614 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
There will be silence for a particular note whose frequency is =a , if 
h—n*v=0, p—n’p=0, 
where 
4=(Q-R)ST, 
p=(M—N)ST+(Q—R)(GT+HS), 
v=(Q—R)GH+(M—N)(GT+ HS) +SJ?-TP , 
p=(M—N)GH+GJ?—HI. 
A balance of this last kind would enable us to determine our arbitrary unit v 
in terms of a resistance, and hence to find its value in absolute C. G. S. units. 
For it will be observed that \ is of the third degree in resistance, while v is 
of the first degree in resistance, and of the second in coefficients of induction ; 
so that the first of the equations expresses a coefficient of induction in terms of 
n, and certain resistances, provided we can determine the ratios of the different 
coefficients, which we can do by means of the differential telephone itself, as we 
have seen. 
This method would, however, require an instrument for producing a pure 
simple harmonic variation of electromotive force. As no apparatus of this 
kind is at present at my command, I have not attempted to test its practi- 
cability. 
Comparison of Two Capacities. 
To test the equality of the capacities of two condensers, we may proceed 
as follows :— 
Let a balance be obtained with the two circuits of the differential telephone 
as usual, then select two parts of the circuit of equal resistance and equal self- 
induction ; or, what comes to the same thing, introduce two equal resistances 
having equal self-induction, say two 1000 coils from a resistance box, one into 
each circuit, and attach the two condensers by thick wires whose resistance 
and self-induction are negligible, so as to include these identical parts of the 
two circuits between them. There will then be silence when, and only when, 
the capacities are equal. 
From preliminary experiments, I believe that there will be no difficulty in 
comparing in this way capacities of the order of a microfarad to the zo g/gpth 
part. 
The application of this arrangement to the study of electrolytic polarisation 
is obvious, but I do not propose to enter on the matter here. 
Comparison of Capacity with Self-Induction. 
The following method allows us to measure capacity in terms of self- 
induction and resistance, or self-induction in terms of capacity and resist- 
ance :— 
