By the practice already recommended, the beginner should have become fairly able to strike ball 1 in the centre, and familiar with the divisions of ball 2; he may therefore with advantage proceed to play natural or plain strokes. We prefer the term plain, partly because, ball 1 being struck in the centre, no rotation beyond that which is self-acquired or spontaneous is communicated by the cue, and partly because one stroke deserves the name natural as much as another. It is as natural for a ball struck on its side to rotate round its vertical axis as it is for a ball struck in the centre to have no such rotation.

In billiards plain strokes cover a vast field; most of the certainties, or strokes which should seldom be missed, come under that definition. Their number is infinite, and it is impossible to give diagrams of more than a few typical examples. The student can, without great effort, multiply and vary them at will, and it is desirable that he should do so, altering the strength and noting the behaviour of each ball after the stroke. He will thus learn more than he can possibly acquire from any book, however excellent, and will profit much if his practice is occasionally supervised by a competent instructor.

Let us begin with winning hazards. Place ball 2 on the centre spot; it is then opposite the middle pockets. Choose one of them into which the ball is to be played. From what has already been explained, it is known that the ball should travel on a line drawn from its centre to the centre of the pocket—that is, from C to A (fig. 1); also that the point of impact must be where that line prolonged meets the circumference at B, and that the centre of ball 1 must therefore, at the moment of striking, be at P, B P being equal to B C, or the radius of the balls. No matter where ball 1 may be situated, its centre has to be played on P in order that the winning hazard may be perfectly made.

Set ball 1 on the prolongation of A C, which is the line of the cue’s axis. The player must place himself accordingly, and aim full at ball 2. The stroke is precisely similar to that recommended for practice over the spots, but easier, as the distances are shorter. It should be played with various strengths. With a soft No. 1, ball 2 will roll into the pocket, ball 1 following a few inches on the same path. If it diverge there is error in the stroke, and endeavour should be made to correct it. That is, the player should not be satisfied with the mere winning hazard, which is very simple, but should by watching the path of the balls, satisfy himself that the stroke was true. With No. 2 strength, or a free No. 2, ball 1 will follow on, and eventually drop into the same pocket.

When tolerable certainty has been acquired, ball 1 may be moved to 1′, 1″, &c., either to the right or left of the original position. No good can result from giving precise measurements for the various situations of ball 1; it does not, indeed, greatly matter where it is set, so long as the player can reach it with comfort; what is obligatory is that its centre must pass over the point P. The limit of the stroke is when the position 1ⁿ is reached; thence, if correctly played, point B will just be touched, and no motion to ball 2 be communicated. Hence, when the path of ball 1 before impact is at right angles to that which 2 must travel, the winning hazard is impossible. In other words, a right-angled cut is impossible; such strokes sometimes seem to be made, but the explanation will, on examination, be found in the size and shape of the pockets. These winning hazards should be practised into both middle pockets till a tolerable certainty or confidence is acquired. Some persons will make the full, whilst others will play the fine strokes best; and again, it will often be found that, when playing into the right-hand pocket, there is a tendency to error on one or other side, but when playing to the left-hand pocket the mistake is just reversed. If the strokes are taken too full to the right, they will be made too fine to the left. The proper procedure is obvious: by making a very small allowance each way the mistake will be corrected, the eyes will become educated, and the tendency to error will diminish. It need scarcely be added that the kind of stroke in which one has least confidence should receive the most attention; failure indicates where practice is required.

Also, let the path of ball 1, after impact, receive close attention, and as soon as some certainty in making the hazard is felt, let the exercise consist quite as much in playing to leave ball 1 in or near a desired place as in the success of the hazard. The value of this is all but self-evident, and it is as important in pool or pyramids as in billiards.

Similar practice may, with advantage, be made to the top corner pockets, ball 2 being placed on the billiard, and afterwards on the pyramid spot. The rules for finding what point of 2 should be struck and the points of aim are, of course, unaltered, but attention may usefully be given to the following hint, based on the construction of the cushions at the neck of the pocket. Whether a pocket is easy or not depends, perhaps, more on this than on the actual width at the fall. If the channel is gradually rounded off, with but little rubber in the sides, a ball once in the neck is nearly sure to fall into the pocket; but if there is much rubber in the sides, the same ball would expend its energy in rebounding from side to side, and have no disposition to travel forward into the pocket. Cushions cut square, as it is called, make the pockets more difficult than those sloped gently away; the channel is narrower.

Let ball 2 be placed between the spot and the top cushion, or anywhere on a line connecting a point so chosen and the corner pocket into which it is proposed to play. In this case the point of aim is no longer the true centre of the pocket, nor even the centre of the portion of the pocket which is open from position 2, but a point so chosen that ball 2 may impinge on the neck or side of the pocket entrance, and thence drop in. The accompanying sketch will show what is meant. If ball 2 were played on C, the centre of the pocket, it would strike the cushion A, and very probably rebound to the opposite side, and the hazard would fail: but if, on the contrary, it strike the cushion B at a point T, inside the neck of the pocket, then, unless played very hard, the hazard will to a certainty be made.

With reference to the position of ball 2, C is termed a blind pocket, because the full width at the fall is not open. Hazards into blind pockets are therefore more difficult than those into open ones; nevertheless, if the player is careful to observe the required point of impact, and to allow accordingly in aim, such strokes can be played with considerable confidence.

When measurements are given whereby the positions of balls on the billiard-table may be found, they must not be supposed to be absolutely accurate. They no doubt are nearly so for the table and balls with which the stroke was played for the purposes of this volume; but tables, balls, cloth, and climate are subject to variation which may make modification necessary, and, moreover, each man has a mode of using his cue as peculiar to himself as is his handwriting. Therefore, once for all, let it be understood that the diagrams and descriptions must be treated as but approximate. All measurements from a cushion are from the edge on which balls impinge to the centre of the ball whose position is to be fixed; those from a pocket are from the middle of the fall. The dotted lines with figures marked in Diagram I., example A, show the measurements whereby the position of ball 2 is determined. Many mistakes are made by inaccurate reading of instructions, and by failure to use the measure correctly, but the eye will prove a useful check; for if the position of the balls, when placed on the table, does not nearly coincide with that shown in the diagram, there is an error somewhere which a little patience and consideration will cause to be discovered.

A few typical strokes are shown on Diagram I.:—

A. Ball 1, on or near the right corner of the Ｄ; ball 2 7½ in. below the right middle pocket, and 8 in. from cushion 3. The measurements are in this instance shown on the diagram as a guide in other cases.

Play a free No. 1 strength. Ball 1, after pocketing 2, should travel to the top cushion, and so far back as to leave an easy winning hazard on a ball on the billiard spot. With slight variation of the position, the stroke may be played slower or faster, as may be desired. If the strength is misjudged, and ball 1 should stop somewhere between the top cushion and the desired position, a losing hazard in the left top pocket may not improbably be possible. The positions of both balls may be considerably varied, whilst the stroke remains virtually unchanged. The further ball 1 is brought to the left along the baulk-line, the fuller is the hazard, and the position of ball 1 after the stroke will be more to the right of the spot than that shown in the diagram.

B. Ball 1, 25½ in. from cushion 2, and 10 in. from the top cushion.

Ball 2, touching the top cushion and 12 in. from the right top pocket. Play a gentle No. 1, which will leave ball 1 about 7 in. from cushion 2 and 14 in. from the top cushion.

In this stroke ball 2 and the cushion are simultaneously struck, as will be apparent if ball 1 be placed against ball 2 at the proper point of impact; hence a very common rule is to direct the player to aim between ball and cushion. The general rule however for finding the point of impact holds good, and the fact that under the circumstances the cushion is struck at the same time as the ball is merely a coincidence.

C. Ball 1, 3 in. from the left side cushion, and 9 in. from the left top pocket.

Ball 2, touching the left side cushion and 4½ in. from left top pocket. Play a very soft stroke so that ball 1 may be left at 1′; a losing hazard from the spot is then open. This stroke is best made if the player stand close to the balls and lean over the table, making his bridge for the cue bouclée—i.e. the forefinger bent round the cue. If played in the usual way the stroke could not be reached without the long rest, and the eye is then so far from the ball that error and failure are probable. Any ordinary player can show the stroke, which is quite easy and very useful.

