{"collection":"myth-cosmogony","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_43519/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_43519","id":"gutenberg_43519","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/43519","summary":null,"tags":["Category: Archaeology & Anthropology","Category: History - Ancient","Codex Dresdensis Maya","Manuscripts, Maya","Maya calendar","Maya mythology","Mayan languages -- Writing","Mayas -- Antiquities"],"text":"PAPERS\n\n  OF THE\n\n  PEABODY MUSEUM OF AMERICAN ARCHAEOLOGY AND\n  ETHNOLOGY, HARVARD UNIVERSITY\n\n  VOL. IV.--NO. 2\n\n  COMMENTARY\n  ON THE\n  MAYA MANUSCRIPT\n  IN THE\n  ROYAL PUBLIC LIBRARY OF DRESDEN\n\n  BY\n\n  DR. ERNST F\u00d6RSTEMANN\n\n  TRANSLATED BY\n  MISS SELMA WESSELHOEFT\n  AND\n  MISS A. M. PARKER\n\n  Translation revised by the Author\n\n  CAMBRIDGE, MASS.\n  PUBLISHED BY THE MUSEUM\n  OCTOBER, 1906\n\n       *       *       *       *       *\n\nNOTE\n\n----\n\nIn pursuance of the plan of publishing translations of valuable\ncontributions to the study of the Maya hieroglyphs, the Museum Committee on\nCentral American Research has the pleasure of offering the following\ntranslation of Dr. Ernst F\u00f6rstemann's important Commentary on the Maya\nManuscript in the Royal Library of Dresden, generally known as the Dresden\nCodex.\n\nThe translation by Miss Selma Wesselhoeft and Miss A. M. Parker was made\nunder the direction of Mr. Charles P. Bowditch of the Museum Committee.\n\nIn the original German edition, published in 1901, Dr. F\u00f6rstemann used the\nArabic numerals to designate the days, but in this translation, with the\nconsent of the author who has kindly revised the translation, Mr. Bowditch\nhas substituted the corresponding Maya names of the days, in uniformity\nwith the general use of students in this country. It is needless to call\nattention to the importance of this paper by Dr. F\u00f6rstemann whose\nlong-continued study of the intricate system of hieroglyphic writing by the\nancient Mayas makes all he writes of great value to students engaged in\nthis most interesting research.\n\nF. W. PUTNAME.\n\n  HARVARD UNIVERSITY,\n              October, 1906.\n\n       *       *       *       *       *\n\nPREFACE.\n\n--------\n\nSome of those who examine this book will say, that it is too early for a\ncommentary on the \"Dresdensis,\" since Maya research is yet in its infancy,\nand this opinion is certainly justified inasmuch as a final explanation of\nthat remarkable monument is, of course, impossible at the present time. On\nthe other hand the accounts of the numerous investigations and discoveries\nwhich have been made thus far are so isolated and so scattered in the shape\nof a hundred short magazine articles, that it is certainly desirable to\nhave what we know and what we have still to learn gathered together under\none head. This book is intended, therefore, to give an idea of the state of\nour knowledge in this department of research at this time, when the\nnineteenth century is passing into the twentieth, with the definite\nexpectation that this work will soon be far outstripped and will possess an\nhistorical value only.\n\nThe contents of the following pages are of very little value, unless the\nstudent can compare them with an edition of the manuscript. My first\nedition was published in 1880 at Leipsic and the second at Dresden in 1892.\nThe edition in Lord Kingsborough's \"Mexican Antiquities\" (in Volume III of\nthat work, London, 1831) is still of practical use.\n\nAnd since in this work I must premise a knowledge of the elements of the\nsubject, I would recommend, as additional aids to the comprehension of the\nfollowing pages, my \"Erl\u00e4uterungen zur Mayahandschrift der K\u00f6niglichen\n\u00f6ffentlichen Bibliothek zu Dresden\" (Dresden, 1886), and also Brinton, \"A\nPrimer of Mayan Hieroglyphics\" (in the publications of the University of\nPennsylvania. Series in Philology, Literature and Archaeology, Vol. III). I\nwould also mention the very valuable work by Paul Schellhas, \"Die\nG\u00f6ttergestalten der Mayahandschriften\" (Dresden, 1897), which I follow in\nthe designation of the various gods by letters of the alphabet.\n\nIt need hardly be pointed out, that the numerous pioneer articles by Edward\nSeler offer abundant instruction to the student in this field as well as in\nthat of Aztec remains.\n\nI wish to express heartfelt thanks to Mrs. Zelia Nuttall and Mr. Charles P.\nBowditch, who have aided my work in various ways and have thus rendered\npossible the publication of this book.\n\nE. F\u00d6RSTEMANN.\n\n  CHARLOTTENBURG.\n\n       *       *       *       *       *\n\nFIRST PART.\n\nPages 1-45.\n\nPage 1.\n\nAs the first page is almost entirely effaced by abrasion, we know very\nlittle of its contents. Like the second, however, it was doubtless divided\ninto four parts. The two pages have this also in common, that, for lack of\nspace, their contents are not expressed in full, but abbreviated as much as\npossible.\n\nThe top section (a) of page 1 may have been filled with a sort of\nfrontispiece, perhaps a face with a few signs around it.\n\nThe three lower sections (b, e, d,) with the three lower of the second page\ndoubtless formed a whole. Each of these sections contained a normal\nTonalamatl of the commonest kind, which was introduced on the left by five\nday-signs having a difference of 12 and was thus divided into five sections\nof 52 days each. In sections b and d, at least, these periods seem to be\ndivided into equal halves of 26 days each. In d alone we recognize the\ninitial week day, VII, of the Tonalamatl. In each of the three divisions\nthere were two figures of gods, but we can recognize only the first of\nthese in section d as the god D.\n\nPage 2.