#4 
Mr. Hell ins on the Rectification 
A = 
• y — 
05, 
B — 
y 
3 y 
3 
3 
-05, 
2 
2 
2 
• 0 5 — y 
2 
c ~ — 
y 
4- 
sy 
3-5 
*cc—y - ■ 
3-5 
■ 05, 
4 
4 
2.4 
2.4 
j) 
y 
+ - 
7y 
3-5*7 
3-5-7 
0t% 
6 
6 
2.4.6 
' a — j 
2.4.6 
&c. 
&c. 
And, lastly, by writing these values of A, B, C, &c. in the 
Theorem, we have, in this case, 
. aa a* . 3a 6 3.9 a 8 
y. + -ry - — ^ + -rrr-y - - 
% 
aa . 
— oi -4- 
2 1 
2-4 
3 
2.2.4 
05 
But the series y + -^-y — -~*y + 
2.4.6 
3 - 3 - 5 fl6 
2. 2. 4.4.6 
3 a® 
05 “l - * 
y — 
2. 4.6. 8 y 
3 * 3-5 5 7 aS 
, &Co 
’ 05, 
2. 2. 4.4.6. 6. 8 
. , , J &C. is 
2.4 ^ * 2.4.6 2. 4.0. 8 
evidently ==y ^/(l aa), which, by the notation in Art. 1, is 
— ey. We therefore have, in this case. 
% 
ey 
05 x : — 
aa 
2 
3« 4 , 3 - 3 - 5« 6 _ 3 - 3 - 5 - 5 - 7 fl3 o. r 
T ^ o . . a oa '° 
2.2.4 ' 2. 2. 4.4.6 2.2.4.4>6.6.8 
And, since this theorem always gives the correct value of z, we 
have now the satisfaction of seeing a confirmation of the truth 
of our conclusion in Art. 15, by obtaining the very same ex- 
pression by a very different process. 
20. From what has been shewn in Articles 12, 13, &c. it will 
be very evident to any one who runs his eye over the compo- 
nent parts of the series given in Theorem IX, Art. 1 1, that, when 
y becomes immensely great, A becomes = the quadrantal arch 
of a circle , of which the radius is 1, which arch was denoted in, 
the preceding Art. by u ; and that 
B = o — {- 
A 
C = 
D = 
&c. 
o -|-* 
' o + 
2 
3B _ 
4 
$C , 
6 ‘ 
&C. 
x 
2 
2.4 
3-5 
2.4.6 
cc , 
05 5 
06 % 
