I can find no excuse for considering “ahau” as a synonym for “katun” in these Books of Chilan Balam. And _a priori_ it is difficult to conceive of a numeral system being made up by a nation as cultivated as the Mayas, by which the name of a day should be taken to mean a period of time, with all the chances of error which might arise from such use. Moreover, if this were the case, it would be natural to suppose that in the inscriptions and codices the day sign ahau might be found meaning 7200 days, and yet I am unaware that a single instance of this exists on the monuments or in the codices. There are one or two cases in the inscriptions where this has been suggested as being possible, but it is very far from being proved or from even having strong evidence in favor of such an explanation. Dr. Förstemann says that at times the name “katun” was given to the period of 18,980 days; but the only authority for this use is, as far as I know, Pio Perez, who says that some applied the name to a “lustre of 4 years,” while others thought that “13 years completed the katun.”[3] Again Pio Perez speaks of “the cycle of 52 years called by the Indians katun.” In none of these cases is any authority given for this use.[4] [3] Stephens, “Travels in Yucatan,” Appendix, p. 439. [4] Ibid., p. 440. It is probably safe to say that any use of the word “ahau” as meaning a katun, or any use of the word “katun” as meaning anything but 20 times 360 days, or any use of the day symbol ahau as meaning a period of time, does not occur in any evidence which could be called contemporary or even approximately so. Don Pio Perez is, I fear, the only author who can be cited for the other side, and his opinion, though worthy of being listened to, is not to be relied upon without the support of, or against the evidence of, early authorities. The second question as to the name to be given to the period of 360 days must be decided by the same authority. We have found that a katun is probably a score of periods of 360 days each, and it would be natural to suppose that the constituent parts of the katun, as mentioned in the Books of Chilan Balam, would be these periods of 360 days, but of this there is no absolute proof in the Books of Chilan Balam. The proof of this, however, is so strong in the Dresden Codex, where the series runs, 20 of the first order equals 1 of the second order, 18 of the second order equals 1 of the third order, and 20 of the third order equals 1 of the fourth, that no time need be wasted upon this part of the question. We do know, however, that each of these constituent parts is called a tun and that they are numbered as high as 13. The following list gives, I think, all the cases where the word “tun” is used in the Books of Chilan Balam: