396 COMPARISON OF RESISTANCES. 



and a condenser of capacity placed as a shunt. * Let us suppose 

 the two armatures of the condenser joined by a resistance R'. Let 

 I' be the current which traverses this resistance, I the current of the 

 battery, and R the total resistance of the circuit. If at a given 

 instant V is the difference of potential of the two armatures, we 

 have 



(50 



L 



at 



The elimination of V between these equations gives 

 L WI R + R' E 



(52) 



If the electromotive force E is sinusoidal, this equation is also 

 satisfied by a sinusoidal current when, the permanent regime is set 

 up. Moreover, equations (49) and (52) become identical if we 

 suppose R' = oo and C = c that is to say, the shunt R' open and 

 the capacity of polarization of the electrodes equal to that of the 

 condenser. In both cases the condition necessary for the establish- 

 ment of compensation is 



(53) T*-4*L; 



it is independent of the resistance of the circuit and of the ampli- 

 tude of the electromotive force. 



This remarkable result may be put in a form which better brings 

 out the mechanism of the phenomenon. Three electromotive forces 

 are at work in the circuit the principal electromotive force of the 



sources, E = E sin 2ir , and two inverse electromotive forces, con- 

 sequences of the first, which have the values respectively 



E '- L ' 



(54) 



* MAXWELL. Phil. Mag. [4], Vol. xxxv., p. 360. 1868. 