D. Ball 1, 5 in. from cushion 5 and 17 in. below the left middle pocket.

Ball 2, 6 in. from cushion 5 and 7 in. below the left middle pocket.

This is an example of a hazard to a blind pocket. Ball 1 should be struck gently, and its position after the stroke will be in the direction of the right top pocket. It is, in fact, a fine cut, and if played with sufficient strength ball 1 may probably go into the right top pocket. If ball 1 be placed 6 in. from cushion 5, the stroke is slightly fuller and may be played slower; after impact the ball will travel in the direction D E.

Diagram II. shows positions for doubles, with which it is well to accustom the eye. Though such strokes are not very much used in billiards, they are occasionally of great value, and their principle is based on the equality of the angles of incidence and reflexion. It is clear that a double may be set up at almost any part of the table, and it is well that several positions should be selected and played from till some certainty is obtained; those shown in the diagram are merely types. In these cases ball 1 is played full or nearly so on 2, and position for a further score may with attention to strength be attained. Doubles are used more in pool and pyramids than in billiards, and will be treated in detail when the two former games are described.

It may be as well to make a few remarks explanatory of the diagram. A is an example of a double in baulk where the balls are easily reached. The point A on the cushion where impact with ball 2 should take place is half-way between the baulk-line and the bottom cushion. A ball played from B to A should, if truly struck in the centre, fall into the left bottom pocket. Place balls 1 and 2 as shown in the diagram on the line B A, keeping 2 sufficiently far from the cushion to avoid a kiss; play full, and 2 should be doubled. Again, let C be the middle point of cushion 6, and imagine lines joining it with the right middle and right top pockets. On these lines place the balls. A full stroke from ball 1 to 2 should double the latter in the one case into the right top pocket, in the other into the right middle pocket.

Next, D is an instance of a simple double, from which in more ways than one a losing hazard from spot may be left. Ball 1 is 24 in. from cushion 6 and 26½ in. above the middle pocket; ball 2 is 5 in. from the same cushion and 20½ in. above the pocket. A full stroke will double ball 2 into the right middle pocket, and ball 1 may be left near the line from the left middle pocket to the spot.

In the case marked E, ball 2 is just beyond the shoulder of the right middle pocket, ball 1 being so placed nearly in a line from 2 to the left bottom pocket that a full stroke about No. 1 strength will carry 2 to the left top pocket. Ball 1 may be so played as to leave a losing hazard into the left top pocket from a ball on spot.

All these strokes should be played medium strength, say No. 1 or 2; in practice it will be found that the angle of reflexion varies somewhat with the strength, and in a less degree with the table.

As great accuracy is of the highest importance in playing winning hazards, it is evident that, when either ball has a considerable distance to travel, the stroke should not be played too slowly; for in a very slow stroke imperfections of ball or table tell more than when greater strength is used. Also, before leaving the subject, it is desirable to impress the reader strongly with the importance of the remarks on pages 145–6 respecting play into a more or less blind pocket. Attention to them is essential to good spot play and also to what is called play at the top of the table. Clearing the dangerous shoulder of the pocket is the secret of success.

We now proceed to losing hazards, which with most amateurs form the mainstay of the game; partly because being easier than winning hazards, they are usually taught first, but mainly because they are possible with a slovenly style and inaccurate striking which effectually prevent success with winners. In reality, however, they will repay care and accuracy as much as any other stroke, because, unless ball 2 be struck in the proper place, it will not travel in the desired path, and the result of a poor stroke may be success as regards the hazard, coupled with leaving ball 2 hopelessly safe. When played with intelligence and with due regard to the position of ball 2 after the stroke, they form most excellent practice. Following the usual custom, these strokes may be divided into short and long losers, and each will be separately treated; at present, of course, plain strokes only being considered. It is convenient to take the half-ball hazard as the standard or typical stroke; it is the easiest for the reason given at p. 133, because aim is taken at the edge of ball 2, a well-defined mark, instead of at an indefinite point on the ball’s surface. Moreover, on billiard-tables certain positions are recognised as affording half-ball losers, and these are most valuable to a player as supplying the means, during play, of testing and correcting his strokes or his judgment of angles. It often happens from many causes that a man’s eye or nerve partially fails, which failure destroys confidence and begets still worse play; he probably before long gets a stroke from one of the many positions which should be played half-ball. The mere effort to recognise the situation tends to arrest demoralisation, whilst the success which follows correct recognition goes far to restore equanimity and confidence. That is one reason against wantonly altering the positions of the spots on the table, the size of the Ｄ and such matters; though, no doubt, if the game can thereby be certainly improved, the alteration is justified, and in time players will learn similar positions under the altered circumstances. Hitherto such changes have been made rather with the view of cramping the play of one or two men, and so placing others less able or less diligent on a par with them, than with the object of making an undeniable improvement in the game. Such modifications under the pretext of reform are much to be deprecated.

