a the case with gunpowder; but the expansion of elastic fluids will burst solid substances, and throw the fragments a great way off: for this two reasons have been assigned: 1. The immense velocity with which aerial fluids expand, when suddenly affected with high degrees of heat: and t. The great celerity with which they acquire heat, and are affected by it. As an example, air when heated as much as iron, when brought to a white heat, is expanded to four times its bulk, but the metal itself will not be expanded the 50Odth part of the space. In the case of gunpowder, which is well known as an explosive substance, the velocity with which the flame moves, is estimated at 7000 feet in a second. Hence the impulse of the fluid is inconceivably great, and the obstacles on which it strikes are hurried off with vast velocity, viz. at the rate of 27 miles per minute. The velocity of the bullet is also promoted by the sudden propagation of the heat through the whole body of air, as soon as it is extricated from the materials of which the gunpowder is made, so that it strikes at once. Hence it has been inferred, that explosion depends first on the quantity of elastic fluid to be expanded : secondly, on the EXPONENT; in algebra, is a number placed over any power or involved quantity, to shew to what height the root is raised: are called the negative powers of a, which have negative exponents; but they are at the same time positive powers of —, or a-'. Exponent of a ratio, is the quotient arising from the division of the antecedent by the consequent: thus, in the ratio of 5 to 4, the exponent is 1J; but the exponent of 4: 5, is ^. If the consequent be unity, the antecedent itself is the exponent of the ratio: thus the exponent of the ratio 4 : 1 is 4. Wherefore the exponent of a ratio is to unity as the antecedent is to the consequent. Although the quotient of the division of the antecedent by the consequent, is usually taken for the exponent of a ratio, yet in reality the exponent of a ratio ought to be a logarithm. And this seems to be more agreeable to Euclid's definition of duplicate and triplicate ratios, in his fifth book. For 1, 3, 9, are continual proportionals; now if ] be the exponent of the ratio of 1 to'3, and j or ^ the exponent of the ratio of 3 to 9; and ± the exponent of the ratio of 1 to 9; and since, according to Euclid, if three quantities be proportional, the ratio of the first to the third is said to be the duplicate of the ratio of the first to the second, and of the second to the third; therefore according to this, i must be the double of |, which is very false. But it is well known, the logarithm of the ratio of 1 to 9, that is, the logarithm of 9, is the double of the ratio of 1 to 3, or 3 to 9, that is, the logarithm of 3. From whence it appears that logarithms are more properly the exponents of ratios, than numerical quotients; and Dr. Halley, Mr. Cotes, and others, are of the same opinion. Exponent, is also used in arithmetic, in the same sense as index or logarithm. EXPONENTIAL curve, is that whose nature is expressed by an exponential equation. The area of any exponential curve, whose nature is expressed by this exponential equation xr= y (making l -f-u = x) wiU be oTi■c2+5i3,',-i—«.■!■ 1 ., i 0.1.2.3.4 ~ O.l.z.'Xi.'j 0.1.2.3.4.5.6> e*,'&c. Exponential equation, is that wherein there is an exponential quantity. See the next article. Exponential quantity, is a quantity whose power is a variable quantity, as a*,
EXPORTATION, the act of sending goods out of one country into another. In officer of the customs. A limited quantity of wool is, however, permitted to be ex* ported from the port of Southampton to Jersey, Guernsey, Aldcrney, and Sark. The duties on exportation, payable in Great Britain and Ireland, which were formerly the principal branch of the revenue derived from foreign trade, are now of small amount in comparison with the duties payable on goods brought into the country. See CusToms. EXPRESSED oil. See On.. EXPRESSION, in chemistry, or pharmacy, denotes the act of expressing out the juices or oils of vegetables, Expression, in rhetoric, the elocution, diction, or choice of words in a discourse. Beautiful expression is the natural and true light of Expression, in painting, a natural and lively representation of the subject, or of the several objects intended to be shewn. The expression consists chiefly in representing the human body and all its parts, in the action suitable to it: in exhibiting in the face the several passions proper to the figures, and observing the motions they impress on the external parts. See PaintIng. EXSICCATION, in pharmacy, the drying of moist bodies, for which two methods are usually employed, in one the humid
parts are exhaled by heat, in the other they are imbibed or absorbed by substances, whose texture is adapted to the purpose. Bodies combined with, or dissolved in a fluid, require the first: such as are only superficially mixed with it, are separated by the second method. Vegetables are usually exsiccated by the natural warmth of the air, but the assistance of a gentle artificial heat is often found very useful. By a moderate fire the more tender flowers may be dried in a short time without any considerable EXTENSION, in philosophy, one of the common and essential properties of body, or that by which it possesses or takes up some part of universal space, which is called the place of that body. Extension is divided, 1. either into length only, and then it is called a line; or, J. Into length and breadth, which is called a superficies; or, 3. Into length, breadth, and depth, which is called a solid; being the three dimensions according to the quantity of which the magnitude or bulk of bodies are estimated. Extension, according to Mr. Locke, is space considered between the extremities of matter, which fills up its capacity with something solid, tangible, and moveable. Space, says that philosopher, may be conceived without the idea of extension, which belongs to body only. EXTENSOR, an appellation given to several muscles, from their extending or stretching the parts to which they belong. See Anatomy. EXTENT, in law, a writ of execution or commission to the sheriff, of one who being bound by statute, has forfeited his bond, for