are sufficiently visible to the eye, and their returns frequent. We shall detail We shall detail that of the Mexicans only. The year of the Mexicans consisted of 365 days; it was composed of eighteen months of twenty days each, and five additional, called nemontemi, or void. At the end of a cycle of 52 years, 13 days were added, and at the end of another cycle 12 days, and so on, alternately, making an addition of 25 days in 104 years. This made the mean year to consist of 365 days, 5 hours, 46 minutes, 9 3 13 seconds, being only 2 39" shorter than the truth. As the wanton destruction of the Mexican monuments and hieroglyphic records, by their cruel and barbarous conquerors, has left little to study, and the extermination of the Mexicans of superior order has done away with their system, we shall not detail the names of their months and particulars of their cycles, which afford striking coincidences withi those of the Tartars, Japanese, &c. We shall only add, that their first cycle began in the month of January, A. D. 1090. List of the Correspondence of Eras with the Year 1830. [When the commencement of the year coincides with the Christian year, that alone will be given; when it begins at a different season, the month in which the 1st of January, 1830, occurs will be also stated.] EPODE EQUATION OF PAYMENTS. 5th book of the odes of Horace. All the odes in this book, however, are not satirical, and Scaliger therefore supposes, that the name here signifies an appendix to the odes; the epodes having been joined to the other works of the poet after his death. EPOPEE. (See Epic.) EPOPTA (from the Greek ἐπὶ and ὄπτομαι, I see); inspectors, or spectators, i. e., initiated; a name given to those who were admitted to view the secrets of the greater mysteries, or religious ceremonies of the ancient Greeks. 557 ric acid and magnesia. It is found covering the crevices of rocks, in caverns, old pits, &c., in the vicinity of Jena, on the Harz, in Bohemia, &c., in mineral springs, in several lakes in Asia, and in sea-water. It is obtained for use from these sources, or by artificial processes, and is employed in medicine as a purgative. The English name is derived from the circumstance of its having been first procured from the mineral waters at Epsom, England. (See Magnesia.) EQUATION, in algebra, is the expression of the equality of different indications of the same magnitude; as, for instance, 9 and 2 are equal to 11, in mathematical characters is expressed thus: 9+211; or, 3 from 4 leave 1, is 4-3 An equation may contain known quantities and unknown quantities. The latter are usually indicated by the last letters of the alphabet; and it is one of the main objects of mathematics to reduce all questions to equations, and to find the value of the unknown quantities by the known, which is sometimes a difficult, but, at the same time, interesting operation; because x, or the unknown quantity, may be given under so involved a form as to require the greatest tact to determine its value. The work of Meier Hirsch, already mentioned in the article Algebra, is perhaps the best collection of equations for solution. There must always be as many equations as there are unknown quantities; and it is not always easy to form these from the question proposed. The equation is called simple, quadratic, cubic, bicubic, of the fifth, &e. degree, according to the exponent of the unknown quantity; for instance (x2— 4cdy+rp) x1—pq—sin 4p, is an equation of the sixth degree. Equations are the soul of all algebraical operations. EPROUVETTE; the name of an instrument for ascertaining the strength of fired gunpowder, or of comparing the strength of different kinds of gunpowder. One of the best, for the proof of powder in artille-=1. ry, is that contrived by doctor Hutton. It consists of a small brass gun, about 23 feet long, suspended by a metallic stem, or rod, turning by an axis, on a firm and strong frame, by means of which the piece os cillates in a circular arch. A little below the axis, the stem divides into two branches, reaching down to the gun, to which the lower ends of the branches are, fixed, the one near the muzzle, the other near the breech of the piece. The upper end of the stem is firmly attached to the axis, which turns very freely by its extremities in the sockets of the supporting frame, by which means the gun and stem vibrate together in a vertical plane, with a very small degree of friction. The piece is charged with a small quantity of powder (usually about two ounces), without any ball, and then fired; by the force of the explosion, the piece is made to recoil or vibrate, describing an arch or angle, which will be greater or less according to the quantity or strength of the powder. Epsom; a place in England, 15 miles south of London, in Surrey; population, 2890. It is celebrated for its medicinal springs, of a purgative quality, and for the downs, on which horse-races annually take place. Near it Henry VIII built a splendid palace, called Nonsuch. EPSOM SALT (sulphate of magnesia, cathartic salt) appears in capillary fibres or acicular crystals; sometimes presents minute prismatic crystals. The fibres are sometimes collected