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+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: UTF-8
+
+*** 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 Bibliothèque 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.
+
+This text contains a number of tables. It is recommended that a
+fixed-width font be used so the tables display with the correct
+alignment.
+
+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 special characters are used in this version of the book.
+If they do not display properly, try using a different font.
+
+  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
+  Ⓘ  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. Förstemann's introduction to the
+photolithographic copy of the codex,[261-1] he having had an opportunity
+to study the original for a number of years in the Royal Public Library
+of Dresden, of which he is chief librarian:
+
+"Unfortunately, the history of the manuscript begins no further back than
+1739. The man to whom we owe the discovery and perhaps the preservation
+of the codex was Johann Christian Götze, son of an evangelical pastor,
+born at Hohburg, near Wurzen, in the electorate of Saxony. He became a
+Catholic, and received his education first at Vienna, then in Rome;
+became first chaplain of the King of Poland and elector of Saxony; later
+on, papal prothonotary; presided over the Royal Library at Dresden from
+1734, and died holding this position, greatly esteemed for learning and
+integrity, July 5, 1749. This sketch is taken from his obituary notice in
+Neue Zeitungen von gelehrten Sachen, Nr. 62, Leipzig, 1749. In his
+capacity as librarian he went to Italy four times, and brought thence
+rich collections of books and manuscripts for the Dresden library. One of
+these journeys took place in 1739, and concerning its literary results we
+have accurate information from a manuscript, in Götze's handwriting,
+which is found in the archives of the Royal Public Library, under A, Vol.
+II, No. 10, and bears the title: 'Books consigned to me for the Royal
+Library in January, 1740.' Under No. 300 we read: 'An invaluable Mexican
+book with hieroglyphic figures.' This is the same codex which we here
+reproduce.
+
+"Götze also was the first to bring the existence of the manuscript to
+public notice. In 1744 he published at Dresden The Curiosities of the
+Royal Library at Dresden, First Collection. As showing what value Götze
+attributed to this manuscript, the very first page of the first volume of
+this work, which is of great merit and still highly useful, begins as
+follows: '1. A Mexican book with unknown characters and hieroglyphic
+figures, written on both sides and painted in all sorts of colors, in
+long octavo, laid orderly in folds of 39 leaves, which, when spread out
+lengthwise, make more than 6 yards.'
+
+"Götze continues speaking of this book from page 1 to 5, adding, however,
+little of moment, but expatiating on Mexican painting and hieroglyphic
+writing in general. On page 4 he says:
+
+"'Our royal library has this superiority over all others, that it
+possesses this rare treasure. It was obtained a few years ago at Vienna
+from a private person, for nothing, as being an unknown thing. It is
+doubtless from the personal effects of a Spaniard, who had either been in
+Mexico himself or whose ancestors had been there.'
+
+"On page 5 Götze says:
+
+"'In the Vatican library there are some leaves of similar Mexican
+writing, as stated by Mr. Joseph Simonius Asseman, who saw our copy four
+years ago at Rome.'
+
+"Götze therefore received the manuscript as a present on his journey to
+Italy at Vienna and took it with him to Rome. Unfortunately we know
+nothing concerning its former possessor. A more accurate report of the
+journey does not seem to exist; at least the principal state archives at
+Dresden contain nothing concerning it, nor does the General Directory of
+the Royal Collections. As appears from the above note, Götze did not know
+that the Vatican Codex was of an entirely different nature from the
+Dresden Codex.
+
+"In spite of the high value which Götze set upon the manuscript, it
+remained unnoticed and unmentioned far into our century. Even Johann
+Christoph Adelung, who as head librarian had it in his custody and who
+died in 1806, does not mention it in his Mithridates, of which that part
+which treats of American languages (III, 3) was published only in 1816,
+after Adelung's death, by J. S. Vater. This would have been a fitting
+occasion to mention the Dresden Codex, because in this volume (pp. 13 et
+seq.) the Maya language is largely treated of, and further on the other
+languages of Anahuac. Of course it was not possible at that time to know
+that our manuscript belongs to the former.
+
+"After Götze, the first to mention our codex is C. A. Böttiger, in his
+Ideas on Archæology (Dresden, 1811, pp. 20, 21), without, however, saying
+anything that we did not already know from Götze. Still Böttiger rendered
+great and twofold service: first, as we shall see presently, because
+through him Alexander von Humboldt obtained some notice of the
+manuscript, and, second, because Böttiger's note, as he himself explains
+in the Dresden Anzeiger, No. 133, p. 5, 1832, induced Lord Kingsborough
+to have the manuscript copied in Dresden.
+
+"We now come to A. von Humboldt. His Views of the Cordilleras and the
+Monuments of the Indigenous Peoples of America bears on the title page
+the year 1810, which certainly means only the year in which the printing
+was begun, the preface being dated 1813. To this work, which gave a
+mighty impulse to the study of Central American languages and
+literatures, belongs the Atlas pittoresque, and in this are found, on
+page 45, the reproductions of five pages of our manuscript. They are Nos.
+47, 48, 50, 51, and 52 of Lord Kingsborough. In the volume of text
+belonging to this atlas Humboldt discusses our manuscript on pp. 266,
+267. When he began his work he knew nothing as yet of the existence of
+the manuscript. It was brought to his knowledge by Böttiger, whose above
+named work he cites. Here we learn for the first time that the material
+of the manuscript consists of the plant metl (_Agave Mexicana_,) like
+other manuscripts that Humboldt had brought from New Spain. Furthermore,
+he correctly states the length of leaf as 0.295 and the breadth 0.085
+meter. On the other hand, he commits two mistakes in saying that there
+are 40 leaves and that the whole folded table forming the codex has a
+length of almost 6 meters, for there are only 39 leaves and the length in
+question is only 3.5 meters, as calculation will approximately show,
+because the leaves are written on both sides. Humboldt's other remarks do
+not immediately concern our problem.
+
+"In 1822 Fr. Ad. Ebert, then secretary and later head librarian,
+published his History and Description of the Royal Public Library at
+Dresden. Here we find, as well in the history (p. 66) as in the
+description (p. 161), some data concerning this 'treasure of highest
+value,' which indeed contain nothing new, but which certainly contributed
+to spread the knowledge of the subject among wider circles. We may remark
+right here that H. L. Fleischer, in his Catalogue of Oriental Manuscript
+Codices in the Royal Library of Dresden, p. 75, Leipzig, 1831, 4^o, makes
+but brief mention of our codex, as 'a Mexican book of wood, illustrated
+with pictures, which awaits its Œdipus;' whereupon he cites the writing
+of Böttiger. The signature of the manuscript here noted, E 451, is the
+one still in use.
+
+"Between the above mentioned notices by Ebert and Fleischer falls the
+first and so far the only complete reproduction of the manuscript.
+Probably in 1826, there appeared at Dresden the Italian Augustino Aglio,
+a master of the art of making fac similes by means of tracing through
+transparent substances. He visited the European libraries, very probably
+even at that time under orders from Lord Kingsborough, to copy scattered
+manuscripts and pictures from Mexico or seemingly from Mexico.
+
+"Now there arises the question, all important for interpretation, In
+which shape did the manuscript lie before Aglio? Was it a strip only 3.5
+meters in length or did it consist of several pieces?
+
+"To render clear the answer which we proceed to give, it is first
+necessary to remark that of the 39 leaves of the codex 35 are written on
+both sides and 4 on one side only, so that we can speak only of 74 pages
+of manuscript, not of 78. These 74 pages we shall in the following always
+designate by the numbers which they bear in Lord Kingsborough, and it is
+advisable to abide by these numbers, for the sake of avoiding all error,
+until the manuscript can be read with perfect certainty; the 4 empty
+pages I shall designate with 0 when there is need of mentioning them
+expressly.
+
+"Furthermore it is necessary to state which of these pages so numbered
+belong together in such way that they are the front and back of the same
+leaf. This condition is as follows: One leaf is formed of pages 1 45, 2
+44, 3 43, 4 42, 5 41, 6 40, 7 39, 8 38, 9 37, 10 36, 11 35, 12 34, 13 33,
+14 32, 15 31, 16 30, 17 29, 18 0, 19 0, 20 0, 21 28, 22 27, 23 26, 24 25,
+46 74, 47 73, 48 72, 49 71, 50 70, 51 69, 52 68, 53 67, 54 66, 55 65, 56
+64, 57 63, 58 62, 59 61, 60 0. [That is to say, each pair of this series
+forms one leaf, one page on one side and the other on the reverse side of
+the leaf.]
+
+"But now we are justified in the assumption, which at least is very
+probable, that neither did Aglio change arbitrarily the order of the
+original, nor Lord Kingsborough the order of Aglio. Consequently Aglio
+must already have had the manuscript before him in two pieces, be it that
+the thin pellicles by which the single leaves are connected were loosened
+in one place or that the whole was separated only then in order not to be
+obliged to manipulate the whole unwieldy strip in the operation of
+copying. A third possibility, to which we shall presently return, is that
+of assuming two separate pieces from the beginning; in this case Götze
+and the others must be supposed to have seen it in this condition, but to
+have omitted the mention of the circumstance, believing that the original
+unity had been destroyed by tearing.
+
+"Of the two pieces one must have comprised 24, the other 15 leaves. But
+Aglio copied each of the two pieces in such way as to trace first the
+whole of one side and then the other of the entire piece, always
+progressing from left to right, in European style. Therefore Aglio's
+model was as follows:
+
+"_First piece_:
+
+"Front (from left to right): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
+14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.
+
+"Back (from right to left): 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35,
+34, 33, 32, 31, 30, 0, 0, 0, 28, 27, 26, 25.
+
+"_Second piece_:
+
+"Front (from left to right): 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,
+57, 58, 59, 60.
+
+"Back (from right to left): 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64,
+63, 62, 61, 0.
+
+"In considering this, our attention is attracted by the position of the
+four blank pages, three of which are together, the fourth alone. It might
+be expected that the separate blank page began or concluded the second
+piece and was purposely left blank, because in the folding of the whole
+it would have lain outside and thus been exposed to injury; the other
+three would be expected at the end of the first piece. The former, as is
+easily seen, was quite possible, but the latter was not, unless we assume
+that even at the time Aglio took his copy the original order had been
+entirely disturbed by cutting and stitching together again. The four
+blank pages show no trace of ever having contained writing; the red brown
+spots which appear on them are to be found also on the sides that contain
+writing. Perhaps, therefore, those three continuous pages indicate a
+section in the representation; perhaps it was intended to fill them later
+on; in a similar way also page three has been left unfinished, because
+the lower half was only _begun_ by the writer.
+
+"I do not wish to conceal my view that the two pieces which Aglio found
+were separated from the beginning; that they belong even to two different
+manuscripts, though written in the same form; but, since it is human to
+err, I will here and there follow custom in the succeeding pages in
+speaking of one codex.
+
+"My conviction rests especially on the fact that the writer of manuscript
+A (pp. 1-45) endeavors to divide each page by two horizontal lines into
+three parts, which the writer of manuscript B (pp. 46-74) rarely does.
+The more precise statement is as follows: In A, pp. 1-23 and 29-43 always
+show two such lines in red color; pp. 25-28 have no red lines, but
+clearly show a division into three parts; p. 24 is the only one of this
+manuscript that has only writing and no pictures and where the greater
+continuity of the written speech forbids tripartition (here ends one side
+of the manuscript); finally, p. 45 seems to be marked as the real end of
+the whole by the fact that it contains three very light lines, dividing
+it into four parts; moreover, everything on this page is more crowded,
+and the figures are smaller than on the preceding pages, just as in some
+modern books the last page is printed more closely or in smaller type for
+want of space. In the same manner I suspect that p. 1 is the real
+beginning of the manuscript. This is indicated by the bad condition of
+leaf 2 44, which has lost one corner and whose page 44 has lost its
+writing altogether. For, if in folding the codex leaf 1 45 was turned
+from within outward, somewhat against the rule, leaf 2 44 was the outer
+one, and p. 44 lay above or below, and was thus most exposed to injury. I
+will not omit mentioning that my attention has been called by Dr. Carl
+Schultz-Sellack, of Berlin, to the possibility of leaves 1 45 and 2 44
+having been fastened to the rest in a reversed position, so that 43, 1
+and 2 and on the other side 44, 45, 3 were adjoining; then the gods would
+here be grouped together, which follow each other also on pages 29 and
+30. It cannot be denied that this supposition explains the bad condition
+of leaf 2 44 still better, because then it must have been the outermost
+of the manuscript; 44 would be the real title page, so to say, and on p.
+45 the writer began, not ended, his representation, with the closer
+writing of which I have spoken, and only afterward passed on to a more
+splendid style; and this assumption tallies very well with some other
+facts. But all this can only be cleared up after further progress has
+been made in deciphering the manuscript.
+
+"In two places, moreover, this first manuscript shows an extension of the
+drawings from one page over to the neighboring one, namely, from 4 to 5
+and from 30 to 31. This is not found on the second manuscript. From
+continuity of contents, if we are allowed to assume it from similarity of
+pictures and partition, we may suppose this manuscript to be divided into
+chapters in the following manner: pp. 1-2 (then follows the unfinished
+and disconnected page 3), 4-17, 18-23 (here follows p. 24, without
+pictures), 25-28, 29-33, 34-35, 36-41.
+
+"Compared with this, manuscript B rarely shows a tripartition, but on pp.
+65-68 and 51-57 a bipartition by one line. A further difference is this,
+that A out of 45 pages has only one (p. 24) without pictures, while B out
+of 29 pages has 9 without pictures (51, 52, 59, 63, 64, 70, 71, 72, 73),
+nothing but writing being found on them. Page 74, differing from all
+others, forms the closing tableau of the whole; and, similarly, p. 60,
+the last of the front, shows a peculiar character. A closer connection of
+contents may be suspected between pp. 46-50, 53-58, 61-62, 65-68.
+
+"The two manuscripts also differ greatly in the employment of the sign,
+or rather signs, differing little from each other, which resemble a
+representation of the human eye and consist of two curves, one opening
+above and the other below and joined at their right and left ends. These
+signs occur only on 5 out of the 45 pages of Codex A (1, 2, 24, 31, 43),
+while they occur on 16 pages out of the 29 of Codex B (48, 51, 52, 53,
+55, 57, 58, 59, 61, 62, 63, 64, 70, 71, 72, 73).
+
+"I believe that the differences above mentioned, to which others will
+probably be added, are sufficient to justify my hypothesis of the
+original independence of the two codices. Whoever looks over the whole
+series of leaves without preconception cannot escape the feeling, on
+passing from leaf 45 to leaf 46, that something different begins here.
+
+"Thus the copy of Aglio has made it possible to venture a hypothesis
+bordering on certainty concerning the original form of this monument.
+Five years after Aglio had finished the copying there appeared, in 1831,
+the first volumes of Lord Kingsborough's Mexican Antiquities. The work in
+the trade cost 175_l_.; the expense of publication had been over
+30,000_l_. The eighth and ninth volumes followed only in 1848. The
+ponderous work has undoubtedly great value from its many illustrations of
+old monuments of Central American art and literature, which in great part
+had never been published. As regards the Spanish and English text, it is
+of much less value. We may pass in silence over the notes added by Lord
+Kingsborough himself, in which he tries to give support to his favorite
+hypothesis that the Jews were the first settlers of America. Whoever
+wishes to obtain exact information concerning the character and contents
+of the whole work and dreads the labor of lifting and opening the
+volumes, may find a comprehensive review of it in the Foreign Quarterly
+Review, No. 17, pp. 90-124, 8vo, London, January, 1832, where he will
+also find a lucid exposition of the history of the literature of Mexican
+antiquarian studies.
+
+"In the middle of the third volume of the Mexican Antiquities (side
+numbers are here absent) there is found the title 'Fac simile of an
+original Mexican painting preserved in the Royal Library at Dresden, 74
+pages.' These 74 pages are here arranged on 27 leaves in the following
+manner:
+
+  Codex A.         Codex B.
+
+  1, 2, 3,         46, 47, 48,
+  4, 5, 6,         49, 50, 51,
+  7, 8, 9,         52, 53, 54,
+  10, 11,          55, 56, 57,
+  12, 13, 14,      58, 59, 60,
+  15, 16, 17,      61, 62, 63,
+  18, 19,          64, 65, 66,
+  20,              67, 68, 69,
+  21, 22, 23,      70, 71, 72,
+  24, 25,          73, 74.
+  26, 27, 28,
+  29, 30, 31,
+  32, 33, 34,
+  35, 36, 37,
+  38, 39, 40,
+  41, 42, 43,
+  44, 45.
+
+"On the whole, therefore, each leaf in Kingsborough comprises three pages
+of our manuscript. Why the publisher joined only two pages in the case of
+10 and 11, 18 and 19, 24 and 25, and left page 20 entirely separate, I
+cannot say; but when he failed to add 46 to 44 and 45 it was due to the
+fact that here there is indication of a different manuscript.
+
+"On January 27, 1832, Lord Kingsborough wrote a letter from
+Mitchellstown, near Cork, in Ireland, to Fr. Ad. Ebert, then head
+librarian at Dresden, thanking him again for the permission to have the
+manuscript copied and telling him that he had ordered his publisher in
+London to send to the Royal Public Library at Dresden one of the ten
+copies of the work in folio. The original of the letter is in Ebert's
+manuscript correspondence in the Dresden library.
+
+"On April 27, 1832, when the copy had not yet arrived at Dresden, an
+anonymous writer, in No. 101 of the Leipziger Zeitung, gave a notice of
+this donation, being unfortunate enough to confound Humboldt's copy with
+that of Lord Kingsborough, not having seen the work himself. Ebert, in
+the Dresden Anzeiger, May 5, made an angry rejoinder to this "hasty and
+obtrusive notice."[TN-1] Böttiger, whom we mentioned above and who till
+then was a close friend of Ebert, on May 12, in the last named journal,
+defended the anonymous writer (who perhaps was himself) in an extremely
+violent tone. Ebert's replies in the same journal became more and more
+ferocious, till Böttiger, in an article of May 25 (No. 150 of the same
+journal), broke off the dispute at this point. Thus the great
+bibliographer and the great archæologist were made enemies for a long
+time by means of our codex.
+
+"From Kingsborough's work various specimens of the manuscript passed into
+other books; thus we find some in Silvestre, Paléographie universelle,
+Paris, 1839-'41, fol.; in Rosny, Les écritures figuratives et
+hiéroglyphiques des peuples anciens et modernes, Paris, 1860, 4to; and
+also in Madier de Montjou, Archives de la société américaine de France,
+2^de série, tome I, table V.
+
+"In 1834 Ebert died, and was followed as head librarian by K. C.
+Falkenstein. He, unlike his predecessor, strove especially to make the
+library as much as possible accessible to the public. Visits and
+examinations of the library became much more frequent, and our
+manuscript, being very liable to injury, on account of its material, had
+to be withdrawn from the hands of visitors, if it was desired to make it
+accessible to their sight. It was therefore laid between glass plates and
+thus hung up freely, so that both sides were visible. In this position it
+still hangs in the hall of the library, protected from rude hands, it is
+true, but at the same time exposed to another enemy, daylight, against
+which it has been protected only in recent time by green screens. Still
+it does not seem to have suffered much from light during these four
+decades; at least two former officers of the library, who were appointed
+one in 1828 and the other in 1834, affirm that at that time the colors
+were not notably fresher than now. This remark is important, because the
+coloring in Humboldt, as well as in Lord Kingsborough, by its freshness
+gives a wrong impression of the coloring of the original, which in fact
+is but feeble; it may have resembled these copies some 300 years ago.
+
+"In 1836, when the manuscript was being preserved in the manner
+indicated, the two unequal parts, which were considered as a whole and
+which no one seems to have thought susceptible of being deciphered, were
+divided into two approximately equal parts from considerations of space
+and for esthetic reasons.
+
+"The first five leaves of Codex A, that is, pp. 1-5, with the backs
+containing pp. 41-45, were cut off and prefixed to Codex B in such way as
+to have p. 46 and p. 5 adjoining; when I examined the codex more closely
+I found that between 5 and 46, and therefore also between 41 and 74,
+there was no such pellicle as generally connects the other leaves. By
+this change one part was made to contain 20 leaves, the other 19.
+
+"At the same time another change was made. The three blank pages between
+pp. 28 and 29 had a marring effect, and they were put at the end by
+cutting through between leaves 18 0 and 17 29 and turning the severed
+leaves around, so that p. 24 joined on to p. 29 and 17 to 25. The
+pellicle loosened on this occasion was fastened again.
+
+"I must expressly state that I have no written or oral account of these
+two manipulations, but conclude they have taken place merely from a
+comparison of the present arrangement with that which Aglio must have had
+before him.
+
+"Thus the arrangement in which I found the manuscript, which it may be
+best to preserve until my views are recognized, is the following:
+
+"(1) _The diminished Codex A (19 leaves):_
+
+Front: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 25, 26, 27, 28, 0, 0, 0.
+
+Back: 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
+39, 40.
+
+"Or, if we enumerate the numbers on the back from right to left, so that
+the back of each leaf stands beneath its front:
+
+   6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17 | 25, 26, 27, 28,  0,  0,  0.
+  40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29 | 24, 23, 22, 21, 20, 19, 18.
+
+"(2) _The enlarged Codex B (20 leaves):_
+
+Front: 1, 2, 3, 4, 5, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
+59, 60.
+
+Back: 0, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 41, 43,
+43, 44, 45.
+
+"Or, reversing, as in the preceding case, the numbers on the back:
+
+   1,  2,  3,  4,  5 | 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60.
+  45, 44, 43, 42, 41 | 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61,  0."
+
+One of the most difficult things to account for in regard to this codex
+is the immense number of numeral characters it contains, many of which
+appear to have no reference to day or other time symbols.
+
+Although it is not claimed that the key which will fully unlock this
+mystery has been found, it is believed that the discoveries made will
+throw considerable light on this difficult subject and limit the field of
+investigation relating to the signification of the Maya codices.
+
+Before proceeding with the discussion of the subject proposed, it will
+not be amiss to state, for the benefit of those readers not familiar with
+these ancient American manuscripts, that the Maya method of designating
+numbers was by means of dots and lines, thus: . (one dot) signifying one;
+.. (two dots) two, and so on up to four; five was indicated by a single
+short straight line, thus, ----; ten, by two similar lines,
+[Illustration: Two horizontal lines, stacked]; and fifteen, by three such
+lines: [Illustration: Three horizontal lines, stacked]. According to this
+system, a straight line and a dot, thus, [Illustration: Dot above
+horizontal line], would denote 6; two straight lines and two dots,
+[Illustration: Two dots above two stacked horizontal lines], 12; and
+three straight lines and four dots, [Illustration: Four dots in a line
+above 3 stacked horizontal lines], 19. But these symbols do not appear to
+have been used for any greater number than nineteen. They are found of
+two colors in all the Maya codices, one class black, the other red,
+though the latter (except in a few instances, where the reason for the
+variation from the rule is not apparent) are never used to denote a
+greater number than thirteen, and refer chiefly to the numbers of the
+days of the Maya week and the numbers of the years of the "Indication" or
+"week of years." On the other hand, the black numerals appear to be used
+in all other cases where numbers not exceeding nineteen are introduced.
+As will appear in the course of this discussion, there are satisfactory
+reasons for believing that other symbols, quite different from these dots
+and lines, are used for certain other numbers, at least for 20 and for 0.
+
+In order that the reader may understand what follows, it is necessary to
+explain the methods of counting the days, months, and years in the order
+in which they succeed one another. Much relating to this will be found in
+a previous work,[269-1] but a particular point needs further
+explanation.
+
+According to the older and also the more recent authorities, the Maya
+years--there being 20 names for days and 365 days in a year--commenced
+alternately on the first, sixth, eleventh, and sixteenth of the series,
+that is to say, on the days Kan, Muluc, Ix, and Cauac, following one
+another in the order here given; hence they are spoken of as Kan years,
+Muluc years, Ix years, and Cauac years.
+
+Writing out in the form of an ordinary counting house calendar the 365
+days of the year, commencing with 1 Kan and numbering them according to
+the Maya custom (that is, up to thirteen to form their week and then
+commencing again with one) they would be as shown in Table I.
+
+TABLE I.--_Names and numbers of the months and days of the Maya system._
+
+   _______________________________________________________________________
+  |             |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |N t|
+  |             |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |u h|
+  |             |  |  |  |  |  |  |Y |  |  |  |  |  |  |K |  |  |  |  |m e|
+  |             |  |  |  |  |  |  |a |  |  |  |  |  |  |a |  |  |K |C |b  |
+  |             |  |  |  |T |T |  |x |  |C |  |  |  |  |n |M |  |a |u |e d|
+  |             |P |  |Z |z |z |X |k |M |h |Y |Z |C |M |k |u |P |y |m |r a|
+  |             |o |U |i |o |e |u |i |o |e |a |a |e |a |i |a |a |e |h |s y|
+  |             |p |o |p |z |c |l |n |l |n |x |c |h |c |n |n |x |b |u |  s|
+  |             |--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+o  |
+  |             | 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|f  |
+  |-------------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+---|
+  |_Names of the|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   |
+  |    days._   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   |
+  |Kan          | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|  1|
+  |Chicchan     | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|  2|
+  |Cimi         | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|  3|
+  |Manik        | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|  4|
+  |Lamat        | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|  5|
+  |Muluc        | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|  6|
+  |Oc           | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|  7|
+  |Chuen        | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|  8|
+  |Eb           | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|  9|
+  |Been         |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 10|
+  |Ix           |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 11|
+  |Men          |12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 12|
+  |Cib          |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 13|
+  |Caban        | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3| 14|
+  |Ezanab       | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4| 15|
+  |Cauac        | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5| 16|
+  |Ahau         | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6| 17|
+  |Ymix         | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 18|
+  |Ik           | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 19|
+  |Akbal        | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 20|
+  |----------------------------------------------------------------+--+---|
+  |                          _Intercalated days._                  |  |   |
+  |Kan                                                             |10|   |
+  |Chicchan                                                        |11|   |
+  |Cimi                                                            |12|   |
+  |Manik                                                           |13|   |
+  |Lamat                                                           | 1|   |
+   -----------------------------------------------------------------------
+
+Each of these eighteen columns forms one month, and the whole taken
+together, with the 5 days added at the end of the eighteenth month, form
+one continuous series, the second column following the first as though
+placed at the end of it, the third following the second, and so on to the
+end of the eighteenth. Whether or not it was the ancient custom to
+include the 5 added days in the year, as asserted by the old Spanish
+writers, is somewhat doubtful, at least in studying the Dresden Codex, we
+shall find but few occasions, if any, to use them, for there are few if
+any positive indications in this codex that they were added.
+
+As stated, each column of the table forms a month, though the numbering
+is carried to thirteen only; but at present the chief object in view in
+presenting it is to use it in explaining the method of counting the days
+and the intervals of time. The table is in truth a continuous series, and
+it is to be understood as though the 365 days were written in one column,
+thus:
+
+   1. Kan.
+   2. Chicchan.
+   3. Cimi.
+   4. Manik.
+   5. Lamat.
+   6. Muluc.
+   7. Oc.
+   8. Chuen.
+   9. Eb.
+  10. Been.
+  11. Ix.
+  12. Men.
+  13. Cib.
+   1. Caban.
+   2. Ezanab, &c.,
+
+the 20 days being repeated over and over in the order in which they stand
+in the table. This order is never changed; we may commence at whatever
+point in the series occasion may require, but the order here given must
+always be maintained, just as in our calendar the order of our days is
+always Sunday, Monday, Tuesday, &c. In other words, Chicchan must always
+follow Kan, Cimi must always follow Chicchan, &c.
+
+The method of counting intervals in the Maya calendar is very simple, if
+these explanations are borne in mind, and may be illustrated thus:
+Counting 14 days from 1 Kan--the first day of the year given in Table
+I--brings us to 2 Ezanab (the day we count from being excluded); 12 days
+more bring us to 1 Oc, in the second column of our table; 17 days more to
+5 Manik, in the third column; and 17 days more, to 9 Kan, in the fourth
+column.
+
+The number of the day required is readily ascertained by adding together
+the number of the day counted from and the number of days to be counted,
+casting out the thirteens when the sum exceeds this number (excepting
+where the remainder is thirteen); thus: 1 + 14 - 13 = 2, the number of
+the day Ezanab given above. So 1 + 14 + 12 - 13 - 13 = 1, the number of
+the day Oc, second column, Table I; and 1 + 14 + 12 + 17 + 17 - 13 - 13 -
+13 - 13 = 9, the number of the day Kan, fourth column. The reason for
+this is so apparent that it is unnecessary to state it.
+
+Suppose the day counted from is 11 Muluc of the eleventh month, and the
+number of days to be counted (or the interval) is 19; by adding together
+the numbers and casting out the thirteens the following result is
+obtained: 11 + 19 - 13 - 13 = 4. Counting forward on the table 19 days
+from 11 Muluc (the sixth number in the eleventh figure column), we reach
+4 Lamat (the fourth day of the twelfth month). When the sum of the
+numbers is a multiple of 13 the number obtained is 13, as there can be no
+blanks, that is to say, no day without a number.
+
+As the plates of the codices are usually divided into two or three
+compartments by transverse lines, it is necessary to adopt some method of
+referring to these in order to avoid the constant repetition of "upper,"
+"middle," and "lower" division. On the plan proposed by Dr. Förstemann,
+in his late work on the Dresden Codex (Erläuterungen zur Mayahandschrift
+der Königlichen öffentlichen Bibliothek zu Dresden), these divisions are
+designated by the letters _a_, _b_, and _c_; this plan will be adopted in
+this paper. The letter _a_ joined to the number of a plate, therefore,
+will signify that the division referred to is the upper one, as Plate
+12_a_; the letter _b_ signifies the middle one where there are three
+divisions or the lower one where there are but two; and the letter _c_
+signifies the lowest or bottom division where there are three.
+
+Where reference is made to the fac simile of the Dresden Codex,
+Kingsborough's colored edition is always to be understood, except where
+another is specially mentioned.
+
+Running through Plates 36_c_ and 37_c_ is a continuous line of day
+symbols and red and black numeral characters as follows, the numbers and
+names below the characters being explanatory and of course not on the
+original:
+
+[Illustration: FIG. 359. Lines of day and numeral symbols.
+  Pl. 36  10   XI Men | 15  XII Oc |  9  IX Cauac
+
+  Pl. 37  11  VII Oc  | 20    I Oc | 10  XI Ahau]
+
+As colors are not used in these figures the red numerals are indi
+cated[TN-2] by hollow or outline dots and lines and the black numerals by
+solid lines and dots.[272-1]
+
+In order further to assist those unacquainted with the symbols the same
+line is here given in another form, in which the names of the days are
+substituted for the symbols, Roman numerals for the red numbers, and
+Arabic for the black: 10, XI Men; 15, XIII Oc; 9, IX Cauac; 11, VII Oc;
+S, I Oc; 10, XI Ahau.
+
+The S is introduced to represent a numeral symbol different from the
+lines and dots and will be explained when reached in the course of the
+illustration.
+
+Starting from 11 Men, found in the twelfth figure column of Table I, and
+counting forward fifteen days, we come to 13 Oc of the thirteenth figure
+column, the second day of the above quoted line. Counting nine days from
+13 Oc[273-1] brings us to 9 Cauac, the third day of the line; eleven days
+more, to 7 Oc, the fourth day of the line. Following this day in the
+line, instead of a black numeral of the usual form, is this symbol:
+[Illustration: Hieroglyph] represented by S in the second form, where the
+names and numbers are substituted for the symbols. Taking for granted,
+from the position it occupies in the line, that it is a numeral
+character, it must represent 20, as the day which follows is 1 Oc, and
+counting twenty days from 7 Oc brings us to 1 Oc. Counting ten days more
+we reach 11 Ahau, the last day of the line given above.
+
+In this example the black numerals appear to have been used simply as
+counters, or as numbers indicating intervals; for example, 15 is the
+interval between 11 Men and 13 Oc.[273-2]
+
+This furnishes a clew which, if followed up, may lead to important
+results. That it explains the signification of one symbol undetermined
+until this relation of the numerals to one another was discovered, is now
+admitted. In the work of Dr. Förstemann before alluded to the discovery
+of the symbol for 20 is announced. Although I was not aware of the
+signification of this symbol until after my second paper, "Notes on
+certain Maya and Mexican manuscripts," was written, I had made this
+discovery as early as 1884.[273-3]
+
+As there will be occasion to refer to the days of the four different
+series of years (the Cauac, Kan, Muluc, and Ix years), a combined
+calendar, similar to an ordinary counting house calendar, is introduced
+here. For the Cauac years the left or Cauac column is to be used; for the
+Kan years, the Kan column, and so on.
+
+TABLE II.--_Names and numbers of the four series of years of the Maya
+system._
+
+  __________________________________________________________________________________
+          |        |        |        |                                      {Numbers
+   Cauac  | Kan    | Muluc  |  Ix    | 1  2  3  4  5  6  7  8  9 10 11 12 13{of the
+  column. |column. |column. |column. |14 15 16 17 18                        {months.
+  --------+--------+--------+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+-------
+          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |Days of
+          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |month.
+  Cauac   |Kan     |Muluc   |Ix      | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|   1
+  Ahau    |Chicchan|Oc      |Men     | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|   2
+  Ymix    |Cimi    |Chuen   |Cib     | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|   3
+  Ik      |Manik   |Eb      |Caban   | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|   4
+  Akbal   |Lamat   |Been    |Ezanab  | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|   5
+  Kan     |Muluc   |Ix      |Cauac   | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|   6
+  Chicchan|Oc      |Men     |Ahau    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|   7
+  Cimi    |Chuen   |Cib     |Ymix    | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1|   8
+  Manik   |Eb      |Caban   |Ik      | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2|   9
+  Lamat   |Been    |Ezanab  |Akbal   |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|  10
+  Muluc   |Ix      |Cauac   |Kan     |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|  11
+  Oc      |Men     |Ahau    |Chicchan|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|  12
+  Chuen   |Cib     |Ymix    |Cimi    |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|  13
+  Eb      |Caban   |Ik      |Manik   | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|  14
+  Been    |Ezanab  |Akbal   |Lamat   | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|  15
+  Ix      |Cauac   |Kan     |Muluc   | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|  16
+  Men     |Ahau    |Chicchan|Oc      | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|  17
+  Cib     |Ymix    |Cimi    |Chuen   | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|  18
+  Caban   |Ik      |Manik   |Eb      | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|  19
+  Ezanab  |Akbal   |Lamat   |Been    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|  20
+  ----------------------------------------------------------------------------------
+
+As this table has been explained in my previous papers it is only
+necessary to add here that the thirteen figure columns form a single
+series; therefore, when we reach the bottom of the thirteenth column we
+go back to the top of the first. The day reached will be the one directly
+opposite (that is, in the same horizontal line) in the day column for the
+given year.
+
+For example, taking the fifth column of numbers (the one having 3 for the
+top figure) and counting down nine days from the top number we reach the
+number 12. This will be 12 Lamat if a Cauac year, 12 Been if a Kan year,
+12 Ezanab if a Muluc year, and 12 Akbal if an Ix year. Therefore it is
+necessary in counting to refer always to the year (year column) with
+which the count begins. So long as the particular year referred to is
+unknown (as is Usually the case, the day series being apparently of
+general rather than of special application) it is immaterial which day
+column is selected, as the result will be the same with any. This will be
+apparent if we bear in mind that, when 260 days with their numbers
+attached have been written down in proper order as a series, we have
+therein all the possible combinations of days and numbers. This, it is
+true, does not give us all the months and years (to include these it is
+necessary to write out fifty-two entire years), but the same series of
+numerals will be applicable to each of the four year series (Kan, Muluc,
+Ix, and Cauac years). As any one of the thirteen figure columns of the
+table may be taken as the commencement of a year and any of the four day
+columns may be used, it is apparent that we have all the possible
+combinations (4 × 13 = 52).
+
+I say above that "it is necessary in counting to refer always to the year
+(year column) which the count begins." This I admit does not agree with
+the generally received idea of the Maya calendar, upon which Table II is
+constructed, as, according to this theory (which I have accepted in my
+previous papers), after passing through a year of one series
+(corresponding with one of the day columns of the table), we should enter
+upon a year of the next series; for example, when the year 1 Kan is
+completed we should enter upon the year 2 Muluc.
+
+Although this calendar system seems to have been in vogue at the time of
+the conquest and is indicated in one or two of the codices, and possibly
+in the one now under consideration, the chronological series of the
+latter, as will hereafter appear, do not seem to be based upon it or to
+agree with it.
+
+These explanations, with the further statement that the lines in the
+codex are to be read from left to right and the columns from the top
+downward, except where variations from this rule are noted, will enable
+the reader to follow the discussion. Another reason for using a table
+with only thirteen columns (though it would be difficult to devise a
+combined calendar of any other form) is that the 260 days they contain
+form one complete cycle, which, as will appear in the course of this
+discussion, was one of the chief periods in Maya time computations.
+
+Examining Plates 33 to 39 of the codex the reader will observe that the
+line already alluded to extends continuously through division _c_,
+commencing with the two characters over the figure (picture) in the lower
+right hand corner of Plate 33.
+
+The first of these characters as given in Kingsborough's work is the
+symbol of the day Ezanab, with the red numeral 13 to the left of it and
+the black numeral 9 over it; but referring to Förstemann's
+photolithographic copy of the codex it is found to be the symbol of Ahau.
+
+The entire line, with this correction (that is to say, as given by
+Förstemann), is represented in Fig. 360. In order to assist the reader,
+the names of the days and numbers of the symbols have been added
+immediately below the characters.
+
+As the year to which the line relates is unknown, we select the Muluc
+series, designated "Muluc column" in Table II, and commence with 13 Ahau,
+the twelfth number of the third figure column. Counting 9 days from this
+brings us to 9 Muluc, the top number of the fourth figure column and also
+the second day of the line above given. (the symbol is a face in
+Kingsborough's copy, but is plainly the Muluc sign in Förstemann's
+photograph). Eleven days more bring us to 7 Ahau, the third day of the
+above line; 20 more to 1 Ahau, the fourth day of the line (the 20 here is
+the symbol represented by S); 10 more to 11 Oc, the fifth day of the
+line; 15 more to 13 Chicchan, the sixth day of the line; 9 more to 9 Ix,
+the seventh day of the line; 11 more to 7 Chicchan, the eighth day of the
+line; line; 20 (S) more to 1 Chicchan, the ninth day of the line; 10 more
+to 11 Men, the tenth day of the line, and so on to the end.
+
+[Illustration: FIG. 360. Line of day and numeral characters.
+  Pl. 33      XIII Ahau IX Muluc
+  Pl. 34  11   VII  Ahau | 20 I Ahau | 10 XI Oc | 15 XIII Chicchan
+  Pl. 35   9    IX  Ix     | 11  VII  Chicchan | 20    I  Chicchan
+  Pl. 36  10    XI  Men    | 15 XIII  Oc       |  9   IX  Cauac
+  Pl. 37  11   VII  Oc     | 20    I  Oc       | 10   XI  Ahau
+  Pl. 38  15  XIII  Men    |  9   IX  Kan      | 11  VII  Men
+  Pl. 39  20     I  Men(?) | 10   XI  Chicchan | 15 XIII  Ahau]
+
+That the order of the series may be clearly seen the numbers are given
+here as they stand in the line, omitting the days: XIII; 9, IX; 11, VII;
+20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII; 9, IX;
+11, VII; 20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15,
+XIII.
+
+By adding together a black numeral and the preceding red one and casting
+out thirteen (or thirteens, as the case maybe), when the sum exceeds this
+number, we obtain the following red one, thus: XIII + 9 - 13 = IX; IX +
+11 - 13 = VII; VII + 20 - 13 - 13 = I; I + 10 = XI, and so on through the
+entire series. Attention is also called to the fact that the sum of the
+black (Arabic) numbers 9, 11, 20, 10, 15, 9, 11, 20, 10, 15, 9, 11, 20,
+10, 15, 9, 11, 20, 10, 15, is 260, a multiple of 13.
+
+If this relation of days and numerals holds good as a general thing
+throughout the codex, it is apparent that where the break is not too
+extensive it will enable the student to restore the missing and defective
+numerals and day symbols, to detect the errors of both copyists and
+original artists, and to determine the proper relation of the plates to
+one another. By it he learns, as before stated, that the symbol (see page
+273) denotes 20, and if phonetic probably stands for the Maya word _Kal_.
+
+Comparing Plates 42 and 43 with Plates 1 and 2, the resemblance is found
+to be so strong as to lead to the belief that they belong together. It is
+apparent from the figures, numerals, and characters[277-1] in the middle
+division (_b_) of Plates 1 and 2 that they belong together, as they now
+stand in Kingsborough's work and Förstemann's copy; that Plates 42 and 43
+are properly placed in regard to each other is also apparent from the
+figures and numerals in divisions _a_ and _b_.
+
+Taking for granted that the lines are to be read from left to right and
+the plates to follow each other in the same order, our next step is to
+ascertain on which side of the pair (Plates 42 and 43) Plates 1 and 2
+should be placed.
+
+The series of days and of numbers in Plate 43_b_ and Plate 1_b_, which
+evidently belong together, can only be brought into proper relation by
+placing the latter to the right of the former. Yet, strange as it may
+appear, the days and numerals in this division are to be read from right
+to left, while all the other numeral series of these four plates are to
+be read as usual, from left to right. This change in the order of the
+pages also brings together the similar figures in the upper division of
+these plates. That Plate 42 properly follows Plate 41 is apparent from
+the line of alternate red and black numerals in division _b_. As shown in
+a previous work[278-1] and as will appear hereafter, these horizontal
+lines of alternate red and black numerals without day symbols
+interspersed are usually, if not always, connected at the left with a
+column of days over which there is a red numeral, as in the Codex Troano.
+Running back along the line of numerals in the middle division of Plates
+42 and 41, the day column with which it is connected is found at the left
+margin of Plate 38. Unfortunately the red numeral over this column is
+obliterated, but can easily be restored. Starting with the first black
+numeral to the right of this, the entire line, which ends in the second
+column of the middle division of Plate 43 (representing the black
+numerals by Arabic numbers and the red by Roman numbers), is as follows:
+16, IX; 8, IV; 11, II; 10, XII; 1, XIII; 12, XII; 6, VI(?); 12, IV; 11,
+II; 11, XIII; 6, VI; 12, V; 7, XII; 6, V; S + 1, XIII; 6, VI.
+
+The number over the day column, Plate 38, must have been VI, as VI + 16 -
+13 = 9, a conclusion which is sustained by Förstemann's copy, which shows
+here very plainly the red character for VI.
+
+By adding the black (Arabic) numeral to the preceding red (Roman) one and
+casting out the thirteens, as heretofore explained, we obtain the
+following red (Roman) numerals, thus: VI + 16 - 13 = IX; IX + 8 - 13 =
+IV; IV + 11 - 13 = II; II + 10 = XII; XII + 1 = XIII; XIII + 12 - 13 =
+XII; XII + 6 - 13 = V.
+
+Here the result differs from what is found at this point in the line, as
+we obtain V instead of VI. In this case the mistake, if one has been
+made, cannot be attributed to Lord Kingsborough's copyist; the Maya
+artist must have made a mistake or there must be an error in the theory
+here advanced. But let us continue according to our own figures: V + 12 -
+13 = IV; IV + 11 - 13 = II; II + 11 = XIII; XIII + 6 - 13 = VI; VI + 12 -
+13 = V; V + 7 = 12; XII + 6 - 13 = V; V + 20 + 1 - 13 = XIII; XIII + 6 -
+13 = VI.
+
+There is no doubt, therefore, that the line forms one continuous series,
+and if so it links together pages 38 and 43 as they are now numbered. It
+follows, then, that if Plates 1 and 2 and Plates 42 and 43 belong
+together, the former pair must be placed to the right of 43. This is
+conceded by Dr. Förstemann,[278-2] as he says that, Dr. Karl
+Schultz-Sellack having pointed out the error in his paging, he changed
+pages 1 and 2 to 44 and 45 and pages 44 and 45 to 1 and 2; that is to
+say, the two leaves containing these pages were loosened from the strip
+and reversed, so that page 1 would be 44 and page 2 would be 45.
+
+Having brought together these plates so that 1 and 2 stand to the right
+of 43, attention is called to the lines of day symbols running through
+division _c_. Substituting names and numbers as heretofore, they are as
+follows:
+
+Plate 42:
+  IV Ahau; XII Lamat; VII Cib; II Kan; X Eb; V Ahau; XIII Lamat.
+     17        8         8        8      8      8         8
+
+Plate 43:
+  IV Chicchan; XII Been; VII Ymix; II Muluc; X Caban; V Chicchan; XIII Been.
+       17          8         8         8        8          8          8
+
+Plate 1:
+  IV Oc; XII Ezanab; VII Cimi; II Ix; X Ik; V Oc; (?) Ezanab.
+    17         8         8       8      8     8        8
+
+Plate 2:
+  IV Men; XIII Akbal; VII Chuen; II Cauac; X Manik; V Men; XIII Akbal.
+    17        8           8          8         8      8        8
+
+The chief objects in view at present in selecting this series are, as
+before indicated, to prove the relation of the plates to one another and
+to determine the use of the black numerals which stand under the day
+symbols. These numerals consist of but two different numbers, the first
+on each page being 17, the rest 8's.
+
+As the particular year or years to which the series refers is unknown we
+turn to our calendar--Table II--and select the Kan column, as we find
+that 4 Ahau, the first day of the series, is the seventeenth day of the
+year 1 Kan. This corresponds with the first black numeral. Counting 8
+days from this we reach 12 Lamat, the second day of our series; 8 more
+bring us to 7 Cib, the third day of the series; 8 more to 2 Kan; 8 more
+to 10 Eb; 8 more to 5 Ahau; 8 more to 13 Lamat, and 17 more to 4
+Chicchan. The red numeral at this point in some of the colored copies of
+Kingsborough's work is III, but a close inspection shows the missing dot
+which has not been colored. IV Chicchan is therefore correct.
+
+Continuing our count, 8 days more bring us to 12 Been: 8 more to 7 Ymix;
+8 more to 2 Muluc; 8 more to 10 Caban; 8 more to 5 Chicchan; 8 more to 13
+Been; 17 more to 4 Oc; 8 more to 12 Ezanab; 8 more to 7 Cimi; 8 more to 2
+Ix; 8 more to 10 Ik; 8 more to 5 Oc, and 8 more to 13 Ezanab. Here the
+red numeral is wanting, but a comparison of the numbers on the different
+plates and the order of the series make it evident that it should be
+XIII.
+
+Continuing our count, 17 more bring us to 4 Men (here a dot is missing in
+Kingsborough's copy, but is present in the photograph); 8 more to 12
+Akbal. Here there is one dot too many, which we may attribute to a
+mistake of the original artist. Assuming XII to be correct, 8 more bring
+us to 7 Chuen; 8 more to 2 Cauac; 8 more to 10 Manik; 8 more to 5 Men; 8
+more to 13 Akbal, and to the end of our table; thus, if we include the
+first seventeen days, completing the series of thirteen months or 260
+days.
+
+These illustrations will probably satisfy any one that the black numerals
+in these lines denote the intervals between the days indicated by the
+symbols and that the series so far examined are to be read from left to
+right.
+
+Although the succession of days and numbers in the lines of the last
+example would seem to furnish conclusive evidence that the whole is one
+continuous series, yet the peculiar combinations of numbers used by the
+Maya priests render these series very deceptive. There can be no doubt
+that the black numbers--8's--are used to indicate the intervals between
+the days specified; but there is another possible way of explaining the
+17 with which the lines on the different plates begin.
+
+Here are four plates, evidently closely related to one another; the lines
+of days and numbers in the lowest division of each are precisely alike,
+except as to the days indicated; in the left hand column of characters of
+each is one of the cardinal point symbols. It is possible, therefore,
+that these four plates relate to the four different years or series of
+years; that is to say, one to the Kan years, one to the Muluc years, and
+so on. This view is somewhat strengthened by the fact that 4 Ahau, first
+of the line on Plate 42, is the seventeenth day of the first month of the
+year 1 Kan; 4 Chicchan, first of the line on plate 43, the seventeenth
+day of the first month of the year 1 Muluc; 4 Oc, the seventeenth day of
+1 Ix, and 4 Men the seventeenth day of 1 Cauac. The four figures in the
+middle division of Plates 1 and 2 seem also to favor this idea, not so
+much by the peculiar animals represented (of which we have no explanation
+to give) as by the double symbols from which they are suspended, which I
+am quite confident denote the union of years or the time at which two
+years meet--the close of one and the commencement of another--although
+fully aware that Dr. Förstemann has interpreted them as symbols of the
+heavenly bodies.[280-1]
+
+In the text above these figures are seen two characters or symbols of
+this type, which in all probability, as will hereafter appear, denote or
+symbolize the "tying of the years." We may also add that the five days of
+each plate or group are the five assigned, as I have explained in "Notes
+on certain Maya and Mexican manuscripts," to the cardinal points. For
+example, those on Plate 42 are Ahau, Eb, Kan, Cib, Lamat.[280-2] Still it
+must be admitted, on the other hand, that as the four lines form
+precisely one complete cycle of 13 months or 260 days there is a very
+strong inference that they together form one continuous series and that
+the arrangement into four parts or divisions has reference to the four
+seasons or four cardinal points. The final decision on this point
+therefore still remains in doubt.
+
+As it has been shown that Plates 33 to 39 and Plates 38 to 43 are
+properly placed as they stand in Kingsborough's copy and also in
+Förstemann's and that Plates 1 and 2 follow Plate 43, we have proof that
+the following plates succeed one another to the right, as here given: 33,
+34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 2.
+
+A slight inspection is sufficient to show that Plates 29 to 33 follow one
+another in the same order, a conclusion which is easily verified by
+testing the lines of numerals in the manner explained. It is apparent,
+therefore, that the following plates form one unbroken series, running
+from left to right: 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
+42, 43, 1, 2; a conclusion which Dr. Förstemann, who has had the
+opportunity of studying the original, has now reached.
+
+Having ascertained the object and use of at least one class of black
+numerals and the relation they bear to the days and day numbers, it may
+be well to test further the discovery by other examples, in order to see
+how far it holds good and what new facts it may bring out. In doing this
+it will be necessary to repeat in part what has already been shown by Dr.
+Förstemann in his late work; but as these discoveries were made
+independently and before this work came to hand, and as our conclusions
+differ in some respects from those reached by him, the plan and scope of
+this paper would be incomplete without these illustrations.
+
+Commencing with the day column in the middle of Plate 35_b_ and extending
+through Plates 36_b_ and 37_b_ to the right margin of the latter, is a
+line of alternate red and black numerals, which may be taken as an
+example of the most common series found in the Dresden and other codices.
+It is selected because it is short, complete, and has no doubtful symbols
+or numerals in it.
+
+Using names and numbers in place of the symbols, it is as follows:
+
+    I.
+  Caban, 11, XII; 6, V; 9, I; 4, V; 7, XII; 9, VIII; 6, I.
+  Muluc.
+  Ymix.
+  Been.
+  Chicchan.
+
+In this case the red numeral over the day column is I. It is to be
+observed that the last number of the series is also I, a fact which it
+will be well to keep in mind, as it has an important bearing on what is
+now to be presented. But it is proper to show first that this series is
+continuous and is connected with the day column.
+
+Adding the I over the column to the 11, the first black numeral; gives
+XII, the red numeral following the 11. That this holds good in all cases
+of this kind will become apparent from the examples which will be given
+in the course of this discussion. Adding together the remaining pairs, as
+follows: XII + 6 - 13 = V; V + 9 - 13 = 1; 1 + 4 = V; V + 7 = XII; XII +
+9 - 13 = VIII; VIII + 6 - 13 = I, we obtain proof that the line is one
+unbroken series. It is apparent that if the black numerals are simply
+counters used to indicate intervals, as has been suggested, then, by
+adding them and the red numerals over the column together and casting out
+the thirteens, we should obtain the last red number of the series. In
+this case the sum of the numbers 1, 11, 6, 9, 4, 7, 9, 6, is 53; casting
+out the thirteens the remainder is 1, the last of the series. If we take
+the sum of the black numbers, which in this case is 52, and count the
+number of days on our calendar (Table II) from 1 Caban, the fourteenth
+day of the first month of the year 1 Kan, we shall find that it brings us
+to 1 Muluc, the sixth day of the fourth month; 52 days more to 1 Ymix; 52
+more to 1 Been, and 52 more to 1 Chicchan, thus completing the day column
+in the example given. This proves, in this case at least, that the red
+numeral over the day column applies to all the days of the column and
+that the whole numeral series--that is to say, the sum of the
+counters--represents the interval between the successive days of the
+column. The total number of days from 1 Caban, first of the column, to 1
+Chicchan, the last, is 208. Adding 52 more gives 260 and brings us back
+to 1 Caban, our starting point.
+
+It will be observed that the sum of the black numbers--which denotes the
+interval between the days of the column--is 52, which is a multiple of
+13, the number of days in a Maya week. It follows, therefore, that so far
+as this rule holds good the last red numeral of the series must be the
+same as that over the day column. In a former work[282-1] I explained the
+method of ascertaining the relations of the days of a column to one
+another by means of the intervals without reference to the numbers
+attached to them, a subject to which Charency had previously called
+attention;[282-2] by the explanation now given we ascertain the true
+intervals between the days _as numbered_. The two modes therefore form
+checks to each other and will aid very materially in restoring
+obliterated and doubtful days.
+
+There is another point in regard to these series which may as well be
+illustrated by means of the example given as any other. What is the
+signification of the red numerals of the series? They are unnecessary if
+the only object in view was to indicate the intervals between the days of
+the column. Nor will the supposition that the Mayas had not discovered a
+means of representing higher numbers than 20 suffice, as the introduction
+of 13 would have lessened the labor and shortened the calculation. But
+one answer to this inquiry appears possible, viz, that these numbers are
+intended to denote certain intermediate days to which importance was for
+some reason attached. These intermediate days can readily be determined
+from the data given, and in the present example are as follows:
+
+    (1) Between 1 Caban and 1 Muluc they are 12 Lamat, 5 Ix, 1 Akbal, 5
+    Manik, 12 Ix, and 8 Akbal.
+
+    (2) Between 1 Muluc and 1 Ymix they are 12 Ahau, 5 Cimi, 1 Men, 5
+    Cauac, 12 Cimi, and 8 Men.
+
+    (3) Between 1 Ymix and 1 Been they are 12 Eb, 5 Ezanab, 1 Manik, 5
+    Chuen, 12 Ezanab, and 8 Manik.
+
+    (4) Between 1 Been and 1 Chicchan they are 12 Kan, 5 Oc, 1 Cauac, 5
+    Akbal, 12 Oc, and 8 Cauac.
+
+These, as will be readily perceived, are found by counting on the
+calendar from 1 Caban, 1 Muluc, &c., as heretofore explained.[283-1]
+
+Our interpretation of the series of this particular class is now
+complete, except as to their application or the object in view in forming
+them and the determination of the particular years to which they apply.
+Possibly they may be of general application, so far as consistent with
+the calendar system. The conclusion on this point depends largely upon
+the conclusion as regards the system, as it is evident their location in
+time--if the year of 365 days and the four series of years formed the
+basis of the system--would not correspond with their position in a system
+based upon the year of 360 days, in which the four year series does not
+play any necessary part.
+
+Dr. Förstemann calls attention to the fact that the pairs of numerals
+representing the intermediate days are usually placed in separate
+compartments, each containing a figure or a picture generally symbolic or
+of a priest dressed to indicate some particular god. It is therefore very
+probable that these intermediate days are to be devoted to ceremonies
+relating to the divinities or subjects indicated by these figures.
+
+In order to confirm the theory we are now discussing and at the same time
+show some of the different varieties of the series of the type now under
+consideration, the following additional examples are given.
+
+In the middle division of Plate 5 is a day column and a numeral series,
+as follows:
+
+    I.
+  Manik }
+  Cauac } 16, IV; 9, XIII; S + 5, XII; 2, I.
+  Chuen }
+  Akbal
+  Men
+
+This series terminates with I, as it should according to the theory. The
+sum of the black numerals--16, 9, 20, 5, 2--is 52, a multiple of
+thirteen, and the interval between the successive days, reading
+downwards, is 52, agreeing in these particulars with the theory. It will
+also be observed that the symbol represented by S answers to the number
+20.
+
+In the lowest division of the same plate is another similar series, as
+follows:
+
+   XII
+  Ezanab }
+  Akbal  } 20 + 9, II; 11, XIII; 18, V; 7, XII.
+  Lamat  }
+  Been
+  Ezanab
+
+This terminates with XII, the number over the column; the sum of the
+black numbers is 65, a multiple of thirteen and precisely the interval
+between the successive days of the column, taking the week numbers into
+consideration, which is always to be understood in speaking of these
+intervals unless the contrary is expressly stated.
+
+[Illustration: FIG. 361.]
+
+In the middle division of Plate 8 is a short series connected with a day
+column containing the following days, reading downwards, as usual: Manik,
+Cauac, Chuen, Akbal, Men. The symbol for Akbal (Fig. 361), is a very
+unusual one, reminding us strongly of a skull, which may possibly have
+given origin to the symbol. The numerals of the series are as follows: 20
++ 6, VIII; 20 + 6, VIII; the number over the column, VIII; and the
+interval between the days, 52.
+
+In Plate 15, division _c_, is the following series, which differs from
+those given in having two day columns instead of one:
+
+   III      III
+  Lamat    Ix
+  Ahau     Cimi   }
+  Eb       Ezanab } 12, II; 14, III.
+  Kan      Oc
+  Cib      Ik
+
+The final number is the same as that over the columns; the sum of the
+black numbers is 26, which is a multiple of 13; but in this case in
+counting the intervals the days are to be taken alternately from the two
+columns.
+
+Commencing with 3 Lamat on our calendar and counting 26 days brings us to
+3 Ix; 26 more to 3 Ahau; 26 more to 3 Cimi, and so on to the end.
+
+In the lower division of Plate 9 is a series arranged as follows:
+
+   III      III      VI   VIII
+  Cauac    Been       3     2
+                    {XI    II
+  Chuen    Chicchan { 3     4
+                    {VI   VII
+  Akbal    Caban    { 4     1
+  Men      Muluc      I   III
+  Manik    Ymix       7     2
+
+The sum of the black numerals is 26 and the final red number is III, the
+same as that over the columns. The interval between the days, taken
+alternately from the two columns, as in the preceding example, is 26. The
+numbers are also to be taken alternately from the two number columns.
+
+It is apparent that these examples sustain the theory advanced. This will
+also be found true in regard to all the series of this type in this and
+the other codices where the copy is correct. Brasseur's copy of the
+Manuscript Troano is so full of mistakes that no satisfactory examination
+of this codex can be made until a photographic copy is obtained;
+nevertheless a few examples are given as proof of the above statement.
+
+In the third division of Plate XI* is the following series:
+
+   IV
+  Ahau }
+  Eb   } 17, VIII; 13, VIII; 10 V; 12, IV.
+  Kan  }
+  Cib
+  Lamat
+
+As will be readily seen, after the explanations given, this agrees with
+the theory advanced.
+
+The last red number is the same as that over the day column, the sum of
+the black numbers is 52, and the interval between the days 52.
+
+Commencing in the right margin of the lowest division of Plate XXIII* and
+running through Plates XXII* and XXI*, is the series here represented:
+
+   VII     VII
+  Cib      Cimi   }
+  Ik       Eb     } 7, I; 7, VIII; 7, II; 5, VII.
+  Lamat    Ezanab }
+  Ix       Kan
+  Ahau     Oc
+
+An examination of this shows it to be of the type of the double column
+series of the other codex, except that here the days of one column are to
+be taken in the order in which they stand before proceeding to the other
+column. The sum of the black numbers is 26 and the interval between 7 Cib
+and 7 Ik 26 days. The interval between 7 Ik and 7 Lamat, 7 Lamat and 7
+Ix, and between 7 Ix and 7 Ahau is, in each case, 26 days. The interval
+between 7 Ahau, last day of the left hand column, and 7 Cimi, the first
+day of the right hand column, is also 26 days.
+
+The order in which the days of these double column series of this
+manuscript follow one another is not uniform, as in some cases (see Plate
+XXV*, division _a_) they are to be taken alternately from the two
+columns, as in the examples heretofore given from the Dresden Codex.
+
+In the middle division (Plate XXXIII*, same codex) is a series of the
+following form, but with the days so nearly obliterated that restoration
+is necessary:
+
+           { VI   I
+           { 5    8
+   I       { VI   I
+  Ymix (?) { 5    8
+  Cimi (?) { VI   I
+  Chuen    { 5    8
+  Cib (?)  { VI   I
+    (?)    { 5    8
+           { VI   I
+           { 5    8
+
+The symbol of the first day has only the upper circle of dots to indicate
+that it is Ymix, that of the second day is almost obliterated, the third
+is clearly Chuen, the lower half of the fourth is obliterated, and the
+interior of the fifth is a blank.
+
+Fortunately there are sufficient data by which to make the restoration.
+Chuen, we observe, is the middle of the column; that is, two days are
+above it and two days below it; the sum of the black numerals is 65;
+hence the interval between the days, considering the week numbers as
+attached, is 65, and the simple interval in the month series, without
+regard to the week numbers, is 5. Counting back on our calendar (Table
+II) 65 days from 1 Chuen we reach 1 Cimi, and 65 more bring us to 1
+Ymix. In like manner we find the fourth day to be 1 Cib and the fifth 1
+Ymix. The numbers in the figure columns are to be taken alternately,
+thus: 5, VI; 8, I; 5, VI; 8, I, &c.
+
+These examples are sufficient to show that the series of the Manuscript
+Troano are arranged upon the same plan and based upon the same system as
+those of the Dresden Codex. The following examples from the Codex
+Cortesianus prove the same thing to be true in reference to the series
+found in it.
+
+The first is taken from the lower division of Plates 10 and 11, Rosny's
+reproduction:
+
+  XIII
+  Ahau     } 11, XI; 5, III; 5, VIII; 5, XIII; 9, IX; 3, XII; 6, V;
+  Chicchan } 1, VI; X, XIII.
