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Electronic Theses and Dissertations, 2004-2019
2007
Maya Eclipses: Modern Data, The Triple Tritos And The Double Tzolkin
William Earl Beck University of Central Florida
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STARS Citation Beck, William Earl, "Maya Eclipses: Modern Data, The Triple Tritos And The Double Tzolkin" (2007). Electronic Theses and Dissertations, 2004-2019. 3078. https://stars.library.ucf.edu/etd/3078
MAYA ECLIPSES: MODERN ASTRONOMICAL DATA, THE TRIPLE TRITOS AND THE DOUBLE-ZTOLKIN
by
WILLIAM E. BECK B.A. University of Central Florida, 2001
A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Arts in the Department of Liberal Studies in the College of Graduate Studies at the University of Central Florida Orlando, Florida
Fall Term 2007
© William E. Beck
ii ABSTRACT
The Eclipse Table on pages 51-58 of the Dresden Codex has long fascinated Maya scholars.
Researchers use the mean-value method of 173.3 days to determine nodal passage that is the place where eclipses can occur. These studies rely on Oppolzer’s Eclipse Canon and Schram’s
Moon Phase Tables to verify eclipse occurrences. The newer canons of Jean Meeus and Bao-Lin
Liu use decimal accuracy. What would be the effect of modern astronomical data on the previous studies and the Maya Eclipse Table?
The study utilizes a general view of eclipses that includes eclipses not visible to the Maya.
Lunar eclipses are also included. This inquiry differs from previous studies by calculating the
Maya dates of eclipses instead of nodal passage. The eclipse dates are analyzed using the three eclipse seasons, of the 520 days, which is the Double Tzolkin or twice the Sacred Calendar of the
Maya. A simulation of the Eclipse Table, using the 59-day calendar, is created to test modern data against the Dresden Table. The length of the Table is the Triple Tritos of 405 lunations. The use of the Tritos instead of the Saros suggests the Table is independent of Western Astronomy.
Advanced Astronomy is not needed to produce this Table; a list of eclipses could produce this
Table.
The result of this inquiry will be to create a facsimile of the Eclipse Table, which can be compared to the Eclipse Table to test the structure, function and purpose of the Table.
iii
In the loving memory of my parents Harold and Virginia Beck
iv ACKNOWLEDGMENTS
I wish to thank my committee members, Drs. Arlen Chase, Diane Chase and Elayne Zorn, for
their help and advice. I also wish thank the staff of the University of Central Florida Library for
their tireless work in finding the resources for this project and the Office of Instructional
Resources for their help with formatting the thesis and images in this study.
v TABLE OF CONTENTS
CHAPTER ONE: BACKGROUND...... 1 Introduction...... 1 Dresden Codex...... 2 Science ...... 15 CHAPTER TWO: DISCUSSION...... 26 Calendars and Maya Math ...... 26 Eclipse Data ...... 31 Eclipse Periods...... 38 Simulation...... 51 Chapter Three: Conclusion ...... 57 Appendix A Meeus Lunar Data ...... 60 Appendix B Liu Lunar Data ...... 63 Appendix C Oppolzer Lunar Data ...... 66 Appendix D Meeus Solar Data ...... 69 Appendix E Oppolzer Solar Data ...... 72 Appendix F Lunar-Solar Data...... 75 Appendix G Meeus Lunar Season Distribution...... 79 Appendix H Meeus Solar Season Distribution ...... 81 Appendix I Teeple Season Distribution...... 83 Appendix J Solar-Lunar Season Distribution ...... 85 Appendix K Table Simulation ...... 87 Appendix L Glossary ...... 90 LIST OF REFERENCES...... 95
vi LIST OF FIGURES
Figure 1 Solar and Lunar Eclipse Glyphs Pages 53a and 58b of the Dresden Codex after Thompson (1972)...... 6 Figure 2 “Bookend Gods” Page 68 of the Dresden Codex after Thompson (1972)...... 18 Figure 3 Serpent Images Pages 56b and 57b of the Dresden Codex after Thompson (1972) ..... 19 Figure 4 Ah Tzul Ahau Page 58b of the Dresden Codex after Thompson (1972) ...... 21 Figure 5 Teeple Arc after Teeple (1930:89) ...... 34 Figure 6 Meeus Arc following Teeple (1930:89) ...... 37
vii LIST OF TABLES
Table 1 Picture Intervals after Guthe (1978:11) ...... 13 Table 2 Lunar Semesters after Guthe (1932:275)...... 43 Table 3 Eclipse Periods after Table 4 Van Den Berg (1955:28) ...... 50 Table 4 Guthe's Semesters after Guthe (1932:275) ...... 53 Table 5 Tritos Simulation of Table 2...... 54
viii
CHAPTER ONE: BACKGROUND
Introduction
The purpose of this study is to compare modern astronomical data against the Dresden Eclipse
Table on pages 51-58 of the Dresden Codex. The Dresden Codex is 405 lunations or 46 Tzolkins in length. A Tzolkin is the 260 day calendar used by the Maya. This duration of time is three times the Tritos eclipse period of 135 lunations or a Triple Tritos. The Dresden Codex is one of three surviving Maya texts that display charts believed to contain astronomical data. The
Dresden Eclipse Table is one of the most studied and least understood pieces of Maya
Iconography. Is it a lunar calendar; a solar warning table; a sysygy, (a list of actual eclipses) or just a list of potential eclipses? For this reason the chart on pages 51-58 will be referred to as the
Eclipse Table in this thesis.
This inquiry differs from earlier studies by computing the Maya Date of modern eclipses instead of nodal passage, the area where eclipses are most likely to occur. This method will allow for the elimination of the use of the mean-value method of 173.31 days, prominent in previous studies of Maya eclipses. Three times the mean-value is a close approximation to the 520-day period, the Double Tzolkin. This study will also investigate other eclipse periods and not just the
Saros period used in the earlier studies. The Saros is very prominent in Western Astronomy but
not in Maya astronomy.
A secondary purpose is to compare modern astronomical data against the astronomical data used in the previous studies of the Eclipse Table. This data is Oppolzer’s Eclipse Canon (1887) and Schram’s Moon Phase Tables (1908). To test the validity of these texts, two newer eclipse
1 canons, one by Bao-Lin Liu (1992) and another by Jean Meeus (1966, 1979) will be compared to
Oppolzer’s Canon. These newer canons are more accurate due to decimal approximations but the
Maya did not use decimal numbers. Would this increased accuracy be of any importance to the
Eclipse Table’s structure or function?
This study uses a general approach, including eclipses observed in the Maya area and those not visible in this area. Other questions open to investigation are; are the eclipses observed or computed; and does the Table list solar or lunar eclipses?
The first chapter introduces the history and structure Eclipse Table. It investigates Maya beliefs about eclipses and compares this to modern scientific knowledge of eclipses. The second chapter investigates Maya and Western calendars. Calendars are important tools in developing eclipse periodicity. Modern eclipse dates are converted into Maya dates using the Goodman-Martinez-
Thompson correlation constant of 584285 days, equating to November 12, 755. These dates are
evaluated using the three eclipse seasons of 520 days. A 59-day Lunar Count is used to create a
simulation of the Eclipse Table. A simulation is also created using the Meeus lunar data.
Simulations are needed because; the Codex is a one of a kind artifact. There is nothing to
compare the Table with, except dates in an ephemeris.
Dresden Codex
The background of the Dresden Codex is not fully known. Some facts have been presented by
J.E.S. Thompson (1972:15-19) and George Dicken Everson (1995:57-58). The Codex was acquired by the Royal Public Library of Dresden from Vienna, Austria. It first appeared in a
1739 catalog of the Dresden Library, produced by Johann Christian Goetz, the Library’s
2 Director. In the catalog, the Codex was believed to be of Mexican (Aztec) origin because of
similarities to the Mexican codices in the Vatican, but its origins are Maya. The Codex is
believed to have been sent in the first Royal Fifth, the Spanish portion of the New World
treasure, around the date of 1519, according to (Everson 1995:57). In Thompson, this shipment is
referred to as Cortes’ Gift to Emperor Charles V. This act did save the Codex from the burning of Maya books in July of 1562 by Friar Diego de Landa. The Habsburg Dynasty, to which Spain belonged, did have a villa in Vienna, Austria. The Codex was observed by visitors to the Royal
Court and very well could have been brought to Vienna by the Royal Court.
In 1880, Ernst Förstemann, the Head Librarian of the Dresden Library, started his classic translation of the Dresden Codex. He was the first researcher to identify pages 51-58 as being eclipse related material. The Dresden Library was damaged in World War II by the fire bombing of Dresden. The Codex received some water damage, but no fire damage. The Codex was rescued by a Russian soldier, who was a student of languages, named Yuri Knorsov. Mr.
Knorsov later became Russia’s pre-eminent Mayanist and epigrapher.
The Dresden Codex may have had four different scribes recording information in it. The Codex also may have contained additional pages (Thompson 1972:20). The date of the Codex is also not known. The Codex contains eight, nine, and ten cycle dates. Some researchers place it in the eleventh century. Thompson places it between 1200 and 1250 (Thompson 1972:15). Everson places it in the thirteenth century (Everson 1995:4). Satterthwaite places it no earlier than A.D.
1345 (Thompson 1972:15). Some researchers have speculated that this is a copy of an earlier work ca. A.D. 755. Any definite date in the Eclipse Table would help to understand some of the questions and inconsistencies of the Codex.
3 The history of the Eclipse Table is covered by Thompson (1975:233-236). The study of Maya
eclipses parallels the history of the study of Maya epigraphy as described by Morley (1940). The early study of epigraphy was focused on aligning the Maya calendar with the Western calendar.
The study of the Eclipse Table began with Ernst Förstemann (1967; see Thompson 1975:29,
1972:71-77). Bowditch (1910) brought Förstemann’s work to America. Guthe (1978), Willson
(1974; see Spinden 1969, 1928, 1928a) and Teeple (1930) are all prominent researchers in the early investigations of the Codex and Eclipse Table. Villacorta and Villacorta (1976) and Gates
(1932) created reproductions of the Dresden Codex. Thompson (1972) continued Gates’ work.
Makemson (1943), Satterthwaite (1947), Lounsbury (1978, 1986),; Bricker and Bricker (1983),
Kelly (1976), Justeson (1986), Campbell (1992), Everson (1995) and Smither (1986) all continued the research of the earlier scholars. Although all of the researchers believe that the
Eclipse Table is associated with eclipse periods, exactly which eclipses match those periods is still in question. All of the newer researchers believe that the Dresden Table is solar in nature.
Smiley (1973:175, 1771975:248) calls the Lunar Table a Solar Eclipse Warning Table and viewed the Venus Table as a Solar Prediction Table. Spinden states that “the Eclipse Table is a calendar of the moon” (Spinden 1928a:148). A study of the lunar calendar is investigated in the
Simulation Section of Chapter Two. Guthe believed the Table served both for predicting eclipses and for lunar reckonings (Thompson 1975:234). MacPherson (1987:443) considered the Table to be a chart of observations of sunsets and moonsets.
“It is either a record of observed results over a thirty-three year period or a computation made for a given thirty-three year period, but cannot possibly be a formal calendar for repeated reuse”
4 (Teeple 1930a:138). Carlson believes that it “is a canonical, quasi-astronomical calendar rather
than a true astronomical ephemeris” (Carlson 1984:241).
The Table is a table of solar sysygies, according to Teeple (1930a:137). A sysygy or ephemeris
is a list of dates when eclipses are likely to occur. The Maya Tables are tables of mean motion
rather than ephemerides, according to Kelly and Kerr (1973:182).
The Table is an Eclipse Warning Table, according to Schove (1982:241, 1984:304), Aveni
(1981:80), and Malmstrom (1977:147). Kelly (1976:43) stated that “it is a Prediction Table
rather than a record of past events.” Satterthwaite (1962:255) also called it an Eclipse Predicting
Table.
The Eclipse Table covers pages 51-58 of the Dresden Codex. It contains an upper register
designated “a” and a lower register designated “b.” This is the old pagination which is still used because of all the past studies which use this system. One must remember to read the Table starting with 51a-58a then 51b-58b. The Table can be divided into four sections: glyphic text; pictures; numbers (bars and dots); and dates. The dates divide the numbers into a bottom section of eclipse intervals and an upper section of totals. The totals, intervals, and dates make up the heart of the Eclipse Table.
Kelly states that “our knowledge of the mechanism of various astronomical tables and of the calendar is quite adequate but our understanding of the associated glyphs has lagged far behind”
(Kelly 1976:52).The eclipse glyphs in the codices (Figure 1) are the Kin (sun) and Uo (moon) signs enclosed in white and black elbow elements.
5
Figure 1 Solar and Lunar Eclipse Glyphs Pages 53a and 58b of the Dresden Codex after Thompson (1972)
There is only one glyph from the monuments, identified by Juan Palacios at Santa Poco Unic.
It has a kin sign in brackets (Teeple 1930:115). The glyphs of eclipses are from the codices.
There are in the references monuments to the sun being in his house; could the bracket in the eclipses glyphs signify his house? There is also a reference to New-Sun-at-horizon.
Coincidently, there occurred a nearly total eclipse at sunrise on December 11, 847 (Schove
1982:251). Schove thought this proved his theory of the Table. The sky-in-hand glyph (Figure 1) also appears quite frequently with eclipses. These glyphs are repeated in a phrase which opens and closes the Eclipse Table.
The Eclipse Table is 405 lunations or 11,960 days in length. This is equivalent to forty-six tzolkins. There are sixty-nine eclipses in three sections of 3,986. This is a total of 11,958. Some researchers also list an 11,959 total, giving a three day spread for the totals. The Table is further divided into “six months” of thirty days and “six months” of twenty nine days for a total of 177 days. There are six parts of 177 to one of 148 days. There are nine parts of 177 to one of 178 days (Förstemann 1967:200-202). The big question has been where to place the 148 and 178-day periods.
The Eclipse Table on pages 51a and 52a opens with an Introductory Section which lists the starting date of the Maya Long Count, 4 Ahau 8 Cumhu. To this date eight days are added to
6 give the date 12 Lamat. Lamat is linked to the planet Venus. Some researchers believe that the
12 Lamat date is a ritual starting date for the Eclipse Table and have tried other dates involving
12 Lamat. Any change of ten tzolkins would return the Lamat date to the base date. The ten- tzolkin interval is 1.31 days more than one of the subdivisions of the Saros, the 88-lunations
(Lounsbury 1992:204).
The major problem with the Table is that the eclipse dates change over time. The Table is supposed to have a self-correction system, but no one has described precisely how it works.
These questions are complicated by the fact that only one version of the Eclipse Table has survived. Another version of the Table would answer some of the questions about the base date and whether the 12 Lamat date is a ritual date for the Table.
It is impossible to determine from the Table’s form whether it is used for solar or lunar eclipses
(Beyer 1933:305). The Table could be employed by both with the addition or subtraction of fifteen days. The Introductory Section contains a series of five Maya dates repeated seven times.
Campbell (1992:51) speculated these “year bearer” dates became eclipse bearer dates. Saros eclipses can be predicted by using the first full or new moon of the year
(http://www.astro.uu.nl/~strous/AA/en/saros.html). The Maya may also have developed a way to predict eclipses with their year bearer date. Additional studies will have to be done to determine the nature and function of this group of 15-day dates. Meinhausen suggested that pictures come after the 148-day eclipse periods because when a solar eclipse occurs at an interval of 148 days, then a lunar eclipse will follow fifteen days later (Everson 1995:160; Thompson 1972:72,
1975:233). Makemson states that “the fifteen days indicates pairs of solar eclipses” (Makemson
1943:206-207).
7 On page 52a, there is a series of thirteen thirteens. This creation number is also recorded on
Stela 1 at Coba, Mexico (Freidel, Schele and Parker 1993:62-63). The thirteen thirteens are also
listed on pages 23 and 24 of the Paris Codex (Willson 1974:19). The thirteens are Oxlahun-ti-Ku,
“Gods of the Thirteen Heavens” (Jakeman 1947:9). Oxlahun-ka’an-ub is “thirteen-sky-moon,” a reference for a full moon (Marci 1996:285-286). In the Motul dictionary, Oxlahun-caan-u is
“thirteen heaven moon” (Campbell 1992:52). There are several instances of the thirteen gods and the thirteen heavens. There are thirteen variations of the head-variant glyphs, which are seen as having had a lunar significance (Marci 1996:278-279). A period of thirteen days is the average number of days from visible first crescent until full moon (waxing moon). The Maya could incorporate a seven day waning period to third quarter and a nine day period through invisibility.
There are nine moonless nights, signified by the Lords of the Night (Marci 1996:275, 278-279).
Thirteen times thirteen is 169 days, a close approximation to the 177-day eclipse cycle (Smiley
1975:248).
The Chilam Balam of Chumayel, the Maya Book of the Jaguar Priests, tells of the creation of
the unial, or thirteen entities added to seven making twenty (Jakeman 1947:8). A variant moon
sign Uo (Frog) is often used for the number twenty. With this change, the calendar became
divorced from observed phenomena, but had to be tracked by specialists (Marci 1996:286).
The Eclipse Table does contain numerous errors. These have been discussed by Förstemann
(1967), Bowditch (1910), Guthe (1921) and Thompson (1972) as “copying errors.” Most involve
dropped bars and dots. Some day signs are incorrect. Fortunately, the Maya used a redundant
system of distance numbers. Some of the dates are correct but the numbers are off, or the
8 numbers correct and the dates are wrong. Both situations are easily corrected and pose no problem to this investigation.
There is also an eleven day error (Appendix F) between the lunar date of the Table and that of the nearest lunar eclipse date. This error may be caused by the date being a “vague date.” The
Maya did not add a day for leap years. There is an expression that “in the thirteenth Ahau; Pop was set in order” (Long 1921:37). Altar U, at Copán, contains two different 0 Pop dates (Carlson
1977:104-106). Kelly speculated on an eclipse date of 9.17.0.0.0 13 Ahau 18 Cumhu, is January
24, 771. The 9.17 date also occurs on Stela E at Quirigua (Kelly 1977:62; Teeple 1925a:115;
Closs 1986:236, 1989:232, 1992:140; Milbrath 1999:115. This date is believed to be an eclipse date, but is in the next cycle of the Eclipse Table used in this study. This eclipse date may hold clues to the ordering of Pop.
The introduction contains a series of numbers that are multiples of 11,960 (1.13.4.0 vigesimal).
This is the length of the Eclipse Table. The most prominent number is eighteen times the Eclipse
Table. This number is the date Satterthwaite uses in his study (1947). These multiples could have been used for recycling the Eclipse Tables or predicting future eclipses. The dates in the Table became obsolete over time due to the accumulated fractional part of the eclipse cycle. How the
Maya recycled the Table is still not fully known. How many times could the Table be used?
There have been suggestions that the Table could be used for some 800 years, but the Maya could have redone the Table more frequently. Teeple (1930a:138) believed the Table was used only once. Makemson (1943:194) stated the Table could be used four times from 1083 to 1214.
Spinden (1969:69), Bowditch (1910:224) and Thompson (1972:74) suggested eight times
(Satterthwaite 1947:77). The four times is due to the 1.6 day regression in the node. The reason
9 for eight times is that the Table of 405 lunations is 0.11 of a day shorter than the 11,960 days.
The .11 days shortfall uses the 11,959.889 day computation (Guthe 1978:3).
The Table includes five Maya Long Count Dates. Two of the dates are questionable dates that do not appear to be eclipse dates. Three of the dates have become vital to the current understanding of the Eclipse Table. These dates are:
9.16.4.10.8 12 Lamat 1 Muan 9.16.4.11.3 1 Akbal 16 Muan 9.16.4.11.18 3 Eznab 11 Pax
These dates are also fifteen days apart. One of the dates is a 12 Lamat date. It has been designated as the Base Date of the Table. The date 12 Lamat is 177 days before the first date in the Table on page 53a. Most of the researchers since Willson have assumed the 12 Lamat date to be that of a solar eclipse. If that date is solar, the Table is a list of new moons. If they are new moons, the Table is solar. This is the circular logic researchers use to determine that the Table is solar. The solar aspect has not been proven, only accepted as fact.
The Base Date used in this study is the 9.16.4.10.8 date without regards to whether it is a solar or lunar date. This date is November 12, 755, using the 584285 constant. The solar proponents believe the 12 Lamat and 3 Eznab dates are solar eclipses with a lunar eclipse in between.
Satterthwaite (1962:256) mentions some studies of the solar-lunar-solar eclipses. Makemson states “it makes no difference whether these dates are two lunar with a solar in the middle or two solar with a lunar in the middle” (Makemson 1943:187). Appendix F combines the solar and lunar data for the period 755. A cursory study of Appendix F does not appear to support this hypothesis. This hypothesis has no relevance to this inquiry but should be further studied in future research.
10 Additional studies are also required for the erroneous Long Count date 9.19.8.7.8 7 Lamat
(Milbrath 1999:115; Thompson 1972:71). The date does not agree with the base date of the
Table. Makemson (1943:189) stated that there was no 7 Lamat to be found among the day names. This date is in conflict with the other 15-day periods of the solar-lunar-solar eclipses.
Other base dates have been proposed. Makemson (1943:194) utilized the date 10.12.16.14.8 12
Lamat 1 Chuen (Lounsbury 1992:203). This date using the 584285 constant is April 19, 1083.
Closs (1989: 234) mentions the date 10.19.6.1.8 12 Lamat 6 Cumhu, which is another tenth cycle date with a 12 Lamat base. Satterthwaite used the date 11.6.2.10.8 12 Lamat 11 Zac, which is eighteen times 405 lunations (Everson 1995:175). This is the date April 12, 1345. Most of the dates are tenth cycle dates and are also 12 Lamat dates. Some base dates use other Ahau constants; (Makemson 489,138; Owen 487,410; Smiley 482,699) Owen (1975:240-241). Smiley
(1975:256) states that the 9.16.4.10.8 date occurred at September 22, 477. These dates are fifth century eclipses. These dates use a different Ahau correlation moving the date back in time.
These dates should be studied because of their high activity of eclipse occurrences.
The structure of the Table consists of sixty-nine eclipses divided into three parts of twenty- three eclipses each, for a total of 405 lunations or 11,960 days. The numbers 11,958 and 11,959 are also mentioned as lengths of the Table, which are derived from different multiples of lunations or mean values. One third of 11,958 days is 3,986 days. One third of 405 lunations are
135 lunations, a period called the Tritos. The 405 lunations are equal to forty-six rounds of Maya tzolkin. The three parts are not the eclipse seasons. The seasons are every third interval of the
177 or 148 numbers.
