Page:Zur Theorie der Strahlung in bewegten Körpern. Berichtigung.djvu/3

 Therefore, the amount $$(2\varkappa-1)$$ stems from the total radiating energy in the moving cavity:

$h\epsilon_{0}(1-\beta^{2})^{-2}\qquad (=h\epsilon_{0}(\varkappa+\tau))$

thus

$h\epsilon_{0}\left(\frac{\beta^{2}}{1-\beta^{2}}+\frac{1}{2\beta}\log\frac{1+\beta}{1-\beta}\right)=\varkappa'h\epsilon_{0}$|undefined

from the heat supply of the walls, while the amount

is gained from the work.

This result is now in full agreement with the one of. Because the work which was spent to bring the system to a certain velocity, can be calculated from momentum by

$\int w\ dt\ \frac{dG}{dt}=\overset{\beta}{\underset{0}{\int}}wd\beta\frac{dG}{d\beta};$|undefined

if one inserts for $$G$$ its value, then the integration indeed provides the value $$h\epsilon_{0}\tau'$$.

If one neglects magnitudes beginning with order $$\beta^4$$, then it is

$\begin{array}{lr} \varkappa'= & 1+\frac{4}{3}\beta^{2},\\ \\\tau'= & \frac{2}{3}\beta^{2}.\end{array}.$

(These values are related to quasi-stationary, reversible velocity changes; twice of the work must be spent at sudden accelerations of the system. In the latter case, one obtains $$\tfrac{8}{3}\tfrac{\epsilon_{0}}{c^{2}}$$ for the apparent mass; the relevant calculation executed by me in an earlier work, is free of the mentioned calculation error. Though the concept of an apparent mass is probably to be confined to quasi-stationary motions.)

The following thermodynamic considerations remain unchanged in principle; one only has to understand by $$\varkappa$$ the