Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/7

the black surface is moving in the positive or negative sense. Only the true relative radiation stems from the heat reservoir of the moving body, by which our terminology may be justified.

We want to denote the difference between the total and true relative radiation, as the apparent relative radiation.

The relation between absolute and total relative radiation is given from purely geometric considerations. Since the density of the radiation energy is a scalar quantity, it has naturally the same value for both reference systems. Thus if we are dealing with parallel radiation, then the relation of absolute radiation to the total relative one is $c:c'$.

If we now consider a light pencil, whose absolute beam direction enclose angles with ${\mathfrak {w}}$, whose magnitude lies between $\varphi$ and $\varphi +d\varphi$, and if the absolute radiation of this pencil is for example given by $2\pi \ J\ sin\varphi \ d\varphi$, then the corresponding total relative radiation is $2\pi \ J\ sin\varphi \ d\varphi \ c'/c$ according to the above; if we write this in the form $2\pi \ J'\ sin\psi \ d\psi$, then the corresponding equation (9) is:

(10)	$J'=J{\frac {c'^{3}}{c^{3}\cos \alpha }}$

Thus if we consider an arbitrary scattered radiation, then the "radiation intensities" of the absolute and total relative radiation behave as $1:c'^{3}/c^{3}\ \cos \alpha$; the densities of radiation, moving in the absolute and relative beam path in the unit of the opening angle, behave as

(11)	${\frac {J}{c}}:{\frac {J'}{c'}}=1:{\frac {c'^{2}}{c^{2}\cos \alpha }}.$

We now want to find out the relation between the total and true relative radiation. For this purpose, we consider a cylindric cavity $R$, whose base surfaces $A$ and $B$ shall belong to two black bodies, while the shell surface of the cylinder, as well as the external boundary of both black bodies, shall be perfectly reflecting surfaces. The cross-section of space $R$ shall be equal to 1; its height equal to $h$. Both space $R$ as well as the exterior space shall be totally free of ponderable