1,386,580 = IV Ahau 13 Muan (12 Muluc),
1,426,360 = IV Ahau 8 Muan (4 Ix).
If we compare the two numbers with the normal date, the curious result
follows that:--
1) 1,386,580 - 1,366,560 = 20,020.
This number is equal to 55 × 364, including therefore the ritual year of
364 days.
2) 1,426,360 - 1,366,560 = 59,800.
This number is five times 11,960 days, which is assumed to be the time in
which the lunar and Mercury revolutions accord. This 59,800 was found once
before on page 24 as the suppressed difference between 68,900 and 9,100.
Thus the separate sections (of the book) are very closely connected.
If the two large numbers be compared with one another their difference will
be found to be 39,780. This is equal first to 51 Mars revolutions of 780
days, and second to 4420 × 9, _i.e._, a multiple of the interval between IV
Ahau and XIII Muluc.
Now we must direct our attention to the seventeen hieroglyphs, which we
find in the two columns on page 58, apart from the matter-of-course
calendar date at the top, which is repeated at the bottom. One column
contains 11 hieroglyphs and the other 6. I will here advance the following
theory in regard to these hieroglyphs, which may serve until a better is
found:--
Since, as a rule, the Tonalamatl is divided into 5 × 52 days, I believe
that each group of three Tonalamatls treated of on page 59, is divided into
15 of these parts; that each hieroglyph, therefore, denotes 52 days and
that the first three parts are separated from the others by the signs of
beginning and end in the first and fifth places, so that three of these
parts, which equal 156 days, always form a separate group. 156 is the 5th
part of 780. With the omission of the first and fifth signs, the passage, I
think, stands thus:--
0 XIII Muluc 2 Kankin (13 Muluc).
1) 0-52 XIII Imix 14 Pax.
2) 53-104 XIII Ben 1 Pop (1 Ix).
3) 105-156 XIII Chicchan 13 Zip.
--------------------------------------
4) 157-208 XIII Caban 5 Xul.
5) 209-260 XIII Muluc 17 Mol.
6) 261-312 XIII Imix 9 Zac.
--------------------------------------
7) 313-364 XIII Ben 1 Kankin.
8) 365-416 XIII Chicchan 13 Pax.
9) 417-468 XIII Caban 25 Cumhu.
--------------------------------------
10) 469-520 XIII Muluc 12 Zip (2 Cauac).
11) 521-572 XIII Imix 4 Xul.
12) 573-624 XIII Ben 16 Mol.
--------------------------------------
13) 625-676 XIII Chicchan 8 Zac.
14) 677-728 XIII Caban 20 Mac.
15) 729-780 XIII Muluc 12 Pax.
If we adopt this arrangement for the present we cannot fail to see that the
author had an aim in view, when we consider the following:--
1. The zero-point lies 15,609 days later than the normal date IV Ahau 8
Cumhu (9 Ix). This is equal to 20 × 780 or 60 × 260 increased by the
interval between IV Ahau and XIII Muluc = 9. There are 86 days between 2
Kankin and 8 Cumhu _i.e._, 15,609 = 43 × 365 - 86, and from 9 Ix to 13
Muluc it is 43 years.
2. The same zero-point, 13 Muluc, lies in the year with the same name, that
is, the very point where a Tonalamatl of the year ends.
3. In this arrangement the first as well as the last day of the year 1 Ix
is exactly reached in the second and ninth groups. While the meaning of the
second is as yet unintelligible to me, the end of the year is appropriately
indicated by the ninth with its compound of Kin and the year-sign, above
which there may be an Ix as a superfix, but misshapen for want of room.
4. Also the fact that it is the first of the two columns, which closes with
this year-end, seems to show a purpose.
5. Several instances of similarity appear among the hieroglyphs in these
groups of three:--an Akbal sign in 1 and 4 suggests the god D, the superfix
and prefix of 2 and 14 the god K and 5 and 11 the screech-owl and therefore
A.
Little else is to be said of these hieroglyphs.
C might be denoted by 3 (13 Zip) and 10 (12 Zip). Group 8, the central
point of the series, has on the left and right the signs for the north and
south as if the time between the north (Muluc) years and the south (Cauac)
years were meant to be indicated here.
I am inclined to consider the crouching personage in 12 as the revolution
of Mercury, which requires 115 days:--573 is 5 × 114 + 3 or 5 × 115 - 2.
Is 7 a sign, as yet unknown, for the year of 364 days?
