COEFFICIENTS OF MUTUAL INDUCTION. 507 



circuit comprises the coils A and A' (Fig. 233). The wires are 

 connected, so that the induced currents on either side add them- 

 selves, and between the two points b and c of the induced circuit a 

 shunt of resistance s, containing a galvanometer G, is inserted. The 

 resistances r and r', on either side of the shunt, are varied until the 

 needle is stationary, when the inducing circuit is opened or closed. 



If I is the inducing current, / and /' the induced currents in the 

 resistances r and r', the coefficients of self-induction of which are 

 L and L', / the coefficient of self-induction of the shunt s, which 

 contains the galvanometer, and / ' - i the corresponding current, we 

 have, in general, equations 



Integrating these equations for the whole duration of the variable 

 state, and calling I the variation of the inducing current, m and m 

 the induced discharges for the currents / and /', we get 



mr + (m' - m} s MI = , 

 m'r' - (m - m)s M'I = . 



The sign + in front of the latter terms corresponds, for instance, 

 to the production of the inducing current, and the sign - to its 

 suppression. The coefficients of self-induction of the various parts 

 of the induced circuit have disappeared, which might be foreseen, as 

 the induced current is null at the two limits. 



If there is no discharge in the galvanometer, we have m = m' t and 

 therefore 



1096. M. Brillouin* has arranged the experiment in a somewhat 

 different manner. The coils a and a' are connected, so that the 

 induced currents are in opposition ; a shunt of resistance s is placed 

 between two points b and c of an induced circuit ; the galvanometer, 

 whose resistance is g, and coefficient of self-induction /, is interposed 



* BRILLOUIN. Ann. de VEcok Normale [2], Vol. XL, p. 352. 1882. 



