### An Observation on Correlating the Mesoamerican and European Calendars

Never does the complexity of correlating the "Maya" calendar with our own become more
apparent than when we try to pin down a particular event in time such as an eclipse. This is because
the days of our calendar have their beginning and end at midnight on the Greenwich Meridian and
the new day moves progressively eastward around the world at the rate of 15º of longitude for
every hour. Thus, Copán, Honduras, near longitude 90º W., is six clock hours behind Greenwich,
so when it is midnight in London, it is 6 PM the previous day in Honduras.

The fact that the Olmecs and the Maya reckoned the beginning and end of their days from
sunset meant, in effect, that as a Christian day was beginning at midnight local time in London, a
new day was also beginning at sunset local time in Mesoamerica. However, what might have
seemed like a convenient coincidence between the two time-counts was, in fact, complicated by
the manner in which each of the two cultures did their counting. The Europeans assigned a new
number to a day as it began, whereas the Mesoamericans did not give a number to a day until it had
been completed. Moreover, the Europeans began their count with "1", whereas the Mesoamericans
started theirs with "0". When we argue that Thompson's initial correlation value of 584,285 is the
correct one to employ, it is because it does indeed mark the beginning of the Maya time-count on a
day they numbered as "0", although it was actually Julian day # 584,286 that coincided with the
day the Maya numbered as "1".

Although the concept of the Julian day was intended to simplify astronomical mathematics --
and does so in most cases -- when it comes to correlating the Mesoamerican and Christian calendars,
it adds an unintended further complication. This is because the Julian day has its beginning and end
in London, not at midnight like a new calendar day, but at noon, in the middle of a given calendar
day. This means that any celestial event which takes place between midnight and noon London time
(that is, between sunset and sunrise Mesoamerican time, when most lunar eclipses visible in that
part of the world would occur) will correlate quite nicely with the Thompson's initial value of
584,285, whereas any event occurring between noon and midnight London time (in other words,
between sunrise and sunset Mesoamerican time, when most solar eclipses visible in that part of
the world would be expected to take place) will correlate instead with a value of 584,286.

Looking at the specifics of the lunar eclipse which was recorded on numerous structures at Copán
late in the month of June in the year 763 -- an event which Morley first characterized as "an
astronomical congress" -- we find the following: the Christian day June 28, 763 began at midnight
in London on what was then Julian day # 1999921. At the same moment, the sun was just going
down in Honduras, completing Maya day # 1415635. At noon London time on June 28, a new
Julian day began -- number 1999922 -- in the middle of which the sun set in Honduras, ending
Maya day # 1415636. Since it was now midnight in London, a new calendar day -- June 29 was
just beginning and Maya day # 1415637 had also gotten started. At noon London time on June 29,
Julian day # 1999923 began and twelve hours later -- at midnight London time, calendar day
June 30 commenced. Over in Honduras the sun had still 26 minutes before it would set on the
western horizon. However, five minutes before it disappeared, the darkened full moon rose over
the eastern horizon, giving the Maya sky-watcher cause to record its eclipse as having occurred on
Maya day # 1415637, even though it did not reach its culmination until about 40 minutes later but
still within the lingering twilight of the previous day. In the Western world the mid-point of the
eclipse was recorded at having taken place at 1:10 Universal Time on June 30, 763, or 7:10 PM
local time on June 29 in Honduras. Although the culmination of the eclipse came on Julian day #
1999923.55, Oppolzer, in keeping with standard astronomical practice, assigned Julian day #
1999924 to the event because it was at noon on June 30 that the new Julian day began.

One of the clearest correlations between a solar eclipse and a Maya calendrical inscription is that
recorded on Stela 3 found at Santa Elena Poco Uinic in Chiapas, Mexico. First mentioned in a
footnote to his paper Maya Astronomy in 1931 by John Teeple, it is also discussed by Floyd
Lounsbury in a footnote to his article published in 1978. Bearing a Long Count date of
9.17.19.13.16. 5 Cib 14 Chen, which is Maya day # 1425516, this inscription most likely records
the total solar eclipse whose path of centrality passed directly over this location at 12:48 P.M.
local time -- an event tabulated as number 4768 in Oppolzer's compendium and which he records
as having occurred on July 16, 790 (Julian day # 2009802). It is obvious that in this instance the
difference between the Maya and Julian counts amounts to 584,286 days, a fact which caused
Lounsbury some puzzlement because, although he found Thompson's original correlation of
584,285 more accurate than he did Thompson's revised value of 584,283, here the two day-counts
differed by an additional day. Had he understood that the Maya day began and ended at sunset, as
explained above, he would have realized that both Thompson's initial value (i.e., 584,285) and
that implied by the inscription at Santa Elena Poco Uinic (584,286) are perfectly correct.

(Note that references for this and the other papers are found on the 'home page' of this article.)