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Title: Aids to the Study of the Maya Codices - Sixth Annual Report of the Bureau of Ethnology to the - Secretary of the Smithsonian Institution, 1884-85, - Government Printing Office, Washington, 1888, pages 253-372
Author: Thomas, Cyrus, 1825-1910
Language: English
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Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

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Transcriber's Note:

This book was originally published as a part of:

  Powell, J. W.
  1888  _Sixth Annual Report of the Bureau of Ethnology to the
        Secretary of the Smithsonian Institution, 1884-'85._ pp.
        253-372. Government Printing Office, Washington, D.C.

The index included in this version of the book was extracted from the
overall volume index.

A number of typographical errors found in the original text have been
maintained in this version. They are marked in the text with a [TN-#].
A description of each error is found in the complete list at the end of
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SMITHSONIAN INSTITUTION--BUREAU OF ETHNOLOGY.


              AIDS TO THE STUDY

                      OF

              THE MAYA CODICES.

                      BY

             PROF. CYRUS THOMAS.



CONTENTS.


  Introduction                                                       259
  CHAP. I. The numerals in the Dresden Codex                         261
       II. Conclusions                                               339
      III. The writing                                               345
             Signification of the characters                         347
             Symbols of animals &c                                   348
             Symbols of deities                                      358
             Discussion as to phonetic features of the characters    365



ILLUSTRATIONS.


FIG. 359. Line of day and numeral symbols from Plates 36_c_ and
            37_c_, Dresden Codex                                     272
     360. Line of day and numeral characters from Plates 33-39,
            Dresden Codex                                            276
     361. Unusual symbol for Akbal from Plate 8 of the Dresden Codex 284
     362. Copy of Plate 50, Dresden Codex                            297
     363. Copy of Plate 51, Dresden Codex                            306
     364. Copy of Plate 52, Dresden Codex                            307
     365. Copy of Plate 53, Dresden Codex                            308
     366. Copy of Plate 54, Dresden Codex                            309
     367. Copy of Plate 55, Dresden Codex                            310
     368. Copy of Plate 56, Dresden Codex                            311
     369. Copy of Plate 57, Dresden Codex                            312
     370. Copy of Plate 58, Dresden Codex                            313
     371. Specimens of ornamental loops from page 72, Dresden Codex  337
     372. Numeral character from the lower division of Plate XV,
            Manuscript Troano                                        343
     373. Turtle from the Cortesian Codex, Plate 17                  348
     374. Jar from the Cortesian Codex, Plate 27                     349
     375. Worm and plant from Manuscript Troano, Plate XXIX          351
     376. Figure of a woman from the Dresden Codex                   351
     377. Copy of middle and lower divisions of Plate XIX,
            Manuscript Troano                                        352
     378. Copy of lower division of Plate 65, Dresden Codex          353
     379. The moo or ara from Plate 16, Dresden Codex                355
     380. The god Ekchuah, after the Troano and Cortesian Codices    358
     381. The long nosed god (Kukulcan) or god with the snake-like
            tongue                                                   359
     382. Copy of head from the Borgian Codex (Quetzalcoatl?)        360
     383. The supposed god of death from the Dresden Codex           361
     384. The supposed god of death from the Troano Codex            361
     385. The god with the banded face from the Troano Codex         362
     386. The god with the old man's face                            363
     387. The god with face crossed by lines                         364
     388. Wooden idol in vessel with basket cover                    371



AIDS TO THE STUDY OF THE MAYA CODICES.

BY CYRUS THOMAS.



INTRODUCTION.


The object of this paper is to present to students of American
paleography a brief explanation of some discoveries, made in regard to
certain Maya codices, which are not mentioned in my previous papers
relating to these aboriginal manuscripts.

It is apparent to every one who has carefully studied these manuscripts
that any attempt to decipher them on the supposition that they contain
true alphabetic characters must end in failure. Although enough has been
ascertained to render it more than probable that some of the characters
are phonetic symbols, yet repeated trials have shown beyond any
reasonable doubt that Landa's alphabet furnishes little or no aid in
deciphering them, as it is evidently based on a misconception of the Maya
graphic system. If the manuscripts are ever deciphered it must be by long
and laborious comparisons and happy guesses, thus gaining point by point
and proceeding slowly and cautiously step by step. Accepting this as
true, it will be admitted that every real discovery in regard to the
general signification or tenor of any of these codices, or of any of
their symbols, characters, or figures, or even in reference to their
proper order or relation to one another, will be one step gained toward
the final interpretation. It is with this idea in view that the following
pages have been written and are now presented to the students of American
paleography.

It is impracticable to present fac simile copies of all the plates and
figures referred to, but it is taken for granted that those sufficiently
interested in this study to examine this paper have access to the
published fac similes of these aboriginal documents.



CHAPTER I.


THE NUMERALS IN THE DRESDEN CODEX.

Before entering upon the discussion of the topic indicated it may be well
to give a brief notice of the history and character of this aboriginal
manuscript, quoting from Dr. Förstemann's introduction to the
photolithographic copy of the codex,[261-1] he having had an opportunity
to study the original for a number of years in the Royal Public Library
of Dresden, of which he is chief librarian:

"Unfortunately, the history of the manuscript begins no further back than
1739. The man to whom we owe the discovery and perhaps the preservation
of the codex was Johann Christian Götze, son of an evangelical pastor,
born at Hohburg, near Wurzen, in the electorate of Saxony. He became a
Catholic, and received his education first at Vienna, then in Rome;
became first chaplain of the King of Poland and elector of Saxony; later
on, papal prothonotary; presided over the Royal Library at Dresden from
1734, and died holding this position, greatly esteemed for learning and
integrity, July 5, 1749. This sketch is taken from his obituary notice in
Neue Zeitungen von gelehrten Sachen, Nr. 62, Leipzig, 1749. In his
capacity as librarian he went to Italy four times, and brought thence
rich collections of books and manuscripts for the Dresden library. One of
these journeys took place in 1739, and concerning its literary results we
have accurate information from a manuscript, in Götze's handwriting,
which is found in the archives of the Royal Public Library, under A, Vol.
II, No. 10, and bears the title: 'Books consigned to me for the Royal
Library in January, 1740.' Under No. 300 we read: 'An invaluable Mexican
book with hieroglyphic figures.' This is the same codex which we here
reproduce.

"Götze also was the first to bring the existence of the manuscript to
public notice. In 1744 he published at Dresden The Curiosities of the
Royal Library at Dresden, First Collection. As showing what value Götze
attributed to this manuscript, the very first page of the first volume of
this work, which is of great merit and still highly useful, begins as
follows: '1. A Mexican book with unknown characters and hieroglyphic
figures, written on both sides and painted in all sorts of colors, in
long octavo, laid orderly in folds of 39 leaves, which, when spread out
lengthwise, make more than 6 yards.'

"Götze continues speaking of this book from page 1 to 5, adding, however,
little of moment, but expatiating on Mexican painting and hieroglyphic
writing in general. On page 4 he says:

"'Our royal library has this superiority over all others, that it
possesses this rare treasure. It was obtained a few years ago at Vienna
from a private person, for nothing, as being an unknown thing. It is
doubtless from the personal effects of a Spaniard, who had either been in
Mexico himself or whose ancestors had been there.'

"On page 5 Götze says:

"'In the Vatican library there are some leaves of similar Mexican
writing, as stated by Mr. Joseph Simonius Asseman, who saw our copy four
years ago at Rome.'

"Götze therefore received the manuscript as a present on his journey to
Italy at Vienna and took it with him to Rome. Unfortunately we know
nothing concerning its former possessor. A more accurate report of the
journey does not seem to exist; at least the principal state archives at
Dresden contain nothing concerning it, nor does the General Directory of
the Royal Collections. As appears from the above note, Götze did not know
that the Vatican Codex was of an entirely different nature from the
Dresden Codex.

"In spite of the high value which Götze set upon the manuscript, it
remained unnoticed and unmentioned far into our century. Even Johann
Christoph Adelung, who as head librarian had it in his custody and who
died in 1806, does not mention it in his Mithridates, of which that part
which treats of American languages (III, 3) was published only in 1816,
after Adelung's death, by J. S. Vater. This would have been a fitting
occasion to mention the Dresden Codex, because in this volume (pp. 13 et
seq.) the Maya language is largely treated of, and further on the other
languages of Anahuac. Of course it was not possible at that time to know
that our manuscript belongs to the former.

"After Götze, the first to mention our codex is C. A. Böttiger, in his
Ideas on Archæology (Dresden, 1811, pp. 20, 21), without, however, saying
anything that we did not already know from Götze. Still Böttiger rendered
great and twofold service: first, as we shall see presently, because
through him Alexander von Humboldt obtained some notice of the
manuscript, and, second, because Böttiger's note, as he himself explains
in the Dresden Anzeiger, No. 133, p. 5, 1832, induced Lord Kingsborough
to have the manuscript copied in Dresden.

"We now come to A. von Humboldt. His Views of the Cordilleras and the
Monuments of the Indigenous Peoples of America bears on the title page
the year 1810, which certainly means only the year in which the printing
was begun, the preface being dated 1813. To this work, which gave a
mighty impulse to the study of Central American languages and
literatures, belongs the Atlas pittoresque, and in this are found, on
page 45, the reproductions of five pages of our manuscript. They are Nos.
47, 48, 50, 51, and 52 of Lord Kingsborough. In the volume of text
belonging to this atlas Humboldt discusses our manuscript on pp. 266,
267. When he began his work he knew nothing as yet of the existence of
the manuscript. It was brought to his knowledge by Böttiger, whose above
named work he cites. Here we learn for the first time that the material
of the manuscript consists of the plant metl (_Agave Mexicana_,) like
other manuscripts that Humboldt had brought from New Spain. Furthermore,
he correctly states the length of leaf as 0.295 and the breadth 0.085
meter. On the other hand, he commits two mistakes in saying that there
are 40 leaves and that the whole folded table forming the codex has a
length of almost 6 meters, for there are only 39 leaves and the length in
question is only 3.5 meters, as calculation will approximately show,
because the leaves are written on both sides. Humboldt's other remarks do
not immediately concern our problem.

"In 1822 Fr. Ad. Ebert, then secretary and later head librarian,
published his History and Description of the Royal Public Library at
Dresden. Here we find, as well in the history (p. 66) as in the
description (p. 161), some data concerning this 'treasure of highest
value,' which indeed contain nothing new, but which certainly contributed
to spread the knowledge of the subject among wider circles. We may remark
right here that H. L. Fleischer, in his Catalogue of Oriental Manuscript
Codices in the Royal Library of Dresden, p. 75, Leipzig, 1831, 4^o, makes
but brief mention of our codex, as 'a Mexican book of wood, illustrated
with pictures, which awaits its Œdipus;' whereupon he cites the writing
of Böttiger. The signature of the manuscript here noted, E 451, is the
one still in use.

"Between the above mentioned notices by Ebert and Fleischer falls the
first and so far the only complete reproduction of the manuscript.
Probably in 1826, there appeared at Dresden the Italian Augustino Aglio,
a master of the art of making fac similes by means of tracing through
transparent substances. He visited the European libraries, very probably
even at that time under orders from Lord Kingsborough, to copy scattered
manuscripts and pictures from Mexico or seemingly from Mexico.

"Now there arises the question, all important for interpretation, In
which shape did the manuscript lie before Aglio? Was it a strip only 3.5
meters in length or did it consist of several pieces?

"To render clear the answer which we proceed to give, it is first
necessary to remark that of the 39 leaves of the codex 35 are written on
both sides and 4 on one side only, so that we can speak only of 74 pages
of manuscript, not of 78. These 74 pages we shall in the following always
designate by the numbers which they bear in Lord Kingsborough, and it is
advisable to abide by these numbers, for the sake of avoiding all error,
until the manuscript can be read with perfect certainty; the 4 empty
pages I shall designate with 0 when there is need of mentioning them
expressly.

"Furthermore it is necessary to state which of these pages so numbered
belong together in such way that they are the front and back of the same
leaf. This condition is as follows: One leaf is formed of pages 1 45, 2
44, 3 43, 4 42, 5 41, 6 40, 7 39, 8 38, 9 37, 10 36, 11 35, 12 34, 13 33,
14 32, 15 31, 16 30, 17 29, 18 0, 19 0, 20 0, 21 28, 22 27, 23 26, 24 25,
46 74, 47 73, 48 72, 49 71, 50 70, 51 69, 52 68, 53 67, 54 66, 55 65, 56
64, 57 63, 58 62, 59 61, 60 0. [That is to say, each pair of this series
forms one leaf, one page on one side and the other on the reverse side of
the leaf.]

"But now we are justified in the assumption, which at least is very
probable, that neither did Aglio change arbitrarily the order of the
original, nor Lord Kingsborough the order of Aglio. Consequently Aglio
must already have had the manuscript before him in two pieces, be it that
the thin pellicles by which the single leaves are connected were loosened
in one place or that the whole was separated only then in order not to be
obliged to manipulate the whole unwieldy strip in the operation of
copying. A third possibility, to which we shall presently return, is that
of assuming two separate pieces from the beginning; in this case Götze
and the others must be supposed to have seen it in this condition, but to
have omitted the mention of the circumstance, believing that the original
unity had been destroyed by tearing.

"Of the two pieces one must have comprised 24, the other 15 leaves. But
Aglio copied each of the two pieces in such way as to trace first the
whole of one side and then the other of the entire piece, always
progressing from left to right, in European style. Therefore Aglio's
model was as follows:

"_First piece_:

"Front (from left to right): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.

"Back (from right to left): 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35,
34, 33, 32, 31, 30, 0, 0, 0, 28, 27, 26, 25.

"_Second piece_:

"Front (from left to right): 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,
57, 58, 59, 60.

"Back (from right to left): 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64,
63, 62, 61, 0.

"In considering this, our attention is attracted by the position of the
four blank pages, three of which are together, the fourth alone. It might
be expected that the separate blank page began or concluded the second
piece and was purposely left blank, because in the folding of the whole
it would have lain outside and thus been exposed to injury; the other
three would be expected at the end of the first piece. The former, as is
easily seen, was quite possible, but the latter was not, unless we assume
that even at the time Aglio took his copy the original order had been
entirely disturbed by cutting and stitching together again. The four
blank pages show no trace of ever having contained writing; the red brown
spots which appear on them are to be found also on the sides that contain
writing. Perhaps, therefore, those three continuous pages indicate a
section in the representation; perhaps it was intended to fill them later
on; in a similar way also page three has been left unfinished, because
the lower half was only _begun_ by the writer.

"I do not wish to conceal my view that the two pieces which Aglio found
were separated from the beginning; that they belong even to two different
manuscripts, though written in the same form; but, since it is human to
err, I will here and there follow custom in the succeeding pages in
speaking of one codex.

"My conviction rests especially on the fact that the writer of manuscript
A (pp. 1-45) endeavors to divide each page by two horizontal lines into
three parts, which the writer of manuscript B (pp. 46-74) rarely does.
The more precise statement is as follows: In A, pp. 1-23 and 29-43 always
show two such lines in red color; pp. 25-28 have no red lines, but
clearly show a division into three parts; p. 24 is the only one of this
manuscript that has only writing and no pictures and where the greater
continuity of the written speech forbids tripartition (here ends one side
of the manuscript); finally, p. 45 seems to be marked as the real end of
the whole by the fact that it contains three very light lines, dividing
it into four parts; moreover, everything on this page is more crowded,
and the figures are smaller than on the preceding pages, just as in some
modern books the last page is printed more closely or in smaller type for
want of space. In the same manner I suspect that p. 1 is the real
beginning of the manuscript. This is indicated by the bad condition of
leaf 2 44, which has lost one corner and whose page 44 has lost its
writing altogether. For, if in folding the codex leaf 1 45 was turned
from within outward, somewhat against the rule, leaf 2 44 was the outer
one, and p. 44 lay above or below, and was thus most exposed to injury. I
will not omit mentioning that my attention has been called by Dr. Carl
Schultz-Sellack, of Berlin, to the possibility of leaves 1 45 and 2 44
having been fastened to the rest in a reversed position, so that 43, 1
and 2 and on the other side 44, 45, 3 were adjoining; then the gods would
here be grouped together, which follow each other also on pages 29 and
30. It cannot be denied that this supposition explains the bad condition
of leaf 2 44 still better, because then it must have been the outermost
of the manuscript; 44 would be the real title page, so to say, and on p.
45 the writer began, not ended, his representation, with the closer
writing of which I have spoken, and only afterward passed on to a more
splendid style; and this assumption tallies very well with some other
facts. But all this can only be cleared up after further progress has
been made in deciphering the manuscript.

"In two places, moreover, this first manuscript shows an extension of the
drawings from one page over to the neighboring one, namely, from 4 to 5
and from 30 to 31. This is not found on the second manuscript. From
continuity of contents, if we are allowed to assume it from similarity of
pictures and partition, we may suppose this manuscript to be divided into
chapters in the following manner: pp. 1-2 (then follows the unfinished
and disconnected page 3), 4-17, 18-23 (here follows p. 24, without
pictures), 25-28, 29-33, 34-35, 36-41.

"Compared with this, manuscript B rarely shows a tripartition, but on pp.
65-68 and 51-57 a bipartition by one line. A further difference is this,
that A out of 45 pages has only one (p. 24) without pictures, while B out
of 29 pages has 9 without pictures (51, 52, 59, 63, 64, 70, 71, 72, 73),
nothing but writing being found on them. Page 74, differing from all
others, forms the closing tableau of the whole; and, similarly, p. 60,
the last of the front, shows a peculiar character. A closer connection of
contents may be suspected between pp. 46-50, 53-58, 61-62, 65-68.

"The two manuscripts also differ greatly in the employment of the sign,
or rather signs, differing little from each other, which resemble a
representation of the human eye and consist of two curves, one opening
above and the other below and joined at their right and left ends. These
signs occur only on 5 out of the 45 pages of Codex A (1, 2, 24, 31, 43),
while they occur on 16 pages out of the 29 of Codex B (48, 51, 52, 53,
55, 57, 58, 59, 61, 62, 63, 64, 70, 71, 72, 73).

"I believe that the differences above mentioned, to which others will
probably be added, are sufficient to justify my hypothesis of the
original independence of the two codices. Whoever looks over the whole
series of leaves without preconception cannot escape the feeling, on
passing from leaf 45 to leaf 46, that something different begins here.

"Thus the copy of Aglio has made it possible to venture a hypothesis
bordering on certainty concerning the original form of this monument.
Five years after Aglio had finished the copying there appeared, in 1831,
the first volumes of Lord Kingsborough's Mexican Antiquities. The work in
the trade cost 175_l_.; the expense of publication had been over
30,000_l_. The eighth and ninth volumes followed only in 1848. The
ponderous work has undoubtedly great value from its many illustrations of
old monuments of Central American art and literature, which in great part
had never been published. As regards the Spanish and English text, it is
of much less value. We may pass in silence over the notes added by Lord
Kingsborough himself, in which he tries to give support to his favorite
hypothesis that the Jews were the first settlers of America. Whoever
wishes to obtain exact information concerning the character and contents
of the whole work and dreads the labor of lifting and opening the
volumes, may find a comprehensive review of it in the Foreign Quarterly
Review, No. 17, pp. 90-124, 8vo, London, January, 1832, where he will
also find a lucid exposition of the history of the literature of Mexican
antiquarian studies.

"In the middle of the third volume of the Mexican Antiquities (side
numbers are here absent) there is found the title 'Fac simile of an
original Mexican painting preserved in the Royal Library at Dresden, 74
pages.' These 74 pages are here arranged on 27 leaves in the following
manner:

  Codex A.         Codex B.

  1, 2, 3,         46, 47, 48,
  4, 5, 6,         49, 50, 51,
  7, 8, 9,         52, 53, 54,
  10, 11,          55, 56, 57,
  12, 13, 14,      58, 59, 60,
  15, 16, 17,      61, 62, 63,
  18, 19,          64, 65, 66,
  20,              67, 68, 69,
  21, 22, 23,      70, 71, 72,
  24, 25,          73, 74.
  26, 27, 28,
  29, 30, 31,
  32, 33, 34,
  35, 36, 37,
  38, 39, 40,
  41, 42, 43,
  44, 45.

"On the whole, therefore, each leaf in Kingsborough comprises three pages
of our manuscript. Why the publisher joined only two pages in the case of
10 and 11, 18 and 19, 24 and 25, and left page 20 entirely separate, I
cannot say; but when he failed to add 46 to 44 and 45 it was due to the
fact that here there is indication of a different manuscript.

"On January 27, 1832, Lord Kingsborough wrote a letter from
Mitchellstown, near Cork, in Ireland, to Fr. Ad. Ebert, then head
librarian at Dresden, thanking him again for the permission to have the
manuscript copied and telling him that he had ordered his publisher in
London to send to the Royal Public Library at Dresden one of the ten
copies of the work in folio. The original of the letter is in Ebert's
manuscript correspondence in the Dresden library.

"On April 27, 1832, when the copy had not yet arrived at Dresden, an
anonymous writer, in No. 101 of the Leipziger Zeitung, gave a notice of
this donation, being unfortunate enough to confound Humboldt's copy with
that of Lord Kingsborough, not having seen the work himself. Ebert, in
the Dresden Anzeiger, May 5, made an angry rejoinder to this "hasty and
obtrusive notice."[TN-1] Böttiger, whom we mentioned above and who till
then was a close friend of Ebert, on May 12, in the last named journal,
defended the anonymous writer (who perhaps was himself) in an extremely
violent tone. Ebert's replies in the same journal became more and more
ferocious, till Böttiger, in an article of May 25 (No. 150 of the same
journal), broke off the dispute at this point. Thus the great
bibliographer and the great archæologist were made enemies for a long
time by means of our codex.

"From Kingsborough's work various specimens of the manuscript passed into
other books; thus we find some in Silvestre, Paléographie universelle,
Paris, 1839-'41, fol.; in Rosny, Les écritures figuratives et
hiéroglyphiques des peuples anciens et modernes, Paris, 1860, 4to; and
also in Madier de Montjou, Archives de la société américaine de France,
2^de série, tome I, table V.

"In 1834 Ebert died, and was followed as head librarian by K. C.
Falkenstein. He, unlike his predecessor, strove especially to make the
library as much as possible accessible to the public. Visits and
examinations of the library became much more frequent, and our
manuscript, being very liable to injury, on account of its material, had
to be withdrawn from the hands of visitors, if it was desired to make it
accessible to their sight. It was therefore laid between glass plates and
thus hung up freely, so that both sides were visible. In this position it
still hangs in the hall of the library, protected from rude hands, it is
true, but at the same time exposed to another enemy, daylight, against
which it has been protected only in recent time by green screens. Still
it does not seem to have suffered much from light during these four
decades; at least two former officers of the library, who were appointed
one in 1828 and the other in 1834, affirm that at that time the colors
were not notably fresher than now. This remark is important, because the
coloring in Humboldt, as well as in Lord Kingsborough, by its freshness
gives a wrong impression of the coloring of the original, which in fact
is but feeble; it may have resembled these copies some 300 years ago.

"In 1836, when the manuscript was being preserved in the manner
indicated, the two unequal parts, which were considered as a whole and
which no one seems to have thought susceptible of being deciphered, were
divided into two approximately equal parts from considerations of space
and for esthetic reasons.

"The first five leaves of Codex A, that is, pp. 1-5, with the backs
containing pp. 41-45, were cut off and prefixed to Codex B in such way as
to have p. 46 and p. 5 adjoining; when I examined the codex more closely
I found that between 5 and 46, and therefore also between 41 and 74,
there was no such pellicle as generally connects the other leaves. By
this change one part was made to contain 20 leaves, the other 19.

"At the same time another change was made. The three blank pages between
pp. 28 and 29 had a marring effect, and they were put at the end by
cutting through between leaves 18 0 and 17 29 and turning the severed
leaves around, so that p. 24 joined on to p. 29 and 17 to 25. The
pellicle loosened on this occasion was fastened again.

"I must expressly state that I have no written or oral account of these
two manipulations, but conclude they have taken place merely from a
comparison of the present arrangement with that which Aglio must have had
before him.

"Thus the arrangement in which I found the manuscript, which it may be
best to preserve until my views are recognized, is the following:

"(1) _The diminished Codex A (19 leaves):_

Front: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 25, 26, 27, 28, 0, 0, 0.

Back: 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40.

"Or, if we enumerate the numbers on the back from right to left, so that
the back of each leaf stands beneath its front:

   6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17 | 25, 26, 27, 28,  0,  0,  0.
  40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29 | 24, 23, 22, 21, 20, 19, 18.

"(2) _The enlarged Codex B (20 leaves):_

Front: 1, 2, 3, 4, 5, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60.

Back: 0, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 41, 43,
43, 44, 45.

"Or, reversing, as in the preceding case, the numbers on the back:

   1,  2,  3,  4,  5 | 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60.
  45, 44, 43, 42, 41 | 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61,  0."

One of the most difficult things to account for in regard to this codex
is the immense number of numeral characters it contains, many of which
appear to have no reference to day or other time symbols.

Although it is not claimed that the key which will fully unlock this
mystery has been found, it is believed that the discoveries made will
throw considerable light on this difficult subject and limit the field of
investigation relating to the signification of the Maya codices.

Before proceeding with the discussion of the subject proposed, it will
not be amiss to state, for the benefit of those readers not familiar with
these ancient American manuscripts, that the Maya method of designating
numbers was by means of dots and lines, thus: . (one dot) signifying one;
.. (two dots) two, and so on up to four; five was indicated by a single
short straight line, thus, ----; ten, by two similar lines,
[Illustration: Two horizontal lines, stacked]; and fifteen, by three such
lines: [Illustration: Three horizontal lines, stacked]. According to this
system, a straight line and a dot, thus, [Illustration: Dot above
horizontal line], would denote 6; two straight lines and two dots,
[Illustration: Two dots above two stacked horizontal lines], 12; and
three straight lines and four dots, [Illustration: Four dots in a line
above 3 stacked horizontal lines], 19. But these symbols do not appear to
have been used for any greater number than nineteen. They are found of
two colors in all the Maya codices, one class black, the other red,
though the latter (except in a few instances, where the reason for the
variation from the rule is not apparent) are never used to denote a
greater number than thirteen, and refer chiefly to the numbers of the
days of the Maya week and the numbers of the years of the "Indication" or
"week of years." On the other hand, the black numerals appear to be used
in all other cases where numbers not exceeding nineteen are introduced.
As will appear in the course of this discussion, there are satisfactory
reasons for believing that other symbols, quite different from these dots
and lines, are used for certain other numbers, at least for 20 and for 0.

In order that the reader may understand what follows, it is necessary to
explain the methods of counting the days, months, and years in the order
in which they succeed one another. Much relating to this will be found in
a previous work,[269-1] but a particular point needs further
explanation.

According to the older and also the more recent authorities, the Maya
years--there being 20 names for days and 365 days in a year--commenced
alternately on the first, sixth, eleventh, and sixteenth of the series,
that is to say, on the days Kan, Muluc, Ix, and Cauac, following one
another in the order here given; hence they are spoken of as Kan years,
Muluc years, Ix years, and Cauac years.

Writing out in the form of an ordinary counting house calendar the 365
days of the year, commencing with 1 Kan and numbering them according to
the Maya custom (that is, up to thirteen to form their week and then
commencing again with one) they would be as shown in Table I.

TABLE I.--_Names and numbers of the months and days of the Maya system._

   _______________________________________________________________________
  |             |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |N t|
  |             |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |u h|
  |             |  |  |  |  |  |  |Y |  |  |  |  |  |  |K |  |  |  |  |m e|
  |             |  |  |  |  |  |  |a |  |  |  |  |  |  |a |  |  |K |C |b  |
  |             |  |  |  |T |T |  |x |  |C |  |  |  |  |n |M |  |a |u |e d|
  |             |P |  |Z |z |z |X |k |M |h |Y |Z |C |M |k |u |P |y |m |r a|
  |             |o |U |i |o |e |u |i |o |e |a |a |e |a |i |a |a |e |h |s y|
  |             |p |o |p |z |c |l |n |l |n |x |c |h |c |n |n |x |b |u |  s|
  |             |--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+o  |
  |             | 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|f  |
  |-------------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+---|
  |_Names of the|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   |
  |    days._   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   |
  |Kan          | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|  1|
  |Chicchan     | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|  2|
  |Cimi         | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|  3|
  |Manik        | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|  4|
  |Lamat        | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|  5|
  |Muluc        | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|  6|
  |Oc           | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|  7|
  |Chuen        | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|  8|
  |Eb           | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|  9|
  |Been         |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 10|
  |Ix           |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 11|
  |Men          |12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 12|
  |Cib          |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 13|
  |Caban        | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3| 14|
  |Ezanab       | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4| 15|
  |Cauac        | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5| 16|
  |Ahau         | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6| 17|
  |Ymix         | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 18|
  |Ik           | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 19|
  |Akbal        | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 20|
  |----------------------------------------------------------------+--+---|
  |                          _Intercalated days._                  |  |   |
  |Kan                                                             |10|   |
  |Chicchan                                                        |11|   |
  |Cimi                                                            |12|   |
  |Manik                                                           |13|   |
  |Lamat                                                           | 1|   |
   -----------------------------------------------------------------------

Each of these eighteen columns forms one month, and the whole taken
together, with the 5 days added at the end of the eighteenth month, form
one continuous series, the second column following the first as though
placed at the end of it, the third following the second, and so on to the
end of the eighteenth. Whether or not it was the ancient custom to
include the 5 added days in the year, as asserted by the old Spanish
writers, is somewhat doubtful, at least in studying the Dresden Codex, we
shall find but few occasions, if any, to use them, for there are few if
any positive indications in this codex that they were added.

