110 Physical Properties [CH. vi 



getting far apart from its neighbours except under the action of disturbing 

 forces greater than any which would occur in a system at the given tempera- 

 ture. In this system, though the oxygen and nitrogen cannot mix, each can 

 make an exchange of molecular energy with the surface molecules of the 

 diaphragm, and exchange of energy can go on within the solid diaphragm 

 itself without any exchange of molecules between distant parts of the 

 diaphragm. 



" Hence in this system, the average kinetic energy of a molecule of 

 oxygen will become equal to that of a molecule of nitrogen in the final state 

 of the system, that is to say, when the temperatures of all parts of the 

 system have become equal, and since in that final state we have pure oxygen 

 on one side and pure nitrogen on the other, we can verify the equality of 

 temperature by means of a thermometer. And we can now assert that the 

 temperatures, not only of oxygen and nitrogen, but of all bodies, are equal 

 when the average kinetic energy of a single molecule of each of these 

 substances is the same." 



Maxwell here rests his proof of the equalisation of temperatures upon 

 his investigation which in turn rests upon the assumption of "continuity of 

 path." This assumption, however, as we have seen, is not altogether satis- 

 factory. Various attempts have been made to establish the theorem of the 

 equalisation of temperatures without relying, in any form, upon this doubtful 

 assumption. In particular, two may be mentioned, due respectively to 

 Professors Bryan and Boltzmann and to Professor J. J. Thomson. 



126. Bryan and Boltzmann* imagine a system in which gases of two 

 different types a and yS occupy two distinct regions A and B. These regions 

 are separated by a layer S of finite thickness which is occupied by a mixture 

 of gases of types a and /8. The gases inside S are, however, acted upon 

 by fields of force, such that no gas of type a can pass into the region B, and 

 no gas of type ft can pass into the region A. 



With reference to this system, the following propositions follow from 

 Chapter V.: 



(i) The mean translational energy of the molecules of type a in the 

 region A is equal to the mean translational energy of the molecules of 

 type a in the region S. 



(ii) The mean translational energy of the molecules of type a in the 

 region S is equal to the mean translational energy of the molecules of type 

 /3 in the region S. 



(iii) The mean translational energy of the molecules of type /3 in the 

 region S is equal to the mean translational energy of the molecules of type 

 {3 in the region B. 



* Wien. Sitzungsber., HI. Dec. 1894. 



