Astronomy, from astros or aster, a star, and nomos, a law, is the science which treats of the laws observed by the stars in their motions. By an extension of signification, it embraces every thing that is known relating to the nature and constitution, as well as to the motions, of the celestial bodies.
The present treatise is divided into Four Parts. In the First, which contains the History of Astronomy, the progressive advancement of the science from the times of the Chaldeans and Egyptians to the present day is briefly sketched, and the labours of those illustrious individuals commemorated, who have either theoretically or practically contributed most to its progress. The Second Part, which we have denominated Theoretical Astronomy, is devoted to a general view of the science,—to the explanation of the different theories and methods by which the motions of the celestial bodies are represented, and their places computed; and the description of such facts as observation has made known respecting their nature and constitution. Part Third treats of Physical Astronomy; and Part Fourth of Practical Astronomy.
PART I.
HISTORY OF ASTRONOMY.
Astronomy, if we dignify by that name the first rude attempts that were made to discover the order and connection of the celestial motions, may probably be regarded as the most ancient of all the sciences. In fact, a certain degree of attention to the heavenly bodies is forced even on the savage who inhabits the forest, and derives his subsistence from the spontaneous productions of the earth. The regular vicissitude of day and night inevitably compels him to observe the diurnal course of the sun; and he cannot fail soon to perceive, that the variety and succession of the seasons is equally dependent on the oblique annual course of the same great luminary. The moon, too, in the absence of the sun, is an object so conspicuous, so consoling, and so useful, that her motions must at all times have been watched with attention and interest; while her various phases, her alternate waxings and wanings, her regular disappearance and return after equal intervals of time, would be contemplated with admiration and delight. Nor are the wonders of the starry firmament less calculated to strike even the most heedless observer of the heavens. The magnificent spectacle of the sky bespangled with brilliant points, and revolving in obedience to eternal and unalterable laws, affords a constant succession of new objects of sublime and exalted contemplation. The occasional recurrence, also, of eclipses and other unusual phenomena, which seem to interrupt the general order and uniformity of the celestial motions, would stimulate to attentive observation; for the vanity of man has in all ages rendered him eager to connect his own destiny with the heavens, while his timidity has prompted him to regard every apparent deviation from the ordinary course of events as an emblem of the wrath, and a precursor of the vengeance, of superior beings.
But though mankind were probably first impelled by motives of mere curiosity to observe the courses of the stars, no great length of time could elapse ere they perceived that the regular and uniform revolutions of the heavens might be rendered subservient to their own wants and conveniences. By the help of the stars the shepherd, during the night, could count the hours, the traveller track his course through the uniform wastes of the desert, and the mariner guide his bark over the ocean: the husbandman, also, learned to regulate his labours by the appearance of certain constellations, which gave him warning of the approaching seasons. The indications derived from the simple observation of such phenomena were doubtless extremely vague; but as civilisation advanced, the necessity of determining accurately the length of the solar year and of the lunar month, in order to regulate the calendar and the religious festivals, led to the accumulation and comparison of different observations, whereby errors were gradually diminished, and the foundations laid of a more perfect acquaintance with the heavenly motions.
Astronomy, presenting so many objects of interesting curiosity, and having so many practical uses, could not fail to be one of the sciences first cultivated by mankind. Its origin is consequently hid amidst the obscurity and traditions of the remotest ages, and is in fact coeval with the origin of society, and the earliest development of the human intellect. The records or traditions of almost every ancient nation furnish some traces of attention to the state of the heavens, and of some rude attempts to discover the laws, the order, and the period of the most remarkable phenomena,—such as eclipses of the sun and moon, the motions of the planets, and the heliacal risings of the principal stars and constellations. The Chaldeans and Egyptians, Chinese and Indians, Gauls and Peruvians, equally regard themselves as the inventors of astronomy; an honour, however, of which Josephus deprives them all, in order to ascribe it to the antediluvian patriarchs. The fables relating to the two columns of brick and marble which these sages are said to have erected, and on which they engraved the elements of their astronomy, to preserve them from the universal destruction by fire and water to which, they are said to have learned from Adam, the earth was doomed, are not worth the trouble of repetition; nor is there any better proof than the assertion of that credulous historian, of their acquaintance with the annus magnus, or, as is most probably supposed, the astronomical cycle of 600 years, which brings back the sun and moon to the same points of the heavens so nearly, that its discovery implies a pretty correct knowledge of the solar and lunar motions. Passing over, therefore, those periods that present us only with a scanty detail of traditional observations or unimportant facts, we will proceed to give a brief account of the state of astronomy among some early nations who have undoubtedly contributed to the improvement of the science, or who, at least, have transmitted to future ages some monuments of their Astronomy of the Chaldeans, Egyptians, Phoenicians, Chinese, and Indians.
According to the unanimous testimony of the Greek historians, the earliest traces of astronomical science are to be met with among the Chaldeans and Egyptians. The spacious level and unclouded horizon of Chaldea afforded the utmost facilities for observing the celestial phenomena; and its inhabitants, enjoying the leisure afforded by a pastoral life, and stimulated by the vain desire of obtaining a knowledge of the future from the aspects of the stars, assiduously cultivated astronomy and astrology. By a long series of observations of eclipses, extending, according to the testimony of some authors, over nineteen centuries, or even a longer period, they had discovered the cycle of 223 lunations, or eighteen solar years, which, by bringing back the moon to nearly the same position with respect to her nodes, her perigee, and the sun, brings back the eclipses in the same order. This is supposed to be the period which they distinguished by the name of Saros. They had others, to which they gave the names of Sossos and Neros; but nothing positive is known with regard to their nature or extent. One thing only is certain, which is, that these Chaldaic periods, whatever they were, were founded on no theoretical knowledge of the celestial motions. They were purely empirical, detected by the comparison of recorded observations, and suppose neither theory nor science, unless, indeed, a simple arithmetical operation is to be considered as such; nor is there any reason to suppose that the Chaldeans employed any process of computation whatever in their predictions of eclipses. Having once established their cycle, they were in possession of a simple means of predicting all those which occurred in the course of it, with as great a degree of accuracy as they considered requisite.
The knowledge of these lunisolar periods among the Chaldeans is doubtless of great antiquity. Simplicius, the commentator of Aristotle, asserts that Callisthenes transmitted to Aristotle from Babylon a collection of observations of all the eclipses which had happened during the nineteen centuries that preceded the conquest of Alexander. This relation, however, is at variance with the accounts given by other historians. Epigenes, cited by Seneca and Pliny, who is supposed to have lived shortly before the time of Alexander, mentions observations of 730 years that had been found preserved on columns of brick. Ptolemy also makes mention of certain observations of eclipses that had been brought from Babylon, several of which he had calculated and verified; but the earliest of these ascends only to the year 720 before our era, or to the 26th of Nabonassar; and if either Hipparchus or himself had been acquainted with others of a more ancient date, they would doubtless have employed them in the determination of the mean motion of the moon. From this circumstance it appears probable that the Chaldeans had no observation sufficiently exact to be of any use to astronomy prior to the time of Nabonassar.
