438 Prof. A. Anderson and Mr. T. Keane on the 



surfaces only, and not on the manner of variation of the 

 specific inductive capacity and specific resistance in the 

 interior of the dielectric, except in so far as these affect 

 the value of the current c. Furthermore, as the residual 

 charge is always of the same sign as the primary charge, it 

 follows that K r is always greater than K^ when a positive 

 current goes from the first plate to the second,, that is, when 

 V is positive. When V is negative K t is always less than 

 KtTj. It is clear, therefore, that the surface values of one 

 or both of the quantities K and r depend on the field of 



Ac 

 force. The charge Q x on the first plate is — - K l r 1 , and the 



Ac 47r 



charge Q on the second plate — -j— K t , the sum of the 



charges on the plates and the charge in the dielectric being, 

 of course, zero. It will be noted that there can be no 

 residual charge if K t = K 1 t 1 , or if c = Q. If q denote the 

 charge in the dielectric, we have 



q K t -K 1 t 1 

 Qi "" K lTl ' 



or assuming K = K 1 , which would seem not to be devoid of 

 probability in an apparently homogeneous dielectric, 



_£ _ T o~~ T i 



Qi "" n 



If this be so, we must explain the existence of q by a 

 difference between t and r l5 and t must be greater than r lm 

 That is to say, the resistance of the dielectric at the cathode 

 must be greater than it is at the anode, and this difference 

 must be produced by the field of force. An explanation is 

 supplied by the electron theory according to which the 

 specific resistance of a conductor is given by the expression 



— yr 2 . Probably the only quantities in this expression which 



can be different for the two surfaces of the dielectric are n 

 and I, n being the number of free electrons per unit volume 

 and I their mean free path. It is easy to understand that 

 the number of free electrons per unit volume close to the 

 anode will be greater than that close to the cathode, just as 

 the density of the atmosphere decreases with an increase of 

 height, ft is possible that I, the mean free path, may be less 

 at the anode than at the cathode, owinsr to the increase in 

 the value of n, but if it be remembered that the motion of a 

 free electron takes place among both fixed atoms and free 



