﻿of Radiation and Line Spectra. 799 



among the different loci is therefore expressed by 



EpOT . . . 



f g ~ *T ,-, 9 , 



TP°T-..— - Ep<TT... * ' ' { L *) 



2 2 2 . , . e yjx 



ooo 



when equilibrium has been attained. 



Equations (5) and (12) give us, for the average energy 

 of a system, 



Eoffr . . . 



V 



2 2... E p ^ . . . <? 



E=^-°~ _= -. . . (13) 



222... ^- /,t 







Theory of Radiation. 



The foregoing results are very general. We shall show 

 that they include Planck's theory (one form of it at any 

 rate) us a special case. We may write the equation of 

 motion of one of Planck's oscillators, when in a steady state, 

 in the form 



The most convenient form of solution for our purpose is 

 q = Hcos(2irpt—0), ..... (14) 



where B, and 6 are the constants of integration, and there- 

 fore 



p^-27TvmUsm(27Tvt-0). . . . (15) 



The energy of such an oscillator is easily shown to be 



2<7rVmR 2 (16) 



Now we have, from (14) and (15), 



(pdq=i**v'mR i ( sin 2 (2 nri -<?)<( 



t 



p/i = 27r 2 j/mR 2 , 



t t 



and consequently 



and therefore, by (10), 



E^pJiv (17) 



