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diff --git a/19777.txt b/19777.txt new file mode 100644 index 0000000..40d9d7a --- /dev/null +++ b/19777.txt @@ -0,0 +1,5943 @@ +Project Gutenberg's Aids to the Study of the Maya Codices, by Cyrus Thomas + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Aids to the Study of the Maya Codices + Sixth Annual Report of the Bureau of Ethnology to the + Secretary of the Smithsonian Institution, 1884-85, + Government Printing Office, Washington, 1888, pages 253-372 + +Author: Cyrus Thomas + +Release Date: November 13, 2006 [EBook #19777] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK STUDY OF THE MAYA CODICES *** + + + + +Produced by PM for Bureau of American Ethnology, Julia +Miller, and the Online Distributed Proofreading Team at +http://www.pgdp.net (This file was produced from images +generously made available by the Bibliotheque nationale +de France (BnF/Gallica) at http://gallica.bnf.fr) + + + + + +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. + +Immediately below each of these four column day series are four lines of +characters (hieroglyphics), and immediately under the latter three +horizontal lines of black numerals, with here and there a red, diamond +shaped symbol inserted. As these numerals stand directly in the vertical +lines of the day columns, it is possible the two have some connection +with each other, a supposition somewhat strengthened by what has been +observed in regard to the red numerals at the bottom of the plates. To +test this and also for the reason that we propose to discuss their +relations and their use, we give here the bottom line of days of each of +the five series (or plates), together with their week numbers attached; +also, the numbers of the three lines of black numerals mentioned, taking +them in the order of the paging as here shown: + +_Plate_ 46: + VIII Cib. VII Cimi. X Cib. V Kan. + 1 1 + 11 16 10 11 + 16 6 16 4 + +_Plate_ 47: + VII Ahau. VI Oc. IX Ahau. IV Lamat. + 2 2 3 3 + 5 9 4 4 + 0 10 0 8 + +_Plate_ 48: + VI Kan. V Ix. VIII Kan. III Eb. + 3 4 4 4 + 16 2 15 15 + 3(?) 14 4 12 + +_Plate_ 49: + V Lamat. IV Ezanab. VII Lamat. II Cib. + 5 5 6 6 + 9 13 8 8 + 8 18 8 16 + +_Plate_ 50: + IV Eb. III Ik. VI Eb. 1 Ahau. + 7 7 8 8 + 3 7 1 2 + 12 2 12 0 + +In considering these horizontal lines it is to be understood that the +series runs through the five pages, 46-50. + +Let us proceed upon the supposition that the figures of the lowest of the +three lines denote days of the month, the numbers of the middle line +months, and those of the upper line years. As already shown, the interval +between 8 Cib and 7 Cimi is 4 months and 10 days; adding 4 months and 10 +days to 11 months and 16 days (bearing in mind that 20 days make a month +and 18 months a year), the sum is found to be 16 months and 6 days, +precisely the figures under 7 Cimi. As already ascertained, the interval +between 7 Cimi and 10 Cib is 12 months and 10 days; this added to 16 +months and 6 days gives 1 year, 10 months, 16 days, precisely the figures +under 10 Cib. The interval between 10 Cib and 5 Kan is 8 days; this added +to the 1 year, 10 months, and 16 days gives 1 year, 11 months, and 4 +days, the figures under 5 Kan. The interval between 5 Kan and 7 Ahau is +11 months, 16 days, which, added to the preceding, gives 2 years, 5 +months, 0 day, agreeing with the figures under 7 Ahau, if the symbol +represented by 0 signifies nought. That this rule holds good throughout +the entire series, by making one correction, is shown by the following +additions: + +Years. Months. Days. + 11 16 Under VIII Cib, Plate 46. + 4 10 + -- -- + 16 6 Under VII Cimi, Plate 46. + 12 10 + -- -- + 1 10 16 Under X Cib, Plate 46. + 8 + -- -- -- + 1 11 4 Under V Kan, Plate 46. + 11 16 + -- -- -- + 2 5 0 Under VII Ahau, Plate 47. + 4 10 + -- -- -- + 2 9 10 Under VI Oc, Plate 47. + 12 10 + -- -- -- + 3 4 0 Under IX Ahau, Plate 47. + 8 + -- -- -- + 3 4 8 Under IV Lamat, Plate 47. + 11 16 + -- -- -- + 3 16 4[300-1] Under VI Kan, Plate 48. + 4 10 + -- -- -- + 4 2 14 Under V Ix, Plate 48. + 12 10 + -- -- -- + 4 15 4 Under VIII Kan, Plate 48. + 8 + -- -- -- + 4 15 12 Under III Eb, Plate 48. + 11 16 + -- -- -- + 5 9 8 Under V Lamat, Plate 49. + 4 10 + -- -- -- + 5 13 18 Under IV Ezanab, Plate 49. + 12 10 + -- -- -- + 6 8 8 Under VII Lamat, Plate 49. + 8 + -- -- -- + 6 8 16 Under II Cib, Plate 49. + 11 16 + -- -- -- + 7 2 12 Under IV Eb, Plate 50. + 4 10 + -- -- -- + 7 7 2 Under III Ik, Plate 50. + 12 10 + -- -- -- + 8 1 12 Under VI Eb, Plate 50. + 8 + -- -- -- + 8 2 0 Under I Ahau, Plate 50. + +The proof of the correctness of the theory advanced may, therefore, be +considered conclusive, as it amounts, in fact, to a mathematical +demonstration. + +Dr. Foerstemann, who considers these lines of black numbers, standing one +above another, as representing different grades of units--thus, the +lowest, single units; the second, units twenty-fold the lower; the third, +eighteen-fold the second; the fourth, twenty-fold the third, &c.--has +found the correct intervals of the series, which he states are 236, 90, +250, and 8 days, agreeing with our 11 months, 16 days; 4 months, 10 days; +12 months, 10 days, and 8 days. + +As all the discoveries mentioned herein were made previous to the receipt +of Dr. Foerstemann's work, I give them according to my own method, +acknowledging any modification due to his work. Although I shall compare +special results from time to time, an explanation of Dr. Foerstemann's +method is reserved for a future paper, as his work was not received until +I was revising my notes for publication. + +The foregoing explanation of the series shows it to be very simple and +makes it clear that it relates to the day columns at the top of the +pages. Still, there is one point somewhat difficult to understand. Are +the numbers of the third or lowest line intended to denote the positions +in the month of the days in the columns above? If so, the month must have +commenced with Ymix, as can readily be shown in the following manner: + +TABLE III. + + 1. Ymix. + 2. Ik. + 3. Akbal. + 4. Kan. + 5. Chicchan. + 6. Cimi. + 7. Manik. + 8. Lamat. + 9. Muluc. + 10. Oc. + 11. Chuen. + 12. Eb. + 13. Been. + 14. Ix. + 15. Men. + 16. Cib. + 17. Caban. + 18. Ezanab. + 19. Cauac. + 20. Ahau. + +If we write in a column in proper order the 20 days of the Maya month, +commencing with Ymix, and number them consecutively, as in Table III, we +shall find by comparison that the numbers in the lower line indicate the +position, in this column, of the days directly over them. Take, for +example, the lower line of black numerals on Plate 46, writing over them +the respective days of the columns, thus: + + Cib. Cimi. Cib. Kan. + 16 6 16 4 + +Referring to Table III we see that Cib is the sixteenth day, Cimi the +sixth, and Kan the fourth. + +The days and numbers of Plate 47 are: + + Ahau. Oc. Ahau. Lamat. + 0 10 0 8 + +Ahau is the twentieth day--here is the diamond shaped symbol--Oc is the +tenth, and Lamat the eighth, and so on to the end of the series on Plate +50. + +It may be justly argued that such relation to some given day of the month +would necessarily follow in any series of this kind made up by adding +together intervals of days and months. Still it is not at all likely that +these series were made up without reference to fitted and determinable +dates. If so, the months given must be months of certain determinable +years, and the days denoted must be days of particular months. In other +words, if we had the proper starting point we should be able to determine +the position in the calendar of any day or month mentioned in the series. + +First. It is easily seen by reference to the calendar (Table II) that Cib +is not the sixteenth day of the month of any of the four years, nor is +Cimi the sixth nor Kan the fourth. The idea that the figures of this +lower line represent the days of the month must, therefore, be given up +unless we assume that the year commenced with Ymix. It may be worthy of +notice at this point that the list of days on the so-called "title page" +of the Manuscript Troano begins with Ymix. It is also true that the +remarkable quadruple series in the Codex Cortesianus on Plates 13-18 +commences with Ymix; as this is evidently some kind of a calendar table, +its bearing on the question now before us is important. + +Second. It can easily be shown that the months referred to in the series, +if the numbers given denote specific months, are not those of the Kan +years. The first, 8 Cib, if in the eleventh month, must be in the year 4 +Kan; counting forward from this 4 months and 10 days to 7 Cimi brings us +into the sixteenth month of the year 4 Kan; this agrees with our figures +on Plate 46. Counting forward 12 months and 10 days to 10 Cib, we reach +the tenth month of the next year; 8 days more carry us to the eleventh +month, which still agrees with the figures in the codex. Counting 11 +months and 16 days more to 7 Ahau, we reach but do not pass the fourth +month of the next year; hence the result does not correspond with the +series, which has at this point a 5 in the middle line. The same will be +found true in regard to the other years as given in our calendar (Table +II). This result, as a matter of course, must follow if the figures in +the lower line of the series do not denote the month days of some one of +the year series as usually given. + +Another fact also becomes apparent here, viz, that the 5 supplemental +days of the year are not brought into the count, the year consisting +throughout of 360 days. There is, in fact, nothing here indicating the +four year series as given in the authorities and as represented in our +calendar table; yet this ought to appear wherever a series extends over +more than one year. + +Dr. Foerstemann says that this entire series of black numerals covers +2,920 days, or 8 years of 365 days. This is true, but the concluding +figures show that it is given by the writer of the codex as 8 years and 2 +months, which would also be 2,920 days, counting the years at 360 days +each and the months 20 days each; moreover, the members of the series are +based throughout upon the year of 360 days. His theory that the intervals +of the series relate to the movements of the planet Venus is, as yet, a +mere hypothesis, which needs further proof before it can demand +acceptance; but his discovery of the methods of identifying the month +symbols on the five plates now under consideration is important. Although +I had noticed that most of the characters which he mentions are month +symbols, I did not succeed in identifying all of them. + +According to his conclusion, which appears to be justified not only by +the evidence he gives but by an additional fact that I shall, presently +mention, there are four of these symbols in the upper row of the middle +group of written characters on each plate and four in the upper and lower +lines of the lower group on each plate (see, for example, Fig. 362). Each +of these symbols (except three or four) has a black number attached to it +which denotes the day of the month represented by the symbol. + +These months and days as given by Dr. Foerstemann are as follows, the +positions of the lines as here given corresponding with those of the +plates: + +TABLE IV.--_Table showing months and days._ + + _____________________________________________________________________ + | Month. Day. | Month. Day. | Month. Day. | Month. Day. + |--------------+--------------+--------------+-------------- + Plate 46 | 7 4 | 11 14 | 5 19 | 6 7 + | 11 8 | 15 18 | 10 4 | 10 12 + | 1 14 | 6 4 | 18 14 | 1 2 + Plate 47 | 18 3 | 4 8 | 16 18 | 17 6 + | 4 3 | 8 13 | 2 18 | 3(not 2) 6 + | 10 10 | 15 3 | 9 8 | 9 16 + Plate 48 | 10 17 | 15 7 | 9 12 | 10 20 + | 15 2 | 1 7 | 13 17 | 14 5 + | 3 7 | 7 17 | 2 2 | 2 10 + Plate 49 | 3 11 | 8 1 | 2 6 | 2 14 + | 7 16 | 12 6 | 6 11 | 6 19 + | 14 6 | 18 16 | 13 1 | 13 9 + Plate 50 | 14 10 | 18 20 | 13 5 | 13 13 + | 18 15 | 5 20 | 17 10 | 17 18 + | 6 20 | 11 10 | 5 15 | 6 3 + --------------------------------------------------------------------- + + +An examination of the plates will show that Dr. Foerstemann has filled out +the following obliterated or wanting day numbers, to wit, the first of +the upper line of Plate 46, the fourth of the upper line of Plate 47, and +the second of the middle line and first of the lower line of Plate 50. He +has also ventured to change the first day number of the lower line of +Plate 46 from 16 to 14. Where the number 20 is found in his list there is +no corresponding number in the codex, the month symbol only being given. +It is evident he has proceeded in these cases upon the theory that the +absence of a number indicated that the month was completed. Although +probably correct in this conclusion, the question will arise, Does the +symbol in such cases denote the _month completed_ or the _month reached?_ + +The intervals between these dates are as follows, the left hand column +being those between the first and second columns of Foerstemann's list +(our Table IV), the second column those between the second and third +columns of his list, the third column those between the third and fourth +columns of his list, and the fourth column those between the last date of +one plate and the first of the next: + +TABLE V.--_Table showing intervals between dates._ + + _____________________________________________________________________ + | Month. Day. | Month. Day. | Month. Day. | Month. Day. + |--------------+--------------+--------------+-------------- + | | | | + Plate 46 | 4 10 | 12 5 | 0 8 | 11 16 + | 4 10 | 12 6_b_| 0 8 | 11 11 + | 4 10 | 12 10 | 0 8 | 9 8_d_ + Plate 47 | 4 5 | 12 10 | 0 8 | 11 11 + | 4 10 | 12 5 | 0 8_c_| 11 16_e_ + | 4 13_a_| 12 5 | 0 8 | 11 11 + Plate 48 | 4 10 | 12 5 | 8 | 11 11 + | 4 5 | 12 10 | 0 8 | 11 11 + | 4 10 | 12 5 | 0 8 | 11 16 + Plate 49 | 4 10 | 12 5 | 0 8 | 11 16 + | 4 10 | 12 5 | 0 8 | 11 16 + | 4 10 | 12 5 | 0 8 | 11 11 + Plate 50 | 4 10 | 12 5 | 0 8 | 11 11 + | 4 5 | 12 10 | 0 8 | 11 10 + | 4 10 | 12 5 | 0 8 | 12 11_g_ + --------------------------------------------------------------------- + +Although it is apparent that the variations from the intervals of the +black numeral and day series above them are too numerous and too uniform +to be considered mistakes, yet there is little reason to doubt that these +month numbers are connected with and depend upon the day series given in +the columns above. + +That there are some errors is quite clear; for instance, the variation at +_a_ arises from the fact that Dr. Foerstemann gives the date here as 10 +months, 10 days, whereas the codex has it 10 months, 13 days. Making this +correction the interval will be 4 months, 10 days. The correction will +make the interval at _d_ 9, 11, instead of 9, 8. Still there is a +variation of two months from the usual interval, which, if corrected on +the supposition that Dr. Foerstemann has mistaken the month, would +necessitate a change of the remainder of the series given in this line. +The interval at _c_, according to the figure given by Dr. Foerstemann, +would be retrograde, that is, minus 12. This arises from the fact that he +gives the last date in the middle line on Plate 47 as 2 months, 6 days, +whereas the symbol is very distinctly that of the third month, and the +eight day series is unbroken if this correction is made. + +When these evident errors are corrected the series of intervals show +very clearly a system and periodicity depending on the day column series +in the upper part of the pages. In the first column (Table V) the +interval is usually 4 months, 10 days, precisely the same as between the +first and second day columns, but occasionally it is 4 months, 5 days, +which will still bring it to one of the four day series, including the +day indicated by the date--4 months, 10 days. This will be understood by +examining our calendar (Table II). The corresponding days in the four +year columns were, by the Maya system, necessarily brought together in +the calendar; for example, they are arranged in the series pictured on +Plates 13-18 of the Cortesian Codex precisely as given in our Table II. +This skip of five days is also apparent in the second and fourth columns +of differences (Table V). Whether Dr. Foerstemann is correct in all his +identifications of months among the symbols on the five plates now under +consideration is a question I feel unqualified to answer without a much +more careful comparison and study of these characters than I have given +them. + +Running through the upper division of Plates 53 to 58 and continued +through the lower division of Plates 51 to 58--that is to say, commencing +in the upper division of 53 and running into 58, then back to the lower +division of 51 and ending in 58--is a remarkable compound series. It +consists, first, of a three line series of black numerals standing above; +second, a middle series of short, three day columns, or columns each of +three day symbols, with red numerals attached; and, third, below, a two +line series of numerals, those of the upper line red and of the lower +black numbers. + +As this series is a very important one in the study of the relations of +the numerals to one another and to the days indicated, an exact copy of +it is given in Figs. 363-370, each figure representing a page and the +whole standing in the same order as in the original. The red numerals and +red symbols are, as usual, given in outline as an indication of their +color. + +[Illustration: FIG. 363. Copy of Plate 51, Dresden Codex.] + +[Illustration: FIG. 364. Copy of Plate 52, Dresden Codex.] + +[Illustration: FIG. 365. Copy of Plate 55, Dresden Codex.] + +[Illustration: FIG. 366. Copy of Plate 54, Dresden Codex.] + +[Illustration: FIG. 367. Copy of Plate 55, Dresden Codex.] + +[Illustration: FIG. 368. Copy of Plate 56, Dresden Codex.] + +[Illustration: FIG. 369. Copy of Plate 57, Dresden Codex.] + +[Illustration: FIG. 370. Copy of Plate 58, Dresden Codex.] + +In order to assist those not familiar with the numeral and day symbols, +the entire series is given in the following tables in names and Arabic +and Roman numerals, as usual. The obliterated symbols and numbers are +restored. + +TABLE VI.--_Table of numeral and day symbols._ (Plate 51_b_.) + + ______________________________________________________________________ + 14 | 15 | 15 | 16 | 16 | 17 + 16 | 7 | 16 | 7 | 16 | 5 + 14 | 11 | 8 | 5 | 2 | 10 + IV Ik. | XII Cauac.| VII Cib. | II Been.| X Oc. | II Ezanab. + V Akbal.|XIII Ahau. |VIII Caban. |III Ix | XI Chuen|III Cauac. + VI Kan. | I Ymix. | IX Ezanab.| IV Men. |XII Eb. | IV Ahau.[VI-1] + VIII | VIII | VIII | VIII | VIII | VII + 17 | 17 | 17 | 17 | 17 | 8 + ---------------------------------------------------------------------- + +[VI-1] The symbol in this case is that of Been, but this is a manifest +error, as Ahau follows Cauac. + +TABLE VII.--_Table of numeral and day symbols._ (Plate 52_b_.) + + ____________________________________________________________ + | 17 | 18 | 18 | 19 + | 14 | 5 | 14 | 4 + | 8 | 5 | 2 | 19 + | XI Cib. | VI Been.| I Oc. | IX Manik. + [Picture.] | XII Caban. | VII Ix. | II Chuen.| X Lamat. + | XIII Ezanab. |VIII Men. |III Eb. | XI Muluc. + | VIII | VIII | VIII | VIII + |17? (18)[VII-1]| 17 | 17 | 17 + ------------------------------------------------------------ + +[VII-1] The variation from the rule found here is explained a little +further on. + +TABLE VIII.