of Edinburgh, Session 1879 - 80 . 687 
must be satisfied in order that there may be silence for all 
frequencies of the interruptor. 
It is also possible to obtain silence for a given frequency by 
satisfying two conditions, which are given. 
The bearings of this theory on practice are pointed out, and the 
reason explained why the induction balance as arranged by Hughes, 
does not give results than can be interpreted satisfactorily. 
The mathematical theory of the measurement of capacities is then 
given. If the armatures of two condensers of capacities X and Y 
be attached, by wires whose resistances may be neglected, to the 
circuits A and B, so as to include between them all the self-induc- 
tion of the circuits except that of the telephone coils, it is shown 
that there cannot be silence for all frequencies unless 
Q = R, M = X, X — Y. 
Another method is described for finding capacities in terms of 
resistances. In the circuit A of the differential telephone is in- 
serted a multiple arc, in one branch of which is a condenser of capa- 
city X, the resistance of this branch is Q". In the other branch 
there is resistance Q' and self-induction M'. The resistance and 
self-induction of the rest of A are Q and M, and the resistance and 
self-induction of B, R and X. The conditions for silence for all 
frequencies is 
M = N, Q' = Q" = R _ Q, and ^ = Q'X . 
This last of these conditions means that the time constants of the 
coil (M', Q') and the condenser (X, Q') shall be equal. When this 
is the case, the multiple arc behaves like a resistance Q', having 
neither induction nor capacity. 
It is proposed to apply the differential telephone to the measure- 
ment of coefficients of induction, and to the comparison of capacities 
and their evaluation in absolute measure. It is also expected to 
prove useful in measuring specific inductive capacity, in investi- 
gating the properties of electrolytes, and in examining the internal 
resistance and polarisation of batteries in action. It is possible that 
the method last described may afford an improved determination of 
the ratio of the electrostatic to the electro-magnetic unit. 
The rest of the paper is occupied with a discussion of the use of 
4 N 
VOL. X. 
