among mathematical instrument-makers, is the process of dividing the arcs of quadrants, theodolites, circular instruments, measures, &c., into degrees, fractions of a degree, &c. Accuracy in this operation is of the utmost importance in practical astronomy and surveying, and no small amount of practical skill is requisite to insure its successful execution. There are two methods employed in the dividing of instruments—the ordinary one consisting in making a copy of a system of divisions already existing; the other and more delicate process is that of original dividing. Straight scales and rules, such as are used in drawing, are divided by placing the particular instrument and the original pattern side by side, then passing a straight edge (with a shoulder fixed at right angles to serve as a guide) along the original, and pausing at each division, when a corresponding line is made on the copy by the dividing knife. Segments of circles may be graduated by making the straight edge revolve on the centre of a divided circle, and marking off the divisions as in the straight scale. This method, which in skilful hands admits of considerable accuracy, was applied to the division of theodolites and common circular instruments until superseded by Ramsden's Dividing Engine. For the invention of this ingenious machine the author received from the Board of Longitude a premium of L300, and L315 for the machine itself, which he was permitted during pleasure to retain in his own possession, on condition of his dividing sextants and octants for other instrument-makers at fixed rates. A description of Ramsden's dividing engine would require a diagram to render it perfectly intelligible; but perhaps some general idea of its mode of action may be formed from the following brief explanation.—A horizontal circle, four feet in diameter, turns upon a vertical axis, and is moved by an endless screw, one revolution of which carries forward the circle ten minutes, or one sixth of a degree; the screw is moved forward by depressing a treadle, at each descent of which the screw, by a series of ingenious mechanical appliances, may be turned through any portion of its revolution; and when the pressure is removed, the position of the several parts is restored without communicating any return motion to the screw. The circle to be graduated is fixed upon the dividing-plate of the machine, and concentric with it, and the lines are cut after each depression of the treadle.

Some idea of the extreme delicacy required for original dividing may be derived from the fact that Ramsden, in laying down the original divisions on his dividing engine, divided his circle first into five parts, and each of these into three; these parts were then bisected four times, but being apprehensive lest some error might arise from quintisection and trisection, in order to test the accuracy of the divisions he described another circle 1/8th inch within the former by continual bisections, when the two sets of divisions were found to exhibit no sensible difference. It was by means of this machine that Ramsden graduated his great theodolite, constructed under the inspection of General Roy for the trigonometrical survey of Great Britain. A description of this fine theodolite, with illustrative plates, may be found in the Philosophical Transactions, Lond., vol. lxxx.

Ramsden's dividing machine is the prototype after which various similar ones (with some alterations and improvements) have been constructed by Troughton, Adie of Edinburgh, and various other artists. The dividing machines of Reichenbach, Gambey, and other continental inventors, differ somewhat from those above mentioned. The German method of division, which admits of the greatest accuracy under skilful management, is performed by copying from a large circle originally divided with extreme precision. Upon this the copy is fixed concentrically; and by the aid of the micrometer-microscope fixed independently over the divided circle, the degrees and their fractional parts are cut in the copy.

Ample details of the different methods employed for graduation are to be found in various published works which treat of this particular subject, such as those of Bird, Ramsden, Troughton, de Chaunies, &c., &c.

the arts, the process of accelerating evaporation by exposing a large surface of the liquid operated on to a current of air.

GRÆCIA MAGNA (ἡ μεγάλη Ἑλλάς), in Ancient Geography, a collective name for the numerous Greek colonies which at an early age were established along the southern, south-eastern, and south-western shores of Italy. The term, however, is never used in a territorial sense to signify the southern half of the Italian peninsula, but is restricted entirely to the Greek cities on coasts.

GRÆVIUS, the Latinized form of GRÆFE, John, George, one of the most learned and laborious writers of his time, was born at Naumburg, in Saxony, Jan. 29, 1632. He began his studies in the gymnasium of Pforta, and Grævius completed them at the university of Leipzig, under Rivinus and Stranch. Grævius was led to the study of letters by his natural inclination, and every day he became more and more devoted to this pursuit. But his father wished that he should study the law; Stranch seconded this view, and Grævius obeyed, though with repugnance. He had the curiosity to visit Holland, while Salmasius, Helinsius, and Frederic Gronovius, were in the zenith of their reputation. The conversation of Gronovius revealed to him the painful truth that his studies had been almost entirely unavailing, that he had been taught according to the principles of a bad school, and that he had no time to lose if he desired to correct the vices of its method of instruction. He entreated Gronovius to become thenceforth his guide; nor could he have chosen one more able; so, having abandoned jurisprudence, he passed two years at Deventer, attending assiduously the lessons of his new master. He then proceeded to Amsterdam to hear Alexander Morus and David Blondel, whose counsels decided him to quit Lutheranism for the sect of Calvin. Peter Burmann, his panegyrist, anxious that this change of religion should not be misrepresented, declares that the new convert listened only to the voice of conscience. Grævius, whose reputation had now begun to be extended, was, in 1656, called to the university of Duisburg; and he had been there two years, surpassing all the hopes which had been conceived of his talents, when Gronovius, who had entered the university of Leyden, solicited the magistrates of Deventer to appoint Grævius his successor. They agreed to this application, and Grævius, notwithstanding the efforts of the elector of Brandenburg, who, in order to retain him, offered an augmentation of fees, quitted a university for a simple gymnasium, influenced probably by the desire of living under a free government. After a stay of three years at Deventer, he yielded to the solicitations of the university of Utrecht, which offered him the chair of history, then vacant by the death of Æmilius. This satisfied all his ambition, and, content with his situation, he declined the invitations of the magistrates of Amsterdam and Leyden, who twice attempted, by brilliant offers, to attach him to the schools in those cities. The elector-palatine, who wished to draw him to Heidelberg, was also refused; the king of Prussia was not more fortunate; and the republic of Venice, which offered him a chair in the university of Padua, had as little success, although, in the hope of inducing him to accept, it had promised him, besides considerable appointments, full liberty on the score of religion, and complete protection against the inquisitors. But none of these offers could overcome his resolution. The eager desire of foreigners to obtain his services was justified by the great reputation which he had attained as professor. Pupils crowded to his lectures, not only from all Holland, but from all Europe. In Germany, particularly, almost all the great lords sent their sons to be educated by him; and he reckoned amongst his auditors sons of princes, and even of kings; for William III., who made him his historiographer, had confided to his care the young Prince of Nassau. Parnot, and before him G. Burmann, in the Trajectum Eruditum, have given a complete list of his works. He died suddenly Jan. 11, 1703.

The following are his principal works—An edition of the Letters of Cassanion, Brunswick, 1655; The Solicit of Lucian, Amsterdam, 1668, in 8vo, with notes rich in grammatical erudition; Heled, with a collection of excellent observations under the title of Lectiones Heledianae; Justin, 1669, cum Notis Variariorum; Catullus, Tibullus, Propertius, 1664; Cicero, 1669, cum Notis Variariorum; Suetonius, 1672; Florus, 1680; The Commentaries of Caesar; The miscellaneous Letters of Cicero, his Letters to Atticus, his Treatise of Offices, and his Discourses, cum Notis Variariorum. But his masterpiece is his Thesaurus Antiquitatum Romanarum, in 12 vols. folio, a work of incredible labour and research, to which he afterwards added Thesaurus Antiq. et Hist. Italicae, printed the year after his