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or deficient. Thus 12 is an abundantimPerfect number, because the sum of its parts 1 + 2 + 3 + 4 + 6 = 16, which is greater than 12. But 10 is a deficient imperfect number, because 1 + 2 + 5 = 8 only, which is less than 10. IMPERSONAL verb, in grammar, a verb to which the nominative of any certain person cannot be prefixed; or, as others define it, a verb destitute of the two first and primary persons. IMPETIGENES, in medicine, descriptive of those disorders, which, from a general bad habit, manifest themselves principally, by disfiguring the skin and external parts of the body. IMPETUS, in mechanics, the force with which one body impels or strikes another. IMPLEAD, to sue or prosecute by course of law. IMPLICATION, in law, is where the law implies something that is not declared between parties in their deeds and agreements, and when our law gives any thing to a man, it gives, by implication, whatever is necessary for enjoying it. An implied contract is such, where the terms of agreement are not expressly set forth in words, but are such as reason and justice dictate, and which therefore the law presumes that every man undertakes to perform. Estates often arise by implication in a will, and sometimes in a deed; but they are more readily implied in the former than in the latter, in which the words must be more strict. IMPONDERABLE substances. SU asTANCEs, imponderable.

See

IMPORTATION, the act of bringing goods into a country from foreign parts. It has generally been considered, that for any country to carry on a profitable trade, it is necessary that the value of the goods sent out of it should be greater than that of the articles imported: this, however, is a very erroneous axiom, unless it is understood with great limitations. All articles of merchandize, imported merely for re-exportation, and also such as are used or worked up in British manufactures, are far from being hurtful to their commerce, and may even, in many respects, be deemed of equal profit with their own native commodities. It is therefore an excess of such importations alone, as are either for mere luxury, or mere necessity, or for both together, which is disadvantageous to the country, and not such importations as, like many of theirs, consist of raw silk, Spanish wool, cotton, wool and yarn, mohair, flax and hemp, oils, potash, dyeing stuffs, naval stores, &c. either used in their ship-building, or worked up in their manufactures, a principal part of which are for exportation: neither can their importations of East India goods and colonial produce, which are chiefly designed to be afterwards exported, be deemed unprofitable, but are, on the contrary, some of the most lucrative branches of their foreign trade. The following statement of the total value of the imports of England, in the year 1354, furnishes a good comparison with their present magnitude.

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part. IMPOSSIBLE roots, in algebra. To discover how many impossible roots are contained in any proposed equation, Sir Isaac Newton gave this rule in his algebra, viz. Constitute a series of fractions, whose denominators are the series of na: tural numbers, 1, 2, 3, 4, 5, &c. continued to the numbershowing the index or expoment of the highest term of the equations, and their numerators the same series of numbers in the contrary order; and divide each of these fractions by that next before it, and place the resulting quotients over the intermediate terms of the equation; then, under each of the intermediate terms, if its square multiplied by the fraction over it be greater than the product of the terms on each side of it, place the sign +3 but if not, the sign and under the first and last term place the sign +. Then will the equation have as many imaginary, roots, as there are changes of the underwritten signs from +to-, and from-to +. So for the equation a 3—4 co -- 4:r-6 =0, the series of fractions is 3,3,4 : then the - - To go second, divided by the first, gives, # or +,

