the projectile force of gunpowder. It consists of a small barrel of great strength, in which a certain quantity of powder is exploded, and the force exerted is measured by the extension it produces upon a spring, or the distance to which a heavy weight is raised. The effect is also estimated by the distance to which a ball of known weight is thrown from a small mortar by a certain quantity of powder. The French formerly used a mortar for an eprouvette of 7 inches calibre, and the test of the powder was for 3 ounces to throw a copper globe weighing 60 lbs. to the distance of 300 feet. EPSOM (Sax. Ebbsham), a market town of Surrey, England, on the margin of Banstead downs, 15 m. S. W. of London, on the London, Croydon, and Epsom railway; pop. in 1851, 3,390. At one time it seemed destined to become a prominent watering place, in consequence of the discovery of medicinal springs, impregnated with sulphate of magnesia, from which the celebrated Epsom salt was manufactured. The springs are no longer visited, but the town has gained another attraction in the great annual races held during the week preceding Whitsuntide on the neighboring downs. They are attended by 300,000 or 400,000 persons of every class of society, and the grand stand on the race course, erected in 1829-30, is capable of holding 7,500 persons. The chief excitement centres in the race for the Derby stakes, which takes place on Wednesday. EPSOM SALT, the name given in pharmacy to the hydrated sulphate of magnesia, which was obtained as far back as the year 1675, by evaporating the waters of some mineral springs at Epsom. Sea water was afterward found to contain it, the brine remaining after the separation of the common salt consisting of the sulphate of magnesia and the chlorides of magnesium and calcium. It was readily obtained by collecting the first crystals which formed, and washing them with a strong solution of the same salt. An excellent quality is manufactured at Baltimore and Philadelphia, from the mineral magnesite, a silicious hydrate of magnesia, which is found in the serpentine of that region. The mineral, reduced to powder, is dissolved in sulphuric acid. The product being dried is calcined in order to decompose the sulphate of iron, and convert it into the peroxide of iron. It is then dissolved in water, and any iron present is precipitated by sulphuret of lime. The crystals of sulphate of magnesia are separated and dissolved again to complete their purification. This salt, and calcined magnesia also, have been prepared from the dolomite or magnesian carbonate of lime, by the process of Mr. William Henry of Manchester. The mineral was calcined, and the lime and magnesia were then converted into hydrates by sprinkling with water; the former was dissolved out by a minimum quantity of hydrochloric acid, and the latter was converted into a sulphate by sulphuric acid.-Epsom salt is also found as a mineral substance, incrust ing the walls of caves, in the form of an efflorescence, and also in silky fibres. In the Mammoth cave in Kentucky, loose masses of it are seen adhering to the roof like snow balls, and in many other caves of the western states it is found upon the walls or mixed with the earth upon the floor. It occurs in some of the gypsum quarries near Paris, and in other parts of France; and wherever water becomes charged with gypsum or sulphate of lime, and flows over rocks containing carbonate of magnesia, the sulphate of magnesia is likely to appear from the result of mutual decomposition of the two salts. Hydrated sulphate of magnesia consists of 1 equivalent of magnesia, 20; 1 of sulphuric acid, 40; and 7 of water, 63=123; or, per cent., magnesia 16.26, acid 35.52, and water 51.22. It crystallizes in 4-sided prisms with reversed dihedral summits, or 4-sided pyramids. Their hardness is 2.25, and specific gravity 1.75. The crystals effloresce slightly in the air, and if they contain any chloride of magnesium this is shown in their deliquescing. They dissolve in their own weight of water at 60°, and in their weight of boiling water. Sulphate of soda is sometimes fraudulently mixed with Epsom salt. Its presence may be detected by dissolving 100 grains in water, and precipitating with a boiling solution of carbonate of potash. Unless this precipitate of carbonate of magnesia amount when dried to 34 grains, sulphate of soda is no doubt present. The salt is much used in medicine as a cathartic, and being of a mild and cooling nature, is particularly adapted to the treatment of fevers and inflammatory affections. The medium dose is an ounce, and this is said to be deprived of its bitter taste, and rendered quite palatable, by being dissolved in about a pint of water, and boiled a few minutes with 1 grains of tannic acid or 2 or 3 drachms of roasted coffee, strained, and sweetened with sugar. EQUATION (Lat. æquo, to make equal), an algebraic sentence affirming the equality of two quantities. Equations, however, are used not only in simple algebra, but in all the higher branches of calculus, according to the general principles explained in the article ALGEBRA.— EQUATION OF PAYMENTS is an arithmetical rule for finding the mean or average time for paying several sums due at separate times: thus, multiply each sum by the number of days, from one day before the first falls due until that sum is due; divide the sum of these products by the whole amount due, and the quotient will be the number of days to be counted from the day before the first falls due.