# Space Time and Gravitation/Index

INDEX
* Absolute, approached through the relative, 82
* Absolute acceleration, 68, 154, 194
* Absolute past and future, 50
* Absolute rotation, 152, 164, 194
* Absolute simultaneity, 12, 51
* Absolute time, in cylindrical world, 163
* Acceleration, a simpler quality than velocity, 195; modifies FitzGerald contraction, 75
* Action, 147; atomicity of, 199; on Weyl's theory, 177
* Action, Principle of Least, 149, 178
* Addition of velocities, 59
* Aether, a plenum with geodesic structure, 164; identified with the "world," 187; non-material nature of, 39; stagnant, 210
* Artificial fields of force, 64
* Atom, vibrating on sun, 128
* Atomicity, law of, 199; of Action, 177
* Aviator, space and time-reckoning of, 23
* Bending of light, effect on star's position, 112; observational results, 118; theory of, 107, 207
* Beta particles, 59, 145
* Brain, constitution of, 191
* Brazil, eclipse expedition to, 117
* Causality, law of, 156
* Causation and free will, 51
* Centrifugal Force, compared with gravitation, 41, 65; debt at infinity, 157; not caused by stars, 153; vibrating atom in field of, 129
* Chess, analogy of, 184
* Christoffel, 89
* Circle in non-Euclidean space, 104
* Clifford, 77, 152, 192
* Cliquishness, 188
* Clock, affected by velocity, 58; on sun, 74, 128; perfect, 13; recording proper- time, 71
* Clock-scale, 58
* Clock-scale geometry, not fundamental, 73, 131, 191
* Coincidences, 87
* Comets, motion through coronal medium, 121; radiation-pressure in, 110
* Conservation of electric charge, 173; of energy and momentum, 139; of mass, 141, 196
* Content contrasted with structural form, 192, 200
* Continuous matter, 91, 140
* Contraction, FitzGerald, 19, 54
* Convergence of physical approximations, 154
* Coordinates, 77
* Coordinate velocity, 107
* Corona, refraction by, 121
* Cottingham, 114
* Crommelin, 114, 122
* Curvature, degrees of, 91; identified with action, 148; merely illustrative, 84; of a globe of water, 148; of space and time, 158; on Weyl's theory, 176; perception of, 190
* Cylinder and plane, indistinguishable in two dimensions, 81
* Cylindrical world, Einstein's, 161, 177
* Davidson, 114
* Deflection of light, effect on star's position, 112; observational results, 118; theory of, 107,207
* Density, effect of motion on, 62
* Displacement of spectral lines, 129; in nebulae, 161 ; in stars, 135
* Displacement of star-images, 112, 115
* Double stars and Einstein effect, 133
* Duration, not inherent in external world, 34 ​
* Eclipse, observations during, 113
* Ehrenfest's paradox, 75
* Electrical theory of inertia, 61
* Electricity and gravitation, 167
* Electromagnetic potentials and forces, 172
* Electron, dimensions of, 177; geometry inside, 91; gravitational mass of, 178; inertia of, 61; Kaufmann's experiment on, 62, 146; singularity in field, 167
* "Elsewhere," 50
* Emptiness, perception of, 190
* Energy, conservation of, 139; identified with mass, 146; inertia of, 61, 146; weight of radio-active, 112
* Entropy, 149
* Eötvös torsion-balance, 112
* Equivalence, Principle of, 76, 131, 212
* Euclidean geometry, 1, 47, 73
* Euclidean space of five dimensions, 84
* Event, definition of, 45, 186
* Evershed, 130
* Extension in four dimensions, 37, 46
* Feeling, elements of, 192
* Fields of force, artificial, 64; due to disturbance of observer, 69; electromagnetic, 171; relativity of, 67
* Field of velocity, 195
* FitzGerald contraction, 19; consequences of, 22; modified by acceleration, 75; relativity explanation of, 54
* Flat space in two dimensions, 80
* Flat space-time, 83; at infinity, 84; conditions for, 89
* Flatfish, analogy of, 95
* Flatland, 57
