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of shield above, and a longitudinal flat dish beneath; aperture placed on the right side, within the shield; four feelers, situate above the mouth, with an eye at the tip of each of the larger ones. There are sixteen species; L. lævis: body black, and almost without wrinkles, found among the moss late in the autumn, five lines long; body glossy, with undulate, transverse striae on the shield; narrower and not so much wrinkled as the next. L. ater; body black and furrowed with deep wrinkles: of this species there are five or six varieties, differing in colour and size; the dusky-brown with a yellowish mouth, a streak on each side; is found in woods, meadows, fields, and gardens; is from one and a half to five inches long; crawls slowly, and leaves a slime upon whatever it passes over. L. alba, is white, and is found in woods and groves; from three to five inches long. L. hyalinus; body hyaline; feelers obselete, with a brown line reaching from the feelers to the shield; inhabits mossy places, and is very destructive to the young shoots of kidneybeans; belly with numerous interrupted wrinkles. L. agrestes; body whitish, with black feelers: five varieties, of which some have the power of secreting a large quantity of mucous from the under surface, and forming it into a thread like a spider's web; by this means it often suspends itself, and descends from the branches of trees, or any height it had crawled up to. It is found in gardens, pastures, and groves, from May till December. One of the varieties of this species is that which has been recommend ed to be swallowed by consumptive persons; it is half an inch long, and when touched it sticks as if dead to the fingers.

LIME, or calcareous earth, predominates in most stones which are soft enough to be scratched with a knife. These are chalk, lime-stone, marble, spars, gypsum, or plasterstone, and various others. As the lime is most frequently combined with carbonic acid, it is usual for mineralogists to drop a small quantity of nitric acid upon the stones they are desirous of classing; and if they froth by the escape of the acid, they conclude that lime enters into the composition. To obtain pure calcareous earth, powdered chalk must be repeatedly boiled in water, which will deprive it of the saline impurities it frequently contains. It must then be dissolved in distilled vinegar, and precipitated by the addition of concrete volatile alkali. The precipitate, when well washed and dried, will consist of lime united

to carbonic acid; the latter of which may be driven off by heat, if necessary.

If chalk, marble, lime-stone, spar, or any other specimens of this earth, containing carbonic acid, be exposed to continued ignition, they give out carbonic acid and water, to the amount of nearly half their weight. The remainder, consisting chiefly of lime, has a strong tendency to combination, and attracts water very powerfully. The addition of water to lime produces a very considerable heat, attended with noise, and agitation of the parts, which break asunder; a considerable vapour arises, which carries up with it part of the lime; and a phosphoric light is seen, if the experiment be made in the dark. Lime thus saturated with water is said to be slaked. Water dissolves about one five-hundredth part of its weight of lime, and is then called lime-water. This solution has an acrid taste, and turns syrup of violets to a green colour. If lime-water be exposed to the open air, the lime attracts carbonic acid, and is by this means converted into chalk; which, not being soluble in water, forms a crust on the surface, formerly called cream of lime, which, when of a certain thickness, breaks, and falls to the bottom: and in this way the whole of the lime will in time be separated. If the fire have been too violent in the burning of lime, the stones become hard, sonorous, and incapable of absorbing water with the requisite degree of avidity. This effect seems to arise from part of the calcareous earth having entered into fusion with the clay, flint, or other contaminating earths, with which it forms a glass that covers and defends the rest.

The paste of lime and water, called mortar, has a degree of adhesion and ductility, though much less than clay. When dry, it is more or less friable, like chalk. A mixture of sand, or broken earthen vessels, greatly increases its firmness, which it seems to effect by rendering it more difficult for the parts to be removed with respect to each other. When mortar is left to dry by the gradual evaporation of its superfluous water, it is very long before it obtains its utmost degree of firmness. But if dry quick-lime be mixed with mortar, it gradually absorbs the superfluous water, and the mass becomes solid in a very short time. See MORTAR.

