Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/399

 

Joule's Calorimetric Method.

767.] The heat generated by a current $\gamma$ in passing through a conductor whose resistance is $R$ is, by Joule's law, Art. 242.

$h={\frac {1}{J}}\int R\gamma ^{2}\,dt$,

(1)

where $J$ is the equivalent in dynamical measure of the unit of heat employed.

Hence, if $R$ is constant during the experiment, its value is

$R={\frac {Jh}{\int \gamma ^{2}\,dt}}$.

(2)

This method of determining $R$ involves the determination of $h$, the heat generated by the current in a given time, and of $\gamma ^{2}$, the square of the strength of the current.

In Joule's experiments^[1], $h$ was determined by the rise of temperature of the water in a vessel in which the conducting wire was immersed. It was corrected for the effects of radiation, &c. by alternate experiments in which no current was passed through the wire.

The strength of the current was measured by means of a tangent galvanometer. This method involves the determination of the intensity of terrestrial magnetism, which was done by the method described in Art. 457. These measurements were also tested by the current weigher, described in Art. 726, which measures $\gamma ^{2}$ directly. The most direct method of measuring $\int \gamma ^{2}\,dt$, however, is to pass the current through a self-acting electrodynamometer (Art. 725) with a scale which gives readings proportional to $\gamma ^{2}$, and to make the observations at equal intervals of time, which may be done approximately by taking the reading at the extremities of every vibration of the instrument during the whole course of the experiment.

1. Report of the British Association for 1867.