-EQUATION OF TIME is the difference of time between a true sun dial and a true clock, as explained under DAY. EQUATOR (Lat. æquo, to make equal), a circle round the earth midway between the poles, so called because when the sun is vertical over this circle (March 20 and Sept. 20) the day and night are equal in all parts of the world. The celestial equator is a circle in the heavens, midway between the poles. When the sun crosses the celestial equator he is vertical at the equator. EQUATORIAL, belonging to the equator, a geographical and astronomical term. An equatorial signifies an equatorial telescope, that is, a telescope which revolves on an axis parallel to the axis of the earth, which renders its motion parallel to the plane of the equator. (See OBSERVATORY.) EQUINOX (Lat. æquus, equal, and nox, night), the moment when the sun's centre crosses the celestial equator; the vernal equinox being about March 20, and the autumnal about Sept. 20.-EQUINOCTIAL LINE is a name sometimes given to the equator.-The EqUINOCTIAL POINTS are the points in the celestial equator at which the sun's path crosses the equator; these points move slowly westward, as explained in the article ECLIPTIC; the movement is called the precession of the equinoxes.-EQUINOCTIAL COLURE is a celestial meridian passing through the equinoctial points. EQUITES (plural of the Lat. eques, horseman), or knights, an order of the people in ancient Rome, which in some respects may be compared with the English gentry. Their origin is attributed by Roman historians to the institution of Romulus, who is said to have selected the first 300 out of the 3 chief divisions of the patricians, and to have divided them into 3 centuries, named Ramnenses, Titienses, and Lucernes, corresponding to similar names of the 3 patrician tribes. Tarquin the Elder added 3 new patrician centuries, and Servius Tullius 12 new ones from among the richest plebeians. They formed a regular military body, being obliged to serve on horseback in time of war, and were divided into turma of 30 men each, subdivided into tens. They were also called celeres, and their chiefs tribuni celerum. Politically they seem to have represented an aristocracy of wealth in opposition to the aristocracy of birth, particularly after they became a distinct body of the people by the institutions of Servius Tullius. Under the republic the knights were enrolled by the censors and consuls for a service of 5 years, being supplied by the state with a large sum for the purchase, equipment, and maintenance of a horse, but with no personal pay. Every dictator, immediately after his appointment by the senate, had to select a commander of the horse, called magister equitum. During service they had no vote in the assemblies of the centuries. At the time of the siege of Veii, when the want of cavalry was much felt by the Romans, a new body was added to the ancient knighthood, consisting of a large number of young volunteers who offered to enter the ranks at their own expense. The new knights received a regular pay, but had no vote, and no share in many distinctions enjoyed by the old order. Gradually they coalesced into a numerous and wealthy middle class, placed politically and socially between the patricians and plebeians, and were so recognized by a law of Caius Gracchus (123 B. C.). Of the privileges as jurymen which the same laws bestowed upon them, they were deprived by Sylla. At VOL. VII.-17 that period they were generally the farmers of the public revenues, under the name of publicani. As such, though their merits are extolled by Cicero, who belonged to their order, they seem to have been despised by the Roman people. Under the empire, owing to the heterogeneous elements of which their increased body was composed, they gradually sank, and in spite of efforts to restore their influence, they disappeared from the stage of political life under the later emperors. In general the history of the Roman knighthood, as a political institution, is involved in great obscurity. EQUITY. In a general sense, equity is natural right, but as used in jurisprudence it denotes an administration of law with reference to the particular circumstances of a case, in contradistinction to the ordinary method of adjudicating by a rule of general application. This, however, is a theoretical rather than a practical view, for equity as distinguished from strict law is necessarily administered by uniform rules. A judgment founded upon the particular circumstances of a case, without any reference to principles applying in common to such case and to others, would hardly deserve the name of a judicial decision, but rather would be an arbitrary opinion unregulated by legal analogy. In other words, it would be the capricious adjudication of a court not bound by any precedent. This has never been the nature of equity as administered in any country where laws have been prescribed for the regulation of society. At an early period, it is true, many cases would occur which were not provided for by legislation. In these a discretion must be exercised; but every case when decided becomes a precedent, and thus in time the equitable or exceptional law acquires a systematic form and obligation. Another class of cases is where a positive law is productive of some individual hardship not contemplated in the en acting of the law. Relief may then be afforded by the intervention of an equitable power, whose office is not to abrogate or interfere with the operation of the law according to its real intent, but to afford exemption in cases