whole terrestrial circumference was 250,000 stadia. The great uncertainty that exists, as to the value of the stadium in question, prohibits any appreciation of the measurement: but several important errors were committed in the practical application of a right principle. No allowance was made for the solar parallax, and instead of Syene being under the tropic of Cancer and on the meridian of Alexandria, it is about 50′ north of the former, and nearly 3o east of the latter. The principle of the method employed is, however, precisely the same as that which has been acted upon in modern times; and our more accurate results in determining the magnitude of the earth are owing to greater nicety in observation, attention to all the elements which the solution of the problem requires, and more perfect instruments for the measurement of linear and angular distances. The inventor of the method was born at Cyrene, in the year 276 B. C. The third Ptolemy invited him to his capital, giving him the charge of its library; but becoming weary of life at the advanced age of eighty, he died by voluntary starvation, and was succeeded in his office of librarian by the author of the Argonautics.

We now come to the greatest astronomical name in antiquity—that of Hipparchus who may be properly regarded, on account of the plans he pursued and the results he obtained, as the father and founder of real astronomy. The invention of spherical trigonometry is supposed to be due to him, and undoubtedly the first application of it is, by which the places of the celestial bodies may be fixed, and the variations of their movements exhibited with precision. He approximated also closely to the true length of the tropical year, which had been previously held to be 365 days. This he discovered to be an error in excess, by comparing one of his own observations of the summer solstice, with another made by Aristarchus of Samos, 145 years before. His own determination of 365 days, 5 hours, 55 minutes, 12 seconds, exhibits a value greater than the truth by 6′ 13′′ only, as according to Laplace, the length of the tropical year at that time must have been about 4"-2 shorter than in the present age. The error can occasion no surprise. It must be remembered, in behalf of the ancients generally-to use the words of Delambre, that their astrolabes were nothing but armillary spheres, of no great diameter, and with very small subdivisions of a degree; and that they had neither telescope, vernier, nor micrometer. "What should we do," he goes on to remark, "even now if deprived of these helps, and if we knew neither the refraction nor the true altitude of the pole, on which point, even at Alexandria, and with armillæ of every sort, an error of a quarter of a degree was committed?" At this day we dispute about a fraction of a second; they could not then answer for any fraction of a degree, and might be wrong by a whole diameter of the sun and moon. The appearance of a new star in the time of Hipparchus is said to have induced him to make a catalogue of the fixed stars, in order that posterity might be able to recognise any changes that might take place in the appearance of the heavens. He was well aware of the importance of such a catalogue, especially for observations of the moon and planets; and in executing the task he rendered essential service to astronomy, and made his most remarkable discovery. Comparing the place of the star Spica Virginis, as determined by himself, with that assigned to it about 170 years previously by two distinguished Alexandrians, he found that this star was six degrees distant from the autumnal equinox, whereas the before-mentioned astronomers had found it eight degrees from the equinox. He saw that there must have been either a movement of the star in longitude during the interval, or a contrary movement of the equinoctial point in the heavens. The same phenomenon was observed in relation to other stars; that while their latitudes had been retained unaltered, they had advanced in longitude; and hence the retrogradation of the equinoctial points along the ecliptic was inferred, the cause of which remained a secret till the age of Newton.

The catalogue formed by Hipparchus contained 1080 stars. The labour it involved,

and its use, called forth the strong language of Pliny, who describes it as a thing even hard for a god to perform-"Ausus rem etiam Deo improbam." Perhaps, had we an accurate catalogue of the stars, dating back four thousand years, some remarkable variations of position would be discovered, transpiring by slow and imperceptible degrees, which would open views of the universe, which will now require the observations and comparisons of future centuries to develope and confirm. After determining the places of the stars, Hipparchus made a representation of the heavens on the surface of an artificial globe, which appears to have been deposited at Alexandria; and with him also the happy idea originated of marking the positions of towns in the same manner, by circles drawn through the poles perpendicularly to the equator, or by latitudes and longitudes. When his brilliant career commenced and terminated, is unknown; but he was born at Nice, in Bithynia, made many of his observations at Rhodes, and was alive in the interval between 160 and 125 B. C. He amply merited the epithet applied to him by Ptolemy," the lover

of labour and truth," φιλόπονος καὶ φιλαλήθης ; and is properly classed in scientific opinion with the Bradleys and Flamsteads of modern times. After him, there is little to invite attention in the history of astronomy for nearly three centuries, when we come to Ptolemy, the first who formally broached a system of the universe which has been handed down to us.

