.:4 : 



NATURE 



[June 5, 1913 



a well-struck ball. But before the experiment was 

 thought of Tait had proved to the mind capable 

 of understanding the dynamics of golf that it is 

 not possible to obtain the distance of flight and 

 the time of flight by balls projected with per- 

 missible velocities at the small angles of elevation 

 which characterise well-driven balls, unless an 

 uplifting force comes into play. 



Mr. Vaile is neither fair to Tait nor true to fact. 

 In his chapter x. he says, quite untruly — for the 

 dates can easily be given " — that Tait did not take 

 underspin into consideration until after a great drive 

 by which his son Freddie proved that the father's 

 calculations were wrong. He then proceeds to 

 point out what he thinks are errors in Tait's article 

 in The Badminton Magazine, which has been 

 already referred to. For example, Tait's remark 

 that "the existence of rotation is manifested at 

 once by the strange effects it produces on the 

 curvature of the path" is branded "as in- 

 correct from a scientific point of view," and "also 

 badly stated." What follows on p. 225 of "The 

 Soul of Golf " shows that our author has not 

 grasped the scientific significance of the problem. 

 He says that it is well known to all golfers that 

 the spin begins to work as the velocity of the ball 

 decreases, and then makes the astounding state- 

 ment that " it is incorrect to refer to the strange 

 effects it (rotation) produces on the curvature of 

 the path, for it is the rotation itself which produces 

 the curvature." 



If this means anything other than Tait meant, 

 it means that the parabola described by a projectile 

 in vacuo has no curvature, nor has the path 

 described in air by a ball devoid of rotation. 

 Gravity apparently is not in it ! Mr. Vaile fails 

 to see that Tait is comparing the path of a rotating 

 golf-ball with the path it would have had if no 

 rotation had existed. The real dynamic truth is 

 that the underspin begins to work from the very 

 beginning of the drive. The curvature of the 

 path is influenced from the start, as witness the 

 upward concavity of the wind-cheater. Not onlv 

 so, but the underspin exerts its greatest influence 

 at the beginning of the drive when the spin and 

 the velocity are both at their greatest. When 

 Mr. Vaile asserts that it is in the second part of 

 the trajectory that the back-spin is exerting its 

 greatest influence, he is confusing what the eye 

 seems to see with what has been really taking 

 place. The ordinary golfer, indeed, is quite 

 ignorant of what any particular path would have 

 been had there been no spin ; also he is badly 

 placed to see the real form of the path, and the 

 initial velocity is too great for him to follow the 



2 See, for example, " A Golf Myth : Prof. Tait's Alleged Error," in Golf 

 Illustrated, January r, 1909 ; or in my " Life and Scientific Work of P. G. 

 'fait," pp. 26-28. 



NO. 22 7^. VOX. SUl 



early details of the flight. Tait's calculated curves 

 bring' out the form of the wind-cheater beautifully 

 (see Nature, June 29, 1893). These calculations 

 are based on the combined effect of gravity and 

 the upward force due to coexistence of transla- 

 tion and spin. Both these motions are present 

 from the beginning, and must dynamically assert 

 themselves from the start. To speak of pace, 

 when there is enough of it, as beating spin, is non- 

 sense. Spin alone has no lifting or swerving 

 power. It must coexist with translational 

 velocity; and the lifting power increases with the 

 amounts of both. 3 The particular instant at which 

 the eye recognises the accumulated effect of the 

 upward lift proves nothing as to the manner in 

 which this lifting force has gone through its 

 successive values. The idea that the spin asserts 

 itself only after the ball has travelled a considerable 

 part of the trajectory is dynamically grotesque and 

 hopelessly erroneous. 



The flight of the golf-ball is not a problem which 

 can be solved by intuition ; and the man who has 

 not mastered Tait's papers on the path of a 

 rotating spherical projectile is not in a position to 

 criticise Tait's conclusions. If Mr. Vaile will 

 take the trouble to turn up the first of these papers 

 he will find pictured a theoretical curve the gradu- 

 ally increasing curvature of which as the linear 

 speed of the projectile falls off will reveal to 

 him all the essential characteristics of the path of 

 the sliced ball. He may then possibly understand 

 the truth which Tait was wont to impress upon 

 his students year by year, that the direct evidence 

 of our senses is frequently misleading unless con- 

 trolled and corrected by reason. 



There are several other statements in Mr. 

 Vaile 's account of the flight of the golf-ball which 

 are scientifically unsound. Thus, on p. 244 he 

 says that the club 



"is nearly always moving either upwards 

 or downwards in a curve at the moment 

 it strikes the ball, so that it stands to reason, 

 especially when the club-face is travelling upwards, 

 which is what it does in the great majority of 

 cases, that the blow is never delivered horizontally, 

 but is always struck more or less upward through 

 the ball's centre of mass." 



This is deliciously loose, for it means grammatically 

 that when the club-face is travelling either upwards 

 or downwards it strikes the ball upward through 

 the centre of mass. Of course, Mr. Vaile does not 

 mean to say so. What he seems to mean to 

 assert is that in the great majority of cases the 

 impulse is through the centre of mass of the ball. 

 If that were so, there could be no underspin, nor, 

 indeed, any spin at all. The great majority of 



3 See, for example. Lord Ravleigh, " On the Irregular Flight of a Tennis 

 Ball," Messenger of Mathematics, 1877; "Scientific Papers," vol. i. 



