84 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



elements must be in order that the Theory of Probabilities may 

 be applicable, the answer is, as many constituents as are necessary 

 to determine the mean values which define the state in the macro- 

 scopic sense (i.e., in the aggregate condition). An idea of the 

 extent to which Nature carries this subdivision is furnished by 

 the fact that one grain (avordupois) of air, under standard con- 

 ditions, contains, 



14 (io 20 ) molecules, 



i.e., millions of billions of particles! 



The last one of said prerequisites is " elementary chaos, " 

 and needs further elucidation and limitation; we will therefore 

 go into this feature at greater length. 



BOLTZMANN has used the term " molekular-ungeordnet " 

 (molecularly disordered) to designate this chaotic condition of 

 the particles, and PLANCK has introduced a more general term 

 still, " elementar-ungeordnet " (elementary disorder or chaos) 

 in order to make the method applicable to phenomena like radia- 

 tion, in which the elements are not atoms or particles but partial 

 oscillations of different periods. The essence of the matter seems 

 to consist in excluding from consideration all such regularities 

 in the conditions of the elements as would lead to results at variance 

 with the well-known laws of physical phenomena, justifying this 

 exclusion by the assumption that no such elementary regularities 

 obtain in Nature. This only means that not all of the many 

 molecular arrangements, which are conceivable from the purely 

 mechanical standpoint, are actually realized. For instance, 

 in an isolated gaseous system we could conceive of a succession 

 of elementary states at variance with the principle of conservation 

 of energy; such a set would obviously not be realized. This 

 exclusion or limitation leaves room for various hypotheses as to 

 said elementary disarrangement, but to be admissible they must 

 all permit -of the legitimate application of the Theory of Prob- 

 abilities, the best one being ultimately determined by its agreement 



