'Extrapolatod' mass of the universe 111 414
'Stationary' lines of calcium 346—348
Acceleration-formula, functional equation for, solved Note 3
Acceleration-formula, physical interpretation of 105—108
Acceleration-formula, stated and derived 101
Accelerations in statistical systems 213
Accelerations of a free particle in the simple kinematic system 96—108
Accelerations, effect of cosmical constant on 497
Accelerations, local 110 181
Accelerations, outward 181
Action at a distance 103 384
Age of the universe 74 112 152
Anderson 223
Apparent brightness of a receding nebula Note 7
Apparent brightness, pursuit of 188—192
Apparent centre of the universe 105 108 183—192 194
Approximation of actual universe to a hyperbolic one 492
Associations of galaxies 325—343 364
Baade 225
Background luminosity finite 112 130 140 Note
Barnes 23
Beals 258
Blackett 223
Bok 259 260
Boltzmann's equation, consequences of 216
Boltzmann's equation, derived Note 5
Boltzmann's equation, generalized 207—209 212
Bothe 221 225
Calcium clouds 346—348
Centrality of each fundamental observer 112 117
Centre of the universe, apparent 105 108
Chandrasekhar 258
Classification of trajectories 237—242
Clay 222
Clerk Maxwell 288
clocks 6 12—14
Clocks, conditions of agreement of 19
Cluster, initial configuration of 82
Clustering of nebulae 119
Collisions, effect of 194 255 285
Comparison of proposed models, method of 421
Comparisons with current cosmology 4 149 198 280 443—447 453 454 463—499 503 505 514
Compton, A.H. 222
Condensations in statistical systems 227—233
Congestion, regions of, not due to instability 259
Conservation of form, role of 2 71 72 89 99 100
Constant of gravitation, sign of 163 223
Constants of gravitation 221 413
Continuity, hydrodynamical equation of 76 92 449
Contraction of a cluster 82
Contraction of a cluster, small probability of 82 86
Convergence of certain integrals 228
Coordinates, 'mixed' 2 31
Coordinates, construction of 16 504
Coordinates, transformations of 2
Corlin 220—225
Cosmic Being, the 148
Cosmic clouds 8 299—364 396
Cosmic clouds, an intrinsic element in the universe 356 363
Cosmic clouds, possible origin of 349—364
Cosmic rays 8 194 235 281—298 395
Cosmic rays, an inevitable element in the universe 292
Cosmic rays, arrival of primary agent in our own neighbourhood 294—296
Cosmic rays, complicated nature of 297
Cosmic rays, difficulties concerning origin of 290 291
Cosmic rays, energy of 286
Cosmic rays, evolutionary consequences of 298
Cosmic rays, nowhere born as such 291
Cosmic rays, observed features 286
Cosmic rays, theories of origin of 287 289
Cosmic time 2 31 62 419 427 434 446 454
Cosmical constant 1 60 103 221 416 417 460—462 512
Cosmological principle 8 11 52—69 135—139 210—212
Cosmological principle and metaphysics 66
Cosmological principle as a definition or principle of selection 8 53
Cosmological principle, equation satisfied by statistical systems obeying 211
Counts of nebulae classified according to Doppler offect 115 426 427 467 468 481 486 487
creation 150—156 502
Creation and deity 154—156
Creation and the zero of timo 83 85
Creation of matter 4 66 86 128
Creation of matter in Einstein — de Sitter model 470—475
Creation of matter in hyperbolic universes 493 494
Creation, all but observable at the expanding frontier 151
Creation, bearing of, on biology 154
Creation, irrationality of 154
Creation, pro-oxporiential 150 475
Curtis 260
Curvature of space, interpretation of, in current cosmology 455 456
de Sitter 2 12 307—309 315 319
Deceleration in Einstein — de Sitter universe 448
Deceleration in Einstein — de Sitter universe in hyperbolic universes 457 458
Deflexion of light 39
Deity, creation and 154—156
Deity, extra-territorial attributes of 154 155
Density of the universe, apparent outward variation of 77 112 119 140 142 Note
