finding the Value of an infinite Series , See. 227 
value, 1.3115028,777,146, &c. x r by only .000,000, 
002, x r, or two thoufand-millionth parts of the radius 
which is indeed a moft minute difference, and thews the 
great exadtnefs and utility of this differential feries. 
Art. 23. Of the nine figures to which the number 
1. 31 1, 028, 779, found by the foregoing procefs,is exadt, 
the laft eight are owing to the differential feries. For if 
we were to multiply the value of the firft twelve terms 
. r . r . BW CZ)* DV 6 E V* 
only 01 the. lenes a- — 4 — — — + — 
J SS / s s 
FV 
-f 8cCe or 
I 1.A.VV Q.'i.BV 
X — ° 
2.2 .SS 
4 
9.9 EV 
+ t0 wit 5 the 
4 4.r 6.6./ ‘ 8.8. / 
number .821,109,079,506', into 7 : x r, or 1.570,796, 
326,794, &c. x r, the product would be only 1.289, 
See. x r, which is true to only one place of figures, the 
fecond figure being a 2 inftead of a 3. This therefore is 
an eminent proof of the utility of the faid differential 
feries. 
Art. 24. In an arch of 90° the verfed fine is equal to 
the radius of the circle, that is, according to the fore- 
going notation, v is = r. Therefore by art. 17. together 
with the foregoing computation, it appears, that the time 
of the defeent of a pendulum, or other heavy body 
(moving freely from a ftate of reft by the force of 
gravity only) through the arch of a whole quadrant 
of a circle is to the time of the fall through the cor- 
Gg 2 
refpondent 
