OCTAGONAL. a. Having eight sides and angles. ŎCTAHEDRON, or OCTAEDRON, in geometry, one of the five regular bodies, consisting of eight equal and equilateral triangles. (See the article BODY.) The square of the edge of the octahedron is to the square of the diameter of the circumscribing sphere, as 1 to 2. If the diameter of the sphere be 2, the solidity of the octahedron inscribed in it will be 1.33333, nearly. The octahedron is two pyramids put together at their bases, therefore its solidity may be found by multiplying the quadrangular base of either of them, by one-third of the perpendicular height of one of them, and then doubling the product. OCTANDRIA. (oxTw, eight, and amp, a man, or husband,) The eighth class in Linnéus's sexual system; consisting of plants with hermaphrodite flowers, which are furnished with eight stamens, or male organs of generation. See BOTANY. OCTANGULAR. a. (octo and angulus, Lat.) Having eight angles. OCTA'NGULARNESS. s. (from octangular.) The quality of having eight angles. OCTANT, or OCTILE, in astronomy, that aspect of two planets, wherein they are distant an eighth part of a circle, or 45° from each other. OCTAPLA, in matters of sacred literature, denotes a polyglot bible consisting of eight columns, and as many different versions of the sacred text; viz. the original Hebrew both in Hebrew and Greek characters, Greek versions, &c. OCTATEUCH, an appellation given to the eight first books of the Old Testament. OCTAVE, in music, an harmonical interval, consisting of eight tones, or degrees of sound. The most simple perception the soul can have of true sounds is that of unison; because the vibrations there begin and end together. The next to this is the octave; wherein the more acute sound makes precisely two vibrations, while the graver or deeper makes one; and wherein, by consequence, the vibrations of the two meet at every vibration of the more grave. Hence unison and octave pass almost for the same concord. Hence also the proportion of the sounds that form the octave is in numbers, or in lines, as 2 to 1, so that two chords or strings of the same matter, thickness, and tension, one whereof is double the length of the other, produce the octave. The octave is called, by the ancients, diapason, because containing all the simple tones and concords; all of which derive their sweetness from it, as they arise more or less directly out of it. To be just, it must contain diatonically seven de , or intervals; and, consequently, eight or sounds: whence its name, ntaining in it all the other simple concords, and the degrees being the dif ferences of these concords; it is evident, the division of the octave comprehends the division of all the rest. By joining, therefore, all the simple concords to a common fundamental, we have the following series: Fund. 3d, 3dg, 4th, 5th, 6th 1, 6th g, 8 ve. 1; : : : 1:1:1: Again, the system of the octave containing all the original concords, and the compound concords being the sum of the octave, and some less concord; in order to have a series to reach beyond an octave we must continue them in the same order through a second octave, as in the first; and so on through a third and fourth octave. Such a series is called the scale of music. Though the composition of octaves may be carried on infinitely, yet three or four octaves are the greatest length we go in ordinary prac tice: the old scales went no farther than two, or at most three octaves, which is the full com. pass of an ordinary voice: and, notwithstanding the perfection of the octave; yet, after the third, the agreement diminishes very fast; nor do they ever go so far at one movement, as from one extreme to the other of a double or triple octave; seldom beyond a single octave: nor is either voice or instrument well able to go beyond. To form a fourth octave, if the acuter string be half a foot, which is but a small length to give a clear sound, the longer must be eight feet. If, then, we go beyond the fourth octave, either the acute term will be too short, or the grave one too long. The octave is not only the greatest interval of the seven original concords, but the first in degree of perfection. As it is the greatest in terval, all the less are contained in it. Indeed, the manner wherein the less concords are found in the octave is somewhat extraordinary; viz. by taking both an harmonical and arith metical mean between the extremes of the oc tave, and then both an arithmetical and barmonical mean between