In order to make this as plain as possible I will give here a table of years for one cycle of 52 years. As there is some doubt as to which of the two years—1 Kan or 1 Cauac—the cycle began with, I give tables (Nos. III and IV) for both.
By this time the reader is sufficiently conversant with this sytem to know that if the cycles commence with 1 Kan, as in the left-hand table (No. Ill), the year following 13 Cauac would be 1 Kan and the commencement of another cycle. If the true method were as given in the right-hand table (No. IV), then 13 Ix would be followed by 1 Cauac, the first year of the next cycle. This follows, as will readily be seen, from the fact that 52 is the least common multiple of 4 and 13.
The importance of knowing which one of these arrangements was that used by the Mayas will be apparent from the following illustration: A certain event is dated a particular day in the year 1 Ix; if the table we have headed 1 Kan be correct it Would then be in the 27th year of the cycle; if the other be the true method it would then be in the 40th year of the cycle, or thirteen years later. These years are marked with a star in Tables III and IV.
As this system admits of fifty-two changes in the day on which the year begins, it would require fifty-two different calendars to cover one cycle, just as fourteen calendars are required to suit all the years of our system, seven for the ordinary years and seven for the leap-years. As it would require much time and space to write these) out in full, I have adopted the expedient shown in the following table (No. V), of abbreviating the work.
First we have at the left four columns, each containing the names of the twenty days of the month. As I am inclined to believe that the author of the manuscript adopted the system which had Cauac as the first day of the cycle, the first or left-hand column commences with this day, the others, Kan, Muluc, and Ix, following in the order in which they are found in the list of days. The first column is therefore the one to be used for all the Cauac years; the second for all the Kan years; the third for all the Muluc years, and the fourth for all the Ix years. The reader must be careful to remember, that when. one day of the month is determined it determines all