Taking the billiard, pyramid, and centre spots as fixed points on the table, Diagram III. shows with sufficient accuracy the lines of half-ball strokes to the top pockets. Let the billiard spot be considered first. From either top pocket there is a half-ball stroke to the opposite one; also from either middle pocket there is similarly a half-ball hazard into the opposite top pocket. Next, from a ball placed on the pyramid spot there are half-ball hazards from either corner of the Ｄ into the top pockets; and, lastly, from a ball on the centre spot, half-ball strokes to either top pocket may be made from positions about 7½ in. to the right and left of the centre spot of baulk. Precise accuracy in definition of these strokes is not attempted; tables and balls vary, whilst no two men strike exactly alike; hence each must work out for himself the exact position for a half-ball stroke; it will in every case be reasonably near the lines indicated.

Diagram IV. illustrates several losing hazards, all good for practice. For the group marked A, place ball 1 on an imaginary line from the centre of the red spot to the upper edge of the shoulder of the left middle pocket about half-way between them, where it can be conveniently reached by the player; it is then in position for a gentle half-ball stroke to the right top pocket. When correctly played, impact with ball 2 takes place on the central longitudinal line of the table, and consequently 2 travels to the top cushion on that line, and returns on the same path a shorter or greater distance according to the strength of stroke. A very gentle one will bring ball 2 back to the spot; a medium stroke will result in leaving it near the pyramid spot, and it can be brought further down the table if desired; but for practice at this stage endeavour should be made to leave ball 2 between the red and pyramid spots on the centre line. If this is effected, ball 2 has been truly struck; should it return to the right of the line it has been struck too full, and if it rests to the left of the line too fine. So that here again we have an index which points out error and shows what is required for its correction. The hazard is so easy that after a little practice it will seldom be missed, and for that reason it should be worked at till it becomes what is called a certainty.

Then from A lay off, in the direction of the right middle pocket, a series of positions marked A′ A″ A‴ A⁗, each about 1¾ in. from the other, and from each of these play the hazard. The point of impact should be the same in every case, therefore the point of aim will vary slightly with the change of position; but the chief variation in the stroke lies in the strength employed.

For the position A′ the strength is about No. 2, and ball 2 should be left on the central line L L between the centre spot and the bottom cushion. For A″ the same stroke a little stronger, ball 2 returning from the bottom cushion towards the centre spot: and so on. It is seldom necessary to practise beyond A‴ in dealing with plain strokes. The strength required for this stroke is considerable approaching No. 4, and ball 2 should travel beyond twice the length of the table. In all these strokes endeavour should be made to keep ball 2 travelling on the line L L; this will be found not quite an easy matter, and sometimes divergence may not be from any fault of striking, for an imperfection in the ball which might account for an error of half an inch or less in 6 ft. would produce a perceptible deviation during a journey of 24 to 30 ft. Nevertheless, the prime source of failure is to be looked for in a faulty method on the part of the player, who, if he cannot easily remedy what is wrong, should without hesitation revert to the practice previously prescribed. After some work at this he will probably find that ball 1 was not being truly struck, and will amend the fault. These strokes should then be transferred to the other side of the table, making the hazards into the left top pocket. They are very conveniently played with the left hand, and the player who can use both hands almost indifferently has a great advantage over a purely one-handed performer. It is entirely, we think, a matter of resolution and of practice. At any rate, these strokes should be played from both sides of the table till they can be made without difficulty.

