Fabricius in the Blbliotheca Graeca. In this it is mentioned that the axes of the ecliptic and equator are separated from each other by the side of a pentedecagon, which is equivalent to saying that they contain an angle of 24. 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.
Calippus 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 Pitane 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 2^ degrees. The observation is, however, interesting, as it is the most ancient of the kind which has been preserved after that of Tcheou-Kong, and as it confirms the successive diminution of the obliquity of the ecliptic. Pytheas undertook several voyages for the purpose of obtaining geographical and astronomical infor mation, and advanced northwards as far as Iceland. His accounts 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.
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 oftheSun 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 dichotomised, 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, he concluded, by the resolution of a right-angled triangle, that the dis tance 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 50 . The estimated distance of the sun is by consequence far too small ; yet the determina tion, 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 Pytha goras respecting the earth s motion, and appears to have entertained juster notions than any of the astronomers who preceded him, regarding 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.
Eratosthenes, the successor of Aristarchus, a native of Cyrene, was invited to Alexandria by Ptolemy Euergetes, 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 42 39", half of which gives 23 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 as 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 as Alexandria, he conceived the idea of determining the amplitude of the celestial arc 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 meri dian. 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 Alexan dria to be 7 12 , or a fiftieth 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 5000x50 = 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.
by the discoveries of some of the distinguished geometricians 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 ns a model for future works of the same kind, and was the first who treated in a geometrical manner the phenomena
of the different inclinations of the sphere. Conon of