and the third divided by the second give: # also ; hence these quotients, placed ëver the intermediate terms, the wholo will stand thus: 1. 3. --to+- -H Now because the square of the second term, multiplied by its superscribed frac. tion, is of r", which is greater than 4 r", the product of the two adjacent orno therefore the sign + is set below the second term, and because the square of the third term, multiplied by its over written fraction, is of r", which is less than 24r, the product of the terms on each side of it; therefore the sign - is placed under that term; also the sign + is set under the first and last terms. Hence the two changes of the underwritten signs ++---, the one from + to -, and the other from - to +, show that the given equation has two impossible roots. When two or more terms are wanting together, under the place of the first of. the deficient terms write the sign —, under the second the sign +, under the third —, and so on, always varyin the signs, except that under the last of the doñcient terms must always be set the sign +, when the adjacent terms on both sides of the deficient terms have contrary signs. As in the equation, ro-Hart # 3: ; +a;=0, + +---- + which has four imaginary roots. IMPOSTS, in architecture, the capitals of pillars, or pilasters, which support arches. An impost, sometimes called chaptrel, is a sort of a plinth, or little corniche, which crowns apier, and supports the first stone whence an arch or vault commences the imposts are conformable to their proer orders. The Tuscan has only * plinth; the Doric has two faces crowned; the Ionic, a larmier, or crown over the two faces, and its mouldings may be oar'. ed; the Corinthian and Composite,ho a larmier, frieze, and other mouldings. See ARchitectURE. IMPOTENCY, in the ecclesiastical law, signifies an inability of generation, or propagating the species, which is a cause of divorce a vinculo matrimonii, as being merely void, and therefore needs only a sentence declaratory of its being so. iMPRESSING men. The power of impressing seamen for the sea-service, by the King's commission; has been a oatter of some dispute, and submitted" with great reluctance, though it has very clearly and learnedly been shown by Sit Michael Foster, that the practice of impressing, and granting power to the Admiralty for that purpose, is of a very ancient date, and has been uniformally continued, by a regular series of precedents, to the present time, whence he concludes it to be part of the common law. The difficulty arises from hence, that no statute has expressly declared this power to be in the crown, though many of them very strongly imply it. The statute 2 Richard Il. c. 4, speaks of mariners being arrested and retained for the king’s service, as of a thing well known and practised without dispute, and provides a remedy against their running away. By statute 2 and 3 Philip and Mary, c. 16, if any waterman, who uses the river. Thames, shall hide himself during the execution of any commission for pressing for the king’s service, he is liable to heavy penalties. By statute 5 Elizabeth, c. 6, no fisherman shall be taken by the queen's commission to serve as a mariner; but the commission shall be first brought to two justices of the peace, inhabiting near the sea coast where the mariners are to be taken, to the intent that the justices may choose out and return such a number of able bodied men as in the commission are contained, to serve her majesty. And by statute 7 and 8 William, c. 21; 2 Anne, c. 6; 4 and 5 Anne, c. 19; 13 George II. c. 17, especial protections are allowed to seamen in particular circumstances, to prevent them from being impressed. All which do most evidently imply a power of impressing to reside o ; and if any where, it must, from the spirit of our constitution, as well as from the frequent mention of the king's commission, reside in the crown alone. The Liverymen of London claim an exemption from being impressed; but, by a late decision of the Court of King’s Bedch, this exemption is denied. Landmen, entering into the merchant service, and apprentices, are exempt for two years from the impress, and all apprentices to the sea-scrvice under eighteen.

IMPRESSION denotes the edition of a book, regarding the mechanical part only: whereas edition, besides this, takes in the care of the editor, who corrected or auginented the copy, adding notes, &c. to render the work more useful.

IMPRISONMENT, is the restraint of a man’s liberty under the custody of another, and extends not only to a gaol, but a house, stocks, or where a man is held in the street, or any other place; for in all these cases the party so restrained is said

to be a prisoner, so long as he hath not his liberty freely to go about his business, as at other times. None shall be imprisoned but by the lawful judgment of his peers, or by the law of the land. IMPROPRIATION, is properly so called, when a benefice ecclesiastical is in the hands of a layman; and appropriation, when in the hands of a bishop, college, or religious house; though sometimes these terms are confounded. It is said there are three thousand eight hundred and fortyfive impropriations in England. IMPULSE, in mechanics, the single and instantaneous action, or force by which a body is impelled, in contradis. tinction to the application of continued forces. INACCESSIBLE, something that cannot be come at, or approached, by reason of intervening obstacles, as a river, rock, &c. . It is chiefly used in speaking of heights and distances. See Sunvexing. INARCHING, in gardening, is a method of grafting, commonly called grafting by approach, and is used when the stock intended to graft on, and the tree from which the graft is to be taken, stand so near, or can he brought so near, that they may be joined together. The method of performing it is as follows: take the branch you would inarch, and having fitted it to that part of the stock where you intend to join it, pare away the rind and wood on one side, about three inches in length. After the same manner cut the stock, or branch in the place where the graft's to be united, so that the rind of both may join equally together; then cut a little tongue upwards in the graft, and make a notch in the stock to admit it; so that when they are joined, the tongue will prevent, their slipping, and the graft will more closely unite with the stock. Having thus placed them exactly together, tie them with some bass, or other soft, tying; then cover the place with grafting clay, to prevent the air from entering to dry the wound, or the wet from getting in to rot the stock: you should also fix a stake in the ground, to which that part of the stock, together with the graft should be fastened, to prevent the win from breaking them asunder, which is often the case when this precaution is not observed. In this manner they are to remain about four months, in which time they will be sufficiently united, and the graft may then be cut from the mother tree, observing to slope it off close to the stock; and if at this time you cover the joined parts with fresh grafting clay, it will be of great service to the graft.