each extreme, and the most distant of the two means last found; i.e. between the last extreme and the first arithmetical, and between the greater extreme and the first harmonical mean, we have all the lesser concords. Mr. Malcolm observes, that any windinstrument being over-blown, the sound will rise to an octave, and no other concord; which he ascribes to the perfection of the octave, and its being next to unison. This ingenious writer was in error with regard to this supposed fact. All the natural harmonics may be produced on a wind-instrument by its being over-blown. Thus, if the breath when propelled into a flute with a certain velocity, with all the holes covered, caused it to emit the tone or sound D; breath impelled with a double velocity will produce the sound D an octave above; a triple velocity will produce the sound G a twelfth above the fundamental tone; a quadruple velocity will produce D the fifteenth, or double octave; a quintuple velocity will produce the sound F sharp, a seventeenth above the primitive tone, and so on. See HARMONICS. OCTAVE denotes also the eighth day after a festival of the church. OCTAVIA, a Roman lady, sister to the emperor Augustus, and celebrated for her beauty and virtues. She married Claudius Marcellus, and after his death M. Antony. Her marriage with Antony was a political step to reconcile her brother and her husband. Antony proved for some time attentive to her, but he soon after despised her for Cleopatra; and when she attempted to withdraw him from this unlawful amour, by going to meet him at Athens, she was totally banished from his presence. This affront was highly resented by Augustus, who resolved to revenge her cause by arms, which he ultimately did. Marcellus, her son by her first husband, was married to a niece of Augustus, and was publicly intended as a successor to his uncle; but his sudden death plunged all his family into the greatest grief. Virgil, upon this occasion, in his Eneid, paid a melancholy tribute to the memory of a young man whom Rome regarded as her future father. He was desired to repeat his composition in the presence of Augustus and of his sister. Octavia burst into tears as soon as the poet began, but when he mentioned Tu Marcellus eris, she swooned away. This pathetic encomium upon the virtues of young Marcellus was liberally rewarded by Octavia, and Virgil received 10,000 sesterces for every one of the verses. Octavia had two daughters by Antony, Antonia Major and Antonia Minor. The death of Marcellus continually preyed upon the mind of Octavia, who died of melancholy about 10 years before the Christian era.-2. Á daughter of the emperor Claudius by Messalina. She was betrothed to Silanus, but by the intrigues of Agrippina, she was married to the emperor Nero in the 16th year of her age, but was soon after divorced on pretence of barrenness. She was afterwards, by the intrigues of Poppaa, banished, and was ordered to kill herself by opening her veins. Her head was cut off, and carried to Poppaa. OCTAVIANUS, or OCTAVIUS CESAR. Vid. AUGUSTUS. OCTAVIUS. This name was common to many eminent Romans, but of celebrity inferior to Octavius Cæsar, afterwards Augustus.2. A man who opposed Metellus in the reduction of Crete, by means of Pompey. He was obliged to retire from the island. OCTA'VO. (Latin.) A book is said to be in octavo when a sheet is folded into eight leaves. OCTENNIAL. a. (from octennium, Lat.) 1. Happening every eighth year. 2. Lasting eight years. OCTOBER, in chronology, the tenth month of the Julian year, consisting of thirtyone days: it obtained the name of October from its being the eighth month in the calendar of Romulus. See the articles MONTH and YEAR. OCTOBLEPHARUM. In botany, a genus of the class cryptogamia, order musci. Capsule ovate, fringe simple, of eight unconnected teeth. One species only, an exotic moss. OCTOE'DRICAL. a. having eight faces. OCTOFID CALYX. In botany, an eight-cleft calyx, as in tormentilla. See CLEFT. OCTO GENARY. a. (from octogeni, Lat.) Of eighty years of age. O'CTONARY. a. (octonarius, Latin.) Belonging to the number eight. OCTONO'CULAR. (octo and oculus, Lat.) Having eight eyes (Derham). OCTOPETALOUS. a. (ox and la) Having eight flower leaves. O'CTOSTYLE. s. (oxw and sux.) The face of a building or ordonnance containing eight columns (Harris). O'CTUPLE. a. (octuplus, Latin.) Eightfold. O'CULAR. a. (from oculus, Latin.) Depending on the eye; known by the eye. OCULARIA. (from oculus, the eye, so called