\n\nThis page contains four much abbreviated Tonalamatls. In the following I\nwill represent each Tonalamatl by setting down in a vertical line those of\nthe twenty days with which the principal divisions of equal length of the\nTonalamatl begin, in a horizontal line with Roman numerals the days of the\nweek of thirteen days on which the separate subdivisions begin, and with\nthe Arabic numerals the distance between these days. I will also remark\nthat the position of the Tonalamatls in the \"Dresdensis\" is not connected\nat all, as in the Aztec, with certain places in the year, and that no rule\nfor this proceeding can be found. It is curious, however, that no\nTonalamatl in this codex begins with the day IX or Eb, which is the more\nimportant in the last pages of the Dresden Codex.\n\n2a.\n\nThis first Tonalamatl has the following form:--\n\n  XIII  5  V  12  IV  11  II  12  I  12  XIII\n  Cauac\n  Chuen\n  Akbal\n  Men\n  Manik.\n\nThe hieroglyphs and the figures show that preparations for a human\nsacrifice are treated of here and that the subject is, therefore, closely\nconnected with page 3a, where the sacrifice itself is represented.\n\nThere are but two pictures of persons, which refer, therefore, only to the\nfirst or to the first two subdivisions and which, for lack of space, are\nwanting for the others. On the left walks the person doomed to sacrifice,\nhis arms are bound on his back, his head is barely visible and his eyes are\napparently torn out. There is an object in front of his breast resembling a\nwreath. Behind this figure crouches a second, who holds an object in his\nhand which probably represents a rattle. The parallel passage in Cod. Tro.\n2b shows the bound prisoner with an axe behind him. Then follows in Tro. 3b\nthe prisoner without a head and behind him the black god with gory lance.\n\nThe hieroglyphs--four for each of the five subdivisions--are arranged in\nthe following order:--\n\n  1  2    5  6     9  13    17\n  3  4    7  8    10  14    18\n                  11  15    19\n                  12  16    20.\n\nOf these 9, 13 and 17-20 are wholly effaced and 14 for the most part. The\nvery first group refers to human sacrifice, for 1 is a head with an axe\naffixed to it, 2 contains the hand (_i_) which so often appears as the sign\nof grasping, especially in representations of the chase; here it has the\nsame superfix as on page 22a, which on pages 4a-10a and 11a, b, appears as\nprefix. 3 is the head of god H, perhaps given here as a symbol of wounding\n(serpent god?). I am unable to explain the meaning of the dot between two\ncrosses in front of this head; perhaps the sign denotes the day Kan, which\nis here arrived at by calculation. We find the same hieroglyph on page 3.\nSign 4 signifies the death-god A = Cimi, who appears again in 12.\n\nIn like manner 2 is repeated in 6 and 14. 7, 11 and 15 (probably also 19)\nare, however, the familiar cross _b_; 8 is the head of E with a prefixed\nknife; the intention here may have been to show that human sacrifice would\nbe likely to have an auspicious influence upon the harvest. 10 and 16 are\nanother unknown head. In 5 we see the familiar Kan-Imix sign, which, for\nthe present, I am inclined to regard as denoting a feast or a sacrificial\nmeal.\n\n2b--c.\n\nThese two sections have something in common. First, 2b (as also 2d) is\ndivided into but two parts and 2c into only three parts. Second, in 2b and\n2c the scribe intended to draw the hieroglyphs for 10 days each, instead of\n5 each, but only drew the outlines of the second five, since they could not\nbe used for these Tonalamatls. Third, the persons represented here are all\nengaged in the same occupation, each holding in his hands an object which\nlooks like a frame for a net or web, and also a large needle with an eye\nthrough which a thread has been passed.\n\nA very similar representation is found in the Codex Troano 34a, 33a and\n23*c, and also in the Sahagun Manuscript of the Bibliotheca Laurentiana at\nFlorence. This can hardly mean anything else than the knotting of cords,\nwhich was the only method of casting lots current among the Mayas; compare\nSeler, \"Altmexikanische Studien II\" (1899), p. 31, and \"Zauberei im alten\nMexiko\" (1900), p. 90, by the same author. This clearly indicates the use\nof these Tonalamatls in soothsaying.\n\nFourth and last, each of the five hieroglyph groups of 2b and 2c begin with\nthe same sign, which must, therefore, denote the casting of lots.\n\nThe Tonalamatl 2b runs thus:--\n\n  XI  34  VI  18  XI\n  Oc\n  Ik\n  Ix\n  Cimi\n  Ezanab.\n\nThe pictures are of three persons. At the left two sit facing one another\nand at the right is the god A. Of the first two, the one at the left is\nprobably feminine, but with an old face. I am inclined here, in spite of\nthe sex, to recall the bald-headed old god (N, according to Schellhas),\nwhom I am inclined to consider, for the present, the representative of the\n5 Uayeyab days at the end of the year. This would account for the sign\nresembling an 8 lying on its side, which appears on the god's head and\nwhich usually represents the change of the year (compare pages 38a, 41b,\n52b, 68a and 72c). I cannot explain the person sitting facing this god\nfurther, than that from his hieroglyph he is either H or allied to H.\n\nOf the 8 hieroglyphs\n\n  1  2    5  6\n  3  4    7  8.\n\nthe first, as stated, seems to refer to the casting of lots, 2 is the sign\nfor H, 3 denotes the female figure pictured beneath it, and 4 is the sign\n_q_ with the Ben-Ik on top of it. In the second group 5 is the same as 1, 6\nis the cross _b_, and 7 and 8 are the hieroglyphs for A.\n\n2c contains the following Tonalamatl:--\n\n  III  20  X  17  I  15  III\n  Oc\n  Ik\n  Ix\n  Cimi\n  Ezanab.