ON THE KINETIC THEORY OF GASES. 213 



because we can raise the temperature by compression alone. 

 So o )3, etc., cannot be independent of g ft, etc. 



18. A step towards the solution of the difficulty, and 

 one which may prove to be important, is taken in 

 Watson's book. He shows, namely, that although the con- 

 dition for permanence is never attained until the distribu- 

 tion of momenta is according to the law £ - h ^ +r \ and any 

 disturbance is gradually effaced by encounters between the 

 molecules, the function B always approaching its minimum, 

 yet the rate at ivJiick this ftrocess takes place depends en- 

 tirely on the nature of the disturbance. If, for instance, 

 the disturbance consists in giving to spheres of mass m 

 greater average energy of translation than those of mass 

 M in a mixture otherwise normal, and under ordinary 

 •conditions of pressure, etc., it will be reduced, as Tait 

 has shown, to half of its original amount in a very small 

 fraction of a second. On the other hand, suppose the sys- 

 tem of elastic discs described in Watson's book, or a 

 •system of elastic spheres, the centre of gravity of each 

 sphere instead of being at the centre of figure, being at a 

 small distance c therefrom. According to the above law the 

 spheres should have energy of rotation on average equal to 

 that of translation. Let the disturbance consist in a small 

 inequality in these average energies. It will be effaced 

 gradually by collisions, but at a rate per unit of time propor- 

 tional to c 2 , and therefore as slowly as we please. 



19. This fact alone will not help us much, because we 

 cannot suppose that the gas subjected to experiments for 

 determining y has not had time during the experiment to 

 attain to its permanent condition. But if it could be shown 

 that any cause exists always increasing the energy of 

 translation and diminishing that of vibration, and so creat- 

 ing a disturbance, while encounters are always effacing the 

 disturbance, the fact that the rate of effacement is very 



slow may be of great importance. For let -jf, be the rate at 

 which the disturbance f is produced by the unknown cause, 



rl f 



~r, the rate at which it is destroyed by encounters. 



