CEN 



CEN 



force of gravity varies in the inverse dupli- 

 cate ratio of the distance, by the rules laid 

 down, it isv/R : ^/r -.: v or 26,000 : 26,000 



= V, the velocity of a body re- 

 volving about the earth at the distance R ; 

 and ^/ r3 . ^/ R3 :: t, or 5078" : 5078 1^1 



^r 7*3 



= T, the time of revolution in the same. 

 So if, for instance, it be the moon revolv- 

 ing about the earth at the distance of 60 

 semi-diameters ; then R = 60 r, and the 

 above expressions become V = 26,000 

 \/-^ 5 =3357 feet per second, or 38 1 miles 

 per minute, for the velocity of the moon 

 in lier orbit; and T = 5078 /5i : 



2,360,051 seconds, or 27 T 3 ^ days nearly, 

 for the periodic time of the moon in her 

 orbit at that distance. 



Thus, also, the ratio of the forces of 

 gravitation of the moon towards the sun 

 and earth may be estimated. For one 

 year, or 3651. days, being the periodic 

 time of the earth and moon about the 

 sun, and 27^3 d a y S , 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 

 semi-diameters of the earth, it is 

 60 23920 23902 27.3* 



27.3> '' 365.25 1 "' r ~6TT~ X o65.25 z 

 = 2.2; that is, the proportion of the moon's 

 gravitation towards the sun is to that to- 

 wards the earth as 21 to 1 nearly. 



Again, we may hence compute the cen- 

 trifugal force of a body at the 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 Ijours, 56 minutes, or 86,160 se- 

 conds, is the period of the earth's rota- 

 tion on its axis; therefore, as 86,160 2 : 

 5078* :: 1 : J.^, the centrifugal force re- 

 quired, 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 to find the 

 center of a circle designed to cut the pa- 

 rabola in as many points, as an equation 

 to be constructed 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 De Latere's methods 

 of constructing equations, in that both 

 these are subject to the trouble of pre- 

 paring the equation, by taking away the 

 second term. 



CENTRIFUGAL force, that force by 

 which all bodies that move round any 

 other body in a curve endeavour to fly off 

 from the axis of their 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 cir- 

 cumference of the curve in which the re- 

 volving body is oarried round. The cen- 

 trifugal force of any body is to the cen- 

 tripetal as the square of the arch which 

 a body describes in a given time, divided 

 by the diameter, 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 

 difference between the specific weight of 

 the medium and the floating body. 



All moving bodies endeavour after a 

 rectilinear motion, because it is the easi- 

 est, shortest, and most simple : whenever 

 therefore they move in any curve, there 

 must be something that draws them from 

 their rectilinear motion, and detains them 

 in their orbits; and were that force to 

 cease, the moving body would go straight 

 off in a tangent 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 

 continually 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 consequently the effect be 

 every where equal to the absolute gravity 

 of the revolving body. 



CENTRIFUGAL J\facMne, a curious ma- 

 chine for raising water by means of a 

 centrifugal force, combined with the pres- 

 sure of the atmosphere. This machine 

 consists of a large tube of copper, &c. in 

 the form of a cross, placed perpendicu- 

 larly in the water, and resting at the bot- 

 tom on a pivot. At the upper part of the 

 tube is an horizontal cog-wheel, which 



