624 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
If the mutual induction be between the adjacent branches AB and BC, 
and if M=0 , N=0, the conditions for absolute silence reduce to 
LT—KU 
ST—RU=0, X= . 
Comparison of two Capacities.—If we attach condensers of capacities X and 
Y respectively by short thick wires to BC and DC, the conditions for absolute 
silence will be 
ST—RU=0, RX—-TY=0, 
provided the self-inductions of all the four arms of the bridge be negligible. 
Comparison af a Capacity with a Coefficient of Self-Induction.—If a con- 
denser of capacity X be attached to B and C, and if the resistance of its 
attachments be 8’, their self-induction being negligible, and if K=0, M=0, 
N=0, then the conditions for absolute silence are 
Sl =RU=0..8(=8,, S576. 
This is the equivalent of one of the methods given above for the differential 
telephone. 
We may also suppose V’=0 , K=0, L=0 , N=0 ; the conditions for 
absolute silence are then . 
ST—RU=0, XST=M. 
This arrangement is described by MAxwe ut, “ Electricity and Magnetism,” 
vol. ii. p. 377. 
All these arrangements are more or less troublesome on account of the 
imperfection of the correction for induction in ordinary resistance boxes. ‘This 
comes out very remarkably when attempts are made (as some have suggested) 
to employ the telephone instead of a galvanometer in measuring resistances 
with Wheatstone’s bridge. At what the galvanometer indicates as a balance 
even with nothing but coils from resistance boxes in the arms, the telephone 
sounds loudly, and alterations of the resistance up to one per cent. affect the 
sound but little. We are measuring, in fact, the inequalities of the coefficients 
of self-induction of the resistance coils. 
Added during printing.—There is yet another source of disturbance which 
will undoubtedly make itself felt in some cases, viz., the electrostatic capacity 
of the coils used for resistance or induction standards. I reserve the mathe- 
matical discussion of this correction until experiment has settled in what cases 
it will be of practical importance. It is scarcely necessary to point out that 
disturbances of this kind are not a peculiar feature in telephonic measure- 
ments; they appear equally in the older methods of dealing with electro- 
magnetic induction. 
