The consideration of the fundamental four-dimensional space as being non-Euclidean where matter is present gives a possibility of an answer to the world old question: Is space finite or infinite? Is time eternal or finite? The fascinating possibility arises that the space may be like the two-dimensional surface of a sphere which to a limited experience seems infinite in extent and flat or Euclidean in character. A new Columbus now asks us to consider other possibilities in which we should have a finite universe--finite not only as to space measurement but as to time (for the space may be such that all of the four coordinates of its points are bounded in magnitude). However, although Einstein speaks of the possibility of a finite universe, we do not, personally, think his argument convincing. Points on a sphere may be located by the Cartesian coordinates of their stereographic projections on the equatorial plane and these coordinates, which might well be those actually measured, are not bounded. THE SPECIAL RELATIVITY THEORY In our account of the Einstein theory we have not followed its historical order of development for two reasons. Firstly, the earlier Special Relativity Theory properly belongs to a school of thought diametrically opposed to that furnishing the "General Theory of Relativity" and, secondly, the latter cannot be obtained from the former by the process of generalization as commonly understood. Einstein, when proposing the earlier theory, adopted the position of the empiricist so that to him the phrase, a point in space, had no meaning without a material framework of reference in which to measure space distances. When he came to investigate what is meant by time and when he asked the question "what is meant by the statement that two remote events are simultaneous?" it became evident that some mode of communication between the two places is necessary; the mode adopted was that by means of light-signals. The fundamental hypothesis was then made that the velocity of such signals is independent of the velocity of their source (some hypothesis is necessary if we wish to compare the time associated with events, when one material reference-system is used, and the corresponding time when another in motion relative to the first is adopted). It develops that time and space measurements are inextricably interwoven; there is no such thing as the length of a body or the duration of an event but rather these are relative to the reference-system. [11] Minkowski introduced the idea of the space of events--of four dimensions--but this space was supposed Euclidean like the three-dimensional space of his predecessors. To Einstein belongs the credit of taking from this representation a purely formal mathematical character and of insisting that the "real" space--whose distances have a physical significance--is the four-dimensional space. But we cannot insist too strongly on the fact that in the gravitational space of the