Counting this number forward from 4 Ahau 13 Yax, the nearest date to it in the text, the terminal date reached will be found to be 6 Ahau 18 Zac, the date which, we have seen, was recorded in A3b B3. It is clear, therefore, that this text records the fact that 3.2.0 has been counted forward from the date 4 Ahau 13 Yax and the date 6 Ahau 18 Zac has been reached, but there is nothing given by means of which the position of either of these dates in the Long Count can be determined; consequently either of these dates will be found recurring like any other Calendar-round date, at intervals of every 52 years. In such cases the first assumption to be made is that one of the dates recorded the close of a hotun, or at least of a tun, in Cycle 9 of the Long Count. The reasons for this assumption are quite obvious.

Fig. 83. Calendar-round dates: A, Altar M, Quirigua; B, Altar Z, Copan.

The overwhelming majority of Maya dates fall in Cycle 9, and nearly all inscriptions have at least one date which closed some hotun or tun of that cycle. Referring to Goodman's Tables, in which the tun endings of Cycle 9 are given, the student will find that the date 4 Ahau 13 Yax occurred as a tun ending in Cycle 9, at 9.15.0.0.0 4 Ahau 13 Yax, in which position it closed not only a hotun but also a katun. Hence, it is probable, although the fact is not actually recorded, that the Initial-series value of the date 4 Ahau 13 Yax in this text is 9.15.0.0.0 4 Ahau 13 Yax, and if this is so the Initial-series value of the date 6 Ahau 18 Zac will be:

9.15.0.0.0 4 Ahau 13 Yax
3.2.0
9.15.3.2.0 6 Ahau 18 Zac

In the case of this particular text the Initial-series value 9.15.0.0.0 might have been assigned to the date 4 Ahau 13 Yax on the ground that this Initial-series value appears on two other monuments at Quirigua, namely, Stelæ E and F, with this same date.

In figure [83], B, is shown a part of the inscription from Altar Z at Copan.[[234]] In A1 B1 appears a number consisting of 1 kin, 8 uinals, and 1 tun, that is, 1.8.1, and following this in B2-A3 is the date 13 Ahau 18 Cumhu, but no record of its position in the Long Count. If 13 Ahau 18 Cumhu is the terminal date of the number 1.8.1, the starting point can be calculated by counting this number backward, giving the date 12 Cauac 2 Zac. On the other hand, if 13 Ahau 18 Cumhu is the starting point, the terminal date reached by counting 1.8.1 forward will be 1 Imix 9 Mol. However, since an ending prefix appears just before the date 13 Ahau 18 Cumhu in A2 (compare fig. [37], a-h), and since another, though it must be admitted a very unusual ending sign, appears just after this date in A3 (compare the prefix of B3 with the prefix of fig. [37], o, and the subfix with the subfixes of l-n and q of the same figure), it seems probable that 13 Ahau 18 Cumhu is the terminal date and also a Period-ending date. Referring to Goodman's Tables, it will be found that the only tun in Cycle 9 which ended with the date 13 Ahau 18 Cumhu was 9.17.0.0.0 13 Ahau 18 Cumhu, which not only ended a hotun but a katun as well.[[235]] If this is true, the unrecorded starting point 12 Cauac 2 Zac can be shown to have the following Initial-series value:

9.17. 0.0. 0 13 Ahau 18 Cumhu
1.8. 1 Backward
9.16.18.9.19 12 Cauac 2 Zac