figures being different views of a single line in the cutting plane; and the part eb cut off by the cones is here represented by the line A B, which joins the vertices of the curves. Bisecting AB in C, any right line (as pq) drawn through C (which is called the centre), and terminating in both curves, is a transverse diameter, and of all these diameters the aris A B is the shortest.

Two points g and h, in the line of the Axis, equally distant from either vertex of the hyperbolas, are their Foci,and these are so situated that, if we take any point m, in either of the curves, and draw the straight lines m g and m h, the difference of the lengths of those lines will be always equal to A B, the shortest transverse diameter. Again, as in the ellipsis and parabola, any straight line mon, in either hyperbola, crossing the axis at right angles, and terminating at both ends in the curve, is a double Ordinate; mo and on are Ordinates, and o B is the Abscissa.

The conic sections have certain properties in common, but the hyperbola possesses a peculiar one, which is often alluded to, and usually considered as paradoxical: two right lines, rs and tu, may be drawn through the centre C, which will pass alongside of the different legs of the two hyperbolas; and although continually approaching nearer and nearer, these curves and straight lines, however much produced, would never meet each other. These lines are called the Asymptotes. The opposite hyperbolas, here described, fill two angles of the cross formed by these asymptotes: and the two blank angles might be filled with two other hyperbolas, of which y z would

be the axis; and the same lines, rs and tu, would also be asymptotes to the new curves. In such a case each opposite pair would be Conjugate hyperbolas to the other, and the shortest Transverse diameter of the one pair would be the Conjugate diameter of the other. A very curious account of coloured rings, crossed by opposite hyberbolic curves, is given at pp. 24, 25, of the Treatise on the Polarisation of Light.

It will be observed, that in every conic section, we have pointed out two lines, at right angles to each other, called the Ordinate and the Abscissa. At whatever point of the axis (in the same sort of curve) the ordinate may be drawn, these two lines will have always the same relation to one another; and the algebraic expression which points out that relation, in each figure respectively, is termed the Equation of that curve. From any one general property of a curve, all its other properties may be ascertained; and the reasoning that enables us to do so, in the Ellipsis, the Parabola, and the Hyperbola, constitutes the whole of the doctrine of Conic Sections.

CONJUGATE DIAMETERS.-See Conic Sections.

See

CONJUGATE HYPERBOLAS. Conic Sections. CONOID. A conoid is a solid which may be conceived as generated by the motion of a parabola or of a hyperbola round its axis. Some have included the spheroid in the class of conoids, but they are more usually limited to the Paraboloid and the Hyperboloid.-See Spheroid. Conoids are of various thicknesses in comparison with their height, according to the pro portions of the parabola, or hyperbola, by which they are generated. The Solid of least resistance, spoken of at page 22 of the Preliminary Treatise, is a Conoid.

CONVERGING RAYS are rays of light, the direction of which is such that they will meet or cross one another at, or near to, a common centre. Their divergence from that centre is termed their aberration.-See Aberration. CONVEX LENSES-See Lens.

MIRRORS-See Mirror. CORUNDUM, or CORINDON, a stone found in India and China, which, when crystallized, has usually the form of a six-sided prism. The diamond was formerly called Adamant; and the crys tals of corundum, being next in hardness, have the name of Adamantine Spar. The Amethyst, Ruby, Sapphire, and Topaz are considered as varieties of this spar, differing from one another chiefly in colour. The amethyst is of a reddish violet colour; the ruby is red; the sapphire is blue, and the opax is yellow. These are termed oriental gems; but stones having

the same names are found in other countries. Topazes, in particular, are of all colours. See Quartz.

CRYSTALLIZATION is that state of certain bodies in which, when passing from the fluid to the solid form, they separate into portions, each portion (or crystal) assuming the same determinate and angular shape. It is a species of congelation, but this last does not necessarily include the idea of separate crystals. Ice was called crystal (crystallos) by the Greeks. An account of certain crystals will be found under their several names in this Glossary; but to have included all that are mentioned in the volume, would have been to have written a work on Crystallization.

