The highly advanced Mayan culture had developed through a complex synthesis of different cultural streams originating form the local agricultural basis affected by cultural values rooted in regions outside the Mayan territory. This culture was forming in the so-called early phase of the initial period spanning from 1500 B.C. to 800 B.C. Gradually, the Mayan culture had spread to cover the territories of Guatemala, South-East Mexico, Belize, Salvador and Honduras. The cultural and economic rise was outwardly reflected in the erection of vast and grandiose cathedral cities, the use of the Mayan own hieroglyphic alphabet, successes in astronomy, the existence of literature and progressive development of industries and trade.

Dating the course of development of the Mayan culture poses one of major problems of its study by correlating the Mayan system of dating with our own Christian system. Currently, the Goodman-Mart¡nez-Thompson correlation is used for the purpose. According to this correlation, the number 584,284 days is added to the Mayan date which stands for the number of days elapsing from an initial point in time to the day to be dated. Thereby, the date is converted to the so-called Julian days to be further converted to our dating system using conversion tables.

For the calculation of the correlation existing between the Mayan and the Christian dating systems the so-called Dresden Codex, one of the few handwritten Mayan books preserved, is of vital importance. E. Foerstemann /1880, 1892/ was one of the first to recognise this fact by pointing out the significance of the tables of visibility of planet Venus, analysed later by J.E. Teeple (1926). The eclipse tables were studied by M. Meinshausen /1913/, C.E. Guthe /1921/ and H.Spinden /1930/. R.W.Willson /1924/assumed that many Mayan dates could relate to observations of Mars, Jupiter and Saturn. The above research workers, like many others, used to work with Mayan dates by either applying the correlation coefficient of 584 284 days according to the Goodman-Martinez-Thompson correlation or attempted to calculate their own conversion patterns, arriving at different results.

Based on their own calculations, the authors believe the Goodman-Mart¡nez-Thompson correlation currently used to convert Mayan dates to the Christian system of dating to be incorrect. To support this view, two Mayan dates from the Dresden Codex relating to major astronomical phenomena s correctly identified by the above authors. The date in question is the Mayan date 1 412 848 days to which the eclipse ephemerides as presented in the tables accompanying this date are assigned. Using the Goodman-Martinez-Thompson correlation the above date corresponds to 7th November 755, a date on which no eclipse, either lunar or solar, took place. To the other Mayan date in question, 1 364 360 days the ephemerides of visibility of the Venus are assigned, i.e. the date is one when the planet, 6-8 days after the lower conjunction with the Sun for the first appeared as the morning star early before the sun rise. Using the Goodman- Mart¡nez-Thompson correlation, the above date would correspond to 5th February 623. On that day, the Venus was positioned only 15 days before its lower conjunction with the Sun and was seen on the sky as the evening star. The ancient Mayas could not have conceivably made a mistake of over 20 days in their observations of this planet.

The above examples have demonstrated that the Goodman- Martinez-Thompson correlation cannot be used for dates relating to actual astronomical phenomena. Therefore, the authors have proceeded to propose a new correlation using Mayan dates from the Dresden Codex and selected inscriptions found in the Mayan cathedral cities for which statistical analyses were taken to indicate that a reference to one of the most important astronomical phenomena, observations of the equinox and solstice during the tropical year, was being made.

by feeding the above Mayan dates to computer programmes for the calculation of the positions of planets on their ecliptics and the positions of the Sun, the Moon and the Earth, several conversion coefficients for the transformation of mayan dates to the Christian dating systems were obtained. The following coefficients were obtained: 530 584 days, 600 070 days and 622 261 days. The last-named coefficient 622 261 days is considered the most likely one. By adding the coefficient to the Mayan date, the number of Julian days can be obtained to be converted to the usual Christian system of dating using days, months and years. For all dates of the Dresden codex, concrete and often highly intriguing conclusions of astronomical observations or calculations were obtained. The new conversion coefficient of 622 261 days was first published at the 12th Global Congress of Prehistory and Protohistory held on 1st to 7th September 1991 in Bratislava, the capital of the Slovak Republic. All the necessary software concerning the calculations of astronomical phenomena were made available to the authors by Ing. Jan Vondrak DrSc. of the Astronomical Institute of Czech Academy of Sciences and we have the pleasure to use this opportunity to thank him for his generous assistance.

The astronomical observations the results of which are listed in the Dresden Codex were made using relatively very simple measuring methods. Moreover, Mayan astronomers knew no decimal numbers. This shortcoming which would otherwise mean a big handicap in calculating periodic phenomena observed in the sky was eliminated by the use of large numbers. Therefore, the recorded phenomena must be studied using statistical methods and respecting the inevitable scatter in the accuracy of the input data. This applies especially to astronomical phenomena apparently calculated backwards and forwards over centuries. Upon converting Mayan dates to the Christian dating system using the proposed conversion coefficient of 622 261 days the astronomical meanings of all were identified as concerning observations of the visibility of the planets and their conjunctions, the course of the tropical year, i.e. identification of the dates of equinox and solstice and solar eclipse. Unfortunately the time available prevents the authors from presenting a detailed analysis of all Mayan dates presented in the Codex and, in particular, the mathematical tables containing multiples of a few basic numerical constants. These used to be applied for the calculation of synodic orbits of the planets and the length of the tropical year.