As stated, each column of the table forms a month, though the numbering
is carried to thirteen only; but at present the chief object in view in
presenting it is to use it in explaining the method of counting the days
and the intervals of time. The table is in truth a continuous series, and
it is to be understood as though the 365 days were written in one column,
thus:

   1. Kan.
   2. Chicchan.
   3. Cimi.
   4. Manik.
   5. Lamat.
   6. Muluc.
   7. Oc.
   8. Chuen.
   9. Eb.
  10. Been.
  11. Ix.
  12. Men.
  13. Cib.
   1. Caban.
   2. Ezanab, &c.,

the 20 days being repeated over and over in the order in which they stand
in the table. This order is never changed; we may commence at whatever
point in the series occasion may require, but the order here given must
always be maintained, just as in our calendar the order of our days is
always Sunday, Monday, Tuesday, &c. In other words, Chicchan must always
follow Kan, Cimi must always follow Chicchan, &c.

The method of counting intervals in the Maya calendar is very simple, if
these explanations are borne in mind, and may be illustrated thus:
Counting 14 days from 1 Kan--the first day of the year given in Table
I--brings us to 2 Ezanab (the day we count from being excluded); 12 days
more bring us to 1 Oc, in the second column of our table; 17 days more to
5 Manik, in the third column; and 17 days more, to 9 Kan, in the fourth
column.

The number of the day required is readily ascertained by adding together
the number of the day counted from and the number of days to be counted,
casting out the thirteens when the sum exceeds this number (excepting
where the remainder is thirteen); thus: 1 + 14 - 13 = 2, the number of
the day Ezanab given above. So 1 + 14 + 12 - 13 - 13 = 1, the number of
the day Oc, second column, Table I; and 1 + 14 + 12 + 17 + 17 - 13 - 13 -
13 - 13 = 9, the number of the day Kan, fourth column. The reason for
this is so apparent that it is unnecessary to state it.

Suppose the day counted from is 11 Muluc of the eleventh month, and the
number of days to be counted (or the interval) is 19; by adding together
the numbers and casting out the thirteens the following result is
obtained: 11 + 19 - 13 - 13 = 4. Counting forward on the table 19 days
from 11 Muluc (the sixth number in the eleventh figure column), we reach
4 Lamat (the fourth day of the twelfth month). When the sum of the
numbers is a multiple of 13 the number obtained is 13, as there can be no
blanks, that is to say, no day without a number.

As the plates of the codices are usually divided into two or three
compartments by transverse lines, it is necessary to adopt some method of
referring to these in order to avoid the constant repetition of "upper,"
"middle," and "lower" division. On the plan proposed by Dr. Förstemann,
in his late work on the Dresden Codex (Erläuterungen zur Mayahandschrift
der Königlichen öffentlichen Bibliothek zu Dresden), these divisions are
designated by the letters _a_, _b_, and _c_; this plan will be adopted in
this paper. The letter _a_ joined to the number of a plate, therefore,
will signify that the division referred to is the upper one, as Plate
12_a_; the letter _b_ signifies the middle one where there are three
divisions or the lower one where there are but two; and the letter _c_
signifies the lowest or bottom division where there are three.

Where reference is made to the fac simile of the Dresden Codex,
Kingsborough's colored edition is always to be understood, except where
another is specially mentioned.

Running through Plates 36_c_ and 37_c_ is a continuous line of day
symbols and red and black numeral characters as follows, the numbers and
names below the characters being explanatory and of course not on the
original:

[Illustration: FIG. 359. Lines of day and numeral symbols.
  Pl. 36  10   XI Men | 15  XII Oc |  9  IX Cauac

  Pl. 37  11  VII Oc  | 20    I Oc | 10  XI Ahau]

As colors are not used in these figures the red numerals are indi
cated[TN-2] by hollow or outline dots and lines and the black numerals by
solid lines and dots.[272-1]

In order further to assist those unacquainted with the symbols the same
line is here given in another form, in which the names of the days are
substituted for the symbols, Roman numerals for the red numbers, and
Arabic for the black: 10, XI Men; 15, XIII Oc; 9, IX Cauac; 11, VII Oc;
S, I Oc; 10, XI Ahau.

The S is introduced to represent a numeral symbol different from the
lines and dots and will be explained when reached in the course of the
illustration.

Starting from 11 Men, found in the twelfth figure column of Table I, and
counting forward fifteen days, we come to 13 Oc of the thirteenth figure
column, the second day of the above quoted line. Counting nine days from
13 Oc[273-1] brings us to 9 Cauac, the third day of the line; eleven days
more, to 7 Oc, the fourth day of the line. Following this day in the
line, instead of a black numeral of the usual form, is this symbol:
[Illustration: Hieroglyph] represented by S in the second form, where the
names and numbers are substituted for the symbols. Taking for granted,
from the position it occupies in the line, that it is a numeral
character, it must represent 20, as the day which follows is 1 Oc, and
counting twenty days from 7 Oc brings us to 1 Oc. Counting ten days more
we reach 11 Ahau, the last day of the line given above.

In this example the black numerals appear to have been used simply as
counters, or as numbers indicating intervals; for example, 15 is the
interval between 11 Men and 13 Oc.[273-2]

This furnishes a clew which, if followed up, may lead to important
results. That it explains the signification of one symbol undetermined
until this relation of the numerals to one another was discovered, is now
admitted. In the work of Dr. Förstemann before alluded to the discovery
of the symbol for 20 is announced. Although I was not aware of the
signification of this symbol until after my second paper, "Notes on
certain Maya and Mexican manuscripts," was written, I had made this
discovery as early as 1884.[273-3]

As there will be occasion to refer to the days of the four different
series of years (the Cauac, Kan, Muluc, and Ix years), a combined
calendar, similar to an ordinary counting house calendar, is introduced
here. For the Cauac years the left or Cauac column is to be used; for the
Kan years, the Kan column, and so on.

TABLE II.--_Names and numbers of the four series of years of the Maya
system._

  __________________________________________________________________________________
          |        |        |        |                                      {Numbers
   Cauac  | Kan    | Muluc  |  Ix    | 1  2  3  4  5  6  7  8  9 10 11 12 13{of the
  column. |column. |column. |column. |14 15 16 17 18                        {months.
  --------+--------+--------+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+-------
          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |Days of
          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |month.
  Cauac   |Kan     |Muluc   |Ix      | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|   1
  Ahau    |Chicchan|Oc      |Men     | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|   2
  Ymix    |Cimi    |Chuen   |Cib     | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|   3
  Ik      |Manik   |Eb      |Caban   | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|   4
  Akbal   |Lamat   |Been    |Ezanab  | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|   5
  Kan     |Muluc   |Ix      |Cauac   | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|   6
  Chicchan|Oc      |Men     |Ahau    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|   7
  Cimi    |Chuen   |Cib     |Ymix    | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1|   8
  Manik   |Eb      |Caban   |Ik      | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2|   9
  Lamat   |Been    |Ezanab  |Akbal   |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|  10
  Muluc   |Ix      |Cauac   |Kan     |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|  11
  Oc      |Men     |Ahau    |Chicchan|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|  12
  Chuen   |Cib     |Ymix    |Cimi    |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|  13
  Eb      |Caban   |Ik      |Manik   | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|  14
  Been    |Ezanab  |Akbal   |Lamat   | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|  15
  Ix      |Cauac   |Kan     |Muluc   | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|  16
  Men     |Ahau    |Chicchan|Oc      | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|  17
  Cib     |Ymix    |Cimi    |Chuen   | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|  18
  Caban   |Ik      |Manik   |Eb      | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|  19
  Ezanab  |Akbal   |Lamat   |Been    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|  20
  ----------------------------------------------------------------------------------

As this table has been explained in my previous papers it is only
necessary to add here that the thirteen figure columns form a single
series; therefore, when we reach the bottom of the thirteenth column we
go back to the top of the first. The day reached will be the one directly
opposite (that is, in the same horizontal line) in the day column for the
given year.

For example, taking the fifth column of numbers (the one having 3 for the
top figure) and counting down nine days from the top number we reach the
number 12. This will be 12 Lamat if a Cauac year, 12 Been if a Kan year,
12 Ezanab if a Muluc year, and 12 Akbal if an Ix year. Therefore it is
necessary in counting to refer always to the year (year column) with
which the count begins. So long as the particular year referred to is
unknown (as is Usually the case, the day series being apparently of
general rather than of special application) it is immaterial which day
column is selected, as the result will be the same with any. This will be
apparent if we bear in mind that, when 260 days with their numbers
attached have been written down in proper order as a series, we have
therein all the possible combinations of days and numbers. This, it is
true, does not give us all the months and years (to include these it is
necessary to write out fifty-two entire years), but the same series of
numerals will be applicable to each of the four year series (Kan, Muluc,
Ix, and Cauac years). As any one of the thirteen figure columns of the
table may be taken as the commencement of a year and any of the four day
columns may be used, it is apparent that we have all the possible
combinations (4 × 13 = 52).

I say above that "it is necessary in counting to refer always to the year
(year column) which the count begins." This I admit does not agree with
the generally received idea of the Maya calendar, upon which Table II is
constructed, as, according to this theory (which I have accepted in my
previous papers), after passing through a year of one series
(corresponding with one of the day columns of the table), we should enter
upon a year of the next series; for example, when the year 1 Kan is
completed we should enter upon the year 2 Muluc.

Although this calendar system seems to have been in vogue at the time of
the conquest and is indicated in one or two of the codices, and possibly
in the one now under consideration, the chronological series of the
latter, as will hereafter appear, do not seem to be based upon it or to
agree with it.

These explanations, with the further statement that the lines in the
codex are to be read from left to right and the columns from the top
downward, except where variations from this rule are noted, will enable
the reader to follow the discussion. Another reason for using a table
with only thirteen columns (though it would be difficult to devise a
combined calendar of any other form) is that the 260 days they contain
form one complete cycle, which, as will appear in the course of this
discussion, was one of the chief periods in Maya time computations.

Examining Plates 33 to 39 of the codex the reader will observe that the
line already alluded to extends continuously through division _c_,
commencing with the two characters over the figure (picture) in the lower
right hand corner of Plate 33.

The first of these characters as given in Kingsborough's work is the
symbol of the day Ezanab, with the red numeral 13 to the left of it and
the black numeral 9 over it; but referring to Förstemann's
photolithographic copy of the codex it is found to be the symbol of Ahau.

The entire line, with this correction (that is to say, as given by
Förstemann), is represented in Fig. 360. In order to assist the reader,
the names of the days and numbers of the symbols have been added
immediately below the characters.

As the year to which the line relates is unknown, we select the Muluc
series, designated "Muluc column" in Table II, and commence with 13 Ahau,
the twelfth number of the third figure column. Counting 9 days from this
brings us to 9 Muluc, the top number of the fourth figure column and also
the second day of the line above given. (the symbol is a face in
Kingsborough's copy, but is plainly the Muluc sign in Förstemann's
photograph). Eleven days more bring us to 7 Ahau, the third day of the
above line; 20 more to 1 Ahau, the fourth day of the line (the 20 here is
the symbol represented by S); 10 more to 11 Oc, the fifth day of the
line; 15 more to 13 Chicchan, the sixth day of the line; 9 more to 9 Ix,
the seventh day of the line; 11 more to 7 Chicchan, the eighth day of the
line; line; 20 (S) more to 1 Chicchan, the ninth day of the line; 10 more
to 11 Men, the tenth day of the line, and so on to the end.

[Illustration: FIG. 360. Line of day and numeral characters.
  Pl. 33      XIII Ahau IX Muluc
  Pl. 34  11   VII  Ahau | 20 I Ahau | 10 XI Oc | 15 XIII Chicchan
  Pl. 35   9    IX  Ix     | 11  VII  Chicchan | 20    I  Chicchan
  Pl. 36  10    XI  Men    | 15 XIII  Oc       |  9   IX  Cauac
  Pl. 37  11   VII  Oc     | 20    I  Oc       | 10   XI  Ahau
  Pl. 38  15  XIII  Men    |  9   IX  Kan      | 11  VII  Men
  Pl. 39  20     I  Men(?) | 10   XI  Chicchan | 15 XIII  Ahau]

That the order of the series may be clearly seen the numbers are given
here as they stand in the line, omitting the days: XIII; 9, IX; 11, VII;
20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII; 9, IX;
11, VII; 20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15,
XIII.

By adding together a black numeral and the preceding red one and casting
out thirteen (or thirteens, as the case maybe), when the sum exceeds this
number, we obtain the following red one, thus: XIII + 9 - 13 = IX; IX +
11 - 13 = VII; VII + 20 - 13 - 13 = I; I + 10 = XI, and so on through the
entire series. Attention is also called to the fact that the sum of the
black (Arabic) numbers 9, 11, 20, 10, 15, 9, 11, 20, 10, 15, 9, 11, 20,
10, 15, 9, 11, 20, 10, 15, is 260, a multiple of 13.

If this relation of days and numerals holds good as a general thing
throughout the codex, it is apparent that where the break is not too
extensive it will enable the student to restore the missing and defective
numerals and day symbols, to detect the errors of both copyists and
original artists, and to determine the proper relation of the plates to
one another. By it he learns, as before stated, that the symbol (see page
273) denotes 20, and if phonetic probably stands for the Maya word _Kal_.

Comparing Plates 42 and 43 with Plates 1 and 2, the resemblance is found
to be so strong as to lead to the belief that they belong together. It is
apparent from the figures, numerals, and characters[277-1] in the middle
division (_b_) of Plates 1 and 2 that they belong together, as they now
stand in Kingsborough's work and Förstemann's copy; that Plates 42 and 43
are properly placed in regard to each other is also apparent from the
figures and numerals in divisions _a_ and _b_.

Taking for granted that the lines are to be read from left to right and
the plates to follow each other in the same order, our next step is to
ascertain on which side of the pair (Plates 42 and 43) Plates 1 and 2
should be placed.

The series of days and of numbers in Plate 43_b_ and Plate 1_b_, which
evidently belong together, can only be brought into proper relation by
placing the latter to the right of the former. Yet, strange as it may
appear, the days and numerals in this division are to be read from right
to left, while all the other numeral series of these four plates are to
be read as usual, from left to right. This change in the order of the
pages also brings together the similar figures in the upper division of
these plates. That Plate 42 properly follows Plate 41 is apparent from
the line of alternate red and black numerals in division _b_. As shown in
a previous work[278-1] and as will appear hereafter, these horizontal
lines of alternate red and black numerals without day symbols
interspersed are usually, if not always, connected at the left with a
column of days over which there is a red numeral, as in the Codex Troano.
Running back along the line of numerals in the middle division of Plates
42 and 41, the day column with which it is connected is found at the left
margin of Plate 38. Unfortunately the red numeral over this column is
obliterated, but can easily be restored. Starting with the first black
numeral to the right of this, the entire line, which ends in the second
column of the middle division of Plate 43 (representing the black
numerals by Arabic numbers and the red by Roman numbers), is as follows:
16, IX; 8, IV; 11, II; 10, XII; 1, XIII; 12, XII; 6, VI(?); 12, IV; 11,
II; 11, XIII; 6, VI; 12, V; 7, XII; 6, V; S + 1, XIII; 6, VI.

The number over the day column, Plate 38, must have been VI, as VI + 16 -
13 = 9, a conclusion which is sustained by Förstemann's copy, which shows
here very plainly the red character for VI.

By adding the black (Arabic) numeral to the preceding red (Roman) one and
casting out the thirteens, as heretofore explained, we obtain the
following red (Roman) numerals, thus: VI + 16 - 13 = IX; IX + 8 - 13 =
IV; IV + 11 - 13 = II; II + 10 = XII; XII + 1 = XIII; XIII + 12 - 13 =
XII; XII + 6 - 13 = V.

Here the result differs from what is found at this point in the line, as
we obtain V instead of VI. In this case the mistake, if one has been
made, cannot be attributed to Lord Kingsborough's copyist; the Maya
artist must have made a mistake or there must be an error in the theory
here advanced. But let us continue according to our own figures: V + 12 -
13 = IV; IV + 11 - 13 = II; II + 11 = XIII; XIII + 6 - 13 = VI; VI + 12 -
13 = V; V + 7 = 12; XII + 6 - 13 = V; V + 20 + 1 - 13 = XIII; XIII + 6 -
13 = VI.

There is no doubt, therefore, that the line forms one continuous series,
and if so it links together pages 38 and 43 as they are now numbered. It
follows, then, that if Plates 1 and 2 and Plates 42 and 43 belong
together, the former pair must be placed to the right of 43. This is
conceded by Dr. Förstemann,[278-2] as he says that, Dr. Karl
Schultz-Sellack having pointed out the error in his paging, he changed
pages 1 and 2 to 44 and 45 and pages 44 and 45 to 1 and 2; that is to
say, the two leaves containing these pages were loosened from the strip
and reversed, so that page 1 would be 44 and page 2 would be 45.

Having brought together these plates so that 1 and 2 stand to the right
of 43, attention is called to the lines of day symbols running through
division _c_. Substituting names and numbers as heretofore, they are as
follows:

Plate 42:
  IV Ahau; XII Lamat; VII Cib; II Kan; X Eb; V Ahau; XIII Lamat.
     17        8         8        8      8      8         8

Plate 43:
  IV Chicchan; XII Been; VII Ymix; II Muluc; X Caban; V Chicchan; XIII Been.
       17          8         8         8        8          8          8

Plate 1:
  IV Oc; XII Ezanab; VII Cimi; II Ix; X Ik; V Oc; (?) Ezanab.
    17         8         8       8      8     8        8

Plate 2:
  IV Men; XIII Akbal; VII Chuen; II Cauac; X Manik; V Men; XIII Akbal.
    17        8           8          8         8      8        8

The chief objects in view at present in selecting this series are, as
before indicated, to prove the relation of the plates to one another and
to determine the use of the black numerals which stand under the day
symbols. These numerals consist of but two different numbers, the first
on each page being 17, the rest 8's.

As the particular year or years to which the series refers is unknown we
turn to our calendar--Table II--and select the Kan column, as we find
that 4 Ahau, the first day of the series, is the seventeenth day of the
year 1 Kan. This corresponds with the first black numeral. Counting 8
days from this we reach 12 Lamat, the second day of our series; 8 more
bring us to 7 Cib, the third day of the series; 8 more to 2 Kan; 8 more
to 10 Eb; 8 more to 5 Ahau; 8 more to 13 Lamat, and 17 more to 4
Chicchan. The red numeral at this point in some of the colored copies of
Kingsborough's work is III, but a close inspection shows the missing dot
which has not been colored. IV Chicchan is therefore correct.

Continuing our count, 8 days more bring us to 12 Been: 8 more to 7 Ymix;
8 more to 2 Muluc; 8 more to 10 Caban; 8 more to 5 Chicchan; 8 more to 13
Been; 17 more to 4 Oc; 8 more to 12 Ezanab; 8 more to 7 Cimi; 8 more to 2
Ix; 8 more to 10 Ik; 8 more to 5 Oc, and 8 more to 13 Ezanab. Here the
red numeral is wanting, but a comparison of the numbers on the different
plates and the order of the series make it evident that it should be
XIII.

Continuing our count, 17 more bring us to 4 Men (here a dot is missing in
Kingsborough's copy, but is present in the photograph); 8 more to 12
Akbal. Here there is one dot too many, which we may attribute to a
mistake of the original artist. Assuming XII to be correct, 8 more bring
us to 7 Chuen; 8 more to 2 Cauac; 8 more to 10 Manik; 8 more to 5 Men; 8
more to 13 Akbal, and to the end of our table; thus, if we include the
first seventeen days, completing the series of thirteen months or 260
days.

These illustrations will probably satisfy any one that the black numerals
in these lines denote the intervals between the days indicated by the
symbols and that the series so far examined are to be read from left to
right.

Although the succession of days and numbers in the lines of the last
example would seem to furnish conclusive evidence that the whole is one
continuous series, yet the peculiar combinations of numbers used by the
Maya priests render these series very deceptive. There can be no doubt
that the black numbers--8's--are used to indicate the intervals between
the days specified; but there is another possible way of explaining the
17 with which the lines on the different plates begin.

Here are four plates, evidently closely related to one another; the lines
of days and numbers in the lowest division of each are precisely alike,
except as to the days indicated; in the left hand column of characters of
each is one of the cardinal point symbols. It is possible, therefore,
that these four plates relate to the four different years or series of
years; that is to say, one to the Kan years, one to the Muluc years, and
so on. This view is somewhat strengthened by the fact that 4 Ahau, first
of the line on Plate 42, is the seventeenth day of the first month of the
year 1 Kan; 4 Chicchan, first of the line on plate 43, the seventeenth
day of the first month of the year 1 Muluc; 4 Oc, the seventeenth day of
1 Ix, and 4 Men the seventeenth day of 1 Cauac. The four figures in the
middle division of Plates 1 and 2 seem also to favor this idea, not so
much by the peculiar animals represented (of which we have no explanation
to give) as by the double symbols from which they are suspended, which I
am quite confident denote the union of years or the time at which two
years meet--the close of one and the commencement of another--although
fully aware that Dr. Förstemann has interpreted them as symbols of the
heavenly bodies.[280-1]

In the text above these figures are seen two characters or symbols of
this type, which in all probability, as will hereafter appear, denote or
symbolize the "tying of the years." We may also add that the five days of
each plate or group are the five assigned, as I have explained in "Notes
on certain Maya and Mexican manuscripts," to the cardinal points. For
example, those on Plate 42 are Ahau, Eb, Kan, Cib, Lamat.[280-2] Still it
must be admitted, on the other hand, that as the four lines form
precisely one complete cycle of 13 months or 260 days there is a very
strong inference that they together form one continuous series and that
the arrangement into four parts or divisions has reference to the four
seasons or four cardinal points. The final decision on this point
therefore still remains in doubt.

As it has been shown that Plates 33 to 39 and Plates 38 to 43 are
properly placed as they stand in Kingsborough's copy and also in
Förstemann's and that Plates 1 and 2 follow Plate 43, we have proof that
the following plates succeed one another to the right, as here given: 33,
34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 2.

A slight inspection is sufficient to show that Plates 29 to 33 follow one
another in the same order, a conclusion which is easily verified by
testing the lines of numerals in the manner explained. It is apparent,
therefore, that the following plates form one unbroken series, running
from left to right: 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 1, 2; a conclusion which Dr. Förstemann, who has had the
opportunity of studying the original, has now reached.

Having ascertained the object and use of at least one class of black
numerals and the relation they bear to the days and day numbers, it may
be well to test further the discovery by other examples, in order to see
how far it holds good and what new facts it may bring out. In doing this
it will be necessary to repeat in part what has already been shown by Dr.
Förstemann in his late work; but as these discoveries were made
independently and before this work came to hand, and as our conclusions
differ in some respects from those reached by him, the plan and scope of
this paper would be incomplete without these illustrations.

Commencing with the day column in the middle of Plate 35_b_ and extending
through Plates 36_b_ and 37_b_ to the right margin of the latter, is a
line of alternate red and black numerals, which may be taken as an
example of the most common series found in the Dresden and other codices.
It is selected because it is short, complete, and has no doubtful symbols
or numerals in it.

Using names and numbers in place of the symbols, it is as follows:

    I.
  Caban, 11, XII; 6, V; 9, I; 4, V; 7, XII; 9, VIII; 6, I.
  Muluc.
  Ymix.
  Been.
  Chicchan.

In this case the red numeral over the day column is I. It is to be
observed that the last number of the series is also I, a fact which it
will be well to keep in mind, as it has an important bearing on what is
now to be presented. But it is proper to show first that this series is
continuous and is connected with the day column.

Adding the I over the column to the 11, the first black numeral; gives
XII, the red numeral following the 11. That this holds good in all cases
of this kind will become apparent from the examples which will be given
in the course of this discussion. Adding together the remaining pairs, as
follows: XII + 6 - 13 = V; V + 9 - 13 = 1; 1 + 4 = V; V + 7 = XII; XII +
9 - 13 = VIII; VIII + 6 - 13 = I, we obtain proof that the line is one
unbroken series. It is apparent that if the black numerals are simply
counters used to indicate intervals, as has been suggested, then, by
adding them and the red numerals over the column together and casting out
the thirteens, we should obtain the last red number of the series. In
this case the sum of the numbers 1, 11, 6, 9, 4, 7, 9, 6, is 53; casting
out the thirteens the remainder is 1, the last of the series. If we take
the sum of the black numbers, which in this case is 52, and count the
number of days on our calendar (Table II) from 1 Caban, the fourteenth
day of the first month of the year 1 Kan, we shall find that it brings us
to 1 Muluc, the sixth day of the fourth month; 52 days more to 1 Ymix; 52
more to 1 Been, and 52 more to 1 Chicchan, thus completing the day column
in the example given. This proves, in this case at least, that the red
numeral over the day column applies to all the days of the column and
that the whole numeral series--that is to say, the sum of the
counters--represents the interval between the successive days of the
column. The total number of days from 1 Caban, first of the column, to 1
Chicchan, the last, is 208. Adding 52 more gives 260 and brings us back
to 1 Caban, our starting point.

It will be observed that the sum of the black numbers--which denotes the
interval between the days of the column--is 52, which is a multiple of
13, the number of days in a Maya week. It follows, therefore, that so far
as this rule holds good the last red numeral of the series must be the
same as that over the day column. In a former work[282-1] I explained the
method of ascertaining the relations of the days of a column to one
another by means of the intervals without reference to the numbers
attached to them, a subject to which Charency had previously called
attention;[282-2] by the explanation now given we ascertain the true
intervals between the days _as numbered_. The two modes therefore form
checks to each other and will aid very materially in restoring
obliterated and doubtful days.

There is another point in regard to these series which may as well be
illustrated by means of the example given as any other. What is the
signification of the red numerals of the series? They are unnecessary if
the only object in view was to indicate the intervals between the days of
the column. Nor will the supposition that the Mayas had not discovered a
means of representing higher numbers than 20 suffice, as the introduction
of 13 would have lessened the labor and shortened the calculation. But
one answer to this inquiry appears possible, viz, that these numbers are
intended to denote certain intermediate days to which importance was for
some reason attached. These intermediate days can readily be determined
from the data given, and in the present example are as follows:

    (1) Between 1 Caban and 1 Muluc they are 12 Lamat, 5 Ix, 1 Akbal, 5
    Manik, 12 Ix, and 8 Akbal.

    (2) Between 1 Muluc and 1 Ymix they are 12 Ahau, 5 Cimi, 1 Men, 5
    Cauac, 12 Cimi, and 8 Men.

    (3) Between 1 Ymix and 1 Been they are 12 Eb, 5 Ezanab, 1 Manik, 5
    Chuen, 12 Ezanab, and 8 Manik.

    (4) Between 1 Been and 1 Chicchan they are 12 Kan, 5 Oc, 1 Cauac, 5
    Akbal, 12 Oc, and 8 Cauac.

These, as will be readily perceived, are found by counting on the
calendar from 1 Caban, 1 Muluc, &c., as heretofore explained.[283-1]

Our interpretation of the series of this particular class is now
complete, except as to their application or the object in view in forming
them and the determination of the particular years to which they apply.
Possibly they may be of general application, so far as consistent with
the calendar system. The conclusion on this point depends largely upon
the conclusion as regards the system, as it is evident their location in
time--if the year of 365 days and the four series of years formed the
basis of the system--would not correspond with their position in a system
based upon the year of 360 days, in which the four year series does not
play any necessary part.

Dr. Förstemann calls attention to the fact that the pairs of numerals
representing the intermediate days are usually placed in separate
compartments, each containing a figure or a picture generally symbolic or
of a priest dressed to indicate some particular god. It is therefore very
probable that these intermediate days are to be devoted to ceremonies
relating to the divinities or subjects indicated by these figures.

In order to confirm the theory we are now discussing and at the same time
show some of the different varieties of the series of the type now under
consideration, the following additional examples are given.

In the middle division of Plate 5 is a day column and a numeral series,
as follows:

    I.
  Manik }
  Cauac } 16, IV; 9, XIII; S + 5, XII; 2, I.
  Chuen }
  Akbal
  Men

This series terminates with I, as it should according to the theory. The
sum of the black numerals--16, 9, 20, 5, 2--is 52, a multiple of
thirteen, and the interval between the successive days, reading
downwards, is 52, agreeing in these particulars with the theory. It will
also be observed that the symbol represented by S answers to the number
20.

