Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/14

 to the emission of a moving surface. The mentioned authors confine themselves, however, to the case of perpendicular incidence or emission. Incidentally, has calculated by a different method the radiation pressure at perpendicular emission with the same result.

If we insert values (26) into (16), then we obtain the pressure upon the surfaces $$A$$ and $$B$$. For example, if we calculate the pressure acting upon surface $$B$$, and express this value for example by the density of the total incident radiation

$\frac{2\pi\ i\ \sin\psi\ d\psi}{c_{-}}=d$,|undefined

then we obtain

which of course is in agreement with the corresponding one of.

The pressure upon a moving mirror incidentally can be derived very easily from the mentioned hypothesis, and one also obtains the law of reflection with one stroke. It follows indeed immediately from it, that the intensities of the incident and reflected light behaves inversely as the wavelengths, and directly as the oscillation numbers.

§ 5.

Now we want to concern ourselves with the fraction of the energy in $$R$$, which is due to the apparent radiation and which is gained from mechanical work. If we set into (19) the values from (26) for $$p_{1}$$ and $$p_{2}$$, it becomes

$\epsilon'=\frac{2\pi wi_{0}}{c^{2}(1-\beta^{2})^{2}}\overset{\pi/2}{\underset{0}{\int}}\sin\psi\ d\psi\frac{\beta\cos^{2}\psi+\beta(1-\beta^{2}\sin^{2}\psi)}{\sqrt{1-\beta^{2}\sin^{2}\psi}}.$|undefined

We put