EFFECT OF ROTATION 339 



different players, but in such wise as to show that the ball makes usually from 

 about i to 3 turns in six feet say from 40 to 120 turns or so per second. This 

 is clearly a circumstance not to be overlooked. 



3. Some 230 years ago, Newton employed the analogy of the curved path 

 of a tennis ball " struck with an oblique racket " to aid him in explaining the separa- 

 tion of the various constituents of white light by a prism. And he says, in words 

 which apply aptly to the behaviour of a golf ball, " a circular as well as a progres- 

 sive 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 than 

 on the other, and there excite a reluctancy and reaction of the air proportionally 

 greater." In other words, the pressure of the air is greater on the advancing than 

 on the retreating side of the ball, so that it is deflected from its course in the same 

 direction as that of the motion of its front part, due to the rotation. This explana- 

 tion has not since been improved upon, though the fact itself has been repeatedly 

 verified by many experimenters, including Robins and Magnus. 



That the deflecting force thus called into play by the rotation of the ball may 

 be of considerable magnitude is obvious from the fact of the frequently observed 

 upward concavity of the earlier part of the path. For this shows that, at first, 

 the new force is greater than the weight of the ball. It is thus greater than one- 

 fifth of the direct resistance when the latter has its maximum value. Its magnitude 

 depends upon the rate of spin, and also upon the speed of the ball, and may be 

 regarded as directly proportional to their product. And we know, from the way in 

 which the ball behaves after falling, that the spin does not diminish very rapidly, 

 for a good deal of it remains at the end of the carry. It is probable that the spin 

 contributes to the direct resistance also ; and this was one of my reasons for assuming 

 a terminal velocity somewhat less than that deduced from the datum of Robins. 

 Two important effects of hammering, or otherwise roughening, the ball are now 

 obvious : it enables the club to " grip " the ball firmly, so as to secure as much spin 

 as possible, and it enables the ball, when free, to utilise its spin to the utmost. 



Some of the effects due to resistance and spin alone are very curious. Thus a 

 top or " pearie " spinning with its axis vertical on a smooth horizontal plane is 

 practically free from the effect of gravity. If it receive a blow which tends to give 

 it horizontal motion only, it moves in an endless spiral, coming back, as it were, 

 to receive a second blow. The sense of the spiral motion is the same as that of the 

 rotation. If its spin were to fall off at the same rate as does its speed of transla- 

 tion, the spiral path would, as it were, uncoil itself into a circular one. 



Closely related to this is Robins' experiment with a pendulum whose bob is 

 supported by two strings twisted together, so that they set it in rotation as they 

 untwist. The plane of the pendulum's vibration constantly turns round in the same 

 sense as does the bob. 



If the bob be supported by a fine wire to whose upper end torsion can be 

 applied, it may be made to move as a conical pendulum. Then its path will shrink, 

 or open out, as the bob is made to rotate in, or against, the sense of the revolution. 



When a narrow, rectangular, slip of paper is let fall, with its greater sides 

 horizontal, it usually begins to spin about its longer axis, and at a rate which is 



43* 



