AND OF THE SECOND LAW 13 



definitions. Indeed he may have feared over-precision and may 

 have trusted to the use he made of the terms at different times 

 to convey their meaning. 



Concerning some of the characteristics of BOLTZMANN'S hap- 

 hazard motion we take the following from Vol. I of his " Vorle- 

 sungen iiber Gas Theorie." 



If in a finite part of. a gas the variables determining the motion 

 of the molecules have different mean values from those in another 

 finite part of the gas (for example if the mean density or mean 

 velocity of a gas in one-half of a vessel is different from those in 

 the other half) , or more generally, if any finite part of a gas behaves 

 differently from another finite part of a gas, then such a dis- 

 tribution is said to be " molar-geordnet " (in molar order). 

 But when the total number of molecules in every unit of volume 

 exists under the same conditions and possesses the same number 

 of each kind of molecules throughout the changes contemplated, 

 then the same number of molecules will leave a unit volume and 

 will enter it so that the total number ever present remains the same; 

 under such conditions we call the distribution " molar-ungeordnet " 

 (in molar disorder) and that finite distribution is one of the 

 characteristics of the haphazard state to which the Theory of 

 Probabilities is applicable. [As another illustration of the excluded 

 molar-geordnet states we may instance the case when all motions 

 are parallel to one plane.] 



But although in passing from one finite part to another of a gas 

 no regularities (of average character) can be discerned, yet infin- 

 itesimal parts (say of two or more molecules) may exhibit certain 

 regularities, and then the distribution would be " molekular- 

 geordnet " (molecularly-ordered) although as a whole the gas 

 is " molar-ungeordnet." For example (to take one of the infinite 

 number of possible cases) suppose that the two nearest mole- 

 cules always approached each other along their line of centers, 

 or if a molecule moving with a particularly slow speed always 

 had ten (10) slow neighbors, then the distribution would be 



