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the cue-ball appears to strike mid-way between the half-ball point and the centre or edge respectively of the object-ball. The half-ball angle is regarded as the standard angle for billiards, other angles being sometimes termed rather vaguely as “rather more or less than half-ball.” The angle of the cue-ball’s new course would be about 45°, were the object-ball fixed, but as the object-ball moves immediately it is struck, the cue-ball is not actually diverted more than 33° from the prolongation of its original course, it being conventional among players to regard the prolongation of the course and not the original track when calculating the angle. The natural angle, and all angles, may be modified by side and screw; the use of strength also makes the ball go off at a wider angle.

Development in Billiard Play.—The modern development of English billiards is due mainly to the skill of such leading players as John Roberts, sen., and his son of the same name. Indeed, their careers form the history of modern billiards from 1849 when the elder Roberts challenged Kentfield (who declined to play) for the championship. No useful comparison can be made between the last-named men, and the change of cushions from list to india-rubber further complicates the question. Kentfield represented the best of the old style of play, and was a most skilful performer; but Roberts had a genius for the game, combined with great nerve and physical power. This capacity for endurance enabled him to practise single strokes till they became certainties, when weaker men would have failed from sheer fatigue; and that process applied to the acquisition of the spot-stroke was what placed him decisively in front of the players of his day until a younger generation taught by him came forward. In 1869 the younger generation had caught him up, and soon afterwards surpassed him at this stroke; both W. Cook and J. Roberts, jun., carried it to greater perfection, but they were in turn put entirely in the shade by W. Mitchell and W. J. Peall. It is curious to realize that John Roberts, sen., developed the game chiefly by means of spot-play, whereas his son continued the process by abandoning it. The public, however, liked quick scoring and long breaks, and therefore a substitute had to be devised. This was provided chiefly by the younger Roberts, whose fertility of resource and manual dexterity eventually placed him by a very long way at the head of his profession. In exhibition matches he barred the spot-stroke and gave his attention chiefly to top-of-the-table play.

The next development was borrowed from the French game (see below), which consists entirely of cannons. Both French and American professors, giving undivided attention to cannons and not being permitted to use the push-stroke, arrived at a perfection in controlling or “nursing” the balls to which English players could not pretend; yet the principles involved in making a long series of cannons were applied, and leading professionals soon acquired the necessary delicacy of touch. The plan is to get the three balls close to each other, say within a space which a hand can cover, and not more than from 4 to 8 in. from a cushion. The striker’s ball should be behind the other two, one of which is nearer the cushion, the other a little farther off and farther forward. The striker’s ball is tapped quietly on the one next the cushion, and hits the third ball so as to drive it an inch or two in a line parallel to the cushion. The ball first struck rebounds from the cushion, and at the close of the stroke all three balls are at rest in a position exactly similar to that at starting, which is called by the French position mère. Thus each stroke is a repetition of the previous one, the positions of the balls being relatively the same, but actually forming a series of short advances along the cushion. With the push-stroke a great number of these cannons could be quickly made, say 50 in 3½ minutes; and, as that means 100 points, scoring was rapid. Most of the great spot-barred breaks contained long series of these cannons, and their value as records is correspondingly diminished, for in such hair’s-breadth distances very often no one but the player, and sometimes not even he, could tell whether a stroke was made or missed or was foul. Push-barred, the cannons are played nearly as fast; but with most men the series is shorter, massé strokes being used when the cannon cannot be directly played.

Championship.—When Kentfield declined to play in 1849, John Roberts, sen., assumed the title, and held the position till 1870, when he was defeated by his pupil W. Cook. The following table gives particulars of championship matches up to 1885:—

  Points.     Date.     Players.     Won  
  Feb. 11, 1870
  April 14, 1870
  May 30, 1870
  Nov. 28, 1870
  Jan. 30, 1871
  May 25, 1871
  Nov. 21, 1871
  March 4, 1872
  Feb. 4, 1874
  May 24, 1875
  Dec. 20, 1875
  May 28, 1877
  Nov. 8, 1880
  Jan. 12, 13, 1881
  March 30, 31, and April 1, 1885  
  June 1, 2, 3, 4, 1885
  Cook b. Roberts, sen.
  Roberts, jun., b. Cook
  Roberts, jun., b. Bowles
  Jos. Bennett b. Roberts, jun.
  Roberts, jun., b. Bennett
  Cook b. Roberts, jun.
  Cook b. Jos. Bennett
  Cook b. Roberts, jun.
  Cook b. Roberts, jun.
  Roberts, jun., b. Cook
  Roberts, jun., b. Cook
  Roberts, jun., b. Cook
  Jos. Bennett b. Cook
  Jos. Bennett b. Taylor
  Roberts, jun., b. Cook
  Roberts, jun., b. Jos. Bennett  

These games were played on three-inch-pocket tables, and John Roberts, jun., fairly contended that he remained champion till beaten on such a table under the rules in force when he won the title or under a new code to which he was a consenting party. A match was played for the championship between Roberts and Dawson, in 1899 of 18,000 up, level. The main departure from a championship game lay in the table, which had ordinary, though not easy pockets, instead of three-inch pockets. The match excited much interest, because Dawson, who had already beaten North for the Billiard Association championship, was the first man for many years to play Roberts even; but Roberts secured the game by 1814 points. After this Dawson improved materially, and in 1899, for the second time, he won the Billiard Association championship. His position was challenged by Diggle and Stevenson, who contested a game of 9000 points. Stevenson won by 2900, but lost to Dawson by 2225 points; he beat him in January 1901, and though Dawson won a match before the close of the spring, Stevenson continued to establish his superiority, and at the beginning of 1907 was incontestably the English champion.

Records.—Record scores at billiards have greatly altered since W. Cook’s break of 936, which included 292 spots, and was made in 1873. Big breaks are in some degree a measure of development; but too much weight must not be given to them, for tables vary considerably between easy and difficult ones, and comparisons are apt to mislead. Peall’s break of 3304 (1890) is the largest “all-in” score on record; and in the modern spot-barred and push-barred game with a championship table, H. W. Stevenson in April 1904 made 788 against C. Dawson. In January 1905 John Roberts, however, made 821 in fifty minutes, in a match with J. Duncan, champion of Ireland; but this was not strictly a “record,” since the table had not been measured officially by the Billiard Association. A break of 985 was made by Diggle in 1895 against Roberts, on a “standard table” (before the reduction in size of the pockets). On the 5th of March 1907 T. Reece began beating records by means of the “anchor” stroke, making 1269 (521 cannons), and he made an unfinished 4593 with the same stroke (2268 cannons) on the 23rd of March. Further large breaks followed, including 23,769 by Dawson on the 20th of April 1907, and even more by Reece; and towards the end of the year the Billiard Association ruled the stroke out.

Handicapping.—The obvious way of handicapping unequal players is for the stronger player to allow his opponent an agreed number of points by way of start. Or he may “owe” points, i.e. not begin to reckon his score till he has scored a certain number. A good plan is for the better player to agree to count no breaks that are below a certain figure. The giver of points scores all forfeits for misses, &c. If A can give B 20 points, and B can give C 25 points, the number of points that A can give C is calculated on the following formula,

20 + 25 −   20 × 25   = 40.

The handicap of “barring” one or more pockets to the better player, he having only four or five sockets to play into, has been abolished in company with other methods that tended to make the game tedious.

Pyramids is played by two or four persons—in the latter case in sides, two and two. It is played with fifteen balls, placed close together by means of a frame in the form of a triangle or pyramid, with the apex towards the player, and a white striking ball. The centre of the apex ball covers the second or pyramid