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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
the text.
Tables XX, XXI, and XXII were too wide to fit within the character limits
of the text file for this ebook. They have been broken into two parts.
Special characters:
The following characters used in the original publication are not
available in the character set used for this version of the book. They
have been replaced with the following codes.
[=h] Small h with stroke
[(1)] Circled 1
[(2)] Circled 2
[(3)] Circled 3
[(4)] Circled 4
[(5)] Circled 5
[(6)] Circled 6
[(7)] Circled 7
[(8)] Circled 8
[(9)] Circled 9
[(10)] Circled 10
[(11)] Circled 11
[(12)] Circled 12
[(13)] Circled 13
[(I)] Circled I
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. Foerstemann'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 Goetze, 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 Goetze'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.
"Goetze 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 Goetze
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.'
"Goetze 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 Goetze 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.'
"Goetze 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, Goetze did not know
that the Vatican Codex was of an entirely different nature from the
Dresden Codex.
"In spite of the high value which Goetze 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 Goetze, the first to mention our codex is C. A. Boettiger, in his
Ideas on Archaeology (Dresden, 1811, pp. 20, 21), without, however, saying
anything that we did not already know from Goetze. Still Boettiger 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 Boettiger'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 Boettiger, 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 OEdipus;' whereupon he cites the writing
of Boettiger. 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 Goetze
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] Boettiger, 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 Boettiger, 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 archaeologist 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, Paleographie universelle,
Paris, 1839-'41, fol.; in Rosny, Les ecritures figuratives et
hieroglyphiques des peuples anciens et modernes, Paris, 1860, 4to; and
also in Madier de Montjou, Archives de la societe americaine de France,
2^de serie, 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. Foerstemann,
in his late work on the Dresden Codex (Erlaeuterungen zur Mayahandschrift
der Koeniglichen oeffentlichen 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. Foerstemann 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 x 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 Foerstemann'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
Foerstemann), 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 Foerstemann'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 Foerstemann'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 Foerstemann'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. Foerstemann,[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. Foerstemann 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
Foerstemann'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. Foerstemann, 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.
Foerstemann 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. Foerstemann 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 Foerstemann'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
Foerstemann'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
Foerstemann.[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 Foerstemann'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. Foerstemann[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 x 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. Foerstemann 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 x 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 x 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. Foerstemann, 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. Foerstemann'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 Foerstemann.
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.