11 Across the bottom of the Table are a series of Maya numbers: 8.17 (8 times 20 = 160 + 17 =
177) and 7.8 (7 times 20 = 140 + 8 = 148). These are the intervals that mark each eclipse and project eclipses into the future and past. A lunation is 29.53 days. Six times the lunation equals
177.18 days, a very close approximation of the eclipse-half-year. Five times 29.53 equals 147.65, a very close approximation of 148. There are seven groups of six lunations (177 days) and a group of five lunations (148 days), and six groups of six lunations and a group of five lunations.
Some of the 177-day groups contain an additional day (178 days). The five lunation groups upset the sequence. The five lunation groupings are important to the structure of the Table. In fact, nine out of the ten pictures are located at these periods. The tenth picture is located at the end of the Table. This may be a new base date if the chart is used more than once. Makemson
(1984:192) believed that the pictures were inserted at points where lunar eclipses would occur.
This may well be true, but it should be remembered that solar and lunar eclipse are separated by fifteen days. Willson (1974:11, 16) tried to find eclipses in Oppolzer’s canon, which he aligned with the pictures in the Table. He was not able to find a match.
The image in picture 10 wears the Venus symbol in the head band. Venus images in picture 3 and 8 indicate Venus is involved in the Eclipse Table (Makemson 1943:191-193). Most symbols are solar in nature, but picture 3 depicts the Moon Goddess. Makemson ignored the Moon
Goddess because she believed that Venus’ importance to the sun proved the solar eclipses.
However, there is a Venus-Moon relationship (Satterthwaite 1962:258). The solar researchers are not looking at the moon.
12 Förstemann (1967:205) listed the intervals between the pictures in the Eclipse Table. Bowditch
(1910:217) created a table of intervals (Table 1) used by most other researchers to find eclipse periods.
Table 1 Picture Intervals after Guthe (1978:11)
Zero picture to the first 502 Fifth to Sixth 1034 First to second 1742 Sixth to Seventh 1210 Second to Third 1034 Seventh to Eighth 1565 Third to Fourth 1210 Eighth to Ninth 1211 Fourth to Fifth 1742 Ninth to end 708
The first column plus the last equals 1210 (Bowditch 1910:217; Kelly 1976:43).
Teeple (1930:63) believed the regularity of the twenty-nine and thirty day moons proved computation, but thought that the irregularities in the intervals proved observation (Teeple
1930:91). The three parts (Tritos) are divided into sections; 1742 equals eight times 177 + 148 +
178; 1034 equals four times 177 + 148 + 178; and 1210 equals six times 177 + 148; for a total of
3986 days Förstemann (1967:202). This is the Maya Sariod (Willson 1974:15).
The bulk of the Table is made up of sets of three consecutive dates. These dates are 176, 177, and 178 days from the preceding set of dates for the six lunation groups, and 147, 148, and 149 days for five lunation groups. This variation has caused some researchers to question whether the dates are a sysygy, which is a list of eclipses for predictions or a warning period of when eclipses are likely to occur. The three day spread does allow wiggle-room for the variations in eclipse periods caused by the accumulation of the fractional part of the eclipse period.
Guthe (1978:27) believed that the one-day error in the calendar was corrected each pass through the Table by moving down from the middle row to the lower row. The three dates were first thought to be three ephemerides (Bowditch 1910:221-224). Eclipses start at the bottom
13 repeating for eight times (Satterthwaite 1947:77, 1962:270). The discrepancy of 11/100 of a day creates, on the ninth time through the Table, a one day correction. The correction was accomplished by moving up one row of dates (Lounsbury 1978:802).
Another theory explaining these dates is the Lunar Variation Theory (Satterthwaite 1947:77).
The rationale behind this theory is that the fraction part of the eclipse period accumulates; resulting in a three-day range of dates (176-178). These variations become apparent in the Meeus data (Appendix A).
The only part of eclipse periods not found in the Table are the one day lunations. These may be the same periods proposed by Satterthwaite (1947:147). The researchers who have been calculating nodal periods from mean values only accept a deviation of twenty-five days. Since one lunation of 29.5 days exceeds this limit, the one lunation eclipses would be fictive or false eclipses. These are like the 148-day eclipse, but only at the other end of the eclipse group. The
148-day eclipses are referred to as “pre-nodal eclipses.” The one-lunation eclipses are referred to as “post-nodal eclipses.” These eclipses are in the Table, but are not as apparent as other eclipses. Some produce the 148 day eclipses in the Table. Others simply recede into the 177- day period and are not differentiated in the Table. The Table contains approximately six one- lunation eclipses.
The three-day groupings in the seasons (Appendix G, H and I) are not readily apparent, but there is a close association between eclipses in the group. The three groupings are controlled by the Base Date of the Table. A change in Base Dates does change the sequence of the lower numbers as well as the upper totals. Appendix J is a combination of solar and lunar eclipses distributions, which shows that the three dates can handle either solar or lunar eclipses.
14 Above the three dates are Maya numerals, which are cumulative totals of the number at the
bottom and the preceding total. This is the same procedure as Meinhausen (1913:221-225) used
in his study on eclipse periods. These numbers are also similar to Table 2 of Schram’s Moon
Table (Morley 1977: 394; Schram 1908:358, and Willson 1974:10).
Science
The first investigations of Maya astronomical data sought to determine a correlation between the Maya and Christian calendars. This is known as the astronomical approach to a correlation.
John Teeple’s (1930:36) work Maya Astronomy sought to determine if it was sufficient to establish a correlation. Willson’s failure to find eclipses to match the pictures in the Eclipse
Table prompted him to say that “no correlation of the Mayan and Julian calendars could be found from the Lunar Series alone” (1974:16). The newest area of research into the astronomical data is the investigation of how much science the Maya actually utilized. David Freidel (1993) and
Dennis Tedlock (1992, 1996) have been investigating the links between the Popol Vuh and astronomy. Charts of recurring astronomical and meteorological events serve as signs for the mythic deeds of the gods (Tedlock 1992:249). The newest hypothesis is that the stories in the
Popol Vuh are based on actual astronomical events some 5,000 years ago. Quiche rites give ample testimony to a long-standing Maya concern with actual astronomical events (Tedlock
1992:269). Aveni (1975, 1977, 1980, and 1992) has become a leading authority in the field of
ArchaeoAstronomy. He states that their literature – in all forms - is filled with celestial knowledge (Aveni 1992:4). Kelly and Kerr (1993:179) state that “there is a considerable amount
15 of astronomical data in the inscriptions.” Unfortunately, the Maya did not leave texts of their celestial knowledge: only charts which are reported to contain astronomical data.
The Maya practiced naked-eye astronomy, which focuses on the helical risings and settings of celestial objects. The Maya did not have the telescope, but may have used sighting sticks during observations. There is also speculation that Maya astronomers aligned stone monuments, called stela, and Maya buildings, called E-groups, as lines of sight for celestial observation.
Maya astronomy is different than Western astronomy in that the Maya priests did not use astronomy as an exact science (Thompson 1975:33). “The Maya were more concerned with numerological commensurations within their calendar than with geometrical and mathematical relationships of positional astronomy” (Carlson 1984:236). Time, not space, is the principal medium of expression for all astronomy (Aveni 1981:85). Another difference in Western astronomy is in the use of the Babylonian eclipse period, the Saros. The Maya use the Triple
Tritos, which is divisible by 260, whereas the Saros is not. The Maya would study the heavens for divination purposes (Landa 1978:13). The celestial bodies exert direct control over the affairs of man (Andrews 1940:150). As far as the Maya were concerned, astronomy was astrology
(Aveni 1981:85). As Thompson (1966:173) stated, “astronomy is the handmaid of astrology.”
Maya priests were obsessed with knowing time. Time is cyclical. Events in the past are the same as events in the present or future. There are good days and bad. The Maya also believed that the conditions in the heavens were a portent of situations on earth. The best way to cope with the bad days was to keep records and search those records for similarities. That way, a proper ritual could be followed to mitigate the bad effects. Careful observation, record keeping, and
16 experimentation are a major part of scientific investigation. The Maya Priest kept records of celestial observation to make predictions.
Other almanacs may have been consulted by the priests making eclipse predictions. This thesis focuses mainly on the Eclipse Table on pages 51-58 of the Dresden Codex. Other studies have been conducted and more should be done on the other almanacs. Eclipse intervals are common between some almanacs and many dates are repeated in more than one almanac. The Moon
Goddess Almanac on pages 16-23 of the Dresden Codex is one of the other almanacs. The Moon
Goddess does have death images suggesting eclipses (Hoflin and O’Neil 1992:102, 118-120).
The Agricultural Almanac on pages 38-41 of the Dresden Codex depicts meteorological and agricultural activities. The almanac is 520 days in length, the Double Tzolkin. It does contain eclipse glyphs (Bricker and Bricker 1986:29-30). The Seasonal Tables on pages 61-69 also have eclipse glyphs on pages 66a and 68a (Figure 2) (Bricker and Bricker 1986a:232-235). Knowlton
(2003:294-298) has also studied the Seasonal Tables to determine if this Table is relevant to eclipses occurring during the rainy season. Weather is always a factor in observing celestial phenomena.
17
Figure 2 “Bookend Gods” Page 68 of the Dresden Codex after Thompson (1972)
The Venus Table on pages 48-50 of the Dresden Codex is another astronomical table located directly in front of the Eclipse Table. Five Venus cycles of 584 days are equal to eight tropical years of 365 days, producing a cycle of 2,920 days (Kelly 1977:58). The 584 days is divided into sections of 236, 90, 250, and 8 days. Venus appears as the Morning star for about eight months after inferior conjunction; it disappears for three months at superior conjunction and reappears as the Evening Star for eight months, then it disappears for two weeks at inferior conjunction
(Teeple 1930:94). The Venus Table does have some connections with eclipses trough moonphases and certain periods of time which Smiley has investigated
Earlier peoples believed that during eclipses the Sun God abandoned them or that a celestial monster devoured the Sun or Moon. On pages 56b and 57b (Figure 3) of the Dresden Codex, a serpent is attempting to devour a Maya solar eclipse symbol.
18
Figure 3 Serpent Images Pages 56b and 57b of the Dresden Codex after Thompson (1972)
The Maya believed that eclipses were caused by fights between the Sun and Moon (Thompson
1939:164, 1975:231). They also believed that eclipses are caused by an agent (that agent is the ant or a jaguar) biting the Sun or Moon (Thompson 1939:164). Closs (1989:229-234) lists that agent as the planet Venus: Venus as Evening Star. The ant and the jaguar are associated with
Venus. The Maya religion has a close relationship with the Sun, Moon, and Venus, the three most brilliant objects in the heavens. “Venus and the Moon marched together” (Aveni 1992:15).
The Moon is a very important clock for the visibility of Venus (Romano 1999:558). D. Juan Pio
Perez states that the Sun, Moon, and Venus all have a prominent role in the Maya universe, while
19 the other planets and stars occupy a relatively minor position (Closs 1978:148). The eclipse overtones of the Venus Table, noted by Spinden and Smiley, are no accident (Kelly and Kerr
1973:188; Schove 1984a:23). Some Venus periods are eclipse period,
To the Maya, eclipses were dreadful times. Both solar and lunar eclipses were portents of the end of time (Closs 1989:234). On page 72 of the Dresden Codex, the flood scene depicts the flood that destroyed the previous creation. At the top of the downpours are glyphs of solar and lunar eclipses. Like another story from the Popol Vuh, total solar or lunar eclipses could cause all of the domestic instruments to be transformed into living creatures that could kill their masters
(Closs 1986:392). Eclipses also caused illness and deformity. Pregnant women and their infants were extremely susceptible to eclipse effects. Infants would get gastrointestinal problems and pregnant women would have their infants born with dark splotches, called sun and moon bites
(Closs 1986:391).
The most dreaded part of eclipses was the monster that would descend to earth to devour people when the sun became obscured. On Page 58b there is an image of the Diving God (Figure
4). This monster is similar to the Mexican Tzitzimime Monster.
20
Figure 4 Ah Tzul Ahau Page 58b of the Dresden Codex after Thompson (1972)
Closs (1978:161; 1986:405, 409; 1989:229; 1992:143) has studied the ethnographic details of
Maya eclipses. He calls the image in Figure 4 the Ah Tzul Ahau, or the Ant Lord or Dog/Spine
Lord (Figure 1). The image is associated with the Venus god, Lahun Cahn. To frighten the eclipse and to defend the moon, the Maya would make noise, shoot arrows into the air, and pinch their dog’s ear to make them howl. This practice is described in a letter by Alfonso Dáavila in
1531. He stated that an eclipse would have inspired fear in the spirit of the Spaniards (Closs
1986:390).
Venus has a period of 584 days, which is a close approximation to the synodic period of
Venus, which is 583.92 days. The planet Venus does not affect the celestial mechanics of eclipses, but there is a strong association between Venus and the phases of the moon. If the
21 Moon is at first quarter at morning helical rising, it will be at the same phase when on its last day as Morning Star. It will reappear as Evening Star at the opposite phase or last quarter (Aveni
1992a:89; Juteson 1986:94-95). The Venus Table on Pages 46-50 of the Dresden Codex is directly in front of the Eclipse Table. It is based on a period of 2,920 days. Lines 14, 20 and 25 are at or near eclipse intervals. Lines 14 and 20 are 11,960 days apart, which is forty-six times the Tzolkin. Lines 20 and 25 are 9,360 days apart, which is thirty-six times the Tzolkin (Aveni
1992a:88). Two prominent dates in the Venus Table are 1 Ahau 18 Kayeb and 1 Ahau 13 Mac.
These dates are 11,960 days apart, the length of the Dresden Eclipse Table. The Maya date 3 Xul to any date 1 Ahau 18 Kayeb is 9360 days (Kelly 1977:58-59).
On page 24 of the Dresden Codex are periods of forty-six times 260 days, which are equal to
104 times 115 days, the synodic period of Mercury (Förstemann 1967:114).
Eclipses are not very important to modern astronomers. The celestial mechanics behind eclipses is fairly well known. Solar eclipses are used to study the sun’s corona. Lunar eclipses are studied to measure the effect of pollution in the earth’s atmosphere. With the aid of modern computers, astronomers are able to improve the accuracy of recording eclipses periods. These improvements create only small changes in the onset, duration, and area covered by the eclipse.
Solar eclipses are very special events. They happen in the daylight and demonstrate dynamic changes in the environment. The levels of light and heat diminish rapidly. Solar eclipses are very fleeting, only lasting up to 7 minutes and 31 seconds in duration as the path of the moon’s shadow sweeps across the earth. An observer would need to travel at speeds greater than 1,000 miles per hour to keep up with the shadow for an hour or more of a solar eclipse (Smiley
1961:212-213). Total solar eclipses occur about every year and a half but they are only seen in
22 the same location on earth about every 300 years. In contrast, lunar eclipses happen at night, so
the effects of the eclipse are not as noticeable as solar eclipses. The Earth’s atmosphere acts like
a prism, which leaks light into the shadow of the earth; producing the rusty red color of lunar
eclipses. Due to size and distance, the eclipse window for solar eclipses is larger, thus producing
more solar than lunar eclipses. Although more frequent, solar eclipses can only be seen in areas
of the earth where the sun’s shadow passes. Lunar eclipses last for several hours and can be
observed by anyone living where the sky is clear and the moon is above the horizon. This gives
an observer a 50% chance of seeing a lunar eclipse, but only an 8% chance of observing a solar
eclipse during their life (Lounsbury 1978:798).
Willson (1974:11) neglects the study eclipses of the moon in the belief that they are
unimportant to the Maya, but he gives no reason for this declaration (Guthe 1932:272; Spinden
1928a:144). “Contemporary Quiches regard the full moon as a nocturnal equivalent of the Sun”
(Tedlock, B. 1992:31; Tedlock, D. 1996:43).
The Sun’s rays shine out into space, illuminating one side of an object in space and creating a
long shadow behind that object. On the earth this process creates day and night; on the moon it
creates the phases of the moon, as seen on earth. The shadow is measured from the center of the
shadow’s vertex (called centrality.) The shadow has two parts; a dark inner region called the umbra and a less dark outer region (called the penumbra). In solar eclipses, each time the moon touches the boundary of a shaded area it is said to bite the sun. If the moon fits into each shaded segment, the eclipse will be total; if not, then partial. This creates the two types of eclipses; the partial and total eclipses. Some astronomers divide total and partial eclipses into four types; total
umbra and total penumbra, and partial umbra and partial penumbra. A fifth type of eclipse in
23 solar eclipses is the annular eclipse. This eclipse is caused by the vertex of the sun’s shadow falling before the Earth, due to the larger distance of the sun from the earth. The shadow does not completely cover the solar disc, creating an outer ring. A sixth type of eclipse, the hybrid, is total or annular depending on the time of day of the eclipse. In hybrid eclipses, the eclipses are total around midday and annular in the early morning and late afternoon due to the curvature of the earth’s surface.
There are two other circumstances that control eclipses, but that are not classifications of eclipses. One is the borderline eclipse, which occurs at the border between zones of totality and partiality. A zone of partiality is at each artic pole with a zone of totality around the equator.
Eclipses that should be partial are total in the partial zone, and partial in the total zone. Another
circumstance is the grazing eclipse. These eclipses are the polar eclipses that occur (or fail to
occur) due to the flattened nature of the Earth’s poles. Eclipses at the poles are partials. In the
artic region the partial eclipses could be seen as total but this eclipse is seen from the opposite
side of the world. The line of centrality does not touch the earth, but the shadow does. Can these
eclipses really be defined as an eclipse? This is why astronomers refer to these types of eclipses
as non-central and central eclipses, where the shadow’s center line touches the Earth (Meeus
1997:43-44).
When discussing eclipses by year, it is important to remember that not all eclipses are visible
from any given point on the Earth. The minimum number of eclipses per year is four; two solar
and two lunar. The maximum is seven; five solar and two lunar, four solar and three lunar, three
solar and four lunar or two solar and five lunar eclipses (Meeus 1997:45-49). One point to be
realized is that one year, the time from January 1st to December 31st, is just a convention of
24 society. January 1st has no astronomical meaning. Due to the leap year addition of one day, the
time changes; therefore, a 365 day cycle may have more than five eclipses compared to a period
from January 1st to December 31st. In one year no more than two solar eclipses can be total, but three lunar eclipses can. Four consecutive lunar eclipses may all be total ones, called Tetrad
(Meeus 1979: xiii). This is why a total lunar eclipse is said to either precede or follow another total eclipse. Two lunar eclipses can occur at one lunation, but both are almost always penumbral. Two successive new moons can be eclipses but most are partial and visible in opposite hemispheres (northern and southern). Clusters of eclipses can be generated during a period of three centuries (293 years) followed by three centuries of few or none. This has been shown by Schiaparelli to be a period of 586 years (Meeus 1979:100).
25 CHAPTER TWO: DISCUSSION
Calendars and Maya Math
The idea of accuracy in Maya data is complicated by the fact that the Maya utilize a different numbering system than Western societies. The Maya use the vigesimal system with a base of twenty instead of ten. The Maya system contains no decimals. The Maya were aware of parts of a whole, but their main concern was with completeness. The Maya did not possess complex mathematics. They were counters and were very good at it. The Maya used a unique form of the vigesimal writing called the bar-dot system. A dot represented one and was used in the numbers
1-4 and 6-9. A bar was used to represent five. A shell was used to represent a zero. The numbers were positional based on the powers of twenty. “They count by fives up to twenty, by twenty to a hundred and by hundreds to four hundred” (Landa 1978:40). This statement blends Western and
Old World ideas; one hundred is decimal, not vigesimal. The blending of ideas is one of the pitfalls of research. It occurs again in eclipse research with the use of the Western idea of the
Saros to explain the Eclipse Table. The math used for calendars is called a modified vigesimal
system, because the tun position has eighteen uinals, instead of twenty, which gives a 360 day
count. For a detailed understanding of the Maya calendar and mathematics, An Introduction to the Study of the Maya Hieroglyphs by Sylvanus G. Morley (1915) or Maya Hieroglyphic Writing by J. Eric Thompson (1975) should be consulted.
Calendars, like eclipses, come in lunar and solar varieties. Time periods have been developed to measure the cyclic motion of the heavens. The motions are variable; there are no uniform processes in nature. The measure of time is simply the aggregate or mean of certain observed motions expressed in arbitrary terms (McGee 1892:331). These problems have caused the need
26 for many different calendars from the Numan calendar, corrected by Julius Caesar, to
aculmination in our present day Gregorian calendar. This calendar did not escape criticism of its
inaccuracy. The Gregorian calendar affords a highly satisfactory compromise between essential
accuracy and much desired simplicity (Moyer 1982:152). The calendar eliminated ten days to
keep March 21 as the vernal equinox at the same date as the First Council of Nicea in 325. The
Church was also interested in having the Paschal full moon fall at Easter. The Paschal full moon
created more criticism than the Gregorian calendar did, but the calendar remains viable after
many centuries.
A second calendar, called the Julian calendar, was developed about the same time as the
Gregorian calendar by Julius Scalinger. Backers of the Julian calendar felt that it was more
astronomical than the Gregorian calendar thus more accurate. The Julian calendar uses three
cycles to calculate the date. Those cycles are the twenty-eight year solar cycle, the nineteen year
lunar cycle, and the fifteen year civil cycle of the Romans. This creates a cycle of 7980 years
(twenty eight times nineteen times fifteen). The calendar starts on the date B.C January 1, 4713.
The Maya also possessed two calendars. There is a 260-day religious calendar made up of thirteen numbers (Trecena) and twenty day names (Vientena). This Sacred Calendar is also
called the Tzolkin or “Count of Days.” The names of the tzolkin are Imix, Ik, Akbal, Kan,
Chicchan, Cimi, Manik, Lamat, Muluc Oc, Chuen, Eb, Ben, Ix, Men, Cib, Cuban, Eznab, Cauac
and Ahau. This calendar always ends on a day named “Ahau.”
The Maya also use a 365-day calendar called the Haab. The haab is made up of twenty
numbers (0-19) attached to eighteen month names, giving a 360-day solar year called a Tun. A
nineteenth month of five days (0-4) called Uayeb makes up the 365-day tropical calendar. The
27 Maya also call the Uayeb, the xma kaba kin, or the days without name. The translation “days not counted” has caused much controversy in the theories of Maya dates. These days need to be counted to keep the Long Count going. This debate caused some researchers to question whether the Maya used the “haab” or the “tun” (Long 1925:575).
