which have been computed, and where you find they agree very well, you may conclude that they are elements of the same comet, it being so extremely improbable that the orbits of two different comets should have the same inclination, the same perihelion distance, and the places of the perihelion and node the same. Thus, knowing the periodic time, we get the major axis of the ellipse; and the perihelion distance being known, the minor axis will be known. When the elements of the orbits agree, the comets may be the same, although the periodic time should vary a little; as that may arise from the attraction of the bodies in our system, and which may also alter all the other elements in a small degree. COMETARIUM, a machine for conveying an idea of the revolution of a comet about the sun. It is contrived in such a manner, as by elliptical wheels to show the unequal motion of a comet in every part of its orbit. COMMENSURABLE, among geometricians, au appellation given to such quantities as are measured by one and the same common 2nleasure. CoMMENsu RABLE Numbers, whether integers, surds, or fractions, are such as can be measured or divided by some other number without any remainder: such are 12, and 18, as being measured by _6 and 3: also 2 V2, and 3 V 2, being measured by V2. CoMMENsu RAble in Power, is said of right lines, when their squares are measured by one and the same space or superficies. Cox M. ENSU R A BLE Surds, those that being reduced to their least terms, become true figurative quantities of their kind; and are therefore as a rational quantity to a ra. tional one. COMMON Measure or Divisor, in Arithmetic, is that number which will divide two other numbers without leaving a remainder; and the greatest of such divisors is called the greatest common measure, or greatest common divisor. CóMMüNiðation of motion, that act of a moving body by which it transfers its motion to another body. COMMUTATION, in Astronomy. Angle of commutation is the distance between the sum’s true place seen from the earth, and the place of a planet reduced to the ecliptic ; and is, therefore, found by subtracting the same longitude front the heliocentric longitude of the planet. COMPASS, or Mariner's Compass, an instrument used at sea by mariners, to direct and ascertain the course of their ship. The invention of this instrument is commonly ascribed to Flavio Gioia, or Flavio, of Malphi, about the year 1302. The common construction of the mariner's compass is extremely simple. It consists of a circular brass box, which contains a paper card, on which is drawn the 32 points of the compass; and this card is fixed on a magnetic needle, which always turns to the north, except a small deviation which is variable at different places, and at the same place at different times. Azimuth CoMPAss. This differs from the common sea compass only in this, that the circumference of the card or box is divided into degrees; also to the box is fitted an index with two sights, which are upright pieces of brass placed , diametrically opposite to each other, having a slit down the middle of thein, through which the sum or star is to be viewed at the time of observation. The use of this instrument is to take the bearing of any celestial object, when it is in or above the horizon, in order to find from the magnetical azimuth, or amplitude, the variation of the needle. These are the thirty-two principal points of divisions drawn on the compass card; and are otherwise called Ithumbs ; each of which has a particular denomination expressed by means of the initials of the four first points, North, East," South, West. Each point contains 11° 15', and is divided into 3 points, containing 2° 48' 51. Cox PAss Es, or Pair of Contpasses, a mathematical instrument for describing circles, measuring and dividing lines, or figures, &c. The common Com PAsses consists of two sharp-pointed branches or legs, joined together at the top. Triangular CoMPAssrs; 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. Beam CoMP Asses consist of a long straight beam or bar, carry. ing two brass cursors; one of these being fixed at one end, the other sliding along the beam, with a screw to fasten it on occasionally. Elliptic Cox PAsses, commonly called a trammel, consists of a cross with two dovetail grooves, at 1 ight 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 inade equal to the semi-transverse (the distance of the nearer knob from the same point being equad to the semiconjugate). Then the cross being laid with its centre over that of the ellipse, and the l; nobs let into the grooves, the turning round of the ruler will trace the ellipse. German CoMPAsses, have their legs a little bent outwards towards the top ; so that when shut the points only meet. Hair Cox PAsses 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 CoM Pass Es, are - 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 conse4uently any proportion whatever easily obtained. 113 Spring CoMP Asses, 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 CoMP Asses, 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 Coxiple M Ent, 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. Coal PLEMENT, in Astronomy, denotes the distance of a star from the zenith. CoM P L E MENT of Lisc, 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. CoM P1, EMENTs 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 multiplication of two or more numbers or factors, and is thus distinguished from a prime mumber, which cannot be so produced. 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. CoM position of Forces, in Mechanics, is the method of finding the quantity * direction of a 3 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 t the 4th. CoM Position of Ratios, in Arithmetic 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. COMPOUND Interest, is that which arises by the continual addition of the interest to the principal as it becomes due. Compoux D 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. CoM Pou ND Quantities, in Algebra, are those connected together by the signs + and — ; they are distinguished into binomials, trinomials, &c. according to the number of terms of which they are composed. CoM Pou ND Ratio, is that which arises from the composition of ra. tios. 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 500 and barometer 29% inclues. Compress, of Mill, pts. Wp grav. Spirits of wine . . 66 . . . . . 846 Oil of olives • - 48 . . . . . . 918 Rain water . . . . 46 . . . . . 1000 Sea water . . . . 49 . . . . . 