. Use of surface plates, squares and levels. Construction and use of vices, machine vices and the simpler chucks. Simple engin- eering workshop appliances. (-D) Smithing, forging, riveted and boiler work. Construction of forge . Description of forging and smithing tools. Forms of welded joints. Fluxes used. Hardening and tempering of tools. Annealing and case- hardening. Machine punching and riveting tools. Arrangement of riveted joints. Methods of dealing with overlapping joints. Templets and methods of setting out riveted work. In Part II. of the examination hand sketches should be used to illustrate the answers ; but no credit will be given for these unless they are fairly well drawn and well proportioned, or unless construction is shown by dotting and sectional shading. fc HONOURS GRADE. Candidates for Honours must have previously passed in the Ordinary Grade. To obtain the certificate in Honours, the Candidate must pass a Written and a Practical Examination, to be taken in the same year. The fee for the Entire Examination (Written and Practical) is Three Shillings and Sixpence. The Written Examination will be held on Tuesday, May 4, from 7 APPENDIX I. 355 1. WRITTEN EXAMINATION. In the Written Examination on the Mechanics of Engineering candidates must select questions from not more than two of the following four divisions : (A) The elasticity and strength of materials, including the more practical and elementary problems in compound stress. Tension, com- pression and torsion. Combined bending and torsion. Combined thrust and bending. Riveted joints and the design of riveted work. Collapse. Behaviour of materials when tested. Ordinary limits of working stress. (5) The theory of the steam engine, including the thermodynamics of the action of steam. The solution of problems relating to the simpler valve gears. Governors and flywheels. The theory of gas engines and hot-air engines. (C) Hydraulics and hydraulic motors. Theory of flow from orifices. Flow in pipes. Water wheels, turbines and pumps. Construction and action of valves. Governors for hydraulic machinery. Hydraulic trans- mission of power. Hydraulic pressure engines. Lifts. (D) Construction of hand and machine tools for engineering work- shops. Lifting and other auxiliary appliances in an engineering work- shop. 2. PRACTICAL EXAMINATION. Candidates will be examined in- one division only, either in (J.) Machine Designing, or (.B) Workshop Practice. (A) Machine Designing. Data for a design in Mechanical Engineer- ing will be given at the time of the written examination. The design to be worked out and drawn, and the drawings and a reasoned description of the design, with a summary of calculations of strength, &c., to be returned not later than May 19th with a certificate from some responsible person, other than the candidate, that it has been done without assistance from any other person. (.B) Workshop Practice. For candidates selecting this branch of practical work, simple castings or forgiugs will be sent with dimensioned sketches of the forms to which they are to be worked, by chipping, filing, turning, or screw-cutting. Candidates may be examined in (a) Fitteis' Work ; (6) Turning ; or (c) Pattern-making ; and it must be stated on the Application Form which section they select. The work to be executed between given dates and returned with a certificate from the shop fore- man * or the class teacher and a member of the School Committee (where the work has been done in a school workshop) that the work has been done without assistance. A candidate may produce, in addition to the exercises set, one piece of work chosen by himself ; but he must state the date when it was executed, and the time occupied. The material for the work will be sent within a week after the written examination, and must be returned, carriage paid, to London not later than May 26th. In the Honours Examination great care should be taken that sketches * It is hoped that masters will co-operate with the Institute by affording facilities to Candidates in Honours for executing the practical test required in their own workshops. In certain cases where there is a technical school pro- vided with the necessary tools and accommodation, the work can be dono in the school workshop. 2 A 2 356 HANDBOOK FOB MECHANICAL ENGINEERS. and drawings are workmanlike and show real knowledge of proportion and construction. Full Technological Certificate. A Provisional Certificate will be granted on the results of the above Examination. For the full Techno- logical Certificate in the Ordinary Grade, the candidate who is not other- wise qualified (see Kules 40-1) will also be required to have passed the Science and Art Department's Examination in the Elementary Stage at least ; and for the full Certificate in the Honours Grade, in the Advanced Stage at least, in one of the following Science subjects : V. Mathematics. X. Inorganic Chemistry. VI. Theoretical Mechanics. | XIX. Metallurgy. Works of Reference. K. H. Smith's Cutting Tools; Hasluck's Metal Turners' Handbook ; Shelley's Workshop Appliances ; Compton's First Lessons in Metal Turning ; Northcott's Lathes and Turning ; Perry's Practical Mechanics ; Northcott's Steam Engine ; Cotterill's Steam Engine ; Ripper's Steam Engine ; Seaton's Manual of Marine Engineering ; Wilson's Steam Boilers ; Robinson's Gas and Petroleum Engines; Unwin's Machine Design; Kennedy's Mechanics of Machinery ; Adams' Handbook for Mechanical Engineers ; Moray and Biggs' Mechani- cal Engineering ; Holmes' Steam Engine ; Article Hydraulics (Ency- clopaedia Britannica, published separately, price 6s.) - ; Marks' Hydraulic Machinery ; Mechanical Engineering, by W. S. Lineham (Chapman & Hall, 10s. 6d. net). 68. MANUAL TRAINING METAL WORK. With the view of certifying to the efficiency of teachers to give instruction in Metal-work, the City and Guilds of London Institute is prepared to issue certificates to qualified teachers of Public Elementary Schools on the following conditions : 1. Candidates must have already passed the Institute's First Year's Examination in Manual Training Woodwork. 2. The candidates will be required to give evidence of having regu- larly attended, during each of two sessions, a course of at least 20 practical metal- working lessons given on separate days, each of not less than two hours' duration, in a school or class registered by, and under an Instructor approved by, the Institute. In order that a class may be registered, it must be under the direction of a Committee of a County or Borough Council, or School Board, or Technical School, or other public body. 3. The candidates will further be required to pass two examinations, one at the end of each year's course, to be conducted by examiners appointed by the Institute, and to pay a fee of ten shillings for each examination. Teachers of Woodwork in Public Elementary Schools (whether Certificated Teachers or not) who give evidence of having satisfactorily taught a class of pupils in Woodwork for a period of not less than one APPENDIX I. 357 year, and who produce a certificate from Her Majesty's Inspector or the Inspector of the Local Authority, to that effect, are eligible under the conditions given in paragraph 2, to sit for 1st Year's Examination and subsequently for the Final Examination in Manual Training Metal- work. Teachers of Metal -work who give evidence of having satisfactorily taught, for a period of two years, a class of pupils in Metal-work at a Public Elementary School, and who produce a certificate from Her Majesty's Inspector to that effect, are eligible without attendance at any class to sit for the 1st Year's Examination in Manual Training Metal- work. FIRST YEAR'S EXAMINATION. The First Year's Examination will consist chiefly of practical exercises in Metal-work, but candidates will also be required to answer in writing a few simple questions, on the tools used and methods employed in working the exercises of the following syllabus, and on the chief properties of the common metals in their relation to workshop processes. The exercises for the practical examination will be such as are included in the following syllabus, and candidates should be able to complete any of the exercises mentioned, but they will be required to pass in two only of the divisions A, B and C, Division A. VICE WORK. The form and use of flat and cross-cut chisels ; flat, round, square and half-round files ; scrapers ; taps, stocks and dies; screw plates; measuring and other tools, including calipers, square, centre punch, scribing and V-blocks, straight-edges and surface plates. Different forms of vices for bench work, and the grinding and keeping in order of the tools used. Chipping, filing and scraping cast iron, wrought iron, steel, brass and gun-metal to simple forms and given dimensions. Cutting keyways and holes from plates or blocks to fit a given gauge, and preparing and fitting taper and headed key, or other piece. Cutting out and filing up a hexagon or octagon gauge from thin plate, filing and preparing a straight-edge. Drilling, tapping and filing to shape, a square or hexagonal nut ; screwing round bar with screw plate and stocks and dies, to fit a given nut. Division B. BENCH WORK. Composition of soft solders; use of copper soldering bit ; composition and use of ordinary fluxes ; soldering simple joints in tin and brass work. The connection of plates and bars, and of joints, with rivets, single and double countersunk, hammered cold. Division C. FORGE WORK. The form and use of the ordinary forge tools, management of fire, precautions to be observed in heating metals, drawing out bars to square and round ends, parallel and taper ; bending iron to simple curves, or to square or circle of given size; jumping up. Forging of simple examples, as headed key, spike nail, &c. ; forging and tempering centre punch, drill and small chipping chisel. Connection of pieces of bar by welding. Case-hardening with prussiate of potash. Annealing. The examination will be held on two days, on Friday, May 21st, and on Saturday, May 22nd, from 10 till 2, or from 2 till 6 each day. Provision for holding the Examinations and arrangements for super- vision must be made by the Committee of each School. Either tools 358 HANDBOOK FOB MECHANICAL ENGINEEKS. must be provided for the Practical Examinations, or the candidates must be required to bring them. Measuring tools (rules, calipers, centre punches, &c.) ought to be brought by candidates. The special material required for the examination will be supplied by the Institute. FINAL EXAMINATION. Candidates for the Final Examination must produce a certificate of having passed the First Year's examination. They will be required to undergo an examination in practical work, and also a written examina- tion and a drawing examination. 1. PRACTICAL WORK. Exercises may be selected from the First Year syllabus A, B and C, only that greater accuracy and finish will be ex- pected; or more difficult exercises of the same character, including examples in brazing, may be set. Candidates will also be required to work exercises requiring a use of the simple lathe and drilling machine to the following syllabus : Form and use of hand tools for turning iron and brass ; centering of work and fixing in lathe ; turning of plain cylindrical rod ; simple taper and collar turning ; use of V centre for drilling ; turning of simple curved pieces to template. Chasing screw threads. Use of slide rest and back gear, and of shifting headstock for taper turning. Methods of screw cutting. Exercises may be set involving forge, vice and lathe work and drilling. 2. WRITTEN EXAMINATION. Forms and angles of cutting edges of tools as used for vice and bench work, and for lathes and drilling machines. Construction and use of simple lathes and drilling machines, including the use of change wheels for screw cutting. The working of steam engines and gas engines, and the arrangement of shafting, pulleys and belting, with some knowledge of speed and methods of running, so far as relates t to their use for driving purposes in school workshops. The fitting and equipment of a school workshop and arrangement of lessons. Workshop methods and properties of materials, so far as relating to the exercises of the practical examination. 3. DRAWING EXAMINATION. Making freehand dimensioned sketches in plan and elevation of hand and machine tools, and other workshop fittings, and of exercises for practical work. Making working drawings to scale, in pencil, from dimensioned sketches. Candidates must pass in each of the three subjects 1, 2 and 3, in order to obtain a certificate. The practical work will receive four times the marks of either of the other subjects. Certificates will be granted on the result of each examination, but the Teacher's certificate will be given to those candidates only who have passed the Final Examination. Provided the necessary arrangements can be made, the Examinations will be held in London and in the Provinces, in the workshops of the Schools where the instruction has been given. The Examinations for the Final Certificate will be held on the following dates : APPENDIX I. 359 Practical Work. Friday, May 28th, and Saturday, May 29th, from 10 till 2, or from 2 till 6. Drawing Examination. Wednesday, June 2nd, 7 till 10. Written Examination. Thursday, June 3rd, 7 till 10. Works of Reference. Principles of Fitting (Whittaker and Co.) ; Metal Turning (Whittaker and Co.) ; Workshop Appliances, by C. P. B. Shelley (Longmans). 