APPENDIX. 



439 



glyphic 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 dis- 

 turbed; since the fifth year would thus be designated by the number 6 in- 

 stead of 5, and the regular order of the years 4 to 6 be thereby interrupted. 

 These interruptions, recurring every fourth year, would render it impossi- 

 ble to preserve that continuous harmony (on which rests the whole system 

 of the Indian computation) between the numbers of the week which desig- 

 nate 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 In- 

 dians, 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 designa- 

 tion 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°. Katun, or Cycle. 



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 



