PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 621 
CoMPARISON OF CAPACITY WITH COEFFICIENT OF INDUCTION. 
In last case (fig. 4) let us suppose the branch of AB, which contains the 
condenser, to be removed, and let R and N now stand for the resistance and 
self-induction of the whole of one circuit of the differential telephone. Farther, 
let us suppose that the condenser branch of AB has resistance Q”, and self- 
induction M”. 
The equations of the systems now become 
(MD? +. Q'D)y'=A-B=(M'D?+Q’D+xy,. 1) 
(iD ODw—-E=E (AB), . . .- = @) 
ees ey PL) 
The condition y=7z gives SS Ean | . | gi 
(A+pD +vD?2+pD?)y=0 , Bos(5) 
where A= ae , 
pay +Q'Q"+(Q'+Q"(Q—B) +434. 
v= Q’M" + Q°M’ + (Q—R)(M’+ M”) + (Q’+.Q”)(M—N) , 
p=(M’+M”)(M—N)+M’M" . 
The condition for absolute silence is that these four expressions shall all vanish. 
Using the first of these conditions to modify the second and third, we may 
write the four 
Pee eas, -- © 
M(Q’—-Q)+(Q’+Q)(M-N)=0,.- © -  . @%) 
——eee 
re a ya ea Se 3) 
Let us first take the ideal case where M’”=0; the conditions then reduce to 
hoe . ©’ =’, M=Q7X , M=N. 
This case is only approximately realisable in practice, because the self- 
induction of the so-called inductionless resistance coils, is quite sensible when 
