332 PETER GUTHRIE TAIT 



the higher or lower quality of a ball, and of a club face, mainly depend. Its value, 

 when good materials are employed, is usually about O'6. Thus the club and ball 

 at last separate with a relative speed six-tenths of that with which the club approached 

 the ball. The ball, therefore, finally acquires a speed about one-third greater than 

 that which the club head originally had. Thus the head must have a pace of about 

 1 80 feet per second in order that it may drive the ball at the rate of 240 feet per 

 second. And, for various values of the co-efficient of restitution, the ultimate pace 

 of the ball can never be less than five-sixths, nor as much as five-thirds, of the 

 initial speed of the club head. We thus get at present about four-fifths of what 

 is (theoretically) attainable ; and we may perhaps, by means of greatly improved 

 materials, some day succeed in utilising a considerable part of this wasted fifth. 



Where, as is almost invariably the case, the face of the club is not moving 

 perpendicularly to itself at impact there is always one perfectly definite plane which 

 passes through the centre of the ball and the point of first contact, and is parallel 

 to the direction of motion of the head. It is in this plane, or parallel to it, that 

 the motions of all parts of the ball and the club head (except, of course, some of 

 the small relative motions due to distortion) take place. Hence if the ball acquire 

 rotation it must be about an axis perpendicular to this plane. The whole circum- 

 stances of the motion can therefore be, in every case, represented diagram matically 

 by the section of the ball and club face made by this plane. The diagram may 

 take one or other of the two forms below, either of which may be derived from the 

 other by perversion and inversion. 



[Thus, if the page be turned upside-down and held before a mirror, the result 

 will be simply to make the first figure into the second, and the second into the first 

 merely, in fact, altering their order. Holding the page erect, before a mirror, we 

 get diagrams specially suited for a left-handed player.] 



In each of the figures the velocity of the club head at impact is represented 

 by the line AB, and the dotted lines AC and CB represent its components parallel 

 and perpendicular to the club face respectively. By properly tilting the figures, 

 AB may be made to take any direction we please, i.e. the club head may be 

 represented as moving in any direction whatever but it is quite sufficient for our 

 purpose to treat it as moving horizontally. It is the existence of the component 

 velocity AC, in a direction parallel to the club face, which (alone) makes the differ- 

 ence between this case and the simple one which we have just treated. And if the 

 ball were perfectly smooth this component would lead to no consequences. But 

 because of friction this component produces a tangential force whose effect is partly 

 to give the ball as a whole a motion parallel to AC, partly to give it rotation in 

 the direction indicated by the curved arrow. The direction of motion of the ball 



