Enriched by the labours and discoveries of Hipparchus, astronomy begins to assume a new form, and to connect into a system the scattered truths of former ages. This illustrious astronomer, who was born at Nice, in Bithynia, flourished at Alexandria about the year 140 A. C. Dis satisfied with the determinations tha• had been already made, he resolved to repeat every observation, and, tin der the guidance of facts, to separate truth from the mass of error in which it was involved. After verifying the obliquity of the ecliptic, as settled by Eratosthenes, and fixing the latitude of Alexandria, he began his suc cessful career, by determining the tropical period of the sun, from the time of its arrival at the tropics and equi noxes ; and he saw the accuracy which would arise from employing two distant observations, which comprehended several revolutions of the sun. With this view he com pared an observation of his own on the solstices with one of Aristarchus, which had been made about 145 years before, and found the length of the tropical year to be 365 days 5 hours 55' 12". When engaged in these ob servations, he discovered that 187 days elapsed between. the vernal and autumnal equinox, while the interval be tween the autumnal and vernal equinox was only 178 days ; and that 94 days 12 hours elapsed between the vernal equinox and summer solstice, while 92 days 12 hours was the interval between the solstice and the autumnal equinox. Misled by the opinion of the an cients respecting the uniform motion of the sun, Hip parchus did not ascribe the inequality of these intervals to any variation in the sun's velocity ; but believing that this luminary described a circle with a uniform velocity, he supposed that the earth was not in the centre of the circular orbit, but removed from it about a 24th part of the radius. Having fixed the apogee of the sun in the 6th degree of Gemini, he had the honour of being the first,who computed tables of the motion of that luminary. In consequence of having assumed too great an eccentri city, he made the equation of the centre too large, an error into which he was probably led from the annual equation of the moon's orbit being always united with the equation of the sun's centre in the tables for eclipses. From these discoveries, Hipparchus was naturally led to the inequality of days, or the equation of time, which he found to be 33' 20". This result is about three times too great, but the merit of the discovery is not dimi nished by any error in calculation. The lunar motiops npixt attracted the notice of Hipparchus. By a com parison of eclipses, he determined the period of her revolution to be 29 days 12 hours 44' 36". He ascer tained the motion of her node and apogee ; and fixed the .};evolution of the moon with regard to the former, at 27 days 5 hours 5' 355", and with regard to the latter, at 27 days 13 hours 18' He discovered the eccentricity and inc,ination of the lunar orbit ; the former producing an equation of and the latter amounting to the same quantity. From the difference of solar eclipses at dif ferent parts of the earth, he detected the parallax of the moon, and endeavoured to determine that of the sun from the breadth of the earth's conical shadow, at the place where it was traversed by the moon in an eclipse of that luminary. From these data lie concluded, that the sun's parailax was about 3 minutes, and that his dis tance from the earth was nearly 1300 or 1400 times great er than the earth's radius. He made the moon's great est distance sometimes 83 and at other times 72 senudiameters of the earth, and the least distance cor responding to these numbers was 71 and 62 semidiame ters. Hipparchus made numerous observations on the planets, nut he does not seem to have attempted an ex planation of their irregular motions. The appearance of a new star in the time of this astronomer, incited him to one of the most magnificent undertakings in the history of science. In order that future astronomers might be acquainted with the changes in the heavens, be resolved to form a catalogue of the fixed stars, containing their apparent magnitudes, and their position in the heavens. He completed this arduous task by fixing the longitudes and latitudes of 1022 stars ; and by a comparison of his own with the observations of Aristillus and Timocharis, lie discovered the precession of the equinoxes. The method which Hipparchus employed in fixing the posi tion of the stars, he transferred to geography ; and he was the first who determined the situation of places on the earth, by their latitudes and longitudes. He fixed upon the Canary Islands as the place of the first meri dian; he pointed out the method of finding the longitude by eclipses of the moon ; and he proposed to form a catalogue of terrestrial longitudes and latitudes, a work which he left to be accomplished by his successors in science. The various investigations in which 'Hippar chus was engaged required numerous calculations, and led him to the resolution of plane and spherical _triangles, a branch of geometry of which he laid the foundation. The principal works of this astronomer perished in the conflagration which destroyed the Alexandrian library. His catalogue of the stars, however, is preserved iu the Almagest of Ptolemy, and his commentary on Aratus and Eudoxus is still extant.
To this brilliant period of discovery a long interval of nearly three centuries succeeded, without being marked by one discovery which extended the boundaries of as tronomy. As if human genius had been strained beyond its ordinary reach, and was anticipating too rapidly the general progress of the mind, it was allowed to recruit its energies by a long period of repose. The names of Geminus, Theodosius, Possidonius, Cleomedes, Agrip pa, Menelaus, 'neon, and Nigidius, occur in the history of the science ; but their labours were scarcely of suf ficient importance Yo entitle them to a separate notice. Geminus maintained that the stars were not all placed at the same distance from the earth ; Theodosius com posed three books on spherical trigonometry ; Possido nius observed the laws of the tides, and their connection with the motions of the sun and moon, and he estimated the height of the atmosphere at fifteen leagues; Cleo medes appears to have understood the refraction of the atmosphere ; and an occultation of a star by the moon, was observed by Menelaus and Agrippa, the former of whom discovered several important theorems in simile rical trigonometry.
