successor of Aristarchus, was a native of Cyrene, and invited to Alexandria by Ptolemy Evergetes, who appointed him keeper of the royal library. He is supposed to have been the inventor of armillary spheres, a species of instrument extensively used by the ancient astronomers. By means of an instrument of this kind he observed the distance between the tropics to be to the whole circumference of a great circle as 11 to 83; a ratio equivalent to $47^\circ 42' 39''$, half of which gives $23^\circ 51' 19.5''$ for the obliquity of the ecliptic. This is a very important observation, and confirms the gradual diminution of the obliquity as indicated by theory. Eratosthenes is celebrated for being the first who attempted, on correct principles, to determine the magnitude of the earth. Having remarked, by some means with which we are unacquainted, that Syene, the most southern of the cities of ancient Egypt, is situated nearly on the same meridian with Alexandria, he conceived the idea of determining the amplitude of the celestial arch intercepted between the zeniths of the two places, and of measuring at the same time their distance on the ground; operations which would afford data for the determination of the whole length of the terrestrial meridian. Syene was known to be situated exactly under the tropic; for at the summer solstice the gnomon had no shadow, and the sun's rays illumined the bottom of a deep well in that city. On the day of the solstice he found the meridional distance of the sun from the zenith of Alexandria to be $7^\circ 12'$, or a fifth part of the circumference. It had also been ascertained by the bematists or surveyors of Alexander and the Ptolemies, that the itinerary distance between Alexandria and Syene was 5000 stadia; therefore $5000 \times 50 = 250,000$ stadia form the circumference of a great circle of the earth, or the length of the terrestrial meridian. Unfortunately, on account of the uncertainty respecting the length of the stadium here employed, we possess no means of estimating the degree of approximation afforded by this rude though ingenious attempt; but the idea does immortal honour to Eratosthenes, and the moderns have added nothing to his method: their better success is owing solely to the progress of the arts and the perfection of astronomical instruments.

About this time the science of astronomy was enriched by the discoveries of some of the distinguished geometers whose labours have so greatly extended the glory of the Alexandrian school. Euclid, the celebrated author of the Elements, lived in the reign of the first Ptolemy. He composed a book on the sphere, which probably served as a model for future works of the same kind, and was the first who treated in a geometrical manner of the phenomena of the different inclinations of the sphere. Conon of Samos, the friend of Archimedes, collected the records of eclipses, which had been observed by the ancient Egyptians; and Callimachus ascribes to him the constellation of Berenice's hair. Archimedes, whose profound Archigenius and deep knowledge of geometry and mechanics entitle him to the appellation of the Newton of the ancients, also claims a high rank among the cultivators of astronomy. His celebrated planetarium, which represented the motions of the sun, moon, planets, and starry sphere, has been a frequent theme of the admiration and praises of the poets:

oli, rerumque fidem, legesque deorum, Ecce Syracusiae transituit arte senex.

Apollonius of Perga solved the important problem of the Apollon stations and retrogradations of the planets by means of epicycles and deferents; and he is entitled to the glory of having formed the alliance between the two sciences of geometry and astronomy, which has been productive of the greatest advantages to both.

Astronomy, which had as yet only consisted of a knowledge of isolated facts, acquired a systematic form, and thus almost a new existence, from the genius and assiduity of Hipparchus, one of the most astonishing men of antiquity, and perhaps the greatest of all in the sciences which are not purely speculative. This illustrious founder of astronomical science was born at Nice in Bythinia, and ob- served at Rhodes. Flamsteed and Cassini, probably misled by some ambiguous expressions of Ptolemy, have related that his observations were made at Alexandria; and this opinion seems generally to have been adopted by historians. The question has been examined carefully, and at considerable length, by Delambre (Astronomie Ancienne), who comes to the conclusion that there is no reason whatever to infer that Hipparchus ever saw Alexandria. Ptolemy, in reporting the observations of Hipparchus, supposed Rhodes and Alexandria to be situated on the same meridian, and consequently does not find it necessary to mention the place at which the observations were made.

ommenced his brilliant career by verifying the determination of the obliquity of the ecliptic made by Eratosthenes. He next directed his attention to the length of the tropical year. By comparing an observation of his own, of the summer solstice, with a similar one made by Aristarchus 140 years before, he found that the anciently received value of 365\(\frac{1}{4}\) days was too great by seven minutes. This leaves the tropical year a value still too great; but it is probable that the error arose from the inaccuracy of the observation of Aristarchus; for the observations of Hipparchus, compared with those of the moderns, make the length of the tropical year amount to 365 days, 5 hours, and 49 minutes, which is only 12 seconds greater than the truth. By a careful observation of the solstices and equinoxes, he discovered that the year is not divided by these points into four equal parts, the sun occupying 94\(\frac{1}{2}\) days in passing from the vernal equinox to the summer solstice, and only 92\(\frac{1}{2}\) from the same solstice to the equinox of autumn. The sun, consequently, remained 187 days in that part of the ecliptic which lies between the equator and the north pole, and therefore only about 178 in the other part. This observation led Hipparchus to the great discovery of the eccentricity of the solar orbit. He accounted for the apparent inequality of the sun's motion, by supposing that the earth is not placed exactly at the centre of the circular orbit of the sun, and that consequently his distance from the earth is subject to variation. When the sun is at his greatest distance, he appears to move more slowly; and when he approaches nearer, his motion becomes more rapid. The distance of the earth from the centre of the orbit is called the eccentricity; it produces an equation between the real and apparent motions, which is called the equation of the centre. He determined the magnitude of this equation in terms of the radius of the ecliptic, and fixed the position of the line of the apsidies, or that which joins the two opposite points of the orbit which are at the greatest and least distance from the earth. With these data he formed the first tables of the sun which are mentioned in the history of astronomy. The discovery of the eccentricity also led Hipparchus to that of the inequality of the lengths of the solar days at different seasons of the year. In the interval which elapses between the sun's passage over the meridian and his return to it the following day, the sun advances by his own proper motion towards the east nearly a degree. But the rate of this motion is unequal, varying between 57 and 61 minutes of a degree; and the accumulation of the inequalities forms what is called the equation of time, that is, the difference between the true time, as shown by the sun, and the mean time, shown by a well-regulated clock, the motions of which are equal and uniform.

The attention of Hipparchus was next directed to the motions of the moon; and on this subject his researches were attended with equal success. From the comparison of a great number of the most circumstantial and accurate observations of eclipses recorded by the Chaldeans, he was enabled to determine the period of the moon's revolution relatively to the stars, to the sun, to her nodes, and to her apogee. These determinations are among the most precious relics of ancient astronomy, inasmuch as they corroborate the results of theory in one of its finest deductions—the acceleration of the mean lunar motion—and thus furnish one of the most delicate tests of the truth of Newton's law of gravitation. It was, indeed, by a comparison of the observations of Hipparchus with those of the Arabian and modern astronomers, that Dr Halley was led to the discovery of that curious and important phenomenon. Hipparchus also determined the eccentricity of the lunar orbit, and its inclination to the plane of the ecliptic; and the values which he assigned to these elements, making allowance for the evaporation and the inequalities of the moon's motion in latitude, are to a few minutes the same as those which are now observed. He had also an idea of the second inequality of the moon's motion, namely, the evaporation, and made all the necessary preparations for a discovery which was reserved for Ptolemy. He likewise approximated to the parallax of the moon, which he attempted to deduce from that of the sun, by determining the length of the frustum cut off from the cone of the terrestrial shadow by the moon when she traverses it in her eclipses. From the parallax he concluded that the greatest and least distances of the moon are respectively equal to 78 and 67 semi-diameters of the earth, and that the distance of the sun is equal to 1300 of the same semi-diameters. The first of these determinations exceeds the truth; the second falls greatly short of it; the distance of the sun being nearly equal to 24,000 terrestrial semi-diameters. It may, however, be remarked that Ptolemy, who undertook to correct Hipparchus with regard to the parallax, deviated still farther from the truth.

The apparition of a new star in the time of Hipparchus induced him to undertake the formation of a catalogue of all the stars visible above his horizon, to fix their relative positions, and mark their configurations, in order that posterity might have the means of observing any changes which might in future take place in the state of the heavens. This arduous undertaking was rewarded by the important discovery of the precession of the equinoxes, one of the fundamental elements of astronomy. By comparing his own observations with those of Arcturus and Timocharis, he found that the first point of Aries, which, in the time of these astronomers, or 150 years before, corresponded with the vernal equinox, had advanced two degrees, according to the order of the signs, or at the rate of 48 seconds a year. This determination is not very far from the truth; for, according to modern observations, the rate of the precession is about 50\(\frac{1}{2}\) seconds annually. His catalogue contained 1080 stars: it is generally, but erroneously, stated to have contained only 1022, after that of Ptolemy, in which the nebulous and some obscure stars are omitted. He also commenced a series of observations to furnish his successors with the means of forming a theory of the planets. Hipparchus likewise invented the planisphere, or method of representing the starry firmament on a plane surface, which afforded the means of solving the problems of spherical trigonometry in a manner often more exact and more commodious than the globe itself. He was the first who demonstrated the methods of calculating triangles, whether rectilineal or spherical; and he constructed a table of chords, from which he drew nearly the same advantages as we derive at present from the tables of sines. Geography is also indebted to him for the happy idea of fixing the position of places on

the earth by means of their latitudes and longitudes; and he was the first who determined the longitude by the eclipses of the moon.

These various labours and brilliant discoveries give a high idea of the industry and genius of Hipparchus. His writings have unfortunately all perished, excepting a commentary on the poem of Aratus; but the principal elements of his theories, together with a few observations, have been preserved in the Almagest of Ptolemy.

After the death of Hipparchus, nearly three centuries elapsed before any successor arose worthy of the name. During this long period astronomy gained no essential advancement. Some rude observations, scarcely superior to those of the Chaldeans, and a few meagre treatises, are the only monuments which exist to testify that science had not fallen into utter oblivion in an age so fertile of poets and orators. Geminus and Cleomedes wrote treatises, which have been preserved to our times; Appigra and Menelaus are said to have observed; the Roman calendar was reformed by Julius Caesar and the Egyptian astronomer Sosigenes; and Posidonius measured a degree, and remarked that the laws of the tides depend on the motions of the sun and moon.

Ptolemy was born at Ptolemais in Egypt, and flourished at Alexandria about the 130th year of our era, under the reigns of Adrian and Antoninus. This illustrious ornament of the Alexandrian school is entitled by his own discoveries to the high rank among astronomers which has universally been assigned to him; but the most signal service which he conferred on science was the collection and arrangement of the ancient observations. Out of these materials he formed the Μεγάλη Σύνταξις, or Great Composition, a collection which exhibits a complete view of the state of astronomy in the time of Ptolemy, and which contains the germ of most of the methods in use at the present day.

The hypothesis which Ptolemy adopted for the purpose of explaining the apparent motions, was that which had been followed by Hipparchus. We have already seen that the genius of Pythagoras, soaring above the illusions of sense, had conceived the sun to be situated at the centre of the universe, and the earth to circulate, like the other planets, about the sun; and that the same opinion was entertained and supported by Aristarchus and a few other astronomers. It would seem, however, that this philosophical idea never gained much ground in antiquity, even among the learned. The vulgar prejudice respecting the immobility of the earth continued to prevail; and it had become an inveterate axiom, that all the celestial motions must be circular and uniform. Ptolemy himself, who felt in its full force the difficulty of reconciling the appearances with the notion of a uniform circular motion, adopted the common opinion without scruple as a primordial law of the universe; for, says he, this perfection belongs to the essence of celestial things, which neither admit of disorder nor irregularity. To save this chimera—the uniform circular motion—Apollonius imagined the ingenious apparatus of epicycles and deferents; and Hipparchus advanced a step farther, by placing the centre of the sun's circle at a small distance from the earth. Ptolemy adopted both hypotheses, and supposed the planet to describe an epicycle by a uniform revolution in a circle, the centre of which was carried forward uniformly in an eccentric round the earth. By means of these suppositions, and by assigning proper relations between the radii of the epicycle and deferent circle, and also between the velocity of the planet and the centre of its epicycle, he was enabled to represent with tolerable accuracy the apparent motions of the planets, and particularly the phenomena of the stations and retrogradations, which formed the principal object of the researches of the ancient astronomers. The notions of Apollonius and Hipparchus were thus reduced to a systematic form, and the proportions of the eccentrics and epicycles of all the planets assigned, by Ptolemy; on which account the system has been generally ascribed to him, and obtained the name of the Ptolemaic System of the universe. As a first attempt to bring the celestial motions within the grasp of geometry, it does infinite honour to the genius of its inventors. It is, however, totally irreconcilable with the precision of modern observations; for it is impossible to represent on this hypothesis the variations of the distances of the planets at the same time with their apparent motions. But this difficulty could scarcely be felt by Ptolemy, inasmuch as it was impossible, before the invention of the telescope and micrometer, to form any accurate estimate of the variations of the apparent diameter of a planet, and consequently of its distance. It must be admitted, however, that the Ptolemaic hypothesis might be sufficient for the wants of practical astronomy, that is, for calculating the places of the planets and forming tables of their motions, were it not for its extreme complication. The discovery of every new irregularity in the planetary motions exacts the addition of a new epicycle; and such was the confusion resulting from this circumstance, that Alphonso X., despairing of being able to comprehend the complicated machinery, was tempted to exclaim, that if the Deity had called him to his counsels at the creation of the world, he could have given good advice. Yet, notwithstanding all its defects, the system of Ptolemy gained a complete ascendancy over the minds of mankind, and, so difficult is it to leave the beaten path, continued to be implicitly followed by every astronomer during fourteen centuries, having been only finally exploded by Kepler's discovery of the elliptic orbit of Mars.

The most important discovery which astronomy owes to Ptolemy is that of the Evection of the moon. Hipparchus had discovered the first lunar inequality, or the equation of the centre, which serves to correct the mean motion at the syzygies, and had also remarked the necessity of another correction for the quadratures. He even undertook a set of observations, with a view to ascertain its amount and its law; but death put a stop to his labours before he had brought them to a successful issue. Ptolemy completed the investigation, and discovered that the eccentricity of the lunar orbit is itself subject to an annual variation, depending on the motion of the line of the apsides. The variation of the position of the apsides produces an inequality of the moon's motion in her quarters, which has been technically denominated the evective. The equation given by Ptolemy, though of course empirical, is remarkably exact.

Ptolemy employed a very simple process for determining the moon's parallax, which was probably suggested to him by the situation of Alexandria, where he observed. He determined the latitude of a place a little to the south of that city, over the zenith of which the moon was observed to pass when her northern declination was the greatest possible. But when the moon is in the zenith, or in the same straight line with the observer and the centre of the earth, she has no parallax; consequently the obliquity of the ecliptic and the latitude of the station being known, the moon's greatest northern latitude was also determined. The next step was to observe the moon's meridian altitude fifteen days after the first observation, when her southern latitude was necessarily the greatest possible. This observation gave the apparent altitude of the moon, but her greatest northern and southern decli- nations being supposed equal, her true altitude, as seen from the centre of the earth, was easily computed from the previous observation, and the difference between the true and apparent altitudes gave the amount of the parallax.

The observations of Hipparchus relative to the motion of the stars in longitude, or the regression of the equinoctial points, were confirmed by Ptolemy, although he mistook its amount, and diminished a quantity which Hipparchus had already estimated too low. According to Hipparchus, the regression is at the rate of two degrees in 150 years. Ptolemy reduced it to one degree in 90 years. This disagreement would seem to indicate an error of more than a degree in the observations, which can with difficulty be admitted, considering the accordance which subsists among the different observations cited by Ptolemy in support of his own determination. For this and some other reasons Ptolemy has been accused of altering the observations of Hipparchus, and accommodating them to his own theory; but there does not appear to be any just ground for the imputation. The error with regard to the regression probably arose from the circumstance, that Hipparchus had assigned too great a value to the length of the year, whence the motion of the sun with regard to the equinoxes would be made too slow, and the longitudes employed by Ptolemy consequently diminished.

Ptolemy has been called the Prince of astronomers—a title which may perhaps be justified by the universal and long-continued prevalence of his system, but to which he has no claim from the number or value of his own observations. After a laborious and minute examination of the Almagest, Delambre doubts whether anything, saving the author's declarations, is contained in that great work, from which it can be decisively inferred that Ptolemy ever observed at all. He indeed frequently makes mention of observations made by himself; but his solar tables, rate of the precession, eclipses, determination of the moon's motion and parallax, and, above all, his catalogue of stars, render it impossible to doubt that the greater part of the results which he has given as observations are merely computed from the tables of Hipparchus. It is therefore difficult to allow to Ptolemy that good faith and "astronomical probity which forms one of the most indispensable qualities of an observer." He never in any instance cites a single observation more than is just necessary for the object he has immediately in view, and consequently, by precluding all comparison of one observation with another, has deprived us of the means even of guessing at the probable amount of the errors of his solar, lunar, and planetary tables. If an astronomer, as Delambre justly remarks, were to adopt the same course at the present day, he would be certain of forfeiting all claim to confidence; but Ptolemy stood alone; he had neither judges nor rivals; he claimed admiration, and received it; and now no one condescends to calculate the few observations he has left us. (Delambre, Astronomie Ancienne, tom. i. Discours Préliminaire.) His catalogue contains only 1029 stars, and is therefore less extensive than that of Hipparchus, but it is exceedingly valuable on account of its details.

The name Almagest (Μαγεστης, with the Arabic prefix) was bestowed on the Syntaxis by the Arabians, into whose language it was translated in the ninth century. The first Latin translation was from the Arabic, and published at Venice in 1515. It abounds in Arabic words and idioms, and is very inaccurate and barbarous. The second Latin translation was made from the original Greek by George of Trebizond, and is greatly superior to the first. It was published at Basle in 1541, and in 1551. The History Greek text was published at the same time in 1538. Ptolemy was the author of numerous other works connected with astronomy, of which his Geography, in eight books, is the best known. It contains a list of all the places of which the latitudes and longitudes had at that time been determined. His treatise on Optics was supposed to be lost, till an imperfect Latin translation, from an Arabic version, was lately discovered in the king's library at Paris. The last book of this work contains a theory of astronomical refraction, more complete than any which existed before that of Cassini. It would seem that Ptolemy had not discovered the refraction at the time he composed the Almagest, no mention being made of the subject in that work. The explanation which he gives of the phenomenon is natural and satisfactory, indeed entirely conformable with that which is now universally adopted. The idea and explanation remained buried in the Optics till reproduced by Alhazen; but neither Ptolemy nor Alhazen attempted to estimate the amount of the refraction. His Planisphere and Analemma, in which he treats of the stereographic and orthographic projections of the sphere, show a perfect acquaintance with spherical trigonometry. In the last-mentioned work he makes use of the sines, and his constructions comprehend three of the four general theorems in modern use. Divers treatises also on music, dialling, chronology, and mechanics, attest the universality of Ptolemy's genius, and his unremitting application to the pursuits of science. Like Archimedes, he had a desire to transmit to posterity the history of his labours by a public monument. In the temple of Serapis, at Canopus, he is said to have consecrated a marble pillar, with an inscription containing the principal elements of his astronomy, such as the length of the year, the eccentricity of the solar and lunar orbits, the dimensions and forms of the epicycles of the planets, &c.

On the death of Ptolemy astronomy ceased to be cultivated among the Greeks. The Alexandrian school subsisted indeed for some centuries after; but genuine science had fled, and its place been usurped by the vain wranglings of theologians and grammarians. During the long period of six or seven centuries, the labours of those who assumed the name of astronomers were confined to needless or trifling commentaries on the works of Hipparchus and Ptolemy, and were productive of no observations, or even remarks, having a tendency to enlarge the boundaries of the science. The genius of the Roman dominion was unfavourable to the development or exercise of the higher faculties of the human intellect; and the natural sciences, with the liberal arts, faded away under the withering influence of military despotism.

From the brief account which has now been given, it will be easily inferred that the Greeks cultivated astronomy rather as a speculative than a practical science. None of their numerous sects ever evinced any taste for observation or experiment; and hence, while geometry made great and rapid advances in their hands, physics and experimental philosophy were entirely neglected. The prevailing passion for speculation pervaded even their astronomy. They explained the doctrine of the sphere, and the apparent motions of the planets; and framed ingenious theories to account for such phenomena as came immediately under the cognizance of their senses; but if we except the observations of Hipparchus and Ptolemy, and perhaps two solstitial distances of the sun from the zenith, observed by Eratosthenes, we remark among them no observations made with instruments capable of measuring angular distances. Before Hipparchus, no mention is made of the astrolabe; and the recorded determinations do not give us a very favourable idea of the accuracy of that instrument. On casting our eyes over the catalogue of Ptolemy, we scarcely ever meet with a fraction of a degree smaller than one-twelfth, that is to say, less than five minutes; whence we may infer that the astrolabe only measured twelfth parts of a degree. Occasionally, indeed, the fractions one-fourth and three-fourths occur; but these were most probably inserted by estimation. The Greeks of Alexandria committed an error of no less than 15' with regard to the altitude of the pole, one of the most essential elements to an observer; and it does not appear that they were ever able to determine the time to within a quarter of an hour. Yet notwithstanding these circumstances, which indicate that the art of observation was still in its infancy, the science of astronomy is vastly indebted to the labours and speculations of the Greeks. The complicated but ingenious hypotheses of Ptolemy prepared the way for the elliptic orbits and laws of Kepler, which, in their turn, conducted Newton to the great discovery of the law of gravitation.

Astronomy of the Arabians.

While the nations of western Europe were involved in the thickest shades of ignorance and barbarism, the torch of science was rekindled, and blazed forth with extraordinary splendour, among the Saracens. The burst of fanaticism which enabled the followers of Mahomet to carry their religion and their arms over the fairest portion of the ancient world subsided, in a great measure, after a century and a half of uninterrupted conquest, and was succeeded by a period of repose, during which they cultivated the arts of peace and civilisation with the same ardour which had characterized their achievements in arms. Under the enlightened and munificent protection of the caliphs, Bagdad became what Alexandria had been under the Ptolemies, the centre of politeness and knowledge.

The accounts which we possess of the Saracen literature are imperfect and scanty; but the first of the caliphs who appears to have encouraged the study of astronomy was Abouigafar, surnamed Almansor, or the Victorious, who reigned in the eighth century. His grandson Almanmon, the seventh of the Abbasides, and second son of the famous Haroun Al Raschid, who reigned at Bagdad from 813 to 833, is celebrated for the protection which he gave to learning, and the zeal with which he laboured to propagate the sciences of the Greeks among his subjects. In granting peace to the emperor Michael III, he stipulated for liberty to collect in Greece all the writings of the philosophers. These he transported into his own country, and caused to be translated into Arabic. Finding it mentioned in the geography of Ptolemy that a degree of the earth was equivalent to 500 stadia, he resolved to have this fact verified by a new measurement; and in obedience to the commands of the caliph, a company of mathematicians assembled in the spacious plain of Sinjar, where, having observed the altitude of the pole, they separated themselves into two parties, and proceeded in opposite directions along the meridian, measuring the distance they passed over till the altitude of the pole varied one degree. Being unacquainted with the nature of the instruments made use of in these geodetic operations, we cannot estimate the probable accuracy of the result; but as it agreed perfectly with the statement of Ptolemy, we have a right to infer that the measurement was executed in a very inadequate manner, and that the mathematicians of the caliph adopted the ancient determination from want of confidence in their own.

