X x 
finding Fluents by Continuation, 437 , 
; hence if the two laft 
_ ft — M-t- r . tft . 
W X X 
r 1 4 - a 
■ 7 ttt 1 jt- m 1 
a-^bx ~f-x 
** a+bx n *x . • . 
fluents be -given, we have the general law of continuation up to 
'*** . in the fame manner as before. 
1 / w 1 *„ 2j 
# 4-&* +<^ 
HI. In general, if we proceed as in the two lad: articles, we 
<hall find J' — — — . — yr x « 4- ^ + &m’ r + ^ 
X f 
a + bx m + &c. x m 
rt—m . 
X X 
a .+ bx” -f &c. # 
__ + ? X 
p 
f= 
U oA-l 
n — 2 *w . 
X X 
4 - &C, =i= 
jX 
/ 
n — m • 
tx 
P 
*4-^+& c * * I 
r~ 
J a + b 
. m 
&c. where the 
^* + &c7^' r ) 
Q^ n _r+ I . w— I 
number of thefe la ft terms Is and M — x ?2 _7+T. ^4- 1 
. . &c omitting, as before, the terms at the end arifing from 
the remainders. Hence if the laft t fluents be given, we can 
by continuation find the required fluent. 
Becaufe the divifion of 
71 
X X 
a+hx m + &c.x tm 
may be expreffed by an 
arcending feries *** - Q£+”*+ R**+“# ~ &<=. it is manifeft, that 
by the fame method we may continue the fluents downwards 
as well as upwards, 
IV Let F z= ** = - x n ~'x - x n ~~*x — - &c. -x n ~’ r x -f 
1 — X 
4- W, where 
n — r . 
X x 
*” *!J c.-* 
ri — r 4- 1 
n — r 4 - 1 
, then F = — - „ 
l-x ’ » K-I n ~ 2 
„ >T x”x XX • M-* 
W is the fluent of the laft term, Now ^ Vi +J ’ 
L 1 1 3 hence 
