As above stated the new Ahau Katun begins in the year 8 Cauac, and as it invariably began on the second day of the year, that day would be 9 Ahau, as Ahau is the next letter in the alphabet after Cauac. An extension of the table will show that the next period will begin in 6 Cauac on 7 Ahau, and so on in the order of the numerals given above. Thirteen Ahau Katunes, as previously stated, constituted a great cycle of three hundred and twelve years. Sr. Perez states that according to all sources of information, confirmed by the testimony of Don Cosme de Burgos, one of the conquerors and a writer (but whose observations have been lost), the year 1392 A. D. corresponded to the Maya year 7 Cauac, and as the second day of that year was the beginning of an era of twenty-four years, it must have been 8 Ahau Katun. By dividing off the time between that date and the beginning of the present century into periods of twenty-four years each, and extending a table of the rotation of the four names of the years, the reader will observe that 13 Ahau will fall in the year 1800; 11 Ahau in 1824; 9 Ahau in 1848; 7 Ahau in 1872, and 5 Ahau in 1896, three hundred and twelve years intervening before this, and any similar combination of Ahau Katunes either have occurred or can be repeated. This would be highly satisfactory if Sr. Perez could be relied upon in this particular, which is doubtful. We are sorry to say that he is certainly chargeable with inaccuracies, which impair the value of his whole system. Most conspicuous of these is one pointed out by Mr. Bancroft, to which we refer the reader below. Señor Perez sets about the verification of his system by citing the death of a notable personage named Ahpula. He states that Ahpula died in the sixth year of 13 Ahau, when the first day of the year was 4 Kan, on the day 9 Imix, the eighteenth of the month Zip. It is seen that 13 Ahau is the second day of the year 12 Cauac which falls in the year 1488, also that the year 1493 is the sixth from the beginning of 13 Ahau, and that its first day is 4 Kan, which is the title of the year. The day is the eighteenth of the month Zip, corresponding to the eleventh of September. The statement is also made that this date fell on 9 Imix. This is tested as follows: The first month of that year commenced on 4 Kan, which combination names the year. The number (of the week of thirteen days) is found by adding seven to the number of the first day of each month successively. The number of the first day of the first month, Pop, in this case being 4, the number of the first day of the second month (Uo) would be 4 + 7 = 11, and that of the first day of the third month (Zip) would be 11 + 7 = 18, but as the week consists of but thirteen days, that number must be substracted, leaving 5 Kan as the first day of Zip. If Zip begins on the twenty-fifth of August, the day 9 Imix will be found to correspond both with the eighteenth of Zip and the eleventh of