+  Oc
+  Men
+
+The S in the line of numerals represents the usual symbol for 20. The sum
+of the black numbers is 65, the interval between the days 65, and the
+last red numeral the same as that over the day column, thus agreeing in
+plan with those in the other codices.
+
+The following double column series is found in the middle division of
+Plate 30:
+
+   XI        XI
+  Ahau     Ymix  }
+  Eb       Been  } 20 + 6, XI; 20 + 6, XI.
+  Kan      Caban }
+  Cib      Chicchan
+  Lamat    Manik
+
+The number 20 is denoted by the usual symbol. The sum of the black
+numbers is 52 and the interval between the days in each column 52, but in
+this case there does not appear to be any connection between the columns,
+there being, in fact, two distinct series.
+
+In the upper division of the same plate is this series:
+
+    XI
+  Ezanab { VI     XI
+         { 8      5
+  Oc     { VI     XI
+         { 8      5
+  Ik     { VI     XI
+         { 8      5
+  Ix     { VI     XI
+         { 8      5
+  Cimi
+
+The order in which these numerals are to be read is as follows: 8, VI; 5,
+XI; 8, VI; 5, XI, &c., which gives, as the final red number of the
+series, XI, the same as that over the column. The sum of the black
+numbers is 52 and the interval between the days 52.
+
+Taking for granted that the correctness of the theory advanced is
+conceded, some attempts at its further application, especially its use in
+making restorations and corrections in defective series and in settling
+doubtful questions relating thereto, will now be presented.
+
+In the upper division of Plate 32, Dresden Codex, are the four day
+columns and lines of numerals over them here represented:
+
+   1
+   4       13       9            4
+  15       13       2           11
+  XIII     XIII     XIII        XIII
+  Manik    Cib      Chicchan    Ix
+  Chuen    Ahau     Muluc       Ezanab
+  Men      Kan      Been        Ik
+  Cauac    Lamat    Caban       Cimi
+  Akbal    Eb       Ymix        Oc
+
+Connected with these numbers is a line of alternate black and red numbers
+running along over the figures of Plates 32 to 39, division _a_. There
+are several breaks and some partially obliterated characters in it which
+must be restored in order to use it. It has been selected partly on this
+account, that the method of filling such breaks and making such
+restorations may be seen.
+
+Representing the numerals and symbols as heretofore and substituting a
+cipher where the numbers are wanting or are too much obliterated to be
+determined by inspection, the series will be as follows: 11, XI; 8 + 20,
+0; 12 (or 13), XIII; 6 + 20, XIII; 12, VII (?); 16 (?), V; 5, X; 1, XI;
+20, V; 12, IV, 6, X; 0, V; 5, X; 7, IV; 12 (?), II; 5, VII; 8, II; 11, 0.
+
+Commencing with the XIII over the day columns and counting as heretofore,
+we obtain the following result: XIII + 11 - 13 = XI; XI + 8 + 20 - 13 -
+13 = XIII. The first blank should therefore be filled with XIII.
+Continuing, XIII + 13 - 13 = XIII; the black numeral in this case should
+be 13, although apparently 12 in the codex; XIII + 6 + 20 - 13 - 13 =
+XIII; XIII + 12 - 13 = XII. Here the result obtained differs from the red
+numeral in the codex, which is apparently one line and two dots, or VII;
+but, by carefully examining it or inspecting an uncolored copy, the two
+lines which have been covered in the colored copy by a single broad red
+line are readily detected. The next black numeral is partially
+obliterated, the remaining portion indicating 16, but it is apparent from
+the following red numeral that it should be 19. Making this correction we
+proceed with our count: XII + 19 - 13 - 13 = V; V + 5 = X; X + I = XI; XI
++ 20 - 13 - 13 = V; V + 12 - 13 = IV; IV + 6 = X. The next black numeral
+is obliterated, but is readily restored, as X + 8 - 13 = V; V + 5 = X; X
++ 7 - 13 = IV. The next step presents a difficulty which we are unable to
+explain satisfactorily. The black numeral to be counted here, which
+stands over the animal figure in the upper division of Plate 39, is 12,
+both in Kingsborough's copy and in Förstemann's photograph, and is clear
+and distinct in each, and the following red numeral is as distinctly II,
+whereas IV + 12 - 13 = III. Moreover it is evident from the remaining
+numbers in the line that this red numeral should be II. We may assume
+that the Maya artist has made a mistake and written 12 instead of 11,
+which is evidently the number to be used in the count; but this
+arbitrary correction should not be resorted to so long as any other
+explanation is possible. From the fact that immediately under these
+numbers there are certain symbols which appear to have some reference to
+the termination of one year or cycle and the commencement of another, it
+is possible that a supplemental, unnumbered, but not uncounted day has
+been added. The fact that this interval of twelve days includes the day
+Ymix lends some probability to this supposition. Using 11 instead of 12,
+we continue our count as follows: IV + 11 - 13 = II; II + 5 = VII; VII +
+8 - 13 = II; II + 11 = XIII. Thirteen is, therefore, the last number of
+the series, which is wanting in the codex. The 8 and II next to the last
+pair of the series are not in line with the other numbers, but thrust
+into and near the bottom of the column of characters in the upper
+division of Plate 39. Adding together the black numbers as thus amended
+and restored, viz, 11, 8, 20, 13, 6, 20, 12, 19, 5, 1, 20, 12, 6, 8, 5,
+7, 11, 5, 8, 11, the sum is found to be 208, which is a multiple of 13,
+and the final number of the series is 13. On the other hand, the sum of
+the series does not indicate the interval between the days of a column
+counting downwards, nor between two consecutive days or the corresponding
+days of two adjoining columns in any direction. The number of days from
+13 Manik to 13 Chuen is 104, but counting 208 days from 13 Manik brings
+us to 13 Men, the third day of the first (left hand) column; 208 more to
+13 Akbal, the fifth; 208 more to 13 Chuen, the second; and 208 more to 13
+Cauac, the fourth, thus completing the column.
+
+As these columns do not appear to form a continuous series it is possible
+they pertain to four different series of years, though the fact that each
+includes more than one year would seem to forbid this idea. It is more
+probable that they pertain to four different series, to each of which the
+line of numerals is to be considered as belonging.
+
+The black numerals above the columns present a problem which I am unable
+to explain. The numbers stand in the original as follows:
+
+   1
+   4    13    9    4
+  15    13    2    11
+
+If we suppose that the lowest line denotes days, the one next above,
+months, and the uppermost, in which there is but a single number, years,
+the series will appear to be ascending toward the left, with the
+difference 4 months and 11 days, as shown by addition, thus:
+
+  Y.    M.     D.
+         4     11 Numbers over the fourth column.
+         4     11
+  ---------------
+         9      2 Numbers over the third column.
+         4     11
+  ---------------
+        13     13 Numbers over the second column.
+
+Doubling the difference and adding we obtain the numbers over the first
+column:
+
+  Y.    M.    D.
+        13    13
+         9     2
+  ---------------
+   1     4    15
+
+What adds to the difficulty is the fact that if the columns are taken in
+reverse order the interval between the corresponding days is 4 months and
+11 days; that is to say, counting from 13 Ix, first day of the fourth
+column, to 13 Chicchan, first day of the third column, we find the
+interval to be exactly 4 months and 11 days; and the same rule holds good
+throughout, so that reading across the upper line of days, from right to
+left, and following with the second line in the same way, ending with
+Akbal, the interval will be 4 months and 11 days between the consecutive
+days. Another significant fact is that by counting 4 months and 11 days
+from the first day of the year 1 Kan we reach 13 Ix; counting 9 months
+and 2 days from the same date brings us to 13 Chicchan; 13 months and 13
+days, to 13 Cib; and 1 year and 4 days, to 13 Manik, which corresponds
+with the regular interval; it is therefore probable that there is an
+error in the numerals over the first or left hand column.
+
+It is apparent from the illustrations given that in numeral series of the
+preceding type restorations can be made where not more than two numbers
+in succession are wanting. Even three can generally be restored if the
+numbers preceding and those following the break are distinct, but such
+restorations should be cautiously made.
+
+In the middle division of Plate 9 is a short series where the number over
+the day column is wanting; moreover, there is uncertainty as to the
+number of days in the column and as to the signification of the red
+numerals, which are in pairs in Kingsborough's work instead of single as
+usual. Is it possible to explain these uncertainties and to reduce them
+to the usual simple form? Let us make the trial.
+
+The days in the column are apparently the following: Ahau, Muluc, Ix,
+Cauac, Kan. The symbols, except that for Cauac, are too plain to admit of
+doubt, and there is no difficulty in reference to Cauac, the question of
+doubt being with regard to the Ahau, which is partially surrounded by
+other characters and may, apparently, be as correctly considered a part
+of the hieroglyphic inscription as of the day column.
+
+Counting on the list of days in the calendar (Table II), as, for example,
+the Muluc column, we find the interval from Muluc to Ix is 5 days, from
+Ix to Cauac is 5 days, and from Cauac to Kan 5 days; but the interval
+from Ahau to Muluc is 9 days. From this fact we may reasonably infer that
+Ahau does not belong to the column. Moreover, the other 4 days are the
+four year bearers, and when they occur together the column usually
+consists of but 4 days, as, for example, in the lowest division of Plate
+29 of this codex and Plate XXXII* of the Manuscript Troano. The numerals
+are 20; XIII, X; 20, XII, III; the number over the day column, as before
+stated, is wanting. The interval from 1 Muluc (or 2 or 3 Muluc) to Ix of
+the same number is 65 days. It is evident, therefore, that one of each
+pair of red numerals of the series given must be a counter and has been
+colored red by mistake. As the numbers in the last pair are III and XII,
+the number over the column must be 3 or 12. Suppose it is 12 and that
+XIII of the first pair is a counter, then XII + 20 + 13 - 13 - 13 - 13 =
+VI. As the number in the series is X this will not do. Supposing the X of
+the first pair of red numerals to be the counter, colored by mistake, the
+result is as follows: XII + 20 + 10 - 13 - 13 - 13 = III. This is also
+wrong, as the remainder should be XIII. Supposing the number over the
+column to be III and the XIII of the first pair and XII of the second to
+be the counters, the result agrees with the theory in every particular.
+Thus, III + 20 + 13 - 13 - 13 = X; X + 20 + 12 - 13 - 13 - 13 = III; and
+20 + 13 + 20 + 12 = 65, the interval between 3 Muluc and 3 Ix. In
+Förstemann's copy the XIII and XII are black, thus verifying the
+conclusion here reached.
+
+The series running through Plates 10_c_ and 11_c_ presents some
+difficulties which I have, so far, been unable to solve. The day columns
+and numerals are as follows:
+
+   I          XIII
+  Ymix        Cimi   }
+  Been        Ezanab } 1, I; 5, VI; 10, III; 13, III; 15, V; 9 (?), XIII.
+  Chicchan    Oc     }
+  Caban       Ik
+  Muluc       Ix[290-1]
+
+The numerals in this case are very distinct, especially in the
+photographic copy, and there can be no doubt as to the days. Here the
+last black number, 9, is wrong; it should be 8, a fact noticed by
+Förstemann.[290-2] Making this correction, the series is regular and
+consistent, so far as it relates to the right hand column, which has the
+red thirteen over it. But there is no series for the left hand column.
+Can it be that those who used the manuscript were expected to find the
+proper numbers by the line given? Possibly this is the reason the other
+series is not written out, as by adding one to each red number we obtain
+the proper result, which, if written out, would be as follows: 1, II; 5,
+VII; 10, IV; 13, IV; 15, VI; 3, I.
+
+In Plate 30_c_ are the four day columns here given, with the numeral
+eleven over each:
+
+   XI         XI         XI       XI
+  Ahau     Chicchan    Oc         Men
+  Caban    Ik          Manik      Eb
+  Ix       Cauac       Kan        Muluc
+  Chuen    Cib         Ymix       Cimi
+  Lamat    Been        Ezanab     Akbal.
+
+Extending from the right of this group is a numeral series consisting of
+nine pairs of numbers, each pair the same, 13, XI. The sum of the black
+numbers (nine 13's) is 117 and the interval between the successive days
+of each column is 117; thus, from 11 Ahau to 11 Caban is 117 days, and so
+on down to Lamat, the last of the left hand column. From 11 Lamat to 11
+Chicchan (first day of second column) is also 117, and so on to the end
+of the fourth column. These four columns, therefore, form one continuous
+series of 2,223 days, commencing with 11 Ahau and ending with 11 Akbal;
+but, by adding 117 days more, so as to bring us back to 11 Ahau--which
+appears to be in accordance with the plan of these series--the sum is
+2,340 days, or nine cycles of 260 days each.[291-1]
+
+The interval between the days, without reference to the numbers attached
+to them, is 17. It may be well to notice here the relation of the
+intervals between the days when counted in the two ways: (1) the apparent
+interval, or that which indicates their position in the month; (2) the
+true interval between the days, indicated by the symbols and numbers.
+When the first is 6 the latter, as we have found, is 20; when the first
+is 12 the latter is 52; when the first is 5 the latter is 65, and when it
+is 17 the latter is 117.
+
+Particular attention is also called here to the fact that so far no
+indications of the use of the year period of 365 days have been observed;
+on the contrary the cycle of 260 days appears to be the period to which
+reference is chiefly made.
+
+Attached to the day column in Plate 29_c_ and running into 30_c_ is a
+series which presents a difficulty I am unable to explain. The days and
+numerals in this case are as follows:
+
+   III
+  Ix
+  Cauac } 16, VI; 16, IX; 16, XII; 16, (?)
+  Kan   }
+  Muluc
+
+The red numeral over the day column is very distinctly III in
+Kingsborough's work, but is II, though somewhat blurred, in Förstemann's
+photograph. As III + 16 - 13 = VI, and the remaining numerals agree with
+this result, III must be correct. Adding together the pairs and casting
+out the thirteens, thus, III + 16 - 13 = VI; VI + 16 - 13 = IX; IX + 16 -
+13 = XII; XII + 16 - 13 - 13 = II, we find the last red number, which is
+wanting in both copies of the codex, to be II, whereas, according to the
+theory advanced, it should be III. The sum of the black numerals (four
+16's) is 64, while the interval between the days is 65. The only way of
+correcting the mistake, if one has been made, is by arbitrarily changing
+the last 16 to 17; but uniformity in the black numerals apparently
+forbids this change and and[TN-3] indicates that the variation from the
+usual rule must be accounted for in some other way.
+
+In reference to this series, Dr. Förstemann[292-1] remarks:
+
+     The column of the days has the difference 5; the fifth sign (in this
+     case really superfluous), that of the thirteenth day, appears in a
+     remarkable form, apparently as an inscription on a vessel. The black
+     figures ought to give the sum 65, but we get only 4 × 16, or 64. But
+     this appears to be merely an oversight by the copyist, for although
+     in the Codex Troano, also, we find 64 several times instead of 65,
+     still this has always appeared to me merely as a sign of the great
+     negligence of the copyist of that manuscript.
+
+Turning to the Manuscript Troano, Plate XXVIII*_b_, we find a column
+consisting of the four terminal days of the year, Been, Ezanab, Akbal,
+and Lamat, which of course have the same relation to one another as the
+first days. It is evident from the space that only four were intended to
+be given. The numerals in Brasseur's fac simile are XI; 20, 12, IV; 9,
+XIII; 10, X; 13, XI.
+
+The red numeral over the column is XI, as is also the last of the series,
+but the sum of the black numbers is only 64, which would give X as the
+final number, as is evident from the following operation: XI + 32 - 13 -
+13 - 13 = IV; IV + 9 = XIII; XIII + 10 - 13 = X; X + 13 - 13 = X. The
+interval between the days is 65. We have, therefore, precisely the same
+difficulty in this instance as in the case from the Dresden Codex under
+consideration. Moreover, the only method of correcting the mistake, if
+there is one, is by adding _one_ to the last black number. It would be
+hazardous to assume that two mistakes, precisely the same in every
+respect, should have been made in regard to these exactly similar series.
+The probability that a mistake has been made is lessened by the fact that
+on Plate XXIX*_b_ of the manuscript is another four day column, the last
+days of the years, as the preceding. The numeral over the column is XIII
+and the series is as follows: 13, XIII; 20, 18, XII; 13, XIII. Adding
+these and casting out the thirteens, we have this result: XIII + 13 - 13
+= XIII; XIII + 20 + 18 - 13 - 13 - 13 = XII; XII + 13 - 13 = XII. This
+gives XII as the last number when it should be XIII. If a mistake has
+been made the only method of correcting it is by increasing the last
+black number by one, as in the other two cases alluded to.
+
+It is proper to state that on the other hand there is another four day
+column on Plate XXXII*_a_ of the last mentioned codex, the days of which
+are precisely the same as those on Plate 29_c_ of the Dresden Codex, to
+wit, Ix, Cauac, Kan, Muluc. The numeral over it is XII and the series is
+as follows: 13, XII; 13, XII; 13, XII; 13, XII; 13, XII. This presents no
+difficulty, as it conforms in every respect to the rules given, but only
+serves to deepen the mystery in the other cases.
+
+Going back to the series on Plate 29_c_ of the Dresden Codex, we observe
+not only that the days of the column are the four year bearers, but also
+that one of the four cardinal symbols is found--in the superscription--in
+each of the four compartments through which the series extends. It is
+possible, therefore, that the series is intended to be applied separately
+to each of the four years. Supposing this to be the case, counting 64
+days from 3 Ix would bring us to 2 Ezanab; 64 days from 3 Cauac to 2
+Akbal; 64 days from 3 Kan to 2 Lamat; and 64 days from 3 Muluc to 2 Been.
+It is significant that in each case the day reached is that on which the
+given year terminates; for example, the Ix years (counting the five added
+days) terminate on Ezanab; the Cauac years on Akbal &c. If the intention
+was to have the series terminate with the end of the respective years,
+then these years must necessarily have been 2 Ix, 2 Cauac, 2 Kan, and 2
+Muluc. I must confess that this explanation is not satisfactory; it is
+thrown out simply as a suggestion.
+
+Running through the middle division of Plates 30 and 31 is this series:
+
+  3,    VIII;    3, VIII;    3, VIII;    3, VIII
+  5,    Oc       5, Men      5, Ahau     5, Chicchan.
+
+Commencing with 8 Oc (omitting for the present the 3 and 5 to the left)
+and counting thence 3 months and 5 days we reach 8 Men; 3 months and 5
+days more and we reach 8 Ahau; 3 months and 5 days more bring us to 8
+Chicchan, and 3 months and 5 days more bring us again to 8 Oc, thus
+completing a cycle of 260 days (13 months) and also accounting for the
+first pair of numerals--3 and 5 in the series. It appears to be a pretty
+general rule to commence a series of this type with the difference
+between the numbers of the series. One reason for this is apparent: that
+is, to complete the cycle of 260 days, to which most, if not all, of
+these groups appear to refer.
+
+Dr. Förstemann says in regard to this line:[293-1]
+
+     This is the place where I first discovered how numbers of several
+     figures are to be read; here for the first time I understood that
+     the figure 3 with 5 below it is nothing but 3 × 20 + 5, or 65, and
+     that they mean nothing else than the interval between the days, such
+     as we have frequently met with so far; 4 × 65 is again the well
+     known period of 260 days.
+
+Plate 3 appears to be isolated and unfinished; at least it presents
+nothing on its face by which it can be directly connected with any other
+plate of the codex, notwithstanding the change made by Dr. Förstemann, by
+which 45 was brought next to it. The day column in this case is in the
+middle compartment of the upper division and consists of the following
+days: Ahau, Eb, Kan, Cib, Lamat; the red numeral over it is I. The
+numerals and days are arranged as follows:
+
+  (?)     (?)        4,  V(?)        15, XIII
+
+                       I
+                      Ahau
+  8,     XIII         Eb
+                      Kan
+                      Cib             14 (?)
+                      Lamat
+
+As numerals belonging to two different series are never found in the same
+compartment it is fair to assume that those of the middle and right
+compartments pertain to one series. But what shall we say in reference to
+those in the left compartment, the upper pair of which is almost entirely
+obliterated? So far we have found no series extending to the left of the
+day column. Is this an exceptional case? I am inclined to believe it is,
+for the following reasons:
+
+Taking the 4, V over the bird as the first pair of the series, we have
+I + 4 = V, which is so far correct; after this follows the pair in the
+lower left hand corner, 8, XIII, as V + 8 = XIII. It is probable that the
+obliterated pair in the upper left hand corner followed next, then the
+pair in the upper right hand corner, and last the partly obliterated one
+in the lower right hand corner. In this case the obliterated pair in the
+upper left hand corner should be 11, XI, as XIII + 11 - 13 = XI, and XI +
+15 - 13 = XIII, and XIII + 14 - 13 - 13 = I, which makes the terminal red
+number of the series the same as that over the day column. This
+restoration requires no change of any of the numbers which can be
+distinctly read. By adding together the black numbers 4, 8, 11, 15, 14,
+the sum is found to be 52, precisely the interval between the days of the
+column. These facts are sufficient to render it more than probable that
+the restoration and the order as here given are correct. The series as
+thus given, including the number over the day column, is: I; 4, V; 8,
+XIII; 11, XI; 15, XIII; 14, I.
+
+This is repeated, because on turning to Dr. Förstemann's comment on this
+series I find that he has restored and amended it so as to read thus: I;
+10, XI; 4, V; 15, XIII; 9, XIII; 14, I; and he remarks that all would be
+plain sailing if, for the V before and the XIII after 15, we could read
+II and IV. This is true, but these numbers are too distinct to justify
+such change; moreover his "9" is not to be found on the page; it is true
+that the three dots over the line are not exactly spaced, but there are
+no indications of a fourth; the number is 8 and should, I think, be so
+read. His 10 is the obliterated black numeral; of course the value
+attributed to it depends upon the order given to the series. The
+fragments remaining of the red number of this pair I think warrant his
+making it XI.
+
+Plates 46, 47, 48, 49, and 50 are peculiar and seemingly have no direct
+relation to any other part of the codex. In the upper left hand corner of
+each are four day columns, all more or less injured, but each column
+evidently contained, originally, thirteen days, or, more correctly
+speaking, the symbol for one day repeated thirteen times. In every case
+the day in the first (left hand) column and that in the third column are
+the same. As the numbers attached to them are absolutely unreadable in
+Kingsborough and much obliterated in the photograph, I give here
+restorations for the benefit of those studying this codex. This
+restoration is easily made by finding the order of the series, which can
+be obtained from Plates 49 and 50 of the photographic copy.
+
+_Plate_ 46:
+     III Cib.        II Cimi.        V Cib.      XIII Kan.
+      XI Cib.         X Cimi.     XIII Cib.      VIII Kan.
+      VI Cib.         V Cimi.     VIII Cib.       III Kan.
+       I Cib.      XIII Cimi.      III Cib.        XI Kan.
+      IX Cib.      VIII Cimi.       XI Cib.        VI Kan.
+      IV Cib.       III Cimi.       VI Cib.         I Kan.
+     XII Cib.        XI Cimi.        I Cib.        IX Kan.
+     VII Cib.        VI Cimi.       IX Cib.        IV Kan.
+      II Cib.         I Cimi.       IV Cib.       XII Kan.
+       X Cib.        IX Cimi.      XII Cib.       VII Kan.
+       V Cib.        IV Cimi.      VII Cib.        II Kan.
+    XIII Cib.       XII Cimi.       II Cib.         X Kan.
+    VIII Cib.       VII Cimi.        X Cib.         V Kan.
+
+_Plate_ 47:
+     II Ahau.         I Oc.         IV Ahau.      XII Lamat.
+      X Ahau.        IX Oc.        XII Ahau.      VII Lamat.
+      V Ahau.        IV Oc.        VII Ahau.       II Lamat.
+   XIII Ahau.       XII Oc.         II Ahau.        X Lamat.
+   VIII Ahau.       VII Oc.          X Ahau.        V Lamat.
+    III Ahau.        II Oc.          V Ahau.     XIII Lamat.
+     XI Ahau.         X Oc.       XIII Ahau.     VIII Lamat.
+     VI Ahau.         V Oc.       VIII Ahau.      III Lamat.
+      I Ahau.      XIII Oc.        III Ahau.       XI Lamat.
+     IX Ahau.      VIII Oc.         XI Ahau.       VI Lamat.
+     IV Ahau.       III Oc.         VI Ahau.        I Lamat.
+    XII Ahau.        XI Oc.          I Ahau.       IX Lamat.
+    VII Ahau.        VI Oc.         IX Ahau.       IV Lamat.
+
+As the arrangement and the order of the series are readily seen from the
+two examples given, only the top and bottom lines of the remaining series
+will be presented.
+
+_Plate_ 48:
+      I Kan.       XIII Ix.        III Kan.        XI Eb.
+         *           *  *           *   *          *  *   [TN-4]
+     VI Kan.          V Ix.       VIII Kan.       III Eb.
+
+
+_Plate_ 49:
+   XIII Lamat.      XII Ezanab.     II Lamat.       X Cib.
+     *   *           *   *          *   *           *  *
+      V Lamat.       IV Ezanab.    VII Lamat.      II Cib.
+
+_Plate_ 50:
+    XII Eb.          XI Ik.          I Eb.         IX Ahau.
+     *   *           *   *           *  *           *  *
+     IV Eb.         III Ik.         VI Eb.          I Ahau.
+
+A careful examination of these groups will bring to light the following
+relations of the numbers, days, columns, and series to one another:
+
+The numerals of any one column, counting downwards, differ from one
+another by 8; that is to say, by adding 8 to any one and casting out 13
+when the sum exceeds that number, the next lower number will be obtained;
+or, reversing the operation and counting upward, the difference is found
+to be 5. The true interval between the days of the columns (counting
+downwards) is 3 months (60 days), a rule which holds good as to all the
+series and each column. Thus, from 3 Cib to 11 Cib is 3 months, or 60
+days; from 11 Cib to 6 Cib, 3 months; from 2 Cimi to 10 Cimi, 3 months,
+and from 13 Kan to 8 Kan, 3 months.
+
+Counting on the list of the days of the month, without reference to the
+week numbers attached to them, it will be found that from Cib to Cimi is
+an interval of 10 days, and from Cib to Kan is an interval of 8 days.
+This rule holds good as to all the series, showing that all are arranged
+upon precisely the same plan. The true interval between any day of the
+first column of either series (the week number attached being considered)
+and the opposite or corresponding day in the second column, is 4 months
+and 10 days, that between the corresponding days of the second and third
+columns is 12 months and 10 days, that between the days of the third and
+fourth columns is 8 days, and that between the corresponding days of the
+fourth or last column of one series or plate and the first column of the
+following series or plate (taking the plates in the order they are paged)
+is 11 months and 16 days.
+
+In order to illustrate this we will run through the lowest line of each
+series, taking them in the order of the pages.[296-1]
+
+These are as follows:
+
+_Plate_ 46: VIII Cib.        VII Cimi.        X Cib.         V Kan.
+
+_Plate_ 47:  VII Ahau.        VI Oc.         IX Ahau.       IV Lamat.
+
+_Plate_ 48:   VI Kan.          V Ix.       VIII Kan.       III Eb.
+
+_Plate_ 49:    V Lamat.       IV Ezanab.    VII Lamat.      II Cib.
+
+_Plate_ 50:   IV Eb.         III Ik.         VI Eb.          I Ahau.
+
+[Illustration: FIG 362. Copy of Plate 50, Dresden Codex.[TN-5]]
+
+By counting on the calendar (our Table II), as heretofore explained, the
+reader will observe that the interval from 8 Cib to 7 Cimi is 4 months
+and 10 days; from 7 Cimi to 10 Cib is 12 months and 10 days; from 10 Cib
+to 5 Kan is 8 days; from 5 Kan to 7 Ahau is 11 months and 16 days; from 7
+Ahau to 6 Oc, 4 months and 10 days; from 6 Oc to 9 Ahau, 12 months and 10
+days; from 9 Ahau to 4 Lamat, 8 days; from 4 Lamat to 6 Kan, 11 months
+and 16 days, and so on to the end of the series on Plate 50. Referring to
+the codex the reader will observe at the bottom of each plate and
+directly under--that is to say, in the same vertical lines as the day
+columns--two lines of red numerals. It is impossible to determine these
+in Kingsborough's copy (except on Plate 50), but they can readily be made
+out on the photographed plates. (See the copy of Plate 50, given in
+Fig. 362.) Those on a single plate are as follows:
+
+  {  XI, IV, XII,    0,
+  { XVI,  X,   X, VIII.
+
+The 0 here represents a red, diamond shaped symbol.
+
+If the upper line represents months and the lower line days, these
+numbers will indicate the intervals between the columns and are properly
+placed. For example, the XI and XVI signify 11 months and 16 days, the
+interval between the last column of the preceding plate and the first
+column of the plate on which they stand; the IV and X, the interval of 4
+months and 10 days between the first and second columns; XII and X, the
+interval of 12 months and 10 days between the second and third columns;
+and 0, VIII, the interval of 8 days between the third and fourth columns.
+It is apparent from this that the red, diamond shaped symbol represented
+by 0 over the VIII denotes a cipher or nought, a conclusion reached
+independently by Förstemann.
+
+If this supposition as to the arrangement of the series and the
+signification of these numbers be correct, it is apparent that the
+plates are to be taken in the order in which they are paged, that is,
+from left to right, as the others so far noticed, an inference borne
+out by another fact now to be mentioned.
+
+Immediately below each of these four column day series are four lines of
+characters (hieroglyphics), and immediately under the latter three
+horizontal lines of black numerals, with here and there a red, diamond
+shaped symbol inserted. As these numerals stand directly in the vertical
+lines of the day columns, it is possible the two have some connection
+with each other, a supposition somewhat strengthened by what has been
+observed in regard to the red numerals at the bottom of the plates. To
+test this and also for the reason that we propose to discuss their
+relations and their use, we give here the bottom line of days of each of
+the five series (or plates), together with their week numbers attached;
+also, the numbers of the three lines of black numerals mentioned, taking
+them in the order of the paging as here shown:
+
+_Plate_ 46:
+   VIII Cib.    VII Cimi.       X Cib.      V Kan.
+                                  1            1
+      11           16            10           11
+      16            6            16            4
+
+_Plate_ 47:
+   VII Ahau.     VI Oc.        IX Ahau.    IV Lamat.
+       2            2             3            3
+       5            9             4            4
+       0           10             0            8
+
+_Plate_ 48:
+    VI Kan.      V Ix.        VIII Kan.     III Eb.
+       3            4             4            4
+      16            2            15           15
+       3(?)        14             4           12
+
+_Plate_ 49:
+   V Lamat.    IV Ezanab.    VII Lamat.     II Cib.
+       5            5             6            6
+       9           13             8            8
+       8           18             8           16
+
+_Plate_ 50:
+    IV Eb.       III Ik.       VI Eb.       1 Ahau.
+       7            7             8            8
+       3            7             1            2
+      12            2            12            0
+
+In considering these horizontal lines it is to be understood that the
+series runs through the five pages, 46-50.
+
+Let us proceed upon the supposition that the figures of the lowest of the
+three lines denote days of the month, the numbers of the middle line
+months, and those of the upper line years. As already shown, the interval
+between 8 Cib and 7 Cimi is 4 months and 10 days; adding 4 months and 10
+days to 11 months and 16 days (bearing in mind that 20 days make a month
+and 18 months a year), the sum is found to be 16 months and 6 days,
+precisely the figures under 7 Cimi. As already ascertained, the interval
+between 7 Cimi and 10 Cib is 12 months and 10 days; this added to 16
+months and 6 days gives 1 year, 10 months, 16 days, precisely the figures
+under 10 Cib. The interval between 10 Cib and 5 Kan is 8 days; this added
+to the 1 year, 10 months, and 16 days gives 1 year, 11 months, and 4
+days, the figures under 5 Kan. The interval between 5 Kan and 7 Ahau is
+11 months, 16 days, which, added to the preceding, gives 2 years, 5
+months, 0 day, agreeing with the figures under 7 Ahau, if the symbol
+represented by 0 signifies nought. That this rule holds good throughout
+the entire series, by making one correction, is shown by the following
+additions:
+
+Years.    Months.    Days.
+            11        16    Under VIII Cib, Plate 46.
+             4        10
+            --        --
+            16         6    Under VII Cimi, Plate 46.
+            12        10
+            --        --
+   1        10        16    Under X Cib, Plate 46.
+                       8
+  --        --        --
+   1        11         4    Under V Kan, Plate 46.
+            11        16
+  --        --        --
+   2         5         0    Under VII Ahau, Plate 47.
+             4        10
+  --        --        --
+   2         9        10    Under VI Oc, Plate 47.
+            12        10
+  --        --        --
+   3         4         0    Under IX Ahau, Plate 47.
+                       8
+  --        --        --
+   3         4         8    Under IV Lamat, Plate 47.
+            11        16
+  --        --        --
+   3        16         4[300-1] Under VI Kan, Plate 48.
+             4        10
+  --        --        --
+   4         2        14    Under V Ix, Plate 48.
+            12        10
+  --        --        --
+   4        15         4    Under VIII Kan, Plate 48.
+                       8
+  --        --        --
+   4        15        12    Under III Eb, Plate 48.
+            11        16
+  --        --        --
+   5         9         8    Under V Lamat, Plate 49.
+             4        10
+  --        --        --
+   5        13        18    Under IV Ezanab, Plate 49.
+            12        10
+  --        --        --
+   6         8         8    Under VII Lamat, Plate 49.
+                       8
+  --        --        --
+   6         8        16    Under II Cib, Plate 49.
+            11        16
+  --        --        --
+   7         2        12    Under IV Eb, Plate 50.
+             4        10
+  --        --        --
+   7         7         2    Under III Ik, Plate 50.
+            12        10
+  --        --        --
+   8         1        12    Under VI Eb, Plate 50.
+                       8
+  --        --        --
+   8         2         0    Under I Ahau, Plate 50.
+
+The proof of the correctness of the theory advanced may, therefore, be
+considered conclusive, as it amounts, in fact, to a mathematical
+demonstration.
+
+Dr. Förstemann, who considers these lines of black numbers, standing one
+above another, as representing different grades of units--thus, the
+lowest, single units; the second, units twenty-fold the lower; the third,
+eighteen-fold the second; the fourth, twenty-fold the third, &c.--has
+found the correct intervals of the series, which he states are 236, 90,
+250, and 8 days, agreeing with our 11 months, 16 days; 4 months, 10 days;
+12 months, 10 days, and 8 days.
+
+As all the discoveries mentioned herein were made previous to the receipt
+of Dr. Förstemann's work, I give them according to my own method,
+acknowledging any modification due to his work. Although I shall compare
+special results from time to time, an explanation of Dr. Förstemann's
+method is reserved for a future paper, as his work was not received until
+I was revising my notes for publication.
+
+The foregoing explanation of the series shows it to be very simple and
+makes it clear that it relates to the day columns at the top of the
+pages. Still, there is one point somewhat difficult to understand. Are
+the numbers of the third or lowest line intended to denote the positions
+in the month of the days in the columns above? If so, the month must have
+commenced with Ymix, as can readily be shown in the following manner:
+
+TABLE III.
+
+   1. Ymix.
+   2. Ik.
+   3. Akbal.
+   4. Kan.
+   5. Chicchan.
+   6. Cimi.
+   7. Manik.
+   8. Lamat.
+   9. Muluc.
+  10. Oc.
+  11. Chuen.
+  12. Eb.
+  13. Been.
+  14. Ix.
+  15. Men.
+  16. Cib.
+  17. Caban.
+  18. Ezanab.
+  19. Cauac.
+  20. Ahau.
+
+If we write in a column in proper order the 20 days of the Maya month,
+commencing with Ymix, and number them consecutively, as in Table III, we
+shall find by comparison that the numbers in the lower line indicate the
+position, in this column, of the days directly over them. Take, for
+example, the lower line of black numerals on Plate 46, writing over them
+the respective days of the columns, thus:
+
+  Cib.       Cimi.       Cib.        Kan.
+   16          6          16          4
+
+Referring to Table III we see that Cib is the sixteenth day, Cimi the
+sixth, and Kan the fourth.
+
+The days and numbers of Plate 47 are:
+
+  Ahau.       Oc.        Ahau.      Lamat.
+    0         10           0          8
+
+Ahau is the twentieth day--here is the diamond shaped symbol--Oc is the
+tenth, and Lamat the eighth, and so on to the end of the series on Plate
+50.
+
+It may be justly argued that such relation to some given day of the month
+would necessarily follow in any series of this kind made up by adding
+together intervals of days and months. Still it is not at all likely that
+these series were made up without reference to fitted and determinable
+dates. If so, the months given must be months of certain determinable
+years, and the days denoted must be days of particular months. In other
+words, if we had the proper starting point we should be able to determine
+the position in the calendar of any day or month mentioned in the series.
+
+First. It is easily seen by reference to the calendar (Table II) that Cib
+is not the sixteenth day of the month of any of the four years, nor is
+Cimi the sixth nor Kan the fourth. The idea that the figures of this
+lower line represent the days of the month must, therefore, be given up
+unless we assume that the year commenced with Ymix. It may be worthy of
+notice at this point that the list of days on the so-called "title page"
+of the Manuscript Troano begins with Ymix. It is also true that the
+remarkable quadruple series in the Codex Cortesianus on Plates 13-18
+commences with Ymix; as this is evidently some kind of a calendar table,
+its bearing on the question now before us is important.
+
+Second. It can easily be shown that the months referred to in the series,
+if the numbers given denote specific months, are not those of the Kan
+years. The first, 8 Cib, if in the eleventh month, must be in the year 4
+Kan; counting forward from this 4 months and 10 days to 7 Cimi brings us
+into the sixteenth month of the year 4 Kan; this agrees with our figures
+on Plate 46. Counting forward 12 months and 10 days to 10 Cib, we reach
+the tenth month of the next year; 8 days more carry us to the eleventh
+month, which still agrees with the figures in the codex. Counting 11
+months and 16 days more to 7 Ahau, we reach but do not pass the fourth
+month of the next year; hence the result does not correspond with the
+series, which has at this point a 5 in the middle line. The same will be
+found true in regard to the other years as given in our calendar (Table
+II). This result, as a matter of course, must follow if the figures in
+the lower line of the series do not denote the month days of some one of
+the year series as usually given.
+
+Another fact also becomes apparent here, viz, that the 5 supplemental
+days of the year are not brought into the count, the year consisting
+throughout of 360 days. There is, in fact, nothing here indicating the
+four year series as given in the authorities and as represented in our
+calendar table; yet this ought to appear wherever a series extends over
+more than one year.
+
+Dr. Förstemann says that this entire series of black numerals covers
+2,920 days, or 8 years of 365 days. This is true, but the concluding
+figures show that it is given by the writer of the codex as 8 years and 2
+months, which would also be 2,920 days, counting the years at 360 days
+each and the months 20 days each; moreover, the members of the series are
+based throughout upon the year of 360 days. His theory that the intervals
+of the series relate to the movements of the planet Venus is, as yet, a
+mere hypothesis, which needs further proof before it can demand
+acceptance; but his discovery of the methods of identifying the month
+symbols on the five plates now under consideration is important. Although
+I had noticed that most of the characters which he mentions are month
+symbols, I did not succeed in identifying all of them.
+
+According to his conclusion, which appears to be justified not only by
+the evidence he gives but by an additional fact that I shall, presently
+mention, there are four of these symbols in the upper row of the middle
+group of written characters on each plate and four in the upper and lower
+lines of the lower group on each plate (see, for example, Fig. 362). Each
+of these symbols (except three or four) has a black number attached to it
+which denotes the day of the month represented by the symbol.
+
+These months and days as given by Dr. Förstemann are as follows, the
+positions of the lines as here given corresponding with those of the
+plates:
+
+TABLE IV.--_Table showing months and days._
+
+  _____________________________________________________________________
+           | Month.  Day. | Month.  Day. | Month.  Day. | Month.   Day.
+           |--------------+--------------+--------------+--------------
+  Plate 46 |   7       4  |  11      14  |   5      19  |   6        7
+           |  11       8  |  15      18  |  10       4  |  10       12
+           |   1      14  |   6       4  |  18      14  |   1        2
+  Plate 47 |  18       3  |   4       8  |  16      18  |  17        6
+           |   4       3  |   8      13  |   2      18  |   3(not 2) 6
+           |  10      10  |  15       3  |   9       8  |   9       16
+  Plate 48 |  10      17  |  15       7  |   9      12  |  10       20
+           |  15       2  |   1       7  |  13      17  |  14        5
+           |   3       7  |   7      17  |   2       2  |   2       10
+  Plate 49 |   3      11  |   8       1  |   2       6  |   2       14
+           |   7      16  |  12       6  |   6      11  |   6       19
+           |  14       6  |  18      16  |  13       1  |  13        9
+  Plate 50 |  14      10  |  18      20  |  13       5  |  13       13
+           |  18      15  |   5      20  |  17      10  |  17       18
+           |   6      20  |  11      10  |   5      15  |   6        3
+  ---------------------------------------------------------------------
+
+
+An examination of the plates will show that Dr. Förstemann has filled out
+the following obliterated or wanting day numbers, to wit, the first of
+the upper line of Plate 46, the fourth of the upper line of Plate 47, and
+the second of the middle line and first of the lower line of Plate 50. He
+has also ventured to change the first day number of the lower line of
+Plate 46 from 16 to 14. Where the number 20 is found in his list there is
+no corresponding number in the codex, the month symbol only being given.
+It is evident he has proceeded in these cases upon the theory that the
+absence of a number indicated that the month was completed. Although
+probably correct in this conclusion, the question will arise, Does the
+symbol in such cases denote the _month completed_ or the _month reached?_
+
+The intervals between these dates are as follows, the left hand column
+being those between the first and second columns of Förstemann's list
+(our Table IV), the second column those between the second and third
+columns of his list, the third column those between the third and fourth
+columns of his list, and the fourth column those between the last date of
+one plate and the first of the next:
+
+TABLE V.--_Table showing intervals between dates._
+
+  _____________________________________________________________________
+           | Month.  Day. | Month.  Day. | Month.  Day. | Month.  Day.
+           |--------------+--------------+--------------+--------------
+           |              |              |              |
+  Plate 46 |   4     10   |  12      5   |   0      8   |  11     16
+           |   4     10   |  12      6_b_|   0      8   |  11     11
+           |   4     10   |  12      10  |   0      8   |   9      8_d_
+  Plate 47 |   4      5   |  12     10   |   0      8   |  11     11
+           |   4     10   |  12      5   |   0      8_c_|  11     16_e_
+           |   4     13_a_|  12      5   |   0      8   |  11     11
+  Plate 48 |   4     10   |  12      5   |          8   |  11     11
+           |   4      5   |  12     10   |   0      8   |  11     11
+           |   4     10   |  12      5   |   0      8   |  11     16
+  Plate 49 |   4     10   |  12      5   |   0      8   |  11     16
+           |   4     10   |  12      5   |   0      8   |  11     16
+           |   4     10   |  12      5   |   0      8   |  11     11
+  Plate 50 |   4     10   |  12      5   |   0      8   |  11     11
+           |   4      5   |  12     10   |   0      8   |  11     10
+           |   4     10   |  12      5   |   0      8   |  12     11_g_
+  ---------------------------------------------------------------------
+
+Although it is apparent that the variations from the intervals of the
+black numeral and day series above them are too numerous and too uniform
+to be considered mistakes, yet there is little reason to doubt that these
+month numbers are connected with and depend upon the day series given in
+the columns above.
+
+That there are some errors is quite clear; for instance, the variation at
+_a_ arises from the fact that Dr. Förstemann gives the date here as 10
+months, 10 days, whereas the codex has it 10 months, 13 days. Making this
+correction the interval will be 4 months, 10 days. The correction will
+make the interval at _d_ 9, 11, instead of 9, 8. Still there is a
+variation of two months from the usual interval, which, if corrected on
+the supposition that Dr. Förstemann has mistaken the month, would
+necessitate a change of the remainder of the series given in this line.
+The interval at _c_, according to the figure given by Dr. Förstemann,
+would be retrograde, that is, minus 12. This arises from the fact that he
+gives the last date in the middle line on Plate 47 as 2 months, 6 days,
+whereas the symbol is very distinctly that of the third month, and the
+eight day series is unbroken if this correction is made.
+
+When these evident errors are corrected the series of intervals show
+very clearly a system and periodicity depending on the day column series
+in the upper part of the pages. In the first column (Table V) the
+interval is usually 4 months, 10 days, precisely the same as between the
+first and second day columns, but occasionally it is 4 months, 5 days,
+which will still bring it to one of the four day series, including the
+day indicated by the date--4 months, 10 days. This will be understood by
+examining our calendar (Table II). The corresponding days in the four
+year columns were, by the Maya system, necessarily brought together in
+the calendar; for example, they are arranged in the series pictured on
+Plates 13-18 of the Cortesian Codex precisely as given in our Table II.
+This skip of five days is also apparent in the second and fourth columns
+of differences (Table V). Whether Dr. Förstemann is correct in all his
+identifications of months among the symbols on the five plates now under
+consideration is a question I feel unqualified to answer without a much
+more careful comparison and study of these characters than I have given
+them.
+
+Running through the upper division of Plates 53 to 58 and continued
+through the lower division of Plates 51 to 58--that is to say, commencing
+in the upper division of 53 and running into 58, then back to the lower
+division of 51 and ending in 58--is a remarkable compound series. It
+consists, first, of a three line series of black numerals standing above;
+second, a middle series of short, three day columns, or columns each of
+three day symbols, with red numerals attached; and, third, below, a two
+line series of numerals, those of the upper line red and of the lower
+black numbers.
+
+As this series is a very important one in the study of the relations of
+the numerals to one another and to the days indicated, an exact copy of
+it is given in Figs. 363-370, each figure representing a page and the
+whole standing in the same order as in the original. The red numerals and
+red symbols are, as usual, given in outline as an indication of their
+color.
+
+[Illustration: FIG. 363. Copy of Plate 51, Dresden Codex.]
+
+[Illustration: FIG. 364. Copy of Plate 52, Dresden Codex.]
+
+[Illustration: FIG. 365. Copy of Plate 55, Dresden Codex.]
+
+[Illustration: FIG. 366. Copy of Plate 54, Dresden Codex.]
+
+[Illustration: FIG. 367. Copy of Plate 55, Dresden Codex.]
+
+[Illustration: FIG. 368. Copy of Plate 56, Dresden Codex.]
+
+[Illustration: FIG. 369. Copy of Plate 57, Dresden Codex.]
+
+[Illustration: FIG. 370. Copy of Plate 58, Dresden Codex.]
+
+In order to assist those not familiar with the numeral and day symbols,
+the entire series is given in the following tables in names and Arabic
+and Roman numerals, as usual. The obliterated symbols and numbers are
+restored.
+
+TABLE VI.--_Table of numeral and day symbols._ (Plate 51_b_.)
+
+  ______________________________________________________________________
+     14    |    15     |    15      |   16    |   16    |   17
+     16    |     7     |    16      |    7    |   16    |    5
+     14    |    11     |     8      |    5    |    2    |   10
+  IV Ik.   | XII Cauac.| VII Cib.   | II Been.|  X Oc.  | II Ezanab.
+   V Akbal.|XIII Ahau. |VIII Caban. |III Ix   | XI Chuen|III Cauac.
+  VI Kan.  |   I Ymix. |  IX Ezanab.| IV Men. |XII Eb.  | IV Ahau.[VI-1]
+    VIII   |   VIII    |   VIII     |  VIII   |  VIII   |   VII
+     17    |    17     |    17      |   17    |   17    |    8
+  ----------------------------------------------------------------------
+
+[VI-1] The symbol in this case is that of Been, but this is a manifest
+error, as Ahau follows Cauac.
+
+TABLE VII.--_Table of numeral and day symbols._ (Plate 52_b_.)
+
+  ____________________________________________________________
+             |      17       |    18    |   18     |    19
+             |      14       |     5    |   14     |     4
+             |       8       |     5    |    2     |    19
+             |    XI Cib.    |  VI Been.|  I Oc.   | IX Manik.
+  [Picture.] |   XII Caban.  | VII Ix.  | II Chuen.|  X Lamat.
+             |  XIII Ezanab. |VIII Men. |III Eb.   | XI Muluc.
+             |      VIII     |   VIII   |  VIII    |   VIII
+             |17? (18)[VII-1]|    17    |   17     |    17
+  ------------------------------------------------------------
+
+[VII-1] The variation from the rule found here is explained a little
+further on.
+
+TABLE VIII.--_Table of numeral and day symbols._ (Plate 53_a_.)
+
+  ______________________________________________________________________________________
+                |    1     |     1     |          |       2       |   2        |
+       7        |   17     |     7     |          |      15       |   6        |  15
+      17        |   18     |     2     |          |14?(19)[VIII-1]|  16        |  13
+    VI Kan.     |  I Ymix. |  VI Muluc.|[Picture.]|    I Cimi.    |IX Akbal.   |IV Ahau.
+   VII Chicchan.| II Ik.   | VII Oc.   |          |   II Manik.   | X Kan.     | V Ymix.
+  VIII Cimi.    |III Akbal.|VIII Chuen.|          |  III Lamat.   |XI Chicchan.|VI Ik.
+     VIII       |  VIII    |   VII     |          |     VIII      | VIII       | VIII
+      17        |   17     |     8     |          |      17       |  17        |  17
+  --------------------------------------------------------------------------------------
+
+[VIII-1] The 14 here is manifestly an error, one of the lines in the
+number symbol having been omitted; it should be 19.
+
+TABLE IX.--_Table of numeral and day symbols._ (Plate 53_b_.)
+
+  _____________________________________________________________________
+              |   1    |          |    1    |     1     |     1
+    19        |   0    |          |    0    |     1     |     1
+    13        |   3    |          |   12    |     2     |    11
+    16        |   4    |          |    1    |    18     |    15
+  IV Kan.     |IX Eb.  |[Picture.]|IV Muluc.| XII Cimi. | VII Akbal.
+   V Chicchan.| X Been.|          | V Oc.   |XIII Manik.|VIII Kan.
+  VI Cimi.    |XI Ix.  |          |VI Chuen.|   I Lamat.|  IX Chicchan.
+   VIII       |  VII   |          |  VIII   |   VIII    |   VIII
+    17        |   8    |          |   17    |    17     |    17
+  ---------------------------------------------------------------------
+
+TABLE X.--_Table of numeral and day symbols._ (Plate 54_a_.)
+
+  ____________________________________________________________________________________
+       3      |     3     |    4    |     4     |     5      |     5       |    6
+       6      |    15     |    6    |    15     |     5      |    10       |    4
+      11      |     8     |    5    |     5     |    19      |    16       |    4
+  XIII Ezanab.|VIII Men.  |III Eb.  |  XI Muluc.|  VI Cib.   |  I Akbal.   | VI Chuen.
+     I Cauac. |  IX Cib.  | IV Been.| XII Oc.   | VII Caban. | II Kan.     | VII Eb.
+    II Ahau.  |   X Caban.|  V Ix.  |XIII Chuen.|VIII Ezanab.|III Chicchan.|VIII Been.
+     VIII     |   VIII    |  VIII   |   VIII    |   VIII     |   VIII      |   VII
+      17      |    17     |   17    |    17     |    17      |    17       |    8
+  ------------------------------------------------------------------------------------
+
+
+TABLE XI.--_Table of numeral and day symbols._ (Plate 54_b_.)
+
+  _______________________________________________________________
+      1    |    1      |    1   |    1     |         |    1
+      2    |    2      |    3   |    3     |         |    4
+      2    |   11      |    2   |    9     |         |    0[XI-1]
+     12    |    9      |    6   |   14     |         |   11
+   II Ahau.|  X Caban. |  V Ix. |  X Ik.   |[Picture]|  V Cauac.
+  III Ymix.| XI Ezanab.| VI Men.| XI Akbal.|         | VI Ahau.
+   IV Ik.  |XII Cauac. |VII Cib.|XII Kan.  |         |VII Ymix.
+    VIII   |  VIII     |  VIII  |  VII     |         |  VII[XI-2]
+     17    |   17      |   17   |    8     |         |   17
+  ---------------------------------------------------------------
+
+[XI-1] The 0 inserted at various points in these tables denotes as usual
+the red, diamond shaped symbol, which apparently signifies "nought."
+
+[XI-2] The numeral symbol in this case, both in Kingsborough's copy and
+in the photograph, is VII, one dot having been omitted by a mistake of
+the original artist.
+
+TABLE XII.--_Table of numeral and day symbols._ (Plate 55_a_.)
+
+  ____________________________________________________________________________
+           |    8            |    7     |    7        |     8    |     8
+           |   13            |    3     |   12        |     3    |    12
+           |    2            |   18     |   16        |    13    |    10
+           | II Muluc.[XII-1]|  X Cimi. |  V Akbal.   |XIII Ahau.|VIII Caban.
+  [Picture]|III Oc.          | XI Manik.| VI Kan.     |   I Ymix.|  IX Ezanab.
+           | IV Chuen.       |XII Lamat.|VII Chicchan.|  II Ik.  |   X Cauac.
+           |  VIII           |  VIII    |  VIII       |   VIII   |   VIII
+           |   17            |   17     |   17        |    17    |    17
+  ----------------------------------------------------------------------------
+
+[XII-1] In Kingsborough's work the symbol in this case is that of Been,
+but should be Muluc, as it is in the photograph.
+
+TABLE XIII.--_Table of numeral and day symbols._ (Plate 55_b_.)
+
+  __________________________________________________________________________________________
+       1      |   1   |   1     |     1     |     1        |    1     |    1     |    1
+       4      |   5   |   5     |     6     |     6        |    6     |    7     |    7
+       9      |   0   |   9     |     0     |     8        |   17     |    8     |   15
+       8      |   6   |   3     |     0     |    17        |   14     |   11     |   19
+  XIII Cib.   |IX Ix. |IV Chuen.| XII Lamat.| VII Chicchan.| II Ik.   |  X Cauac.| II Manik.
+     I Caban. | X Men.| V Eb.   |XIII Muluc.|VIII Cimi.    |III Akbal.| XI Ahau. |III Lamat.
+    II Ezanab.|XI Cib.|VI Been. |   I Oc.   |  IX Manik.   | IV Kan.  |XII Ymix. | IV Muluc.
+     VIII     | VIII  | VIII    |   VIII    |   VIII       |  VIII    |  VIII    |   VII
+      17      |17?(18)|  17     |    17     |    17        |   17     |   17     |    8
+  ------------------------------------------------------------------------------------------
+
+TABLE XIV.--_Table of numeral and day symbols._ (Plate 56_a_.)
+
+  ____________________________________________________________
+       9        |         |     9     |   10     |    10
+       1        |         |    10     |    1     |    10
+      18        |         |    15     |   12     |     9
+  XIII Chicchan.|         |VIII Ik.   |III Cauac.|  XI Cib.
+     I Cimi.    |[Picture]|  IX Akbal.| IV Ahau. | XII Caban.
+    II Manik.   |         |   X Kan.  |  V Ymix. |XIII Ezanab.
+      VII       |         |    VIII   |   VIII   |   VIII
+       8        |         |    17     |   17     |    17
+  ------------------------------------------------------------
+
+TABLE XV.--_Table of numeral and day symbols._ (Plate 56_b_.)
+
+  _________________________________________________________
+           |    1        |      1    |    1     |   1
+           |    8        |      8    |    9     |   9
+           |    6        |     15    |    6     |  15
+           |   16        |     14    |   11     |   8
+  [Picture]|  X Kan.     |  VI Ik.   |  I Cauac.|IX Cib.
+           | XI Chicchan.| VII Akbal.| II Ahau. | X Caban.
+           |XII Cimi.    |VIII Kan.  |III Ymix. |XI Ezanab.
+           |  VIII       |    VIII   |  VIII    |  VIII
+           |   17        |   17?(8)  |   17     |  17
+  ---------------------------------------------------------
+
+TABLE XVI.--_Table of numeral and day symbols._ (Plate 57_a_.)
+
+  ______________________________________________________
+      11   |   11     |   12     |   12       |
+       1   |   10     |    1     |    8       |
+       6   |    4     |    0     |    8       |
+   VII Ix. | II Chuen.|  X Lamat.| II Cib.    |
+  VIII Men.|III Eb.   | XI Muluc.|III Caban.  |[Picture]
+    IX Cib.| IV Been. |XII Oc.   | IV Ezanab. |
+      VIII |   VIII   |   VIII   | VIII[XVI-1]|
+      17   |   17     |   17     |   17[XVI-2]|
+  ------------------------------------------------------
+
+[XVI-1] This should be VII.
+
+[XVI-2] This should be 8.
+
+TABLE XVII.--_Table of numeral and day symbols._ (Plate 57_b_.)
+
+  __________________________________________________________________
+       1    |     1     |   1      |         |     1     |     1
+      10    |    10     |  11      |         |    11     |    12
+       6    |    15     |   4      |         |    13     |     4
+       5    |     2     |  10      |         |     7     |     4
+    IV Been.| XII Oc.   |IV Ezanab.|[Picture]| XII Men.  | VII Eb.
+     V Ix.  |XIII Chuen.| V Cauac. |         |XIII Cib.  |VIII Been.
+    VI Men. |   I Eb.   |VI Ahau.  |         |   I Caban.|  IX Ix.
+      VIII  |   VIII    |  VII     |         |   VIII    |   VIII
+      17    |    17     |   8      |         |    17     |    17
+  ------------------------------------------------------------------
+
+TABLE XVIII.--_Table of numeral and day symbols._ (Plate 58_a_.)
+
+  ____________________________________________
+     12    |   13     |   13     |  14
+     17    |    8     |   17     |   7
+      5    |    2     |    0     |  17
+    X Been.|  V Oc.   |  I Lamat.|II Chicchan.
+   XI Ix.  | VI Chuen.| II Muluc.| X Cimi.
+  XII Men. |VII Eb.   |III Oc.   |XI Manik.
+    VIII   |  VIII    |  VIII    |  VIII
+     17    |   17     |   17     |  17
+  --------------------------------------------
+
+TABLE XIX.--_Table of numeral and day symbols._ (Plate 58_b_.)
+
+  ________________________________
+      1     |    1     |
+     12     |   13     |
+     13     |    3     |
+      1     |   18     |
+   II Muluc.|  X Cimi. |[Picture.]
+  III Oc.   | XI Manik.|
+   IV Chuen.|XII Lamat.|
+    VIII    |  VIII    |
+     17     |   17     |
+  --------------------------------
+
+The spaces in the lists indicate the positions of the pictures of persons
+and curtain-like ornaments inserted here and there, as seen in Figs.
+363-370.
+
+In order to explain this series, we commence with that portion of it
+found in the lower division of Plate 51 (Fig. 363).
+
+Omitting any reference for the present to the black numbers over the day
+columns, we call attention first to the days and to the red numerals
+attached to them. Those in the division selected as an illustration are
+as follows:
+
+  IV Ik.     XII Cauac.  VII Cib.     II Been.   X Oc.     II Ezanab.
+   V Akbal. XIII Ahau.  VIII Caban.  III Ix.    XI Chuen. III Cauac.
+  VI Kan.      I Ymix.    IX Ezanab.  IV Men.  XII Eb.     IV Ahau.[317-1]
+
+It will be observed that the week numbers of the days in each single
+column follow one another in regular arithmetical order, thus: in the
+first column, 4, 5, 6; in the second, 12, 13, 1; in the third, 7, 8, 9;
+and so on throughout the entire series. The interval, therefore, between
+the successive days of a column is 1; or, in other words, the days follow
+one another in regular order, as in the month series, so that having the
+first day of a column given we know at once the other two. It is
+apparent, therefore, that the intervals between the three correspondingly
+opposite days of any two associate columns are the same; that is to say,
+the interval between 5 Akbal and 13 Ahau, in the first two columns given
+above is the same as that between 4 Ik and 12 Cauac, and also as that
+between 6 Kan and 1 Ymix. This is also true if the attached week numbers
+are omitted; for instance, the interval between Ik and Cauac, counting on
+the list of days forming the month, is 17 days, and it is the same
+between Kan and Ymix. Taking the second and third columns we find here
+the same interval. This holds good in that part of the series above given
+until we reach the last two columns; here the interval between Oc and
+Ezanab is 8 days and it is the same between the other days of these two
+columns.
+
+This being ascertained, the next step is to determine the true interval
+between the first days of these columns, taking the numbers attached to
+them into consideration. Referring to our calendar (Table II) and (for
+reasons which will be given hereafter) using the Muluc column and
+counting from 4 Ik, as heretofore explained, we find the interval between
+this and 12 Cauac to be 8 months and 17 days; counting in the same way
+from 12 Cauac, 8 months and 17 days more bring us to 7 Cib; 8 months and
+17 days more to 10 Oc. So far the intervals have been the same; but at
+this point we find a variation from the rule, as the interval between 10
+Oc and 2 Ezanab (first of the next column) is 7 months and 8 days.
+
+These intervals furnish the explanation of the red and black numerals
+below the day columns.
+
+These numerals, as the reader will observe by reference to Fig. 363 or
+the written interpretation thereof in Table VI, are 8 and 17 under the
+first five columns, but 7 and 8 under the sixth column, the red (8 under
+the first five and 7 under the sixth) indicating the months and the black
+(17 under the first five and 8 under the sixth) the days of the
+intervals. This holds good throughout all that portion of the series
+running through the lower divisions of Plates 51 to 58, with three
+exceptions, which will now be pointed out.
+
+In order to do this it will be necessary to repeat here a part of the
+series on Plate 51_b_ and part of that on Plate 52_b_; that is, the two
+right hand columns of the former and the two left hand columns of the
+latter, between which is the singular picture shown in the _lower left
+hand corner_ of our Fig. 364:
+
+  ___________________________________________________________________
+          Plate 51_b_.      ||                Plate 52_b_.
+  --------------------------++---------------------------------------
+    X Oc.     |  II Ezanab. ||            |   XI Cib.    |   VI Been.
+    XI Chuen. | III Cauac.  ||            |  XII Caban.  |  VII Ix.
+   XII Eb.    |  IV Ahau.   || [Picture.] | XIII Ezanab. | VIII Men.
