Part 23

THE BEDS.—The simplest as well as the longest parts of the framework are called “beds” (Fig. 104). Each bed is made of two wooden bars. These bars are united by strong screws passing through small blocks of hard wood so as to keep the bars full ⅜" asunder, and thus allow the shanks of the bolts to pass freely through the slit The scantling of each bar is 2½" × 1½", and the beds are of various lengths from 1' to 10' or even longer. The beds can be attached together in any required position by bolts 6" long. The rectangles and the brackets are attached to the beds by 4" bolts. In one conjunction or another the beds will be found represented in almost every figure in the book. We may specially refer to Figs. 20, 44, 48, 49, 50, 65, 83.

THE STOOL.—Most of the larger pieces of apparatus have the _stool_ as their foundation (see Figs. 11, 39, 102). It is often convenient as in Fig. 65 to employ a pair of stools, while one stool superposed on another gives the convenient stand in Fig. 80. The stool is a stout wooden frame, providing a choice of slits to which beds or other pieces may be attached by bolts. The structure of the frame is shown in Fig. 105. It is 2' 6" high and its extreme horizontal dimensions are 2' 6" × 1' 9" of which the greater is A E. In other words, the longer sides of the stool are those open at the top. Each top corner is strengthened by an iron plate of which a separate sketch is shown. The scantlings of the parts of the stool are as follows:—The legs and horizontal top rails are 3" × 2⅛". Two of these rails with the intervening ⅜" slit make the top and legs to be 4⅝" wide. The bottom front rail I is 3" wide and 4" deep. The double side rails D, H are 1¾" wide and 2½" deep, being made thinner than the legs into which they are mortised in order to allow the washers of the bolts to pass behind them. The slits are to be full ⅜" wide throughout. Beech or birch are very suitable materials, but softer woods will answer if large washers are invariably used.

THE RECTANGLE.—The useful element of the Willis system known by this name is of iron cast in one piece (Fig. 106). The rectangles are used in the attachment of beds to each other under special conditions, or they are often attached to the stools or to brackets. Indeed their uses are multifarious, see for examples Figs. 12, 58, 62, 89, 97, 102 and many others. The faces of the rectangle are 2½" broad. The outside dimensions are 6" and 9", and the thickness of metal is ⅝". Each side of the rectangle has the usual bolt slit ⅜" clear. Rectangles of a larger size are often found useful, their weight makes them effective stands (see Figs. 35, 43, 52, 65).

THE TOOTHED WHEEL.—The most convenient type of toothed wheel for our present purpose is that known as the cast iron _ten-pitch_. In all such wheels the number of teeth is simply ten times the number of inches in the diameter. For example a wheel with 120 teeth is 12 inches in diameter. A number of ten-pitch wheels large and small must be provided. The actual assortment that will be necessary depends upon circumstances. For most purposes it will be sufficient to have the multiples of 5 from 25 upwards to 120, and then a few larger sizes such as 150, 180, 200. Duplicates of the constantly recurring numbers such as 30, 60, 120 are convenient. _Arm_ wheels are always preferable to _plate_ wheels in lightness and appearance as well as in price. All wheels are to be 1" thick at the boss which is faced in the latter at each side, and bored with a hole full 1" diameter, in which a key groove is cut. A pair of mitre wheels such as are used in Fig. 80 are sometimes useful.

THE PULLEY.—We have frequent occasion to use the pulley for conveying a cord, and a somewhat varied stock is convenient Thus light brass pulleys are used in the apparatus shown in Fig. 3, and a stout pulley in Fig. 71. A cast iron pulley about 10" in diameter is seen in Figs. 32 and 34. It is bored 1" in diameter with a key groove, and the boss is 1" thick. Some small pulley-blocks similar to those used on yachts are often very useful.

