228 P L U P L U not unfrequently reaching the Cape Colony, Ceylon, Australia, and even Tasmania. Charadrius pluvialis has a much narrower distribution, though where it occurs it is much more numerous as a species. Its breeding quarters do not extend further than from Iceland to western Siberia, but include the more elevated tracts in the British Islands, whence in autumn it spreads itself, often in immense flocks, over the cultivated districts if the fields be sufficiently open. Here some will remain so long as the absence of frost or snow permits, but the majority make for the Mediter ranean basin, or the countries beyond, in which to winter ; and, as with the Grey Plover, stragglers find their way to the southern extremity of Africa. The same may be said, mutatis mutandis, of what are usually deemed to be two other cognate forms, C. virginicus and C. fulvus, which respectively represent C. pluvialis in America and eastern Asia, where they are also known by the same English name. The discrimination of these two birds from one another requires a very acute eye, and room is here wanting in which to specify the minute points in which they differ ; a but both are easily distinguished from their European ally by their smaller size, their greyish-brown axillary feathers, and their proportionally longer and more slender legs. All, however, and the same is the case with the Grey Plover, undergo precisely the same seasonal change of colour, greatly altering their appearance and equally affecting both sexes. In the course of 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. This is partly due to the growth of new feathers, but partly to some of the old feathers actually changing their colour, though the way in which the alteration is brought about is still uncertain. 2 A corresponding alteration is at the same season observable in the upper plumage ; but this seems chiefly due (as in many other birds) to the shed ding of the lighter-coloured margins of the feathers, and does not produce so complete a transformation of appear ance, though the beauty of the wearer is thereby greatly increased. Though the birds just spoken of are those most emphati cally entitled to be called Plovers, the group of Ringed Plovers before mentioned (KILLDEER, vol. xiv. p. 76) and the LAPWING (vol. xiv. p. 308), with its allies, have, 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 rpo^ Aos of Herodotus (see HUMMING-BIRD, vol. xii. p. 358, n. 3), the Pluvianus or Hyas &yyptius 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 probably belongs to the small section generally known as Coursers, Cursoiius, of which some eight or ten species inhabit the deserts of Africa and India, while one, C. yallicus, occasionally strays to Europe and even to England. Allied to them are the curious PRATINCOLES (q.v.), also peculiar to the Old World, while 1 Schlegel (Mus. Pays-Bas, Cursores, p. 53) states that in some examples it seems impossible to determine the form to which they belong ; but ordinarily American specimens are rather larger and stouter, and have shorter toes than those from Asia. 2 It is much to be regretted that ornithologists favourably situated in regard to zoological gardens have not more extensively used oppor tunities which might thus be accorded to them of conducting useful observations on this subject and others of similar kind. Elsewhere it would be hardly possible to carry on such an investigation, and even under the best circumstances it would not be easy and would require unremitting attention. The results of some partial observations superintended by Yarrell in the gardens of the Zoological Society of London are given in its Transactions (i. pp. L3-19). Little has been done there since of this nature. the genera Thinocoris and Attaais form an outlying group peculiar to South America, that is by some systematists regarded as a separate Family Thinocoridx, near which are often placed the singular SHEATH BILLS (q.v.). By most authorities the Stone-Curlews (CoiiLEW, vol. vi. p. 712), the OYSTER-CATCHERS (vol. xviii. p. Ill), and TURNSTONES (q.v.} are also regarded as belonging to the Family Char- adriidx, and some would add the Avocets (Recurvirostra) and STILTS (q.v.), among which the Cavalier, Dromas 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 TERNS (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 SANDPIPERS and SNIPES (q.v.). United, however, with both of the latter, under the name of Limicokv, 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 not inclined to treat as its nearest relations the Bustards on the one hand and the Gavix on the other, as before suggested (ORNITHOLOGY, vol. xviii, p. 45). (A. N.) PLUCKER, JULIUS (1801-18G8), mathematician and physicist, was born at Elberfeld on the 16th June 1801. After being educated at the gymnasium at Diisseldorf and studying at the universities of Bonn, Heidelberg, and Berlin, he went in 1823 for a short time to Paris, where he came under the influence of the great school of French geometers, whose founder, Monge, was only recently dead ; and there can be no doubt that his intercourse with the mathematicians of that school, more particularly with Poncelet and Gergonne, greatly helped to determine the earlier part at least of his career. In 1825 he was received as " privat-docent " at Bonn, and after three years he was made professor extraordinary. The title of his "habilitationsschrift," Generalem analyseos applicationem ad ea quse yeometrise, altioris et mechanics basis ft funda- menta sunt e serie Tayloria deducit Julius Pliidcer (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 Descrip tive and the Application de V Analyse (I la Geometrie. Although fully master of those general ideas of modern geometry whose development began with the publication of the former of these works, Pliicker s actual labours lay more in the direction of the latter. It was his aim to furnish modern geometry with suitable analytical methods and thus to give it an independent analytical development. In this effort he was as successful as were his great con temporaries Poncelet and Steiner in cultivating geometry in its purely synthetical form. From his lectures and researches at Bonn sprang his first great work Analytisch- Geomdrische Entwickelungen (voL i. 1828, vol. ii. 1831). hi the first volume of this treatise Pliickcr introduced for the first time 3 the method of abridged notation which has become one of the characteristic features of modern analytical geometry. The peculiarity of this method consists in this, that the letters used in the equations of curves and surfaces represent, not coordinates of a point with respect to arbitrary chosen axes, but straight lines, or it may be curves or surfaces, intrinsically related to the figure 3 The independent development of a similar idea by the brilliant young French geometer Bobillier (1797-3 832) was cut short by his
premature death.