C E N
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CEN
People., tho under different Names : that of the common People was call'd Ccnfus, or Lnftrum 5 that of the Knights Cenfus, Rccenfio, Recognitio 5 that of the Senators, Lettio, RelcBio.
In the Vcconian Law, Cenfus is us'd for a Man, whofe Eltate, in the Cenjbr's Books, is valu'd at 1 00000 Seflerces.
CENTAUR, in Aftronomy, a Part, or Moiety of a Sou-
neithcr of them
can move the
fide will equi-ponderatc, other. See Gravity.
Hence, if the Defcent of the Centre of Gravity be pre- vented, or if the Body be fufpended by its Centre of Gravity, it will continue at reft. See Motion, and Rest.
The whole Gravity of a Body may be^conceiv'd united its Centre ; and therefore, in Demonftrations, 'tis ufual,
thern Conftellation, in form, half Man, half Horfe, ufually for the Body, to fubftitute the Centre.
join'd with the Wolf. See Centaurus CUM Lufo.
The Word comes from the Greek jW7«vf©* 5 form'd of x&flt&i pttngo, and TOt'p©-, taunts.
Centaurus cumLufo, Centaur tmth the Wolf \ in Agro- nomy, a Conftellation of the Southern Hemifphere. See Constellation.
The Stars in the Conftellation Centrums cum Lupo, in 'Ptolemy's Catalogue, are 19 5 in Tycbo's 4 •> ' ln the Sri- tannic Catalogue, they are 15. The Order, Names, Lon- gitudes, Latitudes, Magnitudes, gfc, whereof, are as follow.
Stars in the Conjiellation Centaurus cum Lupo. Names and Situation of J£ Longitude. . Latitude. the Stars. £
Inform, before the Head :
Preced. in the Head of the Centaur 1 South, in the Head
Middle Subfeq. and North, in the Head
In hind Shoulder of the Centaur South. of :. in anterior Foot of Wolf Subfeq. and North, of the fame Precox cdtlt. before Neck of Lupus Subsequent 10 Preced. of 1 in the Wolf's Nofe Contiguous to that Subfeq. in the Nofe
CENTRE, or CENTER, Centrum, in Geometry, or CENTRE of a Circle, is a Point in the Middle of a Cir- cle, or circular Figure, from which all Lines drawn to the Circumference are equal. See Circle.
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Thro the Centre of Gravity paffes a right Line, call'd the Diameter of Gravity : the Interferon, therefore, of two fuch Diameters, determines the Centre.
The Plane whereon the Centre of Gravity is plac'd, is call'd the "Plane of Gravity : fo that the common Inter- feflion of two fuch Planes, determines the Diameter of Gravity.
In homogeneal Bodies, which may be divided length- wife into fimilar and equal Parts, the Centre of Gravity is the fame with the Centre of Magnitude. If, therefore, a Line, v.g. or a Cylinder be biffefled, the Point of Section will be the Centre of Gravity.
Common Centre of Gravity of two Bodies, is a Point fo fituated, in the right Line, joining the Centres of the two Bodies, as that, if the Point be fufpended, the two Bodies will equi-ponderate, and reft in any Situation -. Thus, the Point or Sufpenfion in a common Balance, or in a Roman Steelyard, where the two Weights equi-ponderate, is the common Centre of Gravity of the two Weights. larw of the Centre of Gravity.
1. If the Centres of Gravity of tmoBodies AandB, (Tab. Mecbanicks, Fig. 15.) be join 'd by the right Line AB, the Diftances BCandCA, of the common Centre of Gravity C, from the p articular Centres of Gravity B and A, are re- ciprocally as the Weights A and B : See this demonstrated under Balance.
Hence, if the Gravities of the Bodies A and B be equal, the common Centre of Gravity C, will be in the Middle of the right Line A B. Again, fince A : B : : B C : AC ; A will be to A C : : B : B C ; whence, it appears, that the Powers of equi-ponderating Bodies, are to be eftimated by the Factum of the Mats, multiply'd into its Diftance from the Centre of Gravity ; which Factum is ufually call'd
Euclid demonftrates, that the Angle at the Centre is the Momentum of the Weights. See Moment
Further, fince A -. B : : BC : AC, A + B:A:: BC + AC :BC.
The common Centre of Gravity, therefore C, of two Bo- dies, will be found, if the Factum of one Weight A, into the Diftance of the feparate Centres of Gravity A B, be
double to that of the Circumference ; i. e. the Angle made by two Lines drawn from the Extremes of an Arch to the Centre, is double that made by two Lines drawn from thefe Extremes to a Point in the Circumference. See Circum- ference, and Angle.