Example B exhibits a valuable stroke of common occurrence. Ball 1 is on the line from the left top pocket to the spot. That line should be taken from a point nearer the top than the side cushion. Ball 2 should be struck so as to drive it as indicated, half a foot or more above the right middle pocket on to the cushion, whence it rebounds and comes to rest conveniently over that pocket. A similar stroke should be played from the right top pocket, and there is as usual a little license as to the position of ball 1; it may be further from or nearer to the pocket than is shown in the diagram, and also a little above or below the line indicated, and still be a plain stroke; when the divergence is greater, side is required, and the methods of play will be hereafter explained.

The strokes marked C on this diagram afford admirable practice for middle pocket losing hazards; for their results record plainly the errors committed. They have been selected because the point of impact on ball 2 is in the central line of the table; therefore, as has been already shown, its path should lie on that line. Another advantage these strokes possess is that from each position of ball 2 precisely similar hazards may be made into the right and left middle pocket.

Place ball 2 in the central line of the table, 24 in. from the baulk-line. A half-ball hazard is open from either the right or left corner of the Ｄ. Ball 2 should pass up and down the central line, the distance varying with the strength; for simple hazard practice it should be brought back to its place before the stroke was made. Next bring ball 2 1½ in. down the central line; place ball 1 10 in. from the centre of baulk; play as before.

This stroke may be repeated by bringing ball 2 down the central line 1½ in. each time, till a position 18 in. from the baulk-line is reached. When nearer than this the stroke is so far changed that the strength must be reduced, so that ball 2 shall not return from the top cushion, but shall be cut towards one of the top pockets, and as the position of ball 2 approaches the baulk-line it will be found desirable to place ball 1 further and further back in the baulk within the limits of the Ｄ. Ball 1 is placed 1½ in. towards the centre for each stroke up to the fifth when ball 2 is 18 in. from baulk. Whilst accuracy should be aimed at, its perfect attainment is impossible; in playing these strokes occasionally a very good one may be made, and ball 2 may keep very close to the central line. Oftener, however, there will be divergence, and hence it is well to recognise limits within which the stroke, though not very good, may yet suffice to leave ball 2 in play. In the diagram the lines P M and Q N, drawn from the corners of the Ｄ parallel to the sides of the table, form such boundaries. If ball 2 be left anywhere in the space so enclosed, and as far down the table as the spot, there is almost certainly a plain hazard to be made off it from baulk into either top or middle pockets.

Other and easier middle pocket hazards may be indefinitely multiplied, and should be practised till the person playing acquires confidence, not merely that he can make the stroke, but that he can vary the strength at will from such delicacy as scarcely to move ball 2 to one which will bring it in and out of baulk. A few examples are given in Diagram V.

A. Ball 2, 16½ in. from cushion 3, 12½ in. below right middle pocket; ball 1 on right corner of the Ｄ. Play half-ball about No. 2 strength, leaving ball 2 placed for a hazard in the left middle pocket. Ball 2 can be brought back nearly over the centre spot, and the danger of the stroke is that, if played too fine, ball 2 will lie near cushion 6 and be practically out of play.

B. Ball 2, 15½ in. from cushion 3, 6 in. below right middle pocket; ball 1 on baulk centre spot. Play half-ball No. 2 strength, leaving ball 2 with hazard into right middle pocket.

C. Ball 2, 21 in. from cushion 5, 10 in. below left middle pocket; ball 1 on baulk centre spot. Play half-ball No. 2 strength, bringing ball 2 back over or near the centre spot of the table. With slight variation of strength and aim ball 2 can be brought back into almost any desired position on the table.

D. Ball 2, 9 in. from cushion 5, 23½ in. below left middle pocket; ball 1, 5½ in. to the right of the centre of baulk, or on position 5 of Example C, Diagram IV. Play a half-ball slow No. 1. Ball 2 will travel to the side cushion on a line at right angles to its face, or, in other words, parallel to the baulk-line, and will return on the same line to a distance varying with the strength. A medium No. 1 strength will bring the ball back from 24 to 30 in. from the side cushion. There is great latitude in placing ball 1 for this stroke, which can be made as far as 8½ in. to the right of baulk centre, the difference in play being merely in strength. The further ball 1 is placed from 2 the greater is the strength required, and as a consequence the further does ball 2 return from the side cushion. This stroke is of the class called ‘jennies.’ Each stroke here recommended for practice can be played from either side of the table; and this should always be done in order that the eye may become equally familiar with the angles into either side pocket.

