of the parobola is.................. x = y3 Where a is an axis, and p the parameter. And in like manner for any other curves.

This method of expressing the nature of curves by algebraical equations was first introduced by Des Cartes, who, by thus connecting together the two sciences of algebra and geometry, made them mutually assisting to each other, and so laid the foundation of the greatest improve. ments that have been made in every branch of them since that time.

EQUATION of time, in astronomy and chronology, the reduction of the apparent time or motion of the sun to equable, mean, or true time. The difference between true and apparent time arises from two causes, the excentricity of the earth's orbit, and the obliquity of the ecliptic. See TIME, equation of.

EQUATOR, in geography, a great circle of the terrestrial globe, equidistant from its poles, and dividing it into two equal hemispheres; one north and the other south. It passes through the east and west points of the horizon, and at the

meridian is raised as much above the horizon as is the complement of the latitude of the place. From this circle the latitude of places, whether north or south, begin to be reckoned in degrees of the meridian. All people living on this circle, called by geographers and navigators the line, have their days and nights constantly equal. It is in degrees of the equator that the longitude of places are reckoned; and as the natural day is measured by one revolution of the equator, it follows that one hour answers to 360

15

degrees: hence one degree of the equator will contain four minutes of time; 15 minutes of a degree will make a minute of an hour; and, consequently, four seconds answer to one minute of a degree.

EQUATIONAL. See OBSERVATORY. 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.

EQUISETUM, in botany, English horsetail, a genus of the Cryptogamia Filices class and order. Natural order of Filices or Ferns. There are seven species. They are natives of most parts of Europe, in woods and shady places.

EQUIANGULAR, in geometry, an epithet given to figures, whose angles are all equal; such are, a square, an equilate ral triangle, &c.

EQUICRURAL, in geometry, the same with isosceles. See IsosCELES TRIAN

GLE.

EQUIDIFFERENT numbers, in arith. metic, are of two kinds. 1. Continually equidifferent, is when, in a series of three numbers, there is the same difference be tween the first and second, as there is between the second and third; as 3, 6, 9. And 2. Discretely equidifferent, is when, in a series of four numbers or quantities, there is the same difference between the first and second as there is between the

third and fourth such are, 3, 6, 7, 10.

EQUIDISTANT, an appellation given to things placed at equal distance from some fixed point, or place, to which they are referred.

EQUILATERAL, in general, something that hath equal sides, as an equilateral angle.

EQUILATERAL hyperbola, one whose transverse diameter is equal to its parameter; and so all the other diameters equal to their parameters: in such an hyperbola, the asymptotes always cut one another at right angles in the centre. Its most simple equation, with regard to the transverse axis, is y = x-a2; and with regard to the conjugate, y2 = = x2 + a2, when a is the semitransverse, or semiconjugate. The length of the curve cannot be found by means of the quadrature of any space, of which a conic section is any part of the perimeter.

EQUILIBRIUM, in mechanics, is when the two ends of a lever or balance hang so exactly even and level, that neither doth ascend or descend, but keep in a position parallel to the horizon, which is occasioned by their being both charged with an equal weight.

EQUIMULTIPLES, in arithmetic and geometry, are numbers and quantities multiplied by one and the same number or quantity. Hence, equimultiples are

always in the same ratio to each other, as the simple quantities before multiplication: thus, if 6 and 8 are multiplied by 4, the equimultiples 24 and 32 will be to each other as 6 to 8.

EQUINOCTIAL, in astronomy, a great circle of the celestial globe, whose poles are the poles of the world. It is so call ed, because, whenever the sun comes to this circle, the days and nights are equal all over the globe; being the same with that which the sun seems to describe at the time of the two equinoxes of spring and autumn. All stars directly under this circle have no declination, and always rise due east, and set full west. The hour circles are drawn at right angles to it, passing through every fifteenth degree; and the parallels to it are called parallels of declination.

EQUINOX, the time when the sun enters either of the equinoctial points, where the ecliptic intersects the equinoctial. It was evidently an important problem in practical astronomy, to determine the exact moment of the sun's Occupying these stations; for it was natural to compute the course of the year from that moment. Accordingly, this has been the leading problem in the astronomy of all nations. It it susceptible of considerable precision, without any apparatus of instruments. It is only necessary to observe the sun's declination on the noon of two or three days before and after the equinoctial day. On two consecutive days of this number, his declination must have changed from north to south, or from south to north. If his declination on one day was observed to be 21' north, and on the next 5' south, it follows that his declination was nothing, or that he was in the equinoctial point about 23 minutes after 7 in the morning of the second day. Knowing the precise moments, and knowing the rate of the sun's motion in the ecliptic, it is easy to ascertain the precise point of the ecliptic in which the equator intersected it. By a series of such observations made at Alexandria, between the years 161 and 127 before Christ, Hipparchus, the father of our astronomy, found that the point of the autumnal equinox was about six degrees to the eastward of the star called spica virginis. Eager to determine every thing by multiplied observations, he ransacked all the Chaldean, Egyptian, and other records to which his travels could procure him access, for observations of the same kind; but he does not mention his having found any.

