Page:Die Grundhypothesen der Elektronentheorie.djvu/3

as the quasi-elastic forces. This is the case according to H. A. Lorentz, when the dynamics of the electrons which oscillate in the interior of moving matter, is based on the following hypothesis:

E remains.

F and G are replaced by:

K. The electron filled with uniform volume- or surface charge when at rest, oblates when in motion, by contracting its diameter parallel to the direction of motion in the ratio ${\sqrt {1-\beta ^{2}}}:1$. It becomes a so-called Heaviside-Ellipsoid. H. A. Lorentz calculated the electromagnetic momentum for such an ellipsoid, from which both masses are given by my methods without further ado. He finds the longitudinal mass $\mu _{s}=\mu _{0}\cdot \left(1-\beta ^{2}\right)^{-3/2}$, the transverse mass $\mu _{r}=\mu _{0}\cdot \left(1-\beta ^{2}\right)^{-1/2}$. H. A. Lorentz shows, that his formula for the transverse mass is not substantially less in agreement with Kaufmann's experiments than the formulas of mine.

Due to K, on the other hand, the ratio of transverse and longitudinal mass is given equal to $\left(1-\beta ^{2}\right)$, yet because of F, G is is equal to $\left(1-{\tfrac {4}{5}}\beta ^{2}\right)$, when terms of fourth and higher order are neglected; thus when F, G are introduced instead of K into Lorentz's system of hypotheses, a birefringence of order ${\tfrac {1}{5}}\beta ^{2}=2\cdot 10^{-9}$ would be given for such bodies, for whose optical behavior the inertia of the electrons is decisive.

H. A. Lorentz finally remarks, that this influence of Earth's motion vanishes also for bodies with molecular motion, when the latter hypothesis is added.

L. The masses of the molecules are of electromagnetic nature.

We now want to examine hypothesis K more closely. H. A. Lorentz announces it with all restraint; he doesn't go so far as to state it as probable. Indeed, most serious objections can be raised against this hypothesis.

If such an electron is accelerated, its oblateness becomes increased; thus work must be performed against the electric forces. While (for the undeformable electron) the increase of energy is equal to the work performed by the external electric forces, this is not taken place here any more; the energy increase when the velocity increases, is greater as the work of the external forces.

The consequent development of hypothesis K forces us to assume (besides the inner electromagnetic forces) other inner forces which are non-electromagnetic, which determine the shape of the electrons together with the other ones. They would perform the necessary work during the contraction, being equivalent to the increase of electromagnetic energy of the electron together with the work of the external forces. The system of hypotheses A, B, C, D, E, K is incomplete, as long as one is not stating, according to which law these forces shall act.

The incompleteness of this system of hypotheses has the consequence, that one cannot be sure about the stability of an electron being subjected to those hypotheses. The motion of an oblate rotational ellipsoid of invariable form parallel to its rotation axis, is (as mentioned above) unstable. The confirmation is missing, that the non-electromagnetic supplementary forces are rendering stable the motion of the deformable electron.

The necessity to introduce non-electromagnetic forces shows, that the hypothesis of the deformable Heaviside ellipsoid, although it is mathematically simpler in a certain sense, is physically far more complicated though, as the hypothesis of the rigid spherical electron. The former fails indeed with respect to several equations, to which the latter gives a quite definite answer. I only mention the consequence drawn by P. Hertz^[1] from hypotheses A to G, that the electron can be brought by finite forces arbitrarily close to the speed of light, or even to the speed of light. The experiments of F. Paschen^[2] show, that negative electrons contained in the radiation of radium, possessing a much greater penetration capability and a much lower deflectability, as the quickest of the $\beta$ rays studied by Kaufmann. Here, the speed of light actually seems to be almost, if not entirely, reached. Here the paths followed (independently from one another) by the mathematical and experiments research, meet each other. – Hypothesis K, however, completely fails with respect to the question after the attainment of the speed of light.

From all of these reasons, it would be highly premature to abandon hypotheses F, G without further ado in favor of hypothesis K. Of course, the dynamics of the electron is, as any physical theory, subject to the continuing tests by experiment. It is to be hoped, that the experiments which are now started again by W. Kaufmann with tireless

1. P. Hertz, this journal, 6, 109, 1904. Untersuchungen über unstetige Bewegungen eines Elektrons. Inauguraldissertation. Göttingen 1904.
2. F. Paschen, Ann. d. Phys. 14, 164 and 389, 1904.