Balam" are rudely drawn, but for all that, two or three of them are evidently identical with those in the calendar preserved by Landa. Some years ago, Professor de Rosny expressed himself in great doubt as to the fidelity in the tracing of these hieroglyphs of the months, principally because he could not find them in the two codices at his command.[9] As he observes, they are composite signs, and this goes to explain the discrepancy; for it may be regarded as established that the Maya script permitted the use of several signs for the same sound, and the sculptor or scribe was not obliged to represent the same word always by the same figure.

In close relation to chronology is the system of numeration and the arithmetical signs. These are discussed with considerable fullness, especially in the "Book of Chilan Balam of Káua." The numerals are represented by exactly the same figures as we find in the Maya manuscripts of the libraries of Dresden, Pesth, Paris and Madrid; that is, by points or dots up to five, and the fives by single straight lines, which may be indiscriminately drawn vertically or horizontally. The same book contains a table of multiplication in Spanish and Maya which settles some disputed points in the use of the vigesimal system by the Mayas.

A curious chapter in several of the books, especially those of Káua and Mani, is that on the thirteen ahau katuns, or epochs of the greater cycle of the Mayas. This cycle embraced thirteen periods, which, as I have before remarked, are computed by some at twenty years each, by others at twenty-four years each. Each of these katuns was presided over by a chief or king, that being the meaning of the word ahau. The books above-mentioned give both the name and the portrait, drawn and colored by the rude hand of the native artist, of each of these kings, and they suggest several interesting analogies.

They are, in the first place, identical, with one exception, with those on an ancient native painting, an engraving of which is given by Father Cogolludo in his "History of Yucatan," and explained by him as the representation of an occurrence which took place after the Spaniards arrived in the peninsula. Evidently, the native in whose hands the worthy father found it, fearing that he partook of the fanaticism which had led the missionaries to the destruction of so many records of the nation, deceived him as to its purport, and gave him an explanation which imported to the scroll the character of harmless history.

The one exception is the last or thirteenth chief. Cogulludo appends to this the name of an Indian who probably did fall a victim to his friendship to the Spaniards. This name, as a sort of guarantee for the rest of his story, the native scribe inserted in place of the genuine one. The peculiarity of the figure is that it has an arrow or dagger driven into its eye. Not only is this mentioned by Cogolludo's informant, but it is represented in the paintings in both the "Books of the Chilan Balam" above noted, and also, by a fortunate coincidence, in one of the calendar-pages of the "Codex Troano," plate xxiii., in a remarkable cartouche, which, from a wholly independent course of reasoning, was some time since identified by my esteemed correspondent, Professor Cyrus Thomas, of Illinois, as a cartouche of one of the ahau katuns, and probably of the last of them. It gives me much pleasure to add such conclusive proof of the sagacity of his supposition.[10]

[9] "Fe dois déclarer que l' examen dans tous leurs détails du 'Codex Troano' et du ' Codex Peresianus' m'invite de la façon la plus sérieuse à n'accepter ces signes, tout au moins au point de vue de l'exactitude de leur tracé, au'avec une certaine réserve."—Leon de Rosny's "Essai sur le Déchiffrement de l'Ecriture Hiératique de l'Amérique Centrale," page 21 (Paris, 1876). By the "Codex Peresianus," he does not mean the "Codice Perez," but the Maya manuscript in the Bibliothêque Nationale. The identity of the names is confusing and unfortunate.

[10] "The Manuscript Troano," published in The American Naturalist, August, 1881, page 640. This manuscript or codex was. published in chromo-lithograph, Paris, 1879, by the French Government.

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