--_Table of numeral and day symbols._ (Plate 53_a_.) + + ______________________________________________________________________________________ + | 1 | 1 | | 2 | 2 | + 7 | 17 | 7 | | 15 | 6 | 15 + 17 | 18 | 2 | |14?(19)[VIII-1]| 16 | 13 + VI Kan. | I Ymix. | VI Muluc.|[Picture.]| I Cimi. |IX Akbal. |IV Ahau. + VII Chicchan.| II Ik. | VII Oc. | | II Manik. | X Kan. | V Ymix. + VIII Cimi. |III Akbal.|VIII Chuen.| | III Lamat. |XI Chicchan.|VI Ik. + VIII | VIII | VII | | VIII | VIII | VIII + 17 | 17 | 8 | | 17 | 17 | 17 + -------------------------------------------------------------------------------------- + +[VIII-1] The 14 here is manifestly an error, one of the lines in the +number symbol having been omitted; it should be 19. + +TABLE IX.--_Table of numeral and day symbols._ (Plate 53_b_.) + + _____________________________________________________________________ + | 1 | | 1 | 1 | 1 + 19 | 0 | | 0 | 1 | 1 + 13 | 3 | | 12 | 2 | 11 + 16 | 4 | | 1 | 18 | 15 + IV Kan. |IX Eb. |[Picture.]|IV Muluc.| XII Cimi. | VII Akbal. + V Chicchan.| X Been.| | V Oc. |XIII Manik.|VIII Kan. + VI Cimi. |XI Ix. | |VI Chuen.| I Lamat.| IX Chicchan. + VIII | VII | | VIII | VIII | VIII + 17 | 8 | | 17 | 17 | 17 + --------------------------------------------------------------------- + +TABLE X.--_Table of numeral and day symbols._ (Plate 54_a_.) + + ____________________________________________________________________________________ + 3 | 3 | 4 | 4 | 5 | 5 | 6 + 6 | 15 | 6 | 15 | 5 | 10 | 4 + 11 | 8 | 5 | 5 | 19 | 16 | 4 + XIII Ezanab.|VIII Men. |III Eb. | XI Muluc.| VI Cib. | I Akbal. | VI Chuen. + I Cauac. | IX Cib. | IV Been.| XII Oc. | VII Caban. | II Kan. | VII Eb. + II Ahau. | X Caban.| V Ix. |XIII Chuen.|VIII Ezanab.|III Chicchan.|VIII Been. + VIII | VIII | VIII | VIII | VIII | VIII | VII + 17 | 17 | 17 | 17 | 17 | 17 | 8 + ------------------------------------------------------------------------------------ + + +TABLE XI.--_Table of numeral and day symbols._ (Plate 54_b_.) + + _______________________________________________________________ + 1 | 1 | 1 | 1 | | 1 + 2 | 2 | 3 | 3 | | 4 + 2 | 11 | 2 | 9 | | 0[XI-1] + 12 | 9 | 6 | 14 | | 11 + II Ahau.| X Caban. | V Ix. | X Ik. |[Picture]| V Cauac. + III Ymix.| XI Ezanab.| VI Men.| XI Akbal.| | VI Ahau. + IV Ik. |XII Cauac. |VII Cib.|XII Kan. | |VII Ymix. + VIII | VIII | VIII | VII | | VII[XI-2] + 17 | 17 | 17 | 8 | | 17 + --------------------------------------------------------------- + +[XI-1] The 0 inserted at various points in these tables denotes as usual +the red, diamond shaped symbol, which apparently signifies "nought." + +[XI-2] The numeral symbol in this case, both in Kingsborough's copy and +in the photograph, is VII, one dot having been omitted by a mistake of +the original artist. + +TABLE XII.--_Table of numeral and day symbols._ (Plate 55_a_.) + + ____________________________________________________________________________ + | 8 | 7 | 7 | 8 | 8 + | 13 | 3 | 12 | 3 | 12 + | 2 | 18 | 16 | 13 | 10 + | II Muluc.[XII-1]| X Cimi. | V Akbal. |XIII Ahau.|VIII Caban. + [Picture]|III Oc. | XI Manik.| VI Kan. | I Ymix.| IX Ezanab. + | IV Chuen. |XII Lamat.|VII Chicchan.| II Ik. | X Cauac. + | VIII | VIII | VIII | VIII | VIII + | 17 | 17 | 17 | 17 | 17 + ---------------------------------------------------------------------------- + +[XII-1] In Kingsborough's work the symbol in this case is that of Been, +but should be Muluc, as it is in the photograph. + +TABLE XIII.--_Table of numeral and day symbols._ (Plate 55_b_.) + + __________________________________________________________________________________________ + 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 + 4 | 5 | 5 | 6 | 6 | 6 | 7 | 7 + 9 | 0 | 9 | 0 | 8 | 17 | 8 | 15 + 8 | 6 | 3 | 0 | 17 | 14 | 11 | 19 + XIII Cib. |IX Ix. |IV Chuen.| XII Lamat.| VII Chicchan.| II Ik. | X Cauac.| II Manik. + I Caban. | X Men.| V Eb. |XIII Muluc.|VIII Cimi. |III Akbal.| XI Ahau. |III Lamat. + II Ezanab.|XI Cib.|VI Been. | I Oc. | IX Manik. | IV Kan. |XII Ymix. | IV Muluc. + VIII | VIII | VIII | VIII | VIII | VIII | VIII | VII + 17 |17?(18)| 17 | 17 | 17 | 17 | 17 | 8 + ------------------------------------------------------------------------------------------ + +TABLE XIV.--_Table of numeral and day symbols._ (Plate 56_a_.) + + ____________________________________________________________ + 9 | | 9 | 10 | 10 + 1 | | 10 | 1 | 10 + 18 | | 15 | 12 | 9 + XIII Chicchan.| |VIII Ik. |III Cauac.| XI Cib. + I Cimi. |[Picture]| IX Akbal.| IV Ahau. | XII Caban. + II Manik. | | X Kan. | V Ymix. |XIII Ezanab. + VII | | VIII | VIII | VIII + 8 | | 17 | 17 | 17 + ------------------------------------------------------------ + +TABLE XV.--_Table of numeral and day symbols._ (Plate 56_b_.) + + _________________________________________________________ + | 1 | 1 | 1 | 1 + | 8 | 8 | 9 | 9 + | 6 | 15 | 6 | 15 + | 16 | 14 | 11 | 8 + [Picture]| X Kan. | VI Ik. | I Cauac.|IX Cib. + | XI Chicchan.| VII Akbal.| II Ahau. | X Caban. + |XII Cimi. |VIII Kan. |III Ymix. |XI Ezanab. + | VIII | VIII | VIII | VIII + | 17 | 17?(8) | 17 | 17 + --------------------------------------------------------- + +TABLE XVI.--_Table of numeral and day symbols._ (Plate 57_a_.) + + ______________________________________________________ + 11 | 11 | 12 | 12 | + 1 | 10 | 1 | 8 | + 6 | 4 | 0 | 8 | + VII Ix. | II Chuen.| X Lamat.| II Cib. | + VIII Men.|III Eb. | XI Muluc.|III Caban. |[Picture] + IX Cib.| IV Been. |XII Oc. | IV Ezanab. | + VIII | VIII | VIII | VIII[XVI-1]| + 17 | 17 | 17 | 17[XVI-2]| + ------------------------------------------------------ + +[XVI-1] This should be VII. + +[XVI-2] This should be 8. + +TABLE XVII.--_Table of numeral and day symbols._ (Plate 57_b_.) + + __________________________________________________________________ + 1 | 1 | 1 | | 1 | 1 + 10 | 10 | 11 | | 11 | 12 + 6 | 15 | 4 | | 13 | 4 + 5 | 2 | 10 | | 7 | 4 + IV Been.| XII Oc. |IV Ezanab.|[Picture]| XII Men. | VII Eb. + V Ix. |XIII Chuen.| V Cauac. | |XIII Cib. |VIII Been. + VI Men. | I Eb. |VI Ahau. | | I Caban.| IX Ix. + VIII | VIII | VII | | VIII | VIII + 17 | 17 | 8 | | 17 | 17 + ------------------------------------------------------------------ + +TABLE XVIII.--_Table of numeral and day symbols._ (Plate 58_a_.) + + ____________________________________________ + 12 | 13 | 13 | 14 + 17 | 8 | 17 | 7 + 5 | 2 | 0 | 17 + X Been.| V Oc. | I Lamat.|II Chicchan. + XI Ix. | VI Chuen.| II Muluc.| X Cimi. + XII Men. |VII Eb. |III Oc. |XI Manik. + VIII | VIII | VIII | VIII + 17 | 17 | 17 | 17 + -------------------------------------------- + +TABLE XIX.--_Table of numeral and day symbols._ (Plate 58_b_.) + + ________________________________ + 1 | 1 | + 12 | 13 | + 13 | 3 | + 1 | 18 | + II Muluc.| X Cimi. |[Picture.] + III Oc. | XI Manik.| + IV Chuen.|XII Lamat.| + VIII | VIII | + 17 | 17 | + -------------------------------- + +The spaces in the lists indicate the positions of the pictures of persons +and curtain-like ornaments inserted here and there, as seen in Figs. +363-370. + +In order to explain this series, we commence with that portion of it +found in the lower division of Plate 51 (Fig. 363). + +Omitting any reference for the present to the black numbers over the day +columns, we call attention first to the days and to the red numerals +attached to them. Those in the division selected as an illustration are +as follows: + + IV Ik. XII Cauac. VII Cib. II Been. X Oc. II Ezanab. + V Akbal. XIII Ahau. VIII Caban. III Ix. XI Chuen. III Cauac. + VI Kan. I Ymix. IX Ezanab. IV Men. XII Eb. IV Ahau.[317-1] + +It will be observed that the week numbers of the days in each single +column follow one another in regular arithmetical order, thus: in the +first column, 4, 5, 6; in the second, 12, 13, 1; in the third, 7, 8, 9; +and so on throughout the entire series. The interval, therefore, between +the successive days of a column is 1; or, in other words, the days follow +one another in regular order, as in the month series, so that having the +first day of a column given we know at once the other two. It is +apparent, therefore, that the intervals between the three correspondingly +opposite days of any two associate columns are the same; that is to say, +the interval between 5 Akbal and 13 Ahau, in the first two columns given +above is the same as that between 4 Ik and 12 Cauac, and also as that +between 6 Kan and 1 Ymix. This is also true if the attached week numbers +are omitted; for instance, the interval between Ik and Cauac, counting on +the list of days forming the month, is 17 days, and it is the same +between Kan and Ymix. Taking the second and third columns we find here +the same interval. This holds good in that part of the series above given +until we reach the last two columns; here the interval between Oc and +Ezanab is 8 days and it is the same between the other days of these two +columns. + +This being ascertained, the next step is to determine the true interval +between the first days of these columns, taking the numbers attached to +them into consideration. Referring to our calendar (Table II) and (for +reasons which will be given hereafter) using the Muluc column and +counting from 4 Ik, as heretofore explained, we find the interval between +this and 12 Cauac to be 8 months and 17 days; counting in the same way +from 12 Cauac, 8 months and 17 days more bring us to 7 Cib; 8 months and +17 days more to 10 Oc. So far the intervals have been the same; but at +this point we find a variation from the rule, as the interval between 10 +Oc and 2 Ezanab (first of the next column) is 7 months and 8 days. + +These intervals furnish the explanation of the red and black numerals +below the day columns. + +These numerals, as the reader will observe by reference to Fig. 363 or +the written interpretation thereof in Table VI, are 8 and 17 under the +first five columns, but 7 and 8 under the sixth column, the red (8 under +the first five and 7 under the sixth) indicating the months and the black +(17 under the first five and 8 under the sixth) the days of the +intervals. This holds good throughout all that portion of the series +running through the lower divisions of Plates 51 to 58, with three +exceptions, which will now be pointed out. + +In order to do this it will be necessary to repeat here a part of the +series on Plate 51_b_ and part of that on Plate 52_b_; that is, the two +right hand columns of the former and the two left hand columns of the +latter, between which is the singular picture shown in the _lower left +hand corner_ of our Fig. 364: + + ___________________________________________________________________ + Plate 51_b_. || Plate 52_b_. + --------------------------++--------------------------------------- + X Oc. | II Ezanab. || | XI Cib. | VI Been. + XI Chuen. | III Cauac. || | XII Caban. | VII Ix. + XII Eb. | IV Ahau. || [Picture.] | XIII Ezanab. | VIII Men. + VIII | VII || | VIII | VIII + 17 | 8 || | 17 | 17 + ------------------------------------------------------------------- + +As before stated, the interval between 10 Oc and 2 Ezanab is 7 months and +8 days, as indicated by the red and black numerals under the latter. +According to the red and black numbers under the column commencing with +11 Cib, the interval between 2 Ezanab and 11 Cib should be 8 months and +17 days, the usual difference, when, in fact, as we see by counting on +the calendar, it is 8 months and 18 days. That this variation cannot be +attributed to a mistake on the part of the author or of the artist is +evident from the fact that the interval between 11 Cib and 6 Been (first +of the next column) is 8 months and 17 days and that the difference +throughout the rest of the series follows the rule given; that is to say, +each is 8 months and 17 days, except at two other points where this +variation is found and at the regular intervals where the difference of +7 months and 8 days occurs.[319-1] Precisely the same variation occurs on +Plate 55_b_ in passing from the first to the second column and on Plate +56_b_ between columns 1 and 2. + +Why these singular exceptions? It is difficult, if not impossible, for +us, with our still imperfect knowledge of the calendar system formerly in +vogue among the Mayas, to give a satisfactory answer to this question. +But we reserve further notice of it until other parts of the series have +been explained. + +Reference will now be made to the three lines of black numerals +immediately above the day columns. Still confining our examinations to +the lower divisions, the reader's attention is directed to these lines, +as given in Tables VI, VII, IX, XI, XIII, XV, XVII, and XIX. As there are +three numbers in each short column we take for granted, judging by what +has been shown in regard to the series on Plates 46-50, that the lowest +of the three denotes days, the middle months, and the upper years, and +that the intervals are the same between these columns as between the day +columns under them. The correctness of this supposition is shown by the +following additions: Starting with the first or left hand column on Plate +51_b_, we add successively the differences indicated by the corresponding +red and black numbers under the day columns. If this gives in each case +(save the two or three exceptions heretofore referred to) the numbers in +the next column to the right throughout the series, the demonstration +will be complete. + +Years. Months. Days. + 14 16 14 First column on Plate 51_b_. + 8 17 + -- -- -- + 15 7 11 Second column on Plate 51_b_. + 8 17 + -- -- -- + 15 16 8 Third column on Plate 51_b_. + 8 17 + -- -- -- + 16 7 5 Fourth column on Plate 51_b_. + 8 17 + -- -- -- + 16 16 2 Fifth column on Plate 51_b_. + 7 8 + -- -- -- + 17 5 10 Sixth column on Plate 51_b_. + 8 18[319-1] + -- -- -- + 17 14 8 First column on Plate 52_b_. + 8 17 + -- -- -- + 18 5 5 Second column on Plate 52_b_. + 8 17 + -- -- -- + 18 14 2 Third column on Plate 52_b_. + 8 17 + -- -- -- + 19 4 19 Fourth column on Plate 52_b_. + 8 17 + -- -- -- + 19 13 16 First column on Plate 53_b_. + 7 8 + -- -- -- + 20 3 4 Second column on Plate 53_b_. + +At this point in the original, instead of 20 in the year series, we find +a diamond shaped symbol, represented by 0 in our tables, with one black +dot over it. From this it would seem that when this codex was written the +Maya method of counting years was by periods of 20 each, as in the case +of the month days. Whether there is any reference here to the ahaues is +uncertain. I am inclined to think with Dr. Foerstemann that it was rather +in consequence of the use of the vigesimal system in representing +numbers. It would have been very inconvenient and cumbersome to represent +high numbers by means of dots and lines; hence a more practicable method +was devised. It is evident, from the picture inserted at this point in +the series, that some important chronological event is indicated. Here +also in the written characters over this picture is the symbol for 20. +The last number given in the above addition may therefore, in order to +correspond with the method of the codex, be written as follows: + +Twenty year periods. Years. Months. Days. + 1 0 3 4 + +Continuing the addition in this way the result is as follows: + +Twenty year periods. Years. Months. Days. + 1 0 3 4 + 8 17 + -- -- -- -- + 1 0 12 1 Third column on Plate 53_b_. + 8 17 + -- -- -- -- + 1 1 2 18 Fourth column on Plate 53_b_. + 8 17 + -- -- -- -- + 1 1 11 15 Fifth column on Plate 53_b_. + 8 17 + -- -- -- -- + 1 2 2 12 First column on Plate 54_b_. + 8 17 + -- -- -- -- + 1 2 11 9 Second column on Plate 54_b_. + 8 17 + -- -- -- -- + 1 3 2 6 Third column on Plate 54_b_. + 7 8 + -- -- -- -- + 1 3 9 14 Fourth column on Plate 54_b_. + 8 17 + -- -- -- -- + 1 4 0 11 Fifth column on Plate 54_b_. + 8 17 + -- -- -- -- + 1 4 0 8 First column on Plate 55_b_. + 8 18[321-1] + -- -- -- -- + 1 5 0 6 Second column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 5 9 3 Third column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 6 0 0 Fourth column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 6 8 17 Fifth column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 6 17 14 Sixth column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 7 8 11 Seventh column on Plate 55_b_. + 7 8 + -- -- -- -- + 1 7 15 19 Eighth column on Plate 55_b_. + 8 17 + -- -- -- -- + 1 8 6 16 First column on Plate 56_b_. + 8 18[321-2] + -- -- -- -- + 1 8 15 14 Second column on Plate 56_b_. + 8 17 + -- -- -- -- + 1 6 6 11 Third column on Plate 56_b_. + 8 17 + -- -- -- -- + 1 9 15 8 Fourth column on Plate 56_b_. + 8 17 + -- -- -- -- + 1 10 6 5 First column on Plate 57_b_. + 7 8 + -- -- -- -- + 1 10 15 2 Second column on Plate 57_b_. + 7 8 + -- -- -- -- + 1 11 4 10 Third column on Plate 57_b_. + 8 17 + -- -- -- -- + 1 11 13 7 Fourth column on Plate 57_b_. + 8 17 + -- -- -- -- + 1 12 13 1 Fifth column on Plate 57_b_. + 8 17 + -- -- -- -- + 1 12 13 1 First column on Plate 58_b_. + 8 17 + -- -- -- -- + 1 13 3 18 Second column on Plate 58_b_. + +The proof, therefore, that the theory advanced in regard to the order and +the plan of the series is correct seems to be conclusive. This probably +would have been conceded without the repeated additions given, but these +were deemed necessary because of several irregularities found in that +portion running through Plates 53_a_-58_a_, which constitutes the first +half of the series. + +Turning back to our Table VIII, representing that part of the series on +Plate 53_a_, we will consider the three lines of black numerals above the +day columns, discussing the irregularities as we proceed. + +The numbers in the first column are 7/17,[TN-6] or, according to the +explanation given, 7 months and 17 days. There is apparently a mistake +here, the correct numbers being 8 months and 17 days, as it is the usual +custom of the codex to commence numeral series with the prevailing +interval; moreover this correction, which has also been made by Dr. +Foerstemann, is necessary in order to connect rightly with what follows; +the counters under this first column require this correction, as they are +8 months, 17 days. Making this change we proceed with the addition. + +Years. Months. Days. + 8 17 First column, Plate 53_a_ (corrected). + 8 17 + -- -- + 17 14 Second column. Plate 53_a_. + +Here the author of the codex has made another mistake or varied from the +plan of the series. As several similar variations or errors occur in this +part of the series, it will be as well to discuss the point here as +elsewhere. Dr. Foerstemann, in discussing the series, takes it for granted +that these variations are errors of the aboriginal scribe; he remarks +that "It is seen here that the writer has corrected several of his +mistakes by compensation. For instance, the two first differences should +be 177 [8 months, 17 days] and 148 [7 months, 8 days], not 176 and 149," +&c. + +This is a strained hypothesis which I hesitate to adopt so long as any +other solution of the difficulty can be found. It is more likely that the +writer would have corrected his mistakes, if observed, than that he would +compensate them by corresponding errors. + +Going back to that part of the series in the lower divisions which has +already been examined and commencing with Plate 51_b_ (see Table VI), we +observe that the numbers in the lowest of the three lines of black +numerals, immediately over the day columns, and the first day of these +columns are as follows (omitting the week days attached): + + 14 11 8 5 2 10 + Ik. Cauac. Cib. Been. Oc. Ezanab. + +Turning to the calendar (Table II) and using the Muluc column, we notice +that the figures of this third line of black numerals denote respectively +the month numbers of the days under them; that is to say, Ik is the +fourteenth day of the month in Muluc years, Cauac the eleventh, Cib the +eighth, Been the fifth, Oc the second, and Ezanab the tenth. This holds +good through Plates 52_b_ to 58_b_ without a single exception, provided +the diamond shaped symbol in the fourth column of Plate 55_b_ is counted +as 20. This test, therefore, presents fewer exceptions than are found in +counting the intervals as before explained; yet, after all, this would +necessarily result from the fact that the day Muluc was selected as the +commencement of the series, and hence may have no signification in +reference to or bearing on the question of the year series, especially as +the years counted are evidently of 360 days. + +Returning now to our Table VIII, representing Plate 53_a_, we observe +that the number immediately over Kan in the first column is 17, whereas +Kan is the sixteenth day of the month. Is it not possible that the +intention was to designate as the ceremonial day Chicchan, standing +immediately below, which is the seventeenth day of the month in Muluc +years? Even though there is no reference to Muluc years, the intervals +may be given upon the same idea, that of reaching, for some particular +reason, the second or third day of the column instead of the first. This +would account for the compensation of which Dr. Foerstemann speaks, +without implying any mistake on the part of the writer. These +irregularities would then be intentional variations from the order of the +series, yet so as not to break the general plan. + +The interval between 6 Kan of the first column (with the month number +corrected) and 1 Ymix of the second is 8 months and 17 days, as it should +be; between 6 Muluc and 1 Cimi, 8 months and 17 days; and between 1 Cimi +and 9 Akbal, 8 months and 17 days, thus conforming to the rule heretofore +given, a fact which holds good as a general rule throughout that portion +of the series in the upper division. + +Continuing the addition as heretofore we note the variations. + +Years. Months. Days. Column. Plate. + 17 14 Second. 