This important principle may be presented under another aspect, which will perhaps render it more apparent. Suppose the weight W were actually divided into 50 equal parts, or suppose it were a vessel of liquid weighing 50 ounces, and containing 50 equal measures; if these 50 measures were successively lifted through a height of 1 foot; the efforts necessary to accomplish this would be the same as those used to move the power P through 50 feet, and it is obvious, that the total expenditure of force would be the same as that which would be necessary to lift the entire contents of the vessel through 1 foot. When the nature and properties of the mechanic powers and other machines have been explained, the force of these observations will be more distinctly perceived. The effects of props and fixed points in sustaining a part of the weight, and sometimes the whole, both of the weight and power, will then be manifest, and every machine will furnish a verification of the remarkable proportion between the velocities of the weight and power, which has enabled us to explain what might otherwise be paradoxical and difficult of comprehension. (227.) The most simple species of machines are those which are commonly denominated the MECHANIC POWERS. These have been differently enumerated by different writers. If, however, the object be to arrange in distinct classes, and in the smallest possible number of them, those machines which are alike in principle, the mechanic powers may be reduced to three. 1. The lever. 2. The cord. 3. The inclined plane. To one or other of these classes all simple machines whatever may be reduced, and all complex machines may be resolved into simple elements which come under them. (228.) The first class includes every machine which is composed of a solid body revolving on a fixed axis, although the name lever has been commonly confined to cases where the machine affects certain particular forms. This is by far the most useful class of machines, and will require in subsequent chapters very detailed development. The general principle, upon which equilibrium is established between the power and weight in machines of this class has been already explained in (183.) The power and weight are always supposed to be applied in directions at right angles to the axis. If lines be drawn from the axis perpendicular to the directions of power and weight, equilibrium will subsist, provided the power multiplied by the perpendicular distance of its direction from the axis, be equal to the weight multiplied by the perpendicular distance of its direction from the axis. This is a principle to which we shall have occasion to refer in explaining the various machines of this class.