578 
(v is the frequency, 7’ the mean value of the kinetic energy with 
respect to the time), which in the special case of harmonic vibrations 
of one degree of liberty coincides with’) : 
The purpose of the considerations in this paper is: 
1. To formulate the adiabatic law as sharply as possible, at the 
same time indicating where this sharpness is failing especially with 
respect to non-periodie motions. 
2. sto indicate what great significance must be ascribed to the 
“adiabatic invariants” in the quantum theory. The discussion of the 
above mentioned invariant — especially will show how it forms 
Y 
a link between the adiabatic hypothesis on the one hand and the 
quantum hypothesis of Pranck, DeBije, BOHR, SOMMERFELD on the 
other hand. 
3. To point out difficulties, which rise at the application of the 
adiabatic hypothesis, as soon as the adiabatic reversible changes 
lead through singular motions. 
4. To show at least how the adiabatic problems are connected 
with the statistical mechanical bases of the second law of thermo- 
dynamics. The statistical mechanical explanation BoLTzMANN gave of 
it rests on statistical foundations which are destroyed by the intro- 
duction of the quanta. 
Since then a statistical deduction has been given of the second 
law for some special systems (e.g. for those with harmonic vibrations) 
but not for more general systems ®). 
Hoping that others may succeed in removing the difficulties I 
was not able to surmount, I will publish my considerations. 
Perhaps a close investigation will show that the adiabatic law 
may not be maintained in general. At all events W. Wien’s law 
seems to show that in the quantum theory a special place is taken 
by the reversible, adiabatic processes; that for them the classic 
foundations can be of most use. 
§ 1. Definition of the reversible adiabatic influence on a system. 
Adiabatic related motions: Ba) and B(a'). 
1) See A § 2, GS 2. The existence of this adiabatic invariant may be con- 
sidered as the root of Wien’s law. 
2?) Comp. P. EHRENFEST. Zum BoLTZMANN schen Entropie-Walirsch Theorem. 
Phys. Zschr. 15 (1914) p. 657 and § 8 of this paper. 
