4 258] The Structure of tJie Sidereal System 335 



of the stars may be admitted in certain calculations ; but when 

 we examine the Milky Way, or the closely compressed clusters 

 of stars of which my catalogues have recorded so many instances, 

 this supposed equality of scattering must be given up." 



The method of star-gauging was intended primarily to give 

 information as to the limits of the sidereal system or the 

 visible portions of it. Side by side with this method Herschel 

 constantly made use of the brightness of a star as a probable 

 test of nearness. If two stars give out actually the same 

 amount of light, then that one which is nearer to us will 

 appear the brighter ; and on the assumption that no light 

 is absorbed or stopped in its passage through space, the 

 apparent brightness of the two stars will be inversely as the 

 square of their respective distances. Hence, if we receive 

 nine times as much light from one star as from another, 

 and if it is assumed that this difference is merely due to 

 difference of distance, then the first star is three times as 

 far off as the second, and so on. 



That the stars as a whole give out the same amount of 

 light, so that the difference in their apparent brightness is 

 due to distance only, is an assumption of the same general 

 character as that of equal distribution. There must neces- 

 sarily be many exceptions, but, in default of more exact 

 knowledge, it affords a rough-and-ready method of estimating 

 with some degree of probability relative distances of stars. 



To apply this method it was necessary to have some 

 means of comparing the amount of light received from 

 different stars. This Herschel effected by using telescopes of 

 different sizes. If the same star is observed with two reflect- 

 ing telescopes of the same construction but of different 

 sizes, then the light transmitted by the telescope to the eye 

 is proportional to the area of the mirror which collects the 

 light, and hence to the square of the diameter of the mirror. 

 Hence the apparent brightness of a star as viewed through 

 a telescope is proportional on the one hand to the inverse 

 square of the distance, and on the other to the square of 

 the diameter of the mirror of the telescope ; hence the 

 distance of the star is, as it were, exactly counterbalanced by 

 the diameter of the mirror of the telescope. For example, 

 if one star viewed in a telescope with an eight-inch mirror 

 and another viewed in the great telescope with a four-foot 



