The True Year.
The base line at Copan yielded accurate data on the exact length of the tropical year, a period varying by a difficult fraction from 365 full days. The tropical year is the time measured by the revolution of the earth around the sun and by the recurring seasons. No agricultural people could neglect this natural time period with its obvious relation to planting and harvest.
Reference has already been made to the notational 360 day year (tun) of the Mayas and to their formal calendar year (haab) of exactly 365 days. The calendar year kept running ahead of the true year by the accumulating amount of the days which we intercalate on leap years but the Mayas wisely made no such intercalations since to have done so would have thrown their day count out of gear with the moon and other planets and the somewhat defective calendar based upon these minor heavenly bodies. Therefore the months of the Mayan year like those of the ancient Egyptian year slowly moved through the seasons. But the Mayas calculated an almost exact correction for the excess of the true year over the vague 365 day year. This excess amounts to about .24 of a day and their correction seems to have been one day in four years for short periods while for long periods they made 29 calendar rounds (1508 calendar years or 550,420 days) equal 1507 tropical years. This is a remarkably accurate adjustment, much closer, in fact, than that of our present Gregorian calendar. This great cycle is comparable to the 1460 year Sothic cycle of the Egyptians in so far as that relates to the flooding of the Nile, but the Egyptian arrangement has an error of about twelve days for the cycle while the Mayan arrangement is accurate to a very small fraction of a day.
In the calendars of various Guatemalan and Mexican tribes the slow shifting of the months is attested by actual statements of early Spanish writers. But the conventional 365 day year was, after all, sufficiently accurate for most purposes since associations between the months and the seasons would hold reasonably true for the average lifetime.
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. | 0 = | 7200 days |
| 13. | 0 = | 260 days | ||
| 19. | 5. | 0 = | 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.