Strabo states that he discovered that the solar year is longer than 365 days by 6 hours; Vitruvius that he invented a sun-dial.
Both festivals, of course, belong to a lunar calendar, and move through the solar year every thirty-two years.
The civil year consisted in general of twelve months or lunations, but occasionally a thirteenth was added in order to preserve its correspondence with the solar year.
The Harrari are Mahommedans of the Shafa'i or Persian sect, and they employ the solar year and the Persian calendar.
The Mayas had a calendar of 360 days, with intercalary days; this solar year was intersected by their sacred year of twenty weeks of thirteen days each, and these assembled in bewildering cycles.