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C E N
In folid and pjanc Figures agitated laterally, i.e. about the Axis of Ofcillation, perpendicular to the Plane of the Figure, the Investigation or the Centre of Ofcillation is fomewhat difficult; in regard, all the Parts of the Weight, by reafon of their unequal DHtance from the Point of Suf- penficn, den't move with the fame Velocity ; as is fhewn by Kngens, in his Horol. OfcitL He found, in this Cafe, the Diila-ncc of the Centre of Ofcillation, from the Axis in a Circle, to be % of the Diameter : In a Rectangle, fufpended by one of its Angles, } of the Diagonal : In a Parabola, fufpended by its Vertex, y of its Axis, and } of the Parameter ; fulpended from a Point in the Middle of the Balls, > of the Axis, and | the Parameter : In the Scttor of a Circle, £ of a right Line ; which is to the Ra- dius, as the Arch to the Subtenfe : In a Cone, % of the Axis, and \ of the third proportional to the Axis, and the Semidiameter of the Bafe j In a Sphere, fufpended from a Point in the Surface, ^ of the Diameter : in the fame, fufpended from a Point without the Sphere, (as is ulually the Cafe in Pendulums) \ of a third proportional ro that compos'd of the Semidiameter and length of the Thread, and the Semidiameter it felf : In a Cylinder, f of the Altitude, and ~ the Line, which is to the Semidiame- ter of the Bafe, as that is to the Altitude.
Centre of Percuffion, in a moving Body, is that Point wherein the Percuffion is the greatclt, wherein the whole percutient Force or the Body is fuppos'd to be collected 5 or about which the Impetus of the Parts is balanc'd on every fide. See Percussion.
Laws of the Centre of Percuffion.
1. The Centre of 'Percuffion, is the fame with the Centre of Ofcillation, where the percutient Body revolves round a fix'd Point; and is determined in the fame manner, viz. by considering the Impetus of the Parts, as fo many Weights apply'd to an inflexible right Line, void of Gra- vity 5 i. e. by dividing the Sum of the FaMams of the Im- petus's of the Parts, multiply'd by their Diffances from the Point of Sulpenfion, by the Sum of the Impetus's. What, therefore, has been above fhewn of the Centre of Ofcilla- tion, will hold of the Centre of Percuffion, where the per- cutient Body moves round a fix'd Point. See Centre of Ofcillation.
1 . Tfhe Centre of Percuffion is the fame -with the Centre of Gravity, if all the Pares of the percutient Body be carry'd with a parallel Motion, or with the fame Celerity : for the Momenta, are the Facia of the Weights into the Celerities. Wherefore, to multiply equi-ponderating Bodies by the fame Velocity, is the fame thing as to take equimulti- ples : But the equi-multiples of equi-ponderating Bodies, thcmfclves equi-ponderate ; therefore, equivalent Momenta are difpus'd about the Centre of Gravity: consequently the Centre of Percuffion in this Cafe, coincides with that of Gravity ; and what is fhewn of the one, will hold of the other. See Centre of Gravity.
Centre of Converfion, in Mechanicks, a Term firft us'd by M. Parent. Its Signification is thus conceiv'd : If a Stick be laid on a ilagnant Water, ?nd drawn by a Thread faflen'd to it, fo that the Thread always makes the fame Angle with the Stick ; always, v. g. a right Angle 5 the Stick will be found to turn on one of its Points, which will be immoveable 5 which Point is tcrm'd the Centre of Con- verfion. For the greater eafe, the Thread may be con- ceiv'd faflen'd to one End of the Stick.
This Effed arifes from the Refinance of the Fluid, and the manner wherein it divides : for, imagine the firft Mo- ment of Traction ; 'tis certain, here, the Refinance of the Parts of the Fluid to be difplac'd, tends to turn the Stick around the Point to which the Thread is faflen'd, as on a Centre: So that in the prefent Initance, the Staff wou'd defcribe precifcly the Quadrant of a Circle : after which, the Fluid wou'd no longer bear the Stick lengthwife ; but in a circular Motion, in fuch manner, as that the free End of the Stick, and the Parts neareft it, wou'd defcribe larger Arches of Circles than the reft, and have a greater Velocity. The Refinance, therefore, of the Fluid, which tends to im- prefs a circular Motion on the Stick, around the Point to which the Thread is failcn'd, tends to imprefs a greater Velocity on the Parts next the other Extremity 5 or, which is the fame thing, thole Parts require a greater Velocity to fur- mount the Refinance of the Fluid : So that the Stick will not have that circular Motion around the Point to which the Thread is faflen'd h or, the Refinance of the Fluid is greater towards the free Extreme of the Stick, and ftill lef- fens towards the other Extreme. Now, all the Columns, or Threads of Water which refift the Stick, muff be fuppos'd of the fame Length, or the fame Ma fs. One may there- fore find on the Stick fuch a Point, as that taking a great number of thofe Threads on that Side which refiffs the leafl, and a lefs number on that Side where they refift the moft 5 there will be an exact Compenfation, and the For- ces be equal on each Side : 'Tis this Point is the Cen- tre of Converfion. And as the fame Reafoning has place
in all Motions of Traction made in the fame manner, this Centre is always the fame Point.
