Electrons concerned in Metallic Conduction. 107 



hardly probable that an}' approach to the exactness apparently 

 expected by Nicholson can be obtained from any theory of 

 the present type ; and the more complete examination of the 

 results of a theory which takes full account of all actions 

 which are certainly known to be in operation only tends to 

 substantiate this view. It is, therefore, the opinion of the 

 present writer that precision in this direction cannot possibly 

 be obtained with the data at present at our disposal, and we 

 must therefore, at present at least, be content with the 

 roughest calculations on this basis as representing the 

 probable order of magnitude of the quantities. It is not 

 suggested that proper and more exact estimates can never be 

 obtained, but it is insisted that far more knowledge is re- 

 quired concerning the details of the behaviour of the substance 

 in these respects before such exactness can be expected. 



It appears, however, at the present stage sufficiently 

 interesting to examine how the various factors which enter 

 in a full expression of the theory are effective in modifying 

 the calculations usually made on the present basis. This is 

 all that is attempted in the present paper. 



The general formula obtained in the previous paper, from 

 which all the circumstances of optical dispersion and absorption 

 can be obtained, was written in the form 



(fi — itc)-= . . 1 -+(1+- -I, 



where /x is the index of refraction, k the extinction or 

 absorption coefficient, p the frequency of the light used, and 

 C is a function of p and the usual electron constants of the 

 metal which is given by 



If. 



wherein e denotes the charge of an electron, m its mass, N 

 the required total number of free electrons per unit volume 

 of the metal, and <j is a constant connected with the mean 

 square of the velocities of the electrons (v m 2 ) by the relation 



2u* 



and l m is a constant which may bo taken to be the length of 

 the mean free path of the electrons in their undisturbed 

 motion. 



