s 



792 Prof. J. H. Jeans on the 



Thus in equation (39), instead of an integral of the form 



2e9 cos 2p0d{26), (44) 



we have an integral of the form 



§cf>{26) cos 2p9d{20) (45) 



The value of the integral (44) is 



2e 



e 2 +p 2 ' 



but, in virtue of the fact that -^ =0 when £ = 0, the value 



at 



of the integral (45) falls off as e~P p (where /3 is independent 

 of p) when ^? is very great*. 



This is perfectly in accordance with observation, and it 

 seems to be as far as the theory can be carried without 

 introducing special laws of force between electrons and 

 matter. This will be done in another paper. 



Conclusion. 



22. The result of § 20 seems to prove beyond reasonable 

 doubt that there is equipartition of energy between the 

 different vibrations of great wave-length, both in the interior 

 of the matter and in a cavity in the matter. 



Each vibration has the energy appropriate to a temperature 

 T which has been introduced into our analysis as the 

 temperature determined by the kinetic energy of the free 

 electrons. 



Two pieces of evidence identify this temperature T with 

 what we call the temperature of the matter. There is 

 first the evidence provided by the observed energy of radia- 

 tion of great wave-length f ; there is, secondly, the evidence 

 provided by the observed energy of the electrons escaping 

 from hot metals J. 



Thus we can say that the temperature of a solid is defined 

 equally well either by 



(i.) the mean energy of vibrations of great wave-length 

 in its interior ; or 



(ii.) the mean kinetic energy of the free electrons in its 

 interior. 



* ' Dynamical Theory of Gases,' § § 237-240. 



t Lumnier and Pringsheim, Verhand. d. deutscher phys. Gessellschaft, 

 1900, p. 163. 



% Richardson and Brown, Phil. Mag. xvi. p. 353. 



