Attraction of a spherical surface with den-
sity varying inversely as the cube
of the distance from a given point,
II. 474-476

of a sphere whose density varies
inversely as the fifth power of the
distance from a point, 11. 518

of a sphere composed of concentric
shells of uniform density, 11. 480,
491 (d)

of a uniform circular disc on a par-
ticle in its axis, I. 477, 517

of a cylinder on a particle in its axis,
II. 477

of a right cone on a particle at its
vertex, 11. 477

of a uniform circular arc, II. 481
of a straight line, 11. 481

of a uniform hemisphere on a particle
at its edge, 11. 478

of matter arranged in infinite paralle
planes of uniform density, 11. 491
(ƒ)

of coaxal cylinders of uniform density
to infinite lengths, I. 491 (e)
of a homogeneous ellipsoid, II. 494 (j)
-(0); 11. 519-532

of a shell bounded by similar con-
centric and similarly situated ellip-
soids, 11. 519-521, 523

of an infinite homogeneous elliptic
cylinder, 11. 494 (p) (q)

of a heterogeneous ellipsoid, n. 527
of a particle on a distant body, 1.
540, 541

inverse problem of, 11. 494 (a)--(ƒ)

Compressibility, defined, 11. 680; 1. (C) l.
Conservative system, defined, 1. 271
Constraint, of a point with two or one
degrees of free lom, 1. 196

of a rigid body with various degrees
of freedom, I. 197, 199

of a rigid body, five degrees of, 1. 198
of a rigid body, one degree of, most
general form of, 1. 200; mechanical
illustration of, 1. 201; analytical
expression of, 1. 201

Gauss's principle of least, 1. 293
kinetic, cases of motion governed by,
1. 319

Continuity, integral equation of, 1. 192

differential equation of, 1. 193, 194
Co-ordinates, Rodrigues, 1. 95

generalized, of a point, 1. 202, 203
generalized, of a system. 1. 204
generalized, kinetic energy expressed
in, 1. 313

generalized, equations of motion in,
1. 318

ignoration of, 1. 319

generalized orthogonal transforma-
tion of, 1. 337 note

D'Alembert's principle, 1. 264

Density, line, surface and volume, 11. 460
of the Earth, 11. 774, 831

Determinant, expression for the square of,
1. p. 166 4, (k)

minors of a, 1. 343 (b)

relations between the minors of an

evanescent, 1. 343 (b)

square root of skew symmetric, 1.
345 (ix)

Diagonal scale, 1. 419

Direction, integral change of, in a surface,
I. 135

Displacement, in one plane, equivalent to
a rotation, 1. 79, 80, 83; or a trans-
lation, 1. 81

in one plane, examples of, 1. 84,

85

of a non-rigid solid with one point
fixed, general analytical investiga-
tion of, 1. 181, 190 (e), (f), (i)
tangential, defined, 1. 186; of dis-
placed and undisplaced curve com-
pared, 1. 187-189; of a closed
curve, due to rotation, 1. 190; of
a closed curve due to strain, 1. 190
(a)—(d)
Dissipativity, 1. 345 (ii)

Earth, The, as a time-keeper, 11. 830
figure of, as determined by geodesy,
11. 797

rigidity of, 11. 832-848

distribution of land on, 11. 848

secular cooling of, 11. (D)

Edge of regression, 1. 148

Elastic curve, 11. 611, 612

Elastic body, perfectly, defined, 11. 672

Elasticity, of volume, 11. 680

of figure, 11. 680

Elastic solid, equations of equilibrium of,
II. 697, 698; 11. (C)

integration of equations of equi-
librium of infinite, 11. 730
displacements of, by stress applied to
an infinitely small part, 11. 731
displacements of, by stress applied
over the boundary, 11. 732-734
displacement of, when the strain is
plane, 11. 739

Green's theory of, 11. (C) (4), (h)
sphere, deformation of, by rotation,
II. 837, 838

spherical shell, equilibrium of, under

surface tractions, n. 735-737
Ellipticity of strata of equal density within
the earth resulting from Laplace's
law, II. 824, 824'

Energy, kinetic, defined, 1. 213

kinetic, rate of change of, 1. 214;
analytical expression for, 1.280
potential, defined and explained, 1.
241, 273, 274

conservation of, 1. 269-278
apparent loss of, 1. 275-277
equation of, 1. 293, 318

kinetic and potential, expressed as
functions of the time in the case of
small motions, 1. 337

potential, exhaustion of, 11.547-549
Eolotropy, 11. 676–678
Epicycloid, 1. 49, 94

Equilibrant, of a system of forces, 11.558
Equilibrium, neutral, stable and unstable,
examples of, 1. 291

of a particle, 11. 455, 456
of three forces, II. 564.

