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Title: Commentary on the Maya Manuscript in the Royal Public Library of Dresden
Author: Försteman, Ernst
Language: English
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  PAPERS

  OF THE

  PEABODY MUSEUM OF AMERICAN ARCHAEOLOGY AND
  ETHNOLOGY, HARVARD UNIVERSITY

  VOL. IV.--NO. 2

  COMMENTARY
  ON THE
  MAYA MANUSCRIPT
  IN THE
  ROYAL PUBLIC LIBRARY OF DRESDEN

  BY

  DR. ERNST FÖRSTEMANN

  TRANSLATED BY
  MISS SELMA WESSELHOEFT
  AND
  MISS A. M. PARKER

  Translation revised by the Author

  CAMBRIDGE, MASS.
  PUBLISHED BY THE MUSEUM
  OCTOBER, 1906

       *       *       *       *       *

NOTE

----

In pursuance of the plan of publishing translations of valuable
contributions to the study of the Maya hieroglyphs, the Museum Committee on
Central American Research has the pleasure of offering the following
translation of Dr. Ernst Förstemann's important Commentary on the Maya
Manuscript in the Royal Library of Dresden, generally known as the Dresden
Codex.

The translation by Miss Selma Wesselhoeft and Miss A. M. Parker was made
under the direction of Mr. Charles P. Bowditch of the Museum Committee.

In the original German edition, published in 1901, Dr. Förstemann used the
Arabic numerals to designate the days, but in this translation, with the
consent of the author who has kindly revised the translation, Mr. Bowditch
has substituted the corresponding Maya names of the days, in uniformity
with the general use of students in this country. It is needless to call
attention to the importance of this paper by Dr. Förstemann whose
long-continued study of the intricate system of hieroglyphic writing by the
ancient Mayas makes all he writes of great value to students engaged in
this most interesting research.

F. W. PUTNAME.

  HARVARD UNIVERSITY,
              October, 1906.

       *       *       *       *       *

PREFACE.

--------

Some of those who examine this book will say, that it is too early for a
commentary on the "Dresdensis," since Maya research is yet in its infancy,
and this opinion is certainly justified inasmuch as a final explanation of
that remarkable monument is, of course, impossible at the present time. On
the other hand the accounts of the numerous investigations and discoveries
which have been made thus far are so isolated and so scattered in the shape
of a hundred short magazine articles, that it is certainly desirable to
have what we know and what we have still to learn gathered together under
one head. This book is intended, therefore, to give an idea of the state of
our knowledge in this department of research at this time, when the
nineteenth century is passing into the twentieth, with the definite
expectation that this work will soon be far outstripped and will possess an
historical value only.

The contents of the following pages are of very little value, unless the
student can compare them with an edition of the manuscript. My first
edition was published in 1880 at Leipsic and the second at Dresden in 1892.
The edition in Lord Kingsborough's "Mexican Antiquities" (in Volume III of
that work, London, 1831) is still of practical use.

And since in this work I must premise a knowledge of the elements of the
subject, I would recommend, as additional aids to the comprehension of the
following pages, my "Erläuterungen zur Mayahandschrift der Königlichen
öffentlichen Bibliothek zu Dresden" (Dresden, 1886), and also Brinton, "A
Primer of Mayan Hieroglyphics" (in the publications of the University of
Pennsylvania. Series in Philology, Literature and Archaeology, Vol. III). I
would also mention the very valuable work by Paul Schellhas, "Die
Göttergestalten der Mayahandschriften" (Dresden, 1897), which I follow in
the designation of the various gods by letters of the alphabet.

It need hardly be pointed out, that the numerous pioneer articles by Edward
Seler offer abundant instruction to the student in this field as well as in
that of Aztec remains.

I wish to express heartfelt thanks to Mrs. Zelia Nuttall and Mr. Charles P.
Bowditch, who have aided my work in various ways and have thus rendered
possible the publication of this book.

E. FÖRSTEMANN.

  CHARLOTTENBURG.

       *       *       *       *       *

FIRST PART.

Pages 1-45.

Page 1.

As the first page is almost entirely effaced by abrasion, we know very
little of its contents. Like the second, however, it was doubtless divided
into four parts. The two pages have this also in common, that, for lack of
space, their contents are not expressed in full, but abbreviated as much as
possible.

The top section (a) of page 1 may have been filled with a sort of
frontispiece, perhaps a face with a few signs around it.

The three lower sections (b, e, d,) with the three lower of the second page
doubtless formed a whole. Each of these sections contained a normal
Tonalamatl of the commonest kind, which was introduced on the left by five
day-signs having a difference of 12 and was thus divided into five sections
of 52 days each. In sections b and d, at least, these periods seem to be
divided into equal halves of 26 days each. In d alone we recognize the
initial week day, VII, of the Tonalamatl. In each of the three divisions
there were two figures of gods, but we can recognize only the first of
these in section d as the god D.

Page 2.

This page contains four much abbreviated Tonalamatls. In the following I
will represent each Tonalamatl by setting down in a vertical line those of
the twenty days with which the principal divisions of equal length of the
Tonalamatl begin, in a horizontal line with Roman numerals the days of the
week of thirteen days on which the separate subdivisions begin, and with
the Arabic numerals the distance between these days. I will also remark
that the position of the Tonalamatls in the "Dresdensis" is not connected
at all, as in the Aztec, with certain places in the year, and that no rule
for this proceeding can be found. It is curious, however, that no
Tonalamatl in this codex begins with the day IX or Eb, which is the more
important in the last pages of the Dresden Codex.

2a.

This first Tonalamatl has the following form:--

  XIII  5  V  12  IV  11  II  12  I  12  XIII
  Cauac
  Chuen
  Akbal
  Men
  Manik.

The hieroglyphs and the figures show that preparations for a human
sacrifice are treated of here and that the subject is, therefore, closely
connected with page 3a, where the sacrifice itself is represented.

There are but two pictures of persons, which refer, therefore, only to the
first or to the first two subdivisions and which, for lack of space, are
wanting for the others. On the left walks the person doomed to sacrifice,
his arms are bound on his back, his head is barely visible and his eyes are
apparently torn out. There is an object in front of his breast resembling a
wreath. Behind this figure crouches a second, who holds an object in his
hand which probably represents a rattle. The parallel passage in Cod. Tro.
2b shows the bound prisoner with an axe behind him. Then follows in Tro. 3b
the prisoner without a head and behind him the black god with gory lance.

The hieroglyphs--four for each of the five subdivisions--are arranged in
the following order:--

  1  2    5  6     9  13    17
  3  4    7  8    10  14    18
                  11  15    19
                  12  16    20.

Of these 9, 13 and 17-20 are wholly effaced and 14 for the most part. The
very first group refers to human sacrifice, for 1 is a head with an axe
affixed to it, 2 contains the hand (_i_) which so often appears as the sign
of grasping, especially in representations of the chase; here it has the
same superfix as on page 22a, which on pages 4a-10a and 11a, b, appears as
prefix. 3 is the head of god H, perhaps given here as a symbol of wounding
(serpent god?). I am unable to explain the meaning of the dot between two
crosses in front of this head; perhaps the sign denotes the day Kan, which
is here arrived at by calculation. We find the same hieroglyph on page 3.
Sign 4 signifies the death-god A = Cimi, who appears again in 12.

In like manner 2 is repeated in 6 and 14. 7, 11 and 15 (probably also 19)
are, however, the familiar cross _b_; 8 is the head of E with a prefixed
knife; the intention here may have been to show that human sacrifice would
be likely to have an auspicious influence upon the harvest. 10 and 16 are
another unknown head. In 5 we see the familiar Kan-Imix sign, which, for
the present, I am inclined to regard as denoting a feast or a sacrificial
meal.

2b--c.

These two sections have something in common. First, 2b (as also 2d) is
divided into but two parts and 2c into only three parts. Second, in 2b and
2c the scribe intended to draw the hieroglyphs for 10 days each, instead of
5 each, but only drew the outlines of the second five, since they could not
be used for these Tonalamatls. Third, the persons represented here are all
engaged in the same occupation, each holding in his hands an object which
looks like a frame for a net or web, and also a large needle with an eye
through which a thread has been passed.

A very similar representation is found in the Codex Troano 34a, 33a and
23*c, and also in the Sahagun Manuscript of the Bibliotheca Laurentiana at
Florence. This can hardly mean anything else than the knotting of cords,
which was the only method of casting lots current among the Mayas; compare
Seler, "Altmexikanische Studien II" (1899), p. 31, and "Zauberei im alten
Mexiko" (1900), p. 90, by the same author. This clearly indicates the use
of these Tonalamatls in soothsaying.

Fourth and last, each of the five hieroglyph groups of 2b and 2c begin with
the same sign, which must, therefore, denote the casting of lots.

The Tonalamatl 2b runs thus:--

  XI  34  VI  18  XI
  Oc
  Ik
  Ix
  Cimi
  Ezanab.

The pictures are of three persons. At the left two sit facing one another
and at the right is the god A. Of the first two, the one at the left is
probably feminine, but with an old face. I am inclined here, in spite of
the sex, to recall the bald-headed old god (N, according to Schellhas),
whom I am inclined to consider, for the present, the representative of the
5 Uayeyab days at the end of the year. This would account for the sign
resembling an 8 lying on its side, which appears on the god's head and
which usually represents the change of the year (compare pages 38a, 41b,
52b, 68a and 72c). I cannot explain the person sitting facing this god
further, than that from his hieroglyph he is either H or allied to H.

Of the 8 hieroglyphs

  1  2    5  6
  3  4    7  8.

the first, as stated, seems to refer to the casting of lots, 2 is the sign
for H, 3 denotes the female figure pictured beneath it, and 4 is the sign
_q_ with the Ben-Ik on top of it. In the second group 5 is the same as 1, 6
is the cross _b_, and 7 and 8 are the hieroglyphs for A.

2c contains the following Tonalamatl:--

  III  20  X  17  I  15  III
  Oc
  Ik
  Ix
  Cimi
  Ezanab.

There are illustrations for only the first two of the three subdivisions;
the two figures composing them are engaged in the occupation mentioned
under 2b. At the left sits a deity, who is probably E, whose head develops
into a second, which is that of an animal; on the right sits the god D.

The three groups of four hieroglyphs each are arranged as follows:--

  1  2    5  6     9
  3  4    7  8    10
                  11
                  12.

Of these hieroglyphs 1, 5 and 9 are the head already numbered 1 and 5 on
2b; 2, 6 and 10 are the cross _b_; 3, 7 and 11 are three different heads,
all, as it seems, having the Akbal sign, and 11 having also the numeral 6.
4 is again (see 5 on 2a above) the Kan-Imix sign, 8 a Kin with suffix (the
east?) and the numeral 16 as prefix; finally 12 is Cimi (A). Do the numbers
16 and 6 refer to the 16th and 6th of the 17 and 15 days standing below
them? The beginning of this Tonalamatl III Oc seems to me to fall on an
especially auspicious day (hieroglyph _a_).

2d has the following Tonalamatl:--

  XIII  28  II  24  XIII
  Lamat
  Ahau
  Eb
  Kan
  Cib.

This refers probably to the section devoted to women, pages 13-23. For the
picture on the left is a woman sitting and holding an unknown object in one
hand; on her right stands the death-god A holding in his hands what may be
an apron or breech-clout; there is a similar representation in Cod. Tro.
29*b.

The hieroglyphs are

  1  2    5  6
  3  4    7  8.

Of these 1, 6 and 8 are one of the signs of A, 7 another, and 4 may be a
third, recalling the Moan, which, as on page 14c, rests on a hand held
beneath it. 2 and 5 seem to signify a carpet or other fabric (or a lying-in
bed?), on the one hand suggesting the occupation of the figures in 2b and
2c, and on the other the checkered hieroglyph, which is so common in the
Palenque inscriptions. Finally 3 is the woman pictured beneath.

Page 3.

We come now to the sacrificial scene proper, which practically fills the
upper half of the page. The victim, a woman, lies bound hand and foot, on
the sacrificial stone, just as in the Cortes. 41-42; the incision above the
stomach is already made and the eyes are closed. Behind her rises the tree
of life with a bird (vulture?) sitting in its branches, which holds in its
bill one end of an object, resembling a ribbon (entrails) issuing from the
eyes of the victim, just as in Tro. 26*a and 27*a.

This picture is surrounded by four gods, who, however, differ very much
from the other four in the second sacrificial scene, page 34a. At the right
above is K, who, I think, is the storm-god; the figure at the left above is
almost entirely destroyed, and its hieroglyph wholly; I prefer to consider
it a rain deity, so that these two gods shall signify the productive
season. The two gods below may refer to the blessing upon the harvest and
chase resulting from the season and the sacrifice. For, at the left below,
we see the maize deity E, holding a dish of fruit, while her head-ornament
contains a second head. At the right below sits the serpent deity H and in
front of him is an animal with the noose still around its neck, with which
it was caught.

The hieroglyphs are in the following order:--

  1  2    5  6     9  10    13  14
  3  4    7  8    11  12    15  16
      17  18           21  22
      19  20           23  24.

Of these, 1-5 are wholly effaced and also the most essential part of 6.

Of these hieroglyphs four (1-4, 13-16, 17-20 and 21-24) clearly belong to
each of the four deities, for 15, 18, and 22 (the last again with the dot
between two crosses as on page 2a) certainly belong to the picture. From
this it seems to follow that Hieroglyphs 5 to 12 refer to the sacrifice
itself. As a matter of fact 9 and 11, which are directly above the
sacrifice, also refer particularly to that part of the representation.

I wish also to call special attention to the two signs 8 and 16 which seem
to correspond to one another. They are the two which I have designated with
_q_ and _a_, which are met with here for the first time (aside from the _q_
with the Ben-Ik, which is not in question here) and which, I think, denote
the good and evil days, _q_ referring to the sacrifice and _a_ to its
results.

In regard to the rest of these hieroglyphs, 7 and 9 are Cimi; 10, 14, 17
and 24 the cross _b_ and 11 and 23 the hieroglyph c. 12 is the head with
the Akbal eye, having for its prefix the uplifted arm, which is joined thus
to the most diverse signs, and which also occurs in the Tro-Cort. 13 is a
similar head, 19 again Imix, 20 the sign _o_ and 21 a hieroglyph, which is
without doubt a simplified head.

Here, too, we have a Tonalamatl, and one beginning on an especially
ceremonial day I Ahau, which seems to play the same role in celestial
affairs as IV Ahau does in terrestrial matters. On the sacrificial stone we
read the days Ahau, Eb, Kan, Cib and Lamat, and I think it likely that the
same days occur in the passage of the Cortes. referred to above; the
passage evidently contains some errors. The subdivisions of this Tonalamatl
are not known to us, for here the manuscript is somewhat confused. I
propose to read it as follows:--

  I  10  XI  4  II  15  IV  9  XIII  14  I

but Cyrus Thomas, "Aids," p. 294, has

  I  4  V  8  XIII  11  XI  15  XIII  14  I.

Either reading is dubious. The scribe divided the lower half of page 3 into
two parts, and drew in each the outline of five days; but then he saw that,
to continue his work, he needed a long surface extending from left to
right, and he therefore omitted filling in these two sections.

Pages 4a--10a.

We have here a normal Tonalamatl, which, however, was evidently meant by
the author to serve a very special purpose, since he divided the first
section of 52 days into no less than 20 parts of 2, 3 or 4 days. I give the
following arrangement here, remarking, at the same time, that in one
doubtful case (between the third and fourth groups) I deviate from my
former plan:--

    X 2, XII 4, III 3, VI 2, VIII 4, XII 2, I 2, III 4, VII 2, IX 2, XI 2,
    XIII 4, IV 2, VI 3, IX 2, XI 3, I 2, III 3, VI 2, VIII 2, X.

Since the five sections on page 4a begin with the days Imix, Ben, Chicchan,
Caban, and Muluc, we have resulting from this and from the intervals
specified, the following days:--

    X Imix, XII Akbal, III Manik, VI Oc, VIII Eb, XII Cib, I Ezanab,
    III Ahau, VII Kan, IX Cimi, XI Lamat, XIII Oc, IV IX, VI Cib, IX Cauac,
    XI Imix, I Kan, III Cimi, VI Muluc, VIII Chuen, X Ben.

Now, however, in the "Globus," Vol. LXXIII, in my two articles entitled
"Die Tagegötter der Mayas," I have expressed the opinion that there is good
reason to believe that the scribe has made a grave mistake here.

I assume that the scribe simply transferred the so-called month days from
the year just past to the year in which he was writing, in doing which they
were, of course, moved five days on (since 365 = 20 × 18 + 5), but he did
not bear in mind, that the pictures and the hieroglyphs could then no
longer correspond. Hence the days must be not

    Imix, Akbal, Manik, Oc, Eb, Cib, Ezanab, Ahau, Kan, Cimi, Lamat, Oc,
    Ix, Cib, Cauac, Imix, Kan, Cimi, Muluc, Chuen, Ben,

but

    Cib, Ezanab, Ik, Chicchan, Manik, Chuen, Ben, Men, Cauac, Imix, Akbal,
    Chicchan, Muluc, Chuen, Ix, Cib, Cauac, Imix, Kan, Cimi, Lamat.

Let us now consider the 20 groups, disregarding the first (really zero)
which has no figure and no hieroglyphs. We will leave out of the question
also the first two hieroglyphs of each group, which are the same twenty
times and form, as it were, merely a superscription, in which the first
sign is a head, also occurring elsewhere (4b-5b), with suffix and affix,
and the second is the hieroglyph _i_, which might readily denote a
sacrifice. Thus only the usual four signs remain for each picture.

1. Day 15 = Ezanab; Aztec Tecpatl, flint, lance point. The figure of the
god does not correspond with this at all; it is a god in a gala cloak,
holding before him a serpent and bearing a quetzal bird on his back. This
figure, which resembles none other in our manuscript, strongly recalls
Kukulcan, who, in fact, is often placed by the scribes at the head of the
20 Maya gods (cf. Dres. 36) in which manner he appears in this place quite
without reference to the day and the hieroglyphs. In this interpretation I
follow Seler, in the main, who in his treatise "Quetzalcouatl-Kukulcan in
Yucatan" (1898) expresses this opinion on page 403 of the separate edition.
But possibly the ear-ornament may refer to Ezanab. Of the hieroglyphs, 1
and 2 are the familiar sign of the serpent deities H or I, though here they
are not drawn exactly alike. They also appear together on page 6a. 3 ( =
_r_) I think is the sign for the week of 13 days, which recurs in groups 5,
11, 14 and 16, and hence is distributed 4 times, though not regularly,
among the 4 × 13 days. Sign 4 is the death bird.

2. Day 19 = Ik; Aztec Ehecatl, wind, air, breath. The deity pictured is B,
the god who is found the most frequently, and with the most varied
attributes, of all the gods in our manuscript. He is the god proper of
breathing and living and was, perhaps, the local god in the region where
this manuscript originated. The second hieroglyph is his sign; the first,
with a prefixed 9, is _p_ the third _q_ and the fourth _a_ with the usual 3
before it; their relations to B are still unknown.

3. Day 3 = Cimi; Aztec Miquiztli, death. The deity with a black line about
the mouth is certainly the bald-headed old god N, whom we shall find on
pages 12c, 14b, 17a, 21c, and 37a. His hands are much deformed; perhaps
indicating the bite of a serpent? Of the hieroglyphs, 1, 2 and 4 are
effaced; 3 is surely the sign of the god, differing, it is true, from his
usual hieroglyph, but recurring with a 4 also on pages 21c and 24. This 4
might refer to the four kinds of years, but here, perhaps, to the fourth of
the five Uayeyab days, and would thus agree with the 24th day of Cumku,
which should lie here (in the year 9 Kan), if I have begun the Tonalamatl
correctly.

4. Day 4 = Manik; Aztec Mazatl. The significance is stag or roe, game or
the chase. The first picture on page 5 is one of the forms of F, which
seems to stand here not merely for human sacrifice, but also for war and
the chase, and especially for the act of killing in general. Of the
hieroglyphs, unfortunately only the fourth can be read in full (the sign
_c_), the upper part of the second is the cross _b_ and the lower part the
sign Ahau; the number 11, which is peculiar to the god F, probably stood
before the second sign. Did this god rule the eleventh of the 13 months of
28 days, as Moan ruled the thirteenth?

5. Day 8 = Chuen; Aztec Ozomatli, ape, then probably the constellation of
Ursa Minor, and hence belonging to the god C. The figure is unquestionably
his, and the first hieroglyph is surely his sign. The other three are the
familiar _a_, _o_ and _r_.

6. Day 10 = Ben; Aztec Acatl, the fundamental significance of which is
reed, rush, etc. The connection between this day and the god B pictured
here must be left undecided. Of the hieroglyphs, the first points rather to
the sun-god G, the second, with the numeral 7 as a prefix, is entirely
destroyed, the third is the sign _u_, and the fourth, which is half
obliterated, was _q_.

7. Day 12 = Men; Aztec Quauhtli, eagle. The figure to which the first
hieroglyph with the numeral 11 belongs, is a form of the god F, but has the
nose-ornament of the sun-god G. Hieroglyph 2, which we shall find again on
22c, may refer especially to the eagle; the third is the sign of the day
Caban with a prefixed 3, and the fourth is the sign _o_.

8. Day 16 = Cauac; Aztec Quiahuitl. The meaning in the different languages
points to rain, storm and summer, of which the tortoise and serpent are
special symbols. I shall not venture to decide positively upon the deity
pictured here; perhaps the object in his hand may be a tortoise; Seler,
"Quetzalcouatl-Kukulcan" (1898), p. 403, calls him the young god. In the
hieroglyphs we find the serpent sign Chicchan twice, just as in the first
group on page 4; then follow _a_ and Kan-Imix.

9. Day 18 = Imix; Aztec Cipactli. In my treatise on the day-gods, I have
referred to the variations in the significance of this day. The Mayas
connected with it the idea of the female breast, of drink, and, in
particular, of the intoxicating beverage pulque. The deity pictured here,
which is certainly a female deity, has a kind of vessel in her hand, from
which the serpent resting on her head appears to be drinking. Hieroglyphs 2
and 4 are wholly obliterated, and 1 partly; there is a lock of hair, the
sign of femininity, before 1 and 3. It is to be noted further that 3 is the
sign of the death-god and that the deity pictured here has the death-sign
on its cheek. Can this possibly suggest deathlike intoxication?

10. Day 20 = Akbal; Aztec Calli. The meaning is that of darkness, night,
dark hole, then that of house as an artificial cave or as a place of
shelter at night. The first picture on page 7, the black deity L with the
beard fits admirably here. The black paint still visible proves that the
first hieroglyph, which is almost effaced, was his sign, and the second may
be a head more definitely identifying him. The third was the sign _q_, the
fourth is an Ahau, perhaps intimating that Akbal belonged to the days
beginning the Uinal sections of 20 days, and to the lords of the same. In
addition to appearing with these 5th, 10th, 15th, and 20th days, an Ahau is
found with the 1st, 6th, 11th and 16th as regent of the year, and lastly,
but especially, with the 17th, which bears the name Ahau, and with the god
D belonging to it.

11. Day 2 = Chicchan; Aztec Cohuatl, serpent. With this would agree also
the third and fourth hieroglyphs (the latter _r_), which are the two we
found in the first representation on page 4 belonging to the deity holding
the serpent. But what is the meaning here of the dog-head of the figure,
and of the first two hieroglyphs corresponding to it? And what does this
creature hold in its hand? The lightning? The hieroglyphs seem to
correspond to the seventh day, as if the scribe had recognized his mistake
and referred here to the present and not to the past year.

12. Day 6 = Muluc; Aztec Atl, water, cloud. With this corresponds the image
of the storm deity K and his two hieroglyphs 1 and 2, the first of which
occurs frequently, and the second is found on pages 20 b and 47, while 3
(Ahau) designates the day as regent of the year and 4 is the hieroglyph a.
The curious sign 2 is also given on Cort. 32 b.

13. Day 8 = Chuen; Aztec Ozomatli, ape. There is no agreement at all here,
but everything points to the day 3 lying 5 days back, the picture of the
Cimi as well as the hieroglyphs, even the third with the Akbal sign and the
uplifted arm (as on page 36a), also the fourth (_c_) which is generally
thought to be the death-bird. It even seems here as if the scribe had had
the preceding year in mind; possibly he did not want to repeat the fifth
group.

14. Day 11 = Ix; Aztec Ocelotl, jaguar. Here there is an admirable
correspondence between the figure and the first hieroglyph, which on page
26, top, also refers to the jaguar represented there; the other three
hieroglyphs are _r_, Kan-Imix and _q_.

15. Day 13 = Cib; Aztec Cozcaquauhtli, vulture. The bird is actually
pictured here and its sign is the first hieroglyph; the third is _q_, the
second and fourth are obliterated.

16. Day 16 = Cauac; Aztec Quiahuitl, meaning, as in the eighth group, rain,
storm, summer. The figure, the first on page 9, seems, however, to indicate
the day Ahau, as does also the second hieroglyph, which is Ahau; the first
and third are effaced and the fourth is _r_. Perhaps the scribe did not
wish to repeat the eighth group.

17. Day 18 = Imix; Aztec Cipactli, as in the ninth group. Here the allusion
to pulque is still plainer than it is there. The picture is that of a woman
with bound eyes and uncertain position of the hands, and here too with the
death-sign, and on her head a bee from whose honey the beverage was
prepared. I shall not venture to explain the first two hieroglyphs; the
second with uplifted arm appears again on page 8c. The third is Cimi and
the fourth _q_.

18. Day 1 = Kan; Aztec Cuetzpalin, denoting maize with the Mayas. The
representation consists of the maize deity with the Kan sign on her head,
the first hieroglyph is hers, then follows Kan-Imix, which I am inclined to
interpret as meaning a meal, next the sign _a_ and finally a head, which is
uncommon and undetermined, with the leaf-shaped prefix as on pages 4c, 6c,
9c, 34b, 61a, 67b and 69a.

19. Day 3 = Cimi; Aztec Miquiztli, death. The first figure on page 10 is a
deity with the head of the death-bird Moan and above the head is the
death-sign. As has long been known, the first and third hieroglyphs
unquestionably belong to this god, also the fourth with the Akbal sign
agrees with it, and the second likewise recalls the Moan.

20. Day 5 = Lamat; Aztec Tochtli, meaning rabbit in the latter language.
Neither the figure, which represents Cimi, death, nor the corresponding
hieroglyphs, excepting the second one agree with this day. This second
hieroglyph has both in front and above it the number 6. Two numbers added
thus to the common Uinal sign usually designate the Uinal period plus days,
as is so very common on the inscriptions, so that the sign appearing here
would denote 6 × 20 + 6 = 126 days. The hieroglyph here, however, is _not_
the usual sign for 20 days. On the contrary, it has in the centre a
straight line and on either side of it a parallel line ending in a little
knob (or loop?). I propose to regard these lines as representing the
ecliptic and the moon, which takes its course now to the north and now to
the south of the ecliptic, and the sign as a whole as signifying the lunar
month of 28 days. This is confirmed on pages 51, 55, 56 and 57. In that
case this hieroglyph would denote 6 × 28 + 6 = 174 days.

Now bear in mind that in this passage the day X Lamat, which equals the
Aztec Tochtli, is referred to.

In the year named after this day, and indeed on the 174th day of the same
(1 Cipactli), in February 1502, the emperor Ahuitzotzin died; compare
especially Brinton, "Essays of an Americanist" (1890), pp. 274-283.

Should this association in our manuscript of Cimi = death, X Tochtli and
the numeral 174, be considered accidental? Or did the scribe, writing in
the year after the event, actually record it in the year 1503 and,
departing from his real subject, immortalize it in this place at the end of
the greatest Tonalamatl? I will not refrain from expressing the conjecture
I have long entertained, though I am quite prepared for differences of
opinion.

Seler attempts to explain this series of 20 gods in another way; see his
"Monumente von Copan und Quirigua" (1899), p. 729. (Cf. his collected
papers p. 781.)

Pages 4b--5b.

It is my opinion that the Tonalamatl just now discussed connects with
another, which is recorded directly below the beginning of the first, and
which also differs from all the other ordinary Tonalamatls. It likewise
divides the first 52 days into a large number of small parts (14) and has
the following form, if we adopt Seler's correction in the last member:--

  XII 4 III 4 VII 4 XI 3 I 4 V 3 VIII 4 XII 3 II 6 VIII 3 XI 4 II 4 VI 4 X
      2 XII
  Ix
  Cimi
  Ezanab
  Ik
  Oc.

The two days Ik and Oc should be read Oc and Ik. There is only one picture
here:--a scaly green monster with the head of the principal god D. There
are six hieroglyphs on its body, the first is that of Eb and the second
that of Cimi, the fourth is the sign c. The others I shall not venture to
determine.

According to a conjecture expressed verbally by Dieseldorff, this figure
may represent the god who continually recreates himself. We are reminded
here of the two-headed serpent (Seler, "Tonalamatl der Aubinschen
Sammlung," 1900, pp. 65-66). There are two rows of hieroglyphs above the
monster, the upper contains 8 and the second 6, but the second hieroglyph
in the upper row belongs in the lower. Thus there are 14 hieroglyphs
corresponding to the subdivisions noted above.

The upper seven signs are all alike and are also identical with the one,
which, in the great Tonalamatl, recorded above, begins the heading of all
the 20 groups; this likewise points to a close connection between the two
Tonalamatls.

The remaining 7 hieroglyphs should be considered as only 6, for it is
improbable that C occurs twice in this series. They are the gods D, C, H,
N, A and B, to which perhaps an E or F or G is to be mentally added in
place of the second C. They are all principal gods with the exception of N
(as always, according to Schellhas's nomenclature). This N, an old man,
denotes, as it seems, the five Uayeyab days at the end of the year, as he
does also on page 21c. This sign with the number 4 has already been seen on
page 4a. If in 4b this sign signifies the last day of the year, then this
Tonalamatl falls in the year XIII Kan. The sign 5 Zac also appears in the
Tro-Cort., _e.g._, Cort. 29 c, Tro. 9*b and 28*b.

Now I shall proceed to examine all that has not yet been discussed to the
end of page 12, taking up first the remainder of sections a and b and then
all those of 4c-12c.

Pages 10a--12a.

  XI  12  X  8  V  12  IV  8  XII  12  XI
  Lamat
  Ahau
  Eb
  Kan
  Cib.

The period of 52 days is thus divided into five sections of 12 and 8 days
each, alternating regularly. A deity and four hieroglyphs belong to each of
these sections, viz:--

1. D sitting, with his right hand pointing upward and his left downward; on
his head is the Akbal sign as on page 15c. The hieroglyphs are destroyed
with the exception of the third, which is the sign of D (Ahau). The fact
that the 12 days happen to end with the day belonging to D (Ahau) is
accidental.

2. R, a human figure with the head of the Moan (as on page 7c and 10a) and
with the copal pouch around his neck. Of the hieroglyphs only the fourth,
one of the common signs of Moan (_c_), is legible.

3. H, or, according to Seler, "the young god," as on 12b and 14b, with
nose-peg and copal pouch. On his (her?) head sits a bird with an object,
which I do not recognize, in its bill; compare page 12b. Of the
hieroglyphs, the first is destroyed, the second is the unmistakable sign of
H, the fourth is the common _a_, and the third I cannot as yet decipher.

4. A, with the usual design issuing from his mouth (the expiring breath of
life?). Of the hieroglyphs, the first is a double Manik with prefixes,
which probably denotes violent death; the other three are very common
symbols of A.

5. E, holding a vessel containing plants (agave?) and with the cross _b_ on
his head-ornament. The first hieroglyph is an unexplained compound design
apparently referring to the Moan, an Imix and two prefixes, the second is
the monogram of E, whom the third hieroglyph, Imix-Kan, designates as
dispensing nourishment, and the fourth, Ahau, as a leading deity.

Page 12a.

The scribe evidently wishing to carry out his material in some conclusive
form in the top, middle and bottom sections of page 12, found insufficient
space in the top section. He, therefore, condensed two independent
unconnected Tonalamatls, by arranging them in such a manner, that the
period of 52 days was divided, for the sake of brevity, into only two
parts, viz:--

  VIII  27  (IX)  25  (VIII)
  Ahau      Oc
  Eb        Ik
  Kan       Ix
  Cib       Cimi
  Lamat     Ezanab.

I have supplied the two numbers enclosed in parentheses; they are wanting
in the Manuscript.

The hieroglyphs

  1  2  5
  3  4  6
        7
        8.

are sufficient for the two figures one expects to see here; but they are,
in fact, intended for four figures--two for each of the two Tonalamatls.
For the first of the two Tonalamatls we have only one figure, God K, who,
however, from the dish held in his hand, probably containing honey (compare
10b), seems to stand here also in place of E. In agreement with this,
Hieroglyph 2 and probably also 1 (_s_, which occurs again on page 13a, and
also on page 10b) refers to K, while 3 clearly refers to E and 4 is the
sign a. Hieroglyphs 5-8 belong to the second of the two Tonalamatls. The
first two of these hieroglyphs, which are entirely erased, refer to an
unknown deity, and the last two unquestionably relate to A.

Pages 5b--6b.

  I  16  IV  9  XIII  25  XII  2  I
  Manik
  Cauac
  Chuen
  Akbal
  Men.

Four hieroglyphs belong to each of the four subdivisions:--

  1  2    5  6     9  10    13  14
  3  4    7  8    11  12    15  16.

These four parts, however, form a whole, inasmuch as they all relate to
making fire, as it is also represented in the Troano 6, 19 and 14*c. Hence
the upper row of hieroglyphs contains signs which are repeated. 1, 5 and 9
are the same head, the last two cases have the sign for darkness (Akbal);
this Akbal appears again in the parallel passages of the Tro. and in 13 it
is somewhat enlarged simply owing to the absence of a head. The act of
making fire seems to be denoted here rather by the second sign (2, 6, 10,
14), which I designate by _k_ and which, originally, doubtless consisted of
two hands (double Manik sign); the prefix is the same in 6 and 14, and
different in 2 and 10.

The eight lower hieroglyphs are merely the monograms of the four gods
making the fire. The first deity is F, the second either A or one of the
black deities L or M, the third D and the fourth apparently F again, but
conceived as feminine. In the third picture there is a second object,
apparently a head (of D?), below the piece of wood in which the fire-stick
is being whirled. Hieroglyph 11 belonging to this deity has an Akbal as a
prefix.

Pages 6b--7b.

  X  13  X  13  X  13  X  13  X
  Kan
  Cib
  Lamat
  Ahau
  Eb.

This Tonalamatl is divided, by way of exception, into four equal parts,
which all begin with the same week day X.

Here too, as in the preceding Tonalamatl, there are four subdivisions, and
also 16 hieroglyphs arranged in the same way. And here too the upper line
is a condensation of the whole, the same two signs being repeated four
times. The first of these is _q_, which is still a problem and which occurs
inverted also on Cort. 20d-21d (where there are figures with bird-heads);
there too it is the characteristic hieroglyph. The second, however, is
again the double Manik sign referring to activity of some kind, as in the
preceding Tonalamatl. But the occupation of the four deities represented
here is of very different kinds and altogether problematical. E, conceived
as feminine, occupies the first place, with a Kan sign on her head and
holding in her hand a vessel exactly like the one held by the figure just
above on the same page. The third hieroglyph is hers and the fourth is the
sign a.

The second figure is A with a hook-shaped object hanging around his neck.
His hands also seem to be deformed, as are those of the third and fifth
figures of the great Tonalamatl (on pages 4 and 5). His two hieroglyphs are
among those usually belonging to him.

The third god is D sitting, by way of exception, on some object (stone?).
Something resembling the pestle of an ordinary mortar is hanging down in
front of his headdress, and he is holding a very similar object to his
mouth. His two hieroglyphs are also those which usually refer to him.

The most striking figure is that of the fourth god, whom I do not
recognize. He seems to be attracting to himself a bird flying down from
above, whose bill almost touches his mouth. His hieroglyph has the sign Yax
(strength) for a prefix and the fourth hieroglyph is c.

Page 8b.

  VIII  26  VIII  26  VIII
  Manik
  Cauac
  Chuen
  Akbal
  Men.

Again we have a Tonalamatl divided into equal parts, this time, however,
into but two, and it seems thus to be closely connected with the preceding.

While hitherto four hieroglyphs have usually belonged to each figure, we
find here ten in all and in the following order:--

  1  2    5  6
  3  4    7  8
             9
            10.

There are two figures here, which stand in some relation to one
another,--two persons sitting facing each other. The one at the left is
certainly D, the one at the right can hardly be the old woman, whom
Schellhas designates with O, but rather N, the old god of the Uayeyab days.
The former seems to be about to take something from the hand of the latter.
I surmise that it is one of the prophetic weaving implements. which we
found on page 2. The two hieroglyphs _e_ and _h_ must refer to this; they
are repeated, as usual, in the two groups, _e_ in places 2 and 8, and _h_
in 1 and 6.

Signs 3 and 4 refer unquestionably to D and hence 5 and 7 (the first _q_
with Ben-Ik, and the latter unknown) must be the designation of the person
sitting on the right. We shall meet the latter sign again on pages 15b and
18a, with the same person, and on pages 27a and 39b with entirely different
persons. Sign 7 is an object, which also appears on 15b and 18a, held in
the hands of women and may denote some special sacrificial offering; on 9b
Kan-Imix appears in place of this sign, and on 39b beside it. It should be
noted that sign 7 stands here in exactly the same proximity to 1 and 6 as
on page 27a.

The hieroglyphs 9 and 10 stand outside the two groups, and since, as we
know, they belong to the god A, this prophecy must concern death, as is
more clearly indicated by the corresponding hieroglyphs on page 9b.

Page 9b.

Here, for the first time in this manuscript, we have a Tonalamatl in which
the 260 days are not divided into five fifths of 52 days each, but into
four quarters of 65 days. This may be represented as follows, if we supply
the III, which is wanting at the beginning:--

  III  33  X  32  III
  Muluc
  Ix
  Cauac
  Kan.

In the first place, the close connection of this Tonalamatl with that
recorded on page 8b, just now discussed, is striking, for

    1. Here too we find a division into two equal parts is intended, but
    which, of course, as the number is 65, cannot be mathematically exact.

    2. Here too we not only find 10 hieroglyphs, but we find them in the
    same order as on page 8b, and here too the sign _e_ stands in places 2
    and 8, and _h_ in 1 and 6; again 3, 4 and 9 are exactly the same
    hieroglyphs here as there, so that only 5, 7 and 10 are different.

    3. The picture is again that of two persons sitting facing each other.
    Here D sits on the right and facing him is the grain deity E. D is
    speaking to E as is indicated by the sign before his face and by the
    position of his right hand. The signs belonging to E are Hieroglyphs 5
    and 7, while those of D are 3 and 4. It seems, therefore, that D is
    announcing to E the prophecy contained in the preceding Tonalamatl.

    4. Two hieroglyphs, 9 and 10, are again added, both relating to
    death--9 to god A and 10 to F.

Now what especially distinguishes this passage from the preceding one, is
the fact that the four days are the so-called regents of the year, Muluc,
Ix, Cauac and Kan, above which, perhaps to emphasize this circumstance,
there is a particularly elaborate Ahau. Seler ("Einiges mehr über die
Monumente von Copan und Quiriguá," p. 210), however, thinks that this sign
is the hieroglyph for the numeral three, which should stand here.

The fact that the tenth sign, which is the last, is 13 Moan in the
preceding Tonalamatl, while here it is 11 F, will be of special
significance in deciding the interpretation.

Page 10b.

The manuscript gives the following:--

  XIII  22  III  22
  Oc
  Ik
  Ix
  Cimi
  Ezanab.

This cannot be correct, for 22 + 22 is not 52, and from XIII to III is not
22 days, while the last Roman numeral is wanting. I, therefore, propose to
make a 6 of the numeral 2, which occurs twice, by changing the lower dot
into a line, and to change the III into a XIII by the addition of two
lines. This gives the series the form XIII 26 XIII 26 XIII. Then by its
division into three equal parts, this Tonalamatl accords with the three
preceding ones, which it also resembles in other respects. For here too we
find two persons pictured; this time, however, they do not face each other,
but are placed one behind the other. The first is B, the god of life
strictly speaking, the second is F, who is represented by his hieroglyph in
the preceding Tonalamatl, and who is the god of the chase and probably of
death by violence. Both hold offerings in their hands, which have been
presented to them, and this also seems to be suggested by the two pendent
copal pouches. The dish in B's hand probably contains honey, while F holds
a plant (agave?)--the very same articles, which we find on page 12a in the
hands of other gods. It looks as if the gods had been propitiated and as if
this were the conclusion of a drama running through four Tonalamatls. Again
the two death-hieroglyphs, which were added on pages 8 and 9, are wanting
here, and we find only the usual eight signs:--

  1  2    5  6
  3  4    7  8.

Of these, 1, 2 and 5, 6 are the usual comprehensive heading; 1 and 5 are
the Manik sign, which must denote the offering, while 2 and 6 are the
characters, which perhaps, not incorrectly, has been thought to denote a
repetition, a kind of plural; we have already seen it on pages 12a-13a. 3
is the monogram of B, yet it looks more like a fist with the thumb
prominent--a figure I have frequently found in the inscriptions of
Palenque. It must also refer to the sacrifice offered to B, which is
confirmed by the _a_ added to it in 4 and probably denoting a good day. 7
is the hieroglyph of F to which the sign in 8 corresponds, while the
prefixed arm in 8 seems to refer to the presentation of the sacrifice.

Pages 10b--11b.

  VIII  8  III  9  XII  9  VIII  10  V  16  VIII
  Chuen
  Akbal
  Men
  Manik
  Cauac.

I have corrected the 15 in the manuscript by making it 16.

20 hieroglyphs correspond regularly to the five sections in the following
order:--

  1    5  6     9  10    13    17
  2    7  8    11  12    14    18
  3                      15    19
  4                      16    20.

This section seems to refer chiefly to the harvest. First the Muluc sign
with suffix and affix, which is repeated in 1, 5, 9, 13 and 17 at regular
intervals, suggests rain as a preliminary condition of the harvest. Next in
2 the hieroglyph of K, the wind-god, is added to this Muluc sign, and K is
the patron of the day Muluc. Then the signs _a_ and _o_ follow in 3 and 4.
There is no picture belonging to this group; it ought to be the god K. The
second group adds to the Muluc in 6 the glyph of the sun, which is the
second preliminary condition of the harvest. This is followed in 7 by the
sign _u_ apparently denoting wind and cloud and having the prefix of the
storm-god, and in 8 is the sign, which, strange to say, stands also in the
last Tonalamatl in the eighth place. I am not very clear in regard to this
sign. The sun-god G with copal pouch and a vessel containing grains of
maize is appropriately represented with this group. With equal fitness the
third group contains E, the harvest-god proper, with copal pouch and grains
of maize, and, as usual, a Kan sign on his head, but also with a parrot,
probably as an enemy of the harvest. Sign 10 is E's hieroglyph, to which,
as is so often the case, sign 11 (Imix-Kan) is added and in 12 the double
Manik (_i_). The last two groups are without figures of deities; the double
Manik (14 and 18), possibly a repeated summons to sacrifice, is common to
both groups. There seems here to be a further reference to the _enemies_ of
the harvest, for 15 is the hieroglyph of the vulture, 16 that of the
death-bird and 19 that of the night-god, after which this section closes
with the quite universal sign a. If space had permitted, the vulture and
the night-god would have been represented here.

Page 12b.

  I  13  I  26  I  13  I
  Ix
  Cimi
  Ezanab
  Oc
  Ik.

This is again a regular arrangement, half of the 52 days being in the
middle and a quarter each at the beginning and end.

The first four days refer to the purport of the prediction, Ix, the tiger,
Cimi, death, Ezanab, the wounding lance point, and Oc, the lightning dog.
The 12 hieroglyphs indicate the connection with the foregoing Tonalamatl,
for 1, 5 and 9 contain the same Muluc sign which we found there in the same
places.

The three figures, it seems to me, signify the approach of death, the wound
occasioning death, and the arrival of death.

The first picture represents the god probably as feminine, with which the
illustration on page 9c should be compared. The lock of hair before sign 3,
the death hieroglyph, agrees with this as do also the familiar signs 2 and
4. The god is making sounds, which is indicated by the figure issuing from
his mouth. Is the snail in his head-ornament to be understood as the sign
for retarded motion?

The second figure is the wounding serpent deity H, likewise represented
here as feminine, with a lock of hair; the copal pouch hangs from her neck,
her nose-peg resembles a flower as on page 19a. A bird is sitting on her
head and is devouring a piece of an animal's body; we have already met this
representation in the preceding Tonalamatl. Hieroglyph 6 designates the
deity H, 7 (Imix-Kan) probably denotes the devouring of the flesh and sign
8, which is an Ahau with a prefixed knife, may also refer to this.

Finally, the third picture is again the death-god, who is clad in a gala
cloak and, in contrast to the first picture, where the deity is sitting on
some object, is squatting on the ground. The three hieroglyphs 10, 11 and
12 fit here admirably.

We will now turn back to page 4 and consider the lowest section (c) of
pages 4 to 12, which like pages 5b-12b (I omit 4b here because its contents
are of an entirely different nature) contain 7 Tonalamatls, that is, five
ritual years of 364 days. If, however, we add 4b to these and bear in mind
that 10c-11c contain a double Tonalamatl, we will have 9 Tonalamatls. We
find a group of 7 Tonalamatls also on pages 51a-52a.

Pages 4c-5c.

  XII  10  IX  22  V  11  III  9  XII
  Cauac
  Chuen
  Akbal
  Men
  Manik.

The incorrect 10 of the manuscript has been changed to 9. The hieroglyphs
are as follows:--

  1  2    5  6     9  10    13  14
  3  4    7  8    11  12    15  16.

and there are four figures of gods.

The sign of the rising Moan with its usual prefix and superfix (_d_) forms
the principal part of this section, the meaning of which, however, is not
yet very intelligible. This sign appears not merely as the 1st, 5th, 9th
and 13th hieroglyphs, but all the four gods hold it in their hands. Placed
after each of these signs are hieroglyphs 2, 6, 10 and 14, which are the
double Manik or hand sign denoting a sacrifice (_i_).

