the Old Testament, the Targum of Onkelos, and other Aramaic paraphrases, the Vulgate, and the Greek and a Syriac version of the New Testament. It is of no special value for purposes of historical criticism, and is rare now owing to the early loss of a great many copies by accident. (3) The Paris Polyglot, in ten great folio volumes, issued between 1628 and 1645 in Paris by Antoine Vitré at the expense of Guy Michel le Jay. Its critical value is very slight. It presents the Samaritan Pentateuch, another Syriac, and an Arabic version of the Old Testament, in addition to the material contained in the Antwerp volumes. (4) The London or Walton's Polyglot, published in six folio volumes, from 1654 to 1657, under the editorship of Brian Walton. The first copies were dedicated to Oliver Cromwell, who had been personally interested in their publication and had allowed the paper on which they were printed to be imported without duty. The second set was dedicated to King Charles II. and the former patron, Cromwell, is branded as 'the great Dragon.' It contains the entire Bible, or some portion of it, in Hebrew, Samaritan, Aramaic, Syriac, Arabic, Ethiopic, Persian, Greek (with a literal Latin translation of each), and Latin. This is the most valuable polyglot ever issued. The greatest scholars worked upon it, and Walton's Prolegomena is a very able work which has been republished (Canterbury, 1828). A dictionary of all the languages represented except the Greek and Latin, called Lexicon Heptaglotton, was published by Edmund Cartell in 1669. Of minor polyglots mention may be made of Bagster's (London, 1831), which contains the entire Bible in Hebrew, Greek, English, Latin, French, Italian, Spanish, and German, with a Syriac version of the New Testament in addition. Consult Tregelles, An Account of the Printed Text of the Greek New Testament (London, 1854).

POLYGNO'TUS (Lat., from Gk. Holywтos, Polygnotos). A Greek painter of the second quarter of the fifth century B.C. He was the son of Aglaophon, and a native of the island of Thasos, where his family were artists. He seems to have come to Athens shortly after the Persian wars, and found abundant scope for his talents in the decoration of the great buildings which mark this period. Along with the Ionian Micon, and Pananos, brother of Phidias, he is said to have decorated the Theseum, Stoa Poecile (or painted portico), and Anakeion, or temple of the Dioscuri, with paintings from legend and recent history, though the division of the paintings among the artists was not certain. The first building contained the battles of the Athenians with the

tle of Theseus with the Amazons, the battle of Marathon, and the victory of the Athenians and Argives over the Spartans at Enoe, of which the second was by some attributed to Polygnotus. In the Anakeion he painted the Dioscuri carrying off the daughters of Leucippus. In the temple of Athena Areia at Platæa was a painting by him representing the slaughter of the suitors by Odysseus, and some frescoes in the Propylæa at Athens were attributed to him. Most celebrated and best known from the descriptions by Pausanias are the great paintings in the Lesche (or porch) at Delphi, representing the departure of the Greeks from Troy and the descent of Odysseus to the lower world. As is clear from these subjects, Polygnotus devoted himself to extensive compositions containing many figures whose grouping and characterization required careful study. At the same time his means were simple. Black, white, red, yellow, blue, and green were his colors, light and shade were unknown, and the strength of the artist lay in his beauty of outline and coloring, and above all in his delineation of character. His subjects led him to arrange his figures on various levels, and for this reason he chose when possible sloping ground, which could be easily indicated by waving lines and the partial concealment of some figures. His influence was very marked not only on painting, as is clear from a group of Attic vases, but also on sculpture, and it is probable that the reliefs at Tryso (Gyöl-bashi) reflect his art, or that of the Ionian school, of which he was the greatest exponent.

Consult Brunn, Geschichte der griechischen Künstler (Stuttgart, 1853-59). The earlier works on the paintings of Polygnotus, though of some value, are in general superseded by later investigations, especially those of Robert, Schöne, Schreiber, and Weizsäcker: Robert, Die Nekyia des Polygnot (Halle, 1892); Die Iliupersis des Polygnot (ib., 1893); Die Marathonschlacht in der Poikile und Weiteres über Polygnot (ib., 1895); Schöne, "Zur Polygnots delphischen Bildern," in Jahrbuch des archäologischen Instituts (Berlin, 1893); Schreiber, Die Wandbilder des Polygnot in Delphi (Leipzig, 1897); Weizsäcker, Polygnot's Gemälde in der Lesche der Knidier in Delphi (Stuttgart, 1895). For reconstructions, see Robert, and Wiener Vorlegeblätter (Vienna, 1888).

