The beginning of the year is variously stated. Among the Mexicans it seems that, while the authors differ very much, all but one places it on some day between the second day of February and the tenth of April. As their word for year means “new green,” it is probable they placed its commencement about the time new grass appeared. The Mayas are said to have placed the commencement of the year about the sixteenth of July. As this happens to be just about the time that the sun is directly overhead in Yucatan, it has been surmised that the natives took astronomical observations, and tried to have their year commence at that time. But it must be manifest that, if they did not possess a knowledge of the true length of the year, and so make allowance for the leap-year, in the course of a very few years they would have to revise this date.

Refer once more to the Maya table of days. Suppose the first day of the year to commence with the day Kan. As there are twenty days in a month, we see that the second month would also commence with Kan. In like manner, Kan would be the first day of every month of that year. When the eighteen months were past, there would still remain the five days to complete the year. Now, although they were said to be nameless days, the Mayas gave them names. The first day was Kan, the second day Chichan, the third day Quimij, the fourth day Manik, the fifth day Lamat. The regular order of days we see. They were now ready to commence a new year.

The next day in the list is Muluc. This becomes the first day of the first month of the new year. But, being the first day of the first month, it was the first day of every month of that year. At the end of the eighteen months of that year, the five days would have to be named in their order again, which would carry us down to Gix, the first day of the first month of the third year. It would also be the first day of every month of that year. Similarly we see that Cavac would be the first day of every month of the fourth year. The fifth year would commence again with Kan. So we see that four of these twenty days became of more importance than the others. The years were named after them. The year in which the month commenced with Kan was also called Kan. The same way with the other days. So the name of the year was either Kan, Muluc, Gix, or Cavac. These four days were called “carriers of the year;” because they not only gave the name to the year, but because the name of the year was also the name of the first day of every month of that year.

The foregoing will help us to understand the Mexican method. Let us refer now to the list of Mexican days. The first day of the first month was Cipac. For the same reason as above set forth, this would be the first day of every month of the year. The five extra days either were not named at all, or at any rate they were not counted off in the table of days. The consequence was that Cipac was the first day of every month; for we have just seen that it was the first day of every month of the first year. At the end of the eighteen months the five nameless days would come in; but, as they did not form part of a month, were not named. The first day of the first month of the next year would be named as if they had not occurred.72 But, when they came to name the years, we find they proceeded on exactly the same principle as the Mayas. Thus four of the twenty days, occurring just five days apart, were taken to name the years. These days were Tecpatl, Calli, Tochtli, and Acatl.73

Mr. Bandelier, who made the valuable suggestion in regard to the origin of the names of the days, has also suggested that, inasmuch as there are four of the days more prominent than the others, they may signify four original gentes, from which the others have come. It seem to us, however, when we notice they are just five days apart, that the system pursued by the Mayas in naming their years explains the whole matter.

Before we mention the longer periods of time in use among them we must refer to another mode of reckoning time, and trace the influence of this second method on the one already named. The method already explained seems to have been a perfectly natural one—the second method is founded on superstition. A large part of the duties of the priests, we remember, was to determine lucky and unlucky days, and in soothsaying. For this purpose they made a peculiar division of time, which we will now try and explain.

For some cause or other, thirteen was a number continually recurring in their calendar. We can perceive no reason why it should have been chosen. It has been suggested that it was just about the time from the appearance of a new moon to its full. Be that as it may, the number of days thirteen comes very near to what we would call a week. Among the Mexicans, and probably among the Mayas, these thirteen days were divided into lucky, unlucky, and indifferent days, and were supposed to be under the guidance of different gods. The priests had regularly painted lists of them, with the deities which governed them. These lists were used in fortune telling.

We must now inquire as to how they kept track of the years. The Mayas named their next longer period of time an ahau. There is some dispute as to what number of years it meant. Most of the early writers decide that it was twenty years;74 but Perez, whose work we have already referred to, contends that it was twenty-four years. And this conclusion seems to be confirmed by a careful study of some of their old manuscripts.75 Thirteen of these ahaus embraced their longest period of time, known as an ahau-katun. It had a length of either two hundred and sixty or three hundred and twelve years, according as we reckon either twenty or twenty-four years to an ahau. It may be that the length of an ahau varied among the different tribes of the Mayas.

The Mexicans also had this week of thirteen days. Twenty of these weeks, or two hundred and sixty days, formed that part of the year they called the moon-reckoning; the remainder of the year was the sun-reckoning. Their longer period of time was also based on this number. A period of thirteen years they called a tlapilli; four of these constituted a cycle equal to fifty-two years. The end of this cycle was anxiously awaited by the Mexicans. They supposed the world was to come to an end on one of these occasions. As the time drew near, the furniture was broken, the household gods were thrown into the water, the houses were cleaned, and finally, all the fires were extinguished. As the last day of the cycle drew to a close, the priests formed a procession, and set out for a mountain about six miles from Mexico. There an altar was built. At midnight a captive, the bravest and finest of their prisoners, was laid on it. A piece of wood was laid on his breast, and on this fire was built by twirling a stick. As soon as fire was produced, the prisoner was killed as a sacrifice. The production of new fire was proof that the gods had granted them a new period of fifty-two years.

To understand how the years in this cycle were arranged and numbered, we must refer once more to the Mayas, for though they did not use the cycle themselves, yet they give us a hint as to how it was obtained, and afford one more reason why we should think the Mayas were the originators of this calendar system. We give a table showing the arrangement of the days of the year among the Mayas. We will take the year Kan—that is, we remember, when Kan was the first day of every month. We would naturally think they would describe a day by giving the name of the day and the month—as, the day Kan, of the month Xul, or the first day of the month Xul—but instead of so doing, they made use of the period of thirteen days.