have had an opportunity of seeing them in America and the East Indies, their native places of growth. EPIDERMIS, in anatomy, the same with the cuticle. See Curis. EPIGAEA, in botany, a genus of the Decandria Monogynia class and order. Natural order of Bicornes. Erica, Jussieu. Essential character: calyx outer three-leaved; inner five-parted; corolla salver-form; capsule five-celled. There are but two species, viz. E. repens, creeping epigaea, or trailing arbutus, and E. cordifolia, heart-leaved epigaea: the former, remarkable for its fine odour, is a native of Virginia and Canada, and the latter of Guadaloupe. EPIGLOTTIS, one of the cartilages of the larynx or wind-pipe. See ANAToMY. EPIGRAM, in poetry, in short poem or composition in verse, treating only of one thing, and ending with some lively, ingenious, and natural thought or point. EPILEPSY, in medicine, the same with what is otherwise called the falling sickness, from the patient’s falling suddenly to the ground. EPILOBIUM, in botany, a genus of the Octandria Monogynia class and order. Natural order of Calycanthema. Onagrae, Jussieu. Essential character: calyx four-cleft; petals four; capsule oblong, inferior; seeds downy. There are fourteen species. These plants are hardy perennials, not void oft' beauty; they are, however, commonly considered only as weeds, and are rarely cultivated in gardens. The American species are, 1. E. estoratum ; 2. E. spicatum ; 3. E. strictum ; 4. E. linerate. EPILOGUE, in dramatic poetry, a speech addressed to the audience after the play is over, by one of the principal actors therein, usually containing some reflections on certain incidents in the play, especially those in the part of the erson that speaks it. EPIMEDIUM, in botany, English bar. renwort, a genus of the Tetrandria Monogynia class and order. Natural order of Corydales. Berberides, Jussieu. Essential character: nectary four, cup-form, leaning on the petals; corolla four petalled; calyx very caducous; fruit a silique. There is but one species, viz. F. alpinum, alpine barrenwort. EPIPHANY, a christian festival, otherwise called the manifestation of Christ to the Gentiles, observed on the sixth of January, in honour of the appearance of our Saviour to the three magi, or wise men, who came to adore him, and bring him presents. The feast of Epiphany was not originally a distinct festival, but made a part of that of the nativity of Christ, which being celebrated twelve days, the first and last of which were high or chief days of solemnity, either of these might properly be called Epiphany, as that word signifies the appearance of Christ in the world. The kings of England and Spain offer gold, frankincense, and myrrh, on Epiphany, or twelfth day, in memory of the offerings of the wise men to the infant Jesus. The festival of Epiphany is called by the Greeks the feast of lights, because our Saviour is said to have been baptised on this day and baptism is by them called illumination. EPISCOPALIANS, in the modern acceptation of the term, belong more especially to members of the Church of England, and derive this title from episcopus, the Latin word for bishop; or, if it be referred to its Greek origin, implying the care and diligence with which bishops are expected to preside over those committed to their guidance and direction. They insist on the divine origin of their bishops, and other church officers, and on the alliance between church and state. Respecting these subjects, however, Warburton and Hoadley, together with others of the learned amon them, have different opinions, as they have also on the thirty-nine articles, which were established in the reign of Queen Elizabeth. These are to be found in most Common Prayer-Books; and the Episcopal Church in America has reduced their number to twenty. By some the articles are made to speak the language of Calvinism, and by others they have been interpreted in favour of Arminianism. The Church of England is governed by the King, who is the supreme head: by two archbishops, and twenty-four bishops. The benefices of the bishops were converted by William the Conqueror into temporal baronies; so that every prelate has a seat and vote in the House of Peers. Dr. Benjamin Hoadley, however, in a sermon preached from this text, “My kingdom is not of this world,” insisted that the clergy had no pretensions to temporal jurisdiction, which gave rise to various publications, termed, by way of eminence, the Bangorian Controversy, Hoadley being then bishop of Bangor. There is a bishop of Sodor and Man, who has no seat in the House of Peers. Since the death of the intolerant Archo Laud, men of moderate principles have been raised to the see of Canterbury, and this hath tended not a little to the tranquillity of church and state. The established Church of Ireland is the same as the Church of England, and is governed by four archbishops, and eighteen bishops. EPISODE, in poetry, a separate incident, story or action, which a poet invents and connects with his principal action, that his work may abound with a greater diversity of events; though, in a more limited sense, all the particular incidents whereof the action or narration is compounded are called episodes. EPITAPH, a monumental inscription in honour or memory of a person defunct, or an inscription engraven or cut on a tomb, to mark the time of a person's decease, his name, family, and, usually, some eulogium of his virtues, or good qualities. EPITHALAMIUM, in poetry, a nuptial song, or composition, in praise of the bride and bridegroom, praying for their prosperity, for a happy offspring, &c. EPITHET, in poetry and rhetoric, an . expressing some quality of a substantive to which it is joined; or such an adjective as is annexed to substantives by way of ornament and illustration, not to make up an essential part of the description. “Nothing,” says Aristotle, “tires the reader more than too great a redundancy of epithets, or epithets placed improperly; and yet nothing is so es: sential in poetry as a proper use of them.” EPITOME, in literary history, an abridgment or summary of any book, particularly of a history. EPOCHA, in chronology, a term or fixed point of time, whence the succeeding years are numbered or accounted. See Chaoxology. EPODE, in lyric poetry, the third or hast part of the ode, the ancient ode being .