APPARATUS WITH VARIABLE COEFFICIENT OF INDUCTION. 515 



It would have been the same thing if the change of resistance 

 had been made in the branch b'. 



Instead of breaking or making the current, it would be better 

 to reverse it each time ; twice the effect would then be obtained. 

 Moreover, the circuit of the battery is permanently closed, except 

 during the very short time of the reversal, and we have the ad- 

 vantage of obtaining a more uniform current. The principal diffi- 

 culties of the method arise in fact from variations in the intensity 

 of the principal current. 



1101. Let us consider, in the same circuit, traversed by a 

 sinusoidal current, the portions AB and A'B', formed respectively 

 of the resistances R and R' with the coefficients of self-induction 

 L and L'.* The differences of potential between A and B and 

 between A' and B' are, at a given moment, if there were no mutual 

 induction, 



RI + L and R'I + L' . 



dt dt 



If then the two ends of the resistance R and R' are successively 

 connected with the electrodes of an electrometer arranged so as 

 to measure the mean of the squares of potentials (905), the cor- 

 sponding deflections satisfy the equation 



Assume, as a particular case, that the resistances R and R' are 

 equal and the coefficient L' is null, we shall have 



1102. APPARATUS WITH VARIABLE COEFFICIENT OF INDUC- 

 TION. In certain circumstances it is useful to have apparatus with 

 variable coefficient of induction, standardised like boxes of resistance 

 or of capacity. The two following arrangements have been used by 

 M. Brillouin.f 



* JOUBERT. Ann. de VEcol. Normale [2], Vol. x., p. 131. 1881. 

 f BRILLOUIN. Ann. de VEcol. Normale [2], Vol. XL, p. 352. 1882. 



LL2 



