46 A Short History of Astronomy [Cn. n. 



the lengths of two of the seasons of the year, i.e. of the 

 intervals into which the year is divided by the solstices 

 and the equinoxes ( n). By means of his own observa- 

 tions, and of others made by his predecessors, he ascer- 

 tained the length of the spring (from the vernal equinox to 

 the summer solstice) to be 94 days, and that of the summer 

 (summer solstice to autumnal equinox) to be 92^ days, the 

 length of the year being 365^ days. As the sun moves 

 in each season through the same angular distance, a rign't 

 angle, and as the spring and summer make together more 

 than half the year, and the spring is longer than the 

 summer, it follows that the sun must, on the whole, be 

 moving more slowly during the spring than in any other 

 season, and that it must therefore pass through the apogee 

 in the spring. J} If, ' therefore, in fig. t8, we draw two 

 perpendicular lines Q E s, P E R to represent the directions 

 of the sun at the solstices and equinoxes, P corresponding 

 to the vernal equinox and R to the autumnal equinox, the 

 apogee must lie at some point A between P and Q. So 

 much can be seen without any mathematics : the actual 

 calculation of the position of A and of the eccentricity is 

 a matter of 'some complexity. The angle PEA was found 

 to be about 65, so that the sun would pass through its 

 apogee about the beginning of June ; and the eccentricity 

 was estimated at ^ T . 



The motion being thus represented geometrically, it 

 became merely a matter of not very difficult calculation to 

 construct a table from which the position of the sun for 

 any day in the year could be easily deduced. This was 

 done by computing the so-called equation of the centre, 

 the angle c s E of fig. 17, which is the excess of the actual 

 longitude of the sun over the longitude which it would 

 have had if moving uniformly. 



Owing to the imperfection of the observations used 

 (Hipparchus estimated that the times of the equinoxes and 

 solstices could only be relied upon to within about half a 

 day), the actual results obtained were not, according to 

 modern ideas, very accurate, but the theory represented 

 the sun's motion with an accuracy about as great as that 

 of the observations. It is worth noticing that with the 

 same theory, but with an improved value of the eccentricity, 



