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Chap. 2. PHILOSOPHY. 81

which the weight is upheld,’ is annexed by one extremity to ahook C, and at the other end is held by the power D. Herethe weight is fupported by a cord doubled; infomuch thatalthough the cord were not ftrong enough to hold the weighthngle, yet being thus doubled it might fupport it. If theend of the cord held by the power D were hung on the hookC, as well as the other end; then, when both ends of the cordwere tied to the hook, it is evident, that the hook wouldbear the whole weight; and each end of the firing wouldbear againfl the hook with the force of half the weight only,feeing both ends together bear with the force of the whole.Hence it is evident, that, when the power D holds one end ofthe weight, the force, which it mufl exert to fupport theWeight, mufl be equal to juft half the weight. And the fameproportion between the weight and power might be colledt-ed from comparing the refpedtive velocities, with which theyWould move ; for it is evident, that the power mufl movethrough a fpace equal to twice the diftance of the pulley fromthe hook, in order to lift the pulley up to the hook.

4.9. It is equally eafy to eftimatc the effedt, when manypulleys are combined together, as in fig. 3 9, 40 ; in the firft°f which the under fet of pulleys, and confequently theWeight is held by fix firings; and in the latter figure by five:therefore in the firft of thefe figures the power to fupport theWeight, mufl be one fixth part only of the weight, and inthe latter figure the power muft be one fifth part.

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