A Latin edition of the Kreüterbuch was published by Kyber in 1552. This edition has a learned preface written by Conrad Gessner. It is sometimes spoken of as a separate work of Tragus. It has for its title, Hieronymi Tragi de Stirpium maxime earum quæ in Germannia nostra nascuntur, &c. libri tres in Latinam linguam conversi, interprete David Kyber Argentinensi, Argent.,' 4to. Several editions of the German book have been published; the best of these is that of 1695, which was edited by Melchior Sebitz and Nicolas Agerius. Tragus died at Hornbach in 1554. Haller, Bibliotheca Botanica; Adanson, Familles des Plantes; Biog. Univ.) TRAJAN'S COLUMN, a celebrated work at Rome, which has served as a precedent rather than as a model for other triumphal or honorary pillars. [TRAJANUS.] The idea of employing a column for such purpose-probably derived from Egyptian obelisks [OBELISK]—seems to have been first adopted by the Romans, but neither manifests much invention nor regard to propriety. An obelisk is evidently complete in itself; is not intended to bear any support, or to be kept steady by it, but is calculated to stand by itself. A column, on the contrary, is only a member of a structure, detached from which and from its entablature it has no meaning nor any particular grace, being apt to look tottering and top-heavy.' It is chiefly as forming a lofty and conspicuous object that a single colossal column recommends itself as a triumphal monument; yet such geneal outline might be preserved without adhering to the precise shape and details derived from examples from any cae of the orders. In this respect Trajan's pillar is not so great an architectural solecism as many of the numerous eclamns professing to be in imitation of, or after' it, Lecause, owing to its shaft being entirely embossed with sculptures, which, as Dyer happily expresses it -wind aloft And lead through various toils up the rough steep Its hero to the skies' the ordinary column character is done away with, and a degree of variety and magnificence is produced which may be allowed to silence the objections of criticism. There certainly was something poetical in the idea of making the shaft which bore the emperor's statue record his conquests and military exploits; and the sculptures emselves are not only superior specimens of Roman art, bat highly interesting and valuable as historical documents of costume. At the same time they serve to make evident how very ill the surface to which they are applied is calcalated to display them; for, instead of being extended horizontally, this vast bas-relief is coiled spirally from the se to the summit, so that the figures on the upper part of the shaft can hardly be made out; nor can those on the wer one be viewed consecutively, without going round round the column. This historical poem, as it has been called, addresses itself therefore more to the imagination an to actual inspection. Still the idea is magnificent, and the general effect of this column, as it stood originally in the centre of a regular area (Trajan's Forum), enclosed by rulonnades, must have been equally grand and picturesque. Trajan's column and the surrounding forum were the work of Apollodorus of Damascus; and the former was completed A.D. 114, six years after its commencement. It is ased upon a pedestal of rather low proportions, which is also embellished with sculpture, as is likewise the base; therefore although it is usually described as being of the Tuscan order, its character is altogether different, it being that of extreme richness and decoration. It has a staircase within, and is constructed of white Luna, or what is called Carrara marble. Semper, a German architect, who had lately an opportunity of minutely examining the pper part of the shaft, discovered traces of polychromy the mouldings of the capital. Though not so lofty, e Trajan Column is very far superior to the Antonine. ANTONINE.] There are engravings, by Piranesi, of both, an exceedingly large scale, the plates showing the evations of the columns, opening to an extent of 10 feet. The statue of St. Peter, which now stands on the Trajan Column, was erected by Domenico Fontana, in 1588, by Great Obelisk in front of St. Peter's, 132. [See OBELISK, p. 386, for the dimensions of others at Rome.] TRAJANO'POLIS (Τραϊανόπολις, οι Τραϊανούπολις), ε town in Thrace, was most probably built by the emperor Trajan, who adorned it with beautiful buildings. Trajanopolis was situated on the river Hebrus, at a little distance north of the pass which is formed by this river through the range of Mount Rhodope, and about 40 miles from its mouth. According to the Itinerarium Antonini,' this town was situated between Bricires and Cypsela, 37 miles from Bricires, and 29 miles from Cypsela. Ptolemy mentions Trajanopolis (iii. 11). In the fourth century A.D. Trajanopolis was still a considerable town, and