It seems to me that here we have a fairly direct proof that the stars of our universe are really limited in number.
There are thus four distinct lines of argument all pointing with more or less force to the conclusion that the stellar universe we see around us, so far from being infinite, is strictly limited in extent and of a definite form and constitution. They may be briefly summarised as follows:—
(1) Professor Newcomb shows that, if the stars were infinite in number, and if those we see were approximately a fair sample of the whole, and further, if there were not sufficient dark bodies to shut out almost the whole of their light, then we should receive from them an amount of light theoretically greater than that of sunlight. I have shown, at some length, that neither of these causes of loss of light will account for the enormous disproportion between the theoretical and the actual light received from the stars; and therefore Professor Newcomb's argument must be held to be a valid one against the infinite extent of our universe. Of course, this does not imply that there may not be any number of other universes in space, but as we know absolutely nothing of them—even whether they are material or non-material—all speculation as to their existence is worse than useless.
(2) The next argument depends on the fact that all over the heavens, even in the Milky Way itself, there are areas of considerable extent, besides rifts, lanes, and circular patches, where stars are either quite absent or very faint and few in number. In many of these areas the largest telescopes show no more stars than those of moderate size, while the few stars seen are projected on an intensely dark background. Sir William Herschel, Humboldt, Sir John Herschel, R.A. Proctor, and many living astronomers hold that, in these dark areas, rifts, and patches, we see completely through our stellar universe into the starless depths of space beyond.
(3) Then we have the remarkable fact that the steady increase in the number of stars, down to the ninth or tenth magnitudes, following one constant ratio either gradually or suddenly changes, so that the total number from the tenth down to the seventeenth magnitudes is only about one-tenth of what it would have been had the same ratio of increase continued. The conclusion to be drawn from this fact clearly is, that these faint stars are becoming more and more thinly scattered in space, while the dark background on which they are usually seen shows that, except in the region of the Milky Way, there are not multitudes of still smaller invisible stars beyond them.
(4) The last indication of a limited stellar universe—the estimate of numbers by the light-ratio of each successive magnitude—powerfully supports the three preceding arguments.
The four distinct classes of evidence now adduced must be held to constitute, as nearly as the circumstances permit, a satisfactory proof that the stellar universe, of which our solar system forms a part, has definite limits; and that a full knowledge of its form, structure, and extent, is not beyond the possibility of attainment by the astronomers of the future.