IN AUTER DROIT, in another's right, as where executors or administrator sue for a debt or duty, &c. of the testator or intestate. INCEST, is the carnal knowledge of persons within the Levitical degrees of kindred. These, by our law, are totally prohibited to marry with each other; and sentence of divorce, in such case, is only declatory of the illegality of the marriage, for the marriage itself is void ab initio. INCH, a well known measure of length, being the twelfth part of a foot, and equal to three barley-corns in length. See MEAsunre. INch of candle, or sale by inch of candle. See CAN ble. INCHASING. See Exch. As ING. INCIDENCE, in mechanics, denotes the direction in which one body strikes on another. See MechAN1cs and Optics. It is demonstrated that the angle of incidence is equal to the angle of reflection, and that they both lie in the same plane. That the sines of the angles of incidence and refraction are to each other, either accurately or nearly, in a given or constant ratio: that from air to glass, the sine of the angle of incidence is to the sine of the angle of refraction as 14.9. INCIDENT, signifies a thing necessarily depending upon another as , more rincipal. For instance, a court baron, is an incident to a manor, and a court of pye-powder, to a fair, so inseparably, that they cannot be severed by grant. INCINERATION, in chemistry, a term applied to the burning of vegetables for the sake of their ashes: it is usually referred to the burning of kelp on the coasts for making mineral alkali. INCLINATION, is a word frequently used by mathematicians, and signifies the mutual approach, tendency, or leaning of two lines, or two planes, towards each other, so as to make an angle. , Inclination of a right line to a plane, is the acute angle which that line makes with another right line drawn in the plane through the point where the inclined line intersects it, and through the point where it is also cut by a perpendicular, drawn from any point of the inclined line. . Inclination of the axis of the earth, is the angle which it makes with the plane of the ecliptic; or the angle contained between the planes of the equator and ecliptic. Inclination of a planet, is an arch of the circle of inclination, comprehended between the ecliptic and the plane of a planet in its orbit. See AsraoxoMr.

INCLINED plane, in mechanic, some that makes an oblique angle with the horizon. If a force, with a given direction, supports a weight upon an inclined plane, that force is to the weight as the sine of the inclination of the plane to the sine of the angle which is made by the line in which the force acts, and the line perpendicular to the plane. See MechAN1cs.

INCLOSURES. Any person who shall wilfully or maliciously demolish, pull down, or otherwise destroy or damage, any fence raised or made for dividing or inclosing any common, waste, or other lands, in pursuance of any act of parliament, or shall cause or procure the same to be done, shall be guilty of felony, and transported for seven years. Prosecution to be commenced in eighteen months af. ter the offence committed.

INCOMBUSTIBLE. Something that cannot be burnt, or consumed by fire. Authors talk much of an incombustible cloth, made of the asbestus. See Asbes

TUs. INCOMBUSTIBLES, simple. See Sunst Ances, simple. INCOME tar, a direct contribution of a certain proportion of the annual gains of individuals for the public service, which has recently become an important branch of the revenue of Great Britain. An attempt was made in 1702 to levy a tax of this description; but it proved very unproductive, and therefore was discontinued. Towards the end of the year 1798, Mr. Pitt proposed, in lieu of the addition. al assessed taxes, a general tax on income, whether arising from land, personal property, or from any profession, office, trade, or other employment. The act was passed 9th January, 1799; and the duties imposed by it were ten per cent. on all incomes of 2001 per annum and upwards, and lesser proportions on incomes between that amount and 601 per annum, which paid a one-hundred and twentieth [. or ten shillings per annum : incomes elow 60l. a year were wholly exempt. The great object of this tax was, to raise a considerable proportion of the public supplies within the year, and to liquidate within a short time what might be further raised by loan; with the latter view, the payment of the interest, and redemption of the capital, of part of the loans for the years 1798, 1799, and 1800, was charged on the produce of the tax; but it being a tax, which, from its commencement, had been very unpopular, both from its weight and the disclosure of the circumstances of individuals with which it was attended, it was repealed in April, 1802, and the charges upon it transferred to the Convolidated Fund.

