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This view is not in harmony with the theory of Newton. The latter theory rather requires that the universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards from this centre the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space.^[1]

This conception is in itself not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined to become gradually but systematically impoverished.

1. Proof.—According to the theory of Newton, the number of “lines of force” which come from infinity and terminate in a mass $m$ is proportional to the mass $m$. If, on the average, the mass-density $\rho _{o}$ is constant throughout the universe, then a sphere of volume $V$ will enclose the average mass $\rho _{0}V$. Thus the number of lines of force passing through the surface $F$ of the sphere into its interior is proportional to $\rho _{0}V$. For unit area of the surface of the sphere the number of lines of force which enters the sphere is thus proportional to $\rho _{0}{\tfrac {v}{F}}$ or to $\rho _{0}R$. Hence the intensity of the field at the surface would ultimately become infinite with increasing radius $R$ of the sphere, which is impossible.