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sided in man, the one good and the other evil; and who were zealous in expelling the evil soul or dæmon, and hastening the return of the good spirit of God, by contemplation, prayer, and singing of hymns. They also embraced opinions, nearly resembling the Manichean doctrine, which they derived from the tenets of the oriental philosophy.

EUCHITES, another sect of fanatics, who, in the twelth century, infested the Greek and eastern churches, and who were charged with believing a double Trinity, rejecting wedlock, abstaining from flesh, treating with contempt the sacraments of baptism and the Lord's supper, and the various branches of external worship, placing the essence of religion solely in external prayer, and maintaining the efficacy of perpetual supplications to the Supreme Being for expelling an evil genius, who dwelt in the breast of every mortal. This sect is said to have been founded by one Lucopetrus, whose chief disciple was named Tychicus. By degrees the title Euchites became a general and invidious appellation for persons of eminent piety and zeal for genuine Christianity, who opposed the vicious practices and insolent tyranny of the priesthood; as the Latins afterwards comprehended all the adversaries of the Roman pontiff under the general terms of Waldenses and Albigenses.

EUCHOLOGIUM, Gr. evxoλoytov, i. e. a discourse on prayer; from eux, prayer, and Aoyos, discourse; the Greek ritual, wherein are prescribed the order and manner of every thing relating to the administration of their ceremonies, sacraments, ordinations, &c. F. Goar has given an edition of it in Greek and Latin, with notes, at Paris.

EUCHO'LOGY, n. s. Gr. Evxoλoylov. A formulary of prayers.

EUCLID OF ALEXANDRIA, the celebrated mathematician, flourished in the reign of Ptolemy Lagus, about A. A. C. 280. He reduced all the fundamental principles of pure mathematics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, into regularity and order, and added many others of his own discovering; on which account he is said to be the first who reduced arithmetic and geometry into the form of a science. He likewise applied himself to the study of mixed mathematics, and especially to astronomy and optics, in which he also excelled. His works, as we learn from Pappus and Proclus, are The Elements of Geometry; Data; Introduction to Harmony; Phenomena; Optics; Catoptrics; a Treatise of the Division of Superficies; Loci ad Superficiem; Porisms; Fallacies; and four books of Conics. Of these the most celebrated is his Elements, of which there have been numberless editions in all languages. A fine edition of all his works, now extant, was printed in 1703, by David Gregory, Savilian professor of astronomy at Oxford. Euclid was greatly esteemed by king Ptolemy; who once asking him if there was any shorter way of coming at geometry than by his Elements, Euclid answered that there was no royal road to geometry.'

EUCLID OF MEGARA, a celebrated "hilosopher

and logician, flourished about A.A. C. 400. Thes Athenians having prohibited the Megarians from, entering their city on pain of death, this philosopher disguised himself in female clothes to attend the lectures of Socrates. After the death of Socrates, Plato and other philosophers went to Euclid of Megara, to she'ter themselves from the tyrants who governed Athens. Euclid admitted but one chief good; which he sometimes called God, sometimes Spirit, and sometimes Providence. EU'CRASY, n. s. Gr. ευκρασία. An agree

able well-proportioned mixture of qualities, whereby a body is said to be in a good state of health.

EUDIOMETER, an instrument for ascertaining the purity of the atmospherical air, or the quantity of oxygenous gas or vital air contained in it, chiefly from its diminution on a mixture with nitrous air. See AEROLOGY. Several kinds of these have been invented, of several of which we shall give a short account:

The first eudiometer, as invented and used by Dr. Priestley, was a divided glass tube, into which, after having filled it with water, and inverted it into the same, one measure or more of common air, and an equal quantity of nitrous air, are introduced by a small phial, which is called the measure; and thus the diminution of the volume of the mixture, which is seen at once by the gradations of the tube, discovers the purity of the air required. Dr. Priestley's discovery was announced to the public in 1772; and several persons, both at home and abroad, presently availed themselves of it, by framing other more accurate instruments.

