Circles Sentence Examples

The driver had driven in circles and down every back alley he could find until Jule was confident there was no one tailing them.

Dark circles underlined her eyes.

She had dark circles under her eyes.

She was pale beneath her warm color with dark circles beneath her eyes.

She didn't say that she thought Damian would run circles around the boy and find a better solution.

It's wandering around in circles and it's not at all afraid of us.

There were dark circles beneath her light eyes, her hair was in a half-assed lumpy ponytail, and her face was so pale and drawn, she looked ill.

Most…well, all but you come from the elitist circles of their times.

Mismatched chairs, crates, and one couch had been arranged in two circles around stacks of antique books and lanterns.

Of course, she'd spent the last twenty years in the competitive upper-class circles, learning how to keep out of the way of those who would use her to get to Mr. Tim.

He looked as tired as she felt, his hair disheveled and dark circles beneath his blazing golden eyes.

The warlord was pale, her eyes faded and lined with dark circles.

There were dark circles under her eyes today, as if she hadn't slept.

They also Photoshopped away the dark circles that had been under her eyes since meeting Jonny in the hospital.

These Hebrew translations were, in their turn, rendered into Latin (by Buxtorf and others) and in this form the works of Jewish authors found their way into the learned circles of Europe.

The province is divided for administration into 42 circles (Kreise), 24 in the government of Cassel and 18 in that of Wiesbaden.

The province is divided into the six Regierungsbezirke (or departments) of Hanover, Hildesheim, Luneburg, Stade, Osnabruck and Aurich, and these again into Kreise (circles, or local government districts)-76 in all.

In 63 it suited the policy of Pompey that he should be restored to the high priesthood, with some semblance of supreme command, but of much of this semblance even he was soon again deprived by the arrangement of the pro-consul Gabinius, according to which Palestine was in 57 B.C. divided into five separate circles (auv060c, vvv&3pca).

Probably the religious opinions of Irving, originally in some respects more catholic and truer to human nature than generally prevailed in ecclesiastical circles, had gained breadth and comprehensiveness from his intercourse with Coleridge, but gradually his chief interest in Coleridge's philosophy centred round that which was mystical and obscure, and to it in all likelihood may be traced his initiation into the doctrine of millenarianism.

But it does not, like theirs, sacrifice our personality; because, according to Fechner, the one divine consciousness includes us as a larger circle includes smaller circles.

Only in the very highest circles were attempts made to keep in mind the difficulties of the actual position.

When the summits of these are worn by mastication their surfaces present circles of dentine surrounded by a border of enamel, and as attrition proceeds different patterns are produced by the union of the bases of the cusps, a trefoil form being characteristic of some species.

Many other fungi in addition to the fairy-ring champignon grow in circles, so that this habit must merely be taken with its other characters in cases of doubt.

In 1500 the diet had divided Germany into six circles, for the maintenance of peace, to which the emperor at the diet of Cologne in 1512 added four others.

Circles of these radii are usually marked around the jack for convenience' sake.

A strike of the Newcastle miners, after lasting twenty-nine weeks, came to an end in January 1890, and throughout the rest of the year there was great unrest in Labour circles.

It faded away in the great Church, and probably Celsus was describing Montanist circles (though Origen assumed that they were ordinary believers) when he wrote 3 of the many Christians of no repute who at the least provocation, whether within or without their temples, threw themselves about like inspired persons; while others did the same in cities or among armies in order to collect alms, roaming about cities or camps.

For purposes of measurement the polar boundaries are taken to be the Arctic and Antarctic circles, although in discussing the configuration and circulation it is impossible to adhere strictly to these limits.

Austrias petty persecutions of her Italian subjects in the irredente provinces, her active propaganda incompatible with Italian interests in the Balkans, and the antiItalian war talk of Austrian military circles, imperilled the relations of the two allies; it was remarked, indeed, that the object of the alliance between Austria and Italy was to prevent war between them.

In the petiole these strands may increase in number by branching, and thotigh usually reducible to the outline of the primitive horseshoe, more or less elaborated, they may in some of the complex polycylic dictyostelic types (Marattiaceae) be arranged in several concentric circles, thus imitating the arrangement of strands formed in the stem.

Near Bennachie (1619 ft.) are stone circles and monoliths supposed to be of Druidical origin.

When, then, Basilides identified the highest angel of the seven, the creator of the worlds, with the God of the Jews, this is a development of the idea which did not occur until late, possibly first in the specifically Christian circles of the Gnostics.

With increase of speeds this matter has become important as an element of comfort in passenger traffic. As a first approximation, the centre-line of a railway may be plotted out as a number of portions of circles, with intervening straight tangents connecting them, when the abruptness of the changes of direction will depend on the radii of the circular portions.

The circles A'A', which are struck with 2-inch radius, define the first portion of the knuckle.

These semicircles and the circles A'A' are joined by tangents and short arcs struck from the centre of the figure.

The "spiritualistic" movement spread like an epidemic. "Spirit circles" were soon formed in many families.

He was somewhat reserved in manner, and this led to the charge in political circles that he was cold and unsympathetic; but no one gathered around him more devoted and loyal friends, and his dignified bearing in and out of office commanded the hearty respect of his countrymen.

Schwenkfeld, whose gentle birth and courtly manners won him many friends in high circles, left behind him a sect (who were called subsequently by others Schwenkfeldians, but who called themselves "Confessors of the Glory of Christ") and numerous writings to perpetuate his ideas.

He had become possessed with the idea of addressing wider circles and of forming an order whose vocation should be to preach and missionize throughout the whole world.

The fish is also said to be represented in the oval-shaped figure, pointed at both ends, and formed by the intersection of two circles.

The ganglia are crowded at the posterior end of the body as in leeches, and there is much tendency to the obliteration of the coelom as in that group. Pterodrilus and Cirrodrilus bear a few, or circles of, external processes which may be branchiae; Bdellodrilus and Astacobdella have none.

When several rings or circles were combined representing the great circles of the heavens, the instrument became an armillary sphere.

The horror aroused by this crime did not long deaden the feeling, at least in official circles, that something must be done to introduce the principle of heredity, as the surest means of counteracting the aims of conspirators.

The contents of such a circular group are symbolically (or analogically) represented by the contents of all other circles in the animal kingdom.

