<;I;ADI ATIOX 



<;i; A i I.M.KIM; 



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which one part of tliu frame holding the needle fit* 

 \\lien at the end >f its possible range of motion; 

 every tenth notch ]>eing deeper than the otliri- 

 l>t tin- fifth .-i- al>ove), the range of marking 

 i^ longer in this cane than tlu- others. This wheel 

 is luiucd hy ratchet- work in tin- to-aml-fro motion 

 of tin' marking point. Tlie carriage attached to 

 tin- tia\ elling screw may also support a small 

 reading microscope: tlniB tl>e linear dividing-engine 

 ma\ he used t.i ;est with great accuracy tin- dis 

 liet ween two points, each lyinff at the inter- 

 section of the cross- wires in the field of view; all 

 that is necessary is to focus one of the points, count 

 the number of whole and fractional turns of tlie 

 sciew required to hi in;,' (lie second point into focus, 

 and thus the distance may he obtained. 



For the purpose of dividing circles the circular 

 dividing engine is employed. This instrument was 

 lir>t constructed l>v Kamsden, afterwards improved 

 hy Troiighton, and more recently hy Simms. The 

 essential features of a circular dividing-engine are 

 a circular plate carefully divided hy original gradua- 

 tion, and capable of rotation on its axis; a tangent- 

 MTCW, working in a ratched edge of the circle, and 

 thus capahle of turning it through any required 

 angle ; a dividing-knife worked radially, so that, 

 when the tangent-screw turns the circle .through 

 successive equal angles, radial lines may be drawn 



Fig. 2. Dividing-engine. 



on any work laid on the divided circle. Fig. 2 

 represents one form of the instrument. A, A 

 i- the circle, usually 4 or 5 feet in diameter, 

 divided at its edge, and ratched into teeth at 

 its lower edge, C. The axis of the circle is in 

 i he column, E. TT' is the tangent -screw ; T', a 

 handle for turning it; T, a disc-shaped head, the 

 division* on the 'Mrcumference of which allow of 

 the nninher of whole and fractional turns of the 

 screw being counted. Tlie carriage, D, in which 

 works the dividing-knife (not seen in the figure), 

 may be adjusted to different heights by the screws 

 on the pillars, P, which support the parallel beams 

 on which the dividing-knife carriage moves ; it 

 uiay also be adjusted to circles of different radii 



hy moving the carriage along these beams to the 

 requisite amount from the centre. When in action 

 the tangent-screw in pressed against the iat<-h<-.| 

 edge of the circle by a hand Ic, K , with an eccentric 

 knoh. This pressure may, of course, !* relieve,) 

 when the screw in not in use. The tangent-screw 

 is sometimes turned by a treadle, or even hy clock- 

 work. Its pitch being accurately known, the angle 

 through which the circle turns, due to one revolu- 

 tion of the tangent screw, as noted hy the divided 

 head, T, is determined once for all for any machine. 

 The work to be divided is fixed down on and con- 

 centric with the circle, A ; a mark is made as origin 

 with the dividing-knife, the tangent-screw is then 

 made to turn the circle through one of the smallest 

 divisions, and another mark is made ; another equal 

 turn of the screw is made and another mark cut on 

 the circle, and so on until the division of the whole 

 circle is completed. This is the method by which 

 the large circles used in astionomical instruments 

 are graduated, and such is the perfection to which 

 these have l>een brought that the circular dividing- 

 engine may be looked upon as being one of the 

 most perfect of scientific measuring instruments. 

 For graduation in universities, see, in Vol. III., the 

 article DEGREES (UNIVERSITY). 

 Gradus ad Parnassiim (Lat., 'a step to 



Parnassus '), a dictionary of prosody used in making 

 Latin and Greek verse. The 

 best known is the Latin one by 

 John Carey, LL.I). (1756-1826), 

 teacher of the classics and author 

 of school-books, which was pub- 

 lished in 1824. 



Grrecia, MAGNA. See 

 MAGNA GILECIA. 



Graetz, HEINRICH, Jewish 

 theologian, was born in 1817 at 

 Xions in Posen, and studied at 

 Breslau, where in 1854 he be- 

 came teacher in the Jewish sem- 

 inary, and in 1870 also extra- 

 ordinary professor in the Uni- 

 versity. He died 7th September 

 1891. He wrote commentaries 

 on Ecclesiastes.Songof Solomon, 

 Joel, the Psalms, and a work on 

 Gnosticism and Judaism ; but is 

 remembered by his great Ge- 

 schichte derJuden (11 vols. 1853- 

 75 ; 4th ed. 1892 ; abridged in 3 

 vols. 1888-89 and translated in 5 

 by Bella Lowy in 1891-92). 



Graf* ARTURO, Italian poet 

 of German extraction, was born 

 at Athens in 1848, spent his 

 youth in Roumania, studied law 

 at Naples, and in 1874 began to 

 lecture on law in the University 

 of Rome. Meanwhile he became 

 eminent as a poet, has published 

 several volumes of verse, and 

 numerous works on literary history, myths, legends; 

 and since 1882 is Professor of Italian literature at 

 Turin. 



Graf, HEINRICH, professor of theology at Leipzig, 

 studied under Heuss at Strashurg, and died 16th 

 July 1869. His name is identified with the theory 

 of the Pentateuch taught by Reuss in 1833 that 

 the ' Priestly Document ' of the Pentateuch was 

 written after the exile. See PENTATEUCH. 



Grafenberg* a village in the north-west corner 

 of Austrian Silesia, 50 miles N. of Olmiitz. It is 

 celebrated as the spot where the water-cure (see 

 HYDROPATHY) was introduced in 1826 by Vinceni 

 Priessnitz ( 1799-1851). It still is visited yearly by 

 some 1500 persons. 



