The practice prescribed in the preceding chapter had for its chief object the attainment of certainty in striking ball 1 truly in the centre; we now proceed to study some of the elementary facts concerning the impact of one ball with another.

In the first place, the conditions of impact should be recognised, and what is termed the division of balls must be explained.

Now, for practical purposes the cloth and bed of the table are level, and the balls are of the same size; hence when they touch one another the point of contact is invariably on the line of their greatest horizontal circumference, which, as all know, is precisely at half their height. It will hereafter be shown that ball 1 may be caused to leap, and so strike ball 2 above this; but for present purposes, when a plain stroke alone is being considered, it may be accepted as a fact that the point of impact is always at half the ball’s height. That fixes the location of impact vertically; but horizontally it is evident that there is considerable latitude. Ball 1 may hit ball 2 either precisely full, when the centre of one is played on the centre of the other, or it may strike either to the right or left of the centre of ball 2; the limit on either side being the finest possible touch. The accompanying figure will show what is meant. When ball 1 hits ball 2 full, at the moment of impact it occupies the position 1″; and the part of 2 which can be struck by a ball situated at 1 is from P″ to P; if ball 1 occupies the position 1′, then the part of 2 which may be touched is restricted to that marked P″ P′; but should ball 1 be placed at 1″, then the only point on 2 it can touch is P″. Therefore the nearer 1 is to 2 the less of the latter can be struck, and the further away the more.

As regards the division of balls, for the English game at any rate, the simpler it is the better. The larger balls on a smaller table, as used in the French game, admit of more minute subdivision than do our smaller balls, which may be, and often are, further from the player’s eye. To attempt a division which the eye cannot easily appreciate is a mistake. For purposes of play both balls 1 and 2 must be divided; and although at this early stage of the manual we are not concerned with the division of ball 1 (for all practice at present is confined to centre strokes), yet it is convenient now to record the divisions of both balls.

Ball 1 is divided by its vertical and horizontal diameters into four parts. The centre stroke is delivered at C, and is of all strokes by far the commonest and most important.

A ball struck high and right is struck in the sector C A E; low and left in C D B; high and left in C A D; low and right in C E B.

The vertical and horizontal lines are divided from the centre where they intersect, into four equal parts each way. Thus a ball ¼ high is struck on the line C A at the point marked ¼; ½ low is struck on C B at the point marked ½; ¾ right is struck on C E at the point marked ¾; ¼ left is struck on C D at the point marked ¼. Combinations of these divisions are of course possible: thus ½ high and right would indicate a point P; ¾ left and ½ low is represented by P′. That division is quite as minute as the eye can follow; indeed, for general purposes it will probably suffice to indicate the sector only; to say, for example, ball 1 should be struck high and right.

In respect to ball 2 the matter is different; it cannot, as has already been shown, be struck save on the line C C′ A, the height moment of reaching 2, then its position will be that of the dotted circle 1″, whose centre is C″, and P′ is the point of impact. For any stroke between full and half-ball the point of impact will lie between P and P′; between half-ball and the extreme of fineness the point of impact will lie beyond P′ in the direction of E.

Ball 2 being struck by ball 1 at P′ must travel in the direction P′ B F, the line from the point of impact passing through B the centre. There is practically no departure from this rule. Hence it follows that if it be desired that ball 2 should travel in the direction B F, say to a pocket, imagine a line from the pocket passing through the ball’s centre; this cuts the circumference at P′, which is manifestly the point which must be struck by ball 1. Where is the centre of ball 1 to be aimed at in order that P′ may be struck? Produce the imaginary line F B P′ to C″, making P′ C″ equal to B P′ or in other words equal to the radius of the ball. If the centre of ball 1, C, be aimed on C″, ball 2 must be struck at P′ and must travel in the direction required.

Pray realise that it is impossible to hit ball 2 at the point aimed at save when the stroke is full; in every other case the aim must be beyond the point of impact, and the rule above given will enable anyone to determine precisely where aim should be taken.

When a ball is struck by the cue its first impulse is to slide forward, and if there were no friction between the ball and the cloth it would do so till arrested by other causes; but as there always is this friction, the lower part of the ball is thereby retarded, and the result is the rolling or revolving motion with which all are familiar. This will be further considered when the subject of rotation is discussed, but it is mentioned here as the cause of certain effects which will be observed in some of the strokes recommended for practice. When one ball impinges on another the immediate result is a greater or lesser flattening of both surfaces at the point of impact; this is instantaneously followed by recoil,^[14] the result of each ball reassuming its spherical form. The greater the strength of stroke the greater the flattening and the greater the recoil; the converse likewise holds good.

Further, the force or strength with which ball 1 strikes ball 2 is immediately divided on impact; if ball 2 be struck full it appears to acquire from ball 1 the whole of its energy save that due to naturally developed rotation, the result being that ball 2 travels fast whilst ball 1 remains comparatively stationary. If the distance between the two balls be very small, little rotation is acquired and ball 1 transmits its motion to ball 2 and stops on or near the spot which that ball occupied; if the distance be considerable, ball 1 acquires rotation which, overcoming the recoil on impact, causes it to travel slowly in its original direction. When impact is other than full, ball 1 parts with more or less of its force, which is transmitted to ball 2. What the one loses the other gains.

These general remarks will seem to many self-evident and superfluous; to others they may prove difficult to realise and distasteful; but students, whether beginners or those who have already acquaintance with the game, may rest assured that a careful consideration of them can do no harm and may be of much advantage; for practice is assisted by an intelligent appreciation of the behaviour of balls under certain conditions; in short, by a consideration of cause and effect.

For practice: place ball 1 on the centre of the Ｄ on the baulk-line, put ball 2 a foot up the table in the central line, play 1 full on 2 with varying strength, at first with strength to carry 2 to the top cushion; the truth of the stroke will be shown by 2 passing over all the spots in the central line and 1 following slowly in the same line for a short distance. When tolerable certainty is acquired play the same stroke harder, and if correctly struck ball 2 will return from the top cushion and meet ball 1, kiss as it is called, in the central line. The stroke can be made more difficult by placing ball 2 further up the table, say on the centre spot, and playing as before, and again by placing it on the pyramid spot. This practice, though it may seem uninteresting, is most useful; it combines and continues that recommended for one ball with that required for truth of stroke on another. It also, as will hereafter be shown, is directly useful in the matter of cannons, hence it should be assiduously practised.

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.

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.