ARISTARCHUS ON THE YEAR AND “GREAT YEAR”.

Aristarchus is said to have increased by 1/1623rd of a day Callippus’s figure of 365¼ days as the length of the solar year, and to have given 2484 years as the length of the Great Year or the period after which the sun, the moon and the five planets return to the same position in the heavens. Tannery has shown reason for thinking that 2484 is a wrong reading for 2434 years, and he gives an explanation which seems convincing of the way in which Aristarchus arrived at 2434 years as the length of the Great Year. The Chaldæan period of 223 lunations was well known in Greece. Its length was calculated to be 6585⅓ days, and in this period the sun was estimated to describe 10⅔° of its circle in addition to 18 sidereal revolutions. The Greeks used the period called by them exeligmus which was three times the period of 223 lunations and contained a whole number of days, namely, 19756, during which the sun described 32° in addition to 54 sidereal revolutions. It followed that the number of days in the sidereal year was—

19756/(54 + 32/360) = 19756/(54 + 4/45) = (45 × 19756)/2434 = 889020/2434= 365¼ + 3/4868.

Now 4868/3 = 1623 - ⅓, and Aristarchus seems to have merely replaced 3/4868 by the close approximation 1/1623. The calculation was, however, of no value because the estimate of 10⅔° over 18 sidereal revolutions seems to have been an approximation based merely on the difference between 6585⅓ days and 18 years of 365¼ days, i.e. 6574½ days; thus the 10⅔° itself probably depended on a solar year of 365¼ days, and Aristarchus’s evaluation of it as 365¼ 1/1623 was really a sort of circular argument like the similar calculation of the length of the year made by Œnopides of Chios.