the results from the two classes of objects can be brought to converge harmoniously toward the same conclusion.
We have collected abundant evidence that, separate from the accumulations of stars in the Milky Way, perhaps extending beyond them, there is a vast collection of scattered stars, spread out in the direction of the galactic plane, as already described, which fill the celestial spaces in every direction. We have shown that when, from any one area of the sky, we abstract the stars contained in clusters, this great mass is not seriously diminished. We have also collected abundant evidence that the distances of this great mass are very unequal; in other words, there is no great accumulation, in a superficial layer, at some one distance. The question which now arises is whether the darker areas which we see in the Milky Way are vacancies in this mass. Although some of the counts seem to show that they are, yet a general comparison leads to the contrary conclusion. In the darkest areas of the Milky Way, when of great extent, the stars are as numerous as on each side of the galactic zone. Our general conclusion is this:
If we should remove from the sky all the local aggregations of stars, and also the entire collection which forms the Milky Way, we should have left a scattered collection, constantly increasing in density toward the galactic belt.
THE INCREASING NUMBER OF STARS WITH DIMINISHING BRIGHTNESS.
We mentioned in an earlier chapter that, when we compare the number of stars of each successive order of magnitude with the number of the order next lower, we find it to be, in a general way, between three and four times as great. The ratio in question is so important that a special name must be devised for it. For want of a better term, we shall call it the star ratio. It may easily be shown that there must be some limit of magnitude at which the ratio falls off. For, a remarkable conclusion from the observed ratio for the stars of the lower order of magnitude is, that the totality of light received from each successive order goes on increasing. Photometric measures show, as we have seen, that a star of magnitude m gives very nearly 2.5 times as much light as one of magnitude m+1. The number of stars of magnitude m+1 being, approximately, from 3 to 3.75 times as great as those of magnitude m, it follows that the total amount of light which they give us is some 40 or 50 per cent, greater than that received from magnitude m. Using only rough approximations, the amount of light will be about doubled by a change of two units of magnitude; thus the totality of stars of the sixth magnitude gives twice as much light as that of the fourth; that of the eighth twice as much light as that of the sixth; that of the tenth twice as much again as of the eighth, and so on as far as accurate observations and count have been made.