In the lowest division of the same plate is another similar series, as
follows:

   XII
  Ezanab }
  Akbal  } 20 + 9, II; 11, XIII; 18, V; 7, XII.
  Lamat  }
  Been
  Ezanab

This terminates with XII, the number over the column; the sum of the
black numbers is 65, a multiple of thirteen and precisely the interval
between the successive days of the column, taking the week numbers into
consideration, which is always to be understood in speaking of these
intervals unless the contrary is expressly stated.

[Illustration: FIG. 361.]

In the middle division of Plate 8 is a short series connected with a day
column containing the following days, reading downwards, as usual: Manik,
Cauac, Chuen, Akbal, Men. The symbol for Akbal (Fig. 361), is a very
unusual one, reminding us strongly of a skull, which may possibly have
given origin to the symbol. The numerals of the series are as follows: 20
+ 6, VIII; 20 + 6, VIII; the number over the column, VIII; and the
interval between the days, 52.

In Plate 15, division _c_, is the following series, which differs from
those given in having two day columns instead of one:

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

The final number is the same as that over the columns; the sum of the
black numbers is 26, which is a multiple of 13; but in this case in
counting the intervals the days are to be taken alternately from the two
columns.

Commencing with 3 Lamat on our calendar and counting 26 days brings us to
3 Ix; 26 more to 3 Ahau; 26 more to 3 Cimi, and so on to the end.

In the lower division of Plate 9 is a series arranged as follows:

   III      III      VI   VIII
  Cauac    Been       3     2
                    {XI    II
  Chuen    Chicchan { 3     4
                    {VI   VII
  Akbal    Caban    { 4     1
  Men      Muluc      I   III
  Manik    Ymix       7     2

The sum of the black numerals is 26 and the final red number is III, the
same as that over the columns. The interval between the days, taken
alternately from the two columns, as in the preceding example, is 26. The
numbers are also to be taken alternately from the two number columns.

It is apparent that these examples sustain the theory advanced. This will
also be found true in regard to all the series of this type in this and
the other codices where the copy is correct. Brasseur's copy of the
Manuscript Troano is so full of mistakes that no satisfactory examination
of this codex can be made until a photographic copy is obtained;
nevertheless a few examples are given as proof of the above statement.

In the third division of Plate XI* is the following series:

   IV
  Ahau }
  Eb   } 17, VIII; 13, VIII; 10 V; 12, IV.
  Kan  }
  Cib
  Lamat

As will be readily seen, after the explanations given, this agrees with
the theory advanced.

The last red number is the same as that over the day column, the sum of
the black numbers is 52, and the interval between the days 52.

Commencing in the right margin of the lowest division of Plate XXIII* and
running through Plates XXII* and XXI*, is the series here represented:

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

An examination of this shows it to be of the type of the double column
series of the other codex, except that here the days of one column are to
be taken in the order in which they stand before proceeding to the other
column. The sum of the black numbers is 26 and the interval between 7 Cib
and 7 Ik 26 days. The interval between 7 Ik and 7 Lamat, 7 Lamat and 7
Ix, and between 7 Ix and 7 Ahau is, in each case, 26 days. The interval
between 7 Ahau, last day of the left hand column, and 7 Cimi, the first
day of the right hand column, is also 26 days.

The order in which the days of these double column series of this
manuscript follow one another is not uniform, as in some cases (see Plate
XXV*, division _a_) they are to be taken alternately from the two
columns, as in the examples heretofore given from the Dresden Codex.

In the middle division (Plate XXXIII*, same codex) is a series of the
following form, but with the days so nearly obliterated that restoration
is necessary:

           { VI   I
           { 5    8
   I       { VI   I
  Ymix (?) { 5    8
  Cimi (?) { VI   I
  Chuen    { 5    8
  Cib (?)  { VI   I
    (?)    { 5    8
           { VI   I
           { 5    8

The symbol of the first day has only the upper circle of dots to indicate
that it is Ymix, that of the second day is almost obliterated, the third
is clearly Chuen, the lower half of the fourth is obliterated, and the
interior of the fifth is a blank.

Fortunately there are sufficient data by which to make the restoration.
Chuen, we observe, is the middle of the column; that is, two days are
above it and two days below it; the sum of the black numerals is 65;
hence the interval between the days, considering the week numbers as
attached, is 65, and the simple interval in the month series, without
regard to the week numbers, is 5. Counting back on our calendar (Table
II) 65 days from 1 Chuen we reach 1 Cimi, and 65 more bring us to 1
Ymix. In like manner we find the fourth day to be 1 Cib and the fifth 1
Ymix. The numbers in the figure columns are to be taken alternately,
thus: 5, VI; 8, I; 5, VI; 8, I, &c.

These examples are sufficient to show that the series of the Manuscript
Troano are arranged upon the same plan and based upon the same system as
those of the Dresden Codex. The following examples from the Codex
Cortesianus prove the same thing to be true in reference to the series
found in it.

The first is taken from the lower division of Plates 10 and 11, Rosny's
reproduction:

  XIII
  Ahau     } 11, XI; 5, III; 5, VIII; 5, XIII; 9, IX; 3, XII; 6, V;
  Chicchan } 1, VI; X, XIII.
  Oc
  Men

The S in the line of numerals represents the usual symbol for 20. The sum
of the black numbers is 65, the interval between the days 65, and the
last red numeral the same as that over the day column, thus agreeing in
plan with those in the other codices.

The following double column series is found in the middle division of
Plate 30:

   XI        XI
  Ahau     Ymix  }
  Eb       Been  } 20 + 6, XI; 20 + 6, XI.
  Kan      Caban }
  Cib      Chicchan
  Lamat    Manik

The number 20 is denoted by the usual symbol. The sum of the black
numbers is 52 and the interval between the days in each column 52, but in
this case there does not appear to be any connection between the columns,
there being, in fact, two distinct series.

In the upper division of the same plate is this series:

    XI
  Ezanab { VI     XI
         { 8      5
  Oc     { VI     XI
         { 8      5
  Ik     { VI     XI
         { 8      5
  Ix     { VI     XI
         { 8      5
  Cimi

The order in which these numerals are to be read is as follows: 8, VI; 5,
XI; 8, VI; 5, XI, &c., which gives, as the final red number of the
series, XI, the same as that over the column. The sum of the black
numbers is 52 and the interval between the days 52.

Taking for granted that the correctness of the theory advanced is
conceded, some attempts at its further application, especially its use in
making restorations and corrections in defective series and in settling
doubtful questions relating thereto, will now be presented.

In the upper division of Plate 32, Dresden Codex, are the four day
columns and lines of numerals over them here represented:

   1
   4       13       9            4
  15       13       2           11
  XIII     XIII     XIII        XIII
  Manik    Cib      Chicchan    Ix
  Chuen    Ahau     Muluc       Ezanab
  Men      Kan      Been        Ik
  Cauac    Lamat    Caban       Cimi
  Akbal    Eb       Ymix        Oc

Connected with these numbers is a line of alternate black and red numbers
running along over the figures of Plates 32 to 39, division _a_. There
are several breaks and some partially obliterated characters in it which
must be restored in order to use it. It has been selected partly on this
account, that the method of filling such breaks and making such
restorations may be seen.

Representing the numerals and symbols as heretofore and substituting a
cipher where the numbers are wanting or are too much obliterated to be
determined by inspection, the series will be as follows: 11, XI; 8 + 20,
0; 12 (or 13), XIII; 6 + 20, XIII; 12, VII (?); 16 (?), V; 5, X; 1, XI;
20, V; 12, IV, 6, X; 0, V; 5, X; 7, IV; 12 (?), II; 5, VII; 8, II; 11, 0.

Commencing with the XIII over the day columns and counting as heretofore,
we obtain the following result: XIII + 11 - 13 = XI; XI + 8 + 20 - 13 -
13 = XIII. The first blank should therefore be filled with XIII.
Continuing, XIII + 13 - 13 = XIII; the black numeral in this case should
be 13, although apparently 12 in the codex; XIII + 6 + 20 - 13 - 13 =
XIII; XIII + 12 - 13 = XII. Here the result obtained differs from the red
numeral in the codex, which is apparently one line and two dots, or VII;
but, by carefully examining it or inspecting an uncolored copy, the two
lines which have been covered in the colored copy by a single broad red
line are readily detected. The next black numeral is partially
obliterated, the remaining portion indicating 16, but it is apparent from
the following red numeral that it should be 19. Making this correction we
proceed with our count: XII + 19 - 13 - 13 = V; V + 5 = X; X + I = XI; XI
+ 20 - 13 - 13 = V; V + 12 - 13 = IV; IV + 6 = X. The next black numeral
is obliterated, but is readily restored, as X + 8 - 13 = V; V + 5 = X; X
+ 7 - 13 = IV. The next step presents a difficulty which we are unable to
explain satisfactorily. The black numeral to be counted here, which
stands over the animal figure in the upper division of Plate 39, is 12,
both in Kingsborough's copy and in Förstemann's photograph, and is clear
and distinct in each, and the following red numeral is as distinctly II,
whereas IV + 12 - 13 = III. Moreover it is evident from the remaining
numbers in the line that this red numeral should be II. We may assume
that the Maya artist has made a mistake and written 12 instead of 11,
which is evidently the number to be used in the count; but this
arbitrary correction should not be resorted to so long as any other
explanation is possible. From the fact that immediately under these
numbers there are certain symbols which appear to have some reference to
the termination of one year or cycle and the commencement of another, it
is possible that a supplemental, unnumbered, but not uncounted day has
been added. The fact that this interval of twelve days includes the day
Ymix lends some probability to this supposition. Using 11 instead of 12,
we continue our count as follows: IV + 11 - 13 = II; II + 5 = VII; VII +
8 - 13 = II; II + 11 = XIII. Thirteen is, therefore, the last number of
the series, which is wanting in the codex. The 8 and II next to the last
pair of the series are not in line with the other numbers, but thrust
into and near the bottom of the column of characters in the upper
division of Plate 39. Adding together the black numbers as thus amended
and restored, viz, 11, 8, 20, 13, 6, 20, 12, 19, 5, 1, 20, 12, 6, 8, 5,
7, 11, 5, 8, 11, the sum is found to be 208, which is a multiple of 13,
and the final number of the series is 13. On the other hand, the sum of
the series does not indicate the interval between the days of a column
counting downwards, nor between two consecutive days or the corresponding
days of two adjoining columns in any direction. The number of days from
13 Manik to 13 Chuen is 104, but counting 208 days from 13 Manik brings
us to 13 Men, the third day of the first (left hand) column; 208 more to
13 Akbal, the fifth; 208 more to 13 Chuen, the second; and 208 more to 13
Cauac, the fourth, thus completing the column.

As these columns do not appear to form a continuous series it is possible
they pertain to four different series of years, though the fact that each
includes more than one year would seem to forbid this idea. It is more
probable that they pertain to four different series, to each of which the
line of numerals is to be considered as belonging.

The black numerals above the columns present a problem which I am unable
to explain. The numbers stand in the original as follows:

   1
   4    13    9    4
  15    13    2    11

If we suppose that the lowest line denotes days, the one next above,
months, and the uppermost, in which there is but a single number, years,
the series will appear to be ascending toward the left, with the
difference 4 months and 11 days, as shown by addition, thus:

  Y.    M.     D.
         4     11 Numbers over the fourth column.
         4     11
  ---------------
         9      2 Numbers over the third column.
         4     11
  ---------------
        13     13 Numbers over the second column.

Doubling the difference and adding we obtain the numbers over the first
column:

  Y.    M.    D.
        13    13
         9     2
  ---------------
   1     4    15

What adds to the difficulty is the fact that if the columns are taken in
reverse order the interval between the corresponding days is 4 months and
11 days; that is to say, counting from 13 Ix, first day of the fourth
column, to 13 Chicchan, first day of the third column, we find the
interval to be exactly 4 months and 11 days; and the same rule holds good
throughout, so that reading across the upper line of days, from right to
left, and following with the second line in the same way, ending with
Akbal, the interval will be 4 months and 11 days between the consecutive
days. Another significant fact is that by counting 4 months and 11 days
from the first day of the year 1 Kan we reach 13 Ix; counting 9 months
and 2 days from the same date brings us to 13 Chicchan; 13 months and 13
days, to 13 Cib; and 1 year and 4 days, to 13 Manik, which corresponds
with the regular interval; it is therefore probable that there is an
error in the numerals over the first or left hand column.

It is apparent from the illustrations given that in numeral series of the
preceding type restorations can be made where not more than two numbers
in succession are wanting. Even three can generally be restored if the
numbers preceding and those following the break are distinct, but such
restorations should be cautiously made.

In the middle division of Plate 9 is a short series where the number over
the day column is wanting; moreover, there is uncertainty as to the
number of days in the column and as to the signification of the red
numerals, which are in pairs in Kingsborough's work instead of single as
usual. Is it possible to explain these uncertainties and to reduce them
to the usual simple form? Let us make the trial.

The days in the column are apparently the following: Ahau, Muluc, Ix,
Cauac, Kan. The symbols, except that for Cauac, are too plain to admit of
doubt, and there is no difficulty in reference to Cauac, the question of
doubt being with regard to the Ahau, which is partially surrounded by
other characters and may, apparently, be as correctly considered a part
of the hieroglyphic inscription as of the day column.

Counting on the list of days in the calendar (Table II), as, for example,
the Muluc column, we find the interval from Muluc to Ix is 5 days, from
Ix to Cauac is 5 days, and from Cauac to Kan 5 days; but the interval
from Ahau to Muluc is 9 days. From this fact we may reasonably infer that
Ahau does not belong to the column. Moreover, the other 4 days are the
four year bearers, and when they occur together the column usually
consists of but 4 days, as, for example, in the lowest division of Plate
29 of this codex and Plate XXXII* of the Manuscript Troano. The numerals
are 20; XIII, X; 20, XII, III; the number over the day column, as before
stated, is wanting. The interval from 1 Muluc (or 2 or 3 Muluc) to Ix of
the same number is 65 days. It is evident, therefore, that one of each
pair of red numerals of the series given must be a counter and has been
colored red by mistake. As the numbers in the last pair are III and XII,
the number over the column must be 3 or 12. Suppose it is 12 and that
XIII of the first pair is a counter, then XII + 20 + 13 - 13 - 13 - 13 =
VI. As the number in the series is X this will not do. Supposing the X of
the first pair of red numerals to be the counter, colored by mistake, the
result is as follows: XII + 20 + 10 - 13 - 13 - 13 = III. This is also
wrong, as the remainder should be XIII. Supposing the number over the
column to be III and the XIII of the first pair and XII of the second to
be the counters, the result agrees with the theory in every particular.
Thus, III + 20 + 13 - 13 - 13 = X; X + 20 + 12 - 13 - 13 - 13 = III; and
20 + 13 + 20 + 12 = 65, the interval between 3 Muluc and 3 Ix. In
Förstemann's copy the XIII and XII are black, thus verifying the
conclusion here reached.

The series running through Plates 10_c_ and 11_c_ presents some
difficulties which I have, so far, been unable to solve. The day columns
and numerals are as follows:

   I          XIII
  Ymix        Cimi   }
  Been        Ezanab } 1, I; 5, VI; 10, III; 13, III; 15, V; 9 (?), XIII.
  Chicchan    Oc     }
  Caban       Ik
  Muluc       Ix[290-1]

The numerals in this case are very distinct, especially in the
photographic copy, and there can be no doubt as to the days. Here the
last black number, 9, is wrong; it should be 8, a fact noticed by
Förstemann.[290-2] Making this correction, the series is regular and
consistent, so far as it relates to the right hand column, which has the
red thirteen over it. But there is no series for the left hand column.
Can it be that those who used the manuscript were expected to find the
proper numbers by the line given? Possibly this is the reason the other
series is not written out, as by adding one to each red number we obtain
the proper result, which, if written out, would be as follows: 1, II; 5,
VII; 10, IV; 13, IV; 15, VI; 3, I.

In Plate 30_c_ are the four day columns here given, with the numeral
eleven over each:

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

Extending from the right of this group is a numeral series consisting of
nine pairs of numbers, each pair the same, 13, XI. The sum of the black
numbers (nine 13's) is 117 and the interval between the successive days
of each column is 117; thus, from 11 Ahau to 11 Caban is 117 days, and so
on down to Lamat, the last of the left hand column. From 11 Lamat to 11
Chicchan (first day of second column) is also 117, and so on to the end
of the fourth column. These four columns, therefore, form one continuous
series of 2,223 days, commencing with 11 Ahau and ending with 11 Akbal;
but, by adding 117 days more, so as to bring us back to 11 Ahau--which
appears to be in accordance with the plan of these series--the sum is
2,340 days, or nine cycles of 260 days each.[291-1]

The interval between the days, without reference to the numbers attached
to them, is 17. It may be well to notice here the relation of the
intervals between the days when counted in the two ways: (1) the apparent
interval, or that which indicates their position in the month; (2) the
true interval between the days, indicated by the symbols and numbers.
When the first is 6 the latter, as we have found, is 20; when the first
is 12 the latter is 52; when the first is 5 the latter is 65, and when it
is 17 the latter is 117.

Particular attention is also called here to the fact that so far no
indications of the use of the year period of 365 days have been observed;
on the contrary the cycle of 260 days appears to be the period to which
reference is chiefly made.

Attached to the day column in Plate 29_c_ and running into 30_c_ is a
series which presents a difficulty I am unable to explain. The days and
numerals in this case are as follows:

   III
  Ix
  Cauac } 16, VI; 16, IX; 16, XII; 16, (?)
  Kan   }
  Muluc

The red numeral over the day column is very distinctly III in
Kingsborough's work, but is II, though somewhat blurred, in Förstemann's
photograph. As III + 16 - 13 = VI, and the remaining numerals agree with
this result, III must be correct. Adding together the pairs and casting
out the thirteens, thus, III + 16 - 13 = VI; VI + 16 - 13 = IX; IX + 16 -
13 = XII; XII + 16 - 13 - 13 = II, we find the last red number, which is
wanting in both copies of the codex, to be II, whereas, according to the
theory advanced, it should be III. The sum of the black numerals (four
16's) is 64, while the interval between the days is 65. The only way of
correcting the mistake, if one has been made, is by arbitrarily changing
the last 16 to 17; but uniformity in the black numerals apparently
forbids this change and and[TN-3] indicates that the variation from the
usual rule must be accounted for in some other way.

In reference to this series, Dr. Förstemann[292-1] remarks:

     The column of the days has the difference 5; the fifth sign (in this
     case really superfluous), that of the thirteenth day, appears in a
     remarkable form, apparently as an inscription on a vessel. The black
     figures ought to give the sum 65, but we get only 4 × 16, or 64. But
     this appears to be merely an oversight by the copyist, for although
     in the Codex Troano, also, we find 64 several times instead of 65,
     still this has always appeared to me merely as a sign of the great
     negligence of the copyist of that manuscript.

Turning to the Manuscript Troano, Plate XXVIII*_b_, we find a column
consisting of the four terminal days of the year, Been, Ezanab, Akbal,
and Lamat, which of course have the same relation to one another as the
first days. It is evident from the space that only four were intended to
be given. The numerals in Brasseur's fac simile are XI; 20, 12, IV; 9,
XIII; 10, X; 13, XI.

The red numeral over the column is XI, as is also the last of the series,
but the sum of the black numbers is only 64, which would give X as the
final number, as is evident from the following operation: XI + 32 - 13 -
13 - 13 = IV; IV + 9 = XIII; XIII + 10 - 13 = X; X + 13 - 13 = X. The
interval between the days is 65. We have, therefore, precisely the same
difficulty in this instance as in the case from the Dresden Codex under
consideration. Moreover, the only method of correcting the mistake, if
there is one, is by adding _one_ to the last black number. It would be
hazardous to assume that two mistakes, precisely the same in every
respect, should have been made in regard to these exactly similar series.
The probability that a mistake has been made is lessened by the fact that
on Plate XXIX*_b_ of the manuscript is another four day column, the last
days of the years, as the preceding. The numeral over the column is XIII
and the series is as follows: 13, XIII; 20, 18, XII; 13, XIII. Adding
these and casting out the thirteens, we have this result: XIII + 13 - 13
= XIII; XIII + 20 + 18 - 13 - 13 - 13 = XII; XII + 13 - 13 = XII. This
gives XII as the last number when it should be XIII. If a mistake has
been made the only method of correcting it is by increasing the last
black number by one, as in the other two cases alluded to.

It is proper to state that on the other hand there is another four day
column on Plate XXXII*_a_ of the last mentioned codex, the days of which
are precisely the same as those on Plate 29_c_ of the Dresden Codex, to
wit, Ix, Cauac, Kan, Muluc. The numeral over it is XII and the series is
as follows: 13, XII; 13, XII; 13, XII; 13, XII; 13, XII. This presents no
difficulty, as it conforms in every respect to the rules given, but only
serves to deepen the mystery in the other cases.

Going back to the series on Plate 29_c_ of the Dresden Codex, we observe
not only that the days of the column are the four year bearers, but also
that one of the four cardinal symbols is found--in the superscription--in
each of the four compartments through which the series extends. It is
possible, therefore, that the series is intended to be applied separately
to each of the four years. Supposing this to be the case, counting 64
days from 3 Ix would bring us to 2 Ezanab; 64 days from 3 Cauac to 2
Akbal; 64 days from 3 Kan to 2 Lamat; and 64 days from 3 Muluc to 2 Been.
It is significant that in each case the day reached is that on which the
given year terminates; for example, the Ix years (counting the five added
days) terminate on Ezanab; the Cauac years on Akbal &c. If the intention
was to have the series terminate with the end of the respective years,
then these years must necessarily have been 2 Ix, 2 Cauac, 2 Kan, and 2
Muluc. I must confess that this explanation is not satisfactory; it is
thrown out simply as a suggestion.

Running through the middle division of Plates 30 and 31 is this series:

  3,    VIII;    3, VIII;    3, VIII;    3, VIII
  5,    Oc       5, Men      5, Ahau     5, Chicchan.

Commencing with 8 Oc (omitting for the present the 3 and 5 to the left)
and counting thence 3 months and 5 days we reach 8 Men; 3 months and 5
days more and we reach 8 Ahau; 3 months and 5 days more bring us to 8
Chicchan, and 3 months and 5 days more bring us again to 8 Oc, thus
completing a cycle of 260 days (13 months) and also accounting for the
first pair of numerals--3 and 5 in the series. It appears to be a pretty
general rule to commence a series of this type with the difference
between the numbers of the series. One reason for this is apparent: that
is, to complete the cycle of 260 days, to which most, if not all, of
these groups appear to refer.

Dr. Förstemann says in regard to this line:[293-1]

     This is the place where I first discovered how numbers of several
     figures are to be read; here for the first time I understood that
     the figure 3 with 5 below it is nothing but 3 × 20 + 5, or 65, and
     that they mean nothing else than the interval between the days, such
     as we have frequently met with so far; 4 × 65 is again the well
     known period of 260 days.

Plate 3 appears to be isolated and unfinished; at least it presents
nothing on its face by which it can be directly connected with any other
plate of the codex, notwithstanding the change made by Dr. Förstemann, by
which 45 was brought next to it. The day column in this case is in the
middle compartment of the upper division and consists of the following
days: Ahau, Eb, Kan, Cib, Lamat; the red numeral over it is I. The
numerals and days are arranged as follows:

  (?)     (?)        4,  V(?)        15, XIII

                       I
                      Ahau
  8,     XIII         Eb
                      Kan
                      Cib             14 (?)
                      Lamat

As numerals belonging to two different series are never found in the same
compartment it is fair to assume that those of the middle and right
compartments pertain to one series. But what shall we say in reference to
those in the left compartment, the upper pair of which is almost entirely
obliterated? So far we have found no series extending to the left of the
day column. Is this an exceptional case? I am inclined to believe it is,
for the following reasons:

Taking the 4, V over the bird as the first pair of the series, we have
I + 4 = V, which is so far correct; after this follows the pair in the
lower left hand corner, 8, XIII, as V + 8 = XIII. It is probable that the
obliterated pair in the upper left hand corner followed next, then the
pair in the upper right hand corner, and last the partly obliterated one
in the lower right hand corner. In this case the obliterated pair in the
upper left hand corner should be 11, XI, as XIII + 11 - 13 = XI, and XI +
15 - 13 = XIII, and XIII + 14 - 13 - 13 = I, which makes the terminal red
number of the series the same as that over the day column. This
restoration requires no change of any of the numbers which can be
distinctly read. By adding together the black numbers 4, 8, 11, 15, 14,
the sum is found to be 52, precisely the interval between the days of the
column. These facts are sufficient to render it more than probable that
the restoration and the order as here given are correct. The series as
thus given, including the number over the day column, is: I; 4, V; 8,
XIII; 11, XI; 15, XIII; 14, I.

This is repeated, because on turning to Dr. Förstemann's comment on this
series I find that he has restored and amended it so as to read thus: I;
10, XI; 4, V; 15, XIII; 9, XIII; 14, I; and he remarks that all would be
plain sailing if, for the V before and the XIII after 15, we could read
II and IV. This is true, but these numbers are too distinct to justify
such change; moreover his "9" is not to be found on the page; it is true
that the three dots over the line are not exactly spaced, but there are
no indications of a fourth; the number is 8 and should, I think, be so
read. His 10 is the obliterated black numeral; of course the value
attributed to it depends upon the order given to the series. The
fragments remaining of the red number of this pair I think warrant his
making it XI.

Plates 46, 47, 48, 49, and 50 are peculiar and seemingly have no direct
relation to any other part of the codex. In the upper left hand corner of
each are four day columns, all more or less injured, but each column
evidently contained, originally, thirteen days, or, more correctly
speaking, the symbol for one day repeated thirteen times. In every case
the day in the first (left hand) column and that in the third column are
the same. As the numbers attached to them are absolutely unreadable in
Kingsborough and much obliterated in the photograph, I give here
restorations for the benefit of those studying this codex. This
restoration is easily made by finding the order of the series, which can
be obtained from Plates 49 and 50 of the photographic copy.

_Plate_ 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.

_Plate_ 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.

As the arrangement and the order of the series are readily seen from the
two examples given, only the top and bottom lines of the remaining series
will be presented.

_Plate_ 48:
      I Kan.       XIII Ix.        III Kan.        XI Eb.
         *           *  *           *   *          *  *   [TN-4]
     VI Kan.          V Ix.       VIII Kan.       III Eb.


_Plate_ 49:
   XIII Lamat.      XII Ezanab.     II Lamat.       X Cib.
     *   *           *   *          *   *           *  *
      V Lamat.       IV Ezanab.    VII Lamat.      II Cib.

_Plate_ 50:
    XII Eb.          XI Ik.          I Eb.         IX Ahau.
     *   *           *   *           *  *           *  *
     IV Eb.         III Ik.         VI Eb.          I Ahau.

A careful examination of these groups will bring to light the following
relations of the numbers, days, columns, and series to one another:

The numerals of any one column, counting downwards, differ from one
another by 8; that is to say, by adding 8 to any one and casting out 13
when the sum exceeds that number, the next lower number will be obtained;
or, reversing the operation and counting upward, the difference is found
to be 5. The true interval between the days of the columns (counting
downwards) is 3 months (60 days), a rule which holds good as to all the
series and each column. Thus, from 3 Cib to 11 Cib is 3 months, or 60
days; from 11 Cib to 6 Cib, 3 months; from 2 Cimi to 10 Cimi, 3 months,
and from 13 Kan to 8 Kan, 3 months.

Counting on the list of the days of the month, without reference to the
week numbers attached to them, it will be found that from Cib to Cimi is
an interval of 10 days, and from Cib to Kan is an interval of 8 days.
This rule holds good as to all the series, showing that all are arranged
upon precisely the same plan. The true interval between any day of the
first column of either series (the week number attached being considered)
and the opposite or corresponding day in the second column, is 4 months
and 10 days, that between the corresponding days of the second and third
columns is 12 months and 10 days, that between the days of the third and
fourth columns is 8 days, and that between the corresponding days of the
fourth or last column of one series or plate and the first column of the
following series or plate (taking the plates in the order they are paged)
is 11 months and 16 days.

In order to illustrate this we will run through the lowest line of each
series, taking them in the order of the pages.[296-1]

These are as follows:

_Plate_ 46: VIII Cib.        VII Cimi.        X Cib.         V Kan.

_Plate_ 47:  VII Ahau.        VI Oc.         IX Ahau.       IV Lamat.

_Plate_ 48:   VI Kan.          V Ix.       VIII Kan.       III Eb.

_Plate_ 49:    V Lamat.       IV Ezanab.    VII Lamat.      II Cib.

_Plate_ 50:   IV Eb.         III Ik.         VI Eb.          I Ahau.

[Illustration: FIG 362. Copy of Plate 50, Dresden Codex.[TN-5]]

By counting on the calendar (our Table II), as heretofore explained, the
reader will observe that the interval from 8 Cib to 7 Cimi is 4 months
and 10 days; from 7 Cimi to 10 Cib is 12 months and 10 days; from 10 Cib
to 5 Kan is 8 days; from 5 Kan to 7 Ahau is 11 months and 16 days; from 7
Ahau to 6 Oc, 4 months and 10 days; from 6 Oc to 9 Ahau, 12 months and 10
days; from 9 Ahau to 4 Lamat, 8 days; from 4 Lamat to 6 Kan, 11 months
and 16 days, and so on to the end of the series on Plate 50. Referring to
the codex the reader will observe at the bottom of each plate and
directly under--that is to say, in the same vertical lines as the day
columns--two lines of red numerals. It is impossible to determine these
in Kingsborough's copy (except on Plate 50), but they can readily be made
out on the photographed plates. (See the copy of Plate 50, given in
Fig. 362.) Those on a single plate are as follows:

  {  XI, IV, XII,    0,
  { XVI,  X,   X, VIII.