of forces proportional and perpen-
dicular to the sides of a polygon
at their middle points, or the faces
of a polyhedron at their centres of
inertia, 11. 559 (e)

of a free rigid body, 11. 551-553
of a constrained rigid body, II. 554—
557

of a body moveable about an axis, II.
567

of a body resting on a fixed surface,
II. 568

of a body capable of a single screw
motion, 11. 556

simple examples of, 11. 572

of a floating body, stability of, 11. 763
-768

of a rotating gravitational fluil ellip-
soid of equilibrium, 11. 770-773,
775-777, 778'

of a rotating gravitational fluid ellip-
soid with three unequal axes, 11. 778

Equilibrium of a rotating fluid mass gene.
rally, 11. 778'

of a rotating heterogeneous liquid
spheroid, enclosing a rigid spherical
nucleus and subjected to disturb-
ance, 11. 822-824

of rotating spheroid of two incom-
pressible non-mixing fluids, 11. 831
energy criterion for, 1. 289, 290, 292
slightly disturbed, application of the
Lagrange equation to, 1. 337

general solution of any case of slightly
disturbed, 1. 343 (ƒ)—(p)
Equipotential surfaces, defined, 11. 491 (g)
of homogeneous harmonic spheroids,
II. 789, 790

for approximately spherical mass due

to gravitation and rotation con-
jointly, II. 794

of rotating fluid covering a spherical
nucleus, 11. 800-802

of fluid covering a fixed spherical
nucleus, and disturbed by the attrac-
tion of a distant body, II. 803
Ergometer, 1. 436, 437
Error, law of, 1. 391

probable, 1. 392, 393
Errors, theory of, 1. 387-394
Evolute, 1. 17-19

Experiment, remarks on, 1. 373–382

Flexure, of a bar, 11. 711-713
of a plate, I. 719-729

of a plate bounded by an infinite
plane edge, 11. 728

Fluid, perfect, defined, 1. 320; 11. 742
cases of motion in a perfect, 1. 320-
325

equations of equilibrium of a perfect,
II. 753

equilibrium of, in a closed vessel, 11.
754, 755

equilibrium of, under non-conserva-
tive forces, 11. 757-759

equilibrium of, possibility of, under
given forces, II. 755, 756

density of, in terms of potential of
applied forces, 11. 760

impulsive generation of motion in an
incompressible, 1. 312, 317
Fluxions, 1. 24, 203
Foci, kinetic, 1. 357-364
Force, measure of, 1. 220, 413

specification of, 1. 218
accelerative effect of, 1. 219
measurement of, 1. 258
unit of, 1. 221

Gauss's absolute unit of, 1. 223
British absolute unit of, 1. 225
ideal units of, 1. 223

Force, comparison of absolute and gravi-
tational measures of, 1. 226
effective component of, 1. 228
moment of, 1. 232

time-integral of, 1. 297

line of, defined and illustrated, 11.
489, 490

Forces, composition of, 1. 255

parallel, composition of, 11. 561, 563
parallelogram and polygon of, 1. 256
system of, reduced to two, 11. 560
system of, reduced to a force and a
couple, 11. 559 (c)

Freedom, degrees of, 1. 195–201; (see
Constraint)

Friction, laws of, between solids, 11. 450

-452

laws of fluid, 1. 340

Function, simple harmonic, 1. 54

complex harmonic, 1. 75, 76; repre-
sentation of the results of experi
ment by means of a, 1. 338'
plane harmonic, 11. 739
displacement, 1. 190 (k)
spherical harmonic, 1. p. 171 B. (see
Spherical harmonics)

Laplace's, I. p. 208 B. (e') (see Sphe-
rical harmonics)

Hamilton's characteristic, 1. 331;
complete solution derived from a
knowledge of, 1. 331
cyclic, 11. 755, note

Harmonic motions, mechanical composi
tion of, in one line, 1. 62

graphical representation of, 1. 62, 69,
72, 74

composition of, in different lines, 1.
63-73

Harmonic, spheroid, defined, 11. 779
nodal cone, defined, 11. 779; proper-
ties of, 11. 780

spherical (see Spherical harmonics)
Heat, specific, defined, 11. (E) 1 note
Hodograph, definition of, 1. 37

elementary properties of, 1. 37

for the undisturbed motion of a planet
is a circle, 1. 38

physical applications of, 1. 39
Homogeneousness, defined, u. 675
Hooke's joint, 1. 109

Horograph, defined, 1. 136

exercises on, 1. 137

Horse-power, 1. 268
Hypocycloid, 1. 91, 94
Hypotheses, use of, 1. 383-386

Laplace's law of density of the earth's
strata, 11. 824; applied to determine
the constant of precession, 11. 827,
828; compressibility involved in,
II. 829
Laplace's differential equation for the
potential, etc., with Poisson's ex-
tension, II. 491 (b) (c)

expressed in generalized co-ordinates
by physical considerations, 1. A ̧
p. 160 (a)-(e)

expressed in generalized co-ordinates
by algebraical transformation, 1.
p. 166 A。 (j)—(m)