Absorption of Energy by Electrons. 79 



Now 



And 



"=• rf ,„ iN d 2 (b d?d> d 2 d> , /OG . 



2 M MT - (V r <£) = r-^" + lv + T/ b - v ( 38 )- 

 K =i d/c„ apa# </^ay drdz 



Thus the expression (30) reduces to its first term only 

 and the absorption between the time t h and t a is 



( u _J_ j/Q) n=6 ( l r rt a -\ 



iota 



where . f ( , rfr 1>(l , 



This cannot be reduced further without assuming a certain 

 average distribution of the electrons. I take now for the 

 six constants k the coordinates and momenta in an un- 

 disturbed orbit. Since the radiation causes only an infini- 

 tesimal deviation, the distribution is that brought about by 

 the internal forces. Choosing the k's thus /\ = 1, and T shall 

 suppose that the number tZN in the sextuple element is 



rfN =f(H^) dici d/c 2 dic z dic± dx 5 dtc G . 



Then the absorption between t a and t h is for all the electrons 



- V, * . M^^dtj-dS + Conj. (41) 

 Through the undisturbed orbit the total energy is constant, 



H=H h . 



And as in (37) and (38) 



R =l d&n 



71 = 6 fJTJ 



v 9 n= 2 M,^p. 



r n=l "*» 



If we integrate (41) by parts, remembering the value of 