Apart from his theory, Ptolemy has great merits. He was the best scholar of his age a practical astronomer, mathematician, and geographer the author of the important discovery of the evection or libration of the moon. Born in Egypt, and flourishing at Alexandria through the reigns of the emperors Adrian and Antoninus, he there became acquainted with the writings and observations of Hipparchus. The former, with one exception, unfortunately perished

at the destruction of the Alexandrian library; but the chief of the latter have been preserved by Ptolemy in his own works, and they have largely contributed to his fame. In a celebrated production which ruled the mind of Europe for fifteen centuries, the Great Collection, or Almagest, as it was called by the Arabic translator, he recorded the advances of past ages in astronomy, the state of the science in his own time, and developed a plan of the celestial movements. It recognised the earth to be a spherical body for reasons similar to those that are now alleged in proof of its convexity-to be the immovable centre of the universe-the sun, moon, planets, and fixed stars, prosecuting a daily revolution around it, in perfect circles, and with uniform velocities. This is in accordance with the appearance presented by the first blush of the universe to the physical eye. The sun is seen daily pursuing a course through the heavens in the segment of a circle from cast to west. The same path is ap

celestial bodies its servants, moving in circular orbits, and with uniform velocities, and

comets simply meteors generated in the terrestrial atmosphere. The "divine" Plato indeed, the master of Aristotle, is said to have renounced his opinion upon one of these points in his old age, and to have admitted that the centre ought to be appropriated to some more noble object than the earth, or, rather, than terrestrial substance. It is a plausible conjecture, that the elements of his own system were first suggested to the mind of Copernicus by notices of the opinions of the disciples of Thales and Pythagoras. They won few converts, however, among the Greeks, and in some instances exposed their professors to persecution. The Athenians condemned

Anaxagoras to death for his philosophical views, a fate from which he was saved by the interest of Pericles, but he was sentenced to perpetual banishment, and died in an obscure town on the Hellespont. Philolaus also suffered persecution on account of his doctrine of the earth's annual revolution, which so shocked the prejudices of men as to subject him who maintained it to the suspicion of impiety.

Egypt became the chief seat of astronomical science in the ancient world soon after the age of Aristotle. Alexandria had risen by the delta of the Nile at the command of the conqueror from whom its name is derived, and under the superintendence of the architect who proposed cutting mount Athos into the figure of a man. Upon the death of Alexander it became the capital of one of the kingdoms formed out of the ruins of his empire. The first of the Ptolemies laid the foundation of its celebrated library-perhaps the most extensive collection of books ever brought together before the invention of printing. His successor established in connection with it a college for the cultivation of the pure sciences, invited the most accomplished of the Greeks to repair to it, supplied them with whatever instruments could be furnished necessary to their pursuits, and thus arose the Alexandrian school, which received the flattering epithet of Divine, on account of the acquirements of its professors, and the philosophical character of its investigations. It originated a connected series of observations relative to the constitution of the universe. The positions of the fixed stars were determined, the paths of the planets carefully traced, and the solar and lunar inequalities more accurately ascertained. Angular distances were calculated with instruments suitable to the purpose by trigonometrical methods, and, ultimately, the school of Alexandria presented to the world the first system of theoretical astronomy that had ever comprehended an entire plan of the celestial motions. The system we know to be false, and inferior to the Pythagorean notions; but it had the merit of being founded upon a long and patient observation of phenomena, a principle which finally brought about its own destruction, while the previous theories were the results of pure hypothesis.

The most interesting circumstances connected with the early history of the Alexandrian school are the attempts made to determine the distance of the earth from the sun, and the magnitude of the terrestrial globe. Aristarchus of Samos is the author of an ingenious plan to ascertain the former. Suppose the centre of the circle s to represent the centre of

M

E

the sun, м that of the moon, E being the position of an observer on the surface of the earth. It is easy to perceive that, when the moon has half her disc illuminated by the sun, a line drawn from E to м will be perpendicular to another line drawn from s to M, making with each other a right angle. The plan of Aristarchus was, that the angular distance SE M should at that time be taken, which is possible, because both the sun and moon may then be seen at once above the horizon, from whence the ratio of E S to E м may be determined. He obtained the general result, that the distance of the sun from the earth is about nineteen times as great as that of the moon from the earth. We now know that the distance is much greater; but notwithstanding the inaccuracy of the result, the method employed is undoubtedly just, and reflects the highest honour upon the genius of its proposer. He failed in practice, owing to the difficulty of ascertaining the exact time of the bisection of the moon's disc, and the imperfect instruments then in use for the measurement of angular distances. The determination of the sun's distance from the earth, with any thing like precision, is only of recent date, and has been effected by means of which the ancients could have had no conception. Aristarchus held the Pythagorean doctrine of the motion of the earth in space, and gave the right answer to the formidable objection long afterwards made to it, that of the non-existence of an annual parallax. The answer recognised the earth's orbit as being an insensible point in comparison with the vast distance of the fixed stars. The boundaries of the universe were thus extended to his mind far beyond any limits conceived by his predecessors. There is great obscurity resting upon his life. The era of his birth and death is unknown; but he was alive B. C. 280, as an observation of the solstices made by him at that date has been preserved. The Greek text of his only surviving work, "On the Magnitudes and Distances of the Sun and Moon," was edited in this country by Dr. Wallis in 1688. He estimated the apparent diameter of the sun at 30',—about 2′ too little.