The 0 here represents a red, diamond shaped symbol.

If the upper line represents months and the lower line days, these
numbers will indicate the intervals between the columns and are properly
placed. For example, the XI and XVI signify 11 months and 16 days, the
interval between the last column of the preceding plate and the first
column of the plate on which they stand; the IV and X, the interval of 4
months and 10 days between the first and second columns; XII and X, the
interval of 12 months and 10 days between the second and third columns;
and 0, VIII, the interval of 8 days between the third and fourth columns.
It is apparent from this that the red, diamond shaped symbol represented
by 0 over the VIII denotes a cipher or nought, a conclusion reached
independently by Förstemann.

If this supposition as to the arrangement of the series and the
signification of these numbers be correct, it is apparent that the
plates are to be taken in the order in which they are paged, that is,
from left to right, as the others so far noticed, an inference borne
out by another fact now to be mentioned.

Immediately below each of these four column day series are four lines of
characters (hieroglyphics), and immediately under the latter three
horizontal lines of black numerals, with here and there a red, diamond
shaped symbol inserted. As these numerals stand directly in the vertical
lines of the day columns, it is possible the two have some connection
with each other, a supposition somewhat strengthened by what has been
observed in regard to the red numerals at the bottom of the plates. To
test this and also for the reason that we propose to discuss their
relations and their use, we give here the bottom line of days of each of
the five series (or plates), together with their week numbers attached;
also, the numbers of the three lines of black numerals mentioned, taking
them in the order of the paging as here shown:

_Plate_ 46:
   VIII Cib.    VII Cimi.       X Cib.      V Kan.
                                  1            1
      11           16            10           11
      16            6            16            4

_Plate_ 47:
   VII Ahau.     VI Oc.        IX Ahau.    IV Lamat.
       2            2             3            3
       5            9             4            4
       0           10             0            8

_Plate_ 48:
    VI Kan.      V Ix.        VIII Kan.     III Eb.
       3            4             4            4
      16            2            15           15
       3(?)        14             4           12

_Plate_ 49:
   V Lamat.    IV Ezanab.    VII Lamat.     II Cib.
       5            5             6            6
       9           13             8            8
       8           18             8           16

_Plate_ 50:
    IV Eb.       III Ik.       VI Eb.       1 Ahau.
       7            7             8            8
       3            7             1            2
      12            2            12            0

In considering these horizontal lines it is to be understood that the
series runs through the five pages, 46-50.

Let us proceed upon the supposition that the figures of the lowest of the
three lines denote days of the month, the numbers of the middle line
months, and those of the upper line years. As already shown, the interval
between 8 Cib and 7 Cimi is 4 months and 10 days; adding 4 months and 10
days to 11 months and 16 days (bearing in mind that 20 days make a month
and 18 months a year), the sum is found to be 16 months and 6 days,
precisely the figures under 7 Cimi. As already ascertained, the interval
between 7 Cimi and 10 Cib is 12 months and 10 days; this added to 16
months and 6 days gives 1 year, 10 months, 16 days, precisely the figures
under 10 Cib. The interval between 10 Cib and 5 Kan is 8 days; this added
to the 1 year, 10 months, and 16 days gives 1 year, 11 months, and 4
days, the figures under 5 Kan. The interval between 5 Kan and 7 Ahau is
11 months, 16 days, which, added to the preceding, gives 2 years, 5
months, 0 day, agreeing with the figures under 7 Ahau, if the symbol
represented by 0 signifies nought. That this rule holds good throughout
the entire series, by making one correction, is shown by the following
additions:

Years.    Months.    Days.
            11        16    Under VIII Cib, Plate 46.
             4        10
            --        --
            16         6    Under VII Cimi, Plate 46.
            12        10
            --        --
   1        10        16    Under X Cib, Plate 46.
                       8
  --        --        --
   1        11         4    Under V Kan, Plate 46.
            11        16
  --        --        --
   2         5         0    Under VII Ahau, Plate 47.
             4        10
  --        --        --
   2         9        10    Under VI Oc, Plate 47.
            12        10
  --        --        --
   3         4         0    Under IX Ahau, Plate 47.
                       8
  --        --        --
   3         4         8    Under IV Lamat, Plate 47.
            11        16
  --        --        --
   3        16         4[300-1] Under VI Kan, Plate 48.
             4        10
  --        --        --
   4         2        14    Under V Ix, Plate 48.
            12        10
  --        --        --
   4        15         4    Under VIII Kan, Plate 48.
                       8
  --        --        --
   4        15        12    Under III Eb, Plate 48.
            11        16
  --        --        --
   5         9         8    Under V Lamat, Plate 49.
             4        10
  --        --        --
   5        13        18    Under IV Ezanab, Plate 49.
            12        10
  --        --        --
   6         8         8    Under VII Lamat, Plate 49.
                       8
  --        --        --
   6         8        16    Under II Cib, Plate 49.
            11        16
  --        --        --
   7         2        12    Under IV Eb, Plate 50.
             4        10
  --        --        --
   7         7         2    Under III Ik, Plate 50.
            12        10
  --        --        --
   8         1        12    Under VI Eb, Plate 50.
                       8
  --        --        --
   8         2         0    Under I Ahau, Plate 50.

The proof of the correctness of the theory advanced may, therefore, be
considered conclusive, as it amounts, in fact, to a mathematical
demonstration.

Dr. Förstemann, who considers these lines of black numbers, standing one
above another, as representing different grades of units--thus, the
lowest, single units; the second, units twenty-fold the lower; the third,
eighteen-fold the second; the fourth, twenty-fold the third, &c.--has
found the correct intervals of the series, which he states are 236, 90,
250, and 8 days, agreeing with our 11 months, 16 days; 4 months, 10 days;
12 months, 10 days, and 8 days.

As all the discoveries mentioned herein were made previous to the receipt
of Dr. Förstemann's work, I give them according to my own method,
acknowledging any modification due to his work. Although I shall compare
special results from time to time, an explanation of Dr. Förstemann's
method is reserved for a future paper, as his work was not received until
I was revising my notes for publication.

The foregoing explanation of the series shows it to be very simple and
makes it clear that it relates to the day columns at the top of the
pages. Still, there is one point somewhat difficult to understand. Are
the numbers of the third or lowest line intended to denote the positions
in the month of the days in the columns above? If so, the month must have
commenced with Ymix, as can readily be shown in the following manner:

TABLE III.

   1. Ymix.
   2. Ik.
   3. Akbal.
   4. Kan.
   5. Chicchan.
   6. Cimi.
   7. Manik.
   8. Lamat.
   9. Muluc.
  10. Oc.
  11. Chuen.
  12. Eb.
  13. Been.
  14. Ix.
  15. Men.
  16. Cib.
  17. Caban.
  18. Ezanab.
  19. Cauac.
  20. Ahau.

If we write in a column in proper order the 20 days of the Maya month,
commencing with Ymix, and number them consecutively, as in Table III, we
shall find by comparison that the numbers in the lower line indicate the
position, in this column, of the days directly over them. Take, for
example, the lower line of black numerals on Plate 46, writing over them
the respective days of the columns, thus:

  Cib.       Cimi.       Cib.        Kan.
   16          6          16          4

Referring to Table III we see that Cib is the sixteenth day, Cimi the
sixth, and Kan the fourth.

The days and numbers of Plate 47 are:

  Ahau.       Oc.        Ahau.      Lamat.
    0         10           0          8

Ahau is the twentieth day--here is the diamond shaped symbol--Oc is the
tenth, and Lamat the eighth, and so on to the end of the series on Plate
50.

It may be justly argued that such relation to some given day of the month
would necessarily follow in any series of this kind made up by adding
together intervals of days and months. Still it is not at all likely that
these series were made up without reference to fitted and determinable
dates. If so, the months given must be months of certain determinable
years, and the days denoted must be days of particular months. In other
words, if we had the proper starting point we should be able to determine
the position in the calendar of any day or month mentioned in the series.

First. It is easily seen by reference to the calendar (Table II) that Cib
is not the sixteenth day of the month of any of the four years, nor is
Cimi the sixth nor Kan the fourth. The idea that the figures of this
lower line represent the days of the month must, therefore, be given up
unless we assume that the year commenced with Ymix. It may be worthy of
notice at this point that the list of days on the so-called "title page"
of the Manuscript Troano begins with Ymix. It is also true that the
remarkable quadruple series in the Codex Cortesianus on Plates 13-18
commences with Ymix; as this is evidently some kind of a calendar table,
its bearing on the question now before us is important.

Second. It can easily be shown that the months referred to in the series,
if the numbers given denote specific months, are not those of the Kan
years. The first, 8 Cib, if in the eleventh month, must be in the year 4
Kan; counting forward from this 4 months and 10 days to 7 Cimi brings us
into the sixteenth month of the year 4 Kan; this agrees with our figures
on Plate 46. Counting forward 12 months and 10 days to 10 Cib, we reach
the tenth month of the next year; 8 days more carry us to the eleventh
month, which still agrees with the figures in the codex. Counting 11
months and 16 days more to 7 Ahau, we reach but do not pass the fourth
month of the next year; hence the result does not correspond with the
series, which has at this point a 5 in the middle line. The same will be
found true in regard to the other years as given in our calendar (Table
II). This result, as a matter of course, must follow if the figures in
the lower line of the series do not denote the month days of some one of
the year series as usually given.

Another fact also becomes apparent here, viz, that the 5 supplemental
days of the year are not brought into the count, the year consisting
throughout of 360 days. There is, in fact, nothing here indicating the
four year series as given in the authorities and as represented in our
calendar table; yet this ought to appear wherever a series extends over
more than one year.

Dr. Förstemann says that this entire series of black numerals covers
2,920 days, or 8 years of 365 days. This is true, but the concluding
figures show that it is given by the writer of the codex as 8 years and 2
months, which would also be 2,920 days, counting the years at 360 days
each and the months 20 days each; moreover, the members of the series are
based throughout upon the year of 360 days. His theory that the intervals
of the series relate to the movements of the planet Venus is, as yet, a
mere hypothesis, which needs further proof before it can demand
acceptance; but his discovery of the methods of identifying the month
symbols on the five plates now under consideration is important. Although
I had noticed that most of the characters which he mentions are month
symbols, I did not succeed in identifying all of them.

According to his conclusion, which appears to be justified not only by
the evidence he gives but by an additional fact that I shall, presently
mention, there are four of these symbols in the upper row of the middle
group of written characters on each plate and four in the upper and lower
lines of the lower group on each plate (see, for example, Fig. 362). Each
of these symbols (except three or four) has a black number attached to it
which denotes the day of the month represented by the symbol.

These months and days as given by Dr. Förstemann are as follows, the
positions of the lines as here given corresponding with those of the
plates:

TABLE IV.--_Table showing months and days._

  _____________________________________________________________________
           | Month.  Day. | Month.  Day. | Month.  Day. | Month.   Day.
           |--------------+--------------+--------------+--------------
  Plate 46 |   7       4  |  11      14  |   5      19  |   6        7
           |  11       8  |  15      18  |  10       4  |  10       12
           |   1      14  |   6       4  |  18      14  |   1        2
  Plate 47 |  18       3  |   4       8  |  16      18  |  17        6
           |   4       3  |   8      13  |   2      18  |   3(not 2) 6
           |  10      10  |  15       3  |   9       8  |   9       16
  Plate 48 |  10      17  |  15       7  |   9      12  |  10       20
           |  15       2  |   1       7  |  13      17  |  14        5
           |   3       7  |   7      17  |   2       2  |   2       10
  Plate 49 |   3      11  |   8       1  |   2       6  |   2       14
           |   7      16  |  12       6  |   6      11  |   6       19
           |  14       6  |  18      16  |  13       1  |  13        9
  Plate 50 |  14      10  |  18      20  |  13       5  |  13       13
           |  18      15  |   5      20  |  17      10  |  17       18
           |   6      20  |  11      10  |   5      15  |   6        3
  ---------------------------------------------------------------------


An examination of the plates will show that Dr. Förstemann has filled out
the following obliterated or wanting day numbers, to wit, the first of
the upper line of Plate 46, the fourth of the upper line of Plate 47, and
the second of the middle line and first of the lower line of Plate 50. He
has also ventured to change the first day number of the lower line of
Plate 46 from 16 to 14. Where the number 20 is found in his list there is
no corresponding number in the codex, the month symbol only being given.
It is evident he has proceeded in these cases upon the theory that the
absence of a number indicated that the month was completed. Although
probably correct in this conclusion, the question will arise, Does the
symbol in such cases denote the _month completed_ or the _month reached?_

The intervals between these dates are as follows, the left hand column
being those between the first and second columns of Förstemann's list
(our Table IV), the second column those between the second and third
columns of his list, the third column those between the third and fourth
columns of his list, and the fourth column those between the last date of
one plate and the first of the next:

TABLE V.--_Table showing intervals between dates._

  _____________________________________________________________________
           | Month.  Day. | Month.  Day. | Month.  Day. | Month.  Day.
           |--------------+--------------+--------------+--------------
           |              |              |              |
  Plate 46 |   4     10   |  12      5   |   0      8   |  11     16
           |   4     10   |  12      6_b_|   0      8   |  11     11
           |   4     10   |  12      10  |   0      8   |   9      8_d_
  Plate 47 |   4      5   |  12     10   |   0      8   |  11     11
           |   4     10   |  12      5   |   0      8_c_|  11     16_e_
           |   4     13_a_|  12      5   |   0      8   |  11     11
  Plate 48 |   4     10   |  12      5   |          8   |  11     11
           |   4      5   |  12     10   |   0      8   |  11     11
           |   4     10   |  12      5   |   0      8   |  11     16
  Plate 49 |   4     10   |  12      5   |   0      8   |  11     16
           |   4     10   |  12      5   |   0      8   |  11     16
           |   4     10   |  12      5   |   0      8   |  11     11
  Plate 50 |   4     10   |  12      5   |   0      8   |  11     11
           |   4      5   |  12     10   |   0      8   |  11     10
           |   4     10   |  12      5   |   0      8   |  12     11_g_
  ---------------------------------------------------------------------

Although it is apparent that the variations from the intervals of the
black numeral and day series above them are too numerous and too uniform
to be considered mistakes, yet there is little reason to doubt that these
month numbers are connected with and depend upon the day series given in
the columns above.

That there are some errors is quite clear; for instance, the variation at
_a_ arises from the fact that Dr. Förstemann gives the date here as 10
months, 10 days, whereas the codex has it 10 months, 13 days. Making this
correction the interval will be 4 months, 10 days. The correction will
make the interval at _d_ 9, 11, instead of 9, 8. Still there is a
variation of two months from the usual interval, which, if corrected on
the supposition that Dr. Förstemann has mistaken the month, would
necessitate a change of the remainder of the series given in this line.
The interval at _c_, according to the figure given by Dr. Förstemann,
would be retrograde, that is, minus 12. This arises from the fact that he
gives the last date in the middle line on Plate 47 as 2 months, 6 days,
whereas the symbol is very distinctly that of the third month, and the
eight day series is unbroken if this correction is made.

When these evident errors are corrected the series of intervals show
very clearly a system and periodicity depending on the day column series
in the upper part of the pages. In the first column (Table V) the
interval is usually 4 months, 10 days, precisely the same as between the
first and second day columns, but occasionally it is 4 months, 5 days,
which will still bring it to one of the four day series, including the
day indicated by the date--4 months, 10 days. This will be understood by
examining our calendar (Table II). The corresponding days in the four
year columns were, by the Maya system, necessarily brought together in
the calendar; for example, they are arranged in the series pictured on
Plates 13-18 of the Cortesian Codex precisely as given in our Table II.
This skip of five days is also apparent in the second and fourth columns
of differences (Table V). Whether Dr. Förstemann is correct in all his
identifications of months among the symbols on the five plates now under
consideration is a question I feel unqualified to answer without a much
more careful comparison and study of these characters than I have given
them.

Running through the upper division of Plates 53 to 58 and continued
through the lower division of Plates 51 to 58--that is to say, commencing
in the upper division of 53 and running into 58, then back to the lower
division of 51 and ending in 58--is a remarkable compound series. It
consists, first, of a three line series of black numerals standing above;
second, a middle series of short, three day columns, or columns each of
three day symbols, with red numerals attached; and, third, below, a two
line series of numerals, those of the upper line red and of the lower
black numbers.

As this series is a very important one in the study of the relations of
the numerals to one another and to the days indicated, an exact copy of
it is given in Figs. 363-370, each figure representing a page and the
whole standing in the same order as in the original. The red numerals and
red symbols are, as usual, given in outline as an indication of their
color.

[Illustration: FIG. 363. Copy of Plate 51, Dresden Codex.]

[Illustration: FIG. 364. Copy of Plate 52, Dresden Codex.]

[Illustration: FIG. 365. Copy of Plate 55, Dresden Codex.]

[Illustration: FIG. 366. Copy of Plate 54, Dresden Codex.]

[Illustration: FIG. 367. Copy of Plate 55, Dresden Codex.]

[Illustration: FIG. 368. Copy of Plate 56, Dresden Codex.]

[Illustration: FIG. 369. Copy of Plate 57, Dresden Codex.]

[Illustration: FIG. 370. Copy of Plate 58, Dresden Codex.]

In order to assist those not familiar with the numeral and day symbols,
the entire series is given in the following tables in names and Arabic
and Roman numerals, as usual. The obliterated symbols and numbers are
restored.

TABLE VI.--_Table of numeral and day symbols._ (Plate 51_b_.)

  ______________________________________________________________________
     14    |    15     |    15      |   16    |   16    |   17
     16    |     7     |    16      |    7    |   16    |    5
     14    |    11     |     8      |    5    |    2    |   10
  IV Ik.   | XII Cauac.| VII Cib.   | II Been.|  X Oc.  | II Ezanab.
   V Akbal.|XIII Ahau. |VIII Caban. |III Ix   | XI Chuen|III Cauac.
  VI Kan.  |   I Ymix. |  IX Ezanab.| IV Men. |XII Eb.  | IV Ahau.[VI-1]
    VIII   |   VIII    |   VIII     |  VIII   |  VIII   |   VII
     17    |    17     |    17      |   17    |   17    |    8
  ----------------------------------------------------------------------

[VI-1] The symbol in this case is that of Been, but this is a manifest
error, as Ahau follows Cauac.

TABLE VII.--_Table of numeral and day symbols._ (Plate 52_b_.)

  ____________________________________________________________
             |      17       |    18    |   18     |    19
             |      14       |     5    |   14     |     4
             |       8       |     5    |    2     |    19
             |    XI Cib.    |  VI Been.|  I Oc.   | IX Manik.
  [Picture.] |   XII Caban.  | VII Ix.  | II Chuen.|  X Lamat.
             |  XIII Ezanab. |VIII Men. |III Eb.   | XI Muluc.
             |      VIII     |   VIII   |  VIII    |   VIII
             |17? (18)[VII-1]|    17    |   17     |    17
  ------------------------------------------------------------

[VII-1] The variation from the rule found here is explained a little
further on.

TABLE VIII.--_Table of numeral and day symbols._ (Plate 53_a_.)

  ______________________________________________________________________________________
                |    1     |     1     |          |       2       |   2        |
       7        |   17     |     7     |          |      15       |   6        |  15
      17        |   18     |     2     |          |14?(19)[VIII-1]|  16        |  13
    VI Kan.     |  I Ymix. |  VI Muluc.|[Picture.]|    I Cimi.    |IX Akbal.   |IV Ahau.
   VII Chicchan.| II Ik.   | VII Oc.   |          |   II Manik.   | X Kan.     | V Ymix.
  VIII Cimi.    |III Akbal.|VIII Chuen.|          |  III Lamat.   |XI Chicchan.|VI Ik.
     VIII       |  VIII    |   VII     |          |     VIII      | VIII       | VIII
      17        |   17     |     8     |          |      17       |  17        |  17
  --------------------------------------------------------------------------------------

[VIII-1] The 14 here is manifestly an error, one of the lines in the
number symbol having been omitted; it should be 19.

TABLE IX.--_Table of numeral and day symbols._ (Plate 53_b_.)

  _____________________________________________________________________
              |   1    |          |    1    |     1     |     1
    19        |   0    |          |    0    |     1     |     1
    13        |   3    |          |   12    |     2     |    11
    16        |   4    |          |    1    |    18     |    15
  IV Kan.     |IX Eb.  |[Picture.]|IV Muluc.| XII Cimi. | VII Akbal.
   V Chicchan.| X Been.|          | V Oc.   |XIII Manik.|VIII Kan.
  VI Cimi.    |XI Ix.  |          |VI Chuen.|   I Lamat.|  IX Chicchan.
   VIII       |  VII   |          |  VIII   |   VIII    |   VIII
    17        |   8    |          |   17    |    17     |    17
  ---------------------------------------------------------------------

TABLE X.--_Table of numeral and day symbols._ (Plate 54_a_.)

  ____________________________________________________________________________________
       3      |     3     |    4    |     4     |     5      |     5       |    6
       6      |    15     |    6    |    15     |     5      |    10       |    4
      11      |     8     |    5    |     5     |    19      |    16       |    4
  XIII Ezanab.|VIII Men.  |III Eb.  |  XI Muluc.|  VI Cib.   |  I Akbal.   | VI Chuen.
     I Cauac. |  IX Cib.  | IV Been.| XII Oc.   | VII Caban. | II Kan.     | VII Eb.
    II Ahau.  |   X Caban.|  V Ix.  |XIII Chuen.|VIII Ezanab.|III Chicchan.|VIII Been.
     VIII     |   VIII    |  VIII   |   VIII    |   VIII     |   VIII      |   VII
      17      |    17     |   17    |    17     |    17      |    17       |    8
  ------------------------------------------------------------------------------------


TABLE XI.--_Table of numeral and day symbols._ (Plate 54_b_.)

  _______________________________________________________________
      1    |    1      |    1   |    1     |         |    1
      2    |    2      |    3   |    3     |         |    4
      2    |   11      |    2   |    9     |         |    0[XI-1]
     12    |    9      |    6   |   14     |         |   11
   II Ahau.|  X Caban. |  V Ix. |  X Ik.   |[Picture]|  V Cauac.
  III Ymix.| XI Ezanab.| VI Men.| XI Akbal.|         | VI Ahau.
   IV Ik.  |XII Cauac. |VII Cib.|XII Kan.  |         |VII Ymix.
    VIII   |  VIII     |  VIII  |  VII     |         |  VII[XI-2]
     17    |   17      |   17   |    8     |         |   17
  ---------------------------------------------------------------

[XI-1] The 0 inserted at various points in these tables denotes as usual
the red, diamond shaped symbol, which apparently signifies "nought."

[XI-2] The numeral symbol in this case, both in Kingsborough's copy and
in the photograph, is VII, one dot having been omitted by a mistake of
the original artist.

TABLE XII.--_Table of numeral and day symbols._ (Plate 55_a_.)

  ____________________________________________________________________________
           |    8            |    7     |    7        |     8    |     8
           |   13            |    3     |   12        |     3    |    12
           |    2            |   18     |   16        |    13    |    10
           | II Muluc.[XII-1]|  X Cimi. |  V Akbal.   |XIII Ahau.|VIII Caban.
  [Picture]|III Oc.          | XI Manik.| VI Kan.     |   I Ymix.|  IX Ezanab.
           | IV Chuen.       |XII Lamat.|VII Chicchan.|  II Ik.  |   X Cauac.
           |  VIII           |  VIII    |  VIII       |   VIII   |   VIII
           |   17            |   17     |   17        |    17    |    17
  ----------------------------------------------------------------------------

[XII-1] In Kingsborough's work the symbol in this case is that of Been,
but should be Muluc, as it is in the photograph.

TABLE XIII.--_Table of numeral and day symbols._ (Plate 55_b_.)

  __________________________________________________________________________________________
       1      |   1   |   1     |     1     |     1        |    1     |    1     |    1
       4      |   5   |   5     |     6     |     6        |    6     |    7     |    7
       9      |   0   |   9     |     0     |     8        |   17     |    8     |   15
       8      |   6   |   3     |     0     |    17        |   14     |   11     |   19
  XIII Cib.   |IX Ix. |IV Chuen.| XII Lamat.| VII Chicchan.| II Ik.   |  X Cauac.| II Manik.
     I Caban. | X Men.| V Eb.   |XIII Muluc.|VIII Cimi.    |III Akbal.| XI Ahau. |III Lamat.
    II Ezanab.|XI Cib.|VI Been. |   I Oc.   |  IX Manik.   | IV Kan.  |XII Ymix. | IV Muluc.
     VIII     | VIII  | VIII    |   VIII    |   VIII       |  VIII    |  VIII    |   VII
      17      |17?(18)|  17     |    17     |    17        |   17     |   17     |    8
  ------------------------------------------------------------------------------------------

TABLE XIV.--_Table of numeral and day symbols._ (Plate 56_a_.)

  ____________________________________________________________
       9        |         |     9     |   10     |    10
       1        |         |    10     |    1     |    10
      18        |         |    15     |   12     |     9
  XIII Chicchan.|         |VIII Ik.   |III Cauac.|  XI Cib.
     I Cimi.    |[Picture]|  IX Akbal.| IV Ahau. | XII Caban.
    II Manik.   |         |   X Kan.  |  V Ymix. |XIII Ezanab.
      VII       |         |    VIII   |   VIII   |   VIII
       8        |         |    17     |   17     |    17
  ------------------------------------------------------------

TABLE XV.--_Table of numeral and day symbols._ (Plate 56_b_.)

  _________________________________________________________
           |    1        |      1    |    1     |   1
           |    8        |      8    |    9     |   9
           |    6        |     15    |    6     |  15
           |   16        |     14    |   11     |   8
  [Picture]|  X Kan.     |  VI Ik.   |  I Cauac.|IX Cib.
           | XI Chicchan.| VII Akbal.| II Ahau. | X Caban.
           |XII Cimi.    |VIII Kan.  |III Ymix. |XI Ezanab.
           |  VIII       |    VIII   |  VIII    |  VIII
           |   17        |   17?(8)  |   17     |  17
  ---------------------------------------------------------

TABLE XVI.--_Table of numeral and day symbols._ (Plate 57_a_.)

  ______________________________________________________
      11   |   11     |   12     |   12       |
       1   |   10     |    1     |    8       |
       6   |    4     |    0     |    8       |
   VII Ix. | II Chuen.|  X Lamat.| II Cib.    |
  VIII Men.|III Eb.   | XI Muluc.|III Caban.  |[Picture]
    IX Cib.| IV Been. |XII Oc.   | IV Ezanab. |
      VIII |   VIII   |   VIII   | VIII[XVI-1]|
      17   |   17     |   17     |   17[XVI-2]|
  ------------------------------------------------------

[XVI-1] This should be VII.

[XVI-2] This should be 8.

TABLE XVII.--_Table of numeral and day symbols._ (Plate 57_b_.)

  __________________________________________________________________
       1    |     1     |   1      |         |     1     |     1
      10    |    10     |  11      |         |    11     |    12
       6    |    15     |   4      |         |    13     |     4
       5    |     2     |  10      |         |     7     |     4
    IV Been.| XII Oc.   |IV Ezanab.|[Picture]| XII Men.  | VII Eb.
     V Ix.  |XIII Chuen.| V Cauac. |         |XIII Cib.  |VIII Been.
    VI Men. |   I Eb.   |VI Ahau.  |         |   I Caban.|  IX Ix.
      VIII  |   VIII    |  VII     |         |   VIII    |   VIII
      17    |    17     |   8      |         |    17     |    17
  ------------------------------------------------------------------

TABLE XVIII.--_Table of numeral and day symbols._ (Plate 58_a_.)

  ____________________________________________
     12    |   13     |   13     |  14
     17    |    8     |   17     |   7
      5    |    2     |    0     |  17
    X Been.|  V Oc.   |  I Lamat.|II Chicchan.
   XI Ix.  | VI Chuen.| II Muluc.| X Cimi.
  XII Men. |VII Eb.   |III Oc.   |XI Manik.
    VIII   |  VIII    |  VIII    |  VIII
     17    |   17     |   17     |  17
  --------------------------------------------

TABLE XIX.--_Table of numeral and day symbols._ (Plate 58_b_.)

  ________________________________
      1     |    1     |
     12     |   13     |
     13     |    3     |
      1     |   18     |
   II Muluc.|  X Cimi. |[Picture.]
  III Oc.   | XI Manik.|
   IV Chuen.|XII Lamat.|
    VIII    |  VIII    |
     17     |   17     |
  --------------------------------

The spaces in the lists indicate the positions of the pictures of persons
and curtain-like ornaments inserted here and there, as seen in Figs.
363-370.