from its uses in disorders of the eye.) In botany. See EUPHRASIA. O'CULARLY. ad. (from ocular.) To the observation of the eye (Brown). O'CULATE. a. (oculatus, Latin.) Having eyes; knowing by the eye. OCULI ADDUCTOR. In myology, see RECTUS INTERNUS OCULI. OCULI ATTOLLENS. See RECTUS SU- OCULI CANCRORUM. See CANCER. OCULI DEPRESSOR. See RECTUS SU See RECTUS SUPE- LIQUUS INFERIOR OCULI. OCULI OBLIQUUS MAJOR. OCULI OBLIQUUS MINOR. See OBLI See OBLI O'CULIST. s. (from oculus, Latin.) One who professes to cure distempers of the eyes (Bacon). The most celebrated oculists of the present day are Mr. Ware and Mr. Phipps. OCULUS. See ANATOMY and EYE. OCYPETE, one of the harpies, who infected whatever she touched. The name signifies swift flying. OCYROE, a daughter of Chiron, who had the gift of prophecy. She was changed into a mare. (Vid. Melanippe.) OCZAKOW, or ОczAKOFF, a town and fortress, lately of Turkey in Europe, but now included in the Russian government of Catha rinenslaf. It is seated at the mouth of the his readers by the variety of verse, and the deDnieper, opposite Kinhurn, 50 miles W. of licacy of words; the beauty of numbers, and Cherson and 190 N. by E. of Constantinople. the description of things most delightful in Lon. 30. 50 E. Lat. 46. 50 N. themselves. Variety of numbers is essential to the ode. ODA, in the Turkish seraglio, signifies a class, order, or chamber. Hence Oda Bachi, is an officer in the Turkish service. ODD. a. (udda, Swedish.) 1. Not even; not divisible into equal numbers (Brown). 2. More than a round number (Burnet). 3. Particular; uncouth; extraordinary (Pope). 4. Not noted; not taken into the common account; unheeded (Shakspeare). 5. Strange; unaccountable; fantastical (Swift). 6. Uncommon; particular (Ascham). 7. Unlucky (Shakspeare). 8. Unlikely; in appearance improper (Addison). O'DDLY. ad. (from odd.) 1. Not evenly. 2. Strangely; particularly; unaccountably; uncouthly (Locke). ODDLY-ODD. A number is said to be oddly-odd, when an odd number measures it by an odd number. So 15 is a number oddlyodd, because the odd number 3 measures it by the odd number 5. O'DDNESS. s. (from odd.) 1. The state of being not even. 2. Strangeness; particularity; uncouthness; irregularity (Dryden. Collier). ODDS. s. (from odd.) 1. Inequality; excess of either compared with the other (Hook.). 2. More than an even wager; more likely than the contrary (Swift). 3. Advantage; superiority (Hudibras). 4. Quarrel; debate; dispute (Shakspeare). ODE. s. (win.) A poem written to be sung to music; a lyric poem. Ode, in the modern poetry, is a lyric poem, consisting of long and short verses, distinguished into stanzas, or strophes, wherein the same measure is preserved throughout. The odes of the ancients, Vossius observes, had a regular return of the same kind of verse, and the same quantity of syllables, in the same place of every similar verse: "But there is nothing (says he) but confusion of quantities in the modern odes; so that, to follow the natural quantity of our syllables, every stanza will be a different song." 66 He should have observed, however, that all the ancient odes were not of such kind. But he proceeds: The moderns have no regard to the natural quantity of the syllables, and have introduced an unnatural and barbarous variety of long and short notes, which they apply without any regard to the natural quantity of syllables; so that it is no wonder our vocal music has no effect." De Poem. Cantu. Among the ancients, ode signified no more than a song; with us, they are different things. The ancient odes were generally in honour of their gods, as are many of those of Pindar and Horace: sometimes on other subjects, as those of Anacreon, Sappho, &c. The English odes are generally composed in praise of heroes, and great exploits; as those of Dryden, Prior, &c. The distinguishing character of the ode is sweetness: the poet is to sooth the minds of At first, indeed, the verse of the ode was but of one kind; but for the sake of pleasure, and the music to which they were sung, they by degrees so varied the numbers and feet, thai their kinds are now almost innumerable. One of the most considerable is the Pindaric, dis tinguished by the boldness and rapidity of in flights. The ancient ode had originally but cre stanza, or strophe: but was at last divided into three parts; strophe, antistrophe, and exde. The priests going round the altar, singing the praise of the gods, called their first entrance strophe, i. e. turning