494 BUREAU OF AMERICAN ETHNOLOGY [bdll. 28 



super rinoiis, and, as with us, the value of the numbers is indicated by 

 their position. This is also the case in Codex Peresianus, but I can 

 not interpret the numbers, owing to the condition of the manuscript. 

 In Codex Troano-Cortesianus we find only timid attempts at num- 

 bers consisting of many figures, as in the page which connects both 

 parts and in the Troano codex, pages 20 to 23. 



AMien at last it became patent that 360 days by no means consti- 

 tuted a full 3^ear the numeric system could not be changed, because 

 a nndtiple of 20 was needed for the third degree; but in order to be 

 able to compute by years it was necessary to add to the length of the 

 year. In all probability the number 364 was chosen because it is 

 divisible by 4, and thus had a certain relation to the four cardinal 

 points and to everything connected with them in mythology. 



Many portions of the Dresden codex are based upon this year of 

 4X01 days, most distinctly on pages 65 to 69, as I have shown in 

 the Zeitschi'ift fur Ethnologic, 1891, page 144. To it also pertain 

 the series ^^ ith the difference 91 on pages 31 to 32 and 63 to 64. The 

 number 364, however, is not only 4X91, but also 28X13, and this 

 seems to iia ve given rise to the custom of dividing the year into periods 

 of 13 days each, just as the period of 20 daj^s was a natural division 

 of the 360-day year. I^'or nature does not seem to have furnished 

 the number 13, unless the most important parts of the human body, 

 l^erhaps the ten fingers, together Avith eye, ear, and mouth, might have 

 suggested it. Otherwise, there may have been a mythologic basis 

 (13 heavens?) for the number 13. 



There may have been a time when they wavered between the 360- 

 and the 364-day year, and consequently between the periods of 20 and 

 of 13 days. In order to meet the difficulties arising from this, it 

 was necessary to introduce a period which could be divided by both 20 

 and 13 days. Thus doubtless originated, not among the people, but 

 among the priesthood, the sacred tonalamatl of 260 days, which had 

 no connection with the duration of either the one or the other year. 

 I believe that I have found a glyph which rejDresents the tonal- 

 amatl, combined with the figure 8, in the inscription of the Cross of 

 Palenque, C, 2. The days of the 20-day period were then designated 

 by their already established glyphs and those of the later 13-day 

 period by merely adding numbers; thus 260 different characters for 

 days were easih^ obtained, just as they are in the Aztec, which there- 

 fore thus far agrees both with the method of the Mayas and with that 

 of the Kiches. 



The need must now have been felt of bringing these periods of 

 260 days into accord with the year, and particularly wdth the old 

 3^ear of 360 days. For this a period of 4,680 days would have been 

 sufficient, in which the tonalamatl is repeated 18 times, the 360 days 

 13 times, that is, a period in which the 13-day period recurs 360 times. 



