See also:

• JULIUS

JULIUS See also:

• JULIUS PLUCKER (18or-1868)

PLUCKER (18or-1868)  , See also:

• GERMAN
• GERMAN, DUTCH AND SCANDINAVIAN

German mathematician and physicist, was See also:

• BORN, IGNAZ, EDLER VON (1742–1791)

born at See also:

• ELBERFELD

Elberfeld on the 16th of See also:

• JUNE

June 18oI . After being educated at See also:

• DUSSELDORF

Dusseldorf and at the See also:

• UNIVERSITIES

universities of See also:

• BONN

Bonn, See also:

• HEIDELBERG

Heidelberg and See also:

• BERLIN
• BERLIN, CONGRESS AND TREATY OF
• BERLIN, ISAIAH (1725–1799)

Berlin he went in 1823 to See also:

• PARIS
• PARIS (also called ALEXANDROS)
• PARIS, ALEXIS PAULIN (1800-x881)
• PARIS, BRUNO PAULIN GASTON (1839-1903)
• PARIS, FRANCOIS DE (169o-1727)
• PARIS, LOUIS PHILIPPE ALBERT
• PARIS, TREATIES OF (1814-1815)

Paris, where he came under the See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence of the See also:

• GREAT

great school of See also:

• FRENCH
• FRENCH, DANIEL CHESTER (1850– )
• FRENCH, NICHOLAS (1604-1678)

French geometers, whose founder, Gaspard See also:

• MONGE, GASPARD (1746-1818)

Monge, was only recently dead . In 1825 he was received as Privatdozent at Bonn, and after three years he was made See also:

• PROFESSOR (the Latin noun formed from the verb profiteri, to declare publicly, to acknowledge, profess)

professor extraordinary The See also:

• TITLE (0. Fr. title, mod. titre, from Lat. titulus)

title of his " habilitationsschrift," Generalem analyseos applicationem ad See also:

• EA(nar...), (p.s„,.,.)
• EA(psr...), (p, „...)• (pqr...)

ea quae geometriae altioris et mechanicae basis et fundamenta sunt a serie Tayloria deducit See also:

• JULIUS

Julius See also:

• PLUCKER, JULIUS (18or-1868)

Plucker (Bonn, 1824), indicated the course of his future researches . The mathematical influence of Monge had two sides represented respectively by his two great See also:

• WORKS

works, the Geometrie descriptive and the Application de l'analyse d la geometrie . Plucker aimed at furnishing See also:

• MODERN

modern See also:

• GEOMETRY

geometry with suitable See also:

• ANALYTICAL

analytical methods so as to give it an See also:

• INDEPENDENT

independent analytical development . In this effort he was as successful as were his great contemporaries See also:

• PONCELET, JEAN VICTOR (1788-1867)

Poncelet and J . See also:

• STEINER, JAKOB (1796-1863)

Steiner in cultivating geometry in its purely synthetic See also:

• FORM (Lat. forma)

form . From his lectures and researches at Bonn sprang his first great See also:

• WORK

work, Analytisch-geometriscke Entwickelungen (vol. i., 1828; vol. ii., 1831) . In the first See also:

• VOLUME

volume of this See also:

• TREATISE

treatise Plucker introduced for the first See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

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 See also:

• LINE

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 See also:

• FIRM

firm and independent basis the great principle of duality . Another subject of importance which Plucker took up in the Entwickelungen was the curious See also:

• PARADOX (Gr. treat, beyond, contrary to, Sofia, opinion)

paradox noticed by L .

