and the Theory of Quanta. 511 



As yet I have not been able to tell if also for molecules of 

 more than one degree of freedom the sam^ necessary and suf- 

 ficient relations hold between the adiabatic invariants on the one 

 hand and the fulfilment of Boltzmanns theorem on the oilier. 



Remarks. — A. In recent years it has become usual to 

 introduce the relations between probability and entropy (or 

 free energy) 



S = HogW (30) 



F=E-.T*logW (31) 



simply as a postulate. It might seem that in this case the 

 problem discussed in this paragraph becomes superfluous. 

 However, this method of treating only shifts the difficulty 

 to another point, as I have shown *. 



B f . A reversible adiabatic compression transforms black 

 body radiation into black body radiation, by which process 

 it is immaterial if a little piece of a black body is present 

 to act as a " catalyzator " or not. Similarly Maxwell's 

 velocity distribution in a gas consisting of point molecules 

 which exert no forces on each other is transformed into a 

 velocity distribution of the same kind by a reversible adia- 

 batic compression of the gas (in a rough-walled vessel), 

 independently of the occurrence of collisions between the 

 molecules %. Hence we may ask more generally: Does a 

 most probable distribution of states in an ensemble of mole- 

 cules (resonators) pass always into a most probable distribu- 

 tion when the ensemble is subjected to an adiabatic reversible 

 affection independently of the occurrence of interaction 

 between the molecules during the affection ? With the 

 exception of special cases, this question must be answered in 

 the negative §. 



* Paper D, Introduction. f Cf. paper C, § 4. 



\ Both examples have the following property in common : The pressure 

 depends only on the total energy of the system, it is independent of the 

 distribution of the energy over the different principal modes of vibration 

 or over the molecules. In the cycle compression, catalytic process, 

 dilatation, adiabatic process, the same amount of work is given to the 

 system as is taken from it. For general systems this is no longer the case. 



§ Without any calculation this maybe shown by means of the follow- 

 ing example : — Imagine an ideal gas with rigid ellipsoidal molecules ; the 

 walls of the vessel are replaced by a field of force which reflects only 

 the centre of gravity of the molecules (the reflexion is perfectly elastic) ; 

 if the gas is compressed adiabatically, without collisions between the 

 molecules taking place, the kinetic energy of the translators motion is 

 increased, but not the energy of the rotatory motion. If collisions 

 between the molecules do take place, this is otherwise. By a short 

 calculation it may be shown by the following example : — Point molecules 

 move up and down along a straight line between two fixed points A 

 and B, uninfluenced by any force. An elastic field of force is excited 

 infinitely slowly, so that in the end the molecules perform harmonic 

 vibrations about the centre of the line. 