360 HANDBOOK FOR MECHANICAL ENGINEERS. APPENDIX II. Session 1896-97. SYLLABUS OF GOVERNMENT DEPARTMENT OP SCIENCE AND ART IN (II.) Machine Construction and Drawing. (VI.) Theoretical Mechanics. (VII.) Applied Mechanics. (XXII.) Steam. Subject II. MACHINE CONSTKUCTION AND DEAWING. This subject includes a knowledge of the form of the parts of machines, the physical characteristics of the materials used in machine construction, the various workshop processes employed in giving the materials the required shape and size, the magnitude of the straining actions to which they are exposed, and the methods of estimating the dimensions necessary to withstand those straining actions. In addition to this knowledge, the possession of which may be shown by means of written descriptions, freehand sketches and calculations, a candidate for examination in this subject will be required to be able to draw neatly, to scale, the whole or part of a machine either from dimen- sioned sketches, which are provided, or from his own design. IN THE ELEMENTARY STAGE. A candidate will be required to draw in simple or orthographic projec- tion neatly in pencil to a given scale, two or more views (sectional or outside), of a simple portion of a machine in common use. The sketches from which the drawings are to be produced will be given. They will in general be incomplete, and be drawn purposely somewhat out of propor- tion, and the candidate will be required to set off, correctly to scale, dimensions, some of which are given on the view he is drawing, the remainder being obtained from the other views. He will be expected to add parts which are omitted from some of the sketches, but shown in shape and size in others. He will further be expected to draw from his own knowledge the fastenings which are suitable for connecting together the machine parts which are the subject of the example, and, in sectional views, to draw lines neatly by freehand to indicate parts cut by the planes of section, taking care to slope the lines on all the parts of the same piece in the same direction, and of contiguous pieces in directions differing from one another. APPENDIX II. 361 In some simple cases an additional new view (outside or sectional), which is not shown in the sketches will be required to be drawn, and details which are shown in separate detached sketches will be required to be inserted in their proper places in the general drawing. The various views required must be placed in position so as to project from one another in order to show that the candidate appreciates the fact that he is producing a representation of a solid piece of machinery and not merely copying a sketch. No credit whatever will be given unless the candidate shows some knowledge of projection by drawing two views of at least one subject in their proper relative situations. Teachers are enjoined not to rely too much on drawings in giving instruction to their classes, but to make use also of actual simple machine parts or models of them. It is desirable that centre lines should be shown distinctly, and the parts of other lines continued too far, and not needed in the finished drawing, should be rubbed out. In order to save time during the examination the drawings should not be inked in, nor should the figured dimensions be inserted. The following list of examples which have been set in previous years will give a general indication of what may be expected and prepared for: Parts of an Engine. Piston. Piston rod end and guide block. Con- necting rod. Crank shaft, Excentric and rod. Valve rod end. Simple form of loaded governors. Parts of a Boiler. Gusset stay. Mud hole door. "Water gauge cock. Simple feed pump. Portions of Machine Tools. Fast headstock and spindle of a lathe. Rest for a hand-tool for a lathe. Jaw of a dog-chuck for a lathe. Quadrant for carrying change wheels for a lathe. Earn of a slotting machine. Parallel jaw vice. Mill Work. Footstep bearing for an upright shaft. Joint for segments of large spur wheel. Bearing for turbine shaft. Wall bracket. General Fittings. Hooke's coupling. Ball bearing for a tricycle. Hydraulic pipe joint. Union joint. Besides making drawings, candidates will be required to answer some of a number of questions on machine construction, and illustrate those answers by sketches. Unless specially instructed to the contrary the sketches should be drawn freehand. The capability of making freehand sketches of parts of machines from memory is of the greatest value to an engineer, and when the sketches are drawn to a tolerable proportion they will be estimated by the examiners at at least as high a value as those drawn more accurately by means of instruments with a much larger expenditure of time. The details of this portion of the subject may be classified as follows : Formation of Parts of Machineslwhich are in Working Contact : Journals of Shafts and Searings. Constructions to facilitate adjust- ment for wear and renewal by cylindrical bushes, cones and brasses, or steps with caps. Methods of preventing end movement by groove and pin, by collars and by simple forms of footstep or pivot bearings. Joint pin. Knuckle joint. Methods of fixing pin rigidly to the fork portion of the joint. Simple forms of lubricators. 362 HANDBOOK FOB MECHANICAL ENGINEERS. Rubbing Surfaces of Sliding Pieces. Method of adjustment for wear as in the slide rest of a lathe or other machine tool. Helical or Screw Motion. Construction of a helical curve. Meaning of the terms pitch and angle of thread. Surfaces suitable for Rolling Contact. Cylinders, frustums of cones and spheres. Surf aces for a Combination of Boiling and Sliding Contact. Elementary information relative to the form of spur and bevil wheels. Belt Gearing. Advantage of a rounded surface. Methods of connect- ing the ends of a belt. Constructions to permit of the Application of the Urging Force and the Working Eesistance to the Moving Parts. Sim pie forms of pistons, plungers and stuffing boxes. Use of leather in hydraulic work. Simple forms of slide, lift and screw down valves, and two-way turn cocks. Methods of Construction to facilitate the Manufacture of Machine Parts : Connections, whereby parts more easily manufactured and more readily renewed when detached, are joined together more or less permanently and rigidly to compose one single piece of a machine. Use of chipping strips. Riveted Joints. Forms of rivets. Junction of plates by single and double riveting in chain and zig-zag with lap and butt joints. Use of angle, tee and channel irons. Bolted Joints. Bolts with various forms of heads and nuts. Studs and screws. Use of washers. The Whitworth and square form of screw threads. Raised threads. Methods of preventing nuts from working loose. Prevention of bolts from turning when screwing up the nut. Forms of spanners. Cotters. Draw of cotter and clearance. Use of gib. Methods of preventing cotters from working loose. Flanged Joints of pipes and cylinders. Methods of making them steam and water tight. Use of a centering ring in a cylinder cover. Union joint for small pipes. Socket joint. Construction of the Frame of a Machine. Methods of securing frames to foundations. Simple forms of pedestals for supporting a shaft, and methods of attachment to the frame or to a bracket. Simple forms of brackets, hangers and wall boxes. Boilers. Elementary knowledge of their construction. The methods of uniting the plates. The strengthening of a boiler by the use of bar and gusset stays. Primary Pieces. Connection of the parts of a shaft. Crank pin to crank arm and arm to shaft. Use of sunk, saddle and feather keys. Methods of withdrawing keys. Box and flange couplings. Connection of the two parts of an excentric sheave, excentric radius, travel of valve. Connection of the parts of sliding pieces. Piston to rod. Rod to cross- head or guide-block, and slide valve to valve rod. Secondary Pieces. Parts of a connecting rod. Construction of an excentric strap and rod. Physical Characteristics of the Common Materials used in Machine Construction. Elementary information as to the relative strength, dura- bility under wear, resistance to corrosion, and capability of being cast or forged of iron, steel, brass and copper. Any question which may be get APPENDIX II. 363 on the strength and proportions of machine parts will be only of a very elementary character. Workshop Processes. Elementary information of the processes by which the desired shape is given to machine parts, including the use of the lathe, the planing, shaping, slotting and drilling machiues. THE ADVANCED STAGE. Will include all that has been detailed for the Elementary Stage. The examples to be drawn to scale will be a piece of machinery of more complicated construction, requiring the candidate to possess more capability of reading dm wings, and the greater part of the drawing required will consist of views not shown, but which will have to be deduced from information given in other views. A greater facility of execution will be expected to be shown by a larger quantity of drawing of a better finish than in the Elementary Stage. The following is a list of examples which have been set in some previous years : Parts of an Engine. Link reversing gear. Kegulator valve. Hydraulic engine. Double-ported slide valve. Parts of a Boiler. Giffard's injector. Safety valve. Double acting pump. Mill Work. Wall fixing with shafts and bevel wheels. Collar bearing for suspended vertical shaft. To answer the questions a more intimate and detailed knowledge of the parts of machines previously enumerated will be required, and of the following in addition : Formation of Parts of Machines which are in Working Contact. Bearings and Journals of Shafts. Methods of completely providing for wear in any direction. Bearings in which the direction of the centre line of the shaft is capable of automatic adjustment. Bearings for work- ing under water ; for very high speeds; for locomotive carriages. Con- struction permitting the use of antifriction soft metal. Rubbing Surfaces of Sliding Pieces. Use of renewable slipper piece with the guide block of an engine. Automatic lubrication of slides. Guide or valve rods. Helical or Screw Motion. Screw and nut for transmitting energy. Adjustment for wear of nut. Surfaces Suitable for Rolling Contact. Methods of keeping in place live rollers used in cranes and heavy revolving pieces. Surfaces for a Combination of Rolling and Sliding Contact. Simple forms of cams and ratchets. Formation of teeth of wheels. Mortice wheels. Belt Gearing. Fast and loose pulleys and strap fork arrangements. Length of belt. Rope pulleys. Gearing chains and pulleys. Constructions to Permit of the Application of the Urging Force and Working Resistance to the Moving Parts. Metallic gland packing. Hydraulic pistons. Pump buckets and valves. Mechanically controlled pump valves. Stop and throttle valves. Arrangements for relieving the pressure on slide valves. Expansion valves for steam engines. Methods of Construction to Facilitate the Manufacture of Machine Parts. Riveted Joints. Treble riveted joints. Arrangement where three or 364 HANDBOOK FOR MECHANICAL ENGINEERS. more plates overlap. Caulking. Joints in the bars. Connection of parts in girder work. Ordinary proportions of joints and simple calculations of strength. Bolted Joints. Ordinary proportions of bolts and nuts and simple calculations of strength. Buttress form of screw thread. Foundation and wall bolts and washers. Double ended bolts. Cotters. Ordinary proportions of fcteel and iron cotters. Flanged Joints of pipes and cylinders. Diameter and number of bolts. Joints in copper pipes. Expansion joint for steam pipes. Construction of the Frame of a Machine in Parts. Fixings. Hangers and brackets for carrying pedestals of shafts connected by bevel wheels. Engine beds. Boilers. Use of bridge or girder stays for strengthening flat surfaces of boilers. Primary Pieces. Ordinary proportions of keys. Simple forms of disen- gaging couplings and friction clutches. Methods of constructing fly- wheels, pulleys and spur-wheels in parts. Secondary Pieces. Forms of section suitable for transmitting a tensile force and a thrust. Form of section suitable for a locomotive coupling rod. Physical Characteristics of the common Materials used in Machine Construction. Simple questions will be set on the strength and proportions of elementary machine parts and of the pressures at surfaces in working contact. Workshop Processes. Use of the milling machine. Conditions suitable for its application. IN THE HONOURS STAGE. The examination is twofold. A paper will be set which may include any question relating to the design, the method of construction, and the use of any machine. As the subject is large, and includes all the various branches of engineering practice, a considerable choice of questions is provided, the candidate being restricted to answering only a limited number. In general about half the questions will be set on the theoretical portion of the subject, and will require a knowledge of how to apply the principles of Applied Mechanics in the calculations relating to machines. This part of the subject will apply equally to the machines employed in all branches of engineering. The other questions will require answers of a descriptive character involving an intimate knowledge of special machines. Those candidates who answer the questions in this paper in a suffi- ciently satisfactory way will be permitted to enter for a practical examination which will be held at South Kensington about four weeks after the written examination. No candidate can be classed in Honours who is not successful in the practical examination. At the practical examination the candidate will be required to execute a drawing, or design a portion of some machine from given data. In this part of the examination the candidate will in general be allowed the free use of text and note books so that he may to a large extent be working under condi- tions similar to those which obtain in an engineer's drawing office. Candidates must themselves provide drawing instruments and all necessary materials, except drawing paper and drawing boards, which will be supplied by the Department, APPENDIX II. 365 Subject VI. THEORETICAL MECHANICS. There are two distinct nomenclatures applicable to Subject VI. According to one, the science that investigates the action of force is called mechanics, and is divided into (a) statics, treating of the equili- brium of particles and bodies, (6) dynamics, treating of the motion of particles and bodies, (c) hydrostatics, (d) hydrodynamics, treating respectively of the rest and motion of fluids, i.e. liquids and gases. This nomenclature is adopted by many writers of authority, e.g. by Poisson. According to the other, the term dynamics takes the place of mechanics, and the division is into : (i) statics, (ii) kinetics, (iii) hydrostatics, (iv) hydrokinetics. This is a question of words only, but of course one ter- minology may be better than another. It is, however, to be observed that a considerable number of questions, formerly treated under the head of (&) dynamics, relate to motion without reference to the forces producing it. These questions form a distinct branch of pure mathematics to which the name of kinematics is now commonly given. Certain parts of kinematics come into Subject VI., but they occupy a subordinate position in it. Subject VI. can be taken in two divisions, the first corresponding to (a) and (&) defined above, the second corresponding with modifications to (c) and (d). In most cases it would be best for students to take up the first stage, or even first and second stages of the first division, before at- tempting the second division, However, students have their choice, and to enable them to take up the second division as a separate subject, the syllabus contains several articles which also come into the first division. In each division there is a first stage, second stage and honour stage. The distinction between the stages is much the same in the two divisions. ^ In the First Stage the student is required to make himself acquainted with the axioms and the elementary propositions and formulae of the science, as simple matters of fact, independently of their formal proof. For instance, he must know the proposition, called the parallelogram of forces, as a matter of fact, and must be able to apply his knowledge ; but he will not be required to prove the proposition. In like manner he will be required to know what is the inetacentre of a floating body, but not to prove the formula for finding its position. In a word, he will be required to make brief exact statements, and to work out easy examples. With perhaps an occasional exception, the examples will be either arith- metical, or capable of being answered by an easy construction drawn to scale. No question involving complicated algebra or geometry will be set. The student should be able to substitute numerical values in an algebraical formula, and to solve a simple equation. He should also have accurate notions of ratios. Every student should bring to the examination a pair of compasses, a scale of equal parts and a protractor. In the Second Stage of either course the student will be concerned with the mathematical treatment of the principles which form the subject of the first stages respectively, so far as the subject can be discussed with the aid of what is generally called elementary mathematics. He should pay particular attention to the proofs of the mechanical propositions referred to in the synopsis of the courses. Thus, he should not merely know that when a particle moves in a circle the force acting towards the 366 HANDBOOK FOR MECHANICAL ENGINEERS. centre is given by the formula wv 2 -j-r, but he should be able to state the reasoning by which the fact is proved, and to apply his knowledge to a moderately hard example. He should not merely know the rule for finding the magnitude of the resultant pressure of a liquid on a plane area, but be able to state the proof of it. In the Honours Stage of either course it will be assumed that the student has a fair knowledge of what is commonly understood by the higher mathematics, though in drawing up the questions it will be endeavoured to exclude those which have a merely geometrical or algebraical interest. It is of course understood that in any stage of either division any question may be asked, which fairly arises out of the contents of any previous stage. It may be added that in all stages the student should bring to the examination the drawing instruments that are necessary for the first stage. DIVISION I. FIRST STAGE OB ELEMENTARY COURSE. 