In the lapse of time, and by constant observations, they obtained a better knowledge of the solar course, perceiving that the 26 days, or two periods of 13 days, did not give a complete lunation, and that the year could not be regulated exactly by lunations, inasmuch as the solar revolutions do not coincide with those of the moon, except at long intervals. Adding this knowledge to more correct principles and data, they finally constructed their calendar in accordance with the course of the principal luminary, preserving always their periods of 13 days, not in order to make them agree with the apparent course of the moon, but to use them as weeks, and for their chronological divisions.
2°. The Weeks.
It must not be supposed that the weeks of the ancient Indians were similar to ours, that is to say, that they were the revolution of a period of days, each having a particular name: they were only the revolution or successive repetition of thirteen numbers applied in arithmetical progression to the twenty days of the month. The year being composed of 28 weeks and one additional day or number, the course of the years, on account of that excess, followed the arithmetical progression of the thirteen weekly numbers; so that if a year commenced with the number 1, the next would commence with number 2, and so on to the close of the 13 years, which formed an indiction, or week of years, as will be explained hereafter.
3°. The Month.
"Month" is called in the Yucateco language "U," which means also "the moon;" and this corroborates the presumption that the Indians went on from the computation of lunations to determine the course of the sun, calling the months "moons." But in some manuscripts, the name of Uinal in the singular and Uinalob in the plural is given to the eighteen months which compose the year; applying this comprehensive term to the series, and to each one of the particular names assigned to the twenty days that composed the month.
The day was called Kin, "the sun;" and the particular names by which the 20 days composing the month were designated are stated in the following table, in which they are divided into sets of five, for the better understanding of the subsequent explanations.
| 1st. | 2d. | 3d. | 4th. |
| Kan. | Muluc. | Gix (Hix) | Ca-uac. |
| Chicchan. | Oc. | Men. | Ajau (Ahau). |
| Quimí (Cimí). | Chuen. | Quib (Cib). | Ymix. |
| Manik. | Eb. | Caban. | Yk. |
| Lamat. | Been. | Edznab. | Akbal. |
As those names corresponded in number with the days of the month, it followed that, the name of the first day of the year being known, the names of the first days of all the successive months were equally known; and they were distinguished from each other only by adding the number of the week to which they respectively belonged. But the week consisting of thirteen days, the month necessarily consisted of a week and seven days; so that if the month began with the first number of a week, it ended with the seventh number of the week ensuing.
[In order to know the number of the week corresponding with the first day of each month respectively, it is necessary only to know the number of the week with which the year begins, and to add successively seven, but subtracting thirteen whenever the sum of this addition exceeds thirteen, which gives the following series for the first days of the eighteen months: 1, 8, 2 (15-13), 9, 3 (16-13), 10, 4, 11, 5, 12, 6, 13, 7, 1, 8, 2, 9, 3, supposing the first day of the year to be the first day of the week, and generally taking for the first number of the series the number of the week by which the year begins.]
4°. The Year.