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



ball struck with an oblique racket describe such a curved line. For 

 a circular as well as progressive motion being communicated 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 

 reluctancy and reaction of the air proportionately greater." This 

 letter has more than a scientific interest — it shows that Newton set an 

 excellent precedent to succeedino^ 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 Flight of a 

 Tennis-Bail," pubUshed 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 augles to the 

 direction of motion of the ball, and also to the axis of spin, and that 

 the magnitude of the force is proportioned 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 investigation of the effects which a force of this type 

 would produce on the movement of a golf ball has been discussed 

 very fully by Professor Tait, who also made a very interesting series 



Fig. 13. 



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 P Q, 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 

 'iarry 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 



