The Lorentz transformation continues to hold for a limited region. Since the advent of the general theory, it has been recognised that the special theory only applies to particular regions where the~$g_{\mu\nu}$ can be treated as constants, so that it scarcely suffers by the fact that it cannot be applied to the whole domain of spherical space. Moreover the special principle is now brought into line with the general principle. The transformations of the theory of relativity relate to the differential equations of physics; and our tendency to choose simple illustrations in which these equations are integrable over the whole of space-time (as simplified in the mathematical example) is responsible for much misconception on this point. The remaining features of Einstein's world require little comment. His spherical space is commonplace compared with de~Sitter's. Each observer's coordinate-system covers the whole world; so that the fields of their finite experience coincide. There is no scattering force to cause divergent motions. Light performs the finite journey round the world in a finite time. There is no passive ``horizon,'' and in particular no mass-horizon, real or fictitious. Einstein's world offers no explanation of the red shift of the spectra of distant objects; and to the astronomer this must appear a drawback. For this and other reasons I should be inclined to discard Einstein's view in favour of de~Sitter's, if it were not for the fact that the former appears to offer a distant hope of accounting for the occurrence of a very large pure number as one of the constants of nature. \Section{72.}{The problem of the homogeneous sphere} \index{Homogeneous sphere, problem of}% \index{Problem!of homogeneous sphere}% \index{Sphere, problem of homogeneous}% For comparison with the results for naturally curved space, we consider a problem in which the curvature is due to the presence of ordinary matter.