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53 calculation, the epochs from the years 682–1303 A, D., or from the taking of Champotou to the first destruction of Mayapan by the assistance of the foreign Uitzes. This compact period of time touches a very remote epoch in the history of the civilized nations of Central America. It reaches backwards to an epoch when in Europe, Pepin D'Heristal and his family laid the foundation to their future ascendancy on the throne of France. If we look still further backward in our table, we notice another long period of time (sections 3 and 4) which represents the sum of eight uninterrupted Ahaues, equal to 160 years. The connection of these two great periods was re-established by the interpolation of the three Ahaues, 8, 10 and 12 in section 5, a correction for which there should be not the least question. Groping our way, we should reach the epochs when Bacalar was founded, with a date as early as between 462 and 482 A. D. At this point we are no longer able to follow the conquerors on their route. The location of Bacalar is well known to us, but that of Chacnouitan and Tnlapan has escaped our investigation. Notwithstanding, by the aid of the quoted Ahaues we are able to fix the time for the long rest and residence in Chacnouitan, and for their remote starting from Tulapan. It comprises the epochs backwards from the year 462 to that of 162, and since the text reports' that eighty years were spent in the migration, we are entitled to fix the time for the arrival in the peninsula with the year 242 A. D. It is, of significance for our purpose, that this settling on the peninsula can be computed with the year 242 A. D. It represents, as will be seen, the 13th Ahau,a date always assumed by the Maya chronologists as one with which they designate the commencement of a new cycle.