PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 625 
PART IL. 
ON CERTAIN EXPERIMENTS, MAINLY WITH THE DIFFERENTIAL TELEPHONE. 
The following experiments appear to me to be of interest, because they 
show that the theory of the telephone, in so far as it is purely electrical, comes 
well under recognised principles. In saying this I do not mean to prejudice 
the important acoustical questions that are as yet unsettled, or the difficult 
question as to the exact role of the magnetism of the core. 
I shall assume that there is a disturbing electromotive force, which is a 
simple harmonic function of the time, so that under all circumstances the 
current in the telephone circuit will also be a simple harmonic function of the 
time, of the same period, but in general of different phase. Representing the 
harmonic disturbance of the electromotive force by A sin né, I shall suppose in 
all that follows that A is independent of x. This corresponds practically with 
the case of a microphone-sender, where the variation is really in the resistance 
however.* In the case of the telephone-sender, or a sine-inductor, A is pro- 
portional to m, within certain limits. Neither of these laws, of course, is exact, 
for it must be remembered that magnetisation lags behind magnetising force,*t 
so that in all probability the amount of magnetism developed by rapidly alter- 
nating forces gets less and less as the frequency increases. In the case of a 
telephone-sender and a telephone-receiver this tells twice over. 
I shall further assume that, for a given bobbin, core, and vibrating plate, 
the intensity of the sound is proportional to the square of the amplitude of the 
harmonic variation of the current in the receiving telephone. In the case of the 
differential telephone, the two coils of which may be regarded as exactly alike, 
and similarly placed with regard to the core and plate, the square of the 
amplitude of the algebraic sum of the currents is. taken. 
It is needless to discuss the physical grounds for the above assumptions, for 
in all that follows the question is one merely of greater and less. Besides, the 
experimental basis for such a discussion is wanting, inasmuch as there is, so 
far as I am aware, no definite idea among physicists as to how the ear com- 
pares the intensities of notes of different pitch. 
Experiment 1.—If we use the differential telephone as a receiver, we may 
arrange it three different ways :—I. with only one coil in the circuit, the other 
being open ; II. with two coils in series (aiding each other, of course); III. with 
the two coils in circuit abreast, so as to form a multiple arc. 
Under all circumstances, the sound is louder with III. than with L., but in 
* See Aron, Wied. Ann. N.F., vi. p. 403. 
+ On this subject see two very interesting articles by Lord Rayueien, Phil. Mag., 1869, p. 8, 
and ser. 5, vol, iii. p. 46 (1877). 
VOL. XXIx, PART In 70 