The first god portrayed here is G, the sun-god, and the third hieroglyph is
his sign, which is rendered yet more unmistakable here by the laterally
elongated head _q_, the meaning of which is not yet wholly determined.

The second god is D with his two signs in 7 and 8. 7 designates him rather
as night and moon-god and 8 more as the old god and lord of the gods.

The third god is the serpent deity H or Seler's "young god." His sign is
hieroglyph 11, with which, to be sure, the unusual sign 12 (_v_) appears as
a not very intelligible determinative.

The fourth god is A and his usual signs are given in 15 and 16.

Pages 5c--6c.

This is the second example in our manuscript of a Tonalamatl divided into
four parts:--

  XII  29  II  11  XIII  18  V  7  XII
  Ezanab
  Akbal
  Lamat
  Ben
  Ezanab.

The repetition of the 15th day at the end is superfluous.

Here, then, we have the four days with which the 18 Uinals can begin; in
the Tonalamatl on page 9b, the four regents of the year were given instead.
Now, whether the beginning of these periods of 20 days was celebrated by a
banquet or not, at all events, a feast is suggested by the sign Imix-Kan,
which is repeated in hieroglyphs 1, 5, 9 and 13. The four vessels in the
hands of the four deities, two of whom are sitting and two standing, would
agree with the idea of a feast. The first vessel is a cup filled apparently
with foaming pulque, and the other three are larger vessels meant to be
hung up. The first deity is D with a snail on his head. Compare page 12b.
His hieroglyphs are 2 and 3, and sign _a_ is added as fourth. The next
deity is A with his usual signs in 6, 7 and 8. C follows with his
hieroglyph in 10 and lastly F with the sign 14 which belongs to him.

There still remain as the 11th and 15th signs, the elongated head _q_ with
the Ben-Ik superfix belonging to C and with another superfix belonging to F
(with which he likewise appeared as sign 4 in the preceding Tonalamatl).
The 12th sign (_v_), which occurs in exactly the same place in the
preceding Tonalamatl, is no more intelligible to me here than there.

Pages 6c--7c.

  I  17  V  19  XI  6  IV  10  I
  Chuen
  Akbal
  Men
  Manik
  Cauac.

Four sitting gods with the regular 16 hieroglyphs. There is no collective
sign, however, among these. It seems exactly as if the intention had been
to represent the _different_ offerings usually presented to the various
deities. At all events the sacrifices are designated by hieroglyphs 1, 5, 9
and 13, and the same objects are also held in the hands of the four gods
respectively, although they are clearly recognizable only in the case of
the second and third gods.

Now what are these four different sacrificial gifts?

The principal part of the first looks like the sign of the month Mol. In
excellent agreement with its appearance is the fact, that this word
signifies egg in the Quecchi language. The god receiving the sacrifice here
is A. Hieroglyph 2 is his monogram and 3 is that of his companion F and 4
fits both deities.

The second figure is D and his signs are hieroglyphs 6 and 7 to which 8 is
added quite superfluously. The sacrifice proper is denoted by 5, which, I
think, is a sign of multiplicity and which was originally the fin of a
fish. In the manuscripts and inscriptions, when this sign is added to the
sign for 360 days, it enhances the value to 20 × 360 = 7200 days.

The third picture represents the god with the bird-head of the Moan and his
signs are hieroglyphs 10, 11 and 12. One of these, signifying rising birds,
is also the offering in 9.

Lastly, the fourth picture is, according to Schellhas, the serpent deity H,
and, according to Seler, the "young god," with the snail on his head. His
sign is hieroglyph 14. Added to this is the sign _a_ in 15, and in 16 it is
_q_ again with the same superfix as in sign 15 of the preceding Tonalamatl.
The sacrifice in 13 is represented by a Kan sign, which is equivalent to
maize, maize bread or tortilla.

Repeatedly, as on page 23b or 29b-31b of our manuscript, we see a portion
of game (deer), a bird, a lizard and a fish represented as sacrifices. With
this the fish and bird in our second and third pictures agree very well. I
shall not venture to explain the other two in the first and fourth
pictures. Perhaps future explanations of the curious head-ornament of the
four gods will shed further light on the subject.

Page 8c.

  III  9  XII  9  VIII  9  IV  9  XIII  9  IX  7  III
  Cib
  Lamat
  Ahau
  Eb
  Kan.

The horizontal line should be read in this order; in the manuscript the
numbers are in a somewhat unusual order.

An attempt has been made to divide the 52 days into sections of 9 days
each, and in doing this the sixth subdivision has fallen short of two days.
Since this passage has but two pictures, six of the 12 hieroglyphs must
belong to each of the figures. I read the hieroglyphs in the following
order:--

  1  2  5      7   8  11
  3  4  6      9  10  12.

Each of the two pictures contains a building and a deity in front of it,
each of whom seems to have placed another deity in the building. In the
first picture D is putting C inside and in the second F is doing the same
to A or the Moan. I will add also, that the day belonging to C (Chuen) is
actually 9 days distant from that of D (Ahau). I am uncertain in regard to
the other two. In the back of each building we see a cross.

A similar association of two gods appears again elsewhere, as on page 35a,
where D lies on a building in which C is sitting, thus showing an
association of the same two gods as in our first group.

In both groups the first two hieroglyphs form the common heading, since 1
corresponds in general to 7 and 2 to 8. In the first group 3 and 4 are the
hieroglyphs of D and 5 and 6 are the signs _q_ and _v_; does one of these
last signs refer to the god C? In the second group 9 is the sign of F, who
stands in front of the house and 10 that of the god in the house, as
perhaps is also 11, when we consider the closed eye; this is one of the
many hieroglyphs having an uplifted arm as a prefix. On page 9a we find
exactly the same sign. The last sign is the hieroglyph _q_, which sometimes
seems to be used merely to fill space; it corresponds, but with a different
superfix, to the fifth hieroglyph of the first group.

The last three parts of this section of the manuscript all differ
appreciably from the usual form (5 × 52 = 260 days).

Page 9c.

Here for the first time the manuscript contains a Tonalamatl, which is
divided into 10 × 26 days. It is true the position of both the days and
numbers is quite irregular. The manuscript presents the following order:--

  III      III          VI    VIII
                         3       2
  Cauac    Ben          XI      II
  Chuen    Chicchan      3       4
  Akbal    Caban        VI     VII
  Men      Muluc         4       1
  Manik    Imix.         I     III
                         7       2

I read it thus:--

  III  3  VI  2  VIII  3  XI  4  II  4  VI  1  VII  7  I  2  III
  Cauac
  Chicchan
  Chuen
  Caban
  Akbal
  Muluc
  Men
  Imix
  Manik
  Ben.

Two figures and eight hieroglyphs are given here. I do not venture to
decide whether each of the two figures with its hieroglyphs relates only to
a period of 26 days or to the half of the whole, 130 days. I think the
latter is more likely to be the case. The sign Imix-Kan, which I am
inclined to refer to a sacrificial meal, is common to both groups and
connects them. The two gods seem also to have a sign pertaining to a meal
in their hands; this may be a cup.

The first deity is D or I, but with a female breast and with a serpent on
his head. His signs are 2 and 3. The second god is A with a snail on his
head and his signs are 6 and 7.

In addition to these, sign 4 of the first group is _v_ and sign 8 of the
second group is c.

Pages 10c--11c.

  I    3   XIII  1  I  5  VI  10  III  13  III  15  V  8 (in error 9)  XIII
  Imix     Cimi
  Ben      Ezanab
  Chicchan Oc
  Caban    Ik
  Muluc    Ix.

Here we have two independent Tonalamatls as on page 12a. There are
subdivisions only for the second; the first should be regarded either as
entirely invalid or else its division has merely been omitted.

6 gods with 4 hieroglyphs each are represented on these pages:--

  1  2    5  6     9  10    13  14    17  18    21  22
  3  4    7  8    11  12    15  16    19  20    23  24.

Here too Hieroglyphs 1, 5, 9, 13, 17 and 21 are the common factor; they
have the form of the month Mol, but here, as on page 6c, they probably
designate the particular object constituting the sacrifice. The following
details are to be noted regarding the six divisions:--

1. The god A with his two signs in 2 and 3.

2. D with the signs 6 and 7.

3. F with the signs 10 and 11 (the latter _c_).

4. E with the signs 14 and 15, having on his head a structure, which is
compounded apparently of a Kan sign, a snail and the suggestion of the
maize plant.

5. G, clad in the gala cloak and the copal bag. His sign is 18, while 19
suggests rather the Moan or K.

6. B, his headdress displays the little circles, which often occur in
connection with him, _e.g._, pages 30c, 40a and 41a, and which may suggest
the starry sky. His sign is 22; the hieroglyph _m_ is added to it in 23 as
a determinative.

As usual, the fourth sign of each group is the most puzzling. 4 and 12 are
Imix with the uplifted arm as a prefix, as on page 13a, 8 is the hieroglyph
_o_, 16 is _a_, 20 is _c_ and the principal part of 24 is _r_. This sign
_r_ seems to me to suggest the week of 13 days (see above the explanation
of page 4a); four weeks of this kind end here.

It is to be noted further that all the six gods are holding one hand
outstretched:--A downward, B upward and the four in the centre forward.

Page 12c.

  XIII  26  XIII  26  XIII  13  XIII
  Chuen
  Cib
  Imix
  Cimi
  Chuen.

This is another Tonalamatl divided into 4 × 65, the subdivisions being
transferred to the end of the second, fourth and fifth weeks. The Chuen at
the bottom is superfluous.

The twelve hieroglyphs standing here according to rule are grouped together
in fours by the three pairs of the first row. Of these 1, 5 and 9 are the
fist, familiar from the inscriptions, and which we also see on page 10b of
this manuscript, where, to be sure, it occurs with the sign of B, as often
happens, but here it has the closed eye of the death-god A. On the other
hand, 2, 6 and 10 are the sign Kin = sun, with merely a dotted outline, and
the three gods pictured below all hold the same Kin sign in their hands.
This passage, may refer to the dying sun, the winter solstice.

The first god is D, who, however, has B's head on top of his own. An object
like a spyglass projects from the eye of B, which one could hardly venture
to pronounce a nose-peg. The sign 4 (Ahau) refers to D; but what is the
meaning of 3, the hieroglyph of the serpent deity H? Is the sun wounded?

The second god is the baldheaded old deity, whom Schellhas designates as N.
The hieroglyph 7, apparently referring to the five Uayeyab days, is his
sign; we found it on page 4b and shall again find it on page 21c, and this
time likewise with the old man. What is the meaning of the grain-goddess E
denoted by sign 8? As N is connected with the close of the year, so E seems
to be in various ways connected with the beginning of the new year.

The third picture is unmistakably the sun-god G with the copal pouch
hanging from his neck. His sign is 11, while sign 12, which suggests the
wind-god K and balled-up clouds, is as difficult to explain here as it was
on page 11c. The signs 8 and 12 seem, therefore, to refer to one another,
and, if I do not see too much, look like a promise of rain and harvest.

On page 12 the Tonalamatls of the three sections of the page come to an end
and a new part of the manuscript begins.

Page 13a.

I shall here group together pages 13 and 14, the top third of 14 encroaches
a little upon page 15. 13a has the following Tonalamatl:--

  Imix
  Ben
  Chicchan
  Caban
  Muluc.

I have supplied the first day, which is effaced. The week days are wanting.
The 52 days are divided into halves of 26 days each.

Of the 8 hieroglyphs the fifth seems to be the same as the destroyed first;
aside from the prefix, it is the sign _s_.

The two halves of the period have two gods, the first is B with a very
singular head-ornament, and the second A, perhaps with the symbol of a
snail on his head. Both hold a plant (agave) in their hands, as on pages
10b and 12a. Hieroglyph 2, which is mostly destroyed, must have been B's
monogram, 4 has the Ahau as its determinative, and 3 is the elongated head
_q_ with Ben-Ik.

In the second group 6 and 8 are the signs of A, and 7 is an Imix with the
uplifted arm prefixed, as on page 10c.

Pages 14a--15a.

  VIII  13  VIII  13  VIII  13  VIII  13
  Ahau
  Eb
  Kan
  Cib
  Lamat.

The month days 13 and 5 have changed places in the manuscript. The initial
day VIII Ahau will prove to be of especial importance in the second part of
the manuscript (compare page 70). Here, as in the preceding Tonalamatl, the
period is divided into equal parts.

Little can be said of the hieroglyphs, 16 in number, since 6, 9, 10, 12,
13, 14, 15 and 16 are wholly or mostly destroyed. 3, 7 and 11 seem here to
be a comprehensive element, as is also probably 15, but I am unable to
refer this head to a particular god; 2, 6, 10 and 14 may also be alike, but
this is very uncertain. 1, 5, 9 and 13 may have denoted the four cardinal
points, at least 1 suggests the south and 5 the north.

Thus we have left for the four deities E, H, A and G, only the signs 4, 8,
12 and 16; 4 surely belongs to E, and 8 to H, but the other two are erased.

Pages 13b--14b.

  VI  13  VI  9  II  7  IX  7  III  7  X  9  VI
  Ahau
  Eb
  Kan
  Cib
  Lamat.

There are 24 hieroglyphs for the 6 divisions:--

  1  2    5  6     9  10    13  14    17  18    21  22
  3  4    7  8    11  12    15  16    19  20    23  24.

Of these the upper row again contains the comprehensive signs, and the
lower the discriminating characters. The closed eye in 1, 5, 9, 13, 17 and
21 suggests A, who also appears below as the first of the six gods, and the
superfix of these signs suggests the south. 2, 6, 10, 14, 18 and 22 are the
Kan sign, and we also find this sign in the hand of each of the six gods.
Thus the subject of this passage seems strictly speaking to be harvest or
food.

The six gods are A, E, C, L, F and D; the second, third fourth and fifth
have a bird on their heads. The first and fourth birds are eating, as on
pages 11a and 12b, and thus probably represent enemies of the harvest. The
first is of a different species from the other two. The four gods in the
centre have the copal pouch about their necks. Signs 3 and 4 are the common
hieroglyphs for A; 7 that for E, to which _o_ is added as a determinative;
11 is C's hieroglyph with an _a_ added to it, and L is undoubtedly denoted
by sign 15; 16 is _r_ (equal to 13 days; it is meant here for the day III
Cib). F appears quite according to rule in 19, which is appropriately
followed by the sign _c_ in 20. Finally the hieroglyphs for D in 23 and 24
are the usual ones.

We come now to the large section extending to page 23, which, owing to the
numerous pictures of women, forms a section quite by itself. It is not
likely that this contains anything else than oracles relating to pregnancy;
in fact, the period of 260 days represented here with great frequency is in
excellent accord with this subject. In the Codex Tro-Cort. there is also a
section devoted to women, which corresponds to this chapter and
particularly page 19* of the Troano affords remarkable parallels to the
Dresdensis, even in details.

Pages 13c--14c.

  II        II  7  IX  3  XII  3  II  13  II
  Men       Chicchan
  Imix      Chuen
  Manik     Caban
  Ben       Akbal
  Cauac     Muluc.

The second of the two vertical rows on the left should be considered as
immediately joined to the first. Thus we have here the second example in
this manuscript of a Tonalamatl of ten parts; the first was on page 9c.

The entire representation on 13c and 14c looks like an introduction to the
following section, as though treating in general of the relation to one
another of pairs of animals, of human beings and of deities. Corresponding
with the Tonalamatl, there are four pairs of this kind represented.

The hieroglyphs belonging to these pictures are distributed among the four
sections as follows:--

  1  2    5  6     9  10  11    15  16  17
  3  4    7  8    12  13  14    18  19  20.

Apparently, the first two pictures have only 4 signs each, and the other
two 6, but this is equalized by the fact, that hieroglyphs 1, 3, 5, and 7
are clearly each composed of two signs. The comprehensive sign appearing in
2, 6, 9 and 16, is, properly speaking, the sign _t_, which may denote
coition, and, not unsuitably, contains in its centre two black figures side
by side.

Passing now to the separate four groups, I think the male figure is always
on the right and the female on the left. In the first and second groups the
two face each other, and in the other two groups the male is behind the
female.

1. The female figure is an animal, perhaps a deer, the male is a black and
white spotted deity having a human form and his head appropriately
embellished with horns. The hieroglyphs belonging to these are:--1, a
combination of Manik and Chuen with a prefixed 4, just as on page 21b; 3,
likewise a compound sign, with a prefixed 7, which occurs also on page 46c
on the left, and which I do not venture to explain, but which seems to
denote horns, and lastly the hieroglyph c.

2. The female figure is an animal (on page 19a the female is represented
more in resemblance to the human form) with a bird-head, to which belongs
the compound sign _s_, still unexplained; the male figure is a barking (or
howling?) dog, as on page 21b. Hieroglyph 7 is composite and contains first
the sign generally belonging to the dog and suggesting a skeleton, which
also represents the 14th month, and secondly, a Cimi closely related to it,
precisely the same as in the parallel passage 21b. The well-known _q_
follows in the 8th place.

3. The god D holds in front of himself an animal, which may be a rabbit.
His signs are hieroglyphs 11 and 12, while 13, the principal part of which
is a grasping hand, clutching a Moan sign, seems to refer to the animal in
the picture. 10 is _b_ and 14 is a.

4. Lastly, two beings in human guise, showing thus a closer connection with
what follows. They are the black god L with his hieroglyph in 18 enlarged
by an Imix, and a woman holding a Kan sign in her hand, hieroglyph 20
likewise showing the ordinary combination of Imix-Kan. Sign 15, however,
refers to the woman, and lastly 17 and 19 are the signs _m_ and _r_; I note
that _r_ ends a period of 13 days.

The contents of the following seem to suggest that we should first read
page 15 (including the middle section of 16) from top to bottom, then pages
16-23, partly from left to right and partly from top to bottom, according
to the subject.

Page 15a.

  V  34  XIII  18  V
  Ahau
  Eb
  Kan
  Cib
  Lamat.

There are two pictures with 4 hieroglyphs each.

The two pictures represent D and A, the latter probably as feminine. Both
are falling headfirst, and both have leaves about them as if they were
falling from a tree and a cry is issuing from A's mouth. The common element
is given in hieroglyphs 2, 3 and 7, which are all signs of D. Further, 4 is
the Chuen sign, the ape (as the animal living on trees?), its prefix is
hieroglyph _r_, which I regard as denoting the week of 13 days and which
falls here exactly on the day XIII. And the same Chuen sign is repeated in
the second group as the first part of sign 6, the second part of which is
illegible. 8 is the sign of A and 1 is effaced.

Pages 15b--16b.

  I  13  I  31  VI  8  I  13  I
  Ik
  Manik
  Eb
  Caban
  Ik.

That is 4 × 65 = 260 days. Hence the sign of Ik repeated at the bottom, as
is usual in such cases, is superfluous.

The Tonalamatl contains 4 figures, of which 1 and 2 form one pair and 3 and
4 another.

As on page 15a, the pair at the left are falling down and also have leaves
about them. They are god B, who holds a Kan sign in his hand, and a woman,
whose eyes are closed and who holds the sign of death before her breast. B
is falling down in a similar fashion in Cort. 17. Hieroglyphs 1-8 belong to
this pair. Of these, 1, 5 and 8 and also 7 refer to death, 3 with the
determinative sign, 4, added (which is the sign _q_ with a Ben-Ik), refers
to B, while signs 2 and 6 belonging to god D, who occurred in the preceding
Tonalamatl, should be noted.

The pair at the right on the other hand is _seated_, the woman apparently
on the curved handle of a vessel. The head-ornament and hieroglyph of the
female figure prove that she is the serpent deity H, while the male figure
is the rare black deity M, whom we find again with his sign on page 43a for
example; he holds a bone in his hand. Hieroglyphs 9 and 13 agree. The lower
part of these hieroglyphs is the fist with the thumb unfolded, the sign at
the top seeming to be merely an empty outline (Muluc?) and thus, like 1 and
5 of the preceding group, they seem to refer to a sacrifice offered to the
death-god. 10 and 14 are again, strange to say, like 2 and 6 of the
preceding group, the sign of D. 11 is the hieroglyph of H, who is
represented below as feminine, and that 12 is a complement of 11 is proved
by the upper part of this uncommon hieroglyph, which corresponds to the
object in H's hand, and which is repeated on page 18a with the same figure;
compare also page 8b. 15 is surely the hieroglyph of M, who is pictured
below, as in the Tro. 2a and 22*a where the same M appears with the same
hieroglyph, and to him belongs in 16 the sign _r_, which I am inclined to
consider the week of 13 days, and which here, as on 14c, ends a section of
13 days.

Page 15c.

  III       III  12  II  14  III
  Lamat     Ix
  Ahau      Cimi
  Eb        Ezanab
  Kan       Oc
  Cib       Ik.

This is a Tonalamatl of ten parts, the days are to be read in the following
order:--Lamat, Ix, Ahau, Cimi, etc.

There are two figures, A probably conceived as feminine and D with the same
head-ornament as on page 10; both hold in their hands a Kin = sun.
Hieroglyphs 2 and 6 are also the Kin sign, while 1 and 5 have the closed
eye of A, but differ in their secondary parts, the sign suggesting the
south being a suffix in 1 and a superfix in 5; 1, however, has an affix,
while 5 has as a prefix a sign differing from the affix in 1. 3 and 4 are
the signs of A, 7 that of D, next to which in 8 one would expect to see an
Ahau, but instead of this there is again the sign of H (borrowed from page
15b?).

This seems to end the subject of coition; now, in natural course, follows
the subject of pregnancy, to which I believe the following Tonalamatl is
exclusively devoted.

Page 16a.

  Kan  21  31
  Cib
  Lamat
  Ahau
  Eb.

There are no red numerals, hence the Tonalamatl seems to apply to any one
of the initial week days.

Two women are portrayed, both of whom are stretching a hand forward and
upward. There are 8 hieroglyphs of which, however, the top row is almost
entirely obliterated; 3 and 7 in the lower row are just alike, being the
usual sign for woman.

There is a decided contrast between the two figures, which might suggest
barrenness and fruitfulness. Observation of their physical differences
would give us that idea. Furthermore, the first carries on her back an
unfamiliar head, perhaps A's, while the second has the Ahau, Imix and Kan
signs, from which plants seem to be sprouting. The first is represented in
the fourth hieroglyph by the sign _c_, which is closely allied to the death
deities, while the second woman is denoted by hieroglyph 8 which is the
sign of the deity E, the grain-god.

Pages 16a--17a.

In the following I will group together all the pages from page 16-23 as
follows:--First, I shall discuss the top thirds, then the middle and lastly
the lower thirds. The sense, however, often seems to require that the first
third should connect with the second, and the second with the third; but I
find it impossible to determine exactly the intended order.

On pages 16a-17a, we find for the first time in this manuscript not a
Tonalamatl, but in its stead all the twenty days arranged in four columns,
each of which ends with one of the regents of the year:--

  Men        Ahau      Chicchan     Oc
  Cib        Imix      Cimi         Chuen
  Caban      Ik        Manik        Eb
  Ezanab     Akbal     Lamat        Ben
  Cauac      Kan       Muluc        Ix.

This seems to establish the fact that the day of its birth was of
importance to a new-born child.

Between each column and the next there is a picture and above each picture
four hieroglyphs, which, however, are mostly destroyed, so that much of the
meaning of this passage is lost to us.

The first is an old man walking, who beyond doubt is N, the Uayeyab god,
with a staff in his hand and the signs Imix and Kan on his back. He is
looking upward and is also pointing upward with his right hand. Of his
hieroglyphs only enough of the fourth is visible to enable us to recognize
in it the regular sign of N, 5 Zac. The second picture is again an old man
walking with a stick, he is baldheaded and hence is probably also N, as on
page 12c. His hieroglyph might be the fourth of those written above him,
the other three are entirely unrecognizable. He has a carrying-frame on his
back, but it is uncertain whether he is carrying anything upon it.

The third figure is a woman who is pointing upward with one hand and with
the other holding the bundle on her back, which I am unable to explain
(does it refer to the 14th Uinal--the end of pregnancy?) and from which
rises an object resembling a flame. Her sign is in the fourth place and _q_
is in the third. 1 and 2 are not legible and perhaps may be supplemented by
the third picture on page 19c. Finally, the fourth figure is F, who is
sitting and has a Cimi sign on his back. His monogram is the second of the
hieroglyphs above him, the third is very appropriately _b_ and the other
two are not very clear to me.

The first two pictures might designate a male birth, the first indicating
wealth and the second poverty, the third might denote a female birth and
the fourth a still birth. But who can positively assert this!

Pages 18a--19a.

  VIII  12  VII  12  VI  9  II  10  XII  9  VIII
  Ik
  Ix
  Cimi
  Ezanab
  Oc.

This is a Tonalamatl of five parts with 20 hieroglyphs, which unfortunately
are so much injured that no signs comprehending the whole can be
distinguished.

There are five women in a sitting attitude.

The first woman corresponds exactly to the third figure on page 15b. She is
sitting on a bench, the same implement is in her hand and there is also a
serpent on her head, for which reason she likewise reminds us of H. The
third hieroglyph is hers, and the 4th sign is an Ahau.

The second woman holds in her hand the Kin sign; above it is the Yax sign
and above this a little cross between two dots (the numeral 18?). Compare
pages 18c, 19c and 27b, and in the second part, 46b and 50c. I shall
venture no opinion regarding the hieroglyphs.

The third woman with the copal pouch hanging from her neck has nothing in
her hand. She is pointing upward with her right hand. Her hair seems to be
wound in the shape of an 8 in horizontal position and above her is a sign
denoting the union of two parts. The hieroglyphs are entirely destroyed.
Does this represent the birth of twins?

The eyes of the fourth woman are closed, she is pointing forward with her
hand and there is a bird on her head. Nothing is left of the hieroglyphs.

Finally, the fifth is distinguished by a large nose-peg, which, as on 12b,
resembles a flower. Her hand is extended forward. The fourth of the
hieroglyphs above her is her sign. There is nothing to be said regarding
the three others. Are these five women engaged here in presenting their
thankofferings and prayers of thanksgiving for the birth which has taken
place?

Pages 19a--21a.

  XI  13  XI  13  XI  13  XI  13  XI  13  XI
  Ahau
  Chicchan
  Oc
  Men
  Ahau.

Instead of Men the Manuscript has incorrectly Eb. Ahau in the fifth place
is superfluous, since we have here a Tonalamatl divided into four equal
parts.

The hieroglyphs are so nearly obliterated that we can no longer distinguish
a common sign. There were in all six signs for the first picture, of which
the first two are above the day-signs, while the figures from the second to
the fifth have only four signs each, as follows:--

  1  2  5    7   8    11  12    15  16    19  20
  3  4  6    9  10    13  14    17  18    21  22.

All that can be distinguished here is that the 4th and 13th have the same
cross _b_ and that 6 and 10 probably contain the same head.

Each of the five pictures contains a woman sitting. In the first
representation she sits opposite a male figure, who bends down to her with
his bird-head, which we have already seen on page 13c. In the other four
pictures the woman is holding the figure of a god on her lap. I do not
recognize the god in the first picture on page 20. In the second and third
pictures he is related to A or the Moan and the first figure on page 21 may
represent the god D. These can only be new-born children represented by the
gods under whose signs they were born. It should also be noted that the
second woman on page 20 has a serpent on her head and the third a bird. The
bird's head resembles that on page 16c.

Pages 21a--22a.

The Cimi and Eb of the second column have changed places in the Manuscript.
Instead of the X there is an erroneous 2 and there is no initial VII.

  VII       VII  3  X  2  XII  7  VI  9  II  3  V  2  VII
  Oc        Ahau
  Cib       Cimi
  Ik        Eb
  Lamat     Ezanab
  Ix        Kan.

We have here a Tonalamatl consisting of 10 × 26 days, and the 26 days are
subdivided into six parts. I have just assumed that the 2 is wrong and the
initial VII is wanting over the first column, yet the 2 followed by the
laterally elongated head _q_ might here, perhaps, be explained in some
manner as the sign of the day VII Oc.

Apart from this sign which occupies an entirely exceptional position, we
have here 24 hieroglyphs, _i.e._, 4 for each of the six groups.

The fourth sign in the first five groups is in each case a Chuen combined
with the cross _b_ and the suffix, which seems to be a knife, and also with
a numeral, which, however, is not recognizable in the first group; in the
second it is a 3, in the third a 7, in the fourth a 5 and in the fifth a 3.
What can these numbers mean? 3 + 7 + 5 + 3 = 18, and Chuen with the meaning
of 20 (especially in the inscriptions) would be 18 × 20 = 360.

In the fourth place of the sixth group there is a compound character, the
main part of which (top, right) seems to be the sign for the thirteenth
month, Mac, and which may also, as we shall see on page 24, denote the
entire Tonalamatl. It is again compounded with a Chuen, an uplifted arm and
a kind of suffix, and hence might denote the end of a Tonalamatl.

The remaining 18 signs are in the main destroyed. In the second of the
fourth group we recognize the lock of hair denoting a woman, in the third
of the second group the superfix suggesting the south, which we find above
the Cimi sign, for example on page 13b. Lastly, the other third signs are
in the third group Imix-Kan, in the fourth group the head _q_, in the fifth
the bird c and in the sixth a Manik sign with prefix and superfix
resembling the sign _i_; in a few places (24, 39a, 53a, 56b, 58b, 61a, 61c,
68c) the prefix might have the meaning of 20.

Since the intention was to close this section on the next page, the space
had to be used as economically as possible, and instead of the six pictures
to be expected, there is only one and that is the first. It is a woman in
whom I observe nothing characteristic except that she has a kind of cloak,
which has fallen down over the lower part of her body, and who therefore
remains unexplained.

Pages 22a--23a.

  II        II        II        II  2  IV  8  XII  7  VI  10  III  12  II
  Men       Cib       Caban     Ezanab
  Chuen     Eb        Ben       Ix
  Manik     Lamat     Muluc     Oc
  Akbal     Kan       Chicchan  Cimi

The Tonalamatl is no doubt to be read in this way after the correction of a
few inaccuracies in the Manuscript.

The 20 days, all of which occur again here as on pages 16a-17a, should be
read from the right top to the left bottom, since they form but one series.

As a matter of fact Ezanab is distant 19 days from the future Caban, but 39
days distant from the desired weekday of the same name (see my
"Erläuterungen," p. 24). Thus we have here a period of 20 × 39 days = 780,
_i.e._, a three-fold Tonalamatl. The three Tonalamatls represented on the
pages between the preceding passage (pages 16a-17a), where all the 20 days
appear, and this, are of three _different_ kinds (5 × 52, 4 × 65, and 10 ×
26). This in itself is very remarkable. Furthermore a fourth kind of
Tonalamatl seems to be introduced here, which embraces, as it were, these
three Tonalamatls.

The hieroglyphs, which are mostly destroyed, were arranged in groups of
four for each subdivision, in the following order:--

         II    II    II    II
  1  2    5     9    13    17
  3  4    6    10    14    18
          7    11    15    19
          8    12    16    20.

Of the above the third hieroglyph of each group, _i.e._, 7, 11, 15, 19
(probably also 3) is always the same and is the sign of D, the moon and
night-god. In detail we should expect to find five pictures here, but owing
to lack of space only the first of these is given. It represents a deity
with a Kan sign in its hand and a serpent on its head, who is probably E,
and he is falling down here in exactly the same manner as the four deities
on page 15 at the beginning of this section.

Now, which were the other four deities? Signs 8, 12, 20 refer to A, H and
C. 16 is the laterally elongated head _q_, to which Seler is inclined to
refer the day Men, and Schellhas an undetermined deity I. On account of its
frequency this sign must have besides a more general significance. In
addition, however, we have in 14 and 18 the signs of F and B. 6 is
uncertain, 10 is probably C, and the top row is entirely illegible. If to
these deities is added the D repeated five times in the third row, it will
be seen that all the important gods are grouped together here on the last
page of this section.

Pages 16b--17b.

I will now attempt (for it cannot be more than an attempt) to separate into
three parts, according to their contents, the middle and lowest thirds of
pages 16 to 23. The first part, 16b to 18b and 16c to 20c, contains six
Tonalamatls with pictures of women, each of whom carries on her back the
figure or symbol of a deity. This deity can hardly be any other than the
one to which the horoscope of the child especially refers.

The first of these Tonalamatls, on pages 16b-17b, runs as follows:--

  Muluc  13  4  35 (or 20  15)
  Imix
  Ben
  Chicchan
  Caban.

The red numerals are wanting and were probably forgotten.

The hieroglyphs stand thus:--

  1  2    5  6     9    13
  3  4    7  8    10    14
                  11    15
                  12    16.

Of these 3, 7, 11 and 15 are the sign for women, 2, 6, 10 and 14 are
likewise all the same sign, which is repeated in the same places on pages
17c to 18c. I do not understand its meaning; it may have reference merely
to the carrying-frame. Instead of the four women, whom we should expect to
find here, only the first two are portrayed. The first carries B, whose
sign is the first hieroglyph, while the fourth hieroglyph is the sign _q_.

The second woman carries A to whom hieroglyphs 5 and 8 refer. The third
woman would have carried D, which is plainly proved by hieroglyphs 9 and
12, and the fourth, F, as follows from sign 13 and probably also from 16
(_q_).

Pages 17b--18b.

  Eb  11  7  6  16  8  4.
  Kan
  Cib
  Lamat
  Ahau.

Here again there are no red numerals.

The 24 hieroglyphs of the six divisions stand thus:--

  1  2    5   9    13  14    17  18    21  22
  3  4    6  10    15  16    19  20    23  24.
          7  11
          8  12

Again, six women should be portrayed here, but there are only four; the
second and third are wanting. The signs for the women are given in 3, 7,
11, 15, 19 and 23, but in 15 and 19 the prefix is different from that of
the rest. As from here on the women repeatedly carry a bird, the signs for
this are 2, 6, 10, 14, 18 and 22, which are the symbol of a rising bird, as
in the sign of the 15th Uinal (Moan), which in my opinion generally
coincides with the 13th month of 28 days.

The women pictured here have nothing in their hands, which they hold
stretched forward, as is usually the case in this section. The first woman
carries a vulture on her head. Compare 8a. In regard to it see also
Schellhas, "Göttergestalten," p. 31. The hieroglyph of the vulture, which
we find repeated on page 17c, 24, 37b, 46, 50, 65, is here hieroglyph 1,
usually regarded as the sign of the bat deity, and near it in 4 is _q_.

The second woman would have carried the black deity L (hieroglyph 5), to
which _q_ is added in 8.

The third would have had the dog, _i.e._, the lightning dog, which we find
in hieroglyph 9 and in the month sign Kankin; an _a_ is added to them in
12.

The fourth woman carries A, as is proved by his signs in 13 and 16.

The fifth carries nothing; according to the hieroglyphs 17 and 20 she ought
to carry D.

Lastly the sixth carries the Moan as is proved by signs 21 and 24.

Pages 16c--17c.

  Muluc  8  13  13  13  8  10
  Ix
  Cauac
  Kan
  Muluc.

This is a Tonalamatl of 4 × 65 days. The Muluc at the bottom is, therefore,
superfluous. I have been obliged to correct the 12 in the last column of
the Manuscript by changing it into a 10. The red numerals are again
wanting.

This passage admirably continues the one in the preceding Tonalamatl
containing the women carrying birds, and is also divided into six parts.

The hieroglyphs stand thus:--

  1  2    5  6     9  10    13    17    21
  3  4    7  8    11  12    14    18    22
                            15    19    23
                            16    20    24.

Signs 3, 7, 11, 14, 19 and 23 (14 and 15 have changed places) denote women.
Of the six women only the first three are here portrayed.

The first carries the Moan with which signs 1, 2 and 4 agree perfectly. The
second and third carry two birds, which may be parrots of a different
species. They are very seldom represented elsewhere and hence their
hieroglyphs, 5 and 9, with the added determinative 10 are unfamiliar. In 8
and 12 the well-known determinatives _a_ and _c_ are added.

Judging by sign 13 the fourth woman would have carried the same vulture,
which we see in the middle section of this page; 15 and 16 are again signs
_c_ and _q_.

The fifth woman would have carried an unknown bird of prey, the signs of
which are 17 and 18, and 18=10; 20 is again _q_, but with a superfix
different from that in 16.

Finally the sixth woman, like the third in 17b, seems to have carried the
dog, as is proved by sign 21, but in 22 the symbol of a bird is again
added. This passage ends in 24 with the well-known Imix-Kan.

Pages 17c--18c.

  IV  15  VI  33  XIII  4  IV
  Ahau
  Eb
  Kan
  Cib
  Lamat.

Here we again find the regular red numerals (Roman in my transcription of
the text), which were wanting in the last three Tonalamatls. That they were
not added until after the black script and drawings were completed, is
evident in several passages of our Manuscript and also in this one, where
they have been faintly indicated in black by the scribe (or corrector). The
absence of red numbers in the passages 17b-18b and 16c-17c is an evidence
that I was right in proceeding directly from the former to the latter.

Of the 12 hieroglyphs, 2, 6 and 10 have again the form which we found on
pages 16b-17b, and which seems to refer to a carrying-frame; compare,
however, the explanation of pages 25-28 below. The women themselves are
designated by hieroglyphs 3, 8 and 12. The first woman carries the god A
and hieroglyphs 1 and 4 are his regular signs. The second woman has on her
back a Kin sign, above that a Yax, and this combination overtopped by a
cross between two dots also forms hieroglyph 5; compare the upper section
of the same page. That this hieroglyph is nothing else than a designation
of god D follows from hieroglyph 7. Finally the fourth woman carries a
figure, which has a Moan sign for a head and to which hieroglyphs 9 and 11
certainly refer.

Pages 18c--19c.

  XIII  32  VI  20  XIII
  Ahau
  Eb
  Kan
  Cib
  Lamat.

The first woman carries the god A, who is denoted by hieroglyphs 4 and 1,
though somewhat irregularly by the latter. 2 is the carrying-frame and 3
the woman herself.

The second woman has again the Yax-Kin sign on her back as in the preceding
Tonalamatl, and hieroglyph 5 is also a combination of these signs, but here
in 7 we find, not the sign of D, but that of E, to which also the Imix-Kan
in 8 corresponds. 6 is again the carrying-frame, though, as is also the
case in 2, more indistinctly drawn than in the earlier Tonalamatls.

Pages 19c--20c.

  XIII  11  XI  11  IX  11  VII  10  IV  9  XIII
  Ahau
  Eb
  Kan
  Cib
  Lamat.

This is a Tonalamatl divided into five parts, to which 20 hieroglyphs
belong. The hieroglyphs are in the following order:--

  1  2    5  6     9  10    13  14    17  18
  3  4    7  8    11  12    15  16    19  20.

At places 2, 7 (6 and 7 have changed places), 10, 14 and 18 we find again
the sign which we think means a carrying-frame, while signs 3, 6, 11, 15
and 19 are those of the five women.

The first carries a figure with a Moan head and agreeing with this is the
second death-god F in hieroglyph 1 and his determinative in 4.

The second woman, who is seated, carries the same object regarding which I
am still uncertain, which is carried by the standing woman on page 17a.
This object is denoted by hieroglyph 5 (_w_). Its determinative is probably
8. It may perhaps be a step in the right direction to point out that this
sign suggests the god K.

The third, like the first, has a figure with a Moan head, with which a
female form of A in 12 and hieroglyph 9 accord.

The fourth woman carries the maize deity E. 13 is his sign and the food
hieroglyphs, Imix-Kan in 16, agree with it.

The fifth woman seems to carry the somewhat indistinct form of D, if this
may be inferred from the Ahau of the 17th sign. 20 is the universal sign a.

This ends the six Tonalamatls, which are represented in what I have called
the section of the burden-bearing women. Five other Tonalamatls follow,
which again suggest the idea of conception, which we met once before on
pages 13c-14c.

Page 19b.

  X  29  XIII  23  X
  Ik
  Ix
  Cimi
  Ezanab
  Oc

The most frequent sign in the five Tonalamatls, which I have grouped
together, is the cross _b_, which plays the most important part in all the
Tonalamatls, excepting the third, which differs from the rest also in other
respects. It is essentially the sign for union, referring in the case of
the stars to their conjunction and here to sexual union.

In this Tonalamatl we see the cross in hieroglyphs 1 and 5, the sign for
woman in 2 and 6, and their determinatives in 3 and 7.

The first woman has a deity facing her who is devoid of all characteristic
marks, and sign 4 is also nothing but the universal a.

The second woman whose eyes are closed, sits facing A, whose hieroglyph is
in 8.

Pages 19b--20b.

  VI  28  VIII  24  VI
  Cib
  Lamat
  Ahau
  Eb
  Kan.

The arrangement of this Tonalamatl is very similar to that of the
preceding.

Hieroglyphs 1 and 5 are again the cross, and 2 and 6 the signs for woman.

The first picture is wanting; hieroglyph 3 with the number 7 as a prefix
denotes a deity with whom I am not familiar. The same sign is found on page
50, left, middle; in 4 the usual head _q_ is added.

Beside the woman in the second group--not facing her--is the serpent deity
H, again, as on pages 11c and 12b, with the nose-peg resembling a flower.
His sign is 7 to which in 8 the familiar Ahau is again added.

Page 20b.

  II  20  IX  19  II  13  II
  Cauac
  Chuen
  Akbal
  Men
  Manik.

The hieroglyphs stand thus:--

  1  2    5     9
  3  4    6    10
          7    11
          8    12.

The subject now passes into the province of astronomy. This is already
proved by sign 1, which represents the clouds, between which the sun or
moon is usually pictured; the sun is probably omitted here merely owing to
limited space. Sign 3 suggests the storm-god K (compare pages 7a and 47
left) to which in 2 the Ahau might be appropriately added, inasmuch as it
rules the year here under consideration as on pages 25b to 26c. On account
of the Ben-Ik sign I see in 4 one of the months of 28 days as a more exact
determination of time. Below the Ben-Ik a head is represented with eyes
apparently closed, and this head is repeated in 6 and 10, though, probably
for lack of space, without the Ben-Ik. In each of the three places a sign
is used as an affix which might readily be the year sign, contracted
laterally.

The two similar hieroglyphs 5 and 9, which have the following form, are
especially worthy of consideration:--

[Illustration]

The part on the right recalls by its trisection the sign _r_, which I
regard as the week of 13 days and, in fact, the interval between the two
hieroglyphs is 13 days. On the left is the inverted figure of a person in a
squatting attitude, the head surrounded by stars as on pages 57b and 58b
and a sign on the back which may be a suggestion of the sun-glyph. In this
figure, which occurs also in the Tro-Cort. and in the inscriptions, I see
the planet Mercury and I believe that that planet's retrogression (which
lasts 17-18 days) or disappearance into the light of the sun during this
week, is the subject of this passage. 7 and 8 are the sign for D with the
usual Ahau, and 11 and 12 are the hieroglyphs of the death-god A.

Instead of three pictures there is only one here, viz:--a woman with
nose-peg, sitting on a mat and apparently waiting for something. We also
find figures sitting on mats elsewhere, for example on pages 7b and 68b.

Page 21b.

  VII       VII  7  I  7  VIII  7  II  5  VII
  Oc        Ahau
  Cib       Cimi
  Ik        Eb
  Lamat     Ezanab
  Ix        Kan.

This is also a Tonalamatl of 10 parts (10 × 26). The first column should be
read first from top to bottom and then the second. The days are exactly the
same as on page 21a, and here too Cimi and Eb have changed places.

The hieroglyphs run thus:--

  1    5  6     9    13
  2    7  8    10    14
  3            11    15
  4            12    16.

The signs forming the hieroglyphs into groups are, in addition to the cross
in 2, 6, 10 and 14, the heads in 1, 5, 9 and 13 with an Akbal sign
(indistinct in 9) which, by the lock of hair in 5, 9 and 13, refer to a
woman. This lock of hair is replaced by a hand in 1.

Sign 3, with which _m_ in 4 is associated as a determinative, shows that
the first group ought to have a picture of the black god L grouped with a
female figure.

The second group is the only one with a picture. On the right there is a
female figure, which, judging by the headdress, we have already met on page
19a. Opposite her sits the dog which we saw on page 13c. Here (in sign 7),
as on page 13c, the hieroglyph of the dog is combined with a Cimi sign, and
this hieroglyph is repeated in 8 with the sign _c_, which is so closely
allied to Cimi.

For the third group the god A should have been represented with the woman,
as is proved by sign 11 so peculiarly combined with _r_ as a superfix. To
this hieroglyph _a_ is added, doubtless referring to the good days, as if
merely to fill space.

The hieroglyphs of the fourth group do not, I think, convey a clear idea as
to which deity belongs here. His sign is 15, which is compounded of Manik
and Chuen with a superfix, nor does the Cimi added in 16 shed light on the
subject. As for 15 we have already found it on page 13c with the prefixed
4, which I find prefixed in this way in at least 12 different signs.

Pages 21c--22c.

  Caban  5  21  16  10
  Muluc
  Imix
  Ben
  Chicchan.

This is a Tonalamatl of five parts in which the red numerals are wanting.

The hieroglyphs are in the following order:--

  1  2    5  6     9  11    13
  3  4    7  8    10  12    14
                            15
                            16.

Among these are hieroglyphs which are common to all the groups:--the cross
in 1, 5 and 9 and the woman in 3, 7 and 15. In 13 this cross is replaced by
another sign, perhaps that for the year of 360 days, and in 12 the sign for
woman is replaced by the universal a.

Each of the three pictures contains a woman facing a deity. I will consider
first the second picture in which H is the deity, as is proved by
hieroglyph 6 to which an Imix is added in 8, with the uplifted arm prefixed
as in 10c and 13a.

Between the first and third pictures there is some confusion. The first is
D, for while his type inclines more to that of N, the other old god of the
Maya Olympus, comparison with 23c clearly shows that D is intended here.
But the year-sign on his head also suggests in some measure the Uayeyab god
N and moreover this sign does not belong to D and only occurs again with
him on page 23c. Further, there is no hieroglyph at all for D and instead
we find in 2, 5 Zac, the regular sign of N. Also sign 4 fits N better than
it does D. Furthermore this passage relates to the day Ik, which might very
well be the last day of the year.