The Maya combined the tzolkin and haab to create the Calendar Round. The Calendar Round repeats itself every fifty-two years (365 times 52 equals 18,980 days). This equates to seventy- three revolutions of the tzolkin (260 times 73 equals 18,980). Since the Calendar Round repeats every fifty-two years, the Maya needed a way to identify which Calendar Round was referred to.
This was accomplished in two ways. One method, starting around the tenth century, was the
Mexican Katun Ahau method, sometimes referred to as the Short Count. This method identified the Calendar Round by the ending tzolkin date. If the date was 3 Ahau, the Calendar Round was said to be a Katun 3 Ahau. This date repeats itself every 260 tuns or about 256 years.
The other uniquely Maya method was the creation of the Maya Long Count or Initial Series date. From right to left there are five columns of numbers. The first position is the count of days or Kins. The second column to the left is the Uinals, which are twenty kins. The third column is the Tuns, which are eighteen uinals of twenty days, giving the 360-day solar calendar. The fourth is the Katun, which equals twenty tuns. The fifth position is the Baktun, which is twenty katuns.
The baktuns are also called cycles. In the Long Count system the base date of the Dresden
Eclipse Table is 9.16.4.10.8 12 Lamat 1 Muan.
The Maya Date is a count of days from a starting point of 4 Ahau 8 Cumhu. The Maya did possess other calendars with different starting dates. Maya mathematics also possesses a system to add and subtract dates known as Distance Numbers. These dates are written in reverse order to
28 distinguish them from Initial Series Dates. They could be added to or subtracted from the starting date to create the new starting date. The Maya scribes would make charts of multiples of numbers to calculate dates. Another series of numbers, also in reverse order, is the
Supplementary Series.
J. T. Goodman was the first to call attention to the glyphs that contained lunar information, but it is Charles P. Bowditch who gave the glyphs the name, “the Supplementary Series” (Andrews
1951; Morley 1940, 1977). This information is sometimes placed before and sometimes after the
Calendar Round date. The majority of times this data is placed between the tzolkin and haab portion of the calendar round. Not all Long Count Dates contained lunar information. The proximity to the Initial Series Date made it appear to supplement the Initial date. The glyphs are lettered A through G in reverse order. Later researchers found new information that they identified as X, Y and Z. The Glyphs F through A are called the Lunar Series and provide information on the moons age. Linden (1986:123) lists the sequence of the series as G, F, Z, Y,
E, D, C, X, B, A.
For this study only Glyphs A and C will be used. Glyph A represents either 29 or 30 days, signifying the length of the month. Glyph C is never higher than six, indicating the number of lunations. A zero indicates one or the current lunation.
The Ahau Equation was first suggested by the astronomer Willson (1974:17). The Ahau
Equation is a quantity of days that have to be added to the Maya date to get the Julian date; JD
(Julian Date) = MD (Maya Date) + Ahau Equation. Satterthwaite (1962:253) called the Ahau
Equation the Correlation Constant. This equation backs the Maya date to the starting point of the
29 Julian Count. The Long Count date of the Eclipse Table is 9.16.4.10.8 12 Lamat 1 Muan. The
above date is 9 Baktun, 16 Katun, 4 Tuns, 10 Uinals and 8 Kins.
9 Baktuns are 9 X 144,000 days = 1,296,000 16 Katuns are 16 X 7200 = 115,200 4 Tuns are 4 X 360 days, 1440 days 10 Uinals are 10 X 8 days = 180 8 Kins are 8 X 1 day = 8 The Maya date is equal to 1,412,848 days.
The JD (Julian date) = MD (Maya Date) + constant (584285). This is 1,412,848 plus 584,285
which equals 1,997,133 days or Nov 12, 755, the difference is the Ahau equation of 584285
days. This is the constant used in the Goodman-Martinez-Thompson (GMT) correlation.
Different constants move the date forward and back in time by changing the Julian Date.
Numerous constants have been tried for correlating the Maya and Julian Dates with little
success. The GMT constant (584285) is the most accepted. J. E. S. Thompson also came up with
a modification of the GMT, called the Thompson modified (584283). This constant is only one of many in the GMT Family of constants (584281-584288). The following researchers have suggested constants that place the eclipse dates in the fifth Century: Willson (438906); Smiley
(482699); Makemson (489138); and; Spinden (489384).
The Maya calendar did not add leap years. Several theories have been proposed as to how the
Maya handled the leap year problem. Without adding leap years, the days drop back one day every four years and create a Vague Year.
30 Eclipse Data
To compare the eclipse data, Excel worksheets have been prepared for each of the three canons
Oppolzer (1962), Liu and Fiala (1992) and Meeus (1966, 1979) for both lunar eclipses
(Appendix A – C) and solar eclipses (Appendix D, E). Liu and Fiala’s Canon does not have a
solar eclipse. Meeus’ Solar Canon only extends back to the year 1898. These Canons utilize
different methods for calculating eclipse occurrences. Oppolzer uses the mean-value method. Liu
and Fiala use the 1/50th Rule, which adds 1/50th the radius of the Earth to the eclipse computation. Meeus uses the French Method, which compensates for perceived errors in the
1/50th rule. Small penumbral eclipses, found by the 1/50th rule for the enlargement of the penumbra, do, in fact, not exist (Meeus 1979: x). Besides the different methods of computation,
the cannons also use different time measurements. Oppolzer’s Canon uses Universal Time,
whereas Liu and Fiala and Meeus use Ephemeris Time (Meeus, Grosjean and Vandreleen
1966:1; Sadler 1966:1121). Ephemeris time is an astronomical measurement of time not
dependent on movements of the sun. The difference between the two time periods is no more than six hours and is listed in the ephemeris as ∆T. Fredrick Martin (1993:74-83) has studied solar/lunar eclipse pairs. His chart uses U.S. Naval Observatory Ephemerides for the years 1970-
1992. This data appears compatible with the other Canons in this study (Martin 1993:86-92).
Debate has arisen about whether the Dresden Table is solar or lunar in nature. Willson
(1974:11) was one of the first to say that the Eclipse Table was solar. Most researchers since have followed his lead. Martinez, Pogo, and Spinden thought the Table to be lunar.
Pogo (1937:159) made the comment that 33 years is sufficient to create an eclipse table from observed lunar eclipses. Even the solar proponents agree that the Table must have been created
31 from lunar eclipse data. Visible solar eclipses are extremely rare and would require an extremely long period of time to collect enough data to construct a Table. This question will not be fully explored until observed eclipses are isolated for the general eclipse data. Nuclear physicist
Robert Smither has studied this question and concluded it could have been done in a single lifetime (Campbell 1992:47). Justeson (1986:84) states that two or three decades of observation and recording are necessary and sufficient to produce a model for the timing of eclipses so complete that a system for anticipating all eclipse-possible dates would be revealed. This debate about solar and lunar eclipses is the reason that both solar and lunar eclipses are analyzed.
These worksheets contain the Gregorian and Julian Dates of modern eclipses. The Gregorian
Dates of the canons are converted into Maya Dates utilizing the calculator http://www.pauahtun.org/Calendar/tools.html. This site uses the Goodman-Martinez-Thompson
(GMT) constant of 584285 (an explanation of Maya Dates is given in the Calendars Section of
Chapter 2).
A column in the worksheets calculates the difference in days between Julian Dates. In this column, the numbers 29, 30, 148, 176, 177 and 178 appear repeatedly. All of these dates, except for the twenty-nine and thirty days, are major time periods of the Eclipse Table. Lounsbury
(1978:791; Satterthwaite 1947:147) mentions the instances of two solar eclipses one month apart. The twenty-nine and thirty days are not readily apparent in the Table; however, the eclipses are there and will be explained later. Another column in the worksheets calculates the sum of the differences. These sums are similar to the totals in Schram’s Table. (Schram’s Table is the repeated sums of 29.5.) This method of creating sums is also the method that Meinhausen
(1913) uses; however his totals are of 177 days. Meinhausen’s totals are used by other
32 researchers to identify eclipse periods. Except for the Long Count Dates, these worksheets are
similar to Guthe’s Table II (1921:6-7), which is used by all researchers of Maya eclipses.
The three charts of modern eclipse data are quite similar, with only slight variations due to the
differing methods of computing eclipse occurrences. The solar charts of Meeus and Oppolzer are
extremely similar, despite the decimal accuracy of Meeus. There is only one date that is different
between the charts. That date is September 1, 1997 in Meeus, and September 2, 1997 in
Oppolzer. The lunar charts have the most variance. Oppolzer’s chart contains forty-seven instead
of seventy-five eclipses. Oppolzer’s lunar charts have gaps where the non-visible eclipses are
located. Eclipses that are less than .07 in magnitude are not visible to the human eye. Magnitude
is a mathematical designation and cannot be detected by the naked-eye. These gaps are not a
problem when searching for observed eclipses but may be statistically valuable in other studies
of eclipses. Van den Berg (1955:20, 169) states that “Oppolzer’s Canon at once proves its
validity.” He even creates a version of his Eclipse Panorama using Oppolzer’s data. “Oppolzer’s monumental work remains excellent for historical research” (Meeus 1979: xi).
There are four dates in Liu and Fiala that are different than Meeus. Those dates are December
10, 1973, December 20, 1983, April 4, 1996, and November 9, 2003. These differences are caused by the increases in the Earth’s shadow due to the 1/50th Rule. This study will utilize
Meeus’ Canon for comparison with Maya data.
The Maya Tzolkin dates from the conversions are charted on a wheel similar to one Teeple
uses in his classic work, Maya Astronomy (1930). Teeple (1930:89, 1930a:138) was the first to demonstrate the link between the three Eclipse Seasons and the Double Tzolkin. Spinden and
Ludendorf investigated this phenomenon, but did not complete the whole table, focusing instead
33 on the date 1 Imix. Three times the mean value of 173.31 days is 519.93 days, a close
approximation to the Double Tzolkin of 520 days and the three eclipse seasons.
Figure 5 Teeple Arc after Teeple (1930:89)
Teeple’s chart lists the dates from the Eclipse Table. These are not dates of actual eclipses but rather date when eclipses could occur. The dates cluster around three groups which Teeple calls arcs. Lounsbury refers to them as eclipse seasons and Bricker refers to them as danger windows
(Bricker and Bricker 1983:7). These clusters produce fail-safe areas where eclipses would not
occur. Not all the eclipses predicted would be visible in the Maya area, thus producing false- alarms. The false-alarms cause the debate between the predictions versus the warning aspects of the Table (Bricker and Bricker 1983:7-8).
34 Every other dangerous period in a single tzolkin is passed over, thus creating a Double Tzolkin
(Satterthwaite 1947:144-145). Teeple believed the eclipses distributed themselves around the mean value of the seasons (the inner spokes in figure 5.). One of his papers mentions 166, 339, or 512 as the dates of the mean-value (Teeple 1930a:138). His famous paper on Maya astronomy places the dates one day later at 167 (11 Manik), 340 (2 Ahau), and 514 (7 Ix) (Teeple 1925:546-
548, 1928:547, 1930:90-91). Thompson (1975:234) provides the days numbers and dates of 168
(12 Lamat); 341 (3 Imix), and 514 (7 Ix), which would return to 12 Lamat after the next eclipse half-year. Theses dates of nodes are nearly stationary. These nodes recede with each pass through the Table. A regression of 1.61 days occurs in the Table (Teeple 1930:90, 1930a:138).
The eclipses would occur eighteen days on either side of the mean-value. Lunar eclipse would be within a narrower limit of thirteen days (Teeple 1925:547). Bricker and Bricker (1983:6) believe the first half of the eclipse arcs contain null predictions. The true predictions are in the last half of the arcs.
Another Excel chart of the Double Tzolkin was used to sort the dates created by the conversion of modern eclipse data. Entering dates into this chart works so well that it is possible to identify errors in the conversions. The data has been rechecked on several occasions to insure its correctness. While placing data in the chart, sequentially, the distribution of eclipses within the three groups of seasons became apparent. (This process can be observed by following the eclipse number (Ecl) in Meeus’ lunar season chart in Appendix G.) This process works equally well for either solar or lunar eclipses. The only difference is the dates involved. By merging the two season charts of lunar and solar eclipses (Appendix J), the same grouping of dates emerges. This
35 demonstrates that the three dates in the Eclipse Table could be used for either lunar or solar eclipses.
The first trial of the Excel chart contained thirty-three years of eclipses. This is slightly larger than the thirty-two and three-quarters years of the Maya Eclipse Table. The additional eclipses have no effect on the three eclipse periods. The fewer number of eclipses in the Oppolzer Canon also have no effect on these periods. The only differences in the seasons are the number of eclipses in each group. A chart was also made of one half the previous Excel chart (appendix A).
This was done to simulate the effects of observed eclipses. The basic structure of the three seasons remains fairly intact. There are noticeable changes in the outer boundaries of the seasons and gaps where the missing eclipses should have been. These gaps would have been present in the development of the Chaldean Table from visible eclipses (Pannekok 1961:60-62).
The copy of the chart is modified to the 32 and ¾ years for comparison against Teeple’s work and the Dresden Eclipse Table. A chart was also made of the dates in the Dresden Eclipse Table from Table II of Guthe (1978:6-7) to retest Teeple’s original work. These dates are found Table
8 of Maya Astronomy (Teeple 1930:87-88).
36
Figure 6 Meeus Arc following Teeple (1930:89)
The eclipses do distribute themselves in the seasons: not randomly, but sequentially by the
177/78 and 148 values plus the accumulated fractions of the eclipse period. The first feature that becomes apparent is that the 148-eclipses are distributed at the beginning of the season. This is the area of the “fictive” or “pre-nodal” eclipses. The 29 and 30 eclipses are distributed at the end of the season, in the area of post-nodal eclipses.
Some of the 148-day events are followed by an eclipse one lunation later. This is at perigee, the point in the earth’s orbit nearest the sun. The 29 and 30 eclipses are not readily apparent in the
Dresden Table. Some are hidden in the 177/178-day eclipse periods. There are only about six
37 eclipses of this type in the 33-year period. It is a problem of correlation studies that the
information that could specifically identify time periods is not available in the extant record.
Some of these early eclipses are not 148-day eclipses and eclipses at the end of the season are not
29 and 30 days. Some from time to time naturally distribute themselves at the beginning or end
of the season. Some of these eclipses do have a secondary relationship to the 148-day eclipses.
They either proceed or follow the 148-day eclipses.
Eclipse Periods
Sadler (1966:1119) stated that there are two methods to calculate eclipses. One method is to precisely predict eclipse occurrences by using the theories of motions for the sun and moon. The other is to use the mean periods derived from past observations. The former method of celestial
mechanics may well be needed to finally clarify the Eclipse Table, but further study of the mean
periods will aid the understanding of the how the Maya astronomers created the Table without an
understanding of celestial mechanics.
According to Liu and Fiala (1992:6-7) and Sadler (1966:1119-1120), there are three
requirements for an eclipse to occur; the moon must be in the same phase; the moon must be in
the same place with respect to the node, and the sun and moon must be at the same relative
distance. The distance is controlled by the orbit of the earth around the sun. The rotation of the
earth controls the time of day and the location of the eclipse.
The three periods that satisfy these requirements for eclipses are called the synodic month,
draconic month, and eclipse year. Another period involved in eclipses is the anomalistic month
of 27.55455 days. This is the period required for the moon to move from perigee to perigee, the
38 nearest point of the earth’s orbit around the sun. It is this cycle that determines if the central eclipse will be a total or annular eclipse. (In an annular eclipse the shadow does not cover the entire sun).
The smallest period for eclipses is the month or lunation. The sidereal cycle is the time it takes for the moon to revolve around the earth relative to the stars. The sidereal month is 27.321661 days. Due to the fractional part of the moon’s orbit, the moon returns to the same place but at a different time of day. In three sidereal cycles the moon returns to the same constellation at the same time of day. The sidereal month does not meet the requirement of the same phase, but the synodic month does.
The synodic month is the period of the moon’s revolution relative to the same phase of the moon. The synodic month is 29.53058877315 days (Spinden 1928a:141). It is slightly larger than the sidereal month. To the Maya, the Young Moon Goddess and an Old Moon Goddess represented the waxing and waning moon (Thompson 1975:231). Eclipses can only occur at new moon for solar and at full moon for lunar. A big debate has lingered over which phase of the moon starts the Maya month (Guthe 1932:272). A month could be counted from full moon to full moon or from new moon to new moon. The new moon can create problems because some societies use the last visible crescent moon; some use the astronomer’s new moon at conjunction, while other societies use the first visible crescent to start a lunar cycle. This creates about a three- day spread for the lunar count. Barbra Tedlock (1992:30) has stated that the full moon is used by
Maya midwives because of the comparative ease of observation. Teeple (1930a:137) and
Spinden (1930:63-66) debated whether the Maya used the new or full moon. Landa (1978:59) stated that “the Maya counted from the rising of new moon.” Teeple (1928:396, 1930:46, 49)
39 followed Landa’s lead. The Maya keep track of the moon’s age with glyphs D and E (Weitzel
1935:14). D and E show the age of the moon counted from the last new moon (Roys 1933:411).
Most scholars do agree that the Maya used the new moon for astronomy, but there is still much debate about whether they use disappearance, conjunction, or first crescent for new moon for the beginning of the cycle. Satterthwaite (1949:230, 1962:254) called the conjunction, “the Dark
Days” or the “Dark Phase.” This spread also creates debate about whether Maya astronomy is based on observation or computation (Guthe 1932:272). Both observation and computation have their own inherent problems. However, both may not be mutually exclusive.
Teeple’s (1925a:111-114) Table 1 of the Supplementary Series of moon ages shows complete agreement. Roys’ (1969:165, 169) Table 2 charts moon ages by five tun intervals. Guthe
(1932:276-277) believed that the Supplementary Series was a computed record instead of one based on observation. Weitzel (1935: 23) stated that the moon glyphs did not constitute an observational record of new moons. Lounsbury (1978:774) “concluded that at many Maya sites that moon age was reckoned from the first visibility of new crescent.” Shove (1984a:21-22) lists deviations between the recorded and predicted moon ages. Satterthwaite (1951:142, 143, 152) noted that some sites have double dates for moon ages. There is also a seven-day range of moon ages that is excessive whether observed or calculated. He assumed that incorrect ages were sometimes recorded for esoteric reasons (Satterthwaite 1951:142). Roys believed that certain days were taboo as new moons and that an alternate had to be found. Teeple believed that the errors are records of observation not of computation (Gibbs 1977:31).
The second requirement for eclipse periods is the node or the place where the moon crosses the ecliptic. The ecliptic is the plane where the earth orbits the sun. If the moon were in the same
40 plane as the earth and sun, there would be a solar eclipse at new moon (conjunction) and a lunar
eclipse at full moon (opposition) every month. The moon actually orbits the earth at an angle of
5° 8´ and only intersects the plane of the ecliptic at two points: one node for lunar eclipses and
one for solar eclipses.
The draconic month is the period the moon takes to return to the same position relative to the nodes of its orbit. Draconic refers to the dragon on pages 56 and 57, which eats the sun. The draconic month is 27.212220 days: slightly less than the sidereal month due to the westerly drift
of the node. The nodes are not static. This drift is one of the reasons for the 148-day period of
eclipses. The nodes are classified by the orbit of the moon as it passes the node. If the moon is
going up in the orbit as it crosses the ecliptic, it is said to be an ascending node; if going down
the node is descending. Eclipses are measured from the ascending node. The shifting nodes
create problems in identifying which node is active. There is a solar node and a lunar node that
controls which type of eclipse occurs. The Saros period is such that the node does not shift. At a
half-Saros, the node will shift to the lunar node from a solar eclipse. In some other periods the
shift of nodes does not always change the eclipse from lunar to solar. The change in nodes is
between the Northern and Southern hemispheres.
It is only at or near these nodes that the sun, moon, and earth are aligned so their shadows
create eclipses. The nearness is called an eclipse window and is measured in angular distance.
Eclipses occur at an angle of 11° to 18°. From 11° to 14° the eclipses are total. Larger than 14°,
the eclipses are partial. Because of the size and distances involved, the solar eclipse window is slightly larger than the lunar window. This means there is a statistical advantage for solar
eclipses over lunar. One would think lunar eclipses would be more prevalent, since the lunar
41 eclipse is visible to anyone when the moon is above the horizon. The solar eclipse is only visible to the area of the earth that is covered by the Moon’s shadow. Due to the seasons when eclipses occur, there is also a slight statistical advantage in the Northern Hemisphere.
The third requirement, which is distance, is controlled by the yearly revolution of the earth around the sun. The eclipse year is 354 days, which is slightly shorter than a tropical year of 365 days. This allows an occasional three eclipses in one tropical year. Although eclipses can occur after one lunation, the main periods for eclipses is the semester or eclipse half-year (Berlin
1943:156). The eclipse half-year could, as the ancient Chaldean astronomers pointed out, function as a means of eclipse warning (Aveni 1981:80; Pannekoek 1961:57).
The semester consists of six lunations for a total of 177 or 178 days (8.17 or 8.18 vigesimal).
The semester also has an occasional period of five lunations or 148 days (7.8 vigesimal). The
148-day period was noted by Bowditch (1910:213) on page 53a of the Table (Pannekoek
1961:60). There must be one five-month season for each 6.623 six-month seasons (MacPherson
1987:444). Where to place the 178 and 148-days has been a problem for researchers. The 148- day semester has been viewed as an adjustment and not as a part of the eclipse cycle. The mean- value method has ignored this period. These periods are at the end of the seasons and are considered fictive or potential eclipses. The mean-value would work on a static node system, however; in a static system most 148-day semesters would not exist. The semester is six months of alternating twenty-nine and thirty days. Table 2 demonstrates the semester alternations. The twenty-nine and thirty days could be in any order. There is no right way or wrong way, but there usually is a fixed way. The semester is set up this way because of the Supplementary Series glyphs. If glyph C (1-6) is odd then glyph A (29 or 30) is even. If Glyph C is even then glyph A
42 is odd. An occasional extra day is added to the last position of the semester to create two periods of 30 days. This gives an occasional Glyph C and Glyph A, which are both even. This is displayed on line 5 of Table 2.
Table 2 Lunar Semesters after Guthe (1932:275)
1 2 3 4 5 6 1 30 29 30 29 30 29 177 2 30 29 30 29 30 29 177 3 30 29 30 29 30 29 177 4 30 29 30 29 30 29 177 5 30 29 30 29 30 30 178 6 30 29 30 29 30 148
Glyph C = 1- 6 Glyph A = 29 or 30
Linden (1986:125) suggested an eighteen month calendar was used with Glyph X, which has a strong association with Glyph C. The Glyph X cycle is keyed directly to the moon number
(Justeson 1986:91). This relationship to the moon should be studied further.