The Syntax of Ptolemy was translated into Arabic History, under the reign of Almamon, by Isaac Ben Honain. The translation was afterwards revised by Thabet or Thebith Ben Korah, and it was about this time that it received the appellation of Almagest. Astronomical observations, which, as we have had occasion to remark, had been greatly neglected by the successors of Hipparchus, formed a principal object of the attention of the Arabians. By the orders of Almamon, the obliquity of the ecliptic was observed, and found to be $23^\circ 33'$. According to the modern tables, the obliquity at that time was $23^\circ 36' 34''$, so that the error was less than that of Hipparchus and Ptolemy, in their determination of the same element. This observation supposes instruments of some accuracy. Among the astronomers whom Almamon drew to his court, we find the names of Habash of Bagdad, who composed three books of astronomical tables; Ahmed, or Mohammed Ben Cothair, better known by the name of Alfragran, or Alfranius, who, from his great expertise in computing, was styled the calculator. He composed an elementary treatise on astronomy, which was only an abridged extract of the works of Ptolemy; and likewise wrote on sun-dials, and gave a description of the astrolabe. The Jew Meshula, whose treatise on the elements was published at Nuremberg in 1549, also lived in the time of Almansor or Almamon.

The most celebrated of the Arabian astronomers was Albateg-Albategnius, or Muhammed Ben Geber Albattani, so called from Batan, a city of Mesopotamia, where he was born. He was a prince of Syria, and resided at Aracte or Racha, in Mesopotamia; but many of his observations were made at Antioch. Having studied the Syntax of Ptolemy, and made himself acquainted with the methods practised by the Greek astronomers, he began to observe, and soon found that the places assigned to many of the stars in Ptolemy's tables were considerably different from their actual situations, in consequence of the error which that great astronomer had committed with regard to the precession of the equinoxes. Albategnius measured the rate of the precession with greater accuracy than had been done by Ptolemy; and he had still better success in his attempt to determine the eccentricity of the solar orbit, his value of which differs extremely little from that which results from modern observations. In assigning the length of the year, however, he fell into an error of more than two minutes; but this proceeded, as has been shown by Dr Halley, from too great confidence in the observations of Ptolemy. Albategnius also remarked that the place of the sun's apogee is not immovable, as former astronomers had supposed, but that it advances at a slow rate, according to the order of the signs—a discovery which has been confirmed by the theory of gravitation. A new set of astronomical tables, more accurate than those of Ptolemy, likewise resulted from the indefatigable labours of Albategnius; and his observations, important in themselves, are doubly interesting on account that they form a link of connection between those of the astronomers of Alexandria and of modern Europe. The works of Albategnius were published in 1537, under the title of De Scientia Stellarum.

Thebith Ben Korah, another Arabian, acquired celebrity Thebith by proposing an explanation of the motions of the stars, Ben Korah, which, under the name of the "System of Trepidation," was eagerly received by the astronomers of the middle ages, and disfigured the tables of Alphonso, and even those of Copernicus. He ascribed to the eighth sphere, or that of the fixed stars, two motions; one the diurnal motion, the other that of trepidation, performed in small circles round the first points of Aries and Libra, and of History, which the radii were $4^\circ 18' 33''$. He therefore supposed two ecliptics, one fixed in the ninth sphere, the other movable in the eighth. According to this construction, the motion of the stars is sometimes direct and sometimes retrograde.

The Arabians have been said to be not only the cultivators but the apostles of the sciences, on account of the activity with which they propagated them among all the nations subjected to their dominion. The Fatimites caliphs, who reigned in Egypt during two centuries, rivalled their predecessors the Ptolemies in the encouragement which they gave to astronomy. Under the caliph Hakem, who reigned from 996 to 1021 of our era, Ebn Jounis acquired a splendid reputation. He constructed a set of tables, and composed a sort of celestial history, in which he has recorded numerous observations of his own and of other astronomers belonging to the same country. This work, imperfectly known through some extracts, long excited the curiosity of astronomers, as it was supposed to contain observations tending to establish the acceleration of the mean motion of the moon. A manuscript copy of it, belonging to the university of Leyden, was, in 1804, transmitted to the French Institute, and translated by Professor Caussin. It contains 28 observations of eclipses from the year 829 to 1004; seven observations of the equinoxes; one of the summer solstice; one of the obliquity of the ecliptic made at Damascus, by which the value of that element is found to be $23^\circ 35''$; and likewise a portion of tables of the sun and moon, with some other matter illustrative of the state of astronomy among the Arabians.

The observations which regard the acceleration of the mean lunar motion are two eclipses of the sun and one of the moon, observed by Ebn Jounis, near Cairo, in the years 977, 978, and 979, and they agree with theory in confirming the existence of that phenomenon.

The Saracen conquests in Spain were attended with the same happy results as in Egypt, and science flourished in that country while the rest of Europe was involved in the darkest shades of ignorance. Arzachel is supposed to be the author of the Toledo Tables, constructed about the year 1180, but which, on account of the established reputation of those of Albategnius, were never in great estimation. He made some changes in the dimensions which had been assigned by Hipparchus and Ptolemy to the solar orbit, and deserves the praise of having been an exact and attentive observer. Alhazen, who flourished in the same country about the same period, contributed to the progress of astronomy by a treatise on Optics, in which he clearly indicated the necessity of making an allowance for the celestial refraction in astronomical observations. His treatise contained a theory of reflection and refraction, an explanation of the cause of the twilight, and of the magnitude of the horizontal moon. Averroes, a physician of Cordova, made an abridgement of the Almagest in the twelfth century, and Almansor found the obliquity of the ecliptic to be $23^\circ 33' 30''$, which proves that practical astronomy had now attained to a tolerable degree of exactness.

e inquire what effect the labours of the Arabians and their disciples had on the progress of astronomy, we shall find that their services were confined entirely to the practical part. In point of theory they did absolutely nothing. They admitted all the hypotheses of Ptolemy without the slightest alteration, even with timid and superstitious respect, and did not advance a single step towards the discovery of the solar system. But with regard to instruments and methods of calculation, their improvements were numerous and important. They constructed instruments on a larger scale, and divided them with greater care; and, even from the time of Almamon, we remark among them new and more exact determinations of the obliquity of the ecliptic, of the positions of some stars, of the precession, of the length of the year, and of the eccentricity of the sun's orbit. To these fundamental points they added numerous observations of eclipses and conjunctions; they industriously sought out and corrected the errors of Ptolemy's tables; they perceived the necessity of marking the instant of each phenomenon with greater care; and their determinations of the commencement and end of eclipses are in general accompanied with the altitude of a star, which afforded them the means of calculating the hour, angle, and the true time. In cases where less precision was wanted, they made use of their clepsydrae and solar dials, to the construction of which they paid particular attention. Trigonometry derived signal advantages from their constant care to facilitate the calculations of spherical astronomy. Albategnius substituted the sines for the chords,—a most important improvement, the idea of which was probably suggested to him by the Analemma of Ptolemy. By this happy substitution the solution of all rectangular spherical triangles was reduced to four general formulae, of which the Greeks had the equivalent in a much less commodious form. The same astronomer also appears to have invented a very remarkable rule for the oblique-angled triangles, perfectly identical with one of the four general formulae now in use. Ebn Jounis, and his contemporary Aboul Wefa, were acquainted with the tangents and secants, and employed them very dexterously in reducing complicated binomial expressions to a single and simpler term. They also employed subsidiary arcs and other artifices in the calculus of the sines, in order to facilitate the labour of computation. These substitutions are now common; but they remained long unknown in Europe; and 700 years after they were employed by the Arabians, we first meet with some examples of their use in the writings of Thomas Simpson.

The zeal of the Arabians for astronomical observations was communicated by them to the Persians and Tartars. About the year 1072, Omar Cheyam determined the length of the tropical year, and introduced the calendar which has ever since been used in Persia. Hulegu-Ilecou-Khan, who conquered that country about the year 1264, caused an observatory to be built at Maragha, near Tauris, where he assembled the most celebrated astronomers who could be found within his dominions, and employed them in forming new astronomical tables. This work was directed by the famous Nassirreddin, and brought to a conclusion in the year 1269. With the exception of some trifling corrections of the mean motions, the whole of these tables are copied from Ptolemy.

Ulugh Beigh, a Tartar prince, and grandson of the great Ulugh Tamerlane, not only encouraged the study of astronomy, but was himself a diligent and successful observer. At Samarcand, the capital of his dominions, he established an academy of astronomers, and caused the most magnificent instruments to be constructed for their use. By means of a gnomon 180 feet in height, he determined the obliquity of the ecliptic to be $23^\circ 30' 20''$, the precession of the equinoxes at $1^\circ$ in 70 years, and obtained elements for the construction of tables which have been found to be scarcely inferior in accuracy to those of Tycho Brahe. The ancient astronomy had produced only one catalogue of the fixed stars, that of Hipparchus. Ulugh Beigh has the honour of having formed a second, after an interval of sixteen centuries. This learned and munificent prince, whose virtue and talents deserved the esteem of mankind, was assassinated by his own son in the 58th year of his age. After the death of Ulugh Beigh, astronomy received no farther accessions in the east. But the seeds of knowledge had now begun to take root in a more propitious soil, and Europe, destined to carry the development of the human energies to its fullest extent, began to awake from the lethargy in which it had continued during so many ages. The first dawnsings of returning day appeared in Spain. In spite of the horror inspired by the Moslem religion, the Christians began to perceive and acknowledge the superiority and utility of the science of the Moors; and the schools of Cordova became the resort of all those whom curiosity, or love of knowledge, induced to seek abroad for that information which could not be obtained in their own countries. Geber, afterwards Pope Silvester II., acquired the knowledge of arithmetic from that source; and John of Halifax, better known by the name of Sacrobosco, after having studied some time in Spain, made an abridgement of the Almagest, which was long famous under the title of a Treatise of the Sphere.

The emperor Frederick II. is no less celebrated for his protection of the sciences, than for the continual struggles in which he was involved with the popes. He founded the university of Naples, and caused Latin translations to be made of the works of Aristotle and the Almagest of Ptolemy. About the same time astronomy was zealously encouraged and cultivated by Alphons X., king of Castile. This monarch, whose liberal mind seems to have been far superior to the age in which he lived, formed a college or lyceum at Toledo, the capital of his dominions, whither he assembled the most eminent astronomers that could be found, whether Christians, Moors, or Jews, and engaged them in the task of correcting the errors of the ancient tables. From their united labours were produced the Alphonsine Tables, which obtained great celebrity, and were, in some respects, superior in accuracy to any which had preceded them. They are supposed to have been chiefly the work of the Rabbi Isaac Aben Sid, surnamed Hazan, inspector of the synagogue of Toledo. They are said to have cost the king 40,000 ducats,—a sum certainly far exceeding their real value, which is confined to the correction of some epochs, and a more accurate determination of the sun's motions and the length of the year.

The same century gave birth to several other individuals distinguished by their attachment to the sciences. Campanus of Nivari translated Euclid, and left a treatise on the sphere. Vitello, a native of Poland, composed a treatise on optics, in ten books; and Albert, bishop of Ratisbon, whom his contemporaries styled the great, was the author of some works on arithmetic, geometry, astronomy, and mechanics. But the greatest luminary of that age was Roger Bacon, a Franciscan friar, whose numerous works contain many indications of a powerful and inventive genius. He made many important discoveries in optics; but his knowledge of natural philosophy and chemistry, uncommon in those days, had nearly proved fatal to him; for he was suspected of necromancy, and thrown into a dungeon, from which he did not escape till he had satisfied his superiors and the pope that he had never held unlawful intercourse with the devil. He composed a work on the utility of astrology, the places of the stars, and the aspects of the moon; and he had the merit of perceiving the necessity of reforming the calendar.

The fourteenth century produced no astronomer from Purbach, born 1423, whose labours the science gained any accessions. George died 1461. Purbach, or Beurbach, so named from a small town in Austria, where he was born in 1428, obtained great celebrity as a professor. He studied at Vienna, and after giving proofs of distinguished talents, he travelled into Italy, where he was favourably received by the cardinal of Cusa, who himself cultivated astronomy. On his return to Vienna he undertook a translation of the Almagest; and although ignorant both of Greek and Arabic, his perfect acquaintance with the subject enabled him to correct many errors which had been introduced through the carelessness or ignorance of former translators. He published a table of sines for every ten minutes to a radius of 6,000,000 parts, which was afterwards extended by his scholar Regiomontanus to every minute of the quadrant. The most celebrated of his works is his Theorica Nova Planetarum, which was published in 1460. He constructed a celestial globe, on which was represented the motion of the stars in longitude from the time of Ptolemy to the year 1450. He also measured the obliquity of the ecliptic, and is considered as the inventor of decimal arithmetic. He died in 1461, having only reached his 38th year, with the reputation of being, at that time, the first astronomer in Europe.

Purbach had the good fortune to form a disciple who executed many of the plans which had been interrupted by his premature death. This was the celebrated John Muller of Königsberg, better known by the name of Regiomontanus. Attracted in his youth to Vienna by the great reputation of Purbach, he continued to study there during ten years, and on the death of his master repaired to Rome for the purpose of acquiring the Greek language, and of making himself, through it, acquainted with the Almagest. At Rome he continued his observations, and translated into Latin the works of Ptolemy, the Conics of Apollonius, and some other treatises of ancient science. In 1471 he retired to Nuremberg, where, with the aid of Bernard Walther, a wealthy burgess, he founded an observatory, and furnished it with excellent instruments, principally of his own invention, by means of which he was enabled to detect many errors in the ancient tables. On the invitation of Pope Sixtus IV., who wished to reform the calendar, he again repaired to Rome; but after a few months' abode there he died suddenly, according to some accounts, of the plague, according to others, through the effects of poison administered to him by the sons of George of Trebizond, who adopted this execrable method of revenging the exposure which he had made of their father's errors in the translation of the Almagest. Regiomontanus was a learned and skilful man, but the great expectations which his early labours gave of future services to astronomy were disappointed by his untimely death. He paid great attention to trigonometrical calculation; and, although he did not reach the point which had been attained by the Arabs, he had the merit of introducing some useful theorems which till then were entirely unknown in Europe. His genius, however, did not enable him to rise above the prejudices of his age, for he was an astrologer as well as an astronomer, and is said to have most lamented the errors of the Alphonsine Tables on account of the uncertainty which they occasioned in the calculation of genitures or horoscopes.

After the death of Regiomontanus, Walther continued Walther to observe at Nuremberg during thirty years. His observations were collected by order of the senate of Nuremberg, and published by Schönner in 1544, a second time by Snellius, and, lastly, along with those of Tycho Brahe. In 1484 Walther began to make use of clocks, then a recent invention, to measure time in celestial observations. He was also the first who employed the planet Venus as a term of comparison for determining the longitudes of the stars.

Nuremberg had the honour of producing another astro- We are now come down to a period in the history of astronomy when the science was destined to undergo a total renovation, and the system which had been so laboriously established by Ptolemy, and blindly followed as an article of religious belief by Arabs, Persians, Tartars, and Europeans, during so many centuries, was about to be exploded for ever. In proportion as the observations became more numerous and accurate, the difficulty of representing them by the Ptolemaic system became greater; and astronomers were obliged to have recourse to the most violent and improbable suppositions in order to explain the phenomena, and, in the language of Ptolemy, sure the appearances. We have mentioned that Pythagoras and his disciples entertained an idea very different from that which commonly prevailed, and supposed the sun to be the immovable centre of the celestial motions. It appears, however, from Aristotle, that this opinion was not founded on any analysis of the phenomena, but on certain metaphysical notions respecting the comparative dignity of the several elements. For example, fire, being a nobler substance than earth, ought to occupy the centre or place of honour. But such arguments could have little weight except in the schools, and accordingly were rejected by Ptolemy as too absurd to require a serious refutation. In order to give any probability to the Pythagorean doctrine, it was necessary to explain the succession of the seasons and the precession of the equinoxes on the hypothesis of the annual revolution of the earth about the sun; to show how the unequal motions of the planets in concentric orbits would give rise to the phenomena of the stations and retrogradations; to account, in short, for all the appearances, and point out their coherence and mutual connection. All this was effected by Copernicus, who had thereby the glory of first making known the true system of the universe, and of leading the way in that career of astronomical discovery in which the genius of the human race has gained its noblest trophies.

Nicholas Copernicus was born at Thorn, a city of Prussia, on the confines of Poland, according to Junctinus on the 19th of January 1472, and according to others on the 19th February 1473. From his earliest years he displayed a great fondness and aptitude for mathematical studies, and pursued them with corresponding success at the university of Cracow. Stimulated by the desire of acquiring a reputation equal to that of Regiomontanus, he set out for Italy at the age of 23 years, in order to study astronomy at Bologna under the celebrated Dominic Maria. He afterwards removed to Rome, where he employed himself in studying and teaching the mathematics, and where he made several astronomical observations about the year 1500. On his return to his native country he was made a canon of Ermland by his uncle the bishop of Worms, and took up his residence at Frauenberg, a small Prussian town near the mouth of the Vistula, where he passed 36 years of his life in observing the heavens and meditating on the system of the world. In this retirement he composed his famous work entitled Astronomia Restaurata, sive de Revolutionibus Orbium Coelestium, in which he explained the celestial motions in a manner as simple and connected as the system of Ptolemy was complicated and incoherent. The system which Copernicus adopted in this work is now so familiar to everyone, that it is almost unnecessary to describe it. The heaven, composed of stars perfectly at rest, occupies the remotest bounds of space, then the orbit of Saturn, next Jupiter, Mars, the Earth accompanied by its moon, Venus, Mercury, and, lastly, the Sun immovable at the centre. By this arrangement the stations and retrogradations of the planets became simple mathematical corollaries, following from the differences of the radii of their orbits and their unequal motions. The diurnal rotation of the earth explained more simply and rationally the apparent daily revolution of the heavens; and the precession of the equinoxes was referred to a small variation in the inclination of the earth's axis to the plane of the ecliptic. But the simplicity of the system, and its consequent probability, were the only arguments which Copernicus was able to bring forward in proof of its reality. The motion of the earth can indeed never be made an object of sense; but after Richer's discovery of the diminution of gravity towards the equator, it was impossible to doubt longer of the existence of its rotary motion; and when Roemer had measured the velocity of light, and Bradley observed the phenomena of the aberration, the evidences of its annual revolution were rendered equally convincing. Great, however, as were the merits of Copernicus, it must be acknowledged that he left his system in a very imperfect state. After the example of the ancients, he assumed as an axiom the uniform circular motion of the planets; and as the only motions which are observed are in a state of incessant variation, he was obliged, in order to save the inequalities, to suppose a different centre to each of his orbits. The sun was placed within the orbit of each of the planets, but not in the centre of any of them, consequently he had no other office to perform than to distribute light and heat; and, excluded from any influence on the system, he became as it were a stranger to all the motions. Yet notwithstanding these and other imperfections, the establishment of the doctrine of the earth's motion, with an evidence which dissipated the illusions of sense, was a great step towards the true knowledge of the planetary system; and when we consider the ignorance and prejudices of the age, and that Copernicus was moreover a priest, we cannot hesitate to admit his claim to a high rank among philosophers. But whether the actual services which he rendered to astronomy are commensurate with the great fame he has obtained, may admit of doubt. He revived an ancient opinion opposed to the prejudices and religious dogmas of his times, and fortified it with new and strong, though not absolutely convincing, proofs. It seldom happens, however, with regard to those sciences which ultimately appeal to experience, that general reasoning, even of the soundest kind, tends much to their real advancement; and there is little reason for thinking that astronomy would have been less perfect, or that any discoveries since made in it would have been retarded a single day, even if Copernicus had never lived. His great merit, like that of Lord Bacon, consists in the sound views which he took of nature, and in advancing so far before the general attainments of his age.

Fearing the opposition which was likely to arise from religious bigotry to opinions so much at variance with vulgar prejudice, Copernicus long delayed the publication of his great work; and it was only at the urgent request of his friends that he at last allowed it to be printed. He is said to have received the last sheet of it only on the day of his death. He was buried in the cathedral of Frauenberg, and his only epitaph consisted of some spheres cut out in relief on his tombstone. The ideas of Copernicus soon spread over Germany, where astronomy was at that time diligently cultivated; but they do not seem to have met with general favour before the commencement of the seventeenth century. The art of observing was, however, gradually receiving improvement; instruments were constructed on better principles, and more accurately divided; and the methods of computation were rendered much less laborious. Nonius, or Nunez, a Portuguese, invented the ingenious method of subdividing the small divisions of instruments which still retains his name; Reinhold extended the table of tangents of Regiomontanus to every minute of the quadrant, reformed the tables of Copernicus, and composed many works of practical utility; but of the immediate successors of Copernicus, no one deserves to be more honourably mentioned than William IV., landgrave of Hesse. This prince built a magnificent observatory on the top of his palace at Cassel, which he furnished with excellent instruments of copper, and is said to have calculated himself the positions of no less than 400 stars. He was aided in the labours of the observatory by some astronomers of great merit whom his liberality drew to his court; among others, by Rothman, and Justus Byrgius, a distinguished artist, to whom Kepler has ascribed some idea of the logarithms.

Tycho Brahe, one of the best and most indefatigable observers of whom practical astronomy can boast, was born at Knudstorp, in Scania, the 13th of December 1546. His family was one of the most ancient and noble in Denmark; and his father, probably thinking that illustrious birth superseded the necessity of education, refused his consent to have his son instructed in Latin. Through the kindness of a maternal uncle, however, he was rescued from the state of barbarous ignorance to which he had been doomed by his parent; and, after having received the requisite preliminary instruction, he was sent to the university of Leipzig to study jurisprudence and scholastic philosophy. The tastes of the future astronomer were first excited by an eclipse of the sun which happened in 1560. Struck with astonishment at the accuracy of the prediction, he conceived a vehement desire to become acquainted with the principles of so certain a science, and exerted his utmost ingenuity to elude the obstacles which were interposed by his parents and governor to prevent him from acquiring the elementary notions of mathematics and astronomy. By placing the hinge of a common compass near his eye, he contrived to guess at the distances of the planets from the stars, and by this means, according to his own account, detected several errors in the Ephemerides of Stadius. By his persevering efforts he at last obtained the consent of his family to study according to his own inclinations; and from that moment he divided his time between the observation of the heavens, and chemical experiments. He visited the different cities of Germany where he hoped to meet with astronomers and skilful mechanicians, and was received with flattering attention by the landgrave of Hesse-Cassel, with whom he contracted an intimate friendship. On his return to Denmark he obtained from Frederick II. a grant of the small island of Huen, in the strait of Sunda, together with a pension and some presents, by means of which, and an expenditure of 100,000 crowns of his own patrimony, he was enabled to build the castle of Uraniburg, and procure a magnificent collection of the largest and most accurate instruments which could then be constructed. In this celebrated retreat he passed twenty-five years, actively employed in making observations, and attracting by his discoveries the attention of the learned throughout Europe. On the death of his protector Fre- ambition of appearing as the author of a new system, he restored to the earth its immobility, and placed it in the centre of the motions of the sun and moon. The Tycho- nic system was an unsuccessful attempt to reconcile the incongruous hypotheses of Ptolemy and Copernicus. It never enjoyed any real estimation; and its followers were only found among those who dreaded the anathemas of the church, or who, belonging to some university or religious corporation, were deprived of the liberty of expressing their real opinions.

Tycho was assisted in his observations at Huen, during eight years, by Longomontanus, who afterwards became professor of the higher mathematics at Copenhagen, died 1647. This astronomer composed a large work, entitled Astronomia Danica, in which he deduced the elements of the different theories from the observations made at Uranibourg, and gave formulae for computing the planetary motions, according to the three systems of Ptolemy, Copernicus, and Tycho.

The great mass of accurate observations accumulated by Tycho furnished the materials out of which his disciple Kepler may be said to have constructed the edifice of the world. This great man, the true founder of modern astronomy, was born at Wiel, in the kingdom of Wurtenberg, on the 27th of December 1571. He studied philosophy at Tubingen, and was instructed in mathematics and astronomy by Moestlin, whose name deserves a place in the history of science, on account of his having been one of the first who had the courage to adopt and to teach the system of Copernicus. The philosophical mind of Kepler, disgusted with the improbabilities and absurdities of the ancient system, received with transport the novel doctrines explained by Moestlin. The appointment of mathematician to the emperor, which he procured on the death of Stadius, confirmed him in the resolution which he had taken to devote himself to astronomical pursuits; and the energy of his character enabled him in a very short time to make himself thoroughly master of the different hypotheses and principal discoveries which had been made prior to his time. In the year 1596 he published a Prodromus of Dissertations on the properties and causes of the celestial orbits, which procured him the friendship of Tycho, and an invitation to take part in the observations and researches of that great astronomer at Prague. On the death of Tycho, which happened soon after, Kepler obtained possession of his invaluable collection of observations, and was charged with the task of completing and publishing the Rudolphine Tables.

