and many operations of husbandry were fixed by the rising of constellations, etc. The relative position of the two would be found to change as the lunar years fell behind the true time.
It may have been Solon to whom the Athenians owed the regular arrangement of full and hollow months in the year (Ideler, i. 266). He also named the last day of the month ἕνη καί νέα as belonging to both months, the old and the new, and gave the name νουμηυία to the day on which the moon was first visible, i.e. to the day after the conjunction from which the month really dates.
A month calculated at 29½ days is 44' 3" short of the full length, hence a year of 12 such months is about 9 hours too short for the lunar time. It is also 11¼ days behind the solar year. The first attempt at correction was to insert every other year an intercalary month of 30 days. This gave 354 + 354 + 30 = 738 days for 25 months; i.e. each month averaged 29½3⁄5 days, which was nearly correct. But two solar years amount to 730½ days, so that the double year of 25 lunar months was in excess of two solar years by 7½ days.
This was perhaps the system of Solon. It could have been made tolerably correct by leaving out a month of 30 days in every eight years, i.e. by intercalating three, not four, months in the eight years. This consideration may have led the Greeks to their octennial cycle, of which Geminus gives the following account (Ideler, i. 294).
"Discovering the imperfection of their trieteric system (such is the Greek form for a system extending to two years, διἀ τρίτου ἒτους), the Greeks established an octennial cycle, containing 2922 days in 99 months, three being intercalary. The lunar year contains 354 days, the solar year 365¼; the latter therefore has 11¼ days in excess of the former. Now 11¼ days, if multiplied by eight, gives 90 days, or three months of 30 days; thence in eight years the lunar time is three months (90 days) behind the solar. This led to the insertion of three months in a cycle of eight years. These intercalary months
