36 BUKEAU OF AMERICAN ETHNOLOGY [bull. 2S 



can Xochitl). But as the figure 13 only goes into 7,200 with a remain- 

 der of 11, the figure of the first day of the period had to be two less 

 than that of the first day of the previous period. Jn a word, the 

 initial days of the successive periods of 7,200 days are 1 Ahau, 2 Ahau, 

 13 Ahau, 11 Ahau, Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1 Ahau, 12 

 Ahau, 10 Ahau, S Ahau, 6 Ahau, and then again 4 Ahau. Such a 

 period was called katun. It is still an open question upon what circum- 

 stances it depended tiiat just such a period of 20 X 360 days was chosen. 

 But, at any rate, this is the true length of the so-called ahau katun 

 periods, whose computation is clearly stated in the Dresden manu- 

 script, but whose meaning has been very much misunderstood even 

 down to the present time. 



In later times, when the connection with old traditions, if it had not 

 entirely disappeared, had yet been impaired in many ways, the katun 

 was taken, not as 20 X 360 days, but as 20 years. And thence it became 

 evident that the periods could not begin in the way indicated, with 

 4 Ahau, 2 Ahau, 13 Ahau, etc., for the number 13 goes into 7,300 with 

 a remainder of 7. Hence the initial days of the successive periods of 

 20 years (reckoning 365 days to a 3'ear) must by turns begin with 

 4 Ahau, 11 Ahau, 5 Ahau, etc. In order to meet this difficulty the 

 theory was evolved that the katun consisted, not of 20 years, but of 24 

 years, for 24x365, or 8,760, is also divisible by 20, and the number 13 

 goes into it with a remainder of 11, as it does into the true katun, the 

 period of 20x360 days. And hence arose the dispute, in which much 

 ink and paper have been wasted, as to whether the katun consisted of 

 20 or 24 years. As a fact, it contained neither 20 nor 24 years (the 

 old chroniclers did not take j^ears directly into their calculation), but 

 it contained 20 X 360 days. 



Now that the relation of the tonalamatl to the other chronology has 

 been made clear, I will once more turn back to the tonalamatl itself. 

 In my work on the character of the Aztec and Maya manuscripts 

 (Zeitschrift fiir Ethnologic, volume 10, page 1 etseq.) I tried to prove 

 that even the apparently quite dissimilar and differently named 20 

 day signs of the. Mayas could be brought into conformity with the 

 linguistically and hieroglyphicall}^ distinct signs of the Mexicans. 

 But I then overlooked one calendar, because it was not then acces- 

 sible, or at least not intelligible, to me, namely, the Zapotec, which 

 is recorded in the grammar of Father Juan de Cordova, which was — 

 imfortunatel}^, as it seems, very incorrectly and inexactly — republished 

 a few years ago by Doctor Leon. 



I have already mentioned that the Zapotec calendar is of an extremely 

 ancient type. This is shown on the one hand by the ancient form of 

 the words, w^hich are hardly explicable by the language spoken at 

 l)resent or that recorded soon after the Conquest; also by the fact 

 that the relation of the signs to the thirteen figures has become to 



