(282.) It will in all cases be found, that that quantity by which the weight exceeds the power is supported by fixed points; and therefore, although it be commonly stated that a small power supports a great weight, yet in the pulley, as in all other machines, the power supports no more of the weight than is exactly equal to its own amount. It will not be necessary to establish this in each of the examples which have been given: having explained it in one instance, the student will find no difficulty in applying the same reasoning to others. In _fig. 126._, the fixed pulley sustains a force equal to twice the power, and by it the power giving tension to the first rope sustains a part of the weight equal to itself. The first hook sustains a portion of the weight equal to the tension of the first string, or to the power. The second hook sustains a force equal to twice the power; and the third hook sustains a force equal to four times the power. The three hooks therefore sustain a portion of the weight equal to seven times the power; and the weight itself being eight times the power, it is evident that the part of the weight which remains to be supported by the power is equal to the power itself. (283.) When a weight is raised by any of the systems of pulleys which have been last described, the proportion between the velocity of the weight and the velocity of the power, so frequently noticed in other machines, will always be observed. In the system of pulleys represented in _fig. 126._ the weight being eight times the power, the velocity of the power will be eight times that of the weight. If the power be moved through eight feet, that part of the rope between the fixed pulley and the first moveable pulley will be shortened by eight feet. And since the two parts which lie above the first moveable pulley must be equally shortened, each will be diminished by four feet; therefore the first pulley will rise through four feet while the power moves through eight feet. In the same way it may be shown, that while the first pulley moves through four feet, the second moves through two; and while the second moves through two, the third, to which the weight is attached, is raised through one foot. While the power, therefore, is carried through eight feet, the weight is moved through one foot. By reasoning similar to this, it may be shown that the space through which the power is moved in every case is as many times greater than the height through which the weight is raised, as the weight is greater than the power.