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THE

BRITISH ENCYCLOPEDIA.

ELLIPSIS.

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ellipsis, are called conjugate diameters. Any right line, not passing through the centre, but terminated by the ellipsis, and bisected by a diameter, is called the ordinate, or ordinate-applicate, to that diameter; and a third proportional to two conjugate diameters is called the latus rectum, or parameter of that diameter, which is the first of the three proportionals. The reason of the name is this : let B A, E D, be any two conjugate diameters of an ellipsis (fig. 2, where they are the two axes) at the end A, of the diameter A B, raise the perpendicular A F, equal to the latus rectum, or parameter, being a third proportional to A B, E D, and draw the right line B F : then, if any point P be taken in B A, and an ordinate PM be drawn, cutting B F in N, the rectangle under the absciss A P, and the line P N will be equal to the square of the ordinate P M. Hence drawing NO parallel to A B, it appears that this rectangle, or the square of the ordinate, is less than that under the absciss A P, and the parameter A F, by the rectangle under A P and O F, or N O and OF; on account of which deficiency, Appollonius first gave this curve the name of an ellipsis, from taxes rely, to be deficient. In every ellipsis, as A E B D, (fig. 2), the squares of the semi-ordinates MP, m p, are as the rectangles under the segments of the transverse axis A.P × P B, A p x p B, made by these ordinates re. spectively; which holds equally true of

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the circle, where the squares of the ordinates are equal to such rectangles, as being mean proportionals between the segments of the diameter. In the same manner, the ordinates to any diameter whatever are as the rectangles under the segments of that diameter. As to the other principal properties of the ellipsis, they may be reduced to the following propositions. 1. If from any point M in an ellipsis, two right lines, M. F., M. f. (fig. 1.) be drawn to the foci F, j, the sum of these two lines will be equal to the transverse axis A. B. This is evi. dent from the manner of describing an ellipsis. 2. The square of half the lesser axis is equal to the rectangle under the segments of the greater axis, contained between the foci and its verticles; that is, D C = A F x FB = Afz f B. 3. Every diameter is bisected in the centre C. 4. The transverse axis is the greatest, and the conjugate axis the least, of all diameters. 5. Two diameters, one of which is parallal to the tangent in the vertex of the other, are conjugate diameters; and, vice versa, a right ‘. drawn through the vertex of any diameter, parallel to its conjugate diameter, touches the ellipsis in that vertex. 6. If four tangents be drawn through the vertices of two conjugate diameters, the parallelo: gram contained under them will be equal to the parallelogram contained under tangents drawn through the vertices of any other two conjugate diameters. 7. If a right line, touching an ellipsis, meet two conjugate diameters produced, the rectangle under the segments of the tangent, between the point of contact and these diameters, will be equal to the square of the semi-diameter, which is conjugate to that passing through the point of contact. 8. In every ellipsis, the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the two axes. 9. In every ellipsis, the angles FG I, f G H, o 1), made by the tangent H I, and the lines FG, f G, drawn from the foci to the point of contact, are equal to each other. 10. The area of an ellipsis is to the area of a circumscribed circle, as the lesser axis is to the greater, and vice versa with respect to an inscribed circle ; so that it is a mean proportional between two circles, having the transverse and conjugate axes for their diameters. This holds equally true of all the other corresponding parts belonging to an ellipsis. The curve of any ellipsis may be obtained by the following series. Suppose the

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&c. is to 1, where d is equal to the difference of the squares of the axis applied to the square of the transverse axis. Ellipsis, in grammar, a figure of syntax, wherein one or more words are not expressed; and from this deficiency it has got the name ellipsis. Ellipsis, in rhetoric, a figure nearly allied to preterition, when the orator, through transport of passion, passes over many things, which, had he been cool, ought to have been mentioned. In preterition, the omission is designed ; which, in the ellipsis, is owing to the vehemence of the speaker's passion, and his tongue not being able to keep pace with the emotion of his mind. ELLIPTIC, or ELLIPT1cAL, something belonging to an ellipsis. Thus we meet with elliptical compasses, elliptic conoid, elliptic space, elliptic stairs, &c. The elliptic space is the area contained within the curve of the ellipsis, which is to that of a circle described on the transverse axis, as the conjugate diameter is to the transverse axis; or it is a mean proportional between two circles, described on the conjugate and transverse axis. ELLIPTOIDES, in geometry, a name: used by some to denote infinite ellipses, m—H·m defined by the equation au

