Table 12.9. Continued.

Dresden lunar table: Calculated to middle line of table


65. 5 Cauac 17 Zac-Two-legged Sky

Ah Cimil. 13 Muluc 17 Yax-day after last in table

Picture 9. Diving Star Glyph B-kinil

Picture 10. Diving Star, picture and glyph. Royal throne. Half dark sun, moon. Sky-in-hand. Ah ahpo tzu Next table section begins with 13 Muluc.

Table 12.10. Periodicities involving 12 Lamat 1 Muan.

N.B.: The dates arrived at have been referred to the era base 4 Ahau 8 Cumku. See p. 359.

9. 16. 4. 10. 8 12 Lamat 1 Muan difference between the Mesoamerican year and the tropical year cumulatively amounts to exactly one year i.e., 1508 My equal 1507 tropical years. This means that the Mayan year is back to the same season. The interval is also a moderately good eclipse interval (in the sense that there are nearly an integral number of nodal months—20,226.96—in this interval, and it is only 0.64 days more than 18,639 lunations by Spinden's correlation), and a very good Mercury interval (-6257.01 synodic revolutions). Spinden (1930, p. 94) argued that the Venus cycle could be related to this formula, but the evidence of Maya calculations on this is lacking and the structural argument is too complex to be very convincing.

DHK does not think that the Thompson correlation is correct, but that calculation of this interval probably entered into the establishment of the CR as it was known in the colonial period (after the postulated calendar reform). The half-period of 29 CRs (otherwise emphasized at Palenque) is 275,210. Counted forward from the 753 b.c. date, this interval reaches JDN 1,721,922, May 14, 2 a.d. (Julian calendar), the day before a lunar eclipse and 16 days before a solar eclipse (Maya 3 Etz'nab 1 Muan).

Satterthwaite (1947) suggested that the Mayas evolved their eclipse system on a hit-or-miss cyclical basis without ever really understanding what they were doing. Because lunar eclipses are more widely visible than solar eclipses, it is possible that the Mayas worked out a theory based on lunar cycles and transferred it to solar eclipses. Although Satterthwaite's hypothesis is ingenious and persuasive in detail, it involves a combination of long periods of accurate record-keeping, mathematical sophistication in averaging, and minimal understanding. The general sophistication of Mayan astronomical concepts that seems to Kelley to be indicated in the sources is against this view. More recently, Smither (1986) has studied the distribution of both lunar and solar eclipses in Mesoamerica between a.d. 505 and 932 in an attempt to determine how eclipse prediction might have been achieved. He found that lunar eclipses would provide a readily recognizable pattern of repetition over 88 lunations (15 eclipse seasons, 10 tzolkin rounds or 7 Maya years, and 44 days). Smither (1986, p. 102) defined the area of investigation as that part of North America lying between 14° and 22° north lattitude. He defined a visible solar eclipse as one in which 50% or more of the Sun's surface was hidden. Of 1022 solar eclipses during the period investigated, 56 were visible in the area of interest. His published data deal with the period from 712 a.d. to 861 a.d., during which there were

13 total or annular eclipses, and 11 partial eclipses. During the same time period, there were 130 visible lunar eclipses— more than five times as many as the solar eclipses and visible from a given locality for much longer periods of time. Smither (1986, figure 2) compares these data with the eclipse table of the Dresden codex. His further contention that the positions of the five-lunar-month intervals in the codex would work better as predictors of lunar eclipses than of solar eclipses is valid but does not consider the fact that such intervals are necessarily times when it is more probable for a solar eclipse to fall in the same month as a lunar eclipse, which DHK thinks is probably the Maya interest. Smither's belief that lunar eclipses were intended leads him to propose a new correlation constant, 584,301, shifted 16 days from the Thompson constant, 584,285. This would imply that lunations throughout the Classic Period were counted from full moons, as Spinden argued. This does not seem to agree with DHK's postulates on the identities of lunar goddesses. Smither thinks that the table should have been adjusted every 52 years for most effective use, but does not explain the references in the introduction to the table to much longer intervals. Smither argues that the 52-year cycle and the 104-year cycle are evident as actual points where the 88 lunar month pattern "breaks."

