Louis Schwendler — On Differential Galvanometers. 
[No. 2, 
US 
and G ' = E 
9 + 10 
N 
where N = (g + w) (y / + w 7 ) +y + w + g' -f- w')- 
Thus substituting in I and I ' we get either 
A 
:m n E 
^ (V + „._ («, + „,) i 
N V «» » v9 / 
t'E 
and either A or A 
The coefficient 
^r( {gl+wl) ^L i ^L- {g+w) \ r 
N \ u m n' ffg' ) 
on 
on ' n ' ffg ' 
is the factor which at balance becomes zero. 
m n means, therefore, nothing else than what is 
on n */ g 
generally called the constant of the differential galvanometer, i. e., the num- 
ber by which the total resistance in one branch of the differential galvanometer 
has to be multiplied, in order to obtain the total resistance in the other branch, 
when balance is established. This constant of the differential galvanometer 
is a given function of g and g the resistance of the coils, and as g and g ' 
are to be determined, by being variable, it cannot be considered a constant 
-) ft I 
in this investigation. But the 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 
designated by p. It must be borne in mind that p represents an absolute 
number, which theoretically may be anything with the exception of o and oo. 
If p has 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 
K (g' + W '—P~^ C 9 + w )) = K 
A' 
_A 
:Iv 
+ v7 ( + w) \ = 
N V p o/g' y ' 7 
K' 
v7 A 
IT A 
•Sg' 
N 
I 
I' 
p v7' 
K and K ' being independent of g and g ', and also of w and w 
N is a known function of all the resistances in the differential circuit. 
A and A ' arc similar functions of g and g\ w and w' and which functions 
become both zero at balance. 
For the further investigation, only one of the two possible expressions 
of a will be used, viz. equation I. 