\n\nThere are illustrations for only the first two of the three subdivisions;\nthe two figures composing them are engaged in the occupation mentioned\nunder 2b. At the left sits a deity, who is probably E, whose head develops\ninto a second, which is that of an animal; on the right sits the god D.\n\nThe three groups of four hieroglyphs each are arranged as follows:--\n\n  1  2    5  6     9\n  3  4    7  8    10\n                  11\n                  12.\n\nOf these hieroglyphs 1, 5 and 9 are the head already numbered 1 and 5 on\n2b; 2, 6 and 10 are the cross _b_; 3, 7 and 11 are three different heads,\nall, as it seems, having the Akbal sign, and 11 having also the numeral 6.\n4 is again (see 5 on 2a above) the Kan-Imix sign, 8 a Kin with suffix (the\neast?) and the numeral 16 as prefix; finally 12 is Cimi (A). Do the numbers\n16 and 6 refer to the 16th and 6th of the 17 and 15 days standing below\nthem? The beginning of this Tonalamatl III Oc seems to me to fall on an\nespecially auspicious day (hieroglyph _a_).\n\n2d has the following Tonalamatl:--\n\n  XIII  28  II  24  XIII\n  Lamat\n  Ahau\n  Eb\n  Kan\n  Cib.\n\nThis refers probably to the section devoted to women, pages 13-23. For the\npicture on the left is a woman sitting and holding an unknown object in one\nhand; on her right stands the death-god A holding in his hands what may be\nan apron or breech-clout; there is a similar representation in Cod. Tro.\n29*b.\n\nThe hieroglyphs are\n\n  1  2    5  6\n  3  4    7  8.\n\nOf these 1, 6 and 8 are one of the signs of A, 7 another, and 4 may be a\nthird, recalling the Moan, which, as on page 14c, rests on a hand held\nbeneath it. 2 and 5 seem to signify a carpet or other fabric (or a lying-in\nbed?), on the one hand suggesting the occupation of the figures in 2b and\n2c, and on the other the checkered hieroglyph, which is so common in the\nPalenque inscriptions. Finally 3 is the woman pictured beneath.\n\nPage 3.\n\nWe come now to the sacrificial scene proper, which practically fills the\nupper half of the page. The victim, a woman, lies bound hand and foot, on\nthe sacrificial stone, just as in the Cortes. 41-42; the incision above the\nstomach is already made and the eyes are closed. Behind her rises the tree\nof life with a bird (vulture?) sitting in its branches, which holds in its\nbill one end of an object, resembling a ribbon (entrails) issuing from the\neyes of the victim, just as in Tro. 26*a and 27*a.\n\nThis picture is surrounded by four gods, who, however, differ very much\nfrom the other four in the second sacrificial scene, page 34a. At the right\nabove is K, who, I think, is the storm-god; the figure at the left above is\nalmost entirely destroyed, and its hieroglyph wholly; I prefer to consider\nit a rain deity, so that these two gods shall signify the productive\nseason. The two gods below may refer to the blessing upon the harvest and\nchase resulting from the season and the sacrifice. For, at the left below,\nwe see the maize deity E, holding a dish of fruit, while her head-ornament\ncontains a second head. At the right below sits the serpent deity H and in\nfront of him is an animal with the noose still around its neck, with which\nit was caught.\n\nThe hieroglyphs are in the following order:--\n\n  1  2    5  6     9  10    13  14\n  3  4    7  8    11  12    15  16\n      17  18           21  22\n      19  20           23  24.\n\nOf these, 1-5 are wholly effaced and also the most essential part of 6.\n\nOf these hieroglyphs four (1-4, 13-16, 17-20 and 21-24) clearly belong to\neach of the four deities, for 15, 18, and 22 (the last again with the dot\nbetween two crosses as on page 2a) certainly belong to the picture. From\nthis it seems to follow that Hieroglyphs 5 to 12 refer to the sacrifice\nitself. As a matter of fact 9 and 11, which are directly above the\nsacrifice, also refer particularly to that part of the representation.\n\nI wish also to call special attention to the two signs 8 and 16 which seem\nto correspond to one another. They are the two which I have designated with\n_q_ and _a_, which are met with here for the first time (aside from the _q_\nwith the Ben-Ik, which is not in question here) and which, I think, denote\nthe good and evil days, _q_ referring to the sacrifice and _a_ to its\nresults.\n\nIn regard to the rest of these hieroglyphs, 7 and 9 are Cimi; 10, 14, 17\nand 24 the cross _b_ and 11 and 23 the hieroglyph c. 12 is the head with\nthe Akbal eye, having for its prefix the uplifted arm, which is joined thus\nto the most diverse signs, and which also occurs in the Tro-Cort. 13 is a\nsimilar head, 19 again Imix, 20 the sign _o_ and 21 a hieroglyph, which is\nwithout doubt a simplified head.\n\nHere, too, we have a Tonalamatl, and one beginning on an especially\nceremonial day I Ahau, which seems to play the same role in celestial\naffairs as IV Ahau does in terrestrial matters. On the sacrificial stone we\nread the days Ahau, Eb, Kan, Cib and Lamat, and I think it likely that the\nsame days occur in the passage of the Cortes. referred to above; the\npassage evidently contains some errors. The subdivisions of this Tonalamatl\nare not known to us, for here the manuscript is somewhat confused. I\npropose to read it as follows:--\n\n  I  10  XI  4  II  15  IV  9  XIII  14  I\n\nbut Cyrus Thomas, \"Aids,\" p. 294, has\n\n  I  4  V  8  XIII  11  XI  15  XIII  14  I.\n\nEither reading is dubious. The scribe divided the lower half of page 3 into\ntwo parts, and drew in each the outline of five days; but then he saw that,\nto continue his work, he needed a long surface extending from left to\nright, and he therefore omitted filling in these two sections.\n\nPages 4a--10a.