53_a_. + 7 8 + -- -- -- + 1 7 3 Third. 53_a_. + 8 17 + -- -- -- + 1 15 19[323-1] Fourth. 53_a_. + 8 17 + -- -- -- + 2 6 16 Fifth. 53_a_. + 8 17 + -- -- -- + 2 15 13 Sixth. 53_a_. + 8 18[323-2] + -- -- -- + 3 6 11 First. 54_a_. + 8 17 + -- -- -- + 3 15 8 Second. 54_a_. + 8 17 + -- -- -- + 4 6 5 Third. 54_a_. + 8 17 + -- -- -- + 4 15 2[324-1] Fourth. 54_a_. + 8 17 + -- -- -- + 5 5 19 Fifth. 54_a_. + 8 17 + -- -- -- + 5 14[324-2] 16 Sixth. 54_a_. + 7 8 + -- -- -- + 6 4 4 Seventh. 54_a_. + 8 18[324-3] + -- -- -- + 6[324-4] 13 2 First. 55_a_. + 8 17 + -- -- -- + 7 3 19[324-5] Second. 55_a_. + 8 17 + -- -- -- + 7 12 16 Third. 55_a_. + 8 17 + -- -- -- + 8 3 13 Fourth. 55_a_. + 8 17 + -- -- -- + 8 12 10 Fifth. 55_a_. + 7 8 + -- -- -- + 9 1 18 First. 56_a_. + 8 17 + -- -- -- + 9 10 15 Second. 56_a_. + 8 17 + -- -- -- + 10 1 12 Third. 56_a_. + 8 17 + -- -- -- + 10 10 9 Fourth. 56_a_. + 8 17 + -- -- -- + 11 1 6 First. 57_a_. + 8 17 + -- -- -- + 11 10 3 Second. 57_a_. + 8 17 + -- -- -- + 12 1 0 Third. 57_a_. + 7 8[325-1] + -- -- -- + 12 8 8 Fourth. 57_a_. + 8 17 + -- -- -- + 12 17 5 First. 58_a_. + 8 17 + -- -- -- + 13 8 2 Second. 58_a_. + 8 18[325-2] + -- -- -- + 13 17 0 Third. 58_a_. + 8 17 + -- -- -- + 14 7 17 Fourth. 58_a_. + 8 17 + -- -- -- + 14 16 14 First. 51_b_.[325-3] + +We have in what has thus far been given a satisfactory explanation of the +meaning and use of the lines of numerals and also of their relation to +the day columns, but we still fall short of a complete interpretation, +inasmuch as we are unable to give the series a definite location in the +Maya calendar or in actual time. It is apparent, however, that the series +cannot by any possible explanation be made to agree with the calendar +system as usually accepted, as there is nothing in it indicating the four +series of years or the year of 365 days. It may be safely assumed, I +think, from what has been shown, that the year referred to in the series +is one of 360 days, with probably a periodic addition of one day, but the +reason of the addition is not yet apparent. + +If the numbers in the lowest line of numerals over the day columns +indicate the days of the month, and those of the middle line the +respective months of the year, it is evident, as before stated, that +Muluc is the first day of the year throughout, a conclusion +irreconcilable with the Maya calendar as hitherto understood. It is +probable, however, that the month and day numbers do not refer to +particular months and days, but are used only as intervals of time +counted from a certain day, which must in this case have been Muluc. + +The sum of the series as shown by the numbers over the second column of +Plate 58_b_ is 33 years, 3 months, and 18 days. As this includes only the +top day of this column (10 Cimi), we must add two days to complete the +series, which ends with 12 Lamat. This makes the sum of the entire +series 33 years, 4 months, or 11,960 days, precisely 46 cycles of 13 +months, or 260 days each, the whole and also each cycle commencing with +13 Muluc and ending with 12 Lamat. It is also worthy of notice that in +the right hand column of characters (hieroglyphics) over the inverted +figure in Plate 58_b_ two numbers, 13 and 12, are found attached to +characters which appear to be abnormal forms of month symbols. + +On Plates 63 and 64 are three series of ten day columns each and three +lines of numerals over each series. These are as follows, so far as they +can be made out, the numbers over the upper series being mostly +obliterated. The 0 denotes the red, diamond shaped symbol which is here +sometimes given in fanciful forms. + +TABLE XX.--_Table showing series of day columns, with lines of numerals._ + + UPPER DIVISION. + __________________________________________________________________________ + | | + Plate 63. | Plate 64. | + --------------------------------------------+-----------------------------| + 4 | 3 | | | 0 | + 8 | 6 | | 0 | 16 | + 0 | 0 | 0 | 0 | 0 | + III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| + Kan. | Kan. | Kan. | Kan. | Kan. | + Ix. | Ix. | Ix. | Ix. | Ix. | + Cimi. | Cimi. | Cimi. | Cimi. | Cimi. | + XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. | + ______________|______________|______________|______________|______________| + | + Plate 64. | + ____________________________________________ _____________________________| + | | | | | + 0 | 0 | | | | + 12 | 8 | 3 | 3 | | + 0 | 0 | 0 | 0 | 0 | + III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| + Kan. | Kan. | Kan. | Kan. | Kan. | + Ix. | Ix. | Ix. | Ix. | Ix. | + Cimi. | Cimi. | Cimi. | Cimi. | Cimi. | + XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. | + ______________|______________|______________|______________|______________| + + MIDDLE DIVISION.[TN-7] + ___________________________________________________________________________ + | | | | | + XIX 5 | 4 | 4 | 4 | 4 | + IV 1 | 14 | 9 | 5 | 0 | + IV 0 | 0 | 0 | 7 | 16 | + III Chicchan.| III Ix. | III Akbal. | III Eb. | III Ymix. | + Kan. | Been. | Ik. | Chuen. | Ahau. | + Ix. | Akbal. | Eb. | Ymix. | Oc. | + Cimi. | Men. | Kan. | Been. | Ik. | + XIII Akbal. |XIII Eb. |XIII Ymix. |XIII Oc. |XIII Cauac. | + ______________|______________|______________|______________|______________| + | | | | | + 3 | 3 | 3 | 3 | 2 | + 14 | 9 | 5 | 0 | 14 | + 5 | 14 | 3 | 12 | 1 | + III Oc. | III Cauac. | III Lamat. | III Caban. | III Cimi. | + Muluc. | Ezanab. | Manik. | Cib. | Chicchan.| + Cauac. | Lamat. | Caban. | Cimi. | Men. | + Chuen. | Ahau. | Muluc. | Ezanab. | Manik. | + XIII Lamat. |XIII Caban. |XIII Cimi. |XIII Men. |XIII Kan. | + ______________|______________|______________|______________|______________| + + LOWER DIVISION.[TN-7] + ___________________________________________________________________________ + | | | | | + 2 | 2 | 2 | 1 | 1 | + 9 | 4 | 0 | 13 | 9 | + 10 | 19 | 8 | 17 | 6 | + III Men. | III Kan. | III Been. | III Ik. | III Chuen. | + Ix. | Akbal. | Eb. | Ymix. | Oc. | + Kan. | Been. | Ik. | Chuen. | Ahau. | + Cib. | Chicchan.| Ix. | Akbal. | Eb. | + XIII Been. |XIII Ik. |XIII Chuen. |XIII Ahau. |XIII Muluc. | + ______________|______________|______________|______________|______________| + | | | | | + 1 | 1 | | | | + 4 | 0 | 13 | 9 | 4 | + 15 | 4 | 13 | 2 | 11 | + III Ahau. | III Muluc. | III Ezanab. | III Manik. | III Cib. | + Cauac. | Lamat. | Caban. | Cimi. | Men. | + Muluc. | Ezanab. | Manik. | Cib. | Chicchan.| + Ymix. | Oc. | Cauac. | Lamat. | Caban. | + XIII Ezanab. |XIII Manik. |XIII Cib. |XIII Chicchan.|XIII Ix. | + ______________|______________|______________|______________|______________| + +By examining carefully the lines and columns of the middle and lower +divisions of the plates--those represented in Tables XXI and XXII--we +ascertain that the two together form one series; but, contrary to the +method which has prevailed in those examined, it is to be read from +_right_ to _left_, commencing with the right hand column of the lower and +ending with the left hand column of the middle division. + +As proof of this we have only to note the fact that the series of black +numerals over the day columns ascends towards the left. Assuming the +lowest of the three lines to be days, the middle one months, and the +upper one years, the common difference is 4 months and 11 days. Numbering +the ten columns of each of our tables from left to right as usual and +adding successively the common difference, commencing with the tenth +column of the lowest division, of which Cib is the first day, the result +will be as follows: + +Years. Months. Days. + 4 11 Over tenth column, lower division. + 4 11 + -- -- + 9 2 Over ninth column, lower division. + 4 11 + -- -- + 13 13 Over eighth column, lower division. + 4 11 + -- -- + 1 0 4 Over seventh column, lower division. + 4 11 + -- -- -- + 1 4 15 Over sixth column, lower division. + 4 11 + -- -- -- + 1 9 6 Over fifth column, lower division. + 4 11 + -- -- -- + 1 13 17 Over fourth column, lower division. + 4 11 + -- -- -- + 2 0 8 Over third column, lower division. + 4 11 + -- -- -- + 3 4 19 Over second column, lower division. + 4 11 + -- -- -- + 2 9 10 Over first column, lower division. + 4 11 + -- -- -- + 2 14 1 Over tenth column, middle division. + 4 11 + -- -- -- + 3 0 12 Over ninth column, middle division. + 4 11 + -- -- -- + 3 5 3 Over eighth column, middle division. + 4 11 + -- -- -- + 3 9 14 Over seventh column, middle division. + 4 11 + -- -- -- + 3 14 5 Over sixth column, middle division. + 4 11 + -- -- -- + 4 0 16 Over fifth column, middle division. + 4 11 + -- -- -- + 4 5 7 Over fourth column, middle division. + 4 11 + -- -- -- + 4 9 18 Over third column, middle division. + 4 11 + -- -- -- + 4 14 9 Over second column, middle division. + 4 11 + -- -- -- + 5 1 0 Over first column, middle division. + +The red numerals over the first column of the middle division, except the +lowest diamond shaped one, are omitted, as they do not appear to belong +to the series. + +It must be borne in mind that the 4 months and 11 days form the common +difference between the corresponding days of the columns counting from +right to left; that is to say, counting 4 months and 11 days from the top +day of any column will bring us to the first or top day of the next +column to the left. The interval between the other corresponding days of +the columns is also the same if the same week numbers are assigned them. + +This question arises here, Does the difference include the time embraced +in the entire column? That is to say, Is this interval of 4 months and 11 +days (referring, for example, to the tenth and ninth columns of the lower +division, our table) the sum of the intervals between 3 Cib and Men; Men +and Chicchan; Chicchan and Caban; Caban and 13 Ix, and 13 Ix of the tenth +column and 3 Manik of the ninth column? If not, the columns do not form a +continuous series or must be taken in some other order. + +Although Dr. Foerstemann discovered the order in which the series as a +whole was to be read, and also the common difference--given, as is his +custom, in days--he failed to furnish further explanation of the group. + +In answer to the question presented I call attention to the following +facts: + +Commencing again with the uppermost day, 3 Cib, of the tenth column, +lowest division, and counting on the calendar to 13 Ix of the same year, +the interval is found to be 10 months and 18 days, which is much more +than the interval between 3 Cib and 3 Manik (first of the ninth column), +and of course cannot be included in it. + +Reversing the order in reading the columns, but counting forward on the +calendar as usual, we find the interval between 13 Ix and 3 Cib to be 2 +months and 2 days, and, what is another necessary condition, the +intermediate days of the column are included in this period in the order +in which they stand, if read upwards. The interval between 3 Cib, +uppermost day of the tenth column, and 13 Chicchan, bottom day of the +ninth column, is 2 months and 9 days. The sum of these two intervals is 4 +months and 11 days, as it should be on the supposition that the entire +columns follow one another in regular succession. This proves beyond +question that the columns are to be read from _bottom_ to _top_ and that +they follow one another from _right_ to _left_. This enables us to fix +the week numbers to the intermediate days and to determine the day to +which the entire series is referred as its starting point. The days and +their numbers of the tenth and ninth columns of the lower division, +writing them in reverse order, that is, from bottom to top, are as +follows: 13 Ix; 3 Caban; 11 Chicchan; 8 Men; 3 Cib; 13 Chicchan; 3 Lamat; +11 Cib; 8 Cimi; 3 Manik. + +These numbers hold good throughout the series. + +Commencing with 13 Ix, the lowest day of the tenth column, lower +division, but first day of the series, and ending with 13 Akbal, the +bottom of the first column, middle series, the time embraced is 5 years, +1 month, 0 day, less 4 months and 11 days--that is, 4 years, 14 months, 9 +days (years of 360 days being understood). This is easily proved by +counting on the calendar 4 years, 14 months, and 9 days from 13 Ix, as it +brings us to 13 Akbal. If we add to this time 2 months and 2 days--the +interval between 13 Akbal and 3 Chicchan (top day of first column, middle +division)--we have, as the entire period embraced in the series as it +stands--from 13 Ix (first of the series) to 3 Chicchan (the last)--4 +years, 16 months, 11 days. Add to this 4 months and 11 days, in order to +reach the day with which the count begins, and we have as the entire +period 5 years, 3 months, 2 days = 5 years, 1 month, 0 day + 2 months, 2 +days. If we count back 4 months and 11 days from 13 Ix (first of the +series), we reach 1 Kan, the day to which the series is referred as its +starting point. Counting forward from this date 5 years, 3 months and 2 +days brings us to 3 Chicchan, the last day of the series. + +It is worthy of notice that, although this series appears to be referred +to Kan years, it is at variance with the idea of passing from one to the +other of the four year series, and is, moreover, based upon the year of +360 days. The order in which it is to be read, which is true also of some +other pages, indicates that these extracts pertain to a different +original codex than those to which we have heretofore alluded, a +conclusion reached by Dr. Foerstemann soon after he commenced the study of +the Dresden manuscript. + +I was for a time inclined to believe there was a break between Plates 64 +and 65, as there appeared to be no day columns with which the lines of +numerals running through Plates 65-69 could be connected, but the fact +that the sum of the black numbers in each is 91, precisely the interval +between the corresponding days of the columns in Plates 63 and 64, will +probably warrant the conclusion that they are connected with them. This +conclusion is strengthened, so far as those in the lower division are +concerned, by the fact that by taking the XIII attached to the lowest +days of the columns the numbers properly succeed one another and the +series conforms to the rule heretofore given. As proof of this I give +here the lower line of the lower division, prefixing the XIII, thus: +XIII; 9, IX; 5, I; 1, II; 10, XII; 6, V; 2, VII; 11, V; 7, XII; 3, II; +12, I; 8, IX; 4, XIII; 13, XIII. + +Adding together the numbers and casting out the thirteens, thus, XIII + 9 +- 13 = IX; IX + 5 - 13 = I, &c., the connection is seen to be regular. +The final red numeral is XIII, the same as that with which the series +begins, and the sum of the black numbers, 9, 5, 1, 10, 6, 2, 11, 7, 3, +12, 8, 4, 13, is 91, a multiple of 13. The middle line of numerals also +connects with the XIII attached to the bottom symbols of the day columns; +and the upper line of numerals connects with the III attached to the top +symbols of the day columns. + +Plates 70 to 73 present some peculiarities difficult to account for. That +these pages belong to the same type as 62, 63, and 64 cannot be doubted, +and that as a general rule they are to be read from right to left is +easily proved; but this method does not seem to be adopted throughout, +the order being apparently reversed in a single series. + +The aboriginal artist has apparently made up these pages from two older +manuscripts or changed and added to his original. The last two columns of +Plate 70 and first five of 71 appear to have been thrust in here as an +afterthought or as a fragment from some other source, forming apparently +no legitimate connection with the series to either the right or to the +left of them. It is true, as will be shown, that there is some connection +with the lowest series on the right, but it would seem that advantage was +here taken of accidental correspondence rather than that this +correspondence was the result of a preconceived plan. + +Commencing in the lower part of the middle division of Plate 73 and +running back (to the left) to the sixth column of 71 and returning to the +lower part of the lower division of 73 and ending with the sixth column +of 71, is the following series. The columns are given in the order in +which they stand on the respective plates, but the plates are taken in +reverse order: + +TABLE XXIII.--_Table giving comparison between Plates 71, 72, and 73._ + + _______________________________________________________________________________ + | First | Second | Third | Fourth | Fifth | | + | column. | column. |column. | column. | column. | | + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 73,| 16 | 13 | 9 | 6 | 3 | -- | -- + middle | 5 | 0 | 15 | 10 | 5 | -- | -- + division |IV Caban.| IV Eb. |IV Manik.| IV Ik. |IV Caban.| -- | -- + ------------------------------------------------------------------------------- + _______________________________________________________________________________ + | First | Second | Third | Fourth | Fifth | Sixth |Seventh + | column. | column. | column. | column. | column. | column. |column. + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 72,| 2 | 1 | 1 | 1 | 1 | 1 | -- + middle | 3 | 17 | 14 | 11 | 8 | 4 | 19 + division | 0 | 15 | 10 | 5 | 0 | 15 | 10 + | IV Eb. |IV Manik.| IV Ik. |IV Caban.| IV Eb. |IV Manik.