On the other hand the third picture contains, unquestionably, the figure of
N. I look for his sign in the 11th hieroglyph, which is the head of an old
man with a prefixed 4, referring to the four different forms of N in the
Kan, Muluc, Ix and Cauac years. The Ahau in 12, however, does not fit N,
but D.

This confusion can only be adjusted by transferring D from the first group
to the third and also, perhaps, the sign of the woman in 3, which applies
to all the three groups, and by transferring to the first group N and the
11th sign of the third group.

The fourth group has no picture. It should have, as hieroglyph 14 shows,
the god F, who represents death by violence in human sacrifice and the
chase. The hieroglyph Cimi in the 16th place is a suitable sign for this
deity.

Pages 22c--23c.

  II  10  XII  12  XI  9  VII  6  XIII  7  VII  8  II
  Oc
  Ik
  Ix
  Cimi
  Ezanab.

The hieroglyphs are arranged in the following order:--

  1  2    5  6     9    13  14    17  18    21  22
  3  4    7  8    10    15  16    19  20    23  24.
                  11
                  12

This Tonalamatl, the fifth and last of this section, presents much that is
irregular and puzzling.

It can hardly be said that there are comprehensive hieroglyphs here,
forming the heading of the six groups. The sign for woman occurs only in 2,
8 and 24, and the cross _b_ only in 14 and 18, but it is sufficient to make
it clear that here, too, connection with a woman is the principal theme.
Let us pass, therefore, directly to the single groups.

The first group contains A and a woman. The god, however, is not facing the
woman but sits beside her. The Cimi sign in 1, the familiar _c_ in 3 and
the unknown sign in 4 (=6) hardly explain this particular proceeding.

The second group contains two persons who sit facing each other, but the
representation is so obscure and peculiar that it is difficult to determine
which is the male figure and which the female. The hair of the person
sitting on the right stands up in a manner not found elsewhere. It forms a
figure similar to that which is issuing from the mouth of the dog on pages
13c and 21b. The Cimi sign in 5 and the sign _c_ in 7 are familiar, but the
infrequent 6=4 remains a puzzle.

Uncertainty regarding the third group is increased by the fact that there
is no picture belonging to it. The well-known signs, 10 (Cimi) and 12 (_q_)
afford no explanation, nor does the head with the uplifted arm in 11, which
we find with the same hieroglyph on pages 8a and 36a. The most puzzling is
the 9th sign, which is composed of two crouching persons leaning back to
back, and who also appear in the astronomical sections of the Manuscript on
page 68a, not merely in the form of a hieroglyph, but also carried out in a
picture. In my article on the Maya chronology published in the Zeitschrift
für Ethnologie of the year 1891, I attempted to explain this Janus picture
as meaning the change of the year, but that interpretation would make no
sense here.

The fourth group contains the woman opposite D, who is clad in the gala
mantle and has on his head a bird and apparently the sign for a year, and
is designated by the Ahau in 16, while Imix-Kan in 13, _b_ in 14 and _a_ in
15 are rather meaningless.

The fifth group represents the woman united with A, who is designated by
the Cimi sign in 17. 18 with its _b_ and 19 with its _q_ display little
that is characteristic, _r_ in 20, which I think is the sign for the week
of 13 days, invites further study. The sixth picture, which is the last, is
very peculiar; it represents three women sitting side by side denoting
perhaps the virgins who still remain. Sign 21 as Imix-Kan, 23 as _a_ and 24
as sign of femininity supply nothing in the way of explanation. As 6, 9 and
20 are the characteristic signs in the preceding groups, so here the
characteristic sign is 22--an open hand holding the day Ben--which perhaps
designates these virgins by referring to the house in which they are held
fast by the hand. Cf. Tro. 23* d.

Now of the entire woman section closing with page 23 only the two
Tonalamatls on pages 22b-23b remain. These Tonalamatls again display very
many peculiarities and seem to be but loosely connected with the five
Tonalamatls last discussed.

Page 22b.

  III  13  III  13  III  13  III  13  III
  Akbal
  Men
  Manik
  Cauac
  Chuen.

This is a regular Tonalamatl, in which the 52 days are divided into four
equal parts.

The hieroglyphs are in the following order:--

  1  2    5  6     9  10    13
  3  4    7  8    11  12    14
                            15
                            16.

An Ahau is added here as the 17th sign, which is very unusual.

We find elements here forming the hieroglyphs into groups in three
different ways.

1. The signs 1, 5, 9 and 13 designate the four cardinal points as they so
often stand together in this Manuscript in the order of East, North, West
and South, _i.e._, in the sequence of the annual and not of the diurnal
course of the sun.

2. The hieroglyphs 2, 6, 10 and 14 are all alike and are the head with the
Akbal eye, which in 6 is closed.

3. The three persons pictured here all carry a Kan sign in their hands,
probably as the offering they have received. Similarly we found the Kan
sign held in the hand twice on page 16b.

The first picture is B; his sign is the third with the _q_ in 4 as a
determinative, which has above it a Ben-Ik sign.

The second figure is a goddess with a serpent as head-ornament, though we
find in the 7th sign, not her hieroglyph, but merely the one generally used
to denote a woman. 8 is the usual _a_, which in my opinion is the sign for
the _good_ days, to which also the Kan sign refers in the hands of the
three personages.

The third picture is that of the sun-god G; his hieroglyph is the 11th, to
which in 12 is added the sign _q_, the sign for the bad days, with a
superfix.

The fourth picture is wanting. According to the 15th hieroglyph it should
be the maize deity E. My theory that 16 is the sign for the week of 13 days
is supported by the fact that the division into 4 × 13 days is the
prevailing one.

Page 23b.

  VIII  12  VII  12  VI  12  V  12  IV  12  III  5  VIII
  Kan
  Muluc
  Ix
  Cauac
  Lamat.

This is a Tonalamatl of 4 × 65 days divided as evenly as possible into 5 ×
12 + 5. The 5th day added after the 16th must be a mistake (suggested by
the 5th day of the last section) for it is usually the first of the days,
which is repeated superfluously.

The hieroglyphs are:--

  1  2     7   11    15    19    23
  3  4     8   12    16    20    24
  5  6     9   13    17    21    25
          10   14    18    22    26.

Contrary to practice the first section has six hieroglyphs, and the other
five but four each.

As the characteristic hieroglyph we find in 1, 7, 11, 15, 19 and 23 a sign,
the meaning of which is still undetermined and which we shall meet again on
page 60, where it may refer to darkness.

The groups have in common, furthermore, the head without an underjaw and
the hair gathered up in a tuft in 4, 10, 14, 22 and 25 (in 18 perhaps
represented by _q_, the evil days). We shall find this sign on pages 25,
28, 30-35, 42-44 and 65-69, repeated a number of times in many instances. I
consider it the sign for fast-days. It appears also in the Tro-Cort.
Associated with this sign here as in other passages are the four sacrifices
derived from the animal kingdom:--a haunch of venison, a bird, an iguana
and a fish. The fish is beyond doubt denoted by 3, the mammal by 21 and the
bird by 13, and I believe, therefore, that the iguana with its spiny back
is denoted by 9. We find the four animals, though in a different order,
also on pages 29b-30b, 30b-31b and 40c-41c, as well as in Cort. 3-6 and 8,
for example. They seem to have a certain reference also to the four
cardinal points.

Only the first of the six groups has a picture (I?). This represents a
woman with a serpent in her hair, holding in her hand a dish containing a
fish. The woman is denoted by the fifth hieroglyph and the fish by the
third. The 6th sign is an Ahau, which is not quite intelligible here. Sign
2=5 Zac is very remarkable; it is the hieroglyph of the Uayeyab days and of
their god N. If this Ahau refers, as it often does, to the god D, it
suggests the relation between D and N, which follows from page 21c.

According to the 8th sign, the second group might refer to the serpent
deity H, and the 9th sign would not improperly denote the iguana.

In the same way sign 12 in the third group probably denotes the storm-god
K, with whom the bird in 13 accords very well.

In the fourth group both the animal and the sign of fasting, belonging to
it, are wanting, while 16 and 17 as well as the unlucky day in 18 clearly
refer to the death-deity A.

The fifth passage belongs, as sign 20 shows, to the maize deity E and to
this is added the haunch of venison in 21.

In the sixth group we recognize Imix-Kan, the sign for food derived from
the vegetable kingdom. It stands beside the grain-deity E of the fifth
group. I do not understand the vulture-head in 26.

The five deities specified here may be compared with those on page 24,
which are denoted by hieroglyphs 21-25 of the second column, though the
agreement is not perfect.

This ends the first great section of the Manuscript, in which Tonalamatls
are represented in uninterrupted succession. We come now to a page which
stands quite alone, being the first which treats of astronomy and which
ends the front of the first part of the Manuscript.

Page 24.

In my article "Zur Entzifferung IV" I discussed this remarkable page in
detail and in what follows I shall conform to that treatise, though
omitting many things which since then have become the established
possession of science, and shall endeavor to shed a still clearer light
upon other points.

This page presents in brief the subject which is more fully treated of on
the front of the second part of the Manuscript (pages 46-60).

The first problem it presents is to find periods in which the solar year
(365 days) is brought into accord with the apparent Venus year (584 days).
This takes place in a term of 2920 days = 8 × 365 = 5 × 584. Sequent to
this is the still higher aim of bringing the Tonalamatl (260) into harmony
with this period, which is accomplished in 37,960 days (= 146 × 260 = 104 ×
365 = 65 × 584).

The revolution of the moon (28), the ritual year (364 = 28 × 13) and the
apparent revolution of Mercury (115) come in question as secondary matters.

I will now give an approximate reproduction of the page:--

   Hieroglyphs.

   1   17   29    151,840        113,880         75,920         37,960
   2   18   30   (4 × 37,960)   (3 × 37,960)   (2 × 37,960)   (13 × 2920)
   3   19   31    I Ahau         I Ahau          I Ahau         I Ahau

   4   20   32    185,120         68,900         33,280          9100
   5   21   33    I Ahau         I Ahau          I Ahau         I Ahau

   6   22   34     35,040         32,120         29,200         26,280
   7   23   35   (12 × 2920)    (11 × 2920)    (10 × 2920)    (9 × 2920)
   8   24   36     VI Ahau       XI Ahau        III Ahau      VIII Ahau

   9   25   37     23,360         20,440         17,520         14,600
  10   26   38   (8 × 2920)     (7 × 2920)     (6 × 2920)     (5 × 2920)
  11   27   39    XIII Ahau       V Ahau        X Ahau         II Ahau
  12   28   40
  13               11,680          8,760          5,840          2920
  14             (4 × 2920)     (3 × 2920)     (2 × 2920)
                  VII Ahau        XII Ahau      IV Ahau        IX Ahau
  15
  16                2,200         1,366,560            1,364,360
                  IV Ahau          I Ahau               I Ahau
                  8 Cumhu         18 Kayab              18 Zip.

First let me observe that I have restored the four large numbers at the
top, which are almost entirely effaced, as follows:--

   1   15   10   5
   1   16   10   5
   1    6   16   8
  14    0    0   0.
   0

And furthermore, at the right, bottom, I have substituted the third month
for the second of the Manuscript, which proceeding will be justified later
on.

The least difficult portion of the contents of this page is the first
series consisting of 16 members, each being a multiple of 2920. It begins
with the date I Ahau (which is always concealed in these series), regularly
stops at the month day Ahau (since 2920 = 146 × 20), but necessarily
advances in the week days by 8 days each (since 2920 = 224 × 13 + 8), until
37,960 is reached, when the day I Ahau again appears (since 37,960 = 146 ×
260).

According to my method of filling in the numbers, the top row of the page
consists only of multiples of 37,960.

On the other hand, the four numbers of the second row from the top are more
difficult. They are, it is true, all divisible without remainder by 260,
but otherwise they seem to be without rule, and they give one somewhat the
impression of a subsidiary computation such as one might jot down on a slip
of paper in the course of some important mathematical work.

Nevertheless, the following remarkable results are obtained when the first
and third and the second and fourth numbers are combined by addition or
subtraction:--

1) 185,120 + 33,280 = 218,400, which is just 600 years of 13 × 28 = 364
days, 280 Mars years of 780 days, 840 Tonalamatls of 260 days or 7800
months of 28 days.

2) 185,120 - 33,280 = 151,840, _i.e._, precisely the highest number of the
top row, = 416 solar years of 365 days each or 260 Venus years of 584 days
each, _i.e._, the product of the days of the Tonalamatl multiplied by the
Venus years. We shall again find the 151,840 on page 51, and Seler
("Quetzalcoatl and Kukulcan," p. 400) finds this same period on a relief of
Chichen Itza.

3) 68,900 + 9100 = 78,000, _i.e._, 100 Mars years or 300 Tonalamatls. The
half of this number, or 39,000, we shall find again on pages 69-73 by
computation; also the whole 78,000.

4) 68,900 - 9100 = 59,800, _i.e._, 520 Mercury years of 115 days, or 230
Tonalamatls, or five times the period of 11,960 days, in which these two
periods are united. By computation again we find the 59,800 on page 58.
This period of 11,960 days is, however, to the period of 37,960 in the
proportion of 23:73, _i.e._, 23 × 520:73 × 520. 23 is the fifth part of the
apparent Mercury year, as 73 is of the solar year.

Let us now turn to the numbers, which form the bottom of my transcription,
but only the left hand lower corner in the Manuscript. Here, in the latter,
we find the following (with the correction already mentioned of the second
to the third month):--

   2200      1,366,560    1,364,360
  IV Ahau      I Ahau      I Ahau
  8 Cumhu     18 Kayab     18 Zip.

The first thing to be done is to arrange and fill out these numbers to suit
our purpose.

The 2200 is clearly nothing more than the difference between the two high
numbers. We can therefore dispense with it.

Further, we find by the usual computation, that the second number belongs
to the first date and the third to the second. Hence the number
corresponding to the third date is wanting from lack of space. This number
can be calculated from that date; it is 1,352,400. It would suit this date
equally well if the number were higher or lower by 18,980 or a multiple of
18,980; but it will be seen directly that it agrees with the other two
numbers only at the value given above.

Now, if we add to this passage the years in which the dates must lie, they
are in the case of the date on the left, the year 9 Ix, in the case of the
middle date, the year 3 Kan, and of that on the right hand, the year 10
Kan.

Then if we arrange the three numbers with the dates and years belonging to
them, according to the value of the first, this part of the page will run
as follows:--

  1,352,400    1,364,360    1,366,560
   I Ahau        I Ahau      IV Ahau
   18 Zip       18 Kayab     8 Cumhu
   10 Kan        3 Kan         9 Ix.

Let us now consider the properties of the three numbers individually.

1) 1,352,400 = 28 × 48,300 and = 115 × 11,760, hence it is divisible by the
month days of the year of 364 days and by the Mercury year. At all events
this is the least important of the three numbers.

2) 1,364,360. This looks as if it referred particularly to the moon and to
Mercury; to the latter since it is equal to 115 × 11,864, and to the former
if we assume that the lunar revolution has been fixed at 29-2/3 days, in
which case this number is exactly equal to 46,000 such lunations. If this
last number be again divided by 115, the number of days required for a
revolution of Mercury, the quotient is 400, which is a round number in the
vigesimal system and which was therefore denoted by a single word, by Bák
in the Maya (according to Stoll) and by Huna in the Cakchiquel (according
to Seler). 1,364,360, therefore, is a Huna of lunar revolutions multiplied
by the number of days in the Mercury period. Later on we shall find the
lunar revolution fixed at 29-2/3 days.

3) 1,366,560. This is the most comprehensive number of the entire
Manuscript, for it is divisible into each of the following periods:--Those
of the Señores de la noche or Lords of the Cycle (9 × 151,840; this is,
however, the first number of the top row), the Tonalamatls (260 × 5256),
the old official years (360 × 3796), the solar years (365 × 3744), the
Venus years (584 × 2340), the Mars years (780 × 1752), the Venus-solar
periods (2920 × 468), the solar year-Tonalamatls (18,980 × 72), the Venus,
solar, Tonalamatl periods (37,960 × 36), and the periods which are
generally designated Ahau-Katuns (113,880 × 12).

We have next to consider the intervals which elapse between the three
dates.

1) From 1,352,400 to 1,364,360 is 11,960 days, which period we have already
found once on this page by computation. 11,960, however, is equal to 104 ×
115 and 46 × 260, _i.e._, the Mercury revolution and the Tonalamatl
combined. 11,960 is again equal to 32 × 365 + 280, and from the year 10 Kan
to 3 Kan it is actually 32 years, and from the date 18 Zip to 18 Kayab it
is, in fact, 280 days. The day I Ahau must be common to both dates.

2) From 1,364,360 to 1,366,560 is 2200 days, as the Manuscript expressly
states. 2200, however, is equal to 8 × 260+120, and the distance from the
day I Ahau to IV Ahau is in fact exactly 120 days. Further 2200=6 × 365+10;
from the year 3 Kan to 9 Ix it is 6 years and from the date 18 Kayab to 8
Cumhu it is 10 days.

3) From these two statements the third follows. The distance from 1,352,400
to 1,366,560 is 14,160. This contains first the 14040, in which both the
Tonalamatl and the old official year of 360 days meet, and second 120,
which is again the interval between I Ahau and IV Ahau. But 14,160 is also
equal to 38 × 365 + 290, and the interval between 10 Kan and 9 Ix is of
course 38 years, and from 18 Zip to 8 Cumhu it is 290 days.

The numbers with which we have had to do here will again occupy our
attention further on, especially the 2920 and the 37,960 on pages 46-50,
the 11,960 and 115 on pages 51-58, and the 14,040 on page 73.

That these computations are not confined to the Dresden Manuscript is
proved by the cross of Palenque, where we find in signs A B 16 precisely
the date I Ahau 18 Zotz, a Tonalamatl before 18 Kayab, in D 1 C 2 exactly
the difference 2200 and in D 3 C 4 the date IV Ahau 8 Cumhu. This is in
favor of the theory that our Manuscript did not originate far from
Palenque.

Now, the question finally arises as to what may, strictly speaking, be
considered the significance of these numbers, dates and differences.

In the first place, I would recall the fact that the dates of the monuments
of Copan and Quirigua, which doubtless refer to present time, are in the
neighborhood of 1,400,000. The high numbers of our Manuscript, so far as
they are in question here, form first a group, which extends from about
1,200,000 to 1,280,000, and then there is a blank, and next a large group
extending from about 1,350,000 to 1,480,000, then another blank and lastly
a group extending from about 1,520,000 to 1,580,000. If we assume that our
Manuscript belonged to about the same date as these inscriptions, then the
three numbers discussed here would extend over a past period lying about
160-170 years back, when a new period of importance had begun probably
dating from the immigration of the Aztecs into Mexico, which they placed in
the first half of the 14th century (see "Weltall," Vol. 5. pp. 374-377).
Now, however, the number 1,366,560 contains the statement that 3744 years
ago (each year having 365 days) an event must have occurred, which can
hardly be anything other (according to the belief of the Mayas) than the
creation of mankind. Hence all the _historical_ dates of the Mayas were
computed from this starting-point. But how did this event come to have the
date IV Ahau 8 Cumhu?

In my opinion this date is to be regarded only as the result of the far
more important date I Ahau 18 Kayab, lying 2200 days earlier. Day 17, Ahau,
belongs, without doubt, to the chief of the gods, and as the first week day
it must have been especially sacred. The prophecies of the Tonalamatl
preferably begin with the Ahau and with the I. The series on the page under
discussion, constructed with the difference 2920 as a basis, begins with I
Ahau, and the three series on pages 46-50 also have the same day as the
zero point of departure. I Ahau is therefore the starting-point of the
astronomical computations as IV Ahau is of the historical.

Now, however, all the periods of 260 days end each time with I Ahau. Why is
precisely this day chosen here, which is the 18th day of the month Kayab,
therefore in the year 3 Kan, and lying 2200 days earlier than the
historical date?

Day 18 Kayab is our June 18th. In my treatise "Schildkröte und Schnecke in
der Mayaliteratur" (1892), I have sought to prove that the tortoise served
as symbol of the summer solstice, that the sign of Kayab was the head of a
tortoise, and that probably the 18th of June was regarded as the longest
day. The middle one of the three series on pages 46-50 begins with exactly
this date, I Ahau 18 Kayab.

But whence come the 2200 days? I will offer a suggestion which may serve
until a better theory is propounded. Let us assume that each of the five
principal planets had in succession regulated its time of revolution by
this astronomical starting-point, thus:--sun 365, moon 356, Mercury 115,
Venus 584, and Mars 780 days, these numbers added together give exactly
2200. It will scarcely excite surprise that I should set down the lunar
year at 356 days (and not at the usual 354 days) for there are 12 × 29-2/3
lunations in a year and we thought we had already found this period on this
page, while discussing the number 1,364,360; also on pages 51-58, in
addition to the half lunar year of 177 days, we shall find one of 178 days.
Were the planets therefore created 2200 days before the appearance of
mankind? Jupiter and Saturn, of course, with their 397 and 380 days are
probably not considered here, because their periods of revolution so nearly
correspond to that of the sun, and on pages 51-60 they are also treated as
of secondary importance.

I confess I am quite unable to discover what may have happened 11,960 days
before the creation of the stars--possibly the birth of one of the
principal deities. Perhaps one of my fellow-students may succeed in finding
an answer in one of the creation myths.

We come now to the 40 hieroglyphs on the left half of the page. These are
intended simply to familiarize the reader with those signs which are of
importance in the calendrical-astronomical portions of the Manuscript.
Since no phonetic system of writing existed, we cannot, of course, expect
that the scribe should have explained these signs.

Signs 1-4, which are mostly destroyed, can hardly denote anything other
than the four quarters of the globe, at least we can still recognize in 4
the sign for the east, which has also the fourth place in pages 46-50. They
stand thus together five times in the middle of the left side of pages
46-50, which pertain to this subject. 5 to 9 are the sign for Venus
repeated 5 times, probably denoting the four parts of its revolution as on
pages 46-50 and also the revolution as a whole. In connection with this
first appearance of the Venus sign, I would mention that the same
hieroglyph also occurs in the Tro-Cort., _e.g._, Cort. 25c, though this
Manuscript contains little else that is astronomical, yet it also has the
rectangular heavenly shields.

10. This is a well-known form of the Moan sign. In the Globus, Volume LXV,
1894, I sought to make it appear probable that the Moan also denoted the
Pleiades, with whose disappearance and reappearance the beginning of the
years seems to be connected. Likewise on page 50, where the 2920-period
ends, the Venus and Moan signs appear at the top on the right-hand side.

11 and 12 are the same sign, being that of the 13th Uinal (Mac), with which
260 days of the year end, and hence this sign is also used as the sign of
the Tonalamatl. The repetition seems to show, that not until the 73
Tonalamatls of the period of 18,980 days are doubled--thus obtaining the
number 37,960 of such importance here--are the sun and Venus periods
brought into unison (with the whole system).

13. The Kin sign (sun, day) with the superfix, which in all probability
expresses conjunction, union, and which, in my opinion, we also see on page
51, combined with Kin and Imix, as the sign for 18,980 days, is used here
after the two Tonalamatls to denote the doubling of this period.

14-18. If the preceding signs led us to the Venus-solar period and to the
continuation of this subject on pages 46-50, these five hieroglyphs bring
us to the Mercury-lunar period and later, on pages 51-58, which are devoted
to the same period, we shall find a parallel especially on the last page.
First comes 14, which, as has been acknowledged, is the sign for 20 × 360 =
7200 days. 15, a hand holding a rectangle divided by a cross into four
parts, is, I believe, the sign for the period of 20 days augmented to 21 by
the 1 in front of it. The much more distinct form of sign 16 on the middle
of page 58 and also at the top of page 53, should be compared with the sign
as given here. The top part is the familiar Ben-Ik sign denoting the 10th
and 19th days, and the bottom is the sign of the 14th division of 20 days,
which make up the year. Now, however, the 10th day, when it becomes the
19th of the next 20 days, is distant from the first 29 days. The prefix
consists of two parts:--First two small circles joined by a zigzag line,
which I think denotes the division of a day into halves; the sign would
then equal 29½ days, _i.e._, very nearly the true lunar month. Second, of
two vertical lines, which might denote a doubling. The whole would then be
equal to 2 × 29½ = 59. I admit that this interpretation is very artificial
and I should be very glad if a better explanation could be found. On the
other hand the 17th hieroglyph becomes quite clear when it is compared with
the parallel passage on page 58; it is 13 × 360 = 4680 days, a third of the
remarkable period of 14,040 days.

Thus we have

  Hieroglyph 14 = 7200
      "      15 =   21
      "      16 =   59
      "      17 = 4680
                 -----
                 11960,

which is exactly the lunar-Mercury period.

The sign Xul = conclusion, end, is fittingly added in 18 to the end of this
period, as also on page 58. This sign is very common on pages 61 and 62 at
the end of the long periods.

From signs 19 and 20 we see that the four parts of the Venus year are also
about to be treated of here, that is, the periods of 236, 90, 250 and 8
days respectively, which are discussed on pages 46-50. For 19 is the sign
for Venus, and 20 is a hand with a knife as a superfix, which divides the
Venus revolution. This hand appears 20 times in like manner on the pages
mentioned above.

Signs 21-25 represent five gods, who in all probability are N, F, H, the
bat-god and A. These are the same signs which are repeated twice on the
left-hand side of pages 46-50, both times at the beginning and end of the
period of 236 days, that is, the period during which Venus is the morning
star and which is under the dominion of the east. The fact that there is a
4 with N has reference to the four forms which this Uayeyab god assumes.
Now we ought to expect a similar treatment of the periods of the planet,
which are under the rule of the south, west and north, but there is no room
for this. Instead, we find in 26, 27 and 28 three different signs plainly
belonging together, the first of which is the day Caban, _i.e._, the earth;
the second may be Muluc denoting rain and water; the third is Chuen (the
ape) which fittingly denotes the north, for Chuen denotes the little bear,
as I have proved in my treatise on the day-signs of the Mayas. The Chuen
sign in 28 also has a prefix, which probably refers to the night-god D. I
find exactly the same combination in signs 8 A and 8 B of the inscription
on the Cross of Palenque, but I must leave to others the task of connecting
26 and 27 likewise with the north, which is very evident in 27 (Muluc).

Sign 29 is entirely effaced. Nevertheless, I am positive that it
represented the day IV Ahau, the beginning of Maya chronology, for 30 may
still be identified as 8 Cumhu belonging to IV Ahau, and sign 31 is the
same sign as 18, _i.e._, the sign Xul = the end, and denoting here the end
of the long period.

The comprehensive hieroglyphs, 29-31, stand here in the wrong place. A more
suitable position for them would be before 19 or just after 35. For they
are intended to specify the periods during which Venus is in the west and
south, _i.e._, the time during which it is the evening star and the period
of its inferior conjunction.

Sign 32 is the black deity, L according to Schellhas, here denoting the
west, and 33 is the Venus sign with the prefix denoting division. In the
same way we find these two signs together on page 46 at the right in the
middle series, where presumably the four Venus periods are specified in
close succession. The black deity is also found on page 50 in the middle of
the page in the beginning, at the end of a period of 250 days. On page 24
it has as a prefix the sign Imix with three rows of dots proceeding from
it. Imix, however, among the Mayas and Aztecs (as Cipactli), under some
circumstances often, and under others always, denotes the first of the 20
days. Hence this sign may mean:--here begins the Venus period of 250 days.

34-35. The sign for the south still remains to be found. Sign 35 is again
the Venus hieroglyph. In 34 we should expect to find one of the five gods
of the south, which are found on pages 46-50, _e.g._, the Moan, who is
represented on page 47 as the regent of this cardinal point. But there is
no figure of a god here, and in place of it we find set down here, as on
page 47, middle, right-hand, an actual date as the beginning of this short
southern period of only eight days. It is the date 10 Zip (third month),
the month sign of which does indeed suggest a hieroglyph of the Moan. Now,
if we recall that in hieroglyph 21 the god N is designated in exactly the
same way by an actual date, viz:--4 Zac (11th month), then we see that the
interval between 4 Zac and 10 Zip of the second year following, is exactly
236 + 90 + 250 = 576 days, and this corresponds exactly to the interval of
time from the beginning of the period when Venus is in the east to the
beginning of the period when she is in the south. If we knew in what years
the morning star made its first appearance on February 4th and disappeared
as the evening star on the 3d of September, we should make some progress in
the comprehension of this subject, but not much, since these events fall
approximately on the same dates after each period of 8 years.

36-40. The last five of the 40 signs appear in the same order again on
pages 46-50, _one_ sign on each page, in the middle group of the right-hand
half of the page at the beginning of the third line, but with this
difference, that on page 24 each sign has the same prefix, which is wanting
on pages 46-50, where a similar hieroglyph always _follows_. From their
position on pages 46-50 it follows that these are hieroglyphs of five gods,
each of whom belongs to a whole Venus year of 584 days. I am not very sure
in regard to these gods. I prefer to call 36 K, 37 F, 38 E and 40 A. Sign
39 with the person crouching, I am obliged to leave entirely unsettled. We
shall find this hieroglyph again, _e.g._, on pages 47 and 49 right, middle.
Let it suffice that in these five signs we have a repetition of the
Venus-solar period of 2920 days, with which we will end the discussion of
this page. Only F and A have already been met with among the five gods
denoted by hieroglyphs 21-25.

Pages 25--28.

As these four pages, which are the beginning of the back of the first part
of the Manuscript, not only belong together, but also display a parallel
arrangement of their separate parts, the corresponding parts will be
considered together as a whole.

There are seven of these parts on each page, viz:--the column of day-signs
on the left hand; the top, middle and bottom pictures, and lastly the top,
middle and bottom groups of hieroglyphs; but I will consider the pictures
and hieroglyphs of the same section as belonging together.

1. The Columns of Day-Signs.

On the left-hand side of each page two days are repeated 13 times. They are
as follows:--On page 25 Eb and Ben, on page 26 Caban and Ezanab, on page 27
Ik and Akbal, and on page 28 Manik and Lamat. Cyrus Thomas first made the
important discovery that these pages represent the transition from one year
into the next, but held the erroneous opinion that the last two days of
each of the four kinds of years were treated of on each page. While Seler,
on the other hand, found that we have here to do with the last day of one
year and the first of the following year, and that, therefore, Ben, Ezanab,
Akbal and Lamat are the beginnings of the years and thus of the 20-day
periods. The years, however, were always named after their second day
(_i.e._, Kan, Muluc, Ix and Cauac years), since the New Year's Day was
considered unlucky and it was the practice of the Mayas to conceal the real
starting-point.

These four pages, therefore, extend over 13 × 52 years, that is, over a
period of 18,980 days, after which period all the calendar dates are
repeated. A list of all these dates is given in "The Maya and Tzental
Calendars" by William E. Gates (Cleveland, 1900).

The transition from the Muluc to the Ix years is represented on page 25;
from the Ix to the Cauac years on page 26; from the Cauac to the Kan years
on page 27, and from the Kan to the Muluc years on page 28. The Ix years
are represented first, because the beginning of the historical chronology
lies in an Ix year (IV Ahau; 8 Cumhu). This section treats of ceremonies,
especially of the setting up of the idols at the changing of the year,
which I can pass over here since they have already been described by Diego
de Landa and in our own day by Cyrus Thomas in his "Study of the Manuscript
Troano," and elsewhere.

2. The Top Pictures.

The principal representation on all the four pages is a priest, but
disguised as an animal with the head of a beast of prey as a mask (always
the same one) and also with a tail. He is pictured with the same three
articles in each of the four representations, viz:--First, in his right
hand, the staff of office with the hand at the top, which, according to
Seler, "Mittel-Amerik. Musikinstrum.," p. 112, is the rattle-stick, second
the incense-pouch, _i.e._, for copal, and third in his left hand a rattle,
or, according to Schellhas, "Vergleichende Studien" (1880), a fan. There is
one point, however, in which the first two pages differ from the other two;
on the first two the priest is walking on dry land and on the second two
through a stream of water. Was the city, to which this calendar especially
refers, bordered in two directions by water, so that the road led across
it?

On all the four pages, however, the priest carries on his back a different
deity, and I cannot find out by what rule these gods are connected with one
another, or with the one which is represented below them, or with the
years. On page 25 the god is B, on 26 he has the form of a jaguar (Ix), on
27 he is undoubtedly E, and on page 28 he is the god A, Cimi.

Now to the left of the priest on each page there is one of the familiar
Chuen bundles, such as are also frequently found in the the
Tro-Cortesianus. Here, on pages 25-28, there are always three of these
Chuen signs in a bunch. If Chuen really denotes the eighth day (which, of
course, is only possible when Kan = 1), and at the same time the period of
8 days, then in this passage these three Chuen signs would properly
designate the 24 days which elapse _before_ the last day of the year, which
is the last day of the 18th month. In the same way we shall find the Chuen
bundle appropriately given this meaning on pages 42c-45c. Likewise the
simple Chuen sign at the top of page 52 seems to denote 8 days. But what do
the Chuen bundles in the Tro-Cortesianus mean, some of which are much
larger?

In close proximity to these Chuen bundles we find numbers as follows:--on
page 25 numbers 8 and 9, on 26 number 13, on 27 number 2 and on 28 number
13. I can offer no opinion, which would be even approximately acceptable in
regard to the meaning of these numerals, but we shall discuss them later.

3. The Top Hieroglyphs.

I shall discuss these glyphs in this place, although each group seems to
relate not merely to the top picture, but to the whole page. There are 16
on each page, and arranged as follows:--

  1  2     9  10
  3  4    11  12
  5  6    13  14
  7  8    15  16.

Unfortunately, the writing at the top is obliterated, which makes it
impossible to understand not merely this passage, but also those on all the
rest of these pages. Of the 16 signs in the top line only one is legible,
and that is the first on page 28. This is the usual cross _b_; as a
comprehensive heading it perhaps occupied places 1 and 9 on each page,
alternating with another sign in 2 and 10.

In spite of this obliteration there are a few points which can be
profitably discussed here.

I would call attention first to signs 7 and 8 on page 25. The first seems
to contain twice repeated the figure, which is thought to represent eagle
feathers, and which we found on pages 10b and 13a, for example. As this
double character is also used to change the 360-sign into a 7200-sign, so
it may also combine the 52 years of this passage. The 8th sign on page 25
is the head with the tuft of hair and no underjaw, which I think refers to
fast-days, such as might properly occur at the transition point of one long
period to another.

The sign for the year stands five times on the other three pages, which is
in keeping with their contents. On page 26 it appears three times. This
page treats of the transition of the Ix to the Cauac years. In the 6th
place the Ix sign seems actually to be used as a prefix, in 7 the prefix is
plainly the Kin-Cauac sign, just as on page 37a, and in 5 the prefix is
probably Ezanab, the beginning-day of the Cauac years. At this last place
the suffix is the same as that which we often see with the year sign on
pages 13c-14c. On page 27, in the 7th place, the year sign has a prefix and
a suffix, which seem to indicate that here it was intended to represent 365
as separated into 5 × 73 or 360 + 5. Lastly, on page 28 the 8th sign can be
explained as meaning that the ritual year of 364 days is separated into 4
Bacab periods of 91 days each.

Resembling the year sign in form, and placed near it on these pages, is the
following sign:--

[Illustration]

This sign frequently appears on pages 8b-9b, 16b-17b, 17c-20c. We find it
with slight variations once on each of the four pages 25-28. It is the 6th
on page 25; the 8th on 26; the 6th on 27; the 6th on 28. Its lower part,
especially the (phallic?) sign added at the left, suggests the hieroglyphs
of the Bacabs, as we find them on pages 52, 55, 56, etc.; they might refer
to the separation of the ritual year of 364 days into 4 × 91 days. On the
other hand it has been considered simply as the reproduction of the
carrying-frame pictured below it (compare above under page 17c.)

While the hieroglyphs, hitherto discussed, demonstrate the connection
between the parts on the left of the four pages, two other signs prove the
connection of the portions on the right.

One of these looks like the Ik sign surrounded by a dotted circle; it
occurs on page 25 as the 13th sign, on page 26 as the 15th, on page 27 as
the 14th and on page 28 as the 15th. To this sign are prefixed successively
the numbers 9, 7, 11 and 6.

The second is unquestionably the hieroglyph for the numeral 20 or for the
moon. It is effaced on page 25 and on pages 27 and 28 has a prefix, which
on page 26 is used as a superfix. This sign is the 14th on page 25, the
16th on page 26, the 15th on page 27 and the 16th on page 28. The prefixed
numbers are 7, 16, 5 and 6.

The meaning of these two signs and that of the apparently irregular numbers
is still a mystery. The latter will be discussed presently.

The 4th sign on all the four pages seems to refer to a period like the one
hitherto discussed. On page 26 the sign resembles that for the 13th Uinal
(Mac) and hence appears to refer to the Tonalamatl, as in the first column
on page 24. Above it is the sign for the south. The corresponding
hieroglyphs of the other pages are obliterated, but strange to say the
vestiges suggest that they too had _below_ them the sign for the south. Now
the south and the Bacab of the south preside over the fourth quarter of the
year from which ensues the transition to the new year in question here.

Among the signs on the left side we should expect to find those of the gods
to whom the expiring year belonged. On page 25 it ought to be B. Sign 5,
however, though it can with difficulty be identified, points rather to god
K. Sign 3 on page 26 corresponds better; this is the hieroglyph of the
tiger already known to us, which is carried by the priest in the upper
section of page 8a; here its prefix is the sign for the west. On page 27 we
ought to see the grain-god E carried by the priest; his hieroglyph may be
destroyed, but sign 5, which is Kan-Imix (food and drink) is his
determinative. Finally the 5th sign on page 28 is, just as we should
expect, the hieroglyph of A and, in addition, we find his determinative in
7.

But what is to be said of the fact that the tiger appears again on page 28
in sign 3, and this time with the sign for the east?

The Ahau on page 27, sign 16, refers to the god D of the middle section.

There maybe some reference here to sacrifice, thus:--the 11th sign on page
25 is Kan-Imix, the 12th on page 27 is Kan, which is followed in the 13th
sign on page 27 by another one with a Yax and a suggestion of a second
Kan-Imix. Also the curious sign in the 8th place on page 27, which we have
already discussed under page 8b, is used to denote the sacrifice on pages
18a and 15b. Here its position with reference to sign 6 is the same as on
page 8b. On page 26 the prefix of sign 13, which is half destroyed, may be
recognized as a serpent. Signs 12 and 15 on page 25 are unintelligible.
Unfortunately the following signs are entirely effaced:--Sign 1 on pages
25, 26 and 27, as well as 2 on all the four pages, 3 on page 25, 9 and 10
on all the four pages, 11 on pages 26, 27 and 28, 12 on pages 26 and 28, 13
on page 28, 14 on pages 26 and 28, and 16 on page 27.

4. The Middle Pictures.

On each page at the right there is a house, the back wall of which is
always marked with the cross often met with. In front of the house with his
back turned towards it, sits a deity. Each of the four deities has the
front of his body covered with a gala mantle. Now we know that the god of
the new year was set up before the house of the chieftain. On page 25 the
god is K with his eyes apparently destroyed, and on page 26 it is B with a
Kin sign on his head covering, hence designated here as a sun or day-god.
On page 27 the god is D, and on page 28, A with the cross-bones on his
robe, his own hieroglyph on his cheek, and the Akbal sign on his forehead.
Only on the last page, therefore, and apparently by mistake, the god in the
top picture is the same as in the middle picture.

At the left of each page, _i.e._, opposite the house and the god, is a
flaming altar, bearing the sign Ix equivalent to fire.

The centre, between the gods and the altars, is occupied by vessels of
which there are two on each of the first three pages and but one on the
fourth; they contain food, without doubt intended for the sacrificial
feast. On page 25 the lower vessel contains Kan (maize) and the upper
probably a food prepared from Kan. Or are the spines on the back of the
iguana indicated on this vessel? (Compare 40c and Cort. 8 and 12c). The
contents of the lower vessel on page 26 are still unknown (birds?). The
upper vessel contains a Kan, but the sign has a superfix, which corresponds
to the sign for the west. On page 27 the lower vessel contains a fish and
the upper the sign for the south. Lastly, the single vessel on page 28
contains the cross-bones (mammal?) and above them the Kan sign repeated
three times.

Finally here on the last three pages, we find some numbers, which are still
undetermined; on page 26 there is a 7 with the lower vessel, and on page 27
with the upper vessel two dots with a cross between them (perhaps this may
mean 20 - 2 = 18, which is used in place of the usual clumsy numeral?). On
page 28 we see above the vessel a 6, and below it, in place of a second
vessel, a double Chuen sign, as in the upper section of the page, therefore
it can hardly be the Akbal sign resembling Chuen.

5. The Middle Hieroglyphs.

On each page these signs consist of but _one_ line containing 5, 6, 3 and 3
glyphs respectively. The first of these signs in all of the four places is
the same (_o_), which very suitably refers to the change in the year. The
second sign is always the hieroglyph of the god represented in the middle
section:--K on page 25, B as the sun-god on page 26, and D on page 27. The
second sign on page 28, which is the head without an underjaw and with the
prefixed four, probably referring to four fast-days, must, therefore, be an
uncommon sign for A, who was similarly designated on page 25 in sign 8 of
the upper section.

If the gods in the top thirds are those of the past year and those in the
middle the gods of the year just beginning, we should expect to find in
each top third the deity who is represented in the middle of the preceding
page. But this does not hold good. For then we should expect to find K on
page 26 and not the tiger, on page 27 B or G and not E, on page 28 D and
not A, and on page 25 A and not B.

Hence there is some confusion here. Yet it seems to be in the nature of a
correction, that on page 26 the third sign, next to that of the sun-god, is
actually the sign for E who is in the top section on page 27, and that the
sixth sign is Kan-Imix belonging to this god.

On pages 25 and 26 this line also refers to the past year, _i.e._, to the
year set down in the top third. The fourth sign on page 25 is a Manik,
_i.e._, originally a grasping hand denoting taking away, disappearance, and
the fifth sign on this page is a Muluc, which seems to denote the ending of
the Muluc years. The fifth sign on page 26, is, in fact, the tiger pictured
above.

The lunar hieroglyph as the third sign on page 25 and the _a_ as the fourth
on page 26 are strange and unaccountable. Both appear to be almost without
significance here and seem almost like mere points between the names of
gods in groups of two each.

The Ahau as the third sign on page 27 is the usual determinative of D,
whose hieroglyph stands beside it.

On page 28 the main part of the third sign corresponds to the sixth of the
upper section. I do not know, however, how to explain either the upper part
suggesting a mat or the familiar leaf-shaped prefix.

6. The Bottom Pictures.

In the left-hand lower corner of each page we see the sign for the year of
360 days, which at the same time designates the heap of stones, on which
the stelae were erected, the two thick black lines indicating the two
columns of hieroglyphs usually found on them. A tree is growing out of this
sign, having on its trunk an abbreviated Cauac sign, at least, on pages 26,
27 and 28, which probably refers to rain as the most desired event of the
year. The tree on page 25 has no leaves, but the top is carved into the
shape of the head of the god B. In the other three cases it has leaves, but
instead of ending in the god's head the tree is draped with a mantle and a
breech-clout, and a serpent is coiled about it denoting a period of time
(here, the year). Furthermore there are foot-prints on the trunk or the
drapery of the tree, which represent it as the goal of a pilgrimage.

If the top and middle thirds refer to the mere transportation of the idols,
the bottom thirds refer to the feasts connected with this act, or, at any
rate, to those dedicated to the _new_ god. For we see here on page 25 the
god B, on 26 the god K, on 27 A and on 28 D, _i.e._, the same deities as in
the middle sections, yet so placed that the first two and the last two have
changed places.

Each of the four deities hold in one hand a hen with its head cut off;
"degollavan una gallina" is the statement made by Landa concerning these
feasts. Perhaps all four gods, at any rate the last three, are scattering
grain; this was one form of divination; we found the other on page 2. There
are besides, on every page, several small objects between the two pictures,
just as in the middle section. On page 25 the object is probably an altar,
but instead of the flame it has the number 19. Above this is the sign for
the west (the Ix days) with that for the sun, and on top of them the sign
which we found in the middle section of page 26 as the contents of the
lower vessel. On page 26 we see a vessel containing a bird, then another
whose contents are indicated by Yax and a double Kan sign. Above it is the
sign for the moon or for 20 with a prefix, and above this a 9. At the
bottom of page 27 there is a vessel containing two Kan signs and a fish;
above this another vessel the contents of which are the same as we found in
the vessel in the middle section of page 26 and in that of the lower
section of page 25. Above these is again the sign for the moon or 20 with a
superfix, which is the same as the prefix on page 26, and beside it is a
16. Page 28 has the usual haunch of venison (Landa:--"una pierna de
venado"), above this is a vessel with a bird and Kan and above this again
the sign for the moon or for 20 with the same superfix and the numeral 15.
I shall discuss below the numbers scattered over these four pages.

7. The Bottom Hieroglyphs.

These hieroglyphs also form but _one_ line on each page and each line
contains six hieroglyphs. The _first_ of each line is always the same
(_p_). It consists of a surface divided into four quadrants thus suggesting
the four cardinal points, the four Bacabs presiding over them and the four
kinds of years. The superfix seems to be the abbreviated hieroglyph of the
north; the sign for the north, however, is Muluc and these four pages begin
with the Muluc years.

The _second_ sign is the head of D as the supreme god; to this a Yax is
joined on pages 26-28 as the symbol of strength, and on page 25, but
probably by mistake, the abbreviated sign for the west.

The _third_ sign always represents one of the four cardinal points:--on
page 25 the east, on page 26 the south, on page 27 the west and on page 28
the north; here then the usual order is reversed and the signs are set down
according to the diurnal instead of the annual course of the sun, probably
occasioned merely by exchanging the sign for the west (Ix), which belongs
on page 25, with that for the east (Kan), which belongs on page 27.

The other three signs do not stand in the same order on every page.

The _fifth_ sign on pages 26 and 28 and the _fourth_ on page 27 show
correspondence most clearly. This sign is always a head, undoubtedly that
of the god pictured in the bottom third. But on page 25 it is the
hieroglyph of E, who is pictured on the top of page 27, instead of that of
B.

