The Indians made (painted) a small wheel, in which they placed the four hieroglyphics of the initial days, _Kan_ in the east, _Muluc_ in the north, _Gix_ in the west, and _Cauac_ in the south, to be counted in that order. Some suppose that when the fourth year was accomplished, and _Kan_ was again in order, a _Katun_ or lustre of four years, was completed; others, that three revolutions of the wheel, with its four signs, were reckoned, with one (sign) more, which made 13 years, and that this completed the _Katun_; others, again, that the four complete weeks of years, or indictions, constituted the _Katun_; and this is probable. Besides the small wheel aforesaid, they made another great wheel, which they also called _buk xoc_ and in which they placed three revolutions of the four signs of the small wheel, making 12 signs; beginning to count by the first _Kan_, and continuing to reckon all until the fourth naming of the same Kan, which was included, thus making thirteen years, and forming one indiction, or week (of years); the second reckoning began with _Muluc_, ending in the same, which formed the next thirteen; and so on, till they came to Cauac, which formed a Katun. 7 deg.. _Of the Indiction and Cycle of 52 Years, or Katun._ As in the preceding explanations sufficient idea has been given of what constituted the indiction and the cycle of 52 years, called by the Indians _Katun_, the facts are briefly recapitulated here, that the reader may not be fatigued hereafter with new explanations. 1st. The name of indiction is given to each one of the four weeks of years composing the cycle of 52 years. 2d. The American week was formed by the course of 13 numbers, applied indiscriminately to the 20 days of the month. 3d. It has been explained, that as the year was formed of 26 weeks and one day, by this overplus the years succeeded each other, following the correlative order of their numbers up to 13, in order to form a week, or indiction; for if the year had been composed of exactly 28 weeks, the numbers of the new years would never have formed a correlative week, because they would have commenced with the number 1, and finished with 13; by the other method, one year begins with the first, and terminates in the same; the second year commences with the number 2 and also finishes with it; and so on successively, until the 13 are completed.