PER 
3*8 
Nov/, if the bodies have no elasticity, they 
■wili move together as one mass B -\- b after they 
meet, with some common velocity, which call y, 
in the direction AD : therefore the momentum 
in that direction after the shock, being the pro- 
duct of the mass and velocity, will be (B -{- b) 
X v. But the momenta, in the same direction, 
before and after the impact, are equal, that is, 
BV -(- bv — (B -f- b) v ; from which equation 
any one of the quantities may be determined 
when the rest are given. So, if we would find 
the common velocity after the stroke, it will be 
«, — ^ . equal to the sum of the momenta 
y — B _J_ b ’ 1 
divided by the sum of the bodies ; which is also 
equal to the velocity of the common centre of 
gravity of the two bodies, both before and after 
the collision. The signs of the terms, in this 
value of y, will be all positive, as above, when 
the bodies move both the same way AD but 
one term bv must be made negative when the 
motion of b is the contrary way ; and that term 
will be absent or nothing, when b is at rest be- 
fore the shock. 
Again, for the case of elastic bodies, which 
will separate after the stroke, with certain ve- 
locities, .v and z, viz. x the velocity of B, and 2 
the velocity of b after the collision, both esti- 
mated in the direction AD, which quantities will 
be either positive, or negative, or nothing, ac- 
cording to the circumstances of the masses B 
and b , with those of their celerities before the 
stroke. Hence then, Bv and bz are the separate 
momenta after the shock, and Bx -{- bz their 
sum, which must be equal to the sum BV bv 
in the same direction before the stroke : also 
.. x is the relative velocity with which the 
bodies separate after the blow, and which must 
be equal to V — v, the same with which they 
meet ; or, which is the same thing, that V -j- x 
__ v _L z ; that, is, the sum of the two velocities 
bf the one body, is equal to the sum of the ve- 
locities of the other, taken before and after the 
stroke ; which is another notable theorem. 
Hence then, for determining the two unknown 
quantities x and 2, there are these two equa- 
tions, viz. 
BV - 4 - bv zz: B v -)- bz, 
and V — v = z — x; 
or V -{-xzzK-f-z; 
the resolution of which equations gives those 
two velocities as below, 
2 bv (b — b)\ 
viz. x — — — 7 , 
B — j- b 
^ 2BV — (B — b)v 
“ B — |— b 
From these general values of the velocities, 
which are to be understood in the direction AD, 
any particular cases may easily be drawn. As, 
if the two bodies B and b are equal, then B — b 
— 0 and B -f- b zz 2B, and the two velocities 
jg that case become, after ^impulse, x — v, and 
z . — v, the very same as they were before, but 
changed to the contrary bodies, i. e. the bodies 
hjve taken each other’s velocity that it had be- 
fore, and with the same sign also. So that, if 
the equal bodies were before both moving the 
same way, or towards D, they will do the same 
after, but with interchanged velocities. But if 
they before moved contrary ways, B towards D, 
an d b towards A, they will rebound contrary 
ways, B back towards^A, and b towards D, each 
with the other’s velocity. And, lastly, if one 
body, as b, was at rest before the stroke, then 
the other B will be at rest after it, and b will 
go on with the motion that B had before. And 
thus may any other particular cases be deduced 
from the first general values of x and z. . 
PELtDICIUM, a genus of. the class and 
order syngenesia polygamia superflua. The 
cordhts are bilabiate; down simple; re- 
teptacle naked. There are six species. 
PER 
PERENNIAL, in botany, is applied to 
those plants whose roots will abide many 
years, whether they retain their leaves in win- 
ter or not; those which retain their leaves 
are called evergreens; but such as cast their 
leaves, are called deciduous. 
PER GALES I A, a genus of the pentandria 
digynia class and order. Contorted nect. 
surrounding the genitals with li ve-sagittated 
cups; corolla salver-shaped. There are live 
species, twining plants of the Cape, &c. 
PERIANTHIUM. See Botany. 
PERICARDIUM. See Anatomy. 
PERICARPiUJM, among botanists, a co- 
vering or case for tits seeds of plants. See 
Botany. 
PERICRANIUM. See Anatomy. 
PERIGJEUM, perigee. See Astro- 
nomy. 
PERIHELIUM. See Astronomy. 
PEllILLA, a genus of the class and order 
didynamia gynmospermia. The calyx upper- 
most; segment very short ; stamina distant; 
styles two, connected. There is one species, 
an annual of the East Indies. 
PERIMETER, in geometry, the bounds 
or limits of any figure or body. Ihe pe- 
rimeters of Surfaces or figures are lines, those 
of bodies are surfaces. In circular figures, 
instead of perimeter, we say circumference, 
or periphery. 
PERINEUM, or Perineum. See Ana- 
tomy. 
