Billiards

by William Broadfoot

Hence it follows that in considering the motion and rotation of billiard balls on a table, we must picture to ourselves a toothed-wheel working on a toothed-plane, and one toothed-wheel working into another, rather than a perfectly smooth surface on a similarly perfectly smooth plane, or two perfectly smooth spherical surfaces in contact.

The accompanying drawings, in which the roughness is purposely exaggerated, will convey the idea better than much elaborate description. No. 1 shows a ball in contact with the cloth, and No. 2 one ball in contact with another. From these it is easy to realise that a ball rotating has a bite of the cloth, and will travel along it in the direction of the rotation, and also that a ball rotating round its vertical axis brought into contact with another must transmit a portion of its rotation, the effect of which is to make the second ball revolve in the opposite direction, precisely after the manner of one toothed-wheel working into another. Such transmitted side is no doubt very small and difficult to perceive, save in the matter of results which cannot otherwise be accounted for. It is indeed probable that side can in this way be communicated to a third ball provided it be touching the second ball. By its means certain kiss strokes can be made which without the use of side are impossible. The subject is undoubtedly complicated, and the suggestions here offered may be wrong; they are those which, after much consideration, have commended themselves as most in agreement with known facts concerning the rotation of bodies, and as accounting for the behaviour of billiard balls in a manner which is not repugnant to common-sense. Nevertheless it must be admitted that absolute proof of transmitted side can scarcely be said to exist, that many experienced persons deny its existence, and, moreover, it is never safe to jump to conclusions.

Let us now consider the four classes of rotation which have already been defined, and begin with forward rotation or follow. This is the most important of all; for, as will be seen, it is present and active in almost every stroke unless special means are employed to counteract it. It is generated in two ways—spontaneously, and by striking the ball above its centre.

When a ball is struck by a cue in the centre, no rotation is thereby communicated. Its first impulse is to slide along with a velocity and for a distance proportionate to the force employed. But the instant that motion is communicated, resistance to sliding forward is experienced. The ball then is subjected to two forces, one from the cue impelling it forward, and the other a retarding force caused by the friction of the cloth. The impelling force drives C in the direction M, and the friction or retarding force acts on B in the direction B N. The point B is thereby retarded, and the result of the two forces is that C travels towards M, whilst A advancing, B being retarded, a rotatory motion is produced whereby A at the top gradually lowers its position till it reaches the bottom and rests on the cloth. It is evident that this spontaneous rotation exists in every plain stroke; it is separate from the mere displacing or translating force, and has a separate life. One may outlive the other; an ordinary example of this is when ball 1 is played full on ball 2. When the distance between them is small, little or no rotation has been acquired and the force of ball 1 is transmitted to ball 2, the former remaining nearly stationary, or dead, after impact; but when there is considerable distance between 1 and 2, rotation is well established and asserts itself after impact, which destroys the life of the force of displacement or translation. Thus ball 1 on impact stops merely for a moment, for rotation coming into play carries it forward on its original path. A very common illustration of this is unpleasantly familiar to young pool players. They cannot prevent their own ball from following into a pocket after a long straight hazard.

Fig. 3

But follow can be increased or accelerated artificially, and the object of doing so is to augment the progress of ball 1 after impact. No gain in propulsion results from hitting a ball over the centre, for what rotation gains translation loses, and when there is no obstacle to run or follow through it is a mistake to strike above the centre, for a ball will travel less truly when so struck, and further, should it encounter unperceived obstacles, such as grit, or dust, or tobacco, the tendency to leap is enhanced by follow, and the result is greater or less deviation from the true path.

The chief use, then, of follow is to control deviation and prevent stagnation after impact. When a fine stroke becomes dangerous a follow may not only be safe, but may be played so as to leave a good game. The stroke should be delivered gently, smoothly, and the cue should be held as horizontal as possible, the butt being lowered, and the bridge raised so as to bring the tip opposite the part of ball 1 to be struck. After impact the point of the cue should be permitted to follow on with a flowing motion. Another and at first sight quite different use of follow is to decrease the velocity of rebound from a cushion or from a ball touching a cushion. The reason is that after impact rotation is reversed, and a stroke which reaches a cushion with follow rebounds with retrograde or drag. If played with strong follow, the ball will not improbably leap in the air after impact, and either stop short on reaching the bed or even return towards the cushion. As is perhaps evident from what has been explained, follow is very useful when balls 1 and 2 are so close that little or no rotation can be spontaneously acquired; its absence is supplied by striking ball 1 above the centre.

The next rotation to be considered is round the same axis—horizontal—as follow, but is in the opposite or backward direction, whereby what we call ‘screw’ and ‘drag,’ the French ‘retrograde,’ and the Americans ‘draw,’ are effected. The point of aim is on the line C B (p. [191], fig. 1), and the lower the ball is struck the greater the rotation, the limit being as usual where a miss-cue would ensue. To ensure striking low, the cue should be made to bear somewhat heavily on the bridge between the thumb and forefinger, and the butt should be slightly raised. The result of the stroke is that ball 1 is forced forward but does not acquire spontaneous rotation, that being counteracted by the inverse rotation or screw communicated by the cue. If the stroke be played the length of the table close observation will disclose a different behaviour of the ball from that which results from a plain stroke. In the first place, the ball will start for an equal transit or length of path with greater initial velocity, it will slow down much more abruptly, will apparently stop for a moment, and then continue its course till it comes finally to rest. Analysing this path, the first portion is traversed by the ball with inverse rotation and under the influence of a stronger stroke than would have been necessary had it been struck in the centre; the slowing down is the struggle between the screw or backward rotation artificially given and the spontaneous or forward rotation naturally acquired; the momentary check or stop is when the one rotation exactly counterbalances the other, and the ball on an instant slides forward without any rotation; and the final part of the course is when (the backward rotation being dead) the spontaneous rotation has conquered, and in turn dies with the force of displacement or translation. That is what is seen when a master of the art plays with drag. He uses it to overcome irregularities in the ball or bed, and is by its means enabled to combine the advantages of a strong and of a gentle stroke. If ball 1 cannot be trusted the length of the table for a slow hazard or cannon, the player strikes it comparatively hard with drag; the ball then runs fast over the greater length of its course, but pulls up in the manner and for the reasons above described, and reaching ball 2 with gentleness does not displace it to any great extent.

That is the complete stroke; but if it should happen that ball 2 is so near ball 1 that impact takes place before the backward rotation is dead, if the stroke be full the whole of the forward motion (translation) is communicated to ball 2, and ball 1, which has apparently stopped for a moment on the spot which ball 2 occupied, will return towards the point of the cue by reason of its inverse rotation or screw. The result is what is known as a ‘screw back stroke.’ The more full ball 1 is played on ball 2, the further will that ball travel and the greater will be the recoil and screw back. The finer ball 2 be taken, the less velocity will be imparted to it and the less will be the return of ball 1. Screw back is not possible, unless, perhaps, the balls are very near each other, if ball 2 be struck half-ball or finer.