without order, and alternate only as on the boundary of the wheel aforesaid."
Cogolludo (Hist, de Yucathan, Lib. IV, Cap. 5) says:
"They compute their eras and ages, which they write down in their books, by 20 and 20 years and by lustres of 4 and 4. They fix the first year at the east, to which they give the name Cuch-haab. The second, at the west, is called Hiix; the third, at the south, is named Cauac, and the fourth, Muluc, at the north. Five of these lustres being completed, make twenty years; this is what they call a Katun. They place a sculptured stone upon another stone, equally sculptured, fixed with lime and sand in the walls of the temples."
The Perez manuscript, as is well known, counts twenty years to an Ahau. Most of the recent writers have also decided in favor of the same number. Two or three of the most recent authorities, as Dr, Brinton, Charency, and Rosny, are disposed to follow the opinion of Perez, that it contained twenty-four years. I am satisfied that the opinion which holds twenty-four years to be the number is the correct one, and will now proceed to give the proof I have been able to obtain bearing upon this point.
First. If I am correct in my interpretation of the numerals, then the groups of years obtained by using these, as heretofore shown, will necessarily require twenty-four years to the Ahau, no matter with which of the four year-bearing days we begin the cycle; for, although these groups contain but twenty years there is an interval of four years between each two that is not counted.
Second. The method of numbering these periods cannot, as I believe, be accounted for on any other supposition. According to all authorities who have mentioned the subject they were numbered, as I have already stated, thus: 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, the number 13 being the first, 11 the next, and so on. It is not reasonable to suppose that this singular series was wholly an arbitrary selection; on the contrary, it is more than probable that it was obtained in some way through the use of the "13 series." If we examine the table of years. No. XVII, we will see that, commence where we may, and divide it into periods of twenty-four years by transverse lines, the first years of these periods taken in the order they come will accord exactly with this series. Take for example the
