portions didn't lead to any correct result, since at that time, only the equation of Searle[1] for the energy of the electron was at our disposal as a theoretical foundation, from which the "longitudinal" mass indeed could be calculated by means of the energy theorem, i.e. the relevant mass for tangential acceleration, though not the "transverse" mass with which we have to do with respect to the electric or magnetic deflection perpendicular to the original trajectory as observed by me.
After the theory was supplemented by M. Abraham[2] by stating the strict formula for the transverse mass, the experiments have been repeated with improved setup[3], with the result, that the measuring-results are sufficiently represented by Abraham's formula within the margin of errors, i.e. that one can consider the mass of the electron as purely electrical.
In the calculation of the field for a rapidly moving electron, Abraham made the kinematic fundamental assumption, that the field of the electron is infinitely extended into the exterior, however, into the interior it is extended up to the surface of a sphere of constant radius . Within this sphere, the field shall be either zero (surface charge), or shall be decreasing according to a certain law (uniform volume charge). Thus the electron should behave the same way as a rigid sphere would behave, when Maxwell's equations for empty space are employed; in other words: the macroscopic behavior of electrons properly distributed on a certain surface or in a certain space, was formally transfered to the microscopic image of the individual electrons. The fundamental assumption on the constitution of the electron shall be denoted in the following as
rigid electron.
- ↑ G. Searle, Phil. Mag. (5) 44. p. 340. 1897.
- ↑ M. Abraham, Gött. Nachr. 1902.
- ↑ l. c.
