OF THE ENERGIES OF A SYSTEM. 97 



That is, V is the same function of e# as - - of e. 



When n is large, approximate formulae will be more avail- 

 able. It will be sufficient to indicate the method proposed, 

 without precise discussion of the limits of its applicability or 

 of the degree of its approximation. For the value of e^ cor- 

 responding to any given e, we have 



/ = e 



* de q = 6**+** de p , (308) 



where the variables are connected by the equation (300). 

 The maximum value of <f) p + <f> Q is therefore characterized by 

 the equation 



(309) 



de, de, 



The values of e p and e q determined by this maximum we shall 

 distinguish by accents, and mark the corresponding values of 

 functions of e p and e q in the same way. Now we have by 

 Taylor's theorem 



If the approximation is sufficient without going beyond the 

 quadratic terms, since by (300) 



P ~ P' = - ( e * - /) 

 we may write 



+^( d ^ P \'( d \}'-\(^ii^ 



2 *. ( 312 > 



where the limits have been made oo for analytical simplicity. 

 This is allowable when the quantity in the square brackets 

 has a very large negative value, since the part of the integral 



7 