A preferable method of discovering the purity of the air by an eudiometer, is recommended by M. Fontana. The first simple eudiometer consisted only of a glass tube, as uniformly cylindrical as possible in its cavity, about eighteen inches long, and three-fourths of an inch in diameter in the inside, hermetically sealed at one end. The outside had circles drawn round it, marked with a diamond, three inches from one another, or at such distances as are exactly filled by equal measures of elastic fluids. When the parts of these divisions were required, the edge of a ruler, divided into inches and smaller parts, was held against the tube; so that the first division of the ruler might coincide with one of the marks on the tube. The nitrous and atmospherical air are introduced into this tube to be diminished, and the purity of the atmospheric air thus ascertained; but, that an equal quantity of elastic fluid may always be certainly introduced, M. Fontana contrived a curious instrument as a measure. Notwithstanding the accuracy of this instrument, M. Fontana found that it was still liable to some errors, which he endeavoured in vain to remedy.

M. Saussure of Geneva invented an eudiometer which he thought more exact than any of those above described. His apparatus consists of the following parts:-1. A cylindrical glass bottle with a ground stopple, containing about five ounces and a half, which serves as a receiver for mixing the two airs. 2. A small glass phial, about one-third of the size of the receiver, to serve as a measure. 3. A small pair of scales which

must weigh exactly. 4. Several glass bottles for containing the nitrous or other air to be used, and which may supply the place of the receiver when broken. The whole of this apparatus may be easily packed into a box, and thus transported from place to place, and even to the summits of very high mountains. The method of using it is as follows:-The receiver is to be filled with water, closed exactly with its glass stopple, wiped dry on the outside, and weighed very exactly. Being then immerged in a vessel full of water, and held with the mouth downwards, the stopple is removed, and two measures of common and one of nitrous air are introduced into it by a funnel, one after another: these diminish as soon as they come into contact; in consequence of which the water enters the recipient in proportionable quantity. After being stopped and well shaken, to promote the diminution, the receiver is to be opened under water; then stopped and shaken, and so on for three times successively. At last the bottle is stopped under water, taken out, wiped very clean and dry, and weighed exactly as before. It is plain, that now when the bottle is filled partly with elastic fluid and partly with water, it must be lighter than when quite full of water; the weight of it then being subtracted from the former, the difference shows that quantity of water which would fill the space occupied by the diminished elastic fluid. Now, in making experiments with airs of different degrees of purity, the difference will be greater when the diminution is less, or when the air is less pure, and vice versâ ; and thus the comparative purity between two different kinds of airs may be determined. This eudiometer, however, is liable to some errors, principally arising from the inaccuracy of the measure, and the difficulty of stopping the bottle without occasioning a pressure upon the contained elastic fluid.

To avoid the inconveniences to which all the above instruments are subject, Mr. Cavallo employs a glass tube with its scale and measures, the length of the tube being about sixteen or seventeen inches, and between one-half and twothirds of an inch in diameter, and of as equal a bore as possible throughout; having one end sealed hermetically, and the other shaped like a funnel, though not very wide. The following directions are given by Mr. Cavallo for marking these divisions: When the tube is filled with water, a measure of air should be thrown into it; the tube must then be suspended to a hook over the pneumatic trough, by a loop, as represented, so high that the surface of the water within the tube may be very near the surface of the water in the trough, two inches, for instance, above it; then, looking horizontally through the tube, a mark should be made by sticking a bit of soft wax upon the tube, just coinciding with the lower part of the surface of the water within it; in which place afterwards a circular mark should be made with a piece of agate or diamond. Thus the first measure is marked, and in like manner may the rest. The practitioner, however, should never venture to mark the tube with an indelible stroke after one trial, lest he should be mistaken. The proper method is to mark them first with wax, and then repeat the operation

