﻿of Radiation in any Material System. 529 



where we assign to each configuration at time t the probability 

 fdV 2 n- Neglect as before in the calculation of (62) the 

 differences $p r $q r &c. between the actual values of p r q r , 

 and those which belong to the undisturbed motion. Then 



• dV 2n =dq x dq 2 . . . dq n , dp x dp ... dp 2n 

 = dci dc 2 ... dc 2n . 

 And (62) can now be transformed by partial integration 

 with respect to the c's, 



2 n 



dt JJ r = i \dq r dp r dp r dq r J J 



2« 



Using (57) and (58), or 



A -=%ff^WfW-^'^2n. (63) 



2n 



And the lower limit in the integration for t need only be 

 chosen so as to include all elements in the integral which 

 are c >ordinated with (/', (f> m ) the Poisson-bracket expression. 

 a m is periodic in the time 27r(fc m c)~ l . Hence for a large 

 number of periods write 



/da m \ 



U m = (to) COS CK m t -j Sin CK m t ', 



where (a m ) and \~-jf) are the values of a m and — j- at 

 time£ = 0. V ^ /o m 



We require the average value of 



da m C b , , 



—TT 1 a>m<pm at 5 



it is — ( sr ) \ 4> m ^ os CKmt Sin CK nt £' dt' 



cfc m \ at /oj 



- c%(«m) 2 </>»> Sin c/c m £ Cos CK m t' 



1 /doL m \ 2 C* a- / / 7 / 



= - s^varJJ *- s,n ( c "»*- e *™ e ) * > 



P/ii/. 1%. S. 6. Vol. 23. No. 136. A/m7 1912. 2 N 