which were probably not foreseen, and therefore could not have been intended. Again, there may be an omission in a law, whether it be statutory or derived from custom, to provide for cases of non-compliance by reason of casualty or some cause not involving serious fault. Thus where forfeitures or penalties are consequent upon the failure of strict performance of an agreement, there is an obvious distinction between intentional neglect and accidental failure, especially if in the latter case it was by inevitable misfortune. There is here room for equitable relief in the one case without impairing the operation of the law in the other, to which alone it justly applies. It is indeed difficult to distinguish with exact precision the line that divides culpable negligence from excusable omission; or again, to determine how far actual disability should be a ground of relief from legal obligation. A man of small capacity for business may make improvident contracts which he cannot fulfil, or another who has ordinary sagacity may still by accident be deprived of the means of paying debts which he has fairly incurred. Where no fraud is involved, the obligation of contracts cannot as a general rule be abrogated by a court of equity. Hardship will sometimes occur, and there is a natural impulse to give relief in the individual case; but such leniency often repeated is found to be productive of counterbalancing consequences not at first anticipated, and the necessity of a general rule becomes apparent. The discretionary power of the Roman prætor was at first unrestricted. Soon, however, his discretion was brought under certain rules from which he was not allowed to depart. It is true that annually when each prætor went into office he made a formal publication of the rules by which he would be gov. erned in his administration of the laws during his term of office, which might allow the inference that he had an arbitrary liberty to disregard former precedents; but practically it was but the adoption of the edict of his predecessors, with occasional modifications suggested by enlarging experience. The English equity system was early dissevered from the ordinary administration of law, and has ever since remained separate. Yet the equitable principles maintained in the court of chancery could have been applied by the common law courts, and to some extent the latter have been compelled to admit modifications into their practice by analogy to equitable proceedings. Thus the penalty of a bond was formerly held to be the debt, and to be recoverable; yet after the court of chancery gave relief upon the payment of the real debt, which was usually specified in the condition of the bond, the common law courts gave the same relief at any time before judgment; though if payment of the amount really due was not prior to that time tendered, judgment could be entered for the penalty and enforced by execution for the whole amount. A similar change has also taken place with regard to mortgages. (See EQUITY OF REDEMPTION.) Again, the conveyance of lands to uses became a peculiar subject of equity jurisdiction; the use not being recognized at law, but being enforced in chancery. The statute of uses (27 Henry VIII.) was intended to make the use cognizable as the real title in courts of common law, but this effect was defeated by the over-nice scruple of the judges, whereby a limitation of a second use, as if a conveyance was made to A for the use of B, in trust for C, was held not to be within the statute; and the court of chancery again intervened to enforce such second use under the name of a trust, and has ever since retained exclusive jurisdiction of that class of cases in England. Another peculiarity of the English equity system was formerly the right of calling upon the defendant in the action to testify, first by a sworn answer to the coinplaint, and then by examination upon accounting, and in various other cases, at the election of the complainant. But this distinction has been superseded by the recent statutory provisions in England and the United States, by which parties are made competent witnesses in all the courts. (See EVIDENCE, and also CHANCERY.) EQUITY OF REDEMPTION, the interest which the owner of lands retains after having mortgaged them, or rather after the mortgage has become due. By the common law, upon the non-payment of the sum secured by the mortgage at the day when due, there was an absolute forfeiture of the mortgaged property; but courts of equity interfered and compelled the mortgagee upon tender to him of the amount really due to deliver up the premises, and he was also obliged to account for the profits if he had been in possession. At an early period a mortgage was considered to be a conveyance subject to be defeated by the payment of a specified sum at a certain time, the mortgagee being in the mean time entitled to the possession as the legal owner; and even since the change introduced by the courts of equity in respect to the right of the mortgageor to redeem, the old theory has still so far prevailed in England that the right of possession was deemed to pass with the mortgage. Although latterly the mortgageor has usually retained possession until the debt has become due, yet this is only by the assent of the mortgagee; and unless a stipulation to that effect is contained in the mortgage, there is nothing to prevent the mortgagee from maintaining an action of ejectment to obtain possession. Yet notwithstanding this apparent legal ownership, the equitable