into masses; and it also occurs in a loose, mealy powder: its color, white, grayish or yellowish: it is transparent, or translucent, with a saltish, bitter taste. It is soluble in its own weight of cold water, and effloresces on exposure to the air. It is composed of water, sulphu (x2 EQUATION OF PAYMENTS, in arithmetic, is the finding the time to pay at once several debts due at different times, and bearing no interest till after the time of payment, so that no loss shall be sustained by either party. The rule commonly given for this purpose is as follows:Multiply each sum by the time at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the time required. Thus, for example, A owes B £190, to be paid as follows; viz. £50 at 6 months, £60 at 7 months, and £80 at 10 months: what is the equated time at which the whole ought to be paid, that no loss may arise, either to debtor or creditor? By the rule, 558 EQUATION OF PAYMENTS-EQUESTRIAN ORDER. 50 X 6 300 420 60 X 7 190 1520 ) 1520 (8 months, equat. time. This rule, however, is founded on a supposition, that the interest of the several debts which are payable before the equated time, from their terms to that time, ought to be equal to the sum of the interest of the debts payable after the equated time, from that time to their terms respectively, which, however, is not correct, as it is the discount that is to be considered, and not the interest, in the latter sums. In most cases, however, that occur in business, the error is so trifling, that the popular rule will probably always be made use of, as being by far the most eligible and expeditious method that we could suggest. and its axis is the axis of the earth. It divides the celestial sphere into the northern and southern hemispheres. During his apparent yearly course, the sun is twice in the equator, at the beginning of spring and of autumn. (See Equinox, and Day.) Then the day and night are equal,-whence the name of equator. The situation of the stars, with respect to the equator, is determined by their declension and right ascension. (q. v.) The equator, or equinoctial, called by mariners simply the line, is that great circle of our globe, every point of which is 90 degrees from the poles, which are also its poles, and its axis is the axis of the earth. It is in the plane of the celestial equator. All places which are on it, have invariably equal days and nights. (See Day.) Our carth is divided by it into the northern and southern hemispheres. The diurnal revolution of the earth is in the diEQUATION OF TIME, in astronomy, de- rection of it. It crosses the centre of notes the difference between mean and Africa, the islands of Sumatra, Borneo, apparent time, or the reduction of the ap- Celebes, &c., in Asia, then traverses the parent unequal time, or motion of the Pacific ocean, and crosses South Amerisun or a planet, to equable and mean ca, in Colombia, thence proceeds through time or motion. If the earth had only a the Atlantic back to Africa. To cross diurnal motion, without an annual, any the line, in navigation, is to pass over the given meridian would revolve from the equator. The equatorial regions are subsun to the sun again in the same space ject to long calms, alternating with frightof time as from any star to the same star ful hurricanes. As equal or mean time again, because the sun would never is estimated by the passage of arcs of the change his place with respect to the stars. equator over the meridian, it frequently But as the earth advances almost a de- becomes necessary to convert parts of gree eastward in its orbit in the time that the equator into time, and the converse, it turns eastward round its axis, what- which is performed by the following ever star passes over the meridian on any analogy, viz.—as 15° : 1 hour: : any arc day with the sun, will pass over the same of the equator: the time it has been in meridian on the next day, when the sun passing. Or, conversely, 1 hour: 15° is almost a degree short of it, that is, 3:: any given time to the are of the minutes 56 seconds sooner. If the year contained only 360 days, as the ecliptic does 360 degrees, the sun's apparent place, so far as his motion is equable, would change a degree every day, and then the sidereal days would be 4 minutes shorter than the solar. The mean and apparent solar days are never equal, except when the sun's daily motion in right ascension is 59"; which is nearly the case about the 15th of April, the 15th of June, the 1st of September, and 24th of December, when the equator is 0, or nearly so; and it is at its greatest about the 1st of November, when it is 16′ 14′′. EQUATOR. By the celestial equator is understood that imaginary great circle in the heavens, the plane of which is perpendicular to the axis of the earth; it is everywhere 90° distant from the poles of the earth, which are therefore its poles, equator.