Partition of Kinetic Energy, 117 



rather to a small value, only because the conditions, or phases 

 as we have called them, corresponding to small values are 

 more probable, L e. more numerous. If there is considerable 

 available energy at any moment, it is because the condition 

 is then exceptional and peculiar. After a short interval of 

 time the condition may become more peculiar still, and the 

 available energy may increase, but this is improbable. The 

 probability is that the available energy will, if not at once, at 

 any rate after a short interval, decrease owing to the substitu- 

 tion of a more nearly normal state of things. 



There is, however, another side to this question, which 

 perhaps has been too much neglected. Small values of the 

 available energy are indeed more probable than large ones, 

 but there is a degree of smallness below which it is improbable 

 that the value will lie. If at any time the value lies extremely 

 low, it is an increase and not a decrease which is probable. 

 Maxwell showed long ago how a being capable of dealing 

 with individual molecules would be in a position to circumvent 

 the second law. It is important to notice that for this end it 

 is not necessary to deal with individual molecules. It would 

 suffice to take advantage of local reversals of the second law, 

 which will involve, not very rarely, a considerable number of 

 neighbouring molecules. Similar considei ations apply to other 

 departures from a normal state of things, such, for example, as 

 unequal mixing of two kinds of molecules, or such a departure 

 from the Waterston relation (of equal mean kinetic energies) as 

 has been investigated by Maxwell and by Tait and Burbury. 

 The difficulties connected with the application of the law 

 of equal partition of energy to actual gases have long been felt. 

 In the case of argon and helium and mercury vapour the ratio 

 of specific heats (1*67) limits the degrees of freedom of each 

 molecule to the three required for translatory motion. The 

 value (1*4) applicable to the principal diatomic gases gives 

 room for the three kinds of translation and for two kinds of 

 rotation. Nothing is left for rotation round the line joining 

 the atoms, nor for relative motion of the atoms in this line. 

 Even if we regard the atoms as mere points, whose rotation 

 means nothing, there must still exist energy of the last- 

 mentioned kind, and its amount (according to the law) should 

 not be inferior. 



We are here brought face to face with a fundamental 

 difficulty, relating not to the theory of gases merely, but 

 rather to general dynamics. In most questions of dynamics 

 a condition whose violation involves a large amount of 

 potential energy may be treated as a constraint. It is on this 



