Page:Zur Theorie der Strahlung bewegter Koerper.djvu/9

 and

or

If we insert this into (2), then:

If we additionally put the energy content of the resting cavity $$R$$:

$\frac{4\pi i_{0}D}{\mathfrak{B}}=E_{0},$|undefined

then after execution of the integration

$L=E_{0}\frac{c^{2}}{\mathfrak{B}^{2}}\frac{1}{(1-\sigma^{2})^{2}}\left[\frac{1}{2}+\frac{1}{2\sigma^{2}}-\frac{(1-\sigma^{2})^{2}}{4\sigma^{3}}\log\frac{1+\sigma}{1-\sigma}\right].$|undefined

If we neglect herein magnitudes of order $$\sigma^3$$, then it becomes

$L=E_{0}\frac{c^{2}}{B^{2}}\cdot\frac{4}{3}.$|undefined

This expression has now the form and the dimension of a kinetic energy. Thus one can say, that the kinetic energy of our system was apparently increased by $$L$$,