1203 
Vp--p,’ 
a (o—9,) — ENE (20) 
it follows from (3) that 
p* po cos@ p'—p, sing 
e= : U — —. . (21) 
B 1—€cosw B 1—€cos 
For a motion of elliptic type (¢< 1) r and y are periodic in 
p and w witb a period 27; p and w are therefore angular coordi- 
nates of the problem and a Fourier-expansion is possible’). Passing 
to the case ¢ >1 the angle w becomes limited and varies between 
| ats 
the limits + arc cos (~) = +y. Only between these limits «and y 
é 
have the meaning of the functions given in (21); hence they may 
now be represented by a Fourrer-integral 
2 en 2 
ae DB on fear i 
a sE 
The case is different for p: this angle isi varies between two 
Bin 
Vp po 
a physical periodicity: on changing @ by the amount 2a the same 
point of space is reached, so that # and remain periodic with 
respect to p. We may continue the dependence on in the ranges 
extreme values == + p; but in contrast with w it possesses 
PS pa and —a<p<— p, where no motion takes place, just 
as we like. It would be simplest to assume the continuance of the 
law expressed by cosp and sin p over the whole range from 0 to 
2a, in which case we should get 
te 
* cossh 
p) + cos (s p—q) | ds 
& cos 2 
“ahd 
It seems to me that in this result lies a confirmation of the 
reasoning of § 4. The coefficient of w is the number s which may 
assume any value, whereas the coefficient of is the whole number 
1. Extending Bour’s principles to this case we might conclude that 
the radial quantum which is subordinated to yw underlies no limi- 
tations, whereas the azimuthal quantic number can only change by 
1) These coordinates are not linear functions of the time. If we wish them to 
satify the latter condition, they have to be defined differently. But the conclusions 
to be drawn remain valid with this change in the definition. 
