THE MACHINES OF THE ANCIENT WORLD 17 



Now, we know that when we push or pull, the work 

 we do depends not only upon how hard but upon how 

 far. When one pushes on the long arm of a lever and 

 lifts a larger weight at the end of the short arm, he 

 must push a correspondingly greater distance than the 

 weight rises. 



The inclined plane is strictly speaking not a machine. 

 Its serviceability was probably evident to man fairly 

 early in his development. He would have noticed 

 that he could drag a burden up the smooth inclined 

 face of a rock more easily than lift it through the same 

 vertical distance. lii his building operations he learned 

 something of what builders to-day call the " angle of 

 repose" of a loose material. When we try to make 

 a pile of sand or gravel we notice that if the sides 

 become too steep, what we put on slips down. If 

 we do not exceed a certain steepness, that is, a certain 

 angle of repose, then the friction which the surface 

 offers prevents what we add to the pile from sliding 

 down. The steeper the inclined plane, the more easily 

 do things slide down and the greater the difficulty 

 of dragging them up. For this reason the slope of 

 the incline should be gradual. It is also desirable 

 to reduce as much as possible the friction between the 

 body and the surface of the incline. Of course, on 

 roads this is usually accomplished by making the 

 friction between the two surfaces rolling rather than 

 sliding friction. With these ideas the ancients were 

 familiar. 



It is our common knowledge as to friction that it is 

 greater the harder the two sliding surfaces are pressed 

 together and the more irregularities there are upon 



