Bohumil Böhm, Vladimír Böhm

In the area of Southeastern Mexico, Guatemala, Belize, western Honduras and Salvador lived a highly developed Indian nation we know as the Mayas. The beginnings of their cultural and economic development go back to approximately the second half of second millenium B.C. Influences of the ancient Olmec culture from the area of Veracruz and Tabasco, and the culture of Izapa influenced a part of the Guatemala Highlands and played an important role. The climax of the cultural and economic rise of the Mayan era was represented by the building of grandiose Temple Complexes and by an abundant usage of hieroglyphic writing containing calendar dates and astronomical knowledge.

The basic Mayan time counting system consisted of determining how many days had elapsed since the Predetermined First Day until the day which was to be dated. This method is analogous to the dating system, used by present astronomers, with the help of the Julian dating system developed by the French scientist Joseph Scaligera in 1583. He determined January 1st, 4 173 B.C. as the beginning of the Julian Period. Since that date, days have been continually counted without being divided into years. For example midnight on November 17th, 1989 corresponds with the Julian Date 2 447 847.5.

In a number of experiments intended to correlate the Mayan System of dating with that of the Julian period the correlation of Goodman, Martinez and Thompson was accepted as standard.

According to the Thompson correlation the First Day of the Mayan chronology falls on the 584 284th day of the Julian Period. This sum of days as a constant coefficient is necessary to add to each Mayan date so that its value might be converted into our calendar system.

The correct determination of this date is very important for the exact dating of the course of the development of the Mayan culture. When investigating its calculation, we used the established dates from the Dresden Codex with ephemerides for determination of the visibility of Venus and the solar or lunar eclipse. The type of the eclipse, whether lunar or solar, understandably could not have been determined at that phase. All those who tried to calculate the correlation of both dating systems worked with these data. These data do not, however, seem to be unambiguous as a starting point since the synodic periods of Venus and the Moon, i.e. synodic periods related to the Earth: meet after a certain time-they can be expressed by common integer multiples. For that reason there are many shifted correlations between the Mayan and the Julin Dating Systems, besides the accepted one mentioned above. Therefore it was necessary to research and determine further fixed Mayan dates to confidently describe other astronomical phenomena.

The Mayan maize-growing agricultural system respected the course of the tropical year whose length is 365.24219878 days. This was of vital importance for them. A tropical year is divided according to the positions of the rising and setting of the Sun at the horizon into the vernal and autumnal equinoxes with night and day of equal length; and with a summer solstice as the longest day and a winter solstice as the shortest day.

We assumed that in Mayan texts certain dates would be connected with the Tropical Year. Some of the dates occur in the inscriptions of the temple complexes, which means that they were of such great importance that they have been recorded many times. On the basis of an analysis of time intervals between them, it was possible to determine that they were related to the vernal and autumnal equinoxes and summer and winter solstices.In order to eliminate subsequent mistakes we considered all four possibilities when calculating the correlation of each of these dates.
They are e.g. the dates as follows:

1 379 662 days, Piedras Negras, five times
1 383 136 days, Piedras Negras, three times
1 4O1 577 days, Quirigu , five times
1 415 637 days, Cop n, eight times

In order to find the solstices or equinoxes in the Mayan dates we also used statistical methods. For the calculation itself we created such an algorithm consisting of the following method:

Every single date from the established number of 4OO dates was divided by the length of the Tropical Year. The integer part was then subtracted from each quotient /from the result of each division/. The decimal remainders obtained in this calculation were ranged according to their size. A large group of nearly congruent remainders was found. Such a large group of congruent remainders in mathematical model situations is very unusual. This phenomenon evidently describes the solstices or equinoxes.

An analogous situation was found also in relation to full moons or new moons, when Synodic Month was used as divisor.

