Returning from such theoretical applications of the principle of motion, to the practicalities of every-day mechanisms, we must note some of the applications through which the principle of the lever is made available. Of these some of the most familiar are wheels, and the various modifications of wheels utilized in pulleys and in cogged and bevelled gearings. A moment's reflection will make it clear that the wheel is a lever of the first class, of which the axle constitutes the fulcrum. The spokes of the wheel being of equal length, weights and forces applied to opposite ends of any diameter are, of course, in equilibrium. It follows that when a wheel is adjusted so that a rope may be run about it, constituting a simple pulley, a mechanism is developed which gives no gain in power, but only enables the operator to change the direction of application of power. In other words, pound weights at either end of a rope passed about a simple pulley are in equilibrium and will balance each other, and move through equal distances in opposite directions. [Illustration: HORSE AND CATTLE POWER. The large picture shows a model of a familiar mechanism for utilizing horse power. The small picture shows a similar apparatus in actual operation, actuated by cattle, in contemporary Brittany.] If, however, two or more pulley wheels are connected, to make the familiar apparatus of a compound pulley, we have accomplished by an interesting mechanism a virtual application of the principle of the long and short arm of the lever, and the relations between the weight at the loose end of the rope and the weight attached to the block which constitutes virtually the short end of the lever, may be varied indefinitely, according to the number of pulley-wheels that are used. A pound weight may be made to balance a thousand-pound weight; but, of course, our familiar principle still holding, the pound weight must move through a distance of a thousand feet in order to move a thousand-pound weight through a distance of one foot. Familiar illustrations of the application of this principle may be seen on every hand; as when, for example, a piano or a safe is raised to the upper window of a building by the efforts of men whose power, if directly expended, would be altogether inefficient to stir the weight. The pulley was doubtless invented at a much later stage of human progress than the simple lever. It was, however, well known to the ancients. It was probably brought to its highest state of practical perfection by Archimedes, whose experiments are famous through the narrative of Plutarch. It will be recalled that Archimedes amazed the Syracusan general by constructing an apparatus that enabled him, sitting on shore, to drag a ponderous galley from the water. Plutarch does not describe in detail the apparatus with which this was accomplished, but it is obvious from his description of what took place, that it must have been a system of pulleys.