Conditions necessary for Equipartition of Energy. 585 



The only consideration which is opposed to this view is the 

 existence of polonium. The radiations of this body resemble 

 closely the non-separable radioactivity of uranium, both in 

 penetrating power and the absence of deviable rays. But all 

 attempts (Soddy, he. cit.) have so far failed to separate 

 polonium from uranium, and until this is done its existence 

 does not of itself affect the present question. 



Tt seems as if a more satisfactory explanation of the residual 

 activities common to both uranium and thorium, and of the 

 connexion between the emanating power and radioactivity of 

 ThX, is obtained on the modified view. But further work, 

 both on this latter point and on the nature of polonium, must 

 be awaited before the connexion between radioactivity and 

 chemical change can be considered exactly determined. 



Macdonald Physics Building, 



Id Chemistry and Alining- Bui " 



McGill University, Montreal. 



LXT. On the Conditions necessary for Equipartition of Energy . 

 By J. H. Jeaxs, B.A.. Isaac Newton Student and Fellow 

 of Trinity College. Cambridge *. 



Introduction. 



§ 1. rjlHE object of the present paper is, firstly, to give a 

 Jl proof of Boltzmamr's Theorem on the Equiparti- 

 tion of Energy from a somewhat new point of view ; and, 

 secondly, to examine what are the precise conditions under 

 which equipartition will take place, and whether these con- 

 ditions are such as will occur in an actual gas. 



At the outset it must be explained that the equations 

 leading to the law of distribution admit of a simple hydro- 

 dynamical interpretation in generalized space of n-dimensions. 

 I have made use of the hydrodynamical analogy for two 

 reasons. In the first place it is easier to think in terms of 

 generalized space than in terms of multiple integrals ; and in 

 the second place the terminology and results of hydro- 

 dynamics being ready to hand, a great deal of obscurity and 

 repetition may be saved by starting at once from the hydro- 

 dynamical standpoint. So long as we only use hydrodyna- 

 mical results and conceptions which have a mathematical (as 

 opposed to a physical) basis, there will be no danger of a 

 faulty ' ; argument by analogy." 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 4. No. 23. Tor. 1902. 2 Q 



