402 
An Essay on the Game of Billiards. 
[Dec. 
as the distance in which it is made to act, that is greatest when the stroke isshort- 
est, because, the ball having less time to make its escape, the resistance arising 
from inertness, and other impediments to motion, which bend the cue, is increased 
by suddenness of opposition ; but, if the stroke be extended, or lengthened by 
continuation to a greater distance, as when playing for a walk, though the 
quantity of power employed remain the same, by the time the fifth or sixth degree 
arrives, the resistance will be subdued, and the elastic force beginning to expand 
itself, the ball will either be driven too fast for the successive numbers to overtake 
it ; or should it not be detached, the opposition being so small, they will discharge 
themselves to little purpose, merely pushing it forward, while the elastic force, 
instead of being augmented, relaxes, and the cue immediately recovers its form. 
It will he endeavoured to render visible how the measure of aggression, which 
evidently depends upon the power, is increased by contracting the distance wherein 
that power is exerted. Suppose, therefore, b , (see fig. 25,) the point of a cue 
drawn back to c, with any degree of quickness, and immediately returned for the 
purpose of striking the ball A. If its motion (assuming the power of the hand 
or that of gravity) be admitted as uniformly accelerated, in the order of 1,3, 5, 7,9, 
, &c. like that of bodies falling from a state of rest ; an Isosceles in analysis, as 
, , <?, taking the first division of the arenas comprising a given degree of celerity, 
P ve qu&ntity of power, represents the same ratio of arithmetical increase 
< ur.ng its emotion : and under the above law of acceleration, by supposing the 
cue uither removed to/, (that is twice the distance,) with bd produced tog be 
to A and then joining- g h, the relative spaces, degrees of celerity, and quantities 
the lnTt n Ry ’ y trans l ,osition be obtained at each consecutive interval, and 
construe ^gate on its return to the ball. Or two triangles, 
bit the q " S an< Slm ‘ “ l ° tlle s ‘ vcn one ’ and P'aced as in the figure, will exhi- 
i^ Tr:" ,n ° re C °“ Cise ^ "’ ith » initial of the like proportion, as 1, 3, 
within ^ ‘ angle f0r Unity - Blit if twice the quantity of power be excited 
. , . ' sanle stance, the increments ot acceleration will he doubled also, and 
rZ rftw T" Pai '“" elS “ tSi,nil8r inte ™ ,8 > dri '-™ hito lateral expansion, and 
cue drawn l* v 7™° '° aS may be seen in fl S- 26 - Again, suppose the 
Z t 2 O U,C ’* S 2 (m (See fi »* aad tba ". for an instant stopped 
sion be I IC f ' l ltl some P l; *y crs ), tile momentum will by this interims. 
originate thereT ’ /' r, ‘ nta?c “paired from it lost, and the force inns, 
be no mm tl 'i °’ >’ "thtoh the aggressive effect (as the spaces indicate) will 
why bodil lan >a ’ l, ' 0 " Sh the active Power be unimpaired. Hence it append, 
powers bv a hlU ^ tldal strength, without the art or knack of compressing its 
powe, by „ sudden jerk or the like, is so „f ten unaeHiliag , 
it is usual] i 1 1 ' 1 Wa *, S * l l ' e a btl ' e preponderance forward from the part where 
same weiW.t will a 2rl ‘I' 0 We!ght shouM chiefl y be i for if behind it, the 
too much , T P re l>o"'lerance to the other end, or ,f before, it will press 
-elr Trrl b :' d?e \ t0 m ° Ve With 8u ® CIea t lightness; and educing the 
the momentii Tl "•' t ' tte d,sta "ce, is cutting off a principal source whence 
momentum and elastic force take rise. 
section there ^ °V ^ 1,6 USed> U 1S often material to know the transverse 
intrio J " J ? V the tlme ° f Stnki "« “-e ball, it makes with the .aide the 
middle* if ' 6SS 4 ian H one > point of aggression will be under the 
con c„;l? '’,,° Ver S bUt if neitl,er - ,he middle -ill be struck exactly, and the 
"sequences resulting-, wistmg, walking, aud the progTessive respec tively, as 
* (That i.s) the angle opening towards the player. 
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