The next two examples (Diagram VI.) are of an importance which the beginner may not at once realise, but which is abundantly clear to a professional or to an advanced amateur. The hazards are in themselves so easy that a very poor player can have no difficulty in making them; but mark the difference between the right and wrong method of play. In the first example the paths of ball 2 after impact are drawn, both when rightly and when wrongly struck; and an examination of them will show that if the proper method is followed, error in strength has much less effect in leaving the ball out of play, and if the stroke is wrongly played the margin for such error is comparatively small. The principle here illustrated applies to many positions, and consequently the strokes deserve close study.

Example A.—Place ball 1, 40 in. from the top cushion, 7 in. from cushion 6; ball 2, 16 in. from the top cushion, 11 in. from cushion 6; play a free stroke rather finer than half-ball; it is a bad stroke indeed which leaves ball 2 out of play. Another good example is shown at B; ball 1, 24 in. from cushion 4, 4½ in. from cushion 3; ball 2, 13 in. from cushion 4, 9 in. from cushion 3. Play a free stroke finer than half-ball on 2, which will follow a course somewhat resembling that indicated.

Diagram VII. may be thus set up:—Ball 2, 5 in. from left middle pocket, ½ in. above a line joining the centres of the two middle pockets; place ball 1 7 in. to the right of the centre spot in baulk; play half-ball on ball 2 a free stroke. Ball 2 must be very badly struck if it is left out of play; it should strike the left side and top cushions and return to position. If played improperly, it returns from the top cushion only, and unless the strength is very exact is probably lost to play. Many accidents may happen; it may be holed in the left top pocket, or, still worse, catch in it and run safe under the top cushion; it may return close to cushion 6 and come to rest either above or below the middle pocket; in each case it is left in a more or less undesirable position. If played too full, ball 2 will probably be left safe near cushion 2; hence there are at least two types of wrong paths which might be shown, but they have been omitted to avoid complicating the diagram.

Having fairly mastered short losing hazards, the next step is to study similar strokes into the top pockets from baulk. They are called long losing hazards, and form an excellent test of a performer’s capacity at the game of billiards, in which they fill an important part. They require greater accuracy than the short hazards, because the balls have to travel over a greater distance, so that correctness in placing ball 1 for a plain half-ball stroke on ball 2 is of the greatest consequence. Smoothness and truth in the delivery of the cue must not be lost sight of, and a short reversion to the practice recommended in Chapters III. and IV. for the attainment of these objects will prove to be of much benefit.

The typical long losing hazard is made from ball 2 on the centre spot, ball 1 being about 7½ in. from the centre of the baulk. Differences in the elasticity of the balls will make a slight alteration in the best position for ball 1; where it is considerable, 8 in. may not be too far from baulk-spot, and where it is less 7 in. will suffice; the position also varies with the strength of stroke. This hazard is rightly considered a difficult one, and it cannot be mastered without much application; it is indeed now of more value than of old, because in a break when ball 1 is left touching another ball, the game is continued by placing the adversary’s ball on the centre spot, the red on spot, and playing from baulk.

The stroke can be made with considerable difference of strength, which varies of course with the position desired for ball 2. Ball 1 should be struck in the centre (not below) about No. 2 strength; this will bring ball 2 back over the middle pocket, the stroke being played half-ball. If it be made ten or twelve times in succession on a clean table, the path travelled by 1 after impact will be fairly visible, and it is an instructive subject of study. First there is a straight line to within the length of a radius of the point of impact, next there is a somewhat violent curve, the result of the forward course suddenly modified by impact, the rebound due to elasticity and the frictional action between ball and cloth, and this in turn is merged into a second straight line. The action described is not peculiar to this stroke, but is visible in many others, and exists more or less in all, but this one forms a favourable opportunity for observation. The path travelled by ball 1 is roughly indicated in fig. 3, and the practical lesson to be learned therefrom is that in playing cannons the curve must never be overlooked or forgotten when the third ball lies within the sphere of its influence. Reference has just been made to the impact of two balls and the rebound which follows, a subject which was referred to in the last chapter; it is of interest, and at this moment appropriate, to consider the matter a little further.