to the left; the second, turning to the right, they called antistrophe, q. d. returning: lastly, standing still before the altar, they sung the remainder; which they called epode. Among the modern English odes the most distinguished are Dryden's ode on St. Cecilia's day, and Collins's ode on the Passions. ODE (Alcaic). See ALCAIC. ODENATUS, a celebrated prince of Pal myra. He early inured himself to bear fatigues, and accustomed himself to the labor of a military life. He was faithful to the Romans, and when Aurelian had been taken prsoner by Sapor, king of Persia, Oderates warmly interested himself in his cause. Sapr ordered him, in consequence of his solicits tions in favour of Aurelian, to appea nuclore him, on pain of being devoted to instant de struction with all his family. Odenatus dis dained the summons of Sapor, opposed force to force, and obtained some advantages over the troops of the Persian monarch. For these services, Gallienus, the then reigning empe ror, named Odenatus as his colleague on the throne, and gave the title of Augustus to children, and to his wife the celebrated Zenbia. He perished, some time after, by the dag ger of one of his relations, at Emessa, about the 267th year of the Christian æra. Zenobia succeeded to all his titles and honours. ODENSEE, a town of Denmark, capit of the isle of Funen, and a bishop's see. It supplies the greatest part of the army with all their leather accoutrements, and is particularly famous for gloves. Here are also manufac tures of cloth, sugar, and soap. It is situate on a river, six miles from the bay of Stege trand, and go W. by S. of Copenhagen. Len 10. 17 E. Lat. 55. 30 N. ODER, a river of Germany, which has in source in the mountains of Moravia, and Abas N. to Oderberg: then passes by Ratibor, Op peln, Breslau, and Glogau, in Silesia; Crossen, Frankfort, Lebus, Custrin, and Frinwalt, in Brandenburg; and Gartz, Stettin, Carin, Wollin, Usedom, and Wolgast, in Pomerania. Below Stettin it forms large lake or hay, called Gross Haff, and then enters the Balde sea by three channels, called Peene, Swin, and Jiwenow; between which lie the islands of Usedom and Wollin. ODESSA, a fortified seaport of Russia, in The government of Catherinenslaf, seated on gulf of the Black Sea, 44 miles W. by S. of Oczakow. Lon. 29. 24 E. Lat. 46. 28 N. Odessa is now rising into great opulence. When Mr. Macgill visited it in 1805, though had then scarcely existed four years, it conined a population of 10,000 persons. The ouses are well built of freestone, and the reets are regular. There is a secure harbour or vessels of considerable burthen, and a mole ↑ quay extending above a quarter of a mile to the sea. A thousand ships have been aded in this port in a single year; and the sort of the Polish nobles to this thriving wn renders it a very gay and lively place. ODEUM, in Grecian antiquity, a musiceatre, built by Pericles; the inside of which as filled with seats and ranges of pillars, and the outside the roof descended shelving wnwards from a point in the centre, with any bendings, in imitation of the king of ersia's pavilion. Here the musical prizes ere contended for; and here also, according Aristophanes, was a tribunal. ODEYPOUR, a town of Hindostan, capital Jushpour, in the province of Orissa. It is miles N.E. of Ruttunpour, and 220 N.W. Cattack. Lon. 83. 22 E. Lat. 22. 37 N. O'DIBLE. a. (from odi, Lat.) Hateful. ODIHAM, a town in Hampshire, with a arket on Saturday. Here are the remains of ancient castle, and of a royal palace, barns, c. It is seated on the Basingstoke canal, 24 iles N.E. of Winchester, and 42 W. by S. London. ODIN (see FREA), in mythology, called 30 in the dialect of the Anglo-Saxons Woden Wodan, a name given by the ancient Scyians to their supreme god, and assumed, out.70 years before the Christian era, by ge, a Scythian prince, who conquered the orthern nations, made great changes in their wernment, manners, and religion, enjoyed reat honours, and had even divine honours aid him. According to the account given f this conqueror by Snorro, the ancient histoan of Norway, and his commentator Torfæus, din was a Scythian, who withdrew himself, ith many others in his train, by flight, from e vengeance of the Romans under the conact of Pompey and having officiated as riest in his own country, he assumed the diection of the religious worship, as well as the ivil government, of the nations which he conquered. Having subdued Denmark, Sweden, nd Norway, he retired to