(24); you are to call your tierces, &c., next. The sentences are not involved; but, according to the Cavendish mode of construing laws, he says, Hoyle means you are not to call your point first. You may call it after your sequence or quartorze; in other words, you may call it second or third. In Law 23 Cavendish says, first means second or third, or both, and in Law 24 "next" means "before" not "after" the point, and this is the lawyer we are to take in Hoyle's place. In the Happy Land the Chancellor of the Exchequer is chosen because she says two and two make five or three at discretion; may we suggest that Cavendish's system of construction entitles him to the rank of Chancellor.

We hope that it is not too late even now to go once more over the code. The Committee has not dissolved. We are not in the secrets of the Club, and we can only judge by what Cavendish writes, and that gentleman is never very precise in what he says. In the preface, the Committee of the Club and the Special Committee are each spoken of as "The Committee." If the Special Committee is still in existence, they have reported to the General Committee. One of these Committees has sanctioned the publication of the laws, but if it be the Special Committee that has done so, the General Committee can still interpose and stop the publication, until the rules are again revised. If it be the General Committee that has authorised the publication, they might still sanction any alteration that the Special Committee might suggest; and failing here, there is but one appeal, viz. to the General Meeting. Will the members spare one moment for the consideration of the game as played in every other place in the world? We do not wish to repeat our argument of last month, but we would ask the members to consider that up to this moment the English laws are the groundwork of all Piquet laws. That Hoyle, an Englishman, took the lead, and made the laws that govern the game; Hoyle's mantle has fallen to the Portland, and the advantage that he gained his successors are about to throw away, by the introduction of a most imperfect code, and by the adherence to rules obsolete everywhere but amongst the Portland members. Is the game worth the candle? We, the outside public, are asked to give up certain rights. For example, the copyright in the laws of Piquet is now ours, and we are asked to give this up, and to take in exchange what we venture to describe as ill a constructed code as the ingenuity of man could make. If there were no laws in existence, we could understand the first set being ill arranged, ill digested and imperfect. Omissions might abound, and we should not be surprised, because no man can call to mind at once all the intricate points that go to make up the Laws of a game. But these Laws ignore all the difficulties that have been raised in the past. To read them through one would fancy that Cavendish or the Committee had never heard that there were any difficulties on the subject. We get 82 Laws instead of 26, and we are not one whit the wiser. We scarcely get a description of the game. Some of the technical terms are described, and some are not; a knowledge of the game is assumed at one time, and ignored at another. It is true the game is referred to, but the whole Laws are written on the assumption that we play a partie. The game is treated as of no consequence, and the Rubicon is unknown. Hoyle did much the same thing, but two wrongs do not make one right, nor do two swallows make a summer. After giving so many Laws that we consider imperfect, our readers may assume that those Laws to which we have not referred are remarkably good. We wish this were so. Laws as to cutting and dealing there are in plenty? Laws about the fringe of the game, there are in abundance; but the substance of the game, and the laws that govern it, are never dealt with; they are slurred over or evaded. We cannot find a difficulty removed. Doubts in abundance are raised that no one ever thought of before, but no single doubt has been solved-no difficulties faced-and the question arises, what is to be done? It is the Portland alone that can get us out of the difficulty. Hitherto we had no claim upon them. Now, having got us into the mess, by their carelessness, they are bound to help us out, as best they can; and this can only be done by a further revision. Unless this is done, we shall have another set of laws issued by some enterprising firm, and we shall have the same trouble that we had in Croquet and Bezique. If the Portland refuse to amend and make the laws clear, the question arises, will the Clubs adopt this code? We have pointed out what we conceive its imperfections, but we have given the laws themselves, and our reasons for our belief. Our readers will, we trust, not be led away by our strictures. Let them read the laws, and if on doing so they can come to any other conclusion than we have done, we shall only be too happy (hopeless as we think the task) to assist in every way in our power to make the code work. To account for such a miserable fiasco we are quite at a loss. We are satisfied that with the new code we shall have ten difficulties raised where one arose under the old law. The difficulties of the old laws have been removed to the satisfaction of the bulk of the players, either by Mr. Clay, Cavendish, or ourselves, and now we have our work to do over again, with ten times the labour, and with nothing to guide us. If the code be adopted, all the old decisions are at an end, and we start in the race so overweighted by these miserable laws that no one can expect successfully to reach the goal.

