334 
Proceedings of the Royal Society 
Hence for the case 
i — n 
a 
V 
which, according to the preceding formulas, gives T, its greatest 
value, we have 
T.=— 1 . ; 
sJZirnef 
where 
e 
a 
a + b 
and / = 
b 
a -j- b 
Thus, for example, let n = 2 x 10 12 ; 
e= '2, / = -8, 
we have 
T = 1 _ 1 
1 800000 Jtt 1418000 * 
This expresses the chance of there being 4 x 10 11 molecules of 
oxygen in A, and 16 x 10 11 in B. Just half this fraction expresses 
the probability that the molecules of nitrogen are distributed in 
exactly the same proportion between A and B, because the number 
of molecules of nitrogen is four times greater than of oxygen. 
If n denote the molecules of one gas, and n that of the mole- 
cules of another, the probability that each shall he distributed 
between A and B in the exact proportion of the volume, is 
_\_1 
2 rref Jnn 
The value for the supposed case of oxygen and nitrogen is 
1 _ 1 
27rx*16x -4xl0 12 4021 X l0® ’ 
which is the result stated at the conclusion of the text above. 
