Page:The New International Encyclopædia 1st ed. v. 18.djvu/889

* SYMMETRY. 775 SYMONDS. and are symmetric. The theory of symmetric tiyures is closely related to that of similarity (q.v.). SYMMETRIC POLYHEDRAL ANGLES. OPPOSITE POLYHE- DKAL ANGLES. In algebra, an algebraic function is said to be summciric with respect to certain letters %vhen these letters can be interchanged Yithout cliang- ing the form of the expression. E.g. jr + 2xy + y' is symmetric as to x and y, because if x and _i/ are interchanged it becomes y- -^ 2yx + ar, which is the same as the original expression. A knowledge of symmetry and liomogeneity (q.v.) is of great value in factoring. E.g. to factor f{x,y,z) = x(if — ^) + yi.z' — oc') + z(a? — y'). The expression vanishes for a' = j/, hence x — y is a factor by the remainder the- orem (q.v.). But f(j,j/,i) is symmetric with re- spect to x,y,z, therefore y — z, : — x, are also factors. And f{x. y, s) being homogeneous of the fourth degree, it must contain another factor of the first degree : but such a homogeneous sym- metric factor can he x -^ y -{- z only. Whence the literal factors are x — y, y — z, z — x. x -- y -+- z. On algebraic symmetry consult Beman and Smith, Elements of Algchra (Boston, 1900). SYMMETRY. The general tendency in ani- mals tow ard a symmetrical arrangement of part.s. Thus man is bilaterally symmetrical, i.e. the external parts or limbs are arranged in pairs on each side of his body. So with the annelid worms, the lobster, centipede, and scorpion. On the other hand, this symmetry is wanting in some of the internal organs — those which are single. Haeckel has elaborated a scheme of fundamental forms of which the following is a summary. (1) Anaxial or symmetrical forms, with no fixed central point or definite axis (many Pro- tozoa and most sponges ) . (2) Homaxial or spherical animals have the fundamental shape of a sphere, the parts of the body being arranged concentrically around a fixed central point (a few spherical Protozoa, chiefly Eadiolaria ) . (3) Moiiaxial or Radial Symmetry. In polyps, owing to their becoming fixed in larval life, the digestive canal opens upward, the parts ■ being arranged around the single or main axis, radiating from it. In cross-section the radial symmetry is seen to be very marked. The parts are like reentering wedges and were called by Agassiz spheromeres (eoelenterates and echino- derms ) . (4) Bilateral !?ymmetry. Here the parts are symmetrically arranged on each side of the main or sagittal axis (annelid worms, arthropods, vertebrates) . Internai. and External Segmentation. This is due to the division of the body into segments, indicated externally by infoldings of the integu- ment (annelids, ta|)eworms, artliropods). The external signs of segmentation may be ell'aced or wanting. Thus in inan the body is segmented only internally; in the lancelet the muscles are arranged scgmentally and can be seen on the out- side of tlic body. In the annelid worms (earth- worm, etc.) not only is the body segmented externally, bearing seta; or parapodia on each segment, but the nerve-ganglia, nepliridia or segmental organs, the vascular arelies or trans- verse arteries, and the septa of the body, i.e. the partition^ between the segments, are repeated metamerieally. HoMONOMOrS AND IlETEROMEKOf.S SEGMENTA- TION. The earthworm, the galley-worm (.Julus), and the centipedes afford examples where the trunk-segments are for the most part alike in size and appearance, and bear similar locomotive seta> or jointed appendages. In most eru^taccii and insects, as well as in the higher vertebrates, ■hetcronomy' prevails. Homonomy is character- istic of the more primitive forms, lieteronomy of later more specialized types. Thus the trans- fer of parts headwards in crabs (cephalization) , due to the excessive development of certain of the head segments and the atrophy of those be- hind, brings about a decided irregularity in the size and shape of the segments. Heteronomy is thus accompanied by a division of physiological labor due to the specialization of the seg- ments and their appendages. It is owing to the hypertrophy of certain segments and partial or total reduction and even in some cases loss of segments or portions of segments, with their ap- pendages, that the varied forms of arthropods are produced. Consult Haeckel, Oenerelle Mar- phologie (Berlin, 18G6). SYMONDS, sim'ondz or si'mondz, .Tohn Ad- DiKt:TOX (1840-93). An English critic and lit- erary historian, born at Bri-stol. From Harrow he passed to Balliol College, Oxford, where he graduated with distinction, winning the Newdi- gate prize, with a poem on The Eseorial (1860), and a fellowship at Magdalen College (1862). He began the study of law, which ill health compelled him to abandon. He settled at Clifton and began literary work in earnest. Subsequently he passed much time on the Continent, and for several years lived at Davos, in Switzerland. Our Life in the Swiss nighlaiirls (1891) tells charmingly of his moun- tain home. He died in Rome. Symonds's repu- tation rests mainly on The History of the Italian Renaissance (7 vols., 187.'5-S6), and the excel- lent translations of the ^'ita di Rrnrenuto Cel- lini (1887) and the Sonnets of Miehelanyelo and Campanella (1878). Other striking books are the Introduction to the Study of Dante (1872), Essays, Speculatire and Siirjfiestire (1890), In the Key of Blue (1893), and Walt Whitman (1803). Symonds also contributed to the "Eng- lish Men of Letters" good lives of Shellev (1878) and of Sir Philip Sidney (1886). Besides all these and much other miscellaneous work, he composed a considerable bodv of verse, admirable in technique, but wanting in inspiration. This includes Many Moods (1S78): Nero and Old (1880): Animi Fiftiira (1882): and Varmhun- dull Lihelhis (18S4K Both his verse and his prose show the thorough interpenetration of his