MAYA INSCRIPTIONS: FURTHER NOTES ON THE SUPPLEMENTARY SERIES IN BY JOHN E. TEEPLE NA previous article1 I was able to show the method of reading and the meaning of Glyphs C, D and E of the Supplementary Series. Glyph D shows the number of days that had elapsed since the last point of observation of the moon (presumably the new moon) provided the days are less than 20; Glyph E records the days in case they are 20 or more, E itself representing 20; Glyph C records the number of complete lunations in addition that had elapsed since the end of the last moon group (of 5 or 6 lunations). Ample proof was presented in the case of Glyphs D and E, but in the case of C we have only some examples, and the inference of extreme probability, but no actual proof. I think, however, that we can tentatively accept the reading of Glyph C also with perfect safety. The next step was to apply the above readings to various inscriptions and see what could be developed. First, did the Maya exhibit the meticulous accuracy that some writers would have us believe? I think not. Stela 12 at Copan states that the date 9.10.15.0.0 occurred 3 days after a new moon, while Stela 13 Copan gives 9.11.0.0.0 as 5 days after a new moon. It is hardly likely that both statements are correct. If the last date was 5 days after a new moon then the first was probably 6 days after instead of 3 days. More definitely, take date 9.16.5.0.0 which Stela J at Quirigua says occurred 4 days after a new moon. Stela M at Copan gives the same date as 5 days after a new moon. Again, 9.16.10.0.0 is given by Stela N at Copan as 1 day and by Stela 1 at Yaxchilan as 3 days after a new moon. Stelae 24 and 29 at Naranjo give the date 9.12.10.5.12, respectively, as 18 and as 19 days after new moon. Stela J at Copan and 4 at Piedras Negras 1 American Anthropologist, 1925, pp. 108-115. give 9.13.10.0.0 in one case as 18 days and in the other as 20 days after new moon. These discrepancies are not large, only 2 or 3 days at most, but they serve to show that absolute accuracy to a day is too much to expect from a people in their state of development and with their means of recording and filing data. We may assume that they could observe the new moon accurately enough, but a 2 or 3 day inaccuracy in their calendar count was not uncommon, and in fact is exactly what we should expect. I think we may safely assume too that they had means of checking the calendar count at frequent intervals, by observation and computation, so that except in times of war or great public disturbance the calendar variation rarely exceeded a couple of days. The age of the moon in days seems to have been a matter of considerable interest and importance to the Maya for we find several references in the inscriptions to moons of the same age. For example, Stela 3 at Piedras Negras reads in part "9.12.2.0.16.5 Cib 14 Yaxkin, 27 days after the second lunation after the end of a moon group, is the same moon day as katun 12." Now Katun 12 is shown by Stela 37 at Piedras Negras (courtesy of Dr. Sylvanus G. Morley) to be 28 days after new moon. We assume that the former date represents 27 days of a 29 day month and the latter 28 days of a 30 day month, i.e. the moon was the same age in both cases. We read further on Stela 3 above "12.10.0 (from 5 Cib 14 Yaxkin) is 1 Cib 14 Kankin, also the same moon day as Katun 12; 1.1.11.10 (after 1 Cib) is 4 cimi 14 Uo." Here a statement is made about the moon day which I cannot yet read, but the inscription no longer states that it is the same moon day as Katun 12 because at this point we are about 6 days short of that age. No moon days appear in the rest of the inscription and no others are reached by the dates. Stela I at Copan is another interesting one. It reads in part "9.12.3.14.0 5 Ahau (8 Uo) is a new moon day 4 lunations after the close of the last moon group. 10 Ahau 13 Chen (9.12.7.4.0) is also a new moon day the same as Katun 12 (or Katun 6) was. 10.8 (from 10 Ahau) is 10 Lamat (16 Pop 9.12.7.14.8)." The rest is obliterated or I think we should find it explained that 10 Lamat was also a new moon day. Apparently according to the Copan calendar the end of Katun 12 (or 6) was a new moon day. We saw above that according to the Piedras Negras calendar the new moon did not come till a day or two later than Katun 12. 9.12.16.7.8. 3 Lamat 6 Yax on Altar K at Copan is the only other initial series date so far found in the inscriptions, with the exception of two or three hotun endings, which occurred on a new moon day. Consequently these two dates 9.12.3.14.0 and 9.12.16.7.8 with two or three hotun ending dates in addition are the only initial series dates among more than a hundred known ones which could possibly have commemorated an eclipse of the sun. From the position of these two dates in the Tzolkin however, day 200 and day 68 respectively, it does not seem probable that an eclipse occurred on either date. Nor is it probable for the same reason that any initial series date represents an eclipse of the moon although several of these dates occur 14 or 15 days after a new moon. The Maya Tzolkin becomes a beautiful instrument for following eclipse dates if we have any fixed starting point, and I think we have one in Dresden Codex pages 51-58. Taking the table as finally worked out by Prof. Willson and Dr. Guthe, the zero day is 11 Manik, day 167 of the Tzolkin; the first group of 6 moons ends at 6 Kan, day 84 of the