In order to explain this series, we commence with that portion of it
found in the lower division of Plate 51 (Fig. 363).

Omitting any reference for the present to the black numbers over the day
columns, we call attention first to the days and to the red numerals
attached to them. Those in the division selected as an illustration are
as follows:

  IV Ik.     XII Cauac.  VII Cib.     II Been.   X Oc.     II Ezanab.
   V Akbal. XIII Ahau.  VIII Caban.  III Ix.    XI Chuen. III Cauac.
  VI Kan.      I Ymix.    IX Ezanab.  IV Men.  XII Eb.     IV Ahau.[317-1]

It will be observed that the week numbers of the days in each single
column follow one another in regular arithmetical order, thus: in the
first column, 4, 5, 6; in the second, 12, 13, 1; in the third, 7, 8, 9;
and so on throughout the entire series. The interval, therefore, between
the successive days of a column is 1; or, in other words, the days follow
one another in regular order, as in the month series, so that having the
first day of a column given we know at once the other two. It is
apparent, therefore, that the intervals between the three correspondingly
opposite days of any two associate columns are the same; that is to say,
the interval between 5 Akbal and 13 Ahau, in the first two columns given
above is the same as that between 4 Ik and 12 Cauac, and also as that
between 6 Kan and 1 Ymix. This is also true if the attached week numbers
are omitted; for instance, the interval between Ik and Cauac, counting on
the list of days forming the month, is 17 days, and it is the same
between Kan and Ymix. Taking the second and third columns we find here
the same interval. This holds good in that part of the series above given
until we reach the last two columns; here the interval between Oc and
Ezanab is 8 days and it is the same between the other days of these two
columns.

This being ascertained, the next step is to determine the true interval
between the first days of these columns, taking the numbers attached to
them into consideration. Referring to our calendar (Table II) and (for
reasons which will be given hereafter) using the Muluc column and
counting from 4 Ik, as heretofore explained, we find the interval between
this and 12 Cauac to be 8 months and 17 days; counting in the same way
from 12 Cauac, 8 months and 17 days more bring us to 7 Cib; 8 months and
17 days more to 10 Oc. So far the intervals have been the same; but at
this point we find a variation from the rule, as the interval between 10
Oc and 2 Ezanab (first of the next column) is 7 months and 8 days.

These intervals furnish the explanation of the red and black numerals
below the day columns.

These numerals, as the reader will observe by reference to Fig. 363 or
the written interpretation thereof in Table VI, are 8 and 17 under the
first five columns, but 7 and 8 under the sixth column, the red (8 under
the first five and 7 under the sixth) indicating the months and the black
(17 under the first five and 8 under the sixth) the days of the
intervals. This holds good throughout all that portion of the series
running through the lower divisions of Plates 51 to 58, with three
exceptions, which will now be pointed out.

In order to do this it will be necessary to repeat here a part of the
series on Plate 51_b_ and part of that on Plate 52_b_; that is, the two
right hand columns of the former and the two left hand columns of the
latter, between which is the singular picture shown in the _lower left
hand corner_ of our Fig. 364:

  ___________________________________________________________________
          Plate 51_b_.      ||                Plate 52_b_.
  --------------------------++---------------------------------------
    X Oc.     |  II Ezanab. ||            |   XI Cib.    |   VI Been.
    XI Chuen. | III Cauac.  ||            |  XII Caban.  |  VII Ix.
   XII Eb.    |  IV Ahau.   || [Picture.] | XIII Ezanab. | VIII Men.
       VIII   |   VII       ||            |    VIII      |   VIII
       17     |     8       ||            |     17       |    17
  -------------------------------------------------------------------

As before stated, the interval between 10 Oc and 2 Ezanab is 7 months and
8 days, as indicated by the red and black numerals under the latter.
According to the red and black numbers under the column commencing with
11 Cib, the interval between 2 Ezanab and 11 Cib should be 8 months and
17 days, the usual difference, when, in fact, as we see by counting on
the calendar, it is 8 months and 18 days. That this variation cannot be
attributed to a mistake on the part of the author or of the artist is
evident from the fact that the interval between 11 Cib and 6 Been (first
of the next column) is 8 months and 17 days and that the difference
throughout the rest of the series follows the rule given; that is to say,
each is 8 months and 17 days, except at two other points where this
variation is found and at the regular intervals where the difference of
7 months and 8 days occurs.[319-1] Precisely the same variation occurs on
Plate 55_b_ in passing from the first to the second column and on Plate
56_b_ between columns 1 and 2.

Why these singular exceptions? It is difficult, if not impossible, for
us, with our still imperfect knowledge of the calendar system formerly in
vogue among the Mayas, to give a satisfactory answer to this question.
But we reserve further notice of it until other parts of the series have
been explained.

Reference will now be made to the three lines of black numerals
immediately above the day columns. Still confining our examinations to
the lower divisions, the reader's attention is directed to these lines,
as given in Tables VI, VII, IX, XI, XIII, XV, XVII, and XIX. As there are
three numbers in each short column we take for granted, judging by what
has been shown in regard to the series on Plates 46-50, that the lowest
of the three denotes days, the middle months, and the upper years, and
that the intervals are the same between these columns as between the day
columns under them. The correctness of this supposition is shown by the
following additions: Starting with the first or left hand column on Plate
51_b_, we add successively the differences indicated by the corresponding
red and black numbers under the day columns. If this gives in each case
(save the two or three exceptions heretofore referred to) the numbers in
the next column to the right throughout the series, the demonstration
will be complete.

Years.    Months.    Days.
  14        16        14    First column on Plate 51_b_.
             8        17
  --        --        --
  15         7        11    Second column on Plate 51_b_.
             8        17
  --        --        --
  15        16         8    Third column on Plate 51_b_.
             8        17
  --        --        --
  16         7         5    Fourth column on Plate 51_b_.
             8        17
  --        --        --
  16        16         2    Fifth column on Plate 51_b_.
             7         8
  --        --        --
  17         5        10    Sixth column on Plate 51_b_.
             8        18[319-1]
  --        --        --
  17        14         8    First column on Plate 52_b_.
             8        17
  --        --        --
  18         5         5    Second column on Plate 52_b_.
             8        17
  --        --        --
  18        14         2    Third column on Plate 52_b_.
             8        17
  --        --        --
  19         4        19    Fourth column on Plate 52_b_.
             8        17
  --        --        --
  19        13        16    First column on Plate 53_b_.
             7         8
  --        --        --
  20         3         4    Second column on Plate 53_b_.

At this point in the original, instead of 20 in the year series, we find
a diamond shaped symbol, represented by 0 in our tables, with one black
dot over it. From this it would seem that when this codex was written the
Maya method of counting years was by periods of 20 each, as in the case
of the month days. Whether there is any reference here to the ahaues is
uncertain. I am inclined to think with Dr. Förstemann that it was rather
in consequence of the use of the vigesimal system in representing
numbers. It would have been very inconvenient and cumbersome to represent
high numbers by means of dots and lines; hence a more practicable method
was devised. It is evident, from the picture inserted at this point in
the series, that some important chronological event is indicated. Here
also in the written characters over this picture is the symbol for 20.
The last number given in the above addition may therefore, in order to
correspond with the method of the codex, be written as follows:

Twenty year periods.  Years.  Months.  Days.
                 1      0        3       4

Continuing the addition in this way the result is as follows:

Twenty year periods.  Years.  Months.  Days.
                 1       0       3       4
                                 8      17
                --      --      --      --
                 1       0      12       1   Third column on Plate 53_b_.
                                 8      17
                --      --      --      --
                 1       1       2      18   Fourth column on Plate 53_b_.
                                 8      17
                --      --      --      --
                 1       1      11      15   Fifth column on Plate 53_b_.
                                 8      17
                --      --      --      --
                 1       2       2      12   First column on Plate 54_b_.
                                 8      17
                --      --      --      --
                 1       2      11       9   Second column on Plate 54_b_.
                                 8      17
                --      --      --      --
                 1       3       2       6   Third column on Plate 54_b_.
                                 7       8
                --      --      --      --
                 1       3       9      14   Fourth column on Plate 54_b_.
                                 8      17
                --      --      --      --
                 1       4       0      11   Fifth column on Plate 54_b_.
                                 8      17
                --      --      --      --
                 1       4       0       8   First column on Plate 55_b_.
                                 8      18[321-1]
                --      --      --      --
                 1       5       0       6   Second column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       5       9       3   Third column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       6       0       0   Fourth column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       6       8      17   Fifth column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       6      17      14   Sixth column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       7       8      11   Seventh column on Plate 55_b_.
                                 7       8
                --      --      --      --
                 1       7      15      19   Eighth column on Plate 55_b_.
                                 8      17
                --      --      --      --
                 1       8       6      16   First column on Plate 56_b_.
                                 8      18[321-2]
                --      --      --      --
                 1       8      15      14   Second column on Plate 56_b_.
                                 8      17
                --      --      --      --
                 1       6       6      11   Third column on Plate 56_b_.
                                 8      17
                --      --      --      --
                 1       9      15       8   Fourth column on Plate 56_b_.
                                 8      17
                --      --      --      --
                 1      10       6       5   First column on Plate 57_b_.
                                 7       8
                --      --      --      --
                 1      10      15       2   Second column on Plate 57_b_.
                                 7       8
                --      --      --      --
                 1      11       4      10   Third column on Plate 57_b_.
                                 8      17
                --      --      --      --
                 1      11      13       7   Fourth column on Plate 57_b_.
                                 8      17
                --      --      --      --
                 1      12      13       1   Fifth column on Plate 57_b_.
                                 8      17
                --      --      --      --
                 1      12      13       1   First column on Plate 58_b_.
                                 8      17
                --      --      --      --
                 1      13       3      18   Second column on Plate 58_b_.

The proof, therefore, that the theory advanced in regard to the order and
the plan of the series is correct seems to be conclusive. This probably
would have been conceded without the repeated additions given, but these
were deemed necessary because of several irregularities found in that
portion running through Plates 53_a_-58_a_, which constitutes the first
half of the series.

Turning back to our Table VIII, representing that part of the series on
Plate 53_a_, we will consider the three lines of black numerals above the
day columns, discussing the irregularities as we proceed.

The numbers in the first column are 7/17,[TN-6] or, according to the
explanation given, 7 months and 17 days. There is apparently a mistake
here, the correct numbers being 8 months and 17 days, as it is the usual
custom of the codex to commence numeral series with the prevailing
interval; moreover this correction, which has also been made by Dr.
Förstemann, is necessary in order to connect rightly with what follows;
the counters under this first column require this correction, as they are
8 months, 17 days. Making this change we proceed with the addition.

Years.    Months.    Days.
             8        17    First column, Plate 53_a_ (corrected).
             8        17
            --        --
            17        14    Second column. Plate 53_a_.

Here the author of the codex has made another mistake or varied from the
plan of the series. As several similar variations or errors occur in this
part of the series, it will be as well to discuss the point here as
elsewhere. Dr. Förstemann, in discussing the series, takes it for granted
that these variations are errors of the aboriginal scribe; he remarks
that "It is seen here that the writer has corrected several of his
mistakes by compensation. For instance, the two first differences should
be 177 [8 months, 17 days] and 148 [7 months, 8 days], not 176 and 149,"
&c.

This is a strained hypothesis which I hesitate to adopt so long as any
other solution of the difficulty can be found. It is more likely that the
writer would have corrected his mistakes, if observed, than that he would
compensate them by corresponding errors.

Going back to that part of the series in the lower divisions which has
already been examined and commencing with Plate 51_b_ (see Table VI), we
observe that the numbers in the lowest of the three lines of black
numerals, immediately over the day columns, and the first day of these
columns are as follows (omitting the week days attached):

  14      11      8       5      2      10
  Ik.   Cauac.   Cib.   Been.   Oc.   Ezanab.

Turning to the calendar (Table II) and using the Muluc column, we notice
that the figures of this third line of black numerals denote respectively
the month numbers of the days under them; that is to say, Ik is the
fourteenth day of the month in Muluc years, Cauac the eleventh, Cib the
eighth, Been the fifth, Oc the second, and Ezanab the tenth. This holds
good through Plates 52_b_ to 58_b_ without a single exception, provided
the diamond shaped symbol in the fourth column of Plate 55_b_ is counted
as 20. This test, therefore, presents fewer exceptions than are found in
counting the intervals as before explained; yet, after all, this would
necessarily result from the fact that the day Muluc was selected as the
commencement of the series, and hence may have no signification in
reference to or bearing on the question of the year series, especially as
the years counted are evidently of 360 days.

Returning now to our Table VIII, representing Plate 53_a_, we observe
that the number immediately over Kan in the first column is 17, whereas
Kan is the sixteenth day of the month. Is it not possible that the
intention was to designate as the ceremonial day Chicchan, standing
immediately below, which is the seventeenth day of the month in Muluc
years? Even though there is no reference to Muluc years, the intervals
may be given upon the same idea, that of reaching, for some particular
reason, the second or third day of the column instead of the first. This
would account for the compensation of which Dr. Förstemann speaks,
without implying any mistake on the part of the writer. These
irregularities would then be intentional variations from the order of the
series, yet so as not to break the general plan.

The interval between 6 Kan of the first column (with the month number
corrected) and 1 Ymix of the second is 8 months and 17 days, as it should
be; between 6 Muluc and 1 Cimi, 8 months and 17 days; and between 1 Cimi
and 9 Akbal, 8 months and 17 days, thus conforming to the rule heretofore
given, a fact which holds good as a general rule throughout that portion
of the series in the upper division.

Continuing the addition as heretofore we note the variations.

Years.    Months.    Days.  Column.  Plate.
            17        14    Second.  53_a_.
             7         8
  --        --        --
   1         7         3    Third.   53_a_.
             8        17
  --        --        --
   1        15        19[323-1] Fourth. 53_a_.
             8        17
  --        --        --
   2         6        16    Fifth.   53_a_.
             8        17
  --        --        --
   2        15        13    Sixth.   53_a_.
             8        18[323-2]
  --        --        --
   3         6        11    First.    54_a_.
             8        17
  --        --        --
   3        15         8    Second.   54_a_.
             8        17
  --        --        --
   4         6         5    Third.    54_a_.
             8        17
  --        --        --
   4        15         2[324-1]  Fourth.  54_a_.
             8        17
  --        --        --
   5         5        19    Fifth.    54_a_.
             8        17
  --        --        --
   5        14[324-2] 16   Sixth.    54_a_.
             7         8
  --        --        --
   6         4         4    Seventh.  54_a_.
             8        18[324-3]
  --        --        --
   6[324-4] 13         2    First.    55_a_.
             8        17
  --        --        --
   7         3        19[324-5] Second.  55_a_.
             8        17
  --        --        --
   7        12        16    Third.    55_a_.
             8        17
  --        --        --
   8         3        13    Fourth.   55_a_.
             8        17
  --        --        --
   8        12        10    Fifth.    55_a_.
             7         8
  --        --        --
   9         1        18    First.    56_a_.
             8        17
  --        --        --
   9        10        15    Second.   56_a_.
             8        17
  --        --        --
  10         1        12    Third.    56_a_.
             8        17
  --        --        --
  10        10         9    Fourth.   56_a_.
             8        17
  --        --        --
  11         1         6    First.    57_a_.
             8        17
  --        --        --
  11        10         3    Second.   57_a_.
             8        17
  --        --        --
  12         1         0    Third.    57_a_.
             7         8[325-1]
  --        --        --
  12         8         8    Fourth.   57_a_.
             8        17
  --        --        --
  12        17         5    First.    58_a_.
             8        17
  --        --        --
  13         8         2    Second.   58_a_.
             8        18[325-2]
  --        --        --
  13        17         0    Third.    58_a_.
             8        17
  --        --        --
  14         7        17    Fourth.   58_a_.
             8        17
  --        --        --
  14        16        14    First.    51_b_.[325-3]

We have in what has thus far been given a satisfactory explanation of the
meaning and use of the lines of numerals and also of their relation to
the day columns, but we still fall short of a complete interpretation,
inasmuch as we are unable to give the series a definite location in the
Maya calendar or in actual time. It is apparent, however, that the series
cannot by any possible explanation be made to agree with the calendar
system as usually accepted, as there is nothing in it indicating the four
series of years or the year of 365 days. It may be safely assumed, I
think, from what has been shown, that the year referred to in the series
is one of 360 days, with probably a periodic addition of one day, but the
reason of the addition is not yet apparent.

If the numbers in the lowest line of numerals over the day columns
indicate the days of the month, and those of the middle line the
respective months of the year, it is evident, as before stated, that
Muluc is the first day of the year throughout, a conclusion
irreconcilable with the Maya calendar as hitherto understood. It is
probable, however, that the month and day numbers do not refer to
particular months and days, but are used only as intervals of time
counted from a certain day, which must in this case have been Muluc.

The sum of the series as shown by the numbers over the second column of
Plate 58_b_ is 33 years, 3 months, and 18 days. As this includes only the
top day of this column (10 Cimi), we must add two days to complete the
series, which ends with 12 Lamat. This makes the sum of the entire
series 33 years, 4 months, or 11,960 days, precisely 46 cycles of 13
months, or 260 days each, the whole and also each cycle commencing with
13 Muluc and ending with 12 Lamat. It is also worthy of notice that in
the right hand column of characters (hieroglyphics) over the inverted
figure in Plate 58_b_ two numbers, 13 and 12, are found attached to
characters which appear to be abnormal forms of month symbols.

On Plates 63 and 64 are three series of ten day columns each and three
lines of numerals over each series. These are as follows, so far as they
can be made out, the numbers over the upper series being mostly
obliterated. The 0 denotes the red, diamond shaped symbol which is here
sometimes given in fanciful forms.

TABLE XX.--_Table showing series of day columns, with lines of numerals._

                               UPPER DIVISION.
  __________________________________________________________________________
                                              |                             |
                   Plate 63.                  |          Plate 64.          |
  --------------------------------------------+-----------------------------|
         4      |       3      |              |              |       0      |
         8      |       6      |              |       0      |      16      |
         0      |       0      |       0      |       0      |       0      |
   III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
       Kan.     |     Kan.     |     Kan.     |     Kan.     |     Kan.     |
       Ix.      |     Ix.      |     Ix.      |     Ix.      |     Ix.      |
       Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |
  XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |
  ______________|______________|______________|______________|______________|
                                                                            |
                                   Plate 64.                                |
  ____________________________________________ _____________________________|
                |              |              |              |              |
         0      |       0      |              |              |              |
        12      |       8      |       3      |       3      |              |
         0      |       0      |       0      |       0      |       0      |
   III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
       Kan.     |     Kan.     |     Kan.     |     Kan.     |     Kan.     |
       Ix.      |     Ix.      |     Ix.      |     Ix.      |     Ix.      |
       Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |
  XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |
  ______________|______________|______________|______________|______________|

                               MIDDLE DIVISION.[TN-7]
  ___________________________________________________________________________
                |              |              |              |              |
   XIX   5      |       4      |       4      |       4      |       4      |
    IV   1      |      14      |       9      |       5      |       0      |
    IV   0      |       0      |       0      |       7      |      16      |
   III Chicchan.| III Ix.      | III Akbal.   | III Eb.      | III Ymix.    |
       Kan.     |     Been.    |     Ik.      |     Chuen.   |     Ahau.    |
       Ix.      |     Akbal.   |     Eb.      |     Ymix.    |     Oc.      |
       Cimi.    |     Men.     |     Kan.     |     Been.    |     Ik.      |
  XIII Akbal.   |XIII Eb.      |XIII Ymix.    |XIII Oc.      |XIII Cauac.   |
  ______________|______________|______________|______________|______________|
                |              |              |              |              |
         3      |       3      |       3      |       3      |       2      |
        14      |       9      |       5      |       0      |      14      |
         5      |      14      |       3      |      12      |       1      |
   III Oc.      | III Cauac.   | III Lamat.   | III Caban.   | III Cimi.    |
       Muluc.   |     Ezanab.  |     Manik.   |     Cib.     |     Chicchan.|
       Cauac.   |     Lamat.   |     Caban.   |     Cimi.    |     Men.     |
       Chuen.   |     Ahau.    |     Muluc.   |     Ezanab.  |     Manik.   |
  XIII Lamat.   |XIII Caban.   |XIII Cimi.    |XIII Men.     |XIII Kan.     |
  ______________|______________|______________|______________|______________|

                                LOWER DIVISION.[TN-7]
  ___________________________________________________________________________
                |              |              |              |              |
         2      |       2      |       2      |       1      |       1      |
         9      |       4      |       0      |      13      |       9      |
        10      |      19      |       8      |      17      |       6      |
   III Men.     | III Kan.     | III Been.    | III Ik.      | III Chuen.   |
       Ix.      |     Akbal.   |     Eb.      |     Ymix.    |     Oc.      |
       Kan.     |     Been.    |     Ik.      |     Chuen.   |     Ahau.    |
       Cib.     |     Chicchan.|     Ix.      |     Akbal.   |     Eb.      |
  XIII Been.    |XIII Ik.      |XIII Chuen.   |XIII Ahau.    |XIII Muluc.   |
  ______________|______________|______________|______________|______________|
                |              |              |              |              |
         1      |       1      |              |              |              |
         4      |       0      |      13      |       9      |       4      |
        15      |       4      |      13      |       2      |      11      |
   III Ahau.    | III Muluc.   | III Ezanab.  | III Manik.   | III Cib.     |
       Cauac.   |     Lamat.   |     Caban.   |     Cimi.    |     Men.     |
       Muluc.   |     Ezanab.  |     Manik.   |     Cib.     |     Chicchan.|
       Ymix.    |     Oc.      |     Cauac.   |     Lamat.   |     Caban.   |
  XIII Ezanab.  |XIII Manik.   |XIII Cib.     |XIII Chicchan.|XIII Ix.      |
  ______________|______________|______________|______________|______________|

By examining carefully the lines and columns of the middle and lower
divisions of the plates--those represented in Tables XXI and XXII--we
ascertain that the two together form one series; but, contrary to the
method which has prevailed in those examined, it is to be read from
_right_ to _left_, commencing with the right hand column of the lower and
ending with the left hand column of the middle division.

As proof of this we have only to note the fact that the series of black
numerals over the day columns ascends towards the left. Assuming the
lowest of the three lines to be days, the middle one months, and the
upper one years, the common difference is 4 months and 11 days. Numbering
the ten columns of each of our tables from left to right as usual and
adding successively the common difference, commencing with the tenth
column of the lowest division, of which Cib is the first day, the result
will be as follows:

Years.    Months.    Days.
             4        11    Over tenth column, lower division.
             4        11
            --        --
             9         2    Over ninth column, lower division.
             4        11
            --        --
            13        13    Over eighth column, lower division.
             4        11
            --        --
   1         0         4    Over seventh column, lower division.
             4        11
  --        --        --
   1         4        15    Over sixth column, lower division.
             4        11
  --        --        --
   1         9         6    Over fifth column, lower division.
             4        11
  --        --        --
   1        13        17    Over fourth column, lower division.
             4        11
  --        --        --
   2         0         8    Over third column, lower division.
             4        11
  --        --        --
   3         4        19    Over second column, lower division.
             4        11
  --        --        --
   2         9        10    Over first column, lower division.
             4        11
  --        --        --
   2        14         1    Over tenth column, middle division.
             4        11
  --        --        --
   3         0        12    Over ninth column, middle division.
             4        11
  --        --        --
   3         5         3    Over eighth column, middle division.
             4        11
  --        --        --
   3         9        14    Over seventh column, middle division.
             4        11
  --        --        --
   3        14         5    Over sixth column, middle division.
             4        11
  --        --        --
   4         0        16    Over fifth column, middle division.
             4        11
  --        --        --
   4         5         7    Over fourth column, middle division.
             4        11
  --        --        --
   4         9        18    Over third column, middle division.
             4        11
  --        --        --
   4        14         9    Over second column, middle division.
             4        11
  --        --        --
   5         1         0    Over first column, middle division.

The red numerals over the first column of the middle division, except the
lowest diamond shaped one, are omitted, as they do not appear to belong
to the series.

It must be borne in mind that the 4 months and 11 days form the common
difference between the corresponding days of the columns counting from
right to left; that is to say, counting 4 months and 11 days from the top
day of any column will bring us to the first or top day of the next
column to the left. The interval between the other corresponding days of
the columns is also the same if the same week numbers are assigned them.

This question arises here, Does the difference include the time embraced
in the entire column? That is to say, Is this interval of 4 months and 11
days (referring, for example, to the tenth and ninth columns of the lower
division, our table) the sum of the intervals between 3 Cib and Men; Men
and Chicchan; Chicchan and Caban; Caban and 13 Ix, and 13 Ix of the tenth
column and 3 Manik of the ninth column? If not, the columns do not form a
continuous series or must be taken in some other order.

Although Dr. Förstemann discovered the order in which the series as a
whole was to be read, and also the common difference--given, as is his
custom, in days--he failed to furnish further explanation of the group.

In answer to the question presented I call attention to the following
facts:

Commencing again with the uppermost day, 3 Cib, of the tenth column,
lowest division, and counting on the calendar to 13 Ix of the same year,
the interval is found to be 10 months and 18 days, which is much more
than the interval between 3 Cib and 3 Manik (first of the ninth column),
and of course cannot be included in it.

Reversing the order in reading the columns, but counting forward on the
calendar as usual, we find the interval between 13 Ix and 3 Cib to be 2
months and 2 days, and, what is another necessary condition, the
intermediate days of the column are included in this period in the order
in which they stand, if read upwards. The interval between 3 Cib,
uppermost day of the tenth column, and 13 Chicchan, bottom day of the
ninth column, is 2 months and 9 days. The sum of these two intervals is 4
months and 11 days, as it should be on the supposition that the entire
columns follow one another in regular succession. This proves beyond
question that the columns are to be read from _bottom_ to _top_ and that
they follow one another from _right_ to _left_. This enables us to fix
the week numbers to the intermediate days and to determine the day to
which the entire series is referred as its starting point. The days and
their numbers of the tenth and ninth columns of the lower division,
writing them in reverse order, that is, from bottom to top, are as
follows: 13 Ix; 3 Caban; 11 Chicchan; 8 Men; 3 Cib; 13 Chicchan; 3 Lamat;
11 Cib; 8 Cimi; 3 Manik.

These numbers hold good throughout the series.

Commencing with 13 Ix, the lowest day of the tenth column, lower
division, but first day of the series, and ending with 13 Akbal, the
bottom of the first column, middle series, the time embraced is 5 years,
1 month, 0 day, less 4 months and 11 days--that is, 4 years, 14 months, 9
days (years of 360 days being understood). This is easily proved by
counting on the calendar 4 years, 14 months, and 9 days from 13 Ix, as it
brings us to 13 Akbal. If we add to this time 2 months and 2 days--the
interval between 13 Akbal and 3 Chicchan (top day of first column, middle
division)--we have, as the entire period embraced in the series as it
stands--from 13 Ix (first of the series) to 3 Chicchan (the last)--4
years, 16 months, 11 days. Add to this 4 months and 11 days, in order to
reach the day with which the count begins, and we have as the entire
period 5 years, 3 months, 2 days = 5 years, 1 month, 0 day + 2 months, 2
days. If we count back 4 months and 11 days from 13 Ix (first of the
series), we reach 1 Kan, the day to which the series is referred as its
starting point. Counting forward from this date 5 years, 3 months and 2
days brings us to 3 Chicchan, the last day of the series.

It is worthy of notice that, although this series appears to be referred
to Kan years, it is at variance with the idea of passing from one to the
other of the four year series, and is, moreover, based upon the year of
360 days. The order in which it is to be read, which is true also of some
other pages, indicates that these extracts pertain to a different
original codex than those to which we have heretofore alluded, a
conclusion reached by Dr. Förstemann soon after he commenced the study of
the Dresden manuscript.

I was for a time inclined to believe there was a break between Plates 64
and 65, as there appeared to be no day columns with which the lines of
numerals running through Plates 65-69 could be connected, but the fact
that the sum of the black numbers in each is 91, precisely the interval
between the corresponding days of the columns in Plates 63 and 64, will
probably warrant the conclusion that they are connected with them. This
conclusion is strengthened, so far as those in the lower division are
concerned, by the fact that by taking the XIII attached to the lowest
days of the columns the numbers properly succeed one another and the
series conforms to the rule heretofore given. As proof of this I give
here the lower line of the lower division, prefixing the XIII, thus:
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.

Adding together the numbers and casting out the thirteens, thus, XIII + 9
- 13 = IX; IX + 5 - 13 = I, &c., the connection is seen to be regular.
The final red numeral is XIII, the same as that with which the series
begins, and the sum of the black numbers, 9, 5, 1, 10, 6, 2, 11, 7, 3,
12, 8, 4, 13, is 91, a multiple of 13. The middle line of numerals also
connects with the XIII attached to the bottom symbols of the day columns;
and the upper line of numerals connects with the III attached to the top
symbols of the day columns.

Plates 70 to 73 present some peculiarities difficult to account for. That
these pages belong to the same type as 62, 63, and 64 cannot be doubted,
and that as a general rule they are to be read from right to left is
easily proved; but this method does not seem to be adopted throughout,
the order being apparently reversed in a single series.

