288 NEW SERIES for the 
I-+cofA ~~” Top cole Oe CO aes 
r+ cofA et 0% 
2 I+?t 
~/1+cofA 
2 
I a 4, 
3 alfo cof = A=i—, now cof 7 A 
2 
+t 
he IT 
» therefore Oia tp 
1+¢ Vi-+t 
» and hence 
pi Lele a Se 
ie pe oe 
22. Uron the whole, then, the refult of the inveftigation of 
the fecond feries may be ftated briefly as follows. Let a de- 
note any arch of a circle, its radius being unity, then 
( 1 1+cofa L 
41—cola 6 
= (1 1—cofta, 11—cof;a, 1 1—cofya & 
Cc. 
_ JY rfeolga" Brfeotsa” 44 1Feols a" 
{ 4a? Leaay 
ee ed 
where T(m) and T(m+1) denote any two fucceflive terms of the 
{eries in the parenthefis, and S denotes the fum of all the fol- 
lowing terms ; and here S will always be between the limits 
I I __ (Tim) — 16 Tem) Tomer) 
13 re ere 15 (T(m) — T(m+1)) 
that is, it will be lefs than the former, but greater than the lat- 
ter quantity. 
Tue feries of cofines are to be deduced one from another by 
means of the formula 
fA 
cof ~ ees ites. 
Or, 
