THE TRUE TRAJECTORY 341 



out upon too high an estimate of the resistance, and the initial data also were 

 chosen with reference to this. Thus, when reduced to 108 feet as the terminal 

 velocity, the paths have been virtually worked out for intervals of about 9 feet 

 instead of 6, and the initial data appear of a rather haphazard character. 



We see from what precedes that the full investigation of the path of a golf 

 ball, even when it is restricted to a vertical plane, would require voluminous tables 

 of at least triple entry ; for the form and dimensions of the path are now seen to 

 depend quite as essentially upon the amount of spin as upon the initial speed and 

 elevation. There are now no longer two, but innumerable, paths, which involve a 

 definite carry even when they are confined to a vertical plane, and the initial speed 

 is given. Of course no tables for their computation are in existence, and it would 

 prove a somewhat laborious, and therefore costly, work to prepare such tables, even 

 for a few judiciously selected values of elevation, speed, and initial diminution of 

 weight. In their absence it is impossible to make any statements more definite 

 than such very general ones as those above. But (as soon as trustworthy deter- 

 minations of the resistance of air and of the rate at which the spin of a golf ball 

 falls off are obtained) a couple of good computers, working in duplicate for a month 

 or two, would supply sufficient material for at least a rough approximation to any 

 path affected under the ordinary limits of the initial data of fairly good driving. 

 Let us hope that some wealthy club, or some enthusiastic patron of the game, may 

 be induced to further such an undertaking, at least so far as to enable us to give 

 a fairly approximate answer to such a question as, " Other things being the same, 

 what values of elevation and of initial diminution of weight will together secure the 

 maximum carry ? " When we are in a position to give an answer, the clearing up 

 of the whole subject may be regarded as at least fairly commenced. 



30 C'O 90 120 150 180 yds 



Meanwhile, as a specimen of what may be done in this direction, I give in 

 the annexed plate an approximate sketch of the path of a golf ball under the 

 following initial conditions, the spin being regarded as unaltered during the flight : 



Initial speed 240 feet-seconds 



Initial relief of weight ... ... 2 fold 



Elevation 5-2" 



This is fig. i on the plate, and it will be at once recognised as having at least 

 considerable resemblance to that class of really good, raking drives in which the 

 ball's path is concave upwards for more than a third of the range. Its one obvious 



