208, 209] CONDUCTION IN DIELECTRICS. 407 



If the circuit be again broken, the circumstances are the same 

 as in stage 2, so that if the condenser is subsequently again short- 

 circuited, we obtain a new instantaneous discharge, called the 

 residual discharge, and this may be repeated as often as we please. 

 It will be seen that the residual discharge arises from the charge 

 <j 3 that has accumulated by conduction on the plane 3, and that 

 there will accordingly be no residual discharge in a condenser in 

 which the relaxation-time is the same in every part. This is a type 

 of what would occur in any non-homogeneous dielectric, and it is 

 in this manner that Maxwell gave a possible explanation of the 

 phenomena of electric absorption, and of residual charge (Ruck- 

 stand). Maxwell's explanation has found confirmation in experi- 

 mental results of Rowland and Nichols, Hertz, Arons, and Muraoka*, 

 all of whom found that when the dielectric was perfectly homo- 

 geneous there was no residual charge. 



209. Total and Displacement current. In the funda- 

 mental equation 206 (4), we see that the vector 



whose components are 



1 d$ I d$) I d% 



U T , V -\ , W + j~ , 



is solenoidal. If we consider the condition at the surface of an 

 ordinary conductor, in which we consider 8 = 0, surrounded by an 

 insulator (in which q = 0), we have 



= \u cos (n$c) + v cos (niy) + w cos 



- {# cos (n&) + g) cos (n e y) + 3 cos 



i 



so that here also the solenoidal condition is fulfilled. The vector 

 q -f j -T7 is called by Maxwell the total current. It is a funda- 



TcTT Cut 



mental principle of Maxwell's theory that the magnetic effects of 



* Eowland and Nichols, Phil. Mag. (5) 11, p. 414, 1881 ; Hertz, Wied. Ann. 20, 

 p. 279, 1883; Arons, Wied. Ann. 35, p. 291, 1888; Muraoka, Wied. Ann. 40, 

 p. 328, 1890. 



