590 
off, and tlie other by the paint received ; and, 
as the balls retain their spherical figure after 
the impact, it is dear that the parts of the 
surface not only lost, but recovered their 
figure. 
1 wo glass balls may, with a proper de- 
cree of velocity, so impinge on each other, 
that the interior parts of the ball will be bro- 
ken, though the exterior contiguous to the 
point of impact, be unbroken. 
Suspend two ivory balls from the same 
point, by strings of the same length, and let 
the smaller ball A, impinge upon 13, at rest, 
with a given velocity. A will be reflected 
always to the same height, and 13 will be im- 
pelled to the same height. But if either A or 
J3 is hollowed, and lead inserted in the cen- 
tre or near to the posterior surface, neither 
ball, though the weight be the same, will as- 
cend as high as before the insertion of the 
lead. The progressive motion of the parts 
from the point of impact is stopped by the 
insertion of the lead ; and consequently, the 
force of restitution and the change of figure, 
is less than before it was inserted. 
1 he motion diffused from the point of im- 
pact to the remote parts of an elastic body, is 
continued for some time, and diminishes gra- 
dually till it vanishes: and there seem to be 
.two kinds of vibrations in the parts of an elas- 
tic body ; one of which is quick, and called a 
tremor of its minute parts ; and the other 
slower and longer, by which its figure is 
■changed, and an impinging body repelled. 
A stroke or friction upon the edge of a 
glass, communicates a tremulous motion to 
the parts of the glass, which is visibly com- 
municated to the water it may contain. A reed 
or stick placed across the bottom of a large 
glass bell, will fall when the glass is struck, the 
stroke producing a change of figure. If you 
hold a piece of metal near the brim or lip of a 
bell, without touching it, and the bell is 
stricken by a hard body, you will see it touch 
the piece of metal, and will hear a succession 
of sounds gradually decaying. If the edge of 
the bell is pinched, and the Angers suddenly 
withdrawn, the same sound is heard, without 
producing any sensible motion, towards the 
piece of metal, or displacing the reed across it. 
Those laws according to which alterations 
-are produced in the rest and motion of bodies 
upon their collision, are called the laws of 
•communication of motion. 
When one body strikes against another, if 
the fine of direction of the impulse passes 
through the centre of gravity of both the bo- 
dies, tlie impulse is called full or direct, other- 
wise it is called an oblique impulse. 
'fhe relative velocity of two bodies, is 
that velocity with which they approach to, or 
recede from, each other ; and is equal either 
to the difference of the velocities of bodies 
moving the same way, or to the sum of the ve- 
locities of bodies moving contrary ways ; for, 
if one of the bodies was at rest, and the other 
moved towards it or from it, with the fore- 
mentioned difference or sum of velocities, the 
body in motion would approach to, or recede 
from, the body at rest, just as fast as the two 
moving bodies approached to, or receded 
from, each other. 
If two bodies move in the same direction 
wit h equal velocities, they are relatively at rest. 
When the iupulse is direct, and the bodies 
are void of elasticity, the laws of the com- 
piumcation of motion are as follow: 
ELASTICITY. 
(1.) In all cases, the velocities after the 
stroke are equal ; for the impulse ceases 
when the impinging bodies are relatively at 
rest, and not before. (2.) If two bodies move 
the same way, and in the same right line, 
that which moves fastest will overtake the 
other, and the sum oftheir motions will be the 
same after the stroke as before : for, by the 
third law ot motion, so much motion as the 
slowest body gains, the swiftest body loses. 
(3.) If two bodies move contrary ways, the 
sum of their motions after the stroke will be 
equal to the difference oftheir motions before 
the stroke ; for, whilst the strongest motion de- 
stroys the weakest, it also loses an equal part of 
itself, the third law of motion. (4.) If thesum 
of two conspiring motions, or the difference of 
two contrary motions, be divided by the sum 
of the quantities of matter in both the moving- 
bodies, the quotient will give their common ve- 
locity after the stroke. (5.) If the velocity after 
the stroke be multiplied into the quantity of 
matter in each body, the product will' ex- 
press the quantities of motion in each body 
after the stroke. (6.) The difference between 
me quantities of motion in either of the mov- 
ing bodies before and after the stroke, is equal 
to the quantity of the stroke. 
Lxample 1. Let a ball of three ounces 
moving with nine degrees of velocity, over- 
take another ball, of two ounces, moving with 
four degrees of velocity: then will the°quan- 
tities of motion before the stroke be 27 and 
8, the common velocity after the stroke 
will be 7, the quantities of motion after the 
strode will be 21 and 14, and the quantity 
of the stroke will be 6. 
