INDEX.

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Aberration gives hodograph of Earth's

orbit 53

Abscissae 452

Absolute acceleration 64

- motion 63

-unit of force, Gauss's, 188; British 190
Acceleration, definition 34; uniform 32;
variable 33; average 33; angular 57;
composition and resolution 34, 37
directed to a fixed centre 45

- in a fixed direction 44

in logarithmic spiral with uniform
angular velocity about the pole 295
- in Simple Harmonic Motion 74
in straight line, uniform 43

- in uniform circular motion 36, 39, 42
- of momentum 178

Accurate measurements, necessity for

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--

-

-

-

-

--

Attraction not modified by interposition
of other matter 474

- is normal to equipotential surfaces
506

- integral of normal, over a closed
surface 510

direct analytical calculation of 494
- law of, when a uniform spherical
shell exerts no attraction on an in
ternal point 541

law of gravitation 475

of gravitating, electric, or magnetic
masses 478

variation of, in crossing an attracting
surface 495

of a circular arc for a particle at its
centre 499

- of a right cone for a particle at its
vertex 494 (c)

of a cylinder on a particle in its axis
494 (6)

of a cylindrical distribution of matter
508

of a uniform circular disc on a par-
ticle in its axis 494 (a)

of an infinite disc 494

of two equal uniform discs, one posi-
tive, other negative 494 (d)

of an Ellipsoid 535, 537; of homo-
geneous ellipsoid 538; Maclaurin's
Theorem 539; Ivory's Theorem 540;
Duhamel's application of Ivory's The-
orem 541

of an ellipsoidal shell 535; on an in-
ternal particle 536

- of a uniform limited straight line on
an external particle 499 (b)

- of a mountain on a plumb line
496 (a)

at the top and the bottom of a pit
496 (b)

of infinite parallel planes 508

of a sphere composed of concentric
shells of uniform density 498

- of a uniform sphere on an external
particle infinitely near its surface 488

cor.

- of a uniform sphere 534, 541

Confocal ellipsoids, corresponding points

on 535; Chasles' proposition 537
Conical pendulum, Appendix f
Conical surface 480

Conservation of energy 250

Conservative system 243
Constancy of a balance 384

Constraint of a point 165, of a body
167; one degree of constraint of the
most general character 170
Contrary forces 555 note
Continuity, equation of 162
Conversion of units:-pounds per sq.
inch to grammes per sq. centimetre
661; other units 362-366
Co-ordinates 452; propositions in co-
ordinate geometry 459
Cord round cylinder 592, 603
Corresponding points in confocal ellip-
soids 535

Cosines, sum of the squares of the direc-
tion, of a line, equal to unity 460
Couple 201, axis of 201, moment of
201, direction of 560

composition of in same or parallel
planes 561; any number 564; any
number not in parallel planes 566;
conditions of equilibrium of 567;
and a force, composition of 568 et seq.
Curvature of a plane curve 9; integral
14; average 14; of a surface 120
oblique sections, Meunier's Theorem,
121; principal, Euler's Theorem 122
Curvature of a lens, how to measure 381
Curve, plane 11; tortuous 13; of double

curvature 11; continuous 35; closed
443

Curves use of, in representing experi-
mental results 347

Cycloid 66, 103; properties of 104;
prolate 103; curtate 103

D'Alembert's Principle 230
Day, Sidereal and Mean Solar 357
Degrees of freedom and constraint 165,
of a point 165, of a body 167; one
degree of freedom of most general
character 170

Density 174; linear, surface, volume,
477; mean density of the earth ex-
pressed in attraction units 715
Developable surface 125; practical con-
struction of a, from its edge 133
Diagonal scale 372

Direction of motion 8

Direction of rotation, positive 455
Direction cosine 463; sum of squares
of, equal to unity 460; of the common
perpendicular to two lines 464
Displacement of a plane figure in its

of

-

plane 91, examples 96; of a rigid
solid 100

Dissipation of Energy, instances 247,
292, 683

Dissipative systems 292

Distortion, places of maximum, in a
cylinder 678

Distribution of the weight of a solid on
points supporting it 626
Double-weighing 384

Duhamel's application of Ivory's theo.
rem 541
Dynamics I

Edge of regression 132
Elastic body, a perfectly 643

centre of a section of a wire 608;
line of elastic centres, 608; rotation
of a wire about 628

curve transmitting force and couple
619, properties of 620; Kirchoff's ki-
netic comparison, common pendulum
and elastic curve 620

solid equilibrium of 667
wire or fibre 605

Elasticity, co-efficient of 265 note; of
volume 651; of figure 651

Electric images 528; definition 530;
transformation by reciprocal radius
vectors 531; electric image of a
straight line, an angle, a circle, a
sphere, a plane 531; application to the
potential 532; of any distribution of
attracting matter on a spherical shell
533; uniform shell eccentrically re-
flected 533; uniform solid sphere
eccentrically reflected 534
Elements of a force 184
Ellipse, how to draw an 19
Ellipsoid, central 237
Ellipsoid, attraction of a, 535; corre-
sponding points on two 535; Ellips-
oidal shell defined 535; attraction of
homogeneous ellipsoidal shell on in-
ternal point 536; Potential constant
inside 536; Chasles' Proposition con-
cerning 537; equipotential surfaces of
a 537; Maclaurin's Theorem 539;
Ivory's 540; comparison of the po-
tentials of two 537