During his short residence with Tycho, Kepler learned to check the fanciful suggestions of his brilliant imagination, and to draw his conclusions from observations alone, by rigorous and patient induction. The observations of the Danish astronomer had furnished him with the means of establishing with certainty the truth or inaccuracy of the various hypotheses which he successively imagined; and the diligence with which he laboured in comparing and calculating these observations during 20 years, was finally rewarded by some of the most important discoveries which had yet been made in astronomy. Deceived by an opinion which had been adopted by Copernicus, and had never been called in question by the ancients, that all the celestial motions are performed in circles, he long fruitlessly endeavoured to represent, by that hypothesis, the irregular motions of Mars; and after having computed with incredible labour the observations of seven oppositions of that planet, he at length succeeded in breaking down the barrier which had so long obstructed the progress of knowledge, and found that the motions could only be accurately represented by supposing the planet to move in an ellipse, having the sun in one of its foci. Having arrived at this important result, he next proceeded to consider the angular motion of the planet, and finding that it was not uniform in respect of any point situated within the orbit, he concluded that the uniform motion, till then universally received as an axiom, was a vain chimera, which had no existence in nature. He perceived, however, that the areas described by the radius vector of the planet, at its greatest and least distances, were equal in equal times; and subsequent observations enabled him to demonstrate that this equality extended to every point of the orbit. It was therefore discovered that Mars moves in an elliptic orbit, of which the sun occupies a focus, and in such a manner, that the area described by a line drawn from the centre of the planet to that of the sun is always proportional to the time of description. The same conclusions he found to be true in respect of the orbit of the earth; and therefore he could no longer hesitate to extend them by analogy to the other planets. These are two of the three general principles which are known by the name of the Laws of Kepler.

It was some years later before Kepler arrived at the knowledge of the analogy which subsists between the distances of the several planets from the sun, and the periods in which they complete their revolutions. To the discovery of this analogy he attached the greatest importance, and regarded all his other labours as incomplete without it. After having imagined numberless hypotheses, it at last occurred to him to compare the different powers of the numbers which express the distances and times of revolutions; and he found, to his infinite satisfaction, that the squares of the periodic times of the planets are always in the same proportion as the cubes of their mean distances from the sun. This is the third law of Kepler. He demonstrated it to be true of all the planets then known. It has been found to be equally true in regard to those which have been since discovered, and likewise to prevail in the systems of the satellites of Jupiter and Saturn. It is indeed, as can be shown mathematically, a necessary consequence of the law of gravitation, directly as the masses, and inversely as the squares of the distances.

By these brilliant discoveries, the solar system was reduced to that degree of beautiful simplicity which had been conceived by Copernicus, but from which that great astronomer had found himself constrained to depart. The sun could not occupy the common centre of the circular orbits, but his place is in the common focus of the elliptic orbits of all the planets; and it is to this focus that every motion is to be referred, and from which every distance is to be measured. The discovery of the elliptic motion, of the proportionality of the areas to the times, and the method of dividing an ellipse, by straight lines drawn from the focus to the periphery, into segments having a given ratio, formed the solution of a problem which had been the constant object of the labours of all astronomers from Ptolemy to Tycho, namely, to assign the place of a planet at any instant of time whatever. The tables which he computed for the elliptic motions form the model of those in present use. Some additions have been made in consequence of the perturbations, which the geometry of Kepler was inadequate to estimate, and which were only partially detected by the genius of Newton. It has been considered matter of surprise that Kepler did not think of extending the laws of the elliptic motion to the comets. Prepossessed with the idea that they never return after their passage to the sun, he imagined that it would only be a waste of time to attempt the calculation of the orbits of bodies which had so transitory an existence. He supposed History. The tail to be produced by the action of the solar rays, which, in traversing the body of the comet, continually carry off the most subtile particles, so that the whole mass must be ultimately annihilated by the successive detachment of the particles. He therefore neglected to study their motions, and left to others a share of the glory resulting from the discovery of the true paths of the celestial bodies.

The observations of eclipses had formed the principal object of the earliest astronomers, but it was Kepler who first showed the practical advantages which may be derived from them, by giving an example of the method of calculating a difference of meridians from an eclipse of the sun. The method extends to occultations of the stars, and is deservedly considered as the best we possess for determining geographical longitudes and correcting the tables. He composed a work on optics, replete with new and interesting views, and gave the first idea of the telescope with two convex glasses, which has since been advantageously substituted for that of Galileo. Prompt to seize every happy idea of his contemporaries, he perceived with delight the advantages which practical astronomy would derive from the new invention of the logarithms, and he immediately constructed a table, from which the logarithms of the natural numbers, sines, and tangents could be taken at once.

as not merely an observer and calculator; he inquired with great diligence into the physical causes of every phenomenon, and made a near approach to the discovery of that great principle which maintains and regulates the planetary motions. He possessed some very sound and accurate notions of the nature of gravity, but unfortunately conceived it to diminish simply in proportion to the distance, although he had demonstrated that the intensity of light is reciprocally proportional to the surface over which it is spread, or inversely as the square of the distance from the luminous body. In his famous work *De Stella Martis*, which contains the discovery of the laws of the planetary motions, he distinctly states that gravity is a corporeal affection, reciprocal between two bodies of the same kind, which tends, like the action of the magnet, to bring them together, so that when the earth attracts a stone, the stone at the same time attracts the earth, but by a force feebler in proportion as it contains a smaller quantity of matter. Further, if the moon and the earth were not retained in their respective orbits by an animal or other equilibrant force, the earth would mount towards the moon one fifty-fourth part of the interval which separates them, and the moon would descend the fifty-three remaining parts, supposing each to have the same density. He likewise very clearly explains the cause of the tides in the following passage. "If the earth ceased to attract its waters, the whole sea would mount up and unite itself with the moon. The sphere of the attracting force of the moon extends even to the earth, and draws the waters towards the torrid zone, so that they rise to the point which has the moon in the zenith." It is not difficult to imagine how much these views must have contributed to the immortal discovery of Newton.

It is afflicting to consider how frequently the just rewards of true merit are usurped by charlatanism and pretension. While the fire-eaters and astrologers of Rudolph were basking in the sunshine of imperial favour, Kepler, from whose labours the sciences derived the most signal benefits, passed his life in extreme indigence. Born without fortune, the only revenue he possessed, and out of which he had to maintain a numerous family, arose from the precarious produce of his writings, and his pension of mathematician to the emperor,—a pension which, owing to the calamities of the times, was seldom duly paid. On this account he was obliged to prefer frequent solicitations, and undertake long journeys, whereby he lost his time, always precious to genius, and exhausted his mind in anxiety. He died on the 15th of November 1630, at Ratishon, whither he had gone to solicit the arrears that were due to him. In the present century a marble monument has been erected to his memory by an enlightened prince, Charles of Alberg. It contains his bust and the eclipse of Mars; a monument more glorious and more imperishable than brass or marble.

Contemporary with Kepler was the illustrious Galileo, Galileo, whose discoveries, being of a more popular nature, and born 1564, far more striking and intelligible to the generality of mankind, had a much greater immediate effect on the opinions of the age, and in hastening the revolution which was soon about to change the whole face of physics and astronomy. Galileo-Galilei, a Florentine patrician, was born at Florence in the year 1564. He passed his youth at Venice, where he continued till he was appointed to a professor's chair at Padua. After a residence of eighteen years in that city, he was induced to remove to Pisa by Cosmo II., who assigned him a pension, and conferred on him the title of his first mathematician. While residing at Venice, he heard it reported that Metius, a Dutch optician, had discovered a certain combination of lenses, by means of which distant objects were approximated to the sight. This vague and scanty intelligence sufficed to excite the curiosity of Galileo, who immediately set about inquiring into the means whereby such an effect could be produced. His researches were attended with prompt success, and on the following day he had a telescope which magnified about three times. It was formed by the combination of two lenses, a plano-convex and plano-concave, fitted in a leaden tube. In a second trial he obtained one which magnified seven or eight times; and subsequent essays enabled him to increase the magnifying power to 32 times. On directing his telescope to the moon, he perceived numerous inequalities on her surface, the diversified appearances of which led him to conclude almost with certainty that the moon is an opaque body similar to the earth, and reflecting the light of the sun unequally, in consequence of her superficial asperities. The planet Venus exhibited phases perfectly similar to those of the moon. These phases had been formerly announced by Copernicus as a necessary consequence of his system; and the actual discovery of their existence made it impossible to doubt of the revolution of Venus round the sun. He detected the four satellites or moons of Jupiter, and, in honour of his patron, gave them the name of the Medicean Stars. The discovery of these little bodies circulating round the huge orb of Jupiter afforded him a strong analogical proof of the annual revolution of the earth, accompanied by its moon. He perceived spots on the disk of the sun, from the motions of which he concluded the rotation of that body about its axis in the space of 27 days. The singular appearances of Saturn were beheld by him with no less pleasure than astonishment. His telescope was not sufficiently powerful to separate the ring from the body of the planet; and to explain the appearances he supposed Saturn to be composed of three stars almost in contact with one another. These discoveries proved that the substances of the celestial bodies are similar to that of the earth, and demolished the Aristotelian doctrine of their divine essence and incorruptible nature. They enlarged the ideas of mankind respecting the planetary system, and furnished the most convincing arguments in favour of the doctrines of Copernicus.

The discoveries of Galileo excited the envy of his History, contemporaries, and stirred up against him a persecution which embittered the last days of his life. The motion of the earth, which he had proved so triumphantly, was considered contrary to many express declarations of Scripture; it was also considered as a heresy in the schools, where the doctrines of Aristotle were followed with implicit submission. In defending the Copernican system, Galileo had incurred the bitterest resentment, both of theologians and peripatetics. His great reputation, his title of professor and first mathematician, gave them reason to dread that the new doctrines, recommended by such an advocate, would spread too rapidly, and finally overthrow the altars of Aristotle. They therefore combined to check their progress, and to procure the ruin of Galileo by injurious representatives to the Grand Duke and the court of Rome. Soon after his first telescopic discoveries he was cited to appear before the Inquisition, and a promise extorted from him that he would never, either by word or writing, support the opinion of the motion of the earth. But in a great mind the love of truth is the most imperious of all passions, and cannot be restrained by the frowns of despotism, or the persecution of a fanatical tribunal. The evidences of the motion of the earth burst forth from every point of the heavens; and Galileo, in his celebrated Dialogues on the system of the world, exposed them in so clear and forcible a manner, that, although he appeared to put them forth for the purpose of refuting them, it was not difficult to perceive that he regarded them as complete and indubitable. For this relapse into heresy he was again brought before the tribunal of the Inquisition, and, in the seventieth year of his age, condemned formally to retract and abjure the doctrine of the earth's motion, and to be imprisoned during the pleasure of the Inquisition. This scandalous proceeding has called forth the indignant reprobation of every lover of truth and freedom. "What a spectacle," exclaims Bailly, "an old man, whose hairs were blanched with study, watchings, and benefits to mankind, on his knees before the sacred Scriptures, abjuring the truth in the eyes of Italy, which he had enlightened, in opposition to the testimony of his conscience, and in spite of the manifestations given by nature through all her works."

The sentence passed on Galileo was not inflicted with great severity. At the end of a year the Grand Duke had the influence to procure his release from prison; but he was prohibited from returning to Florence, and obliged to confine himself to the Tuscan territory. He retired to the village of Arcetri, where he resumed his observations, and shortly afterwards discovered the libration of the moon. The satellites of Jupiter continued also to engage his attention, and he commenced a table of their motions, and pointed out the method of determining the longitude by means of their eclipses. The states of Holland, aware of the great benefit of his researches to commerce and navigation, sent two astronomers, Hortensius and Blaeu, to present him with a gold chain, and encourage him to persevere in his useful labours. A short time after receiving this honourable mark of esteem from a foreign country, Galileo suddenly became blind; and the task of forming the tables of the satellites was reserved for Cassini. He survived this misfortune only a few years, and expired in 1642, in the seventy-eighth year of his age.

Science is indebted to Galileo for two other discoveries of a different kind, less brilliant perhaps, but of far greater importance than those which we have yet enumerated. These are the isochronism of the vibrations of the pendulum, and the law of the acceleration of falling bodies. His telescopic discoveries could not have remained long unknown; in fact, with the exception of those of the phases of Venus, and of the triple form of Saturn, they were all History fiercely disputed, even during his own lifetime. It is now universally admitted that he was the first who discovered the satellites of Jupiter, and the spots of the sun; but the very circumstance of other claimants to these discoveries having arisen, proves that they were within the reach of ordinary attention. No one ever thought of disputing with Kepler the discovery of the laws of the planetary motions. Those of Galileo required only eyes, and may be regarded as following of course from the discovery of the telescope; but his persecution, his condemnation, and his being compelled to retract and abjure a doctrine of which he had given the physical proof, inspire a hallowed interest in his history, and contributed much to the great reputation which he acquired throughout Europe.

While astronomy was making these rapid advances in Scotland which contributed, though less directly, no less powerfully, to the acceleration of its progress. This was the invention of the logarithms by Lord Napier, baron of Merchiston; "an admirable artifice," says Laplace, "which, by reducing to a few days the labour of many months, doubles the life of the astronomer, and spares him the errors and disgust inseparable from long calculations; an invention of which the human mind has the more reason to be proud, inasmuch as it was derived exclusively from its own resources." It may be added, that without this, or some equivalent artifice, the computations rendered necessary by more correct observations would far exceed the limits of human patience or industry, and astronomy could never have acquired that precision and accuracy by which it is now distinguished above all the other branches of human knowledge.

The same epoch presents to us a great number of excellent observers, who, although they did not produce any different revolution in the state of astronomy, still rendered it useful service. Scheiner is celebrated for his observations on the solar spots, and his disputes with Galileo. John Bayer of Augsburg published a description of the constellations, accompanied by maps, in which the stars are marked by a Greek letter; a simple idea, which has been universally adopted. Lansberg, a Flemish mathematician, published in 1632 a set of astronomical tables, which, though filled with inaccuracies, rendered good service to science by apprising Horrox of the transit of Venus over the sun's disk, which that young astronomer and his friend Crabtree had the satisfaction of observing on the 24th of November 1639. They were the first who ever witnessed that interesting but rare phenomenon. Snellius is celebrated for his measure of the earth. Gassendi, who had the merit, along with Descartes, of hastening the downfall of the Aristotelian philosophy in France, made some useful observations, particularly one of a transit of Mercury in 1631. His works, which fill six folio volumes, abound with curious and useful researches. Riccioli, a Jesuit, born at Ferrara in 1598, contributed to the progress of astronomy, not so much by his own discoveries, as by collecting and rendering an account of those of others. He rejected the system of Copernicus, and was more zealous in maintaining the doctrines of the church than in investigating nature; but his works form a vast repertory of useful information. His Novum Almagestum is a collection of the observations, opinions, and physical explanations of the phenomena, together with all the methods of computation then known. He was assisted in his labours by Grimaldi, who discovered the inflection of light, and gave the names to the principal spots of the moon which are now used by astronomers. The most accurate observations that were ever made prior to the adaptation of the telescope to astronomical instruments were those of Hevelius, a rich citizen of Dantzig, who devoted his life and a large fortune to the service of astronomy. Having fitted up an observatory, and furnished it with the best instruments which could be procured, he commenced a course of observations, which he followed assiduously upwards of forty years. In his *Selenographia* he has given an accurate description of the face and spots of the moon, accompanied with excellent delineations of her appearance in her different phases and librations. The idea of making drawings of the different phases of the moon had previously occurred to Gassendi and Peiresc, but they had not been able to execute the project; indeed the difficulty attending it was such, that it occupied Hevelius, who was an excellent draughtsman, as well as observer, during a great number of years. Hevelius made an immense number of researches on comets; and finding that the observations could not be represented by rectilinear or circular orbits, he supposed them to move in parabolas. During a temporary absence from Dantzig, this indefatigable astronomer had the misfortune to lose, in a great fire which occurred in the city, his observatory, instruments, manuscripts, and almost the entire edition of the second volume of his *Machina Coelestis*, which contained the results of his long labours and numerous observations. He was now in his old age, but his zeal did not give way under the terrible calamity. He patiently recommenced all his calculations, reconstructed tables of the sun, and prepared for publication his *Firmamentum Sobiescianum*, or celestial chart, which did not appear till after his death. Towards the latter part of his life, the use of telescopic sights began to be generally adopted. Hevelius, however, resisted the innovation, and continued to employ plain sights. This preference given to the ancient method by so skilful an observer induced Dr Halley to visit him at Dantzig, for the purpose of ascertaining, by a comparison of observations made at the same time and place, which of the two methods gave the most correct results. Dr Halley observed with the telescope, and Hevelius with his own instruments; but such was the dexterity he had acquired through long practice, that the difference of their observations seldom amounted to more than a few seconds, and in no case to so much as a minute. Notwithstanding this agreement, it is to be regretted that Hevelius did not adopt the new method; for, on account of the greater precision given to instruments by the use of the telescope, his observations, which were made without it, cannot now be admitted in the construction of tables, and consequently are for the most part useless to astronomy.

Few individuals have rendered more important services to science than Huygens. Born at the Hague in 1629, he studied geometry under Schooten, the commentator of Descartes, and gave early proofs of proficiency in that science by a treatise on the quadrature of the conic sections. Having passed into France, he studied law at the university of Angers; but his principal attention was directed to the physical sciences, particularly to optics. He employed himself in grinding and polishing lenses; and constructed a telescope of ten feet, with which he discovered one of the satellites of Saturn. His application of the pendulum to clocks deserves to be considered as one of the best gifts which genius has ever conferred on science. He seems to have conceived the idea of this application in 1656; and he presented the first description of the pendulum clock to the states of Holland in 1657. He endeavoured to make this invention subservient to the problem of the longitudes; and if his efforts were not attended with the desired success, it may be said, that without another invention, in which also he had a principal share, that of the spiral spring, the object would never have been accomplished so nearly as it was a hundred years later. By means of his excellent telescopes he discovered that the extraordinary appearance exhibited by Saturn was occasioned by a ring surrounding the body of the planet, and inclined to the ecliptic in an angle which he estimated at 21°. He published his observations on this planet in a work entitled *Systema Saturnium*, which still shows some traces of that species of reasoning from final causes which so greatly disfigures the writings of Kepler. For example, on discovering the satellite, he conceived that as the number of satellites now equalled the number of planets, it was in vain to look for more, the equality being necessary to the harmony of the system. He lived, however, to witness the discovery of four more satellites belonging to the same planet. Huygens was invited to settle in France by Colbert, the patriotic minister of Louis XIV., who assigned him a pension and a seat in the academy of sciences. He continued in that country till the revocation of the edict of Nantz in 1681, when he resigned his pension and retired to Holland. After this he contributed several papers to the *Philosophical Transactions*, and in 1690 published a treatise on light and gravitation. Geometry, mechanics, and optics, are indebted to the genius of Huygens for many important discoveries. His theorems on central forces, his researches on the doctrine of probabilities and continued fractions, and his theory of involutes and evolutes, raise him to the highest rank among the mathematicians of his age. He died on the 8th of June 1695, at the age of 66 years.

The application of telescopes and micrometers to graduated instruments forms an important epoch in the history of astronomy. This happy improvement was first brought into use by Picard in 1667. Morin, indeed, had applied a telescope to the quadrant so early as 1634, and perceived the stars in full day in 1635. In 1669 Picard began to observe the stars on the meridian in the daytime, with a quadrant, to which, in concert with Azout, he had applied an astronomical telescope having cross wires in its focus. Huygens invented the plate micrometer in 1650; Malvasia that with the fixed wires in 1662; and Azout that with the movable wire in 1666. (See Delambre, *Astronomie du Moyen Age*, p. 618. Note by Bovard.) It is principally to the happy discoveries and ingenious inventions just referred to, and the fine application of the pendulum to clocks by Huygens in 1656, that we must attribute the rapid progress since made in practical astronomy, and the extreme precision of modern observations. Picard was also the first who introduced the modern method of determining the right ascensions of the stars, by observing their meridional passages, and employed the pendulum for that purpose. He likewise introduced the method of corresponding altitudes, and is entitled to be regarded as the founder of modern astronomy in France.

Roemer, the friend and pupil of Picard, discovered the progressive motion of light in 1675, and measured its velocity by means of the eclipses of Jupiter's satellites. He was the first who erected a transit instrument, which gave a new accuracy to observations of right ascension.

The Royal Observatory of Paris was completed in 1670, and its direction intrusted to Dominic Cassini. This celebrated astronomer was born at Perinaldo, in the county of Nice, and educated in a college of the Jesuits at Genoa. He acquired an early passion for astronomical observations; and in 1644 was invited to Bologna by the marquis Malvasia, where, in 1650, he succeeded Cavalleri. History, as professor of astronomy. In this situation he continued till 1669, when he went to Paris on the invitation of Louis XIV. He was naturalized in France in 1673, and continued in the charge of the observatory till his death, which happened in 1712.

Cassini enriched astronomy with a great number of curious observations and discoveries. He determined the motions of Jupiter's satellites from observations of their eclipses, and constructed tables of them, which were found to be remarkably exact. He observed that the ring of Saturn is double, and discovered four of the satellites of that planet. He also determined the rotation of Jupiter and Mars, and made a number of observations on Venus with the same view. He observed the zodiacal light, and made a near approximation to the parallax of the sun. We also owe to him the first table of refractions, calculated on correct principles; and a complete theory of the libration of the moon. Galileo had only observed the libration in latitude; Hevelius explained the libration in longitude, by supposing that the moon always presents the same face to the centre of her orbit, of which the earth occupies a focus. Cassini made the important remark, that the axis of rotation of the moon is inclined to the ecliptic, and that its nodes coincide with those of the lunar orbit, so that the poles of the orbit, ecliptic, and equator of the moon, are on the same circle of latitude, the pole of the ecliptic being situated between the other two. The greater number of these discoveries are, however, only of secondary importance; and it must be confessed that Cassini took no part in the great and permanent improvements which astronomy received in that age. He has, nevertheless, obtained an extraordinary reputation. Lalande remarks, that in his hands astronomy underwent the most signal revolutions, and that his name is, in France, almost synonymous with that of creator of the science. Delambre has, however, taken a different and far more accurate view of the real services of Cassini. "The revolution in Astronomy," this judicious critic observes, "was brought about by Copernicus, by the laws of Kepler, by the pendulum of Huygens, the micrometers of Azout and Picard, by the sectors and mural of Picard, and his method of corresponding altitudes, by the transit instruments of Roemer; and Cassini appears to us an entire stranger to all these innovations. He followed another route; he devoted a long life to painful observations, which at last deprived him of sight. Let us not refuse him the praise which he has so well merited, but let us reserve a place in our esteem for labours less brilliant perhaps, but of greater and more permanent utility, and which evince at least equal talent and sagacity."

Maraldi. Cassini was assisted in his observations by his nephew, James Philip Maraldi, who determined the regression of the nodes, and the progressive motion of the apsides of the orbit of Jupiter. This astronomer also corrected the theory of Mars, and observed the sun's parallax. He rejected the hypothesis of the progressive motion of light, as being insufficient to explain the inequalities of Jupiter's satellites; and he conceived the design of forming a new catalogue of the stars, which, however, was never executed. He died in 1729.

