The Lunar Calendar.

The apparent revolution of the moon around the earth was taken by the Mayas as the basis of a lunar calendar distinct from the civil calendar, but used in combination with it for various ceremonial purposes. Now the average duration of a lunar revolution is 29 days, 12 hours, 44 minutes, 2.87 seconds. Twelve lunations amount to a little more than 354 days and are therefore far short of a true year. Primitive peoples whose principal interest is to keep the moon in adjustment with the seasons have an occasional thirteenth month in their luni-solar calendars.

The Metonic cycle of the Greeks, an equation of 19 tropical years, 235 lunations and 6940 days, has been regarded as a remarkable achievement in observation. The Mayas discovered the same equation and with their system of designating days were able to use it with much greater ease than the Greeks since one katun minus one tzolkin gives exactly the required number of days:—

1.	0.	0.	7200 days
		13.	260 days
	19.	5.	6940 days

This interval is used prominently in several calculations at Copan and Quirigua.

On pages 51 to 58 of the Dresden Codex is found a remarkable lunar calendar covering 405 lunations or nearly 33 years. The lunar revolutions are arranged in groups of five or six, the former calculated at 148 days and the latter at 177 or 178 days. These are the necessary intervals between eclipses. The total amounts to 11,960 days which exactly contains the tzolkin and therefore forms a cycle. It is a remarkable fact that 405 lunar revolutions amount, according to modern calculations, to 11,959.888 or only O.112 of a day less than the Mayan lunar calendar. Therefore this re-entering series can be used nine times, or nearly 300 years, before an error amounting to one whole day has accumulated. There is also evidence that the Mayas used the great cycle of 29 × 52 calendar years, or 1507 tropical years, in connection with the moon and here the error for 18,639 lunations is about .64 of a day.

The Supplementary Series in Long Count dates is probably to be interpreted as the statement of the day reached by the Initial Series in a lunar calendar with an accumulated error; that is, the Mayas had an uncorrected lunar count as well as an uncorrected calendar year. Glyph C records a number of complete lunations which is never in excess of six; Glyph D gives the number of days in the current lunation when these are 19 or less and Glyph E, which has the basic value of 20, finishes the count of a current lunation. There is some evidence that the Mayan lunar calendar in the fifth century A. D. had receded about four days from the true positions of the moon, the count being made from the new or conjunctional phase. When, however, a new or full phase actually coincided with an important round number in the day count special record of the fact was made.

Fig. 50. Representations of the Moon: a, sun and moon hieroglyphs; b, moon from a “celestial band”; c, moon hieroglyph used for 20 in codices.

Fig. 51. The Last Glyph of the Supplementary Series: a, moon glyph; combined with the numeral 9 or 10 to indicate a 29 or a 30 day lunar month.

The lunar table in the Dresden Codex does not apply precisely to records of the First Empire but possibly may be adjusted to the times of the Second Empire. The indications are, however, too complicated to be examined in detail.