The semesters can be added together to derive other periods of eclipse occurrences. Since the
Maya do not have decimals, they needed to find an integral number of moons in order to calculate eclipses (Teeple 1930:65).
Meinhausen (1913) was the German astronomer who proved that the Dresden Codex Table contained eclipse cycles. His data used the dates A.D. 1775 to A.D. 1808. He calculated the difference between dates and the sum of those differences. These periods (sums) have become the standard of eclipse periodicity for other researchers of Maya eclipses. He also noted a sum of
502 days (1.7.2. vigesimal). This sum is also prominent in the Oppolzer canon. The 502 days is the sum of 177, 177 and 148. The 502-day period is prominent on page 53 of the Dresden Codex
43 (Bowditch 1910:213). The 502-day cycle is also the amount of time needed for the eclipses to travel though the polar region. There is also a 325-day period in Oppolzer, which is 177 + 148 days. These are the hidden 148-day eclipses in Oppolzer’s canon. There are other periods of time when eclipses can occur. Most eclipse cycles start without names. They are identified by the lunations of the eclipse cycle or an approximation of the years in the cycle (Table 3). It should be remembered that all eclipse periods have distinct advantages and disadvantages. The disadvantages do not necessarily make these periods incorrect, but rather inappropriate for the situation.
Because of its simplicity and accuracy, the Saros has become the preeminent eclipse reckoning period. The Saros is used because this is the cycle that not only answers the when question of eclipses but also informs us as to where an eclipse will occur. If an eclipse occurs, another will occur 6585 1/3 days later, 120° to the west. The Saros cycle is 223 lunations (29.530588 times
223 equals 6585.321124). This is a period of 18 years 11 and 1/3 days. This third of a day is what causes the next occurrence of the eclipse to be about 120° to the west. It is derived from the
Babylonians, but Chinese astronomers knew about it much earlier. The Saros is also involved in the Numan cycle of the ancient Roman lunar calendar (Magini 2001:73). It takes three Saros cycles to return to the same longitude. The Babylonians also knew the importance of the triple or
Mega-Saros of 54 years and one month.
The Saros is made up of six lunations. Some periods can be five lunations (Pannekok 1961:57-
60). Two consecutive new moons can each give rise to partial eclipses called a Nova (Van Den
Berg 1955:10). Babylonian science developed the Saros-Canon by noticing eclipses in
44 succession (Pannekok 1961:60-62). Researchers believe the Maya astronomers did the same with
their Table.
Saros eclipses are given numbers to denote families or series of eclipses. Families are eclipses
separated by one Saros period. There are thirty-eight different families active at any given time.
There can be 69 to 86 eclipses in each family. Odd number eclipses are at ascending nodes and
even number eclipses are at descending nodes. It is important not to confuse Saros families and
the Saros period. Families of Saros eclipses are born, can live for 1226 to 1532 years, and then
die. They disappear and are replaced by a new family. Families are separated by a 29-year
period. The Saros period is such that it does not produce a node shift as in other periods. The
node shift causes the eclipses to jump from the northern to southern hemisphere. A new Saros
series will be born on July 1, 2011 (Meeus 1997:49-51). It will contain sixty-nine eclipses. This
is the same number of eclipses as in the Eclipse Table. The 38th eclipse in the Table is the Saros.
It is the 41st in Appendix A. The 61st eclipse is the length of the Schram Table or 10,571 days
(Makemson 1943:190). Researchers were glad to find the Saros period in the Table. The other periods are also there, but no one actually looked for them.
In the first section of the Eclipse Table (page 52b, column D) is the number 18.5.5 vigesimal.
This is 6585 days in length: the same period as the Saros (Milbrath 1999:114). The Saros is not a popular system with the Maya because the Saros is not divisible by 260. The Table can only express one Saros because the Table is only 33 years in length and two Saros periods are 36 years. The Numan Cycle has been compared to the Dresden Eclipse Table in Table 11 (Magini
2001:106). There is a period of one half of the Saros cycle. At this point there is a shift in nodes,
45 from solar to lunar eclipses. This is how one creates a lunar eclipse table from solar eclipse data.
In like manner, the Maya could make a solar eclipse table from a lunar table.
Stockwell (1901:185) lists an unnamed cycle of seven years or eighty-eight lunations for 2598
days. Van Den Berg (1955:28) calls this period the anonymous. The seven-year cycle is good for
predicting eclipses over short periods of time, but loses accuracy after about 250 years. The
nodes change so that 14 ½ years are required for eclipses in the same area. Robert Smither
(1986:104) has studied the 88-month cycle to predict periods of minimal lunar activity indicating solar eclipses. Campbell (1992:53) has also studied the relationship between lunar activity and solar eclipses. Low lunar activity is believed to be where the five-lunation periods are located.
The 88-lunations period is made up of 41 and 47 lunations: a missing part of the Saros eclipse period (Pannekoek 1961:58; Smither 1986:99-111). The Table is forty-one lunations short of two
Saros periods (Satterthwaite 1978:799). It is not known if the Maya were aware of this 88- lunation eclipse period, but these are the dates in the Season Tables (Appendix G, H, and I) which have duplicate occurrences.
After 19 years and 11 days the moon returns to the same position in the sky. This cycle is also referred to as the Metonic cycle or the Meton. It is named for the Greek philosopher Meton, but all societies that have lunar calendars were aware of this cycle. The Chinese called it the Tchang
(Mcgee 1892:329). The Metonic cycle is 235 lunations or 6,940 (19-5-0 vigesimal) days
(Spinden 1930:49). The Meton is an easy way of predicting phases of the moon, but it does not take into account the drift of the nodal line. The five- lunation period creates some dates that should be eclipse dates, but the actual eclipse has occurred one lunation earlier. Not all full moons are eclipse full moons; since the Meton only predicts 9 out of 10 eclipses, some have
46 called it the so-called eclipse period (Carlson 1984:236). The Meton is the basis of the Golden
Number of the Greeks. The Golden Number is one more than the remainder of the year divided by nineteen (Pannekoek 1961:218). The Meton is the nineteen-year cycle of the Julian calendar.
The Maya may also have known about the Meton, but Lounsbury (1978:804) states “the Metonic cycle appears to have attracted no particular attention.”
Teeple (1928:392-394, 1930:56-69, 1930a:137) researched the Lunar Series dates and noticed a Period of Uniformity in lunar data. Prior to Uniformity, sometime around the Maya date
9.12.15.0.0 - 9.13.0.0.0, there was a period when each area had its own system for moon numbering. During Uniformity, between 9.13.0.0.0 and 9.16.0.0.0, all areas used the same system for moon the numbering system. The system was called the “Palenque System.” The system uses an 81-moon count (6.11.12 equals 2392 days) to calculate moon numbering (Beyer
1935:66). This ratio of 81 moons to 2,392 days gives a mean lunar month of 25.530864 days
Lounsbury 1978:775). This system counted lunar half-years of six moons each
(Justeson1986:86-91; Satterthwaite 1959:200). Berlin (1943:156) has doubted some of Teeple’s finding about Glyph C and the 6 moon groupings because two dates did not match what should have been expected. The 81 lunations are one-fifth of the Eclipse Table of 405 lunations. This period is not an eclipse period, but the nine lunations may have a connection with Venus (Aveni
1986:315).
The Palenque System fell to a new system instituted at Copán. This system uses 149 moons
(12.4.0) equaling 4,400 days. The ratio of 149 moons to 4,400 days gives a mean lunar month of
29.530201 (Lounsbury 1978:775). This is the number some people use to claim the increased accuracy of the Maya calendar over the Gregorian calendar. At Copán, the Meton period shows
47 up in the monument dates. The Meton is one katun minus one tzolkin, which equal 6,940 days
(Spinden 1928:49, 1930:49). Stela A has the date 9.14.19.5.0 4 Ahau 18 Muan. This is 19.5.0
after the katun ending date of 9.14.0.0.0. This date is linked to the date 9.11.19.5.0 10 Ahau 13
Ceh on Stela I. This date is 3 Katuns earlier. The period 19.5.0 is the Meton (Chambers
1965:350-351; Milbrath 1999:106; Morley 1920:178, 222; and Teeple 1930:71). This period is
also associated with Stela C and H and with altar U (Spinden 1928a:145). Stela H has the date
9.14.19.5.0 4 Ahau 18 Muan (Baudez 1994:59).
On Copán’s Altar Q on the Maya date 9.16.12.5.17 6 Caban 10 Mol, a supposed astronomical
congress took place at Copán, on the Gregorian date July 2, 763 (Carlson 1977:101). The ruler is
interpreted as New-Sun-at-Horizon. On December 11, 847, there was a nearly total eclipse at sunrise (Schove 1982:251). Schove claimed confirmation of his method because of these dates and the “at Horizon” clause. The major problem of this theory concerning Altar Q is that the altar has no dates of astronomical significance (Baudez 1994:97).
The cycle of 135 lunations is the Tritos (Stockwell 1901:186). This is a period of 3,986 2/3 days. Willson (1974:15) calls this period the Maya Saroid (Spinden 1969:71; 1928a:145;
1930:52). The Maya appear to have used the Tritos (Smiley 1973:179). The Dresden Codex is made up of three sections of Tritos for a period 11,960 days or 405 lunations. This period is given the name Maya (Van Den Berg 1955:24).
Van Den Bergh (1955) studied a twenty-nine year period that is described by Stockwell
(1901:186) and Crommelin (1901:380), but did not have a name at that time. Oppolzer knew about this period, but did not use it. Van Den Berg calls this period the Inex because it was the
time that an eclipse enters or exits an eclipse zone (In-Exit). This period is twenty-nine years
48 minus twenty days or 358 lunations which equals 6,940 days. The period consists of no fewer
than seventy families co-exist at one time. Each family has 780 members. The lifetime of each
family is 22,600 years (780 times 29 years). The family member enters at one of the poles,
entering a zone of partiality. After 140 partial eclipses, the family enters a zone of centrality at
the tropical area of the earth. After 250 eclipses, the family reaches the equator. After 250 more
central eclipses, the family enters the other zone of partiality at the opposite pole. The eclipses
alternate between the north and south partial zones due to the alternation of ascending and
descending nodes (as opposed to the Saros, which does not change nodes). The Central eclipses
alternate between the northern and southern hemispheres. Since multiple families are active at
the same time, it is possible for one family that enters a zone later than another family to produce an eclipse sooner than another family. Also, there is a gap of time from when one family leaves a zone and another family enters that zone. The Inex has an advantage over the Saros over long periods, but has unfavorable results with the anomalistic month. All eclipse periods have strengths and weakness. That is why researchers should look at more periods than just the Saros.
It is not that the Inex should replace the Saros, but that both can be used to create new periods of eclipses.
One last fact about the Inex is the Inex law, which states that when a family enters a zone, it stays in that zone until it exits it. One situation that seems to disprove that law is the border eclipses. Although the family has not entered the other zone, circumstances can cause a partial eclipse in the central zone or total eclipse in a partial zone. This creates undulations or clusters in the number of eclipses. These clusters seem to follow a cycle of 358 years. Van Den Bergh
(1955) created a Panorama of eclipses, by organizing eclipses in rows and columns. The
49 columns are Tritos periods and the rows are Saros periods. The Inex is the diagonal, one Saros plus one Tritos (Meeus, Grosjean and Vandreleen 1966:41). With this panorama of eclipses Van
Den Bergh was able to develop a formula, T = mS + nI, to find the time intervals between eclipses. The Inex minus the Saros is 358-223 equals 135 lunations, or a Tritos. A Saros minus
Tritos (223 – 135) equals eighty-eight lunations called an Anonymous. With this formula, any eclipse period could be found since all are combinations of Inex and Saros periods.
Table 3 Eclipse Periods after Table 4 Van Den Berg (1955:28)
Name Lunations Time Formula 1 1 month 5 5 months Semester 6 6 month 5T-3S or 5I-8S Anonymous 88 7 years Saros - Tritos Tritos 135 11 years - 1 month Inex - Saros Saros 223 18 months + 11 days Meton 235 19 months Inex 358 29 years Saros + Tritos
Astronomer Charles Smiley was not impressed with George Van Den Bergh’s formula for eclipse periods. He believed that the statement amounted to nothing more than stating that a solar eclipse occurs at new moon (Smiley 1975a:133). Jean Meeus (1975) and Charles H. Smiley
(1975) debated each other in articles about the Saros–Inex eclipse periods. Smiley (1973, 1975, and 1975a) introduced two periods of solar observation coordinated with the Maya sacred calendar of 260 days. These periods he called the Thix and the Fox. The Thix is THirty-sIX times
260 days and equals 9360 days. The Fox is FOrty-siX times 260 and equals 11,960 days. These are the periods (11,960 and 9360) mentioned by Aveni in the Venus section of this thesis (Kelly
50 1977:59, 1992:88). This is why Smiley (1973:177-178) called the Venus Table a Solar Eclipse
Prediction Table. In Konnen and Meeus (1976:81), the authors state that the Maya Thix period
(317 lunations) can be expressed as 4I – 5S as well as 227I – 363S. The second equation
produces a shift in the node.
Smiley also describes a period of forty-one times the 260 days, equaling 10,660 days. He
called this period the Fone (pronounced phony) because it is not a solar eclipse interval (Smiley
1975:255; 1975a:134). The Thix minus the Fox is equal to ten tzolkin. This interval is 1.31 days
more than one subdivision of the Saros, or the 88 lunations. Subtracting 2600 days from any 12
Lamat date will locate another 12 Lamat date, 1 day prior to another new moon (Lounsbury
1992:204).
Simulation
The origins of the Eclipse Table point to a lunar calendar as the origin of the Table. Belmont
(1935:147) called it “a Lunar Eclipse Count.” Spinden (1930:42) called it the so-called Lunar
Calendar of the Maya. Miles (1949:275) found evidence of a survival of a lunar count of fifty- nine days in Chiapas Mexico. The lunar calendar is 354 days, or twice the length of the eclipse half-year of 177 days. Lunar calendars also have the fifty-nine day periods, as those in Table 2.
Lunar calendars are tied to the seasons rather than to eclipses. However, studying the eclipse half-years, a pattern of eclipses would appear.
Morley (1977:395) states that “the next point to be determined is the sequence of the twenty-nine and thirty-day lunar months as they actually occurred.” Many researchers have studied the twenty-nine and thirty day periods. Table VIII of Guthe (1978:19) lists the days in a thirtyfour
51 month period. Table XI of Guthe (1978:25) arranges the periods in the 177 and 148 day patterns.
Table I of Belmont (1934:145-146) arranges the Table by the sixty-nine eclipses. Beyer’s Table I
(1935:71) creates the eclipse half year periods without the 148-lunation periods. Beyer’s,
(1937:78-80) Table II does list the 148 period, but Tables III and IV only expresses the 177 and
178-day periods. Lounsbury’s (1978:800) study of the twenty-nine and thirty-day eclipses found that 11,960 days minus the 405 lunations times 29.5 are 12.5 days short of the total.
Satterthwaite’s (1947:71; 1948:61) study of the twenty-nine and thirty-day groupings is made up of sixty 6-moon groups (177 days) and nine 5-moon groups (148 days). Merrill (1946:40) creates a chart of the twenty-nine and thirty days, which contains no 148-day periods. The occasional double thirty-day grouping is a correction to the chart. This created a debate between
Satterthwaite (1948:61) and Merrill (1949:228) about half-day and full-day corrections. Do you add a half or subtract one half? Does the half day matter? A high degree of accuracy was never sought and not required for the Maya problem (Satterthwaite 1948:62).
Guthe (1932:274-275) did look into the Tritos, but later rejected it because of the problems with the 59-day cycle and the five lunations. Western astronomy is based on the Saros and the six lunations, not five.
52 Table 4 Guthe's Semesters after Guthe (1932:275)
1 2 3 4 5 6 30 29 30 29 30 29 177 30 29 30 29 30 29 177 30 29 30 29 30 30 178 30 29 30 29 30 29 177 30 29 30 29 30 30 178 30 29 30 29 30 30* 148 29 30 29 30 29 30 177 29 30 29 30 29 148
Glyph C = 1- 6 Glyph A = 29 or 30
Moon groups are arranged in six lunation sets, while five lunation groups upset the parallelism
(Beyer 1933:309). At the 148-day group, the relationship between the Glyph A and C reverses
from odd to even (line 7 of Table 4). The five lunations also upset the belief in the six lunations
of the Saros. There is a five-lunation period in the Saros called a Nova (Van Den Berg 1955:10).
Guthe (1932:276) stated “the manuscript table can not be applied to the record of the inscriptions
as it stands because of the existence of the five-month groups which were not in use during the
Period of Uniformity.”
The six lunation groupings are compatible with glyph X of the Supplementary Series. Linden
(1896:125) created an eighteen-month calendar based on three lunar semesters. Although not
associated with eclipses, further studies need to be done in relation to Glyph X and the moon.
In computing a series of lunations in a Tritos fashion, more than 11,960 days (11,981)
appeared. The 23rd eclipse was at 4,013, not at 3,986, days. This was done by using seven grouping of 177 days to one of 148. The problem is that the eclipses alternate between six and seven groups of the 177 days. The key to the Tritos structure is the five lunation groupings.
53 Properly adding the 148-groups gives a total slightly smaller than the required number. This is due to the missing 178-day corrections. This discrepancy was amajor question that early researchers faced; where to add the 178 and 148-groupings? This also provides a clue about one of the questions that has not been fully explained. Is the Eclipse Table computed or is it created by observation of eclipses? At some point, computations would have to be checked against actual observations, but computation and observation are not mutually exclusive.
Table 5 Tritos Simulation of Table 2
1 1 30 29 30 29 30 29 177 177 2 2 30 29 30 29 30 29 177 354 3 3 30 29 30 29 30 29 177 531 4 4 30 29 30 29 30 29 177 708 5 5 30 29 30 29 30 29 177 885 6 6 30 29 30 29 30 29 177 1062 7 7 30 29 30 29 30 29 177 1239 8 8 30 29 30 29 30 148 1387 9 9 30 29 30 29 30 29 177 1564 10 10 30 29 30 29 30 29 177 1741 11 11 30 29 30 29 30 29 177 1918 12 12 30 29 30 29 30 29 177 2095 13 13 30 29 30 29 30 29 177 2272 14 14 30 29 30 29 30 29 177 2449 15 15 30 29 30 29 30 29 177 2626 16 16 30 29 30 29 30 148 2774 17 17 30 29 30 29 30 29 177 2951 18 18 30 29 30 29 30 29 177 3128 19 19 30 29 30 29 30 29 177 3305 20 20 30 29 30 29 30 29 177 3482 21 21 30 29 30 29 30 29 177 3659 22 22 30 29 30 29 30 29 177 3836 23 23 30 29 30 29 30 148 3984
54 24 1 30 29 30 29 30 29 177 4161 25 2 30 29 30 29 30 29 177 4338 26 3 30 29 30 29 30 29 177 4515 27 4 30 29 30 29 30 29 177 4692 28 5 30 29 30 29 30 29 177 4869 29 6 30 29 30 29 30 29 177 5046 30 7 30 29 30 29 30 148 5194 31 8 30 29 30 29 30 29 177 5371 32 9 30 29 30 29 30 29 177 5548 33 10 30 29 30 29 30 29 177 5725 34 11 30 29 30 29 30 29 177 5902 35 12 30 29 30 29 30 29 177 6079 36 13 30 29 30 29 30 29 177 6256 37 14 30 29 30 29 30 29 177 6433 38 15 30 29 30 29 30 148 6581 39 16 30 29 30 29 30 29 177 6758 40 17 30 29 30 29 30 29 177 6935 41 18 30 29 30 29 30 29 177 7112 42 19 30 29 30 29 30 29 177 7289 43 20 30 29 30 29 30 29 177 7466 44 21 30 29 30 29 30 29 177 7643 45 22 30 29 30 29 30 29 177 7820 46 23 30 29 30 29 30 148 7968
47 1 30 29 30 29 30 29 177 8145 48 2 30 29 30 29 30 29 177 8322 49 3 30 29 30 29 30 29 177 8499 50 4 30 29 30 29 30 29 177 8676 51 5 30 29 30 29 30 29 177 8853 52 6 30 29 30 29 30 29 177 9030 53 7 30 29 30 29 30 29 148 9178 54 8 30 29 30 29 30 177 9355 55 9 30 29 30 29 30 29 177 9532 56 10 30 29 30 29 30 29 177 9709 57 11 30 29 30 29 30 29 177 9886 58 12 30 29 30 29 30 29 177 10063 59 13 30 29 30 29 30 29 177 10240 60 14 30 29 30 29 30 148 10388 61 15 30 29 30 29 30 29 177 10565 62 16 30 29 30 29 30 29 177 10742 63 17 30 29 30 29 30 29 177 10919 64 18 30 29 30 29 30 29 177 11096 65 19 30 29 30 29 30 29 177 11273 66 20 30 29 30 29 30 29 177 11450 67 21 30 29 30 29 30 29 177 11627 68 22 30 29 30 29 30 148 11775 69 23 30 29 30 29 30 29 177 11952
55 After creating Table 5, the next step is to separate the Meeus Solar data into the three Tritos groupings at 3,986 and 7,972 days. This task is rather simple; the tricky part is in matching the
177 and 148 lunations with those found in the Dresden Table. The problem is that the Meeus chart is not aligned with the Table’s sequence. The problem is created by the one-lunation (29.5) eclipses. The 29.5 lunation is used to differentiate these twenty-nine and thirty-day lunations, but it should be remembered that the 29.5 can be either of these lunations. The 29.5 lunations are hidden within the 177-day period. It is this group that causes the alternations between the six and seven groupings of the 177-day period. The 29.5 period occurs between two 148-day periods.
With two 148-day periods, which 148-day grouping is pictured in the Table?
When comparing the Dresden Eclipse Table with the Meeus data (Appendix K), other periods than the six and seven groupings appear in the Eclipse Table. The Dresden Eclipse Table is not laid out in a six-seven groupings of 177 days. This would assume that observation played a big part in the 148-day periods placement, as Teeple (1930:91) believes. Combining the one-lunation groups with a 148- day period reduces seventy-five eclipses to sixty-seven. This would suggest that at least two eclipses in the Eclipse Table are at the 29.5 day lunations; the others are hidden in the 177-day groups. The Lunar eclipses of Meeus (Appendix K) appear to be a closer fit to the
Table, but like Willson’s study are not perfect matches. This is as far as general data will be useful for studying the Maya eclipses. A further investigation of observed eclipses may better establish some benchmarks to aid this investigation.
