58 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



is a simple question of aritlimetic. Since the clay 2 Ik can not return 

 to its original position in A until after 260 days shall have passed, 

 and smce the day Pop can not return to its original position in B 

 until after 365 days shall have passed, it is clear that the day 2 Ik 

 Pop can not recur until after a number of days shall have 

 passed equal to the least common multiple of these numbers, which is 



^X^X5, or 52X73X5=18,980 days. But 18,980 days = 52 X 



365 = 73X260; in other words the day 2 Ik Pop can not recur 

 until after 52 revolutions of B, or 52 years of 365 days each, and 73 

 revolutions of A, or 73 tonalamatls of 260 days each. The Maya 

 name for this 52-year period is unknown; it has been called the 

 Calendar Round by modern students because it was only after this 

 interval of time had elapsed that any given day could return to the 

 same position in the year. The Aztec name for this period was 

 xiuhmolpilli or toxiuhmolpia.^ 



The Calendar Round was the real basis of Maya chronology, since 

 its 18,980 dates included all the possible combinations of the 260 days 

 with the 365 positions of the year. Although the Maya developed 

 a much more elaborate system of counting time, wherein any date of 

 the Calendar Round could be fixed with absolute certainty within a 

 period of 374,400 years, this truly remarkable feat was accomplished 

 only by using a sequence of Calendar Rounds, or 52-year periods, in 

 endless repetition from a fixed point of departure. 



In the development of their chronological system the Aztec prob- 

 ably never progressed beyond the Calendar Round. At least no 

 greater period of time than the round of 52 years has been found in 

 their texts. The failure of the Aztec to develop some device which 

 would distinguish any given day in one Calendar Round from a day 

 of the same name in another has led to hopeless confusion in regard 

 to various events of their history. Since the same date occurred 

 at intervals of every 52 years, it is often difficult to determine the 

 particular Calendar Round to which any given date with its corre- 

 sponding event is to be referred; consequently, the true sequence of 

 events in Aztec history stiU remains uncertain. 



Professor Seler says in this connection : ^ 



Anyone who has ever taken the trouble to collect the dates in old Mexican history 

 from the various sources must speedily have discovered that the chronology is very 

 much awry, that it is almost hopeless to look for an exact chronology. The date of the 

 fall of Mexico is definitely fixed according to both the Indian and the Christian chro- 

 nology . . . but in regara to all that precedes this date, even to events tolerably near 

 the time of the Spanish conquest, the statements differ widely. 



I The meanings of t hese words in NahuatI, the language spoken by the Aztec, are "year bundle " and "our 

 years will be bound," respectively. These doubtless refer to the fact that at the expiration of this period 

 the Aztec calendar had made one complete round ; that is, the years were bound up and commenced anew. 



^Bulletin 28, p. 330. 



