336 A Short History of Astronomy [CH. xn. 



mirror appear equally bright, then the second star is on 

 the fundamental assumption six times as far off. 



In the same way the size of the mirror necessary to make 

 a star just visible was used by Herschel as a measure of 

 the distance of the star, and it was in this sense that he 

 constantly referred to the " space-penetrating power " of his 

 telescope. On this assumption he estimated the faintest 

 stars visible to the naked eye to be about twelve times as 

 remote as one of the brightest stars, such as Arcturus, while 

 Arcturus if removed to 900 times its present distance would 

 just be visible in the 2o-foot telescope which he commonly 

 used, and the 4o-foot would penetrate about twice as far 

 into space. 



Towards the end of his life (1817) Herschel made an 

 attempt to compare statistically his two assumptions of 

 uniform distribution in space and of uniform actual bright- 

 ness, by counting the number of stars of each degree of 

 apparent brightness and comparing them with the numbers 

 that would result from uniform distribution in space if 

 apparent brightness depended only on distance. The 

 inquiry only extended as far as stars visible to the naked 

 eye and to the brighter of the telescopic stars, and indicated 

 the existence of an excess of the fainter stars of these 

 classes, so that either these stars are more closely packed 

 in space than the brighter ones, or they are in reality smaller 

 or less luminous than the others ; but no definite con- 

 clusions as to the arrangement of the stars were drawn. 



259. Intimately connected with the structure of the sidereal 

 system was the question of the distribution and nature of 

 nebulae (cf. figs. 100, 102, facing pp. 397, 400) and star 

 clusters (cf. fig. 104, facing p. 405). When Herschel began 

 his work rather more than 100 such bodies were known, 

 which had been discovered for the most part by the French 

 observers Lacaille (chapter x., 223) and Charles Messier 

 (1730-1817). Messier maybe said to have been a comet- 

 hunter by profession ; finding himself liable to mistake 

 nebulae for comets, he put on record (1781) the positions 

 of 103 of the former. Herschel's discoveries carried out 

 much more systematically and with more powerful instru- 

 mental appliances were on a far larger scale. In 1786 

 he presented to the Royal Society a catalogue of 1,000 



