This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau, were each equal to a score of years of 365 days each. When, however, we try to account for the numbering of the katuns on this basis, we find that the numbers of the ahaus ending each katun would come in the following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc., while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12. 10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”[2] which occurs in paragraph 3, is taken literally, there would seem to be no explanation of this difficulty; but if we consider that these books used these words as we often use them now as meaning approximately “years,” and if we substitute the third term of the numeral series as found in the codices for the word “years”—in other words, if we substitute 360 for 365—we find then that the katuns or scores of 360 days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12. 10, etc., as has been said and as given in the Books of Chilan Balam. This has been shown by Seler, Goodman, and others.
[2] It is very probable that “años” is merely a gloss—and an erroneous one at that.
It will then be a good working theory that the score of 360 days is called a katun, and that each katun is distinguished by the name of an ahau with its proper number, with which a katun ended. That the ahau and its number are merely the name of the katun and not the katun itself is shown in No. 5 of Brinton’s Books of Chilan Balam,—the Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau” was a synonym for “katun” would be as foolish as to say of a family containing John Smith, Mary Smith, and James Smith, that John and Mary and James were all synonyms of Smith, when they were merely names to distinguish one Smith from another.
This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s “Maya Chronicles”), where
Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”
” 9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”
” 10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”
” 12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”
” 15 says “u katunil ho ahau,” “In the katun 5 Ahau.”
Also in the Book of Tizimin (pp. 139 et seq. of Brinton):
Par. 6, “Uaxac ahau—lay u katunil,” “8 Ahau—in this katun.”
” 14, “Bolon ahau—lai—u katunil,” “9 Ahau—in this katun.”
” 15, “Vuc ahau—u katunil,” “7 Ahau—in this katun.”
Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):
Par. 2, “Uaxac ahau—layli u katunil,” “8 Ahau—in this katun.”
” 8, “Bolon ahau—u katunil,” “9 Ahau—in this katun.”
Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):