4. The first three numbers are each divisible without a remainder by 17,
the interval from XIII Akbal to IV Ahau, which was true also of the
1,268,540 in the second column on page 63, although only this last number
has anything to do with these important days, of which the other three
numbers are independent.
On the other hand, a notable difference between the first serpent and the
other three is, that the day XI Kan is the starting-point of the first and
IX Kan of the others. There are, however, 80 days between IX Kan and XI
Kan. Hence the numbers 2a and 1b are separated from each other by 66,640 =
256 × 260 + 80, although they have the same end III Chicchan.
Further it is to be noted that the largest of the eight numbers,
12,489,781, is separated from the lowest, 12,388,121, _i.e._, the black
number from the red one of the first serpent, by only 101,660, _i.e._, by
not a full one per cent of the entire magnitude. 101,660 = 5 × 18,980 + 26
× 260 or 391 × 260 or 7820 × 13.
It is to be noted also that the differences between the black and red
numbers in the second and third serpents (60,021 and 28,132) are divisible
by 13 (4617 × 13 and 2164 × 13). They _must_ be, since all six numbers
refer to the day III.
Finally the question naturally arises, how did the computer obtain these
values, _i.e._, how was the whole structure built up? On page 63 we found a
136,864 (not 136,884) set down in strikingly small characters and crowded
between the other numbers, which would remain a mystery unless one assumed
that it was reserved there for this structure; it is 91 × 1504. At first I
thought it possible that this 136,864 had been again multiplied by 91, the
real basal number of this section; for we had found a second power once
before (on pages 46-50) by computation, viz:--2 × 260 × 260. The result of
multiplication in this case would be 12,454,624, and the differences
between the eight numbers in the serpents would be as follows:--1a +
35,157, 1b - 66,503, 2a + 137, 2b and 4b - 60,884, 3a - 17,814, 3b +
12,318, 4a - 165. But these differences are doubtful, inasmuch as they bear
no relation to the dates beginning and ending the serpent numbers.
On the other hand, another number contains the desired properties. I refer
to the 12,412,920, _i.e._, it is 109 times the so-called Ahau-Katun of
113,880 days, and I believe I have found that the Ahau-Katun and its
multiples were mostly used in the formation of the large numbers. In the
following table I have placed this number beside each of the serpent
numbers, have then found the difference between the two and have added to
it the interval between the first and last day of each serpent number:--
1a) 12,489,781 1b) 12,388,121
12,412,920 12,412,920
---------- ----------
76,861 = 295 × 260 + 161 -24,799 = 95 × 260 + 99
XI Kan - III Chicchan = 161. III Chicchan - XI Kan = 99.
2a) 12,454,761 2b) 12,394,740
12,412,920 12,412,920
---------- ----------
41,841 = 160 × 260 + 241 -18,180 = 69 × 260 + 240
IX Kan - III Chicchan = 241. III Kan - IX Kan = 240.
3a) 12,438,810 3b) 12,466,942
12,412,920 12,412,920
---------- ----------
25,890 = 99 × 260 + 150 54,022 = 207 × 260 + 202
IX Kan - III Ix = 150. IX Kan - III Cimi = 202.
4a) 12,454,459 4b) = 2b
12,412,920
----------
41,539 = 159 × 260 + 199
IX Kan - XIII Akbal = 199.
Where the serpent number is less than 12,412,920, I have had to place the
last day before the initial day.