50 Mr. S. B. McLaren on the 



§ 4. Emission and Absokption. 

 The rate of increase of the sethereal energy of wave-length 



2w?u.>,^ (23) 



In a steady state this vanishes on the average, the emission 

 balances the absorption. I calculate each directly, and by 

 equating the results arrive at a formula for complete 

 radiation. ^ a 



In calculating the absorption -~ is treated as a simple- 

 harmonic function of period 27r(c/e m )~ 1 . The absorption is 

 due to the disturbance produced by the presence in (16) of 



the'terms involving u m and — ~ . The rate of absorption is 

 the! average value of 



~di 



— °9m-jr, 



01 -^TS^N, 



d i?M% mdt ■ ■ ■ (24) 



The rate of emission is found by treating <f> m in (23) as a 

 given function of the time and of the initial values of # l5 

 x 2i &c. (1) may then be regarded as the equation of motion 

 of a simple pendulum slightly disturbed. I have already 

 shown that the average rate of emission is 



2 \ <j>m \ 



Jtf Jo 



c 2 \ <fm (j>m cos(cK m e)dedN, . . (25) 

 J is" Jo (*-*) 



€ is a time taken large enough to ensure that in (23) cj) m (t — e) 

 is included so long as it is correlated with (p m (t) (Phil. Mag. 

 April 1912, p. 532, equation (72)). 



To calculate (24) use (15), (5), (16), retaining in the last 



da 

 only the terms which involve a m and _J2 , since only these 



are correlated in value with -^- ' 



Then (24) becomes - 



-*^J>I.f""™' 



