1853. Apparition of a brilliant comet in the northern hemisphere. Cooper's Catalogue of 30,168 stars observed at Markree. The method of recording transits of the stars by means of electro-galvanism introduced at Greenwich. Airy's researches on ancient eclipses. Adam's researches on the secular inequality in the mean motion Hansen's researches on the theory of the pendulum, taking into account the figure and motion of the earth. Publication of the American Lunar Tables. Encke gives a new solution of the problem of planetary perturbation. Apparition of a conspicuous comet. Discovery of four new asteroids. Hansen's Solar Tables.

of the moon.

1854. Occurrence of a total eclipse of the sun which was visible in Chili. Discovery of six new asteroids. Lubbock's Researches on Refraction. Captain Jacob's Catalogue of 1440 stars. Airy's Pendulum experiments in the Harton coal mine for determining the mean density of the earth. Determination of the difference of longitude of Greenwich and Paris by galvanic signals.

1855. Greenwich Catalogue of 1576 stars. Bond's Zone Observations of Small Stars near the equator (First Part). Main's Researches on Aberration and Nutation. Commencement of the publication of the Annales de l'Observatoire Impérial,' Paris. Main's Researches on the dimensions of the Rings of Saturn. Commencement of the American Nautical Almanac. Discovery of four new asteroids.

1856. Discovery of five new asteroids. Researches of Professor Challis on the problem of three bodies. Main's researches on the diameters of the planets. 1857. Discovery of eight new asteroids. Airy's researches on ancient eclipses. Main's researches on refraction. Carrington's catalogue of circumpolar stars. Hansen's Lunar Tables. The application of photography to astronomy makes sensible progress. De La Rue and Secchi execute photographs of the moon. Bond obtains photographs of double stars.

1858. Discovery of six new asteroids. De La Rue succeeds in executing a stereographic photograph of the moon. Le Verrier's Solar Tables. The first comet of the year found by Dr. Bruhns to be periodic, and to be identical with a comet which appeared in 1790. Dr. Winnecke discovers a comet, which he finds to be periodic, the time of revolution being somewhat more than five years. Professor Encke establishes beyond doubt the existence of a continued diminution in the time of revolution of the comet which bears his name, by means of researches prosecuted during a period of nearly thirty years. Occurrence of a total eclipse of the sun which was visible in Brazil, An annular eclipse of the sun observed in England. Completion of the calculations for determining the principal triangles of the Trigonomettrical Survey of the British Isles, and deduction of the definitive results relative to the dimensions, ellipticity, and mean density of the earth. Maclear, having re-measured and extended Lacaille's are of the meridian at the Cape of Good Hope, obtains a result which accords with the generally admitted value of the earth's figure. Apparition of a comet of unusual splendour (Donati's), which continued visible to the naked eye for several weeks.

1859. Airy's researches on the motion of the solar system in space. The following list of public observatories now in action is taken from the 'Nautical Almanac' for 1862:

The materials of modern astronomy are contained-1st, In the publications of scientific societies; 2nd, In the introductions to the volumes which emanate from public observatories; Srd, In the appendices to the annual volumes of ephemerides; 4th, In journals devoted exclusively to astronomical subjects; and lastly, in the independent publications of individual authors. By far the greater part of the science is to be found recorded in the third and fourth of these distinct repositories.

The ephemerides, chiefly remarkable for the papers on astronomical subjects contained in them, are:-The Connaissance des Temps,' of Paris; the Berlin Jahrbuch,' and the Effemeridi di Milano.' During the course of the present century a great number of valuable papers by Lagrange, Laplace, Poisson, &c., have appeared in the Connaissance des Temps,' but recently the volumes have been falling off somewhat in this respect. The Berlin Jahrbuch,' of which Professor Encke is superintendent, maintains in the present day a decided pre-eminence among publications of this class, in so far as relates to the papers appended to each volume. The volumes of the 'Effemeridi di Milano, for the years corresponding to the close of the last century and the beginning of the present, contain many valuable papers by Oriani, Carlini, &c. A very small number of papers only have been published in the form of supplements to the Nautical Almanac.'

The greater part of the astronomy of the present day is to be found in the periodicals devoted exclusively to astronomical subjects. These are:-The Astronomische Nachrichten,' published at Altona; the Monthly Notices,' of the Royal Astronomical Society; and Gould's Astronomical Journal,' published at Cambridge, U. S.

