Page:Über die Konstitution des Elektrons (1906).djvu/44

2. Comparison with the theories of Abraham, Lorentz and Bucherer.

The function $\Phi (\beta )$ expressing the dependency of mass from velocity, has the following value (according to the three theories mentioned in the headline of this paragraph and which were closer described in the introduction):

I.	(Abraham)	$\Phi (\beta )={\frac {3}{4}}{\frac {1}{\beta ^{2}}}\left({\frac {1+\beta ^{2}}{2\beta }}\cdot lg{\frac {1+\beta }{1-\beta }}-1\right)$
II.	(Lorentz)	$\Phi (\beta )=\left(1-\beta ^{2}\right)^{-1/2}$
III.	(Bucherer)	$\Phi (\beta )=\left(1-\beta ^{2}\right)^{-1/3}$

The theory of Einstein leads to the same formula as the one of Lorentz, when one sticks to the equations of motion given by Einstein (l.c.); the somewhat deviating definition of mass for an observer co-moving with the electron given by Einstein, does not correspond