ON THE HISTORY OF ASTRONOMY. 455 



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the solstices divided each of these seasons a little unequally. In order to 

 explain this, Hipparchus supposed the sun to move uniformly in an 

 eccentric circle, the distance of its centre from that of the earth being -^ of 

 the radius, and placed the apogee in the sixth degree of gemini. Probably 

 the annual equation of the moon, which has some influence on the time of 

 eclipses, was the cause of his making the eccentricity too great ; had he 

 assumed it but one fifth part less, the supposition would have represented 

 the sun's place with tolerable accuracy. Hipparchus appears to have been 

 the first that employed astronomical observations for determining the lati- 

 tudes and longitudes of places. 



The interval of three centuries, which elapsed between Hipparchus and 

 Ptolemy, offers us little that is remarkable in the progress of astronomy, 

 except the reformation of the calendar by Julius Caesar, who was assisted 

 in making the arrangement by Sosigenes, an astronomer of the same 

 school that gave birth to all the preceding discoveries, as well as to the 

 improvements of Ptolemy. This great astronomer was born at Ptolemais 

 in Egypt, and flourished about the year 140 of our era. He continued the 

 vast project, begun by Hipparchus, of reforming the whole science which 

 he studied. He discovered the evection of the moon, or the change of her 

 velocity, occasioned by the position of the apogee with respect to the sun ; 

 he determined the quantity of this equation with great precision ; and in 

 order to represent it, he supposed the moon to perform a subordinate revo- 

 lution in an epicycle, or a smaller circle, of which the centre was carried 

 round in the line of the general orbit, which he considered as an eccentric cir- 

 cle. This mode of approximation is exceedingly ingenious ; it is said to have 

 been the invention of Apollonius of Perga, the mathematician, and although 

 it sometimes becomes complicated, yet it is very convenient for calculation ; 

 and it may be employed with advantage in the representation of the plane- 

 tary motions by machinery. Ptolemy adopted the most ancient opinion 

 with respect to the solar system, supposing all the heavenly bodies to 

 revolve round the earth ; the moon being nearest, then Mercury, Venus, 

 the Sun, Mars, Jupiter, and Saturn. This opinion had long been the most 

 general, although some astronomers had placed Mercury and Venus at 

 greater distances than the sun, and some attributed to the earth a diurnal 

 motion only ; but the doctrine of the Pythagoreans appears to have been 

 wholly exploded or forgotten. Ptolemy determined the quantity of the 

 precession of the equinoxes from a comparison of his own observations 

 with those of Hipparchus ; but he made it smaller than the truth ; and he 

 probably formed his table of the places of the stars by applying this 

 erroneous correction to the tables of Hipparchus, in order to accommodate 

 them to his own time. Both these errors may, however, be otherwise 

 explained, by supposing him to have followed Hipparchus in the length of 

 the tropical year, which being somewhat too great, caused an error in the 

 calculation of the sun's place, to which that of the stars was referred ; but 

 upon this supposition, he must also have been mistaken in three obser- 

 vations of the place of the equinoctial points. Ptolemy's principal work is 

 nis mathematical system of astronomy, which was afterwards called the 

 great syntax or body of astronomy, and is at present frequently quoted by 



