Page:Cyclopaedia, Chambers - Volume 1.djvu/735

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Sins ; and after feveral Ceremonies, made an Atonement for all the People to waSh them from their Sins.

Expiation, among the Heathens, was a Purification ufed for effacing, or abolishing of a Crime.

It was pracfifed with divers Ceremonies : The mcft ufual was Ablution. See Aelution.

Expiations were perform'd for whole Cities, as well as particular Perfons.

After the young Horatius had been abfblved by the People from the Murther of his Sitter ; he was further pu- rified by the feveral Expiations prefcribed by the Laws of the Pontifices for involuntary Murthers. Halicarnafs.

EXPILATION, in the Civil Law, the Afl of With- drawing, or diverting any Thing belonging to an Inheri- tance, before any Body had declared himfelf Heir thereof. This made a peculiar Species of Theft : For there cou'd not properly be a Theft in taking a Thing not pof- fefs'd by any Body ; or ere the Inheritance was accepted. For this Reafon, the Roman Legislature introduced the Action of Expilation, for the Punishment of this Crime.

EXPIRATION, in Medicine, that Motion in an Ani- mal, whereby the Air, infpired into the Lungs, is expell'd, or thruft out of the fame, and the Cavity of the Brcaft contracted. See Lungs.

Refpiration confifts of two alternate Motions, or Actions of the Lungs, correfponding to thofe of a Pair of Bel- lows 5 Inspiration, whereby the Air is drawn in ; and Expiration, whereby 'tis driven out again. See Respi- ration.

By Means of this .Alternation, the Circulation of the Blood, and the Motions of the Heart are maintained. See Circulation and Heart.

Expiration, is alfo ufed figuratively, for the End of a Term of Time granted, agreed on, or adjudged. — 'Tis not above eight Days, till the Expiration of the Term of his Imprilbnment. The Term of fuch a Bill of Ex- change is expired, i.e. it is fallen due. See Bill.

EXPLICIT, in the Schools, fomcthing clear, diltinfl, formal, and unfolded. — The Will, Intention, &c. is faid to be Explicit, when 'tis fully explain'd, in proper Terms ; and implicit, when 'tis only learnt by Deductions and Confequences.

The Jews had not all an Explicit Knowledge of Jefus Chrift, but they had at leaSt an implicit one.

Such a Teflator has declared his Will explicitly, i. e. in formal Terms ; there is 110 need to have Recourfe to Explications.

EXPLOSION, in Phyficks, the Action of a Thing that drives another out of the Place it before poffefs'd.

The Term is chiefly ufed for the going off of Gun- Powder, and the Expulsion of the Ball, Shot, or the like Confequent thereon. See Gun-Powder.

Hence the Word comes likewife to be figuratively ufed to exprefs Such fudden Actions of other Bodies, as have fome Refemblance thereto ; as thofe which ferment with Violence, immediately upon their Mixture, and occafion a crackling Sound.

Some Writers have likewife applied it to the Excursions of the Animal Spirits, and inSSantaneous Motions of the Fibres, arising without the Direction of the Mind; but the Term then becomes too figurative to exprefs any determinate Idea, fo as really to inform the Understanding.

EXPOLITION, in Rhetoric, a Figure, whereby we explain the fame Thing in different PhraSes and Expres- sions, in order to Shew it more fully.

Expolition was the favourite Figure of "Balzac — A Man, but moderately verfed in the Style of Scripture, will 'perceive that this is no more than an Expolition ; that is, a Figure whereby the facred Author explains the fame Thing in different Terms. The Scriptures are full of fuch Figures 5 and I fcarce think there is any one more ordinary. Souciet.

EXPONENT, in Arithmetic, or Exponent of a •Power, the Number which expreffes the Degree of the Power ; or which Shews how often a given Power is to be divided by its Root, ere it be brought down to Unity. See Power. , -

Thus the Exponent of a Square Number is 2 ; ot a Cube 3 : The Square being sa Power of the fecond De- gree ; the Cube of the third, ©c.

Exponent, is alfo ufed in Arithmetic, in the Same Senfe with Index, or Logarithm.

Thus a Series of Numbers in Arithmetical Progression, being placed under another Series in Geometrical Pro- greffion, are call'd the Exponents, Indices, or Logarithms thereof. See Index.

E. gr. In the two Progefflons,

Geom. 1, 2, 4, 8, 16, 32, 64, 128, 2.56, 512 jirith. o, 1, 2, s, 4, 5, 6, 7, 8, 9 o is the Exponent, Index, or Logarithm, oi the tint Term 1 ; ; that of the 6 th. 32, ckc.

