1,486,923, XIII Akbal.
1,483,585, III Chicchan.
Difference 3338 = 12 × 260 + 218 (VII Kan to IV Ik, III Chicchan to XIII
Akbal).
1,268,523, XIII Akbal.
1,233,985, III Chicchan.
Difference 34,538 = 132 × 260 + 218 (as above).
1,272,423, XIII Akbal.
1,272,465, III Chicchan.
Difference 42 (which is 260 - 218); 42 = IV Kan to IV Imix.
On the other hand the three pairs specified in the Manuscript are as
follows:--
1,538,342, IV Ik.
1,535,004, VII Kan.
Difference 3338 = 12 × 260 + 218 as above, by reason of the encircled
number 51,419 which is common to both numbers.
1,268,540, IV Ahau.
1,234,220, IV Ahau.
Difference 34,320 = 132 × 260, on account of the same day.
1,272,544, IV Kan.
1,272,921, IV Imix.
Difference 117 = IV Kan to IV Imix; strictly speaking 377 = 260 + 117.
The upper part of the five columns just now under discussion still remains
to be examined. Here are five vertical rows of hieroglyphs, the first four
each containing seven, and the fifth only six owing to lack of space.
The two rows at the top are as usual much obliterated, which is the more to
be deplored since they consisted of five calendar dates, which would have
contributed materially to the comprehension of the entire section.
Fortunately, however, one of these dates is preserved complete, and we are
able to see in what relation it stands to the rest. Thus we find in the
third column of page 63 the date XIII Imix 9 Uo. It comes in the year 12 Ix
and represents the number 1,523,921 (or a number separated from it by a
multiple of 18,980). Now 1,523,921 = 4175 × 365 + 46 and = 5861 × 260 + 61.
This agrees with the lower number inserted in red:--1,538,342 = IV Ik 15
Zac (12 Muluc), which comes later by 14,421 = 39 × 365 + 186 and = 55 × 260
+ 121. 121, however, is the difference between both XIII Imix and IV Ik and
the days XIII Akbal and IV Kan in the last column of page 62. If we set
down with these two numbers, those of the normal date just preceding and
the normal date next following, we have
1,518,400 = 80 × 18980.
1,523,921,
1,538,342,
1,556,360 = 82 × 18980.
This is a period of 37,960 = 2 × 18,980 days. It is possible that at some
future time an indication of such a transition from one Katun to the other
will be found in the writings. Now these two top lines contain two dates;
on page 62 we find 13 Ceh, and on page 63, 13 Xul, but nothing further is
to be learned from this than that one or the other of the day-signs, 2, 7,
12, 17, must have been set down in the effaced indication of the position
in the Tonalamatl. All else is obliterated. From the third to the seventh
row of these five columns it is all extremely simple. The third row
consists only of five signs for beginning, the fourth, of five for end, the
sixth of B's sign five times and the seventh of the elongated head _q_ four
times. But in the fifth, two deities alternate, one is apparently male and
the other female; the god is in columns 1, 3 and 5 and the goddess in 2 and
4; the god probably belonging to the days III Chicchan and the goddess to
XIII Akbal.
If we look upon this series as the first story of a structure and the large
numbers just now discussed as the second, then we find the third story
here, as we shall find it again on page 69. In the passage on page 31,
which is so closely related to the present one, a timid attempt has already
been made with the number 2,804,100 to erect a third story of this kind,
which however barely attained to a quarter of the height of the one which
now engages our attention. If the numbers hitherto examined refer to a time
not very far from the present, we now come to numbers which lie in so
remote a future that they can hardly suggest anything else than the
destruction of the world or a sort of twilight of the gods. Nevertheless
the starting-point of the whole, the series, which is built up with the
number 91, _i.e._, the Bacab period or the quarter of a ritual year,
continually comes to view. Indeed, the number of serpents is suggestive of
this.
There are four large serpents, which fill most of the space on the left
half of page 62 and the right of page 61. The two outer ones are bluish and
the two inner ones white. They rise in several coils, their tails below and
their heads above. A deity is represented above the gaping jaws of each of
the four serpents, having apparently been vomited up. Above the first and
third serpents B is represented in a fashion very similar to that which we
have already seen on pages 33-35. Above the first serpent B has the pouch
hanging from his neck and his hatchet is held downward; above the third he
wears the pouch and the gala mantle and his hatchet is raised. Above the
second fourth serpents, on the other hand, there are four-footed animals,
but of a species not represented elsewhere. They might suggest a
(four-footed?) walrus and a bear. We have here a double contrast,
apparently referring to the four cardinal points.
