1872 ] Louis Schwendler — On Differential Galvanometers. 151 
would be those which would make the reading most delicate near balance, 
when the variation takes place in w', i. e., the external resistance belonging 
to the coil g 
If instead of differentiating the expression for a with respect to tv by 
using the expression I, we had done so with respect to w by using the expres- 
sion I we should have obtained in a similar way the following relation 
between g and g' 
(tv 1 — g') ( w + g) + / (w + io' + g — ff') 2 (g + iv J_)_ — , 
~g „ /-/ u JrU \ 
n' 
r 
which equation connected with the other 
2 -Jg Vh' 
P 
Cl(f) 
dg ' 
further we will substitute : 
dg 
- + 
dA_ 
E y/f> dg ' 
N 2 
= — (P ' + Q ') 
d A 
d g 
d A 
d g • 
= $ 
Thus we have the following differential equation : 
(P_Q)d 3 _(P'+Q')^'+ « dg + /3dg ,y )= 0 
\ being the undetermined factor. From this equation we have . 
P_ Q + Aa = 0 
and — (P' + QO + X 0 = 0 
or A. eliminated : p _ Q p/ + Q / 
5 -8 
but we have always : n y 
Q hs 
ot £ 
thus we have as end-equation : 
P __ P' 
ot 0 
or the value for P, P a and 0 substituted we have : 
2 g dN 2 dN . 
N “ ST _ 
further substituting 
p g'(g — W) 
dN 
dg 
dN 
dg' 
and reducing as much as possible, we have 
(w - g) (w' + g ')+/(«’ + >«' + !>'— g) 
a s/g n/s ' — p (? + M ) 
= g'+ w'+/ 
— g + w +f 
2 (g + w + f) 
II 
p (s - u-7? a V? >/»'— P(3 + ,u ) 
which is the equation II as given above. 
In quite a similar manner, equation II ' can be found, it must only be remembered 
that it is more simple to use expression I ' for the purpose than I. 
