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



where I have written t — t' = e and e in the upper limit is 

 to be determined as already explained. I have also assumed 

 that on the average 



« m —j- = and 



go:-* 



(63) reduces to 



>&)'o$V' *-)j**-C(*-^ S^ (cK, n e))dedV, 



pe 



A 2C 1 



° 2n ° ... (64) 



(64) can be put in another form when the wave-length 

 2ttk„i is very small compared with the dimensions of the 

 enclosure, as may always be ensured by making the enclosure 

 large enough. 



E\dX is the total energy per unit volume of the radiation 

 of wave-length in the interval d\ and X for the m'th normal 

 function is to be 2ir/e~\ Then we shall have 



V^=V^ 2 i^y (65) 



This expresses the fact that in the interval dX there are 

 VSirX~ 4 dX normal vibrations each having a total energy 



equal to ^(—nr) which is twice the kinetic energy. (S 



Rayleigh on u Complete Radiation," Phil. Mag. xlix. p. 540.) 

 The result may be compared with Rayleigh's formula for 

 the radiation of great wave-length in accordance with which 



E x dX = S7rU6\- i dX ¥ ". 



Since JR0 is the kinetic energy of an atom at the 

 temperature 6 it follows that the total energy of radiation in 

 the volume V is 



V167r\- 4 d\ 



times the kinetic energy of an atom. Allowing equal 

 kinetic and potential energies to each " sethereal " degree 

 of freedom there must be the number 



YSirX-^dX 

 in the interval dX. 



* The numerical factor 8n- is left undetermined in Rayleigh's paper. 