There is no period in the history of mankind so distinguished by great and important discoveries, or so remarkable for the rapid development of the human intellect, as the seventeenth century. We have already noticed the invention of the pendulum, and its application to regulate the motion of time-keepers; of the telescope, and some of the phenomena of the new worlds it has exposed to view; of the logarithms, by which computations are so much abridged; and of the mechanical contrivances for measuring minute angles in the heavens. The same century witnessed the application of algebra to geometry, the discovery of the laws of the planetary motions, of the infinitesimal calculus, the acceleration of falling bodies, the sublime theory of central forces, and the great principle of gravitation which connects the celestial orbs, and regulates the motions which it had been the business of the astronomer to observe since the earliest ages of the world. The different steps which conducted to this important discovery, and the immediate consequences deduced from it by its immortal author, are so fully developed in the admirable Dissertation on the Progress of the Physical Sciences, in this Encyclopedia, that it is unnecessary to enter into any detail respecting them here; we may only remark, that if observation has furnished the data for the discovery of the mechanical principle and primordial laws of the universe, the knowledge of these laws has been, in turn, of the most essential service to observation, by guiding and directing it to its most important objects. Many of the inequalities of the planetary motions, in consequence of their minuteness and the slowness with which they vary, could not have been detected by observation; others might perhaps have been perceived, but we should still have been ignorant whether their constant accumulation might not ultimately change the state of the system, and, by destroying all confidence in the tables, demolish the fabric which had been reared at such a vast expense of time and labour. But when these inequalities are detected by theory, and separated from the mean motions with which they were blended, it becomes an object of the highest interest to confirm their existence by the most delicate and accurate observations. Hence, a more refined practice has constantly followed every theoretical discovery. Besides, it is the perfection of theory, and not the mere knowledge of isolated facts, which gives astronomy its greatest value in the eyes of the philosopher. Numerous and important as its applications are, they have but a subordinate interest, in comparison of the knowledge of those general laws to which every particle of matter in the universe is subject, and by the discovery of which man has penetrated so deeply into the mysteries of nature.

By the discovery of the law of gravity Newton laid the foundations of physical astronomy; and by the consequences which he deduced from that law, proceeded far in the erection of the superstructure. He showed that the motions of all the bodies of the planetary system are regulated by its influence; he determined the figure of the earth on the supposition of its homogeneity; he gave a theory of the tides, discovered the cause of the precession of the equinoxes, and determined some of the principal lunar inequalities and planetary perturbations. Many of his theories were left in an imperfect state; for it is not in matters of science that it is given to the same individual to invent and bring to perfection: their complete development required that several subsidiary sciences should be farther advanced; but it has been the triumph of his system, that every subsequent discovery has only tended to strengthen and confirm it. This bright ornament of the human genius was born on the 25th of December 1642, the day of the death of Galileo, and died on the 20th of March 1727, in the 85th year of his age.

While physical astronomy was undergoing a complete revolution in the hands of Newton, the practical part was receiving great improvement from Flamsteed, the first astronomer royal, who conducted the Greenwich Observatory. This celebrated institution, from which so many important discoveries have emanated, was erected under the reign of Charles II. in 1675. Flamsteed was appoint- History, ed to it in 1676, and continued with indefatigable zeal to discharge the duties of the office during the long period of 38 years. In the course of this time he made an immense number of excellent observations, the results of which are given in the *Historia Coelestis*, the first edition of which was published in 1712, at the expense of Prince George of Denmark, the husband of Queen Anne. The second appeared in 1723, some time after the death of the author, in three volumes folio. The first volume contains the observations which he made, first at Derby, and afterwards at Greenwich, on the fixed stars, planets, comets, spots of the sun, and Jupiter's satellites. The second volume contains the transits of the planets and stars over the meridian, and the places of the planets deduced from these observations. The third contains an historical notice, in which he gives a description of the instruments used by Tycho and himself; catalogues of fixed stars by Ptolemy, Ulugh Beigh, Tycho, the landgrave of Hesse, and Hevelius; together with the British Catalogue, containing the places of 2884 stars. The labours of Flamsteed were, however, confined entirely to the practical part of astronomy. He made no improvements in theory; but he is entitled to the merit of having been the first who brought into common use the method of simultaneously observing the right ascension of the sun and a star, a method by means of which the determination of the positions of the stars is reduced to the observation of meridional transits and altitudes. He was likewise the first who explained the true principles of the equation of time; and he improved the lunar tables by introducing into them the annual equation which had been suggested by Horrox. The *Atlas Coelestis*, another posthumous work of Flamsteed, was published in 1753.

as succeeded in the observatory by Dr Halley, a philosopher whose inventive genius and indefatigable activity rendered him one of the brightest ornaments of his country. Halley was the son of a wealthy citizen of London, where he was born on the 8th of November 1656. From his earliest years he applied himself with ardour to the study of mathematics and astronomy; and having procured a few instruments, he began to make observations, by which he was led to remark the inaccuracy of the tables of Jupiter and Saturn. In his 19th year he published a direct and geometrical method of finding the eccentricities and aphelia of the orbits of the planets; and in the year following he undertook a voyage to St Helena, with a view to form a catalogue of the stars in the southern hemisphere. The station was unfortunately chosen, for owing to the incessant rains and foggy atmosphere of that island, he was able to determine the places of only 360 stars in the course of a whole year. He had, however, the satisfaction of observing a transit of Mercury over the sun's disk, a phenomenon which suggested to him the important remark, that the transits of the inferior planets might be advantageously employed in determining one of the most essential elements of the planetary system, viz. the parallax of the sun, and consequently the diameters of the orbits. The method has since been successfully employed in the case of Venus: the transits of Mercury, though much more frequent, are not so well adapted to the purpose. On his return from St Helena he was commissioned by the Royal Society to visit Hevelius at Dantzic, and determine, by a direct comparison of observations, the dispute which had arisen between that astronomer and Dr Hooke respecting the relative advantages of plain and telescopic sights. After this Halley for some time travelled on the Continent, and on his return to England devoted himself entirely to scientific pursuits. The fruits of his leisure soon began to appear in the multitude of treatises which he published from time to time in every department of the mathematical and physical sciences. The most important of those connected with astronomy was his *Synopsis Astronomiae Cometicæ*—a work abounding in profound and original views, and which, in respect of theory, formed perhaps the most remarkable accession to the science that had been made since the time of Kepler. In this work he revived an ancient opinion, that the comets belong to the solar system, and move in very eccentric orbits round the sun, returning after stated but long intervals. He also ventured to predict that the comet of 1681 would again return to its perihelion in 1759,—the first prediction of the kind that was verified. In 1720 Dr Halley was appointed to succeed Flamsteed in the Royal Observatory; and though now in the 64th year of his age, he undertook, with a view to improve the lunar theory, to observe the moon through a whole revolution of her nodes, erroneously supposing, that after such a revolution the errors of the tables would again appear in the same order. He was the first who, by a comparison of ancient and modern observations, remarked the acceleration of the mean motion of the moon, and thus called the attention of mathematicians to an important and curious phenomenon, the physical cause of which was at length detected by the powerful analysis of Laplace. He was also the first who pointed out the secular inequalities of Jupiter and Saturn, occasioned by their mutual perturbations,—a theory that formed the subject of several profound memoirs of Euler and Lagrange, and for the complete development of which astronomy is likewise indebted to Laplace. Besides these important discoveries in astronomy, the labours of Dr Halley also greatly contributed to the promotion of geometry and navigation. He undertook two long voyages, and traversed the Pacific Ocean to observe the deviations of the magnetic needle; and posterity will gratefully recollect that it was through his pressing solicitations that Newton consented to the publication of the *Principia*. In 1703 he succeeded Dr Wallis as professor of geometry at Oxford. He became secretary of the Royal Society in 1713, and died at Greenwich in 1742.

The discoveries of Bradley, who succeeded Halley as astronomer-royal, form a memorable epoch in the history of the science. This great astronomer was born at Sherborne in Gloucestershire in 1692, and acquired from his uncle, Mr Pound, an early taste for astronomical observation. He was destined for the church, and for some time held a curacy, which he resigned in 1721, on being appointed to succeed Keill as Savilian professor of astronomy at Oxford. His first essays indicated no extraordinary talent; but an opportunity having presented itself of engaging in more important researches, he embraced it with ardour; and by his sagacity and perseverance was conducted to two discoveries which have entirely changed the face of astronomy.

A singular motion of the polar star had been observed by Picard, of which, however, that astronomer could neither assign the law nor give any satisfactory explanation, ratione of He only remarked that the inequality was annual, and light amounted to about 40 seconds. Hooke, in 1674, a few years after the observations of Picard, imagined that he had discovered a parallax in some of the stars; and Flamsteed, following the ideas of Hooke, explained, by means of parallax, the minute changes of position which he had observed in Polaris and some circumpolar stars. Manfredi and Cassini demonstrated the error of Flamsteed, but were not more successful in their attempts to explain the motion in question. Samuel Molyneux conceived the idea of verifying all that had been said respecting the History, supposed parallaxes, and for this purpose commenced a series of observations at Kew, with an excellent 24 feet sector constructed by Graham. Bradley, who happened at that time to reside at Kew, took part in these observations, the result of which was, that the remarks of Picard were confirmed beyond the possibility of doubt. It was, however, abundantly evident that the apparent motions alluded to were not connected in any manner with parallax; it therefore became an object of the greatest interest to determine their physical cause, and assign their law and period. The first idea that occurred was to inquire whether they arose from a change of position in the earth's axis; but this supposition was found to be inadequate to the explanation of the phenomena. Molyneux having been in the mean time appointed a lord of the admiralty, the observations were discontinued at Kew; they were, however, shortly after resumed by Bradley at Wanstead, with a smaller but more convenient instrument; and after they had been continued several years, it was found that the star (γ draconis) on which they were principally made, appeared to describe annually a small ellipse, the transverse axis of which amounted to 40°. This was an important determination; for the ellipse afforded the means of computing at all times the aberration of any star whatever, whether in longitude, latitude, declination, or right ascension. Bradley also pointed out the physical cause of the aberration, and demonstrated that it resulted from the combination of the motion of light with the annual motion of the earth. This capital discovery was made in 1728.

Bradley, anxious to verify his ingenious theory, continued his observations, and soon felt the difficulty that had so much embarrassed Picard. The places of the stars, calculated according to his formula for the aberration, could not be reconciled with the observations. The errors continued to augment during nine years, after which they went on diminishing during the nine years following. This inequality, of which the period, like that of the nodes of the moon, was 18 years, was readily explained by supposing a slight oscillation of the earth's axis, occasioned by the action of the moon on the protuberant parts surrounding the equator of the terrestrial spheroid. After assiduously observing its effects during twenty years, Bradley found that the phenomena could be accurately represented by giving the pole of the equator a retrograde motion about its mean place in an ellipse whose axes are 18° and 16°, and completing its revolution in the period of 18 years. This result was communicated to the Royal Society in 1748. To these two grand discoveries of Bradley, the aberration and nutation, modern astronomy is wholly indebted for all its accuracy and precision; and, as Delambre remarks, they assure to their author a distinguished place, after Hipparchus and Kepler, above the astronomers of all ages and all countries.

Bradley was appointed astronomer royal in 1741, and from this time to the period of his death made an immense number of observations, which were presented by his heirs to the university of Oxford, on condition that they should forthwith be published. The first volume appeared only in 1798, edited by Dr Hornsby. The rest were committed to the care of the late Dr Abraham Robertson, and appeared in 1805. Dr Bradley was chosen a corresponding member of the Academy of Sciences in 1748. In 1752, twenty-four years after his great discovery of the aberration of light, he was admitted into the Royal Society. He died on the 13th of July 1762, in the 70th year of his age.

While England was deriving so much glory from the brilliant discoveries of Bradley, France produced a multitude of excellent astronomers, by whose successful labours every department of the science was signalized. Among these Lalande is pre-eminently distinguished, both by the variety and importance of his observations, and the indefatigable zeal with which, during twenty-two years, he prosecuted the most laborious researches. He commenced his astronomical career in 1739, by assisting Cassini de Thury (grandson of the first Cassini) in the verification of the measurement of the meridian through France. In 1751 he undertook a voyage to the Cape of Good Hope, the primary objects of which were to determine the sun's parallax, by means of observations on the parallaxes of Mars and Venus, while similar observations were made in Europe; and to form a catalogue of the southern circumpolar stars. No undertaking for the benefit of science was ever more successfully executed. In the course of a single year, Lalande, without assistance, observed upwards of ten thousand stars, situated between the tropic of Capricorn and the pole, and computed the places of 1942 of them; a labour which would scarcely be credited, if the details of his observations had not been published in the Catalogue Astrale Stelliferum, a work which was given to the world in 1763. Our admiration of the rapid execution of this vast undertaking will be increased, when we consider, that during the same time he measured a degree of the meridian, and made numerous observations on the moon simultaneous with those of Lalande, who observed at Berlin, in order to determine the moon's parallax, by means of direct observations made at the extremities of a meridional arc of upwards of 85 degrees. Before his return to Europe, he visited the isles of France and Bourbon, where he measured the length of the pendulum, and made numerous remarks on the natural and civil history of those countries. Astronomy is likewise indebted to Lalande for a table of refractions which he computed from a comparison of above 300 observations made at the Cape and at Paris. In 1757 he published his Astronomiae Fundamenta, in which he gave rules and tables for computing the apparent motions of the stars, which continued to be employed till Lambert supplied the corrections depending on the nutation, and Delambre those depending on the aberration. To defray the expense attending the publication of this important work, which he distributed in presents to the different observatories and astronomers in Europe, he submitted to the drudgery of calculating ephemerides during ten years. Lalande composed several elementary works for the use of the students in the college of Mazarin, where he occupied the chair of astronomy, and inserted a great number of memoirs in the volumes of the Academy of Sciences. This great astronomer, distinguished as much by the excellence of his moral qualities as his profound knowledge and indefatigable zeal, died suddenly in 1762.

The Royal Observatory of Paris continued under the direction of the family of Dominic Cassini during 120 years. James Cassini, the second of that name, is principally known by a work on the magnitude and figure of the earth, and his Elements of Astronomy. He seems not to have duly appreciated the new discoveries which were daily making around him. His Elements, published in 1740, contains no mention of the aberration; and he adopted the opinion that the earth is elongated instead of being flattened at the poles. His son, Cassini de Thury, was chiefly occupied with the meridian, and the geometrical survey of France. The last astronomer of the family, the Count de Cassini, was obliged to resign the observatory at the revolution.

The question of the figure of the earth furnished ample materials for the practical as well as the speculative measurement of the earth. The results of the measurement of the meridian by Cassini were at variance with the theories of Newton and Huygens; and the Academy of Sciences resolved on making a decisive experiment by the actual measurement of the lengths of two degrees, one at the equator, and another in as high a latitude as could be reached. In the year 1735, three astronomers, Godin, Bouguer, and La Condamine, were commissioned by the French government to accomplish the first of these objects in Peru; and the year following, Maupertuis, Clairaut, Camus, and Lemonnier, went to Lapland to execute the second under the polar circle. Notwithstanding the greater difficulties they had to contend with, the first party were the most successful; but the result of both operations established the compression of the earth at the poles. Bouguer published the details of the Peruvian measurement in an admirable work on the Figure of the Earth, in which he has also inserted an account of a great number of experiments made by him in the same country to determine the length of the seconds' pendulum, and the effects of the attraction of mountains on the plumb-line. Bouguer is likewise the author of an excellent treatise on light. This accomplished mathematician and experimenter did not adopt the Newtonian theory of gravitation, but he was the last apostle of the Cartesian philosophy in the Academy of Sciences.

It would greatly exceed the limits of this article to give even an abridged account of the numerous observers who, about this period, contributed to the improvement of every department of practical astronomy. We must therefore content ourselves with merely noticing the names of some of the most distinguished, leaving the details of their labours to be given in the biographical articles interspersed throughout the work.

Delisle formed a school of astronomy in Russia, and has left a method of computing the heliocentric places of the sun's spots, and of Mercury and Venus in their transits over the sun's disk, and likewise of determining, by means of the stereographic projection, the directions of their path when they enter and leave the disk. Lemonnier introduced the discoveries of Bradley into his Astronomical Institutions, and was the instructor of Lacaille and Lalande. He published a Histoire Celeste, containing a collection of observations from 1666 to 1685, and a number of other works and memoirs connected with astronomy. He made an immense number of observations, but their accuracy is far inferior to those of Bradley. Wargentin, secretary of the Academy of Sciences of Stockholm, devoted the whole of his life to the correction of the tables of the satellites of Jupiter. The theory of the satellites was not then far advanced; but when theory failed him, he profited by the remarks of others and by his own reflections, and endeavoured by repeated trials to find empirical equations capable of conciliating the tables with the best observations. By confining himself almost exclusively to this subject, he acquired a high reputation, and was ranked among the first astronomers of an epoch which abounds in great names. His tables of the satellites have, on account of their superior accuracy, been employed in determining the masses, and other elements, which serve as the basis of the analytical theories.

One of the most celebrated astronomers of the last century was Lalande. He commenced his early career by a set of lunar observations at Berlin, undertaken simultaneously with those of Lacaille at the Cape, for the purpose of determining the moon's horizontal parallax. On his return to Paris he was received, though only twenty-one years of age, into the Academy of Sciences; and on the resignation of Delisle was appointed professor of astronomy in the college of France. By his extraordinary zeal, indefatigable activity, and the care which he took to have his name constantly before the public, Lalande soon became one of the most distinguished men of his day; but his reputation, acquired in a great measure from attention to subjects which had only an ephemeral interest, and not through any permanent or fundamental additions to science, has already begun to wane; and his works, many of which are of considerable utility, seem to have fallen into unmerited neglect. His character as an astronomer is fairly and impartially summed up by Delambre in the following terms:—"If Lalande did not renew the foundations of astronomical science, like Copernicus and Kepler,—if he did not, like Bradley, immortalize himself by two brilliant discoveries,—if he was not so learned and accurate a theorist as Mayer,—if he was not to the same degree as Lacaille an exact, expert, scrupulous, industrious, and indefatigable observer and calculator,—if he had not the constancy to attach himself, like Wargentin, to a single object, in order to become the first in a particular department,—and if, in all these respects, he was only an astronomer of the second rank,—he was the first of all as a professor. No one ever did more to propagate the knowledge and love of astronomy. It was his object to be useful and celebrated; and he succeeded, through his labours, his activity, his credit, and his solicitations: by means of a most extensive correspondence he incessantly laboured for the benefit of science: he even endeavoured to serve it after his death, by founding a medal, which the Academy of Sciences adjudges annually to the astronomer who has made the most interesting observation, or written the most useful memoir." (Delambre, Astronomie du Moyen Age.)

Bradley was succeeded in the Greenwich Observatory by Dr Bliss, who died in the course of a few years after Lyne, born his appointment. Dr Bliss was in turn succeeded by Dr Maskelyne, the late astronomer royal, under whose care the observatory maintained the high character which it acquired from the immortal labours of his illustrious predecessors. Dr Maskelyne began his astronomical career in 1761, when he was appointed to observe the transit of Venus at the island of St Helena, and endeavour to verify the existence of a small parallax of the star Sirius, which seemed to be indicated by the observations of Lacaille at the Cape. Unfortunately the state of the weather prevented him from observing the transit; and his observations on Sirius were abandoned in consequence of the discovery of a defect in the zenith sector which he had carried out with him for the purpose of making the observations in question. The main objects of his voyage were thus frustrated; but some indirect advantages resulted from it, which compensated in some measure for the disappointment. The attention of Ramsden was called to the sector, and a better method of constructing these instruments was devised. At St Helena he made several interesting observations on the tides, the variation of the compass, the moon's horary parallaxes, &c. In going out and returning home, he paid particular attention to the different methods of finding the longitude at sea, and practised that which depends on observations of the lunar distances from known stars, taken with a Hadley's sextant, or other reflecting instrument. He also composed a set of rules for the use of the seamen, which he published on his return, first in the Philosophical Transactions, and afterwards in the British Mariner's Guide. In the year 1765 he was appointed astronomer royal, and soon after recommended to the Board of Longitude the general adoption in the navy of the lunar method of finding the Herschel was led to conclude that the whole solar system is in motion about some distant centre, and that its direction is at present towards the constellation Hercules—a conclusion which recent investigations have amply verified. His observations on nebulae and double stars opened up a new field of research, boundless in extent and interesting by reason of the variety of the objects it presents to the attention of the observer. The extraordinary activity with which he pursued his favourite occupations is attested by 67 memoirs communicated from time to time to the Royal Society. A great part of these, however, are filled with speculations of no value to astronomy; and his taste was rather to observe astronomical phenomena than to engage in computations, or the more arduous and essential, though less fascinating, labours through which the science can be really benefited. In the course of the following chapters we shall have frequent occasion to allude to his discoveries, and his ingenious speculations concerning the constitution of the sun and the sidereal heavens.

Few individuals have contributed so eminently to the perfection of modern astronomy as Delambre, the late perpetual secretary of the Academy of Sciences. The scientific life of this illustrious astronomer did not commence till he had attained his 40th year; but from that time till his death it was occupied by a series of unremitting labours to enlarge the boundaries, and ameliorate the practice and theory of the science. Associated with Mechain, he was employed during the troubles of the revolution in measuring the meridian from Dunkirk to Barcelona,—a labour which was prosecuted with admirable zeal in the face of innumerable difficulties, and even dangers of the most formidable kind. By an immense number of excellent observations he determined the constants which enter into the formulae deduced from theory by the profound researches of Lagrange and Laplace, and also formed a set of tables much more exact than any that had appeared before them. His *Astronomie Théorique et Pratique*, in three quarto volumes, contains the best rules and methods which have yet been devised for the guidance of the practical astronomer; and his *Histoire*, in six large volumes 4to, gives an account of every successive improvement which has been made in the science, and a full abstract of every work of celebrity which has been written respecting it, since the first rude observations of the Greeks to the end of the last century. It is invaluable to the historian, and will ever remain a proud monument of the profound learning and laborious research of its author.

The observatory which was established at Palermo about the year 1790, under the active superintendence of Piazzi, holds a distinguished rank among the similar institutions of Europe. Piazzi, born in 1746, took the habit of the religious order of the Theatins at Milan, and finished his noviciate in the convent of St Anthony. Among his preceptors he had the advantage of counting Tiraboschi, Beccaria, Le Scour, and Jacquier; and from these illustrious masters he speedily acquired a taste for mathematics and astronomy. After filling several professors' chairs in the colleges of the Jesuits at Rome and Ravenna, he was appointed in 1780 professor of the higher mathematics in the academy of Palermo. Here his first care was to reform the general system of education; and, by the alterations which he introduced, he contributed powerfully to dissipate the shades of ignorance, which, under the double influence of the Jesuits and the Inquisition, still lowered over the soil of Sicily. After having rendered this service to literature, he obtained from the prince of Caramanico, viceroy of the island, permission to found an observatory, and undertook a voyage to France and England, in order to provide the instruments necessary for the new establishment. Having procured a vertical circle, a transit, and some other instruments from Ramsden, he returned to Palermo and commenced his observations. His first care was to prepare a new catalogue of stars, the exact positions of which he justly considered as the basis of all true astronomy. In prosecuting this object he did not content himself with a single observation, but before he fixed the position of any star, observed it several times successively; and, by this laborious but accurate method, he constructed his first great catalogue of 6748 stars, which was crowned by the Academy of Sciences of France, and received with admiration by the astronomers of all countries. His constant practice of repeating his observations led to another brilliant result, the discovery of an eighth planet. On the 1st of January 1801, Piazzi, searching for the star 87 of the catalogue of Mayer, cursorily observed a small star of the eighth magnitude, between Aries and Taurus. On the following day he remarked that the star had changed its position, and accordingly supposed it to be a comet. He communicated his observations to Oriani, who, seeing that this luminous point had no nebulosity like the comets, and that it had been stationary and retrograded within comparatively small limits like the planets, computed its elements on the hypothesis of a circular orbit. He found that this hypothesis agreed with the observations, and other astronomers soon confirmed its accuracy. He gave the planet the name of Ceres Ferdinandea, in honour of Ferdinand, king of Naples, in whose dominions it was discovered, and who proposed to consecrate the event by a gold medal, struck with the effigy of the astronomer; but Piazzi, nobly preferring the interests of science to vain honours which could add nothing to his glory, requested that the money destined for this purpose should be employed in the purchase of an equatorial, which was still wanting to his observatory. In 1814 he published a new catalogue, extended to 7646 stars,—a splendid monument of indefatigable zeal and activity. He made an uninterrupted series of solstitial observations from 1791 to 1816, for the purpose of determining the obliquity of the ecliptic, which, compared with those of Bradley, Mayer, and Lacaille, in 1750, give a diminution of 44" in a year. Besides these labours, sufficient to occupy a life of ordinary industry, Piazzi composed a number of memoirs for the different societies of which he was a member, and was intrusted by the Neapolitan government with several important commissions respecting the public instruction and the regulation of weights and measures in Sicily. He died in 1826, after having bequeathed his library and all his instruments to the observatory at Palermo, and assigned a liberal annuity to be devoted to the instruction of young men who evince a decided taste for astronomy.

