PEN 
not complying with the regulations of cer- 
tain acts of parliament ; a penalty is also 
annexed to secure the performance of cer- 
tain covenants in a deed, articles of agree- 
ment, copartnership, &c. In a bond also 
for payment of money, it is usual to annex a 
penalty in double the amount of the obliga- 
tion. See Bond. 
PENCIL, an instrument used by painters 
for laying on their colours. Pencils are of 
various kinds, and made of various mate- 
rials ; the larger sorts are made of boars 
bristles, the thick ends of which are bound 
to a stick, bigger or less according to the 
uses they are designed for ; these, when 
large, are called brushes. The finer sorts 
of pencils are made of camels, badgers, 
and squirrels hair, and of the down of 
swans ; these are tied at the upper end with 
■a piece of strong thread, and inclosed in the 
barrel of a quill. All good pencils on 
being drawn between the lips come to a 
fine point. 
• Pencil is also an instrument used in 
drawing, writing, &c. made of long pieces 
of black-lead, or red-chalk, placed in a 
groove cut in a slip of cedar, on which other 
pieces of cedar being glued, the whole is 
planed round, and one of the ends being cut 
to a point, it is fit for use. 
PENDANT, an ornament hanging at the 
ear, frequently consisting of diamonds, 
pearls, and other precious stones. 
Pendants, in heraldry, parts hanging 
down from the label, to the number of 
three, four, five, or six at most, resembling 
the drops in the Doric frieze. When they are 
more than three, they must be specified in 
blazoning. 
Pendants, of a ship, are those streamers 
or long colours which are split and divided 
into two parts ending in points, and hung at 
the head of masts, or at the yard-arm ends. 
PENDULOUS, a term applied to any 
thing tlrat bends or hangs downwards ; 
thus, the flowers, w'hose slender stalks are 
not able to sustain their heads upright, are 
called pendulous flowers. See Botany and 
Flower. 
PENDULUM, in mechanics, denotes 
any heavy body, so suspended as that it may 
vibrate or swing backwards and forwards, 
about some fixed point, by the force of gra- 
vity. The vibrations of a pendulum are 
called its oscillations. See Oscillation. 
A pendulum, therefore, is any body. B, 
(Plate Misccll. fig. 8), suspended 
upon, and moving about a fixed point. A, 
as a 'centre. The nature of a pendulum 
PEN 
consists in the following particulars ; I- 
The times of the vibrations of a pendulum, 
in very small arches, are all equal. 2. The 
velocity of the bob, in the lowest point, 
will be nearly as the length of the chord of 
the arch which it describes in the descent, 
3. The times of vibration in different pen- 
dulums, A B, A C, are as the square roots 
of the times of their vibrations. 4. The 
time of one vibration is to the time of the 
descent, throngh half the length of the pen- 
dulum, as the circumference of a circle to 
its diameter. .5. IVIience the length of a 
pendulum, vibrating seconds, will be found 
39.2 inches nearly ; and that of an half se- 
cond pendulum 9.8 inches. 6. An uniform 
homogeneous body B G (fig. 9) has a rod, 
staff, &c. which is one-third part longer 
than a pendulum A D, will vibrate in the 
same time with it. 
From these properties of the pendulum 
we may discern its use as an imiversal 
chronometer, or regulator of time, as it is 
used in clocks, and such-like machines. See 
Chronometer, Horology, &c. 
By this instrument also we can measure 
the distance of a ship, by measuring the in- 
terval of time between the fire and the 
sound of the gun ; also the distance of a 
cloud, by numbering the seconds, or half- 
seconds, between the lightning and thunder. 
Thus, suppose between the lightning and 
thunder, we number 10 seconds ; then, be- 
cause sound passes through 1142 feet in 
one second, we have the distance of the 
cloud equal to 11420 feet. Again, the 
height of any room, or other object, may be 
measured by a pendulum vibrating from the 
top thereof. Thus, suppose a pendulum 
from the height of a room vibrates once in 
three seconds ; then say, as 1 is to the 
square of 3, viz. 9, so is 39.2 to 352.8 feet, 
the height required. Lastly, by the pendu- 
lum we discover tlie different force of gra- 
vity on different parts of tlie earth’s sur- 
face, and thence the true figure of the 
earth. 
When pendulums were first applied to 
clocks, they were made very short ; and, 
the arches of the circle being large, the 
time of vibration through different arches 
could not in that case be equal ; to effect 
which, the pendulum was contrived to vi- 
brate in the arch of a cycloid, by making it 
play between two semi-cycloids C B, C D 
(fig. 10), whereby it describes the cycloid 
BEAD; the property of which curve is, 
that a body vibrating in it will describe all 
its arches, great or small, in equal times. 
