8 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



bination of these minute elements has always given the important 

 result that the vast majority of these micro-states belong to one 

 and the same macro-state or aggregate, and that only compara- 

 tively few of the said micro-states furnish an anomalous result, 

 and these few are characterized by very special and far-reaching 

 conditions existing between the locations and the velocities of 

 adjacent atoms. And, furthermore, it has appeared that the 

 almost invariably resulting macro-event is just the very one 

 perceived by the macroscopic observer, the one in which' all 

 the measureable mean values have a unique sequence, and con- 

 sequently and in particular satisfies the second law of thermody- 

 namics." 



" Herewith is revealed the bridge of reconciliation betv/een 

 the two observers. The micro- observer needs only to take up 

 in his theory the physical hypothesis, that all such particular 

 cases (which premise very special, far-reaching conditions between 

 the states of adjacent and interacting atoms) do not occur in 

 Nature; or in other words, the micro-states are in c elementary 

 disorder* (elemmtar ungzordnet). This secures the unique 

 (unambiguous) character of the macroscopic event and makes 

 sure that the Principle of the Growth of Entropy will be satisfied 

 in every direction." 



Before elaborating all that is implied in this hypothesis of 

 " elementary disorder " we will again point out that for each 

 macro-state (even with settled values of density and temperature) 

 there may be many micro-states which satisfy it in the aggregate. 



According to PLANCK, " it is easy to see that the macro-observer 

 deals with mean values; for what he calls density, visible velocity, 

 temperature of the gas, are for the micro-observer certain averages, 

 statistical data, which have been suitably obtained from the 

 spatial arrangement and the velocities of the atoms. But with 

 these averages the micro-observer at first can do nothing even 

 if they are known for a certain time, for thereby the sequence 

 of events is by no means settled; on the contrary, he can easily 



