The numbers refer to pages.
Eolotropy, defined, 71; produced by
permanent set, 104; curvilinear dis-
tributions of, 99, 229; for different
kinds of phenomena, 346.
After-strain: see Elastic After-working.
Amagat, 18, 77.
Amorphous bodies, constants for, 98.
Axes, Crystallographic, 79; equivalent,
Axis, neutral, introduction of by Galilei,
3; determination of, 181.
Bars: see Beams.
Barytes, constants for, 97.
Beams, theories of, 31. See also Exten-
sion, Torsion, and Flexure.
Bernoulli, Daniell, on vibrations of bars,
3.
Bernoulli, James (the elder), discoverer
of the elastic line, 3; originator of
stress-strain curve, 101.
Beryl, constants for, 97.
Betti, theorem, 127; method of integra-
tion, 30, 239, 347; particular integrals
for the bodily forces, 233.
Blanchet, on wave-motion, 26.
Bodily forces, two classes of, 235; par-
ticular integrals for, 237, 238, 258.
Borchardt, solution of general equations,
29.
Boundary-conditions, in terms of stress-
components, 60; for isotropic solids,
77; for surface of discontinuity, 136;
for torsion of prisms, 160; for flexure
of prisms, 185; for spherical surface,
277; for equilibrium of sphere, 292;
for vibrations of sphere, 316.
Boussinesq, problem, 27, 248; theory of
local perturbations, 28, 259; simple
types of solutions, 253, 269.
Brass, Wertheim on, 18; constants for,
77.
Braun, on elastic after-working, 109.
Bresse, theorem on position of neutral
axis, 182.
Butcher, on elastic after-working, 104.
Cast-iron, Hodgkinson on, 20; elastic
character of, 70, 102.
Cauchy, analysis of strain and stress,
6; on the general equations, 8, 11,
110; on Poisson's assumption con-
cerning inter-molecular force, 10; re-
lations among the constants, 15, 79,
114; constants for isotropic solids, 21;
torsion of rectangular prism, 31; theo-
rem of stress, 59, 64.
Cerruti, 28, 248.
Chree, general method of solution, 29,
277; polar coordinates, 216; rotating
circular cylinder, 226; rotating circu-
lar disc, 228; rotating ellipsoids, 277;
tendency to rupture in strained gravi-
tating sphere, 300.
Christoffel, wave-motion in crystalline
media, 26, 135, 139.
Clapeyron: see Lamé and Clapeyron.
Clausius, explains Cauchy's analysis,
9.
Clebsch, on the general equations, 14;
on the theory of vibrations, 26; on
Saint-Venant's problem, 33, 149.
Compression, modulus of: see Modulus.
Conical refraction, 347.
Conjugate functions, for torsion problem,
159; for flexure problem, 193; ortho-
gonal surfaces derived from, 214; for
plane strain, 334.
Constants: see Elastic Constants.
Copper, constants for, 77.
Coulomb, theories of flexure and torsion,
4; theory of rupture, 4, 106.
Crystal forms, 79; not identical with
boundaries, 81.
Crystallography, sketch of, 79.
Crystals, systems of, 81-90; theory of
elasticity of, 81; moduluses of, 90-
94; values of elastic constants of, 96.
Cubic crystals, energy-function for, 87;
rigidities of, 347.
Curvilinear coordinates, history of, 25;
general theory of, 199; strain in terms
of, 205; stress-equations referred to,
206; strain-equations referred to, 213;
systems of, 213.
Cylinder, rotating, 224; radial vibrations
of, 226. See also Beams and Plane
Strain.
Cylindrical cavity in infinite solid, 340.
Cylindrical shell, under pressure, 226,
229; radial vibrations of, 226.
Darwin, G. H., on stress produced by
the weight of continents and moun-
tains, 300; on the tidal effective
rigidity of the earth, 307, 308.
Deflexion, of beams, 179, 181.
Dilatation, cubical, 51, 54, 55; mean
value of, 129; in curvilinear coordi-
nates, 205; in polar coordinates, 215;
in a solid with given surface-displace-
ments or surface-tractions, 244; in
solid bounded by plane, 250, 261;
in vibrating sphere, 312; in solid of
revolution, 332; in plane strain, 335.
