Page:EB1911 - Volume 21.djvu/886

Rh change of colour, greatly altering their appearance and equally affecting both sexes. In spring or early summer nearly the whole of the lower plumage from the chin to the vent, which during winter has been nearly pure white, becomes deep black. A corresponding alteration is at the same season observable in the upper plumage.

Though the birds just spoken of are those most emphatically entitled to be called plovers, the group of ringed plovers (see and ), with its allies, has, according to usage, hardly less claim to the name, which is also extended to some other more distant forms that can here have only the briefest notice. Among them one of the most remarkable is the “ Zickzack " (so-called from its cry)—the of Herodotus (see ), the Pluvianus or Hyas aegyptius of ornithologists, celebrated for the services it is said to render to the crocodile—a small bird whose plumage of delicate lavender and cream colour is relieved by markings of black and white. This belongs to the small family Glareolidae, of which the members best known are the coursers, Cursorius, with some eight or ten species inhabiting the deserts of Africa and India, while one, C. gallicus, occasionally strays to Europe and even to England. Allied to them are the curious  (q.v.), also peculiar to the Old World, while the genera Thinocoris and Attagis form an outlying group peculiar to South America, that is by some systematists regarded as a separate family Thinocoridae, near which are often placed the singular  (q.v.). By most authorities the Stone-curlews (see ), the (q.v.) and (q.v.) are also regarded as belonging to the family Charadriidae, and some would add the Avocets (Recurvirostra) and (q.v.), among which the Cavalier, or Crab-plover, Dramas ardeola—a form that has been bandied about from one family and even order to another—should possibly find its resting-place. It frequents the sandy shores of the Indian Ocean and Bay of Bengal from Natal to Aden, and thence to Ceylon, the Malabar coast, and the Andaman and Nicobar Islands—a white and black bird, mounted on long legs, with webbed feet, and a bill so shaped as to have made some of the best ornithologists lodge it among the (q.v.).

Though the various forms here spoken of as plovers are almost certainly closely allied, they must be regarded as constituting a very indefinite group, for hardly any strong line of demarcation can be drawn between them and the and  (q.v.). United, however, with both of the latter under the name of Limicolae, after the method approved by the most recent systematists, the whole form an assemblage the compactness of which no observant ornithologist can hesitate to admit, even if he be uncertain of the exact kinship.

 PLUCK, to pull or pick off something, as flowers from a plant, feathers from a bird. The word in O. Eng. is pluccian or ploccian and is represented by numerous forms in Teutonic languages, cf. Ger. pflücken, Du. plukken, Dan. plakke, &c. In sense and form a plausible identification has been found with Ital. piluccare, to pick grapes, hair, feathers, cf. Fr. éplucher, pick. These romanic words are to be referred to Lat. pilus, hair, which has also given “peruke” or “periwig” and “plush.” Difficulties of phonology, history and chronology, however, seem to show that this close similarity is only a coincidence. “Pluck,” in the sense of courage, was originally a slang word of the prize-ring, and Sir W. Scott (Journal, Sept. 4, 1827) speaks of the “want of that article blackguardly called pluck.” In butcher's parlance the “pluck” of an animal is the heart, liver and lungs, probably so called from their being “plucked” or pulled out of the carcase immediately after slaughtering. The heart being the typical seat of courage, the transference is obvious. In university colloquial or slang use, “to pluck” is to refuse to pass a candidate on examination; the more usual colloquial word is now “to plough.” At the granting of degrees at Oxford objection to a candidate could be taken for other reasons than failure at examination, and the person thus challenging drew the attention of the proctor in congregation by “plucking” a piece of black silk attached to the back of his gown.

PLÜCKER, JULIUS (1801–1868), German mathematician and physicist, was born at Elberfeld on the 16th of June 1801. After being educated at Düsseldorf 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 e serie Tayloria deducit Julius Plücker (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 Géométrie descriptive and the Application de l'analyse à la géométrie. Plücker 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., 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 ). 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 Plücker 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. Plücker 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 Plücker's discovery of the six equations connecting the numbers of singularities in algebraical curves (see ). Plücker 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 Kurven (1839).

In 1833 Plücker 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 gegründet, und insbesondere eine ausführliche Theorie der Curven dritter 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+μs=0. He gives a complete enumeration of them, including two hundred and nineteen species. In 1836 Plücker 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 Plücker'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