-From this circle is reckoned the latitude of places, both north and south, in degrees of the meridian. (See Latitude, and Longitude.) EQUATORIAL, UNIVERSAL, or PORTA BLE OBSERVATORY is an instrument intended to answer a number of useful purposes in practical astronomy, independent of any particular observatory. It may be employed in any steady room or place, for performing many useful problems. EQUERRY, in the British customs; an officer of state, under the master of the horse. There are five equerries, who ride abroad with his majesty; for which purpose, they give their attendance monthly, one at a time, and are allowed a table. EQUESTRIAN ORDER, in Roman antiquities (ordo equestris). The equites did not at first form a distinct order, but were EQUESTRIAN ORDER-EQUINOX. merely selected, 100 from each tribe, as the body-guard of the king, and were called celeres, because they were mounted. Their number was afterwards increased; but when the equites became a distinct order, or class, is not known with certainty; it was probably soon after the expulsion of the kings. None but those who were named by the censor belonged to the order of equites; they were taken from plebeian or patrician families, and those who were of illustrious descent were called illustres, speciosi, &c. Their number was not fixed. In the latter periods of the republic, property of the value of 400 sestertia was required for admission into it. The privileges of a knight or eques were, 1. to receive a horse from the state; 2. a gold ring (hence annulo aureo donari, i. e. to be made a knight); 3. angustus clavus, a narrow strip of purple on the tunic; 4. a particular seat on public occasions. At first, their duty was to serve the republic in war; but, at a later period, they became judges, and farmers of the public revenues. Caius and Tiberius Gracchus wrested the right of being judges from the senate, and gave it to the equites. Some authors date the elevation of the equites to a third class at this period. Every fifth year, the censor held a review of the equites, on which occasion they passed before him, leading their horses. If any one of their number had been guilty of any offence, even if he had only neglected his horse, the censor ordered it to be sold, which was equivalent to degrading him from the order; hence adimere equum, to degrade a knight. Others, who had committed slighter offences, for which they were to be deprived of their rank, were omitted in the list, which was read aloud by the censor. The first on the list was called princeps. The farmers of the revenue were divided into classes, each having a president, called magister societatis: the members were called publicani. They were hated in the provinces. EQUILIBRIST (from the Latin æquilibrium); one who keeps his balance, in unnatural positions and hazardous movements. The equilibrist entertains the spectator by his artful motions, attitudes, leaps, &c. Every rope-dancer is an equilibrist. India is the native country of equilibrists; and the accounts given by travellers of the Indian balancers border on the incredible. The French, too, are distinguished as equilibrists. Such performers are met with in all the large cities of Europe and America. The equilibrists 559 are frequently also buffoons, jugglers, conjurers, &c. EQUINOCTIAL, in astronomy; a great circle of the sphere, under which the equator moves in its diurnal motion. It is the same as the celestial equator. (See Equator.) EQUINOCTIAL GALES; storms which are observed generally to take place about the time of the sun's crossing the equator or equinoctial line, at which time there is equal day and night throughout the world. EQUINOCTIAL POINTS are the two points wherein the equator and ecliptic intersect each other: the one, being in the first point of Aries, is called the vernal point; and the other, in the first point of Libra, the autumnal point. EQUINOX is that time of the year when the day and night are equal: the length of the day is then 12 hours; the sun is ascending 6 hours, and descending the same time. This is the case twice a year, in the spring and in autumn, when the sun is on the equator. When the sun is in this situation, the horizon of every place is, of course, divided into two equal parts by the circle bounding light and darkness; hence the sun is visible every where 12 hours, and invisible for the same time in each 24 hours. (See Day.) The vernal equinox marks the beginning of spring, the autumnal that of autumn: at all other times, the lengths of the day and of the night are unequal, and their difference is the greater the more we approach either pole, and in the same latitude it is every where the same. Under the line, this inequality entirely vanishes: there, during the day, which is equal to the night, the sun always ascends 6 hours, and descends 6 hours. In the opposite hemisphere of our earth, the inequality of the days increases in proportion to the latitude: the days increase there, while they diminish with us, and vice versa. The points where the ecliptic comes in contact with the equator are called equinoctial points. The vernal equinoctial point was formerly at the entrance of the constellation of Aries; hence the next 30 degrees of the eeliptic, reckoned eastward from it, have been called Aries; but this point long ago deserted the constellation of Aries, and now stands under Pisces; for it is found by observation, that the equinoctial points, and all the other points of the celiptic, are