and the Theory of the Induction-balance. 133 



is never accurately true, as the electromotive force begins 

 to fall off the instant the circuit is closed, and some dis- 

 crepancies between theory and experiment may arise from 

 this cause. Let us see what happens when the battery is 

 not constant, or when a polarizable voltameter forms part 

 of the circuit. According to Kohlrausch, the electromotive 

 force of polarization is proportional to the amount of decompo- 

 sition, and therefore a short time t after the current has been 

 established it is 



p 1 idt, 

 Jo 



o 



where p is the electromotive force produced by the passage 

 of a unit of electricity. The equation to the current is there- 

 fore 



L^+B 



dt 



:=E— p j idt, 



L d? +n dt + 2 )l=0 '> ( 14 > 



and the integral of this, remembering that i=0 when £=0, 



is 



2E 

 i=-^e-**Bmh0t, (15) 



where E 



-S-"V(£-& 



E 2 

 If/>=7j-, there could never be any current; and it is im- 



E 2 



possible for p to be greater than jy-. Practically, however, 



p would always be very small compared with this quantity; 

 and so we may write 



P 2L E 



Hence in any ordinary polarizable circuit the strength of the 

 current at any time after " make " is 



. E/ -? t fP-*)t\ 



l=z n{ e R ~^ R ). • • • • ( 16 ) 



On the Law of Variation of a Battery-current when a closed 

 secondary circuit is stationary in its neighbourhood. 

 12. So far we have considered a primary circuit in space 

 by itself ; but now we will arrange near it a secondary coil 

 with a resistance r and a coefficient of self-induction /, and 



