686 Proceedings of the Royal Society 
there are in general more than one condition of balance, and in the 
former case, although one will very often suffice, two may occasion- 
ally be necessary. In the former class of cases we get relations 
between electric quantities of the same dimension, in the latter 
relations between quantities of different dimensions, e.g ., between 
coefficients of induction and resistances : so that when the 
frequency is known we can find a coefficient of induction in terms 
of a resistance, and so on. 
A new instrument is described called the differential telephone. 
It is an ordinary telephone only wound double like a differential 
galvanometer. The peculiar difficulties attending the construction 
of an instrument of this kind which will give no sound when the 
same current passes round its two parallel circuits in opposite direc- 
tions are explained, and the means of overcoming them pointed out. 
The method of using the instrument is explained. A multiple 
circuit of two branches A and B is inserted in a circuit containing 
a battery and an interruptor. A and B each contain one coil of the 
differential telephone, so that the currents pass in opposite direc- 
tion round it. A and B have self-induction coefficients, M and N, 
which can be varied at will by altering the configuration of certain 
coils in the two circuits. If the resistances of A and B be Q and B, 
then the conditions of equilibrium are shown to be M = N, and 
Q = K. There cannot be silence if either of these is unfulfilled, and 
if both are fulfilled there is silence for all frequencies of the in- 
terruptor. 
It is pointed out that the instrument, and in fact the telephone 
generally, is better suited for measuring coefficients of induction 
than for measuring resistance. 
A practical method for procuring a graduated scale of coefficients 
of induction is then explained. 
The mathematical theory of the disturbance of the balance in the 
differential telephone by two independent circuits E and F neigh- 
bouring to A and B is given. If S and T be the resistances, G and 
H the coefficients of self-induction, and I and J the coefficients of 
mutual induction with A and B of E and E respectively, then 
the following four conditions 
Q = R SJ 2 = TI 2 
M = 1ST GJ 2 4 HI 2 