Lime has an affinity for tannin, whence it is probable that a portion of it is retained in tanned leather, perhaps not to the improvement of its quality. It has an edul

corative power with respect to animal oils, by combining with the putrid gelatine in them; but its action on them in forming a soap is too strong to admit of its being used for this purpose with advantage, unless in small quantities. Feathers, however, may be very conveniently cleaned by steeping three or four days in strong lime-water, and afterward washing and drying them.

Though infusible in the strongest heats of our furnaces, it is nevertheless a very powerful flux with regard to mixtures of the other earths. These are all fusible by a proper addition of lime. Compounds are still more fusible; for any three of the five well-known earths may be fused into perfect glass, if they be mixed together in equal portions, provided the calcareous be one of them.

The earthy part of animals is chiefly, if not altogether, calcareous: in most cases it is united with phosphoric acid, but frequently with the carbonic.

LIME-stone. The native indurated carbonate of lime. It is usually more or less bluish from iron, and of a granulated fracture; and it is connected with lime by ignition in lime-kilns, for the purpose of making mortar. See LIME; also MORTAR.

LIMEUM, in botany, a genus of the Heptandria Digynia class and order. Natural order of Holoracæ. Portulaceæ, Jussieu. Essential character: calyx five-leaved; petals five, equal; capsule globular, twocelled. There are three species, all natives of the Cape of Good Hope.

LIMIT, in a restrained sense, is used by mathematicians for a determinate quantity to which a variable one continually approaches; in which sense the circle may be said to be the limit of its circumscribed and inscribed polygons. In algebra, the term limit is applied to two quantities, one of which is greater, and the other less, than another quantity; and in this sense it is used in speaking of the limits of equations, whereby their solution is much facilitated.

Let any equation, as x3-px × q x — r=o be proposed, and transform it into the following equation:

y'+Sey's c2y+e1 ́
-py-2pey — pe2
+qy+qe

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= 0.

Where the values of y are less than the respective values of x, by the difference e. If you suppose e to be taken such as to make all the coefficients of the equation of y positive, viz. e3 — pe2 + ge—r, 3 e2

2 pe+q, 3e -p; then there being no variation of the signs in the equation, all the values of y must be negative; and conse. quently the quantity e, by which the values of x are diminished, must be greater than the greatest positive value of x; and, consequently, must be the limit of the roots of the equation x3— p x2 + q x · -r=0.

It is sufficient, therefore, in order to find the limit, to inquire what quantity substituted for x, in each of these expressions x-p x2 + q x−r, 3 x2 - 2 p x + q, 3 x -P, will give them all positive; for the quantity will be the limit required.

m

Having found the limit that surpasses the greatest positive root, call it m. And if you assume y=m— -x, and for x substitute -y, the equation that will arise will have all its roots positive; because m is supposed to surpass all the values of x, and consequently m- x(y) must always be affirmative. And, by this means, any equation may be changed into one that shall have all its roots affirmative.

Or, if - n represent the limit of the negative roots, then by assuming y=x+n the proposed equation shall be transformed into one that shall have all its roots affirmative; forn being greater than any negative value of x, it follows that y=x+n must be always positive.

What is here said of the above cubic equation, may be easily applied to others; and of all such equations, two limits are easily discovered, viz. o, which is less than the least; and e, found as above, which surpasses the greatest root of the equation. But besides these, other limits still nearer the roots may be found; for the method of doing which, the reader may consult Maclaurin's Algebra.

LIMITATION, a certain time prescribed by statute, within which an action must be brought, which is generally twofold; first in writs, by several acts of parliament, and, secondly, to make a title to any inhe ritance, and that is by the common law.

