138 JAMES CLERK MAXWKU, 



referred to, extended it (under certain limitations) to 

 the parts of which a molecule is composed. According 

 to Maxwell the average kinetic energy of the centre 

 of gravity of each molecule tends to become the same. 

 According to lioltzmanii the average kinetic energy 

 of each part of the molecule tends to become tho 

 same, 



Maxwell, in the last paper ho wrote on the subject 

 ("On Boltzmann's Theorem on the Average Distri- 

 bution of Energy in a System of Material Points/ 1 

 Ca % nb. Phil. Trans., XII.), took up this proble:u. 

 Watson had given a proof of it in ls7G di tiering from 

 ]> iltzinann's, but still limited by the stipulation that 

 the time, during which a particle is encountering other 

 particles, is very small compared with the time during 

 which there is no sensible action between it and other 

 particles, and also that tho time during which a 

 particle is simultaneously within the distance of more 

 than one other particle may bo neglected. 



Maxwell claims that his proof is free from any 

 such limitation. Tho material points may act on 

 each other at all distances, and according to any law 

 which is consistent with the conservation of energy ; 

 they may also be acted on by forces external to tho 

 system, provided these are consistent with that law. 



The only assumption which is necessary for tho 

 direct proof is that the system, if left to itself in its 

 actual state of motion, will sooner or later pass 

 through every pluuse which is consistent with tho 

 conservation of energy. 



In this paper Maxwell finds in a very general 

 manner an expression for the number of molecules 



