To the Editor.
Please grant me space to thank Col. Western for the reference he makes in his letter to the subject about which I had previously written you.
I certainly measured on the circumference of the ball, as the point of contact is on the circumference, and, moreover, if the remark in Stevenson's book was intended to apply to the diameter it should have been so stated. I submit, however, that the diagrams in Col. Western's book, to which he refers me, clearly show that even if the measurements are taken on the diameter, the statement I made still remains absolutely correct.
The problem is how to aim when the balls are some distance apart, so that the point of contact shall be at a spot on the circumference from which a perpendicular falls on the diameter of the object ball at a spot midway between the centre of the sphere and the point aimed at on the diameter (or diameter produced). This can only be accomplished by supposing a line drawn from the point of the cue through the desired point of contact on to a spot on the diameter of the object ball, and then measuring from that spot for the point of aim.
Now this spot on the radius cannot be midway between the point of aim and the centre of the sphere; it must be nearer the centre.
It follows, therefore, that whether the measurements be taken on the circumference or on the diameter, the point of aim must be distant from the line passing through centre of object ball more than twice the distance of the centre line from the point of contact.
I have read Col. Western's book with great interest and am pleased to find that it confirms some of my own theories.
Everyone who takes an interest in the scientific and mathematical side of billiards should order the book at once.
A. Long Brown.
Muswell Hill,
24th July, 1012.
To the Editor.
Working through Roberts' book and trying to copy the specimen" break "after placing the balls according to the measurements given, I was troubled with the half-ball angles, which I could only get by greater strength or with side, when the leaves were, of course, all wrong. I was puzzling over this and at last noticed in Roberts's book that his measurements are given for bonzoline balls, which explains my difficulty.
I knew that the throw-off of ivory balls is slightly less than that of bonzoline, but it is not easy to allow for this when following bonzoline instructions. One has to allow for the narrower throw off of ivory not only from the object ball, but also from the second ball, for position, when playing a cannon. The examples are difficult enough to execute with precision without any added difficulty, and I was curious to see how I got on when I could place the balls as directed. Hitherto I had used ivory balls, so decided to obtain also a set of bonzolines.
With the bonzoline balls I missed at first the greater elasticity of ivory, although the throw-off is very slightly greater when playing gently. All-round cannons do not seem so easy, but quiet position play is, I am sure, easier. The bonzoline balls seem to run truer, and their angles are more certain. Any attempt at forcing is disastrous. The balls are heavier than ivory, and that, I think, makes for greater precision. They do not seem to carry side so well or so long as ivory balls. It seems to me that with practice a surer game can be played with bonzoline balls as soon as the peculiar feel of them has been mastered. My own set of ivories varies in weight quite 1/8 of an oz., and even after an hour's play I feel the confidence that equal weights give.
But what a nuisance are the different kinds of balls one has to pay with on different tables. I wish everything in relation to billiards was standardized. Indeed I would go so far as to make a one weight cue, and that 15½ oz.
A Lover of the Game.