580 
(comp. $ 9) T am not able to say whether the adiabatic law might 
be generalized to the real aperiodie motions and how this would 
have to be done. 
B. Some forms of adiabatic influence may be realized without 
difficulties, e.g. the increase of an electric or magnetic field in the 
neighbourhood of an atom (Stark and ZeEMan effect). Some others 
are more fictitious e.g. the change of a central force, (comp, § 7). 
At all events from the example of Wien’s law it is evident, that 
such a fiction may show the right way. Only further investigation 
and the control by experiment can teach where the “natural” adia- 
batie influencing becomes “unnatural”. At any rate the adiabatic 
law gives a statement that is the more positive the more multiple 
influencing we allow. 
§ 3. The adiabatic invariants and their application. 
Every use of the adiabatic proposition induces us to seek for 
“adiabatic invariants’, viz. quantities which remain constant at the 
change of a motion (a) into an adiabatically related motion p(@’). 
From the adiabatic proposition namely the following conclusion 
may be immediately drawn. 
If we assume that for the admissible motions Ba) a definite adiabatic 
invariant 2 has the discrete numerical values 2’, £2" for the special 
values (,,, dye, then it has exactly the same values for the admissible 
motions belonging to the arbitrary values of the parameters a, q,. 
2T € 
. . . . ed » ’ . . 
§ 4. The adiabatie invariant — for periodic motions and — 
p p 
especially for harmonic motions. *) 
Let us suppose that the considered system has the following 
properties: For fixed but arbitrarily chosen values of the parameters 
(sl, all motions of the systems that have to be considered, 
are periodic, for any phase (q10,-- ++ 0. (10, ---- Qno) the motion 
1) Comp. communication G $$ 1, 2. Other examples of adiabatic invariants 
are the cyclic moments, if the system has cyclic coordinates. If the rotation of a 
ring of electrons is influenced by an increasing magnetic field, this is the sum of 
its moment of momentum and its electro kinetic moment (ZEEMAN-effect, magneli- 
zation). If an increasing electric field acts on a hydrogen atom of Borr, then it 
is the moment of momentum with respect to the direction of the lines of force, 
At the change of the field of a central force (comp § 7) it is the moment of 
momentum. 