PERIOD, in astronomy, the time taken 
up by a star or planet in making a revolution 
round the sun; or the duration of its course 
till it returns to the same point of its orbit, 
i See Astronomy. 
Period. See Chronology. 
Period, in grammar, denotes a small com- 
pass of discourse, containing a perfect sen- 
tence, and distinguished at the end by a point, 
or full stop, thus (.); and its members or di- 
visions marked by commas, colons, &c. 
PERICECr. See Geography. 
PERIOSTEUM. See Anatomy. 
PERIPHERY, in geometry, the circum- 
ference of a circle, ellipsis, or any other re- 
gular curvilinear figure. See Circle, &c. 
PERIPLOCA, Virginian silk, a genus of 
the digynia order, in the pentandria class of 
plants; and in the natural method ranking 
under the 30th order, contorta?. The nec- 
tarium surrounds the genitals, and sends out 
five filaments. There are 13 species, some 
of which are natives of warm climates: one, 
however, is sufficiently hardy forthis climate. 
The periploca is a fine climbing plant, that 
will wind itself with its ligneous branches 
about whatever tree, hedge, pale, or pole, is 
near it, and will arise, by the assistance of 
such support, to the height of above 30 feet ; 
and where no tree or support is at hand to 
wind about, it will knit or entangle itself to- 
gether in a most complicated manner. The 
stalks of the older branches, which are most 
woody, are covered with a dark brown bark, 
whilst the younger sliqots are more mottled 
with the different colours of brown and grey, 
and the ends of the youngest shoots are oiten 
of a light green. The leaves are the greatest 
ornament to this plant, for they are large, and 
of a shining green colour on their upper sur- 
face, and cause a variety by exhibiting their 
under surface of a-hoary cast. Their figure 
is oblong, or rather more inclined to the shape 
of a spear, as their ends are pointed, anti they 
PER 
stand opposite, by pairs, on short footstalks. 
Their flowers afford pleasure to the curious 
examiner of nature. Each of them singly has 
a star-like appearance; for, though it is com- 
posed of one petal only, yet the rim is divided 
into segments, which expand in such a man- 
ner as to form that figure. Their inside is 
hairy, as is also the neetarium which sur- 
rounds the petal. The propagation of this 
cl mber is very easy ; for, if the cuttings are 
planted in a light moist soil, in the autumn or 
in the spring, they will readily strike root. 
PER IPN EU MONA”. See Medicine, 
PEEIPTERE. See Architecture. 
PEEISCn. See Geography. 
PERISTALTIC. See Physiology, 
PERISTYLE. See Architecture. 
PERITONEUM. See Anatomy. 
PERU ROCHIUM. See Mechanics, 
PERJURY, is a crime committed when a 
lawful oath is administered, by any one who 
has authority, to a person in any judicial pro- 
ceeding, who swears wilfully, absolutely, and 
falsely, in a matter material to the issue or 
cause in question, by his own act, or by the 
subornation of others. To constitute perjury, 
it is essential that the oath is wilfully taken ; 
that it is in a judicial proceeding, or some 
other public proceeding of a similar nature: 
the oath must betaken before persons lawfully 
authorized to administer it, and also by a 
person sworn to depose the truth ; it must also 
be taken absolutely and directly, and upon 
something material to the point in issue. It 
is not material whether the false oath is 
credited or not ; or whether the party in whose 
prejudice it was taken, was in the event da- 
maged by it; for the prosecution is not 
grounded upon the damage, but on the abuse 
of public justice. By stat. 5 Eliz. c. 9, per- 
sons guilty of perjury, or subornation of per- 
jury, are to be punished with one year’s im- 
prisonment, and stand in the pillory where 
the offence was commifted. This offence is 
also punished by transportation. 
PERU'. INK LE. See Turbo. 
PERM l 'I ATION of quantities, in alge- 
bra. See Combination. 
PERORATION. See Rhetoric. 
PEROTIS, a genus of the digynia order, in 
the triandria class of plants, and in the na- 
tural method ranking under the fourth order, 
gramina. There is no calyx; the corolla 
consists of a bivalvular glume; the valves are 
oblong, acute, somewhat unequal, and ter- 
minating in a sharp beard. There are two 
species, natives of the East Indies. 
PEROXIDE, in chemistry, denotes the 
maximum of oxidizement. See Oxide. 
PERPEN DI CU L A R . See C e o m e t r y. 
Perpendicular to a parabola, is a right 
line cutting the parabola in the point in which 
any other right line touches it, and is also it- 
self perpendicular to that tangent. 
PERPETUITY, in annuities, the number 
of years purchase to be given for an annuity 
which is to continue forever. It is found by 
dividing 100/. by the rate of interest, and,, 
consequently, is, at the most usual rates, as 
follows : 
At 3 percent. 33,3333 
3£ 28,5714 
4 25,0000 
4i 22,2222 
5 20,0000 
§ 1 6,0606 
14,28577 