In fig. 3 ball 1 played on 2 impinges at T; 2 travels from T as shown by the arrow. B C shows the line travelled by 1 after impact as it is exhibited in the diagrams; but the true path is more nearly B D. Hence it is clear that a cannon on ball 3 would just be missed, the position of 1 being indicated in the act of passing 3. The tendency of the lines B D and B C to approach each other and ultimately to coincide is apparent. It is also clear that the magnitude of the curve B D depends on the strength of stroke as well as on the elasticity of the balls. If played very hard, it will be greater; if very soft, it will almost disappear, the line of travel approximating to B C, in which case it is evident the cannon would be made.

The balls may for our purpose be assumed to be of equal density and perfectly elastic; that is, they are equally hard, equally heavy, and when they receive the shock of impact they recover their figure or shape with a force equal to that which caused the momentary compression. What happens more or less in every stroke in which one ball is made to strike another is that at the moment of collision the round surfaces are flattened by the shock, and impact is not confined to what is accurately called a point, but is extended to this flattened surface, which varies in size according to the strength of the stroke, the hardness of the balls, and the part of ball 2 struck. In using a very perfect set of ivory balls 2³⁄₃₂ in. diameter, in a stroke rather fuller than half-ball with strength from No. 3 to 4, this temporary flattening was found to extend to about the size of the head of a small tin-tack, say ⅒ in. in diameter; nearly but not quite as large as the billiard balls shown in the diagrams. The rebound is due to the reaction whereby the balls recover their normal shape; in the case of ball 2, which was at rest before impact, the effect is to make it travel on a line from the point of impact through its centre; the effect on ball 1, which was not only moving forward but also revolving, being to check its velocity, some of which is imparted to ball 2, to rebound, and to assume a new path, the first part of which is curved as a result of the blending of the various forces to which it is subjected. In this explanation no pretence to a mathematical solution is made; it is simply the result of watching the behaviour of the balls and endeavouring to account for it by an exercise of common-sense. Most persons who have played much must have noticed occasional stains of red on the white ball; these were the results of impact, and if carefully examined would be found to be small circular spots; similarly all persons are familiar with the fact that the red ball gradually loses its colour, which it parts with in the way here noticed.

Now to return to the long losing hazards; the usual mistake is to place ball 1 for a stroke finer than half-ball, the result being that it strikes the side cushion on the dangerous shoulder; therefore, when in doubt, allow for this and place the ball for a full rather than for a fine stroke. The hazard from ball 2 on the central point of the table should be constantly practised, first into one top pocket and next into the other, till it can be made with considerable facility and with varied strength. Then let ball 2 be placed on the pyramid spot and ball 1 on or near the corner of the Ｄ; a half-ball stroke will make the losing hazard into either top pocket. Care should be taken not to hit ball 1 above the centre, and the strength should be about a soft No. 2. Ball 2, after striking the top and side cushions, should come to rest so that a middle pocket hazard may be left.

Between these two hazards a number of others may be interpolated, the most satisfactory plan being to set ball 2 at intervals of 6 in. from the centre spot up the central line towards the pyramid spot as shown in Diagram VIII. By this means six separate hazards are provided for practice, or four are inserted between the two already described. Taking these four 6 in. in succession above the centre spot; for the first, ball 1 should be placed about 7 in. from baulk centre; for the second about 5 in.; for the third about 2½ in.; and for the fourth on the centre spot of the baulk. As before explained, these positions for ball 1 are but approximate; they require modification proportioned to the elasticity of the balls, the personality of the player, and the strength used. For example, from the position when ball 2 is on the centre spot and for the next two positions, in playing with bonzoline balls it would be prudent to place ball 1 from ½ to ¼ in. further from centre of the Ｄ than the positions indicated.

When the eye has become acquainted with the half-ball angle, ball 2 should be set up anywhere within the lines P M, Q N (Diagram IX.), between the centre and billiard spots, and practice continued. Unless for some special purpose, endeavour should be made to leave ball 2 within the space enclosed by these lines.