56 CHAPTER THREE: CONCLUSION
The Eclipse Table has great flexibility. It can be a sysygy, a lunar calendar, and a warning table, all at once. The Table can easily be made by a list of eclipses, either solar or lunar. It would be very valuable to have the source material that the Maya used to create this Table. The other unfortunate problem is that the Dresden Codex contains the only copy of a Maya Eclipse
Table. Another copy would answer questions about the Base Date and the ritual nature of day
Lamat, in the Table.
The origins of the Table cannot be determined by general data, but this data is compatible with a lunar origin for the Eclipse Table. As Pogo and Smither have suggested thirty years worth of data is sufficient to create the Table, but how long would it take to acquire a list of thirty years worth of eclipses by observation, in order to fill in the gaps. This method was the way the
Chaldean Tablets revealed the Saros period. McGee (1892) has noticed that all societies which observed the moon have recognized different periods associated with the moon. Some are more relevant and are given names. The three groupings of the Eclipse Table are the Maya Sariod of
3896 days, the Tritos. The difference between the Saros and Tritos suggests an independent development of the Maya calendar and astronomy.
Observation, record keeping, and experimentation make eclipse prediction possible. Increased accuracy is not needed for eclipse predictions. Oppolzer’s data serves well for most studies. With the many different methods of eclipse approximation, the key to eclipse predictions is the new moons and full moons. Not all new moons and full moons produce eclipses.
The three sections of 69 eclipses are not divided by the seasons, but by the 135-lunation period
Tritos. The Table is not a list of eclipse dates, but rather dates when eclipses could occur. The
57 Table does chart all but six eclipses. These are the eclipses at one month intervals. They may be picked up by the 15-day dates. These dates need further study. What are their importance, function and relationship to the 148-day period? These dates may help determine the relationship between solar and lunar eclipse. It is curious that the Maya, who had no interest in lunar eclipses, would place a lunar eclipse glyph along side the solar eclipse glyph suspended from sky-band images in the flood scene elsewhere in the Dresden Code (Figures 2 and 4).
In summary, this thesis expands the examination of eclipse data beyond the mean-value of
173.31 days. This will further the investigation of eclipse dates instead of nodal passage. The
148-day and 29.5 day periods, ignored by earlier researchers, may hold clues to proper date alignment of the Eclipse Table. These periods have been overlooked by earlier researchers; their only importance has been related to the location of the pictures in the Table. The 148-day eclipses are caused by the rotation of the nodes. They are also produced by the sun at perigee, which allows the eclipse window to remain open at one lunation, producing another 148 and 29 day eclipse from the 177-day period. This is the reason for the six and seven groups of 177-day eclipses found in the eclipse data. Unfortunately, the Eclipse Table does not have the six and seven groupings. The task now is to find specific eclipses visible in the Maya area that will match the computations of eclipse periods.
More attention is required concerning the three sequential dates in the Table. Meeus’ data
(Appendix A) does appear to support the Lunar Variation Theory. The dates have been overlooked in earlier studies. The emphasis has been on the numbers and totals.
The fifth century eclipse need further study since they are at the time of the other correlations that have been suggested. What is the function of the multiples of the Dresden Eclipse Table?
58 How many times could the Table be used? Even Glyph X with its six lunation periods should be investigated thoroughly.
A deeper understanding of the role Venus plays in eclipse prediction should be investigated. As
Satterthwaite (1962:258) states, the Maya were interested in the relationship of Venus to solar eclipses; the Venus Table implies an interest in the Venus-moon relationships. The Thix and Fox are eclipse periods in the Venus Table. More studies are needed into the other charts of the
Dresden Codex and their relationship to eclipse predictions.
As Guthe said, “The Indigenous records of the Maya lunar count still contain many interesting, unsolved problems” (1932:277).
59
APPENDIX A MEEUS LUNAR DATA
60 Lunar 1971 to 2003 Meeus P 1 Year MM DD Julian Diff Sum Tzolkin Haab
1 1971 8 6 2441170.32 177.5 177.5 12 17 18 0 5 8 Chicchan 13 Xul 2 1972 1 30 2441346.95 176.63 354.13 12 17 18 9 2 3 Ik 10 Muan 3 1972 7 26 2441524.8 177.85 531.98 12 17 19 0 0 12 Ahau 3 Xul 4 1973 1 18 2441701.39 176.59 708.57 N 12 17 19 8 16 6 Cib 19 Kankin 5 1973 6 15 2441849.37 147.98 856.55 N 12 17 19 16 4 11 Kan 2 Zotz 6 1973 7 15 2441878.99 29.62 886.17 N 12 17 19 17 14 2 Ix 12 Tzec 7 1973 12 10 2442026.57 147.58 1033.8 X* 12 18 0 7 2 7 Ik 0 Mak 8 1974 6 4 2442203.43 176.86 1210.6 * 12 18 0 15 18 1 Eznab 11 Zip 9 1974 11 29 2442381.13 177.7 1388.3 12 18 1 6 16 10 Cib 9 Ceh 10 1975 5 25 2442557.74 176.61 1564.9 12 18 1 15 13 5 Ben 1 Zip 11 1975 11 18 2442735.43 177.69 1742.6 * 12 18 2 6 10 13 Oc 18 Zac 12 1976 5 13 2442912.33 176.9 1919.5 12 18 2 15 7 8 Manik 10 Uo 13 1976 11 6 2443089.46 177.13 2096.6 N* 12 18 3 6 4 3 Kan 7 Zac 14 1977 4 4 2443237.68 148.22 2244.9 12 18 3 13 13 9 Ben 16 Cumhu 15 1977 9 27 2443413.85 176.17 2421 N 12 18 4 4 9 3 Muluc 7 Chen 16 1978 3 24 2443592.18 178.33 2599.4 12 18 4 13 7 12 Manik 5 Cumhu 17 1978 9 16 2443768.29 176.11 2775.5 12 18 5 4 3 6 Akbal 16 Mol 18 1979 3 13 2443946.38 178.09 2953.6 * 12 18 5 13 1 2 Imix 14 Kayeb 19 1979 9 6 2444122.95 176.57 3130.1 12 18 6 3 18 10 Eznab 6 Mol 20 1980 3 1 2444300.37 177.42 3307.6 N 12 18 6 12 15 5 Men 3 Kayeb 21 1980 7 27 2444448.3 147.93 3455.5 N 12 18 7 2 3 10 Akbal 6 Xul 22 1980 8 26 2444477.65 29.35 3484.8 N 12 18 7 3 13 1 Ben 16 Yaxkin 23 1981 1 20 2444624.83 147.18 3632 N 12 18 7 11 0 5 Ahau 3 Muan 24 1981 7 17 2444802.7 177.87 3809.9 12 18 8 1 18 1 Eznab 16 Tzec 25 1982 1 9 2444979.33 176.63 3986.5 12 18 8 10 14 8 Ix 12 Kankin 26 1982 7 6 2445156.81 177.48 4164 12 18 9 1 12 4 Eb 5 Tzec 27 1982 12 30 2445333.98 177.17 4341.2 12 18 9 10 9 12 Muluc 2 Kankin 28 1983 6 25 2445510.85 176.87 4518 * 12 18 10 1 6 7 Cimi 14 Zotz 29 1983 12 20 2445688.58 177.73 4695.8 XN* 12 18 10 10 4 3 Kan 12 Mac 30 1984 5 15 2445835.7 147.12 4842.9 N 12 18 10 17 11 7 Chuen 14 Uo 31 1984 6 13 2445865.1 29.4 4872.3 N 12 18 11 1 0 10 Ahau 3 Zotz 32 1984 11 8 2446013.25 148.15 5020.4 N 12 18 11 8 8 2 Lamat 11 Zac 33 1985 5 4 2446190.33 177.08 5197.5 12 18 11 17 5 10 Chicchan 3 Uo 34 1985 10 28 2446367.24 176.91 5374.4 12 18 12 8 2 5 Ik 0 Zac 35 1986 4 24 2446545.03 177.79 5552.2 12 18 12 17 0 1 Ahau 13 Pop 36 1986 10 17 2446721.3 176.27 5728.5 12 18 13 7 16 8 Cib 9 Yax 37 1987 4 14 2446899.6 178.3 5906.8 N 12 18 13 16 15 5 Men 3 Pop 38 1987 10 7 2447075.67 176.07 6082.9 12 18 14 7 11 12 Chuen 19 Chen 39 1988 3 3 2447224.18 148.51 6231.4 N 12 18 14 14 19 4 Cauac 7 Kayeb 40 1988 8 27 2447400.96 176.78 6408.1 12 18 15 5 16 12 Cib 19 Yaxkin
61 Lunar 1971 to 2003 Meeus P 2 Year MM DD Julian Diff Sum Tzolkin Haab
41 1989 2 20 2447578.15 177.19 6585.3 12 18 15 14 13 7 Ben 16 Pax 42 1989 8 17 2447755.63 177.48 6762.8 12 18 16 5 11 3 Chuen 9 Yaxkin 43 1990 2 9 2447932.3 176.67 6939.5 12 18 16 14 7 10 Manik 5 Pax 44 1990 8 6 2448110.09 177.79 7117.3 12 18 17 5 5 6 Chicchan 18 Xul 45 1991 1 30 2448286.75 176.66 7293.9 N 12 18 17 14 2 1 Ik 15 Muan 46 1991 6 27 2448434.64 147.89 7441.8 N 12 18 18 3 10 6 Oc 18 Zotz 47 1991 7 26 2448464.26 29.62 7471.4 N 12 18 18 4 19 9 Cauac 7 Xul 48 1991 12 21 2448611.94 147.68 7619.1 12 18 18 12 7 1 Manik 15 Mak 49 1992 6 15 2448788.71 176.77 7795.9 12 18 19 3 4 9 Kan 7 Zotz 50 1992 12 9 2448966.49 177.78 7973.7 * 12 18 19 12 1 4 Imix 4 Mac 51 1993 6 4 2449143.04 176.55 8150.2 12 19 0 2 18 12 Eznab 16 Zip 52 1993 11 29 2449320.77 177.73 8328 12 19 0 11 16 8 Cib 14 Ceh 53 1994 5 25 2449497.65 176.88 8504.8 12 19 1 2 13 3 Ben 6 Zip 54 1994 11 18 2449674.78 177.13 8682 N 12 19 1 11 10 11 Oc 3 Ceh 55 1995 4 15 2449823.01 148.23 8830.2 12 19 2 0 18 3 Eznab 6 Pop 56 1995 10 8 2449999.17 176.16 9006.4 N 12 19 2 9 14 10 Ix 2 Yax 57 1996 4 4 2450177.51 178.34 9184.7 X* 12 19 3 0 13 7 Ben 1 Uayeb 58 1996 9 27 2450353.62 176.11 9360.8 12 19 3 9 9 1 Muluc 12 Chen 59 1997 3 24 2450531.69 178.07 9538.9 12 19 4 0 7 10 Manik 10 Cumhu 60 1997 9 16 2450708.28 176.59 9715.5 12 19 4 9 3 4 Akbal 1 Chen 61 1998 3 13 2450885.68 177.4 9892.9 N 12 19 5 0 1 13 Imix 19 Kayeb 62 1998 8 8 2451033.6 147.92 10041 N 12 19 5 7 9 5 Muluc 2 Yaxkin 63 1998 9 6 2451062.97 29.37 10070 N 12 19 5 8 18 8 Eznab 11 Mol 64 1999 1 31 2451210.18 147.21 10217 N 12 19 5 16 5 12 Chicchan 18 Muan 65 1999 7 28 2451387.98 177.8 10395 12 19 6 7 3 8 Akbal 11 Xul 66 2000 1 21 2451564.7 176.72 10572 12 19 6 16 0 3 Ahau 8 Muan 67 2000 7 16 2451742.08 177.38 10749 12 19 7 6 17 11 Caban 0 Xul 68 2001 1 9 2451919.35 177.27 10927 12 19 7 15 14 6 Ix 17 Kankin 69 2001 7 5 2452096.12 176.77 11103 12 19 8 6 11 1 Chuen 9 Tzec 70 2001 12 30 2452273.94 177.82 11281 N 12 19 8 15 9 10 Muluc 7 Kankin 71 2002 5 26 2452421 147.06 11428 N 12 19 9 4 16 1 Cib 9 Zip 72 2002 6 24 2452450.39 29.39 11458 N 12 19 9 6 5 4 Chicchan 18 Zotz 73 2002 11 20 2452598.57 148.18 11606 N* 12 19 9 13 13 9 Ben 6 Ceh 74 2003 5 16 2452775.65 177.08 11783 12 19 10 4 11 5 Chuen 19 Uo 75 2003 11 9 2452952.56 176.91 11960 X* 12 19 10 13 8 13 Lamat 16 Zac
Night Eclipse * Not Liu X Not Oppolzer N
62
APPENDIX B LIU LUNAR DATA
63 Lunar 1971 to 2003 Liu P 1 Year MM DD Julian Diff Sum Tzolkin Haab
1 1971 8 6 2441170 177 177 12 17 18 0 5 8 Chicchan 13 Xul 2 1972 1 30 2441347 177 354 12 17 18 9 2 3 Ik 10 Muan 3 1972 7 26 2441525 178 532 12 17 19 0 0 12 Ahau 3 Xul 4 1973 1 18 2441701 176 708 N 12 17 19 8 16 6 Cib 19 Kankin 5 1973 6 15 2441849 148 856 N 12 17 19 16 4 11 Kan 2 Zotz 6 1973 7 15 2441879 30 886 N 12 17 19 17 14 2 Ix 12 Tzec 7 1973 12 9 2442026 147 1033 X* 12 18 0 7 1 6 Imix 19 Ceh 8 1974 6 4 2442203 177 1210 * 12 18 0 15 18 1 Eznab 11 Zip 9 1974 11 29 2442381 178 1388 12 18 1 6 16 10 Cib 9 Ceh 10 1975 5 25 2442558 177 1565 12 18 1 15 13 5 Ben 1 Zip 11 1975 11 18 2442735 177 1742 * 12 18 2 6 10 13 Oc 18 Zac 12 1976 5 13 2442912 177 1919 12 18 2 15 7 8 Manik 10 Uo 13 1976 11 6 2443089 177 2096 N* 12 18 3 6 4 3 Kan 7 Zac 14 1977 4 4 2443238 149 2245 12 18 3 13 13 9 Ben 16 Cumhu 15 1977 9 27 2443414 176 2421 N 12 18 4 4 9 3 Muluc 7 Chen 16 1978 3 24 2443592 178 2599 12 18 4 13 7 12 Manik 5 Cumhu 17 1978 9 16 2443768 176 2775 12 18 5 4 3 6 Akbal 16 Mol 18 1979 3 13 2443946 178 2953 * 12 18 5 13 1 2 Imix 14 Kayeb 19 1979 9 6 2444123 177 3130 12 18 6 3 18 10 Eznab 6 Mol 20 1980 3 1 2444300 177 3307 N 12 18 6 12 15 5 Men 3 Kayeb 21 1980 7 27 2444448 148 3455 N 12 18 7 2 3 10 Akbal 6 Xul 22 1980 8 26 2444478 30 3485 N 12 18 7 3 13 1 Ben 16 Yaxkin 23 1981 1 20 2444625 147 3632 N 12 18 7 11 0 5 Ahau 3 Muan 24 1981 7 17 2444803 178 3810 12 18 8 1 18 1 Eznab 16 Tzec 25 1982 1 9 2444979 176 3986 12 18 8 10 14 8 Ix 12 Kankin 26 1982 7 6 2445157 178 4164 12 18 9 1 12 4 Eb 5 Tzec 27 1982 12 30 2445334 177 4341 12 18 9 10 9 12 Muluc 2 Kankin 28 1983 6 25 2445511 177 4518 12 18 10 1 6 7 Cimi 14 Zotz 29 1983 12 19 2445688 177 4695 XN 12 18 10 10 3 2 Akbal 11 Mac 30 1984 5 15 2445836 148 4843 N 12 18 10 17 11 7 Chuen 14 Uo 31 1984 6 13 2445865 29 4872 N 12 18 11 1 0 10 Ahau 3 Zotz 32 1984 11 8 2446013 148 5020 N 12 18 11 8 8 2 Lamat 11 Zac 33 1985 5 4 2446190 177 5197 12 18 11 17 5 10 Chicchan 3 Uo 34 1985 10 28 2446367 177 5374 12 18 12 8 2 5 Ik 0 Zac 35 1986 4 24 2446545 178 5552 12 18 12 17 0 1 Ahau 13 Pop 36 1986 10 17 2446721 176 5728 12 18 13 7 16 8 Cib 9 Yax 37 1987 4 14 2446900 179 5907 N 12 18 13 16 15 5 Men 3 Pop 38 1987 10 7 2447076 176 6083 12 18 14 7 11 12 Chuen 19 Chen 39 1988 3 3 2447224 148 6231 N 12 18 14 14 19 4 Cauac 7 Kayeb 40 1988 8 27 2447401 177 6408 12 18 15 5 16 12 Cib 19 Yaxkin 41 1989 2 20 2447578 177 6585 12 18 15 14 13 7 Ben 16 Pax 42 1989 8 17 2447756 178 6763 12 18 16 5 11 3 Chuen 9 Yaxkin 43 1990 2 9 2447932 176 6939 12 18 16 14 7 10 Manik 5 Pax
64
Lunar 1971 to 2003 Liu P 2 Year MM DD Julian Diff Sum Tzolkin Haab
44 1990 8 6 2448110 178 7117 12 18 17 5 5 6 Chicchan 18 Xul 45 1991 1 30 2448287 177 7294 N 12 18 17 14 2 1 Ik 15 Muan 46 1991 6 27 2448435 148 7442 N 12 18 18 3 10 6 Oc 18 Zotz 47 1991 7 26 2448464 29 7471 N 12 18 18 4 19 9 Cauac 7 Xul 48 1991 12 21 2448612 148 7619 12 18 18 12 7 1 Manik 15 Mak 50 1992 12 9 2448966 177 7973 * 12 18 19 12 1 4 Imix 4 Mak 51 1993 6 4 2449143 177 8150 12 19 0 2 18 12 Eznab 16 Zip 52 1993 11 29 2449321 178 8328 12 19 0 11 16 8 Cib 14 Ceh 53 1994 5 25 2449498 177 8505 12 19 1 2 13 3 Ben 6 Zip 54 1994 11 18 2449675 177 8682 N 12 19 1 11 10 11 Oc 3 Ceh 55 1995 4 15 2449823 148 8830 12 19 2 0 18 3 Eznab 6 Pop 56 1995 10 8 2449999 176 9006 N 12 19 2 9 14 10 Ix 2 Yax 57 1996 4 3 2450177 178 9184 X* 12 19 3 0 12 6 Eb 0 Uayeb 58 1996 9 27 2450354 177 9361 12 19 3 9 9 1 Muluc 12 Chen 59 1997 3 24 2450532 178 9539 12 19 4 0 7 10 Manik 10 Cumhu 60 1997 9 16 2450708 176 9715 12 19 4 9 3 4 Akbal 1 Chen 61 1998 3 13 2450886 178 9893 N 12 19 5 0 1 13 Imix 19 Kayeb 62 1998 8 8 2451034 148 10041 N 12 19 5 7 9 5 Muluc 2 Yaxkin 63 1998 9 6 2451063 29 10070 N 12 19 5 8 18 8 Eznab 11 Mol 64 1999 1 31 2451210 147 10217 N 12 19 5 16 5 12 Chicchan 18 Muan 65 1999 7 28 2451388 178 10395 12 19 6 7 3 8 Akbal 11 Xul 66 2000 1 21 2451565 177 10572 12 19 6 16 0 3 Ahau 8 Muan 67 2000 7 16 2451742 177 10749 12 19 7 6 17 11 Caban 0 Xul 68 2001 1 9 2451919 177 10926 12 19 7 15 14 6 Ix 17 Kankin 69 2001 7 5 2452096 177 11103 12 19 8 6 11 1 Chuen 9 Tzec 70 2001 12 30 2452274 178 11281 N 12 19 8 15 9 10 Muluc 7 Kankin 71 2002 5 26 2452421 147 11428 N 12 19 9 4 16 1 Cib 9 Zip 72 2002 6 24 2452450 29 11457 N 12 19 9 6 5 4 Chicchan 18 Zotz 73 2002 11 19 2452598 148 11605 N* 12 19 9 13 13 9 Ben 6 Ceh 74 2003 5 16 2452776 178 11783 12 19 10 4 11 5 Chuen 19 Uo 75 2003 11 8 2452952 176 11959 X* 12 19 10 13 7 12 Manik 15 Zac
