iBB Mr. Hell i ns's new Method of computing 
R 
I 
X 
" 2 5 ’ 
1 -f? X? 
, p 
X 
• 26 
I +x* 
. 2 0 ~ 
X 
2 7 
I -f X 
_ 3R 
X 
28 
I -f X 
&c. 
which form is well adapted to arithmetical calculation. And,, 
that a similar form for that purpose may always be obtained, 
when the coefficients of the proposed series are the reciprocals 
of any arithmetical progression, has been shewn by Mr. Simp- 
son, in his Mathematical Dissertations, p. 64. 
Having premised these observations, I now proceed to the 
arithmetical work ; in which I shall use, and explain,, such other 
devices as have occurred to me for facilitating it. 
5. Since the work of computing the value of the proposed 
series is so much shortened,. by first finding the sum of a mo- 
derate number of initial terms, and then resolving the remain- 
ing terms into several series, in the manner described in Art. 2, 
I will begin with computing the first twenty-four terms of it ; 
and, to facilitate this part of the work, I will separate these 
terms into three parts ; viz. 
!■ 
+ 
+ 
X 
x 9 
9 
x 11 
l 7 
+ 
+ 
+ 
x 
2 
+ -T + 
j : 10 . x 11 
10 ' 11 
x 
15 
18 
+ 
*9 
+ 
+ 
X 
12 
,.ao 
20 
which are evidently equal to 
x' 
x 
16 
x + 
+ 
+ 
x 
~9 
x 
"*7 
x x 
2 
X 1 
10 
.r* 
18 
-h 
+ 
+ 
3 
X 3 
1 1 
X 3 
"19 
+ 
+ 
+ 
XT 
12 
20 
■ + 
+ ■ 
I 
+ ' 
+ ■ 
4 ~ 
X^_ 
13 
,ai 
X 
21 
5 
x 5 
X s 
IT 
+ 
+ 
+ 
+ 
+ 
+ 
X u 
6 
.r 14 
22 
x 6 
6 
jL 
*4 
X 6 
22 
+ ■ 
• + 
+ ' 
+ 
+ ■ 
+ 
K .15 
l S 
23 
x‘ 
7 
X 7 
*5 
x 7 
+ 
1 + 
“t 
+ 
+ 
■ + 
x? 
T“ 5 ' 
16 * 
x %,v 
8 * 
16 I * 
X s 
