C 565 ] 
El 
H 
TT 
**Q. 
, bx'X bx* , l , bX 
■ ■■ j — ’ - - rnmmmmm - . ■ — — ' l — — — 1 — . ■ ■■ 
2 1 4 4 1 4 4 
# 4 - — 
‘ 4 
.— 3 
A 
— 5 
&C. 
i 2 -3 2 3 2 -5 2 5 2 -7 2 ' 
And hence, by multiplying by x x, and taking 
the correct fluents, we have 
nr 
II 
A 4 O , b A 4 X. 
+ 
C b x 
,+ 
8 
16 
64 
I b a* j b x % X , A 
1 T7T * y~ T 
fl 1_LAL 
3 9 1 9 ^ 
a 7 x~ 
16 
341 ( 
64 
nr 
4 S -j- 
. — 3 
, — 5 
8 16 ' 1 1 1.32.5* 
nr 
3-5 2 7 2 
, G?f. S being put for the ferics 
1 , 
J z -3 2 -5 2 
3 2 -5 2 -7 2 
— - — , &c. 
5 2, 7 2 *9 2 
ill !U. 
Now, this value of H being equal to the value of H 
in art. i y. when both feries converge, it follows, that 
5 * 5 
X 
I 7 A 7 — 3 A- 3 . 9 A 9 
5 *' 
I ‘-3 2 -5 2 ' 3 2 -5 2 -7 2 
a 4 j 7 x 4 X 5 b a -4 | 
‘ 16 ^ - 1 
2 -7 2 9 2 
b - 7 
8 
+ 
Z ,.2 
r? -- a 
v r 
+ 
64 
3 ° z 
x 
7b 
nr 
4,S. 
J_ 
bx 7 X 
, £?c. is theft 
b 
,3 
K + 6* 
9 ■ ' ■ 8 16 
Hence, by taking x equal to — i , we hnd — 4 S 
tt.1 
O h 2 111 111 O /7^ 
— — -f- i + 4 S ; and, confequently, S = — 
r 
" 9 “ 
Many other inftances of the ulc of this method 
might be given ; but thefe may fuffice to enable the 
intelligent reader to purfue the fpeculation farther, at 
his pleafure. 
4-D % 
LV. Coif, 
