finding Fh tents by Continuation . 
439 
F x - — when we fubftitute for r its value ; therefore, If we 
i+* [ 
&c. — x - — we Aral! have 
8 -T+J 
putM=-l- 
r, — i n — 2 
= M±I^_L ± &c. i- x IHZf _ I x/^Ji 
vi + 2 n n — l n — r+ I l -px[ ^ ^ Ki-/ 
j__L ~ -J— x — - X - I - --L- ! — L- x / J L 1 gr C 
^ n «-I J V —* n n-l^n-Z */ V'TZT^ + ' 
^ — _ rt: &c. — x n ~ f ~f” I + 1 K / • — 
h— I » — r-f-i ^ V i ^ 
- =±: — — r^&c + — - - x n — r x f y l f . Hence, if the 
n— i zz — r+i %J v ' I __# 2 
two laft fluents be given, we have the general law of conti- 
nuation up to the fluent of 
/ 
, W'here the index of ’ x with- 
I — X 
out the vinculum increafes by unity each time. And in the 
fame manner we may (by increaiing the index of x without by 
m ) find the fluent of - ~ if we have given the fluents of 
W / 
a zm -x %m 
n — rm . 
_ X x 
V 2 <, im 
a —x 
and 
r i . 
k/ im 2 m 
y a — x 
~ . Thus we have a general law of coin 
tinuation, where the index of x without is increafed by half 
the index under the vinculum. 
V. Affume F = 
n „ 
X X 
m / 
X — o 
=: x n ~~ m x + bx n ~~ 2m x -f- b 2 x n —3 m x - f &c. + : 
b r x n ~ rm x , ^ n—zm+ I ,a n-^m+r 
- *, then F — + &c. 4- W, 
n — m-\- I + i 
where W is put for the fluent of the laft term. Now 
fix”x \j . = yi___ x vV 1 ~ a x F x v'V* - a x x a 4b 
m j 
X ~~V 
tfi s 
X —D 