Works on the History of Astronomy.-Sherburn's edition of Manilius, London, 1675, contains a list and short account of a very large number of astronomers, and has been much used by succeeding authors. A somewhat similar account is given by De Chales in tome i. (pp. 74-108) of his Cursus seu Mundus Mathematicus,' Lugdini, 1690. Weidler, 'Historia Astronomiæ,' Vittemb., 1741, contains a valuable collection of facts and dates. Heathcote, Historia Astronomia,' Cantab., 1747. Esteve, 'Histoire Générale et Particulière de l'Astronomie,' Paris, 1755. Costard, 'History of Astronomy,' London, 1767. Bailly, 'Histoire de l'Astronomie Ancienne,' 4to, Paris, 1775; Traité de l'Astronomie Indienne et Orientale,' 4to, Paris, 1787; 'Histoire de l'Astronomie Moderne,' 3 vols., 4to, Paris, 1779-82. Pingré's Cometographie,' 2 vols., Paris, 1783. Lalande's Astronomie,' Paris, 1792, contains a considerable number of historical facts. Bibliographie Astronomique, avec l'Histoire de l'Astronomie, depuis 1781 jusqu'à 1802:' this work gives a list of every known astronomical publication, and also an enormous alphabetical list of astronomers. The historians of mathematicsVossius, Montucla, Kästner, Bossut, and Delambre, 'Rapport Historique,' &c., Paris, 1810-treat astronomy as a part of their subject. Hutton's Mathematical Dictionary,' and Martin's Biographia Philosophica,' contain information on English astronomers which is not to be found in foreign works; and there is a good deal in the histories of the Royal Society, written respectively by Sprat, Birch, and Thomson. Small's 'Account of the Discoveries of Kepler,' 1804, contains valuable information on the earlier systems of astronomy. Laplace's' Précis sur l'Histoire de l'Astronomie,' Paris, 1821, which is also appended to his 'Exposition du Système du Monde,' is delightfully written; and there is also much information in the historical chapters of the fifth volume of the 'Mécanique Celeste.' Voiron, 'Histoire de l'Astronomie, depuis 1781 jusqu'à 1811,' Paris, 1811, is a continuation of Bailly's 'Histoire de l'Astronomie Moderne.' Delambre, 'Histoire de l'Astronomie Ancienne,' 2 vols., 4to, Paris, 1817; 'Histoire de l'Astronomie du Moyen Age,' 4to, 1819; 'Histoire de l'Astronomie Moderne,' 2 vols., 4to, 1821; Histoire de l'Astronomie au dixhuitième siècle,' 4to, 1827 (a posthumous work): these various works of Delambre contain a vast amount of critical research; they are indispensable to the student of astronomical history. Airy's 'Report on the Progress of Astronomy, published in the British Association Report' for 1882, contains a great mass of valuable facts relative to the history of astronomy in the present century. Narrien's 'Account of the Origin and Progress of Astronomy,' 8vo, London, 1835, contains an excellent account of the progress of astronomy, especially down to Kepler's time. Whewell's History of the Inductive Sciences,' 1847, and the 'Supplement,' 1857, may also be consulted with advantage. Professor De Morgan, in a series of papers which have been published from time to time in the Companion to the British Almanac,' has thrown much valuable light on the history of astronomy in modern Europe. We give the titles of the following: Old Arguments against the Motion of the Earth' (Comp. 1836); Notices of English Mathematical and Astronomical Writers between the Norman Conquest and the year 1600' (Comp. 1837); 'References for the History of the Mathematical Sciences' (Comp. 1843); 'On the Difficulty of Correct Description of Books' (Comp. 1853); The Progress of the Doctrine of the Earth's Motion between the times of Copernicus and Galileo' (Comp. 1855). Jahn's Geschichte der Astronomie,' 2 vols., 1844. Grant's History of Physical Astronomy, from the Earliest Ages to the Middle of the Nineteenth Century,' 8vo, London, 1852, comprises a detailed account of the progress of the theory of gravitation; besides a history, more or less extensive, of the various other branches of astronomical science. Much historical information will be found in the Annual Reports of the Council of the Royal Astronomical Society. For the general reader,

