198 ON THE DETERMINATION OF THE ATTRACTIONS 



JV 

 j i 'n * 1 



L ax, . . . dx 8 u =-*- 

 du 



, - a,")" + fo - o 1 + - + (* - O* + 



i 



'2) 2 



In this equation V is supposed to be such a function of x v 

 x z ...x s and w, that the equation (2) and condition (9) are both 

 satisfied. Moreover V" = 0, and F ' is the particular value of V 

 for which 



x t = x" ; #2 = a? 2 " ;. ..... a? g = a;,", and u = 0. 



Let us now make, for abridgment, 



and afterwards change a? into a/, and x" into x in the expression 

 immediately preceding, there will then result 



.'2) 2 



P' being what P becomes by changing generally x r into a?/, the 

 unit attached to the foot of P' indicating, as before, that the 

 multiple integral comprises only the values admitted by the 

 condition (a), and V' being what V becomes when we make 

 w = 0. 



The equation just given supposes u' evanescent ; but if we 

 were to replace u with the general value u in the first member, 

 and make a corresponding change in the second by replacing V 

 with the general value F, this equation would still be correct, 

 and we should thus have 



