and Cherkess is said to signify as much as 'brigand'; but over against this may be set their hospitality and brave struggle for liberty against the Russians. When the Russian conquest was completed in 1864, more than 300,000 of them left the Caucasus for various parts of Asiatic and European 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. The higher classes of the Circassians have adopted Islam, while among the lower exists a certain kind of Christianity or Islamism in combination with survivals of ancient heathenism. The languages of the Circassian tribes are thought by some authorities to be incorporating rather than agglutinative. Since Neumann's Russland und die Tscherkessen (1840), the literature about the Circassians has grown considerably. Especial reference may be made to R. von Erckert's Der Kaukasus und seine Völker (Leipzig, 1887), and the fourth volume of Chantre's comprehensive Recherches anthropologiques dans le Caucase (Lyons, 1885 87). CIRCE, ser'sê (Lat., from Gk. Kípкŋ, Kirkē). In Homer, the sister of Eætes, and daughter of Helios and the ocean nymph Perse. She lived in a valley of the island of Eæa, surrounded by human beings whom she had transformed into wolves and lions. Here she transformed into swine the companions of Odysseus, and when the hero came to her palace she sought to exercise the same enchantment upon him. Protected by the magic herb, moly, 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 homeward 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 transformed her rival into a monster, by pouring her magic drugs into the water where Scylla bathed. CIRCE'I, or CIRCEII. A town of ancient Latium, situated on the promontory known as Mons Circeius (Monte Circeo). Though of ancient date, Circei was never very famous, but Tiberius and Domitian had villas there. On the hill, about three miles from the sea, are remains of early walls of polygonal masonry. CIRCENSIAN (sẽr-sen'shan) GAMES. See CIRCUS. CIRCLE (from Lat. circulus, dim. of circus, Gk. Kipkos, kirkos, кpixos, krikos, circle). The locus (q.v.) of all points 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, or, more properly, its measure, 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 through the centre, O, is called a diameter, as A'B'. The centre bisects any diameter, and the halves are called radii. Any 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 does not intersect it when produced, as B'T, is called a tangent. Any portion of the area limited by two radii, 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 into segments; the segments are equal if the chord is a diameter. A plane passing through B FIG. 1. P B H the centre of a sphere cuts the surface in a circle called a great circle of the sphere. 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 applied to the space inclosed. In modern geometry, at least above the elements, the word circumference' is not used, and the word 'circle' applies to the curve. In coördinate geometry (see ANALYTIC GEOMETRY), the circle ranks as a curve of the second order (see CURVE), 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 2+ y2= r2. The constructions 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 geometry. A few of the leading properties of the circle are: (1) The ratio of the circumference to the has diameter is a constant; this is designated by This ratio is approximately the symbol. 3.141592; 3.1416 and even 34 are sufficiently accurate for ordinary purposes; thus the area of a circle of radius 5 inches is 3.1416 X 52 square inches, or 78.54 square inches. The ratio an interesting history. The papyrus of Ahmes (q.v.) (before B.C. 1700) contains the value (16) or 3.1605; Archimedes (B.C. 287-212) described it as lying between 34 and 3; the Almagest (q.v.) gives it as 8 3+ + 60 30 60.60 the Romans often used 3%; Aryabhatta (q.v.) gave 3.1416; Bhaskara (q.v.), 3.14166; and the Chinese of the sixth century A.D., 22. Ludolph van Ceulen (1586) computed to 35 decimal places, and in recent times it has been carried to over 700 places. In 1794 Legendre proved that is an irrational number. Furthermore, it is not only incommensurable-that is, not expressible as the quotient of two integers but it has been proved by Lindemann (1882) to be transcendental. This means that π cannot be a root of an algebraic equation with integral coefficients. Certain irrational (incommensurable) numbers may be represented by elementary geometric lines; e.g. 2 is represented by the diagonal of a square of side 1; but T, being transcendental, cannot be represented by any construction depending solely upon the straight-edge and compasses. It requires a transcendental curve, such as the integraph of Abdank-Abakanowicz. Thus, through labors like those of Gauss, Hermite, and Lindemann, the true nature of T has been determined, and efforts at circle-squaring by the instruments of elementary geometry have been proved futile. Modern analysis has shown to be expressible by certain infinite series; e.g. 1 1 T=4 5 dependent of the length of the radius; thus producing an angle measure, the basis of the protractor (q.v.). For scientific purposes, however, it would be more convenient to divide a quadrant into 100 equal parts, called grades, and each of