328 ANNUAL OF SCIENTIFIC DISCOVERY. 



no difficulty in proving that, unless the light were absorbed in its 

 passage through space, the whole celestial vault would be one blaze 

 of light, brilliant as the noon-day sun, on which the moon and planets 

 would appear as dark patches. It was therefore concluded by Che- 

 seaux and Olbers, that the celestial spaces probably contained some 

 ether, which possessed the power of absorbing light. This theory 

 was subjected to a test by Struve, in his work entitled Etudes de I'As- 

 tronomie Stellaire, in the following manner. If the stars are equally 

 distributed through space, and are of equal absolute brilliancy, the 

 number of stars of each magnitude would be at least four times as 

 great as that of the next larger magnitude, supposing that no light 

 were lost. An extinction of light would lessen the proportionate 

 number of small stars. Now this is precisely what is found to be the 

 case : whence it is concluded, either that the stars are more numerous 

 in the neighborhood of our system, or that light is absorbed. Con- 

 sidering the former horn of the dilemma very improbable, Struve 

 adopts the latter, though it cannot yet be considered as an established 

 theory. One object of Struve's investigation was to show that the 

 idea of an infinite universe was not incompatible with the appear- 

 ance of the heavens. But this is not the only difficulty to which the 

 hypothesis of such an infinite universe as we have supposed would 

 lead. Unless heat as well as light is absorbed we should experience 

 a temperature compared with which that of a reverberatory furnace 

 would be as the frozen pole. The principal difficulty, however, would 

 be that resulting from the attraction of the infinite mass of stars. 

 The attractions of the different parts of such a mass could not coun- 

 terbalance themselves anywhere, and some systems would be exposed 

 to an infinite attraction. True, it is difficult exactly to define what 

 stars would come into this category. At first sight it might appear 

 that, since each star is equally surrounded by an infinite series of 

 other stars, each ought to be equally attracted in all directions. This 

 conclusion would be correct, if the combined attractions of the more 

 distant stars gradually diminished, so as to vanish at infinity. But, 

 although the attractions of the separate bodies do diminish as we 

 increase the distance, yet the entire number which will be con- 

 tained in a spherical surface, at any given distance, will increase in 

 the same proportion that the attraction will diminish, so that the 

 combined attraction will not vary at all. Now, if we examine the 

 reasoning on which the conclusion cited above is based, we shall find 

 that it tacitly assumes that for every attracting mass of stars on one 

 side of any star, taken at pleasure, there is an equal attracting mass 

 on the other side to counterbalance it. "We thus profess to compare 

 two infinite magnitudes, and pronounce them absolutely equal. But 

 two magnitudes can be pronounced absolutely equal only when cer- 

 tain relations exist between their boundaries. Now, by hypothesis, 

 our magnitudes are infinite, therefore without bounds, and therefore 

 without means of comparison, so that the whole reasoning is illusory. 

 Moreover, it is mathematically demonstrable that, if the stars in any 

 one position were in an equilibrium as to the opposing forces, this 

 could be the case in no other position. 



It must be understood that we have thus far spoken of the infinite 

 system of stars as scattered indiscriminately, but with a certain ap 