Night Eclipse * Not Muess X Not Oppolzer N
65
APPENDIX C OPPOLZER LUNAR DATA
66 Lunar 1971 to 2003 Oppolzer P 1 Year MM DD Julian Diff Sum Tzolkin Haab
1 1971 8 6 2441170 177 177 12 17 18 0 5 8 Chicchan 13 Xul 2 1972 1 30 2441347 177 354 12 17 18 9 2 3 Ik 10 Muan 3 1972 7 26 2441525 178 532 12 17 19 0 0 12 Ahau 3 Xul 4 1973 12 10 2442027 502 1034 X* 12 18 0 7 2 7 Ik 0 Mak 5 1974 6 4 2442203 176 1210 * 12 18 0 15 18 1 Eznab 11 Zip 6 1974 11 29 2442381 178 1388 12 18 1 6 16 10 Cib 9 Ceh 7 1975 5 25 2442558 177 1565 12 18 1 15 13 5 Ben 1 Zip 8 1975 11 18 2442735 177 1742 * 12 18 2 6 10 13 Oc 18 Zac 9 1976 5 13 2442912 177 1919 12 18 2 15 7 8 Manik 10 Uo 10 1977 4 4 2443238 326 2245 12 18 3 13 13 9 Ben 16 Cumhu 11 1978 3 24 2443592 354 2599 12 18 4 13 7 12 Manik 5 Cumhu 12 1978 9 16 2443768 176 2775 12 18 5 4 3 6 Akbal 16 Mol 13 1979 3 13 2443946 178 2953 * 12 18 5 13 1 2 Imix 14 Kayeb 14 1979 9 6 2444123 177 3130 12 18 6 3 18 10 Eznab 6 Mol 15 1981 7 17 2444803 680 3810 12 18 8 1 18 1 Eznab 16 Tzec 16 1982 1 9 2444979 176 3986 12 18 8 10 14 8 Ix 12 Kankin 17 1982 7 6 2445157 178 4164 12 18 9 1 12 4 Eb 5 Tzec 18 1982 12 30 2445334 177 4341 12 18 9 10 9 12 Muluc 2 Kankin 19 1983 6 25 2445511 177 4518 * 12 18 10 1 6 7 Cimi 14 Zotz 20 1985 5 4 2446190 679 5197 12 18 11 17 5 10 Chicchan 3 Uo 21 1985 10 28 2446367 177 5374 12 18 12 8 2 5 Ik 0 Zac 22 1986 4 24 2446545 178 5552 12 18 12 17 0 1 Ahau 13 Pop 23 1986 10 17 2446721 176 5728 12 18 13 7 16 8 Cib 9 Yax 24 1987 10 7 2447076 355 6083 12 18 14 7 11 12 Chuen 19 Chen 25 1988 8 27 2447401 325 6408 12 18 15 5 16 12 Cib 19 Yaxkin 26 1989 2 20 2447578 177 6585 12 18 15 14 13 7 Ben 16 Pax 27 1989 8 17 2447756 178 6763 12 18 16 5 11 3 Chuen 9 Yaxkin 28 1990 2 9 2447932 176 6939 12 18 16 14 7 10 Manik 5 Pax 29 1990 8 6 2448110 178 7117 12 18 17 5 5 6 Chicchan 18 Xul 30 1991 12 21 2448612 502 7619 12 18 18 12 7 1 Manik 15 Mak 31 1992 6 15 2448789 177 7796 12 18 19 3 4 9 Kan 7 Zotz 32 1992 12 9 2448966 177 7973 * 12 18 19 12 1 4 Imix 4 Mak 33 1993 6 4 2449143 177 8150 12 19 0 2 18 12 Eznab 16 Zip 34 1993 11 29 2449321 178 8328 12 19 0 11 16 8 Cib 14 Ceh 35 1994 5 25 2449498 177 8505 12 19 1 2 13 3 Ben 6 Zip
67
Lunar 1971 to 2003 Oppolzer P 2 Year MM DD Julian Diff Sum Tzolkin Haab
36 1995 4 15 2449823 325 8830 12 19 2 0 18 3 Eznab 6 Pop 37 1996 4 4 2450178 355 9185 X* 12 19 3 0 13 7 Ben 1 Uayeb 38 1996 9 27 2450354 176 9361 12 19 3 9 9 1 Muluc 12 Chen 39 1997 3 24 2450532 178 9539 12 19 4 0 7 10 Manik 10 Cumhu 40 1997 9 16 2450708 176 9715 12 19 4 9 3 4 Akbal 1 Chen 41 1999 7 28 2451388 680 10395 12 19 6 7 3 8 Akbal 11 Xul 42 2000 1 21 2451565 177 10572 12 19 6 16 0 3 Ahau 8 Muan 43 2000 7 16 2451742 177 10749 12 19 7 6 17 11 Caban 0 Xul 44 2001 1 9 2451919 177 10926 12 19 7 15 14 6 Ix 17 Kankin 45 2001 7 5 2452096 177 11103 12 19 8 6 11 1 Chuen 9 Tzec 46 2003 5 16 2452776 680 11783 12 19 10 4 11 5 Chuen 19 Uo 47 2003 11 9 2452953 177 11960 X* 12 19 10 13 8 13 Lamat 16 Zac
Night Eclipse * Not Liu X
68
APPENDIX D MEEUS SOLAR DATA
69
Solar 1971 to 2003 Meeus P 1 Year MM DD Julian Diff Sum Tzolkin Haab
1 1971 7 22 2441154.9 147 147 12 17 17 17 10 6 Oc 18 Tzec 2 1971 8 20 2441184.44 29.54 176.54 12 17 18 0 19 9 Cauac 7 Yaxkin 3 1972 1 16 2441332.96 148.52 325.06 12 17 18 8 8 2 Lamat 16 Kankin 4 1972 7 10 2441509.32 176.36 501.42 12 17 18 17 4 9 Kan 7 Tzec 5 1973 1 4 2441687.16 177.84 679.26 12 17 19 8 2 5 Ik 5 Kankin 6 1973 6 30 2441863.99 176.83 856.09 12 17 19 16 19 13 Cauac 17 Zotz 7 1973 12 24 2442041.13 177.14 1033.2 12 18 0 7 16 8 Cib 14 Mac 8 1974 6 20 2442218.7 177.57 1210.8 12 18 0 16 14 4 Ix 7 Zotz 9 1974 12 13 2442395.18 176.48 1387.3 12 18 1 7 10 11 Oc 3 Mac 10 1975 5 11 2442543.8 148.62 1535.9 12 18 1 14 19 4 Cauac 7 Uo 11 1975 11 3 2442720.05 176.25 1712.1 12 18 2 5 15 11 Men 3 Zac 12 1976 4 29 2442897.93 177.88 1890 12 18 2 14 13 7 Ben 16 Pop 13 1976 10 23 2443074.72 176.79 2066.8 12 18 3 5 10 2 Oc 13 Yax 14 1977 4 18 2443251.94 177.22 2244 12 18 3 14 7 10 Manik 5 Pop 15 1977 10 12 2443429.35 177.41 2421.5 12 18 4 5 4 5 Kan 2 Yax 16 1978 4 7 2443606.13 176.78 2598.2 12 18 4 14 1 13 Imix 19 Cumhu 17 1978 10 2 2443783.77 177.64 2775.9 12 18 5 4 19 9 Cauac 12 Chen 18 1979 2 26 2443931.2 147.43 2923.3 12 18 5 12 6 13 Cimi 19 Pax 19 1979 8 22 2444108.22 177.02 3100.3 12 18 6 3 3 8 Akbal 11 Yaxkin 20 1980 2 16 2444285.87 177.65 3278 12 18 6 12 1 4 Imix 9 Pax 21 1980 8 10 2444462.3 176.43 3454.4 12 18 7 2 17 11 Caban 0 Yaxkin 22 1981 2 4 2444640.42 178.12 3632.5 12 18 7 11 15 7 Men 18 Muan 23 1981 7 31 2444816.66 176.24 3808.8 12 18 8 2 12 2 Eb 10 Xul 24 1982 1 25 2444994.7 178.04 3986.8 12 18 8 11 10 11 Oc 8 Muan 25 1982 6 21 2445142 147.3 4134.1 12 18 9 0 17 2 Caban 10 Zotz 26 1982 7 20 2445171.28 29.28 4163.4 12 18 9 2 6 5 Cimi 19 Tzec 27 1982 12 15 2445318.9 147.62 4311 12 18 9 9 14 10 Ix 7 Mac 28 1983 6 11 2445496.7 177.8 4488.8 12 18 10 0 12 6 Eb 0 Zotz 29 1983 12 4 2445673.02 176.32 4665.1 12 18 10 9 8 13 Lamat 16 Ceh 30 1984 5 30 2445851.2 178.18 4843.3 12 18 11 0 6 9 Cimi 9 Zip 31 1984 11 22 2446027.45 176.25 5019.6 12 18 11 9 2 3 Ik 5 Ceh 32 1985 5 19 2446205.4 177.95 5197.5 12 18 12 0 0 12 Ahau 18 Uo 33 1985 11 12 2446382.09 176.69 5374.2 12 18 12 8 17 7 Caban 15 Zac 34 1986 4 9 2446529.76 147.67 5521.9 12 18 12 16 5 12 Chicchan 3 Uayeb 35 1986 10 3 2446707.3 177.54 5699.4 12 18 13 7 2 7 Ik 15 Chen 36 1987 3 29 2446884.03 176.73 5876.1 12 18 13 15 19 2 Cauac 12 Cumhu 37 1987 9 23 2447061.63 177.6 6053.7 12 18 14 6 17 11 Caban 5 Chen 38 1988 3 18 2447238.58 176.95 6230.7 12 18 14 15 14 6 Ix 2 Cumhu 39 1988 9 11 2447415.7 177.12 6407.8 12 18 15 6 11 1 Chuen 14 Mol 40 1989 3 7 2447593.26 177.56 6585.4 12 18 15 15 8 9 Lamat 11 Kayeb
70
Solar 1971 to 2003 Meeus P 2 Year MM DD Julian Diff Sum Tzolkin Haab
41 1989 8 31 2447769.73 176.47 6761.8 12 18 16 6 5 4 Chicchan 3 Mol 42 1990 1 26 2447918.31 148.58 6910.4 12 18 16 13 13 9 Ben 11 Muan 43 1990 7 22 2448094.63 176.32 7086.7 12 18 17 4 10 4 Oc 3 Xul 44 1991 1 15 2448272.5 177.87 7264.6 12 18 17 13 7 12 Manik 0 Muan 45 1991 7 11 2448449.3 176.8 7441.4 12 18 18 4 4 7 Kan 12 Tzec 46 1992 1 4 2448626.46 177.16 7618.6 12 18 18 13 1 2 Imix 9 Kankin 47 1992 6 30 2448804.01 177.55 7796.1 12 18 19 3 19 11 Cauac 2 Zek 48 1992 12 24 2448980.52 176.51 7972.6 12 18 19 12 16 6 Cib 19 Mac 49 1993 5 21 2449129.1 148.58 8121.2 12 19 0 2 4 11 Kan 2 Zip 50 1993 11 13 2449305.41 176.31 8297.5 12 19 0 11 0 5 Ahau 18 Zac 51 1994 5 10 2449483.22 177.81 8475.3 12 19 1 1 18 1 Eznab 11 Uo 52 1994 11 3 2449660.07 176.85 8652.2 12 19 1 10 15 9 Men 8 Zac 53 1995 4 29 2449837.23 177.16 8829.3 12 19 2 1 12 4 Eb 0 Uo 54 1995 10 24 2450014.69 177.46 9006.8 12 19 2 10 10 13 Oc 18 Yax 55 1996 4 17 2450191.44 176.75 9183.5 12 19 3 1 6 7 Cimi 9 Pop 56 1996 10 12 2450369.09 177.65 9361.2 12 19 3 10 4 3 Kan 7 Yax 57 1997 3 9 2450516.56 147.47 9508.7 12 19 3 17 12 8 Eb 15 Kayeb 58 1997 9 2 2450693.5 176.94 9685.6 12 19 4 8 9 3 Muluc 7 Mol 59 1998 2 26 2450871.23 177.73 9863.3 12 19 4 17 6 11 Cimi 4 Kayeb 60 1998 8 22 2451047.59 176.36 10040 12 19 5 8 3 6 Akbal 16 Yaxkin 61 1999 2 16 2451225.77 178.18 10218 12 19 5 17 1 2 Imix 14 Pax 62 1999 8 11 2451401.96 176.19 10394 12 19 6 7 17 9 Caban 5 Yaxkin 63 2000 2 5 2451580.04 178.08 10572 12 19 6 16 15 5 Men 3 Pax 64 2000 7 1 2451727.31 147.27 10719 12 19 7 6 2 9 Ik 5 Tzec 65 2000 7 31 2451756.59 29.28 10749 12 19 7 7 12 13 Eb 15 Xul 66 2000 12 25 2451904.23 147.64 10896 12 19 7 14 19 4 Cauac 2 Kankin 67 2001 6 21 2452082 177.77 11074 12 19 8 5 17 13 Caban 15 Zotz 68 2001 12 14 2452258.37 176.37 11250 12 19 8 14 13 7 Ben 11 Mac 69 2002 6 10 2452436.49 178.12 11429 12 19 9 5 11 3 Chuen 4 Zotz 70 2002 12 4 2452612.81 176.32 11605 12 19 9 14 8 11 Lamat 1 Mac 71 2003 5 31 2452790.67 177.86 11783 12 19 10 5 6 7 Cimi 14 Zip 72 2003 11 23 2452967.45 176.78 11960 12 19 10 14 2 1 Ik 10 Ceh
71
APPENDIX E OPPOLZER SOLAR DATA
72
Solar 1971 to 2003 Oppolzer P1 Year MM DD Julian Diff Sum Tzolkin Haab
1 1971 7 22 2441155 147 147 12 17 17 17 10 6 Oc 18 Tzec 2 1971 8 20 2441184 29 176 12 17 18 0 19 9 Cauac 7 Yaxkin 3 1972 1 16 2441333 149 325 12 17 18 8 8 2 Lamat 16 Kankin 4 1972 7 10 2441509 176 501 12 17 18 17 4 9 Kan 7 Tzec 5 1973 1 4 2441687 178 679 12 17 19 8 2 5 Ik 5 Kankin 6 1973 6 30 2441864 177 856 12 17 19 16 19 13 Cauac 17 Zotz 7 1973 12 24 2442041 177 1033 12 18 0 7 16 8 Cib 14 Mac 8 1974 6 20 2442219 178 1211 12 18 0 16 14 4 Ix 7 Zotz 9 1974 12 13 2442395 176 1387 12 18 1 7 10 11 Oc 3 Mac 10 1975 5 11 2442544 149 1536 12 18 1 14 19 4 Cauac 7 Uo 11 1975 11 3 2442720 176 1712 12 18 2 5 15 11 Men 3 Zac 12 1976 4 29 2442898 178 1890 12 18 2 14 13 7 Ben 16 Pop 13 1976 10 23 2443075 177 2067 12 18 3 5 10 2 Oc 13 Yax 14 1977 4 18 2443252 177 2244 12 18 3 14 7 10 Manik 5 Pop 15 1977 10 12 2443429 177 2421 12 18 4 5 4 5 Kan 2 Yax 16 1978 4 7 2443606 177 2598 12 18 4 14 1 13 Imix 19 Cumhu 17 1978 10 2 2443784 178 2776 12 18 5 4 19 9 Cauac 12 Chen 18 1979 2 26 2443931 147 2923 12 18 5 12 6 13 Cimi 19 Pax 19 1979 8 22 2444108 177 3100 12 18 6 3 3 8 Akbal 11 Yaxkin 20 1980 2 16 2444286 178 3278 12 18 6 12 1 4 Imix 9 Pax 21 1980 8 10 2444462 176 3454 12 18 7 2 17 11 Caban 0 Yaxkin 22 1981 2 4 2444640 178 3632 12 18 7 11 15 7 Men 18 Muan 23 1981 7 31 2444817 177 3809 12 18 8 2 12 2 Eb 10 Xul 24 1982 1 25 2444995 178 3987 12 18 8 11 10 11 Oc 8 Muan 25 1982 6 21 2445142 147 4134 12 18 9 0 17 2 Caban 10 Zotz 26 1982 7 20 2445171 29 4163 12 18 9 2 6 5 Cimi 19 Tzec 27 1982 12 15 2445319 148 4311 12 18 9 9 14 10 Ix 7 Mac 28 1983 6 11 2445497 178 4489 12 18 10 0 12 6 Eb 0 Zotz 29 1983 12 4 2445673 176 4665 12 18 10 9 8 13 Lamat 16 Ceh 30 1984 5 30 2445851 178 4843 12 18 11 0 6 9 Cimi 9 Zip 31 1984 11 22 2446027 176 5019 12 18 11 9 2 3 Ik 5 Ceh 32 1985 5 19 2446205 178 5197 12 18 12 0 0 12 Ahau 18 Uo 33 1985 11 12 2446382 177 5374 12 18 12 8 17 7 Caban 15 Zac 34 1986 4 9 2446530 148 5522 12 18 12 16 5 12 Chicchan 3 Uayeb 35 1986 10 3 2446707 177 5699 12 18 13 7 2 7 Ik 15 Chen 36 1987 3 29 2446884 177 5876 12 18 13 15 19 2 Cauac 12 Cumhu 37 1987 9 23 2447062 178 6054 12 18 14 6 17 11 Caban 5 Chen 38 1988 3 18 2447239 177 6231 12 18 14 15 14 6 Ix 2 Cumhu 39 1988 9 11 2447416 177 6408 12 18 15 6 11 1 Chuen 14 Mol 40 1989 3 7 2447593 177 6585 12 18 15 15 8 9 Lamat 11 Kayeb
73 Solar 1971 to 2003 Oppolzer P 2 Year MM DD Julian Diff Sum Tzolkin Haab
41 1989 8 31 2447770 177 6762 12 18 16 6 5 4 Chicchan 3 Mol 42 1990 1 26 2447918 148 6910 12 18 16 13 13 9 Ben 11 Muan 43 1990 7 22 2448095 177 7087 12 18 17 4 10 4 Oc 3 Xul 44 1991 1 15 2448272 177 7264 12 18 17 13 7 12 Manik 0 Muan 45 1991 7 11 2448449 177 7441 12 18 18 4 4 7 Kan 12 Tzec 46 1992 1 4 2448626 177 7618 12 18 18 13 1 2 Imix 9 Kankin 47 1992 6 30 2448804 178 7796 12 18 19 3 19 11 Cauac 2 Zek 48 1992 12 24 2448981 177 7973 12 18 19 12 16 6 Cib 19 Mac 49 1993 5 21 2449129 148 8121 12 19 0 2 4 11 Kan 2 Zip 50 1993 11 13 2449305 176 8297 12 19 0 11 0 5 Ahau 18 Zac 51 1994 5 10 2449483 178 8475 12 19 1 1 18 1 Eznab 11 Uo 52 1994 11 3 2449660 177 8652 12 19 1 10 15 9 Men 8 Zac 53 1995 4 29 2449837 177 8829 12 19 2 1 12 4 Eb 0 Uo 54 1995 10 24 2450015 178 9007 12 19 2 10 10 13 Oc 18 Yax 55 1996 4 17 2450191 176 9183 12 19 3 1 6 7 Cimi 9 Pop 56 1996 10 12 2450369 178 9361 12 19 3 10 4 3 Kan 7 Yax 57 1997 3 9 2450517 148 9509 12 19 3 17 12 8 Eb 15 Kayeb 58 1997 9 1 2450693 176 9685 12 19 4 8 8 2 Lamat 6 Mol 59 1998 2 26 2450871 178 9863 12 19 4 17 6 11 Cimi 4 Kayeb 60 1998 8 22 2451048 177 10040 12 19 5 8 3 6 Akbal 16 Yaxkin 61 1999 2 16 2451226 178 10218 12 19 5 17 1 2 Imix 14 Pax 62 1999 8 11 2451402 176 10394 12 19 6 7 17 9 Caban 5 Yaxkin 63 2000 2 5 2451580 178 10572 12 19 6 16 15 5 Men 3 Pax 64 2000 7 1 2451727 147 10719 12 19 7 6 2 9 Ik 5 Tzec 65 2000 7 31 2451757 30 10749 12 19 7 7 12 13 Eb 15 Xul 66 2000 12 25 2451904 147 10896 12 19 7 14 19 4 Cauac 2 Kankin 67 2001 6 21 2452082 178 11074 12 19 8 5 17 13 Caban 15 Zotz 68 2001 12 14 2452258 176 11250 12 19 8 14 13 7 Ben 11 Mac 69 2002 6 10 2452436 178 11428 12 19 9 5 11 3 Chuen 4 Zotz 70 2002 12 4 2452613 177 11605 12 19 9 14 8 11 Lamat 1 Mac 71 2003 5 31 2452791 178 11783 12 19 10 5 6 7 Cimi 14 Zip 72 2003 11 23 2452967 176 11959 12 19 10 14 2 1 Ik 10 Ceh
74
APPENDIX F LUNAR-SOLAR DATA
75 Lunar Eclipse 755 Oppolzer 755 P 1 Year Month Day Julian Interval
725 1 19 1985883 178 9 14 13 5 14 3 Ix 2 Cumhu G6 725 7 14 1986059 176 9 14 13 14 10 10 Oc 13 Mol G2 725 12 24 1986222 163 9 14 14 4 13 4 Ben 16 Pax G3 726 1 8 1986237 15 9 14 14 5 8 6 Lamat 11 Kayeb G9 726 6 19 1986399 162 9 14 14 13 10 12 Oc 8 Yaxkin G9 726 7 4 1986414 15 9 14 14 14 5 1 Chicchan 3 Mol G6 726 12 13 1986576 162 * 9 14 15 4 7 7 Manik 5 Pax G6 726 12 28 1986591 15 9 14 15 5 2 9 Ik 0 Kayeb G3 727 5 25 1986739 148 9 14 15 12 10 1 Oc 3 Xul G7 727 6 8 1986753 14 9 14 15 13 4 2 Kan 17 Xul G3 727 6 23 1986768 15 9 14 15 13 19 4 Cauac 12 Yaxkin G9 727 11 17 1986915 147 9 14 16 3 6 8 Cimi 19 Kankin G3 727 12 3 1986931 16 9 14 16 4 2 11 Ik 15 Muan G1 728 5 13 1987093 162 9 14 16 12 4 4 Kan 12 Tzec G1 728 5 27 1987107 14 * 9 14 16 12 18 5 Eznab 6 Xul G6 728 11 6 1987270 163 9 14 17 3 1 12 Imix 9 Kankin G7 729 4 18 1987433 163 9 14 17 11 4 6 Kan 7 Zotz G8 729 5 2 1987447 14 9 14 17 11 18 7 Eznab 1 Tzec G4 729 10 27 1987625 178 9 14 18 2 16 3 Cib 19 Mac G2 730 4 7 1987787 162 * 9 14 18 10 18 9 Eznab 16 Zip G2 730 4 22 1987802 15 9 14 18 11 13 11 Ben 11 Zotz G8 730 10 1 1987964 162 X* 9 14 19 1 15 4 Men 13 Ceh G8 730 10 16 1987979 15 9 14 19 2 10 6 Oc 8 Mac G5 731 3 12 1988126 147 9 14 19 9 17 10 Caban 10 Uo G8 731 3 28 1988142 16 9 14 19 10 13 13 Ben 6 Zip G6 731 9 6 1988304 162 9 15 0 0 15 6 Men 8 Zac G6 731 9 20 1988318 14 9 15 0 1 9 7 Muluc 2 Ceh G2 732 3 1 1988481 163 9 15 0 9 12 1 Eb 0 Uo G3 732 8 25 1988658 177 9 15 1 0 9 9 Muluc 17 Yax G9 733 2 3 1988820 162 9 15 1 8 11 2 Chuen 19 Cumhu G9 733 2 19 1988836 16 9 15 1 9 7 5 Manik 10 Pop G7 733 7 31 1988998 162 9 15 1 17 9 11 Muluc 12 Chen G7 733 8 14 1989012 14 9 15 2 0 3 12 Akbal 6 Yax G3 734 1 10 1989161 149 9 15 2 7 12 5 Eb 15 Kayeb G8 734 1 24 1989175 14 9 15 2 8 6 6 Cimi 9 Cumhu G4 734 2 8 1989190 15 9 15 2 9 1 8 Imix 4 Uayeb G1 734 7 5 1989337 147 9 15 2 16 8 12 Lamat 6 Mol G4 734 7 20 1989352 15 9 15 2 17 3 1 Akbal 1 Chen G1 734 8 3 1989366 14 9 15 2 17 17 2 Caban 15 Chen G6 734 12 30 1989515 149 9 15 3 7 6 8 Cimi 4 Kayeb G2 735 1 13 1989529 14 9 15 3 8 0 9Ahau 18Kayeb G7 735 6 25 1989692 163 9 15 3 16 3 3 Akbal 16 Yaxkin G8 735 7 9 1989706 14 9 15 3 16 17 4 Caban 10 Mol G4 735 12 19 1989869 163 9 15 4 7 0 11 Ahau 13 Pax G5