On penal statutes, all actions, suits, bills, indictments, or informations, for any forfeiture limited to the king, his heirs or successors only, shall be brought within two years after the offence committed, and not after. All such actions, &c. except the statutes of tillage, which give the penalty to the king and a common informer, are limited to one year next after the offence committed; and if not sued for by the informer, they may be sued for by the king, any time within the two years, after that

year is ended: and where a shorter time is limited by any penal statute, the prosecution must be within that time. 31 Eliz. c. 5.

All actions of trespass, of assault, battery, wounding, imprisonment, or any of them, are to be commenced within four years next after the cause of such actions or suits, and not after: 21 James I. c. 16. All actions of trespass, quare clausum fregit; all actions of trespass, detinue, trover, and replevin; all actions of account, and upon the case, (other than such accounts as concern the trade of merchandise between merchant and merchant); all actions of debt, grounded upon any lending, or contract without specialty (that is, not being by deed or under seal); all actions of debt for arrearages of rent; and all actions of as sault, menace, battery, wounding, and imprisonment, shall be commenced within the time and limitation as followeth, and not after that is to say, the said actions upon the case (other than for slander), and the said actions for account, and the said actions for trespass, debt, detinue, and replevin, and the said action for trespass quare clausum fregit, within six years after the cause of such action; 21 James I. c. 16. In all these statutes there is an exception in relation to infants, lunatics, and femes coverts, allowing them a further time after they are in a situation which enables them to sue. As to the exception with respect to merchant's accounts, it extends to actions on accounts current only, in which the giving credit on one side is an acknowledgement of the debt on the other; but when the account is settled between merchant and merchant, it must be sued for like any other debt; and if all the articles are on one side, the account is not taken out of the statute. An acknowledgment of the debt prevents the operation of the statute of limitations, and also a payment upon account; but as it is convenient that suits should not be delayed so long that vouchers cannot be produced, settlements should regularly be enforced. A writ also may be sued out to save the statute of limitation, as it is called, and though never sued, yet, if it is regularly entered, and continued upon the record, the suit may be effectually prosecuted long after, and being commenced within time, the action may be maintained out. This is in conscience rather a mode of evading the statute. It is generally considered as an unfair defence to rely upon the statute, when the party has the

actual means of knowing whether the debt is due, and therefore a very slight acknowledgment removes the objection to the suit.

LIMNING, the art of painting in water colours, in contradistinction to painting, which is done in oil colours. See PAINT

ING.

LIMODORUM, in botany, a genus of the Gynandria Diandria class and order. Natural order of Orchideæ. Essential character: nectary one-leafed, concave, pedicelled, within the lowest petal. There are thirteen species.

LIMONIA, in botany, a genus of the Decandria Monogynia class and order. Essential character: calyx five-parted ; petals five; berry three-celled; seeds solitary. There are seven species, of which L. pentaphylla, five-leaved limonia, is an elegant fragrant shrub, very common in most uncultivated lands in Coromandel, but chiefly under large trees, where birds have dropped the seeds. It flowers all the year. The whole plant, when drying in the shade, diffuses a pleasant permanent scent; the flowers are exquisitely fragrant; birds eat the berries greedily.

LIMOSELLA, in botany, a genus of the Didynamia Angiospermia class and order. Natural order of Preciæ. Lysimachiæ, Jussieu. Essential character: calyx five cleft; corolla five-cleft, equal; stamina approximating by pairs; capsule one-celled, two-valved, many-seeded. There are two species, viz. L. aquatica, common mudwort, or bastard plantain; and L. diandria.

LINCONIA, in botany, a genus of the Pentrandria Digynia class and order. Essential character: petals five, with a necta reous excavation at the base; capsule twocelled. There is but one species, viz. L. alopecuroidea, a native of the Cape of Good Hope, in watery places among the mountains.

LINDERA, in botany, so named from J. Linder, a Swede, a genus of the Hexandria Monogynia class and order. Essential character: corolla six-petalled; capsule. There is only one species, viz. L. umbellata, a native of Japan.

