206 ON THE DETERMINATION OF THE ATTRACTIONS 



and by a second differentiation 



-** * 



+ i rff?-^W 



O O I -L. 1 



2) as before comprising all the * combinations of the s 



1*3 



indices taken in pairs. 



Hence, the quantity on the right side of the equation (17), 



when we make H=E^ becomes 



" V 



a r 



* 



But if we recollect that we have generally 



(24) ' 



it is easy to perceive that in consequence of the equation (18) 

 the quantity (23) will vanish, and therefore the foregoing value 

 of ZT will always satisfy the equation (17). 



Having thus a particular value of H, we immediately get the 

 general one by assuming 



In fact, there thence results 



H=KHA n , ^ dh , 



J -&Q a i ) a 2 ' a 3 a 8 



the two arbitrary constants which the general integral ought to 

 contain being K, and that which enters implicitly into the in- 

 definite integral. But the condition = V" requires that H 

 should vanish when h is infinite, and consequently the particular 

 value adapted to the present investigation is 



H t = K.H.[ 



<f a 



