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