334 PETER GUTHRIE TAIT 



also represents the natural action of a spoon, or a "grassed" play club, AB being 

 horizontal. In all these cases the spin is about a horizontal axis, and therefore the 

 skewing is upwards or downwards. Thus, we have traced out generally, and also 

 specially for the most important cases, the processes of the second scene, which 

 usher the ball into the third with a definite speed and a definite rotation. 



In the discussion of the third scene, in which the ball is left to its own 

 resources, to struggle as best it can against the persistent downward pull of gravity 

 and the ever-varying resistance of the air, we will treat fully of really good drives 

 i.e., those in which the spin, if there be any, is about a horizontal axis perpen- 

 dicular to the plane of flight, and is such as to cause the ball to "soar," not to 

 "dook." Incidentally, however, we will notice (though with much less detail) the 

 causes which produce departures of various kinds from a high standard of driving. 



We will treat, first, of the path as affected by gravity alone ; second, of the path 

 under gravity and resistance alone (the ball having no rotation) ; third, of the 

 path as it would be if the ball were spinning, but not affected by gravity ; fourth, 

 as it is when all these agents are simultaneously at work ; and, finally, the effects 

 of wind. The first and third of these, in each of which one of the most important 

 agents is left wholly out of account, though of less consequence than the others, 

 are necessary to the proper development of the subject, inasmuch as their prelimi- 

 nary treatment will enable us to avoid complications which might embarrass the 

 reader. 



i. If there were no resistance, the path of a golf ball would be part of a 

 parabola, BAG, whose axis, AD, is vertical. The vertex, A, of the path would be 

 always midway along the range, BC; and the ball would reach the ground with 

 the speed given it from the tee. A golf ball would therefore be an exceedingly 

 dangerous missile. For fairish but high driving would easily make the range BC 

 something like a quarter of a mile ! And at that distance the ball would fall with 

 precisely the same speed as that with which it left the tee The range for any 

 definite " elevation " (i.e. angle at which the path was inclined to horizon at starting) 

 would be proportional to the square of the initial speed, so that double speed 

 would give quadruple range ; and for any given speed, it would increase with the 

 elevation up to 45, and thence diminish with greater elevation. Any one can test 

 this last result by means of the jet from a garden engine. The speed of such a jet 

 is so small that the resistance is inconsiderable. 



For comparison with some of the numerical results to be given below, we will 

 here give a few simple particulars. 



