THE FINITE UNIVERSE OF GENERAL RELATIVITY The mean density of space can be used to determine the dimensions of the finite but boundless universe of general relativity. De Sitter[27] made the calculations some years ago, but used values for the density, 10^{–26} and greater, which are of an entirely different order from that indicated by the present investigations. As a consequence, the various dimensions, both for spherical and for elliptical space, were small as compared with the range of existing instruments. For the present purpose, the simplified equations which Einstein has derived for a spherically curved space can be used.[28] When R, V, M, and ρ represent the radius of curvature, volume, mass, and density, and k and c are the gravitational constant and the velocity of light, $R = \frac{c}{\sqrt{4πk}} \cdot \frac{1}{\sqrt{\rho}},$ (14) $V = 2π^2R^3,$ (15) $M = πc^2/2k · R.$ (16) Substituting the value found for ρ, 1.5×10^{–31}, the dimensions become R = 8.5×10^{28} cm = 2.7×10^{10} parsecs, (17) V = 1.1×10^{88} cm = 3.5×10^{32} cubic parsecs, (18) M = 1.8×10^{57} grams = 9×10^{22} ☉. (19) The mass corresponds to 3.5×10^{15} normal nebulae. The distance to which the 100-inch reflector should detect the normal nebula was found to be of the order of 4.4×10^{75} parsecs, or about 1⁄600 the radius of curvature. Unusually bright nebulae, such as M 31, could be photographed at several times this distance, and with reasonable increases in the speed of plates and size of telescopes it may become possible to observe an appreciable fraction of the Einstein universe. Mount Wilson Observatory September 1926 [1] _Contributions from the Mount Wilson Observatory_, No. 324. [2] These are the two Magellanic Clouds, M 31, and M 33. [3] Bailey, _Harvard Annals_, ❰60❱, 1908. [4] Hardcastle, _Monthly Notices_, ❰74❱, 699, 1914. [5] This estimate by Seares is based on a revision of Fath’s counts of nebulae in Selected Areas (_Mt. Wilson Contr._, No. 297; _Astrophysical Journal_, ❰62❱, 168, 1925). [6] “A General Study of Diffuse Galactic Nebulae,” _Mt. Wilson Contr._, No. 241; _Astrophysical Journal_, ❰56❱, 162, 1922.