On Diagram X. two hazards, when ball 2 is further up the table than the pyramid spot, are shown. They are types of two classes, either soft or strong strokes—forcing hazards, as they are called. A is of the latter class; that is, though the hazard can be played quite gently by the use of side, yet as a plain stroke from the left corner of the Ｄ the strength required would be such as to make it probable that ball 2 would be left in baulk after the stroke. To avoid this, place ball 1 so that the hazard may be played with strength sufficient to bring ball 2 in and out of baulk. Place ball 2 about 16 in. from the top cushion, and 26 in. from cushion 2; ball 1 should be played from baulk 8 in. to the left of the centre, a free No. 2 or No. 3 strength. Ball 2 will travel somewhat as shown by the dotted line; if struck fuller it will go further and keep better within the lines P M, Q N.

B is an example of a gentle stroke, and of a type which frequently occurs in the course of a game. Ball 2, 4 in. from the left side cushion and 4 in. from the top cushion. Place ball 1 on the baulk-line on the left corner of the Ｄ. Play on to the left top cushion so as to rebound on 2 about half-ball. As in most other strokes, there is considerable latitude both as regards strength and the fulness or fineness with which ball 2 may be struck. A few trials will show where it is desirable to place ball 1 if a very gentle stroke is required, and where it should be put if a stronger one is wanted. That the latitude both as to the position of ball 2 and to the point of aim is great is clear from the results of a number of trials, ball 1 being played at a point on the left side cushion about 18 in. below the top cushion; the path taken by ball 2 varied generally between the two shown on the diagram; when it was struck full or nearly so, it impinged on the top cushion at R, and travelled towards the pyramid spot, and sometimes beyond it; when struck fine it was cut towards M, and of course did not travel so far. It is useful to be able to play this stroke when ball 2 is at some distance from the pocket until, in fact, the direct losing hazard becomes possible, and therefore it should be practised till the eye can select with tolerable accuracy the point of the cushion at which ball 1 should be aimed. This method of playing by first striking a cushion or bricole is too much neglected in the English game, which suffers thereby; when played it is often considered a fancy stroke, whereas numerous plain strokes, specially cannons, are advantageously made by its judicious use. Seeing that play from a cushion is sometimes imperative, as, for example, when player’s ball is in hand and a certainty left in baulk, bricole practice from a variety of positions will well repay the labour bestowed.

What has been mentioned about the elasticity of balls and the consequent rebound after impact has a special importance in treating of cannons. This class of strokes has a tendency in the recent development of the game of billiards to supersede in a measure losing hazards which formerly, without doubt, were the mainstay of our players. The inferiority of losing to winning hazards in respect to influencing the game was conclusively shown when the spot stroke was played, but that stroke was rarely formidable save in professional hands; the amateur, as might be expected, clinging to the easier losing hazard. When the spot stroke was barred, a substitute had to be found, and in a great measure this has been supplied by the cannon, chiefly, no doubt, in runs or series of strokes called nurseries (of which more will be said hereafter), but also by strokes which have the result of leaving the three balls close together, gathering them, as the Americans say. To deal fully with these involves the use of side and of other refinements of play with which as yet the student is not supposed to be familiar; at present attention is confined to plain strokes, which include those made direct from ball to ball and those made after impact with one or more cushions, but all played without side.

The general rule to be observed as to strength is to make it proportional to the distance to be traversed and to the angle between the paths of ball 1. That is to say, the smaller the angle between balls 1, 2, and 3, the greater the strength required. Figure 4 shows at a glance what is meant. Ball 1, played half-ball on 2, cannons on 3, as indicated by the lines. The nearer 3 approaches the position 3′, which is nearly at right angles to a line joining the centres of 1 and 2, the harder must the stroke be played. When it passes the right angle and approaches to 3″, screw is required in addition to strength; that is, ball 1, though still truly struck in its vertical central line, must be struck below its true centre. Hence it may be said that, the greater the angle or the finer the stroke, the more gently should it be played; the smaller the angle, or the fuller the stroke, the greater is the required strength.

The other point of importance is common to all plain strokes, but may here be usefully repeated; the player should stand for the stroke so that the line from 1 to 2 prolonged through 1 backwards shall form the axis of his cue.

Another matter never to be forgotten is that the finer the stroke the less velocity ball 1 loses, and consequently the less is imparted to ball 2; the fuller the stroke the more 1 loses and 2 gains.