so it was in the time of Constantine Porphyrogenitus. Mannert thinks that this town was destroyed by the Turks in the fifteenth century, and he states that nobody has examined the ruins of it. Paul Lucas however discovered an antient aqueduct at a short distance from the present town of Trajanopoli. This modern town is situated on the banks of the Maritza, or Hebrus, on or very near the site of antient Trajanopolis. Trajanopoli, the see of a Greek archbishop, is a small town of no importance: in 1829 it was taken by the Russians on their march from Adrianople to Enos. (Mannert, Geographie der Griechen und Römer, vii., p. 224.) TRAJANO'POLIS, or SELI'NUS (Zeλvõõç), was the most western town of Cilicia. The emperor Trajanus having died at Selinus, this town was for some time called Trajanopolis. It was situated at the mouth of the river Selinus, on a steep rock, surrounded on three sides by the sea, and it was renowned for its commerce and navigation. According to Ptolemy, the district in which this town was situated had the name of Selentis. Its present name is Selenti, which must not be confounded with Zelina, a considerable town east of Selenti. (Strabo, p. 682, Cas.; Dion Cassius, lxviii. 33; Livius, xxxiii. 20; Mannert, cited above, vi. 1, p. 85; Cellarius, Notitia Orbis Antiqui, ii., p. 196; Beaufort's Karamania.) TRAJANO'POLIS, a town in Mysia, between Antandrus and Adramyttium, according to the maps in the editions of Ptolemy, who mentions it among the towns of Mysia, but he puts it in 50° E. long. and in 40° 40′ N. lat. The longitude is apparently an error, because this point would be situated a little north of Thessalonica in Thrace, and not in Asia. The error being manifest, almost all editions of Ptolemy have adopted 56° instead of 50°; but in the edition of Joh. Noviomagus, Coloniae, 1540, 8vo. (p. 214), there is 50°: Mercator has 56°. Some geographers have made two towns of it, one in Mysia, and the other in Thrace. Cellarius thinks that Trajanopolis was not situated in Mysia, but farther east in Phrygia Major (ii., p. 40); and Mannert (vi., 2, p. 542) thinks that Trajanopolis is only another name of Melitopolis, in the mountains of Mysia, east of 56° E. long. TRAJA'NUS, MARCUS ULPIUS NERVA, was most probably born in 53 A.D., at Italica, the present Alcalà del Rio, on the Guadalquivir, not far from Seville in Spain. He was the son of one Trajan, who was descended from an old Spanish or Iberian family, and who is said to have been a consul (Eutropius, viii., c. 2); but his name is not found in the Fasti Consulares. Eutropius gives to Ulpius Trajanus the surname of Crinitus,' perhaps because he wore his hair long, as did his countrymen the Iberians. Trajan the elder having obtained a command in Asia Minor, went there, accompanied by his son, who distinguished himself at an early age in the wars against the Parthians and the Jews. He became consul in A.D. 91, together with Acilius Glabrio. After he had discharged his function he went to Spain, and he afterwards commanded the legions on the Lower Rhine. His military talents and his amiable character made him popu Jar with the troops; and though we know very little about | rous colonists. [WALLACHIA.] Trajan returned to Rome his early life, we must suppose that his merits were great. in the same year, and celebrated his second Dacian This we may conclude from the circumstance that the triumph. In memory of his victories over the Dacians a emperor Nerva, an old man without issue, adopted him in column was erected, in 114, by the architect Apollodorus, A.D. 97, and chose him for his successor, although there were on the Forum Trajani, which, having been preserved from several relations of Nerva who had perhaps more claims ruin, is still admired as one of the finest remnants of to the throne than Trajan. But, says Dion Cassius (lxviii., antient art. The column was 144 Roman feet high, acc. 4), Nerva was exclusively led in his choice by his care cording to Eutropius (viii., c. 2), and on the base of it is for the welfare of the empire; and he considered Trajan's the following inscription:Iberian origin as a matter of indifference. Yet Trajan's nomination as Cæsar was a new thing in Roman history, the imperial throne having hitherto been exclusively occupied by members of the old Roman aristocracy, so that Trajan was the first emperor who was born beyond the limits of Italy. Trajan received the news of his nomination in Cologne, and three months later (Aurelius Victor, Epitome, c. 12) the death of Nerva, which took place on the 27th of January, 98, made him master of the Roman empire. On his arrival at Rome the people received him with great demonstrations of joy, and Trajan soon proved that he deserved his high station. He appointed distinguished and honest men as public functionaries; he curbed the turbulent body of the Praetorians; he issued an edict against