808 Professor Sir J. J. Thomson [March 18, 



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

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

 A in the direction A B, but is sliced ; let us find the side\yays motion 

 B C due to slice. The sidcAyays 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 B C would have been 

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

 velocity halves the force, B C is doubled when the velocity is halved : 

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

 halved. 



Fig. 24. Fig. 25. 



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

 the curvature Ayould 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 he deduced f com 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 

 pronounced \yhen there is a head-wind tlian on a calm day. All golfers 

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

 illustration is found in cricket : many boAvlers are able to swerve when 

 bowling against the wind who cannot do so to any considerable 

 extent on a calm day. 



Let us now consider the effect of a cross-wind. Suppose the wind 

 is blowing from left to right, then, if the ball is pulled, it will be 



