AND OF THE SECOND LAW 85 



in the whole with known facts or laws. Evidently by prearrange- 

 ment and precomputation there could be obtained molecular 

 arrangements which would establish long-continued regularities, 

 which would furnish mean results in the aggregate, that would 

 be at variance with the well-known behavior of Nature. All 

 such cases are here excluded. 



According to PLANCK the unregulated, confused and whirring 

 intermingling of very many atoms (in the case of a monatomic 

 gas) is the prerequisite for the validity of this hypothesis of 

 " elementary chaos." 



(2) Differences in the States of " Elementary Chaos " 



When we consider the general state of a gas we need not think 

 of the state of equilibrium, for this is still further characterized 

 by the condition that its entropy is a maximum. 1 



Hence in the general or unsettled state of the gas an unequal 

 distribution of density may prevail, any number of arbitrarily 

 different streams (whirls and eddies) may be present, and we 

 may in particular assume that there has taken place no sort of 

 equalization between the different velocities of the molecules. 

 To conceive of said differences we may assume beforehand, in 

 perfectly arbitrary fashion, the velocities of the molecules as well 

 as their co-ordinates of location. But there must exist (in order 

 that we may know the state in the macroscopic sense), certain 

 mean values of density and velocity, for it is through these very 

 mean values that the state is characterized from the aggregate 

 (macroscopic) standpoint. The differences that do exist in the 

 successive stages of disorder of the unsettled state are mainly 

 due to the molecular collisions that are constantly taking place, 

 thus changing the velocity and locus of each molecule. 



Let us for sake of brevity speak of the state of permanence 



1 The rest of the paragraph is a repetition of what was stated at middle of p. 19. 