#. into strophe, antistrophe, and epode. EPOPOEIA, in poetry, the story, fable, or subject, treated of in an epic poem. The word is commonly used for the epic poem itself. See Epic. EPSOM salt, another name for sulphate of magnesia. EQUABLE, an appellation given to such motions as always continue the same in degree of velocity, without being either accelerated or retarded. When two or more bodies are uniformly accelerated or retarded, with the same in crease or diminution of velocity in each, they are said to be equally accelerated, or retarded. EQUAL, a term of relation between two or more things of the same magnitude, quantity, or quality. Mathematicians speak of equal lines, angles, figures, circles, ratios, solids, &c. EQUALITY, that agreement between two or more things whereby they are denominated equal. The equality of two quantities, in algebra, is denoted by two parallel lines placed between them; thus, 4 + 2 = 6, that is, 4 added to 2 is equal to 6. EQUANIMITY, in ethics, denotes that even and calm frame of mind and temper, under good or bad fortune, whereby a man appears to be neither puffed up or overjoyed with prosperity, nor dispirited, soured, or rendered uneasy, by adversity. EQUATION, in algebra, the mutual comparing two equal things of different denominations, or the expression denoting this equality; which is done by setting the one in o to the other, with the sign of equality ( = ) between them: thus, 3s. = 36d. or 3 feet = 1 yard. Hence, if we put a for a foot, and b for a yard, we shall have the equation 3 a = b, in algebraical characters. See ALG Ebn A. EQUATIONS, construction of, in algebra, is the finding the roots or unknown quantities of an equation, by geometrical construction of right lines or curves, or the reducing given equations into geometrical figures. And this is effected by lines or curves, according to the order or rank of the equation. The roots of any equation may be determined, that is, the equation may be constructed, by the intersections of a straight line with another line or curve of the same dimensions as the equation to be constructed : for the roots of the equation are the ordinates of the curve at the points of intersection with the right line; and it is well known that a curve may be cut by a right line in as many points as its dimensions amount to. Thus, then, a simple equation will be constructed by the intersection of one right , line with another; a quadratic equation, or an affected equation of the second rank, by the intersections of a right line with a circle, or any of the conic sections, which are all lines of the second order; and which may be cut by the right line in two points, thereby giving the two roots of the quadratic equation. A cubic equation may be constructed by the intersection of the right line with a line of the third order, and so on. But if, instead of the right line, some other line of a higher order be used, then the second line, whose intersections with the former are to determine the roots of the equation, may be taken as many dimensions lower as the former is taken higher. And, in general, an equation of any height will be constructed by the intersection of two lines, whose dimensions multiplied together produce the dimension of the given equation. Thus, the intersections of a circle with the conic sections, or of these with each other, will construct the biquadratic equations, or those of the fourth power, because 2 × 2 = 4; and the intersections of the circle, or conic sections, with a line of the third order, will construct the equations of the fifth and sixth power, and so on.—For example: To construct a quadratic equation. 1. If it be a simple quadratic, it may be reduced to this form, x* = a b : and hence as a :: * ; b, or a = v a b, a mean proportional between a and b. #.. upon a straight line take A B = a, and B C = b, then upon the diameter A C describe a semicircle, and raise the perpendicular B D to meet it in D; so shall B D be = ar, the mean proportional sought between A B and B C, or between a and b. 2. If the quadratic be affected, let it first be aca + 2 ax = bo; then form the right-angled triangle, whose base A B is a, and perpendicular B C is b , and with the centre A To construct cubic and biquadratic equations. These are constructed by the intersections of two conic sections; for the equation will rise to four dimensions, by which are determined the ordinates from the four points in which these conic sections may cut one another; and the conic sections may be assumed in such a manner as to make this equation coincide with any proposed biguadratic ; so that the ordinates from these four intersections will be equal to the roots of the proposed biquadratic. When one of the intersections of the conic section falls upon the axis, then one of the ordinates vanishes, and the equation by which these ordinates are determined will then be of three dimensions only, or a cubic to which any proposed cubic equation may be accommodated; so that the three remaining ordinates will be the roots of that proposed cubic. The conic sections for this purpose should be such as are most easily described t the circle may be one, and the parabola is usually assumed for the other. See Simpson's and Maclaurin's Algebra. Equations, nature of . Any equation involving the powers of one unknown quantity may be reduced to the form 2n— p zo-1 + q z*-*, &c. = 0, here the whole expression is equal to nothing, and the terms are arranged according to the dimensions of the unknown quantity, the coefficient of the highest dimension is unity, understood, and the coefficients p, q, r, and are effected with the proper signs. An equation, where the index is of the highest power of the unknown quantity is n, is said to be of n dimensions, and in speaking simply of an equation of n dimensions, we understand one reduced to the above form. Any quantity zo- p 2n-1 + q 2n-2, &c. --P 2–Q may be supposed to arise from the multiplication of z – a xz – b x z – c. &c. |