A MEETING of the Piquet Players of the Westminster Chess Club will be held on Wednesday, the 4th June, in the Club Room, at Five o'clock, to consider the advisability of adopting the New Code, with or without amendments. It is particularly requested that all the Piquet Players will attend.

ANGLES

AT BILLIARDS.-No. III.

SECTION 15.-FINE AND SIDE STROKES.

FROM the last section it will be evident that the conduct of the white, after a straight stroke upon red, depends solely upon the rotatory motion it has at the time of striking. The direct motion is wholly transferred to red, and were the table without friction, the white would continue its rotation on the spot which red had quitted. The friction however restrains the rotation of white at the point next the cloth, and thus causes the white to roll, forwards or backwards, according to the direction of the rotation. Should the white have a spinning motion—that is to say, if it has been played with side, so that the rotation is round a perpendicular axis-the friction of the cloth has no tendency to reproduce a direct motion in white after it has been once brought to rest by the collision. Straight strokes therefore, with side, cause the white to remain spinning on the spot from which the red has been driven. The effect of side in strokes not straight is the same on the white as a dead stroke, for this reason, as long as the ball does not strike a cushion. The effect then, which is very marked, will be considered later, when we come to explain the peculiar properties of the cushions. Indeed, we might have postponed our consideration of side strokes altogether till then, were it not for the slight effect they have sometimes on the path of white (see Section 9), and their power of acting in restraint of the cloth's friction, so as to prevent the effects of follow until the side is exhausted. It is sufficient now for the learner to remember that a ball struck with side sufficient to preserve its spinning motion until it strikes red, will act like a ball struck dead, which will be the subject of the next section. In very fine strokes, the strength and the manner of the stroke are unimportant, as far as the direction taken by either ball is concerned, and the white, after impact, leaves the red in the direction of the common tangent.

SECTION 16.-DEAD STROKE OBLIQUE IMPACT.

The dead stroke is the simplest in its result of any, as the direct motion is all that has to be considered. When the white struck in this manner impinges on red, its motion is resolved into two, according to the well-known law of the composition and resolution of motion. One of these is in the direction of the resistance, the other at right angles to it. The first of these is transferred wholly to red, which is therefore driven in the direction of the common diameter; the other part of the motion continues in white, and carries it in the direction of the common tangent. As this is absolutely true only of perfectly elastic bodies, the allowance for ivory must be made according to the principle explained in Section 5. For practical purposes, it will be enough to remember that, for all dead strokes between quarter ball and full, the path of red and white form an angle of 86 deg. with each other. The deviation of white from the direction of the common tangent is from nothing to half an inch for every foot it runs after striking red. The extreme deviation of red from the direction of the common diameter amounts to about an inch in three feet, and diminishes to nothing. SECTION 17.-FOLLOWING STROKES-HALF BALL.

S

K

Fig 3

The conduct of the white ball after an oblique following stroke is the most complex question presented by the present part of our subject. It will be more easy to follow if we confine ourselves for the time to a consideration of one angle only. We can easily afterwards extend our conclusions to fuller and finer strokes. For the purpose, it will be most convenient to select the half ball stroke, because it is the most frequently required by the player. It is generally the best angle to play at the red where there is power of choice, and the effects are more strongly marked at this angle than at most others. In the accompanying diagram, Fig. 3, the line of direction is represented by ASK. W shews the position of White at the time of striking the red ball, after advancing along the line SW; R is the red ball, and W T the common diameter, which, as we have seen (Section 11), make an angle of 30 deg. with the line of direction. WA is then the common tangent. It is along this line, with the small allowance necessary for imperfect elasticity, that white will diverge if the stroke has been dead. If struck with follow, white will follow one of the paths between W B and W F, according to the strength of the stroke. The