According to Apollonius of Myndus, the Chaldeans supposed the comets to be substances of the same nature as the planets; that they are visible only during a portion of their revolutions, and that they re-appear after certain intervals. But this statement, which argues some just notions respecting the celestial bodies, is contradicted by Epigenes, who himself studied among the Chaldeans, and who affirms, that instead of regarding the comets as subjected like the planets to the operation of eternal laws, History, they attributed their formation to vortices of inflamed matter, supposing them to have only a temporary existence, and to move in random directions through the fields of space. Diodorus says, that they regarded the world as eternal and imperishable, and held that its order is due, not to chance, but to a divine providence; that the planets, which have peculiar motions, announce future events by their various aspects and colours; that they portend rains, tempests, excessive heats; sometimes also the appearance of comets, eclipses, earthquakes, and, in short, whatever has a beneficial or hurtful influence on the fortunes of nations or individuals.
From the few facts that can be gleaned from the vague accounts given by ancient authors of the astronomy of the ancient Chaldeans, it may be inferred that their boasted science was confined to observations of the simplest and rudest kind, neither guided by theory, nor assisted by instruments; for, notwithstanding the assertion of Herodotus, it is doubtful if they were acquainted even with the gnomon, the simplest of all instruments for determining the obliquity of the ecliptic, the altitude of the pole, and the length of the tropical year. If to the knowledge of their lunisolar periods, the result of ages of observation, we add the notion of a spherical revolution about an inclined axis, and an idea of the principal circles of the sphere and the position of the poles, the sum will comprehend all that constituted the science of a people regarded by antiquity as having made the greatest progress in the science of the stars. Astronomy, however, owes some obligations to their humble labours. The observations which they recorded served to correct the theories that were afterwards imagined by the more brilliant genius of the Greeks, and thereby furnished some materials for the edifice of the world.
The Egyptians were in ancient times the rivals of the Egyptians-Chaldeans in the cultivation of astronomy; and although they have left behind them still fewer monuments of their labours, they have obtained, through the exaggerated statements of the Greeks, even a greater reputation. The Greeks acknowledge themselves indebted to the Egyptians for their science and civilisation; but regarding themselves likewise as descendants of that ancient people, they indulged their vain-glory in magnifying the accounts of the antiquity and knowledge of their supposed ancestors. It is not improbable that some traditional observations of the heavens, along with some arts indispensable to society even in its earliest stages, were carried into Europe by tribes migrating from the banks of the Nile; and it is certain that the early philosophers of Greece travelled into Egypt for the purpose of acquiring a more perfect knowledge of astronomy than could be obtained in their own country. But the facts from which it can be inferred that the Egyptians had much to communicate, are few and ill attested. They are also blended with so much absurdity and fable, that no accurate notions can be formed, from the accounts that have been transmitted to us, of the real advances which that people had made in astronomical science. The priests were the depositaries of the national knowledge; and they carefully concealed it from the vulgar by shrouding it in allegories, traces of which, it has been remarked, may be detected in the institutions even of the present day.
According to Diogenes Laertius, the Egyptians reckoned 48,853 years from Vulcan to Alexander, during which they had observed 373 eclipses of the sun, and 832 of the moon. These numbers in fact nearly express the relative proportion of the eclipses of the two luminaries; but the enormous length of the period altogether exceeds History, the bounds of credibility; and it has been remarked that the same number of eclipses might have been observed within the more probable period of twelve or thirteen centuries. Supposing the numbers to be accurately stated, it will follow that, as the observations terminated with the conquest of Alexander, the Egyptians must have been in the habit of observing eclipses at least 1600 years before the commencement of our era. By attentively observing the heliacal rising of the star Sirius, to which they gave the name of Thaat, or Thoth (the Watch-Dog), because its appearance shortly preceded the overflow of the waters of the Nile, the Egyptians had discovered that the year consists of 365\(\frac{1}{4}\) days. This was their religious or sacred year. Their civil year consisted of only 365 days; consequently the sacrifices and feasts, which were regulated by it, successively corresponded to the different seasons. Instead of attempting to obviate this inconvenience by intercalation, they imposed an oath on their kings to maintain the use of the civil year, superstitiously imagining that each of the seasons would be blessed and rendered prosperous by enjoying in its turn the celebration of the feast of Isis. The difference between the lengths of the sacred and civil year suggested to them their famous sothic or canicular period of 1460 solar years, corresponding to 1461 civil years of 365 days, and which consequently brings back the months and festivals to the same seasons. Dion Cassius ascribes the week to the Egyptians, and says that they first dedicated a day to each of the planets; but it is sufficiently proved that this short cycle was in use among the Chinese and Indians from the remotest times, and was even known to the Druids of Gaul and Britain. It was more probably suggested to different nations by the phases of the moon. The Egyptians had likewise been attentive to the courses of the planets. Diodorus Siculus affirms that they could explain the phenomena of the stations and retrogradations; and Macrobius ascribes to them the knowledge of the real motions of Mercury and Venus, and says that they regarded these planets as satellites of the sun. This notion would do credit to their philosophy; but it is unfortunately not mentioned by any other author, and for this reason the testimony of Macrobius is suspected. The state of their practical astronomy may in some measure be inferred from the means they employed to determine the magnitude of the sun's apparent diameter. By comparing the time, observed by means of a clepsydra, which the sun takes to mount above the horizon at the equinox, with that in which he makes a complete revolution of the sky, they estimated his diameter at \(28^\circ 48'\). An observation of this kind is liable to great uncertainty; and as there is no evidence that the Egyptians possessed the slightest knowledge of spherical trigonometry, they would probably make no allowance for the obliquity of the equator to their horizon; and if this correction was left out of the calculation, as it probably was, their diameter, already too small, ought to have been still farther reduced, and to have amounted only to \(24^\circ 42'\).
It has been conjectured by Goguet, that the obelisks of Egypt were intended to serve the purpose of gnomons; and this conjecture acquires some probability from their needle-shaped form, and the narrowness of their bases relatively to their heights. It has however been proved by MM. Jollois and Devilliers, in their description of Thebes, that the obelisks were connected with the walls of temples and palaces; a disposition which rendered them entirely unfit for the purposes of astronomical observation. Their summits were also of so unfavourable a form, that the Romans were obliged to surmount them with a ball in order to obtain a distinct and well-defined shadow. The pyramids have also been adduced as evidences of the early progress of astronomy among the Egyptians; for History, the faces of these stupendous masses are turned directly towards the four cardinal points, from which it is evident that the people by whom they were constructed were at least acquainted with the method of tracing a meridional line.
