Euclid's and Newton's systems stand as first and second approximations to that world. The Special Relativity Theory constitutes a correction of Newton, presumably because it is a third approximation. We must seek in it those features which we may most hopefully carry along, into the still more general case. Newton's system retained the geometry of Euclid. But Minkowski's invariant expression tells us that Einstein has had to abandon this; for in Euclidean geometry of four dimensions the invariant takes the form: $$\sqrt{(X-x)^2 + (Y-y)^2 + (Z-z)^2 + (T-t)^2}\,,$$ analogous to that of two and three dimensions. It is not the presence of the constant $C$ in Minkowski's formula that counts; this is merely an adjustment so that we may measure space in miles and time in the unit that corresponds to a mile. It is the minus sign where Euclidean geometry demands a plus that makes Minkowski's continuum non-Euclidean. The editor has told us what this statement means. I think he has made it clear that when we speak of the geometry of the four-dimensional world, we must not read into this term the restrictions surrounding the kind of geometry we are best acquainted with--that of the three-dimensional Euclidean continuum. So I need only point out that if we are to make a fourth (and we hope, final) approximation to the reality, its geometry must preserve the generality attained by that of the third step, if it goes no further. EINSTEIN'S TIME-SPACE WORLD Einstein accordingly examined the possible non-Euclidean geometries of four dimensions, in search of one displaying fundamental characteristics which, interpreted in terms of space-time, would lead to the observed facts of gravitation. The mathematics of this investigation is that part of his work which, we are told, but twelve men can follow; so we may only outline his conclusions. If we assume that in the neighborhood of matter the world of space-time is non-Euclidean, and that its curvature or distortion or non-Euclideanism is of a certain type already known to mathematicians; that the curvature of this world in the neighborhood of matter increases with the mass, and decreases as the distance from the matter increases; and that every particle of matter that is not interfered with travels through space-time in the most direct path possible in that continuum; then the observed facts of gravitation are accounted for as an inherent geometric property of this space-time world. We usually say that the presence of matter distorts this world, and that this distortion gives the track of particles through the region affected its non-uniform character.