Coefficients of Self-induction and Mutual Induction. 231 



Method III. — Using the differential galvanometer. 

 The coil whose resistance is R is put in circuit with one coil 

 of the galvanometer ( Gr) ; and an additional resistance in AF = c, 



B, 



oqooooq J^.2? 



.. -^ 



-^4^ 



'X 





» wv p ~py 



m -^ 





ii 



E' 



the other coil of the galvanometer being put into circuit with- 

 similar resistances. The poles of the condenser are moved 

 along AF and AE ; or one only till the galvanometer gives no 

 kick. 



The steady current in each branch is- 



2E 

 2B + R+G + C* 

 and we have in this case 

 T=iL^ 2 , 



¥ = \{a.x — u +R + G + C— a.x 2 + b.y + u + R + G + c — b.y 2 + Kx~+y 2 \ r 



n ~ 2 c 



The equations for the transient current at make are 



a . x — w + R + G + c — a .x + B . x+y = — -1jx 0} 

 b.y + u + R+G + c — b.y + B.x+y = % 



-(a-b)x + ^=0; 

 whence 



(E+G+c)(2B*R+G+cy 



The condition for no deflection is 



a 2 -6 2 .C-L = 0. 



It may happen, however, that if the galvanometer have a 

 high resistance the deflections produced are always small, 

 even when the condenser is not introduced : in this case we 

 may improve matters by shunting each coil of the galvano- 

 meter. In this case G will stand for the combined resistance 

 of the galvanometer and shunt ; and if S be the shunt, G the 