In 1803 the income tax was revived, with some alterations in the mode of collecting it, under the title of the property tax: the rate at which it was now imposed was 5 per cent. on all incomes above 150l. per annum, and lesser proportions on incomes between that amount and 60l. per annum. In 1805 it was increased to 64 per cent.; and in 1806 it was raised to the original rate at which it had been imposed, or 10 per cent., while the scale of lesser rates was made to comprehend all incomes amounting to 50l. per annum. By this means, and by deducting the tax on the dividends of the public funds at the Bank, and abolishing most of the former abatements and exemptions, the sum raised by it has been considerably augmented, the estimated produce being as follows:

1804 at 1s. in the pound L. 4,650,000 1805 at 1s. 3d. ditto........ 5,937,500 1806 at 2s.......ditto........ 11,500,000

An income tax, if it could be so regulated as to bear a just proportion to the different modes in which the incomes of individuals arise, and did not extend to such amounts of income as are absolutely necessary for subsistence, would become the most equitable, as well as the most productive mode of taxation. INCOMMENSURABLE, a term in geometry, used where two lines, when compared to each other, have no common measure, how small soever, that will exactly measure them both. And in general two quantities are said to be incommensurable, when no third quantity can be found that is an aliquot part of both. Such are the diagonal and side of a square; for though each of those lines have infinite aliquot parts, as the half, the third, &c. yet not any part of the one, be it ever so little, can possibly measure the other, as is demonstrated in prop. 117. lib. x, of Euclid. IN.com MENsu RABLE numbers, are such as have no common divisor that will divide them both equally. INCOMPLETE, in botany, a term used to denote the sixteenth class of the Linnaen “methodus calycina,” consisting of lants whose flowers want either the cayx or petals. INCORPORATION, power of To the erection of any corporation the King’s consent is necessary, either impliedly or expressly given: the King's implied con

sent is to be found in corporations which

exist by force of the common law, to which the former kings are supposed to have given their concurrence ; of this sort are all bishops, parsons, vicars, churchwar. ‘lens, and some others, who, by common law, have ever been held to have been corporations by virtue of their office. Another method of implied consent is with regard to all corporations by prescription ; such as the city of London, and many others, which have existed as corporations for time immemorial; for though the members thereof can show no legal charter of incorporation, yet, in cases of such high antiquity, the law presumes there once was one, and that, by variety of accidents, which a length of time may produce, the charter is lost or destroyed. The methods by which the King's consent is expressly given are either by act of parliament or charter; but the immediate creative act is usually F. by the King alone, in virtue of is royal prerogative. See further, Joint Stock. INCREMENT, is the small increase of a variable quantity. Sir Isaac Newton calls these increases “moments,” and observes, that they are proportional to the velocity or rate of increase of the flowing or variable quantities, in an indefinitely small time. The notation of increment is different by different authors. The method of increments is a branch of analytics, in which a calculus is founded on the properties of successive values of variable quantities, and their differences, or increments. It is nearly allied to the doctrine of fluxions, and, in truth, arises out of it. Of the latter the great Newton was the inventor; of the former we have different treatises by Dr. Taylor, Mr. Emerson, and . others. We shall give Mr. Emerson’s observations on the distinction between the method of increments and fluxions. “From the method of increments,” he says, “the principal foundation of the method of fluxions may be easily derived; for, as in the method of increments, the increment may be of any magnitude, so in the method of fluxions it must be suposed infinitely small; whence all preceding and successive values of the variable uantity will be equal, from which equality the rules for performing the principal operations of fluxions are immediately deduced. That I may give the reader,” continues he, “a more perfect idea of the nature of this method: suppose the ab

'scissa of a curve be divided into any num

ber of equal parts, each part of which is called the increment of the abscissa, and

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