it may be well to mention the History of Astronomy,' and the 'Lives of Galileo and Kepler,' in the Library of Useful Knowledge; and the 'History of Natural Philosophy,' in Lardner's' Cabinet Cyclopædia. ASTY'LAR, one of the numerous compound architectural terms from the Greek stylos (σrûλos), column; which, having the Greek privative a prefixed to it, signifies without columns. It is a term of recent introduction, but very convenient and expressive, inasmuch as it explains at once that the building described by it is without any order of columns or pilasters, however ornate it may be in all other respects. Thus, we speak of Astylar Italian in contradistinction from the columnar class of buildings in that style, or such as are decorated with the orders. Astylar composition is not only susceptible of a very high degree of embellishment, but of a species of grandeur not attainable (that is, on the same scale) in the Palladian style, or that where an order is raised upon a basement, or even more than a single order is employed for a façade, because in the former the cornice is proportioned to the entire elevation; sometimes of greatly increased proportions, and then distinguished by the name of cornicione. In this country we had no examples of such astylar class of design, until it was introduced by Mr. Barry, in the Travellers' and Reform Clubhouses. ASYLUM, the Latin and English form of the Greek "Aσvλov, which is generally supposed to be made up of a privative and the root of the verb ovλáw,' to plunder,' and therefore to signify, properly a place free from robbery or violence. Some, however, have derived the Greek word from the Hebrew, 'a grove;' the earliest asylums, it is said, having been usually groves sacred to certain divinities. It is a pretty, rather than perhaps a very convincing illustration of this etymology, which is afforded by Virgil's expression as to the asylum opened by Romulus,

"Hinc lucum ingentem, quem Romulus acer asylum

Retulit."-ÆN. VIII. v. 343.

The tradition was, that Romulus made an asylum of the Palatine Hill preparatory to the building of Rome. Plutarch tells us that he dedicated the place to the god Asylæus. (Plut. 'Romul.' 9.)

Probably all that is meant by these stories is, that in those ages whoever joined a new community received shelter and protection; and even if he had committed any crime, was neither punished by those whose associate he had become, nor surrendered to the vengeance of the laws or customs he had violated. Such an asylum was not an appointed place of refuge established by general consent; it was merely a congregation of outlaws bidding defiance to the institutions of the country in which they had settled, and proclaiming their willingness to receive all who chose to come to them.

But both in the Grecian states, and in Rome, the temples, or at least some of them, were endowed with the privilege of affording protection to all who fled to them, even although they had committed the worst crimes. The practice seems to have been, that they could not be dragged from these sanctuaries; but that, nevertheless, they might be forced to come out, not only by being prevented from receiving food while they remained, but even by such compulsory measures as the application of fire to the building. (See Thucyd.' i. 126, 134; 'Herodot.' vi. 80.) Anything appears to have been permitted except the actual dragging forth of the criminal. Eventually, these places of refuge became great nuisances, being, especially among the Greek cities, established in such numbers as sometimes almost to put an end to the administration of justice. After Greece had become a part of the Roman empire, an attempt was made to repress this evil by an order of the senate, directed to all the pretended asylums, to produce legal proofs of the privilege which they claimed. (Tacit. 'Annal.' iii. 60, &c.) Many were put down in consequence of not being able to satisfy this demand. At last, all the asylums throughout the empire were abolished by an edict of the Emperor Tiberius. (Sueton. in Vitâ Tiberii.' cap. 37.)

The term "Arvλos was given as an epithet to certain divinities; as, for example, to the Ephesian Diana. It is also found on medals as an epithet of certain cities; in which application it probably denoted that the city or district was under the protection of both of two otherwise belligerent powers, and enjoyed accordingly the privileges of neutral ground.

After the decline and fall of Paganism, the privilege of serving as asylums for malefactors was obtained by the Christian temples. The credit of conferring this honour upon churches in general is attributed to Pope Boniface V., in the beginning of the 7th century; but more than two hundred years before, certain sacred buildings of the new religion are said to have been declared asylums by the Emperor Honorius. The asylums thus established eventually grew throughout all Christendom to be a still more intolerable abuse than those of the ancient world had been. In most countries, not only churches and convents, with their precincts, but even the houses of the bishops, came to be at length endowed with the privilege of sanctuary. In all these places the most atrocious malefactors might be found bidding defiance to the civil power. At the same time, there can be no doubt, that while in this way criminals were frequently rescued from justice, protection was also sometimes afforded to the innocent, who would not otherwise have been enabled to escape the oppression or private enmity which pursued them under the perverted forms of law. The institu