\n\nWe have here a normal Tonalamatl, which, however, was evidently meant by\nthe author to serve a very special purpose, since he divided the first\nsection of 52 days into no less than 20 parts of 2, 3 or 4 days. I give the\nfollowing arrangement here, remarking, at the same time, that in one\ndoubtful case (between the third and fourth groups) I deviate from my\nformer plan:--\n\n    X 2, XII 4, III 3, VI 2, VIII 4, XII 2, I 2, III 4, VII 2, IX 2, XI 2,\n    XIII 4, IV 2, VI 3, IX 2, XI 3, I 2, III 3, VI 2, VIII 2, X.\n\nSince the five sections on page 4a begin with the days Imix, Ben, Chicchan,\nCaban, and Muluc, we have resulting from this and from the intervals\nspecified, the following days:--\n\n    X Imix, XII Akbal, III Manik, VI Oc, VIII Eb, XII Cib, I Ezanab,\n    III Ahau, VII Kan, IX Cimi, XI Lamat, XIII Oc, IV IX, VI Cib, IX Cauac,\n    XI Imix, I Kan, III Cimi, VI Muluc, VIII Chuen, X Ben.\n\nNow, however, in the \"Globus,\" Vol. LXXIII, in my two articles entitled\n\"Die Tageg\u00f6tter der Mayas,\" I have expressed the opinion that there is good\nreason to believe that the scribe has made a grave mistake here.\n\nI assume that the scribe simply transferred the so-called month days from\nthe year just past to the year in which he was writing, in doing which they\nwere, of course, moved five days on (since 365 = 20 \u00d7 18 + 5), but he did\nnot bear in mind, that the pictures and the hieroglyphs could then no\nlonger correspond. Hence the days must be not\n\n    Imix, Akbal, Manik, Oc, Eb, Cib, Ezanab, Ahau, Kan, Cimi, Lamat, Oc,\n    Ix, Cib, Cauac, Imix, Kan, Cimi, Muluc, Chuen, Ben,\n\nbut\n\n    Cib, Ezanab, Ik, Chicchan, Manik, Chuen, Ben, Men, Cauac, Imix, Akbal,\n    Chicchan, Muluc, Chuen, Ix, Cib, Cauac, Imix, Kan, Cimi, Lamat.\n\nLet us now consider the 20 groups, disregarding the first (really zero)\nwhich has no figure and no hieroglyphs. We will leave out of the question\nalso the first two hieroglyphs of each group, which are the same twenty\ntimes and form, as it were, merely a superscription, in which the first\nsign is a head, also occurring elsewhere (4b-5b), with suffix and affix,\nand the second is the hieroglyph _i_, which might readily denote a\nsacrifice. Thus only the usual four signs remain for each picture.\n\n1. Day 15 = Ezanab; Aztec Tecpatl, flint, lance point. The figure of the\ngod does not correspond with this at all; it is a god in a gala cloak,\nholding before him a serpent and bearing a quetzal bird on his back. This\nfigure, which resembles none other in our manuscript, strongly recalls\nKukulcan, who, in fact, is often placed by the scribes at the head of the\n20 Maya gods (cf. Dres. 36) in which manner he appears in this place quite\nwithout reference to the day and the hieroglyphs. In this interpretation I\nfollow Seler, in the main, who in his treatise \"Quetzalcouatl-Kukulcan in\nYucatan\" (1898) expresses this opinion on page 403 of the separate edition.\nBut possibly the ear-ornament may refer to Ezanab. Of the hieroglyphs, 1\nand 2 are the familiar sign of the serpent deities H or I, though here they\nare not drawn exactly alike. They also appear together on page 6a. 3 ( =\n_r_) I think is the sign for the week of 13 days, which recurs in groups 5,\n11, 14 and 16, and hence is distributed 4 times, though not regularly,\namong the 4 \u00d7 13 days. Sign 4 is the death bird.\n\n2. Day 19 = Ik; Aztec Ehecatl, wind, air, breath. The deity pictured is B,\nthe god who is found the most frequently, and with the most varied\nattributes, of all the gods in our manuscript. He is the god proper of\nbreathing and living and was, perhaps, the local god in the region where\nthis manuscript originated. The second hieroglyph is his sign; the first,\nwith a prefixed 9, is _p_ the third _q_ and the fourth _a_ with the usual 3\nbefore it; their relations to B are still unknown.\n\n3. Day 3 = Cimi; Aztec Miquiztli, death. The deity with a black line about\nthe mouth is certainly the bald-headed old god N, whom we shall find on\npages 12c, 14b, 17a, 21c, and 37a. His hands are much deformed; perhaps\nindicating the bite of a serpent? Of the hieroglyphs, 1, 2 and 4 are\neffaced; 3 is surely the sign of the god, differing, it is true, from his\nusual hieroglyph, but recurring with a 4 also on pages 21c and 24. This 4\nmight refer to the four kinds of years, but here, perhaps, to the fourth of\nthe five Uayeyab days, and would thus agree with the 24th day of Cumku,\nwhich should lie here (in the year 9 Kan), if I have begun the Tonalamatl\ncorrectly.\n\n4. Day 4 = Manik; Aztec Mazatl. The significance is stag or roe, game or\nthe chase. The first picture on page 5 is one of the forms of F, which\nseems to stand here not merely for human sacrifice, but also for war and\nthe chase, and especially for the act of killing in general. Of the\nhieroglyphs, unfortunately only the fourth can be read in full (the sign\n_c_), the upper part of the second is the cross _b_ and the lower part the\nsign Ahau; the number 11, which is peculiar to the god F, probably stood\nbefore the second sign. Did this god rule the eleventh of the 13 months of\n28 days, as Moan ruled the thirteenth?\n\n5. Day 8 = Chuen; Aztec Ozomatli, ape, then probably the constellation of\nUrsa Minor, and hence belonging to the god C. The figure is unquestionably\nhis, and the first hieroglyph is surely his sign. The other three are the\nfamiliar _a_, _o_ and _r_.\n\n6. Day 10 = Ben; Aztec Acatl, the fundamental significance of which is\nreed, rush, etc. The connection between this day and the god B pictured\nhere must be left undecided. Of the hieroglyphs, the first points rather to\nthe sun-god G, the second, with the numeral 7 as a prefix, is entirely\ndestroyed, the third is the sign _u_, and the fourth, which is half\nobliterated, was _q_.\n\n7. Day 12 = Men; Aztec Quauhtli, eagle. The figure to which the first\nhieroglyph with the numeral 11 belongs, is a form of the god F, but has the\nnose-ornament of the sun-god G. Hieroglyph 2, which we shall find again on\n22c, may refer especially to the eagle; the third is the sign of the day\nCaban with a prefixed 3, and the fourth is the sign _o_.