From this brief account it appears, that the only circumstances with which we are acquainted that imply the knowledge of astronomical methods among the Egyptians, are the length of the year, the doubtful discovery of the true motions of Mercury and Venus, and the position of the pyramids. The Chaldean observations were of use to Hipparchus and Ptolemy in the determination of some important elements; but those of the Egyptians exercised no influence whatever on the future progress of the science.
The Phoenicians are also generally enumerated among the nations who cultivated astronomy at a very early date. Period, though it does not appear, from any facts mentioned by ancient authors, that they addicted themselves to the observation of the heavens, or made any discoveries relative to the motions of the planets. That they excelled in the art of navigation is certain, from the commercial intercourse which they carried on with many places on the coasts of Africa and Spain, and in the principal islands of the Mediterranean; and it may readily be allowed that in their long voyages they would direct their course during the night by the circumpolar stars. If they had any speculative notions of astronomy, these were probably derived from the Chaldeans or Egyptians.
In China, astronomy has been cultivated from the remotest ages, and always been considered as a science indispensably necessary to the civil government of the state. The Chinese boast of a series of eclipses, recorded in the annals of the nation, extending over a period of 3858 years, all of which, they pretend, were not only carefully observed, but calculated and figured previous to their occurrence. The same motives which led the Chaldeans and Egyptians to attend to the celestial phenomena, namely, the regulation and division of time, had equal influence among the Chinese; and we accordingly find the care of the calendar occupying the attention of their earliest princes. The emperor Fou-Hi, whose reign commenced about 2857 years before our era, is said to have assiduously studied the motions of the celestial bodies, and laboured to instruct his ignorant subjects in the mysteries of astronomy. But as they were yet in too rude a condition to be able to comprehend his theories, he was obliged to content himself with giving them a rule for the computation of time by means of the numbers 10 and 12, the combination of which produces the cycle of 60 years, which is the standard or unit from which they deduce their hours, days, and months. Tradition is silent with respect to the sources from which Fou-Hi derived his own knowledge. The Chinese attribute to him also the invention of arithmetic and music. In the year 2808 B.C., Hoang-Ti caused an observatory to be built, for the purpose of correcting the calendar, which had already fallen into great confusion, and appointed one set of astronomers to observe the course of the sun, another that of the moon, and a third that of the stars. It was then discovered that the twelve lunar months do not exactly correspond with a solar year; and that, in order to restore the coincidence, it was necessary to intercalate seven lunations in the space of nineteen years. If this fact rested on undoubted evidence, it would follow that the Chinese had anticipated the Greeks by 2000 years in the discovery of the Metonic cycle. The reign of Hoang-Ti is also rendered memorable by the institution of the Mathematical Tribunal, for promoting the science of History. astronomy, and regularly predicting eclipses, to which an extraordinary importance has always been attached in China. The members of this celebrated tribunal were made responsible with their lives for the accuracy of their predictions, by a law of the empire, which ordained that, "whether the instant of the occurrence of any celestial phenomenon was erroneously assigned, or the phenomenon itself not foreseen and predicted, either negligence should be punished with death." In the reign of Tchong-Kang, the two mathematicians of the empire, Ho and Hi, were the victims of this absurd and sanguinary law; an eclipse having taken place which their skill had not enabled them to foresee.
The emperor Yao, who mounted the throne, according to the Chinese annals, about the year 2317 B.C., gave a new impulse to the study of astronomy, which had begun already to decline. He ordered his astronomers to observe with the utmost care the motions of the sun and moon, of the planets and the stars, and to determine the exact length of each of the four seasons. He sent Hi-Tchong to the east to observe the star situated at the point of the vernal equinox, Hi-Tchou to the south to examine that at the summer solstice, Ho-Tchong to the west, and Ho-Tchou to the north, to observe those situated respectively at the autumnal equinox and winter solstice. These docile observers found stars in the positions assigned by the emperor; but the extraordinary resemblance of their names imparts a fabulous air to the whole relation, and excites a very excusable incredulity even with regard to those statements which involve no improbability. To this emperor are attributed the Chinese division of the zodiac into 28 constellations, called the houses of the moon, and the severe laws already noticed in regard to the erroneous prediction of the celestial phenomena.
From the time of Yao the Chinese year consisted of 365\(\frac{1}{4}\) days. They also divided the circle into 365\(\frac{1}{4}\) degrees, so that the sun daily described in his orbit an arc of one Chinese degree. Their common lunar year consisted of 364\(\frac{3}{4}\) days; and by combining this number with 365\(\frac{1}{4}\), they formed the period of 4617 years, after which the sun and moon again occupy the same relative positions.
The earliest Chinese observations we are acquainted with, sufficiently precise to afford any result useful to astronomy, were made by Tchou-Kong, whose reign commenced about the year 1100 before our era. Two of these observations are meridional altitudes of the sun, observed with great care at the village of Loyang, at the time of the summer and winter solstices. The obliquity of the ecliptic thus determined at that remote epoch is 23° 54' 3½"; a result which perfectly agrees with the theory of universal gravitation. Another observation, made about the same time, relates to the position of the winter solstice in the heavens; and it also corresponds to within a minute of a degree with the calculations of Laplace. Laplace considers this extraordinary conformity as an indubitable proof of the authenticity of those ancient observations.
The golden age of Chinese astronomy extended from the reign of Fou-Hi to the year 480 B.C.; that is, over a space of 2500 years. It is only, however, towards the latter part of this long period that the history of China becomes in any degree authentic; and the true date which must be assigned for the commencement of observations on which any reliance can be placed, is the year 722 B.C.; that is, 25 years posterior to the era of Nabonassar. From that period to the year 400 B.C. Confucius reckons a series of 36 eclipses, and of these 31 have been verified by modern astronomers. After this the science fell into great neglect, notwithstanding the inveterate tenacity with which the Chinese in general adhere to their ancient customs. The decline of their astronomy is ascribed, whether justly or not, to the barbarous policy of the emperor Tsin-Chi-Hong-Ti, who, in the year 221 B.C., ordered all the books to be destroyed, excepting those only which related to agriculture, medicine, and astrology, the only sciences which he considered as being of any use to mankind. His fury, it is true, was principally directed against those of Confucius, the stern morality of which he felt to be a censure on his own profigacy; but those of science and astronomy were included in the general destruction. In this manner, it is said, the precious mass of astronomical observations and precepts which had been accumulating for ages was irretrievably lost.