In the same way the 6th sign on page 25, the 4th on page 26, the 5th on
page 27 and the 4th on page 28 have something in common. One element of the
hieroglyph is always the sign for the year of 360 days, combined on page 25
with cross-bones and the Cauac sign, on 26 with Yax and Kan, and on 27 and
28 simply with Yax.

The most puzzling and divergent of these hieroglyphs are the remaining
ones. The 4th on page 25 has an oblique cross (or bones?) and the
abbreviated glyph for the west, the 6th on page 26 is the head of E, the
6th on page 27 is the 360-day sign combined with Kin and Cauac, and the 6th
on page 28 is the usual Kan-Imix sign. Here, too, there seems to have been
a displacement.

Before I leave the four pages 25-28, I will glance at the numerals, which
are scattered over them and which apparently have no connection with one
another. I have discussed these numerals in my article "Die
Mayahieroglyphen" in Volume LXXI, No. 5, of the Globus, and the following
is borrowed therefrom.

First of all, I believe that I proved there, that the sign composed of two
dots with a cross between them is an abbreviation for the usual clumsy
representation of the numeral 18 and designates it like a duodeviginti by
20 - 2. Next, that in this passage as on pages 18a, 18c, 19c, 46b and 50c,
the sign is combined with the hieroglyphs Yax-Kin. Third, that it is
closely related to the god D, inasmuch as it stands on page 27b close
beside the picture of that god.

Assuming this as a known fact, we find scattered over these four pages the
following numbers:--

  25:    9,    7,    8,    9,   19,
  26:    7,   16,   13,    7,    9,
  27:   11,    5,    2,   18,   16,
  28:    6,    6,   13,    6,   15.

It is very remarkable that the sum of the numbers on each of the first
three pages is equal to 52, and as an accidental freak it would be most
surprising; somewhere on the fourth page six units may have been omitted;
but perhaps the 6, which stands above the _two_ Chuen signs in the centre,
is to be counted twice. The 52, however, designates the very 52 years,
which are treated of on these four pages.

As yet I know no reason to account for the fact that the 52 is here
separated into these apparently very irregular numbers. The discovery of
this reason would be an important step in advance. Or does it means 52
_days_, perhaps those which follow a Tonalamatl coming in the middle of the
year?

Page 28 is followed in the Manuscript by three empty pages. The scribe's
object in reserving them is beyond our ken; possibly they were intended to
represent the period of 8 years.

Pages 29-45 (_i.e._, to the end of the first part of the Manuscript) all
belong together. After the Maya manner there is very little system
displayed in their arrangement, and though here and there there may be
occasion to consider the three parts of each page consecutively, I will
discuss them here as follows:--First, the top thirds, which are most
difficult owing to the destruction of a large portion of them; then the
middle, and last the bottom thirds. They all consist in great part, with a
few interruptions, of representations of the regular Tonalamatl, such as we
find represented from the beginning of the Manuscript to page 23.

The element which these pages have in common is the fact that the god B,
who can hardly be Kukulcan or Quetzalcoatl, occurs on almost all of them.
He is the god of wind, fire, breath, _i.e._, the true god of life and is
here represented in his relation to the most varied manifestations and
activities of a human being, so that this section bears a certain
resemblance to the Tro-Cortesianus. With this is closely connected his
relation to all four cardinal points, which so often occur. He may have
been the local god of the region from whence this Manuscript came; in the
Tro-Cort. It seems rather to be C who lays claim to this office.

Pages 29a--30a.

  XI  13  XI  13  XI  13  XI  13  XI  13  XI
  Lamat
  Ben
  Ezanab
  Akbal.

This is a Tonalamatl of 4 × 65 days, each part subdivided into 5 × 13 days.
The four days written on the left are those which may begin the year.

In each of the five sections B is pictured in a sitting posture, the first
four times on a tree (the tree of life rather than the sacrificial tree).

In the first picture he holds in one hand the haunch of venison, so often
occurring as an offering, the last time on page 28; the object above it is
probably the Kan sign. There is a vessel at the god's feet, probably a
receptacle for the venison, bearing the hieroglyph of the 13th day Cib,
which, however, refers rather to a bird.

In the second picture an animal with a protruding tongue lies on its back
at the feet of the god, who kneels upon its stomach. This probably
represents the lightning-dog as vanquished. The same animal is pictured on
the next page and also on page 40b and perhaps on page 60. There are a
number of small dots around B's head, which on page 11c we attempted to
interpret as the starry sky.

I can find nothing of special importance in the third and fourth pictures,
but in the fifth, B is sitting in a house, which is marked repeatedly with
the sign Caban (ground). Here the god is holding the hatchet (machete) in
his hand, as if prepared for some terrestrial activity. Four hieroglyphs in
the usual order belong to each of the five pictures. They are almost
entirely destroyed, but the vestiges show that the fourth sign was always
that of B, while the third sign with the first picture had the abbreviated
hieroglyph of the west as a prefix; with the second picture it had that of
the south, and therefore with the third and fourth it must certainly have
had the signs of the east and north. We should expect the signs with these
prefixes to contain references to Ix, Cauac, Kan and Muluc, but they are
not distinguishable.

Thus B is represented in pictures 1-4 as ruler of the four cardinal points
and in 5 as the ruler of the earth in general.

Pages 30a--31a.

This passage looks like an amplification of the middle picture on page 29a.
Here B is represented with the hatchet in his left hand and holding aloft
by the tail with his right hand the animal, which is spitting out something
upon a stepped pyramidal structure, probably the pyramid of a teocalli.
That this is probably meant to represent lightning is rendered almost a
certainty by the picture on page 40b. In this passage there are several red
and black numerals scattered around the animal in an irregular manner,
which we find nowhere else in our Manuscript, but with which the
Tro-Cortesianus has made us familiar. The sum of the black numbers still
legible is 23, probably a 3 is effaced and the sum should be 26, the sum
which so often occurs in the Cod. Troano 8-13 with the animal represented
there. The red numbers likewise do not admit of exact determination. This
passage also contained hieroglyphs, four standing side by side on each of
the two pages. The legible portion is limited to the Cimi sign in the third
place, perhaps an Imix in the second, and possibly an Ahau in the first.

Pages 31a--32a.

In my article "Zur Entzifferung, etc., VI," published in the year 1897, I
discussed this passage more in detail, and the following will be in
continuation of what I stated there.

The real aim of the computation on these pages is to find a number in which
the following periods of time are united with the Tonalamatl of 260
days:--1. The ritual year of 364 days, and consequently also a quarter of
it, the Bacab period of 91 days. 2. The period of 104 days, being the
number of days which remain after a Tonalamatl has been deducted from a
ritual year. The hypothesis advanced by Mrs. Zelia Nuttall ("Note on the
Ancient Mexican Calendar System," Stockholm, 1894) and also the entirely
different opinion held by Mr. Charles P. Bowditch ("The Lords of the Night
and the Tonalamatl of the Codex Borbonicus" in the American Anthropologist,
N. S., Vol. II, New York, 1900) prove the existence not only of merely
arbitrary Tonalamatls for the purpose of prediction, as those in our
Manuscript, but also of Tonalamatls having a fixed position in certain
years. But after the manner peculiar to priestcraft, the number sought is
found only by an indirect and mysterious process.

In the first place we find on page 32a all the days set down in the
following manner:--

  XIII      XIII      XIII         XIII
  Manik     Cib       Chicchan     Ix
  Chuen     Ahau      Muluc        Ezanab
  Men       Kan       Ben          Ik
  Cauac     Lamat     Caban        Cimi
  Akbal     Eb        Imix         Oc.

That is to say, a series counting from the day XIII Akbal, the New Year's
day of the year I Kan, recurring every 52 years, furthermore a series which
shows the same difference of 91 from the day XIII Akbal to XIII Ix, XIII
Chicchan, etc., and finally ends with XIII Akbal again, after it has run
through a period of 20 × 91, _i.e._, 1820 days = 7 Tonalamatls, like a
similar representation of 7 Tonalamatls on page 51. Above these 20 days,
and to the left of them, numbers are set down rather irregularly, which
begin with 91 and are multiples of that number. The signs of the days
corresponding to these numbers are joined to them; but they are omitted
with the numbers of lowest value. Hence we have:--91, 182, 273, 364 (4),
455 (5), 546 (6), 637 (7), 728 (8), 819 (9), 910 (10). Then with a bound
follow 1456 and 1820; with the last number Akbal is reached in the natural
way, which day the scribe had erroneously set down again with 1456 in place
of Cauac.

The number 728 already united the numbers 91, 104 and 364, but did not
include the number 260. This inclusion is accomplished by the number 3640
on page 32, quite on the left where we find the numbers 10 and 2, under
which only a 0 has been omitted. With the usual hiatuses this series seems
to end on page 31, where I think the numbers 4, 0, 16 and 0 ought to stand,
but they are almost wholly effaced; this would then be 320 × 91, 280 × 104,
112 × 260, 80 × 364 = 29,120.

We have thus gone far in advance of the first problem, but a second always
presents itself in these series, it is that of using these periods for
larger numbers, which refer to a not too remote past or to a future not too
distant. The first numbers are, as a rule, in the neighborhood of
1,252,680, the close of the eleventh Ahau-Katun, and the latter in the
neighborhood of 1,480,440, the close of the thirteenth Ahau-Katun. The
Manuscript presents the following:--

   1,272,544      1,268,540     1,538,342.
  XIII Akbal     XIII Akbal     XIII Akbal
     121             17          51,419
   IV Ahau        IV Ahau
   8 Cumhu        8 Cumhu        IV Ahau.

In connection with this it should be noted first that I have restored the 8
in the statement of the months, and second that the two numbers on the
right were found with the aid of page 63 only by an easy conjecture. For
with the reading of the Manuscript 10, 13, 3, 13, 2, I do not agree, but
read instead 10, 13, 13, 3, 2; the number below, however, is given in the
Manuscript as 7, 2 and then a black 14 joined to a red 5; I read this 7, 2,
14, 19.

The three numbers nearest the bottom have red circles around them,
indicating subtraction, or, according to my present point of view,
addition.

Now let us see how the computer arrived at the large numbers.

Day XIII Akbal, the New Year's day of the 1 Kan years, is given; also the
differences of the series 91 and 104, therefore also in the proportion of 7
to 8. If we combine these last two numbers by addition and then by
multiplication with 260, the result is (7 + 8) × 260 = 3900. If, however,
7, 8 and 3900 be combined by multiplication the product is 7 × 8 × 3900 =
218,400 = 2400 × 91 = 2100 × 104 = 840 × 260 = 600 × 364 = 1120 × (91 +
104). We have already met with the 218,400 on page 24, which was obtained
by the addition of 33,280 + 185,120.

My opinion is as follows:--First 11 Ahau-Katuns = 1,252,680, were taken as
a point of departure, and to this sum was added 15,600 = 4 × 3900, and 243
as the interval between the normal date IV Ahau and XIII Akbal. The result
was 1,268,523. The position of this day, however, is XIII Akbal 11 Xul (1
Ix).

Then the 3900 mentioned above was added to this number and the result was
1,272,423 = XIII Akbal 16 Pop (12 Muluc).

Then to the 1,268,523 was added the 218,400 and the sum was 1,486,923 =
XIII Akbal 1 Kankin (1 Kan), the very place in that year where a Tonalamatl
ends.

The following numbers were thus obtained:--

  1,272,423     1,268,523     1,486,923.

These numbers are suppressed in the Manuscript. But if the encircled
numbers are added to them, viz:--121 (interval between XIII Akbal and IV
Kan), 17 (interval between XIII Akbal and IV Ahau), and 51,419 (= 197 × 260
+ 199; 199, however, is the interval between XIII Akbal and IV Ik), the
result is the three large numbers set down in the Manuscript, which have
the following properties:--

1) 1,272,544 = IV Kan 17 Xul (12 Muluc). This number = 13,984 × 91 = 12,236
× 104 = 3496 × 364. It also = 4894 × 260 + 104, the interval between IV
Ahau and IV Kan.

2) 1,268,540 = IV Ahau 8 Mol (1 Ix) = 4879 × 260 = 3485 × 364 = 74,620 ×
17. 17 is the interval between XIII Akbal and IV Ahau.

3) 1,538,342 = IV Ik 15 Zac (12 Muluc). It also = 5916 × 260 + 182. The
182, however, the half of the ritual year of 364 days, is the interval
between IV Ahau and IV Ik and between IV Ik and IV Kan. The fact that the
interval is the same in each case is clearly the reason for the choice of
the days IV Kan and IV Ik, which are otherwise not at all prominent.

It is remarkable that the third number is obtained by the addition of
51,419, _i.e._, of 197 × 260 + 199 (there are 199 days between XIII Akbal
and IV Ik). But it was evidently desirable to obtain as large a number as
this. On page 63 a number of nearly similar value is associated with it,
viz:--1,535,004. It is set down almost in the middle between the 13th and
14th Ahau-Katuns, for it is 57,902 days greater than 1,480,440, and 55,978
days less than 1,594,320.

Now, however, the Manuscript presents in the last column but one of page 31
a number, 2,804,100, which occupies a very unique position, since it is
nearly twice as great as all the other large numbers, with the exception of
those in the serpents. It must refer to the year 9 Muluc, and to the date
IV Ahau 13 Mol. It has many remarkable properties, for it is:--

1) = 10,785 × 260

2) = 17,975 × 156 (156 = IV Kan - IV Ahau).

3) = 35,950 × 78 (78 = IV Ik - IV Ahau and IV Kan - IV Ik).

4) = 719 × 3900. We have already met with this 3900 above. Now, however,
the 2,804,100 by virtue of its magnitude creates the suspicion that it may
be composed of two ordinary large numbers. It might be

5) 1,308,580 + 1,495,520, therefore 14,380 (91 + 104).

6) 1,380,600 + 1,423,500, therefore 3,900 (354 + 365).

That is to say, the important 3900 multiplied by the days of the lunar year
and also by those of the solar year, hence the 719, referred to under 4,
separates into these two parts. The lunar year of 354 = 6 × 29 + 6 × 30
days was not unknown to the Mayas. We shall find its half, 177 days,
several times on pages 51-58.

We might also use the two important numbers 14,040 and 18,980, the first of
which is divisible by 260 and 360, and the second by 260 and 365, without
remainder.

Then we have the large number desired:--

7) 147 × 18,980 + 14,040.

8) 200 × 14,040 - 3900.

What future student will penetrate more deeply into the meaning and purpose
of these numbers?

We might now expect to interpret also the upper right-hand corner of page
31, but here almost everything is in a deplorable state of obliteration. In
the first three of the five columns over each of the three large numbers
there was a date consisting of a numeral and a hieroglyph, but these admit
of no certain nor even probable determination.

Four hieroglyphs still remain in the fourth column, respecting which
compare my treatise "Zur Maya-Chronologie" in the Berliner Zeitschrift für
Ethnologie XXIII, pp. 141-155.

In the top sign I recognize an Imix with a prefix and probably also a
superfix. I think this denotes the period of 18,980 days.

I am forced to pass over the second entirely, inasmuch as a red 6 inserted
in it remains a mystery (6 × 18,980 = 113,880?).

As I stated in the above-named work, I think the third is three times the
sacred period of 2920, _i.e._, 8760 days.

Finally, the fourth sign certainly denotes the period of 7200 days.

Whether or not there was a fifth sign above the one now at the top is as
uncertain as the meaning of the whole.

The most remarkable thing about it is that in three other passages of this
Manuscript these three signs appear in close proximity to another. On page
61 we find the third in the 11th place in the second column, the first in
the 12th place in the same column, and the fourth in the 14th place in the
first column. Page 70 has the first sign in the middle of the 4th column;
the second somewhat lower down in the 3d column and the 4th two places
below. Finally all three signs appear in succession on the top of page 73
in the same order as on page 31.

The fifth column on page 31 may have contained another numeral belonging to
the series, the loss of which is not so serious a matter, but there may
have been one or two hieroglyphs above it, the obliteration of which is
greatly to be deplored.

Pages 32a--39a.

This is a large section extending over eight pages, which is difficult of
interpretation owing to the prevailing disorder and because a large part of
the hieroglyphs are effaced. Here, too, the principal subject is the god B,
who is represented in manifold activity. A series of numbers extends
through the entire representation. I read them as follows:--

  I 11 XII 28 I 12 XIII 26 XIII 12 XII 19 V 5 X 1 XI 20 V 12 IV 6 X 8 V 5 X
      7 IV 12 III 5 VIII 8 III 11 I.

There are thus 18 divisions, the different lengths of which reveal no rule.
They embrace 208 days, _i.e._, 2 × 104, which may well be considered as a
continuation of the computation in the preceding section, of which the 104
was so important a number. The red numbers are entirely lacking in the
beginning, then they are very slightly indicated, and finally they are
distinctly written out on pages 36-39. I assume that the scribe has set
down the 4th, 3d and 2nd numbers from the end, one too little. The last
number has been entirely omitted. I have supplied these omissions though in
a manner somewhat different from that adopted by Cyrus Thomas, "Aids," p.
28. I would note in addition that a period such as this, consisting of 208
days = 16 weeks, might be explained in an entirely different way, if there
were a column of five days at the left having a difference of 8 days; then
the whole would signify four Tonalamatls. But there is no such series of
days.

Another point of view presents itself, however. If we take cognizance of
the fact that a group of four hieroglyphs usually belongs to a picture,
then it is evident that here there are such groups not for 18, but for
about 22 subdivisions. It may, therefore, be assumed that about four
subdivisions averaging 13 days are not specified, in which case this
passage would extend not over 208, but over 260 days. The very irregularity
in the arrangement of these numbers is an argument in favor of this
hypothesis; it may be occasioned by the fact, that the pictures do not
correspond exactly to the subdivisions. For the present, however, we shall
discuss the single pictures assuming that there are 18 subdivisions.

1. Pages 32a-33a. Here at the very beginning it is uncertain whether the
signs at the end of page 32 and at the beginning of page 33 are to be
regarded as a single group of 8 hieroglyphs, as seems to follow from the
numbers, or as two groups of 4 hieroglyphs each. At the end of page 32 we
see two persons facing one another, one of whom, to be sure, is barely
visible. The other wears a head-covering like a man's silk hat, similar to
that worn by the priests on the inscriptions of Palenque. It is a
remarkable fact that of the four hieroglyphs above these figures, 1, 2 and
4 (the last probably the god C) seem to have the sign for the west as a
prefix, while the prefix of 3 (Imix) suggests the usual representation of
the tortoise head. Below the persons there is a Kan sign, the prefix of
which is also the sign for the west.

On page 33, B is represented walking and carrying the Caban sign in his
hand. The first of the four hieroglyphs is the sign for B, the second is
Imix, probably again with the sign for the west as a prefix, the third is
an Akbal sign with Kin, and the fourth is the cross-hatched sign with Kan.

2. The rest of 33a is occupied by two persons, one of whom is clad in a
gala mantle, but neither admit of further identification. They are occupied
in fishing, inasmuch as they are sitting on the shore of a body of water
and are either casting a net or drawing it in. There is a fish between them
and above it is a vessel with something apparently cooking in it. Of the 8
hieroglyphs belonging to this picture, only the following are
distinguishable:--the 1st containing an Akbal, the 3d, which is the common
cross _b_ with a 9, the 4th, an Imix also with 9, and of the 7th only the
prefix Yax. The 3d and 4th appear again on page 35a, 28 days later.

3. Page 34, like page 3, represents a human sacrifice. The victim, very
vaguely drawn, lies on a step-shaped sacrificial stone, or on the pyramid
of a teocalli. There is a Caban (earth) sign between the sacrifice and the
pyramid, and also on the walls of the buildings; the shrieking of the
victim is plainly indicated. As on page 3, there are four persons in the
form of gods surrounding the sacrifice, but here they are different ones.
The one at the left above is the black god (L?), holding the rattle-stick
(Seler, "Mittelamer. Musikinstrumente," p. 111), and at the right, above,
F, the companion of the death-god, is sitting with a rattle in his hand.
Below, the two have changed places, F is on the left and L on the right.
The former is beating the drum and the latter blowing a wind-instrument.
The sounds emitted by the two instruments are represented by drawings. This
may, therefore, be regarded as an instrumental quartette. The following
objects are also in this picture:--at the left above is a vessel the
contents of which are cooking; at the left below, another vessel with three
Kan signs, and at the right above, a Kan sign with a bird's head and below
the food known to us from pages 27b and 29b. These four objects refer to
the sacrificial feast. Lastly, at the bottom on the right there is a
ladder, probably intended for scaling the pyramid. Ten hieroglyphs in the
upper line belong to this picture:--the first, which is effaced, is
followed by a Cauac, then comes the cross _b_, then a Cimi appropriate to
the sacrifice, and lastly a head with an Akbal eye, probably D's. The first
sign in the lower row is likewise destroyed, the second sign is a Kan, the
next is the cross _b_, both having a different prefix, then here too is the
hieroglyph of B with Yax as a prefix, and the last is an unknown sign.

4 and 5. Page 35a. According to the numbers there are two sections here,
but neither the pictures nor the hieroglyphs can with certainty be assigned
to either. On the left is a house in which C sits holding a Kan sign in his
hand; on the roof, as if guarding him, and also holding a Kan sign, lies
the god B. In the Cort. 24b-25b, there are six gods lying on houses, within
which other gods are also represented in a recumbent position. Then follow
two vessels, again denoting the sacrificial feast, the contents of which
are probably cooking, and which, from the sign on the second, are probably
liquid. Above these are three others, one with the Cimi sign (human
flesh?), one with a bird and the third with the haunch of venison. At the
right of these is an implement, which is unfamiliar to me and is similar to
that held in the god's hand on pages 5c and 6c. And quite on the right sits
B with foot-prints pictured below him and on his clothing.

The hieroglyphs on page 35, when they were all legible, numbered 14 and
were arranged in two rows. 4 of the upper row are preserved, the lower part
of the first is a year-sign (?), similar to that which often appears on
pages 25-28, the upper element is the cross, and the prefix is the one
resembling a leaf, which occurs so frequently. The second sign is an Imix
with a prefixed 9, the third a cross and the fourth a head (probably D's)
with Akbal. In the second row there is a cross with a prefixed 9 (sign of
the second or third month?). These two signs with the prefixed 9 are
perhaps to be read as a calendar date IX Imix 9 Zip (1 Ix), as on page 33a.
Ix, however, belongs to the west, which is the predominant cardinal point
from 32a onward. The second sign is a compound of Kin and Akbal (day and
night) which often occurs here, the third is the compound of the Moan and
Caban signs with the number 1 above each, and the fourth is the hieroglyph
of B. The fifth sign is unfamiliar to me. The sixth contains an Imix with
the sign for the west as a prefix, and the seventh is effaced.

At this point the representations begin to display a more orderly
arrangement.

6. Page 36a. Here the head of B forms the head of a serpent (cf. pages 61
and 62) represented in pouring rain, while on page 35b it is emerging from
the water. Of the four hieroglyphs 1 and 2 are entirely and 3 for the most
part destroyed, and 4 is the usual Kan-Imix.

7. The lightning-beast with flames pouring forth from his forepaws and
tail, is plunging down from the rectangle, which primarily designates stars
and then the sky in general. This rectangle occurs for the first time here,
but will often be met with later. Here it may be a combination of Mars and
Venus. Of the four hieroglyphs, 1 is effaced, 2 is a compound of Kan and
Kin, 3 a head with Akbal and Kin (D?) with the uplifted arm as a prefix,
and 4, corresponding with the picture, is the compound of the rain sign
Cauac with the prefix of the storm-god K.

8. Here B himself is the bringer of lightning. In one hand he holds a
burning torch and flames are bursting from his carrying-frame. The third
hieroglyph is his sign. It is doubtful whether the fourth is the hatchet
(machete) or is not rather intended for an ear pierced for the purpose of
ritual blood-letting, as on pages 44b and 45b; the first and second signs
are rather indistinct.

9. Page 37a. Unless I am entirely mistaken, B is here represented with his
arms bound behind his back. Cf. the pictures on page 2, top, and 60,
bottom. Are the ends of the rope fluttering in front of the god intended to
render this still more plain? Hieroglyph 1 contains the sign _t_, which
resembles, but is not the same as, the year sign. This sign has already
occurred frequently, especially on pages 25a-28a, and the last time on page
35 in the first hieroglyph. As on page 35, hieroglyph 4 is the compound
Kin-Cauac, but here it is joined to the year-sign, _i.e._, it denotes the
Kin-Cauac year, just as it does on page 26a. 3 is again Cauac and 2 is the
hieroglyph for B.

10. Rain is falling from the heavenly shield, already seen on page 36, here
however designating different planets (Mars and Mercury?) and the figure
represented in the rain is the one which we have already seen on pages 12c,
17a and 21c. It is that of the old Uayeyab god N with a hatchet in one hand
and an unfamiliar object in the other like the one on page 39a, and with
another unknown object on his back shaped like a shield marked with a Kin.
That this figure is really meant to represent N follows from the fourth
hieroglyph (which, however, is not his regular sign 5 Zac), which is
repeated on the head of the figure. The lower part of the hieroglyph is
replaced by the year-sign just as it is in the hieroglyph on page 47, left,
middle. The third hieroglyph contains 2 Caban signs, the first and second
cannot be clearly identified.

11. This is a deity which I hardly think appears elsewhere. It has an
animal's head resembling that of a bear, thus recalling page 7a, and it
also has the paws of a bear. Of the hieroglyphs only a Kin-Akbal is
recognizable.

12. Page 38a. Here we have another heavenly shield (Mars and Venus?) and
under this shield B is represented seated and strangely enough facing
himself, the figures not being back to back as on page 68a. Hieroglyphs 1
to 3 are wholly and 4, which is a head, is for the most part destroyed.

13. B is here represented in very close connection with a female figure.
Cf. pages 21c-23c. The representation on page 68b is a still closer
parallel to this passage. The first hieroglyph is destroyed for the most
part, the second is B, the third is probably only a determinative of the
latter, but has the sign for the west, and the fourth is Kan-Imix.

14. B holding a Kan sign is sitting on an object, which may be meant for
the stone on which the idols were set up at the change of the year. Of the
hieroglyphs the third is again B, and the fourth is probably the frequent
sign a. The first sign is the most remarkable. In the Zeitschrift für
Ethnologie, Vol. XXIII, p. 147, I stated that this was the sign for the
change of the year, which is its meaning on pages 41b, 52b and 68a. The Kan
year follows here after the Cauac year of page 37. The prefix of the sign
is the hieroglyph for the east to which the Kan years belong. The Kan sign
in B's hand also corresponds to this. The second hieroglyph is destroyed.

15. Page 39. The picture represents the lightning-beast with two flaming
torches walking under the heavenly shield (Mercury and Jupiter?). Of the
hieroglyphs the third belongs to B, the fourth has as a prefix the sign of
the storm-god K, but otherwise admits as little of determination as do the
first and second.

16. Here we see B in the rain holding in one hand a machete, and in the
other a strange implement similar to that on page 37a. Of the hieroglyphs
the second was the god's sign, the third is _a_, and the fourth may be an
Akbal sign with Kin. The first sign somewhat suggests the sign for the
Moan; its prefix is curious.

17. Here in place of the picture and the superscription, owing perhaps to
lack of space and in order not to omit the last picture, we have a vertical
row of seven hieroglyphs interrupted between the sixth and seventh by the
red and black numeral belonging here. The top sign is effaced and the
second is B's. I will not venture to determine the third, which contains a
Yax. Could it belong to the serpent deity H? The fourth is probably
Kan-Imix and the fifth is indistinct. And the same is true of the sixth,
the prefix of which we have already met with as the sixteenth hieroglyph on
page 24, and shall meet with again on pages 53, 56, 58, 61, etc. The
seventh sign, which is quite at the bottom, consists of a vessel with a
foot-print beneath it; it seems to be in the place of the picture.

18. The entire section ends with a picture of B, who carries the hatchet
and probably the copal pouch. The hieroglyphs are wholly obliterated.

Pages 40a--41a.

The following Tonalamatl, one of the form of 10 × 26, has suffered much
from the carelessness of the scribe and from injury. I have attempted to
restore it as follows:--

  X         X  7  IV  4  VIII  4  XII  2  I  1  II  8  X
  Ahau      Oc
  Cimi      Cib
  Eb        Ik
  Ezanab    Lamat
  Kan       Ix.

The first row should be read from top to bottom, and then the second in the
same order.

The six subdivisions all refer to some activity of B. Among the 6 × 4
hieroglyphs his sign occurs five times as the fourth and only in the last
group as the third. Let us now examine the six groups individually.

1. B is traversing the water in a canoe, as on pages 29c and 40c, with the
paddle in his hand. All the hieroglyphs belonging to him are obliterated.

2. B is sitting on the laterally elongated head _q_, which here, as on page
69, is enlarged and drawn with special care. Seler ("Charakter der
aztekischen, etc. Handschrift" in the Zeitschrift für Ethnologie, 1888, p.
83) discusses this sign in connection with the day Men. It seems to me to
denote unlucky days, the influence of which may here be checked by B. B
holds in his hand a hatchet. The head (_q_) is repeated in the third sign,
perhaps also in the second, and the superfix of these two signs is probably
the same as that of the sign beneath the picture of B. The first sign is
mostly destroyed.

3. As on pages 30a and 31c, and again just as on page 69a, B is sitting on
the tree of life or sacrificial tree. A branch of this, which he grasps in
one hand, ends in a serpent-head, and the root of the tree also represents
B's head. Around the god's head are again the familiar dots, probably
signifying stars. Of the hieroglyphs, the first is probably _f_, the second
is destroyed, the third may be a variant of _a_, although it recalls the
sign which, I believe, has the meaning of 73 days on pages 46-50; the
prefix of 1 also suggests this meaning.

4. B's head is again surrounded by stars and he holds in one hand the
outline of a hieroglyph. He is sitting on a peculiar ornamented structure
resembling the crenelations of a wall. This wall displays the spiral which
we found also on pages 33b-35b, and which in the treatise, "Zur
Maya-Chronologie" (Zeitschrift für Ethnologie XXIII, p. 147), I regarded as
an abbreviation for a serpent and hence as a symbol of time. It is further
to be noted that B is wet with rain and with this the third hieroglyph is
in keeping, if it is actually intended to denote the rainy season and not
the week of 13 days ("Zur Entzifferung" V, 6); still the red numeral 13
below is more in keeping with the second meaning. The second sign is an
Ahau with the leaf-shaped prefix, which also appears in the first sign of
the third group. The first is effaced.

5. B, represented with a gala mantle hanging down in front and with the
copal pouch, is sitting on a head, which looks like his own, especially as
to the eyes, but which notwithstanding probably belongs to D and is marked
with Ik (wind) and Cauac (cumulus clouds). Of the hieroglyphs the first and
second do not admit of positive identification, and the third is Kan-Imix.

6. The god is sitting on a mat in a house. All the hieroglyphs except his
own are obliterated.

Pages 42a--44a.

Another Tonalamatl of the form of 10 × 26; I have restored the effaced
day-signs as follows:--

  XIII     XIII 3 III 2 V 2 VII 6 XIII 2 II 2 IV 2 VI 7 XIII
  Oc       Cib
  Ik       Lamat
  Ix       Ahau
  Cimi     Eb
  Ezanab   Kan.

Thus the month days are the same as in the preceding Tonalamatl, but should
be read in a different order:--Oc, Cib, Ik, Lamat, etc.

Here each of the 8 subdivisions has 6 hieroglyphs, and the order is as
follows:--

  1  2
  3  4
  5  6.

A few of these signs are common to all the groups. Thus the first sign
(_v_), as far as what remains is distinguishable, seems to occur in all the
groups. It has the leaf-shaped prefix, but I cannot understand the rest of
it; we shall find it again several times on pages 29c-41c.

Again the sign in the sixth place, as far as we can see, is always the head
without an underjaw and the tuft of hair tied up on top of it (O, according
to Schellhas), which we found above on page 25 and which we shall meet
again on pages 65-69 no less than 13 times, with regular intervals of 6
signs between them. Indeed that passage is a remarkable parallel to this
one.

That the sign for B, who here too plays the most important part, occurs
often, is self-evident. It appears in the fourth place, in the 1st, 3d,
4th, and 7th groups, and in the third of the 8th group; in the 6th group it
is destroyed. In the 2nd and 5th groups B has neither picture nor sign.

The hieroglyphs of the cardinal points I shall mention in connection with
the separate groups. They are especially conspicuous in this section, being
sometimes represented in full and sometimes in an abbreviated form as mere
prefixes.

1. B with arms crossed sits above a serpent denoting time, and holding in
its coils the cross _b_, which so often refers to astronomical conditions.
Above the head of the serpent is the vessel with the three Kan signs, which
we have already found several times on pages 25-28. It is remarkable that
the flourish, which usually appears as the nose-ornament of the sun-god G
(_e.g._, pages 11b and c), is added to these Kan signs. As the stars are
again indicated on B's head, he plainly denotes a time-god here. The third
hieroglyph, the sign of the east, corresponds with this meaning, and the
Kan sign, which we see in the fifth hieroglyph probably combined with Ahau,
also belongs to the east; the prefix of the fourth hieroglyph is the sign
for the west.

2. A deity whom we shall probably have to call F, the god of human
sacrifice, is sitting on a stepped pyramidal structure (a teocalli as a
place of sacrifice?). He holds something in his hands, resembling a long
and broad scroll, joined to which is the head of the god of the north, C,
and in the third hieroglyph of this group the sign for the north also
appears, prefixed to the head of F, who seems to be repeated in the fourth
hieroglyph. The fifth hieroglyph with an Imix is unintelligible to me.

3. Page 43. B is sitting in the water, the copal pouch hangs from his neck
and the hatchet is raised as if ready to attack. The second hieroglyph
clearly denotes water, while the third is the sign for the west and the
fourth is the sign for B, its prefix being the sign for the east
abbreviated; the order of the cardinal points is thus exactly the reverse
of that in the first group. The fifth hieroglyph is not clear to me, but it
appears to be repeated in the same place in the next group.

4. B is sitting here astride a sort of bench again holding the hatchet in
his hand. Belonging to this picture in the third hieroglyph is the sign for
the south, which is repeated in an abbreviated form in the fourth
hieroglyph.

The fifth is Kan, joined to what appears to be the same sign as the one
found in this place in the preceding group. The second sign is indistinct.

5. This is an aged deity, probably M according to Schellhas, seated on an
indefinite object. In front of the deity is a Cauac sign, which contains
exactly the same cumulus clouds as those in the sign 5 Zac, which belongs
to N. Cauac, however, belongs to the south, and therefore corresponds with
the north of the second group on page 42. Sign 5, a Kan, corresponds
exactly with the same sign in the fifth place of the preceding group.

6. Page 44. B seems to be in a state of collapse. Behind him is a second
person, who is either trying to support him or to pull him up by some kind
of a sling. I think the second person is E, the grain-deity, if it is not
Seler's young god. If the hieroglyphs were not completely effaced, they
would probably shed some light on this interesting passage.

7. Here we see B, holding a fish in his hand, and sitting on a hieroglyph,
which is compounded of Imix and a prefix, which resembles the tortoise head
and which appeared once before in this combination on page 32a. This
passage recalls page 40a, where B is seated on the laterally elongated head
_q_. Nothing more can be said of the hieroglyphs, than that 6 is the head
without an underjaw.

8. B is sitting here in a house; his sign in the third place has Yax as a
prefix. Hieroglyph 5, with the number 4 prefixed, recalls the one which we
found on page 21c belonging to the baldheaded old man. Hieroglyph 4 is the
common Kan-Imix.

Page 45a.

The last page on the front of the first section of this Manuscript is used
for a series, which presents itself as a second improved edition of the
series which was found on pages 31a-32a. The very fact that the writing is
so much better proclaims it an amendment. The chief aim of both series is
the same, viz:--to bring into unison the numbers 91, 104, 260 and 364. But
the two series gain this end by different means. On page 32 the series
begins with 91, and at first has only 91 as a difference, until with 728 a
multiple of 104 and 364 is obtained, then it returns to the simple
difference 91, in 1456 it obtains again the 104 and 364, loses these two
last numbers once more in 1820 and finally in 3640 obtains the desired
multiple of all four numbers, which is retained in 7280, 14,560, 21,840 and
29,120. The series on page 45a proceeds much more briefly. It begins at
once with 728 (91, 104, 364), loses the 104 in 1092, gains the 260 and
loses the 104 in 1820, arrives at divisibility by all four numbers in the
3640, loses the 104 again in 5460, but then comes to a standstill after
having obtained the same multiples (double at that) of 3640, which I
mentioned just now in the preceding series. Indeed it can be seen from what
is legible in the third column above, that the series went still further.
But so much is obliterated that I have obtained the numbers 14,560 and
21,840 in both series only by conjecture.

In the earlier passage the starting-point of the series is the day XIII
Akbal and in the one before us it is the day XIII Oc. In the former the
days specified were 91 days apart from each other, and here they are
separated by 104, _i.e._, XIII Ezanab, XIII Ik, XIII Cimi, XIII Oc.

The initial days of the two series, XIII Oc-XIII Akbal, are separated by 13
days, and the reversed series, XIII Akbal-XIII Oc, by 247 days. Hence the
subject of both passages is essentially the week of thirteen days, _i.e._,
the year of 364 (28 × 13) days.

Now this series is also accompanied by a number amounting to millions. It
is in the second column of page 45; only, in order to understand it, we
must add a zero as the bottom figure; then it becomes 1,278,420. XIII Oc
stands below this number as the beginning of the series. The first column
has 30 as an encircled number and below it the normal day IV Ahau.

The large number must have been formed as follows:--

The point of departure was 230, the interval between IV Ahau and XIII Oc,
to this was added 98 × 260 = 25,480, the sum being 25,710. The result of
this number added to 11 Ahau-Katuns = 1,252,680, was 1,278,390, which
number is not revealed in the Manuscript. It is concealed in XIII Oc 3 Mol
(2 Muluc). But 1,278,390 = 42,613 × 30, _i.e._, it is divisible by the
interval XIII Oc-IV Ahau.

Now if we add to this large number the 30 set down in the Manuscript, the
result will be the above-mentioned 1,278,420. This number in the Manuscript
has the date IV Ahau 13 Chen. (2 Muluc). It is, of course, divisible by 30
and by 260, hence = 42,614 × 30 and 4917 × 260. It corresponds not merely
in this respect with the largest number on page 31a, viz:--2,804,100, but
also with regard to its divisibility by 78, 156, 195, which are all
multiples of 13.

On page 45a, top left, there were doubtless five hieroglyphs, of which the
two topmost ones are effaced. First we see only the sign of the eleventh or
twelfth month, Zac or Ceh, with an uncertain number prefixed, then the
signs for beginning and end are distinctly legible. Ceh begins and Zac ends
the year of 364 days; see page 4 of my treatise "Zur Entzifferung V."

Pages 29b--30b.

We come now to the middle section of pages 29-45, in which we shall not be
so hampered by obliteration in our attempts at interpretation, as we were
in the upper section.

We have here first a Tonalamatl of the usual kind, arranged as follows:--

  III  13  III  13  III  13  III  13  III
  Ix
  Cimi
  Ezanab
  Oc
  Ik.

That is to say, the 52 days divided into four equal parts.

To these four divisions, as on page 23b, belong the four usual forms of
animal food, which are joined in three places to Kan (bread) and probably
denote sacrifice. They are, first a mammal, which, however, is erroneously
represented by a fish; second, a fish, third an iguana and lastly a bird. I
would add, that in the hieroglyphs above, the east, north, west and south
correspond in turn with these representations of food.

The hieroglyphs are arranged as follows:--

  1  2    5  6     9  10    13  14
  3  4    7  8    11  12    15  16.

Of these, 2, 6, 10 and 14 are the cardinal points just mentioned; 4, 8, 12
and 16 are the sign for B, and 1, 5, 9 and 13 are the head with the tuft of
hair and the Akbal eye to which I attribute the meaning of _beginning_.
Likewise the remaining four signs, 3, 7, 11 and 15, although they are not
exactly alike, have something in common, the 15th being a distinct Imix;
they are not yet wholly intelligible to me.

Four pictures of B belong to these hieroglyphs. In the first the god is
seated with crossed arms on two of the ordinary astronomical signs (Jupiter
and Mars?). In the second, where he is pointing forward with his hand,
there are footprints on his seat, as, for example, on page 35a. In the
third the seat contains the usual cumulus clouds in clusters. Finally, in
the fourth, he is seated on the tree of life or of sacrifice, the hatchet
is in his hand and he is clad in the gala mantle; cf. pages 31c, 40a, 69a.

Pages 30b--31b.

This passage is in some respects closely related to the preceding
Tonalamatl, but in other respects it differs significantly from this and
from what is usual, for the Tonalamatl is divided here into only four
principal divisions of 65 days each, which begin very regularly with the
days VIII Oc, VIII Men, VIII Ahau and VIII Chicchan. There are neither
subdivisions nor the usual pictures belonging to them. But on the other
hand each of the longer periods of time written down here have eight
hieroglyphs for each section in the usual order.

B's sign occupies the places 6, 4, 4 and 4; from this it follows that here
too he forms the principal subject.

Here, as in the preceding Tonalamatl, the first place in each group
contains the sign denoting beginning, while the eighth sign is invariably
the head without an underjaw, which seems to me to refer to _fasting_, as
if a fast-day fell at the end of every 65 days.

In the fifth place we see in succession the four animals, which in the
preceding Tonalamatl are not included in the groups of hieroglyphs. Here
they stand in the order of mammal, bird, amphibian and fish, but the bird
in the second group is replaced by the sign which usually occurs with the
dog (lightning-beast).

The signs in the second place are those of the cardinal points, and they
are given in the same order as in the preceding Tonalamatl, _i.e._, east,
north, west and south, so that they do not belong to the same animals as
they do there.

The third signs are the cardinal points again, but in the abbreviated form
discovered first by Schellhas, and in a different order:--west, north, east
and south, and always joined to the head of C around which everything
revolves as around the polar star. The Kan sign with different accompanying
signs occupies the seventh place in the first group, and the sixth in the
other three.

Four signs still remain:--the fourth of the first group I am inclined to
consider the abbreviated sign for the sun; the seventh of the second, rain
with the sign for the west as a prefix; the seventh of the third, Caban,
ground, with the sign for the east as a prefix; the seventh of the fourth
is Kan with the Yax sign above it, probably denoting the vegetable kingdom.

Pages 31b--35b.

This entire passage is devoted to a single Tonalamatl, which is divided and
written out in an unusual manner. Like the preceding it is divided into
four parts of 65 days each, but the remarkable thing about it is that these
divisions of 65 days are each subdivided into two periods of 46 and 19
days, and the 46 days again into eight unequal parts, which are exactly the
same each time, while the 19 days run their course without further
subdivision. On pages 33, 34 and 35 this 19 is always on the left at the
bottom, on page 32 it is wanting, probably because it was self-evident and
there was no suitable place for it.

We shall next discuss the division of these four periods of 46 days each.
This division is indicated with especial exactness on these pages, since
not merely the length of the separate divisions and the week days are
specified, but also the month days. This representation has the additional
peculiarity, that the two columns on each page must be read from bottom to
top, and of each group of two days standing side by side, the one on the
right is to be read first and then the one on the left. If the Tonalamatl
were written in the usual manner, it would have the following form:--

  X  9  VI  9  II  9  XI  2  XIII  4  IV  9  XIII  4  IV  19  X
  Ben
  Ezanab
  Akbal
  Lamat.

Instead of this we read in greater detail as follows (the pages and the
stated _length_ of time are in parentheses):--

  (31) X Ben (9)     VI Ik (9)     II Chuen (9)  XI Ahau (2)
         XIII Ik (4)     IV Cimi (9)   XIII Men (4)       IV Cauac (19).
  (32) X Ezanab (9)  VI Manik (9)  II Cib (9)    XI Chicchan (2)
         XIII Manik (4)  IV Chuen (9)  XIII Ahau (4)      IV Kan (19).
  (33) X Akbal (9)   VI Eb (9)     II Imix (9)   XI Oc (2)
         XIII Eb (4)     IV Cib (9)    XIII Chicchan (4)  IV Muluc (19).
  (34) X Lamat (9)   VI Caban (9)  II Cimi (9)   XI Men (2)
         XIII Caban (4)  IV Imix (9)   XIII Oc (4)        IV Ix (19).

In spite of the seemingly wholly irregular division of time, the following
relation, which is certainly not accidental, results from this
arrangement:--the first of the eight members of each row is one of the days
which may begin the year and the months, and the eighth, on the other hand,
one of the four regents of the year. The remaining six members are the
remaining 12 of the 20 days repeated twice and the second always
corresponds with the fifth of its own series, and the third to the sixth
and the fourth to the seventh of the following series.

Two pictures of god B belong to each of these periods of 65 days, the first
of these pictures referring to the divided period of 46 days and the second
to the undivided one of 19. It is also in agreement with this that on pages
61 and 62 the fourth, sixth and eighth pictures represent the god as rising
from the jaws of a serpent--the serpent being represented each time as
lying in water which invariably contains the number 19.

As the hieroglyphs belonging to the periods of 46 days are allied to one
another, and as this is also true of those belonging to the periods of 19
days, I will first consider the hieroglyphs of the first period by
themselves, then those of the second, and the pictures shall be treated in
the same manner.

Therefore, let us first examine the four pictures (1, 3, 5 and 7) on the
right side of the pages:--

1. The first page shows the god walking with the official staff in his
right hand, in his left the hatchet raised for a blow and with the copal
pouch hanging from his neck.

2. He is walking and holding a flaming torch reversed in his right hand, in
his left the hatchet is raised aloft, the pouch hangs from his neck, the
mantle is indicated and around his head are the little circles which are so
frequently his adjuncts and probably signify stars.

3. He is walking and holding the reversed torch in his left hand and the
hatchet in his right.

4. He is walking and holding a torch in each hand. He wears on his head the
head of K. He seems to be bringing storm and fire.

Now let us examine the hieroglyphs, which I have numbered thus:--

  1  3  5
  2  4  6.

