﻿672 Electron Theory of Optical Properties of Metals. 

 is i<x'E 2 . We thus conclude that 



~ v dv 



, = 2 ,/ 2 N*»kf» e~ 

 W V 3tt mu m \ 



•Jo 1 -f 



pV#' 



In the above discussion and also in a previous papergl 

 find, however, that the more consistent value for a is 



s= 2\/— ^ eHm C" ve~ v dv 

 " v 3-7T mu m \ pHJi 

 Jo 1 + : 



Wilson obtains by both of his methods formube which 



3 

 differ from the first of these by a factor ^, but his deductions 



are I believe both incomplete. 



There is unfortunately a mistake in my previous work 

 which considerably affects the final formula. The result of 

 the integration at the top of page 182 of the paper mentioned 

 should have its denominator squared. On making this cor- 

 rection a formula for the conductivity is obtained which is 

 perfectly consistent with that given above, so that there is 

 no real discrepancy*. 



11. Conclusion. — It thus appears that a detailed analysis 

 of the motion of the electrons in the metal along lines 

 suggested by Thomson and Lorentz enables us to formulate 

 a complete theory for the action of the most rapidly altern- 

 ating fields in the metal. Moreover, this theory is perfectly 

 consistent with the special deductions given by Lorentz in 

 the particular case of steady fields, and in this respect shows a 

 distinct advantage over the form of theory proposed by 

 H. A. Wilson. 



A discussion of the actual bearing of the present form of 

 theory on the fundamental question as to the number of free 

 electrons taking part in conduction will be reserved for a 

 future communication. 



The University, Sheffield, 

 Nov. 14, 1914. 



* This mistake was kindly pointed out to me by Dr. Bohr. I must 

 also add that through the kindness of Dr. Bohr I have, since the above 

 was written, had the pleasure of reading his Dissertation on the present 

 subject, published in 1911. Reference will be made to this work in 

 future papers. 



