292 G. H. BUY AN. 



mies, it is now obvious tliat a studj of tlie accélérations or second dill'e- 

 rential coefficients with respect to the time of tlie squares and products 

 of velocities of a dynamical system, will eûable us to détermine the law 

 of partition of energy in tliat System, and to lind the mean values of 

 thèse squares and ])roducts in order tliat the state may be stationary, if 

 we know the law of probabiiity of distribution of the coordinates of 

 the particles or bodies forming the system. 



(2) The présent method enables us to account for irréversible phe- 

 nomena in a system the éléments of whicli satisfy the équations of réver- 

 sible dynamies, According to this hypothesis, the property that „heat 

 always tends to flow from a liotter to a colder body" would hâve the 

 following dynamical interprétation: „When two Systems Â and B 

 are brought witliin each other^s influence, then if a certain inequality is 

 satisfied, energy will be accelerated from one system to the other and 

 the sign of the inequality will détermine whether the accélération takes 

 place from Â to B or from B to A." The inequality involving, as it 

 will, only squares and ])roducts of velocities, its sign will be unaltered by 

 reversing ail the velocities of the system, lience the difficulties encoun- 

 tered in connection with the study of the kinetic theory when the ques- 

 tion of reversibility isint roduced in connection with Boltzmann's Mini- 

 mum or //.-Theorem, will be obviated, 



(3) We hâve seen (Example 2) that in the case of binary encounters 

 in one dimension in a field of external force, Maxwell's Law of Partition 

 of Energy does not necessarily hold good. Erom the nature of the 

 mathematical reasoning it should be évident that what holds good in 

 this case, where the field of force is suj^^josed to be due to a fixed distur- 

 bing body, is also true in the more gênerai case when the disturbing 

 body is moving. Without examining more coinplicated cases, we can see 

 liow it may happen that in the case of a polyatomic gas, in wliich the 

 intermolecular forces are fiuite, the partition of energy between the 

 varions atoms of a molécule may not necessarily follow Maxwell^s Law. 



(4) The considération (Example 3) of a single particle moving in a 

 field of force leads us to généralise for the case of a particle in a field 

 due to the action of other particles. The results discussed above afi'ord 

 évidence for the possibility tliat in a non-isotropic solid, the mean squa- 

 res of the velocity components of an atom in difierent directions may 

 be unequal, and the mean products of the velocity components may 

 not vanisli unless the axes of référence are cliosen in certain directions. 



