[ 493 ] 



LXVIII.— FUETHEE EEMAEKS ON STAE-DISTEIBUTION. 

 By W. H. S. MONCK. 



[Read, June 15, 1885.] 



In a Paper, read before this Society [antea, p. 470), I assumed 

 that, although the brightness of an individual star is no test of its 

 distance from us, the average distance of the stars of any given 

 magnitude is less than that of the stars of the next succeeding 

 magnitude. As this assumption did not appear to meet with uni- 

 versal acceptance, I desire, on the present occasion, to state some 

 reasons in its favour. I need hardly say that the very faintest of 

 fixed stars would appear brighter than Sirius, if it approached us 

 sufficiently, while Sirius itself might be removed to such a distance 

 as to become invisible to our most powerful telescopes. Keasons 

 more definite than this will, however, be expected from me, and 

 these I proceed to give. 



Assuming that there is no medium in space which absorbs light, 



l.s 

 the general expression for the brightness of a star will be 



d 



2' 



where / represents the illuminating power of each unit of surface, 

 and s the area of the illuminated surface. If there is an absorbing 

 medium, the expression will, of course, be somewhat different ; but 

 into this I shall not at present enter. Now, if we compare a con- 

 siderable number of instances taken at random, in which the value 



l.s 

 of -V is high, with a considerable number, likewise taken at ran- 



d 



dom, in which the same value is much lower, is it reasonable to 

 suppose that the difference depends wholly on the factors / and s, 

 and that the average value of d is either unaltered or increases 

 when the average value of the fraction diminishes ? I think not. 

 But we are able to take another step. There is probably no 

 instance in which we are able to ascertain the value of s or the ex- 

 tent of illuminated surface which the star turns towards us ; but 

 we can form a very fair estimate of the value of I, and are thus 

 enabled to conclude positively that several of the stars of the first 



