It may be here stated that the inscriptions all show that where an even uinal is given (and therefore where an even tun, katun, or cycle is given) the day is Ahau. If then it was desirable to distinguish the katuns from each other, two methods could be used: either count them numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with which the preceding katun had ended. The former method is found in the inscriptions and the Dresden Codex, the latter in the Books of Chilan Balam. The second method would not be possible if each katun ended with the same numbered ahau. But 7200 is not divisible by 13 without a remainder, but equals 13 × 553 + 11. If then a particular katun ended with 13 Ahau, the next would end with Ahau, but the number attached to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun would end with 9, the next with 7, and so on. The katuns then would be known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1 Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc. Taking up, therefore, No. I. of the Books of Chilan Balam, published by Brinton--that of Mani--we find in the paragraph numbered 1 by Brinton “This is the arrangement of the katuns” not “of the ahaus,” and in paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.” This is followed by the statement “When they set out for this country, it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau, 2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when, etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear, and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau are called fourscore years is equally clear. In paragraph 4 we have “4 Ahau, 2 Ahau, 13 Ahau--threescore years they ruled Ziyan caan, etc.” Here three katuns are called threescore years. 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.