POLYGON (Lat. polygonum, from Gk. nokvywvov, polygonon, polygon, neu. sg. of moλúyros, polygōnos, having many angles, from woλvę, polys, much, many+ywvla, gōnia, angle). If the two end-points of a broken line coincide, the figure ob

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Amazons, and of the Lapitha with the Centaurs, and the descent of Theseus to Amphitrite in the depths of the sea. In the Stoa were represented the capture of Troy and the council of the Greeks to judge Ajax for his outrage on Cassandra, which was certainly by Polygnotus, also the bat

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tained is called a polygon, and the broken line its perimeter. The vertices of the angles made by the various segments of the perimeter are called the vertices of the polygon, and the segments themselves the sides of the polygon. The perimeter of. a polygon divides the plane into two

amphibium, one of the species of the section or suborder Persicaria, is abundant about margins of ponds and ditches throughout the Northern Hemisphere. It has two forms of leaves; those upon the erect stems being broad and smooth, those which float in the water narrow and rough, differences which might be held to indicate distinct species, yet both may be found growing from one root. The stems have been used on the Continent of Europe as a substitute for sarsaparilla. Several species are occasionally used for dyeing, as the spotted persicaria (Polygonum Persicaria), a very common weed on manure heaps and in waste places in Europe and also naturalized in the United States. The only species really important on this account is that called dyers' buckwheat (Polygonum tinctorium), a Chinese biennial, with ovate leaves and slender spikes of reddish flowers. It has been successfully cultivated in France and Flanders. It yields a blue dye scarcely inferior to indigo. Coccoloba, another genus of this order, has a wide distribution throughout the tropics, Coccoloba uvifera and other species producing edible fruits. POLYGONAL NUMBERS. See NUMBER. POLYHEDRON (from Gk. Пoλúedpos, polyedros, having many bases, from Toλús, polys, much, many + éopa, hedra, base). A solid whose bounding surface consists entirely of planes. The polygons which bound it are called its faces; the sides of those polygons, its edges; and the points where the edges meet, its vertices. If a polyhedron is such that no straight line can be drawn to cut its surface more than twice, it is said to be convex; otherwise it is said to be concave. Unless the contrary is stated the word polyhedron means convex polyhedron. If the faces of a polyhedron are congruent and regular polygons, and the polyhedral angles are all congruent, the polyhedron is said to be regular. A polyhedron which has for bases any two polygons in parallel

having 8 faces, 6 vertices, and 12 edges, the equation becomes 12+2=8+ 6. For every polyhedron there is another which, with the same number of edges, has as many faces as the first has vertices, and as many vertices as the first has faces. There cannot be more than five regular convex polyhedra. These solids are represented by the accompanying figures, and are sometimes known as the Platonic bodies, from the attention they received among the Platonists.

For these five polyhedra, if s be the number of sides in each face, n the number of plane angles at each vertex, then, following the other notation above given, sf=nv = 2e. Also the sum of all the plane angles in each figure is 2 (v—2). These formulas may easily be verified from the following table of elements:

POLYHEDRA.

planes, and for lateral faces triangles or trapezoids which have one side in common with one base and the opposite vertex or side in common with the other base, is called a prismatoid. ( (See MENSURATION.) In accordance with the definition, also all prisms and pyramids (q.v.) are included among the prismatoids. Among the general relations of polyhedra, the following are the most remarkable: If a convex polyhedron has e edges, v vertices, and f faces, then e+ 2 = ƒ + v. (A theorem known to Descartes, but bearing Euler's name.) E.g., in a regular octahedron, a solid

POLYHYMNIA, or POLYMNIA (Lat., from Gk. Пoλvýμna or Пoλúμvia). One of the nine Muses (q.v.). When in late times the functions of the Muses were specialized, she became the Muse of the pantomime, and was represented without special attribute, but closely wrapped in her mantle, and sometimes with her hand upon her

mouth.

POLYMASTODON

(Neo-Lat., from Gk. Toλús, polys, much, many + parrós, mastos, breast, +ódovs, odous, tooth). A fossil multi-tuberculate animal of the size of a beaver, of which fragmentary remains have been found in the basal Eocene or Puerco beds of New Mexico. The jaws and dentition have some resemblances to those of rodents.

