_xel u ca katun_, thirty years. _xel u yox katun_, fifty years. Literally these expressions are, "dividing the second katun," "dividing the third katun," _xel_ meaning to cut in pieces, to divide as with a knife. They may be compared to the German _dritthalb_, two and a half, or "the third a half."[54-1] The Katun of 20 years was divided into five lesser divisions of 4 years each, called _tzuc_, a word with a signification something like the English "bunch," and which came to be used as a numeral particle in counting parts, divisions, paragraphs, reasons, groups of towns, etc.[54-2] These _tzuc_ were called by the Spaniards _lustros_, from the Latin _lustrum_, although that was a period _five_ years. Cogolludo says: "They counted their eras and ages, which they entered in their books, by periods of 20 years each, and by _lustros_ of four years each. The first year they placed in the East [that is, on the Katun-wheel, and in the figures in their books], calling it _cuch haab_; the second in the West, called _Hijx_; the third in the South, _Cavac_; and the fourth, Muluc, in the North, and this served them for the Dominical letter. When five of the _lustros_ had passed, that is 20 years, they called it a _Katun_, and they placed one carved stone upon another, cemented with lime and sand, in the walls of their temples, or in the houses of their priests."[55-1] The historian is wrong in saying that the first year was called _cuchhaab_; that was the name applied to all the Dominical days, and as I have said, means "year bearer." The first year was called _Kan_, from the first day of its first month. This is but one of many illustrations of how cautious we must be in accepting any statement of the early Spanish writers about the usages of the natives. There is, however, some obscurity about the length of the _Katun_. All the older Spanish writers, without exception, and most of the native manuscripts, speak of it distinctly as a period of twenty years. Yet there are three manuscripts of high authority in the Maya which state that it embraced twenty-four years, although the last four were not reckoned. This theory was adopted and warmly advocated by Pio Perez, in his essay on the ancient chronology of Yucatan, and is also borne out by calculations which have been made on the hieroglyphic Codex Troano, by M. Delaporte, in France, and Professor Cyrus Thomas, in the United States.[56-1]