it 
1 — tt 
X x 
2t~ 
3 
I — tt 
y x 
2 1 ~ 
✓ 
I — tt 
Z X 
It 
1 — tl 
a x 
2t 

1 —tt: 
4 * 
[ 28 3 ] 
2/ 3 4 - US -}- 2 f 4 - U\ frc. 
%xts+24,xts+4.Zxts+%oxl*, &c. 
W‘ ! +i6oyP+4.$oy(*, &c, 
it 83^4- 8963;’, &c. 
fiiup, tire. 
And (by making an equation, between tx the 
coefficient of P in the firft found value of ia\ and 
2 + 8 x, tlie fum of the coefficients of P in the latter 1 
2x = 2 -f- 8 *; whence — 4 =*. 
1# 
And, by proceding in the fame manner, with the 
coefficients of t \ t\ & c . and fupplying the places 
of x, y , z, &c. (as they arife) by the numbers (To 
found) we fhall have ■- ' 
2 )~ 2 ~fH 2 ) , i whence y=-f f . 
2z~ 2 28,5 ; whence z=— ± 
And iu=2-if + ^-:-ij* +f l2u . whence a=+ ,_‘ 
Therefore we may conclude, that t — ' ii-L± ,s~. 
f P-Hfi, (?c.=a. 1 ‘ 
The application of this feries to the redification 
of the circle is extant in many authors ; particularly 
in Sherwtn’s tables of logarithms, above-quoted 
folio ff. ^ * 
When the arc is juft 45 degrees, then t— 1, and 
the feries becomes 4—44-4-44-4, <v? c . which con _ 
verges exceedingly flow; but, by the afliftance of a 
N n 2 method. 