The veil enveloping this representation would be lifted to a considerable
extent, if all the eight hieroglyphs written above each serpent, were still
legible. But, unfortunately, the second group is wholly and the third
almost wholly effaced, while the first is partially effaced and only the
fourth is preserved in its entirety. I read these groups in the following
order:--
1 2
3 4
5 6
7 8.
Of these 7 and 8 in the first and fourth groups form the date IX Kan 12
Kayab, which is in the year 4 Ix; this same date probably occurred also in
the other two groups. That it is of special importance here, is shown by
the two columns of hieroglyphs on the left side of page 61, where this date
occurs again in the lowest place. The last three large numbers are not
computed from the normal date IV Ahau 8 Cumhu, but from this very date and
the other five from a similar one. The sixth hieroglyph in the first group
seems to correspond to the fifth in the fourth, since both contain the
elongated head _q_, though with different accompaniments.
In the first group the fourth hieroglyph is the Bacab sign familiar to us
from pages 51-58, suggesting that the series here is closely connected with
the one which had the difference 91. The fifth sign of the same group is
that for _beginning_, probably to confirm the fact that this section begins
here. The third sign of the first group is probably an Imix, as it is in
the first and fourth of the fourth group, combined here with the woman's
head, which we saw repeated on pages 62 and 63 at the top; and over it in
the second place of the fourth group is B's hieroglyph, which is also
repeated on pages 62 and 63 at the top. The third place of the fourth group
is occupied by a head, which may be C's and which is distinguished by the
same kind of circle which on page 9b surrounded the Ahau.
Eight complete dates are set down below the serpents, among which are the
XIII Akbal already found with the previous large numbers, and III Chicchan
(repeated three times), and then III Kan (twice), forming the beginning and
end of the series (page 64), and also III Cimi and III Ix. As we shall see
directly these are the end dates of the large numbers, and Xul = end
repeated eight times at the extreme bottom corresponds with this. On the
other hand, the starting-points must be found by computation, with the
exception of the date IX Kan 12 Kayab, which is actually written down and
is the point of departure for three of the numbers.
I will designate the black numbers by _a_ and the red by b. Seven of the
eight numbers are undoubtedly absolutely correct; but I must alter the
number 1b, the red number belonging to the first serpent. I assume that a
line is wanting in the lowest figure, _i.e._, it should be 8 instead of 3,
and that the conspicuously large 1 further down on the page serves also as
the red number, which belongs here. Only one slight change is necessary in
the dates on the bottom of the pages, which were mentioned above. To the 16
in the date 4b I add a dot, and read it 17.
I will now give a table of the numbers, the starting-points of the periods
obtained by computation, and the ends of the latter which are indicated
below the serpents:--
1a: 12,489,781; XI Kan 12 Kankin (1 Ix); III Chicchan 18 Xul (4 Muluc).
1b: 12,388,121; XI Kan 12 Muan (7 Ix); III Chicchan 13 Pax (4 Ix).
2a: 12,454,761; IX Kan 7 Kankin (4 Cauac); III Chicchan 13 Yaxkin
(2 Ix).
2b: 12,394,740; IX Kan 2 Chen (5 Kan); III Kan 12 Ceh (7 Ix).
3a: 12,438,810; IX Kan 12 Xul (3 Ix); III Ix 7 Zac (9 Muluc).
3b: 12,466,942; IX Kan 12 Kayab (4 Ix); III Cimi 14 Kayab (9 Ix).
4a: 12,454,459; IX Kan 12 Kayab (4 Ix); XIII Akbal 1 Kankin (1 Kan).
4b: 12,394,740; IX Kan 12 Kayab (4 Ix); III Kan 17 Uo (7 Muluc).
See my treatise, "Die Schlangenzahlen in der Dresdener Mayahandschrift"
(Weltall, year 5, pages 199-203).
Several details show how this number-structure forms a definite, closely
connected whole.
1. The beginning day in each case is the day Kan, which thereby indicates
its position as the first.
2. The last three starting-points are the same; the first three end dates,
at least, are the same in the Tonalamatl, though not in the year.