220 
-1 
+ 
Mr. Hellins's Improvement of 
+ -£- 4. J!L + 
” 9 1 7 1 
+ 
+ 4r + 
J1L 
25 
<•» 
29 
_}_ J!L 4- & c . 
~ 33 1 
+ — + &C. 
~ 37 1 
+ 4r + 
-f + ^r + 
t 19 
~W 
J!L 
23 
— 
35 
39 
-f &C. 
4- &c. 
All which series are evidently of the first form in article 3, 
and therefore their values may be expressed in the second 
form there given, or more neatly in the Newtonian nota- 
tion mentioned in art. 6. In each of these series the value of 
fin the first series, is 1 ; 
I in the second series, is 5 ; 
n is 8; and the value of m,< jn the tWrd serie s, is g ; 
^in the fourth series, is 7. 
If now we take t = the tangent of 30°, which was 
chosen by Dr. Halley, we shall have the arch of 30“ 
= < 
- • TP. 1 »**•* ' J'-* 1 * • 39 8,4 
Six times this quantity will be = the semicircumference when 
radius is 1, and = the whole circumference when the diameter 
is 1. If therefore we multiply the last series by 6 , and write 
for and express their value in the form given in 
art. 6, we shall have the circumference of a circle whose dia- 
meter is 1, 
3 + 11.81 + 19-81 
