and side, we will illustrate them by means of a diagram.
In Fig. 1 we will suppose the red ball to be placed on the middle spot in the table, M. The player places his own ball in the centre spot in the baulk-line, K, and aims his ball, first of all, so as to strike the object ball with the ordinary Half-ball Stroke—that is, the centre of his ball advances towards the extreme edge of the object ball.
In Fig. 2, O is the object ball; S, the striker's ball. In order to play the half-ball stroke, it is necessary that the player should aim at the point E, the extreme edge of the horizontal diameter of the object ball. Of course, as the diagram shows, he will not strike the ball in the point at which he aims (this is never done save in the case of the ball being struck exactly in the centre), but as S1, in the point C. When the object ball is thus struck, the striker's ball, supposing there is no screw on the ball, will take the direction indicated in Fig. 2 as S2. This angle is called the natural angle; about this natural angle we shall have to say more by-and-by. Suppose the stroke played thus. After playing, the ball will follow the line M P (Fig. 1). Now suppose some strong screw had been put on the ball by hitting it low down. The ball, owing to the hit, and to its after-contact with the ball at M, would follow the line M P; but, owing to the rotatory motion making the ball revolve or spin backwards, it has a tendency to run back again towards K, the point from which it started. Under the influence of these two forces, the ball takes the medium course shown by the dotted line M P1. In other words, the striker, although he hits the object ball a half-ball stroke, screws into the middle pocket.
Now suppose, instead of hitting the ball below the centre, he hits it high up above the centre, so as to make the ball rotate forwards. After the balls have come in contact, the rotatory motion forwards has a tendency to make the striker's ball run onwards
towards the top cushion and away from K, the point from which it started; but the contact with the object ball would—did no rotatory motion exist—cause it to follow the direction of the line M P. Under the influence of these two forces the ball takes a medium course, and follows the line M P2.
If the player hit the ball at M full, that is, played at it quite straight and hit the ball at M in its nearest point, then, if he put on screw, his own ball would, after striking the ball at M, stop and run back towards K, fast or not according to the amount of rotatory motion he succeeded in putting on his own ball when he struck it.
If the player hit the ball at M full, and hit his own ball high up and above the centre—the following stroke—his ball, after striking the ball at M, would follow on, and, if he hit it exactly, would go on in the direction of the spots, P and S.
In putting on side, the ball is caused to rotate on a perpendicular axis. For instance (vide Fig. 1), suppose the player places his ball on the centre spot in baulk, K, and hits the cushion in the point T without putting on any side, then the ball would rebound in the direction of T R, just as the angles of incidence and reflection are equal. Suppose, however, the player strikes his ball on the right-hand side, causing it to rotate on a perpendicular axis. When the ball touches the cushion at T, this rotation, owing to the friction between the ball and the cushion, causes the ball to take the direction shown in the diagram by the line T R1. If, on the other hand, the player hits his ball on the left-hand side, the ball will rebound in the contrary direction shown by line T R2. This latter stroke is what every player