Cases where tun endings are recorded are exceedingly rare. The bare statement that a certain tun, as Tun 10, for example, had come to its end left much to be desired in the way of accuracy, since there was a Tun 10 in every katun, and consequently any given tun recurred after an interval of 20 years; in other words, there were three or four different Tun 10's to be distinguished from one another in the average lifetime. Indeed, to keep them apart at all it was necessary either to add the particular katun in which each fell or to add the date on which each closed. The former was a step away from the brevity which probably prompted the use of Period-ending dating in the first place, and the latter imposed too great a task on the memory, that is, keeping in mind the 60 or 70 various tun endings which the average lifetime included. For these reasons tun-ending dates occur but rarely, only when there was little or no doubt concerning the particular katun in which they fell.
In plate [21], F, is figured a tun-ending date from the tablet in the Temple of the Inscription at Palenque.[[208]] In glyph 1 appears an ending sign showing the hand element and the grotesque flattened head (for the latter see fig. [37], i, r, u, v), both common ending signs. The remaining element, another grotesque head with a flaring postfix, is an unusual variant of the tun head found only at Palenque (see fig. [29], h). The presence of the tun sign with these two ending signs indicates probably that some tun ending follows. Glyphs 2 and 3 record the date 5 Ahau 18 Tzec, and glyph 4 records Tun 13. We have here then the record of a Tun 13, which ended on the date 5 Ahau 18 Tzec. But which of the many Tun 13s in the Long Count was the one that ended on this particular date? To begin with, we are perfectly justified in assuming that this particular tun occurred somewhere in Cycle 9, but this assumption does not aid us greatly, since there were twenty different Tun 13s in Cycle 9, one for each of the twenty katuns. However, in the full text of the inscription from which this example is taken, 5 Ahau 3 Chen is the date next preceding, and although the fact is not recorded, this latter date closed Katun 8 of Cycle 9. Moreover, shortly after the tun-ending date here under discussion, the date "3 Ahau 3 Zotz, end of Katun 9," is recorded. It seems likely, therefore, that this particular Tun 13, which ended on the date 5 Ahau 18 Tzec, was 9.8.13.0.0 of the Long Count, after 9.8.0.0.0 but before 9.9.0.0.0. Reducing this number to units of the first order, and applying the several rules given for solving Initial Series, the terminal date of 9.8.13.0.0 will be found to agree with the terminal date recorded in glyphs 2 and 3, namely, 5 Ahau 18 Tzec,
and this tun ending corresponded, therefore, to the Initial Series 9.8.13.0.0 5 Ahau 18 Tzec.
Another tun-ending date from Stela 5 at Tikal is figured in plate 21, G.[[209]] In glyphs 1 and 2 the date 4 Ahau 8 Yaxkin appears, the month sign being represented as a head variant, which has the essential elements of the sign for Yaxkin (see fig. [19], k, l). Following this in glyph 3 is Tun 13, to which is prefixed the same ending-sign variant as the prefixial or superfixial elements in figure [37], i, r, u, v. We have recorded here then "Tun 13 ending on 4 Ahau 8 Yaxkin," though there seems to be no mention elsewhere in this inscription of the number of the katun in which this particular tun fell. By referring to Great Cycle 54 of Goodman's Tables (Goodman, 1897), however, it appears that Tun 13 of Katun 15 of Cycle 9 closed with this date 4 Ahau 8 Yaxkin, and we may assume, therefore, that this is the correct position in the Long Count of the tun-ending date here recorded. This date corresponds to the Initial Series 9.15.13.0.0 4 Ahau 8 Yaxkin.
There is a very unusual Period-ending date on the west side of Stela C at Quirigua[[210]] (see pl. [21], H). In glyphs 1 and 2 appears the number 0 kins, 0 uinals, 5 tuns, and 17 katuns, which we may write 17.5.0.0 and following this in glyphs 3 and 4 is the date 6 Ahau 13 Kayab. At first sight this would appear to be a Secondary Series, the number 17.5.0.0 being counted forward from some preceding date to reach the date 6 Ahau 13 Kayab recorded just after it. The next date preceding this on the west side of Stela C at Quirigua is the Initial-series terminal date 6 Ahau 13 Yaxkin, illustrated together with its corresponding Initial-series number in figure [68], A. However, all attempts to reach the date 6 Ahau 13 Kayab by counting either forward or backward the number 17.5.0.0 from the date 6 Ahau 13 Yaxkin will prove unsuccessful, and we must seek another explanation for the four glyphs here under discussion. If this were a Period-ending date it would mean that Tun 5 of Katun 17 came to an end on the date 6 Ahau 13 Kayab. Let us see whether this is true. Assuming that our cycle coefficient is 9, as we have done in all the other Period-ending dates presented, we may express glyphs 1 and 2 as the following Initial-series number, provided they represent a period ending, not a Secondary-series number: 9.17.5.0.0. Reducing this number to units of the 1st order, and applying the rules previously given for solving Initial Series, the terminal date reached will be 6 Ahau 13 Kayab, identical with the date recorded in glyphs 3 and 4. We may conclude, therefore, that this example records the fact that "Tun 5 of Katun 17 ended on the date 6 Ahau 13 Kayab," this being identical with the Initial Series 9.17.5.0.0 6 Ahau 13 Kayab.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 22
EXAMPLES OF PERIOD-ENDING DATES IN CYCLES OTHER THAN CYCLE 9