See also:

• EULER, LEONHARD (1707-1783)

Euler and G . See also:

• CRAMER, JOHANN BAPTIST (1771—1858)
• CRAMER, JOHN ANTONY (1793—1848)
• CRAMER, KARL VON (1818—r9o2)

Cramer, that, when a certain number of the intersections of two algebraical curves are given, the See also:

• REST (O. Eng. rest, reste, bed, cognate with other Teutonic forms, e.g. Ger. Rast, Riiste, rest, and probably Gothic Rasta, league, i.e. resting or stopping place)

rest are thereby determined . Gergonne had shown that when a number of the intersections of two curves of the (p+q)th degree See also:

• LIE, JONAS LAURITZ EDEMIL (1833—1908)
• LIE, MARIUS SOPHUS (1842–1899)

lie on a See also:

• CURVE (Lat. curvus, bent)

curve of the pth degree the rest lie on a curve of the qth degree . Plucker finally (Gergonne See also:

• ANN

Ann., 1828–1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite in number) may be See also:

• DRAWN

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 See also:

• ORIGINAL

original choice . Later, simultaneously with C . G . J . See also:

• JACOBI, FRIEDRICH HEINRICH (1743-1819)
• JACOBI, JOHANN GEORG (1740-1814)
• JACOBI, KARL GUSTAV JACOB (1804-1851)

Jacobi, he extended these results to curves and surfaces of unequal See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order . Allied to the See also:

• MATTER

matter just mentioned was Plucker's See also:

• DISCOVERY

discovery of the six equations connecting the See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

numbers of singularities in algebraical curves (see CURVE) . Plucker communicated his formulae in the first See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place to Crelle's See also:

• JOURNAL
• JOURNAL (through Fr. from late Lat. diurnalis, daily)

Journal (1834), vol. xii., and gave a further See also:

• EXTENSION (Lat. ex, out ; tendere, to stretch)

extension and See also:

• COMPLETE

complete See also:

• ACCOUNT
• ACCOUNT (through O. Fr. acont, Late Lat. comptum, cornputare, to calculate)

account of his theory in his Theorie der algebraischen Curven (1839) . In 1833 Plucker See also:

• LEFT

left Bonn for Berlin, where he occupied a See also:

• POST

post in the See also:

• FRIEDRICH, JOHANN (1836— )

Friedrich Wilhelm's Gymnasium . He was then called in 1834 as See also:

• ORDINARY (med. Lat. ordinarius, Fr. ordinaire)

ordinary professor of See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics to See also:

• HALLE (known as HALLE-AN-DER-SAALE, t0 distinguish it from the small town of Halle in Westphalia)
• HALLE, SIR CHARLES (originally KARL HALLE) (1819-1895)

Halle .

While there he published his See also:

• SYSTEM

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 co-ordinates; he also made the fullest use of the principles of collineation and See also:

• RECIPROCITY (Lat. reciprocus, returning back the same way, alternating, probably from re back and pro forward)

reciprocity . His discussion of curves of the third order turned mainly on the nature of their asymptotes, and depended on the fact that the See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation to every such curve can be put into the form pgr+p.s=o . He gives a complete enumeration of them, including two See also:

• HUNDRED

hundred and nineteen See also:

• SPECIES

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 See also:

• PART

part in modern geometrical researches . From this time Plucker's geometrical researches practically ceased, only to be resumed towards the end of his See also:

• LIFE

life . It is true that he published in 1846 his System der Geometric See also:

• DES

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 See also:

• ANATOLIA (Gr. avaroX,7, sunrise, i.e. eastern land)

Anatolia and the See also:

• CAUCASUS

Caucasus, and is See also:

• CON

con-earlier results . In 1847 he was made professor of physics at sidered to be the only species naturalized in See also:

• EUROPE

Europe . P. insititia Bonn; and from that time his scientific activity took a new and is See also:

• WILD, JONATHAN (c. 1682-1725)

wild in See also:

• SOUTHERN

southern Europe, in See also:

• ARMENIA (old Persian Armina, Armenian Hayasdan, or Hayq)

Armenia, and along the shores of astonishing turn. the See also:

• CASPIAN

Caspian . In the Swiss See also:

• LAKE
• LAKE, GERARD LAKE, 1ST VISCOUNT (1744-1808)

lake-dwellings stones of the P . His first See also:

• PHYSICAL

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 See also:

• ROMANS
• ROMANS, EPISTLE TO THE

Romans cultivated large See also:

