Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/406

 

and the charge of electricity produced in the condenser, whose capacity in electromagnetic measure is $C$, will be

$Q=EC$.

Now let the electrodes of the condenser, and then those of the galvanometer, be disconnected from the circuit, and left the magnet of the galvanometer be brought to rest at its position of equilibrium. Then let the electrodes of the condenser be connected with those of the galvanometer. A transient current will flow through the galvanometer, and will cause the magnet to swing to an extreme deflexion $\theta$. Then, by Art. 748, if the discharge is equal to the charge,

$Q={\frac {H}{G}}{\frac {T}{\pi }}2\sin {\frac {1}{2}}\theta$.

We thus obtain as the value of the capacity of the condenser in electromagnetic measure

$C={\frac {T}{\pi }}{\frac {1}{R}}{\frac {2\sin {\frac {1}{2}}\theta }{\tan \phi }}$.

The capacity of the condenser is thus determined in terms of the following quantities:—

$T$, the time of vibration of the magnet of the galvanometer from rest to rest.

$R$, the resistance of the coil.

$\theta$, the extreme limit of the swing produced by the discharge.

$\phi$, the constant deflexion due to the current through the coil $R$.

This method was employed by Professor Fleeming Jenkin in determining the capacity of condensers in electromagnetic measure^[1].

If $c$ be the capacity of the same condenser in electrostatic measure, as determined by comparison with a condenser whose capacity can be calculated from its geometrical data,

$c=\nu ^{2}C$.

Hence

$\nu ^{2}=\pi R{\frac {c}{T}}{\frac {\tan \phi }{2\sin {\frac {1}{2}}\theta }}$.

The quantity $\nu$ may therefore be found in this way. It depends on the determination of $R$ in electromagnetic measure, but as it involves only the square root of $R$, an error in this determination will not affect the value of $\nu$ so much as in the method of Arts. 772, 773.

 

Intermittent Current.

775.] If the wire of a battery-circuit be broken at any point, and

1. Report of British Association, 1867.