﻿666 Mr. G. H. Livens on the Electron 



and it is then an interesting verification of our present 

 analysis to show that if SN is given by our previous general 

 law, viz., 



V ^ L m J r m J f=t _ T J 



then the equation is identically satisfied. 



6. The polarization currents and the total electric field at 

 a point in the meted. — It must now be remembered that in 

 the case of most metals to be dealt with, there is usually 

 a contribution to the total current of electricity not only as 

 the result of the motion of the various free electrons, but also 

 as a result of the relative displacement of the neutralizing 

 charges in each atom, caused by the electric field pulling the 

 opposite charges in opposite directions. This part of the 

 current is easily calculated, as has already been explained in 

 great detail in a previous communication on absorption 

 in dielectric media, and turns out to be of the form 



dF 

 dV 



where P is a vector defining what is analogous to the 

 polarization in dielectrics and whose intensity is given by 



where 



1 — aA 



A=2 



n- — n "-\-inn 



wherein X denotes a sum taken over all the electronic 

 resonators in the atoms per unit volume for the typical one 

 of which n is the period of free vibration and mn ' the 

 coefficient of the damping force in its equation of motion. 

 The constant a is a numerical constant whose value in an 

 ideal case is \ and in any real case is at least of this order of 

 magnitude. 



In addition to this current there is, of course, as always, 

 to be added the sethereal displacement or polarization 

 current, which is measured by 



dE 



dV 



as in the Maxwellian theory. 



Now we know that the resonance electrons in the atoms 



