of Electric Induction and Conduction. 361 



' cr 12 [the surface-density of electricity on the surface which 

 separates the first and second strata] . The length of cord 

 in excess of the normal length, which exists between the 

 first and second buttons. 

 R the regular Ohmic resistance of the dielectric, or 



a*p x + a 2 r 2 + .... + a n r n . 

 C the capacity of the dielectric measured instantaneously, 

 i. e. without allowing time for any slipping between cord 



and buttons, or -^ : it equals . 



ah a-iKi + a 2 K 2 + .... + a n K n 



§ 9. Maxwell then goes on to consider what happens in any 

 one stratum (say, the first) when the electric forces are brought 

 to bear on the dielectric. 



By Ohm's law we must have 



a 1 X 1 = a 1 r 1 p 1 (1) 



Maxwell's theory assumes 



Xi = K lt /i; (2) 



and by definition of total current, 



'■*«»+■! (3) 



Also evidently 



*n=fi-fu (4) 



and 



dcr-,2 >k\ 



-&=*-*> ( 5 ) 



These equations being given, certain consequences follow, 

 of which the most obvious are 



U 1 = U 2 =^.... = U n = U, .... (7) 



and 



E = « 1 X 1 + « 2 X 2 + ...., .... (10) 



while the most important is a relation between E and u, which 

 is obtained by substituting in (3) the values of p and / from (1) 

 and (2), and then adding up in accordance with (10) thus, 



E = (« 1 D 1 + « 2 D 2 + ...>, . . . (11) 



where T) 1 stands for the operator ( 1 ) . 



\?'i k x dt) 



Equations (4) and (2) give us 



_ X 2 X x 



^12— ■ , 



which shows that internal charges will appear unless the stretch- 



