shown in figure [57], a, b, but also satisfactorily provides for the enumeration of the cycles from 1 to 13, inclusive.
If the date "4 Ahau 8 Cumhu ending Cycle 13" be regarded as a Period-ending date, not as indicating that the number of cycles in a great cycle was restricted to 13, the next question is—Did a great cycle also come to an end on the date 4 Ahau 8 Cumhu—the starting point of Maya chronology and the closing date of a Cycle 13? That it did the writer is firmly convinced, although final proof of the point can not be presented until numerical series containing more than 5 terms shall have been considered. (See pp. [114]-[127] for this discussion.) The following points, however, which may be introduced here, tend to prove this condition:
1. In the natural course of affairs the Maya would have commenced their chronology with the beginning of some great cycle, and to have done this in the Maya system of counting time—that is, by elapsed periods—it was necessary to reckon from the end of the preceding great cycle as the starting point.
2. Moreover, it would seem as though the natural cycle with which to commence counting time would be a Cycle 1, and if this were done time would have to be counted from a Cycle 13, since a Cycle 1 could follow only a Cycle 13.
On these two probabilities, together with the discussion on pages [114]-[127], the writer is inclined to believe that the Maya commenced their chronology with the beginning of a great cycle, whose first cycle was named Cycle 1, which was reckoned from the close of a great cycle whose ending cycle was a Cycle 13 and whose ending day fell on the date 4 Ahau 8 Cumhu.
The second point (see p. [108]) on which rests the hypothesis of "13 cycles to a great cycle" in the inscriptions admits of no such plausible explanation as the first point. Indeed, it will probably never be known why in two inscriptions the Maya reckoned time from a starting point different from that used in all the others, one, moreover, which was 13 cycles in advance of the other, or more than 5,000 years earlier than the beginning of their chronology, and more than 8,000 years earlier than the beginning of their historic period. That this remoter starting point, 4 Ahau 8 Zotz, from which proceed so far as known only two inscriptions throughout the whole Maya area, stood at the end of a great cycle the writer does not believe, in view of the evidence presented on pages [114]-[127]. On the contrary, the material given there tends to show that although the cycle which ended on the day 4 Ahau 8 Zotz was also named Cycle 13,[[79]] it was the 8th division of the grand cycle which ended on the day 4 Ahau 8 Cumhu,
the starting point of Maya chronology, and not the closing division of the preceding grand cycle. However, without attempting to settle this question at this time, the writer inclines to the belief, on the basis of the evidence at hand, that the great cycle in the inscriptions was of the same length as in the codices, where it is known to have contained 20 cycles.
Let us return to the discussion interrupted on page [107], where the first method of expressing the higher numbers was being explained. We saw there how the higher numbers up to and including 1,872,000 were written, and the digression just concluded had for its purpose ascertaining how the numbers above this were expressed; that is, whether 13 or 20 units of the 5th order were equal to 1 unit of the 6th order. It was explained also that this number, 1,872,000, was perhaps the highest which has been found in the inscriptions. Three possible exceptions, however, to this statement should be noted here: (1) On the east side of Stela N at Copan six periods are recorded (see fig. [58]); (2) on the west panel from the Temple of the Inscriptions at Palenque six and probably seven periods occur (see fig. [59]); and (3) on Stela 10 at Tikal eight and perhaps nine periods are found (see fig. [60]). If in any of these cases all of the periods belong to one and the same numerical series, the resulting numbers would be far higher than 1,872,000. Indeed, such numbers would exceed by many millions all others throughout the range of Maya writings, in either the codices or the inscriptions.
Before presenting these three numbers, however, a distinction should be drawn between them. The first and second (figs. [58], [59]) are clearly not Initial Series. Probably they are Secondary Series, although this point can not be established with certainty, since they can not be connected with any known date the position of which is definitely fixed. The third number (fig. [60]), on the other hand, is an Initial Series, and the eight or nine periods of which it is composed may fix the initial date of Maya chronology (4 Ahau 8 Cumhu) in a much grander chronological scheme, as will appear presently.