tion was one of the many which then existed, having the effect of throwing the regulating power of society into the hands of the clergy, who certainly were, upon the whole, the class in whose hands such a discretion was by far least likely to be abused. When communities, however, assumed a more settled state, and the law became strong with the progress of civilisation, the rights which had at one time armed the church as a useful champion against tyranny, became not only unnecessary but mischievous. The church maintained a long and hard struggle in defence of its old supremacy; and in the face of the stand thus made, and in opposition to ancient habits, and the popular superstition by which they were guarded, it was only very cautiously that attempts could be made to mitigate the evil. For a long time the legal extent of the privilege of sanctuary appears to have been matter of violent dispute between the church and the civil power. In this country, it was not till the year 1487, in the reign of Henry VII, that by a bull of Pope Innocent VIII. it was declared, that if thieves, robbers, and murderers, having taken refuge in sanctuaries, should sally out and commit fresh offences, and then return to their place of shelter, they might be taken out by the king's officers. It was only by an Act of Parliament passed in 1534, after the Reformation, that persons accused of treason were debarred of the privilege of sanctuary. After the complete establishment of the Reformation, however, in the reign of Elizabeth, neither the churches nor sanctuaries of any other description were allowed to become places of refuge for either murderers or other criminals. But various buildings and precincts in and near London, continued for a long time after this to afford shelter to debtors. At length, in 1697, all such sanctuaries, or pretended sanctu aries, were finally suppressed by the Act 8 & 9 Will. III. chap. 26.

In Scotland, the precincts of the palace of Holyrood in Edinburgh still remain a sanctuary for debtors. The boundaries of this privileged place are somewhat extensive, comprehending the whole of what is called" the King's Park," in which is the remarkable hill called "Arthur's Seat." The debtors find lodgings in a short street, the privileged part of which is divided from the remainder by a kennel running across it. Holyrood retains its privilege of sanctuary as being a royal palace; but it is singular as being now the only palace in this country any part of the precincts of which is the property, or at least in the occupation, of private individuals, and therefore open to the public generally.

In England, a legal asylum, or privileged place, is called a sanctuary; and this use of the word sanctuary appears to be peculiar to the English language. Both in this country and in America, the name of asylum is commonly given to benevolent institutions intended to afford shelter neither to criminals nor to debtors, but to some particular description of the merely unfortunate or destitute.

The Jewish Cities of Refuge, established by Moses and Joshua, may be quoted as the most remarkable instance on record of a system of asylum founded and protected by the state itself for the shelter of persons who had violated the law. These cities, as we are informed in the twentieth chapter of the Book of Joshua, were six in number, three on each side of the Jordan. They only, however, protected the person who had killed another unawares. This institution may be regarded as an ingenious device for protecting, on the one hand, the guiltless author of the homicide from the popular resentment, which his unfortunate act would have been likely to draw upon him: and cherishing, on the other, in the public mind, that natural horror at the shedding of human blood, which, in such a state of society, it would have been so dangerous to suffer to be weakened. We see the same principle in the deodand formerly awarded by our law in the case of the accidental destruction of life by any inanimate object.

One of the most curious instances of the privilege of sanctuary, is that long enjoyed in Scotland by the descendants of the celebrated Macduff, Thane of Fife, the dethroner of the usurper Macbeth. It is said to have been granted at the request of the thane by Malcolm III. (Canmore), on his recovery of the crown of his ancestors soon after the middle of the 11th century. By this grant it was declared that any person, being related to the chief of the clan Macduff within the ninth degree, who should have committed homicide without premeditation, should have his punishment remitted for a fine, on flying to Macduff's Cross, which stood near Lindores, in Fifeshire. Although this, however, is the account of the old Scottish historians, it is probable that the privilege only conferred upon the offender a right of being exempted from all other courts of jurisdiction, except that of the Earl of Fife. Sir Walter Scott (Minstrelsy of the Scottish Border,') has printed a Latin document of A.D. 1291, in which the privilege to this latter extent is pleaded. The original deed still exists. Of Macduff's Cross, only the pedestal now remains, the cross itself having been destroyed at the Reformation. It bore a metrical inscription, in a strange half Latin jargon, the varying copies of which, still preserved, have given much occupation to the antiquaries.

(Sibbald's History of Fife, second ed., 8vo, Cupar-Fife, 1802; Cunninghame's Essay upon Macduff's Cross; Camden's Britannia, by Gough).

A'SYMPTOTE (àσúμптwтоs), a compound Greek word signifying which does not fall with: if taken literally with respect to two lines, it would mean that they do not meet one another. But it is used only in speaking of two lines (one of which at least must be curved) which continually approach each other, but never meet; so that the dis

tance between them diminishes without limit, or they may be brought to any degree of nearness, without ever actually meeting.