Disc, rotating, 227.
Discontinuity, surface of, 134.
Displacement, components of, 52; in
beam, 153; for extension, 154; for
uniform flexure, 155; for torsion,
157; for non-uniform flexure, 179;
for asymmetric loading, 181; in ro-
tating disc, 228; for weight at single
point of surface of solid, 255, 270;
due to force at a point, 258; in sphere
with given surface-displacements, 276;
in sphere with given surface-tractions,
280; in solid with spherical cavity,
283; in sphere strained by bodily
forces, 292; in vibrating sphere, 314;
in sphere forced to vibrate, 325; in
case of surface-waves, 329; in solid of
revolution, 333; in plane strain, circles,
339; in plane strain, elliptic boundary,
342; produced by rotation of ellipse,
343.
Distortion: see Waves, Flexure, Tor-
sion.
Disturbance, propagation of, in isotropic
media, 130; in æolotropic media, 134.
Dufour, discoverer of yield-point, 102.
Duhamel, on the thermo-elastic equa-
tions, 24, 115.
Dupin's theorem, 204.
Elastic after-working, 103, 109.
Elastic constants, controversy concern-
ing, 14; variation of with change of
temperature, 23; for isotropic solids,
72; relations among, 73; table of, 77;
for æolotropic solids, 78; for amor-
phous bodies, 98. See also Crystals
and Modulus.
Elastic limits, 69, 102.
Elastic-line, 3.
Elasticity, curvilinear distributions of,
23, 99; cylindrical distribution, 229;
spherical distribution, 230.
Ellipsoid, strain, 7, 36, 40; stress, 64;
rotating, 277.
Elliptic cylinder, torsion, 163; flexure,
193; strain produced by rotation of,
343.
Elongation-quadric, 46; for strain in
solid bounded by plane, 256.
Energy-function, for isotropic solids, 75,
90; for monoclinic crystals, 81; for
rhombic crystals, 84; for tetragonal
crystals, 86; for cubic crystals, 87;
for hexagonal crystals, 88; for rhom-
bohedral crystals, 90; existence of,
116; for solid strained by unequal
heating, 118; form of, 119. See also
General Equations.
Equipollent loads, principle of equiva-
lence of, 33, 177, 228, 259.
Euler, on vibrations of bars, 3.
Everett, 77.
Extension, principal, 40; strain-quadric
for, 41; stress-strain curve for, 101;
of a cylinder, 154.
Factor of safety, 107.
Fatigue, 105.
Flaws, effects of on strength, 108; cylin-
drical, 161, 162; spherical, 284.
Flexure, Saint-Venant's theory of, 32; uni-
form, 155; non-uniform, 174; strength
of beam under, 182; cross-sections do
not remain plane, 179; asymmetric
load, 180; of circular bar, 187; of
hollow circular bar, 192; of elliptic
bar, 193; of rectangular bar, 196.
Flow, of solids, 103.
Fluor-spar, constants for, 96.
Frequency-equation, has always real
positive roots, 143; for radial vibra-
tions of spherical shell, 223; for
cylinder or cylindrical shell, 226; for
sphere, 317; for spherical shell, 324.
Fresnel's Wave-surface, 140.
General equations, history of, 7; in terms
of stress-components, 60, 207; for
isotropic solids, 76; deduced from en-
ergy-function, 119, 208.
Glass, Wertheim on, 18; constants for, 77.
Gravitation, compression of sphere due
to, 219.
Green, his principle, 12; constants for
isotropic solids, 22; on waves in
crystalline media, 25, 140; his trans-
formation, 58; reduction of the num-
ber of constants, 78; his method, 118.
Hagen, on the elasticity of wood, 98.
Hemihedrism, 80.
Hexagonal crystals, 87.
Hooke's Law, discovery of, 3; disputed,
20; generalised, 70; proofs of, 70.
Hydrodynamical analogy, for torsion,
33, 158, 161; for flexure, 186.
Invariants, of strain, 41, 47, 211; of
stress, 64.
Iron (wrought), constants for, 77.
Isotropy, defined, 71; transverse, 347.
