Page:Über die scheinbare Masse der Ionen.djvu/2

$10^{-12}$ cm, that is certainly not an arbitrarily small magnitude, but a lower limit.

The question of whether or not a real mass exists besides the apparent mass of an ion, is extremely important; because by that we touch the question of the relation of ponderable matter with ether and electricity. I am far away to announce a decision, but I would like to cite but a few questions whose resolution can potentially bring us further in that question.

The first question is whether an ion rotates in a magnetic field. Actually, we should expect that. Since if an ion is present, and if a magnetic field is caused, then a rotation arises, as it can easily be derived from the formation of induced currents. Of course this is also the case when the ion flies into an already existing magnetic field. The velocity of rotation will depend on the magnitude of the mass; if only apparent mass is present, and even a corresponding moment of inertia, then the rotation velocity has a certain value. If, however, a real moment of inertia is added, the rotation is slowing down. Unfortunately I can not find any phenomenon, from which we could conclude anything about this rotation.

A second means by which we maybe could decide the question of the relationship between the apparent and real mass is the following:

The value for the apparent mass was given above only in first approximation. If the velocity is such that it is comparable to the velocity of light, then additional magnitudes will be added. For a straight path of the ion we can calculate the intensity of the field and the size of the energy and deduce from that the mass factor. In general, the trajectory will be curvilinear through the influence of the magnetic field, e.g. circular; then the calculation of the mass factor will become more complicated, but it can be carried out. If we denote by $m_{0}$ the expression above and $q$ is defined as the ratio of the ion velocity to that of light, it follows in second approximation for the apparent mass of the ion in linear motion:

$m_{0}\left(1+{\frac {6}{5}}q^{2}\right){,}$

while in a circular motion the term with $q^{2}$ yields a different coefficient.

These terms of the second order could now perhaps become observable, because the velocity of cathode rays increases up to a third of that of light, hence $q={\tfrac {1}{3}}$ and $q^{2}={\tfrac {1}{9}}$. To come to a decision, we could think of experiments as they were done by Lenard, to examine the influence of electric forces on the velocity of cathode rays. He has shown that the magnetic deflectability of the cathode rays, which is of course the smaller, the greater the speed, will change when the rays can pass through the space between two charged capacitor plates in the direction of the electric force lines.

We could measure the magnetic deflection in the case of an uncharged capacitor, then in the case of charge in one direction and then for the other direction. Thus we would obtain three different values of deflectability, between which a simple relation should exist, if the terms of second order could be neglected. If we measure each time the magnetic field-force required for a particular deflection, then the squares of these three field forces should form an arithmetic row. A deviation from this relationship would indicate that the terms with $q^{2}$ shall not be neglected, and that therefore in any case the apparent mass is noticeable. Detailed specifications could decide concerning the ratio between the real and the apparent mass, and concerning the question whether a real mass exists. It turns out that by Lenard's experiments we were near to decide about the existence of terms of the second order.

(Self-lecture of the lecturer.)

Discussion. (Reviewed by the participants.)

W. Wien. I was recently concerned with similar issues, and would like to stress that Lenard has observed cathode rays at low velocities, triggered under the influence of ultraviolet light. There, he found a small value for the ratio of mass to charge, namely the decrease lies in the sense which is required by the theory.

I have tried to transcend over Lorentz's position, by posing me the question, whether it would suffice when we only consider the apparent mass and omit the inertial mass, and replace it with the electromagnetically defined apparent mass to present the mechanical and electromagnetic phenomena in an uniform way. Because the magnetic and mechanical phenomena are only connected by the energy principle so far. I've tried to pose the question as to whether we could try by Maxwell's theory,