+       VIII   |   VII       ||            |    VIII      |   VIII
+       17     |     8       ||            |     17       |    17
+  -------------------------------------------------------------------
+
+As before stated, the interval between 10 Oc and 2 Ezanab is 7 months and
+8 days, as indicated by the red and black numerals under the latter.
+According to the red and black numbers under the column commencing with
+11 Cib, the interval between 2 Ezanab and 11 Cib should be 8 months and
+17 days, the usual difference, when, in fact, as we see by counting on
+the calendar, it is 8 months and 18 days. That this variation cannot be
+attributed to a mistake on the part of the author or of the artist is
+evident from the fact that the interval between 11 Cib and 6 Been (first
+of the next column) is 8 months and 17 days and that the difference
+throughout the rest of the series follows the rule given; that is to say,
+each is 8 months and 17 days, except at two other points where this
+variation is found and at the regular intervals where the difference of
+7 months and 8 days occurs.[319-1] Precisely the same variation occurs on
+Plate 55_b_ in passing from the first to the second column and on Plate
+56_b_ between columns 1 and 2.
+
+Why these singular exceptions? It is difficult, if not impossible, for
+us, with our still imperfect knowledge of the calendar system formerly in
+vogue among the Mayas, to give a satisfactory answer to this question.
+But we reserve further notice of it until other parts of the series have
+been explained.
+
+Reference will now be made to the three lines of black numerals
+immediately above the day columns. Still confining our examinations to
+the lower divisions, the reader's attention is directed to these lines,
+as given in Tables VI, VII, IX, XI, XIII, XV, XVII, and XIX. As there are
+three numbers in each short column we take for granted, judging by what
+has been shown in regard to the series on Plates 46-50, that the lowest
+of the three denotes days, the middle months, and the upper years, and
+that the intervals are the same between these columns as between the day
+columns under them. The correctness of this supposition is shown by the
+following additions: Starting with the first or left hand column on Plate
+51_b_, we add successively the differences indicated by the corresponding
+red and black numbers under the day columns. If this gives in each case
+(save the two or three exceptions heretofore referred to) the numbers in
+the next column to the right throughout the series, the demonstration
+will be complete.
+
+Years.    Months.    Days.
+  14        16        14    First column on Plate 51_b_.
+             8        17
+  --        --        --
+  15         7        11    Second column on Plate 51_b_.
+             8        17
+  --        --        --
+  15        16         8    Third column on Plate 51_b_.
+             8        17
+  --        --        --
+  16         7         5    Fourth column on Plate 51_b_.
+             8        17
+  --        --        --
+  16        16         2    Fifth column on Plate 51_b_.
+             7         8
+  --        --        --
+  17         5        10    Sixth column on Plate 51_b_.
+             8        18[319-1]
+  --        --        --
+  17        14         8    First column on Plate 52_b_.
+             8        17
+  --        --        --
+  18         5         5    Second column on Plate 52_b_.
+             8        17
+  --        --        --
+  18        14         2    Third column on Plate 52_b_.
+             8        17
+  --        --        --
+  19         4        19    Fourth column on Plate 52_b_.
+             8        17
+  --        --        --
+  19        13        16    First column on Plate 53_b_.
+             7         8
+  --        --        --
+  20         3         4    Second column on Plate 53_b_.
+
+At this point in the original, instead of 20 in the year series, we find
+a diamond shaped symbol, represented by 0 in our tables, with one black
+dot over it. From this it would seem that when this codex was written the
+Maya method of counting years was by periods of 20 each, as in the case
+of the month days. Whether there is any reference here to the ahaues is
+uncertain. I am inclined to think with Dr. Förstemann that it was rather
+in consequence of the use of the vigesimal system in representing
+numbers. It would have been very inconvenient and cumbersome to represent
+high numbers by means of dots and lines; hence a more practicable method
+was devised. It is evident, from the picture inserted at this point in
+the series, that some important chronological event is indicated. Here
+also in the written characters over this picture is the symbol for 20.
+The last number given in the above addition may therefore, in order to
+correspond with the method of the codex, be written as follows:
+
+Twenty year periods.  Years.  Months.  Days.
+                 1      0        3       4
+
+Continuing the addition in this way the result is as follows:
+
+Twenty year periods.  Years.  Months.  Days.
+                 1       0       3       4
+                                 8      17
+                --      --      --      --
+                 1       0      12       1   Third column on Plate 53_b_.
+                                 8      17
+                --      --      --      --
+                 1       1       2      18   Fourth column on Plate 53_b_.
+                                 8      17
+                --      --      --      --
+                 1       1      11      15   Fifth column on Plate 53_b_.
+                                 8      17
+                --      --      --      --
+                 1       2       2      12   First column on Plate 54_b_.
+                                 8      17
+                --      --      --      --
+                 1       2      11       9   Second column on Plate 54_b_.
+                                 8      17
+                --      --      --      --
+                 1       3       2       6   Third column on Plate 54_b_.
+                                 7       8
+                --      --      --      --
+                 1       3       9      14   Fourth column on Plate 54_b_.
+                                 8      17
+                --      --      --      --
+                 1       4       0      11   Fifth column on Plate 54_b_.
+                                 8      17
+                --      --      --      --
+                 1       4       0       8   First column on Plate 55_b_.
+                                 8      18[321-1]
+                --      --      --      --
+                 1       5       0       6   Second column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       5       9       3   Third column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       6       0       0   Fourth column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       6       8      17   Fifth column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       6      17      14   Sixth column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       7       8      11   Seventh column on Plate 55_b_.
+                                 7       8
+                --      --      --      --
+                 1       7      15      19   Eighth column on Plate 55_b_.
+                                 8      17
+                --      --      --      --
+                 1       8       6      16   First column on Plate 56_b_.
+                                 8      18[321-2]
+                --      --      --      --
+                 1       8      15      14   Second column on Plate 56_b_.
+                                 8      17
+                --      --      --      --
+                 1       6       6      11   Third column on Plate 56_b_.
+                                 8      17
+                --      --      --      --
+                 1       9      15       8   Fourth column on Plate 56_b_.
+                                 8      17
+                --      --      --      --
+                 1      10       6       5   First column on Plate 57_b_.
+                                 7       8
+                --      --      --      --
+                 1      10      15       2   Second column on Plate 57_b_.
+                                 7       8
+                --      --      --      --
+                 1      11       4      10   Third column on Plate 57_b_.
+                                 8      17
+                --      --      --      --
+                 1      11      13       7   Fourth column on Plate 57_b_.
+                                 8      17
+                --      --      --      --
+                 1      12      13       1   Fifth column on Plate 57_b_.
+                                 8      17
+                --      --      --      --
+                 1      12      13       1   First column on Plate 58_b_.
+                                 8      17
+                --      --      --      --
+                 1      13       3      18   Second column on Plate 58_b_.
+
+The proof, therefore, that the theory advanced in regard to the order and
+the plan of the series is correct seems to be conclusive. This probably
+would have been conceded without the repeated additions given, but these
+were deemed necessary because of several irregularities found in that
+portion running through Plates 53_a_-58_a_, which constitutes the first
+half of the series.
+
+Turning back to our Table VIII, representing that part of the series on
+Plate 53_a_, we will consider the three lines of black numerals above the
+day columns, discussing the irregularities as we proceed.
+
+The numbers in the first column are 7/17,[TN-6] or, according to the
+explanation given, 7 months and 17 days. There is apparently a mistake
+here, the correct numbers being 8 months and 17 days, as it is the usual
+custom of the codex to commence numeral series with the prevailing
+interval; moreover this correction, which has also been made by Dr.
+Förstemann, is necessary in order to connect rightly with what follows;
+the counters under this first column require this correction, as they are
+8 months, 17 days. Making this change we proceed with the addition.
+
+Years.    Months.    Days.
+             8        17    First column, Plate 53_a_ (corrected).
+             8        17
+            --        --
+            17        14    Second column. Plate 53_a_.
+
+Here the author of the codex has made another mistake or varied from the
+plan of the series. As several similar variations or errors occur in this
+part of the series, it will be as well to discuss the point here as
+elsewhere. Dr. Förstemann, in discussing the series, takes it for granted
+that these variations are errors of the aboriginal scribe; he remarks
+that "It is seen here that the writer has corrected several of his
+mistakes by compensation. For instance, the two first differences should
+be 177 [8 months, 17 days] and 148 [7 months, 8 days], not 176 and 149,"
+&c.
+
+This is a strained hypothesis which I hesitate to adopt so long as any
+other solution of the difficulty can be found. It is more likely that the
+writer would have corrected his mistakes, if observed, than that he would
+compensate them by corresponding errors.
+
+Going back to that part of the series in the lower divisions which has
+already been examined and commencing with Plate 51_b_ (see Table VI), we
+observe that the numbers in the lowest of the three lines of black
+numerals, immediately over the day columns, and the first day of these
+columns are as follows (omitting the week days attached):
+
+  14      11      8       5      2      10
+  Ik.   Cauac.   Cib.   Been.   Oc.   Ezanab.
+
+Turning to the calendar (Table II) and using the Muluc column, we notice
+that the figures of this third line of black numerals denote respectively
+the month numbers of the days under them; that is to say, Ik is the
+fourteenth day of the month in Muluc years, Cauac the eleventh, Cib the
+eighth, Been the fifth, Oc the second, and Ezanab the tenth. This holds
+good through Plates 52_b_ to 58_b_ without a single exception, provided
+the diamond shaped symbol in the fourth column of Plate 55_b_ is counted
+as 20. This test, therefore, presents fewer exceptions than are found in
+counting the intervals as before explained; yet, after all, this would
+necessarily result from the fact that the day Muluc was selected as the
+commencement of the series, and hence may have no signification in
+reference to or bearing on the question of the year series, especially as
+the years counted are evidently of 360 days.
+
+Returning now to our Table VIII, representing Plate 53_a_, we observe
+that the number immediately over Kan in the first column is 17, whereas
+Kan is the sixteenth day of the month. Is it not possible that the
+intention was to designate as the ceremonial day Chicchan, standing
+immediately below, which is the seventeenth day of the month in Muluc
+years? Even though there is no reference to Muluc years, the intervals
+may be given upon the same idea, that of reaching, for some particular
+reason, the second or third day of the column instead of the first. This
+would account for the compensation of which Dr. Förstemann speaks,
+without implying any mistake on the part of the writer. These
+irregularities would then be intentional variations from the order of the
+series, yet so as not to break the general plan.
+
+The interval between 6 Kan of the first column (with the month number
+corrected) and 1 Ymix of the second is 8 months and 17 days, as it should
+be; between 6 Muluc and 1 Cimi, 8 months and 17 days; and between 1 Cimi
+and 9 Akbal, 8 months and 17 days, thus conforming to the rule heretofore
+given, a fact which holds good as a general rule throughout that portion
+of the series in the upper division.
+
+Continuing the addition as heretofore we note the variations.
+
+Years.    Months.    Days.  Column.  Plate.
+            17        14    Second.  53_a_.
+             7         8
+  --        --        --
+   1         7         3    Third.   53_a_.
+             8        17
+  --        --        --
+   1        15        19[323-1] Fourth. 53_a_.
+             8        17
+  --        --        --
+   2         6        16    Fifth.   53_a_.
+             8        17
+  --        --        --
+   2        15        13    Sixth.   53_a_.
+             8        18[323-2]
+  --        --        --
+   3         6        11    First.    54_a_.
+             8        17
+  --        --        --
+   3        15         8    Second.   54_a_.
+             8        17
+  --        --        --
+   4         6         5    Third.    54_a_.
+             8        17
+  --        --        --
+   4        15         2[324-1]  Fourth.  54_a_.
+             8        17
+  --        --        --
+   5         5        19    Fifth.    54_a_.
+             8        17
+  --        --        --
+   5        14[324-2] 16   Sixth.    54_a_.
+             7         8
+  --        --        --
+   6         4         4    Seventh.  54_a_.
+             8        18[324-3]
+  --        --        --
+   6[324-4] 13         2    First.    55_a_.
+             8        17
+  --        --        --
+   7         3        19[324-5] Second.  55_a_.
+             8        17
+  --        --        --
+   7        12        16    Third.    55_a_.
+             8        17
+  --        --        --
+   8         3        13    Fourth.   55_a_.
+             8        17
+  --        --        --
+   8        12        10    Fifth.    55_a_.
+             7         8
+  --        --        --
+   9         1        18    First.    56_a_.
+             8        17
+  --        --        --
+   9        10        15    Second.   56_a_.
+             8        17
+  --        --        --
+  10         1        12    Third.    56_a_.
+             8        17
+  --        --        --
+  10        10         9    Fourth.   56_a_.
+             8        17
+  --        --        --
+  11         1         6    First.    57_a_.
+             8        17
+  --        --        --
+  11        10         3    Second.   57_a_.
+             8        17
+  --        --        --
+  12         1         0    Third.    57_a_.
+             7         8[325-1]
+  --        --        --
+  12         8         8    Fourth.   57_a_.
+             8        17
+  --        --        --
+  12        17         5    First.    58_a_.
+             8        17
+  --        --        --
+  13         8         2    Second.   58_a_.
+             8        18[325-2]
+  --        --        --
+  13        17         0    Third.    58_a_.
+             8        17
+  --        --        --
+  14         7        17    Fourth.   58_a_.
+             8        17
+  --        --        --
+  14        16        14    First.    51_b_.[325-3]
+
+We have in what has thus far been given a satisfactory explanation of the
+meaning and use of the lines of numerals and also of their relation to
+the day columns, but we still fall short of a complete interpretation,
+inasmuch as we are unable to give the series a definite location in the
+Maya calendar or in actual time. It is apparent, however, that the series
+cannot by any possible explanation be made to agree with the calendar
+system as usually accepted, as there is nothing in it indicating the four
+series of years or the year of 365 days. It may be safely assumed, I
+think, from what has been shown, that the year referred to in the series
+is one of 360 days, with probably a periodic addition of one day, but the
+reason of the addition is not yet apparent.
+
+If the numbers in the lowest line of numerals over the day columns
+indicate the days of the month, and those of the middle line the
+respective months of the year, it is evident, as before stated, that
+Muluc is the first day of the year throughout, a conclusion
+irreconcilable with the Maya calendar as hitherto understood. It is
+probable, however, that the month and day numbers do not refer to
+particular months and days, but are used only as intervals of time
+counted from a certain day, which must in this case have been Muluc.
+
+The sum of the series as shown by the numbers over the second column of
+Plate 58_b_ is 33 years, 3 months, and 18 days. As this includes only the
+top day of this column (10 Cimi), we must add two days to complete the
+series, which ends with 12 Lamat. This makes the sum of the entire
+series 33 years, 4 months, or 11,960 days, precisely 46 cycles of 13
+months, or 260 days each, the whole and also each cycle commencing with
+13 Muluc and ending with 12 Lamat. It is also worthy of notice that in
+the right hand column of characters (hieroglyphics) over the inverted
+figure in Plate 58_b_ two numbers, 13 and 12, are found attached to
+characters which appear to be abnormal forms of month symbols.
+
+On Plates 63 and 64 are three series of ten day columns each and three
+lines of numerals over each series. These are as follows, so far as they
+can be made out, the numbers over the upper series being mostly
+obliterated. The 0 denotes the red, diamond shaped symbol which is here
+sometimes given in fanciful forms.
+
+TABLE XX.--_Table showing series of day columns, with lines of numerals._
+
+                               UPPER DIVISION.
+  __________________________________________________________________________
+                                              |                             |
+                   Plate 63.                  |          Plate 64.          |
+  --------------------------------------------+-----------------------------|
+         4      |       3      |              |              |       0      |
+         8      |       6      |              |       0      |      16      |
+         0      |       0      |       0      |       0      |       0      |
+   III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
+       Kan.     |     Kan.     |     Kan.     |     Kan.     |     Kan.     |
+       Ix.      |     Ix.      |     Ix.      |     Ix.      |     Ix.      |
+       Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |
+  XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |
+  ______________|______________|______________|______________|______________|
+                                                                            |
+                                   Plate 64.                                |
+  ____________________________________________ _____________________________|
+                |              |              |              |              |
+         0      |       0      |              |              |              |
+        12      |       8      |       3      |       3      |              |
+         0      |       0      |       0      |       0      |       0      |
+   III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
+       Kan.     |     Kan.     |     Kan.     |     Kan.     |     Kan.     |
+       Ix.      |     Ix.      |     Ix.      |     Ix.      |     Ix.      |
+       Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |     Cimi.    |
+  XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |XIII Akbal.   |
+  ______________|______________|______________|______________|______________|
+
+                               MIDDLE DIVISION.[TN-7]
+  ___________________________________________________________________________
+                |              |              |              |              |
+   XIX   5      |       4      |       4      |       4      |       4      |
+    IV   1      |      14      |       9      |       5      |       0      |
+    IV   0      |       0      |       0      |       7      |      16      |
+   III Chicchan.| III Ix.      | III Akbal.   | III Eb.      | III Ymix.    |
+       Kan.     |     Been.    |     Ik.      |     Chuen.   |     Ahau.    |
+       Ix.      |     Akbal.   |     Eb.      |     Ymix.    |     Oc.      |
+       Cimi.    |     Men.     |     Kan.     |     Been.    |     Ik.      |
+  XIII Akbal.   |XIII Eb.      |XIII Ymix.    |XIII Oc.      |XIII Cauac.   |
+  ______________|______________|______________|______________|______________|
+                |              |              |              |              |
+         3      |       3      |       3      |       3      |       2      |
+        14      |       9      |       5      |       0      |      14      |
+         5      |      14      |       3      |      12      |       1      |
+   III Oc.      | III Cauac.   | III Lamat.   | III Caban.   | III Cimi.    |
+       Muluc.   |     Ezanab.  |     Manik.   |     Cib.     |     Chicchan.|
+       Cauac.   |     Lamat.   |     Caban.   |     Cimi.    |     Men.     |
+       Chuen.   |     Ahau.    |     Muluc.   |     Ezanab.  |     Manik.   |
+  XIII Lamat.   |XIII Caban.   |XIII Cimi.    |XIII Men.     |XIII Kan.     |
+  ______________|______________|______________|______________|______________|
+
+                                LOWER DIVISION.[TN-7]
+  ___________________________________________________________________________
+                |              |              |              |              |
+         2      |       2      |       2      |       1      |       1      |
+         9      |       4      |       0      |      13      |       9      |
+        10      |      19      |       8      |      17      |       6      |
+   III Men.     | III Kan.     | III Been.    | III Ik.      | III Chuen.   |
+       Ix.      |     Akbal.   |     Eb.      |     Ymix.    |     Oc.      |
+       Kan.     |     Been.    |     Ik.      |     Chuen.   |     Ahau.    |
+       Cib.     |     Chicchan.|     Ix.      |     Akbal.   |     Eb.      |
+  XIII Been.    |XIII Ik.      |XIII Chuen.   |XIII Ahau.    |XIII Muluc.   |
+  ______________|______________|______________|______________|______________|
+                |              |              |              |              |
+         1      |       1      |              |              |              |
+         4      |       0      |      13      |       9      |       4      |
+        15      |       4      |      13      |       2      |      11      |
+   III Ahau.    | III Muluc.   | III Ezanab.  | III Manik.   | III Cib.     |
+       Cauac.   |     Lamat.   |     Caban.   |     Cimi.    |     Men.     |
+       Muluc.   |     Ezanab.  |     Manik.   |     Cib.     |     Chicchan.|
+       Ymix.    |     Oc.      |     Cauac.   |     Lamat.   |     Caban.   |
+  XIII Ezanab.  |XIII Manik.   |XIII Cib.     |XIII Chicchan.|XIII Ix.      |
+  ______________|______________|______________|______________|______________|
+
+By examining carefully the lines and columns of the middle and lower
+divisions of the plates--those represented in Tables XXI and XXII--we
+ascertain that the two together form one series; but, contrary to the
+method which has prevailed in those examined, it is to be read from
+_right_ to _left_, commencing with the right hand column of the lower and
+ending with the left hand column of the middle division.
+
+As proof of this we have only to note the fact that the series of black
+numerals over the day columns ascends towards the left. Assuming the
+lowest of the three lines to be days, the middle one months, and the
+upper one years, the common difference is 4 months and 11 days. Numbering
+the ten columns of each of our tables from left to right as usual and
+adding successively the common difference, commencing with the tenth
+column of the lowest division, of which Cib is the first day, the result
+will be as follows:
+
+Years.    Months.    Days.
+             4        11    Over tenth column, lower division.
+             4        11
+            --        --
+             9         2    Over ninth column, lower division.
+             4        11
+            --        --
+            13        13    Over eighth column, lower division.
+             4        11
+            --        --
+   1         0         4    Over seventh column, lower division.
+             4        11
+  --        --        --
+   1         4        15    Over sixth column, lower division.
+             4        11
+  --        --        --
+   1         9         6    Over fifth column, lower division.
+             4        11
+  --        --        --
+   1        13        17    Over fourth column, lower division.
+             4        11
+  --        --        --
+   2         0         8    Over third column, lower division.
+             4        11
+  --        --        --
+   3         4        19    Over second column, lower division.
+             4        11
+  --        --        --
+   2         9        10    Over first column, lower division.
+             4        11
+  --        --        --
+   2        14         1    Over tenth column, middle division.
+             4        11
+  --        --        --
+   3         0        12    Over ninth column, middle division.
+             4        11
+  --        --        --
+   3         5         3    Over eighth column, middle division.
+             4        11
+  --        --        --
+   3         9        14    Over seventh column, middle division.
+             4        11
+  --        --        --
+   3        14         5    Over sixth column, middle division.
+             4        11
+  --        --        --
+   4         0        16    Over fifth column, middle division.
+             4        11
+  --        --        --
+   4         5         7    Over fourth column, middle division.
+             4        11
+  --        --        --
+   4         9        18    Over third column, middle division.
+             4        11
+  --        --        --
+   4        14         9    Over second column, middle division.
+             4        11
+  --        --        --
+   5         1         0    Over first column, middle division.
+
+The red numerals over the first column of the middle division, except the
+lowest diamond shaped one, are omitted, as they do not appear to belong
+to the series.
+
+It must be borne in mind that the 4 months and 11 days form the common
+difference between the corresponding days of the columns counting from
+right to left; that is to say, counting 4 months and 11 days from the top
+day of any column will bring us to the first or top day of the next
+column to the left. The interval between the other corresponding days of
+the columns is also the same if the same week numbers are assigned them.
+
+This question arises here, Does the difference include the time embraced
+in the entire column? That is to say, Is this interval of 4 months and 11
+days (referring, for example, to the tenth and ninth columns of the lower
+division, our table) the sum of the intervals between 3 Cib and Men; Men
+and Chicchan; Chicchan and Caban; Caban and 13 Ix, and 13 Ix of the tenth
+column and 3 Manik of the ninth column? If not, the columns do not form a
+continuous series or must be taken in some other order.
+
+Although Dr. Förstemann discovered the order in which the series as a
+whole was to be read, and also the common difference--given, as is his
+custom, in days--he failed to furnish further explanation of the group.
+
+In answer to the question presented I call attention to the following
+facts:
+
+Commencing again with the uppermost day, 3 Cib, of the tenth column,
+lowest division, and counting on the calendar to 13 Ix of the same year,
+the interval is found to be 10 months and 18 days, which is much more
+than the interval between 3 Cib and 3 Manik (first of the ninth column),
+and of course cannot be included in it.
+
+Reversing the order in reading the columns, but counting forward on the
+calendar as usual, we find the interval between 13 Ix and 3 Cib to be 2
+months and 2 days, and, what is another necessary condition, the
+intermediate days of the column are included in this period in the order
+in which they stand, if read upwards. The interval between 3 Cib,
+uppermost day of the tenth column, and 13 Chicchan, bottom day of the
+ninth column, is 2 months and 9 days. The sum of these two intervals is 4
+months and 11 days, as it should be on the supposition that the entire
+columns follow one another in regular succession. This proves beyond
+question that the columns are to be read from _bottom_ to _top_ and that
+they follow one another from _right_ to _left_. This enables us to fix
+the week numbers to the intermediate days and to determine the day to
+which the entire series is referred as its starting point. The days and
+their numbers of the tenth and ninth columns of the lower division,
+writing them in reverse order, that is, from bottom to top, are as
+follows: 13 Ix; 3 Caban; 11 Chicchan; 8 Men; 3 Cib; 13 Chicchan; 3 Lamat;
+11 Cib; 8 Cimi; 3 Manik.
+
+These numbers hold good throughout the series.
+
+Commencing with 13 Ix, the lowest day of the tenth column, lower
+division, but first day of the series, and ending with 13 Akbal, the
+bottom of the first column, middle series, the time embraced is 5 years,
+1 month, 0 day, less 4 months and 11 days--that is, 4 years, 14 months, 9
+days (years of 360 days being understood). This is easily proved by
+counting on the calendar 4 years, 14 months, and 9 days from 13 Ix, as it
+brings us to 13 Akbal. If we add to this time 2 months and 2 days--the
+interval between 13 Akbal and 3 Chicchan (top day of first column, middle
+division)--we have, as the entire period embraced in the series as it
+stands--from 13 Ix (first of the series) to 3 Chicchan (the last)--4
+years, 16 months, 11 days. Add to this 4 months and 11 days, in order to
+reach the day with which the count begins, and we have as the entire
+period 5 years, 3 months, 2 days = 5 years, 1 month, 0 day + 2 months, 2
+days. If we count back 4 months and 11 days from 13 Ix (first of the
+series), we reach 1 Kan, the day to which the series is referred as its
+starting point. Counting forward from this date 5 years, 3 months and 2
+days brings us to 3 Chicchan, the last day of the series.
+
+It is worthy of notice that, although this series appears to be referred
+to Kan years, it is at variance with the idea of passing from one to the
+other of the four year series, and is, moreover, based upon the year of
+360 days. The order in which it is to be read, which is true also of some
+other pages, indicates that these extracts pertain to a different
+original codex than those to which we have heretofore alluded, a
+conclusion reached by Dr. Förstemann soon after he commenced the study of
+the Dresden manuscript.
+
+I was for a time inclined to believe there was a break between Plates 64
+and 65, as there appeared to be no day columns with which the lines of
+numerals running through Plates 65-69 could be connected, but the fact
+that the sum of the black numbers in each is 91, precisely the interval
+between the corresponding days of the columns in Plates 63 and 64, will
+probably warrant the conclusion that they are connected with them. This
+conclusion is strengthened, so far as those in the lower division are
+concerned, by the fact that by taking the XIII attached to the lowest
+days of the columns the numbers properly succeed one another and the
+series conforms to the rule heretofore given. As proof of this I give
+here the lower line of the lower division, prefixing the XIII, thus:
+XIII; 9, IX; 5, I; 1, II; 10, XII; 6, V; 2, VII; 11, V; 7, XII; 3, II;
+12, I; 8, IX; 4, XIII; 13, XIII.
+
+Adding together the numbers and casting out the thirteens, thus, XIII + 9
+- 13 = IX; IX + 5 - 13 = I, &c., the connection is seen to be regular.
+The final red numeral is XIII, the same as that with which the series
+begins, and the sum of the black numbers, 9, 5, 1, 10, 6, 2, 11, 7, 3,
+12, 8, 4, 13, is 91, a multiple of 13. The middle line of numerals also
+connects with the XIII attached to the bottom symbols of the day columns;
+and the upper line of numerals connects with the III attached to the top
+symbols of the day columns.
+
+Plates 70 to 73 present some peculiarities difficult to account for. That
+these pages belong to the same type as 62, 63, and 64 cannot be doubted,
+and that as a general rule they are to be read from right to left is
+easily proved; but this method does not seem to be adopted throughout,
+the order being apparently reversed in a single series.
+
+The aboriginal artist has apparently made up these pages from two older
+manuscripts or changed and added to his original. The last two columns of
+Plate 70 and first five of 71 appear to have been thrust in here as an
+afterthought or as a fragment from some other source, forming apparently
+no legitimate connection with the series to either the right or to the
+left of them. It is true, as will be shown, that there is some connection
+with the lowest series on the right, but it would seem that advantage was
+here taken of accidental correspondence rather than that this
+correspondence was the result of a preconceived plan.
+
+Commencing in the lower part of the middle division of Plate 73 and
+running back (to the left) to the sixth column of 71 and returning to the
+lower part of the lower division of 73 and ending with the sixth column
+of 71, is the following series. The columns are given in the order in
+which they stand on the respective plates, but the plates are taken in
+reverse order:
+
+TABLE XXIII.--_Table giving comparison between Plates 71, 72, and 73._
+
+  _______________________________________________________________________________
+           |  First  | Second  | Third   | Fourth  | Fifth   |         |
+           | column. | column. |column.  | column. | column. |         |
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 73,|   16    |   13    |    9    |    6    |    3    |   --    |   --
+  middle   |    5    |    0    |   15    |   10    |    5    |   --    |   --
+  division |IV Caban.|  IV Eb. |IV Manik.| IV Ik.  |IV Caban.|   --    |   --
+  -------------------------------------------------------------------------------
+  _______________________________________________________________________________
+           |  First  | Second  |  Third  | Fourth  | Fifth   | Sixth   |Seventh
+           | column. | column. | column. | column. | column. | column. |column.
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 72,|    2    |    1    |    1    |    1    |    1    |    1    |   --
+  middle   |    3    |   17    |   14    |   11    |    8    |    4    |   19
+  division |    0    |   15    |   10    |    5    |    0    |   15    |   10
+           | IV Eb.  |IV Manik.|  IV Ik. |IV Caban.|  IV Eb. |IV Manik.|IV Ik.
+  -------------------------------------------------------------------------------
+  _______________________________________________________________________________
+           |         |         |         |         |         | Sixth   | Seventh
+           |         |         |         |         |         | column. | column.
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 71,|   --    |   --    |   --    |   --    |   --    |    2    |    2
+  middle   |   --    |   --    |   --    |   --    |   --    |    9    |    6
+  division |   --    |   --    |   --    |   --    |   --    |   10    |    5
+           |   --    |   --    |   --    |   --    |   --    |  IV Ik. |IV Caban.
+  -------------------------------------------------------------------------------
+  _______________________________________________________________________________
+           |  First  | Second  |  Third  | Fourth  | Fifth   |         |
+           | column. | column. | column. | column. | column. |         |
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 73,|    3    |    3    |    3    |    2    |    2    |   --    |   --
+  lower    |    7    |    3    |    1    |   16    |   12    |   --    |   --
+  division |   15    |   10    |    5    |    0    |   15    |   --    |   --
+           |IV Manik.| IV Ik.  |IV Caban.|  IV Eb. |IV Manik.|   --    |   --
+  -------------------------------------------------------------------------------
+  _______________________________________________________________________________
+           |  First  | Second  |  Third  | Fourth  | Fifth   | Sixth   |Seventh
+           | column. | column. | column. | column. | column. | column. |column.
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 72,|    4    |    4    |    4    |    4    |    2    |    3    |    3
+  lower    |   12    |    9    |    6    |    2    |   17    |   14    |   11
+  division |   10    |    5    |    0    |   15    |   10    |    5    |    0
+           | IV Ik.  |IV Caban.|  IV Eb. |IV Manik.| IV Ik.  |IV Caban.| IV Eb.
+  -------------------------------------------------------------------------------
+  _______________________________________________________________________________
+           |         |         |         |         |         | Sixth   | Seventh
+           |         |         |         |         |         | column. | column.
+  ---------+---------+---------+---------+---------+---------+---------+---------
+  Plate 71,|   --    |   --    |   --    |   --    |   --    |    5    |    4
+  lower    |   --    |   --    |   --    |   --    |   --    |    1    |   15
+  division |   --    |   --    |   --    |   --    |   --    |    0    |   15
+           |   --    |   --    |   --    |   --    |   --    |  IV Eb. |IV Manik.
+  -------------------------------------------------------------------------------
+
+The interval between the successive days, counting to the left, is in
+each case 3 months and 5 days, corresponding with the numbers over IV
+Caban, fifth column, middle division, Plate 73. Commencing with this
+number and adding it successively, we obtain the numbers over the various
+columns:
+
+Years.    Months.    Days.
+             3         5    Over fifth column, middle division, Plate 73.
+             3         5
+            --        --
+             6        10    Over fourth column, middle division, Plate 73.
+             3         5
+            --        --
+             9        15    Over third column, middle division, Plate 73.
+             3         5
+            --        --
+            13         0    Over second column, middle division, Plate 73.
+             3         5
+            --        --
+            16         5    Over first column, middle division, Plate 73.
+             3         5
+            --        --
+   1         1[333-1] 10    Over seventh column, middle division, Plate 72.
+             3         5
+  --        --        --
+   1         4        15    Over sixth column, middle division, Plate 72.
+             3         5
+  --        --        --
+   1         8         0    Over fifth column, middle division, Plate 72.
+             3         5
+  --        --        --
+   1        11         5    Over fourth column, middle division, Plate 72.
+             3         5
+  --        --        --
+   1        14        10    Over third column, middle division, Plate 72.
+             3         5
+  --        --        --
+   1        17        15    Over second column, middle division, Plate 72.
+             3         5
+  --        --        --
+   2         3         0    Over first column, middle division, Plate 72.
+             3         5
+  --        --        --
+   2         6         5    Over seventh column, middle division, Plate 71.
+             3         5
+  --        --        --
+   2         9        10    Over sixth column, middle division, Plate 71.
+             3         5
+  --        --        --
+   2        12        15    Over fifth column, lower division, Plate 73.
+             3         5
+  --        --        --
+   2        16         0    Over fourth column, lower division, Plate 73.
+             3         5
+  --        --        --
+   3         1         5    Over third column, lower division, Plate 73.
+             3         5
+  --        --        --
+   3         4        10    Over second column, lower division, Plate 73.
+             3         5
+  --        --        --
+   3         7        15    Over first column, lower division, Plate 73.
+             3         5
+  --        --        --
+   3        11         0    Over seventh column, lower division, Plate 72.
+             3         5
+  --        --        --
+   3        14         5    Over sixth column, lower division, Plate 72.
+             3         5
+  --        --        --
+   3        17        10    Over fifth column, lower division, Plate 72.
+             3         5
+  --        --        --
+   4         2        15    Over fourth column, lower division, Plate 72.
+             3         5
+  --        --        --
+   4         6         0    Over third column, lower division, Plate 72.
+             3         5
+  --        --        --
+   4         9         5    Over second column, lower division, Plate 72.
+             3         5
+  --        --        --
+   4        12        10    Over first column, lower division, Plate 72.
+             3         5
+  --        --        --
+   4        15        15    Over seventh column, lower division, Plate 71.
+             3         5
+  --        --        --
+   5         1         0    Over sixth column, lower division, Plate 71.
+
+It is worthy of notice that the sum of the series as expressed by the
+final numbers is precisely that of the series on the middle and lower
+divisions of Plates 63 and 64, heretofore given, and embraces seven
+complete cycles of 13 months, or 260 days each. Counting back three
+months and five days from 4 Caban (the day in the fifth column, middle
+division, of Plate 73) we reach 5 Been as the starting point of the
+series.
+
+As there can be no doubt that the lines and days of the two divisions
+form together one unbroken series, it is evident there is no connection
+between that portion of it in the middle division and what lies to the
+left of it in Plate 71; but there does appear to be, as before indicated,
+some connection between the conclusion and what follows to the left in
+the lower portion of 71. The series which lies to the left at this point
+is as follows:
+
+TABLE XXIV.--_Table showing relations of Plates 70 and 71._
+
+  ________________________________________________________________
+      Plate 70.   |                   Plate 71.
+  ----------------+-----------------------------------------------
+    5th  |  6th   |  1st  |  2d   |  3d   |  4th  |  5th  |  6th
+  column.|column. |column.|column.|column.|column.|column.|column.
+     6   |   5    |   4   |   3   |   2   |       |       |
+     1   |   1    |   0   |   0   |   0   |  15   |  10   |   5
+     6   |   2    |  16   |  12   |   8   |   3   |   2   |   1
+     0   |   0    |   0   |   0   |   0   |   0   |   0   |   0
+   IV Eb.| IV Eb. | IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb.| IV Eb.
+  ---------------------------------------------------------------
+
+For the purpose of assisting the reader to see the relation more clearly,
+the last column of the preceding series--sixth of the lower division on
+Plate 71--is added at the right as it stands in the original.
+
+It is apparent that the figures in the fifth column of 71 are exactly
+double those in the sixth column. This and the fact that the day IV Eb is
+the same as those following are the only indications that there is any
+connection between the series. Using the 5 years and 1 month as the
+common difference and adding, the result is as follows:
+
+Years.    Months.    Days.
+   5         1         0     Sixth column, lower division, Plate 71.
+   5         1         0
+  --        --        --
+  10         2         0     Fifth column, lower division, Plate 71.
+   5         1         0
+  --        --        --
+  15         3         0     Fourth column, lower division, Plate 71.
+
+At this point another change occurs: the former difference is added to
+the last figures and the sum is doubled.
+
+Twenty year periods.  Years.  Months.  Days.
+                        15       3       0
+                         5       1       0
+                --      --      --      --
+                 1       0       4       0
+                                         2
+                --      --      --      --
+                 2       0       8       0   Third column lower division,
+                                                    Plate 71.
+                 1       0       4       0
+                --      --      --      --
+                 3       0      12       0   Second column, lower division,
+                                                    Plate 71.
+                 1       0       4       0
+                --      --      --      --
+                 4       0      16       0   First column, lower division,
+                                                    Plate 71.
+                 1       0       4       0
+                --      --      --      --
+                 5       1       2       0   Sixth column, lower division,
+                                                    Plate 70.
+                 1       0       4       0
+                --      --      --      --
+                 6       1       6       0   Fifth column, lower division,
+                                                    Plate 70.
+
+This series does not end at this point, but is continued in the lines
+immediately above, which are as follows:
+
+TABLE XXV.--_Table showing relations between Plates 70 and 71._
+
+  ________________________________________________________
+      Plate 70.   |               Plate 71.
+  ----------------+---------------------------------------
+    5th     6th   |  1st     2d      3d      4th     5th
+  column. column. |column. column. column. column. column.
+     1            |
+     0       8(?) |  15      13      10       9       7
+                  |                  XII
+    12       1    |   3       2       2       2       1
+                  |                  II
+     3      10    |   6      16       4       0      10
+                  |                  XII
+     0       0    |   0       0      (?)      0       0
+   IV Eb.  IV Eb. | IV Eb.  IV Eb.  IV Eb.  IV Eb.  IV Eb.
+  --------------------------------------------------------
+
+Adding the difference, 1, 0, 4, 0, to the final result of the preceding
+addition we obtain the figures of the right hand column (fifth column,
+Plate 71) of this series:
+
+   6   1   6   0
+   1   0   4   0
+  --  --  --  --
+   7   1  10   0
+
+To obtain the figures of the fourth column this difference must be
+doubled, thus
+
+   7   1  10   0
+   2   0   8   0
+  --  --  --  --
+   9   2   0   0
+
+To obtain the black numbers of the next (third) column, the lower cipher
+symbol of which is wanting, we add the former difference:
+
+   9   2   0   0
+   1   0   4   0
+  --  --  --  --
+  10   2   4   0
+
+This decrease in the difference is unusual and indicates some error. This
+idea seems to be confirmed in the following way: In order to obtain the
+numbers of the next (second) column it is necessary to add three times
+the former difference, thus:
+
+  10   2   4   0
+   3   0  12   0
+  --  --  --  --
+  13   2  16   0   Second column, Plate 71.
+
+If the increased difference, 2, 0, 8, 0, were retained after its
+appearance the result would be as follows:
+
+   7   1  10   0   Fifth column, Plate 71.
+   2   0   8   0
+  --  --  --  --
+   9   2   0   0   Fourth column, Plate 71.
+   2   0   8   0
+  --  --  --  --
+  11   2   8   0   Third column, Plate 71.
+   2   0   8   0
+  --  --  --  --
+  13   2  16   0   Second column, Plate 71.
+   2   0   8   0
+  --  --  --  --
+  15   3   6   0   First column, Plate 71.
+
+Adding the difference, 2, 0, 8, 0, to the third column, Plate 71, thus:
+
+  10   2   4   0
+   2   0   8   0
+  --  --  --  --
+  12   2  12   0
+
+we obtain the red numerals inserted in the third column. It is probable
+that the original or some subsequent scribe, observing an error at this
+point, inserted these figures as a correction. If so, he failed to remedy
+the confusion apparent in this portion of the series. The sum of the
+entire series is 303 years (360 days each) and six months, equal to 420
+cycles of 260 days.
+
+I am strongly inclined to believe that this section and also pages 24 and
+59 are interpolations by some aboriginal artist of a mathematical turn
+and advanced ability in this direction, who has given these high series
+more as curiosities than with reference to any specific dates or periods
+of time.
+
+[Illustration: FIG. 371. Specimens of ornamental loops from page 72,
+Dresden Codex.]
+
+Commencing in the sixth column of Plate 71_a_ and running through 72_a_
+to the second column of 73_a_, is a numeral series which presents some
+peculiarities that baffle all attempts at explanation. Contrary to the
+rule which prevails in these pages it ascends from left to right and has
+no day symbols connected with it. In addition to this, the numbers of its
+lowest line are inclosed in loops of the form here shown (Fig. 371) and
+have no apparent connection with the other lines of the series, but, on
+the contrary, if taken from right to left, they present in the order
+usually given the numbers of the ahaues or katunes.[337-1] It is as
+follows:
+
+                                   1    1    1    1    1    1    1
+     2    5    8   10   13   16    0    3    6    9   11   14   17
+                                                                     II.
+    14    8    2   16   10    4   18   12    6    0   14    7(?) 2   XIV
+    ⑪    ⑬   ②   ④   ⑥    ⑧   ⑩   ⑫    ①   ③   ⑤   ⑦    ⑨
+
+The last (thirteenth) column of this series is not in a line with the
+others, but is found in the lower part of the right hand column of Plate
+73, and in connection with it we find the red numerals II and XIV,
+denoting the difference between the columns, as is apparent from the
+additions here given:
+
+Years.    Months.    Days.
+             2        14         First or left hand column.
+             2        14
+            --        --
+             5         8         Second column.
+             2        14
+            --        --
+             8         2         Third column.
+             2        14
+            --        --
+            10        16         Fourth column.
+             2        14
+            --        --
+            13        10         Fifth column.
+             2        14
+            --        --
+            16         4         Sixth column[TN-8]
+             2        14
+            --        --
+   1         0        18         Seventh column.
+             2        14
+  --        --        --
+   1         3        12         Eighth column.
+             2        14
+  --        --        --
+   1         6         6         Ninth column.
+             2        14
+  --        --        --
+   1         9         0         Tenth column.
+             2        14
+  --        --        --
+   1        11        14         Eleventh column.
+             2        14
+  --        --        --
+   1        14         8[338-1]  Twelfth column.[TN-9]
+             2        14
+  --        --        --
+   1        17         2         Thirteenth column.
+
+
+FOOTNOTES:
+
+[261-1] The work here referred to is entitled Die Mayahandschrift der
+Königlichen öffentlichen Bibliothek zu Dresden, herausgegeben von Prof.
+Dr. E. Förstemann, Hofrat und Oberbibliothekar. It contains, besides the
+chromolithographs of the 74 plates, an introduction published at Leipzig,
+1880, 4^o.
+
+[269-1] A Study of the Manuscript Troano, by Cyrus Thomas, pp. 7-15.
+
+[272-1] This method will be adopted throughout this paper where figures
+containing numerals are introduced.
+
+[273-1] In the representations of lines and columns of the codex Roman
+numbers are necessarily used to distinguish the class of numerals, yet in
+the text, as in this case, the Arabic numbers will be used as most
+convenient.
+
+[273-2] Strictly speaking, the interval between 11 Men and 13 Oc is
+fourteen days, but throughout this paper, by "_interval between_" two
+days, is to be understood the number of days to be counted _from_ one _to
+and including_ the other. The one counted from is always _excluded_ and
+the one reached or with which the interval terminates is always
+_included_.
+
+[273-3] Science, p. 459, April 11, 1884.
+
+[277-1] Throughout this paper when the words "figure" and "character" are
+used in reference to what appears in the codex, they are to be understood
+as follows: "figure" refers to the picture, as of a person, animal, or
+other object in the spaces; "character" refers to the hieroglyphics or
+written symbols.
+
+[278-1] Study of the Manuscript Troano, by Cyrus Thomas, Chapters II and
+VII.
+
+[278-2] Erläuterungen zur Mayahandschrift, p. 2.
+
+[280-1] Erläuterungen zur Mayahandschrift, p. 16.
+
+[280-2] Bureau of Eth., Third Ann. Rep., pp. 16 et seq.
+
+[282-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 15, 16.
+
+[282-2] Déchiffrement des écritures calculiformes ou Mayas, par M. le
+C^te H. de Charency, Alençon, 1849; also, Mélanges, pp. 185-195.
+
+[283-1] For an explanation of the principle upon which these day columns
+were formed, see "Notes on certain Maya and Mexican manuscripts," by
+Cyrus Thomas, published in the Third Annual Report of the Bureau of
+Ethnology.
+
+[290-1] The symbol for this day in Kingsborough resembles Lamat, but the
+photographic copy makes it Ix, as it should be.
+
+[290-2] Förstemann, Erläuterungen zur Mayahandschrift, p. 42.
+
+[291-1] Erläuterungen zur Mayahandschrift, p. 36.
+
+[292-1] Erläuterungen zur Mayahandschrift, p. 60.
+
+[293-1] Erläuterungen zur Mayahandschrift, p. 56.
+
+[296-1] The bottom lines are selected because they are less injured in
+the codex than the top lines, which are in most cases entirely
+obliterated.
+
+[300-1] 3 days in ms., should be 4.
+
+[317-1] The third symbol in the last day column of Plate 51_b_ is Been in
+the codex; but this is an evident mistake, as shown by the order of the
+days, since Ahau, which has been substituted above, always follows Cauac.
+This may be seen by reference to the middle column of 57_b_.
+
+[319-1] This is one of the exceptional cases.
+
+[321-1] Second exception.
+
+[321-2] Third exception.
+
+[323-1] One line has been omitted in the numeral symbol.
+
+[323-2] Here we have again the added day.
+
+[324-1] The 8 at this point in the codex is an evident error.
+
+[324-2] Here is also an error in the original, this being 10.
+
+[324-3] The symbols require an additional day here.
+
+[324-4] The 8 in the year line in the original is a manifest error, as 6
+precedes and 7 follows.
+
+[324-5] The 18 in the day line at this point is also an error, as the
+interval between 2 Muluc and 10 Cimi is 8 months and 17 days. Moreover,
+the next day number being 16 requires this to be 19.
+
+[325-1] The counters in the original at this point are certainly wrong,
+for here should be 7 months and 8 days, whereas the symbols are those for
+8 months and 17 days.
+
+[325-2] Here we have again the additional day.
+
+[325-3] Added to show connection with the lower series.
+
+[333-1] Codex has 19, which is equivalent to 1 year and 1 month.
+
+[337-1] While reading the final proof I fortunately discovered what may
+prove to be the correct explanation of the numbers in the loops.
+
+At the commencement of the series on Plate 71 and at its close on Plate
+73 we observe the symbol of the day, 9 Ix. Starting from this date and
+counting forward on the calendar two months and fourteen days, we reach
+11 Lamat. This gives the number in the first loop of the series. Two
+months and fourteen days more bring us to 13 Ik, the number in the second
+loop; two months and fourteen days to 2 Cib, the number in the third
+loop, and so on to the end. It is therefore probable that the numerals in
+the loops indicate the week numbers of the days, though these are usually
+expressed in red symbols.
+
+[338-1] The 7 in the twelfth column is an error; it should be 8, as an
+inspection shows the place of the missing dot. The additions make it
+clear that the numbers of the second line refer to months, those of the
+line below them to days, and those of the line above to years. The series
+is, therefore, apparently complete without the numbers inclosed in the
+loops.
+
+
+
+
+CHAPTER II.
+
+CONCLUSIONS.
+
+
+The conclusions to be drawn from the foregoing discussion may be briefly
+stated as follows:
+
+First. That the codex in its present form is composite, being made up
+from two or more different original manuscripts, as Dr. Förstemann has
+suggested.
+
+Second. That a number of minor changes and additions have been made by a
+subsequent hand, possibly after it had assumed its present form.
+
+Third. That the year referred to in the larger series is one of 360 days;
+also, that in instances of this kind the count is continuous, and hence
+not consistent with the generally received idea of the Maya calendar, in
+which, the four year series forms a necessary part of the system, unless
+some other method of accounting for the five supplemental days can be
+discovered than that which has hitherto been accepted.
+
+Fourth. On the other hand, indications of the four year series are
+certainly found in all of the Maya manuscripts; for example, in Plates
+25-28 of the Dresden Codex and Plates XX-XXIII of the Manuscript
+Troano,[339-1] which seem to be based on this series; in fact, the
+numbers attached to the days in the latter can be accounted for in no
+other way. Plates 3-6 of the Cortesian Codex are apparently based upon
+the same system. The numbers in the loops on Plates 71, 72, and 73,
+Dresden Codex, heretofore alluded to and represented in Fig. 371,
+apparently defy explanation on any supposition except that they refer to
+the numbers of the ahaues, which are based upon the four year
+series.[339-2] The frequent occurrence in connection and in proper order
+of both the first and the terminal days of the year apparently refers to
+the same system. Many of the quadruple series no doubt relate to the four
+cardinal points and the four seasons; yet there are some which cannot be
+explained on this theory alone.
+
+It is impossible, therefore, to exclude this system from consideration in
+studying the chronology of the codices, although there are a number of
+the numerical series of the Dresden manuscript which cannot be made to
+fit into it on any hypothesis so far suggested. The same thing is also
+found to be true in regard to some, in fact most, of the series found in
+the Mexican manuscripts. This confusion probably arises in part from the
+apparently well established fact that two methods of counting time
+prevailed among both Mexicans and Mayas: one, the solar year in ordinary
+use among the people, which may be termed the vulgar or common calendar;
+the other, the religious calendar used by the priests alone in arranging
+their feasts and ceremonies, in which the cycle of 260 days was taken as
+the basis. But this supposition will not suffice as an explanation of
+some of the long series of the Dresden Codex, in which the year of 360
+days appears to have been taken as a unit of measure, unless we
+assume--as Förstemann seems to have done--that what have been taken as
+years are simply high units and counting the whole as so many days, refer
+the sum to the cycle of 260 days, which will in almost every case measure
+them evenly as a whole, or by its leading factor, 13. That the smaller
+series attached to day columns are all multiples of 13 and referable to
+the cycle of 260 days has been shown by Förstemann as well as in the
+preceding part of this paper. But it is worthy of note that the
+difficulty mentioned occurs only in reference to series found in that
+portion of the Dresden manuscript which Förstemann has designated Codex B
+(page 24 being considered as belonging thereto).
+
+The red unit number symbol, with a circle of dots around it, seen
+occasionally in the Manuscript Troano, seems to have some connection with
+the four year series. Take, for example, the one in the lowest division
+of Plate VII.
+
+The series commences in the lower right hand corner of Plate VIII, where
+the day column with which it is connected is found. The days of this
+column, reading downward, are as follows: Ahau, Eb, Kan, Cib, Lamat, and
+the number over them is I, but without any dots around it, while the
+terminal I of the series is inclosed in the circle of dots. What is the
+meaning of this marked distinction? It is evident that it is something
+which does not apply equally to all the days of the columns; yet, as it
+is the terminal number, it must relate to some one of them. If we examine
+the series carefully I think the reason for the distinction will be
+explained; Written out in full, it is as follows:
+
+   I.
+  Ahau
+  Eb   }
+  Kan  } 10, XI; 10, VIII; 10, V; 10, II; 12[?], Ⓘ.
+  Cib
+  Lamat
+
+The last black number is 10 in Brasseur's fac simile, but should be 12.
+Making this correction, the series is regular and of the usual form. The
+sum of the black numbers is 52, which is the interval between the days,
+and the number over the column is the same as the final red number.
+
+If we turn now to the calendar (Table II) and select Ahau of the Kan
+column, and 1, the seventeenth number of the eighth figure column, and
+count 52 days, we reach 1 Eb, the second day of our column as given
+above; 52 days more bring us to 1 Kan, the first day of the first month
+in the calendar and third day of our column. If the theory of the four
+year series be correct, then 1 Kan of the Kan series must be the first
+day of the first year of an Indication or week of years. This fact was
+probably considered by the aboriginal artist of sufficient importance to
+give this day a mark of distinction. As it is not possible for any of the
+other days of the column to be thus distinguished, it is fair to presume
+this peculiar marking of the final number refers to Kan. Moreover, this
+distinction would not occur if any other than the Kan series were used.
+
+In the upper division of Plate IX of the same manuscript is the following
+series:
+
+   XIII
+  Men   }
+  Manik } 20, VII; 20 Ⓘ; 1, II; 4, VI; 7, XIII.
+  Cauac }
+  Chuen
+  Akbal
+
+In this, I, the second red number of the series, has the circle of dots
+around it. The number over the column is partially obliterated, but is
+readily restored, and should be XIII.
+
+If we select, on our calendar, the Cauac column, or series, a reason for
+this distinction will appear. The sum of the black numbers is 53, which
+is also the interval between the days. As has heretofore been shown, the
+red numbers of the series refer to certain days selected by the priests,
+for special reasons unknown to us, which occur between the days of the
+column.
+
+In this case the intermediate days are as follows:
+
+     Between 13 Manik and 13 Cauac: 7 Manik, 1 Manik, 2 Lamat, and 6 Eb.
+
+     Between 13 Cauac and 13 Chuen: 7 Cauac, 1 Cauac, 2 Ahau, and 6 Kan.
+
+Here we find the explanation for which we are seeking, as in the interval
+between 13 Cauac and 13 Chuen is 1 Cauac, which, if the Cauac column of
+the calendar be selected, is the first day of the year 1 Cauac, the first
+year of an Indication. As this occurs only when a year commencing with
+Cauac is selected, we infer that the series is based upon the system with
+the four year series.
+
+The best illustration of this peculiarity and the strongest evidence of
+its signification is probably found in the series contained in the middle
+division, Plate XI, same manuscript. This, when written out and the
+numbers properly arranged, is as follows:
+
+   Ⓘ        Ⓘ
+  Oc       Ahau  }
+  Cib      Cimi  } 1, II; 2, IV; 2, VI; 5, XI; 2, XIII; 4, IV; 9(?) Ⓘ.
+  Ik       Eb    }
+  Lamat    Ezanab
+  Ix       Kan
+
+The last black number of the series is 9, but should be 10 to render the
+series complete. Making this correction, the series is of the usual type;
+the sum of the black numerals is 26, the interval between the days of
+the columns is 26, and the final red numeral is the same as that over the
+columns.
+
+As the circle of dots is around the final red number and also around each
+of those over the columns, the distinction indicated must refer to one or
+more days of each column.
+
+As the last days only of the columns are year bearers, the mark of
+distinction probably applies to them. Selecting for the left hand column
+the Ix series of years and commencing with 1 Oc, the seventeenth day of
+the eighth month, we count 26 days. This brings us to 1 Cib, the third
+day of the tenth month, or tenth figure column of our calendar and second
+day of the first day column of the series; 26 days more to 1 Ik; 26 more
+to 1 Lamat, and 26 more to 1 Ix, the first day of the year 1 Ix, which,
+according to the four year series, will be the first year of an
+Indication. Selecting the Kan series for the second column and counting
+in the same way from 1 Ahau, the seventeenth day of the eighth month, or
+eighth figure column of the calendar, the last day is found to be 1 Kan,
+the first day of the year 1 Kan, which must also be the first year of an
+Indication.
+
+Unit numerals marked in this manner are found in two or three places in
+the Cortesian Codex, but there is none in the Dresden Codex. The series
+with which they are connected in the former, except that in the middle
+division of Plate 24, are too much obliterated to be traced throughout.
+This, by making two slight and apparently authorized corrections, is as
+follows:
+
+    Ⓘ
+  Cimi   }
+  Ezanab } 11, XII(?); 11, X; 6, III; 8, XI; 7(?), V; 9, I.
+  Oc     }
+  Ik
+  Ix
+
+The first red numeral of the line is X in the original and the next to
+the last black number is 6. By changing the former to XII and the latter
+to 7 the sum of the series will be 52, which is the interval between the
+days of the column.
+
+Using the Ix column in the calendar and commencing with 1 Cimi, counting
+as heretofore, the last day of the column of the series is found to be 1
+Ix, the first day of the year 1 Ix and the first year of an Indication,
+according to the four year system.
+
+A somewhat remarkable confirmation of the theory here advanced is
+presented in a series found in the middle division of Plate II of the
+Manuscript Troano.
+
+The series, when written out with the substitutes heretofore used, is as
+follows:
+
+    Ⓘ          Ⓘ
+  Manik      Ymix     }
+  Men (?)    Been     } 9, X; 6, III; 11, I.
+  Chuen      Chicchan }
+  Akbal      Caban
+  Men        Muluc
+
+In Brasseur's fac simile the second symbol of the left hand column is
+clearly that for Men. If this be accepted as correct, then no year bearer
+(Kan, Muluc, Ix, Cauac) would be found in either column and the theory we
+have advanced regarding the signification of the dots around the red unit
+over the column would fall to the ground. Nor is this the only difficulty
+we meet with in attempting to apply the theory to this series. The sum of
+the black numbers is 26, which should also be the interval between the
+days of the columns. Counting 26 days from 1 Manik brings us to 1 Been
+instead of 1 Men; 26 more to 1 Cauac, a day not found in either column as
+given in the original. Taking the second column and counting 26 days from
+1 Ymix, we reach 1 Manik, instead of 1 Been. This gives us the key to the
+series and solves the riddle. We must commence with 1 Ymix, then take 1
+Manik, then 1 Been, and so on, going alternately from column to column.
+
+Adopting this method and using the Cauac column of our calendar, Table
+II, the result is as follows: Commencing with 1 Ymix, the third day of
+the tenth figure column, and counting 26 days, we reach 1 Manik; 26 days
+more bring us to 1 Been, and 26 more to 1 Cauac, the first day of the
+first year of an Indication. The 1 Men of the left hand column should
+therefore be 1 Cauac, which is also proved by counting the intervals,
+without regard to the week numbers. For example, from Ymix to Been is 12
+days, from Been to Chicchan 12 days, from Manik to Cauac 12 days, and so
+on through each column. Or, if we take the columns alternately, the
+interval is six days, thus: From Ymix to Manik, 6 days; from Manik to
+Been, 6 days; from Been to Cauac, 6 days; from Cauac to Chuen, 6 days,
+and so on to the end.
+
+Although the proof is not absolutely conclusive that these red unit
+numerals have this mark of distinction for the reason given, it
+nevertheless furnishes what would seem to be a satisfactory explanation,
+and, if so, affords proof that the calendar system, based upon the four
+year series, was in vogue when the Manuscript Troano and the Codex
+Cortesianus were written.
+
+This mark of distinction is found in a strange and unusual relation in
+the lower division of Plate XV, Manuscript Troano. The first red numeral
+of the series is given thus:
+
+[Illustration: FIG. 372. Numeral character from the lower division of
+Plate XV, Manuscript Troano.]
+
+Most of the day and about half of the numeral symbols are obliterated,
+but all that are necessary for present purposes remain distinct and
+uninjured, as follows:
+
+  III, }
+  Ix   } 10, XIⒾI.
+  Cimi }
+
+Judging by these and the few numbers remaining, the entire series was as
+follows:
+
+  III,   }
+  Ix     }
+  Cimi   }
+  Ezanab } 10, XIII; 4, IV; 20, XI; 9, VII; 9, III
+  Oc     }
+  Ik     }
+
+The only doubt in reference to the restoration is whether the second and
+third pairs of numerals should be as given, or 2, II, and 22, XI. If we
+select the Kan column of our Table II and count from 3 Ix of the eleventh
+figure column, we reach 13 Kan. If the four year series was the system
+used 13 Kan might be the first day of a year, but not the first day of an
+Indication. As this is the only day referred to by the XIII which could
+have been the first of a year we must seek an explanation in something
+else. Counting ten days from 3 Ezanab will bring us to 13 Lamat, which is
+the last day (counting the five added days) of an Indication, commencing
+with the year 1 Kan and ending with the year 13 Kan.
+
+According to my theory of the ahaues,[344-1] the year 13 Kan would have
+corresponded with the Gregorian years 1376, 1438, 1480, and 1532.
+According to the theory advanced by Perez,[344-2] it would have
+corresponded with 1385, 1437, 1489, and 1541.
+
+It is therefore possible that this mark of distinction may be of some
+value in determining the relation of the Maya to the Gregorian calendar.
+
+
+FOOTNOTES:
+
+[339-1] See Study of the Manuscript Troano, by Cyrus Thomas.
+
+[339-2] See note on page 337.
+
+[344-1] See Table XVII, Study of the Manuscript Troano, by Cyrus Thomas,
+p. 44.
+
+[344-2] See Table XVIII, ibid., p. 45.
+
+
+
+
+CHAPTER III
+
+THE WRITING.
+
+
+It must be admitted that none of the attempts made at deciphering the
+writing in these manuscripts has proved entirely satisfactory; in fact
+there is still some doubt as to whether any of the characters are truly
+phonetic; nevertheless it is believed that what is here shown will tend
+to lessen this doubt. It must be conceded, however, notwithstanding these
+drawbacks and difficulties, that some material progress has been made
+towards a better understanding of its type and of the nature of the
+characters.
+
+The direction in which it is to be read must of course be determined
+before any progress can be made in deciphering it. This was, until
+recently, a matter of speculation, but now may be considered settled. As
+this has been explained[345-1] it is unnecessary to repeat that
+explanation here.
+
+A certain parallelism in the sentences or groups of characters has also
+been discovered. Attention was first called to this by me in the work
+referred to, but is more fully explained by Dr. P. Schellhas in his paper
+entitled "Die Mayahandschrift der königlichen Bibliothek zu Dresden." It
+will readily be understood from a single illustration. Take for example
+the lower division of Plate XV of the Manuscript Troano (see Study Ms.
