768 The Maya Calendar and the Age of MS. Troano, (October, 
Cauac, Kan, Muluc, Ix, which followed each other in the order 
here given, it is evident this Ahau must have ended on 10 Ix, and 
must have commenced with 13 Cauac, if we count 24 years to 
the Ahau. As I have shown in the previous paper that this 
period consisted of 24 years, I shall assume that point as settled, 
and will give, opposite, a table of years sufficiently extended to 
cover one entire grand cycle, also the closing cycle of the prece- 
ding, and the first of the following grand cycles, showing the 
position of the Ahaues. 
As the grand cycle includes just 13 Katunes—312 years—I 
take for granted that the first year of this period coincides with 
the first year of a Katun, and consequently the close of the for- 
mer coincides with the close of a Katun. By dividing the for- 
mer into periods of twenty-four years, we will obtain the positions 
of the Katunes, and our next step will be to find their respective 
numbers. . 
The commencement and ending of the great cycle are marked 
thus —mgime-— + the divisions between the Ahaues with single 
transverse solid black lines. According to the quotation just 
made from the Perez manuscript, the 13th Ahau was one that 
required six years to complete it after the year 4 Kan. This can 
only be found in the one I have numbered xi (the Roman 
numerals indicate the numbers of the Ahaues or Katunes). If 
we take for granted that the periods were numbered thus, 13, ob 
9,7, 5, 3, 1, 12, 10, 8, 6, 4, 2—a point in reference to which all the © 
authorities agree—having determined the number of one in the 
grand cycle, it is an easy matter to number the rest. 
I call special attention to the fact that the one numbered XI 
found as above stated, begins with the year 13 Cauac; also that 
the first years of the others correspond with numbers and order 
as given in the above series. The selection of XIII as the ont 
with which to begin the series, was, as Dr. Valentini has giver 
good reasons for believing, an arbitrary proceeding on the part © 
the Maya priests. 
II, 
This numbering, as any one can see, agrees precisely with the 
position and numbers of the periods marked in table X1 of my 
previous article (p. 639). The position and numbers of these 
periods, as I have given them here (Table x11) agree exactly with 
the dates in the Manuscript Troano and the Perez manuscript. ‘ = 
As 4 Kan of the 13th Ahau coincides with the yeat 15 3° ae 