Jaërisch, on vibrations of sphere, 30.
Kelvin, Lord: see Thomson, Sir W.
Kirchhoff, experiments on steel, 18;
constants for isotropic solids, 22;
theorems on energy-function, 120;
theory of thin rods, 174.
Lagerhjelm, on static and kinetic modu-
luses, 24.
Lamb, on vibrations of sphere, 30, 309.
Lamé, geometrical theorems on stress,
6, 64; on the general equations, 12;
constants for isotropic solids, 22; on
curvilinear coordinates, 25, 200; on
free vibrations, 27; his problem, 28,
273.
Lamé and Clapeyron, on the general
equations, 12; on solid bounded by
plane, 27.
Larmor, on gyrostatic inertia, 61; on
the influence of flaws on strength,
161; on Betti's method of integration,
347.
Lead, constants for, 77.
Limit of elasticity: see Elastic Limit.
Load, strain linear in terms of, 70;
effect of repeated, 105; sudden ap-
plication or reversal of, 108, 144;
equivalence of statically equipollent
systems of, 177.
Marriotte, on Galilei's problem, 3.
Matter, kinetic theory of, 16.
Maxwell, method of obtaining general
equations, 11; on viscosity and elas-
tic after-working, 104.
Modulus, static and kinetic, 24, 120;
defined, 71; of compression, 72, 91;
of rigidity, 72, 92; Young's, 73, 75, 93.
Molecular force, hypothesis of, 8; stress
deduced from, 112; elastic constants
deduced from, 113.
Monoclinic crystals, 81.
Navier, on the general equations, 8;
on torsion and flexure, 31; Leçons,
Neumann, F. E., theory of elastic cry-
stals, 22, 81; thermo-elastic equa-
tions, 24, 115.
Neutral line: see Axis.
Nodal surfaces, of vibrating sphere, 318,
320.
Normal coordinates, explained, 141.
Normal functions, explained, 142; for a
vibrating sphere, 311, 320.
Notations, double suffix, 99; symbolical,
120, 136.
Orthogonal surfaces, theory of, 200;
line element, 201; rotations of nor-
mals, 203; systems of, 213. See also
Curvilinear Coordinates.
Pearson, on the methods of the older
writers on Mechanics, 3; on rari-
constancy and multi-constancy, 14;
on the equivalence of statically equi-
pollent systems of load, 33; on beams
subject to continuous load, 34; on
the yield-point, 102; on Wöhler's ex-
periments, 105; on the Bernoulli-
Eulerian theory of beams, 180; Elas-
tical Researches of Barré de Saint-
Venant, 196, 230.
Perturbations, local, 28, 259.
Piezometer, 231.
Plane, solid bounded by, history of
problem, 27; Cerruti's solution, 251,
267.
Plane-strain, general equations for, 335;
polar coordinates, 336; elliptic co-
ordinates, 340.
Plasticity: see Flow.
Poisson, on the general equations, 9;
criticised by Stokes, 10; integral of
the equations of wave-motion, 25, 130.
Poisson's ratio, 75, 95.
Poncelet, on stress-strain diagrams, 101;
theory of rupture, 106; on load sud-
denly applied, 108.
Potassium Chloride, constants for, 96.
Potential, direct, 253; logarithmic, 269.
Pressure, arrived at kinematically, 67.
See also Stress.
Prism see Beams.
Purser, 168.
Pyrites, constants for, 19, 96.
Quartz, elastic character of, 90; con-
stants for, 97.
Quasi-nodal surfaces, 311, 321.
Radial strain, polar coordinates, 217;
cylindrical coordinates, 224.
Ray, equations of, 139.
Rayleigh, Lord, theory of free vibrations,
26, 141, 320; reciprocal theorem, 128;
on waves at surface of solid, 328.
Rhombic crystals, 83.
Rhombohedral crystals, 89.
Rigidity, introduced by Vicat and Navier,
21; defined, 72; depends on two di-
rections, 93; torsional, 158; flexural,
178; of the earth, 29, 308.
Rock-salt, constants for, 96.
Rods: see Beams.
Rotation, of a figure, 48; of the normals
to orthogonal surfaces, 203.
