76 Dr. W. F. G. Swann on Equipartition of 



hotter gas increases the motion o£ the molecules of the 

 cooler gas not by a sort of knocking process directed at 

 the centre of gravity, but by a very complex electromagnetic 

 process involving the structure of the atom. We do not 

 escape the difficulty by defining a perfect gas molecule 

 as one whose actions are representable in terms of the 

 positions and motions of its centre of gravity alone ; for 

 such a molecule would have its power of interacting with 

 radiation defined out of it. Neither do we escape the 

 difficulty by observing that the energy is approximately 

 expressible as the sum of terms corresponding to the motion 

 of the gas molecules alone. Indeed, the matter stands 

 somewhat in the following light : — The whole energy of the 

 system is approximately expressible as the sum of squared 

 terms corresponding to the molecules alone, and we may 

 reasonably expect approximate equipartition between these 

 terms, together with an approximate conformity to the 

 so-called perfect gas laws. Such a specification can, how- 

 ever, tell us nothing about the radiation or its relation to 

 the gas constant ; for it is only by the neglect of the 

 radiation that the approximate equipartition results. The 

 energy may, however, be expressible approximately, or 

 possibly exactly, in a much more fine-grained manner as 

 the sum of squared terms, some of which correspond to the 

 modes of setherial vibrations, and some of which owe their 

 origin in some way to the matter, and are apart from what 

 is ordinarily understood as radiation. When this mode 

 of expression is adopted, it becomes necessary to introduce 

 into the statistical theory determining the partition of 

 energy between the different terms, those restricting 

 relations, whatever they are, which provide for the per- 

 manent existence of the molecule as such. It may be that 

 some law other than equipartition will result ; but even if 

 equipartition does result, it is not to be anticipated that the 

 average energy of one of the coordinates which correspond 

 to the system as expressed in this fine-grained manner will 

 have any connexion with the average energy of a coordinate 

 of the system when the latter is expressed in the entirely 

 different and approximate manner in terms of the ordinary 

 coordinates and momenta of the molecules. It might be 

 thought that, although for the purposes of the radiation 

 theory it is necessary to represent the molecule in terms 

 of a large number of additional coordinates, yet the average 

 energy of one of these coordinates would be the same as the 

 average energy of the centre of gravity of the molecule 

 itself, just as the average energy of the centres of gravity 