|IV Ik. + ------------------------------------------------------------------------------- + _______________________________________________________________________________ + | | | | | | Sixth | Seventh + | | | | | | column. | column. + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 71,| -- | -- | -- | -- | -- | 2 | 2 + middle | -- | -- | -- | -- | -- | 9 | 6 + division | -- | -- | -- | -- | -- | 10 | 5 + | -- | -- | -- | -- | -- | IV Ik. |IV Caban. + ------------------------------------------------------------------------------- + _______________________________________________________________________________ + | First | Second | Third | Fourth | Fifth | | + | column. | column. | column. | column. | column. | | + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 73,| 3 | 3 | 3 | 2 | 2 | -- | -- + lower | 7 | 3 | 1 | 16 | 12 | -- | -- + division | 15 | 10 | 5 | 0 | 15 | -- | -- + |IV Manik.| IV Ik. |IV Caban.| IV Eb. |IV Manik.| -- | -- + ------------------------------------------------------------------------------- + _______________________________________________________________________________ + | First | Second | Third | Fourth | Fifth | Sixth |Seventh + | column. | column. | column. | column. | column. | column. |column. + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 72,| 4 | 4 | 4 | 4 | 2 | 3 | 3 + lower | 12 | 9 | 6 | 2 | 17 | 14 | 11 + division | 10 | 5 | 0 | 15 | 10 | 5 | 0 + | IV Ik. |IV Caban.| IV Eb. |IV Manik.| IV Ik. |IV Caban.| IV Eb. + ------------------------------------------------------------------------------- + _______________________________________________________________________________ + | | | | | | Sixth | Seventh + | | | | | | column. | column. + ---------+---------+---------+---------+---------+---------+---------+--------- + Plate 71,| -- | -- | -- | -- | -- | 5 | 4 + lower | -- | -- | -- | -- | -- | 1 | 15 + division | -- | -- | -- | -- | -- | 0 | 15 + | -- | -- | -- | -- | -- | IV Eb. |IV Manik. + ------------------------------------------------------------------------------- + +The interval between the successive days, counting to the left, is in +each case 3 months and 5 days, corresponding with the numbers over IV +Caban, fifth column, middle division, Plate 73. Commencing with this +number and adding it successively, we obtain the numbers over the various +columns: + +Years. Months. Days. + 3 5 Over fifth column, middle division, Plate 73. + 3 5 + -- -- + 6 10 Over fourth column, middle division, Plate 73. + 3 5 + -- -- + 9 15 Over third column, middle division, Plate 73. + 3 5 + -- -- + 13 0 Over second column, middle division, Plate 73. + 3 5 + -- -- + 16 5 Over first column, middle division, Plate 73. + 3 5 + -- -- + 1 1[333-1] 10 Over seventh column, middle division, Plate 72. + 3 5 + -- -- -- + 1 4 15 Over sixth column, middle division, Plate 72. + 3 5 + -- -- -- + 1 8 0 Over fifth column, middle division, Plate 72. + 3 5 + -- -- -- + 1 11 5 Over fourth column, middle division, Plate 72. + 3 5 + -- -- -- + 1 14 10 Over third column, middle division, Plate 72. + 3 5 + -- -- -- + 1 17 15 Over second column, middle division, Plate 72. + 3 5 + -- -- -- + 2 3 0 Over first column, middle division, Plate 72. + 3 5 + -- -- -- + 2 6 5 Over seventh column, middle division, Plate 71. + 3 5 + -- -- -- + 2 9 10 Over sixth column, middle division, Plate 71. + 3 5 + -- -- -- + 2 12 15 Over fifth column, lower division, Plate 73. + 3 5 + -- -- -- + 2 16 0 Over fourth column, lower division, Plate 73. + 3 5 + -- -- -- + 3 1 5 Over third column, lower division, Plate 73. + 3 5 + -- -- -- + 3 4 10 Over second column, lower division, Plate 73. + 3 5 + -- -- -- + 3 7 15 Over first column, lower division, Plate 73. + 3 5 + -- -- -- + 3 11 0 Over seventh column, lower division, Plate 72. + 3 5 + -- -- -- + 3 14 5 Over sixth column, lower division, Plate 72. + 3 5 + -- -- -- + 3 17 10 Over fifth column, lower division, Plate 72. + 3 5 + -- -- -- + 4 2 15 Over fourth column, lower division, Plate 72. + 3 5 + -- -- -- + 4 6 0 Over third column, lower division, Plate 72. + 3 5 + -- -- -- + 4 9 5 Over second column, lower division, Plate 72. + 3 5 + -- -- -- + 4 12 10 Over first column, lower division, Plate 72. + 3 5 + -- -- -- + 4 15 15 Over seventh column, lower division, Plate 71. + 3 5 + -- -- -- + 5 1 0 Over sixth column, lower division, Plate 71. + +It is worthy of notice that the sum of the series as expressed by the +final numbers is precisely that of the series on the middle and lower +divisions of Plates 63 and 64, heretofore given, and embraces seven +complete cycles of 13 months, or 260 days each. Counting back three +months and five days from 4 Caban (the day in the fifth column, middle +division, of Plate 73) we reach 5 Been as the starting point of the +series. + +As there can be no doubt that the lines and days of the two divisions +form together one unbroken series, it is evident there is no connection +between that portion of it in the middle division and what lies to the +left of it in Plate 71; but there does appear to be, as before indicated, +some connection between the conclusion and what follows to the left in +the lower portion of 71. The series which lies to the left at this point +is as follows: + +TABLE XXIV.--_Table showing relations of Plates 70 and 71._ + + ________________________________________________________________ + Plate 70. | Plate 71. + ----------------+----------------------------------------------- + 5th | 6th | 1st | 2d | 3d | 4th | 5th | 6th + column.|column. |column.|column.|column.|column.|column.|column. + 6 | 5 | 4 | 3 | 2 | | | + 1 | 1 | 0 | 0 | 0 | 15 | 10 | 5 + 6 | 2 | 16 | 12 | 8 | 3 | 2 | 1 + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + IV Eb.| IV Eb. | IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb. + --------------------------------------------------------------- + +For the purpose of assisting the reader to see the relation more clearly, +the last column of the preceding series--sixth of the lower division on +Plate 71--is added at the right as it stands in the original. + +It is apparent that the figures in the fifth column of 71 are exactly +double those in the sixth column. This and the fact that the day IV Eb is +the same as those following are the only indications that there is any +connection between the series. Using the 5 years and 1 month as the +common difference and adding, the result is as follows: + +Years. Months. Days. + 5 1 0 Sixth column, lower division, Plate 71. + 5 1 0 + -- -- -- + 10 2 0 Fifth column, lower division, Plate 71. + 5 1 0 + -- -- -- + 15 3 0 Fourth column, lower division, Plate 71. + +At this point another change occurs: the former difference is added to +the last figures and the sum is doubled. + +Twenty year periods. Years. Months. Days. + 15 3 0 + 5 1 0 + -- -- -- -- + 1 0 4 0 + 2 + -- -- -- -- + 2 0 8 0 Third column lower division, + Plate 71. + 1 0 4 0 + -- -- -- -- + 3 0 12 0 Second column, lower division, + Plate 71. + 1 0 4 0 + -- -- -- -- + 4 0 16 0 First column, lower division, + Plate 71. + 1 0 4 0 + -- -- -- -- + 5 1 2 0 Sixth column, lower division, + Plate 70. + 1 0 4 0 + -- -- -- -- + 6 1 6 0 Fifth column, lower division, + Plate 70. + +This series does not end at this point, but is continued in the lines +immediately above, which are as follows: + +TABLE XXV.--_Table showing relations between Plates 70 and 71._ + + ________________________________________________________ + Plate 70. | Plate 71. + ----------------+--------------------------------------- + 5th 6th | 1st 2d 3d 4th 5th + column. column. |column. column. column. column. column. + 1 | + 0 8(?) | 15 13 10 9 7 + | XII + 12 1 | 3 2 2 2 1 + | II + 3 10 | 6 16 4 0 10 + | XII + 0 0 | 0 0 (?) 0 0 + IV Eb. IV Eb. | IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. + -------------------------------------------------------- + +Adding the difference, 1, 0, 4, 0, to the final result of the preceding +addition we obtain the figures of the right hand column (fifth column, +Plate 71) of this series: + + 6 1 6 0 + 1 0 4 0 + -- -- -- -- + 7 1 10 0 + +To obtain the figures of the fourth column this difference must be +doubled, thus + + 7 1 10 0 + 2 0 8 0 + -- -- -- -- + 9 2 0 0 + +To obtain the black numbers of the next (third) column, the lower cipher +symbol of which is wanting, we add the former difference: + + 9 2 0 0 + 1 0 4 0 + -- -- -- -- + 10 2 4 0 + +This decrease in the difference is unusual and indicates some error. This +idea seems to be confirmed in the following way: In order to obtain the +numbers of the next (second) column it is necessary to add three times +the former difference, thus: + + 10 2 4 0 + 3 0 12 0 + -- -- -- -- + 13 2 16 0 Second column, Plate 71. + +If the increased difference, 2, 0, 8, 0, were retained after its +appearance the result would be as follows: + + 7 1 10 0 Fifth column, Plate 71. + 2 0 8 0 + -- -- -- -- + 9 2 0 0 Fourth column, Plate 71. + 2 0 8 0 + -- -- -- -- + 11 2 8 0 Third column, Plate 71. + 2 0 8 0 + -- -- -- -- + 13 2 16 0 Second column, Plate 71. + 2 0 8 0 + -- -- -- -- + 15 3 6 0 First column, Plate 71. + +Adding the difference, 2, 0, 8, 0, to the third column, Plate 71, thus: + + 10 2 4 0 + 2 0 8 0 + -- -- -- -- + 12 2 12 0 + +we obtain the red numerals inserted in the third column. It is probable +that the original or some subsequent scribe, observing an error at this +point, inserted these figures as a correction. If so, he failed to remedy +the confusion apparent in this portion of the series. The sum of the +entire series is 303 years (360 days each) and six months, equal to 420 +cycles of 260 days. + +I am strongly inclined to believe that this section and also pages 24 and +59 are interpolations by some aboriginal artist of a mathematical turn +and advanced ability in this direction, who has given these high series +more as curiosities than with reference to any specific dates or periods +of time. + +[Illustration: FIG. 371. Specimens of ornamental loops from page 72, +Dresden Codex.] + +Commencing in the sixth column of Plate 71_a_ and running through 72_a_ +to the second column of 73_a_, is a numeral series which presents some +peculiarities that baffle all attempts at explanation. Contrary to the +rule which prevails in these pages it ascends from left to right and has +no day symbols connected with it. In addition to this, the numbers of its +lowest line are inclosed in loops of the form here shown (Fig. 371) and +have no apparent connection with the other lines of the series, but, on +the contrary, if taken from right to left, they present in the order +usually given the numbers of the ahaues or katunes.[337-1] It is as +follows: + + 1 1 1 1 1 1 1 + 2 5 8 10 13 16 0 3 6 9 11 14 17 + II. + 14 8 2 16 10 4 18 12 6 0 14 7(?) 2 XIV + [(11)][(13)][(2)][(4)][(6)][(8)][(10)][(12)][(1)][(3)][(5)][(7)][(9)] + +The last (thirteenth) column of this series is not in a line with the +others, but is found in the lower part of the right hand column of Plate +73, and in connection with it we find the red numerals II and XIV, +denoting the difference between the columns, as is apparent from the +additions here given: + +Years. Months. Days. + 2 14 First or left hand column. + 2 14 + -- -- + 5 8 Second column. + 2 14 + -- -- + 8 2 Third column. + 2 14 + -- -- + 10 16 Fourth column. + 2 14 + -- -- + 13 10 Fifth column. + 2 14 + -- -- + 16 4 Sixth column[TN-8] + 2 14 + -- -- + 1 0 18 Seventh column. + 2 14 + -- -- -- + 1 3 12 Eighth column. + 2 14 + -- -- -- + 1 6 6 Ninth column. + 2 14 + -- -- -- + 1 9 0 Tenth column. + 2 14 + -- -- -- + 1 11 14 Eleventh column. + 2 14 + -- -- -- + 1 14 8[338-1] Twelfth column.[TN-9] + 2 14 + -- -- -- + 1 17 2 Thirteenth column. + + +FOOTNOTES: + +[261-1] The work here referred to is entitled Die Mayahandschrift der +Koeniglichen oeffentlichen Bibliothek zu Dresden, herausgegeben von Prof. +Dr. E. Foerstemann, Hofrat und Oberbibliothekar. It contains, besides the +chromolithographs of the 74 plates, an introduction published at Leipzig, +1880, 4^o. + +[269-1] A Study of the Manuscript Troano, by Cyrus Thomas, pp. 7-15. + +[272-1] This method will be adopted throughout this paper where figures +containing numerals are introduced. + +[273-1] In the representations of lines and columns of the codex Roman +numbers are necessarily used to distinguish the class of numerals, yet in +the text, as in this case, the Arabic numbers will be used as most +convenient. + +[273-2] Strictly speaking, the interval between 11 Men and 13 Oc is +fourteen days, but throughout this paper, by "_interval between_" two +days, is to be understood the number of days to be counted _from_ one _to +and including_ the other. The one counted from is always _excluded_ and +the one reached or with which the interval terminates is always +_included_. + +[273-3] Science, p. 459, April 11, 1884. + +[277-1] Throughout this paper when the words "figure" and "character" are +used in reference to what appears in the codex, they are to be understood +as follows: "figure" refers to the picture, as of a person, animal, or +other object in the spaces; "character" refers to the hieroglyphics or +written symbols. + +[278-1] Study of the Manuscript Troano, by Cyrus Thomas, Chapters II and +VII. + +[278-2] Erlaeuterungen zur Mayahandschrift, p. 2. + +[280-1] Erlaeuterungen zur Mayahandschrift, p. 16. + +[280-2] Bureau of Eth., Third Ann. Rep., pp. 16 et seq. + +[282-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 15, 16. + +[282-2] Dechiffrement des ecritures calculiformes ou Mayas, par M. le +C^te H. de Charency, Alencon, 1849; also, Melanges, pp. 185-195. + +[283-1] For an explanation of the principle upon which these day columns +were formed, see "Notes on certain Maya and Mexican manuscripts," by +Cyrus Thomas, published in the Third Annual Report of the Bureau of +Ethnology. + +[290-1] The symbol for this day in Kingsborough resembles Lamat, but the +photographic copy makes it Ix, as it should be. + +[290-2] Foerstemann, Erlaeuterungen zur Mayahandschrift, p. 42. + +[291-1] Erlaeuterungen zur Mayahandschrift, p. 36. + +[292-1] Erlaeuterungen zur Mayahandschrift, p. 60. + +[293-1] Erlaeuterungen zur Mayahandschrift, p. 56. + +[296-1] The bottom lines are selected because they are less injured in +the codex than the top lines, which are in most cases entirely +obliterated. + +[300-1] 3 days in ms., should be 4. + +[317-1] The third symbol in the last day column of Plate 51_b_ is Been in +the codex; but this is an evident mistake, as shown by the order of the +days, since Ahau, which has been substituted above, always follows Cauac. +This may be seen by reference to the middle column of 57_b_. + +[319-1] This is one of the exceptional cases. + +[321-1] Second exception. + +[321-2] Third exception. + +[323-1] One line has been omitted in the numeral symbol. + +[323-2] Here we have again the added day. + +[324-1] The 8 at this point in the codex is an evident error. + +[324-2] Here is also an error in the original, this being 10. + +[324-3] The symbols require an additional day here. + +[324-4] The 8 in the year line in the original is a manifest error, as 6 +precedes and 7 follows. + +[324-5] The 18 in the day line at this point is also an error, as the +interval between 2 Muluc and 10 Cimi is 8 months and 17 days. Moreover, +the next day number being 16 requires this to be 19. + +[325-1] The counters in the original at this point are certainly wrong, +for here should be 7 months and 8 days, whereas the symbols are those for +8 months and 17 days. + +[325-2] Here we have again the additional day. + +[325-3] Added to show connection with the lower series. + +[333-1] Codex has 19, which is equivalent to 1 year and 1 month. + +[337-1] While reading the final proof I fortunately discovered what may +prove to be the correct explanation of the numbers in the loops. + +At the commencement of the series on Plate 71 and at its close on Plate +73 we observe the symbol of the day, 9 Ix. Starting from this date and +counting forward on the calendar two months and fourteen days, we reach +11 Lamat. This gives the number in the first loop of the series. Two +months and fourteen days more bring us to 13 Ik, the number in the second +loop; two months and fourteen days to 2 Cib, the number in the third +loop, and so on to the end. It is therefore probable that the numerals in +the loops indicate the week numbers of the days, though these are usually +expressed in red symbols. + +[338-1] The 7 in the twelfth column is an error; it should be 8, as an +inspection shows the place of the missing dot. The additions make it +clear that the numbers of the second line refer to months, those of the +line below them to days, and those of the line above to years. The series +is, therefore, apparently complete without the numbers inclosed in the +loops. + + + + +CHAPTER II. + +CONCLUSIONS. + + +The conclusions to be drawn from the foregoing discussion may be briefly +stated as follows: + +First. That the codex in its present form is composite, being made up +from two or more different original manuscripts, as Dr. Foerstemann has +suggested. + +Second. That a number of minor changes and additions have been made by a +subsequent hand, possibly after it had assumed its present form. + +Third. That the year referred to in the larger series is one of 360 days; +also, that in instances of this kind the count is continuous, and hence +not consistent with the generally received idea of the Maya calendar, in +which, the four year series forms a necessary part of the system, unless +some other method of accounting for the five supplemental days can be +discovered than that which has hitherto been accepted. + +Fourth. On the other hand, indications of the four year series are +certainly found in all of the Maya manuscripts; for example, in Plates +25-28 of the Dresden Codex and Plates XX-XXIII of the Manuscript +Troano,[339-1] which seem to be based on this series; in fact, the +numbers attached to the days in the latter can be accounted for in no +other way. Plates 3-6 of the Cortesian Codex are apparently based upon +the same system. The numbers in the loops on Plates 71, 72, and 73, +Dresden Codex, heretofore alluded to and represented in Fig. 371, +apparently defy explanation on any supposition except that they refer to +the numbers of the ahaues, which are based upon the four year +series.