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 commencement 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 attention 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 positively that these periods are Ahaues, or that they are even embraced in or coincide with them; still, the oftrepeated 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 these 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, without 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 they did by 20 and 20 years, computing 13 twenties with one 'of the twenty letters of their month called Ahau, but
