456 BUREAU OF AMERICAN ETHNOLOGY [bull. !i8 



true of all the succeeding members of the series. The real zero point, 

 which is always concealed in this manuscript, is XIII 20, the same as 

 the last day of the series. This day is, however, the new year's day 

 which recurs every 52 years, followed by I 1 as the second day, which 

 gives the name to the whole year, for, according to the Maya view, the 

 new year's day is not the first, but the zero da3^ It is not counted. 

 Day XIII 20 is, therefore, highly significant in this passage. 



The difference 91 is equally significant. It is a Bacab period, a 

 quarter of the ritual year of 364 days. This entire list of 20 days, 

 therefore, includes a period of 20X91=^1,820, or 7 tonalamatls. 



The rest of the upper third of page 32 and the column on tlie right 

 of page 31 are filled by a series which begins with 91, and 91 or a 

 multiple of this number always appenrs as the difference. This 

 shows an attempt to obtain numbers divisible by the tonalamatl, 

 260. This attempt is uniformly adhered to in all these series. At 

 the same time a number divisible by 10-1 is sought, 104 being the 

 remainder of a ritual year of 304 days when a tonalamatl, 2()0. is 

 subtracted from it. This division of the year into 260-)-104 recalls 

 the hypothesis of Mrs Zelia Nuttall, which assumes that the Aztec 

 year was separated into 52-)-260-j-52." 



It is unnecessary to repeat the entire twenty terms of the series 

 in the manuscript, some of which are destroyed, since it concerns 

 merely an auxiliary calculation. It is sufficient to give the principle. 

 Here the two numbers 728 and 3,640 on page 32, on the left, need 

 a passing allusion. They are of special importance, since with the 

 former the combination of 91 and 104 is obtained and with the latter, 

 besides this, the agreement with 2()0. It is as follows: 



728=8X91 (therefore also 2 X 3(54)== 7 X 104. 

 3,640=40x01 (therefore also 10x364)=35X 104 = 14x260. 



Our chief concern noAV is to represent what has thus far been stated 

 as the germ of what is to follow. 



The writer has added two superfluous signs at the end of the five 

 columns of page 31 which belong here, in order to avoid an empty 

 space. In the fourth and fifth columns he twice sets down the day 

 XIII 20, the importance of which is already sufficiently conspicuous. 

 In the first three columns he sets down the day IV 17 three times, and, 

 besides, on the first and second he has twice set doAvn the sign of the 

 eighteenth month, Cumku. But we know that only the beginning of 

 Maya chronology, upon which all numbers are based, is here meant, 

 for it fell on the eighth day of the eighteenth month and was a day 

 IV 17 in the year 9 Ix. 



Before we consider the three large numbers with which the three 

 first columns begin I must make a more general observation. The 



" Note on the Ancient Mexican Calendar System, Stockholm, 1894. 