It is the envelope of circles described on the central radii of an ellipse as diameters.

Rude stone monuments (circles and dolmens) and other prehistoric remains show that Syria must have been inhabited from a very early period.

Such a conception has a Greek tinge, and would be found in Jewish circles, probably, not before the 2nd century B.C.

Treating the earth as a sphere, the meridians of longitude are all great circles.

The body is ringed, and often has circles of spines, which are continued into the slightly protrusible pharynx.

His family was known among judicial circles in the 16th century, and maintained the Roman Catholic faith after the official introduction of the Reformed religion into Navarre.

His great work The American Commonwealth, which appeared in 1888, was the first in which the institutions of the United States had been thoroughly discussed from the point of view of a historian and a constitutional lawyer, and it at once became a classic. His Studies in History and Jurisprudence (1901) and Studies in Contemporary Biography (1903) were republications of essays, and in 1897, after a visit to South Africa, he published a volume of Impressions of that country, which had considerable weight in Liberal circles when the Boer War was being discussed.

It must further be supposed that the name and the very existence of this genius were totally forgotten in Christian circles fifty years after he wrote.

The three provinces are divided for local administration into 18 circles and 989 communes.

Near Balliasta are the remains of three stone circles.

Of the original Pictish inhabitants remains exist in the form of stone circles (three in Unst and two in Fetlar) and brochs (of which 75 examples survive).

Of the fortress built by William the Conqueror in 1068 some portions were probably incorporated in Clifford's tower, the shell of which, showing an unusual ground plan of four intersecting circles, rises from an artificial mound.

There was nothing in their general position to make them in- 'hospitable to ethical conceptions of the future life, as is shown by the fact that so soon as the Egyptian-Greek idea of immortality made itself felt in Jewish circles it was adopted by the author of the Wisdom of Solomon; but prior to the 1st century B.C. it does not appear in the Wisdom literature, and the nationalistic dogma of resurrection is not mentioned in it at all.

In one of the literary and fashionable circles of Berlin he had met a Fraulein von Ddnniges, for whom he at once felt a passion, which was ardently reciprocated.

It was a mile in diameter, built in concentric circles, with the mosque and palace of the caliph in the centre, and had four gates toward the four points of the compass.

The black circles represent one ion and the white circles the other.

This step, which caused him to be ostracized for a time from the Boston circles in which he had been reared, brought him the cases of the fugitive slaves, Shadrach, Sims and Burns, and of the rescuers of Shadrach.

Proselytes are still not allowed, in Orthodox circles, to become the wives of reputed descendants of the priestly families, but otherwise marriage with proselytes is altogether equal to marriage between born Jews.

If the wire consists of a ferromagnetic metal, it will become " circularly magnetized by the field, the lines of magnetization being, like the lines of force, concentric circles.

According to his view, all mountain ranges parallel to the same great circle of the earth are of strictly contemporaneous origin, and between the great circles a relation of symmetry exists in the form of a pentagonal reseau.

Hungary proper, according to ancient usage, was generally divided into four great divisions or circles, and Transylvania up to 1876 was regarded as the fifth.

According to this division Hungary proper is divided into seven circles, of which Transylvania forms one.

Tisza's policy on both these occasions increased his unpopularity in Hungary, but in the highest circles at Vienna he was now regarded as indispensable.

He was highly esteemed in devout circles as the author of De la aficiOn y amor de Jesus (1630), and De la aficion y amor de Maria (1630), both of which were translated into Arabic, Flemish, French, German, Italian and Latin.

It seems to have arisen in Gnostic circles, and its tendency is wholly in favour of asceticism and celibacy.

Hitherto Fontenelle had made his home in Rouen, but in 1687 he removed to Paris; and in the same year he published his Histoire des oracles, a book which made a considerable stir in theological and philosophical circles.

Gentz, who from the winter of 1806 onwards divided his time between Prague and the Bohemian wateringplaces, seemed to devote himself wholly to the pleasures of society, his fascinating personality gaining him a ready reception in those exalted circles which were to prove of use to him later on in Vienna.

There are antiquarian remains (cromlechs, stone circles and the like) at Slievemore and elsewhere.

The education department is under a director of public instruction, and there are three circles - eastern, western and Upper Burma, each under an inspector of schools.

The Burma forests are divided into three circles each under a conservator, with twenty-one deputy conservators.

There are three circles - Eastern, Central and Upper Burma.

The glass is made in cylinders and in " crowns " or circles.

The lower part has four rows of circles united to the vessel at those points alone where the circles touch each other.

All the other examples have the lower portion covered in like manner by a network of circles standing nearly a quarter of an inch from the body of the cup. An example connected with the specimens just described is the cup belonging to Baron Lionel de Rothschild; though externally of an opaque greenish colour, it is by transmitted light of a deep red.

This is decorated with circles of rosettes of blue, green and red enamel, each surrounded by lines of gold; within the circles are little figures evidently suggested by antique originals, and precisely like similar figures found on carved ivory boxes of Byzantine origin dating from the II th or 12th century.

Normandy glass was made from glass circles or disks.

Nor was the knowledge confined to these pious circles; the name continued to be employed by healers, exorcists and magicians, and has been preserved in many places in magical papyri.

Under his influence the order spread rapidly, and he soon found himself the supreme director (Oberhauptdirektor) of some 26 "circles," which included in their membership princes, officers and high officials.

This fact was not observed (that is, the collections of examples were not made) till recently, when experiments in private non-spiritualist circles drew attention to crystal-gazing, a practice always popular among peasants, and known historically to have survived through classical and medieval times, and, as in the famous case of Dr Dee, after the Reformation.

This does not mean that visions and significant dreams may not have been of frequent occurrence in Montanistic circles.'

In this paper Vieta made use of the centre of similitude of two circles.

He was an adviser to Mazarin in the negotiations which terminated in the treaty of the Pyrenees (1659) He amassed a considerable fortune, and was unpopular, even in court circles.

The disease steadily spread outwards in concentric circles from its first place of lodgment near Roquemaure.

Measures 1 The circles by Reichenbach, then almost exclusively used in Germany, were read by verniers only.

The circles for position angle and declination are read by micrometer-microscopes illuminated by the lamp L; the scales are illuminated by the lamp 1.

The microscopes adjoining 82 read the position and declination circles; for, by an ingenious arrangement of prisms and screens, the images of both circles can be read by each single microscope as shown in fig.