1. Units of time and distance; measurement of velocity, whether constant or variable ; measurement of acceleration, particularly of con- stant acceleration ; acceleration due to gravity ; mass or quantity of matter, unit of mass, density, specific gravity (or specific density) ; momentum; measurement of force; absolute units of force, particularly the poundal or British absolute unit ; distinction between the mass and the weight of a body. 2. Specification of a force. Composition of forces, particularly of two forces, whether acting along intersecting or parallel lines. Equilibrium of two or three forces. Statical couples. Moment of a force. Centre of parallel forces. Work done by a force. Units of work, foot-pound, units of power, horse- power. 3. Different states of matter. Elasticity. Resistance to (1) elongation, (2) compression, (3) bending and (4) torsion. 4. Centre of gravity, and its position in simple cases. Reaction of smooth surfaces, points and hinges. Equilibrium of a body capable of turning on a fixed point or fulcrum. Levers ; the steelyard ; the balance and its sensibility. Tension of a thread. Pulleys. Equilibrium of a body resting on a smooth plane, horizontal or inclined. Stable and unstable equilibrium. 5. Laws of uniformly accelerated motion, and the formulas embodying them, viz. v = V+ft, 8 = Vt+^ff, v* = V* +2/ a. Atwood's machine. 6. Composition of two velocities. Uniform motion in a circle ; centri- fugal force. Small oscillations of a simple pendulum and of a compound pendulum. Convertibility of the centres of oscillation and suspension. Determination of the numerical value of the acceleration due to gravity. Force exerted by the earth on the same mass at different places. 7. Definition of energy. Distinction between potential and kinetic energy. Absolute units of work, particularly the foot-poundal. Equation of work and energy for a constant force acting on a particle. APPENDIX II. 367 SECOND STAGE OB ADVANCED COURSE. 1. Kelative rest and motion. Composition of velocities. Determination of the velocity of a moving point, relatively to another moving point. Angular velocity. 2. Newton's three laws of motion, and his proof of the parallelogram of forces. 3. The composition of forces including parallel forces and couples acting in one plane, and the conditions of their equilibrium. Centre of parallel forces. 4. Determination of the centre of gravity in ordinary cases. Proper- ties of the centre of gravity. 5. Friction and laws of friction ; co-efficient and angle of friction. 6. Equilibrium of simple machines when friction is not, and when it is, taken into account. Inclined plane, wedge, screw, pulleys. Equili- brium of body resting on axle, whether smooth or rough. 7. Virtual velocities (or virtual work). Stable and unstable equili- brium. 8. "Work done by a variable force ; diagrams of work in simple cases ; the indicator diagram. 9. Kectilinear motion under the action of constant forces, particularly on smooth or rough inclined planes. 10. Motion of projectiles ; motion in a circle ; motion of a simple pendulum. 11. Impulsive forces. Direct and oblique impact of smooth spheres. HONOURS. Owing to the great extent of the science of theoretical mechanics, it may be of use to the student to have those parts of the subject marked out to which his attention should, in the first place, be directed. It cannot be too strongly urge I on him that the study of the higher branches of mechanics cannot be attempted with advantage unless it is preceded by a thorough knowledge of the elements of the science. The candidate for honours should therefore be prepared to answer readily any question on the advanced course. Supposing this degree of proficiency obtained, his attention should next be directed to the subjects named below, or some of them. It may be added that there will always be a sufficient number of questions arising out of Nos. 1, 6, 8, of the following articles, and out of Stages 1 and 2, to enable a student to obtain a second class with sound knowledge of these parts of the subjects. 1. The general theory of the composition and resolution of forces, and of the equilibrium of a rigid body. Centre of gravity. 2. Virtual velocities (or virtual work). 3. The equilibrium of flexible, inextensible threads. 4. Simpler oases of the deflection and rupture of beams. 5. The elements of uniplanar kinematics. 6. Moments and products of inertia. 7. General differential equations of the motion of a particle and of a rigid body. 368 HANDBOOK FOE MECHANICAL ENGINEERS. 8. Constrained motion of a particle ; motion of a rigid body about a fixed axis, including a case when the forces are impulsive. 9. Motion in space of two dimensions. U.O. The general principles of dynamics. DIVISION II. FIRST STAGE OB ELEMENTARY COURSE. The subject of Division II. cannot be understood unless the student has a preliminary acquaintance with the fundamental notions of force and motion, on which all parts of the science are based. These are given in Section 1 of the following syllabus. He should also understand what is meant by the resultant of two or more forces, and that in the ease of two or more parallel forces the resultant equals the sum of the forces. He should know what is meant by the centre of gravity of a body, some of its elementary properties, and its position in the case of such bodies as sphere, prism, cylinder, circle, parallelogram. 1. Units of time and distance ; measurement of velocity, whether con- stant or variable ; measurement of acceleration, particularly of constant acceleration ; acceleration due to gravity ; mass or quantity of matter, unit of mass, density, specific gravity (or specific density); momentum; measure- ment of force ; absolute units of force, particularly the poundal or British absolute unit ; distinction between the mass and the weight of a body. 2. Definition of energy ; distinction between potential and kinetic energy ; the work done by a force ; absolute units of work, particularly the foot-poundal ; equation of work and energy for a constant force acting on a particle. 3. Definition of fluid and liquid ; transmission of pressure through a fluid ; measurement of pressure at any point of a fluid ; surface of a liquid acted on by gravity, and pressure at any point within the liquid ; distinction between the whole pressure and the resultant pressure of a liquid on a given surface ; magnitude and line of action of resultant pressure in the case of a rectangular area, one edge of which is on the surface of the liquid ; also in the case of a body wholly or partly immersed in a liquid. 4. Conditions of equilibrium of a floating body ; definition of the meta- centre ; position of a metacentre in the case of a sphere, and of a cylinder with its axis vertical (the formula 4 HM .hs r 2 being assumed) ; stability of floatation. 5. Determination of the specific gravity of insoluble solids and of liquids, (1) by the balance, (2) by the specific gravity bottle, (8) by Nicholson's hydrometer; specific gravity of solids lighter than water by the balance ; weight of a body in air and in vacuo. 6. Distinction between heat and temperature ; definition of higher and lower temperature, and of equal temperature ; the mercurial thermometer, and its graduation ; Fahrenheit's, the Centigrade and Eeaumur's scales. Definition of absolute zero. 7. Air is a heavy elastic fluid ; the barometer ; pressure of air on the sides of a vessel containing it ; variations in this pressure consequent on change of volume and temperature, i.e. Boyle's Law and Dalton's Law, and the formula in which they are embodied, viz. VP = CT ; limitation APPENDIX II. 369 of Boyle's law ; contents of the " vacuum-space " in barometers of different liquids. 8. Hydrometer of variable immersion; suction-pump; force-pump; siphon; air-pump and mercurial gauge; compressed air manometer; hydraulic press. SECOND STAGE OB ADVANCED COURSE. The demonstrations and additional subjects of the second stage require corresponding extensions in the preliminary part of the course, as men- tioned below. But besides this the student should extend his knowledge of the centre of gravity, and learn how to find the moment of inertia in such simple cases as involve no more than finding the limiting value of 2 (x n A x) by integration or otherwise, including the case in which n = -1. 1. Composition and resolution of forces acting on a body, and the general conditions of their equilibrium. Angular velocity. Uniform circular motion. Work done by a variable force. 2. Resultant pressure of a liquid on an immersed surface plane or curved. Centre of pressure in simple cases. Equilibrium of bodies floating freely or partly supported. Metacentre in simple cases (the for- mula HM . V = A fc 2 being assumed). Tension of thin flexible cylinder or sphere under internal fluid pressure. 3. Pressure and elasticity of air; height of the homogeneous atmo- sphere ; variations of the height due to variations of gravity and tem- perature ; pressure of mixed gases ; vapours in contact with the liquid producing them; saturation; the dew point ; densities of dry and moist air. Work of gas expanding at a constant temperature. 4. Elementary notions of surface tension ; rise of a liquid between two plates, and in a capillary tube. 5. Surface of a liquid in a vessel rotating steadily, under the action of gravity ; pressure at any point of the liquid, 6. Velocity of liquid issuing from hole in the side of a vessel (Torricelli' s Theorem) ; velocity of the descending surface of the fluid. 7. Elementary notions of the propagation of an aerial disturbance along a straight tube; geometrical representation of the motion of the aerial particles constituting a wave; explanation of the interference of two waves ; corresponding representation and explanation by means of a sine function (e.g. A sin (n t + ) ). HONOURS. The parts of this course are to some extent alternative. The student will be at liberty to answer questions in any part of the paper, but it will be possible for him to obtain a first class by answering questions arising out of previous stages, and out of the first six or out of the last four of the following articles. The honours stage consists in great part of the subjects of the previous stages, but treated more generally. 1. General conditions of the equilibrium of fluids acted on by any forces. 2. Resultant pressure of a liquid on plane and curved surfaces. 2 B. 370 HANDBOOK FOR MECHANICAL ENGINEEKS. 3. Centre of pressure of a plane area. 4. Condition of stability of floatation in respect of small displacements. 5. Stability of floatation when the displacement is large. 6. Formula for finding distances of altitude by the barometer and the necessary corrections. 7. Sudden compression and expansion of gases ; ratio of specific heat of air at constant pressure to specific heat of air at constant volume. 8. Motion of aerial waves in a straight tube ; investigation and integra- d 2 z d? z tion of the equation -T-J = a 2 - -, and interpretation of results. (.It ct oCf 9. Elements of the kinetic theory of gases. Subject VII. APPLIED MECHANICS. In order to prepare for this examination the student should carefully inform himself as to the details and construction of the various contrivances, machines and appliances, referred to in the list given below ; and in doing so, he must seek to understand the manner in which certain natural laws or mechanical principles receive their useful application. The list for the first stage is necessarily comprehensive, but the questions will be framed in such a manner that a candidate who has ob- tained a fair knowledge of a portion only of the subjects may hope to pass with some credit. Easy questions involving arithmetical results may arise, and in particular the student should be able to solve simple mechanical problems by graphic construction. The list for the second stage refers also to a wide range of subjects, and he will be liable to questions involving only a very limited knowledge of mathematics. In the honours paper a fair amount of mathematical knowledge may be required. FIRST STAGE OB ELEMENTARY COURSE. The subjects for examination will be : Measurement. Line and end measure. Rules, callipers, gauges. True Plane Surfaces. Surface plates. Method of surfacing. Applica- tions in machinery. The principle of Work and its Application to simple Machines. Levers. Balances. t Safety valves. Pulleys. The snatchblock. Sheaves. The inclined plane. Screws, forms of thread, mechanical characteristics of screw threads. Right and left handed screws, single and double threaded screws. The screw and lever in combination. Screw presses. Lifting jacks. Endless screw and worm-wheel. Wheel and axle, its applications. Winch or crab. Power gained by wheelwork. The Conversion of Motion. Endless bands, straps, fast and loose pulleys, guide pulleys. Toothed wheels. Rack and pinion. The crank and connecting rod. Cams. Mangle motions. Ratchet wheels, detents. Special Contrivances. Such as : The fusee. The wheel and compound axle. Weston's pulley block. Escapements. Geneva stop. Fast and Blow motion in the Deadstock of a lathe. APPENDIX II. 371 Energy. What it means. The measure of work stored up in a raised weight or in a heavy mass in motion. The fly-wheel. Fly-presses. The Pressure of Water, Estimation of water pressure on plane surfaces such as sluice gates. Pressure gauges. The hydrostatic pnss. The accumulator, or vessel for obtaining a supply of water under pressure. Machines for Raising Water. Pumps. Lift pumps. Force pumps. The use of an air vessel. Materials. Iron ; qualities required for diiferent purposes. Testing of iron for strength and ductility. Steel ; hardening and tempering. Copper and tin ; their alloys. Gun-metal. Brass. Strength of Materials. Power of resistance of different materials to tensile and compressive stresses. Power of resistance to forces acting trans- versely. Influence of form or dimensions of section. Influence of length, of position of load, of distribution of load. Friction. The laws of friction. Contrivances for lessening the effect of friction. In answering the questions, students will be required to make hand sketches of the details of the various parts in a clear and intelligible manner. Great importance will be attached to this requirement. SECOND STAGE OR ADVANCED COURSE. The subjects for examination will include everything mentioned in the first course, but candidates will be expected to possess a more extended and thorough knowledge of the various details, as well as of theoretical principles. The additional matter will be the following : Miscellaneous Details. The forging of iron. Welding. The casting of iron. Moulding. Soldering. Brazing. The expansion and contrac- tion of metals. Friction. Examples where friction is useful. Rolling friction. Brakes. Strap-brakes. Friction and other dynamometers. The efficiency of machines. Friction grips. Holding power of ropes when coiled. Friction clutches. Strength of Materials. Estimation of stresses in a rectangular timber beam. Cast and wrought iron girders. Cantilevers. Buckled plates. The deflection of beams. Stresses in Framework. Simple examples of framework, with corre- sponding diagrams of stress. Travellers, roofs. Lattice girders. Trussed beams. Shearing Stresses. Cotters, rivets, joints of plates. Strength of shafting to resist torsion. Hollow or solid shafting. Compressive Stress. Pillars. Piers. T and angle iron struts. Tie- bars. The Conversion of Motion. Quick return movements. Linkwork and parallel motions. Peaucellier's invention. Trains of wheels for screw- cutting, clockwork. Epicyclic trains. Rope-making machinery. Dif- ferential motion of three bevil wheels. Universal joints. Pressure of Air. Fans, blowers, air pumps. Gauges for measuring the pressure of air. Construction and efficiency of windmills. The diving-bell. 2 B 2 372 HANDBOOK FOE MECHANICAL ENGINEERS. Hydraulic Machines. Water wheels. Forms of buckets. Pendulum governor for water wheels. Turbines. Centrifugal pumps. Hydraulic press. The hydraulic jack. Hydraulic cranes, different powers. Force pump for feeding the accumulator. The water ram. Description of Machines in Common Use. Such as : Cranes. Ma- chines for weighing. Counting and numbering machines, Corn mills. Clocks. Dead beat escapement. The lever escapement. The chrono- meter escapement. The keyless watch. Hand printing presses. Principles and construction of Hand Tools. Such as: Chisels. Planes. Gimlets. Augers. Saws. Drills. Files. Machine Tools Such as : Lathes, ordinary and screw cutting. Planing, shaping and slotting machines. Reversing motions. Drilling and boring machines. Punching and shearing machines. Feed motions. The observations already made with reference to hand sketching apply equally here, and details of machines, such as feed motions, reversing motions, &c., might form the subject of questions, the answers 'to which will be of no value unless the sketches are correctly given. HONOURS. The above syllabus will sufficiently indicate the nature of the subjects that form the basis for the examination in honours. Candidates must be versed in mechanical principles, and will be asked to give theoretical investigations which may bear upon the subject matter under con- sideration. Subject XXII. STEAM. FIRST STAGE OB ELEMENTARY COURSE. Students in this course will be required to possess some knowledge of the effects of heat on matter, such as changes of temperature, expansion, change of elasticity, vaporisation, liquefaction ; they must also know something of the phenomena of the radiation, absorption, conduction and convection of heat; they will be liable to questions relating to the mechanical equivalent of heat, as well as to the conversion of work into heat and of heat into work ; they must also inform themselves on the following subjects, viz. the ca.uses which influence the boiling tempera- ture of water, the boiling points of fresh and salt water, high pressure steam, measure of steam pressure by atmospheres, the relation between the pressure, density and temperature of steam, the specific volume of steam, the latent heat of steam, the quantity of water required to pro- duce condensation, the distinction between saturated and superheated steam. Early Engines.-^ Newcoinen's atmospheric engine, its defects. The discoveries of Watt. Hornblower's compound engine. The Single-acting Condensing Pumping Engine. Details connected with this engine; the steam cylinder, the steam, equilibrium and eduction valves, their action; the steam-jacket, the clothing of the cylinder ; the condenser, the air-pump, the foot-valve, the delivery-valve. APPENDIX II. 373 the snifting valve, the hot well; the piston rod, stuffing boxes and glands ; the construction of the beam in large engines, the plug rod, the parallel motion ; the method of starting the engine, and of regulating its speed, the construction and action of the cataract. Double-acting Condensing Engine. Details of the various parts, the cylinder, how constructed, the ports or openings into the cylinder ; the various forms of valves in common use, the methods of balancing valves, the three-ported valve, the lap on a valve, the lead of a valve, the eccentric ; details of the piston, metallic packing rings ; the air-pump, jet condenser, the surface condenser, gauges for the condenser, the baro- meter gauge, method of estimating pressure by it, errors in this method, and correction of the same ; the crank and connecting rod, the strap, gib and cotter, the beam, parallel motion in beam engines, the governor, the fly-wheel; stopping and starting gear. Various types of direct-acting condensing engines. The Non-condensing Engine. Various types of direct-acting engines. The Expansion of Steam. Saturated and super-heated steam ; law of expansion ; the object of expanding steam; modes of carrying out expan- sive working. Expansion valves; double beat valve, crown valve, gridiron valve; wire drawing of steam, the throttle valve. Stationary Boilers. The Cornish boiler, the Lancashire boiler, the vertical boiler ; heating and fire-grate surfaces, the evaporative power of boilers, boiler chimneys : the strength of boilers, the use of stays, the proving of boilers. Boiler appendages; safety valves, reverse or atmo- spheric valves, communication or stop valves ; the glass water gauge, steam pressure gauge, various forms, the heating of feed water, feed pumps. Priming, its causes and remedies. The Marine Steam Engine. Various types of paddle-wheel engines ; the oscillating and inclined engine, various types of screw propeller engines. Details of parts connected with the working of marine engines, expansion and reversing gear ; bilge and feed pumps. Marine Boilers. General forms and construction ; tubes and flues ; the funnel and its casing ; fire-bridge and ashpit, waste steam pipe, water gauge, gauge cocks, pressure gauges, safety valves, reverse valves, stop valves, feed pumps, boiler hand-pump ; feed or donkey-engine ; Kingston's valves, blow-out cocks, brine-pumps and brine-valves; the methods of ascertaining the degree of saltness of the water in a boiler, amount of saltness permissible ; formation of scale ; superheating apparatus ; surface condensation. The Locomotive Engine. The general construction of a locomotive engine and boiler before the invention of Stephenson ; description of the Rocket engine as the type of tha modern locomotive, the tubular boiler, the draught produced by the discharge of waste steam. Details. Inside cylinders, outside cylinders, steamways, ports, slide valve; water cocks, grease cocks, the piston and packing-rings, piston- rod, guides, connecting rod, eccentrics, the reversing or link motion, reversing lever, sector, expansive working ; crank axle and driving wheels, power required for traction, adhesion of the driving wheels, counter weights to cranks, wheels and axles, axle-boxes, bearing-springs, buffer and draw springs, friction brakes. The Boiler. The fire-box, the inner and outer shell, the cylindrical barrel, the tubes, mode of fixing them, fire-box stays, gusset stays ; the 374 HANDBOOK FOR MECHANICAL ENGINEERS. ash-pit, the smoke box, the blast pipe, mechanical action of the blast ; the steam chest, the outer dome, the steam pipe, the regulator, safety valves, pressure gauges ; whistles, blow-off cocks, feed pumps, Giffurd's injector ; evaporative power of the boiler, fire-grate and heating surface, combustion of fuel ; the tender, water-tank, tank-engines, brake, feed pipes ; coke-burning engines, methods of consuming smoke in coal- burning engines. Ramsbottom's method of filling the tender. In this examination it is essential that the student should acquire the power ot making hand sketches of the various parts which he may be called upon to describe. The observations made in the syllabus for Applied Mechanics hold equally in this subject, and it is further to be noted that the student is liable to be questioned as to the mechanical principles involved in any of the matters herein mentioned. SECOND STAGE OR ADVANCED COURSE. Students will be examined in the subjects already set forth, but will be expected to show a more extended knowledge of the same, and they should now be prepared also to answer questions in accordance with the second part of the syllabus as follows : Valves and Valve Gears. Various types of valves, the double and treble ported, the piston, the Trick, and other valves. Meyer's expan- sion valve. The position of eccentrics on the ciank-shaft; Zeuner's valve diagrams ; effect of length of rod in modifying stt-am distribution. The valve motions or gears of Stephenson, Hackworth, Marshall, Corliss, Joy, arid others. Expansion valves for compound engines. The distribution of steam in various types of compound engines. Condensation. Surface and jet condensers. Extent of surface re- quired in surface condensers. Amount of water necessary for the condensation of steam. Construction of air pumps and circulation pumps. Ejector condensers. Compound Engines. Various types of compound engines, triple and quadruple expansion engines. Webb's compound locomotive engine. Fly- Wheel and Governors. Theory of their action. Proper diameter and weight for fly-wheels, details of construction of the fly-wheel. Construction and action of Watt's pendulum governor, of the Porter governor, and of other high speed governors. The parabolic governor. The Indicator. Description of the instrument, the atmo.-pheric line. Method of taking a diagram. The general configuration of diagram to be expected under various circumstances. Examination of the indicator diagram when the steam is throttled ; when expansive gear alone used, and in other cases. To ascertain the horse-power of an engine by means of the indicator. The indicator diagram in engines of various types. The combining of the indicator cards of a compound engine. Propellers. Paddle wheels, feathering of the floats, disconnection and immersion of wheels. The screw propeller, various forms, length, angle, pitch and area of screw blade, disconnecting and raising the screw ; the position of the screw propeller in the vessel, twjn screws, the slip of the screw ; the method of receiving the thrust upon the vessel, soft metal and hard wood bearings. TJieoretical Portion. Work done during the conversion of water into APPENDIX II. 375 steam ; work done in a steam cylinder when the steam is expanded ; work done in the air-pump ; work developed by a crank ; inertia of reciprocating parts, diagram of crank pin effort. Method of measuring the efficiency of a steam engine ; meaning of absolute temperature ; isothermal and adiabatic curves ; efficiency of heafc engines ; experimental testing of engines; estimation of loss of fuel by "blowing out"; calculations re- lating to parallel motions, such as Watt's and Peaucellier's ; estimation of the relative positions of the piston and crank in any part of the stroke ; diagram showing the relative motions of the slide and piston ; dynamo- meter, its use in finding the horse-power of an engine. In order to encourage the study of the gas engine some questions will be set in the advanced course, which will embrace the following subject- matter ; but these questions will not be compulsory. Hot-air and Gas Engines. General principles underlying the action of such engines. Stirling's hot-air engine ; the regenerator ; the con- struction of refrigerating machines. The efficiency of air engines. Explosive mixtures of gas and air. The Lenoir engine. The Otto engine. Details of construction of the Otto engine. The valves required, their construction and action. The charging of the cylinder. The firing of the charge. Mechanism for operating the valves, for regulating the speed, and for admitting the gas. Fittings of the engine. The cycle of operations. The indicator diagram. The efficiency of the engine. HONOTJKS. The range of subjects will comprise the whole syllabus, and students will be expected to show a more extended knowledge, both in a theoretical and practical direction, than is required of them in the second stage. 376 HANDBOOK FOR MECHANICAL ENGINEERS. APPENDIX III. SYLLABUS OF THE CITY OF LONDON COLLEGE ENGINEEBING DEPARTMENT. Subject to revision annually, ready first week in September, and forwarded gratis on application to the Secretary, City of London College, White Street, Moorfields, London, E.G. INDEX. ABSOLUTE pressure, 181 unit of force, 7 zero of temperature, 170 Accelerating force of gravity, 5 Acceleratrix of gravity, 5 Accumulated work, 8 Accumulator, friction of, 294 hydraulic pressure, 292 pressure, mechanical value of, 291 variation of pressure in, 293 Accumulators, air pressure, 295 Action of oils on metals, 167 Actual energy, 8 horse-power, 240 of boiler, 194 Adhesion, attraction of cohesion and, 5 of locomotive wheels, 272 Adiabatic curve, 181 Admiralty horse-power, 241 Advantage, mechanical, 24 Aerostatics, 23 Air accumulators, 295 bulk of, 181 composition of, 200 condensers, 274 pump and condenser, 262 required to burn fuel, 200-204 space occupied by 1 lb., 181 vessels and accumulators, 295 weight of, 7, 200 Allan's link motion, 253 Allotropic substances, 3 Alloying with copper, effect of, 49 Alloys, 49 antimony, 51 brass, 50 bronze, 50 for tempering bath, 115 fusible, 52 Alloys, fusible below 212 F., 53 nickel, 51 ultimate strength of various, 63 various, 52 Aluminium, 48 America, unit of boiler horee-powei in, 194 Amorphous substances, 4 Ampere, definition of, 310 Amplitude of vibration, 18 Analyses of iron and steel, 64 of pig iron, 36, 108 Angle and tee iron, strength of, 66, 67 of relief in tools, 129 of repose, 162 of twist, 125 Angles of tools, 129 Angular advance, 249 measurement of forces, 124 motion, work in terms of, 123 velocity, 123 Anhydrous steam, 185 Animal power, comparison of, 28 Ankarsrurns (Swedish) cast iron, 64 Antimony alloys, 51 Apertures, discharge through vari- ous, 279 Archimedes, principle of, 278 Architectural drawing, colours for, 326 Areas of circles, 336 of ports in hydraulic slide valves, 306 of steam ports, 250 of valves for machinery under accumulator pressure, 306 Simpson's rule for, 246 Arithmetical mean, 319 series, 321 terms, 319 378 HANDBOOK FOR MECHANICAL ENGINEERS. Armstrong crane steelyard, 27 Armstrong's accumulator, 292 Atmospheric pressure, 181, 296 Atoms, particles, molecules and, 2 Attraction of cohesion and adhesion, 5 of gravitation, 5 Average force, 12 Avogadro's law of gases, 177 BABCOCK and Wilcox boiler, 193 B.A.G., or British Association gauge for screws, 332 E.G., or standard sheet and hoop- iron gauge, 334 B.W.G., or Birmingham wire gauge, 333 Balance or scales, principle of, 27 Balk timber, sizes of, 86 Balloon or haystack boiler, 192 Basic steel, 45 Batteries, galvanic, 310 Beams, approximate proportions, 84 deflection of, 93 under impact, 97 experiments on rectangular pine, 83 proportions for strength and stiffness, 84 rectangular, constants for, 83 Bearing area of rivets, pins and bolts, 103 Bearings for shop shafting, 166 gun-metal for, 50 wood for, 55 Belt gearing, notes on, 140 Belts, large double, 142 strength of leather, 142 to find length of, 143 Bending moment, 72, 74 tests of iron and steel, 67 Bent lever balance, 27 Bessemer iron, 37 steel, 44 Best iron, single, double and treble, 39 Bevel wheels, 151 Birmingham wire gauge (B.W.G.), 333 Blast furnace, chemical action of, 35 Blister steel, 43 classification of, 43 Block and tackle, 25, 160 Blow and scum, 219 Blowing off to prevent incrustation, 219 Board of Trade electrical unit, 31 1 Boiler cocks, taper of plugs for, 219 condition of, affecting heat trans- mission, 198 Cornish, 215 comparison with I.H.P. of engine, 216 evaporative power of, 195 furnaces, 206 heat in, 206 locomotive, 229, 235 power, cost of, 195 scale, 220 seatings, 217 shell, ultimate strength of, 232 stays, 230 to calculate size of, 214 tubes, 218 collapsing pressure of, 233 Boilers, comparison of collapsing and bursting pressures, 234 of transverse and longitudinal strength, 232 Cornish and Lancashire, sizes of, 216 corrosion of, 222 cylindrical, 218 early forms of, 192 economical draught for, 201 effect of supervision of, 210 efficiency of, 195 experiments on evaporation in, 210 factor of safety, 228 fall in setting, 218 feed water required for, 212, 222 grease in, 222 heating surface of, 199 helical joints for, 233. horse-power of, 193 of, from dimensions, 194 incrustation in, 220, 221 loss of heat in, 207 production of steam in, 193 riveting for, 229 safety valves for, 223 INDEX. 