+Troano). Omitting from consideration the numerals and the day column at
+the left, there are here two short columns on the left and two on the
+right over the animal figures, and three longer columns between. As
+explained in the work referred to, the short columns are to be read as
+lines from left to right and the longer columns separately, from the top
+downward. There are, in all, five groups or sentences, each containing
+four compound characters. Representing these by letters, repeating those
+which indicate similar characters, and arranging as in the plate, the
+result is as follows:
+
+   ___________________________________________
+  |            |     |     |     |            |
+  | _b_   _a_  | _h_ | _l_ | _m_ |  _w_   _a_ |
+  |            |     |     |     |            |
+  | _r_   _n_  | _a_ | _a_ | _a_ |  _r_   _s_ |
+  |____________|     |     |     |____________|
+               | _r_ | _r_ | _r_ |
+               |     |     |     |
+               | _p_ | _k_ | _t_ |
+               |_____|_____|_____|
+
+In this case the characters represented by _a_ and _r_ are repeated in
+each group and in the same relation to the other characters. It is
+apparent, therefore, that each group is to be read separately, and, as
+each repeats in part what is given in the others, it is more than
+probable that they are simply short formulas to be repeated in certain
+religious ceremonies. This parallelism, though not always so apparent as
+in the case presented, is nevertheless found running through all the
+codices. The advantage to the attempts at decipherment which results from
+this fact is evident, as it will often justify the restoration of blurred
+or obliterated characters, and, what is of still more importance, will
+enable the investigator to test his conclusions by comparing the
+different characters and pictures with which they are associated.
+
+Although it appears to be well settled that, as a rule, the writing, when
+in lines, is to be read from left to right--the lines following each
+other downward and the columns to be read from the top downward, but the
+groups, as before explained, to be read separately--it does not follow
+that the _groups_ succeed one another from left to right. This has
+generally been taken for granted, but there are some reasons to doubt the
+correctness of this conclusion as regards a number of plates and possibly
+one entire codex.
+
+The facts that the lines of numerals attached to the day columns extend
+to the right and that the written characters, when in lines, follow one
+another in the same direction lead us to infer that the groups and
+pictures follow one another in the same order, but the apparent movement
+of the latter towards the left would seem to indicate that _they_ follow
+one another in _this_ direction. This inference appears to be confirmed
+by the following evidence: As is well known, the plates of the Manuscript
+Troano are to be taken in reverse order to the paging. Turning to Plate
+II, we observe in the middle department of the middle division a bound
+captive or victim, on whose neck a machete is descending to sever the
+head from the trunk. Turning to Plate III, which properly stands to the
+left of Plate II, we see a headless trunk covered with blood and the
+fatal machete near the neck. It is fair to presume that this is the same
+individual that is figured in the preceding plate, and, if so, that the
+pictures follow one another toward the left.
+
+Placing Plates XV* and XVI* of the same manuscript in the proper relation
+to each other and carefully examining the figures in the second division,
+we notice that the idol heads which the artisans are carving approach
+completion as we move toward the left, those in Plate XV* and the right
+hand one in XVI* being simply blocked out, while the middle one in the
+latter plate is completely rounded and is receiving the second ornamental
+line and the one at the left hand is receiving the third and final line.
+
+The female figures in the second division of Plate XIX* indicate the same
+order, as shown by the increasing girth as we proceed toward the left.
+
+The same order appears to be indicated in numerous places by the symbols
+of the cardinal points inserted in the text, as they (supposing the
+conclusion as to their assignment in my "Notes on certain Maya and
+Mexican manuscripts," accepted by Drs. Förstemann and Schellhas, to be
+correct) follow one another in the proper order if read towards the left,
+to wit, south, east, north, west.
+
+As the writing over each figure, consisting usually of four compound
+characters, appears to refer to that over which it is placed, it follows
+that these character groups must be taken in the same order as the
+pictures. The suggestions on this point are presented here more as proper
+subjects of investigation by students of American paleography than as
+fixed conclusions of the writer. If found to be justified by the facts,
+they will furnish some additional aid in the work of deciphering these
+manuscripts.
+
+
+SIGNIFICATION OF THE CHARACTERS.
+
+As Landa's alphabet has so far proved useless as an aid in deciphering
+these manuscripts, our only hope of accomplishing this end is by long and
+careful study of these records and laborious comparisons of characters
+and the relations in which they stand to one another and to the figures.
+
+Some discoveries made while preparing this paper for the press, which are
+mentioned further on, may possibly give us the key to the method used by
+Landa in forming his alphabet, and, if so, will probably furnish some
+slight additional aid in our investigations.
+
+The direction in which the writing is to be read having been ascertained,
+our next step is to determine by comparison the probable signification of
+as many characters as possible before discussing the question of
+phoneticism. The relation of the characters to the pictorial
+representations forms our chief reliance in this branch of the
+investigation.
+
+As a commencement in this work and as a basis for further attempts in the
+same direction, attention is now called to some characters, other than
+the day and month symbols, whose signification seems to be satisfactorily
+determined. As there is still some difference of opinion as to the
+assignment of the symbols of the cardinal points they are also omitted
+from the list. M. Léon de Rosny has given, as a supplement to his edition
+of the Cortesian Codex, a list of characters with their supposed
+signification. It is not my intention to discuss here the merits of this
+vocabulary, although I shall avail myself of so much found therein as
+appears to warrant acceptance.
+
+The question of phoneticism will not be considered in connection with the
+list, as the subject will be briefly discussed at the close, the only
+object in view in giving the list being to indicate the signification of
+the characters alluded to. The Maya names appended are therefore to be
+understood simply as the supposed names applied to them or the objects
+they denote.
+
+
+SYMBOLS OF ANIMALS &C.
+
+[Illustration: No. 1]
+
+  _Kal._ The symbol for the number 20. Found in all of the codices and
+     explained in the preceding portion of this paper.
+
+[Illustration: No. 2]
+
+  The symbol for 0 (nought), always red. Found only in the Dresden Codex
+     and always in the numeral series.
+
+[Illustration: No. 3]
+
+  _Kin._ Sun, and probably day also. It is not known positively that it
+     has this signification except in connection with the equatorial
+     cardinal point symbols and the symbol of the month _Yaxkin;_ yet it
+     is reasonable to suppose it has.
+
+[Illustration: No. 4 _a_ _b_ _c_ _d_]
+
+  _Aac_ or _Ac_. A turtle. That this symbol as shown in _a_ and _b_
+     denotes the turtle is conclusively proved by its resemblance to the
+     head of that animal, as figured in the Cortesian Codex (see Fig.
+     373) and its relation to these figures. Found only in this codex,
+     unless two doubtful symbols on Plate XXV*, Manuscript Troano, are to
+     be considered as variants.
+
+[Illustration: FIG. 373. Turtle from the Cortesian Codex.]
+
+There can be no doubt that Landa's _A_, an exact copy of which is given
+in the margin, in both varieties, _c_ and _d_, is nothing more nor less
+than this symbol; for, in addition to the very close general resemblance,
+we see in it the eye and the dot indicating the nostril. This fact is
+important, as it gives us some clew to the method adopted by Landa in
+forming his alphabet.
+
+[Illustration: No. 5]
+
+  _Uech._ Symbol or head of the armadillo of Yucatan. Appears but once or
+     twice and in the Manuscript Troano only. (See Study of the
+     Manuscript Troano, by Cyrus Thomas, pp. 98 and 145).
+
+[Illustration][TN-10]
+
+  _Che._ Wood. (See Study of the Manuscript Troano, by Cyrus Thomas, p.
+     144).
+
+[Illustration: No. 7]
+
+  _Cab._ Earth, soil; also honey. (See Study of the Manuscript Troano, by
+     Cyrus Thomas, p. 150.)
+
+[Illustration: No. 8]
+
+  _Piz._ Stone or stone heap. (See Study of the Manuscript Troano, by
+     Cyrus Thomas, p. 144). The Maya name of the thing indicated is
+     uncertain, though I am inclined to believe _Piz_, as given in the
+     work alluded to, is correct.
+
+[Illustration: No. 9]
+
+  _U._ The left symbol of this figure appears to stand for vase, and is
+     also used to indicate a pronoun or article when joined to another
+     symbol, as here shown. (See op. cit., p. 145.)
+
+[Illustration: No. 10]
+
+  _Xicim._ The ear. Rosny, Vocabulaire hiératique, No. 185.
+
+[Illustration: No. 11]
+
+  _Hau._ The quarter of a deer. Usually represented as an offering to the
+     gods; in all the manuscripts.
+
+[Illustration: No. 12]
+
+  _Ikilcab._ The bee. Although the figure bears a much stronger
+     resemblance to a beetle than to a bee, there can be no longer any
+     doubt that Brasseur's supposition that it represents a bee is
+     correct.
+
+[Illustration: No. 13]
+
+  Honey in the comb. (See Study of the Manuscript Troano, by Cyrus
+     Thomas, Fig. 20); in the Manuscript Troano only, and always in red.
+
+[Illustration: No. 14]
+
+  _Xamach or Chimix._ A vessel. This symbol, found in all the codices, is
+     apparently explained by its use in the upper division of Plate 27,
+     Cortesian Codex, where it stands over each of four vessels or jars
+     of the form represented in Fig. 374.
+
+[Illustration: FIG. 374. Jar from the Cortesian Codex.]
+
+This conclusion is greatly strengthened by the fact that the only other
+symbols in this connection are those of the cardinal points, one to each
+vessel. These figures are probably intended to denote here the four
+sacred vessels or amphoræ of the Bacab, though not surmounted, as
+Brasseur supposed, by human or animal figures.
+
+The symbol appears to be used also in the ordinary sense, or at least to
+signify other vessels than the sacred four, if we may judge by its
+frequent repetition in Plate XIV, Manuscript Troano. But it is worthy of
+notice that here also, in both the middle and lower divisions, four of
+the symbols are connected with the cardinal point symbols; there is also
+in the former the figure of a vessel.
+
+[Illustration: Hieroglyph]
+
+If this identification be correct it is important, as it has a strong
+bearing on the question of phoneticism. It will be observed that,
+although the right hand member resembles closely the symbol of the day
+Ymix, there are some differences, as may be seen by comparison. In the
+former the little figure at the top is divided as in Kan, and on each
+side of it there is a large dot, usually, and apparently by intention,
+circular or hollow. These differences are permanent in the different
+codices.
+
+In the upper division of Plates X and XI, Manuscript Troano, where this
+symbol appears in connection with each of the four cardinal symbols, that
+relating to the east presents this remarkable variation:
+
+[Illustration: Hieroglyph]
+
+[Illustration: No. 15 _a_ _b_]
+
+  (?) A conventional figure of sprouting maize, never inserted in the
+     text, but frequently in the Manuscript Troano and in the Peresian
+     Codex made a part of the head gear of figures of deities, in which
+     case the Kan symbol is generally omitted.
+
+The Kan symbol in this connection cannot be intended, as Dr. Schellhas
+supposes, to indicate the field or milpa in which the corn is growing,
+but the grain from which the plant is springing. (On this subject see
+Study of the Manuscript Troano, by Cyrus Thomas, pp. 105 and 107.)
+
+[Illustration: No. 16]
+
+  (?) Symbol of a worm which gnawed the roots of the growing agave or
+     maguey; appears but once, on Plate XXIX_c_ of the Manuscript Troano.
+
+The animal head and teeth show the erroneous idea the natives had of the
+gnawing apparatus of insects. The worm is shown on the next page in Fig.
+375.
+
+[Illustration: FIG. 375. Worm and plant from Manuscript Troano.]
+
+[Illustration: FIG. 376. Figure of a woman from the Dresden Codex.]
+
+[Illustration: No. 17]
+
+  _Chuplal._ Woman or female. This symbol is found in the Dresden and
+     Troano Codices, but most frequently in the former. The appendage at
+     the right is sometimes wanting, and occasionally that at the left,
+     but when this is the case some other prefix is generally
+     substituted.
+
+If we examine carefully Plates 16-20 of the Dresden Codex, where this
+symbol is most frequently repeated, and compare it with the heads of the
+females there figured, it soon becomes apparent that the scrolls with the
+heavy black dot are intended to denote the locks of hair and that the
+symbol as a whole is, as usual, a modified or conventional form of the
+head (see Fig. 376).
+
+[Illustration: No. 18 _a_ _b_ _c_]
+
+  _Otoch._ A house or dwelling, or _Tabay;_ a hut or hunting lodge. The
+     symbol marked _a_ is found in the Cortesian Codex on Plate 29; that
+     marked _b_, on Plates 29, 32, and 34, same codex, and on Plates XVI*
+     and XXII* of the Manuscript Troano. The one marked _c_ is the usual
+     form in the latter, as on Plates V*, VII*, and X*. It is also on
+     Plate 38 of the Dresden Codex.
+
+The relation of these symbols to the conventional figures of houses or
+huts inserted at the points where they are found, together with the form,
+which shows an attempt to represent the thatched or leaf covered roof,
+leaves no doubt that they are used for the purpose indicated.
+
+[Illustration: No. 19 _a_ _b_]
+
+  _Buk_ (?). There are good and, it is believed, satisfactory reasons for
+     concluding that these symbols are intended to denote the action of
+     whirling a stick to produce fire or rolling a pestle in grinding
+     paint. The first, marked _a_, is found only on Plate XIX of the
+     Manuscript Troano, and the second, on Plates 5 and 6 of the Dresden
+     Codex.
+
+A copy of part of Plate XIX of the Manuscript Troano is introduced here
+(see Fig. 377) to show the relation of the figures to the characters. If
+this interpretation be correct, we see here an evident attempt on the
+part of the aboriginal artist to indicate by the symbol the action
+necessary in the work to be performed. It is probably a conventional
+sign, and not a phonetic character.
+
+[Illustration: FIG. 377.]
+
+[Illustration: No. 20]
+
+  (?) In all probability one of the symbols used to denote the act of
+     walking or taking steps. Found but seldom in this particular form,
+     though each portion occurs frequently alone or in other
+     combinations.
+
+[Illustration: FIG. 378. Copy of lower division of Plate 65, Dresden
+Codex.]
+
+A remarkable series of figures and written characters runs through the
+lower division of Plates 65 to 69 of the Dresden Codex, apparently
+devoted entirely to the representation of incidents in the life of the
+culture hero Kukulcan, or deity mentioned on a subsequent page as the
+"long nosed god" or "god with the snake-like tongue," or to ceremonies to
+be performed in honor of this deity. Over the figure are three lines of
+written characters, as shown in Fig. 378, which is a copy of the lower
+division of Plate 65. These, as is readily seen, are in groups, one group
+of six compound characters over each figure of the god. There are
+thirteen figures of the god and thirteen of these groups of characters in
+the series. The characters of a group, as may be seen by reference to the
+figure, are arranged in the following manner:
+
+   ___________
+  |     |     |
+  | _a_ | _b_ |
+  |_____|_____|
+  |     |     |
+  | _c_ | _d_ |
+  |_____|_____|
+  |     |     |
+  | _e_ | _f_ |
+  |_____|_____|
+
+to be read (presumably) in the alphabetic order of the letters given;
+though the order in which they are to be read is not essential at
+present. Examining the series carefully we find that the first character
+of each group corresponding with _a_ in the above diagram is the same
+throughout. The same thing is true in reference to the third, or that
+occupying the place of _c_ in the diagram, which is the symbol of the
+deity. The sixth, or that corresponding with _f_ in the diagram, is also
+the same throughout the series; the fifth, corresponding with _e_, is
+substantially the same throughout, though subject to more variations than
+any of the other characters. It follows, therefore, that the chief and
+almost the only differences in the readings of the groups are to be found
+in the second and fourth characters, or those represented by _b_ and _d_
+in the above diagram; the others (at least those represented by _a_, _c_,
+and _f_), if referring at all to the figures, must relate to something
+found in or applicable to each. The third (_c_), as stated, is the symbol
+of the deity and corresponds in the text with the figure of the god in
+the pictures. As this deity figure is the only thing found in all of the
+representations, we must seek for the explanation of the other two
+permanent characters in something else than what is figured.
+
+Comparing the second character (_b_) of each group with that upon which
+the god is seated or standing, we find sufficient evidence to satisfy us
+that this symbol is the one which is used throughout to indicate this
+object. For example, the second symbol in the group on Plate 69 is an
+exact copy of the object on which the deity is seated. The same thing is
+substantially true of that in the left hand group of Plate 66, the middle
+group of 67, and the right hand group of 68.
+
+Assuming, on account of the remarkable regularity of this series and the
+fact that the deity is in each case seated or standing on something, that
+this rule holds good throughout, we have a clew to those corresponding
+symbols which are not simple copies of the things they are used to
+indicate.
+
+Turning to Fig. 378, we observe in the right hand department the marks of
+footsteps under the deity and the character shown in the margin (No. 20)
+as the second of the group above the deity. It is worthy of notice that
+in the two we find precisely Landa's two characters for the letter B. Is
+it possible that the two principal parts of this compound character
+denote the Maya words _oc be_, "foot journey" or "enters upon the
+journey"? Attention will be called to this further on, but it is proper
+to state here that as the prefix is found in three other corresponding
+characters it cannot be a necessary part of that which represents the
+footsteps in this case.
+
+[Illustration: No. 21.]
+
+  Assuming the theory above given as to the characters in the inscription
+     which represent the things under the deity figures to be correct,
+     the second character in the middle group of the lower division of
+     Plate 65, shown in Fig. 378, will be the symbol for the substance
+     represented by scrolls under the figure of the deity.[354-1]
+
+The prefix in this case is the same as that to the symbol above described
+(No. 20), and of course has the same signification. The other portion of
+No. 21 must therefore represent the substance in which the god is
+walking. This appears to be dust, sand, or mud.
+
+[Illustration: No. 22. _a_ _b_ _c_]
+
+  _Cacauak_ or _cacauche_. The wild or cultivated cacao. Found a number
+     of times in the Dresden Codex, sometimes as represented in the
+     marginal figure _a_ and sometimes as in _c_, and always in
+     connection with figures holding in the hand a fruit of some kind. It
+     appears once in the Cortesian Codex (Plate 36), as shown in _b_, in
+     connection with a fruit of precisely the same kind as that figured
+     in the Dresden Codex. It is found also on Plate XVIII* of the
+     Manuscript Troano, but is apparently used here to denote an action.
+
+There can be little, if any, doubt, judging by the figures in connection
+with which it is found, that this symbol is used in the Dresden and the
+Cortesian Codices to denote the cacao. Whether it refers to the tree or
+to the fruit is uncertain; possibly the different forms in which it is
+found are intended to denote these distinctions. In some of the figures
+the capsule appears to be indicated; in others the seed. The prefix to
+figure _c_ apparently indicates the heaping or piling up of the fruit on
+the dish held in the hands of the individuals figured in the same
+connection, as, for example, on Plates 12 and 13 of the Dresden Codex. If
+this supposition be correct it gives us a key to the signification of
+this prefix. Reference to its use in the upper division of Plate XVIII*,
+Manuscript Troano, will be made further on.
+
+In this symbol we find another of Landa's letters, and, if phonetic,
+agreeing precisely with his interpretation.
+
+[Illustration: No. 23. _a_ _b_]
+
+  _Ekbalam_ according to Rosny. The variety marked _a_ is found twice in
+     the Manuscript Troano, Plates XVI and XVII, and that marked _b_ once
+     in the Dresden Codex, Plate 8, each time in connection with a
+     spotted, leopard-like animal.
+
+The black markings on the symbols render it probable that Rosny's
+interpretation is correct. The numeral before the first form may possibly
+be explained by the fact that this symbol is used once (Manuscript
+Troano, Plate XII) to indicate the day Ix.
+
+[Illustration: No. 24.]
+
+  _Moo._ The ara, a large species of parrot. This symbol is found but
+     once, and that in Plate 16_c_, Dresden Codex, in connection with the
+     bird shown in Fig. 379.
+
+[Illustration: FIG. 379. The moo or ara from Plate 16. Dresden Codex.]
+
+The conclusion in this case is based on the following evidence: In this
+series there are six groups of characters, four compound characters in
+each group, arranged as in the annexed diagram:
+
+   __________________________________________________
+  |          |          |          |     |     |     |
+  | _a_  _b_ | _e_  _d_ | _g_  _h_ | _i_ | _m_ | _o_ |
+  |          |          |          |     |     |     |
+  | _c_  _d_ | _c_  _f_ | _c_  _d_ | _c_ | _n_ | _b_ |
+  |__________|__________|__________|     |     |     |
+                                   |     |     |     |
+        1          2          3    | _k_ | _c_ | _c_ |
+                                   |     |     |     |
+                                   | _l_ | _l_ | _p_ |
+                                   |_____|_____|_____|
+
+Similar characters in the different groups are represented by the same
+letter; for example, the symbol for woman, heretofore shown (No. 17), is
+represented by _c_, and an unknown character by _d_. Different letters
+represent different symbols. It is apparent that we have here the
+parallelism heretofore spoken of and are justified in basing conclusions
+on this fact.
+
+At 1, 2, and 3 are female figures with a bird in each case perched on the
+back. At _a_ is the head of a bird, evidently the symbol of the bird on
+the female below; at _i_, in the fourth group, is precisely the same
+symbol as the one found in the same relative position in the middle
+division of Plate 17 over another bird, and at _m_, in the fifth group,
+is another bird's head. From these facts we conclude that the first
+symbol in each of these groups denotes a bird, and, as no two are alike,
+that they refer to different species, the one at _g_ corresponding with
+symbol No. 24, the bird beneath being the great parrot or ara. Other
+facts, derived from a careful study of the various groups of this portion
+of the codex, which would require much space and numerous illustrations
+to explain, lead to the same belief.
+
+According to this conclusion, the following symbols also denote birds,
+probably of the species here indicated.
+
+[Illustration: No. 25.]
+
+  _Icim_? The horned owl. This is represented by _a_ in the first group
+     in the above diagram.
+
+The bird in the figure under the group, although horned, bears but slight
+resemblance to an owl; yet, comparing the marks on the tail with those of
+two of the birds on Plate XVIII* of the Manuscript Troano, I think the
+interpretation is justified.
+
+[Illustration: No. 26.]
+
+  _Kukuitz_? The Quetzal. The symbol is apparently incomplete, but the
+     bird figured under it justifies this conclusion. This symbol is
+     represented by _e_ in the above diagram.
+
+If this interpretation be correct, we find in this symbol another of
+Landa's letters.
+
+[Illustration: No. 27. _a_ _b_]
+
+  _Kuch._ A vulture or bird of prey much like the sopilote. These two
+     symbols (_a_ and _b_) appear to refer to the same bird, evidently a
+     vulture. (See Manuscript Troano, Plates XVII_a_ and XXVI*_a_.) The
+     first form (_a_) is found but once (Manuscript Troano, Plate
+     XVII_a_), the other at several points, both in the Manuscript Troano
+     and the Dresden Codex, and is represented by _m_ in the preceding
+     diagram.
+
+If this determination be correct, the first of these symbols (_a_) is
+probably phonetic and agrees with the interpretation of No. 26.
+
+[Illustration: No. 28.]
+
+  _Cħom_, _Xchom_, or _Hcħom_. The sopilote or vulture. Found only in
+     Plates 16 and 17, Dresden Codex. The bird figure in Plate 17
+     appears to be intended to represent a vulture. The symbol
+     corresponds to _i_ in the preceding diagram.
+
+If phonetic, the word indicated should, according to Landa's alphabet, be
+aspirated, which is found to be true of one of the forms given by Perez.
+
+In certain series of the Dresden Codex, which appear to relate to the
+four year series or to the four seasons, especially those on Plates
+29-31, a certain class of food animals seems to be assigned to each. The
+four following symbols are those used to express this idea:
+
+[Illustration: No. 29.]
+
+  _Ceh_? The symbol for game quadrupeds. The same idea appears to be
+     indicated by the folded and tied quarter of a deer, as shown in No.
+     11. The head shown in the symbol is probably intended for that of
+     the deer, though more like that of the rabbit.
+
+[Illustration: No. 30.]
+
+  _Cutz_ or _Cax_. The symbol for game birds, the head being probably
+     that of the wild turkey (_Cutz_ or _Ahcutz_).
+
+[Illustration: No. 31.]
+
+  _Huh._ The symbol for food reptiles or the iguana.
+
+As the Kan figure is admitted to be a maize or bread symbol, it is
+readily seen that the object in view in connecting it with the animal
+figures is to indicate that they are used for food, and hence are proper
+offerings to the gods, which is equivalent to saying, to the priests.
+
+[Illustration: No. 32.]
+
+  _Cay._ The symbol for food fishes, or fishes in general, though as
+     often on the Kan symbol or without any suffix.
+
+[Illustration: No. 33.]
+
+  _Cutz_ or _Cax_. In one of the two series of these food symbols, in
+     Plates 29-31 of the Dresden Codex, in place of the bird symbol No.
+     30 is that shown in symbol No. 33. It probably has, as Rosny
+     supposes, the same signification, a supposition which is
+     strengthened by the fact that it is found in the bird series on
+     Plates 16_c_ and 17_c_, same codex, and is represented by _o_ in the
+     preceding diagram.
+
+
+SYMBOLS OF DEITIES.
+
+[Illustration: No. 34.]
+
+  _Ekchuah._ The symbol or hieroglyph of the deity named "Ekchuah" by
+     the Mayas and considered the patron and protector of peddlers or
+     traveling merchants (Fig. 380).
+
+[Illustration: FIG. 380. The god Ekchuah, after the Troano and Cortesian
+Codices.]
+
+The signification of the name of this deity is "The Black Calabash." The
+form and the shading of the symbol render it more than probable that it
+is a conventional representation of a divided or halved black calabash or
+gourd, cut for the purpose of forming it into a cup or dipper, which, in
+this form, is considered a symbol of this deity.
+
+The evidence upon which this determination is based is that the symbol
+constantly accompanies the red mouthed, black deity. It is found, with a
+single exception, only in the Manuscript Troano, and chiefly in Plates II
+to V, relating to the traveling merchants. The single exception alluded
+to is on Plate 15 of the Cortesian Codex; here the god bears upon his
+back the traveling pack, indicating the vocation of which he is the
+special guardian.
+
+It occurs unconnected with the figure of the deity only on Plates IX*,
+XIV*, XV*, and XXV* of the Manuscript Troano. In the last the figure of
+the god is in the same division, but in the adjoining compartment. In
+Plate XV* it apparently refers to the idol the priest is carving, which
+is probably a black one intended to represent this god. Landa,[358-1]
+speaking of the artists carving idols from wood, says:
+
+     They took also that which they used for scarifying their ears and
+     drawing blood from them, and also the instruments which they needed
+     for sculpturing their _black divinities_.
+
+Its appearance in Plate XIV* is apparently in connection with the
+ceremonies relating to the manufacture of idols. Neither the symbol nor
+the god it represents is to be fond in the Dresden Codex.
+
+[Illustration: No. 35. _a_ _b_ _c_]
+
+  _Kukulcan._ (?) This is the symbol of the long nosed god, which Dr.
+     Schellhas designates "the god with the snake-like tongue," of which
+     representations appear so frequently in the different codices (see
+     Fig. 381).
+
+The snake-like appendages hanging from the side of the mouth may possibly
+be intended to represent a curved fang rather than part of a divided
+tongue. A remarkable figure on Plate 72 of the Borgian Codex deserves
+special notice here. This is the representation of a deity supposed by
+Kingsborough and others to be Quetzalcoatl, in which the head is as
+represented in Fig. 382. Here we see both tongue and fang, and also an
+eye precisely of the form found in the Maya symbol.
+
+[Illustration: FIG. 381. The long nosed god (Kukulcan) or "god with the
+snake-like tongue."]
+
+Whether Kukulcan is the god indicated is uncertain, unless he is
+identical with the long nosed god, or Maya Tlaloc, so frequently figured
+in the Manuscript Troano and the Cortesian Manuscript. It is only
+necessary to compare the figures on Plates 2 to 5 of the latter codex
+with the long nosed, green figures of Plates XXVI, XXVII, XXIX, XXX, and
+XXXI of the former to be convinced that they represent the same deity,
+and that this is the Maya Tlaloc or rain god, whatever may be the name by
+which he was known.
+
+As the symbol which accompanies these is the same as that found in
+connection with the "snake tongued," long nosed god of the Dresden Codex,
+there is no doubt that the same deity is referred to. It is worthy of
+notice in this connection that Plates 29-41 of the Dresden Codex, which
+are devoted almost exclusively to this deity, refer very largely to
+water, the god being figured in connection with water no less than
+twenty-eight times. He is also twice colored black, probably to symbolize
+the dark rain cloud, and twice blue, denoting water. It is therefore fair
+to conclude that the author of this codex considered him the giver of
+rain.
+
+[Illustration: FIG. 382. Copy of head from the Borgian Codex
+(Quetzalcoatl).]
+
+The following reasons given by Dr. Schellhas for supposing that the deity
+indicated is Kukulcan apparently justify his conclusion, though it is
+possible some other name may have been applied to him:
+
+     He is represented in all the manuscripts, and far more frequently
+     than any other deity. His characteristic marks are always
+     unmistakable. An entire section of the Dresden Codex, pp. 29-43, and
+     pp. 1 and 2, belonging thereto, treat almost exclusively of this
+     god, and wherever he is pictured there we also find his name
+     hieroglyph. He is always characterized by the double, snake-like
+     tongue hanging from his mouth and by the peculiar eye, two marks
+     that are never absent, how numerous and varied soever may be his
+     representations, his symbols, and attributes. We also find him with
+     torches in his hands as symbols of fire; he sits on water; he stands
+     or sits in water or in falling rain; he rides in a boat; he appears
+     in company with a fish as symbol of water or in company of a bird's
+     head as symbol of the atmosphere, upon the day sign _Cab_ as symbol
+     of the earth, sitting, with the ax (machete) in his hand, with
+     arrows or spears, with a scepter, and finally, also, with the body
+     of a snake. Considering the immense variety of this god's
+     representations and the numerous symbols of power in the various
+     elements which the deity rules, we may well be justified in assuming
+     that there are indications here of one of the most important figures
+     in Maya mythology, with one of the principal deities of the people.
+     The most important god of the Mayas was Kukulcan, the creator of the
+     country's civilization, who had come from the far, unknown east, the
+     Mexican Quetzalcohuatl, the Gucumatz of the Kiche, the Kukulcan of
+     the Tzendals. All these names mean "feathered snake," "bird snake."
+     Now, in the above mentioned section of the Dresden manuscript, pp.
+     29-43, there is found on page 36, middle, the representation of a
+     bird and a snake, the two symbols of the god Kukulcan, which, at the
+     same time, denote his name in the manner of a rebus. That this
+     representation is to be referred to the god with the snake's tongue
+     is rendered probable on the one hand by the fact that this whole
+     section treats of him and is proved on the other hand by the
+     circumstance that in the same place the same snake is found
+     represented with the head of the god; thus, page 35, middle, and 36,
+     above. In the same way this snake with the god's head is also found
+     in the Codex Cortesianus, page 10, middle, a passage which is
+     rendered notable also by the fact that in the writing above the
+     picture there is expressly found as a second sign the name
+     hieroglyph of the god.
+
+[Illustration: No. 36. _a_ _b_]
+
+  _Cimi_ (?). Supposed symbols of the god of death. Occurring very
+     frequently in all the codices, but with several variations (see
+     Figs. 383 and 384).
+
+These are given chiefly on the authority of Drs. Förstemann and
+Schellhas, as I have some doubt in reference to this conclusion, for
+reasons which will here be given.
+
+[Illustration: FIG. 383. The supposed god of death, from the Dresden
+Codex.]
+
+[Illustration: FIG. 384. The supposed god of death, from the Troano
+Codex.]
+
+As Dr. Schellhas remarks, this is "the most characteristic and most
+easily recognized deity of the Maya Codices"; but this statement will not
+apply to the symbols, as the variations are such as to render it
+exceedingly doubtful whether precisely the same idea is embodied in each.
+Even the two forms here given, both of which are found in all the codices
+and often together, present variations too marked for us to believe,
+except upon strong evidence, that they represent the same thing. Nor do
+the figures of this deity or supposed deity appear to embody throughout
+the same idea. In fact, they leave us in doubt as to whether any one
+recognized deity is to be understood. Was there in the Maya pantheon such
+a deity as the god of death? I have so far been unable to find any
+satisfactory reason for answering this question in the affirmative.
+
+In the first part of the Dresden Codex, which is devoted, in part at
+least, if not chiefly, to the maladies of the country, the skeleton
+figures undoubtedly have reference to death, much like the skull and
+cross bones in our day. In other places, as Plates XXVII and XXII* of the
+Manuscript Troano and Plate 7 of the Cortesian Codex, the parched earth
+appears to be intended, but it must be conceded that here also the idea
+of death is included. Substantially the same idea, or at least the
+relation of this god to the earth, appears to be indicated in Plate 8 of
+the Cortesian Codex, where he is represented as beneath and holding up
+that upon which another deity, bearing the bread symbol, is seated.
+
+As before stated the two symbols frequently appear in connection,
+sometimes where the god is figured and often where he is not. It is,
+therefore, unsafe to conclude as yet that either variety indicates a
+particular deity known as the god of death.
+
+[Illustration: No. 37.]
+
+  Symbol of the god with the banded face; seen chiefly in the Manuscript
+     Troano; not found in the Dresden Codex (Fig. 385). This is not the
+     deity which Dr. Schellhas designates as "the god with face crossed
+     by lines."
+
+[Illustration: FIG. 385. The god with the banded face, from the Codex
+Troano.]
+
+This deity evidently pertains to the underworld and is closely allied to
+the so-called god of death. The symbol and the figure are found together
+in but few instances, yet the peculiar markings are such as to leave no
+doubt on the mind, that the symbol is intended to denote what is
+represented by the figure, being simply the head of the deity as
+invariably figured. They appear together in Plates III_c_, V_a_, and
+V_b_, XXVIII*_c_, and XXIX_c_ of the Manuscript Troano, in the first two
+as having some relation to the traveling merchants, but in the last two
+in a very different rôle. The dotted lines with which the bodies of these
+figures are marked and the peculiar anklets appear to have been
+introduced to signify relationship to the god of death. Perhaps the most
+direct evidence of this relation is found in Plate 42 of the Cortesian
+Codex, where the two deities are brought together at the sacrifice here
+indicated. The two appear to be united in one in the lower division of
+Plate XXVI* of the Manuscript Troano.
+
+Figures of this god are also found in some of the Mexican codices, as on
+Plate 73 of the Borgian manuscript, where the relation to death and to
+the underworld is too apparent to be mistaken. On Plate 10, same codex,
+the head of death is marked with the distinguishing black band.
+
+Unfortunately for investigations in this line, the early Spanish notices
+of the Maya mythology are so brief and confused that we can derive but
+little aid from them in our efforts to identify the deities figured in
+these manuscripts. Possibly the one with the banded face may represent
+Cumahau or Hunhau, the prince of the lower regions; but the rôle he
+appears to play where figured, with the exception of Plate II, Manuscript
+Troano, and Plate 73 of the Borgian Codex, would scarcely justify the
+name.
+
+[Illustration: No. 38.]
+
+  (?) Symbol of the deity which Dr. Schellhas designates "the god with
+     the old man's face." Found in all the codices and almost invariably
+     in connection with the representation of the deity shown in our Fig.
+     386.
+
+[Illustration: FIG. 386. The god with the old man's face.]
+
+The deity denoted by this symbol and by the figure which it accompanies
+is possibly Zamna or Ytzamna, a deified Maya hero, but the various rôles
+in which he is found make it difficult to decide on this point. He
+appears comparatively few times in the Dresden Codex, and only in the
+first few pages. In none of these is there anything to indicate his
+functions. In Plates 12_c_ and 15_c_ he holds a sun symbol in his hand,
+which might be supposed to refer to his attributes as "Kinich-Kakmo" but
+for the fact that the same thing is true of one or two other deities
+figured in the same codex. In the Manuscript Troano, where he is oftenest
+represented, his figure and his symbol appear most frequently in
+connection with the bee or honey industry; for example, on Plate V_c_,
+the only place in the first part of the manuscript where honey appears to
+be referred to, and twenty-two times in that section of the second part,
+Plates I* to X*, relating to bees. He also appears to take an active part
+in the manufacture of idols, engages in painting, aids in the culture or
+gathering of cacao, engages in predatory excursions, and acts in various
+other relations. In the left compartment of Plate XXIV*_a_ he bears on
+his head the head of a bird. In the remarkable double plate (41-42) of
+the Cortesian Codex he is twice figured, in the central area and at the
+east (top), and in each case is accompanied by a female deity. In the
+latter case both god and goddess are bearing in their hands the Kan or
+corn symbol. In Maya mythology Zamua was given a spouse named Ix
+Kan-Leox, which signifies the yellow frond or silk of maize.
+
+[Illustration: FIG. 39.[TN-11]]
+
+  Symbol, according to Dr. Schellhas, of the deity which he names "the
+     god with face crossed by lines," found in all the codices, but most
+     frequently in the Manuscript Troano and the Cortesian manuscript.
+     The deity is usually represented as in Fig. 387.
+
+[Illustration: FIG. 387. The god with face crossed by lines.]
+
+This is introduced here on the authority of Dr. Schellhas, although I
+have considerable doubt as to the correctness of his conclusion.
+
+He remarks in regard to it as follows:
+
+     Another characteristic and easily recognized deity, which, it is
+     true, is comparatively rare in the Dresden manuscript, but occurs
+     with extraordinary frequency in other codices, and whose sign it is
+     not hard to find, is the god whose face is crossed [surrounded] by
+     peculiar parallel lines, representations of whom are given in the
+     Cortesian Codex (p. 11, below) and Dresden Codex (p. 13, middle).
+     The deity is always male and is found in the Dresden Codex five
+     times, Cortesian Codex eighteen times, Manuscript Troano twenty
+     times, and Codex Peresianus five times.
+
+     The sign of this god, as was the case with the others and as seems
+     to be the general rule, consists merely of a representation of the
+     god's head, combined with a sign which probably represents an affix.
+     The sign is found wherever the deity is represented and is an exact
+     rendering of the god's head, so that there can be no doubt as to its
+     being the name hieroglyph. True variations are not found, the
+     hieroglyph being perfectly alike in all the manuscripts.
+
+     The nature of this deity is not easily determined, though it occurs
+     in the Codices Troano and Cortesianus with extraordinary frequency,
+     so that it would be seen that these two manuscripts, which evidently
+     belong together, treat principally of this deity. No analogous deity
+     is found in Aztec picture writing. * * * To all appearances we have
+     here a momentous figure of Maya mythology, of which, unfortunately,
+     we know nothing.
+
+It is true that this symbol is found in almost every instance where the
+figure of the god appears--in fact, with fewer exceptions than others in
+reference to which there is probably little doubt. It is also true that
+the symbol is an exact copy of the god's head; but on the other hand
+there are strong reasons for doubting the correctness of Dr. Schellhas's
+conclusion.
+
+The first is that the figure of the supposed deity seems to have more
+indications of being the conventional representation of an idol than of a
+deity. The lines of the head are precisely the same as those on the heads
+of the carved idols.[365-1]
+
+We also find it in connection with the wood symbol (marginal No. 6) at
+the only points where the latter is found in the Cortesian Codex, and,
+what is significant, in wholly inappropriate places unless connected with
+an idol figure. These are found in the lower division of Plates 10 and
+11, two on the top of thatched roofs and another on the head of the deity
+called the "god with the old man's face," the head in the latter case
+being apparently carved from a block of wood.
+
+The second is to the same effect, the symbol being found over each of the
+figures of the lower division of Plates 26, 27, and 28 of the Cortesian
+Codex and the middle division of Plates XXXI* and XXXII* of the
+Manuscript Troano, where there appear to be processions of the different
+deities. It is also significant that in the latter case each deity is
+bearing in his hands what seems to be a block of wood from which in all
+probability an idol is to be carved.
+
+Third, we find rows or lines composed entirely of this symbol, as in the
+so-called title page of the Manuscript Troano.
+
+
+DISCUSSION AS TO PHONETIC FEATURES OF THE CHARACTERS.
+
+It must be admitted, as heretofore intimated, that this question has not
+as yet been satisfactorily answered. Whether what is here presented will
+suffice to settle this point in the minds of students of American
+paleography is doubtful; nevertheless, it is believed that it will bring
+us one step nearer the goal for which we are so earnestly striving.
+Something is said on this subject in my former work,[365-2] which need
+not be repeated here.
+
+As it is evident from the preceding list of characters that conventional
+signs and symbols, often nothing more than abbreviated pictographs, were
+used in many cases to designate objects and persons, the inference to be
+drawn, unless other evidence is adduced, is, that this method prevailed
+throughout. Nevertheless there is some evidence that at the date when
+these manuscripts were written Maya culture was in a transition state;
+that is to say, conventional symbols were passing into true
+ideographs[366-1] and possibly into phonetic characters.
+
+The lack of any satisfactory key to assist us in deciphering them makes
+it exceedingly difficult to decide how far this change had progressed. We
+are therefore left wholly to deductions to be drawn from the facts
+obtained by laborious comparisons of the various relations in which the
+characters are found and the uses which appear to be made of them in the
+manuscript.
+
+It will be admitted without question that a large number of these
+characters are ideographs or conventional symbols, as distinguished from
+pictures, as, for example, most of those denoting the days, months, and
+cardinal points. I say most of these, as it is yet possible to learn from
+some of them the objects they were intended to represent, the
+characteristic features not being entirely lost, as the symbol for the
+day Cimi, the "death's head" or skull; that of the day Ymix, "the grain
+of maize;" that of the month Moan, "the head of the moo or ara," a
+species of parrot, &c.
+
+It is also possible to show from the manuscripts themselves evidences of
+the changes from conventional pictographs to true or mnemonic symbols.
+
+Take, for instance, the bird symbols on Plates 16, 17, and 18 of the
+Dresden Codex, presented in the preceding marginal figures numbered 24,
+25, 26, 27, 28, and 33. If the determination be correct as given, it is
+apparent that, while one of the birds is indicated by the head as a
+symbol, the others are denoted by ideographs, or by phonetic characters
+bearing no resemblance to their forms or peculiar features. That numerous
+examples of this kind are to be found in these manuscripts will be
+admitted by all who have carefully studied them.
+
+Another fact bearing upon this point is the difference between the
+Dresden Codex and the Manuscript Troano in regard to marking with symbols
+the things represented in the pictures. We fail to find in the former
+(unless that on Plate 30 be a possible exception) the earth or soil
+represented by any symbol, though frequently occurring in the latter and
+also occasionally in the Cortesian Codex. The symbol for wood or that
+appearing so often on wooden articles in the latter, and occasionally in
+the Cortesian Codex, is wanting in the Dresden Codex, though wooden
+articles are several times represented. From this we infer that the
+Manuscript Troano is a more recent production than the Dresden Codex,
+notwithstanding the evidences of greater skill in drawing and higher
+mathematical attainments shown in the latter.
+
+Before discussing the question of phonography we ask attention to one or
+two facts regarding Landa's alphabet which do not appear to have been
+previously noticed, yet have an important hearing on the subject.
+
+The failure to reach any satisfactory results with this alphabet proves,
+beyond a reasonable doubt, that this author was mistaken as to the
+character of the Maya writing; yet the frequent occurrence in the
+manuscripts of most, if not all, of the elements he presents renders it
+certain that there is a basis of truth on which it rests. It is probable,
+therefore, if we can find the key to his method, we may, after all,
+obtain some satisfactory results by means of his alphabet.
+
+I have already stated as my belief that--
+
+     He has undertaken to pick out of their compound or syllabic
+     characters the letter elements; hence it is that, while we find it
+     impossible to decipher the manuscripts by using them, yet we find
+     such frequent resemblances as to compel us to admit a fundamental
+     relationship.[367-1]
+
+This opinion I still believe to be correct, but was, until very recently,
+unable to get any positive evidence as to his method of obtaining these
+elements.
+
+While examining the Cortesian Codes I came across (on Plate 17) the
+symbol for a turtle (the different varieties of which are shown in
+marginal figure No. 4), which is nothing more or less than an attempt to
+represent the head of the animal. In the more abbreviated form (_b_) I at
+once recognized Landa's A (compare with _c_ and _d_, No. 4). As the Maya
+name of the turtle is _Ac_ or _Aac_ it is apparent that in this instance
+the old Spanish priest selected a symbol representing an object the name
+of which contains a single syllable having, as its chief letter element,
+A. As this symbol is simply a representation of the animal's head there
+is no reason to infer that it is phonetic; on the contrary, it is more
+reasonable to assume that it was used only as a conventional sign. It is
+possible that after long usage it may have been adopted as a phonetic
+character, though its exceedingly rare occurrence in the manuscripts
+(being found only in the Cortesian Codex and with the turtle figure) and
+the fact that it is seldom, if ever, used as part of a compound character
+would seem to forbid this idea.
+
+Precisely the same method was adopted in obtaining his B, which is given
+in two forms, first as a foot print and second as a circle inclosing four
+circular dots. The first, as all are aware, is only a conventional sign
+and presumably not phonetic. The second may be phonetic, though
+apparently but an abbreviation of the first. In Plate 65_c_ (see marginal
+No. 20) and Plate 41_c_ the two forms are brought into such relation to
+each other as to show that the latter is used as a symbol to represent
+the idea conveyed by the first. The proof in these cases is too strong
+to admit of doubt and explains Landa's method of obtaining his B, which,
+as before stated, was by selecting the symbol of that which is denoted by
+a Maya word of one syllable having B as its chief letter element, _Be_
+being the Maya word for "way," "journey," "walking," &c.
+
+The symbol for the cacao given above in marginal No. 22 contains his
+eleventh letter _Ca_ twice and is probably that from which it was taken;
+likewise that of the _Kukuitz_ or Quetzal (marginal No. 26) and of the
+_Kuch_ or vulture (marginal No. 27_a_), each of which contains his _Ku_,
+being double in the former and single in the latter. I am as yet unable
+to trace these two symbols to their origin; we might suppose, from
+Landa's figure of the latter, that it was intended to represent a bird's
+nest containing eggs, but an examination of the symbol as found in the
+manuscript renders this conclusion doubtful.
+
+The evidences of phonography are few and, as must be admitted, not
+entirely satisfactory; yet they are apparently sufficient to justify the
+somewhat general belief that the writing of the Mayas had reached that
+stage where characters are sometimes used to indicate sounds. That
+comparatively little advance had been made in this direction at the time
+of the conquest is possible; moreover there is nothing to justify the
+belief that they made use of true letters as Landa supposed. If they had
+a phonographic system of any kind it was very imperfect and was only in
+that primary stage in which syllables are represented by single
+characters and words of more than one syllable by compound characters.
+Judging by the changes observed in the relation of the parts of compound
+characters to one another, we conclude that the order of arranging these
+parts was not uniform or essential. It is also doubtful, if any of these
+characters are phonetic, whether the parts of the longer words were
+always written out in full. I am led to believe, from a few slight
+indications, that, in forming words of more than one syllable, they often
+used only the leading phonetic elements of the single words of which they
+are composed; in other words, that they followed the rebus method of the
+Mexicans.
+
+Descending to particulars and examples, the following are, perhaps, the
+strongest proofs which can be presented on this point:
+
+As there can no longer be any doubt that the symbols for the cardinal
+points have been ascertained and that those relating to the polar points
+are distinguishable from those relating to the equatorial points, we are
+justified in referring to them in this discussion. As each of the two
+assigned to the equatorial points contains the symbol for "sun" or "day"
+and as the two Maya words for these points--_Likin_ or _Lakin_ and
+_Chikin_--contain the Maya term for sun or day ("kin"), there is some
+reason for believing that the characters are phonetic. There is to be
+added to this evidence the fact that the symbol of the month _Yaxkin_
+contains the same sun symbol. It would be somewhat remarkable to find the
+same single character in three different combinations, representing three
+different ideas expressed by words containing the same sound, yet having
+no reference to the sound.
+
+It is now generally admitted by students of American paleography, on what
+appears to be satisfactory evidence, that symbol No. 7 of the preceding
+list, _Cab_, is used to signify "earth" or "land" and "honey," both of
+which are designated by the same Maya term, _Cab_. As there is no
+similarity in the things denoted the character is probably phonetic. The
+"bee" appears also to be frequently indicated by the same character with
+an affix, as may be seen by reference to the lower divisions of Plates
+III*--X* of the Manuscript Troano.
+
+The symbol No. 9 (U) of the preceding list is found repeatedly on vases
+and also as a prefix to both simple and compound characters. As _U_ in
+Maya signifies "moon," "vase," and certain pronouns and is also used as a
+euphonic particle before vowels, we are perhaps justified in concluding
+that the symbol is phonetic and denotes the word _U_. I am aware that
+neither Perez nor Dr. Brinton gives "vase" as one of the meanings of this
+word, yet its constant appearance on vessels seems to leave no doubt that
+Brasseur is correct. Even admitting that he is mistaken and that we are
+in error as to the signification of the symbol, its various uses justify
+the belief that it is phonetic.
+
+The symbol No. 34 of the preceding list, which is supposed to be that of
+the god Ekchuah, is probably phonetic. The name of this deity is composed
+of two Maya words, _ek_, "black," and _chu_, "calabash," and hence
+signifies "the black calabash," and the form and coloring of the symbol
+are apparently intended to denote this signification. If this
+interpretation be correct it is phonetic, as there is nothing in or
+pertaining to the figure of the deity which corresponds with it, except
+the color.
+
+If the interpretation given of the preceding symbols Nos. 22, 24, 26,
+27_a_, and 33 be correct, there can be scarcely a doubt that they are
+phonetic. In the first--_cacau_, _cacauak_, or _cacauche_, the "cacao"--we
+see Landa's letter _Ca_, which is doubled in each of the three forms taken
+from the different codices. In the twenty-sixth--_Kukuitz_, the
+Quetzal--Landa's _Ku_ is duplicated, as it should be if phonetic, while in
+27_a_, _Kuch_, it appears but once. There is here also an additional
+evidence of phoneticism in the fact that, while one of the symbols used to
+denote this bird shows simply its head, and is surely not phonetic, the
+other is entirely different and bears no resemblance whatever to any
+feature or characteristic of the bird. Moreover, both parts of it are used
+in other combinations referring to entirely different things.
+
+If my interpretation of No. 14 (_Xamach_ or _Chimix_) be right, it is
+probably phonetic also. It is composed, as will be seen by reference to
+the figure, of two symbols closely resembling that for the day Ymix,
+except that the top portion of one is omitted. The resemblance in sound
+to a duplication of Ymix is apparent. The slight but permanent variation
+of the right hand portion from the usual Ymix symbol and the omission of
+the top portion of the left hand one are scarcely explainable on the
+supposition that they form simply a conventional sign; but if phonetic
+the reason is apparent, as the _m_ sound is not repeated in the Maya
+name. This conclusion is strengthened by the fact that the month _Mac_,
+found in the last or bottom line of Plate 49, is precisely the same as
+the right portion of No. 14, with Landa's symbol for _Ca_ added. This
+probably justifies us in concluding that the true name of this month is
+_Camach_, "the jaw" or "jaws," and that Landa's figure is simply a rude
+representation of the lips or mouth.
+
+I have expressed the opinion[370-1] that the chief phonetic element of
+No. 8 (the stone symbol), if used to represent sound, is _p_ or _pp_.
+This opinion seems to be confirmed by the fact that this character is
+found as a part of the symbol for the month _Pop_ on Plate 50 of the
+Dresden Codex. (See the second character in the first transverse line
+below the day columns in the preceding Fig. 362.) The method of
+determining the months referred to in these plates of the codex has been
+given in the preceding part of this paper.
+
+The interpretation given above of symbol No. 24 (the moo or ara) will
+probably be accepted by all students of these manuscripts, and if so its
+phonetic character must be conceded. That it is used in the place above
+alluded to (Dresden Codex, Plate 16_c_) to denote this bird is proved by
+the parallelism of the groups and the figure of the parrot under it. If
+we turn now to Plate 48 of this codex we observe that the second
+character of the first line below the day columns and the first character
+in the upper line of the lower group or square is, in each case, a bird's
+head. It is easily proved by means of the numeral series with which these
+are connected that they denote, in both cases, the month Moan (from the
+moo), proving that Brasseur's surmise was correct.[370-2] If the same
+bird is represented by two symbols, one pictorial and the other having no
+resemblance to any feature or character of the thing denoted, it is
+probable the latter is phonetic. This conclusion is strengthened in this
+case by the strong resemblance of the first part of No. 24 to the symbol
+for the month Mol.
+
+I have shown above that the right portion of No. 20 of the list is
+Landa's letter B, and also that in the lower division of Plate 65,
+Dresden Codex (see Fig. 378), it signifies "footsteps" or the act of
+walking. As the Maya word _Be_ signifies "journey," "wood," "march," and
+also "journeying" and "marching," it is possible that this symbol is also
+phonetic, although apparently only a modified form of the footprint. This
+supposition is strongly supported by the fact that it is found in
+numerous and varied relations, single and in combination.
+
+The symbol for 20 (_Kal_), No. 1 of the preceding list, is apparently
+phonetic. This view appears to be confirmed by its use otherwise than as
+a numeral symbol at several points in the text of the Manuscript Troano.
+For example, in the third division of Plate XVII* it appears in this
+form, [Illustration: Hieroglyph] while immediately below is the
+representation of an idol head in a vessel covered with a screen or
+basket, as shown in Fig. 388. The Maya verb _Kal_ signifies to "imprison"
+or "inclose," which is certainly appropriate to what we see in the
+figure. As the symbol is over each of the three similar figures in the
+division, it is probable that it is intended to denote something relating
+to or observable in them. In the second division of Plates XV* and XVI*,
+same codex, is this symbol, [Illustration: Hieroglyph] several times
+repeated, and below each the figure of a priest or deity at work, each
+carving, with a machete or hatchet, the head of an idol. The probable
+signification is "Give twice twenty strokes with a machete," and hence is
+but partially phonetic.
+
+[Illustration: FIG. 388. Wooden idol in vessel with basket cover.]
+
+Other examples bearing on this question may be found, but these are
+believed to be sufficient to warrant the belief that at the time these
+codices were written Maya culture had reached that stage where the idea
+of phoneticism was being introduced into the writing. Yet it is certain,
+and even susceptible of demonstration, that a large portion, perhaps the
+majority, of the characters are symbols. The more I study these
+characters the stronger becomes the conviction that they have grown out
+of a pictographic system similar to that common among the Indians of
+North America. The first step in advance appears to have been to
+indicate, by characters, the gesture signs.
+
+
+FOOTNOTES:
+
+[345-1] See Chapter VI, Study of the Manuscript Troano, by Cyrus Thomas.
+
+[354-1] Unfortunately the scrolls were overlooked in preparing the cut.
+
+[358-1] Relacion de las cosas de Yucatan, p. 308.
+
+[365-1] See Plates XVI*_b_ and XVII*_c_, Manuscript Troano.
+
+[365-2] Study of the Manuscript Troano, pp. 141-161.
+
+[366-1] As the term "ideograph" is somewhat broad and comprehensive, it
+may be well enough to state that I use it as expressing that stage of
+symbolic writing where the picture characters have so changed that all
+resemblance to the objects they were originally intended to represent is
+lost, and therefore they can only be considered as mnemonic signs.
+
+[367-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 142, 143.
+
+[370-1] Study of the Manuscript Troano, p. 147.
+
+[370-2] Landa's Relacion, pp. 382, 383, Note 1.
+
+
+
+
+INDEX
+
+
+Adelung, J. C. cited 262
+
+Aglio, Augustina, fac simile of Dresden Codex by 263-266
+
+
+Böttiger, C. A., mention of Dresden Codex by 262
+  controversy with Abert concerning Dresden Codex 267
+
+Brasseur, copy of the Manuscript Troano by 284, 286, 343
+  cited 350
+
+
+Calendar system, tabular view of 270-374
+
+Charency, H. de, cited 282
+
+Codex Cortesianus, similarity of, to Manuscript Troano and Dresden
+Codex 286
+
+
+Dresden Codex, numerals in 261-338
+
+
+Ebert, F. A., description of Dresden Codex by 263
+  controversy with Böttiger concerning Dresden Codex 267
+
+
+Falkenstein, K. C., preservation of Dresden Codex by 268
+
+Fleischer, H. L., mention of Dresden Codex by 263
+
+Förstemann, E., citation from Die Mayahandschrift of 261-269
+  cited 272, 278, 280, 281, 283, 290, 292, 293, 300, 301, 302, 303, 304,
+  305, 320, 322, 329, 330, 339, 340
+
+
+Götze, J. C., preservation of Dresden Codex by 261
+  biographical sketch of 261, 262
+
+
+Humboldt, A. von, notice of Dresden Codex by 262, 263
+
+
+Kingsborough, Lord, Dresden Codex copied by order of 262
+  Mexican Antiquities of, cited 266
+
+
+Landa, cited 348
+
+Landa's alphabet, insufficiency of 259, 347
+
+
+Manuscript Troano, copy of, by Brasseur 285, 286, 343
+  study of, by C. Thomas, cited 339, 343, 344, 345, 350, 365, 366, 367, 370
+
+Maya and Mexican manuscripts, C. Thomas on, cited 280
+
+Maya Codices, aids to the study of, by C. Thomas 253-371
+
+Mexican Antiquities, by Lord Kingsborough, cited 266, 267
+
+
+Rosny, L. de, cited 267, 347, 355, 357
+
+
+Schellhas, P., cited 345, 359, 360, 361, 362, 364
+
+Schultz-Sellack, K., cited 278
+
+Silvestre, É., Paléographie universelle of, cited 267
+
+
+Thomas, C., paper on aids to the study of the Maya codices by 253-371
+
+Troano Manuscript, copy of, by Brasseur 285, 286, 343
+
+
+Vater, J. S., cited 262
+
+
+
+
+Transcriber's Note:
+
+  TN-1   267  "hasty and obtrusive notice." should read 'hasty and
+              obtrusive notice.'
+  TN-2   272  indi cated should read indicated
+  TN-3   291  "and" repeated.
+  TN-4   295  Plate 48, 2nd line first asterisk is missing.
+  TN-5   296  Period missing after FIG
+  TN-6   322  In the original text, the 7 is printed above the 17, with
+              no horizontal line separating the two numbers.
+  TN-7   327  Tables XXI and XXII are not labeled in the original
+              publication but, by context, appear to be the two sections
+              of table following Table XX.
+  TN-8   338  Sixth column should read Sixth column.
+  TN-9   338  Footnote number for 338-1 was missing. It was inserted
+              based on the context of the note.
+  TN-10  348  Illustration No. 6 was missing the caption.
+  TN-11  364  Fig. 39 should read No. 39
+
+
+
+
+
+End of the Project Gutenberg EBook of Aids to the Study of the Maya Codices, by 
+Cyrus Thomas
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diff --git a/19777-0.zip b/19777-0.zip
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+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: ISO-8859-1
+
+*** 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 Biblioth�que 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. F�rstemann'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 G�tze, 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 G�tze'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.
+
+"G�tze 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 G�tze
+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.'
+
+"G�tze 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 G�tze 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.'
+
+"G�tze 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, G�tze did not know
+that the Vatican Codex was of an entirely different nature from the
+Dresden Codex.
+
+"In spite of the high value which G�tze 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 G�tze, the first to mention our codex is C. A. B�ttiger, in his
+Ideas on Arch�ology (Dresden, 1811, pp. 20, 21), without, however, saying
+anything that we did not already know from G�tze. Still B�ttiger 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 B�ttiger'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 B�ttiger, 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 B�ttiger. 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 G�tze
+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] B�ttiger, 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 B�ttiger, 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 arch�ologist 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, Pal�ographie universelle,
+Paris, 1839-'41, fol.; in Rosny, Les �critures figuratives et
+hi�roglyphiques des peuples anciens et modernes, Paris, 1860, 4to; and
+also in Madier de Montjou, Archives de la soci�t� am�ricaine de France,
+2^de s�rie, 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. F�rstemann,
+in his late work on the Dresden Codex (Erl�uterungen zur Mayahandschrift
+der K�niglichen �ffentlichen 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. F�rstemann before alluded to the discovery
+of the symbol for 20 is announced. Although I was not aware of the
+signification of this symbol until after my second paper, "Notes on
+certain Maya and Mexican manuscripts," was written, I had made this
+discovery as early as 1884.[273-3]
+
+As there will be occasion to refer to the days of the four different
+series of years (the Cauac, Kan, Muluc, and Ix years), a combined
+calendar, similar to an ordinary counting house calendar, is introduced
+here. For the Cauac years the left or Cauac column is to be used; for the
+Kan years, the Kan column, and so on.
+
+TABLE II.--_Names and numbers of the four series of years of the Maya
+system._
+
+  __________________________________________________________________________________
+          |        |        |        |                                      {Numbers
+   Cauac  | Kan    | Muluc  |  Ix    | 1  2  3  4  5  6  7  8  9 10 11 12 13{of the
+  column. |column. |column. |column. |14 15 16 17 18                        {months.
+  --------+--------+--------+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+-------
+          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |Days of
+          |        |        |        |  |  |  |  |  |  |  |  |  |  |  |  |  |month.
+  Cauac   |Kan     |Muluc   |Ix      | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|   1
+  Ahau    |Chicchan|Oc      |Men     | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|   2
+  Ymix    |Cimi    |Chuen   |Cib     | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|   3
+  Ik      |Manik   |Eb      |Caban   | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|   4
+  Akbal   |Lamat   |Been    |Ezanab  | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|   5
+  Kan     |Muluc   |Ix      |Cauac   | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|   6
+  Chicchan|Oc      |Men     |Ahau    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|   7
+  Cimi    |Chuen   |Cib     |Ymix    | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1|   8
+  Manik   |Eb      |Caban   |Ik      | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2|   9
+  Lamat   |Been    |Ezanab  |Akbal   |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|  10
+  Muluc   |Ix      |Cauac   |Kan     |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|  11
+  Oc      |Men     |Ahau    |Chicchan|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|  12
+  Chuen   |Cib     |Ymix    |Cimi    |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|  13
+  Eb      |Caban   |Ik      |Manik   | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7|  14
+  Been    |Ezanab  |Akbal   |Lamat   | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8|  15
+  Ix      |Cauac   |Kan     |Muluc   | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9|  16
+  Men     |Ahau    |Chicchan|Oc      | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10|  17
+  Cib     |Ymix    |Cimi    |Chuen   | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11|  18
+  Caban   |Ik      |Manik   |Eb      | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12|  19
+  Ezanab  |Akbal   |Lamat   |Been    | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13|  20
+  ----------------------------------------------------------------------------------
+
+As this table has been explained in my previous papers it is only
+necessary to add here that the thirteen figure columns form a single
+series; therefore, when we reach the bottom of the thirteenth column we
+go back to the top of the first. The day reached will be the one directly
+opposite (that is, in the same horizontal line) in the day column for the
+given year.
