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Let q,--Gn be the coordinates of a system, while the potential 
energy depends not only on the coordinates g, but also on certain 
“slowly changing parameters” @,.7,.... Suppose the kinetic energy 7 
to be a homogeneous quadratic function of the velocities sli 
while in its coefficients there occur besides the q,,q,.... eventually 
also the a,,a,.... Some original motion a) can be transformed into 
a definite other motion 2(«') by an infinitesimal slow change of the 
parameters from the values a,,a,.... to the values a,',a,'.... This 
special way of influencing the system may be termed “reversible 
adiabatic”, the motions @(a) and pa’) “adiabatically related”. 
Remarks: A. The addition “reversible” needs no further justification, 
if all motions that are considered are periodic. It becomes different 
if under the considered motions there are aperiodic ones as e.g. the 
motion in a hyperbola under the attraction according to Nrwron’s 
law. Here the addition loses its original meaning. By the introdue- 
tion of well-chosen coordinates, quasi-periodic motions as e.g. the 
oscillations of a conical pendulum or irrational motions of LrssaJovs 
may be treated as periodic ones. 
B. The definition given above needs generalization if the influence 
of a magnetic field has to be considered (Zerman-effect) or if we 
have to do with an electro-magnetic system (reversible, adiabatic 
compression of radiation by a mirror). 
§ 2. Formulation of the adiabatic hypothesis for systems with 
periodic or quasi-periodic motions. 
Let the values a,,,a,,..... of the parameters if the system be 
determined in any way. The quantum theory will not allow every 
motion 3(4,), Which can exist with these parameter values according 
to the fundamental equations of mechanics, but only some of them *). 
Therefore we speak of the motions Bfa,} as ‘‘admissible” for the para- 
meter values @,,,@,,..... To another set of values of the parameters 
a,,a,.... there belong then ‘admissible’ motions Bat. 
Now the adiabatic hypothesis may be formulated as follows: 
For a general set of parameter values a,,a,,... only those motions 
are possible that are adiabatically related with motions possible for 
the special values a, a,,... (that is which can pass into these 
by a reversible change). 
Remarks: A. Because of some difficulties rising in that question, 
1) In order to avoid too many details, we leave aside that in PLANCK’s recent 
treatment of the theory of radiation only “eritieal’ motions are considered, besides 
which also the other motions are ‘admissible’. It is obvious how our discussion 
might be adapted to this new treatment 
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