292 Journal of the Asiatic Society of Bengal. [N.S., XVIII, 
space so that in periodic orbits the integration is over one com- 
plete cycle. In Newtonian orbits of the relativistic type or other 
quasi-periodic orbits, where there is a regular forward or back- 
ward motion of the perihelion, this means a path of integration 
for | Pdr from Pin tO Tain through fnax, Of What amounts to 
the same thing, double the path from Ppp tO finaez. For the 
azimuthal phase-integral } pyip the path is taken to be just 
one cycle of 27 and not from Prin tO fin through free. 
The reason for this variation, as given by Sommerfeld, seems 
to be that attention should be directed not so much to the 
: It is at once possible, however, to raise certain theoretical 
objections to Sommerfeld’s theory. In the first place the 
elementary volume | dq,dp, .. dq,dp, which is h/ after Planck 
cannot be represented as J dq.dp, . J dq,dp,... J dqydpy. This 
objection is met partially if on the authority of Epstein and 
Schwarzschild—and to this Sommerfeld agrees—the choice of the 
coordinates is determined by the possibility of separation of the 
prdr. On the other hand having in view the concepts of the 
time-total (Zeitgesamtheit) of phases and of the space-total 
(Raumgesamtheit) of phases employed in statistical mechanics 
and the proposition ! that the time-total of phases of a single 

| Ganz und Weber: Repertorium der Physik, p. 455 (1916). 

