finding the Value of an infinite Series, Sec. 229 
the radius of the circle, or the whole length of the pern 
dulum, as 1.570,796, &c. is to 1.414,213, ,&c. But 
we have Teen in the laft article that the time of the fall 
of a heavy body through the radius of the circle is to 
the time of defeent of a pendulum through the arch of 
a whole quadrant as 1 to 1.311,028,779,- Sec. There- 
fore the limit of the time of defeent of a pendulum 
through a very finall arch at the bottom of the quadrant 
is to the time of delcent through the arch of the whole, 
quadrant as 1.570,796,326, Sec. x 1 is to 1 .414,2 1 3,, 
<kc. x 1.3 1 1,028,779, - &c., or as 1.570,796,32.6, 8cc. 
is to 1.414,213, Sec. x 1. 31 1,028,779, - See., that is, 
by art. 21. as 1.570,796,326, Sec. is to 1.414,213, Sec. 
x 1.570,79.6,326, Sec. x .834,626,843, - &c., or as 
1 to 1.414,213, &c. x .834,626,843, - Sec., or as 1 to 
1.180,340, 8cc., or, in fmaller numbers, as 1 to 1.180, 
or as 1000 to 1 180, or as 100 to 1 1 8, or as 50 to 59. 
Art, 26. This proportion of the times of the de- 
feent of a pendulum through an infinitely fmall arch 
at the bottom of the quadrant, and through the arch 
of the whole quadrant, agrees pretty nearly with 
that afligned for them by Mr. huygens in the pre- 
face to his admirable Treadle on Pendulum-clocks, 
or De Horologia Of dilator io , which is that of 29 to 
34. For 50 is to 59 as 29 25 to 34.2, or 34}; or 
(negle&ing the fraction j) as 29 is to 34; Mr. huygens 
meaning 
