Billiards

by William Broadfoot

Next set ball 2 upon the central line at such a distance from the baulk-line as the player can imagine its division described on page [133], and play ball 1 so as to make three-quarter, half, and quarter-ball strokes with some confidence. This distance will no doubt vary with the stature and sight of the player, but 2 feet may be tried as about average. If P, P′, P″ be the points of impact for the various divisions, ball 2 will, after the strokes, travel in the directions R, R′, R″, each being the prolongation of a line from the point of impact through the centre. Ball 1 will behave differently according to the strength with which it is struck; what is always true is that it will travel in a contrary direction to ball 2. If the one ball goes to the left after impact the other will go to the right. Played with strength 1 or 2, impact being at P, ball 1 will follow through the space which ball 2 covered, and will stop slightly to the right of the line A B. With impact at P′ or a half-ball stroke, ball 1 will deviate further from the line A B, and travel in the direction D, A C D being the half-ball angle; when played quarter-ball, impact being at P″, ball 1 will deviate less from A B and travel towards E. The object of this practice is to accustom the eye to recognise approximately the directions taken by both balls after impact.

A small matter which is a little obscure connected with the language of billiards should here be noticed. In placing ball 1 for a stroke, it is usual, and generally desirable, to select a spot from which the angle 1 C D shall be what is known as the half-ball angle, and certainty in play is greatly based on the power of recognising this position. Consequently in time players, perhaps unconsciously, refer almost every stroke to that angle as a standard. If a hazard or cannon is on the table, they consider for a moment whether the angle contained between the two paths of ball 1 is greater or less than the half-ball angle, and to the best of their ability they apply compensations to meet the difference, playing fuller and harder when the angle is less, finer and slower when the angle is greater, until a following stroke becomes necessary. Nevertheless, the universal custom is to define the situation when the angle is smaller as wider, and when the angle is greater as narrower. Thus the position 1 C D is called wider than 1 C E. Clearly it is so only as regards the deviation of ball 1 from the prolongation of its original path—that is, from the path which would have been followed if there had been no impact—consequently the angle of deviation must be defined as that between the new actual path of ball 1 and the path that would have been described if the deviation had not taken place. This being accepted, the ordinary use of the terms wider and narrower is appropriate.

In this and in all diagrams as far as possible the lines followed by the centres of balls are shown; hence, as the centres cannot touch each other or the cushions, the lines do not reach to the surface of either, but are necessarily short of the point of impact by the length of the ball’s radius. Ball 1, after impact other than full, describes a curve due to the forces to which it is subject; this is greater in proportion to the strength of stroke, and though in practice its effect must not be neglected, it is not ordinarily shown in the diagrams, which do not pretend to absolute accuracy, but merely to such measure of correctness as is required for practical purposes. An illustration of the curve, and a warning when its existence must not be overlooked, will be found in Chapter V.

Fig. 6

From the strokes recommended in Chapter III. for practice it will have been learnt that in a general way a ball played against a cushion will return therefrom, so that the angle of reflexion shall be nearly equal to the angle of incidence. A useful two-ball practice based on this is to place balls 1 and 2 on the table and endeavour to play on 2, having first struck a cushion. The difficulty is to determine the point on the cushion on which 1 must impinge so as to rebound on 2.

The solution is approximately:—From ball 1 let fall 1 A perpendicular to the cushion A C D; produce 1 A to B, making A B = 1 A. Join B with the centre of 2; where that line cuts the cushion at C is the point required. Play 1 so that it shall strike C and it will rebound on 2. Similarly, if the second ball occupy the position 2′ the line from B to its centre intersects the cushion at D; ball 1 played to touch the cushion at D will travel to 2′. In a game of course the cushion must not be marked, but in practice it will at first be found advantageous to mark the spot sufficiently to guide the stroke and educate the eye. This is easily done by placing a piece of chalk on the wooden frame of the cushion just behind the spot to be hit, thus doing away with the need of marking the cushion with chalk, which it is well to avoid. When it is necessary to mark the cloth of bed or cushion, pipeclay such as tailors use is preferable to chalk. Special attention is necessary to two facts: first, the angle of reflexion varies with the strength; that is, a soft stroke will come off very nearly at the same angle as that of incidence, whilst with a hard stroke there is a perceptible difference; second, the point on the cushion which should be hit must not be aimed at. This is merely a modification of what has already been explained with reference to the points of aim and of impact. Fig. 7 shows how very far a ball on the line 1 P played, i.e. aimed at P, is from hitting that point; instead of doing so it strikes the cushion at T; hence allowance must be made in aiming, the length allowed on the cushion diminishing as the angle approaches a right angle. When the stroke is at a right angle to the cushion the points P and T coincide and no allowance is required.

One reason why the angle of reflexion varies with the strength is that, on impact with the cushion, the ball, being harder than the rubber, indents it—makes a sort of cup, in fact, deeper as the stroke is stronger. Friction with the cloth of the cushion has also some effect on the angle, and there may be other causes at work; fortunately, it is probable that one to some extent counteracts another. This practice from a cushion is interesting as well as useful; at first the beginner will be satisfied if he hits ball 2 anywhere and anyhow; but soon he will be able to hit it on one side or the other, as he may wish, when the distance ball 1 has to travel is not very great. Hereafter both cannons and hazards will be mentioned, which must be played bricole, or off a cushion before ball 2 is struck, and the practice proposed will make their execution fairly easy and certain. We conclude this chapter, which has covered important ground, with four illustrations of the division of ball 2 at the moment of impact. A shows ball 1 applied to 2 for a quarter-ball stroke, B for a half-ball, C for a three-quarter-ball, and D for a full ball stroke; the phases varying between partial and total eclipse.

Fig. 7