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52 have adopted, which is repeated on the annexed Table XXI, does not preclude us from accepting Perez's theory that they were numbered from the second day of the first year, which, as the periods begin with Cauac, would be Ahau. This would change the position of the Ahaues so far as their numbers are concerned, and they would then stand as shown in this table; that is, the first one in the grand cycle would be No. II, the next XIII, and so on in the usual order. But one very serious objection to this plan of numbering is that 4 Kan of the XIIIth Ahau would be the sixth instead of the eighteenth year.

I am of the opinion that the only foundation Perez had for thus numbering these periods is the fact that the name "Ahau" was applied to them. It is probable that it was sometimes so applied on account of their importance, but a careful study of the language of Landa and Cogulludo lead me to believe that Katum was the name by which they were usually designated. The latter author gives this term only. Landa simply remarks that "they counted 13 twenties with one of the twenty letters of their month which is called Ahau, without order and alternate only as on the border of the wheel above; they called these, in their language, Katunes."

The most serious objection which, so far as I see, can be urged against my theory is that the series of Ahaues does not begin with XIII, or, in other words, that the first of the grand cycle is not XIII. But this objection applies with equal force to Perez's scheme. If we adopt the division shown in Table XVIII, and suppose the numbering to correspond with the first year (Cauac) of each period, we would then commence the grand cycle with the XIIIth Ahau. To illustrate this I give a table (XXII) similar to XVIII so far as the division of the grand cycle is concerned, but numbered as above suggested.