1873.] Louis Schwendler — On Differential Galvanometers. 3 



obviously make y and g' negative, values which cannot solve the physical 

 question. — 



Further, if we introduce the ratio 



a' w' . 



— = — , given by equation IV, into equation I, and develope f we get : 



i?^ = — c. 



w 



This latter expression shows the very simple relation which must exist 

 between the mecJianical arrangement of ani/ differential galvanometer and 

 the two resistances at which balance is arrived at, in order to make a simul- 

 taneous maximum sensitiveness possible. 



Thus if the ratio of the two resistances at which balance arrives is 

 fixed, the mechanical arrangement p cannot be chosen arbitrarily, but must 

 be identical with this ratio. This is in fact the answer to the question put 

 at the beginning of this paper. 



However, the meaning of this result will be made even still clearer if 

 we revert to equation I, by which we have 



^^=t±J^_^ I. 



expressing the ratio between the total resistances in the two differential 

 branches, when balance is established, and which ratio is generally known 

 under the name Constant of tlie Differential Galvanometer. 



Substituting in the above expression I the value of — = — from equa- 



if 



tion IV we get at once 



*-:^' = c d. 



w 

 and as a second answer to the question put at the beginning of this paper 

 we have therefore : 



A simultaneous maximum sensitiveness with respect to an alteration of 

 external resistance in either hranch of any differential galvanometer can he 

 ohtained only, if the constant of the differential galvanometer is equal to the 

 ratio of the two resistances at which halance arrives, and this clearly necessi- 

 tates that the resistances of the respective coils to which iv and w' belong 

 should stand in the same ratio. 



The general problem may now be considered as solved by the following 

 four general expressions : 



w' J 



q' =^ — q O' 



