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Showing the present Value of 11, to be received at the end of any Number of Years not exceeding a Hundred, discounting at the rate of 5 per cent. Compound

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Er. 1. A person is entitled to receive 1000l. at the end of seven years from the present time; what sum paid him immediately would be equivalent thereto 1000 x .710681 = 710l. 13s. 7+d. Er. 2. What is the present worth of 2221. 10s. payable 15 years hence 2 222.5 × .481017 = 1071. 0s. 64d.

Fr. 3. What is the present value of 13921. 19s. 7d. to be received at the expiration of 21 years 2 1392.98 × .358942 = 500l.

Tables showing the present value or amount of annual payments of compound interest are given under the articles ANNutti Es and LEAs Es.

It is not legal to lend money at compound interest, but in granting or pur

chasing annuities, either for lives or terms
of years, it is always usual to compute
their value at compound interest; this is
particularly the case with respect to sums
of money which are not receivable till
some future period. See Revensions.
INTERest, in law, is usually taken for a
term, or chattel real, and more particu-
larly for a future term.
INTERest of money, is the premium paid
for the use of a sum, and is by law, in this
country, limited strictly to five per cent.
per annum. See Usuay.
Where an estate is devised for pay-
ment of debts, chancery will not allow in-
terest for book debts. In case of a vested
legacy, due immediately, and charged on
land, or money in the funds, which yield
an immediate profit, interest shall be pay-

able thereon from testator's death; but if charged only on the personal estate, which cannot be immediately got in, it shall carry interest only from the end of the year after the death of the testator. Where lands are charged with payment of a sum in gross, they are also chargeable in equity with payment of interest for such sum. INTERJECTION, in grammar, an indeclinable part of speech, signifying some passion or emotion of the mind. As the greatest part of the expressions used on these occasions are taken from nature alone, the real interjections, in most languages, are monosyllables ; and as all nations agree in these natural passions, so do they agree in the signs and indications of them, as of love, mirth, &c. See GRAMIn Art. INTERLOCUTORY judgments, in law, are such as are given in the middle of a cause, upon some plea, proceeding, or default, which is only intermediate, and does not finally determine or complete the suit. INTERLUDE, an entertainment exhibited on the theatre between the acts of a play, to amuse the spectators while the actors take breath and shift their dress, or to give time for changing the scenes and decorations. INTERMEDIATES, in chemistry, a term made use of when speaking of chemical affinity. Oil, for example, has no affinity to water, unless it be previously combined with an alkali, it then becomes soap, and the alkali is said to be the intermedium which causes the union. INTERNAL, in general, signifies whatever is withi" a thing. Euclid (lib. i. prop. 32) proves, that the sum of the three angles of every triangle is equal to two right angles; whence he deduces several useful corollaries.—He likewise deduces from the same proposition, this theorem, viz. that the sum of the angles of every rectilinear figure is equal to twice as many right angies as the figure hath sides, excepting or subtracting four. INTERPOLATION, among critics, denotes a spurious passage, inserted into the writings of some ancient author.— One great rule with regard to the expunging interpolations is, that the restitution be perfectly agreeable to the rest of the work. INTERPolation, in algebra, is used for finding an intermediate term of a series, its place in the series being given. INTERROGATION, or point of INTEnWOL. VI.

noGATION, in grammar, a character of this form (?) serving to denote a question. INTERRogation, in rhetoric, is a figure, whereby the orator proposes something by way of question; which, it must be owned, greatly enlivens the discourse. INTERSECTION, in the mathematics, signifies the cutting of one line or plane by another. Thus, we say, that the mutual intersection of two planes is a right line. The centre of a circle, or conic section, &c. is the intersection of two diameters; and the central point of a quadrangle is the intersection of two diagonals. INTERVAL, in music, the difference between two sounds, in respect of acute and grave; or that imaginary space terminated by two sounds, differing in acuteness or gravity. When two or more sounds are compared in this relation, they are either equal or unequal in the degree of time; such as are equal are called unisons, with regard to each other, as having one tune; the other, being at a distance from each other, constitute what we call an interval in music; which is properly the distance in time between two sounds. Intervals are distinguished into simple and compound. A simple interval is without parts or divisions. Such are the octave, and all that are within it; as the second, third, fourth, fifth, sixth, and seventh, with their varieties. A compound interval consists of several lesser intervals; such are all those greater than the octave, as the ninth, tenth, eleventh, twelfth, &c. with their varieties. INTESTINA, in natural history, the first of the five orders of the class Ver