R

Y

manner of the stroke is of little importance in the case of a follow, as we have seen (Section 10). A glance at the figure shows us that the line W B is straight, but that all the rest are more or less curved. We have now to examine the cause, the nature and the amount of this curvature. In doing this, we must take account of the twofold motion, direct and rotatory, of white at the moment of striking. The impact, as we have already abundantly seen, affects the direct motion only, which is resolved, according to the law we have explained in the last section, into a motion, which is wholly transferred to red, in the direction of the resistance, and a tangental motion, which remains in white to associate itself with the motion of rotation, which remains unaltered, either in its amount or in the direction of its axis. But these two parts of the residual motion, on which the course of white after impact depends, are acted upon very differently by the friction of the table. The direct motion. remaining in white causes it immediately to slide along the table in the direction of the common tangent; but this sliding motion is rapidly weakened by the friction of the cloth (Section 3). The rotatory motion continues to cause the ball to turn round the same axis until the retarding action of the cloth on the lowest point of the ball changes this into a rolling motion. But this effect of friction is much diminished by the sliding motion with which the ball begins, and reaches its full effect only when the sliding motion is completely arrested. From this it happens that when the white is struck as gently as possible, no sliding motion is apparent whatever, and white follows the direction of the line W B in the figure, which forms an angle of 30 degrees with the line of direction S K. When white is struck very strongly the sliding motion lasts till white has travelled about three feet, when it becomes imperceptible. In the meantime the rotatory motion has been gradually converted into a rolling one in a direction always parallel to W B, and its course after three feet is always very nearly in this direction. So that the path W F is made up of a curved portion three feet in length, the tangent to which curve is at first W A, and which finally merges into its tangent at its termination parallel to W B.

The five lines marked in the figure W B, W C, W D, W E and W F show the course of the white with the five strengths we have taken as references (Section 8). W B shows the direction of the gentlest possible stroke, and what we have called a very gentle stroke varies from it to an amount scarcely appreciable. W C is the path taken by white after a gentle stroke. In this case the curved portion of the path has a length of about nine inches, and the terminal straight part lies parallel to W B, at a distance of about two inches, or the diameter of a ball. W D, the course after a medium stroke, has eighteen inches of curvature, and the straight part lies about two inches from that of W C. Twenty-seven inches of curved path are produced by a strong stroke, which is shown in W E. The very strong stroke, causing the white to travel along W F, has been already described. In all we have said in this section, it must be remembered we have been assuming that the stroke is a true follow; that is, the white makes one rotation round its axis while advancing the length of its circumference. But, by striking the white nearer its centre, any lesser amount of rotation may be given it. in proportion to its direct velocity. In such cases the curve is longer and flatter the less the rotation, and the terminal straight path becomes less and less inclined to W A. As the rotation is given less and less till it becomes a dead stroke, the line gradually approaches W A until it finally coincides with it.

SECTION 18.-FOLLOWING STROKES AT OTHER ANGLES,

In the half ball stroke we have seen that the course of white, in all strokes without back rotation, is confined within the limits W A and W B. The position of WA is defined as forming an angle of 86 deg. with W T, and W B makes the angle B W K, on one side of the line of direction, equal to the angle T W K on the other. Now, as you play finer on red, the angle T W K increases gradually, and B W K, which represents the most forward path W can be made to take, increases with it. At the same time A W K, the other limit, diminishes. When white strikes red at an angle of 45 deg., WA and W B coincide. We have seen (Section 11) that the angle of quarter ball is 48 deg. ; and so it is strictly true of all balls finer than quarter ball, and even 4 deg. fuller, that no difference of strength, or of manner of stroke, or no difference in point of white aimed at, will alter the path of white after its collision with red. Of strokes at an angle intermediate (between 30 deg. and 45 deg.), it will be enough guide to the learner to remark, that the curves become longer and flatter as the angle diminishes, and the terminal straight path is always parallel to the limiting line W B. When the stroke is at an angle less than half ball, a less portion of the direct motion remains in white after collision. The sliding motion in white will therefore be sooner destroyed by friction. This causes the curve to be sharper than a like strength would produce at the greater angle. Also, as the stroke is made fuller, a greater strength may be given without causing any perceptible sliding motion. When we get as full as a three-quarter ball with follow, scarcely any amount of strength we can conveniently give will cause much deflection from the limiting line W B. In the three-quarter ball stroke this line will occupy the position marked W K, as the line of direction is inclined only 14 deg. to the common diameter W T. We are now in a position to express the general law of oblique impact with follow. When the white strikes the red fuller-that is, at a less angle--than three-quarter ball, the direction taken by white forms the same angle with the line of direction as that taken by red, at any strength. When the white strikes the red at an angle greater than 45 deg.--that is, finer-the directions taken by white and red form an angle of from 86 to 90 deg. At any angle between 45 deg. and.15 deg. the finish of white's path will always be

parallel to the line, making the same angle on the other side of the line of direction as the common diameter. The first portion of its path will be in the direction of the common tangent, and the length of the curve which connects the beginning with the end of the path will depend on the strength of the stroke.

