This discrepancy may arise from the custom of counting the katuns by two different systems, ground for which supposition is furnished by various manuscripts; but for purposes of chronology and ordinary life, it will be evident that the writers of the annals in the present volume adopted the Katun of twenty years' length; while on the other hand the native Pech, in his History of the Conquest, which is the last piece in the volume, gives for the beginning and the end of the Katun the years 1517-1541, and therefore must have had in mind one of twenty-four years' duration. The solution of these contradictions is not yet at hand. This great cycle of 13 × 20=260 years was called an _ahau Katun_ collectively, and each period in it bore the same name. This name, _ahau Katun_, deserves careful analysis. _Ahau_ is the ordinary word for chief, king, ruler. It is probably a compound of _ah_, which is the male prefix and sign of the _nomen agentis_, and _u_, collar, a collar of gold or other precious substance, distinguishing the chiefs. _Katun_ has been variously analyzed. Don Pio Perez supposed it was a compound of _kat_, to ask, and _tun_, a stone, because at the close of these periods they set up the sculptured stone, which was afterwards referred to in order to fix the dates of occurrences.[57-1] This, however, would certainly require that _kat_ be in the passive, _katal_ or _kataan_, and would give _katantun_. Beltran in his Grammar treats the word as an adjective, meaning very long, perpetual.[57-2] But this is a later, secondary sense. Its usual signification is a body or batallion[TN-7] of warriors engaged in action. As a verb, it is to fight, to give battle, and thus seems related to the Cakchiquel _[k]at_, to cut, or wound, to make prisoner.[58-1] The series of years, ordered and arranged under a controlling day and date, were like a row of soldiers commanded by a chief, and hence the name _ahau katun_. Each of these _ahaus_ or chiefs of the Katuns was represented in the native calendars by the picture or portrait of a particular personage who in some way was identified with the Katun, and his name was given to it. This has not been dwelt upon nor even mentioned by previous writers on the subject, but I have copies of various native manuscripts which illustrate it, and give the names of each of the rulers of the Katuns. The thirteen _ahau katuns_ were not numbered from 1 upward, but beginning at the 13th, by the alternate numbers, in the following order:-- 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2 Various reasons have been assigned for this arrangement. It would be foreign to my purpose to discuss them here, and I shall merely quote the following, from a paper I wrote on the subject, printed in the _American Naturalist_, Sept., 1881:--