The Fundamental Hypotheses of the Theory of Electrons.

By M. Abraham.

The theory of electrons, the most promising continuation of Maxwell's electrodynamics, is based on the following general presuppositions:

**A**. *The Maxwell-Hertz equations hold in space devoid of matter and electricity*. They postulate a reference system, in which plane electromagnetic waves are propagating in all directions with the same velocity cm/sec; motions related to this reference frame are called *absolute motions*.

**B**. *Electricity consists of discrete positive and negative particles, called "electrons"*. These are the ones, that convey the interaction of matter and aether.

**C**. *Every electric current is a convection current of moving electrons*. The density of the convection current is the product of density of electricity and its absolute velocity. *The convection current excites the same magnetic field, as the equivalent conduction current of the Maxwell-Hertz theory.*

From hypotheses **A, B, C** the field equations follow, specifying the velocity of electricity of the electromagnetic field at a given distribution. A statement is supplemented to them concerning the force (at a given field) acting upon a volume element filled by electricity:

**D**. *The electromagnetic force is additively composed of forces, acting in the electric field upon resting electrons, and in the magnetic field upon moving electrons.*

These four statements represent the general fundamental hypotheses of the theory of electrons.^{[1]} Every investigation based on them, and only such one, is to be denoted as belonging to the framework of the theory of electrons.

The phenomena observed at cathode rays, can be interpreted on the basis of **D**, when one considers the electromagnetic force of the external field as an external force, and one ascribes an inertial mass to the free electrons which are assumed to be in the cathode rays. On the other hand, the fundamental hypotheses **A, B, C, D** have led to the consequence, that this mass (at least partially) is the result of the field excited by the electron itself. The experiments of W. Kaufmann have shown, that at great velocities, the electromagnetic mass of the electron becomes of considerable influence.

In my investigations^{[2]} I have given a form to the dynamics of the electron, which suits to explain the experiments of Kaufmann on a purely electromagnetic basis. Thereby I have, besides the general fundamental hypotheses of the electron theory, introduced the following special hypotheses:

**E**. *The electromagnetic forces of the external field and the field excited by the electron itself, are in equilibrium at the electron in the sense of the mechanics of rigid bodies*.