INDEX
A
Accelerated masses, inductive
action of, 108
Addition and subtraction of
tensors, 14
—theorem of velocities, 38
B
Biot-Savart force, 44
C
Centrifugal force, 64
Clocks, moving, 38
Compressible viscous fluid, 22
Concept of space, 3
—time, 28
Conditions of orthogonality, 7
Congruence, theorems of, 3
Conservation principles, 54
Continuum, four-dimensional, 31
Contraction of tensors, 14
Contra-variant vectors, 69
—tensors, 71
Co-ordinates, preferred systems
of, 8
Co-variance of equation of
continuity, 21
Co-variant, 12 et seq.
—vector, 68
Criticism of principle of inertia, 62
Criticisms of theory of
relativity, 29
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
—Radius of, 113
V
Vector, co-variant, 69
—contra-variant, 69
Velocities, addition theorem of, 38
Viscous compressible fluid, 22
W