\n\n8. Day 16 = Cauac; Aztec Quiahuitl. The meaning in the different languages\npoints to rain, storm and summer, of which the tortoise and serpent are\nspecial symbols. I shall not venture to decide positively upon the deity\npictured here; perhaps the object in his hand may be a tortoise; Seler,\n\"Quetzalcouatl-Kukulcan\" (1898), p. 403, calls him the young god. In the\nhieroglyphs we find the serpent sign Chicchan twice, just as in the first\ngroup on page 4; then follow _a_ and Kan-Imix.\n\n9. Day 18 = Imix; Aztec Cipactli. In my treatise on the day-gods, I have\nreferred to the variations in the significance of this day. The Mayas\nconnected with it the idea of the female breast, of drink, and, in\nparticular, of the intoxicating beverage pulque. The deity pictured here,\nwhich is certainly a female deity, has a kind of vessel in her hand, from\nwhich the serpent resting on her head appears to be drinking. Hieroglyphs 2\nand 4 are wholly obliterated, and 1 partly; there is a lock of hair, the\nsign of femininity, before 1 and 3. It is to be noted further that 3 is the\nsign of the death-god and that the deity pictured here has the death-sign\non its cheek. Can this possibly suggest deathlike intoxication?\n\n10. Day 20 = Akbal; Aztec Calli. The meaning is that of darkness, night,\ndark hole, then that of house as an artificial cave or as a place of\nshelter at night. The first picture on page 7, the black deity L with the\nbeard fits admirably here. The black paint still visible proves that the\nfirst hieroglyph, which is almost effaced, was his sign, and the second may\nbe a head more definitely identifying him. The third was the sign _q_, the\nfourth is an Ahau, perhaps intimating that Akbal belonged to the days\nbeginning the Uinal sections of 20 days, and to the lords of the same. In\naddition to appearing with these 5th, 10th, 15th, and 20th days, an Ahau is\nfound with the 1st, 6th, 11th and 16th as regent of the year, and lastly,\nbut especially, with the 17th, which bears the name Ahau, and with the god\nD belonging to it.\n\n11. Day 2 = Chicchan; Aztec Cohuatl, serpent. With this would agree also\nthe third and fourth hieroglyphs (the latter _r_), which are the two we\nfound in the first representation on page 4 belonging to the deity holding\nthe serpent. But what is the meaning here of the dog-head of the figure,\nand of the first two hieroglyphs corresponding to it? And what does this\ncreature hold in its hand? The lightning? The hieroglyphs seem to\ncorrespond to the seventh day, as if the scribe had recognized his mistake\nand referred here to the present and not to the past year.\n\n12. Day 6 = Muluc; Aztec Atl, water, cloud. With this corresponds the image\nof the storm deity K and his two hieroglyphs 1 and 2, the first of which\noccurs frequently, and the second is found on pages 20 b and 47, while 3\n(Ahau) designates the day as regent of the year and 4 is the hieroglyph a.\nThe curious sign 2 is also given on Cort. 32 b.\n\n13. Day 8 = Chuen; Aztec Ozomatli, ape. There is no agreement at all here,\nbut everything points to the day 3 lying 5 days back, the picture of the\nCimi as well as the hieroglyphs, even the third with the Akbal sign and the\nuplifted arm (as on page 36a), also the fourth (_c_) which is generally\nthought to be the death-bird. It even seems here as if the scribe had had\nthe preceding year in mind; possibly he did not want to repeat the fifth\ngroup.\n\n14. Day 11 = Ix; Aztec Ocelotl, jaguar. Here there is an admirable\ncorrespondence between the figure and the first hieroglyph, which on page\n26, top, also refers to the jaguar represented there; the other three\nhieroglyphs are _r_, Kan-Imix and _q_.\n\n15. Day 13 = Cib; Aztec Cozcaquauhtli, vulture. The bird is actually\npictured here and its sign is the first hieroglyph; the third is _q_, the\nsecond and fourth are obliterated.\n\n16. Day 16 = Cauac; Aztec Quiahuitl, meaning, as in the eighth group, rain,\nstorm, summer. The figure, the first on page 9, seems, however, to indicate\nthe day Ahau, as does also the second hieroglyph, which is Ahau; the first\nand third are effaced and the fourth is _r_. Perhaps the scribe did not\nwish to repeat the eighth group.\n\n17. Day 18 = Imix; Aztec Cipactli, as in the ninth group. Here the allusion\nto pulque is still plainer than it is there. The picture is that of a woman\nwith bound eyes and uncertain position of the hands, and here too with the\ndeath-sign, and on her head a bee from whose honey the beverage was\nprepared. I shall not venture to explain the first two hieroglyphs; the\nsecond with uplifted arm appears again on page 8c. The third is Cimi and\nthe fourth _q_.\n\n18. Day 1 = Kan; Aztec Cuetzpalin, denoting maize with the Mayas. The\nrepresentation consists of the maize deity with the Kan sign on her head,\nthe first hieroglyph is hers, then follows Kan-Imix, which I am inclined to\ninterpret as meaning a meal, next the sign _a_ and finally a head, which is\nuncommon and undetermined, with the leaf-shaped prefix as on pages 4c, 6c,\n9c, 34b, 61a, 67b and 69a.\n\n19. Day 3 = Cimi; Aztec Miquiztli, death. The first figure on page 10 is a\ndeity with the head of the death-bird Moan and above the head is the\ndeath-sign. As has long been known, the first and third hieroglyphs\nunquestionably belong to this god, also the fourth with the Akbal sign\nagrees with it, and the second likewise recalls the Moan.\n\n20. Day 5 = Lamat; Aztec Tochtli, meaning rabbit in the latter language.