Page:Über die Möglichkeit einer elektromagnetischen Begründung der Mechanik.djvu/10

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here only 0,07 perc. An increase of mass compared to the electric charge at cathode rays of great velocity, is indeed contained in Lenard's observations.[1] Though the differences found by Lenard are much too great, to find their explanation in the electromagnetic inertia.

However, these quantitative measurements are still not to be seen as decisive.

If we confine ourselves to small velocities, then we have the same expression for the kinetic energy, that is stated by mechanics for the living force. The magnitude of acceleration, however, cannot be derived from that without further ado.

Acceleration presupposes a variability of velocity. The expressions for electromagnetic energy, however, are only derived under the assumption of a time-independent value of velocity.

For variable velocities, the problem of a moving electric quantum is not rigorously solved thus far.

Though we obtain from Maxwell's equations a criterion concerning the magnitude of the error made by us when we apply the expressions for energy to variable velocities as well.

The electric and magnetic polarizations are in our case, when the motion occurs in the direction x,

X=\frac{\partial U}{\partial x}\left(1-A^{2}v^{2}\right),\quad Y=\frac{\partial U}{\partial y},\quad Z=\frac{\partial U}{\partial z},

M=-Av\frac{\partial U}{\partial z},\quad N=Av\frac{\partial U}{\partial y},\quad L=0,

U=\frac{e}{\sqrt{r^{2}-A^{2}v^{2}\varsigma^{2}}},\quad\varrho^{2}=x^{2}+y^{2}.

Here, the coordinate system is rigidly connected with the moving point.

  1. P. Lenard, Wied. Ann. 64. p. 287. 1898 and l. c.