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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 velocity it acquires by a certain degree of beat; and thirdly, on the celerity with which the degree of heat affects the whole expansile fluid.

EXPONENT; in algebra, is a number placed over any power or involved quantity, to shew to what height the root is raised: thus, 2 is the exponent of jr1, and 4 the exponent of a4, or zxxx. The rule for dividing powers of the same quantity, is to subtract the exponents, and make the difference the exponent of the quotient: if, therefore, a lesser power is divided by a greater, the exponent of the quotient must, by this rule; be negative: thus,

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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

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there is an exponential quantity. See the next article.

Exponential quantity, is a quantity whose power is a variable quantity, as a*, P. Exponential quantities are of several degrees and orders, according as the exponents themselves are more or less involved. If the exponent be a simple quantity, as V, it is called an exponential of the first or lowest degree; but when the exponent itself is an exponential of the first degree, as v", it is called an exponential of the second degree. In like manner, if the exponent itself be an exponential of the second dc

grep, as i' , it is called an exponential of the third degree, &c.

EXPORTATION, the act of sending goods out of one country into another. In modern times it has been the principal object of commercial policy, in almost every country, to encourage exportation, except with respect to a few particular articles; the export of manufactured goods has been promoted with a view of encouraging the internal industry of the country, and the export of foreign produce, as a means of drawing wealth from other countries by the profits of the carrying trade. The excess of the value of goods exported, beyond that of the imports, has usually been considered as a criterion of the profits which a country derives from foreign trade; but this is a very fallacious mode of determining a point of great importance; advantageous foreign trade might long exist, even if the imports constantly exceeded the value of the exports. The laws in force relating to exportation, consist principally of prohibitory, or restrictive regulations respecting bullion, corn, wool, machinery, and tools used in various branches of manufactures, the exportation of which, it is thought, might diminish the necessary supply of provisions for the consumption of the country, or enable foreigners to rival valuable branches of its manufactures. The acts relative to the exportation of wool, prohibit the exportation, not only of the article itself, but also of live sheep, rams, or lambs, from Great Britain, Ireland, Jersey, Guernsey, Alderney, Sark, or Man, on penalty of the forfeiture thereof, and of the ships conveying the same; also 31. for every sheep, &c. and the offender to suffer three months solitary imprisonment; for a second offence 5/. per sheep, &c. and six months imprisonment: except wether sheep for ships' use only, put on board by licence of the port

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, which is one of the three ways of obtaining them ; the other two being by infusion and decoction. The hard fruits require to- be well bruised previously to expression, but herbs are only to be moderately bruised. They are then to be included in a hair bag, and pressed between wooden plates in the common screw press, till the juice ceases to run. The expression of oils is performed nearly in the same manner as that of juices, only iron plates are to be used instead of wooden ones. The insipid oils of all unctuous seeds are obtained uninjured by this operation, if performed without the aid of heat, which, though it promotes the extraction of the oil, gives it an ungrateful flavour. The oils expressed from aromatic substances, generally carry with them a portion of their essential oil. Hence the smell and flavour of the expressed oils of nutmegs and mace.

Expression, in rhetoric, the elocution, diction, or choice of words in a discourse. Beautiful expression is the natural and true light of our thoughts: it is to this we owe all the excellencies in discourse, which gives a kind of vocal life and spirit. As the principal end of discourse is to be understood, the first thing we should endeavour to obtain is a richness of expression, or habit of speaking so well as to make our thoughts easily understood.

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 loss, either of their odour or lively colour, which would be injured, or perhaps destroyed, by the more slow exsiccation in the air. Some plants, particularly those of the acrid kind, lose their virtues by that process.ever a right, title, or interest is destroyed, or taken away by the act of God, operation of law, or act of the party, it is called an extinguishment; a creditor's accepting a higher security than he had before is an extinguishment of the first debt of c consonant, and was wrote inverted

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 -\- My =ic x: so again to take away the sign of the square, or cube, or other root, as ^V + y2 = 4s we raise the 4z to 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 = b -j- y 3 o = 2x + y subtract the upper equation from the under and there remains St — a — x = 2x — b,

hence3x =46—a and 4= 1 —-—.

Suppose also two equations given involving two unknown quantities, as

ax -l-by = c) ,. ... afdc

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; and

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

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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 use of. Therefore extraction is performed by dissolutions, macerations, infusions, &c.

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 roots, in algebra and arithmetic, the method of finding the root of any power or number. See Algebra.

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 fossils, and more properly called extraneous, or marine fossils. EYE. See Anatomy and Optics. Eye, in architecture, is used to signify any round window made in a pediment, an attic, the reins of a vault, or the like.

Eye of a dome.au aperture at the top of a dome, as that of the Pantheon at Rome, or of St. Paul's at London: it is usually covered with a lantern.

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 the shoots or sprigs proceed.

EYE-trig-Ar. See Euphrasia.

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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 does (or forte 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, vs. the flat, marked with a 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 used for the plot of an epic or dramatic poem, and is, according to Aristotle, the principal part, and, as it were, the soul of a poem.

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 speciesi tie. the myrtifolia and the I.vvisrata, both found in New Holland.

FACE, comprehends all that part of the head which is not covered with the common long hair. See Anatomy.

Face, or facade, in architecture, the fr out of a building, or the side which contains the chief entrance. Sometimes, however, it is used for whatever side presents to the street, garden, court, &c, or is opposite to the eye.

Face, in fortification, an appellation given to several parts of a fortress, as the face of a bastion, &c.

FACET, or Facette, among jewellers, the name of the little faces or planes to be found in brilliant and rose diamonds.

FACTITIOUS, any filing made by art, in opposition to what is the produce of nature. Thus, factitious cinnabar is opposed to native cinnabar. See Cinnabar.

FACTOR, in commerce, is an agent or correspond, nt residing beyond the seas, or in some remote part, commissioned by merchants to buy or sell goods on their account, or assist them in carrying on their trade.

A factor, in law and in merchandise, is one authorized to sell goods and merchandise, and otherwise act for his principal, with an allowance or commission

for, his care. He must pursue his orders strictly. He is accountable for all lawful goods coming to his hands ; yet if the factor buy goods for his principal, and they receive damage in his possession, through no negligence of his, the principal shall bear the loss; and if a factor is robbed, he shall be discharged: if a factor act contrary to his orders in selling goods, he is liable for the loss, though there may be a probability of advantage by his act: so he is liable for not making insurance, if ordered to do so.

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, Peters burgh, Dantzic, and Amsterdam, all endowed with certain privileges. The ascendency of the French Emperor, for the present, at least, has put an end to these, or to the most of them. We trust, however, that 'd change of circumstances may hereafter place things on their old footing.

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 fitculties, who has a power of granting dispensations in divers cases, as to marry without the bans being first published; to eat flesh on days prohibited; to ordain a deacon under age; for a son to succeed his father in his benefice; a clerk to hold two or more livings, &c.

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 there

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