THE STUD SOCKET.—For mounting toothed wheels on the larger pulleys or for almost any rotating or oscillating pieces the stud socket is used (see Fig. 107). The socket A B may be made of brass or of cast iron. It is 1" in diameter so as to pass through the bosses of the wheels that have been bored to 1" with this object:—The socket is provided with a shoulder at one end (A) which is 1½" diameter, and with a strong screw B and octagonal nut at the other end. The extreme length of the socket is 3½", and the plain part of the 1" cylinder is 1¾" long. When two wheels are placed on the socket each of which has a boss 1" thick, the tightening of the nut will secure the wheels against the shoulder. A feather is screwed on the plain part which enters the key grooves in the wheels, and thus ensures that the wheels shall turn together. This feather should be small enough to slip _easily_ into the key groove. If only a single wheel or if any peculiar piece such as a wooden cam or a disk of sheet iron has to be mounted, then collars or large thick washers must be placed on the socket so as permit the screw to bind the whole together. The socket revolves upon a stout iron stud C D, which is ⅝" in diameter. It bears a shoulder or flange C at the back of the same diameter as the base of the socket The stud bears on the other side of the shoulder a strong screw and nut which project 1⅝" so as to allow the stud to be secured in a hole 1" deep in one of the brackets (to be presently described). The plain part of this screw near the shoulder must be ⅝" diameter. The front end of the stud is pierced with a hole to receive a spring pin to keep the socket from sliding off the stud. Among the many applications of the stud socket we may mention those shown in Figs. 30, 73, 74.

THE BRACKET.—There are six different forms of cast iron brackets represented in the adjoining figures (Figs. 108-113).

The brackets are primarily intended as the supports of the stud sockets. For this purpose each has a head 1" thick bored with a hole ⅝" diameter, and thus fitted to receive the screw on any of the studs. Each bracket stands on a base or _sole_ with a slit full ⅝" wide for the bolts. The thickness of the sole is ⅝". The larger of the brackets I., II., and IV. have also slits in their vertical faces. Brackets can be fastened either to the stool or to the beds or rectangles, and the variety of their forms enables the wheel-work carried on the stud sockets to be disposed in any desired fashion. Brackets avail for many other purposes besides those of supporting rotating mechanism. (Look at Figs. 11, 12, 17, 20, 33, 38, 39, 73 and many others.)

THE SHAFTS AND TUBE-FITTINGS.—The stud sockets will not provide for every case in which wheels have to be mounted and driven. We must often employ shafts (see for instance Figs. 30, 47, 101). The shafts we use are turned iron rods ¾" in diameter, and of various lengths from 6" up to 4'. To support the shafts we use for bearings the _tube fitting_ (Fig. 114). This is a brass casting which consists of a tube M N 2" long, and 1¼" in external diameter, bored ¾" so as to fit the shaft. The back of this tube is a flat surface parallel to the bore, and from it projects a screw ⅝" diameter, and 1⅝" long with a nut which is however omitted in the drawing. This screw may be of the same size as that of the studs, and it is intended for the same purpose, namely to attach the bearing to the hole in a bracket. The tube may of course be fixed at any desired angle in the plane parallel to the face of the bracket. To prevent the endlong motion of the shaft cast iron or brass rings are employed (Fig. 115). These are bored ¾", and furnished with a binding screw by which they may be tightened on the shaft in any position. To avoid injury to the shaft it is well to have a narrow flat surface filed along it to receive the end of the binding screw. The use of the rings is shown in Fig. 47. If as often happens (see for example Fig. 102) a barrel has to be set in motion by a shaft the required attachment can be made by simply slipping on the barrel, and then putting at each end of it two of the pinned rings (Fig. 115). The pins enter holes bored into the barrel for their reception so that when the rings are bound to the shaft by their screws the barrel must revolve with the shaft.

THE ADAPTER.—For the attachment of wheels or other rotating pieces to the shaft an adapter is employed (Fig. 116). It is bored with a ¾" hole to fit the shaft, and the external diameter is 1". At one end is a shoulder through which the binding screw is tapped, and there is a nut and screw at the opposite end. A feather will prevent the wheel from turning round on the adapter which is itself made to revolve with the shaft by screwing the binding screw down on the shaft. Some adapters are only large enough for a single wheel 1" thick in the boss, but it is useful to have others that will take two wheels. Adapters are shown in use in Figs. 46 and 101.

