Diagram VII.
Fig. 3
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.
Diagram VIII.