VOL. V.

He found, however, some observations of Arisulius and Timochares, made about 150 years before. From these it appeared evident that the point of the autumnal equinox was then about eight degrees east of the same star. He discusses these observations with great sagacity and rigour; and, on their authority, he asserts that the equinoctial points are not fixed in the heavens, but move to the westward about a degree ih 75 years, or some what less.

This motion is called the procession of the equinoxes, because by it the time and place of the sun's equinoctial station precedes the usual calculation: it is fully confirmed by all subsequent observations. In 1750, the autumnal equinox was observed to be 20° 21' westward of spica virginis. Supposing the motion to have been uniform during this period of ages, it follows that the annual precession is about 50" and one-third; that is, if the celestial equator cuts the ecliptic in a particular point on any day of this year, it will on the same day of the following year cut it in a point 50′′ and one-third to the west of it, and the sun will come to the equinox 20′ 23′′ before he has completed his round of the heavens. Thus the equinoctial, or tropical year, or true year of seasons, is so much shorter than the revolution of the sun, or the sidereal year. It is this discovery that has chiefly immortalized the name of Hipparchus, though it must be acknowledged that all his astronomical researches have been conducted with the same sagacity and intelligence. It was natural, therefore, for him to value himself highly for the discovery. It must be acknowledged to be one of the most singular that has been made, that the revolution of the whole heavens should not be stable, but its axis continually changing. For it must be observed, that since the equator changes its position, and the equator is only an imaginary circle, equidistant from the two poles, or extremities of the axis, these poles, and this axis, must equally change their positions. The equinoctial points make a complete revolution in about 25,745 years, the equator being all the while inclined to the ecliptic in nearly the same angle. Therefore the poles of this diurnal revolution must describe a circle round the poles of the ecliptic, at the distance of about 23 degrees in 25,745 years; and in the time of Timochares, the north pole of the heavens must have been 30 degrees eastward of where it now is.

G

EQUITY, quasi æqualitas, is generally understood, in law, a liberal correction, or qualification of the law, where it is too strict, too confined, or severe, and is sometimes applied, where, by the words of a statute, a case does not fall within it, yet being within the mischief, the judges, by an equitable construction, have extended its application to that case. Equity is understood as a correction of the law: the difference between courts of equity and law is known only in this country, and arises principally, if not entirely, from the different modes of trial, which must ever render them essentially distinct. For it is obvious, that where men form contracts in the ordinary course of law, the legal consequence, and the enforcement of them, must be, according to general rules, applicable to general cases; and the nature of our mode of trial by jury is so strict in the evidence which it requires, that a strict legal decision alone can justly be founded upon it. There are, however, many cases, in which there are particular circumstances between the different parties peculiar to their case, which give rise to exceptions and equitable decisions wholly different from the general rule. These cases of exception are such, that unless the judge can inquire into all the circumstances affecting the conscience of the several parties, a perfectly equitable decision cannot be given. For this purpose the court of equity is empowered to examine all the itigant parties upon their oaths, and to make every one answer to the full, as to all the circumstances affecting the case, which is not done in a court of law, where no person can be a witness in his

own cause.

In equity, however, the plaintiff by filing his bill waves the objections, and submits to take the answer of each defendant, though he cannot be admitted to give evidence himself. This is the process by what is called English bill in equity; and the form of proceeding, though somewhat tardy, gives the parties the fullest opportunity of obtaining a final decision according to good conscience. It is this difference in the proceeding, which has rendered the best judges in courts of law averse to introducing equitable distinctions and principles, applicable to courts of equity, in courts of law, because they have not the same means of informing their consciences upon all the circumstances necessary to induce them to alter the strict law according to the peculiar facts,

case.

or conscientious circumstances of the Formerly, it is supposed, the King, upon petition, referred the case upon a harsh decision at law to a committee, together with the Chancellor ; but in the time of Edward III. when uses, or trusts of lands, which were discountenanced at common law, were considered as binding in conscience by the clergy, John Waltham, Chancellor to Richard II. introduced the writ of subpana, returnable in the Court of Chancery only, to make the tenant, or feoffee to uses, answerable for the confidence reposed in him, and this writ is the commencement of a suit in equity, which has been chiefly modelled by Lord Ellesmere, the great Lord Bacon, and Sir Heneage Finch, in the time of Charles I. Lord Hardwicke followed, at some dis tance, after these great men, and by his decisions, together with those of his successors, has established a practical system of equity, which is as definite and well understood as the law itself; and taking into consideration the leading circumstances above mentioned, is nothing more than the law administered according to the justice of the case. There are some cases which belong more peculiarly to a court of chancery, as the care of infants, and appointing guardians to them; so of lunatics and charities, in which the Chancellor acts for the King as keeper of his conscience. In other cases, as in cases of trust, matters of fraud, account, suits for a discovery, matters of accident, and the like, courts of equity act, in aid of the courts of law, and give relief, where, from the nature of the case, a court of law cannot relieve. Thus, where an agreement is to be performed, courts of law can only give da mages for the breach; but a court of equity, taking all the circumstances into consideration, directs and enjoins a specific performance of it according to good conscience. So, where it apprehends an injury likely to be done, it will interfere to prevent it.

