AND OF THE SECOND LAW 11 



(2) Further Elucidation of this Essential Condition of " Elemen- 

 tary Chaos." Sundry Aspects of Haphazard 



To gain as complete an understanding as possible of this funda- 

 mental idea we will now give the views of the several investigators 

 as to the physical features of this chaotic state. We have seen 

 how PLANCK, the chief expositor of BOLTZMANN, boldly excludes 

 from consideration all cases leading to anomalous results, because 

 of the very special conditions existing between the molecular data, 

 by assuming that these cases do not occur in Nature. PLANCK 

 reminds the physicists who object to the hypothesis of elementary 

 disorder because they feel it is unnecessary or even unjustifiable, 

 that the hypothesis is already much used in Physics, that tacitly 

 or otherwise it underlies every computation of the constants 

 attached to friction, diffusion and the conduction of heat. On 

 the other hand he reminds others, those inclined to regard the 

 hypothesis of " elementary disorder " as axiomatic, of the theorem 

 of H. POINCARE, which excludes this hypothesis for all times from 

 a space surrounded with absolutely smooth walls. PLANCK says 

 that the only escape from the portentous sweep of this proposition 

 is that absolutely smooth walls do not exist in Nature. 



The foregoing thought PLANCK has also put in a slightly dif- 

 ferent way. Appreciating that all mechanically possible simul- 

 taneous arrangements and velocities of molecules are not realized 

 in Nature, the concept of " elementary dirorder " implies one 

 limitation of the conceivable molecular states, namely that, 

 between the numerous elements of a physical system there exist 

 no other relations than those conditioned by the existing measurable 

 mean values of the physical features of the system in question. 



Another, briefer but equivalent, definition is that: " In Nature 

 all states and processes which contain numerous independent 

 (unkontrollierbar) constituents are in ' elementary disorder ' 

 (elementar ungeordnet)" The constituents are molecular ele- 



