Page:Messungen an Becquerelstrahlen.djvu/4

 By means of this arrangement, rays of a certain velocity find quite automatically the angle, at which the compensation occurs at a given field strength, and which allows them to leave the condenser. Thus electrons of all velocities and corresponding masses will hit upon the film, and thus produce a curve which allows to determine the mass as a function of velocity. Consequently, a single exposition suffices to test the various theories of the electron. The equations of motion of the electrons assume the following form:

Here, $$\epsilon,\ m$$ mean the specific charge and mass of the electron. The direction of increasing $$x$$ is the direction of the magnetic field $$\mathfrak{H}$$. While the $$X$$- and $$Y$$-axes coincide with the plane of the condenser plates, $$z$$ is perpendicular to this plane. Within the condenser, the direction of motion forms the angle $$\alpha$$ with $$\mathfrak{H}$$. Due to the spiral motion in the pure magnetic field, however, the direction deviates from the initial one, so that the impact point $$P$$ upon the film, lies in the direction $$\theta$$ which somewhat deviates from $$\alpha$$. If one integrates the preceding equations and if one sets $$\varphi=\tfrac{\epsilon}{m}Ht$$, then it follows:

If one furthermore sets $$OD=DP=\alpha$$, and

$u=\frac{F}{H\ \sin\alpha},$

then one obtains by repeated integration:

If one denotes the values of $$x, y, z$$ and $$\varphi$$ (present at the impact point of the electron) by index $$\Theta$$, and if one furthermore sets $$\tfrac{F}{2\alpha H^{2}}=K$$, then one finds:

By insertion of (3) into (1) and (2) it follows:

$$\alpha$$ is given from these equations, and from that the velocity of the ray hitting at $$P$$.

Since $$\theta$$ slightly differs from $$\alpha$$, one proceeds just so, as if the electron (which is hitting at $$P$$) would have moved with the previously calculated velocity at a circular path in a vertical plane, which passes through the radium granule and $$P$$.

Now, the force acting in the magnetic field is:

However, as it is shown by a simple calculation, it is:

Now if one considers, that according to :

then the relations (4), (5) and (6) give

While according to under employment of 's formula, and when we set $$\tanh\delta=\beta$$:

Obviously only that theory is valid, for which $$\tfrac{\epsilon}{m_{0}}$$ is a real constant for any value of $$\beta$$ within the observational errors.

The experiments.

I omit at this place the experiments, which I have undertaken to test my relativity principle. The report shall suffice,