Page:A Dynamical Theory of the Electromagnetic Field.pdf/34

The quantity $v$ may be determined by experiment in several ways. According to the experiments of MM. Weber and Kohlrausch,

$v$=310,740,000 metres per second.

(81) It appears from this investigation, that if we assume that the medium which constitutes the electromagnetic field is, when dielectric, capable of receiving in every part of it an electric polarization, in which the opposite sides of every element into which we may conceive the medium divided are oppositely electrified, and if we also assume that this polarization or electric displacement is proportional to the electromotive force which produces or maintains it, then we can show that electrified bodies in a dielectric medium will act on one another with forces obeying the same laws as are established by experiment.

The energy, by the expenditure of which electrical attractions and repulsions are produced, we suppose to be stored up in the dielectric medium which surrounds the electrified bodies, and not on the surface of those bodies themselves, which on our theory are merely the bounding surfaces of the air or other dielectric in which the true springs of action are to be sought.

Note on the Attraction of Gravitation.

(82) After tracing to the action of the surrounding medium both the magnetic and the electric attractions and repulsions, and finding them to depend on the inverse square of the distance, we are naturally led to inquire whether the attraction of gravitation, which follows the same law of the distance, is not also traceable to the action of a surrounding medium.

Gravitation differs from magnetism and electricity in this; that the bodies concerned are all of the same kind, instead of being of opposite signs, like magnetic poles and electrified bodies, and that the force between these bodies is an attraction and not a repulsion, as is the case between like electric and magnetic bodies.

The lines of gravitating force near two dense bodies are exactly of the same form as the lines of magnetic force near two poles of the same name; but whereas the poles are repelled, the bodies are attracted. Let $E$ be the intrinsic energy of the field surrounding two gravitating bodies $M_{1}$, $M_{2}$, and let $E'$ be the intrinsic energy of the field surrounding two magnetic poles $m_{1}$, $m_{2}$ equal in numerical value to $M_{1}$, $M_{2}$, and let X be the gravitating force acting during the displacement $\delta x$, and $X'$ the magnetic force,

$X\delta x=\delta E,\ X'\delta x=\delta E';$

now $X$ and $X'$ are equal in numerical value, but of opposite signs; so that

$\delta E=-\delta E'\,$

or

${\begin{array}{ll}E&=C-E\\\\&=C-\sum {\frac {1}{8\pi }}\left(\alpha ^{2}+\beta ^{2}+\gamma ^{2}\right)dV\end{array}}$