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relatively to the vertical, that is to say, whatever be s and r, the
... & . ratio - is therefore constant; and r
consequently we have at the same time r = 0, s = 0; which shows that the centre of oscillation, the centre of gravity, and the point of suspension are in one and the same right line. Hence it results that s = r, and that A are + B be + C co (A + B - C). A ‘ The same kind of reasoning applies exactly, however many the number of particles may be : therefore, to find the centre of oscillation of a system of particles or of bodies, we must multiply the weight of each of them by the square of its distance from the point of suspension, and divide the sum of these products by the weights multiplied by the distance of the centre of gravity from the centre of suspension : this quotient expresses the disuance of the centre of oscillation from the point of suspension measured on the continuation of the line i. the centre of gravity and that point. Call S the point of suspension, O the centre of oscillation, or SO the distance of the centre of oscillation from the point of suspension ;
in which the whole percutiem. force of the body is supposed to be collected. When the percutient body revolves about a fixed point, the cen tre of percussion is the same with the centre of oscillation. For instance, when the body moves with a parallel motion, or all its parts with the same celerity, then the centre of percussion is the same as the centre of gravity. Centre of Position, in Mechanics, denotes a point of any body, or system of bodies, so selected, that we may properly estimate the situation and motion of the body, or system, by those of this point. CENTRE of Pressure, is that point against which a force being applied equal and contrary to the whole pressure, will sustain it, so as that the body pressed on will not incline to either side. CENTRE of spontaneous Rotation, is that point which remains at rest the instant a body is struck, or about which the body begins to revolve. CENTRIFUGAL Force, is that by which a body revolving about a centre or about another body, has a tendency to recede from it. CENTRIPETAL Force, is that by which a body is perpetually urged towards a centre, and thereby made to revolve in a curve instead of a right line. CENTRIPETATION, a term used by Sir Richard Phillips to indicate the tendency which bodies or planets, and parts of planets, have to fall or move towards their centres, which tendency he ascribes to the orbicular and rotatory motions of the entire masses. e uses the term Centripetation, as descriptive of the local effect, to avoid the ambiguity of the term Attraction, which is used to express a cause, and the term universal Gravitation, used to express a universal cause ; which cause is local and particular in each planet, as resulting from its own motions. Centripetation, therefore, according to the new system, is a local effect, , producing aggregation in the planetary masses, while the mutual action and re-action of distant planets, and of the sun on the planets, and the re-actions of the latter arise from their several and respective impulses on the medium of space within which they are situated. Of course, the diverging action and re-action, through a gazeous medium, is inversely as the squares of the distances, and directly on the masses; and hence the laws of the two systems accord with each other and with nature, though the explications are very different. CENTRO Baryco, is the same as the Centre of Gravity. CENTRO BARYC Method, in Mechanics, is a method of measuring or determining the quantity of any surface or solid, by considering it as generated by motion, and multiplying the generating line or surface into the path of its centre of gravity, viz. Every figure, whether superficial or solid, generated by the motion of a line or surface, is equal to the product of the generating magnitude into the path of its cen. tre of gravity. CERES, the name given by Piazzi, of Palermo, to a planet which he discovered on the 1st of January, 1801.
From the number of links point off 5 figures to the right-hand for decimals, and those on the left will be acres. CHALDRON, an English dry measure of capacity, mostly used in measuring coals. The chaldron contains 36 bushels, and it weighs about 28 cwt. By act of parliament, the Newcastle chaldron is 52 cwt. CHANCES, a branch of analysis, which treats of the probability of events taking place, by contemplating the different ways in which they may happen or fail. The probability of an event is the ratio of the chance for its happening to all the chances, both for its happening and failing. The expectation of an event, is the present value of any sum or thing which depends either on the happening or on the failing of such an event. Events are independent, when the happening of any one of them neither increases or lessens the probability of the rest. Prop. 1. If an event may take place in n different ways, and each of these be equally likely to happen, the probability that it will take place in a specified way is
- 1. properly represented by ; cer
tainty being represented by unity For the sum of all the probabi. lities is certainty, or unity, because the event must take place in some one of the ways, and the probabilities are equal, therefore each of
And if the certainty
be a, the value of the expectation
... 1 them is -72
that a given number of things as admits of, is equal to the continued product, thus the number of changes of 6 things = 188.8.131.52.5.6 = 720. CHARGE, in Electricity, the supposed accumulation of the electric matter on one surface of an electric, whilst an equal quantity passes off from the opposite surface. CHARGE, in Gunnery, is the quantity of powder and ball, or shot, put into a piece of ordnance, in order to prepare it for execution. Different charges of powder, with the same weight of ball, produce different velocities in the ball, which are in the subduplicate ratio of the weights of powder; and when the weight of powder is the same, and the ball varied, the velocity protiuced is in the reciprocal subduplicate ratio of the weight of the ball. Calling the length of the bore of the gun b, the length of the charge producing the feates: velocity ought to be
