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

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9. Application to cavity radiation.

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

we call the true (relative) radiation. The true radiation intensity

i = J(1-\beta \cos\varphi) (19)

is crucial for the heat transport between bodies of equal velocity.[2]

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)
  1. M. Abraham, Boltzmann-Festschrift, p. 90, 1904. Compare for instance F. Hasenöhrl, Jahrb. d. Radioaktivität, 2, p. 281 (1905).
  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).