398 
The splendid structure at Dzibilno- 
cac was built, I think, to celebrate 
this concordance and the opening of 
Venus Calendar A featured in the 
Dresden Codex. Carried back to its 
beginning, the year is O Pop at sunset 
December 21, 574 B. C. The Venus 
dates also repeat at 6X251=1,506 
tropical years. 
The Tropical Year 
We think of the tropical year as 
something in nature which compels 
us to correct our calendar by inserting 
extra days. For the Maya, the tropi- 
cal year was one of several natural 
cycles equally deserving of attention. 
To measure all these without fear or 
favor, days were numbered, named, 
and given places in the 365-day 
calendar which in itself could not be 
amended. In this way the Maya, long 
before the time of Christ, obtained the 
same kind of control over diverse 
phenomena that Scaliger gave to 
European historians and astronomers 
in his Julian Period and Julian Day. 
The Maya calculated rather closely 
the recession of 365 days from a tropi- 
cal year of approximately 365.2423 
days, corresponding to about A. D. 
ANNUAL REPORT SMITHSONIAN INSTITUTION, 1948 
200. Mostly they did this by restating 
for any current year the anniversary 
of Maya zero, October 15, 3373 B. C. 
Obviously they could not do this with- 
out previously acquired knowledge ac- 
cruing after Baktun 7, August 6, 613 
Ba: 
Instead of trying our method of 
intercalations, they preferred year 
dials. These give better adjustments, 
everything considered, than are possi- 
ble with any leap-year system. We 
glance at evidence of their skill in using 
the tropical year, for this had an im- 
portant reaction on the year dial 
itself. At Palenque in the Temple of 
the Cross, a series of dates indicate 
betterment as time goes on in reaching 
the anniversary of Maya zero. As an 
earnest of their ability in astronomical 
matters, the earliest date, placed 20 
days before the initial series, strikes a 
lunar eclipse. The initial series, also 
placed before Maya zero, strikes a 
close conjunction of Venus and Mars. 
After this, zero is itself declared. 
Among some 30 dates, 7 deal with 
Maya zero and the tropical year meas- 
ured from it. I think the one record- 
ing October 10, A. D. 162, especially 
interesting for on this day took place 
a lunar eclipse visible at Palenque. 
TABLE 3.—Anniversaries of Maya zero, Temple of the Cross, Palenque 
The Tropical Year is 365.2423 days for all parts of this table. 
Date Maya day number Maya calendar Gregorian calendar Error 
ACH rato stoterotees 0 4 Ahau 8 Cumhu Oct. 15, 3373 B.C. 0.00 
Badgers tysnstae) emcxopent 295482 9 Ik 0 Yax Oct. 15, 2564 +0.98 
OS ago ote chs sets: ov 1291128 11 Lamat 6 Xul Oct. 10, A. D162" 33.53 
1D eneedrciteae ersten cio 1295878 2 Caban 10 Xul Octit; 175 —1.68 
Bit Phe cistsraet lores 1295879 3 Eznab 11 Xul Octi12! 175 —0.68 
Bins Soaee- sere. «8 1366007. 7 Kan 17 Mol Oct. 12; 367 +0.80 
CGA Gs Radasnes 1385365 11 Chicchan 13 Chen Oct. 14, 420 -+0.96 
References to the place of Maya 
zero are concentrated at Palenque on 
the tablet of the Temple of the Cross. 
I will not comment on three other 
possible ones. This tablet like those 
of the Foliated Cross and of the Sun 
probably were carved about A. D. 
430 although mounted in buildings 
of the seventh century. 
Other statements which give ap- 
proximately the place of Maya zero 
in historic times occur at most of the 
important cities on monuments of the 
first order. At Naranjo, Stela 32 has 
such a date which combines with 
others in the year-dial complex yet 
to be explained. On this monument 
a theocrat is seated above several tiers 
of stars and planets. 
The most accurate measurement of 
