826 B. A. Gould—Number and Distribution 
Could we assume, Ist, that, in general, the apparent bright- 
ness of a star depends upon its distance from us, all being of 
the same order of intrinsic brilliancy, and 2dly, that stars are dis- 
tributed through space with approximate uniformity, the total 
number visible, down to any given magnitude, would be pro- 
portional to the contents of the sphere within which stars of 
this magnitude are contained. Thus the degree of approxima- 
tion to the truth, which is fairly attributable to the hypothesis 
mentioned, may be inferred from the degree of accordance 
which can be obtained between two series of numbers, the one 
the same ratio for different degrees of brightness, and other 
ing from this inquiry, to regions outside of the distance of 9th 
magnitude stars. H'rdm a discussion of the numbers given by 
the Durchmusterung as far as the 8th magnitude, assorte 
according to whole units, he obtains the value 0423 as the 
b 
comprising all stars to the 8th magnitude inclusive, he obtains 
] 1. Each of these computations gives, for the 
_ average distance of a star of the 9th magnitude, about 26 times 
that of the most distant first magnitude star. 
:) 
