Mechanics. 117

are, at the lowest Point C, as the Lengthsof those Chords. (5.) The Times of De-scent through Chords of similar ArchesDB, EC, are as the Square Roots of theSemidiamcters AB, AC, of the respectiveCircles.

From these Properties, and their Corol- p] a te V.laries, the Doctrine of Pendulums is de- Fi g- 3 -rived. A Pendulum is any Body B, sus-pended upon, and moveable about a PointA, as a Centre. The Nature of a Pendu-lum consists in the following Particulars.

(1.) The Times of the Vibrations of aPendulum in very small Arches are allequal. (2.) The Velocity of the Bob inthe lowest Point will be nearly as theLength of the Chord of the Arch which itdescribes in the Descent. (3.) The Timesof Vibration in different Pendulums, AB,

AC, are as the Square Roots of theirLengths. (4.) Hence the Lengths of Pen-dulums AB, AC, are as the Squares of theTimes of their Vibrations. (5.) The Timeof one Vibration is to the Time of De-scent through half the Length of the Pen-dulum, as the Circumference of a Circle toits Diameter. (6.) Whence the Length ofa Pendulum vibrating Seconds will befound 39 Inches nearly ; and of an Half-I 3 Second