20 THE REALITIES OF MODERN SCIENCE 



pebbles and bowlders rolling down a hillside, or from 

 the turning of bits of branches under foot. From the 

 use of rollers to wheels was possibly the line evolution 

 took. From wheels to pulleys is another possible 

 step. A wheel, rolling along the ground, comes into 

 contact with successive points, and the rotating 

 axle moves forward. In the pulley successive points 

 of the rope pass from one side to the other of a rotating 

 axle. In both cases the rotation of the wheel about 

 its axis is accompanied by a translation of the con- 

 tacting surface relative to the axle. 



The pulley was of special value in early building 

 operations because there were no sources of energy, 

 like steam engines, which could exert large forces. 

 Large forces were derived from a large number of men ; 

 and a pulley allowed their combined force to be exerted 

 in the desired direction. It is important to notice 

 that with a single pulley the only effect is that of 

 changing the direction of the force. With a combina- 

 tion of pulleys we may obtain mechanical advantage 

 which was apparently unknown to the ancients. 1 In 

 such a case we arrange the system so that the weight 

 to be lifted moves a smaller distance than the end of 

 the rope which is being pulled. In this way we make 

 use of the principle which applies to the lever and the 

 inclined plane. This "work principle" states that in 

 any machine the work of the acting force is equal to 

 the work done against the resisting force. The work 

 in each instance is measured by the product of the 

 force and the distance. 



1 The story of page 43 indicates that Archimedes was familiar 

 with it, but this was much later than the building of the pyramids. 



