﻿Theory of the Optical Properties of Metals. 661 



practically identical with that given by Maxwell's original 

 law, which is just what we should expect, as in such circum- 

 stances the alternations or.' the field are too rapid to take 

 effective hold on the "inertia of the electrons. 



4. The expression for the current density, — We are now in 

 a position to calculate the conduction current density under 

 the assumptions we have specified above. This is done 

 exactly along the lines laid down by Lorentz, and is therefore 

 given by its components (l x , I y , l z ) parallel to the coordinate 

 axes, where 



the integrals being extended over all values of (f, 77, £) for 

 all the electrons per unit volume. 



On inserting the value of SN we find that this gives 



while I y = T z = 0. 



This gives us the general formula for the current at time t. 

 Particular cases are worth noticing. 



(i.) If E is constant for a time large compared with the 

 mean time between two collisions, then we have at once 



m V 7T 3 J-ooJ-oo^-00 

 Now noticing that we can put, as a good approximation, 





we see that we can at once transform the triple integral with 

 respect to (£, rj, f) by a spherical polar transformation into 

 a single integral with respect to u from to infinity, if we 

 put 



d%dr)dX=4:7rirJi< and | 2 = 5 5 



