CHAPTERS ON THE STARS. 423 



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 accumu- 

 lations 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 num- 

 ber 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 

 mu2h again as of the eighth, and so on as far as accurate observations 

 and count have been made. 



