226 Prof. C. Niven on Determining and Comparing 



solution of the second problem only compares the coefficient 

 of self-induction of a coil with that of the mutual induction 

 between this coil and another. 



It seemed desirable so to extend these methods that in the 

 first two cases the adjustments for no permanent and no 

 transient current should be independent of each other, and to 

 obtain the means of comparing the self-induction of any coil 

 with that of the mutual induction of any two other coils. 



The differential galvanometer appears at first sight to possess 

 special advantages for these problems ; but the methods are 

 easily adapted to the Wheatstone-bridge, which practically 

 converts the ordinary into a differential galvanometer ; and 

 the adjustments with it are more easily effected than with the 

 other, which usually requires for these methods that the coils 

 of the galvanometer should be suitably shunted. 



I shall therefore begin by giving methods adapted to the 

 ordinary galvanometer, reserving to the end of each article an 

 account of those which may be employed with the differential 

 galvanometer. 



§ 2. In these inquiries it is useful to know not only the 

 condition that there should be no current through the instru- 

 ment, but also the expression for the total flow when this 

 condition is not satisfied, in order to be able to select the best 

 arrangement of the bridge so that the galvanometer shall be 

 most sensitive, and in the case of the differential galvanometer 

 to ascertain what shunts should be used with it. And for this 

 purpose Maxwell's method is particularly suitable. 



Let a network of conductors be considered to form a system 

 of meshes the currents round which are B 9 y y > , . . , and let elec- 

 tromotive forces E X3/ . . act along the sides of these : let also 



T = i(L^ 2 + 2Mi^ + ]^ 2 +...), >j 



F = i(a 11 x* + 2a l2 xi / + a 22 y* + ...), V . . (1) 



E=E^-^)+..., J 



T being work dissipated in heat in the conductors. 

 The general equations of the system are typified by 



d/dT\ dF_dE 

 dt \dx ) die ~~ dx ' 



If we have also condensers, the poles of which are attached 

 to the network, each of these may be considered as forming 

 an additional mesh ; and if u be the charge of one of these at 

 any time, the current round the corresponding mesh is w, and 

 must be included in the expressions for T, F, E. The energy 

 employed in charging the condensers will usually be of the form 



