The inhabitants of this peninsula, which, at the time of the arrival of the Spaniards, was called _Mayapan_, and by its first inhabitants or settlers _Chacnouitan_, divided time by calculating it almost in the same manner as their ancestors the Tulteques, differing only in the particular arrangement of their great ages (siglos). The period of 13 days, resulting from their first chronological combinations, afterward became their sacred number, to which, introducing it ingeniously in their reckonings, they made all those divisions subordinate which they devised to adjust their calendar to the solar course; so that the days, years, and ages were counted by periods of thirteen numbers. It is very probable that the Indians, before they had corrected their computation, used the lunations (neomenias) to regulate the annual course of the sun, counting (senalando) 26 days for each lunation; which is a little more or less than the time during which the moon is seen above the horizon in each of its revolutions; dividing this period into two of 13 days, which served them as weeks, giving to the first the first 13 days during which the new moon is seen till it is full; and to the second, the other thirteen, during which the moon is decreasing until it cannot be seen by the naked eye. 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 deg.. _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 deg.. _The Month._