CHAPTERS ON THE STARS. 309 



proportional to the square of the diameters of the spheres which bound 

 it. Hence, supposing an equal distribution of the stars, each of these 

 regions will contain a number of stars increasing as the square of the 

 radius of the region. Since the amount of light which we receive from 

 each individual star is as the inverse square of its distance, it follows 

 that the sum total of the light received from each of these spherical 

 shells will be equal. Thus, as we include sphere after sphere, we add 

 equal amount of light without limit. The result of the successive addi- 

 tion of these equal quantities, increasing without limit, would be that 

 if the system of stars extended out indefinitely the whole heavens would 

 be filled with a blaze of light as bright as the sun. 



Now, as a matter of fact, such is very far from being the case. It 

 follows that infinite space is not occupied by the stars. At best there 

 can only be collections of stars at great distances apart. 



The nearest approximation to such an appearance as that described 

 is the faint, diffused light of the Milky Way. But so large a frac- 

 tion of this illumination comes from the stars which we actually 

 see in the telescope that it is impossible to say whether any visible 

 illumination results from masses of stars too faint to be individually 

 seen. Whether the cloud-like impressions, which Barnard has found 

 in long-exposed photographs of the Milky Way, are produced by 

 countless distant stars, too faint to impress themselves even upon the 

 most sensitive photographic plate, is a question of extreme interest 

 which cannot be answered. But even if we should answer it in the 

 affirmative, the extreme faintness of light shows that the stars which 

 produce it are not scattered through infinite space; but that, although 

 they may extend much beyond the limits of the visible stars, they 

 thin out very rapidly. The evidence, therefore, seems to be against 

 the hypothesis that the stars we see form part of an infinitely extended 

 universe. 



But there are two limitations to this conclusion. It rests upon the 

 hypothesis that light is never lost in its passage to any distance, how- 

 ever great. This hypothesis is in accordance with our modern theories 

 of physics, yet it cannot be regarded as an established fact for all 

 space, even if true for the distances of the visible stars. About half a 

 century ago Struve propounded the contrary hypothesis that the 

 light of the more distant stars suffers an extinction in its passage to 

 us. But this had no other basis than the hypothesis that the stars were 

 equally thick out to the farthest limits at which we could see them. 



It might be said that he assumed the hypothesis of an infinite 

 universe, and from the fact that he did not see the evidence of infinity, 

 concluded that light was lost. The hypothesis of a limited universe 

 and no extinction of light, while not absolutely proved, must be regarded 



