104 MECHANICAL RECREATIONS [CH. V 



its centre of figure, and the friction of the surface of the ball on 

 the air produces a sort of whirlpool. This rotation is in addition 

 to its motion of translation. Suppose the ball to be spherical 

 and rotating about an axis through its centre perpendicular to 

 the plane of the paper in the direction of the arrow-head, and at 

 the same time moving through still air from left to right 

 parallel to PQ. Any motion of the ball perpendicular to PQ 

 will be produced by the pressure of the air on the surface of the 

 ball, and this pressure will, by Hauksbee's Law, be greatest 

 where the velocity of the air relative to the ball is least, and vice 

 versa. To find the velocity of the air relative to the ball we may 

 reduce the centre of the ball to rest, and suppose a stream 

 of air to impinge on the surface of the ball moving with a 

 velocity equal and opposite to that of the centre of the ball. 



The air is not frictionless, and therefore the air in contact with 

 the surface of the ball will be set in motion by the rotation of 

 the ball and will form a sort of whirlpool rotating in the direction 

 of the arrow-head iu the figure. To find the actual velocity of 

 this air relative to the ball we must consider how the motion 

 due to the whirlpool is affected by the motion of the stream of 

 air parallel to QP. The air at A in the whirlpool is moving 

 against the stream of air there, and therefore its velocity is 

 retarded : the air at B in the whirlpool is moving in the same 

 direction as the stream of air there, and therefore its velocity is 

 increased. Hence the relative velocity of the air at A is less 

 than at B, and, since the pressure of the air is greatest where 

 the velocity is least, the pressure of the air on the surface of the 

 ball at A is greater than on that at B. Hence the ball is forced 

 by this pressure in the direction from the line PQ, which we may 



