To the Editor.
With reference to Mr. Long Brown's letter, and your footnote in the June issue, perhaps I can help. Both are quite right. The variance is that you measure in different manners. Mr. Long Brown measures round the circumference of the ball, and you on the radius or diameter of the ball. In the case of the half-ball the distance of the point of contact from the nearest point of the circumference of the ball, from which Mr. Long Brown measures, is only one-third of the circumference to the aiming point, which is the edge of the ball, but it is half the radius measuring from the centre of the ball.
If Mr. Long Brown will drop perpendiculars from the points of contact on the diameter of the object ball in Figs. 2, 2a, and 2b, pages 13, 14, and 15, of my book, he will, I think, see what you mean by your footnote, which is also correct.
With reference to Query 155 in the same issue asking whether it is possible to make a right angled screw at a finer than half-ball contact, it will be seen on reference to Table 9, page 97, in my book" Practical Science on Billiards," that with a 5/8 contact with 60 per cent. of screw the angle is 94 deg. 27'; and with a J contact and 70 per cent. of screw the angle is 91 deg. 3', and, of course, it could be carried further. It is possible theoretically, but these amounts of screw are difficult to put on.
With reference to Query 153, asking whether for a finer and fuller than half-ball shot, the aim is taken at the same distance off and on the object ball, in order to get the same direction for the cue ball, the answer will be found in Chapters V. and VI.; and graphically so in Chapter XII. of my book. Approximately it is the case, but not exactly.
With regard to "W's" lucid article on "Why the Half Ball is the Amateur's Sheet Anchor," I would suggest that the amount of variation due to error will possibly be found more clearly set forth in Chapter XII., headed, "On, the proportionate variation in direction of the cue ball, due to the division of the object ball it strikes," and in Figs. 24, 24a, 25, 26, and 27, rather than in Figs. 15 and 18 to which he refers. And in his reference to the clock face, it must be remembered that the point of divergence of the cue ball, and not the centre of the object ball, is the centre of the clock, and that the centre of the object ball must be supposed to be on the circumference of a little circle struck, with 2 1/16 inches radius from the clock centre.
C. M. WESTERN, COL.,
Author "Practical Science of Billiards."