CEN 
face are equal. Hermes Trismegistus de- 
fines God an intellectual sphere, whose 
center is every where, and circumference 
no where. 
CENTINEL or Gentry, in military 
language, is aprivate soldier, from the guard 
posted upon any spot of ground, to stand 
and watch carefully for the security of the 
said guard, or of any body of troops, or 
post, and to prevent any surprise from the 
enemy. All centinels are to be very vigi- 
lant on their posts ; neither are they to sing, 
smoke, or suffer any noise to be made 
near them. Tliey are not to sit down, 
lay their arras out of their hands, or sleep ; 
but keep moving about their posts during 
the two hours they stand, if the weather 
will allow of it. No centry to move more 
than 50 paces to the right, and as many to 
tlie left of his post, and let the weather be 
ever so bad, he must not get under any 
other cover but that of the centry-box. No 
one to be allowed to go from his post with- 
out leave from his commanding officer ; 
and, to prevent desertion or marauding, 
the centries and vedettes must be charged 
to let no soldier pass. 
CENTRAL forces, the powers which 
cause a moving body to tend towards, or 
recede from, the center of motion. 
If a body A (plate III. Miscel. fig. 10,) be 
suspended at the end of a string AC, 
moveable about a point C, as a center, and 
in that position it receive an impulse in 
an horizontal direction, it will be thereby 
compelled to describe a circle about tlie 
central point. While the circular motion 
continues, the body will certainly endea- 
vour to recede from the center, which is 
called its centrifugal force, and arises from 
the horizontal impetus. With this force it 
acts upon the fixed center-pin, and that, 
by its immobility, re-acts with an equal 
force on the body, by means of the string, 
and solicits it towards the center of mo- 
tion ; whence it is called the centripetal 
force ; and when we speak of either or 
both indefinitely, they are called the cen- 
tral forces of the revolving body. 
The doctrine of central forces makes a 
considerable branch of the Newtonian phi- 
losophy, and has been greatly cultivated by 
matlieraaticians, on account of its extensive 
use in the theory of gravity, and other phy- 
sical and mathematical sciences. 
In this doctrine it is supposed that matter 
is equally indifferent to motion or restj or 
that a body at rest never moves itself, and 
that a body in motion never of itself changes 
either the velocity or the direction of its 
CEN 
motion ; but that every motion would con- 
tinue uniformly, and its direction rectilinear, 
unless some extemal force or resistance 
should affect it, or act upon it. Hence, 
when a body at rest always tends to move, 
or when the velocity of any rectilinear mo- 
tion is continually accelerated or retarded, 
or when the direction of a motion is conti- 
nually changed, and a curve line is thereby 
described, it is supposed that these circum- 
stances proceed from the influence of some 
power that acts incessantly ; which power 
may be measured, in the first case, by the 
pressure of the quiescent body against the 
obstacle which prevents it from moving, or 
by the velocity gained or lost in the second 
case, or by the flexure of the curve described 
in the third case : due regard being had to 
the time in which these effects are produced, 
and other circumstances, according to the 
principles of mechanics. Now the power 
or force of gravity produces effects of each 
these kinds, which fall under our constant 
observation near tlie surface of the earth ; 
for the same power which renders bodies 
heavy, while they are at rest, accelerates 
their motion when they descend perpendi- 
cularly ; and bends the track of the motion 
into a curve line, when they are projected 
in a direction oblique to that of their gravity. 
But we can judge of the forces or powers 
that act on the celestial bodies by effects of 
the last kind only. And hence it is, tliat 
the doctrine of central forces is of so much 
use in the theoiy of the planetary mo- 
tions. 
Sir Isaac Newton has treated of central 
forces in his Principia, and has demonstrat- 
ed this fundamental theorem, viz. that the 
areas which revolving bodies describe by 
radii drawn to an immoveable center, lie in 
the same immoveable planes, and are pro- 
portional to the- times in which they are 
described. 
The theory of this species of motion is 
comprised in the following propositions. 
1. When two or more bodies revolve at 
equal distances from the center of the circle 
they describe, but with unequal velocities, 
the central forces necessary to retain them 
will be to each other as the squares of their 
velocities. That is, if one revolves twice 
as fast as the other, it will require four times 
the retaining force the other does; if with 
three times the velocity, it will require nine 
times the force to retain it in its orb, Uc. 
2. When two or more bodies move with 
equal velocities, but at unequal distances 
from the center they revolve about, their 
central forces must be inversely as their 
