﻿Theory of the Optical Properties of Metals. 671 



so that we have, with Lorent?, 



or using 



we have 



,=, 8tB' 

 E * = T A' 



p l m 



3 



( J — 9„ 2» 



27T6' 



E; 



X 4 



The present analysis thus verifies completelv what was 

 surmised in a former communication, viz. that KirchhofFs 

 law, which affirms that E A is independent of the particular 

 metal under consideration, is absolutely true on the basis of 

 the present theory. The incompatibility of the previous 

 results rested in the formula adopted for the conductivity 

 which has in the present instance been considerably modified. 



It thus appears that the variation from the above law 

 obtained by Wilson in his analysis is not, as he says, due to 

 the neglect of the motion of the atoms and the mutual in- 

 fluence of the electrons, but rather to an incompleteness in 

 his analytical investigation of the statistical motions of the 

 electrons themselves. 



The reason why the present form of theory fails to give an 

 appropriate form of E A has been fully discussed in another 

 place and need not detain us any longer here. 



10. On the dissipation of energy. — Before closing this paper 

 I think it is necessary to point out an apparent discrepancy in 

 the present form of theory, which at first escaped my notice. 



According to Thomson the energy dissipated per second in 

 a unit volume of the metal is equal to the work done by the 

 electric force on the electrons during the whole of their free 

 path motions, and according to a calculation I made of this 

 work in the case when the electric force E is given by 



E = E cos^, 



I found that the energy dissipated per unit time and 

 volume is 



V 37r mu m ] 1 + /f 



diich is taken to be equal to the mean value of a'E : . which 

 * Phil. Mao-. January 1915. 