SECTION 19.-SCREW.

The screw produces in white a back rotation round a horizontal axis, in addition to the direct motion. As the ball advances towards the red, the friction of the table is acting strongly against both these motions, as they each tend to produce a slide. If the direct motion is first arrested, whether by friction or by striking another ball, the back rotation, acted upon by the friction of the cloth, causes the white to roll back along the line of its advance. If the rotatory motion is first exhausted, the stroke becomes first dead, and subsequently a drag or slow follow. At Billiards, if we exclude from consideration the masse, it is not possible to give with the cue a rotatory back motion so great in proportion to the direct motion, as to remain in the white after the latter is exhausted by friction, although it is possible to do so with the hand. By striking sharply down on the edge of the ball, it will advance a few inches, and, after stopping for a moment, begin to roll back, often with considerable velocity. The same effect is produced by the down stroke of the cue, called the masse.

As we are concerned with English Billiards alone, we need not take into consideration this extreme amount of screw. We have to do only with the back rotation remaining in white after the direct motion has been stopped or altered in direction by collision with red. In Section 18 we have seen that at an angle of 45 deg. or less, no amount of follow or forward rotation has any effect on the path of white after impact. The same is true of such back rotation as we are able to give with the cue. We have also seen in the same section that the part of the direct motion remaining in white after striking red causes it at first to move in the direction of the common tangent, which direction is gradually changed by the rotation into one parallel with W B in the illustration (Fig. 3). Exactly the same effect takes place in the case of screw at angles between 45 deg. and 15 deg. The path of white begins by taking the direction of the common tangent, and is gradually drawn into a direction parallel to W X, which makes the angle T W X equal to T W S. This is the case only when the balls are very close, so that the amount of rotatory motion is a maximum; in other, and by far the most numerous cases, the terminal path of white, after a screw at these angles, is much nearer to WA in direction. If the screw is quite exhausted on striking, of course the stroke is a dead one, and the direction truly WA. When the red is struck with screw fuller than three-quarter ball, the white returns along a line making the same angle with the common diameter as the line of direction. So that the angles which limit the formation of curved paths in following strokes are the same as those which have the same effect on screw. Owing to the powerful retarding effect of the cloth on back rotation, it is difficult to preserve screw in a ball for any great distance. It is rarely good play to attempt to get the effects of screw when the balls are more than two and a-half feet apart; although an expert player can extend the distance considerably, it requires an enormous amount of practice to regulate the effect of the stroke at a greater distance with the necessary precision. As the learner now understands that the effect of screw depends on the proportion which the two motions given to white bear to each other, it is unnecessary to repeat and insist on the remark (Section 14) that strong play is fatal to the effects of screw.

SECTION 20.-LIMITS OF VARIATION.

It is often useful for the player to know within what limits the course of one ball is confined when the other must be driven to a given point. Let us suppose the course of the red fixed-either that it is intended to go into a given pocket, or to be sent in a certain direction that a break may be left. The course that white will take will then depend on the way it has been struck. We have seen that at angles greater than 45 deg. there is no power of varying the direction of white, and at angles less than 15 deg. the white may be played either with screw or follow. At 15 deg. about three-quarter ball, we have the greatest range possible for white. It may take the line W K with slow follow, or the line W Y with great screw, or the line W A if played a strong dead stroke. And we have explained how any intermediate direction may be got. As the angle increases from 15 deg. to 45 deg. the limiting lines, W K and W Y, approach, leaving gradually less range for white till they coincide at the latter angle. If white must reach a certain point, the amount to which we may vary the direction of red is much more limited. Perhaps its greatest amount is, when playing from S at R, white has to arrive at E (Fig 3). In this case red may be sent, by a quarter ball stroke, at an angle of 45 from the line of direction, or by a three-quarter ball, with appropriate strength, this may be reduced to 15 deg.

SECTION 21.-ADVANTAGES OF HALF-BALL STROKES.