false accusers, and he banished those who were convicted of this crime to the barren islands of the Mediterranean. Corn being dear in Rome, he allowed its entrance duty-free, and he thus won the hearts of the people, while those whom he honoured with his intercourse were delighted by his affability. Yet the emperor never forgot his dignity. His virtues and eminent qualities became conspicuous in the first years of his reign, as we may see from the panegyric of Trajan, which Pliny the younger read in the senate as early as 100, after he had been made consul. In 103 Pliny, who was a personal friend of the emperor, was appointed proconsul of Bithynia and Pontus; and having inquired into the state of the Christians, he recommended them to the emperor, and thus mitigated the persecutions to which they had hitherto been exposed by Pliny himself. The letters that passed between Pliny and Trajan are the best sources with regard to the private character of this emperor. SENATUS. POPULUSQUE. ROMANUS IMP. CAESARI. DIVI. NERVE. F.NERVÆ Another column, which is likewise extant, was erected in honour of Trajan by the inhabitants of Beneventum after his victories over the Parthians. After the conquest of Dacia, eight years of peace elapsed, which Trajan employed in a careful administration, and in adorning Rome with beautiful buildings; he also founded a library, the Bibliotheca Ulpia, and an institution for the education of poor children of Italian parents. (Fr. A. Wolf, Von einer milden Stiftung Trajan's, Berlin, 1808, 4to.) In 114 Trajan left Rome to lead his armies against the Parthians. In the Asiatic part of the empire peace had already several times been disturbed, principally by the Arabs, who however were subdued by Cornelius Palma, the proconsul of Syria, who, in 105, conquered Arabia Petræa, and made it a Roman province. Some years later Cosrhoes, or Khosrew, king of the Parthians, deprived Exedares, king of Armenia, of his dominions, and created his brother Parthamaspes, or Parthamasiris, king of Armenia. The Romans having always been anxious to maintain their influence in Armenia-the independence, or rather dependence of this country on Rome was necessary for the security of the East-Trajan declared war against Khosrew. The Parthians were defeated, and in one campaign Trajan conquered Mesopotamia and delivered Armenia. He took up his winter-quarters at Antioch, relieved the Syrians, who were suffering from the consequences of a violent earthquake, and in the following year, 115, opened a new campaign. He crossed the Tigris, in the province of Adiabene, and the Parthians having again been defeated, he took the towns of Nisibis, Edessa, Ctesiphon, and Seleucia; Babylonia, Assyria, Armenia, and Mesopotamia became Roman provinces; a rebellion of the Jews in Egypt and Cyrenaica was quelled; Khosrew was deposed, and his brother Parthamasiris was put by Trajan on the throne of Parthia. As early as 100 Trajan was engaged in a war with Decebalus, king of the Dacians; at the head of a numerous army Trajan crossed the Danube, defeated the enemy, and in 101 took their capital, Zermizegethusa (Dion Cassius, lxviii., c. 9), which was most probably situated on the site of the present village of Varhely, not far from the pass of the Iron Porte, in Transylvania. In 102 Decebalus was compelled to purchase peace by the cession of a part of his territory; and on his return to Rome Trajan celebrated his first triumph, and was saluted with the name Dacicus. Lucius Quintus and Hadrianus, afterwards emperor, distinguished themselves in this war. Annoyed by his dependence on Rome, Decebalus violated the peace as early as 104, and Trajan hastened to the Danube, resolved to finish the war by the conquest of Dacia. He ordered a bridge to be constructed over the Danube, which was the largest work of this kind mentioned by the antients. According to Dion Cassius it consisted of twenty piers, 150 feet high, 60 wide, and 170 feet apart; the piers were united by wooden arches. (Dion Cass., lxviii., c. 13, ed. Reimar, and the note.) The whole length of it has been calculated at 4770 Roman feet. If the statement of Dion Cassius is true, this bridge seems not only to have served for the passage of the river, but the immense height of the pillars, of which scarcely more than seventy feet can have been under water, leads to the supposition that it was at the same time a strong fortification destined to command the navigation. At a height of eighty feet above the water, soldiers were protected against the missiles of the Dacian ships, while the fleet of the enemy in passing that bridge ran the risk of destruction. This bridge was either at Szernecz in Hungary, or five leagues above the junction of the Alt with the Danube, in Wallachia, not far from Nicopolis, where ruins of the Roman colonies of Romula and Castra Nova, and a Roman road, which is pretty well