379 Boilers, size of chimney for, 203 of manholes for, 218 testing, 229 varieties of, 192 weight of per horse-power, 214 Boiling water and steam, tempera- ture of, 182 Bolt stays, 230 Bolts and nuts, Whitworth stan- dard, 331 nuts and washers, in carpentry, proportions of, 101 strength of, 102 Bower-Barff process, 57 Bowling iron, 40 Boyle and Marriotte's law of ga s s, 177 Brachystochrone or curve of quickest descent, 30 Brake blocks, wood for, 55 horse-power, 242 Brass alloys, 50 castings, 111 composition of, 49 Breaking weights, 62 Breeches-flued boiler, 192 Brick chimney shafts, 201 piers, safe load on, 78 Bridge and girder work, specifica- tion tests, 66 Bridges and girders, 65 load on, 96 British gravitation units, 8 kinetic unit, 7 Bronze alloys, 50 castings, 111 composition of, 49 Buffer beams, wood for, 55 Building, units of work in, 9 Built-up crank shafts, 269 Bursting and collapsing pressures on boilers, 234 Butterley boiler, 192 C.G.S., or centimetre-gramme- second system, 8, 328 Calculations, units employed in engineering, 329 Calorie, or French unit of heat, 172 Calories compared with British heat units, 196 Calorific power, definition of, 197 value of fuels, 196 Camber and deflection, 93 Capacity of bodies for heat, 173 Capillary attraction, 5 Carbon in iron, effect of, 34 Carnot's law or function, 184 Sir W. Thompson's modifica- tion of, 184 Carpentry, proportions of bolts, nuts and washers, 101 Carriage building, wood for, 56 springs, flat, strength of, 97 Cartesian co-ordinates, 30 Cart shafts, wood for, 56 Case hardening, 41 Cast iron, breaking stress and safe load, 62 characteristics of, 33 chilled and malleable, 47 for pipes, tests of, 61 malleable, strength of, 65 notes on, 47 plates, strength of, 77 qualities of, 47 specification tests of, 61 testing, 60 to distinguish from wrought iron and steel, 33 toughened, 48 weight of, handy numbers for, 91 steel, 43 Castings, notes on moulding and, 106 weight of, from pattern, 105 wrought iron, Mitis process, 42 Castings, allowance on, for machin- ing, 105 bronze and brass, 111 cleaning, 107 contraction of, 110 expansion of, 111 melting metal for, 110 Catenary curve, 147 Caulking, notes on, 119 tools, 119 Celo, definition of, 13 Cement, rust joint for iron, 191 Centimetre-gramme-second (C.G.S.) system, 8, 328 Centre of gravity, 14, 15, 16 380 HANDBOOK FOR MECHANICAL ENGINEERS. Centre of gyration, 17 of oscillation, 18 of percussion, 20 of pressure, 277 of spontaneous rotation, 20 Centrifugal and centripetal forces, 16 force, 6, 17 pumps, 286 Centripetal force, 16 Centrobaryc theorem, 16 Centroid or centre of gravity of form, 14 Chain-riveting, 116 Chains, counterweight for crane, 307 examination of, at docks in London, 150 remarks on crane, 150 strength of, 149 Change of temperature, effect of, 171 wheels for screw-cutting, 134 Charcoal iron, 40 Charles' law of gases, 177 Check or lock nuts, to secure, 103 nuts, 103 Chemical action of blast furnace, 35 composition of fuels, 196 compounds, 3 elements, 3 Chilled cast iron, 47 Chimney for boilers, size of, 203 force of draught in, 205 furnace, London County Council rules for, 205 shafts, brick, 201 velocity of gases in, 204 Choke-damp, 36 Circular rings, strength of, 151 Circulating pump, 262 water required for condensation, 263 Classification of pig iron, 37 Cleaning castings, 107 Clearance in cylinder, 244 Cleveland list of limits for plates and angles, 92 plates, sizes of, 92 Coal, angle for shoots and screens, 195 bunkers, Navy allowance for, 195 burnt per square foot of fire grate, 205 Coal con sumption, possible economy in, 213 gas, 316 space occupied by, 195 stores, capacity of, 195 weighing cranes, 304 weight of, 195 Coefficient of friction, definition of, 162 of steam engines, 296 Coefficients of friction, mean, 166 Cohesion and adhesion, 5 Collapsing pressure, comparison between bursting and, 234 of boiler tubes, 233 of flues, 234 Cold-blast pig iron, 36 Cold-shortness, 41 Colours, composition of, for me- chanical drawing, 327 corresponding to temperature, 114 used in architectural and me- chanical drawing, 326 Columns, notes on iron, 79 safe load on, 78 strength of cast iron, 78, 80 Combustion, products of, 200 rate of, 205 Comparison of animal power, 28 of steam engines, 263 Compos- ition and resolution offerees, 22 Dr. Angus Smith's, 57 for coating pipes, 300 of water, 3 Compound engine, mean effective pressure, 247 engines, economy of, 238 progress of, 238 Compressed gas, cylinders for, 316 Compressibility of water, 279 Condensation of steam, 185 water required for, 263 Condenser, air, 274 and air pump, 262 water, 263 Conduction of heat, 171 Cone, centre of gravity of, 16 Connecting rod, thrust in, 248 Conservation of energy, 9 of mass, 2 INDEX. 381 Consumption of fuel per I.H.P., 213 of steam in engines, 211 Continuous girders, load on supports of, 78 Contraction of castings, 110 of metals in cooling, 110 Convection of heat, 171 Convertibility of energy, 9 Convexity of pulleys, 141 Co-ordinates, Cartesian, 30 Copper, 48 effect of alloying with, 49 plates, loss of strength when heated, 198 sheet, 90 Core sand, composition of, 106 Cornish and Lancashire bo , size of, 216 boiler, 192, 215 comparison with I.H.P. of engine, 216 duty, 208 Corrosion of boilers, 222 Corrugated flues, strength of, 235 iron roofing, 89 Cost of transmitting power by vari- ous methods, 309 Cotters through bars, proportion of, 157 Cotton rope, 147 Coulomb, definition of a, 310 Counter-efficiency of a machine, 121 Counterweights for crane chains, 307 Couples, 23 Coupling bolts for screw shaft, 100 in series and parallel, 310 Couplings, proportions of, on screw shaft, 101 Crab winches, 159 Crane chains, counterweight for, 307 remarks on, 151 strength of, 149 hand power, 159 Cianeman, power of, 158 Cranes, height of lift for, 304 lifting rama for hydraulic, 305 stress allowed on wrought iron for, 307 turning rams for hydraulic, 305 Crank and piston notes, 247 Crank pin, strength of, 259 shafts, built up, 269 strength of, 101 Crowds, weight of men in, 76 Crown wheel, 151 Crucible cast steel, 43 Crude wrought iron, 39 Cube measure, 319 Cubical strain, 71 Cup leathers, 294, 297 friction of, 294 Curvature, radius of, 93 Curve, hyperbolic expansion, 245 of quickest descent, 30 of rope or chain, 147 Cut-off, point of, 251 Cutting speeds and feeds, 129-133 tools, Holtzapffel's classification, 129 Cylinder lagging, wood for, 55 ratios, 252, 263 thickness of, 262 Cylinders for storing gases, 316 \ hydraulic press, 301 D'ALEMBERT'S principle, 11 Dalton's law of gases, 177 Danish balance, principle of, 27 Dannemora cast steel, 45 Dead load, usual allowance for, 62 Deal, fir, pine, &c., 56 Decimal equivalents to fractions of an inch, 330 Deduction contrasted with induc- tion, 1 Defects in wrought iron, 41 Deflection, 93 and camber, 93 coefficients for rectangular beams, 94 of reaction for, 94 of beams under impact, 97 of girders, 95 of solid beams, 93 of springs, 97, 225-228 of wrought-iron girders, formula for, 95 Delivery cranes, 159 of water in pipes, 290 Delta metal, 52 OF THE 382 HANDBOOK FOE MECHANICAL ENGINEERS. Density, mass and weight, 6 T>e Pambour's principles, 243 Derrick poles, safe load on, 160 Descartes' doctrine of conservation of motion, 1 Diagonal riveting, 1 19 Diametral pitch, 155 Diaphragm regulator for hydraulic machinery, 302 Differential pulley calculations, 160 screw, 26 Dimensions of engine details, 261 Dimorphism, 4 Discharge of steam through pipes, 187 of water, practical, 280 over weirs, 282 through pipes from natural head, 287 various apertures, 279 Displacement of ships, 271 Distributed loads on continuous girders, 78 Dock gates, 307 Dr. Angus Smith's composition, 57, 300 Double belts, large, 142 Drains, rivers, sewers, &c., flow in, 283 Draught in chimney, force of, 205 stack, 204 Drawings, colours used in, 326 composition of colours for, 327 section lines in, 327 Dry puddling, 38 sand moulding, 105 Drying stove, foundry, 106 Duckham's weighing machine, 27 Dulong and Petit' s law, 174 Duplicate ratio of velocity, 12 Duty of engines, 208 compared with coal used, 209 progress in, 208 Dynamic energy, 8 Dynamical theory of heat, Rankine, 169 Dynamics, modern notation in, 12 statics and, 23 Dynamometers, 124 Dyne, or metrical kinetic unit, 8 E.M.F., or electromotive force, 311 Earth wagons and barrows, wood for, 56 Economic efficiency of steam boiler, 195 Economical working of machines, 121 Economy of compound engines, 238 of hi^h-pressure steam, 238 Effect of carbon in iron, 34 Effective horse-power, 242 pressure for hydraulic cranes and hoists, 302 for hydraulic machinery, 302 Efficiency of boilers, 195 of paddle wheels, 270 of pumps and accumulator, 296 of riveted joint, 116 of steam engines, 242, 243 of thermodynamic engine, law of, 184 of water-raising machines, 284 useful work and, 121 Egg-ended boiler, 192 Eidsfos Stobestaal cast steel, 46 Elasticity, definition of modulus of, 70 elongation by, 70 explanation of modulus of, 69 Hooke's law of, 69 limit of, 68 moduli of, 71 of bulk, modulus of, 71 torsional modulus of. 99 Young's modulus of, 70 Electric lighting, 313 power required for, 314 transmission, 308 wiring, 315 Electrical equations, 312 terms, 311 units, 310 work, measure of, 312 Electricity, comparison of, with other powers, 308 Elephant boiler, 192 Elongation under stress, 69, 70 Endless screw, or worm, 26 Energy, conservation of, 9 convertibility of, 9 kinetic, 8 INDEX. 383 Energy of fly-wheel, 255-259 of motion, 9 potential, 8 Engine shafts, calculation of, 260, 261 Engines, compound, economy of, 238 progress of, 238 duty of, 208 compared with coal used, 209 early forms of, 237 horse-power of, 240 resistance in, 246 triple expansion, 252 Entropy, 173 Epitome of mensuration, 324 Equality of moments, principle of the, 22 Equilibrant of forces, 21 Equilibrum, 14 of floating bodies, as ships, 270 of forces, 20 Estimating, weight of materials for, 89 . Ether, universal, 169 hypothesis of, 308 Ether-monads, combination of, 3 Evaporation, fuel required for, 204 heat required for, 1 82 in boilers, experiments on, 211 of steam, solution and, 182 of water, natural, 284 Evaporative efficiency, 195 power of boiler, 195 value of different temperatures, 209 Expanding alloy, 51 Expansion curves, 181 hyperbolic, 245 of bridges by change of tem- perature, 66 of castings, 111 of gases, 177 of metals by heat, 54 of steam pipes, 188 Expansions, number of, in various engines, 251 FACTOR of safety, 59 steam boilers, 228 Factors, solving roots by, 323 Factory chimneys, 201-205 Fairbairn boiler, 193 Falling bodies, formulae for, 28 Fastest mile, the, 32 Farad, definition of, 310 Fatigue of wrought iron, 69 Feed water, advantage of heating, 212 required in boiler, 212 Fender and rubbing pieces, wood for, 56 Field boiler, 193 Firj deal and pine, 56 posts, strength of, 80, 81, 82 Fire bars, 217 grate, coal burnt per square foot of, 205 Fire-damp, 36 Flange couplings for screw shaft, 100, 101 Flanges of steam cylinders, studs in, 102 Flat carriage springs, strength of, 97 plates, strength of, 231, 232 ropes, 147 Flexure, moment of, 72 Floatation power of water, 278 Floating bodies, equilibrium of, 270 Floats for paddle wheels, wood for, 55 Floor plates, strength of, 77 Floors, safe load on, 76 Flue, heat in, 201 Flues, collapsing pressure of, 233- 235 corrugated, strength of, 235 Fluids under pressure, mechanical value of, 291 velocity of, flowing into vacuum, 186 Fly ropes, 146 wheels, notes and formula, 255 investigation of, 258 Foot-poundals, 13 Foot-pounds, 8, 10, 13 Foot-second-pound system, 8 Force, absolute unit of, 7 centrifugal, 17 matter and motion, 1 moment of a, 22 of draught in chimney, 205 384 HANDBOOK FOB MECHANICAL ENGINEERS. Force of gravity, 5 pumps, packing for, 297 transmissibility of, 20 units of, 7 Force-polygon, 21 Forces, angular measurement of, 123 composition and resolution of, 22 equilibrant of, 21 equilibrium of, 20 parallelogram of, 20 polygon of, 21 resultant of, 21 sense of, 20 triangle of, 20 Forge iron, 37 Forging, 113 presses, 138 hydraulic, 301 Formulae for electricians, 312, 314 Forth bridge, experiments on wire ropes, 148 Foundry drying stove, 106 iron, 37 moulding in, 105 pig, 109 Fox's corrugated flues, 235 Fraction, reduction of, to lowest terms, 322 Fractions and decimals, 330 of an inch and decimal equiva- lents, 330 types of, 321 Freezing of water, 289 French horse-power. 242 measurements, basis of, 327 measures, 327 or elephant boiler, 192 terms for weight and gravity, poids and pesanteur, 6 Friction and heat, 164 Ball's experiments on, 164 coefficient of, 163 definitions of, 163 laws of, 162 mean coefficients of, 166 of accumulators, 294 of cup leathers, 294 of journals, 165 of motion, 163 Morin's experiments on, 163 Friction of steam engines, 263 of water in pipes, 287 rolling, 168 statical, 163 Fuel, absolute heating power of, 197 air required to burn, 200 consumption, evaporation from increased, 206 of, per I.H.P., 213 economisers, 213 units of heat per Ib. by experi- ment, 197 theoretical, 196 thickness of, in furnace, 206 Fuels, calorific value of, 196 chemical composition of, 196 Funicular polygon, 21 Furnaces, boiler, 206 Fusee, 152 Fusible alloys, 52 below'212 F., 53 safety plugs for boilers, 52 gr, value of, 6 G.C.M., or greatest common mea- sure, 322 Galileo's law of inertia, 10 laws of motion, 13, 14 Galloway boiler, 192 Galvanic batteries, 310 Galvanised iron roofing, 89 Galy-Calazat steel, 45 Gas, coal, 316 engines, 275 threads, Whitworth standard, 331 volume of, at given pressure and temperature, 177 Gases and vapours, 175 cylinders for storing, 316 heating by contact of, 197 kinetic theory of, 176 laws of, 177 ordinary, 176 permanent, 175 solids, liquids and, 4 Gauge, Birmingham wire (B.W.G.), 333 for screws," British Association (B.A.G.), 332 INDEX. 385 Gauge, sheet and hoop iron (B.G.)