ALL SYSTEMS HAVE THE SAME ENERGY. 119 

 From the last equation, with (298), we get 



= e~* V. (375) 



But by equations (288) and (289) 



-V,-?*. (376) 



Therefore 



e~* V e~ P "Pjj e = - ep\e . (377) 



Again, with the aid of equation (301), we get 



= (378) 



Vq=0 



if n > 2. Therefore, by (289) 



These results are interesting on account of the relations of 

 the functions e~$ V and -^ to the notion of temperature in 



thermodynamics, a subject to which we shall return here- 

 after. They are particular cases of a general relation easily 

 deduced from equations (306), (374), (288) and (289). We 

 have 



' ' r : , . w < 



f* 



=J 



The equation may be written 



g=< 



material points with this particular value of the energy as nearly as possible 

 in statistical equilibrium, or if we ask : What is the probability that a point 

 taken at random from an ensemble in statistical equilibrium with this value 

 of the energy will be found in any specified part of the circle? 



