THE HALF-BALL ANGLE
Fig. 38
A piece of wood of about the thickness of half a ball (say 1¹⁄₃₂ in.), as shown in fig. 38, is to be bought, and will be found exceedingly useful to beginners. The idea of this invention is that by its means the angle by which a ball (fairly struck in the middle without side, No. 1 strength) is deflected from its course by colliding a half-ball with another is accurately shown (fig. 39).
Let A be the striker’s ball, and let it be required to hit the ball B exactly half-ball. Clearly the line of progression of ball A will be along the line A D. At D it is deflected in the direction of the arrow F; and the angle between F D and E D, the original course of the ball, is the amount of deflection due to collision. This will be found to amount to 33°.
Suppose, then, it is required to find the proper place to spot a ball, so as to go into a pocket half-ball off another (fig. 40).
Let O be the object ball, P a pocket. It is required to spot a player’s ball somewhere near the line A B to go into the pocket off O. Place the angle A of the instrument against the ball O in such fashion that the side A D points for the centre of the pocket. Then a ball with its centre upon the line A E produced will, if it strikes the ball O half-ball, proceed towards the centre of the pocket.
Fig. 39
The course of the player’s ball will not be along A D, but converging upon it from a point half a diameter distant from the ball O. Hence the angle of deviation as shown by the instrument is made slightly greater than that described by the ball; that of the instrument being about 35°, the real angle being about 33°.