To this day the Indians call the year Jaab or Haab, and, while heathens, they commenced it on the 16th of July. It is worthy of notice that their progenitors, having sought to make it begin from the precise day on which the sun returns to the zenith of this peninsula on his way to the southern regions, but being destitute of instruments for their astronomical observations, and guided only by the naked eye, erred only forty-eight hours in advance. That small difference proves that they endeavoured to determine, with the utmost attainable correctness, the day on which the luminary passed the most culminating point of our sphere, and that they were not ignorant of the use of the gnomon in the most tempestuous days of the rainy season.

They divided the year into 18 months, as follows:

1st, Pop, beginning on the 16th of July.
2d, Uóó, beginning on the 5th of August.
3d, Zip, beginning on the 25th of August.
4th, Zodz, beginning on the 14th of September.
5th, Zeec, beginning on the 4th of October.
6th, Xul, beginning on the 24th of October.
7th, Dze-yaxkin, beginning on the 13th of November,
8th, Mol, beginning on the 3d of December.
9th, Dchen, beginning on the 23d of December.
10th, Yaax, beginning on the 12th of January.
11th, Zac, beginning on the 1st of February.
12th, Quej, beginning on the 21st of February,
13th, Mac, beginning on the 13th of March.
14th, Kankin, beginning on the 2d of April.
15th, Moan, beginning on the 22d of April.
16th, Pax, beginning on the 12th of May.
17th, Kayab, beginning on the 1st of June.
18th, Cumku, beginning on the 21st of June.

As the 18 months of 20 days each contained but 360 days, and the common year consists of 365, five supplementary days were added at the end of each year, which made part of no month, and which, for that reason, they called "days without name," xona kaba kin (= Neg. Name. Days.). They called them also uayab or uayeb Jaab (= Year. ); which may be interpreted two different ways. The word uayab may be derived from uay, which means "bed" or "chamber," presuming that the Indians believed the year to rest during those days; or uayab may equally be derived from another signification of uay, viz., to be destroyed, wounded, corroded by the caustic juice of plants, or with ley and other strong liquids. And on this account the Indians feared those days, believing them to be unfortunate, and to carry danger of sudden deaths, plagues, and other misfortunes. For this reason these five days were assigned for the celebration of the feast of the god Mam, "grandfather." On the first day they carried him about, and feasted him with great magnificence; on the second they diminished the solemnity; on the third they brought him down from the altar and placed him in the middle of the temple; on the fourth they put him at the threshold or door; and on the fifth, or last day, the ceremony of taking leave (or dismissal) took place, that the new year might commence on the following day, which is the first of the month Pop, corresponding with the 16th of July, as appears by the preceding table. The description of the god Mam may be seen in Cogolludo.

The division of the year into 18 months of 20 days would have given only the sum of 360 days; and the first day of the year falling on Kan, the last would have fallen on Akbal, so as to begin again the next year with the same Kan, making all the years alike. But as, in order to complete the year, they added five days, the result was that the year which commenced in Kan ended in Lamat, the last of the first series of five days; the ensuing year commenced in Muluc, the first of the second series of five days; the third commenced in Gix, the first of the third series; and the fourth in Cauac (the first ending in Akbal), the last of the fourth series of five days; so that the fifth year again began with Kan. It has also been stated that the year consisted of 28 weeks of 13 days each, and of one additional day; so that, if the year commenced with the number one of the week, it ended with the same number, and the ensuing year began with number two; and so on through the thirteen numbers of the week, thus forming, with the four initial days, the week of years, or indiction, of which we shall speak hereafter.

The following is the order of the twenty days in each of the 18 months composing the years formed by the four initial days together with the intercalary or complementary days.

Year beginning with the day Kan.Year beginning with the day Muluc.Year of Gix.Year of Cauac.
Kan.Muluc.Gix.Cauac.
Chicchan.Oc.Men.Ajau.
Quimí.Chuen.Quib.Ymix.
Manik.Eb.Caban.Yk.
Lamat.Ben.Edznab.Akbal.
Muluc.Gix.Cauac.Kan.
Oc.Men.Ajau.Chicchan.
Chuen.Quib.Ymix.Quimí.
Eb.Caban.Yk.Manik.
Ben.Edznab.Akbal.Lamat.
Gix.Cauac.Kan.Muluc.
Men.Ajau.Chicchan.Oc.
Quib.Ymix.Quimí.Chuen.
Caban.Yk.Manik.Eb.
Edznab.Akbal.Lamat.Ben.
Cauac.Kan.Muluc.Gix.
Ajau.Chicchan.Oc.Men.
Ymix.Quimí.Chuen.Quib.
Yk.Manik.Eb.Caban.
Akbal.Lamat.Ben.Edznab.
Intercalary days.Intercalary days.Intercalary days.Intercalary days.
Kan.Muluc.Gix.Cauac.
Chicchan.Oc.Men.Ajau.
Quimí.Chuen.Quib.Ymix.
Manik.Eb.Caban.Yk.
Lamat.Ben.Edznab.Akbal.

5°. The Bissextile.

The connexion between the days or numbers of the week which designate the beginning of the year, and the four initial or first days of the series of five, is so intimate that it is very difficult to intercalate an additional day for the bissextile, without disturbing that correlative order of the initials which is constantly followed in the denomination of the years, and forms their indictions, or weeks. But as the bissextile is necessary to complete the solar course, and as I have not any certain knowledge of the manner in which the Indians effected that addition, I will exhibit the method adopted by the Mexicans, their computation being very analogous to that of Yucatan, which in its origin probably emanated from Mexico.

Veyta asserts, in ch. x. of his "Historia Antigua de Mexico," that the bissextile was made by adding at the end either of the 18 months or of the five supplementary days, a day which was marked with the same hieroglyphic as the one preceding, but with a different number of the week, viz., with the succeeding number. But in each way that numerical order by which the years follow each other till they form the week of years, is disturbed; since the fifth year would thus be designated by the number 6 instead of 5, and the regular order of the years 4 to 6 be thereby interrupted. These interruptions, recurring every fourth year, would render it impossible to preserve that continuous harmony (on which rests the whole system of the Indian computation) between the numbers of the week which designate the ending year and its successor, as shown in the uniform succession of the four initial days.