THE THEORY OF DIABOLO 



By C. V. BOYS, F.R.S. 



It would be an interesting subject for a course of lectures 

 or a series of articles to trace the effects of rotation in balls 

 and other objects used in games and in other pursuits. Some 

 of these are fairly obvious, as, for instance, the effect of a spin 

 on a cricket-ball causing it to break after contact with the 

 ground, or the effect of a screw in billiards, where the ball has 

 a rotation about an inclined axis and bounces from the cushion 

 at an angle which by no means obeys the laws of reflection. 

 Here also, in consequence of the rotation the height of the 

 cushion has to be seven-tenths of the diameter of the ball, for 

 in the case of pure rolling the upper part of the ball may be 

 considered to be travelling more quickly than the lower part, 

 and so, if the cushion were only the height of the centre the upper 

 part of the ball would go on and take the rest of the ball with it. 

 Less simple than these are the effects of the air in causing a 

 spinning ball to veer away from the course that it would take 

 if it did not spin. The best known of these is that shown by 

 the flight of a golf-ball, which was first carefully investigated 

 by the late Professor Tait. When the ball is fairly struck 

 by the club, the front face of which slopes somewhat backwards, 

 it is struck at a point below its centre. The rotation imparted 

 is in such a direction as to cause the lower part to move forward 

 most quickly and the front part to move upward. At one time 

 it was supposed, and I believe clearly proved in the armchair 

 in an analogous case, that the front portion moving upward 

 would cause the ball to roll, as it were, upon the air compressed 

 in front of it, and so cause a departure from the natural trajectory, 

 which in the case of the golf-ball would be downwards. As 

 every one knows, the exact reverse is the case, and a proper 

 consideration of the action shows that it should be so, for the 

 air-pressure can be shown, both by theory and by experiment, 

 to be greater below a ball spinning and moving in the directions 

 followed by a golf-ball than above. Professor Tait established 



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