THE LEVER ARM.—To give motion to the mechanism a lever arm with a handle is frequently required (Fig. 117). It is bored 1" and has a key groove, and the hole is 1" long, so that the lever arm can be fixed on a stud socket like a wheel. By the aid of an adapter the lever arm is attached to a shaft. For the use of the handle see Figs. 30 and 101. There are however many other uses to which the lever arm is occasionally put. It can be used as a crank, and in linkage arrangements a pair of lever arms are very convenient. Studs A or C can replace the handle when necessary.

Such are the parts of the Willis apparatus which are adapted for our present purpose. It remains to add that the fits should be very easy, and the parts should be readily interchangeable.

INDEX.

A. Accident, risk of, 32 Action, 6 Adapter, Willis apparatus, 352 Angle of friction, 78 of statical friction, 80 Apparatus for centre of gravity, 62 for equilibrium of three forces, 7 to show friction, 65, 78 the Willis, 345 Appendix I., 339 Atwood’s machine, 232 Axes, permanent, 279

B. Balance, defective, 48 spring, 16 Bar, equilibrium of a, 38 Bat, cricket, 309 Beam, breadth of, 193 breaking load of, 193, 196 cast iron, 222 collapse of, 186 deflection of, 179 elasticity of, 184 load on, 197 placed edgewise, 193 strained, 178 strength of, 190 uniformly loaded, 198 with both ends secured, 200 with one end secured, 201 Beds in Willis apparatus, 346 Bob, raising or lowering the, 320 Bolts, use of, in Willis apparatus, 346 Bracket, Willis apparatus, 350 Brass, specific gravity of, 56 Breaking load, 177 Bridge, deflection of, 208 mechanics of, 218 Menai, 218 suspension, 225 the Wye, 215 tubular, 223 with four struts, 210 two struts, 206 two ties, 211 Brunei, Sir J., the Wye bridge, 215

C. Capstan, 151 Cast iron beam, 222 Catenary, 226 Cathetometer, 180 Centre of gravity, 57 of a wheel, 61 position of, 59 oscillation, 304 percussion, 307 Circular motion, 267 action of, 271 applications of, 276 cause of, 270 in governor-balls, 276 in sugar refining, 276 nature of, 267 on liquids, 271 on the earth, 276 Circular pendulum, 284 Clamps, 203 Clock pendulum, 299 principles of, 318 rate of, 322 Coefficient of friction, 74, 82 Collapse of a beam, 186 Compensating pendulum, 319 Composition of forces, 1, 9 parallel forces, 35, 37, 42 vibrations, 299, 315 Conical pendulum, 310 Couple, 44 Crane, 29, 162 friction in, 166 mechanical efficiency of, 165 Table XXI. 165 XXII. 166 velocity, ratio of, 163 Cricket bat, 309 Crowbar, 123 Cycloid, 295

D. Dead-beat escapement, 328 Definition of force, 2 Deflection of a beam, Table XXIII. 182 Differential pulley, 112 Table XI. 114 Direction of a force, 5

E. Eade, Mr., epicycloidal pulley-block, 116 Easter Island, 100 Elasticity of beam, 184 Energy, 85, 94 storage of, 256, 258 unit of, 95 Engine, locomotive, 83 Epicycloidal pulley-block, 80, 116 Table XII. 118 Equilibrium, neutral, 61 of a bar, 38, 41 three forces, 6 two forces, 6 stable, 59 unstable, 59 Escapement, 324 dead-beat, 328 recoil, 328 Expansion of bodies, 321 Experiment by M. Plateau, 273

