1199 
two successive curves be equal to h. In the region outside the curve 
a =O each one of the curves possesses two asymptotes parallel to 
the axis of abscissae. The strip between two curves whose energy- 
constants differ by a finite amount has an infinite area. Just as in 
the case of the spiral orbits we may conclude that the energy stages 
of the stationary motions must be infinitely dense. very positive 
value of the energy-constant is therefore a “selected” value in the 
sense of the quantum theory. That hyperbolic orbits with all values 
of the energy are present, was already enunciated by Bonr on the 
ground of experimental results (by WaGner and others). From our 
point of view this does not prove that the hyperbolic motion is 
beyond the controll of the quantum theory; on the contrary this 
fact is a natural inference of a consistent application of this theory. 
This view naturally implies that the azimuthal impulse must also 
be subjected to quantic conditions. What these are cannot immedi- 
ately be deduced from the case of the elliptic motion. Two possibi- 
lities seem to present themselves: we must extend the integral | pdp 
either over the range of change of the codrdinate y, i.e. over the 
angle enclosed between the asymptotes, or, as in the case of the 
elliptic motion, from Oto 2. The former assumption would according 
to 2’ give 
nh (92) 
P=): . ail eee’ ve Bh ES a 
2p 
the latter 
nh 
De gone (95) 
7 
In $ 7 we shall meet with an argument in favour of the second 
assumption, but a decision between the two can ultimately only be 
brought by experiment. 
§ 5. Collision between an a-particle and an atomic nucleus. We 
shall now investigate the case of repulsive forces in detail and 
thereby take into account the motion of the nucleus, neglecting the 
relativistie correction which is of no importance for our purpose. 
In the usual manner by means of the principle of the centre of 
mass we eliminate the co-ordinates of the one body and so reduce 
the problem to that of a system of two degrees of freedom. We 
shall choose as the variables the relative polar co-ordinates of the 
two particles, i.e. their distance and the angle p under which the 
«-particle appears for an observer moving with the atomic nucleus, 