preserved, still exist. The war proved fatal to Decebalus. Defeated wherever he encountered the Romans, he killed himself in despair (105); and in 106 all Dacia was conquered and made a Roman province by Trajan, who sent there nume conquest of these extensive sailed with his fleet on the Tigris to the Persian Gulf, and cok up his winter-quarters in the town of Spasinus. When he had reached the sea, the example of Alexander suggested to him the idea of conquering India, but remembering his advanced age, he renounced that scheme. (Dion Cassius, lxviii., c. 29.) In 117 Trajan made an incursion into Arabia, and ordered a fleet to be kept on the Red Sea. Suffering from dropsy, he set out for Rome, but he died on his way at Selinus, a town in Cilicia [TRAJANOPOLIS], in the month of August, 117, at the age of sixtythree years nine months and four days, according to Eutropius (viii., c. 2). are Trajanth the bay; it is liable from its situation to be flooded when spring-tides in the bay and the stream of the Lee is swollen. The streets are repaired by county presentment, and are partially paved and flagged, but not lighted neither is there any nightly watch. An attempt to introduce the provisions of the new paving and lighting act (9 Geo. IV., c. 82) was resisted by the inhabitants. The sewers in the town are bad, and the streets are very dirty. There is no regular market-place, and the business of the market is conducted in the streets. Some of the streets are lined with respectable dwelling-houses (several of them of a superior description) and good shops; and the town has undergone great improvement within the last few years. The church is a large and handsome building, with a square tower crowned with pinnacles: the congregation averages 700 persons, and is increasing. There is a large and handsome Roman Catholic chapel (attended by 3000 persons), a small Methodist meeting-house, and another small one for Independents. Detached from the town, half a mile to the south-east, are the county gaol and a barrack; they are both substantial buildings; the gaol, built on the radiating principle, is capable of accommodating more than 200 prisoners; the barrack is capable of accommodating nearly 500 men, and has an hospital for 30 patients. A considerable brewery and a distillery are (Aurelius Victor, De Cæsaribus, c. 13; Epitome, c. 13; near the gaol. The county court-house, a handsome buildSextus Rufus, Breviarium, c. 8, 14, 20; H. Francke, Zuring of modern erection, is in the town; and in the same Geschichte Trajans und seiner Zeitgenossen, 1837, is a street as the court-house is the county club and newsvery valuable book.) room. There are an extensive hrewery, besides that already mentioned, and a smaller brewery, both in the town. Trajan was one of the greatest emperors of Rome. He is said to have been addicted to women and wine; but his public character was without reproach, except his passion for warfare and conquest. However he undertook no war for frivolous motives. He deserved the title of Optimus,' which the senate conferred on him. The memory of his name lasted for centuries, and two hundred years later the senators used to receive the emperors with the acclamation, Be happier than Augustus, and better than Trajan!' The body of Trajan was transported to Rome, where it was deposited under the Columna Trajani. His successor was Hadrian. TRAJECTORY, the technical name which was formerly given to a curve, that is, to a curve required to be found by means of given conditions; most frequently used for the required path of a particle acted on by given forces. The term is now seldom used. TRALEE, the assize-town of the county of Kerry, in the province of Munster in Ireland, 159 miles in a direct line south-west of Dublin, or 192 miles by the mail-road through Naas, Maryborough, Roscrea, Nenagh, Limerick, Rathkeale, Tarbert, and Listowel; 73 miles south-west of Limerick, and 74 miles west-north-west of Cork, through facroom and Killarney; in 52° 15′ N. lat. and 9° 38′ W. long. Tralee derives its name (Traigh-lee,'' the strand or shore of the Lee') from its position near the outfall of the little river Lee into the shallow and unsafe bay of Tralee. There was antiently a Dominican friary, under the invocation of the Holy Cross, founded (A.D. 1213) by John FitzThomas, one of the great Geraldine family. The knights of St. John of Jerusalem had also a commandery in this neighbourhood. In the Irish wars of Queen Elizabeth a body of Irish was routed at Tralee (A.D. 1600) with great slaughter by Sir Charles Wilmot. The earl of Desmond had a castle here, which having come, on the forfeiture of the earl, into the hands of Sir Edward Denny, served as a place of refuge for the English families resident in and about the town when Tralee was entered by the insurgents in the great rebellion of 1641. The castle held out for six months, but was