It appears only that the Chevalier Boturini had some knowledge, though imperfect, of that mode of reckoning time; inasmuch as Don Mariano Veytia, in the second chapter of his "Historia Antigua de Mexico," transcribes literally the explanation which Boturini gives at page 122 of the work which he published under the title of "Idea of a New History of North America," and says, "that the Mexican Indians, when they reckoned in their calendar the first sign of their indiction under number 1, as, for instance, Ce Tecpatl (1 Tecpatl), it was understood that it was (so placed) only one time in every four cycles, because they spoke then of the initial characters of each cycle; and thus, according to the contrivance of their painted wheels, Ce (1) Tecpatl was but once the commencement of the four cycles" [meaning--began a cycle but once in four cycles. But the fact is not so: both in the Mexican and the Yucatec calendar, every cycle of 52 years begins with the same initial character of the year]; "for which reason, any character of those initial signs placed in their history means that four Indian cycles of 52 years each have elapsed, which makes 208 years before they can again occur as initial, because, in this way, no account is taken of characters which are in the body of the four cycles; and though the same characters are found there, they have not the same value." Veytia affirms that he did not find any similar explanation, or anything alluding to the system of Boturini, in any of the ancient monuments which he had collected or examined, or mentioned by any Indian historian, not even in order to designate the epochs of the most remarkable events. But I believe that, in answer to this remark of Veytia, it may be said that Boturini, as Veytia states elsewhere, had examined the calendars used in old times by the Indians of Oaxacac, Chiapas, and Soconusco, and these being similar to that of the Yucatecos, it is not unreasonable to suppose that they, like the Yucatecos, computed by cycles greater than the Mexicans employed; and that Boturini took from them the idea, though confused and incorrect, of our Ajaus, or great cycles. This incorrectness might arise either from his not understanding the mechanism of their mode of computing, owing to the defective explanation given by the Indians, or from the manuscripts which Boturini had before him being mutilated, or, finally, from the possible fact that the Indians in those provinces had a particular custom of counting by cycles of four indictions, or of 208 years, which, notwithstanding the difference observed in their calculation, and the number of years which it produces, have a great analogy with the Yucateco cycles of 312 years. The only thing for which Boturini may be censured, if the Mexicans had no knowledge of that cycle, and did not use it, was the ascribing of it to them as being in common use for the computation of the greater periods of time.