Ahaues as there given: the first commences with the year 1 Cauac, the second with 12 Cauac, the third with 10 Cauac, and so on. As the great cycle contains thirteen of these periods, it follows that we shall find all these numbers in it by thus dividing it. It is true this does not prove that the first period was numbered 13; moreover it is possible (though I do not think probable) that the number was not taken from that of the first day of the year, but from the second, as suggested by Perez. According to the theory advanced by this author these periods were numbered from the second day of the Cauac years, which would necessarily be Ahau, because as he supposes, some notable event in their history occurred on that da,j. Even on this supposition the series could not commence with the first period of the grand cycle, as this would be Ahau No. 2, but would begin with the second, which would be Ahau No. 13.
It may not be improper to call attention at this point to a remark made by Dr. Valentini in his article on the Perez manuscript (Proc. Am. Ant. Soc. No. 74): "Nor do we understand the reason why, just here, the topic of the succession of the numbers 13, II, 9, 7, 5, 3, 1, Ti, 10, 8, 6, 4, 2, was introduced. Could it have been with the intention of showing that this singular enumeration of alternating Ahaues, which we shall hereafter speak of, occurred only in cycles of twenty-four years, and that therefrom a proof might be derived for establishing the pretended cycle of twenty-four and three hundred and twelve years? Evidence of this should have been given by a table showing the series, and by still another table in which should be shown that such an alternating succession did not occur in cycles composed of twenty years. Not one single fact can be detected in Señor Perez's text by which the long established assumption of a twenty years' cycle has been disproved."
The object Señor Perez had in view in introducing this series at this point was for the very purpose of showing that this "singular enumeration" could be obtained only by dividing the series into periods of twenty-four years. As he was not fortunate enough to hit upon the plan of a table that would bring this clearly before the eye, I call attention to Table XVII, which meets precisely the requirements of Dr. Valentini. Dividing it into periods of twenty-four years will give this singular enumeration, while dividing it into periods of twenty years will not.
