Page:Zur Theorie der Strahlung bewegter Koerper.djvu/2

These modes of conception were already spoken out by different authors.^[1]

In the following I've tried now, to apply these theorems upon the radiation in a moving cavity. Except the radiation provided by the walls, also radiation energy must be present within it, which is gained from mechanical work and which is transformed into such work again. It is essentially determined by the motion of the cavity; its amount is, as it will be shown, proportional to the square of the system's velocity (in first approximation), thus it apparently increases the kinetic energy of the system. Circumstances are thus present, that are quite analogous to the motion of an electron. In the same way as the concept of "electromagnetic mass" is introduced there, one could also speak about an "apparent mass" here, which is caused by radiation. In the same way, as the electromagnetic mass is proportional to the static energy of the stationary electron, also the apparent mass caused by radiation is proportional to the energy content of the stationary cavity. Namely, the proportionality factor is in both cases of the same order of magnitude. Now, since the heat content of every body partly consists of radiation energy, then every body must possess such an apparent mass depending on the temperature, and which is added to the mass in the ordinary sense.

1.

Now, we consider a cylindric cavity $R$, moving with constant velocity $c$ in the direction of the arrow (Fig. 1). Let ${\mathfrak {B}}$ be the velocity of light and $\sigma ={\tfrac {c}{\mathfrak {B}}}$. Furthermore, let $A$ and $B$ be two black surfaces.

The shell surface of the cavity as well as the outer boundary of the black body shall be formed by

1. See J. H. Poynting, Phil. Trans. 202, p. 525, 1904; Vl. v. Türin, Ann. d. Naturphil., III, p. 270, 1904; M. Abraham, Boltzmann-Festschrift, p. 84, and Drude, Ann. XIV, p. 236, 1904.