214 ON THE DETERMINATION OF THE ATTRACTIONS 



If now we suppose moreover 



D ^ 1 <?F r 



!-' du J ' 



n'+l J 

 2 



the method before explained (No. 1 1) will immediately give 



271-1 T (1) ", 



, 



, , . abcu 

 ri + 



and therefore if for abridgment we make 



*m ' 



the total differential of V may be written 



which being integrated in the usual way by first supposing h 

 constant, and then completing the integral with a function of h, 

 to be afterwards determined by making every thing in Fvariable, 

 we get 



abc J x abc 



k being a quantity absolutely constant, which is equal to zero 

 when ri> 1. What has just been advanced will be quite clear 

 if we recollect that h may be regarded as a function of x, y, z 

 and u, determined by the equation 



- 2 



seeing that 2 = a' 2 + h\ V = b f * + Ji\ and c 2 = c' 2 + tf. 