length of the bore. CHART, or Sea Chart, a hydrographical or sea-map for the use of navigators; being a projection of some part of the sea in plano, shewing the sea-coasts, rocks, sands, bearings, &c. Plain CHARTs have the meridian, as well as the parallels of latitudes, drawn parallel to each other, and the degrees of longitude and latitude every where equal to those at the equator. Mercator’s CHART, like the plain charts, has the meridians represented by parallel right lines, and the degrees on the parallels, or of longitude, every where equal to those at the equator, so that they are increased more and more, above their natural size, as they approach towards the pole; but then the degrees of the meridians, or of latitude, are increased in the same proportion at the same part; so that the same proportion is preserved between them as on the globe itself. CHORD in Geometry, is the right line joining the extremities of any arc of a circle. A line drawn from the centre to
bisect a chord, is perpendicular to the chord; or if perpendicular to the chord, it bisects both the chord and the arch. Chords equally distant from the centre are equal; or if they are equal, they are equally distant from the centre. The chord is a mean proportional between the diameter and versed sine. CHROMATICS, that part of optics which explains the several properties of the colours of light, and of natural bodies. CHRONOLOGY, the art of measuring time, and distinguishing its several constituent parts, such as centuries, ages, years, months, weeks, &c. by appropriate marks and characters. C H R O N O M ETER, a kind of clock, so contrived as to measure very small portions of time with great accuracy. CIRCLE, in Geometry, a plane figure bounded by a curve-line, every where equally distant from a point within it, called the centre. The periphery or circumference, is sometimes called the circle, though that name denotes the space contained within the circumference, and not the circumference itself.
through the point of section draw a line at right angles. This line is a diameter, which bisected, gives the centre. To describe a circle through any three given points not in the same straight line. Join the points by two straight lines, bisect those lines at right angles, and the intersection of the bisecting lines is the centre. To divide a given circle into any number of co-centric parts, equal to each other. Divide the radius into as many equal parts as are required ; and from the parts of division, erect perpendiculars upon the radius; describe a semicircle meeting the perpendiculars; and through the points of contact draw the circles. To divide a circle into any num ber of parts, equal both in area and periphery. Divide the diameter into the number of parts, and describe a semicircle upon the alternate sides of each division, so as to touch the point of contact, and also the extremities of the diameter.
Quadrature and Rectification of the
The simplest and most ancient approximation is as follows: As 7 to 22, so is the diameter to the circumference. Other approximations, nearer than the above, but in larger numbers, are as follows: as 106:333 113: 355 1702:5347 1815: 5702 of which each is more accurate than the preceding. Vieta shows, that if the diameter of the circle he 1000, the circumference will be greater than 3141-5926,535 but less than 3141-5926,537 a greater and greater degree of approximation. Van Ceulen carried the approximation to thirty-six places of figures; Sharp, to seventy-two places of figures; Machin, to 100 places; and Lagny, to 128; that is, if the diameter of a circle be one, the circumference will be
so is diam. to the cir.
A great CIncle of the Sphere, is that which divides it into two equal parts or hemispheres, having the same centre and diameter with it; as the horizon, meridian, &c. A small of the Sphere, divides the sphere into two unequal parts, having neither the same centre nor diameter with the sphere; its diameter being only some chord of the sphere less than its axis. Such as the parallels of latitude, &c. C1R cles of Altitude. Parallels to the horizon. C1RcLEs of Declination, are great circles intersecting each other in the poles. IDiurnal Circles, are parallels to the equinoctial, supposed to be described by the stars, and other points of the heavens, in their ap parent diurnal rotation about the earth. It may here be observed, that most circles of the sphere are trans ferred from the heavens to the earth; and have thus a place in geography, as well as in astronomy; all the points of each circle being conceived as let fall perpendicularly on the surface of the terrestrial globe, and hence tracing our circles perfectly similar to them. C1R cle of Illumination, a circle passing through the centre of the earth or moon, perpendicular to a line drawn from the sun to the respective body. C1Rcles of Celestial Latitude, are great circles perpendicular to the plane of the ecliptic, passing through its poles, and through every star and planet. C1R cle of perpetual Apparition, one of the less circles, parallel to the equator; described by any point of the sphere touching the northern or southern point of the horizon; and carried about with the diurnal motion. Circle of perpetual Occultation, is another circle at a like distance from the equator; and contains all those stars which never appear at the place to which it refers. Polar C1R cles, are at a distance from the poles equal to the greatest declination of the ecliptic. CIRCULAR, any thing relating to the circle. I 3