* Force, compared with inertia, 137; electromagnetic, 172; elementary conception of, 63; fields of, 64; relativity of, 43, 67, 76
* Form contrasted with content, 192, 200
* Formalism of knowledge, 175
* Foucault's pendulum, 152
* Four-dimensional order, 35, 56, 186
* Four-dimensional space-time, geometry of, 45, 82; reality of, 181
* Fourth dimension, 13
* Frame, inertial, 156
* Frames of reference, "right" and "wrong," 42
* Freewill, 51
* Freundlich, 212
* Future, absolute, 50
* Galilean potentials, 83
* Gauge, effect on observations, 31; provided by radius of space, 177
* Gauge-system, 169
* Geodesic, absolute significance of, 70, 150; definition of, 75; motion of particles in, 138, 151; in regions at infinity, 157
* Geodesic structure, absolute character of, 155, 164; acceleration of, 195
* Geometrical conception of the world, 176, 183
* Geometry, Euclidean, 1; hyperbolic, 47; Lobatchewskian, 1, 9; natural, 2; non-Euclidean, or Riemannian, 6, 73, 84, 90; non-Riemannian, 169; semi-Euclidean, 47
* Ghosts of stars, 161
* Globe of water, limit to size of, 148
* Gravitation, Einstein's law of, differential formula, 90; integrated formula for a particle, 97; macroscopic equations, 140, 193
* Gravitation, Newton's law of, ambiguity of, 93; approximation to Einstein's law, 103; deflection of light, 109, 111
* Gravitation, propagation with velocity of light, 94, 147; relativity for uniform motion, 21, 125
* Gravitational field of Sun, 97; deflection of light, 107, 118, 207; displacement of spectral lines, 129; motion of perihelion, 122, 206; Newtonian attraction, 102; result of observational verification, 126
* Grebe and Bachem, 130
* Greenwich, Royal Observatory, 114
* Gyro-compass, 152
* Hummock in space-time, 97
* Hurdles, analogy of counts of, 104
* Hyperbolic geometry, 47 ​
* Identities connecting $G_{\mu \nu }$, 141
* Identity permanent, 40, 193
* Imaginary intervals, 150, 187
* Imaginary time, 48, 181
* Inertia, compared with force, 137; electrical theory of, 61; in regions at infinity, 157; infinite, 56; Mach's views, 164; of light, 110; relativity theory of, 139
* Inertia-gravitation, 137
* Inertial frame, 156
* Infinity, conditions at, 157
* Integrability of length and direction, 174
* Interval, 46, 150, 187; general expression for, 82; practical measurement of, 58, 75
* Interval-length, geometrical significance essential, 127; identified with proper time, 71; tracks of maximum, 70, 150; zero for velocity of light, 71
* Invariant mass, 145; of light, 148
* Kaufmann's experiment, 62, 146
* Kinds of space, 81
* Laplace's equation, 96, 140
* Larmor, 19, 211
* Length, definition of, 2; effect of motion on, 19; relativity of, 34
* Le Verrier, 124
* Levi-Civita, 89
* Lift, accelerated, 64
* Light, bending of, 107, 112, 118, 207; coordinate velocity of, 107; mass of, 62, 110, 148; voyage round the world, 161; weight of, 111
* Light, velocity of, an absolute velocity, 59; importance of, 60; system moving with, 26, 56
* Lobatchewsky, 1, 9
* Lodge, 32, 125, 211
* Longest tracks, 70
* Lorentz, 19, 211
* Mach's philosophy, 163
* Macroscopic equations, 92, 139; interval, 187
* Map of sun's gravitational field, 99
* Mass, conservation of, 141, 195; electrical theory of, 61; gravitational, 98; identified with energy, 146; invariant, 145; of light, 62, 110, 148; variation with velocity, 145
* Mathematics, Russell's description of, 14
* Matter, continuous, 91; definition of a particle, 98; extensional relations of, 8; gravitational equations in, 141; perception of, 190; physical and psychological aspects, 192
* Mercury, perihelion of, 123, 125
* Mesh-systems, 77; irrelevance to laws of nature, 87