F. Fall in a second, 239 Falling body, motion of, 230 Feet, how represented, 7 Fibres in state of compression, 184 tension, 184 First law of motion, 230 Fly-wheel, 260 in steam-engine, 262 Foot-pound, 95 Force, a small, and two larger, 12 definition of, 2 destroying motion, 3 direction of a, 5 magnitude of a, 4 measurement of, 4 of friction, 65 gravity, 50 one, resolved into three, 26 two, 17 representation of, 5 standard of, 4 Forces, composition of, 1, 9 equilibrium of three, 6 two, 6 illustrations of, 3 in inclined plane, 136 parallel, 34 parallelogram of, 10 resolution of, 16 Formula for pulley-block, 109, 114 Framework, 203, 345 Friction, 65 accurate law of, 75 a force, 66 and pressure, 72 angle of, 78 angle of statical, 80 apparatus to show, 65, 68, 78 caused by roughness, 66 coefficient of, 74, 82 diminished, 66 excessive, 115 experimenting on, 66 in crane, 166 differential pulley-block, 113 inclined plane, 132 lever, 123 pulleys, 89 law of, 91 rope and iron bar, 87 wheel and axle, 153 wheel and barrel, 158 laws of, 73, 81, 82 mean, 75 motion impeded by, 70 nature of, 65 overcoming, 93 Table I. 69 II. 71 III. 74 IV. 76 V. 78 VI. 81 VII. 81 VIII. 81 upon axle, 155 wheels, 93

G. Galileo and falling bodies, 235 kinetics, 230 the pendulum, 284 tower of Pisa, 233 Gathering pallet, 336 Girder, 219 as slight as possible, 221 Governor-balls, 276 Graham, dead-beat escapement, 328 Graphical construction, 339 Gravity, 50 action of, 243 and the pendulum, 292 and weight, 52 centre of, 57 defined, 246 different effects of, 53 independent of motion, 241 in London, 292 specific, 53 Grindstone, treadle of, 128

H. Hammer, 252 theory of the, 252 Hands of a clock, 331 Horse-power, 96

I. Illustration of parallelogram of forces, 10 Illustrations of forces, 10 resolution, 19 Inches, how represented, 7 Inclination of thread, 140 Inclined plane, 131 forces on, 136 friction in, 132 mechanical efficiency of, 139 Table XIII. 134 XIV. 137 XV. 138 velocity, ratio of, 139 Inertia, 250 inherent in matter, 252 Iron girders, 219 specific gravity of, 55 Isochronous simple pendulum, 303 Ivory, specific gravity of, 56

J. Jib, 29, 163

K. Kater, Captain, 305 Kinetics, 230

L. Large wheels, advantages of, 93 Law of falling bodies, 238 friction in pulleys, 91 lever of first order, 122 pressure, 37 Laws of friction, 73, 81, 82 Lead, specific gravity of, 56 Leaning tower of Pisa, 233 Level, 56 Lever, 119 and friction, 123 applications of, 123 arm, Willis apparatus, 352 laws of, 130 of first order, 119 law of, 122 of second order, 124 of third order, 128 weight of, 121 Lifting crane, 29 Line and plummet, 56 Load, breaking, 177 Locomotive engine, 83

M. Machine, Atwood’s, 232 punching, 263 Machines, pile-driving, 255 Magnitude of a force, 4 Margin of safety, 33 Mass, 236 Mean frictions, 75 Measurement of force, 4 Mechanical powers, 85, 100 apparatus, Willis, 345 Menai Bridge, 218 Method of least squares, 342 Moment, 130 Monkey, 257 Motion, first law of, 230 of falling body, 230

N. Neutral equilibrium, 61 Newton and gravity, 289 Nut, 140

O. Oscillation, centre of, 304

P. Pair of scales, 48 testing, 48 Parabola, 226 Parallel forces, 34 composition of, 35, 37, 42 opposite, 44 resultant of, 43 Parallelogram of forces, 10 Path of a projectile, 247 Pendulum and gravity, 292 circular, 284 compensating, 319 compound, 299, 301 conical, 310 formula for, 292 Galileo and the, 286 isochronous simple, 303 length of the seconds, 292, 318 motion of the, 285 of a clock, 299 simple, 284 time of oscillation, 286, 289 Percussion, centre of, 307, 309 Permanent axes, 279 Pile-driving machines, 255 Plateau, M., experiment by, 273 Plummet, 56 Powers, mechanical, 85 Pressure and friction, 72 law of, 37 of a loaded beam, 35, 37 Principles of framework, 203 Projectile, path of, 247 Pulley-block, 99 differential, 110 epicycloidal, 80 three-sheave, 106 velocity, ratio of, 112 Pulley, ordinary form of, 86 single movable, 101 fixed, 86 use of, 88 velocity, ratio of, 103 Pulleys, friction in, 89 in windows, 86 in Willis apparatus, 349 Punching machine, 263 force of, 265