This appears a paradox to beginners in geometry, who are generally unable to imagine it possible that two lines should continue to approach one another for ever, without absolute contact. But this arises from their confounding the thing called a straight line in practice (which is not a straight line, but a thin stroke of black lead or ink, as the case may be) with the straight line of geometry, which has neither breadth nor thickness, but only length. And they also imagine that if two lines might be asymptotic, the fact might be made visible, which is impossible, unless the eye could be made to distin

guish any distance, however small. But if the unassisted eye cannot detect a white space between two black lines, unless that space be a thousandth of an inch in breadth, which is about the truth, it is evident that two geometrical surfaces with asymptotic boundaries, such as ABC, DE C, would appear to coincide from the point where the distance between them is about the thousandth part of an inch. The idea of a geometrical asymptote is therefore an effort of pure reason, and the possibility of it must be made manifest to the mind, not to the senses. ALMBCD is a vessel of water, of which the sides and

bottom are extended indefinitely towards G and R; the end AL is fixed, but the end BM is moveable parallel to its first position, so as always to form a water-tight obstacle; by which means the length of the vessel may be increased to any extent, while its breadth and height remain the same. Let the water be a perfect fluid, without any adhesion to the sides of the vessel (which is mathematically possible, though not physically), and let the bottom of the vessel be geometrically horizontal. Then, as the end MB changes its position and moves towards GR, it is manifest that the vessel will grow larger, and the level of the water will fall. Suppose the side LK to be of glass. Thus, when the vessel ends at EP, the water may stand at sv; when the end is at FQ, the water may stand at rw, and so on. But the level of the water never can fall absolutely to the bottom CK; for so long as the preceding mathematical suppositions hold good, and there is some water in the vessel, it must stand at some determinate height above the bottom. As the end BM moves to the right, let the curve м v w, &c., mark out the positions of the level upon the edge of the moving end, as is done in the diagram. Then for the reason above given, this curve never can meet the line c K, though obviously in a state of continual approach towards it. Hence the curve MV W and the line с K are asymptotes.

As another illustration, let there be two parallel lines A B, C D, the perpendicular distance of which is AC; and from A, with different

radii, describe arcs of circles p1, qq, Rr, ss, &c. From A B on all these circles measure arcs equal in length to the straight line ac; that is, let P 1, Q2, R 3, . . . . w 7, &c., be all equal to ▲ C. Now it is plain that the arcs qq, Rr, &c., are all greater than a c, and will continue so, however great the radius may be; for A c is the shortest distance which can be drawn from one parallel to the other. But as the radius is extended, the arcs Tt, vv, &c., become more upright, as a person unused to geometrical phraseology would say, that is, more and more nearly coincident with a perpendicular drawn from AB; they also become more and more nearly equal to a C. Hence the points 5, 6, 7, &c., come nearer and nearer to CD, with which they would actually coincide, if it were possible that one of the arcs could become equal to A C. Hence the curve, 1, 2, 3, &c., is an asymptote to CD.

The mathematical theory of asymptotes will be found in all works on the theory of curves, and in most on the differential calculus. The following are the most general notions which it will be within our limits to give, and will be understood by a moderately well-informed mathematician. If the equation of a curve be y= (x), and if the function 4 (x) can be separated into two others, say (x) and x (x), of |

similar reasoning will show that the straight line whose equation is xa is also an asymptote. If the first expression be developed in inverse powers of x, giving

Ꮖ

+ &c.

ba ba2 b a3 y=b+ + + x2 23 the equations of curves which are asymptotes to the preceding may be found by taking any of the preceding terms for y, provided b be always one. Such are ba x

y=b+

or generally, any curve whose equation is y=b+x(x)

where x (x) diminishes without limit, when x is increased without limit, is an asymptote to the preceding. Observe that a curve may first cut another, then recede from it, and afterwards become an asymptote to it.

The following is a mere sketch of the most general method of finding asymptotes to algebraical curves. The first part of the method detects the number and direction of the rectilinear asymptotes, those only excepted which are parallel to either axis of co-ordinates, which will easily admit of a separate determination.

Clear the equation of all radicals. Suppose it then of the second degree, though the same reasoning applies to all degrees. Its form will then be (putting all the highest terms on one side) a y2+ b xy + c x2=dy + ex+f.

The following theorem can then be demonstrated. If the equation (A)

a y2+ b xy + c x2=0

be possible, then it is the collective equation of two lines passing through the origin of co-ordinates, which two lines are parallel to two asymptotes of the curve and the curve can have no others. It is a well-known theorem that any algebraical equation between x and y, which is homogeneous with respect to these letters, is not the equation of a curve, but of a collection of straight lines passing through the origin. Thus the asymptotes of the curve of the third degree will be determined by the solution of an equation of the form ax3+b x2y+c xy2 + dy3=0

which may belong either to one or three straight lines.

If y=kx+l be the equation of an asymptote, the value of k may be any one of the values of determined from the equation (A). To find l, remember that any homogeneous algebraical expression of the mth degree, containing x and y, may be expressed by the form

x