The grand Qucftion here arifing, is to know preciTely in what Point the Centre of Converfion is found : This M. Parent has dctermin'd by an infinite deal of Calculation. If the Stick drawn by one Extremity be a ftrait Line di- vided into 20 Parts, reckoning from the Thread, the Cen- tre of Converfion, he finds, will be nearly on the 13 th. If it ben't a Line, but a Surface or a Solid, there will be fome change in the Situation of the Centre of Converfion, ac- cording to the Surface or the Solid.
If in lieu of a Body fwimming in a Fluid, we fuppofe it laid on a rough uneven Plane 5 the Refinance of this Plane to the Motion of the Body, will always be divided in the fame manner, and determine the fame Centre of Converfion. This Refinance is, precifely, what we call Friction, fo prejudicial to the Effects of Machines. See Friction.
CENTO, in Poetry, a Work wholly compos'd of Verfes, or Paffages promifcuoufly taken from other Authors 5 only difpos'd in a new Form, or Order. Proba Falconia has wrote the Life of Jcfus Chrifr, in Centos taken from Virgil. Alex. Roffe has done the like in his Chrijliados ; and Stephen dc Pleurre the fame : An Inftance of whofe Centos on the Adoration of the Magi, is as follows.
Adoratio Magorum, Matt. 2.
\ Scc.JEn.iff. Ecct autem primi fab lumina foLis, is ortus t
,JE.6g^.. Stella facem ducens multa cum luce cucurrit :
, JE. 5116, Signavitque Viam. * call in regione ferena.
, JE. 333. Tum Regcs * (credo quia fit divinitus iUis
, 31,4-16". Jngenium, & rerum fato prudentia m.ijor)
, JE.. 58. Extemi ventunt * qua cuique eft copia latl
I, JE. 333. Mutiera p-.rtantes ; * molles faa thura Sah&i
, JE. 4.64.. Dona, debinc atiro gravia,* myrrbaque madentes
1, JE. 659. tAgnayere Deum Regem, * Regumque Parentcm.
, 9.4.18. Mutttve re vias, * perfeffis ordine votis ;
', &. 16. Injuetum fey iter,* fpatia in faa. quifq; recent.
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Aufon'ms has laid down the Rules to be obferv'd in com- pofing Centos. The Pieces, he fays, may be taken either from the fame Poet, or from feveral ; and the Verfes may be either taken entire, or divided into two j one half to be connected, with another half taken elfewhere : but two Verfes never to be us'd running, nor much lefs than half a Verfe to be taken. Agreeable to thefe Rules, he has made a pleafant Cento from Virgil.
The Politicks of Liffius are only Centos ; there being nothing of his own but Conjunctions and Particles.
The Word comes from the Latin Cento, a Cloak made of Patches ; and that from the Greek Ktvjoew. The Roman Soldiers us'd thefe Centos, or old Stuffs patch'd over each, other, to guard themfelves from the Strokes of their Enemies* Others fay, that Centos were properly us'd for the patch- es of Leather, &c. wherewith their Galleries or Skreens, called Vine<s, were cover'd 5 under which the Befiegers made their Approaches towards any Place.
Hence Centonarii, the Perfons whofe Bufinefs was to prepare thefe Centos.
CENTRAL, fomething relating to a Centre $ fee Centre. Thus, we fay, Ce?ztral Eclipfe, Central Fire, Central Forces, Central Rule, &c. See Central Forces, Cen- tral i?;//;?, ckc. See alfo Fire, Eclipse,^.
Central Forces, theVires, or Powers whereby amoving Body either tends towards the Centre of Motion, or recedes from it. See Centre of Motion; fee alfo Force, and Vis.
Central Forces are divided into two Kinds, with regard to their different Relations to the Centre, viz. Centripetal, and Centrifugal.
Centrifugal Force, is that whereby a Body revolv- ing round a Centre, endeavours to recede from it.
'Tis one of the eltabli/h'd Laws of Nature, That all Motion is of it felf rectilinear ; (fee Motion) and that the moving Body never recedes from its firft fight Line, till fome new Impulfe be fuperadded in a different Direction : After that new Impulfe, the Motion becomes compound- ed, but continues ftill rectilinear ; tho the Direction of the Line be alter'd. See Compound Motion. To move in a Curve, it muft receive a new Impulfe, and that in a diffe- rent Direction, every Moment ; a Curve not being redu- cible to right Lines, unlefs infinitely fmall ones. If then a Body continually driven towards a Centre, be projected in a Line that does not go thro that Centre, it will defcribe a Curve ; in each Point whereof, A (Tab. Mechanicks^ Fig. 15.) it will endeavour to recede from the Curve, and proceed in the Tangent AD: and, if nothing hinder'd, wou'd actually proceed ; fo as in the fame Time wherein it defcribes the Arch AE, it wou'd recede the length of the Line DE, perpendicular to AD, by its Centrifug^ Force. The Centrifugal Force, therefore, is as the right Line D E, perpendicular to A D 5 fuppofing the Arch A £ infinitely fmall. See Infinite,
3 The