15 looks like two signs for the month Mac, placed back to back, which here
designates the Tonalamatl as it does on page 24. The superfix of three
parts might denote three Tonalamatls = 780 days. The familiar sign in the
fifth place in connection with the expiration of the first Tonalamatl is
striking; it is the one usually identified as that of the screech-owl or
death-bird.
Page 60.
This is the last page of the front of the second part and is divided into
four sections:--at the top we find hieroglyphs, below these a picture, then
hieroglyphs again and in the lowest section another picture.
The upper picture contains first a rectangular elevation like a platform.
Enclosed in this rectangle is the picture of the animal resembling a dog
lying down, which we have often met with, the last time on page 47. In
front of the dog is a hieroglyph, which, I regret to say, is still unknown
and which occurred six times as a heading on page 23b. On the platform two
personages are fighting; one is in war-dress holding in his left hand the
throwing-stick or atlatl, and in his right probably arrows; the other
figure, whose back is somewhat indistinct owing to obliteration, is
apparently unarmed and is making a defensive gesture with one hand. Beside
the platform, and therefore on a lower level, is a second person walking
behind the armed person as if to help him. He too is in war-dress and
likewise holds an atlatl. A black 3 is set down between the two combatants,
and there may also have been a red 2, which is indistinct owing to the red
background of the picture.
Let us next examine the lower picture. A blindfolded personage is kneeling
on the left. A serpent's head rises from the ground in front of him. A
second serpent rises in several coils on the shoulders of the blindfolded
personage and on the serpent's neck sits enthroned another personage, who
is rather indistinct, holding a spear and a shield. On the right, opposite
this group and facing it, is a second. A personage with arms bound and
bowed head is sitting on the ground. There is a black ring around his eye.
Behind him stands the victor in war-dress and again equipped with spear and
shield. There is a red 11 and a black 2 between the two groups.
We see that the reference here is to combat, just as it was on the right
side of pages 46-50. And since the subject of these pages like that of
46-59 is confined to the revolutions of the planets, it is natural that the
pursuit of one by the other, their periodical disappearance, the crossing
of their orbits and the variation in the length of their revolutions should
be looked upon as a contest. Therefore, since the sun, the moon and the
five planets have hitherto been treated of on these pages, I look for these
seven heavenly bodies in the seven personages pictured here on page 60. I
will attempt to explain them, hoping that my interpretation may be replaced
by a better one.
The sun and moon stand on the platform in the upper picture; their combat
is equivalent to the eclipses to which they at times succumb. The moon is
the assailant and the sun makes only a proud defensive gesture. The person
behind the moon must be Mars. The animal under the two persons is the
embodiment of the eclipses, which the Aztecs interpreted as the act of
being devoured by the jaguar. The hieroglyph in front looks very much like
the meeting of two circles. Does it refer to the day Lamat (Aztec tochtli =
rabbit)?
At the left, bottom, the powerful Venus triumphs over the weak Mercury. The
two planets are real chronometers by reason of the regular alternation of
their appearance as morning and evening stars, and also by their
disappearance twice in each revolution and finally even in the variation in
the length of the two periods of invisibility. Hence they are each
accompanied by a serpent as the usual symbol of time.
On the right, on the other hand, Jupiter as the stronger has vanquished
Saturn, whose bound arms symbolize his slowness of motion and the fact that
he is confined to the same region of the sky. Should not the ring around
his eye have a very special meaning? But we must guard against an excess of
imagination. Jupiter and Saturn are the last to be represented, as they
were of but secondary importance, on pages 51-58 and perhaps also in the
2200 on page 24.
I will not deny that yet another interpretation of this page is possible.
The top picture may be Venus and the moon opposing one another, and the
bottom picture may represent the sun as victor over Mercury. There are some
things in favor of this point of view.
The correct order of the twenty-four hieroglyphs is the following, in my
opinion, which is borne out by the different colors of the four groups:--
1 2 | 7 8
3 4 | 9 10
5 6 | 11 12
-----------------
13 14 | 19 20
15 16 | 21 22
17 18 | 23 24
These signs can have no relation to mythology. There is not a hieroglyph of
a god among them, for if sign 6 could be taken for B's hieroglyph, the
resemblance to the sign of the fist, familiar from the inscriptions, as
well as the Imix and the cross-hatching as a prefix, makes this doubtful.
