"At the end of each Ajau Katun, or period o/ 24 years," says a manuscript, "great feasts were celebrated in honour of the god thereof, and a statue of the god was put up, with letters and inscriptions." It must be supposed that these were expressed by means of signs or hieroglyphics.
The use of this cycle was of very great advantage and importance, because when, for example, the 8th Ajau was referred to in their histories in describing some event which it was necessary to distinguish from others, the 8th Ajau was established as a distinct date, and it was understood that the 312 years had elapsed, which made up the whole Katun, in order to return to the same number; this was more clear, if the writer explained that a uudz Katun had elapsed, which is the sum total of the thirteen Katunes, or the great cycle. They had various modes of quoting the Ajaues, as by saying generally the beginning, middle, or end of such an Ajau, or by mentioning the years of the Katun which had elapsed, without stating the month or day of the year, or by specifying all the particulars of the epoch, the year, month, and day. Such is the passage in which is noticed the death of a certain, without doubt very notable, Ajpula. It is said that he died in the 6th year of 13 Ajau, when the first day of the year was 4 Kan at the east end of the wheel, in the day of 9 Ymix, 18th of the month Zip. This date being so circumstantial, we will trace it out, that it may serve as an example.
Looking at the series of years which belong to the 13 Ajau, and which we have given above, it will be seen that 12 Cauac falls in the year 1488, the second day of that year being, therefore, the beginning of the 13th Ajau; that the year 1493 is the sixth from the beginning of the said Ajau, and that its first day is designated as 4 Kan, which is the title of that year, "18th of the month Zip." As this month begins on the 25th of August, the 18th corresponds with the 11th of September. Let us see now whether this 18th day falls on 9 Ymix. The first month of that year commenced with 4 Kan, since 4 Kan designates that year (see the rule given in treating of the months). We find the numbers (of the week) annexed to the first days of the following months by successively adding 7 to each month, &c. (or, which is the same thing, by the rule buk xoc). The number of the 1st day of the 1st month being in this case 4, the number of the 1st day of the 2d month will be 4+7=11, and that of the 1st day of the 3d month, viz., of Zip, will be 11+7-13=5. That month begins, therefore, in that year, with 5 Kan, and the following days are,
| Days of | Days of the Week. | Days of | Days of the Week. | Days of | Days of the Week. | |||
| Aug. | Zip. | Sept. | Zip. | Sept. | Zip. | |||
| 25 | 1 | 5. Kan. | 1 | 8 | 12. Chuen. | 8 | 15 | 6. Edznab. |
| 26 | 2 | 6. Chicchan. | 2 | 9 | 13. Eb. | 9 | 16 | 7. Cauac. |
| 27 | 3 | 7. Quimí. | 3 | 10 | 1. Ben. | 10 | 17 | 8. Ajau. |
| 28 | 4 | 8. Manik. | 4 | 11 | 2. Gix. | 11 | 18 | 9. Ymix. |
| 29 | 5 | 9. Lamat. | 5 | 12 | 3. Men. | |||
| 30 | 6 | 10. Muluc. | 6 | 13 | 4. Quin. | |||
| 31 | 7 | 11. Oc. | 7 | 14 | 5. Caban. | |||
Thus the 11th of September was the 18th of Zip, which does fall on 9 Ymix, and accords with the date given in the MS. This date appears, therefore, to have been very correct.
Of the Origin of this Cycle.
The origin and use of this species of age, epoch, or cycle, and (the time) when it commenced, are not known. Neither the Mexican nor Toltecan authors, nor those who corrected the chronological system for the computation of time, ever used it, nor had their writers any knowledge of its existence. The few and incomplete manuscripts which exist in this peninsula make no mention of it; so that there is neither record nor even conjecture to guide us, unless there be something on the subject in the work written by Don Cristobal Antonio Xiu, son of the King of Mani, by order of the then government, which, according to the padre Cogolludo, existed in his time, and some allege to be even yet extant.
It appears only that the Chevalier Boturini had some knowledge, though imperfect, of that mode of reckoning time; inasmuch as Don Mariano Veytia, in the second chapter of his "Historia Antigua de Mexico," transcribes literally the explanation which Boturini gives at page 122 of the work which he published under the title of "Idea of a New History of North America," and says, "that the Mexican Indians, when they reckoned in their calendar the first sign of their indiction under number 1, as, for instance, Ce Tecpatl (1 Tecpatl), it was understood that it was (so placed) only one time in every four cycles, because they spoke then of the initial characters of each cycle; and thus, according to the contrivance of their painted wheels, Ce (1) Tecpatl was but once the commencement of the four cycles" [meaning—began a cycle but once in four cycles. But the fact is not so: both in the Mexican and the Yucatec calendar, every cycle of 52 years begins with the same initial character of the year]; "for which reason, any character of those initial signs placed in their history means that four Indian cycles of 52 years each have elapsed, which makes 208 years before they can again occur as initial, because, in this way, no account is taken of characters which are in the body of the four cycles; and though the same characters are found there, they have not the same value."
Veytia affirms that he did not find any similar explanation, or anything alluding to the system of Boturini, in any of the ancient monuments which he had collected or examined, or mentioned by any Indian historian, not even in order to designate the epochs of the most remarkable events. But I believe that, in answer to this remark of Veytia, it may be said that Boturini, as Veytia states elsewhere, had examined the calendars used in old times by the Indians of Oaxacac, Chiapas, and Soconusco, and these being similar to that of the Yucatecos, it is not unreasonable to suppose that they, like the Yucatecos, computed by cycles greater than the Mexicans employed; and that Boturini took from them the idea, though confused and incorrect, of our Ajaus, or great cycles. This incorrectness might arise either from his not understanding the mechanism of their mode of computing, owing to the defective explanation given by the Indians, or from the manuscripts which Boturini had before him being mutilated, or, finally, from the possible fact that the Indians in those provinces had a particular custom of counting by cycles of four indictions, or of 208 years, which, notwithstanding the difference observed in their calculation, and the number of years which it produces, have a great analogy with the Yucateco cycles of 312 years. The only thing for which Boturini may be censured, if the Mexicans had no knowledge of that cycle, and did not use it, was the ascribing of it to them as being in common use for the computation of the greater periods of time.
The great similarity between the names of the days in the calendar of Oajaca, Chiapas, and Soconusco, and those of the Yucatecos, has been mentioned, and appears clearly by comparing the latter with those of the said provinces, which Veytia has transcribed in his history, chap. xi., at the end.