400 
An Essay on the Game of Billiards. 
[Dec. 
its centre, or touching the cushion above its most prominent part, rises, and is 
carried by the progressive over the table. 
Should the active ball by any means hop on the passive, somewhere about half 
way in or near the arch between its middle and summit, with only a small degree 
of progressive force, it will be driven backwards : for as in this case, it urges the 
other to pass through the table, its forward motion is impeded, not only by the 
resistance and re-action of the passive ball; but by similar properties in the table 
also, and must be returned from their ascendency, and according to that direction 
wherein they are assailed. 
.The active ball after hitting the passive has (caeteris par ibus) the same degree 
of latitudinal range with it : but, if the interval between them be small, and 
the active ball invested with those subsidiary powers, from which the other is 
debarred, it may have more than twice as much, and traverse a circle entirely, 
(as shewn at the beginning of this essay, see fig. 2 :) whereas, the passive ball 
is subject to a government, the limits whereof cannot by any means or situation 
be extended to half the compass, and its influence diminishing in direct propor- 
tion with the interval, the space accordingly will become contracted as they are 
approximated, till distance vanishes, and it be reduced to a single line. Or (by 
conversion) supposing them thus in contact : as the hitting point cannot be 
altered by any manner of striking the active ball, neither can the direction of 
the passive be capable of latitudinal variation ; and, in proportion as they are 
removed, the arch intercepted between the tangents b, c, and d, e, (see fig. 18.) 
formed on opposite sides by the motion of the active ball, will increase; but on 
account of their divergency after intersection, as at f, or any where else, as at g, 
cannot (however great the distance) be equal to a semicircle. Hence a losing 
hazard occurs much oftener than a winning one, and dexterity the effect of 
practice, gives it with most players the preference. Yet they cannot well be 
compared ; at least, their comparative facility should not be decided by the 
distance from the pocket only, but also by the arch, on the surface of the passive 
ball intercepted between the middle, and the part which it is necessary to hit for 
the respective purposes. However a person executes that best, which he is 
most accustomed to play for, and fancy the offspring from success, assists execu- 
tion. Players therefore equally good may have different design. 
A cannon, or losing hazard, is made with less certainty, if the first ball be 
within the distance of an inch or two from the second, and the third one or 
p. c. somewhat remote, than when extended to that of so many feet ; because 
t ie mannei of striking the ball must be more precise, to avoid complication 
ioni the vaiious motions which are in the beginning more particularly apt to 
occupy it, as before explained. 
A cannon is more easily made than a hazard, if the distance be the same ; 
c ve, should the first ball after hitting the second, .move within three 
' teis of the thiid, it must be made; but no table has the opening of its 
pockets so wide. 6 
It the progressive motion of a ball be slow before it hits a cushion, it is often 
j C * t0 ,^ e soaunv hat accelerated after; the increase arises from a coinci- 
motions bj. reflection, which had been at variance in progression. 
ball '■ Wmi ! ing aUt * ,0sin o a winning hazard made of the adversary’s 
tabic ^ e, * eid l ess value than a losing one, as the fewer balls left upon the 
good ni. ' f 88 °^ i0US, y must be the remaining chance; on which account, 
‘3 wi fiequently give it up in favour of a worse hazard, and relin- 
