AND OF THE SECOND LAW 9 



with said given averages ascertain a whole host of different values 

 for the location and velocities of the individual atoms, all of which 

 correspond to said given averages, and yet some of these lead to 

 wholly different sequences of events even in their mean values," 

 events which do not at all accord with experience. It is evident, 

 if any progress is to be made, that the micro-observer must in 

 some suitable way limit the manifold character of the multi- 

 farious micro-states. This he accomplishes by the hypothesis 

 of " elementary disorder " about to be more fully defined. 



In passing we may here note for future use, that what has 

 just been said concerning macro-states (aggregates) with " settled " 

 mean velocity, density and temperature, applies also to states 

 unsettled in the aggregate, so far as concerns the manifold char- 

 acter of the conceivable constituent micro-states and the dif- 

 ferences in the mean character of their sequences. Even after 

 the above limiting hypothesis removes all illegitimate micro- 

 states, an enormously greater number of legitimate ones will be 

 left to constitute the number of complexions properly belonging 

 to the state contemplated. We may also add that it seems quite 

 evident that the numbers representing these complexions will 

 be different in the settled and unsettled states even if the latter 

 should ultimately possess the mean velocity, density and tem- 

 perature of the former. 



On the other hand, we also point out that for one and the same 

 set of external conditions the macro-state may itself vary very 

 greatly. When it has a settled density and temperature, it is 

 said to be in a stationary state, to be in thermal equilibrium and, 

 anticipating, we may add that it is then has maximum entropy, 

 in short we may say it is in a " normal " condition. But the 

 external conditions remaining the same, before attaining to 

 said " normal " ultimate state, it may pass through a whole 

 series of so-called " abnormal " states after it leaves its initial 

 condition. While it is in any one of these " abnormal " states, 

 it may be said to be in a more or less turbulent condition 5 