Lieou-Pang, the successor of Tsin-Chi-Hong, endeavoured to repair the disaster, by re-establishing the tribunal of the mathematicians, and ordering a new series of observations to be undertaken. About the year 104 B.C. the astronomer Sse-Ma-Tsien gave some precepts for the calculation of eclipses, the motions of the planets, and the syzygies. He employed instruments of copper, the nature and construction of which are however not very well understood, for measuring the extent of the 28 zodiacal constellations; and he observed the meridional altitudes of the sun, by means of a gnomon 8 feet high. The differences of right ascensions, and the intervals between the risings, settings, and culminations of the stars, were measured by clepsydrae. It would appear that after this period astronomical observations continued for some time to be made in China with considerable regularity. In the 164th year of our era the astronomer Tchang-Heng constructed armillary spheres and a celestial globe. He also formed a catalogue of stars, which is said to have contained 2500, but without either latitudes or longitudes; a circumstance which gives us a very unfavourable idea of the state of practical astronomy at that time. About the eighth century of our era, all knowledge of the science seems to have been again lost. The predictions were erroneous; and the Chinese witnessed, with superstitious terror, eclipses of which their astronomers had given them no intimation. This induced the emperor Hieng-Tsong to call to his court the astronomer Y-Hang, by whose indefatigable activity a reform was speedily effected. With a view to determine the situations of the principal places of the empire, this astronomer constructed gnomons, spheres, astrolabes, quadrants, and other instruments; and sent one company of mathematicians to the south, and another to the north, with directions to observe daily the altitudes of the sun and the polar star. The latitudes of the cities were determined by observing the shadow of the gnomon, and the longitudes by eclipses of the moon. Y-Hang had the mortification of announcing two eclipses which did not take place. On these occasions he alleged the usual excuse, namely, that his calculus was not in error, but that the celestial bodies had deviated from their ordinary courses out of respect to the virtues of the emperor. The fate of Ho and Hi had probably suggested to the Chinese astronomers this ingenious mode of disarming the emperor's resentment by flattering his vanity.
On considering attentively the accounts which have been given of the Chinese astronomy, we find that it consisted only in the practice of observations which led to nothing more than the knowledge of a few isolated facts. The missionaries who were sent out by the Jesuits about the end of the seventeenth century, to whom we are indebted for what is known of the early history History of China, either seduced by some appearances of truth, or thinking it prudent to conciliate the people whom they were attempting to convert, adopted their marvelous relations regarding the antiquity of their science, and spread them over Europe. As the history of the nation begins to become more authentic, their astronomy shrinks into its real but insignificant dimensions. Superstitiously attached to their ancient usages, and blindly adopting the habits of their ancestors, the Chinese continued to observe the heavens from century to century without making the slightest advances in theoretical knowledge. In later times they have adopted many improvements, for which they are entirely indebted to foreigners. During the time of the caliphs many Mahometans passed into China, carrying with them the astronomical methods and knowledge of the Arabians. The missionaries introduced the science of Europe; and the most that can be said in praise of the Chinese is, that their government sometimes relaxed so far its spirit of jealousy and exclusion, as to afford protection to these strangers, adopt their arts, and place them at the head of the mathematical tribunal.
The astronomy of the Indians forms one of the most curious problems which the history of science presents to the consideration of the learned, and one which, notwithstanding the numerous dissertations to which it has given rise, still continues involved in great uncertainty. Of the science of the ancient nations, of which we have already spoken, the accounts which have come down to our times are founded on conjecture and tradition; for few monuments remain to confirm or confute the glowing descriptions which authors have given of its high antiquity and great perfection. But the claims of the Indians rest on more solid foundations. We are in possession of the tables from which they compute the eclipses and places of the planets, and of the methods by which they effect the computation: we have, in short, an Indian astronomy committed to writing, which represents the celestial phenomena with considerable exactness, and which, therefore, could only be produced by a people far advanced in science. But the difficulty of the problem consists in determining the sources from which this science originated, and the epoch of its existence; whether it was created by the people who now blindly follow its precepts without understanding its principles, or was communicated to them by another race of a bolder and more original genius, through channels with which we are unacquainted. Some authors regard India as the cradle of all the sciences, particularly of astronomy, which they suppose to have been cultivated there from the remotest ages; others date the origin of the Indian astronomy from the period when Pythagoras travelled into that country, and carried thither the arts and sciences of the Greeks; a third opinion is, that astronomy was conveyed to India by the Arabians in the ninth century of our era, and that the Brahmins are only entitled to the humble merit of adapting the rules and practices of that people to their own peculiar methods of calculation. We shall endeavour to describe very briefly the existing monuments of the Indian astronomy, which furnish the only data from which a rational conjecture can be formed relative to its antiquity and precision.
We possess four different sets of tables of Indian astronomy. The first which were known in Europe were brought from Siam by La Loubère, who had resided in that country as ambassador from Louis XIV. They were communicated by him to the celebrated Cassini, who, notwithstanding the difficulties arising from the complicated and useless operations which they directed, succeeded in detecting the principles on which they were constructed, and in explaining their use and signification. The date of these tables corresponds to the 21st of March in the year 638 of our era. They suppose two species of years, the solar tropical year, which they make to consist of 365 days 5 hours 50 min. and 4 sec., and the solar anomalistic year, that is, the period in which the sun returns to its apogee, which they estimate at 365 days 6 hours 12 min. 36 sec. This determination of the length of the solar year is too great only by 1 min. 15 sec. By means of the same tables the longitudes of the sun and moon are determined with considerable accuracy. They contain a correction for the sun's mean place, which corresponds to the equation of the centre. At 90° from the apogee, where the inequality of the sun's motion is greatest, they estimate the requisite correction at 2° 12', which is about 16' too great. This determination deserves to be particularly remarked, because, on account of a secular inequality of the eccentricity of the sun's orbit, there was once a time when the greatest value of the equation of the centre was nearly 2° 12'; and this fact is adduced as a proof of the remote antiquity of the observations from which the tables in question have been constructed. These tables suppose the apogee to retain always the same position relatively to the fixed stars; in reality it advances or gains on the stars about 10" annually; but the supposition is still much nearer the truth than in the system of Ptolemy, where the apogee is supposed to be absolutely at rest with regard to the plane of the sun's orbit, and consequently to fall back among the stars by the whole quantity of the precession of the equinoxes, or about 50" annually. With regard to the motions of the moon, they are deduced from a period of 19 years, in which are comprehended nearly 235 lunations; so that the cycle of Meton appears to have been known in Siam as well as in China. The moon's apogee is supposed to have been in the beginning of the movable zodiac 621 days after the epoch of the 21st of March 638, and to make an entire revolution in the heavens in the space of 3232 days. The first of these suppositions agrees with Mayer's tables to within a degree, and the second differs from them only by 11 hours 14 min. 31 sec. They contain only one correction for the two principal inequalities of the moon's motion, the equation of the centre and the excentricity.
