probable that the Tutul Xiu themselves did not use the long count, but reckoned time, as in the books of Chilan Balam, by the “short count,” i.e. by the initial day of the katun alone. It is an interesting fact that in more than one of the versions we find a statement that, after their arrival at Chichen Itza, “Pop was first counted in order,” with the variant “Pop was set in order,” and this is, I think, capable of explanation in one of two ways. In the first place, it may refer to some change in the calendar, necessitated by the fact that the absence of intercalary days had brought the commencement of the year noticeably out of tune with the seasons. In the second, it may indicate the actual adoption of the early Maya month-system, which they found prevailing at Chichen. We may assume, from what evidence exists, that the month-names were never expressed in dating in the Mexican valley, and we know that the Tutul Xiu placed their original home within the realm of “Tulan.” It may be remarked in passing that, whichever explanation be adopted, this was probably the occasion when the change in the “year-bearers,” from the early system to the later, was made, and it may further be noted that such a change would not necessarily affect the katun count. In any case the essential point on which I would lay stress is that the initial date at Chichen belongs to the period before the arrival of the Tutul Xiu. Now the katun expressed in this initial date would be termed in the short count “katun 3. ahau,” and I think it reasonable to assume that this corresponds with the last “katun 3. ahau” of the Tutul Xiu chronology _before_ they arrived at Chichen Itza. It may of course be earlier, but I think this extremely unlikely, having regard to the similarity between such buildings as the Monjas group and those of the central Mayan area. If this assumption be admitted, then the dates of the monuments can be brought into line with historical chronology as appears in the Appendix.