708 
MR, J. J. THOMSON ON THE NUMBER OF ELECTROSTATIC 
with S, the condenser will be charged, and until it is fully charged, electricity will 
flow into it from the battery; this will produce a momentary current through the 
various arms of the bridge. When the moving piece P is in contact with Pi, the two 
plates of the condenser are connected, and the condenser will discharge itself through 
D Pi, and as the resistance of D R is infinitesimal in comparison with the resistance 
of any other circuit, the discharge of the condenser will not send an appreciable 
amount of electricity through the galvanometer. Thus, if we make the moving piece 
P oscillate quickly from R to S, there will, owing to the flow of electricity to the 
condenser, be a succession of momentary currents through the galvanometer. The 
resistances are so adjusted that the deflection of the galvanometer produced by these 
momentary currents is balanced by the deflection due to the steady current through 
the galvanometer, and the resultant deflection is zero. When this is the case there 
is a relation between the capacity of the condenser, the number of times the condenser 
is charged and discharged per second, and the resistances in the various arms of the 
bridge. 
As the investigation of this relation given in Maxwell’s c Treatise on Electricity 
and Magnetism’ is only an approximation, it may be worth while to give here an exact 
investigation of the relation between the capacity of the condenser and the resistances 
in the arms of the bridge; though we shall find that when the resistances have the 
values which they had in the present investigation, Maxwell’s formula is very nearly 
correct. This relation will enable us to calculate the electromagnetic measure of the 
capacity of the condenser. 
Let x be the current in A B 
y „ B S 
z „ DC 
then the currents in 
A C=x— (y+z) 
A D —y-\-z 
C B —x—y 
Let b be the resistance of A B 
a „ „ AC 
c „ „ AD 
(J „ » AC 
d „ „ B C 
The resistances of D hi, SB are so small in comparison with the other resistances 
that they may be neglected. 
