Chapter I: The Numerals in the Dresden Codex (1)

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, ; and fifteen, by three such lines: . According to this system, a straight line and a dot, thus, , would denote 6; two straight lines and two dots, , 12; and three straight lines and four dots, , 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:

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: 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.

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.