continually moving backward, or westward; which retrograde motion of the equinoctial points is what is called the precession of the equinoxes. (See Precession.) It appears from the result of calculations, that the path of either of the poles is a circle, the poles of which coincide with those of the ecliptic, and that the pole will move along that circle so slowly as to accomplish the whole revolution in about 25,791 years, nearly. The diameter of this circle is equal to twice the inclination of the ecliptic to the equator, or about 47 degrees. Now, as the ecliptic is a fixed circle in the heavens, but the equator, which must be equidistant from the poles, moves with the poles, therefore the equator must be constantly changing its intersection with the ecliptic. And from the best observations, it appears, that the equator cuts the ecliptic every year 50 seconds .25 more to the westward than it did the year before; hence the sun's arrival at the equinoctial point precedes its arrival at the same fixed point of the heavens every year by 20 minutes 23 seconds of time, or by an arc of 50 seconds 25. Thus, by little and little, these equinoctial points will cut the ecliptic more and more to the westward, till, after 25,791 years, they return to the same point. EQUISETUM; a genus of plants, belonging to the Linnæan class cryptogamia. The species are very common in wet places, and are commonly called horse-tails. The fructification is in terminal oval or conical heads, composed of peltate scales; the seeds numerous and very minute; the stein simple or branched, striate, and composed of articulations, each surrounded at base with a scarious sheath, which is toothed on the margin; the branches are verticillate and destitute of leaves. Five species are natives of the U. States, all common to the Eastern continent. The E. hyemale (shave-grass or scouringrush) has a remarkably rough stem, and is used for polishing wood, ivory, and the metals; for this purpose, a piece of iron wire is introduced into the hollow of the stem, which is then rubbed against the substance under operation. The asperity of the cuticle is owing to its containing a proportion of silex. Being a rare plant in England, it is imported into that country in considerable quantities from Holland, and is an article of commerce in other parts of Europe: the value of that exported from the Rhone is estimated at nearly $2000 annually. We are not aware that this plant has been found very abundantly at any particular locality in the U. States, though it occurs sparingly throughout a great portion of the Union. EQUITY. We call that, in a moral sense, equity, which is founded in natural justice, in honesty, and in right, ex æquo et bono. So, in an enlarged view (as Mr. Justice Blackstone has observed, 3 Comm. 429), "equity, in its true and genuine meaning, is the soul and spirit of all law; positive law is construed, and rational law is made by it. In this, equity is synonymous with justice; in that, to the true and sound interpretation of the rule.” Hence Grotius has defined it to be the correction of that, wherein the law, by reason of its generality, is deficient. It is applied to cases which the law does not exactly define, but which it submits to the sound judgment of the proper interpreter, arbitrio boni viri permittit. In this sense, equity must have a place in every rational system of jurisprudence; if not in name, at least in substance. It is impossible, that any code, however minute and particular, should embrace or provide for the infinite variety of human affairs, or should furnish rules applicable to all of them. Every system of laws must necessarily be defective; and cases must occur, to which the antecedent rules cannot be applied without injustice, or to which they cannot be applied at all. It is the office, therefore, of a judge, to consider whether the antecedent rule does apply, or ought, according to the intention of the lawgiver, to apply to a given case; and, if there be two rules, nearly approaching to it, but of opposite tendency, which ought to govern; and, if there exist no exact rule applicable to all the circumstances, whether the party is remediless, or the rule furnishing the closest analogy ought to be followed. The general words of a law may embrace all cases; and yet it may be clear that all could not have been intentionally embraced; for, if they were, it would defeat the obvious objects of the legislation. So words of doubtful import may be employed, and of a more or less extensive meaning. The question, in such cases, must be, in what sense the words were used; and it is the part of a judge to look to the objects of the legislature, and to give such a construction of the words as will further those objects. He is not at liberty to set aside the law, but to expound it. Custos non conditor juris, juvare, supplere, interpretari, mitigare jus civile potuit; mutare vel tollere non potuit (Taylor's Elements of Civil Law, ́214). This is an exercise of equitable construction. It is the administration of equity. Hence arises a variety of rules of interpretation of laws according to their nature and operation, whether they are remedial |