Physics. — “On the principles of the theory of quanta. By Paur 
S. Epstein. (Communicated by Prof. P. Esrenrust). 
(Communicated at the meeting of January, 29, 1921.) 
1. Introduction. The quantum-theory in the form, which in 1911 
Pranck *) has given it, depends on the application of statistical mechanies 
in the so-called “phase-space” of the canonical position- and impulse- 
coordinates q,q,-...Qf; Pi P.--++- py, and consists in dividing this 
space into elementary regions of probability. The method obtains 
a considerable simplification for the soluble mechanical systems, 
since for them each impulse-coordinate p; = p;(q;). Instead of the 
2f-dimensional phase-space (f being the number of degrees of freedom 
of the system) it is then sufficient to consider the f ‘‘phase-planes” 
(pi, gi), which, as the author showed a few years ago’), gives great 
advantages in the treatment of these systems. In each of these planes 
the successive conditions of the system are represented by a curve. 
For the class of the “conditioned-periodic motions”, the only ones 
for which so far quantum-conditions have been established, the 
curves in question are as a rule closed. The only exception is formed 
by the “cyclic coordinates” which bear the character of a plane 
angle; a cyclic coordinate varies from 0 to 2a and the corresponding 
impulse is constant; hence the representive curve becomes a segment 
of a straight line parallel to the axis of abscissae. *) 
Puanck’s hypothesis, as extended by SommurreLp and the author, 
consists in the assumption of the existence among the states of the 
system of certain preferential or ‘‘stationary” motions, which are 
represented by discrete curves in the diagram, the area of the phase- 
plane between two successive stationary curves being equal to the 
universal constant / 
[fea SPT leh A rte 4 
If the area of the narrowest of these curves (or for cyclic coor- 
1) M. Pranck. Verhandelingen van het Solvay-congres. 
2) P. S. Epstein. Ann. d. Phys. 50, p. 489; 51, p. 168, 1916. 
3) This case was discussed for the first time by P. EHRENFEST. Verh. d. 
D. phys. Ges. 15, p. 451. 1913. 
(A 
Proceedings Roval Acad. Amsterdam Vol. XXIII. 
