PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 623 
WHEATSTONE’S BRIDGE. 
As an example of the application of the foregoing theory to Wheatstone’s 
bridge, consider the case where all the arms have self-induction and two 
opposite arms have mutual induction. 
Let the current, resistance, and self-induction in the 
branches of the bridge be y,R,K, y,8,L, &c., the current in 
the circuit BD in which the telephone is inserted being 
supposed zero; and let the coefficient of mutual induction 
of AB and DC be X. We have, since B=D, in order that 
there may be silence in the telephone, 
(KD+R)y+XDz=A—B=A—D=(MD+T)z . . (1) 
(LD +8)y=B=0=D—C=(ND+U)z4#XDy Ss QQ) 
Hence 
(KD +R)y= (M+ X)D+Tiz, 
(L—X)D+S}y=(ND+0U)z, 
which gives 
[{(L—X)D+S}{(M—X)D+T}—(KD+R)(ND+U)|smvt=0  . (8) 
The conditions for silence are therefore 
h—vn?=0, 
|! (4) 
we =0, 
where 
A\=ST—RU, 
p=LT+MS—KU—NR—(S+T)X, { pnt) 
v=LM—KN—(L =P M)X + X?2, 
For absolute silence we must have 
ESS my ale aaa ad ean (5) 
Comparison of two Coefficients of Self-Induction If M=0, N=0, X=0, (6) 
reduce to 
ST—RU=0 , LT—KU=0. 
This case is given by MaxweE tt, “ Electricity and Magnetism,” vol. ii. p. 357. 
Comparison of Coefficients of Mutual with Coefficients of Self-Induction.—If 
L=0 , M=0, (6) reduce to 
KU+NR 
a0) x — KN 