LINDERNIA, in botany, a genus of the Didynamia Angiospermia class and or der. Natural order of Personatæ. ScroEssential character: phulariæ, Jussieu. calyx five-parted; corolla ringent, with the upper lip very short; stamina the two lower with a terminating tooth, and a sub-lateral

anther; capsule one-celled. There are three species.

LINE, in geometry, a quantity extended in length only, without any breadth or thickness. It is formed by the flux or notion of a point. See FLUXION.

LINES in perspective, are, 1. Geometrical line, which is a right line drawn in any manner on the geometrical plane. 2. Terrestrial line, or fundamental line, is a right line wherein the geometrical plane, and that of the picture or draught intersect one another, formed by the intersection of the geometrical plane, and the perspective plane. 3. Line of the front, is any right line parallel to the terrestrial line. 4. Vertical line, the common section of the vertitical and of the draught. 5. Visual line, the line or ray imagined to pass from the object to the eye. 6. Line of station, according to some writers, is the common section of the vertical and geometrical planes. 7. Objective line, the line of an object from whence the appearance is sought for in the draught or picture.

LINES, in dialling, are, 1. Horizontal line, the common section of the horizon and the dial plane. See DIALLING. 2. Horary lines, or hour-lines, the common intersections of the hour-circles of the sphere, with the plane of the dial. See HORARY. 3. Substylar line, that line on which the style or cock of a dial is duly erected, and the representation of such an hour circle as is perpendicular to the plane of that dial. 4. Equinoctial line, the common intersection of the equinoctial and plane of the dial.

LINE of measures, is used by Onghtred, to denote the diameter of the primitive circle in the projection of the sphere in plano, or that line in which the diameter of any circle to be projected falls. In the stereographic projection of the sphere in plano the line of measures is that line in which the plane of a great circle perpendicular to the plane of the projection, and that oblique circle which is to be projected, intersects the plane of the projection; or it is the common section of a plane passing through the eye point and the centre of the primitive at right angles to any oblique circle which is to be projected, and in which the centre and pole of such circle will be found.

LINE of direction on the earth's axis, in the Pythagorean system of astronomy, the line connecting the two poles of the eclipVOL. IV.

tic and of the equator when they are pro jected on the plane of the former.

LINE of direction, in mechanics, that wherein a body actually moves, or would move, if it were not hindered. It also denotes the line that passes through the cen tre of gravity of the heavy body to the centre of the earth, which must also pass through the fulcrum, or support of the heavy body, without which it would fall.

LINE of gravitation, of any heavy body, a line drawn through its centre of gravity, and according to which it tends downwards. LINE of the swiftest descent, of a heavy body is the cycloid. See CYCLOID.

LINES on the plain scale, are the line of chords, line of sines, line of tangents, line of secants, line of semitangents, line of leagues; the construction and application of which see under MATHEMATICAL INSTRUMENTS, SAILING, &C.

LINES on Gunter's scale, are the line of numbers, line of artificial sines, line of artificial tangents, line of artificial versed sines, line of artificial sines of rhumbs, line of artificial tangents of the meridian line, and line of equal parts; for the construction and application whereof. See GUNTER'S scale.

LINES of the sector, are the line of equal parts, or line of lines, line of chords, line of sines, line of tangents, line of secants, line of polygons, line of numbers, line of hours, line of latitudes, line of meridians, line of metals, line of solids, line of planes; for the construction and use whereof, see SECTOR.

LINES, in fortification, are those of approach, capital, defence, circumvallation, contravallation, of the base, &c. See APPROACH, &c.

To LINE a work, signifies to strengthen a rampart with a firm wall; or to encompass a parapet or moat with good turf, &c.

LINE, in the art of war, is understood of the disposition of an army, ranged in order of battle, with the front extended as far as may be, that it may not be flanked. See ARMY.

LINE of battle, is also understood of the disposition of a fleet on the day of engagement, on which occasion the vessels are usually drawn up as much as possible in a straight line, as well to gain and keep the advantage of the wind, as to run the same board.