The discovery of Ceres led to that of three other little planets, circulating at nearly the same distance from the sun,—a circumstance unique in the construction of the solar system. On account of the smallness of the new planet, and the nebulosity by which it is surrounded, the difficulty of finding it after it had for some time ceased to be observed, was so considerable, that Dr Olbers of Bremen was induced to examine, with particular care, the configurations of all the small stars situated in the vicinity of its path, in order to have the means of detecting it at any time with greater facility. While engaged in making observations for this purpose, he discovered, on the 28th of March 1802, and nearly in the same place where he had before observed Ceres, another planet similar in size and appearance, to which he gave the name of Pallas. The extraordinary circumstance of the discovery of two planets having nearly the same mean distance, and performing their revolutions nearly in the same time, led Dr Olbers to imagine that Ceres and Pallas were fragments of a larger planet which had revolved in the same place, and been shattered by some external force or internal convulsion. The immediate consequence of this hypothesis was the probability of the existence of other fragments of the original planet, hitherto undiscovered; and that if such fragments existed, the planes of their orbits would pass through the points in which the orbits of Ceres and Pallas intersect each other. This bold idea acquired some probability from the subsequent discovery of two other planets in the very quarter of the heavens to which Dr Olbers had directed the attention of astronomers. Juno was discovered by M. Harding of Lilienthal, on the 2d of September 1804; and Vesta, by Dr Olbers himself, on the 29th of March 1807. Diligent observation did not for many years add to their number.

Astronomy is a science which borrows the aid of several improvements, with which its advancement is simultaneous. Instruments capable of appreciating, or measuring optical instruments, the exceedingly minute quantities about which the observer now concerns himself, could only be produced in a very advanced state of mechanics. In the accurate graduation of large instruments, our English artists have long maintained an unrivalled superiority. Graham, a celebrated watch-maker, united to great dexterity in the mechanical arts a decided taste for observation; and the extraordinary improvements which he effected in the art of dividing form an era in the history of practical astronomy. The sector used by Bradley, in the observations which led to the discovery of the nutation, was of his construction, and he was also the inventor of the first compensation pendulum. Sisson, who succeeded him, maintained in this department the honour and pre-eminence of England. Bird was originally a weaver in Durham, and first gave proof of his mechanical genius by dividing dials for the watch-makers in a manner far superior to what had been commonly practised. He was employed by Sisson in the division of mathematical instruments, and recommended by that artist to Graham, who instructed him in his methods. He constructed the 8 feet quadrants employed in the Greenwich and Paris observatories, and another of 6 feet for Mayer at the observatory of Göttingen. Ramsden invented a Ramsden machine for the more accurate division of instruments, on account of which he received a premium from the Board of Longitude. The mural quadrants of this artist were held in high estimation, and the transit instrument, sextant, and refracting micrometer, in passing through his hands, received considerable ameliorations. His astronomical instruments in general were considered the best that could be procured in Europe. Mr Troughton, who in his day stood the foremost of our British opticians, more than rivalled his predecessors. In the hands of this distinguished artist and astronomer, the division of instruments was carried to a degree of precision which at the time seemed incapable of being surpassed; while the great improvements he has introduced into the methods of constructing and mounting large instruments, and his ingenious inventions to elude natural obstacles, and guard against the accidental derangements from which it is impossible altogether to protect them, entitled him to the high place which he held by universal consent among the most eminent philosophers and original mechanicians of the age. The numerous circles and other instruments of his manufacture, whether in the hands of private individuals or deposited in the different public observatories, are considered still as the finest specimens of what art has yet accomplished for the advancement of astronomical science. (See Supplement to Part I. for accounts of Modern Instruments.)

Progress of Physical Astronomy.

Having now endeavoured to give an account of the labours of those astronomers who have principally contributed to make us acquainted with the state of the heavens, and the order and succession of the various phenomena they exhibit, we will conclude this part of the article by briefly adverting to the profound researches of some illustrious mathematicians who have developed the theory of Newton, and raised the fabric of physical astronomy to its present proud elevation.

Although the law of gravitation, as proposed by Newton, had from the first been admitted by all the most eminent astronomers of Britain, it was for a long time either opposed or neglected on the Continent. In fact, great improvements were required both in analysis and mechanics before it admitted of other applications than had been made by its great author, or could be regarded as anything more than a plausible hypothesis. Newton demonstrated, that if two bodies only were projected in space, mutually attracting each other with forces proportional directly to their masses, and inversely to the squares of their distance, they would each accurately describe an ellipse round the common centre of gravity; and the spaces described by the straight line joining that centre and the moving body, would be proportional to the time of description, according to the second law of Kepler. But when it is attempted to apply Newton's law to the case of the solar system, great difficulties immediately present themselves. Any one planet in the system is not only attracted by the sun, but also, though in a greatly smaller degree, by all the other planets, in consequence of which it is compelled to deviate from the elliptic path which it would pursue in virtue of the sun's attraction alone. Now, the calculation of the effects of this disturbing force was the problem which geometers had to resolve. In its most general form it greatly transcends the power of analysis; but there are particular cases of it, and those too the cases presented by nature, in which, by reason of certain limitations in the conditions, it is possible to obtain an approximate solution to any required degree of exactness. For example, the Sun, Moon, and Earth form in a manner a system by themselves, which is very slightly affected by the aggregate attractions of the other planets. In the same way the Sun, Jupiter, and Saturn form another system, in which the motions are very little influenced by the action of any other body. In these two cases, then, the number of bodies to be taken into consideration is only three; and in this restricted form, the problem, celebrated in the history of analysis under the denomination of the Problem of the Three Bodies, is susceptible of being treated mathematically. With the hope of ameliorating the lunar tables, and of completing the investigations which Newton had commenced in the Principia, three distinguished geometers, Clairaut, D'Alembert, and Euler, about the middle of the last century, undertook, simultaneously, and without the knowledge of each other, the investigation of the problem of the three bodies, and commenced that series of brilliant discoveries which it is the glory of our own times to have seen completed.

Clairaut's solution of the problem of the three bodies was presented to the Academy of Sciences in 1747, and was applied to the case of the moon. From this solution he deduced with great facility, not only the inequality of the variation, which Newton had obtained by a more complicated, though at the same time a very ingenious method, but also the erection, the annual equation, and many other inequalities which Newton had not succeeded in connecting with his theory. It happened, however, curiously enough, that in the calculation of one effect of the disturbing force, namely, the progression of the moon's apogee, Clairaut was led into an error which produced a result that threatened to overturn the system of gravitation. The error consisted in the omission of some of the terms of the series expressing the quantity in question, which he wrongly supposed to have only an insensible value; and by reason of this omission, his first approximation gave only half of the observed progressive motion of the apogee. As this result was confirmed by D'Alembert and Euler, who had both fallen into the same error, it seemed to follow, as a necessary consequence, either that the phenomenon depended on some other cause than the disturbing force of the sun, or that the law of gravity was not exactly proportional to the inverse square of the distance. The triumph which this result gave to the Cartesians was not of long duration. Clairaut soon perceived the cause of his error; and by repeating the process, and carrying the approximations farther, he found the computed to agree exactly with the observed progression,—a result which had the effect of dissipating for ever all doubt respecting the law of gravity. The researches of Clairaut were followed by a set of lunar tables, much more correct than any which had been previously computed.

The return of the comet of 1682, which Halley had predicted for the end of 1758, or beginning of 1759, afforded an excellent opportunity for putting to the test both the theory of gravity and the power of the new calculus. Clairaut applied his solution of the problem of the three bodies to the perturbations which this comet sustained from Jupiter and Saturn, and, after calculations of enormous labour, announced to the Academy of Sciences, in November 1758, that the comet would return in the beginning of the following year, and pass through its perihelion about the 15th of April. It returned according to the prediction, but passed its perihelion on the 13th of March. The correction of an error of computation reduced the difference to nineteen days; and if Clairaut had been aware of the existence of the planet Uranus, he might have come still nearer the truth.

Besides these important researches on the system of the world, Clairaut composed an admirable little treatise on the figure of the earth, in which he gave the differential equations, till then unknown, of the equilibrium of fluids, whether homogeneous or heterogeneous, supposing an attractive force, following any law whatever, to exist among the molecules. He applied these equations to the earth; demonstrated that the elliptic figure satisfies the conditions of equilibrium; assigned the ellipticity of the different strata of which the earth may be supposed to be formed, together with the law of gravitation at the exterior surface. He likewise discovered the important theorem which establishes a relation between the oblateness of the terrestrial spheroid and the increase of gravitation towards the poles, on every supposition which can be imagined relative to the interior construction of the earth. By means of this theorem the ellipticity of the spheroid is deduced from observations of the lengths of the seconds pendulum at different points of the earth's surface.

D'Alembert, as has already been mentioned, presented a solution of the problem of the three bodies to the Academy of Sciences at the same time with Clairaut. In the year 1749 he published his treatise on the precession of the equinoxes,—a work remarkable in the history of analysis and mechanics. By means of his newly invented calculus of Partial Differences, and the discovery of a fertile principle in dynamics, he determined from theory the rate of the precession, which is nearly 50° in a year. He also determined the nutation of the earth's axis, which had been discovered by Bradley, and assigned the ratio of the axes of the small ellipse which the true pole of the earth describes around its mean place, in the same time in which the nodes of the lunar orbit complete a revolution. The solution of this problem led to the determination of the ratio of the attractive forces of the sun and moon, which D'Alembert found to be that of seven to three very nearly; whence he inferred that the mass of the earth is 70 times greater than that of the moon. He proved likewise that the precession and nutation are the same in every hypothesis concerning the interior constitution of the earth. In 1754 he published the first two volumes of his Researches on the System of the World. In this work he applied the formulae by which he had calculated the motions of the moon to the motions of the planets disturbed by their mutual attraction, and pointed out the simplest method of determining the perturbations of the motions of a planet occasioned by the action of its own satellites. D'Alembert also treated the subject of the figure of the earth in a much more general manner than had been done by Clairaut, who had confined his investigations to the case of a spheroid of revolution. He determined the attraction of a spheroid of small eccentricity, whose surface can be represented by an algebraic equation of any order whatever, and even supposing the spheroid to be composed of strata of different densities.

The works of D'Alembert, which are extremely numerous, abound generally in profound and original views, and contributed greatly to the advancement of the physical and mathematical sciences; but it is to be regretted that they are very frequently deficient in that perspicuity and order so necessary in abstruse speculations, and that the course of his reasoning can be followed with difficulty when he descends into the detail of analytical operations. He had a horror of calculation, and delighted in general considerations and speculations which frequently turned on matters of pure curiosity.

The first memoir of Euler on the planetary perturbations was transmitted to the secretary of the Academy of Sciences in July 1747, some months before Clairaut and D'Alembert had communicated their solutions of the problem of the three bodies, and it carried off the prize which the academy had proposed for the analytical theory of the motions of Jupiter and Saturn. In this memoir Euler gave the differential equations of the elements of the disturbed planet, but suppressed the analysis by which he had been conducted to them. This analysis, however, he subsequently expanded in two memoirs, the first of which appeared in the Berlin Memoirs in 1749, and the second in those of Petersburg in 1750. Of these supplementary memoirs the first is remarkable on several accounts. It contains the first example of a method which has been fruitful of important consequences—namely, that of the variation of the arbitrary constants in differential equations, and the development of the radical quantity which expresses the distance between two planets in a series of angles, multiples of the elongations. The expressions which he gave for the several terms of this series were simple and elegant; and he demonstrated a curious relation subsisting among any three consecutive terms, by means of which all the terms of the series may be calculated from the first two. He was thus enabled to develop the perturbing forces in terms of the sines and cosines of angles increasing with the time, and thereby to surmount a very great analytical difficulty. Notwithstanding, however, the great merit of Euler's memoir, several of the formulae expressing the secular and periodic inequalities were found to be inaccurate; and in order to procure a correction of these errors, and give greater perfection to so important a theory, the academy again proposed the same subject for the prize of 1752. This prize was also carried off by Euler. In the memoir which he presented on this occasion, he considered simultaneously the motions of Jupiter and Saturn, and determined, in the first instance, the amount of their various inequalities, independently of the consideration of the eccentricities of their orbits. Pushing the approximations farther, and having regard to the inequalities depending on the eccentricities, he arrived at a most important result relative to the periodic nature of the inequalities occasioned by the mutual perturbations of the planets; which laid the foundation of the subsequent discovery by Lagrange and Laplace of the permanent stability of the planetary system. He demonstrated that the eccentricities and places of the aphelia of Jupiter and Saturn are subject to constant variation, confined, however, within certain fixed limits, which it never exceeds; and he computed that the elements of the orbits of the two planets recover their original values after a lapse of about 30,000 years.

In the year 1756 the Academy of Sciences crowned a third memoir of Euler on the same subject as the two former, namely, the inequalities of the motions of the planets produced by their reciprocal attractions. This memoir, analytically considered, is also of great value. The method which he followed and illustrated has since been generally adopted in researches of the same nature, and consists in regarding as variable, in consequence of the disturbing forces, the six elements of the elliptic motion, viz. 1st, the greater axis of the orbit, which, by the law of Kepler, gives the ratio of the differential of the mean longitude to the element of the time; 2d, the epoch of this longitude; 3d, the eccentricity of the orbit; 4th, the motion of the aphelion; 5th, the inclination of the orbit to a given fixed plane; and, 6th, the longitude of the node. By considering separately the variations introduced into each of these elements by the disturbing forces, Euler obtained some important results; but even in this memoir his theory was not rendered complete. He did not consider the variation of the epoch; and the expression which he gave for the motion of the aphelion did not include that part of it which depends on the ratio of the eccentricities of the orbits of the disturbed and disturbing planet. Besides, the present memoir, like the two former, contained several errors of computation, which, by leading to results known to be wrong, probably prevented the author himself from being aware of the full value of the ingenious methods of procedure which he had exposed. Euler concluded this important memoir by making an extended application of his formulae to the orbit of the earth as disturbed by the action of the planets. From some probable suppositions, first employed by Newton, relative to the ratios of the masses of the planets to that of the sun, he determined the variation of the obliquity of the ecliptic at 48° in a century,—a result which agrees well with observation. By this determination the secular variation of the obliquity of the ecliptic, which had been regarded by Lahire, Lemonnier, D'Alembert, and other eminent astronomers, as uncertain, was placed beyond doubt. The three memoirs which we have mentioned contain the principal part of Euler's labours on the perturbations; but physical astronomy is indebted to him for many other researches. He gave a solution of the problem of the precession of the equinoxes, and made several important steps in the lunar theory, with which he seems to have History, occupied himself before he undertook the investigation of the planetary perturbations. In the year 1772, when entirely blind, he directed his son, Albert Euler, and two illustrious pupils, Krafft and Lexell, in the composition of a work of enormous labour on the same subject, which was undertaken with a view to discover the cause of the moon's acceleration. This work was concluded with a set of lunar tables deduced entirely from theory; but they were found to be far inferior to those of Mayer, and in some respects hardly equal to those of Clairaut.

The labours of Euler form an epoch in the history of the mathematical sciences. From the arithmetic of sines, and the simplest formulae of trigonometry up to the variation of the arbitrary constants of differential equations, there is hardly an analytical theory which has not received extension or improvement from the creative powers of his great mind. The transactions of the Berlin and Petersburg Academies are filled with his inestimable productions; and if fecundity were not itself one of the attributes of genius, the number of the profound and laborious researches in which he was engaged would appear altogether incredible.

The first theory of Euler formed the basis of the excellent lunar tables which were calculated by Tobias Mayer, and first published in the Memoirs of the Academy of Göttingen in 1753. Mayer was a skilful astronomer, and determined the co-efficients of the arguments of the different lunar inequalities from his own observations. He continued to correct and improve his tables till the time of his death, which happened in 1762, when a copy of them, containing his last corrections, was presented by his widow to the Board of Longitude in London. Bradley ascertained their accuracy by comparing them with a great number of his own observations, and made so favourable a report concerning them, that the Board of Longitude presented the widow of Mayer with a gratuity of L3000. They were printed along with the author's lunar theory in 1765. Subsequently, the Board of Longitude directed Mason, who had been assistant to Bradley, to revise them, under the superintendence of Dr Maskelyne. Mason compared them with about 1200 of Bradley's observations; he corrected the co-efficients of Mayer, and introduced some new equations which had been indicated by that astronomer, but which he had considered as too uncertain, or of too small a value, to render it necessary to load his tables with them. Mayer's tables, thus corrected, were published in 1784, and for a long time continued to be the most accurate that had appeared.

The solution of the problem of the three bodies by Clairaut, D'Alembert, and Euler, gave rise to many other important works relative to the theory of the moon, into the merits of which, however, our limits will not permit us to enter. Thomas Simpson, Walmsley, Frisi, Lambert, Schulze, and Matthew Stewart, treated the subject with more or less success; but the complete explication of the theory of the lunar and planetary perturbations was reserved for two mathematicians, whose discoveries perfected the theory of gravitation, and explained the last inequalities which remained to be accounted for in the celestial motions,—we mean Lagrange and Laplace.

In the year 1764, the Academy of Sciences of Paris, which had so successfully promoted the great efforts that had already been made to perfect the theory of attraction, proposed for the subject of a prize the theory of the libration of the moon. This was considered as an appeal to the genius of Lagrange, whose splendid talents had suddenly shone forth in two profound papers on the theory of sound, inserted among the Memoirs of the Turin Academy, and in which the calculus of variations was first explained and made use of. Lagrange had the honour of carrying off the prize; but although he treated the subject in a manner altogether new, and with extraordinary analytical skill, he did not on this occasion arrive at a complete solution of the problem. In 1766 he obtained another prize for a theory of Jupiter's satellites. In the admirable memoir which Lagrange presented to the academy on this subject, he included in the differential equations of the disturbed motion of a satellite, the attracting force of the sun, as well as of all the other satellites, and thus, in fact, had to consider a problem of six bodies. His analysis of this problem is remarkable, inasmuch as it contained the first general method which was given for determining the variations which the mutual attractions of the satellites produce in the forms and positions of their orbits, and pointed out the route which has since been so successfully followed in the treatment of similar questions.

Of all the grand discoveries by which the name of Lagrange has been immortalized, the most remarkable is that of the invariability of the mean distances of the planets from the sun. We have already mentioned that Euler had perceived that the inequalities of Jupiter and Saturn, in consequence of their mutual actions, are ultimately compensated, though after a very long period. In prosecuting this subject, which Euler had left imperfect, Laplace had discovered that, on neglecting the fourth powers in the expressions of the eccentricities and inclinations of the orbits, and the squares of the disturbing masses, the mean motions of the planets, and their mean distances from the sun, are invariable. In a short memoir of 14 pages, which appeared among those of the Berlin Academy for 1776, Lagrange demonstrated generally, and by a very simple and luminous analysis, that whatever powers of the eccentricities and inclinations are included in the calculation of the perturbations, no secular inequality, or term proportional to the time, can possibly enter into the expression of the greater axis of the orbit, or, consequently, into the mean motion connected with it by the third law of Kepler. From this conclusion, which is a necessary consequence of the peculiar conditions of the planetary system, it results that all the changes to which the orbits of the planets are subject in consequence of their reciprocal gravitation, are periodic, and that the system contains within itself no principle of destruction, but is calculated to endure for ever.

In 1780 Lagrange undertook a second time the subject of the moon's libration; and it is to the memoir which he now presented to the Berlin Academy that we must look for the complete and rigorous solution of this difficult problem, which had not been resolved before in a satisfactory manner, either on the footing of analysis or observation. In the same year he obtained the prize of the Academy of Sciences on the subject of the perturbations of comets. In 1781 he published, in the Berlin Memoirs, the first of a series of five papers on the secular and periodic inequalities of the planets, which together formed by far the most important work that had yet appeared on Physical Astronomy since the publication of the Principia. This series did not, properly speaking, contain any new discovery; but it embodied and brought into one view all the results and peculiar analytical methods which had appeared in his former memoirs, and contained the germs of all the happy ideas which he afterwards developed in the Mécanique Analytique.

On account of the brilliant discoveries and important labours which we have thus briefly noticed, Lagrange must be considered as one of the most successful of those illustrious individuals who have undertaken to perfect the theory of Newton, and pursue the principle of gravi- With the name of Lagrange is associated that of Laplace, whose rival labours divided the admiration of the scientific world during half a century. Like Newton and Lagrange, Laplace raised himself at an early age to the very highest rank in science. Before completing his 24th year, he had signalized himself by the capital discovery of the invariability of the mean distances of the planets from the sun, on an hypothesis restricted, indeed, but which, as we have already mentioned, was afterwards generalized by Lagrange. About the same time he was admitted into the Academy of Sciences, and thenceforward devoted himself to the development of the laws which regulate the system of the world, and to the composition of a series of memoirs on the most important subjects connected with astronomy and analysis. His researches embraced the whole theory of gravitation; and he had the high honour of perfecting what had been left incomplete by his predecessors.

Among the numerous inequalities which affect the motion of the moon, one still remained which no philosopher as yet had been able to explain. This was the acceleration of the mean lunar motion, which had been first suspected by Dr. Halley, from a comparison of the ancient Babylonian observations, recorded by Hipparchus, with those of Albategnius and the moderns. The existence of the acceleration had been confirmed by Dunthorne and Mayer, and its quantity assigned at 10° in a century, but the cause of it remained doubtful. Lagrange demonstrated that it could not be occasioned by any peculiarity in the form of the earth; Bossut ascribed it to the resistance of the medium in which he supposed the moon to move; and Laplace himself at first explained it on the supposition that gravity is not transmitted from one body to another instantaneously, but successively in the manner of sound or light. Having afterwards remarked, however, in the course of his researches on Jupiter's satellites, that the secular variation of the eccentricity of the orbit of Jupiter occasions a secular variation of the mean motions of the satellites, he hastened to transfer this result to the moon, and had the satisfaction to find that the acceleration observed by astronomers is occasioned by the secular variation of the eccentricity of the terrestrial orbit. This was the last celestial phenomenon which remained to be accounted for on the principle of gravitation.

Another discovery relative to the constitution of the planetary system, which does infinite honour to the sagacity of Laplace, is the cause of the secular inequalities indicated by ancient and modern observations in the mean motions of Jupiter and Saturn. On examining the differential equations of the motions of these planets, Laplace remarked, that as their mean motions are nearly commensurable (five times the mean motion of Saturn being nearly equal to twice that of Jupiter), those terms of which the arguments are five times the mean longitude of Saturn, minus twice that of Jupiter, may become very sensible by integration, although multiplied by the cubes and products of three dimensions of the eccentricities and inclinations of the orbits. The result of a laborious calculation confirmed his conjecture, and showed him that in the mean motion of Saturn there existed a great inequality, amounting at its maximum to $48'2''3$, and of which the period is 920 years; and that in the case of Jupiter there exists a corresponding inequality of nearly the same period, of which the maximum value is $19'46''$, but which is affected by a contrary sign, that is to say, diminishes while the first increases, and vice versa. He also perceived that the magnitude of the co-efficients of these inequalities, and the duration of their periods, are not always the same, but participate in the secular variations of the elements of the orbits.

