368 
An Essay on the Game of Billiards. 
[Nov. 
rotary motion, and their imperfectly elastic nature which will not retribute in 
adequate proportion as the quantity of aggressive force increases, it would be 
always of this magnitude : But, although to this extent they cannot separate 
these circumstances (granting a choice of situation) render them efficient of any 
angle less, till they coincide : or to be more explicit ; one ball, as A (see Fig. 
17) being driven from the point b, in a tangent to another as P, the angle 
which both thus make after bitting, is the nearest to a right one, and greatest 
that can be made ; but, if driven from the several positions c, d , e,f, g, h, i, 
b, notwithstanding the opposition, and of consequence the reflection also, be 
increased with each advance, the vertical angle will be in the same order progres- 
sively diminished, till at k, whence they hit centrally, it vanishes altogether, the 
active ball following in a line coincident or corresponding with that wherein 
the passive ball moves. 
This may be further illustrated by supposing A and P, divided into eight or any 
other number of parts, and only the two divisions immediately adjoining to be 
excited when the active ball A is driven from the point b, whence the opposition 
must be least ; consequently the quantity of direct force turned towards reflection, 
will be affected by no more of that deficiency from elastic perfection, than resides 3 
in those parts which receive the impression ; and a situation necessary to increase 
that opposition, will also add to the quantity of that latent principle which proves 
a drawback on the reflecting line ; for, by altering it from b to c, &c. to It, 
though the absolute reflective power be enhanced at each promotion, the opposition 
becoming more direct; the concussion which the balls undergo, penetrating at 
the same time further from the point of contact, will rouse into action this attenu- 
ating quality of matter which lies dormant in the portions behind ; and thereby 
deteriorate reflection, without a suitable or any alteration in the direction of the 
passive ball — the other constituent line of the angle in the proposition. It must 
therefore be diminished in the like ratio. 
An effort, or tendency towards lateral rotation, arises from this indirect oppo- 
sition also ; and may sometimes be perceived ; but that it always exists, will 
appear, by supposing c, d, (fig. 15) equal portions cut off from the balls on opposite 
sides, changing their centres to the line of direction, e, f, as in fig. 14; then 
likewise, the portion on one side being opposed by an equal portion on the other, 
and no predominating influence to turn the scale, the balls may be said to be in 
equilibrio. It is plain therefore, that, not only a difference in direction must take 
place, by restoring these crescents, which alter the centre of gravity, and destio) 
this equilibrium ; but also, that the crescent of the active ball, being unopposed, 
is warped from its rectilineal course, by the violence its complement receives m 
reaction from the passive ball, and carried by its momentum, horizontally and 
slowly round, having that part of its surface, which came in contact with the 
other, as a centre or focus point of its motion. A similar effect is produced in the 
passive ball, but its crescent having no momentum at the time of contact, d ls 0 
much less consideration. 
Lateral rotation acting, as it seems, obliquely against progressive motion, 111 a J 
be conceived as somewhat analogous to the power of gravity, making the ball, in 
subservience to the law of projectiles, describe a parabola, whose principal ' ei 
3 Giving to a negative quality a positive place, may be a crust for a Cllt ^.’ 
but the author’s chief aim is to be explicit, and if that abuse administeistot 
purpose, he will readily admit bis acumen; with the same view only? he has som 
times ventured to express his meaning figuratively, Theory having a littlo clai 
to this indulgence, beyond the bounds of Practice. 
