passes, a mathematical instrument for describing circles, measuring and dividing lines, or figures, &c. The common COMPASSES consists of two sharp-pointed branches or legs, joined together at the top. Triangular COMPASSES; the construction of which is like that of the common compasses, with the addition of a third leg or point, which has a motion every way. Their use is to take three points at once, and so to form triangles, and lay down three positions of a map to be copied at the same time. of Beam COMPASSES Consist of a long straight beam or bar, carry. ing two brass cursors; one these being fixed at one end, the other sliding along the beam, with a screw to fasten it on occasionally. Elliptic COMPASSES, commonly called a trammel, consists of a cross with two dovetail grooves, at right angles, and a ruler with two dovetail knobs and a tracing point. The two knobs are adjusted to the local distance of the ellipse, and the distance between the remotest one and the tracing point is made equal to the semi-transverse (the distance of the nearer knob from the same point being equal to the semiconjugate). Then the cross being laid with its centre over that of the ellipse, and the knobs let into the grooves, the turning round of the ruler will trace the ellipse. German COMPASSES, have their legs a little bent outwards to wards the top; so that when shut the points only meet. Hair COMPASSES have an adjusting screw attached to one of the legs, by means of which measures may be taken to a very great degree of accuracy. Proportional Spring COMPASSES, or Dividers, are made of hardened steel, with an arched head, which by its springs opens the legs; the opening being directed by a circular screw fastened to one of the legs, let through the other, and worked with a nut. Geometry of the COMPASSES, a species of geometry invented by M. Mascheroni, of Milan, by which all the elementary problems of plane geometry are performed by the compasses only, without the use of the ruler; it is, however, more ingenious than profound, and may be considered rather as a subject of curiosity than of real utility. COMPLEMENT of an Arch or Angle, is what it wants of 90 degrees. Arithmetical COMPLEMENT, of a logarithm, is what the logarithm wants of 10-00000, &c.; and the easiest way to find it is, beginning at the left hand, to subtract every figure from 9, and the last from 10. COMPLEMENT, in Astronomy, denotes the distance of a star from the zenith. COMPLEMENT of Life, a term much used in the doctrine of lifeannuities, by De Moivre; to denote the number of years which a given life wants of 86, this being the age which he considered as the utmost probable extent of life. COMPLEMENTS of a Parallelogram, are the two smaller parallelograms made by drawing two right lines through a point in the diagonal, and parallel to the sides of the parallelogram. In every parallelogram these complements are equal to each other. COMPOSITE Number, is that which is produced by the multipliCOMPASSES, are cation of two or more numbers or factors, and is thus distinguished from a prime number, which cannot be so produced. those in which the joint lies, not at the end of the legs, but be tween the points terminating each leg. These are either simple or compound. In the former sort the centre or place of the joint is fixed; so that one pair of them serves only for one proportion. In the compound ones the joint may be set at any distance, and consequently any proportion whatever casily obtained. COMPOSITION, is a species of reasoning by which we proceed. from things that are known and given, step by step, till we arrive at others, which were before unknown. COMPOSITION of Forces, în Mechanics, is the method of finding the quantity and direction of a single force, equivalent to two or more forces of which the quantity and direction are given. It is thus distinguished from Resolution of Forces, which is the method of resolving a given force into two or more forces, the combined effect of which shall be equivalent to the single given force. COMPOSITION of Proportion, is when, of four proportionals, the sum of the 1st and 2d is to the 2d, as the sum of the 3d and 4th is to the 4th. to denote the curvilinear vacuity of hollow bodies. CONCAVE Lenses, or Mirrors, have either one or both sides con• cave. See LENS and MIRROR. CONCAVITY, from concave, the hollow or vacuity of bodies. CONCAVO-Concave Lens, is that which is concave on both sides. CONCAVO-Convex Lens, is that which is concave on one side, and convex on the other. CONCENTRIC, having a common centre, as concentric circles, COMPOSITION Of Ratios, in Arith-ellipses, &c. metic and Algebra, is performed by multiplying the quantities or exponents of two or more ratios together, which product is