AND OF THE SECOND LAW 21 



of the remaining motions are concerned, we might stop right here, 

 for the very nature of this hypothesis insures results in harmony 

 with experience, i.e., with the undisturbed operation of the laws 

 of probability. 



But if we do not stop here, preferring to examine some of the 

 special features of fortuitous motion, as detailed on pp. 10, 13, 14 

 and 17, we still see that by this hypothesis we have not removed 

 the haphazard character of the remaining motions in either the 

 unsettled or the settled state. For instance, we have not 

 removed BURBURY'S condition A. We must remember, too, that 

 in PLANCK'S briefest statement of "elementary disorder" (bot. of 

 p. n), two important features of haphazard are emphasized, viz.: 

 the independence and great number of the constituents. BOLTZ- 

 MANN in his Gas Theorie of course considers the special features 

 which underlie the application of the Calculus of Probabilities; 

 thus he says they are, the great number of molecules and the 

 length of their paths, which together make the laws of the colli- 

 sion of a molecule in a gas independent of the place where it 

 collided before. Neither has the introduction of the hypothesis 

 of " elementary disorder" done away with these special features. 

 There have simply been excluded rrom consideration such pre- 

 computed and prearranged regularities in the paths and direc- 

 tions of molecules as purposely interfere with the operation of 

 the laws of probability. We are still free to consider all the imagin- 

 able positions and velocities of the individual molecules which are 

 compatible with the mean velocity, density, and temperature 

 properly characteristic of each stage of the passage from the 

 unsettled to the settled state. For adequate haphazard we only 

 need the assumption that the molecules fly so irregularly as to 

 permit the operation of the laws of probabilities. Such a presen- 

 tation as this of course calls for complete trust that all the specified 

 requirements have been adequately met and BOLTZMANN'S emi- 

 nence as a mathematical physicist and the endorsement of his peers 

 must be our guarantee for such confidence and trust. 