• ACTION

action . Then followed a See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long See also:

• SERIES (a Latin word from serere, to join)

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 See also:

• GROUPS
• GROUPS, THEORY

groups, such as the greengages, the damsons and diamagnetic bodies, establishing results which are now part and the See also:

• EGG (O.E. aeg, cf. Ger. Ei, Swed. aegg, and prob. Gr. u,ov, Lat. ovum)
• EGG, AUGUSTUS LEOPOLD (1816-1863)

egg plums being very distinct, and sometimes reproducand See also:

• PARCEL (Fr. parcelle, Ital. particella, Lat. particela, diminutive of pars, part)

parcel of our magnetic knowledge . In 1858 (Fogg . Ann. See also:

• ING

ing themselves from See also:

• SEED (from the root seen in Lat. serere, to sow)

seed . The See also:

• COLOUR (Lat. color, connected with celare, to hide, the root meaning, therefore, being that of a covering)

colour of the See also:

• FRUIT (through the French from the Lat. fructus; frui, to enjoy)

fruit varies from vol. ciii.) he published the first of his classical researches on the See also:

• GREEN, A
• GREEN, ALEXANDER HENRY (1832—1896)
• GREEN, DUFF (1791—1875)
• GREEN, JOHN RICHARD (1837—1883)
• GREEN, MATTHEW (1696-1737)
• GREEN, THOMAS HILL (1836-1882)
• GREEN, VALENTINE (1739–1813)
• GREEN, WILLIAM HENRY (.1825–1900)

green to deep See also:

• PURPLE

purple, the See also:

• SIZE

size from that of a small See also:

• CHERRY

cherry to action of the magnet on the electric See also:

• DISCHARGE (adapted from the O. Fr. discharge, modern decharge, from a med. Lat. discargare, to unload, dis- and earn care, to load, cf. " charge ")

discharge in rarefied gases. that of a See also:

• HEN

hen's egg; the form is oblong acute or obtuse at both Plucker, first by himself and afterwards in See also:

• CONJUNCTION (from Lat. conjungere, to join together)

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, See also:

• SEASON (0. Fr. seson, seison, mod. saison, Lat. satio, sowing time, the spring, from serere, to sow; in Late Lat. the word is found with its present meaning, the spring being considered as particularly the season of the year)

season of ripening and duration are all subject to scopy of gases . He was the first to use the vacuum See also:

• TUBE (Lat. tuba)

tube with variation . From its hardihood the See also:

• PLUM

plum is one of the most the capillary part now called a See also:

• GEISSLER, HEINRICH (1814-1879)

Geissler's tube, by means of which valuable fruit trees, as it is not particular as to See also:

• SOIL

soil, and the the luminous intensity of feeble electric discharges was raised See also:

• CROP (a word common. in various forms, such as Germ. Kropf, to many Teutonic languages for a swelling, excrescence, round head or top of anything; it appears also in Romanic languages derived from Teutonic, in Fr. as troupe, whence the English " crupper "

crop is less likely to be destroyed by See also:

• SPRING (from " to spring," " to leap or jump up," " burst out," O. Eng., springau, a common Teut. word, cf. Ger. springer, possibly allied to Gr. QnrFpxecOac, to move rapidly)

spring frosts . Prunes sufficiently to allow of spectroscopic investigation . He antici- and French plums are merely plums dried in the See also:

• SUN
• SUN (0. Eng. sonne, Ger. sonne. Fr. soleil, Lat. sol, Gr. ijXior, from which comes helio- in various English compounds)

sun .

