196 THE POPULAR SCIENCE MONTHLY 



One very familiar property of slicing and pulling is that the 

 curvature due to them becomes much more pronounced when the 

 velocity of the ball has been reduced, than it was at the beginning 

 when the velocity was greatest. We can easily understand why this 

 should be so if we consider the effect on the sideways motion of 

 reducing the velocity to one half. Suppose a ball is projected from 

 A in the direction AB, but is sliced; let us find the sideways motion 

 BC due to slice. The sideways force is, as we have seen, proportional 

 to the product of the velocity of the ball and the velocity of spin, or 

 if we keep the spin the same in the two cases, to the velocity of the 

 ball; hence, if we halve the velocity we halve the sideways force, 

 hence, in the same time the displacement would be halved too, but 

 when the velocity is halved the time taken for the ball to pass from 

 A to B is doubled. Now the displacement produced by a constant 

 force is proportional to the square of the time; hence, if the force 

 had remained constant, the sideways deflection BC would have been 

 increased four times by halving the velocity, but as halving the 



Fig. 26. Fig. 27. 



velocity halves the force, BC is doubled when the velocity is halved; 

 thus the sideways movement is twice as great when the velocity is 

 halved. 



If the velocity of spin diminished as rapidly as that of translation 

 the curvature would not increase as the velocity diminished, but the 

 resistance of the air has more effect on the speed of the ball than on 

 its spin, so that the speed falls the more rapidly of the two. 



The general effect of wind upon the motion of a spinning ball 

 can easily be deduced from the principles we discussed in the earlier 

 part of the lecture. Take, first, the case of a head-wind. This wind 

 increases the relative velocity of the ball with respect to the air; since 

 the force due to the spin is proportional to this velocity, the wind 

 increases this force, so that the effects due to spin are more pro- 

 nounced when there is a head-wind than on a calm day. All golfers 

 must have had had only too many opportunities of noticing this. 

 Another illustration is found in cricket; many bowlers are able to 

 swerve when bowling against the wind who can not do so to any con- 

 siderable extent on a calm day. 



