412 BUREAU OP AMERICAN ETHNOLOGY [bull. 28 



by addition or subtraction should be made, and in tlie manuscript we 

 find these corrections in the numbers which are encircled with red 

 whenever the space permits. 



In our section we must consider the distance of the days III 2 and 

 XIII 20 from the noi-mal day IV 17, and also from the days IV 1, 

 IV 18, IV 19, and VII 1. I do not yet know why these last four days 

 were selected, but a close examination shows that the first three of 

 them preceded the normal day IV 17 by 156, 39, and 78 days. These 

 intervals have the ratio 4:1:2, but this is merely incidental. 



From III 2 to IV 17 there are 235 days 

 From XIII 20 to IV 17 there are 17 days 

 From III 2 to IV 18 there are 196 days 

 From XIII 20 to IV 1 there are 121 days 

 From III 2 to VII 1 there are 199 days 

 From XIII 20 to IV 19 there are 199 days 



The last two intervals are the same, Avhich doubtless has a hidden 

 meaning. 



The effect is exactly the same whether we make these corrections in 

 the amounts given or in these increased by a number divisible by 260, 

 since after 260 days the same daj^s recur. Thus we actually find on 

 pages 62 and 63 the numbers 235 and 121 inclosed in circles, but 

 instead of 196 we find 456=260+196, and instead of 199 we have 

 51,419=197X260+199. The last number is perfectly reliable, for 

 it has alread}^ occurred in the same connection on page 31 of the 

 manuscript. Instead of the 17, above which there is a quite incom- 

 prehensible zero, I now read 537=2X260+17, the correctness of 

 Avhich I shall prove later on. 



The numbers to which these encircled numbers are added do not 

 occur in the manuscript. I have given them in my earlier treatise 

 and will omit them here. 



THE LARGE NUMBERS 



With regard to this subject I can also be brief, as it has already 

 been discussed in my previous article. I refer to the numbers scat- 

 tered throughout the manuscript, always lying between 1,200,000 and 

 1,600,000, whose true mean and point of departure, unless we are 

 wholly mistaken, lies in 12 ahau katuns 1,366,560 (page 24 of the 

 manuscript). Perhaps it may be an aid to their better comprehension 

 if, in connection with the days belonging to them, I specify these num- 

 bers somewhat more particularly by some of their properties. 



IV 17. 1,2:54.220 = 4,747x260=235x5,252x235 is the distance from III 

 2 to IV 17. The number is 1:32,340 less tlian 12 ahau l^atuns. 



IV 17. 1,268,540=4,879X200 = 17X74,020. 17 is the distance from 

 XIII 20 to IV 17. The number is 08,020 less than 12 ahau katuns. 