these into 100 equal parts, called centesimal minutes, and each of these into 100 equal parts, called centesimal seconds. This plan, attempted in France as part of the metric system, is known as the centesimal division of the circle. For example, 35 45′ 17′′ (read 3 grades, 45 centesimal minutes, and 17 centesimal seconds) may be written 3.4517. To translate this into sexagesimal notation, 38 equals 3 X 900 or in the form of a continued fraction, as in centesimal minutes 45 X = 2.7°, 45 18800 = 0.405' or 0.00675°; and so on. The sexagesimal system is, however, so well established that the centesimal has only very recently, in France, come to take important rank. (1 -+ 1 7 1 + — — ...) (Leibnitz); (Brouncker) 4 T= 1+ 1 2 + 25 The method of approximating this ratio commonly used before the introduction of calculus (q.v.) consisted in computing the perimeters of the circumscribed and inscribed polygons of a circle of diameter 1. For, since the length of the circumference in this case is the desired ratio, the value of lies between the values of the perimeters of the given polygons. A history of the development of this important problem of geometry will be found in Rudio, Archimedes, Huygens, Lambert, Legendre: vier Abhandlungen über die Kreismessung (Leipzig, 1892). (2) The centre of the circle is a centre of symmetry, and any diameter is an axis of symmetry (q.v.). (3) The perimeter of a circle of radius r is 2r, and its area r2. The area is greater than that of any plane figure of the same perimeter. (4) Concentric circles-that is, those having the same centre-never intersect. (5) Circles are similar figures (see SIMILARITY), and their areas are proportional to the squares of their radii or diameters. (6) Arcs of a circle are proportional to the angles subtended at the centre, and conversely. This property forms the basis of angular meas ure. CIRCULAR MEASURE. The supposed number of days in the year early led to the division of the circle into 360 equal parts, for use in astronomical instruments. A knowledge of the regular hexagon probably led to the further division of 360 degrees into six parts of 60 degrees each. The Babylonians divided each degree into 60 equal parts, and each subdivision into 60 equal parts, thus producing the sexagesimal scale. (See NOTATION.) Thus the circumference of a circle is divided into 360 equal parts, called degrees; each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. Further divisions are better represented by decimal fractions. The circle is also commonly divided into four equal parts of 90 seconds each, called quadrants. By connecting the centre of a circle with the points of equal division on the circumference, equal unit angles are formed, whose magnitude is in RADIAN MEASURE. In higher mathematics, especially in anal ytic trigonometry, radian equals X 4 right angles == X 1 right angle. In degrees one radian is 2 The word radian is commonly omitted in discus- (1) Co-axal Circles.-The radical axis XX, (Fig. 3) of two circles of radii r1, r, is the line perpendicular to their centre line C,C1, and dividing this line so that the difference of the squares on the segments equals the difference of the squares on the radii. The common chord of two intersecting circles is a segment of their radical axis. All circles having a common radical axis pass through two real or two imaginary points, and such a group of circles is called a co-axal system. If two circles are concentric, their rocal triangle with respect to the circle, the three vertices being the poles of the opposite sides. (4) Involution.-Pairs of inverse points, P, P'; Q, Q'; etc., on the same straight line, form a system in involution, the relation between them being OP OP' = OQ OQ′ = . . . = p2. Here the inverse points are usually called conjugate points. Any four points whatever of a system in involution on a straight line have their anharmonic ratio (q.v.) equal to that of their four conjugates. (5) Nine-Points Circle.-The intersection of the three altitudes of a triangle is called the orthocentre. The mid-points of the segments from the orthocentre to the vertices constitute three points, the feet of the altitudes three more, and the mid-points of the sides of the triangle three more-all nine lying on the circumference of a circle, called the nine-points circle. In Fig. 5, O is the orthocentre and K, L, G, D, M, E, H, N, F are the nine points. FIG. 4. (2) Inversion.-Let O (Fig. 4) be the centre of a circle of radius r, and P, Q two points on a line through O, such that OP OQ= r2. P and Q are called inverse points with respect to the circle. Either point is said to be the inverse of the other. The circle and its centre are called the circle and centre of inversion, and r the constant of inversion. If every point of a plane figure be inverted with respect to a circle, or every point of a figure in respect to a sphere, the resulting figure is called the inverse image of the given one. The inverse of a circle is either a straight line or a circle, according as the centre of inversion is or is not on the given circle. The centre of inversion is then the centre of similitude of the original circle and its inverse; and the circle, its inverse, and the circle of inversion are co-axal. The theory of inversion was invented by Stubbs and Ingram in 1842, and has been made use of by Lord Kelvin in several important propositions of mathematical physics. (3) Pole and Polar.