It is quite impossible to verify directly such a theory, for we know the actual distance of only about forty-three stars. We are unable, therefore, definitely to assure ourselves whether, as the grindstone theory presupposes, the stellar universe actually reaches out very much further from us in the direction of the Milky Way than in the other parts of the sky. The theory is clearly founded upon the supposition that the stars are more or less equal in size, and are scattered through space at fairly regular distances from each other.

Brightness, therefore, had been taken as implying nearness to us, and faintness great distance. But we know to-day that this is not the case, and that the stars around us are, on the other hand, of various degrees of brightness and of all orders of size. Some of the faint stars—for instance, the galloping star in Pictor—are indeed nearer to us than many of the brighter ones. Sirius, on the other hand, is twice as far off from us as α Centauri, and yet it is very much brighter; while Canopus, which in brightness is second only to Sirius out of the whole sky, is too far off for its distance to be ascertained! It must be remembered that no parallax had yet been found for any star in the days of Herschel, and so his estimations of stellar distances were necessarily of a very circumstantial kind. He did not, however, continue always to build upon such uncertain ground; but, after some further examination of the Milky Way, he gave up his idea that the stars were equally disposed in space, and eventually abandoned the grindstone theory.

Since we have no means of satisfactorily testing the matter, through finding out the various distances from us at which the stars are really placed, one might just as well go to the other extreme, and assume that the thickening of stars in the region of the Milky Way is not an effect of perspective at all, but that the stars in that part of the sky are actually more crowded together than elsewhere—a thing which astronomers now believe to be the case. Looked at in this way, the shape of the stellar universe might be that of a globe-shaped aggregation of stars, in which the individuals are set at fairly regular distances from each other; the whole being closely encircled by a belt of densely packed stars. It must, however, be allowed that the gradual increase in the number of stars towards the Milky Way appears a strong argument in favour of the grindstone theory; yet the belt theory, as above detailed, seems to meet with more acceptance.

There is, in fact, one marked circumstance which is remarkably difficult of explanation by means of the grindstone theory. This is the existence of vacant spaces—holes, so to speak, in the groundwork of the Milky Way. For instance, there is a cleft running for a good distance along its length, and there is also a starless gap in its southern portion. It seems rather improbable that such a great number of stars could have arranged themselves so conveniently, as to give us a clear view right out into empty space through such a system in its greatest thickness; as if, in fact, holes had been bored, and clefts made, from the boundary of the disc clean up to where our solar system lies. Sir John Herschel long ago drew attention to this point very forcibly. It is plain that such vacant spaces can, on the other hand, be more simply explained as mere holes in a belt; and the best authorities maintain that the appearance of the Milky Way confirms a view of this kind.

Whichever theory be indeed the correct one, it appears at any rate that the stars do not stretch out in every direction to an infinite distance; but that the stellar system is of limited extent, and has in fact a boundary.

In the first place, Science has no grounds for supposing that light is in any way absorbed or destroyed merely by its passage through the "ether," that imponderable medium which is believed to transmit the luminous radiations through space. This of course is tantamount to saying that all the direct light from all the stars should reach us, excepting that little which is absorbed in its passage through our own atmosphere. If stars, and stars, and stars existed in every direction outwards without end, it can be proved mathematically that in such circumstances there could not remain the tiniest space in the sky without a star to fill it, and that therefore the heavens would always blaze with light, and the night would be as bright as the noonday.[36] How very far indeed this is from being the case, may be gathered from an estimate which has been made of the general amount of light which we receive from the stars. According to this estimate the sky is considered as more or less dark, the combined illumination sent to us by all the stars being only about the one-hundreth part of what we get from the full moon.[37]

Secondly, it has been suggested that although light may not suffer any extinction or diminution from the ether itself, still a great deal of illumination may be prevented from reaching us through myriads of extinguished suns, or dark meteoric matter lying about in space. The idea of such extinguished suns, dark stars in fact, seems however to be merely founded upon the sole instance of the invisible companion of Algol; but, as we have seen, there is no proof whatever that it is a dark body. Again, some astronomers have thought that the dark holes in the Milky Way, "Coal Sacks," as they are called, are due to masses of cool, or partially cooled matter, which cuts off the light of the stars beyond. The most remarkable of these holes is one in the neighbourhood of the Southern Cross, known as the "Coal Sack in Crux." But Mr. Gore thinks that the cause of the holes is to be sought for rather in what Sir William Herschel termed "clustering power," i.e. a tendency on the part of stars to accumulate in certain places, thus leaving others vacant; and the fact that globular and other clusters are to be found very near to such holes certainly seems corroborative of this theory. In summing up the whole question, Professor Newcomb maintains that there does not appear any evidence of the light from the Milky Way stars, which are apparently the furthest bodies we see, being intercepted by dark bodies or dark matter. As far as our telescopes can penetrate, he holds that we see the stars just as they are.

Also, if there did exist an infinite number of stars, one would expect to find evidence in some direction of an overpoweringly great force,—the centre of gravity of all these bodies.

It is noticed, too, that although the stars increase in number with decrease in magnitude, so that as we descend in the scale we find three times as many stars in each magnitude as in the one immediately above it, yet this progression does not go on after a while. There is, in fact, a rapid falling off in numbers below the twelfth magnitude; which looks as if, at a certain distance from us, the stellar universe were beginning to thin out.

Again, it is estimated, by Mr. Gore and others, that only about 100 millions of stars are to be seen in the whole of the sky with the best optical aids. This shows well the limited extent of the stellar system, for the number is not really great. For instance, there are from fifteen to sixteen times as many persons alive upon the earth at this moment!