the valueing of lands or tenements; sometimes the act of the sheriff upon this writ. EXTERMINATION, in general, the extirpating or destroying something. In algebra, surds, fractions, and unknown quantities are exterminated by the rules for reducing equations. Thus to take away the fractional form from these equations r =z -; and —-1— = -; in both cases 5 «' 2c y we multiply the numerator of one fraction by the denominator of the other, and the equations become ay = hi and a'y -\- the second power, and take off the sign of the root on the other side of the equation thus a1 -}- if — 16V: and when n */ a -J- b — i: then «-)-'' = P. To exterminate a quantity from any equation there are divers rules. See Algebra. We shall however give an instance in this place: thus to exterminate y out of these two equations a -f- x = hence3x =46—a and 4= 1 —-—. Suppose also two equations given involving two unknown quantities, as ax -l-by = c) ,. ... af—dc 3 S then shall y= — , dx -f-ey=/S ae — do. Where the numerator is the difference of the products of the opposite coefficients, in the orders in which ;/ is not found; the denominator is the difference of the products of the opposite coefficients, taken from the orders that involve the unknown quantities. For from the first equation it appears that ax = c — by, and x = -; and from the second equation, ey EXTORTION, in law, any oppression by colour or pretence of right EXTRA judicial, in law, is when judgment is given in a cause or case not depending in that court, where such judgment is given, or wherein the judge has no jurisdiction. Extra parochial, out of any parish; privileged or exempted from the duties of a parish. EXTRACT, in pharmacy, the soluble parts of vegetable substances, first dissolved in spirit or water, and then reduced to the consistence of a thick syrup, or paste, by evaporation. See Pharmacy. EXTRACTION, in chemistry, is the general operation by means of which we separate and extract from very compounded bodies of the vegetable and animal kingdoms, different matters contained in them. For this purpose alcohol, water, acids, and alkalies are made Extraction, in surgery, is the drawing any foreign matter out of the body by the hand, or by the help of instruments. Extraction, in genealogy, implies the stock or family from which a person is descended. Extraction of EXTRACTOR, in midwifery, an instrument, or forceps, for extracting children by the head. See Midwifery. EXTRAVASATION, in contusions, fissures, depressions, fractures, and other ac cidents of the cranium, a when one or more of the blood-vessels that are distributed on the dura mater, is broke or divided, whereby there is such a discharge of blood as greatly oppresses the brain, and disturbs its offices; frequently bringing on violent pains, and other mischiefs; and, at length, death itself, unless the patient is timely relieved. EXTREME and mean proportion, in geometry, is when a line is so divided into two parts, that the rectangle under the whole line, and the lesser segment, is equal to the square of the greater segment. EXU VMS, among naturalists, denote the cast-off' parts or coverings of animals, as the skins of serpents, caterpillars, and other insects. See Entomology. M. Reaumur is very particular in describing the manner in which the caterpillar tribe throw off, or extricate themselves from their exuviae. See vol. i. of the "History of Insects." The crab, as is well known, can even throw off its limbs at pleasure, which are again replaced by new ones. See Cancer. Excvi.-e is also used for the remains of sea animals, found Eye of a dome.au aperture at the top of a dome, as that of the Eye, in agriculture and gardening, signifies a little bud, or shoot, inserted into a tree, by way of graft. Eye of a tree, a small pointed knot to which the leaves stick, and from which EYE-trig-Ar. See Euphrasia. a As a numeral, F denotes 40, and with a dash over it thus F, 40,000: in music, it .••lands for the bass clef; and frequently for forte, As an abbreviation, F stands for filius, fellow, and the like: thus F. R. S. signifies Fellow of the Royal Society. FA, in music, one of the syllables invented by Oiiido Arctine, to mark the fourth note of the modern scale, which rises thus, at, re, mi, fa. Musicians distinguish two/a's, j , ui'(., •. and the sharp or natural, marked thus q, and called biquadro.FABER, a fish of the zeus kind, called in English doree, or John doree. See Zeus. FABLE is FABR1CIA, in botany, a genus of the Tcosandria Mouogynia class and ruler. Caljx five-cleft, half superior; five petals, without claws; stigma capitate; capsule many-celled; seeds winged. There are two species FACE, comprehends all that part of the head which is not covered with the common long hair. See Anatomy.
Face, in fortification, an appellation given to several parts of a fortress, as the face of a bastion, &c. FACET, or Facette, among jewellers, FACTITIOUS, any FACTOR, in commerce, is an agent or correspond, nt residing beyond the seas, or in A factor,
Factor, in multiplication, a name given to the multiplier and multiplicand, because they constitute the product See ArithMetic. FACTORAGE, called also commission, is the allowance given to factors*by the merchant who employs them. FACTORY is a place where a considerable number of factors reside, to negotiate for their masters and employers. The most considerable factories belonging to the British are those established in the East Indies, There were also factories in Portugal, Turkey, and at Hamburgh, FACULfii, in astronomy, certain bright and shining parts, which the modern astronomers have, by means of telescopes, observed upon or about the surface of the sun; they are but very seldom seen. One was seen by Hevelius in 1634, whose breadth was said to be equal to a third part of the sun's diameter. FACULTY, in law, a privilege granted to a person, by favour and indulgence, of doing what, by law, he ought not to do. For granting these privileges, there is a court under the Archbishop of Canterbury, called the court of the faculties, the chief officer whereof is styled master of" the Faculty, in the schools, a term applied to the different members of an university, divided according to the arts and sciences taught there; thus in most universities |