-The polar of any point P, with respect to a circle, is the perpendicular to the diameter OP drawn through the inverse point. Hence the polar of a point exterior to a circle is the chord joining the points of contact of the tangents drawn from the external point. Any point P lying on the polar of a point Q' has its own polar passing through Q'. The polars of any two points, and the line joining the points, form a triangle called the self-recip. together with S and the circumcentre of the triangle, lie on a circle called the seven-points or Brocard circle. P, P' are called the Brocard points. Consult: McClelland, Geometry of the Circle (London, 1891); Casey, Sequel to Euclid (Dublin, 1888); Catalan, Théorèmes et problèmes de géométrie élémentaire (Paris, 1870). CIRCLE, MAGIC. A space in which sorcerers were wont, according to the ancient popular belief, to protect themselves from the fury of the evil spirits they had raised. This circle was usually formed on a piece of ground from seven to nine feet square, in the midst of some dark forest, in a churchyard, vault, or other lonely and dismal spot. The circle was described at midnight in certain conditions of the moon and weather. Inside the outer circle was another somewhat less. in the centre of which the CIRCULAR PARTS. The five elements involved in a rule for solving rightangled spherical formutriangles, lated by John Napier (q.v.). The five parts, c, a, complement of A, complement of C, and complement of sorcerer had his seat. The spaces between the CIRCLE, MERIDIAN. See MERIDIAN CIRCLE. CIRCLEVILLE. A city and the county-seat of Pickaway County, Ohio, 25 miles (direct) south of Columbus; on the Scioto River, the Ohio and Erie Canal, and the Cincinnati and Muskingum Valley and the Norfolk and Western railroads (Map: Ohio, E 6). It was laid out in 1810, on the site of a prehistoric circular fortification (described in Howe's History of Ohio), from which the name is taken. The surrounding country is very fertile, and the city has extensive straw-board works, canneries, and flour and corn meal mills. Settled in 1806, Circleville was incorporated as a village in 1814, and as a city in 1853. It is now governed, under the Ohio Municipal Code of 1902, by a mayor, elected biennially, and a council. Population, 1890, 6556; 1900, 6991. CIRCUIT (Fr. circuit, from Lat. circuitus, from circuire, circumire, to go around; from circum, around + ire, to go). A territorial division, within which a court of justice is to be held, at stated times and places. The practice of dividing England into circuits, and assigning to each division judges whose duty it is to hold court therein at prescribed places and terms, became settled during the reign of Edward I. As early as the first Magna Charta, in 1215, it was provided that certain assizes (q.v.) for the recovery of lands should always be taken in the counties in which the lands were situated, and that two justices of the King should be sent to each county four times a year for that purpose. But the evils arising from the remote and irregular sittings of the King's Court (curia regis) were not obviated until the end of that century. This early arrangement of circuits has been modified from time to time, and it is now regulated by the Judicature Act of 1875, and an order in council of 1876. In the United States there are two classes of circuits-one belonging to the judicial system of the Federal co-b a Co-C circumference of a circle, admit of the following co-b mnemonic: The a CIRCULATING DECIMALS. Decimals in which one or more figures are continually repeated in the same order; e.g. 0.333 ...., 0.25666 0.3172172...., are circulating decimals. These are sometimes called repeating decimals, and the figure or set of figures repeated is called the repetend. If the repetend begins at the decimal point, the decimal is called a pure circulate; otherwise the decimal is called a mixed circulate; eg. 0.2727 is a pure circulate. but 0.25999 is mixed. If the repetend contains but one figure, it is called simple-otherwise, compound. If the first figures of repetends are of the same order, the repetends are said to be similar; and if they end with figures of the same order, they are said to be conterminous; e.g. 0.639292 .. and 0.253232 .... are both similar and conterminous. Periods over the first and last figures of the repetend serve to indicate that a decimal is a circulate; thus, 0.273 = 0.27373 . . . . Operations with circulating decimals may be performed in the usual way, or the circulates may be reduced to common fractions. This is usually done by applying the formula for the sum of an infinite geometric progression. (See SERIES.) Thus, 0.35 is the same as 0.35+ 0.0035 + 0.000035+... in which the first term is 0.35 and the rate 0.01; hence, the sum is That this fraction is the same as the decimal 0.35 may be seen by division. CIRCULATING LIBRARY. See LIBRARY. CIRCULATING MEDIUM. See MONEY. CIRCULATION (Lat. circulatio, circular course, from circulus, circle, dim. of circus, circle). A term used in anatomy and physiology to designate the course of