( 494 ) 



same cases occur in such an ensemble, with regard to the distribu- 

 tion of velocities, as are considered as equally possible cases by 

 Boi.tzmann and Jeans. The difference in the way of treatment of 

 Gibbs on one side, and that of Boltzmann and Jeans on the other 

 consists besides in the fact that the one occupies himself with separate 

 velocities and the other not, in this that Gibbs treats the configuration 

 and the distribution of velocities at the same time (both belong to the 

 idea phase), whereas Jeans treats the latter separately, and Boltz- 

 mann does not occupy himself with the configuration in this connection. 



Every phase of Boltzmann (combination of velocities) corresponds 

 with as many phases of Gibbs (combination of velocities and con- 

 figuration) as the molecules can be placed in different ways with 

 that special combination of velocities. This number being the same 

 for every combination of velocities according to the independence of 

 the distribution of velocities and configuration following from the 

 fundamental assumption, it will be of no consequence, comparing 

 the different combinations of velocities inter se, whether we also take 

 the configuration of the molecules into account or not. So when 

 seeking the most probable distribution of velocities (that, with which 

 the most combinations of velocities coincide), we must arrive at the 

 same result whether we follow Gibbs or Boltzmann. 



It is obvious that the phases of the microcanonical ensemble meant 

 here are what Gibbs calls the specific phases. Gibbs distinguishes 

 namely between specific and generic phases : in the former we con- 

 sider as different cases those where we find at the same place and 

 with the same velocity, other, even though quite equal molecules, 

 in the latter we do not. In other words : in the former we consider 

 also the individual molecules, in the second only the number of the 

 molecules. So we may now say that in such a microcanonical 

 ensemble the most probable distribution of velocities and that which 

 will also occur in the great majority of cases (compare Jeans' 

 analysis discussed in the first paper) will be that of Maxwell. 

 When therefore an arbitrary mass of gas in stationary state may be 

 considered as taken at random out of such a microcanonic ensemble, 

 Maxwell's distribution of velocities or one closely resembling it will 

 most probably occur in it. In this way a derivation of' the law 

 has been obtained to which the original objection no longer applies, 

 though, of course, the assumption of the microcanonical ensemble 

 remains somewhat arbitrary *). 



] ) With the more general assumption of a canonical ensemble Maxwell's law is 

 derived by Lorentz: "Abhandlungen über Theoretische Physik", Lpzg. 1906 I, 

 p. 295. 



