196 Mr . Hellins’s new Method of computing 
11. The part now remaining, of the proposed series, is x 
x 
zx° 
— + — + TT + — + — + &c- ad infinitum, 
which may very conveniently be resolved into x* s x these two 
,r 4 ° x 48 r , 
— &C. 
12 9 
zx 
.24 
zx 
zx 4 ' 
zx 
48 
f-L- 4 - 
. 6 T 
series^ 
' | 
l 
+ 
* + 
2.T 
16 
9 
* -f* 
— + 
IO 1 II 
zx 
32 
* + + &c - 
48 
IO 
the value of the first of which will quickly be obtained, by means 
of the theorem which has been repeatedly used in the preceding 
operations. The terms of it are as below, in which the decimal 
is used, for the reason mentioned in 
value of — ■ — « = 
4304672! 
1 -f- x a 143046721 
the preceding article. 
Q 
R 
X 
Y 
I 
6 
1 
7 
P 
S 
9 
3 R 
10 
4 -S 
1 1 
5 T 
12 
6 U 
13 
7 V 
H 
8 W 
’iS 
9 X 
****** 
16 
0*16666,66667 
x 0-30092,77018 = 0-00161,70979 
x 0-30092,77018 = 0-00010,81399 
x 0-30092,77018 = 0*00000,00005 
x 0-30092,77018 = O-OOOOOjOOOOl 
The sum of these terms is 0-21139,25631 = l 