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Of these there are several sorts: thus, is a y = b x* (a—r) it is a cubical eliptoid; and if a y = b r- (a–c)", it denotes a biquadratic elliptoid, which is an ellipsis of the third order in respect of the appollonian ellipsis. ELLISIA, in botany, so called in memory of John Ellis, F. R. S. a genus of the Pentandria Monogynia class and order. Natural order of Luridae. Borraginee, Jussieu. Essential character: corolla funnel-form, narrow; berry dry, two-celled, two valved; seeds two, dotted, one placed over the other. There is only one species, viz. E. nyctelea, cutleaved ellisia, a native of Virginia. ELM. See Ulmus. The elm is very serviceable in places where it may lie continually dry or wet in extremes. Accordingly, it is proper for water-works, mills, the ladles and soles of the wheel. pipes, pumps, aqueducts, pales, and shipplanks beneath the water-lines. It is also of use for wheel-rights, handles for singke saws, axle-trees, and the like. The elearness of the grain makes it also fit for all kinds of carved works, and most ornaments relating to architecture. ELOCUTION, in rhetoric, the adapting words and sentences to the things or sentiments to be expressed. It consists of elegance, composition, and dignity. The first, comprehending the purity and perspicuity of language, is the foundation of elocution. The second ranges the words in proper order; and the last adds the ornaments of tropes and figures, to give strength and dignity to the whole. ELOGY, a praise or panegyric bestowed on any person or thing, in consideration of its merit. The beauty of elogy consists in an expressive brevity. Elogiums should not have so much as one epithet, properly so called, nor two words synonimous. They should strictly adhere to truth: for extravagant and improbable elogies rather lessen the character of the person or thing they would extol. ELONGATION, in astronomy, the digression or recess of a planet from the sun, with respect to an eye placed on our earth. The term is chiefly used in speaking of Venus and Mercury, the arch of a great circle intercepted between either of these planets and the Sun being called the elongation of that planet from the Sun, Buthere it is to be observed, that it is only a circle which has the sun for its centre; that the greatest elongation is in a line touching the planet's orbit. For in an elliptic orbit it may be, that the

elongation from the sun may grow still greater, even after it has left the place where the line joining the earth and planet touches the orbit. For after that, the true distance of the planet from the Sun may increase, whilst the distance of the Sun and planet from the earth does not increase, but rather decrease. But because the orbits of the planets are nearly circular, such small differences may be neglected in astronomy. The greatest elongation of Venus is found by observation to be about forty-eight degrees, and the greatest elongation of Mercury about twenty-eight degrees, upon which account this planet is rarely to be seen with the naked eye. Eloxgation, angle of; is an angle contained under lines drawn from the centre of the sun and planet to the centre of the earth. ELOPEMENT, is when a married woman of her own accord departs from her husband, and dwells with an adulterer; for which, without voluntary reconciliation to the husband, she shall lose her dower by the statute of Westminster, 2. c. 34. Except that her husband willingly, and without coercion of the church, reconcile her, and suffer her to dwell with him, in which case, she shall be restored to her action, 13 Ed. I. st. 1. c. 34. By eloping in this manner, or living in adultery apart from the husband, he is discharged of her future debts, and no longer liable to support her. To ELOQUENCE, the art of speaking well, so as to affect and persuade. Cicero defines it the art of speaking with copiousness and embellishment. Eloquence and rhetoric differ from each other, as the theory from the practice; rhetoric being the art which describes the rules of eloquence, and eloquence that art which uses them to advantage. See RhErortic. ELOPS, in natural history, a genus of fishes of the order Abdominales. Generic character: head smooth, edges of the jaws and palate rough, with teeth ; gilt membrane with thirty rays, and armed on the outside in the middle with five teeth. The saury elops, the only species, bears a considerable resemblance to a salmon, from which it differs principally in wanting the fleshy back fin. It inhabits the shores of Carolina and the West Indies; in Jamaica it passes by the name of the sun-fish. It is in general about fourteen inches long. ELY MUS, in botany, lymegrass, a genus of the Triandria Digynia class and order. Natural order of Gramina, or Grasses. Essential character: calyx late

