16 THE REALITIES OF MODERN SCIENCE 



stone he probably selected a bar which looked about 

 long enough and tried. If it didn't work he pushed 

 the fulcrum a little closer to the block and tried again. 

 If the force he was capable of applying was still too 

 small, he tried a longer lever. He thus made the lever 

 arm of his force sufficiently greater than that of the 

 weight he was trying to lift. Of course, if he chose too 

 long a bar it may have bent in such a way as really to 

 make his lever arm shorter. In some such manner the 

 ancients probably obtained their knowledge of the lever 

 and incidentally some ideas as to the bending and 

 elasticity of beams. 



We know to-day another property of the lever of which 

 they made use, although it was not formally and com- 

 pletely described in words for centuries. We recognize 

 that the motion of a lever is a rotation about its fulcrum, 

 the path which any point travels being a part of a circle 

 about the fulcrum. Obviously, in any motion, the 

 more distant points must move through the greater 

 distances. But the time it takes each point to move 

 through the arc of its circle is the same. Hence the 

 point that moves the farther must also move the faster. 

 This is the property which we use whenever we want to 

 strike faster than we can with the levers afforded us in 

 the bones of our bodies, as in using an ax, a sword, or 

 a golf club. The system of levers involved in an 

 ordinary typewriter is an interesting illustration of 

 a slow motion of the point where the force is applied 

 producing a faster motion of another point of the 

 system. 



In the case of the lever, as of all machines, work is 

 done by the machine only because work is done on it. 



