Although, as shown by Table XVII, the grand cycles, if counted from the year 1 of each period, would begin with the 1st Ahau, yet, as the Indians chose, for some reason, to begin these periods with the 13th, our calculations must correspond with this arbitrary selection. I therefore give here a brief table of cycles, with the corresponding years of our era, running backward:
| Years. | |
| Fourth grand cycle | 1519-1830 |
| Third grand cycle | 1207-1518 |
| Second grand cycle | 895-1206 |
| First grand cycle | 583-894 |
The numbers given the grand cycles are (for the present, at least) arbitrary, given simply as a means of reference. We see from this table that the year 935 would fall in the grand cycle numbered 2, and, as before stated, in the 11th Ahau. Referring to this manuscript again, we see that Mayapan is first mentioned in the 7th paragraph, where it is stated that "the 2d Ahau, 13th, 11th, 9th, 7th, 5th, 3d, 1st, 12th, and 10th Ahau, 200 years, they [the Tutul Xiu] governed in Uxmal with the governors of Chichen-Itza and Mayapan."
Here we find our 11th with but two Ahaues preceding it, or, as we judge from the preceding clause—"In this Katun of the 2d Ahau"—but one and part of another. Supposing Mayapan to have been in existence at the commencement of the periods here named, it would carry us back only some forty or fifty years beyond Herrera's general statement; but this is more than accounted for by the difference in the estimated length of the Ahau.
If we count the Ahaues necessary to complete the number from the 2d in the commencement of the seventh paragraph to the 2d in the eleventh paragraph when the Spaniards first appeared, filling up the lacunæ and making the correction in the eighth paragraph suggested by Dr. Valentini, we shall find the number to be as follows:
| 2, 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2. | |
| 13, 11, 9, 7, 6, 3, 1, 12, 10, 8, 6, 4, 2. | |
Making 27 Ahaues, or 648 years.
