1872.] 



Louis Schwendler- 



-On Differential Galvanometers. 

 Fisr. 1. 



145 



Now, as far as the 

 magnetic effect of the 

 two coils is concerned, 

 we may substitute for the 

 parallel circuit, Fig. 1, 

 the simple circuit, Fig. 2, 

 if we only reverse the \V 

 magnetic action of one 

 of the two coils, (say the 

 right one). 



§" 



— snnnnf 



%C C 



I 



w 



And in order to have, in 

 this case, for the same 

 electromotive force E the 

 same current C flowing 

 through the coils as be- 

 fore, (see Fig. 1), we 

 must necessarily intro- 

 duce a resistance x 

 hence — 



C 



E 



UJUL> 



X 



B 



E 



g + w 2g -f x 



therefore to = g -f- ® (I) 



But to obtain the maximum magnetic effect in any single circuit (Fig. 2), 

 it is necessaiy that the resistance of the coil should be equal to the total 

 external resistance* and therefore in this case (Fig. 2) 



• =2y (II) 



Eliminating x from equation I and II we have 



*=T ; CO 



To obtain the most delicate reading with a differential galvanometer, the 

 two coils of which have equal magnetic momenta, and also equal resistances, 



* This law holds good, — as can easily be shown, — for any number of coils con- 

 nected into a single circuit, no matter if the magnetic effects of these coils have the 

 same or opposite sign with respect to a given magnetic point. 