Dawes found the best method for the purpose in question was to limit the aperture of the object-glass by a diaphragm having a double circular aperture, placing the line joining the centres of the circles approximately in the position angle under measurement.

And yet the Apocalypse shows in many of its phrases an undoubted affinity to the latter a fact which requires for its explanation the assumption that the book emanated from certain literary circles influenced by John.

These, Swete holds, "create a strong presumption of affinity" between the two books, while Bousset infers that they "justify the assumption that the entire circle of Johannine writings spring from circles which stood under the influence of the John of Asia Minor."

A committee of the Royal Geographical Society - the deliberations of which were interrupted by the departure on his last voyage of Sir John Franklin, one of the members - suggested these meridians as boundaries; the north and south boundaries of the Atlantic and Pacific Oceans being the polar circles, leaving an Arctic and an Antarctic Ocean to complete the hydrosphere.

If the whole globe were covered with a uniformly deep ocean, and if there were no difference of density between one part and another, the surface would form a perfect ellipsoid of revolution, that is to say, all the meridians would be exactly equal ellipses and all parallels perfect circles.

During this sojourn of five years in England he had made many valuable friends outside of court and political circles, among whom Hume, Robertson and Adam Smith were conspicuous.

His dress, the simplicity of his external appearance, the friendly meekness of the old man, and the apparent humility of the Quaker, procured for Freedom a mass of votaries among the court circles who used to be alarmed at its coarseness and unsophisticated truths.

It may be regarded as an epicycloid in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.

During his life at Paris he had opportunities of mixing in the circles of the philosophers and of others who frequented the salon of Madame de Geniis, and he there formed those ideas in favour of political and social reform which he retained through life.

This fluctuation, due partly to the different circles in which the biblical narratives took shape, and partly to definite reshaping of the traditions of the past, seriously complicates all attempts to combine the early history of Israel with the external evidence.

His Autonomies ecclesiastiques; eglises separees (1897), in which he speaks of the origin of the Anglican Church, but treats especially of the origin of the Greek Churches of the East, was received with scant favour in certain narrow circles of the pontifical court.

A collection of circles such as is the armillary sphere, if each circle were fitted with a view-tube, might be considered a complete astrolabe.

Still, a good deal of semi-congregationalism probably did exist in obscure circles which preluded the wider Reformation and were merged in it.

In certain Anabaptist circles the primitive idea of a " covenant " between believers and God as conditioning all their life, especially one with another, was revived (Champlin Burrage, The Church-Covenant Idea, Philadelphia, 1904).

To a large extent the native forms of government are maintained under European administrators responsible for the preservation of order, the colony for this purpose being divided into a number of "circles" each with its local government.

Chebichev further constructed an instrument for drawing large circles, and an arithmetical machine with continuous motion.

From these points as centres, circles are drawn in succession, each with radius greater than the last by a fixed amount, say 4 or 5 mm.

The disk being started, then by means of a tube held at one end between the lips, and applied near to the disk at the other, or more easily with a common bellows, a blast of air is made to fall on the part of the disk which contains any one of the above circles.

Hence the note produced with any given circle of holes rises in pitch as the disk revolves more rapidly; and if, the revolution of the disk being kept as steady as possible, the tube be passed rapidly across the circles of the first series, a series of notes is heard, which, if the lowest be denoted by C, form the sequence C, C1, El, G1, C2, &c. In like manner, the first circle in which we have two sets of holes dividing the circumference, the one into say 8 parts, and the other into Io,.

To its educational advantages, already conspicuous, he added the three Fi rstenschulen at Pforta, Grimma and Meissen, and for administrative purposes, especially for the collection of taxes, he divided the country into the four circles of the Electorate, Thuringia, Meissen and Leipzig.

He increased the area of the country by the " circles " of Neustadt and the Vogtland, and by parts of Henneberg and the silver-yielding Mansfeld, and he devoted his long reign to the development of its resources.

The determination of the shortest distance between two small circles on a sphere is given in the article Variations, Calculus Of.

The solid enclosed by a small circle and the radii vectores from the centre of the sphere is a "spherical sector"; and the solid contained between two spherical sectors standing on copolar small circles is a "spherical cone."

Systems of spheres have characters analogous to those of systems of circles.

Corresponding to the radical centre of three circles, it may be shown that four spheres have a radical centre, i.e.

The new baronies and countships, owing their existence entirely to the crown, introduced a strong solvent into aristocratic circles.

The worship of Odin seems to have prevailed chiefly, if not solely, in military circles, i.e.

For, by representing the prosecution of its party-political objects as a championship of the Catholic Church, Ultramontanism seeks to acquire the support of the official organs of that Church, and the good will of all circles interested in her welfare; while at the same time it strives to discredit any attempt at opposition by branding it as an assault on the orthodox faith.

There is no doubt that the absence of a royal residence in Ireland was felt as a slur upon the Irish people in certain circles.

This affair caused no little agitation in royal circles, but in the end state reasons were allowed to prevail and the _ chancellor had his way.

The liberal school of thought of which Mohler was a prominent exponent was discouraged in official circles, while Protestants, on the other hand, complain that the author failed to grasp thoroughly the significance of the Reformation as a great movement in the spiritual history of mankind, while needlessly dwelling on the doctrinal shortcomings, inconsistencies and contradictions of its leaders.

Just within the Lion Gate is a projection of the wall surrounding a curious circular enclosure, consisting of two concentric circles though the historical identity of the persons actually buried in them is a more difficult question.

It is bounded by two circles equidistant from the ecliptic, about eighteen degrees apart; and it is divided into twelve signs, and marked by twelve constellations.

Each muang is subdivided into ampurs under assistant commissioners, and these again are divided into village circles under headmen (kamnans), which circles comprise villages under the control of elders.

The secret of the enthusiasm of the masses for the analogous expression Theotokos is to be sought not so much in the Nicene doctrine of the incarnation as in the recent growth in the popular mind of notions as to the dignity of the Virgin Mary, which were entirely unheard of (except in heretical circles) for nearly three centuries of the Christian era.

In some circles the serpent was identified with Prunikos.

He proposed to divide the country into five circles, corresponding to the five provinces, each of which was to undertake to defend the realm in turn should occasion arise.