The length of a Tropical Year can also be quite exactly determined by the transit of the Sun through its zenith, which happens twice a year in those geographical areas lying between 23^26' Latitude North and 23^26' Latitude South. In the extensive inscription in the Temple of the Rood in Palengue there are the following calendar dates: the date 1 291 128 days a subsequent time interval of 4 749 days and the date 1 295 877 days. Each of them is accompanied with the same hieroglyph /see the figure 1/. The interval of 4 749 days between the two dates corresponds to 13 Tropical Years. During the calculations of correlation we found out that at these the Mayan dates the declination of the Sun is equal to 18^ latitude so that at noon the Sun stood right over Palengue which lies at 17^3O' Latitude North.

The miscalculation of O.5' is negligible and was unascertainable for Mayan astronomers.

The position of the rising of the Moon at the horizon changes from one day to the next. At the zero declination it rises exactly in the east, to the maximum northern and maximum southern declinations. This cycle takes 27.3215816 days and can be easily observed. In some inscriptions of the towns of Quirigu  and Yaxchil n, the Mayan dates are again accompanied by recurrent hieroglyphs. The time intervals between them are periods of the Tropical Month. They are the following dates: 1 4O1 577 days; 1 4O6 446 days; 1 411 569 days and others /see the figure 2/. The Mayan dates relating to the observation the length of the Tropical Year and the length of the Tropical Month were not sufficient to establish a correlation between the Julian & Mayan Calendars. So when calculating this, we used known Mayan dates from the Dresden Codex.

First we used the date 1 364 36O days to which the Mayan ephemerides of the visibility of the Venus were added. This falls on the first day when the planet is sighted after the lower conjunction of the Morning Star before the sun-rise in the morning sky. The second date has the value of 1 412 848 days. The Mayan cycle of the eclipse of the Moon or the Sun is added to that date. These periods of the eclipses are 177;178 or 148 days. Within the first phase of the calculation of correlation we took both possibilities of the solar or lunar eclipse into account.

Some dates of the inscriptions of the Temple Complex of Palengues accompanied with the same hieroglyphs /see the fig.3/, are connected with the synodic run of the Moon which has a period of 29.53O5882 days. They establish two groups of numbers fifteen days apart. This means that one group represents full moons and the other new moons. Some Mayan dates from the first group are 295 482; 1 386 61O days. Some dates from the other group are 1 295 877; 1 34O 763 days.

The date 1 412 848 days from the Dresden Codex is also related to that group. The Mayan dates obtained with the help of the analysis of hierohlyphic texts were ordered into groups according to certain astronomical phenomena. One typical date was then picked up from each group:

1 412 848 days - the eclipse of the Sun or the Moon
1 4O1 577 days - a Tropical Month, i.e. a zero, maximum northern or maximum southern declination
1 415 637 days - Tropical Year, i.e. vernal or autumnal equinox, summer or winter solstice
1 364 36O days - the Venus visible for the first time in the morning star in the morning sky after the lower conjunction.

The calculation of correlation between the Mayan and Christian systems of dating was carried out on a computer with the help of programs on determination of ephemerides of planets, the Sun and the Moon, and the tables of solar and lunar eclipses. We calculated that, for each of the astronomical phenomena assumed above, in a quite wide range of several hundreds of years, there was a set of Julian days during which a certain phenomenon was repeated in cycles. The difference between each individual Julian day and the related Mayan date represented a possible correlation. There were left only three coefficients from several tens of converting coefficients. They are as follows: 53O 584 days, 6OO O7O days and 622 261 days. Those coefficients are always to be added to the assumed Mayan dates so that they can equate to The Julian days and to our system of dating.

The last converting coefficient of 622 261 days, when applied to other dates from the inscriptions in Mayan towns and especially the Dresden Codex demonstrates such a high occurrence of significant locations of planets and celestial phenomena that this value is considered to be an essential correlation between both systems of dating.

Therefore we consider the converting coefficient of 584 284 days according to Thompson's Correlation which is used at present to convert the Mayan dates into the Christian system of dating, to be incorrect.

When using Thompson's Correlation for converting the dates relating to celestial phenomena into our calendar we find that the observed phenomenon would not take place.

The correctness of our converting coefficient of 622 261 days can also be supported by the historical continuity. Its analysis, however, reaches far beyond the frame of this study.