once or twice, to correct such errors as might escape the first time; after which the mark may be made with a diamond, flint, or perhaps more conveniently with a file. The polish of the inside of both tube and measure should be taken off with emery; which is a very laborious operation, though it is particularly necessary that the measure should be done in this manner.' To use this eudiometer, fill the tube with water, taking care that no bubbles of air remain in it; and, inverting it with the mouth downwards, leave it in the water leaning against the side of the trough. Fill the measure then with the elastic fluid whose purity is to be tried. Put the eudiometer upon the shelf of the trough, keeping it perpendicular, and with the mouth exactly upon the hole of the shelf, and throw the measure of air into it: fill it again with the same air, and throw this likewise into the tube. Then fill it with nitrous air, and throw this also into the tube, which must be shaken immediately after the operation by moving it alternately up and down in the water of the tub for about a quarter of a minute. It is then left a short time at rest, and suspended by the hook, so that the surface of the water in the inside may be about two inches above that in the tub; when the brass scale is slided upon it till the upper edge of the lower ring coincide with the middle part of the surface of the water within the tube, and then we may observe which division of the scale coincides with any of those on the tube; by which means the quantity of elastic fluid remaining in the tube may be clearly seen, even to the 1-100th part of a measure.' Mr. Cavallo, after giving directions for noting down the results, advises that, in this operation, care should be taken to shake the tube immediately after the nitrous air has been thrown into it, and to leave it at rest afterwards for some time; otherwise the results of similar experiments are far from being alike. By holding the measure or the eudiometer with the hand, which is warmer than the water of the trough, the elastic fluid undergoes some degree of rarefaction, so that the event of the experiments may often be rendered precarious. For this reason the instruments should be held only with the extremities of the fingers and thumb.

In vol. LXXIII. of the Philos. Trans. we have an account of an eudiometer by Mr. Cavendish. He preferred the abbé Fontana's to all the rest; the great improvement in which is, that as the tube is long and narrow, and the orifice of the funnel not much less than the bore of the tube, and the measure made to deliver its contents very quick, the air rises slowly up the tube in one continued column; so that there is time to take the tube off the funnel, and to shake it before the airs come quite into contact; by which means the diminution is much greater and more certain than it would otherwise be. Thus, if equal measures of nitrous and common air are mixed in this manner, the bulk of the mixture will, in general, be about one measure; but, if the airs are suffered to remain in contact about a quarter of a minute before they are shaken, the bulk will hardly be less than one measure and one-fifth; and it will be very different according the time they are suffered to remain before they are shaken.

In like manner, if, through any fault in the apparatus, the air rises in bubbles, as in that case it is impossible to shake the tube soon enough, the diminution is always less than it ought to be. Another very considerable advantage arising from the method of mixing the airs just mentioned is, that the diminution takes place in its full extent almost instantaneously; but, if they are allowed to remain for some time in contact before they are shaken, the mixture will continue diminishing for many hours afterwards. The reason of these differences is, that, in the abbé Fontana's method, the water is shaken briskly up and down in the tube while the airs are mixing; by which means every small portion of nitrous air must be in contact with water, either at the instant it mixes with the common air, or at least immediately after; and it seems that the water, by absorbing the nitrous acid the moment it is formed, greatly contributes to the quickness of the diminution, as well as to the quantity of it. Hence Mr. Cavendish was induced to try whether the diminution would not be more certain and regular, if one of the airs were added to the other slowly and in small bubbles, the vessel being kept shaking all the while that the mixture was made: and on trial he found that this method fully answered his expectations. In some of his experiments, Mr. Cavendish had occasion to use a larger apparatus, which is represented in the annexed diagram. A repre

C

B

the specific gravity of the air; for the thing found by weighing the vessel is the difference of weight of the included air and an equal bulk of water; which, as air is no less than 800 times lighter than water, is very nearly equal to the weight of a quantity of water equal in bulk to the included air. A common balance is not convenient for weighing the bottles under water, without some addition to it: for the lower the vessel of air sinks under water, the more the air is compressed; which makes the vessel heavier, and thereby causes that end of the beam to preponderate. Hence we must either have the index placed below the beam, as in assay balances; or by some other means remove the centre of gravity of the beam so much below the centre of suspension as to make the balance vibrate, notwithstanding the tendency which the compressibility of the air in the vessels has to prevent it.

Scheele's eudiometer is merely a graduated glass cylinder, containing a given quantity of air, exposed to a mixture of iron filings and sulphur, formed into a paste with water. The substances may be made use of in the following manner:

Make a quantity of sulphur in powder, and iron filings, into a paste with water, and place the mixture in a saucer, or plate, over water, on a stand raised above the fluid; then invert over it a graduated bell-glass, and allow this to stand for a few days. The air contained in the bellglass will gradually diminish, as will appear from the ascent of the water.

