PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 617 
Differential Telephone, with a Neighbouring Circuit to each Branch. 
Let the current, resistance, and coefficient of self-induction be denoted as 
follows :— 
For the line, : ‘ ‘ ee ee een ae 
,, 1st branch of differential telephone, soe pO 
Ape a do. d : : Seer kuN ; 
,, Ist neighbouring circuit, ; ay vot WSs Gis 
Ka ek do. : : : 5 SEE aM 
Farther, let the coefficients of mutual induction of the two neighbouring 
circuits, each with its corresponding branch, be I and J; and that of the coils 
of the differential telephone K. 
If U and V be the potentials, at any time ¢ at the two points UV, then 
we have 
(LD + P)z=Asinnt+ V—U : = Ch) 
(MD+Q)y—KDz+IDu=U—V . ; 7 (2) 
—KDy+(ND+R)z+JDv=U-V : . (3) 
(GD+S)u+IDy=0 . . (4) 
(HD+T)v+JDz=0 . : . (5) 
L=yt+z  . ; . (6) 
Here D is used for shortness instead of =, We may at once replace (1), (2), 
(3), and (6) by the following :— 
{(L+M)D+P+Q}y+ {(L—K)D + P}z+IDu=Asinnt wap Ch) 
{(L—K)D+P}y+ {(L+N)D+P+R}2+JDv=Asinni me) 
There is no difficulty in finding y and z by means of (4), (5), (7), and (8); but 
the expressions are complicated, and I avoid them here. 
VOL. XXIX. PART IL. TN 
