62 Dr. waring on Interpolations. 
correfponding to the values t, f, a, r, 8ec. of the above- 
-mentioned quantity x. 
Afllime j v — s’ r -=T ff , s e = t?, J T -s r = T T , 
See.; then the errors of the function X will be refpec- 
tively t t , t?, t 0 , t t , 8ec.; and the correcting quantity 
fought may be 
# — 00 Xx— (3 X X — yXx — <t X x— 
■ 6 X &C. 
x — {XX — *XX — TX &C. 
tt — a X 9r — 13 X v — yX v— S Xw— e X &C. 
X 
^ — fX7T— <rxn — tX &C. 
X 
x — ooX x — (3 X x — y X x — $Xx- 
- £ X &C. 
X — nx X—o-X X—TX &C. 
T* 
£ — a X § — -j3 X £ — 7 X £ — ^ X § — £ X &C# 
X 
$ — w x f — ff X f — T X &c. 
X 
# — a X x — & X x — y X X — % X X — 
£ X &C. 
x — w X x — g X x — r X &C. 
rp/ 
cr — ooXtr — @X cr — yX^ — ^X cr — 
£ X &C. 
X 
cr — w X cr — £ X cr — r X &C. 
X 
T 
X—aXX—8XX—yXx—$XX— 
■ £ X &C. 
X tr X x — • g X X — j-X &C. 
T t 
r — a Xr—fix r — yX'r — ^X r — 
■ £ X &C. 
X 
r — ttX — X r — cr X &C. 
X 
+ See. 
Aliter. 
Let x — a. x x — xx — y x x — S' x x — ex &c. x x — 7; 
X X — gX X—ax X-TX Sce.= N ; 7T—XX Tt-fix-K—yx It— fix 7T—£ 
x Scc.xn-exn—crxn—Tx 8ec.=ri; g—xxg—fixg—yxg—ftx 
g-sx Sec. xt-TTxg—crxf-Tx Sec. = P; cr- axa— fixer— yx 
<j—d' x <x—e x 8cc. x<j—7rxa—()x<7— rx 8ec. =2; T—otxT—fix 
1 -yxr—^x t—s x &c. x r-7T x r-^x t-ctx 8ec.=T,8cc.; then 
( x r x? 
rjiff T r 
4- — = + — = + 8ec.). 
£ X a: — <r T x * — r 
This 
