MECHANICAL PARADOXES. 



common, it can be shown that they are similar, 

 and therefore L N has to L M the same propor- 

 tion as M O has to M N. M N, therefore, is as 

 much greater proportionally than M O as L N 

 is less than L M ; so that M N represents the 

 magnitude of a force which, applied tangentially 

 that is, vertically at N, would have the same 

 turning effect as M O applied tangentially at M. 



But M O, as we have seen, is the tangential 

 component at M of the force M N applied verti- 

 cally at N and transmitted to M in the bent 

 crank L M N. Whether, therefore, the foot- 

 pressure at N be applied directly to the straight 

 crank L N, or indirectly through M N to the 

 angle at M, in both cases it exercises exactly 

 the same turning effect, M N at the shorter 

 leverage, or its equivalent M O at the longer 

 leverage. 



Yet the inventor who showed this crank 

 was able to print recommendations from 

 people who had actually used it, testifying to 

 the increase of power that it had given them 

 in their riding, so that they had been in some 

 cases enabled by it to ride hills which they had 

 vainly tried to mount before. 



What is the explanation of this paradoxical 

 result ? 



Partly, it is that which applies to many 

 quack remedies : more favourable circumstances 

 at the time of trial. The machine may be a 

 new one, more perfectly made in other respects. 



no 



