The evaluation of the cosmical number

Source abstract

1. The cosmical number N = . 136 . 2 256 is most picturesquely described as ‘the number of protons and electrons in the universe’. This in itself would be a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae; it determines the ratio of the electrical to the gravitational forces between particles, the range and magnitude of the non-Coulombian forces in atomic nuclei, and the cosmical repulsion manifested in the recession of the nebulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; this total is N . We cannot say with the same confidence that the number of particles in the actual universe is precisely N , because the admission of radiation, complex nuclei, and unsteady conditions takes the problem outside the range of rigorously developed theory; but to the best of our belief these complications do not affect the total number of protons and electrons composing the matter of the universe.