1831.1 
An Essay on the Gam? of Billiards. 
3(>7 
quiescent at b, the point of contact: but, should it hit obliquely (see fig. 1 .'») 
the passive ball P, at whatever distance, will bedriven in a right line draw n through 
its centre from the point of contact, and with a velocity inversely as its deviation 
from the line of direction, compounded with the loss of motion in A, the active 
hall, which is carried oft’ by the difference, making an angle with the line of acci- 
dence always greater than a right one, and inversely commensurate with the por- 
tions opposed. 
It is obvious this angle of reflection cannot be so small as a right one ; for since, 
in the former case, where the balls are centrally and completely in opposition, the 
active one is not driven back beyond the point of contact ; therefore (a fortiori) 
it cannot take place where the opposition is less ; and the angle must increase ac- 
cording to that diminution. Besides, otherwise the balls must have an elastic 
force more than equal to the aggressive; whereas, on the contrary, reflection 
simply 2 , (that is) without these rotary motions which influence it conformably 
with their characters, as already described, has ever proved it to be interior. Iho 
walking power operates over this angle with a tendency to enlarge it ; and, although 
it may be increased at the same time with the progressive ; not only, its increments 
of motion are always proportionably small, but the quantity performed in any 
definite distance, regularly less, as the other becomes augmented : so that increas- 
ing the violence counteracts the means of enlarging it. 
The twisting power influences this angle to an opposite purpose : but, as it may 
be increased by violence, in a definite distance, without adding to the pi ogr< suite 
also, the active ball may be drawn back upon the line of accidence or towards 
it, and the angle accordingly in a great measure reduced. This power is 
most efficient when the balls are not further asunder than a free use ol the 
cue make necessary, because, in that case, having less attrition to contend 
with, it will therefore be less diminished, and consequently return with a greater 
quantity. Moreover, the angle resulting from such a situation appears n *? 
smaller than if the balls were more removed, though no twisting should hau 
taken place ; because the active ball struck at different distances upon thc saine 
right line, between the centres of both, will be most reflecte rom 1 , w icn i 
interval is shortest ; though the passive ball be bit in the same par ■ prw ,s j V 
But this conclusion (admitting the statement) is drawn erroneousl y ;fbr Bo. 
of accidence from which the angle should be measured, also «-^the 
distance. This may be seen in fig. 16, by putting A, A, to represen j 
and P, the passive, at different distances upon the same line h, c ; 
lines l e , those of accidence and reflection respectively ; and though the 
Portions opposed, viz./,/, increase with the interval as 1 ie / ^ ' J jh 
reflection from the original line b, c, will not be equivalent to the an,le w 
attends a diminution of the distance. both 
Hence i, is obvious, that giving back the ^ 
Produced, when not within reach of the cue s p . . j t0 
!“ «"*'«» Play). the angular relation with, cushion or J» 
leave the position with respect to both unchangc , 
that the centre may occupy some place in the parallel g , h, aSI - ^ w j t (, t |, c 
But the active ball can never make so great an angle as a ng ^ ^ ^ ^ 
lotion of the passive ball, except by means of twisting ; 5 > 
. i Units from the same or adjacent 
a This may be shown by suspending two equa ^ ^ between the 
Points, and letting one fall against the other: tie -mg couse quently a proof 
mes of accidence aud reflection will always be o > 
this inferiority. 
