Coefficients of Self-induction and Mutual Induction. 235 



circuits will be G 



Go 

 This may be made a maximum in the usual way. 



G»: y - 



§ 5. To Compare the Coefficient of Mutual Induction of Two 

 Coils with the Coefficient of Self-induction of a Third Coil. 



One of the coils of the pair is placed in the battery- circuit, 

 and the other is connected to BD as a shunt to the galvano- 

 meter. The resistance of this part will be called R, that of 



D 



the other will be included in the battery. The self-induction 

 of the latter coil produces no effect on the galvanometer ; this 

 is likewise the case with R, because there is no permanent 

 current through it. The coefficient of mutual induction will, 

 as usual, be denoted by M ; the other coil is placed in AD, as 

 in the figure. 



In dealing with this case the galvanometer, coil R, BC, CD 

 must be looked upon as lying in one plane. 



Thus, 



T=i(Li* + 2Ms.ti-y), 



Y = i{cx 2 + a.k-z + dy <2 + b.i/-£ + a.x-u +R.w-y +Bi 2 }, 

 We observe also that 



Thus, 



w = 0, x=y Q . 



a . x- 



+ ex + G . x — u = — L^o, 



b.y— z + dy + ~R.y— u= -Mi , 

 -G(x-u) -R(*/-w) = -M* . 



