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1911 Encyclopedia Britannica

Julius Plucker

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JULIUS PLUCKER (r801-1868), German mathematician and physicist, was born at Elberfeld on the 16th of June r 801. After being educated at Dusseldorf and 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, was only recently dead. In 1825 he was received as Privatdozent at Bonn, and after three years he was made professor extraordinary. The title of his "habilitationsschrift," Generalem analyseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundaments sunt e serie Tayloria deducit Julius Plucker (Bonn, 1824), indicated the course of his future researches. The mathematical influence of Monge had two sides represented respectively by his two great works, the Geometric descriptive and the Application de l'analyse a la geometrie. Plucker aimed at furnishing modern geometry with suitable analytical methods so as to give it an independent analytical development. In this effort he was as successful as were his great contemporaries Poncelet and J. Steiner in cultivating geometry in its purely synthetic form. From his lectures and researches at Bonn sprang his first great work, Analytisch-geometrische Entwickelungen (vol. i., 18 28; vol. ii., 1831).

In the first volume of this treatise Plucker introduced for the first time the method of abridged notation which has become one of the characteristic features of modern analytical geometry (see Geometry, Analytical). In the first volume Of the Entwickelungen he applied the method of abridged notation to the straight line, circle and conic sections, and he subsequently used it with great effect in many of his researches, notably in his theory of cubic curves. In the second volume of the Entwickelungen he clearly established on a firm and independent basis the great principle of duality.

Another subject of importance which Plucker took up in the Entwickelungen was the curious paradox noticed by L. Euler and G. Cramer, that, when a certain number of the intersections of two algebraical curves are given, the rest are thereby determined. Gergonne had shown that when a number of the intersections of two curves of the ( p+q)th degree lie on a curve of the pth degree the rest lie on a curve of the qth degree. Plucker finally ( Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice. Later, simultaneously with C. G. J. Jacobi, he extended these results to curves and surfaces of unequal order. Allied to the matter just mentioned was Plucker's discovery of the six equations connecting 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 Theorie der algebraischen Curven (1839).

In 1833 Plucker left Bonn for Berlin, where he occupied a post in the Friedrich Wilhelm's Gymnasium. He was then called in 1834 as ordinary professor of mathematics to Halle. While there he published his System der analytischen Geometrie, auf neue Betrachtungsweisen gegrundet, and insbesondere eine ausfuhrliche Theorie der Curven driller Ordnung enthaltend (Berlin, 1835). In this work 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. His discussion of curves of the third order turned mainly on the nature of their asymptotes, and depended on the fact that the equation to every such curve can be put into the form pqr-hus = o. He gives a complete enumeration of them, including two hundred and nineteen species. In 1836 Plucker returned to Bonn as ordinary professor of mathematics. Here he published his Theorie der algebraischen Curven, which formed a continuation of the System der analytischen Geometrie. The work falls into two parts, which treat of the asymptotes and singularities of algebraical curves respectively; and extensive use is made of the method of counting constants which plays so large a part in modern geometrical researches.

From this time Plucker's geometrical researches practically ceased, only to be resumed towards the end of his life. It is true that he published in 1846 his System der Geometrie des Raumes in newer analytischer Behandlungsweise, but this contains merely a more systematic and polished rendering of his earlier results. In 1847 he was made professor of physics at Bonn; and from that time his scientific activity took a new and astonishing turn.

His first physical memoir, published in Poggendorffs Annalen (1847), vol. lxxii., contains his great discovery of magnecrystallic action. 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. In 1858 ( Pogg. Ann. vol. ciii.) he published the first of his classical researches on the action of the magnet on the electric discharge in rarefied gases.

Plucker, first by himself and afterwards in conjunction with W. Hittorf, made many important discoveries in the spectroscopy of gases. He was the first to use the vacuum tube with the capillary part now called a Geissler's tube, by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated R. W. Y. Bunsen and G. 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.

Hittorf tells us that Plucker never attained great manual dexterity as an experimenter. He had always, however, very clear conceptions as to what was wanted, and possessed in a high degree the power of putting others in possession of his ideas and rendering them enthusiastic in carrying them into practice. Thus he was able to secure from the Sayner Hutte in 1846 the great electromagnet which he turned to such use in his magnetic researches; thus he attached to his service his former pupil the skilful mechanic Fessel; and thus he discovered and fully availed himself of the ability of the great glass-blower Geissler.

Induced by the encouragement of his mathematical friends in England, Plucker in 1865 returned to the field in which he first became famous, and adorned it by one more great achievement - the invention of what is now called "line geometry." His first memoir on the subject was published in the Philosophical Transactions of the Royal Society of London. It became the source of a large literature in which the new science was developed. 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 constructed which are now so well known to the student of the higher mathematics. He was engaged in bringing out a large work embodying the results of his researches in line geometry when he died on the 22nd of May 1868. The work was so far advanced that his pupil and assistant Felix Klein was able to complete and publish it (see Geometry, Line). Among the very numerous honours bestowed on Plucker by the various scientific societies of Europe was the Copley medal, awarded to him by the Royal Society two years before his death.

See R. F. A. Clebsch's obituary notice (Abh. d. kon. Ges. d. Wiss. z. Gottingen, 1871, vol. xvi.), to which is appended an appreciation of Plucker'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 Plucker's life by A. Dronke (Bonn, 1871).

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Bibliography Information
Chisholm, Hugh, General Editor. Entry for 'Julius Plucker'. 1911 Encyclopedia Britanica. 1910.

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