A second set of Indian tables was sent from Chrismabouram, a town in the Carnatic, by Father Du Champ, to De Lisle, about the year 1750. They are fifteen in number. They give the mean motions of the sun, moon, and planets; equations of the centre for the sun and moon; and two corrections for each of the planets, one of which corresponds to the apparent, the other to the real inequality. The epoch of these tables is not so ancient as that of the former. It corresponds to the 10th of March, at sunrise, in the year 1491 of our era, when the sun and moon were in conjunction.
A third set of astronomical tables was sent from India by Father Patonillet, and received by De Lisle about the same time with those of Chrismabouram. These have not the name of any particular place affixed to them; but being calculated for the latitude of 16° 16', Bailly thinks it probable that they came from Narsapur. Their epoch is midnight, between the 17th and 18th of March 1569.
The fourth and last set of Indian tables which we possess have been published in the Memoirs of the Academy of Sciences. They were communicated by a learned Brahmin of Tirvalore, a small town on the Coromandel coast, to the French astronomer Legentil, who had gone to India to observe the transit of Venus in 1769. The tables History of Tirvalore, though somewhat different in form, present many points of resemblance with those formerly known in Europe. They suppose the same length of the year, the same inequalities of the sun and moon, and they are adapted nearly to the same meridian. But while they correspond with the other tables in these elements, they differ from them greatly in the antiquity of their epoch, which goes back to the famous era of the Calyougham, that is, the beginning of the year 3102 before Christ.
Now, the only question to be determined with regard to the antiquity of the Indian astronomy is, whether this epoch is real or fictitious; that is, whether the state of the heavens at the commencement of the Calyougham, as assumed in these tables, was actually determined by observation, or computed backwards from observations of more modern date. The solution to this question can only be obtained from the internal evidence afforded by the tables themselves; by examining whether the elements and precepts which they furnish are of sufficient accuracy to enable the places of the sun, moon, and planets to be calculated through a period of 44 centuries, without involving errors which the refined accuracy of the modern tables furnishes the means of detecting. A comparison of the Indian with the modern tables has been made at great length by Bailly, who imagines that he finds ample evidence of the reality of the era in question, and of the existence of an astronomy prior to that period, hardly yielding in accuracy to that which modern science has built on the theory of universal gravitation. The theory of Bailly has been adopted, and put forth with additional clearness and evidence, by the late Professor Playfair.
One of the principal arguments which these illustrious authors bring forward in support of it is founded on the longitudes of the sun and moon. The mean place of the moon at the commencement of the Calyougham, that is, at midnight, between the 17th and 18th of February 3102 B.C., is stated by the Indian tables to be 306°. Her mean place, computed from Mayer's tables, without taking into account the acceleration, with which the Indians in the 15th century were of course unacquainted, is 300° 51' 16". Hence there would be a discrepancy of 5° 8' 44". But, according to the theory and last tables of Laplace, the moon, in virtue of the acceleration of her mean motion, has passed over an arc of very nearly 6° more than she would have done had her mean motion continued uniform from the period of the Calyougham to the date of Mayer's tables. This added to 300° 51' 16" gives 306° 51' 16" for the mean longitude of the moon at the epoch of the Calyougham, differing from the Indian determination by only 51' 16". Now, it is argued that this is a degree of accuracy which could have been reached only by actual observation, especially since, if the tables had been computed backwards, the error arising from the acceleration alone would have amounted to more than 5°. Bailly computes the place of the moon at the same epoch, from all the tables, Greek and Arabian, to which the Indians can be supposed to have had access, and the discrepancies are so great as to render his conclusion almost inevitable, that the Indian tables could not possibly have been drawn from such sources. The tables of Ptolemy make the moon's longitude at that time 11° 52' 7" greater than the Indian tables; and those of Ulugh-Beigh, constructed at Samarqand in 1437, give a difference of 6° also in excess.
Similar results are obtained from the consideration of other elements. According to the tables of Tirvalore, the tropical year consists of 365 days 5 hours 50 min. 35 sec. Lalande makes it 365 days 5 hours 48 min. 49 sec. The difference is 1 min. 46 sec. Now the tropical year, being affected by the precession of the equinoxes, History is subject to a secular inequality, which, according to the theory of Lagrange, renders it actually shorter by 40.5 sec. at the present time than it was at the commencement of the Calyougham. The error of the Indian tables is thus reduced to 1 min. 55 sec. In like manner, the obliquity of the ecliptic, which has been gradually diminishing during a great number of centuries, is supposed in the Indian tables to be greater than it is now found to be by observation. The Brahmins estimate it at 24°. The formula of Lagrange makes the variation, in 4800 years, amount to 22° 32'. This therefore must be added to its obliquity in 1700, that is, to 23° 28' 41", in order to have the true obliquity at the commencement of the Calyougham. The sum is 25° 51' 13", and falls short of the Indian determination by 8' 47". We shall mention only another element, the equation of the centre of the sun. Bailly calculates that, according to the theory of Lagrange, the equation of the sun's centre, at the epoch of the tables, was 2° 6' 28". The Indians make it 2° 10' 32". The difference is only about 4', and incomparably less than could have resulted from calculation by any methods which we can suppose the Indians to have possessed.
These arguments, it must be admitted, are exceedingly specious, but they are not by any means convincing. Even with the best modern tables we could not, as Bailly himself acknowledges, answer for the accuracy of the places of the sun and moon computed for so remote an epoch. The corrections for the secular inequalities amount in that long period to considerable quantities; and these corrections are deduced by theory from elements with respect to which there exists great uncertainty. And if we cannot be sure of the true places by computing backwards from our own tables, with what degree of confidence can we pronounce upon the accuracy of the places assigned in the tables of the Indians? It may be said that comparisons of this kind can never be supposed to give results perfectly alike. Granted; but if the discrepancies are such that the lapse of a thousand years more or less is required to establish a rigorous conformity, what becomes of the famous epoch of the Calyougham? Some of the elements of the Indian tables could not have the values assigned to them but at a long period before that epoch. In order to find their equation of the sun's centre, for example, it is necessary, according to the results of modern theory, to go back to 6000 years before our era. The argument, therefore, proves too much, and is consequently inconclusive. The different sets of tables of which we have spoken are closely allied with each other, and the most probable supposition is, that they are all derived from those of Chrismabouram, of which the epoch is 1491. At that era the Indians were acquainted with the instruments, the geometry, and the researches of the Arabians and Greeks. Through this channel the tables seem to have come into their possession. The Brahmins adapted them to their own particular methods of computation, and threw back their epoch to the period when, according to these tables, all the planets were in conjunction with the sun. Every circumstance connected with the science of the Indians conspires to give us the humblest ideas of its value. Their methods of computation are encumbered with the unnecessary multiplications and divisions of enormous numbers, endless additions, subtractions, and reductions, for the purpose of obtaining numbers which could be put into technical verses, and even adapted to songs; so that the astronomer might be enabled to effect his calculations from memory alone, without its being necessary to have History. recourse to tables or books. But simple and rude as these methods are, if they were really invented by the Brahmans, the science of that people must have greatly retrograded; for at present they merely follow a blind routine, utterly ignorant of theory, or the principles on which their processes are founded. Their astronomy, whether of ancient or recent origin, has produced no effect whatever on that of Europe; it has no filiation or connection with the science of the present day, and therefore has no other claim on our attention than such as may result from motives of mere curiosity.
