Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/816

750 the truth ; for, according to modern observations, the rate of the precession is about 50 1 seconds annually. His catalogue contained 1080 stars, not, as has sometimes been erroneously stated, 1022, the number in that of Ptolemy, in which the nebulous and some obscure stars are omitted. He also commenced a series of observations to furnish his successors with the means of forming a theory of the planets. Hipparchus likevise invented the plani sphere, or method of representing the starry firmament on a plane surface, which afforded the means of solving the problems of spherical trigonometry in a manner often more exact and more convenient than the globe itself. He was the first who demonstrated the methods of calculating triangles, whether rectilineal or spherical ; and he con structed a table of chords, from which he drew nearly the same advantages as we derive at present from the tables of sines. Geography is also indebted to him for the happy idea of fixing the position of places on the earth by means of their latitudes and longitudes; and lie was the first who determined the longitude by the eclipses of the moon. After the death of Hipparchus nearly three centuries elapsed before any successor arose worthy of the name. During this long period astronomy made no essential advancement. Some rough observations, scarcely superior to those of the Chaldeans, and a few meagre treatises, are the only monuments which exist to testify that science had not fallen into utter oblivion in an age so fertile of poets and orators. Geminus and Cleomedes wrote treatises, which have been preserved to our times ; Agrippa and Menelaus are said to have observed ; the Roman calendar was reformed by Julius Caesar and the Egyptian astronomer Sosigenes ; and Posidonius measured a degree, and re marked that the laws of the tides depend on the motions of the sun and moon.

was born at Ptolemais in Egypt, and flourished at Alexandria about the 130th year of our era, under the reigns of Hadrian and Antoninus. This illustrious ornament of the Alexandrian school is entitled by his own discoveries to the high rank among astronomers which lias universally been assigned to him; but the most signal service which he conferred on science was the collection and arrangement of the ancient observations. Out of these materials he formed the ~MeydX.rj Swrafts, or Great Composition, a col lection which exhibits a complete view of the state of astronomy in the time of Ptolemy, and which contains the germ of most of the methods in use at the present day. The hypothesis which Ptolemy adopted for the purpose of explaining the apparent motions, was that which had been followed by Hipparchus. To account for the uniform circu lar motion, Apollonius imagined the ingenious apparatus of epicycles and deferents; and Hipparchus advanced a step farther, by placing the centre of the sun s circle at a small distance from the earth. Ptolemy adopted both hypotheses, and supposed the planet to describe an epicycle by a uni form revolution in a circle, the centre of which was carried forward uniformly in an eccentric round the earth. By means of these suppositions, and by assigning proper rela tions between the radii of the epicycle and deferent circle, and also between the velocity of the planet and the centre of its epicycle, he was enabled to represent with tolerable accuracy the apparent motions of the planets, and parti cularly the phenomena of the stations and retrogradations, which formed the principal object of the researches of the ancient astronomers. The notions of Apollonius and Hip parchus were thus reduced to a systematic form, and the proportions of the eccentrics and epicycles of all the planets assigned, by Ptolemy ; on which account the system has &quot;been generally ascribed to him, and has obtained the name of the Ptolemaic System of the universe. The most important discovery which astronomy ewes to Ptolemy is that of the evection of the moon. Hipparchus had discovered the first lunar inequality, or the equation of the centre, which serves to correct the mean motion at the syzygies, and had also remarked the necessity of another correction for the quadratures. He even undertook a set of observations, with a view to ascertain its amount and its law ; but death put a stop to his labours before he had brought them to a successful issue. Ptolemy completed the investigation, and discovered that the eccentricity of the lunar orbit is itself subject to an annual variation, depending on the motion of the line of the apsides. The variation of the position of the apsides produces an inequality of the moon s motion in her quarters, which has been technically denominated the evection. The equation given by Ptolemy, though of course empirical, is remarkably exact. Ptolemy employed a very simple process for determining the moon s parallax, which was probably suggested to him by the situation of Alexandria, where he observed. He determined the latitude of a place a little to the south of that city, over the zenith of which the moon was observed to pass when her northern declination was the greatest possible. But when the moon is in the zenith, or in the same straight line with the observer and the centre of tho earth, she has no parallax ; consequently the obliquity of the ecliptic and the latitude of the station being known, the moon s greatest northern latitude was also determined. The next step was to observe the moon s meridian altitude fifteen days after the first observation, when her southern latitude was necessarily the greatest possible. This obser vation gave the apparent altitude of the moon, but her greatest northern and southern declinations being supposed equal, her true altitude, as seen from the centre of the earth, was easily computed from the previous observation, and the difference between the true and apparent altitudes gave the amount of the parallax. The observations of Hipparchus relative to the motion of the stars in longitude, or the regression of the equinoctial points, were confirmed by Ptolemy, although he mistook his amount, and diminished a quantity which Hipparchus had already estimated too low. According to Hipparchus the regression is at the rate of two degrees in 150 years. Ptolemy reduced it to one degree in 90 years. This dis agreement would seem to indicate an error of more than a degree in the observations, which can with difficulty be admitted, considering the accordance which subsists among the different observations cited by Ptolemy in support of his own determination. For this and some other reasons Ptolemy has been accused of altering the observations of Hipparchus, and accommodating them to his own theory ; and there would appear to be but too just grounds for the imputation. The error with regard to the regression may, however, have arisen from the circumstance, that Hipparchus had assigned too great a value to the length of the year, whence the motion of the sun with regard to the equinoxes would be made too slow, and the longitudes employed by Ptolemy consequently diminished. Ptolemy has been called The Prince of Astronomers, a title which may perhaps be justified by the universal and long-continued prevalence of his system, but to which he has no claim from the number or value of his own observations. After a laborious and minute examination of the Almagest, Delambre doubts whether anything is contained in that great work, beyond the author s own statement, from which it can be decisively inferred that Ptolemy ever observed at all. He, indeed, frequently makes mention of observations made by himself ; but his solar tables, rate of the precession, eclipses, determination of the moon s motion and parallax, arid above all, his catalogue of stars, render it impossible to doubt that the greater part of the 