move over six times as much space as the nail during the time of drawing it out of the wood. Corollary. In all the mechanical powers it will be found, that the advantage gained is in proportion to the space passed over by the moving power. OF THE WHEEL AND AXIS. 70. The wheel and axis, though made in many forms, consists of a cylinder, and a wheel fastened to it, as in fig. 14, or of a cylinder, with projecting spokes that answer the same purpose as a wheel, as in fig. 15. 71. The advantage gained, is in proportion as the circumference of the wheel is greater than that of the axis; or as the diameter of the wheel is greater than the diameter of the axis. Illustration. If the diameter of the wheel fig. 14, or the length of the spokes fig. 15, be four feet, and the diameter of the axis only 8 inches, then the power P of one hundred pounds, or the strength of a man applied to the spokes S equivalent to a hundred pounds, will balance a weight W of six hundred pounds. In this case, as in the lever, the power will travel over six times as much space as the weight, when the machine is put in motion. Example 1. To this engine, cranes of all kinds for raising heavy weights may be referred. 2. Sometimes the axis is turned by a winch fastened to it, which serves for a wheel, and the power gained is in proportion as the winch is larger than the axis. 3. A capstan is a cylinder of wood, with holes in it, into these bars are put to turn it round. The bars are made to act something like the spokes, fig. 15. OF THE PULLEY. 72. The pulley is a small wheel turning on an axis, with a rope passing over it. See fig. 16. 73. The small wheel x is called a sheeve, and is so fixed to a block a, as to be moveable round a pin passing through the centre. 74. Pullies are either fixed, or moveable. 75. The fixed pulley gives no mechanical advantage, but is used only to change the direction of a power. By it a man may raise a weight to any height, without moving from the place in which he is, as a stone to the top of a building, otherwise he must ascend with the weight. 76. The moveable pulley represented by x, fig. 16, is fixed to the weight, and rises and falls with it, and the advantage gained by it is as 2 to 1; that is, a power exerted by the hand h of 10 lbs. will balance a weight W of 20 lbs. Illustration. The reason of this is evident, for in raising the weight one inch, foot, or yard, both sides of the rope must be shortened as much, that is, the hand h must move through two inches, feet, or yards, which shews, as before, that the space through which the power moves must be always in proportion to the advantage gained. on 77. When the upper fixed block z, fig. 17, contains two pullies, which only turn their axis, and the lower moveable block x contains also two, which turn, and rise with the weight W, the advantage gained is as four to one. Illustration. For each pulley in the lower block will be acted upon by an equal part of the weight, and since in each pulley that moves with the weight, a double increase of power is gained, therefore the advantage gained is as four to one. 78. In general, the advantage gained by pullies is found by multiplying the number of pullies in the lower block by 2. Example 1. A weight W of 72 lb. may be balanced with a set of pullies, having four in the lower block, by a power of nine pounds, because 72 divided by 8 gives |