Curvilinear co-ordinates, 65 D Differentiation of tensors, 73, 76 Displacement of spectral lines, 97 E Energy and mass, 45, 49 —tensor of electromagnetic field, 50 —of matter, 54 Equation of continuity, co-variance of, 21 Equations of motion of material particle, 50 Equivalence of mass and energy, 49 Equivalent spaces of reference, 25 Euclidean geometry, 4 F Finiteness of universe, 105 Fizeau, 28 Four-dimensional continuum, 31 Four-vector, 41 Fundamental tensor, 71 G Galilean regions, 62 —transformation, 27 Gauss, 65 Geodetic lines, 82 Geometry, Euclidean, 4 Gravitation constant, 95 Gravitational mass, 60 H Homogeneity of space, 17 Hydrodynamical equations, 54 Hypotheses of pre-relativity physics, 73 I Inductive action of accelerated masses, 108 Inert and gravitational mass, equality of, 60 Invariant, 9 et seq. Isotropy of space, 17 K Kaluza, 104 L Levi-Civita, 73 Light-cone, 41 Light ray, path of, 98 Light-time, 33 Linear orthogonal transformation, 7 Lorentz electromotive force, 44 —transformation, 31 M Mach, 59, 105, 106, 109, 114 Mass and Energy, 45, 49 —equality of gravitational and inert, 60 —gravitational, 60 Maxwell's equations, 23 Mercury, perihelion of, 99, 103 Michelson and Morley, 28 Minkowski, 32 Motion of particle, equations of, 50 Moving measuring rods and clocks, 38 Multiplication of tensors, 14 N Newtonian gravitation constant, 95 O Operations on tensors, 13 et seq. Orthogonal transformations, linear, 7 Orthogonality, conditions of, 7 P Path of light ray, 98 Perihelion of Mercury, 99, 103 Poisson's equation, 87 Preferred systems of co-ordinates, 8 Pre-relativity physics, hypotheses of, 26 Principle of equivalence, 61 —inertia, criticism of, 62 Principles of conservation, 54 R Radius of Universe, 113 Rank of tensor, 13 Ray of light, path of, 98 Reference, space of, 3 Riemann, 68 —tensor, 79, 82, 105 Rods (measuring) and clocks in motion, 38 Rotation, 63 S Simultaneity, 17, 29 Sitter, 28 Skew-symmetrical tensor, 15 Solar Eclipse expedition (1919), 99 Space, concept of, 2 —Homogeneity of, 17 —Isotropy of, 17 Spaces of reference, 3 —equivalence of, 25 Special Lorentz transformation, 34 Spectral lines, displacement of, 97 Straightest lines, 82 Stress tensor, 22 Symmetrical tensor, 15 Systems of co-ordinates, preferred, 8 T Tensor, 12 et seq., 68 et seq. —Addition and subtraction of, 14 —Contraction of, 14 —Fundamental, 71 —Multiplication of, 14 —operations, 13 et seq. —Rank of, 13 —Symmetrical and Skew-symmetrical, 15 Tensors, formation by differentiation, 73 Theorem for addition of velocities, 38 Theorems of congruence, 3 Theory of relativity, criticisms of, 29 Thirring, 109 Time-concept, 28 Time-space concept, 31 Transformation, Galilean, 27 —Linear orthogonal, 7 U Universe, Finiteness of, 105