254 



NATURE 



[December 22, 1910 



•O- 



Fig. 12. 



a circular as well as progressive motion being communi- 

 cated to it by that stroke, its parts on that side where 

 the motions conspire must press and beat the contiguous 

 air more violently, and there excite a rcluctancy and re- 

 action of the air proportionately greater." This letter has 

 more than a scientific interest — it shows that Newton set 

 an excellent precedent to succeeding mathematicians and 

 physicists by taking an interest in games. The same 

 explanation was given by Magnus, and the mathematical 

 theory of the effect is given by Lord Rayleigh in his paper 

 on "The Irregular F'light of a Tennis Ball," published in 

 the Messenger of Mathematics, vol. vi., p. 14, 1877. Lord 

 Rayleigh shows that the force on the ball resulting from 

 this pressure difference is at right angles 

 to the direction of motion of the ball, and 

 also to the axis of spin, and that the mag- 

 nitude of the force is proportional to the 

 velocity of the ball multiplied by the velocity 

 of spin, multiplied by the sine of the angle 

 between the direction of motion of the ball 

 and the axis of spin. The analytical in- 

 vestigation of the effects which a force of 

 this type would produce on the movement 

 of a golf ball has been discussed very fully 

 by Prof. Tait, who also made a very 

 interesting series of experiments on the 

 velocities and spin of golf balls when 

 driven from the tee, and the resistance they 

 experience when moving through the air. 

 As I am afraid I cannot assume that all my hearers 

 are expert mathematicians, I must endeavour to give a 

 general explanation, without using symbols, of how this 

 difference of pressure is established. 



Let us consider a golf ball (Fig. 13) rotating in a 

 current of air flowing past it. The air on the lower side 

 of the ball will have its motion checked by the rotation 

 of the ball, and will thus in the neighbourhood of the 

 ball move more slowly than it would do if there were no 

 golf ball present, or than it would do if the golf ball 

 were there but was not spinning. Thus if we consider a 

 stream of air flowing along the channel PQ, its velocity 

 when near the ball at Q must be less than its velocity 

 when it started at P ; there must, then, have been 

 pressure acting against the motion of the air as it moved 

 from P to Q, i.e. the pressure of the air at Q must be 

 greater than at a place like P, which is some distance 

 from the ball. Now let us consider the other side of the 

 ball ; here the spin tends to carry the ball in the direction 

 of the blast of air ; if the velocity of the surface of the 

 ball is greater than that of the blast, the ball will increase 

 the velocity of the blast on this side, and if the velocity 

 of the ball is less than that of the blast, though it will 

 diminish the velocity of the air, it will not do so to so 

 great an extent as on the other side of the ball. Thus 

 the increase in pressure of the air at the top of the ball 

 over that at P, if it exists at all, will be less than the 

 increase in pressure at the bottom of the ball. Thus the 

 pressure at the bottom of the ball will be greater than that 

 at the top, so that the ball will be acted on by a force 

 tending to make it move upwards. 



side of the boat they have to face the wind, on the other 

 side they have the wind at their backs. Now when they 

 face the wind, the pressure of the wind against them is 

 greater than if they were at rest, and this increased 

 pressure is exerted in all directions, and so acts against 

 the part of the ship adjacent to the deck ; when they an- 

 moving with their backs to the wind the pressure against 

 their backs is not so great as when they were still, st) 

 the pressure acting against this side of the ship will not 

 be so great. Thus the rotation of the passengers will 

 increase the pressure on the side of the ship when they 

 are facing the wind and diminish it on the other side. 

 This case is quite analogous to that of the golf ball. 



Fig. 13. 



We have supposed here that the golf ball is at rest, and 

 the air rushing past it from right to left ; the forces are 

 just the same as if the air were at rest, and the golf ball 

 rushing through it from left to right. As in Fig. 13, such 

 a ball rotating in the direction shown in the figure will 

 move upwards, i.e. it will follow its nose. 



It may perhaps make the explanation of this difference 

 of pressure easier if we take a somewhat commonplace 

 example of a similar effect. Instead of a golf ball, let us 

 consider the case of an Atlantic liner, and, to imitate the 

 rotation of the ball, let us suppose that the passengers 

 are taking their morning walk on the promenade deck, all 

 circulating round the same way. When they are on one 



NO. 2147, VOL. 85] 



Fig. 14. 



The difference between the pressures on the two sides 

 of the golf ball is proportional to the velocity of the ball 

 multiplied by the velocity of the spin. As the spin 

 imparted to the ball by a club with a given loft is pro- 

 portional to the velocity with which the ball leaves the 

 club, the difference of pressure when the ball starts 

 proportional to the square of its initial velocity. The 

 difference between the average pressures on the two sides 

 of the ball need only be about one-fifth of i per centJ 

 of the atmospheric pressure to produce a force on the ball 

 greater than its weight. The ball leaves the club ii 

 good drive with a velocity sufficient to produce far greater 

 pressures than this. The consequence is that when the 

 ball starts from the tee spinning in the direction shown 

 in Fig. 14, this is often called underspin ; the upward 

 force due to the spin is greater than its weight, thus the 

 resultant force is upwards, and the ball is repelled from 

 the earth instead of being attracted to it. The consequence 

 is that the path of the ball curves upward as in the curve 

 A instead of downwards as in B, which would be its path 

 if it had no spin. The spinning golf ball is, in fact, a 

 very efficient heavier-than-air flying machine ; the lifting 

 force may be many times the weight of the ball. 



The path of the golf ball takes very many interesting 

 forms as the amount of spin changes. We can trace all 

 these changes in the arrangement which I have here, and 

 which I might call an electric golf links. With thi« 

 apparatus I can subject small particles to forces of exactly 

 the same type as those which act on a spinning golf ball. 



Fig. 15. 



These particles start from what may be called the tee A 

 (Fig. 15). This is a red-hot piece of platinum with a 

 spot of barium oxide upon it ; the platinum is connected 

 with an electric battery which causes negatively electrified 

 particles to fly off the barium and travel down the glass 

 tube in which the platinum strip is contained ; nearly all 

 the air has been exhausted from this tube. These particles 

 are luminous, so that the path they take is very easily 

 observed. We have now got our golf balls off from the 

 tee ; we must now introduce a vertical force to act upon 

 them to correspond to the force of gravity on the golf 

 ball. This is easily done by the horizontal plates BC, 

 which are electrified by connecting them with an electric 



