Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/400



COMPARISON OF THE ELECTROSTATIC WITH THE ELECTROMAGNETIC UNITS..

Determination of the Number of Electrostatic Units of Electricity in one Electromagnetic Unit.

768.] absolute magnitudes of the electrical units in both systems depend on the units of length, time, and mass which we adopt, and the mode in which they depend on these units is different in the two systems, so that the ratio of the electrical units will be expressed by a different number, according to the different units of length and time.

It appears from the table of dimensions, Art. 628, that the number of electrostatic units of electricity in one electromagnetic unit varies inversely as the magnitude of the unit of length, and directly as the magnitude of the unit of time which we adopt.

If, therefore, we determine a velocity which is represented numerically by this number, then, even if we adopt new units of length and of time, the number representing this velocity will still be the number of electrostatic units of electricity in one electromagnetic unit, according to the new system of measurement.

This velocity, therefore, which indicates the relation between electrostatic and electromagnetic phenomena, is a natural quantity of definite magnitude, and the measurement of this quantity is one of the most important researches in electricity.

To shew that the quantity we are in search of is really a velocity, we may observe that in the case of two parallel currents the attraction experienced by $$a$$ length a of one of them is, by Art. 686, where $$C$$, $$C^\prime$$ are the numerical values of the currents in