( 631 ) 



another meaning-, and that the cirenmstance that H is minimum 

 implies that the probability of the corresponding distribution of velo- 

 cities, indicated by the function ƒ, is maximum. Afterwards the 

 connection between H and the entropy is indicated in § 8 on the 

 "Physikalische Bedeiitung der Grosse H" . 



The meaning of H in question being very incompletely derived 

 in ^ 6, we shall have to consult Vol. 76 of the Sitzungsberichte der 

 Wiener Akad., to which Boltzmann refers, and Vol. 72, to whicii 

 he refers in Vol. 76. 



In ^ 6 p. 40, Boltzmann begins with the following reasoning: 

 "Fur alle Zusammenstösse, für welche der Geschvvindigkeitspunkt 

 des einen der stossenden Moleküle ver dem Zusammenstösse in einem 

 unendlich kleinen Volumelemente lag, beflndet sich derselbe, wie 

 wir sahen, bei Constanz aller anderen, den Zusammenstoss charakte- 

 risirenden Variabeln nach dem Stosse wieder in einem Volumelement 

 von genau gleicher Grosse. Theilen wir daher den ganzen Raum 

 in sehr viele (§) gleichgrosse Volumenelemente w (Zeilen), so ist die 

 Anwesenheit des Geschwindigkeitspunktes eines Molekuls in jedem 

 solchen Volumenelemente mit der Anwesenheit in jedem anderen 

 Volumenelemente als ein gleichmöglicher Fall zu betrachten, gerade 

 so wie früher der Zug einer weissen oder einer schwarzen oder 

 einer blauer Kugel." 



So it is as if the velocities were assigned to the molecules by 

 taking for every molecule a slip of paper from a box, w'hich box 

 would be filled with slips of paper each indicating a unit of volume 

 of the "whole space". The probabilities a priori are therefore equal 

 that the components of the velocity è', 'i, ? He between two values 

 which differ d^, ch], f/?. 



Here at least something has been adduced to account for the fact 

 that these probabilities are equal, which has not been attempted in 

 Vol. 76 of the W. S. We have to derive it from the fact, that at 

 a collision the "points of velocity" skip from a certain volume into 

 one of the same size (cf. the "daher" of the quotation). For me 

 this has, however, by no means convincing force; for that one point 

 always skips from a volume to one of the same size does not prove 

 that it can just as well be found in any volume of the same size. 

 We shall presently show that this can hardly be assumed. 



But let us first proceed. Let us assume n molecules are to have 



a velocity, then the probability a priori that of them n, cu have their 



"point of velocity" in the first volume co, n, to in the second volume 



. , ., n! 



etc. IS proportional to Z = ; -— , where Cn.+n.-f...) io=zn. 



(«1 Oi) \ {n, to) ! . . . 



44* 