He also entered into relations with the well-known French Liberal Catholic Lamennais, whose views on the reconciliation of the Roman Catholic Church with the principles of modern society had aroused much suspicion in Ultramontane circles.

But if the tradition of the consulship was thus, it would seem, already an old one about the year 200, there is at least some reason to conclude that trustworthy information in early Christian circles pointed, independently of the Gospels, to the year 29 as that of the Crucifixion.

It was not till the time came nearer for the introduction of the budget for 1909-1910 that opinion in financial circles showed the change which was afterwards to become so marked.

The well-established doctrine that the House of Lords could not amend, though it might reject, a money-bill, coupled with the fact that it never had gone so far as to reject a budget, was relied on by the extremists as dictating the obvious party tactics; and before the year 1909 opened, the possibility of the Lords being driven to compel a dissolution by standing on their extreme rights as regards the financial provision for the year was already canvassed in political circles, though it was hardly credited that the government would precipitate a constitutional crisis of such magnitude.

And a strange division of the shekel in 10 (probably therefore connected with this decimal mina) is shown by a series of bronze weights (44) with four curved sides and marked with circles (British Museum, place unknown), which may be Romano-Gallic, averaging 125/10.

Since Neoplatonism originated in Alexandria, where Oriental modes of worship were accessible to every one, and since the Jewish philosophy had also taken its place in the literary circles of Alexandria, we may safely assume that even the earliest of the Neoplatonists possessed 1 The resemblance would probably be still more apparent if we thoroughly understood the development of Christianity at Alexandria in the 2nd century; but unfortunately we have only very meagre fragments to guide us here.

The totality of being may thus be conceived as a series of concentric circles, fading away towards the verge of non-existence, the force of the original Being in the outermost circle being a vanishing quantity.

Numerous small suburbs fill the space between the two circles, the chief being Northcote, Preston, Camberwell, Toorak, Caulfield, Elsternwick and Coburg.

It was laid down in wonderful mystic writings, which were in the possession of the various circles (Liechtenhahn, Die Offenbarung im Gnosticismus, 1901).

We also meet with speculations of this kind about man in the circles of non-Christian Gnosis.

Reitzenstein has shown (p. 81 seq.) that very probably the system of the Naasseni described by Hippolytus was originally derived from purely pagan circles, which are probably connected in some way with the mysteries of the Attis cult.

Gnosticism itself is a free, naturally-growing religion, the religion of isolated minds, of separate little circles and minute sects.

The homogeneity of wide circles, the sense of responsibility engendered by it, and continuity with the past are almost entirely lacking in it.

The Aztec numerals, which were vigesimal or reckoned by scores, were depicted by dots or circles up to 20, which was represented by a flag, 400 (a score of scores) by a feather, and 8000 (a score of scores of scores) by a purse; but for convenience these symbols might be halved and quartered, so that 534 might be shown by one feather, one quarter of a feather, one flag, one-half of a flag, and four dots.

An interesting picture-writing, to be seen in Kingsborough, shows the details of the boy's and girl's education, from the early time when three small circles over the child show it to be three years old, and a drawing of half a tortilla or corn-cake shows its allowance for each meal; as.

Solemn and gay dances were frequent, and a sport called the bird-dance excited the admiration of foreigners for the skill and daring with which groups of performers dressed as birds let themselves down by ropes wound round the top of a high mast, so as to fly whirled in circles far above the ground.

These consist of combinations of faces, circles, lines, &c., arranged in compartments in so complex a manner that hardly two are found alike.

He was well known in fashionable circles, where his witty conversation and his pleasant manners made him a favourite.

Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (f - f')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.

The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.

The introduction of these lines and points constitutes a striking achievement in geometry, and from their association with circles they have been named the " circular lines " and " circular points."

A further deduction from the principle of continuity follows by considering the intersections of concentric circles.

The equations to such circles may be expressed in the form x 2 +y 2 = a 2, x 2 +y 2 = /3 2 .

These equations show that the circles touch where they intersect the lines x 2 +y 2 = o, i.e.

In various systems of triangular co-ordinates the equations to circles specially related to the triangle of reference assume comparatively simple forms; consequently they provide elegant algebraical demonstrations of properties concerning a triangle and the circles intimately associated with its geometry.

It may be readily shown that the external and internal centres are the points where the line joining the centres of the two circles is divided externally and internally in the ratio of their radii.

It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

With a system of three circles it is readily seen that there are six centres of similitude, viz.

A system of circles is coaxal when the locus of points from which tangents to the circles are equal is a straight line.

A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis - considered as a circle of infinite radius.

In the case of two non-intersecting circles it may be shown that the radical axis has the same metrical relations to the line of centres.

To construct circles coaxal with the two given circles, draw the tangent, say XR, from X, the point where the radical axis intersects the line of centres, to one of the given circles, and with centre X and radius XR describe a circle.

Then circles having the intersections of tangents to this circle and the line of centres for centres, and the lengths of the tangents as radii, are members of the coaxal system.

In the case of non-intersecting circles, it is seen that the minimum circles of the coaxal system are a pair of points I and I', where the orthogonal circle to the system intersects the line of centres; these points are named the " limiti,ng points."

The circles intersect in real or imaginary points according to the lower or upper sign of k 2, and the limiting points are real for the upper sign and imaginary for the lower sign.

The centres of circles forming a coaxal system are collinear 2.

Every circle through the limiting points cuts all circles of the system orthogonally; 5.

John Casey, professor of mathematics at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of similitude and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.

Here we may notice that there are eight circles which solve the problem.

This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.

For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

The most difficult case, and the most interesting from its historical associations, is when the three given things are circles.

De Locis Planis is a collection of propositions relating to loci which are either straight lines or circles.

The chief conclusions of astronomers concerning the .spherical figure and dimensions of the earth, its relation to the heavenly bodies, and the great circles of the globe - the equator, the ecliptic and the tropics - were considered as well established.

The original inhabitants were Picts, evidence of whose occupation still exists in numerous weems or underground houses, chambered mounds, barrows or burial mounds, brochs or round towers, and stone circles and standing stones.

Before him the whole Christian literature in the Latin language consisted of a translation of the Bible, the Octavius of Minucius Felix (q.v.) - an apologetic treatise written in the Ciceronian style for the higher circles of society, and with no evident effect for the church as a whole, the brief Acts of the Scillitan martyrs, and a list of the books recognized as canonical (the so-called Muratorian fragment).

