THERMODYNAMICS OF RADIATION 
43 
Hence by (33-71) and (33-72) 
vl(v, T) = F {v/T). 
By (33-74) v oc T~ 3 , so that absorbing the constant of proportion in F 
1 (y, T) = T S F ( v/T ). 
Finally, if /j ( x ) = F ( x)/x s 
I (v, T) = V»/, (v/T) 
which proves the required theorem. 
To review this rather lengthy investigation we note four steps : ( 1) Proof 
that the change of constitution of equilibrium radiation with temperature 
is brought about by reflection at moving walls independently of absorption 
and emission processes ; (2) Proof that the number of quanta is unchanged ; 
(3) Formulation and integration of the partial differential equation ex 
pressing the fact that there is no correlation between s and v ; (4) Determina 
tion of one of the two functions introduced, by the condition that the 
total density of the radiation must agree with Stefan’s law.