Chap. 2. PHILOSOPHY. $9

ference juft in the fame time, as would be imployed by thebody in falling perpendicularly down through the diameterC A. But the time in which the body will defcend throughthe arch, is different from the time, which it would take upin falling through the line A B.

6 o. It has been thought by fome, that becaufe in veryfmall arches this correfpondent ftraight line differs but littlefrom the arch itfelf; therefore the defcent through thisftraight line would be performed in fuch fmall arches nearlym the fame time as through the arches themfdves: fo thatif a pendulum were to fwing in fmall arches, half the timeof a ftngle fwing would be nearly equal to the time, in whicha body would fall perpendicularly through twice the lengthof the pendulum. That is, the whole time of the fwing, ac-cording to this opinion, will be four fold die time requiredfor the body to fall through half the length of the pendu-lum ; becaufe the time of the body’s falling down twice thetangth of the pendulum is half the time required for the fallthrough one quarter of this fpace, diat is through half thependulum’s length. However there is here a miftake ; forthe whole time of the fwing, when the pendulum movesftnough fmall arches, bears to the time required for a bodyto fall down through half the length of the pendulum verynearly the fame proportion, as the circumference of a circlehears to its diameter ; that is very nearly the proportion ofSTY to ixg s or pttle more than the proportion of 3 to 1.If the pendulum takes fo great a fwing, as to pafs over an archequal to one ftxth part of the whole circumference of the

N circle,

1