The aboriginal artist has apparently made up these pages from two older
manuscripts or changed and added to his original. The last two columns of
Plate 70 and first five of 71 appear to have been thrust in here as an
afterthought or as a fragment from some other source, forming apparently
no legitimate connection with the series to either the right or to the
left of them. It is true, as will be shown, that there is some connection
with the lowest series on the right, but it would seem that advantage was
here taken of accidental correspondence rather than that this
correspondence was the result of a preconceived plan.

Commencing in the lower part of the middle division of Plate 73 and
running back (to the left) to the sixth column of 71 and returning to the
lower part of the lower division of 73 and ending with the sixth column
of 71, is the following series. The columns are given in the order in
which they stand on the respective plates, but the plates are taken in
reverse order:

TABLE XXIII.--_Table giving comparison between Plates 71, 72, and 73._

  _______________________________________________________________________________
           |  First  | Second  | Third   | Fourth  | Fifth   |         |
           | column. | column. |column.  | column. | column. |         |
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 73,|   16    |   13    |    9    |    6    |    3    |   --    |   --
  middle   |    5    |    0    |   15    |   10    |    5    |   --    |   --
  division |IV Caban.|  IV Eb. |IV Manik.| IV Ik.  |IV Caban.|   --    |   --
  -------------------------------------------------------------------------------
  _______________________________________________________________________________
           |  First  | Second  |  Third  | Fourth  | Fifth   | Sixth   |Seventh
           | column. | column. | column. | column. | column. | column. |column.
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 72,|    2    |    1    |    1    |    1    |    1    |    1    |   --
  middle   |    3    |   17    |   14    |   11    |    8    |    4    |   19
  division |    0    |   15    |   10    |    5    |    0    |   15    |   10
           | IV Eb.  |IV Manik.|  IV Ik. |IV Caban.|  IV Eb. |IV Manik.|IV Ik.
  -------------------------------------------------------------------------------
  _______________________________________________________________________________
           |         |         |         |         |         | Sixth   | Seventh
           |         |         |         |         |         | column. | column.
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 71,|   --    |   --    |   --    |   --    |   --    |    2    |    2
  middle   |   --    |   --    |   --    |   --    |   --    |    9    |    6
  division |   --    |   --    |   --    |   --    |   --    |   10    |    5
           |   --    |   --    |   --    |   --    |   --    |  IV Ik. |IV Caban.
  -------------------------------------------------------------------------------
  _______________________________________________________________________________
           |  First  | Second  |  Third  | Fourth  | Fifth   |         |
           | column. | column. | column. | column. | column. |         |
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 73,|    3    |    3    |    3    |    2    |    2    |   --    |   --
  lower    |    7    |    3    |    1    |   16    |   12    |   --    |   --
  division |   15    |   10    |    5    |    0    |   15    |   --    |   --
           |IV Manik.| IV Ik.  |IV Caban.|  IV Eb. |IV Manik.|   --    |   --
  -------------------------------------------------------------------------------
  _______________________________________________________________________________
           |  First  | Second  |  Third  | Fourth  | Fifth   | Sixth   |Seventh
           | column. | column. | column. | column. | column. | column. |column.
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 72,|    4    |    4    |    4    |    4    |    2    |    3    |    3
  lower    |   12    |    9    |    6    |    2    |   17    |   14    |   11
  division |   10    |    5    |    0    |   15    |   10    |    5    |    0
           | IV Ik.  |IV Caban.|  IV Eb. |IV Manik.| IV Ik.  |IV Caban.| IV Eb.
  -------------------------------------------------------------------------------
  _______________________________________________________________________________
           |         |         |         |         |         | Sixth   | Seventh
           |         |         |         |         |         | column. | column.
  ---------+---------+---------+---------+---------+---------+---------+---------
  Plate 71,|   --    |   --    |   --    |   --    |   --    |    5    |    4
  lower    |   --    |   --    |   --    |   --    |   --    |    1    |   15
  division |   --    |   --    |   --    |   --    |   --    |    0    |   15
           |   --    |   --    |   --    |   --    |   --    |  IV Eb. |IV Manik.
  -------------------------------------------------------------------------------

The interval between the successive days, counting to the left, is in
each case 3 months and 5 days, corresponding with the numbers over IV
Caban, fifth column, middle division, Plate 73. Commencing with this
number and adding it successively, we obtain the numbers over the various
columns:

Years.    Months.    Days.
             3         5    Over fifth column, middle division, Plate 73.
             3         5
            --        --
             6        10    Over fourth column, middle division, Plate 73.
             3         5
            --        --
             9        15    Over third column, middle division, Plate 73.
             3         5
            --        --
            13         0    Over second column, middle division, Plate 73.
             3         5
            --        --
            16         5    Over first column, middle division, Plate 73.
             3         5
            --        --
   1         1[333-1] 10    Over seventh column, middle division, Plate 72.
             3         5
  --        --        --
   1         4        15    Over sixth column, middle division, Plate 72.
             3         5
  --        --        --
   1         8         0    Over fifth column, middle division, Plate 72.
             3         5
  --        --        --
   1        11         5    Over fourth column, middle division, Plate 72.
             3         5
  --        --        --
   1        14        10    Over third column, middle division, Plate 72.
             3         5
  --        --        --
   1        17        15    Over second column, middle division, Plate 72.
             3         5
  --        --        --
   2         3         0    Over first column, middle division, Plate 72.
             3         5
  --        --        --
   2         6         5    Over seventh column, middle division, Plate 71.
             3         5
  --        --        --
   2         9        10    Over sixth column, middle division, Plate 71.
             3         5
  --        --        --
   2        12        15    Over fifth column, lower division, Plate 73.
             3         5
  --        --        --
   2        16         0    Over fourth column, lower division, Plate 73.
             3         5
  --        --        --
   3         1         5    Over third column, lower division, Plate 73.
             3         5
  --        --        --
   3         4        10    Over second column, lower division, Plate 73.
             3         5
  --        --        --
   3         7        15    Over first column, lower division, Plate 73.
             3         5
  --        --        --
   3        11         0    Over seventh column, lower division, Plate 72.
             3         5
  --        --        --
   3        14         5    Over sixth column, lower division, Plate 72.
             3         5
  --        --        --
   3        17        10    Over fifth column, lower division, Plate 72.
             3         5
  --        --        --
   4         2        15    Over fourth column, lower division, Plate 72.
             3         5
  --        --        --
   4         6         0    Over third column, lower division, Plate 72.
             3         5
  --        --        --
   4         9         5    Over second column, lower division, Plate 72.
             3         5
  --        --        --
   4        12        10    Over first column, lower division, Plate 72.
             3         5
  --        --        --
   4        15        15    Over seventh column, lower division, Plate 71.
             3         5
  --        --        --
   5         1         0    Over sixth column, lower division, Plate 71.

It is worthy of notice that the sum of the series as expressed by the
final numbers is precisely that of the series on the middle and lower
divisions of Plates 63 and 64, heretofore given, and embraces seven
complete cycles of 13 months, or 260 days each. Counting back three
months and five days from 4 Caban (the day in the fifth column, middle
division, of Plate 73) we reach 5 Been as the starting point of the
series.

As there can be no doubt that the lines and days of the two divisions
form together one unbroken series, it is evident there is no connection
between that portion of it in the middle division and what lies to the
left of it in Plate 71; but there does appear to be, as before indicated,
some connection between the conclusion and what follows to the left in
the lower portion of 71. The series which lies to the left at this point
is as follows:

TABLE XXIV.--_Table showing relations of Plates 70 and 71._

  ________________________________________________________________
      Plate 70.   |                   Plate 71.
  ----------------+-----------------------------------------------
    5th  |  6th   |  1st  |  2d   |  3d   |  4th  |  5th  |  6th
  column.|column. |column.|column.|column.|column.|column.|column.
     6   |   5    |   4   |   3   |   2   |       |       |
     1   |   1    |   0   |   0   |   0   |  15   |  10   |   5
     6   |   2    |  16   |  12   |   8   |   3   |   2   |   1
     0   |   0    |   0   |   0   |   0   |   0   |   0   |   0
   IV Eb.| IV Eb. | IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb.
  ---------------------------------------------------------------

For the purpose of assisting the reader to see the relation more clearly,
the last column of the preceding series--sixth of the lower division on
Plate 71--is added at the right as it stands in the original.

It is apparent that the figures in the fifth column of 71 are exactly
double those in the sixth column. This and the fact that the day IV Eb is
the same as those following are the only indications that there is any
connection between the series. Using the 5 years and 1 month as the
common difference and adding, the result is as follows:

Years.    Months.    Days.
   5         1         0     Sixth column, lower division, Plate 71.
   5         1         0
  --        --        --
  10         2         0     Fifth column, lower division, Plate 71.
   5         1         0
  --        --        --
  15         3         0     Fourth column, lower division, Plate 71.

At this point another change occurs: the former difference is added to
the last figures and the sum is doubled.

Twenty year periods.  Years.  Months.  Days.
                        15       3       0
                         5       1       0
                --      --      --      --
                 1       0       4       0
                                         2
                --      --      --      --
                 2       0       8       0   Third column lower division,
                                                    Plate 71.
                 1       0       4       0
                --      --      --      --
                 3       0      12       0   Second column, lower division,
                                                    Plate 71.
                 1       0       4       0
                --      --      --      --
                 4       0      16       0   First column, lower division,
                                                    Plate 71.
                 1       0       4       0
                --      --      --      --
                 5       1       2       0   Sixth column, lower division,
                                                    Plate 70.
                 1       0       4       0
                --      --      --      --
                 6       1       6       0   Fifth column, lower division,
                                                    Plate 70.

This series does not end at this point, but is continued in the lines
immediately above, which are as follows:

TABLE XXV.--_Table showing relations between Plates 70 and 71._

  ________________________________________________________
      Plate 70.   |               Plate 71.
  ----------------+---------------------------------------
    5th     6th   |  1st     2d      3d      4th     5th
  column. column. |column. column. column. column. column.
     1            |
     0       8(?) |  15      13      10       9       7
                  |                  XII
    12       1    |   3       2       2       2       1
                  |                  II
     3      10    |   6      16       4       0      10
                  |                  XII
     0       0    |   0       0      (?)      0       0
   IV Eb.  IV Eb. | IV Eb.  IV Eb.  IV Eb.  IV Eb.  IV Eb.
  --------------------------------------------------------

Adding the difference, 1, 0, 4, 0, to the final result of the preceding
addition we obtain the figures of the right hand column (fifth column,
Plate 71) of this series:

   6   1   6   0
   1   0   4   0
  --  --  --  --
   7   1  10   0

To obtain the figures of the fourth column this difference must be
doubled, thus

   7   1  10   0
   2   0   8   0
  --  --  --  --
   9   2   0   0

To obtain the black numbers of the next (third) column, the lower cipher
symbol of which is wanting, we add the former difference:

   9   2   0   0
   1   0   4   0
  --  --  --  --
  10   2   4   0

This decrease in the difference is unusual and indicates some error. This
idea seems to be confirmed in the following way: In order to obtain the
numbers of the next (second) column it is necessary to add three times
the former difference, thus:

  10   2   4   0
   3   0  12   0
  --  --  --  --
  13   2  16   0   Second column, Plate 71.

If the increased difference, 2, 0, 8, 0, were retained after its
appearance the result would be as follows:

   7   1  10   0   Fifth column, Plate 71.
   2   0   8   0
  --  --  --  --
   9   2   0   0   Fourth column, Plate 71.
   2   0   8   0
  --  --  --  --
  11   2   8   0   Third column, Plate 71.
   2   0   8   0
  --  --  --  --
  13   2  16   0   Second column, Plate 71.
   2   0   8   0
  --  --  --  --
  15   3   6   0   First column, Plate 71.

Adding the difference, 2, 0, 8, 0, to the third column, Plate 71, thus:

  10   2   4   0
   2   0   8   0
  --  --  --  --
  12   2  12   0

we obtain the red numerals inserted in the third column. It is probable
that the original or some subsequent scribe, observing an error at this
point, inserted these figures as a correction. If so, he failed to remedy
the confusion apparent in this portion of the series. The sum of the
entire series is 303 years (360 days each) and six months, equal to 420
cycles of 260 days.

I am strongly inclined to believe that this section and also pages 24 and
59 are interpolations by some aboriginal artist of a mathematical turn
and advanced ability in this direction, who has given these high series
more as curiosities than with reference to any specific dates or periods
of time.

[Illustration: FIG. 371. Specimens of ornamental loops from page 72,
Dresden Codex.]

Commencing in the sixth column of Plate 71_a_ and running through 72_a_
to the second column of 73_a_, is a numeral series which presents some
peculiarities that baffle all attempts at explanation. Contrary to the
rule which prevails in these pages it ascends from left to right and has
no day symbols connected with it. In addition to this, the numbers of its
lowest line are inclosed in loops of the form here shown (Fig. 371) and
have no apparent connection with the other lines of the series, but, on
the contrary, if taken from right to left, they present in the order
usually given the numbers of the ahaues or katunes.[337-1] It is as
follows:

                                   1    1    1    1    1    1    1
     2    5    8   10   13   16    0    3    6    9   11   14   17
                                                                     II.
    14    8    2   16   10    4   18   12    6    0   14    7(?) 2   XIV
    ⑪    ⑬   ②   ④   ⑥    ⑧   ⑩   ⑫    ①   ③   ⑤   ⑦    ⑨

The last (thirteenth) column of this series is not in a line with the
others, but is found in the lower part of the right hand column of Plate
73, and in connection with it we find the red numerals II and XIV,
denoting the difference between the columns, as is apparent from the
additions here given:

Years.    Months.    Days.
             2        14         First or left hand column.
             2        14
            --        --
             5         8         Second column.
             2        14
            --        --
             8         2         Third column.
             2        14
            --        --
            10        16         Fourth column.
             2        14
            --        --
            13        10         Fifth column.
             2        14
            --        --
            16         4         Sixth column[TN-8]
             2        14
            --        --
   1         0        18         Seventh column.
             2        14
  --        --        --
   1         3        12         Eighth column.
             2        14
  --        --        --
   1         6         6         Ninth column.
             2        14
  --        --        --
   1         9         0         Tenth column.
             2        14
  --        --        --
   1        11        14         Eleventh column.
             2        14
  --        --        --
   1        14         8[338-1]  Twelfth column.[TN-9]
             2        14
  --        --        --
   1        17         2         Thirteenth column.


FOOTNOTES:

[261-1] The work here referred to is entitled Die Mayahandschrift der
Königlichen öffentlichen Bibliothek zu Dresden, herausgegeben von Prof.
Dr. E. Förstemann, Hofrat und Oberbibliothekar. It contains, besides the
chromolithographs of the 74 plates, an introduction published at Leipzig,
1880, 4^o.

[269-1] A Study of the Manuscript Troano, by Cyrus Thomas, pp. 7-15.

[272-1] This method will be adopted throughout this paper where figures
containing numerals are introduced.

[273-1] In the representations of lines and columns of the codex Roman
numbers are necessarily used to distinguish the class of numerals, yet in
the text, as in this case, the Arabic numbers will be used as most
convenient.

[273-2] Strictly speaking, the interval between 11 Men and 13 Oc is
fourteen days, but throughout this paper, by "_interval between_" two
days, is to be understood the number of days to be counted _from_ one _to
and including_ the other. The one counted from is always _excluded_ and
the one reached or with which the interval terminates is always
_included_.

[273-3] Science, p. 459, April 11, 1884.

[277-1] Throughout this paper when the words "figure" and "character" are
used in reference to what appears in the codex, they are to be understood
as follows: "figure" refers to the picture, as of a person, animal, or
other object in the spaces; "character" refers to the hieroglyphics or
written symbols.

[278-1] Study of the Manuscript Troano, by Cyrus Thomas, Chapters II and
VII.

[278-2] Erläuterungen zur Mayahandschrift, p. 2.

[280-1] Erläuterungen zur Mayahandschrift, p. 16.

[280-2] Bureau of Eth., Third Ann. Rep., pp. 16 et seq.

[282-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 15, 16.

[282-2] Déchiffrement des écritures calculiformes ou Mayas, par M. le
C^te H. de Charency, Alençon, 1849; also, Mélanges, pp. 185-195.

[283-1] For an explanation of the principle upon which these day columns
were formed, see "Notes on certain Maya and Mexican manuscripts," by
Cyrus Thomas, published in the Third Annual Report of the Bureau of
Ethnology.

[290-1] The symbol for this day in Kingsborough resembles Lamat, but the
photographic copy makes it Ix, as it should be.

[290-2] Förstemann, Erläuterungen zur Mayahandschrift, p. 42.

[291-1] Erläuterungen zur Mayahandschrift, p. 36.

[292-1] Erläuterungen zur Mayahandschrift, p. 60.

[293-1] Erläuterungen zur Mayahandschrift, p. 56.

[296-1] The bottom lines are selected because they are less injured in
the codex than the top lines, which are in most cases entirely
obliterated.

[300-1] 3 days in ms., should be 4.

[317-1] The third symbol in the last day column of Plate 51_b_ is Been in
the codex; but this is an evident mistake, as shown by the order of the
days, since Ahau, which has been substituted above, always follows Cauac.
This may be seen by reference to the middle column of 57_b_.

[319-1] This is one of the exceptional cases.

[321-1] Second exception.

[321-2] Third exception.

[323-1] One line has been omitted in the numeral symbol.

[323-2] Here we have again the added day.

[324-1] The 8 at this point in the codex is an evident error.

[324-2] Here is also an error in the original, this being 10.

[324-3] The symbols require an additional day here.

[324-4] The 8 in the year line in the original is a manifest error, as 6
precedes and 7 follows.

[324-5] The 18 in the day line at this point is also an error, as the
interval between 2 Muluc and 10 Cimi is 8 months and 17 days. Moreover,
the next day number being 16 requires this to be 19.

[325-1] The counters in the original at this point are certainly wrong,
for here should be 7 months and 8 days, whereas the symbols are those for
8 months and 17 days.

[325-2] Here we have again the additional day.

[325-3] Added to show connection with the lower series.

[333-1] Codex has 19, which is equivalent to 1 year and 1 month.

[337-1] While reading the final proof I fortunately discovered what may
prove to be the correct explanation of the numbers in the loops.

At the commencement of the series on Plate 71 and at its close on Plate
73 we observe the symbol of the day, 9 Ix. Starting from this date and
counting forward on the calendar two months and fourteen days, we reach
11 Lamat. This gives the number in the first loop of the series. Two
months and fourteen days more bring us to 13 Ik, the number in the second
loop; two months and fourteen days to 2 Cib, the number in the third
loop, and so on to the end. It is therefore probable that the numerals in
the loops indicate the week numbers of the days, though these are usually
expressed in red symbols.

[338-1] The 7 in the twelfth column is an error; it should be 8, as an
inspection shows the place of the missing dot. The additions make it
clear that the numbers of the second line refer to months, those of the
line below them to days, and those of the line above to years. The series
is, therefore, apparently complete without the numbers inclosed in the
loops.



CHAPTER II.

CONCLUSIONS.


The conclusions to be drawn from the foregoing discussion may be briefly
stated as follows:

First. That the codex in its present form is composite, being made up
from two or more different original manuscripts, as Dr. Förstemann has
suggested.

Second. That a number of minor changes and additions have been made by a
subsequent hand, possibly after it had assumed its present form.

Third. That the year referred to in the larger series is one of 360 days;
also, that in instances of this kind the count is continuous, and hence
not consistent with the generally received idea of the Maya calendar, in
which, the four year series forms a necessary part of the system, unless
some other method of accounting for the five supplemental days can be
discovered than that which has hitherto been accepted.

Fourth. On the other hand, indications of the four year series are
certainly found in all of the Maya manuscripts; for example, in Plates
25-28 of the Dresden Codex and Plates XX-XXIII of the Manuscript
Troano,[339-1] which seem to be based on this series; in fact, the
numbers attached to the days in the latter can be accounted for in no
other way. Plates 3-6 of the Cortesian Codex are apparently based upon
the same system. The numbers in the loops on Plates 71, 72, and 73,
Dresden Codex, heretofore alluded to and represented in Fig. 371,
apparently defy explanation on any supposition except that they refer to
the numbers of the ahaues, which are based upon the four year
series.[339-2] The frequent occurrence in connection and in proper order
of both the first and the terminal days of the year apparently refers to
the same system. Many of the quadruple series no doubt relate to the four
cardinal points and the four seasons; yet there are some which cannot be
explained on this theory alone.

It is impossible, therefore, to exclude this system from consideration in
studying the chronology of the codices, although there are a number of
the numerical series of the Dresden manuscript which cannot be made to
fit into it on any hypothesis so far suggested. The same thing is also
found to be true in regard to some, in fact most, of the series found in
the Mexican manuscripts. This confusion probably arises in part from the
apparently well established fact that two methods of counting time
prevailed among both Mexicans and Mayas: one, the solar year in ordinary
use among the people, which may be termed the vulgar or common calendar;
the other, the religious calendar used by the priests alone in arranging
their feasts and ceremonies, in which the cycle of 260 days was taken as
the basis. But this supposition will not suffice as an explanation of
some of the long series of the Dresden Codex, in which the year of 360
days appears to have been taken as a unit of measure, unless we
assume--as Förstemann seems to have done--that what have been taken as
years are simply high units and counting the whole as so many days, refer
the sum to the cycle of 260 days, which will in almost every case measure
them evenly as a whole, or by its leading factor, 13. That the smaller
series attached to day columns are all multiples of 13 and referable to
the cycle of 260 days has been shown by Förstemann as well as in the
preceding part of this paper. But it is worthy of note that the
difficulty mentioned occurs only in reference to series found in that
portion of the Dresden manuscript which Förstemann has designated Codex B
(page 24 being considered as belonging thereto).

The red unit number symbol, with a circle of dots around it, seen
occasionally in the Manuscript Troano, seems to have some connection with
the four year series. Take, for example, the one in the lowest division
of Plate VII.

The series commences in the lower right hand corner of Plate VIII, where
the day column with which it is connected is found. The days of this
column, reading downward, are as follows: Ahau, Eb, Kan, Cib, Lamat, and
the number over them is I, but without any dots around it, while the
terminal I of the series is inclosed in the circle of dots. What is the
meaning of this marked distinction? It is evident that it is something
which does not apply equally to all the days of the columns; yet, as it
is the terminal number, it must relate to some one of them. If we examine
the series carefully I think the reason for the distinction will be
explained; Written out in full, it is as follows:

   I.
  Ahau
  Eb   }
  Kan  } 10, XI; 10, VIII; 10, V; 10, II; 12[?], Ⓘ.
  Cib
  Lamat

The last black number is 10 in Brasseur's fac simile, but should be 12.
Making this correction, the series is regular and of the usual form. The
sum of the black numbers is 52, which is the interval between the days,
and the number over the column is the same as the final red number.

If we turn now to the calendar (Table II) and select Ahau of the Kan
column, and 1, the seventeenth number of the eighth figure column, and
count 52 days, we reach 1 Eb, the second day of our column as given
above; 52 days more bring us to 1 Kan, the first day of the first month
in the calendar and third day of our column. If the theory of the four
year series be correct, then 1 Kan of the Kan series must be the first
day of the first year of an Indication or week of years. This fact was
probably considered by the aboriginal artist of sufficient importance to
give this day a mark of distinction. As it is not possible for any of the
other days of the column to be thus distinguished, it is fair to presume
this peculiar marking of the final number refers to Kan. Moreover, this
distinction would not occur if any other than the Kan series were used.

In the upper division of Plate IX of the same manuscript is the following
series:

   XIII
  Men   }
  Manik } 20, VII; 20 Ⓘ; 1, II; 4, VI; 7, XIII.
  Cauac }
  Chuen
  Akbal

In this, I, the second red number of the series, has the circle of dots
around it. The number over the column is partially obliterated, but is
readily restored, and should be XIII.

If we select, on our calendar, the Cauac column, or series, a reason for
this distinction will appear. The sum of the black numbers is 53, which
is also the interval between the days. As has heretofore been shown, the
red numbers of the series refer to certain days selected by the priests,
for special reasons unknown to us, which occur between the days of the
column.

In this case the intermediate days are as follows:

     Between 13 Manik and 13 Cauac: 7 Manik, 1 Manik, 2 Lamat, and 6 Eb.

     Between 13 Cauac and 13 Chuen: 7 Cauac, 1 Cauac, 2 Ahau, and 6 Kan.

Here we find the explanation for which we are seeking, as in the interval
between 13 Cauac and 13 Chuen is 1 Cauac, which, if the Cauac column of
the calendar be selected, is the first day of the year 1 Cauac, the first
year of an Indication. As this occurs only when a year commencing with
Cauac is selected, we infer that the series is based upon the system with
the four year series.

The best illustration of this peculiarity and the strongest evidence of
its signification is probably found in the series contained in the middle
division, Plate XI, same manuscript. This, when written out and the
numbers properly arranged, is as follows:

   Ⓘ        Ⓘ
  Oc       Ahau  }
  Cib      Cimi  } 1, II; 2, IV; 2, VI; 5, XI; 2, XIII; 4, IV; 9(?) Ⓘ.
  Ik       Eb    }
  Lamat    Ezanab
  Ix       Kan

The last black number of the series is 9, but should be 10 to render the
series complete. Making this correction, the series is of the usual type;
the sum of the black numerals is 26, the interval between the days of
the columns is 26, and the final red numeral is the same as that over the
columns.

As the circle of dots is around the final red number and also around each
of those over the columns, the distinction indicated must refer to one or
more days of each column.

As the last days only of the columns are year bearers, the mark of
distinction probably applies to them. Selecting for the left hand column
the Ix series of years and commencing with 1 Oc, the seventeenth day of
the eighth month, we count 26 days. This brings us to 1 Cib, the third
day of the tenth month, or tenth figure column of our calendar and second
day of the first day column of the series; 26 days more to 1 Ik; 26 more
to 1 Lamat, and 26 more to 1 Ix, the first day of the year 1 Ix, which,
according to the four year series, will be the first year of an
Indication. Selecting the Kan series for the second column and counting
in the same way from 1 Ahau, the seventeenth day of the eighth month, or
eighth figure column of the calendar, the last day is found to be 1 Kan,
the first day of the year 1 Kan, which must also be the first year of an
Indication.

Unit numerals marked in this manner are found in two or three places in
the Cortesian Codex, but there is none in the Dresden Codex. The series
with which they are connected in the former, except that in the middle
division of Plate 24, are too much obliterated to be traced throughout.
This, by making two slight and apparently authorized corrections, is as
follows:

    Ⓘ
  Cimi   }
  Ezanab } 11, XII(?); 11, X; 6, III; 8, XI; 7(?), V; 9, I.
  Oc     }
  Ik
  Ix

The first red numeral of the line is X in the original and the next to
the last black number is 6. By changing the former to XII and the latter
to 7 the sum of the series will be 52, which is the interval between the
days of the column.

Using the Ix column in the calendar and commencing with 1 Cimi, counting
as heretofore, the last day of the column of the series is found to be 1
Ix, the first day of the year 1 Ix and the first year of an Indication,
according to the four year system.

A somewhat remarkable confirmation of the theory here advanced is
presented in a series found in the middle division of Plate II of the
Manuscript Troano.

The series, when written out with the substitutes heretofore used, is as
follows:

    Ⓘ          Ⓘ
  Manik      Ymix     }
  Men (?)    Been     } 9, X; 6, III; 11, I.
  Chuen      Chicchan }
  Akbal      Caban
  Men        Muluc

In Brasseur's fac simile the second symbol of the left hand column is
clearly that for Men. If this be accepted as correct, then no year bearer
(Kan, Muluc, Ix, Cauac) would be found in either column and the theory we
have advanced regarding the signification of the dots around the red unit
over the column would fall to the ground. Nor is this the only difficulty
we meet with in attempting to apply the theory to this series. The sum of
the black numbers is 26, which should also be the interval between the
days of the columns. Counting 26 days from 1 Manik brings us to 1 Been
instead of 1 Men; 26 more to 1 Cauac, a day not found in either column as
given in the original. Taking the second column and counting 26 days from
1 Ymix, we reach 1 Manik, instead of 1 Been. This gives us the key to the
series and solves the riddle. We must commence with 1 Ymix, then take 1
Manik, then 1 Been, and so on, going alternately from column to column.

Adopting this method and using the Cauac column of our calendar, Table
II, the result is as follows: Commencing with 1 Ymix, the third day of
the tenth figure column, and counting 26 days, we reach 1 Manik; 26 days
more bring us to 1 Been, and 26 more to 1 Cauac, the first day of the
first year of an Indication. The 1 Men of the left hand column should
therefore be 1 Cauac, which is also proved by counting the intervals,
without regard to the week numbers. For example, from Ymix to Been is 12
days, from Been to Chicchan 12 days, from Manik to Cauac 12 days, and so
on through each column. Or, if we take the columns alternately, the
interval is six days, thus: From Ymix to Manik, 6 days; from Manik to
Been, 6 days; from Been to Cauac, 6 days; from Cauac to Chuen, 6 days,
and so on to the end.

