﻿of Radiation in any Material System. 527 



If ^ bo any function whatever of the p's and ^'s 



dc s r= i \dq r dc s dp r dcsj - 7 



And on solving these equations 



d X = d X 

 ,=i dc s dq 



4c. dc 



TM'„p.= & ..... (58) 

 ,=i dc, dp r 



= f {I J (^ 7 ) g ives 



s=2n 



s=1 rs dc s \dp r ) dq r dp r ' 



and putting %— ~ (58) gives also 



«=1 ? S d(T s \dfjrj dprd(Jr * 



Then the last term in (56) disappears and 



r =idp r du r ,. =1 s=1 de s ( \ dp,. di/,.JJ ) 



.... (59) 



§6. The Absorption of Radiation. 



In order to arrive at the nature of complete radiation I 

 suppose the radiating material system enclosed in a very 

 much larger volume of space devoid of matter. The 

 boundary surface S is at a great distance. The nature of 

 complete radiation is of course unaffected but the formula 

 (47) is greatly simplified. Since F r satisfies the equation 



it appears that the average value of F m decreases inversely 



as V*. On the other hand, the average value of ^~( c a "' ) is 



the kinetic energy belonging to a single degree of freedom. 

 On the theory of equipartition this is always equal to the 

 average kinetic energy of an atom, in fact it is something 

 less than this in a ratio which depends upon the wave-length 

 27t(k iii )- 1 , but does not depend upon the volume V. Thus by 