Repsold introduced essential improvements in the meridian circles by substituting microscopes (on Jesse Ramsden's plan) for the verniers to read the circles, and by making the various parts perfectly symmetrical.

For a number of years the firm furnished meridian circles to the observatories at Hamburg, Konigsberg, Pulkova, &c.; later on its activity declined, while Pistor and Martins of Berlin rose to eminence.

That they found favour outside Catholic circles is proved by Thomas Nash's imitation of Mary Magdalen's Tears in Christ's Tears over Jerusalem.

Owing to these circumstances, the rise and further development of the Kulturkampf were viewed in Jesuit and Vatican circles with feelings of the utmost complacency.

During the whole tenure of office the Marquis di San Giuliano was an ardent believer in the Triple Affiance, on which he thought that Italy's foreign policy should be based, and attached the greatest importance to a good understanding with Austria, an attitude not calculated to win him popularity in many circles; under his guidance consequently Italy opposed Serbia's desire for a port on the Adriatic and Greece's aspirations in Epirus, and supported the policy of creating an independent Albanian State.

Eight miles from the town is Lough Gur, near which are numerous stone circles and other remains.

Encircling the sun or moon (S), there are two circles, known as FIG.

Montanism also brought these apocalyptic expectations into discredit in orthodox ecclesiastical circles.

Stevinus printed little circles round the exponents of the different powers of one-tenth.

He was partially successful in improving the condition of the country; and in 1500 Bavaria formed one of the six circles into which Germany was divided for the maintenance of peace.

The provinces are subdivided into " classes," and the classes again into " circles " (ringen), each circle comprising from 5 to 25 congregations, and each congregation being governed by a " church council " or session.

The meetings of the circles have no administrative character, but are mere brotherly conferences.

His researches in hydrodynamics were highly useful for marine engineering, while the reflecting and repeating circles, as improved by him, were of great service in nautical astronomy.

This ideal it has not been possible permanently to maintain in the great body of the order, but only in limited circles, as Trappists.

It can scarcely be doubted that the favour which was at once accorded to the views of Malthus in certain circles was due in part to an impression, very welcome to the higher ranks of society, that they tended to relieve the rich and powerful of responsibility for the condition of the working classes, by showing that the latter had chiefly themselves to blame, and not either the negligence of their superiors or the institutions of the country.

The circles in the centre indicate a rectilinear series of indicate the five turns of the spiral, scales and two lateral secondand show the insertion of each of the ary spirals, one turning from leaves.

They lived in very different circles, one surrounded by dukes and earls, the other by starving pamphleteers and indexmakers.

The Life of Savage was anonymous; but it was well known in literary circles that Johnson was the writer.

About the beginning of 1775 his Journey to the Hebrides was published, and was, during some weeks, the chief subject of conversation in all circles in which any attention was paid to literature.

Of these areas the provinces, circles and communes are for the purposes both of the central administration and of local self-government, and the bodies by which they are governedare corporations.

Common to allis the president(Regierungsprasident, Kreishauptmann in Saxony), an official who, with a committee of advisers, is responsible for the oversight of the administration of the circles and communes within his jurisdiction.

In 1500 Germany had been divided into six circles (Kreise) or districts, for the purpose of sending representatives to the Reic/isregiment.

These circles were now increased in number to ten and an official (Hauptmann) was placed over each, his duties being to enforce the decisions of the Reichskammergericht.

But it was some time before the circles came into working order; the only permanent reform of the reign was the establishment of the imperial court of justice, and even this was not entirely satisfactory, I\Iaximilians remaining diets loudly denouncing it for delay and incompetence.

The Swedes, whose leader was now the chancellor Oxenstjerna, were stunned by this catastrophe, but in a desultory fashion they maintained the struggle, and in April 1633 a Th new league was formed at Heilbronn betweenthem and Ieaue of the representatives of four of the German circles, ileiihronn while by a new agreement France continued to furnish and the monetary aid.

The Anglo-Boer War had then but recently ended, and in Germany generally, and especially in military circles, it had provoked much adverse criticism on the inability of the British to bring the contest to a speedier conclusion.

As these would inevitably bring about a large increase in the importation of corn from Rumania and Russia, a great agitation was begun in agricultural circles, and the whole influence of the Conservative party was opposed to the treaties.

The violence with which it was conducted, coming, as it did, from the highest circles of the Prussian nobility, appeared almost an imitation of Socialist methods; but the emperor, with his wonted energy, personally rebuked the leaders, and warned them that the opposition of Prussian nobles to their king was a monstrosity.

Antiquarian remains are somewhat numerous, such as forts and cairns in Cromarty parish, and stone circles in Urquhart and Logie Wester and Knockbain parishes, the latter also containing a hut circle and rock fortress.

Both probably arose in Syria (so Lightfoot), but in circles varying a good deal in religious standpoint.'

But the different circles represented by the two make relative dating precarious.

Table-turning is still in vogue amongst spiritualist circles.

These most commonly resemble segments of circles, but are not infrequently elliptical or irregular in outline.

Bodies were established for executive, financial and judicial purposes, the Austrian lands constituted one of the imperial circles which were established in 1512, and in 1518 representatives of the various diets (Landtage) met at Innsbruck, a proceeding which marks the beginning of an organic unity in the Austrian lands.

At the same time the prevalent tone of the populace was, no doubt, Hellenistic, as is shown by the fact that the Jews who settled there acquired Greek in place of Aramaic as their mother-tongue, and in its upper circles Alexandrian society under the Ptolemies was not only Hellenistic, but notable among the Hellenes for its literary and artistic brilliance.

The antiquities include stone circles, duns, the ruins of Breachacha Castle, once a fortress of the Lords of the Isles.

From 1860 to 1864 academical and clerical circles were agitated by the storm which followed the publication of Essays and Reviews, a volume to which two of his most valued friends, Benjamin Jowett and Frederick Temple, had been contributors.

He was continually engaged in theological controversy, and, by his advocacy of all efforts to promote the social, moral, and religious amelioration of the poorer classes and his chivalrous courage in defending those whom he held to be unjustly denounced, undoubtedly incurred much and grow- ing odium in influential circles.

