CONDITIONS OF IMPACT 331 



dynamical calculation, and Scene II. would be absolutely instantaneous. If, in ad- 

 dition, the ball were perfectly spherical, smooth, and of homogeneous material, no 

 blow could possibly set it in rotation ; if it were defective in any of these particulars, 

 we could easily calculate the direction of the axis of rotation and the amount of 

 spin produced in it by any assigned blow. But, unfortunately, neither balls nor 

 clubs can make an approach to perfect hardness. For there is never, even in a 

 gentle stroke, a mere point of contact between ball and club. In good drives the 

 surface of contact may often, as we see by an occasional trace from undried paint 

 or by the pattern impressed by the first drive on a new leather face, be as large 

 as a shilling. The exact mathematical treatment of so large a distortion is an 

 exceedingly complex and difficult matter. But fortunately we are not called upon 

 to attack it, for it is obvious, from the facts of common observation already cited, 

 that the final effect on the ball is of the same general character as if it had been 

 perfectly hard, though the speed of projection, and notably that of spin, will be 

 materially less. And it is with the character rather than with the amount of the 

 effect that we are mainly concerned, as will be seen farther on. Thus, in a great 

 part of what follows, we will argue as if both club and ball were hard, since we 

 seek to explain the character of the results and are not for the time concerned with 

 their magnitiides. 



When we reflect on the very brief duration of the impact, during which the 

 average force exerted is about three tons' weight (while the player is, for an instant, 

 working at two or three horse-power at least), we see at once that we may practi- 

 cally ignore the effects of gravity, of the continued pushing forward of the club head, 

 and even of the resistance of the air (though amounting to, say, five-fold the weight 

 of the ball) during that short period ; so that we are concerned only with the 

 velocity and the orientation of the club face at the moment of impact. 



The simplest case which we have to consider is that in which the club face, 

 at the instant of meeting the ball, is moving perpendicularly to itself. If the ball 

 be spherical and homogeneous, there can be no spin ; and thus we are concerned 

 only with the steps of the process by which the ball ultimately leaves the club in 

 the common direction of motion. The first effect is the impulsive pushing forward 

 of the part of the ball which is struck, the rest, by its inertia, being a little later in 

 starting. Thus the ball and club face are both distorted until they, for an instant, 

 form, as it were, one body, which has the whole momentum which the club head 

 originally possessed. As the club head is usually about five times more massive 

 than the ball, the common speed is five-sixths only of the original speed of the 

 head. [In the case of a more massive club head a correspondingly less fraction 

 of its speed would be lost, but a proportionately greater effort would be required 

 to give it a definite speed to begin with. A sort of compromise must thus be 

 made, and experience has led to the proportion cited above so long, at least, as 

 we are dealing with balls of about ten or eleven to the pound.] But the ball and 

 club both tend to recover from their distortion, and experiment shows that they 

 exert on one another, during this recovery, an additional impulsive pressure which 

 is a definite fraction of that already exerted between them. This fraction is tech- 

 nically called the " co-efficient of restitution," and it is upon its magnitude that 



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