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DIGNANO — DIMENSIONS

Reibung und Warmeleitung verdiinnter Gase,” Pogg. Ann. civ.— Loschmidt. “ Experimentaluntersuchungen iiber Diffusion,” W.S. Ixi. Ixii. 1870.—Magnus. “Leitung der Warme durch die Gase,” Pogg. Ann. cxii.—J. C. Maxwell. Scientific Papers, Camb. Univ. Press, 1890.—0. E. Meyer. The Kinetic Theory of Gases, translated by Robert E. Baynes, London, 1899; De Gasorum Theoria, Breslau, 1866; “ Ueber die innere Reibung der Gase,” Pogg. Ann. vols. cxxv. cxxvii. cxliii. cxlviii.—L. Natan sox. “Interpretation cinetique de la fonction de dissipation,” Bulletin de I’Acad. de Cracovie, 1893 ; “On the Laws of Irreversible Phenomena,” Phil. Mag., May 1896; “Ueber die kinetische Energie der Bewegung der AVarme,” Zeitschrift fur phys. Ghemie, 1895, pp. 289-302.—Von Obermayer. “ Ueber die Abhangigkeit der Reibungscoeflicienten von der Temperatur,” Carl's licpertorium, xii., W.S. Ixxiii.—J. Planck. “Ueber das Leitungsvermogen,” W.S. Ixiv. 1870, and Ixxii. July 1875.—Pulyj. “Ueber die Reibungsconstante der Luft,” W.S. Ixix. Ixx. Ixxiii. — Lord Rayleigh. “On Maxwell’s Law of Partition of Energy,” Phil. Mag., Jan. 1900.—R. Ruhlmann. Handbuch der mechanischen Wdrmetheorie. Braunschweig, Vieweg, 2 vols. 1885. —J. Stefan. “ Ueber das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasmengen,” W.S. Ixiii. January ; “ Untersuchungen iiber die Warmeleitung in Gasen,” W.S. Ixv! February 1872 ; “Ueber die dynamische Theorie der Diffusion der Gase,” W.S. Ixv. April 1872 ; “Relative Bestimmung des Warmeleitungsvermbgens,” W.S. Ixxii. June.—P. G. Tait. “The Foundations of the Kinetic Theory of Gases,” Trans. Roy. Soc. Edin. xxxiii. pts. 1, 2, 1886 ; xxxv. pt. 4, 1889 ; xxxvi. pt. 2, 1891; Scientific Papers, ii. Camb. Univ. Press, 1900.—M. Toefler. “ Gas-Diflusion,” Wied. Ann. Iviii. 1896, p. 599.—J. J. Waterston. “The Physics of Media,” Phil. Trans. Roy. Soc., (A.) 1892.— Rev. H. W. Watson. A Treatise on the Kinetic Theory of Gases. Oxford, 1893.—Winkelmann. “Ueber die Warmeleitung der Gase,” Pogg. Ann. clvi. clvii. clix. — Wretschko. “Experimentaluntersuchungen iiber die Diffusion von Gasmengen,” W.S. lxii (a H. Br.) Di^nano (Slavonic, Vodnjan), a town in the government district of Pola, Istria (Austria), about 8 miles north of Pola, on the railway from Trieste. It is situated on a gentle slope overlooking the Gulf of Venice, a few miles from the shore. The principal resource of the inhabitants (in 1890, 9151 ; in 1900, 9684—mostly Italian) is the cultivation of the vine, olive, fruit, and the silkworm, together with a considerable trade in timber. The socalled rose-vine, one of the best of the Istrian varieties, is grown in the vicinity. Dijon, chief town of department Cote-d’Or, France, 196 miles south-east of Paris, on railway from Paris to Lyon. It is the seat of a court of appeal for the departments of Cote d’Or, Haute Marne, and Seine-et-Loire, and has schools of medicine and pharmacy. Since the FrancoPrussian War it has been strongly fortified, and it is now protected by eight forts. The bathing establishment or casino was rebuilt in ornate style in 1886. The manufacture of heavy iron goods and machinery has become extensive, and there are large soap works, while blackcurrant liqueur (“ cassis de Dijon ”) is a speciality; cottonspinning is still carried on, but textile industries are no longer of any account. Population (1881), 46,344 : (1891), 55,673; (1901), 70,428. Dillmann, Christian Friedrich August (1823-1894), German theologian and Orientalist, was born at Illingen, Wurtemberg, 25th April 1823. He commenced the study of theology at Tubingen, where he was a favourite pupil of Ewald, who encouraged him to pursue the study of the Oriental languages, of which, after having for some years been a Privat-docent, he became extraordinary professor in 1853. In 1854 he removed to Kiel, where he was made regular professor in 1860. Having, however, signalized himself as a divine as well as an Oriental scholar, he was in 1864 invited to fill the post of professor of biblical exegesis at Giessen, and in 1869 succeeded the celebrated Hengstenberg as exegetical professor at Berlin. His lectures were much esteemed, but his principal distinction was