Sir H. Davy passes the nitrous gas into a saturated solution of green muriate of iron, which becomes black and opaque when fully impregnated with the gas. The air to be tried is contained in a small graduated tube, largest at the open end, which is introduced into the solution, and then gently inclined, to accelerate the action, which will be complete in a few minutes, so as to have absorbed all the oxygen. He observes, that the measure must be taken as soon as this is done, otherwise the bulk of the air will be increased by a slow decomposition of the nitric acid formed.

sents a bottle containing nitrous air inverted into the trough of water D E. Bis a bottle fitted with Volta had recourse to the ascension of hydroa bent glass tube C. This bottle is to be filled gen gas. For this purpose, two measures of hywith common air without any water, and is first drogen, with three of the air to be examined, slightly warmed by the hand: the end of the are introduced into a graduated tube, and fired glass tube is then put into the bottle of nitrous by the electric spark. The diminution of bulk, air as represented in the figure. As the bottle observed after the vessel has returned to its oriB cools, a little nitrous air runs into it, which ginal temperature, divided by three, gives the instantly loses its elasticity in consequence of quantity of oxygen consumed. coming into contact with the atmospherical air. This condensation occasions an influx of fresh nitrous air, and so on till the whole is exhausted. Thus the nitrous air is added slowly to the other without coming into contact with water, till the whole of it has run out from the bottle A into B; after which the water flows in to supply the vacancy occasioned by the diminution.

In mixing the airs together, Mr. Cavendish commonly added the respirable slowly to the nitrous. The quantities of air made use of, and the diminution of the mixture, are determined by weighing the vessels under water. No sensible error can arise from any difference in

Phosphorus and sulphuret of potassa have likewise been employed in eudiometry. A piece of phosphorus may be introduced by means of a glass rod into a tube containing the air to be examined, standing over water, and suffered to remain till it has absorbed its oxygen; which, however, is a slow process. Or a glass tube may be filled with mercury and inverted, and a piece of phosphorus, dried with blotting paper, introduced, which will of course rise to the top. It is there to be melted, by bringing a red-hot iron near the glass, and the air to be admitted by a little at a time. At each addition the phosphorus inflames; and, when the whole has been admitted,

the red-hot iron may be applied again, to ensure the absorption of all the oxygen. In either of these modes one-fortieth of the residuum is to be deducted, for the expansion of the nitrogen, by means of a little phosphorus which it affords. Seguin's eudiometer, consists of a glass tube, of about one inch in diameter, and eight or ten inches high, closed at the upper extremity. It is filled with mercury, and kept inverted in this fluid in the mercurial trough. A small bit of phosphorus is introduced into it, which, on account of its specific gravity being less than that of mercury, will rise up in it to the top. The phosphorus is then melted by means of a red hot poker, or burning coal applied to the outside of the tube. When the phosphorus is liquefied, small portions of air destined to be examined, and which have been previously measured in a vessel graduated to the cubic inch, or into grains, are introduced into the tube. As soon as the air which is sent up reaches the phosphorus, a combustion will take place, and the mercury will rise again. The combustion continues till the end of the operation; but, for the greater exactness, Seguin directs the residuum to be heated strongly. Instead of the rapid combustion of phosphorus, Berthollet has substituted its spontaneous combustion, which absorbs the oxygen of atmospheric air completely; and, when the quantity of air operated on is small, the process is accomplished in a short time.

Berthollet's apparatus consists of a narrow graduated glass tube, containing the air to be examined, into which is introduced a cylinder, or stick of phosphorus, supported upon a glass rod, while the tube stands inverted in water. The phosphorus thould be nearly as long as the tube. Immediately after the introduction of the phosphorus white vapors are formed, which fill the tube; these vapors gradually descend, and become absorbed by the water. When no more white vapors appear, the process is at an end, for all the oxygen gas which was present in the confined quantity of air, has united with the phosphorus; the residuum is the quantity of nitrogen of the air submitted to examination.

