1922.] Theory of Generalised Quanta. 295 
rdr 
Be rdr 
ne mad 0 = 0 mans 7) = 1 min 
B ) Vener ee 
1 
n cols n E ne 
m= rata -se.,/™.| et en ac. 
2 E? 
0 ee 0 
H, = —E,= = which is in perfect accord with 
Sommerfeld’s expression BE niin if it is noticed that the 
(n + n’)*h® 
single number n really absorbs n’ and stands for n +n’. 
For the azimuthal phase-integral | Bip we have 
2n Pn’! = nh. 
THEORETICAL CONSIDERATIONS UNDERLYING THE PRESENT 
MODE OF WRITING THE QUANTA CONDITIONS. 
(i) One degree of freedom; phase-integral :— 
I$ dt. 8H. 
In integrating with respect to ¢ over the whole period it is evi- 
ent that we are taking account of all phases through which a 
particular system passes with constant energy and in so doing 
we are also taking the space-total of all phases which all 
systems with a given energy siege in phase-space. In 
subsequent integration with respect to H, therefore, we om 
accounting for the whole of phase-space corresponding to 
every variation of the energy. The poem cell in this 
phase-space having a volume equal to h we 
[fusn or [T8H=%. 
The phase- -space and the cell may be represented on a plane 
a oN I for the oscillator and by Fig. II for the rotator as 
oll Sse 