\nNeither the figure, which represents Cimi, death, nor the corresponding\nhieroglyphs, excepting the second one agree with this day. This second\nhieroglyph has both in front and above it the number 6. Two numbers added\nthus to the common Uinal sign usually designate the Uinal period plus days,\nas is so very common on the inscriptions, so that the sign appearing here\nwould denote 6 \u00d7 20 + 6 = 126 days. The hieroglyph here, however, is _not_\nthe usual sign for 20 days. On the contrary, it has in the centre a\nstraight line and on either side of it a parallel line ending in a little\nknob (or loop?). I propose to regard these lines as representing the\necliptic and the moon, which takes its course now to the north and now to\nthe south of the ecliptic, and the sign as a whole as signifying the lunar\nmonth of 28 days. This is confirmed on pages 51, 55, 56 and 57. In that\ncase this hieroglyph would denote 6 \u00d7 28 + 6 = 174 days.\n\nNow bear in mind that in this passage the day X Lamat, which equals the\nAztec Tochtli, is referred to.\n\nIn the year named after this day, and indeed on the 174th day of the same\n(1 Cipactli), in February 1502, the emperor Ahuitzotzin died; compare\nespecially Brinton, \"Essays of an Americanist\" (1890), pp. 274-283.\n\nShould this association in our manuscript of Cimi = death, X Tochtli and\nthe numeral 174, be considered accidental? Or did the scribe, writing in\nthe year after the event, actually record it in the year 1503 and,\ndeparting from his real subject, immortalize it in this place at the end of\nthe greatest Tonalamatl? I will not refrain from expressing the conjecture\nI have long entertained, though I am quite prepared for differences of\nopinion.\n\nSeler attempts to explain this series of 20 gods in another way; see his\n\"Monumente von Copan und Quirigua\" (1899), p. 729. (Cf. his collected\npapers p. 781.)\n\nPages 4b--5b.\n\nIt is my opinion that the Tonalamatl just now discussed connects with\nanother, which is recorded directly below the beginning of the first, and\nwhich also differs from all the other ordinary Tonalamatls. It likewise\ndivides the first 52 days into a large number of small parts (14) and has\nthe following form, if we adopt Seler's correction in the last member:--\n\n  XII 4 III 4 VII 4 XI 3 I 4 V 3 VIII 4 XII 3 II 6 VIII 3 XI 4 II 4 VI 4 X\n      2 XII\n  Ix\n  Cimi\n  Ezanab\n  Ik\n  Oc.\n\nThe two days Ik and Oc should be read Oc and Ik. There is only one picture\nhere:--a scaly green monster with the head of the principal god D. There\nare six hieroglyphs on its body, the first is that of Eb and the second\nthat of Cimi, the fourth is the sign c. The others I shall not venture to\ndetermine.\n\nAccording to a conjecture expressed verbally by Dieseldorff, this figure\nmay represent the god who continually recreates himself. We are reminded\nhere of the two-headed serpent (Seler, \"Tonalamatl der Aubinschen\nSammlung,\" 1900, pp. 65-66). There are two rows of hieroglyphs above the\nmonster, the upper contains 8 and the second 6, but the second hieroglyph\nin the upper row belongs in the lower. Thus there are 14 hieroglyphs\ncorresponding to the subdivisions noted above.\n\nThe upper seven signs are all alike and are also identical with the one,\nwhich, in the great Tonalamatl, recorded above, begins the heading of all\nthe 20 groups; this likewise points to a close connection between the two\nTonalamatls.\n\nThe remaining 7 hieroglyphs should be considered as only 6, for it is\nimprobable that C occurs twice in this series. They are the gods D, C, H,\nN, A and B, to which perhaps an E or F or G is to be mentally added in\nplace of the second C. They are all principal gods with the exception of N\n(as always, according to Schellhas's nomenclature). This N, an old man,\ndenotes, as it seems, the five Uayeyab days at the end of the year, as he\ndoes also on page 21c. This sign with the number 4 has already been seen on\npage 4a. If in 4b this sign signifies the last day of the year, then this\nTonalamatl falls in the year XIII Kan. The sign 5 Zac also appears in the\nTro-Cort., _e.g._, Cort. 29 c, Tro. 9*b and 28*b.\n\nNow I shall proceed to examine all that has not yet been discussed to the\nend of page 12, taking up first the remainder of sections a and b and then\nall those of 4c-12c.\n\nPages 10a--12a.\n\n  XI  12  X  8  V  12  IV  8  XII  12  XI\n  Lamat\n  Ahau\n  Eb\n  Kan\n  Cib.\n\nThe period of 52 days is thus divided into five sections of 12 and 8 days\neach, alternating regularly. A deity and four hieroglyphs belong to each of\nthese sections, viz:--\n\n1. D sitting, with his right hand pointing upward and his left downward; on\nhis head is the Akbal sign as on page 15c. The hieroglyphs are destroyed\nwith the exception of the third, which is the sign of D (Ahau). The fact\nthat the 12 days happen to end with the day belonging to D (Ahau) is\naccidental.\n\n2. R, a human figure with the head of the Moan (as on page 7c and 10a) and\nwith the copal pouch around his neck. Of the hieroglyphs only the fourth,\none of the common signs of Moan (_c_), is legible.\n\n3. H, or, according to Seler, \"the young god,\" as on 12b and 14b, with\nnose-peg and copal pouch. On his (her?) head sits a bird with an object,\nwhich I do not recognize, in its bill; compare page 12b. Of the\nhieroglyphs, the first is destroyed, the second is the unmistakable sign of\nH, the fourth is the common _a_, and the third I cannot as yet decipher.\n\n4. A, with the usual design issuing from his mouth (the expiring breath of\nlife?). Of the hieroglyphs, the first is a double Manik with prefixes,\nwhich probably denotes violent death; the other three are very common\nsymbols of A.\n\n5. E, holding a vessel containing plants (agave?) and with the cross _b_ on\nhis head-ornament. The first hieroglyph is an unexplained compound design\napparently referring to the Moan, an Imix and two prefixes, the second is\nthe monogram of E, whom the third hieroglyph, Imix-Kan, designates as\ndispensing nourishment, and the fourth, Ahau, as a leading deity.