CEN 
S;.14159 &c. the circumference of the earth 
being 2 cr= 26,000 miles, or 132,000,000feet, 
ft will be : 2cr :: l" ; c\/ — = 
6078 seconds nearly, or ih 24” 38', the pe- 
riodic time at the circumference ; also the 
velocity there, or is = 26,000 feet 
per second nearly. Then, since the force of 
gravity varies in the inverse duplicate ratio 
of the distance, by the rules laid down, it is 
y/R :y^r::o or 26,000: 26,000 ,y/ — ^ — 
V, the velocity of a body revolving about 
the earth at the distance R; and^ri : 
/ R’ 
^R’ :: t, or 6078" : 6078 \/ -p = T, tlie 
time of revolution in the same. So if, for 
instance, it be the moon revolving about 
tlie earth at the distance of 60 semi-diame- 
ters ; then R = 60 r, and the above expres- 
sions become V = 26,000 = 3367 feet 
per second, or 38} miles per minute, for the 
velocity of the moon in her orbit ; and T 
5078 V —=2,360,051 seconds, or 27-'5 
days nearly, for the periodic time of the 
moon in her orbit at that distance. 
Thus also the ratio of the forces of gra- 
vitation of the moon towards the sun and 
earth may be estimated. For one year, or 
366J days, being the periodic time of the 
earth and moon about the sun, and 27fi 
days the periodic time of the moon 
about the earth, also 60 being the distance 
of the moon from the earth, and 23,920 the 
distance from the sun, in seraidiameters of 
the earth, it is 
60 239i0 „ ^ 23902 _ 27.3^ 
27.3“^ ’ 366.‘26‘‘ ’ 60 366.25^ 
= 2f ; that is, the proportion of the moon’s 
gravitation towards the sun is to that to- 
wards the earth as 2f to 1 nearly. 
Again, we may hence compute the centri- 
fugal force of a body at tlie equator, arising 
from the earth’s rotation. For, the periodic 
time when the centrifugal force is equal to 
the force of gravity, it has been shown 
above, is 5078 seconds ; and 23 hours, 66 
minutes, or 86,160 seconds, is the period of 
the earth’s rotation on its axis ; therefore, as 
86,160’ : 6078’ :: 1 : the centrifugal 
force required, which therefore is the 289th 
part of gravity at the earth’s surface. See 
Simpson’s Fluxions, vol. i. 
Central rule, a rule discovered by Mr. 
Thomas Baker, whereby td find the cen- 
ter of a circle designed to cut the parabola 
m as many points, as an equation to be con- 
CEN 
structed hath real roots. Its principal use 
is in the construction of equations, and he 
has applied it with good success as far as 
biquadratics. 
The central rule is chiefly founded on 
the property of the parabola, that if a line 
be inscribed in that curve perpendicular to 
any diameter, a rectangle formed of the 
segments of the inscript is equal to the 
rectangle of the intercepted diameter and 
parameter of the axis. 
The central rule has the advantage over 
Des Cartes and Ue Latere’s methods of con- 
structing equations, in that both these are 
subject to the trouble of preparing the equa- 
tion, by taking away the second terra. 
CENTRIFUGAL Jorce, that force by 
which all bodies that move round any other 
body in a curve endeavour to fly off from 
the axis of tlieir motion in a tangent to the 
periphery of the curve, and that in every 
point of it. 
Mr. Huygens demonstrates, that this 
force is always proportional to the circum- 
ference of the curve in which the revolving 
body is carried round. The centrifugal 
force of any body is to the centripetal as 
the square of the arch which a body de- 
scribes in a given time, divided by the diame- 
ter, to the space through which a heavy 
body moves in falling from a place where 
(it was at rest in the same time. 
If any body swim in a medium heavier 
than itself, the centrifugal force is the dif- 
ference between the specific weight of the 
medium and the floating body. 
All moving bodies endeavour after a rec- 
tilinear motion, because it is the easiest, 
shortest, and most simple : whenever there- 
fore they move in any curve, there must be 
something that draws them from their rec- 
tilinear motion, and detains them in their 
orbits; and were that force to cease, the 
moving body would go straight olf in a tan- 
gent to the curve in that very point, and so 
would get still further and further from the 
focus, or center of its curvilinear motion. 
It may be, that in a curve where the force 
of gravity in the describing body is continu- 
ally variable, the centrifugal force may also 
continually vary in the same manner, and so 
that one may also supply the defect, or 
abate for the excess of the other, and con- 
sequently the effect be every where equal 
to the absolute gravity of the revolving 
body. 
Centrifugal Machine, a curious ma- 
chine, for raising water by means of a 
centrifugal force, combined with the pres- 