+
+For example, taking the fifth column of numbers (the one having 3 for the
+top figure) and counting down nine days from the top number we reach the
+number 12. This will be 12 Lamat if a Cauac year, 12 Been if a Kan year,
+12 Ezanab if a Muluc year, and 12 Akbal if an Ix year. Therefore it is
+necessary in counting to refer always to the year (year column) with
+which the count begins. So long as the particular year referred to is
+unknown (as is Usually the case, the day series being apparently of
+general rather than of special application) it is immaterial which day
+column is selected, as the result will be the same with any. This will be
+apparent if we bear in mind that, when 260 days with their numbers
+attached have been written down in proper order as a series, we have
+therein all the possible combinations of days and numbers. This, it is
+true, does not give us all the months and years (to include these it is
+necessary to write out fifty-two entire years), but the same series of
+numerals will be applicable to each of the four year series (Kan, Muluc,
+Ix, and Cauac years). As any one of the thirteen figure columns of the
+table may be taken as the commencement of a year and any of the four day
+columns may be used, it is apparent that we have all the possible
+combinations (4 � 13 = 52).
+
+I say above that "it is necessary in counting to refer always to the year
+(year column) which the count begins." This I admit does not agree with
+the generally received idea of the Maya calendar, upon which Table II is
+constructed, as, according to this theory (which I have accepted in my
+previous papers), after passing through a year of one series
+(corresponding with one of the day columns of the table), we should enter
+upon a year of the next series; for example, when the year 1 Kan is
+completed we should enter upon the year 2 Muluc.
+
+Although this calendar system seems to have been in vogue at the time of
+the conquest and is indicated in one or two of the codices, and possibly
+in the one now under consideration, the chronological series of the
+latter, as will hereafter appear, do not seem to be based upon it or to
+agree with it.
+
+These explanations, with the further statement that the lines in the
+codex are to be read from left to right and the columns from the top
+downward, except where variations from this rule are noted, will enable
+the reader to follow the discussion. Another reason for using a table
+with only thirteen columns (though it would be difficult to devise a
+combined calendar of any other form) is that the 260 days they contain
+form one complete cycle, which, as will appear in the course of this
+discussion, was one of the chief periods in Maya time computations.
+
+Examining Plates 33 to 39 of the codex the reader will observe that the
+line already alluded to extends continuously through division _c_,
+commencing with the two characters over the figure (picture) in the lower
+right hand corner of Plate 33.
+
+The first of these characters as given in Kingsborough's work is the
+symbol of the day Ezanab, with the red numeral 13 to the left of it and
+the black numeral 9 over it; but referring to F�rstemann'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
+F�rstemann), 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 F�rstemann'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 F�rstemann'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 F�rstemann'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. F�rstemann,[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. F�rstemann 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
+F�rstemann'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. F�rstemann, 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.
+F�rstemann 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. F�rstemann 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 F�rstemann'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
+F�rstemann'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
+F�rstemann.[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 F�rstemann'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. F�rstemann[292-1] remarks:
+
+     The column of the days has the difference 5; the fifth sign (in this
+     case really superfluous), that of the thirteenth day, appears in a
+     remarkable form, apparently as an inscription on a vessel. The black
+     figures ought to give the sum 65, but we get only 4 � 16, or 64. But
+     this appears to be merely an oversight by the copyist, for although
+     in the Codex Troano, also, we find 64 several times instead of 65,
+     still this has always appeared to me merely as a sign of the great
+     negligence of the copyist of that manuscript.
+
+Turning to the Manuscript Troano, Plate XXVIII*_b_, we find a column
+consisting of the four terminal days of the year, Been, Ezanab, Akbal,
+and Lamat, which of course have the same relation to one another as the
+first days. It is evident from the space that only four were intended to
+be given. The numerals in Brasseur's fac simile are XI; 20, 12, IV; 9,
+XIII; 10, X; 13, XI.
+
+The red numeral over the column is XI, as is also the last of the series,
+but the sum of the black numbers is only 64, which would give X as the
+final number, as is evident from the following operation: XI + 32 - 13 -
+13 - 13 = IV; IV + 9 = XIII; XIII + 10 - 13 = X; X + 13 - 13 = X. The
+interval between the days is 65. We have, therefore, precisely the same
+difficulty in this instance as in the case from the Dresden Codex under
+consideration. Moreover, the only method of correcting the mistake, if
+there is one, is by adding _one_ to the last black number. It would be
+hazardous to assume that two mistakes, precisely the same in every
+respect, should have been made in regard to these exactly similar series.
+The probability that a mistake has been made is lessened by the fact that
+on Plate XXIX*_b_ of the manuscript is another four day column, the last
+days of the years, as the preceding. The numeral over the column is XIII
+and the series is as follows: 13, XIII; 20, 18, XII; 13, XIII. Adding
+these and casting out the thirteens, we have this result: XIII + 13 - 13
+= XIII; XIII + 20 + 18 - 13 - 13 - 13 = XII; XII + 13 - 13 = XII. This
+gives XII as the last number when it should be XIII. If a mistake has
+been made the only method of correcting it is by increasing the last
+black number by one, as in the other two cases alluded to.
+
+It is proper to state that on the other hand there is another four day
+column on Plate XXXII*_a_ of the last mentioned codex, the days of which
+are precisely the same as those on Plate 29_c_ of the Dresden Codex, to
+wit, Ix, Cauac, Kan, Muluc. The numeral over it is XII and the series is
+as follows: 13, XII; 13, XII; 13, XII; 13, XII; 13, XII. This presents no
+difficulty, as it conforms in every respect to the rules given, but only
+serves to deepen the mystery in the other cases.
+
+Going back to the series on Plate 29_c_ of the Dresden Codex, we observe
+not only that the days of the column are the four year bearers, but also
+that one of the four cardinal symbols is found--in the superscription--in
+each of the four compartments through which the series extends. It is
+possible, therefore, that the series is intended to be applied separately
+to each of the four years. Supposing this to be the case, counting 64
+days from 3 Ix would bring us to 2 Ezanab; 64 days from 3 Cauac to 2
+Akbal; 64 days from 3 Kan to 2 Lamat; and 64 days from 3 Muluc to 2 Been.
+It is significant that in each case the day reached is that on which the
+given year terminates; for example, the Ix years (counting the five added
+days) terminate on Ezanab; the Cauac years on Akbal &c. If the intention
+was to have the series terminate with the end of the respective years,
+then these years must necessarily have been 2 Ix, 2 Cauac, 2 Kan, and 2
+Muluc. I must confess that this explanation is not satisfactory; it is
+thrown out simply as a suggestion.
+
+Running through the middle division of Plates 30 and 31 is this series:
+
+  3,    VIII;    3, VIII;    3, VIII;    3, VIII
+  5,    Oc       5, Men      5, Ahau     5, Chicchan.
+
+Commencing with 8 Oc (omitting for the present the 3 and 5 to the left)
+and counting thence 3 months and 5 days we reach 8 Men; 3 months and 5
+days more and we reach 8 Ahau; 3 months and 5 days more bring us to 8
+Chicchan, and 3 months and 5 days more bring us again to 8 Oc, thus
+completing a cycle of 260 days (13 months) and also accounting for the
+first pair of numerals--3 and 5 in the series. It appears to be a pretty
+general rule to commence a series of this type with the difference
+between the numbers of the series. One reason for this is apparent: that
+is, to complete the cycle of 260 days, to which most, if not all, of
+these groups appear to refer.
+
+Dr. F�rstemann says in regard to this line:[293-1]
+
+     This is the place where I first discovered how numbers of several
+     figures are to be read; here for the first time I understood that
+     the figure 3 with 5 below it is nothing but 3 � 20 + 5, or 65, and
+     that they mean nothing else than the interval between the days, such
+     as we have frequently met with so far; 4 � 65 is again the well
+     known period of 260 days.
+
+Plate 3 appears to be isolated and unfinished; at least it presents
+nothing on its face by which it can be directly connected with any other
+plate of the codex, notwithstanding the change made by Dr. F�rstemann, 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. F�rstemann'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 F�rstemann.
+
+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. F�rstemann, 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. F�rstemann'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. F�rstemann'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. F�rstemann 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. F�rstemann 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. F�rstemann 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 F�rstemann'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. F�rstemann 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. F�rstemann 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. F�rstemann,
+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. F�rstemann 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. F�rstemann 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.
+F�rstemann, 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. F�rstemann, 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. F�rstemann 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. F�rstemann 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. F�rstemann 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
+K�niglichen �ffentlichen Bibliothek zu Dresden, herausgegeben von Prof.
+Dr. E. F�rstemann, 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] Erl�uterungen zur Mayahandschrift, p. 2.
+
+[280-1] Erl�uterungen 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] D�chiffrement des �critures calculiformes ou Mayas, par M. le
+C^te H. de Charency, Alen�on, 1849; also, M�langes, 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] F�rstemann, Erl�uterungen zur Mayahandschrift, p. 42.
+
+[291-1] Erl�uterungen zur Mayahandschrift, p. 36.
+
+[292-1] Erl�uterungen zur Mayahandschrift, p. 60.
+
+[293-1] Erl�uterungen 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. F�rstemann 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 F�rstemann 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 F�rstemann 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 F�rstemann 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 k�niglichen 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. F�rstemann 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. L�on 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 hi�ratique, 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 amphor� 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. F�rstemann 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 r�le. 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 r�le 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 r�les
+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
+
+
+B�ttiger, 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 B�ttiger concerning Dresden Codex 267
+
+
+Falkenstein, K. C., preservation of Dresden Codex by 268
+
+Fleischer, H. L., mention of Dresden Codex by 263
+
+F�rstemann, 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
+
+
+G�tze, 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, �., Pal�ographie 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 
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+<pre>
+
+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: ISO-8859-1
+
+*** 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 Biblioth�que nationale
+de France (BnF/Gallica) at http://gallica.bnf.fr)
+
+
+
+
+
+
+</pre>
+
+
+<div style="background-color: #EEE; color: inherit; padding: 0.5em 1em 0.5em 1em;">
+<p class="center"><b>Transcriber&#8217;s&nbsp;Note</b></p>
+
+<p class="noindent">This book was originally published as a part of:</p>
+
+<p class="noindent">Powell, J.&nbsp;W.<br />
+1888  <i>Sixth Annual Report of the Bureau of Ethnology to the
+Secretary of the Smithsonian Institution 1884-&#8217;85.</i> pp. 253-372.
+Government Printing Office, Washington, D.C.</p>
+
+<p class="noindent">The index included in this version of the book was extracted from the
+overall volume index.</p>
+
+<p class="noindent">A number of typographical errors have been maintained
+in the current version of this book. They are <ins class="correction" title="correction">marked</ins>
+and the corrected text is shown in the popup. A <a href="#trans_note">list</a> of these
+errors is found at the end of this book.</p>
+
+<p class="noindent">Tables XX, XXI, and XXII were too wide to fit within a single screen width.
+They have been broken into two parts with a link to an image showing the complete
+tables.</p>
+
+
+<p class="noindent">Special characters:</p>
+
+<p class="noindent">The original publication used several characters that may not be
+available in all fonts. If the following characters do not display
+correctly, please try changing the font: &#295; (h with stroke) &#9312; &#9313;
+&#9314; &#9315; &#9316; &#9317; &#9318; &#9319; &#9320; &#9321;
+&#9322; &#9323; &#9324; (numbers 1 to 13 in circles) &#9406; (I in circle)</p>
+</div>
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_253" id="Page_253">[253]</a></span></p>
+
+
+<div class="tpborder">
+<div class="tpborder2">
+<h3 style="font-weight: normal;">SMITHSONIAN INSTITUTION&mdash;BUREAU OF ETHNOLOGY.</h3>
+
+<hr style='width: 45%; border: solid 1px;' />
+
+<h2 style="font-weight: normal;">AIDS TO THE STUDY</h2>
+
+<p class="titlepage">OF</p>
+
+<h1 style="font-weight: normal; letter-spacing: 0.2em;">THE MAYA CODICES.</h1>
+
+<p class="titlepage">BY</p>
+
+<h2 style="font-weight: normal;">PROF. CYRUS THOMAS.</h2>
+
+</div>
+</div>
+
+<p><span class='pagenum'><a name="Page_254" id="Page_254">[254]</a></span></p>
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_255" id="Page_255">[255]</a></span></p>
+
+
+
+<h2 class="chapterhead">CONTENTS.</h2>
+
+<table width="80%" border="0" cellpadding="0" cellspacing="0" summary="Table of Contents">
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#INTRODUCTION">Introduction</a></td>
+  <td><a href="#INTRODUCTION">259</a></td>
+</tr>
+<tr>
+  <td class="tdr padr1"><span class="smcap">Chap.</span> I.</td>
+  <td><a href="#CHAPTER_I">The numerals in the Dresden Codex</a></td>
+  <td><a href="#CHAPTER_I">261</a></td>
+</tr>
+<tr>
+  <td class="tdr padr1">II.</td>
+  <td><a href="#CHAPTER_II">Conclusions</a></td>
+  <td><a href="#CHAPTER_II">339</a></td>
+</tr>
+<tr>
+  <td class="tdr padr1">III.</td>
+  <td><a href="#CHAPTER_III">The writing</a></td>
+  <td><a href="#CHAPTER_III">345</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td style="padding-left: 1.5em;"><a href="#characters">Signification of the characters</a></td>
+  <td><a href="#characters">347</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td style="padding-left: 1.5em;"><a href="#animals">Symbols of animals &amp;c.</a></td>
+  <td><a href="#animals">348</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td style="padding-left: 1.5em;"><a href="#deities">Symbols of deities</a></td>
+  <td><a href="#deities">358</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td style="padding-left: 1.5em;"><a href="#phonetics">Discussion as to phonetic features of the characters</a></td>
+  <td><a href="#phonetics">365</a></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_256" id="Page_256">[256]</a></span></p>
+
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_257" id="Page_257">[257]</a></span></p>
+
+<h2 class="chapterhead"><a name="ILLUSTRATIONS" id="ILLUSTRATIONS"></a>ILLUSTRATIONS.</h2>
+
+<table width="80%" border="0" cellpadding="0" cellspacing="0" summary="Illustrations">
+<tr>
+  <td><span class="smcap">Fig.</span></td>
+  <td><a href="#Fig_359">359.</a> Line of day and numeral symbols from Plates 36<i>c</i> and 37<i>c</i>,
+      Dresden Codex</td>
+  <td><a href="#Fig_359">272</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_360">360.</a> Line of day and numeral characters from Plates 33-39, Dresden Codex</td>
+  <td><a href="#Fig_360">276</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_361">361.</a> Unusual symbol for Akbal from Plate 8 of the Dresden Codex</td>
+  <td><a href="#Fig_361">284</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_362">362.</a> Copy of Plate 50, Dresden Codex</td>
+  <td><a href="#Fig_362">297</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_363">363.</a> Copy of Plate 51, Dresden Codex</td>
+  <td><a href="#Fig_363">306</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_364">364.</a> Copy of Plate 52, Dresden Codex</td>
+  <td><a href="#Fig_364">307</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_365">365.</a> Copy of Plate 53, Dresden Codex</td>
+  <td><a href="#Fig_365">308</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_366">366.</a> Copy of Plate 54, Dresden Codex</td>
+  <td><a href="#Fig_366">309</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_367">367.</a> Copy of Plate 55, Dresden Codex</td>
+  <td><a href="#Fig_367">310</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_368">368.</a> Copy of Plate 56, Dresden Codex</td>
+  <td><a href="#Fig_368">311</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_369">369.</a> Copy of Plate 57, Dresden Codex</td>
+  <td><a href="#Fig_369">312</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_370">370.</a> Copy of Plate 58, Dresden Codex</td>
+  <td><a href="#Fig_370">313</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_371">371.</a> Specimens of ornamental loops from page 72, Dresden Codex</td>
+  <td><a href="#Fig_371">337</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_372">372.</a> Numeral character from the lower division of Plate XV, Manuscript Troano</td>
+  <td><a href="#Fig_372">343</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_373">373.</a> Turtle from the Cortesian Codex, Plate 17</td>
+  <td><a href="#Fig_373">348</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_374">374.</a> Jar from the Cortesian Codex, Plate 27</td>
+  <td><a href="#Fig_374">349</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_375">375.</a> Worm and plant from Manuscript Troano, Plate XXIX</td>
+  <td><a href="#Fig_375">351</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_376">376.</a> Figure of a woman from the Dresden Codex</td>
+  <td><a href="#Fig_376">351</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_377">377.</a> Copy of middle and lower divisions of Plate XIX, Manuscript Troano</td>
+  <td><a href="#Fig_377">352</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_378">378.</a> Copy of lower division of Plate 65, Dresden Codex</td>
+  <td><a href="#Fig_378">353</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_379">379.</a> The moo or ara from Plate 16, Dresden Codex</td>
+  <td><a href="#Fig_379">355</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_380">380.</a> The god Ekchuah, after the Troano and Cortesian Codices</td>
+  <td><a href="#Fig_380">358</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_381">381.</a> The long nosed god (Kukulcan) or god with the snake-like tongue</td>
+  <td><a href="#Fig_381">359</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_382">382.</a> Copy of head from the Borgian Codex (Quetzalcoatl?)</td>
+  <td><a href="#Fig_382">360</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_383">383.</a> The supposed god of death from the Dresden Codex</td>
+  <td><a href="#Fig_383">361</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_384">384.</a> The supposed god of death from the Troano Codex</td>
+  <td><a href="#Fig_384">361</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_385">385.</a> The god with the banded face from the Troano Codex</td>
+  <td><a href="#Fig_385">362</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_386">386.</a> The god with the old man&#8217;s face</td>
+  <td><a href="#Fig_386">363</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_387">387.</a> The god with face crossed by lines</td>
+  <td><a href="#Fig_387">364</a></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td><a href="#Fig_388">388.</a> Wooden idol in vessel with basket cover</td>
+  <td><a href="#Fig_388">371</a></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_258" id="Page_258">[258]</a></span></p>
+
+
+
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_259" id="Page_259">[259]</a></span></p>
+
+<h2 class="chapterhead"><a name="AIDS_TO_THE_STUDY_OF_THE_MAYA_CODICES" id="AIDS_TO_THE_STUDY_OF_THE_MAYA_CODICES"></a>AIDS TO THE STUDY OF THE MAYA CODICES.</h2>
+
+<hr class="bbox" style="width: 5em;" />
+
+<p class="titlepage"><span class="smcap">By Cyrus Thomas.</span></p>
+
+<hr class="bbox" style="width: 5em;" />
+
+
+<p class="sectionhead"><a name="INTRODUCTION" id="INTRODUCTION"></a>INTRODUCTION.</p>
+
+
+<p>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.</p>
+
+<p>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&#8217;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.</p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_260" id="Page_260">[260]</a></span></p>
+
+
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_261" id="Page_261">[261]</a></span></p>
+
+<h2 class="chapterhead"><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I.</h2>
+
+
+<p class="sectionhead">THE NUMERALS IN THE DRESDEN CODEX.</p>
+
+<p>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. F&ouml;rstemann&#8217;s introduction to the
+photolithographic copy of the <span class="nowrap">codex,<a name="FNanchor_261-1_9" id="FNanchor_261-1_9"></a><a href="#Footnote_261-1_9" class="fnanchor">261-1</a></span> 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:</p>
+
+<p>&#8220;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 G&ouml;tze, 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 G&ouml;tze&#8217;s handwriting,
+which is found in the archives of the Royal Public Library, under A, Vol.
+II, No. 10, and bears the title: &#8216;Books consigned to me for the Royal
+Library in January, 1740.&#8217; Under No. 300 we read: &#8216;An invaluable Mexican
+book with hieroglyphic figures.&#8217; This is the same codex which we here
+reproduce.</p>
+
+<p>&#8220;G&ouml;tze 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 G&ouml;tze
+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: &#8216;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.&#8217;</p>
+
+<p><span class='pagenum'><a name="Page_262" id="Page_262">[262]</a></span>&#8220;G&ouml;tze 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:</p>
+
+<p>&#8220;&#8216;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.&#8217;</p>
+
+<p>&#8220;On page 5 G&ouml;tze says:</p>
+
+<p>&#8220;&#8216;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.&#8217;</p>
+
+<p>&#8220;G&ouml;tze 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, G&ouml;tze did not know
+that the Vatican Codex was of an entirely different nature from the
+Dresden Codex.</p>
+
+<p>&#8220;In spite of the high value which G&ouml;tze 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&#8217;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.</p>
+
+<p>&#8220;After G&ouml;tze, the first to mention our codex is C. A. B&ouml;ttiger, in his
+Ideas on Arch&aelig;ology (Dresden, 1811, pp. 20, 21), without, however, saying
+anything that we did not already know from G&ouml;tze. Still B&ouml;ttiger 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 B&ouml;ttiger&#8217;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.</p>
+
+<p>&#8220;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<span class='pagenum'><a name="Page_263" id="Page_263">[263]</a></span> 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 B&ouml;ttiger, whose above
+named work he cites. Here we learn for the first time that the material
+of the manuscript consists of the plant metl (<i>Agave Mexicana</i>,) 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&#8217;s other remarks do
+not immediately concern our problem.</p>
+
+<p>&#8220;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 &#8216;treasure of highest
+value,&#8217; 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<sup class="a">o</sup>, makes
+but brief mention of our codex, as &#8216;a Mexican book of wood, illustrated
+with pictures, which awaits its &OElig;dipus;&#8217; whereupon he cites the
+writing of B&ouml;ttiger. The signature of the manuscript here noted, E 451,
+is the one still in use.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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?</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;Furthermore it is necessary to state which of these pages so num<span class='pagenum'><a name="Page_264" id="Page_264">[264]</a></span>bered
+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.]</p>
+
+<p>&#8220;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 G&ouml;tze
+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.</p>
+
+<p>&#8220;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&#8217;s
+model was as follows:</p>
+
+<div class="blockquot"><p>&#8220;<i>First piece</i>:</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;<i>Second piece</i>:</p>
+
+<p>&#8220;Front (from left to right): 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56,
+57, 58, 59, 60.</p>
+
+<p>&#8220;Back (from right to left): 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64,
+63, 62, 61, 0.</p></div>
+
+<p>&#8220;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<span class='pagenum'><a name="Page_265" id="Page_265">[265]</a></span> page three has been left unfinished, because
+the lower half was only <i>begun</i> by the writer.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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:<span class='pagenum'><a name="Page_266" id="Page_266">[266]</a></span> 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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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).</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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&#8217;s Mexican Antiquities. The work in
+the trade cost 175<i>l</i>.; the expense of publication had been over
+30,000<i>l</i>. 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.</p>
+
+<p>&#8220;In the middle of the third volume of the Mexican Antiquities (side
+numbers are here absent) there is found the title &#8216;Fac simile of an
+original Mexican painting preserved in the Royal Library at Dresden,<span class='pagenum'><a name="Page_267" id="Page_267">[267]</a></span> 74
+pages.&#8217; These 74 pages are here arranged on 27 leaves in the following
+manner:</p>
+
+<table width="200" border="0" cellpadding="0" cellspacing="0" summary="Codex pages">
+<tr>
+  <td style="width: 100px;">Codex A.</td>
+  <td style="width: 100px;">Codex B.</td>
+</tr>
+<tr>
+  <td>1, 2, 3,</td>
+  <td>46, 47, 48,</td>
+</tr>
+<tr>
+  <td>4, 5, 6,</td>
+  <td>49, 50, 51,</td>
+</tr>
+<tr>
+  <td>7, 8, 9,</td>
+  <td>52, 53, 54,</td>
+</tr>
+<tr>
+  <td>10, 11,</td>
+  <td>55, 56, 57,</td>
+</tr>
+<tr>
+  <td>12, 13, 14,</td>
+  <td>58, 59, 60,</td>
+</tr>
+<tr>
+  <td>15, 16, 17,</td>
+  <td>61, 62, 63,</td>
+</tr>
+<tr>
+  <td>18, 19,</td>
+  <td>64, 65, 66,</td>
+</tr>
+<tr>
+  <td>20,</td>
+  <td>67, 68, 69,</td>
+</tr>
+<tr>
+  <td>21, 22, 23,</td>
+  <td>70, 71, 72,</td>
+</tr>
+<tr>
+  <td>24, 25,</td>
+  <td>73, 74.</td>
+</tr>
+<tr>
+  <td>26, 27, 28,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>29, 30, 31,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>32, 33, 34,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>35, 36, 37,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>38, 39, 40,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>41, 42, 43,</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>44, 45.</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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&#8217;s
+manuscript correspondence in the Dresden library.</p>
+
+<p>&#8220;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&#8217;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 <a name="corr1" id="corr1"></a><ins class="correction" title="&#8216;hasty and obtrusive notice.&#8217;">&#8220;hasty and
+obtrusive notice.&#8221;</ins> B&ouml;ttiger, 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&#8217;s replies in the same journal became more and more
+ferocious, till B&ouml;ttiger, 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 arch&aelig;ologist were made enemies for a long
+time by means of our codex.</p>
+
+<p>&#8220;From Kingsborough&#8217;s work various specimens of the manuscript passed into
+other books; thus we find some in Silvestre, Pal&eacute;ographie universelle,
+Paris, 1839-&#8217;41, fol.; in Rosny, Les &eacute;critures figuratives<span class='pagenum'><a name="Page_268" id="Page_268">[268]</a></span> et
+hi&eacute;roglyphiques des peuples anciens et modernes, Paris, 1860, 4to; and
+also in Madier de Montjou, Archives de la soci&eacute;t&eacute; am&eacute;ricaine de France,
+2<sup class="b">de</sup> s&eacute;rie, tome I, table V.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;Thus the arrangement in which I found the manuscript, which it may be
+best to preserve until my views are recognized, is the following:</p>
+
+<p>&#8220;(1) <i>The diminished Codex A (19 leaves)</i>:</p>
+
+<div class="blockquot"><p>Front: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 25, 26, 27, 28, 0, 0, 0.</p>
+
+<p>Back: 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
+39, 40.</p></div>
+
+<p><span class='pagenum'><a name="Page_269" id="Page_269">[269]</a></span>&#8220;Or, if we enumerate the numbers on the back from right to left, so that
+the back of each leaf stands beneath its front:</p>
+
+<div class="blockquot">
+<table border="0" cellpadding="4" cellspacing="0" summary="Order of Codex">
+<tr>
+  <td class="tdr">6,</td><td class="tdr">7,</td><td class="tdr">8,</td><td class="tdr">9,</td><td class="tdr">10,</td><td class="tdr">11,</td><td class="tdr">12,</td><td class="tdr">13,</td><td class="tdr">14,</td><td class="tdr">15,</td><td class="tdr">16,</td><td class="brright" style="padding-right: 6px;">17</td><td class="tdr" style="padding-left: 6px;">25,</td><td class="tdr">26,</td><td class="tdr">27,</td><td class="tdr">28,</td><td class="tdr">0,</td><td class="tdr">0,</td><td class="tdr">0.</td>
+</tr>
+<tr>
+  <td class="tdr">40,</td><td class="tdr">39,</td><td class="tdr">38,</td><td class="tdr">37,</td><td class="tdr">36,</td><td class="tdr">35,</td><td class="tdr">34,</td><td class="tdr">33,</td><td class="tdr">32,</td><td class="tdr">31,</td><td class="tdr">30,</td><td class="brright" style="padding-right: 6px;">29</td><td class="tdr" style="padding-left: 6px;">24,</td><td class="tdr">23,</td><td class="tdr">22,</td><td class="tdr">21,</td><td class="tdr">20,</td><td class="tdr">19,</td><td class="tdr">18.</td>
+</tr>
+</table>
+</div>
+
+<p>&#8220;(2) <i>The enlarged Codex B (20 leaves)</i>:</p>
+
+<div class="blockquot"><p>Front: 1, 2, 3, 4, 5, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
+59, 60.</p>
+
+<p>Back: 0, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 41, 43,
+43, 44, 45.</p></div>
+
+<p>&#8220;Or, reversing, as in the preceding case, the numbers on the back:</p>
+
+<div class="blockquot">
+<table border="0" cellpadding="4" cellspacing="0" summary="Order of Codex reassembled">
+<tr>
+  <td class="tdr">1,</td><td class="tdr">2,</td><td class="tdr">3,</td><td class="tdr">4,</td><td class="brright" style="padding-right: 6px;">5</td><td class="tdr" style="padding-left: 6px;">46,</td><td class="tdr">47,</td><td class="tdr">48,</td><td class="tdr">49,</td><td class="tdr">50,</td><td class="tdr">51,</td><td class="tdr">52,</td><td class="tdr">53,</td><td class="tdr">54,</td><td class="tdr">55,</td><td class="tdr">56,</td><td class="tdr">57,</td><td class="tdr">58,</td><td class="tdr">59,</td><td class="tdr">60.</td>
+</tr>
+<tr>
+  <td class="tdr">45,</td><td class="tdr">44,</td><td class="tdr">43,</td><td class="tdr">42,</td><td class="brright" style="padding-right: 6px;">41</td><td class="tdr" style="padding-left: 6px;">74,</td><td class="tdr">73,</td><td class="tdr">72,</td><td class="tdr">71,</td><td class="tdr">70,</td><td class="tdr">69,</td><td class="tdr">68,</td><td class="tdr">67,</td><td class="tdr">66,</td><td class="tdr">65,</td><td class="tdr">64,</td><td class="tdr">63,</td><td class="tdr">62,</td><td class="tdr">61,</td><td class="tdr">0.&#8221;</td>
+</tr>
+</table>
+</div>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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: <img src="images/image01.png" width="7" height="5" alt="dot" title="dot" /> (one dot) signifying one;
+<img src="images/image02.png" width="17" height="9" alt="two dots" title="two dots" /> (two dots) two, and so on up to four; five was indicated by a single
+short straight line, thus, <img src="images/image03.png" width="21" height="8" alt="Two horizontal lines, stacked" title="Two horizontal lines, stacked" />; ten, by two similar lines,
+<img src="images/image04.png" width="21" height="11" alt="Three horizontal lines, stacked" title="Three horizontal lines, stacked" />; and fifteen, by three such
+lines: <img src="images/image05.png" width="21" height="18" alt="Dot above horizontal line" title="Dot above horizontal line" />. According to this
+system, a straight line and a dot, thus, <img src="images/image06.png" width="17" height="12" alt="Two dots above two stacked horizontal lines" title="Two dots above two stacked horizontal lines" />, would denote 6; two straight lines and two dots,
+<img src="images/image07.png" width="16" height="17" alt="Four dots in a line above 3 stacked horizontal lines" title="Four dots in a line above 3 stacked horizontal lines" />, 12; and
+three straight lines and four dots, <img src="images/image08.png" width="31" height="20" alt="4 dots over 3 lines" title="4 dots over 3 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 &#8220;Indication&#8221; or
+&#8220;week of years.&#8221; 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.</p>
+
+<p>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 <span class="nowrap">work,<a name="FNanchor_269-1_10" id="FNanchor_269-1_10"></a><a href="#Footnote_269-1_10" class="fnanchor">269-1</a></span> but a particular point needs further
+explanation.</p>
+
+<p><span class='pagenum'><a name="Page_270" id="Page_270">[270]</a></span>According to the older and also the more recent authorities, the Maya
+years&mdash;there being 20 names for days and 365 days in a year&mdash;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.</p>
+
+<p>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 <a href="#Table_I">Table I</a>.</p>
+
+<p class="tabletitle"><a name="Table_I" id="Table_I"></a><span class="smcap">Table I.</span>&mdash;<i>Names and numbers of the months and days of the Maya system.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table I">
+<tr>
+  <td class="btl">&nbsp;</td>
+  <td class="btl" valign="bottom">P<br />o<br />p<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">U<br />o<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">Z<br />i<br />p<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">T<br />z<br />o<br />z<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">T<br />z<br />e<br />c<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">X<br />u<br />l<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">Y<br />a<br />x<br />k<br />i<br />n<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">M<br />o<br />l<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">C<br />h<br />e<br />n<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">Y<br />a<br />x<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">Z<br />a<br />c<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">C<br />e<br />h<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">M<br />a<br />c<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">K<br />a<br />n<br />k<br />i<br />n<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">M<br />u<br />a<br />n<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">P<br />a<br />x<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">K<br />a<br />y<br />e<br />b<br /><sup>.</sup></td>
+  <td class="btl" valign="bottom">C<br />u<br />m<br />h<br />u<br /><sup>.</sup></td>
+  <td class="btl" rowspan="2">N<br />u<br />m<br />b<br />e<br />r<br />s</td>
+  <td class="btr" rowspan="2">o<br />f<br /> <br />d<br />a<br />y<br />s</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="btlright">1</td>
+  <td class="btlright">2</td>
+  <td class="btlright">3</td>
+  <td class="btlright">4</td>
+  <td class="btlright">5</td>
+  <td class="btlright">6</td>
+  <td class="btlright">7</td>
+  <td class="btlright">8</td>
+  <td class="btlright">9</td>
+  <td class="btlright">10</td>
+  <td class="btlright">11</td>
+  <td class="btlright">12</td>
+  <td class="btlright">13</td>
+  <td class="btlright">14</td>
+  <td class="btlright">15</td>
+  <td class="btlright">16</td>
+  <td class="btlright">17</td>
+  <td class="btlright">18</td>
+</tr>
+<tr>
+  <td class="btl">&nbsp;<i>Names of the days.</i></td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btlright">&nbsp;</td>
+  <td class="bblright br" colspan="2">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">Kan</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blrright" colspan="2">1</td>
+</tr>
+<tr>
+  <td class="bl">Chicchan</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blrright" colspan="2">2</td>
+</tr>
+<tr>
+  <td class="bl">Cimi</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blrright" colspan="2">3</td>
+</tr>
+<tr>
+  <td class="bl">Manik</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blrright" colspan="2">4</td>
+</tr>
+<tr>
+  <td class="bl">Lamat</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blrright" colspan="2">5</td>
+</tr>
+<tr>
+  <td class="bl">Muluc</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blrright" colspan="2">6</td>
+</tr>
+<tr>
+  <td class="bl">Oc</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blrright" colspan="2">7</td>
+</tr>
+<tr>
+  <td class="bl">Chuen</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blrright" colspan="2">8</td>
+</tr>
+<tr>
+  <td class="bl">Eb</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blrright" colspan="2">9</td>
+</tr>
+<tr>
+  <td class="bl">Been</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blrright" colspan="2">10</td>
+</tr>
+<tr>
+  <td class="bl">Ix</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blrright" colspan="2">11</td>
+</tr>
+<tr>
+  <td class="bl">Men</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blrright" colspan="2">12</td>
+</tr>
+<tr>
+  <td class="bl">Cib</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blrright" colspan="2">13</td>
+</tr>
+<tr>
+  <td class="bl">Caban</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blrright" colspan="2">14</td>
+</tr>
+<tr>
+  <td class="bl">Ezanab</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blrright" colspan="2">15</td>
+</tr>
+<tr>
+  <td class="bl">Cauac</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blrright" colspan="2">16</td>
+</tr>
+<tr>
+  <td class="bl">Ahau</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blrright" colspan="2">17</td>
+</tr>
+<tr>
+  <td class="bl">Ymix</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blrright" colspan="2">18</td>
+</tr>
+<tr>
+  <td class="bl">Ik</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blrright" colspan="2">19</td>
+</tr>
+<tr>
+  <td class="bl">Akbal</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blrright" colspan="2">20</td>
+</tr>
+<tr>
+  <td class="btlcent" colspan="18"><i>Intercalated days.</i></td>
+  <td class="btlright">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btr">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">Kan</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="blright">10</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">Chicchan</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">Cimi</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">Manik</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="blright">13</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bbl">Lamat</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">1</td>
+  <td class="bblright">&nbsp;</td>
+  <td class="bbr">&nbsp;</td>
+</tr>
+</table>
+
+<p>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<span class='pagenum'><a name="Page_271" id="Page_271">[271]</a></span> 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.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Day order">
+<tr>
+  <td class="tdr" style="padding-right: 4px;">1.</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">2.</td>
+  <td>Chicchan.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">3.</td>
+  <td>Cimi.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">4.</td>
+  <td>Manik.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">5.</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">6.</td>
+  <td>Muluc.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">7.</td>
+  <td>Oc.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">8.</td>
+  <td>Chuen.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">9.</td>
+  <td>Eb.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">10.</td>
+  <td>Been.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">11.</td>
+  <td>Ix.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">12.</td>
+  <td>Men.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">13.</td>
+  <td>Cib</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">1.</td>
+  <td>Caban.</td>
+</tr>
+<tr>
+  <td class="tdr" style="padding-right: 4px;">2.</td>
+  <td>Ezanab, &amp;c.,</td>
+</tr>
+</table>
+
+<p class="noindent">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, &amp;c. In other words, Chicchan must always
+follow Kan, Cimi must always follow Chicchan, &amp;c.</p>
+
+<p>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&mdash;the first day of the year given in <a href="#Table_I">Table
+I</a>&mdash;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.</p>
+
+<p>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, <a href="#Table_I">Table I</a>; and 1 + 14 + 12 + 17 + 17 - 13 - 13 -
+13 - 13 = 9, the number of the day<span class='pagenum'><a name="Page_272" id="Page_272">[272]</a></span> Kan, fourth column. The reason for
+this is so apparent that it is unnecessary to state it.</p>
+
+<p>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.</p>
+
+<p>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 &#8220;upper,&#8221;
+&#8220;middle,&#8221; and &#8220;lower&#8221; division. On the plan proposed by Dr. F&ouml;rstemann,
+in his late work on the Dresden Codex (Erl&auml;uterungen zur Mayahandschrift
+der K&ouml;niglichen &ouml;ffentlichen Bibliothek zu Dresden), these divisions are
+designated by the letters <i>a</i>, <i>b</i>, and <i>c</i>; this plan will be adopted in
+this paper. The letter <i>a</i> joined to the number of a plate, therefore,
+will signify that the division referred to is the upper one, as Plate
+12<i>a</i>; the letter <i>b</i> signifies the middle one where there are three
+divisions or the lower one where there are but two; and the letter <i>c</i>
+signifies the lowest or bottom division where there are three.</p>
+
+<p>Where reference is made to the fac simile of the Dresden Codex,
+Kingsborough&#8217;s colored edition is always to be understood, except where
+another is specially mentioned.</p>
+
+<p>Running through Plates 36<i>c</i> and 37<i>c</i> 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:</p>
+
+<div class="figcenter" style="width: 383px;">
+<a name="Fig_359" id="Fig_359"></a><img src="images/image09.png" width="383" height="174" alt="Fig. 359. Lines of day and numeral symbols." title="Fig. 359. Lines of day and numeral symbols." />
+<span class="caption"><span class="smcap">Fig.</span> 359. Lines of day and numeral symbols.</span>
+</div>
+
+<p>As colors are not used in these figures the red numerals are <a name="corr2" id="corr2"></a><ins class="correction" title="indicated">indi
+cated</ins> by hollow or outline dots and lines and the black numerals by
+solid lines and <span class="nowrap">dots.<a name="FNanchor_272-1_11" id="FNanchor_272-1_11"></a><a href="#Footnote_272-1_11" class="fnanchor">272-1</a></span></p>
+
+<p><span class='pagenum'><a name="Page_273" id="Page_273">[273]</a></span>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.</p>
+
+<p>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.</p>
+
+<p>Starting from 11 Men, found in the twelfth figure column of <a href="#Table_I">Table I</a>, 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 <span class="nowrap">Oc<a name="FNanchor_273-1_12" id="FNanchor_273-1_12"></a><a href="#Footnote_273-1_12" class="fnanchor">273-1</a></span> 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:
+<img src="images/image10.png" width="55" height="43" alt="Hieroglyph" title="Hieroglyph" style="vertical-align: middle;" /> 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.</p>
+
+<p>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 <span class="nowrap">Oc.<a name="FNanchor_273-2_13" id="FNanchor_273-2_13"></a><a href="#Footnote_273-2_13" class="fnanchor">273-2</a></span></p>
+
+<p>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. F&ouml;rstemann 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, &#8220;Notes on
+certain Maya and Mexican manuscripts,&#8221; was written, I had made this
+discovery as early as <span class="nowrap">1884.<a name="FNanchor_273-3_14" id="FNanchor_273-3_14"></a><a href="#Footnote_273-3_14" class="fnanchor">273-3</a></span></p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_274" id="Page_274">[274]</a></span></p>
+
+<p class="tabletitle"><a name="Table_II" id="Table_II"></a><span class="smcap">Table II.</span>&mdash;<i>Names and numbers of the four series of years of the Maya
+system.</i></p>
+
+<table border="0" cellpadding="2" cellspacing="0" summary="Table II">
+<tr>
+  <td class="btcent">Cauac<br />column.</td>
+  <td class="btlcent">Kan<br />column.</td>
+  <td class="btlcent">Muluc<br />column.</td>
+  <td class="btlcent">Ix<br />column.</td>
+  <td class="btlright">1<br />14</td>
+  <td class="btlright">2<br />15</td>
+  <td class="btlright">3<br />16</td>
+  <td class="btlright">4<br />17</td>
+  <td class="btlright">5<br />18</td>
+  <td class="btlright">6<br />&nbsp;</td>
+  <td class="btlright">7<br />&nbsp;</td>
+  <td class="btlright">8<br />&nbsp;</td>
+  <td class="btlright">9<br />&nbsp;</td>
+  <td class="btlright">10<br />&nbsp;</td>
+  <td class="btlright">11<br />&nbsp;</td>
+  <td class="btlright">12<br />&nbsp;</td>
+  <td class="btlright">13<br />&nbsp;</td>
+  <td class="btl"><span class="triple">{</span></td>
+  <td class="btcent">Numbers<br />of the<br />months.</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">Days of<br />month.</td>
+</tr>
+<tr>
+  <td class="padlr">Cauac</td>
+  <td class="bl">Kan</td>
+  <td class="bl">Muluc</td>
+  <td class="bl">Ix</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright padr1" colspan="2">1</td>
+</tr>
+<tr>
+  <td class="padlr">Ahau</td>
+  <td class="bl">Chicchan</td>
+  <td class="bl">Oc</td>
+  <td class="bl">Men</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright padr1" colspan="2">2</td>
+</tr>
+<tr>
+  <td>Ymix</td>
+  <td class="bl">Cimi</td>
+  <td class="bl">Chuen</td>
+  <td class="bl">Cib</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright padr1" colspan="2">3</td>
+</tr>
+<tr>
+  <td>Ik</td>
+  <td class="bl">Manik</td>
+  <td class="bl">Eb</td>
+  <td class="bl">Caban</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright padr1" colspan="2">4</td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td class="bl">Lamat</td>
+  <td class="bl">Been</td>
+  <td class="bl">Ezanab</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright padr1" colspan="2">5</td>
+</tr>
+<tr>
+  <td>Kan</td>
+  <td class="bl">Muluc</td>
+  <td class="bl">Ix</td>
+  <td class="bl">Cauac</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright padr1" colspan="2">6</td>
+</tr>
+<tr>
+  <td>Chicchan</td>
+  <td class="bl">Oc</td>
+  <td class="bl">Men</td>
+  <td class="bl">Ahau</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright padr1" colspan="2">7</td>
+</tr>
+<tr>
+  <td>Cimi</td>
+  <td class="bl">Chuen</td>
+  <td class="bl">Cib</td>
+  <td class="bl">Ymix</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright padr1" colspan="2">8</td>
+</tr>
+<tr>
+  <td>Manik</td>
+  <td class="bl">Eb</td>
+  <td class="bl">Caban</td>
+  <td class="bl">Ik</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright padr1" colspan="2">9</td>
+</tr>
+<tr>
+  <td>Lamat</td>
+  <td class="bl">Been</td>
+  <td class="bl">Ezanab</td>
+  <td class="bl">Akbal</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright padr1" colspan="2">10</td>
+</tr>
+<tr>
+  <td>Muluc</td>
+  <td class="bl">Ix</td>
+  <td class="bl">Cauac</td>
+  <td class="bl">Kan</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright padr1" colspan="2">11</td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td class="bl">Men</td>
+  <td class="bl">Ahau</td>
+  <td class="bl">Chicchan</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright padr1" colspan="2">12</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td class="bl">Cib</td>
+  <td class="bl">Ymix</td>
+  <td class="bl">Cimi</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright padr1" colspan="2">13</td>
+</tr>
+<tr>
+  <td>Eb</td>
+  <td class="bl">Caban</td>
+  <td class="bl">Ik</td>
+  <td class="bl">Manik</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright padr1" colspan="2">14</td>
+</tr>
+<tr>
+  <td>Been</td>
+  <td class="bl">Ezanab</td>
+  <td class="bl">Akbal</td>
+  <td class="bl">Lamat</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright padr1" colspan="2">15</td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td class="bl">Cauac</td>
+  <td class="bl">Kan</td>
+  <td class="bl">Muluc</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright padr1" colspan="2">16</td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td class="bl">Ahau</td>
+  <td class="bl">Chicchan</td>
+  <td class="bl">Oc</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright padr1" colspan="2">17</td>
+</tr>
+<tr>
+  <td>Cib</td>
+  <td class="bl">Ymix</td>
+  <td class="bl">Cimi</td>
+  <td class="bl">Chuen</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright padr1" colspan="2">18</td>
+</tr>
+<tr>
+  <td>Caban</td>
+  <td class="bl">Ik</td>
+  <td class="bl">Manik</td>
+  <td class="bl">Eb</td>
+  <td class="blright">6</td>
+  <td class="blright">13</td>
+  <td class="blright">7</td>
+  <td class="blright">1</td>
+  <td class="blright">8</td>
+  <td class="blright">2</td>
+  <td class="blright">9</td>
+  <td class="blright">3</td>
+  <td class="blright">10</td>
+  <td class="blright">4</td>
+  <td class="blright">11</td>
+  <td class="blright">5</td>
+  <td class="blright">12</td>
+  <td class="blright padr1" colspan="2">19</td>
+</tr>
+<tr>
+  <td class="bb">Ezanab</td>
+  <td class="bbl">Akbal</td>
+  <td class="bbl">Lamat</td>
+  <td class="bbl">Been</td>
+  <td class="bblright">7</td>
+  <td class="bblright">1</td>
+  <td class="bblright">8</td>
+  <td class="bblright">2</td>
+  <td class="bblright">9</td>
+  <td class="bblright">3</td>
+  <td class="bblright">10</td>
+  <td class="bblright">4</td>
+  <td class="bblright">11</td>
+  <td class="bblright">5</td>
+  <td class="bblright">12</td>
+  <td class="bblright">6</td>
+  <td class="bblright">13</td>
+  <td class="bblright padr1" colspan="2">20</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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<span class='pagenum'><a name="Page_275" id="Page_275">[275]</a></span> day
+columns may be used, it is apparent that we have all the possible
+combinations (4 &times; 13 = 52).</p>
+
+<p>I say above that &#8220;it is necessary in counting to refer always to the year
+(year column) which the count begins.&#8221; This I admit does not agree with
+the generally received idea of the Maya calendar, upon which <a href="#Table_II">Table II</a> 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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>Examining Plates 33 to 39 of the codex the reader will observe that the
+line already alluded to extends continuously through division <i>c</i>,
+commencing with the two characters over the figure (picture) in the lower
+right hand corner of Plate 33.</p>
+
+<p>The first of these characters as given in Kingsborough&#8217;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 F&ouml;rstemann&#8217;s
+photolithographic copy of the codex it is found to be the symbol of Ahau.</p>
+
+<p>The entire line, with this correction (that is to say, as given by
+F&ouml;rstemann), is represented in <a href="#Fig_360">Fig. 360</a>. In order to assist the reader,
+the names of the days and numbers of the symbols have been added
+immediately below the characters.</p>
+
+<p>As the year to which the line relates is unknown, we select the Muluc
+series, designated &#8220;Muluc column&#8221; in <a href="#Table_II">Table II</a>, 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&#8217;s copy, but is plainly the Muluc sign in F&ouml;rstemann&#8217;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<span class='pagenum'><a name="Page_276" id="Page_276">[276]</a></span> 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.</p>
+
+<p><span class='pagenum'><a name="Page_277" id="Page_277">[277]</a></span></p>
+
+<div class="figcenter" style="width: 399px;">
+<a name="Fig_360" id="Fig_360"></a><a href="images/image11-full.png"><img src="images/image11.png" width="399" height="671" alt="Fig. 360. Line of day and numeral characters." title="Fig. 360. Line of day and numeral characters." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 360. Line of day and numeral characters.</span>
+</div>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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
+<a href="#Page_273">273</a>) denotes 20, and if phonetic probably stands for the Maya word <i>Kal</i>.</p>
+
+<p>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 <span class="nowrap">characters<a name="FNanchor_277-1_15" id="FNanchor_277-1_15"></a><a href="#Footnote_277-1_15" class="fnanchor">277-1</a></span> in the middle
+division (<i>b</i>) of Plates 1 and 2 that they belong together, as they now
+stand in Kingsborough&#8217;s work and F&ouml;rstemann&#8217;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 <i>a</i> and <i>b</i>.</p>
+
+<p>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.</p>
+
+<p>The series of days and of numbers in Plate 43<i>b</i> and Plate 1<i>b</i>, 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<span class='pagenum'><a name="Page_278" id="Page_278">[278]</a></span>
+the line of alternate red and black numerals in division <i>b</i>. As shown in
+a previous <span class="nowrap">work<a name="FNanchor_278-1_16" id="FNanchor_278-1_16"></a><a href="#Footnote_278-1_16" class="fnanchor">278-1</a></span> 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.</p>
+
+<p>The number over the day column, Plate 38, must have been VI, as VI + 16 -
+13 = 9, a conclusion which is sustained by F&ouml;rstemann&#8217;s copy, which shows
+here very plainly the red character for VI.</p>
+
+<p>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.</p>
+
+<p>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&#8217;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.</p>
+
+<p>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. F&ouml;<span class="nowrap">rstemann,<a name="FNanchor_278-2_17" id="FNanchor_278-2_17"></a><a href="#Footnote_278-2_17" class="fnanchor">278-2</a></span> 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.</p>
+
+<p>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<span class='pagenum'><a name="Page_279" id="Page_279">[279]</a></span> through
+division <i>c</i>. Substituting names and numbers as heretofore, they are as
+follows:</p>
+
+<div class="blockquot"><table border="0" cellpadding="0" cellspacing="0" summary="Day name and number correspondence">
+<tr>
+  <td>Plate 42:</td>
+  <td>IV Ahau;</td>
+  <td>XII Lamat;</td>
+  <td>VII Cib;</td>
+  <td>II Kan;</td>
+  <td>X Eb;</td>
+  <td>V Ahau;</td>
+  <td>XIII Lamat.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">17</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>Plate 43:</td>
+  <td>IV Chicchan;</td>
+  <td>XII Been;</td>
+  <td>VII Ymix;</td>
+  <td>II Muluc;</td>
+  <td>X Caban;</td>
+  <td>V Chicchan;</td>
+  <td>XIII Been.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">17</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>Plate 1:</td>
+  <td>IV Oc;</td>
+  <td>XII Ezanab;</td>
+  <td>VII Cimi;</td>
+  <td>II Ix;</td>
+  <td>X Ik;</td>
+  <td>V Oc;</td>
+  <td>(?) Ezanab.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">17</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+ <td>Plate 2:</td>
+  <td>IV Men;</td>
+  <td>XIII Akbal;</td>
+  <td>VII Chuen;</td>
+  <td>II Cauac;</td>
+  <td>X Manik;</td>
+  <td>V Men;</td>
+  <td>XIII Akbal.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">17</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+</table>
+</div>
+
+<p>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&#8217;s.</p>
+
+<p>As the particular year or years to which the series refers is unknown we
+turn to our calendar&mdash;<a href="#Table_II">Table II</a>&mdash;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&#8217;s work is III, but a close inspection shows the missing dot
+which has not been colored. IV Chicchan is therefore correct.</p>
+
+<p>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.</p>
+
+<p>Continuing our count, 17 more bring us to 4 Men (here a dot is missing in
+Kingsborough&#8217;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.</p>
+
+<p>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.</p>
+
+<p>Although the succession of days and numbers in the lines of the last
+example would seem to furnish conclusive evidence that the<span class='pagenum'><a name="Page_280" id="Page_280">[280]</a></span> 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&mdash;8&#8217;s&mdash;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.</p>
+
+<p>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&mdash;the close of one and the commencement of another&mdash;although
+fully aware that Dr. F&ouml;rstemann has interpreted them as symbols of the
+heavenly <span class="nowrap">bodies.<a name="FNanchor_280-1_18" id="FNanchor_280-1_18"></a><a href="#Footnote_280-1_18" class="fnanchor">280-1</a></span></p>
+
+<p>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 &#8220;tying of the years.&#8221; We may also add that the five days of
+each plate or group are the five assigned, as I have explained in &#8220;Notes
+on certain Maya and Mexican manuscripts,&#8221; to the cardinal points. For
+example, those on Plate 42 are Ahau, Eb, Kan, Cib, <span class="nowrap">Lamat.<a name="FNanchor_280-2_19" id="FNanchor_280-2_19"></a><a href="#Footnote_280-2_19" class="fnanchor">280-2</a></span> 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.</p>
+
+<p>As it has been shown that Plates 33 to 39 and Plates 38 to 43 are
+properly placed as they stand in Kingsborough&#8217;s copy and also in
+F&ouml;rstemann&#8217;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.</p>
+
+<p>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<span class='pagenum'><a name="Page_281" id="Page_281">[281]</a></span>
+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. F&ouml;rstemann, who has had the
+opportunity of studying the original, has now reached.</p>
+
+<p>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.
