147 
1872.] 
Louis Schwendler — On Differential Galvanometers. 
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'D' G' 
U and U' being the number of convolutions in the coils g and ^'respec- 
tively, and m, 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 — 
D —n a/ g 
U'= n Vy 7 
as can he easily proved. 
n and n 1 are quantities independent of g and g ', so long as it may he 
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° a in n >Jg G — m 1 n‘ g ' G ' I 
which general expression for the deflection we may write in two different forms 
either 
a a m n 
m n 
i/0 / 
a° oc in ' n 
■Jj ( 
v J \ m‘ n’ Vy 
) 
r 
which means that any deflections observed may he naturally considered due 
to either coil. In the first form (equation I) it is considered due to the 
coil g, when a current Gr 
m‘ n 1 \/g' 
G / flows through it, in the latter 
in n \/ g 
form (equation I') it is considered due to the coil g\ when a current 
_ “/JL G — G ' flows through it. 
m ' n ' \/g ' 
Now considering that the same battery E has to supply the current 
to both the coils we have 
, g' + v>' 
N 
G = E 1 