> 334 standard Imperial wire (S.W.G.) 335 Gaussian unit, 7 Gay-Lussac's law of gases, 177 Gearing, determining the propor- tions of, 156 formula for strength of, 154 Manchester pitch, 155 mill, 155 notes on belt, 140 toothed, notes on, 152 strength and weight of, 154 varieties of, 151 Geneva stop, 152 Geometrical mean, 319 series, 321 German silver, 51 Gilchrist-Thomas steel, 45 Girders, approximate strength of, 65 deflection of, 95 formula for deflection of wrought- iron flanged, 95 Gooch's link motion, 253 Governor, efficiency of, 255 Watt's, 254 Gravitation, laws of, 5 units, 8 Gravity, centre of, 14 force of, 5 Grease in boilers, 222 Green-sand moulding, 105 Green's fuel economiser, 213 Grinding and polishing, speed of, 136 Guide bar, pressure on, 248, 249 Gun-metal composition of, 49 Gyration, centre of, 17 radius of, 17, 73 H.C.F., or highest common factor, 322 Hair felt, 189 Hammer shafts, wood for, 56 Hammers, 125 steam, 137 work of, 126 Hand firing and mechanical stoking, 210 Hand pump for hydraulic press, 300 Hand-power crane, 159 Hardness of minerals, scale of, 35 of water, 220 Hauling machines, power and speed of hydraulic, 303 Haystack or balloon boiler, 192 Heat, capacity of bodies for, 173 comparative transmission of, 189 engine, general view of, 185 expansion of metals by, 54 horse-power of boiler, 193 in boiler furnaces, 206 in flue, 201 latent and total, 175 loss of, by pipes, 188 in boiler, 207 mechanical equivalent of, 171 per Ib. of fuel, theoretical units of, 196 quantity of, 172 Rankine's dynamical theory of, 169 rate of transmission of, 197, 198 required for evaporation, 182 sensible, 170 sources of, 170 specific, 173 of various bodies, 174 units of, per Ib. of fuel by experi- ment, 197 utilised in boilers, 207 transfer of, 171 Heating by contact of gases, 197 by hot water, 190 by steam, 190 power of fuel, absolute, 197 surface of boilers, 199 surfaces, comparative value of, 199 Heaton steel, 45 Helical joints for boilers, 233 Helmholtz' " sum of the tensions," 8 Hemisphere, centre of gravity of, 16 Hemispheroid, centre of gravity of, 16 Hemp ropes, notes on, 144 strength of, 145, 147 Hide ropes, 146 2 386 HANDBOOK FOB MECHANICAL ENGINEERS. High-pressure cylinders for storing gases, 316 * steam, economy of, 237 tension system of electric trans- mission, 309 Holtzapffel's classification of cutting tools, 129 Hooke's law of elasticity, 69 Hoop-iron gauge (B.G.), 334 Horse-power, 8, 240 effective or brake, 242 estimated, 241 French, 242 from one cubic foot of water, 194 indicated, 241 nominal, 193, 240 of boilers, 193 from dimensions, 194 of engines, 240 per ton weight of boilers, 214 to drive machine tools, 133, 138 Hot blast pig iron, 36 Hot-shortness, 41 Hot-water, heating by, 190 Hunter's differential screw, 26 Hunting-cog, 152 Hydraulic cranes and hoists, effec- tive pressure for, 302 lifting rams for, 305 stress allowed on wrought iron in, 307 turning rams for, 305 forging presses, 301 hauling machines, power and speed of, 303 lilting, speed of, 304 machinery, 276 areas of valves for, 306 diaphragm regulator for, 302 effective pressure for, 302 power required to work, 292 mains, thickness of pipes for, 298 pipes, proportions of, 298 power, speed of lifting with, 304 press cylinders, 301 invention of, 301 with hand pump, 300 pressure accumulator, 292 variation of, 293 ram, 285 riveting, 117 Hydraulic slide valves, area of ports in, 306 valves, area of, 306 water-raising machines, effi- ciency of, 284 Hydraulics, 23 summary of, 276 Hydrodynamics, 23 Hydrokinetics, 23 Hydrostatic paradox, 278 Hydrostatics, 23 Hyperbolic expansion curves, ordi- nates to, 245 logarithms, table of, 244 Hypothesis of a universal ether, 308 IMPACT of moving bodies, 12, 126- 128 on beams, 85 deflection under, 97 Imperial standard wire gauge, 335 Imponderables, 169 Impulse, definition of an, 13 Impurities in water, deposition of. 220 Inclined plane, principle of, 26 velocity of descent on, 30 planes, rolling on, 30 Incrustation, blowing off to prevent, 219 in boilers, 221 Indestructibility of matter, 2 Indicated horse-power, 241 Indicator diagrams, piston-constant for, 247 Induction and deduction contrasted, 1 Inertia, 9 and momentum, 10 law of, 10 moment of, 72, 73 Initial pressure, 243 Intensity of motion, 1 of sound, 31 of stress, 59 Intermediate wheel, 152 Iron and steel shipbuilding, 68 common ores of, 34 defects in wrought, 41 effect of carbon in, 34 expansion of, by heat, 54 INDEX. 387 Iron, handy numbers for weight of, 90 molecular condition of, 39 ores, classification of, 108 plates, loss of strength when heated, 198 roasting and smelting, 35 rolling mills, 40 roofing, galvanised, 89 sheet and hoop, gauge, 334 single and double sheet, 40 squeezing, shingling and rolling, 39 varieties of, 33 Ironwork, designing, 65 Irrational numbers or surds, 321 Isomeric substances, 4 Isomorphous substances, 4 Isothermal curve, 181 JOINERS' tools, wood for, 55 Joints for boilers, helical, 233 for hot- water pipes, 191 notes on riveted, 116 Joule, definition of a, 310 Joule's equivalent, 171 Journals for shafts and axles, 158 friction of, 164 Joy's valve motion, 253 KEPLEB'S law of motion, 13 Keys, ordinary proportions of, 157 Kinematics, 23 Kinetic energy, 8 theory of gases, 176 Kinetics, 23 Knots, speed in, 264 LANCASHIRE boiler, 192 boilers, sizes of, 216, 217 Landing cranes, 159 Landore-Siemens steel, 44 Lantern wheel, 151 Lap of slide valve, 249, 250 Latent and total heat, 175 Lathe, power required to drive, 133 speeds and feeds, 132 Lattens, 40 Law of efficiency of thermodynamic engine, 184 of elasticity, Hooke's, 69 of inertia, 10 Laws of friction, 162 of gases, 177 of gravitation, 5 of heat, 182, 183 of motion, 13 of thermodynamics, 182, 183 Lead, effect of alloying with copper, 49 of slide valve, 249, 250 sheet, 90 Least resistance, Moseley's prin- ciple of, 23 Leather belts, strength of, 142 rope, 147 Leverage, orders of, 24 Lifting rams for hydraulic cranes, 305 with hydraulic power, speed of, 304 Lifts, wire ropes for, 148 Light testing, 316 visibility of, at a distance, 316 Lighting, electric, 313 power required for, 314 Limit of elasticity, 68 Limiting angle of resistance, 163 Lineal measure, 318 Link motions, 253 Link-polygon, 21 Liquids, solids and gases, 4 Load not axial, effect of, 79 on bridges, 96 on supports of continuous girders, 78 Loam moulding, 105 Lock gates, 307 nuts, to secure, 103 Locomotive boiler, 229, 235 boilers, 193 express engines, dimensions of, 273 wheels, adhesion of, 272 Locomotives, effect of speeds aud gradients, 273 tractive force of, 271 Logarithms, hyperbolic, table of, 244 principle of, 323 2 c 2 588 HANDBOOK FOR MECHANICAL ENGINEERS. Loss of head in bends, 277 of heat by pipes, 188 by boiler scale, 198 in boilers, 207 of strength by load not being axial, 79 in copper platen when heated, 198 in iron plates when heated, 198 Low tension system of electric transmission, 309 Lowmoor iron, 40 Lubricants for various cases, 167 MACHINE riveting, 117 tools, resistances in, 132 speed of, 129-133 Machinery in motion, 121 Machines, economical working of, 121 object of, 120 theory of, 24 use of, 120 Machining, allowance for, 105 Malleable cast iron, 47 strength of, 65 Manchester pitch, wheel gearing, 155 Manholes in boilers, size of, 218 Manila rope, strength of, 145, 147, 148 Manual power, comparison of, 28 Marine boilers, 193 engines, cylinder diameters, 252, 263 Market sizes of plates, 91 Marlborough wheel, 152 Mass acceleration, 13 density and weight, 6 velocity or momentum, 13 Materials, weight of, for estimating, 89, 90 Mathematical concepts, 318 signs, 319 Matter, constitution of, 2 force and motion, 1 indestructibility of, 2 states of, 2, 3, 4 Mayer's experiment, 172 Mean centre of gravity, 14 Mean effective pressure, compound engines, 247 pressure, 243 without logarithms, 245 Measurement of forces, 2 Measures, French, 327 Mechanical advantage, 24, 122 drawing, colours for, 326 efficiency, 121 elements, 24 equivalent of heat, 171 horse-power of boiler, 193 powers, 24 stoking and hand firing, 210 value of fluids under pressure, 291 of water under accumulator pressure, 291 Mechanics, classification of, 23 Melting metal for castings, mode of, 110 points of various metals, 53 Men in crowds, weight of, 76 useful work of, in ft.-lbs. per minute, 28 Mensuration, epitome of, 324 Merchant bar, 39 Metals, expansion of, by heat, 54 melting-point of, 53 weight of, 55 Metric system, equivalents of, 328 measurements in, 327 units in, 328 Metrical absolute unit of force, 8 Mild steel cylinders for high-pres- sure gases, 316 strength of, 62, 63 Mill gearing, 155 speed of, 156 Milling cutters, speed of, 132, 133 Minerals, scale of hardness of, 35 Mitis process of casting wrought iron, 42 Mitre wheels, 151 Mixtures of pig iron, 109 Modes of motion, 9 Moduli of elasticity, 71 Modulus, definition of, 68 of elasticity, definitions of, 70 explanation of, 69 of bulk, 71 torsional, 99 INDEX. 389 Modulus of elasticity, Young's, 70 of rigidity, 68 of rupture for transverse strains, 74 of section or strength modulus, 73 of steam engine, 242 Molar motion, 4 Molecular condition of iron, 39 motion, 4 Molecules, particles and atoms, 2 Moment of a force, 22 of a section, 75 of flexure or bending moment, 72 of inertia, 72, 73 of load, 74 of resistance, 74, 75 working load for given, 75 of rupture, 74 Moments, 22 principle of equality of, 22 Momentum, 11 and inertia, 10 and vis viva, 12 Mooring rings, strength and dia- meter of, 151 Morin's experiments on friction of motion, 163 Mortice wheels, 152 Moseley's principle of least resist- ance, 23 Motion, definition of, 1 laws of, 13 transmission of, 140 varieties of, 2 Motive power, 120 Moulding and casting, notes on, 107 in foundry, 105 sand, nature of, 106 Moving bodies, impact of, 12, 126- 128 force, 12 Muntz metal, composition of, 49 NAVIER'S modification of Boyle and Marriotte's law, 179 Negative slip, 266 Neutral axis, 72 Newcomen's engine, 237 Newton's law of universal gravita- tion, 5 laws of motion, 13 Nickel alloys, 51 Nomenclature of large numbers, 320 Nominal horse-power of boilers, 193 of engines, 240 Notation in dynamics, modern, 12 Number of expansions in various engines, 251 Nuts, standard sizes of, 331 OAK posts, strength of, 80, 81, 82 Object of machines, 120 Ohtn, definition of an, 310 Ohm's law, 312 Oils, action of, on melals, 167 Orders of leverage, 24 Ores, classification of iron, 108 of iron, common, 34 Oscillation and vibration, 18 centre of, 18 Otto cycle of gas engines, 275 PACKING for force pumps, 297 Paddle wheels, 269 efficiency of, 270 Painting ironwork, 56 Paraboloid, centre of gravity of, 16 Parallelogram of forces, 20 Particles, molecules and atoms, 2 Parting sand, nature of, 106 Pascal's principle, 279 Pattern making, 104 wood for, 55 Patterns, allowance for machining, 105 black varnish for, 105 Pendulum, formulae for, 19 length of London seconds, 18 Percussion, centre of, 20 Permanent gases, 175 set, 59 Petroleum, calorific value of, 196 Phosphor bronze, 52 Phosphorus, effect of alloying with copper, 49 390 HANDBOOK FOB MECHANICAL ENGINEEKS. Photometry, 316 Pig iron, 36, 109 analyses of, 36, 108 charges employed at Dowlais, 108 classification of, 37 mixtures of, 109 relative production of, in dif- ferent countries, 46 Pile-driving, formulae for, 87 notes on, 87 Pillars and struts of wood, 81 Pine, fir and deal, 56 Pinions, 151 Pipe main, pressure in, 293 delivery of water in, 290 Pipes, discharge of steam through, 187 through, from natural head, 287 Dr. Angus Smith's composition for coating, 300 expansion of steam, 188 friction of water in, 288 general rule for thickness of, 299 how measured and marked, 300 loss of heat by, 188 proportions of hydraulic, 298 steam, expansion of, 188 tests of metal for, 61, 289 thickness of, for hydraulic mains, 298 of, for water companies' mains, 298 of steam, 188 velocity of steam in, 188 of water through, 290 Piston and crank notes, 247 point of maximum velocity, 243 Piston-constant for indicator dia- grams, 247 Pitch of screw propeller, 267 alteration of, 268 of sound, 31 Planing machine, speeds and feed, 132 Plates, cast-iron, strength of, 77 encastre', strength of, 231, 2:i2 iron and steel, market sizes of, 91 strength of iron and steel, 63 when heated, 198 Plumb line, 7 Plumber's solder, 53 Pneumatics, 23 Poids and pesanteur, use of, 6, 7 Point of cut-off, 251 Polarity, 3 Polishing and grinding, speed of, 136 Polygon, force, 21 funicular, 21 link, 21 of forces, 20 Pooley's weighing machine, 27 Ports, area of steam, 250 Positional energy, 8 Posts, timber, safe load on, 80 Potential energy, 8 Poundal, definition of, 7, 13 Poundal-second or pulse, 13 Pound-celo and pound-velo, 13 Power, definition of, 99 of craneman, &c., 158 of men in various operations, 28 required to work hydraulic machinery, 292 transmission of, by shafting, 99 Powers and roots, 322 mechanical, 24 Preserving ironwork, 56 Press cylinders, 301 hydraulic, with hand pump, 300 Presses, steel forging, 138 Pressure, atmospheric, 181 effective, for hydraulic machi- nery, 302 in pipe mains, 293 of water, 277 of wind, 88 on bearing area, 103 on moving surfaces, safe work- ing, 164 to close rivet, 117 to temperature of steam, relation of, 178 Pressures and reactions, 2 Prices, limits of ordinary, Cleveland district, 92 limits of ordinary, Staffordshire district, 91 Prime numbers, 152, 321 Priming, causes of, 222 Principle of Archimedes, 278 of least resistance, 23 INDEX. 391 Principle of the equality of mo- ments, 22 of virtual velocities, 122 definition of, 123 Production of iron and steel by different countries, 46 Products of combustion, 200 Proof strength, 59 Propellers, alteration of pitch, 268 definitions relating to, 264 formula for pitch of, 268 I.H.P. required for, 268 notes on screw, 265 pitch of screw, 267 slip of screw, 266 Proportion, ratio and, 322 Proportions of beams for strength and stiffness, 84 of bolts and nuts in carpentry, 101 of cotters through bars, 157 of flange couplings on s^rew shaft, 101 of gearing, determining the, 156 of hydraulic pipes, 298 of keys, 157 of rivets to thickness of plates, 118 of wheel teeth, 157 Puddled bar, 39 Puddling, 38 Pulley block sheaves, wood for, 55 calculations, differential, 160 principle of the, 25 Pulley-gear, 25 Pulleys, convexity of, 141 Pulse, definition of a, 13 Pumping, speed of, 295 Pumps, air and circulating, 262 and accumulator, efficiency of, 296 centrifugal, 286 packing for force, 297 Punching, loss of strength by, 116 shearing, &c., 136 Purchase, 121 Pyramid, centre of gravity of, 16 QUALITIES of cast iron, 47 of wrought iron, 40 Quantity of motion, 11 KADIAL valve gears, 254 Radian, definition of, 124 Radiation, comparative, 190 of heat, 171 Radius of curvature, 93 of gyration, 17, 73 Rag-wheel, 152 Railway curves, 274 work done in moving truck, 10 Railways, resistance on, 272 Rams, lifting, for hydraulic cranes, 305 turning, for hydraulic cranes, 305 Rastrick boiler, 192 Ratio and proportion, 322 Reciprocals, 319 Record speeds, 32 Red shortness, 41 Reduction of fraction to lowest terms, 322 Refining pig-iron, 37 Regular solids, centre of gravity of, 16 Regulator for hydraulic machinery, 302 Relative velocities, 32 volume of steam, 179 Relief, angle of, in tools, 129 Repose, angle of, 162 Resilience, 85 Resistance in machine tools, 132 in steam engines, 246 limiting angle of, 163 moment of, 74, 75 on railways, 272 principle of least, 23 Resolution and composition of forces, 22 Resultant of forces, 21 Retaining wall, centre of gravity of, 15 Rigidity, modulus of, 68 Rings, strength of, 150, 151 Rivers, sewers, drains, &c., flow in, 283 Rivet iron, strength of, 62, 66, 67 length to form head of, 116, 118 tension in, 116,118 Riveted joint, efficiency of, 116 joints, notes on, 116 Riveting, 116-119 392 HANDBOOK FOR MECHANICAL ENGINEERS. Hireling, diagonal, 119 for boilers, 229 hydraulic and machine, 117 single, 118 Rivets, pressure to close, 1 17 proportions of, to thickness of plate, 118 weight of, 90 Roads, traction or friction on, 168 Roasting and smelting, 35 Rolled joists, strength of, 65 Rolling friction, 168 iron, 39 mill, fly-wheel shaft, 260 speeds, 136 mills, iron, 40 on inclined planes, 30 Roman statera, principle of, 27 Roofing, galvanised iron, 89 Roofs, timber, 88 weight of timber, approximate, 89 Roots, solving by factors, 323 Rope, curve of, 147 driving, 146 tackle for lifting, 160 wire, experiments on at Forth Bridge, 148 Ropes, fly, 146 formula for strength of hemp, 145 hide, 146 Lang's patent wire, 148 leather, cotton, steel and hemp, 147 notes on hemp, 1 44 R. S. Newall & Go's wire, 149 tensile strength of, 148 tests of, 147 Rotation of the earth, effect on plumb line, 7 effect on weight, 6 Rough gangways, wood for, 56 Round, definition of, 124 Rupture, modulus of ? 