256 



NATURE 



[December 22, 1910 



here a ball A made of very thin indiarubber of the kind 

 used for toy balloons, filled with air, and weighing very 

 little more than the air it displaces ; on striking this with 

 the hand, so as to put underspin upon it, you see that it 

 describes a loop, as in Fig. 24. 



Striking the ball so as to make it spin about a vertical 

 axis, you see that it moves off with a most exaggerated 

 slice when its nose is moving to the right looking at it 

 from the tee, and with an equally pronounced pull when 

 its nose is moving to the left. 



One very familiar property of slicing and pulling is 

 that the curvature due to them becomes much more pro- 

 nounced when the velocity of the ball has been reduced 

 than it was at the beginning when the velocity was 

 gi-eatest. 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 pro- 



FlG. 24. 



Fig. 25. 



jected from .\ in the direction .VB, 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 displace- 

 ment would be halved too, but when the velocitv 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 pro- 

 portional 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 velocitv, but as 

 halving the 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 the 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 dis- 

 cussed 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 



Fig. 26. 



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

 more pronounced when there is a head-wind than on a 

 calm day. All golfers must have 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 cannot do so to any con- 

 siderable 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 rotating in the direction shown in 

 Fig. 26 ; the rules we found for the effect of rotation on 

 the difference of pressure on the two sides of a ball in a 

 blast of air show that in this case the pressure on the 

 front half of the ball will be greater than that on the rear 

 half, and thus tend to stop the flight of the ball. If, 



NO. 2147, VOL. 85] 



however, the spin was that for a slice, the pressure on 

 the rear half would be greater than the pressure in front, 

 so that the difference in pressure would tend to push on 

 the ball and make it travel further than it otherwiso 

 would. The moral of this is that if the wind is coming 

 from the left we should play up into 'the wind and slin 

 the ball, while if it is coming from the right we should 

 play up into it and pull the ball. 



Fig. 27. 



I have not time for more than a few words as to hov> 

 the ball acquires the spin from the club. But if you grasp 

 the principle that the action between the club and the ba" 

 depends only on their relative motion, and that it is tli 

 same whether we have the ball fi.xed and move the club 

 or have the club fixed and project the ball against it, thf 

 main features are very easily understood. 



Suppose Fig. 27 represents the section of the head of a 



< -- 



Fig. 28. 



Fig. 29. 



lofted club moving horizontally forward from right to left, 

 the effect of the impact will be the same as if the club 

 were at rest and the ball were shot against it horizontally 

 from left to right. Evidently, however, in this case th 

 ball would tend to roll up the face, and would thus g- 

 spin about a horizontal axis in the direction shown in th 

 figure ; this is underspin, and produces the upward fori 

 which tends to increase the carry of the ball. 



Fig. 30. 



Fig. 31 



Suppose, now, the face of the club is not square to if_ 

 direction of motion, but that, looking down on the club, 

 its line of motion when it strikes the ball is along PQ 

 (Fig. 28), such a motion as would be produced if the arm- 

 were pulled in at the end of the stroke, the effect of th 

 impact now will be the same as if the club were at re.-: 

 and the ball projected along RS, the ball will endeavour 

 to roll along the face away from the striker ; it will spin 



