Page:Zur Theorie der Strahlung bewegter Koerper.djvu/15

 This becomes by differentiation of equation (3):

Since this energy is located in a cylinder of height $$D$$, then the energy quantity falling upon $$B$$ in this direction is:

$\frac{2\pi i_{0}D}{\mathfrak{B}^{3}}\cdot\frac{\mathfrak{B}_{-}^{2}}{\sqrt{1-\sigma^{2}\sin^{2}\phi}}\sin\phi\ d\phi$|undefined

Previously (§ 1) we saw, that from the incident radiation $$2\pi\ i\ cos\phi\ sin\phi\ d\phi$$, the fraction $$2\pi\ i_{0}\ \cos\phi \sin\phi\ d\phi$$ is absorbed, while the fraction $$2\pi\ p_{1}\ \cos\phi \sin\phi d\phi$$ is transformed into work. Thus from the totality of the incident energy quantity, the fraction $$\tfrac{i_{0}}{i}$$ is absorbed and the fraction $$\tfrac{p_{1}c}{i}$$ is transformed into work.

Thus from the just incident energy quantity, the fraction

$\frac{2\pi i_{0}D}{\mathfrak{B}^{3}}\cdot\frac{\mathfrak{B}_{-}^{2}}{\sqrt{1-\sigma^{2}\sin^{2}\phi}}\sin\phi\ d\phi\cdot\frac{i_{0}}{i}$|undefined

is absorbed; the fraction

$\frac{2\pi i_{0}D}{\mathfrak{B}^{3}}\cdot\frac{\mathfrak{B}_{-}^{2}}{\sqrt{1-\sigma^{2}\sin^{2}\phi}}\sin\phi\ d\phi\cdot\frac{p_{1}c}{i}$|undefined

is transformed into work.

In a similar way one recognizes, that the energy quantity

$\frac{2\pi i_{0}D}{\mathfrak{B}^{3}}\cdot\frac{\mathfrak{B}_{+}^{2}}{\sqrt{1-\sigma^{2}\sin^{2}\phi}}\sin\phi\ d\phi$|undefined

falls upon $$A$$, and that we have to multiply this energy quantity with $$\frac{i_{0}}{i}$$ and $$-\frac{p_{2}c}{i}$$ respectively, to obtain the fraction of them