[30]. The North Americans of Antiquity, their origin, migrations, and type of civilization considered. By John T. Short, 1880.

[31]. Historia de Yucatan. By Eligio Ancona, Mérida, 1879, Vol. I., page 95, note 1.

[32]. Historia de Yucatan, Eligio Ancona, Mérida, 1879, Vol. II., page 78.

[33]. Historia de Yucatan, Eligio Ancona, Mérida, 1879, Vol. I., page 156. “Landa in Relacion de las cosas de Yucatan, § viii., also speaks of the tranquillity and good harmony which reigned among the chiefs of those cities, and we notice that concerning the epochs referred to, his report is in accordance, in many details, with that of the anonymous author of the ‘Maya Epochs.’”

[34]. Diego Lopez de Cogolludo, Historia de Yuacathan. Madrid, 1683, Lib. IV., Cap. 5. “The count they kept in their books was by 20 to 20 years, and also by lustros of 4 to 4 years. When five of these lustros had passed, or twenty years elapsed, they called this time Katun, and set one hewn stone (piedra labrada) upon another, well cemented by lime and sand. This can be noticed in their temples and ecclesiastical buildings, and especially on some ancient walls of our convent in Mérida, upon which the cells have been built.”

The expression Katun, mentioned in this passage, and to which we have assigned a place in our title, requires a few words of explanation. As far as we know, it occurs only three times in our Central American authors; in Cogolludo, Landa, and in our manuscript. The first gives Katun the meaning of a period of twenty years. The second (§ XLI.), uses the following phraseology: “Contando XIII. veyntes con una de las XX. letras de los meses que llaman Ahau, sin orden, sino retruecandolos como pareceran en las siguiente raya redonda, llaman les a estos en su lengua Katunes.” This phraseology is somewhat obscure, nevertheless it will be admitted that his intention was to state that each of the images of the thirteen Ahaues, depicted on the surface of the wheel, represented twenty years, this being a period which they also called Katunes. We arrive at this definite conclusion by the consideration that if Landa says that the period of twenty years was called Ahau, and another one, that of 260 years, Katun, he would have stated the latter fact in expressive words; the occasion for doing so being too urgent to let it pass. The third author uses the word Katun in his introductory lines, without giving it any numerical value. But it will be noticed that in the text which follows, the expression Katun is used interchangeably with that of Ahau for a period of 20 years. This concordance of the three authors allows us to conclude that whenever the word Katun is employed, the short period of 20 years was meant. In this connection a question arises: How is it that no author has made mention of the long period of 260 years, with which we become acquainted in Señor Perez’s chronological essay. It is probable he found it mentioned in some Maya manuscripts in which this long period appeared under the name of Ahau Katun. Though this fact of itself may be considered of no importance, still, as it would bring to light another of the many numerical combinations (13×20=260) in which those people indulged, with the fundamental figures of their calendar system, we must feel a great interest in the asserted fact, hoping it will turn out to be a correct statement. Our researches have been directed for a long time towards the discovery of the symbols which the Maya annalists or sculptors would have employed for their chronological periods. It was in connection with these studies that we discovered the Nahuatl symbols for the same, of which we gave account in our discussion on the Calendar Stone. Yet while this discovery only corroborates the suspicion long entertained that a certain set of Maya symbols represented the lustra of 5, and another the period of 20 years, we have not yet been able to recognize a Maya symbol for the period of 260 years.

The word Katun is a compound of Kat, to ask, to consult, and tun, stone; hence the stone, which when asked, gives account. Thus it was also understood by Cogolludo, who, when mentioning the word Katun (see above), was referring to the square stones incrusted into walls, upon which the convent was built. What traditions he followed in this is still better illustrated by the words in continuation of this passage: “In a place called Tixualahtun, which means a spot where one hewn stone is set upon another one, the Archives of the Indians are said to have existed, to which they resorted for all questions of historical interest (recurso de todos los acaecimientos), as we should do to Simancas, in Spain.” The stone columns found on the spot named, can be seen pictured in J. L. Stephens’ Incidents of travel in Yucatan, Vol. II., page 318.

[35]. Señor Orozco y Berra, the learned and laborious author of the “Carta ethnografica de México, México, 1864,” has made this matter a subject of special investigation in “Anales del Museo Nacional de México,” 1879, Tom. I., Entrega 7, page 305.

[36]. Las cosas de Yucatan. Diego de Landa. Edition B. de Bourbourg. Paris, 1864. Page 315, § XL.

[37]. A specimen of such an instrument with a surface inscribed as the cut shows would hardly have been preserved. We think that the box enclosed a round disk turning on a pivot; this contrivance, evidently served as an aid to the memory in enumerating the alternating Ahaues. To-day, we should obtain the same result by writing the Ahaues in a horizontal or vertical line, but the Nahuatls and Mayas, having solely a symbolical or pictorial manner of representation, made use of this ingenious arrangement by painting the series of the Ahaues on the circumference of a circle. Thus the idea of an uninterrupted sequence of time and the connection of the 2d Ahau with the 13th were brought to notice.