ox COLLISION'. , 81 



tliat of the hammer, besides some further dimmution, on accoiiut of the want 

 of perfect elasticity, and from the effect of the larger surface of the anvil, in 

 dividing the pressure occasioned hy the blow, so as to enable a greater por- 

 tion of the chest to cooperate in resisting it. 



When a body strikes another, in a direction which does not pass through 

 its centre of gravity, the effect produced involves the consideration of rotatory 

 motion, since in this case the body is made to revolve on an axis. But this 

 can never happen when the borly is spherical, and its surface perfectly polish- 

 ed; since every impulse must then be perpendicular to the surface, and must 

 consequently be directed to the centre of the body. If the motion of a ball, 

 which strikes another, is not directed to its centre, the surface of contact must 

 be oblique with respect to its motion, and the second ball will only receive an 

 imptdse in a direction perpendicular to this surface, while the first receives, 

 from its reaction, an equal impulse in a contrary direction, which is com- 

 bined with its primitive motion. The magnitude of this impulse may be de- 

 termined by resolving the motion of the first ball into two parts, the one pa- 

 rallel to the surface of contact, and the other perpendicular; the first part re- 

 maining always unaltered, the second being modified by the collision. If, for 

 example, the balls were equal, this second part of the motion would be de- 

 stroyed, and the remaining motion would be in the direction of the surface 

 of contact, and perpendicular to that of the ball impelled. 



Hence it follows, that if we wish to impel a billiard ball in a given direc- 

 tion, by the stroke of another ball, we have only to imagine a third ball to 

 be placed in contact Avith the first, immediately behind it in the line of the 

 required motion, and to aim at the centre of this imaginary ball: the first 

 ball will then be impelled in the required direction, and the second will also 

 continue to move in a direction perpendicular to it. 



By a similar resolution of the motion of an elastic ball, we may determine 

 its path, when it is refiected from a fixed obstacle. That part of the motion, 

 which is in a direction parallel to the surface of the obstacle, remains undi- 

 minished: the motion perpendicular to it is changed for an equal motion 

 in a contrary direction, and the joint result of these constitutes a motion, 

 in a direction, which is equally inclined to the surface, with the first motion, 



VOL. I. M 