Two suggestions have been made with respect to the interpretation of the pictures, which appear following 148-day intervals. The first view was that they marked locally visible eclipses. Willson (1924, pp. 9-16) checked the entire series of eclipses visible in Yucatan between 12 b.c. and 1520 a.d. and found that there was no series of 10 visible eclipses at the intervals shown in the codex. Indeed, Willson (1924, p. 15, fn. 1) points out that the interval between the 9th and 10th pictures is 708 days and that "no central eclipse visible in the tropics can be followed in 708 days by an eclipse whose shadow passes over tropical countries."Willson found four cases of seven visible eclipses at the intervals indicated, but no greater number of eclipses. He thought that the eclipses may be predicted eclipses, with errors up to 1/10 day, and found one series that included 10 eclipses that might have been predicted at the appropriate intervals. However, although not known in Willson's time, the verb accompanying the 5th picture has an affix that indicates that it refers to an event in the past. Because this indicates that it is unlikely that the text was directly designed to refer to the future, this makes it very unlikely that the pictures were intended to refer to visible eclipses.

The alternative explanation is that the pictures refer to a lunar month in which one may have found a lunar and a solar eclipse together. Because an interval of 148 days implies just such a condition, DHK thinks that Meinshausen (1913) was correct in making this suggestion. Indeed, the glyphs and details of the pictures seem to support this view. In particular, five of the pictures are accompanied by glyphs of both Sun and Moon, each in a curious frame, in which one is half-black, and another, half-white. These were accepted as "eclipse" glyphs by most early and present scholars, Eric Thompson's insistence that the frames indicate only "darkness" notwithstanding (such a view was consistent with Thompson's arguments that various "almanacs" were essentially agricultural with little or no astronomical content).

Severin (1981, p. 17) proposed that the "wings" of these symbols in their four variants marked the positions of the Sun—both white, summer solstice; both black, winter solstice; left white and right black, autumn equinox; left black and right white, spring equinox. This was part of his argument that the Maya knew and used calculations of precession over 26,000 years. Severin based his work on the Paris codex, where there is little chronological control. Closs (1983) shows that the forms in the Dresden eclipse table (not considered by Severin) are utterly inconsistent and would remain so whatever correlation is accepted and whatever base is accepted for the table, with the "autumn equinox" appearing in seven different months of the tropical year.

Teeple (1930, pp. 90-93) analyzed the sequence of intervals in the eclipse table and concluded that they do indeed refer to eclipse half-year intervals and that the instant of a solar node-crossing most probably occurred on the day before the 12 Lamat date which was the base of the table (see § for detailed discussion of the circumstances for eclipses to occur). The table is immediately preceded by the date 12 Lamat 1 Muan, which it is reasonable to suppose is the 12 Lamat date, the base of the table. However, neither the Thompson nor the Spinden correlations (which seemed most likely on historical grounds, at that time) put the instant of a node passage of the Sun even near this date; so various explanations were devised that removed the table by various amounts from its supposed base. Makemson (1943, pp. 187-188) argued that the three dates 12 Lamat 1 Muan, 1 Akbal 16 Muan (15 days later), and 3 Etz'nab 11 Pax (30 days after the first date), which appear just prior to the table depictions, could represent two solar eclipses flanking a lunar eclipse (or conceivably a solar between two lunar eclipses). In either case, a node passage of the Sun must be near the middle date. From the discrepancy between this node passage instant and that of Teeple, she argued that the 12 Lamat base of the table was different from 12 Lamat 1 Muan and that the table must belong to a substantially later date, corresponding to a different date of nodal crossing. However, she failed to point out that

(1) in the case of a lunar eclipse between two solar eclipses, one of the solar eclipses would be visible too far to the north for the Mayas to see it and the other would be too far south to be visible;

(2) two lunar eclipses with a solar eclipse between them could not be separated by more than 30 days; and

(3) there are actually four dates, not three, at the beginning of the table; the 4th seems out of place in this context, although reading is doubtful. In any case, the dates seem to be in two pairs, rather than a set of three and an extra date.

These circumstances would make it seem that the Makem-son interpretation is unlikely and that the most straightforward interpretation would be that 12 Lamat 1 Muan was the table base, as Teeple thought, that it is very near an instant of solar node passage, and that the date is that of a new Moon. If so, the paired date 1 Akbal 16 Muan (15 d later) could serve as a base for calculating associated lunar eclipses, which would be in accord with the

Figure 12.12. (a) A prototype of the Nahua old Moon god, Tec-ciztecatl, "He of the Snail Shell," from Teotihuacan. Drawing by Sean Goldsmith. (b) The head of a Sun god growing on a gourd tree and another head already largely turned into a gourd, from a Mayan pot. Drawing by Sharon Hanna.

suggested interpretation of the pictures. However, that interpretation is incompatible with either the Thompson correlation or with the Spinden correlation, which once seemed the most likely competitor with the Thompson correlations. It was suggested earlier in this section that 12 Lamat 1 Muan was based on a formal cyclical recurrence of a date 12 Lamat 1 Muan back-calculated before the Maya era base, which would allow any correlation.

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