206 Mr. Adams on [Sept 



fl2 f x m-1 $ x 



m— I 



x m a x 



— + r + 



m m — 1 x — a 



x" ax™- 1 n'j;"-! a?J x m ~t 



— -4- -|- -f- — - 



m m — I nt — 2 x — a 



&C. 



By comparing with formula A, we write m + 1 for ?rc, and 

 make a = — a, b = 1, » = 1, and P = — 1. 



Fluent 9. — To find the fluent of 1 -, where r is a whole 



positive number. 



P xrm ~' Ax _ /*af m - , da:(a:--a-)- , 



J x™ — a™ J v 



T T * 



r tn /2"» 



(r — l)m 



x (r— l)m a m z (r-2)m jl» Alr-Di.-! ,J j 



= 1 U :i . 



(r — ljnt (r — 2)?» i" - a" 



x (r— m a m x (r — 2) nt „lmj.(r-!)» a 3 m ^ x( r — 3 ' m ""' dX 



~ (r — 1) 7» (r — 2) m (r — 3) m x m — a m 



&C. 



By comparing with formula A, we write r m for m, m for n } 

 — a'" for a, 1 for b, and — 1 for p. 



Fluent lO.-To find the fluent of UlLzl^ll, 



c + b y* 



J c + by* b J c + by" 1 2 6 



6c+rc S* 2 y dy ry* 



= 2 b- J f + c_ ~ Tb 



= »-^f.h y p,iog.(y + J)-^ 



By making m = 4, n = 2, a = c, and P = — 1 ; in formula A. 

 Fluent 13. — Required the fluent of ^ 



^ 3 »/ 3 n/V V ^ y 



The same as Mr. Dealtry's when reduced j m sr n, &c. in 

 formula A. 



