1922.] Theory of Generalised Quanta. 303 
co-ordinates are known the quanta-integrals may be written in 
the forms 
age n! +n! 
| ron=nn \ Bip, =Wh, | Wop =n"h, ete. 
0 0 0 
It is evident that a quanta-integral would tend to become 
infinite if the periodic time or the period of the positional 
coordinate is infinite, i.e. if the motion of the system in respect 
of that particular coordinate is not periodic. It would thus 
appear allowable to suggest that quantaic changes of energy- 
or momenta are a property of periodic or quasi-periodic mo- 
tions and that in cases where there is no periodicity the energy- 
changes or momenta-changes must be gradual—a fact which 
ensures finite values for the quanta-integrals. 
SumMMaARY. 
In this paper the suggestion has been made on theoretical 
grounds of statistical mechanics that the quanta integral in the 
case of one degree of freedom should be written in the form 
a 
\ TsH = nh 
0 
and that in the case of Newtonian elliptic motion both of the 
ordinary and the relativistic type quanta-integrals should be 
written in the forms 
| Td3H = nh, \ Dip =n'h 
7G 
lines of hydrogen and it is shewn that while the doublets and 
triplets receive no explanation, the behaviour of the Rydberg 
number may be regarded as equally satisfactory if not more so. 