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We refer the reader to the articles under these words in the alphabetical order; but having omitted CARyophyllous, we insert it here : Body round; mouth dilated and fringed. One species, viz. C. piscium, which inhabits the intestines of various fresh water fish, as the carp, tench, bream, &c.; the body is clay colour, about an inch long, rounded at the hind part, and broader before.

INTESTINES, in anatomy, long cylindrical, hollow, and membranaceous bodies; or rather one such continued body, or tube, reaching from the stomach to the anus. See ANAToMr.

INTORSION, in botany, a term used to denote the bending of any of the parts of a plant towards one side. This admits of certain distinctions. 1. Twining stems which bend towards the left, as in hops, honey-suckle, &c.; but in the kidneybean, convolvulus, &c. they bend to the right. 2. Twining tendrils, which bend to the right and back again ; of this kind are the tendrils of most of the pea-bloom or leguminous tribe of plants. 3. Twisted flowers in the periwinkle ; the petals bend to the left; the pointal in the viscous campion is twisted to the left, as the seed-bud is in the screw-tree. In oats, the beard which terminates the husk is twisted like a rope. This species of contortion being effected by the moisture or dryness of the atmosphere is denominated by Linnaeus, “intorsio hygrometrica.” Another species of intorsion is the ap

earance of the petals in the violet, basil, K. in which the upper lip of the corolla looks to the ground, and the under lip upwards.

INTRA1)0S, in architecture the interior and lower side, or curve, of the arch of a bridge; in contradistinction from the extrados, or exterior curve, or line, on the upper side of the arch.

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intervention of any other; in which case the mind perceives the truth as the eye doth the light, only by being directed to. wards it. Thus the mind perceives that white is not black, that three are more than two, and equal to one and two. This part of knowledge, says Mr. Locke, is irresistible, and, like the sunshine, forces itself immediately to be perceived, as soon as ever the mind turns its view that way. It is on this intuition that all the certainty and evidence of our other know. ledge depends; this certainty every one finds to be so great, that he cannot imagine, and therefore cannot require, a greater. INVECTED, in heraldry, denotes a thing fluted, or furrowed. Invected is just the reverse of ingrailed, in which the points are turned outward to the field, whereas in invected, they are turned inward to the ordinary, and the small semicircles outward to the field. INVECTIVE, in rhetoric, differs from reproof, as the latter proceeds from a friend, and is intended for the good of the erson reproved; whereas the invective is the work of an enemy, and entirely designed to vex and give uneasiness to the person against whom it is directed. INVENTION, denotes the act of finding anything new, or even the thing thus found. Invention is, according to lord Bacon, of two very different kinds, the one of arts and sciences, the other of arguments and discourse : the former he sets down as absolutely deficient. That the other part of knowledge is wanting, says he, seems clear; for logic professes not, nor pretends to yo, either mechanical or liberal arts; nor to deduce the operations of the one, or the axioms of the other, but only leaves us this instruction, “To believe every artist in his own art.” His lordship further maintains, that men are hitherto more obliged to brutes than reason for inventions. Whence those who have written concerning the first inventors of things, and origin of sciences, rather celebrate chance than art, and o beasts, birds, fishes, and serpents, rather than men, as the first teachers of arts. No wonder, therefore, as the manner of antiquity was to consecrate the inventors of useful things, that the Egyptians, to whom many arts owe their rise, had their temples filled with the images of brutes, and but a few human idols amongst them. Invention is, therefore, used for a subtlety of mind, or somewhat peculiar in a man's genius, which leads him to the discovery of things new ; whence we say a man of invention. Invention, according to Du Bos, is that part which constitutes the principal merit of works, and distinguishes the great genius from the simple artist. Investion, in rhetoric, being one of the second divisions of invention, according to Bacon, signifies the finding out and choosing of arguments which the orator is to use for proving his point, in moving his hearers’ passions. This invention, in the opinion of that philosopher, cannot properly be called invention, which is the discovery of things not yet known, and not the recollecting things that are known: the only use and office of this rhetorical invention being, out of the stock of knowledge already laid up, to select such articles as ... make for the purpose. The same author divides the method of procuring a stock of matter for discourse into two; the first of which is either by marking out and indicating the parts wherein a thing is to be searched after, which he calls the topical way; and the second is by laying up arguments for use that were composed before hand, and which he calls the promptuary way. INvention, in poetry, is o: to whatever the poet adds to the history of the subject he has chosen, as well as to the new turn he gives it. INvestron, in painting, is the choice which the painter makes of the objects that are to enter the composition of his piece. IN VENTRE SA MERE, is where a woman is with child at the time of her husband’s death; which child, if he had been born, would be heir to the land of the husband. A devise to an infant in ventre sa mere is good, by way of future executory devise. And where a daughter comes into land by descent, the son, born after, shall put her out, and have the land. INVERSE, is applied to a manner of working the rule of three, or proportion, which seems to go backward, or contrary to the order of the common or direct rule. See PRoPontiox. INvehse proportion, or INvensE ratio, in philosophy, is that in which more requires jess, or less requires more. Thus, in the case of light and heat flowing from a luminous body, the light and heat are less at a greater distance, and greater at a less distance ; so that in this instance more gives less, or a greater distance receives sess light and heat; and less gives more, that is, a person coming nearer the illuminated body receives more light and

