Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/8

matter. This system shall move with velocity $w$ in the direction of the arrow (Fig. 2). The exterior space shall have the temperature 0° A (so that the system experiences no external resistance in its motion), while the black surfaces $A$ and $B$ shall have a certain temperature different from zero. (When the system described is at rest, it is completely closed with respect to the outside.)

Now, surface $A$ is left in unit time by a certain amount of total relative radiation; we pick out the radiation whose relative direction encloses angles between $\psi$ and $\psi +d\psi$ with the normal (and thus also with ${\mathfrak {w}})$). Let its amount be:

(12a)

$2\pi \ i\ \cos \psi \ \sin \psi \ d\psi .$

This radiation exerts a certain pressure upon $A$, whose component coinciding with the direction of the negative normal, we want to denote by:

(13)	$2\pi \ p_{1}\ \cos \psi \ \sin \psi \ d\psi .$

Since $A$ is moving in the positive sense, the work

(14)	$w\cdot \ 2\pi \ p_{1}\cos \psi \ \sin \psi \ d\psi$

must be performed form the outside in unit time, so that the uniform motion of surface $A$ remains conserved. If we denote the true radiation of $A$ by

(15)	$2\pi \ i_{0}\ \cos \psi \ \sin \psi \ d\psi .$

then according to the things said earlier:

$i=i_{0}+wp_{1}.$

The emphasized total relative radiation (12a) now hits plane $B$ moving in the negative sense, and there it will be partly transformed in mechanical work and partly it is absorbed. Namely, the relation of these two parts depends on the magnitude of the pressure exerted upon this surface by the radiation (12a) incident in $B$. So if we think for a