266 Mr. Louis Schwendler on Differential Galvanometers. 



The general problem may now be regarded as solved by 

 the following four general expressions : — i 



g = - -^ +/ __j + -y ^ + _ (w + ^ )/+ l___L A 



4**.** C») 





r w s> •••••• w 



c=^ M 



■ • « • -Additional Remarks, 



In the foregoing it has not been shown that the values g 

 and g' expressed by equations (a) and (b) must necessarily cor- 

 respond to a maximum sensitiveness of the differential galva- 

 nometer, 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 ar- 



y / q 



rived at, we had a°cc K -^rr A; and as the increase of deflection 



at or near balance is identical with the deflection itself, and, 

 further, as the law which binds the resistance of the differ- 

 ential 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 f , if we only suppose A constant and small enough ; and 

 as K is known to be independent of g and g' 3 the deflection 



'a° will be a maximum if —r~ is a maximum for any constant 



A (zero included). 



Further, we know that g ! =Cg, which value for g' in N sub- 

 stituted will make the latter a function of g only, and con- 

 sequently -^p also. We have therefore to deal with a single 



maximum or minimum ; and, according to well-known rules, we 

 have 



