PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 6135 
The instrument is now ready for measuring coefficients of self-induction 
that do not exceed twice the coefficient of mutual induction of either pair of 
coils when in close proximity. 
We can now proceed by the process of continual doubling to make standards 
and prolong the scale beyond this limit. Thus we completely solve the problem 
of measuring coefficients of self-induction, and hence, of course, the problem of 
measuring induction coefficients generally. All that remains to be done is to 
get the absolute value of our arbitrary unit v. 
Since the above was written, I have had an instrument constructed for 
giving varying self-induction with constant resistance. It is so devised as to 
give a scale of approximately constant sensibility, and at the same time to have 
a considerable range. I hope to be able soon to lay before the Society a 
description of this instrument, and of some results obtained with it. 
Action of Neighbouring Circuits. 
Another class of experiments of some interest may be made with the 
differential telephone. 
If a conducting body, say a coin or a closed circuit of wire, be placed upon 
one of the pairs of coils, or, better still, between the members of one pair, the 
balance is disturbed. The sensitiveness of the instrument to influences of this 
kind is very great. A penny placed between the coils restores the sound very 
markedly, a half-crown still more so; in fact, a single circlet of thin copper 
wire of the diameter of one’s middle finger, gives a sound which can be heard 
quite distinctly. These effects are analogous to those produced in HUGHES’ 
instrument. & 
I append to this paper the mathematical theory of these experiments, from 
which it appears that a disturbance produced by a neighbouring circuit in one 
branch of the differential telephone cannot be compensated for all frequencies 
of the current variation, by merely adjusting the resistances and induction 
coefficients within the two branches. This is another instance of multiple 
adjustment. 
The effect of a neighbouring circuit on one branch can be compensated by 
adjusting properly a neighbouring circuit to the other branch. If S and T 
denote the resistances, G and H the coefficients of self-induction, and I and J 
the coefficients of mutual induction with the respective branches, then the 
conditions for silence for all disturbances are 
\ G H 
Q=R, MEN, SJ2=TE, g=7- 
The last of these conditions is that the time constants of the two neighbour- 
ing circuits must be equal, a condition which might easily have been foreseen. 
We shall have other instances of a similar condition. 
