﻿of Radiation in any Material System. 531 



Writing therefore in accordance with (65) 



1 (da m \ 2 A, 4 2 7t . ,-„ 



2?U 7 = m^ and x= i~ m (64) ' 



Am= " l£" 2 ^if (/; *0^x(*-e) Sin(^e)dedV*, . (66) 



2« 



writing <£\ for <£ m . 



§7. The Emission of Radiation and Complete Radiation. 



The rate of emission R m to the m'th sethereal degree of 

 freedom can be found by (47). Integration gives 



detm 

 dt 



or 



= *jp+ *.*)§ (***- ?3?) Sin <s**-«*W! 



And 



r =__^ fjy> _i^ArY^ m _i^Mcos(^6)^, 



.... (69) 

 with the same significance for e as before t f — t — e. 



p^k Cos (c«»6)rf6= [^ Cos c«„e] 6 + eicS^Bm CK m e de 



= I" ^ Cos cic m e + CK m $ m Sin c Km e~] " - •J**- 1 ( * <£» Cos c«»e efe. 



,° . . . . (70) 



Now in (70) the terms at the limits and e contribute 

 nothing to the emission R m . The term at the upper limit e 

 can be omitted because at the time t — e there is no longer any 

 correlation with the first factor on the right-hand side of (69) 

 which refers to the time t. At the lower limit e = we 



have on the right of (70) only the term — -^ or — ^ This 



a€ tit 



contributes nothing to R, M because the average values of 

 ^f'andf^ are both zero. 



2N2 



