For instance, we see, by looking at the table, that the day ten Kan can not be any other day during the year than the day above mentioned; so that, for all purposes, it is sufficient to give the day and its number in the week. We notice, however, that the last five columns of figures for week days of thirteen are just the same as the first five. But this did not confuse any, for the last five columns of days belong to the “sun-reckoning,” the others to the moon-reckoning. And though the number of the day in the week was the same, yet a different deity ruled over them than in the corresponding days of the first five columns. We can not affirm that we know this to be true of the Mayas. Such, however, we know to be the case among the Mexicans.76
Now we notice in this almanac that the last day of the year Kan, is number one of the week. As the count goes right along, the first day of the next year, Muluc, must be number two. If we would make an almanac for that year, we would find the first day of the third year would be number three of the week. If we were to continue this, we would find that the first days of the years, would range from one to thirteen. This table shows the number in the week of the first day of the first fourteen years. The first day of the fourteenth year would be number one of the week again, but this time one Muluc, and not Kan. If we would continue our researches, we would quickly discover that fifty-two years would go by before we would have a year Kan in which the first day of the year would be number one again.
We think the above explains the origin of the Mexican cycle of fifty-two years. The Mayas either never had this cycle, or had abandoned its use.77 The Mexicans however, used this period of time, and they numbered their years in it in such a way that we can not explain it, unless we suppose they derived it in some such a way as just set forth. We give a table showing the order of the years in a cycle, and also notice that all that was needed was the number and name of the year to show at once what year of the cycle it was. The year seven Calli, for instance, could never be any other year than the twentieth of the cycle.78
To express the dates, they of course painted the hieroglyphic of the day, and dots for the number of days. This cut, for instance, expresses the day-date “seven Acatl.” They generally wrote the dots in sets of five. Seven was sometimes expressed in the above manner. When they wished to express a year-date, they made a little frame and painted in the hieroglyphics of the year, and dots for the number. This date here expressed is their thirteen Acatl, which, by the above table, is seen to be the twenty-sixth year of the cycle.
We have already dwelt too long on this part of the subject. Glancing back over the ground, we see there is nothing implying astronomical knowledge, more than we would expect to find among a rude people. We find there are several particulars of the Mexican system which we could not understand, except by reference to the Maya system. It would bother us to explain why they should choose the days Tochli, Acatl, Tecpatl, and Calli, to be the names of their years, if we did not know how the Mayas proceeded. We would be at a loss to explain why they choose the number of fifty-two years for the cycle, and arranged their years in it as they did, if we had not learned the secret from the construction of the Mayas’ almanac. From this comparison, we should say the Mexican calendar was the simpler of the two. As the Mayas had twenty days in the month, and, for priestly use, weeks of thirteen days, so they took twenty years, which, as they imagined, were supported by four other years, as a pedestal for their next longer period, the ahau; and for apparently no other reason than that they had weeks of thirteen days, they took thirteen of these ahuas for their longest period of time. They did not use the cycle of fifty-two years, but they numbered their years in such a way that, in effect, they were possessed of it. The Mexican did away with all but the cycle of fifty-two years.