Absorption of Energy by Electrons, 77 



expressions for D and P require the terms conjugate to those 

 written. Ilemembering (19), (20), and (21), 



-'-A^ 1 M » ^lj, ^ ***J +C0nJ ' (32) 



Where ( 1 2 j— e^'J denotes the value at £ n . 



o 



§ 5. The Absorption of Radiation. 



The rate of absorption of energy is the electric force multi- 

 plied by the velocity. In the undisturbed motion this is 



e~Ej or <?EVp#, 



and, on the average, it is zero between t b and t a , because 

 only by the deviation produced is energy absorbed. Write 



£ = EVp#". (33) 



<£> is therefore expressed as a function of the time momenta 

 and position, the time entering explicitly through E. If 

 in the disturbed motion <£ becomes <£ + £</>, the total absorp- 

 tion between t h and t is 



o a 



e{ ta ^dt = e{ ta T>Vx<t>dt + e \ a V\7v<l>dt, . (31) 



and in (31) the values of D and P given by (31) and (32) 

 are to be used. 



It is plain that only terms which contain the product of 

 the conjugates a + i/3 and a — ?/3 will contribute to (34). 

 The first terms in (31) and (32), those which involve t . will 

 yield nothing, for the time t Q antedates t b by at least the 

 length of a free path. Even if we are considering light 

 waves whose period is long compared with the time t b — 1 , 

 our definition of free path requires that there should be 



no 



correlation between the factors M w and ( -=— ) . Foi 



\dfc n /o 



