USEOFSINUSOIDALCURRENTS FORMEASURING LIQUID RESISTANCES. 395 



If the polarization is always below its maximum value, it may 

 be assumed that the electromotive force which corresponds to it 

 is proportional to the quantity of electricity which has passed from 

 the origin. If c is the capacity of the electrodes that is to say, 

 the inverse of the potential to which they would be raised by unit 

 electricity on the assumption of a strict proportionality, we may 

 write then 



-if 



de I 



Idt, or - = - 

 dt c 



Replacing this value in equation (48), we deduce from it 



dl I </E 



The electromotive force E being of the form 

 E = E sin 27T - , 



the current is thus periodic ; and when once the stable condition 

 is established, it may be represented by the expression 



A sin 27r ( - 



As the equation (49) should be satisfied by this value of I for 

 any given epoch, it gives 



F 2 



A 2 : 

 (50) 



T 



.. 





It will be seen that for given values of L and of c there is 

 always one value of T that is, a velocity of the sinusoidal inductor 

 for which the effects of self-induction and of polarization mutually 

 destroy themselves. When this condition is realised, the change 

 of phase is null, and the intensity is every instant equal to the 

 quotient of the electromotive force by the true resistance. 



993. We may point out in passing the analogy of this problem 

 with that of a circuit which contained a variable electromotive force, 



