1872.] 
Louis Schwendler — On Differential Galvanometers. 
149 
s°aK^i 
N 
Differentiating this expression with respect to w the external resistance 
belonging to the coil g ', we get 
da 
= K 
( \/ff __ A hi \/;t ) 
In n* 
i 
where II = 
dN 
dw' 
or the variation of the deflection a, when w 1 varies, is 
Sat = K {^- Jdw' = K^5w'. 
Now it is clear that the instrument is most sensitively constructed 
when, for the slightest variation in w / , the variation in a is greatest, lliis 
will he the case if the factor <f> = ^ is as great as possible. 
This factor <f> is a known function of the resistances in the circuit, and as 
w and w ' are given, <f> can only be made a maximum with respect to g and 
g ', the resistances of the two coils. 
Thus our physical problem is reduced to the following mathematical 
one : 
A function <j> containing two variables is to be made a maximum, while 
the two variables are fixed to each other by the relation 
k/<]' 
A = g ' + w' — j> ( g + id), 
A being a constant with respect to g and g ' and becoming zero at balance. 
Solving this question (relative maxima), we get 
y _L etr -4- f 1 
... II.* 
(10 — g) (w ' + g') +f(w + to ' + g ' — g) _ 2 (y 4- w +/ ) 
v (y — «’)y' 
2 ffg v/y '— p (y + «0 
* To some of the readers, a more detailed working out of the mathematical pro. 
blem may, perhaps, be welcome; and as this will also prove to be an easy control 
over the equations (II) and (II'), I will give it here in a somewhat condensed form. 
We had 
„ A 
“ K ^r A ' 
where K represents a constant, i. e. a quantity independent of any of the resistances 
/o' 
in the differential circuit (Fig. 3), while 6 = g’ + w f — p A_ (</ + w), i. c. a re- 
sistance which at balance becomes = 0 ; and further 
n = (g + w) (s' +»') + / (a + w +/ + “')• 
Differentiating a with respect to w', and remembering that -A_ = 1, and substitut- 