Astronomy of the Greeks.
The origin of astronomy in Greece, as in other early nations, ascends beyond the period of authentic history, and is concealed amidst the fables and traditions of the remotest times. During the darkness of the heroic ages some gleams of an acquaintance with the motions of the stars occasionally burst forth; and some traces appear of astronomical observations, probably derived from Egypt, the country which also furnished Greece with its gods and its arts. The Greeks seem to have divided the heavens into constellations about 13 or 14 centuries before the Christian era; for the sphere of Eudoxus, which is probably one of the fruits of the famous voyage of the Argonauts, must be referred to that period. Their early attention to the appearances of the heavens is sufficiently attested by their mythological fables, the greater part of which are only allegories of the celestial motions, and of the operations of nature. The lively fancy and brilliant imagination of this ingenious people strewed flowers in the most rugged paths, and spread agreeable images over the driest and most uninviting subjects; hence the sky was quickly covered with legends of the loves and exploits of gods and heroes. It would be foreign to our present purpose to enter into an enumeration of these fables, or attempt to trace their connection with the first dawns of astronomy; we shall content ourselves with barely alluding to Uranus, to Atlas and his son Hesperus, who gave his name to the planet Venus; also to his daughters the Atlantides, from whom the Pleiades received their appellation; to Endymion, who, on the summit of Mount Latmos, held nocturnal converse with the chaste Diana; to Hercules; and Chiron the centaur, who taught men the use of the constellations; Museus, who imagined the figures of men and animals which cover the celestial sphere; Orpheus and Linus, who explained the theogonies; Atreus, from whose banquet the sun fled back with horror; and Tiresias, who was struck blind for having witnessed some secret of the gods.
The true foundations of Grecian science were laid by Thales, who was born at Miletus 640 years before our era. He was descended from an illustrious family, which had formerly reigned in Phoenicia, and inherited an ample fortune, which he expended in collecting the expiring embers of oriental science. Instigated by the love of knowledge, he travelled first into Crete, and afterwards into Egypt, where he was initiated into the mysteries of the priests, to whom, in return, he is said to have taught the method of measuring the height of the pyramids by comparing their shadows with those of known objects. Returned to his own country, he publicly taught the truths he had collected during his travels, and formed a sect which has been distinguished by the title of the History Ionian School. His doctrines regarding astronomy contain a few truths which do honour to his sagacity and observation, though they are mixed with much error and absurdity. He taught that the stars are formed of fire; that the moon receives her light from the sun, and is invisible at her conjunctions, because she is hid in the sun's rays. He also taught the sphericity of the earth, which he placed at the centre of the world. He divided the sphere into five zones, by the arctic and antarctic circles, and the two tropics; and held that the equator is cut obliquely by the ecliptic, and perpendicularly by the meridian. He is also said to have observed eclipses; and Herodotus relates that he predicted the famous one which put a stop to the war between the Medes and the Lydians. It does not appear, however, that he ventured to assign either the day or the month of the eclipse, so that his prediction must have been confined to the year. According to Callimachus, he determined the positions of the stars which form the Lesser Bear, by which the Phoenicians guided themselves in their voyages. It is difficult, however, to conceive how Thales, unacquainted with instruments, could determine the positions of stars with so much accuracy as to render any essential assistance to the navigator. It is probable that he only pointed out the configuration, and some of the more brilliant stars of that constellation, among which he might remark that which is nearest the pole of the world.
Thales was succeeded by Anaximander, to whom is also attributed the invention of the sphere, and the knowledge of the zodiac. According to Diogenes Laertius, he supposed, like his master Thales, the earth to be spherical, and placed at the centre of the universe; but Plutarch ascribes to him the less philosophical opinion of its resemblance to a column. He supposed the sun to be of equal magnitude with the earth. He invented the gnomon, and placed one at Lacedemon to observe the solstices and equinoxes. But the circumstance which does most honour to Anaximander, and which entitles him to the gratitude of posterity, is the invention of geographical charts. He is said also to have believed in the plurality of worlds,—a sublime idea, which was adopted by almost every succeeding philosopher of Greece.
Anaximenes succeeded Anaximander in the Ionian school, and maintained nearly the same doctrines. Pliny, born says he was the first who taught the art of constructing dials,—an invention which, as we have just seen, has also been ascribed to Anaximander. These two philosophers probably revived the knowledge of an instrument the use of which had been forgotten amidst the general rudeness and ignorance of their countrymen. Before their time the Greeks only marked the divisions of the day by the different lengths of the sun's shadow.
Anaxagoras was the disciple and successor of Anaximenes. If this philosopher really entertained the ridiculous opinions ascribed to him by Plutarch, the Ionian school must rather have retrograded than advanced in sound philosophy from the time of Thales. He is said to have believed that the sun is a mass of red-hot iron, or of heated stone, somewhat bigger than the Peloponnese,—that the heaven is a vault of stones, which is prevented from tumbling only by the rapidity of its circular motion,—and that the sun is prevented from advancing beyond the tropics by a thick and dense atmosphere, which forces
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1 For an account of the Indian astronomy, see Bailly, Astronomie Indienne; also a Memoir by Professor Playfair, in the Edinburgh Transactions, vol. ii., or in the 3d volume of his Works; and the Papers of Jones, Bentley, and Davis, in the Calcutta Memoirs. The theory of Bailly is most satisfactorily refuted by Delambre. See his Histoire de l'Astronomie Ancienne, tom. i. him to retrace his course. These absurd notions are probably greatly exaggerated; but it does not appear that Anaxagoras contributed much to extend the knowledge of the heavens. A melancholy interest is, however, excited in his behalf; on account of the persecution which he suffered in consequence of his liberal opinions and his disregard for the superstitious notions of his age. Having shown the reason of the eclipses of the moon, he was accused of ascribing to natural causes the attributes and power of the gods. Having taught the existence of only one God, he was accused of impiety and treason towards his country. Sentence of death was pronounced on the philosopher and all his family; and it required the powerful interest of his friend and disciple Pericles to obtain a commutation of this iniquitous sentence into one of perpetual banishment.