The Dresden Codex is structured into pages numbered according to the older version defined by E. Foerstemann (F) and the newer version used by Ju. V. Knorozov (D). The parenthesis with some dates indicate that the corresponding date is not expressed directly a a number of elapsing days but have been derived instead in accordance with the rules of the so-called calendar circle comprising a combination of the sacred 260-day and the astronomical 365-day cycles.

Pages F24 (D24) of the Dresden Codex show Mayan dates in the following format:

To the date B multiples of 2 920 days are added. This is the typical period in which the concurrence of 5 synodic orbits of the Venus (as observed from the Earth), 13 sideric orbits (the actual duration of the planet's orbit around the Sun) and 8 tropical years are contained. Upon lapsing the time, two days given or taken, the Venus again rises and sets in the same point in the sky with the same stars in its background. Mayan dates B and C above stand for the point in time when the planet, following a period of invisibility of a few days duration, shone for the first time as the morning star in the early morning sky shortly before the sunrise. During the time the planet remained invisible, it was positioned in its lower conjunction with the Sun.

1 364 360 days (27th January 727)

the Venus is 8 days after its lower conjunction. It rises 56 minutes before sunrise as the morning star

1 397 640 days (11th March 818)

the Venus is 5 days after its lower conjunction. It rises 35 minutes before sunrise as the morning star

Between the two above dates (A and B) the time interval of 2,200 days is indicated in the Mayan text. This interval is typical for the repeatability of the same mutual positions of Mercury, the Earth and the Sun. The interval contains 19 synodic and 25 sideric orbits of the planet which coincide again after 6 tropical years. After such time, Mercury rises or sets in the same point in the sky and approximately on the same day in the year. A similar cyclic pattern was discovered by Mayan astronomers to exist for the Venus with which the repeatability of the process takes 2 920 days.

Observations of Mercury are very difficult as its orbit has the shape of a highly eccentric ellipse with the average length of the synodic orbit as observed from the Earth equalling 115.877484 days. Due to the eccentricity, the planet's speed differs in different parts of its orbit and hence the different synodic orbits durations range from 104 to 132 days. Moreover, the closeness of the Mercury to the Sun causes its visibility being obscured by the glare of the Sun. This was why Mayan astronomers could watch the planet only when it reached its extreme angular distances from the Sun (the so-called elongations) during its orbit. These can be either the western elongation with which the mercury rises in the morning over the horizon less than an hour before the Sun or the eastern elongation when the mercury can be seen shortly immediately upon sunset. The extreme angular distances of the planet from the Sun usually range from 18 to 23 degrees. The maximum deviation of 27 degrees and 49 minutes is reached when the elongation observed from the Earth takes place in the apohelion position i.e. at the biggest distance of the planet from the Sun, a position reached by the planet once in its sideric orbit (87.9693 days) along its eccentric trajectory. In the perihelion, i.e. at the point of the minimum distance from the Sun, the maximum deviation from the Sun as observed from the Earth is only 15 degrees 55 minutes. At the time around its maximum elongations the planet appears as if standing motionless for 4-6 days. Its angular distance from the Sun changes only slightly and the motion could have been hardly identified by Mayan astronomers given their crude observation methods. Therefore also their identification of the elongations of the Mercury tends to range within this error.

The above Mayan dates entry in the Dresden Codex describes at the same time the maximum elongations of the Mercury at the time the planet was positioned close to its maximum distance form the Sun and was hence the best to be seen.

1 366 560 days (4th February 733)

The Mercury in its western elongation with angular distance from the Sun 27 degrees. Rising 97 minutes before the Sun in the morning. Full moon.

2 200 days

Concurrence of 19 synodic and 25 sideric orbits of the Mercury with 6 tropical years.

1 364 360 days (27th January 727)

The Mercury in its western elongation with angular distance from the Sun 26 degrees. Rising 98 minutes before the Sun in the morning. The Moon in the new phase.

The observations of the visibility of the Mercury by Mayan astronomers is truly remarkable as their conditions to watch the planet were highly difficult. Therefore, their cognizance of the 2 200 days periodicity with which the concurrence of the synodic and sideric orbit times with the tropical year takes place deserves recognition as a major achievement.

