10 A STUDY OF TDE MANUSCRIPT TROANO. 



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. 

 Ill 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 commence- 

 ment 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 cer- 

 tain 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 requii-ed 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 the}^ 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 



