1872.] Louis Sehwendler — On Differential Galvanometers. 147 



and which may be positive, zero or negative, depending on the relative 

 strength of the currents which at the time are acting through the coils, on 

 the relative position of the needle towards the coils, and on the shape and 

 size of the latter. 



Approximately we have further 



Y =m U G 

 Y' = m / U / G' 

 U and U ' being the number of convolutions in the coils g and g ' respec- 

 tively, and in, m ' representing the magnetic momenta of an average convolu- 

 tion (one of mean size and mean distance from the needle) in the coils g and 

 g' respectively, when a current of unit strength passes through them. 



Further, as the space of each coil to be filled with wire of constant 

 conductivity is given, we have — 



U = n A/'g 

 TJ'=n'</g~ 

 as can be easily proved. 



n and n ' are quantities independent of g and g ', so long as it may be 

 allowed to neglect the thickness of the insulating covering of the wire against 

 its diameter, which for brevity's sake we will suppose to be the case. 

 "With this reservation n and n ' depend entirely on the size of the coils and 

 on the manner of coiling. 



Substituting these values, we get 



a° <xm n A/g G — m' n' */g ' G ' I 



which general expression for the deflection we may write in two different forms 

 either 



/ m 1 n 1 \/g'\ 



n a/ a ( Gr — ■ — j- Gr J ) 



u \ m 11 A/g / 



v,y Xm'n 1 A/g' ) 



which means that any deflections observed may be naturally considered due 

 to either coil. In the first form (equation I) it is considered due to the 



/ Wb % A / O 



coil a, when a cm-rent Gr — — G 7 flows through it, in the latter 



m n A/g 



form (equation I ') it is considered due to the coil g ', when a current 



vJ-Hl ^L a — Gf' flows through it. 

 m n A/g ' 



Now considering that the same battery E has to supply the current 



to both the coils we have 



G-E-^— 



