notation as a Factor of Motion. 



237 



with the velocity of translation the deflection from a perpendicu- 

 lar will be very great and vice versa. 



When the ball is propelled against the vertical plane at any 

 other angle than a right angle with a rotary motion besides, the 

 problem becomes somewhat more complicated. Let the ball 

 be propelled from a 

 with a positive rota- ' 

 tion. By its motion of 

 translation it ought 

 to rebound in the 

 path which makes 

 the angle of reflec- 

 tion, equal to the 

 angle of incidence 

 But by its rotation -^ 

 against the fixed point; 6, it would tend toward c ; hence it 

 will take the direction i-e, and be measured by the diagonal 

 parallelogram of forces, represented by h-a and he. Here it is 

 plain that the angle of reflection is much less than the angle of 

 incidence. If the rotation be a negative or left-hand rotation 

 from the same point, a, following the same path, a-J, the result- 

 ant will be nearer a perpendicular — that is, the angle of reflec- 

 tion will be greater than the angle of incidence. 



If a ball be thrown perpendicularly against a vertical plane sur- 

 face with a positive rotation it will rebound to the left, if the rota- 

 tion be negative it will rebound to the right, if the rotation be for- 

 ward the ball will rise, if backward it will fall. If the ball be 

 thrown obliquely to the left, with positive rotation, the angle of 

 reflection will be less than that of incidence. If thrown obliquely 

 to the right, with same rotation, the angle of reflection will be 

 greater than that of incidence. The combinations are almost in- 

 finite, and afford a variety of valuable observations. 



There are some very curious and interesting experiments in 

 compound direct motion. If a ball lying upon a plane surface be 

 struck by a mallet so as to produce translation with forward rota- 

 tion on its horizontal transverse axis, and at the same time a ro- 

 tation about a vertical axis, the ball will neither rotate upon the 



