500 



PROFESSOR TAIT ON 



As the last five values of <p have been increasing steadily by nearly 3° for each 

 dement, it is clear that the direction of motion again rises above the horizontal; but 

 whether the path has next a point of contrary flexure, or another kink, can only be 

 found by carrying the calculation several steps further. [The second kink is very 

 unlikely, as the speed is so much reduced at the point where the calculations were 

 arrested. Mr Wood has gone to Australia, and I had unfortunately told him to stop 

 the numerical work in this particular example as soon as he found that S(cos^), 

 after becoming negative, had recovered its former maximum (positive) value.] 



The trajectories represented in figs. 5 and 6 may be taken as fairly representative 

 of ordinary good play by the two classes of drivers. For we have in both a = 360, 

 V— 200. These are the new data, representing (as above explained) the best informa- 

 tion I have yet acquired. In fig.5 k= 1/3, <p = 10° ; but in fig.6 Jc — 0, <f> =l5°. In 

 spite of its 50 per cent, greater angle of initial elevation, the carry of the non-rotating 

 projectile is little more than half that of the other : — and it takes only one-third of the 

 time spent by the other in the air. But the contrast shows how much more important (so 

 far as carry is concerned) is a moderate amount of underspin than large initial elevation. 

 And we can easily see that initial elevation, which is always undesirable (unless there 

 is a hazard close to the tee) as it exposes the ball too soon to the action of the wind where 

 it is strongest, may be entirely dispensed with. This point is discussed in next section. 



On account of their intimate connection with actual practice, I give a few of the 

 numerical results for these two closely allied yet strongly contrasted cases, belonging 

 to two different classes of driving: — choosing sides of each polygon passed at intervals 

 of about I s , as well as those near the vertices and the point of contrary flexure. The 

 formulas for these cases are those given at the end of § 17 above : — the second term in 

 the expression for cf>' being omitted for the latter of the two trajectories. 



For Fig. 5. 



s/6 



v l 



V 



1. 



40,000 



* 



200 



25. 



15,497 

 * 



124-5 



39. 



8,216 

 * 



90-6 



42. 



7,042 



83-9 



54. 



3,511 



59-3 



61. 

 62. 



2,387 



2,296 



* 



48-9 

 47-9 



70. 



2,249 



* 



474 



79. 



3,157 

 * 



562 



89. 



4,338 



* 



659 



94. 



4,853 



69-7 



1/v 



00500 



* 



00803 



* 



01103 



* 



01192 



* 



01687 

 * 



02046 



02088 

 * 



02109 



* 



01780 



* 



01519 



* 



01436 



2(1/0) 



4> 



sin cf> 



2(sin #) 



cos<£ 



2(cos <j>) 



•00500 



10° 



•1736 



•1736 



•* 



•9848 



•9848 



* 



•16549 



17-552 



•3015 



6-2345 



•9534 



25-2200 



* 



•29869 



19-789 



3388 



10-7983 



9410 



38-4544 

 * 



•33353 



19-665 



3366 



11-8116 



* 



•9417 



41-2783 



* 



•50626 



13-611 



•2354 



15-3925 



•9719 



52-7246 

 * 



•63904 

 •65992 



1-727 

 - 0-675 - 



•0303 

 •0120 



16-3078 

 16-2958 



•9996 

 •9999 



59-6508 



606507 



* 



•83155 



-21-807 - 



•3714 



14-5533 



■9285 



68-4117 



00513 



- 35-890 - 



■X- 



5862 



9-9647 



8103 



76-1309 



* 



•16748 



- 40-840 - 



-X- 



6538 



3-6521 



7566 



83-8830 

 * 



•24081 



-41-548 - 



6633 



0-3507 



7484 



87-6381 