The concluding sentence of the last section will explain to us why half-ball strokes are to be preferred to all others on the Billiard table. The width of a pocket is only 3 inches, and this, at a distance of three feet from the red, allows a range of error in the angle of 3 deg. only, in fine and following strokes. But if the three balls, white, red and spot white, form the angles of a triangle, which has an angle at red equal to

135 deg. we have seen that a half-ball stroke—that is, one which strikes the red at an angle of 30 degreesstrong and high, will make the cannon, and a stroke at 45 deg. will take the white to the same point. It can be further seen that on hitting red at any angle between 45 deg. and 30 deg. high and strong, the deviation of white will never exceed 2 deg. from the mean position at a distance of three feet from red. If then the player's eye is sufficiently trained to find the point in balk (when his ball is in hand) which makes this angle, and if he strike properly he has a range of error of 15 deg., measured on the circumference of red, without missing his object. If it is desirable to play with medium strength, the angle between the line of direction and the path of white is increased to one of 139 deg., and a gentle stroke increases it still further, in each case diminishing the amount of error, which may be made without failure.

DRAMATIC NOTES.

THE performances of Hamlet, by Mr. Tom Taylor, have ceased for the present at the Crystal Palace. Considering that Mr. Taylor is a man not easily daunted, and that one or two theatres are going begging for a tenant, it is possible that he may again present his revised edition of Shakspeare's tragedy on a more suitable stage than that of the Transept at Sydenham. Much curiosity was felt as to the venture, and a decided difference of opinion was expressed, ranging from the contemptuous hostility of the Era, to the astounding verdict of the Spectator, that no finer performance had been given, and no better Hamlet than Mr. Mackaye had been seen since the days of Macready. Making every allowance for extremes, we think that the professional organ went nearest to the truth, and that the drawbacks far outnumber the merits. Some of these drawbacks are no doubt beyond Mr. Taylor's control; for instance, he is not to blame that the actors, when speaking from the back of the stage, are quite inaudible, owing to some defect in the roofing; nor that the visitors to the Palace walk in and out during the progress of the play in the most easy and club-like manner; nor that the Palace officials disturb your enjoyment of the famous soliloquies by flourishing a book of the (Taylorian) text before your eyes, with the whispered assurance that the price is only a shilling. But, as Mr. Taylor ostentatiously announced that he himself had selected his troupe, he must be held responsible for exhibiting about the weakest company of performers that ever acted in a Shaksperian play. It is true that on the 21st May, when we had the pleasure of attending the representation, Polonius was not taken by Mr. Flockton, but by an actor of the most conventional type; nor did Mr. Archer appear as Claudius, though his name was conspicuously printed on the bill, and no apology was given for his absence. How Messrs. Archer and Flockton therefore would have comported themselves we do not know, but it may be safely said of the rest that not a single one of them deserved the honour of being thus paraded before the public, with the partial exception of Mr. Mackaye (Hamlet), who has the making of a good actor in him, and will be much improved by the apprenticeship which other and less vaunted tragedians have been compelled to serve. With regard to Mr. Taylor's omissions and alterations, we cannot speak critically, as we have not carefully compared his version with the ordinary one; but we noticed two very arbitrary omissions. Will it be believed that a performance of Hamlet was given with the advice to the players, than which no better advice was ever given, left out? As this passage is in Mr. Taylor's book, it may be hoped that its omission on the 21st May was accidental, but it certainly was omitted. But neither on Mr. Taylor's stage, nor in Mr. Taylor's book, is heard or written the very humorous language with which Hamlet, when calling on his friends to swear silence, attempts to pacify the interrupting ghost. Does Mr. Taylor think that ghosts are not fit subjects for chaff, or actors for advice; and does he consider it levity in Hamlet to address his father's shade as "mole" and "old truepenny?" He may think what he pleases, but most people will hold him guilty of a most unwarrantable liberty in thus suppressing important passages of the great work.

The season being just now at its height, managers are content to rest for a while on their oars, and leave novelty aside till the tide of visitors has left London. The public taste seems to be mostly in a right direction, theatres with good plays being patronised strongly, those with bad ones feebly. Mdlle. Aimée Desclée, who is now in London, has not astonished the English world to the degree that was expected, partly perhaps because certain critics, by their immoderate anticipatory eulogy, led playgoers to expect that something very wonderful indeed would be found in her. It is discouraging too to an actress, more especially to one of such nervous sympathy as Mdile. Desclée, to play in a theatre where the pit and gallery are very sparsely occupied ; for the appreciation of the stalls and boxes, though it may be deep, is rarely expressed save by a gentle patting of the palm of one hand by the finger of the other. But on no account should a visit to the Princess's be neglected by those who wish to compare, without prejudice, the merits of French and English artistes. It will probably be found that though we are weak (numerically speaking) in actresses, our actors will hold their own.