Non-Euclidean geometry, however, showed other possibilities. The surface of a sphere has no boundary, yet it is not infinite. In traveling round the earth, we never reach “the edge of the world,” and yet the earth is not infinite. The surface of the earth is contained in three-dimensional space, but there is no reason in logic why three-dimensional space should not be constructed on an analogous plan. What we imagine to be straight lines going on for ever will then be like great circles on a sphere: they will ultimately return to their starting point. There will not be in the universe anything straighter than these great circles; the Euclidean straight line may remain as a beautiful dream, but not as a possibility in the actual world. In particular, light rays in empty space will travel in what are really great circles. If we could make measurements with sufficient accuracy, we should be able to infer this state of affairs even from a small part of space, because the sum of the angles of a triangle would always be greater than two right angles, and the excess would be proportional to the size of the triangle. The suggestion we have to consider is the suggestion that our universe may be spherical in this sense. The reader must not confuse this suggestion with the non-Euclidean character of space upon which the new law of gravitation depends. The latter is concerned with small regions such as the solar system. The departures from flatness which it notices are like hills and valleys on the surface of the earth, local irregularities, not characteristics of the whole. We are now concerned with the possible curvature of the universe as a whole, not with the occasional ups and downs due to the sun and the stars. It is suggested that on the average, and in regions remote from matter, the universe is not quite flat, but has a slight curvature, analogous, in three dimensions, to the curvature of a sphere in two dimensions.