1028 Mercury . . . . . 3 . . . . 13595 CONCAVE, an expression used to denote the curvilinear vacuity of hollow bodies. Conc Avg. Lenses, or Mirrors, have either one or both sides concave. See LENs and M1R RoR. CONCAVITY, from concave, the hollow or vacuity of bodies. CONCAVO-Concave Lens, is that which is concave on both sides. CoN cAvo-Conver Lens, is that which is concave on one side, and convex on the other. CONCENTRIC, having a connmon centre, as concentric circles, ellipses, &c. 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 point draw any number of lines, each cutting another line, then 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 Come hoid the first, or external one, on the side opposite to the point; and the second, or internal one, on the side next the point. Of the second there are two forms, 1st. pointed, when the curve passes between the line and the point; and 2d looped, when it passes beyond the point. If a be the portion cut off from the lines, b the perpendicular distance of the point from the line cut by the others, op the angle which any of the lines cut makes with the perpendicular, and Z the total length of the line so cut; b + a. In which COS. + answers for the first conchoid, and — for the second. The swell of architectural columns is usually a first conchoid. Newton approves of the use of this curve for the trisection of angles, finding two mean proportionals, and in the construction of problems, for which purposes it was employed by the ancients. co ND ENS AT I o N, the act
whereby a body is rendered more dense, compact, and heavy. CONDENSER, a pneumatic engine, or syringe, whereby an uncommon quantity of air may be condensed into a given space. CONDUCTOR, in Electricity, a term used to denote those substances which are capable of receiving and transmitting electricity, in opposition to electrics, in which the matter or virtue of electricity may be excited and accumulated, or retained. The former are also called non-electrics, and the latter non-conductors. And all bodies are ranked under one or other of these two classes, though none of them are perfect electrics, nor perfect conductors, so as wholly to retain, or freely and without resistance to transmit electricity. To the class of conductors belong all metals and semi-metals, 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 dis. charged 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 vacuum 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. CoN Ductor Prime, is an insulated conductor, so connected with the •oical machine, as to re s ceive the electricity immediately from the excited electric. . CoNDUctors of Lightning, are pointed metallic rods fixed to the upper parts of buildings, to secure them from strokes of lightning. CONE, is a solid body, having a circular base, and its other extremity terminated in a single point or vertex. Cones are either right, or oblique. A Right Con E, is that in which the right line joining the vertex and centre of the base, is perpendicular to the plane of the base. It may be conceived to be generated by revolution of the rightangled triangle, about its perpendicular. And thus, Euclid defines a cone to be a solid figure, whose base is a circle, and is produced by the entire revolution of the plane of a right-angled triangle about its perpendicular, being called the axis of the cone. Right comes 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 come 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 rule 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 MATHIEMATICAL AND PHYSICAL SCIENCE. - perpendiculars, drawn from the point in which the axis of the right cone intersects the ellipse; and it is also equal to one-third of the height of the cone multip.ied by the area of the elliptic base. Consequently, the above perpendicular is to the height of the cone, as the elliptic base is to the curve surface. Its curve surface is equal to half the sum of the circumferences multiplied by the slant side; and its solidity to the sum of the squares and product of the diameters multiplied by ,7854, and by § the perpendicular height. Frustrum of a Con E, is that which is formed by cutting off the upper part of a coine, 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 + Da + de) Solidi h4. Po-o: olidity = |ph+ 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, congelation and treezing mean the same thing. Water congeals at 32°; and there are few liquids that will not congeal, if the temperature be brought sufficiently low. Every particular kind of substance requires a different degree of temperature for its congelation. CON G R U O U S Quantities, are those which are of the same kind, and therefore admit of comparison ; and quantities which cannot be so compared, are incongruous quan1ities. All abstract. numbers are congruous; but concrete numbers are not congruous, unless the quantities they represent be so. Thus, three and four, as abstract numbers, are congruous; but if they denote three pounds and four miles, they are incongruous. CONICAL, any thing of a conical form, or relating to the cone. CoNic AL Ellipse, Hyperbola, Parabola, denote those figures, under their most simple form, as cut from the •o to distinguish them from the same figures of a higher order. See the respective articles. CoN ic Al Ungula, or Conic Ungula, is a solid formed by a plane passing through the side and base of a cone. - CoN1c 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 an ise five different sections; viz. a triangle, circle, ellipse, parabola, and hyper. bola. 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. lf it pass through neither, it is a circle when parallel to the base, and an clipse 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. 4. The vertices of any section are the points where the cutting plane meets the opposite sides of the cone. Hence the ellipse and hyperbola have each two vertices, but the parabola only one, unless we consider the other as at an infinite distance. 5. The aris, or transverse diameter, of a comic 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 intimite in length. 6. The centre of a comic section is in that point which bisects the axis. Hence the centre of an ellipse is within the figure, of the hyperbola without the figure, and in the parabola it is at an 15 finite distance from the vertex. The definition of the other lines, in and about the conic sections, will be found under their respective heads. The conic sections are of themselves a system of regular curves |