331 
of Edinburgh, Session 1873 - 74 . 
readily calculated. Let a hermetically sealed glass jar of air con- 
tain 2,000,000,000,000 molecules of oxygen, and 8,000,000,000,000 
molecules of nitrogen. If examined any time in the infinitely 
distant future, what is the number of chances against one that 
all the molecules of oxygen and none of nitrogen shall be found 
in one stated part of the vessel equal in volume to |th of the 
whole? The number expressing the answer in the Arabic notation 
has about 2,173,220,000,000 of places of whole numbers. On the 
other hand, the chance against their being exactly -^ths of the 
whole number of particles of nitrogen, and at the same time 
exactly T %ths of the whole number of particles of oxygen in the 
first specified part of the vessel, is only 4021 x 10 9 to 1. 
APPENDIX. 
Calculation of 'probability respecting Diffusion of Oases. 
For simplicity, I suppose the sphere of action of each molecule 
to be infinitely small in comparison with its average distance from 
its nearest neighbour ; thus, the sum of the volumes of the spheres 
of action of all the molecules will be infinitely small in proportion 
to the whole volume of the containing vessel. For brevity, space 
external to the sphere of action of every molecule will be called 
free space : and a molecule will be said to be in free space at 
any time when its sphere of action is wholly in free space ; 
that is to say, when its sphere of action does not overlap the 
sphere of action of any other molecule. Let A, B, denote any 
two particular portions of the whole containing vessel, and let 
a , b , be the volumes of those portions. The chance that at 
any instant one individual molecule of whichever gas shall be 
in A is — qLj , however many or few other molecules there may be 
in A at the same time; because its chances of being in any speci- 
fied portions of free space are proportional to their volumes ; and, 
according to our supposition, even if all the other molecules were 
in A, the volume of free space in it would not be sensibly diminished 
by their presence. The chance that of n molecules in the whole 
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VOL. VIII. 
