166 Mr. Louis Schwendler on Differential Galvanometers, 



Til n 

 factor is entirely independent of any of the resistances, it 



represents what may appropriately be called the ^'mechanical 

 arrangement '' of the differential galvanometer, and may be de- 

 signated by/?. It must be borne in mind that^ represents an 

 absolute number, which theoretically may be any thing with the 

 exception of and gc. \i j^ had a value equal to either of these 

 two limits, the instrument would be a simple galvanometer with 

 a shunt, and not a differential galvanometer. 



The deflection a may now be written more simply as follows : — 



A 



a°ocK^(y + z.'-;.^(^-rz.))=K^A, . (I. 



or 



\/g 

 A' 



K and K' being independent of _^ and g\ and also of w and wK 



N is a known function of all the resistances in the differential 

 circuit. 



A and A' are similar functions of ^ and y\ iv and y, and 

 which both become zero at balance. 



For the further investigation only one of the two possible ex- 

 pressions of « will be used, viz. equation (L). 



«°ocK^^A. . (I.) 



Differentiating this expression with respect to iv\ the external 

 resistance belonging to the coil g\ w^e get 



where 



da ^^f Vg A'R\/g'\ 

 M" {If N^J ' 





or the variation of the deflection a, when lu' varies, is 



ga = K U^ - ^y } dw'= K^chu'. 



Now it is clear that the iustrument is most sensitively con- 

 structed when, for the slightest variation in w', the variation in a 



is greatest. This will be the case if the factor (p = -^ rp"^ 



is as great as possible. This factor d> is a known function of the 



