SIMPLE THEORY OF PROJECTILES 335 



Suppose the ball to have an initial speed of 200 feet per second ; we have 



The lengths are in feet and the times in seconds. Notice that for elevation 15" 

 we get a range of 207 yards, with a maximum height of 14 yards. These, so far, 

 are not very unlike what may sometimes occur in an actual drive. But we must 

 look to all the facts ; and this closer comparison shows the resemblance to be only 

 superficial. For, first, the vertex is midway along the path ; second, the ball comes 

 down, as it rose, at 200 feet per second. These are utterly contrary to experience. 

 But, third, this long journey is effected in little more than three seconds. A golfer 

 finds that it requires nearly seven seconds. The unresisted projectile theory is thus 

 completely at fault, so far as application to golf is concerned, 



2. Let us next consider the effect of atmospheric resistance, the ball having 

 no spin. [This was, and unfortunately must continue to be, a matter of grave 

 concern to myself. For when I began to learn golf, my instructor (an elderly man, 

 but a very fair player for all that) urged me to bear constantly in mind that "all 

 spin is detrimental" This was, he told me, the definite result of his long experience. 

 It cost me much thought, and long practice, to carry out his recommendation, and 

 it is possible that I have more personal experience of the behaviour of balls almost 

 free from spin than has any other player. The more nearly I approached this 

 ideal the greater was the proportion of run to carry in my driving. I understand 

 it now too late by thirty-five years at least.] 



It has already been said that want of homogeneity in a spherical ball almost 

 certainly leads to its getting spin from the very tee. But, even should it be pro- 

 jected without rotation, it will soon acquire some as it moves through the air. The 

 spin so acquired will be of an uncertain and variable nature, and the flight of the 

 ball will be unsteady and erratic. [I have elsewhere explained how to test balls 

 for this defect, by merely making them oscillate while floating on mercury. Any 

 which oscillate quickly are absolutely useless.] 



It seems to be pretty well established that, for the range of speed common in 

 golf, the resistance is as the square of the speed. In fact, the faster a ball moves 

 the more air does it displace in a given time and also the faster does it make that 

 air move. The most convenient mode of expressing the amount of resistance is 

 to assign the "terminal velocity" of the ball, i.e. its speed when the resistance is 

 just equal to its weight If a sack full of golf balls were emptied at a height of 

 three or four miles, the balls would reach the ground with their terminal velocity. 



