Wave-trains through a Conducting Dielectric. 311 



hereinafter generally referred to as " the dielectric/' and the 

 conducting slab as " the plate " or " electrolyte." 



II. The Phenomena at the First Surface of the Plate. 



In this section we will deal with the phenomena occurring 

 at the first surface of the " electrolyte " only. 



The direction of propagation of the ray is chosen as the 

 positive direction of the axis of z and the origin is taken in- 

 definitely close to the interface. 



The suffix 1 always refers to the dielectric and the suffix 2 

 to the plate. 



Fig. 2. 



*/ / £> 



<\ ( *r O 



Let X : be the electric force in the dielectric and X 2 that in 

 the plate. Under the limitations we have set ourselves — 

 plane waves and non-conducting dielectric— -Maxwell's equa- 

 tions assume the simple forms 



** (1) 



A^- 



dt 2 



dz* 



(«5 



+A 



d\dX 9 __ d 2 X 2 



(2) 



% dt) dt ~ dz* ' 

 where we have abbreviated Maxwell's notation by putting 



£i=Pi*i> &2 =f^2 fC 2, a 2 = 47r^ 2 2? . . (3; 



/jl 2 being the magnetic permeability of the plate, k 2 its dielectric 

 constant, 2 its conductivity; fi x k x are the same constants 

 referring to the dielectric, 0, being zero. As already stated, 



Y2 



