﻿174 Mr. Gr. H. Livens on the 



the theory have thereby received verification and justifi- 

 cation from several entirely independent investigations, 

 although it must be admitted that some of the results of 

 these investigations have not always been so happily coinci- 

 dent as one might desire. This remark applies particularly 

 to the formula for the electrical conductivity which expresses 

 it in terms of the electron constants of the metal. After 

 Drude's initial attempt to deduce a formula for the conduc- 

 tivity, the problem appeared to be finally settled, at least as 

 far as its application in the theory of steady currents, by 

 the very general and elaborate investigations by Lorentz *. 

 The formulae obtained by Lorentz, however, appear to require 

 modification and amplification in order to make them 

 applicable for very rapidly alternating fields, particularly 

 those associated with radiation. The application of the 

 theory of electrons to these extensions, initiated by Thom- 

 son f, was fully carried out and in great detail by Jeans % 

 and H. A. Wilson §, their method of procedure being, how- 

 ever, essentially different from that followed by Lorentz. 

 It appears, however, that the formula obtained for the con- 

 ductivity by Wilson, who alone carries the calculation right 

 through on the statistical basis, does not agree with Lorentz's 

 formula in the limiting case, being in fact half as big 



It is maintained by Nicholson || that as far as the optical 

 properties of metals are concerned Wilson's formula is more 

 satisfactory than any other yet proposed. He also considers 

 that Wilson's treatment is the most satisfactory yet pub- 

 lished and that from the theoretical standpoint it is 

 complete ! IF 



The object of the present communication is to prove that 

 a rigorous treatment of the problem along the lines laid 

 down by Wilson and Thomson leads to a formula differing 

 trom Wilson's by a factor 2/3, which is just what is required 

 to make it consistent with Lorentz's result in the limiting 

 case. There is a discrepancy in Wilson's treatment of the 

 problem which has considerable bearing on the final result 

 obtained. 



The discussion of the actual bearing of the results of the 

 present discussion on the optical side of the question will 

 be reserved for a future communication, as it is merely 

 desired to show that the principles underlying the discussions 



* Vide ' The Tkeorv of Electrons.' t Phil. Mag. Aug. 1907. 



X Phil. Mag. June and Julv, 1909. § Phil. Mag. Nov. 1910. 



|| Phil. Mag. Aug. 1911. 



«j] Nicholson informs me that he has subsequently modified his views 

 as to the exactness of the formula? under dispute. 



