Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/22

 states considered earlier were quite independent from the constitution of the boundary of the cavity.

To avoid this difficulty, we want to imagine adiabatic changes of the radiation state in our cavity as of such kind, that a black body is present in the space surrounded at all sides by mirrors, yet whose capacity is so small, that its heat content can be neglected against the energy content of space $$R$$. The purpose of it is only to regulate the distribution of radiation in different directions, so that they remain in stable equilibrium when the velocity of the system is changed; simultaneously, it can serve to define the temperature of the radiation on the moving cavity, by setting the latter equal to the temperature of this small body.

Now we consider such a space moving with velocity $$w$$, which for example was earlier in connection with an extended black body, which had the same velocity (thus with a heat reservoir of certain temperature). Then the energy density

$\epsilon+\epsilon'=\epsilon_{0}\varkappa+\epsilon_{0}\tau.$

is present in this space. Now, if the velocity is changed by $$\delta w$$ to $$w\epsilon_1$$, then the black body absorbs the fraction $$h\epsilon=h\epsilon_{0}\varkappa$$ from the energy $$h(\epsilon+\epsilon')$$ initially present. (Let $$h$$ again be the volume of that space). However, due to the vanishing capacity of that body, this heat quantity must be equal to the heat given off by it when the velocity is changed. Yet according to the things said earlier, the latter must be proportional to $$\varkappa_1$$ ; thus $$\epsilon_0$$ must have been changed, for example to $$\epsilon_{0,1}$$, so that

$\epsilon_{0,1} = \epsilon_{0}\varkappa$.

The amount of true radiation thus remains unchanged, which actually was already clear from the outset. However, since $$\varkappa$$ changes with velocity, also $$\epsilon_{0}$$