18 THE REALITIES OF MODERN SCIENCE 



them. Automobile tires have specially shaped surfaces 

 or chains. Because of the fact that the amount of 

 friction which will oppose the action of a sliding body 

 depends upon the character of the two surfaces, it is 

 easier when we wish to develop the law for an inclined 

 plane to consider first a case where there is no friction. 

 But such a case is impossible ; even between the most 

 highly polished and oiled surfaces there would be some 

 friction. Nevertheless it is a method of science to 

 consider first an " ideal problem/' "the limiting case" 

 of the general problem. Thus in the present instance, 

 of all the possible cases of bodies on inclined planes, 

 we decide to discuss first that case which lies just at 

 the limit of the physically possible, where the friction 

 is so small that we may entirely neglect it. 



Consider the work of moving a body from one end 

 a to the other end c of the inclined plane shown in 

 Fig. 3. Experience tells us that as we push the body 

 upward the plane supports part of its weight. If there 

 is no frictional opposition to sliding, the work we do 

 is that of lifting. In sliding it along the side ac we do 

 not have to push as hard, but we must push farther, so 

 that we do just as much work as if we lifted the body 

 vertically through the distance be. In both the in- 

 clined plane and the lever the principle is the same, 

 namely, a small force exerted for a long distance does 

 the same work as a larger force for a shorter distance. 



The wedge is a sort of double inclined plane. Of 

 all the elementary machines it was probably the earliest, 

 for it is really a cutting tool like a chisel. Some primi- 

 tive man in trying to scrape a hole through a block of 

 wood by using a sharp stone may have got it stuck in 



