# Page:Zur Thermodynamik bewegter Systeme (Fortsetzung).djvu/4

We base our calculation on the relative ray path. We consider radiation that encloses angles between $\phi$ and $\phi+d\phi$ with the direction of motion; it carries – in unit volume through the unit surface of a perpendicular (co-moving) plane – the energy amount:

$2\pi J\ \sin\phi\ \cos\phi\ d\phi.$

We call $J$ the intensity of the total (relative) radiation. If this radiation is incident upon an absorbing surface, it performs the pressure work:[1]

$q\cdot\frac{2\pi J\sin\phi\cos\phi\ d\phi}{c}\cdot \cos\varphi=2\pi J\sin\phi\cos\phi\ d\phi\ \beta\cos\varphi,$

where $\varphi$ is the angle between the absolute radiation direction and the direction of motion. The difference:

$2\pi J\ \sin\phi\ \cos\phi\ d\phi(1-\beta\ \cos\varphi) = 2\pi i\ \sin\phi\ \cos\phi\ d\phi$

 $i = J(1-\beta \cos\varphi)$ (19)
We employ the standpoint of Lorentz's contraction hypothesis and introduce the angle $\phi'$ by the equation
 $\begin{array}{rl} \operatorname{tg}\ \phi'= & \varkappa\ \operatorname{tg}\ \phi\\ \varkappa{}^{2}= & 1-\beta^{2}\end{array}$ (20)
2. This terminology agrees with the one used in an earlier paper (Ann. d. Phys., 15 [1904]). There, $i$ and $i_0$ was written instead of $J$ and $i$. See also Jahrb. d. Radioaktivität und Elektronik, 2, p. 283 (1905).