589 
in a vessel with rough walls impacts between the molecules occur 
Or. noe*): 
yeneralizing the question might be put as follows: Is in an 
ensemble of molecules one most probable state converted into an 
other most probable one, if the molecules are subjected to a reversible 
adiabatic change also when no mutual action exists between the 
molecules ? In general this question must be denied. This is evident 
for the case that can be treated completely viz for that of molecules 
with one degree of liberty. The above mentioned supposition is only 
true, (but then always) when between the invariant for adiabatic 
processes and e and « there exists a relation of the special form 
ann 
e= AM +B) Eten ne ae AGN 
§ 9. Difficulties which occur, if the adiabatic reversible change 
gues rise to a singular motion. Non-periodic motions. 
These difficulties are already met with at the adiabatic change 
of an oscillation into a uniform rotation (remark § 6). In somewhat 
different form they occur, when the vibrations in an anisotropic 
field of force are changed in an adiabatic reversible way into those 
of an zsotropic field’). Let the mass of the moving point be one, 
the potential energy of the field of force 
D= ee an 
For the case of isotropy 
EN EE PE ek ee 
SOMMERFELD’s way of introducing the quanta may be characterized 
as follows’) : 
Only those motions are admissible, for which the moment of 
momentum 77° p and the total energy satisfy the equations: 
Za mr? f ot || eT a rr ee ce) 
a (alen AOR ien on € at ah oe ee oA) 
. 
(n and nw’ are arbitrary whole numbers). 
h The two mentioned cases have this in common, that the pressure depends 
only on the total energy of the system and not on the distribution over the diffe- 
rent principal vibrations (molecules). 
*) Already in 1912 in a paper “On energy elements” (Versl. Kon. Akad. 1912, 
DI. XX p. 1103), H.A. Lorentz drew the attention to the fact that in the quantum 
theory difficulties arise for isotropic resonators with two or three degreesof liberty. 
*) Comp Appendix. II. 
