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



Hence 



R ™ = # I K 3 \f&n ~ - 2 ~^r) I (j> m (t-e) Cos c/c m €de . (71) 



Reasoning similar to that which gives the reduction 

 from (69) to (70) shows that the average value of R m at 

 time t is 



R m = c 2 <£ m l (j> m (t — e) Cos cK m € de . . . (72) 

 A result independent of k. The average total emission is 



° 2 n/0™ \ 4>m(t — e) COS GKm€ de dV 2ll • . (73) 

 2n 



And the equilibrium of radiation involve^ that the expression 



(73) be equal to A m in (66). Hence 



Ex^if, *x) j* &(«.-«) Si" (^)^V 2 „ 



2w 



= _ ^jJ7*A j* *x («-■«) Cos ^ e rfe ,/V 2 „ . . (74, 



2n 



Writing as before </>\ for <f> m and X for 27T*" 1 . If it is 

 assumed that the distribution function / depends merely 

 upon the energy H, then 



\J ? r- dH r =\ \ dp r d</ r dgv dp r I 



— iL r y H ( C H^ tyr , d<j>\ dq r \ 

 dUr^i \dp r dt d(j r dt J 



And on integration by parts since the average value of 



ff^-^H 2 ^)^ -£*j; w-o cos(^ 6 ), £ 



(74) becomes 



2n 



= 5(V/^xf^A(?-6)Cos( 2 ^e)rf6, . . (75) 