POLYMORPHISM (from Gk. Toλús, polys, much, many + μoppń, morphe, form). The differentiation either of one animal into two or more incomplete undetached individuals (pseudindividuals) or zooids, as in the Siphonophores or Physalia; or that of the animal into two separate sexes, or of the latter into castes, as in the termites and ants. Instead of the functions of the whole animal or plant being equally distributed to the individual organs, some of the organs or parts of the animal are set apart for this or that function. In the hydra the individual is monomorphic, not divided into male and female individuals, but in Hydractinia, a fixed, vegetative form, there arise sexual or reproductive zooids, some female and others male, and also hydra-like or nutritive zoöids or incomplete individuals. In the Portuguese man-of-war (q.v.) we have a still better example of incomplete polymorphism. Thus, as Hertwig states, division of labor leads to greater centralization, "the more polymorphic an animal colony becomes, the more unified it is, the more it gives the impression of being a single animal instead of an aggregation of single animals."

In the hydroids alternation of generations (q.v.) has arisen from a division of labor or polymorphism of individuals originally of equivalent value, in which some individuals (the sexual ones) have separated and acquired a peculiar structure. Moreover, while alternation of generations has arisen from polymorphism, it can again produce it. Hertwig illustrates this by the case of certain medusa, which, instead of separating, remain permanently attached to the colony. They then degenerate into 'sporosacs,' in which a mouth, tentacles, and a velum are wanting.

A second kind of polymorphism is that seen in the males and the females of most animals. This is sexual dimorphism, which may pass into sexual polymorphism. This is complete polymorphism. Reproduction by budding involves the differentiation of the animal form into three kinds of individuals-i.e. males, females, and 'neuters,' as among insects. Among the cœlenterates and worms the forms reproducing by parthenogenesis (q.v.) are usually larval or immature, as if they were prematurely hurried into existence, and their reproductive organs had been elaborated in advance of other systems or organs, for the sudden production, so to speak, of large numbers of individuals like themselves.

Among insects dimorphism is intimately connected with organic reproduction. Thus the summer wingless asexual aphis and the perfect winged autumnal aphis may be called 'dimor

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phic' forms. The perfect female may assume two forms, so much so as to be mistaken for two distinct species.

DIMORPHISM IN BIRDS. Besides ordinary sexual dimorphism, depending on sex, and comprised under the head of secondary sexual characters (see SEX; SEXUAL SELECTION), a few special cases are known, due probably to climate or local causes. Thus, in some species of skua, a particolored bird may frequently be found mated with a uni-colorous form, either male or female. In the guillemots at nearly every breeding station about one in twenty may be marked with a white circle around the eye, and a white line extending bridled backward from it, these ringed or guillemots being of either sex and apparently paired with birds of normal plumage, no intermediate forms being known. (See DICHROMATISM IN BIRDS.) A striking example of dimorphism in respect to the beak is furnished by the huia (q.v.).

DIMORPHISM AND POLYMORPHISM IN INSECTS.

Although sexual dimorphism is very prevalent in insects, there are many instances of dimorphism, resulting from local causes, as temperature. (See TEMPERATURE VARIETIES, especially as relating to seasonal dimorphism, wet and dry forms.) Certain species of grasshoppers are dimorphic. In the honey-ant (Myrmecocystus Mexicanus), besides the usual workers, there occur individuals with enormous spherical abdomens filled with honey. Here the cause is evidently connected with the food. See, for other examples, EVOLU TION, paragraph Polymorphism.

The chief initial or determining causes of dimorphism and polymorphism, besides sexual selection (q.v.), are changes in temperature, of light, and of other physical agents.

POLYMORPHOUS (in geology). See Iso

MORPHISM.

POL'YNE'SIA (Neo-Lat., from Gk. Tohức, polys, much, many moos, nesos, island). A name once applied to all the islands in the Pacific Ocean, lying between Asia and America. By modern geographers the name is used to designate a division of Oceanica comprising all the islands not included under Micronesia or Melonesia. The most important of them are the Tonga, Samoan, Ellice, Cook, Society, Hawaiian, and Marquesas Islands, and Low Archipelago. The Fiji Islands are included by some in Polynesia and by others in Melanesia, all of which are described in separate articles. For a description of the inhabitants of these islands, consult: Stevenson, In the South Seas (New York, 1896); Becke, Wild Life in Southern Seas (London, 1897); Mager, Le monde polynesien (Paris, 1902). See POLYNESIANS.

POLYNESIANS. A term used diversely by various writers. By some it is employed as a synonym of Malayo-Polynesian (q.v.) and made to include all the so-called brown race of the regions known as Malaysia, Micronesia, Melanesia, and Polynesia, also known as the Malayan race. F. Müller (1879) made the Poly-Melanesians one of the branches of his Malay race, while Brinton (1890) divides his Malayic stock into a Western (Malayan) and an Eastern (Polynesian) group. Deniker makes the Polynesians properly so called one of the great ethnic groups of the Indo-Pacific area. Keane (1896) holds that the Eastern Polynesians are a branch of