332 
Proceedings of the Royal Society 
space there shall be i stated individuals in A, and that the other 
n — i molecules shall be at the same time in B, is 
/ a V / b V“ i a i b n ~' i 
\a + b) \a + b) ’ ° (a + b) n ' 
Hence the probability of the number of molecules in A being 
exactly i, and in B exactly n-i, irrespectively of individuals, is a 
fraction having for denominator (a + by, and for numerator the term 
involving a 1 b n ~ { in the expansion of this binomial ; that is to say, 
it is — 
n(ii- 1) . . . . {n-i + 1) / a V / b \ n_i 
1.2 .... i -f- b) \<x -f - b) 
If we call this , we have 
T 
i + l 
71 — 'Id m 
i+l b ■ 
Hence is the greatest term if i is the smallest integer, which 
makes 
n-i b 
i + 1 < a ’ 
this is to say, if i is the smallest integer which exceeds 
a b 
n . 
a+b a+b 
Hence if a and b are commensurable, the greatest term is that for 
which 
n 
a 
a + b 
To apply these results to the cases considered in the preceding 
article, put in the first place 
n = 2 x 10 12 , 
this being the number of particles of oxygen ; and let i — n. 
Thus, for the probability that all the particles of oxygen shall be 
in A, we find 
/ a \8xl0» 
+ b, 
