Louis Schvvendler — On Differential Galvanometers. [No. 1, 



2 '^ 





Additional reonarJcs, 



In the foregoing it has not been shewn that the values g and g', ex- 

 pressed by equations a and 1), must necessarily correspond to a maximum 

 sensitiveness of the differential galvanometer, because it was clear a priori^ 

 that the function by which the deflection is expressed is of such a nature 

 that no minimum with respect to g and g' is possible. However, to complete 

 the solution mathematically, the following is a very short proof that the 

 values of g and g' really do correspond to a maximum sensitiveness of the 

 differential galvanometer under consideration. 



Reverting to one of the expressions for the deflection a^ which any 

 differential galvanometer gives before balance is arrived at, we had : 



fl° a K — |- A and as the increase of deflection at or near balance is 



N- 



identical with the deflection itself, and further as the law which binds the 

 resistance of the differential coils to the other resistances in the circuit, in 

 order to have a maximum sensitiveness, is of practical interest only when 

 the needle is at, or very nearly at, balance, we can solve the question at once 

 by making a° a maximum with respect to g and g\ if we only suppose A 

 constant and small enough, and as K is known to be independent of y andy', 



the deflection a^ will be a maximum if -— - is a maximum for any con- 

 stant A (zero included). 



Fui-ther we know that g' = Cg which value for g' in N substituted will 



make the latter a function of g only and consequently -—- also. We have 



therefore to deal with a single maximum or minimum, and according to well- 

 known rules we have : 



and 



da 



* 



^ dg 



u 



dg- 



2v/y 



W 



■~ V 



d'^a 



^7- 



dg 



- U 



dg 



dg' y 