74 moment of, 74 Rust joint cement, 191 SAFE load on columns and piers, 78 on floors, 76 on iron and steel, 62 Safe load on posts, 80 on structures, 76 on timber, direct compression, 82 stresses in machinery, 62 Safety, factor of, 59 plugs, fusible, 52 valves for boilers, 223 B. of T. rules for, 224 initial compression of springs for, 227 lift of, 224, 227 spiral springs for, 227 spring balance, 228 to calculate leverage of, 225 springs for, 228 Salt water feed, 222 Sample bars of cast iron, 61 Sand for moulding, 106 Saturated steam, properties of, 180 Savery's engine, 237 Scaffold poles, wood for, 56 Scale, boiler, 220 of hardness of minerals, 35 Screw cutting, 134 for worm wheel, 135 principle of, 26 propellers, definitions relating to, 264 formula for pitch of, 268 I.H.P. required for, 268 notes on, 265 pitch of, 267 relative efficiency of, 265 relation of pitch to diameter, 267 slip of, 266 shaft flange coupling, 100, 101 Screws, B.A. gauge for, 332 Scumming boilers, 219 Sea water, 221 Seatings, boiler, 217 Section lines on mechanical draw- ings, 327 Sector of disc or cylinder, centre of gravity of, 16 Segment of disc or cylinder, centre of gravity of, 16 Semicylinder, centre of gravity of, 16 Sense of forces, 20 Sensible heat, 170 INDEX. 393 Sewers, rivers, drains, &c., flow r in, 283 Shaft couplings, 101 Shafting, approximate strength of, 99 formula for strength of, 100 Molesworth's formula for wrought iron, TOO notes on torsion and, 98 transmission of power by, 99 velocity of, 141 Shafts, built-up crank, 269 calculation of engine, 260 journals for, and axles, 158 transverse strength of, 101 Shapton's hydrostatic weighing machine, 27 Shear legs, safe load on, 160 steel, 43 Shearing and punching, 136 compared with tensile strength, 65 Sheet copper, 90 iron, single and double, 40 lead, 90 zinc, 90 Sheet-iron gauge (B.G.), 334 Shell wheel, 152 Shingling, squeezing and rolling, 39 Shipbuilding in steel, reduction in weight, 68 specification tests of iron and steel, 67 steel and iron, 68 Ships, displacement of, 271 Shop shafting, bearings for, 166 velocity of, 141 tools, horse-power required, 138 Siemens steel, 44 Siemens-Martin steel, 44 Simple machines, 24 Simpson's rule for area of irregular figure, 246 Single and double sheet iron, 40 double and treble best iron, 39 Sizes of fir timber in balk, 86 of timber for strength, stiffness and convenience, 84 Slide valves, explanation of terms, 249 hydraulic, area of, 306 Slide-valve notes, 250 Sling chain rings, strength of, 151 strength of, 149 Slip, negative, 266 of screw propellers, 266 Sluice paddles, wood for, 55 Smith's, Dr. Angus, composition, 300 Snatch block, 26, 160 Solders, 53 Solids, liquids and gases, 4 Solution and evaporation of steam, 182 Sound, velocity of, 31 waves, 31 Sources of heat, 170 Specific gravity, 7 heat, 173 of various bodies, 174 Specification tests, cast iron, 61 common wrought iron, 67 wrought iron, bridge and girder work, 66 and steel for ship- building, 67 Speed in knots, 264 of hydraulic hauling machines, 303 of lifting with hydraulic power, 304 of machine tools, 129-133 of mill gearing, 156 of polishing and grinding, 136 of pumping, 295 Speeds, cutting, 129-133 in cutting metals, 129 rolling mill, 136 Spelter, 53 Spiegel s, 37 Spiral springs, 225-228 Spontaneous rotation, centre of, 20 Spring balance, 27 safety valve, 228 beams, wood for, 56 steel, 43 Springs, flat carriage, strength of, 97 for safety valves, initial com- pression of, 227 to calculate, 228 spiral, 227 spiral, 225-228 Spur wheels, 151 391 HANDBOOK FOR MECHANICAL ENGINEERS. Square measure, 318 Squared paper, use of, 30 Squeezing, shingling and rolling, 39 Staffordshire iron, 63, 64 plates, sizes of, 91 Stame or superheated steam, 185 Standard candle, 316 States of matter, 2, 3, 4 Statical energy, 8 Statics and dynamics, 23 Stay bolts, strength of, 230 Stays, boiler, 230 Steam, advantage of expanding, 238, 243 boilers, 192-236 condensation of, 185 discharge through pipes, 187 economy of high -pressure, 238 engine dimensions, 261 modulus of, 242 engines, coefficient of, 296 comparison of, 263 friction of, 263 multipliers for various sizes of same type, 263 resistances in, 246 hammers, 137 heatiug by, 190 jacketing, advantage of, 253 pipes, diameter of, 187 expansion of, 1 88 thickness of, 188 ports, area of, 250 pressure and temperature of, 179, 182 and volume of, by Boyle and Marriotte's law, 179 production of, in Cornish and Lancashire boilers, 193 properties of saturated, 180 relation of pressure to tempera- ture, 178 relative volume of, 179 ships, Scott Russell's rules, 269 solution and evaporation of, 182 superheated, 185 velocity of, in pipes, 188 worked expansively, 243 Steel and iron shipbuilding, 68 bending tests, 67 Bessemer and Siemens, 44 blister and spring, 43 Steel, blister, classification of, 43 breaking stress and safe load, 62 characteristics of, 33 cylinders for storing gases, 316 Dannemora cast, 45 definition of, 42 effect of carbon in, 45, 46 Eidsfos Stobestaal cast, 46 forging presses, 138 Galy-Calazat, Heaton, Gilchrist- Thomas and basic, 45 relative production of various countries, 46 ropes, 147 sheer and crucible, 43 Siemens-Martin and Landore- Siemens, 44 specification tests of (ship- building),-67 tempering of, 114 weight of, handy numbers for, TO wrought, and cast iron, to dis- tinguish, 33 Steelyard for coal cranes, 304 principle of, 27 Steelyards and weighing machines, 27 Stephenson's link motion, 253 Stiction or statical friction, 163 Stiffness of timber, 84, 85 Stoking boilers, 206 Stone piers, safe load on, 78 Strain allowed on wrought iron in hydraulic cranes, 307 and stress, definition of, 58 Strains, classification of, 58 Streams, velocities of, 281 Strength and deflection of springs, 97, 225-228 and stiffness of timber, 85 definition of, 58 modulus, 73, 75 of boiler-shell, ultimate, 232 of bolts and studs, 102 of cast-iron columns, 78, 79, 80 of chains, 149 of gearing, formula for, 154 of girders, approximate, 65 of iron and steel plates, 63 of manila rope, 145 of ropes, average tensile, 148 formula for, 145 INDEX. 395 Strength of structures, 76 of timber, 82 beams, formula for, 82 of toothed gearing, 154 of various metals and alloys, 63 Stress, definitions of strain and, 58 Structures, safe load on, 76 strength of, 76 Struts and pillars of wood, 81 wrought iron, 79 Stud chains, strength of, 150 Studs, stress allowed on, 102 Suction in chimney shaft, 205 Superheated steam, 185 Supervision of boiler, effect of, 210 Surcharged steam, 185 Surds, 321 Swaging, 113 Swedish iron, 64 Systems of electric transmission, 309 TACKLE for lifting, 160 Tanks, riveting for, 1 1 8 Taper of plugs for boiler cocks, 219 Tapered girder web, centre of gravity of, 15 Tee-iron, centre of gravity of, 15 Teeth of wheels, proportions of, 157 Temperature and pressure of steam, 177-180 colours corresponding to, 114 definition of, 170 effect of change of, 171 on bridges, 66 in boiler flue, 201 of boiling water and steam", 182 of steam, relation of pressure to, 178, 179 Tempering, 114 steel, colours in, 115 Tensile and shearing strength, 65 Terminal pressure, 243 Test bars of cast iron, 61 Testing boilers, 229 cast iron, 60 for pipe making, 61 wrought iron, CO Tests of iron and steel, physical and chemical, 64 of metal for pipes, 61, 289 Tests of ropes, 147 Terms, arithmetical, 319 electrical, 311 Theorem of three moments, 77 Theory of heat, Kankine's djnami- cal, 169 of machines, 24 Thermal unit, British, 171 Thermodynamic engine, formula for perfect, 185 engines, law of efficiency of, 184 function, 173 Thermodynamics, first law of, 182 second law of, 183 Thermometer, mercurial, 170 Thermometers, comparison of, 170 Three moments, theorem of, 77 Tie bars, rivets in, 119 Tilted steel, 43 Timber beams, formula for strength of, 82 framing, wood for, 56 in balk, size of fir, 86 piling, notes and formula, 87 wood for, 56 posts, safe load on, 80 roofs, 88 safe load on, 82 size, for strength, stiffness and convenience, 84 strength and stiffness of, 85 trees, diameter and length of, 86 ultimate strength of, 82 Timbre of sound, 31 Tin, effect of alloying with copper, 49 Tinmen's solder, 53 Tomlinson's centrobaryc theorem, 16 Tool handles, wood for, 56 steel, carbon in, 45 Tools and fittings, workshop, 129 angles of, 129 caulking, 119 cutting speed of machine, 129- 133 Holtzapffel's classification of cutting, 129 resistances in machine, 132 workshop, classification of, 125 Toothed gearing, notes on, 152 396 HANDBOOK FOR MECHANICAL ENGINEERS. Toothed gearing, principle of, 25 strength and weight of, 154 varieties of, 151 Torque, definition of, 124 Torricelli's theorem, 277 Torsion and shafting, notes on, 98 Torsional modulus of elasticity, 99 resistance, 68 strength of various metals, 99 Toughened cast iron, 48 Traction or friction on roads, 168 Tractive force of locomotives, 271 Transfer of heat, 171 Transmissibility of force, 20 Transmission dynamometers, 124 of heat, comparative, 189 rate of, 197, 198 of motion, 140 of power by belting, 140-143 by gearing, 151-157 by ropes, 144-149 by shafting, 99 electric, 308, 309 Transmitting power by various methods, comparative cost of, 309 Transverse impact, resistance to, 85 strain, modulus of rupture for, 74 strength of shafts, 101 Trapezium, centre of gravity of, 15 Travel of slide valve, 249, 250 Trees, timber, sizes of, 86 Trial of engines, 210 Triangle, centre of gravity of, 1 5 of forces, 20 Triple expansion engines, 251, 252 Tubes, boiler, 218 Turbines, 285 Turning effort on crank, 248 rams for hydraulic cranes, 305 Twist, angle of, in shafting, 1 25 drill, pressure to work, 132 Two-cylinder compounds, 251, 252 ULTIMATE strength of iron and steel, 62 of various metals and alloys, 63 Unit, British thermal, 171 of heat, French, 172 Unit of work, 8 Units, C.G.S. or metric system, 8, 328 electrical, 310 employed in engineering calcu- lations, 329 gravitation, 8 in foot-second-pound system, 329 kinetic, 8 modern, in dynamics, 12 of force, 7 of heat per Ib. of fuel, by experi- ment, 197 theoretical, 196 Universal ether, 169, 308 Upsetting, 113 Use of wood in engineering, 55 Useful numbers, 55, 281, 314, 323 work and efficiency, 121 of men in tbot-lbs. per minute, 28 Utilisation of heat in boiler furnaces, 206, 207 VACUTJM, velocity of fluids flowing into, 186 Valve, notes on slide, 250 Valves, area of, for hydraulic ma- chinery, 306 ports in hydraulic slide, 306 B. of T. rules for safety, 224 safety, for boilers, 225 velocity of water through pipes and, 290 Vapours, gases and, 175 Variation of accumulator pressure due to working of machinery, 293 Varieties of boilers, 192 of iron, 33 of steel, 43-46 Varnish for patterns, 105 Velocity, definition of, 1, 12 of falling bodies, 28 of fluids flowing into vacuum, 186 of gases in chimney, 204 of sound, 31 of steam in pipes, 188 INDEX. 397 Velocity of water through pipes and valves, 290 of wood- working machinery, 135 ratio, 122 Velocities of streams, 281 relative, 32 Velo, definition of, 12 Vena contracta, 276 Vibration and oscillation, 18 Vibrations of strings, 31 Vicars' mechanical stokers, 210 Virtual velocities, definition of prin- ciple of, 123 principle of, 122 Visibility of light at a distance, 316 Vis inertise, 9 viva, 9 Volt, definition of a, 310 Volume of a gas at given pressure and temperature, 177 of steam, relative, 179 pressure and, of steam by Boyle and Marriotte's law, 179 Vulgar fractions, types of, 321 WAGON boiler, 192 Water as steam to give one horse- power, 252 chemical composition of, 3 companies' mains, pressure in, 293 sizes of, 289 thickness of pipes for, 298 compressibility of, 279 delivery of, in pipes, 290 expansion of, by heat, 54 floatation power of, 278 freezing of, 289 friction of, in pipes, 287 hardness of, 220 natural evaporation of, 284 pressure of, 277 required for condensation, 263 sea, 221 supply, 288 under accumulator pressure, me- chanical value of, 291 useful numbers in connection with, 281 practical discharge of, 280 Water, velocity of, through pipes and valves, 2~90 weight and bulk of, 280 wheels, 284 Water-gauge, glass, 219 Water-tube boiler, 193 Watt, definition of a, 310 Watt's first engine, 237 governor, 254 horse-power, 8 Wedge, principle of, 26 Weigh-beam for coal cranes, 304 Weighing machines, steelyards and, 27 Weight and bulk of water, 280 density, mass and, 6 of air, 7, 200 of casting from patttern, 105 of coal, 195 of iron, handy numbers for, 90 of materials for estimating, 89, 90 of men in crowds, 76 of sheet copper, 90 lead, 90 zinc, 90 of timber roofs, approximate, 89 of toothed gearing, 154 of various metals, 55 Weirs, discharge over, 282 with rectangular notch, 283 with triangular notch, 283 Welding, 113 loss of strength in, 114 Wet puddling or pig-boiling, 38 Wheel and axle, principle of, 25 gearing, Manchester pitch, 155 teeth, proportions of, 157 wood for, 55 Whitworth standard, bolts and nuts, 331 gas threads, 331 Wind, force of, 202 pressure, 88 Wire gauge (B.W.G.), 333 imperial (W.G.), 335 ropes, experiments on, at Forth Bridge, 148 for lifts, 148 Lang's patent, 148 K. S. Newall & Co.'s, 149 Wiring, electric, 315 398 HANDBOOK FOB MECHANICAL ENGINEERS. Wbhler's experiments, safe stress in machinery, 62 Wood, use of, in engineering, 55 Wood-working machinery, velocity of, 135 Work, accumulated, 8 definition of, 8 dependent on resistance, a electrical, measure of, 312 in terms of angular motion, 123 mechanical, 8 of hammers, 126 unit of, 8 Working load for given moment of resistance, 75 loads, 59, 62 strength of materials for machi- nery, 62 Workshop tools and arrangement of workshop, 125 and fittings, 129 World-substance or ultimate form of matter, 3 Worm, or endless screw, 26 wheel, screw for, 135 Wrought iron, breaking stress and safe loads, 62 bridge and girder work, spe- cification tests, 66 casting, 42 characteristics of, 33 crude, 39 Wrought iron, defects in, 41 fatigue of, 69 handy numbers for weight of, 90 limit of elasticity in, 68 qualities of, 40 safe load on, 62 shafting, Molesworth's for- mula for, 100 single, double and treble best, 39 specification tests of common, 67 for shipbuilding, 67 steel and cast iron, to distin- guish, 33 stress allowed on, in hy- draulic cranes, 307 struts, 79 testing, 60 YOKKSHIBE iron, 63, 64 Young's modulus of elasticity, 70 Z.G., or zinc gauge, 90 Zero of temperature, absolute, 170 Ziz-zag riveting, 116, 119 Zinc, effect of alloying with copper, 49 sheet, 90 LONDON: fBINTED BY WILLIAM CLOWES AND SONS, LIMITED, STAMFOBD STREJCt AND CHAJtING CBO6B. 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Details of Engines Displacement Nos. .. 34 and 35 .. 35 .. 35 to 37 .. 37, 38 38 Distilling Apparatus . . 38 and 39 Diving and Diving Bells .. 39 Docks . . . . . . 39 and 40 Drainage 40 and 41 Drawbridge .. .. ..41 Dredging Machine .. ..41 Dynamometer .. .. 411043 Electro-Metallurgy .. 43, 44 Engines, Varieties .. 