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
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.