Mr. Louis Schwendler on Differential Galvanometers. 265 



16w' 2 



the negative signs of the square roots having been omitted, since 

 they would obviously make g and g' negative, values which cannot 

 solve the physical question. 



o 11) 



Further, if we introduce the ratio ^- = — , given by equation 



(IV.), into equation (I.), and develop^, we get 



w 

 p*=~. (c) 



This latter expression shows the very simple relation which 

 must exist between the mechanical arrangement of amj differen- 

 tial galvanometer and the two resistances at which balance is 

 arrived at in order to make a simultaneous maximum sensitive- 

 ness 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 



4' = ^=C ; .... (I.) 

 " */g g + w 3 K J 



expressing the ratio between the total resistances in the two 



differential branches when balance is established, which ratio 



is generally known under the name Constant of the Differential 



Galvanometer. 



Substituting in the above expression (I.) the value of- = — , 



from equation (IV.) we get at once 



^=C; id) 



IV 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 alte- 

 ration of external resistance in either branch of any differen- 

 tial galvanometer can be obtained only if the constant of the 

 differential galvanometer is equal to the ratio of the two resist- 

 ances at which balance arrives; and this clearly necessitates 

 that the resistances of the respective coils to which w and io J 

 belong should stand in the same ratio. 

 * See note at end. 



