MoNCK — On Star-Distribution. 501 



their position, not to their distance, but to their great brilliancy 

 at the unit of distance, but they will also contain stars whose dis- 

 tance is less than the average, but whose want of absolute brilliancy 

 has prevented them from figuring in a higher class. How far we 

 should have to go before this kind of compensation would become 

 perfect it is not easy to determine, but at all events we would ap- 

 proach nearer to the theoretic value at every stage — the average 

 increase of distance being below the theoretic value during the 

 earlier stages of the process. This theoretic value is easily com- 

 puted if we assume that no light is absorbed in passing from the 

 stars to us. The average light of the stars of any magnitude 

 being taken as -| of that of the stars of the preceding magnitude, 

 the average distance will be found by multiplying the average 

 distance of the stars of the preceding magnitude by-i-v/lO or 1'58 

 nearly. This value of f, I may add, is closely approached by the 

 recent computations of M. Littrow and Mr. Pogson, as well as 

 being very nearly the mean of Dr. Ball's authorities. This theo- 

 retic value of 1'58, however, is liable to be reduced at the earlier 

 stages of the process by the cause which I have mentioned, while 

 if there is in a space a widely-diffused medium which absorbs light 

 it would also be affected by the absorption, especially at the later 

 stages. To what extent this would affect the theoretic value 

 would depend on the law of absorption. 



It occurred to me since my former Paper that the effects of 

 this supposed absorptive medium might be revealed in a somewhat 

 different way. On the hypothesis of uniformity the entire number 

 of stars up to any given magnitude would be included in a sphere 

 having the earth as its centre. The total light of all these stars 

 would be proportional to the radius of this sphere, while the total 

 number of the stars in question would be proportional of the cube 

 of the radius (assuming that no light was lost in the passage) . We 

 would thus have two modes of calculating the proportion which 

 the radius of any of these spheres bore to the radius of any pre- 

 ceding sphere, viz. : — 1st., by computing the total light in each 

 case (which could be easily done when we know the number of 

 stars of each magnitude and their proportionate brilliancy) ; and 

 2nd, by finding the total number of stars comprised in each sphere, 

 and comparing the values of the cube roots of these numbers. If 

 there was no absorption, and the averages derived from the hypo- 