Although the proof is not absolutely conclusive that these red unit
numerals have this mark of distinction for the reason given, it
nevertheless furnishes what would seem to be a satisfactory explanation,
and, if so, affords proof that the calendar system, based upon the four
year series, was in vogue when the Manuscript Troano and the Codex
Cortesianus were written.

This mark of distinction is found in a strange and unusual relation in
the lower division of Plate XV, Manuscript Troano. The first red numeral
of the series is given thus:

[Illustration: FIG. 372. Numeral character from the lower division of
Plate XV, Manuscript Troano.]

Most of the day and about half of the numeral symbols are obliterated,
but all that are necessary for present purposes remain distinct and
uninjured, as follows:

  III, }
  Ix   } 10, XIⒾI.
  Cimi }

Judging by these and the few numbers remaining, the entire series was as
follows:

  III,   }
  Ix     }
  Cimi   }
  Ezanab } 10, XIII; 4, IV; 20, XI; 9, VII; 9, III
  Oc     }
  Ik     }

The only doubt in reference to the restoration is whether the second and
third pairs of numerals should be as given, or 2, II, and 22, XI. If we
select the Kan column of our Table II and count from 3 Ix of the eleventh
figure column, we reach 13 Kan. If the four year series was the system
used 13 Kan might be the first day of a year, but not the first day of an
Indication. As this is the only day referred to by the XIII which could
have been the first of a year we must seek an explanation in something
else. Counting ten days from 3 Ezanab will bring us to 13 Lamat, which is
the last day (counting the five added days) of an Indication, commencing
with the year 1 Kan and ending with the year 13 Kan.

According to my theory of the ahaues,[344-1] the year 13 Kan would have
corresponded with the Gregorian years 1376, 1438, 1480, and 1532.
According to the theory advanced by Perez,[344-2] it would have
corresponded with 1385, 1437, 1489, and 1541.

It is therefore possible that this mark of distinction may be of some
value in determining the relation of the Maya to the Gregorian calendar.


FOOTNOTES:

[339-1] See Study of the Manuscript Troano, by Cyrus Thomas.

[339-2] See note on page 337.

[344-1] See Table XVII, Study of the Manuscript Troano, by Cyrus Thomas,
p. 44.

[344-2] See Table XVIII, ibid., p. 45.



CHAPTER III

THE WRITING.


It must be admitted that none of the attempts made at deciphering the
writing in these manuscripts has proved entirely satisfactory; in fact
there is still some doubt as to whether any of the characters are truly
phonetic; nevertheless it is believed that what is here shown will tend
to lessen this doubt. It must be conceded, however, notwithstanding these
drawbacks and difficulties, that some material progress has been made
towards a better understanding of its type and of the nature of the
characters.

The direction in which it is to be read must of course be determined
before any progress can be made in deciphering it. This was, until
recently, a matter of speculation, but now may be considered settled. As
this has been explained[345-1] it is unnecessary to repeat that
explanation here.

A certain parallelism in the sentences or groups of characters has also
been discovered. Attention was first called to this by me in the work
referred to, but is more fully explained by Dr. P. Schellhas in his paper
entitled "Die Mayahandschrift der königlichen Bibliothek zu Dresden." It
will readily be understood from a single illustration. Take for example
the lower division of Plate XV of the Manuscript Troano (see Study Ms.
Troano). Omitting from consideration the numerals and the day column at
the left, there are here two short columns on the left and two on the
right over the animal figures, and three longer columns between. As
explained in the work referred to, the short columns are to be read as
lines from left to right and the longer columns separately, from the top
downward. There are, in all, five groups or sentences, each containing
four compound characters. Representing these by letters, repeating those
which indicate similar characters, and arranging as in the plate, the
result is as follows:

   ___________________________________________
  |            |     |     |     |            |
  | _b_   _a_  | _h_ | _l_ | _m_ |  _w_   _a_ |
  |            |     |     |     |            |
  | _r_   _n_  | _a_ | _a_ | _a_ |  _r_   _s_ |
  |____________|     |     |     |____________|
               | _r_ | _r_ | _r_ |
               |     |     |     |
               | _p_ | _k_ | _t_ |
               |_____|_____|_____|

In this case the characters represented by _a_ and _r_ are repeated in
each group and in the same relation to the other characters. It is
apparent, therefore, that each group is to be read separately, and, as
each repeats in part what is given in the others, it is more than
probable that they are simply short formulas to be repeated in certain
religious ceremonies. This parallelism, though not always so apparent as
in the case presented, is nevertheless found running through all the
codices. The advantage to the attempts at decipherment which results from
this fact is evident, as it will often justify the restoration of blurred
or obliterated characters, and, what is of still more importance, will
enable the investigator to test his conclusions by comparing the
different characters and pictures with which they are associated.

Although it appears to be well settled that, as a rule, the writing, when
in lines, is to be read from left to right--the lines following each
other downward and the columns to be read from the top downward, but the
groups, as before explained, to be read separately--it does not follow
that the _groups_ succeed one another from left to right. This has
generally been taken for granted, but there are some reasons to doubt the
correctness of this conclusion as regards a number of plates and possibly
one entire codex.

The facts that the lines of numerals attached to the day columns extend
to the right and that the written characters, when in lines, follow one
another in the same direction lead us to infer that the groups and
pictures follow one another in the same order, but the apparent movement
of the latter towards the left would seem to indicate that _they_ follow
one another in _this_ direction. This inference appears to be confirmed
by the following evidence: As is well known, the plates of the Manuscript
Troano are to be taken in reverse order to the paging. Turning to Plate
II, we observe in the middle department of the middle division a bound
captive or victim, on whose neck a machete is descending to sever the
head from the trunk. Turning to Plate III, which properly stands to the
left of Plate II, we see a headless trunk covered with blood and the
fatal machete near the neck. It is fair to presume that this is the same
individual that is figured in the preceding plate, and, if so, that the
pictures follow one another toward the left.

Placing Plates XV* and XVI* of the same manuscript in the proper relation
to each other and carefully examining the figures in the second division,
we notice that the idol heads which the artisans are carving approach
completion as we move toward the left, those in Plate XV* and the right
hand one in XVI* being simply blocked out, while the middle one in the
latter plate is completely rounded and is receiving the second ornamental
line and the one at the left hand is receiving the third and final line.

The female figures in the second division of Plate XIX* indicate the same
order, as shown by the increasing girth as we proceed toward the left.

The same order appears to be indicated in numerous places by the symbols
of the cardinal points inserted in the text, as they (supposing the
conclusion as to their assignment in my "Notes on certain Maya and
Mexican manuscripts," accepted by Drs. Förstemann and Schellhas, to be
correct) follow one another in the proper order if read towards the left,
to wit, south, east, north, west.

As the writing over each figure, consisting usually of four compound
characters, appears to refer to that over which it is placed, it follows
that these character groups must be taken in the same order as the
pictures. The suggestions on this point are presented here more as proper
subjects of investigation by students of American paleography than as
fixed conclusions of the writer. If found to be justified by the facts,
they will furnish some additional aid in the work of deciphering these
manuscripts.


SIGNIFICATION OF THE CHARACTERS.

As Landa's alphabet has so far proved useless as an aid in deciphering
these manuscripts, our only hope of accomplishing this end is by long and
careful study of these records and laborious comparisons of characters
and the relations in which they stand to one another and to the figures.

Some discoveries made while preparing this paper for the press, which are
mentioned further on, may possibly give us the key to the method used by
Landa in forming his alphabet, and, if so, will probably furnish some
slight additional aid in our investigations.

The direction in which the writing is to be read having been ascertained,
our next step is to determine by comparison the probable signification of
as many characters as possible before discussing the question of
phoneticism. The relation of the characters to the pictorial
representations forms our chief reliance in this branch of the
investigation.

As a commencement in this work and as a basis for further attempts in the
same direction, attention is now called to some characters, other than
the day and month symbols, whose signification seems to be satisfactorily
determined. As there is still some difference of opinion as to the
assignment of the symbols of the cardinal points they are also omitted
from the list. M. Léon de Rosny has given, as a supplement to his edition
of the Cortesian Codex, a list of characters with their supposed
signification. It is not my intention to discuss here the merits of this
vocabulary, although I shall avail myself of so much found therein as
appears to warrant acceptance.

The question of phoneticism will not be considered in connection with the
list, as the subject will be briefly discussed at the close, the only
object in view in giving the list being to indicate the signification of
the characters alluded to. The Maya names appended are therefore to be
understood simply as the supposed names applied to them or the objects
they denote.


SYMBOLS OF ANIMALS &C.

[Illustration: No. 1]

  _Kal._ The symbol for the number 20. Found in all of the codices and
     explained in the preceding portion of this paper.

[Illustration: No. 2]

  The symbol for 0 (nought), always red. Found only in the Dresden Codex
     and always in the numeral series.

[Illustration: No. 3]

  _Kin._ Sun, and probably day also. It is not known positively that it
     has this signification except in connection with the equatorial
     cardinal point symbols and the symbol of the month _Yaxkin;_ yet it
     is reasonable to suppose it has.

[Illustration: No. 4 _a_ _b_ _c_ _d_]

  _Aac_ or _Ac_. A turtle. That this symbol as shown in _a_ and _b_
     denotes the turtle is conclusively proved by its resemblance to the
     head of that animal, as figured in the Cortesian Codex (see Fig.
     373) and its relation to these figures. Found only in this codex,
     unless two doubtful symbols on Plate XXV*, Manuscript Troano, are to
     be considered as variants.

[Illustration: FIG. 373. Turtle from the Cortesian Codex.]

There can be no doubt that Landa's _A_, an exact copy of which is given
in the margin, in both varieties, _c_ and _d_, is nothing more nor less
than this symbol; for, in addition to the very close general resemblance,
we see in it the eye and the dot indicating the nostril. This fact is
important, as it gives us some clew to the method adopted by Landa in
forming his alphabet.

[Illustration: No. 5]

  _Uech._ Symbol or head of the armadillo of Yucatan. Appears but once or
     twice and in the Manuscript Troano only. (See Study of the
     Manuscript Troano, by Cyrus Thomas, pp. 98 and 145).

[Illustration][TN-10]

  _Che._ Wood. (See Study of the Manuscript Troano, by Cyrus Thomas, p.
     144).

[Illustration: No. 7]

  _Cab._ Earth, soil; also honey. (See Study of the Manuscript Troano, by
     Cyrus Thomas, p. 150.)

[Illustration: No. 8]

  _Piz._ Stone or stone heap. (See Study of the Manuscript Troano, by
     Cyrus Thomas, p. 144). The Maya name of the thing indicated is
     uncertain, though I am inclined to believe _Piz_, as given in the
     work alluded to, is correct.

[Illustration: No. 9]

  _U._ The left symbol of this figure appears to stand for vase, and is
     also used to indicate a pronoun or article when joined to another
     symbol, as here shown. (See op. cit., p. 145.)

[Illustration: No. 10]

  _Xicim._ The ear. Rosny, Vocabulaire hiératique, No. 185.

[Illustration: No. 11]

  _Hau._ The quarter of a deer. Usually represented as an offering to the
     gods; in all the manuscripts.

[Illustration: No. 12]

  _Ikilcab._ The bee. Although the figure bears a much stronger
     resemblance to a beetle than to a bee, there can be no longer any
     doubt that Brasseur's supposition that it represents a bee is
     correct.

[Illustration: No. 13]

  Honey in the comb. (See Study of the Manuscript Troano, by Cyrus
     Thomas, Fig. 20); in the Manuscript Troano only, and always in red.

[Illustration: No. 14]

  _Xamach or Chimix._ A vessel. This symbol, found in all the codices, is
     apparently explained by its use in the upper division of Plate 27,
     Cortesian Codex, where it stands over each of four vessels or jars
     of the form represented in Fig. 374.

[Illustration: FIG. 374. Jar from the Cortesian Codex.]

This conclusion is greatly strengthened by the fact that the only other
symbols in this connection are those of the cardinal points, one to each
vessel. These figures are probably intended to denote here the four
sacred vessels or amphoræ of the Bacab, though not surmounted, as
Brasseur supposed, by human or animal figures.

The symbol appears to be used also in the ordinary sense, or at least to
signify other vessels than the sacred four, if we may judge by its
frequent repetition in Plate XIV, Manuscript Troano. But it is worthy of
notice that here also, in both the middle and lower divisions, four of
the symbols are connected with the cardinal point symbols; there is also
in the former the figure of a vessel.

[Illustration: Hieroglyph]

If this identification be correct it is important, as it has a strong
bearing on the question of phoneticism. It will be observed that,
although the right hand member resembles closely the symbol of the day
Ymix, there are some differences, as may be seen by comparison. In the
former the little figure at the top is divided as in Kan, and on each
side of it there is a large dot, usually, and apparently by intention,
circular or hollow. These differences are permanent in the different
codices.

In the upper division of Plates X and XI, Manuscript Troano, where this
symbol appears in connection with each of the four cardinal symbols, that
relating to the east presents this remarkable variation:

[Illustration: Hieroglyph]

[Illustration: No. 15 _a_ _b_]

  (?) A conventional figure of sprouting maize, never inserted in the
     text, but frequently in the Manuscript Troano and in the Peresian
     Codex made a part of the head gear of figures of deities, in which
     case the Kan symbol is generally omitted.

The Kan symbol in this connection cannot be intended, as Dr. Schellhas
supposes, to indicate the field or milpa in which the corn is growing,
but the grain from which the plant is springing. (On this subject see
Study of the Manuscript Troano, by Cyrus Thomas, pp. 105 and 107.)

[Illustration: No. 16]

  (?) Symbol of a worm which gnawed the roots of the growing agave or
     maguey; appears but once, on Plate XXIX_c_ of the Manuscript Troano.

The animal head and teeth show the erroneous idea the natives had of the
gnawing apparatus of insects. The worm is shown on the next page in Fig.
375.

[Illustration: FIG. 375. Worm and plant from Manuscript Troano.]

[Illustration: FIG. 376. Figure of a woman from the Dresden Codex.]

[Illustration: No. 17]

  _Chuplal._ Woman or female. This symbol is found in the Dresden and
     Troano Codices, but most frequently in the former. The appendage at
     the right is sometimes wanting, and occasionally that at the left,
     but when this is the case some other prefix is generally
     substituted.

If we examine carefully Plates 16-20 of the Dresden Codex, where this
symbol is most frequently repeated, and compare it with the heads of the
females there figured, it soon becomes apparent that the scrolls with the
heavy black dot are intended to denote the locks of hair and that the
symbol as a whole is, as usual, a modified or conventional form of the
head (see Fig. 376).

[Illustration: No. 18 _a_ _b_ _c_]

  _Otoch._ A house or dwelling, or _Tabay;_ a hut or hunting lodge. The
     symbol marked _a_ is found in the Cortesian Codex on Plate 29; that
     marked _b_, on Plates 29, 32, and 34, same codex, and on Plates XVI*
     and XXII* of the Manuscript Troano. The one marked _c_ is the usual
     form in the latter, as on Plates V*, VII*, and X*. It is also on
     Plate 38 of the Dresden Codex.

The relation of these symbols to the conventional figures of houses or
huts inserted at the points where they are found, together with the form,
which shows an attempt to represent the thatched or leaf covered roof,
leaves no doubt that they are used for the purpose indicated.

[Illustration: No. 19 _a_ _b_]

  _Buk_ (?). There are good and, it is believed, satisfactory reasons for
     concluding that these symbols are intended to denote the action of
     whirling a stick to produce fire or rolling a pestle in grinding
     paint. The first, marked _a_, is found only on Plate XIX of the
     Manuscript Troano, and the second, on Plates 5 and 6 of the Dresden
     Codex.

A copy of part of Plate XIX of the Manuscript Troano is introduced here
(see Fig. 377) to show the relation of the figures to the characters. If
this interpretation be correct, we see here an evident attempt on the
part of the aboriginal artist to indicate by the symbol the action
necessary in the work to be performed. It is probably a conventional
sign, and not a phonetic character.

[Illustration: FIG. 377.]

[Illustration: No. 20]

  (?) In all probability one of the symbols used to denote the act of
     walking or taking steps. Found but seldom in this particular form,
     though each portion occurs frequently alone or in other
     combinations.

[Illustration: FIG. 378. Copy of lower division of Plate 65, Dresden
Codex.]

A remarkable series of figures and written characters runs through the
lower division of Plates 65 to 69 of the Dresden Codex, apparently
devoted entirely to the representation of incidents in the life of the
culture hero Kukulcan, or deity mentioned on a subsequent page as the
"long nosed god" or "god with the snake-like tongue," or to ceremonies to
be performed in honor of this deity. Over the figure are three lines of
written characters, as shown in Fig. 378, which is a copy of the lower
division of Plate 65. These, as is readily seen, are in groups, one group
of six compound characters over each figure of the god. There are
thirteen figures of the god and thirteen of these groups of characters in
the series. The characters of a group, as may be seen by reference to the
figure, are arranged in the following manner:

   ___________
  |     |     |
  | _a_ | _b_ |
  |_____|_____|
  |     |     |
  | _c_ | _d_ |
  |_____|_____|
  |     |     |
  | _e_ | _f_ |
  |_____|_____|

to be read (presumably) in the alphabetic order of the letters given;
though the order in which they are to be read is not essential at
present. Examining the series carefully we find that the first character
of each group corresponding with _a_ in the above diagram is the same
throughout. The same thing is true in reference to the third, or that
occupying the place of _c_ in the diagram, which is the symbol of the
deity. The sixth, or that corresponding with _f_ in the diagram, is also
the same throughout the series; the fifth, corresponding with _e_, is
substantially the same throughout, though subject to more variations than
any of the other characters. It follows, therefore, that the chief and
almost the only differences in the readings of the groups are to be found
in the second and fourth characters, or those represented by _b_ and _d_
in the above diagram; the others (at least those represented by _a_, _c_,
and _f_), if referring at all to the figures, must relate to something
found in or applicable to each. The third (_c_), as stated, is the symbol
of the deity and corresponds in the text with the figure of the god in
the pictures. As this deity figure is the only thing found in all of the
representations, we must seek for the explanation of the other two
permanent characters in something else than what is figured.

Comparing the second character (_b_) of each group with that upon which
the god is seated or standing, we find sufficient evidence to satisfy us
that this symbol is the one which is used throughout to indicate this
object. For example, the second symbol in the group on Plate 69 is an
exact copy of the object on which the deity is seated. The same thing is
substantially true of that in the left hand group of Plate 66, the middle
group of 67, and the right hand group of 68.

Assuming, on account of the remarkable regularity of this series and the
fact that the deity is in each case seated or standing on something, that
this rule holds good throughout, we have a clew to those corresponding
symbols which are not simple copies of the things they are used to
indicate.

Turning to Fig. 378, we observe in the right hand department the marks of
footsteps under the deity and the character shown in the margin (No. 20)
as the second of the group above the deity. It is worthy of notice that
in the two we find precisely Landa's two characters for the letter B. Is
it possible that the two principal parts of this compound character
denote the Maya words _oc be_, "foot journey" or "enters upon the
journey"? Attention will be called to this further on, but it is proper
to state here that as the prefix is found in three other corresponding
characters it cannot be a necessary part of that which represents the
footsteps in this case.

[Illustration: No. 21.]

  Assuming the theory above given as to the characters in the inscription
     which represent the things under the deity figures to be correct,
     the second character in the middle group of the lower division of
     Plate 65, shown in Fig. 378, will be the symbol for the substance
     represented by scrolls under the figure of the deity.[354-1]

The prefix in this case is the same as that to the symbol above described
(No. 20), and of course has the same signification. The other portion of
No. 21 must therefore represent the substance in which the god is
walking. This appears to be dust, sand, or mud.

[Illustration: No. 22. _a_ _b_ _c_]

  _Cacauak_ or _cacauche_. The wild or cultivated cacao. Found a number
     of times in the Dresden Codex, sometimes as represented in the
     marginal figure _a_ and sometimes as in _c_, and always in
     connection with figures holding in the hand a fruit of some kind. It
     appears once in the Cortesian Codex (Plate 36), as shown in _b_, in
     connection with a fruit of precisely the same kind as that figured
     in the Dresden Codex. It is found also on Plate XVIII* of the
     Manuscript Troano, but is apparently used here to denote an action.

There can be little, if any, doubt, judging by the figures in connection
with which it is found, that this symbol is used in the Dresden and the
Cortesian Codices to denote the cacao. Whether it refers to the tree or
to the fruit is uncertain; possibly the different forms in which it is
found are intended to denote these distinctions. In some of the figures
the capsule appears to be indicated; in others the seed. The prefix to
figure _c_ apparently indicates the heaping or piling up of the fruit on
the dish held in the hands of the individuals figured in the same
connection, as, for example, on Plates 12 and 13 of the Dresden Codex. If
this supposition be correct it gives us a key to the signification of
this prefix. Reference to its use in the upper division of Plate XVIII*,
Manuscript Troano, will be made further on.

In this symbol we find another of Landa's letters, and, if phonetic,
agreeing precisely with his interpretation.

[Illustration: No. 23. _a_ _b_]

  _Ekbalam_ according to Rosny. The variety marked _a_ is found twice in
     the Manuscript Troano, Plates XVI and XVII, and that marked _b_ once
     in the Dresden Codex, Plate 8, each time in connection with a
     spotted, leopard-like animal.

The black markings on the symbols render it probable that Rosny's
interpretation is correct. The numeral before the first form may possibly
be explained by the fact that this symbol is used once (Manuscript
Troano, Plate XII) to indicate the day Ix.

[Illustration: No. 24.]

  _Moo._ The ara, a large species of parrot. This symbol is found but
     once, and that in Plate 16_c_, Dresden Codex, in connection with the
     bird shown in Fig. 379.

[Illustration: FIG. 379. The moo or ara from Plate 16. Dresden Codex.]

The conclusion in this case is based on the following evidence: In this
series there are six groups of characters, four compound characters in
each group, arranged as in the annexed diagram:

   __________________________________________________
  |          |          |          |     |     |     |
  | _a_  _b_ | _e_  _d_ | _g_  _h_ | _i_ | _m_ | _o_ |
  |          |          |          |     |     |     |
  | _c_  _d_ | _c_  _f_ | _c_  _d_ | _c_ | _n_ | _b_ |
  |__________|__________|__________|     |     |     |
                                   |     |     |     |
        1          2          3    | _k_ | _c_ | _c_ |
                                   |     |     |     |
                                   | _l_ | _l_ | _p_ |
                                   |_____|_____|_____|

Similar characters in the different groups are represented by the same
letter; for example, the symbol for woman, heretofore shown (No. 17), is
represented by _c_, and an unknown character by _d_. Different letters
represent different symbols. It is apparent that we have here the
parallelism heretofore spoken of and are justified in basing conclusions
on this fact.

At 1, 2, and 3 are female figures with a bird in each case perched on the
back. At _a_ is the head of a bird, evidently the symbol of the bird on
the female below; at _i_, in the fourth group, is precisely the same
symbol as the one found in the same relative position in the middle
division of Plate 17 over another bird, and at _m_, in the fifth group,
is another bird's head. From these facts we conclude that the first
symbol in each of these groups denotes a bird, and, as no two are alike,
that they refer to different species, the one at _g_ corresponding with
symbol No. 24, the bird beneath being the great parrot or ara. Other
facts, derived from a careful study of the various groups of this portion
of the codex, which would require much space and numerous illustrations
to explain, lead to the same belief.

According to this conclusion, the following symbols also denote birds,
probably of the species here indicated.

[Illustration: No. 25.]

  _Icim_? The horned owl. This is represented by _a_ in the first group
     in the above diagram.

The bird in the figure under the group, although horned, bears but slight
resemblance to an owl; yet, comparing the marks on the tail with those of
two of the birds on Plate XVIII* of the Manuscript Troano, I think the
interpretation is justified.

[Illustration: No. 26.]

  _Kukuitz_? The Quetzal. The symbol is apparently incomplete, but the
     bird figured under it justifies this conclusion. This symbol is
     represented by _e_ in the above diagram.

If this interpretation be correct, we find in this symbol another of
Landa's letters.

[Illustration: No. 27. _a_ _b_]

  _Kuch._ A vulture or bird of prey much like the sopilote. These two
     symbols (_a_ and _b_) appear to refer to the same bird, evidently a
     vulture. (See Manuscript Troano, Plates XVII_a_ and XXVI*_a_.) The
     first form (_a_) is found but once (Manuscript Troano, Plate
     XVII_a_), the other at several points, both in the Manuscript Troano
     and the Dresden Codex, and is represented by _m_ in the preceding
     diagram.

If this determination be correct, the first of these symbols (_a_) is
probably phonetic and agrees with the interpretation of No. 26.

[Illustration: No. 28.]

  _Cħom_, _Xchom_, or _Hcħom_. The sopilote or vulture. Found only in
     Plates 16 and 17, Dresden Codex. The bird figure in Plate 17
     appears to be intended to represent a vulture. The symbol
     corresponds to _i_ in the preceding diagram.

If phonetic, the word indicated should, according to Landa's alphabet, be
aspirated, which is found to be true of one of the forms given by Perez.

In certain series of the Dresden Codex, which appear to relate to the
four year series or to the four seasons, especially those on Plates
29-31, a certain class of food animals seems to be assigned to each. The
four following symbols are those used to express this idea:

[Illustration: No. 29.]

  _Ceh_? The symbol for game quadrupeds. The same idea appears to be
     indicated by the folded and tied quarter of a deer, as shown in No.
     11. The head shown in the symbol is probably intended for that of
     the deer, though more like that of the rabbit.

[Illustration: No. 30.]

  _Cutz_ or _Cax_. The symbol for game birds, the head being probably
     that of the wild turkey (_Cutz_ or _Ahcutz_).

[Illustration: No. 31.]

  _Huh._ The symbol for food reptiles or the iguana.

As the Kan figure is admitted to be a maize or bread symbol, it is
readily seen that the object in view in connecting it with the animal
figures is to indicate that they are used for food, and hence are proper
offerings to the gods, which is equivalent to saying, to the priests.

[Illustration: No. 32.]

  _Cay._ The symbol for food fishes, or fishes in general, though as
     often on the Kan symbol or without any suffix.

[Illustration: No. 33.]

  _Cutz_ or _Cax_. In one of the two series of these food symbols, in
     Plates 29-31 of the Dresden Codex, in place of the bird symbol No.
     30 is that shown in symbol No. 33. It probably has, as Rosny
     supposes, the same signification, a supposition which is
     strengthened by the fact that it is found in the bird series on
     Plates 16_c_ and 17_c_, same codex, and is represented by _o_ in the
     preceding diagram.


SYMBOLS OF DEITIES.

[Illustration: No. 34.]

  _Ekchuah._ The symbol or hieroglyph of the deity named "Ekchuah" by
     the Mayas and considered the patron and protector of peddlers or
     traveling merchants (Fig. 380).

[Illustration: FIG. 380. The god Ekchuah, after the Troano and Cortesian
Codices.]

The signification of the name of this deity is "The Black Calabash." The
form and the shading of the symbol render it more than probable that it
is a conventional representation of a divided or halved black calabash or
gourd, cut for the purpose of forming it into a cup or dipper, which, in
this form, is considered a symbol of this deity.

The evidence upon which this determination is based is that the symbol
constantly accompanies the red mouthed, black deity. It is found, with a
single exception, only in the Manuscript Troano, and chiefly in Plates II
to V, relating to the traveling merchants. The single exception alluded
to is on Plate 15 of the Cortesian Codex; here the god bears upon his
back the traveling pack, indicating the vocation of which he is the
special guardian.

It occurs unconnected with the figure of the deity only on Plates IX*,
XIV*, XV*, and XXV* of the Manuscript Troano. In the last the figure of
the god is in the same division, but in the adjoining compartment. In
Plate XV* it apparently refers to the idol the priest is carving, which
is probably a black one intended to represent this god. Landa,[358-1]
speaking of the artists carving idols from wood, says:

     They took also that which they used for scarifying their ears and
     drawing blood from them, and also the instruments which they needed
     for sculpturing their _black divinities_.

Its appearance in Plate XIV* is apparently in connection with the
ceremonies relating to the manufacture of idols. Neither the symbol nor
the god it represents is to be fond in the Dresden Codex.

[Illustration: No. 35. _a_ _b_ _c_]

  _Kukulcan._ (?) This is the symbol of the long nosed god, which Dr.
     Schellhas designates "the god with the snake-like tongue," of which
     representations appear so frequently in the different codices (see
     Fig. 381).

The snake-like appendages hanging from the side of the mouth may possibly
be intended to represent a curved fang rather than part of a divided
tongue. A remarkable figure on Plate 72 of the Borgian Codex deserves
special notice here. This is the representation of a deity supposed by
Kingsborough and others to be Quetzalcoatl, in which the head is as
represented in Fig. 382. Here we see both tongue and fang, and also an
eye precisely of the form found in the Maya symbol.

[Illustration: FIG. 381. The long nosed god (Kukulcan) or "god with the
snake-like tongue."]

