Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/20

to the latter, while the difference of the amount of apparent radiation, thus the energy quantity

$h\epsilon _{0}(\tau _{1}-\tau )$,

is the equivalent of the work to be performed in order to accelerate our system. Namely, the sign of $\delta w$ played no role at all in our reasoning; the process is thus reversible. The same is also true for a finite velocity change, which one indeed can imagine as caused by several repetitions of arbitrarily small changes of that kind. It's only necessary that it must be executed so slowly, that the radiation in $R$ is always in the state of equilibrium corresponding to the momentary value of velocity. Only then, the energy transformations accompanying the finite velocity change, are reversible.

This work, which is performed at any velocity increase, and gained at any velocity decrease, and which of course is added to the work against the inertial resistance in the ordinary sense, shows us that the ordinary kinetic energy of our system appears to be increased by the amount $h\epsilon _{0}\tau$; the state of facts is such, as if the mass of our system were increased by the amount $2h\epsilon _{0}\tau /w^{2}$. If we insert herein for $\tau$ its approximate value form (30), then this apparent increase of mass becomes independent from velocity, and namely equal to:

(32)	${\frac {8}{3}}{\frac {h\epsilon _{0}}{c^{2}}}.$

Namely, the introduction of this concept of an apparent mass caused by radiation, is completely analogous to the introduction of the electromagnetic mass. We also mention, that the relation of this apparent mass to the energy of the resting cavity is equal to $8/3c^{2}$: the relation of the electromagnetic mass of a spherical electron to the energy of the resting electron is (in the case of surface charge) equal to $4/3c^{2}$,^[1] thus of the same order of magnitude.

1. See for example, M. Abraham, Ann. d. Phys. 10. p, 151. 1903.