Density of the universe, local value of 76 110 119 145 415 438 450 452 483
Differential equations, role of 319
Dingle 20
Dirac 236
Discrete systems, impossibility of satisfying cosmological principle with, in three dimensions 8 397 Note
Discrete universe in one dimension 46—60
Discreteness, effect of 8 397
Distance, definition of 16
Distribution function for statistical systems 211
Distribution-theorems 261
Doppler effects 21 73 425 448 458 466 479 481
Doterminacy 214
Eddington 3 19 104 115 119 120 128 205 274 275 286 341 342 346
Einstein 1 2 6—8 19 24 33 39 64 65 111 116 182 299—301 307—309 343
Einstein — de Sitter universe 443—448 464—476
Einstein — de Sitter universe, consideration of negative times in 471—472
Einstein — de Sitter universe, creation of matter in 470 473—476
Einstein — de Sitter universe, observable relations in 468 469
Einstein — de Sitter universe, ultimate rest in 448
Einstein's universe, instability of, discussed 258
Elliptic universes 449—459
entropy 402
Epoch, definition of 16
Equivalence of observers 2 9—51 372
Equivalence, conditions of 18 373
Equivalence, definition of 11
Equivalence, solution of equations for 20
Evolution and cosmic rays 298
Evolution and cosmic rays of the universe 152 154
Expanding space of negative curvature 477-494
Expansion of a cluster of the universe 1 8 70—86 91—95 112
Expansion of a cluster, high probability of 82
Expectation, cosmological principle as an 137
Extrapolation of observations 138 139
Extrapolation, cosmological principle as a means of 134—139
Field equations 5 509—513
Finsler space 197
Free particle in inter-galactic space 194
Free particle in inter-galactic space, motion of, in the simple kinematic system 167—198
Friedmann 2 319
Fundamental particles, uniformity of motion of 69 202
Future of the universe 153
Future, impossibility of prior experience of the 116
Galactic dust-clouds 350—354
Galaxies, dissolution and re-formation of 363
Galaxies, recession of 1 8
Galaxies, rotations of 8 346 397
Galaxy, spherical form of our own 251
Galaxy, structure of 200 260—280
General relativity 2 76 100 102 103 198 221 375—378 504—514
Geometry of trajectories 183—187
Geometry, arbitrary 5 142
Gerasimovic 258
Gilbert 224
| Gravitation, comparison with local Newtonian 412
Gravitation, Einstein's law of 1 5 221 509
Gravitation, law of, for a statistical system 218
Gravitation, local, essentially attractive 163
Gravitation, nature of 2 3 103 143 218—222 381—385
Hartmann 257
Heat-death, avoidance of any ultimate 402
Hodgkinson 357
Hodograph of a free trajectory 174 186 334—340
Homogeneity 58—64 109
Homogeneity and simultaneity 61
Hubble 1 74 78 113 114 123 213 259 260 354
Hydrodynamical motion 76 81 205 206
Hyperbolic models, rejected 493
Hyperbolic universes 449—459 477—494
Hyperbolic universes, observable properties of 482—491
Hyperbolic universes, properties of, for large and small  486—487
Immortality of the universe 153
Indeterminacy, principle of 215
Inge 286
Integrals of motion 160—171 178
Integrals of motion, properties of 180 193
Integration of trajectories (table of results) 311
Integration-constants of a trajectory 158 176 312—315 317
Intensity of impingeing particles 234
Interaction, absence of, between interior and exterior of expanding light-spliere 162 193
Interlopers 253
Invariant velocity-distribution 89
Invariant velocity-distribution, functional equation for, solved Note 2
Invariant velocity-distribution, limiting spatial distribution of 91
Invariant velocity-distribution, properties of 90
Isopliotic lines (in nebulae), circular nature of 274 389
Jeans 2 3 18 19 21 205 206 225 227 286 325 360
Jeffreys 74
K-effoct 252 391
Kelvin 288
Keplerian problem 367 382 434
Kermack 333 334
Kinematic systems, abstract characteristics of 369—385
