If a rope were applied only to sustain, and not to move a weight, this would be sufficient to remove the inconveniences arising from its rigidity. But when motion is to be produced, the rope, in passing over the curved surface, would be subject to excessive friction, and consequently to rapid wear. This inconvenience is removed by causing the surface on which the rope runs to move with it, so that no more friction is produced than would arise from the curved surface rolling upon the rope. (268.) All these ends are attained by the common pulley, which consists of a wheel called a _sheave_, fixed in a block and turning on a pivot. A groove is formed in the edge of the wheel in which the rope runs, the wheel revolving with it. Such an apparatus is represented in _fig. 113._ We shall, for the present, omit the consideration of that part of the effects of the stiffness and friction of the machine which is not removed by the contrivance just explained, and shall consider the rope as perfectly flexible and moving without friction. From the definition of a flexible cord, it follows, that its tension, or the force by which it is stretched throughout its entire length, must be uniform. From this principle, and this alone, all the mechanical properties of pulleys may be derived. Although, as already explained, the whole mechanical efficacy of this machine depends on the qualities of the cord, and not on those of the block and sheave, which are only introduced to remove the accidental effects of stiffness and friction; yet it has been usual to give the name pulley to the block and sheave, and a combination of blocks, sheaves, and ropes is called a _tackle_. (269.) When the rope passes over a single wheel, which is fixed in its position, as in _fig. 113._, the machine is called a _fixed pulley_. Since the tension of the cord is uniform throughout its length, it follows, that in this machine the power and weight are equal. For the weight stretches that part of the cord which is between the weight and pulley, and the power stretches that part between the power and the pulley. And since the tension throughout the whole length is the same, the weight must be equal to the power.