[339-2] The frequent occurrence in connection and in proper order +of both the first and the terminal days of the year apparently refers to +the same system. Many of the quadruple series no doubt relate to the four +cardinal points and the four seasons; yet there are some which cannot be +explained on this theory alone. + +It is impossible, therefore, to exclude this system from consideration in +studying the chronology of the codices, although there are a number of +the numerical series of the Dresden manuscript which cannot be made to +fit into it on any hypothesis so far suggested. The same thing is also +found to be true in regard to some, in fact most, of the series found in +the Mexican manuscripts. This confusion probably arises in part from the +apparently well established fact that two methods of counting time +prevailed among both Mexicans and Mayas: one, the solar year in ordinary +use among the people, which may be termed the vulgar or common calendar; +the other, the religious calendar used by the priests alone in arranging +their feasts and ceremonies, in which the cycle of 260 days was taken as +the basis. But this supposition will not suffice as an explanation of +some of the long series of the Dresden Codex, in which the year of 360 +days appears to have been taken as a unit of measure, unless we +assume--as Foerstemann seems to have done--that what have been taken as +years are simply high units and counting the whole as so many days, refer +the sum to the cycle of 260 days, which will in almost every case measure +them evenly as a whole, or by its leading factor, 13. That the smaller +series attached to day columns are all multiples of 13 and referable to +the cycle of 260 days has been shown by Foerstemann as well as in the +preceding part of this paper. But it is worthy of note that the +difficulty mentioned occurs only in reference to series found in that +portion of the Dresden manuscript which Foerstemann has designated Codex B +(page 24 being considered as belonging thereto). + +The red unit number symbol, with a circle of dots around it, seen +occasionally in the Manuscript Troano, seems to have some connection with +the four year series. Take, for example, the one in the lowest division +of Plate VII. + +The series commences in the lower right hand corner of Plate VIII, where +the day column with which it is connected is found. The days of this +column, reading downward, are as follows: Ahau, Eb, Kan, Cib, Lamat, and +the number over them is I, but without any dots around it, while the +terminal I of the series is inclosed in the circle of dots. What is the +meaning of this marked distinction? It is evident that it is something +which does not apply equally to all the days of the columns; yet, as it +is the terminal number, it must relate to some one of them. If we examine +the series carefully I think the reason for the distinction will be +explained; Written out in full, it is as follows: + + I. + Ahau + Eb } + Kan } 10, XI; 10, VIII; 10, V; 10, II; 12[?], [(I)]. + Cib + Lamat + +The last black number is 10 in Brasseur's fac simile, but should be 12. +Making this correction, the series is regular and of the usual form. The +sum of the black numbers is 52, which is the interval between the days, +and the number over the column is the same as the final red number. + +If we turn now to the calendar (Table II) and select Ahau of the Kan +column, and 1, the seventeenth number of the eighth figure column, and +count 52 days, we reach 1 Eb, the second day of our column as given +above; 52 days more bring us to 1 Kan, the first day of the first month +in the calendar and third day of our column. If the theory of the four +year series be correct, then 1 Kan of the Kan series must be the first +day of the first year of an Indication or week of years. This fact was +probably considered by the aboriginal artist of sufficient importance to +give this day a mark of distinction. As it is not possible for any of the +other days of the column to be thus distinguished, it is fair to presume +this peculiar marking of the final number refers to Kan. Moreover, this +distinction would not occur if any other than the Kan series were used. + +In the upper division of Plate IX of the same manuscript is the following +series: + + XIII + Men } + Manik } 20, VII; 20 [(I)]; 1, II; 4, VI; 7, XIII. + Cauac } + Chuen + Akbal + +In this, I, the second red number of the series, has the circle of dots +around it. The number over the column is partially obliterated, but is +readily restored, and should be XIII. + +If we select, on our calendar, the Cauac column, or series, a reason for +this distinction will appear. The sum of the black numbers is 53, which +is also the interval between the days. As has heretofore been shown, the +red numbers of the series refer to certain days selected by the priests, +for special reasons unknown to us, which occur between the days of the +column. + +In this case the intermediate days are as follows: + + Between 13 Manik and 13 Cauac: 7 Manik, 1 Manik, 2 Lamat, and 6 Eb. + + Between 13 Cauac and 13 Chuen: 7 Cauac, 1 Cauac, 2 Ahau, and 6 Kan. + +Here we find the explanation for which we are seeking, as in the interval +between 13 Cauac and 13 Chuen is 1 Cauac, which, if the Cauac column of +the calendar be selected, is the first day of the year 1 Cauac, the first +year of an Indication. As this occurs only when a year commencing with +Cauac is selected, we infer that the series is based upon the system with +the four year series. + +The best illustration of this peculiarity and the strongest evidence of +its signification is probably found in the series contained in the middle +division, Plate XI, same manuscript. This, when written out and the +numbers properly arranged, is as follows: + + [(I)] [(I)] + Oc Ahau } + Cib Cimi } 1, II; 2, IV; 2, VI; 5, XI; 2, XIII; 4, IV; 9(?) [(I)]. + Ik Eb } + Lamat Ezanab + Ix Kan + +The last black number of the series is 9, but should be 10 to render the +series complete. Making this correction, the series is of the usual type; +the sum of the black numerals is 26, the interval between the days of +the columns is 26, and the final red numeral is the same as that over the +columns. + +As the circle of dots is around the final red number and also around each +of those over the columns, the distinction indicated must refer to one or +more days of each column. + +As the last days only of the columns are year bearers, the mark of +distinction probably applies to them. Selecting for the left hand column +the Ix series of years and commencing with 1 Oc, the seventeenth day of +the eighth month, we count 26 days. This brings us to 1 Cib, the third +day of the tenth month, or tenth figure column of our calendar and second +day of the first day column of the series; 26 days more to 1 Ik; 26 more +to 1 Lamat, and 26 more to 1 Ix, the first day of the year 1 Ix, which, +according to the four year series, will be the first year of an +Indication. Selecting the Kan series for the second column and counting +in the same way from 1 Ahau, the seventeenth day of the eighth month, or +eighth figure column of the calendar, the last day is found to be 1 Kan, +the first day of the year 1 Kan, which must also be the first year of an +Indication. + +Unit numerals marked in this manner are found in two or three places in +the Cortesian Codex, but there is none in the Dresden Codex. The series +with which they are connected in the former, except that in the middle +division of Plate 24, are too much obliterated to be traced throughout. +This, by making two slight and apparently authorized corrections, is as +follows: + + [(I)] + Cimi } + Ezanab } 11, XII(?); 11, X; 6, III; 8, XI; 7(?), V; 9, I. + Oc } + Ik + Ix + +The first red numeral of the line is X in the original and the next to +the last black number is 6. By changing the former to XII and the latter +to 7 the sum of the series will be 52, which is the interval between the +days of the column. + +Using the Ix column in the calendar and commencing with 1 Cimi, counting +as heretofore, the last day of the column of the series is found to be 1 +Ix, the first day of the year 1 Ix and the first year of an Indication, +according to the four year system. + +A somewhat remarkable confirmation of the theory here advanced is +presented in a series found in the middle division of Plate II of the +Manuscript Troano. + +The series, when written out with the substitutes heretofore used, is as +follows: + + [(I)] [(I)] + Manik Ymix } + Men (?) Been } 9, X; 6, III; 11, I. + Chuen Chicchan } + Akbal Caban + Men Muluc + +In Brasseur's fac simile the second symbol of the left hand column is +clearly that for Men. If this be accepted as correct, then no year bearer +(Kan, Muluc, Ix, Cauac) would be found in either column and the theory we +have advanced regarding the signification of the dots around the red unit +over the column would fall to the ground. Nor is this the only difficulty +we meet with in attempting to apply the theory to this series. The sum of +the black numbers is 26, which should also be the interval between the +days of the columns. Counting 26 days from 1 Manik brings us to 1 Been +instead of 1 Men; 26 more to 1 Cauac, a day not found in either column as +given in the original. Taking the second column and counting 26 days from +1 Ymix, we reach 1 Manik, instead of 1 Been. This gives us the key to the +series and solves the riddle. We must commence with 1 Ymix, then take 1 +Manik, then 1 Been, and so on, going alternately from column to column. + +Adopting this method and using the Cauac column of our calendar, Table +II, the result is as follows: Commencing with 1 Ymix, the third day of +the tenth figure column, and counting 26 days, we reach 1 Manik; 26 days +more bring us to 1 Been, and 26 more to 1 Cauac, the first day of the +first year of an Indication. The 1 Men of the left hand column should +therefore be 1 Cauac, which is also proved by counting the intervals, +without regard to the week numbers. For example, from Ymix to Been is 12 +days, from Been to Chicchan 12 days, from Manik to Cauac 12 days, and so +on through each column. Or, if we take the columns alternately, the +interval is six days, thus: From Ymix to Manik, 6 days; from Manik to +Been, 6 days; from Been to Cauac, 6 days; from Cauac to Chuen, 6 days, +and so on to the end. + +Although the proof is not absolutely conclusive that these red unit +numerals have this mark of distinction for the reason given, it +nevertheless furnishes what would seem to be a satisfactory explanation, +and, if so, affords proof that the calendar system, based upon the four +year series, was in vogue when the Manuscript Troano and the Codex +Cortesianus were written. + +This mark of distinction is found in a strange and unusual relation in +the lower division of Plate XV, Manuscript Troano. The first red numeral +of the series is given thus: + +[Illustration: FIG. 372. Numeral character from the lower division of +Plate XV, Manuscript Troano.] + +Most of the day and about half of the numeral symbols are obliterated, +but all that are necessary for present purposes remain distinct and +uninjured, as follows: + + III, } + Ix } 10, XI[(I)]I. + Cimi } + +Judging by these and the few numbers remaining, the entire series was as +follows: + + III, } + Ix } + Cimi } + Ezanab } 10, XIII; 4, IV; 20, XI; 9, VII; 9, III + Oc } + Ik } + +The only doubt in reference to the restoration is whether the second and +third pairs of numerals should be as given, or 2, II, and 22, XI. If we +select the Kan column of our Table II and count from 3 Ix of the eleventh +figure column, we reach 13 Kan. If the four year series was the system +used 13 Kan might be the first day of a year, but not the first day of an +Indication. As this is the only day referred to by the XIII which could +have been the first of a year we must seek an explanation in something +else. Counting ten days from 3 Ezanab will bring us to 13 Lamat, which is +the last day (counting the five added days) of an Indication, commencing +with the year 1 Kan and ending with the year 13 Kan. + +According to my theory of the ahaues,[344-1] the year 13 Kan would have +corresponded with the Gregorian years 1376, 1438, 1480, and 1532. +According to the theory advanced by Perez,[344-2] it would have +corresponded with 1385, 1437, 1489, and 1541. + +It is therefore possible that this mark of distinction may be of some +value in determining the relation of the Maya to the Gregorian calendar. + + +FOOTNOTES: + +[339-1] See Study of the Manuscript Troano, by Cyrus Thomas. + +[339-2] See note on page 337. + +[344-1] See Table XVII, Study of the Manuscript Troano, by Cyrus Thomas, +p. 44. + +[344-2] See Table XVIII, ibid., p. 45. + + + + +CHAPTER III + +THE WRITING. + + +It must be admitted that none of the attempts made at deciphering the +writing in these manuscripts has proved entirely satisfactory; in fact +there is still some doubt as to whether any of the characters are truly +phonetic; nevertheless it is believed that what is here shown will tend +to lessen this doubt. It must be conceded, however, notwithstanding these +drawbacks and difficulties, that some material progress has been made +towards a better understanding of its type and of the nature of the +characters. + +The direction in which it is to be read must of course be determined +before any progress can be made in deciphering it. This was, until +recently, a matter of speculation, but now may be considered settled. As +this has been explained[345-1] it is unnecessary to repeat that +explanation here. + +A certain parallelism in the sentences or groups of characters has also +been discovered. Attention was first called to this by me in the work +referred to, but is more fully explained by Dr. P. Schellhas in his paper +entitled "Die Mayahandschrift der koeniglichen Bibliothek zu Dresden." It +will readily be understood from a single illustration. Take for example +the lower division of Plate XV of the Manuscript Troano (see Study Ms. +Troano). Omitting from consideration the numerals and the day column at +the left, there are here two short columns on the left and two on the +right over the animal figures, and three longer columns between. As +explained in the work referred to, the short columns are to be read as +lines from left to right and the longer columns separately, from the top +downward. There are, in all, five groups or sentences, each containing +four compound characters. Representing these by letters, repeating those +which indicate similar characters, and arranging as in the plate, the +result is as follows: + + ___________________________________________ + | | | | | | + | _b_ _a_ | _h_ | _l_ | _m_ | _w_ _a_ | + | | | | | | + | _r_ _n_ | _a_ | _a_ | _a_ | _r_ _s_ | + |____________| | | |____________| + | _r_ | _r_ | _r_ | + | | | | + | _p_ | _k_ | _t_ | + |_____|_____|_____| + +In this case the characters represented by _a_ and _r_ are repeated in +each group and in the same relation to the other characters. It is +apparent, therefore, that each group is to be read separately, and, as +each repeats in part what is given in the others, it is more than +probable that they are simply short formulas to be repeated in certain +religious ceremonies. This parallelism, though not always so apparent as +in the case presented, is nevertheless found running through all the +codices. The advantage to the attempts at decipherment which results from +this fact is evident, as it will often justify the restoration of blurred +or obliterated characters, and, what is of still more importance, will +enable the investigator to test his conclusions by comparing the +different characters and pictures with which they are associated. + +Although it appears to be well settled that, as a rule, the writing, when +in lines, is to be read from left to right--the lines following each +other downward and the columns to be read from the top downward, but the +groups, as before explained, to be read separately--it does not follow +that the _groups_ succeed one another from left to right. This has +generally been taken for granted, but there are some reasons to doubt the +correctness of this conclusion as regards a number of plates and possibly +one entire codex. + +The facts that the lines of numerals attached to the day columns extend +to the right and that the written characters, when in lines, follow one +another in the same direction lead us to infer that the groups and +pictures follow one another in the same order, but the apparent movement +of the latter towards the left would seem to indicate that _they_ follow +one another in _this_ direction. This inference appears to be confirmed +by the following evidence: As is well known, the plates of the Manuscript +Troano are to be taken in reverse order to the paging. Turning to Plate +II, we observe in the middle department of the middle division a bound +captive or victim, on whose neck a machete is descending to sever the +head from the trunk. Turning to Plate III, which properly stands to the +left of Plate II, we see a headless trunk covered with blood and the +fatal machete near the neck. It is fair to presume that this is the same +individual that is figured in the preceding plate, and, if so, that the +pictures follow one another toward the left. + +Placing Plates XV* and XVI* of the same manuscript in the proper relation +to each other and carefully examining the figures in the second division, +we notice that the idol heads which the artisans are carving approach +completion as we move toward the left, those in Plate XV* and the right +hand one in XVI* being simply blocked out, while the middle one in the +latter plate is completely rounded and is receiving the second ornamental +line and the one at the left hand is receiving the third and final line. + +The female figures in the second division of Plate XIX* indicate the same +order, as shown by the increasing girth as we proceed toward the left. + +The same order appears to be indicated in numerous places by the symbols +of the cardinal points inserted in the text, as they (supposing the +conclusion as to their assignment in my "Notes on certain Maya and +Mexican manuscripts," accepted by Drs. Foerstemann and Schellhas, to be +correct) follow one another in the proper order if read towards the left, +to wit, south, east, north, west. + +As the writing over each figure, consisting usually of four compound +characters, appears to refer to that over which it is placed, it follows +that these character groups must be taken in the same order as the +pictures. The suggestions on this point are presented here more as proper +subjects of investigation by students of American paleography than as +fixed conclusions of the writer. If found to be justified by the facts, +they will furnish some additional aid in the work of deciphering these +manuscripts. + + +SIGNIFICATION OF THE CHARACTERS. + +As Landa's alphabet has so far proved useless as an aid in deciphering +these manuscripts, our only hope of accomplishing this end is by long and +careful study of these records and laborious comparisons of characters +and the relations in which they stand to one another and to the figures. + +Some discoveries made while preparing this paper for the press, which are +mentioned further on, may possibly give us the key to the method used by +Landa in forming his alphabet, and, if so, will probably furnish some +slight additional aid in our investigations. + +The direction in which the writing is to be read having been ascertained, +our next step is to determine by comparison the probable signification of +as many characters as possible before discussing the question of +phoneticism. The relation of the characters to the pictorial +representations forms our chief reliance in this branch of the +investigation. + +As a commencement in this work and as a basis for further attempts in the +same direction, attention is now called to some characters, other than +the day and month symbols, whose signification seems to be satisfactorily +determined. As there is still some difference of opinion as to the +assignment of the symbols of the cardinal points they are also omitted +from the list. M. Leon de Rosny has given, as a supplement to his edition +of the Cortesian Codex, a list of characters with their supposed +signification. It is not my intention to discuss here the merits of this +vocabulary, although I shall avail myself of so much found therein as +appears to warrant acceptance. + +The question of phoneticism will not be considered in connection with the +list, as the subject will be briefly discussed at the close, the only +object in view in giving the list being to indicate the signification of +the characters alluded to. The Maya names appended are therefore to be +understood simply as the supposed names applied to them or the objects +they denote. + + +SYMBOLS OF ANIMALS &C. + +[Illustration: No. 1] + + _Kal._ The symbol for the number 20. Found in all of the