46. Transition to continuous matter 47. Experiment and deductive theory CHAPTER IV RELATIVITY MECHANICS 48. The antisymmetrical tensor of the fourth rank 107 49. Element of volume. Tensor-density 109 50. The problem of the rotating disc 112 51. The divergence of a tensor 113 52. The four identities 115 53. The material energy-tensor 116 54. New derivation of Einstein's law of gravitation 119 55. The force 122 56. Dynamics of a particle 125 57. Equality of gravitational and inertial mass. Gravitational waves 128 58. Lagrangian form of the gravitational equations 131 59. Pseudo-energy-tensor of the gravitational field 134 60. Action 137 61. A property of invariants 140 62. Alternative energy-tensors 141 63. Gravitational flux from a particle 144 64. Retrospect 146 CHAPTER V CURVATURE OF SPACE AND TIME 65. Curvature of a four-dimensional manifold 66. Interpretation of Einstein's law of gravitation 67. Cylindrical and spherical space-time 68. Elliptical space 69. Law of gravitation for curved space-time 70. Properties of de Sitter's spherical world 71. Properties of Einstein's cylindrical world 72. The problem of the homogeneous sphere \PageSep{ix} CONTENTS CHAPTER VI ELECTRICITY SECTION PAGE 73. The electromagnetic equations 74. Electromagnetic waves 75. The Lorentz transformation of electromagnetic force 76. Mechanical effects of the electromagnetic field 77. The electromagnetic energy-tensor 78. The gravitational field of an electron 79. Electromagnetic action 80. Explanation of the mechanical force 81. Electromagnetic volume 82. Macroscopic equations CHAPTER VII WORLD GEOMETRY Part I. Weyl's Theory 83. Natural geometry and world geometry 84. Non-integrability of length 85. Transformation of gauge-systems 86. Gauge-invariance 87. The generalised Riemann-Christoffel tensor 88. The in-invariants of a region 89. The natural gauge 90. Weyl's action-principle Part II. Generalised Theory 91. Parallel displacement 92. Displacement round an infinitesimal circuit 93. Introduction of a metric 94. Evaluation of the fundamental in-tensors 95. The natural gauge of the world 96. The principle of identification 97. The bifurcation of geometry and electrodynamics 98. General relation-structure 99. The tensor *B_{\mu\nu\sigma}^{\eps}. 100. Dynamical consequences of the general properties of world-invariants 101. The generalised volume 102. Numerical values 103. Conclusion Bibliography Index \fi%**** \PageSep{x} \PageSep{1} \MainMatter \Matter{Introduction} \index{Differentiation|seealso{Derivative}} \index{Distance|see{Length}} \index{Gravitation|seealso{Einstein's law}} \index{Ponderomotive force|see{Mechanical force}} \index{Proper-|see{Invariant mass \emph{and} Density}}