﻿Theory of the Optical Properties of Met als . 667 



are effective in modifying the electric field at any point 

 inside the metal, so that they will by such means also in- 

 directly affect the currents o£ conduction. In fact, at any 

 point in any homogeneous medium polarized to intensity P, 

 there is an additional electric force of intensity 



a? 



in the direction of P, arising solely from the distribution of 

 the immediately surrounding polarized molecules or atoms. 

 We must therefore include this part of the electric field in 

 the general expression for E, which therefore now becomes 



E + aP. 



This is the complete expression for the total electric force 

 which is effective in driving the electric current. 



7. The electro-optical equations. — The fundamental equa- 

 tions of the optical theory are the generalized Maxwell 

 equations which, expressed in their differential form and 

 using the Hertz-Heaviside system of units, are simply, for 

 non-magnetic media 



JjI' = Cnrl H, - ^?=CurlE, 



wherein E, H denote as usual the electric and magnetic 

 force vectors at any point in the field, 1' the total current 

 density at the same point which is, inside the metal ex- 

 pressed by 



Let us now examine the propagation of light in a medium 

 where these equations are satisfied. In order to simplify the 

 equations we adopt the standard convention and consider as 

 previously the propagation of plane homogeneous waves 

 taking place in the direction of the axis Oz, so that the 

 components of E, H, and I' involve the coordinates of space 



and time by the exponential factor t %p \ <?/, where n is in 

 general a complex quantity, a function of p, the frequency 

 of the light disturbance used. 



Since in this case all differentials with respect to X and u 

 vanish, the general equations reduce io 



ipn J, lj. / ftEg 11 7 