SA

The attempt to determine the magnitude of the earth was made by Eratosthenes, and we have reason to believe this was the first attempt ever made to solve the problem, as certainly it was to do it upon a true principle. Syene, in Upper Egypt, then a flourishing city, now Assouan, has acquired an interest from its connection with this experiment. It was supposed to lie exactly under the tropic of Cancer, as it had been observed that, on the day of the summer solstice, at noon, a well there was enlightened to the bottom, while vertical bodies threw no shadow for the space of about three hundred stadia around it. At Alexandria, therefore, which was conceived to lie under the same meridian, on the same day at noon, when the sun was believed to be vertical at Syene, Eratosthenes measured his zenith distance, or the value of an arc of the meridian between the two cities. Let E be the centre of the earth, A Alexandria, s the sun, and s' Syene. The celestial arc contained between the zeniths of the two places, Alexandria and Syene, was found to be equal toth of the circumference of a circle, that is, to 7° 12′. Now, admitting the earth to be of a spherical form, Eratosthenes would obtain the measure of its circumference, by multiplying fifty times the distance between the cities. This distance was ascertained by order of the government to be 5000 stadia, and consequently the result obtained for the length of the

whole terrestrial circumference was 250,000 stadia. The great uncertainty that exists, as to the value of the stadium in question, prohibits any appreciation of the measurement: but several important errors were committed in the practical application of a right principle. No allowance was made for the solar parallax, and instead of Syene being under the tropic of Cancer and on the meridian of Alexandria, it is about 50′ north of the former, and nearly 3o east of the latter. The principle of the method employed is, however, precisely the same as that which has been acted upon in modern times; and our more accurate results in determining the magnitude of the earth are owing to greater nicety in observation, attention to all the elements which the solution of the problem requires, and more perfect instruments for the measurement of linear and angular distances. The inventor of the method was born at Cyrene, in the year 276 B. C. The third Ptolemy invited him to his capital, giving him the charge of its library; but becoming weary of life at the advanced age of eighty, he died by voluntary starvation, and was succeeded in his office of librarian by the author of the Argonautics.

We now come to the greatest astronomical name in antiquity—that of Hipparchus who may be properly regarded, on account of the plans he pursued and the results he obtained, as the father and founder of real astronomy. The invention of spherical trigonometry is supposed to be due to him, and undoubtedly the first application of it is, by which the places of the celestial bodies may be fixed, and the variations of their movements exhibited with precision. He approximated also closely to the true length of the tropical year, which had been previously held to be 365 days. This he discovered to be an error in excess, by comparing one of his own observations of the summer solstice, with another made by Aristarchus of Samos, 145 years before. His own determination of 365 days, 5 hours, 55 minutes, 12 seconds, exhibits a value greater than the truth by 6′ 13′′ only, as according to Laplace, the length of the tropical year at that time must have been about 4"-2 shorter than in the present age. The error can occasion no surprise. It must be remembered, in behalf of the ancients generally-to use the words of Delambre, that their astrolabes were nothing but armillary spheres, of no great diameter, and with very small subdivisions of a degree; and that they had neither telescope, vernier, nor micrometer. "What should we do," he goes on to remark, "even now if deprived of these helps, and if we knew neither the refraction nor the true altitude of the pole, on which point, even at Alexandria, and with armille of every sort, an error of a quarter of a degree was committed?" At this day we dispute about a fraction of a second; they could not then answer for any fraction of a degree, and might be wrong by a whole diameter of the sun and moon. The appearance of a new star in the time of Hipparchus is said to have induced him to make a catalogue of the fixed stars, in order that posterity might be able to recognise any changes that might take place in the appearance of the heavens. He was well aware of the importance of such a catalogue, especially for observations of the moon and planets; and in executing the task he rendered essential service to astronomy, and made his most remarkable discovery. Comparing the place of the star Spica Virginis, as determined by himself, with that assigned to it about 170 years previously by two distinguished Alexandrians, he found that this star was six degrees distant from the autumnal equinox, whereas the before-mentioned astronomers had found it eight degrees from the equinox. He saw that there must have been either a movement of the star in longitude during the interval, or a contrary movement of the equinoctial point in the heavens. The same phenomenon was observed in relation to other stars; that while their latitudes had been retained unaltered, they had advanced in longitude; and hence the retrogradation of the equinoctial points along the ecliptic was inferred, the cause of which remained a secret till the age of Newton.

The catalogue formed by Hipparchus contained 1080 stars.

The labour it involved,