V" Centre of a 'Parallelogram, or 'Polygon, the Point divided by the Sum of the Weights A and B. Suppofe, v.&
wherein its Diagonals interfect. See Parallelogram, A= 12, B = 4, AB = 24 ; therefore, B C — 14,12:15 —
and Polygon. 18. IftheWeightA be given, and the Diftance of the par-
Centre of Magnitude, is a Point equally remote from ticular Centres of Gravity AB, together with the common
the extreme Parts of a Line, Figure, or Body; or the Centre of Gravity C ; the Weight of B will be found = to A.
Middle of a Line, or Plane, by which a Figure or Body is AC : BC ; that is, dividing the Moment of the given Weight,
divided into two equal Parts. See Magnitude. by the Diftance of the Weight requir'd. Suppofe, A = 1 2,
Centre of a Sphere, is a Point from which all the B C = 18, A C = 5 ; then B = 5. n : 18 : : 12:3=4. Lines drawn to the Surface, are equal. See Sphere. 1. To determine the common Centre of Gravity of fever A
The Centre of the Semicircle, by whofe Revolution the given Bodies a, b, c, d, (Fig. 13.) in the tight Line AB.
Sphere is generated, is alfo that of the Sphere. See Se- Find the common Centre of Gravity of the two Bodies
micircle. a and b, which fuppofe in F 5 conceive a Weight a-\-b.
Centre of a Baflion, is a Point in the middle of the apply'd in F ; and in the Line FE, find the common Centre
\- of the Weights a~\-b and c; which fuppofe in G. Laft-
Gorge of the Baftion, whence the Capital Line commen ces ; and which is ordinarily at the Angle of the inner Po lygon of the Figure. See Bastion, &c.
Centre of a Battalion, the Middle of a Battalion ; where is ufually left a large fquare Space, for lodging the Clothes and Baggage. See Battalion.
ly, in BG, fuppofe a Weight a-\-b-\-c apply'd, equal to the two a -f- b and c ; and find the common Centre of Gra- vity between this and the Weight d, which fuppofe in H; this H will be the common Centre of Gravity of the Bodies b,c, d. And in the fame manner might the common Cen-
Centre of a Dial, is that Point where its Gnomen or tre of Gravity of any greater number of Bodies be found.
Style, which is plac'd parallel to the Axis of the Earth, 3. TivoWeightsT) and E, (Fig. 14.) being fufpended ixith-
interfect s the Plane of the Dial ; and from thence, in thofe out their common Centre of Gravity in C, to determine
Dials which have Centres, all the Hour-Lines are drawn, -which of them preponderates, and horn much. Multiply
If the Plane of the Dial be parallel to the Axis of the each into its Diftances, from the Centre of Sufpenfion ;
Earth, it can have no Centre at all, but all the Hour-Lines that Side on which the Factum is greateft, will prepon-
will be parallel to the Style, and to one another. See Dial, derate; and the Difference between the two, will be the
Centre of a Conic Section, is the Point wherein all the Weight wherewith it preponderates.
Diameters concur. See Diameter ; fee alfo Conic Section. Hence, the Momentum of the Weights D and E, fuf-
This Point, in the Ellipjis, is within the Figure ; and, pended without the Centre of Gravity, are in a Ratio com-
in the Hyperbola, without. Sec Centre of an Ellipjis, Sec. pounded of the Weights D and E, and the Diftances from
Centre of an Ellipjis, is that Point where the two the Point of Sufpenfion. Hence alfo the Momentum of a
Diameters, the Tranfverfe and the Conjugate, interfect Weight fufpended in the very Point C, will have no effect
each other. See Ellipsis. at all in refpect of the reft D E.
Centr e of an Hyperbola, is a Point in the Middle of the 4. To determine the Prefonderation --.there fever al Bodies
Tranfverfe Axis. See Hyperbola ; and Transverse Axis. a,b,c,d, (Fig. 15.) are fufpended -without the common
Centre of a Curve, of the higher Kind, is the Point Centte of Gravity in C. Multiply the Weights c and d
where two Diameters concur. Sec Diameter. into their Diftances from the Point of Sufpenfion CE and
Where all the Diameters concur in the, fame Point, Sir EB ; the Sum will be the Momentum of their Weights, or
Jfaac Newton calls it, the general Centre. See Curve. their Ponderation towards the right: Then multiply the
Centre of Gravitation, or Attraction, in Phyficks, is Weights a and b into their Diftances, A C and C D, the
that Point to which a revolving Planet, or Comer, is im- Sum will be the Ponderation towards the left : Subrra£ftng,
pell'd, >r attracted by the Force, or Impetus of Gravity, therefore, the one from the other, the Remainder will be
See Gravitation, and Attraction. the Preponderation requir'd.
Centre of Gravity, in Mechanicks, is a Point within a 5. Any Number of Weights a, b, c, d, being fufpended
Body, thro which if a Plane pafs, the Segments on each without the common Centre of Gravity in C, and prepon- derating
