PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 615 
To make the principles involved clearer, I shall suppose that we can obtain 
resistances absolutely without self-induction (a method for applying correction 
for residual induction is given below). 
G H is a multiple arc, one branch contains a condenser of capacity X, and 
has resistance Q”, but no self- 
induction ; the other branch has 
self-induction M’, and resistance Q’. 
The self-induction and resistance 
of the rest of the circuit EABF are 
M and Q; the corresponding quantities for the other circuit EDCF are N 
and R. The necessary and sufficient conditions for silence for all notes are 
Q’=%, R=Q+Q’, 
MEI, pa XO 
Q 
The last condition is simply that the time constant of the two branches of 
GH shall be equal; and we have the interesting result that a condenser and a coil 
can be so combined as to be equivalent jor all disturbances to a simple resist- 
ance. The action of the two is reciprocal; at first the current passes entirely 
into the condenser, then more and more passes through the coil, and at last 
when the current is stationary (wholly or for the moment) it passes entirely 
through the coil. The one acts as a sort of spring or buffer to the other. 
I believe that this method could be made most useful in practical testing, 
and that by means of a small coil with a movable iron core* empirically 
graduated, and a differential telephone capacity or self-induction could be 
measured with even greater ease than resistance. 
Fig. 2. 
General Theory. 
The following general discussion of the theory of the induction currents in 
a system of linear conductors, in one branch of which there is a harmonically 
varying electromotive force, will help to bring out the fundamental principles 
which underlie all the applications that follow. These priciples I believe furnish 
the key to the theory of the telephone, in so far as it is purely electrical; and it 
is on them that we must proceed in forming null methods of electrical measure- 
ment in which the telephone is to be used. 
et ara, £4 Sh x, denote the current strengths at time ¢ in the different 
circuits, and Asinné the varying external electromotive force in the first cir- 
cuit, there being no external electromotive force in any other circuit; then 2, 2,, 
* Strictly speaking, an iron core is inadmissible in measurements with the telephone, because it acts 
as a neighbouring circuit, and introduces disturbances that cannot be compensated in a simple manner. 
I have found, however, in practice that, when the core is made of thin wires well insulated from one 
another, these residual effects are so small as not to interfere with the results, where the utmost nicety 
is not required. 