But public opinion still insists, in considerable circles even in Europe, on restrictions of a more or less defined kind, both as to marriage and as to eating together.

But since the re-establishment of the German empire in 1871 there has been, at least in intellectual circles, a certain waning of his popularity, the Germans of to-day realizing that Goethe more fully represents the aspirations of the nation.

This found few admirers outside Socialist circles, and was hooted by the ordinary playgoer.

So when the king was preparing the way for ennobling her, in order to introduce her into court circles, which were unwilling to receive her, the ministry protested in the famous memorandum of the 11th of February 1847 against the king's demand for her naturalization as a Bavarian, the necessary prcliminary to her ennoblement.

A friend of his mother's, Susanne Katharina von Klettenberg, who belonged to pietist circles in Frankfort, turned the boy's thoughts to religious mysticism.

It left room for rival schools and sects, both within and without the priestly circles, and for continued development of the older and non-priestly thought.

Specific influence on the part of Babylonia is not excluded; but the absence of striking points of agreement in other portions of the Old Testament may not be due to anything else than the particular character of the circles to which they belonged.

In studying the internal peculiarities and the different circles of thought involved, it is found that they often imply written traditions which have a perspective different from that in which they are now placed.

Historical Value.-The book of Judges consists of a number of narratives collected by Deuteronomic editors; to the same circles are due accounts of the invasions of Palestine and settlement in Joshua, and of the foundation of the monarchy in I Samuel.

It was felt in British circles at the time that a very considerable concession to Habibullah's independence of attitude was displayed in the fact that he was styled in the treaty " His Majesty "; but, in the circumstances, it seems to have been thought diplomatic to accede to the amir's determination to insist on this matter of style.

Since the transit circle is preferable to the equatorial for such observations wherein great accuracy is required, the declination and hour circles of an equatorial are employed, not for the determination of the right ascensions and declinations of celestial objects, but for directing the telescope with ease and certainty to any object situated in an approximately known position, and which may or may not be visible to the naked eye, or to define approximately the position of an unknown object.

The hour circle has two toothed circles cut upon it, one acted upon by a worm screw mounted on the pier and driven by clockwork, the other by a second worm screw attached to the polar axis, which can be turned by a handle in the observer's hand and thus a slow movement can be given to the telescope in right ascension inde FIG.

Telescopes of such dimensions can be conveniently directed to any object by the circles without the observer being under the necessity to climb a special ladder.

But when much larger instruments are required the hour circle becomes inaccessible from the floor, and means have to be devised for reading both circles from the eyeend.

The observer at the eye-end can also read off the hour and declination circles and communicate quick or slow motions, to the telescope both in right ascension and declination by conveniently Pulkovo, placed handles.

The eye end presents an refractor appearance too complicated to be figured here; it has a micrometer and its illumination for the position circle, a micrometer head, and a bright or dark field, clamps in right ascension and declination and quick and slow motion in the same, a finder, microscopes for reading the hour and declination circles, an illuminated dial showing sidereal time and driven by an electric current from the sidereal clock, and counter weights which can be removed when a spectroscope or other heavy appliance is added.

Until the plebiscite should take place the administration of these Circles was taken over by interallied commissions for East and West Prussia respectively.

In ordinary life we may say, " All men are mortal," " All centaurs are figments," " All square circles are impossibilities," " All candidates arriving five minutes late are fined " (the last proposition being an example of the identification of categorical with hypothetical in Keynes's Formal Logic).

His reception by literary circles in France was very flattering.

Excepting in relatively narrow circles these theories have been seriously studied only by professed theologians.

Even in the official circles of the Church, not excepting corn- the Roman Church, there are many scholars who find Y promises.

This spirit manifests itself in wide circles in our day.

The religious myths are generally identifiable with the Polynesian, but a belief in the gods proper is overshadowed by a general deification of ancestors, who are supposed from time to time to occupy certain blocks of stone, set up near the family dwelling, and surrounded by circles of smaller ones.

It was foreordained that Messiah's witnesses should be borne by Divine power through all obstacles and to ever-widening circles, until they reached and occupied Rome itself for the God of Israel - now manifest (as foretold by Israel's own prophets) as the one God of the one race of mankind.

Among the principal residence streets are Massachusetts, especially between Dupont and Sheridan circles, New Hampshire, Connecticut and Vermont Avenues and 16th Street, all in the N.W.

The particular case where both centrodes are circles is specially important in mechanism.

The herpolhode curve in the fixed plane is obviously confined between two concentric circles which it alternately touches; it is not in general a re-entrant curve.

Hence the path will be confined between two horizontal circles which it touches alternately, and the direction of motion is never horizontal except at these circles.

In the case of disturbed steady motion, just considered, these circles are nearly coincident.

The coupling rod remains always parallel to itself, and all its points describe equal and similar circles relatively to the frame of the engine, and move in parallel directions with equal velocities at the same instant.

The moment of friction of this pivot is at first almost C, inappreciable from the extreme smallness of the T radius of the circles of contact of the ball and cups, but, as they wear, that radius and the moment of friction increase.

When we leave the higher circles of the twice-born, the difficulty of finding a uniform basis of classification becomes apparent.

A special feature of the Sakti cult is the use of obscure Vedic mantras, often changed so as to be quite meaningless and on that very account deemed the more efficacious for the acquisition of superhuman powers; as well as of mystic letters and syllables called bija (germ), of magic circles (chakra) and diagrams (yantra), and of amulets of various materials inscribed with formulae of fancied mysterious import.

At the Dutch university, where he matriculated on the 27th of October 1745, he associated with a small knot of English youths, afterwards well known in various circles of life, among whom were Dowdeswell, his subsequent rival in politics, Wilkes, the witty and unprincipled reformer, and Alexander Carlyle, the genial Scotchman, who devotes some of the pages of his Autobiography to chronicling their sayings and their doings.

But the Slavophil movement, with its motto, " one law, one church, one tongue," acquired great influence in official circles, and its aim was, in defiance of the pledges of successive tsars, to subject Finland to Orthodoxy and autocracy.

We may likewise conclude that this conflict performs circles round the wire, for without this condition it seems impossible that one part of the wire when placed below the magnetic needle should drive its pole to the east, and when placed above it, to the west."

He was introduced to pietistic circles in Berlin, and came specially under the influence of Baron Hans Ernst von Kottwitz (1757-1843), who became his "spiritual father," and of the historian Neander.

