AND OF THE SECOND LAW 15 



independence could be maintained for an indefinite time only 

 by an infinite number of molecules. 



The place of collision of a pair of molecules must in our 

 Theory of Probabilities be independent of the locality from 

 which either molecule started. 



From all the preceding we must infer what measure of hap- 

 hazard BOLTZMANN considers necessary for the legitimate use of 

 the Theory of Probabilities. 



BOLTZMANN in proving his H-Theorem, 1 which establishes the 

 one-sidedness of all natural events, makes the explicit assumption 

 that the motion at the start is both "molar- und molekular- 

 ungeordnet " and remains so. Later on, he assumes the same 

 things but adds that if they are not so at the start they will soon 

 become so; therefore said assumption does not preclude the con- 

 sideration by Probability methods of the general case or the 

 passage from " ordnete " to ts ungeordnete " conditions which 

 characterizes all natural events. 



In fact these very definitions show solicitude for securing the 

 uninterrupted operation of the laws of probability. BOLTZMANN 

 intimates his approval of S. H. BURBURY'S statement of the con- 

 dition of independence underlying his work. 



Here S. H. BURBURY 2 simplifies the matter by assuming that 

 any unit of volume of space contains a uniform mixture of 

 differently speeded molecules and then says: 



" Let V be the velocity of the center of gravity of any pair of 

 molecules and R their relative velocity. Then the following 

 condition (here called ^4) holds: For any given direction of R 

 before collision, all directions of R after collision are equally 

 probable. Then BOLTZM ANN'S H- theorem proves that if con- 

 dition A be satisfied, then if all directions of the relative velocity 

 R for given V are not equally likely, the effect of collisions 



1 In BOLTZMANN'S H-Theorem we have a process (consisting of a number of 

 separately reversible processes) which is irreversible in the aggregate. 



2 Nature, Vol. LI, p. 78, Nov. 22, 1894. 



