1052 



said above on the extrapolation of the curve may possibly hold very 

 well for a curve with nol too many ups and downs. It quite loses 

 its validity when we have to do with a zigzag line. And the kinetic 

 conception exactly assumes in general such a zigzag course of the diffe- 

 rent macroscopic quantities — this course being always compared 

 with one that would be obtained by means of a lottery drawing. 



This objection brings into prominence a characteristic of the kinetic 

 theory which does not belong to its fundamental properties, but to 

 the desperate auxiliary methods of calculation. The foundations of 

 the theory teach us that the course of the processes takes place 

 according to mechanical laws. In order to calculate some results 

 however we suppose that some elements of the calculation may be 

 replaced by certain formulae borrowed from the theory of probability. 

 In every separate case the different intuitive images have to make 

 clear which foruiulae from this theory must be taken. We may 

 directly add that these formulae give just as regular natural laws 

 as those obtained in the ordinaiy way, so that until now the practical 

 kinetic theory does not show any deviations from tiie other physical 

 theories. 



In theoretical discussions however the applicability of the theory 

 of probability is generalized so far as to request that all possibilities 

 must be expected which would occur when at any moment the 

 values of the above mentioned 6iV microscopic quantities would be 

 determined by means of an ideal lottery. 



Now we can immediately give examples which are in contra- 

 diction with this demand. 



A closed vessel be divided into two by a wall. One part may 

 contain a gas in which Maxwell's partition law is fulfiled ; the 

 other part be emj)ty. At a definite moment a rather large opening 

 be made in the wall. Then it is impossible that the second part of 

 the vessel remains always empty in the following time. 



It is also excluded, that at an arbitrary moment determined by 

 lottery the molecules entered in this latter part will all have crept back 

 through the opening: the mechanical laws demand, that there exists 

 an inferior limit for the time which these molecules want to proceed 

 to the walls of the vessels and to return to the opening, this limit 

 being determined by the velocities and their directions of these 

 molecules, by the form and the extension of the vessel. 



Intuitively we are inclined to draw still much farther reaching 

 conclusions as to the further distribution of the gas over the two 

 halves of the vessel. On the other hand no one has ever calculated 

 in how far it is mechanically possible that e.g. after a homogeneous 