doctrine is that the mortgageor is the real owner until foreclosure, so far at least that his estate descends to his heirs, or may be devised or otherwise conveyed by him, subject only to the right of the mortgagee, which right is to hold the land as a security for payment of the debt. An incongruity is however still suffered to exist in several particulars. Thus a lease made by the mortgageor can be avoided by the mortgagee, while on the other hand a lease by the mortgagee is subject to the limitation of his estate, and on payment of the mortgage will cease. So the wife of the mortgageor was held not entitled to dower because he had only an equity of redemption, yet the wife of the mortgagee was also excluded on the ground that the estate which he had was in the nature of a trust. But now, by the statute 3 and 4 William IV., c. 105, the equity of redemption is subject to dower and curtesy. In the United States the equity doctrine has been long since carried out with more consistency. The mortgage is considered merely as a security, which can be made available only by a sale under a decree of a court or under a power of sale contained in the mortgage itself. Until such sale the fee of the estate is in the mortgageor, and he has the entire disposition of it, except that the lien of the mortgage will continue as against all persons to whom the lands may descend or be conveyed; the mortgageor retains possession until such sale, unless his right is divested by a court of equity, by reason of the insufficiency of the mortgaged lands as a security. So the estate of the mortgageor is subject to the lien of a judgment, and may be sold on execution, and his wife is entitled to dower except as against the mortgagee, and even as against him unless she joined in the mortgage. This is on the supposition that the mortgage was made subsequent to marriage; if made before, the dower of the wife would of course be subject to the right of the mortgagee. Such in the state of New York are the incidents of the estate of the mortgageor, usually though not with strict propriety termed the equity of redemption; the same system has been generally adopted in the other states. tions, which are convenient in calculations, and can be easily retained by the memory. Another table, in which the equivalent weight of oxygen is assumed to be 100, has been much used on the continent of Europe. It was proposed by Berzelius, mainly it would seem for the purpose of discountenancing a theory advanced by Prout, that all the equivalent numbers are simple multiples of that of hydrogen; superiority was claimed for it on the ground that as oxygen is the most abundant of all the elements, and since the greater number of bodies studied by chemists are compounds of it, calculations would be simplified if its equivalents were regarded EQUIVALENT, CHEMICAL. It is a matter as equal to 100; in which case it is only necesof experience, that when an element enters into sary to add 100, 200, 300, &c., to the equivalent chemical combination with another element, weight of the element with which oxygen is it does so in a fixed proportion which may be combined, in order to ascertain the equivalent expressed in numbers. This ratio is termed weights of its several oxides. The equivalent the combining equivalent, combining propor- of sulphur, a very common element, would also tion, equivalent weight, or simply the equiva- have a simple expression, being equal to 200. lent of the element. The term atomic weight These instances, however, do not at all comis also used synonymously by those who accept pensate for the high numbers by which the the atomic theory. Each of the elements has other equivalents must be represented; numits own special combining equivalent, and is bers which cannot be remembered without incapable of uniting with other elements except great difficulty, and which render even the most in this proportion or some multiple of it. The common calculations extrémely laborious unless equivalents of compound bodies are represented logarithms are resorted to. Berzelius, who beby the sums of the equivalent numbers of all lieved that the equivalent numbers should be the elements which enter into their composi- regarded as entirely accidental and unconnecttion. The weights of the equivalents of the ed with each other, desiring to give them the elements are ascertained by determining experi- most accurate possible expression, introduced mentally how much of each is required to re- the custom of attaching to them large decimal place the others in their combinations with fractions; indeed, the power to do this which some well-known element, the weight of the is afforded by the high numbers of his system equivalent of which has been assumed. Thus, has always been claimed as one of its advanthe quantity by weight of each element which tages. The accuracy of thus employing several unites with one equivalent of oxygen to form a decimals, in cases where the process by which protoxide, analogous to water, is usually con- the result has been obtained is liable to errors sidered to represent its equivalent. A knowl- of considerable magnitude, was long since edge of the exact weights of the equivalents is pointed out by Erdmann, who has called attenof the first importance to chemists; all calcu- tion to the fact that no greater or lesser numlations regarding the composition of bodies, ber of decimals ought to be given than the exas in analysis, or of the quantities of materials periment justifies. All tables of equivalents to