codices and + explained in the preceding portion of this paper. + +[Illustration: No. 2] + + The symbol for 0 (nought), always red. Found only in the Dresden Codex + and always in the numeral series. + +[Illustration: No. 3] + + _Kin._ Sun, and probably day also. It is not known positively that it + has this signification except in connection with the equatorial + cardinal point symbols and the symbol of the month _Yaxkin;_ yet it + is reasonable to suppose it has. + +[Illustration: No. 4 _a_ _b_ _c_ _d_] + + _Aac_ or _Ac_. A turtle. That this symbol as shown in _a_ and _b_ + denotes the turtle is conclusively proved by its resemblance to the + head of that animal, as figured in the Cortesian Codex (see Fig. + 373) and its relation to these figures. Found only in this codex, + unless two doubtful symbols on Plate XXV*, Manuscript Troano, are to + be considered as variants. + +[Illustration: FIG. 373. Turtle from the Cortesian Codex.] + +There can be no doubt that Landa's _A_, an exact copy of which is given +in the margin, in both varieties, _c_ and _d_, is nothing more nor less +than this symbol; for, in addition to the very close general resemblance, +we see in it the eye and the dot indicating the nostril. This fact is +important, as it gives us some clew to the method adopted by Landa in +forming his alphabet. + +[Illustration: No. 5] + + _Uech._ Symbol or head of the armadillo of Yucatan. Appears but once or + twice and in the Manuscript Troano only. (See Study of the + Manuscript Troano, by Cyrus Thomas, pp. 98 and 145). + +[Illustration][TN-10] + + _Che._ Wood. (See Study of the Manuscript Troano, by Cyrus Thomas, p. + 144). + +[Illustration: No. 7] + + _Cab._ Earth, soil; also honey. (See Study of the Manuscript Troano, by + Cyrus Thomas, p. 150.) + +[Illustration: No. 8] + + _Piz._ Stone or stone heap. (See Study of the Manuscript Troano, by + Cyrus Thomas, p. 144). The Maya name of the thing indicated is + uncertain, though I am inclined to believe _Piz_, as given in the + work alluded to, is correct. + +[Illustration: No. 9] + + _U._ The left symbol of this figure appears to stand for vase, and is + also used to indicate a pronoun or article when joined to another + symbol, as here shown. (See op. cit., p. 145.) + +[Illustration: No. 10] + + _Xicim._ The ear. Rosny, Vocabulaire hieratique, No. 185. + +[Illustration: No. 11] + + _Hau._ The quarter of a deer. Usually represented as an offering to the + gods; in all the manuscripts. + +[Illustration: No. 12] + + _Ikilcab._ The bee. Although the figure bears a much stronger + resemblance to a beetle than to a bee, there can be no longer any + doubt that Brasseur's supposition that it represents a bee is + correct. + +[Illustration: No. 13] + + Honey in the comb. (See Study of the Manuscript Troano, by Cyrus + Thomas, Fig. 20); in the Manuscript Troano only, and always in red. + +[Illustration: No. 14] + + _Xamach or Chimix._ A vessel. This symbol, found in all the codices, is + apparently explained by its use in the upper division of Plate 27, + Cortesian Codex, where it stands over each of four vessels or jars + of the form represented in Fig. 374. + +[Illustration: FIG. 374. Jar from the Cortesian Codex.] + +This conclusion is greatly strengthened by the fact that the only other +symbols in this connection are those of the cardinal points, one to each +vessel. These figures are probably intended to denote here the four +sacred vessels or amphorae of the Bacab, though not surmounted, as +Brasseur supposed, by human or animal figures. + +The symbol appears to be used also in the ordinary sense, or at least to +signify other vessels than the sacred four, if we may judge by its +frequent repetition in Plate XIV, Manuscript Troano. But it is worthy of +notice that here also, in both the middle and lower divisions, four of +the symbols are connected with the cardinal point symbols; there is also +in the former the figure of a vessel. + +[Illustration: Hieroglyph] + +If this identification be correct it is important, as it has a strong +bearing on the question of phoneticism. It will be observed that, +although the right hand member resembles closely the symbol of the day +Ymix, there are some differences, as may be seen by comparison. In the +former the little figure at the top is divided as in Kan, and on each +side of it there is a large dot, usually, and apparently by intention, +circular or hollow. These differences are permanent in the different +codices. + +In the upper division of Plates X and XI, Manuscript Troano, where this +symbol appears in connection with each of the four cardinal symbols, that +relating to the east presents this remarkable variation: + +[Illustration: Hieroglyph] + +[Illustration: No. 15 _a_ _b_] + + (?) A conventional figure of sprouting maize, never inserted in the + text, but frequently in the Manuscript Troano and in the Peresian + Codex made a part of the head gear of figures of deities, in which + case the Kan symbol is generally omitted. + +The Kan symbol in this connection cannot be intended, as Dr. Schellhas +supposes, to indicate the field or milpa in which the corn is growing, +but the grain from which the plant is springing. (On this subject see +Study of the Manuscript Troano, by Cyrus Thomas, pp. 105 and 107.) + +[Illustration: No. 16] + + (?) Symbol of a worm which gnawed the roots of the growing agave or + maguey; appears but once, on Plate XXIX_c_ of the Manuscript Troano. + +The animal head and teeth show the erroneous idea the natives had of the +gnawing apparatus of insects. The worm is shown on the next page in Fig. +375. + +[Illustration: FIG. 375. Worm and plant from Manuscript Troano.] + +[Illustration: FIG. 376. Figure of a woman from the Dresden Codex.] + +[Illustration: No. 17] + + _Chuplal._ Woman or female. This symbol is found in the Dresden and + Troano Codices, but most frequently in the former. The appendage at + the right is sometimes wanting, and occasionally that at the left, + but when this is the case some other prefix is generally + substituted. + +If we examine carefully Plates 16-20 of the Dresden Codex, where this +symbol is most frequently repeated, and compare it with the heads of the +females there figured, it soon becomes apparent that the scrolls with the +heavy black dot are intended to denote the locks of hair and that the +symbol as a whole is, as usual, a modified or conventional form of the +head (see Fig. 376). + +[Illustration: No. 18 _a_ _b_ _c_] + + _Otoch._ A house or dwelling, or _Tabay;_ a hut or hunting lodge. The + symbol marked _a_ is found in the Cortesian Codex on Plate 29; that + marked _b_, on Plates 29, 32, and 34, same codex, and on Plates XVI* + and XXII* of the Manuscript Troano. The one marked _c_ is the usual + form in the latter, as on Plates V*, VII*, and X*. It is also on + Plate 38 of the Dresden Codex. + +The relation of these symbols to the conventional figures of houses or +huts inserted at the points where they are found, together with the form, +which shows an attempt to represent the thatched or leaf covered roof, +leaves no doubt that they are used for the purpose indicated. + +[Illustration: No. 19 _a_ _b_] + + _Buk_ (?). There are good and, it is believed, satisfactory reasons for + concluding that these symbols are intended to denote the action of + whirling a stick to produce fire or rolling a pestle in grinding + paint. The first, marked _a_, is found only on Plate XIX of the + Manuscript Troano, and the second, on Plates 5 and 6 of the Dresden + Codex. + +A copy of part of Plate XIX of the Manuscript Troano is introduced here +(see Fig. 377) to show the relation of the figures to the characters. If +this interpretation be correct, we see here an evident attempt on the +part of the aboriginal artist to indicate by the symbol the action +necessary in the work to be performed. It is probably a conventional +sign, and not a phonetic character. + +[Illustration: FIG. 377.] + +[Illustration: No. 20] + + (?) In all probability one of the symbols used to denote the act of + walking or taking steps. Found but seldom in this particular form, + though each portion occurs frequently alone or in other + combinations. + +[Illustration: FIG. 378. Copy of lower division of Plate 65, Dresden +Codex.] + +A remarkable series of figures and written characters runs through the +lower division of Plates 65 to 69 of the Dresden Codex, apparently +devoted entirely to the representation of incidents in the life of the +culture hero Kukulcan, or deity mentioned on a subsequent page as the +"long nosed god" or "god with the snake-like tongue," or to ceremonies to +be performed in honor of this deity. Over the figure are three lines of +written characters, as shown in Fig. 378, which is a copy of the lower +division of Plate 65. These, as is readily seen, are in groups, one group +of six compound characters over each figure of the god. There are +thirteen figures of the god and thirteen of these groups of characters in +the series. The characters of a group, as may be seen by reference to the +figure, are arranged in the following manner: + + ___________ + | | | + | _a_ | _b_ | + |_____|_____| + | | | + | _c_ | _d_ | + |_____|_____| + | | | + | _e_ | _f_ | + |_____|_____| + +to be read (presumably) in the alphabetic order of the letters given; +though the order in which they are to be read is not essential at +present. Examining the series carefully we find that the first character +of each group corresponding with _a_ in the above diagram is the same +throughout. The same thing is true in reference to the third, or that +occupying the place of _c_ in the diagram, which is the symbol of the +deity. The sixth, or that corresponding with _f_ in the diagram, is also +the same throughout the series; the fifth, corresponding with _e_, is +substantially the same throughout, though subject to more variations than +any of the other characters. It follows, therefore, that the chief and +almost the only differences in the readings of the groups are to be found +in the second and fourth characters, or those represented by _b_ and _d_ +in the above diagram; the others (at least those represented by _a_, _c_, +and _f_), if referring at all to the figures, must relate to something +found in or applicable to each. The third (_c_), as stated, is the symbol +of the deity and corresponds in the text with the figure of the god in +the pictures. As this deity figure is the only thing found in all of the +representations, we must seek for the explanation of the other two +permanent characters in something else than what is figured. + +Comparing the second character (_b_) of each group with that upon which +the god is seated or standing, we find sufficient evidence to satisfy us +that this symbol is the one which is used throughout to indicate this +object. For example, the second symbol in the group on Plate 69 is an +exact copy of the object on which the deity is seated. The same thing is +substantially true of that in the left hand group of Plate 66, the middle +group of 67, and the right hand group of 68. + +Assuming, on account of the remarkable regularity of this series and the +fact that the deity is in each case seated or standing on something, that +this rule holds good throughout, we have a clew to those corresponding +symbols which are not simple copies of the things they are used to +indicate. + +Turning to Fig. 378, we observe in the right hand department the marks of +footsteps under the deity and the character shown in the margin (No. 20) +as the second of the group above the deity. It is worthy of notice that +in the two we find precisely Landa's two characters for the letter B. Is +it possible that the two principal parts of this compound character +denote the Maya words _oc be_, "foot journey" or "enters upon the +journey"? Attention will be called to this further on, but it is proper +to state here that as the prefix is found in three other corresponding +characters it cannot be a necessary part of that which represents the +footsteps in this case. + +[Illustration: No. 21.] + + Assuming the theory above given as to the characters in the inscription + which represent the things under the deity figures to be correct, + the second character in the middle group of the lower division of + Plate 65, shown in Fig. 378, will be the symbol for the substance + represented by scrolls under the figure of the deity.[354-1] + +The prefix in this case is the same as that to the symbol above described +(No. 20), and of course has the same signification. The other portion of +No. 21 must therefore represent the substance in which the god is +walking. This appears to be dust, sand, or mud. + +[Illustration: No. 22. _a_ _b_ _c_] + + _Cacauak_ or _cacauche_. The wild or cultivated cacao. Found a number + of times in the Dresden Codex, sometimes as represented in the + marginal figure _a_ and sometimes as in _c_, and always in + connection with figures holding in the hand a fruit of some kind. It + appears once in the Cortesian Codex (Plate 36), as shown in _b_, in + connection with a fruit of precisely the same kind as that figured + in the Dresden Codex. It is found also on Plate XVIII* of the + Manuscript Troano, but is apparently used here to denote an action. + +There can be little, if any, doubt, judging by the figures in connection +with which it is found, that this symbol is used in the Dresden and the +Cortesian Codices to denote the cacao. Whether it refers to the tree or +to the fruit is uncertain; possibly the different forms in which it is +found are intended to denote these distinctions. In some of the figures +the capsule appears to be indicated; in others the seed. The prefix to +figure _c_ apparently indicates the heaping or piling up of the fruit on +the dish held in the hands of the individuals figured in the same +connection, as, for example, on Plates 12 and 13 of the Dresden Codex. If +this supposition be correct it gives us a key to the signification of +this prefix. Reference to its use in the upper division of Plate XVIII*, +Manuscript Troano, will be made further on. + +In this symbol we find another of Landa's letters, and, if phonetic, +agreeing precisely with his interpretation. + +[Illustration: No. 23. _a_ _b_] + + _Ekbalam_ according to Rosny. The variety marked _a_ is found twice in + the Manuscript Troano, Plates XVI and XVII, and that marked _b_ once + in the Dresden Codex, Plate 8, each time in connection with a + spotted, leopard-like animal. + +The black markings on the symbols render it probable that Rosny's +interpretation is correct. The numeral before the first form may possibly +be explained by the fact that this symbol is used once (Manuscript +Troano, Plate XII) to indicate the day Ix. + +[Illustration: No. 24.] + + _Moo._ The ara, a large species of parrot. This symbol is found but + once, and that in Plate 16_c_, Dresden Codex, in connection with the + bird shown in Fig. 379. + +[Illustration: FIG. 379. The moo or ara from Plate 16. Dresden Codex.] + +The conclusion in this case is based on the following evidence: In this +series there are six groups of characters, four compound characters in +each group, arranged as in the annexed diagram: + + __________________________________________________ + | | | | | | | + | _a_ _b_ | _e_ _d_ | _g_ _h_ | _i_ | _m_ | _o_ | + | | | | | | | + | _c_ _d_ | _c_ _f_ | _c_ _d_ | _c_ | _n_ | _b_ | + |__________|__________|__________| | | | + | | | | + 1 2 3 | _k_ | _c_ | _c_ | + | | | | + | _l_ | _l_ | _p_ | + |_____|_____|_____| + +Similar characters in the different groups are represented by the same +letter; for example, the symbol for woman, heretofore shown (No. 17), is +represented by _c_, and an unknown character by _d_. Different letters +represent different symbols. It is apparent that we have here the +parallelism heretofore spoken of and are justified in basing conclusions +on this fact. + +At 1, 2, and 3 are female figures with a bird in each case perched on the +back. At _a_ is the head of a bird, evidently the symbol of the bird on +the female below; at _i_, in the fourth group, is precisely the same +symbol as the one found in the same relative position in the middle +division of Plate 17 over another bird, and at _m_, in the fifth group, +is another bird's head. From these facts we conclude that the first +symbol in each of these groups denotes a bird, and, as no two are alike, +that they refer to different species, the one at _g_ corresponding with +symbol No. 24, the bird beneath being the great parrot or ara. Other +facts, derived from a careful study of the various groups of this portion +of the codex, which would require much space and numerous illustrations +to explain, lead to the same belief. + +According to this conclusion, the following symbols also denote birds, +probably of the species here indicated. + +[Illustration: No. 25.] + + _Icim_? The horned owl. This is represented by _a_ in the first group + in the above diagram. + +The bird in the figure under the group, although horned, bears but slight +resemblance to an owl; yet, comparing the marks on the tail with those of +two of the birds on Plate XVIII* of the Manuscript Troano, I think the +interpretation is justified. + +[Illustration: No. 26.] + + _Kukuitz_? The Quetzal. The symbol is apparently incomplete, but the + bird figured under it justifies this conclusion. This symbol is + represented by _e_ in the above diagram. + +If this interpretation be correct, we find in this symbol another of +Landa's letters. + +[Illustration: No. 27. _a_ _b_] + + _Kuch._ A vulture or bird of prey much like the sopilote. These two + symbols (_a_ and _b_) appear to refer to the same bird, evidently a + vulture. (See Manuscript Troano, Plates XVII_a_ and XXVI*_a_.) The + first form (_a_) is found but once (Manuscript Troano, Plate + XVII_a_), the other at several points, both in the Manuscript Troano + and the Dresden Codex, and is represented by _m_ in the preceding + diagram. + +If this determination be correct, the first of these symbols (_a_) is +probably phonetic and agrees with the interpretation of No. 26. + +[Illustration: No. 28.] + + _C[=h]om_, _Xchom_, or _Hc[=h]om_. The sopilote or vulture. Found only + in Plates 16 and 17, Dresden Codex. The bird figure in Plate 17 + appears to be intended to represent a vulture. The symbol + corresponds to _i_ in the preceding diagram. + +If phonetic, the word indicated should, according to Landa's alphabet, be +aspirated, which is found to be true of one of the forms given by Perez. + +In certain series of the Dresden Codex, which appear to relate to the +four year series or to the four seasons, especially those on Plates +29-31, a certain class of food animals seems to be assigned to each. The +four following symbols are those used to express this idea: + +[Illustration: No. 29.] + + _Ceh_? The symbol for game quadrupeds. The same idea appears to be + indicated by the folded and tied quarter of a deer, as shown in No. + 11. The head shown in the symbol is probably intended for that of + the deer, though more like that of the rabbit. + +[Illustration: No. 30.] + + _Cutz_ or _Cax_. The symbol for game birds, the head being probably + that of the wild turkey (_Cutz_ or _Ahcutz_). + +[Illustration: No. 31.] + + _Huh._ The symbol for food reptiles or the iguana. + +As the Kan figure is admitted to be a maize or bread symbol, it is +readily seen that the object in view in connecting it with the animal +figures is to indicate that they are used for food, and hence are proper +offerings