First of all I should like to say that the dates are not intended to be more than approximate; even the records of Mexican history are not in absolute accordance, and contradictions become more frequent and serious in proportion with the remoteness of particular events from the date of the conquest. However, the history of the valley can be compiled with some degree of probability when the different accounts are studied from the point of view detailed on p. 19, though the dates of Toltec history, before the fall of the city, are in the highest degree problematical. The books of Chilan Balam give a chronology for the history of the Tutul Xiu which can be related to European time, though they do not agree exactly among themselves, and interpolations of a whole cycle appear to occur in places. The dating which I have adopted, which is in the main that of the book of Chilan Balam of Mani, is a conservative interpretation of these records, and may, I believe, be credited with reasonable probability. The dating of the monuments, the most important question of all, is unfortunately the most problematical, and the chain of evidence by which I seek to assign them a place in chronology has two weak links, one considerably weaker than the other. The first of these is the assumption that the initial dates on stelæ refer to the erection of the monuments in question. In considering this question I would omit Palenque, which is obviously, from the architectural and artistic point of view, one of the latest ruins in the central Mayan area. Further, the dates do not occur on stelæ, but for the most part on mural tablets in temples, and may well be “mythical,” and based upon calculations into past time made at a period when the art of chronology, if such a phrase be permitted, had attained a great development in the hands of a specialist priesthood. At other sites the fact that the dates form more or less connected series, and correspond on the whole to the development of architecture, lends a certain probability to the theory that they are “historical” and the theory receives some support, in a negative way, from the extreme difficulty of assigning them any other reasonable function. The other link, which I frankly admit is far weaker, consists in an attempt to correlate them with the dating of the books of Chilan Balam, and this I will now explain. I have tried to show that the buildings at Chichen Itza may be divided into three main classes, corresponding in a rather remarkable manner to the principal epochs of Tutul Xiu tradition; and I have pointed out that what may be considered the earliest group is distinguished by a date in the “long count” characteristic of the central Mayan region. I have also explained that there is reason to believe that Chichen was inhabited before the arrival of the Tutul Xiu, and the presence of the early Maya in Yucatan is supported by the “long count” date at Tulum. It seems