This eudiometer, though excellent of the kind, is nevertheless not absolutely to be depended upon; for, as soon as the absorption of oxygen is completed, the nitrogen gas exercises an action upon the phosphorus, and thus its bulk becomes increased. 'It has been ascertained, that the volume of nitrogen gas is increased by one-fortieth part; consequently the bulk of the residuum, diminished by one-fortieth, gives us the bulk of the nitrogen gas of the air examined; which bulk subtracted from the original mass of air, gives us the proportion of oxygen gas contained in it. The same allowance must be made in the eudiometer of Seguin.

The following account of Dr. Ure's eudiometer for measuring the combustible gases by explosion with the electric spark, we extract (by permission) from his well known Dictionary of Chemistry.

It consists of a glass syphon, having an interior diameter of from two-tenths to four-tenths of an inch. Its legs are of nearly equal length, each being from six to nine inches long. The

open extremity is slightly funnel-shaped; the other is hermetically sealed; and has inserted near it, by the blow-pipe, two platina wires. The outer end of the one wire is incurvated across, so as nearly to touch the edge of the aperture; that of the other is formed into a little book, to allow a small spherical button to be attached to it, when the electrical spark is to be transmitted. The two legs of the syphon are from one-fourth to half an inch asunder.

The sealed leg is graduated by introducing successively equal weights of mercury from a measure glass tube. Seven ounces troy, and sixty-six grains, occupy the space of a cubic inch; and 344 grains represent part of that column. The other leg may be graduated also, though this is not necessary. The instrument is then finished.

To use it, we first fill the whole syphon with mercury or water, which a little practice will render easy. We then introduce into the open leg, plunged into a pneumatic trough, any convenient quantity of the gases, from a measure glass tube, containing them previously mixed in determinate proportions. Applying a finger to the orifice, we next remove it from the trough in which it stands, like a simple tube; and, by a little dexterity, we transfer the gas into the sealed leg of the syphon. When we conceive enough to have been passed up, we remove the finger, and next bring the mercury to a level in both legs, either by the addition of a few drops, or by the displacement of a portion, by thrusting down into it a small cylinder of wood. We now ascertain, by careful inspection, the volume of included gas. Applying the fore-finger again to the orifice, so as also to touch the end of the platina wire, we then approach the pendent ball or button to the electrical machine, and transmit the spark. Even when the included gas is considerable in quantity, and of a strongly explosive power, we feel at the instant nothing but a slight push or pressure on the tip of the finger. After explosion, when condensation of volume ensues, the finger will feel pressed down to the orifice by the superincumbent atmosphere. On gradually sliding the finger to one side, and admitting the air, the mercurial column in the sealed leg will rise more or less above that in the other. We then pour in this liquid metal, till the equilibrium be again restored, when we read off as before, without any reduction, the true resulting volume of gas.

As we ought always to leave two inches or more of air, between the finger and the mercury, this atmospheric column serves as a perfect recoil spring, enabling us to explode very large quantities without any inconvenience or danger. The manipulation is also, after a little practice, as easy as that of the single tube. But a peculiar advantage of this detachable instrument is, to enable us to keep our pneumatic troughs, and electrical machine, at any distance which conve nience may require; even in different chambers, which, in the case of wet weather, or a damp apartment, may be found necessary to ensure electrical excitation.

We may analyse the residual gaseous matter, by introducing either a liquid or a solid re-agent.

We first fill the open leg nearly to the brim with quicksilver, and then place over it the substance whose action on the gas we wish to try. If liquid, it may be passed round into the sealed leg among the gas, but if solid, fused potassa; for example, the gas must be brought round into the open leg, its orifice having been previously closed with a cork or stopper. After a proper interval, the gas being transferred back into the graduated tube, the change of its volume may be accurately determined. With this eudiometer, and a small mercurial pneumatic cistern, we may perform pneumatic analyses on a very considerable scale.