to the gods, which is equivalent to saying, to the priests. + +[Illustration: No. 32.] + + _Cay._ The symbol for food fishes, or fishes in general, though as + often on the Kan symbol or without any suffix. + +[Illustration: No. 33.] + + _Cutz_ or _Cax_. In one of the two series of these food symbols, in + Plates 29-31 of the Dresden Codex, in place of the bird symbol No. + 30 is that shown in symbol No. 33. It probably has, as Rosny + supposes, the same signification, a supposition which is + strengthened by the fact that it is found in the bird series on + Plates 16_c_ and 17_c_, same codex, and is represented by _o_ in the + preceding diagram. + + +SYMBOLS OF DEITIES. + +[Illustration: No. 34.] + + _Ekchuah._ The symbol or hieroglyph of the deity named "Ekchuah" by + the Mayas and considered the patron and protector of peddlers or + traveling merchants (Fig. 380). + +[Illustration: FIG. 380. The god Ekchuah, after the Troano and Cortesian +Codices.] + +The signification of the name of this deity is "The Black Calabash." The +form and the shading of the symbol render it more than probable that it +is a conventional representation of a divided or halved black calabash or +gourd, cut for the purpose of forming it into a cup or dipper, which, in +this form, is considered a symbol of this deity. + +The evidence upon which this determination is based is that the symbol +constantly accompanies the red mouthed, black deity. It is found, with a +single exception, only in the Manuscript Troano, and chiefly in Plates II +to V, relating to the traveling merchants. The single exception alluded +to is on Plate 15 of the Cortesian Codex; here the god bears upon his +back the traveling pack, indicating the vocation of which he is the +special guardian. + +It occurs unconnected with the figure of the deity only on Plates IX*, +XIV*, XV*, and XXV* of the Manuscript Troano. In the last the figure of +the god is in the same division, but in the adjoining compartment. In +Plate XV* it apparently refers to the idol the priest is carving, which +is probably a black one intended to represent this god. Landa,[358-1] +speaking of the artists carving idols from wood, says: + + They took also that which they used for scarifying their ears and + drawing blood from them, and also the instruments which they needed + for sculpturing their _black divinities_. + +Its appearance in Plate XIV* is apparently in connection with the +ceremonies relating to the manufacture of idols. Neither the symbol nor +the god it represents is to be fond in the Dresden Codex. + +[Illustration: No. 35. _a_ _b_ _c_] + + _Kukulcan._ (?) This is the symbol of the long nosed god, which Dr. + Schellhas designates "the god with the snake-like tongue," of which + representations appear so frequently in the different codices (see + Fig. 381). + +The snake-like appendages hanging from the side of the mouth may possibly +be intended to represent a curved fang rather than part of a divided +tongue. A remarkable figure on Plate 72 of the Borgian Codex deserves +special notice here. This is the representation of a deity supposed by +Kingsborough and others to be Quetzalcoatl, in which the head is as +represented in Fig. 382. Here we see both tongue and fang, and also an +eye precisely of the form found in the Maya symbol. + +[Illustration: FIG. 381. The long nosed god (Kukulcan) or "god with the +snake-like tongue."] + +Whether Kukulcan is the god indicated is uncertain, unless he is +identical with the long nosed god, or Maya Tlaloc, so frequently figured +in the Manuscript Troano and the Cortesian Manuscript. It is only +necessary to compare the figures on Plates 2 to 5 of the latter codex +with the long nosed, green figures of Plates XXVI, XXVII, XXIX, XXX, and +XXXI of the former to be convinced that they represent the same deity, +and that this is the Maya Tlaloc or rain god, whatever may be the name by +which he was known. + +As the symbol which accompanies these is the same as that found in +connection with the "snake tongued," long nosed god of the Dresden Codex, +there is no doubt that the same deity is referred to. It is worthy of +notice in this connection that Plates 29-41 of the Dresden Codex, which +are devoted almost exclusively to this deity, refer very largely to +water, the god being figured in connection with water no less than +twenty-eight times. He is also twice colored black, probably to symbolize +the dark rain cloud, and twice blue, denoting water. It is therefore fair +to conclude that the author of this codex considered him the giver of +rain. + +[Illustration: FIG. 382. Copy of head from the Borgian Codex +(Quetzalcoatl).] + +The following reasons given by Dr. Schellhas for supposing that the deity +indicated is Kukulcan apparently justify his conclusion, though it is +possible some other name may have been applied to him: + + He is represented in all the manuscripts, and far more frequently + than any other deity. His characteristic marks are always + unmistakable. An entire section of the Dresden Codex, pp. 29-43, and + pp. 1 and 2, belonging thereto, treat almost exclusively of this + god, and wherever he is pictured there we also find his name + hieroglyph. He is always characterized by the double, snake-like + tongue hanging from his mouth and by the peculiar eye, two marks + that are never absent, how numerous and varied soever may be his + representations, his symbols, and attributes. We also find him with + torches in his hands as symbols of fire; he sits on water; he stands + or sits in water or in falling rain; he rides in a boat; he appears + in company with a fish as symbol of water or in company of a bird's + head as symbol of the atmosphere, upon the day sign _Cab_ as symbol + of the earth, sitting, with the ax (machete) in his hand, with + arrows or spears, with a scepter, and finally, also, with the body + of a snake. Considering the immense variety of this god's + representations and the numerous symbols of power in the various + elements which the deity rules, we may well be justified in assuming + that there are indications here of one of the most important figures + in Maya mythology, with one of the principal deities of the people. + The most important god of the Mayas was Kukulcan, the creator of the + country's civilization, who had come from the far, unknown east, the + Mexican Quetzalcohuatl, the Gucumatz of the Kiche, the Kukulcan of + the Tzendals. All these names mean "feathered snake," "bird snake." + Now, in the above mentioned section of the Dresden manuscript, pp. + 29-43, there is found on page 36, middle, the representation of a + bird and a snake, the two symbols of the god Kukulcan, which, at the + same time, denote his name in the manner of a rebus. That this + representation is to be referred to the god with the snake's tongue + is rendered probable on the one hand by the fact that this whole + section treats of him and is proved on the other hand by the + circumstance that in the same place the same snake is found + represented with the head of the god; thus, page 35, middle, and 36, + above. In the same way this snake with the god's head is also found + in the Codex Cortesianus, page 10, middle, a passage which is + rendered notable also by the fact that in the writing above the + picture there is expressly found as a second sign the name + hieroglyph of the god. + +[Illustration: No. 36. _a_ _b_] + + _Cimi_ (?). Supposed symbols of the god of death. Occurring very + frequently in all the codices, but with several variations (see + Figs. 383 and 384). + +These are given chiefly on the authority of Drs. Foerstemann and +Schellhas, as I have some doubt in reference to this conclusion, for +reasons which will here be given. + +[Illustration: FIG. 383. The supposed god of death, from the Dresden +Codex.] + +[Illustration: FIG. 384. The supposed god of death, from the Troano +Codex.] + +As Dr. Schellhas remarks, this is "the most characteristic and most +easily recognized deity of the Maya Codices"; but this statement will not +apply to the symbols, as the variations are such as to render it +exceedingly doubtful whether precisely the same idea is embodied in each. +Even the two forms here given, both of which are found in all the codices +and often together, present variations too marked for us to believe, +except upon strong evidence, that they represent the same thing. Nor do +the figures of this deity or supposed deity appear to embody throughout +the same idea. In fact, they leave us in doubt as to whether any one +recognized deity is to be understood. Was there in the Maya pantheon such +a deity as the god of death? I have so far been unable to find any +satisfactory reason for answering this question in the affirmative. + +In the first part of the Dresden Codex, which is devoted, in part at +least, if not chiefly, to the maladies of the country, the skeleton +figures undoubtedly have reference to death, much like the skull and +cross bones in our day. In other places, as Plates XXVII and XXII* of the +Manuscript Troano and Plate 7 of the Cortesian Codex, the parched earth +appears to be intended, but it must be conceded that here also the idea +of death is included. Substantially the same idea, or at least the +relation of this god to the earth, appears to be indicated in Plate 8 of +the Cortesian Codex, where he is represented as beneath and holding up +that upon which another deity, bearing the bread symbol, is seated. + +As before stated the two symbols frequently appear in connection, +sometimes where the god is figured and often where he is not. It is, +therefore, unsafe to conclude as yet that either variety indicates a +particular deity known as the god of death. + +[Illustration: No. 37.] + + Symbol of the god with the banded face; seen chiefly in the Manuscript + Troano; not found in the Dresden Codex (Fig. 385). This is not the + deity which Dr. Schellhas designates as "the god with face crossed + by lines." + +[Illustration: FIG. 385. The god with the banded face, from the Codex +Troano.] + +This deity evidently pertains to the underworld and is closely allied to +the so-called god of death. The symbol and the figure are found together +in but few instances, yet the peculiar markings are such as to leave no +doubt on the mind, that the symbol is intended to denote what is +represented by the figure, being simply the head of the deity as +invariably figured. They appear together in Plates III_c_, V_a_, and +V_b_, XXVIII*_c_, and XXIX_c_ of the Manuscript Troano, in the first two +as having some relation to the traveling merchants, but in the last two +in a very different role. The dotted lines with which the bodies of these +figures are marked and the peculiar anklets appear to have been +introduced to signify relationship to the god of death. Perhaps the most +direct evidence of this relation is found in Plate 42 of the Cortesian +Codex, where the two deities are brought together at the sacrifice here +indicated. The two appear to be united in one in the lower division of +Plate XXVI* of the Manuscript Troano. + +Figures of this god are also found in some of the Mexican codices, as on +Plate 73 of the Borgian manuscript, where the relation to death and to +the underworld is too apparent to be mistaken. On Plate 10, same codex, +the head of death is marked with the distinguishing black band. + +Unfortunately for investigations in this line, the early Spanish notices +of the Maya mythology are so brief and confused that we can derive but +little aid from them in our efforts to identify the deities figured in +these manuscripts. Possibly the one with the banded face may represent +Cumahau or Hunhau, the prince of the lower regions; but the role he +appears to play where figured, with the exception of Plate II, Manuscript +Troano, and Plate 73 of the Borgian Codex, would scarcely justify the +name. + +[Illustration: No. 38.] + + (?) Symbol of the deity which Dr. Schellhas designates "the god with + the old man's face." Found in all the codices and almost invariably + in connection with the representation of the deity shown in our Fig. + 386. + +[Illustration: FIG. 386. The god with the old man's face.] + +The deity denoted by this symbol and by the figure which it accompanies +is possibly Zamna or Ytzamna, a deified Maya hero, but the various roles +in which he is found make it difficult to decide on this point. He +appears comparatively few times in the Dresden Codex, and only in the +first few pages. In none of these is there anything to indicate his +functions. In Plates 12_c_ and 15_c_ he holds a sun symbol in his hand, +which might be supposed to refer to his attributes as "Kinich-Kakmo" but +for the fact that the same thing is true of one or two other deities +figured in the same codex. In the Manuscript Troano, where he is oftenest +represented, his figure and his symbol appear most frequently in +connection with the bee or honey industry; for example, on Plate V_c_, +the only place in the first part of the manuscript where honey appears to +be referred to, and twenty-two times in that section of the second part, +Plates I* to X*, relating to bees. He also appears to take an active part +in the manufacture of idols, engages in painting, aids in the culture or +gathering of cacao, engages in predatory excursions, and acts in various +other relations. In the left compartment of Plate XXIV*_a_ he bears on +his head the head of a bird. In the remarkable double plate (41-42) of +the Cortesian Codex he is twice figured, in the central area and at the +east (top), and in each case is accompanied by a female deity. In the +latter case both god and goddess are bearing in their hands the Kan or +corn symbol. In Maya mythology Zamua was given a spouse named Ix +Kan-Leox, which signifies the yellow frond or silk of maize. + +[Illustration: FIG. 39.[TN-11]] + + Symbol, according to Dr. Schellhas, of the deity which he names "the + god with face crossed by lines," found in all the codices, but most + frequently in the Manuscript Troano and the Cortesian manuscript. + The deity is usually represented as in Fig. 387. + +[Illustration: FIG. 387. The god with face crossed by lines.] + +This is introduced here on the authority of Dr. Schellhas, although I +have considerable doubt as to the correctness of his conclusion. + +He remarks in regard to it as follows: + + Another characteristic and easily recognized deity, which, it is + true, is comparatively rare in the Dresden manuscript, but occurs + with extraordinary frequency in other codices, and whose sign it is + not hard to find, is the god whose face is crossed [surrounded] by + peculiar parallel lines, representations of whom are given in the + Cortesian Codex (p. 11, below) and Dresden Codex (p. 13, middle). + The deity is always male and is found in the Dresden Codex five + times, Cortesian Codex eighteen times, Manuscript Troano twenty + times, and Codex Peresianus five times. + + The sign of this god, as was the case with the others and as seems + to be the general rule, consists merely of a representation of the + god's head, combined with a sign which probably represents an affix. + The sign is found wherever the deity is represented and is an exact + rendering of the god's head, so that there can be no doubt as to its + being the name hieroglyph. True variations are not found, the + hieroglyph being perfectly alike in all the manuscripts. + + The nature of this deity is not easily determined, though it occurs + in the Codices Troano and Cortesianus with extraordinary frequency, + so that it would be seen that these two manuscripts, which evidently + belong together, treat principally of this deity. No analogous deity + is found in Aztec picture writing. * * * To all appearances we have + here a momentous figure of Maya mythology, of which, unfortunately, + we know nothing. + +It is true that this symbol is found in almost every instance where the +figure of the god appears--in fact, with fewer exceptions than others in +reference to which there is probably little doubt. It is also true that +the symbol is an exact copy of the god's head; but on the other hand +there are strong reasons for doubting the correctness of Dr. Schellhas's +conclusion. + +The first is that the figure of the supposed deity seems to have more +indications of being the conventional representation of an idol than of a +deity. The lines of the head are precisely the same as those on the heads +of the carved idols.[365-1] + +We also find it in connection with the wood symbol (marginal No. 6) at +the only points where the latter is found in the Cortesian Codex, and, +what is significant, in wholly inappropriate places unless connected with +an idol figure. These are found in the lower division of Plates 10 and +11, two on the top of thatched roofs and another on the head of the deity +called the "god with the old man's face," the head in the latter case +being apparently carved from a block of wood. + +The second is to the same effect, the symbol being found over each of the +figures of the lower division of Plates 26, 27, and 28 of the Cortesian +Codex and the middle division of Plates XXXI* and XXXII* of the +Manuscript Troano, where there appear to be processions of the different +deities. It is also significant that in the latter case each deity is +bearing in his hands what seems to be a block of wood from which in all +probability an idol is to be carved. + +Third, we find rows or lines composed entirely of this symbol, as in the +so-called title page of the Manuscript Troano. + + +DISCUSSION AS TO PHONETIC FEATURES OF THE CHARACTERS. + +It must be admitted, as heretofore intimated, that this question has not +as yet been satisfactorily answered. Whether what is here presented will +suffice to settle this point in the minds of students of American +paleography is doubtful; nevertheless, it is believed that it will bring +us one step nearer the goal for which we are so earnestly striving. +Something is said on this subject in my former work,[365-2] which need +not be repeated here. + +As it is evident from the preceding list of characters that conventional +signs and symbols, often nothing more than abbreviated pictographs, were +used in many cases to designate objects and persons, the inference to be +drawn, unless other evidence is adduced, is, that this method prevailed +throughout. Nevertheless there is some evidence that at the date when +these manuscripts were written Maya culture was in a transition state; +that is to say, conventional symbols were passing into true +ideographs[366-1] and possibly into phonetic characters. + +The lack of any satisfactory key to assist us in deciphering them makes +it exceedingly difficult to decide how far this change had progressed. We +are therefore left wholly to deductions to be drawn from the facts +obtained by laborious comparisons of the various relations in which the +characters are found and the uses which appear to be made of them in the +manuscript. + +It will be admitted without question that a large number of these +characters are ideographs or conventional symbols, as distinguished from +pictures, as, for example, most of those denoting the days, months, and +cardinal points. I say most of these, as it is yet possible to learn from +some of them the objects they were intended to represent, the +characteristic features not being entirely lost, as the symbol for the +day Cimi, the "death's head" or skull; that of the day Ymix, "the grain +of maize;" that of the month Moan, "the head of the moo or ara," a +species of parrot, &c. + +It is also possible to show from the manuscripts themselves evidences of +the changes from conventional pictographs to true or mnemonic symbols. + +Take, for instance, the bird symbols on Plates 16, 17, and 18 of the +Dresden Codex, presented in the preceding marginal figures numbered 24, +25, 26, 27, 28, and 33. If the determination be correct as given, it is +apparent that, while one of the birds is indicated by the head as a +symbol, the others are denoted by ideographs, or by phonetic characters +bearing no resemblance to their forms or peculiar features. That numerous +examples of this kind are to be found in these manuscripts will be +admitted by all who have carefully studied them. + +Another fact bearing upon this point is the difference between the +Dresden Codex and the Manuscript Troano in regard to marking with symbols +the things represented in the pictures. We fail to find in the former +(unless that on Plate 30 be a possible exception) the earth or soil +represented by any symbol, though frequently occurring in the latter and +also occasionally in the Cortesian Codex. The symbol for wood or that +appearing so often on wooden articles in the latter, and occasionally in +the Cortesian Codex, is wanting in the Dresden Codex, though wooden +articles are several times represented. From this we infer that the +Manuscript Troano is a more recent production than the Dresden Codex, +notwithstanding the evidences of greater skill in drawing and higher +mathematical attainments shown in the latter. + +Before discussing the question of phonography we ask attention to one or +two facts regarding Landa's alphabet which do not appear to have been +previously noticed, yet have an important hearing on the subject. + +The failure to reach any satisfactory results with this alphabet proves, +beyond a reasonable doubt, that this author was mistaken as to the +character of the Maya writing; yet the frequent occurrence in the +manuscripts of most, if not all, of the elements he presents renders it +certain that there is a basis of truth on which it rests. It is probable, +therefore, if we can find the key to his method, we may, after all, +obtain some satisfactory results by means of his alphabet. + +I have already stated as my belief that-- + + He has undertaken to pick out of their compound or syllabic + characters the letter elements; hence it is that, while we find it + impossible to decipher the manuscripts by using them, yet we find + such frequent resemblances as to compel us to admit a fundamental + relationship.