192 Mechanich Powers. Book IX.Eighthly, Oregter Clocks which are furniſht with greaterPendulums, in like manner require weights in the ſame pro-portion, or alſo in a greater than the times of the Vübrationshave, or which is the fame, in ſubduplicate proportion of thelengths of the bendulums; for Example, let a Clock have a pen-dulum or 36 inches, or 3 feet, which makes each Vibration inone ſecond, and another with a pendulum of 9 inches, whichabfolves the vibrations in half a ſecond, ſo that in one hourthat makes 3600 vibrations, and this makes 7200; ſince thependulum of the firſt Clock is quadruple of the other, to agi-tate it, is required a quadruple force or weight; becauſe itought to move but doubly ſlower, alſo the Serpentine Wheel,or that which incites the pendulum, muſt be moved doublynower, and therefore the weight hung to the Iower Wheel willhave a double weight, therefore a double weight ſuffices to movea pendulum of quadruple length through like Arches; for àdouble weight, if it have over and above a double poiſe of a-nother weight, is equivalent to a quadruple weight.Fig. 133. Notwithſtanding tis to be Noted, if the longerpendulum be inforced in a point proportionally di-ſtant from the centre of the pendulum, a weight as little againwill ſuffice to move the long pendulum, as if the pendulum AC, receive an impulſe from the upper wheel in the point B, andanother longer pendulum D F, receive an impulſe in the pointE, and let the proportion be the ſame of A C to D B as of PF to DE, a weight doubly leſſer is required to move thelonger pendulum than to move the ſhorter pendulum; for ifthe diſpoſition of the wheels be the ſame, oi the velocity thelame as the upper wheel, an equal weight is required as ap-pars, but in a longer pendulum the upper wheel is moveddoubly flower, and ſo the weight hung to the Clock hath adouble poiſe, therefore a weight doubly leſs ſuffices. But itthe pendulum D F be impelled in G, ſo that D G be a meanproportional between AB and D E, than an equal weight ineach Clock is required, and only double the weight is requir-ed in the Clock of the pendulum D F, when the pendulum 10incited in the point H, ſo that D H be equal to AB, and theGlobes C and Fare ſuppoſed of equal weight, but if the weightsare unequal, then their proportion ought to be had, Whichmay vary diverlly. ö

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