76 Lunar Eclipse 755 Oppolzer 755 P 2 Year Month Day Julian Interval
736 6 13 1990046 177 9 15 4 15 17 6 Caban 5 Yaxkin G2 736 11 23 1990209 163 9 15 5 6 0 13 Ahau 8 Muan G3 736 12 7 1990223 14 9 15 5 6 14 1 Ix 2 Pax G8 737 5 18 1990385 162 *915514167Cib 19TzecG8 737 6 3 1990401 16 9 15 5 15 12 10 Eb 15 Xul G6 737 10 28 1990548 147 9 15 6 4 19 1 Cauac 2 Kankin G9 737 11 12 1990563 15 9 15 6 5 14 3 Ix 17 Kankin G6 737 11 26 1990577 14 9 15 6 6 8 4 Lamat 11 Muan G2 738 4 23 1990725 148 9 15 6 13 16 9 Cib 14 Zotz G6 738 5 8 1990740 15 9 15 6 14 11 11 Chuen 9 Tzec G3 738 10 18 1990903 163 9 15 7 4 14 5 Ix 12 Mac G4 738 11 1 1990917 14 9 15 7 5 8 6 Lamat 6 Kankin G9 739 4 12 1991079 162 9 15 7 13 10 12 Oc 3 Zotz G9 739 10 7 1991257 178 9 15 8 4 8 8 Lamat 1 Mac G7 740 3 18 1991420 163 9 15 8 12 11 2 Chuen 19 Uo G8 740 4 1 1991434 14 9 15 8 13 5 3 Chicchan 13 Zip G4 740 9 10 1991596 162 9 15 9 3 7 9 Manik 15 Zac G4 740 9 25 1991611 15 9 15 9 4 2 11 Ik 10 Ceh G1 741 2 20 1991759 148 9 15 9 11 10 3 Oc 13 Pop G5 741 3 7 1991774 15 9 15 9 12 5 5 Chicchan 8 Uo G2 741 3 21 1991788 14 9 15 9 12 19 6 Cauac 2 Zip G7 741 8 31 1991951 163 91510 3 213Ik 5Zac G8 741 9 14 1991965 14 9 15 10 3 16 1 Cib 19 Zac G4 742 2 10 1992114 149 9 15 10 11 5 7 Chicchan 3 Pop G9 742 2 24 1992128 14 9 15 10 11 19 8 Cauac 17 Pop G5 742 8 5 1992290 162 9 15 11 2 1 1 Imix 19 Chen G5 742 8 20 1992305 15 91511 216 3Cib 14Yax G2 743 1 30 1992468 163 9 15 11 10 19 10 Cauac 17 Cumhu G3 743 7 25 1992644 176 9 15 12 1 15 4 Men 8 Chen G8 744 1 4 1992807 163 9 15 12 9 18 11 Eznab 11 Kayeb G9 744 1 19 1992822 15 9 15 12 10 13 13 Ben 6 Cumhu G6 744 6 29 1992984 162 9 15 13 0 15 6 Men 3 Mol G6 744 7 14 1992999 15 9 15 13 1 10 8 Oc 18 Mol G3 744 12 24 1993162 163 9 15 13 9 13 2 Ben 1 Kayeb G4 745 1 7 1993176 14 9 15 13 10 7 3 Manik 15 Kayeb G9 745 6 4 1993324 148 9 15 13 17 15 8 Men 8 Xul G4 745 6 18 1993338 14 91514099Muluc 12YaxkinG9 745 7 4 1993354 16 9 15 14 1 5 12 Chicchan 8 Mol G7 745 11 28 1993501 147 9 15 14 8 12 3 Eb 15 Muan G1 745 12 13 1993516 15 91514975Manik 10Pax G7 746 5 25 1993679 163 9 15 14 17 10 12 Oc 8 Xul G8 746 6 8 1993693 14 91515 0 413Kan 2YaxkinG4 746 11 17 1993855 162 9 15 15 8 6 6 Cimi 4 Muan G4 747 4 29 1994018 163 9151516 913Muluc 2Tzec G5
77 Lunar Eclipse 755 Oppolzer 755 P 3 Year Month Day Julian Interval
747 5 14 1994033 15 9 15 15 17 4 2 Kan 17 Tzec G2 747 11 7 1994210 177 9 15 16 8 1 10 Imix 14 Kankin G8 748 4 18 1994373 163 9 15 16 16 4 4 Kan 12 Zotz G9 748 5 2 1994387 14 9 15 16 16 18 5 Eznab 6 Tzec G5 748 10 11 1994549 162 91517 7 011Ahau 8Mak G5 748 10 26 1994564 15 9 15 17 7 15 13 Men 3 Kankin G2 749 3 23 1994712 148 9 15 17 15 3 5 Akbal 6 Zip G6 749 4 7 1994727 15 9 15 17 15 18 7 Eznab 1 Zotz G3 749 9 16 1994889 162 9 15 18 6 0 13 Ahau 3 Ceh G3 749 9 30 1994903 14 * 9 15 18 6 14 1 Ix 17 Ceh G8 750 3 12 1995066 163 9 15 18 14 17 8 Caban 15 Uo G9 750 9 5 1995243 177 9 15 19 5 14 3 Ix 17 Zac G6 751 2 15 1995406 163 91519131710Caban 10Pop G7 751 3 2 1995421 15 9 15 19 14 12 12 Eb 5 Uo G4 751 8 11 1995583 162 916 0 414 5Ix 7Yax G4 751 8 25 1995597 14 9 16 0 5 8 6 Lamat 1 Zac G9 752 1 21 1995746 149 9 16 0 12 17 12 Caban 10 Cumhu G5 752 2 4 1995760 14 9 16 0 13 11 13 Chuen 4 Uayeb G1 752 2 20 1995776 16 9 16 0 14 7 3 Manilk 15 Pop G8 752 7 15 1995922 146 9 16 1 3 13 6 Ben 1 Chen G1 752 7 31 1995938 16 X* 9 16 1 4 9 9 Muluc 17 Chen G8 752 8 14 1995952 14 9 16 1 5 3 10 Akbal 11 Yax G4 753 1 9 1996100 148 9 16 1 12 11 2 Chuen 19 Kayeb G8 753 1 24 1996115 15 X* 9 16 1 13 6 4 Cimi 14 Cumhu G5 753 7 5 1996277 162 9 16 2 3 8 10 Lamat 11 Mol G5 753 7 20 1996292 15 X* 9 16 2 4 3 12 Akbal 6 Chen G2 753 12 29 1996454 162 9 16 2 12 5 5 Chicchan 8 Kayeb G2 754 6 25 1996632 178 9 16 3 3 3 1 Akbal 1 Mol G9 754 12 4 1996794 162 9 16 3 11 5 7 Chicchan 3 Pax G9 754 12 18 1996808 14 9 16 3 11 19 8 Cauac 17 Pax G5 755 5 30 1996971 163 9 16 4 2 2 2Ik 15Xul G6 755 6 14 1996986 15 9 16 4 2 17 4 Caban 10 Yaxkin G3 755 11 23 1997148 162 9 16 4 10 19 10 Cauac 12 Muan G3 755 12 8 1997163 15 9 16 4 11 14 12 Ix 7 Pax G9 756 5 4 1997311 148 9 16 5 1 2 4 Ik 10 Tzec G4 756 5 18 1997325 14 * 9 16 5 1 16 5 Cib 4 Xul G9 756 10 28 1997488 163 9 16 5 9 19 12 Cauac 7 Kankin G1 756 11 11 1997502 14 9 16 5 10 13 13 Ben 1 Muan G6 757 4 23 1997665 163 9 16 6 0 16 7 Cib 19 Zotz G7 757 5 8 1997680 15 9 16 6 1 11 9 Chuen 14 Tzec G4 757 10 17 1997842 162 9 16 6 9 13 2 Ben 16 Mac G4 758 3 29 1998005 163 9 16 6 17 16 9 Cib 14 Zip G5 758 4 12 1998019 14 9 16 7 0 10 10 Oc 8 Zotz G1 758 9 21 1998181 162 916 7 812 3Eb 10Ceh G1 758 10 7 1998197 16 9 16 7 9 8 6 Lamat 6 Mac G8
78
APPENDIX G MEEUS LUNAR SEASON DISTRIBUTION
79
Meeus Lunar 2003 P1 Season 1 Season 2 Season 3 Ecl Num Day Tzolkin Ecl Num Day Tzolkin Ecl Num Day Tzolkin
1 62 109 5 Muluc l 21 283 10 Akbal l 71 456 1 Cib l 2 46 110 6 Oc l 5 284 11 Kan l 457 2 Caban 3 30 111 7 Chuen l 64 285 12 Chicchan l 55 458 3 Eznab l 4 112 8 Eb 286 13 Cimi 39 459 4 Cauac l 5 14/73 113 9 Ben ll 48 287 1 Manik l 23 460 5 Ahau l 6 56 114 10 Ix l 32 288 2 Lamat l 461 6 Imix 7 115 11 Men 15 289 3 Muluc l 7 462 7 Ik I 8 40 116 12 Cib l 290 4 Oc 65 463 8 Akbal l 9 117 13 Caban 74 291 5 Chuen l 49 464 9 Kan l 10 8/24 118 1 Eznab ll 292 6 Eb 33 465 10 Chicchan l 11 119 2 Cauac 41/57 293 7 Ben lI 466 11 Cimi 12 66 120 3 Ahau l 25 294 8 Ix l 16 467 12 Manik l 13 50 121 4 Imix l 295 9 Men 75 468 13 Lamat I 14 34 122 5 Ik l 9 296 10 Cib l 58 469 1 Muluc l 15 17 123 6 Akbal l 67 297 11 Caban l 470 2 Oc 16 124 7 Kan 51 298 12 Eznab l 42 471 3 Chuen l 17 1 125 8 Chicchan l 299 13 Cauac 26 472 4 Eb l 18 126 9 Cimi 35 300 1 Ahau l 10 473 5 Ben l 19 43/59 127 10 Manik ll 18 301 2 Imix l 68 474 6 Ix l 20 128 11 Lamat 2 302 3 Ik l 475 7 Men 21 27 129 12 Muluc l 60 303 4 Akbal l 36/52 476 8 Cib ll 22 11 130 13 Oc l 304 5 Kan 477 9 Caban 23 69 131 1 Chuen l 44 305 6 Chicchan l 19 478 10 Eznab l 24 132 2 Eb 28 306 7 Cimi l 479 11 Cauac 25 53 133 3 Ben l 12 307 8 Manik l 3 480 12 Ahau l 25 134 4 Ix 308 9 Lamat 61 481 13 Imix l 27 20/37 135 5 Men ll 70 309 10 Muluc l 45 482 1 Ik l 28 4 136 6 Cib l 54 310 11 Oc l 483 2 Akbal 29 137 7 Caban 38 311 12 Chuen l 13/29 484 3 Kan ll 30 63 138 8 Eznab l 312 13 Eb 72 485 4 Chicchan l 31 47 139 9 Cauac l 22 313 1 Ben l 32 31 140 10 Ahau l 6 314 2 Ix l
26 25 24
80
APPENDIX H MEEUS SOLAR SEASON DISTRIBUTION
81 Meeus Solar 2003 P1 Season 1 Season 2 Season 3 Num Day Tzolkin Num Day Tzolkin Num Day Tzolkin
1 110 6 Oc l 282 9 Ik l 457 2 Caban l 2 111 7 Chuen 283 10 Akbal 458 3 Eznab 3 112 8 Eb l 284 11 Kan l 459 4 Cauac ll 4 113 9 Ben l 285 12 Chicchan l 460 5 Ahau l 5 114 10 Ix l 286 13 Cimi l 461 6 Imix 6 115 11 Men l 287 1 Manik 462 7 Ik l 7 116 12 Cib 288 2 Lamat l 463 8 Akbal l 8 117 13 Caban l 289 3 Muluc l 464 9 Kan l 9 118 1 Eznab l 290 4 Oc l 465 10 Chicchan 10 119 2 Cauac l 291 5 Chuen 466 11 Cimi l 11 120 3 Ahau 292 6 Eb l 467 12 Manik l 12 121 4 Imix l 293 7 Ben ll 468 13 Lamat l 13 122 5 Ik l 294 8 Ix 469 1 Muluc 14 123 6 Akbal l 295 9 Men l 470 2 Oc l 15 124 7 Kan l 296 10 Cib 471 3 Chuen l 16 125 8 Chicchan 297 11 Caban ll 472 4 Eb l 17 126 9 Cimi l 298 12 Eznab 473 5 Ben 18 127 10 Manik l 299 13 Cauac l 474 6 Ix l 19 128 11 Lamat l 300 1 Ahau 475 7 Men l 20 129 12 Muluc 301 2 Imix ll 476 8 Cib l 21 130 13 Oc l 302 3 Ik l 477 9 Caban l 22 131 1 Chuen l 303 4 Akbal 478 10 Eznab 23 132 2 Eb l 304 5 Kan l 479 11 Cauac l 24 133 3 Ben 305 6 Chicchan 480 12 Ahau l 25 134 4 Ix l 306 7 Cimi ll 481 13 Imix l 26 135 5 Men l 307 8 Manik 482 1 Ik l 27 136 6 Cib l 308 9 Lamat l 483 2 Akbal 28 137 7 Caban l 309 10 Muluc 484 3 Kan l 29 138 8 Eznab 310 11 Oc ll 485 4 Chicchan l 30 139 9 Cauac ll 311 12 Chuen 486 5 Cimi l 31 140 10 Ahau 312 13 Eb l 487 6 Manik
24 24 24
82
APPENDIX I TEEPLE SEASON DISTRIBUTION
83
Table 755 Teeple P1 Season 1 Season 2 Season 3 Num Day Tzolkin Num Day Tzolkin Num Day Tzolkin
1 62 10 Ik l 236 2 Cib l 409 6 Muluc l 2 63 11 Akbal 237 3 Caban 410 7 Oc 3 64 12 Kan 238 4 Eznab l 411 8 Chuen 4 65 13 Chicchan l 239 5 Cauac l 412 9 Eb ll 5 66 1 Cimi l 240 6 Ahau 413 10 Ben l 6 67 2 Manik l 241 7 Imix 414 11 Ix 7 68 3 Lamat 242 8 Ik l 415 12 Men l 8 69 4 Muluc l 243 9 Akbal l 416 13 Cib l 9 70 5 Oc l 244 10 Kan l 417 1 Caban 10 71 6 Chuen l 245 11 Chicchan 418 2 Eznab l 11 72 7 Eb l 246 12 Cimi l 419 3 Cauac l 12 73 8 Ben 247 13 Manik 420 4 Ahau l 13 74 9 Ix l 248 1 Lamat l 421 5 Imix 14 75 10 Men 249 2 Muluc ll 422 6 Ik l 15 76 11 Cib ll 250 3 Oc 423 7 Akbal l 16 77 12 Caban 251 4 Chuen l 424 8 Kan 17 78 13 Eznab l 252 5 Eb 425 9 Chicchan l 18 79 1 Cauac l 253 6 Ben l 426 10 Cimi ll 19 80 2 Ahau l 254 7 Ix l 427 11 Manik 20 81 3 Imix 255 8 Men l 428 12 Lamat l 21 82 4 Ik l 256 9 Cib l 429 13 Muluc 22 83 5 Akbal l 257 10 Caban l 430 1 Oc l 23 84 6 Kan l 258 11 Eznab 431 2 Chuen l 24 85 7 Chicchan l 259 12 Cauac l 432 3 Eb l 25 86 8 Cimi 260 13 Ahau l 433 4 Ben l 26 87 9 Manik l 261 1 Imix l 434 5 Ix l 27 88 10 Lamat l 262 2 Ik l 435 6 Men 28 89 11 Muluc l 263 3 Akbal 436 7 Cib l 29 90 12 Oc l 264 4 Kan l 437 8 Caban l 30 91 13 Chuen 265 5 Chicchan 438 9 Eznab 31 92 1 Eb 266 6 Cimi l 439 10 Cauac l 32 93 2 Ben l 267 7 Manik 440 11 Ahau 33 94 3 Ix 268 8 Lamat 441 12 Imix 34 269 9 Muluc l 442 13 Ik 35 270 10 Oc l 443 1 Akbal l 22 24 24
84
APPENDIX J SOLAR-LUNAR SEASON DISTRIBUTION
85
Meeus Lunar AND Solar 2003 Season 1 Season 2 Season 3
282 9 Ik S 1 109 5 Muluc L 283 10 Akbal LS 456 1 Cib L 2 110 6 Oc LS 284 11 Kan LS 457 2 Caban S 3 111 7 Chuen L 285 12 Chicchan LS 458 3 Eznab L 4 112 8 Eb S 286 13 Cimi S 459 4 Cauac LSS 5 113 9 Ben LLS 287 1 Manik L 460 5 Ahau LS 6 114 10 Ix LS 288 2 Lamat LS 461 6 Imix 7 115 11 Men S 289 3 Muluc LS 462 7 Ik LS 8 116 12 Cib L 290 4 Oc S 463 8 Akbal LS 9 117 13 Caban S 291 5 Chuen L 464 9 Kan LS 10 118 1 Eznab LLS 292 6 Eb S 465 10 Chicchan L 11 119 2 Cauac S 293 7 Ben LLSS 466 11 Cimi S 12 120 3 Ahau L 294 8 Ix L 467 12 Manik LS 13 121 4 Imix LS 295 9 Men S 468 13 Lamat LS 14 122 5 Ik LS 296 10 Cib L 469 1 Muluc LS 15 123 6 Akbal LS 297 11 Caban LSS 470 2 Oc LS 16 124 7 Kan S 298 12 Eznab L 471 3 Chuen LS 17 125 8 Chicchan L 299 13 Cauac S 472 4 Eb LS 18 126 9 Cimi S 300 1 Ahau L 473 5 Ben L 19 127 10 Manik LL 301 2 Imix LSS 474 6 Ix LS 20 128 11 Lamat S 302 3 Ik LS 475 7 Men S 21 129 12 Muluc L 303 4 Akbal L 476 8 Cib LS 22 130 13 Oc LS 304 5 Kan S 477 9 Caban LS 23 131 1 Chuen LS 305 6 Chicchan L 478 10 Eznab L 24 132 2 Eb S 306 7 Cimi LSS 479 11 Cauac S 25 133 3 Ben L 307 8 Manik L 480 12 Ahau LS 26 134 4 Ix S 308 9 Lamat S 481 13 Imix LS 27 135 5 Men LLS 309 10 Muluc L 482 1 Ik LS 28 136 6 Cib LS 310 11 Oc LSS 483 2 Akbal 29 137 7 Caban S 311 12 Chuen L 484 3 Kan LLS 30 138 8 Eznab L 312 13 Eb S 485 4 Chicchan LS 31 139 9 Cauac LSS 313 1 Ben L 486 5 Cimi S 32 140 10 Ahau L 314 2 Ix L
86
APPENDIX K TABLE SIMULATION
87 Lunar Eclipse 755 P 1 Year Month Day Julian Interval Page 148 First Second
1 177 177.85 177.85 177.85 2 177 176.59 176.59 176.59 3 148 147.98 177.6 147.98 4 177 29.62 147.58 177.2 5 177 147.58 176.86 176.86 6 177 53 176.86 177.7 177.7 7 177 177.7 176.61 176.61 8 177 176.61 177.69 177.69 9 177 177.69 176.9 176.9 10 177 176.9 177.13 177.13 11 177 177.13 148.22 148.22 12 177 148.22 176.17 176.17 13 148 54 176.17 178.33 178.33 14 177 178.33 176.11 176.11 15 177 176.11 178.09 178.09 16 177 178.09 176.57 176.57 17 177 176.57 177.42 177.42 18 177 55 177.42 177.28 147.93 19 148 147.93 147.18 176.53 20 177 29.35 177.87 177.87 21 177 147.18 176.63 176.63 22 177 56 177.87 177.48 177.48 23 178 176.63 177.17 177.17 24 177 177.48 176.87 176.87 25 177 177.17 177.73 177.73 26 177 57 176.87 176.52 147.12 27 177 177.73 148.15 177.55 28 177 147.12 177.08 177.08 29 177 29.4 176.91 176.91 30 177 58 148.15 177.79 177.79 31 177 177.08 176.27 176.27 32 177 176.91 178.3 178.3 33 177 177.79 176.07 176.07 34 177 176.27 148.51 148.51 35 177 178.3 176.78 176.78
88 Lunar Eclipse 755 P 2 Month Day Julian Interval
36 148 51 176.07 177.19 177.19 37 177 148.51 177.48 177.48 38 177 176.78 176.67 176.67 39 177 177.19 177.79 177.79 40 177 52 177.48 176.66 176.66 41 177 176.67 177.51 147.89 42 148 177.79 147.68 177.3 43 177 176.66 176.77 176.77 44 177 147.89 177.78 177.78 45 177 53 29.62 176.55 176.55 46 177 147.68 177.73 177.73 47 177 176.77 176.88 176.88 48 177 177.78 177.13 177.13 49 148 176.55 148.23 148.23 50 177 54 177.73 176.16 176.16 51 177 176.88 178.34 178.34 52 177 177.13 176.11 176.11 53 177 148.23 178.07 178.07 54 177 176.16 176.59 176.59 55 177 178.34 177.4 177.4 56 177 176.11 177.29 147.92 57 177 178.07 147.21 176.58 58 148 55 176.59 177.8 177.8 59 177 177.4 176.72 176.72 60 177 147.92 177.38 177.38 61 177 29.37 177.27 177.27 62 177 56 147.21 176.77 176.77 63 177 177.8 177.82 177.82 64 177 176.72 176.45 147.06 65 148 177.38 148.18 177.57 66 177 177.27 177.08 177.08 67 177 57 176.77 176.91 176.91 68 177 177.82 69 177 147.06 29.39 148.18 177.08 176.91
89
APPENDIX L GLOSSARY
90 Ah Tzul Ahau A name given to a cannibal monster that descended to earth during eclipses. This monster is similar to the Mexican Tzitzimine Monster.
