Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/402

 

The ratio of the attraction to the repulsion is equal to that of $\nu \nu ^{\prime }$ to $n^{2}$. Hence, since the attraction and the repulsion are quantities of the same kind, $n$ must be a quantity of the same kind as $\nu$, that is, a velocity. If we now suppose the velocity of each of the moving planes to be equal to $n$, the attraction will be equal to the repulsion, and there will be no mechanical action between them. Hence we may define the ratio of the electric units to be a velocity, such that two electrified surfaces, moving in the same direction with this velocity, have no mutual action. Since this velocity is about 288000 kilometres per second, it is impossible to make the experiment above described.

770.] If the electric surface-density and the velocity can be made so great that the magnetic force is a measurable quantity, we may at least verify our supposition that a moving electrified body is equivalent to an electric current.

It appears from Art. 57 that an electrified surface in air would begin to discharge itself by sparks when the electric force $2\pi \sigma$ reaches the value 130. The magnetic force due to the current-sheet is $2\pi \sigma {\frac {\nu }{n}}$. The horizontal magnetic force in Britain is about 0.175. Hence a surface electrified to the highest degree, and moving with a velocity of 100 metres per second, would act on a magnet with a force equal to about one-four-thousandth part of the earth's horizontal force, a quantity which can be measured. The electrified surface may be that of a non-conducting disk revolving in the plane of the magnetic meridian, and the magnet may be placed close to the ascending or descending portion of the disk, and protected from its electrostatic action by a screen of metal. I am not aware that this experiment has been hitherto attempted.

 

I. Comparison of Units of Electricity.

771.] Since the ratio of the electromagnetic to the electrostatic unit of electricity is represented by a velocity, we shall in future denote it by the symbol $\nu$. The first numerical determination of this velocity was made by Weber and Kohlrausch^[1].

Their method was founded on the measurement of the same quantity of electricity, first in electrostatic and then in electromagnetic measure.

The quantity of electricity measured was the charge of a Leyden jar. It was measured in electrostatic measure as the product of the

1. Elektrodynamische Maasbestimmungen; and Pogg. Ann. xcix, (Aug. 10, 1856.)