150 
Louis Schwendler — On Differential Galvanometers . 
[No. 2, 
which equation with the other 
g ' +■ w ' — p (g + w) — A = 0 1 
v 9 
gives all that is required to determine g and g and the values thus obtained 
d a 
d w‘ 
= K 
j^-A 
l N 
W8 ) 
N 2 I 
Sa = K 
l N 
A ^ j Sw‘ 
N a 
“v~ 
Set = K </> Siv ' 
Thus the variation of a is always directly proportional to </>, a known function of g 
and g’, and to make 8<x for any Sw' as large as possible, we have to make <p a maxi- 
mum with respect to g and g’, while g and g' are connected by the following equation 
/ / 
A= gr' + w'— p — j- (gf + w) I 
v0 
p being a constant with respect to g and g ', as also is A. 
We have, therefore, to deal here with a relative maximum, and in accordance with 
well known rules, we have to form the following partial differential coefficients : 
d tj> _ 
d g 
N — 2 g 
d N 
d g 
R \ /g 
d A 
d g 
2 v'-jN 2 
N 2 
+ A S 
d N 
R = — ' = 3 + W + / 
s _ n/3 
S “TF 
d (p 
d g ' 
2 R. 
d N 
d g 
\/s. 
N 
d N 
d R R_ ( 
dg 2 g ) 
d g' 
N 2 
d R 
dg 
R n /g 
d A 
Tf' 
N 2 
V-7 /dR 2Ri£x 
= -w(jp--±L) 
+ A S' 
d A 
d g 
d A 
Tp 
— g p \/g' 
g 2 */g 
. 2 */g s/g* — p (a + ">) 
2 */g >Jg' 
At or near balance when A is = 0, or very small, the terms A S and A S' in the re. 
spective differential coefficients are to be neglected, because neither S nor S' become 
infinite for any finite values of g and g'. 
Thus we have approximately : 
d 
N-2 g 
d N 
d g 
R s/g 
d A 
d g 
VjN' 
N 2 
= P-Q 