The first hieroglyph on each page certainly represents one of the cardinal
points. They are in the usual order:--east, north, south and west.

2 is the same sign on each page. I take it to be the sign for Xul = end,
denoting, it may be, the end of the period of each cardinal point.

In each group 3 is the head with tuft of hair and the Akbal eye; probably
the sign denoting _beginning_. This beginning and end occur most distinctly
repeated on page 63, and the end alone eight times at the bottom of pages
61-62.

On page 31, 4 is B's sign, on page 32 B's with the prefix of the north, on
page 33 it is B's sign again and although quite indistinct its is plainly
joined with the east. On page 34 there is another indistinct sign which may
be that of the serpent deity H.

Owing to indistinctness I do not venture to determine the fifth sign on
pages 31 and 33; on page 32 it is the laterally elongated head _q_ with the
Ben-Ik superfix, and on page 34 the ordinary Kan-Imix.

The sixth sign varies as much as the fifth; it seems here to denote four
different gods, perhaps the four given on pages 25-28. On page 31 it is a
Cauac, the prefix of which here, however, suggests K, on 32 it is certainly
the hieroglyph of E and on 33 possibly of A, on 34 it most resembles Muluc
of the day-signs, but also suggests the line crossing F's face from top to
bottom.

We come now to the four pictures 2, 4, 6 and 8 and to the hieroglyphs
belonging to them, which are on the left side of the pages and belong to
the periods of 19 days.

1. B is pictured walking, raising the hatchet in his right hand, and
holding an uncertain object in his left; the serpent with the 19 set down
in its coils does not appear here. The 2nd, 3d and 4th pictures belong
together. In each picture on these three pages there is a serpent with
water in its coils and the number 19 in the water, denoting the number of
days belonging here. As on pages 61 and 62 B is emerging from the open jaws
of the serpent. In each case he is brandishing the uplifted axe in his left
hand. The difference in the three pictures consists, first, in the fact
that only in the 2nd and 3d B wears the copal pouch, second, that only in
the 3d and 4th he has an implement in his right hand (the two implements
differ somewhat but are both, apparently, adapted for hanging up) and
third, that only in 3 the whole picture is painted blue, which means that
the entire scene is enacted under water.

The hieroglyphs are as follows:--

The first in all four cases is a Manik, _i.e._, originally a grasping hand,
perhaps referring to the chase; on page 32 it has a prefix and on pages
33-35 a superfix corresponding to the first.

The second sign on each page is simply B's.

The Cauac sign in the third refers in all four cases to the water
represented at the bottom of pages 33b-35b. On page 32 it has an Akbal as a
superfix, on 33-35 a prefix, which is familiar and in keeping with the sign
and probably also the same suffix, though it is indistinct on page 34.

The fourth sign shows, as do several other things, that the representation
on page 32 differs from that on pages 33-35. On the first of these pages we
see an Imix with a puzzling 1 prefixed. If the numbering of the days really
begins with Kan, as is probable in this Manuscript, then Imix is the 18th
day and 1 + 18 might denote the 19, which is not set down here. On pages
33-35 this sign contains the spiral, which refers to the serpent in the
picture below (and probably therefore to time). A curious element, however,
is the numeral 9 prefixed three times to the spiral. This number is rarely
a prefix, but it occurs, for example, on pages 33a and 35a before the cross
_b_ and on page 60 right, middle, prefixed to Xul (= end). The interval 9
occurs in this Tonalamatl 16 times, including therefore 117 of the 260
days.

The fifth sign each time contains the head without the under jaw, just as
it recurs regularly in the preceding passage, pages 30-31.

The sixth sign in each group is the not uncommon compound of Caban and the
sign, which resembles Muluc and which we saw before in the sixth place
among the hieroglyphs on the right side of page 34.

Pages 35b--37b.

  I  11  XII  6  V  9  I  4  V  7  XII  9  VIII  6  I
  Caban
  Muluc
  Imix
  Ben
  Chicchan.

That is, a regular Tonalamatl of five parts, 5 × 52. That the 52 days are
divided into two halves (11 + 6 + 9 = 4 + 7 + 9 + 6), may only be
accidental.

I will designate the hieroglyphs of the seven divisions thus:--

  1  2  |  5  6   9  10  13  14  |  17  18  21  22  25  26
  3  4  |  7  8  11  12  15  16  |  19  20  23  24  27  28.

I will first consider those signs, which are repeated and by means of which
the sections seem to be brought into connection with one another. But I
shall attend in detail to those hieroglyphs which contain characteristic
references to each picture, when I discuss the latter.

The first place both among the pictures and among the hieroglyphs again
belongs unquestionably to B. He is plainly designated in the 10th, 17th,
21st and 26th hieroglyphs, but, for an unknown reason, C's sign is joined
to B's in the 16th, probably also in the 6th and perhaps in the 9th, and in
20 and 28 C's sign forms an integral part of a hieroglyph. Now in
discussing the great Tonalamatl, pages 4a-10a, I attempted to make it
appear probable that C belongs to the eighth day (Chuen) and in that case
the Chuen sign in the thirteenth hieroglyph may be probably set down here.
Further, in discussing pages 25 to 28, I expressed the conjecture that this
Chuen sign might simply mean eight days, if we begin with Kan as the first
day, for which proceeding there is some warrant in the "Dresdensis." Now,
in hieroglyphs 8 and 24 we find an 8 inscribed; in hieroglyph 8 it is
joined to an Imix, exactly as on page 39c; on page 65a it is joined to Kin,
and on 67a and 68a to a hand. Is it possible that here also the 8 is
intended as a sign for Chuen = C?

Then the familiar Kin-Akbal sign (day and night) is in the fourth place as
well as in the eleventh and nineteenth.

The other signs which appear but once, I will discuss in connection with
each of the seven pictures:--

1. A serpent in the water, with B emerging from its head, exactly as on
pages 36a, Tro. 26 and Cort. 10.

The third sign, that of the serpent-deity H, refers to the serpent. The
first sign is the one which I think may be Caban-Muluc, while the second,
owing to its indistinctness, eludes interpretation.

2. This also represents a deity sitting in the water, whom we are probably
safe in calling H, for the top of his head changes into a serpent, ending,
however, in a bird's bill holding a fish. The deity holds up both hands.
The union of serpent and bird should be noted in connection with the fourth
picture. The deity is represented in the fifth sign; the sixth, seventh and
eighth signs have already been discussed.

3. B is traversing the water in a boat, exactly as on pages 29c, 40a and c,
and 43c. Here, however, there is a person beside him (probably a woman)
whom, from the ninth hieroglyph we recognize as the deity E, unless this
sign is C's. In 12 we see with Kan a sign which may suggest the usual
hieroglyph denoting a year.

4. A serpent is pictured here, with a bird sitting upon it. We met with the
same bird on page 17b. Schellhas, "Maya-handschr.," p. 51, has already
expressed the opinion that this is probably a rebus for the name
Quetzalcoatl or Kukulcan, and this theory is certainly worthy of
consideration. In this connection I would call to mind that it is probably
also Kukulcan with serpent and bird who occupies the first place on page
4a. The bird appears again in the fourteenth sign, while the thirteenth is
a Chuen, which, according to the statement made above, may be connected
with the C in the sixteenth. The fifteenth sign is the cross _b_, which
probably denotes the connection between the thirteenth and sixteenth or
else between the bird and serpent. Or is Chuen intended here to represent
the serpent and not the ape?

5. This picture represents B carrying a burning torch, with the copal pouch
hanging from his neck. His left hand touches a strange object, a kind of
frame, the top of which ends in the head of a bird of prey.

The eighteenth sign is obliterated and the twentieth is a curious
combination of Caban, C and the front part of K.

6. B is walking, with the hatchet in his left hand and in his right an
object which looks like the representation of sounds issuing from musical
instruments, as on page 34a. Perhaps B is represented here as the air-god.

The twenty-second sign is the familiar Kan-Imix. The twenty-third sign
(_w_) is not intelligible to me; it occurs on pages 19c, 40b, 58, on the
right, with a superfix suggesting K.

7. Water, in which a small human being seems to be emerging from a snail
(the symbol of birth). Above the water is B, grasping a serpent which is in
the water, as if to protect the new-born being from the serpent. The
twenty-fifth (with Kin) is the so-called bat-god, who on page 50 at the
left ends the series of twenty gods. The twenty-seventh sign (with Yax) is
still undetermined.

Pages 38b--41b.

  VI 16 IX 8 IV 11 II 10 XII 1 XIII 12 XII 6 V 12 IV 11 II 11 XIII 6 VI
  Cauac
  Akbal
  Manik
  Chuen
  Men.

The sum of the black numbers is 104, the whole is, therefore, a double
Tonalamatl = 5 × 104 = 520. While the series on pages 31a-32a primarily
brought the 91 and the 104 together, and the series on page 45a
accomplished the same result with the 104 and the 364, here, though the
process is a different one, the 104 is combined with the 260 in another
number.

It is characteristic of this part of the Manuscript, that the astronomical
rectangles, which are very rare in the preceding pages, appear here in no
less than five of the eleven divisions and six of them represent showers of
rain. One is very readily, therefore, led to infer that the 104 days have
reference to the rainy season and to its dependence upon the position of
the planets. I will now analyse the eleven sections separately.

1. Rain is streaming down from two astronomical signs (Mars and Jupiter?
Day and night?) and in the rain stands a black human form, grasping an
implement with the right hand held downward and pointing upward with the
left. It has the vulture head which occurred on pages 8a and 13c.

Hieroglyphs 1 and 2 represent the sun and moon, both surrounded by half
white and half black envelopes, which must denote clouds. The third sign is
Imix, which just here might refer to the rainy season productive of
nourishment. The fourth sign is the vulture head of the picture.

2. B is walking in the rain and holds in one hand a stick pointed at the
lower end. This is doubtless a farming implement, likewise occurring
frequently in the Tro-Cort., which was used for making furrows or holes in
the ground.

The second hieroglyph is B's, the first is Caban = earth, the fourth might
be a compound of Caban and Muluc, referring to the rain, and the third is
the familiar Kan-Imix, which, as the designation of food and drink, would
be especially appropriate here.

3. B is apparently resting from tilling the soil, since he is sitting on a
support consisting of the signs just spoken of, _i.e._, Caban and Muluc
(?).

The latter signs are repeated in the second hieroglyph, while the third is
B's with the sun-glyph (?) prefixed; the first is the head apparently open
on top with the Akbal eye, probably the sign for beginning, and the fourth
is the familiar sign _a_, which I think signifies a good, auspicious day.

4. Page 39. This represents a violent shower of rain, which might be
pronounced a cloud-burst. The old red goddess with tiger-claws and a
serpent on her head is pouring water in a stream from a jug. The same
goddess occurs on page 43b and on the last page, 74.

Her hieroglyph is the second; it is more distinct in the two other
passages. The first part of the third hieroglyph is indistinct, and the
second part is the hieroglyph denoting the year. The first hieroglyph is a
head with the Akbal sign, and the fourth is the usual compound of Kin and
Akbal.

5. The cloud-burst seems to have destroyed the cultivation of the field,
for B walks forth again with the implement for tilling the soil, as in the
second picture. The second hieroglyph is B's with the prefix of the west,
therefore probably denoting sunshine, the first again contains Caban and
Muluc and the fourth is Kan-Imix referring again to the produce of the
field. I shall not venture to explain the third sign here any more than I
did in the previous passages. Compare page 8b.

6. B is again sitting in the rain and under the same astronomical signs as
before on page 38. He is pointing downward (to the sprouting seed?). He has
the sun-glyph on his back. The first two hieroglyphs are unfamiliar to me
(Yax); the third is Imix with the sign for the west, and the fourth is
again Muluc.

7. Page 40. B is plunging down headfirst from the same astronomical signs
and is brandishing the hatchet.

Hieroglyph 1 is the cross _b_, 2 is B's sign, 3 probably that of the
grain-god E, and 4 being Kan-Imix refers to grain. Favorable weather seems
to have set in.

8. The astronomical signs are not the same as those in the three preceding
instances (Mercury and sun?). Below them is a deity with tortoise-head--in
my opinion, the sign for the longest day--holding a torch in each hand and
thus referring to the heat.

Hieroglyph 1 (_w_) with the superfix suggesting K still puzzles me. 2 is
the cross _b_, 3 is the tortoise-head with the number 4, which probably
refers to the Kan, Muluc, Ix and Cauac years, as the 4 sometimes appears
prefixed to N's hieroglyph. In exactly the same way the tortoise-head with
the tortoise itself occurs frequently in the Cortesianus. 4 is the sign of
the year with prefixed Kin and Cauac, _i.e._, day-Cauac-year.

9. A thunder-storm, which is very appropriate after the longest day. The
lightning-beast, likewise holding a burning torch, is plunging down from
the astronomical signs, which are different ones again (Venus and the
moon?).

The second hieroglyph contains the sign of the dog together with the cross
_b_, while the third is that of the north-god C, and the fourth is Muluc. I
cannot explain the first sign; its prefix, which rarely occurs, appears
also on pages 23b, 25a, 37b, 63a, and possibly on pages 53b, 62-63a, 69b.

10. Page 41. Another representation of rain. There is an old deity in the
rain, who is N rather than F, denoting the end of the old year. He is
emerging from a snail (cf. with this page 37b), and is pointing upward; a
part of the first hieroglyph is on his head.

This first hieroglyph recalls the sign which, in the Zeitschrift für
Ethnologie, XXIII, p. 145, I ventured to connect with the change of the
year; but it also suggests the snail pictured below, hence the birth of the
new year. The beginning of the year for the Mayas, although of course not
for all parts of the country, is fixed, as a rule, to fall on the 16th of
July. This would agree admirably with the eighth and ninth sections, which
represent the time of the longest day and of thunder-storms.

The second hieroglyph is B's, the fourth the cross _b_, probably referring
here to a union of two years, and the third with its Cauac to the duration
of the rainy season or to the god N.

11. The rain seems to fall with less violence. B is seated, clad in the
gala mantle with a Kan on his head, as the sign of grain. His headdress
also strongly recalls that of the grain-deity E (which is also the case of
the headdress on the preceding picture.)

Hieroglyph 1, the upper part of which is very like that of the first sign
of the preceding group, looks like a plaited mat. Does it not suggest that
the name of the first month of the new year is Pop and that this word is
denoted by carpet, mat? Hieroglyph 2 is B's, 3 is the sun between a dark
and a bright sky, and 4 is the common Kin-Akbal, day and night.

If the seventh picture really refers to the beginning of the year, then the
entire period of 104 days extends from April 15th to August 2nd, which,
with the addition of the five days not counted at the end of the year, does
indeed make 109 days. All this, however, is only true on the supposition
that I have not seen more in these representations than they contain.

Pages 41b--43b.

  VI  12  V  7  XII  6  V  21  XIII  6  VI.
  Caban
  Muluc
  Imix
  Ben
  Chicchan.

Another regular Tonalamatl, and like the preceding one apparently referring
to the change of the year, the tilling of the soil and the rainy season.
B's sign is regularly repeated in the second place of all five groups of
hieroglyphs, and moreover each of these groups has six signs. The head with
the missing under jaw is in the fourth place of groups 2 and 3, in the
sixth of group 5 and might perhaps be intended also in the fourth of 1 and
4. The usual Kan-Imix is in the third sign of group 2, in the fifth of 4,
and the fourth of 5; possibly also in the fifth of 1; the third hieroglyph
in group 3, at any rate, contains Imix.

Let us now consider the five groups individually:--

1. The rainy season seems to have been delayed; the beginning of the year
draws near. B is kneeling on a kind of footstool, the hatchet is in his
right hand and his left hand holds a kind of chisel with which he is
carving something out of the trunk of a tree. The purpose of the work is
indicated by the god's own head directly below (probably placed in front of
the tree as a model?). No doubt this is intended to represent the making of
the statue of the god of the new year destined for the beginning of the
year, as we know it from pages 25-28.

Corresponding with this is the first hieroglyph denoting the year with Yax
as a superfix, and also the sixth being the sign to which in the article in
the Zeitschrift für Ethnologie cited above, I attributed the meaning of
change of the year. I cannot decide whether the third sign is intended for
an Imix-Chuen with the sign of the south as a superfix, the fifth for a
Kan-Imix and the fourth for the head without the under jaw.

2. Page 42. Prayer for rain. B (that is to say, his priest) is seated
apparently on the same footstool. He is gazing upward and presenting a
vessel containing an offering, the nature of which is uncertain. The vessel
ends in a tube; cf. page 67b.

The first, fifth and sixth hieroglyphs are not finished, and the third is
Kan-Imix.

3. The rain-goddess promises aid. B is seated opposite the old red goddess,
who is holding intercourse with him. The god is seated on the Caban sign
(earth) and the goddess on Muluc (rain?).

The first, fifth and sixth hieroglyphs are also unfinished; the third is
Imix with its meaning intensified by the prefixed Yax (the luxuriantly
growing grain?).

4. B is again tilling the ground in the manner already familiar to us.
Under him lies his own head with the Imix-Kan sign, denoting food and
drink, as a superfix. The first hieroglyph is the sign of the eighteenth
month Cumhu, _i.e._, of the end of the year. The third is a Kin-Akbal, the
fifth a Kan-Imix, the sixth is not finished, and the fourth may be intended
for the head without the lower jaw, but it is carelessly drawn.

5. Page 43. The solicited rain begins. The goddess with the serpent on her
head is pouring streams of water from her vessel.

The first hieroglyph repeats the month Cumhu, denoting the beginning of
rain, before the close of the year; the third is the sign of the goddess
met with on page 39b, here also with the sign for the west as a prefix; the
fifth is her determinative, the serpent, and the fourth is Kan-Imix.

If the first sign in the first group is not regarded as the sign of the
year, but as that of the sixteenth month (Pax) resembling it, and the fact
is taken into consideration that there is an interval of 34 days between
the second and fourth groups and of 40 days between the second and fifth,
this would be found to correspond with the interval between the months Pax
and Cumhu.

Pages 43b--44b.

This is the fourth and last series of the first part of the Manuscript; the
first is on page 24, the second on pages 31a to 32a, and the third on page
45a. The first series is quite by itself, but the second and third are
similar in form to this fourth, though their initial days are different
from those of the latter:--XIII Akbal, XIII Oc and III Lamat. All three
begin with differences which are divisible by 13:--91, 104 and 78, equal to
7, 8, and 6 × 13. All three aim and arrive at numbers which are common
factors of 260, 104 and 364, and therefore also of 3640, which last number
is written out in the other two series, while in this series it can only
appear later on and then, increased by multiplication.

Since this series has the difference 78, the week day numbers remain the
same, while those of the month days must advance by 18 each, that is, from
the hidden starting-point III Lamat they go on to III Cimi, III Kan, III
Ik, III Ahau, etc., until the tenth member of the series is 10 × 78,
_i.e._, 3 × 260 and thus comes again to the day III Lamat.

From 780 onward this number is itself always the difference of the higher
terms of the present series. At the same time 780 days are the duration of
the apparent revolution of Mars, which is here supplementary, as it were,
since page 24 treated of the revolutions of the sun and of Venus, and also
of those of the moon and of Mercury. Hence in the present passage we find
the numbers 1560, 2340, 3120 and 3900, always accompanied by the day III
Lamat. The larger numbers require a few corrections; I read them 13,260 (17
× 780), 15,600 (20 × 780), 31,200 (40 × 780), 62,400 (80 × 780) and 72,540
(93 × 780). The very largest again are correctly set down; first 109,200
equal to 140 × 780, but here also equal to 1050 × 104 and 300 × 364, so
that in this series the goal aimed at is not reached until later than it is
in the two preceding series. Then follows 131,040 = 168 × 780, 1260 × 104,
360 × 364, but finally 151,320, which number = 1455 × 104 and 194 × 780,
but is not divisible by 364.

Detached in the usual way from this series on the left of page 43 is the
number 1,435,980. Above and below it is the day III Lamat, further down IV
Ahau, and between them is 352 in a red circle. This number seems to have
been obtained in the following way:--The writer began with the distance
between III Lamat and IV Ahau, which is 92, added to it 172 × 260 = 44,720,
and subtracted the result 44,812 from 13 Ahau-Katuns = 1,480,440. The
remainder was 1,435,628, which number would correspond to the date III
Lamat 6 Zotz (4 Kan), which, however, is suppressed in the Manuscript. The
352 = 260 + 92 was added to this sum, and the result was the 1,435,980
written out in the Manuscript, _i.e._, a day IV Ahau 13 Zip (5 Muluc). Now
this number is the one sought; it is 5523 × 260 = 1841 × 780 = 3945 × 364,
and hence must also be equal to 263 × 5460, since the 780 and 364 are
united in 5460. According to our present knowledge, it would seem to lie in
the future, but not far from the present; the solar and Mars revolutions
are united in it. There is but a single hieroglyph here, the hieroglyph of
the animal which is the chief subject of the next section; from which it
appears that the two sections are closely connected.

Pages 44b--45b.

This section supplements the pictures and hieroglyphs belonging to the
series just examined. Therefore it likewise extends over 78 days and
divides them as follows:--

  III  19  IX  19  II  19  VIII  21  III.

These five days are plainly intended to be the days III Lamat, IX Manik, II
Cimi, VIII Chicchan, III Cimi.

With regard to the real purport of this section, it is my opinion that it
has reference to the time of the shortest day and also to the four winds
and that this section therefore forms, in a measure, a contrast to pages
38-41, where attention was called to the rainy season, the longest day and
the thunderstorms.

We see here in the first place four of the ordinary heavenly shields, with
two astronomical signs each. I cannot decide, at present, whether these are
1st, the moon and Saturn, 2nd, Mars and Mercury, 3d, the moon and Mars, and
4th, Jupiter and Venus.

From each of these shields hangs a figure not unlike an heraldic beast. It
cannot be the canine lightning-beast; it has no flames, it is cloven-footed
and with the upper lip bent upward and the lower lip curved downward
suggesting the storm-god K, and therefore probably represents the four
winds; this wind-beast repeated four times also occurs on Cort. 2.

Six hieroglyphs belong to each picture. Those in the first place are
pierced ears and refer therefore to the ritual bloodletting, which may have
been performed at this season. In Tro. 5*b we also find the pierced ear; a
pierced _tongue_ (Tro. 17*b), however, does not occur in the Dresdensis.
The second place always contains the sign of the beast like the one
instance on page 43.

The third place seems to be devoted to the four cardinal points, _i.e._, to
the four winds. First we see Akbal-Kin, _i.e._, the transition from night
to day, the east. The north-god, C, is here in the second group; in the
third we see Kin and beside it in the fourth place Akbal, both enveloped by
clouds denoting the transition from day to night, the west. The fourth
group, it is true, has the year-sign here, but with the compound Kin-Cauac
prefixed, and Cauac always belongs to the south. I believe I have found a
distinct reference to the season of the year in two other places. The
fourth hieroglyph of the second group and the sixth of the fourth both have
the familiar prefix suggesting K, the storm-god. The first of the two
contains the month Mol (December 3d-22nd); the second might very well be
the month Yax (January 12th-31st). This is quite in keeping with the
distances 19 + 21 = 40 set down below.

In my "Tagegöttern der Mayas" (Globus LXXIII, 10) and above in my
discussion of the great Tonalamatl under pages 4a-10a, I have assigned the
day Chuen to C, and Muluc to K, _i.e._, the first to the dark north and the
latter to the wind, which are both under consideration here. In fact, we
find the Chuen sign in the fifth place of the fourth group with the same
prefix that C has in the second group. The Muluc sign, however, seems to
occur three times:--1st, group 1, sign 6, where it may be joined to the
month Mol belonging here; 2nd, group 3, sign 5, joined to the Akbal, which
also belongs here; 3d, group 4, sign 4, with a usual prefix. In the second
group it may be included in the very similar month sign of Mol. Four
hieroglyphs remain:--1st, Akbal in group 1, sign 5, hence probably denoting
the darker time of the year in general; 2nd, A in 2, sign 5; 3d, E in 2,
sign 6; _i.e._, probably referring to the death of the grain (I do not know
to what extent this expression may be used in relation to the Maya
country); 4th, Kan-Imix in 3, sign 6, perhaps expressing the hope of new
harvests.

This finishes the middle sections of the pages of the first part of the
Manuscript, and we must now turn back again to page 29 in order to examine
the lower sections.

Pages 29c--30c.

  III  16  VI  16  IX  16  XII  17  III
  Ix
  Cauac
  Kan
  Muluc.

Here is a Tonalamatl of four quarters, 4 × 65.

In the Manuscript 16 is again erroneously set down for 17 and the III
following it is omitted. The initial day is exactly the same III Ix, as in
section 29b above it, to which in other respects the passage now under
consideration shows a great likeness, since the four familiar animals occur
here as well as there. But in spite of beginning in the same way the days
here are different ones, being the four regents of the year, as on page 9b.

The four parts are grouped together by the sign, which always occupies the
first place in each part; I have denoted this sign by _f_, and I think it
must have a very general significance, since from pages 29c to 40c it
always begins the groups. The connection between the four parts is further
shown by the four cardinal points in the second place:--the north in the
first group, the west in the second, the south in the third and the east in
the fourth. In the third place these cardinal points are again indicated by
their usual abbreviations; the east is erroneously set down in the second
group. These abbreviations are here invariably joined to the head of C as
the representative of the north, the first of the cardinal points occurring
in this passage; the others revolve about the north pole.

As B's sign always occurs in the fourth place, there is nothing further to
be said concerning the hieroglyphs. We now come to the pictures:--

1. B is rowing a boat, as we have already seen him several times (36b, 40a,
_c_, and 43c). To the left of his head there is a bird's head and in the
left, bottom, corner, a pot in which apparently a soup of fowl is cooking,
emitting bubbles. The Cib sign on the pot refers to the cooking or
bubbling.

2. B, with his head surrounded by the familiar stars, is seated in water,
in which are represented the iguana over a Kan sign, and the familiar
spiral probably denoting a serpent. He is painted black (perhaps
corresponding to the west?) and holds in his hand an implement not yet
determined. Perhaps it may be intended for a tree, _past_ which the water
is flowing.

3. The god is seated, holding in one hand the spiral with a Kin sign over
it and a Yax on top of that, and in the other hand something which looks
like a bird's feather or a fish's fin. Above him is a fish with a Kan sign,
as on page 27, where the fish and Kan are also combined.

4. Holding a hunting-spear, he is sitting on an animal slain in the chase,
as on page 45c.

Finally, I have remarked that pages 42c-45c, the last part of the first
division of the Manuscript, look like an enlargement or amendment of the
section just considered.

Pages 30c--33c.

To begin with, the day signs are set down in the following order:--

   XI        XI           XI        XI
  Ahau      Chicchan     Oc        Men
  Caban     Ik           Manik     Eb
  Ix        Cauac        Kan       Muluc
  Chuen     Cib          Imix      Cimi
  Lamat     Ben          Ezanab    Akbal.

Here then, as is frequently the case in this Manuscript, all the twenty
days are specified. But in order to obtain equal periods of time, the left
column should first be read from top to bottom and the following ones
should be treated in the same way. Then each succeeding day is 17 days
distant from the preceding, but in reality the interval is 117 days, since
the same week-day is always implied. The hieroglyphs seem to indicate that
these 117 days are divided into three distinct parts, 52, 39 and 26.

117 days, however, are equal to 9 × 13 and hence in what follows we find a
black 13 set down 9 times as the interval between the days, and a red XI
being the number of the week-day an equal number of times. Now, since the
whole series extends over 20 such sections of 117 days, the duration of
this calendar is 2340 days or 9 Tonalamatl.

Consequently we find nine pictures of the same god B. In five of them (in
Groups 1-4 and 9) he is sitting before or on a sacrificial tree or tree of
life; cf. 30b. It is probably not accidental that in these five cases the
hieroglyphs refer to the cardinal points. In the eighth group the god is
surrounded by the suggestion of one or more trees; he is sitting in water
as if in a forest; or in a cave bordered by trees? In the remaining groups,
5, 6 and 7 he is seated on various supports, in 5 on an object, which is
not completed and which cannot, therefore, be explained, in 6 on
astronomical figures (Mars and Venus?) and in 7 on agave leaves. In 1 and 3
his head is again surrounded by those dots suggesting stars, in 4 there
seems to be a bird (quetzal?) seated upon it and in 2 it bears what may be
the Kin sign. In 1 and 5 he has the pouch for incense in his hand, while in
3 alone he wears the gala mantle and is painted black, just as he appears
in connection with the same hieroglyphs on page 29c. He carries a hatchet
in repose in 2, 6 and 9, and raised for a blow in 1 and 7. In 7 he also
holds the Imix sign.

The hieroglyphs form nine groups of four signs each. The first hieroglyph,
as is always the case in this part of the Manuscript, is the sign which I
have denoted by _f_, and the second is always B's hieroglyph. The cardinal
points are everywhere specified by two signs each; in places 3 and 4 of
group 1, the west comes first and beside it is the sign for the east,
erroneously used for that of the west (a like error occurred in the
preceding Tonalamatl); in group 2 there are two signs for the north; in
group 3 that for the east with the sign for the west beside it erroneously
given for the east, and in group 4 two signs for the south. In groups 5, 6
and 7 we find in the 4th place the head of C, and the same sign in group 7
in the 3d place, where it is joined to another head, which may be that of a
woman. The 3d sign of group 5 is incomplete and cannot be determined. The
3d sign of group 6 displays a repetition of the astronomical signs
represented below. There still remain the 3d and 4th signs of groups 8 and
9. Of these the 3d in group 8 is _w_, which is as yet unexplained. The 4th
might be interpreted either as Oc (day 7) or as Xul (end). Its prefix is a
Yax sign. Finally, in group 9 the 3d sign is Manik (day 4), the 4th the
elongated head _q_ with the Ben-Ik superfix, which Seler assigns to Men
(day 12).

Pages 33c--39c.

The beginning of this Tonalamatl is indicated by a large red dot on page
33. It resembles the Tonalamatl almost exactly above it on pages 31b-35b,
inasmuch as its arrangement is an unusual one. I will here, as I did above,
give it the form in which it would present itself if it were set down in
the usual order:--

  XIII  9  IX  11  VII  20  I  10  XI  15  XIII
  Ahau
  Chicchan
  Oc
  Men.

In this passage as in the earlier one, instead of employing the above
concise order, a preference has been shown throughout for carrying out the
whole series in such a manner that the week days are set down each time and
not merely in the left column. It, therefore, has the following form in the
Manuscript:--

  XIII Ahau (9)     IX Muluc (11) VII Ahau (20)     I Ahau (10)
                                                           XI Oc (15)
  XIII Chicchan (9) IX Ix (11)    VII Chicchan (20) I Chicchan (10)
                                                           XI Men (15)
  XIII Oc (9)       IX Cauac (11) VII Oc (20)       I Oc (10)
                                                           XI Ahau (15)
  XIII Men (9)      IX Kan (11)   VII Men (20)      I Men (10)
                                                           XI Chicchan (15)

I have arranged the whole series in four parallel periods of 65 days each,
for the 65 appears throughout the computation, although the entire
Tonalamatl is written out in _one_ continuous line. On the right of page 35
the scribe seems to have wished to erase an entirely incongruous 4, and in
writing the last 15, on page 39, he began to use the red paint prematurely,
so that the top one of the three lines is red.

Attention should also be called to the fact that the second of my vertical
columns contains the year-regents, the others only the days following
immediately after them, while 12 month days do not occur at all. Also the
intervening periods 9 + 11 (= 20), 20, 10, 15 doubtless reveal some design.

In order to avoid repetition, I think it proper to mention first, that in
the twenty groups of four hieroglyphs each, the sign _f_ always stands in
the first place, but the hieroglyph of B, who is represented 20 times,
usually appears in the second place, in the first and second groups in the
third place, and in the 18th and 19th his sign does not appear at all. I
will discuss the remaining hieroglyphs in their place in each of the 20
groups.

1. B is sitting in a house and holding the Kan sign in his hand.

The second hieroglyph is apparently meant for the Ahau sign (referring to
the 17th day), which usually does not belong to B. This hieroglyph, which
certainly bears a resemblance to Ahau and with which we have become very
familiar in the inscriptions, occurs again in this Manuscript on pages 46b,
c, 50b, 54b, 65a and 66a. The fourth sign is a combination of Cauac and
Manik.

2. B is seated on what may be a tree, below him is the cross _b_, and he
holds the hatchet in his left hand.

The second sign with an emphasized 6 as a prefix (cf. the same sign with
the 6 on page 48, bottom, left, below the gods), has the usual Ben-Ik
superfix, perhaps to denote that a lunar month has now elapsed, for this
passage extends from the 20th to the 40th day of the Tonalamatl. The rest
of the hieroglyph is unintelligible. In the 4th place we see a vessel with
Imix, probably denoting pulque.

3. B is sitting in water, the hatchet raised in his right hand and his face
turned upward.

The 3d hieroglyph is again Imix and the 4th a compound of Ik and
Muluc:--wind and clouds.

4. B is seated on a reproduction of his own head or D's, beating a drum
with his hand.

The 3d hieroglyph denotes the serpent-god H with the number 3 as a prefix.
The 4th hieroglyph is a Chuen with the sign for the south prefixed,--at any
rate the upper part of that sign.

5. B is standing in the pouring rain and looking backward.

The 3d sign here is a Caban apparently in a vessel. Following this in 4 is
the hieroglyph which I have proposed to interpret as the sign for
_beginning_ (Globus, Vol. LXVI, page 79). This sign occurs again in groups
7, 12, 15, 17 and 19, and must therefore be connected with the principal
idea embodied in this Tonalamatl.

6. B with folded arms is sitting in a house.

Aside from the usual leaflike prefix, the third sign is composed of two
parts. The upper part looks like a plaited mat and suggests that the word
for the first month of the year (Pop) is expressed by mat. The lower part
is the sign, which occurs frequently especially on pages 25-28, and which
very much resembles the familiar sign for a year of 360 days. We shall meet
it again in the continuation of this Tonalamatl on pages 36 and 38. The
three passages refer to the 74th, 139th, and 204th days of the Tonalamatl,
and hence are 65 days apart.

The 4th sign is the cross _b_, with possibly the sign of the east as a
prefix.

7. B is seated on the cross _b_, which is here undoubtedly meant for an
astronomical sign. He holds a Kan sign in his hand and there is an Ahau
sign on his back.

The naked crouching personage, pointing upward, should have especial
mention here. The same figure recurs above as a prefix to the 4th
hieroglyph. We have already seen it in the 39th hieroglyph on page 24, and
shall meet it with especial frequency in the second part of the Manuscript.
It is placed sometimes, as in this case, _before_ a sign, sometimes _after_
a sign and again two of these figures are placed back to back as on page
22c, and one of them is even placed upside down before another sign, where
it seemed to me to be a sign for Mercury ("Zur Entzifferung VII," p. 11).
This figure is represented independently only on the right of page 58. In
the passage under present consideration this personage appears again on
page 38. The two figures are connected one with the 85th and the other with
the 215th day, and are, therefore, divided by exactly half a Tonalamatl or
130 days. Here we find it as a prefix of the supposed sign for _beginning_
of which mention was made in discussing the 5th group. The 3d sign is the
same astronomical one, which we saw below under B. It might refer to the
Moan and to the change of the year, and thus indicate that a Mercury
revolution was coincident here with the beginning of the solar year.

8. B is walking in the rain, both arms are stretched upward, and the pouch
hangs from his neck. At the left top there is a black spot suggesting those
which usually occur beside the sun and moon.

The 3rd sign is Manik, with a prefix. The 4th is an indistinct head, which
may be C's, with an Imix sign as a prefix.

9. B is walking with the pouch hanging from his neck, and the hatchet in
his hand.

The 3d sign, which is unusual, is very obscure, but suggests the fish on
page 44c or that on page 36b. The 4th sign with the prefix of the north is
very indistinct.

10. B is standing in _water_, his face turned upward while water is pouring
from a cloud. The third sign is very complex. The top, left, suggests a
serpent, the right a hand, the bottom, left, a Chuen and the element at the
bottom, right, may be intended for a bird's head. Exactly the same sign,
with the 4th part merely indicated, occurs 65 days later on page 38. The
4th sign is the familiar compound Kin-Akbal.

11. B is sitting in a tent, on the roof of which there is a vessel
containing food of some kind.

The third sign, which is very complex, is indistinct. The 4th sign likewise
consists of four parts, the left, bottom, part is probably the vessel,
above it is a spiral (which usually means serpent or time). The right,
bottom, is again the sign resembling the year-sign which was spoken of in
discussing group 6. The component at the right, top, is indistinct.

12. B is sitting here on no less than four astronomical signs, he has the
hatchet in his hand and the design on his back may be a shield or the
elaborately ornamented sun-glyph Kin.

The third sign (denoting _beginning_?) has already been discussed in
connection with group 7, which is 65 days earlier. The fourth is the sign
of the year of 360 days or the month Pax with the Ben-Ik as a prefix. These
signs are here suggestive of the beginning and end of the year.

13. _Above_ B are astronomical signs (Jupiter and Mercury?) and also the
sun and moon. The rain is pouring down upon the god, and a fish is placed
beside him. He seems to have the same chisel in his hand which we saw him
using on page 41b in connection with the beginning of the year. This again
would correspond to the date indicated in the preceding picture. The shield
(?) also is the same here as in the preceding group.

The third sign ought to represent the fish; the drawing seems to have been
unsuccessful and the sign looks more like a bird and also resembles the
third sign in the ninth group on page 36. The fourth sign is a Kin-Akbal.

14. B is seated on the elongated head _q_, which has an ordinary prefix. He
is pointing upward with his right hand and the left looks as if opened to
receive something.

The third hieroglyph contains a _q_ like the one under the god, the fourth
is an indistinct head (C's?) with an unintelligible prefix.

15. B is standing in water while rain is again pouring down upon him. He
holds the hatchet raised in his left hand, while the fingers of the right
are extended upward in an unusual manner. This is repeated in the third
hieroglyph.

The third hieroglyph, however, is the same as the third in the tenth group
65 days earlier, only here the hand is more distinct, while the element
below it is vague. The fourth sign is again the one denoting beginning.
Compare the fifth group (130 days earlier).

16. B with arms folded is sitting in a house with the Cauac sign below.

The third and fourth hieroglyphs contain the sign resembling that for the
year, which was mentioned in discussing the sixth group (130 days earlier).
In the third a Kin is prefixed to this sign, while the superfix of the
fourth is what I take to be a mat, which also occurred in the sixth group.
The prefix is a figure suggesting the serpent-deity, which we have already
met with in the tenth and fifteenth groups.

17. B, holding the hatchet, is seated on a Moan head, and the third sign is
probably intended to represent the same Moan head, in front of which we
find the same crouching person met with in the seventh group, 130 days
earlier.

The fourth hieroglyph is again the sign for beginning, which we have
already often met with, as, for example, 65 days earlier in the twelfth
group.

18. B is sitting in the pouring rain under astronomical signs (Mars and
Mercury?) to which those of the sun and moon are added. The god's face is
upturned and he holds the hatchet in his hand.

The third hieroglyph may be the vulture head, to which a part of the
unintelligible second hieroglyph may also refer. This second sign stands in
the place of B's hieroglyph, which is wanting here.

The fourth sign contains the enigmatical numeral 8, which we found on pages
36b and 37b, and has the Imix sign as a prefix, as in the first of these
two passages. The same compound appears on pages 67a-68a.

19. B is seated here on his own head, as in the fourth group he is sitting
on D's. His hands are empty.

The second sign is again the vulture head instead of B's hieroglyph. The
third is probably the head of the lightning beast, and the fourth is again
the sign supposed to denote beginning.

20. B is sitting in water and holding in his hands a vessel with a Kan sign
upon it.

The water (with Imix prefixed) is denoted by the third sign, while the
fourth represents a head (with what is probably a hand pointing to the
right above it), which I should prefer to consider the grain-deity E.

In conclusion I would call attention to the remarkable fact that every four
pictures, which are separated from each other by four of the other
pictures, _i.e._, after every 65 days, correspond in certain respects with
one another, _viz_:--

1. Pictures 1, 6, 11 and 16. In all, and _only_ in these, B is sitting in a
house or tent, in 6 and 16 with his arms folded.

2. Pictures 2, 7, 12 and 17. In the first three the god is seated on
astronomical signs and in the fourth on the Moan head, which I think refers
to the Pleiades.

3. Pictures 3, 8, 13 and 18. Here in the last two B is sitting _beneath_
astronomical signs. In all four pictures water, clouds and rain are
represented.

4. Pictures 4, 9, 14 and 19. In the first and fourth the god is seated on
D's head and on his own, and in the third on the elongated head _q_.

5. Pictures 5, 10, 15 and 20. Like the third of these five classes, these
pictures are likewise distinguished by water, clouds and rain.

Now the first set of pictures is between the week days XIII and IX, the
second between IX and VII, the third between VII and I, the fourth between
I and XI, the fifth between XI and XIII, while the month days are quite
different. Hence the conjecture is but natural that the pictures and week
days bear some relation to one another, though that relation is still
shrouded in obscurity.

Pages 40c--41c.

  I  10  XI  10  VIII  10  V  10  II  3  V  9  I
  Ahau
  Eb
  Kan
  Cib
  Lamat.

This is a Tonalamatl of the most ordinary kind, in which an unsuccessful
attempt has been made to divide the subdivisions into equal parts.

In the groups of four hieroglyphs each, which belong to each of the six
parts, the sign _f_ always occupies the first place, and B the third. Let
us now examine the six parts separately.

1. B is sitting in a boat and rowing (as on the top of the same page).
Around his head there is again the suggestion of what may denote the starry
sky, and in this picture his nose-peg is unusually large.

The second sign is an Imix, but it might also denote the thirteenth month
Mac and therefore the Tonalamatl (13 × 20). The fourth sign is a fish
forming a connecting link between the water represented below and the rest
of the group.

2. B is seated on the Caban sign and his arms are apparently resting on an
altar standing in front of him, on which fire is burning, indicated by the
Ik sign, while the moon is placed below the altar.

The Caban sign below is repeated in the second hieroglyph, combined here as
usual with a sign which may be Muluc.

The fourth sign is a head. I think the scribe meant to set down an 8 before
it, but as there was not sufficient space for the heavy line _after_ the
three small circles, he indicated it by a black dot _below_ the circles.
Now, if we call the head D's, which of course cannot be asserted
positively, this would be day VIII Ahau, and this, in fact, is twenty days
from the beginning day I Ahau, as it is meant to be in this passage. There
is no representation of food; can this have been a fast day?

3. B is seated on four astronomical signs. He wears the gala mantle and
holds a serpent in his hand.

The second sign is _b_, and at the same time one of the astronomical signs.
The fourth is the iguana prepared as food, recognizable by the spines on
its back, as on page 25b. It is drawn in precisely the same curious fashion
in Cort. 8 and 12c; hence it is represented in the picture by the serpent.

4. B is falling down from above headfirst. I believe that the numerous
footprints below him are only intended to represent swift motion. The
descent from above may only be intended here to bring the god into closer
relationship with the head of the bird of prey in the fourth sign. That
this head is again as usual joined to Kan, may refer merely to the fact
that it was the Maya custom to eat bread with animal food. Compare page
27b. The second sign might be the abbreviation for the south.

5. B is seated on a mat with his hand extended as if to receive something.
He is wet with water.

The second sign contains the mat, with what may be the sign below it, and
the leaf-shaped prefix probably denoting the plant from which the mat is
plaited. The very same combination is given on page 35c and a similar one
on 38c. The fourth sign has the prefix of the west followed by two Kans, as
if on this day (V Akbal) it had been the custom to eat tortillas without
meat.

6. B is standing holding the hatchet. The fourth sign must denote venison,
the fourth article of animal food. The second seems to represent the day
Eb, with which the remaining 52 days begin, and if the prefixed 9 indicates
nothing more than that the ninth day of the month is here meant, it is
further evidence that the "Dresdensis" began the days with Kan and not with
Imix.

In the discussion of this Tonalamatl I have omitted the mention of a very
peculiar feature, which as yet does not admit of explanation. I refer to
the numbers below the pictures. With the first picture we find 6 + 20, with
the second 20, with the third 19 + 20, with the fourth 6 + 20, with the
fifth 19 + 20, and with the sixth 6 + 20, _i.e._, with the exception of the
second, 26 or 39, two multiples of 13. Now the question arises, should not
one of these multiples have been set down with the second picture? There
was no space left for a prefixed 19. Therefore the idea suggests itself
that what we took to be an altar with the sign Ik above it, is intended for
nothing else than this 19, and Ik is the 19th day, if we count from Kan as
the starting-point.

Pages 42c--45c.

This is a Tonalamatl consisting of 4 × 65 days. If written out in the usual
way it would run as follows:--

  XIII  17  IV  8  XII  8  VII  8  II  8  X  8  V  8  XIII
  Akbal
  Lamat
  Ben
  Ezanab.

Since, however, the subdivisions are divided and the individual month days
also are given for all the parts of the whole Tonalamatl, the
representation follows the order which we have already found on pages
31b-35b and 33c-39c. In this place, as in the two former ones, I will
reproduce in four lines what is set down in the Manuscript in one single
line extending over all four pages.

  XIII Akbal (17)  IV Ahau (8)     XII Lamat (8)  VII Cib (8)
                                     II Kan (8)   X Eb (8)    V Ahau (8)
  XIII Lamat (17)  IV Chicchan (8) XII Ben (8)    VII Imix (8)
                                     II Muluc (8) X Caban (8) V Chicchan(8)
  XIII Ben (17)    IV Oc (8)       XII Ezanab (8) VII Cimi (8)
                                     II Ix (8)    X Ik (8)    V Oc (8)
  XIII Ezanab (17) IV Men (8)      XII Akbal (8)  VII Chuen (8)
                                     II Cauac (8) X Manik (8) V Men (8)

Thus the days Chicchan, Lamat, Oc, Ben, Men, Ezanab, Ahau, and Akbal are
repeated here twice, and the others occur but once. The 4 (17 + 48)
strongly recalls the 4 (19 + 46) on pages 31b-35b. The repetition of six
times eight days in each quarter of the Tonalamatl is closely connected
with the fact that there are six Chuen signs on each page, two of which,
however, are omitted on page 44. From this it follows, as we have already
found on pages 25-28, that Chuen really denotes 8 days and that the count
of the days in the "Dresdensis" begins with Kan. But the numbers 12, 15, 16
and 17 are entirely unexplained. They show no recognizable order and always
stand near the bundle of Chuen signs. They recall the numbers on pages
25-28, which are equally irregular and unintelligible, and upon which, it
is probable, light will break at the same time as it does upon these now
under consideration.