* Michelson-Morley experiment, 18
* Minkowski, 30, 212
* Mirror, distortion by moving, 22
* Momentum, conservation of, 141; re-definition of, 144; of light, 111
* Moon, motion of, 93, 134
* Motion, insufficiency of kinematical conception, 194; Newton's first law, 136
* Natural frame, 155
* Natural gauge, 176
* Natural geometry, 2
* Natural tracks, 70
* Nebulae, atomic vibrations in, 161
* Newton, absolute rotation, 41; bending of light, 110; law of gravitation, 93; law of motion, 136; relativity for uniform motion, 40; super-observer, 68
* Non-Euclidean geometry, 6, 73, 84, 90
* Non-Riemannian geometry, 169
* Observer, an unsymmetrical object, 57
* Observer and observed, 30
* Orbits under Einstein's law, 123
* Order and dimensions, 14, 186
* Ordering of events in external world, 35, 54, 184
* Past, absolute, 50
* Perceptions, as crude measures, 10, 15, 31 ​
* Perihelia of planets, motions of, 123
* Permanence of matter, 196
* Permanent identity, 40, 193
* Permanent perceptual world, 141, 198
* Poincaré, 9
* Point-event, 45, 186
* Potentials, 80; Galilean values, 83
* Potentials, electromagnetic, 172
* Principe, eclipse expedition to, 114
* Principle of Equivalence, 76, 131, 212
* Principle of Least Action, 149, 178
* Principle of Relativity (restricted), 20
* Probability, a pure number, 178
* Projectile, Jules Verne's, 65
* Propagation of Gravitation, 94, 147
* Proper-length, 11
* Proper-time, 71
* Pucker in space-time, 85
* Radiation-pressure, 110
* Real world of physics, 37, 181
* Receding velocities of B-type stars, 135; of spiral nebulae, 161
* Reflection by moving mirror, 22
* Refracting medium equivalent to gravitational field, 109
* Refraction of light in corona, 121
* Relativity of force, 43, 76; of length and duration, 34; of motion, 38; of rotation, 152, 155; of size, 33
* Relativity, Newtonian, 40; restricted Principle of, 20; standpoint of, 28
* Repulsion of light proceeding radially, 102, 108
* Retardation of time, 24, 55; in centrifugal field, 129; in spherical world, 160
* Ricci, 89
* Riemann, 2, 89, 167
* Riemann-Christoffel tensor, 89
* Riemannian, or non-Euclidean, geometry, 6, 73, 84, 90
* Rigid scale, definition of, 3
* Rotation, absolute, 152, 164, 194
* Rotation of a continuous ring, 194
* Russell, 14, 197
* St John, 130
* Semi-Euclidean geometry, 47
* Simultaneity, 12, 51
* de Sitter, 134, 159, 179
* Sobral, eclipse expedition to, 117
* Space, conventional, 9; kinds of, 81; meaning of, 3, 8, 15; relativity of, 34
* Space-like intervals, 60, 187
* Space-time, 45; due to Minkowski, 212; partitions of, 54
* Spherical space-time, 159
* Standard metre, comparison with, 168
* Stresses in continuous matter, 193
* Structure opposed to content, 197, 200
* Structure, geodesic, absolute character of, 155, 164; acceleration of, 195; behaviour at infinity, 157
* Super-observer, Newton's, 68
* Synthesis of appearances, 31, 182
* Tensors, 89, 189
* Thomson, J. J., 61
* Time, absolute, 163; depends on observer's track, 38, 57; for moving observer, 24; imaginary, 48; measurement of, 13; past and future, 51; "standing still," 26, 160
* Time-like intervals, 60, 187
* Tracks, natural, 70
* Vacuum, defined by law of gravitation, 190
* Vector, non-integrable on Weyl's theory, 174
* Velocity, addition-law, 59; definition of, 193; static character, 194
* Velocity of gravitation, 94, 147
* Velocity of light, importance of, 60; in gravitational field, 108; system moving with, 26, 56
* Warping of space, 8, 126
* Wave-front, slewing of, 108
* Weight, of light, 107, 111; of radio-active energy, 111; proportional to inertia, 137; vanishes inside free projectile, 65
* Weyl, 174
* World, 186, 187
* World-line, 87