Kinematic systems, possible observations on 419—428
Kinematics of a cluster of a 'homogeneous' system 70—77
Kinematics of a cluster of particles 78-85
Kirchhoff 287
Kolhoerster 221 225
Larmor 199 279 287
Law of gravitation 103 218
Law's of naturo 2 5 100 402—403
Lemaitre 2 223 319 340
Life 154
Limiting velocity of a particle 320—324
Lindemann 178
Lobatchevsky 10
Local density 110 119 145 415 438 450 452 483
Lorentz formulae, content of 51 374
Lorentz formulae, derivation of 15 28 32—34 36
Lorentz formulae, generalized 27
Lorentz — FitzGerald contraction 36
Luminosity-distribution in nebulae 274
Mass of the universe, 'extrapolated' 111
Mathematics and humbug 319
Mathematics and humbug and metaphor 1
Maxwell's sorting demon 81
McCrea 71 296 303 311 333 334
McVittie 10
Metric, meaning of adoption of 143 506—513
Millikan 221 225 227
Milner 11 166
Minkowski 18 287
Motion of a cluster of particles 78—86
Motion of a cluster of particles, ultimate hydrodynamical character of 79 81
Natural zero of time 82 471—473
Nature, laws of 2 5 100 402 403
Nebulae, accelerations of 74 471 472 500
Nebulae, apparent brightness of Note 7
Nebulae, equivalence of 24 77 119 201
Nebulae, evolution of 152 363
Nebulae, infinity of number of 58 90 112
Nebulae, number of, observed 119
Nebulae, outward motions in 194
Nebulae, predicted properties of 140
Nebulae, recession of 1 73 74 119
Nebulae, represented by an open set of points 112
Newtonian elliptic universes 449—452
Newtonian elliptic universes, hyperbolic universes 449—452
Newtonian elliptic universes, parabolic universe 436—442
Newtonian elliptic universes, universes 68 411 430—462
Newtonian elliptic universes, universes, formal equivalence to universes of relativistic cosmology 434 443—448
Newtonian elliptic universes, universes, valid for local astronomical purposes 433 446 454
Nuclear agglomerations 231
Observations, totality of 15 366
Observers, centrality of fundamental 112 117
Observers, equivalence of 2 9—51
Observers, linear systems of equivalent 39—50
Occhialini 223
Oort 257 279
Oscillating universes 495 496
Particle-observer 10
Past, impossibility of re-experience of the 116
Peano 14
Photographic counts of nebulae 77
Photons, system of satisfying the cosmological principle 300
Plaskett, J.S. 257 279
Plummer 212
Poincare, H. 10 23 129
Principle of indeterminacy 215
Principle of indeterminacy of least action 5 195—198
Principle of indeterminacy of relativity 2 214 220 376
Principle of indeterminacy of superposition 398
Quadratic forms, invariance of 30
Radial velocity, definition of 23
Radius of the universe 112
Random systems, expansion of 82
Reciprocity theorems 327—333
Relativity, general 2 76 100 102 103 198 221 375—378
Relativity, nature of 6 371
Rest, absence of absolute standard of, in simple kinematic system 117
Rest, absolute standard of 60 448
Reynolds 212 213
Riemannian space 197 221 506
Rigid bodies 9
Robb 15
Robertson 315 319 333 334
Rogener 221
Rossi 222 223
Russell, Bertrand 12 14
Russell, H.N. (Dugan and Stewart) 326
Rutherford 221
Sample principle, rotation of, to cosmological principle 135
Sample principle, the 134
Schwarzschild 7
Seares 113
Seeliger 301 326
Segregation of particles 79—84
Shapley 113 279
Signalling between observers 15
Simple kinematic system 87—118 411—429
Simple kinematic system, formulae of 92
Simple kinematic system, invariance of 94
Simple kinematic system, possible observations on 419—428
Simple kinematic system, properties of 112
Simultaneity 31
Simultaneity and homogonoity 61 64
Singularities in density, removal of 398
Singularity, nature of, near a nucleus 232 272 398
Slipher 1
Solipsism 6
Space, arbitrary 5 141 142
Space, choice of flat 5
Space, curvature of 5 128 385
Space, curvod 1 58 118 128
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