IX  
    R = radius of the sphere

The fact, that this path (seen from direction e - f) and its spatial derivative as well are continuous, needs no detailed explanation, since it was calculated under this condition. To prove the absence of kinks over the entire surface of the sphere, we have to look at this curve from two other directions as well, and check the continuity of the derivative. It will be sufficient if it is proven for the direction a - b. If the continuity of the derivative can be shown here, then it will be identical with the third independent view (eg. b - c). It can easily be shown that (Fig. 7).

Therefore, we have a completely continuous and kink-free closed path before us that circumscribes an octahedron that fits into the sphere. Further, we will have achieved the spherically symmetrical charge distribution required by quantum theory if we conduct the electron (initially by force) along this orbit. This orbit is even by pieces.

Now, we cheerfully tackle the answer to the question of how the electron shall be caused to wobble. In any case, there must be a force that does not perform any work (i.e. no changes in speed); only changes in direction should be permitted. This must be - as we assume - the Lorentz' force and we will look around for magnetic fields. They are also there; we only have to look in the direction of the arrows 1, 2, 3, or 4 and we will see continuous and in terms of their spatial derivative closed continuous ellipses that do not contradict our magnetic field theorem formulated at the beginning. Should the electron really swim on its own magnetic fields without the nucleus becoming aware of (Fig. 8)?

This will be the explanation for the standing De Broglie waves that had to serve as a model for the idea of steady orbits so far. Thus, these "standing waves" would turn out to be rotating magnetic fields.