A third division of time employed by the Mayas was the great cycle of 312 years, composed, according to Señor Perez,[631] of thirteen periods of time, each embracing twenty-four years. Each of these thirteen periods was called an Ahau Katun, and was divided into two parts. The first part, embracing twenty years, was enclosed in a square and called _Amaytum lamayte_, or _lamaytum_; and the other part of four years, which formed as it were a pedestal for the first, was called _Chek oc Katun_, or _lath oc Katun_, meaning “stool” or “pedestal.” He affirms that the latter were intercalated, therefore believed to be unfortunate as were the five supplementary days of the year. This may account for their not being reckoned with the Ahau Katun by any other writer. Just here lies the discrepancy which has created most of the confusion in the investigation of this subject. However, if we accept the statement of Señor Perez, that the Ahau Katun embraced twenty-four years instead of the testimony of every other writer that it included but twenty years, we shall have moderately fair sailing until we split upon the rock of his inaccuracies as to dates. He tells us that these periods took their name from Ahau, the second of those years that began in Cauac, and from the order of the numerals accompanying those days would succeed each other according to the numbers 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2. The Indians established the number 13 Ahau as the first, because some great event happened in that year. If the 13 Ahau Katun began on a second day of the year, it must have been the year which began on 12 Cauac, and the 12th of the indiction. The next or the 11 Ahau would commence in the year 10 Cauac, which combination in its rotation would happen after a lapse of twenty-four years. The third or 9 Ahau would begin in 8 Cauac twenty-four years later, in illustration of which we follow out the rotation of the four names of the years, Kan, Muluc, Ix and Cauac, through the indictions of thirteen years each, until we have noted the numerals accompanying them during twenty-four years. Our starting point will be the commencement of the second Ahau Katun on the second day of 10 Cauac.