CUBIZITE.-See Analcime.
CURVATURE.-See Curve.
CURVE. A straight (or stretched) line is

the measure of the shortest distance between two points. A curve or curved line is that of which no portion, however small, is straight. A crooked line may be either a curved line or the junction of two or more straight lines drawn in different directions. The varieties of curve lines are innumerable; that is, they have different degrees of bending or CURVATURE. The curves most generally referred to, beside the circle, are the Ellipsis, the Parabola, and Hyperbola, to which we may add the Cycloid. CURVES, Evolutes and Involutes of. Let a thread be wound round the curve

stretched out in the line CE) is termed the Involute. The thread, during the progress of unwinding, is, at every point, a tangent to the Evolute; thus, at the point D, it is a tangent to CBA at B. The Involute of a Circle is described, with its use, in Mechanics, Treatise ii. page 29. It is a spiral.-See Spiral. CURVES, EQUATION OF.-See Conic Sections.

CURVILINEAL, or CURVILINEAR, designates figures that are bounded by curve lines. Thus a Curvilinear surface is that which can be touched by a plane only in one point.-See Tangential Plane. A cone and a cylinder are rightlined surfaces in the direction of their length. A sphere and a spheroid are wholly curvilinear. CYCLOID.

If we conceive the circle b na c d to roll along the line A B; the point a being first at A, and ending at B, this point (a) will describe, or pass through the curved line A h pak B, which curve is termed a Cycloid. Seeing that the circle rolls over the whole line, it is obvious that the length A B is equal to its circumference, and the general properties of the curve are these: that taking any point h and drawing the line hg (parallel to the line on which the circle rolls) to meet the circle, when in the middle of its motion, at g; and joining g a, the line h g is always equal in length to the circular arc g na; and the portion of the cycloidal arch p a is always double the length of the chord g a. Further, the area of the whole cycloidal space A B k a ph is equal to thrice that of the circle g na cd, by which it is formed. See Preliminary Treatise, p. 21 Fig. 10.

α

h

CBA, fixing one end at C, and carrying the other round to A. If we unwind this thread, keeping it tight upon the convexity of the curve, its end A will describe another curve A D E, passing further and further from the former curve CBA, as the string gradually lengthens, until it reaches the point C, where it is supposed to be fixed. If carried further on to F, the length of the thread would continue the same, and the arch EF would be part of a circle. The primary curve CBA, that round which the thread was wound, is called the Evolute, and the secondary curve A D E, formed by the unrolling of the thread (now

d

CYLINDER. A cylinder is a solid having a circular base, and which base may be considered as carried upwards in a straight line, and continuing the circle in a parallel direction. It is a circular prism, as a cone is a circular pyramid. When the base is elliptical, it is a Cylindroid. When the sides are perpendicular to the base, it is a Right cylinder or cylindroid; otherwise it is an O blique one. D'ALEMBERT'S PRINCIPLE. Principle D'Alembert's. DEAD LEVEL.-See Level. DEGREES AND MINUTES. Angle. DENSITY (Latin densitas, closeness) is a relative term, and denotes the com

See

See

parative quantity of matter, in different bodies, which is contained in the same space. (See Volume.) Gravity is understood to act in proportion to the relative quantity of the matter of bodies; and, hence, the specific gravities of bodies are presumed to be the measure of their densities. See Gravity. DE-OXYDATION is the depriving a substance of the oxygen, or vital air which it contains. Concerning the de-oxydating power of the solar rays, see Optics, p. 29. DIAMETERS, TRANSVERSE AND CONJUGATE.-See Conic Sections. DIGESTER, a strong vessel of iron, or other metal, having a screwed-down and air-tight lid, into which substances, either fluid or solid, are inclosed, and are therein submitted to a much higher degree of heat than they could be subjected to in the open air.

DIOPTRICS is that division of the science

of Optics which treats of the Refraction of Light.

