The earth completes its orbit about the sun in 365 days 5 hr 48 min 46 secthe length of the solar year. The moon passes through its phases in about 29 12 days; therefore, 12 lunar months (called a lunar year) amount to more than 354 days 8 hr 48 min. The discrepancy between the years is inescapable, and one of the major problems since early days has been to reconcile and harmonize solar and lunar reckonings. Some peoples have simply recorded time by the lunar cycle, but, as skill in calculation developed, the prevailing calculations generally came to depend upon a combination.

The fact that months and years cannot be divided exactly by days and that the years cannot be easily divided into months has led to the device of intercalation (i.e., the insertion of extra days or months into a calendar to make it more accurate). The simplest form of this is shown in ancient calendars which have series of months alternating between 30 and 29 days, thus arriving at mean months of 29 12 days each. Similarly four

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