( 632 ) 



If we now assume (lifit for ^>! may be taken \/2pjt{ — j , we get 

 IZ ^^ — (o (hj Z/ij -\- «2 In^ -\- . . .) A^ C, and so Z is maximum when 

 to (?Ji i/ij-f «, Z ?ij-j-- •) 'S minimum or when \ f {^t\^) I f {^r^^) dï, dt] dC, 



is minimum, or when ^is minimum, if we have a simple gas. 



The distribution of the velocities ƒ (g ij ?) for which i/^is minimum, 

 is therefore also that with the greatest probability, concludes Boltzmann. 

 So the stationary state with Maxwell's distribution of velocities is at 

 the same time the most probable (p. 42). 



This, however, follows by no means from the above, for the 

 stationary state is that, for which the change of H luith the time in 

 consequence of the collisions = 0, whereas the most probable state 

 here is that for which every conceivable variation of the numerator 

 of Z= 0. 



Not before the condition is taken into consideration that the kinetic 

 energy of n molecules must have a deliuite value, as Boltzmann does 

 in Vol. 76 and 72, it can appear whether the result is the same. 



Now 



+ .0 +00 +CO 



// = ƒ ƒ ƒƒ (§ 7, g) i/iS ,i S) d§ dn </s 



must be minimum, while the conditions 



+ » +» +CC 



■•=SSS^ 



and 



+«> +=0 +CO 



L = '!ƒ ƒ ƒ (^^ + n' + il/iS n S) dè dn di 



00 — 00 — 00 



exist, when m is the mass of every molecule, and L the kinetic 

 energy of n molecules. 



In Vol. 72 p. 450 Boltzmann giv«s the solution of this, and it 

 appears that when no external forces exist, 



ifiê ni) + ^ + i^-i»^{è' + n' + g^) = o 



where X and fi are constants which are still to be determined. 



From this follows Maxwell's distribution of velocities. 



But what probability problem has now been solved ? I cannot see 

 that any has been solved but the following: From a box with slips 

 of paper, each indicating a volume element, one has been taken at 



