( 634) 



dll 

 this not incompatible witli § 5, where it is proved that — can only 



be negative or zero? No, says Boltzman, for the reversed motion is 

 not one for which this theorem holds, because the motion is "molecular 

 geordnet". For the molecules, which a molecule with a certain velocity 

 meets, are not taken at haphazard from the whole number but 

 their velocities are connected with that of the molecule under con- 

 sideration. This is specially clear when at the moment of reversal 

 the motion had not yet lasted long. 



Now, however, Boltzmann meets with another dfiiculty, which is 

 to be removed. Does the increase of H not also clash with the laws 

 of probability, as the smallest H gives the most probable state ? 



No, for the increase of H is only improbable, not impossible. 



This diflTiculty seems to me to have only been raised by the in- 

 correct view discussed above. The smallest H is not the most pro- 

 bable. Moreover we do not do justice to the subjectivity of statements 

 concerning probability, when we speak of a transition from pro- 

 bable to improbable states, as if objective properties of substances 

 are expressed in this way. Boltzmann loses repeatedly sight of this; 

 particularly at the end of the second part of his "Gastheorie". 



In my opinion the views on this matter of Dr. A. Pannekoek, occurring 

 in these Proceedings, Vol. VI, p. 42 ') are not perfectly correct either. 



The latter assumes also that in the above mentioned case of 

 reversal the reversed motion is "molecular-geordnet", and tries now to 

 make clear what this means. With perfect justice he says, that it 

 does not mean, as seems to be sometimes assumed, that the state 

 may be calculated beforehand; this might also be done in the original 

 case if the initial state was known. Now, however, we get the im- 



1) Another remark on this subject. Under 2 we read : "one more remark, however 

 is to be added", on which something follows, that does not supplement what has 

 been said, but is in direct opposition to it. Moreover, tlie author seems to con- 

 found the collisions in the fictitious system (after reversal of the motions) and what 

 Boltzmann calls the collisions of the opposite kind. 



For it is not correct that the points QiQ/, R-^Bi return to Pj Pi' in the reversed 

 system; by reversal of the velocity we get a point of velocity lying diametrically 

 opposite to the first. 



Also 3 gives rise to different questions. As e. g. is it altogether correct that in 

 the statistical way of treatment the direction of the normal of collision is consi- 

 dered as independent of the velocities? It can certainly not be independent of the 

 relative velocity ? And further : does the fact, that in the calculations it is assumed 

 that the molecules do not hinder each other when colliding against a third, give 

 sufticient justification for calling the radius of a molecule small of the first order 

 with respect to the distances of the molecules? 



