Page:Über die Möglichkeit einer elektromagnetischen Begründung der Mechanik.djvu/7

This would only make sense, when one was able to increase or decrease gravitation, and to observe the disturbances caused by that.

However, since gravitation always acts invariably, only the extraordinary small changes caused by motion can come into question, which are of second order as shown by Lorentz.

The inertia of matter, which represents the second independent definition of matter besides gravitation, can be derived without further hypotheses from the concept of electromagnetic inertia, which is already employed many times.

We think of the electric elementary quantum as an electrified point. The forces and polarizations emanating from such a moving point, were derived by Heaviside.^[1]

Since equal amounts of positive and negative quanta are always moving together, thus, in a distance great against the their mutual distance, the forces emanating from them and the polarizations are neutralizing each other, except gravitation discussed before. Though we will assume in the following, that the extension of the quanta is so small compared to their distance, that the energy of any of them is so great, as if the second one would not be present.

According to a calculation by Searle,^[2] those polarizations emanate from an ellipsoid moving in the direction of its axis $a$ with velocity $v$, whose other two axes are $a/{\sqrt {1-A^{2}v^{2}}}$, and which carries the same charge upon its surface. The ratio of the axes therefore depends on the velocity.

The energy of such an ellipsoid is according to Searle

$E={\frac {e^{2}}{2a}}\left(1+{\frac {1}{3}}A^{2}v^{2}\right).$

The ellipsoid with the same axes, has the energy in a state of rest

${\mathfrak {E}}={\frac {e^{2}{\sqrt {1-A^{2}v^{2}}}}{2a\quad Av}}\arcsin Av.$

1. O. Heaviside, Electrical papers 2.
2. G. F. C. Searle, Phil. Mag. 44. p. 340. 1897.