the blood through the blood-vessels. A knowledge of the heart, arteries, capillaries, and veins (qq.v.) is, of course, essential to a complete understanding of the subject of circulation; but by means of a diagram (Fig. 1), we can indicate the circulation of the blood in a general way. The shaded part of Fig. 1 represents the vessels carrying the impure or venous blood, which has already given up its oxygen to the body and taken in exchange the carbonic-acid gas. The unshaded diagram represents the vessels filled with pure blood, which is freely supplied with oxygen (arterial blood). The heart is shown here as composed of four chambers, of the blood: h, heart; v, which the two right ones right ventricle; v', left ven- belong to the circulation tricle; c, right auricle; c, of venous blood and the left auricle; a, aorta; d, FIG. 1. Circulation of vena cava; e. greater cir- two left to that of arculation; b, smaller circu- terial blood. Now the lation; f, pulmonary, ar- blood from the whole tery; g, pulmonary veins. body is brought to the right auricle of the heart (c) by two large veins, the superior vena cava and the inferior vena cava, both of which are here represented by d. By the contraction of this chamber, the blood is forced through the right auriculo-ventricular opening into the second chamber of the right side of the heart, the right ventricle (v), and this by its contraction drives the blood to the lungs in the direction of the arrow pointing to f. The blood is prevented from returning into the auricle by the tricuspid valve, which completely closes the auriculo-ventricular opening during the contraction of the ventricle. In its passage through the lungs the blood is purified and oxygenated, and then is brought back to the heart again by the four pulmonary veins, entering the auricle on the left side. When this contracts, the blood is forced onward into the left ventricle, and then by ventricular contraction into the aorta for general arterial distribution. The mitral valve prevents regurgitation into the left auricle, and the semi-lunar valve at the beginning of the aorta stops any reflux into the ventricle. (Similar valves are present in the pulmonary artery.) The aorta divides into branches, and these in turn into smaller ones, until the whole body is supplied by a minute arterial plexus, or network; the smallest arteries divide into a finer network of still more minute vessels, the capillaries, which have extremely delicate walls, so that the blood can come into the closest relation with the cells of the body-tissues. It is in these capil laries that the oxygen is given off, the nourishment furnished to the body elements, and the waste products taken up into the blood. The capillaries then unite to form a venous plexus, and later small veins which unite with each other to form larger ones until we have all the blood collected into the superior and inferior venæ cave, and thus brought to the heart again. We see, from this description, that there are in reality two circulations-one, a short circuit, from the right side of the heart through the lungs to the left side of the heart; and the second, a longer circuit, from the left side of the heart through the body back to the right side of the heart. In the heart the two circulations connect with each other, and become continuous. In addition to the pulmonary and systemic circulations, described above, we have another subsidiary to the venous system, and known as the portal circulation. This is not indicated in the diagram. A certain amount of the blood of the intestines is collected into the portal vein and carried to the liver, where it traverses a capillary network in intimate relation with the liver-cells. Bile is formed and other important changes are effected in the blood, which is highly charged with foodstuffs recently absorbed in its passage through the intestinal capillaries. The blood is collected a second time into veins, and carried to the inferior vena cava, where it again joins the general circulation. In its passage through other special organs, the blood undergoes further modifications. See KIDNEY; SPLEEN; etc. The anatomy of the organs concerned is given elsewhere, and we can consider them here only in their mechanical relation to the circulation. The FIG. 2. The lungs, heart, and principal blood-vessels in man; a, h, veins from right and left arms; b, f, right and left jugular veins, returning the blood from head and neck. These four veins unite to form a single trunk, the vena cava superior, which enters the right auricle 1; c, e, the right and left carotid arteries, the latter rising directly from the arch of the aorta, a'; the former from a short trunk called the arteria innominata; g, the left subclavian artery, rising directly from the aorta, while the right subclavian artery rises from the arteria innominata; d, the trachea or windpipe; i, k, right and left lungs; 1, 1, the right and left auricles; p, the right ventricle; o, the apex of the ventricle; m, the inferior or ascending vena cava; n, the descending aorta, emerging from behind the heart; q, the pulmonary artery. heart is situated in the anterior part of the chest, lying between the right and left lungs, and inclosed in a membranous sac (the peri |