\n\nPage 12a.\n\nThe scribe evidently wishing to carry out his material in some conclusive\nform in the top, middle and bottom sections of page 12, found insufficient\nspace in the top section. He, therefore, condensed two independent\nunconnected Tonalamatls, by arranging them in such a manner, that the\nperiod of 52 days was divided, for the sake of brevity, into only two\nparts, viz:--\n\n  VIII  27  (IX)  25  (VIII)\n  Ahau      Oc\n  Eb        Ik\n  Kan       Ix\n  Cib       Cimi\n  Lamat     Ezanab.\n\nI have supplied the two numbers enclosed in parentheses; they are wanting\nin the Manuscript.\n\nThe hieroglyphs\n\n  1  2  5\n  3  4  6\n        7\n        8.\n\nare sufficient for the two figures one expects to see here; but they are,\nin fact, intended for four figures--two for each of the two Tonalamatls.\nFor the first of the two Tonalamatls we have only one figure, God K, who,\nhowever, from the dish held in his hand, probably containing honey (compare\n10b), seems to stand here also in place of E. In agreement with this,\nHieroglyph 2 and probably also 1 (_s_, which occurs again on page 13a, and\nalso on page 10b) refers to K, while 3 clearly refers to E and 4 is the\nsign a. Hieroglyphs 5-8 belong to the second of the two Tonalamatls. The\nfirst two of these hieroglyphs, which are entirely erased, refer to an\nunknown deity, and the last two unquestionably relate to A.\n\nPages 5b--6b.\n\n  I  16  IV  9  XIII  25  XII  2  I\n  Manik\n  Cauac\n  Chuen\n  Akbal\n  Men.\n\nFour hieroglyphs belong to each of the four subdivisions:--\n\n  1  2    5  6     9  10    13  14\n  3  4    7  8    11  12    15  16.\n\nThese four parts, however, form a whole, inasmuch as they all relate to\nmaking fire, as it is also represented in the Troano 6, 19 and 14*c. Hence\nthe upper row of hieroglyphs contains signs which are repeated. 1, 5 and 9\nare the same head, the last two cases have the sign for darkness (Akbal);\nthis Akbal appears again in the parallel passages of the Tro. and in 13 it\nis somewhat enlarged simply owing to the absence of a head. The act of\nmaking fire seems to be denoted here rather by the second sign (2, 6, 10,\n14), which I designate by _k_ and which, originally, doubtless consisted of\ntwo hands (double Manik sign); the prefix is the same in 6 and 14, and\ndifferent in 2 and 10.\n\nThe eight lower hieroglyphs are merely the monograms of the four gods\nmaking the fire. The first deity is F, the second either A or one of the\nblack deities L or M, the third D and the fourth apparently F again, but\nconceived as feminine. In the third picture there is a second object,\napparently a head (of D?), below the piece of wood in which the fire-stick\nis being whirled. Hieroglyph 11 belonging to this deity has an Akbal as a\nprefix.\n\nPages 6b--7b.\n\n  X  13  X  13  X  13  X  13  X\n  Kan\n  Cib\n  Lamat\n  Ahau\n  Eb.\n\nThis Tonalamatl is divided, by way of exception, into four equal parts,\nwhich all begin with the same week day X.\n\nHere too, as in the preceding Tonalamatl, there are four subdivisions, and\nalso 16 hieroglyphs arranged in the same way. And here too the upper line\nis a condensation of the whole, the same two signs being repeated four\ntimes. The first of these is _q_, which is still a problem and which occurs\ninverted also on Cort. 20d-21d (where there are figures with bird-heads);\nthere too it is the characteristic hieroglyph. The second, however, is\nagain the double Manik sign referring to activity of some kind, as in the\npreceding Tonalamatl. But the occupation of the four deities represented\nhere is of very different kinds and altogether problematical. E, conceived\nas feminine, occupies the first place, with a Kan sign on her head and\nholding in her hand a vessel exactly like the one held by the figure just\nabove on the same page. The third hieroglyph is hers and the fourth is the\nsign a.\n\nThe second figure is A with a hook-shaped object hanging around his neck.\nHis hands also seem to be deformed, as are those of the third and fifth\nfigures of the great Tonalamatl (on pages 4 and 5). His two hieroglyphs are\namong those usually belonging to him.\n\nThe third god is D sitting, by way of exception, on some object (stone?).\nSomething resembling the pestle of an ordinary mortar is hanging down in\nfront of his headdress, and he is holding a very similar object to his\nmouth. His two hieroglyphs are also those which usually refer to him.\n\nThe most striking figure is that of the fourth god, whom I do not\nrecognize. He seems to be attracting to himself a bird flying down from\nabove, whose bill almost touches his mouth. His hieroglyph has the sign Yax\n(strength) for a prefix and the fourth hieroglyph is c.\n\nPage 8b.\n\n  VIII  26  VIII  26  VIII\n  Manik\n  Cauac\n  Chuen\n  Akbal\n  Men.\n\nAgain we have a Tonalamatl divided into equal parts, this time, however,\ninto but two, and it seems thus to be closely connected with the preceding.\n\nWhile hitherto four hieroglyphs have usually belonged to each figure, we\nfind here ten in all and in the following order:--\n\n  1  2    5  6\n  3  4    7  8\n             9\n            10.\n\nThere are two figures here, which stand in some relation to one\nanother,--two persons sitting facing each other. The one at the left is\ncertainly D, the one at the right can hardly be the old woman, whom\nSchellhas designates with O, but rather N, the old god of the Uayeyab days.\nThe former seems to be about to take something from the hand of the latter.\nI surmise that it is one of the prophetic weaving implements. which we\nfound on page 2. The two hieroglyphs _e_ and _h_ must refer to this; they\nare repeated, as usual, in the two groups, _e_ in places 2 and 8, and _h_\nin 1 and 6.