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



old view o£ things, in which the coordinates of a hydrogen 

 and of an oxygen molecule were pictured as of different 

 classes, the theorem did really lead to a definite conclusion, 

 viz., that the average energy of the hydrogen molecule was 

 the same as that of the oxygen molecule ; for if we imagine 

 the p group of coordinates as drawn from the oxygen mole- 

 cules and the q group as drawn from the hydrogen molecules,. 

 then no matter how long may be the time for which we ob- 

 serve these groups, the^ group will always be exclusively 

 oxygen, and the q group will be hydrogen, so that the 

 equality of the averages as predicted by the theorem is, in 

 this case, a result of interest. 



Thus, as we have seen above, the absence of equipartition 

 of energy between the electrons inside and outside atoms 

 would not in itself lead to any contradiction with what might 

 be expected from a proper application of the theorem of equi- 

 partition. An apparent contradiction, to the application to 

 ordinary matter, of the general theory discussed on pp. 65-67, 

 would arise, however, when we found, as we should find, that 

 at any instant the number of coordinates in the system, 

 having magnitudes between assigned limits, was not given 

 by a formula of the type (2), with p replaced by the total 

 number of coordinates. The failure of the truth of this 

 result would mean that the system was not in the normal 

 state. 



Does equipartition of energy require that the energy of a 

 dynamical system with an infinite number of coordinates 

 should be infinite ? 



The chief field in which the question here referred to 

 becomes involved is that of temperature radiation, where 

 the coordinates of the system are associated with the modes 

 of vibration into which the radiation field can be analysed. 

 It is generally maintained that equipartition does lead to the 

 above conclusion, the argument being somewhat as follows: — 

 " Suppose that a perfect gas forms part of the system. If 

 T is the temperature, and if, further, we write RT/2 for the 

 average energy of a degree of freedom of the perfect gas, 

 then equipartition requires that the average energy of any 

 of the other degrees of freedom shall be RT/2. Since, in 

 the case of radiation, the number of modes of motion in the 

 aether — and so the number of coordinates — is infinite, and 

 since R can be measured and is found to be finite, th& 



