344 PETER GUTHRIE TAIT 



with it, is then moving as a whole, and in it the path of a golf ball depends only 

 upon the relative speed and elevation with which it was started. Find, then, with 

 these data, the path of the ball relatively to the air, and then compound with the 

 results the actual motion of the air, and we have the path of the ball as it appears 

 to a spectator. If, then, the ball be struck from with velocity represented by 

 OA, and the reversed velocity of the air be represented by AB, the velocity of the 

 ball relatively to the air is given by OB 1 or OB 3 according as the wind is with the 

 ball or against it. Trace the successive positions of the ball in the moving air for 

 each of these, say at intervals of a second, and then displace these horizontally, 

 forward or backward, to the amount by which the air itself has advanced during 

 the time elapsed. The result is of course merely to compress or to lengthen each 

 portion of the path in proportion to the time which the ball took in traversing it. 

 There is no effect on the height of any part of the path, nor on the time of passing 

 through it. It is clear that the path, whose initial circumstances are shown by OB t 

 in the figure, will rise higher than that corresponding to OB t . Hence a ball 

 which has no spin rises higher when driven with a following wind than against an 

 equally strong head wind. This is in the teeth of the general belief, which is 

 probably based on the fact that the vertex of the path against a head wind is 

 brought closer to the spectator at the tee, and therefore its angular elevation is 

 increased. When the ball has spin, the conditions of this question become very 

 complex and no general statement can be made ; though a calculation can, of 

 course, be carried out for the data of each particular case. 

 I conclude, as I began, with the much-needed warning : 



False views abound, the "cracks" are all mistaken; 

 In figures, only, rests our trust unshaken. 



It seems appropriate to note, with regard to Tait's article on long 

 driving, how completely his theory has stood the test of later investi- 

 gations. In an interesting lecture on the dynamics of a golf ball delivered 

 at the Royal Institution on March 18, 1910, Sir J. J. Thomson 1 went over 

 much of the ground covered by Tait in the preceding article and in his 

 papers on the path of a rotating spherical projectile, reproducing also by 

 way of illustration some of the experiments due to Robins and to Magnus. 

 The most novel feature of Sir J. J. Thomson's lecture was the practical 

 realisation of the possible paths calculated by Tait and shown on page 341. 

 The cusp and kink figured on page 342 were also demonstrated by 

 Sir J. J. Thomson by means of the same ingenious experiment. A stream 

 of negatively charged particles from a red-hot piece of platinum with a spot 

 of barium oxide upon it was caused to travel along the vacuum tube in 

 which the platinum strip was contained. This stream of particles was 

 1 See Nature of December 22, 1910, Vol. LXXXV, pp. 251-257. 