The theory of the figures of the planets, scarcely less interesting than that of their motions, was also greatly advanced by the researches of Laplace. He confirmed the results of Clairaut, Maclaurin, and D'Alembert, relative to the figure of the earth, and treated the question in a much more general way than had been done by those three great mathematicians. From two lunar inequalities depending on the non-sphericity of the earth, he determined the ellipticity of the meridian to be $\frac{1}{357}$ very nearly.

the Principia, explained the cause of the tides, phenomena of the tides, and laid the foundations of a theory which was prosecuted and extended by Daniel Bernoulli, Maclaurin, Euler, and D'Alembert; but as no one of these geometers had taken into account the effects of the rotatory motion of the earth, the subject was in a great measure new when it was taken up by Laplace in 1774. Aided by D'Alembert's recent discovery of the calculus of Partial Differences, and by an improved theory of hydrodynamics, he succeeded in obtaining the differential equations of the motion of the fluids which surround the earth, having regard to all the forces by which these motions are produced or modified, and published them in the Memoirs of the Academy in 1775. By a careful examination of these equations, he was led to the curious remark, that the differences between the heights of two consecutive tides about the time of the solstices, as indicated by Newton's theory, are not owing, as Newton and his successors had supposed, to the inertia of the waters of the ocean, but depend on a totally different cause, namely, the law of the depth of the sea, and that it would disappear entirely if the sea were of a uniform and constant depth. He also arrived at the important conclusion, that the fluidity of the sea has no influence on the motions of the terrestrial axis, which are exactly the same as they would be if the sea formed a solid mass with the earth. The same analysis conducted him to the knowledge of the conditions necessary to insure the permanent equilibrium of the waters of the ocean. He found that if the mean density of the earth exceeds that of the sea, the fluid, deranged by any causes whatever from its state of equilibrium, will never depart from that state but by very small quantities. It follows from this, that, since the mean density of the earth is known to be about five times greater than that of the sea, the great changes which have taken place in the relative situation of the waters and dry land must be referred to other causes than the instability of the equilibrium of the ocean.

Closely connected with the problem of the tides is that of the precession of the equinoxes, which also received similar improvements in passing through the hands of Laplace. He demonstrated, as has just been mentioned, that the fluidity of the sea has no influence on the phenomena of precession and nutation. He considered some of the effects of the oblate figure of the earth which had not been attended to by D'Alembert, and showed that the annual variation of the precession causes a corresponding variation in the length of the tropical year, which at present is about 9 or 10 seconds shorter than it was in the time of Hipparchus. He proved that the secular inequa- lities of the motions of the earth and moon have no sensible effect in displacing the axis of the earth's rotation; and he determined the nutation of the lunar orbit corresponding to the nutation of the terrestrial equator.

Physical astronomy is also indebted to Laplace for a complete theory of the system of Jupiter's satellites, from which Delambre constructed a set of tables which represent the motions of these bodies with all desirable accuracy. And when to these numerous and most important researches we add the mathematical theories of molecular attraction, and the propagation of sound, together with many great improvements in analysis,—and reflect, besides, that he is the author of the Mécanique Céleste, the Système du Monde, and the Théorie des Probabilités,—we shall not hesitate to rank him next to Newton among the greatest benefactors of the mathematical and physical sciences.

By the brilliant discoveries of Laplace, the analytical solution of the great problem of physical astronomy was completed. The principle of gravity, which had been discovered by Newton to confine the moon and the planets to their respective orbits, was shown to occasion every apparent irregularity, however minute, in the motions of the planets and satellites; and those very irregularities which were at first brought forward as objections to the hypothesis have been ultimately found to afford the most triumphant proofs of its accuracy, and have placed the truth of the Newtonian law beyond the reach of all future cavil. Such is the state to which analysis has now attained, that the geometer embraces in his formulæ every circumstance which affects the motions or positions of the different bodies of the planetary system; and the conditions of that system being made known to him at any given instant of time, he can determine its conditions at any other instant in the past or future duration of the world. He ascends to remote ages to compare the results of his theories with the most ancient observations; he passes on to ages yet to come, and predicts changes which the lapse of centuries will hardly be sufficient to render sensible to the observer. But notwithstanding the proud elevation to which the theory of astronomy has been raised, it is still far from having reached the limit beyond which further refinement becomes superfluous. The masses of the planets, and some other elements, remain to be determined with still greater precision, by a diligent comparison of the analytical formulæ with good observations; and the labours of the geometer may still be beneficially employed in giving greater simplicity to the calculus, or in extending its power over subjects which have hitherto eluded its grasp. The recent discovery of several periodic comets completing their revolutions in comparatively short intervals of time, opens up an interesting field for speculation and research, and will doubtless be the means of throwing light over some curious and as yet very obscure, points, respecting the appearances, motions, and physical constitution of those strange bodies.

In the other departments of the science, also, numerous questions still remain to be discussed, the solution of which will occupy and reward the future labours of the astronomer, and in which much progress has been made during the present century, by means of the powerful instruments now employed at the great observatories of every civilized country, and the improved methods of analysis brought to bear upon the results of observation. The curious phenomena of double and multiple stars, some of which appear to form connected systems of bodies revolving about one another, or a common centre of motion,—the variable stars,—the proper motions of the stars,—the translation of the solar system in space,—the progressive condensation of nebulae,—are subjects still in a great measure new; for it is only of late years that observers have begun to direct the requisite attention towards them, or indeed have been in possession of instruments of sufficient power and delicacy to observe and measure the minute changes which take place beyond the boundaries of our own system.

(T.G.)

**Supplement to Part I.—1853.**

The discoveries in astronomy during the present century have been so brilliant and numerous, and the progress in every department is so rapid, and involves so many details, that we should despair of adequately representing even the outlines of the leading features in such a way as to benefit the reader within the compass of the few pages which can be allotted to the extension of the history which has already been given. We propose, instead of attempting this, to give as briefly as possible an account of the journals, institutions, and observatories which have been chiefly instrumental in producing this rapid progress of the science, and especially to draw the attention of the English student to the works of those great German astronomers, with which he must make himself conversant if he would ever desire to understand the nature of the advances which have been made, and which are absolutely indispensable if he hope to add anything to the fabric which has been erected. The supplement thus given will familiarize the reader with the sources of the various discoveries and investigations which he will meet with in the subsequent parts of the article; and there is scarcely a subject of importance in any department of astronomy which will not receive some elucidation.

**Account of Serial Works or Journals, Institutions, and Observatories which have chiefly contributed to the improvement of Astronomy in the nineteenth century.**

The history of astronomy has been given with sufficient detail to the beginning of the present century; and, in conformity with the plan already indicated, we propose to exhibit the sources of its rapid advancement since that time, by giving short notices of the principal publications and institutions which have mainly contributed to its progress.

Of the serial works in question, the first to be mentioned is Zach's Monatliche Correspondenz, which, commencing with the year 1800, was, till 1813, the leading astronomical journal in Europe. The basis of this work was one conducted previously by Zach, entitled Allgemeine Geographische Ephemeriden. This work was devoted chiefly to geographical researches; but Zach was induced to alter his plan, and to commence, on a more extended scale, the celebrated Correspondenz, or, as it was entitled by its able editor, Monatliche Correspondenz zur Förderung der Erd und Himmel's Kunde. Soon after its commencement (that is at the beginning of 1801), Piazzi discovered the planet Ceres, the complete history of which discovery, as well as of the discoveries of Juno, Pallas, and Vesta, must be looked for in its pages.

At the end of 1813 this journal was discontinued, having been really conducted from the year 1807 by Lindenaus, though Zach was still the responsible editor. Its abrupt termination was due to the French war, in which Lindenaus felt himself called upon to take part on the staff of the Duke of Weimar. This war produced a suspension of many of the literary and scientific works of Germany; and it was not till the beginning of 1816 that a new journal was commenced, under Lindenaus's direction, bearing the title of Zeitschrift für Astronomie und verwandte Wissenschaften. This work, in which Lindenaus was assisted by Bohnenberger, differed from its predecessor chiefly in being of a more strictly astronomical character, each number consisting of articles comprehended under one or another of the three divisions, Original Treatises on Astronomical Subjects, Critical Notices of Astronomical Works, and Correspondence.

One of the most valuable portions of this work, which was not carried on beyond the year 1818, is the elaborate introduction by Lindeman. It contains a long historical summary of the progress of astronomy during the period of suspension of Zach's Correspondenz from 1813 to 1816, thus supplying a gap in the continuous history of the astronomy of the present century.

Amongst the most remarkable of the contributions to the Zeitschrift, we may mention the following:

In vol. I., a paper by Gauss on the Theory of Certainty in Observations; also two or three papers by Bohnenberger on the Precessional Motion of Stars for long Intervals of Time; and a complete list of the works of Lagrange.

In vol. ii., amongst other interesting papers and letters, an essay by Littrow, On the Correction to the Mean Refraction due to the Thermometer; A Catalogue of the Arabic Names of the Stars, by Zach; Observations by Bessel, especially of Right Ascension, for the Determination of the Parallax of 61 Cygni; A History of the Greenwich Observatory by Lindeman; and an Investigation of the Orbit of the Comet of Pons.

In vol. iii., a paper by Zach, On Tobias Mayer's Observations of Uranus; and one by Littrow, On the Correction of the Solar Tables.

In vol. iv., Westphal On the Periods of Variable Stars; Plana On the Changes in the Places of the Fixed Stars, produced by the Secular Motion of the Plane of the Ecliptic; A letter from Struve On the Commencement of his Operations at the Observatory at Dorpat.

In vol. vi., the most important article is by Encke, On the most probable Orbit of the Comet of 1850. Other works worthy of notice are.—On the Accurate Computation of Nutation and Aberration, by Bessel. On the General Formula for Computation of the Corrections of Six Elements, according to the Method of Least Squares, by Plana.

The Zeitschrift was brought suddenly to a conclusion with the sixth volume, at the end of the year 1818.

The epoch of this journal was one of very great importance to astronomy. Old instruments and old methods were being superseded by new ones. Telescopes of greater power were mounted equatorially in several observatories; and meridian instruments of improved construction were erected. At Greenwich, Trigonometrical mural circle and transit instrument had been erected, and a series of excellent observations had been begun under Pond's direction. On the continent, Reichenbach's meridian circles were being introduced into every observatory; and the first series of the Königsberg observations, made by Bessel with an instrument of this class, had been published.

But above all, the incomparable Fundamenta Astronomiae of Bessel was published at this time, giving the accurate results of Bradley's star observations, and new values of every element necessary for their reduction, by investigations based on the observations themselves.

The Tabula Regiomontanae, or synopsis of all the fundamental quantities needed by the astronomer, which is still indeed an indispensable text book, was published by Bessel in 1830.

Another serial work which must be mentioned, is Zach's Correspondance Astronomique, Geographique, Hydrographique, et Statistique, of which the first letter is dated June 1818. This was published in the French language, and was issued from Genoa where Zach was residing. The series terminated with the thirteenth volume in 1825.

In connection with Zach's journals, it may be mentioned, that a complete index to the Monatliche Correspondenz was compiled recently by Dr Galle, and published in 1848, preceded by a short memoir of the Baron de Zach.

The journal which succeeded the Zeitschrift, was the celebrated Astronomische Nachrichten, which is continued at the present time with unremitting utility. It was commenced in 1821 at Altona, under the editorship of Professor Schumacher. The abilities and untiring zeal of its editor, who continued his services till the time of his death in 1850, were mainly instrumental in raising the Nachrichten to the high rank which it possesses.

For a biographical account of Schumacher, the reader may consult the eleventh volume of the Notices of the Royal Astronomical Society. It will suffice here to mention his principal works. They are, 1. A Collection of Astronomical Tables; 2. Ephemerides of the bright planets from 1820 to 1829, and of the distances of the bright planets from the moon, from 1822 to 1831, inclusive; 3. His Astronomical Jahrbuch, from 1836 to 1844, which, in addition to a variety of useful tables, contains numerous popular scientific views and summaries by the greatest geometers of the continent.

In 1829, the Royal Astronomical Society of London awarded to Schumacher their gold medal for the Nachrichten; and, in illustration of the acknowledged character of the work, we quote the following extract from the eulogium pronounced by Sir J. Herschel on that occasion:—"Amongst those numerous and talented individuals throughout the continent and in England, who are attached to astronomy professionally, or from love to the science, the Astronomische Nachrichten of Professor Schumacher establishes a point of concurrence—a complete bond of reunion. We have there a theatre of discussion of whatever is most new and refined in the theory and practice of astronomy; the utmost delicacies of computation and scrupulous investigation of instrumental errors are given by those most competent to reply and judge of them. To its pages, observations of every kind find their way, especially those which depend for their utility on corresponding observations, or which lose their interest or importance by long suppression. Not a comet appears, but there we find its elements handed in from all quarters with wondrous rapidity. Occultations, moon-eliminating observations, computations of longitudes and latitudes, disquisitions on practical points, descriptions, advertisements, and prices of instruments,—in a word, everything which can awaken and keep alive attention to the science,—everything that can facilitate the contact of mind with mind."

The Astronomische Nachrichten, in fact, contains the history of astronomical science for the last thirty years; it is the necessary complement and commentary of almost every astronomical publication of value, and is the complete repertory of modern theory and practice, not of Europe, but of the civilized world."

This excellent serial still flourishes under the able editorship of Dr Petersen, and continues to be the great medium of communication for astronomers.

A serial work of the same character as the Nachrichten, and performing similar services for the science of astronomy in America, has lately appeared under the editorship of Mr B. A. Gould of Cambridge University, Massachusetts. The first volume was completed in April 1851, and the work has gone on uninterruptedly to the present time.

In proceeding to give some account of the principal ephemerides, we shall confine ourselves chiefly to the French Connaissance des Temps; the English Nautical Almanac; the Berlin Jahrbuch; the Effemeridi di Milano; and the American Ephemeris and Nautical Almanac, of which the first volume for 1855 has recently been published.

The series of the Connaissance des Temps commenced in the seventeenth century, under the superintendence of Picard. Lalande in the following century introduced great changes and improvements, and the work remains substantially as he left it. In both the ancient and the modern volumes, the places of the planets are given only approximately at intervals of several days, though in the modern volumes the daily places of the sun and moon, and other solar and lunar elements, are given with more detail and precision, and provision is made for the determination of the longitude at sea by a copious table of lunar distances for every three hours for the bright stars and the planets. The places are given of a copious catalogue of fixed stars, and particular attention has been paid to render the work useful for maritime purposes. It has always been the vehicle for the publication of some of the most valuable papers of the French astronomers; and in particular we may mention, that it contains the whole of Leverrier's admirable discussions leading to the discovery of the planet Neptune. For many years it was published under the direction of the Academy of Sciences; but was afterwards placed under the direction of the Bureau des Longitudes. The modern volumes contain an excellent list of geographical latitudes and longitudes, well determined.

The English Nautical Almanac dates from 1767, for which year the first volume was issued in 1766. It was undertaken in connection with the parliamentary commission for the "Discovery of the Longitude at Sea." Dr Maskelyne, the Astronomer-Royal, conducted it for many years. It was afterwards succes- sively under the direction of the celebrated Dr Thomas Young, secretary to the Board of Longitude, and the Astronomer-Royal, Mr Pond.

About the year 1830, however, the construction of the Almanac was found to be defective, and reference was made by the Lords Commissioners of the Admiralty to the Royal Astronomical Society, requesting that body to consider what improvements it would be desirable or necessary to make in the work. A committee was consequently appointed by the society, including every eminent astronomer in the British Isles, together with Professor Struve of Dorpat, to report upon the subject; and in consequence of their recommendations, the work was brought to its present excellent form. One of the greatest changes in principle made in the Almanac was its adaptation to the wants of the theoretical and practical, as well as of the nautical astronomer, to which last it was formerly almost exclusively devoted. This scheme introduced a great deal of additional computation of the accurate places of the sun, moon, and planets for every day of the year; the introduction of mean time instead of apparent; the supplying of the constants for the corrections of the mean places of the stars; and finally, a more extensive list of fundamental or well-observed stars, with their mean places deduced with scrupulous accuracy for every year, and with the elements of their reduction. In addition, the times of all the phenomena of Jupiter's satellites are given; a list of moon-eliminating stars, and of all stars down to the sixth magnitude which could be occulted by the moon, together with the elements for facilitating the computations of the occultations; and lastly, a list of remarkable phenomena likely to be useful. Every possible information with regard to the places of the large planets, and of the four small planets first discovered, is given, and complete elements for every solar and every lunar eclipse during the year; supplying, in fact, every reasonable want of the general as well as of the nautical astronomer. One important addition to this work is the construction of ephemerides of the planets calculated for the meridian of Greenwich. By this means the observed and the tabular places of these bodies can be immediately compared, and a very easy reduction renders these places almost equally applicable for other observatories not differing greatly in longitude, including all in the British Isles, and several of the continental observatories. The Nautical Almanac is so conducted that the volume is always published about three years in advance of the current year, and its price has recently been reduced from five shillings to half that sum.

The first volume of the Berlin Jahrbuch was published in 1774 for the year 1776. Its object was twofold, viz., to supply the want of such a work in which Germany had been for some time singular, and "to obtain a repertory for all observations, information, remarks, and treatises connected with astronomical science." From its commencement the Jahrbuch was published under the inspection and sanction of the Royal Academy of Sciences at Berlin. The volumes from 1776 to 1783 inclusive, bear on their title-page the name of no responsible superintendent; but the volume for 1784, and those that followed it for a long period, were under the immediate editorship of Bode, and after he relinquished the office, it was put into the hands of Encke, its present superintendent. It has always been famed for the valuable collections of observations and astronomical papers contained in its second part, which forms one of the great storehouses of astronomical data from its establishment to the present time. Its contents are particularly valuable in this respect for the period before the establishment of the Monatliche Correspondenz, and it is here that the astronomer must look for the records of his science in the last century.

Almost all the articles in the second part of the first volume are by Lambert, and though this and several succeeding volumes are anonymous, yet it would appear that they were under his management. At the present time it is one of the most useful publications of its class, and is the only one which provides original ephemerides for the recently discovered small planets. Those given in the supplements to the Nautical Almanac are taken from the Jahrbuch, only adapted to the meridian of Greenwich.

The Milan Ephemeris (Ephemeridi di Milano) is a useful publication commencing with the year 1800. The modern volumes are sometimes found useful from their supplying some elements of the planetary motions which are wanting in other ephemerides. It contains many valuable observations and papers of the Italian astronomers. Other ephemerides are those of Bologna, Coimbra, and Cadiz; but these require no particular mention.

Very recently an American Ephemeris and Nautical Almanac has appeared, which promises to be of great service. It is printed in a large octavo volume, and is published under the authority of the Secretary of the Navy. It is at present under the superintendence of Lieutenant C. H. Davis, U.S.N., the theoretical part being placed under the special direction of Professor Povesh of Harvard College, Cambridge.

This work does not copy implicitly any existing nautical almanac, but, retaining what is best in our own and others, modifies the arrangement in a way which promises to be more generally convenient. One great peculiarity in this work is the separation between the part designed exclusively for the purpose of navigation, and that which is generally useful for the theoretical or practical astronomer. In the second part the places of the stars and the planets are referred to the meridian of Washington, and in the computations, the best elements at present known are scrupulously employed. Thus, for the star corrections, Peters's constants of precession, nutation, &c., have been adapted to Bessel's formulae; and with regard to the lunar computations, the elements are based on Plana's theory, but include Hansen's inequalities and secular changes of the mean motion and the perigee; and Airy's corrections of the elements derived from the reduction of the ancient Greenwich observations. For the planetary computations, the latest corrections of the elements of each planet have been employed. For Mercury, Leverrier's theory has been used (Com. des Temps for 1845); for Venus and Mars, Mr H. Breen's corrections have been applied to Lindeman's elements (Memoirs of Royal Astronomical Society, vols. xviii. and xx.); for Jupiter and Saturn, Bouvard's tables have been used with some changes, and Bessel's value of the mass of Jupiter is employed; for Uranus the elliptic elements of Bouvard are used as the basis, with Leverrier's corrections and perturbations caused by Jupiter and Saturn (Com. des Temps for 1849), and with Peirce's corrections and perturbations arising from the action of Neptune; finally, for Neptune, Peirce's theory and Walker's orbit have been used in the construction of the ephemeris.

Another very useful work is the French Annuaire, which contains some valuable articles by Arago, and the Annuaire de Bruxelles which, since 1835, has been published yearly under the superintendence of M. Quetelet, director of the observatory of that city.

Finally, we must make mention of the Comptes Rendus of the French Institute, which furnishes abstracts of all papers read at the meetings of that body, and contains very many valuable articles by the best French astronomers. This series is, however, too generally known to require more than this passing notice.

We will now proceed to give some account of such modern societies and institutions as have most tended to advance the science of astronomy; and it will be sufficient to advert to two of the most prominent of those connected with England, namely, the Royal Astronomical Society of London, and the British Association for the Advancement of Science.

The Royal Astronomical Society dates its existence from the year 1820. Previously to this time the greater number of papers relating to English astronomical research were presented to the Royal Society, and many valuable articles appeared from time to time in the Philosophical Transactions, particularly those of Sir William Herschel. It was evident, however, that astronomy involved so vast a field of research as to require a totally independent organization. The Astronomical Society, accordingly, was founded; and, at its first meeting in 1821, it enrolled amongst its members every astronomer of reputation in England, and amongst its associates, several of the most distinguished philosophers of the continent. Amongst its officers at this time were Sir William Herschel (president), and Sir John Herschel, Mr Baily, Mr Babbage, and Dr Pearson; and History amongst its associates were found the names of Arago, Biot, Delambre, Laplace, Bossel, Ganss, Harding, Littrow, Olbers, Schumacher, Zach, and Piazzi—in fact, every continental astronomer of acknowledged reputation.

From the first establishment of the Society, its serial publications were two, namely, the Memoirs, published from time to time in quarto volumes, and the Monthly Notices. In the former are printed papers, either practical or theoretical, having more than a temporary interest, and declared by a committee appointed for the purpose to be worthy of a permanent record; in the latter are given abstracts of all papers presented to the Society, and a full account of all the proceedings at the monthly meetings. At the present time the Monthly Notices take rather a wider range; and omitting such observations as are sure to appear in the Nachrichten, they supply abstracts and reviews of all astronomical papers or books whatever, which appear either at home or abroad.

The quarto volumes of the Memoirs, now twenty-one in number, are exceedingly rich in the contributions of both English and foreign astronomers. Amongst the most valuable papers contained in them may be mentioned some of the contributions of the late Mr Francis Baily, including his compiled catalogue of stars (commonly called the Catalogue of the Astronomical Society); his Report on the Pendulum Experiments made by Captain Foster; his edition of the catalogues of Ptolemy, Ulugh Beigh, Tycho Brahe, and Hevelius; and finally, his account of his repetition of the Cavendish experiment for determining the mean density of the earth.

The volumes contain also many valuable papers by Sir John Herschel, Mr Airy, and many other distinguished astronomers, which it would be inviolate to particularize.

The Monthly Notices communicate to the Society generally every astronomical circumstance of interest; they give the correspondence of its members with foreign associates, and accounts of every class of observations communicated to the Society by its fellows or correspondents; and, in fact, perform all the offices of a monthly journal for the science in relation to the English scientific public.

In the annual report of the council to the Society, a good retrospect is taken of the events of the past year; and from the date of its establishment, its pages contain perhaps the best materials extant for a history of the science, including memoirs and accounts of all eminent astronomers who have died in the interval.

At the end of 1830 the society obtained a royal charter of incorporation, enabling them to amass property, to receive bequests, and to insure its perpetuity; and, generally, to augment its consideration and sphere of usefulness. It has taken ever since the title of the Royal Astronomical Society of London, and has the sovereign for its patron.

Of all the societies for the advancement of separate physical sciences which have branched off from the Royal Society, as the Astronomical Society was one of the first, so it has been probably the most practically useful. Its reputation has been constantly increasing; and the influence of its works, and of the operations set on foot through its agency, extends to every part of Europe and America, and has produced a marked effect in every department of the science.