Even after leaving prison he was necessarily an outcast from decent circles, and he lived mainly on the Continent, under the name of "Sebastian Melmoth."

There are remains of ancient chapels, Danish duns and Druidical circles on the island.

They do not, however, exclude the possibility that by the side of the scholasticism of the early Jewish academical circles was the more popular thought which, forming a link between Jews and Christians, ultimately fell into neglect as Judaism and Christianity formulated their theologies.

In the 15th century it was divided into upper and lower Barnim, and these names are now borne by two, circles (Kreise) in the kingdom of Prussia.

Piles of rocks are made on the muddy bottoms of these salt-water lakes, and around these are arranged circles of stakes, to which are often attached bundles of twigs.

The ten books of Symmachus' Epistolae, so highly esteemed in the cultured circles of the 4th century, may be contrasted with the less elegant but more forceful epistles of Jerome.

In this spirit he offered the most decided opposition to those circles at the court of Vienna which advocated a bloody reckoning with Serbia.

The pure gospel, however, Marcion found to be everywhere more or less corrupted and mutilated in the Christian circles of his time.

He was occasionally seen in London during the first years of the century, and wherever he appeared he was the delight of admiring circles.

On wing the movements of the condor, as it wheels in majestic circles, are remarkably graceful.

But his reputation in court circles was increasing; he was appointed a member of the committee for the reform of the criminal law in 1840; and, the same year with a letter of recommendation from Metternich in his pocket, visited England and France, Holland and Belgium, made the acquaintance of Thiers and Heine in Paris, and returned home with an immense and precious store of practical information.

The railroad in making this ascent makes curves equivalent to forty-two whole circles in a distance of 81 m., at one place paralleling its track five times in a space of about 300 ft.

This point of view was not widely shared even in circles appreciative of his actual work.

For traces of the wider sense of "apostle" in Gnostic, Marcionite and Montanist circles, see Monnier (as below).

To the clerical and ultra-royalist faction which was supreme in the Lower Chamber and in the circles of the court after the second Restoration, Gregoire, as a revolutionist and a schismatic bishop, was an object of double loathing.

Looking at Stonehenge from the architectural standpoint, there can be no hesitancy in regarding it as an advanced representative of the ordinary stone circles, some two hundred of which, great and small, are known within the British Isles.

The ancient books, preserved in the Pali Pitakas, being mainly occupied with the details of Arahatship, lost their exclusive value in the eyes of those whose attention was being directed to the details of Bodhisatship. And the opinion that every leader in their religious circles, every teacher distinguished among them for his sanctity of life, or for his extensive learning, was a Bodhisat, who might have and who probably had inherited the karma of some great teacher of old, opened the door to a flood of superstitious fancies.

He thus made it possible for the half-converted and rude tribes to remain Buddhists while they brought offerings, and even bloody offerings, to these more congenial shrines, and while their practical belief had no relation at all to the Truths or the Noble Eightfold Path, but busied itself almost wholly with obtaining magic powers (Siddhi), by means of magic phrases (Dhdrani), and magic circles (Mandala).

In the annexed figure, there are shown various examples of the curves named above, when the radii of the rolling and fixed circles are in the ratio of I to 3.

The hypocycloid derived from the same circles is shown as curve d, and is seen to consist of three cusps arranged internally to the fixed circle; the corresponding hypotrochoid consists of a three-foil and is shown in curve e.

Leonhard Euler (Acta Petrop. 1784) showed that the same hypocycloid can be generated by circles having radii of; (a+b) rolling on a circle of radius a; and also that the hypocycloid formed when the radius of the rolling circle is greater than that of the fixed circle is the same as the epicycloid formed by the rolling of a circle whose radius is the difference of the original radii.

The epicychid when the radii of the circles are equal is the cardioid (q.v), and the corresponding trochoidal curves are limacons.

For the religious aspect of vegetarianism in these and other circles, see von Dobschiitz's Christian Life in the Primitive Church (1904), pp. 125 f., 396 f.

We must imagine him devoted to the great task which he had set himself to perform, with a mind free from all disturbing cares, and in the enjoyment of all the facilities for study afforded by the Rome of Augustus, with its liberal encouragement of letters, its newlyf ounded libraries and its brilliant literary circles.

In 1869 appeared his Hereditary Genius, its Laws and Consequences, a work which excited much interest in scientific and medical circles.

The ornamentation of the period is as a rule confined to spirals, bosses and concentric circles.

A most singular habit possessed by this bird is that of rising in the air and soaring there in circles at an immense altitude, uttering at intervals the very loud cry of which its local name is an imitation.

In Switzerland, on the contrary, there is an organized body of the New Church; divine service being held in the Society at Zurich and by circles at Berne, Herisau and Nesslau.

The apparatus when liberated flies into the air sometimes to a height of 50 ft., and gyrates in large circles for a period varying from 15 to 30 seconds.

In both cases the curves are epicycloids; in the first case the radii of the rolling and the fixed circles are a(2n - I) /4n and a/2n, and in the second, an/(2n+ I) and a/(2n4-I), where a is the radius of the mirror and n the number of reflections.

Whatever the currency in classical circles of the epistle as a literary form, it is irrational to put first in the development of Christian literature a general epistle, couched in fluent, even rhetorical, Greek, and afterwards the Pauline letters, which both as to origin and subsequent circulation were a product of urgent conditions.

In some bamboos they are very numerous from the lower nodes of the erect culms, and pass downwards to the soil, whilst those from the upper nodes shrivel up and form circles of spiny fibres.

The success of his pamphlet gained him ready access to all Whig circles; but already his confidence in that party was shaken, and he was beginning to meditate that change of sides which has drawn down upon him so much but such unjustifiable obloquy.

Swift was afraid of the reception the book would meet with, especially in political circles.

God reveals to Enoch the history of the creation of the earth and the seven planets and circles of the heaven and of man, the story of the fallen angels, the duration of the world through 7000 years, and its millennium of rest.

It is quite certain that Bunyan was, at eighteen, what, in any but the most austerely puritanical circles, would have been considered as a young man of singular gravity and innocence.

In puritanical circles, from which plays and novels were strictly excluded, that effect was such as no work of genius, though it were superior to the Iliad, to Don Quixote or to Othello, can ever produce on a mind accustomed to indulge in literary luxury.

