1922.) Theory of Generalised Quanta. : 293 
orbit is equal to the space-total of phases of all similar orbits 
we should rather have the path of integration extended over the 
complete cycle from ryj, tO Min through nae, seeing that al- 
though p, is constant the phase-point in phase-space does not 
come back to itself until starting from rp;, we come back 
tO Tain through Pnow- ; 
A third objection to Sommerfeld’s treatment of the relati- 
vistic motion is that advanced by Planck and Schwarzschild also 
in regard to the azimuthal phase-integral. According to Som- 
merfeld himself the integral [aap is reducible to the form 
i pdq= nh only when a path may be obtained such that along it 
a, 
J pdqg=0. This however is not vossible owing to a minimum 
the relativistic Newtonian ellipse. While they meet all the 
objections stated against Sommerfeld’s theory they give results 
identical with those of Planck and Sommerfeld in the first 
three cases. The results obtained, however, in the case of 
the relativistic ellipse are at variance alike with those of 
Planck and of Sommerfeld as well as with those which Sommer- 
feld would have if he took the path of integration for the 
azimuthal phase-integral (as he at first did) from 7p, to Tnin 
through re. The central idea in this investigation is still 
that of Planck namely the structure of phase-space must 
ONE DEGREE OF FREEDOM. LINEAR OSCILLATOR, ROTATOR. 
We may write the quanta condition in the form 
[fae.a=nh ox | TeH=nb 
where H is the energy and T is the periodic time. 