The British Association for the Advancement of Science has been also very instrumental in assisting the progress of Astronomy. With its general objects and constitution our present subject is not concerned; and we shall confine ourselves to a mention of such astronomical books or works as it has been the means of producing. The Association was indebted for its existence chiefly to the exertions of the Yorkshire Philosophical Society, and to the convictions of that body of the utility of organizing the efforts of the various societies for the advancement of science existing in London as well as in the provincial towns of our empire.

The first meeting of the Association was held at York in September 1831; and, as concerns the science under consideration, a report on the state and progress of physical and practical astronomy was requested from Professor Airy for the meeting of the next year to be held at Oxford. Mr Lubbock was also requested to furnish a report "on the means which we possess, or which we want, for forming accurate tables for calculating the time and height of high water at a given place."

The former of these reports, which is a most valuable synopsis of the progress of astronomy from the beginning of the present century to the date of the report, is printed in the first volume of the Reports of the Association.

The astronomical works of greatest importance, performed by aid of the funds, and under the auspices of the Association, are, 1st. The compiled catalogue of 3877 stars, formed under the direction of Mr Baily, with an elaborate introduction written by that astronomer; 2dly, the catalogue of Lalande, containing more than 40,000 stars, formed by the reduction of the observations of the Histoire Celeste; and 3dly, the catalogue derived from Lacaille's Southern Observations, containing 9763 stars.

The formation of the above-mentioned catalogues, and the reduction of the ancient observations of Lalande and Lacaille, necessary thereto, are works of that magnitude and importance which only such a society could have undertaken, and which rank amongst the most valuable boons to astronomy in the present century.

We come now to the most important class of institutions tending to promote astronomy, namely, the great Observatories, of which almost every country in the civilized world has one or more. Our limits oblige us to confine ourselves chiefly to those observatories which have produced in the present century important changes and advances in the science, merely adverting to the others by way of reference.

Of observatories of the first class are those of Greenwich, Cambridge, Oxford, Edinburgh, and the Cape of Good Hope, in the British dominions; of Dorpat and Pulkowa in Russia; of Berlin and Konigsberg in Prussia; and, finally, the observatory of Paris; and of these we shall give short notices.

The Observatory of Greenwich is sufficiently well known to prevent any necessity for dwelling upon its early history; and our remarks will be confined to its operations since the accession of the present Astronomer-Royal, Mr Airy, near the end of the year 1835. At that time the instruments consisted mainly of a 10-foot transit instrument, and a 6-foot mural circle, both by Troughton; of a 5-foot equatorially-mounted telescope by Ramsden, and of another small equatorial (since dismounted) by Sisson. There was also a gigantic 25-foot zenith tube by Troughton, which has been since dismounted. The working staff of the establishment consisted, in addition to the Astronomer-Royal and the first assistant (the Rev. R. Main), of five subordinate assistants. Since that time very little alteration has taken place in the staff or organization of the establishment, excepting in the employment of additional computers.

In 1840 magnetical and meteorological observations were commenced in an observatory built for the purpose, of which the superintendence was given to Mr Glaisher, one of the assistants in the astronomical department, and observations have been carried on up to the present time; for the last few years they have been made, however, by a photographic process.

The principal changes and additions to the instruments are the following:

In 1838 was erected an equatorial instrument, of which the telescope has an object-glass of 7 inches diameter, with a focal length of 8 feet, presented by the Rev. R. Sheepshanks. This instrument has a clockwork movement attached, and many valuable observations have been made with it.

In 1847 was erected a very massive altitude and azimuth instrument, constructed by the Astronomer-Royal on peculiar principles of solidity and strength, for the purpose of making extra-meridional observations of the moon with as great accuracy as those usually made on the meridian, and thus securing generally a far greater number of observations in each lunation, as well as a good supply of observations near the conjunctions, which was totally impracticable before. Every object intended by this instrument has been amply realized. The observations made with it are of equal excellence with those made on the meridian, and they are more than double in number;—in addition, observations have been made occasionally within thirty hours, and frequently within two days, of the time of conjunction on either side. In 1850 was erected a large transit circle, intended to replace the transit instrument and mural circle then in use. This instrument, which was brought into use early in 1851, occupies very nearly the same position as the mural circle formerly in use, its centre being 6 feet S. of the point corresponding to the centre of that instrument. It is also 20 feet E. of the position occupied by the transit instrument. The focal length of the telescope is 12 feet, and the diameter of the object-glass is 8 inches. In connexion with the instrument are two collimating telescopes of 5 feet focal length, one to the N. and the other to the S. of it. For the determination of the zenith-point, observations are made daily of the coincidence of the horizontal wire with its image reflected in mercury, as well as observations of stars by reflection. The pivots of the axis are 6 inches in diameter, and the instrument is of very great weight and solidity. It is found that ordinarily as many observations can be made with it by one observer as could be made formerly with the transit instrument and mural circle by the employment of two observers; and that they are of unexceptionable excellence.

We must not here omit to mention the system of galvanic communications now in operation. Wires were laid in the spring of 1852, connecting the observatory with the general system of wires of the South-Eastern Railway Company; and since that time a communication has also been made between the wires of the Electric Telegraph Company crossing Blackheath, and the observatory. It is thus enabled to communicate at pleasure (with the concurrence of the companies above named) with any place to which the wires of these companies extend; and successful experiments have already been made for the determination of the longitudes of the observatories of Cambridge and Edinburgh. From the observatory hourly time-signals are transmitted to the stations of the South-Eastern Railway at London Bridge, Tunbridge, Deal, and Dover. For the transmission of these signals the circuit is closed by means of a clock whose maintaining power is galvanic; and by a combination of the same agency and of electro-magnets fixed near the trigger which drops the Greenwich time-ball at 1 o'clock, the ball is dropped by electro-magnetic power. A bell erected at the office of the Electric Telegraph Company in the Strand is also dropped by the same agency, the wires in connexion with its electro-magnets being included in the circuit. Several sympathetic clocks in the observatory beat in coincidence with the motor-clock, especially one of which the dial is exposed to the public; and it is intended that ultimately clocks at London Bridge and other railway stations shall be put in connexion.

To the Greenwich Observatory, and to the untiring labours of its present eminent director, are due some of the most important works of modern astronomy. The ordinary production of each year is a thick folio volume, averaging from 600 to 700 pages. The star-observations, as far as the year 1847, are incorporated in a catalogue of 2156 stars, named the Twelve Year Catalogue. Recently observations have been made of all stars down to the fourth magnitude included in the British Association catalogue, and visible at Greenwich; a copious list has been observed for the determination of clock error, and is now in ordinary use in addition to the list of the Nautical Almanac; and finally, a good list of circumpolar stars has been observed for the determination of the azimuthal errors of the transit instrument.

A great many comets have been in former years well observed with the equatorials, as well as a small catalogue of double stars. The bright planets have all been well measured, and, in particular, the ellipticity of the planet Saturn has been determined by means of measures made with a double-image micrometer, in a paper by Mr Main, printed in the eleventh volume of the Memoirs of the Royal Astronomical Society.

Besides the ordinary work of the observatory, many great works have been undertaken and completed by the Astronomer-Royal. Of these the most important is the reduction of the ancient lunar and planetary observations made at Greenwich by his predecessors, beginning with Bradley. Both these works are of a most important character; and the former, immediately after its publication, was instrumental in detecting a remarkable inequality of the lunar orbit, depending upon the action of Venus, on the results being put into the hands of M. Hansen. The ancient lunar and planetary observations form three thick quarto volumes.

Another work of considerable importance was the determination, in 1845, of a large arc of parallel on the earth's surface, by means of chronometrical determinations of the longitudes of stations at Kingstown (Dublin), and the island of Valentia on the west coast of Ireland.

The Observatory of Cambridge.—The building was completed in 1824, and the first director of the observatory was Professor Woodhouse. Professor Airy succeeded him in 1828, and continued till the autumn of 1835, when he became Astronomer-Royal. He was succeeded by Professor Challis, the present director.

The observatory was at first furnished only with a 10-foot transit instrument by Dollond. To this was added in 1832 an 8-foot mural circle by Troughton and Simms, and a 5-foot equatorial by Jones. Finally, the Northumberland equatorial (so called from the title of its donor the Duke of Northumberland) was erected under the direction of Mr Airy in 1838. The telescope of this fine instrument is of nearly 20 feet focal length, and the clear aperture of its object-glass is 11½ inches. It is mounted with its telescope in the plane of the polar axis, which is supported above and below by pivots resting in Y's.

At the accession of Professor Airy, he introduced a very important principle, vigorously followed by himself up to the present time, and now imitated in the greater number of British observatories, namely that of thoroughly reducing every observation before its publication. The elements of reduction are uniform throughout; and, these being explicitly stated in the introduction to each volume of observations, it is comparatively easy to compare the results with those of any other set of reduced observations, even if the elements be somewhat different, by making the requisite alterations.

Mr Airy, while at Cambridge, introduced an important alteration in the use of the mural circle, by observing the reflected as well as the direct image of a star at the same transit, and thus determining the zenith point.

He also introduced the practice of observing the planets when at a considerable distance from opposition on either side. By this means errors in the orbits were rendered capable of detection, for which no data existed previously, especially such as depend upon an error in the radius-vector.

The results of Mr Airy's star-observations, made at Cambridge, were afterwards collected by himself, and published in a catalogue of 726 stars, named the First Cambridge Catalogue.

The planetary observations were also grouped by him, and the normal results published in various papers of the Memoirs of the Royal Astronomical Society.

The activity of the observatory has continued undiminished to the present time; but, on account of the erection of the Northumberland Equatorial, the chief subjects for observation have become necessarily different. This instrument has been employed systematically for several years in observations of double stars, and of the small planets which recent discoveries have rendered so numerous. Our readers will also remember, and we shall have farther occasion to notice in our history of the planet Neptune (Supplement to Part II.), the active part taken by Professor Challis in the search for that planet, and the fact that it was twice actually observed by him before Galle's discovery, although it was not recognised till after the discovery.

The Radcliffe Observatory at Oxford.—This observatory was erected about the year 1774. Its directors have been successively Dr Hornsby, Dr Robertson, Professor Rigaud, and Manuel J. Johnson, Esq., the present director. The observations which have given an honourable distinction to this observatory have been made during the directorship of Mr Johnson, and are inferior to none produced at any establishment with an equal amount of observing force, in number, in accuracy, or in punctuality of publication. They are also published in a reduced state, which adds considerably to their value. The instruments consist mainly—1st, Of a transit instrument of 8 feet focal length, and 4 inches aperture of object-glass, constructed essentially in 1843 by Simms; 2dly, Of a meridian circle of 6 feet in diameter, erected in 1836 by Jones; 3dly, Of a fine heliometer erected in 1850, by the Messrs Repsold of Hamburg, the object-glass of which is by Messrs Merz of Munich, and is of 10½ feet focal length and 7½ inches aperture.

Mr Johnson's great work has been, since his accession to the directorship in 1839, the re-observation of the stars in Groombridge's Circumpolar Catalogue, and the careful determination of their magnitudes. This, with the aid of only one assistant, he has completed, and is preparing to arrange the collected results in a catalogue.

This work, when completed, will be a great boon to science on many accounts, but especially for the accurate determination of the proper motions of the stars, more than 4000 in number, contained in the catalogue.

Another assistant has recently been added to the establishment, for the working of the heliometer.

Of the observatories in the British dominions, we will next mention that at the Cape of Good Hope. This observatory was established by order in council in 1820, at the instigation of the then existing Board of Longitude. The Rev. Fearon Fallows was appointed the astronomer, with a salary of £600 per annum, and he was to be supplied with an assistant to carry on the observations. He was instructed to make observations of the same kind and in the same manner as those made at Greenwich, so that "the whole might constitute two corresponding series capable of comparison in all their parts."

Mr Fallows arrived at the Cape in August 1821, and after some unavoidable delays, the observatory was erected on a site he had selected between Liesbeek River and Zwart or Salt River. Notwithstanding innumerable disadvantages and annoyances against which he had to struggle, he contrived to observe a catalogue of 273 stars, the reception of which was announced at a meeting of the Board of Longitude in November 1823.

A new clock by Hardy was shipped for him at the end of 1822, and the transit instrument and mural circle intended for the observatory were progressing; but no steps had been taken for the building of the observatory, which was not completed till 1827, and the instruments were not mounted and ready for use till 1829.

The instruments at that time were,—1st, A transit instrument by Dollond, of 10 feet focal length, and 5 inches aperture; 2dly, a mural circle by Jones, of 6 feet in diameter, which proved a very faulty instrument, and caused most serious annoyance, not only to Mr Fallows, but to other astronomers.

Mr Fallows did not live long after the completion of his observatory, when he might have expected to reap some rewards of his previous labours and anxieties. He died on the 25th July 1831, deeply regretted in all scientific circles in England.

Mr Henderson succeeded Mr Fallows at the Cape, but resigned his appointment in 1833. During his brief directorship, however, he materially advanced the reputation of the observatory. The bright double star α Centauri was found to have a considerable proper motion; and this induced him to make a series of observations for the purpose of detecting its parallax, which he ultimately found to be about one second of space. This result has since been confirmed by his successor, Mr Maclear.

Mr Henderson was succeeded by the present director, Mr Maclear, who had for his assistant, Mr C. Piazzi Smyth, the present Astronomer-Royal of Scotland. The observations of Mr Maclear for 1834 were published in 4to in 1840, but only one additional volume has appeared since. He has, however, been actively employed, and many valuable results have been printed in the Memoirs of the Royal Astronomical Society, of which we may mention, in particular, the details relating to the measurement of Lacaille's arc of meridian.

Two more assistants have at different times been added to the staff, and more recently a magnetic and meteorological observatory has been added, provided with one additional assistant.

A good equatorial, with clock movement, of which the telescope is of 8½ feet focal length, and 6½ inches aperture, was erected in 1849; and a large transit circle similar to that at Greenwich, and intended to supersede the present meridian instruments, is in course of construction.

Mr Maclear is at present engaged in observing approximately, with the mural circle, all the stars of the catalogue of the British Association which are visible at the Cape, and has already cleared up a great many errors and inconsistencies in Lacaille's observations.

The Royal Observatory of Edinburgh.—This observatory is situated on the Calton Hill of Edinburgh. It had its origin in an astronomical institution, whose members built on the Calton Hill a small observatory, and placed it in the charge of the Professor of Astronomy and Natural Philosophy, Dr Wallace. At this time there existed a sinecure Professorship of Practical Astronomy; but, at the death in 1828 of Dr Blair, who had for some time occupied the chair, the government declined to fill up the vacancy immediately. The office remained vacant from 1828 till 1834; when an agreement was made between the government and the members of the Institution, whereby the latter gave up to the university the use of the observatory on the Calton Hill, which the former undertook to convert into a public establishment, by furnishing it with suitable instruments, and making provision for an observer and an assistant. It was then resolved to fill up the office of Professor of Practical Astronomy, and to combine with it the direction and superintendence of the observatory; and this arrangement has continued till the present time, though until lately no attempt was made to form a class of practical astronomy.

Mr Henderson, on resigning his appointment at the Cape, was appointed to the office, and continued to fill it until his death, which took place in 1844. Under his able directorship, and by his unremitting labours, the Edinburgh Observatory immediately took its place amongst the best institutions of the kind. The observations made with the transit instrument and mural circle rivalled those made at Greenwich in accuracy and in number, taking into account its small establishment; while the director illustrated and extended astronomy generally by a long series of papers on various branches of the science, many of which are of great value, and are reckoned amongst the most valuable contributions of the time. He had considered it an indispensable duty to reduce the observations which he had made at the Cape of Good Hope; and at this he worked diligently as long as his life lasted, and his other duties would permit.

It has been already mentioned that he determined the parallax of α Centauri. By comparison of his observations of the moon made at the Cape with those made in Europe, he established the necessity of a considerable augmentation of the moon's parallax; while, by observations of very low stars, he has produced materials for a new set of refraction tables. Finally, he deduced from his observations a catalogue of the declinations of 172 principal stars, chiefly in the southern hemisphere. Indeed, he seems to have done for his epoch in some degree the same thing which was done by the illustrious Bessel; he redetermined and corrected some of the most important astronomical elements, and his papers remain as models of elegance and accuracy to future inquirers.

At the time of Mr Henderson's death he left five published volumes of observations, namely, those from 1834 to 1839, and a sixth nearly ready for publication. His successor, Professor Piazzi Smyth, took upon himself the charge of reducing the observations of the remaining years up to the time of his decease. This task he has accomplished; and the Edinburgh Observations now form an uninterrupted series from 1834 to 1844, printed in ten volumes 4to, and inferior to none yet produced in accuracy or utility.

The principal instruments of the observatory consist of a transit instrument by Repsold and Son of Hamburg; a mural circle by Troughton and Simms; and an altitude and azimuth

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1 For a complete catalogue of his works, see the Monthly Notices of the Royal Astronomical Society, vol. vi. p. 190. instrument by the same artist. The transit telescope is of nearly 8½ feet focal length, and 6½ inches aperture. The 6-foot mural circle is similar to those formerly used at Greenwich.

Since the accession of Professor Smyth, a new arrangement has been made with the government. The town authorities have consented to make over the building to the crown, on condition of the latter taking upon itself the sole charge of defraying the expenses of the establishment, and of providing for its adequate and perpetual maintenance. A general repair of the building and the instruments has since been made, and at the same time a board of visitors was appointed, so as to render the management of the observatory in most respects similar to that of Greenwich.

The Observatory of Paris was built by order of Louis XIV. during the years 1668 to 1671. It had for its first directors successively the four Cassinis; namely, the celebrated Dominique Cassini, and after him Jacques Cassini, Cesar Francois Cassini, or Cassini de Thury, and finally Jean Dominique Cassini, or the Comte de Cassini. For the ancient history of this observatory, the reader may refer to Delambre's Astronomie du dis-buillitine siècle, p. 311; we have space only for a few remarks on its modern condition.

The instruments have consisted for some years chiefly of a transit instrument by Gamby; of a mural circle, completed by Fortin in 1822, and of another since erected by Gamby; and finally of a good equatorial of moderate size by the latter artist.

Several volumes of unreduced observations have recently been published in folio, which give ample evidence of the skill and industry of the observers, but they do not appear to be made on any settled plan, and the introductions defend the principle of publishing them in the unreduced state. Individually, the astronomers of the Paris Observatory have taken a good part in the recent discoveries and rapid progress of the science. Faye, Languier, and Mauvais have been distinguished by their cometary discoveries, as well as for other valuable works; Leverrier is the famed discoverer of the planet Neptune; and, finally, Villarceau is distinguished for his researches on the orbits of double stars.

For many years the Paris observations were printed in the Connaissance des Temps. The observations from 1800 to 1803 are printed in the volumes for 1823, 1824, and 1825. From 1803 to the commencement of 1810, they are printed in the volumes extending from 1808 to 1812.

Afterwards they were printed in two distinct folio volumes, the first of which contains the observations from 1810 to 1819, and the second from 1820 to 1828. Finally, a new series has been published in folio, containing, in ten volumes, the observations from 1837 to 1846.

The Observatory of Berlin is of comparatively recent date, but the institution was contemporary with that of the Academy of Sciences, which dates from the commencement of the seventeenth century. Omitting the history of the institution before the erection of the modern building, which is only interesting in connexion with the publication of the Jahrbuch unter Bode, and which may be found in Encke's introduction to the first volume of his observations, we shall confine ourselves to a short description of the modern observatory.

Encke succeeded Bode about 1822, but it was not till 1828 that, on the representations of Humboldt, measures were taken for the erection of a suitable observatory, of which the foundation-stone was laid in 1832.

The building is situated in the Lindenstrasse, near the north boundary of the city wall, and the instruments are placed in apartments above the ground floor, on solid piers of masonry carried up from the foundation. It contains—

1. A large refracting telescope by Fraunhofer, mounted equatorially, of the same dimensions with that at Dorpat, the mounting being similar to that of the Königsberg heliometer. 2. A 3½-feet meridian circle by Pistor, the telescope of which is of 5 feet focal length, and of 5½ inches aperture. 3. A 3½-feet transit instrument by Dollond, placed in the prime vertical. 4. A heliometer of 42 inches focal length, by Utzschneider and Fraunhofer, mounted equatorially.

There are as usual several smaller instruments, and a magnetic observatory has been added to the establishment.

Three folio volumes of observations, commencing with 1838, have been published.

The importance of this observatory is chiefly due to the labours of Professor Encke. We have already mentioned his researches on the comet of 1860, and he is still more celebrated for those on the comet bearing his name, which have been the means of bringing into evidence the existence of a very thin resisting medium pervading the planetary spaces. Recently he has published a very ingenious method of calculating the disturbances of the small planets. This memoir has been translated by Mr Airy, and is published as an appendix to the Nautical Almanac for 1856.

Dr Galle, who was till lately attached to the observatory, has also added to its reputation by the discovery of two comets, and still more by the discovery of the planet Neptune, on the first evening of his search, near the position indicated by Leverrier.

The Observatory of Königsberg was finished in 1813, and none has contributed more during the present century to the improvement of every branch of astronomy than this observatory, under the direction of Bessel.

It is situated on the summit of a hill on the N.W. of the city, and at first was but moderately equipped with instruments. In 1820 there was added a good meridian circle by Reichenschuh, and with this instrument were made those observations of small stars lying between 45° N. declination and 15° S. declination, known by the name of Bessel's Zones. These observations have been recently reduced (as far as 15° N. declination) by Dr Weisse, and the resulting catalogue is printed in 4to.

In 1829 was erected the celebrated heliometer by Fraunhofer, which is described in the Memoirs of the Royal Astronomical Society, vol. xii. The most celebrated work performed with it by Bessel, was the detection of the parallax of the binary star 61 Cygni. It has been since used by Wichmann in the attempt to detect the parallax of the star No. 1830 of Groomebridge's catalogue.

In 1841, a new and improved meridian circle, by the Brothers Repsold of Hamburg, was erected, and in the use of it Bessel introduced the practice of obtaining the nadir point by means of observations of the coincidence of the direct and reflected images of the horizontal wire of the telescope.

The fame of this observatory is so intimately connected with that of Bessel, that a full account of the works performed in it would be but a record of part of the life of that great man, and for this we would refer the reader to the Notices of the Astronomical Society.

Our limits oblige us to be brief in our accounts of the Russian observatories at Dorpat and Pulkowa, which have both attained the highest possible distinction through the labours of Struve.

The Observatory of Dorpat was built about 1811, and in 1813 Struve was appointed to it. For some time its chief instrument was an 8-feet transit instrument; but in 1822 a large meridian circle by Reichenschuh was added; and at that time Struve began those researches in sidereal astronomy which have rendered him so famous.

In 1824 was added the great Fraunhofer refractor, of which a particular description, accompanied with plates, is given in Part iv. of this article.

The results of Struve's labours with regard to double stars are contained in a large folio volume, entitled, Stellarum duplicium et multiplicitum mensurae micrometricae per magnum Fraunhoferti tubum, annis a 1824 ad 1837 in Speculā Dorpatensi, Petropoli, 1837. This volume is accompanied by a smaller work of reference, entitled Catalogus Novus Stellarum Duplicium.

Very recently, M. Struve has published another large folio, giving the mean places for 1830 of the stars observed at Dorpat. The title is Stellarum fixarum imprimis duplicium et multiplicitum positiones medice pro epocha 1830, deducta ex observationibus meridianis, annis 1522 ad 1843, in Speculā Dorpatensi institutis. M. Struve was appointed in 1839 to the new observatory to be erected at Pulkowa, and was succeeded by M. Müller, who has well sustained the reputation of the observatory of Dorpat.

The foundation-stone of the Observatory of Pulkowa was laid in 1835; and in the autumn of 1839 this best endowed and most perfectly organized of all European observatories was completed and in working order. We must be content to give only a few details concerning this admirable institution.

The instruments are the following:

1. A large transit instrument by Ertel, with provision for reversing the position of the eye-piece and object-glass, and with a collimating mark placed on a pier to the S. of the instrument.

