COMPLEX NUMBER. 237 COMPOSITE. for the use of such (juantities as a +!)t/ — 1, Ijut fouiulefl no theory. Wallis (168.5) made the first attempt to give a geometric iiiterjjreta- tjon. Euler (1770) still regarded these (|uanli- ties impossible. Thus it was reserved for Casper Wessel (1797), a Xorwegian surveyor, to invent a graphic treatment of eomph-x numbers. His method is contained in a memoir, presented to the Royal Academy of Science and Letters of Denmark, entitled On the Analytic Rcprc.icnta- lion of Direction. For the early development of the subject, however, credit nnist be given to Argand. Gauss, Servois, and others, since Wes- feel's article (i)ul)lished in 1700 by the Royal Academy ol' Denmark) did not a])pear in French until 1897. one hundred years after its presen- tation. Oauss did nnich to establish the under- lying principles. Argand's memoir (ISOO), un- questionably an original and independent pro- duction, supplied the graphic theory that lay neglected in the work of Wessel. Francois, Ser- vois, Gergonne. and Cauehy did much to correct the errors of their predecessors and to generalize the theory of directed lines. Complex number, being the most general type of algebraic number, has come to occupy the pUice of highest importance in modern analysis. It has led in recent times to the establishment of the theory of functions (q.v. ) and quaternions (q.v. ). Consult: Beman, ""A Chapter in the His- tory of Jlathematics," in the Proceed inr/s of the American Asxociation for the Arlra)icenient of •Science (Salem. 1897) ; Cauehy, fours d'anah/se (Paris, 1821) : Warren, A Treatise on the Geo- metric Representation of the Hqiiare Roots of Xcgatire Quantities (Cambridge, 1827): Chrvs- tal, Algehra, part i. (Edinburgh, 1889) ; Hankel, Vorlesunfien iiber die complexcn Zahlen (Leip- zig, 1867); Dur&ge, Theorie der Functioncn einer complexen veriinderlichen Grosse (Leip- zig. 1873), trans, by Fisher and Schwatt as Ete- ments of the Throni of Functions of a Complex Variable (Philadelphia, 1896). COMPLU'VIUM. See Atrium; Implvvium. COMPONE, kom-po'na (Fr., composed), or GoBOXY. In heraldry, a term describing a field or charge Iiearing a row of small squares, con- sisting of alternate metals and colors, COMPOSIT.ffi. kom-poz'I-te (Lat. nom. pi., from conipositns, p.p. of componcre, to put to- gether, from com-, together + ponerr, to ])ut, from po-, Gk. a-6, apo, oft' + sinerc, to allow). An order of dicotyledonous plants, variously called the composite family, aster family, sun- flower family, and sometimes divided and known as the chicory and thistle families, embracing nearly 1000 genera and more than 11,000 species, making it the largest family of flowering plants. Although a large order, the flowers of the Com- positiE are so characteristic and distinctive as not to be confused with those of any other order, the only ones bearing even a superficial resem- blance being Dipsacere, represented with us by the teasel. The flowers of the order Compositic are rather small and are grotiped together upon a ('oninion receptacle, surroimded hy bracts which form a leafy or scaly invohicre. so as to give the ap- pearance of a single flower. The conuuon term 'flower' is applied to the aggregation instead of to the individtials making tip the so-called 'head.' The flowers, or florets, as they are tisually known, are often of (wo kinds, those of the cen- tral part being called disk florets, and those of the circumference ray florets. These often differ in size, shape, and color, and the disk florets are usually fertile, while those of the ray are often sterile, or at least without stamens. The caly.v is united with the. ovary, and its divisions crown the ovary with awns, teeth, bristles, etc all of which are called the pappus (q.v.) ; or the pap- pus may be wholly wanting. The coridla is situated above the ovary, an<l is united into a tube (tubular), or may be strap-shaped (ligu- late), both forms commonly occnrring in the same flower, the tubular florets com])osing the disk, and the ligulate florets the rays of the 'flower.' The corolla may be, and usually is, di- vided at its summit into five teeth or lobes. The stamens are usually five in number, and are inserted upon the corolla, and are united together by their anthers into a tube around the single style, which is two-cleft at its siniiniit. The ovary is one-celled and one-ovulcd, the ovules ripening into a dry fruit called an akene or achene (q.v.). Growing among the flowers are often found numerous bracts which are spoken of as chaff or palete. When these are not present, the receptacle is said to be naked. The fonn of the receptacle may vary from flat, eon- vex, conical, or, in some cases, elongated to the length of an inch or more. The fonn of the corolla, shape of the receptacle, presence and nature of the chaflT, are all important characters in the classiflcation of the members of (his order. The plants are herbaceous, shrubby, or even trees, and are found in nearly all parts of the world where plant life exists to any extent, and they frequent almost every condition of soil and surroundings. The tree forms are confined to the tropics, many of the shrubby species occur in hot. dry regions, while the herbaceous species ])revail in temperate climates, extending well within the colder zones. In general the leaves are alternate and without stipules, but are some- times opposite or whorled; or they may all be radical, as in the dandelion, etc, Numerous sys- tems of classification have been proposed from time to time, that of Hoffmann (with some modi- fication) being the one most current at present. HofTmann divides the order into two suliordcrs — TuljuJiflora. in which the disk llorets are never ligulate. and Lir/iiliftora:, in which all the florets .■ire ligulate. The plants of the first stibdivision do not bear any latex in their stems, while those of the second are conspictioiis on account of the milky or reddish-colored juice which they exude when injured. The first suborder is by far the largest in number of species. The two great di- visions are again subdivided into thirteen tribes, as follows: Tubi'i.iflor.k: (1) Ternoniefr. rep- resented by the genus Vernonia; (2) Eiipatoriew, embracing Ageratum, Eupatorium, and Mikania; (3) Asterew, the principal genera of which are Aster, Solidago. Erigcron. Bellis, Baccharis; etc: (4) Inulew, which contains among its prominent representatives the genera Pluchea, Filago, An- tennaria, Gnaphalium. Inula, llelichrysnm. etc.; (.■>) Helianthecr. represented in our flora by Helianthus. Silphium, Iva. Ambrosia. Rudlieckia, Echinacea. Coreopsis. Bidens, Xanthium, Zinnia, Dahlia, etc.: (6) Helenicre. with Actinella. He- lenium. Tagetes. Gaillardia. Dysodia. etc.: (7) AuthemidefF, which embraces .chillea, Anthemis, .Matricaria, Chrvsanthemiiiii. 'I'anacetum. .Arte-
