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* SYMBIOSIS. 772 SYMBOLS. line between symbiosis and the parasitism, for instance, of the itch mite which burrows under the skin between the fingers. Social Symbiosis. Wheeler applies this term to the relations between ants and the various beetles, crickets, cockroaches, etc, which live at their expense. Of those beetles (Claviger, Paus- sus, etc.) that live in ant and termite nests cer- tain ones seem to be tolerated or ignored by the ants. So completely agreeable to the ants is the presence of certain of the Staphylinida? that the ants regurgitate food which they give to the beetles, and the beetles in the same manner share their supply with hungry ants. The ants feed the larval beetles with as much care as they do their own larvae. They even clean the young beetles by licking them. See Ant; Bee; Com- MENSALISM; EPIPHYTE; IXSECT ; LiCHEN : MU- TUALISM: Parasite: Eove-Beetle: Termite. Consult: O. Hertwig, Die Symbiosis (Jena, 1883) ; Geddes, 'Nature, vol. xxv.n882) : Brandt, Archiv fur Anatomie nnd Physiologie ( 1882), and Mittheilungen der zofjlofiischen Station, Naples, iv. (1883) ; Lankester, .A''af»re, vol. xxvii. (1882). Tor symbiosis in insects, see tbe papers of Forel, Wasniann, Wheeler, etc. SYMBOLISM (from symbol, from Lat. syin- holus, si/iiiholitin, from Gk. cri/j-PoXos, ain^oKov, mark, token, signal, sign, confession of faith, from ffviipdWcii/, si/mhalleiii, to compare, put together, from aiv, syi), together -|- pdWeiv, iaUein, to throw). In its broadest sense, the representation of one thing by another, as of a sovmd by a letter, of a word or a concrete idea by a hieroglyph. Symbolism is most important in the history of art, especially of Christian art. Obviously no doctrine of religion can take form in outward act without some kind of symbolism; and accordingly every detail of the ancient Ro- man Catholic or Eastern rites is so planned as to suggest to the worsliiper one or anotlicr aspect of abstract truth. In the plan and construction of the older churches the same idea is carried out as in their cruciform shape. Early Christian art represented Jesus under nxunerous symbols, among the commonest being the lamb, the fish, and the Greek letters Aljiha and Omega (the be- ginning and the end). Similarly, the Holy Ghost was represented by a dove; and the olive branch denoted peace ; the palm, triumph ; and the anchor, faith or hope. In later art each one of the saints depicted may be recognized by some appropriate symbol, e.g. Saint Andrew by a cross in the shape of an X, or Saint Dominic by the lily and the star above his forehead. Consult: Clement, Handbook of Leqendary and Mythologi- cal Art (2d ed., Boston, 1881); Knight, The Symbolic Language of Ancient Art and Myth- ology (2d ed., New York, 1876). See Deca- dents. SYMBOLISTS. The name of a class of writers which sprang up after 1880 notably in France and in connection with verse. The sym- bolists regard symbolism as the expression of an idea by the introduction of a being or an object merely for the purposes of such expression. The characteristic means are the allegory, transposi- tion, and allusion. The symbolists were in ef- fect reactionists against realism. They concern themselves with general truths in contrast with actualities. They court erudition, adore the metaphysical and mysterious, and especially ex- alt the magic power and charm of music. Identi- fied with tiie inlluence of Wagner, they seek music in language and accordingly the sonorousness of words; they suggest but do not name. Dreams, visions, and mythological tales are their proper subjects, and lyricism their favorite form of poetic expression. In their aim to unify and blend the arts and the functions of the senses, the ex- tremists among them, like Arthur Rimbaud, as- sociated the vowels with colors, etc. The metri- cal reforms of the French Sj'mbolists have re- sulted in making French verse more free and large in its possibilities of effect, more subtle, in- timate, and musical. The S3'mbolists, despite the vagaries which attend all new schools of lit- erature and art, have left a permanent and de- sirable mark. Their general inlluence has been for the exclusive, the refined, the delicate, and the mystic beauties of the supranatural. Their verse has represented idealism, religious senti- ment, a return to the ancient, and an inherent preference for solemn or fatalistic themes. Ver- laine, Mallarme, and Maeterlinck are the most noteworthy of the French and Belgian Symbolists. Among Symbolist plays those of De Curel may be noted. S.ymbolism reaches also into the domain of contemporary painting. For a state- ment of certain particular phases or develop- ments of Symbolism, see D£c.4.dents. SYMBOLS, Mathematical. The various signs and abbreviations used to facilitate mathe- matical expression. They are of the following kinds : Of value. Hindu and other numerals. See Numerals. Of operation. Addition, -f, 2. Subtraction, —. Multiplication, as in a X 6, a-b, (a -{- b) , M or a! . .- (=a. Division, as in a -t- 5, a:b, ^/b % (as in 6% = -j-ts). Involution, as in x°. 1- Evolution, as m x" or ■^/x. Differentation, d, 5, D. Integration, i . Of function. f(x), V(x]. for f — function of x, F — function of cr; ')(" greater than b), a <^ b (a not less than 5),a}> * '" "ot greater than h), a ^ b (a not equal to 6). Of continuation. as in a, a', a',