Sweden, where he lied. There is nothing certain in this account; but it is probable, that the god, whose prophet or priest this Scythian pretended to be, was named Odin, and that the ignorance of succeeding ages confounded the deity with his priest, composing out of the attributes of the one, and the history of the other, the character of the northern conqueror. He deluded the people by his enchantments and skill in magic: VOL. VIII. having cut off the head of one Mimer, who in his lifetime was in great reputation for wisdom, he caused it to be embalmed, and persuaded the Scandinavians that he had restored it to the use of speech; and he caused it to pronounce whatever oracles he wanted. The Icelandic chronicles represent Odin as the most eloquent, and persuasive of men; they ascribe to him the introduction of the art of poetry among the Scandinavians, and likewise the invention of the Runic characters. He had also the address to persuade his followers, that he could run over the world in the twinkling of an eye; that he had the direction of the air and tempests; that he could transform himself into all sorts of shapes, could raise the dead, could foretel things to come, deprive his enemies, by enchantment, of health and vigour, and discover all the treasures concealed in the earth. They add, that by his tender and melodious airs he could make the plains and mountains open and expand with delight; and that the ghosts, thus attracted, would leave their infernal caverns, and stand motionless about him. Nor was he less dreadful and furious in battle; changing himself into the shape of a bear, a wild bull, or a lion, and amidst ranks of enemies committing the most horrible devastation, without receiving any wound himself. ODINUS, a celebrated hero of antiquity, who flourished about 70 years before Christ, in the northern parts of ancient Germany, or the modern kingdom of Denmark. He was at once a priest, a soldier, a poet, a monarch, and a conqueror. He imposed upon the credulity of his superstitious countrymen, by the manner of his death, and made them believe as he expired that he was going into Scythia, where he should become one of the immortal gods. O'DIOUS. a. (odiosus, Latin.) 1. Hateful; detestable; abominable (South). 2. Exposed to hate (Clarendon). 3. Causing hate; invidious (Milton). O'DIOUSLY. ad. (from odious.) 1. Hatefully; abominably (Milton). 2. Invidiously; so as to cause hate (Dryden). O'DIOUSNESS. s. (from odious.) 1. Hatefulness (Wake). 2. The state of being hated (Sidney). O'DIUM. s. (Latin). Invidiousness; qua◄ lity of provoking hate (King Charles). ODO (Saint), second abbot of Clugni, was born at Tours, 879. The sanctity of his life was such, that even kings and popes referred their disputes to his unbiassed judgment. He wrote some religious books, and died 943. ODOMETER, is an instrument for meas suring the ground or distance passed over by a carriage. The best contrivance for this purpose with which we are acquainted was invented by Richard Lavell Edgeworth, Esq. His description of it is as follows. This instrument may be easily fixed to the axletree bed of a post-chaise, gig, or any other carriage. Ope turn and a half of a screw is framed round the nave of one of the hinder wheels by a slip of iron three quarters of an inch broad, and one-eighth of an inch thick; this is wound round the nave, and fastened to it by screws passing through five or six cocks, which are turned up at right angles on the slip of iron. The helix so formed on the nave of the carriage wheel acts as a worm or screw upon the teeth of the wheel A, upon the arbor of which another screw of brass B is formed, which acts upon the brass wheel C (fig. I. pl. 122). This wheel C serve also as a dial-plate, and is divided into miles, halves, quarters, and furlongs; the figures indicating the miles are nearly three quarters of an inch long, so as to be quite distinct; they are pointed out by the index D, which is placed as represented in the plate, in such a manner as to be easily seen from the carriage. These two brass wheels are mounted by the irons E E upon a block of wood F, eight inches long, two inches thick, and five inches broad. This block may be screwed upon the axletree-bed by two strong square-headed wood screws. If the carriage permits, this block should be fixed obliquely on the axletree-bed, so that the dial-plate may be raised up toward the eye of the person looking out from the carriage. H is a ratchet wheel attached to