PROFESSOR CHRYSTAL ON: THE DIFFERENTIAL TELEPHONE. 611 
the core in AB and CD, so that when the currents are equal at every instant 
there is silence. 
In the single part of the line there is a battery G, and an interruptor F, 
which was sometimes a microphone attached to a clock, sometimes a tuning 
fork, but oftenest a piece of watch spring attached to the pendulum of a small 
clock which grated over a milled head at the lowest part of each swing, and 
thus made a momentary contact. The last arrangement uses the least current, 
which is an advantage, but it also has the great virtue of being the most power- 
ful noise-producer that I have been able to find. 
The mathematical theory of the above arrangement, which is appended to 
this paper, shows that there can be silence in the differential telephone when, 
and only when, the resistances of both branches of the multiple arc are equal, 
and also their coefficients of self-induction. It is of no consequence what 
induction there is between the two branches. 
When these two conditions are fulfilled there is silence for all frequencies, 
so that it is of no consequence what kind of interruptor we use. 
There are thus two adjustments. If either of the two be not perfect, 
alteration of the other will produce a minimum of sound, but never absolute 
silence. 
This is a simple instance of a principle in telephone measurements, the 
neglect of which has, I believe, hindered the success of many experimenters. 
They have tried to do that with one adjustment which could be done only with 
several. Hughes’ induction balance, as used with the sonometer, is an instance 
in point; severalinstances of multiple adjustment are given below, and the 
general theory of the matter is discussed (see p. 615). 
The mathematical expression for the square of the amplitude of the 
difference of the currents in the two coils, is a fraction whose denominator is 
essentially positive, and whose numerator is 
4n’n'(M—N)’ + (Q—R); 
where M and N are the coefficients of self-induction of the two branches, Q and 
R the resistances, and 7 is the frequency of the harmonic disturbance of the 
current. From this formula it is clear that the differential telephone is more 
sensitive to differences of coefficients of induction than to differences of resist- 
ances. Its proper use, therefore, is to compare induction coefficients, and not 
as a delicate resistance measurer. 
In practice Q and R are first made equal by some of the ordinary methods, 
and then the equality of M and N is adjusted. 
I have found that with 1000 ohms in each branch, the differential telephone 
is sensitive to differences of resistance up to about 1 per cent. only; whereas 