Not till many years after Sumner's death was any other American received so intimately into the best, English circles, social, political and intellectual.

He was an admirable lecturer and writer of popular books on his subject, as well as of more learned works such as his Treatise on Spherical Astronomy (1885) and Treatise on the Theory of Screws (1900); and he was a congenial figure in all circles.

In the most general case two points may be chosen on the line of intersection of the diametral planes, and tangents drawn to the pitch circles of the pulleys.

By this arrangement he was able to be frequently in Edinburgh, and to cultivate the literary and scientific society for which it was at that time specially distinguished; and through Maskelyne, whose acquaintance he had first made in the course of the celebrated Schiehallion experiments in 1774, he also gained access to the scientific circles of London.

Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

It often accompanies a ship for days - not merely following it, but wheeling in wide circles round it - without ever being observed to alight on the water, and continues its flight, apparently untired, in tempestuous as well as in moderate weather.

In the military classes it was felt that the honor of the realm was lost; in mercantile circles it was thought that the continuance for a few years more of such government would make an end of English trade.

Consider two circles partially drawn so that it does not appear whether the circles, if completed, would or would not intersect in real points, say two arcs of circles; then we can, by means of a third circle drawn so as to intersect in two real points each of the two arcs, determine a right line, which, if the complete circles intersect in two real points, passes through the points, and which is on this account regarded as a line passing through two (real or imaginary) points of intersection of the two circles.

The construction in fact is, join the two points in which the third circle meets the first arc, and join also the two points in which the third circle meets the second arc, and from the point of intersection of the two joining lines, let fall a perpendicular on the line joining the centre of the two circles; this perpendicular (considered as an indefinite line) is what Gaultier terms the " radical axis of the two circles "; it is a line determined by a real construction and itself always real; and by what precedes it is the line joining two (real or imaginary, as the case may be) intersections of the given circles.

The intersections which lie on the radical axis are two out of the four intersections of the two circles.

Gunter's Quadrant, an instrument made of wood, brass or other substance, containing a kind of stereographic projection of the sphere on the plane of the equinoctial, the eye being supposed to be placed in one of the poles, so that the tropic, ecliptic, and horizon form the arcs of circles, but the hour circles are other curves, drawn by means of several altitudes of the sun for some particular latitude every year.

Augustine's (erroneous) interpretation of the Millennium (Rev. xx.), as a parable of the Church's historic triumph, stands for the final eradication of primitive " enthusiasm " in the great Church, though of course millenarianism has had many revivals in special circles.

The doctrine of Atonement, destined to be the focus of Protestant evangelicalism, has remained undefined in Catholic circles,' an implicate or presupposition, but no part of the explicit and authorized creeds.

The "mandarin language" is the Chinese, which is spoken in official and legal circles; it is also spoken over a considerable portion of the country, particularly the northern and central parts, though not perhaps with the same purity.

A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

He was already known in literary circles by several essays and poems, when the revolution opened a wider career.

The city is furthermore divided into ten municipal circles as follows.

This way of solving, or passing over, the ultimate problems of thought has had many followers in cultured circles imbued with the new physical science of the day, and with disgust for the dogmatic creeds of contemporary orthodoxy; and its outspoken and even aggressive vindication by physicists of the eminence of Huxley had a potent influence upon the attitude taken towards metaphysics, and upon the form which subsequent Christian apologetics adopted.

When Germany was divided into circles by the emperor Maximilian I.

The appointment caused much surprise at the time, as Billow was little known outside diplomatic circles.

The anatomy of the stele in the stem exhibits on the whole a progression from a solid protostele through a tubular solenostele to one or more circles of separate steles derived by the breaking up of the solenostele.

The stem, from the ground tissue of which sclerenchyma is absent, has a complicated system of steles arranged in concentric circles; the thick roots, the central cylinders of which have several alternating groups of xylem and phloem, arise in relation to these.

Among the principal buildings are the ancient castle, formerly the residence of the counts of Hanau; the church of St John, dating from the 17th century, with a handsome tower; the old church of St Mary, containing the burial vault of the counts of Hanau; the church in the new town, built by the Walloons in the beginning of the 17th century in the form of two intersecting circles; the Roman Catholic church, the synagogue, the theatre, the barracks, the arsenal and the hospital.

Humped cattle are widely spread over Africa, Madagascar and India, and form a distinct species, Bos indicus, characterized by the presence of a fleshy hump on the shoulders, the convexity (instead of concavity) of the first part of the curve of the horns, the very large size of the dewlap, and the general presence of white rings round the fetlocks, and light circles surrounding the eyes.

When at the pole his zenith coincides with the celestial pole, and as the earth revolves on its axis, the heavenly bodies perform their apparent diurnal revolutions in horizontal circles round the zenith.

As he travels South, his zenith moves along the celestial sphere, and the circles of diurnal rotation become oblique to the horizon.

The circles in which the heavenly bodies appear to revolve are then vertical.

Finally, at the south pole the circles of diurnal revolution are again apparently horizontal, but are described in a direction apparently (but not really) the reverse of that near the north pole.

From of old, in China, circles were divided into 3654 parts, so that the sun described daily one Chinese degree; and the equator began to be employed as a line of reference, concurrently with the ecliptic, probably in the second century B.C. Both circles, too, were marked by star-groups more or less clearly designated and defined.

They were provided with large graduated circles adapted for measurements of declination and right ascension, and prove the Chinese to have anticipated by at least three centuries some of Tycho Brahe's most important inventions.

He further elaborated it by the introduction of " eccentrics," which accounted for the changes in orbital velocity of the sun and moon by a displacement of the earth, to a corresponding extent, from the centre of the circles they were assumed to describe.

He long adhered to the traditional belief that all celestial revolutions must be performed equably in circles; but a laborious computation of seven recorded oppositions of Mars at last persuaded him that the planet travelled in an ellipse, one focus of which was occupied by the sun.

More immediately efficacious was the innovation made by John Pond (astronomer royal, 1811-1836) of substituting entire circles for quadrants.

Still retaining his connexion with the Moravians, he was appointed court preacher at Konigsberg in 1691 by the elector of Brandenburg, Frederick III., and here, entering upon a career of great activity, he soon became a person of influence in court circles.