R. Rack, 334 Reaction, 6 Recoil escapement, 328 Rectangle in Willis apparatus, 348 Representation of a force, 5 Resistance to compression, 172, 175 extension, 172 Resolution of forces, 16 one force into three, 26 two, 17 Resultant, 9 of parallel forces, 43 Rings in Willis apparatus, 352 Risk of accident, 32

S. Safety, margin of, 33 Sailing, 21 against the wind, 24 Scales, 46 Screw, 139 and wheel and axle, 167 form of, 139 Table XVI. 142 velocity, ratio of, 143 Screw bolt and nut, 148 jack, 131, 145 Table XVII. 146 Second, fall in a, 239 Seconds, pendulum, 318 Shafts, Willis apparatus, 351 Shears, 126 Simple pendulum, 284 Single movable pulley, Table IX. 104 Snail, 334 Specific gravity, 53 of brass, 56 iron, 55 ivory, 56 lead, 56 Spirit-level, 56 Spring balance, 16 Stable equilibrium, 59, 282 Standard of force, 4 Statical friction, angle of, 80 Stool in Willis apparatus 347 Storage of energy, 256, 258 Stored-up energy exhibited, 261 Strength of a beam, 190 Striking parts, 333 Structures, 169 Strut, 28 Stud socket in Willis apparatus, 349 Sugar refining, 276 Suspension bridge, 225 mechanics of, 225 tension in, 228

T. Table I. 69 II. 71 III. 74 IV. 76 V. 78 VI. 78 VII. 81 VIII. 81 IX. 104 X. 108 XI. 114 XII. 118 XIII. 134 XIV. 137 XV. 138 XVI. 142 XVII. 146 XVIII. 154 XIX. 159 XX. 162 XXI. 165 XXII. 166 XXIII. 182 XXIV. 190 Tacking, 25 Tension along a cord, 17 Three-sheave pulley-block, 106 Tie, 28, 175 rod, 29, 32 Timber, bending, 171 compression of, 172 extension of, 172 properties of, 170 rings in, 171 seasoning, 171 warping, 171 Tin, 223 Toothed wheels, 160 Tower of Pisa, 233 Train of wheels, 330 Transverse strain, 181 Treadle of a grindstone, 128 Tripod, 28 strength of, 28 Truss, simple form of, 212 Tube fitting, Willis apparatus, 351 Tubular bridge, 223

U. Unstable equilibrium, 59, 282

V. Velocity, 231 ratio of inclined plane, 139 pulley, 103 pulley-block, 112 screw, 143 wheel and axle, 152 wheel and pinion, 161 Vibrations, composition of, 299, 315

W. Wedge, 139 Weighing machines, 123 scales, 46, 48 Weight caused by gravity, 52 of water, 54 Wheel and axle, 149 and differential pulley, 167 screw, 167 experiments on, 152 formula for, 154 friction in, 153 Table XVIII. 154 velocity, ratio of, 152 Wheel and barrel, 158 formula for, 160 friction in, 158 Table XIX. 159 Wheel and pinion, 160 efficiency of, 161 Table XX. 162 velocity, ratio of, 161 Wheel, centre of gravity of, 61 Wheels, 92 friction, 93 Wheels in Willis apparatus, 348 Willis system of apparatus, 345 Winch, 151 Wind, direction of, 22 Work, 85, 94 Wye Bridge, 215

THE END.

RICHARD CLAY AND SONS, LIMITED, LONDON AND BUNGAY.

End of Project Gutenberg's Experimental Mechanics, by Robert Stawell Ball