Their pated R . W . Y . See also:

• BUNSEN, CHRISTIAN CHARLES JOSIAS, BARON VON (1791-186o,)
• BUNSEN, ROBERT WILHELM VON (1811-1899)

Bunsen and G . See also:

• KIRCHHOFF, GUSTAV ROBERT (1824-1887)
• KIRCHHOFF, JOHANN WILHELM ADOLF (1826-1908)

Kirchhoff in announcing that the preparation is carried on on a large See also:

• SCALE
• SCALE (1) A

scale in Bosnia and See also:

• SERVIA

Servia, lines of the spectrum were characteristic of the chemical sub- as well as in See also:

• SPAIN
• SPAIN (Espana)

Spain, See also:

• PORTUGAL

Portugal and southern See also:

• FRANCE
• FRANCE, ANATOLE (1844– )

France . stance which emitted them, and in indicating the value of this Plums are propagated chiefly by budding on See also:

• STOCKS

stocks of the discovery in chemical See also:

• ANALYSIS (Gr. avci and Meta, to break up into parts)

analysis . According to Hittorf he was See also:

• MUSSEL (0. Eng. muscle, Lat. musculus, diminutive of mus, mouse, applied to small sea fish and mussels)

Mussel, See also:

• BRUSSELS (Fr. Bruxelles, Flem. Brussel)

Brussels, St See also:

• JULIEN, STANISLAS (1797?-1873)

Julien and See also:

• PEAR (Pyrus communis)

Pear plums . The damson, the first who saw the three lines of the See also:

• HYDROGEN [symbol H, atomic weight x-oo8 (0=16)]

hydrogen spectrum, See also:

• WINE (Lat. vinum, Gr. oivos)

wine-sour and other varieties, planted as See also:

• STANDARDS

standards, are generally which a few months after his See also:

• DEATH

death were recognized in the spec- increased by suckers . For planting against walls, trees which trum of the See also:

• SOLAR, SOLLER (Lat. solarium, Fr.• galetas, Ital. solaio)

solar protuberances, and thus solved one of the have been trained for two years in the nursery are preferred, mysteries of modern See also:

• ASTRONOMY (from Gr. &arpov, a star, and v ,usiv, to classify or arrange)

astronomy, but See also:

• MAIDEN, or MAID

maiden trees can be very successfully introduced, and by Hittorf tells us that Plucker never attained great See also:

• MANUAL

manual liberal treatment may be speedily got to a fruiting See also:

• STATE
• STATE, GREAT OFFICERS OF

state . Any dexterity as an experimenter . He had always, however, -very See also:

• GOOD, JOHN MASON (1764-1827)

good well-drained loamy soil is suitable for plums, that of clear conceptions as to what was wanted, and possessed in a high See also:

• MEDIUM

medium quality as to lightness being decidedly preferable. degree the See also:

• POWER [WILLIAM GRATTAN] TYRONE (1797-1841)

power of putting others in See also:

• POSSESSION
• POSSESSION (Lat. possessio, possidere, to possess)

possession of his ideas Walls with an See also:

• EAST
• EAST, ALFRED (1849- )

east or See also:

• WEST
• WEST, BENJAMIN (1738-1820)
• WEST, NICHOLAS (1461-1533)

west aspect are generally allowed to and rendering them enthusiastic in carrying them into practice. them . The See also:

• HORIZONTAL

horizontal mode of training and the See also:

• FAN (Lat. vannus; Fr. eventail)

fan or See also:

• HALF

half-fan 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 See also:

• PUPIL (Lat. pupillus, orphan, minor, dim. of pupus, boy, allied to puer, from root pm- or peu-, to beget, cf. "pupa," Lat. for " doll," the name given to the stage intervening between the larval and imaginal stages in certain insects)

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 See also:

• GLASS
• GLASS (O.E. glees, cf. Ger. Glas, perhaps derived from an old Teutonic root gla-, a variant of glo-, having the general sense of shining, cf. " glare," " glow ")
• GLASS, STAINED

glass-blower Geissler. continue fruitful for several years . See also:

• STANDARD
• STANDARD, BATTLE OF THE

Standard plum trees should Induced by the encouragement of his mathematical See also:

• FRIENDS, SOCIETY
• FRIENDS, SOCIETY OF

friends in be planted 25 ft. apart each way, and dwarfs 15 or 20 ft . The See also:

• ENGLAND
• ENGLAND, THE CHURCH OF

England, Plucker in 1865 returned to the See also:

• FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
• FIELD, CYRUS WEST (1819-1892)
• FIELD, DAVID DUDLEY (18o5-1894)
• FIELD, EUGENE (1850-1895)
• FIELD, FREDERICK (18o1—1885)
• FIELD, HENRY MARTYN (1822-1907)
• FIELD, JOHN (1782—1837)
• FIELD, MARSHALL (183 1906)
• FIELD, NATHAN (1587—1633)
• FIELD, STEPHEN JOHNSON (1816-1899)
• FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)

field in which he first latter are now largely grown for See also:

• MARKET (Lat. mercatus, trade or place of trade)

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 See also:

• DWARF (A.S. dweorg, D. dwerg, Icel. dvergr)

dwarf See also:

• BUSH

bush first memoir on the subject was published in the Philosophical than from standard trees . Transactions of the Royal Society of See also:

• LONDON

London . It became the The following is a selection of good varieties of plums, with source of a large literature in which the new See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

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 See also:

• EARLY
• EARLY, JUBAL ANDERSON (1816-1894)

Early Green-See also:

• GAGE
• GAGE, LYMAN JUDSON (1836– )
• GAGE, THOMAS (1721–1787)

gage . e . See also:

• JULY

July Transparent Gage . . b . See also:

• SEPT

Sept . Early Transparent Gageb .

Aug . See also:

• JEFFERSON
• JEFFERSON, JOSEPH (1829-1905)
• JEFFERSON, THOMAS (1743-1826)

Jefferson b . Sept . See also:

• MODELS

models to -be constructed which are now so well known to the Denniston's Superb . b . Aug . See also:

• KIRKE, PERCY (c. 1646-1691)

Kirke's . . . m . Sept . student of the higher mathematics . He was engaged in bringing Oullin's See also:

• GOLDEN

Golden . . . m . Aug .

See also:

• COE

Coe's GoldenDrop . . e . Sept . out a large work embodying the results of his researches in line Green-gage m.e.Aug . Reine See also:

• CLAUDE, JEAN (1619-1687)

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 See also:

• FELIX
• FELIX, ANTONIUS
• FELIX, LIA (1830– )

Felix See also:

• KLEIN, JULIUS LEOPOLD (1810–1876)

Klein was M'Laughlin's e . Aug . Ickworth Imperatrice b .

Oct . Oct . able to complete and publish it (see GEOMETRY, LINE) . Among Angelina See also:

• BURDETT, SIR FRANCIS (1770-1844)

Burdett b . Sept . See also:

• LATE

Late See also:

• RIVERS
• RIVERS, ANTHONY WOODVILLE, or WYDEVILLE, 2ND EARL (c. 1442—1483)
• RIVERS, EARL
• RIVERS, RICHARD SAVAGE, 4TH EARL (c. 1660—1712)

Rivers . . . • Nov . the very numerous honours bestowed on Plucker by the various scientific See also:

• SOCIETIES, LEARNED

societies of Europe was the See also:

• COPLEY, JOHN SINGLETON (1737—1815)

Copley See also:

• MEDAL (Fr. medaille, from Lat. metallum)

medal, awarded to him by the Royal Society two years before his death . See R . F . A .

Clebsch's obituary See also:

• NOTICE

notice (Abh. d. kon . Ges. d . Wiss. z . See also:

• GOTTINGEN

Gottingen, 1871, vol. xvi.), to which is appended an appreciation of Plucker's physical researches by Hittorf, and a See also:

• LIST (O.E. lisle, a Teutonic word, cf. Dut. lust, Ger. Leiste, adapted in Ital. lista and Fr. lisle)
• LIST, FRIEDRICH (1789-1846)

list of Pliicker's works by F . Klein . See also C . I . See also:

• GERHARDT, CHARLES FREDERIC (1816-1856)
• GERHARDT, PAUL (c. 1606–1676)

Gerhardt, Geschichte der Mathematik in Deutschland, p . 282, and Plucker's life by A . Dronke (Bonn, 1871) .