Page:The New International Encyclopædia 1st ed. v. 01.djvu/871

ARCHIMAGE. hood. (2) The jiorsmiilicatioii of Indolence in Thomson, Cunllc of Indnlcncc (1748). ARCHIMANDRITE, ar'kiman'drlt (Late Ck. (2/3,/iai't5p/V;/^', archimandritf's, from Gk. api[i-, archi-, fhiet' + fiuviSpa, mandni. a fold, i.e., a convent). The title of the highest order of superiors of convents in the tJrcck Church, cor- responding to abbot (<i.v. ) in the Latin C'hurcli; except that, strictly speaking, an arcliimandrite presides over several monasteries, whereas the litfliimcnos was over onlj- one, and so the latter was nearer to an ordinary abbot. The Russian bishops are chosen from among the archimandrites. ARCHIMEDEAN MIR'ROR, ar'ki-me-de'un. See iliiiiiOK.  ARCHIMEDES, iir'ki-me'dez (from Arclii- iiicdes' Scrcir: see below). A genus of fossil Hryozoa of the family Fenestellida?, common in some so-called '"Archimedes Limestones" of the early Carboniferous age in the Mississippi Valley and in some of the southwestern States. The minute animals of this genus dwelt in colonies at- tached to the ocean floor, and secreted acalcareous framework of spiral form, the a.is of which re- sembles llu> Arehiiuodes" screw (q.v.) . Continuing the comparison — the thread of the screw is pro- duced as a reticulated expansion, upon the ujiper surface of which are situated the cells that served as dwelling-places for the individuals. The cell-bearing portion of the colony is seldom found connected with the spiral axis, having, by reason of its delicacy, been usually broken off by the action of the waves. Some nearly complete examples have l)een found in the .soft shales of the Keokuk group at Crawfordsville, Ind. See also Bryozo.; CARnoNiFEROus System; and for illustration, see plate PoLyzoA. ARCHIMEDES (Gk. 'Apx'MiiS))!. Archimedes) (B.C. 287-212). A tireek geometrician and mechanician, the greatest mathematician of an- tiquity. He was born in the State of Syracuse, in the Island of Sicily. He studied probably under (.'onon at the University of Alexandria, sjjcnding the major part of his life in Sicily. He was killed in the sack of Syracuse. The most im- portant among his extant worlcs include three on plane geometry, three on solid geometry, one on arithmetic, and three on mechanics. In the treatise on the measurement of the circle, the value of If is given as a number less than SI and greater than 3'". He also gave formiilas for the area of the circle and the ellipse, and for the sector of a sjiiral whose equation is r = c0. His demonstration that the area of a segment of a ])arabola is two-thirds that of the inclosing parallelogram is the first real example of the quadrature (q.v.) of a curvilinear surface. His method of exhaustion is suggestive of the modern methods of calculus. In the works on solid geometry are treated the volumes of spheroids and conoids. His aritlimetical work, known by its L.atin title, AiTiiaiius (sand-reckoner), con- tains his famous attempt to express the amount of sand required to fill the universe. This work has given rise to the conjecture that Archimedes invented a new and powerful system of notation, all knowledge of which perished with the work itself. Besides his work in pure mathematics, Archimedes also made valuable contributions to applied mathematics, including applications of geometry to the theory of machines, as levers, pulleys, and screws. He also improved the methods iif lindiiig centres of gravity. In accord- ance with a wish of Archimedes, Jlarcellus rai.sed in his honor a tomb, on which was engraved a sphere inscribed in a cylinder. Cicero, in his Tuscan Uisputations, gives a charming account of his discover}^ of the tomb in B.C. 75. The most noted editions of Archimedes' works are those of .1. Torelli (Oxford. 1792): .T. L. Hciberg (Leipzig, 1881); and T. L. Heath (Caiiil)ridge, 1897). ARCHIMEDES' SCREW (called also Spiral, Pump). A machine for raising water, said to liave been invented by Archimedes, during liis stay in Egypt, for draining and irrigating the land. Its simplest form consists of a llexible tube bent spirally round a solid cylinder, the ends of which are furnished with pivots, so as to admit of the whole turning round its axis, as is shown in Fig. I. The machine is placed in an inclined position, so that the lower mouth of the tube may dip below the surface of the water to be raised. The lowest bend of the tube will be tilled with water, and if now the handle be made to turn in the direction of the hands of a watch, the mouth of the spiral tube will be raised above the surface; and the water inclosed in the tube, having no means of escape, will flow within it until, after one revolution, it will occupy the second bend. The first bend has meanwhile

Fig. I. Fig. II.

received a second charge, which, after a second revolution, flows up into the second bend, and takes the place of the first charge, which has now-moved up to the third bend. When, therefore, as many revolutions of the cylinder have been made as there are turns in the spiral tube, each of the lower bends will be filled with water; and in the course of another revolution, there being no higher bend for the water of the first charge to occupy, it will flow out of the tube by its upper mouth. At each succeeding revolution, the lowest bend will be charged, and the highest discharged. It will be seen that there may be room to dispose a second tube side by side with the