LINE, ship of the, a vessel large enough to be drawn up in the line, and to have a place in a sea-fight. See SHIP.

K

LINE, in fencing, that part of the body opposite to the enemy, wherein the shoulders, the right arm, and the sword, ought always to be found; and wherein are also to be placed the two feet at the distance of eighteen inches from each other. In which sense a man is said to be in his line, or to go out of his line, &c.

LINE of the synodical, in reference to some theories of the moon, is a right line supposed to be drawn through the centres of the earth and sun; and, if it be produced quite through the orbits, it is called the line of the true syzygies: but a right line imagined to pass through the earth's centre, and the mean place of the sun, is called the line of the mean syzygies.

LINE, in genealogy, a series or succession of relations in various degrees, all descending from the same commoŋ father. Direct line, is that which goes from father to son; being the order of ascendants and descendants. Collateral line is the order of those who descend from some common father related to the former, but out of the line of ascendants and descendants: in this are placed uncles, aunts, cousins, nephews, &c.

LINE was also formerly a French measure, containing the twelfth part of an inch, or the hundred and forty-fourth part of a foot. Geometricians conceive the line, notwithstanding its smallness, to be subdivided into six points.

LINES, in music, the name of those strokes drawn horizontally on a piece of paper, on and between which the characters and notes of music are disposed: their number is commonly five; when another is added, for one, two, or more notes, it is called a ledger-line.

LINES, in heraldry, the figures used in armories, to divide the shield into different parts, and to compose different figures. These lines, according to their different forms and names, give denomination to the pieces or figures which they form, except the straight or plain lines.

LINEAR numbers, in mathematics, such as have relation to length only; such is a number which represents one side of a plane figure. If the plane figure be a square the linear number is called a root.

LINEAR problem, that which may be solved geometrically, by the intersection of two right lines. This is called a simple problem, and is capable but of one solution.

LINEN, in commerce. The linen manufacture was probably introduced into Britain with the first settlements of the Romans. The flax was certainly first planted by that nation in the British soil. The plant itself indeed appears to have been originally a native of the east. The woollen-drapery would naturally be prior in its origin to the linen, and the fibrous plants from which the threads of the latter are produced, seem to have been first noticed and worked by the inhabitants of Egypt. In Egypt, indeed, the linen manufacture appears to have been very early; for even in Joseph's time it had risen to a considerable height. From the Egyptians the knowledge of it proceeded probably to the Greeks, and from them to the Romans. Even at this day the flax is imported among us from the eastern nations; the western kind being merely a degenerate species of it. In order to succeed in the linen manufacture, one set of people should be confined to the ploughing and preparing the soil, sowing and covering the seed, to the weeding, pulling, rippling, and taking care of the new seed, and watering and dressing the flax till it is lodged at home: others should be concerned in the drying, breaking, scutching, and heckling the flax, to fit it for the spinners; and others in spinning and reeling it, to fit it for the weaver : others should be concerned in taking due care of the weaving, bleaching, beetling, and finishing the cloth for the market. It is reasonable to believe, that if these several branches of the manufacture were carried on by distinct dealers in Scotland and Ireland, where our home-made linens are manufactured, the several parts would be better executed, and the whole would be afforded cheaper, and with greater profit.

LING, in ichthyology, the cirrated gadus with two black fins, and with the upper jaw longest; a fish called by authors asellus longus. See GADUS.

LINGUATALA, in natural history, a genus of the Vermes Intestina class and order. Body depressed, oblong; mouth placed before, surrounded with four pas sages. There is but a single species, viz. L. serrata, inhabiting the lungs of the hare.

LINNEA, in botany, so named in honour of the celebrated Linnæus, a genus of the Didynamia Angiospermia class and or der. Natural order of Aggregatæ. Caprifoliæ, Jussieu. Essential character: calyx double, of the fruit two-leaved, of the

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