## Why the Half-Ball is the Amateur’s Sheet Anchor

##### (Contributed to The Billiard Monthly.)

A very interesting figure in Col. C. M. Western’s book

“The Practical Science of Billiards,” is Fig. 18, page 57,

which shows graphically how a small error in the direction

of the cue ball, when aiming half-ball, makes but little difference

in the direction of the cue ball after contact with

the object ball. It also shows that when playing fine, or

nearly full to follow on, a very small error in the aim, and

consequent contact, has a very large and serious influence

on the direction and divergence of the cue ball after contact

with the object ball. (See also Fig. 15, page 49).

We all know, of course, that among the advantages of

the half-ball are: 1, A definite something, i.e., the outer edge

of the object ball, to aim at; 2, A definite angle to get into

the eye and also into the head (you should be able to

imagine and see the half-ball angle over all the billiard

table, with your eyes shut), not only to play it, when you

can, but also as a standard whereby to judge other angles.

These two advantages are obvious to anyone. Most of us

have also been told that when the shot is a half-ball shot,

error in aim, if only small, will not much affect the direction

of the cue ball after contact. But no one tells us how

much, or how little, it will affect it. Our own experience

may convince us that a small error in a half-ball loser is not

important, but though we get to feel this and to know it,

we don’t know whywhich may not matterand we don’t

know how muchwhich does matter.

These figures 15 and 18 of Col. Western’s exactly show

the “how much.” Anyone can see them and understand

them. Some elementary knowledge of trigonometry and

geometry is required to understand how they are arrived at,

but there are the results in Figs. 15 and 18 for anyone.

Perhaps a brief sketch of Col. Western’s method may be

of interest, and perhaps some idea of it may be conveyed

without bringing in mathematics.

A cue ball, struck in the centre, with medium force, and

aimed half-ball at the object ball strikes it and goes off at

the half-ball anglewhere? and why there? But first let

us follow the object ball. Fortunately its direction is easy

and universally admitted. A line drawn through the centres

of the two balls, and through the point of contact at the

instant of contact gives the direction. And this is always

true for any contactfine, full, or medium.

The direction which the object ball, when struck half-ball,

makes with the original direction of the cue ball is 30

degrees. This is quite certain, but for those who don’t like

degrees, I hasten to add that if you imagine you play from

six o’clock on a clock face half-ball on the right of an

object ball at the centre of the clock, the direction the object

ball will take will be 5 minutes to 12. This is soabsolutely,

theoretically, and practically; and it is nice to find,

sometimes, that theory and practice agree.

But where is the cue ball going? It is hard to say

theoretically, and here, fortunately, the practical billiard

players step in and help us.

It will be readily admitted that all players recognise certain

positions on the table as the half-ball angle. See, for

instance, Mr. Mannock’s book “Billiards Expounded,” or

the Badminton billiards, or Charles Roberts’s book, “The

Complete Billiard Player,” or John Roberts’s book, “The

Game of Billiards.” Perhaps we shall all agree that John

Roberts is a practical billiard player. We find certain

closely approximate half-ball angles duly recognised such as

red on spot and cue ball at a top or middle pocket. We

know the distance of the spot from the top cushion, the

length of cushions, etc (or we can measure these matters),

and now practice must hearken to theory.

Theory does not dispute what practical men say are half-ball

losers, but with facts and measurements theory can

easily and indisputably arrive at the half-ball angle of departure

of cue ball after contact. Theory would give it

exactly if the practical players could state the circumstances

exactly; but the angle varies with the substance of the balls

and the strength of the stroke. We all know that the half-ball

angle varies slightly with ivory, crystalate and bonzoline

balls, but from the different recognised positions of the

half-ball and the variations for the nature of the balls, Col.

Western deduces, and rightly, that 35 degrees is a fair average

angle for the departure of the cue ball from its original

direction, after a half-ball contact with the object ball.

Again, to avoid degrees, I hasten to add that playing halfball

from 6 o’clock on a clock face, on the object ball at the

centre of the clock, the cue ball would go to nearly about

6 minutes past 12 and the object ball to 5 minutes to 12.

You may say, to include the various classes of balls, front

about 5 min. 35 sec. past 12 for ivory, to about 6 minutes

past 12 for bonzoline. I grant the angle looks more like 7 or

7½ minutes past 12 to many people, but it is not so. However,

as Col. Western shows, we have now the two directions

for the two balls after a half-ball contact. As regards the

relative distances the balls will travel, we all know that if you

hit the object ball pretty full, it will go far and the cue ball

will travel but little, and if you hit the object ball fine, it will

not travel far, but the cue ball will. And, for most of us,

this is sufficient, but Col. Western pursues the subject for

those who may be interested to follow it.

Having got the half-ball directions and a given force.

Col. Western, with the assistance of the parallelogram of

forces, is able to give two similar semi-circles, on opposite

sides of the original line of direction of the cue ball, so that

when we know the direction and distance of the travel of

the object ball after an impact by the cue ball (and we can

always find this direction by a straight line through the

centres of the balls at the moment of impact) we can also

find the direction and distance of travel of the cue ball on

the circumference of the opposing semi-circle.

We see, then, from these diagrams, that, playing halfball,

an error of one-eighth diameter of the ball in direction

will make but little difference in the direction of cue ball

after contact, but one-eighth will make a very great difference

when playing fine or full, so the nearer you can keep

to half-ball, the less do your errors matter for losers and

cannons.

On the other hand, as regards the direction of the object

ball, the diagrams, etc., in Col. Western’s book show that

your error matters least when playing nearly full, and goes

on increasing in an increasing ratio, until a very small error

in a fine cut has a very serious effect on the direction.

W.