Theory of Radiation. 51 



Now dH m =™ , da m d / m =*> \ 



since (19) is the expression for the total energy. In the 



value o£ -j- given by (27) only the terms involving ct ni need 



be retained to be substituted in (26), and the rate of absorption 

 reduces to 



i du,n C m C r T l d ' \ d<x ™ j* jk 



+ ^ L **£ '.£ J i (px "' "' )am dt ™' (28) 



The second term of (28) disappears since 



C* d * 



I -j. {tym *m) dt dN= [yjr m cc m ~] dN, 



and the average value of — jr X a »i is zero. 



Substitute in other terms the values of a in and —£■ given 

 by (2). (28) reduces to dt 



111 —r^ I I <$>m\ 4> m cos CfCm€ de <^N, 



V dt J Jx T J (t-e) 



+ ft) 2 ] * w i HI £ 9 <FX!r.«\_™e Km *deiS, 



-r(^n)-M-^j I W J ^-^(pXr,m)smcK m ededN. 



.... (29) 



The formula for complete radiation results by equating (29) 

 to (25). The second and third terms in (29) vanish in the 

 form of electromagnetic theory due to Lorentz. Here (16) 

 become 



dq r dq>- 



dt \du r ) 

 E 2 



dt dpr 

 r = l, 2 ...a-. 