DIRECT PROPORTION, or DIRECT RATIO.-See Ratio.

DIRECTION, LINE OF.-See Force, Direction of.

DIRECTRIX OF A PARABOLA.-See Conic Sections.

DISTILLATION is a process by which a fluid, or portion of a fluid, is converted into vapour by means of heat, and that vapour returned into a state of fluidity by cold, or, as the chemists say, by the abstraction of caloric. Distillation is Evaporation, that is, raising a fluid to the state of vapour, but the latter term does not include the idea of preserving that vapour and condensing it again into a fluid-See Vapour.

DIVERGING RAYS are the opposite of

Converging (which see.) They separate in their progress further and further asunder, as the radii of a circle do from its centre.

DODECAHEDRON.-See Rhombus.

DOUBLE REFRACTION.-See Refrac

tion.

DYNAMICS (Greek dynamis, force) is that division of the science of mechanics which considers bodies as acted upon by forces which are not in equilibrio. It therefore treats of bodies in motion.See Equilibrium. EBULLITION.-See Boiling. ELASTICITY (from a Greek word signifying to push, or drive back) is that quality of a substance, whether solid or fluid, by which, when compressed, or when forcibly expanded, it endeavours, in either case, to re-assume its former bulk. ELASTIC FLUIDS.- See Fluids, and Gas.

ELLIPSIS.-See Cone, and Conic Sections. ELLIPSOID.-See Conoid, and Spheroid. EMERALD. The emerald is ranked among the gems, and is now found only

in Peru. It is of a green colour, rather harder than quartz, and always in crystals, which are translucent and generally transparent. What is called Oriental emerald is a green sapphire. The Beryl is a variety of the emerald, of a paler green, frequently passing into blue, and is much less prized. It is found in various countries, sometimes in Scotland. The Emerald of Brazil is a Tourmaline, which see.

EMPIRICAL (Greek en and peirao, I try) designates any assertion or act which is made or done, merely as an experiment, without any past experience or known principle to direct the choice. EQUATION OF A CURVE.-See Conic Sections. EQUILIBRIUM.

When two or more forces, acting upon a body, are so opposed to each other that the body remains at rest, although either would have moved it if acting alone, those forces are said to be in equilibrio, which is a Latin term signifying equally balanced. ETHER.-See Air, ethereal. EVAPORATION; the state or action of a fluid when its particles are so far sepa rated by caloric as to assume the form of vapour. Evaporation, or (as it is sometimes called) vaporization, is often, but not always, preceded by ebullition.-See Boiling and Vapour.

EVOLUTE OF A CURVE-See Curves. EXHAUSTED RECEIVER.- See Va

cuuma

EXPANSIBILITY is that property of a substance which renders it capable, under certain circumstances, of occupying more space than it usually requires. The grand agent in the expansion of bodies is caloric.

FAHRENHEIT'S THERMOMETER is that arrangement of the scale of the instrument, in which the space between the freezing and the boiling points of water, under a medium pressure of the atmosphere, is divided into 180 parts, or degrees: the freezing being marked 32° and the boiling 2120. This scale was adopted by Fahrenheit, because he supposed, erroneously, that 32 of those divisions below the freezing-point of water (which was therefore (0) on his scale) was the zero, or greatest degree of cold.— See Thermometer. FELDSPAR is, next to quartz, the most abundant stone that exists; being a constituent in granite and other rocks. It scratches glass, and gives out sparks with steel; but all its varieties are inferior to quartz in hardness. The transparent lamina of its crystals have a double refraction; and one of the species, Adularia, or Moonstone, exhibits a pearly lustre. It is the famous Petuntse of the Chinese being the vitrifying ingredient in their porcelain.

FIRST, or PRIME MOVER, in mecha

nics. See Machine. FLUIDITY (Latin fluere, to flow) is that state of a substance in which its constituent particles are indefinitely small; and so slightly cohesive, that they are moveable in every direction, passing over one another with the least impulse. There is a partial fluidity, in which the particles are condensed or thickened into a coherent though tremulous mass. Jellies are of this kind, and may be considered as holding a middle place between liquids and solids.