These trivial accessions to astronomy, the production of nearly 300 years, seemed to hold out the richest lau rels to the first philosopher who had the genius and the courage to seize them. Ptolemy had the good lortune to live at a period so favourable to the developement of great talents, and lie seized the opportunity which it afforded of recovering the science from its fatal relapse.
This philosopher, who was born at Ptolemais in Eg}pt, continued the plan conceived by Hipparchus of reform ing the science of asaonomy, and with this view he collected all the scattered materials which history or tradition had saved horn the ravages of time. These fragments of antiquity are preserved along with his own researches, in his ?llmagest, or Great Composition, a work which contains a complete system of astronomy, and which continued for many ages to be the elemen tary work by which the science was taught in every nation of Europe. The most interesting discovery which we owe to Ptolemy, is that of a second inequality in the moon's motion, which is called the erection. The equa tion of the lunar orbit, amounting to 5° 1', as discovered by Hipparchus, was found sufficiently accurate in the calculation of eclipses, in which it had been chiefly used. Ptolemy, however, followed the moon through every part of her orbit, and found that the tabular differed from the observed longitude as she receded from the syzigies, and that this difference reached its maximum at the quadratures when the whole equation amounted to 7° 40'; a result which scarcely differs a minute from the sum of the two equations as fixed by modern obser vations. Ptolemy applied himself with great assiduity to perfect the theory of the planets, by determining, with an accuracy which had never before been attempted, their irflative positions and distances from the earth, and the apparent paths which they described among the fixed stars. Rejecting the system of Pythagoras, as contrary to the evidence of the senses, and unsupported by positive arguments, he placed the earth in the mid dle of the universe, and supposed it to be the centre. round which the various revolutions of the planets and fixed stars were performed. The stations and retrogra dations of the planets, however, presented difficulties which this theory could not resolve ; and Ptolemy was compelled to surmount them, by assuming the most perplexing hypotheses. He supposed the planets to move uniformly in the circumference of a small circle, called the epicycle, which was carried uniformly round the earth in the circumference of another circle called the dtyrerent, which had the earth at its centre. The inclination of the planetary orbits was explained, by supposing that the epicycle and deferent circles were hi planes different from that of the ecliptic ; and in order to account for the variation in the velocity of the pla nets, Ptolemy placed time earth at a small distance from: the centre of the deferent,—the very same contrivance by which Hipparchus explained the inequalities in the motion of the sun. By increasing the number of these epicycles, and judiciously proportioning their magnitude, the inequalities of the apparent motion may be pretty accurately represented : but though Apollonius had given very useful directions for this purpose, it was not till the 13th century that the doctrine of epicycles was brought to any degree of perfection. This complicated method of explaining the celestial motions, became still more complex in the progress of discovery, as every new inequality that was observed, encumbered the sys tem with an additional epicycle. It is not surprising, therefore, that Alphonso X. should have exclaimed, when contemplating these cumbrous appendanges of the planets, that " if the Deity had called him to his councils at the creation of the world, he could have given him good advice !" a speech whose impiety is directed only against the creative powers of Ptolemy. The order of the planets in the Ptolemaic system, is the same which is adopted by modern astronomers, with the exception of the sun, which occupies the place of the earth. Pto lemy was fortunate in placing Mercury and Venus below the sun : This position was assigned them by the an cients ; but several contemporary astronomers placed them beyond the sun, while the Egyptians made them revolve round that luminary. By comparing his obser vations with those of Hipparchus, Ptolemy confirmed the precession of the equinoxes, and fixed it at 35"9 in a year. This erroneous result has, without any reason, been alleged as a proof that Ptolemy altered the obser vations of Hipparchus ; for the error evidently arose from his determining the longitudes of the stars by comparing them with the sun, a comparison which in volved the length of the tropical year. This element, however, was erroneously determined by Hipparchus ; and therefore if we take the true length of the tropical year, we shall find, that the observations of Ptolemy give a precession of 49", differing very little from the most correct observations. By observing the time in which the moon traversed the earth's shadow, he found the distance of the sun to be 1210 diameters of the earth, and his parallax 51". It does not appear whether we are indebted to Ptolemy or Hipparchus, for the methods of computing eclipses contained in the Abnagest. The reduction of the moon's orbit to the ecliptic, an impor tant equation in the calculation of the moon's place, seems to have been the discovery'of this astronomer. He found that its maximum value was five minutes, but that in eclipses it never exceeded two minutes, which produced an error in time of 4 minutes. The subject of astronomical refractions was first explained by Ptole my, in his Treatise on Optics. This important work, which existed in the days of the Arabian astronomer Alhazen, has not been transmitted to our times : It would appear, however, that Ptolemy made some allowance for the effects of refraction, and advanced a rational expla nation of the magnitude of the horizontal moon. By accomplishing the proposal of Hipparchus, to collect all the known longitudes and latitudes of places on the earth, this astronomer rendered an essential service to geography ; and he had also the merit of laying the foundation of the method of projections in the formation of geographical charts. The sciences of chronology, music, optics, and dialling, were all indebted to the la bours of this universal genius ; and the reveries of judi cial astrology, which he is falsely said to have counte nanced by a treatise on the subject, never gained admittance into his penetrating mind. Sensible of the benefits which he had conferred on science, and proud of the mighty edifice which he had reared, Ptolemy was naturally anxious to transmit to future ages some dura ble monument of his labours. He accordingly conse crated, in the temple of Serapis at Canopus, an inscrip tion cut on marble, which contained the leading features of the system which he had formed.