The density can be reduced to absolute units by substituting the value for the mean mass of a nebula, 2.6×108 ☉. Then, since the mass of the sun in grams is 2×1033 and 1 parsec is 3.1×1018 cm,
| ρ = 1.5×10–31 grams per cubic centimeter. | (13) |
This must be considered as a lower limit, for loose material scattered between the systems is entirely ignored. There are no means of estimating the order of the necessary correction. No positive evidence of absorption by inter-nebular material, either selective or general, has been found, nor should we expect to find it unless the amount of this material is many times that which is concentrated in the systems.
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,
| (14) |
| (15) |
| (16) |
Substituting the value found for ρ, 1.5×10–31, the dimensions become