494 PROFESSOR TAIT ON 



habitual carry is 180 yards or upwards, the circumstances of the trials were somewhat 

 unfavourable, for there was great difficulty in hitting the disc of clay centrally. The 

 pendulum was suspended in an open door- way ; and heavy matting was disposed all 

 about the clay so as (in Robins' quaint language) " to avoid these dangers, to the 

 braving of which in philosophical researches no honour is annexed " ; so that the whole 

 surroundings were absolutely unlike those of a golf-course. I therefore make an allow- 

 ance of 20 per cent., and (as at present advised) regard 240 foot-seconds or something 

 like it as a fair average value of the initial speed of a really well-driven ball : — while 

 thinking it quite possible that, under exceptionally favourable circumstances, this may 

 be increased by 20 or 30 per cent, at least. Now, it is certain that the time of flight 

 is usually about six seconds when the range is about 180 yards: — considerably more 

 for a very high trajectory, and somewhat less for a very flat one. As we have by § 5 

 the approximate formula 



we may take a = 360 as a reasonable estimate. This number is possibly some 10 per 

 cent, in error, but it is very convenient for calculation, and golf-balls differ considerably 

 from one another in density as well as in diameter. With it the "terminal velocity" of 

 a golf-ball is about 108 foot-seconds ; intermediate to the values deduced from the 

 formulae of Robins and of Bashforth, which I make out to be 114 and 95 respectively. 

 With this value of a, it is easy to see that air-resistance, alone, reduces the speed of a 

 golf-ball to half its initial value in a path of 83 yards only. This is the utmost gain of 

 range obtainable (other conditions remaining unchanged) by giving four-fold energy of 

 propulsion ! With the value (282) of a deduced from Bashforth's formula, this gain 

 would have been 65 yards only ! [So far for the higher speeds, but it is obvious from 

 all ordinary experience of pendulums (with a golf-ball as bob) that slow moving bodies 

 suffer greater resistance than that assigned by this law.] 



In passing, I may mention that, on several occasions, I fastened firmly to the bail a 

 long light tape, the further end being fixed (after all twist was removed) to the ground 

 so that the whole was perpendicular to the direction of driving. After the 4 foot flight 

 of the ball, the diameter at first parallel to the tape preserved its initial direction, while 

 the tape was found twisted (in a sense corresponding to underspin) and often through 

 one or two full turns, indicating something like 60 or 120 turns per second. This is 

 clearly a satisfactory verification of the present theory. 



mVj(M+m). Equating the corresponding kinetic energy to the potential energy into which it is transformed, we find 

 at once (M +m)gd 2 j2l = m 2 V 2 j2(M +m) leading to the very simple expression 



M+m - 7r 



With the numerical values given in the text we easily find that this is equivalent to 



r=331j2l'93 = 53-2Z); 



where Via, of course, in foot-seconds, but the deflection is now (for convenience) expressed in inches, and called /'. 

 Hence the numerical result in the text. 