heat than he would at a greater distance. This is expressed in different books, in different ways, sometimes by the term inversely, sometimes by the term reciprocally; as in the case referred to, we say the light and heat are inversely, or reciprocally, as the square of the distance, or in the inverse, or reciprocal, duplicate ratio of the distance. iNVERSION, or, as it is in Euclid, invertendo, or by inversion, is inverting the terms of a proportion by changing the antecedents into consequents, and the consequents into antecedents: thus if a : b :: c : d 4 : 9 ::12: 27 Then by inversion it will be b: a 3: d : c 9 : 4 :: 27 : 12 INVERsion, in music, is a changed position either of a subject or of a chord. The inversion of a subject is produced by giving it a higher or lower situation among the several parts of a score, sometimes making it the bass, at other times the tenor, counter-tenor, or the treble. The inversion of a chord is that changed position of its compotent parts, with respect to its fundamental bass, by which, though the harmony remain the same, the intervals are varied, and the compound assumes another name. INVERsroN, in grammar, is where the words of a phrase are ranged in a manner not so natural as they might be. It is a considerable beauty, either in verse or prose, when we have it from an able hand; it gives vigour and variety to a sentence, and keeps the mind in an agreeable suspense and expectation of a marvellous turn and conclusion. INVESTIGATION, properly denotes the searching or finding anything out by the tracks or prints of the feet; whence mathematicians, schoolmen, and grammarians, come to use the term in their respective researches. INVESTITURE, in law, is the giving possession of lands by actual seisin. The ancient feudal investiture was, where the vassal or descent of lands was admitted in the lord’s court, and there received his seisin, in the nature of a renewal of his ancestor's grant, in the presence of the rest of the tenants; but in after-times, entering on any part of the lands, or other notorious possession, was admitted to be equivalent to the formal grant of seisin or investiture. INULA, in botany, common inula, or elecampane, a genus of the Syngenesia Polygamia Superflua class and order. Natural order of Composita: Discoidex. Corymbiferr, Jussieu. Essential character: receptacle naked : down simple : anthers ending in two bristles at the base. There are thirty-four species; these are generally herbaceous plants; leaves simple, alternate ; flowers yellow, axillary, or terminating frequently in corymbs. I. helenium, common inula, or elecampane, has a perennial, fusiform, branching, aromatic root; according to some botanists it is biennial. It is from three to five feet high, and one of the largest of our herbaceous plants; lower leaves on foot stalks, lanceolate, a foot long, and four inches broad in the middle; flowering heads very large, single, terminating the stem and branches; flow.rets all yellow, those of the ray narrow, linear, from an inch to an inch and an half in length, with three sharp teeth at the end; pappus, egret or down white, twice as long as the seed, appearing to be capillary but when viewed with a glass, finely toothed on one side, shorter than the florets, sessile. Native of Japan, Denmark, Germany, Flanders, &c. The official name is enula campana, whence our English name elecampane is derived. INUNDATAE, in botany, the name of the fifteenth order in Linnaeus’s “ Fragments of a Natural Method,” consisting of plants which grow in the water. Among these may be mentioned, the ceratophyllum, horned pond-weed, and elatine, water-wort. The plants of this order are, as the name imports, aquatic, low, herbaceous, and mostly perennial; the roots are fibrous ; the stem is usually wanting, and in its stead is an assemblage of leaves, which, unfolding one another mutually, form a sheath, from the middle of which is produced the foot-stalk of the flower; the leaves are sometimes alternate, sometimes placed in whorls round the stem ; the flowers are hermaphrodite in some, as the pond-weed ; and on others, the male and female are in the same root; the flowers, in some cases, proceed singly from the wings of the leaves, as in the ceratophyllum, elatine, and hippuris; those of the lower leaves of the myriophillum, water-miltoil, are female ; those of the upper, male. The zannichellia, triple-headed pond-weed, has two flowers in the same wing ; one inaie and the other female. The flowers in potamogeton, pond-weed, and ruppia, are disposed in specks in the wings of the leaves; the flower-cup is either wanting, or consists of three, four, or five divisions or leaves ; the petals are generally wanting, but the elatine and pond-weed have four ; the stamina are in number from one to sixteen

