( 638 ) 



K is now minimum when a^ ^ a^ = etc. or wlien v = constant. 

 It is obvious that this also means "the part of the generalized space", 

 is maximum or tlie chance is maximum. So on the above assump- 

 tion the most probable distribution is that of uniform density. 



Now Jeans proves further, that also by far the greater part of 

 the generalized space contains systems which ditfer infinitely little 

 from these with minimum K, so that this state may be called the 

 normal one. Expressed in the other way this is, that the chance is 

 infinitely great of a state deviating infinitely little from the most 

 probable state. Though Jeans' proof does not seem faultless to me 

 (no sufficient attention is paid, in my opinion, to the order of mag- 

 nitude of infinitesimals) yet the result seems to me to follow from 

 Bernoulli's theorem, provided "systems differing infinitely little" is 

 taken in the proper sense. 



So Jeans concludes -. it is clear that the gas-masses with uniform 

 density will represent (he ordinary case. 



The second problem might be treated in the same way. Instead 



of the molecules Avhich are to be distributed over the elements of 



volume of the vessel, we have now the velocity points of the 



molecules which are to be distributed over the elements of volume 



of the whole space. We get now in the same way for the part of 



the generalized space occupied by systems with a certiiin distribution 



'iV.' 



of velocities, the expression — ; — ; n— ^, but now iV is infinitely 



flj.' ct,.' . . . a„ 



large. According to the other mode of expression this is again the 



chance to that distribution of velocities. 



The treatment of the problem is further the same as that of the 

 first, but now Ave have to do with tlie quantity H. And finally it 

 may be proved, that by far the greater part of the generalized space 

 is occupied by systems which differ very little from that with mini- 

 mum ^ or the normal state is that for which i/ is about minimum, 

 from which, taking into account the condition that the energy = E, 

 Maxwell's distribution of velocities follows. 



Now it is, however, clear that the same objection may be raised 

 to this reasoning as to that of Boltzmann. 



The above expression for the part of the generalized space (or 

 the chance) rests on the assumption that the representative points 

 are distributed uniformly throughout the generalized space also here, 

 or that for every molecule the chance that the point of velocity 

 gets into a certain element of volume, is independent of the place 

 of that element. What now does the condition, that the energy 

 =: B, mean ? Either that attention has been paid to it in the distri- 