Ellipsoid, Strain 141; principal axes
of 142

Empirical formulae, use of 350
Energy, kinetic 179; kinetic energy of
a system 234; energy in abstract
dynamics 241, 251; foundation of
the theory of energy 244; potential
energy of a conservative system 245;
conservation of E. 250; inevitable loss

of forces 221, 418, parallelogram and
polygon of 222, true polygon of 416,
triangle of 410; forces through one
point, resultant of 412; forces in equi-
librium, graphic test of 414; resultant
of three forces acting at a point 465;
resolution of force along three speci-
fied lines 468; resultant of any number
of forces acting at a point 469; con-
ditions of equilibrium of forces acting
at a point 470; resultant of forces
whose lines meet 552; two parallel
forces in a plane 554, in dissimilar
directions 555, of any number 556,
not in one plane 557, conditions of
equilibrium of 558 et seq.; forces and
a couple 568; forces may be reduced
to one force and one couple 570; re-
duction of forces to simplest system
571; parallel forces whose algebraic
sum is zero exert a directive action
only 583; conditions of equilibrium
of three, acting on a rigid body 584;
conservative system of 243
Force in terms of the potential 504; at
any point, due to attraction of a
spherical distribution of matter, a
cylindrical distribution, or a distri-
bution in infinite planes 508, where
it varies as D-2 509

Force of gravity, Clairault's formula for
187, in absolute units 187, average
value in Britain 191, in Edinburgh
191, law of 475

Force, line of, definition 507, instance
of 499; variation of intensity along
a 508

Force, tube of 508

Form of equilibrium of a rotating mass
of fluid 711-719

Formulae, use of empirical, in exhibit-
ing results of experiment 347
Foucault's pendulum 87

Fourier's theorem 88

Freedom of a point, degrees of 165; of
a rigid system 167

Friction brake, White's 390
Friction, laws of statical 403, kinetic
404; effect of tidal friction 248; fric-
tion of liquids varies as the velocity
292; friction of solids 293; of a cord
round a cylinder 592, 603

Gauss's absolute unit of force 188;
theorem relating to potential 515
Geodetic line 124, properties of 601
Glacier Motion, Forbes's Viscous The-

ory of, meaning of Viscous in 683
Gravitation, law of 475; potential 503
Gravity, force of, Clairault's formula

for 187, at Edinburgh, in Britain
191, in absolute units 187, work
done against 509

Gravity, centre of, and centre of inertia
195, 582; centre of gravity 542; pro-
perties of a body possessing a centre of
gravity 544; centre of gravity where
it exists coincides with centre of inertia
550; position of centre of gravity in
a body for stable equilibrium 585, in
rocking stones 586, in a body with
one point fixed: with two points
fixed 587, on a surface 588; Pappus'
theorem concerning, sometimes called
Guldinus' theorem 589

Green 501; problem in potential 517;
the general problem of electric in-
fluence possible and determinate 521
Gyration, radius of 235
Gyroscopes, motion of 116

Hamilton's Characteristic Function 283
Harmonic motion 69; simple harmonic
motion 70, amplitude, argument,
epoch, period, phase, 71, instances of
72; velocity in simple harmonic mo-
tion 73, acceleration in 74; composi-
tion of two simple harmonic motions
in one line 75, examples 77; graphical
representation of simple harmonic
motion in one line 79; composition
of simple harmonic motion in different
directions 80; of different kinds in
different directions 84; in two rect-
angular directions 85

Harton coal mine experiment 498
Hodograph 49, of a planet or comet
49, of a projectile 50, of motion in
a conic section 51, of path where
acceleration is directed to a fixed
point and varies as D-2 61
Homogeneous atmosphere defined 695:
height of 694, at Paris, at Edinburgh
695.
Homogeneous body 646

Homogeneous strain 135; see Strain
Horsepower 240

Hydrodynamics 683; see Fluid
Hydrostatics 685; see Fluid
Hyperbola, how to draw a 19
Hypocycloid and hypotrochoid 105
Hypothesis, use of 332

Image, electric 528; see Electric im-
ages
Impact 259, duration of 259; time in-
tegral 262; ballistic pendulum 263;
direct impact of spheres, Newton's
experiments on 265, loss of kinetic
energy in 266, due to 267, case with