We have thought this explanation of the general principles, which distinguish courts of law and equity, better suited to a work like the present, than an attempt to abridge any more particular account of the practice and principles of courts of equity, which will be found to proceed upon the ordinary rules of good conscience, as far as they can be reduced to practice. An appeal lies from the Chancellor to the House of Lords. The Court of Exchequer has a court of equi

ly, and so have most courts of peculiar jurisdiction.

EQUITY, of redemption. Upon a mortgage, although the estate upon non-payment of the money becomes vested in the mortgagee, yet equity considers it only a pledge for the money, and gives the party a right to redeem, which is called his equity of redemption. If the mortgagee is desirous to bar the equity of redemption, he may oblige the mortgager either to pay the money, or be foreclosed of his equity, which is done by proceedings in the Court of Chancery by bill of foreclosure.

EQUUS, the horse, in natural history, a genus of mammalia of the order of Belluæ. Generic character: upper fore-teeth parallel, and six in number; in the lower jaw six, rather more projecting; tusks on each side, in both jaws, remote from the rest; feet with undivided hoofs. There are six species, and very many varieties. E. caballus, or the common horse. The elegance, grace, and usefulness of the horse entitle him to particular attention, and certainly confer upon him a pre-eminence above all other quadrupeds. There are few parts of the world in which horses are not to be found; and in various parts of Africa they maintain their original independence, and range at pleasure in herds of several hundreds, having always one or more as an advanced guard, to alarm against approaching danger. These alarms are expressed by a sudden snorting, at which the main body gallop off with the most surprising swiftness. In the south of Siberia also, and at the north-west of China, wild horses are to be found in considerable abundance; and it is stated, that different herds will carry on hostilities, and one party frequently surround an enemy inferior in number, and conduct them to the hostile territory, manœuvring perpetually to baffle all their attempts to escape. On each bank of the river Don, towards the Palus Mootis, horses are found wild, but are supposed to be the descendants of domesticated horses, belonging to the Russian army occupied in the siege of Asoph, at the close of the seventeenth century. In America, likewise, horses are found wild in vast abundance, sweeping the extensive plains of Buenos Ayres, and the Brazils particularly, in immense herds. They are taken by the inhabitants, by throwing, with great dexterity, a noosed cord over their heads, at full speed; and are often destroyed merely for their hides, as an arti

cle of commerce. These American horses are the descendants of those which were introduced by the Spaniards on their discovery of America, as none previously existed on that continent. They are, in general, small and clumsily formed, and their height is rarely above fourteen hands. In the deserts of Arabia, it has been stated by several writers, wild horses are extremely abundant; but Shaw and Sonnini, with greater probability, confine their appearance in that country to the borders of the desert, the latter not supplying materials for their subsistence. Mr. Bruce mentions the horses of Nubia as unequalled in beauty, and far superior to those of Arabia. Of the former little notice has been taken but from that observant traveller; of the latter the fame has long been distinguished; and the Arabian horse, celebrated for his beauty and swiftness, has been long exported to the most remote countries of Europe, to correct and improve the native breeds. In Arabia, almost every man possesses his horse, which lives in the same apartment, or tent, with his family, and is considered as constituting by no means the lest important part of it. Harsh and violent applications, such as the whip or spur, are rarely inflicted on it. It is fed with the most regular attention, and cleaned with incessant assiduity. The Arab occasionally appears to carry on a conversational intercourse with his horse, and his external attachment to this animal excites in return a corresponding affection. The horse being purified under his management from every vicious propensity, and guarded against casual injury with the utmost solicitude, suffering the infant children to climb its legs without the slightest attempt to kick or shake them off. The Arabs never cross the breeds of horses, and preserve the genealogies of these animals for a considerable number of generations. The horses of Barbary are in high reputation, also, for speed and elegance, as are likewise those of Spain. In various parts of the East, as in India and in some parts of China, there exists a race of these animals, scarcely exceeding the height of a large mastiff, and with their diminutive size are generally connected not a little intractability and mischievousness. In no country of the globe has the breeding of the horse been attended to on more enlarged and philosophic principles than in Great Britain; and with such success have the efforts of the English on this subject been at