296 Sir William Thomson on the Kinetic 



Take, however, another case, in which the probability may 

 be readily calculated. Let an hermetically sealed glass jar 

 of air contain 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 there being exactly -^ths of the whole number of 

 particles of nitrogen, and at the same time exactly -^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 Gases. 



For simplicity, I suppose the sphere of action of each mole- 

 cule 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 ail 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 wdiolly 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 



7, however many or few other molecules there may be in 



A at the same time ; because its chances of being in any 

 specified 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 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 + b) \o7+b) ' ° r (a + by 