at last obliged to surrender. The town was soon after burned, to prevent its falling into the hands of Lord Inchiquin. It was again burned (A.D. 1691) on the approach of King William's army. Tralee is in the barony of Trughenackmy: the parish is about four miles in length and one and a half in breadth, and has an area of 4391 acres, statute measure: the population in 1831 was as follows: The trade of Tralee is considerable, and it has been for some years rapidly progressive. In 1831, 991 persons were employed in the town and borough in retail trade and handicraft; and there were 214 capitalists, bankers, professional, and other educated men. There are two weekly markets, well supplied, and five yearly fairs. There are three banking establishments. The town is well supplied with fish, and on reasonable terms. Tralee is a port, but vessels have had to take in and discharge their cargoes at Blennerville, on the shore of the bay, a mile and a quarter distant: a ship-canal is in progress, perhaps finished by this time, by which vessels of 300 tons will be enabled to come up to the town, at the west end of which a large basin has been constructed. The port is visited yearly (taking the average of the seven years from 1827 to 1933) by about seven vessels (having a total of 1500 to 1600 tons) from foreign parts; in the same years nearly forty coasters (about 3000 tons) from Great Britain entered inwards, and about twenty-five coasters (800 to 1000 tons) from other ports in Ireland; while about fifty-five coasters (about 4000 tons) cleared out for Great Britain, and about fifteen or sixteen coasters (500 to 700 tons) for other ports in Ireland. The trade with Great Britain, especially the export trade, was steadily increasing through that interval; but the trade with other ports of Ireland was decreasing. The chief foreign goods imported were timber, deals, and staves; the chief article of import from Great Britain was coals; and the chief exports were wheat and oats, both rapidly increasing; barley, also increasing; and butter, which was diminishing. The corporation of Tralee (consisting of a provost, twelve free burgesses, and other officers) was created by charter of James I. It never had any property except the tolls on the Tuesday market and on one of the fairs: it has been abolished by the late act (3 & 4 Vict., c. 108) for regulating the Irish municipal corporations. Before the abolition there was a provost's court, which was a court of record for all personal actions not exceeding the sum of five marks. Petty sessions were held by the provost and some of the county magistrates twice a week. There was no borough gaol. The assizes for the county of Kerry are held here; and the assistant-barrister for the county sits at quarter-sessions and for the trial of civil bills four times in the year. Some of the county police are stationed in the town. Tralee returns one member to parliament. By the Irish Boundary Act (2 & 3 Wm. IV., c. 89), a boundary was adopted for parliamentary purposes, more restricted than the existing municipal boundary, but comprehending all the town, and allowing space for its extension. The num ber of electors on the register in 1839-40 was 296, namely | subjects to which they relate; but in Dr. Thomson's 285 ten-pound householders and 11 freemen. Tralee is a rectory in the diocese of Ardfert, and in the province of Cashel, now united to that of Dublin: the gross yearly value of the living is estimated at 4547. 78. 74d., the net value at 3777. 168.; there is a glebe-house fit for residence. In the Roman Catholic division the parish is united with the greater portion of three adjacent parishes. There is a nunnery of the order of the Presentation. There were in the year 1835 nine day-schools in the parish of Tralee: one of these, a free-school, with an average attendance of 50 children, was under the superintendence of the rector, and was supported by a grant from Erasmus Smith's fund, and by contributions from the clergy of the establishment; a second free-school was under the same superintendence; two others, free-schools, with an average attendance of 500 children, were under the superintendence of the Roman Catholic clergy, and were partly taught by the nuns of the Presentation; the other five schools, with an average attendance of 35 children each, were respectable schools, kept by ladies, and supported by the payments of the pupils. bank. The county fever-hospital, the county infirmary, with a dispensary attached, are at Tralee; and there are two asylums for the poor, a neat row of almshouses, a temporary asylum for lunatics before sending them to the district asylum at Limerick, and a prosperous savings' Races are held near the town, and a yearly regatta in the bay. There is a chalybeate spring about three miles west of the town, it is not in Tralee parish, on the northern shore of the bay, round