Page:Zur Theorie der Strahlung in bewegten Körpern. Berichtigung.djvu/1

On the Theory of Radiation in Moving Bodies. Correction.

By Fritz Hasenöhrl.

In a paper of same title published a short time ago ^[1], I have stated the concept of an apparent mass of cavity radiation, and as its value I have given the quantity^[2]

${\frac {8}{3}}{\frac {h\epsilon _{0}}{c^{2}}}$

where $h\epsilon _{0}$ is the amount of radiation energy contained in the stationary cavity, and $c$ is the speed of light. Namely, this value was only valid when quantities of order $\beta ^{4}$ were neglected.

Now, M. Abraham was so kind to report to me by letter a new method for the calculation of this mass, yet which gives a different result.

Here, I state the simple method of Abraham with his permission, while I am using the notation of my cited paper. The total relative radiation in the cavity is given by^[3]

$2\pi i\sin \psi \ d\psi =2\pi i_{0}{\frac {c}{c'\cos \alpha }}\sin \psi \ d\psi$

The absolute radiation that corresponds to it, is:

1)	$2\pi i_{0}\left({\frac {c}{c'}}\right)^{4}\sin \varphi \ d\varphi$.[4]

Now, according to Abraham, the density of the electromagnetic momentum is equal to the absolute radiation divided by $c^{2}$.^[5] Thus if we calculate the total

1. F. Hasenöhrl, Ann. d. Phys. 15. p. 344. 1904.
2. l. c. p. 368. Equation (32).
3. l. c. p. 355. Equation (25).
4. l. c. p. 350. Equation (10).
5. M. Abraham, Ann. d. Phys. 14. p. 244. 1904.