In making experiments of this kind, several phenomena occur, which should be attended to: 1. When respirable air is mixed with nitrous air their joint bulk is diminished, and the diminution is greater when the air is purer, ceteris paribus, and vice versâ. 2. On mixing the two airs together all at once, the ensuing diminution is greater than if the same quantity of nitrous air be added to an equal quantity of respirable air at different times: and hence it follows, that, the quicker the two sorts of elastic fluids are mixed together, the greater is the diminution, and contrarywise. 4. Nitrous airs of different qualities occasion a different degree of diminution with respirable air; and, therefore, care should be taken to use such materials as afford air always of the same quality. The most proper substance for this purpose is very pure quicksilver; a quarter of an ounce or even less, with a proper quantity of diluted nitrous acid, will produce a great deal of nitrous air, which is always of the same quality, provided the metal be always of equal purity; but with other metals, as brass, copper, &c., the nitrous air made at one time is often different from that made at another, and therefore occasions a greater or less diminution when mixed with common air though precisely of the same sort. 4. The quality of nitrous air is impaired by keeping, especially when in contact with water; and for this reason it ought to be prepared fresh every two or three days. 5. In performing these experiments, it should be carefully remarked, that no mistake arise from heat or cold; as the elastic fluids are easily contracted or expanded by any variation of temperature. 6. Though the greatest diminution takes place immediately after mixing the respirable and nitrous airs together, especially when they are agitated, yet they continue to diminish a little for some time after; for which reason the diminution should be observed always at a certain time after the mixture is made. The whole process indeed ought always to be performed in a uniform manner, otherwise the results will be frequently very dissimilar. 7. It must be remarked, that the surface of the water which lies contiguous to the elastic fluid contained in a small vessel, is very far from being a plane, or even from being always of a similar figure in the same vessel, on account of the attraction or repulsion between the substance of the glass and water. This is altered by many circumstances, particularly by the adhesion of extraneous bodies; whence it is very improper to use common open phials for this purpose.

We must also take into consideration the drops of water adhering to the sides of the vessel, and the quality of the water in which the operation is performed. 8. In case the experiment is to take up some hours, in order to observe the last diminution, it will be proper to notice, by a good barometer, if the gravity of the atmosphere has suffered any alteration during that time; for a difference in its pressure may occasion some difference in the result of the experiments. 9. A simple apparatus is always to be preferred to a more complicated one, even though the latter should appear to have some advantage over it in point of accuracy. Complex machines are not only expensive, and subject to be easily put out of order, but occasion frequent mistakes, on account of the operator having generally many things to do and keep in proper order; whence it is easy to overlook some of them

EUDOCIA, or EUDOSIA, a celebrated lady, the daughter of Leontius, a philosopher of Athens; who gave her a learned education, and at his death left her only a small legacy, saying she was capable of making her own fortune. Pleading at Athens against her two brothers, for a share in her father's estate, without success,' she carried her cause personally by appeal to Constantinople; recommended herself to Pulcheria, the sister of the emperor Theodosius II., embraced Christianity, was baptised by the name of Eudosia, her original name being Athenais, and was soon after married to the emperor. A difference at length taking place, on account of the emperor's jealousy, excited by Chrysapius, the eunuch, she retired to Jerusalem, where she spent many years in building and adorning churches, and in relieving the poor. Dupin says that she did not return thence till after the emperor's death; but Cave informs us, that she was reconciled to him, returned to Constantinople, and continued with him till his death; after which she went again to Palestine, where she spent the remainder of her life in pious works. She died A. D. 459 or 460. She wrote a Paraphrase on the First Eight Books of the Old Testament, in heroic verse; another in prose on Daniel and Zechariah; a History of St. Cyprian and Justina; and a Life of Christ, in heroics, with many other poems, which are lost.

EUDOXIANS, a sect of heretics in the fourth century, who adhered to the errors of the Arians and Eunomians, maintaining that the Son was created out of nothing; that he had a will different from that of the Father, &c.

EUDOXIUS, the founder of the sect of the Eudoxians, was patriarch of Antioch and Constantinople, and succeeded Macedonius in the latter see, A. D. 360. He was a zealous defender of the Arian doctrines, and died A. D. 370.

EUDOXUS, a celebrated astronomer of Cnidus, in Caria, who flourished about A. A. C. 370. He studied geometry under Archytas, and travelled into Egypt to learn the sciences. There he studied, together with Plato, for thirteen years; after which they came to Athens, where Eudoxus taught with great renown. Eudoxus composed Elements of Geometry, from which, Proclus tells us, Euclid himself borrowed liberally. Cicero calls Eudoxus the greatest astro

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