whicha small watering-place has risen up, called the Spa of Tralee,' or more concisely Spa. There is an excellent strand for bathing. There are several gentlemen's seats round Tralee. Good limestone for building is quarried near the town. (Reports of Commissioners, and other Parliamentary Papers; Lewis's and Carlisle's Topographical Dictionaries; Dublin Almanack.) TRAM-ROAD, a road prepared for the easy transit of trams or waggons, by the insertion, in its surface, of smooth beams of wood, blocks of stone, or plates of iron, as wheel-tracks. It is therefore a kind of railway, adapted for the passage of vehicles with wheels of the ordinary form. Of the early kinds of railway which bear the characteristics, and frequently also the name, of tram-roads, an account is given under RAILWAYS, vol. xix., pp. 245, 246; and of the mode of constructing tram-ways in ordinary roads, and their advantages, a notice will be found under ROAD. vol. xx., pp. 33, 34. TRAMMELS, the name of the ELLIPTIC COMPASSES, described in that article, in which a bar carrying a pencil is guided by two pins which move in grooves. TRA'NI, a considerable town of the kingdom of Naples, situated on the coast of Apulia in the province of Terra di Bari, is an archbishop's see, whose archbishop is also bishop in partibus of Nazareth. The Gran Corte Civile, or court of appeal for civil suits, of the two provinces of Terra di Bari and Terra d'Otranto, and the Gran Corte Criminale of the province of Bari, hold their sittings at Trani. The town is well built it has a castle, which was built by the emperor Frederic II.; a handsome cathedral with a lofty tower, and several other churches and convents; a harbour for small vessels; and about 15,000 inhabitants, who carry on a considerable trade in agricultural produce, especially oil and corn. Trani is 8 miles S.E. of Barletta, 26 miles N.W. of Bari, and 120 miles E.N.E. of Naples. (Neigebaur, Gemälde Italiens; Serristori, Statistica dell' Italia.) History of the Society, brief notices of the most important papers will be found, under the particular heads to which those papers belong, and that work must therefore be considered as a valuable guide for those who would trace the progress of scientific discovery in this country during nearly 180 years, which have elapsed since the formation of the Society: it is to be regretted however that the work extends only to the end of the eighteenth century. Dr. Thomson has arranged the subjects of the papers in the Transactions,' under the following divisions:Natural History, Mathematics, Mechanical Philosophy, Chemistry, 6 and to these are added several miscellaneous articles. Under the first of these divisions are placed Botany, Zoology, Mineralogy, Geography, and Topography; and the number of papers on the first of these subjects amounts to about one hundred; it is observed however, that few of these were presented by members of the Society, and that since the formation of the Linnean Society, in 1788, none have been received in the Transactions. Sir Hans Sloane, who was elected in 1684, was the principal contributor, and his botanical papers are still of considerable value. The physiology of plants was first investigated by members of the Royal Society, but the discoveries which have been made during the present century have very much diminished the importance of the earlier papers on this branch of Natural History. The most curious are those of Dr. Grew (1670), on the anatomy of plants; of Mr. Barrel (1727), on the growth of the misseltoe of Dr. Smith (1788), on the irritability of plants; and the several papers by Mr. Knight which were read in 1799 and in subsequent years. Forty papers relate to agriculture, but they are of early dates; and the first is a review (1669) of Evelyn's 'Sylva and Pomona.' In the Transactions' are numerous detached papers on zoology, and these contain descriptions of several species of mammalia, birds, amphibia, fish, zoophytes, &c. Shot notices only of anatomical discoveries occur, and the earliest is a paper (1691), by Clopton Havers, on the structure and growth of bones: the Transactions' are, however, enriched by several papers on comparative anatomy. Of Physiology, or the properties and functions of living bodies, the number of papers is considerable, and they are classed by Dr. Thomson under the following subdivisions:-Circulation of the Blood, Respiration, the Action of the Skin, the Nervous System, Vision, Organs of Motion and Nourishment. The second, third, and filth volumes contain papers by Mr. Boyle on respiration; and among the later volumes will be found those of Dr. Currie (1792), and Mr. Brodie (1811), on animal heat: there are also two curious papers on the temperature which the human body is capable of bearing; and recently (1840), à valuable paper by Sir Charles Bell on the Nervous System. The Medical and Surgical papers