INDUCTION BALANCE. 389 



A telephone (Fig. 203) is placed in the circuit of two induced 

 coils a and a connected so that their currents are in opposite 

 directions. When the coefficients of mutual induction have the 

 same value M , the balance is established, and the telephone is 

 silent. The introduction of any conductor C between the coils 

 A and a forms a partial screen (563) which destroys the equi- 

 librium and makes the sound reappear. 



Let L, R, I be the coefficient of self-induction, the resistance, 

 and the intensity at the time / for the inducing circuit, /, r and / 

 for the induced circuit, A, /o, y for the conductor, or more exactly 

 for a ring which should be equivalent to it; M and m are the 

 coefficients of mutual induction of the conductor in respect of the 

 coils A and a. Taking into account the original equilibrium, we 

 have the equations 



< 44) l 



dy d\ di 



If then the coefficient of mutual induction of the coils A and 

 a is diminished by a quantity m Q , by separating them for example, 

 the two former equations become 



di d\ dy 



In order that there shall always be no current in the induced 

 wire, we must have 



m Q d\ = mdy, 

 or 



-=("*')' 



the simultaneous variations being proportional, the two currents 

 should have the same period, and the same phase, the constant 

 current I being further without action on the telephone. This 



