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. In order to prevent that inconvenience, it is necessary to suppose that the Indians, whether they intercalated the additional day at the end of the 18 months or after the five supplementary days, did not only give to it the same number and hieroglyphic as to the day immediately preceding, but also designated it by some peculiar sign or number, in order that it might not be confounded with any other. In a treatise published by Akerman, the opinion is expressed that the Indians, at the end of their cycle of 52 years, added a week of days in lieu of the bissextile days which had been neglected. This method has not the defect of disturbing the numerical order of the years, but that of deranging the series of the four initial days, which, as has been stated, gives designation to the years. It will be seen by the table of indictions, that each cycle consists of four complete weeks of years, formed by series of each one of the four initial signs, each week of years commencing with number one and ending with number thirteen; consequently, if, at the end of each cycle, a week of days be added, the first day of the ensuing year would be the 14th in the series of the 20 days of the month (instead of being the 1st, 6th, 11th, or 16th), thus abandoning the regular series of the four initial days, and substituting others, changing them again at each new cycle. 6 deg.. _Katun, or Cycle._