44, 45 Engines, Agricultural .. I and 2 Engines, Marine .. .. 74> 75 Engines, Screw .. .. 89, 90 Engines, Stationary .. 91, 92 Escapement .. .. 45, 46 Fan .. .. .. ..46 File-cutting Machine .. ..46 Fire-arms .. .. .. 46, 47 Flax Machinery .. .. 47, 48 Float Water-wheels .. ..48 Forging .. .. .. ..48 Founding and Casting .. 48 to 50 Friction, 50 ; Friction, Angle of 3 Fuel, 50; Furnace .. 50, 51 Fuze, 51 ; Gas 51 Gearing 51, 52 Gearing Belt .. .. 10, II Geodesy 52 and 53 Glass Machinery .. .. --53 Gold, 53, 54 ; Governor . . . . 54 Gravity, 54 ; Grindstone .. 54 Gun-carriage, 54 ; Gun Metal . . 54 Gunnery .. .. .. 541056 Gunpowder .. .. .. 56 Gun Machinery .. .. 56,57 Hand Tools " ,. .. 57,58 Hanger, 58; Harbour .. ..58 Haulage, 58, 59 ; Hinging . . 59 Hydraulics and Hydraulic Ma- chinery 59 to 63 Ice-making Machine .. ..63 India-rubber .. .. ..63 Indicator 63 and 64 Injector .. .. .. ..64 Iron 641067 Iron Ship Building .. ..67 Irrigation .. .. ..67 and 68 Nos. Isomorphism, 68 ; Joints .. 68 Keels and Coal Shipping 68 and 69 Kiln, 69 ; Knitting Machine .. 69 Kyanising .. .. .. ..69 Lamp, Safety .. .. 69, 70 Lead 70 Lifts, Hoists .. .. 70, 71 Lights, Buoys, Beacons .. 71 and 72 Limes, Mortars, and Cements .. 72 Locks and Lock Gates .. 72, 73 Locomotive .. .. 73 Machine Tools .. .. 73,74 Manganese .. .. 74 Marine Engine .. -.74 and 75 Materials of Construction 75 and 76 Measuring and Folding . . . . 76 Mechanical Movements .. 76, 77 Mercury, 77 ; Metallurgy .. 77 Meter 77,78 Metric System 78 Mills 78, 79 Molecule, 79 ; Oblique Arch .. 79 Ores, 79,80; Ovens .. ..80 Over-shot Water-wheel .. 80, 8 1 Paper Machinery .. .. .. 81 Permanent Way .. .. 81,82 Piles and Pile-driving . . 82 and 83 Pipes 83, 84 Planimeter 84 Pumps .. .. .. 84 and 85 Quarrying .. .. .. -.85 Railway Engineering .. 85 and 86 Retaining Walls .. .. ..86 Rivers, 86, 87 ; Riveted Joint .. 87 Roads 87, 88 Roofs 88, 89 Rope-making Machinery .. 89 Scaffolding 89 Screw Engines .. .. 89, 90 Signals, 90; Silver .. 90, 91 Stationary Engine .. 91, 92 Stave-making & Cask Machinery 92 Steel, 92 ; Sugar Mill .. 92, 93 Surveying and Surveying Instru- ments Telegraphy Testing, 95; Turbine .. Ventilation Waterworks Wood- working Machinery Zinc 95: 93,94 94,95 .. 95 96,97 96, 97 96,97 96,97 PUBLISHED BY E. & F. N. SPON, LIMITED. 23 la super-royal 8vo, 1168 pp., "with 2400 illustrations, in 3 Divisions, cloth, price 13*. bd. each ; or i vol., cloth, a/. ; or half-morocco, a/. 8*. A SUPPLEMENT TO SPONS' DICTIONARY OF ENGINEERING. EDITED BY ERNEST SPON, MEMB. Soc. ENGINEERS. Abacus, Counters, Speed Indicators, and Slide Rule. Agricultural Implements and Machinery. Air Compressors. Animal Charcoal Ma- chinery. Antimony, Axles and Axle-boxes. Barn Machinery. Belts and Belting. Blasting. Boilers. Brakes. Brick Machinery. Bridges. Cages for Mines. Calculus, Differential and Integral. Canals. Carpentry. Cast Iron. Cement, Concrete, Limes, and Mortar. Chimney Shafts. Coal Cleansing and Washing. Coal Mining. Coal Cutting Machines. Coke Ovens. Copper. Docks. Drainage. Dredging Machinery. Dynamo - Electric and Magneto-Electric Ma- chines. Dynamometers. Electrical Engineering, Telegraphy, Electric Lighting and its prac- tical details,Telephones Engines, Varieties of. Explosives. Fans. Founding, Moulding and the practical work of the Foundry. Gas, Manufacture of. Hammers, Steam and other Power. Heat. Horse Power. Hydraulics. Hydro-geology. Indicators. Iron. Lifts, Hoists, and Eleva- tors. Lighthouses, Buoys, and Beacons. Machine Tools. Materials of Construc- tion. Meters. Ores, Machinery and Processes employed to Dress. Piers. Pile Driving. Pneumatic Transmis- sion. Pumps. Pyrometers. Road Locomotives. Rock Drills. Rolling Stock. Sanitary Engineering. Shafting. Steel. Steam Navvy. Stone Machinery. Tramways. Well Sinking. 24 CATALOGUE OF SCIENTIFIC BOOKS. In demy 4to, handsomely bound in cloth, illustrated with 220 full f wge flates, Price 1^. ARCHITECTURAL EXAMPLES IN BRICK, STONE, WOOD, AND IRON. A COMPLETE WORK ON THE DETAILS AND ARRANGEMENT OF BUILDING CONSTRUCTION AND DESIGN. BY WILLIAM FULLERTON, ARCHITECT. Containing 220 Plates, with numerous Drawings selected from the Architecture of Former and Present Times. The Details and Designs are Drawn to Scale, |", \" t \" t and Full size being chiefly used. The Plates are arranged in Two Parts. The First Part contains Details of Work in the four principal Building materials, the following being a few of the subjects in this Part: Various forms of Doors and Windows, Wood and Iron Roofs, Half Timber Work, Porches, Towers, Spires, Belfries, Flying Buttresses, Groining, Carving, Church Fittings, Constructive and Ornamental Iron Work, Classic and Gothic Molds and Ornament, Foliation Natural and Conventional, Stained Glass, Coloured Decoration, a Section to Scale of the Great Pyramid, Grecian and Roman Work, Continental and English Gothic, Pile Foundations, Chimney Shafts according to the regulations of the London County Council, Board Schools. The Second Part consists of Drawings of Plans and Elevations of Buildings, arranged under the following heads : Workmen's Cottages and Dwellings, Cottage Resi- dences and Dwelling Houses, Shops, Factories, Warehouses, Schools, Churches and Chapels, Public Buildings, Hotels and Taverns, and Buildings of a general character. All the Plates are accompanied with particulars of the W T ork, with Explanatory Notes and Dimensions of the various parts. Specimen Pages, reduced Jrom the originals. ArcJwftcr^I ExomfJa- Window. 7Z 26 CATALOGUE OF SCIENTIFIC BOOKS With nearly 1500 illustrations, in super-royal 8vo, in 5 Divisions, cloth. Divisions I to 4, 13*. 6d. each ; Division 5, 17^. 6d. ; or 2 vols., cloth, $ lew. SPONS' ENCYCLOPEDIA INDUSTRIAL ARTS, MANUFACTURES, AND COMMERCIAL PRODUCTS, EDITED BY C. G. WARNFORD LOCK, F.L.S. Among the more important of the subjects treated of, are the following : Acids, 207 pp. 220 figs. Alcohol, 23 pp. 1 6 figs. Alcoholic Liquors, 13 pp. Alkalies, 89 pp. 78 figs. Alloys. Alum. Asphalt. Assaying. Beverages, 89 pp. 29 figs. Blacks. Bleaching Powder, 15 pp. Bleaching, 51 pp. 48 figs. Candles, 18 pp. 9 figs. Carbon Bisulphide. Celluloid, 9 pp. Cements. Clay. Coal-tar Products, 44 pp. 14 figs. Cocoa, 8 pp. Coffee, 32 pp. 13 figs. Cork, 8 pp. 17 figs. Cotton Manufactures, 62 pp. 57 figs. Drugs, 38 pp. Dyeing and Calico Printing, 28 pp. 9 figs. Dyestuffs, 16 pp. Electro-Metallun 13 plO! Explosives, 22 pp. 33 figs. Feathers. Fibrous Substances, 92 pp. 79 figs. Floor-cloth, 1 6 pp. 21 figs. Food Preservation, 8 pp. Fruit, 8 pp. Fur, 5 pp. Gas, Coal, 8 pp. Gems. Glass, 45 pp. 77 figs. Graphite, 7 pp. Hair, 7 pp. Hair Manufactures. Hats, 26 pp. 26 figs. Honey. Hops. Horn. Ice, 10 pp. 14 figs. Indiarubber Manufac- tures, 23 pp. 17 figs. Ink, 17 pp. Ivory. Jute Manufactures, 1 1 pp., II figs. Knitted Fabrics Hosiery, 15 pp. 13 figs. Lace, 13 pp. 9 figs. Leather, 28 pp. 3 1 figs. Linen Manufactures, pp. 6 figs. Manures, 21 pp. 30 figs. Matches, 17 pp. 38 figs. Mordants, 13 pp. Narcotics, 47 pp. Nuts, 10 pp. Oils and Fatty Sub- stances, 125 pp. Paint. Paper, 26 pp. 23 figs. Paraffin, 8 pp. 6 figs. Pearl and Coral, 8 pp. Perfumes, 10 pp. Photography, 13 pp. 20 figs. Pigments, 9 pp. 6 figs. Pottery, 46 pp. 57 figs. Printing and Engraving, 20 pp. 8 figs. Rags. Resinous and Gummy Substances, 75 pp. 16 figs. Rope, 1 6 pp. 17 figs. Salt, 31 pp. 23 figs. Silk, 8pp. Silk Manufactures, 9 pp. II figs. Skins, 5 pp. Small Wares, 4 pp. Soap and Glycerine, 39 pp. 45 figs. Spices, 1 6 pp. Sponge, 5 pp. 16 ! Starch, 9 pp. 10 figs. Sugar, 155 pp. 134 figs- Sulphur. Tannin, 1 8 pp. Tea, 12 pp. Timber, 13 pp. Varnish, 15 pp. Vinegar, 5 pp. Wax, 5 pp. Wool, 2 pp. Woollen Manufactures, 58 pp. 39 figs. PUBLISHED BY E. & F. N. SPON, LIMITED. 27 JUST PUBLISHED, SECOND EDITION, Crown Svo, doth, with illustrations, 5s. WORKSHOP RECEIPTS FIRST SERIES. SYNOPSIS OF Alloys Bleaching Bookbinding Bronzing Candle-making Cements and Lutes Cleansing Crayons Drawings Dyeing Electro-plating Engraving Etching Explosives Fireworks Fluxes Fulminates Glass CONTENTS. Graining Gunpowder Iron & Steel Tem- pering Lathing and Plas- tering Marble Working Painting Paper Paper-hanging Papier-M Ache Pavements Photography Plating Polishing Pottery Recovering Waste Metal 28 CATALOGUE OF SCIENTIFIC BOOKS Crown 8vo, cloth, 485 pages, with illustrations, 5*. WORKSHOP RECEIPTS, SECOND SERIES. SYNOPSIS OF CONTENTS. Acidimetry and Alkali- Disinfectants. lodoform. metry. Dyeing, Staining, and Isinglass. Albumen. Colouring. Ivory substitutes. Alcohol . Essences. Leather. Alkaloids. Extracts. Luminous bodies. Baking-powders. Fireproofing. Magnesia. Bitters. Gelatine, Glue, and Size. Matches. Bleaching. Glycerine. I Paper. Boiler Incrustations. Gut. Parchment. Cements and Lutes. 1 Hydrogen peroxide. Perchloric acid. Cleansing.. Ink. Potassium oxalate. Confectionery. Iodine. Preserving. Copying. Pigments, Paint, and Painting : embracing the preparation of Pigments, including alumina lakes, blacks (animal, bone, Frankfort, ivory, lamp, sight, soot), blues (antimony, Antwerp, cobalt, caeruleum, Egyptian, manganate, Paris, Peligot, Prussian, smalt, ultramarine), browns (bistre, hinau, sepia, sienna, umber, Vandyke), greens (baryta, Brighton, Brunswick, chrome, cobalt, Douglas, emerald, manganese, mitis, mountain, Prussian, sap, Scheele's, Schweinfurth, titanium, verdigris, zinc), reds (Brazilwood lake, carminated lake, carmine, Cassius purple, cobalt pink, cochineal lake, colco- thar, Indian red, madder lake, red chalk, red lead, vermilion), whites (alum, baryta, Chinese, lead sulphate, white lead by American, Dutch, French, German, Kremnitz, and Pattinson processes, precautions in making, and composition of commercial samples whiting, Wilkinson's white, zinc white), yellows (chrome, gamboge, Naples, orpiment, realgar, yellow lakes) ; Paint (vehicles, testing oils, driers, grinding, storing, applying, priming, drying, filling, coats, brushes, surface, water-colours, removing smell, discoloration ; miscellaneous paints cement paint for carton-pierre, copper paint, gold paint, iron paint, lime paints, silicated paints, steatite paint, transparent paints, tungsten paints, window paint, zinc paints) ; Painting (general instructions, proportions of ingredients, measuring paint work ; carriage painting priming paint, best putty, finishing colour, cause of cracking, mixing the paints, oils, driers, and colours, varnishing, importance of washing vehicles, re-varnishing, how to dry paint ; woodwork painting). PUBLISHED BY E. & F. N. SPON, LIMITED. 29 Crown 8vo, cloth, 480 pages, with 183 illustrations, WORKSHOP RECEIPTS, THIRD SERIES. Uniform with the First and Second Series. SYNOPSIS OF CONTENTS. Alloys. Iridium. Rubidium. Aluminium. Iron and Steel. Ruthenium. Antimony. Lacquers and Lacquering, Selenium. Barium. Lanthanum. Silver. Beryllium. Lead. Slag. Bismuth. Lithium. Sodium. Cadmium. Lubricants. Strontium. Caesium. Magnesium. Tantalum. Calcium. Manganese. Terbium. Cerium. Mercury. Thallium. Chromium. Mica. Thorium. Cobalt. Molybdenum. Tin. Copper. Nickel. Titanium. Didymium. Niobium. Tungsten. Enamels and Glazes. Osmium. Uranium. Erbium. Palladium. Vanadium. Gallium. Platinum. Yttrium. Glass. Potassium. Zinc. Gold. Rhodium. Zirconium. Indium. Electrics. Alarms, Bells, Batteries. Carbons, Coils, Dynamos, Micro- phones, Measuring, Phonographs, Telephones, &c., 130 pp., 112 illustrations. 30 CATALOGUE OF SCIENTIFIC BOOKS WORKSHOP RECEIPTS, FOURTH SERIES, DEVOTED MAINLY TO HANDICRAFTS & MECHANICAL SUBJECTS. 250 Illustrations, with Complete Index, and a General Index to the Four Series, 5s. Waterproofing rubber goods, cuprammonium processes, miscellaneous preparations. Packing and Storing articles of delicate odour or colour, of a deliquescent character, liable to ignition, apt to suffer from insects or damp, or easily broken. Embalming and Preserving anatomical specimens. Leather Polishes. Cooling Air and Water, producing low temperatures, making ice, cooling syrups and solutions, and separating salts from liquors by refrigeration. Pumps and Siphons, embracing every useful contrivance for raising and supplying water on a moderate scale, and moving corrosive, tenacious, and other liquids. 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SPON, LIMITED. 31 Crown 8vo, cloth, with 373 illustrations, price 5-r. WORKSHOP RECEIPTS, FIFTH SERIES. Containing many new Articles, as well as additions to Articles included in the previous Series, as follows, viz. : Anemometers. Barometers, How to make. Boat Building. Camera Lucida, How to use. Cements and Lutes. Cooling. Copying. Corrosion and Protection of Metal Surfaces. Dendrometer, How to use. Desiccating. Diamond Cutting and Polishing. Elec- trics. New Chemical Batteries, Bells, Commutators, Galvanometers, Cost of Electric Lighting, Microphones, Simple Motors, Phonogram and Graphophone, Registering Appa- ratus, Regulators, Electric Welding and Apparatus, Transformers. Evaporating. Explosives. Filtering. Fireproofing, Buildings, Textile Fa- brics. Fire-extinguishing Compounds and Apparatus. Glass Manipulating. Drilling, Cut- ting, Breaking, Etching, Frosting, Powdering, &c. Glass Manipulations for Laboratory Apparatus. Labels. Lacquers. Illuminating Agents. Inks. Writing, Copying, Invisible, Marking, Stamping. Magic Lanterns, their management and preparation of slides. Metal Work. Casting Ornamental Metal Work, Copper Welding Enamels for Iron and other Metals, Gold Beating, Smiths' Work. Modelling and Plaster Casting. Netting. Packing and Storing. Acids, &c. Percolation. Preserving Books. Preserving Food, Plants, &c. Pumps and Syphons for various liquids. Repairing Books. Rope Tackle. Stereotyping. Taps, Various. Tobacco Pipe Manufacture. Tying and Splicing Ropes. Velocipedes, Repairing. Walking Sticks. Waterproofing. 32 CATALOGUE OF SCIENTIFIC BOOKS. In demy Svo, cloth, 600 pages and 1420 illustrations, 6s. FOUETH EDITION. SPONS' MECHANICS' OWN BOOK; A MANUAL FOR HANDICRAFTSMEN AND AMATEURS. CONTENTS. Mechanical Drawing Casting and Founding in Iron, Brass, Bronze, and other Alloys Forging and Finishing Iron Sheetmetal Working Soldering, Brazing, and Burning Carpentry and Joinery, embracing descriptions of some 400 Woods, over 200 Illustrations of Tools and their uses, Explanations (with Diagrams) of 116 joints and hinges, and Details of Construction of Workshop appliances, rough furniture, Garden and Yard Erections, and House Building Cabinet-Making and Veneering Carving and Fretcutting Upholstery Painting, Graining, and Marbling Staining Furniture, Woods, Floors, and Fittings Gilding, dead and bright, on various grounds Polishing Marble, Metals, and Wood Varnishing Mechanical movements, illustrating contrivances for transmitting motion Turning in Wood and Metals Masonry, embracing Stonework, Brickwork, Terracotta and Concrete Roofing with Thatch, Tiles, Slates, Felt, Zinc, &c. Glazing with and without putty, and lead glazing Plastering and Whitewashing Paper-hanging Gas-fitting Bell-hanging, ordinary and electric Systems Lighting Warming Ventilating Roads, Pavements, and Bridges Hedges, Ditches, and Drains Water Supply and Sanitation Hints on House Construction suited to new countries. E. & F. N. SPON, Limited, 125 Strand, London. New York : SPON & CHAMBERLAIN. CONDON : PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, STAMFORD STREET AND CHARING CROSS. j\ ] am des the De Gai and Gra Fitt Mai illus and and Gla2 Whi and Pav( Supi coun E. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. NOV 25 1941 MAY 2 7 1987 toiro.Disc.ra 27 -$7 LD 21-100m-9,'47(A5702sl6)476 YB 5)975 rj U.C. BERKELEY LIBRARIES