720 Notes on the Codex Troano, and Maya Chronology. [Sept., 
Gallatin explained them as the numerical characters of the 
days “ Ahau”’ following the first day of each year called Cauac;’ 
Dr. Valentini thinks they refer to the numbers of the various 
idols worshiped in the different Ahaus; Professor Thomas that 
they are’ the number of the year (in the indiction of 52 years) 
on which the Ahau begins. Each of these statements is true in 
itself, but each fails to show any practical use of the series; and 
of the last mentioned it is to be observed that the objection 
applies to it that at the commencement of an Ahau Katun the 
numbers would run 1, 12, 10, 8, etc., whereas we know positively 
that the numbers of the Ahaus began with 13 and continued It, 
6; 7, ‘5, etc. 
The explanation which I offer, is, that the number of the Aha 
was taken from the last day Cauac preceding the Kan with which 
the first year of each Ahau began—for, as 24 is divisible by 4, 
the first year of each Ahau necessarily began with the day Kan. 
This number was the “ ruling number” of the Ahau, and not for 
any mystical or ceremonial purpose, but for the practical one of 
at once and easily converting any year designated in the Ahau 
into its equivalent in the current Kin Katun, or 52 year cycle. 
All that is necessary to do this is to add the number of the 
yearin the Ahau to the number of the year Cauac corresponding 1 
this “ruling number.’ When the sum exceeds. 52, subtract that 
number. 
Take an example: To what year in the Kin Katun does 10 
Ahau x1 (the roth year of the 11th Ahau) correspond ? 
On referring to a table, or, as the Mayas did, to a “ Katun 
wheel,” we find the 11th Cauac to be the 24th year of the cy cle; 
add ten to this and we have 34 as the number of the year in the 
cycle to which 10 Ahau x1 corresponds. The great simplicity 
and convenience of this will be evident without further dis 
cussion. 
I now pass to the important question: Can we establish a cot 
rect correspondence between the Kin Katuns and the Ahau Ka- 
tuns with the years of the Christian era ? 
The attempt has been made with widely divergent results. 
Perez makes the 13th Ahau begin in 1488, and Gallatin follows 
him; Valentini has it begin in 1522, but he makes the serious 
error of supposing the 1 3th was the /ast Ahau, whereas it was. 
1 Trans. Am. Ethnol. Soc., Vol. 1, p. 109. 