be employed in the manufacture of com- heretofore published are more or less defecpounds, being based upon them. As the equiv- tive from neglect of this truth. The equivalent alent numbers express nothing but the relative numbers have been recently thoroughly inweights in which the elements unite with each vestigated and revised by Dumas, who has again other, it is evident that the weight of any one brought forward and upheld Prout's theory, equivalent may be arbitrarily chosen as a stand- which, owing to the vigorous opposition of Berard to which all the others shall be referred; zelius, had found but few supporters of late it is essential only that the relation be strictly years. Most of the equivalents thus far studied observed. Tables of equivalents are thus con- by Dumas are simple multiples of that of hystructed, in which the equivalent weight of each drogen. To this rule there are, however, sevof the elements is attached to its name. Several exceptions; among which some are multieral standards have been selected by different chemists; only two, however, have ever been generally used. The equivalent weight of hydrogen, being smaller than that of any other element, was regarded as unity by Dalton, who referred all the other equivalents to it. This system has always been generally adopted by the chemists of Great Britain and the United States. It possesses the very great advantage that in it the equivalents are represented by small numbers, many of them without frac ples of, while others are multiples of of an equivalent of hydrogen. It may be mentioned that it is still a matter of doubt whether the equivalents of several of the elements should not be regarded as twice, or that of others as of those ordinarily admitted; a change which would greatly simplify certain portions of chemical science. This question has been warmly discussed for several years, and many chemists habitually employ equivalents thus modified; in this article, however, the most common usage of chemists will be adhered to. The numbers in the annexed table of equivalents have been taken in part from Dumas' memoir, (Comptes rendus, xlvi., 952), and in part from Kapp and Will's Jahresbericht für Chemie, &c., for 1857. For convenience of reference both the hydrogen and oxygen scales are given; the numbers of the latter being readily obtained by dividing those of the former by the fraction 100. The names of those elements which from their variety are comparatively unimportant, are printed in italics; the equivalents of a few of these have not as yet been determined. 16, and apprenticed himself to a maker of harpsichords. Possessing a remarkable inventive faculty, he soon rose to the position of foreman, and his ingenuity bade fair to be of great benefit to his employer, when the latter, moved by jealousy, dismissed him from his service. Another harpsichord maker who had received an order for an instrument, the construction of which baffled his ingenuity, offered him a certain sum to undertake the work, provided only the employer's name should appear in connection with it. The instrument, when completed, excited so much admiration, that the maker was compelled to confess that it was the production of Erard. Attention was at once drawn to the young workman, who was applied to for a variety of new instruments which people wished to have constructed, and who soon after much increased his reputation by the production of a clavecin mécanique, or mechanical harpsichord, which contained several improvements on the instruments in use. The duchess de Villeroy, a woman of taste in music, wished to retain him in her service; but preferring his liberty, he declined her flattering offers, and remained in her hotel, where a suitable work room had been fitted up for him, only long enough to execute several ideas which she suggested. It was here, in 1780, that he constructed his first pianoforte, an instrument which, though invented a number of years previous, was then almost unknown in France, and the introduction of which into that country may be said to date from this time. In connection with his brother Jean Baptiste, he soon after established a manufactory of pianofortes in Paris, which gradually became the first in Europe. Among his inventions was an instrument with 2 key boards, one for the piano, and one for the organ; one of which was fitted with a sliding key board for transposing the music, for the use of Marie Antoinette. During the revolutionary period, the brothers Erard went to England, and established a manufactory of pianos and harps in London; but in 1796 Sébastien returned to Paris, and thenceforth his life was passed between that city and London. He constructed the first grand pianos with single action ever made in Paris; subsequently in 1808 much improved the mechanism of the instrument, and in 1823 completed his inventions in this department, by the production of his grand piano with repeating movement. In 1811 his double action harp appeared in London, where it became so popular, that in a single year, instruments to the value of £25,000 were sold. His last important work was the grand organ constructed between 1827 and 1830 for the chapel royal of the Tuileries. During the last 40 years of his life his inventive faculty seemed never idle, and of the 15 or 20 inventions for which he took out patents, not one was perfected without close study and repeated experiments. The celebrity which his instruments have gained remains undiminished, and Erard pianos are still unsurpassed for |