Of the several parts of a machine, some are designed to move, while others are fixed; and of those which move, some have motions differing in quantity and direction from those of others. The several parts, whether fixed or movable, are subject to various strains and pressures, which they are intended to resist. These forces not only vary according to the load which the machine has to overcome, but also according to the peculiar form and structure of the machine itself. During the operation the surfaces of the movable parts move in immediate contact with the surfaces either of fixed parts or of parts having other motions. If these surfaces were endued with perfect smoothness or polish, and the several parts subject to strains possessed perfect inflexibility and infinite strength, then the effects of machinery might be practically investigated by the principles already explained. But the materials of which every machine is formed are endued with limited strength, and therefore the load which is placed upon it must be restricted accordingly, else it will be liable to be distorted by the flexure, or even to be destroyed by the fracture of those parts which are submitted to an undue strain. The surfaces of the movable parts, and those surfaces with which they move in contact, cannot in practice be rendered so smooth but that such roughness and inequality will remain as sensibly to impede the motion. To overcome such an impediment requires no inconsiderable part of the moving power. This part is, therefore, intercepted before its arrival at the working point, and the resistance to be finally overcome is deprived of it. The property thus depending on the imperfect smoothness of surfaces, and impeding the motion of bodies whose surfaces are in immediate contact, is called _friction_. Before we can form a just estimate of the effects of machinery, it is necessary to determine the force lost by this impediment, and the laws which under different circumstances regulate that loss. When cordage is engaged in the formation of any part of a machine, it has hitherto been considered as possessing perfect flexibility. This is not the case in practice; and the want of perfect flexibility, which is called _rigidity_, renders a certain quantity of force necessary to bend a cord or rope over the surface of an axle or the groove of a wheel. During the motion of the rope a different part of it must thus be continually bent, and the force which is expended in producing the necessary flexure must be derived from the moving power, and is thus intercepted on its way to the working point. In calculating the effects of cordage, due regard must be had to this waste of power; and therefore it is necessary to enquire into the laws which govern the flexure of imperfectly flexible ropes, and the way in which these affect the machines in which ropes are commonly used.