are numerous; and though they are on miscellaneous subjects, they constitute a valuable repository of information on those branches of knowledge; among them are some remarkable cases of persons being burnt to death without visible cause, and an account of the cases of death from the gaol-fever in 1750 there are also several papers relating to inoculation for the small-pox, of which the first is in the volume for 1714 and a paper by Mr. Cheselden containing an account o the operation performed on the eyes of a boy who was born blind. The Transactions' contain few notices relating Mineralogy: among the earlier papers is one (1671) o the formation of cloth and paper from amianthus, and another (1731) on the first discovery of diamonds in Brazil. TRANQUEBAR. [HINDUSTAN, p. 208.] TRANSACTIONS, PHILOSOPHICAL, are the volumes containing the several papers relating to the sciences, which, after having been read at the meetings of the Royal Society of London, have been thought worthy of being made public at its expense. In the article ROYAL Under the head of Geology may be placed some im SOCIETY there has been given an account of the pubirea-portant papers concerning the rocks which constitute th tion of the first portions of the work, and of the number crust of the earth; and there are several on petrifactions of volumes which have appeared, from the time of its com- on shells and zoophytes, and on fossil bones. Amon mencement in 1665, to the year 1841. them also is a paper (1711) on the origin of peat, by th earl of Cromartie, and on mosses (1772), by Dr. Walker Forty-five papers have been published concerning th earthquake at Lisbon, besides several on volcanoes, burnin The papers are inserted in the volumes according as they were presented, and consequently they are destitute of any arrangement with respect to the nature of the coal-pits, and on the temperature of hot-springs. Mr. | The second great division is that of Mathematics, and on this important subject the papers are numerous. Among those which relate to the antient Geometry are the papers of Dr. Simson (1723), and of Mr. Brougham 1798), on Porisms; a problem by Dr. Pemberton (1763), concerning loci, and a paper by Dr. Horsley (1772), on the invention of Eratosthenes for determining prime numbers. There are nine papers on the origin of the nine digits; in one of which, by Mr. Barlow (1741), it is shown, from a date in the parish church of Romney, that the Arabic numerals must have been known in England about the year 1000. Of the rest, the most important are the logarithmotechnica of Mercator; the papers of Dr. Halley. Mr Cotes, and Mr. Hellins, which relate also to logarithms; the papers on the nature of equations, on series, and on annuities, also those which relate to the conic sections and to the quadrature of curves. In the Eater volumes will be found the important papers which have been contributed by the eminent mathematicians of the present day. Under the third great division, which is that of Mechanical Philosophy, are classed Astronomy, Optics, Dynamics, Mechanics, Hydrodynamics, Acoustics, Navigation, Electricity, and Magnetism; and among the papers relating to astronomy are those of Dr. Halley (1691, 1716), on the junctions of the inferior planets, and on the transits of Venus; those of Dr. Bradley (1723, 1747) describing his covery of aberration and nutation; besides the accounts Sir William Herschel's astronomical observations. The principal optical papers are those which contain Newton's experiments on fight (1672); Dr. Halley's paper (1693) containing formula for finding the foci of optical glasses; Mr. Dollond's account (1758) of his discovery of the achromatic telescope; and the papers on the recent discovery of the polarity of light. To dynamics belong the papers containing the mathematical theory of the collision of odies, by Dr. Wallis, Sir C. Wren, and Mr. Huygens 1668-9); Mr. Smeaton's paper (1776) on the quantity of mechanical power necessary for giving different degrees of velocity to heavy bodies; with those of Mr. Landen 1777) and Mr. Vince (1780) on the rotatory motion of Lodies. There are comparatively few papers on the subject of mechanics: among them are those of Huygens and Hooke (1675) on watches: a valuable paper (1785) by Mr. Viace on friction; and one by Mr. Hodgkinson (1840) on the strength of cast-iron pillars. With respect to hydrodynamics and hydraulics, the most important are those of Mr. Canton (1762-4) on the compressibility and elasticity of fluids; and two by Mr. Atwood (1796-8) on the staLiity of ships. Mr. Smeaton has a valuable paper (1759) in the power of wind and water to turn machines; and Mr. Vince (1798) one on the resistance to bodies moving in fluids. There are several papers on the suspension of water in capillary tubes; and there is one by Mr. Beighton 1731), giving an account of the water-works at London. The