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 centre of gravity. CERES, the name given by Piazzi, of Palermo, to a planet which he discovered on the 1st of January, 1801. Elements. Inclination of orbit 0s 10° 36' 57" Node . 2 21 0 44 Epoch of 1801 .. 2 16 28 0 Mean anomaly Aphelion Eccentricity Equation Distance Revolution 3 15 55 0 10 26 27 38 0.0825017 0° 28/ 2.7355 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 524 cwt. CHANCES, a branch of analy. sis, which treats of the probability of events taking place, by contem plating the different ways in which they may happen or fail. The probability of an event is the ratio of the chance for its hap pening 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 properly represented by - cer tainty being represented by unity 1 n 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 1 them is - And if the certainty n be a, the value of the expectation will be a 1681d 12h 9m CHAIN, an instrument used in surveying, of which there are dif. ferent kinds; but that which is most commonly employed for this purpose, is the Gunter chain, so Prop. 2. If an event happen in called from the name of its inven-ing equally probable, the chance a ways, and fail in b ways, all be tor. This chain is 4 poles, or 66 feet long, and is divided into 100 parts or links, each link being 7.92 inches in length; I square chain 10,000 links = 16 poles = 10 square chains 100,000 links = 160 poles 1 acre. Hence we have the following easy method of converting links or chains to acres. n of its happening is a a+b ·9 and of Thus, the probability of casting an ace with a single die in one throw is 1 of casting an ace or Suppose it were required to determine the probability of drawing out of the 52 cards in a pack the four aces in four draws. Here m 4 and n = 52, whence 1.2.3.4 that a given number of things a admits of, is equal to the continued product, thus the number of changes of 6 things 1.2.3.4.5,6720. CHARGE, in Electricity, the sup the probability is 52.51.50.49 posed accumulation of the electric Prop. 3. If two events be inde-matter on one surface of an elecpendent of each other, and the tric, whilst an equal quantity pasprobability that one will happen ses off from the opposite surface. be; and the probability that the m CHARGE, in Gunnery, is the quan. tity 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 produced is in the reci procal 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 greatest velocity ought to be b 2.718281848 or about ths of the 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. CHRONOMETER, 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. To find the Area, or Circumference, of a Circle, the Diameter being given. 1. Multiply the diameter by 3.14159, and the product will be the circumference. 2. Multiply the square of the diameter by 7854, and the product will be the area. Or general, if we put diameter =D, circumference = C, area = A, and 3.14159 P, we have the following relations between those four quantities; viz. C A 2√ P 1... D= C = 2/PA D 4A To find the centre of a given circle draw any chord, bisect it, and through the point of section draw To describe a circle through any 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 Circle. 31415,92653,58979,32384,62643,38327, A great CIRCLE of the Sphere, is 95028,84197,16939,93751,05820,97494, that which divides it into two 45923,07816,40628,62089,98628,03482, equal parts or hemispheres, having 53421,17067,98214,80865,13272,30664, the same centre and diameter with 70938,446+ or 447 Lord Brounker found the ratio of the square of the diameter, to the area of a circle in a continued fraction, to be as 2+49 &c. If the diameter of a circle be 1, and c be taken to represent the circumference; then C=4 = 4 (: C=V 1 1 1 1 1 + 1 3 &c.) 5 1 1 1 1 √8(1+ 7 ++ C=8 18 (1-1-3 +1-3-5-337 + 5-7-9-&c.) 1 CIRCLES of the higher Orders are curves, the properties of which are expressed by the following equa tions: amym :=:ya-x, or ym+1= xma-x 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. CIRCLES of Altitude. Parallels to the horizon. CIRCLES of Declination, are great circles intersecting each other in the poles. Diurnal 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 perpen. dicularly on the surface of the terrestrial globe, and hence tracing our circles perfectly similar to them. CIRCLE 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. CIRCLES of Celestial Latitude, are great circles perpendicular to the plane of the ecliptic, passing through its poles, and through every star and planet. CIRCLE of perpetual Apparition, xm: ym:=:yn; a-an, or ym+none of the less circles, parallel to =xma where a is the axis, the absciss, and y the ordinate. Curves de fined by this equation will be ovals, when m is an odd number. But when m and n are each equal to one, the equation becomes that of the common circle. CIRCLE of Curvature in Geometry, that circle, the curvature of which is equal to that of any curve at a certain point. See RADIUS of Curvature. CIRCLES of the Sphere, either great or small. 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 CIRCLES, are at a distance from the poles equal to the greatest declination of the ecliptic. CIRCULAR, any thing relating to the circle. CIRCULAR Arc, any part of the circumference. To find the Lengths of Circular Arcs. Let r represent the radius, d the diameter, c the circumference of the circle, s the sine of the arc, and v the versed sine of the half arc, and m its measure, in degrees, &c.; then 1. The arcrm X 0174533. 2. The arc 2 √ dv { + 3.528 + 3v + or 2.3 529 C, &c. 6.7 v where q=ai 2.3d &c. 32q means of reflection, though the instruments themselves are small and portable. Circular instruments may be considered as improvements of Hadley's octant, and the marine sexant, which are for the same purpose; viz. for observing the altitudes, distances, &c. of the heavenly bodies, extremely useful for navigators in finding the moon's distance, and other nautical purposes. The best instruments of this kind, are those of Mayer, Borda, and Rios. CIRCULAR Parts (Napier's), are the legs, the complement of the hypothenuse, and the complements of the two oblique angles of a right angled spherical triangle. Napier's general rule is this: the rectangle, under the radius and the sine of the middle part, is equal to the rectangle under the and A, B, C, &c. are tangents of the adjacent parts, and to the rectangle under the cosines of the opposite parts. The right angle or quadrantal side being neglected, the two sides and the complements of the other three natural parts are called the circular parts; as they follow each other, as it were, in a circular order. Of these, any one being fixed upon as the middle part, those next it are the adjacent, and those farthest from it the opposite parts. This rule contains all the particu where q=; and A, B, C, D, &c. lar rules for the solution of right |