28 A STUDY OF THE MANUSCRIPT TROANO. 



what I mean by "properly locating" these periods, I have extended the 

 table so as to include one complete cycle, the close of another, and the com- 

 mencement of another. I have also located this last period — as a matter of 

 course according to the years obtained — in the only two possible positions 

 in the table; surrounding each by a dotted line. If the table had been 

 extended it could of course have been located in other cycles. I call atten- 

 tion to the fact that both these periods commence with a Muluc year, which 

 would render it impossible for the commencement or ending of an Ahau, if 

 these are Ahaues, to coincide with the commencement or ending of a cycle 

 or grand cycle. If we suppose the Ahau to contain twenty-four years, and 

 the periods marked on Table X to omit two years at the commencement 

 and two at the close ; in other words, extend the upper and lower lines 

 bounding the groups, across the table, we will then have no difficulty in 

 making all the periods agree with each other and with the cycles. After 

 all, we are not yet authorized to say positivel}^ that these periods are Ahaues, 

 or that they are even embraced in or coincide with them; still, the oft- 

 repeated five-character day columns, and the resulting groups of years, 

 justify us in assuming that they do at least coincide with them. 



Before proceeding further in our discussion of the Manuscript it will 

 be necessary for us to decide in reference to the following points relating 

 to the calendar upon which we have incidentally touched: 



First. The number of years contained in an Ahau. 



Second. The position of tlfese periods in the grand cycle or Ahau- 

 Katun. 



Third. The respective numbers of these periods as thus fixed in the 

 Ahau-Katun. 



Fourth. With which one of the four days (year bearers) the grand 

 cycle begins. 



That the older authorities, so far as we are aware, Avithout exception, 

 give 20 years as the length of an Ahau, is admitted. Landa, for example, 

 says (in § XLI), "The Indians had not only the computation of the year 

 and the months, but they had also a certain manner of computing the times 

 and events by ages. This the}' did by 20 and 20 years, computing 13 

 twenties with one of the twenty letters of their month called Ahau, but 



