Chap. XI.
MECHANICS.
937
In a muffle of pulleys, when three are fixed andthree movable, there will always be an equilibriumwhen the weight is to the power, as the number ofropes which bear the lower muffle i« to unity : thereis the same proportion between the power and the re-sistance when the pulleys are in different places, orwhen the fixed pulleys are placed on one axis, and allthe movable ones upon another.
In all movable pulleys whose number is n, when sus-pended on separate ropes, the extremities of each ofwhich are attached to the weight, there will be anequilibrium when P: \V = 1 : 2 n — 1. In a combin-ation of pulleys in which two are supported by onerope, there will be an equilibrium when P : W = 1 : 4,and all others in the same proportion.
There are several arrangements made in the pulleysused to raise weights : in some single-wheeled pulleysthere are means provided to release the rope; a partof the sheeve opens at the edge sufficiently to passthe rope over, or to disengage it: the weight beingattached to the movable block, the fixed one servesonly to apply the power in the desired direction; theformer alone diminishing the power acquired, dividingthe weight equally among all the pulleys; every mov-able pulley requires the application of a force equal to half the weight to produce equi-librium.
Fig. 1280.
USED AT THE MENA I BRIDGE.
The pulley is of great antiquity, and was used by the ancients : we learn from Vitruvius that Ctesibius , whose father was a barber, was born at Alexandria, and that beiDg endowedwith extraordinary talent and industry, he acquired great reputation for his mechanicalcontrivances: wishing to suspend a mirror in his father’s shop in such a way that it mightbe easily lowered and raised by means of a cord, he used the following expedient:—fixinga wooden tube on the under side of the beam he attached a pulley to it, in such a mannerthat the cord passed and made an angle in descending into the wood which he had hollowedout; there he placed small tubes, within which a leaden ball attached to the cord was madeto descend. It happened that the weight in its descent in the tube pressed on the enclosedair, and violently driving out at its mouth the quantity of air compressed in the tubes,produced by its obstruction and contact hollow sounds; this afterwards led to his inventionof the organ.
The block or sheeve was much in use by the Romans, and known under the name oftrochlea , though it was sometimes called rechamus. From the description handed down tous by the author above quoted, it would appear that the pulleys were not placed as we have