in Geometry, a plane figure comprehended by a single curve line, called its circumference, to which right lines drawn from a point in the middle, called the centre, are equal to each other. See GEOMETRY.

CIRCLES of the Sphere, are such as cut the mundane sphere, and have their periphery either on its moveable surface, or in another immoveable, continuous, and equidistant surface. See SPHERE. Hence arise two kinds of circles, moveable and immoveable. The first, those whose peripheries are in the moveable surface, and which therefore revolve with its diurnal motion; as, the meridians, &c. The latter having their periphery in the immoveable surface, do not revolve; as the ecliptic, equator, and its parallels, &c. See GEOGRAPHY.

CIRCLES of Altitude, otherwise called almucantars, are circles parallel to the horizon, having their common pole in the zenith, and still diminishing as they approach the zenith. See ALMUCANTAR.

Diurnal CIRCLES, are immoveable circles, supposed to be described by the seven stars, and other points of the heavens, in their diurnal rotation round the earth; or rather, in the rotation of the earth round its axis. The diurnal circles are all unequal: the equator is the biggest.

Horary CIRCLES, in Dialing, are the lines which show the hours on dials; though these be not drawn circular, but nearly straight. See DIALING.

CIRCLES of Latitude, or Secondaries of the Ecliptic, are great circles parallel to the plane of the ecliptic, passing through the poles thereof, and through every star and planet. They are so called, because they serve to measure the latitude of the stars, which is nothing but an arch of one of these circles intercepted between the star and the ecliptic. See LATITUDE.

CIRCLES of Longitude, are several lesser circles, parallel to the ecliptic; still diminishing, in proportion as they recede from it. On the arches of these circles, the longitude of the stars is reckoned.

CIRCLE of perpetual Apparition, one of the lesser circles, parallel to the equator, described by any point of the sphere touching the northern point of the horizon, and carried about with the diurnal motion. All the stars included within this circle never set, but are ever visible above the horizon.

CIRCLE of perpetual Occultation, is another circle at a like distance from the equator, and contains all those stars which never appear in our hemisphere. The stars situated between these circles alternately rise and set at certain times.

Polar CIRCLES, are immoveable circles, parallel to the equator, and at a distance from the poles equal to the greatest declination of the ecliptic. That next the northern pole is called the ARCTIC; and that next to the southern one the ANTARCTIC.

Fairy CIRCLE. See FAIRY-CIRCLE.

Druidical CIRCLES, in British topography, a name given to certain ancient inclosures formed by rude stones circularly arranged, in the manner represented on Plate CXLV. These, it is now generally agreed, were temples, and many writers think also, places of solemn assemblies for councils or elections, and seats of judgment. Mr Borlase is of this opinion. "Instead, therefore (says he), of detaining the reader with a dilute, whether they were places of worship or council, it may with great probability be inferred, that they were used for both purposes; and having for the most part been first dedicated to religion, naturally became afterwards the curiae and fora of the same community." These temples, though generally circular, occasionally differ as well in figure as magnitude: with relation to the first, the most simple were composed of one circle: Stonehenge consisted of two circles and two ovals, respectively concentric, whilst that at Bot-talch near St Just in Cornwall is formed by four intersecting circles. And the great temple at Avebury in Wiltshire, it is said, described the figure of a seraph or fiery flying serpent, represented by circles and right lines. Some besides circles have avenues of stone pillars. Most, if not all of them, have pillars or altars within their penetralia or centre. In the article of magnitude and number of stones, there is the greatest variety, some circles being only twelve feet diameter, and formed only of twelve stones, whilst others, such as Stonehenge and Avebury, contained, the first 140, the second 612, and occupied many acres of ground. All these different numbers, measures, and arrangements had their pretended reference; either to the astronomical divisions of the year, or some mysteries of the druidical religion. Mr Borlase, however, supposes, that those very small circles, sometimes formed of a low bank of earth, sometimes of stones erected, and frequently of loose small stones thrown together in a circular form, inclosing an area of about three yards diameter, without any larger circle round them, were originally places of burial.

in Logic, or Logical CIRCLE, is when the same terms are proved in orbem by the same terms; and the parts of the syllogism alternately by each other, both directly and indirectly.

CIRCLES of the Empire, such provinces and principalities of the German empire as have a right to be present at diets. Maximilian I divided the empire into six, and some years after into ten circles. This last division was confirmed by Charles V. The circles, as they stand in the Imperial Matricula, are as follow: Austria, Burgundy, the Lower Rhine, Bavaria, Upper per Saxony, Franconia, Swabia, Upper Rhine, Westphalia, and the Lower Saxony,

CIRCONCELLIONES; a species of fanatics, so called because they were continually rambling round the houses in the country. They took their rise among the Donatists in the reign of the emperor Constantine. It is incredible what ravages and cruelties these vagabonds committed in Africa through a long series of years. They were illiterate savage peasants, who understood only the Punic language. Intoxicated with a barbarous zeal, they renounced agriculture, professed continence, and assumed the title of "Vindicators of justice, and protectors of the oppressed." To accomplish their mission, they enslaved slaves, scourged the roads, forced masters to alight from their chariots, and run before their slaves, who they obliged to mount in their place; and discharged debtors, killing the creditors if they refused to cancel the bonds. But the chief objects of their cruelty were the Catholics, and especially those who had renounced Donatism. At first they used no swords, because God had forbidden the use of one to Peter; but they were armed with clubs, which they called the clubs of Israel, and which they handled in such a manner as to break a man's bones without killing him immediately, so that he languished a long time and then died. When they took away a man's life at once, they looked upon it as a favour. They became less scrupulous afterwards, and made use of all sorts of arms. Their shout was Praebe to God. These words in their mouths were the signal of slaughter, more terrible than the roaring of a lion. They had invented an unheard-of punishment; which was to cover with lime diluted with vinegar the eyes of those unhappy wretches whom they had crushed with blows, and covered with wounds, and to abandon them in that condition. Never was a stronger proof what horrors superstition can beget in minds destitute of knowledge and humanity. These brutes, who had made a vow of chastity, gave themselves up to wine and all sorts of impurities, running about with women and young girls as drunk as themselves, whom they called sacred virgins, and who often carried proofs of their incontinence. Their chiefs took the name of Chiefs of the Saints. After having glutted themselves with blood, they turned their rage upon themselves, and fought death with the same fury with which they gave it to others. Some scrambled up to the tops of rocks, and cast themselves down headlong in multitudes; others burned themselves, or threw themselves into the sea. Those who proposed to acquire the title of martyrs, published it long before, upon which they were feasted and fattened like oxen for the slaughter; after these preparations they set out to be destroyed. Sometimes they gave money to those whom they met, and threatened to murder them if they did not make them martyrs. Theodoret gives an account of a stout young man, who meeting with a troop of these fanatics, consented to kill them, provided he might bind them first; and having by this means put it out of their power to defend themselves, whipped them as long as he was able, and then left them tied in that manner. Their bishops pretended to balance them, but in reality made use of them to intimidate such as might be tempted to forswear their feet; they even honoured them as saints. They were not, however, able to govern those furious monsters, and more than once found themselves under a necessity of abandoning them, and even of imploring the assistance of the secular power against them. The counts Urfacius and Taurus were employed to quell them; they destroyed a great number of them, of whom the Donatists made as many martyrs. Urfacius, who was a good Catholic and a religious man, having lost his life in an engagement with the barbarians, the Donatists did not fail to triumph in his death, as an effect of the vengeance of heaven. Africa was the theatre of these bloody scenes during a great part of Constantine's life.