igs Mr . Hellins's new Method of computing 
R 
U 
I 
p 
x ■ 
9 
l 9 
9 
1 
26 
A ” 
l 9 
_ *0, 
X * 
9 
27 
*9 
__ 3R 
\s - 
9 
28 
*9 
4 s 
V 0 
9 
29 
19 
5 t 
9 
3° 
A 
19 
6U 
9 
3 1 
A 
19 
r_ 7V 
x ■ 
9 
T- 
3 2 
19 
= 0-01894,73684,2 
0*00001 j 2 1 121,0 
0 *OOOCO,Op 03 l ,7 
0 * 00000 , 00002,9 
0 * 00000 , 00000,3 
The sum of these terms is 0*01930,53338,5, which, for the sake 
of reference, call a. Then we have ax^ = x M x : ^ + ~- 
x* _L * r5 
30 
7. The part of the proposed series which now remains to be 
1 . M 2 SC 1 | 2X^ | 2X | 2X | 2X j 2X j 
computed, isxV:— + — + — + — + — +-rg- + we- 
ed infinitum, or x“x : -£■ + -£• + — - + + -f 
ad infinitum, which may also be divided into two series, 
in the manner above shewn ; but, to obtain a swifter conver- 
gency in the next, as well as the succeeding applications of the 
differential series, it will be convenient first to compute the va- 
lue of four terms at the beginning of this series ; which we may 
quickly do, since all the powers of x requisite in that part of 
the calculation are ready at hand, being set down in Art, 5. 
The work will stand thus : 
