312 
limiting orbit, which will be discussed later (in connection with 
the zero-point energy) *). 
And thus an analogue has been obtained of the possible quantizised 
orbits which a negative electron can describe round the positive 
nucleus. The points D and £ lie in this latter case exceedingly close 
together, so that the discontinuity in the value of the radii of the 
possible orbits is almost complete. 
But for this the assumption is required that also for electron and 
nucleus the force acts periodically, e.g. through this that the positive 
nucleus executes a pulsating movement (analogous to the motion 
studied by BuJerknus)’). It may also be assumed that the nucleus 
always sucks in “ether” from its surroundings (which is led off to the 
4th dimension), the electron expelling ether in the same way. When 
a rotation is assumed to take place of the electron round an axis 
coinciding with the direction of the motiqn, the known equations 
can be derived of the electro-magnetic field *). 
But this cannot yet be fully discussed here. One thing at least 
is certain, that 2f the electrons revolve round the nucleus in definite 
orbits (in which the quantity 2 plays a part in the determination 
of radius and velocity), that then necessarily, in consequence of our 
above considerations, this same quantity 4 must play a part in the 
movement of the molecules in closed orbits round positions of 
equilibrium —- in consequence of which that quantity will naturally 
occur in the relation between E and 7’ which we derived in our 
previous paper, as analogue of PLancx’s relation; while the quantity 
v will be in connection with the time of revolution of the molecules 
in their closed orbits, which in its turn will again be in relation 
with the time of revolution 7’ of the electrons round the nucleus — 
as we saw above. 
Clarens, summer 1921. To be continued. 
1) On decrease of temperature such an abrupt succession of some ever 
narrower orbits is perhaps also possible for solid bodies, and this may 
possibly be brought in connection with some allotropic states, which are 
met with in many elements and compounds. 
*) Very suggestive in this respect is an old Paper, almost entirely forgotten, 
by VoicT in the “Journ. f. reine v. angew. Mathematik”, Band 89, on “Der 
leuchtende Punkt.” Vorar chiefly calculated the state of vibration close to 
this point, when either a periodic translatory movement, or a periodic rotatory 
movement was supposed. Later on KIRCHHOFF (Ibid 90, p. 34) considerably 
simplified Voict’s derivation. 
3) The assumption of expulsion of ether from the electron with the velocity 
of light would then also explain that the velocity of the electron can never 
exceed the velocity of light, and an idea can be obtained of the mechanics 
of relativity (factor 1—v*/c’). 
