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XXL — On the Path of a Rotating Spherical Projectile. By Prof. Tait. 



(With a Plate.) 



(Read 5th June and 3rd July 1893.) 



The curious effects of rotation upon the path of a spherical projectile have been in- 

 vestigated experimentally by Robins and many others, of whom Magnus is one of the 

 more recent. They have also been the subject of elaborate mathematical investiga- 

 tion, especially by Poisson, who has published a large treatise on the question.* For all 

 that, we know as yet very little more about them than Newton did in 1666, when 

 he made his famous experiments on what we now call dispersion. Writing to Olden- 

 burg an account of these experiments in 1 67 l-2,t he says : — 



" Then I began to suspect whether the rays, in their trajection through the prism, 

 did not move in curve lines, and according to their more or less curvity, tend to divers 

 parts of the wall. And it increased my suspicion, when I remembered that I had often 

 seen a tennis-ball, struck with an oblique racket, describe such a curve line. For, a 

 circular as well as a 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 than on the other ; and there excite a reluctancy and re-action of the air pro- 

 portionably greater. And for the same reason, if the rays of light should possibly be 

 globular bodies, and by their oblique passage out of one medium into another acquire a 

 circulating motion, they ought to feel the greater resistance from the ambient aether, on 

 that side where the motions conspire, and thence be continually bowed to the other." 



From this remarkable passage it is clear that Newton was fully aware of the effect of 

 rotation in producing curvature of the path of a ball, also that it could be of sufficient 

 amount to be easily noticed in the short flight of a tennis-ball ; that he correctly described 

 the direction of the deviation, and that he ascribed the effect to difference of air-pressure 

 for which he assigned a cause. All that has since been done experimentally seems merely 

 to have given various more or less striking illustrations of these facts, without any attempt 

 to find how the deflecting force depends upon the velocities of translation and rotation : 

 and I am not aware of any successful attempt to extend or improve Newton's suggestion 

 of a theoretical explanation. It seems in fact to have been altogether unnoticed, perhaps 

 even ignored. 



Thus Robins, | writing some seventy years later than the date of Newton's letter, 

 speaks of 



" the hitherto unheeded effects produced by this resistance ; for its action is not 



* Recherches sur le Mouvement des Projectiles dans VAir. Paris, 1839. 

 + Isaaci Newtoni Opera quae exstant Omnia (Horsley), vol. iv. p. 297. 



X New Principles of Gunnerij (new edit.), 1805, p. 206. The paper referred to is stated to have been read to the 

 Royal Society in 1747. 



VOL. XXXVII. PART II. (NO. 21). 3 T 