Ahau Constant A number that is added to the Maya Day Count that equals the Julian Date.
Ahau Date The last day of the year is always Ahau. The number associated with this date identifies the Katun. If the date is 4 Ahau then the year is identified as a 4 Katun Ahau.
Arcs Three areas where the eclipses dates group, when placed within the Double Tzolkin. Also called danger windows, and eclipse seasons.
Baktun A period equal to 20 Katuns or 144,000 days.
Calendar Round A period combining the Tzolkin and Haab. This is a period of 18,980 days. The period is 52 years or 73 Tzolkins.
Copán Method A lunar period of 149 moons. The ratio of 149 moons to 4,400 days is the basis for the statement of the extreme accuracy of the Maya Calendar.
Conjunction The place of new moon.
Correlation An attempt to synchronize the Maya calendar with the Julian and Gregorian calendars.
Draconic Month The time the moon reaches the same node again 27.212 days. It is less than the sidereal month due to the westerly drift of the node.
Dresden Codex One of three surviving hieroglyphic texts believed to contain astronomical data.
Eclipse The darkening of the sun or moon caused by the shadows produced by the alignment of the earth, sun and moon.
Eclipse Table The chart on pages 51 – 58 of the Dresden Codex. The Table is 11,960 Days 1.13.4.0, 405 lunations, 3 Tritos periods or 46 tzolkins in length.
91 Eclipse Window An area, measured in angular distance around the node where eclipses can occur. This window produces a 148-day period with a corresponding eclipse, one lunation later.
Ecliptic The plane containing the earth and sun.
Ephemeris An astronomical almanac or table of the predicted position of celestial bodies.
Glyph A A part of the Supplementary Series denoting whether the month is twenty-nine or thirty days in length.
Glyph C A part of the supplementary Series that denotes one of six lunar periods. If Glyph A is even, Glyph C is usually odd, if Glyph A is odd, then Glyph C is usually even.
GMT (Goodman-Martinez-Thompson) The most widely accepted Ahau Constant of 584285 days.
Haab The Maya calendar of 365 days produced by the combination of one of 18 numbers and 20 month names, plus the xma-kaba-kin, which are the five unlucky days at the end of the year.
Inex An eclipse period of 358 lunations or 29 years or 10,561 days. This period separates Saros families.
Julian Date A calendar produced by Joseph Scalinger that begins on the date B.C.. January 1, 4713. It is the result of the 12-year solar cycle, the 19-year lunar cycle and the 28-year civil cycle.
Katun A period of 20 Tuns or 7,200 days.
Kin A period equal to one day.
Long Count Also called the Initial Series. This is a count of days from the Maya Calendar Round date of 4 Ahau 8 Cumhu. It is made up of the Baktun, Katun, Tun, Uinals, and Kins.
92 Lunation A lunar period of 29.5 days.
Maya Date The count of days produced by the Maya Long Count.
Mean-value A period of 173.31 days that determines the Nodal Passage.
Meton An eclipse period of 235 lunations or 19 years. Besides eclipses, the Meton is also used to calculate new and full moons. It is 6,940 (19.5.0) days.
Nodal Passage The area in the mean-value system where the eclipses can occur.
Nodes The two places were the moon crosses the ecliptic (one for solar and another for lunar eclipses). The nodes are not static but move producing the 148-day eclipses.
Non-Central Eclipses Eclipses where the center line of the eclipse angle does not intersect the earth. These occur in the Polar Regions.
Opposition The place of the full moon.
Palenque Method A period of 81 moons to 2,396 (6.11.12) days. It is not an eclipse period but may be associated with Venus.
Perigee The point in the earth’s orbit nearest the sun.
Penumbra The light outer portion of the eclipse shadow.
Period of Uniformity A brief 70-year period where all of the lunar data agrees at different sites.
Popol Vuh The Maya book of creation.
Saros A period of 223 lunations or 18 years. It is a period of 6,585 (18.5.5) days.
Semester A period of six lunation of alternating twenty-nine and thirty days.
Sideral Period A period of 27. 3216 days. This is the period of the moon requires to return to the same point in its orbit relative to the stars.
93 Short Count A method of identifying the Calendar Round according to the ending Ahau date.
Supplementary Series Also called the Lunar Series because of its lunar information. The glyphs are located between the Calendar Round date written in reverse order.
Synodic Period A period of 29.5305 days. This is the period the moon requires to return to the same phase.
Sysygy A list of eclipses.
Tritos A eclipse period of 135 lunations or 3,986.days (11.1.6).
Tzolkin Also known as the Sacred Calendar, A period of 260 days created by a combination of one of thirteen numbers and one of the twenty day names.
Tun A period of eighteen Uinals or 360 days.
Uayeb Another name for the five unlucky days.
Uinal A period of 20 kins or days.
Umbra The inner, darker portion of the eclipse shadow.
Vigesimal A number system based on the number twenty.
Xma-Kaba-Kin The five unlucky days at the end of the year.
94 LIST OF REFERENCES
Andrews, E. Wyllys IV 1951 The Maya Supplemental Series. 29th International Congress of Americanists, pp. 123- 141. 1940 Chronology and Astronomy in the Maya Area. In Maya and Their Neighbor, pp. 159- 535. D. Appleton-Century, New York.
Aveni, Anthony F. 1992 Introduction: Making Time. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 3-17. Oxford University Press, New York. 1992a The Moon and the Venus Table: An Example of Commensuration in the Maya Calendar. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 87-101. Oxford University Press, New York. 1986 The Real Kukulacan in Maya Inscriptions and Alignments. In Sixth Palenque Round Table. edited by Merle Greene Robertson, pp. 309-321. University of Oklahoma Press, Norman. 1981 Old and New World Naked-eye Astronomy. In Astronomy of the Ancients, edited by Kenneth Brecher and Michael Feirtag, pp. 61-89. MIT Press, Cambridge.
Baudez, Claude-Francois 1994 Maya Sculpture of Copán: The Iconography. University of Oklahoma Press, Norman.
Belmont, G. E. 1935 The Secondary Series as a Lunar Eclipse Count. Maya Research 2:144-153.
Berlin, Heinrich 1943 Notes on Glyph C of Lunar Series at Palenque. Notes on Middle American Archaeology 79 No. 24, pp. 156-159. Carnegie Institute of Washington, Washington D.C.
Beyer, Hermann 1937 Lunar Glyphs of the Supplemental Series at Piedras Negras. El Mexico Antiguo 4 :75-82. 1935 On the Correlation Between Maya and Christian Chronology. Maya Research 2(1):64-72. 1933 The Relation of the Synodical Month and Eclipses to the Maya Correlation Problem. In Middle American Research Series number 6 of Publication 5, pp 305-319. Middle American Research Institute, Tulane University, New Orleans.
Bowditch, Charles P. 1910 The Numeration, Calendar Systems and Astronomical Knowledge of the Mayas. University Press, Cambridge.
95
Bricker Harvey M. and Victoria R. Bricker 1983 Classic Maya Predictions of Solar Eclipses. Current Anthropology 24(1):1-23.
Bricker Victoria and Harvey Bricker 1986 Archaeoastronomical Implications of an Agricultural Almanac in the Dresden Codex. Mexicon 8(2):29-35. 1986a Astronomical References in the Table on Page 61-69 of the Dresden Codex. In World Archaeoastronomy: selected papers from the 2nd Oxford International Conference on Archaeoastronomy, held at Merida, Yucatan, Mexico, 13-17 January, 1986, edited by Anthony F. Aveni, pp. 232-245. Cambridge University Press, Cambridge.
Campbell, Paul Douglas 1992 Astronomy and the Maya Calendar Correlation. Aegean Park Press, Laguana Hills Ca.
Carlson John B. 1984 The Nature of Mesoamerican Astronomy: A Look at the Native Texts. In Archaeoastronomy and the Roots of Science, edited by E. C. Krupp, pp. 211-252. Published by Westview Press for the American Association for the Advancement of Science, Boulder, Colorado. 1977 Copán Altar Q: The Astronomical Congress of A.D. 763? In Native American Astronomy, edited by Anthony F. Aveni, pp. 100-109. University of Texas Press, Austin.
Chambers, David 1965 Did the Maya know the Metonic Cycle? Isis 56(3):348-351.
Closs, Michael P. 1992 Some Parallels in the Astronomical Events Recorded in the Maya Codices and Inscriptions. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 133-147. Oxford University Press, New York. 1989 A Glyph for Venus as Evening Star. In Seventh Palenque Round Table. edited by Merle Greene Robertson, pp. 229-236. Pre-Colombian Art Research Institute, San Francisco. 1986 Cognitive Aspects of Ancient Maya Eclipse Theory. In World Archaeoastronomy: selected papers from the 2nd Oxford International Conference on Archaeoastronomy, held at Merida, Yucatan, Mexico, 13-17 January, 1986, edited by Anthony F. Aveni, pp.389-415. Cambridge University Press, Cambridge. 1978 Venus in the Maya World: Glyph, Gods and Associated Astronomical Phenomena. In Tercera Mesa Redonda de Palenque, edited by Merle Greene Robertson, pp. 347-365. Pre-Colombian Art Research Institute, San Francisco.
Crommelin A.C.D. 1901 The 29-Year Eclipse-Cycle. The Observatory 379-382.
96 Everson, George Dicken 1995 The Celestial Dresden: Archaeoastronomy in Late Post-Classic Yucatan. University of California, Riverside.
Förstemann, Ernst 1967 [1906] Maya Chronology. Peabody Museum of American Archaeology. Cambridge. Reprinted. Kraus Reprint Corporation, New York.
Freidel, David, Linda Schele & Joy Parker 1993 Maya Cosmos: Three Thousand Years on the Shaman's Path. Morrow and Company, New York.
Gates, William E. 1932 Dresden Codex. Maya Society at the Johns Hopkins University, Baltimore.
Gibbs, Sharon L. 1977 Mesoamerican Calendrics as Evidence of Astronomical Activity. In Native American Astronomy, edited by Anthony F. Aveni, pp. 21-35. University of Texas Press, Austin.
Guthe, Carl E. 1978 [1921] A Possible Solution to the Number Series on Pages 51 to 58 of the Dresden Codex. Peabody Museum of American Archaeology. Cambridge. Reprinted. Kraus Reprint Corporation, New York. 1932 The Maya Lunar Count. Science 75(1941):271-277.
Hofling, Charles A. and Thomas O’Neil 1992 Eclipse Cycles in the Moon Goddess Almanacs in the Dresden Codex. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 102-132. Oxford University Press, New York.
Jakeman, M. Wells 1947 The Ancient Middle-American Calendar System: Its Origin and Development. Brigham Young Publications in Archaeology and Early History 1, Provo.
Juteson, John S. 1986 Ancient Maya Ethonoastronomy: An Overview of Hieroglyphic Sources. In World Archaeoastronomy: selected papers from the 2nd Oxford International Conference on Archaeoastronomy, held at Merida, Yucatan, Mexico, 13-17 January, 1986, edited by Anthony F. Aveni, pp. 8-129. Cambridge University Press, Cambridge.
Kelly, David H. 1977 Maya Astronomical Tables & Inscriptions. In Native American Astronomy, edited by Anthony F. Aveni, pp. 57-73. University of Texas Press, Austin. 1976 Deciphering the Maya Script. University of Texas Press, Austin.
97
Kelly, David and K. Ann Kerr 1973 Mayan Astronomy and Astronomical Glyphs. In Mesoamerican Writing Systems: A Conference at Dumbarton Oaks, October 30th and 31st, 1971, edited by Elizabeth Benson, pp. 179-215. Dumbarton Oaks Research Library and Collections, Washington, D.C.
Knowlton, Timothy 2003 Seasonal Implications of Maya Eclipse and Rain Iconography in the Dresden Codex. Journal for the History of Astronomy 34(3) 116: 291-303.
Konnen, G.P. and Jean Meeus 1976 Periodicities of Eclipses. Journal of the Royal Astronomical Society of Canada 70(2):81- 83.
Landa, Diego de 1978 Yucatan Before and After the Conquest: Translated with Notes by William Gates. Dover Publications, New York.
Linden, John H. 1986 Glyph X of the Maya Lunar Series: An Eighteen-Month Lunar Synodic Calendar. American Antiquity 51(1):122-136.
Liu, Bao-Lin and Alan D. Fiala 1992 Canon of Lunar Eclipses 1500 B.C. – A.D. 3000. Willmann-Bell, Richmond.
Long, Richard C.E. 1925 Some Maya Time Periods. 21st International Congress of Americanists 574-589. 1921 The Setting in Order of Pop in the Maya Calendar. Man 21:37-40.
Lounsbury, Floyd G. 1992 A Derivation of the Mayan to Julian Calendar Correlation from the Dresden Codex Venus Chronology. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 184- 206. Oxford University Press, New York. 1978 Maya Numeration, Computation and Calendrical Astronomy. In Dictionary of Scientific Bibliography Volume XV Supplement I, edited by Charles Coulston Gillispie, pp. 759-818. Charles Scribner’s Sons, New York.
MacPherson, H.G. 1987 The Maya Lunar Season. Antiquity 61(233):440-449.
Magini, Leonardo 2001 Astronomy and Calendar in Ancient Rome: The Eclipse Festivals. Erma di Bretschneider, Roma.
98 Makemson, Maud W. 1943 The Astronomical Tables of the Maya. Carnegie Institute of Washington 546 contr. 42. Washington D.C.
Malmstrom, Vincent H. 1997 Cycles of the Sun, Mysteries of the Moon: The Calendar in Mesoamerican Civilization. University of Texas Press, Austin.
Marci, Marthe J. and D. Beattie, 1996 The Lunar Cycle and the Mesoamerican Counts of Twenty, Nine and Seven. Carolina Academic Press. Durham.
Martin, Frederick 1993 A Dresden Codex Eclipse Sequence: Projections for the Years 1970-1992. Latin American Antiquity 4(1):74-93.
Martinez-Hernandez, Juan 1928 The Mayan Lunar Table. 23rd International Congress of Americanist. pp. 149-154.
McGee, W. J. 1892 Comparative Chronology. American Anthropologist 5(4):327-344.
Meeus, Jean, 1997 Mathematical Astronomy Morsels. Wilmann-Bell, Richmond.
Meeus, Jean, and Hermann Mucke 1979 Cannon of Lunar Eclipses -2002 to + 2526. Astronomisches Buro, Wein.
Meeus, Jean, Carl C. Grosjean and Willy Vandreleen 1966 Cannon of Solar Eclipses. Pergamon Press, New York.
Meinhausen, Martin 1913 Uber Sonnen und Mondfinsternisse in der Dresdener Mayahandschrift. Zetschrift fur Ethnologie 45:221-227.
Merrill, Robert 1949 The Maya Eclipse Table of the Dresden Codex: A Reply. American Antiquity 14(3):228-230. 1946 A Graphic Approach to Some Problems in Maya Astronomy. American Antiquity 12(1):35-46.
Milbrath, Susan 1999 Star Gods of the Maya: Astronomy in Art, Folklore, and Calendars. University of Texas Press, Austin.
99 Miles, Suzanna.W. 1952 An Analysis of Modern Middle American Calendars. 29th International Congress of Americanists. pp. 273-284.
Morley, Sylvanus Griswold 1977 The Maya Supplementary Series in the Maya Inscriptions. In Holmes Anniversary Volume. 1916. Reprint, Cambridge: Peabody Museum. 1940 Maya Epigraphy. In The Maya and Their Neighbors, pp. 139-149. D. Appleton-Century, New York. 1920 Inscriptions of Copán. Carnegie Institution of Washington, Washington D.C. 1915 An Introduction to the Study of the Maya Hieroglyphs. Bureau of American Ethnology Bulletin 57.
Moyer, Gordon 1982 The Gregorian Calendar. Scientific American 246(5):144-152.
Oppolzer, Theodor Ritter von 1962 [1887] Cannon der Finsternisse Translated by Owen Gingerich. Reprinted. Dover Publications, NewYork.
Owen, Nancy Kelly 1975 The Use of Eclipse Data to Determine the Maya Correlation Number. In ArchaeoAstronomy in Pre-Columbian America, pp. 237-246. University of Texas Press, Austin.
Pannekoek Anton 1961 A History of Astronomy. George Allen and Unwin, London.
Pauahtun.org http://www.pauahtun.org/Calendar/tools.html accessed 4/20/2007.
Pogo, Alexander 1937 Maya Astronomy. Carnegie Institute of Washington Yearbook 36:158-159.
Ramano, Guiliano 1999 The Moon in the Classic Maya World. Earth, Moon and Planet 85(1/3) 557-560.
Roys, Lawrence 1945 Moon Age Tables. Notes on Middle American Archaeology and Ethnology no. 50. pp 159-169.AMS Press, New York. 1933 The Maya Correlation Problem Today. American Anthropologist 35(3):403-417.
Sadler, D.H. 1966 Predictions of Eclipses. Nature 211:1119-1121.
100 Saros Prediction www.astro.uu.nl/~strous/AA/en/saros.html accessed 4/20/2007.
Satterthwaite, Linton 1962 An Appraisal of a New Maya-Christian Calendar Correlation. Estudios de Cultura Maya 2:251-275. 1959 Early Uniformity Maya Moon Numbers at Tikal and Elsewhere. 33rd International Congress of Americanist. pp. 200-210. 1951 Moon Ages of the Mayan Inscriptions: the Problem of their Seven-day Range of Deviation from Calculated Mean Ages. 29th International Congress of Americanists. pp. 142- 154. 1949 The Dark Phase of the Moon and Ancient Methods of Solar Eclipse Prediction. Antiquity 14(3):230-234. 1948 Note on the Maya Eclipse Table of the Dresden Codex. American Antiquity 14(1):61-62. 1947 Concepts and Structures of Maya Calendrical Arithmetics. Museum of University of Pennsylvania, Philadelphia.
Schove, Derek Justin 1984 Chronology of Eclipses and Comets AD 1-1000. Boydell Press, Dover. 1984a Maya Correlations, Moon Ages and Astronomical Cycles. Journal for the History of Astronomy 15(1) 42:18-29. 1982 Maya Eclipses and the Correlation Problem. Estudios de Cultura Maya 14:241-260.
Schram Robert 1908 Kalendaiographische und Chronologische Taflin. J.C. Hinrichs, Leipzig.
Smiley, Charles H. 1975 The Solar Eclipse Warning Table in the Dresden Codex. In ArchaeoAstronomy in Pre- Columbian America, edited by Anthony F. Aveni, pp. 237-246. University of Texas Press, Austin. 1975a A Note on the Periodicity of Eclipses. Journal of the Royal Astronomical Society of Canada 69(3):133-135. 1973 The Thix and the Fox, Mayan Solar Eclipse Intervals. Journal of the Royal Astronomical Society of Canada 67(4):175-182.
Smiley, Charles H. and Fred F. Czarnec 1961 Paths of Solar Eclipses. Journal of the Royal Astronomical Society of Canada 55:211- 217. Smither, Robert K. 1986 The 88 Lunar Month Pattern of Solar and Lunar Eclipses and Its Relation to the Calendars. Archaeoastronomy 9(1-4):99-113.
101 Spinden, Herbert J. 1977 [1916] The Maya Supplementary Series in the Maya Inscriptions. In Holmes Anniversary Volume. Peabody Museum Cambridge. Reprinted. Kraus Reprint Corporation, New York. 1969 [1924] The Reduction of Maya Dates. Peabody Museum of Archaeology and Ethnology vol. 6 n 4. Peabody Museum. Cambridge. Reprinted. Kraus Reprint Corporation, New York. 1930 Maya Dates and What They Reveal. Brooklyn Institute of Arts and Sciences 4(1), Brooklyn. 1928 Maya Inscriptions Dealing with Venus and the Moon. Bulletin of the Buffalo Society of Natural Sciences 14:1-59. Buffalo. 1928a The Eclipse Table of the Dresden Codex. 23rd International Congress of Americanist. pp.140-148.
Stockwell, John N. 1901 Eclipse-Cycles. The Astronomical Journal 21(24):185-191.
Tedlock, Dennis 1996 Popol Vuh: The Definitive Edition of the Mayan Book of the Dawn of Life and the Glories of Gods and Kings. Simon and Shuster, New York. 1992 Myth, Math and the Problem of Correlation in Mayan Books. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 247-273. Oxford University Press, New York.
Tedlock, Barbara 1992 Road of Light: Theory and Practice of Mayan Skywatching. In The Sky in Maya Literature, edited by Anthony F. Aveni, pp. 18-42. Oxford University Press, New York.
Teeple, John E. 1930 Maya Astronomy. Carnegie Institute of Washington, Washington, D.C. 1930a Factors that May Lead to a Correlation of the Maya and Christian Calendar. 23rd International Congress of Americanists, pp. 136-139. 1928 Maya Inscription VI: The Lunar Calendar and Its Relation to Maya History. American Anthropologist 30(3):391-407. 1925 Maya Inscriptions: Further Notes on the Supplementary Series. American Anthropologist 27(4):544-549. 1925a Maya Inscriptions: Glyphs C, D and E of the Supplementary Series. American Anthropologist 27(1):108-115.
Thompson, John Eric Sidney 1975 Maya Hieroglyphic Writing. Third Edition, University of Oklahoma Press, Norman. 1972 A Commentary the Dresden Codex: A Maya Hieroglyphic Book. American Philosophical Society, Philadelphia. 1966 The Rise and Fall of Maya Civilization. University of Oklahoma Press, Norman. 1939 The Moon Goddess in Middle America, with Notes on Related Deities. Carnegie Institute of Washington, Washington D.C.
102
Van Den Bergh, George 1955 Periodicity and Variation of Solar (and Lunar) Eclipses. Tjeenk Willink, Haarlem, Netherlands.
Villacorta J. Antonio and Carlos A. Villacorta 1976 Codices Mayas. Segunda Edicion. Dela Sociedad de Geogrfia e Historia de Guatemala, C. A., Guatemala.
Weitzel, Robert B. 1935 Maya Moon Glyphs and New Moons. Maya Research 2(1):14-23.
Willson, Robert W. 1974 [1924] Astronomical Notes on the Maya Codices. Peabody Museum of Archaeology and Ethnology Vol VI n 3. Peabody Museum, Cambridge. Reprinted. Kraus Reprint Corporation, New York.
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