While the Ionian sect was so successfully employed in cultivating and propagating a knowledge of nature in Greece, another, still more celebrated, was founded in Italy by Pythagoras. This renowned philosopher was in early youth a disciple of Thales. In quest of knowledge, which in those days could only be obtained by visiting the sages of foreign lands, he travelled into Egypt, Phoenicia, Chaldea, and India, where his memory is said still to subsist. Through the favour of Amadis, king of Egypt, to whom he was recommended by Polycrates, the tyrant of Samos, he was admitted into the sacred college at Memphis, though with great reluctance on the part of the priests. The severe ordeal through which these charlatans compelled him to pass, before they would consent to initiate him into their mysteries, was sufficient to have deterred the most courageous votary of knowledge; and Pythagoras was probably the only stranger who ever succeeded in fully exploring their secrets. After an absence of thirty years he returned to Greece, and began to give instructions in his native island of Samos. Soon after, he passed over to the Grecian colony established at Tarentum in Italy, and settled at Crotona, where he speedily acquired a splendid reputation. He was the first who assumed the modest title of philosopher, or lover of wisdom: formerly those who devoted themselves to the acquisition of learning were called sophists or sages.
Pythagoras is said to have acquired in Egypt the knowledge of the obliquity of the ecliptic, and that of the identity of the morning and evening stars. What he chiefly deserves to be commemorated for in the history of astronomy, is his philosophical doctrine regarding the motion of the earth. He taught publicly that the earth is placed at the centre of the universe; but among his chosen disciples he propagated the doctrine that the sun occupies the centre of the planetary world, and that the earth is a planet circulating about the sun. This system, which still retains his name, being called the old or Pythagorean system of the universe, is that which was revived by Copernicus. It is, however, only just to the memory of this last mentioned great man to observe, that there is a vast difference between the bare statement of the possibility of a fact, and the demonstration of its existence by irrefragable arguments. Pythagoras having remarked the relation which subsists between the tone of a musical chord and the rapidity of its vibration, was led by analogy to extend the same relation to the planets, and to suppose that they emit sounds proportional to their respective distances, and form a celestial concert too melodious to affect the gross organs of mankind. Another fancy into which he was led by his passion for analogies, was the application of the five geometrical solids to the elements of the world. The cube symbolically represented the earth; the pyramid, fire; the octaedron, air; the icosedron, or twenty-sided figure, water; and the dodecaedron, or figure with twelve faces, the exterior sphere of the universe. Pythagoras left no writings; and it is doubtful whether he really entertained many of the opinions and reveries which have usually been ascribed to him.
Philolaus of Crotona, a disciple of Pythagoras, embraced the doctrine of his master with regard to the revolution of the earth about the sun. He supposed the sun to be a disk of glass which reflects the light of the world. He made the lunar month consist of 29½ days, the lunar year of 354 days, and the solar year of 365½ days.
Nicetas of Syracuse seems to have been the first who openly taught the Pythagorean system of the universe. Cicero, on the authority of Theophrastus, the ancient historian of astronomy, gives him the credit of maintaining that the apparent motion of the stars arises from the diurnal motion of the earth about its axis; but this rational doctrine seems to have been first broached by Heraclides of Pontus, and Ephantus, a disciple of Pythagoras.
The introduction of the Metonic cycle forms an era in the history of the early astronomy of Greece. The Chaldeans, as we have already stated, established several lunar periods; and the difficulty of reconciling the motions of the sun and moon, or of assigning a period at the end of which these two luminaries again occupy the same positions relatively to the stars, had long embarrassed those who had the care of regulating the festivals. Meton and Euctemon had the honour of first obviating this difficulty, at least for a time; for the motions of the sun and moon being incommensurable, no period can be assigned which will bring them back to precisely the same situations. These two astronomers formed a cycle of nineteen lunar years, twelve of which contained each 12 lunations, and the seven others each 13, which they intercalated among the former. It had long been known that the synodic month consisted of 29½ days nearly; and in order to avoid the fraction, it had been usual to make the twelve synodic months, which compose the solar year, to consist of 29 and 30 days alternately; the former being called deficient and the latter full months. Meton made his period to consist of 125 full and 110 deficient months, which gives 6940 days for the 235 lunations, and is nearly equal to 19 solar years. This cycle commenced on the 16th of July in the year 433 B.C. It was received with acclamation by the people assembled at the Olympic games, and adopted in all the cities and colonies of Greece. It was also engraved in golden letters on tables of brass, whence it received the appellation of the golden number, and has been the basis of the calendars of all the nations of modern Europe. It is still in ecclesiastical use, with such modifications as time has rendered necessary.
Eudoxus of Cnidus, about the year 370 B.C., obtained Eudoxus, great reputation as an astronomer. According to Pliny, 370 B.C. he introduced the year of 365½ days into Greece. Archimedes says that he supposed the diameter of the sun to be nine times greater than that of the moon, which shows that he had in some degree overcome the illusions
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1 "Nicetas Syracusius, ut ait Theophrastus, coelum, solem, lunam, stellas, supera denique omnia, stare censet; neque, praeter terram, rem ullam in mundo moveri; quae cum circum axem se summa celerritate convertat et torquet, eadem effici omnia, quasi, stante terra, coelum movetur." (Cicero, Acad. Quest.; Opera, tom. iv, p. 39, edit. Bipont.) Copernicus himself could not have stated the doctrine with greater precision. of sense. The titles of three of his works have been preserved—the Period or Circumference of the Earth, the Phaenomena, and the Mirror. His observatory was still standing at Cnidus in the time of Strabo. His memory deserves to be honoured for the contempt which he evinced for the Chaldean predictions, and for having contributed to separate true astronomy from the reveries of judicial astrology. Eudoxus seems to have been the first who attempted to give a mechanical explanation of the apparent motions of the planets. He supposed each planet to occupy a particular part of the heavens, and that the path which it describes is determined by the combined motion of several spheres performed in different directions. The sun and moon had each three spheres; one revolving round an axis which passes through the poles of the world, and which occasions the diurnal motion; a second revolving round the poles of the ecliptic, in a contrary direction, and causing the annual and monthly revolutions; the third revolving in a direction perpendicular to the first, and causing the changes of declination. Each of the planets had a fourth sphere to explain the stations and retrogradations. As new inequalities and motions were discovered, new spheres were added, till the machinery became so complicated as to be altogether unintelligible.
Although Plato can hardly be cited as an astronomer, yet the progress of the science was accelerated by means of the lights struck out by his sublime and penetrating genius. He seems to have had just notions of the causes of eclipses; and he imagined that the celestial bodies originally moved in straight lines, but that gravity altered their directions, and compelled them to move in curves. He proposed to astronomers the problem of representing the courses of the stars and planets by circular and regular motions. Geometry was assiduously cultivated in the school of Plato; and on this account he claims a distinguished place among the promoters of true astronomy.
