MECHANICAL PARADOXES. 



that of the compression wave and is there- 

 fore (apart from friction losses) equal to the 

 velocity of the striking balls which produced 

 the compression wave. The velocity of the 

 balls starting from one end is therefore (except 

 for friction losses) that of the balls which 

 struck at the other end. 



But the amount or extent of compression 

 between the moving balls at one end and the 

 balls resisting movement at the other end 

 varies with the compressing force that is, for 

 a given velocity with the mass or number 

 of the striking balls. And since this energy 

 must all be represented finally in the move- 

 ment of balls at a velocity which is, as we have 

 seen, identical with the velocity of the striking 

 balls, the mass of these moved balls which 

 take up in starting at the definite speed the 

 definite quantity of energy must equal the 

 mass of the striking balls which gave up that 

 quantity of energy when stopped at that speed. 

 Therefore the number of balls moved must 

 equal the number of balls which struck. 



As to the details of force-application which 

 decide the movement of the last ball that 

 moves, and the inability to move of the ball 

 preceding it, without the help of mathematical 

 figures they might be made fairly intelligible 

 in the following way. 



Suppose the number of striking balls to 

 have been two. As the last ball at the other 



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