and upwards; the seed.buds are from one to four; the style is frequently wanting, as the seed-vessel is universally, except in the elatine, which has a dry capsule, with four external openings, and the same number of cells; there are generally four seeds; but in the ceratophyllum the fruit is a nut or stone, egg-shaped, and containing a single cell. INVOICE, an account, in writing, of the particulars of merchandise, with their value, custom, charges, &c., transmitted by one merchant to another in a distant country. One copy of every invoice is to be inserted verbatim in the invoice-book, for the merchant’s private use ; and another copy must, immediately upon shipping off the goods, be dispatched by post, or otherwise, to the correspondent. This copy is commonly drawn out upon a sheet of large post paper, to the end of which is subjoined a letter of advice. It must here be observed, that when a merchant ships off goods for his own account, the invoice sent to the factor contains only the quantity of goods, but nothing of the cost and charges ; and the letter subjoined consists of instructions, signifying in what manner the employer inclines to have his goods disposed of, and returns made. INvoice book, this book is paged, and contains copies of the invoices of goods sent to sea; for as a merchant is obliged to send his correspondent an invoice of all the goods he consigns to him, so it is reasonable that he should keep a copy of it for himself. For the further uses of invoice-books, see Book of invoices. INVOLUCRUM. See. BotANY. INVOLUTE, figure or curve, in the higher geometry, is that which is traced out by the outer extremity of a string, as it is folded or wrapped upon another figure, or as it is unwound from offit. The involute of a cycloid is also acycloid equal to the former, a part that was discovered by Huygens, and by means of this he fell upon the plan of making a pendulum vibrate in the curve of the cycloid, and in equal times, whatever be the length of the curve. INVOLUTION in algebra, the raising a quantity from its root to any power assigned. See ALGERRA. JOIN FRY, the art of working in wood, or of fitting various pieces of timber together. It differs from the art of the carpenter, inasmuch as the joiner is employed chiefly in the inside work of a house, but the carpenter does the rough work, which, in general, requires more strength and less skill.

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