PERCUSSION. 
slon a body makes in falling or striking upon ’ 
another, or the shock of two bodies in motion. 
Percussion is either direct or oblique ; di- 
rect, when the impulse is given in a line per- 
pendicular to the point of contact ; and ob- 
lique, when it is given in a line obiique to the 
point of contact. 
1 he ratio which an obiique stroke bears 
to a perpendicular one, is as the sine of the 
angle of incidence to the radius, d'hus, let 
ab (Plate Miscel. fig. 185) be the side of any 
body on which an oblique force falls, with the 
direction da; draw dc at right angles to db, 
a perpendicular let fall from d to the body to 
be moved, and make ad- the radius of a circle ; 
it is plain that the oblique force da, by the 
laws ot Composition and resolution of motions, 
will be resolved into the two forces dc and 
hd- \ of which dc, being parallel to ab, has 
wo energy or force to move that body ; and 
consequently, db expresses all the power of 
the stroke or impulse on the body to be 
moved. But db is the right sine of the angle 
of incidence dab ; wherefore the oblique 
force da, to one falling perpendicularly, is as 
the sine ot the angle of incidence to the radius. 
Percussion, centre of, is that part or 
point ol a pendulous body, which will make 
the greatest impression on an obstacle that 
is opposed to it whilst vibrating; for if the 
obstacle is opposed to it at different distances 
from the point of suspension, the stroke or per- 
cussion will not be equally powerful, and it 
will soon appear that this centre of percussion 
does not coincide with the centre of gravity. 
1 he force ot percussion is the same as the 
momentum, or quantity of motion, and is 
represented by the product arising from the 
mass or quantity of matter moved, multi- 
plied by the velocity of its motion ; and that 
without any regard' to the time or duration 
of action ; tor its action is considered totally 
independant of time, or but as for an instant, 
or an infinitely small time. 
i his consideration will enable us to re- 
solve a question that has been greatly can- 
vassed among philosophers and mathema- 
ticians, viz. what is the relation between the 
force of percussion and mere pressure or 
weight? For we hence infer, that the former 
force is infinitely, or incomparably, greater 
than the latter. For, let M denote any mass, 
body, or weight, having no motion or ve- 
locity, but simply its pressure; then will that 
pressure or force be denoted by M itself, 
if it is considered* as acting for some certain 
finite assignable time ; but, considered as a 
force of percussion, that is, as acting but for 
an infinitely small time, its velocity being 0, 
or nothing, its percussive force will be 0 x 
M, khat is 0, or nothing ; and is therefore 
less than any the smallest percussive force 
whatever. Again, let us consider the two 
forces, viz. of percussion and pressure, with 
respect to the effects they produce. Now 
the intensity of any force' is very well mea- 
sured and estimated bv the effect it produces 
in a given time: but 'the effect of the pres- 
sure M, in 0 time, or an infinitely small time, 
is nothing at all ; that is, it will not, in an 
infinitely small time, produce, for example, 
any motion, either in itself, or in any other 
body ; its intensity, therefore, as its effect, 
is infinitely less than any the smallest force 
of percussion. It is true, indeed, that we 
see motion and other considerable effects 
produced by mere pressure, and to couuter- 
Vdl. II. 
» 7 * 
act which it will require the opposition of! The laws of percussion therefore to b 
some considerable percussive force; but then 
it must be observed, that the former lias been 
an infinitely longer time than the latter in 
producing its effect; and it is no wonder in 
mathematics that an infinite number of infi- 
nitely small quantities makes up a finite one. 
ft has therefore only been for want of con- 
sidering the circumstance of time, that any 
question could have arisen on this head'. 
Hence the two forces are related to each 
other, only as a surface is to a solid or body; 
by the motion of the surface through an infi- 
nite number of points, or through a finite 
right line, a solid or body is generated ; and 
by the actiou of the pressure for an infinite 
number of moments, or for some finite time, 
a quantity equal to a given percussive force 
is generated ; but the surface itself is infi- 
nitely less than any solid, and the pressure 
infinitely less than any percussive force. 
1 his point may be easily illustrated by some 
familiar instances, which prove at least the 
enormous disproportion between the two 
forces, it not also their absolute incompa ni- 
hility. And first, the blow of a small ham- 
mer, upon the head of a nail, will drive the 
nail into a board ; when it is hard to conceive 
any weight so great as will produce a like 
effect, i. c. that will sink the nail as far into 
the board, at least unless it is left to act for 
a very considerable time ; and even after 
the greatest weight has been laid as a pres- 
sure on the head of the nail, and has sunk it 
as far as it can as to sense, by remaining for 
a long time there without producing any 
farther sensible effect; let the weight be re- 
moved from the head of the nail, and instead 
of it, let it be struck a small blow with a ham- 
mer, and the nail will immediately sink far- 
ther into the wood. Again, it is also well 
known, that a ship-carpenter, with a blow of 
his mallet, will drive a wedge in below the 
greatest ship whatever, King aground, and 
so overcome her weight, and lift her up. 
