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Attraction not modified by interposition
of other matter 474

- is normal to equipotential surfaces




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 (b)

of a cylindrical distribution of matter

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

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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


- of a uniform sphere 534, 541

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Circuit, linear 443; autotomic 443

Circular measure, unit of 357

Clairault's formula for the amount of

gravity at a place 187

Clocks 367

Closed curve 443

polygon 443

Closed surface, ff Ndo, over a 510
Coarsegrainedness 646

Coefficient of elasticity 265 note, 644
Coefficient of restitution 265; of glass,
iron, wool 265

Comet, hodograph of orbit of 49
Component velocity 29; acceleration
37; of a force, effective 193
Composition of Velocities 31; Accelera-
tions 34; Simple Harmonic Motions in
same direction 75, in different direc-
tions 80; Angular velocities 107,
about axes meeting in a point 108;
Rotations 107, successive finite rota-
tions 109; Forces 221, of two acting
on a point 419, 422, special cases of
423 et seq.; nearly conspiring 427,
nearly opposed 428, at right angles
429, of any set of forces acting on a
rigid body 570; Couples in same plane
or in parallel planes 561, 562, 563, any
number, 564; not in parallel planes
565, any number of 566, and a force
Compound pendulum, Appendix g.
Compressibility 651

Conditions of equilibrium of a particle
408; a material point 470; of parallel
forces 558; of floating bodies 702-9;
of any number of couples 567 et seq.
Cone, orthogonal and oblique section of
very small 486; solid angle of 482;
area of segment cut from spherical
surface by a small cone 487
Cones opposite or vertical 481

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; of
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 II; continuous 35; closed

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

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

Dynamometer 389, Morin's 389

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 energy of visible motion 247; po-
tential energy of a perfectly elastic
body strained 644; energy of a
strained isotropic substance 666
Epicycloid, integral curvature of 14,
motion in 105

Epoch in simple harmonic motion 71
Equation of continuity 162; integral and
differential 163

Equations of motion of any system 258
Equilibrium of a particle, conditions of
408, 470, on smooth and rough curves
and surfaces 473; conditions of equi-
librium of forces acting at a point 470;
conditions of equilibrium of three forces
acting at a point 584; graphic test
of forces in equilibrium 414; condi-
tions for stable equilibrium of a body
585, rocking stones 586, body move-
able about an axis 587, body on a
fixed surface 588; neutral, stable, and
unstable equilibrium, tested by the
principle of virtual velocities 256,
energy criterion of 257; conditions
of equilibrium of parallel forces 558;
conditions of equilibrium of forces
acting on a rigid body 576; equi-
librium of a non-rigid body not af
fected by additional fixtures 584, of
a flexible and inextensible cord 594;
position of equilibrium of a flexible
string on a smooth surface 601, rough
surfaces 602; equilibrium of elastic
solid 667, of incompressible fluid com-
pletely filling rigid vessel 696, under
any system of forces 697; equilibrium
of a floating body 704 et seq., of a
revolving mass of fluid 710
Equipotential surfaces, examples of 499,
505, 526, of ellipsoidal shell 537
Equivalent of pounds per square inch
in grammes per square centimetre
661; other units 362–366.
Experience 320

Experiment and observation 324; rules

for the conduct of experiment 325; use
of empirical formulae in exhibiting
results of experiment 347
Euler's theorem on curvature 122, on
Impact 276
Evolute 20, 22

Flexible and inextensible line, Kine-
matics of a 16; flexible and inexten-
sible surface, flexure of 125, general
property of 134; flexible string on
smooth surface, position of equili-
brium of 601, on rough surface 602
Flexure of flexible and inextensible sur-
face 125, of a wire 605; laws of flexure

and torsion 607; axes of pure flexure
609; case in which the elastic central
line is a normal axis of torsion 609;
where equal flexibility in all directions
610; wire strained to any given spiral
and twist 612; spiral spring 614;
principal axes of 679; distortion of the
cross section of a bent rod 679
Floating bodies, stable equilibrium of,
lemma 704; stability of 705 et seq.;
see Fluid

Fluid, properties of perfect 401, 684;
fluid pressure 685, equal in all di-
rections 686, proved by energy cri-
terion 689; fluid pressure as depending
on external forces 690; surfaces of
equal pressure are perpendicular to
lines of force 691, are surfaces of
equal density and equal potential 692;
rate of increase of pressure 694, in
a calm atmosphere of uniform tem
perature 695 (free surface in open
vessel is level 696); resultant pres-
sure on a plane area 702; moment of
pressure 702; loss of apparent weight
by immersion 703; conditions of equi-
librium of a fluid completely filling a
closed vessel 696, under non-con-
servative system of forces 697, im-
aginary example 699, actual
701; equilibrium of a floating body,
lemma 704, stability 705, work done
in a displacement 705, metacentre,
condition of its existence 709; oblate
spheroid is a figure of equilibrium of
a rotating incompressible homoge-
neous fluid mass 711; relation be-
tween angular velocity of rotation
and density with given ellipticity 712;
table of eccentricities and correspond-
ing angular velocities and moments
of momentum for a liquid of the
earth's mean density 717; equilibrium
of rotating ellipsoid of three unequal
axes 719
Fluxion 28


Forbes's use of Viscous in connection

with glacier motion 683
Force, moment of 46, about a point
199, source of the idea of 173, de-
fined 183, specification of a 184,
measure of a 185, measurement of.
224, by pendulum 387; force of gray-
ity, Clairault's formula for 187, in
absolute units 187, average, in Britain
191; unit of force, gravitation 185,
absolute 188; British absolute unit
191; attraction unit of force 476;
representation of forces by lines 192;
component of force 193; composition

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

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-

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

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