Thermodynamics of Radiation. 873 



law), and also for each component considered separately. 

 The product XT, or the ratio v/T, remains constant for 

 each component, which is Wien/s displacement law. Both 

 laws are summed up in Wien's general expression for the 

 distribution in full radiation, which gives for q as already 

 defined, 



q =Cv*F(v/T) = CTf(v/T), . . . . (1) 



where F and / are undetermined functions expressing the 

 distribution in full radiation. 



Extensions of the Theory. 



So far we have been considering only those theoretical 

 relations which result from the Doppler effect on components 

 of variable frequency which retain their identity in adiabatic 

 expansion. These relations have been verified indirectly, and 

 are universally admitted. The extensions which I have pro 

 posed result, from a consideration of isothermal emission at 

 constant frequency. In experimental work it is impossible 

 to isolate and trace the components of variable frequency 

 (v/T constant), or to perform an adiabatic expansion. We 

 have to deal with rays of constant frequency, separated and 

 measured under the condition of steady flow at constant 

 temperature. 



The main points which I have endeavoured to establish are 

 the following: — 



(1) Since, so far as we know, each frequency is propagated 

 without change in free space, the heat taken from the source 

 by the emission of a steady stream of a particular frequency 

 should, by the first law of thermodynamics, be equal to the 

 heat evolved on condensation of the same stream in the 

 receiver. Although it is not possible to trace all the steps of 

 an irreversible process, such as radiation from a higher to a 

 lower temperature, the change of total heat must be the same 

 as that calculated by a reversible path. The first requisite, 

 therefore, is to find the latent heat of isothermal emission of 

 a particular frequency. 



(2) It has always been tacitly assumed that the energy- 

 density of each frequency in an isothermal enclosure is 

 directly proportional to the heat measured on absorption, 

 which is equivalent to assuming the latent heat of emission 

 per unit volume proportional to the energy-stream q. I have 

 maintained on the contrary, in the paper already quoted, that 

 the latent heat of emission per unit volume for each frequency 

 should be that given by Carnot's principle, namely T(dp/dT) v , 



