PLUCKER, JULIUS (1801-1868), German mathematician and physicist, was born at Elberfeld on June 16, 1801. After studying at the universities of Bonn, Heidelberg and Berlin he went in 1823 to Paris, where he came under the influence of the great school of French geometers, whose founder, Gaspard Monge, had only recently died. In 1825 he was received as Privatdozent at Bonn, and after three years he was made pro fessor extraordinary. He then held the following posts: pro fessor of mathematics at Friedrich Wilhelm's Gymnasium, Ber lin (1833-34), professor of mathematics at Halle (1834-36), professor of mathematics (1836-47) and finally professor of physics at Bonn. He died on May 2 2, 1868.
From his lectures at Bonn sprang his first great work, Analy tisch-geometrische Entwickelungen (vol. i., 1828; vol. ii., 1831), in which he introduced the abridged notation which has since characterized modern analytical geometry. (See ANALYTIC GEOMETRY.) He applied this notation to the straight line, circle and conic sections, and he used it in his theory of cubic curves. Also he established the great principle of duality. PlUcker dis covered the six equations known as "PlUcker's equations" con necting the numbers of singularities in algebraical curves. (See CURVE.) PlUcker communicated his formulae in the first place to Crelle's Journal (1834), vol. xii., and gave a further extension and complete account of his theory in his Tlteorie der algebraischen Curven (1839). In his System der analytischen Geometrie (1835) he introduced the use of linear functions in place of the ordinary co-ordinates; he also made the fullest use of the principles of collineation and reciprocity. He discussed curves of the third order and gave a complete enumeration of them, including two hundred and nineteen species. In 1846 Pllicker published his System der Geometrie des Raumes in newer analytischer Behand lungsweise, but this contains merely a more systematic and polished rendering of his earlier results.
After his appointment as professor of physics at Bonn, Plucker began a series of researches in physics. His first physical memoir, published in Poggendorffs Annalen deals with the be haviour of crystals in a magnetic field. Then followed a long
series of researches, mostly published in the same journal, on the properties of magnetic and diamagnetic bodies, establishing results which are now part and parcel of our magnetic knowledge. This was followed by researches on the discharge tube ; he in vestigated the deflection of the discharge by a magnet and the be haviour of the negative glow in a magnetic field. Plucker, first by himself and afterwards in conjunction with Hittorf, made many important discoveries in the spectroscopy of gases. He anticipated Bunsen and Kirchhoff in announcing that the lines of the spectrum were characteristic of the chemical substance which emitted them, and in indicating the value of this discovery in chemical analysis. According to Hittorf he was the first who saw the three lines of the hydrogen spectrum, which a few months after his death were recognized in the spectrum of the solar protuberances, and thus solved one of the mysteries of modern astronomy. Induced by his mathematical friends in England, Plucker in 1865 returned to "line geometry." His first memoir on the subject was published in the Philosophical Trans actions of the Royal Society of London in 1865. Plucker himself worked out the theory of complexes of the first and second order, introducing in his investigation of the latter the famous complex surfaces of which he caused those models to be con structed which are now so well known to the student of the higher mathematics. He left an uncompleted work on the sub ject which was so far advanced that his pupil and assistant Felix Klein was able to complete and publish it. (See LINE GEOMETRY. 1 See R. F. A. Clebsch's obituary notice (Abh. d. /eon. Ges. d. Wiss. z. Gottingen, 1871, vol. xvi.), to which is appended an appreciation of Pliicker's physical researches by Hittorf, and a list of Pliicker's works by F. Klein. See also C. I. Gerhardt, Geschichte der Mathematik in Deutschland, p. 282, and Pliicker's life by A. Dronke (Bonn, 1871).