DEPAETMENT 



MATHEMATICAL AND PHYSICAL SCIENCES. 



EOTATION AS A FACTOR OF MOTION. 



By Professor J. G. McMURPHY, Kenosha. 



When an elastic ball is thrown against a plane surface it re- 

 bounds from that -surface according to certain fixed laws. Its 

 position at any moment will depend on certain conditions. The 

 elasticity of the ball, the angle of projection, the rotation of the 

 ball on its own axis, the velocity, will all of them affect the re- 

 bounding of the ball. "Velocity and elasticity affect the distance 

 to which it will rebound ; the angle of projection and angular mo- 

 tion will affect the direction of rebounding. 



A ball projected perpendicularly against a plane surface will re- 

 bound in the same line, making due allowance for the attraction 

 of gravitation, which finally comes and controls its motion. The 

 resistance of the air is no inconsiderable factor. (In point of fact, 

 it is the latter only which is opposed to the force with which the 

 ball rebounds, for gravity acts at right angles to this force and is 

 not opposed to it.) 



If the ball, without rotation, is projected against the plane sur- 

 face at any angle, excepting ninety degrees, it will rebound so 

 that the. angle of reflection shall be equal to the angle of inci- 

 dence ; modified, of course, by gravitation and the resistance of 

 the air. 



Let us add another factor and examine the result. Given a hori- 

 zontal plane surface in front of the vertical plane. Let the ball 