The latter component would rather suggest the summer solstice. If sign 12
were intended to denote the Bacab, then it would refer to chronology rather
than to mythology. Also the Cimi in 17 might equally well mean the day as
the god. Indeed several things refer here to chronology and astronomy,
among them the unmistakable union of numbers and month signs, which occur
here repeatedly. Thus from what remains of the almost obliterated signs 1
and 2, they might denote the normal date IV Ahau 8 Cumhu, which always
occupies the first place. Signs 7 and 20 are plainly the same, 9 Xul (sixth
month) and sign 14 is 10 Yaxkin (seventh month). Sign 5 might be Caban
combined with Uo (second month) and a ten. In sign 19 we again see Yaxkin
without a number. Signs 9 and 23 are Zec (fifth month) and signs 21 and 22
may be Kankin (fourteenth month). The days occur in the same manner as the
months. It is true that Kin is only a part of hieroglyph 10, the rest of
which is effaced, but the familiar compound of Caban and Muluc appears in
18 and 24 and Cimi is in 17, as we have seen. In sign 13, Ahau is combined
with a red number, which must lie between X and XV. But this should not be
regarded as forming a calendar date with the 10 Yaxkin near by, for Ahau is
never the tenth day of a month. Can 16 be the sign of the twelfth month,
Ceh, combined with that for 7200? Hieroglyphs 3 and 8 are effaced and I do
not understand 4, 11 and 15.
There are no parallels in the kindred passages 46-50, unless it be 7 Zec on
the bottom of page 49 and here in signs 9 and 23, but without a number. Cf.
my paper on this page 60 in the "Weltall," year 6, pages 251-257.
Page 61--64.
On examining the reverse of the second part of our Manuscript, _i.e._,
pages 61-74, we find an empty page on the left, the back of which is
occupied by page 60. This may be explained by assuming that the scribe
wrote pages 61-64 and possibly even pages 61-74 from right to left, the
great series having occasioned such a proceeding, and that his material
came to an end when he had finished page 61. Nevertheless, it is advisable
to continue with the original numbering in order to avoid confusion.
Aside from the concluding (or beginning) page 74, this whole section of
pages 61-74 consists of three parts:--61-64, 65-69 and 70-73. Let us first
consider the first section, which I have already discussed in my treatise
"Zur Erläuterung der Mayahandschriften II."
The basis of this section is a series, the beginning of which is on the
bottom, right, of page 64. Its primary difference is always that which we
found on pages 31-32, viz:--the Bacab period of 91 days, the quarter of the
ritual year of 364 days = 7 weeks of 13 days each. It ascends by 91 until
it reaches 1820, which number is a multiple of both 364 and 260 and is also
divisible by 28, the number of weeks in a year. Just as on page 32 the
series continues with the new difference 1820 as far as 7280, its fourth
multiple, which then becomes the third difference. Indeed, I believe that
even the partially effaced numbers could be so restored as to carry the
series to the number 36,400 = 400 × 91, which would then become the fourth
difference and the series would close at the top of page 63 with 145,600 =
1600 × 91, _i.e._, with the numbers 1. 0. 4. 8. 0. of which the 1 is
entirely and the 0 half effaced. The series on pages 31-32, however, closed
with 29,120 = 320 × 91, but there is still room for a higher series.
Under this largest number (1600 × 91) there is on page 63 a large red
number consisting of 19. 0. 4. 4. which is crowded into a very small space
between the figures of 1820. I can only understand it by replacing the
first 4 by a 3, for then it is 136,864 = 1504 × 91 or by addition of a
zero. We shall return to this number in the examination of the serpent
numerals.
The series is accompanied in the regular way by five days. At the beginning
of this series, page 64, right bottom, are the days III Cib, III Men, III
Chicchan, III Caban and XIII Ix; the III is set down only with the first of
these days and is to be supplied with the next three. Hence the actual zero
point is to be found 91 days back in the days III Chicchan, III Kan, III
Ix, III Cimi and XIII Akbal, the last of which is also the beginning of the
corresponding series on page 32. From 1820 on, these last-named days, of
course unchanged, accompany the numbers. The most important of these days
are the first and last, but we shall see later in connection with the
serpent numbers that the other three, which are separated from one another
by 39, 130 and 52, _i.e._, 3 × 13, 10 × 13 and 4 × 13, are likewise not set
down here by mere accident.