ral, two-valved, aggregate, many flowered. The American species are 10 in number, viz. 1. E. arenarius. 2. E. philadelphicus. 3. E. canadensis. 4. E. virginicus. 5. E. striatus. 6. E. europæus, 7. E. villosus. 8. E. hystric. 9. E. ciliatus. 10. E. glaucifolius. (.Muhl.) EMARGINATED, among botanists, an appellation given to such leaves as have a little indenting on their summits : when this indenting is terminated on each side by obtuse points, they are said to be obtūsely emarginated ; whereas, when these points are acute, they are called acutely emarginated. EMBALMING, is the opening a dead body, taking out the intestines, and filling the place with odoriferous and desiccative drugs and spices, to prevent its pu: trefying. The Egyptians excelled all other nations in the art of preserving bodies from corruption; for some that they have embalmed upwards of 2000 years ago remain whole to this day, and are often brought into other countries as eat curiosities. Their manner of emalming was thus; they scooped the brains with an iron scoop out at the nostrils, and threw in medicaments to fill up the vacuum ; they also took out the entrails, and having filled the body with myrrh, cassia, and other spices, except frankincense, proper to dry up the humours, they pickled it in nitre, where it lay soaking for seventy days. The body was then wrapped up in bandages of fine linen and gums, to make it stick like glue; and so was delivered to the kindrcd of the deceased, entire in all its features, the very hairs of the eye-lids being preserved. They used to keep the bodies of their ancestors, thus embalmed, in little houses magnificently adorned, and took great pleasure in beholding them alive, as it were, without any change in their size, features, or complexion. The Egyptians also embalmed birds, &c. The prices for embalming were different; the highest was a talent, the next 20 minae, and so decreasing to a very small matter; but those who had not where withall to answer this expense, contented themselves with infusing, by means of a syringe, through the fundament, a certain liquor extracted from the cedar, and, leaving it there, wrapped up the body in salt of nitre : the oil thus preyed upon the intestines, so that, when they took it out, the intestines came away with it, dried, and not in the least putre

fied: the body, being inclosed in nitre, grew dry, and nothing remained besides the skin glued upon the bones. The method of embalming used by the modern Egyptians, according to Maillet, is, to wash the body several times with rose-water, which, he elsewhere observes, is more fragrant in that country than with us. They afterwards perfume it with incense, aloes, and a quantity of other odours, of which they are by no means sparing; and then they bury the body in a winding sheet, made partly of silk and partly of cotton, and moistened, as is supposed, with some sweet-scented water or liquid perfume, though Maillet uses only the term moistened; this they cover with another cloth of unmixed cotton, to which they add one of the richest suits of clothes of the deceased. The expense, he says, on these occasions, is very great, though nothing like what the genuine embalming cost in former times. EMBARG(), in commerce, an arrest on ships, or merchandize, by public authority; or a prohibition of state, commonly on foreign ships, in time of war,

to prevent their going out of port; some-.

times to prevent their coming in ; and sometimes both, for a limited time. The

'king may lay embargoes on ships, or em

ploy those of his subjects, in time of danger, for service and defence of the nation ; but they must not be for the private advantage of a particular trader, or company; and, therefore, a warrant to stay a single ship is no legal embargo. No inference can be made from embargoes which are only in war time, and are a prohibition by advice of council, and not a prosecution of parties. If goods be laden on board, and after an embargo or restraint from the prince or state comes forth, and then the master of the shi breaks ground, or endeavours to sail, if any damage accrues, he must be responsible for the same: the reason is, because his freight is due, and must be paid, nay though the goods be seized as contraband. Embargo differs from quarantine, insomuch as this last is always for the term of forty days, in which persons from foreign parts infected with the plague are not permitted to come on shore. See QUARANT, NE. EMBASSADOR, or AMBAssanoR, a public minister sent from one sovereign prince, as a representative of his person, to another. Embassadors are either ordinary or extraordinary. Embassador in ordinary is he who constantly resides in the court of

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