1198 
But for our purpose it is important that these orbits are possible 
in principle irrespectively of how long an electron can move along it. 
Fig. 2. 
§ 4. Quantization of the hyperbolic curves. The problem becomes 
of greater importance pbysically, if repulsive forces are considered, 
so that the orbits are hyperbolic. The question, how these orbits 
have to be quantizized was discussed by me several years ago (I.c.). 
The method adopted then, which was explicitly stated to be provi- 
sional, I do not wish to adhere to in all its particulars. But the 
fundamental idea of submitting such orbits to quantum-conditions 
still appears to me a sound one. Quite a long time ago I have in 
the Munich colloquium developed certain views on this subject 
which appear to me still to deserve attention. For simplicity we 
shall here disregard the relativity correction (¢c =o): the radial 
impulse according to (7) and (4) then assumes the form: 
1 1 
pa|/ 2ma+ dumei—p Whe strate 
r r 
For a <0 the motion is elliptical, for « =O parabolic, for a > 0 
hyperbolic. The aspect of the curves in the phase-plane (p,7) is 
seen in Fig. 2. The part of the plane, where « <0 is bounded by 
the heavily drawn curve « == 0, both ends of which approach the 
axis of abscissae asymptotically. Inside this region the curves are 
elliptic and it is easy to fulfil the condition that the area between 