Astronomy is also under some obligations to Aristotle. In a treatise which he composed on this science, he recorded a number of observations which he had made; and, among others, mentions an eclipse of Mars by the moon, and the occultation of a star in the constellation Gemini by the planet Jupiter. As such phenomena are of rare occurrence, their observation proves that he had paid considerable attention to the planetary motions.
A great number of astronomers about this time appear on the stage, whose labours and observations prepared the way for the reformation of the science which was shortly after effected by Hipparchus. Helicon of Cizyene is renowned for the prediction of an eclipse, which took place, as Plutarch affirms, at the time announced. History records the names of only three individuals in ancient Greece who predicted eclipses, Thales, Helicon, and Eudemus. Eudemus composed a history of astronomy, a fragment of which, consisting of only a few lines, is preserved by Fabricius in the Bibliotheca Graeca. In this it is mentioned that the axes of the ecliptic and equator are separated from each other by the side of a pentadecagon, which is equivalent to saying that they contain an angle of $24^\circ$. This is the first value which we find assigned by the Greeks to the obliquity of the ecliptic. It is given in round numbers, and may easily be supposed to contain an error of a quarter of a degree.
Callippus is celebrated for the period which he formed of four Metonic cycles. Having observed, by means of an eclipse of the moon which took place about six years before the death of Alexander, that the Metonic cycle contained an error of a fourth of a day, he introduced the period of 940 lunations, containing four Metonic cycles, diminished by one day. He likewise formed a collection of observations on the heliacal risings of the planets. Theophrastus wrote a history of astronomy, and supposed the milky way to be produced by the imperfect junction of the two hemispheres, which allowed the light to penetrate from the firmament beyond. Autolycus of Pitaneas wrote two books, one on the movable sphere, the other on the risings and settings of the stars. These are the most ancient of the astronomical works of the Greeks which have come down to our times.
Pytheas of Marseilles, about the time of Alexander the Great, determined the length of the solstitial shadows in various countries by means of the gnomon. He found the shadows equal at Marseilles and Byzantium—a circumstance which does not give a favourable idea of the accuracy of his observations, inasmuch as the difference of the latitudes of the two places amounts to 24 degrees. The observation is, however, interesting, as it is the most ancient of the kind which has been preserved after that of Techeou-Kong, and as it confirms the successive diminution of the obliquity of the ecliptic. Pythens undertook several voyages for the purpose of obtaining geographical and astronomical information, and advanced northwards as far as Iceland. His relations have been treated as fabulous by Strabo and Polybius, but the accuracy of the greater number of them has been confirmed by modern observation and experience. He was the first who distinguished the climates by the different lengths of the days and nights.
**Astronomy in the School of Alexandria.**
In the history of the various sects which have hitherto come under our review, we meet only with some useful remarks, with numerous hypotheses and conjectures, but with scarcely any appearance of regular and connected science. Up to this date the astronomical knowledge of the Greeks was confined to a few facts, the discovery of which implies no theory, and scarcely the aid even of the simplest instruments. The order and arrangement of the planets, the causes of eclipses, the identity of the morning and evening stars, the approximate length of the year, that of the lunar month, the obliquity of the ecliptic, and the cycles of Meton and Calippus, were almost the sole results of their astronomical speculations. In the Alexandrian school we meet for the first time with regular and systematic observations. We there find angular distances measured with appropriate instruments, and calculations made according to the rules of trigonometry.
After the premature death of Alexander, his principal generals shared among themselves his magnificent conquests, and Egypt fell to the lot of Ptolemy Soter. This prince was distinguished by an ardent love of science, and a desire to promote every species of liberal knowledge. He accordingly invited to his court, which he had established at Alexandria, the most eminent philosophers of Greece, and fixed them there by his liberality and magnificent protection. His son, Ptolemy Philadelphus, who inherited his throne, also inherited his genius and love of science and learning. A superb edifice, styled the Museum, was assigned to the use of the men of science whom he had attracted to his capital, to which he also added an observatory, and the famous library, which had been collected with great care and at a vast expense by Demetrius Phalerius. The prince took great delight in the Museum; he visited it frequently, entered into familiar conversation with its inmates on the subject of their various pursuits, and by his own example stimulated their History. zeal and encouraged their inquiries. This noble institution, which survived all the vicissitudes of nine centuries, was the means of conferring incalculable benefits on the human race; and the name of its founder, Ptolemy Philadelphus, will be gratefully remembered while science and learning occupy a place in the estimation of mankind.
The first astronomers of the Alexandrian school were Aristillus and Timocharis, who flourished under the first Ptolemy, about 300 years before Christ. The chief object of their labours was the determination of the relative positions of the principal stars of the zodiac, instead of merely announcing their risings and settings, as had been the practice of the orientals and the ancient Greeks. The observations of these two astronomers conducted Hipparchus to the important discovery of the precession of the equinoxes, and served as the basis of the theory which Ptolemy, some centuries afterwards, gave of that phenomenon.
Aristarchus of Samos, the next in order of the Alexandrian astronomers, composed a treatise on the Magnitudes and Distances of the sun and moon, which has been preserved to our times. In this treatise he describes an ingenious method which he employed to obtain the relative distances of the two luminaries. At the instant when the moon is dichotomized, that is, when the exact half of her disk appears to a spectator on the earth to be illuminated by the sun's light, the visual ray passing from the centre of the moon to the eye of the observer is perpendicular to the line which joins the centre of the moon and sun. At that instant, therefore, he measured the angular distance of the two bodies, and finding it to be 87 degrees, he concluded, by the resolution of a right-angled triangle, that the distance of the sun is between eighteen and nineteen times greater than that of the moon. This method is perfectly correct in theory, but it is difficult to be assured of the exact instant of the moon's dichotomy, and in an angle of such magnitude a very small error greatly affects the result. The error of Aristarchus is very considerable, the true angle being about $87^\circ 50'$. The estimated distance of the sun is by consequence far too small; yet the determination, faulty as it was, contributed to expand greatly the existing notions relative to the boundaries of the universe, for the Pythagoreans had taught that the sun is only three, or at most three and a half times more distant than the moon. Another delicate observation made by Aristarchus was that of the magnitude of the sun's diameter, which, as we learn from Archimedes, he determined to be the 720th part of the circumference of the circle which the sun describes in his diurnal revolution. This estimate is not very far from the truth, and the observation is by no means an easy one. He embraced the doctrine of Pythagoras respecting the earth's motion, and appears to have entertained juster notions than any of the astronomers who preceded him, on the magnitude and extent of the universe. The treatise on the Magnitudes and Distances is published in the third volume of the works of Dr Wallis, with a Latin translation by Commandine, and some notes.