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UNITS

gained by his researches in the Ethiopic language and literature, upon which he was regarded as the highest living authority. Between 1846 and 1848, and before his first appointment at Tubingen, he visited France and England as a student, and while in England prepared the seventh volume of the Bodleian catalogue of manuscripts, comprising the Ethiopic. This catalogue was published in 1848. Dillmann also catalogued the Ethiopic MSS. in the British Museum. In 1851 he edited the apocryphal Book of Enoch in the Ethiopic version, the only one in which it is extant, and published an annotated translation of it in 1853. In the same year he translated the Ethiopic Book of Adam, and in 1855 edited the ancient Ethiopic translation of the Old Testament. He was also the author of an Ethiopic grammar (1857) and lexicon (1862-65), standard works in their department of philology. Among his Ethiopic labours may also be reckoned two works on. the history of the kingdom of Axum, published in 1879 and 1880. His principal theological writings are On the Origin of the Religion of the Old Testament (1865) and On the Political Activity of the Old Testament Prophets (1868). His investigations are characterized by a prevailing spirit of moderation and sobriety. He died at Berlin, 4th July 1894, leaving the reputation not merely of a great Ethiopic scholar, but of the reviver of a branch of Oriental study which had fallen into neglect. (r. g.) Dilolo, Lake.

See Congo.

Dimensions Of Units.—Measurable entities of different kinds cannot be directly compared. Each one must be specified in terms of a unit of its own kind; a single number attached to this unit forms its measure. Thus if the unit of length be taken to be L centimetres, a line whose length is l centimetres will be represented in relation to this unit by the number f/L; while if the unit is increased [L] times, that is, if a new unit is adopted equal to [L] times the former one, the numerical measure of each length must in consequence be divided by [L]. Measurable entities are either fundamental or derived For example, velocity is of the latter kind, being based upon a combination of the fundamental entities length and time; a velocity may be defined, in the usual form of language expressive of a limiting value, as the rate at which the distance from some fixed mark is changing per unit time. The element of length is thus involved directly and the element of time inversely in the derived idea of velocity; the meaning of this statement being that when the unit of length is increased [L] times and the unit of time is increased [T] times, the numerical value of any given velocity, considered as specified in terms of the units of length and time, is diminished [L]/[T] times. In other words, these changes in the units of length and time involve change in the unit of velocity determined by them, such that it is increased [V] times where [V] = [L][T]_1. This relation is conveniently expressed by the statement that velocity is of +1 dimension in length and of -1 dimension in time. Again, acceleration of motion is defined as rate of increase of velocity per unit time; hence the change of the units of length and time will increase the corresponding or derived unit of acceleration [V]/[T] times, that is [L][T]‘2 times: this expression thus represents the dimensions (1 in length and - 2 in time) of the derived entity acceleration in terms of its fundamental elements length and time. In the science of dynamics all entities are derived from the three fundamental ones, length, time, and mass; for example, the dimensions of force (P) are those of mass and acceleration jointly, so that in algebraic form [P] = [M][L][T]"2. This restriction of the fundamental units to three is therefore applicable to