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oning, and ilhuitl, festival. This last calendar, 

 the only one employed by the priests, and of 

 which we find traces in almost all the hierogiy- 

 phical paintings preserved to our own times, pre- 

 sents a uniform series of small periods of 23 days. 

 These small periods may be considered as half 

 lunations ; they probably took their origin from 

 the two states of watching, ixtozoliztU, and 

 sleep, cochiliztli, which the Mexicans attributed 

 to the Moon ; according as this luminary lights 

 the greater part of the night, or, appearing only 

 by day on the horizon, seems, according to the 

 popular opinion, to repose in the night. This 

 relation, observed between the periods of thir- 

 teen days, and the half of the time that the 

 Moon is visible, before and after her opposition, 

 has undoubtedly given to the ritual calendar the 

 name of the reckoning of the Moon ; but this de- 

 nomination ought not to induce us to look for a 

 lunar year in the series of the small cycles, which 

 follow uniformly, and which have nothing com- 

 mon either with the phases or the revolutions of 

 the Moon. 



The number 13 by its multiples affords pro- 

 portions, which the Mexicans made use of to 

 preserve an agreement between the ritual and 

 civil almanacks. A civil year of 365 days 

 contains a day more than twenty-eight small 

 periods of 13 days ; now the cycle of 52 years 

 being divided into four tlalpilU of 13 years, this 



