Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/405

 

by means of a differential galvanometer with shunts, determines the ratio of the primary to the secondary current.

In this experiment the only measurement which must be referred to a material standard is that of the great resistance, which must be determined in absolute measure by comparison with the Ohm. The other measurements are required only for the determination of ratios, and may therefore be determined in terms of any arbitrary unit.

Thus the ratio of the two forces is a ratio of equality.

The ratio of the two currents is found by a comparison of resistances when there is no deflexion of the differential galvanometer.

The attractive force depends on the square of the ratio of the diameter of the disks to their distance.

The repulsive force depends on the ratio of the diameter of the coils to their distance.

The value of $\nu$ is therefore expressed directly in terms of the resistance of the great coil, which is itself compared with the Ohm.

The value of $\nu$, as found by Thomson's method, was 28.2 Ohms^[1]; by Maxwell's, 28.8 Ohms^[2].

 

III. Electrostatic Capacity in Electromagnetic Measure.

774.] The capacity of a condenser may be ascertained in electromagnetic measure by a comparison of the electromotive force which produces the charge, and the quantity of electricity in the current of discharge. By means of a voltaic battery a current is maintained through a circuit containing a coil of great resistance. The condenser is charged by putting its electrodes in contact with those of che resistance coil. The current through the coil is measured by the deflexion which it produces in a galvanometer. Let $\phi$ be this deflexion, then the current is, by Art. 742,

$\pi ={\frac {H}{G}}\tan \phi$,

where $H$ is the horizontal component of terrestrial magnetism, and $G$ is the principal constant of the galvanometer.

If $R$ is the resistance of the coil through which this current is made to flow, the difference of the potentials at the ends of the coil is

$E=R\gamma$,

1. Report of British Association, 1869, p. 434.
2. Phil. Trans., 1868, p. 643; and Report of British Association, 1869, p. 436.