Page:Über die Konstitution des Elektrons.djvu/6

 alone, and partly from the connection with the value $$\tfrac{\epsilon}{\mu_{0}}$$ found with respect to cathode rays. The more or less precise degree of agreement then decides in favor or against the concerning theory.

The following three theories on the constitution of the electrons will be mutually compared:


 * 1. Rigid electron ,


 * 2. deformable electron ,


 * 3. deformable electron.

No. 1 and 2 are already mentioned; assumes that the electron is (like that of ) deformed into an oblate ellipsoid with axis-ratio $$(1-\beta^{2})^{-\tfrac{1}{2}}:1$$ (so called "Heaviside-Ellipsoid"), however, the perpendicular dimensions are increased and simultaneously the volume remains constant.

The function $$\phi\beta$$ expressing the dependence of mass from velocity, has the following value according to the mentioned three theories:

$\begin{array}{ll} 1. & \phi(\beta)=\frac{3}{4}\frac{1}{\beta^{2}}\cdot\left(\frac{1+\beta^{2}}{2\beta}\cdot\lg\frac{1+\beta}{1-\beta}-1\right)\\ \\2. & \phi(\beta)=(1-\beta^{2})^{-\frac{1}{2}}\\ \\3. & \phi(\beta)=(1-\beta^{2})^{-\frac{1}{3}}\end{array}$|undefined

Eventually, also a theory of electrodynamics recently published by has to be mentioned, which leads to consequences formally identical to those of 's theory, and consequently to which the second equation applies as well.

In the cases (1.) and (3) the following relations between the apparatus constants, the curve constants and $$\tfrac{\epsilon}{\mu_{0}}$$ are given from the equations (1.) to (3.):

In case (2.) (-) a separation of the variables is possible, so that one obtains as the trajectory:

where

and