CIRCASSIANS. 756 CIRCLE. and Cherkt^ss is said to signify as much as "brigand": but over against this ni.iy be set their liospitalily and brave struggle for liberty against llie Itussians. When the ilussian conquest was completed in 18(i4, more than 300,000 of them left the Caucasus for various parts of Asiatic and Eurojiean Turkey, and they are said later to have had a share in the Bulgarian massacres. Those who are still in the old habitat number about 150.000, and are losing more and more of their racial purity. Tlic higher classes of the Circassians have adopted Ishun, while among the lower exists a certain kind of Christianity or Islamism in combination with survivals of ancient lieathcnism. The languases of the Cir- cassian tribes are thought by some authorities to be incorporating rather than agglutinative. Since Xeumaun's Russlaiid und die Tsclicrkessen (1840). the literature about the Circassians has grown considerably. Ksjjecial reference nuiy be made to K. von Erckert's Der Kaiilcasus luid seine V67/,cr (Leipzig, 1887),, and the fourth volume of Chantre's comprehensive Hecherches anthropolofiitjucs duns le Caticase (Lvons, 1885- 87 ) . ' CIRCE, ^^er'se (Lat., from Gk. KlpKii, Kirke). In Homer, the sister of .-E;etes, and daughter of Helios and the ocean nymph Perse. She lived in a valley of the island of .Eica, svirrounded by Inmian beings whom she had transformed into wolves and lions. Here she transformed into swine the comi)anions of Odysseus, and when the hero came to lier palace she sought to exercise the same enchantment upon him. Protected by the magic herb, mohj, which Hermes had given him, he withstood her sorceries, and forced her to disenchant his followers. He then remained with her a year, and received instruction for avoiding the dangers that still beset his home- ward way, A Cyclic epic told of Telegonus. the son of Circe and Odysseus, who, landing in Ithaca, killed his father in battle. Later writers, possibly even Hesiod, placed the island of Circe in the Tyrrhenian Sea, and still later it was identified with the Circean Promontory, In the Alexandrian writers Circe also appears in the story of the Argonauts, and to the same period belongs the story that in jealousy of Scylla, she tran-fiivmed her rival into a monster, by pour- ing hir magic drugs into the water where Scvlla bathed. CIRCE'I, or CIRCEII. A town of ancient Latiimi, situated on the promontory known as Mens Circcius (Monte Circeo). Th(mgh of an- cient date. Circci was never very famous, but Tiberius ami Dumitian had villas there. On the hill, about tliKc miles from the sea, are remains of early wall- if polygonal masonry, CIRCENSIAN (ser-sen'shan) GAMES. See ClRCfS. CIRCLE (from Lat. circulua, dim. of eircus, Cik. KlpKos. hirkns, k-pkos, hrikos. circle). The locus (i|.v.) of all ]iolnts in a plane at an equal finite distance from a fixed point in that plane. The fixed point is called the centre, and the space inclosed, o"r, more 'proi)erly, its meas- ure, the area of the circle. The segment of any straight line intercepted by the circle (AB in Fig. 1 ) is called a chord. Any chord passing thnnigh (he centre. O, is called a diameter, as A'B', The centre bisects any diameter, and the halves arc called radii, Anv line drawn from an external point cutting the circle, as PQ, is called a secant : and any line which has contact with the circle, but docs not intersect it ulieu produced, as B'T, is called a tangent. Any por- tion of the area limited by two ra- 3 p dii, as OA and OB, is called a sector; and any portion of the circle, BA'A, is called an arc, A chord is said A(- to divide the area Fio, 1. into segments; the segments are equal if the chord is a diameter. A plane passing through the centre of a sphere cuts the surface in a circle called a great cir- cle of the sjihere. Circles of longitude are great circles. Other circles of a sphere are called small circles. Ancient writers usually called the circle, as above defined, a circumference, the word 'circle' being ajiplied to the sjiace inclosed. In modern geometry, at least above the elements, the word 'circumference' is not used, and the word 'circle' applies to the curve. In coordinnle geometry (see AxAl-TTlC Geom- etry), the circle ranks as a curve of the second order (see Ci^kve), and belongs to the conic sec- tions; the section of a right circular cone, per- pendicular to the axis of the cone, being a circle. The Cartesian equation of the circle, taking its centre as the origin, is 0"° + )/• =: i~. The con- structions of Euclidean geometry being limited to the use of two instruments, the straight-edge and the compasses, the circle and the straight line are the two basal elements of plane geom- etry. A few of the leading properties of the circle are: (1) The ratio of the circumference to the diameter is a constant; this is designated by the symbol ir. This ratio is approximately 3.141.592: 3.1410 and even 31 arc sufficiently ac- curate for ordiiuirv purposes'; thus the area of a circle of radius ,5 inches is 3.1410 X .5" square inches, or 78.54 square inches. The ratio ir has an intei"esting history. The papyrus of Ahmes (q.v.) (before B.C. 1700) contains the value (J/)' or ."^.leOo: Archimedes (B.C. 287-212) de- sci"ibed it as lying between 3i and 31J; the Almagest (q.v.) gives it as 3 + 4+6So = 3"1^166; the Romans often iised 3t<j; Arvahhatta (q.v.) gave 3. 1410; Bliaskara (q.v.),' 3.14](j6; and the Chinese of the sixth century A.u., >.'. Lu- dolpli van Ceulen (1580) computed ir' to 35 decimal ])laccs, and in recent times it has been carried to over 700 places. In 1704 Legendre proved that ir is an irrational number. Fur- thermore, it is not only incommensurable — that is. not expressible as the quotient of two inte- trers — but it has been ])rovcd by Lindeniann (1882) to be transcendental. This means that ir cannot be a root of an algebraic equation with integral coclhcicnts. Certain irrational ( inconuuensurable) niind)ers may be represented by elementary geometric lines; e.g. (■'2 is repre- sented by the diagonal of a square of side 1 ;
