56 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



the name parts of the days and not their complete designations. Bearing 

 this in mind, we may state the following facts concerning the 20 day- 

 names and their positions in the divisions of the year : 



1. The Maya year and its several divisions could begin only with 

 one of these four day-names: Ik, Manik, Eb, and Caban. 



2. Consequently, any particular position in the divisions of the 

 year could be occupied only by one of four day-names. 



3. Consequently, every fifth year any particular day-name returned 

 to the same position in the divisions of the year. 



4. Consequently, any particular day-name could occupy only one 

 of four positions in the divisions of the year, each of which it held in 

 successive years, returning to the same position every fifth year. 



5. Consequently, the twenty day-names were divided into five 

 groups of four day-names each, any day-name of any group being 

 five days distant from the day-name of the same group next pre- 

 ceding it. 



6. Finally, in any given year any particular day-name occupied 

 the same relative position throughout the divisions of that year. 



Up to this point, however, as above stated, we have not been deal- 

 ing with the complete designations of the Maya days, but only their 

 name parts or name glyphs, the positions of which in the several 

 divisions of the year we have ascertained. 



It now remains to join the tonalamatl, which gives the complete 

 names of the 260 Maya days, to the haab, which gives the positions 

 of the days in the divisions of the year, in such a way that any one 

 of the days whose name-part is Ik, Manik, Eb, or Caban shall occupy 

 the first position of the first division of the year; that is, Pop, 

 or, as we should ^\Tite it, the first day of Pop. It matters little 

 which one of these four name parts we choose first, since in four 

 years each one of them in succession Avill have appeared in the 

 position Pop. 



Perhaps the easiest way to visualize the combination of the tonala- 

 matl and the haab is to conceive these two periods as two cogwheels 

 revolving in contact with each other. Let us imagine that the firet 

 of these, A (fig. 21), has 260 teeth, or cogs, each one of which is 

 named after one of the 260 d&js of the tonalamatl and follows the 

 sequence shown in plate 5. The second wheel, B (fig. 21), is some- 

 what larger, having 365 cogs. Each of the spaces or sockets between 

 these represents one of the 365 positions of the days in the divisions 

 of the year, beginnijig with Pop and ending with 4 Uayeb. See 

 Table IV for the positions of the days at the end of one year and the 

 commencement of the next. Finally, let us imagine that these two 

 wheels are brought into contact with each other in such a way that 

 the tooth or cog named 2 Ik in A shall fit into the socket named 