Rotation, components of, in Cartesian
coordinates, 53; in curvilinear co-
ordinates, 206; in polar coordinates,
215; in a solid with given surface
displacements or surface tractions,
246; in solid bounded by plane, 265;
in solid of revolution, 332; in case of
plane strain, 335.
Rupture, theories of, 106; examples of
theories, 225.
Saint-Venant, on shear, 7; on the gene-
ral equations, 10; objection to Green's
process, 20; on the distribution of
elasticity, 23; semi-inverse method,
31, 146; theory of torsion, 32; on
amorphous bodies, 98; theory of
safety, 107; torsion-factor, 158; ap-
proximate formula for torsion, 171;
on the neutral axis, 182; on piezo-
meter experiments, 231.
Screw-propeller shafts, 107.
Set, defined, 69; Coulomb-Gerstner law
of, 109.
Shear, simple, defined, 37; strain-quadric
for, 42; equivalent to extension and
compression, 7, 43; twofold character
of, 345.
Shearing-stress, defined, 62; cone of, 64;
twofold character of, 345.
Shells: see Spherical Shell and Cylin-
drical Shell.
Solutions, uniqueness of, 123; possibility
of, 125, 186; for bodily forces, equi-
librium, 237; for bodily forces, forced
vibrations, 238; for solid bounded by
plane, 251, 266; simple, of first type,
253; simple, of second type, 268;
in potential functions, 253, 272; in
spherical harmonics, 276; for a solid
of revolution, 331; by conjugate func-
tions, 335.
Sphere, compression of by its own gravi-
tation, 219; with given surface dis-
placements, 274; with given surface
tractions, 277; with normal surface
tractions, 281; under bodily forces,
285, 296; rotating, 303; free vibra-
tions of, 309; radial vibrations, 319;
forced vibrations, 324. See also Radial
Strain and Solutions.
Spherical cavity, in infinite solid, 283.
Spherical shell, radial vibrations, 222;
under pressure, 221, 230; general
theory of vibrations of, 322.
Stability, strength dependent on, 109;
in connexion with theorem of unique-
ness of solution, 124.
State of ease, 69, 102.
Steel, elastic constants for, 77.
Stokes, Sir G., criticism of Poisson, 10;
on the general equations, 13; con-
stants for isotropic solids, 22; on
diffraction, 25, 133.
Strain, history of analysis of, 6; homo-
geneous, defined, 36; ellipsoid, 36;
principal axes of, 36; components of,
38; quadric, 39; transformation of,
40; invariants, 41, 47, 51, 211; pure,
44; composition of, 47; infinitesimal,
50; in a body, 52; produced by heat,
115; conditions of compatibility of
components of, 122; mean values of
components of, 128; in curvilinear
coordinates, 205; in polar coordinates,
215; in cylindrical coordinates, 216;
in solid bounded by plane and sup-
porting a weight, 256. See also Radial
Strain and Plane Strain.
Strength, of materials, 101; of a beam
under torsion, 161; of a beam under
flexure, 182; of a beam under com-
bined strain, 183.
Stress, history of analysis of, 6; at a
point, 56; transformation of, 61;
quadric, 62; principal planes of, 62;
geometrical theorems on, 64; measure-
ment of, 66; in a medium, 66; ther-
mal, 115; in a twisted prism, 157;
in a bent beam, 175; in solid bounded
by plane and supporting a weight,
255, 270; on mean surface of strained
gravitating sphere, 289; due to the
weight of continents, 300.
Stress-difference: see Rupture.
Stress-strain diagrams, 101.
Stress-strain relations, for isotropic solids,
73; for solotropic solids, 78; for
amorphous bodies, 98; deduced from
point-atom hypothesis, 113.
Tetragonal crystals, 84.
Thermo-elastic equations, history of, 24;
establishment of, 114; deduced by
energy-method, 118.
Thomson, Sir W., strain-ellipsoid, 7; on
the energy-function, 13, 116; model
of solotropic molecule, 16; on Lamé's
problem, 29, 298; on the rigidity of
the earth, 29, 308; on cubic crystals,
96, 347; on æolotropy produced by
permanent set, 105; on fatigue, 106;
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