» 
55 8 
Mr. Hellins’s improved Solution of 
~ X + P CC + 
cc c + 
v C 
,6 
8 
&r 
16’ 
2 
c c 
+ A + 
C C — {- v C 4 
±xcc-±pc* 
i cc 
±xc* 
i 
y == 7 ~c+ e +f° c + g°\ &c. 
where ej, and^*, are = a- i, ^ — f a — f, and v _ |a — f, 
respectively; in numbers = 0-1931472, 0*1036802, and 
0*0687064, respectively. And this expression, which is evi- 
dently more simple than the former, is somewhat nearer than 
that to the value of the whole series, as will appear to any one 
who shall compute the value of the next coefficient. 
7. In like manner, the product of the two factors in the 
value of A', in Art. 13. will be 
4 1 5 
3 c + 
+ ■J77 + + p' c c + v'c* 
5 c 8 
c c 
2 
8 
16 
8.16 
, &C. 
4 
3 c* 
+ 
v'c 4 
-JTc + + V-’ cc + . 
— \ — -K'CC — -u.'C i 
6 2 2 I 
3 cc 
1 5 
-7- — — CC 
6 24 
8 A ' C f — 7^4 '•\- — -\-b-l r icC-) r kc* r i 
1 5 4 
- cc -- c 
12 48 
_5_ 
96 
c* 
3 
&C 
which expression also is more simple than that from which it 
is derived, while the accuracy of it is not less, as is pretty evi- 
dent on inspection. And, that the numerical values of h , i, 
and k } are very easily attainable from the values of a 7 , //, and /, 
1 
