594 LECTURE XLVIII. 



astronomical observations for determining the latitudes 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, occasion- 

 ed 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 revolution 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 circle. This mode of approxima- 

 tion is exceedingly ingenious; it is said to have been the invention of Apol- 

 lonius of Perga, the mathematician, and although it sometimes becomes com- 

 plicated, yet it is very convenient for calculation ; and it may be employed 

 with advantage in the representation of the planetary 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 at- 

 tributed to the earth a diurnal motion only; but the doctrine of the Pytha- 

 goreans appears to have been wholly exploded or forgotten. Ptolemy deter- 

 mined the quantity of the precession of the equinoxes from a comparison of 

 his own observations with those of Hipparchus; but he made it sHialler 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 



