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TAR the throne and from the country. Tarquinius died at Cumæ in poverty and wretchedness.—D. M.  TARQUINIUS,, nephew of Tarquinius Superbus, and husband of Lucretia. After the expulsion of the Tarquinii he was made consul along with Lucius Junius Brutus; but the popular hatred of the family was so strong that he was forced to resign his office. He retired to Alba and lived there in voluntary exile.—D. M.  TARTAGLIA (in Latin Tartalea), the surname assumed by an eminent Italian mathematician, whose christian name was , and who was born at Brescia about 1506, and died at Venice in 1559. He taught mathematics in various parts of Italy, edited the works of Archimedes, and published original writings on mechanical and mathematical subjects. Amongst the latter was the discovery of a rule for solving cubic equations, which constituted one of the most remarkable steps in the progress of algebra. It was an improvement and extension of a rule discovered by Scipione del Ferro, and was further improved and extended by Cardan, whose name it now bears.—W. J. M. R.  TARTINI,, a musician, was born at Pirano in April, 1692. His father, having been a great benefactor to the cathedral church at Parenza, had been ennobled. Giuseppe was intended for the law, but mixing music with his other studies, it soon obtained undivided sway. In 1710 he was sent to the university of Padua, to pursue his studies as a civilian; but before he was twenty, having married without the consent of his parents, they abandoned him, and he was obliged to wander in search of an asylum. After many hardships, he found one in a convent at Assisi, where he was received by a monk, who, commiserating his misfortunes, let him remain till something could be done for him. Here Tartini practised the violin to keep off melancholy thoughts; but it was not long till he got his differences accommodated, and settled with his wife at Venice. During his residence here he heard Veracini, whose performance awakened an extraordinary degree of emulation in the young musician. Tartini had never heard a great player before, or conceived it possible for the bow to possess such varied powers of expression. He therefore quitted Venice for Rome, where he held a place in the opera orchestra. This was in 1714, when he discovered the phenomenon of the third sound. This phenomenon was supposed to consist in the united sounds of two notes; as, for example, G and E, comprehending the sound of C, or the fifth below. Here, too, by diligent practice he acquired reputation sufficient to obtain (in 1721) the place of first violin and master of the band to the celebrated church of St. Anthony in Padua. By this time his fame was so far extended that he had repeated offers from Paris and London; but through a singular devotion to his patron saint, to whom he consecrated himself and his instrument, he constantly declined entering any other service. With reference to his celebrated composition, "Il Trillo del Diavolo" (the Devil's Sonata), the following anecdote is said to have been derived from Tartini himself:—"He dreamed one night that he had made a compact with the devil, who promised to be at his service on all occasions; and during this vision everything succeeded according to his mind: his wishes were anticipated, and his desires always exceeded by the assistance of his new servant. In short, he imagined that he presented the devil his violin in order to discover what kind of a musician he was, when, to Tartini's great astonishment, he heard him play a solo so singularly beautiful, and with such superior taste and precision, that it surpassed all the music which he had ever heard or conceived in his life. So great was Tartini's surprise, and so exquisite his delight, that it deprived him of the power of breathing. He awoke with the violence of his sensations, and instantly seized his fiddle, in hopes of expressing what he had just heard, but in vain. He, nevertheless, composed a piece, which is perhaps the best of all his works, and called it the 'Devil's Sonata;' but it was so inferior to what his dream had presented, that he declared he would have broken his instrument, and abandoned music for ever, if he could have subsisted by any other means." By the year 1728 Tartini had formed many excellent scholars, and established a system of practice for students on the violin that became celebrated all over Europe. He died on the 26th of February, 1770, at Padua, where he had resided nearly fifty years.—E. F. R.  TARUTIUS or TARRUNTUS,, a Roman mathematician and astrologer, is said to have flourished during the first century ., and to have practised what may be called retrospective astrology; that is, the deduction of the planetary configuration, and consequently of the date, at the time of the birth of a man or the foundation of a city, from the events in the history of the city or the life of the man. It has been alleged that Marcus Terentius Varro assigned a date to the foundation of Rome on the authority of a retrospective horoscope computed by Tarutius; and that circumstance has been cited as an instance of the insufficient grounds on which history is sometimes based.—W. J. M. R.  TASMAN,, a Dutch navigator of the seventeenth century, whose fortune it was to make, within the limits of a single voyage, some of the most important additions to geographical knowledge that belong to the history of discovery. Scarcely anything is known of Tasman's personal history. It has been stated that he was born at the town of Horn in Holland. The dates of his birth and death are unknown. It is his voyage of 1642 that has alone given him immortality. In that year Tasman was placed by the governor-general of the Dutch East Indies (Van Diemen) in command of two ships with which to ascertain the southerly limit of Terra Australis. He sailed from Batavia on August 14, directing his course in the first instance to the island of Mauritius. Thence sailing to the eastward, and under a more southwardly parallel, he fell in with the land which is now best known by his own name (i.e., Tasmania), but which he called Van Diemen Land, in compliment to his patron. Tasman landed on the shores of this region, and saw evidence of its being inhabited, though he did not fall in with any of the natives. Sailing thence to the east, he discovered a prolonged range of coast, backed by high mountains. The Dutch ships cast anchor within a sheltered opening of this coast. Some natives put off in their canoes, and approached the ships. After some intercourse of this kind, one of the ship's boats (engaged at the time in passing between the two vessels) was attacked by the armed canoes of the natives, and three of the Dutchmen were killed, the body of one of them being carried on shore by the savages. The land with which intercourse was thus, under circumstances so inauspicious, first opened up by Europeans, is the New Zealand of modern geography, and the scene of this unhappy occurrence is the Massacre Bay of our present charts. Tasman gave the country the name of Staten Land, in honour of the States-general of Holland. He kept a northwardly course along the coast which he had discovered, as far as its northernmost extremity, bestowing the name of Three Kings Islands upon the little group still so called. Thence, sailing eastward of north, first Pylstaart island, and afterwards three islands which the Dutch named Amsterdam, Middelburg, and Rotterdam, were discovered. These latter belong to the Friendly islands, and correspond to the Tongataboo, Eoua, and Anamooka of native geography. The Dutch had much amicable intercourse with their inhabitants. Shaping his course in the direction of New Guinea, and passing several groups and extensive shoals by the way, Tasman sailed past the northern shores of that region, and ultimately reached Batavia after a voyage which had occupied nearly ten months. His success on this occasion naturally prompted a second voyage, concerning which we hardly know anything more than the instructions issued for his guidance, dated from Batavia, 29th of January, 1644, and the main object of which appears to have been to ascertain the existence, or otherwise, of a passage between Terra Australis and New Guinea. Some fragments from this second voyage of Tasman, the detailed record of which seems to be lost, appear in the work of a Dutch writer, Witsen, issued in 1705. They are reprinted by Mr. Major, in his admirable volume entitled Early Voyages to Terra Australis (Hakluyt Society, London, 1859). Upon this occasion Tasman coasted the Gulf of Carpentaria, and passed thence by New Guinea towards the island of Ceram, leaving unexplored the now well-known opening of Torres Strait (which had, indeed, been sailed through by the Spanish navigator Torres long previously, in 1606). The chart of Tasman's two voyages is still extant, and has been recently republished in Holland. The name of Maria Van Diemen, given by Tasman to the north-western cape of New Zealand, has been supposed indicative of a love story.—W. H.  TASSI,, an Italian painter at Rome during the pontificate of Paul V. He was born at Perugia in 1566, and is chiefly distinguished now as having been the master of Claude, who originally entered Tassi's service as cook and menial servant. Tassi was distinguished for his decorative works and 