Lastly, let us consider a man with a club to 
strike a small bull, upwards or in any other 
direction ; it is evident that the ball will ac- 
quire a certain determinate velocity by the 
blow, suppose that of 1 0 feet per second or 
minute, or any other time whatever ; now it 
is a law, universally allowed in the communi- 
cation of motion, that when different bodies 
aie struck with equal forces, the velocities 
communicated are reciprocally as the weights 
of the bodies that are struck; that is, that 
a double body, or weight, will acquire half 
the velocity from an equal blow; a body 
ten times as great, one-tenth of the velocity ; 
a body 100 times as great, the 100th part 
of the velocity ; a body a million times, as 
great, the millionth part of the velocity, and 
so on, without end; from whence it follows, 
that there is no body or weight, how great 
soever, but will acquire some finite degree 
of velocity, and be overcome, by any given 
small finite blow, or percussion. 
In percussion, we distinguish at least three 
several sorts of bodies; the perfectly hard, 
the perfectly soft, and the perfectly elastic. 
r I lie two former are considered as utterly 
void of elasticity ; having no force to sepa- 
rate or throw them off from each other 
again, after collision ; and therefore either 
remaining at rest, or elseproceeding uniform- 
ly forward together as one body or mass of 
matter. 
3 B 
considered, are of two kinds ; those ior’elas- 
tic, and those for non-elastic bodies. 
! lie one only general principle for deter- 
li.sMing the motions ot bodies from percus- 
sion, and which belongs equally to both tint 
sorts of bodies, 4. e. both the elastic and non- 
elastic, is this ; viz., that there exists in the 
bodies the same momentum, or quantity' of 
motion, estimated in any one and the same 
dueclion, both before the stroke and after it. 
And Inis principle is the immediate result 
ot the third law of nature or motion, that re- 
action is equal to action, and in a contrary 
direction; from whence it happens, that 
whatever motion is communicated to one 
boc.y by the action of another, exactly the 
same motion does this latter lose in the'same 
direction, or exactly the same dges the former 
communicate to the latter in the contrary di- 
rection. J 
From this general principle too it results, 
hat no alteration takes place in the common 
centre of gravity of bodies by their actions 
upon another; but that the said common 
centre of gravity perseveres in the same state, 
whether of rest or of uniform molion, both 
before and after the shock of bodies 
Now from either of these two laws, viz. 
thrtt of the preservation of the same quantity 
ot motion, in one and the same direction 
and that of the preservation of the same state 
of the centre of gravity, both before and after 
the shock, all the circumstances of the motions 
of both the kinds of bodies after collision may 
be made out ; in conjunction with their own 
peculiar and separate constitutions, namely 
that of the one sort being elastic, and the 
other non-elastic. 
The effects of these different constitutions 
here alluded to, are these: that non-elastic 
bodies, on their shock, will adhere together 
and either remain at rest, or else move to- 
gether as one mass with a common velocity • 
or if elastic they will separate after the 
shock, with the very same relative velocity 
with which they met and shocked. The 
former of these consequences is evident viz 
that non-elastic bodies keep together as one 
mass after they meet; because there exists 
no power to separate them, and without a 
cause there can be no effect. And the latter 
consequence results immediately from the 
very definition and essence of elasticity itself 
being a power always equal to the force of 
compression or shock; and which restorin'* 
force therefore, acting the contrary wav will 
generate the same relative velocity between 
the bodies, or the same quantity of matter 
as before the shock, and the same motion’ 
also of their common centre of gravity. 
-e- 
A w ^ -yy 
P> 7; J) 
To apply now the general principle to the de- 
termination of the motions of bodies after their 
shock; let B and b be any two bodies, and V 
and v their respective velocities, estimated in 
the direction AD; which quantities V and v 
will be Imth positive if the bodies both move 
towards D, but one of them as -a will be nema- 
nve it the body b moves towards A, and will 
the body b is at rest. Hence the 
is the momentum of B towards D, and also 
bv is the momentum of b towards D who'.r 
sum .s BV 4 ~ bv which is the whole quantity of 
motion in the direction AD. and which motnen* 
turn must also be preserved after the ^hock. 