Example 2. Let the same balls move 
with the same velocities contrary ways; then 
will the quantities of motion before tlie stroke 
be as before; the common velocity after the 
stroke will be 3 4, the quantities of motion 
after the stroke will be li|., and and 
the quantity of the stroke 15f. 5 * 
W lierefore, if two equal bodies move in 
contrary directions, with equal velocities, as 
soon as they strike, both motions will be 
destroyed. And if a body in motion strikes 
an equal body at rest, it will communicate half 
its velocity or half its motion. And if one 
moving body overtakes another moving body 
equal to the first, the common velocity after 
the stroke will be equal to half the difference 
of their velocities before the stroke. But if 
lliey move in contrary directions, the velocity 
inter the stroke will be equal to half the 
sum of the velocities before the stroke. (7.) 
If amoving body strikes against an immove- 
able obstacle, after .tlie stroke the whole 
will be destroyed, and the quantity of the 
stroke will be equal to the whole quantity of 
the motion. (8.) If the moving body gravi- 
tates towards tlie immoveable obstacle, as 
when a stone falls upon the earth, the quan- 
tity of the stroke is equal to the sum of the 
quantity of motion added to the weight of the 
moving body ; for the weight remains upon 
the obstacle when the impulse is destroyed. 
I he sum of the motions of two bodies void 
of elasticity, may be less after the stroke than it 
was before, but it cannot be more. (9.) If a 
body moves after the stroke, the same way 
that it moved before, the difference of the ve- 
locities before and after the stroke will be equal 
to the velocity lost or gained. Thus, in the 
first example, the velocity lost is 2, and the 
velocity gained 3. (10.) Tf the direction of 
the motion after the stroke is contrary to 
the direction of the motion before the stroke 
the sum of the velocities before and after the 
stroke will express the quantity of the v- 
locity gamed. Thus, in (he second example 
vie velocity is 5^, the velocity gained 74 
VV nen the impulse is direct, and the bodies 
perfeedy elastic, the laws of the edmmuni- 
cation of motion are different from the fore- 
going. For, 1 
(lOUponthecoifisfon of two elastic bo- 
dies, the force of elasticity is equal to the 
force of compression ; and the force of com- 
piession in each body is equal to the quan- 
tity ol the stroke (2.) Th e whole force of 
elasticity exerted at the restitution of both 
the springs, is double the quantity of the 
stroke ; for it is the result of two forces in con- 
of ^ hich is ec i uai to 
quan tv of the stroke. Or if it may be con- 
"r r )V Um ° f the elasticitl ^ ^ equal 
to the su n of the quantities of the stroke in 
auantKfel ft er; that is > double the 
quantity oi the stroke in each single body (3 'i 
he .fleet of the elasticity m Jch £oX, lii 
be equal to he effect of the stroke, and in 
the same direction; for the two equal and 
contrary elasticities in the former case, are 
equu-alcmt to action and reaction in the lat- 
•f; \ 4 ’) VV herefore, to find the velocity of 
either body after the collision, first find the 
common velocity with which the bodies would ■ 
move after the stroke, if they had been void 
0 elasticity, and find also the velocity lost 
or gamed; then subtract the velocity lost 
fiom the common velocity, or to the' com- 
the^Ifferen^ ^ ^ V ? lot ? y S ained 5 so shall 
1 e oh, ence or sum be the velocity sought. 
But it tlie velocity lost be greater than the 
common velocity, then subtract the common 
velocity from the velocity lost, and the re- ; 
mainder will give the velocity sought in a 
contrary direction. 
I hus, in the first example before stated 
! we su PPose the bodies to be elastic, the ve- 
locities after collision will be 5 and 10 and 
consequently the quantities of motion will be 
15 and 2. j 
In tne second example, the velocities 
alter collision will be l-?- and nil, and 
the quantities of motion 4 % and 23 -t-? 
1 oi a third example, let us suppose two j 
bodies pn proportion as three to two ; tlie ] 
m st at rest, and the second moving towards 
the first with 40 degrees of velocity: then 
\\m the quantities of motion before the stroke 
be 0 and 80, the common velocity after the 
stroke 16 , the quantities of motion after the 
stroke 48 and 32, the quantity of the stroke 
48, the velocity gained 16, the velocity lost 24, 
the velocities after the restitution of the 
springs 32, and 8 in a contrary direction ; the 
quantities of motion after collision 96 and 16. 
In the first example, the sum of the motion 
befoie collision is equal to the sum of the mo- 
tion after collision; in the second, it is 
greater ; in the third, less. 
I wo elastic bodies always recede from each 
othei after collision, and that with the same 
relative velocity with which they tended to- 
wards each other before collision. Thus the 
relative velocity before and after collision, is 5 
in the first example, 13 in the second, and 40 
in the third. 
And in all cases, whether the impinging 