+F&ouml;rstemann 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.</p>
+
+<p>Commencing with the day column in the middle of Plate 35<i>b</i> and extending
+through Plates 36<i>b</i> and 37<i>b</i> 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.</p>
+
+<p>Using names and numbers in place of the symbols, it is as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 35-37 summary">
+<tr>
+  <td class="tdc">I.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Caban,</td>
+  <td class="padl">11, XII; 6, V; 9, I; 4, V; 7, XII; 9, VIII; 6, I.</td>
+</tr>
+<tr>
+  <td>Muluc.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ymix.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Been.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td colspan="2">Chicchan.</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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<span class='pagenum'><a name="Page_282" id="Page_282">[282]</a></span> in this case is 52, and count the
+number of days on our calendar (<a href="#Table_II">Table II</a>) 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&mdash;that is to say, the sum of the
+counters&mdash;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.</p>
+
+<p>It will be observed that the sum of the black numbers&mdash;which denotes the
+interval between the days of the column&mdash;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 <span class="nowrap">work<a name="FNanchor_282-1_20" id="FNanchor_282-1_20"></a><a href="#Footnote_282-1_20" class="fnanchor">282-1</a></span> 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
+<span class="nowrap">attention;<a name="FNanchor_282-2_21" id="FNanchor_282-2_21"></a><a href="#Footnote_282-2_21" class="fnanchor">282-2</a></span> by the explanation now given we ascertain the true
+intervals between the days <i>as numbered</i>. The two modes therefore form
+checks to each other and will aid very materially in restoring
+obliterated and doubtful days.</p>
+
+<p>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:</p>
+
+<div class="blockquot"><p>(1) Between 1 Caban and 1 Muluc they are 12 Lamat, 5 Ix, 1 Akbal, 5
+Manik, 12 Ix, and 8 Akbal.</p>
+
+<p>(2) Between 1 Muluc and 1 Ymix they are 12 Ahau, 5 Cimi, 1 Men, 5 Cauac,
+12 Cimi, and 8 Men.</p>
+
+<p>(3) Between 1 Ymix and 1 Been they are 12 Eb, 5 Ezanab, 1 Manik, 5 Chuen,
+12 Ezanab, and 8 Manik.</p>
+
+<p>(4) Between 1 Been and 1 Chicchan they are 12 Kan, 5 Oc, 1 Cauac, 5
+Akbal, 12 Oc, and 8 Cauac.</p></div>
+
+<p><span class='pagenum'><a name="Page_283" id="Page_283">[283]</a></span>These, as will be readily perceived, are found by counting on the
+calendar from 1 Caban, 1 Muluc, &amp;c., as heretofore <span class="nowrap">explained.<a name="FNanchor_283-1_22" id="FNanchor_283-1_22"></a><a href="#Footnote_283-1_22" class="fnanchor">283-1</a></span></p>
+
+<p>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&mdash;if the year of 365 days and the four series of years formed the
+basis of the system&mdash;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.</p>
+
+<p>Dr. F&ouml;rstemann 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.</p>
+
+<p>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.</p>
+
+<p>In the middle division of Plate 5 is a day column and a numeral series,
+as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 5 summary">
+<tr>
+  <td class="tdc">I.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Manik</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Cauac</td>
+  <td>16, IV; 9, XIII; S + 5, XII; 2, I.</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>This series terminates with I, as it should according to the theory. The
+sum of the black numerals&mdash;16, 9, 20, 5, 2&mdash;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.</p>
+
+<p>In the lowest division of the same plate is another similar series, as
+follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 5 summary 2">
+<tr>
+  <td class="tdc">XII</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ezanab</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td>20 + 9, II; 11, XIII; 18, V; 7, XII.</td>
+</tr>
+<tr>
+  <td>Lamat</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Been</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ezanab</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_284" id="Page_284">[284]</a></span></p>
+
+<div class="figleft" style="width: 45px;">
+<a name="Fig_361" id="Fig_361"></a><img src="images/image12.png" width="32" height="22" alt="Fig. 361." title="Fig. 361." />
+<span class="caption"><span class="smcap">Fig.</span>&nbsp;361.</span>
+</div>
+
+<p>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 (<a href="#Fig_361">Fig. 361</a>), 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.</p>
+
+<p>In Plate 15, division <i>c</i>, is the following series, which differs from
+those given in having two day columns instead of one:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 15 summary">
+<tr>
+  <td class="tdc padr1">III</td>
+  <td class="tdc">III</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Lamat</td>
+  <td>Ix</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Ahau</td>
+  <td>Cimi</td>
+  <td rowspan="2"><span class="double">}</span></td>
+  <td rowspan="2" valign="middle">12, II; 14, III.</td>
+</tr>
+<tr>
+  <td class="padr1">Eb</td>
+  <td>Ezanab</td>
+</tr>
+<tr>
+  <td class="padr1">Kan</td>
+  <td>Oc</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Cib</td>
+  <td>Ik</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>In the lower division of Plate 9 is a series arranged as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 9 summary">
+<tr>
+  <td class="tdc padr1">III</td>
+  <td class="tdc">III</td>
+  <td>&nbsp;</td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">VIII</td>
+</tr>
+<tr>
+  <td class="padr1">Cauac</td>
+  <td>Been</td>
+  <td>&nbsp;</td>
+  <td class="padr1">3</td>
+  <td>2</td>
+</tr>
+<tr>
+  <td class="padr1">Chuen</td>
+  <td>Chicchan</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">XI<br />3</td>
+  <td>II<br />4</td>
+</tr>
+<tr>
+  <td class="padr1">Akbal</td>
+  <td>Caban</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">VI<br />4</td>
+  <td>VII<br />1</td>
+</tr>
+<tr>
+  <td class="padr1">Men</td>
+  <td>Muluc</td>
+  <td>&nbsp;</td>
+  <td class="padr1">I</td>
+  <td>III</td>
+</tr>
+<tr>
+  <td class="padr1">Manik</td>
+  <td>Ymix</td>
+  <td>&nbsp;</td>
+  <td class="padr1">7</td>
+  <td>2</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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&#8217;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.</p>
+
+<p>In the third division of Plate XI* is the following series:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate XI* summary">
+<tr>
+  <td class="tdc">IV</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ahau</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Eb</td>
+  <td>17, VIII; 13, VIII; 10 V; 12, IV.</td>
+</tr>
+<tr>
+  <td>Kan</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Cib</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Lamat</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_285" id="Page_285">[285]</a></span>As will be readily seen, after the explanations given, this agrees with
+the theory advanced.</p>
+
+<p>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.</p>
+
+<p>Commencing in the right margin of the lowest division of Plate XXIII* and
+running through Plates XXII* and XXI*, is the series here represented:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate XXIII* summary">
+<tr>
+  <td class="tdc padr1">VII</td>
+  <td>VII</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Cib</td>
+  <td>Cimi</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+</tr>
+<tr>
+  <td class="padr1">Ik</td>
+  <td>Eb</td>
+  <td>7, I; 7, VIII; 7, II; 5, VII.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Lamat</td>
+  <td>Ezanab</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Ix</td>
+  <td>Kan</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Ahau</td>
+  <td>Oc</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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 <i>a</i>) they are to be taken alternately from the two
+columns, as in the examples heretofore given from the Dresden Codex.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate XXXIII* summary">
+<tr>
+  <td>&nbsp;</td>
+  <td rowspan="10"><table border="0" cellpadding="0" cellspacing="0" summary="brace">
+                   <tr>
+                      <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;</td>
+                   </tr>
+                   </table></td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">I</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc padr1">5</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td class="tdc">I</td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">I</td>
+</tr>
+<tr>
+  <td>Ymix (?)</td>
+  <td class="tdc padr1">5</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>Cimi (?)</td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">I</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td class="tdc padr1">5</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>Cib (?)</td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">I</td>
+</tr>
+<tr>
+  <td class="tdc">(?)</td>
+  <td class="tdc padr1">5</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc padr1">VI</td>
+  <td class="tdc">I</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc padr1">5</td>
+  <td class="tdc">8</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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<span class='pagenum'><a name="Page_286" id="Page_286">[286]</a></span> back on our calendar (<a href="#Table_II">Table
+II</a>) 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, &amp;c.</p>
+
+<p>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.</p>
+
+<p>The first is taken from the lower division of Plates 10 and 11, Rosny&#8217;s
+reproduction:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 10 and 11 summary">
+<tr>
+  <td class="tdc">XIII</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ahau<br />Chicchan</td>
+  <td><span class="double">}</span></td>
+  <td>11, XI; 5, III; 5, VIII; 5, XIII; 9, IX; 3, XII; 6, V; 1, VI; X, XIII.</td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>The following double column series is found in the middle division of
+Plate 30:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 30 summary">
+<tr>
+  <td class="tdc padr1">XI</td>
+  <td class="tdc">XI</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Ahau</td>
+  <td>Ymix</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Eb</td>
+  <td>Been</td>
+  <td>20 + 6, XI; 20 + 6, XI.</td>
+</tr>
+<tr>
+  <td class="padr1">Kan</td>
+  <td>Caban</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Cib</td>
+  <td>Chicchan</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Lamat</td>
+  <td>Manik</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>In the upper division of the same plate is this series:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 30 summary 2">
+<tr>
+  <td class="tdc">XI</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ezanab</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">VI<br />8</td>
+  <td>XI<br />5</td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">VI<br />8</td>
+  <td>XI<br />5</td>
+</tr>
+<tr>
+  <td>Ik</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">VI<br />8</td>
+  <td>XI<br />5</td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td><span class="double">{</span></td>
+  <td class="padr1">VI<br />8</td>
+  <td>XI<br />5</td>
+</tr>
+<tr>
+  <td>Cimi</td>
+</tr>
+</table>
+
+<p>The order in which these numerals are to be read is as follows: 8, VI; 5,
+XI; 8, VI; 5, XI, &amp;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.</p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_287" id="Page_287">[287]</a></span>In the upper division of Plate 32, Dresden Codex, are the four day
+columns and lines of numerals over them here represented:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 32 summary">
+<tr>
+  <td>&nbsp;&nbsp;1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;&nbsp;4</td>
+  <td>13</td>
+  <td>9</td>
+  <td>&nbsp;&nbsp;4</td>
+</tr>
+<tr>
+  <td>15</td>
+  <td>13</td>
+  <td>2</td>
+  <td>11</td>
+</tr>
+<tr>
+  <td>XIII</td>
+  <td>XIII</td>
+  <td>XIII</td>
+  <td>XIII</td>
+</tr>
+<tr>
+  <td>Manik</td>
+  <td>Cib</td>
+  <td>Chicchan</td>
+  <td>Ix</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td>Ahau</td>
+  <td>Muluc</td>
+  <td>Ezanab</td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td>Kan</td>
+  <td>Been</td>
+  <td>Ik</td>
+</tr>
+<tr>
+  <td>Cauac</td>
+  <td>Lamat</td>
+  <td>Caban</td>
+  <td>Cimi</td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td>Eb</td>
+  <td>Ymix</td>
+  <td>Oc</td>
+</tr>
+</table>
+
+<p>Connected with these numbers is a line of alternate black and red numbers
+running along over the figures of Plates 32 to 39, division <i>a</i>. 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.</p>
+
+<p>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.</p>
+
+<p>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&#8217;s copy and in F&ouml;rstemann&#8217;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<span class='pagenum'><a name="Page_288" id="Page_288">[288]</a></span> 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.</p>
+
+<p>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.</p>
+
+<p>The black numerals above the columns present a problem which I am unable
+to explain. The numbers stand in the original as follows:</p>
+
+<table border="0" width="40%" cellpadding="0" cellspacing="0" summary="Problematic numbers">
+<tr>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdr">4</td>
+  <td class="tdr">13</td>
+  <td class="tdr">9</td>
+  <td class="tdr">4</td>
+</tr>
+<tr>
+  <td class="tdr">15</td>
+  <td class="tdr">13</td>
+  <td class="tdr">2</td>
+  <td class="tdr">11</td>
+</tr>
+</table>
+
+<p>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:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="Calendrical addition">
+<tr>
+  <td class="colhead">Y.</td>
+  <td class="colhead">M.</td>
+  <td class="colhead">D.</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td class="tdr">11</td>
+  <td style="padding-left: 1em;">Numbers over the fourth column.</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bbright">4</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td class="tdr">2</td>
+  <td style="padding-left: 1em;">Numbers over the third column.</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bbright">4</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td class="tdr">13</td>
+  <td style="padding-left: 1em;">Numbers over the second column.</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_289" id="Page_289">[289]</a></span>Doubling the difference and adding we obtain the numbers over the first
+column:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="Calendrical addition">
+<tr>
+  <td class="colhead">Y.</td>
+  <td class="colhead">M.</td>
+  <td class="colhead">D.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td class="tdr">13</td>
+</tr>
+<tr>
+  <td class="bbright">&nbsp;</td>
+  <td class="bbright">9</td>
+  <td class="bbright">2</td>
+</tr>
+<tr>
+  <td class="tdr">1</td>
+  <td class="tdr">4</td>
+  <td class="tdr">15</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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&#8217;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.</p>
+
+<p>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.</p>
+
+<p>Counting on the list of days in the calendar (<a href="#Table_II">Table II</a>), 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<span class='pagenum'><a name="Page_290" id="Page_290">[290]</a></span> 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
+F&ouml;rstemann&#8217;s copy the XIII and XII are black, thus verifying the
+conclusion here reached.</p>
+
+<p>The series running through Plates 10<i>c</i> and 11<i>c</i> presents some
+difficulties which I have, so far, been unable to solve. The day columns
+and numerals are as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 32 summary">
+<tr>
+  <td class="tdc padr1">I</td>
+  <td class="tdc">XIII</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Ymix</td>
+  <td>Cimi</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Been</td>
+  <td>Ezanab</td>
+  <td>1, I; 5, VI; 10, III; 13, III; 15, V; 9 (?), XIII.</td>
+</tr>
+<tr>
+  <td class="padr1">Chicchan</td>
+  <td>Oc</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Caban</td>
+  <td>Ik</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="padr1">Muluc</td>
+  <td><span class="nowrap">Ix<a name="FNanchor_290-1_23" id="FNanchor_290-1_23"></a><a href="#Footnote_290-1_23" class="fnanchor">290-1</a></span></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>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
+F&ouml;<span class="nowrap">rstemann.<a name="FNanchor_290-2_24" id="FNanchor_290-2_24"></a><a href="#Footnote_290-2_24" class="fnanchor">290-2</a></span> 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.</p>
+
+<p>In Plate 30<i>c</i> are the four day columns here given, with the numeral
+eleven over each:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 30 summary">
+<tr>
+  <td style="padding-left: 1.2em;">XI</td>
+  <td style="padding-left: 1.5em;">XI</td>
+  <td style="padding-left: 1.2em;">XI</td>
+  <td style="padding-left: 1.2em;">XI</td>
+</tr>
+<tr>
+  <td>Ahau</td>
+  <td>Chicchan</td>
+  <td>Oc</td>
+  <td>Men</td>
+</tr>
+<tr>
+  <td>Caban</td>
+  <td>Ik</td>
+  <td>Manik</td>
+  <td>Eb</td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td>Cauac</td>
+  <td>Kan</td>
+  <td>Muluc</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td>Cib</td>
+  <td>Ymix</td>
+  <td>Cimi</td>
+</tr>
+<tr>
+  <td>Lamat</td>
+  <td>Been</td>
+  <td>Ezanab</td>
+  <td>Akbal.</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_291" id="Page_291">[291]</a></span>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&#8217;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&mdash;which
+appears to be in accordance with the plan of these series&mdash;the sum is
+2,340 days, or nine cycles of 260 days <span class="nowrap">each.<a name="FNanchor_291-1_25" id="FNanchor_291-1_25"></a><a href="#Footnote_291-1_25" class="fnanchor">291-1</a></span></p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>Attached to the day column in Plate 29<i>c</i> and running into 30<i>c</i> is a
+series which presents a difficulty I am unable to explain. The days and
+numerals in this case are as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 32 summary">
+<tr>
+  <td class="tdc">III</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Cauac</td>
+  <td rowspan="2"><span class="double">}</span></td>
+  <td rowspan="2">16, VI; 16, IX; 16, XII; 16, (?)</td>
+</tr>
+<tr>
+  <td>Kan</td>
+</tr>
+<tr>
+  <td>Muluc</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p>The red numeral over the day column is very distinctly III in
+Kingsborough&#8217;s work, but is II, though somewhat blurred, in F&ouml;rstemann&#8217;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&#8217;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 <a name="corr3" id="corr3"></a><ins class="correction" title="and">and and</ins> indicates that the variation from the
+usual rule must be accounted for in some other way.</p>
+
+<p><span class='pagenum'><a name="Page_292" id="Page_292">[292]</a></span>In reference to this series, Dr. F&ouml;<span class="nowrap">rstemann<a name="FNanchor_292-1_26" id="FNanchor_292-1_26"></a><a href="#Footnote_292-1_26" class="fnanchor">292-1</a></span> remarks:</p>
+
+<div class="blockquot"><p>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 &times; 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.</p></div>
+
+<p>Turning to the Manuscript Troano, Plate XXVIII*<i>b</i>, 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&#8217;s fac simile are XI; 20, 12, IV; 9,
+XIII; 10, X; 13, XI.</p>
+
+<p>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 <i>one</i> 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*<i>b</i> 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.</p>
+
+<p>It is proper to state that on the other hand there is another four day
+column on Plate XXXII*<i>a</i> of the last mentioned codex, the days of which
+are precisely the same as those on Plate 29<i>c</i> 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.</p>
+
+<p>Going back to the series on Plate 29<i>c</i> 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&mdash;in the superscription&mdash;in
+each of the four compartments through which<span class='pagenum'><a name="Page_293" id="Page_293">[293]</a></span> 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 &amp;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.</p>
+
+<p>Running through the middle division of Plates 30 and 31 is this series:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Middle division Plates 30 and 31">
+<tr>
+  <td>3,</td>
+  <td>VIII</td>
+  <td rowspan="2">;</td>
+  <td>3,</td>
+  <td>VIII</td>
+  <td rowspan="2">;</td>
+  <td>3,</td>
+  <td>VIII</td>
+  <td rowspan="2">;</td>
+  <td>3,</td>
+  <td>VIII</td>
+</tr>
+<tr>
+  <td>5,</td>
+  <td>Oc</td>
+  <td>5,</td>
+  <td>Men</td>
+  <td>5,</td>
+  <td>Ahau</td>
+  <td>5,</td>
+  <td>Chicchan.</td>
+</tr>
+</table>
+
+<p>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&mdash;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.</p>
+
+<p>Dr. F&ouml;rstemann says in regard to this <span class="nowrap">line:<a name="FNanchor_293-1_27" id="FNanchor_293-1_27"></a><a href="#Footnote_293-1_27" class="fnanchor">293-1</a></span></p>
+
+<div class="blockquot"><p>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 &times; 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 &times; 65 is again the well
+known period of 260 days.</p></div>
+
+<p>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. F&ouml;rstemann, 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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 3">
+<tr>
+  <td style="padding-right: 1.5em;">(?)</td>
+  <td style="padding-right: 4em;">(?)</td>
+  <td class="padr1"> 4,</td>
+  <td style="padding-right: 4em;">V(?)</td>
+  <td>15,</td>
+  <td style="padding-left: 1.5em;">XIII</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td colspan="2" class="tdc" style="padding-right: 4em;">I</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td colspan="2">Ahau</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>8,</td>
+  <td>XIII</td>
+  <td colspan="2">Eb</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td colspan="2">Kan</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td colspan="2">Cib</td>
+  <td>&nbsp;</td>
+  <td style="padding-left: 1.5em;">14 (?)</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td colspan="2">Lamat</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_294" id="Page_294">[294]</a></span>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:</p>
+
+<p>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.</p>
+
+<p>This is repeated, because on turning to Dr. F&ouml;rstemann&#8217;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 &#8220;9&#8221; 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.</p>
+
+<p>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<span class='pagenum'><a name="Page_295" id="Page_295">[295]</a></span> of the series, which can
+be obtained from Plates 49 and 50 of the photographic copy.</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plates 46">
+<tr>
+  <td colspan="2"><i>Plate</i> 46:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdr">III</td>
+  <td>Cib.</td>
+  <td class="tdr">II</td>
+  <td>Cimi.</td>
+  <td class="tdr">V</td>
+  <td>Cib.</td>
+  <td class="tdr">XIII</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">XI</td>
+  <td>Cib.</td>
+  <td class="tdr">X</td>
+  <td>Cimi.</td>
+  <td class="tdr">XIII</td>
+  <td>Cib.</td>
+  <td class="tdr">VIII</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">VI</td>
+  <td>Cib.</td>
+  <td class="tdr">V</td>
+  <td>Cimi.</td>
+  <td class="tdr">VIII</td>
+  <td>Cib.</td>
+  <td class="tdr">III</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">I</td>
+  <td>Cib.</td>
+  <td class="tdr">XIII</td>
+  <td>Cimi.</td>
+  <td class="tdr">III</td>
+  <td>Cib.</td>
+  <td class="tdr">XI</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">IX</td>
+  <td>Cib.</td>
+  <td class="tdr">VIII</td>
+  <td>Cimi.</td>
+  <td class="tdr">XI</td>
+  <td>Cib.</td>
+  <td class="tdr">VI</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td>Cib.</td>
+  <td class="tdr">III</td>
+  <td>Cimi.</td>
+  <td class="tdr">VI</td>
+  <td>Cib.</td>
+  <td class="tdr">I</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">XII</td>
+  <td>Cib.</td>
+  <td class="tdr">XI</td>
+  <td>Cimi.</td>
+  <td class="tdr">I</td>
+  <td>Cib.</td>
+  <td class="tdr">IX</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">VII</td>
+  <td>Cib.</td>
+  <td class="tdr">VI</td>
+  <td>Cimi.</td>
+  <td class="tdr">IX</td>
+  <td>Cib.</td>
+  <td class="tdr">IV</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">II</td>
+  <td>Cib.</td>
+  <td class="tdr">I</td>
+  <td>Cimi.</td>
+  <td class="tdr">IV</td>
+  <td>Cib.</td>
+  <td class="tdr">XII</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">X</td>
+  <td>Cib.</td>
+  <td class="tdr">IX</td>
+  <td>Cimi.</td>
+  <td class="tdr">XII</td>
+  <td>Cib.</td>
+  <td class="tdr">VII</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">V</td>
+  <td>Cib.</td>
+  <td class="tdr">IV</td>
+  <td>Cimi.</td>
+  <td class="tdr">VII</td>
+  <td>Cib.</td>
+  <td class="tdr">II</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">XIII</td>
+  <td>Cib.</td>
+  <td class="tdr">XII</td>
+  <td>Cimi.</td>
+  <td class="tdr">II</td>
+  <td>Cib.</td>
+  <td class="tdr">X</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="tdr">VIII</td>
+  <td>Cib.</td>
+  <td class="tdr">VII</td>
+  <td>Cimi.</td>
+  <td class="tdr">X</td>
+  <td>Cib.</td>
+  <td class="tdr">V</td>
+  <td>Kan.</td>
+</tr>
+</table>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" style="margin-top: 1.5em;" summary="Plate 47">
+<tr>
+  <td colspan="2"><i>Plate</i> 47:</td>
+</tr>
+<tr>
+  <td class="tdr">II</td>
+  <td>Ahau.</td>
+  <td class="tdr">I</td>
+  <td>Oc.</td>
+  <td class="tdr">IV</td>
+  <td>Ahau.</td>
+  <td class="tdr">XII</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">X</td>
+  <td>Ahau.</td>
+  <td class="tdr">IX</td>
+  <td>Oc.</td>
+  <td class="tdr">XII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VII</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">V</td>
+  <td>Ahau.</td>
+  <td class="tdr">IV</td>
+  <td>Oc.</td>
+  <td class="tdr">VII</td>
+  <td>Ahau.</td>
+  <td class="tdr">II</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">XIII</td>
+  <td>Ahau.</td>
+  <td class="tdr">XII</td>
+  <td>Oc.</td>
+  <td class="tdr">II</td>
+  <td>Ahau.</td>
+  <td class="tdr">X</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">VIII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VII</td>
+  <td>Oc.</td>
+  <td class="tdr">X</td>
+  <td>Ahau.</td>
+  <td class="tdr">V</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">III</td>
+  <td>Ahau.</td>
+  <td class="tdr">II</td>
+  <td>Oc.</td>
+  <td class="tdr">V</td>
+  <td>Ahau.</td>
+  <td class="tdr">XIII</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">XI</td>
+  <td>Ahau.</td>
+  <td class="tdr">X</td>
+  <td>Oc.</td>
+  <td class="tdr">XIII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VIII</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">VI</td>
+  <td>Ahau.</td>
+  <td class="tdr">V</td>
+  <td>Oc.</td>
+  <td class="tdr">VIII</td>
+  <td>Ahau.</td>
+  <td class="tdr">III</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">I</td>
+  <td>Ahau.</td>
+  <td class="tdr">XIII</td>
+  <td>Oc.</td>
+  <td class="tdr">III</td>
+  <td>Ahau.</td>
+  <td class="tdr">XI</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">IX</td>
+  <td>Ahau.</td>
+  <td class="tdr">VIII</td>
+  <td>Oc.</td>
+  <td class="tdr">XI</td>
+  <td>Ahau.</td>
+  <td class="tdr">VI</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td>Ahau.</td>
+  <td class="tdr">III</td>
+  <td>Oc.</td>
+  <td class="tdr">VI</td>
+  <td>Ahau.</td>
+  <td class="tdr">I</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">XII</td>
+  <td>Ahau.</td>
+  <td class="tdr">XI</td>
+  <td>Oc.</td>
+  <td class="tdr">I</td>
+  <td>Ahau.</td>
+  <td class="tdr">IX</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td class="tdr">VII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VI</td>
+  <td>Oc.</td>
+  <td class="tdr">IX</td>
+  <td>Ahau.</td>
+  <td class="tdr">IV</td>
+  <td>Lamat.</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 48">
+<tr>
+  <td colspan="2"><i>Plate</i> 48:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdr">I</td>
+  <td>Kan.</td>
+  <td class="tdr">XIII</td>
+  <td>Ix.</td>
+  <td class="tdr">III</td>
+  <td>Kan.</td>
+  <td class="tdr">XI</td>
+  <td>Eb.</td>
+</tr>
+<tr>
+  <td class="tdr"><a name="corr4" id="corr4"></a><ins class="correction" title="This * was missing in the original publication">*</ins></td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+</tr>
+<tr>
+  <td class="tdr">VI</td>
+  <td>Kan.</td>
+  <td class="tdr">V</td>
+  <td>Ix.</td>
+  <td class="tdr">VIII</td>
+  <td>Kan.</td>
+  <td class="tdr">III</td>
+  <td>Eb.</td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top: 1.5em;"><i>Plate</i> 49:</td>
+</tr>
+<tr>
+  <td class="tdr">XIII</td>
+  <td>Lamat.</td>
+  <td class="tdr">XII</td>
+  <td>Ezanab.</td>
+  <td class="tdr">II</td>
+  <td>Lamat.</td>
+  <td class="tdr">X</td>
+  <td>Cib.</td>
+</tr>
+<tr>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+</tr>
+<tr>
+  <td class="tdr">V</td>
+  <td>Lamat.</td>
+  <td class="tdr">IV</td>
+  <td>Ezanab.</td>
+  <td class="tdr">VII</td>
+  <td>Lamat.</td>
+  <td class="tdr">II</td>
+  <td>Cib.</td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top: 1.5em;"><i>Plate</i> 50:</td>
+</tr>
+<tr>
+  <td class="tdr">XII</td>
+  <td>Eb.</td>
+  <td class="tdr">XI</td>
+  <td>Ik.</td>
+  <td class="tdr">I</td>
+  <td style="width: 13%">Eb.</td>
+  <td class="tdr">IX</td>
+  <td>Ahau.</td>
+</tr>
+<tr>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+  <td class="tdr">*</td>
+  <td>*</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td>Eb.</td>
+  <td class="tdr">III</td>
+  <td>Ik.</td>
+  <td class="tdr">VI</td>
+  <td>Eb.</td>
+  <td class="tdr">I</td>
+  <td>Ahau.</td>
+</tr>
+</table>
+
+<p>A careful examination of these groups will bring to light the following
+relations of the numbers, days, columns, and series to one another:</p>
+
+<p>The numerals of any one column, counting downwards, differ from<span class='pagenum'><a name="Page_296" id="Page_296">[296]</a></span> 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.</p>
+
+<p>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.</p>
+
+<p>In order to illustrate this we will run through the lowest line of each
+series, taking them in the order of the <span class="nowrap">pages.<a name="FNanchor_296-1_28" id="FNanchor_296-1_28"></a><a href="#Footnote_296-1_28" class="fnanchor">296-1</a></span></p>
+
+<p>These are as follows:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plates 46-50">
+<tr>
+  <td><i>Plate</i> 46:</td>
+  <td class="tdr">VIII</td>
+  <td>Cib.</td>
+  <td class="tdr">VII</td>
+  <td>Cimi.</td>
+  <td class="tdr">X</td>
+  <td>Cib.</td>
+  <td class="tdr">V</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td><i>Plate</i> 47:</td>
+  <td class="tdr">VII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VI</td>
+  <td>Oc.</td>
+  <td class="tdr">IX</td>
+  <td>Ahau.</td>
+  <td class="tdr">IV</td>
+  <td>Lamat.</td>
+</tr>
+<tr>
+  <td><i>Plate</i> 48:</td>
+  <td class="tdr">VI</td>
+  <td>Kan.</td>
+  <td class="tdr">V</td>
+  <td>Ix.</td>
+  <td class="tdr">VIII</td>
+  <td>Kan.</td>
+  <td class="tdr">III</td>
+  <td>Eb.</td>
+</tr>
+<tr>
+  <td><i>Plate</i> 49:</td>
+  <td class="tdr">V</td>
+  <td>Lamat.</td>
+  <td class="tdr">IV</td>
+  <td>Ezanab.</td>
+  <td class="tdr">VII</td>
+  <td>Lamat.</td>
+  <td class="tdr">II</td>
+  <td>Cib.</td>
+</tr>
+<tr>
+  <td><i>Plate</i> 50:</td>
+  <td class="tdr">IV</td>
+  <td>Eb.</td>
+  <td class="tdr">III</td>
+  <td>Ik.</td>
+  <td class="tdr">VI</td>
+  <td>Eb.</td>
+  <td class="tdr">I</td>
+  <td>Ahau.</td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 177px;">
+<a name="Fig_362" id="Fig_362"></a><a href="images/image13-full.png"><img src="images/image13.png" width="177" height="377" alt="Fig 362. Copy of Plate 50, Dresden Codex." title="Fig 362. Copy of Plate 50, Dresden Codex." /></a>
+<a name="corr5" id="corr5"></a><span class="caption"><ins class="correction" title="FIG."><span class="smcap">Fig</span></ins> 362. Copy of Plate 50, Dresden Codex.</span>
+</div>
+
+<p>By counting on the calendar (our <a href="#Table_II">Table II</a>), 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&mdash;that is to say, in the same vertical lines as the day
+columns&mdash;two lines of red numerals. It is impossible to determine these
+in Kingsborough&#8217;s copy (except on Plate 50), but they can readily be made
+out on the<span class='pagenum'><a name="Page_297" id="Page_297">[297]</a><br /><a name="Page_298" id="Page_298">[298]</a></span> photographed plates. (See the copy of Plate 50, given in
+<a href="#Fig_362">Fig. 362</a>.) Those on a single plate are as follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 50">
+<tr>
+  <td rowspan="2"><span class="double">{</span></td>
+  <td class="tdr">XI,</td>
+  <td class="tdr">IV,</td>
+  <td class="tdr">XII,</td>
+  <td class="tdr">0,</td>
+</tr>
+<tr>
+  <td class="tdr">XVI,</td>
+  <td class="tdr">X,</td>
+  <td class="tdr">X,</td>
+  <td class="tdr">VIII.</td>
+</tr>
+</table>
+
+<p>The 0 here represents a red, diamond shaped symbol.</p>
+
+<p>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 F&ouml;rstemann.</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 46">
+<tr>
+  <td colspan="2"><i>Plate</i> 46:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">VIII Cib.</td>
+  <td class="tdc">VII Cimi.</td>
+  <td class="tdc">X Cib.</td>
+  <td class="tdc">V Kan.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdc">1</td>
+  <td class="tdc">1</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">11</td>
+  <td class="tdc">16</td>
+  <td class="tdc">10</td>
+  <td class="tdc">11</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">16</td>
+  <td class="tdc">6</td>
+  <td class="tdc">16</td>
+  <td class="tdc">4</td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top: 1.5em;"><i>Plate</i> 47:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">VII Ahau.</td>
+  <td class="tdc">VI Oc.</td>
+  <td class="tdc">IX Ahau.</td>
+  <td class="tdc">IV Lamat.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">2</td>
+  <td class="tdc">2</td>
+  <td class="tdc">3</td>
+  <td class="tdc">3</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">5</td>
+  <td class="tdc">9</td>
+  <td class="tdc">4</td>
+  <td class="tdc">4</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="tdc">10</td>
+  <td class="tdc">0</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top:1.5em;"><span class='pagenum'><a name="Page_299" id="Page_299">[299]</a></span><i>Plate</i> 48:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">VI Kan.</td>
+  <td class="tdc">V Ix.</td>
+  <td class="tdc">III Kan.</td>
+  <td class="tdc">III Eb.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">3</td>
+  <td class="tdc">4</td>
+  <td class="tdc">4</td>
+  <td class="tdc">4</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">16</td>
+  <td class="tdc">2</td>
+  <td class="tdc">15</td>
+  <td class="tdc">15</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">3(?)</td>
+  <td class="tdc">14</td>
+  <td class="tdc">4</td>
+  <td class="tdc">12</td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top: 1.5em;"><i>Plate</i> 49:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">V Lamat.</td>
+  <td class="tdc">IV Ezanab.</td>
+  <td class="tdc">VII Lamat.</td>
+  <td class="tdc">II Cib.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">5</td>
+  <td class="tdc">5</td>
+  <td class="tdc">6</td>
+  <td class="tdc">6</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">9</td>
+  <td class="tdc">13</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">8</td>
+  <td class="tdc">18</td>
+  <td class="tdc">8</td>
+  <td class="tdc">16</td>
+</tr>
+<tr>
+  <td colspan="2" style="margin-top: 1.5em;"><i>Plate</i> 50:</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">IV Eb.</td>
+  <td class="tdc">III Ik.</td>
+  <td class="tdc">VI Eb.</td>
+  <td class="tdc">1 Ahau.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">7</td>
+  <td class="tdc">7</td>
+  <td class="tdc">8</td>
+  <td class="tdc">8</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">3</td>
+  <td class="tdc">7</td>
+  <td class="tdc">1</td>
+  <td class="tdc">2</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">12</td>
+  <td class="tdc">2</td>
+  <td class="tdc">12</td>
+  <td class="tdc">0</td>
+</tr>
+</table>
+
+<p>In considering these horizontal lines it is to be understood that the
+series runs through the five pages, 46-50.</p>
+
+<p>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:</p>
+
+<table class="tuk"  border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Under VIII Cib, Plate 46.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>Under VII Cimi, Plate 46.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Under X Cib, Plate 46.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Under V Kan, Plate 46.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Under VII Ahau, Plate 47.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Under VI Oc, Plate 47.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr"><span class='pagenum'><a name="Page_300" id="Page_300">[300]</a></span>
+   3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Under IX Ahau, Plate 47.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Under IV Lamat, Plate 47.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td class="tdl"><a name="FNanchor_300-1_29" id="FNanchor_300-1_29"></a><a href="#Footnote_300-1_29" class="fnanchor">300-1</a></td>
+  <td>Under VI Kan, Plate 48.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Under V Ix, Plate 48.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Under VIII Kan, Plate 48.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Under III Eb, Plate 48.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Under V Lamat, Plate 49.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>Under IV Ezanab, Plate 49.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Under VII Lamat, Plate 49.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Under II Cib, Plate 49.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Under IV Eb, Plate 50.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Under III Ik, Plate 50.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Under VI Eb, Plate 50.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Under I Ahau, Plate 50.</td>
+</tr>
+</table>
+
+<p>The proof of the correctness of the theory advanced may, therefore, be
+considered conclusive, as it amounts, in fact, to a mathematical
+demonstration.</p>
+
+<p>Dr. F&ouml;rstemann, who considers these lines of black numbers, standing one
+above another, as representing different grades of units&mdash;thus, the
+lowest, single units; the second, units twenty-fold the lower; the third,
+eighteen-fold the second; the fourth, twenty-fold the third, &amp;c.&mdash;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.</p>
+
+<p>As all the discoveries mentioned herein were made previous to the receipt
+of Dr. F&ouml;rstemann&#8217;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<span class='pagenum'><a name="Page_301" id="Page_301">[301]</a></span> Dr. F&ouml;rstemann&#8217;s
+method is reserved for a future paper, as his work was not received until
+I was revising my notes for publication.</p>
+
+<p>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:</p>
+
+<p class="tabletitle"><a name="Table_III" id="Table_III"></a><span class="smcap">Table III.</span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table III">
+<tr>
+  <td class="padrright">1.</td>
+  <td class="padl">Ymix.</td>
+</tr>
+<tr>
+  <td class="padrright">2.</td>
+  <td class="padl">Ik.</td>
+</tr>
+<tr>
+  <td class="padrright">3.</td>
+  <td class="padl">Akbal.</td>
+</tr>
+<tr>
+  <td class="padrright">4.</td>
+  <td class="padl">Kan.</td>
+</tr>
+<tr>
+  <td class="padrright">5.</td>
+  <td class="padl">Chicchan.</td>
+</tr>
+<tr>
+  <td class="padrright">6.</td>
+  <td class="padl">Cimi.</td>
+</tr>
+<tr>
+  <td class="padrright">7.</td>
+  <td class="padl">Manik.</td>
+</tr>
+<tr>
+  <td class="padrright">8.</td>
+  <td class="padl">Lamat.</td>
+</tr>
+<tr>
+  <td class="padrright">9.</td>
+  <td class="padl">Muluc.</td>
+</tr>
+<tr>
+  <td class="padrright">10.</td>
+  <td class="padl">Oc.</td>
+</tr>
+<tr>
+  <td class="padrright">11.</td>
+  <td class="padl">Chuen.</td>
+</tr>
+<tr>
+  <td class="padrright">12.</td>
+  <td class="padl">Eb.</td>
+</tr>
+<tr>
+  <td class="padrright">13.</td>
+  <td class="padl">Been.</td>
+</tr>
+<tr>
+  <td class="padrright">14.</td>
+  <td class="padl">Ix.</td>
+</tr>
+<tr>
+  <td class="padrright">15.</td>
+  <td class="padl">Men.</td>
+</tr>
+<tr>
+  <td class="padrright">16.</td>
+  <td class="padl">Cib.</td>
+</tr>
+<tr>
+  <td class="padrright">17.</td>
+  <td class="padl">Caban.</td>
+</tr>
+<tr>
+  <td class="padrright">18.</td>
+  <td class="padl">Ezanab.</td>
+</tr>
+<tr>
+  <td class="padrright">19.</td>
+  <td class="padl">Cauac.</td>
+</tr>
+<tr>
+  <td class="padrright">20.</td>
+  <td class="padl">Ahau.</td>
+</tr>
+</table>
+
+<p>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 <a href="#Table_III">Table III</a>, 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:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 46">
+<tr>
+  <td class="tdc">Cib.</td>
+  <td class="tdc">Cimi.</td>
+  <td class="tdc">Cib.</td>
+  <td class="tdc">Kan.</td>
+</tr>
+<tr>
+  <td class="tdc">16</td>
+  <td class="tdc">6</td>
+  <td class="tdc">16</td>
+  <td class="tdc">4</td>
+</tr>
+</table>
+
+<p>Referring to <a href="#Table_III">Table III</a> we see that Cib is the sixteenth day, Cimi the
+sixth, and Kan the fourth.</p>
+
+<p>The days and numbers of Plate 47 are:</p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Plate 47">
+<tr>
+  <td class="tdc">Ahau.</td>
+  <td class="tdc">Oc.</td>
+  <td class="tdc">Ahau.</td>
+  <td class="tdc">Lamat.</td>
+</tr>
+<tr>
+  <td class="tdc">0</td>
+  <td class="tdc">10</td>
+  <td class="tdc">0</td>
+  <td class="tdc">8</td>
+</tr>
+</table>
+
+<p>Ahau is the twentieth day&mdash;here is the diamond shaped symbol&mdash;Oc is the
+tenth, and Lamat the eighth, and so on to the end of the series on Plate
+50.</p>
+
+<p><span class='pagenum'><a name="Page_302" id="Page_302">[302]</a></span>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.</p>
+
+<p>First. It is easily seen by reference to the calendar (<a href="#Table_II">Table II</a>) 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 &#8220;title page&#8221;
+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.</p>
+
+<p>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 (<a href="#Table_II">Table
+II</a>). 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.</p>
+
+<p>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.</p>
+
+<p>Dr. F&ouml;rstemann 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<span class='pagenum'><a name="Page_303" id="Page_303">[303]</a></span> 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.</p>
+
+<p>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, <a href="#Fig_362">Fig. 362</a>). 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.</p>
+
+<p>These months and days as given by Dr. F&ouml;rstemann are as follows, the
+positions of the lines as here given corresponding with those of the
+plates:</p>
+
+<p class="tabletitle"><a name="Table_IV" id="Table_IV"></a><span class="smcap">Table IV.</span>&mdash;<i>Table showing months and days.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table IV">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btl">Month.</td>
+  <td class="bt">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt">Day.</td>
+</tr>
+<tr>
+  <td>Plate 46</td>
+  <td class="btlright">7</td>
+  <td class="btright">4</td>
+  <td class="btlright">11</td>
+  <td class="btright">14</td>
+  <td class="btlright">5</td>
+  <td class="btright">19</td>
+  <td class="btlright">6</td>
+  <td class="btright">7</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">8</td>
+  <td class="blright">15</td>
+  <td class="tdr">18</td>
+  <td class="blright">10</td>
+  <td class="tdr">4</td>
+  <td class="blright">10</td>
+  <td class="tdr">12</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">1</td>
+  <td class="tdr">14</td>
+  <td class="blright">6</td>
+  <td class="tdr">4</td>
+  <td class="blright">18</td>
+  <td class="tdr">14</td>
+  <td class="blright">1</td>
+  <td class="tdr">2</td>
+</tr>
+<tr>
+  <td>Plate 47</td>
+  <td class="blright">18</td>
+  <td class="tdr">3</td>
+  <td class="blright">4</td>
+  <td class="tdr">8</td>
+  <td class="blright">16</td>
+  <td class="tdr">18</td>
+  <td class="blright">17</td>
+  <td class="tdr">6</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">3</td>
+  <td class="blright">8</td>
+  <td class="tdr">13</td>
+  <td class="blright">2</td>
+  <td class="tdr">18</td>
+  <td class="blright">3(not 2)</td>
+  <td class="tdr">6</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">10</td>
+  <td class="tdr">10</td>
+  <td class="blright">15</td>
+  <td class="tdr">3</td>
+  <td class="blright">9</td>
+  <td class="tdr">8</td>
+  <td class="blright">9</td>
+  <td class="tdr">16</td>
+</tr>
+<tr>
+  <td>Plate 48</td>
+  <td class="blright">10</td>
+  <td class="tdr">17</td>
+  <td class="blright">15</td>
+  <td class="tdr">7</td>
+  <td class="blright">9</td>
+  <td class="tdr">12</td>
+  <td class="blright">10</td>
+  <td class="tdr">20</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">15</td>
+  <td class="tdr">2</td>
+  <td class="blright">1</td>
+  <td class="tdr">7</td>
+  <td class="blright">13</td>
+  <td class="tdr">17</td>
+  <td class="blright">14</td>
+  <td class="tdr">5</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">3</td>
+  <td class="tdr">7</td>
+  <td class="blright">7</td>
+  <td class="tdr">17</td>
+  <td class="blright">2</td>
+  <td class="tdr">2</td>
+  <td class="blright">2</td>
+  <td class="tdr">10</td>
+</tr>
+<tr>
+  <td>Plate 49</td>
+  <td class="blright">3</td>
+  <td class="tdr">11</td>
+  <td class="blright">8</td>
+  <td class="tdr">1</td>
+  <td class="blright">2</td>
+  <td class="tdr">6</td>
+  <td class="blright">2</td>
+  <td class="tdr">14</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">7</td>
+  <td class="tdr">16</td>
+  <td class="blright">12</td>
+  <td class="tdr">6</td>
+  <td class="blright">6</td>
+  <td class="tdr">11</td>
+  <td class="blright">6</td>
+  <td class="tdr">19</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">14</td>
+  <td class="tdr">6</td>
+  <td class="blright">18</td>
+  <td class="tdr">16</td>
+  <td class="blright">13</td>
+  <td class="tdr">1</td>
+  <td class="blright">13</td>
+  <td class="tdr">9</td>
+</tr>
+<tr>
+  <td>Plate 50</td>
+  <td class="blright">14</td>
+  <td class="tdr">10</td>
+  <td class="blright">18</td>
+  <td class="tdr">20</td>
+  <td class="blright">13</td>
+  <td class="tdr">5</td>
+  <td class="blright">13</td>
+  <td class="tdr">13</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">18</td>
+  <td class="tdr">15</td>
+  <td class="blright">5</td>
+  <td class="tdr">20</td>
+  <td class="blright">17</td>
+  <td class="tdr">10</td>
+  <td class="blright">17</td>
+  <td class="tdr">18</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">6</td>
+  <td class="bbright">20</td>
+  <td class="bblright">11</td>
+  <td class="bbright">10</td>
+  <td class="bblright">5</td>
+  <td class="bbright">15</td>
+  <td class="bblright">6</td>
+  <td class="bbright">3</td>
+</tr>
+</table>
+
+<p>An examination of the plates will show that Dr. F&ouml;rstemann 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<span class='pagenum'><a name="Page_304" id="Page_304">[304]</a></span> that the month was completed. Although
+probably correct in this conclusion, the question will arise, Does the
+symbol in such cases denote the <i>month completed</i> or the <i>month reached?</i></p>
+
+<p>The intervals between these dates are as follows, the left hand column
+being those between the first and second columns of F&ouml;rstemann&#8217;s list
+(our <a href="#Table_IV">Table IV</a>), 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:</p>
+
+<p class="tabletitle"><a name="Table_V" id="Table_V"></a><span class="smcap">Table V.</span>&mdash;<i>Table showing intervals between dates.</i></p>
+
+<table border="0" width="60%" cellpadding="0" cellspacing="0" summary="Table V">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btl">Month.</td>
+  <td class="bt" colspan="2">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt" colspan="2">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt" colspan="2">Day.</td>
+  <td class="btl">Month.</td>
+  <td class="bt" colspan="2">Day.</td>
+</tr>
+<tr>
+  <td class="bt">Plate 46</td>
+  <td class="btlright">4</td>
+  <td class="btright">10</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlright">12</td>
+  <td class="btright">5</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlright">0</td>
+  <td class="btright">8</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlright">11</td>
+  <td class="btright">16</td>
+  <td class="bt">&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">6</td>
+  <td style="padding-left: 0;"><i>b</i></td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">9</td>
+  <td class="tdr">8</td>
+  <td style="padding-left: 0;"><i>d</i></td>
+</tr>
+<tr>
+  <td>Plate 47</td>
+  <td class="blright">4</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td style="padding-left: 0;"><i>c</i></td>
+  <td class="blright">11</td>
+  <td class="tdr">16</td>
+  <td style="padding-left: 0;"><i>e</i></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">13</td>
+  <td style="padding-left: 0;"><i>a</i></td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Plate 48</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Plate 49</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">16</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>Plate 50</td>
+  <td class="blright">4</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blright">4</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td class="blright">12</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td class="blright">0</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td class="blright">11</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">4</td>
+  <td class="bbright">10</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">12</td>
+  <td class="bbright">5</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">0</td>
+  <td class="bbright">8</td>
+  <td class="bb">&nbsp;</td>
+  <td class="bblright">12</td>
+  <td class="bbright">11</td>
+  <td class="bb" style="padding-left: 0;"><i>g</i></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>That there are some errors is quite clear; for instance, the variation at
+<i>a</i> arises from the fact that Dr. F&ouml;rstemann 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 <i>d</i> 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. F&ouml;rstemann has mistaken the month, would
+necessitate a change of the remainder of the series given in this line.
+The interval at <i>c</i>, according to the figure given by Dr. F&ouml;rstemann,
+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.</p>
+
+<p>When these evident errors are corrected the series of intervals show<span class='pagenum'><a name="Page_305" id="Page_305">[305]</a></span>
+very clearly a system and periodicity depending on the day column series
+in the upper part of the pages. In the first column (<a href="#Table_V">Table V</a>) 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&mdash;4 months, 10 days. This will be understood by
+examining our calendar (<a href="#Table_II">Table II</a>). 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 <a href="#Table_II">Table II</a>.
+This skip of five days is also apparent in the second and fourth columns
+of differences (<a href="#Table_V">Table V</a>). Whether Dr. F&ouml;rstemann 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.</p>
+
+<p>Running through the upper division of Plates 53 to 58 and continued
+through the lower division of Plates 51 to 58&mdash;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&mdash;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.</p>
+
+<p>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. <a href="#Fig_363">363-370</a>, 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.</p>
+
+<p><span class='pagenum'><a name="Page_306" id="Page_306">[306]</a></span></p>
+
+<div class="figcenter" style="width: 166px;">
+<a name="Fig_363" id="Fig_363"></a><a href="images/image14-full.png"><img src="images/image14.png" width="166" height="391" alt="Fig. 363. Copy of Plate 51, Dresden Codex." title="Fig. 363. Copy of Plate 51, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 363. Copy of Plate 51, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_307" id="Page_307">[307]</a></span></p>
+
+<div class="figcenter" style="width: 171px;">
+<a name="Fig_364" id="Fig_364"></a><a href="images/image15-full.png"><img src="images/image15.png" width="171" height="393" alt="Fig. 364. Copy of Plate 52, Dresden Codex." title="Fig. 364. Copy of Plate 52, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 364. Copy of Plate 52, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_308" id="Page_308">[308]</a></span></p>
+
+<div class="figcenter" style="width: 172px;">
+<a name="Fig_365" id="Fig_365"></a><a href="images/image16-full.png"><img src="images/image16.png" width="172" height="388" alt="Fig. 365. Copy of Plate 55, Dresden Codex." title="Fig. 365. Copy of Plate 55, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 365. Copy of Plate 55, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_309" id="Page_309">[309]</a></span></p>
+
+<div class="figcenter" style="width: 177px;">
+<a name="Fig_366" id="Fig_366"></a><a href="images/image17-full.png"><img src="images/image17.png" width="177" height="392" alt="Fig. 366. Copy of Plate 54, Dresden Codex." title="Fig. 366. Copy of Plate 54, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 366. Copy of Plate 54, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_310" id="Page_310">[310]</a></span></p>
+
+<div class="figcenter" style="width: 181px;">
+<a name="Fig_367" id="Fig_367"></a><a href="images/image18-full.png"><img src="images/image18.png" width="181" height="390" alt="Fig. 367. Copy of Plate 55, Dresden Codex." title="Fig. 367. Copy of Plate 55, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 367. Copy of Plate 55, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_311" id="Page_311">[311]</a></span></p>
+
+<div class="figcenter" style="width: 179px;">
+<a name="Fig_368" id="Fig_368"></a><a href="images/image19-full.png"><img src="images/image19.png" width="179" height="400" alt="Fig. 368. Copy of Plate 56, Dresden Codex." title="Fig. 368. Copy of Plate 56, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 368. Copy of Plate 56, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_312" id="Page_312">[312]</a></span></p>
+
+<div class="figcenter" style="width: 180px;">
+<a name="Fig_369" id="Fig_369"></a><a href="images/image20-full.png"><img src="images/image20.png" width="180" height="397" alt="Fig. 369. Copy of Plate 57, Dresden Codex." title="Fig. 369. Copy of Plate 57, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 369. Copy of Plate 57, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_313" id="Page_313">[313]</a></span></p>
+
+<div class="figcenter" style="width: 173px;">
+<a name="Fig_370" id="Fig_370"></a><a href="images/image21-full.png"><img src="images/image21.png" width="173" height="390" alt="Fig. 370. Copy of Plate 58, Dresden Codex." title="Fig. 370. Copy of Plate 58, Dresden Codex." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 370. Copy of Plate 58, Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_314" id="Page_314">[314]</a></span>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.</p>
+
+<p class="tabletitle"><a name="Table_VI" id="Table_VI"></a><span class="smcap">Table VI.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 51<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table VI">
+<tr>
+  <td class="btcent" colspan="2">14</td>
+  <td class="btlcent" colspan="2">15</td>
+  <td class="btlcent" colspan="2">15</td>
+  <td class="btlcent" colspan="2">16</td>
+  <td class="btlcent" colspan="2">16</td>
+  <td class="btlcent" colspan="2">17</td>
+</tr>
+<tr>
+  <td class="tdc" colspan="2">16</td>
+  <td class="blcent" colspan="2">7</td>
+  <td class="blcent" colspan="2">16</td>
+  <td class="blcent" colspan="2">7</td>
+  <td class="blcent" colspan="2">16</td>
+  <td class="blcent" colspan="2">5</td>
+</tr>
+<tr>
+  <td class="tdc" colspan="2">14</td>
+  <td class="blcent" colspan="2">11</td>
+  <td class="blcent" colspan="2">8</td>
+  <td class="blcent" colspan="2">5</td>
+  <td class="blcent" colspan="2">2</td>
+  <td class="blcent" colspan="2">10</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td>Ik.</td>
+  <td class="blright">XII</td>
+  <td>Cauac.</td>
+  <td class="blright">VII</td>
+  <td>Cib.</td>
+  <td class="blright">II</td>
+  <td>Been.</td>
+  <td class="blright">X</td>
+  <td>Oc.</td>
+  <td class="blright">II</td>
+  <td>Ezanab.</td>
+</tr>
+<tr>
+  <td class="tdr">V</td>
+  <td>Akbal.</td>
+  <td class="blright">XIII</td>
+  <td>Ahau.</td>
+  <td class="blright">VIII</td>
+  <td>Caban.</td>
+  <td class="blright">III</td>
+  <td>Ix</td>
+  <td class="blright">XI</td>
+  <td>Chuen</td>
+  <td class="blright">III</td>
+  <td>Cauac.</td>
+</tr>
+<tr>
+  <td class="tdr">VI</td>
+  <td>Kan.</td>
+  <td class="blright">I</td>
+  <td>Ymix.</td>
+  <td class="blright">IX</td>
+  <td>Ezanab.</td>
+  <td class="blright">IV</td>
+  <td>Men.</td>
+  <td class="blright">XII</td>
+  <td>Eb.</td>
+  <td class="blright">IV</td>
+  <td><span class="nowrap">Ahau.<a name="FNanchor_VI-1_1" id="FNanchor_VI-1_1"></a><a href="#Footnote_VI-1_1" class="fnanchor">VI-1</a></span></td>
+</tr>
+<tr>
+  <td class="tdc" colspan="2">VIII</td>
+  <td class="blcent" colspan="2">VIII</td>
+  <td class="blcent" colspan="2">VIII</td>
+  <td class="blcent" colspan="2">VIII</td>
+  <td class="blcent" colspan="2">VIII</td>
+  <td class="blcent" colspan="2">VII</td>
+</tr>
+<tr>
+  <td class="bbcent" colspan="2">17</td>
+  <td class="bblcent" colspan="2">17</td>
+  <td class="bblcent" colspan="2">17</td>
+  <td class="bblcent" colspan="2">17</td>
+  <td class="bblcent" colspan="2">17</td>
+  <td class="bblcent" colspan="2">8</td>
+</tr>
+<tr>
+  <td colspan="12" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_VI-1_1" id="Footnote_VI-1_1"></a><a href="#FNanchor_VI-1_1"><span class="label">VI-1</span></a> The symbol in this case is that of Been, but this is a
+manifest error, as Ahau follows Cauac.</td>
+</tr>
+</table>
+
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_VII" id="Table_VII"></a><span class="smcap">Table VII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 52<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table VI">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">      17</td>
+  <td class="btlcent">    18</td>
+  <td class="btlcent">   18</td>
+  <td class="btlcent">   19</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blcent">      14</td>
+  <td class="blcent">     5</td>
+  <td class="blcent">   14</td>
+  <td class="blcent">    4</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blcent">       8</td>
+  <td class="blcent">     5</td>
+  <td class="blcent">    2</td>
+  <td class="blcent">   19</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blcent">    XI Cib.</td>
+  <td class="blcent">  VI Been.</td>
+  <td class="blcent">  I Oc.</td>
+  <td class="blcent">IX Manik.</td>
+</tr>
+<tr>
+  <td style="padding-left: 5em; padding-right: 5em;">  [Picture.]</td>
+  <td class="blcent">   XII Caban.</td>
+  <td class="blcent"> VII Ix.</td>
+  <td class="blcent"> II Chuen.</td>
+  <td class="blcent"> X Lamat.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blcent">  XIII Ezanab.</td>
+  <td class="blcent">VIII Men.</td>
+  <td class="blcent">III Eb.</td>
+  <td class="blcent">XI Muluc.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="blcent">      VIII</td>
+  <td class="blcent">   VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bblcent">17? (<span class="nowrap">18)<a name="FNanchor_VII-1_2" id="FNanchor_VII-1_2"></a><a href="#Footnote_VII-1_2" class="fnanchor">VII-1</a></span></td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+</tr>
+<tr>
+  <td colspan="5" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_VII-1_2" id="Footnote_VII-1_2"></a><a href="#FNanchor_VII-1_2"><span class="label">VII-1</span></a> The variation from the rule found here is explained a
+little further on.</td>
+</tr>
+</table>
+
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_VIII" id="Table_VIII"></a><span class="smcap">Table VIII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 53<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table VIII">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">       2</td>
+  <td class="btlcent">   2</td>
+</tr>
+<tr>
+  <td class="tdc">      7</td>
+  <td class="blcent">  17</td>
+  <td class="blcent">    7</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">     15</td>
+  <td class="blcent">  6</td>
+  <td class="blcent"> 15</td>
+</tr>
+<tr>
+  <td class="tdc">      17</td>
+  <td class="blcent">  18</td>
+  <td class="blcent">    2</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">14?(<span class="nowrap">19)<a name="FNanchor_VIII-1_3" id="FNanchor_VIII-1_3"></a><a href="#Footnote_VIII-1_3" class="fnanchor">VIII-1</a></span></td>
+  <td class="blcent"> 16</td>
+  <td class="blcent"> 13</td>
+</tr>
+<tr>
+  <td class="tdc">   VI Kan.</td>
+  <td class="blcent"> I Ymix.</td>
+  <td class="blcent"> VI Muluc.</td>
+  <td class="blcent">[Picture.]</td>
+  <td class="blcent">   I Cimi.</td>
+  <td class="blcent">IX Akbal.</td>
+  <td class="blcent">IV Ahau.</td>
+</tr>
+<tr>
+  <td class="tdc">  VII Chicchan.</td>
+  <td class="blcent">II Ik.</td>
+  <td class="blcent">VII Oc.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  II Manik.</td>
+  <td class="blcent">X Kan.</td>
+  <td class="blcent">V Ymix.</td>
+</tr>
+<tr>
+  <td class="tdc"> VIII Cimi.</td>
+  <td class="blcent">III Akbal.</td>
+  <td class="blcent">VIII Chuen.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent"> III Lamat.</td>
+  <td class="blcent">XI Chicchan.</td>
+  <td class="blcent">VI Ik.</td>
+</tr>
+<tr>
+  <td class="tdc">    VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">  VII</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">    VIII</td>
+  <td class="blcent">VIII</td>
+  <td class="blcent">VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">      17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">     8</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">      17</td>
+  <td class="bblcent">  17</td>
+  <td class="bblcent">17</td>
+</tr>
+<tr>
+  <td colspan="7" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_VIII-1_3" id="Footnote_VIII-1_3"></a><a href="#FNanchor_VIII-1_3"><span class="label">VIII-1</span></a> The 14 here is manifestly an error, one of the lines in
+the number symbol having been omitted; it should be 19.</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_IX" id="Table_IX"></a><span class="smcap">Table IX.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 53<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table IX">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">   1</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">     1</td>
+</tr>
+<tr>
+  <td class="tdc">   19</td>
+  <td class="blcent">  0</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   0</td>
+  <td class="blcent">    1</td>
+  <td class="blcent">    1</td>
+</tr>
+<tr>
+  <td class="tdc">   13</td>
+  <td class="blcent">  3</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  12</td>
+  <td class="blcent">    2</td>
+  <td class="blcent">   11</td>
+</tr>
+<tr>
+  <td class="tdc">   16</td>
+  <td class="blcent">  4</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   1</td>
+  <td class="blcent">   18</td>
+  <td class="blcent">   15</td>
+</tr>
+<tr>
+  <td class="tdc"> IV Kan.</td>
+  <td class="blcent">IX Eb.</td>
+  <td class="blcent">[Picture.]</td>
+  <td class="blcent">IV Muluc.</td>
+  <td class="blcent">XII Cimi.</td>
+  <td class="blcent">VII Akbal.</td>
+</tr>
+<tr>
+  <td class="tdc">  V Chicchan.</td>
+  <td class="blcent">X Been.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">V Oc.</td>
+  <td class="blcent">XIII Manik.</td>
+  <td class="blcent">VIII Kan.</td>
+</tr>
+<tr>
+  <td class="tdc"> VI Cimi.</td>
+  <td class="blcent">XI Ix.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">VI Chuen.</td>
+  <td class="blcent">  I Lamat.</td>
+  <td class="blcent"> IX Chicchan.</td>
+</tr>
+<tr>
+  <td class="tdc">  VIII</td>
+  <td class="blcent"> VII</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">    17</td>
+  <td class="bblcent">   8</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_315" id="Page_315">[315]</a></span></p>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_X" id="Table_X"></a><span class="smcap">Table X.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 54<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table X">
+<tr>
+  <td class="btcent">       3</td>
+  <td class="btlcent">     3</td>
+  <td class="btlcent">    4</td>
+  <td class="btlcent">     4</td>
+  <td class="btlcent">     5</td>
+  <td class="btlcent">     5</td>
+  <td class="btlcent">    6</td>
+</tr>
+<tr>
+  <td class="tdc">      6</td>
+  <td class="blcent">   15</td>
+  <td class="blcent">   6</td>
+  <td class="blcent">   15</td>
+  <td class="blcent">    5</td>
+  <td class="blcent">   10</td>
+  <td class="blcent">   4</td>
+</tr>
+<tr>
+  <td class="tdc">     11</td>
+  <td class="blcent">    8</td>
+  <td class="blcent">   5</td>
+  <td class="blcent">    5</td>
+  <td class="blcent">   19</td>
+  <td class="blcent">   16</td>
+  <td class="blcent">   4</td>
+</tr>
+<tr>
+  <td class="tdc"> XIII Ezanab.</td>
+  <td class="blcent">VIII Men.</td>
+  <td class="blcent">III Eb.</td>
+  <td class="blcent"> XI Muluc.</td>
+  <td class="blcent"> VI Cib.</td>
+  <td class="blcent"> I Akbal.</td>
+  <td class="blcent">VI Chuen.</td>
+</tr>
+<tr>
+  <td class="tdc">    I Cauac.</td>
+  <td class="blcent"> IX Cib.</td>
+  <td class="blcent">IV Been.</td>
+  <td class="blcent">XII Oc.</td>
+  <td class="blcent">VII Caban.</td>
+  <td class="blcent">II Kan.</td>
+  <td class="blcent">VII Eb.</td>
+</tr>
+<tr>
+  <td class="tdc">   II Ahau.</td>
+  <td class="blcent">  X Caban.</td>
+  <td class="blcent"> V Ix.</td>
+  <td class="blcent">XIII Chuen.</td>
+  <td class="blcent">VIII Ezanab.</td>
+  <td class="blcent">III Chicchan.</td>
+  <td class="blcent">VIII Been.</td>
+</tr>
+<tr>
+  <td class="tdc">    VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VII</td>
+</tr>
+<tr>
+  <td class="bbcent">      17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">     8</td>
+</tr>
+</table>
+
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XI" id="Table_XI"></a><span class="smcap">Table XI.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 54<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XI">
+<tr>
+  <td class="btcent">      1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">    1</td>
+</tr>
+<tr>
+  <td class="tdc">     2</td>
+  <td class="blcent">   2</td>
+  <td class="blcent">   3</td>
+  <td class="blcent">   3</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   4</td>
+</tr>
+<tr>
+  <td class="tdc">     2</td>
+  <td class="blcent">  11</td>
+  <td class="blcent">   2</td>
+  <td class="blcent">   9</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent" style="padding-left: 2em;">   <span class="nowrap">0<a name="FNanchor_XI-1_4" id="FNanchor_XI-1_4"></a><a href="#Footnote_XI-1_4" class="fnanchor">XI-1</a></span></td>
+</tr>
+<tr>
+  <td class="tdc">    12</td>
+  <td class="blcent">   9</td>
+  <td class="blcent">   6</td>
+  <td class="blcent">  14</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  11</td>
+</tr>
+<tr>
+  <td class="tdc">  II Ahau.</td>
+  <td class="blcent"> X Caban.</td>
+  <td class="blcent"> V Ix.</td>
+  <td class="blcent"> X Ik.</td>
+  <td class="blcent">[Picture]</td>
+  <td class="blcent"> V Cauac.</td>
+</tr>
+<tr>
+  <td class="tdc"> III Ymix.</td>
+  <td class="blcent">XI Ezanab.</td>
+  <td class="blcent">VI Men.</td>
+  <td class="blcent">XI Akbal.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">VI Ahau.</td>
+</tr>
+<tr>
+  <td class="tdc">  IV Ik.</td>
+  <td class="blcent">XII Cauac.</td>
+  <td class="blcent">VII Cib.</td>
+  <td class="blcent">XII Kan.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">VII Ymix.</td>
+</tr>
+<tr>
+  <td class="tdc">   VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VII</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent" style="padding-left: 2em;"> <span class="nowrap">VII<a name="FNanchor_XI-2_5" id="FNanchor_XI-2_5"></a><a href="#Footnote_XI-2_5" class="fnanchor">XI-2</a></span></td>
+</tr>
+<tr>
+  <td class="bbcent">     17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    8</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">   17</td>
+</tr>
+<tr>
+  <td colspan="6" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_XI-1_4" id="Footnote_XI-1_4"></a><a href="#FNanchor_XI-1_4"><span class="label">XI-1</span></a> The 0 inserted at various points in these tables denotes
+as usual the red, diamond shaped symbol, which apparently signifies
+&#8220;nought.&#8221;</td>
+</tr>
+<tr>
+  <td colspan="6" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_XI-2_5" id="Footnote_XI-2_5"></a><a href="#FNanchor_XI-2_5"><span class="label">XI-2</span></a> The numeral symbol in this case, both in Kingsborough&#8217;s
+copy and in the photograph, is VII, one dot having been omitted by a
+mistake of the original artist.</td>
+</tr>
+</table>
+
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XII" id="Table_XII"></a><span class="smcap">Table XII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 55<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XII">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">    8</td>
+  <td class="btlcent">    7</td>
+  <td class="btlcent">    7</td>
+  <td class="btlcent">     8</td>
+  <td class="btlcent">     8</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">  13</td>
+  <td class="blcent">   3</td>
+  <td class="blcent">  12</td>
+  <td class="blcent">    3</td>
+  <td class="blcent">   12</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">   2</td>
+  <td class="blcent">  18</td>
+  <td class="blcent">  16</td>
+  <td class="blcent">   13</td>
+  <td class="blcent">   10</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent" style="padding-left: 2em;">II <span class="nowrap">Muluc.<a name="FNanchor_XII-1_6" id="FNanchor_XII-1_6"></a><a href="#Footnote_XII-1_6" class="fnanchor">XII-1</a></span></td>
+  <td class="blcent"> X Cimi.</td>
+  <td class="blcent"> V Akbal.</td>
+  <td class="blcent">XIII Ahau.</td>
+  <td class="blcent">VIII Caban.</td>
+</tr>
+<tr>
+  <td class="tdc"> [Picture]</td>
+  <td class="blcent">III Oc.</td>
+  <td class="blcent">XI Manik.</td>
+  <td class="blcent">VI Kan.</td>
+  <td class="blcent">  I Ymix.</td>
+  <td class="blcent"> IX Ezanab.</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">IV Chuen.</td>
+  <td class="blcent">XII Lamat.</td>
+  <td class="blcent">VII Chicchan.</td>
+  <td class="blcent"> II Ik.</td>
+  <td class="blcent">  X Cauac.</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+</tr>
+<tr>
+  <td class="bb">&nbsp;</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+</tr>
+<tr>
+  <td colspan="6" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_XII-1_6" id="Footnote_XII-1_6"></a><a href="#FNanchor_XII-1_6"><span class="label">XII-1</span></a> In Kingsborough&#8217;s work the symbol in this case is that
+of Been, but should be Muluc, as it is in the photograph.</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XIII" id="Table_XIII"></a><span class="smcap">Table XIII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 55<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XIII">
+<tr>
+  <td class="btcent">       1</td>
+  <td class="btlcent">   1</td>
+  <td class="btlcent">   1</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">    1</td>
+</tr>
+<tr>
+  <td class="tdc">      4</td>
+  <td class="blcent">  5</td>
+  <td class="blcent">  5</td>
+  <td class="blcent">    6</td>
+  <td class="blcent">    6</td>
+  <td class="blcent">   6</td>
+  <td class="blcent">   7</td>
+  <td class="blcent">   7</td>
+</tr>
+<tr>
+  <td class="tdc">      9</td>
+  <td class="blcent">  0</td>
+  <td class="blcent">  9</td>
+  <td class="blcent">    0</td>
+  <td class="blcent">    8</td>
+  <td class="blcent">  17</td>
+  <td class="blcent">   8</td>
+  <td class="blcent">  15</td>
+</tr>
+<tr>
+  <td class="tdc">      8</td>
+  <td class="blcent">  6</td>
+  <td class="blcent">  3</td>
+  <td class="blcent">    0</td>
+  <td class="blcent">   17</td>
+  <td class="blcent">  14</td>
+  <td class="blcent">  11</td>
+  <td class="blcent">  19</td>
+</tr>
+<tr>
+  <td class="tdc"> XIII Cib.</td>
+  <td class="blcent">IX Ix.</td>
+  <td class="blcent">IV Chuen.</td>
+  <td class="blcent">XII Lamat.</td>
+  <td class="blcent">VII Chicchan.</td>
+  <td class="blcent">II Ik.</td>
+  <td class="blcent"> X Cauac.</td>
+  <td class="blcent">II Manik.</td>
+</tr>
+<tr>
+  <td class="tdc">    I Caban.</td>
+  <td class="blcent">X Men.</td>
+  <td class="blcent">V Eb.</td>
+  <td class="blcent">XIII Muluc.</td>
+  <td class="blcent">VIII Cimi.</td>
+  <td class="blcent">III Akbal.</td>
+  <td class="blcent">XI Ahau.</td>
+  <td class="blcent">III Lamat.</td>
+</tr>
+<tr>
+  <td class="tdc">   II Ezanab.</td>
+  <td class="blcent">XI Cib.</td>
+  <td class="blcent">VI Been.</td>
+  <td class="blcent">  I Oc.</td>
+  <td class="blcent"> IX Manik.</td>
+  <td class="blcent">IV Kan.</td>
+  <td class="blcent">XII Ymix.</td>
+  <td class="blcent">IV Muluc.</td>
+</tr>
+<tr>
+  <td class="tdc">    VIII</td>
+  <td class="blcent">VIII</td>
+  <td class="blcent">VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">  VII</td>
+</tr>
+<tr>
+  <td class="bbcent">      17</td>
+  <td class="bblcent">17?(18)</td>
+  <td class="bblcent">  17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    8</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_316" id="Page_316">[316]</a></span></p>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XIV" id="Table_XIV"></a><span class="smcap">Table XIV.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 56<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XIV">
+<tr>
+  <td class="btcent">       9</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">     9</td>
+  <td class="btlcent">   10</td>
+  <td class="btlcent">    10</td>
+</tr>
+<tr>
+  <td class="tdc">      1</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   10</td>
+  <td class="blcent">   1</td>
+  <td class="blcent">   10</td>
+</tr>
+<tr>
+  <td class="tdc">     18</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   15</td>
+  <td class="blcent">  12</td>
+  <td class="blcent">    9</td>
+</tr>
+<tr>
+  <td class="tdc"> XIII Chicchan.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">VIII Ik.</td>
+  <td class="blcent">III Cauac.</td>
+  <td class="blcent"> XI Cib.</td>
+</tr>
+<tr>
+  <td class="tdc">    I Cimi.</td>
+  <td class="blcent">[Picture]</td>
+  <td class="blcent"> IX Akbal.</td>
+  <td class="blcent">IV Ahau.</td>
+  <td class="blcent">XII Caban.</td>
+</tr>
+<tr>
+  <td class="tdc">   II Manik.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  X Kan.</td>
+  <td class="blcent"> V Ymix.</td>
+  <td class="blcent">XIII Ezanab.</td>
+</tr>
+<tr>
+  <td class="tdc">     VII</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">       8</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">    17</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XV" id="Table_XV"></a><span class="smcap">Table XV.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 56<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XV">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">      1</td>
+  <td class="btlcent">    1</td>
+  <td class="btlcent">   1</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">   8</td>
+  <td class="blcent">     8</td>
+  <td class="blcent">   9</td>
+  <td class="blcent">  9</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">   6</td>
+  <td class="blcent">    15</td>
+  <td class="blcent">   6</td>
+  <td class="blcent"> 15</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">  16</td>
+  <td class="blcent">    14</td>
+  <td class="blcent">  11</td>
+  <td class="blcent">  8</td>
+</tr>
+<tr>
+  <td class="tdc"> [Picture]</td>
+  <td class="blcent"> X Kan.</td>
+  <td class="blcent"> VI Ik.</td>
+  <td class="blcent"> I Cauac.</td>
+  <td class="blcent">IX Cib.</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">XI Chicchan.</td>
+  <td class="blcent">VII Akbal.</td>
+  <td class="blcent">II Ahau.</td>
+  <td class="blcent">X Caban.