We come now to the purport of this passage, which seems to be a further
amplification of the contents of pages 29c-30c. The meaning is simply as
follows:--every 65 days the god B discards a cardinal point and the deity
presiding over it and installs another.

From this point of view let us now examine the four pictures.

1. Page 42. B is represented here as a warrior with the front of his body
painted red. He is aiming a blow with his hatchet at a person sunk down
before him, who, from the ornament above his head, seems to be the
grain-deity E, the ruler of Kan and of the east, although the contents of
this passage really demand a deity of the south, a ruler of Cauac. In a
very similar way on page 27, E occurs with the completed Cauac years,
instead of with the Kan years just beginning. Behind B's head is the sign
of the discarded cardinal point, the south, while below it is a vessel with
food, clearly a piece of venison with Kan.

2. Page 43 deals not with the removal of the old cardinal point, but with
the introduction of the new one. Here B is rowing in a boat, as in other
passages (29c), and Muluc, the north, has certainly a close relation to
water. We see here two kinds of food, while none is represented on page 45.
The same bird's head, which we find at the bottom of the corresponding page
28, is placed in front of the canoe, and on 29c it is combined with the
representation of rowing a boat. On the left is the picture of a vessel
with Kan and the iguana. There is something resembling a net between the
boat and the bird.

3. Page 44 likewise refers to the introduction of the new cardinal point,
west, which is represented on page 26 by the tiger Ix. The two hieroglyphs
in the middle of this passage must surely refer to an animal; the lower is
the skeleton of an animal, which we so often find as the sign of the
lightning-dog, but also as that of the month Kankin, and the upper I take
to be a rather vague picture of the day Oc, which certainly denotes the
dog. Below these two signs the fish is represented as the fourth species of
animal food.

The picture belonging to these hieroglyphs is very remarkable. B stands
opposite a seated personage wearing an animal's snout, which somewhat
resembles that of the wind-beast on pages 44b and 45b and also the nose of
the storm-god K, who occurs on the corresponding pages 25 and 26 both with
the coming and the departing Ix years, as he does here with the coming
years. In the picture before us, the two personages seem to be throwing
something resembling a rope at each other, as if these ropes were to be
tied together. Is this meant to suggest the casting of lots by means of the
knotting of cords, as it is represented on page 2? Or of hunting with
snares?

Page 45 refers to the displacement of the Ix period by the Cauac period,
_i.e._, of the west by the south. The end of the former is represented
here. The lightning-beast, which occurred in the preceding period, here
lies on his back and B sits astride his body brandishing in each hand a
burning torch as an appropriate symbol of the south. On pages 29a and 30c
we already saw the god riding on the lightning-dog.

Finally the six interesting hieroglyphs set down in a vertical row on the
left of each of the four pages are still to be examined. I will give here
in the following table what I think is a correct interpretation of them:--

                   Page 42.          43.          44.          45.
                  South (1)     East (7)   North (13)     West (9).
                It ends (2)          (8)         (14)         (20)
                      B (3)          (9)         (15)         (21)
  the time of the Cauac (4),    Kan (10),  Muluc (16),     Ix (22),
              while Kan (5),  Muluc (11),     Ix (17),  Cauac (23)
                 begins (6)         (12)         (18)         (24).

If that which is actually set down in the Manuscript be compared with this,
it will be seen that in 11 of the 24 places the Manuscript corresponds to
my hypothesis:--1, 7 and 19 are the familiar signs for the three cardinal
points, 8 and 20 are the sign Xul = end, which I have already frequently
mentioned, 9 and 21 are the sign for B, 11 is Muluc, 23 is Cauac, where the
scribe has added to the correct Kin-Cauac the sign for the year, as if the
Cauac _years_ were treated of here as on pages 26 and 27. Finally the two
agree in 12 and 18, where the Manuscript has the compound Kan-Imix to
denote beginning, _i.e._, the two days beginning the series of twenty days,
one of them according to this Manuscript, and the other according to the
method resembling that used by the Aztecs.

The other cases have the correct signs, but set down in the wrong place,
thus B is changed from 3 to 2, from 15 to 16, the north from 13 to 14, the
Xul from 2 to 3, 14 to 15, the E (Kan) from 5 to 4 and 6 and Cauac from 4
to 5, _i.e._, pushed along every time to the next place. This is all in
favor of my theory. As one series began at the top, the scribe incorrectly
placed the sign for beginning in the thirteenth place.

Strange to say in the tenth place we have the very general sign _a_ in
place of Kan. In the 4th, 17th and 22nd, and probably also in the half
destroyed 6th sign, the scribe thoughtlessly put down a sign for E, which
is proper only with Kan and should come after 5 or 10. Finally in the 24th
place he put a sign for A, as if it were the intention that this passage
should end exactly like its parallel on page 28. For, as a matter of fact,
the two principal sections of the first part of the Dresdensis do end in a
very similar way.

       *       *       *       *       *

PART II.

Pages 46--74.

The first glance at the form and contents of the second part of the
Manuscript shows that it is very different from the first. The pages are no
longer divided into the usual three parts and there are fewer pictures. The
Tonalamatls, which form the principal contents of the first part, disappear
wholly, and with them both the vertical columns of day-signs and the
horizontal lines of numerals alternating between red and black. On the
other hand, the large number series as well as the high numbers
significantly increase and we note the appearance of the large vertical
columns of hieroglyphs, which were impossible in the triple division of the
earlier pages. We also find a large number of hieroglyphs which did not
occur in the first part. The contents are essentially astronomical.

And yet the two parts are so closely connected with one another that the
idea of two independent Manuscripts must be dismissed. Especially the front
side of the second part as far as page 60 is nothing more than an
amplification of page 24. The contents of pages 61-74 are of a more
independent nature, but special attention should be called to the relation
of 31a-32a to 62-63.

Pages 46--50.

The entire contents of these pages must be represented as a unit, for what
is in the main true of page 24 is also true of these pages, namely that
they treat exclusively of the period of 2920 days, in which five Venus
years of 584 days each are brought into accord with eight solar or
terrestrial years of 365 days each. Each page is a direct continuation of
the preceding one. Each period of 2920 days is taken 13 times, the result
being 37,960 days, which are equal to 146 Tonalamatls.

I will give here first a reproduction, as it were, of the left side of the
five pages, omitting for greater clearness a few indifferent matters, which
are intended only to fill the blank spaces, viz:--

1. The twenty hands pointing to the right, with a knife placed over them,
in the middle of the pages, which mean nothing more than that these parts
of the Venus year are to be read from left to right.

2. The Venus hieroglyph three lines below, repeated twenty times with the
sign of the knife, to denote the _division_ of the Venus revolution.

3. The _Akbal_ sign occurring further down, four times on each page, except
on pages 46 and 47. This is the last of the day-signs, again counting
forward from the day Kan, and means only that henceforth the _close_ of the
four periods of the Venus year is indicated below, as the beginning is
indicated above.

4. The sixteen Venus signs also occurring below, except on page 48. This
sign likewise occurs in a very similar form on Altar R of Copan.

With these omissions, the left side of these pages presents the following
appearance:--

                            Page 46.

     III Cib         II Cimi         V Cib       XIII Kan
      XI Cib          X Cimi      XIII Cib       VIII Kan
      VI Cib          V Cimi      VIII Cib        III Kan
       I Cib       XIII Cimi       III Cib         XI Kan
      IX Cib       VIII Cimi        XI Cib         VI Kan
      IV Cib        III Cimi        VI Cib          I Kan
     XII Cib         XI Cimi         I Cib         IX Kan
     VII Cib         VI Cimi        IX Cib         IV Kan
      II Cib          I Cimi        IV Cib        XII Kan
       X Cib         IX Cimi       XII Cib        VII Kan
       V Cib         IV Cimi       VII Cib         II Kan
    XIII Cib        XII Cimi        II Cib          X Kan
    VIII Cib        VII Cimi         X Cib          V Kan

    4 Yaxkin         14 Zac         19 Zec         7 Xul
      North.          West           South          East
      Gods.
       236            326             576           584
    9[1] Zac      19[1] Muan         4 Yax        12 Yax
       Gods
       East          North            West         South
    19 Kayab        4 Zotz           14 Pax       2 Kayab
       236            90              250            8

                            Page 47.

     II Ahau            I Oc       IV Ahau      XII Lamat
      X Ahau           IX Oc      XII Ahau      VII Lamat
      V Ahau           IV Oc      VII Ahau       II Lamat
   XIII Ahau          XII Oc       II Ahau        X Lamat
   VIII Ahau          VII Oc        X Ahau        V Lamat
    III Ahau           II Oc        V Ahau     XIII Lamat
     XI Ahau            X Oc     XIII Ahau     VIII Lamat
     VI Ahau            V Oc     VIII Ahau      III Lamat
      I Ahau         XIII Oc      III Ahau       XI Lamat
     IX Ahau         VIII Oc       XI Ahau       VI Lamat
     IV Ahau          III Oc       VI Ahau        I Lamat
    XII Ahau           XI Oc        I Ahau       IX Lamat
    VII Ahau           VI Oc       IX Ahau       IV Lamat

    3 Cumhu           8 Zotz       18 Pax         6 Kayab
     North             West         South           East
     Gods.
      820               910         1160            1168
    3 Zotz             13 Mol       18 Uo          6 Zip
     Gods
     East              North        West           South
    13 Yax             3 Pax       8 Chen         16 Chen
      236               90           250             8

                            Page 48.

       I Kan          XIII Ix       III Kan         XI Eb
      IX Kan          VIII Ix        XI Kan         VI Eb
      IV Kan           III Ix        VI Kan          I Eb
     XII Kan            XI Ix         I Kan         IX Eb
     VII Kan            VI Ix        IX Kan         IV Eb
      II Kan             I Ix        IV Kan        XII Eb
       X Kan            IX Ix       XII Kan        VII Eb
       V Kan            IV Ix       VII Kan         II Eb
    XIII Kan           XII Ix        II Kan          X Eb
    VIII Kan           VII Ix         X Kan          V Eb
     III Kan            II Ix         V Kan       XIII Eb
      XI Kan             X Ix      XIII Kan       VIII Eb
      VI Kan             V Ix      XIII Kan        III Eb

     17 Yax            7 Pax       12 Chen         0 Yax[2]
      North             West         South          East
       Gods
       1404             1494          1744          1752
      2 Pax            7 Pop        17 Mac      5 Kankin
       Gods
       East            North          West         South
      7 Zip        17 Yaxkin          2 Uo         10 Uo
       236               90           250             8

                            Page 49.

  XIII Lamat      XII Ezanab       II Lamat         X Cib
  VIII Lamat      VII Ezanab        X Lamat         V Cib
   III Lamat       II Ezanab        V Lamat      XIII Cib
    XI Lamat        X Ezanab     XIII Lamat       VII Cib
    VI Lamat        V Ezanab     VIII Lamat       III Cib
     I Lamat     XIII Ezanab      III Lamat        XI Cib
    IX Lamat     VIII Ezanab       XI Lamat        VI Cib
    IV Lamat      III Ezanab       VI Lamat         I Cib
   XII Lamat       XI Ezanab        I Lamat        IX Cib
   VII Lamat       VI Ezanab       IX Lamat        IV Cib
    II Lamat        I Ezanab       IV Lamat       XII Cib
     X Lamat       IX Ezanab      XII Lamat       VII Cib
     V Lamat       IV Ezanab      VII Lamat        II Cib

     11 Zip          1 Mol            6 Uo         14 Uo
      North           West           South          East
       Gods
       1988           2078            2328          2336
  16 Yaxkin          6 Ceh          11 Xul        19 Xul
       Gods
       East          North            West         South
   6 Kankin        16 Cumhu           1 Mac         9 Mac
       236            90             250             8

                            Page 50.

      XII Eb            XI Ik          I Eb       IX Ahau
      VII Eb            VI Ik         IX Eb       IV Ahau
       II Eb             I Ik         IV Eb      XII Ahau
        X Eb            IX Ik        XII Eb      VII Ahau
        V Eb            IV Ik        VII Eb       II Ahau
     XIII Eb           XII Ik         II Eb        X Ahau
     VIII Eb           VII Ik          X Eb        V Ahau
      III Eb            II Ik          V Eb     XIII Ahau
       XI Eb             X Ik       XIII Eb     VIII Ahau
       VI Eb             V Ik       VIII Eb      III Ahau
        I Eb          XIII Ik        III Eb       XI Ahau
       IX Eb          VIII Ik         XI Eb       VI Ahau
       IV Eb           III Ik         VI Eb        I Ahau

  10 Kankin         20 Cumhu[3]      5 Mac        13 Mac
      North             West         South          East
       Gods
       2572             2662          2912          2920
   15 Cumhu            0 Zec[4]   10 Kayab      18 Kayab
       Gods
       East            North          West         South
     20 Xul           10 Zac        15 Zec         3 Xul
       236               90           250             8

Let us first examine the numbers which are regularly repeated in the lowest
line:--236, 90, 250, and 8, and we shall find that the 584 days of the
apparent Venus revolution are divided into these four periods.

The number 236 denotes the time of the western elongation, when Venus is
the morning star, 90 the time of the invisibility of the planet, during its
superior conjunction, 250 that of its eastern elongation, when Venus is the
evening star, and 8 the time of its invisibility during inferior
conjunction. The disproportion between 236 and 250 is somewhat striking.
These periods which need not of course be exactly equal are usually
computed at 243 days. The short period of eight days is only calculated for
very sharp eyes; we actually find in the Anales del Museo Nacional de
Mexico II, 341 (Mex. 1882), that the Aztecs calculated only eight days for
the invisibility of Venus, and this period is also mentioned in the Anales
de Quauhtitlan. The repetition of the cardinal points in the 15th and 20th
lines of the extract given above refer to these periods; in the upper line
to their beginning and in the lower to their close. Hence in the lower line
the cardinal points must advance one place and the gods belonging to them
in the 16th and 19th lines must follow the same course.

The numbers in the 17th line indicate to which day of the period of 2920
days the position has advanced.

But now we see that the indication of days in the lines 1-13, the
indication of months in lines 14, 18 and 21, and the numbers in line 17 are
separated from those directly to the right of them by a number of days
equal to the numbers given in the lowest line.

From this it follows that each day of the thirteen top lines is joined to
each of the month dates placed just below them, forming a complete calendar
date. Therefore from the III Cib on the left upper corner of page 46 a III
Cib 4 Yaxkin, a III Cib 8 Zac, a III Cib 19 Kayab must be formed.

All the 4 × 13 × 5 = 260 day indications combined with three month
indications each, show therefore that this whole passage is a huge
abbreviation for 780 calendar dates and that the whole refers to 3 × 37,960
days = 113,880 days. But 37,960 which we already found on page 24, is equal
to 146 × 260, 104 × 365, 65 × 584, 13 × 2920. I am inclined to think that I
also found 113,880 on page 24.

But the 3 × 37,960 = 113,880 days do not form the entire period treated of
here. For the three periods begin and end with the days:--

  I Ahau 13 Mac (10 Muluc),
  I Ahau 18 Kayab (3 Kan),
  I Ahau 3 Xul (4 Cauac).

Hence these three dates, the second of which was found on page 24, prove
that the three periods of 37,960 are not consecutive, but that there is an
interval between them. Now between the first and second of the three dates
the interval is 19 years + 85 days = 7020 days, and between the second and
third, the interval is 26 years + 130 days = 9620 days. If these two
periods be added to the 113,880 days, the sum is the whole period treated
of here, viz:-- 130,520 = 502 × 260 days.

But a truly surprising result is obtained, if, as must often be the case
with series, we begin not with the upper of the three dates, but with the
lower.

From I Ahau 3 Xul (4 Cauac) to I Ahau 18 Kayab (3 Kan) there is a lapse of
9360 days or 12 apparent Mars years of 780 days, such as we shall find as
the principal subject of page 59. 9360, however, equals 25 × 365 + 235
days. We shall meet with this 235 again as a difference on page 63.

But from I Ahau 18 Kayab (3 Kan) to I Ahau 13 Mac (10 Muluc) there are
11,960 days, _i.e._, the 104 Mercury years, which we found on page 24, and
which we shall find again as the principal period on pages 51-58. But this
is equal to 32 years + 280 or 33 years - 85 days. Now if 113,880, 9360,
11,960 are added together, we have for the entire period under discussion
here, 135,200 days, and this is equal to 2 × 260 × 260 days. Thus the Mayas
seem actually to have had an idea of a second power.

Finally I would call attention to a singular double connection between the
numbers occurring here:--

  37,960 - 11,960 = 26,000 = 100 Tonalamatls,
  11,960 -  9,360 =   2600 =  10 Tonalamatls.

But if we subtract 2 × 11,960 = 23,920 from 37,960, the remainder is
14,040, _i.e._, an extraordinary number which often occurs and is equal to
54 × 260, 39 × 360 and 18 × 780.

In short, a Mars and a Mercury-lunar period are inserted in the two spaces
between the three solar-Venus periods.

Now, let us try to gain a clearer understanding of this subject by
approaching from another side.

As we have seen, the beginning of the middle one of the three equal periods
of 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24
furnished us with a day number for this date, 1,364,360, and from this the
beginnings of the other two periods may be computed in the following way:--

  I Ahau  3 Xul  (4 Cauac) = 1,317,040,
  I Ahau 18 Kayab  (3 Kan) = 1,364,360,
  I Ahau 13 Mac (10 Muluc) = 1,414,280.

Between the first number and the second there are 47,320 days = 2^3 × 5 × 7
× 13^2, and between the second and third 49,920 days = 2^8 × 3 × 5 × 13
days.

But, according to what has been stated above, 47,320 = 37,960 + 9360, and
49,920 = 37,960 + 11,960.

The whole period is therefore divided as follows:--

It begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years,
then the great period again followed by 8 × 13 = 104 Mercury years, and
lastly, apparently about the present time, comes the third great period,
which, as already stated, ends 135,200 days after the first date.

The case assumes a different aspect, if we insert between the three dates
the other two from page 24:--

  1,317,040 = I Ahau,
  1,352,400 = I Ahau,
  1,364,360 = I Ahau,
  1,366,560 = IV Ahau,
  1,414,280 = I Ahau.

Here we have again, as examination of page 24 showed, the difference 11,960
between the second and third numbers, while there is no longer any
connection with the periods of 37,960 days.

Of the left halves of the pages we have now examined all except the twenty
hieroglyphs of the gods. I shall mention them according to the upper place
in line 16; the lower in line 19, where the hieroglyphs move forward only
one place, is only referred to when the two signs differ. They offer many
problems still unsolved.

The first sign on page 46 is an unknown sign, which, however, is repeated
several times on the right side of the pages; the second is probably an
Ahau (_i.e._, D) with a prefix suggesting the snail, the symbol of birth;
the third is a head also occurring elsewhere, which I have not yet
determined; the fourth is A; compare page 24, hieroglyph 25.

Page 47. The first sign is probably K; compare the third picture on page 7a
with its hieroglyph; the second is C's hieroglyph with an Akbal appropriate
to it; the third sign is Moan with the 13 belonging to it; the fourth sign
is N's with a prefixed 4; the year-sign in the lower series is replaced by
Zac, which agrees equally well; compare page 24, hieroglyph 21.

Page 48. The first sign is Kin with the Ben-Ik superfix, perhaps denoting
G; the second is a figure similar to the year-sign with a prefixed 6. This
same sign in the line below has a 6, but is very different in other
respects; the third is an Akbal with superfix and prefix, perhaps denoting
D; the fourth is a head which might easily be F's; compare page 24,
hieroglyph 22.

Page 49. The first sign is B's; the second, A's; the 3d, K's; compare page
24, hieroglyph 38; the fourth is H's with a prefixed 1; compare page 24,
hieroglyphs 23 and perhaps 37.

Page 50. The first sign is E's; compare page 24, hieroglyph 38; the second
is L, the black deity; compare page 24, hieroglyph 32; the third is an
unknown hieroglyph with a prefixed 7, which also occurs on page 5a and 19b;
the fourth is the bat-god; compare page 24, hieroglyph 24.

I find it impossible to discover any relation between these hieroglyphs and
the periods and I have as little success with the hieroglyphs apparently
belonging to the same cardinal point. Perhaps we should follow Seler here
(Quetzalcoatl and Kukulcan, p. 403), who thinks these passages suggest
constellations with which Venus is in conjunction; this question, owing to
the retrogression of the planet, raises increased difficulties. It is
curious that the fourth of these signs on page 46 is like the fourteenth on
page 49 (A), and perhaps the two following refer to the same god K; the
first two are separated by 1494 days and the latter by 1508 days.

We come now to the _right_ half of the pages. Interpretation is rendered
impossible by the destruction of the top part. For we do not even know
whether the upper hieroglyphs occupied three or four rows each, the latter
being the case at least in part, and there may have been a superscription
over the day signs in the left half.

These upper signs are always followed by a picture, then three rows of
hieroglyphs, then a second picture and next two rows of hieroglyphs and
lastly a third picture.

Let us first examine the pictures:--

At the top of pages 46-49 there is on each page a deity, who with his right
arm extended is offering or receiving something. He is seated on
astronomical signs; on page 46 B's head accompanies these signs. On pages
46 and 48 the deity is undoubtedly the old woman with tiger claws, who
usually pours streams of water from a jug (compare pages 39, 43 and 74). I
cannot identify the personage on pages 47 and 49. The object in the deity's
hand seems invariably to be a cup of foaming pulque. On page 49 another
object is placed above the cup, which I am unable to determine. The fifth,
page 50, differs from the other four and forms the connecting link, as it
were, between the upper row of pictures and the middle and lower ones.
Here, too, a personage is represented sitting on astronomical signs and
exhibiting symptoms of violent anger toward a second person opposite him
holding the cup in his hands. Both personages are painted as warriors.

The middle pictures on all the pages represent a warrior in a
half-kneeling, half-crouching posture, holding spears or a shield in the
right hand and brandishing a hatchet in the left. The shield on page 46 is
doubtless a representation of the sun-glyph; and on 47 the Venus sign is
combined with the head ornament. The hieroglyphs of these deities occupy
the first place in the middle line of the three lines above the pictures.

The five lower pictures represent a creature lying on the ground, pierced
by arrows and spears. On page 47 it is a jaguar; at any rate it is the same
animal found on pages 29a, 30c and 45c; a very similar creature pierced by
arrows is given in the Cod. Vat. B.; compare also the pictures in Seler's
"Venus-periode," page 371. On the other four pages this creature is in
human guise. On page 50 where, differing from the other four pages, this
figure is represented lying with the head to the right, it is plainly
shedding tears. Seler takes this figure to be E on page 48 and the tortoise
on page 49. The varying periods of time occupied by the revolution of the
planets is plainly conceived of as contest. But who is the victor in this
contest? The planet with the longer or with the shorter period of
revolution? Owing to obliteration only a small part of the hieroglyphs of
the top section is legible.

On page 46 we see the Venus sign and E's hieroglyph; on page 47 the sign
_c_, which occurs frequently on these pages, and is probably always
connected with Moan (the Pleiades and thus with the year). The numeral 1,
prefixed to an obliterated sign on page 47, is still legible, and we find
it repeated on the lower part of the same page. There is rather more to be
seen on page 48:--first the elongated head _q_ with the Ben-Ik superfix,
then the sign _a_, beside it that for the west with a prefix, in the line
below an Ahau, next, an Akbal sign with the prefix of the north, and lastly
a Moan sign.

On page 49 we see sign _c_ again occupying the first place, then o with
Ben-Ik, and in the lower line the year sign with that for 20 or the moon as
a superfix, and to the right of it the head with the Akbal eye, probably
denoting D.

This top part of the page is best preserved on page 50. In the third line
from the bottom we see the Venus sign and beside it the Moan sign, below, a
Cauac, then a Kin with the Ben-Ik superfix, then a Kan-Imix. Finally, in
the first place in the lowest row there is a Kin sign and in the second
place a sign resembling the year-sign, both having the same superfix, the
next sign is again _c_ and the last is a half-effaced sign, of which only a
Muluc is distinguishable.

Our knowledge of the middle section of these pages is somewhat more
definite. There are twelve hieroglyphs on each page, which I will number in
the following order:--

  1   2   3   4
  5   6   7   8
  9  10  11  12.

Unquestionably these 5 × 12 signs refer to a Venus year, more exactly to
the _beginning_ of it, the period of the east. The first sign, which is a
hand pointing to the right, merely refers here, as on the left side, to the
direction in which this is to be read; the second sign is always the sign
for the east, and the sixth invariably that for Venus.

Notice should be taken of the fact that the signs of the Moan and
screech-owl or death-bird are recurrent, that of the Moan appearing on page
46, sign 7; 48, 3; 49, 11; 50, 11; and that of the death-bird on page 47,
sign 3; 48, 11, 49, 3, 50, 3 and 7, _i.e._, only in places 3, 7 and 11,
which indicates that the 12 signs are divided each time into three times
four.

It is further to be noted that the five gods, who are represented on page
24 by hieroglyphs 36-40, always recur in the ninth place in the order of
the pages:--the god represented on page 24 by sign 36 is the 8th on page
49; the 38th on the same page is the 11th on page 46 and the 12th on page
50; the 39th is the 12th on page 47, and the 40th may be the 5th on page
49, though this is hardly possible. On page 49 the 9th hieroglyph seems to
be the 39th on page 24 joined to the sign for the month Kayab.

Of the twenty gods on the left side of these pages, I have already remarked
that E, who on page 24 occupies the 38th place, and the 11th on page 46,
also occurs as the 9th on page 48 and the 12th on page 50.

It is doubtless of special significance that the sign of the first of the
twenty deities on the left side of page 46 is repeated on the right as the
tenth sign on all the pages (on page 47 also in the eleventh place where it
has a prefixed 3). It seems as if this sign, which is otherwise quite
unfamiliar, might be connected with the sun and regarded as a contrast to
the Venus sign in the sixth place.

Also the 9th deity of the left side, the 1st of page 48, reappears in the
4th place on page 49; the 10th deity, the 2nd on page 48, in the 12th on
page 49; the 15th deity, the 3d on page 49, in the 9th on page 46 and the
8th on page 49 (as already stated); the 18th, the 2nd on page 50, in the
5th on page 46.

The 2nd of these deities is suggested by the 8th on page 47, perhaps also
by the 5th on page 50; the 3d and 13th seem to be A and to recur in the 3d
place on page 46.

On the other hand C, the god who, as I believe I have proved, is connected
with the day-sign Chuen, does not appear on the left side. Now the 4th sign
on page 46 contains a Chuen, which in the 12th sign on page 48 is probably
combined with a Muluc, in the 12th on page 49 with Yax and a prefixed 6,
and in the 4th sign on page 50 with C's sign, _i.e._, as a rule Chuen
stands in the 4th place in a line.

As the gods E and K already mentioned also appear on pages 25-28 in
connection with the change of the year, so we find the tiger on the top of
page 26, and I believe this animal occurs again in the 7th sign on page 47.

Of the day-signs I take the 4th on page 47 to be Kan, the 7th on page 48 to
be Caban, and the next sign, the 8th on page 48, to be Muluc. Now if we
take into consideration the fact, that of the three periods of the month
signs on the left side of these pages, the 18th (the middle) line is the
most important, owing to its ending, 18 Kayab, alone, if for no other
reason; furthermore, that in this middle period the second Venus year
always ends with a Kan year and the third with a Muluc year, one is
naturally led to suppose that the illegible sign 12 on page 46 is an Ix
(for thus the first Venus year ends) and that the days Cauac and Kan might
have been found among the obliterated day-signs on pages 49 and 50.

I shall examine the remaining signs in the order of the pages.

Sign 8 on page 46 is the same compound of Yax and Kin having as a superfix
the sign assumed by me to be the numeral 18, which occurs again in the
lower group on page 50 and also on page 27.

In the number 11 prefixed to the fifth sign on page 47, the 1 seems to be
indistinct and may not belong here. If we correctly assume that this number
is 10, then the sign is the same as the 34th on page 24, to the discussion
of which I beg to refer my readers.

Sign 8 on page 47 is an indistinct compound, the first part of which I
supposed above to be the sign of the second deity on page 46.

I cannot explain 4 and 5 on page 48.

As yet I do not understand sign 5 on page 49, which we seem to have met
before on page 22c.

Sign 7 on page 49 is the moon, which is very curious here.

I would like to call special attention to signs 5 to 8 on page 50. I
interpret the passage thus:--At the time of the summer solstice after the
reappearance of the Pleiades, the change of the Venus year takes place
(this time). I have already discussed the Venus sign in the sixth place and
the screech-owl so closely connected with the Moan (Pleiades) in the
seventh place. Sign 5 connects the sun (Kin) with the Ahau (lord) and the
cross-hatching on the left of it, which I have assigned to the tortoise and
thus to the summer solstice (Zur Entzifferung III, 3). Sign 8 is recognized
as very appropriate to the change of year; compare the first sign of the
middle section on pages 25-28. All this points to the day 18 Kayab, of one
of the Kan years, if, as I stated above, we base our computation on the
middle series of dates.

Now we have yet to examine the eight signs of the lower group, which we
will do in the following order:--

  1  2  3  4
  5  6  7  8.

Regarding the beginnings of these groups, I will venture a bold surmise,
which will, I hope, be improved upon by some one else. It concerns the
first sign of four of these five groups, which seem to me to refer to the
end of the Venus year, as those above refer to the beginning. This sign has
the following form:--

[Illustration]

I see in this the term of 73 days, which is the fifth part of the 365 days
of the solar year and the eighth part of the 584 days of the Venus year:--

It is combined with Chuen in all four cases (pages 46, 48, 49 and 50). But
I attribute the meaning of eight days to this Chuen sign, as I did on pages
25-28 and 42c-45c, though I am doubtful in these as in other cases.

Page 46 contains the sign for 73 with a Chuen under it, and a 1 prefixed to
each sign; _i.e._, 1 × 8 × 73 = expiration of the first Venus year.

On page 48 Chuen follows the sign for 73 and each sign has a 3 prefixed to
it; _i.e._, 3 × 8 × 73, expiration of the third Venus year.

On page 49 the two signs again stand side by side, but the prefix is a 7
instead of the expected 4. By an error this 4 has been added to the 3 of
the preceding page, but, for a wholly unintelligible reason, prefixed to
the crouching person below the Chuen, as if to correct the 7.

Page 50 again has the sign for 73 above and the Chuen below. A prefixed 5
would seem to be in order; instead of it, there is a 10, one 5 for the 73
and another 5 for the 8 days. In this connection let me say that I believe
I have found on page 27, top left, the year of 365 days divided into 5 ×
73.

Page 47 differs from the others. Above two oval bodies appears the
cross-hatched figure resembling a clamp, like the one in the middle group
of page 50 in the fifth place, which I ventured to refer to the summer
solstice. There is a 1 prefixed to it. Is this equivalent to a union of two
Venus revolutions?

Next we repeatedly meet here, as we did in the middle groups, with the Moan
sign and that of the screech-owl belonging with it; the former is the 6th
sign on page 46 and page 50, and the latter is the 3d and 7th on page 47,
the 7th on page 49 and finally the 2nd and 4th on page 50.

The moon is represented in the 5th sign on page 48 and in the 3d on page 49
and indistinctly in the 4th on page 48.

The cardinal points occur here several times. The 3d and 7th signs on page
46 have at least the superfix of the south as a prefix; the 8th on page 47
apparently has the east, but with the familiar cross-hatched sign prefixed;
the 7th on page 48 plainly has the east, the 3d on page 50 the prefix of
the north prefixed to the cross _b_, and the 8th on page 50 the west, thus
approximating the usual order and distribution.

Of the gods I note the Akbal head, perhaps intended for D, in the 4th place
on page 46, also in the 3d on page 48, and lastly in the 5th on page 49,
the first two times with the Ben-Ik superfix, and in the 2nd place on page
47 the sign for A.

In the 4th place on page 47 we have the tortoise as the sign of the month
Kayab or of the summer solstice, in the 6th on page 47 the lightning-beast
or the month Kankin with a Ben-Ik superfix; the beast itself is pictured
below, and the same hieroglyph also with the Ben-Ik superfix is the 8th
sign on page 49.

It is hard to decide whether the sign 4 on page 49 represents the god F
owing to the line through the eye, or a female by reason of the prefixed
lock.

Sign 7 on page 50 represents the deity whose sign began the series of
twenty gods on the left of page 46 and which we have already met with
several times in the centre of the right side. We recognize the prefix as
having occurred in the middle group of the same page.

Sign 6 on page 48 is a Kin combined with an unfamiliar sign. Sign 5 on page
50 contains a Kin with a Yax and probably with 18 as a superfix (as on
pages 27 and 46 middle).

Sign 6 on page 49 contains a crouching person with a 4 which is probably
out of place here and to be regarded as a correction of the 7 above it.

Sign 5 on page 46 contains a Mac denoting the thirteenth Uinal or a
Tonalamatl, and having the sign _p_ as a superfix and a double Ik as a
prefix.

Sign 3 on page 46 merits special attention, because it contains the
duplication of the sign, which, at the end of the first part of the
Manuscript, pages 29-41, always began the groups of hieroglyphs on the
lower third of the pages.

I do not understand the second hieroglyph on page 46 and the 5th on page
47.

In conclusion I would call attention to the fact that the last hieroglyph
on page 48 is very peculiar. As on pages 51, 52, 61 and 69 it has the
meaning of 18,980 days and consists of an Imix with a comprehensive
superfix; its prefix is a 7.

But what is the meaning here of 7 × 18,980 = 132,860? When we recall the
statement made above that the whole section of pages 46-50 embraces 130,520
days, or, according to another calculation 135,200 days, it is a striking
fact that 132,860 is exactly the mean of the two numbers, being separated
from each by 2340 days = 9 × 260. Can it be an accident that on the next
page (page 49) the fourth Venus revolution is reached, for 4 × 584 = 2336,
_i.e._, almost 2340? The hieroglyph discussed here would not be so
extraordinary on page 50. I will not venture to assert as to the 511 in
132,860 = 511 × 260, that it is connected with the 511 which will appear as
the difference on page 58.

Before leaving these pages, I will give a brief survey of the two signs of
the screech-owl and the Moan (hieroglyph _c_ and the lower part of _d_)
which occur on these pages with such marked frequency.

In spite of obliteration, the first of these two signs is distinguishable
in the top groups on pages 47, 49 and 50, in the middle groups on pages 47,
48, 49 and twice on page 50, in the lower groups on page 46, twice on page
47, once on 49, twice again on 50, making 14 times in all. A few additional
cases might be added to these where the similar hieroglyph of the moon may
have been set down instead of the one in question.

On the other hand the second sign, always provided with the same prefix and
suffix as the first, occurs in the top groups on page 48 and 50, in the
middle of pages 46, 48, 49 and 50, and in the lowest on pages 46 and 50, 8
times in all.

Since the subject here is astronomical, it is suggestive less of a deity or
a sacrifice than of a period of time to which the allied page 24 has
already referred (see page 110 of this book). The inner meaning of these
pages is of course still enveloped in mystery.

Pages 51a--52a.

I shall begin the discussion of this very peculiar section with the
remarkable fourth column on page 52, which, very possibly, the scribe ought
to have placed at the beginning; for it looks like a repetition of the
section on pages 46-50, while everything else on the left and right of it,
apparently belongs together.

If we omit the two hieroglyphs at the top, which I regard as belonging to
the two rows of hieroglyphs extending over these two pages, we shall have
the following result, according to my point of view:--

    1          5
  Chuen       360
    2       18,980.

Since, as is frequently the case, the Chuen will here have the value of 8
days and the 5 with the sign for 360 may be regarded as 365, this group
might denote 8 × 365 = 2920, but actually be 2 × 18,980 = 37,960. Both
numbers are the basis of the section included on pages 46-50. And in the
same way the 13 repeated 13 times seems to me to refer to the 13 series of
days on those pages, which begin with the 13th day of the Uinal.

The two rows of hieroglyphs are in the main destroyed. We can still
recognize in the second and third columns of page 51 the signs for end and
beginning, which we often find in the vicinity of numbers; in the second
and third columns of page 52, the sun and moon; in the fourth column, the 8
days of such significance here and in the fifth and sixth, the normal date
IV Ahau 8 Cumhu repeated twice.

As the problem on pages 46-50 was to bring into accord the solar year with
the Venus year and consequently also the Tonalamatl, _i.e._, to combine
365, 584 and 260, so the aim here is first of all to bring the Tonalamatl
into unison with the Mercury year (115). For this purpose the number 11,960
is employed. This is equal to 46 × 260 = 104 × 115, including, therefore
just as many Mercury years as there were solar years in the preceding
section. 11,960 is also 8 × 1495, and this 8 is significant here, for, as
we shall see directly, the day forming the basis of this calculation is XII
Lamat, which comes 8 days after the normal date IV Ahau.

The series given here is based, therefore, on 11,960 and consists entirely
of multiples of this number, which, it is true, are recorded with the usual
irregularity. The members of this series, representing the greatest values,
which are set down in red numbers among the black, are the 31st and 39th
multiples of 11,960, which are separated from each other by 8 × 11,960,
viz:--370,760 and 466,440. All these numbers, of course, denote the day IV
Ahau.

The day XII Lamat as the actual starting-point of the Mercury revolution is
not introduced until we come to the dates placed below the series. Here we
find the days XII Lamat, I Akbal, III Ezanab, V Ben and VII Lamat written
one below the other, and repeated seven times. Each of these days is
separated from the next by 15, and the last of one row and the first of the
next on the left are 200 days apart, hence the whole is equal to 7 × 260 =
1820 days. From XII Lamat begins also the Peresianus, pages 21-22.

Now these dates are connected with the four large numbers, which we find on
page 52, but between the third and fourth, one number corresponding to the
day V Ben is omitted for lack of space.

These four numbers, to which I have added the corresponding dates, are as
follows:--

  1,412,848 = XII Lamat I Muan (6 Muluc).
  1,412,863 = I Akbal 16 Muan (6 Muluc).
  1,412,878 = III Ezanab 11 Pax (6 Muluc).
  1,434,748 = VII Lamat I Muan (1 Muluc).

It is curious that while the first three are separated from each other by
15, between the 3d and 4th, or rather between the missing 4th and 5th, 84 ×
260 days are inserted in excess of the required 15, _i.e._, 21,855. This,
however, is not accidental, but is due to the fact that between the first
number and the last exactly 21,900 = 60 × 365 days have elapsed. This
number is, however, = 18,980 + 2920, i. e., the sum of two very important
numbers, in the first of which the Tonalamatl and the solar year accord,
while both the solar and Venus years occur in the second.

I must here call attention to the fact that the four numbers are not
obtained without slight corrections, since in the 20-place of the third, I
have put a 11 instead of 10, while in the 360-place of the fourth, I have
omitted the three dots, _i.e._, set down a 5 instead of the 8.

Of these four dates, which were doubtless not far removed from the time of
the scribe, the three last are only the result of the first. Day XII Lamat
is the most important. As the beginning of a Mercury period it should be
regarded in the same way as I Ahau of the Venus period and IV Ahau of the
solar period; and the very next day, XIII Muluc, will subsequently be seen
to be the beginning day of the Mars period.

The four dates XII Lamat, I Akbal, III Ezanab and VII Lamat are set down in
the Manuscript directly below the numbers.

Now in the first column on page 51 we again find a day XII Lamat, as is
expressly stated beneath it. It has the number 1,578,988 and the
corresponding date is XII Lamat 6 Cumhu (6 Kan). This day, however, is
separated from the same day on page 52 (1,412,848 = XII Lamat I Muan 6
Muluc) by 166,140 days, that is by 8 × 18,980 + 14,300 = 639 × 260, _i.e._,
by 8 so-called Katuns increased by 55 Tonalamatls. Here 58 × 260 = 15,080
seems to have been added to 252 (XII Lamat - IV Ahau) and the sum
subtracted from 14 Ahau-Katuns = 1,594, 320. I could obtain this number
only by substituting 1 for 0 in the 20-place.

In the Manuscript the sign XII Lamat is set down above and below this
number. I must leave undetermined whether the 8 directly above the number
and combined with Kin and the Katun sign refers only to the 8 Katuns or at
the same time also to the 8 days from IV Ahau to XII Lamat.

It is also to be noted here that once before on page 24 of this Manuscript
(which forms the basis of this section) 8 × 18,980 = 151,840 days was found
to be the difference between 185,120 and 33,280, and that there, too, if my
restoration is correct, it was the highest term of the series = 4 × 37,960.

Finally, in the first column of page 51, we have the complete normal date 4
Ahau 8 Cumhu (9 Ix). But below this, between red numerals denoting the
1,578,988 mentioned above, there is set down in black the number 1,268,800.
This corresponds to the date IV Ahau 3 Zip (2 Cauac). It may have been
formed by adding 16,120 = 62 × 260 to 11 Ahau-Katuns = 1,252,680. It is,
however, not only equal to 4880 × 260, but also to 158,600 × 8, therefore
also divisible by the interval between IV Ahau XII Lamat, as well as by 104
= 8 × 13, while on the contrary it is not as we should expect, divisible by
11,960. I have changed the 11, in the 20 × 11, to 8 by omitting one line
and adding two dots, for otherwise the result would not be the one
required.

The magnitude of the number recalls the one on page 31, which is only 260
less, and that on page 62.

Finally it should be noted that the two large numbers on page 51 are
separated from one another by 310,188 days = 849 years and 303 days, which
corresponds exactly to the dates given for each. One may be situated as far
in the future as the other is in the past, but this does not necessarily
mean that the present coincides exactly with 1,423,894.

Pages 51--58.

Thus far we have examined only the upper halves of pages 51 and 52 and have
still to consider the lower, but not until we have finished the upper parts
of pages 53-58 of which the former are the continuation. We have first to
consider the series, then the pictures and lastly the hieroglyphs.

As on page 24 we found multiples of the number 2920 (= 8 × 365 = 5 × 584),
while on pages 46-50 it was divided into four unequal parts, so on pages
51-52 we find multiples of the number 11,960 (104 × 115 = 46 × 260) while
on pages 53-58 it is divided into 69 unequal parts. On pages 51-52 it was
the aim to combine only the Mercury course with the Tonalamatl, but here we
are confronted with the additional problem of bringing the lunar revolution
into accord with these two.

The lunar revolution, which we assume to be 29.53 days, of course requires
fractional computation, of which the Mayas either were ignorant or which
they timorously avoided; like the ancient Egyptians, who were acquainted
only with fractions having 1 as numerator, or beyond these at most with 2/3
(see Hultsch, "Die Elemente der ägyptischen Teilungsrechnung," 1895, page
16).

Now the Mayas had determined the lunar revolution so exactly that they
perceived the incompatibility of the period of 11,960 days with a multiple
of lunar revolutions. They found that 405 lunar revolutions amounted
approximately to 11,958 days, which is, in fact, the largest number on the
second half of page 58. In order not to drop the significant 11,960
altogether, they made use of a very shrewd artifice. They took as the
starting-point the day XII Lamat, corresponding to the number 11,960, and
set down XI Manik before it and XIII Muluc after it. Now if the count began
with XIII Muluc and ended with XI Manik, it actually resulted in 11,958.

Therefore what the Manuscript presents here is, in the first place, the
series, which is this time to be read from left to right. Below it are the
three days belonging to each member of the series and then a number for
each member stating the interval between it and the preceding one. The
members, the days and the differences must correspond with one another. It
is, therefore, no longer necessary to pay especial attention to the two
latter. They will serve merely to control and to correct the manifold
errors.

The entire period of 11,958 days was doubtless first divided into three
equal periods of 3986 days. And in order still further to subdivide these
shorter periods, the term of 177 days was employed as far as it would go;
177, however, is the half of a lunar year of 354 days, made up of 6 months
of 30 days and 6 of 29 days, thus allowing 29.5 days in round numbers for
each month.

Now 177 is = 3 × 29 + 3 × 30. The average, 29.5, however, is too short for
the length of the lunar revolution. In order to raise it as nearly as
possible to the exact time, two other numbers were introduced at certain
points of the series, viz:--148 = 2 × 29 + 3 × 30, 178 = 2 × 29 + 4 × 30.
148 = 5 months of 29.6 days, while 178 = 6 months of 29-2/3 days. Now let
us see in what _proportion_ these 148 and 178 days were distributed among
the periods of 177.

First we see that the period of 3986 days (_i.e._, a third of the whole)
was divided into 3 sections of 1742, 1034 and 1210 days, as follows:--

  1742 =  8 × 177 + 148 + 178
  1034 =  4 × 177 + 148 + 178
  1210 =  6 × 177 + 148
  ----------------------------
  3986 = 18 × 177 + 3 × 148 + 2 × 178.

This is equal to 135 months of 29.526 days each. Now the question arises
how did the Mayas express this fraction?

Perhaps some time in the future it will be found, that following their
vigesimal system, they designated it approximately thus:--

29 + ½ + 1/40 + 1/800.

The _whole_ period of 11,958 days was divided as follows:--

  3 × 1742 = 24 × 177 + 3 × 148 + 3 × 178
  3 × 1034 = 12 × 177 + 3 × 148 + 3 × 178
  3 × 1210 = 18 × 177 + 3 × 148
  ---------------------------------------
  3 × 3986 = 54 × 177 + 9 × 148 + 6 × 178.

Thus for every 6 parts of 177 days there was consequently 1 of 148 and to
every 9 parts of 177, 1 of 178.

Since 177 and 178 include 6 months each, while 148 equals 5 months, the
entire length of the period is 405 months, which are divided into 69
periods.

