NOTE ON THE THEORY OF ELECTRIC ABSORPTION 143 



the direction of the plane YZ, so that m and V will be only functions 

 of the ordinate x. Our equations then become 



d 



A ~- 



dx dx j dt 



Eliminating p we find 



if A _ 



4- dt dx \dx dx dx 

 Now let us make p = x -=- and as t and x are independent, we find 



CvtC 



on integration, 



(P Pj + 4 " (P m jOoWo) = 0, 



where p is the value of p for some initial value of x, say at the surface 

 of the condenser, and is an arbitrary function of t, seeing that we may 

 vary the charge at the surface of the body in any arbitrary manner. 

 This equation establishes p as a function of m and t only, and as we have 



1 dp 

 ~~ - 



p will also be a function of these only. 



Let us now suppose that at the time t = 0, the condenser is charged, 

 having had no charge before, and let us also suppose that the different 

 strata of the dielectric are infinitely thin and are placed in the same 

 order and are of the same thickness at every 'part of the substance, so 

 that a finite portion of the substance will have the same properties at 

 every part. 



In this case m will be a periodic function of x, returning to the same 

 value again and again. As p is a function of this and of t only, at a 

 given time t, it must return again and again to the same value as we 

 pass through the substance, indicating a uniform polarized structure 

 throughout the body. 



This conclusion would have been the same had we not assumed a 

 laminated structure of the dielectric. In all other cases, except that 

 of two planes, electric absorption can take place, as we have before 

 remarked, even in perfectly homogeneous bodies, provided that Ohm's 

 law is departed from or that the electric induction is not proportional 

 to the electric force, as well as in non-homogeneous bodies. But where 

 the body is thus homogeneous, electric absorption is not due to a uni- 



