JULIUS PLUCKER (18or1868), German mathematician and physicist, was born at Elberfeld on the 16th of June 18oI. 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 fundamenta sunt a 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 Geometrie descriptive and the Application de l'analyse d 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, Analytischgeometriscke Entwickelungen (vol. i., 1828; 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 drifter Ordnung enthaltend (Berlin, 1835). In this work he introduced the use of linear functions in place of the ordinary coordinates; 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 pgr+p.s=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 Geometric 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 Geometric des
Raumes in neuer analytischer Behandlungsweise, but this distinctions, however, are not maintained with much constancy. contains merely a more systematic and polished rendering of his P. domestica is a native of Anatolia and the Caucasus, and is conearlier results. In 1847 he was made professor of physics at sidered to be the only species naturalized in Europe. P. insititia Bonn; and from that time his scientific activity took a new and is wild in southern Europe, in Armenia, and along the shores of astonishing turn. the Caspian. In the Swiss lakedwellings stones of the P.
His first physical memoir, published in Poggendorfs Annalen insititia as well as of P. spinosa have been found, but not those (1847), vol. lxxii., contains his great discovery of magnecrystallic of P. domestica. Nevertheless, the Romans cultivated large action. Then followed a long series of researches, mostly numbers of plums. The cultivated forms are extremely numerpublished in the same journal, on the properties of magnetic ous, some of the groups, such as the greengages, the damsons and diamagnetic bodies, establishing results which are now part and the egg plums being very distinct, and sometimes reproducand parcel of our magnetic knowledge. In 1858 (Fogg. Ann. ing themselves from seed. The colour of the fruit varies from vol. ciii.) he published the first of his classical researches on the green to deep purple, the size from that of a small cherry to action of the magnet on the electric discharge in rarefied gases. that of a hen's egg; the form is oblong acute or obtuse at both
Plucker, first by himself and afterwards in conjunction with ends, or globular; the stones or kernels vary in like manner; and J. W. Hittorf, made many important discoveries in the spectro the flavour, season of ripening and duration are all subject to scopy of gases. He was the first to use the vacuum tube with variation. From its hardihood the plum is one of the most the capillary part now called a Geissler's tube, by means of which valuable fruit trees, as it is not particular as to soil, and the the luminous intensity of feeble electric discharges was raised crop is less likely to be destroyed by spring frosts. Prunes sufficiently to allow of spectroscopic investigation. He antici and French plums are merely plums dried in the sun. Their pated R. W. Y. Bunsen and G. Kirchhoff in announcing that the preparation is carried on on a large scale in Bosnia and Servia, lines of the spectrum were characteristic of the chemical sub as well as in Spain, Portugal and southern France.
stance which emitted them, and in indicating the value of this Plums are propagated chiefly by budding on stocks of the discovery in chemical analysis. According to Hittorf he was Mussel, Brussels, St Julien and Pear plums. The damson, the first who saw the three lines of the hydrogen spectrum, winesour and other varieties, planted as standards, are generally which a few months after his death were recognized in the spec increased by suckers. For planting against walls, trees which trum of the solar protuberances, and thus solved one of the have been trained for two years in the nursery are preferred,
mysteries of modern astronomy, but maiden trees can be very successfully introduced, and by
Hittorf tells us that Plucker never attained great manual liberal treatment may be speedily got to a fruiting state. Any dexterity as an experimenter. He had always, however, very good welldrained loamy soil is suitable for plums, that of clear conceptions as to what was wanted, and possessed in a high medium quality as to lightness being decidedly preferable. degree the power of putting others in possession of his ideas Walls with an east or west aspect are generally allowed to and rendering them enthusiastic in carrying them into practice. them. The horizontal mode of training and the fan or halffan Thus he was able to secure from the Sayner Hiftte in 1846 the forms are commonly followed; where there is sufficient height great electromagnet which he turned to such use in his magnetic probably the fan system is the best. The shoots should be laid researches; thus he attached to his service his former pupil the in nearly or quite at full length. The fruit is produced on small skilful mechanic Fessel; and thus he discovered and fully availed spurs on branches at least two years old, and the same spurs himself of the ability of the great glassblower Geissler. continue fruitful for several years. Standard plum trees should
Induced by the encouragement of his mathematical friends in be planted 25 ft. apart each way, and dwarfs 15 or 20 ft. The England, Plucker in 1865 returned to the field in which he first latter are now largely grown for market purposes, being more became famous, and adorned it by one more great achievement easily supported when carrying heavy crops, fruiting earlier, —the invention of what is now called " line geometry." His and the fruit being gathered more easily from the dwarf bush first memoir on the subject was published in the Philosophical than from standard trees.
Transactions of the Royal Society of London. It became the The following is a selection of good varieties of plums, with
source of a large literature in which the new science was de their times of ripening:
veloped. Plucker himself worked out the theory of complexes Dessert Plums.
of the first and second order, introducing in his investigation of
the latter the famous complex surfaces of which he caused those Early Greengage . e. July Transparent Gage . . b. Sept. Early Transparent Gageb. Aug. Jefferson b. Sept.
models to be constructed which are now so well known to the Denniston's Superb . b. Aug. Kirke's . . . m. Sept.
student of the higher mathematics. He was engaged in bringing Oullin's Golden . . . m. Aug. Coe's GoldenDrop . . e. Sept.
out a large work embodying the results of his researches in line Greengage m.e.Aug. Reine Claude de Bavay e. Sept.
geometry when he died on the 22nd of .May 1868. The work was b. Oct.
so far advanced that his pupil and assistant Felix Klein was M'Laughlin's e. Aug. Ickworth Imperatrice b. Oct.
Oct.
able to complete and publish it (see GEOMETRY, LINE). Among Angelina Burdett b. Sept. Late Rivers . . . • Nov.
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).
End of Article: JULIUS PLUCKER (18or1868) 

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