We come now to the five columns, three on page 63 and two on page 62, which
join this series on the left. They contain the large numbers, which
invariably accompany these series. Here there are six numbers, four of
which, in my opinion, refer to the past and two to the future. Two of these
numbers, the two largest, are set down together in the third column on page
63, one with red numbers and the other with black. Of these black numbers,
I take the second from the top to be not 8 but 13, assuming that a line is
omitted. The normal date IV Ahau 8 Cumhu from which, as the starting-point,
all these numbers are to be computed, is set down below at the end of each
of the five columns.
I now give the six numbers, first the two highest, then the other four from
right to left, adding in each case the calendar date and the year in which
they should be situated:--
1,538,342; IV Ik 15 Zac (12 Muluc).
1,535,004; VII Kan 2 Chen (3 Kan).
1,268,540; IV Ahau 8 Mol (1 Ix).
1,234,220; IV Ahau 18 Kayab (11 Kan).
1,272,544; IV Kan 17 Yaxkin (12 Muluc).
1,272,921; IV Imix 9 Mol (13 Ix).
The first, third and fifth numbers are already known from page 31a, and
hence they need no further discussion here.
As these three numbers depend on the day XIII Akbal, so the other three all
proceed from the day III Chicchan in the following positions, which are
again suppressed in the Manuscript:--
1,483,585 = III Chicchan 8 Zac (5 Cauac).
1,233,985 = III Chicchan 8 Kankin (10 Cauac).
1,272,465 = III Chicchan 18 Zip (12 Muluc).
The second date in the manuscript is 13 Kankin and the third is 13 Zip;
hence there is one line too many in the former number and one too few in
the latter. While on page 31a the origin of the numbers belonging to the
day XIII Akbal seems to be quite clear, here their relation to one another
is entirely concealed. I must, therefore, refrain from expressing any
conjecture in regard to them.
Now the numbers set down in the Manuscript are formed only by the addition
of the encircled numbers also found there. The encircled number for the
first expressed number is 51,419, which is the same number we found with
the corresponding day XIII Akbal; the second has 235 and the third 456 =
260 + 196. The 51,419 was 197 × 260 + 199; but 199 is the interval from III
Chicchan to VII Kan, just as it is from XIII Akbal to IV Ik. The 235 is the
interval between III Chicchan and IV Ahau and the 196 that from III
Chicchan and IV Imix.
By the addition of these differences, the numbers written out in the
Manuscript are obtained:--
1,483,585 + 51,419 = 1,535,004 (VII Kan).
1,233,985 + 235 = 1,234,220 (IV Ahau).
1,272,465 + 456 = 1,272,921 (IV Imix).
Keeping in mind what was said in reference to page 31a, let us now examine
the six numbers and dates collectively.
The fact that the days IV Ahau and XIII Akbal occur here and consequently
also III Chicchan is not surprising. Nor is the choice of VII Kan and IV Ik
an accident, for the interval between these days is exactly the same as
that between III Chicchan and XIII Akbal, viz:--218 days.
Hence the distance from III Chicchan to VII Kan is also exactly equal to
that between XIII Akbal to IV Ik, viz:--199 days.
Finally, the distance from VII Kan to III Chicchan is exactly equal to that
between IV Ik and XIII Akbal, viz:--61 days.
IV Imix and IV Kan are separated from the normal date IV Ahau by 3 × 13 =
39 and 8 × 13 = 104 days.
Regarding the encircled numbers, so far as they are independent of 260, I
would note the following:--
17 = XIII Akbal to IV Ahau.
121 = XIII Akbal to IV Kan.
196 = III Chicchan to IV Imix.
199 = III Chicchan to VII Kan and XIII Akbal to IV Ik.
235 = III Chicchan to IV Ahau.
In addition let me remark that 36 = VII Kan to IV Ahau, 39 = IV Imix to IV
Ahau and 104 = IV Ahau to IV Kan.
The following arrangement will prove that these numbers were as usual also
employed to form the large numbers by multiplication:--
17 × 74,620 = 1,268,540 (IV Ahau),
235 × 5,252 = 1,234,220 (IV Ahau),
36 × 42,639 = 1,535,004 (VII Kan),
39 × 32,639 = 1,272,921 (IV Imix),
104 × 12,236 = 1,272,544 (IV Kan).
But the highest number, 1,538,342, was formed in a different way; it =
59,167 × 26; but the interval from IV Ahau to IV Ik = 182 = 7 × 26, and
from IV Ik to IV Ahau = 78 = 3 × 26.
If in conclusion, we now examine the twelve numbers of seven figures given
in this section, we will clearly see that by twos and twos they plainly
belong together in pairs:--