MECHANICAL PARADOXES. 



direction to that of the inner end D ; so that 

 when D moves along the ruler one-sixteenth 

 of an inch to the right, G moves one-sixteenth 

 to the left. F is for the time being the centre 

 of a circle of which D G is a diameter, and 

 the ends of the diameter move in opposite 

 directions. If a point H be marked on the 

 bristle, half way from F to G, it will move 

 backwards only half the distance, and there- 

 fore, since the time is the same, at only half 

 the speed at which D moves forward. If 

 the point K be at one-sixth of the distance 

 from F to G, it will move backwards at one- 

 sixth of the rate at which D moves forward. 



If E F be a wheel, and D the centre of the 

 axle by which it is attached to a carriage, 

 D will necessarily have at all times the same 

 speed as the carriage itself, while F is stationary 

 at the moment when it is the bottom point of 

 the wheel ; and at the same moment a point 

 K, rigidly connected with the wheel at the 

 stated distance beneath the point on which 

 it is rolling, will move backwards at one-sixth 

 of the speed at which the carriage is advancing, 

 whatever that speed may be. 



Such an arrangement we have in the wheel 

 of a railway carriage, which has a flange O P 

 projecting beyond the rolling surface M N. If 

 the radius L N be eighteen inches, and the flange 

 N P be three inches deep, then that point 

 P of the flange which is at any moment three 



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