It was necessary to discuss all this before I could introduce the entire
series itself. In the following table I have set down the numbers and added
to them the differences between each number and the preceding one (to the
first, the interval between it and the zero point), just as they are given
in the Manuscript. An asterisk is added to show that the number has been
corrected by me and is wrong in the Manuscript, owing to a mistake either
in writing or in computation. The three columns correspond to the three
divisions of 3986 days, and the two horizontal lines divide the periods of
1742, 1034 and 1210 days.

    Page 53a:      |  24.  4163* 177   |  47.  8149  177
   1.   177  177   |  25.  4340  177   |  48.  8326  177
   2.   354* 177   |  26.  4488  148*  |  49.  8474  148
   3.   502  148   |    Page 58a:      |  50.  8651  177*
   4.   679* 177   |  27.  4665  177   |    Page 55b:
   5.   856  177   |  28.  4842  177   |  51.  8828  177
   6.  1034* 178*  |  29.  5020  178*  |  52.  9006  178*
    Page 54a:      |  30.  5197  177   |  53.  9183  177
   7.  1211  177   |    Page 51b:      |  54.  9360  177
   8.  1388  177   |  31.  5374  177   |  55.  9537  177
   9.  1565  177   |  32.  5551  177   |  56.  9714  177
  10.  1742* 177   |  33.  5728  177   |
  -----------------+-------------------+-----------------
  11.  1919  177   |  34.  5905  177   |  57.  9891  177
  12.  2096* 177   |  35.  6082  177   |  58. 10068* 177*
  13.  2244* 148   |  36.  6230  148   |    Page 56b:
    Page 55a:      |    Page 52b:      |  59. 10216  148*
  14.  2422* 178   |  37.  6408  178*  |  60. 10394  178*
  15.  2599* 177   |  38.  6585  177   |  61. 10571  177
  16.  2776  177   |  39.  6762  177   |  62. 10748  177
  -----------------+-------------------+-----------------
  17.  2953  177   |  40.  6939  177   |    Page 57b:
  18.  3130  177   |    Page 53b:      |  63. 10925  177
    Page 56a:      |  41.  7116  177   |  64. 11102  177
  19.  3278  148   |  42.  7264  148   |  65. 11250  148
  20.  3455  177   |  43.  7441  177   |  66. 11427  177
  21.  3632  177   |  44.  7618  177   |  67. 11604  177
  22.  3809  177   |  45.  7795  177   |    Page 58b:
    Page 57a:      |    Page 54b:      |  68. 11781  177
  23.  3986  177*  |  46.  7972  177   |  69. 11958  177

No one acquainted with the cursoriness of the Maya Manuscripts will be
surprised that among 138 numbers I have declared 21 to be wrong.
Furthermore the 21 errors are lessened by the fact that six of them are
really only one, for in all 6 cases where the difference is 178, the scribe
has overlooked this and written down the usual 177, although the numbers
and the days of the series very correctly indicate 178. Again the three
errors in groups 58 and 59 are also only one, for the author had confused
the differences 177 and 148 and had, therefore, to write down 10,039
instead of 10,068. In group 4 the error is merely the omission of a line
meaning 5. The scribe must have been at the same time the computer and
therefore the actual author of the Manuscript.

Furthermore I must call attention to the regular position of the
differences 178 and 148. In the three periods of 1742 days the 178 always
occupies the 6th place and in the periods of 1034 it is always in the 4th
place. This difference appears, therefore, in groups 6, 14, 29, 37, 52 and
60, _i.e._, 8, 15, 8, 15 and 8 groups apart; but it is entirely lacking in
the periods of 1210 days. And in all nine sections the 148 occupies the
third place, _i.e._, directly in front of the pictures, which will be
discussed immediately, therefore in groups 3, 13, 19, 26, 36, 42, 49, 59,
65, _i.e._, at intervals of 10, 6, 7, 10, 6, 7, 10 and 6 groups. But I must
point out an error fraught with consequences. Groups 22 and 23 quite
correctly have the difference 177, but in this single instance the scribe
has written down 178 and hence has computed the three days belonging to it
as VII Ix, VIII Men and IX Cib instead of VI Ben, VII Ix and VIII Men, and
from here on to the close he is always one day in advance, so that on page
58 group 69 ends with the days X Cimi, XI Manik and XII Lamat, while it
ought to have ended with IX Chicchan, X Cimi and XI Manik.

So much for the series. Vid. on this series my paper "Zwei
Hieroglyphenreihen in der Dresdener Mayahandschrift" (Zeitschrift für
Ethnologie, 1905, numbers 2 and 3). Let us turn next to the ten pictures
which are inserted in this series, three of which appear at the end of each
period of 2920 days as on pages 46-50. Let us attempt to advance a step
further in the darkness which still surrounds us here.

One of these pictures, the 8th, which is on page 56b, is in the wrong
place, owing to the error in computation in Groups 58 and 59 to which I
called attention above. It belongs not _before_ but _after_ group 59, the
first on page 56b. This is indicated in the Manuscript itself. For in group
59 the two hieroglyphs, usually placed above each group, are missing and we
find instead of them the sign resembling a snail, which is doubtless a very
much emphasized zero (compare my "Erläuterungen," page 29), which indicates
that the section designated by a picture closes with this group.

Having corrected this error we see that the ten pictures are on the
following pages and come after the following numbers of the series:--

   1.   53a     502
   2.   55a    2244
   3.   56a    3278
   4.   57a    4488
   5.   52b    6230
   6.   53b    7264
   7.   54b    8474
   8.   56b   10216
   9.   57b   11250
  10.   58b   11958.

From this it follows that a picture is assigned to each of the nine
sections composing the series. They are placed, however, not at the
beginning or end of the section, but always after the expiration of 502 (=
2 × 177 + 148) days. The pictures are thus separated from one another by
1742, 1034 and 1210 days, which intervals correspond exactly to the length
of the nine sections. But the last picture is separated from the preceding
one by 708 days, and as it has a character quite its own, it must be
discussed separately. But these 708 days with the 502 days of the beginning
quite regularly amount to 1210 days, and the series is therefore to be
considered as a recurring one.

Now these nine pictures might very easily be regarded as forming a new
series, which is inserted in the original one and which has the day 502 as
its zero-point. In that case, we shall have to subtract 502 every time from
the days set down in the Manuscript. This new series may be represented
thus:--

   1.   53a       0
   2.   55a    1742
   3.   56a    2776
   4.   57a    3986
   5.   52b    5728
   6.   53b    6762
   7.   54b    7972
   8.   56b    9714
   9.   57b   10748.

It is certainly remarkable that the last number, 10748, corresponds so
closely to the time of the revolution of Saturn, which is computed at 10753
days. For owing to the slowness of its progress, the Mayas may have known
not only the apparent but also the actual revolution of Saturn. Besides the
apparent revolution of Saturn (378 days from one superior conjunction to
the next) could not be made to coincide very well with the length of the
solar year. I will immediately present a further confirmation of my theory.

All these pictures have rectangles above them, of which I have spoken in my
"Erläuterungen," page 16, and which always enclosed two or three
hieroglyphs in which, with due hesitation, I assumed to be the signs of the
sun, moon, and planets. This theory has as yet called forth no serious
opposition.

Now in the passages just mentioned, I indicated the following figures as
the signs of Saturn:--

[Illustration]

These figures actually occur in all the nine pictures with the exception of
the first, which has no rectangle at all, and where in true Maya fashion,
the zero-point is concealed.

I go still further in my bold hypothesis. The time of the apparent
revolution of Jupiter has been placed at 397 days. The Mayas, I think,
computed it at 398 days. In the passage alluded to I regarded the following
as the sign for Jupiter:--

[Illustration]

We find these signs in pictures 4, 6, 7 and 9. The corresponding numbers
reduced for the revolution of Saturn are 3986, 6762, 7972 and 10,748. I
assume that the third picture, _i.e._, the number 2776, is another
zero-point, in consequence of which the sign is here suppressed, and that
still another is the tenth picture with the number 11,958, which has no
relation to the revolution of Saturn.

If we compare these numbers with the 398, _i.e._, the apparent revolution
of Jupiter, we have the following:--

   3.     2776 =  7 × 398 - 10
   4.     3986 = 10 × 398 +  6
   6.     6762 = 17 × 398 -  4
   7.     7972 = 20 × 398 + 12
   9.    10748 = 27 × 398 +  2
  10.    11958 = 30 × 398 + 18

The differences 10, 6, 4, 12, 2 and 18 are so small in comparison with 398,
that the numbers 2776, etc., might very well have been regarded as
approximate multiples of the revolution of Jupiter. And the remainders in
the seventh and tenth pictures could be still further reduced. In the
seventh picture, the first sign is very unusual and one which I do not
remember having met with elsewhere. If it should be possible to regard it
as the number of the thirteen week days, then it would follow (the Saturn
sign being regarded as unimportant) that the contents of the rectangle
meant:-- 13 + a multiple of 398, by which this remainder would be reduced
to -1.

The tenth picture has the cross _b_ as the beginning of the rectangle. This
is the sign for union, very often denoting especially the union of all the
twenty days. Thus we have here (aside from the middle sign to be discussed
later) the formula:-- 20 + 30 × 398 - 2 = 11,958, or even 20 + 30 × 398 =
11,960.

The regular progression from the 7th multiple to the 10th, 17th, 20th,
27th, and 30th multiples in the above six equations is also somewhat in
favor of my theory, while the four rectangles without the Jupiter sign are
by no means multiples of the Jupiter revolution:--

  1.      502 = 398 + 104
  2.     1742 =   4 × 398 + 150
  5.     5728 =  14 × 398 + 156
  8.     9714 =  24 × 398 + 162.

Let us now try to interpret the meaning of the remaining rectangles (always
omitting the Saturn sign as a matter of course.)

In pictures 2 and 8 the rectangle also contains the sign of the moon or of
the twenty days. Beside it in picture 2 is the sign, which in my
"Erläuterungen," page 16, I regarded as the sign for Mercury. Hence we have
here 20 + 15 × 115 = 1745, _i.e._, only 3 units more than the required
1742.

The rectangle with the eighth picture contains in addition to the moon a
sign which looks as if it were intended for a whole divided into four
parts. Until something better (perhaps the the sign of Venus) is proposed,
I will assume that it is the quarter of the Tonalamatl, _i.e._, 65, and I
take the required number to be 9714 in the form of 20 + 149 × 65 + 9.

Above the third picture I see a Mercury and a Venus sign and I read 584 +
19 × 115 = 2769, which is only 7 units less than the required 2776.

The fifth picture still remains to be discussed, but I do not know how to
unite the Mercury revolution here with the 5728. For the present, however,
I am inclined to believe that there is a mistake in this passage.

We pass now from the obscure contents of the rectangles to the equally
mysterious pictures themselves.

Aside from the tenth picture, I find human forms in four pictures.

Picture 1, page 53a, is the death-god (A) seated and pointing upward, an
appropriate representation for the zero-point of the Saturn series, _i.e._,
for the end of the preceding revolution.

Picture 2, page 55a, contains the head of a deity, probably D's with the
suggestion of a beard and the sun-sign on his forehead. The head is
surrounded by a ring striped black and white.

Picture 3, page 56a, is the head of B, again with a beard and with the sign
Kin (sun) above. The head is surrounded by a design, the left part of which
is black and the right white.

Picture 6, page 53b, represents a hanged woman, which Schellhas,
"Göttergestalten," page 11, takes to be the Maya goddess Ixtab, the goddess
of the halter, _i.e._, of the hanged.

The centre of picture 4 on page 57a, contains the suggestion of a face,
perhaps in place of the Ahau sign, and on either side of it is a black and
white surface.

It is further important to note that four times in this section Kin (sun)
forms the centre of the picture, viz:--pictures 5, 7, 8 and 9, pages 52b,
54b, 56b and 57b. In all four cases there is on either side of Kin a black
and white surface, such as we have already seen in picture 4 and similar to
that in picture 3. Pictures 8 and 9 are vomited up, as it were, by a
serpent placed below them, in the same way as B is represented on pages 34b
and 35b. In pictures 5 and 8, four objects suggesting arrows extend from
the Kin in four directions and probably denote the four cardinal points or
the four Bacabs, of which we shall have more to say presently. Two of these
arrow-like signs also appear in picture 7, page 54b, but only on the black
and not on the white surface.

I will postpone discussing picture 10 until later and pass on to the
hieroglyphs above the first nine pictures, about which it is true I have
nothing satisfactory to say. There are always properly speaking ten of
these hieroglyphs, among them the two signs for the sun and moon. But the
scribe introduced the latter only in pictures 1-4, and also with the more
elaborate last picture 10. With pictures 5 and 9 he omitted these signs in
order to represent the other eight larger and with greater distinctness of
detail. Among these hieroglyphs are several of gods, especially that of A
with pictures 1, 5 and 9, and H with picture 5, and with pictures 1, 3, 5,
7, 8 and 9 there are other heads, some of them bird-heads, regarding which
I am uncertain.

The Ben-Ik sign, to which I have assigned the meaning of a lunar month,
belongs with pictures 4, 8 and 9 and occurs twice each with pictures 1 and
10.

I am inclined to see the sign for Mercury in the crouching figure belonging
to pictures 9 and 10, which is drawn upside down and combined with the half
Venus sign (11958 = 104 × 115 - 2).

Hands grasping a hieroglyph (a sign for 20 days?) are represented in
pictures 1, 7, 8 and 10.

The enigmatical numbers, prefixed to the hieroglyphs, occur several times,
thus a 1 with pictures 1 and 10, and a 4 twice with picture 8 and a 6 with
picture 3.

Now let us examine picture 10 somewhat in detail and also the signs
standing above it, since both are of special significance here. This
representation treats of the period of 11,960 days in which the Mercury and
lunar revolutions meet. And this is proved by the ten hieroglyphs, which I
will number as follows:--

  1   6
  2   7
  3   8
  4   9
  5  10.

I can omit Signs 3 and 8, sun and moon, since they refer to a period of
time only in a general way. Sign 1 seems to me, as I have already stated,
to have reference to the revolutions of Mercury. Then follows sign 2, the
upper part of which is a mat and the lower the Muluc sign. I believe this
sign is intended to denote that the beginning of this period is in a Muluc
year. Indeed, our examination of pages 51-52 showed that it was the year 6
Muluc. The mat (Pop) is very properly the symbol of beginning, since the
first month of the year was likewise called Pop. Sign 7, it seems to me,
indicates that this period should be divided into lunar months (denoted by
Ben-Ik), and, as I have already demonstrated in my examination of page 24,
the length of the period is stated here by Signs 4, 5, 6 and 9, but the dot
before the fifth should be placed before the fourth, as is actually the
case on page 24. Therefore:--

   4 =   21
   5 = 7200
   6 = 4680
   9 =   59
      -----
      11960.

It is perhaps not accidental that the ninth sign is that of the fourteenth
month, which signifies the expiration of the preceding lunar month, for
here the month begins with the first day of the fifteenth month.

Sign 10 is doubtless Xul = end, as it so often is, for example, on pages
61-62 below. But I have not solved the meaning of the two prefixes. The end
would be XII Lamat 16 Yax (13 Ix).

The picture represents a human form, which has in place of a head a design
somewhat resembling the head of a lance. It is sitting with legs spread
apart, and in this respect may be compared with god B of Cort. 9, who is
represented in the same way. In the picture before us, the figure holds in
its upraised hands the sun and moon signs, which are constantly repeated
throughout the series. The Venus sign is placed between the outspread legs.
In the rectangle above the figure, this sign is repeated in a more concise
form, while on the left the cross _b_ appears as the sign of union or
multiplication, and on the right that of Jupiter, whose period of
revolution is here multiplied by 30 (30 × 398 = 11,940). And the two Venus
signs can mean nothing more than that this period of 11,960 also serves the
purpose of filling up the gap between the two large Venus-solar periods of
37,960 days, like the similar process which we saw on pages 46-50.

We have examined first the series and then the pictures with the
hieroglyphs belonging to them. Let us pass now, as the third step, to the
examination of the two rows of hieroglyphs extending above the numbers
throughout the whole section. First of all, I will again set down here the
position of each of the sixty-nine groups:--

  Page 51.          | 52.        | 53.              | 54.
  31.32.33.34.35.36.|37.38.39.40.| 1. 2. 3. 4. 5. 6.| 7. 8. 9.10.11.12.13.
                    |            |41.42. 43.44. 45. |46.47.48.49.50.

  Page 55.             | 56.        | 57.           | 58.
  14.15.16.17.18.      |19.20.21.22.|23.24.25.26.   |27.28.29.30.
  51.52.53.54.56.57.58.|59.60.61.62.|63.64.65.66.67.|68.69.

Since each group contains two hieroglyphs, this makes 138. in all. Of
these, however, about 24 on the upper halves of the pages, are wholly or
almost wholly effaced which very materially hinders the trustworthy
determination of the context.

Furthermore group 59 is entirely lacking or rather group 58, in the place
of which the 59th has been set down. The eighth picture was probably
already drawn, when the artist saw that there was not room enough left for
the 58th and 59th groups. Hence he omitted the 58th, setting down in place
of it the 59th and in the place of the latter he set down the zero
mentioned above.

The question now arises:--Are these hieroglyphs dependent upon the days and
numbers of the series and upon the pictures, or are they entirely
independent of them?

I find but _one_ point in favor of the first possibility, viz:--the Venus
sign in group 4b (I will designate the upper hieroglyphs by _a_ and the
lower by _b_). It is placed in the period indicated in which 502-679 days
elapse, and in which, therefore, Venus has finished a revolution of 584
days. It may be, that by way of exception, this significant date was
intentionally recorded.

On the other hand, there are many things, which favor an entirely different
interpretation of these hieroglyphs. Thus I am of the opinion that the
ritual year of 364 days with its four Bacab periods of 91 days each is
referred to here, as we have already found it referred to on pages 31a-32a
and on page 45a, and shall find it again on pages 65-69 and 71-73. In that
case the single groups would be separated from one another by one Maya week
= 13 days.

I will now arrange the sixty-nine groups in the following order (the reason
for which will become clear directly):--

    I   4  11  18  25  32  39  46  53  60  67
   II   5  12  19  26  33  40  47  54  61  68
  III   6  13  20  27  34  41  48  55  62  69
   IV   7  14  21  28  35  42  49  56  63   1
    V   8  15  22  29  36  43  50  57  64   2
   VI   9  16  23  30  37  44  51  58  65   3
  VII  10  17  24  31  38  45  52  59  66.

The groups in a horizontal row are separated from one another by 7 or a
multiple of 7. If now a hieroglyph is repeated in those places, which are
in the same horizontal row, then this is a confirmation of the supposition
that Bacab periods are meant to be represented here. Hence I will examine
each row in turn. These rows extend over the long period of 69 × 13 days
probably merely for the purpose of filling up the space.

I. In 39b, 46b, 53b and 60b, _i.e._, after every seven groups, perhaps also
in 18b, we find the following sign, which I identified as that of a Bacab,
in Globus, Vol. LXXI:--

[Illustration]

Hence this denotes the beginning of the Bacab period. In 4b the sign is
replaced by that for Venus. In 11b, 25b, 32b and 67b we find other signs,
it is true, nevertheless the regularity stated above cannot be accidental.
The upper signs of groups 39a, 46a, 53a and 60a contain an Imix and
corroborate the connection.

II. 5b and 26b (after 3 × 91 days) contain a head very like the preceding,
which readily suggests the idea that it is merely a Bacab sign pushed one
group ahead, but it also appears in 13b, 50b and 52b.

Then 12b, 54b and 61b correspond, _i.e._, after six groups of 91 days and
one more of the same length, but the same sign appears also in 34b, 48b and
56b.

III. 41b and 69a are Xul = end and are therefore separated by 28 × 13 = 4 ×
91 days, _i.e._, the length of a year. It is singular that both signs of 41
are like those of 47; if we assume that 47 was set down one group too soon,
it would be in excellent keeping with the rest. The Xul also appears in 11b
and 28b. 34b and 48b correspond after 2 × 91 days, as already mentioned
under II.

IV. 42a and 49b both contain the sign for the sun between clouds.

V. 36b and 57b agree after 3 × 91 days; the same sign appears again in 10b
and 20b.

15a and 36a correspond after 3 × 91 days; we shall continue the examination
of this sign under pages 71-73.

VI. 37a and 65a agree, _i.e._, after 4 × 91 days = a year. The sign
contains a human figure stretching both arms aloft. The passing of a year
was likewise indicated in III, but a year coming 52 days later than this.

VII. 10a and 31a agree, _i.e._, after 3 × 91 days. The sign is composed of
the crouching figure prefixed to the cross, which we also find in 12b, 35a
and 65b; it is prefixed to a different hieroglyph in 30a. In 38b, 52b and
59b (58 in the Manuscript) we see bird-like heads resembling the Bacab
sign. We should expect to find a familiar sign in 45, which is drawn
between these, but a Moan appears there instead. These signs seem to
indicate the end of the Bacab period. Does the Moan sign here, too, suggest
the end of the year?

In 38a, 52a and 59a we again see an Imix, and I consider it a corroboration
of my theory that all the four signs of groups 38 and 39 are repeated in 52
and 53 after 2 × 91 days.

I believe a further corroboration is the fact that though many of these
hieroglyphs have no connection with these periods of 7 × 13, _i.e._, with
the divisions of the ritual year, they do correspond with the usual
divisions of the Tonalamatl, _i.e._, 4 × 13 and 5 × 13 days.

After 4 × 13 or a multiple of it the signs recur in 20b, 24b, 40b, 44b-12b,
48b, 56b-16b, 32b, 64b-26b, 50b-10a, 30a-37a, 65a-15b, 51b-11b and 47b.

As examples of 5 × 13 I would mention 3b, 63b-10a, 20a, 30a-5b, 50b-24b,
29b-35b, 65b-15b, 20b, 40b.

Finally, I must mention two more hieroglyphs, which are limited almost
entirely to these pages:--

[Illustration]

In the first sign, which occurred on page 10a, I thought I recognized the
lunar month of 28 days. It occurs in this section in connection with the
third picture on page 56, and besides in the following groups of
hieroglyphs:--16b, 32b and 64b, always combined with a Yax. The regularity
of the intervals is striking, but as yet I can neither explain that, nor
the crouching personage (Mercury?) in the 10th, 20th and 30th groups and
again in the next, the 31st.

The second sign is found _only_ on these pages and here not less than
eleven times, possibly with the addition of the effaced sign in 6b and 27b
which may have been the same hieroglyph. The eleven places in which it
occurs are as follows:--3b, 15b, 17b, 23b, 24b, 29b, 40b, 44b, 49a, 51b and
63b. Two different prefixes are added to it; one in the first two and the
last two places and also in the last but two joined with Kin, and the other
in the six middle places. Of the eleven groups, 17 and 24, 44 and 51 are 7
groups apart, 3 and 17, 15 and 29, 49 and 63 are 14 groups apart, 23 and 44
are 21 groups apart, and hence 23 and 51 are separated by 28 groups or 1
year. Group 40 alone is not concerned with these intervals of seven or
multiples of seven.

Now, how far may all these periods of time be due to accident and how far
to design? Accident _alone_ is quite out of the question. The frequent
repetition of the sun-sign in groups 49, 50 and 51 on pages 54b and 55b,
seems to me to refer to the conjunctions of the sun with certain stars,
which occur at intervals of thirteen days.

Pages 58--59.

This section is also based on a series occupying the whole of page 59,
which contains nothing but number and day signs. This series has the
difference 78, which we found once before on page 44. There the
starting-point was III Lamat, here it is the day XIII Muluc, probably
coming in the year XIII Muluc, as in Cort. 40b, as I shall have occasion to
suggest later. The series extends, with the usual errors and variations, in
four divisions from top to bottom. The days, which are always two days
behindhand, owing to the number 78, in 780 again reach the day XIII Muluc,
at which point the succeeding members remain stationary, since from here on
the difference is always 780 or a multiple of it. 780 days are, however,
the apparent time of the revolution of Mars, which is the only planet now
left to be discussed, the subject of pages 46-50 having been Venus and the
sun, and of pages 51-58, Mercury and the moon with incidental treatment of
Saturn and Jupiter. With 780 as its difference, the series ascends to 19 ×
780 = 14,820, and then continues with this large number as its difference
until the series is lost in the effaced passages.

Curiously enough, however, directly under the line containing the 14,820,
there is a new series composed of nine members, or ten counting the
suppressed starting-point. But this starting-point is again the day IX Ik,
the difference, as proved by the annexed days, is again 78 and the series
ends with 780. Thus the starting-point is the only difference between the
two series. The principal series contains all the even and the secondary
series all the uneven days. Can the starting-point of the revolution of
Mars have been determined according to different principles? Is it possible
that in one case the beginning of the planet's retrogression was adopted as
the starting-point, and in the other case the date on which the planet,
after completing its retrograde course, again reached the degree of right
ascension at which it had begun its retrogression? This is a difficult
matter to decide, since the period of the retrogression of Mars fluctuates
between 62 and 81 days. The interval from IX Ik to XIII Muluc is 147 and in
reversed order 113 days.

It can hardly be assumed that the 19 of the IX 19 or IX Ik is connected
with the 19 × 780 mentioned above or with the 19 + 19 + 19 + 21 into which
the 78 is divided on pages 44-45, or finally with the 19, which four times
forms the principal part of the sub-divisions of 65 on pages 33-34.

Numbers amounting to millions accompany this series in the usual way. Two
of these are on page 58, viz:--1,426,360 and 1,386,580; but with the sign
of the sixth day, which is important here, between them. Below these
numbers, however, are two month dates:--first the normal date IV Ahau 8
Cumhu and, if I have correctly restored the effaced number before the month
sign, which in its turn is indistinct, the second is XIII Muluc 2 Zac,
which would fall in the year VIII Muluc. The encircled numbers also occur
here. They are set down beside the lower number of seven figures. We find
here a red 12 with a black 1 inserted, below this a black 7 and below this
again, enclosed in a red band, a black 11, which I regard as also
representing the value of a red number. We shall find a similar instance
among the serpent numerals. Then we have here 1. 7. 11. = 511 and 12. 11. =
251. But 511 = 260 + 251 and 251 is the interval between XIII Muluc and IV
Ahau.

With the day XIII Muluc and the interval 9 between IV Ahau and XIII Muluc,
numbers for XIII Muluc have been formed amounting to millions, which,
however, have been suppressed in the Manuscript, just as they were on page
31 where, in like manner, numbers were first formed for day XIII Akbal.

I assume that to begin with, 76 Tonalamatls (= 19,760) were added to this 9
and then 228 Tonalamatls (= 59,280), the 228 being = 3 × 76 and the 59,280
including 76 revolutions of Mars.

The result in one case was 19,769 and in the other 59,289. If the 12
Ahau-Katuns, which are specified as 1,366,560 on page 24b be added here, we
have the following numbers:--

  1,386,329 = XIII Muluc 2 Mol (3 Muluc),
  1,425,849 = XIII Muluc 2 Zip (12 Muluc),

and if the two encircled numbers of the Manuscript:--251 and 511 be added,
the sums are 1,386,580 and 1,426,360, _i.e._, the two large numbers of the
Manuscript.

The dates corresponding to these numbers are as follows:--

  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:--

The three pairs of numbers found by computation are as follows:--

  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.

3. The two numbers 2b and 4b are exactly the same.

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.

The work of the Indian computer was, therefore, as follows:--

He took the days for granted. First he determined the differences between
them; then he added to each difference a multiple of 260; and the choice of
the multiple seems to have been quite arbitrary. The number thus obtained
he added to 12,412,920, unless it was the smaller, in which case he
subtracted it from 12,412,920, and the result he wrote down in the
serpents.

We shall find the same process, only somewhat amplified, with the serpent
on page 69.

Are the seven numbers intended to denote the destruction of the seven
planets? I hope this question will be answered in the near future.

There now remains of the contents of these pages only the two columns on
the left of page 61, which we will now examine and at the same time compare
them with the corresponding column of page 69, the upper part of which is
exactly the same, and the lower very nearly so. Each column consists of 18
hieroglyphs, which I count from the top downward, designating those of the
first column by _a_ and those of the second by b.

At the first glance these double columns remind one of the inscriptions in
the temples and on the stelae, especially of their beginnings, the
so-called initial series. Here, in the second column, we find the statement
of the usual periods:--144,000, 7200, 360, 20, 1, but in the first column
we find faces belonging to them. In his work "The Archaic Maya
Inscriptions," 1897, which, on the whole, contains more of imagination than
of science, J. T. Goodman unqualifiedly declares these faces to be numbers
by which the periods indicated beside them are to be multiplied, and this
theory has already found considerable recognition; we will therefore try to
follow where he leads.

1a and 1b are effaced on page 61; they probably contained a sort of
superscription as on the inscriptions. 2a is effaced on page 61, but the
sign may be recognized from page 69 as that with which on page 46 the
series of the twenty deities begins after 236 (4 × 59) days. On pages 61
and 69 it takes the place of a face, to which I am inclined to assign the
numerical value 4. In 2b, which is C's head, I am inclined to look for the
value 2,880,000 = 20 × 20 × 20 × 360 days, which is not at all
inappropriate for C, as the sign of the north pole around which everything
revolves. I therefore propose to read 2ab as 4 × 2,880,000 = 11,520,000.
3b, it seems to me, resembles the sign for 144,000, which I found in the
inscriptions and which is repeated in 12a. It must, however, be left
undecided by what this same number in 3a is to be multiplied; 3a is
repeated besides in 8a and 13b. 4a contains the head of E, and 4b that of
the Moan. 4a seems to refer to 5a, and 4b to 5b. But 5a and 5b are the same
sign, which, inserted between the 144,000 and the 7200, can scarcely mean
anything else than the so-called Ahau-Katun of 6 × 18,980 = 113,880 days.
Have we two such periods here? Were they designated by consecutive numbers?
Now comes the 7200 in 6a, and the number 8 with E's head and the inserted
sign for 360 days in 6b (on page 69 without E's head), therefore 8 × 360 =
2880. Seler also thinks 7a has the numerical value 16 (Einiges mehr über
die Monumente von Copan, etc., page 217); 7b belongs to 7a. 7b, a Kin with
a I and a suffix and a leaf-shaped prefix, is inserted between the 360 and
20. What can it mean? Hardly the 260, for this is represented elsewhere
(_e.g._, page 24) by the thirteenth month Mac. Or can it possibly refer to
the month Yaxkin (days 120-140)?

8b is a Chuen sign, which, with its prefix (superfix on page 69) always
denotes twenty days in the inscriptions. It is multiplied with the same
unknown head in 8a, which we have already met with in 3a. 9a contains H's
head, and 9b is an unknown head with inserted Kin; the two signs must of
necessity indicate the single days still to be added to the period, though
as yet we do not know how.

The normal date IV Ahau 8 Cumhu then follows in 10ab. If it refers to the
signs just now discussed, then they must denote a number of about the same
magnitude as the serpent numbers. 653 or 654 times 18,980 seems to suggest
itself, but we shall have more to say later on this subject. My efforts to
reach a definite result here have failed.

Nor does the lower part of the two columns lead me to the desired goal. As
it seems to consist of several groups, I will first combine 11ab and 12ab.
I look upon 11a as denoting 20, and with regard to 11b I have already
expressed the surmise in the Zeitschrift für Ethnologie XXIII, page 153,
that it may mean 8760 = 24 × 365, _i.e._, three Venus-solar periods. That
would be 20 × 8760 = 480 × 365 = 175,200. The Moan in 12a may have the
value 13, for this number is so often combined with the Moan. As we saw
under page 51, 12b is = 18,980; 13 × 18,980 = 246,740. Accordingly the four
signs taken together may mean 421,940 = 1156 × 365.

The second group, from 13a to 15b, refers, on the other hand, to the year
of 360 days. First 13a = 144,000, having in 13b the unknown multiplier,
which we have already seen in 3a and 8a. Then follows in 14a, 15 × 7200 =
108,000; in 14b, 9 × 360 = 3240; in 15a, a 20 with a prefixed 1 (21?); and
in 15b, three days. It would be more correct to place the 1 beside the
following 3. The whole sum would then end with the number 4, which would
agree with the day Kan, the date specified below.

In the third group the 16a = 19 × 18,980 = 360,620, remains a mystery; an
empty outline of a sign is added in 16b.

17ab also forms a group by itself. 17a contains a sign, which rather
suggests the Bacab, upon whose period of 91 days the series belonging here
is based. The Imix in 17b with a superfix is still unintelligible.

The columns end in 18 with the date IX Kan XII Kayab, the starting-point of
the serpent numbers.

Pages 65--69.

I think it very likely that this section bears the same relation to pages
61-64 as pages 46-50 do to 24 and as 53-58 to 51-52. For here, too, a
period of time forming the basis of the earlier section seems to be divided
into smaller parts. On page 64 we recognize as the basis of the series the
number 91, the quarter of the ritual year of 364 days; here we have to do
with the fourfold division of 91 into 13 unequal parts. And the real
starting-points on these pages, as on the previous ones, are the days III
Chicchan and XIII Akbal.

The four series of numbers, the top one of which I have probably correctly
restored from what still remains, are as follows:--

  9 XII, 5 IV, 1 V, 10 II, 6 VIII, 2 X, 11 VIII, 7 II, 3 V, 12 IV,
    8 XII, 4 III, 13 III.
  11 I, 13 I, 11 XII, 1 XIII, 8 VIII, 6 I, 4 V, 2 VII, 13 VII, 6 XIII,
    6 VI, 8 I, 2 III.
  11 XI, 13 XI, 11 IX, 1 X, 8 V, 6 XI, 4 II, 2 IV, 13 IV, 6 X,
    6 III, 8 XI, 2 XIII.
  9 IX, 5 I, 1 II, 10 XII, 6 V, 2 VII, 11 V, 7 XII, 3 II, 12 I, 8 IX,
    4 XIII, 13 XIII.

The first two lines, forming together a single period of 182 days, refer to
a day III, as we see by the ending, and the last two to XIII, which
undoubtedly refers to the III Chicchan and XIII Akbal, the days so
significant in the preceding section. Hence an interval of 218 days (III
Chicchan to XIII Akbal) is to be assumed between the second and third
lines, with the addition of which interval each of the two periods extends
over 400 days.

The first and fourth series have the same difference; and the second and
third correspond with one another in this respect. In the first and fourth
the differences follow a rule, viz:--as if one were walking in a ring
having on its edge the numbers 1 to 13, and kept stepping backward four
numbers. The differences of the second and third series apparently do not
follow any rule. Hence I think that the fourth series follows the third by
mistake and ought rightfully to precede it. Only the fifth member in the
first and second series has the same day VIII and the day V in the third
and fourth series, otherwise the week-days of each series differ from those
of the others.

As I regard III Chicchan and XIII Akbal as unquestionably the
starting-points, I will here give a table of the days on which each of the
twenty-six members of each series must fall and at the same time I will
indicate for each day its number from the beginning of the series.
Accordingly the first 182 days present the following appearance:--

     III 2.

   1.      9.    XII Ix
   2.     14.    IV Cauac
   3.     15.    V Ahau
   4.     25.    II Oc
   5.     31.    VIII Cib
   6.     33.    X Eznab
   7.     44.    VIII Muluc
   8.     51.    II Cib
   9.     54.    V Cauac
  10.     66.    IV Chuen
  11.     74.    XII Cauac
  12.     78.    III Akbal
  13.     91.    III Cib
  14.    102.    I Manik
  15.    115.    I Ahau
  16.    126.    XII Chuen
  17.    127.    XIII Eb.
  18.    135.    VIII Ahau
  19.    141.    I Cimi
  20.    145.    V Oc
  21.    147.    VII Eb
  22.    160.    VII Chicchan
  23.    166.    XIII Chuen
  24.    172.    V Caban
  25.    180.    I Chicchan
  26.    182.    III Manik

In the same way I will tabulate the second group of 182 days, but in this
case I shall place the fourth line before the third, which is probably
correct, and which shows for the first time parallelism of the two rows:--

    XIII 20.

   1.      9.    IX Eb
   2.     14.    I Caban
   3.     15.    II Ezanab
   4.     25.    XII Lamat
   5.     31.    V Ix
   6.     33.    VII Cib
   7.     44.    V Manik
   8.     51.    XII Ix
   9.     54.    II Caban
  10.     66.    I Muluc
  11.     74.    IX Caban
  12.     78.    XIII Imix
  13.     91.    XIII Ix
  14.    102.    XI Chicchan
  15.    115.    XI Ezanab
  16.    126.    IX Muluc
  17.    127.    X Oc
  18.    135.    V Ezanab
  19.    141.    XI Kan
  20.    145.    II Lamat
  21.    147.    IV Oc
  22.    160.    IV Akbal
  23.    166.    X Muluc
  24.    172.    III Men
  25.    180.    XI Akbal
  26.    182.    XIII Chicchan

It would be very essential now to know what place these days occupy in the
year, and what year is meant; the answer to one of these questions would at
the same time solve the other.

Now I think I come nearer to the solution of this problem by assuming that
the pictures and hieroglyphs refer here only to the more important of the
two days, XIII Akbal, and that III Chicchan is represented only by the
numbers of the series. Thus both the pictures and the hieroglyphs of the
two sections connect without the interval of 218 days, which must be
assumed in the case of the numbers.

Here, as is usually the case of series, we have to begin at the bottom. Now
the first group of the lower half of page 65 contains the sign 9 Kan. If,
as it seems, this actually denotes the year, then the day XIII Akbal must
be the first of the eleventh month, _i.e._, the 201st day of the year.
Hence I will again set down the twenty-six dates, but add to them the
position in the year.

   0.            XIII Akbal I Zac (9 Kan)
   1.      9.    IX Eb 10 Zac
   2.     14.    I Caban 15 Zac
   3.     15.    II Ezanab 16 Zac
   4.     25.    XII Lamat 6 Ceh
   5.     31.    V Ix 12 Ceh
   6.     33.    VII Cib 14 Ceh
   7.     44.    V Manik 5 Mac
   8.     51.    XII Ix 12 Mac
   9.     54.    II Caban 15 Mac
  10.     66.    I Muluc 7 Kankin
  11.     74.    IX Caban 15 Kankin
  12.     78.    XIII Imix 19 Kankin
  13.     91.    XIII Ix 12 Muan
  14.    102.    XI Chicchan 3 Pax
  15.    115.    XI Ezanab 16 Pax
  16.    126.    IX Muluc 7 Kayab
  17.    127.    X Oc 8 Kayab
  18.    135.    V Ezanab 16 Kayab
  19.    141.    XI Kan 2 Cumhu
  20.    145.    II Lamat 6 Cumhu
  21.    147.    IV Oc 8 Cumhu
  22.    160.    IV Akbal 21 Cumhu
  23.    166.    X Muluc 2 Pop (10 Muluc)
  24.    172.    III Men 8 Pop
  25.    180.    XI Akbal 16 Pop
  26.    182.    XIII Chicchan 18 Pop

Let us now prove the correctness of my theory by an examination of groups
22 and 23. In 22 the 160th day of this period, the 361st day of the year is
reached, _i.e._, the first of the five Uayeyab days. The year 9 Kan is
ended and the year 10 Muluc is not yet reached. In the corresponding
picture we see B occupied in conveying in a bag the image of God K to whom
belongs the next year. B is armed with the official staff and the bag also
contains water (rain). In the 23d group the 166th day has passed and the
second of the year 10 Muluc is reached, which gives the name to this year.
The first hieroglyph shows two personages sitting back to back. This
representation is repeated on a larger scale below in the Janus picture of
B who is sitting on signs of planets. The second hieroglyph, with equal
fitness, represents a clamp, which is intended for fastening two objects
together, and which is repeated twice over the Janus picture, black in one
case and white in the other. Rain is pouring over the second half of the
picture, for it has long been known that Muluc and rain belong together,
and in our examination of page 7a we saw that K is the ruler of the day
Muluc (6).

Now, before I begin the examination of the separate pictures and the groups
of six hieroglyphs belonging to each picture, I wish to mention three
things which are often repeated here.

First, B's picture, which appears in all the twenty-six pictures with the
exception of 20, 24 and 25, and represents the god in the most varied
positions and activities. These pictures are very similar to those on pages
29-46 and we shall therefore make frequent reference to the section there
represented.

Second, the first hieroglyph in groups 1 to 13, strange to say, is not
found in the second half. It is hieroglyph _f_, which appears in exactly
the same way in close combination with B in two sections, which differ from
each other but are placed side by side on pages 30c-39c. In the present
passage it has a distinct prefix resembling the beak of a bird or tortoise,
but in the former passage it has rather a stunted appearance. It seems to
refer to the eagle in B's hands in group 13.

Third, the head with no underjaw, which is the sixth hieroglyph in groups 1
to 13, but does not occur in groups 14 to 26. It is repeated in a very
similar fashion in the last hieroglyph but one on page 23b. I propose to
attribute to it the meaning of fasting.

Now for the single groups:--

1. B is seated rowing in a boat, as he is represented also on pages 29c,
36b, 40c and 43c. A creature is swimming beneath him, which may be a
crocodile. The fifth hieroglyph is the important 9 Kan already discussed,
the fourth is _a_ and the second the cross _b_ combined with Caban. The day
is the 210th of the year.

2. B is walking with the atlatl in his hand, and armed with javelins.
Hieroglyph 5, Manik, denotes the chase, but has a prefix, which often seems
to have the meaning of 20. 2 is the elongated head _q_ with the prefix of
the east belonging to the Kan years. 4 is a Moan sign (c) with the
leaf-shaped prefix. Does this perhaps denote the slaying of game in the
forest? It is remarkable that B's feet are hidden, as if he were walking in
sand or in a bog.

3. B is walking, carrying a large stick like that for tilling the field, as
on pages 38b and 39b, and he bears a carrying-frame; there are footprints
below him. Hieroglyph 2 is the compound of the signs for south and east, 4
(_r_) may denote rain, and 5 is two elongated heads with an unknown prefix.

4. B, is seated on astronomical signs as on page 37c. The copal pouch is
hanging from his neck and he is brandishing his hatchet. Sign 2 is _b_, 4
is _a_ and 5 is _r_, but all three signs have unusual prefixes; the first
of these prefixes appears again in the tenth group, 41 days later.

5. B is seated on a head, probably that of D, which, however, is peculiar
owing to the ornaments resembling bunches of grapes in place of both the
eye and the ear (compare pages 39c and 41a). I do not venture to decide
what he holds in his hand nor what are the other objects which he carries.
Sign 2 is _r_ with a prefix, 4 is Imix perhaps with a knife as a prefix, 5
is the skeleton which sometimes belongs to the lightning beast, but also to
the 14th month; its prefix is unknown.

6. B is seated on a support, which contains two cross-bones, down to which
he points with his right hand, while his left hand holds the hatchet on his
knee. Sign 2 is the crouching naked personage, with the cross _b_ prefixed,
4 is the elongated head with a prefixed Yax, and 5 is Kan with a vessel as
a prefix (instead of Imix) from which steam or froth is rising. The day is
the 234th of the year, _i.e._, the end of a week of 18 × 13 days.

7. B is sitting on a tree at the root of which his own head appears
(compare with this the representations on pages 31c, 33c, and especially
40a, and also 41b and 42b). The second sign is Yax with a prefix; 4 is Kin
within which there is a 1, as is several times the case, for example, on
pages 61 and 69. The fifth sign is still a mystery to me. The day here is V
Manik. Do the hieroglyphs suggest that the interval from the day IX Kan,
which gives the name to the year, to V Manik is exactly the same as that
from the normal date IV Ahau to the true starting-point of our passage, the
day XIII Akbal? Both intervals are 243.

8. B is seated in a house, on the roof, wall and floor of which are several
Caban signs, just as on page 30a; he seems to be pointing forward. Sign 2
is Caban with a prefix, the 4th and also the 5th is Kan with two unusual
prefixes.

9. Water is pictured at the bottom of this picture, and in it are a fish, a
mussel and a snail (possibly page 37b may be compared with this). There
seems to be a suggestion of footprints on the margin of the water, back of
which B is walking, his legs hidden as far as the knees. He holds the
hatchet uplifted in his left hand and his right holds what may be a
long-stemmed aquatic plant (compare page 42b). Sign 2 is composed of _b_,
Imix, the mouth and nose of C and the object which apparently is a beak,
previously met with in sign 1. 4 is Kan-Imix, and 5 is Kan with prefix and
suffix.

10. B is seated in an expectant attitude, his hands resting on his knees.
We see a very similar representation of him on page 38a, where he faces
himself, and in general the remaining pictures of that passage furnish a
striking parallel to the present one. Sign 2 is a head (E's?) with a call
seemingly issuing from its mouth. 4 is the elongated head _q_ with the
Ben-Ik superfix and an unusual prefix, which we found on page 66c prefixed
to the cross _b_; 5 is Kan with the same prefix, which I regarded as
denoting a call in sign 2, and which is probably answered here by an
affirmative cry.

11. The expectation has been fulfilled. B is seated on a mat holding a
woman in the same position as on page 38a. Sign 2 is the cross _b_ with the
prefixed beak as in 1, and also with another prefix, which seems sometimes
to denote the number 20. 4 is exactly the same Kin with 1 and the
leaf-shaped prefix, which occurred in the same place with the seventh
picture. 5 contains the sign for 73 days; a new period of this length
begins here on the 74th day.

12. As in the parallel passage on page 38 B seems to be offering a Kan, so
here his gift consists of a kind of wreath, like the one in the fifth
picture; he is seated on astronomical signs, which contain the cross _b_
twice as does also hieroglyph 2. 4 is Kin-Akbal, and 5 is a Kan with the
prefix which generally belongs to the south as a superfix.

13. B is seated on the elongated head _q_ with a superfix and a prefix,
exactly as on pages 37c and 40a, and this sign is repeated in the
hieroglyphs (in 2) just as it is in the two former places. He holds the
eagle on his lap and we see him connected with the same bird in a different
way on page 43c. Is B represented here as the preventer of evil? Hieroglyph
4 is _a_, while 5 is Kan, apparently with the sign of the south as a
prefix. A Bacab period of 91 days ends here. We come now to the upper
series of pictures.

14. B is walking in the rain, with the copal pouch around his neck and the
hatchet uplifted in his left hand. An unknown object, possibly held in his
right hand, is hanging in front of his legs. Hieroglyphs 1 and 3 are
effaced, 2 is indistinct, 5 seems to be a Xul (end, close) and 6 is E's
head.

