Motion of Electrons in Solids. 791 



and equating this to expression (41) we obtain 



which is exactly the value obtained before (equation (35)). 



20. We notice that ~E P depends on the structure of the 

 medium only through the factor 1/V 3 . This is as it should 

 be, by equation (26), to accord with the experimental fact 

 that the radiation in a cavity is independent of the nature 

 of the matter. From equations (25), (26), and (41), it 

 follows that the radiation in the cavity must be given by 



P TT^ 3 ' W 



where V x is the velocity in the cavity. 



If X is the wave-length of radiation of frequency p we 

 have p\=2rrY in metal, and = 27rV! in the cavity. The 



radiation i E p dp in the metal, Ep being given by equation (41) , 



accordingly transforms into 



J8irRT\- 4 d\, (43) 



when expressed in terms of A,, and the energy (42) in air 

 transforms into exactly the same expression. Moreover, 

 expression (43) expresses the partition of energy demanded 

 by the law of equipartition *, both for the metal and the 

 cavity. 



21. When dealing with waves of shorter wave-length the 

 principal modification which has to be made originates in 

 the need for changing equation (38). Other modifications 

 are needed which alter the radiation by an appreciable fraction 

 of its whole amount, but it is easily seen that this particular 

 modification changes the order of magnitude of the radiationf. 



For, by § 5, when p is very great, we must replace 



equation (38), namely 



• —et 



i = i e , 

 by an equation of the form (cf. equation (5)) 



i=i <l>(t), 

 in 



which |£=0 when* = 0. 



dt 



* Phil. Mag. xvii. p. 231. 



t These remarks apply only to natural radiation, and not to the radiation 

 inside an ideal perfectly-reflecting enclosure. For this latter radiation it 

 will he proved, in the second part of this paper, that equations (38) and 

 (43) are true throughout the whole spectrum. 



3H2 