papers on pneumatics consist chiefly of those which were contributed by Dr. Halley (1686), Sir George Shuckbargh, and General Roy (1777), on the measurement of heights by the barometer; with those of Greaves, Halley, Robins, Hutton, and Count Rumford, on the force of fired rapowder. The principal papers relating to acoustics are, one by Dr. Denham (1768) on the velocity of sound; and one by Dr. Young (1800) on sound and light. Those which come under the head of navigation consist almost holly of descriptions relating to the phenomena of tides. Almost every discovery in the science of electricity has been made by members of the Royal Society, and the num ber of papers relating to this subject is considerable. Among them are accounts of the experiments made by the earliest electricians, Hauksbee, Gray, Dufay, and Desaguliers. Dr. Watson has a paper (1748) on the distances to which shocks may be conveyed by conductors, and another (1751) in which an account is given of Franklin's Treatise on Electricity. There is a paper by the Abbé Nollet (1748) on the effect produced by electricity on water flowing through capillary tubes; one by Mr. Wilson (1759) on the heated tourmalin; and another by the same (1773) on the efficacy of blunt conductors: there are also several papers by Dr. Priestley on electrical subjects; Mr. Cavendish's theory of electricity (1771): Volta's account (1800) of the galvanic pile; and Sir Humphry Davy's paper containing his great discovery concerning the agency of galvanism in decomposing compound substances; besides the highly valuable papers by Mr. Faraday concerning his experimental researches in electricity. Among the papers on magnetism are that of Dr. Brook Taylor (1715) on the law of magnetic attraction; the hypothesis of Halley concerning the cause of the dip and variation of the needle; and Lt.-Col. Sabine's recent contributions on terrestrial magnetism. The Transactions are rich in papers on Chemistry, which however are of a miscellaneous nature: among the more important are, the paper of Mr. Brand (1736) on hydrogen gas; that which states the experiments of Mr. Cavendish (1783) to determine the components of atmospherical air. There is a paper by Dr. Henry of Manchester (1797) on the expansion of carburetted hydrogen gas by electricity; and one by Mr. Kirwan (1786), containing an account of his experiments on sulphuretted hydrogen gas. There are many papers on the subject of Meteorology, but most of them are merely diaries of the weather: among them however is a paper by Dr. Heberden (1765) on the rate at which temperatures diminish in the atmo sphere as the distances from the surface of the earth in crease. Among the papers which Dr. Thomson ranks as miscellaneous are the few which relate to Antiquities: these contain accounts of the ruins of Palmyra (1695), Pompey's pillar (1767), the catacombs of Rome and Naples (1760); and there are several papers on the discoveries made in Herculaneum. TRANSCENDENTAL, a mathematical term of description, the meaning of which is not very uniform. When any particular formula is incapable of being expressed by any particular range of algebraical symbols, it is, with respect to those symbols, transcendental, that is, it transcends or climbs beyond the power of these symbols. The word was perhaps first used by Leibnitz (Leipzig Acts.' 1686), who says, placet hoc loco, ut magis profutura dicamus, fontem aperire transcendentium quantitatum, cur nimirum quaedam problemata neque sint plana, neque solida, neque sursolida, aut ullius certigradus, sed omnem aequationem algebraicam transcendant.' Here then is the first meaning of the word; a transcendental problem is one the equation of which is infinitely high, or contains an infinite series of powers of an unknown quantity, so that its highest degree transcends every degree. To form an idea of what is now most commonly meant by transcendental, it will be desirable to recapitulate the steps by which algebra has arrived at its present state of expression; or rather, mathematical analysis, as those would say who do not like to call the differential calculus by the name of algebra. And first we have the state which preceded the time of Vieta, in which formula were mostly described in words, and the adoption of arbitrary symbols of quantity was only of casual occurrence. Next, we have the introduction of arbitrary symbols of quantity by Vieta, but not to the extent of using arbitrary numbers of multiplications, or algebraical exponents. Here what we now call an was transcendental; Vieta could have described as by a cubo-cubum, or a7 by a quadrato-quadrato-cubum, but a had neither name nor symbol. Thirdly, we have the stage which began with Harriot and Descartes, and which brought ordinary algebra into substantially its present form. During these periods however geometry and arithmetic, without help from algebra, |