then said to be compounded of all the other ratios whose exponents were multiplied. CONCHOID, the name of a curve invented by Nicomedes; and hence commonly called the Conchoid of Nicomedes, which was much used by the ancients in the construction of solid problems. It is thus constructed. From a COMPOUND Interest, is that point draw any number of lines, which arises by the continual ad-each cutting another line, then dition of the interest to the principal as it becomes due. COMPOUND Motion, is that which arises from the effect of several conspiring forces, which may render it either rectilinear or curvilinear, according to the nature of the forces and the circumstances under which they act. from this line set off equal distances, either toward the point, or in the opposite direction; when the lines and the curve drawn through these points is the conchoid. There are two kinds of Cone hoid the first, or external one, on the side opposite to the point; and the second, or internal one, on the COMPOUND Quantities, in Algebra, side next the point. Of the seare those connected together by cond there are two forms, 1st. the signs and; they are dis- pointed, when the curve passes be tinguished into binomials, trino-ween the line and the point; and mials, &c. according to the num-2d looped, when it passes beyond ber of terms of which they are the point. composed. COMPOUND Ratio, is that which arises from the composition of ratios. COMPRESSIBILITY, that quality of a body by which it yields to the pressure of another body or force, so as to be brought into 'a narrower compass. The following table shows the quantity of compression of these fluids and mercury, when the thermometer was at 599 and barometer 29 inches. Compress. of Mill. pts. Sp grav. Rain water... Sea water... Mercury 48. - 846 918 1090 1028 13595 CONCAVE, an expression used If a be the portion cut off from the lines, b the perpendicular distance of the point from the line which any of the lines cut makes cut by the others, the angle with the perpendicular, and Z the total length of the line so cut; then Z= ±a. In which b cus. answers for the first conchoid, and for the second. The swell of architectural columus is usually a first conchoid. Newton approves of the use of this curve for the trisection of angles, finding two mean propor tionals, and in the construction of problems, for which purposes it was employed by the ancients. CONDENSATION, the act whereby a body is rendered more dense, compact, and heavy. ceive the e.ectricity immediately from the excited electric. CONDUCTORS of Lightning, are un-pointed metallic rods fixed to the upper parts of buildings, to secure them from strokes of lightning. CONDENSER, a pneumatic en gine, or syringe, whereby an common quantity of air may be condensed into a given space. CONE, is a solid body, having circular base, and its other extremity terminated in a single point or vertex. CONDUCTOR, in Electricity, a term used to denote those sub-a stances which are capable of receiving and transmitting electricity, in opposition to electrics, in Cones are either right, or oblique. which the matter or virtue of A Right CONE, is that in which electricity may be excited and ac- the right line joining the vertex cumulated, or retained. The for- and centre of the base, is perpenmer are also called non-electrics, dicular to the plane of the base. and the latter non-conductors. It may be conceived to be geneAnd all bodies are ranked under rated by revolution of the rightone or other of these two classes, angled triangle, about its perpenthough none of them are perfect dicular. And thus, Euclid defines electrics, nor perfect conductors, a cone to be a solid figure, whose so as wholly to retain, or freely base is a circle, and is produced and without resistance to transmit by the entire revolution of the electricity. plane of a right-angled triangle To the class of conductors be-about its perpendicular, being callong all metals and semi-metals, led the axis of the cone. ores, and all fluids, (except air and oils), the effluvia of flaming bodies, ice (unless very hard frozen), and snow, most saline and stony substances, charcoals, of which the best are those that have been exposed to the greatest heat; smoke, and the vapour of hot water. It is commonly supposed, that the electric fluid passes through the substance, and not merely over the surfaces or metallic conductors; because, if a wire of any kind of metal be covered with some electric substance, as resin, sealing-wax, &c. and a jar be discharged through it, the charge will be conducted as well as without the electric coating. It has also been alleged, that electricity will pervade a vacuum, and be transmitted through it almost as freely as through the