tance number (or interval) that leads forward to a Classic Period date. This is followed by a multiplication table and then by a series of figures associated with a repeating tzolkin or longer period. This strong structural similarity is a good generic reason for supposing that the intellectual content is similar and likewise astronomical in the unidentified or dubiously identified cases.

The best starting point for an understanding of the RNs is the date 1 Ahau 18 Kayab, 2200 days before the Maya era. From this, the count goes forward to 1 Ahau 18 Kayab. The base of the accompanying table of Venus movements (Table 12.10) is a day 1 Ahau 18 Kayab, which may, theoretically, be either of these dates but has always been interpreted as the later of the two. The table covers 104 My and gives cumulative totals of a sequence of numbers: 584 (equal to 0), 236, 326, and 576, associated with CR dates in an unwavering 584-day cycle. These numbers refer to cumulative intervals of days (indicated by "S" in the list below) associated with the following Venus phenomena (see the discussions of general planetary phenomena in §§2.4.3, 5.4,, and

(1) the zero point at heliacal rising four days after inferior conjunction;

(2) 236 days as morning star;

(3) 90-day disappearance around superior conjunction (S = 326);

(5) 8-day disappearance following heliacal setting, around inferior conjunction (S = 584).

In the table, the CR date 3 Kan 17 Mac appears as a "stan dard" date of heliacal setting at "age" 576 and corresponds to the RN 13 Kan 17 Mac. Another RN base, 4 Eb 20 Yaxkin ("seating of" Mol), appears as day 240 of the cycle, 4 days after a standard 236-day interval, and a 4th RN, 13 Cauac 7 Ceh, appears as a day 327 of the cycle, 1 day after the standard 326. This strongly suggests that all four positions were involved in the calculation of the RNs and were being integrated with other phenomena. Over the period of 2079 days separating 1 Ahau 18 Kayab from 13 Cauac 7 Ceh, the accumulated error from use of the standard period of 584 days differs from that obtained from the use of the true synodic period (583.920+ days) by <0.24+ days. Hence, the positions involved may have been conceptualized as either true periods or cycles, or as both.

Of the other planetary phenomena involved in calculating these RN dates, the clearest refers to Mercury. The average synodic period of the planet is 115.87754 days. Counting from the earliest of the RNs, 13 Imix 9 Uo (at 51,419 days before the Maya era base), we find that the RN 9 Ix 2 Kankin has an age1 of 115 days, almost exactly the same Mercury age as that of the base. We also find that RN 9 Ix 7 Xul has an "age" of 55.32 days, ~ V2 Psyn, hence, the mean interval from an inferior conjunction to a superior conjunction or vice versa, and that the RN 9 Ix 2 Ch'en has the same day name at an "age" of 61 days, only 3 days off from that previously discussed. The RN 13 Oc 18 Pax appears at 55 days, or 3 days off in the opposite direction. Finally, the date 4 Eb 20 Yaxkin, mentioned in connection with Venus, has a Mercury "age," reckoning from the earliest date, of 109 days, 6 or 7 days short of a complete cycle. Hence, of the 16 dates of the RN table, six occur at or close to intervals involving the true Mercury synodic period. Of the six dates, three are days 9 Ix from a single table of the codex, emphasizing that day, and another day, 4 Eb, is from a related and adjacent table. It may be more than a coincidence that the true average period of Mercury had shifted during the periods of the RNs approximately halfway around from a cyclical period counted with a round number of 116 days. Thus, the 109-day true average age of 4 Eb 20 Yaxkin would correspond to a cyclical "age" of 55 days; conversely, the true average "age" of 61 days at 9 Ix 9 Ch'en had a cyclical age of 9 days and the true average age of 58 days at 9 Ix 7 Xul would give a cyclical "age" of 5 days. The true average "age" of 55 days at 13 Oc 18 Pax has a cyclical "age" of 1 day.

The average sidereal period of Mercury is 87.96939 days, so that half a Mercury "year" is 44 days. The day 9 Ix 2 Kankin, already noted as being at a true average synodic "age" of 115 days from 13 Imix 9 Uo, was also a sidereal "age" of Mercury of 46 days. The RN dates 1 Ahau 18 Kayab, 3 Lamat 1 uayeb, and 4 Ahau 8 Cumku all have a sidereal "age" of 44 days, as reckoned from 13 Imix 9 Uo. These coincidences suggest to Kelley that both the synodic and sidereal periods of Mercury were involved, whether or not consciously formulated as such, in the construction of the RNs. This is congruent with other evidence from the 9 Ix tables and from the inscriptions.

Calculating the synodic period of Saturn at 378.09208 days, we find that the average "age" of Saturn at

7 The "age" of a given planet is counted in calendar days from a date given as "zero" without any a priori implication that a particular station (configuration) of the planet is involved. Any particular interval is counted in multiples of true mean synodic or sidereal periods with the remainder to the nearest whole day considered as the "age." Thus, the "age" is a given interval modulo some mean period. Astronomers often use the term "phase" instead. Cf. Table 2.9 for period data.

4 Ahau 8 Cumku, counted from 13 Imix 9 Uo was 376 days. A cyclical count of exactly 378 days reached a point 11 days earlier. Put in terms of the table construction, if a Saturn "base" was desired and it was believed that 4 Ahau 8 Cumku was a Saturn base, a strictly cyclical base would have started 11 days after 13 Imix 9 Uo. Alone, this suggestion of a Saturn calculation does not offer much support to an interpretation of RNs in astronomical terms. If such an interpretation seems plausible on other grounds, one would certainly suspect Saturn interest here.

As our discussion in §12.7 on the Dresden Venus table points out, there is good reason to think that that table shows an interest in eclipses as well as an interest in Venus. Because the basic half eclipse year is 173.31 days, it is interesting to note that counting forward from 13 Imix 9 Uo to 13 Cauac 7 Ceh, it has an "age" of 171 days, and 1 Ahau 18 Kayab has an "age" of 172 days. Although Thompson (1950 p. 226) pointed out that the interval between the RN base 1 Ahau 18 Kayab and the table base 1 Ahau 18 Kayab involved a shift of about half a year both in the Tropical Year and in Venus's synodical phase or age (see §12.7), he did not extend this suggestion of a direct astronomical interest here to other RNs. Neither did he discuss why the Mayas should count back to a base off by about a half year from its later Venus position, although he supposed that the late end was in step with Venus's reality (if one applied certain corrections to the base). Willson (1924, p. 35) concluded that "all the planets appear with Ring Numbers and all Ring Numbers appear only with planetary tables." Without agreeing with all the details of his arguments, we think that the evidence supports his position.

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