OF THE ENERGIES OF A SYSTEM. 95 



n n 



-) /o _\9 ^2 ~j if w > 1 ; (294) 



if n > 2 ; (295) 



= . (296) 



If n = 2, e* p = 2 TT, and d<j> p /de p = 0, for any value of e p . 

 The definitions of F, V# and F^, give 



(297) 



where the integrations cover all phases for which the energy 

 is less than the limit e, for which the value of Fis sought. 

 This gives 





V=Cv p dV q , (298) 



and ,-j-r 9= 6 



e* = -~ f e^ p dV n , (299} 



de j 



where V p and e^ p are connected with V q by the equation 



p + e q = constant ~ e. (300) 



If n > 2, e*? vanishes at the upper limit, i. e., for e p = 0, and 

 we get by another differentiation 



q= 



We may also write 



6 2 = e 



F= J "P;/ 9 ^, (302) 



* r 

 =J 



(303) 