2. A large vertical circle by Ertel, in construction similar to an astronomical theodolite. The focal length of the telescope is 77 inches, and the diameter of the object-glass very nearly 6 inches. With this instrument were made M. Peters's observations for determining the parallax of certain stars, of which the results are given in his paper, *Recherches sur la Parallaxe des Étoiles Fixes*, printed in the Transactions of the Petersburg Academy.

3. A meridian circle by Repsold, with all the improvements suggested by M. Struve's experience. The focal length of the telescope is nearly 7 feet, and the aperture of the object-glass 6 inches. "This instrument is designed," says M. Struve, "for the collection of a great mass of observations to serve for the construction of a vast catalogue of stars."

4. A large transit instrument by Repsold, placed in the prime vertical. The telescope is of 71 feet focal length, and 64 inches aperture of object-glass. With this instrument M. Struve made his observations for determining the value of the constant of the aberration of light discussed in his paper, *Sur le Coefficient de l'Aberration des Étoiles Fixes*, 1843.

5. The great refracting telescope by Merz and Mahler, of which the focal length is 22½ feet, and the clear aperture of the object-glass 15 inches. It is mounted equatorially according to the usual method applied to foreign telescopes. It has been used with great effect by M. Otto Struve, son of the director, on the system of Saturn and on other objects. A similar telescope has since been erected at the observatory of Harvard College, Cambridge, Massachusetts, which has added to astronomical discovery.

6. A heliometer by Merz and Mahler, of which the focal length is 10 feet, and the aperture of the object-glass is 7½ inches.

These are the grand Instruments of the establishment, which is also liberally supplied with smaller instruments of every kind. There is also a very fine library attached to the establishment, of which the foundation is that of Olbers, purchased after his decease.

Connected with the observatory are workshops for making the requisite repairs and alterations in the instruments, and to these are attached mechanists and carpenters superintended by proper officers.

Besides the persons on the ordinary staff of the establishment, several others are ordinarily attached, either for instruction or for the carrying on of special works, or in connexion with geodetical or geographical operations. To give some idea of the extent of this noble institution, M. Struve estimated that in 1844 there were no fewer than 103 persons (including the wives and families of the persons employed) residing within its boundaries.

We are obliged to conclude this short account of a few of the leading observatories of Europe, without mention of many others of very considerable importance in the history of astronomy. We should have been glad to have given some detailed notices of that of Bonn, including the labours of Argelander, and of Hamburgh, including those of Rumker. The observatories of Cambridge and Washington in the United States are also of great importance; as well as the private observatories of Mr Bishop, Mr Lassell, Lord Rossie, and Mr Cooper. The preceding sketch may however suffice to show the great activity that during the present century has pervaded every branch of astronomy, and to guide the student in some measure to the sources of astronomical knowledge relating to the present epoch.

The following works may be consulted on the history of astronomy:—Riccioli, *Almagestum Novum*, Bononiae, 1653, 2 vols. folio; Sherburn's *Translation of the Astronomicum of Manilius*, London, 1675; Weidler, *Programma de Veterinomia*, et Nova Astronomiae Discrimine, Wittemberg, 1720; Societ., *Observationes Mathematicae, Astronomicae*, &c., 1729, 2 vols. 4to. The second volume of this work, by Gaubil, contains a history of the Chinese Astronomy, with Dissertations. Weidler, *Historia Astronomiae*, Wittemb., 1741; Idem, *Commentatio de Mechanica Astronomica Medii Evri*, 1742; Long's *Astronomy*, London, 1742; Costard's *Letter to Martin Folkes concerning the Rise and Progress of Astronomy among the Ancients*, London, 1746; Foulques' *History of Astronomy*, London, 1746; Heathcoat, *Historia Astronomiae*, Cantab., 1747, 8vo; Estève, *Histoire Générale et Particulière de l'Astronomie*, Paris, 1755, 3 vols. 12mo; Goguet, *Origine des Lois, des Arts, et des Sciences*, various editions; Jablonski, *De Astronomiae Ortu ac Progressu*, &c., Rome, 1763, 4to; Bailly, *Histoire de l'Astronomie Ancienne et Moderne*, 1770, 1779, 1782, 4 vols. 4to. This work has been published without the notes and calculations in 2 vols. 8vo, Paris, 1805.

Gentil, *Sur l'Astronomie des Indiens*, Hist. Acad., Paris, 1772; Gaubil, *Histoire de l'Astron. Chinoise*, in the Lettres Edifiantes et Curieuses, tom. xxvi.; Bailly, *Traité de l'Astr. Indienne*, Paris, 1775, 4to; Playfair's *Remarks on the Astronomy of the Brahmins*, in the Edinburgh Transactions, republished in the 3d volume of his Works; *Asiatic Researches*, vols. ii., vi., viii.; Adam Smith's *Fragment on the History of Astronomy*; Lalande, *Astronomie*, Paris, 1792, 3 vols. 4to; Idem, *Bibliographie Astronomique, avec l'Histoire de l'Astronomie depuis 1781 jusqués à 1802*; Vince's *Astronomy*, vol. ii., Cambridge, 1799; Kaestner, *Geschichte der Mathematik*, Göttingen, 1796; Schaubach, *Geschichte der Griechischen Astron. bis auf Eratosthenes*, Göttingen, 1802, 8vo; Montucla, *Histoire des Mathématiques*, Paris, an 7, an 10 (1802), 24 edit. 4 vols. 4to; Laplace, *Exposition du Système du Monde*, and Pond's *Translation of the same work*; Small's *History of the Discoveries of Kepler*, 1803; Bossut, *Histoire Générale des Mathématiques*, Paris, 1810, 2 vols. 8vo; Voiron, *Histoire de l'Astronomie depuis 1781 jusqués à 1811*, Paris, 1811, 8vo, a continuation of Bailly; Delambre, *Histoire de l'Astronomie Ancienne*, Paris, 1817, 2 vols. 4to; Idem, *Histoire de l'Astronomie du Moyen Age*, 1819, 4to; Idem, *Histoire de l'Astronomie Moderne*, 1821, 2 vols. 4to; Idem, *Histoire de l'Astronomie du xviie Siècle*, 1827, 4to. These six volumes of Delambre's *Histoire* contain copious extracts of all the principal works which have been published on the subject of astronomy, interspersed with much enlightened criticism; *Geschichte der Astronomie*, von Dr G. A. Jahn, Leipzig, 1844, 2 vols.; Airy's *Report on Astronomy in British Association Report* for 1832, vol. i.; Grant's *History of Physical Astronomy*, 1832, 8vo.

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Bryce—Elements of Algebra. By James Bryce, M.A., F.G.S., One of the Masters of the High School, Glasgow. Second Edition. 12mo, 4s. 6d., bound.

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Christison’s Dispensatory. A Commentary on the Pharmacopœias of Great Britain, comprising the Natural History, Description, Chemistry, Pharmacy, Actions, Uses, and Doses of the Articles of the Materia Medica. By Robert Christison, M.D., Professor of Materia Medica in the University of Edinburgh. New and improved Edition, with a Supplement, containing the most important New Remedies which have come into general use since the publication of the last Edinburgh Pharmacopoeia in 1841. 8vo, 20s., cloth.

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Gunn—Rudiments of the Latin Language. By William M. Gunn, LL.D., late One of the Masters of the High School, Edinburgh. Second Edition. 12mo, 2s., bound.

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Lindsay—High School Vocabulary. By Samuel Lindsay, A.M., late One of the Masters of the High School, Edinburgh. 18mo, 1s. bound. Marshall—Enlisting, Discharging, and Pensioning of Soldiers. With the Official Documents on these Branches of Military Duty. By Henry Marshall, F.R.S.E., Deputy Inspector-General of Army Hospitals. Second Edition. 8vo, 7s. 6d., cloth.

"A most valuable book, and ought to be in the library of every medical officer in the public service, whether of the army or navy."—British and Foreign Medical Review.

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Brown—Views of Canada and the Colonists. Embracing the experience of an Eight Years' Residence; views of the Present State, Progress, and Prospects of the Colony; with detailed and practical Information for intending Emigrants. By James B. Brown. Second Edition, fcp. 8vo, 4s. 6d., cloth.

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Gilly—Valdenses, Valdo, and Vigilantius. By the Rev. W. S. Gilly, D.D., Author of "Waldensian Researches." Post 8vo, 1s. 6d. "An eloquent account, from personal observation, of that small community of Protestants, who, in the secluded valleys of the Cotton Alps, have, for many centuries, maintained the purity of their faith and worship, and kept up the fire of their vestal church, in the midst of privations and persecutions not yet extinguished."—Quarterly Review. MISCELLANEOUS WORKS—(continued).

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"One of the best modern books on Gardening extant."—London's Gardener's Magazine.

Ramsay—Gentle Shepherd. By Allan Ramsay. New Edition. With a Life and Portrait, and numerous Illustrations after David Allan. 18mo, sewed, 1s. 9d.; cloth, 2s. 6d.; cloth, gilt, 3s.; morocco, 5s.; morocco, extra, 5s. 6d.

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Russell—History of Modern Europe. With an Account of the Decline and Fall of the Roman Empire, and a view of the Progress of Society from the Rise of Modern Kingdoms to the Peace of Paris in 1763; in a Series of Letters from a Nobleman to his Son. New Edition, continued to the Accession of Queen Victoria of England. Four Volumes, 8vo, 52s., cloth. MISCELLANEOUS WORKS—(continued).

Scott—Memoir of David Scott, R.S.A. Containing his Journal in Italy, Notes on Art, and other Papers. By William B. Scott. With seven Engravings, Svo, 10s. 6d., cloth.

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Smith—Wealth of Nations. An Inquiry into the Nature and Causes of the Wealth of Nations. By Adam Smith, LL.D. With the Life of the Author, an Introductory Discourse, Notes, and Supplemental Dissertations, by J. R. McCulloch, Esq. Fourth Edition, corrected throughout, and greatly enlarged. With two Portraits. Svo, 16s., cloth.

Thomson—Brewing and Distillation. By Thomas Thomson, M.D., F.R.S. London and Edinburgh, Professor of Chemistry in the University of Glasgow. With Practical Instructions for Brewing Porter and Ales according to the English and Scottish Methods. By William Stewart. With Engravings. Post Svo, 6s., cloth.

Tytler—History of Scotland. By Patrick Fraser Tytler, Esq. Third Edition, Seven Volumes demy Svo, £2, 12s. 6d. cloth. THE SAME.—A Cheap Stereotyped Edition, in nine vols. post Svo, cloth, £2, 5s.

"The Standard History of Scotland."—Quarterly Review.

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"Written in a flowing and animated style. Those who wish to know Scotland in its Coasts and Islands, will derive from this work both instruction and pleasure; those who desire to know the value of their country and its institutions, as shown even in the most inaccessible parts of its remotest provinces, will ponder over its contents; and the general reader, who seeks only for that rational amusement which the personal narrative of a lively and intelligent tourist never fails to yield, will find it in these volumes."—Edinburgh Review.

EDINBURGH: ADAM AND CHARLES BLACK. ENCYCLOPÆDIA BRITANNICA, EIGHTH EDITION.

In every country where Science and Literature have been long and successfully cultivated, and books extensively multiplied, attempts more or less skilful have been made to reduce the mass of information to a compendious and regulated form, and to furnish a ready access to its varied details by means of Encyclopaedias. Of the importance and advantages of such publications, there can scarcely be two opinions. Executed on a plan sufficiently comprehensive, they ought to embrace all the departments of human learning, rendering the Alphabet a ready key, not only to the Arts and Sciences, but to the multiplied details of History, Biography, Geography, and Miscellaneous Literature. A work thus constructed is not only valuable to the Scholar and the man of Science as a Dictionary of Universal Reference, but the subjects being treated in a form consistent with Systematic Exposition, as well as with Alphabetical Arrangement, the book becomes an inestimable treasure to those who, although they cannot afford leisure for very laborious research or profound investigation, are yet desirous to possess that general information on all subjects which constitutes an intelligent and well-informed man.

Among books of this class, the Encyclopædia Britannica has long been conspicuously eminent. As a Great Repertory of Human Knowledge, it has continued since 1771 to accumulate the ever-increasing treasures of Science and Literature. It was first published in three volumes 4to, 1771; next, in ten volumes, in 1778; in eighteen volumes in 1797, to which was added the Supplement, in two volumes, by Bishop Gleig, in 1801; this was followed by an edition in twenty volumes, in 1810; and other two editions during the succeeding ten years; to which was added the celebrated Supplement, in six volumes 4to, edited by Professor Napier, commenced in 1815, and finished in 1824.

The Seventh Edition, which was completed in 1842, embodied whatever remained valuable in the previous editions and in the Supplements, and was further enhanced in value by the addition of some of the most celebrated disquisitions which have adorned the literature of the nineteenth century. The publication thus of Seven Editions with successive improvements, and the Sale of 35,000 copies, not during an excitement raised by a factitious reputation, but during a succession of years, in which the work was tested and approved by the most accomplished and scientific scholars, remains an irrefragable proof of its unquestionable merit, and have given it so decided a preference in public favour, that its popularity, instead of suffer- ing diminution from rivalry, has steadily continued to increase, and never stood higher than at the present time.

It has been the leading object of its conductors to combine abstract with practical, and solid with pleasing information, in such proportions as would be most useful and most acceptable to the public, to deliver the truths of Science in the most accurate and intelligible form, and, at the same time, to pay due attention to those branches of knowledge, which, though not admitting of a scientific shape, are yet deservedly popular, and have a powerful influence on the taste, habits, and character of the individual,—in a word, to render the Work at once a Dictionary of Science, a Copious Abstract of Literature and Philosophy, and a Book of Universal Reference.

The Eighth Edition will undergo careful revision and extensive alterations, so as to be accommodated to the improved taste and advanced intelligence of the times. Arrangements are accordingly made to secure the co-operation of the most eminent living Authors, who have contributed treatises in the various departments of Science, Literature, the Arts, Manufactures, Commerce, Statistics, and General Knowledge, to supersede those now rendered obsolete by the progress of discovery, improvements in the Arts, or the general advancement of society.

In giving effect to the extensive plan of reconstruction thus adopted, due consideration will, at the same time, be given to the great and permanent value of many of those Articles and Treatises with which the former Editions were enriched. The possession of these invaluable contributions forms, indeed, a characteristic feature of the Work, and gives it a decided pre-eminence over every other publication of its class.

To the Gentleman and the Merchant, to the Agriculturist and the Manufacturer, to the Clergyman and the Layman, to the Student of Science or Philosophy and the Cultivator of Literature or the Fine Arts, the Encyclopaedia Britannica will prove an acquisition of the highest value. The great scope of its information also recommends it to Emigrants and other persons resident in quarters where access to books is difficult, or whose fortunes do not permit them the enjoyment of extensive libraries.

To all such the Publishers confidently recommend the Encyclopaedia Britannica, as a Work deserving of their confidence and support, and worthy of the National Name.

EDINBURGH: ADAM AND CHARLES BLACK. Now Publishing, in Monthly Parts, price 8s., and Quarterly Volumes, price 24s.,

ENCYCLOPÆDIA BRITANNICA, EIGHTH EDITION. GREATLY IMPROVED AND BROUGHT DOWN TO THE PRESENT TIME.

EDITED BY THOMAS STEWART TRAILL, M.D., F.R.S.E., Professor of Medical Jurisprudence in the University of Edinburgh; ASSISTED BY NUMEROUS CONTRIBUTORS, WHOSE INITIALS ARE ATTACHED TO THEIR RESPECTIVE ARTICLES.

The ENCYCLOPÆDIA BRITANNICA forms an Alphabetical Repertory of every branch of Human Knowledge, and renders the Alphabet a ready key not only to the Arts and Sciences, but to the multiplied details of History, Philosophy, Biography, Geography, Commerce, Manufactures, Statistics, and Miscellaneous Literature.

The Publishers are fully aware that in a comprehensive work of reference, as this is, it is desirable to obtain Completeness and Accuracy of Detail in all the Articles, of whatever length or consequence they may be. Accordingly, while arrangements have been made to secure the co-operation of some of the most eminent living authors for the more important contributions, the greatest regard will in every respect be paid to those of the smallest size.

LIST OF SOME OF THE CONTRIBUTORS TO THE EIGHTH EDITION.

Rt. Hon. THOMAS BARINGTON MACAULAY, M.P. RICHARD WHATELY, D.D., Archbishop of Dublin. R. DICKSON HAMPDEN, D.D., Bishop of Hereford. WILLIAM WHEWELL, D.D., Professor of Moral Philosophy, Trinity College, Cambridge. BARTON JUSTUS VON LIEBIG. Dr WM. GREGORY, Professor of Chemistry in the University of Edinburgh. WILLIAM SPALDING, Professor of Rhetoric, St Andrews University. Sir ARCHIBALD ALISON, Bart., Author of the History of Europe, &c. &c. JOHN STUART BLACKIE, Professor of Greek, Edinburgh University. EDWARD TROTTON, Esq., Statistical Department, East India House, Author of Guarantee of Science. AUGUSTUS PETERMANN, Esq., Physical Geographer to the Queen. JOHN WILSON, Esq., Farmer, Edlington Mains, Berwickshire, Author of various papers on Agriculture read before the Highland and Agricultural Society. THOMAS ANDERSON, M.D., Professor of Chemistry, Glasgow, and Lecturer on Agricultural Chemistry to the Highland and Agricultural Society. JOHN HILL BURTON, Esq., Advocate, Author of the History of Scotland from the Revolution, &c. REV. WM. LINDSAY ALEXANDER, D.D., Author of Connection and Harmony of Old and New Testaments, &c. &c. GEORGE FARQUHAR GRAHAM, Esq., Author of various Works on Music.

J. R. McCULLOCH, Esq., Member of the Institute of France, Author of Commercial Dictionary, &c. Sir WILLIAM HAMILTON, Bart. GEORGE FERGUSON, LL.D., Professor of Humanity, King's College, Aberdeen. CHARLES MACLAIRN, Esq., F.R.S.E., Author of Topography of the Plain of Troy, Geology of Fife and the Lothians, &c. &c. WILLIAM HOSKING, Esq., Professor of Architecture and Arts of Construction, King's College, London. Rev. ROBERT MAIN, M.A., F.R.A.S., First Assistant, Royal Observatory, Greenwich. Lieut.-Col. PORTLOCK, R.M.A., Woolwich. Rev. WM. SCORESBY, Author of Account of the Arctic Regions, &c. &c. J. H. STOOCQUELL, Esq., Author of British Officer, Military Encyclopaedia, &c. &c. JONATHAN AYLES, Esq., Master Attendant, H.M. Dockyard, Sheerness. JAMES WILSON, Esq., F.R.S.E., Author of various Works on Natural History. DAVID CRAIGIE, M.D., F.R.S.E. HON. LORD COCKBURN, Author of Life of Lord Jeffrey. Dr LEONARD SCHMITZ, F.R.S.E., Rector, High School, Edinburgh, Author of History of Rome. JOHN HUTTON BALFOUR, M.D., Regius Professor of Botany, Edinburgh University. JAMES D. FORBES, F.R.S.E., &c. &c., Professor of Natural Philosophy, Edinburgh University. EMERIC SZABAD, late Secretary under the Hungarian National Government of 1849.

Three Volumes are now published:

VOLUME I. contains the Preliminary Dissertations. By DUGALD STEWART, Sir JAMES MACKINTOSH, RICHARD WHATELY, D.D., JOHN PLAYFAIR, and Sir JOHN LESLIE.

VOLUME II. contains Articles from A to ANATOMY. Illustrated by numerous Engravings on Wood and Steel.

VOLUME III. contains Articles ANATOMY to ASTRONOMY. Illustrated by numerous Engravings on Wood and Steel.

SPECIMENS AND PROSPECTUSES MAY BE HAD OF ANY BOOKSELLER.

EDINBURGH: ADAM AND CHARLES BLACK. LONDON: LONGMEN & COMPANY; SIMPKIN & COMPANY; HAMILTON & COMPANY; WHITTAKER & COMPANY; SMITH, ELDER, & COMPANY, CORNHILL; HATCHARD, PICCADILLY; AND ALL BOOKSELLERS. BOOKS FOR CHRISTMAS.

MESSRS. ADAM & CHARLES BLACK have the following Works in preparation, suitable for Christmas Gifts:

**Lay of the Last Minstrel**, NEW EDITION ILLUSTRATED. Reprinted from the Author's interleaved Copy, and containing his latest Corrections and Additions. With ONE HUNDRED ILLUSTRATIONS from Designs by BIRKET FOSTER and JOHN GILBERT. Mr. Foster last Summer personally visited the District in which the Scenery described is situated, and his Illustrations embrace every Place of Interest noticed in the Poem. EXTRA CLOTH, GILT EDGES, 18s.; MOROCCO ELEGANT OR ANTIQUE, GILT EDGES, 25s. On 1st December.

**Lady of the Lake**, SECOND EDITION ILLUSTRATED. With the Author's latest Copyright Notes, Various Readings, and Additions. Profusely Illustrated by BIRKET FOSTER and JOHN GILBERT, and including several Additional Designs. EXTRA CLOTH, GILT EDGES, 18s.; MOROCCO ELEGANT OR ANTIQUE, GILT EDGES, 25s. On 10th November.

**Library Edition of the Waverley Novels**. Each Volume containing a complete Novel or Novels. This Edition is enriched with Portraits after ZUCCHERO, GODFREY KNELLER, VANDYKE, LE TOCQUE, &c., and Illustrations after WILKIE, LANDSEER, FRITH, WARD, PICKERGILL, ELMORE, EGG, HOOK, STONE, PHILLIPS, FAED, HORSEY, &c. IN TWENTY-FIVE VOLS. DEMY SVO, CLOTH LETTERED, £11:5s. On 15th November.

WORKS FOR CHRISTMAS GIFTS RECENTLY PUBLISHED:

**Uncle Tom's Cabin**, WITH ONE HUNDRED AND THIRTY ILLUSTRATIONS. A Frontispiece by JOHN GILBERT, and Ornamental Title-Page by PHIZ. EXTRA CLOTH, GILT EDGES, PRICE 10s.6d. EXTRACT FROM A LETTER FROM MRS. STOWE TO THE PUBLISHERS. "Accept my thanks for the copy of your Illustrated Edition of Uncle Tom's Cabin. From the examination I have been able to give it, I am disposed to regard it as the best in point of execution, particularly in respect to the woodcuts, which I have yet seen.—GLASGOW, April 14, 1853."

**Life of Sir Walter Scott**, BY J. G. LOCKHART, ESQ. New Edition, in One Vol. 12 Engravings, cloth, 7s. 6d.; extra, gilt edges, 8s. 6d. This contains much new and interesting matter relative to Abbotsford and Sir Walter Scott's Family.

**Poetical Works of Sir Walter Scott**, AUTHOR'S EDITION ILLUSTRATED. Twenty-four Engravings from Turner, cloth, lettered, 18s.; morocco, elegant or antique, gilt edges, 32s.

**Poetical Works of Sir Walter Scott**, AUTHOR'S EDITION. Six Engravings, cloth, gilt edges, 5s.; morocco antique, 10s. Large paper, cloth, gilt edges, 6s.; morocco antique, 10s. 6d.

**Tales of a Grandfather (History of Scotland)**, BY SIR WALTER SCOTT. Numerous Illustrations, 3 vols. cloth, lettered, 12s.; extra, gilt edges, 15s.

**Tales of a Grandfather (History of France)**, BY SIR WALTER SCOTT. Numerous Illustrations, cloth, lettered, 4s.; extra, gilt edges, 5s.

**Beauties of Sir Walter Scott**, (SELECTIONS FROM HIS WRITINGS). Two Engravings, cloth, lettered, gilt edges, 5s.; extra, gilt sides and edges, 6s.

**Readings for the Young**, FROM THE WORKS OF SIR WALTER SCOTT. Numerous Illustrations, 3 vols. in one, cloth, lettered, gilt edges, 7s.; separate vols. 2s. 6d.

ADAM & CHARLES BLACK, EDINBURGH.