Whether Kukulcan is the god indicated is uncertain, unless he is
identical with the long nosed god, or Maya Tlaloc, so frequently figured
in the Manuscript Troano and the Cortesian Manuscript. It is only
necessary to compare the figures on Plates 2 to 5 of the latter codex
with the long nosed, green figures of Plates XXVI, XXVII, XXIX, XXX, and
XXXI of the former to be convinced that they represent the same deity,
and that this is the Maya Tlaloc or rain god, whatever may be the name by
which he was known.

As the symbol which accompanies these is the same as that found in
connection with the "snake tongued," long nosed god of the Dresden Codex,
there is no doubt that the same deity is referred to. It is worthy of
notice in this connection that Plates 29-41 of the Dresden Codex, which
are devoted almost exclusively to this deity, refer very largely to
water, the god being figured in connection with water no less than
twenty-eight times. He is also twice colored black, probably to symbolize
the dark rain cloud, and twice blue, denoting water. It is therefore fair
to conclude that the author of this codex considered him the giver of
rain.

[Illustration: FIG. 382. Copy of head from the Borgian Codex
(Quetzalcoatl).]

The following reasons given by Dr. Schellhas for supposing that the deity
indicated is Kukulcan apparently justify his conclusion, though it is
possible some other name may have been applied to him:

     He is represented in all the manuscripts, and far more frequently
     than any other deity. His characteristic marks are always
     unmistakable. An entire section of the Dresden Codex, pp. 29-43, and
     pp. 1 and 2, belonging thereto, treat almost exclusively of this
     god, and wherever he is pictured there we also find his name
     hieroglyph. He is always characterized by the double, snake-like
     tongue hanging from his mouth and by the peculiar eye, two marks
     that are never absent, how numerous and varied soever may be his
     representations, his symbols, and attributes. We also find him with
     torches in his hands as symbols of fire; he sits on water; he stands
     or sits in water or in falling rain; he rides in a boat; he appears
     in company with a fish as symbol of water or in company of a bird's
     head as symbol of the atmosphere, upon the day sign _Cab_ as symbol
     of the earth, sitting, with the ax (machete) in his hand, with
     arrows or spears, with a scepter, and finally, also, with the body
     of a snake. Considering the immense variety of this god's
     representations and the numerous symbols of power in the various
     elements which the deity rules, we may well be justified in assuming
     that there are indications here of one of the most important figures
     in Maya mythology, with one of the principal deities of the people.
     The most important god of the Mayas was Kukulcan, the creator of the
     country's civilization, who had come from the far, unknown east, the
     Mexican Quetzalcohuatl, the Gucumatz of the Kiche, the Kukulcan of
     the Tzendals. All these names mean "feathered snake," "bird snake."
     Now, in the above mentioned section of the Dresden manuscript, pp.
     29-43, there is found on page 36, middle, the representation of a
     bird and a snake, the two symbols of the god Kukulcan, which, at the
     same time, denote his name in the manner of a rebus. That this
     representation is to be referred to the god with the snake's tongue
     is rendered probable on the one hand by the fact that this whole
     section treats of him and is proved on the other hand by the
     circumstance that in the same place the same snake is found
     represented with the head of the god; thus, page 35, middle, and 36,
     above. In the same way this snake with the god's head is also found
     in the Codex Cortesianus, page 10, middle, a passage which is
     rendered notable also by the fact that in the writing above the
     picture there is expressly found as a second sign the name
     hieroglyph of the god.

[Illustration: No. 36. _a_ _b_]

  _Cimi_ (?). Supposed symbols of the god of death. Occurring very
     frequently in all the codices, but with several variations (see
     Figs. 383 and 384).

These are given chiefly on the authority of Drs. Förstemann and
Schellhas, as I have some doubt in reference to this conclusion, for
reasons which will here be given.

[Illustration: FIG. 383. The supposed god of death, from the Dresden
Codex.]

[Illustration: FIG. 384. The supposed god of death, from the Troano
Codex.]

As Dr. Schellhas remarks, this is "the most characteristic and most
easily recognized deity of the Maya Codices"; but this statement will not
apply to the symbols, as the variations are such as to render it
exceedingly doubtful whether precisely the same idea is embodied in each.
Even the two forms here given, both of which are found in all the codices
and often together, present variations too marked for us to believe,
except upon strong evidence, that they represent the same thing. Nor do
the figures of this deity or supposed deity appear to embody throughout
the same idea. In fact, they leave us in doubt as to whether any one
recognized deity is to be understood. Was there in the Maya pantheon such
a deity as the god of death? I have so far been unable to find any
satisfactory reason for answering this question in the affirmative.

In the first part of the Dresden Codex, which is devoted, in part at
least, if not chiefly, to the maladies of the country, the skeleton
figures undoubtedly have reference to death, much like the skull and
cross bones in our day. In other places, as Plates XXVII and XXII* of the
Manuscript Troano and Plate 7 of the Cortesian Codex, the parched earth
appears to be intended, but it must be conceded that here also the idea
of death is included. Substantially the same idea, or at least the
relation of this god to the earth, appears to be indicated in Plate 8 of
the Cortesian Codex, where he is represented as beneath and holding up
that upon which another deity, bearing the bread symbol, is seated.

As before stated the two symbols frequently appear in connection,
sometimes where the god is figured and often where he is not. It is,
therefore, unsafe to conclude as yet that either variety indicates a
particular deity known as the god of death.

[Illustration: No. 37.]

  Symbol of the god with the banded face; seen chiefly in the Manuscript
     Troano; not found in the Dresden Codex (Fig. 385). This is not the
     deity which Dr. Schellhas designates as "the god with face crossed
     by lines."

[Illustration: FIG. 385. The god with the banded face, from the Codex
Troano.]

This deity evidently pertains to the underworld and is closely allied to
the so-called god of death. The symbol and the figure are found together
in but few instances, yet the peculiar markings are such as to leave no
doubt on the mind, that the symbol is intended to denote what is
represented by the figure, being simply the head of the deity as
invariably figured. They appear together in Plates III_c_, V_a_, and
V_b_, XXVIII*_c_, and XXIX_c_ of the Manuscript Troano, in the first two
as having some relation to the traveling merchants, but in the last two
in a very different rôle. The dotted lines with which the bodies of these
figures are marked and the peculiar anklets appear to have been
introduced to signify relationship to the god of death. Perhaps the most
direct evidence of this relation is found in Plate 42 of the Cortesian
Codex, where the two deities are brought together at the sacrifice here
indicated. The two appear to be united in one in the lower division of
Plate XXVI* of the Manuscript Troano.

Figures of this god are also found in some of the Mexican codices, as on
Plate 73 of the Borgian manuscript, where the relation to death and to
the underworld is too apparent to be mistaken. On Plate 10, same codex,
the head of death is marked with the distinguishing black band.

Unfortunately for investigations in this line, the early Spanish notices
of the Maya mythology are so brief and confused that we can derive but
little aid from them in our efforts to identify the deities figured in
these manuscripts. Possibly the one with the banded face may represent
Cumahau or Hunhau, the prince of the lower regions; but the rôle he
appears to play where figured, with the exception of Plate II, Manuscript
Troano, and Plate 73 of the Borgian Codex, would scarcely justify the
name.

[Illustration: No. 38.]

  (?) Symbol of the deity which Dr. Schellhas designates "the god with
     the old man's face." Found in all the codices and almost invariably
     in connection with the representation of the deity shown in our Fig.
     386.

[Illustration: FIG. 386. The god with the old man's face.]

The deity denoted by this symbol and by the figure which it accompanies
is possibly Zamna or Ytzamna, a deified Maya hero, but the various rôles
in which he is found make it difficult to decide on this point. He
appears comparatively few times in the Dresden Codex, and only in the
first few pages. In none of these is there anything to indicate his
functions. In Plates 12_c_ and 15_c_ he holds a sun symbol in his hand,
which might be supposed to refer to his attributes as "Kinich-Kakmo" but
for the fact that the same thing is true of one or two other deities
figured in the same codex. In the Manuscript Troano, where he is oftenest
represented, his figure and his symbol appear most frequently in
connection with the bee or honey industry; for example, on Plate V_c_,
the only place in the first part of the manuscript where honey appears to
be referred to, and twenty-two times in that section of the second part,
Plates I* to X*, relating to bees. He also appears to take an active part
in the manufacture of idols, engages in painting, aids in the culture or
gathering of cacao, engages in predatory excursions, and acts in various
other relations. In the left compartment of Plate XXIV*_a_ he bears on
his head the head of a bird. In the remarkable double plate (41-42) of
the Cortesian Codex he is twice figured, in the central area and at the
east (top), and in each case is accompanied by a female deity. In the
latter case both god and goddess are bearing in their hands the Kan or
corn symbol. In Maya mythology Zamua was given a spouse named Ix
Kan-Leox, which signifies the yellow frond or silk of maize.

[Illustration: FIG. 39.[TN-11]]

  Symbol, according to Dr. Schellhas, of the deity which he names "the
     god with face crossed by lines," found in all the codices, but most
     frequently in the Manuscript Troano and the Cortesian manuscript.
     The deity is usually represented as in Fig. 387.

[Illustration: FIG. 387. The god with face crossed by lines.]

This is introduced here on the authority of Dr. Schellhas, although I
have considerable doubt as to the correctness of his conclusion.

He remarks in regard to it as follows:

     Another characteristic and easily recognized deity, which, it is
     true, is comparatively rare in the Dresden manuscript, but occurs
     with extraordinary frequency in other codices, and whose sign it is
     not hard to find, is the god whose face is crossed [surrounded] by
     peculiar parallel lines, representations of whom are given in the
     Cortesian Codex (p. 11, below) and Dresden Codex (p. 13, middle).
     The deity is always male and is found in the Dresden Codex five
     times, Cortesian Codex eighteen times, Manuscript Troano twenty
     times, and Codex Peresianus five times.

     The sign of this god, as was the case with the others and as seems
     to be the general rule, consists merely of a representation of the
     god's head, combined with a sign which probably represents an affix.
     The sign is found wherever the deity is represented and is an exact
     rendering of the god's head, so that there can be no doubt as to its
     being the name hieroglyph. True variations are not found, the
     hieroglyph being perfectly alike in all the manuscripts.

     The nature of this deity is not easily determined, though it occurs
     in the Codices Troano and Cortesianus with extraordinary frequency,
     so that it would be seen that these two manuscripts, which evidently
     belong together, treat principally of this deity. No analogous deity
     is found in Aztec picture writing. * * * To all appearances we have
     here a momentous figure of Maya mythology, of which, unfortunately,
     we know nothing.

It is true that this symbol is found in almost every instance where the
figure of the god appears--in fact, with fewer exceptions than others in
reference to which there is probably little doubt. It is also true that
the symbol is an exact copy of the god's head; but on the other hand
there are strong reasons for doubting the correctness of Dr. Schellhas's
conclusion.

The first is that the figure of the supposed deity seems to have more
indications of being the conventional representation of an idol than of a
deity. The lines of the head are precisely the same as those on the heads
of the carved idols.[365-1]

We also find it in connection with the wood symbol (marginal No. 6) at
the only points where the latter is found in the Cortesian Codex, and,
what is significant, in wholly inappropriate places unless connected with
an idol figure. These are found in the lower division of Plates 10 and
11, two on the top of thatched roofs and another on the head of the deity
called the "god with the old man's face," the head in the latter case
being apparently carved from a block of wood.

The second is to the same effect, the symbol being found over each of the
figures of the lower division of Plates 26, 27, and 28 of the Cortesian
Codex and the middle division of Plates XXXI* and XXXII* of the
Manuscript Troano, where there appear to be processions of the different
deities. It is also significant that in the latter case each deity is
bearing in his hands what seems to be a block of wood from which in all
probability an idol is to be carved.

Third, we find rows or lines composed entirely of this symbol, as in the
so-called title page of the Manuscript Troano.


DISCUSSION AS TO PHONETIC FEATURES OF THE CHARACTERS.

It must be admitted, as heretofore intimated, that this question has not
as yet been satisfactorily answered. Whether what is here presented will
suffice to settle this point in the minds of students of American
paleography is doubtful; nevertheless, it is believed that it will bring
us one step nearer the goal for which we are so earnestly striving.
Something is said on this subject in my former work,[365-2] which need
not be repeated here.

As it is evident from the preceding list of characters that conventional
signs and symbols, often nothing more than abbreviated pictographs, were
used in many cases to designate objects and persons, the inference to be
drawn, unless other evidence is adduced, is, that this method prevailed
throughout. Nevertheless there is some evidence that at the date when
these manuscripts were written Maya culture was in a transition state;
that is to say, conventional symbols were passing into true
ideographs[366-1] and possibly into phonetic characters.

The lack of any satisfactory key to assist us in deciphering them makes
it exceedingly difficult to decide how far this change had progressed. We
are therefore left wholly to deductions to be drawn from the facts
obtained by laborious comparisons of the various relations in which the
characters are found and the uses which appear to be made of them in the
manuscript.

It will be admitted without question that a large number of these
characters are ideographs or conventional symbols, as distinguished from
pictures, as, for example, most of those denoting the days, months, and
cardinal points. I say most of these, as it is yet possible to learn from
some of them the objects they were intended to represent, the
characteristic features not being entirely lost, as the symbol for the
day Cimi, the "death's head" or skull; that of the day Ymix, "the grain
of maize;" that of the month Moan, "the head of the moo or ara," a
species of parrot, &c.

It is also possible to show from the manuscripts themselves evidences of
the changes from conventional pictographs to true or mnemonic symbols.

Take, for instance, the bird symbols on Plates 16, 17, and 18 of the
Dresden Codex, presented in the preceding marginal figures numbered 24,
25, 26, 27, 28, and 33. If the determination be correct as given, it is
apparent that, while one of the birds is indicated by the head as a
symbol, the others are denoted by ideographs, or by phonetic characters
bearing no resemblance to their forms or peculiar features. That numerous
examples of this kind are to be found in these manuscripts will be
admitted by all who have carefully studied them.

Another fact bearing upon this point is the difference between the
Dresden Codex and the Manuscript Troano in regard to marking with symbols
the things represented in the pictures. We fail to find in the former
(unless that on Plate 30 be a possible exception) the earth or soil
represented by any symbol, though frequently occurring in the latter and
also occasionally in the Cortesian Codex. The symbol for wood or that
appearing so often on wooden articles in the latter, and occasionally in
the Cortesian Codex, is wanting in the Dresden Codex, though wooden
articles are several times represented. From this we infer that the
Manuscript Troano is a more recent production than the Dresden Codex,
notwithstanding the evidences of greater skill in drawing and higher
mathematical attainments shown in the latter.

Before discussing the question of phonography we ask attention to one or
two facts regarding Landa's alphabet which do not appear to have been
previously noticed, yet have an important hearing on the subject.

The failure to reach any satisfactory results with this alphabet proves,
beyond a reasonable doubt, that this author was mistaken as to the
character of the Maya writing; yet the frequent occurrence in the
manuscripts of most, if not all, of the elements he presents renders it
certain that there is a basis of truth on which it rests. It is probable,
therefore, if we can find the key to his method, we may, after all,
obtain some satisfactory results by means of his alphabet.

I have already stated as my belief that--

     He has undertaken to pick out of their compound or syllabic
     characters the letter elements; hence it is that, while we find it
     impossible to decipher the manuscripts by using them, yet we find
     such frequent resemblances as to compel us to admit a fundamental
     relationship.[367-1]

This opinion I still believe to be correct, but was, until very recently,
unable to get any positive evidence as to his method of obtaining these
elements.

While examining the Cortesian Codes I came across (on Plate 17) the
symbol for a turtle (the different varieties of which are shown in
marginal figure No. 4), which is nothing more or less than an attempt to
represent the head of the animal. In the more abbreviated form (_b_) I at
once recognized Landa's A (compare with _c_ and _d_, No. 4). As the Maya
name of the turtle is _Ac_ or _Aac_ it is apparent that in this instance
the old Spanish priest selected a symbol representing an object the name
of which contains a single syllable having, as its chief letter element,
A. As this symbol is simply a representation of the animal's head there
is no reason to infer that it is phonetic; on the contrary, it is more
reasonable to assume that it was used only as a conventional sign. It is
possible that after long usage it may have been adopted as a phonetic
character, though its exceedingly rare occurrence in the manuscripts
(being found only in the Cortesian Codex and with the turtle figure) and
the fact that it is seldom, if ever, used as part of a compound character
would seem to forbid this idea.

Precisely the same method was adopted in obtaining his B, which is given
in two forms, first as a foot print and second as a circle inclosing four
circular dots. The first, as all are aware, is only a conventional sign
and presumably not phonetic. The second may be phonetic, though
apparently but an abbreviation of the first. In Plate 65_c_ (see marginal
No. 20) and Plate 41_c_ the two forms are brought into such relation to
each other as to show that the latter is used as a symbol to represent
the idea conveyed by the first. The proof in these cases is too strong
to admit of doubt and explains Landa's method of obtaining his B, which,
as before stated, was by selecting the symbol of that which is denoted by
a Maya word of one syllable having B as its chief letter element, _Be_
being the Maya word for "way," "journey," "walking," &c.

The symbol for the cacao given above in marginal No. 22 contains his
eleventh letter _Ca_ twice and is probably that from which it was taken;
likewise that of the _Kukuitz_ or Quetzal (marginal No. 26) and of the
_Kuch_ or vulture (marginal No. 27_a_), each of which contains his _Ku_,
being double in the former and single in the latter. I am as yet unable
to trace these two symbols to their origin; we might suppose, from
Landa's figure of the latter, that it was intended to represent a bird's
nest containing eggs, but an examination of the symbol as found in the
manuscript renders this conclusion doubtful.

The evidences of phonography are few and, as must be admitted, not
entirely satisfactory; yet they are apparently sufficient to justify the
somewhat general belief that the writing of the Mayas had reached that
stage where characters are sometimes used to indicate sounds. That
comparatively little advance had been made in this direction at the time
of the conquest is possible; moreover there is nothing to justify the
belief that they made use of true letters as Landa supposed. If they had
a phonographic system of any kind it was very imperfect and was only in
that primary stage in which syllables are represented by single
characters and words of more than one syllable by compound characters.
Judging by the changes observed in the relation of the parts of compound
characters to one another, we conclude that the order of arranging these
parts was not uniform or essential. It is also doubtful, if any of these
characters are phonetic, whether the parts of the longer words were
always written out in full. I am led to believe, from a few slight
indications, that, in forming words of more than one syllable, they often
used only the leading phonetic elements of the single words of which they
are composed; in other words, that they followed the rebus method of the
Mexicans.

Descending to particulars and examples, the following are, perhaps, the
strongest proofs which can be presented on this point:

As there can no longer be any doubt that the symbols for the cardinal
points have been ascertained and that those relating to the polar points
are distinguishable from those relating to the equatorial points, we are
justified in referring to them in this discussion. As each of the two
assigned to the equatorial points contains the symbol for "sun" or "day"
and as the two Maya words for these points--_Likin_ or _Lakin_ and
_Chikin_--contain the Maya term for sun or day ("kin"), there is some
reason for believing that the characters are phonetic. There is to be
added to this evidence the fact that the symbol of the month _Yaxkin_
contains the same sun symbol. It would be somewhat remarkable to find the
same single character in three different combinations, representing three
different ideas expressed by words containing the same sound, yet having
no reference to the sound.

It is now generally admitted by students of American paleography, on what
appears to be satisfactory evidence, that symbol No. 7 of the preceding
list, _Cab_, is used to signify "earth" or "land" and "honey," both of
which are designated by the same Maya term, _Cab_. As there is no
similarity in the things denoted the character is probably phonetic. The
"bee" appears also to be frequently indicated by the same character with
an affix, as may be seen by reference to the lower divisions of Plates
III*--X* of the Manuscript Troano.

The symbol No. 9 (U) of the preceding list is found repeatedly on vases
and also as a prefix to both simple and compound characters. As _U_ in
Maya signifies "moon," "vase," and certain pronouns and is also used as a
euphonic particle before vowels, we are perhaps justified in concluding
that the symbol is phonetic and denotes the word _U_. I am aware that
neither Perez nor Dr. Brinton gives "vase" as one of the meanings of this
word, yet its constant appearance on vessels seems to leave no doubt that
Brasseur is correct. Even admitting that he is mistaken and that we are
in error as to the signification of the symbol, its various uses justify
the belief that it is phonetic.

The symbol No. 34 of the preceding list, which is supposed to be that of
the god Ekchuah, is probably phonetic. The name of this deity is composed
of two Maya words, _ek_, "black," and _chu_, "calabash," and hence
signifies "the black calabash," and the form and coloring of the symbol
are apparently intended to denote this signification. If this
interpretation be correct it is phonetic, as there is nothing in or
pertaining to the figure of the deity which corresponds with it, except
the color.

If the interpretation given of the preceding symbols Nos. 22, 24, 26,
27_a_, and 33 be correct, there can be scarcely a doubt that they are
phonetic. In the first--_cacau_, _cacauak_, or _cacauche_, the "cacao"--we
see Landa's letter _Ca_, which is doubled in each of the three forms taken
from the different codices. In the twenty-sixth--_Kukuitz_, the
Quetzal--Landa's _Ku_ is duplicated, as it should be if phonetic, while in
27_a_, _Kuch_, it appears but once. There is here also an additional
evidence of phoneticism in the fact that, while one of the symbols used to
denote this bird shows simply its head, and is surely not phonetic, the
other is entirely different and bears no resemblance whatever to any
feature or characteristic of the bird. Moreover, both parts of it are used
in other combinations referring to entirely different things.

If my interpretation of No. 14 (_Xamach_ or _Chimix_) be right, it is
probably phonetic also. It is composed, as will be seen by reference to
the figure, of two symbols closely resembling that for the day Ymix,
except that the top portion of one is omitted. The resemblance in sound
to a duplication of Ymix is apparent. The slight but permanent variation
of the right hand portion from the usual Ymix symbol and the omission of
the top portion of the left hand one are scarcely explainable on the
supposition that they form simply a conventional sign; but if phonetic
the reason is apparent, as the _m_ sound is not repeated in the Maya
name. This conclusion is strengthened by the fact that the month _Mac_,
found in the last or bottom line of Plate 49, is precisely the same as
the right portion of No. 14, with Landa's symbol for _Ca_ added. This
probably justifies us in concluding that the true name of this month is
_Camach_, "the jaw" or "jaws," and that Landa's figure is simply a rude
representation of the lips or mouth.

I have expressed the opinion[370-1] that the chief phonetic element of
No. 8 (the stone symbol), if used to represent sound, is _p_ or _pp_.
This opinion seems to be confirmed by the fact that this character is
found as a part of the symbol for the month _Pop_ on Plate 50 of the
Dresden Codex. (See the second character in the first transverse line
below the day columns in the preceding Fig. 362.) The method of
determining the months referred to in these plates of the codex has been
given in the preceding part of this paper.

The interpretation given above of symbol No. 24 (the moo or ara) will
probably be accepted by all students of these manuscripts, and if so its
phonetic character must be conceded. That it is used in the place above
alluded to (Dresden Codex, Plate 16_c_) to denote this bird is proved by
the parallelism of the groups and the figure of the parrot under it. If
we turn now to Plate 48 of this codex we observe that the second
character of the first line below the day columns and the first character
in the upper line of the lower group or square is, in each case, a bird's
head. It is easily proved by means of the numeral series with which these
are connected that they denote, in both cases, the month Moan (from the
moo), proving that Brasseur's surmise was correct.[370-2] If the same
bird is represented by two symbols, one pictorial and the other having no
resemblance to any feature or character of the thing denoted, it is
probable the latter is phonetic. This conclusion is strengthened in this
case by the strong resemblance of the first part of No. 24 to the symbol
for the month Mol.

I have shown above that the right portion of No. 20 of the list is
Landa's letter B, and also that in the lower division of Plate 65,
Dresden Codex (see Fig. 378), it signifies "footsteps" or the act of
walking. As the Maya word _Be_ signifies "journey," "wood," "march," and
also "journeying" and "marching," it is possible that this symbol is also
phonetic, although apparently only a modified form of the footprint. This
supposition is strongly supported by the fact that it is found in
numerous and varied relations, single and in combination.

The symbol for 20 (_Kal_), No. 1 of the preceding list, is apparently
phonetic. This view appears to be confirmed by its use otherwise than as
a numeral symbol at several points in the text of the Manuscript Troano.
For example, in the third division of Plate XVII* it appears in this
form, [Illustration: Hieroglyph] while immediately below is the
representation of an idol head in a vessel covered with a screen or
basket, as shown in Fig. 388. The Maya verb _Kal_ signifies to "imprison"
or "inclose," which is certainly appropriate to what we see in the
figure. As the symbol is over each of the three similar figures in the
division, it is probable that it is intended to denote something relating
to or observable in them. In the second division of Plates XV* and XVI*,
same codex, is this symbol, [Illustration: Hieroglyph] several times
repeated, and below each the figure of a priest or deity at work, each
carving, with a machete or hatchet, the head of an idol. The probable
signification is "Give twice twenty strokes with a machete," and hence is
but partially phonetic.

[Illustration: FIG. 388. Wooden idol in vessel with basket cover.]

Other examples bearing on this question may be found, but these are
believed to be sufficient to warrant the belief that at the time these
codices were written Maya culture had reached that stage where the idea
of phoneticism was being introduced into the writing. Yet it is certain,
and even susceptible of demonstration, that a large portion, perhaps the
majority, of the characters are symbols. The more I study these
characters the stronger becomes the conviction that they have grown out
of a pictographic system similar to that common among the Indians of
North America. The first step in advance appears to have been to
indicate, by characters, the gesture signs.


FOOTNOTES:

[345-1] See Chapter VI, Study of the Manuscript Troano, by Cyrus Thomas.

[354-1] Unfortunately the scrolls were overlooked in preparing the cut.

[358-1] Relacion de las cosas de Yucatan, p. 308.

[365-1] See Plates XVI*_b_ and XVII*_c_, Manuscript Troano.

[365-2] Study of the Manuscript Troano, pp. 141-161.

[366-1] As the term "ideograph" is somewhat broad and comprehensive, it
may be well enough to state that I use it as expressing that stage of
symbolic writing where the picture characters have so changed that all
resemblance to the objects they were originally intended to represent is
lost, and therefore they can only be considered as mnemonic signs.

[367-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 142, 143.

[370-1] Study of the Manuscript Troano, p. 147.

[370-2] Landa's Relacion, pp. 382, 383, Note 1.



INDEX


Adelung, J. C. cited 262

Aglio, Augustina, fac simile of Dresden Codex by 263-266


Böttiger, C. A., mention of Dresden Codex by 262
  controversy with Abert concerning Dresden Codex 267

Brasseur, copy of the Manuscript Troano by 284, 286, 343
  cited 350


Calendar system, tabular view of 270-374

Charency, H. de, cited 282

Codex Cortesianus, similarity of, to Manuscript Troano and Dresden
Codex 286


Dresden Codex, numerals in 261-338


Ebert, F. A., description of Dresden Codex by 263
  controversy with Böttiger concerning Dresden Codex 267


Falkenstein, K. C., preservation of Dresden Codex by 268

Fleischer, H. L., mention of Dresden Codex by 263

Förstemann, E., citation from Die Mayahandschrift of 261-269
  cited 272, 278, 280, 281, 283, 290, 292, 293, 300, 301, 302, 303, 304,
  305, 320, 322, 329, 330, 339, 340


Götze, J. C., preservation of Dresden Codex by 261
  biographical sketch of 261, 262


Humboldt, A. von, notice of Dresden Codex by 262, 263


Kingsborough, Lord, Dresden Codex copied by order of 262
  Mexican Antiquities of, cited 266


Landa, cited 348

Landa's alphabet, insufficiency of 259, 347


Manuscript Troano, copy of, by Brasseur 285, 286, 343
  study of, by C. Thomas, cited 339, 343, 344, 345, 350, 365, 366, 367, 370

Maya and Mexican manuscripts, C. Thomas on, cited 280

Maya Codices, aids to the study of, by C. Thomas 253-371

Mexican Antiquities, by Lord Kingsborough, cited 266, 267


Rosny, L. de, cited 267, 347, 355, 357


Schellhas, P., cited 345, 359, 360, 361, 362, 364

Schultz-Sellack, K., cited 278

Silvestre, É., Paléographie universelle of, cited 267


Thomas, C., paper on aids to the study of the Maya codices by 253-371

Troano Manuscript, copy of, by Brasseur 285, 286, 343


Vater, J. S., cited 262



Transcriber's Note:

  TN-1   267  "hasty and obtrusive notice." should read 'hasty and
              obtrusive notice.'
  TN-2   272  indi cated should read indicated
  TN-3   291  "and" repeated.
  TN-4   295  Plate 48, 2nd line first asterisk is missing.
  TN-5   296  Period missing after FIG
  TN-6   322  In the original text, the 7 is printed above the 17, with
              no horizontal line separating the two numbers.
  TN-7   327  Tables XXI and XXII are not labeled in the original
              publication but, by context, appear to be the two sections
              of table following Table XX.
  TN-8   338  Sixth column should read Sixth column.
  TN-9   338  Footnote number for 338-1 was missing. It was inserted
              based on the context of the note.
  TN-10  348  Illustration No. 6 was missing the caption.
  TN-11  364  Fig. 39 should read No. 39





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