the arbor of the wheel A, which, by means of the click I, allows the wheel to be set with a key or handle fitted to the squared end of the arbor at K. L is a long spring screwed on the block; it presses on the wheel A, to prevent it from shaking by the motion of the carriage. A small triangular spring is put under the middle of the dial-plate wheel for the same purpose. If the wheel of the carriage is exactly five feet three inches in circumference, the brass toothed wheel which it turns should have twenty teeth, and that which serves as a dialplate should have eighty; it will then count five miles. If the carriage wheel is either larger or smaller, a mile should be carefully measured on a smooth road, and the number of turns which the carriage wheel makes in going this mile may easily be counted by tying a piece of fine packthread to one of the spokes, and letting the wheel, as it moves slowly for ward, wind up the packthread on its nave. When the wheel has proceeded a half or a quarter of a mile, unwind the string, and count the number of turns which it has made. By the addition of another wheel of eightyone teeth, placed under the dial-plate wheel, and moved by the screw C, with a proper hand fitted to it, and proper figures on the dial-plate, this machine would count four hundred miles. ODONTALGIA. (odontalgia, odolanya, from ods, a tooth, and any, pain.) tooth-ache. The ODONTALGICA. (medicamenta odontalgica, odoyranyina, from odlahy, the toothache.) Medicines which relieve the tooth ache. ODONTOID PROCESS. (processus odon toides, from dus, a tooth, and uda;, form, because it is shaped like a tooth.) A process of the second vertebra of the neck. See DesATDONTOLOGY. (odous, očare;, a truth, and eyes, a treatise, or discourse.) The doctne of teething, or dentition. There are few branches of science of so greet consequence that have been so little attended are The different orders of mammalian animals in the Linnéan system are for the most part determined by the peculiarity of the teeth. Much the comfort of human life, as well as much of the beauty of the human face (notwithstanding the the organ is thrown entirely out of the LA of the regular surgeon, and left entirely at the mercy of persons who for the most part hare but slender pretensions to any scientife quaintance with the subject), are to a couserable extent dependent upon the state of the teeth; and much of the general age, and, că--sequently, of the real value of that noble armas the horse, as well as of various other animals, a ascertained by their structure and appear. They are subject to diseases of various kinds, am of the most distressing character: to agony the most excruciating, and to foulness and cel most humiliating, from the fetor they produce. We shall, therefore, take leave to dwelt annewhat more largely, and in a more physiologe point of view, upon this important science, f`-z has ever been done, as we believe, in a wok this kind before, or has often been done in any work even of a professional nature. 1. In the first stages of infancy nature desi us for the softest aliment, so that the gums a are then sufficient for the purpose of mardus tion; but as we advance in life, and require a different food, she wisely provides us with teeth. These are the hardest and whitest of war be and, at full maturity, we usually find thirty-tw both jaws; viz. sixteen above, and as many be low. Their number varies indeed in dife! animals, as well as different human subjects; bat it is seldom seen to exceed thirty-two in the and it will very rarely be found to be less twenty-eight. Each tooth in the human subject may divided into two parts; viz. its body, or that pr which appears above the gums; and its far root, which is fixed into the socket. The ." pression, is called the neck of the tooth. T Every tooth is composed of its corter enamel, and its internal bony substance. enamel, or as it is sometimes called, the vitre part of the tooth, is a very hard and coat substance, of a white colour, and peculiar to “ teeth. It is found only upon the body of th touth, covering the outside of the bony or inten nal substance. When broken it appears fir or striated; and all the strige are directed ir the circumference to the centre of the tot This enamel is thickest on the grinding surace, and on the cutting edges or points of the teeth, becoming gradually thinner as it approaches the neck, where it terminates insensibly. It seem to be au earth, united with a portion of a |