-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
568
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, Appendixƒ

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
443

Curves use of, in representing experi
mental results 347

Cycloid 66, 103; properties of 104;
prolate 103; curtate io3

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

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; con-
ditions of equilibrium of forces acting
on a rigid body 576; equilibrium of a
non-rigid body not affected by ad-
ditional fixtures 584, of a flexible and
inextensible cord 594; position of equi.
librium of a flexible string on a smooth
surface 601. rough surfaces 602; equi
librium of elastic solid 667, of incom-
pressible fluid completely 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.
Ergometer 389, Morin's 389
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 693;
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 703; 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 case
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 grav
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