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.

Footnotes:

[1] We shall often, in these lectures, represent feet or inches in the manner usual among practical men—1' is one foot, 1" is one inch. Thus, for example, 3' 4" is to be read “three feet four inches.” When it is necessary to use fractions we shall always employ decimals. For example, 0"·5 is the mode of expressing a length of half an inch; 3' 1"·9 is to be read “three feet one inch and nine-tenths of an inch.”

[2] I ought to acknowledge the kindness with which Mr. J. Willis Clark, of Cambridge, the literary executor of Professor Willis, has responded to my queries, while I am also under obligations to the courtesy of Messrs. Crosby, Lockwood, & Co.

Transcriber’s Notes:

The illustrations have been moved so that they do not break up paragraphs and so that they are next to the text they illustrate.

Typographical errors have been silently corrected.