F. The Electron is not at all capable of any change of its shape.
G. It is a sphere with uniform volume- or surface charge.
Hypothesis F is thereby to be understood as a conditional equation in the sense of Hertz's mechanics. It by no means obliges us to speak about forces holding together the volume elements of the electron; on the contrary, it says that such a force can never perform work and thus it renders its introduction superfluous.
On the basis of hypotheses A, B, C, D, E, F, the dynamics of the electron of arbitrary shape can be developed in a purely electromagnetic way. The details of the behavior of the electron, however, essentially depend on its form. I have extended the investigation also upon the ellipsoid electrons of invariable shape; it was given, that the translatory motion of such an electron is only stable in the direction of the major axis. An oblate rotational ellipsoid cannot move parallel to the rotation axis; the slightest push would cause it to turn.
On the basis of hypotheses A to G, I have calculated the electromagnetic momentum of the electron. I have shown in general, how to derive from it the electromagnetic masses, namely the longitudinal and transverse mass. The formula obtained for the latter, represents the deflection experiments by Kaufmann with a satisfying precision.
However, the theory of electron has given to itself another goal; it demands to totally enclose the electric and optical properties of the bodies. The optics of transparent bodies satisfying Maxwell's relation, is included in the electron theory by assuming quasi-elastic forces, which pull back the electrons into their equilibrium states. The dispersion of the bodies is interpreted by introduction of the inertial mass of the electrons, which together with those quasi-elastic force, cause the existence of proper oscillations. The oscillating electron represents the simplest image of an illuminating point; the Zeeman effect in its normal form shows, that this image agrees with reality for a great number of spectral lines. The velocity of the electron oscillations is thereby so low, that the variability of mass plays no role. Hypotheses E, F, G thus don't come into play as long as the body itself is at rest.
The matter is different in the optics of moving bodies. The aberration phenomena show, that the universal reference system (see A) doesn't share the orbital motion of Earth around the sun. How does it come, that the electric and optical processes happening on Earth's surface, nevertheless show no influence of Earth's motion? This question was studied by H. A. Lorentz. He has shown, that the absence of an influence of first order in the ratio of Earth's velocity and the speed of light, can very well be brought into agreement with the fundamental hypotheses A to D of electron theory.
The negative result of experiments, whose sensitivity is sufficient to discover an influence of second order, provides considerable difficulties for the electron theory. In two papers, Lorentz sought to overcome these difficulties. In the second of the cited papers, he states a system of hypotheses, which are sufficient to give account for all negative experimental results:
H. Due to Earth's motion, the bodies experience a certain contraction parallel to the direction of motion.
This hypothesis explains the negative result of the interference experiment of Michelson. It also explains the absence of a force-couple upon a condenser obliquely located to the Earth's direction of motion, which Trouton and Nobel tried to detect in vain.
One can render hypothesis H plausible, by interpreting the molecular forces as electrical forces.
I. The quasi-elastic force, which bind the electrons in their equilibrium positions, experience the same change due to Earth's motion, as the electric and the molecular forces.
Hypothesis I can also be made plausible, by considering the quasi-elastic forces themselves as electric forces.
To explain the absence of birefringence in the rest state of isotropic bodies due to Earth's motion, which has been shown by the experiments of Lord Rayleigh and D. B. Brace, it is sufficient to add hypothesis I to hypotheses A, B, C, D, H for bodies satisfying Maxwell's relation. For dispersing bodies, however, at which the inertia of the electrons come into play, birefringence due to Earth's motion is only then excluded when the longitudinal and transverse inertial forces are changed in the same way,
- H. A. Lorentz, Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern. Leiden 1895.
- H. A. Lorentz, K. Akad. van Wetensch. te Amsterdam 1899, p. 507 and 1904, p. 809.