142 Transactions. — Miscellaneous. 



the same direction along the other sides without loss of motion. Let the 

 length of each side be represented by h, and let the length of line passed 

 over by particle H, during the time particle B traverses a side, be 

 represented by h. Then h will be the length of the line drawn from 

 the end of a produced side to the angular point opposite. When B 

 has traversed all the sides of the polygon, it has passed over a distance equal 

 io n y. b and the sum of the distances passed over by the other particles 

 (which are the same as H, and have the same velocity) is equal to n x h. 

 The ratio of the distance passed over by the striking or deflecting particles 

 to the distance passed over by the revolving (struck or deflected) particle is 

 constant. Whether the velocity be augmented or diminished the ratio is the 

 same. The foi'ce necessary to deflect by successive impulses a particle along 

 the sides of a polygon does not therefore have to vary in strength as the 

 square of the velocity of the deflected particle. It is only reasonable, there- 

 fore, to suppose that the force necessary to deflect a particle so as to cause 

 it to move in a circle does not vary as the square of the velocity. 