+</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent">XII Cimi.</td>
+  <td class="blcent">VIII Kan.</td>
+  <td class="blcent">III Ymix.</td>
+  <td class="blcent">XI Ezanab.</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent">   VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">&nbsp;</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17?(8)</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">  17</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XVI" id="Table_XVI"></a><span class="smcap">Table XVI.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 57<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XVI">
+<tr>
+  <td class="btcent">      11</td>
+  <td class="btlcent">   11</td>
+  <td class="btlcent">   12</td>
+  <td class="btlcent">   12</td>
+  <td class="btlcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">1</td>
+  <td class="blcent">  10</td>
+  <td class="blcent">   1</td>
+  <td class="blcent">   8</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">      6</td>
+  <td class="blcent">   4</td>
+  <td class="blcent">   0</td>
+  <td class="blcent">   8</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">  VII Ix.</td>
+  <td class="blcent">II Chuen.</td>
+  <td class="blcent"> X Lamat.</td>
+  <td class="blcent">II Cib.</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc"> VIII Men.</td>
+  <td class="blcent">III Eb.</td>
+  <td class="blcent">XI Muluc.</td>
+  <td class="blcent">III Caban.</td>
+  <td class="blcent">[Picture]</td>
+</tr>
+<tr>
+  <td class="tdc">   IX Cib.</td>
+  <td class="blcent">IV Been.</td>
+  <td class="blcent">XII Oc.</td>
+  <td class="blcent">IV Ezanab.</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">     VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent" style="padding-left: 2em;"><span class="nowrap">VIII<a name="FNanchor_XVI-1_7" id="FNanchor_XVI-1_7"></a><a href="#Footnote_XVI-1_7" class="fnanchor">XVI-1</a></span></td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bbcent">      17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent" style="padding-left: 2em;">   <span class="nowrap">17<a name="FNanchor_XVI-2_8" id="FNanchor_XVI-2_8"></a><a href="#Footnote_XVI-2_8" class="fnanchor">XVI-2</a></span></td>
+  <td class="bblcent">&nbsp;</td>
+</tr>
+<tr>
+  <td colspan="5" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_XVI-1_7" id="Footnote_XVI-1_7"></a><a href="#FNanchor_XVI-1_7"><span class="label">XVI-1</span></a> This should be VII.</td>
+</tr>
+<tr>
+  <td colspan="5" style="padding-top: 0.5em; font-size: 0.9em;"><a name="Footnote_XVI-2_8" id="Footnote_XVI-2_8"></a><a href="#FNanchor_XVI-2_8"><span class="label">XVI-2</span></a> This should be 8.</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XVII" id="Table_XVII"></a><span class="smcap">Table XVII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 57<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XVII">
+<tr>
+  <td class="btcent">       1</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">   1</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">     1</td>
+  <td class="btlcent">     1</td>
+</tr>
+<tr>
+  <td class="tdc">     10</td>
+  <td class="blcent">   10</td>
+  <td class="blcent"> 11</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   11</td>
+  <td class="blcent">   12</td>
+</tr>
+<tr>
+  <td class="tdc">      6</td>
+  <td class="blcent">   15</td>
+  <td class="blcent">  4</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   13</td>
+  <td class="blcent">    4</td>
+</tr>
+<tr>
+  <td class="tdc">      5</td>
+  <td class="blcent">    2</td>
+  <td class="blcent"> 10</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">    7</td>
+  <td class="blcent">    4</td>
+</tr>
+<tr>
+  <td class="tdc">   IV Been.</td>
+  <td class="blcent">XII Oc.</td>
+  <td class="blcent">IV Ezanab.</td>
+  <td class="blcent">[Picture]</td>
+  <td class="blcent">XII Men.</td>
+  <td class="blcent">VII Eb.</td>
+</tr>
+<tr>
+  <td class="tdc">    V Ix.</td>
+  <td class="blcent">XIII Chuen.</td>
+  <td class="blcent">V Cauac.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">XIII Cib.</td>
+  <td class="blcent">VIII Been.</td>
+</tr>
+<tr>
+  <td class="tdc">   VI Men.</td>
+  <td class="blcent">  I Eb.</td>
+  <td class="blcent">VI Ahau.</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  I Caban.</td>
+  <td class="blcent"> IX Ix.</td>
+</tr>
+<tr>
+  <td class="tdc">     VIII</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent"> VII</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">  VIII</td>
+  <td class="blcent">  VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">      17</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">   8</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">    17</td>
+</tr>
+</table>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XVIII" id="Table_XVIII"></a><span class="smcap">Table XVIII.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 58<i>a</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XVIII">
+<tr>
+  <td class="btcent">     12</td>
+  <td class="btlcent">   13</td>
+  <td class="btlcent">   13</td>
+  <td class="btlcent">  14</td>
+</tr>
+<tr>
+  <td class="tdc">    17</td>
+  <td class="blcent">   8</td>
+  <td class="blcent">  17</td>
+  <td class="blcent">  7</td>
+</tr>
+<tr>
+  <td class="tdc">     5</td>
+  <td class="blcent">   2</td>
+  <td class="blcent">   0</td>
+  <td class="blcent"> 17</td>
+</tr>
+<tr>
+  <td class="tdc">   X Been.</td>
+  <td class="blcent"> V Oc.</td>
+  <td class="blcent"> I Lamat.</td>
+  <td class="blcent">II Chicchan.</td>
+</tr>
+<tr>
+  <td class="tdc">  XI Ix.</td>
+  <td class="blcent">VI Chuen.</td>
+  <td class="blcent">II Muluc.</td>
+  <td class="blcent">X Cimi.</td>
+</tr>
+<tr>
+  <td class="tdc"> XII Men.</td>
+  <td class="blcent">VII Eb.</td>
+  <td class="blcent">III Oc.</td>
+  <td class="blcent">XI Manik.</td>
+</tr>
+<tr>
+  <td class="tdc">   VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+  <td class="blcent"> VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">     17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">   17</td>
+  <td class="bblcent">  17</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_317" id="Page_317">[317]</a></span></p>
+
+<p class="tabletitle" style="margin-top: 1.5em"><a name="Table_XIX" id="Table_XIX"></a><span class="smcap">Table XIX.</span>&mdash;<i>Table of numeral and day symbols.</i> (Plate 58<i>b</i>.)</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Table XIX">
+<tr>
+  <td class="btcent">      1</td>
+  <td class="btlcent">   1</td>
+  <td class="btlcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">    12</td>
+  <td class="blcent"> 13</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">    13</td>
+  <td class="blcent">  3</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">     1</td>
+  <td class="blcent"> 18</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">  II Muluc.</td>
+  <td class="blcent">X Cimi.</td>
+  <td class="blcent">[Picture.]</td>
+</tr>
+<tr>
+  <td class="tdc"> III Oc.</td>
+  <td class="blcent">XI Manik.</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">IV Chuen.</td>
+  <td class="blcent">XII Lamat.</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">   VIII</td>
+  <td class="blcent">VIII</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bbcent">     17</td>
+  <td class="bblcent">  17</td>
+  <td class="bblcent">&nbsp;</td>
+</tr>
+</table>
+
+<p>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.
+<a href="#Fig_363">363-370</a>.</p>
+
+<p>In order to explain this series, we commence with that portion of it
+found in the lower division of Plate 51 (<a href="#Fig_363">Fig. 363</a>).</p>
+
+<p>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:</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Plate 51">
+<tr>
+  <td class="tdr">  IV</td>
+  <td>Ik.</td>
+  <td class="tdr"> XII</td>
+  <td>Cauac.</td>
+  <td class="tdr"> VII</td>
+  <td>Cib.</td>
+  <td class="tdr"> II</td>
+  <td>Been.</td>
+  <td class="tdr">  X</td>
+  <td>Oc.</td>
+  <td class="tdr"> II</td>
+  <td>Ezanab.</td>
+</tr>
+<tr>
+  <td class="tdr">   V</td>
+  <td>Akbal.</td>
+  <td class="tdr">XIII</td>
+  <td>Ahau.</td>
+  <td class="tdr">VIII</td>
+  <td>Caban.</td>
+  <td class="tdr">III</td>
+  <td>Ix.</td>
+  <td class="tdr"> XI</td>
+  <td>Chuen.</td>
+  <td class="tdr">III</td>
+  <td>Cauac.</td>
+</tr>
+<tr>
+  <td class="tdr">  VI</td>
+  <td>Kan.</td>
+  <td class="tdr">   I</td>
+  <td>Ymix.</td>
+  <td class="tdr">  IX</td>
+  <td>Ezanab.</td>
+  <td class="tdr"> IV</td>
+  <td>Men.</td>
+  <td class="tdr">XII</td>
+  <td>Eb.</td>
+  <td class="tdr"> IV</td>
+  <td><span class="nowrap">Ahau.<a name="FNanchor_317-1_30" id="FNanchor_317-1_30"></a><a href="#Footnote_317-1_30" class="fnanchor">317-1</a></span></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_318" id="Page_318">[318]</a></span>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 (<a href="#Table_II">Table II</a>) 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.</p>
+
+<p>These intervals furnish the explanation of the red and black numerals
+below the day columns.</p>
+
+<p>These numerals, as the reader will observe by reference to <a href="#Fig_363">Fig. 363</a> or
+the written interpretation thereof in <a href="#Table_VI">Table VI</a>, 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.</p>
+
+<p>In order to do this it will be necessary to repeat here a part of the
+series on Plate 51<i>b</i> and part of that on Plate 52<i>b</i>; 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 <i>lower left
+hand corner</i> of our <a href="#Fig_364">Fig. 364</a>:</p>
+
+<table border="0" width="80%" cellpadding="0" cellspacing="0" summary="Plate 52">
+<tr>
+  <td class="btcent" colspan="2">Plate 51<i>b</i>.</td>
+  <td class="btl" style="width: 1px;">&nbsp;</td>
+  <td class="btlcent" colspan="3">  Plate 52<i>b</i>.</td>
+</tr>
+<tr>
+  <td class="btcent">    X Oc.</td>
+  <td class="btlcent"> II Ezanab.</td>
+  <td class="bl" style="width: 1px;">&nbsp;</td>
+  <td class="btlcent">&nbsp;</td>
+  <td class="btlcent">  XI Cib.</td>
+  <td class="btlcent">VI Been.</td>
+</tr>
+<tr>
+  <td class="tdc">    XI Chuen.</td>
+  <td class="blcent">III Cauac.</td>
+  <td class="bl" style="width: 1px;">&nbsp;</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent"> XII Caban.</td>
+  <td class="blcent">VII Ix.</td>
+</tr>
+<tr>
+  <td class="tdc">   XII Eb.</td>
+  <td class="blcent"> IV Ahau.</td>
+  <td class="bl" style="width: 1px;">&nbsp;</td>
+  <td class="blcent">[Picture.]</td>
+  <td class="blcent">XIII Ezanab.</td>
+  <td class="blcent">VIII Men.</td>
+</tr>
+<tr>
+  <td class="tdc">       VIII</td>
+  <td class="blcent">  VII</td>
+  <td class="bl" style="width: 1px;">&nbsp;</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">   VIII</td>
+  <td class="blcent">VIII</td>
+</tr>
+<tr>
+  <td class="bbcent">       17</td>
+  <td class="bblcent">    8</td>
+  <td class="bbl" style="width: 1px;">&nbsp;</td>
+  <td class="bblcent">&nbsp;</td>
+  <td class="bblcent">    17</td>
+  <td class="bblcent">17</td>
+</tr>
+</table>
+
+<p>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<span class='pagenum'><a name="Page_319" id="Page_319">[319]</a></span> intervals where the difference of
+7 months and 8 days occurs.319-1 Precisely the same variation occurs on
+Plate 55<i>b</i> in passing from the first to the second column and on Plate
+56<i>b</i> between columns 1 and 2.</p>
+
+<p>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.</p>
+
+<p>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&#8217;s attention is directed to these lines,
+as given in Tables <a href="#Table_VI">VI</a>, <a href="#Table_VII">VII</a>, <a href="#Table_IX">IX</a>, <a href="#Table_XI">XI</a>, <a href="#Table_XIII">XIII</a>, <a href="#Table_XV">XV</a>, <a href="#Table_XVII">XVII</a>, and <a href="#Table_XIX">XIX</a>. 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<i>b</i>, 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.</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Fifth column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Sixth column on Plate 51<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td style="padding-left: 0em;"><a name="FNanchor_319-1_31" id="FNanchor_319-1_31"></a><a href="#Footnote_319-1_31" class="fnanchor">319-1</a></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 52<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 52<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td><span class='pagenum'><a name="Page_320" id="Page_320">[320]</a></span>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 52<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 52<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 53<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">20</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 53<i>b</i>.</td>
+</tr>
+</table>
+
+<p>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. F&ouml;rstemann 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:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td class="colhead">Twenty year<br />periods.</td>
+  <td class="colhead">Years.</td>
+  <td class="colhead">Months.</td>
+  <td class="colhead">Days.</td>
+</tr>
+<tr>
+  <td class="tdc">1</td>
+  <td class="tdc">0</td>
+  <td class="tdc">3</td>
+  <td class="tdc">4</td>
+</tr>
+</table>
+
+<p>Continuing the addition in this way the result is as follows:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td class="colhead" colspan="3">Twenty year<br />periods.</td>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 53<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 53<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Fifth column on Plate 53<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 54<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 54<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 54<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 54<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr"><span class='pagenum'><a name="Page_321" id="Page_321">[321]</a></span>1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>Fifth column on Plate 54<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td style="padding-left: 0"><a name="FNanchor_321-1_32" id="FNanchor_321-1_32"></a><a href="#Footnote_321-1_32" class="fnanchor">321-1</a></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>Fifth column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Sixth column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>Seventh column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>Eighth column on Plate 55<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 56<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td style="padding-left: 0"><a name="FNanchor_321-2_33" id="FNanchor_321-2_33"></a><a href="#Footnote_321-2_33" class="fnanchor">321-2</a></td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 56<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 56<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 56<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 57<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 57<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Third column on Plate 57<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>Fourth column on Plate 57<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>Fifth column on Plate 57<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>First column on Plate 58<i>b</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bb">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>Second column on Plate 58<i>b</i>.</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_322" id="Page_322">[322]</a></span>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<i>a</i>-58<i>a</i>, which constitutes the first
+half of the series.</p>
+
+<p>Turning back to our <a href="#Table_VIII">Table VIII</a>, representing that part of the series on
+Plate 53<i>a</i>, we will consider the three lines of black numerals above the
+day columns, discussing the irregularities as we proceed.</p>
+
+<p>The numbers in the first column are <a name="corr6" id="corr6"></a><ins class="correction" title="original printed 7 over 17 with no dividing line">7/17,</ins> 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.
+F&ouml;rstemann, 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.</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>First column, Plate 53<i>a</i> (corrected).</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Second column. Plate 53<i>a</i>.</td>
+</tr>
+</table>
+
+<p>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. F&ouml;rstemann, in discussing the series, takes it for granted
+that these variations are errors of the aboriginal scribe; he remarks
+that &#8220;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,&#8221;
+&amp;c.</p>
+
+<p>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.</p>
+
+<p>Going back to that part of the series in the lower divisions which has
+already been examined and commencing with Plate 51<i>b</i> (see <a href="#Table_VI">Table VI</a>), 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):</p>
+
+<table width="50%" border="0" cellspacing="0" cellpadding="0" summary="Plate 51b">
+<tr>
+  <td class="tdc">14</td>
+  <td class="tdc">11</td>
+  <td class="tdc">8</td>
+  <td class="tdc">5</td>
+  <td class="tdc">2</td>
+  <td class="tdc">10</td>
+</tr>
+<tr>
+  <td class="tdc">Ik.</td>
+  <td class="tdc">Cauac.</td>
+  <td class="tdc">Cib.</td>
+  <td class="tdc">Been.</td>
+  <td class="tdc">Oc.</td>
+  <td class="tdc">Ezanab.</td>
+</tr>
+</table>
+
+<p>Turning to the calendar (<a href="#Table_II">Table II</a>) 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<span class='pagenum'><a name="Page_323" id="Page_323">[323]</a></span> 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<i>b</i> to 58<i>b</i> without a single exception, provided
+the diamond shaped symbol in the fourth column of Plate 55<i>b</i> 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.</p>
+
+<p>Returning now to our <a href="#Table_VIII">Table VIII</a>, representing Plate 53<i>a</i>, 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. F&ouml;rstemann 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.</p>
+
+<p>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.</p>
+
+<p>Continuing the addition as heretofore we note the variations.</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td class="colhead">Column.</td>
+  <td class="colhead" style="text-align: left;">Plate.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Second.</td>
+  <td>53<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>53<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td><a name="FNanchor_323-1_34" id="FNanchor_323-1_34"></a><a href="#Footnote_323-1_34" class="fnanchor">323-1</a></td>
+  <td>Fourth.</td>
+  <td>53<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Fifth.</td>
+  <td>53<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>Sixth.</td>
+  <td>53<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td><a name="FNanchor_323-2_35" id="FNanchor_323-2_35"></a><a href="#Footnote_323-2_35" class="fnanchor">323-2</a></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td><span class='pagenum'><a name="Page_324" id="Page_324">[324]</a></span>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Second.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td><a name="FNanchor_324-1_36" id="FNanchor_324-1_36"></a><a href="#Footnote_324-1_36" class="fnanchor">324-1</a></td>
+  <td>Fourth.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>Fifth.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td><a name="FNanchor_324-2_37" id="FNanchor_324-2_37"></a><a href="#Footnote_324-2_37" class="fnanchor">324-2</a></td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Sixth.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Seventh.</td>
+  <td>54<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td><a name="FNanchor_324-3_38" id="FNanchor_324-3_38"></a><a href="#Footnote_324-3_38" class="fnanchor">324-3</a></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td><a name="FNanchor_324-4_39" id="FNanchor_324-4_39"></a><a href="#Footnote_324-4_39" class="fnanchor">324-4</a></td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>55<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td><a name="FNanchor_324-5_40" id="FNanchor_324-5_40"></a><a href="#Footnote_324-5_40" class="fnanchor">324-5</a></td>
+  <td>Second.</td>
+  <td>55<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>55<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>Fourth.</td>
+  <td>55<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Fifth.</td>
+  <td>55<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>56<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Second.</td>
+  <td>56<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>56<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>Fourth.</td>
+  <td>56<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>57<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td><span class='pagenum'><a name="Page_325" id="Page_325">[325]</a></span>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>Second.</td>
+  <td>57<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>57<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td><a name="FNanchor_325-1_41" id="FNanchor_325-1_41"></a><a href="#Footnote_325-1_41" class="fnanchor">325-1</a></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Fourth.</td>
+  <td>57<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>58<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Second.</td>
+  <td>58<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">18</td>
+  <td><a name="FNanchor_325-2_42" id="FNanchor_325-2_42"></a><a href="#Footnote_325-2_42" class="fnanchor">325-2</a></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Third.</td>
+  <td>58<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>Fourth.</td>
+  <td>58<i>a</i>.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>First.</td>
+  <td>51<i>b</i>.<a name="FNanchor_325-3_43" id="FNanchor_325-3_43"></a><a href="#Footnote_325-3_43" class="fnanchor">325-3</a></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>The sum of the series as shown by the numbers over the second column of
+Plate 58<i>b</i> 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<span class='pagenum'><a name="Page_326" id="Page_326">[326]</a></span> 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<i>b</i> two numbers, 13 and 12, are found attached to
+characters which appear to be abnormal forms of month symbols.</p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_327" id="Page_327">[327]</a></span></p>
+
+<p class="tabletitle"><a name="Table_XX" id="Table_XX"></a><span class="smcap"><a href="images/tablexx.png">Table XX.</a></span>&mdash;<i>Table showing series of day columns, with lines of numerals.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table XX">
+<tr>
+  <td class="tdc" colspan="10">UPPER DIVISION.</td>
+</tr>
+<tr>
+  <td class="btcent" colspan="6">Plate 63.</td>
+  <td class="btlcent br" colspan="4">Plate 64.</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btcent">4</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">3</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent br">0</td>
+</tr>
+<tr>
+  <td></td>
+  <td class="tdc">8</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">6</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdr">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">16</td>
+</tr>
+<tr>
+  <td></td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">0</td>
+</tr>
+<tr>
+  <td class="tdr">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td class="br">Chicchan.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Kan.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Ix.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Cimi.</td>
+</tr>
+<tr>
+  <td class="bbright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="br bb">Akbal.</td>
+</tr>
+<tr>
+  <td class="tdc" colspan="10">Plate 64.</td>
+</tr>
+<tr>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">0</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">0</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">12</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">8</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">3</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">3</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+</tr>
+<tr>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Chicchan.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+</tr>
+<tr>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Akbal.</td>
+</tr>
+<tr>
+  <td class="tdc" colspan="10" style="padding-top: 1em; padding-bottom: 1em;"><a name="Table_XXI" id="Table_XXI"></a><a name="corr7" id="corr7"></a><ins class="correction" title="Table XXI. MIDDLE DIVISION">MIDDLE DIVISION.</ins></td>
+</tr>
+<tr>
+  <td class="btright">XIX</td>
+  <td class="btcent">5</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">4</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">4</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">4</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent br">4</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td class="tdc">1</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">14</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">9</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">5</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">0</td>
+</tr>
+<tr>
+  <td class="tdr">IV</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">7</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">16</td>
+</tr>
+<tr>
+  <td class="tdr">III</td>
+  <td>Chicchan.</td>
+  <td class="blright">III</td>
+  <td>Ix.</td>
+  <td class="blright">III</td>
+  <td>Akbal.</td>
+  <td class="blright">III</td>
+  <td>Eb.</td>
+  <td class="blright">III</td>
+  <td class="br">Ymix.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Been.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ik.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Chuen.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Ahau.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Akbal.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Eb.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ymix.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Oc.</td>
+</tr>
+<tr>
+  <td></td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Men.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Been.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Ik.</td>
+</tr>
+<tr>
+  <td class="bbright">XIII</td>
+  <td class="bb">Akbal.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Eb.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Ymix.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Oc.</td>
+  <td class="bblright">XIII</td>
+  <td class="bbr">Cauac.</td>
+</tr>
+<tr>
+  <td colspan="10">&nbsp;</td>
+</tr>
+<tr>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">3</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">3</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">3</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">3</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">2</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">14</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">9</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">5</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">14</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">5</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">14</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">3</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">12</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">1</td>
+</tr>
+<tr>
+  <td class="blright">III</td>
+  <td>Oc.</td>
+  <td class="blright">III</td>
+  <td>Cauac.</td>
+  <td class="blright">III</td>
+  <td>Lamat.</td>
+  <td class="blright">III</td>
+  <td>Caban.</td>
+  <td class="blright">III</td>
+  <td>Cimi.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Muluc.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ezanab.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Manik.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cib.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Chicchan.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Cauac.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Lamat.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Caban.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Men.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Chuen.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ahau.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Muluc.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ezanab.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Manik.</td>
+</tr>
+<tr>
+  <td class="bblright">XIII</td>
+  <td class="bb">Lamat.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Caban.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Cimi.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Men.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Kan.</td>
+</tr>
+<tr>
+  <td class="tdc" colspan="10" style="padding-top: 1em; padding-bottom: 1em;"><a name="Table_XXII" id="Table_XXII"></a><ins class="correction" title="Table XXII. LOWER DIVISION">LOWER DIVISION.</ins></td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="btcent">2</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">2</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">2</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">1</td>
+  <td class="btl">&nbsp;</td>
+  <td class="tdc bt br">1</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">9</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">4</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">13</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">9</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdc">10</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">19</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">8</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">17</td>
+  <td class="bl">&nbsp;</td>
+  <td class="brcent">6</td>
+</tr>
+<tr>
+  <td class="tdr">III</td>
+  <td>Men.</td>
+  <td class="blright">III</td>
+  <td>Kan.</td>
+  <td class="blright">III</td>
+  <td>Been.</td>
+  <td class="blright">III</td>
+  <td>Ik.</td>
+  <td class="blright">III</td>
+  <td class="br">Chuen.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Akbal.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Eb.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ymix.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Oc.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>Kan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Been.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ik.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Chuen.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Ahau.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>Cib.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Chicchan.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Akbal.</td>
+  <td class="bl">&nbsp;</td>
+  <td class="br">Eb.</td>
+</tr>
+<tr>
+  <td class="bbright">XIII</td>
+  <td class="bb">Been.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Ik.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Chuen.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Ahau.</td>
+  <td class="bblright">XIII</td>
+  <td class="br bb">Muluc.</td>
+</tr>
+<tr>
+  <td colspan="10">&nbsp;</td>
+</tr>
+<tr>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">1</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">1</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">4</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">0</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">13</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">9</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">4</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">15</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">4</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">13</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">2</td>
+  <td class="bl">&nbsp;</td>
+  <td class="tdc">11</td>
+</tr>
+<tr>
+  <td class="blright">III</td>
+  <td>Ahau.</td>
+  <td class="blright">III</td>
+  <td>Muluc.</td>
+  <td class="blright">III</td>
+  <td>Ezanab.</td>
+  <td class="blright">III</td>
+  <td>Manik.</td>
+  <td class="blright">III</td>
+  <td>Cib</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Cauac.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Lamat.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Caban.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cimi.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Men.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Muluc.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Ezanab.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Manik.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cib.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Chicchan.</td>
+</tr>
+<tr>
+  <td class="bl">&nbsp;</td>
+  <td>Ymix.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Oc.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Cauac.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Lamat.</td>
+  <td class="bl">&nbsp;</td>
+  <td>Caban.</td>
+</tr>
+<tr>
+  <td class="bblright">XIII</td>
+  <td class="bb">Ezanab.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Manik.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Cib.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Chicchan.</td>
+  <td class="bblright">XIII</td>
+  <td class="bb">Ix.</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_328" id="Page_328">[328]</a></span>By examining carefully the lines and columns of the middle and lower
+divisions of the plates&mdash;those represented in Tables <a href="#Table_XXI">XXI</a> and <a href="#Table_XXII">XXII</a>&mdash;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
+<i>right</i> to <i>left</i>, commencing with the right hand column of the lower and
+ending with the left hand column of the middle division.</p>
+
+<p>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:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>Over tenth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Over ninth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>Over eighth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Over third column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">19</td>
+  <td>&nbsp;</td>
+  <td>Over second column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over first column, lower division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>Over tenth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Over ninth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>Over eighth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td><span class='pagenum'><a name="Page_329" id="Page_329">[329]</a></span>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>Over third column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>Over second column, middle division.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over first column, middle division.</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>Although Dr. F&ouml;rstemann discovered the order in which the series as a
+whole was to be read, and also the common difference&mdash;given, as is his
+custom, in days&mdash;he failed to furnish further explanation of the group.</p>
+
+<p>In answer to the question presented I call attention to the following
+facts:</p>
+
+<p>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.</p>
+
+<p>Reversing the order in reading the columns, but counting forward<span class='pagenum'><a name="Page_330" id="Page_330">[330]</a></span> 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 <i>bottom</i> to <i>top</i> and that
+they follow one another from <i>right</i> to <i>left</i>. 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.</p>
+
+<p>These numbers hold good throughout the series.</p>
+
+<p>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&mdash;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&mdash;the
+interval between 13 Akbal and 3 Chicchan (top day of first column, middle
+division)&mdash;we have, as the entire period embraced in the series as it
+stands&mdash;from 13 Ix (first of the series) to 3 Chicchan (the last)&mdash;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.</p>
+
+<p>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. F&ouml;rstemann soon after he commenced the study of
+the Dresden manuscript.</p>
+
+<p>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<span class='pagenum'><a name="Page_331" id="Page_331">[331]</a></span> 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.</p>
+
+<p>Adding together the numbers and casting out the thirteens, thus, XIII + 9
+- 13 = IX; IX + 5 - 13 = I, &amp;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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<p><span class='pagenum'><a name="Page_332" id="Page_332">[332]</a></span></p>
+
+<p class="tabletitle"><a name="Table_XXIII" id="Table_XXIII"></a><span class="smcap">Table XXIII.</span>&mdash;<i>Table giving comparison between Plates 71, 72, and 73.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table XXIII">
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">First<br />column.</td>
+  <td class="btlcent">Second<br />column.</td>
+  <td class="btlcent">Third<br />column.</td>
+  <td class="btlcent">Fourth<br />column.</td>
+  <td class="btlcent">Fifth<br />column.</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="3">Plate 73,<br />middle<br />division</td>
+  <td class="bt bb" rowspan="3"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btl" style="text-align: right; padding-right: 1em;">16</td>
+  <td class="btl">1</td>
+  <td class="btl">9</td>
+  <td class="btl">6</td>
+  <td class="btl">3</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bl">5</td>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+  <td class="bl">10</td>
+  <td class="bl">5</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+</tr>
+<tr>
+  <td colspan="8">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">First<br />column.</td>
+  <td class="btlcent">Second<br />column.</td>
+  <td class="btlcent">Third<br />column.</td>
+  <td class="btlcent">Fourth<br />column.</td>
+  <td class="btlcent">Fifth<br />column.</td>
+  <td class="btlcent">Sixth<br />column.</td>
+  <td class="btlcent">Seventh<br />column.</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="4">Plate 72,<br />middle<br />division</td>
+  <td class="bt bb" rowspan="4"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btl" style="text-align: right; padding-right: 1em;">2</td>
+  <td class="btl">1</td>
+  <td class="btl">1</td>
+  <td class="btl">1</td>
+  <td class="btl">1</td>
+  <td class="btl">1</td>
+  <td class="btlcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bl">3</td>
+  <td class="bl">17</td>
+  <td class="bl">14</td>
+  <td class="bl">11</td>
+  <td class="bl">8</td>
+  <td class="bl">4</td>
+  <td class="bl">19</td>
+</tr>
+<tr>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+  <td class="bl">10</td>
+  <td class="bl">5</td>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+  <td class="bl">10</td>
+</tr>
+<tr>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">IV Ik.</td>
+</tr>
+<tr>
+  <td colspan="8">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btlcent">Sixth<br />column.</td>
+  <td class="btlcent">Seventh<br />column.</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="4">Plate 71,<br />middle<br />division</td>
+  <td class="bt bb" rowspan="4"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btl">2</td>
+  <td class="btl">2</td>
+</tr>
+<tr>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="bl">9&nbsp;</td>
+  <td class="bl">6</td>
+</tr>
+<tr>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="bl">10&nbsp;</td>
+  <td class="bl">5</td>
+</tr>
+<tr>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+</tr>
+<tr>
+  <td colspan="8">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">First<br />column.</td>
+  <td class="btlcent">Second<br />column.</td>
+  <td class="btlcent">Third<br />column.</td>
+  <td class="btlcent">Fourth<br />column.</td>
+  <td class="btlcent">Fifth<br />column.</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="4">Plate 73,<br />lower<br />division</td>
+  <td class="bt bb" rowspan="4"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btl">3</td>
+  <td class="btl">3</td>
+  <td class="btl">3</td>
+  <td class="btl">2</td>
+  <td class="btl">2</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bl">7</td>
+  <td class="bl">3</td>
+  <td class="bl">1</td>
+  <td class="bl">16</td>
+  <td class="bl">12</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bl">15</td>
+  <td class="bl">10</td>
+  <td class="bl">5</td>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+</tr>
+<tr>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+</tr>
+<tr>
+  <td colspan="8">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btlcent">First<br />column.</td>
+  <td class="btlcent">Second<br />column.</td>
+  <td class="btlcent">Third<br />column.</td>
+  <td class="btlcent">Fourth<br />column.</td>
+  <td class="btlcent">Fifth<br />column.</td>
+  <td class="btlcent">Sixth<br />column.</td>
+  <td class="btlcent">Seventh<br />column.</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="4">Plate 72,<br />lower<br />division</td>
+  <td class="bt bb" rowspan="4"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btl">4</td>
+  <td class="btl">4</td>
+  <td class="btl">4</td>
+  <td class="btl">4</td>
+  <td class="btl">2</td>
+  <td class="btl">3</td>
+  <td class="btl">3</td>
+</tr>
+<tr>
+  <td class="bl">12</td>
+  <td class="bl">9</td>
+  <td class="bl">6</td>
+  <td class="bl">2</td>
+  <td class="bl">17</td>
+  <td class="bl">14</td>
+  <td class="bl">11</td>
+</tr>
+<tr>
+  <td class="bl">10</td>
+  <td class="bl">5</td>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+  <td class="bl">10</td>
+  <td class="bl">5</td>
+  <td class="bl">0</td>
+</tr>
+<tr>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+  <td class="bblcent">IV Ik.</td>
+  <td class="bblcent">IV Caban.</td>
+  <td class="bblcent">IV Eb.</td>
+</tr>
+<tr>
+  <td colspan="8">&nbsp;</td>
+</tr>
+<tr>
+  <td class="bt">&nbsp;</td>
+  <td class="bt">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btl">&nbsp;</td>
+  <td class="btlcent">Sixth<br />column.</td>
+  <td class="btlcent">Seventh<br />column.</td>
+</tr>
+<tr>
+  <td class="bt bb" rowspan="4">Plate 71,<br />lower<br />division</td>
+  <td class="bt bb" rowspan="4"><table border="0" cellpadding="0" cellspacing="0" summary="bracket">
+     <tr>
+       <td class="bt bl bb">&nbsp;<br />&nbsp;<br />&nbsp;</td>
+     </tr>
+     </table></td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btlcent">&mdash;</td>
+  <td class="btl">5</td>
+  <td class="btl">4</td>
+</tr>
+<tr>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">1</td>
+  <td class="blcent">15</td>
+</tr>
+<tr>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="blcent">&mdash;</td>
+  <td class="bl">0</td>
+  <td class="bl">15</td>
+</tr>
+<tr>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">&mdash;</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Manik.</td>
+</tr>
+</table>
+
+<p>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. Com<span class='pagenum'><a name="Page_333" id="Page_333">[333]</a></span>mencing with this
+number and adding it successively, we obtain the numbers over the various
+columns:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, middle division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, middle division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over third column, middle division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over second column, middle division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over first column, middle division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td colspan="2"><a name="FNanchor_333-1_44" id="FNanchor_333-1_44"></a><a href="#Footnote_333-1_44" class="fnanchor">333-1</a></td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over third column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over second column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over first column, middle division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, middle division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, middle division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, lower division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, lower division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over third column, lower division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over second column, lower division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over first column, lower division, Plate 73.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td><span class='pagenum'><a name="Page_334" id="Page_334">[334]</a></span>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over fifth column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over fourth column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over third column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>Over second column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Over first column, lower division, Plate 72.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>Over seventh column, lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Over sixth column, lower division, Plate 71.</td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<p class="tabletitle"><a name="Table_XXIV" id="Table_XXIV"></a><span class="smcap">Table XXIV.</span>&mdash;<i>Table showing relations of Plates 70 and 71.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table XXIV">
+<tr>
+  <td class="btcent" colspan="2">Plate 70.</td>
+  <td class="btlcent" colspan="6">Plate 71.</td>
+</tr>
+<tr>
+  <td class="btcent">5th column.</td>
+  <td class="btlcent">6th column.</td>
+  <td class="btlcent">1st column.</td>
+  <td class="btlcent">2d column.</td>
+  <td class="btlcent">3d column.</td>
+  <td class="btlcent">4th column.</td>
+  <td class="btlcent">5th column.</td>
+  <td class="btlcent">6th column.</td>
+</tr>
+<tr>
+  <td class="tdc">6</td>
+  <td class="blcent">5</td>
+  <td class="blcent">&nbsp;&nbsp;4</td>
+  <td class="blcent">&nbsp;&nbsp;3</td>
+  <td class="blcent">2</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">&nbsp;</td>
+  <td class="blcent">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">1</td>
+  <td class="blcent">1</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">0</td>
+  <td class="blcent">15</td>
+  <td class="blcent">10</td>
+  <td class="blcent">5</td>
+</tr>
+<tr>
+  <td class="tdc">6</td>
+  <td class="blcent">2</td>
+  <td class="blcent">16</td>
+  <td class="blcent">12</td>
+  <td class="blcent">8</td>
+  <td class="blcent">&nbsp;&nbsp;3</td>
+  <td class="blcent">&nbsp;&nbsp;2</td>
+  <td class="blcent">1</td>
+</tr>
+<tr>
+  <td class="tdc">0</td>
+  <td class="blcent">0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">0</td>
+</tr>
+<tr>
+  <td class="bbcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+</tr>
+</table>
+
+<p>For the purpose of assisting the reader to see the relation more clearly,
+the last column of the preceding series&mdash;sixth of the lower division on
+Plate 71&mdash;is added at the right as it stands in the original.</p>
+
+<p><span class='pagenum'><a name="Page_335" id="Page_335">[335]</a></span>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:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Sixth column, lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fifth column, lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fourth column, lower division, Plate 71.</td>
+</tr>
+</table>
+
+<p>At this point another change occurs: the former difference is added to
+the last figures and the sum is doubled.</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td class="colhead" colspan="3">Twenty year<br />periods.</td>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright"></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright"></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright"></td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Third column lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Second column, lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>First column, lower division, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Sixth column, lower division, Plate 70.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fifth column, lower division, Plate 70.</td>
+</tr>
+</table>
+
+<p>This series does not end at this point, but is continued in the lines
+immediately above, which are as follows:</p>
+
+<p class="tabletitle"><a name="Table_XXV" id="Table_XXV"></a><span class="smcap">Table XXV.</span>&mdash;<i>Table showing relations between Plates 70 and 71.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Table XXIV">
+<tr>
+  <td class="btcent" colspan="2">Plate 70.</td>
+  <td class="btlcent" colspan="6">Plate 71.</td>
+</tr>
+<tr>
+  <td class="btcent">5th column.</td>
+  <td class="btlcent">6th column.</td>
+  <td class="btlcent">1st column.</td>
+  <td class="btlcent">2d column.</td>
+  <td class="btlcent">3d column.</td>
+  <td class="btlcent">4th column.</td>
+  <td class="btlcent">5th column.</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;&nbsp;1</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;&nbsp;0</td>
+  <td class="blcent">8(?)</td>
+  <td class="blcent">15</td>
+  <td class="blcent">13</td>
+  <td class="blcent">10</td>
+  <td class="blcent">9</td>
+  <td class="blcent">&nbsp;&nbsp;7</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="blcent">XII</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">12</td>
+  <td class="blcent">&nbsp;&nbsp;1</td>
+  <td class="blcent">&nbsp;&nbsp;3</td>
+  <td class="blcent">&nbsp;&nbsp;2</td>
+  <td class="blcent">&nbsp;&nbsp;2</td>
+  <td class="blcent">2</td>
+  <td class="blcent">&nbsp;&nbsp;1</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="blcent">II</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;&nbsp;3</td>
+  <td class="blcent">10</td>
+  <td class="blcent">&nbsp;&nbsp;6</td>
+  <td class="blcent">16</td>
+  <td class="blcent">&nbsp;&nbsp;4</td>
+  <td class="blcent">0</td>
+  <td class="blcent">10</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+  <td class="blcent">XII</td>
+  <td class="bl">&nbsp;</td>
+  <td class="bl">&nbsp;</td>
+</tr>
+<tr>
+  <td class="tdc">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+  <td class="blcent">(?)</td>
+  <td class="blcent">0</td>
+  <td class="blcent">&nbsp;&nbsp;0</td>
+</tr>
+<tr>
+  <td class="bbcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+  <td class="bblcent">IV Eb.</td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_336" id="Page_336">[336]</a></span>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:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+</table>
+
+<p>To obtain the figures of the fourth column this difference must be
+doubled, thus</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+</table>
+
+<p>To obtain the black numbers of the next (third) column, the lower cipher
+symbol of which is wanting, we add the former difference:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+</table>
+
+<p>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:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Second column, Plate 71.</td>
+</tr>
+</table>
+
+<p>If the increased difference, 2, 0, 8, 0, were retained after its
+appearance the result would be as follows:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">7</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fifth column, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Fourth column, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Third column, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Second column, Plate 71.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">15</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>First column, Plate 71.</td>
+</tr>
+</table>
+
+<p>Adding the difference, 2, 0, 8, 0, to the third column, Plate 71, thus:</p>
+
+<table class="ktuk" border="0" cellpadding="0" cellspacing="0" summary="Day counts">
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;&nbsp;0</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+</tr>
+</table>
+
+<p class="noindent">we obtain the red numerals inserted in the third column. It is probable
+that the original or some subsequent scribe, observing an error at<span class='pagenum'><a name="Page_337" id="Page_337">[337]</a></span> 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.</p>
+
+<p>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.</p>
+
+<div class="figcenter" style="width: 348px;">
+<a name="Fig_371" id="Fig_371"></a><img src="images/image22.png" width="348" height="73" alt="Fig. 371. Specimens of ornamental loops from page 72,
+Dresden Codex." title="Fig. 371. Specimens of ornamental loops from page 72,
+Dresden Codex." />
+<span class="caption"><span class="smcap">Fig.</span> 371. Specimens of ornamental loops from page 72,
+Dresden Codex.</span>
+</div>
+
+<p>Commencing in the sixth column of Plate 71<i>a</i> and running through 72<i>a</i>
+to the second column of 73<i>a</i>, 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 (<a href="#Fig_371">Fig. 371</a>) 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 <span class="nowrap">katunes.<a name="FNanchor_337-1_45" id="FNanchor_337-1_45"></a><a href="#Footnote_337-1_45" class="fnanchor">337-1</a></span> It is as
+follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="series of numbers">
+<tr>
+  <td></td>
+  <td></td>
+  <td></td>
+  <td></td>
+  <td></td>
+  <td></td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td class="tdr">1</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="tdr">2</td>
+  <td class="tdr">5</td>
+  <td class="tdr">8</td>
+  <td class="tdr">10</td>
+  <td class="tdr">13</td>
+  <td class="tdr">16</td>
+  <td class="tdr">0</td>
+  <td class="tdr">3</td>
+  <td class="tdr">6</td>
+  <td class="tdr">9</td>
+  <td class="tdr">11</td>
+  <td class="tdr">14</td>
+  <td class="tdr">17</td>
+  <td></td>
+</tr>
+<tr>
+  <td colspan="13"></td>
+  <td>II.</td>
+</tr>
+<tr>
+  <td class="tdr">14</td>
+  <td class="tdr">8</td>
+  <td class="tdr">2</td>
+  <td class="tdr">16</td>
+  <td class="tdr">10</td>
+  <td class="tdr">4</td>
+  <td class="tdr">18</td>
+  <td class="tdr">12</td>
+  <td class="tdr">6</td>
+  <td class="tdr">0</td>
+  <td class="tdr">14</td>
+  <td class="tdr">7(?)</td>
+  <td class="tdr">2</td>
+  <td>XIV</td>
+</tr>
+<tr>
+  <td class="tdr">&#9322;</td>
+  <td class="tdr">&#9324;</td>
+  <td class="tdr">&#9313;</td>
+  <td class="tdr">&#9315;</td>
+  <td class="tdr">&#9317;</td>
+  <td class="tdr">&#9319;</td>
+  <td class="tdr">&#9321;</td>
+  <td class="tdr">&#9323;</td>
+  <td class="tdr">&#9312;</td>
+  <td class="tdr">&#9314;</td>
+  <td class="tdr">&#9316;</td>
+  <td class="tdr">&#9318;</td>
+  <td class="tdr">&#9320;</td>
+  <td></td>
+</tr>
+</table>
+
+<p>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<span class='pagenum'><a name="Page_338" id="Page_338">[338]</a></span> XIV,
+denoting the difference between the columns, as is apparent from the
+additions here given:</p>
+
+<table class="tuk" border="0" cellpadding="0" cellspacing="0" summary="addition">
+<tr>
+  <td class="colhead" colspan="3">Years.</td>
+  <td class="colhead" colspan="3">Months.</td>
+  <td class="colhead" colspan="2">Days.</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>First or left hand column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">5</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>Second column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Third column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>Fourth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">13</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">10</td>
+  <td>&nbsp;</td>
+  <td>Fifth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">16</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">4</td>
+  <td>&nbsp;</td>
+  <td>Sixth <a name="corr8" id="corr8"></a><ins class="correction" title="column.">column</ins></td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">18</td>
+  <td>&nbsp;</td>
+  <td>Seventh column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">3</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">12</td>
+  <td>&nbsp;</td>
+  <td>Eighth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">6</td>
+  <td>&nbsp;</td>
+  <td>Ninth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">9</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">0</td>
+  <td>&nbsp;</td>
+  <td>Tenth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">11</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>Eleventh column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">14</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">8</td>
+  <td><a name="FNanchor_338-1_46" id="FNanchor_338-1_46"></a><a name="corr9" id="corr9"></a><ins class="correction" title="Footnote number missing in original"><a href="#Footnote_338-1_46" class="fnanchor">338-1</a></ins></td>
+  <td>Twelfth column.</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="bbright">&nbsp;</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">2</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="bbright">14</td>
+  <td>&nbsp;</td>
+</tr>
+<tr>
+  <td>&nbsp;</td>
+  <td class="tdr">1</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">17</td>
+  <td>&nbsp;</td>
+  <td>&nbsp;</td>
+  <td class="tdr">2</td>
+  <td>&nbsp;</td>
+  <td>Thirteenth column.</td>
+</tr>
+</table>
+
+
+<div class="footnotes" style="margin-top: 2em;">
+
+<p><a name="Footnote_261-1_9" id="Footnote_261-1_9"></a><a href="#FNanchor_261-1_9"><span class="label">261-1</span></a> The work here referred to is entitled Die
+Mayahandschrift der K&ouml;niglichen &ouml;ffentlichen Bibliothek zu Dresden,
+herausgegeben von Prof. Dr. E. F&ouml;rstemann, Hofrat und Oberbibliothekar.
+It contains, besides the chromolithographs of the 74 plates, an
+introduction published at Leipzig, 1880, 4<sup class="a">o</sup>.</p>
+
+<p><a name="Footnote_269-1_10" id="Footnote_269-1_10"></a><a href="#FNanchor_269-1_10"><span class="label">269-1</span></a> A Study of the Manuscript Troano, by Cyrus Thomas, pp.
+7-15.</p>
+
+<p><a name="Footnote_272-1_11" id="Footnote_272-1_11"></a><a href="#FNanchor_272-1_11"><span class="label">272-1</span></a> This method will be adopted throughout this paper where
+figures containing numerals are introduced.</p>
+
+<p><a name="Footnote_273-1_12" id="Footnote_273-1_12"></a><a href="#FNanchor_273-1_12"><span class="label">273-1</span></a> 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.</p>
+
+<p><a name="Footnote_273-2_13" id="Footnote_273-2_13"></a><a href="#FNanchor_273-2_13"><span class="label">273-2</span></a> Strictly speaking, the interval between 11 Men and 13 Oc
+is fourteen days, but throughout this paper, by &#8220;<i>interval between</i>&#8220; two
+days, is to be understood the number of days to be counted <i>from</i> one <i>to
+and including</i> the other. The one counted from is always <i>excluded</i> and
+the one reached or with which the interval terminates is always
+<i>included</i>.</p>
+
+<p><a name="Footnote_273-3_14" id="Footnote_273-3_14"></a><a href="#FNanchor_273-3_14"><span class="label">273-3</span></a> Science, p. 459, April 11, 1884.</p>
+
+<p><a name="Footnote_277-1_15" id="Footnote_277-1_15"></a><a href="#FNanchor_277-1_15"><span class="label">277-1</span></a> Throughout this paper when the words &#8220;figure&#8221; and
+&#8220;character&#8221; are used in reference to what appears in the codex, they are
+to be understood as follows: &#8220;figure&#8221; refers to the picture, as of a
+person, animal, or other object in the spaces; &#8220;character&#8221; refers to the
+hieroglyphics or written symbols.</p>
+
+<p><a name="Footnote_278-1_16" id="Footnote_278-1_16"></a><a href="#FNanchor_278-1_16"><span class="label">278-1</span></a> Study of the Manuscript Troano, by Cyrus Thomas,
+Chapters II and VII.</p>
+
+<p><a name="Footnote_278-2_17" id="Footnote_278-2_17"></a><a href="#FNanchor_278-2_17"><span class="label">278-2</span></a> Erl&auml;uterungen zur Mayahandschrift, p. 2.</p>
+
+<p><a name="Footnote_280-1_18" id="Footnote_280-1_18"></a><a href="#FNanchor_280-1_18"><span class="label">280-1</span></a> Erl&auml;uterungen zur Mayahandschrift, p. 16.</p>
+
+<p><a name="Footnote_280-2_19" id="Footnote_280-2_19"></a><a href="#FNanchor_280-2_19"><span class="label">280-2</span></a> Bureau of Eth., Third Ann. Rep., pp. 16 et seq.</p>
+
+<p><a name="Footnote_282-1_20" id="Footnote_282-1_20"></a><a href="#FNanchor_282-1_20"><span class="label">282-1</span></a> Study of the Manuscript Troano, by Cyrus Thomas, pp. 15,
+16.</p>
+
+<p><a name="Footnote_282-2_21" id="Footnote_282-2_21"></a><a href="#FNanchor_282-2_21"><span class="label">282-2</span></a> D&eacute;chiffrement des &eacute;critures calculiformes ou Mayas, par
+M. le C<sup class="b">te</sup> H. de Charency, Alen&ccedil;on, 1849; also, M&eacute;langes, pp. 185-195.</p>
+
+<p><a name="Footnote_283-1_22" id="Footnote_283-1_22"></a><a href="#FNanchor_283-1_22"><span class="label">283-1</span></a> For an explanation of the principle upon which these day
+columns were formed, see &#8220;Notes on certain Maya and Mexican manuscripts,&#8221;
+by Cyrus Thomas, published in the Third Annual Report of the Bureau of
+Ethnology.</p>
+
+<p><a name="Footnote_290-1_23" id="Footnote_290-1_23"></a><a href="#FNanchor_290-1_23"><span class="label">290-1</span></a> The symbol for this day in Kingsborough resembles Lamat,
+but the photographic copy makes it Ix, as it should be.</p>
+
+<p><a name="Footnote_290-2_24" id="Footnote_290-2_24"></a><a href="#FNanchor_290-2_24"><span class="label">290-2</span></a> F&ouml;rstemann, Erl&auml;uterungen zur Mayahandschrift, p. 42.</p>
+
+<p><a name="Footnote_291-1_25" id="Footnote_291-1_25"></a><a href="#FNanchor_291-1_25"><span class="label">291-1</span></a> Erl&auml;uterungen zur Mayahandschrift, p. 36.</p>
+
+<p><a name="Footnote_292-1_26" id="Footnote_292-1_26"></a><a href="#FNanchor_292-1_26"><span class="label">292-1</span></a> Erl&auml;uterungen zur Mayahandschrift, p. 60.</p>
+
+<p><a name="Footnote_293-1_27" id="Footnote_293-1_27"></a><a href="#FNanchor_293-1_27"><span class="label">293-1</span></a> Erl&auml;uterungen zur Mayahandschrift, p. 56.</p>
+
+<p><a name="Footnote_296-1_28" id="Footnote_296-1_28"></a><a href="#FNanchor_296-1_28"><span class="label">296-1</span></a> The bottom lines are selected because they are less
+injured in the codex than the top lines, which are in most cases entirely
+obliterated.</p>
+
+<p><a name="Footnote_300-1_29" id="Footnote_300-1_29"></a><a href="#FNanchor_300-1_29"><span class="label">300-1</span></a> 3 days in ms., should be 4.</p>
+
+<p><a name="Footnote_317-1_30" id="Footnote_317-1_30"></a><a href="#FNanchor_317-1_30"><span class="label">317-1</span></a> The third symbol in the last day column of Plate 51<i>b</i>
+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<i>b</i>.</p>
+
+<p><a name="Footnote_319-1_31" id="Footnote_319-1_31"></a><a href="#FNanchor_319-1_31"><span class="label">319-1</span></a> This is one of the exceptional cases.</p>
+
+<p><a name="Footnote_321-1_32" id="Footnote_321-1_32"></a><a href="#FNanchor_321-1_32"><span class="label">321-1</span></a> Second exception.</p>
+
+<p><a name="Footnote_321-2_33" id="Footnote_321-2_33"></a><a href="#FNanchor_321-2_33"><span class="label">321-2</span></a> Third exception.</p>
+
+<p><a name="Footnote_323-1_34" id="Footnote_323-1_34"></a><a href="#FNanchor_323-1_34"><span class="label">323-1</span></a> One line has been omitted in the numeral symbol.</p>
+
+<p><a name="Footnote_323-2_35" id="Footnote_323-2_35"></a><a href="#FNanchor_323-2_35"><span class="label">323-2</span></a> Here we have again the added day.</p>
+
+<p><a name="Footnote_324-1_36" id="Footnote_324-1_36"></a><a href="#FNanchor_324-1_36"><span class="label">324-1</span></a> The 8 at this point in the codex is an evident error.</p>
+
+<p><a name="Footnote_324-2_37" id="Footnote_324-2_37"></a><a href="#FNanchor_324-2_37"><span class="label">324-2</span></a> Here is also an error in the original, this being 10.</p>
+
+<p><a name="Footnote_324-3_38" id="Footnote_324-3_38"></a><a href="#FNanchor_324-3_38"><span class="label">324-3</span></a> The symbols require an additional day here.</p>
+
+<p><a name="Footnote_324-4_39" id="Footnote_324-4_39"></a><a href="#FNanchor_324-4_39"><span class="label">324-4</span></a> The 8 in the year line in the original is a manifest
+error, as 6 precedes and 7 follows.</p>
+
+<p><a name="Footnote_324-5_40" id="Footnote_324-5_40"></a><a href="#FNanchor_324-5_40"><span class="label">324-5</span></a> 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.</p>
+
+<p><a name="Footnote_325-1_41" id="Footnote_325-1_41"></a><a href="#FNanchor_325-1_41"><span class="label">325-1</span></a> 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.</p>
+
+<p><a name="Footnote_325-2_42" id="Footnote_325-2_42"></a><a href="#FNanchor_325-2_42"><span class="label">325-2</span></a> Here we have again the additional day.</p>
+
+<p><a name="Footnote_325-3_43" id="Footnote_325-3_43"></a><a href="#FNanchor_325-3_43"><span class="label">325-3</span></a> Added to show connection with the lower series.</p>
+
+<p><a name="Footnote_333-1_44" id="Footnote_333-1_44"></a><a href="#FNanchor_333-1_44"><span class="label">333-1</span></a> Codex has 19, which is equivalent to 1 year and 1
+month.</p>
+
+<p><a name="Footnote_337-1_45" id="Footnote_337-1_45"></a><a href="#FNanchor_337-1_45"><span class="label">337-1</span></a> While reading the final proof I fortunately discovered
+what may prove to be the correct explanation of the numbers in the loops.