15. B is walking, brandishing the hatchet in his left hand, and holding in
his right an object resembling a cornucopia filled with fruit; below this
hangs what appears to be a flower. The god wears the copal pouch.
Hieroglyph 1 is a hand holding K's head; it is curious that this sign
should also occur in the next group as an indication of the approaching
Muluc year. 3 is a sign still undetermined; but the prefix is the crouching
naked personage with dots suggesting stars around its head. I have often
thought that similar figures represented Mercury; it is remarkable that
exactly the 115th day of this section is reached here, corresponding with
the apparent revolution of Mercury = 115 days. Similarly sign 2 invites
computation; it is a face resembling an Ahau sign, with a 3 as a superfix
and a 9 as a prefix; compare the other places containing the same face,
with 33c. After the fashion of the inscriptions this would denote 9 + 3 ×
20 = 69, which by the way is three fifths of the Mercury revolution. 5 is a
compound of Akbal and Imix and 6 a compound of a Moan sign (_c_) with a.

16. B is in a half sitting position and holds a strange object before
himself. On top of his own head is K's, which is repeated in sign 2. I do
not know how to explain 1, unless it is the bat-god; 3 is a Xul = end (but
of what?) combined with Imix, and 5 is the usual Kan-Imix. 6 is a Kin with
an 8 back of it (as 36b, 37b, 67a, 68a) and over it is a hand pointing to
the right, just like those in groups 20 and 25. This looks as if we ought
to count forward 8 days, but what can be the purpose of doing so?

17. B is walking armed with spear and shield. Sign 1 is _b_, 2 the face
resembling an Ahau, which occupied the second place in group 15, 3 is
probably Xul again, but with an effaced prefix; of 5 also only an Imix
remains; while 6 is the usual compound of Muluc-Caban.

18. We have now reached the day 16 Kayab, a day very close to the day 18
Kayab, which on page 24 we recognized as an especially important day, while
in my article "Zur Entzifferung III" I regarded it as the day of the summer
solstice. Computed from the normal date IV Ahau 8 Cumhu it may also have
denoted the end of a lunar year, as on pages 51-58 where it is the basis of
the series. The picture here agrees with this. B is sitting in the pouring
rain of the rainy season and gazing upward at the planets, as on page 36c
and particularly on 39c; the sun and moon are also represented, but below
the planets. The hieroglyphs likewise contain the sun and moon in 1 and 2,
in 3, Ahau and Xul with a prefix, as if this were the end of the increase
of the sun's power; 5 is Kin-Akbal, day and night, and 6 is Caban with the
cross b.

19. B is walking armed with hatchet and shield. He holds a serpent in his
hand as on page 40c, but here with the head downward. Hieroglyphs 1 and 2
are destroyed, 3 is the cross _b_ with a suffix and the horse-shoe prefix
_e_, known to us from pages 5 and 6. 5 is Imix combined with Chuen and
probably with Yax, and 6 is E's head.

20. This is the old red woman with the tiger claws, whom we saw on pages
39b and 43b and shall see again on page 74; she reinforces the water
falling from the planets by pouring a stream from her jug. The first three
hieroglyphs are effaced, 4 is the elongated head _q_, 5 is Kin-Akbal, 6, as
in group 16, is again the enigmatical 8 with a hand pointing to the right.

21. B is walking and bears pouch, spear and shield. Hieroglyph 1 is a hand
holding the sign of the rising Moan, just as in 15 a hand holds the head of
K; 2 is again K, whose sign is probably effaced several times in the last
groups of this series. 3 is E with the sign of the east; 5 is compounded of
Imix, Chuen and _b_, and 6 is Kin with the sign of the north. Here the day
of the normal date is reached, but this may be significant only for the
year 9 Ix.

22. We come now to the representation of the change of the year, which we
have already mentioned. Hieroglyph 1 is curious, consisting of the moon
with a stripe running around it like a strap; 3 and 5 are not clear to me
and are doubtless closely connected with one another; 3 also contains a
trace of K and is perhaps a determinative of the same. 6 is again E, and
suggests the tilling of the fields.

23. This picture as well as the first two hieroglyphs have already been
discussed above. The crouching personage, repeated again in 3 as a prefix
to the cross _b_, is curious. 5 is again E and 6 is Imix, referring to
grain and honey.

24. The picture and three of the hieroglyphs plainly correspond. The grain
deity E holds food and drink in his hand. Rain is pouring from the planets,
and the wind-beast plunges down, as on pages 44 and 45. Sign 3 is E's
hieroglyph, 6 is Kan-Imix and 2 is the wind-beast. B is superfluously added
in 4 and the same is true of the cross _b_ in 1, while Kin-Akbal in 5 seems
to fit almost everywhere. Pages 29a, 30a and 45c show the lightning-beast
in a different form.

25. As is usually the case, rain is pouring from the stars and below them
are the sun and moon as before. This time C is sitting in the rain, clad in
the gala mantle and holding Kan. Hieroglyphs 1, 2 and 4, the latter
apparently representing C, are effaced. The other three are enigmatical, 3
is again Xul with a prefixed 9, 5 a Caban, but with an unintelligible
prefix, and 6 is again the mysterious 8.

26. B is sitting on a tree or sacrificial stone, which is colored half blue
and half red, and may denote the ceasing of the rainy season; he is
brandishing his hatchet. Hieroglyphs 1, 2 and 3 are effaced; 4 is B's sign,
5 might be Xul and 6 is _a_ with _c_ added and thus referring to the Moan.
And here the half of the ritual year ends with the 182nd day, which is XIII
Chicchan 18 Pop (10 Muluc); and it is left to the reader to imagine or to
find hieroglyphs and pictures for the other two series of numeral signs.

I am troubled about the five naked crouching figures of this section, which
I am inclined to regard as the sign for Mercury with its apparent
revolution of 115 days, which, however, seems sometimes (as on pages 54, 56
and 58 in the upper sections) to be raised to the value of half a
Tonalamatl = 130 days. This may be explained by the fact that it is
difficult to determine exactly the length of the revolution of Mercury. In
group 15 this figure appears exactly on the 115th day of this section, but
in group 6 on the 234th day of the year, _i.e._, approximately at the
expiration of two Mercury periods after the beginning of the year. But now
for group 23. Here there are three of these crouching figures. The two
upper ones leaning back to back must serve the purpose of indicating the
change in the year. But they would hardly do so, if the third personage
were not added, which may indicate that the solar year consists
approximately of three Mercury periods. I look upon this view of the matter
merely as the first attempt at an explanation.

Pages 69--73.

The chief subject of the last great section of this Manuscript is two of
the usual series, from which large numbers are developed in the usual way
and the largest of all is finally recorded in a serpent. This section thus
forms a parallel to the contents of pages 61-64, but is somewhat more
composite.

Before I begin the discussion of these series, I wish to examine two
passages, which I think are not connected with these series, but are
independent, like the instance on pages 51-58, where the hieroglyphs were
found to be quite independent of the numerals. The Mayas took advantage of
space wherever it presented itself, which is admissible in ideographic
writing.

The first of these two passages is at the top of pages 71-73. Here there
are four horizontal rows of twelve hieroglyphs each. Since, however, the
top row is entirely effaced and none of the other three are perfectly
preserved, it is quite impossible at present to judge of the
interconnection of the whole. But I must point out a certain resemblance to
the passage on pages 44b-45b, where a period of 78 days is considered with
reference to the wind-deities. The first and sixth columns of pages 71-72
likewise contain the signs for wind and the pierced ears. The fact that the
Bacab sign occurs in the eighth column, and in no other, must attract
'attention; if we knew it to be effaced in the first column, then each
column might refer to 13 days, though 12 × 13, it is true, does not form a
natural whole. C's sign is the only hieroglyph of a god to be found in both
passages. E also occurs on pages 44b-45b and may be one of the effaced
signs on pages 71-72. There is no trace left of the others. The fact that
some hieroglyphs occur in both the passages referred to proves nothing with
regard to signs in frequent use and I can find no cases of correspondence
among those occurring more rarely. Hence this passage must be left for the
present as an almost complete mystery.

I have discussed the second passage in detail in my article "Zur
Entzifferung der Mayahandschriften V," of the year 1895, and from it I will
borrow the following. This second passage fills the middle and lower thirds
of pages 71-73, occupying the same space as the first passage in the upper
third, and offering far more reliable material than the latter.

That these hieroglyphs are not connected with the numerals above and below,
can be deduced from the fact that the numbers follow one another from right
to left and the hieroglyphs in the reversed order. This is proved by the
hand pointing to the right, which occurs here at least eight times like the
one occurring twenty times on pages 46-50.

But the scribe, misled by the direction of the numeral series, began on
page 71 to write the _first_ of these hieroglyphs from the right instead of
from the left, but after the first four groups he corrected his mistake.
Hence I read the groups of three hieroglyphs each, in the following
order:--

  Page 71.          Page 72.                 Page 73.
    2  1 |  5   6   7   8   9  10  11 | 19  20  21  22  23
    4  3 | 12  13  14  15  16  17  18 | 24  25  26  27  28

The number 28 shows that we have to do here with 28 weeks of 13 days each,
_i.e._, with a ritual year of 364 days, as was the case on pages 31-32,
63-64 and 65-69. This year, however, is divided into four parts of 7 x 13 =
91 days, _i.e._, into four so-called Bacab periods. This is very plainly
indicated here, for groups 4, 11, 18 and 25, _i.e._, those separated by
seven groups each, are exactly alike, but in group 4b (I will designate the
three hieroglyphs of each group from top to bottom by _a_, _b_ and _c_)
there is a prefixed 4 which refers to the four Bacabs as does the same 4
prefixed to the Bacab sign at the top of page 72.

Now the question arises as to when this ritual year began. Undoubtedly its
beginning day was very different from that of the civil year (360 days) and
from that of the astronomical year (365 days).

In this matter I follow Mrs. Zelia Nuttall, who has rendered such estimable
service to Aztec science. At the Congress of Americanists at Stockholm in
1894, she submitted an article entitled "Note on the Ancient Mexican
Calendar System," in which with keen discernment she pointed out a year
beginning with the spring equinox and including in its centre the sacred
Tonalamatl, _i.e._, 260 days, which were preceded and followed by 52 days.
I recognize this ritual year also in the present passage of the
"Dresdensis," as the one current in the Maya country. It probably began
about the 10th of March, at that period about the time of the vernal
equinox, according to the Julian Calendar.

Beginning with this date, I will now attempt to tabulate the chronology of
this passage. In the first column I will place the number of the group of
hieroglyphs in question, in the second I will set down to what day of the
Maya year each group refers; in the third, the corresponding day of our
year, and finally in the fourth, the 20-day periods which agree in general
with the dates.

   1.     1-13    March 10-22               Ceh.
   2.    14-26    March 23-April 5          Mac.
   3.    27-39    April 6-18              } Kankin.
   4.    40-52    April 19-May 1          }
   5.    53-65    May 2-14                  Moan.
   6.    66-78    May 15-27,                Pax.
   7.    79-91    May 28-June 9           } Kayab.
   8.    92-104   June 10-22              }
   9.   105-117   June 23-July 5          } Cumhu.
  10.   118-130   July 6-18               }
  11.   131-143   July 19-31                Pop.
  12.   144-156   August 1-13             } Uo.
  13.   157-169   August 14-26            }
  14.   170-182   August 27-September 8     Zip.
  15.   183-195   September 9-21          } Zotz.
  16.   196-208   September 22-October 4  }
  17.   209-221   October 5-17              Zec.
  18.   222-234   October 18-30           } Xul.
  19.   235-247   October 31-November 12  }
  20.   248-260   November 13-25            Yaxkin.
  21.   261-273   November 26-December 8  } Mol.
  22.   274-286   December 9-21           }
  23.   287-299   December 22-January 3   } Chen.
  24.   300-312   January 4-16            }
  25.   313-325   January 17-29             Yax.
  26.   326-338   January 30-February 11  } Zac.
  27.   339-351   February 12-24          }
  28.   352-364   February 25-March 8       Ceh.

In the following I will call attention to a few points by which this
arrangement is justified.

Hieroglyph 1a admits of explanation. It consists of four parts:--the left
top is Kin, meaning sun or day, the right top is the sign of the year, the
right bottom is the knife as symbol of separation or division, and the left
bottom, which is especially decisive, is the month Ceh. Hence I read 1a
thus:--the day of the change of year in the month Ceh. The sign 1b is the
familiar Kin-Akbal signifying either the beginning day or the day Akbal. If
the year should be named from this sign, then this would mean a Kan year,
as in the preceding section the beginning lay in the year 9 Kan. If the
year in the latter section had been as equally divided as the one in
question here, it would have furnished us with some very remarkable
parallels.

Again the four groups:--4, 11, 18 and 25, which are alike, are important.
The cross in sign _a_, combined with the three dotted lines passing from
top to bottom, may refer to the wind and this meaning is further confirmed
by the Ik sign (wind) in c. Further the sign _b_ between them is that for
the Bacab, the wind deity itself.

The most important events of the year are obviously the sowing and
harvesting of the maize together with the beginning and end of the rainy
season. Now we find the first two in connection with the god E, the
maize-god, who is represented in 6c and 13c, 91 days apart, corresponding
to the end of May and the beginning of August. Generally speaking, sixty
days only were reckoned as the time between sowing and reaping, but here a
quarter of a year may have been taken as a round number and it may also
have reference to a more elevated region.

I am inclined to think that the beginning and end of the rainy season are
referred to in signs 8c and 16c, where, as it seems to me, three lines of
drops are falling from a rectangle denoting the sky (as is usual) like the
representation of rain dropping from a cloud at the bottom of page 36
(second picture). The serpent 8b as symbol of water may also refer to the
same thing, especially as it is combined with an Akbal (often denoting
beginning). The sign, which I think denotes the rainy season, is very
similar, but not the same as another one, which is common to the Dresdensis
and Tro-Cortesianus, the significance of which is certainly very close to
the idea of the week of 13 days.

I have some other ideas on this subject, which, however, are mere
conjectures, advanced with some hesitation. If the Chuen sign in 7a is
actually a serpent's jaw, then it might refer to the beginning of the
astronomical year in May, since the serpent so often designates that time.

In 9b we find a crouching figure with the sign which is usually considered
that of the death-bird. In another place (Zur Entzifferung IV, 12) I have
regarded the naked human figure placed upside down on page 58 as the sign
for Mercury, and on page 60 at the bottom, left, I also regarded the
crouching figure as representing Mercury vanquished by Venus. But in 9b,
which belongs to the 105th-117th days of the year, a 115 day revolution of
Mercury is computed. A crouching figure, like that in 9b, likewise appears
on page 65a in the second series of 91 days after 11 + 13 = 24 days of this
series have elapsed, _i.e._, directly after the 115 days of the apparent
revolution of Mercury.

In 10b, and it is the only place in this passage, we find the hieroglyph of
B, the leading god of this Manuscript. This corresponds with the time of
the greatest power of the sun and of the change in the civil year (July
16th). In Group 12, do _a_ and _c_ mean the year and is _b_ the head with
the Akbal eye, thus denoting the beginning of the civil year? It ought
really to have formed group 11, but there was no room for it, since it was
necessary that the signs for the period of 91 days should be set down
there.

Signs 14a and the combined signs 15bc are almost alike and suggest 1a. Is
it intended to designate here the ritual year, the time of the autumnal
equinox (September 10th?). In 15a two hooks, turned in opposite directions
proceed from one side of the sun-glyph. Do they signify two halves of the
year and does the 3 in front of them signify the third quarter of the year?

20b is the sign of the death-god A, probably not placed accidentally here
at the end of the month Xul, which denotes the end; but the end of what?

The hieroglyph in 23a is a black bird, with two hooks, one pointing up and
the other down, projecting from its head. Usually these hooks belong to K,
and by means of them this bird becomes the storm-bird; the year symbol is
below. Does this hieroglyph signify the time of the shortest day, when
darkness predominates?

A peculiarity of this passage is the striking frequency of the sign looked
upon as that of the death-bird as well as of the cognate sign, which is
commonly considered as that of the rising Moan. The first bird is in the
14th group, in the 9th it is combined with the apparent Mercury sign, and
in the 17th with the year sign. The second bird with the prefixed Yax is in
the 2nd group. But it is especially striking that several times both signs,
and this is the case nowhere else, are combined into a single sign in
groups 9, 13 and 26 and also probably in 19 where, however, the Moan sign
seems to be effaced.

This is all I have to say at the present time in reference to this
calendar. Some of my statements are positive and some are only conjectures.
Compare my treatise "Zwei Hieroglyphenreihen in der Dresdener
Mayahandschrift" (Zeitschrift für Ethnologie, 1905, 2 and 3).

Having disposed in this way of the two supplementary subjects of this
section, I will now proceed to consider the principal theme, viz:--the two
series and whatever is connected with them.

1. The 54-Series of the Day IX Ix.

As with the other series, we begin here at the right, _i.e._, with page 73.
There in the last column we find the superscription as it were. It is true
that nothing positive can be gathered from the top part consisting of five
hieroglyphs, which are mostly destroyed. The third hieroglyph seems to be
the sign in group 2a discussed above. The fourth is an Akbal with a
prefixed arm as on pages 8a, 36a, and the fifth is an Ik with a prefix.

Below these are three numbers:--14,040, 702 and 54, which are in the
proportion of 260, 13 and 1, so that the 14,040 is a Tonalamatl, as it
were, of 260 periods of 54 days each. The fact that 54 is chosen here as
the difference of the following series is curious, because usually only
parts of 260 or of 364 are selected. But 54 is probably only a secondary
matter, while 14,040, with its marvellous property of divisibility into the
most varied and important periods, is the chief subject.

There is a 9 in a red circle under the three numbers. It is meant to denote
the starting-point of the series, the day IX Ix. Perhaps these two as well
as the 54 are connected with the 9 "señores de las noches."

In passing on to the left, I shall not consider the hieroglyphs and numbers
in the next two columns in the upper third, since they are only set down
here in order to secure space for them. They will be discussed later.

The series itself begins in the upper third of page 71, in the next to the
last column; it is continued on page 72 and on page 73 as far as the third
column. The first twelve numbers are written from left to right contrary to
the usual practice, doubtless occasioned by the passage above the series,
which has already been discussed. And below, again contrary to rule, we
find not the week and month days, but only the week days and they are in
red circles. If written in the usual way, the series would have the
following form (with the usual omission of the initial day IX Ix):--

     54        108      162      216      270       324        378
  XI Lamat   XIII Ik   II Cib   IV Oc   VI Kan   VIII Ezanab   X Eb
    432        486      540      594      648
  XII Cimi   I Ahau   III Ix   V Lamat   VII Ik.

The series must now continue with the 702 already specified on page 73,
which it proceeds to do from right to left in the middle of page 71, and
continues from there on with regularly added dates and with the 702 itself
as the difference. At the same time, since 702 = 54 × 13, the week-days are
forced to come to a standstill on the IX, while each of the month days
ascends by two (702 = 35 × 20 + 2). The 4914 = 7 × 702 is obtained in the
next to the last column of page 70. On page 71 the 702 is incorrectly set
down as 1. 15. 2. instead of 1. 17. 2. The series continues on page 71 in
the same way beyond the 702, until in 7020 a number is obtained which is
also divisible by 260, so that now the accompanying day must be IX Ix. Now
we ought to expect to see here the double of 7020, the very 14,040
abovementioned, but it is omitted just because it was set down on page 73.
Nevertheless this very number forms the new difference with which the
series returns from page 70 to the top line of page 71, where the numbers
are mostly effaced, but enough remains to enable us to assume that the last
number on page 71 is the 10th multiple of 14,040, and this may be followed
by the 11th and 12th multiples, the last number being 168,480.

2. The 65-Series of the Day IV Eb.

This series begins in the middle of page 73 with the day IV Caban, the
zero-point therefore being IV Eb. It then advances to the left across 28
members, until on page 71 it reaches the number 1820 = 5 years of 364 days
= 7 Tonalamatls. From there on, 1820 itself is the difference, and the
accompanying day therefore remains IV Eb. Then, in the two lowest sections
of pages 71 and 70, the fourth multiple of 1820, _i.e._, 7280, is the third
difference and thus the series advances to 15 × 7280 = 109,200 on page 71,
after which on page 70 the omitted 8 × 7280 = 58,240 is written out. Close
beside this number are the figures 1. 0. 12. 3. and a 0 below the latter,
which was not successfully erased; this would be the number 7443 of which I
can make nothing at all.

The initial dates of the two series, IX Ix and IV Eb, are 138 days apart
and reversely 122 days.

3. The Groups of Hieroglyphs.

The transition, as it were, from the series to the large numbers is formed
by a few groups of hieroglyphs.

The first of these groups is at the top of pages 69-70; its first top line
is completely effaced. The remainder I will designate by the following
numbers:--

  1  2    5  6     9  13
  3  4    7  8    10  14
                  11  15
                  12  16.

The date IX Kan 12 Kayab, set down under 3 and 4 does not belong there but
to the serpent below and will be discussed later.

I take sign 1 to be that of a Bacab, 2 I do not understand and it is half
obliterated; it seems to occur again on page 73 in the column to the
extreme right. 3 and 7 are the elongated head _q_ with an unusual superfix,
4 and 8 correspond with one another, but I cannot explain them. 5, 10 and
14 denote the beginning, 6, 11 and 15, the end. 9 and 13 both designate the
8th day of the month Kayab and over them IV Ahau must have been set down
twice. 12 and 16 are two heads of gods, 12 is probably D's with the sign
for west and 16, B's with that of the east.

On page 70, in the middle of the third and fourth columns, the day IX Ix
occurs twice. In one case it ought to have been IV Eb and the scribe has
really changed the IX to IV, but he omitted changing the Ix to Eb. Directly
below these dates we find the second group, consisting of two rows of four
hieroglyphs.

I think these eight hieroglyphs can be interpreted as follows:--

  1) 13 Pax               2) 20 Pop or 25 Cumhu
  3) VIII Ahau            4) 13 Yaxkin
  5) 10 Muan              6) 37,960
  7) 20                   8) 1 Zec.

The following is to be noted in this connection:--

3 is really set down X Ahau, but an VIII is written above the Ahau by way
of correction. The day VIII Ahau will presently prove to be important.

6, a compound of Imix and the superfix denoting multiplication, is the sign
for 18,980, and its prefix seems to me to denote duplication. We have long
known how important the 37,960 = 146 × 260 = 104 × 365 is, and, if my
theory is correct, we shall see directly that it occurs again here.

8 seems really to be 1 Zec, but the composite prefixes demand further
examination.

Impenetrable darkness still shrouds the meaning of the whole group. Though
it is clear that in several cases certain days are specified according to
their position in the year, their distance apart does not agree with the
interval between days IV Eb, IX Ix and IV Ahau under discussion here.

If signs 3 and 4 ought to be read together as VIII Ahau 13 Yaxkin, then
this date would come in the year 7 Muluc. In the Zeitschrift für Ethnologie
I explained the five hieroglyphs in the third column at the bottom of page
70 (the third group) as civil years of 360 and astronomical years of 365
days:--

  1)       8,760 = 24 × 365 = 15 × 584
  2)       2,920 =  8 × 365 =  5 × 584
  3)       7,200 = 20 × 360
  4)      18,720 = 52 × 360 = 72 × 260
  5)         360
          ------
          37,960.

This, it is true, is a striking explanation and certainly a surprising one!

Now the date IX Ix 12 Kayab is at the very bottom of the fourth column.
This, without apparent reason, would refer to the year 4 Kan. Should it not
be read IX Kan 12 Kayab (4 Ix), thus indicating that the entire passage is
only the preparation for the date from which the serpent numbers proceed?
The scribe may have had in mind the IX Ix of the series.

The fourth and last group on page 73, above the two numbers 83,474 and
34,732, consists of four hieroglyphs. The two upper hieroglyphs on the left
are effaced, and the top one on the right. I think it probable that the day
VIII Ahau, which will be discussed later, may have stood in the top line,
and possibly with a month date. Of the two remaining signs of the fourth
group, the upper is the moon and the lower Imix, probably with the
hieroglyph of the east as a prefix; but there is nothing to be done with it
owing to the obliteration of the sign above it. In the Zeitschrift für
Ethnologie, 1891, page 153, I have endeavored to explain these three signs
on the right above 34,732, by suggesting for them the values

  18,980 = 52 × 365
   8,760 = 24 × 365
   7,200 = 20 × 360
  ------
  34,940

and calling special attention to the fact that between IV Eb and IV Ahau
there are 208 days, and that the 34,732 placed below them in the
Manuscript, increased by 208, is equal to 34,940. This group then seems
really to belong to the day IV Eb and to the 65-series, while manifold
problems are still to be encountered in interpreting the other groups.

4. The Large Numbers.

The Manuscript offers material with which to work, beginning on page 70:--

  1,394,120     1,437,020     1,567,332     1,520,654
    (606)         (1646)        IV Eb         IX Ix
   IV Ahau       IV Ahau       VIII Ahau; 13 Yaxkin (7 Muluc).
   8 Cumhu       8 Cumhu
    IX Ix         IV Eb
  1,201,200     1,202,240       111,554       101,812
     (86)         (208)
   IV Ahau       IV Ahau
   8 Cumhu       8 Cumhu

This is followed at the right top of page 73 by

  83,474     34,732
  IX Ix      IV Eb.

Two of the numbers and two of the dates are conjectural:--

I read the 1,202,240 as 8. 6. 19. 10. 0. while the Manuscript has 16
instead of 6. I read the 101,812 as 14. 2. 14. 12. the Manuscript has 16
instead of the second 14. And in two places in the third column of page 70,
I have restored the day IV Eb, where the Manuscript incorrectly repeats the
IX Ix, and does the same thing on page 73.

Let us now first consider the construction of those large numbers, which
are connected with the day IX Ix and thus with the 54-series. These numbers
are the two upper ones of columns 1 and 2 and the lower one of column 1 on
page 70.

174 is the starting-point, the number of the day is IX Ix, which seems to
have been chosen because it divides the Tonalamatl approximately in the
proportion of 2 to 1. (IV Ahau - IX Ix = 174.)

The 5359th, 5520th and 4619th multiples of 260 have been added to 174; why
precisely these multiples were chosen remains a mystery. In this way were
obtained the following numbers, which the Manuscript suppresses. I will
give them with their corresponding dates:--

  1,393,514 = IX Ix 12 Muan (5 Kan).
  1,435,374 = IX Ix 17 Chen (3 Cauac).
  1,201,114 = IX Ix  7 Mac (11 Muluc).

When we add to the above the three encircled numbers 606, 1,646 and 86, the
resulting sums are the three numbers found in the Manuscript:--

  1,394,120 = IV Ahau  8 Chen (7 Ix).
  1,437,020 = IV Ahau 23 Cumhu (7 Cauac).
  1,201,200 = IV Ahau 13 Kayab (11 Muluc).

I am placing the first two not far from the present and the third in the
past.

As multiples of 260 these three numbers have the following form:--

  1,394,120 = 5362 × 260.
  1,437,020 = 5527 × 260.
  1,201,200 = 4620 × 260.

Some curious facts come to light with regard to their magnitude and their
mutual relation.

The two largest numbers are 165 × 260 = 660 × 65 apart; this recalls the
65-series. The third lowest number is 165 × 7280 and thus contains not only
the 65 but = 165 × 65 × 112.

The ritual year (364) and its excess over the Tonalamatl (104) is likewise
contained in these numbers, at least in the first and third:--

  1,394,120 = 3830 × 364 = 13,405 × 104.
  1,201,200 = 3300 × 364 = 11,550 × 104.

The three encircled numbers are connected with one another because the
first = 2 × 260 + 86, the second = 6 × 260 + 86 and the third is 86 itself.
The larger encircled numbers are, therefore, 1040 = 4 × 260 apart, and this
is also the interval between the two numbers near the bottom. 1040,
however, also = 5 × 208, and 208 is the interval from IV Eb to IV Ahau. Now
it is curious that the two numbers below are 5775 × 208 and 5780 × 208,
though the third belongs to day IX Ix and the fourth to IV Eb. One result
of this is that 1,201,200 = 1155 × 1040 and 1,202,240 = 1156 × 1040.

As these three numbers relate to day IX Ix and the 54-series, so the fourth
relates to IV Eb and the 65-series.

Here the starting-point is the number 52, which belongs to day IV Eb and
this is separated from IV Ahau by 208 days _i.e._, it divides the
Tonalamatl in the proportion of 1 to 4.

To the number 52 then, for unknown reasons was added 4623 × 260 =
1,201,980, and thus the number 1,202,032, suppressed in the Manuscript, was
obtained for the day IV Eb. To this sum the encircled number 208 was then
added and the result was 1,202,240, the number in the Manuscript.

The number = 23,120 × 52 = 4624 × 260, which is self-evident, but it also =
5780 × 208, _i.e._, it is a multiple of the encircled number. It
consequently also = 11,560 × 104, and thus it is related to the first and
third numbers just now discussed.

The position of this number is IV Ahau 18 Kankin (1 Kan) and the position
of the suppressed number is IV Eb 10 Zotz (also 1 Kan).

We ought now to discuss the last two numbers of this section amounting to
millions:--1,567,332 and 1,520,654, which are in the third and fourth
columns at the top of page 70. But before going further, we must examine
four other numbers, two of which, 111,554 and (with my correction) 101,812,
are in column 4 on the lower part of page 70, and the other two, 83,474 and
34,732, are on the top of page 73. Although these four numbers are not
ornamented with circles, they all have the significance of the numbers
enclosed in circles and are designations of differences between suppressed
and specified numbers.

Let us first of all examine their curious relation to one another:--

The Manuscript should have set down under these numbers the day IX Ix twice
and IV Eb twice, from which days the numbers in question must be computed;
but here the two errors already mentioned were made. 111,554 - 101,812 is
9742, the very same number which we shall afterward find as the difference
of the serpent numbers on page 69.

83,474 - 34,732 = 48,742. If 9472 be subtracted from this, the remainder is
exactly 39,000 = 150 Tonalamatls = 50 revolutions of Mars. I have already
found this number on page 31a, and also the double of it, 78,000, on page
24, and this I found by using 68,900 + 9100 for my computation.

111,554 - 83,474 = 28,080, _i.e._, exactly the double of the important
14,040, which is recorded on page 73.

101,812 - 34,732 = 67,080, _i.e._, = 258 Tonalamatls or 86 revolutions of
Mars.

111,554 - 34,732 = 76,822; if 122, the interval from IV Eb to IX Ix be
subtracted from this, the remainder is 76,700 = 295 Tonalamatls.

101,812 - 83,474 = 18,338; if 138, the interval from IX Ix to IV Eb, be
subtracted from 18,338, the remainder is 18,200 = 70 Tonalamatls = 50
ritual years of 364 days each, _i.e._, exactly the double of the 9100
specified on page 24.

Now we also have the following equations for the four numbers:--

  111,554 = 429 × 260 + 14.
   83,474 = 321 × 260 + 14.
  101,812 = 391 × 260 + 152.
   34,732 = 133 × 260 + 152.

A day VIII Ahau is 14 days back of the day IX Ix, and another VIII Ahau is
152 days back of IV Eb.

Thus a day VIII Ahau hitherto unmentioned is introduced into the
computations. This day has no doubt been chosen, because it divides the
Tonalamatl beginning with IV Ahau into two parts of 160 and 100 days, which
are in the proportion of 8 to 5, _i.e._, the same proportion as the Venus
year to the solar year.

This day VIII Ahau may also figure in the large numbers of the first two
columns on page 70, for 1,394,120 and 1,201,200 are both divisible by 14,
the interval between VIII Ahau and IX Ix.

Now I believe that the large numbers were constructed in the following
twofold manner (I add the corresponding dates):--

        160
  1,408,940 = 5419 × 260
  ---------
  1,409,100 = VIII Ahau 3 Yax (9 Cauac).
    111,554
  ---------
  1,520,654 = IX Ix 7 Zip (3 Muluc).

        160
  1,437,020 = 5527 × 260
  ---------
  1,437,180 = VIII Ahau 18 Mol (8 Kan).
     83,474
  ---------
  1,520,654 = IX Ix 7 Zip (3 Muluc).

        160
  1,465,360 = 5636 × 260
  ---------
  1,465,520 = VIII Ahau 8 Uo (8 Ix).
    101,812
  ---------
  1,567,332 = IV Eb 5 Pop (1 Muluc).

        160
  1,532,440 = 5894 × 260
  ---------
  1,532,600 = VIII Ahau 13 Pax (9 Muluc).
     34,732
  ---------
  1,567,332 = IV Eb 5 Pop (1 Muluc).

The last record of the date of VIII Ahau seems to throw light on the date
13 Pax (page 70, column 3), which is directly above the date VIII Ahau, and
which I have already mentioned in the discussion of the groups of
hieroglyphs.

Indeed, it seems as if a day VIII Ahau occurred a fifth time in that
passage, for in consequence of the correction made by the scribe we read
here VIII Ahau 13 Yaxkin. This would point to a year 7 Muluc, the position
of which between the other four is, of course, undetermined.

If the two large numbers in the Manuscript were treated in the same way as
the other large numbers, they would not be recorded at all, but instead of
them there would have been two numbers belonging to the day IV Ahau and
under them would have been the encircled numbers 208 and 86, or these
numbers increased by a multiple of 260. This passage would then read about
as follows:--

  1,567,540 (IV Ahau)     1,520,740 (IV Ahau)
        208 (IV Eb)              86 (IX Ix).

These two numbers for IV Ahau are equal to 6029 and 5849 Tonalamatls. If
5549 × 260 be subtracted from these, the remainders are 480 and 300
Tonalamatls respectively, _i.e._, 124,800 and 78,000, and these are in the
proportion of 8 to 5.

Now the two large numbers have the difference 46,678 = 179 × 260 + 138; the
latter is the interval from IX Ix to IV Eb.

The four numbers of the days VIII Ahau seem to stand in very irregular
relation to one another and yet they show the following striking results,
if the first and third and also the second and fourth numbers be combined
(as I combined them under page 24):--

In the first case we see the following:--

    1,465,520 - 1,409,100 = 56,420 = 3 × 18,980 - 520.
  3 Yax (9 Cauac) to 8 Uo (8 Ix) = 18,460 = 18,980 - 520.
       56,420 - 18,460 = 37,960 = 2 × 18,980.

While in the second case:--

  1,532,600 - 1,437,180 = 95,420 = 5 × 18,980 - 520.
      18 Mol (8 Kan) to 13 Pax (9 Muluc) = 520.
        95,420 - 520 = 94,900 = 5 × 18,980.

5. The Serpent.

As in the section occupying pages 61-64, the single series is crowned by
four serpents with eight large numbers, so in this section the two series
end in a single serpent with two numbers, one for each series, but both
bear some obscure relation to the day VIII Ahau, which has made its
appearance here. The two sections also correspond, inasmuch as the numbers
in both are computed not from the normal date, but from the date IX Kan 12
Kayab (4 Ix).

The serpent pictured here is different from the previous ones, inasmuch as
it is partly black. The god B is sitting on its opened jaws, and this time
he, too, is painted black (as on page 31c); there is an animal's head upon
the god's head, in which we again recognize that of the animal with the
fourth serpent in the preceding section. The god is armed with spear and
shield and recalls his picture at the bottom of page 74.

There are eight hieroglyphs above this picture, just as there are over each
of the first four serpents. The two top hieroglyphs are obliterated. Of the
legible hieroglyphs, the one at the left top is the Bacab sign, which also
occurs over the first of the four serpents. In the third line are the same
two hieroglyphs, which are in the third line of the first and second
columns on page 70. The first of the two also occupies the same place on
page 62 above the fourth serpent. But here at the bottom we find the date
IX Kan 12 Kayab (4 Ix), the same date which we found over the fourth
serpent, which is thus again brought into closer connection with the single
serpent.

There can be no doubt here regarding the two numbers in the serpents, but
notice should be taken of the fact that the figure 1 is barely visible in
the red number.

The black number here has the figures 4. 5. 19. 13. 12. 8. and the red 4.
6. 1. 0. 13. 10. The black is therefore 12,381,728, and the red 12,391,470.
The black number is somewhat less than the eight numbers in the four
serpents, and the red is somewhat larger than the least of them.

The difference of the two is 9742 = 37 × 260 + 122; but 122 is the interval
between days IV Eb and IX Ix. Now this is the same 9742 which we found on
page 70, as the difference between 111,554 and 101,812.

In order not merely to examine these numbers, but also to understand them,
we will again make use of 109 Ahau-Katuns = 12,412,920, as we did in the
first four serpents, and we shall have the following:--

     Black                          Red

  12,381,728                     12,391,470
  12,412,920                     12,412,920
  ----------                     ----------
     -31,192 = 119 × 260 + 252      -21,450 = 82 × 260 + 130
          IV Eb - IX Kan = 252          IX Ix - IX Kan = 130

The date given for both numbers was the day IX Kan, which was likewise the
starting-point for six of the eight numbers in the previous serpents.

Besides this the day IV Eb, the starting-point of the 65-series, is given
for the black number, and therefore also the interval between IV Eb and IX
Kan = 252.

To this 252 was added a multiple of 260, not an arbitrary choice, but one
which combined with 252 resulted in a number divisible by 8, the interval
from IX Kan to IV Eb. 31,192 = 3899 × 8 = 119 × 260 + 252 was thus
obtained.

The subtraction of this number from 12,412,920 resulted in the serpent
number 12,381,728.

In addition to all this the day IX Ix, the starting-point of the 54-series,
is given for the red number; consequently also the interval between IX Ix
and IX Kan = 130, which, at the same time, is reversely the interval from
IX Kan to IX Ix.

To this 130 was added a multiple of 260, which _must_ in every case be a
multiple also of 130. Thus we obtain the 21,450 = 82 × 260 + 130.

The subtraction of this number from 12,412,920 results in the serpent
number 12,391,470.

Reckoned from the starting-point IX Kan 12 Kayab (4 Ix) the black number
corresponds to the date IV Eb 5 Chen (10 Muluc) and the red to IX Ix 12 Zip
(11 Kan), and these two dates must certainly have been under the serpent;
the months unfortunately are effaced.

It is self evident that the black number is exactly divisible by 8 and the
red by 130.

The two events indicated by the two numbers must be to some extent
coincident with the beginning of the seven events recorded in the previous
four serpents. These large numbers pertaining to the destruction of the
world are a reminder of the numbers, which on page 24 we believed were
connected with the creation of the world. Thus here, too, we have the
genesis and the apocalypse of all the mythologies.

6. The Columns of Hieroglyphs.

The last portion of this section is formed by the two middle columns of
hieroglyphs on page 69. They bear an extraordinary resemblance to those
discussed under page 61 even in regard to the fact that each column
contains 18 signs. Besides, the upper 10 lines, _i.e._, the upper 20 signs,
are exactly alike on the two pages, aside from slight variations, and
differ only in so far as the passage on page 69 is written on blue ground
and the one on page 61 on white.

But also the lower part, with eight signs in each column, shows many points
in common with page 61. Here as there the whole is divided into several
groups.

With the four signs 11ab and 12ab, which formed the first group there, I
can compose only the two signs 11ab here. In the cross 11a, as on pages 24
and 58 of the Manuscript, I see the sign for 20 with the prefixed 5 making
25. In 11b we find the sign for 18,980 days, which we have already met with
several times. Hence 11ab would have the value of 25 × 18,980 = 474,500
days, as on page 61 the corresponding four signs seemed to form 421,940.
And as the number there was 1156 × 365, so on page 69 we have 1300 × 365.

I believe there is a disarrangement in what follows, inasmuch as I assume
that the two signs 12b and 13a ought to be placed _before_ and not _after_
12a. Assuming that the two little crosses on either side of the 1 are
meaningless, we should assign the value of 61 to the 3 Chuen, 1 Kin. Here,
in the first place, the intention seems to be to establish some connection
with the two days VII Kan and IV Ik specified with their numbers on page
63, column 3, as well as with the days most important there, III Chicchan
and XIII Akbal, _i.e._, a connection with the previous section of the four
serpents in general; for the interval from VII Kan to III Chicchan, as well
as that between IV Ik and XIII Akbal is 61 and on pages 70-73 the two most
important days, IV Eb and IX Ix, are 122 days apart, and 122 is the second
multiple of 61. I can now put the 144,000 of 12a in the place of the 13a.
Then, secondly, the four signs from 13a to 14b in the one section are
exactly like those in the other section, and therefore need not be
discussed here. Only 15ab differs from the signs in the other passages
inasmuch as on page 69 we find 4 × 20 + 4 × 1. The last 4 agrees even
better than it does there with the distance from IV Ahau to the day Kan
with which the serpent numeral begins.

Nothing on page 69 corresponds to the signs in 16ab and 17ab of page 61. On
the contrary, the initial date of the serpent IX Kan 12 Kayab, which on
page 61 does not appear until 18ab is set down in 16ab. On the other hand
on page 69 the four signs 17ab and 18ab are added, 17a being a sign as yet
unknown with 13 as a superfix. I feel inclined, though with many
misgivings, to treat 17ab like 5a and b of page 61 and to assign to them
the value of an Ahau-Katun of 113,880 days. For then they would denote the
13th Ahau-Katun, which extends from the day 1,366,560 (page 24) to
1,480,440 and which contains the two large numbers on page 70, left, top,
while the two lower numbers in the first and second columns of that page
belong to the 12th Ahau-Katun, and the two in the third and fourth belong
to the 14th Ahau-Katun. The 13th would be the present and the 12th and 14th
the past and future; but all this could only be confirmed by further
research. At all events, the signs for beginning in 17b and for end in 18a
refer to past and future. Unfortunately, 18b is entirely effaced.

Page 74.[5]

Besides the picture, this page contains only 15 hieroglyphs in three
horizontal rows. Only about six of these signs are decipherable. The
second, third and fourth of the lower line are three different heads; the
middle is the familiar head of god B, the one on the left has the Akbal eye
and the abbreviated sign for the south, which is repeated in the affix; the
head on the right has the sign for the west as a prefix. Very little more
is to be said of the other hieroglyphs than that the second and third of
the second line have the sign for the east; the first of the second line,
however, was the one which we found on pages 71-73 as the constant
companion of the Bacabs and which suggested the wind. The last sign of the
second line must have contained that for north, so that the four cardinal
points all came together here.

The picture begins below these signs. Astronomical figures, apparently
Venus, Mars, Mercury and Jupiter, end in the fore part of a crocodile.
Below the astronomical signs are the signs for the sun and moon. Streams of
water are falling from the jaws of the crocodile and also from the sun and
moon. And a fourth stream is being poured from a jug by the old woman with
the tiger claws, and with the serpent on her head, whom we saw on pages 39,
43 and 67 engaged in the same occupation. Cross-bones are represented on
her skirt as the symbol of death. The sign of the ninth day, Eb, appears on
the jug; this is the day which was avoided in the Tonalamatls, for not a
single Tonalamatl begins with Eb in the Dresdensis, nor does one begin with
the week-day IX; does Bolon meaning nine suggest Balam, the jaguar?

Still further down on the page sits a black god, who may be the same as the
god on pages 7a and 16b, with a bird of prey on his head. There are two
arrows in his right hand and his left hand holds what may be an atlatl, but
it is very much longer than is usually the case; at the same time it can be
regarded as a spear.

This page can denote nothing but the end of the world, for which the
serpent numbers have prepared the way. Perhaps what looks like a zero above
the sign Eb in the stream of water may likewise point to this calamity.

       *       *       *       *       *

INDEX.

------

The numbers in the first column refer to the pages of the Manuscript, and
those in the second column to the pages of the Commentary.

  FIRST PART.

       1   |  55  |      16a  |  90  |  42a-44a  | 146
       2   |  55  |  16a-17a  |  90  |      45a  | 148
       3   |  59  |  18a-19a  |  92  |  29b-30b  | 150
   4a-10a  |  61  |  19a-21a  |  93  |  30b-31b  | 151
   4b-5b   |  67  |  21a-22a  |  93  |  31b-35b  | 152
  10a-12a  |  69  |  22a-23a  |  95  |  35b-37b  | 156
      12a  |  69  |  16b-17b  |  96  |  38b-41b  | 159
   5b-6b   |  70  |  17b-18b  |  97  |  41b-43b  | 162
   6b-7b   |  71  |  16c-17c  |  98  |  43b-44b  | 164
      8b   |  72  |  17c-18c  |  99  |  44b-45b  | 165
      9b   |  73  |  18c-19c  | 100  |  29c-30c  | 167
      10b  |  74  |  19c-20c  | 100  |  30c-33c  | 168
  10b-11b  |  75  |      19b  | 101  |  33c-39c  | 170
      12b  |  76  |  19b-20b  | 101  |  40c-41c  | 176
   4c-5c   |  77  |      20b  | 102  |  42c-45c  | 178
   5c-6c   |  78  |      21b  | 103  |
   6c-7c   |  79  |  21c-22c  | 104  |  SECOND PART.
      8c   |  80  |  22c-23c  | 105  |
      9c   |  81  |      22b  | 107  |   46-50   | 182
  10c-11c  |  82  |      23b  | 108  |  51a-52a  | 197
      12c  |  83  |      24   | 110  |   51-58   | 200
      13a  |  84  |   25-28   | 120  |   58-59   | 215
  13b-14b  |  85  |  29a-30a  | 132  |      60   | 219
  13c-14c  |  86  |  30a-31a  | 133  |   61-64   | 222
  14a-15a  |  85  |  31a-32a  | 133  |   65-69   | 235
      15a  |  88  |  32a-39a  | 138  |   69-73   | 245
  15b-16b  |  88  |  40a-41a  | 144  |      74   | 265
      15c  |  89  |           |      |           |

       *       *       *       *       *

[Illustration: GLYPHS REFERRED TO IN THE TEXT.]

[Illustration: CARDINAL POINTS.]

       *       *       *       *       *

Notes

[1] The Manuscript has incorrectly 8 and 18.

[2] = 20 Chen.

[3] The sign denotes the end of the 360-day year.

[4] = 20 Zotz.

[5] Compare the Peresianus, page 20.





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