[ 35a ] 



n-\- in «+ X 



n'K n, n — i \ ex -^ yx -^ay 



WK - - - - - - yx = ay 



&c. &c. 



Then becaufe when x = t>, and^ = Y, jk = Yx we immediately 

 deduce 



Y x^ 3 y^3 ? + ' ex Yx"'>>i-^yx 



y = ;» y = : y = fi. 71 — I - - I + T, y= • , &C. 



X X' X' 



'.' fubftitutin? for :v, ^ : y = Y + Y X _ + t - - 



1.2. -«rf» 



+ == 4- &C. + ^— + : =- + &C. 



1.2. w+io' n j^ I a n + i.n+zat 



This example was given to remark that fometimes by this 

 method we may derive a general folution from the particular 

 one. For although the above folution is only a particular one 

 viz. when x is fuch that the feries will converge, yet becaufe we 

 know that i + — l + &c. = no. the hyp. log. of which is _' 



n-\- 1 B-f 2 



CX C X 



and alfo becaufe == 1- . . .=^=^:^ + &c. — 



n + l 



OC OC A? 



I. i.--n-r I <i 



i.z,--n a. 



