INDUCTION BALANCE. 387 



986. INDUCTION BALANCE. Induced currents in a conductor, 

 other things being equal, are inversely as its resistance; and this 

 property has been already used (936) in comparing resistances 

 by measuring induced charges. The use of induced currents is 

 particularly valuable in a great number of special cases in which 

 ordinary methods would be inapplicable. 



The simplest arrangement consists in counterbalancing the 

 effects of induction in two different circuits. 



Suppose, for instance, that we interpose in a circuit containing 

 a variable electromotive force E (Fig. 202) two equal coils A and A', 

 at such a distance from each other that their mutual induction may 

 be disregarded. 



Above them, and at the same distance, two other equal coils 

 a and a' are placed in the same axis, so that the coefficients of 

 mutual induction are the same for the two systems. 



When the induced coils a and a' have the same coefficient 

 of self-induction, and their circuits are closed respectively by wires 



Fig. 202. 



of equal resistances R and R', the coefficients of self-induction 

 are either equal or may be neglected. The currents induced in 

 each case by any variation of the electromotive force are equal. 

 The addition of two equal resistances r and r', without a coeffi- 

 cient of self-induction or having equal coefficients, does not affect 

 the equality; so that if the induced currents are joined separately 

 to the two coils of a differential galvanometer perfectly equilibrated, 

 the needle should remain stationary. 



As the galvanometer only measures total quantities of electricity, 

 it is sufficient for equilibrium that the discharge or the integral value 

 of the two induced currents is the same, and also approximately 

 their duration, provided this duration is very short in comparison 

 with that of the oscillation of the needle. This condition does not 

 require complete symmetry of the two systems, but simply equality 



CC2 



