After discussing the special theory we shall proceed to examine Einstein’s general theory, which he began to develop in 1912 and which he completed in 1916. The general theory deals more especially with gravitation, though it also sheds new light on the problem of the relativity of motion. It is our opinion that the reader will [Pg xix] save himself much unnecessary trouble if he realises from the start that Einstein, even in the general theory, does not succeed in establishing the complete relativity of all motion. While it is true that acceleration loses much of its absoluteness, we are still far from being able to subscribe to the very wide visual or kinematical principle which the complete relativity of all motion would necessitate. Following the general theory, Einstein entered into cosmological considerations on the form of the universe as a whole. This part of the theory is still highly speculative; and until such time as astronomical observations conducted on the globular clusters and the Milky Way have given their verdict, nothing definite can be said. From the standpoint of the relativity of motion, this last part of Einstein’s theory is of fascinating interest; for should it be proved correct, the relativity of all motion might finally be justified and the bugaboo of absolute rotation dispelled forever. We should then be led to a modified form of the visual or kinematical principle of the complete relativity of motion; namely, to Mach’s mechanics. On the other hand, should astronomical observation deny the correctness of Einstein’s cosmological views, the theory would have failed to establish the complete relativity of all motion. In addition to all this preliminary physical information with which it is necessary to be acquainted (Newtonian mechanics, electrodynamics) before proceeding to a study of Einstein’s theory, a considerable amount of purely mathematical knowledge must be mastered. Here we refer not to the actual technique of calculation, but to the general significance of the mathematical doctrines developed by the great mathematicians of the past. Einstein’s theory, more especially the second part (the general theory), is intimately connected with the discoveries of the non-Euclidean geometricians, Riemann in particular. Indeed, had it not been for Riemann’s work, and for the considerable extension it has conferred upon our understanding of the problem of space, Einstein’s general theory could never have arisen. As Weyl expresses it: “Riemann left the real development of his ideas in the hands of some subsequent scientist whose genius as a physicist could rise to equal flights with his own as a mathematician. After a lapse of seventy years this mission has been fulfilled by Einstein.”