| 
| 

1922.] Theory of Generalised Quanta. 297 - 
The observation nay be made that the canonical coordi- 
determined by the system of coordinates (p,, g,, Ps, Ys - 
The elementary volume of this space would be 
: dq,dp,dq,dp,..dtdH. 
In the present case this volume= [dsopateH which can be re- 
presented as J dddp . J adtsH because p and H are independent 
constants while ® and 7' are functions of p and H respectively 
This volume, therefore, is equal to h? as Planck should have. 
POSSIBILITY OF REDUCTION OF THE pec QUANTA 
NTEGRALS TO SOMMERFELD’S FOR 
Writing the Hamiltonian equations of motion in the 
bilinear ao we 
(dgip — dpéq) = dt. dH. 
where d refers to a variation with the time and therefore _- 
the orbit and 8 refers to a ~ independent of the time 
In the particular case before 
( dq,3p,— dp, 3q, ) + dqgSp,=4 . 8H 
because, Po being constant, apy ace @) 
This may be put in the form 
(2, dq, ee a(», 84, ) + dq,dp,=dt . dH. 
Integrating this form over a complete cycle we have 
8 [¢ P, ia, |- £ »,%, | + 2rdpy =T7 . 3H. 
Since dp, ia, | —Q-—and this may be easily verified—there- 
fore we may write 
a[ ¢ a iu, | + 2ndp, = TSH. 
Integrating this equation from one orbit to another we have 
[¢ ptt, | + [ 2=r ] 7m , es 
