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CHAPTER V. 



MECHANICAL RECREATIONS. 



I proceed now to enumerate a few questions connected with 

 mechanics which lead to results that seem to me interesting 

 from a historical point of view or paradoxical. Problems in 

 mechanics generally involve more difficulties than problems in 

 arithmetic, algebra, or geometry, and the explanations of some 

 phenomena — such as those connected with the flight of birds — 

 are still incomplete, while the explanations of many others of an 

 interesting character are too difficult to find a place in a non- 

 technical work. Here I exclude all transcendental mechanics, 

 and confine myself to questions which, like those treated in the 

 preceding chapters, are of an elementary character. The 

 results are well-known to mathematicians. 



I assume that the reader is acquainted with the funda- 

 mental ideas of kinematics and dynamics, and is familiar with 

 the three Newtonian laws; namely, first that a body will 

 continue in its state of rest or of uniform motion in a straight 

 line unless compelled to change that state by some external 

 force : second, that the change of momentum per unit of time 

 is proportional to the external force and takes place in the 

 direction of it: and third, that the action of one body on 

 another is equal in magnitude but opposite in direction to the 

 reaction of the second body on the first. The first and second 

 laws state the principles required for solving any question on 

 the motion of a particle under the action of given forces. The 

 third law supplies the additional principle required for the 

 solution of problems in which two or more particles influence 

 one another. 



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