FLUIDS are substances, or rather masses of particles, which have the quality of fluidity; and, in consequence, have no fixed shape, but assume that of the vessel by which they are contained. They are usually divided into two kinds; gascous and liquid.

ELASTIC.-See Gas.

NON-ELASTIC.-See Liquid. FLY-WHEEL is an addition to certain machines, for the purpose of equalizing the effect of the moving power. If this power act irregularly, there will be moments in which it will exert more force than is required. This excess is employed in giving motion to the fly-wheel, and part of this communicated excess is returned upon the machine when the power is too languid. In the former case it is a retarding, and in the latter an impelling power.

FOCUS. The Latin focus is a hearth or fire-place; and hence the word has been employed to denote any point in which light, and consequently heat, is concentrated. In optics, it is the point where several rays are collected, whether in consequence of refraction or of reflexion. For the situation of the foci of the ellipsis, parabola, and hyperbola, see Conic Sections.

FORCE is the name of any exertion which,

if applied to a body, has a tendency to move that body when at rest; or to affect, or to stop its progress, if already in motion. This is sometimes termed Active force, in contradistinction to what merely resists or retards the motion of another, but is itself, apparently, inactive. The degree of resistance to any motion may be measured by the active force required to overcome that resistance, and hence writers on mechanics make use of the terms Resisting forces and Retarding forces. FORCE, CENTRIFUGAL.-See Centrifugal Force.

LINE OF DIRECTION OF, is the straight line in which force any tends to make a body move. FORCES, COMPOSITION OF. When two forces act on a body in the same line of direction, the resulting force (or Resultant, as it is called) will be the sum of both. If they act in opposite directions,

the body will remain at rest if the forces be equal; or, if unequal, it will move with a force equivalent to their difference, in the direction of the greater. If the lines of direction make an angle with each other, the resultant will be a mean force in an intermediate direction. Any number of forces may be thus resolved into one resulting force, the effect of which is the absolute motion; and any motion may be assumed to be the result either of a single force, or of a combination of many. This is what writers on mechanics call the Composition and Resolution of forces.

FORCES, ACCELERATED.-See Acceleration.

FREEZING POINT. That point in a thermometer at which the included fluid stands, when the instrument is immersed in another fluid that is in the act of freezing, is the freezing point of the lat

ter.

FRICTION (Latin fricare, to rub) is the rubbing or grating of the surfaces of bodies upon one another. In mechanics, it is considered as one of the causes of the hinderance or stopping of motion,-as a retarding force.

FRIGORIFIC, having the quality of producing extreme cold, or of converting liquids into ice :-from the Latin frigus, coldness.

FULCRUM.-See Lever, and Balance. FUSIBILITY (from the Latin fusus, melted or poured out) is that quality of a solid which renders it capable of being brought to the state of a liquid by heat. FUSION is the state of melting, or softening into a liquid.

GAS is an old Teutonic word, equivalent to the Greek pneuma, air, or spirit, and has been adopted by the modern chemists to denote permanent aëriform (or airlike) fluids generally, for the purpose of distinguishing them more clearly from common air, which is a mixture of two species of gas. Gases are distinguished from liquids by the name of Elastic fluids; while liquids are termed non-elastic, be cause they have, comparatively, no elasticity. But the most prominent distinction is the following:-liquids are compressible to a certain degree, and expand into their former state when the pressure is removed; and in so far, they are elastic: but gases appear to be in a continued state of compression; for when left unconfined, they expand in every direction, to an extent which has not hitherto been determined. Thus, a small portion of common air, inclosed in a thin bladder, will, when the pressure of the atmosphere is removed, expand so as to inflate the whole cavity, stretching out every part of the surface. The expansion of a liquid, under such circumstances, would not be perceptible. Gases retain their elasticity