Pages F 43 (D72) of the Dresden Codex show two dates referring to the maximum elongation of the Mercury. These date again relate also to other planetary phenomena. Similar such efforts of Mayan astronomers to seek links between individual phenomena in the sky and find their mutual correlations viable to be expressed by natural numbers are frequently encountered in the Dresden Codex. Between the two dates treated below the integer interval of 352 days is indicated. This interval stands for the least common multiple of 3 synodic and 4 sideric orbits of the Mercury. At that time, the planet is again positioned in the same point in the sky, this time in the area of its maximum elongation from the Sun, when it is the easiest to observe.

1 435 980 days (27th February 923)

The Mercury in its western elongation with angular distance from the Sun 25 degrees. Rising 77 minutes before the Sun in the morning.

- 352 days

Concurrence of 3 synodic and 4 sideric orbits of the Mercury.

(1 435 628) days (12th March 922)

The Mercury in its western elongation with angular distance from the Sun 27 degrees. Rising 80 minutes before the Sun in the morning. The spring equinox with error of - 4 days.

The other of the Mayan dates describes, besides other astronomical phenomena, also the heliactic rise of the Mars, when the planet was first shortly visible on the morning sky before sunrise, 56 days after its conjunction with the Sun. On the other hand, the heliactic planet setting means the moment when the planet is seen the last time after sunset low over the western horizon, to disappear beyond the sun for several days. The planet is in conjunction. It is clear in this respect that due to changing atmospheric conditions the heliactic planets risings and settings cannot be identified with the accuracy of a single day even if they are regular cyclic phenomena. By long-term observation extending over many years, the method can be used to establish fairly accurately the duration of the synodic orbits of planets. Numerous Mayan dates presented in the Codex relate to the observations of the heliactic risings and settings of planets, particularly the Jupiter and Saturn.

Some dates of the Dresden Codex relate to conjunctions of planets. Watching two astronomical bodies to meet in their trajectories is always an intriguing sight. Based on the observation findings and calculations of Mayan astronomers, close encounters of two planets should be perhaps sometimes referred to. Their values in the ecliptic are indicated in degrees of apparent geocentric rectascence from which their mutual distance is apparent. Page F 45 (D74) includes two dates between which an interval of 30 days is indicated.

To the later date on which the conjunction occurred the constant of 29120 days ia added. The Codex indicates the manner the constant was arrived at. The constant stood for the series of sequential products of 2 * 364 to 80 * 364. The constant contains 73 synodic orbits of the Jupiter and 77 synodic orbits of the Saturn. It is one of the periods at which the conjunction of the two planets recurs in the sky after 80 years. Really, after 29 120 days after date B, i.e. on 5th June 571, the two planets approached one another to under 5 degrees. But also the other way round, 29120 days before date B, i.e. on 22nd December 411 the two planets approached one another to 1.2 degrees.

The six Mayan dates presented in Pages F 51 - 52 (D 30-31) can be subdivided into two groups. The first relate to observations of the synodic orbit of the Moon and the solar eclipse.

1 412 848 days (29th October 859)

Annular eclipse of the Sun. The maximum was reached at 17 hours and 19 minutes of the ephemeride time on 78.79 deg. of western longitude and 2 deg of Northern latitude. Over the Mayan territory with its centre approximately over 90 deg. of Western longitude the maximum was visible at 11 hours and 19 minutes of the local time and virtually the whole course of the eclipse was visible. The eclipse ephemerides are added to the date.

1 412 863 days (13th November 859) Full Moon

1 412 878 days (28th November 859) Moon in the new phase.

The other group of dates relate to the conjunction of the Venus with Mars. Their proximity at the ecliptic is indicated in degrees.

1 578 988 days (10th September 1314)

Conjuction of the Venus (187.99 deg.) with Mars (197.76 deg.)

1 434 748 days (14th October 919)

Conjunction of the Venus (215.48 deg.) with Mars (214 deg.)

1 268 808 days (19th June 465)

Conjunction of the Venus (70.05 deg.) with Mars (57.04 deg.) The summer solstice.

The Mayan date 1 434 748 days can be considered to have been one when the close proximity of the two planets to 1.5 degrees was actually observed. The two other dates were calculated from it, one applying in the future (395 years) and one in the past (454.3 years). This is also why the angular distance between the two planets is bigger and it is more accurate to refer to their close approach in terms of the current astronomy. Mayan astronomers used to calculate with integer numbers only and hence their calculations of astronomical phenomena spanning longer intervals in time tend to be affected with a degree of inaccuracy. The same applies for the use of some numerical tables accompanying Mayan dates in the Codex. While recurring in a cyclic pattern astronomical phenomena can be predicted over centuries using these tables, the calculation error tends to grow.

The Dresden Codex contains numerous other series of Mayan dates and tables referring to major phenomena observed in the sky the system of which was understood by the authors. These concern particularly heliactic risings and settings of planets, their mutual conjunctions or observations of the length of the tropical year spanning as long as 34000 years. This major written artefact is a major document proving the intellectual capabilities of Mayas who created one of the most advanced and most remarkable cultures on the American continent.