54 BUREAU OF AMERICAN ETHNOLOGY [bdll. 57 



the names of the first days of all of its divisions, was shifted forward 

 in the sequence another 5 days, as shown above. 



This leads directly to another important conclusion : Since the first 

 days of all the divisions of any given year always had the same name- 

 part, it follows that the second days of all the divisions of that year 

 had the same name, that is, the next succeeding in the sequence of 

 twenty. The third days in each division of that year must have had 

 the same name, the fourth days the same name, and so on, through- 

 out the 20 days of the month. For example, if a year began with the 

 day-name Ik, all of the divisions in that year also began with the 

 same name, and the second days of all its divisions had the day-name 

 Akbal, the third days the name Kan, the fourth days the name 

 Chicchan, and so forth. This enables us to formulate the following — 



Rule. The 20 day-names always occupy the same positions in all 

 the divisions of any given year. 



But since the year and its divisions must begin with one of four 

 names, it is clear that the second positions also must be filled with 

 one of another group of four names, and the third positions with one 

 of another group of four names, and so on, through all the positions 

 of the month. This enables us to formulate a second — 



Rule. Only four of the twenty day-names can ever occupy any 

 given position in the divisions of the years. 



But since, in the years when Ik is the 1st name, Manik will be the 

 6th, Eb the 11th, and Caban the 16th, and in the years when Manik 

 is the 1st, Eb will be the 6th, Caban the 11th, and Ik the 16th, and 

 in the years when Eb is the 1st, Caban mil be the 6th, Ik the 11th, and 

 Manik the 16th, and in the years when Caban is the 1st, Ik will be 

 the 6th, Manik the 11th, and Eb the 16th, it is clear that any one of 

 this group which begins the year may occupy also three other positions 

 in the di\asions of the year, these positions being 5 days distant from 

 each other. Consequently, it follows that Akbal, lamat, Ben, and 

 Eznab in Table V, the names which occupy the second positions in 

 the divisions of the year, will fill the 7th, 12th, and 17th positions as 

 well. Similarly Kan, Muluc, Ix, and Cauac will fill the 3d, 8th, 13th, 

 and 18th positions, and so on. This enables us to formulate a third — 



Rule. The 20 day-names are divided into five groups of four names 

 each, any name in any group being five days distant from the name 

 next preceding it in the same group, and furthermore, the names of 

 any one group will occupy four different positions in the divisions of 

 successive years, these positions being five days apart in each case. 

 This is expressed in Table VI, in which these groups are shown as 

 well as the positions in the divisions of the years which the names of 

 each group may occupy. A comparison with Table V will demon- 

 strate that this arrangement is inevitable. 



