﻿52S Mr. S. B. McLaren on Emission and Absorption 



increasing V (47) becomes the equation of motion of a simple 

 pendulum disturbed by a very small force ; and for a 

 number of oscillations which can be made as large as we please 

 by taking V large enough the oscillations of this pendulum are 

 simple harmonic, and gradually change their amplitude and 

 phase. In calculating the absorption of radiation by matter 

 we can therefore suppose a m which occurs in <I> to be simple 

 harmonic of period 27r(/e m c) -1 and find the rate of absorption 

 due to this term alone disturbing the material system. The 

 emission of radiation is due to whatever part of cf> m in (17) 

 is of the same period and it can be found by the Fourier 

 Analysis. 



Tne absorption of radiation is at the rate 



- 



dv, 



C Lit 



or taking only the term cc m ¥m in F^ 



F m dV 



da 



_ dan Cp'.l 

 ' dt J c 



clt $•> (°°) 



The absorption is due entirely to the deviation caused by 

 the radiation and in the absence of any deviation the average 

 value of the absorption would be zero. Instead, therefore, 

 of (GO) we may put 



-%%» (61) 



and calculate £<£>,„ by writing <f> m for -yfr in (50). Only the 

 term a m <p m in the series for <I> need be retained since the 



others are not correlated with -— f- in (61). Hence (61) 

 reduces to dt 



da^ndp^J^^d f( M J^_^jI^)0 ( f )mdL I 

 a ' n dt dp r d.U r dt r=l s=1 dc s \\ dp r dqJJ "'^ J 



And the first term vanishes since the average value of 

 a m -j^ is zero in a steady state. Thus putting A m for the 

 average rate of absorption of radiation of wave-length 



.... (02) 



