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LXIII.— THE DISTEIBUTION OF THE STAES IN SPACE, 

 By W. H. S. MONCK. 



[Eead, May 18, 1885.] 



That the fixed stars are not uniformly distributed in space is a 

 fact too obvious to insist upon ; but, nevertheless, I believe some 

 important consequences may be derived from tracing the re- 

 sults of an uniform distribution, and then comparing these with 

 the results of observation, and pointing out where the most re- 

 markable deviations take place. 



Supposing the stars to be all of equal absolute brightness, and 

 to be situated at equal distances from each other throughout all 

 space, it will appear that if we describe a sphere with the earth as 

 centre, the light of the stars which intersect or touch this sphere 

 will be a constant quantity ; for the number of stars which inter- 

 sect or touch the sphere will vary directly as the square of the 

 radius, while the intensity of the light of each star will vary 

 inversely as the square of the radius. This result will not be 

 affected by giving to the surface of each sphere a small but uni- 

 form thickness ; and by adding together a number of such surfaces 

 it becomes evident that the total light of the stars comprised 

 within any sphere will vary directly as the radius of the sphere — 

 this radius measuring the number of surfaces of which the sphere 

 may be considered to be made up. But the number of stars com- 

 prised within each sphere will evidently vary as the cube of the 

 radius. If, taking any sphere as unit, we describe other spheres 

 with twice, three times, four times, &c., its radius, the stars com- 

 prised within these spheres will give twice, three times, four times, 

 &c., the light of the stars comprised within the inner sphere ; 

 whence it follows that the stars comprised in the space included 

 between any two adjacent spheres will give the same amount of 

 light as that of the stars in the inner sphere. Since the total 

 number of stars in each sphere is proportional to the cube of its 

 radius, the number of stars in these interspheral spaces is easily 

 calculated. Representing the number of stars in the inner sphere 



