PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 619 
as may be seen by putting S=o and T=2. In this case there is absolute 
silence. The expression for the maximum value of y—z is 
n®#(M—N)? + (Q—R)? 
A, (p—n'py tnx?” 
where 
¢=MN+NL+LM+2KL—K?, 
“x=P(M+N)+Q(N+L)+R(L+M)+2KP, 
b=QR+RP+PQ. 
On account of their complexity I refrain from giving the corresponding 
formule in the general case, but they can be obtained without difficulty. 
COMPARISON OF CAPACITIES. 
Suppose the two circuits of the differential telephone to branch into 
multiple ares AB and CD, and in one of the branches of each of these multiple 
arcs let there be condensers of capacities X and Y respectively. Let the 
current strengths at any moment 
in these branches be y” and 2”, and 
suppose for the present that the 
wires in these branches are short 
and thick, so that their resistance 
Fig. 4. and self-induction may be neglected. 
Let the current strength, resistance, and coefficient of self-induction of the 
other branches of AB and CD bey’, Q’, M’, 2’, R’, N’ respectively, and the 
corresponding quantities for the rest of the two circuits of the telephone 
y, Q, M, and z, R, N respectively. Then A, B, &c., denoting the potentials 
at the respective points, and A, B, &c., their differential coefficients with 
respect to the time, we have the following equations :— 
(MD?+QDy'=A-B=zy’. . . . 
PE rere anes 1 velorwiiatos Het Gay 
(MD?+QD)y—KD2z=E-F—(A—B) .  .  . @) 
(ND? SRD KDy—Eh-F—(CHD), oa of! of. A) 
i ts Me , ; ! fe 3) 
Z2=2/ 42" : IG) 
