﻿of Radiation in any Material System. 5»59 



in particular we may if we please take 



r=l 



where V involves the q's only. 



d# _ r ^ dHdp r dHdqr _ 

 ~dt r =\dp r dt dq r dt 

 So that H is a constant. Let 



4>r=firl), f(r2) ... f(rs) ■■<f{rn)(s = h % ••• ™X ■ ( 96 ) 



where f {rs) =f (srh (97) 



and / (rs) is a function of p r , q r , and p 8 , q s only. 



The distribution of systems in which the number in the 

 2n'ple volume element dY 2n is pdY 2n will De invariant of 



|(^V 2M )=0, 



which gives the ordinary equation of continuity 



or 



T«f— (■£.)*-£- -— '(£\— V=o. 



r=i \dq r \4>r/ dp r dp r \<l)r/ dq r J 

 This equation can be satisfied by taking 



(99) 



so that p is the product of the distinct functions /(, jS ) each 

 taken once. With this value of p it follows from (96) and 



(97) that -£-- does not involve p r or q r and each term in 



(98) vanishes identically. 



The equipartition of the kinetic energy would require 



2?i 2n 



And this need not be so. 



By taking only two coordinates p Y and p 2 , writing 



fn = ' +a K ,/i2=l, /.=•+**"• 

 it may easily be proved that the ratio in which the energy 



