556 
il 7,7 2 va 
ee Pads == erp: =| dq, +P; = | for dp, 
vp ( 
; eS 0 
27 
SOMMERFELD introduces the quanta by the equations: 
Jonan = Osby vey Kn te Gaye 
[fees dp, phere rt - ay @ oe EE 
These hypotheses are thus actually in harmony with the adiabatic 
hypothesis (comp. the formulation in § 3). 
Remarks. A: We see that the adiabatic invariants (22) and (23) 
do not only exist for the periodic motions about a centre of force 
Which attracts either according to the law of NewronN-Couroms or 
2 
\ a a 8 3 BE 7 
elastically (y= — or x= Sat but also for the quasi-periodic motion 
r 7 
(in a rosette) about a centre of force with general 4 (r, a). But in 
the first case are rn, =v», =v, so that the invariants can be taken 
together to: 
TT PE Ri ane 
+ *" — —_ adiabatically invariant 
vp DY 
(comp. here remark 4 of the appendix). 
B. Now it would be interesting to find the adiabatic invariants 
for more general quasi-periodic motions, (in the first place for 
anisotropie instead of isotropic fields of force). This would at the 
same time furnisb an answer to the question to which system of 
coordinates SOMMERFELD’s quantum hypotheses have to be applied *). 
C. If the attracting force obeys Covroms’s law, the hypothesis 
(23) is equivalent with PLanck’s*) new method of introducing the 
quanta, as has been remarked by SommerreLD (p. 455). This is also 
the case, when we have to do with an elastic attraction *). 
I have not yet succeeded in finding a more general connexion 
between the adiabatic hypothesis and PLanck’s new assumptions. 
D. In the refinement of his theory SommerreLD has still taken 
into consideration the dependency of the mass of the electron on 
1) A, Sommerretp. Zur Theorie d. Balmerschen Serie. Sitzber. Bayr. Ak. 1916 
p. 425—500; See p 455 at the bottom. 
*) M. Prancx. We again leave aside, that Pranck only speaks of “critical” 
motions, beside which also the other motions are “stable”. 
8) Comp. Appendix Il. 
