142 Transactions.— Miscellaneous. 
the same direction along the other sides without loss of motion. Let the 
length of each side be represented by b, and let the length of line passed 
over by particle H, during the time particle B traverses a side, be 
represented by h. Then hf 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 
ton x band the sum of the distances passed over by the other particles 
(which are the same as H, and have the same velocity) is equal ton 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 force 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. 
