108 BUREAU OF AMERICAN ETHNOLOGY [bdll. 57 



mimber was in fact the only unit of progression used, except in the 

 2d order, in which 18 instead of 20 units were required to make 1 

 unit of the 3d order. In other words, in the codices the Maya carried 

 out their vigesimal system to six places without a break other than 

 the one in the 2d place, just noted. See Table VIII. 



In the inscriptions, however, there is some groimd for believing 

 that only 13 units of the 5th order (cycles), not 20, were required to 

 make 1 unit of the 6th order, or 1 great cycle. Both Mr. Bowditch 

 (1910: App. IX, 319-321) and Mr. Goodman (1897: p. 25) incline to 

 this opinion, and the former, in Appendix IX of his book, presents 

 the evidence at some length for and against this hypothesis. 



This hypothesis rests mainly on the two following points : 



1. That the cycles in the inscriptions are numbered from 1 to 13, 

 inclusive, and not from to 19, mclusive, as in the case of all the 

 other periods except the umal, which is numbered from to 17, 

 inclusive. 



2. That the only two Initial Series wMch are not counted from the 

 date 4 Ahau 8 Cumhii, the starting point of Maya chronology, are 

 counted from a date 4 Ahau 8 Zotz, which is exactly 13 cycles in 

 advance of the former date. 



Let us examine the passages in the inscriptions upon which these 

 points rest. In three places ^ in the inscriptions the date 4 Ahau 

 8 Cumhu is declared to have occurred at the end of a Cycle 13; that 

 is, in these three places this date is accompanied by an ''ending sign" 

 and a Cycle 13. In another place in the inscriptions, although the 

 starting point 4 Ahau 8 Cumhu is not itself expressed, the second 

 cycle thereafter is declared to have been a Cycle 2, not a Cycle 15, 

 as it would have been had the cycles been numbered from to 19, 

 inclusive, like all the other periods.^ In still another place the ninth 

 cycle after the starting point (that is, the end of a Cycle. 13) is not a 

 Cycle 2 in the following great cycle, as would be the case if the cycles 

 were numbered from to 19, inclusive, but a Cycle 9, as if the cycles 

 were numbered from 1 to 13. Again, the end of the tenth cycle after 

 the starting point is recorded in several places, but not as Cycle 3 of 

 the following great cycle, as if the cycles were numbered from to 

 19, inclusive, but as Cycle 10, as would be the case if the cycles were 

 numbered from 1 to 13. The above examples leave little doubt that 

 the cycles were numbered from 1 to 13, inclusive, and not from to 19, 

 as in the case of the other periods. Thus, there can be no question 

 concerning the truth of the first of the two above points on which 

 this hypothesis rests. 



1 These are: (1) The tablet from the Temple of the Cross at Palenque; (2) Altar 1 at Piedras Negras; 

 and (3) The east side of Stela C at Quirigua. 



2 This case occurs on the tablet from the Temple of the Foliated Cross at Palenque. 



