577 
the reversible-adiabatic changes for such more general motions might 
e.g. be calculated by the classic method, while in the calculation of 
other changes (e.g. of the isothermal addition of heat) the quanta 
already play a role. 
This was the starting-point in some papers in which partly PLANck’s 
hypothesis of the energy steps (¢ — nhr) was investigated in details") 
and partly its generalization from harmonic to more general motions 
was treated ®). Especially the following hypothesis was used, to which 
Einstein gave the name of adiabatic hypothesis *). 
« Adiabatic hypothesis” *). If a system is exposed to adiabatic influences 
the “admissible”? motions are transformed into ‘admissible’ ones. 
Let us suppose for some class of motions the quantum hypothesis 
to be introduced for the first time. In some cases the adiabatic hy po- 
thesis quite determines which special motions are “admissible”: namely 
in the ease that the new motion can be derived from a former class 
of motions by a reversible adiabatic process, for which has been 
fixed already, which special motions are “admissible” (especially there- 
fore if the new motions can be obtained from harmonic motions 
with one degree of liberty’’).’) 
In other cases the adiabatic hypothesis puts at least limits to the 
arbitrary way in which otherwise the quantum hypothesis might 
be applied. 
In each such application of the adiabatic law a great part is 
played by the “adiabatic invariants’, viz. those quantities which 
before and after the adiabatic process have the same value. Formerly 
there has been shown especially that for arbitrary periodic motions 
(of one or more degrees of liberty) there exists the adiabatic invariant: 
EER aorta nel or pas!) 
1) P, Enrenrest. Welche Züge der Lichtquantenhypothese spielen in der 
Theorie d. Warmestrahlung eine wesentliche Rolle? Ann. d. Phys. 36 (1911) p. 
91—118. [Further cited as communication A]. 
2) P. Enrenrest, Bemerk. betr. d. Spezif. Wärme zweiatomiger Gase. Verh. d. 
deutsch. phys. Ges. 15 (1913) p. 451. (Comm. B). — P. EHRENFEST. Ken 
mechan. theorema van BOLTZMANN en zijne betrekking tot de quanten-theorie. 
Versl. Amsterdam. XXII (1913) p. 586. [Gomm. C]. 
3) A. ErsrerN. Beiträge z. Quantentheorie. Verh. d. deutsch. phys. Ges. 16 
(1914) p. 826. 
4) Por the definition of the expressions used here comp. § Lee 
5) Comp. the transformation used in C § 3 of infinitesimal vibrations in uniform 
rotation, for other examples see $§ 7, 8 of this paper. 
6) Comm. B § 1. 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