Hence, Unity is to the Exponent of the Power, as the Logarithm of the Root, to the Logarithm of its Power : Confequently, the Logarithm of the Power is had, by multiplying the Logarithm of the Root by its Exponent ■ and the Logarithm of the Root is had, by dividing the Logarithm of the Power by its Exponent. See Loga- rithm.

Exponent of a Ratio, is the Quotient arifing upon a Division of the Antecedent by the Confequent.-- Thus, in the Ratio 3 to 2, the Exponent is 1 i ; and the Exponent of the Ratio 3 to 2, is f. See Ratio.

Hence, 1°. If the Confequent be Unity, the Antecedent is the Exponent of the Ratio. E. gr. The Exponent of the Ratio 4 to 1, is 4. And again : The Expo?ient of a Ratio is to Unity, as the Antecedent to the Confequent.

2 . Since, in a rational Ratio, the Exponent of the Ratio is had by dividing a rational Number by another rational ; the Exponent of a rational Ratio, is a rational Number.

EXPONENTIAL Calculus, at Calculus Exponentia- lis, is the Method of differencing Exponential Quantities, and of fumming up the Differentials of Exponentials* See Calculus.

Exponential Curve, is that defined by an Exponen- tial Equation — Tranfcendental Curves partake both of the Nature of Algebraic and Tranfcendent ones 5 Of the former, becaufe they confiSt of a finite Number of Terms,, tho' thofe Terms themfelves are indeteterminate ; and of the latter, becaufe they cannot be Algebraically con- structed. See Curve.

Exponential Equation, is that wherein there is aft Exponential Quantity ; call'd alb a tranfcendental Equation, and by fome, a Geometrical Irrational. See Eqjiation, Transcendental, c^c.

Exponential Quantity, is a Power whofe Exponent is an indeterminate, variable, or flowing Quantity. See Quantity.

Exponential Quantities are of feveral Degrees and Orders; when the Exponent is a Simple indeterminate Quantity, it is call'd an Exponential of the firfl or lowed Degree.

When the Exponent it felf is an Exponential of the firfl: Degree, then the Quantity is an Exponential of the fecond Degree.

Thus *y is an Exponential of the firfl: Degree, be-

i caufe the Quantity y is a Ample Slowing Quantity. But zv is an Exponential Quantity of the Second Degree ; be-

i caufe y* is an Exponential of the firfl: Degree. So alfo z*

is an Exponential of the third Degree, the Exponent y* being one of the fecond.

EXPORTATION, in Commerce, the Aft of fending Commodities out of one Kingdom into another. See Commerce.

The Merchandizes yearly Exported from England are immenfe. — The principal Articles are Corn, Cattle,' Cloth, Iron, Lead, Tin, Leather, Coal, Hops, Flax, Hemp, Hats, Malt Liquors, FiSh, Watches, Ribbands, iSc.

The Woollen Manufacture alone, yearly Exported, is computed to amount to 200C000 Pound Sterling ; and Lead, Tin, and Coals, 500000 Pound. See Woollen.

Wool, Fullers Earth, ^Sc. are contraband Goods, /. e* prohibited to be exported. Sec Contraeand.

For the Duties of Exportation. See Duty.

EXPOSING, the fetting a Thing to publick View.

Perjury, Forgery, Libelling, falfe Weights and Meafures, are puniSh'd, by Expofwg the Criminal in the Pillory, to the Detifion of the People. See Pillory.

In the Romifi Church, the Sacrament is faid to 06 Expofed, when 'tis Shewn in public, uncover'd, on Feflivai Days, and during the Time of plenary Indulgences.

The Term is alfo ufed with a further Latitude : Thus, we fay, 'tis prohibited to Expofe falfe, or clipp'd Money.

Children are fometimes Expofed in the Streets; i. e; are left in the Streets, withDefign to be lofl. — Such a Houfe flands very high, and has a delicious Profpecf, but it is expofed to all the Four Winds. Such a City being on the Frontiers, and not fortified, is Expofed to the In- fults of every Party of Forces.

EXPOSITION, the Ad of Expofwg.— But the Term has a further Meaning; being likewife applied to the Interpretation, or Explication of an Aurhor, or a Paffage therein. r

Thus we fay, an Expofition of the 39 Articles, 0.- the Lord's Prayer, Sc. In which Sen<e we do not fay Expofmg, but Expounding. See Exposure.

EXPOSITOR, or Expository, a Title fome Writers have given to a' little Kind of Dictionaries, or Vocabti-

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