second Tzolkin, or day 344 if we number consecutively through a pair of Tzolkins; Group 2 ends at 1 Imix, day 1 of the third Tzolkin, then follow in order days 149, 326, 503, 161, 338, 515, etc. If we plot them all we find the whole 69 dates falling into 3 groups. The first group of 23 dates (or 24 if we include the zero date) lie between days 149 and 183, and center around day 166; the second group of 23 dates lie between 322 and 353 and center around day 339; and the third group between day 496 and day 10 of the next Tzolkin and center around day 513. Now if we are right in assuming that this table in the Dresden Codex represents a possible eclipse calendar, then days 166, 339, and 513 of the Tzolkin must be the days when the sun passed the moon's nodes, and at the date of the calendar no eclipse either solar or lunar could have occurred except within an extreme limit of 18 days on either side of day 166, 339, or 513. Lunar eclipses would of course be within the narrower limit of 13 days. This agreement between eclipse seasons and Tzolkin becomes easily understandable when we remember that the average eclipse half year is 173.31 days, and that 3 such periods require 519.93 days, just .07 day less than 2 Tzolkins. The discrepancy between average eclipse periods and Tzolkin then is slightly less than one day per katun. If day 166 of the first Tzolkin was the day when the sun passed the moon's nodes around 9.16.0.0.0, then about 9.17.0.0.0 the sun would pass the node on day 165 for a katun, and at 9.18.0.0.0 days 164, 337 and 511 would be the node days. In the other direction no date near, say, 9.11.0.0.0 could possibly be an eclipse day unless (a) it was within 18 days of day 171, 344 or 518 for a solar eclipse or within 13 days for a lunar eclipse; and (b) it was on a new moon day for solar eclipse or 15 days before or after new moon for lunar eclipse. This rather definitely narrows the field and may possibly lead to the identification of some secondary series date as the record of an eclipse and so give another aid to the correlation of the Maya and Christian calendars. We know from two monuments (Stela M Copan and Stela J Quirigua) that a new moon occurred on 9.16.4.10.8 or within one day of it, and Stela M also shows a moon group ending at 11 Manik 9.16.4.10.7. It seems altogether probable that 9.16.4.10.8 was the zero day or beginning day of the table in Dresden Codex. All three of the correlations discussed by Prof. Willson2 are partly based on an eclipse Syzygy at 9.16.4.10.8 and this seems a necessary condition of any final correlation; of course it is not a sufficient condition. On the other hand a correlation such as that so carefully worked out by Dr. Spinden3 which places the date 9.16.4.10.8 on a day where there is no ecliptic conjunction within 40 days and not even a new moon within about 10 days cannot possibly be correct to a day. The arrangement of the moons in groups of 5 and 6, to end on possible eclipse dates as shown in the Dresden Codex was appar "Astronomical Notes on the Maya Codices. 1924. • The Reduction of Maya Dates. 1924. ently a recent discovery. Throughout the inscriptions the moons are arranged in groups of 5 and 6, but the five groups are apparently about as numerous as the six groups, and in the inscriptions there is no apparent attempt to have the moon groups coincide with the eclipse seasons. In the inscriptions moon groups end promiscuously on almost any day of the Tzolkin instead of hovering near days 166, 339 and 513, as they do in Dresden Codex. Only in two cities, at one particular time do we find any series of monuments following the Dresden Codex Table. This is at Copan where the four latest initial series (Stelae D, M and N and Temple 11, 9.15.5.0.0 to 9.16.12.5.17) all conform fully to the Dresden Codex method, and at Naranjo where also the four latest ones (Stelae 30, 13, 14 and 8, 9.14.3.0.0 to 9.18.10.0.0) conform fully. This is hardly sufficient evidence to link the Dresden Codex with Naranjo or Copan, but it is the only indication that I have been able to find so far. The method of the Codex was not in use in Naranjo in 9.13.18.4.18 (Stela 23) nor at Copan in 9.14.19.8.0 (Stela A), but every later legible series in both cities conforms closely with the Dresden Table. What method of grouping the moons was followed in these two cities before the dates given, or in other cities like Quirigua, Piedras Negras, Yaxchilan, Palenque, etc., at all times has so far eluded me entirely. Alternate arrangement of a five and a six, or two fives and two sixes, or six fives and five sixes are all indicated, but indications derived from any one group of monuments fail completely when applied to another series of inscriptions. In addition to the period 1.13.4.0 which apparently was in use before its adjustment to eclipses according to the Dresden Table, the Maya had a number of other convenient approximations for computing a new moon day; for example a tun and a Tzolkin 1.13.0 is a very close approximation to 21 lunations; five tuns and a kin 5.0.1 for 61 lunations; a katun and five kins 1.0.0.5 for 244 lunations. All these or multiples of them will be found in use in the inscriptions. The figure 11.11.13 written on a shield next to a moon ending sign on the inscribed stairway at Palenque (Maudsley 4, 23) is no doubt meant for a period of 142 lunations and is one third of a longer 426 lunation period 1.14.17.0, just |