[367-1] + +This opinion I still believe to be correct, but was, until very recently, +unable to get any positive evidence as to his method of obtaining these +elements. + +While examining the Cortesian Codes I came across (on Plate 17) the +symbol for a turtle (the different varieties of which are shown in +marginal figure No. 4), which is nothing more or less than an attempt to +represent the head of the animal. In the more abbreviated form (_b_) I at +once recognized Landa's A (compare with _c_ and _d_, No. 4). As the Maya +name of the turtle is _Ac_ or _Aac_ it is apparent that in this instance +the old Spanish priest selected a symbol representing an object the name +of which contains a single syllable having, as its chief letter element, +A. As this symbol is simply a representation of the animal's head there +is no reason to infer that it is phonetic; on the contrary, it is more +reasonable to assume that it was used only as a conventional sign. It is +possible that after long usage it may have been adopted as a phonetic +character, though its exceedingly rare occurrence in the manuscripts +(being found only in the Cortesian Codex and with the turtle figure) and +the fact that it is seldom, if ever, used as part of a compound character +would seem to forbid this idea. + +Precisely the same method was adopted in obtaining his B, which is given +in two forms, first as a foot print and second as a circle inclosing four +circular dots. The first, as all are aware, is only a conventional sign +and presumably not phonetic. The second may be phonetic, though +apparently but an abbreviation of the first. In Plate 65_c_ (see marginal +No. 20) and Plate 41_c_ the two forms are brought into such relation to +each other as to show that the latter is used as a symbol to represent +the idea conveyed by the first. The proof in these cases is too strong +to admit of doubt and explains Landa's method of obtaining his B, which, +as before stated, was by selecting the symbol of that which is denoted by +a Maya word of one syllable having B as its chief letter element, _Be_ +being the Maya word for "way," "journey," "walking," &c. + +The symbol for the cacao given above in marginal No. 22 contains his +eleventh letter _Ca_ twice and is probably that from which it was taken; +likewise that of the _Kukuitz_ or Quetzal (marginal No. 26) and of the +_Kuch_ or vulture (marginal No. 27_a_), each of which contains his _Ku_, +being double in the former and single in the latter. I am as yet unable +to trace these two symbols to their origin; we might suppose, from +Landa's figure of the latter, that it was intended to represent a bird's +nest containing eggs, but an examination of the symbol as found in the +manuscript renders this conclusion doubtful. + +The evidences of phonography are few and, as must be admitted, not +entirely satisfactory; yet they are apparently sufficient to justify the +somewhat general belief that the writing of the Mayas had reached that +stage where characters are sometimes used to indicate sounds. That +comparatively little advance had been made in this direction at the time +of the conquest is possible; moreover there is nothing to justify the +belief that they made use of true letters as Landa supposed. If they had +a phonographic system of any kind it was very imperfect and was only in +that primary stage in which syllables are represented by single +characters and words of more than one syllable by compound characters. +Judging by the changes observed in the relation of the parts of compound +characters to one another, we conclude that the order of arranging these +parts was not uniform or essential. It is also doubtful, if any of these +characters are phonetic, whether the parts of the longer words were +always written out in full. I am led to believe, from a few slight +indications, that, in forming words of more than one syllable, they often +used only the leading phonetic elements of the single words of which they +are composed; in other words, that they followed the rebus method of the +Mexicans. + +Descending to particulars and examples, the following are, perhaps, the +strongest proofs which can be presented on this point: + +As there can no longer be any doubt that the symbols for the cardinal +points have been ascertained and that those relating to the polar points +are distinguishable from those relating to the equatorial points, we are +justified in referring to them in this discussion. As each of the two +assigned to the equatorial points contains the symbol for "sun" or "day" +and as the two Maya words for these points--_Likin_ or _Lakin_ and +_Chikin_--contain the Maya term for sun or day ("kin"), there is some +reason for believing that the characters are phonetic. There is to be +added to this evidence the fact that the symbol of the month _Yaxkin_ +contains the same sun symbol. It would be somewhat remarkable to find the +same single character in three different combinations, representing three +different ideas expressed by words containing the same sound, yet having +no reference to the sound. + +It is now generally admitted by students of American paleography, on what +appears to be satisfactory evidence, that symbol No. 7 of the preceding +list, _Cab_, is used to signify "earth" or "land" and "honey," both of +which are designated by the same Maya term, _Cab_. As there is no +similarity in the things denoted the character is probably phonetic. The +"bee" appears also to be frequently indicated by the same character with +an affix, as may be seen by reference to the lower divisions of Plates +III*--X* of the Manuscript Troano. + +The symbol No. 9 (U) of the preceding list is found repeatedly on vases +and also as a prefix to both simple and compound characters. As _U_ in +Maya signifies "moon," "vase," and certain pronouns and is also used as a +euphonic particle before vowels, we are perhaps justified in concluding +that the symbol is phonetic and denotes the word _U_. I am aware that +neither Perez nor Dr. Brinton gives "vase" as one of the meanings of this +word, yet its constant appearance on vessels seems to leave no doubt that +Brasseur is correct. Even admitting that he is mistaken and that we are +in error as to the signification of the symbol, its various uses justify +the belief that it is phonetic. + +The symbol No. 34 of the preceding list, which is supposed to be that of +the god Ekchuah, is probably phonetic. The name of this deity is composed +of two Maya words, _ek_, "black," and _chu_, "calabash," and hence +signifies "the black calabash," and the form and coloring of the symbol +are apparently intended to denote this signification. If this +interpretation be correct it is phonetic, as there is nothing in or +pertaining to the figure of the deity which corresponds with it, except +the color. + +If the interpretation given of the preceding symbols Nos. 22, 24, 26, +27_a_, and 33 be correct, there can be scarcely a doubt that they are +phonetic. In the first--_cacau_, _cacauak_, or _cacauche_, the "cacao"--we +see Landa's letter _Ca_, which is doubled in each of the three forms taken +from the different codices. In the twenty-sixth--_Kukuitz_, the +Quetzal--Landa's _Ku_ is duplicated, as it should be if phonetic, while in +27_a_, _Kuch_, it appears but once. There is here also an additional +evidence of phoneticism in the fact that, while one of the symbols used to +denote this bird shows simply its head, and is surely not phonetic, the +other is entirely different and bears no resemblance whatever to any +feature or characteristic of the bird. Moreover, both parts of it are used +in other combinations referring to entirely different things. + +If my interpretation of No. 14 (_Xamach_ or _Chimix_) be right, it is +probably phonetic also. It is composed, as will be seen by reference to +the figure, of two symbols closely resembling that for the day Ymix, +except that the top portion of one is omitted. The resemblance in sound +to a duplication of Ymix is apparent. The slight but permanent variation +of the right hand portion from the usual Ymix symbol and the omission of +the top portion of the left hand one are scarcely explainable on the +supposition that they form simply a conventional sign; but if phonetic +the reason is apparent, as the _m_ sound is not repeated in the Maya +name. This conclusion is strengthened by the fact that the month _Mac_, +found in the last or bottom line of Plate 49, is precisely the same as +the right portion of No. 14, with Landa's symbol for _Ca_ added. This +probably justifies us in concluding that the true name of this month is +_Camach_, "the jaw" or "jaws," and that Landa's figure is simply a rude +representation of the lips or mouth. + +I have expressed the opinion[370-1] that the chief phonetic element of +No. 8 (the stone symbol), if used to represent sound, is _p_ or _pp_. +This opinion seems to be confirmed by the fact that this character is +found as a part of the symbol for the month _Pop_ on Plate 50 of the +Dresden Codex. (See the second character in the first transverse line +below the day columns in the preceding Fig. 362.) The method of +determining the months referred to in these plates of the codex has been +given in the preceding part of this paper. + +The interpretation given above of symbol No. 24 (the moo or ara) will +probably be accepted by all students of these manuscripts, and if so its +phonetic character must be conceded. That it is used in the place above +alluded to (Dresden Codex, Plate 16_c_) to denote this bird is proved by +the parallelism of the groups and the figure of the parrot under it. If +we turn now to Plate 48 of this codex we observe that the second +character of the first line below the day columns and the first character +in the upper line of the lower group or square is, in each case, a bird's +head. It is easily proved by means of the numeral series with which these +are connected that they denote, in both cases, the month Moan (from the +moo), proving that Brasseur's surmise was correct.[370-2] If the same +bird is represented by two symbols, one pictorial and the other having no +resemblance to any feature or character of the thing denoted, it is +probable the latter is phonetic. This conclusion is strengthened in this +case by the strong resemblance of the first part of No. 24 to the symbol +for the month Mol. + +I have shown above that the right portion of No. 20 of the list is +Landa's letter B, and also that in the lower division of Plate 65, +Dresden Codex (see Fig. 378), it signifies "footsteps" or the act of +walking. As the Maya word _Be_ signifies "journey," "wood," "march," and +also "journeying" and "marching," it is possible that this symbol is also +phonetic, although apparently only a modified form of the footprint. This +supposition is strongly supported by the fact that it is found in +numerous and varied relations, single and in combination. + +The symbol for 20 (_Kal_), No. 1 of the preceding list, is apparently +phonetic. This view appears to be confirmed by its use otherwise than as +a numeral symbol at several points in the text of the Manuscript Troano. +For example, in the third division of Plate XVII* it appears in this +form, [Illustration: Hieroglyph] while immediately below is the +representation of an idol head in a vessel covered with a screen or +basket, as shown in Fig. 388. The Maya verb _Kal_ signifies to "imprison" +or "inclose," which is certainly appropriate to what we see in the +figure. As the symbol is over each of the three similar figures in the +division, it is probable that it is intended to denote something relating +to or observable in them. In the second division of Plates XV* and XVI*, +same codex, is this symbol, [Illustration: Hieroglyph] several times +repeated, and below each the figure of a priest or deity at work, each +carving, with a machete or hatchet, the head of an idol. The probable +signification is "Give twice twenty strokes with a machete," and hence is +but partially phonetic. + +[Illustration: FIG. 388. Wooden idol in vessel with basket cover.] + +Other examples bearing on this question may be found, but these are +believed to be sufficient to warrant the belief that at the time these +codices were written Maya culture had reached that stage where the idea +of phoneticism was being introduced into the writing. Yet it is certain, +and even susceptible of demonstration, that a large portion, perhaps the +majority, of the characters are symbols. The more I study these +characters the stronger becomes the conviction that they have grown out +of a pictographic system similar to that common among the Indians of +North America. The first step in advance appears to have been to +indicate, by characters, the gesture signs. + + +FOOTNOTES: + +[345-1] See Chapter VI, Study of the Manuscript Troano, by Cyrus Thomas. + +[354-1] Unfortunately the scrolls were overlooked in preparing the cut. + +[358-1] Relacion de las cosas de Yucatan, p. 308. + +[365-1] See Plates XVI*_b_ and XVII*_c_, Manuscript Troano. + +[365-2] Study of the Manuscript Troano, pp. 141-161. + +[366-1] As the term "ideograph" is somewhat broad and comprehensive, it +may be well enough to state that I use it as expressing that stage of +symbolic writing where the picture characters have so changed that all +resemblance to the objects they were originally intended to represent is +lost, and therefore they can only be considered as mnemonic signs. + +[367-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 142, 143. + +[370-1] Study of the Manuscript Troano, p. 147. + +[370-2] Landa's Relacion, pp. 382, 383, Note 1. + + + + +INDEX + + +Adelung, J. C. cited 262 + +Aglio, Augustina, fac simile of Dresden Codex by 263-266 + + +Boettiger, C. A., mention of Dresden Codex by 262 + controversy with Abert concerning Dresden Codex 267 + +Brasseur, copy of the Manuscript Troano by 284, 286, 343 + cited 350 + + +Calendar system, tabular view of 270-374 + +Charency, H. de, cited 282 + +Codex Cortesianus, similarity of, to Manuscript Troano and Dresden +Codex 286 + + +Dresden Codex, numerals in 261-338 + + +Ebert, F. A., description of Dresden Codex by 263 + controversy with Boettiger concerning Dresden Codex 267 + + +Falkenstein, K. C., preservation of Dresden Codex by 268 + +Fleischer, H. L., mention of Dresden Codex by 263 + +Foerstemann, E., citation from Die Mayahandschrift of 261-269 + cited 272, 278, 280, 281, 283, 290, 292, 293, 300, 301, 302, 303, 304, + 305, 320, 322, 329, 330, 339, 340 + + +Goetze, J. C., preservation of Dresden Codex by 261 + biographical sketch of 261, 262 + + +Humboldt, A. von, notice of Dresden Codex by 262, 263 + + +Kingsborough, Lord, Dresden Codex copied by order of 262 + Mexican Antiquities of, cited 266 + + +Landa, cited 348 + +Landa's alphabet, insufficiency of 259, 347 + + +Manuscript Troano, copy of, by Brasseur 285, 286, 343 + study of, by C. Thomas, cited 339, 343, 344, 345, 350, 365, 366, 367, 370 + +Maya and Mexican manuscripts, C. Thomas on, cited 280 + +Maya Codices, aids to the study of, by C. Thomas 253-371 + +Mexican Antiquities, by Lord Kingsborough, cited 266, 267 + + +Rosny, L. de, cited 267, 347, 355, 357 + + +Schellhas, P., cited 345, 359, 360, 361, 362, 364 + +Schultz-Sellack, K., cited 278 + +Silvestre, E., Paleographie universelle of, cited 267 + + +Thomas, C., paper on aids to the study of the Maya codices by 253-371 + +Troano Manuscript, copy of, by Brasseur 285, 286, 343 + + +Vater, J. S., cited 262 + + + + +Transcriber's Note: + + TN-1 267 "hasty and obtrusive notice." should read 'hasty and + obtrusive notice.' + TN-2 272 indi cated should read indicated + TN-3 291 "and" repeated. + TN-4 295 Plate 48, 2nd line first asterisk is missing. + TN-5 296 Period missing after FIG + TN-6 322 In the original text, the 7 is printed above the 17, with no + horizontal line separating the two numbers. + TN-7 327 Tables XXI and XXII are not labeled in the original + publication but, by context, appear to be the two sections + of table following Table XX. + TN-8 338 Sixth column should read Sixth column. + TN-9 338 Footnote number for 338-1 was missing. It was inserted + based on the context of the note. + TN-10 348 Illustration No. 6 was missing the caption. + TN-11 364 Fig. 39 should read No. 39 + + + + + +End of the Project Gutenberg EBook of Aids to the Study of the Maya Codices, by +Cyrus Thomas + +*** END OF THIS PROJECT GUTENBERG EBOOK STUDY OF THE MAYA CODICES *** + +***** This file should be named 19777.txt or 19777.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/1/9/7/7/19777/ + +Produced by PM for Bureau of American Ethnology, Julia +Miller, and the Online Distributed Proofreading Team at +http://www.pgdp.net (This file was produced from images +generously made available by the Bibliotheque nationale +de France (BnF/Gallica) at http://gallica.bnf.fr) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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