112 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



Table XI, in wliich the 20 days of the month Pop are enumerated. 

 Now it is evident from this table that, although the coefficients of 

 the days themselves do not rise above 13, the numbers showing the 

 positions of these days in the month continue up through 19. In 

 other words, two different sets of numerals were used in describing 

 the Maya days: (1) The numerals 1 to 13, inclusive, the coefficients 

 of the days, and an integral part of their names ; and (2) The numerals 



to 19, inclusive, showing the positions of these days in the divisions 

 of the year — the uinals, and the xma kaba kin. It is clear from the 

 foregoing, moreover, that the number of possible day coefficients (13) 

 has nothing whatever to do in determining the number of days in 

 the period next higher. That is, although the coefficients of the days 

 are numbered from 1 to 13, inclusive, it does not necessarily follow 

 that the next higher period (the uinal) contained only 13 days. 

 Similarly, the WTiter believes that while the cycles were undoubtedly 

 numbered — that is, named — from 1 to 13, inclusive, like the coefli- 

 cients of the days, it took 20 of them to make a great cycle, just as it 

 took 20 kins to make a uinal. The two cases appear to be parallel. 

 Confusion seems to have arisen through mistaking the name of the 

 period for its position in the period next higher — two entirel}^ different 

 things, as we have seen. 



A somewhat similar case is that of the katuns in the u kahlay 

 katunob in Table IX. Assuming that a cycle commenced mth the 

 first katun there given, the name of this katun is Katun 2 Ahau, 

 although it occupied thej^fs^ position in the cycle. Again, the name 

 of the second katun in the sequence is Katun 13 Ahau, although it 

 occupied the second position in the cycle. In other words, the katuns 

 of the u kahlay katunob were named quite independently of their 

 position in the period next higher (the cycle), and their names do not 

 indicate the corresponding positions of the katun in the period next 

 higher. 



Applying the foregoing explanation to those passages in the 

 inscriptions which show that the enumeration of the cycles was from 



1 to 13, inclusive, we may interpret them as follows: When we find 

 the date 4 Ahau 8 Cumhu in the inscriptions, accompanied by an 

 "ending sign" and a Cycle 13, that ''Cycle 13," even granting that 

 it stands at the end of some great cycle, does not signify that there 

 were only 13 cycles in the great cycle of which it was a part. On the 

 contrary, it records only the end of a particular Cycle 13, being a 

 Period-ending date pure and simple. Such passages no more fix the 

 length of the great cycle as containing 13 cycles than does the coeffi- 

 cient 13 of the day name 13 Ix in Table XI limit the number of days 

 in a uinal to 13, or, again, the 13 of the katun name 13 Ahau in 

 Table IX limit the number of katuns in a cycle to 13. Tliis expla- 

 nation not only accounts for the use of the 14 cycles or 17 cycles, as 



