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