Mention may be made of Donkin's linear dividing engine, in which a compensating arrangement is employed whereby great accuracy is obtained notwithstanding the inequalities of the screw used to advance the cutting tool. Dividing engines have also been made by Reichenbach, Repsold and others in Germany, Gambey in Paris and by several other astronomical instrument-makers. A machine constructed by E. R. Watts & Son is described by G. T. McCaw, in the _Monthly Not. R. A. S._, January 1909.
REFERENCES.--Bird, _Method of dividing Astronomical Instruments_ (London, 1767); Duc de Chaulnes, _Nouvelle Méthode pour diviser les instruments de mathématique et d'astronomie_ (1768); Ramsden, _Description of an Engine for dividing Mathematical Instruments_ (London, 1777); Troughton's memoir, _Phil. Trans._ (1809); _Memoirs of the Royal Astronomical Society_, v. 325, viii. 141, ix. 17, 35. See also J. E. Watkins, "On the Ramsden Machine," _Smithsonian Rep._ (1890), p. 721; and L. Ambronn, _Astronomische Instrumentenkunde_ (1899). (J. Bl.)
GRADUS, or GRADUS AD PARNASSUM (a step to Parnassus), a Latin (or Greek) dictionary, in which the quantities of the vowels of the words are marked. Synonyms, epithets and poetical expressions and extracts are also included under the more important headings, the whole being intended as an aid for students in Greek and Latin verse composition. The first Latin gradus was compiled in 1702 by the Jesuit Paul Aler (1656-1727), a famous schoolmaster. There is a Latin gradus by C. D. Yonge (1850); English-Latin by A. C. Ainger and H. G. Wintle (1890); Greek by J. Brasse (1828) and E. Maltby (1815), bishop of Durham.
GRAETZ, HEINRICH (1817-1891), the foremost Jewish historian of modern times, was born in Posen in 1817 and died at Munich in 1891. He received a desultory education, and was largely self-taught. An important stage in his development was the period of three years that he spent at Oldenburg as assistant and pupil of S. R. Hirsch, whose enlightened orthodoxy was for a time very attractive to Graetz. Later on Graetz proceeded to Breslau, where he matriculated in 1842. Breslau was then becoming the headquarters of Abraham Geiger, the leader of Jewish reform. Graetz was repelled by Geiger's attitude, and though he subsequently took radical views of the Bible and tradition (which made him an opponent of Hirsch), Graetz remained a life-long foe to reform. He contended for freedom of thought; he had no desire to fight for freedom of ritual practice. He momentarily thought of entering the rabbinate, but he was unsuited to that career. For some years he supported himself as a tutor. He had previously won repute by his published essays, but in 1853 the publication of the fourth volume of his history of the Jews made him famous. This fourth volume (the first to be published) dealt with the Talmud. It was a brilliant resuscitation of the past. Graetz's skill in piecing together detached fragments of information, his vast learning and extraordinary critical acumen, were equalled by his vivid power of presenting personalities. No Jewish book of the 19th century produced such a sensation as this, and Graetz won at a bound the position he still occupies as recognized master of Jewish history. His _Geschichte der Juden_, begun in 1853, was completed in 1875; new editions of the several volumes were frequent. The work has been translated into many languages; it appeared in English in five volumes in 1891-1895. The _History_ is defective in its lack of objectivity; Graetz's judgments are sometimes biassed, and in particular he lacks sympathy with mysticism. But the history is a work of genius. Simultaneously with the publication of vol. iv. Graetz was appointed on the staff of the new Breslau Seminary, of which the first director was Z. Frankel. Graetz passed the remainder of his life in this office; in 1869 he was created professor by the government, and also lectured at the Breslau University. Graetz attained considerable repute as a biblical critic. He was the author of many bold conjectures as to the date of Ruth, Ecclesiastes, Esther and other biblical books. His critical edition of the Psalms (1882-1883) was his chief contribution to biblical exegesis, but after his death Professor Bacher edited Graetz's _Emendationes_ to many parts of the Hebrew scriptures.