272 



THE PULLEY. 



than a single one could be, the force requisite for the deflection, as well as the 

 liability of rupturing the cord, would oe considerably diminished. But this 

 end will be still more perfectly attained if the deflection of the cord be pro- 

 duced by bending it over the surface of a curve. 



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 incon- 

 venience 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. 



All these ends are attained by the common pulley, which consists of a wheel 

 called a sheave, fixed in a block and turning on pivots. 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. 2. 



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 con- 

 trivance 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 ma- 

 chine 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. 



When the rope passes over a single wheel, which is fixed in its position, as 

 in fig. 2, 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. 



Hence it appears that no mechanical advantage is gained by this machine. 

 Nevertheless, there is scarcely any engine, simple or complex, attended with 

 more convenience. In the application of power, whether of men or animals, 

 or arising from natural forces, there are always some directions in which it 

 may be exerted to much greater convenience and advantage than others, and 

 in many cases the exertion of these powers is limited to a single direction. A 

 machine, therefore, which enables us to give the most advantageous direction 

 to the moving power, whatever be the direction of the resistance opposed to 

 it, contributes as much practical convenience as one which enables a small 