substance of the best conductor; but Mr. Walsh found that the electric spark or shock would no more pass through a perfect va cuum than through a stick of solid glass; in other instances, however, when the vacuum has been made with all possible care the experiment has not succeeded. CONDUCTOR Prime, is an insulated conductor, so connected with the electrical machine, as to re Right cones are called acute, obtuse, right-angled, or equilateral, according to the species of the vertical angle. An Oblique CoNE, is that in which the line joining the vertex and centre of the base is not perpendicular, but oblique, to the plane of the base. Every cone, whether right or oblique, is equal to one-third of a cylinder of equal base and altitude. And therefore the solidity of a cone is found by multiplying the area of its base by one-third of its perpendicular altitude. The curve surface of a right cone is equal to a circular sector, having its radius equal to the slant height of the cone, and its arc equal to the whole circumference of the cone's base. And therefore this surface is equal to half the product of the slant side into the circumference of the base. The surface of an oblique cone is not quadrable; indeed, no ruie has yet been found that will even lead to a practical approximation of its area, notwithstanding the attempts of several ingenious and able mathematicians. The solidity of a cone with an elliptic base, forming part of a right cone, is equal to the product of its surface by a third of one of the the same figures of a higher order. See the respective articles. CONICAL Ungula, or CONIC Ungula, is a solid formed by a plane passing through the side and base perpendiculars, drawn from the Frustrum of a CONE, is that which is formed by cutting off the upper part of a cone, by a plane parallel to its base. Put the greater diameter D, the less diameter d, the height=h, and 7854=p; then Surface 2p (D+ d Solidity ph (D2 + Dd + d2) D3-d3 Solidity={ph+ CONIC Sections, as the name im plies, are such curve-lines and plane-figures as are produced by the intersection of a plane with a cone. From the different positions of the cutting plane, there arise five different sections; viz. a triangle, circle, ellipse, parabola, and hyperbola. But only the three latter are particularly denominated conic sec tions. 1. If the cutting plane pass through both base and vertex, the section is a triangle. 2. If it pass through neither, it is a circle when parallel to the base, and an ellipse when not; the obliquity determining the eccentricity of the ellipse. 3. If it pass through the base and slant side, it is a parabola when parallel to the opposite side; and an hyperbola when it makes an angle with that side, and would meet it beyond the vertex of the cone. D-d CONGELATION, the transition of a liquid into a solid state, in consequence of an abstraction of heat: thus, metals, oil, water, &c. are said to congeal when they pass from a fluid into a solid state. With regard to fluids, conge- 4. The vertices of any section are lation and freezing mean the same the points where the cutting plane thing. Water congeals at 32°; and meets the opposite sides of the there are few liquids that will not cone. Hence the ellipse and hypercongeal, if the temperature be bola have each two vertices, but brought sufficiently low. Every the parabola only one, unless we particular kind of substance re- consider the other as at an infinite quires a different degree of tempe-distance. rature for its congelation. 5. The axis, or transverse diameter, of a conic section, is the line joining its vertices; therefore the axis of an ellipse is within the figure, of the hyperbola without it, and in the parabola it is infinite in length. CONGRUOUS Quantities, are those which are of the same kind, and therefore admit of comparison; and quantities which cannot be so compared, are incongruous quantities. All abstract, numbers are congruous; but concrete numbers 6. The centre of a conic section.' are not congruous, unless the quan-is in that point which bisects the tities they represent be so. Thus, axis. Hence the centre of an el three and four, as abstract num-lipse is within the figure, of the bers, are congruous; but if they hyperbola without the figure, and denote three pounds and four miles, they are incongruous. in the parabola it is at an afinite distance from the vertex. The definition of the other lines, in and about the conic sections, will be found under their respective heads. CONICAL, any thing of a conical form, or relating to the cone. CONICAL Ellipse, Hyperbola, Parabola, denote those figures, under their most simple form, as cut from The conic sections are of themthe cone, to distinguish them from Iselves a system of regular curves |