+</p><p>
+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.</p>
+
+<p><a name="Footnote_338-1_46" id="Footnote_338-1_46"></a><a href="#FNanchor_338-1_46"><span class="label">338-1</span></a> 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.</p>
+</div>
+
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_339" id="Page_339">[339]</a></span></p>
+
+<h2 class="chapterhead"><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II.</h2>
+
+<p class="sectionhead">CONCLUSIONS.</p>
+
+
+<p>The conclusions to be drawn from the foregoing discussion may be briefly
+stated as follows:</p>
+
+<p>First. That the codex in its present form is composite, being made up
+from two or more different original manuscripts, as Dr. F&ouml;rstemann has
+suggested.</p>
+
+<p>Second. That a number of minor changes and additions have been made by a
+subsequent hand, possibly after it had assumed its present form.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="nowrap">Troano,<a name="FNanchor_339-1_47" id="FNanchor_339-1_47"></a><a href="#Footnote_339-1_47" class="fnanchor">339-1</a></span> 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 <a href="#Fig_371">Fig. 371</a>,
+apparently defy explanation on any supposition except that they refer to
+the numbers of the ahaues, which are based upon the four year
+<span class="nowrap">series.<a name="FNanchor_339-2_48" id="FNanchor_339-2_48"></a><a href="#Footnote_339-2_48" class="fnanchor">339-2</a></span> 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.</p>
+
+<p>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<span class='pagenum'><a name="Page_340" id="Page_340">[340]</a></span> 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&mdash;as F&ouml;rstemann seems to have done&mdash;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 F&ouml;rstemann 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 F&ouml;rstemann has designated Codex B
+(page 24 being considered as belonging thereto).</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate VIII">
+<tr>
+  <td class="tdc">I.</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ahau</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Eb</td>
+  <td rowspan="2"><span class="double">}</span></td>
+  <td rowspan="2">10, XI; 10, VIII; 10, V; 10, II; 12[?], &#9406;.</td>
+</tr>
+<tr>
+  <td>Kan</td>
+</tr>
+<tr>
+  <td>Cib</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Lamat</td>
+  <td></td>
+  <td></td>
+</tr>
+</table>
+
+<p>The last black number is 10 in Brasseur&#8217;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.</p>
+
+<p>If we turn now to the calendar (<a href="#Table_II">Table II</a>) 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<span class='pagenum'><a name="Page_341" id="Page_341">[341]</a></span> 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.</p>
+
+<p>In the upper division of Plate IX of the same manuscript is the following
+series:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate IX">
+<tr>
+  <td>XIII</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Manik</td>
+  <td>20, VII; 20 &#9406;; 1, II; 4, VI; 7, XIII.</td>
+</tr>
+<tr>
+  <td>Cauac</td>
+  <td></td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td></td>
+  <td></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>In this case the intermediate days are as follows:</p>
+
+<div class="blockquot"><p>Between 13 Manik and 13 Cauac: 7 Manik, 1 Manik, 2 Lamat, and 6 Eb.</p></div>
+
+<p>Between 13 Cauac and 13 Chuen: 7 Cauac, 1 Cauac, 2 Ahau, and 6 Kan.</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate IX">
+<tr>
+  <td>&#9406;</td>
+  <td class="tdc">&#9406;</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td>Ahau</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Cib</td>
+  <td>Cimi</td>
+  <td>1, II; 2, IV; 2, VI; 5, XI; 2, XIII; 4, IV; 9(?) &#9406;.</td>
+</tr>
+<tr>
+  <td>Ik</td>
+  <td>Eb</td>
+  <td></td>
+</tr>
+<tr>
+  <td style="padding-right: 1em;">Lamat</td>
+  <td>Ezanab</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td>Kan</td>
+  <td></td>
+  <td></td>
+</tr>
+</table>
+
+<p>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<span class='pagenum'><a name="Page_342" id="Page_342">[342]</a></span> days of
+the columns is 26, and the final red numeral is the same as that over the
+columns.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate IX">
+<tr>
+  <td class="tdc">&#9406;</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Cimi</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ezanab</td>
+  <td>11, XII(?); 11, X; 6, III; 8, XI; 7(?), V; 9, I.</td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ik</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td></td>
+  <td></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>The series, when written out with the substitutes heretofore used, is as
+follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate IX">
+<tr>
+  <td class="tdc">&#9406;</td>
+  <td class="tdc">&#9406;</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Manik</td>
+  <td>Ymix</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td></td>
+</tr>
+<tr>
+  <td style="padding-right: 1em;">Men (?)</td>
+  <td>Been</td>
+  <td>9, X; 6, III; 11, I.</td>
+</tr>
+<tr>
+  <td>Chuen</td>
+  <td>Chicchan</td>
+  <td></td>
+</tr>
+<tr>
+  <td>Akbal</td>
+  <td>Caban</td>
+  <td></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Men</td>
+  <td>Muluc</td>
+  <td></td>
+  <td></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_343" id="Page_343">[343]</a></span>In Brasseur&#8217;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.</p>
+
+<p>Adopting this method and using the Cauac column of our calendar, <a href="#Table_II">Table
+II</a>, 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.</p>
+
+<p>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.</p>
+
+<p>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:</p>
+
+<div class="figcenter" style="width: 200px;">
+<a name="Fig_372" id="Fig_372"></a><img src="images/image23.png" width="43" height="45" alt="Fig. 372. Numeral character from the lower division of
+Plate XV, Manuscript Troano." title="Fig. 372. Numeral character from the lower division of
+Plate XV, Manuscript Troano." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 372. Numeral character from the lower division of
+Plate XV, Manuscript Troano.</span>
+</div>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate XV">
+<tr>
+  <td>III,</td>
+  <td rowspan="3"><span class="triple">}</span></td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td>10, XI&#9406;I.</td>
+</tr>
+<tr>
+  <td>Cimi</td>
+  <td></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_344" id="Page_344">[344]</a></span>Judging by these and the few numbers remaining, the entire series was as
+follows:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate IX">
+<tr>
+  <td>III,</td>
+  <td rowspan="6"><table border="0" cellpadding="0" cellspacing="0" summary="brace">
+                   <tr>
+                      <td class="bt br bb">&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;<br />&nbsp;</td>
+                   </tr>
+                   </table></td>
+</tr>
+<tr>
+  <td>Ix</td>
+  <td></td>
+</tr>
+<tr>
+  <td>Cimi</td>
+  <td rowspan="2">10, XIII; 4, IV; 20, XI; 9, VII; 9, III</td>
+</tr>
+<tr>
+  <td>Ezanab</td>
+</tr>
+<tr>
+  <td>Oc</td>
+  <td></td>
+</tr>
+<tr>
+  <td>Ik</td>
+  <td></td>
+</tr>
+</table>
+
+<p>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 <a href="#Table_II">Table II</a> 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.</p>
+
+<p>According to my theory of the <span class="nowrap">ahaues,<a name="FNanchor_344-1_49" id="FNanchor_344-1_49"></a><a href="#Footnote_344-1_49" class="fnanchor">344-1</a></span> the year 13 Kan would have
+corresponded with the Gregorian years 1376, 1438, 1480, and 1532.
+According to the theory advanced by <span class="nowrap">Perez,<a name="FNanchor_344-2_50" id="FNanchor_344-2_50"></a><a href="#Footnote_344-2_50" class="fnanchor">344-2</a></span> it would have
+corresponded with 1385, 1437, 1489, and 1541.</p>
+
+<p>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.</p>
+
+
+<div class="footnotes">
+
+<p><a name="Footnote_339-1_47" id="Footnote_339-1_47"></a><a href="#FNanchor_339-1_47"><span class="label">339-1</span></a> See Study of the Manuscript Troano, by Cyrus Thomas.</p>
+
+<p><a name="Footnote_339-2_48" id="Footnote_339-2_48"></a><a href="#FNanchor_339-2_48"><span class="label">339-2</span></a> See <a href="#Footnote_337-1_45">note</a> on page 337.</p>
+
+<p><a name="Footnote_344-1_49" id="Footnote_344-1_49"></a><a href="#FNanchor_344-1_49"><span class="label">344-1</span></a> See Table XVII, Study of the Manuscript Troano, by Cyrus
+Thomas, p. 44.</p>
+
+<p><a name="Footnote_344-2_50" id="Footnote_344-2_50"></a><a href="#FNanchor_344-2_50"><span class="label">344-2</span></a> See Table XVIII, ibid., p. 45.</p>
+</div>
+
+
+<hr style="width: 65%;" />
+<p><span class='pagenum'><a name="Page_345" id="Page_345">[345]</a></span></p>
+
+<h2 class="chapterhead"><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III</h2>
+
+<p class="sectionhead">THE WRITING.</p>
+
+
+<p>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.</p>
+
+<p>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 <span class="nowrap">explained<a name="FNanchor_345-1_51" id="FNanchor_345-1_51"></a><a href="#Footnote_345-1_51" class="fnanchor">345-1</a></span> it is unnecessary to repeat that
+explanation here.</p>
+
+<p>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 &#8220;Die Mayahandschrift der k&ouml;niglichen Bibliothek zu Dresden.&#8221; 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:</p>
+
+<table border="0" cellpadding="10" cellspacing="0" summary="Plate XV">
+<tr>
+  <td class="btl pad10"><i>b</i></td>
+  <td class="bt pad10"><i>a</i></td>
+  <td class="btl pad10"><i>h</i></td>
+  <td class="btl pad10"><i>l</i></td>
+  <td class="btl pad10"><i>m</i></td>
+  <td class="btl pad10"><i>w</i></td>
+  <td class="bt br bl pad10"><i>a</i></td>
+</tr>
+<tr>
+  <td class="bbl pad10"><i>r</i></td>
+  <td class="bb pad10"><i>n</i></td>
+  <td class="bl pad10"><i>a</i></td>
+  <td class="bl pad10"><i>a</i></td>
+  <td class="bl pad10"><i>a</i></td>
+  <td class="bbl pad10"><i>r</i></td>
+  <td class="bblr pad10"><i>s</i></td>
+</tr>
+<tr>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="bl pad10"><i>r</i></td>
+  <td class="bl pad10"><i>r</i></td>
+  <td class="blr pad10"><i>r</i></td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+</tr>
+<tr>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="bbl pad10"><i>p</i></td>
+  <td class="bbl pad10"><i>k</i></td>
+  <td class="bl bb br pad10"><i>t</i></td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+</tr>
+</table>
+
+<p>In this case the characters represented by <i>a</i> and <i>r</i> are repeated in
+each group and in the same relation to the other characters. It is<span class='pagenum'><a name="Page_346" id="Page_346">[346]</a></span>
+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.</p>
+
+<p>Although it appears to be well settled that, as a rule, the writing, when
+in lines, is to be read from left to right&mdash;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&mdash;it does not follow
+that the <i>groups</i> 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.</p>
+
+<p>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 <i>they</i> follow
+one another in <i>this</i> 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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_347" id="Page_347">[347]</a></span>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 &#8220;Notes on certain Maya and
+Mexican manuscripts,&#8221; accepted by Drs. F&ouml;rstemann and Schellhas, to be
+correct) follow one another in the proper order if read towards the left,
+to wit, south, east, north, west.</p>
+
+<p>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.</p>
+
+
+<p class="sectionhead"><a name="characters" id="characters"></a>SIGNIFICATION OF THE CHARACTERS.</p>
+
+<p>As Landa&#8217;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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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. L&eacute;on 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.</p>
+
+<p>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 significa<span class='pagenum'><a name="Page_348" id="Page_348">[348]</a></span>tion 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.</p>
+
+
+<p class="sectionhead"><a name="animals" id="animals"></a>SYMBOLS OF ANIMALS &amp;C.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-left: 0;" summary="No. 1">
+<tr>
+  <td class="tdc"><img src="images/image24.png" width="60" height="46" alt="No. 1" title="No. 1" /><br />
+<a name="No_1" id="No_1"></a><span class="caption">No. 1</span></td>
+  <td><p class="hanging"><i>Kal.</i> The symbol for the number 20. Found in all of the codices and
+explained in the preceding portion of this paper.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 2">
+<tr>
+  <td class="tdc"><img src="images/image25.png" width="40" height="21" alt="No. 2" title="No. 2" /><br />
+<a name="No_2" id="No_2"></a><span class="caption">No. 2</span></td>
+  <td><p class="hanging">The symbol for 0 (nought), always red. Found only in the Dresden Codex
+and always in the numeral series.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 3">
+<tr>
+  <td class="tdc"><img src="images/image26.png" width="70" height="65" alt="No. 3" title="No. 3" />
+<a name="No_3" id="No_3"></a><span class="caption">No. 3</span></td>
+  <td><p class="hanging"><i>Kin.</i> 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 <i>Yaxkin;</i> yet it
+is reasonable to suppose it has.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 4">
+<tr>
+  <td class="tdc" rowspan="2"><img src="images/image27.png" width="98" height="219" alt="No. 4 " title="No. 4 " /><br />
+<a name="No_4" id="No_4"></a><span class="caption">No. 4 </span></td>
+  <td><p class="hanging"><i>Aac</i> or <i>Ac</i>. A turtle. That this symbol as shown in <i>a</i> and <i>b</i>
+denotes the turtle is conclusively proved by its resemblance to the
+head of that animal, as figured in the Cortesian Codex (see <a href="#Fig_373">Fig.
+373</a>) 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.</p></td>
+</tr>
+<tr>
+  <td class="tdc"><a name="Fig_373" id="Fig_373"></a><img src="images/image28.png" width="181" height="106" alt="Fig. 373. Turtle from the Cortesian Codex." title="Fig. 373. Turtle from the Cortesian Codex." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 373. Turtle from the Cortesian Codex.</span></td>
+</tr>
+</table>
+
+<p>There can be no doubt that Landa&#8217;s <i>A</i>, an exact copy of which is given
+in the margin, in both varieties, <i>c</i> and <i>d</i>, 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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 5">
+<tr>
+  <td class="tdc"><img src="images/image29.png" width="81" height="60" alt="No. 5" title="No. 5" /><br />
+<a name="No_5" id="No_5"></a><span class="caption">No. 5</span></td>
+  <td><p class="hanging"><i>Uech.</i> 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).</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 6">
+<tr>
+  <td class="tdc"><img src="images/image30.png" width="58" height="118" alt="No. 6" title="No. 6" /><br />
+<a name="No_6" id="No_6"></a><a name="corr10" id="corr10"></a><ins class="correction" title="Figure number missing in original">No. 6</ins></td>
+  <td><p class="hanging"><i>Che.</i> Wood. (See Study of the Manuscript Troano, by Cyrus Thomas, p.
+144).</p></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_349" id="Page_349">[349]</a></span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 7">
+<tr>
+  <td class="tdc"><img src="images/image31.png" width="96" height="44" alt="No. 7" title="No. 7" /><br />
+<a name="No_7" id="No_7"></a><span class="caption">No. 7</span></td>
+  <td><p class="hanging"><i>Cab.</i> Earth, soil; also honey. (See Study of the Manuscript Troano, by
+Cyrus Thomas, p. 150.)</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 8">
+<tr>
+  <td class="tdc"><img src="images/image32.png" width="81" height="83" alt="No. 8" title="No. 8" /><br />
+<a name="No_8" id="No_8"></a><span class="caption">No. 8</span></td>
+  <td><p class="hanging"><i>Piz.</i> 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 <i>Piz</i>, as given in the
+work alluded to, is correct.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 9">
+<tr>
+  <td class="tdc"><img src="images/image33.png" width="91" height="48" alt="No. 9" title="No. 9" /><br />
+<a name="No_9" id="No_9"></a><span class="caption">No. 9</span></td>
+  <td><p class="hanging"><i>U.</i> 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.)</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 10">
+<tr>
+  <td class="tdc"><img src="images/image34.png" width="26" height="40" alt="No. 10" title="No. 10" /><br />
+<a name="No_10" id="No_10"></a><span class="caption">No. 10</span></td>
+  <td><p class="hanging"><i>Xicim.</i> The ear. Rosny, Vocabulaire hi&eacute;ratique, No. 185.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 11">
+<tr>
+  <td class="tdc"><img src="images/image35.png" width="72" height="73" alt="No. 11" title="No. 11" /><br />
+<a name="No_11" id="No_11"></a><span class="caption">No. 11</span></td>
+  <td><p class="hanging"><i>Hau.</i> The quarter of a deer. Usually represented as an offering to the
+gods; in all the manuscripts.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 12">
+<tr>
+  <td class="tdc"><img src="images/image36.png" width="173" height="128" alt="No. 12" title="No. 12" /><br />
+<a name="No_12" id="No_12"></a><span class="caption">No. 12</span></td>
+  <td><p class="hanging"><i>Ikilcab.</i> 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&#8217;s supposition that it represents a bee is
+correct.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 13">
+<tr>
+  <td class="tdc"><img src="images/image37.png" width="84" height="77" alt="No. 13" title="No. 13" /><br />
+<a name="No_13" id="No_13"></a><span class="caption">No. 13</span></td>
+  <td><p class="hanging">Honey in the comb. (See Study of the Manuscript Troano, by Cyrus
+Thomas, Fig. 20); in the Manuscript Troano only, and always in red.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 14">
+<tr>
+  <td class="tdc"><img src="images/image38.png" width="80" height="45" alt="No. 14" title="No. 14" /><br />
+<a name="No_14" id="No_14"></a><span class="caption">No. 14</span></td>
+  <td><p class="hanging"><i>Xamach or Chimix.</i> 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 <a href="#Fig_374">Fig. 374</a>.</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 92px;">
+<a name="Fig_374" id="Fig_374"></a><img src="images/image39.png" width="92" height="125" alt="Fig. 374. Jar from the Cortesian Codex." title="Fig. 374. Jar from the Cortesian Codex." />
+<span class="caption"><span class="smcap">Fig.</span> 374. Jar from the Cortesian Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_350" id="Page_350">[350]</a></span>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 amphor&aelig; of the Bacab, though not surmounted, as
+Brasseur supposed, by human or animal figures.</p>
+
+<p>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.</p>
+
+<div class="figleft" style="width: 63px;">
+<img src="images/image40.png" width="63" height="57" alt="Hieroglyph" title="Hieroglyph" />
+</div>
+
+<p>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.</p>
+
+<p>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:
+<img src="images/image41.png" width="86" height="58" alt="Hieroglyph" title="Hieroglyph" style="vertical-align: middle;" /></p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 15">
+<tr>
+  <td class="tdc"><img src="images/image42.png" width="82" height="194" alt="No. 15" title="No. 15" /><br />
+<a name="No_15" id="No_15"></a><span class="caption">No. 15</span></td>
+  <td><p class="hanging">(?) 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.</p></td>
+</tr>
+</table>
+
+<p>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.)</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 16">
+<tr>
+  <td class="tdc"><img src="images/image43.png" width="57" height="42" alt="No. 16" title="No. 16" /><br />
+<a name="No_16" id="No_16"></a><span class="caption">No. 16</span></td>
+  <td><p class="hanging">(?) Symbol of a worm which gnawed the roots of the growing agave or
+maguey; appears but once, on Plate XXIX<i>c</i> of the Manuscript Troano.</p></td>
+</tr>
+</table>
+
+<p>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 <a href="#Fig_375">Fig.
+375</a>.</p>
+
+<p><span class='pagenum'><a name="Page_351" id="Page_351">[351]</a></span></p>
+
+<table width="80%" border="0" cellpadding="0" cellspacing="0" summary="Fig. 375, 376">
+<tr>
+  <td class="tdc" style="width: 50%; vertical-align: bottom;"><a name="Fig_375" id="Fig_375"></a><img src="images/image44.png" width="135" height="139" alt="Fig. 375. Worm and plant from Manuscript Troano." title="Fig. 375. Worm and plant from Manuscript Troano." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 375. Worm and plant from Manuscript Troano.</span></td>
+  <td class="tdc" style="width: 50%; vertical-align: bottom;"><a name="Fig_376" id="Fig_376"></a><img src="images/image45.png" width="125" height="172" alt="Fig. 376. Figure of a woman from the Dresden Codex." title="Fig. 376. Figure of a woman from the Dresden Codex." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 376. Figure of a woman from the Dresden Codex.</span></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 17">
+<tr>
+  <td class="tdc"><img src="images/image46.png" width="56" height="34" alt="No. 17" title="No. 17" /><br />
+<a name="No_17" id="No_17"></a><span class="caption">No. 17</span></td>
+  <td><p class="hanging"><i>Chuplal.</i> 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.</p></td>
+</tr>
+</table>
+
+<p>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 <a href="#Fig_376">Fig. 376</a>).</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 18">
+<tr>
+  <td class="tdc"><img src="images/image47.png" width="95" height="157" alt="No. 18 " title="No. 18 " /><br />
+<a name="No_18" id="No_18"></a><span class="caption">No. 18 </span></td>
+  <td><p class="hanging"><i>Otoch.</i> A house or dwelling, or <i>Tabay;</i> a hut or hunting lodge. The
+symbol marked <i>a</i> is found in the Cortesian Codex on Plate 29; that
+marked <i>b</i>, on Plates 29, 32, and 34, same codex, and on Plates XVI*
+and XXII* of the Manuscript Troano. The one marked <i>c</i> is the usual
+form in the latter, as on Plates V*, VII*, and X*. It is also on
+Plate 38 of the Dresden Codex.</p></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 19">
+<tr>
+  <td class="tdc"><img src="images/image48.png" width="89" height="131" alt="No. 19" title="No. 19" /><br />
+<a name="No_19" id="No_19"></a><span class="caption">No. 19</span></td>
+  <td><p class="hanging"><i>Buk</i> (?). 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 <i>a</i>, is found only on Plate XIX of the
+Manuscript Troano, and the second, on Plates 5 and 6 of the Dresden
+Codex.</p></td>
+</tr>
+</table>
+
+<p>A copy of part of Plate XIX of the Manuscript Troano is introduced here
+(see <a href="#Fig_377">Fig. 377</a>) 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
+nec<span class='pagenum'><a name="Page_352" id="Page_352">[352]</a><br /><a name="Page_353" id="Page_353">[353]</a></span>essary in the work to be performed. It is probably a conventional
+sign, and not a phonetic character.</p>
+
+<div class="figcenter" style="width: 263px;">
+<a name="Fig_377" id="Fig_377"></a><a href="images/image49-full.png"><img src="images/image49.png" width="263" height="332" alt="Fig. 377." title="Fig. 377." /></a>
+<span class="caption"><span class="smcap">Fig.</span> 377.</span>
+</div>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 20">
+<tr>
+  <td class="tdc"><img src="images/image50.png" width="67" height="46" alt="No. 20" title="No. 20" /><br />
+<a name="No_20" id="No_20"></a><span class="caption">No. 20</span></td>
+  <td><p class="hanging">(?) 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.</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 363px;">
+<a name="Fig_378" id="Fig_378"></a><img src="images/image51.png" width="363" height="357" alt="Fig. 378. Copy of lower division of Plate 65, Dresden
+Codex." title="Fig. 378. Copy of lower division of Plate 65, Dresden
+Codex." />
+<span class="caption"><span class="smcap">Fig.</span> 378. Copy of lower division of Plate 65, Dresden
+Codex.</span>
+</div>
+
+<p>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
+&#8220;long nosed god&#8221; or &#8220;god with the snake-like tongue,&#8221; or to ceremonies to
+be performed in honor of this deity. Over the figure are three lines of
+written characters, as shown in <a href="#Fig_378">Fig. 378</a>, 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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 65">
+<tr>
+  <td class="btl pad10"><i>a</i></td>
+  <td class="bl bt br pad10"><i>b</i></td>
+</tr>
+<tr>
+  <td class="btl pad10"><i>c</i></td>
+  <td class="bl bt br pad10"><i>d</i></td>
+</tr>
+<tr>
+  <td class="bl bt bb pad10"><i>e</i></td>
+  <td class="bl bt br bb pad10"><i>f</i></td>
+</tr>
+</table>
+
+<p class="noindent"><span class='pagenum'><a name="Page_354" id="Page_354">[354]</a></span>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 <i>a</i> in the above diagram is the same
+throughout. The same thing is true in reference to the third, or that
+occupying the place of <i>c</i> in the diagram, which is the symbol of the
+deity. The sixth, or that corresponding with <i>f</i> in the diagram, is also
+the same throughout the series; the fifth, corresponding with <i>e</i>, 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 <i>b</i> and <i>d</i>
+in the above diagram; the others (at least those represented by <i>a</i>, <i>c</i>,
+and <i>f</i>), if referring at all to the figures, must relate to something
+found in or applicable to each. The third (<i>c</i>), 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.</p>
+
+<p>Comparing the second character (<i>b</i>) 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.</p>
+
+<p>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.</p>
+
+<p>Turning to <a href="#Fig_378">Fig. 378</a>, we observe in the right hand department the marks of
+footsteps under the deity and the character shown in the margin (<a href="#No_20">No. 20</a>)
+as the second of the group above the deity. It is worthy of notice that
+in the two we find precisely Landa&#8217;s two characters for the letter B. Is
+it possible that the two principal parts of this compound character
+denote the Maya words <i>oc be</i>, &#8220;foot journey&#8221; or &#8220;enters upon the
+journey&#8221;? 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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 21">
+<tr>
+  <td class="tdc"><img src="images/image52.png" width="60" height="37" alt="No. 21." title="No. 21." /><br />
+<a name="No_21" id="No_21"></a><span class="caption">No. 21.</span></td>
+  <td><p class="hanging">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 <a href="#Fig_378">Fig. 378</a>, will be the symbol for the substance
+represented by scrolls under the figure of the <span class="nowrap">deity.<a name="FNanchor_354-1_52" id="FNanchor_354-1_52"></a><a href="#Footnote_354-1_52" class="fnanchor">354-1</a></span></p></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_355" id="Page_355">[355]</a></span>The prefix in this case is the same as that to the symbol above described
+(<a href="#No_20">No. 20</a>), and of course has the same signification. The other portion of
+<a href="#No_21">No. 21</a> must therefore represent the substance in which the god is
+walking. This appears to be dust, sand, or mud.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 22">
+<tr>
+  <td class="tdc"><img src="images/image53.png" width="105" height="129" alt="No. 22." title="No. 22." /><br />
+<a name="No_22" id="No_22"></a><span class="caption">No. 22.</span></td>
+  <td><p class="hanging"><i>Cacauak</i> or <i>cacauche</i>. The wild or cultivated cacao. Found a number
+of times in the Dresden Codex, sometimes as represented in the
+marginal figure <i>a</i> and sometimes as in <i>c</i>, 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 <i>b</i>, 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.</p></td>
+</tr>
+</table>
+
+<p>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 <i>c</i> 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.</p>
+
+<p>In this symbol we find another of Landa&#8217;s letters, and, if phonetic,
+agreeing precisely with his interpretation.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 23">
+<tr>
+  <td class="tdc"><img src="images/image54.png" width="76" height="102" alt="No. 23." title="No. 23." /><br />
+<a name="No_23" id="No_23"></a><span class="caption">No. 23.</span></td>
+  <td><p class="hanging"><i>Ekbalam</i> according to Rosny. The variety marked <i>a</i> is found twice in
+the Manuscript Troano, Plates XVI and XVII, and that marked <i>b</i> once
+in the Dresden Codex, Plate 8, each time in connection with a
+spotted, leopard-like animal.</p></td>
+</tr>
+</table>
+
+<p>The black markings on the symbols render it probable that Rosny&#8217;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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 24">
+<tr>
+  <td class="tdc"><img src="images/image55.png" width="60" height="38" alt="No. 24." title="No. 24." /><br />
+<a name="No_24" id="No_24"></a><span class="caption">No. 24.</span></td>
+  <td><p class="hanging"><i>Moo.</i> The ara, a large species of parrot. This symbol is found but
+once, and that in Plate 16<i>c</i>, Dresden Codex, in connection with the
+bird shown in <a href="#Fig_379">Fig. 379</a>.</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 200px;">
+<a name="Fig_379" id="Fig_379"></a><img src="images/image56.png" width="67" height="102" alt="Fig. 379. The moo or ara from Plate 16. Dresden Codex." title="Fig. 379. The moo or ara from Plate 16. Dresden Codex." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 379. The moo or ara from Plate 16. Dresden Codex.</span>
+</div>
+
+<p><span class='pagenum'><a name="Page_356" id="Page_356">[356]</a></span>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Plate 16">
+<tr>
+  <td class="btl pad10"><i>a</i></td>
+  <td class="bt pad10"><i>b</i></td>
+  <td class="btl pad10"><i>e</i></td>
+  <td class="bt pad10"><i>d</i></td>
+  <td class="btl pad10"><i>g</i></td>
+  <td class="bt pad10"><i>h</i></td>
+  <td class="btl pad10"><i>i</i></td>
+  <td class="btl pad10"><i>m</i></td>
+  <td class="btl br pad10"><i>o</i></td>
+</tr>
+<tr>
+  <td class="bbl pad10"><i>c</i></td>
+  <td class="bb pad10"><i>d</i></td>
+  <td class="bbl pad10"><i>c</i></td>
+  <td class="bb pad10"><i>f</i></td>
+  <td class="bbl pad10"><i>c</i></td>
+  <td class="bb pad10"><i>d</i></td>
+  <td class="bl pad10"><i>c</i></td>
+  <td class="bl pad10"><i>n</i></td>
+  <td class="blr pad10"><i>b</i></td>
+</tr>
+<tr>
+  <td class="tdc pad10" colspan="2">1</td>
+  <td class="tdc pad10" colspan="2">2</td>
+  <td class="tdc pad10" colspan="2">3</td>
+  <td class="bl pad10"><i>k</i></td>
+  <td class="bl pad10"><i>c</i></td>
+  <td class="blr pad10"><i>c</i></td>
+</tr>
+<tr>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="pad10">&nbsp;</td>
+  <td class="bbl pad10"><i>l</i></td>
+  <td class="bbl pad10"><i>l</i></td>
+  <td class="bblr pad10"><i>p</i></td>
+</tr>
+</table>
+
+<p>Similar characters in the different groups are represented by the same
+letter; for example, the symbol for woman, heretofore shown (<a href="#No_17">No. 17</a>), is
+represented by <i>c</i>, and an unknown character by <i>d</i>. 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.</p>
+
+<p>At 1, 2, and 3 are female figures with a bird in each case perched on the
+back. At <i>a</i> is the head of a bird, evidently the symbol of the bird on
+the female below; at <i>i</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 <i>m</i>, in the fifth group,
+is another bird&#8217;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 <i>g</i> corresponding with
+symbol <a href="#No_24">No. 24</a>, 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.</p>
+
+<p>According to this conclusion, the following symbols also denote birds,
+probably of the species here indicated.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 25">
+<tr>
+  <td class="tdc"><img src="images/image57.png" width="63" height="38" alt="No. 25." title="No. 25." /><br />
+<a name="No_25" id="No_25"></a><span class="caption">No. 25.</span></td>
+  <td><p class="hanging"><i>Icim</i>? The horned owl. This is represented by <i>a</i> in the first group
+in the above diagram.</p></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 26">
+<tr>
+  <td class="tdc"><img src="images/image58.png" width="62" height="40" alt="No. 26." title="No. 26." /><br />
+<a name="No_26" id="No_26"></a><span class="caption">No. 26.</span></td>
+  <td><p class="hanging"><i>Kukuitz</i>? The Quetzal. The symbol is apparently incomplete, but the
+bird figured under it justifies this conclusion. This symbol is
+represented by <i>e</i> in the above diagram.</p></td>
+</tr>
+</table>
+
+<p>If this interpretation be correct, we find in this symbol another of
+Landa&#8217;s letters<span class='pagenum'><a name="Page_357" id="Page_357">[357]</a></span>.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 27">
+<tr>
+  <td class="tdc"><img src="images/image59.png" width="88" height="107" alt="No. 27." title="No. 27." /><br />
+<a name="No_27" id="No_27"></a><span class="caption">No. 27.</span></td>
+  <td><p class="hanging"><i>Kuch.</i> A vulture or bird of prey much like the sopilote. These two
+symbols (<i>a</i> and <i>b</i>) appear to refer to the same bird, evidently a
+vulture. (See Manuscript Troano, Plates XVII<i>a</i> and XXVI*<i>a</i>.) The
+first form (<i>a</i>) is found but once (Manuscript Troano, Plate
+XVII<i>a</i>), the other at several points, both in the Manuscript Troano
+and the Dresden Codex, and is represented by <i>m</i> in the preceding
+diagram.</p></td>
+</tr>
+</table>
+
+<p>If this determination be correct, the first of these symbols (<i>a</i>) is
+probably phonetic and agrees with the interpretation of <a href="#No_26">No. 26</a>.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 28">
+<tr>
+  <td class="tdc"><img src="images/image60.png" width="62" height="42" alt="No. 28." title="No. 28." /><br />
+<a name="No_28" id="No_28"></a><span class="caption">No. 28.</span></td>
+  <td><p class="hanging"><i>C&#295;om</i>, <i>Xchom</i>, or <i>Hc&#295;om</i>. 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>i</i> in the preceding diagram.</p></td>
+</tr>
+</table>
+
+<p>If phonetic, the word indicated should, according to Landa&#8217;s alphabet, be
+aspirated, which is found to be true of one of the forms given by Perez.</p>
+
+<p>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:</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 29">
+<tr>
+  <td class="tdc"><img src="images/image61.png" width="55" height="36" alt="No. 29." title="No. 29." /><br />
+<a name="No_29" id="No_29"></a><span class="caption">No. 29.</span></td>
+  <td><p class="hanging"><i>Ceh</i>? The symbol for game quadrupeds. The same idea appears to be
+indicated by the folded and tied quarter of a deer, as shown in <a href="#No_11">No.
+11</a>. The head shown in the symbol is probably intended for that of
+the deer, though more like that of the rabbit.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 30">
+<tr>
+  <td class="tdc"><img src="images/image62.png" width="60" height="85" alt="No. 30." title="No. 30." /><br />
+<a name="No_30" id="No_30"></a><span class="caption">No. 30.</span></td>
+  <td><p class="hanging"><i>Cutz</i> or <i>Cax</i>. The symbol for game birds, the head being probably
+that of the wild turkey (<i>Cutz</i> or <i>Ahcutz</i>).</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 31">
+<tr>
+  <td class="tdc"><img src="images/image63.png" width="60" height="38" alt="No. 31." title="No. 31." /><br />
+<a name="No_31" id="No_31"></a><span class="caption">No. 31.</span></td>
+  <td><p class="hanging"><i>Huh.</i> The symbol for food reptiles or the iguana.</p></td>
+</tr>
+</table>
+
+<p>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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 32">
+<tr>
+  <td class="tdc"><img src="images/image64.png" width="61" height="43" alt="No. 32." title="No. 32." /><br />
+<a name="No_32" id="No_32"></a><span class="caption">No. 32.</span></td>
+  <td><p class="hanging"><i>Cay.</i> The symbol for food fishes, or fishes in general, though as
+often on the Kan symbol or without any suffix.</p></td>
+</tr>
+</table>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 33">
+<tr>
+  <td class="tdc"><img src="images/image65.png" width="51" height="35" alt="No. 33." title="No. 33." /><br />
+<a name="No_33" id="No_33"></a><span class="caption">No. 33.</span></td>
+  <td><p class="hanging"><i>Cutz</i> or <i>Cax</i>. In one of the two series of these food symbols, in
+Plates 29-31 of the Dresden Codex, in place of the bird symbol <a href="#No_30">No.
+30</a> is that shown in symbol <a href="#No_33">No. 33</a>. 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<i>c</i> and 17<i>c</i>, same codex, and is represented by <i>o</i> in the
+preceding diagram.</p></td>
+</tr>
+</table>
+
+<p><span class='pagenum'><a name="Page_358" id="Page_358">[358]</a></span></p>
+
+
+<p class="sectionhead"><a name="deities" id="deities"></a>SYMBOLS OF DEITIES.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 34">
+<tr>
+  <td class="tdc"><img src="images/image66.png" width="79" height="54" alt="No. 34." title="No. 34." /><br />
+<a name="No_34" id="No_34"></a><span class="caption">No. 34.</span></td>
+  <td><p class="hanging"><i>Ekchuah.</i> The symbol or hieroglyph of the deity named &#8220;Ekchuah&#8221; by
+the Mayas and considered the patron and protector of peddlers or
+traveling merchants (<a href="#Fig_380">Fig. 380</a>).</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 151px;">
+<a name="Fig_380" id="Fig_380"></a><img src="images/image67.png" width="151" height="221" alt="Fig. 380. The god Ekchuah, after the Troano and Cortesian
+Codices." title="Fig. 380. The god Ekchuah, after the Troano and Cortesian
+Codices." />
+<span class="caption"><span class="smcap">Fig.</span> 380. The god Ekchuah, after the Troano and Cortesian
+Codices.</span>
+</div>
+
+<p>The signification of the name of this deity is &#8220;The Black Calabash.&#8221; 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.</p>
+
+<p>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.</p>
+
+<p>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. <span class="nowrap">Landa,<a name="FNanchor_358-1_53" id="FNanchor_358-1_53"></a><a href="#Footnote_358-1_53" class="fnanchor">358-1</a></span>
+speaking of the artists carving idols from wood, says:</p>
+
+<div class="blockquot"><p>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 <i>black divinities</i>.</p></div>
+
+<p>Its appearance in Plate XIV* is apparently in connection with the<span class='pagenum'><a name="Page_359" id="Page_359">[359]</a></span>
+ceremonies relating to the manufacture of idols. Neither the symbol nor
+the god it represents is to be fond in the Dresden Codex.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 35">
+<tr>
+  <td class="tdc"><img src="images/image68.png" width="108" height="159" alt="No. 35." title="No. 35." /><br />
+<a name="No_35" id="No_35"></a><span class="caption">No. 35.</span></td>
+  <td><p class="hanging"><i>Kukulcan.</i> (?) This is the symbol of the long nosed god, which Dr.
+Schellhas designates &#8220;the god with the snake-like tongue,&#8221; of which
+representations appear so frequently in the different codices (see
+<a href="#Fig_381">Fig. 381</a>).</p></td>
+</tr>
+</table>
+
+<p>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 <a href="#Fig_382">Fig. 382</a>. Here we see both tongue and fang, and also an
+eye precisely of the form found in the Maya symbol.</p>
+
+<div class="figcenter" style="width: 184px;">
+<a name="Fig_381" id="Fig_381"></a><img src="images/image69.png" width="184" height="321" alt="Fig. 381. The long nosed god (Kukulcan) or &#8220;god with the
+snake-like tongue.&#8221;" title="Fig. 381. The long nosed god (Kukulcan) or &#8220;god with the
+snake-like tongue.&#8221;" />
+<span class="caption"><span class="smcap">Fig.</span> 381. The long nosed god (Kukulcan) or &#8220;god with the
+snake-like tongue.&#8221;</span>
+</div>
+
+<p>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.</p>
+
+<p>As the symbol which accompanies these is the same as that found in<span class='pagenum'><a name="Page_360" id="Page_360">[360]</a></span>
+connection with the &#8220;snake tongued,&#8221; 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.</p>
+
+<div class="figcenter" style="width: 231px;">
+<a name="Fig_382" id="Fig_382"></a><img src="images/image70.png" width="231" height="385" alt="Fig. 382. Copy of head from the Borgian Codex
+(Quetzalcoatl)." title="Fig. 382. Copy of head from the Borgian Codex
+(Quetzalcoatl)." />
+<span class="caption"><span class="smcap">Fig.</span> 382. Copy of head from the Borgian Codex
+(Quetzalcoatl).</span>
+</div>
+
+<p>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:</p>
+
+<div class="blockquot"><p>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&#8217;s
+head as symbol of the atmosphere, upon the day sign <i>Cab</i> as symbol
+of the earth, sitting, with the ax <span class='pagenum'><a name="Page_361" id="Page_361">[361]</a></span>(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&#8217;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&#8217;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 &#8220;feathered snake,&#8221; &#8220;bird snake.&#8221;
+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&#8217;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&#8217;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.</p></div>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 36">
+<tr>
+  <td class="tdc"><img src="images/image71.png" width="75" height="73" alt="No. 36." title="No. 36." /><br />
+<a name="No_36" id="No_36"></a><span class="caption">No. 36.</span></td>
+  <td><p class="hanging"><i>Cimi</i> (?). Supposed symbols of the god of death. Occurring very
+frequently in all the codices, but with several variations (see
+Figs. <a href="#Fig_383">383</a> and <a href="#Fig_384">384</a>).</p></td>
+</tr>
+</table>
+
+<p>These are given chiefly on the authority of Drs. F&ouml;rstemann and
+Schellhas, as I have some doubt in reference to this conclusion, for
+reasons which will here be given.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="Fig. 383, 384">
+<tr>
+  <td class="tdc" style="vertical-align: bottom; width: 50%;"><a name="Fig_383" id="Fig_383"></a><img src="images/image72.png" width="96" height="165" alt="Fig. 383. The supposed god of death, from the Dresden
+Codex." title="Fig. 383. The supposed god of death, from the Dresden
+Codex." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 383. The supposed god of death, from the Dresden
+Codex.</span></td>
+  <td class="tdc" style="vertical-align: bottom; width: 50%;"><a name="Fig_384" id="Fig_384"></a><img src="images/image73.png" width="216" height="190" alt="Fig. 384. The supposed god of death, from the Troano
+Codex." title="Fig. 384. The supposed god of death, from the Troano
+Codex." /><br />
+<span class="caption"><span class="smcap">Fig.</span> 384. The supposed god of death, from the Troano
+Codex.</span></td>
+</tr>
+</table>
+
+<p>As Dr. Schellhas remarks, this is &#8220;the most characteristic and most
+easily recognized deity of the Maya Codices&#8221;; 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<span class='pagenum'><a name="Page_362" id="Page_362">[362]</a></span> 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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 37">
+<tr>
+  <td class="tdc"><img src="images/image74.png" width="48" height="46" alt="No. 37." title="No. 37." /><br />
+<a name="No_37" id="No_37"></a><span class="caption">No. 37.</span></td>
+  <td><p class="hanging">Symbol of the god with the banded face; seen chiefly in the Manuscript
+Troano; not found in the Dresden Codex (<a href="#Fig_385">Fig. 385</a>). This is not the
+deity which Dr. Schellhas designates as &#8220;the god with face crossed
+by lines.&#8221;</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 148px;">
+<a name="Fig_385" id="Fig_385"></a><img src="images/image75.png" width="148" height="170" alt="Fig. 385. The god with the banded face, from the Codex
+Troano." title="Fig. 385. The god with the banded face, from the Codex
+Troano." />
+<span class="caption"><span class="smcap">Fig.</span> 385. The god with the banded face, from the Codex
+Troano.</span>
+</div>
+
+<p>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<i>c</i>, V<i>a</i>, and
+V<i>b</i>, XXVIII*<i>c</i>, and XXIX<i>c</i> 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 r&ocirc;le. The dotted lines with which the bodies of these
+figures are marked and the peculiar anklets appear to<span class='pagenum'><a name="Page_363" id="Page_363">[363]</a></span> 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.</p>
+
+<p>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.</p>
+
+<p>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 r&ocirc;le 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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 38">
+<tr>
+  <td class="tdc"><img src="images/image76.png" width="68" height="47" alt="No. 38." title="No. 38." /><br />
+<a name="No_38" id="No_38"></a><span class="caption">No. 38.</span></td>
+  <td><p class="hanging">(?) Symbol of the deity which Dr. Schellhas designates &#8220;the god with
+the old man&#8217;s face.&#8221; Found in all the codices and almost invariably
+in connection with the representation of the deity shown in our <a href="#Fig_386">Fig.
+386</a>.</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 115px;">
+<a name="Fig_386" id="Fig_386"></a><img src="images/image77.png" width="115" height="170" alt="Fig. 386. The god with the old man&#8217;s face." title="Fig. 386. The god with the old man&#8217;s face." />
+<span class="caption"><span class="smcap">Fig.</span> 386. The god with the old man&#8217;s face.</span>
+</div>
+
+<p>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 r&ocirc;les
+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<i>c</i> and 15<i>c</i> he holds a sun symbol in his hand,
+which might be supposed to refer to his attributes as &#8220;Kinich-Kakmo&#8221; 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<i>c</i>,
+the only place in the first part of the manuscript where honey appears to
+be referred to, and<span class='pagenum'><a name="Page_364" id="Page_364">[364]</a></span> 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*<i>a</i> 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.</p>
+
+<table border="0" cellpadding="0" cellspacing="0" style="margin-top: 1em; margin-left: 0;" summary="No. 39">
+<tr>
+  <td class="tdc"><img src="images/image78.png" width="73" height="50" alt="No. 39." title="No. 39." /><br />
+<a name="No_39" id="No_39"></a><span class="caption"><a name="corr11" id="corr11"></a><ins class="correction" title="No.">Fig.</ins> 39.</span></td>
+  <td><p class="hanging">Symbol, according to Dr. Schellhas, of the deity which he names &#8220;the
+god with face crossed by lines,&#8221; found in all the codices, but most
+frequently in the Manuscript Troano and the Cortesian manuscript.
+The deity is usually represented as in <a href="#Fig_387">Fig. 387</a>.</p></td>
+</tr>
+</table>
+
+<div class="figcenter" style="width: 77px;">
+<a name="Fig_387" id="Fig_387"></a><img src="images/image79.png" width="77" height="125" alt="Fig. 387. The god with face crossed by lines." title="Fig. 387. The god with face crossed by lines." />
+<span class="caption"><span class="smcap">Fig.</span> 387. The god with face crossed by lines.</span>
+</div>
+
+<p>This is introduced here on the authority of Dr. Schellhas, although I
+have considerable doubt as to the correctness of his conclusion.</p>
+
+<p>He remarks in regard to it as follows:</p>
+
+<div class="blockquot"><p>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.</p>
+
+<p>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&#8217;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&#8217;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.</p>
+
+<p>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. *&nbsp;*&nbsp;* To all appearances we have
+here a momentous figure of Maya mythology, of which, unfortunately,
+we know nothing.</p></div>
+
+<p>It is true that this symbol is found in almost every instance where the
+figure of the god appears&mdash;in fact, with fewer exceptions than<span class='pagenum'><a name="Page_365" id="Page_365">[365]</a></span> others in
+reference to which there is probably little doubt. It is also true that
+the symbol is an exact copy of the god&#8217;s head; but on the other hand
+there are strong reasons for doubting the correctness of Dr. Schellhas&#8217;s
+conclusion.</p>
+
+<p>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 <span class="nowrap">idols.<a name="FNanchor_365-1_54" id="FNanchor_365-1_54"></a><a href="#Footnote_365-1_54" class="fnanchor">365-1</a></span></p>
+
+<p>We also find it in connection with the wood symbol (marginal <a href="#No_6">No. 6</a>) 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 &#8220;god with the old man&#8217;s face,&#8221; the head in the latter case
+being apparently carved from a block of wood.</p>
+
+<p>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.</p>
+
+<p>Third, we find rows or lines composed entirely of this symbol, as in the
+so-called title page of the Manuscript Troano.</p>
+
+
+<p class="sectionhead"><a name="phonetics" id="phonetics"></a>DISCUSSION AS TO PHONETIC FEATURES OF THE CHARACTERS.</p>
+
+<p>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 <span class="nowrap">work,<a name="FNanchor_365-2_55" id="FNanchor_365-2_55"></a><a href="#Footnote_365-2_55" class="fnanchor">365-2</a></span> which need
+not be repeated here.</p>
+
+<p>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<span class='pagenum'><a name="Page_366" id="Page_366">[366]</a></span> were passing into true
+<span class="nowrap">ideographs<a name="FNanchor_366-1_56" id="FNanchor_366-1_56"></a><a href="#Footnote_366-1_56" class="fnanchor">366-1</a></span> and possibly into phonetic characters.</p>
+
+<p>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.</p>
+
+<p>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 &#8220;death&#8217;s head&#8221; or skull; that of the day Ymix, &#8220;the grain
+of maize;&#8221; that of the month Moan, &#8220;the head of the moo or ara,&#8221; a
+species of parrot, &amp;c.</p>
+
+<p>It is also possible to show from the manuscripts themselves evidences of
+the changes from conventional pictographs to true or mnemonic symbols.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p><span class='pagenum'><a name="Page_367" id="Page_367">[367]</a></span>Before discussing the question of phonography we ask attention to one or
+two facts regarding Landa&#8217;s alphabet which do not appear to have been
+previously noticed, yet have an important hearing on the subject.</p>
+
+<p>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.</p>
+
+<p>I have already stated as my belief that&mdash;</p>
+
+<div class="blockquot"><p>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
+<span class="nowrap">relationship.<a name="FNanchor_367-1_57" id="FNanchor_367-1_57"></a><a href="#Footnote_367-1_57" class="fnanchor">367-1</a></span></p></div>
+
+<p>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.</p>
+
+<p>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 <a href="#No_4">No. 4</a>), which is nothing more or less than an attempt to
+represent the head of the animal. In the more abbreviated form (<i>b</i>) I at
+once recognized Landa&#8217;s A (compare with <i>c</i> and <i>d</i>, <a href="#No_4">No. 4</a>). As the Maya
+name of the turtle is <i>Ac</i> or <i>Aac</i> 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&#8217;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.</p>
+
+<p>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<i>c</i> (see marginal
+<a href="#No_20">No. 20</a>) and Plate 41<i>c</i> 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<span class='pagenum'><a name="Page_368" id="Page_368">[368]</a></span> proof in these cases is too strong
+to admit of doubt and explains Landa&#8217;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, <i>Be</i>
+being the Maya word for &#8220;way,&#8221; &#8220;journey,&#8221; &#8220;walking,&#8221; &amp;c.</p>
+
+<p>The symbol for the cacao given above in marginal <a href="#No_22">No. 22</a> contains his
+eleventh letter <i>Ca</i> twice and is probably that from which it was taken;
+likewise that of the <i>Kukuitz</i> or Quetzal (marginal <a href="#No_26">No. 26</a>) and of the
+<i>Kuch</i> or vulture (marginal <a href="#No_27">No. 27<i>a</i></a>), each of which contains his <i>Ku</i>,
+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&#8217;s figure of the latter, that it was intended to represent a bird&#8217;s
+nest containing eggs, but an examination of the symbol as found in the
+manuscript renders this conclusion doubtful.</p>
+
+<p>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.</p>
+
+<p>Descending to particulars and examples, the following are, perhaps, the
+strongest proofs which can be presented on this point:</p>
+
+<p>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 &#8220;sun&#8221; or &#8220;day&#8221;
+and as the two Maya words for these points&mdash;<i>Likin</i> or <i>Lakin</i> and
+<i>Chikin</i>&mdash;contain the Maya term for sun or day (&#8220;kin&#8221;), there is some
+reason for believing that the characters are phonetic. There is to be
+added to this evidence the fact that the<span class='pagenum'><a name="Page_369" id="Page_369">[369]</a></span> symbol of the month <i>Yaxkin</i>
+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.</p>
+
+<p>It is now generally admitted by students of American paleography, on what
+appears to be satisfactory evidence, that symbol <a href="#No_7">No. 7</a> of the preceding
+list, <i>Cab</i>, is used to signify &#8220;earth&#8221; or &#8220;land&#8221; and &#8220;honey,&#8221; both of
+which are designated by the same Maya term, <i>Cab</i>. As there is no
+similarity in the things denoted the character is probably phonetic. The
+&#8220;bee&#8221; 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*&mdash;X* of the Manuscript Troano.</p>
+
+<p>The symbol <a href="#No_9">No. 9</a> (U) of the preceding list is found repeatedly on vases
+and also as a prefix to both simple and compound characters. As <i>U</i> in
+Maya signifies &#8220;moon,&#8221; &#8220;vase,&#8221; 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 <i>U</i>. I am aware that
+neither Perez nor Dr. Brinton gives &#8220;vase&#8221; 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.</p>
+
+<p>The symbol <a href="#No_34">No. 34</a> 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, <i>ek</i>, &#8220;black,&#8221; and <i>chu</i>, &#8220;calabash,&#8221; and hence
+signifies &#8220;the black calabash,&#8221; 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.</p>
+
+<p>If the interpretation given of the preceding symbols Nos. <a href="#No_22">22</a>, <a href="#No_24">24</a>, <a href="#No_26">26</a>,
+<a href="#No_27">27<i>a</i></a>, and <a href="#No_33">33</a> be correct, there can be scarcely a doubt that they are
+phonetic. In the first&mdash;<i>cacau</i>, <i>cacauak</i>, or <i>cacauche</i>, the
+&#8220;cacao&#8221;&mdash;we see Landa&#8217;s letter <i>Ca</i>, which is doubled in each of the
+three forms taken from the different codices. In the
+twenty-sixth&mdash;<i>Kukuitz</i>, the Quetzal&mdash;Landa&#8217;s <i>Ku</i> is duplicated, as it
+should be if phonetic, while in 27<i>a</i>, <i>Kuch</i>, 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.</p>
+
+<p><span class='pagenum'><a name="Page_370" id="Page_370">[370]</a></span>If my interpretation of <a href="#No_14">No. 14</a> (<i>Xamach</i> or <i>Chimix</i>) 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 <i>m</i> sound is not repeated in the Maya
+name. This conclusion is strengthened by the fact that the month <i>Mac</i>,
+found in the last or bottom line of Plate 49, is precisely the same as
+the right portion of <a href="#No_14">No. 14</a>, with Landa&#8217;s symbol for <i>Ca</i> added. This
+probably justifies us in concluding that the true name of this month is
+<i>Camach</i>, &#8220;the jaw&#8221; or &#8220;jaws,&#8221; and that Landa&#8217;s figure is simply a rude
+representation of the lips or mouth.</p>
+
+<p>I have expressed the <span class="nowrap">opinion<a name="FNanchor_370-1_58" id="FNanchor_370-1_58"></a><a href="#Footnote_370-1_58" class="fnanchor">370-1</a></span> that the chief phonetic element of
+<a href="#No_8">No. 8</a> (the stone symbol), if used to represent sound, is <i>p</i> or <i>pp</i>.
+This opinion seems to be confirmed by the fact that this character is
+found as a part of the symbol for the month <i>Pop</i> on Plate 50 of the
+Dresden Codex. (See the second character in the first transverse line
+below the day columns in the preceding <a href="#Fig_362">Fig. 362</a>.) The method of
+determining the months referred to in these plates of the codex has been
+given in the preceding part of this paper.</p>
+
+<p>The interpretation given above of symbol <a href="#No_24">No. 24</a> (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<i>c</i>) 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&#8217;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&#8217;s surmise was <span class="nowrap">correct.<a name="FNanchor_370-2_59" id="FNanchor_370-2_59"></a><a href="#Footnote_370-2_59" class="fnanchor">370-2</a></span> 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 <a href="#No_24">No. 24</a> to the symbol
+for the month Mol.</p>
+
+<p>I have shown above that the right portion of <a href="#No_20">No. 20</a> of the list is
+Landa&#8217;s letter B, and also that in the lower division of Plate 65,<span class='pagenum'><a name="Page_371" id="Page_371">[371]</a></span>
+Dresden Codex (see <a href="#Fig_378">Fig. 378</a>), it signifies &#8220;footsteps&#8221; or the act of
+walking. As the Maya word <i>Be</i> signifies &#8220;journey,&#8221; &#8220;wood,&#8221; &#8220;march,&#8221; and
+also &#8220;journeying&#8221; and &#8220;marching,&#8221; 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.</p>
+
+<p>The symbol for 20 (<i>Kal</i>), <a href="#No_1">No. 1</a> 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, <img src="images/image80.png" width="55" height="46" alt="Hieroglyph" title="Hieroglyph" style="vertical-align: middle;" /> while immediately below is the
+representation of an idol head in a vessel covered with a screen or
+basket, as shown in <a href="#Fig_388">Fig. 388</a>. The Maya verb <i>Kal</i> signifies to &#8220;imprison&#8221;
+or &#8220;inclose,&#8221; 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, <img src="images/image82.png" width="76" height="64" alt="Hieroglyph" title="Hieroglyph" style="vertical-align: middle;" /> 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 &#8220;Give twice twenty strokes with a machete,&#8221; and hence is
+but partially phonetic.</p>
+
+<div class="figcenter" style="width: 103px;">
+<a name="Fig_388" id="Fig_388"></a><img src="images/image81.png" width="103" height="129" alt="Fig. 388. Wooden idol in vessel with basket cover." title="Fig. 388. Wooden idol in vessel with basket cover." />
+<span class="caption"><span class="smcap">Fig.</span> 388. Wooden idol in vessel with basket cover.</span>
+</div>
+
+<p>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.</p>
+
+
+<div class="footnotes">
+
+<p><a name="Footnote_345-1_51" id="Footnote_345-1_51"></a><a href="#FNanchor_345-1_51"><span class="label">345-1</span></a> See Chapter VI, Study of the Manuscript Troano, by Cyrus
+Thomas.</p>
+
+<p><a name="Footnote_354-1_52" id="Footnote_354-1_52"></a><a href="#FNanchor_354-1_52"><span class="label">354-1</span></a> Unfortunately the scrolls were overlooked in preparing
+the cut.</p>
+
+<p><a name="Footnote_358-1_53" id="Footnote_358-1_53"></a><a href="#FNanchor_358-1_53"><span class="label">358-1</span></a> Relacion de las cosas de Yucatan, p. 308.</p>
+
+<p><a name="Footnote_365-1_54" id="Footnote_365-1_54"></a><a href="#FNanchor_365-1_54"><span class="label">365-1</span></a> See Plates XVI*<i>b</i> and XVII*<i>c</i>, Manuscript Troano.</p>
+
+<p><a name="Footnote_365-2_55" id="Footnote_365-2_55"></a><a href="#FNanchor_365-2_55"><span class="label">365-2</span></a> Study of the Manuscript Troano, pp. 141-161.</p>
+
+<p><a name="Footnote_366-1_56" id="Footnote_366-1_56"></a><a href="#FNanchor_366-1_56"><span class="label">366-1</span></a> As the term &#8220;ideograph&#8221; 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.</p>
+
+<p><a name="Footnote_367-1_57" id="Footnote_367-1_57"></a><a href="#FNanchor_367-1_57"><span class="label">367-1</span></a> Study of the Manuscript Troano, by Cyrus Thomas, pp.
+142, 143.</p>
+
+<p><a name="Footnote_370-1_58" id="Footnote_370-1_58"></a><a href="#FNanchor_370-1_58"><span class="label">370-1</span></a> Study of the Manuscript Troano, p. 147.</p>
+
+<p><a name="Footnote_370-2_59" id="Footnote_370-2_59"></a><a href="#FNanchor_370-2_59"><span class="label">370-2</span></a> Landa&#8217;s Relacion, pp. 382, 383, Note 1.</p>
+</div>
+
+<p><span class='pagenum'><a name="Page_372" id="Page_372">[372]</a></span></p>
+
+<hr style="width: 65%;" />
+<h2 class="chapterhead"><a name="INDEX" id="INDEX"></a>INDEX</h2>
+
+
+<ul class="IX">
+  <li>Adelung, J. C. cited <a href="#Page_262">262</a></li>
+  <li>Aglio, Augustina, fac simile of Dresden Codex by <a href="#Page_263">263-266</a></li>
+</ul>
+
+<ul class="IX">
+  <li>B&ouml;ttiger, C. A., mention of Dresden Codex by <a href="#Page_262">262</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>controversy with Abert concerning Dresden Codex <a href="#Page_267">267</a></li>
+  <li>Brasseur, copy of the Manuscript Troano by <a href="#Page_284">284</a>, <a href="#Page_286">286</a>, <a href="#Page_343">343</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>cited <a href="#Page_350">350</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Calendar system, tabular view of <a href="#Page_270">270-374</a></li>
+  <li>Charency, H. de, cited <a href="#Page_282">282</a></li>
+  <li>Codex Cortesianus, similarity of, to Manuscript Troano and Dresden Codex <a href="#Page_286">286</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Dresden Codex, numerals in <a href="#Page_261">261-338</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Ebert, F. A., description of Dresden Codex by <a href="#Page_263">263</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>controversy with B&ouml;ttiger concerning Dresden Codex <a href="#Page_267">267</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Falkenstein, K. C., preservation of Dresden Codex by <a href="#Page_268">268</a></li>
+  <li>Fleischer, H. L., mention of Dresden Codex by <a href="#Page_263">263</a></li>
+  <li>F&ouml;rstemann, E., citation from Die Mayahandschrift of <a href="#Page_261">261-269</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>cited <a href="#Page_272">272</a>, <a href="#Page_278">278</a>, <a href="#Page_280">280</a>, <a href="#Page_281">281</a>, <a href="#Page_283">283</a>, <a href="#Page_290">290</a>, <a href="#Page_292">292</a>, <a href="#Page_293">293</a>, <a href="#Page_300">300</a>, <a href="#Page_301">301</a>, <a href="#Page_302">302</a>, <a href="#Page_303">303</a>, <a href="#Page_304">304</a>,
+   <a href="#Page_305">305</a>, <a href="#Page_320">320</a>, <a href="#Page_322">322</a>, <a href="#Page_329">329</a>, <a href="#Page_330">330</a>, <a href="#Page_339">339</a>, <a href="#Page_340">340</a></li>
+</ul>
+
+<ul class="IX">
+  <li>G&ouml;tze, J. C., preservation of Dresden Codex by <a href="#Page_261">261</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>biographical sketch of <a href="#Page_261">261</a>, <a href="#Page_262">262</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Humboldt, A. von, notice of Dresden Codex by <a href="#Page_262">262</a>, <a href="#Page_263">263</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Kingsborough, Lord, Dresden Codex copied by order of <a href="#Page_262">262</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>Mexican Antiquities of, cited <a href="#Page_266">266</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Landa, cited <a href="#Page_348">348</a></li>
+  <li>Landa&#8217;s alphabet, insufficiency of <a href="#Page_259">259</a>, <a href="#Page_347">347</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Manuscript Troano, copy of, by Brasseur <a href="#Page_285">285</a>, <a href="#Page_286">286</a>, <a href="#Page_343">343</a></li>
+  <li class="subhead"><span class="hidespace">&nbsp;&nbsp;&nbsp;&nbsp;</span>study of, by C. Thomas, cited <a href="#Page_339">339</a>, <a href="#Page_343">343</a>, <a href="#Page_344">344</a>, <a href="#Page_345">345</a>, <a href="#Page_350">350</a>, <a href="#Page_365">365</a>, <a href="#Page_366">366</a>, <a href="#Page_367">367</a>, <a href="#Page_370">370</a></li>
+  <li>Maya and Mexican manuscripts, C. Thomas on, cited <a href="#Page_280">280</a></li>
+  <li>Maya Codices, aids to the study of, by C. Thomas <a href="#Page_253">253-371</a></li>
+  <li>Mexican Antiquities, by Lord Kingsborough, cited <a href="#Page_266">266</a>, <a href="#Page_267">267</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Rosny, L. de, cited <a href="#Page_267">267</a>, <a href="#Page_347">347</a>, <a href="#Page_355">355</a>, <a href="#Page_357">357</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Schellhas, P., cited <a href="#Page_345">345</a>, <a href="#Page_359">359</a>, <a href="#Page_360">360</a>, <a href="#Page_361">361</a>, <a href="#Page_362">362</a>, <a href="#Page_364">364</a></li>
+  <li>Schultz-Sellack, K., cited <a href="#Page_278">278</a></li>
+  <li>Silvestre, &Eacute;., Pal&eacute;ographie universelle of, cited <a href="#Page_267">267</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Thomas, C., paper on aids to the study of the Maya codices by <a href="#Page_253">253-371</a></li>
+  <li>Troano Manuscript, copy of, by Brasseur <a href="#Page_285">285</a>, <a href="#Page_286">286</a>, <a href="#Page_343">343</a></li>
+</ul>
+
+<ul class="IX">
+  <li>Vater, J. S., cited <a href="#Page_262">262</a></li>
+</ul>
+
+
+<hr style="width: 65%;" />
+
+<div style="background-color: #EEE; color: inherit; padding: 0.5em 1em 0.5em 1em;">
+<p class="titlepage"><a name="trans_note" id="trans_note"></a><b>Transcriber&#8217;s&nbsp;Note</b></p>
+
+<p class="noindent">The following errors and inconsistencies have been maintained.</p>
+
+<p class="noindent">Misspelled words and typographical errors:</p>
+
+<table style="margin-left: 0%;" cellpadding="0" cellspacing="0" summary="typos">
+<tr>
+  <td class="padr">Page&nbsp;</td>
+  <td>Error</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr1">267</a></td>
+  <td>&#8220;hasty and obtrusive notice.&#8221; should read &#8216;hasty and obtrusive notice.&#8217;</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr2">272</a></td>
+  <td>indi cated should read indicated</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr3">291</a></td>
+  <td>&#8220;and&#8221; repeated.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr4">295</a></td>
+  <td>Plate 48, 2nd line first asterisk is missing.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr5">296</a></td>
+  <td>Period missing after <span class="smcap">Fig</span></td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr6">322</a></td>
+  <td>In the original text, the 7 is printed above the 17, with no horizontal line separating the two numbers.</td>
+</tr>
+<tr>
+  <td class="padr" style="vertical-align: top;"><a href="#corr7">327</a></td>
+  <td>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.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr8">338</a></td>
+  <td>Sixth column should read Sixth column.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr9">338</a></td>
+  <td>Footnote number for 338-1 was missing. It was inserted based on
+      the context of the note.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr10">348</a></td>
+  <td>Illustration No. 6 was missing the caption.</td>
+</tr>
+<tr>
+  <td class="padr"><a href="#corr11">364</a></td>
+  <td>Fig. 39 should read No. 39</td>
+</tr>
+</table>
+
+</div>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
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+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
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