An Essay on the Game of Billiards. 
116 
[April, 
being excited, rather by a reverse in the mode of application, than a change in the 
nature of the principle, it rules with equal influence. 
The second position of the cue here represented, is chosen only to exhibit the 
Theory more clearly, by making the contrast with its former place more perfect ; 
for it is obvious, the middle at the but-end cannot, by reason of the cue’s thickness 
there, be so much depressed ; neither, perhaps, is it always eligible, as far as it 
can be done ; because, if the violence be considerable, the ball will boimce from 
it, in a line passing through its centre from the point of impulsion, (see o, b, Fig. 
3.) and turn in the air, (see Fig. 4.) with too small a share of the progressive to 
carry it effectually to its object; whereas, by elevating the but-end, and at the 
same time applying the point somewhat higher towards the middle, as c, d, in 
those figures, that line will approach nearer to a coincidence with the progressive ; 
and the ball be less apt to rise ; while, if the direction be equally distant from the 
centre, the twisting power can suffer no diminution. 
Hence a ball is often struck thus, and considerably higher, as e, f, with good 
effect, providing the ball played at be remote ; and the degree of violence, as well 
as the mode of applying it, should be in proportion to the distance between the 
balls, so as to have as little of the progressive, and as much of the twisting motion 
as possible, at the time of contact, their action being in opposite directions. Be- 
cause, if the balls be far asunder, and the impulse small, the twist will be quickly 
overcome by the roughness of the cloth, and sink into the attritive ; but, if it be 
great, the twist will be so likewise, and the ball fly over the same space with less 
interruption from that impediment, as a former observation shews, and conse- 
quently less consumption of the twist imparted. If, on the other hand, the balls be 
not far asunder, and the impulse great, the ball impelled will at first be apt to 
rise (as above explained)^; and to hit the other before it falls into level motion; 
or, should that not be the result, the twist will be counteracted, by the quantity of 
progressive force remaining after contact, with which the ball had been over- 
charged ; and proportionably destroyed. 
These effects also are rotary ; but (abstractedly considered) the centre of motion 
is not confined to the external parts of the ball, as they severally fall in succession 
upon the table, like the attritive ; for the ball, according to the nature, manner, 
and force of the stroke, is often driven with a tendency to move round points beyond 
its surface, and its course may be assimilated to (see Fig. 2.) that which takes place, 
before the progressive be sufficiently subdued, to coalesce, and form the attritive; 
or, the compass may be so reduced, as to have its centre within the ball’s surface, 
(see Fig. 4,) and produce locomotion, by means of repulsive agency against the 
cloth, without much attrition or any progressive aid. 
Tins last effect, a twisting stroke may exhibit very clearly ; for a low appli- 
catton of the po.nt w.ll detach the ball from the table, without imparting almost 
any progress, ve mot, on ; but a temporary separation from the table, with so small 
a W of t.m progression scarcely (if possible) be produced b . waIkin „ 
d ltfoctl ““ P Unt " aftCr reflecti °"- n ° r even then be sees 
with ,b t a Y 35 heretofore dir eeted, in order to make it' twist, 
S absolum d r U T Cpared or serves to little purptfse ; for 
recilinellco 7* be u ‘ wds ’ “ line «, 4, from which 
r: r “ bclng , C ° n,inualI y “« »P°" by the power Of gravity, 
projectiles ! * parabola ’ as according to the law of 
bofolikefoLfd P °'f- '* rOU<?h ’ ate ”POrary hold is taken of the ball, and 
both, like indented maclunery, are for an instant locked together in the inequali- 