\n\nSigns 3 and 4 refer unquestionably to D and hence 5 and 7 (the first _q_\nwith Ben-Ik, and the latter unknown) must be the designation of the person\nsitting on the right. We shall meet the latter sign again on pages 15b and\n18a, with the same person, and on pages 27a and 39b with entirely different\npersons. Sign 7 is an object, which also appears on 15b and 18a, held in\nthe hands of women and may denote some special sacrificial offering; on 9b\nKan-Imix appears in place of this sign, and on 39b beside it. It should be\nnoted that sign 7 stands here in exactly the same proximity to 1 and 6 as\non page 27a.\n\nThe hieroglyphs 9 and 10 stand outside the two groups, and since, as we\nknow, they belong to the god A, this prophecy must concern death, as is\nmore clearly indicated by the corresponding hieroglyphs on page 9b.\n\nPage 9b.\n\nHere, for the first time in this manuscript, we have a Tonalamatl in which\nthe 260 days are not divided into five fifths of 52 days each, but into\nfour quarters of 65 days. This may be represented as follows, if we supply\nthe III, which is wanting at the beginning:--\n\n  III  33  X  32  III\n  Muluc\n  Ix\n  Cauac\n  Kan.\n\nIn the first place, the close connection of this Tonalamatl with that\nrecorded on page 8b, just now discussed, is striking, for\n\n    1. Here too we find a division into two equal parts is intended, but\n    which, of course, as the number is 65, cannot be mathematically exact.\n\n    2. Here too we not only find 10 hieroglyphs, but we find them in the\n    same order as on page 8b, and here too the sign _e_ stands in places 2\n    and 8, and _h_ in 1 and 6; again 3, 4 and 9 are exactly the same\n    hieroglyphs here as there, so that only 5, 7 and 10 are different.\n\n    3. The picture is again that of two persons sitting facing each other.\n    Here D sits on the right and facing him is the grain deity E. D is\n    speaking to E as is indicated by the sign before his face and by the\n    position of his right hand. The signs belonging to E are Hieroglyphs 5\n    and 7, while those of D are 3 and 4. It seems, therefore, that D is\n    announcing to E the prophecy contained in the preceding Tonalamatl.\n\n    4. Two hieroglyphs, 9 and 10, are again added, both relating to\n    death--9 to god A and 10 to F.\n\nNow what especially distinguishes this passage from the preceding one, is\nthe fact that the four days are the so-called regents of the year, Muluc,\nIx, Cauac and Kan, above which, perhaps to emphasize this circumstance,\nthere is a particularly elaborate Ahau. Seler (\"Einiges mehr \u00fcber die\nMonumente von Copan und Quirigu\u00e1,\" p. 210), however, thinks that this sign\nis the hieroglyph for the numeral three, which should stand here.\n\nThe fact that the tenth sign, which is the last, is 13 Moan in the\npreceding Tonalamatl, while here it is 11 F, will be of special\nsignificance in deciding the interpretation.\n\nPage 10b.\n\nThe manuscript gives the following:--\n\n  XIII  22  III  22\n  Oc\n  Ik\n  Ix\n  Cimi\n  Ezanab.\n\nThis cannot be correct, for 22 + 22 is not 52, and from XIII to III is not\n22 days, while the last Roman numeral is wanting. I, therefore, propose to\nmake a 6 of the numeral 2, which occurs twice, by changing the lower dot\ninto a line, and to change the III into a XIII by the addition of two\nlines. This gives the series the form XIII 26 XIII 26 XIII. Then by its\ndivision into three equal parts, this Tonalamatl accords with the three\npreceding ones, which it also resembles in other respects. For here too we\nfind two persons pictured; this time, however, they do not face each other,\nbut are placed one behind the other. The first is B, the god of life\nstrictly speaking, the second is F, who is represented by his hieroglyph in\nthe preceding Tonalamatl, and who is the god of the chase and probably of\ndeath by violence. Both hold offerings in their hands, which have been\npresented to them, and this also seems to be suggested by the two pendent\ncopal pouches. The dish in B's hand probably contains honey, while F holds\na plant (agave?)--the very same articles, which we find on page 12a in the\nhands of other gods. It looks as if the gods had been propitiated and as if\nthis were the conclusion of a drama running through four Tonalamatls. Again\nthe two death-hieroglyphs, which were added on pages 8 and 9, are wanting\nhere, and we find only the usual eight signs:--\n\n  1  2    5  6\n  3  4    7  8.\n\nOf these, 1, 2 and 5, 6 are the usual comprehensive heading; 1 and 5 are\nthe Manik sign, which must denote the offering, while 2 and 6 are the\ncharacters, which perhaps, not incorrectly, has been thought to denote a\nrepetition, a kind of plural; we have already seen it on pages 12a-13a. 3\nis the monogram of B, yet it looks more like a fist with the thumb\nprominent--a figure I have frequently found in the inscriptions of\nPalenque. It must also refer to the sacrifice offered to B, which is\nconfirmed by the _a_ added to it in 4 and probably denoting a good day. 7\nis the hieroglyph of F to which the sign in 8 corresponds, while the\nprefixed arm in 8 seems to refer to the presentation of the sacrifice.\n\nPages 10b--11b.\n\n  VIII  8  III  9  XII  9  VIII  10  V  16  VIII\n  Chuen\n  Akbal\n  Men\n  Manik\n  Cauac.\n\nI have corrected the 15 in the manuscript by making it 16.\n\n20 hieroglyphs correspond regularly to the five sections in the following\norder:--\n\n  1    5  6     9  10    13    17\n  2    7  8    11  12    14    18\n  3                      15    19\n  4                      16    20.\n\nThis section seems to refer chiefly to the harvest. First the Muluc sign\nwith suffix and affix, which is repeated in 1, 5, 9, 13 and 17 at regular\nintervals, suggests rain as a preliminary condition of the harvest. Next in\n2 the hieroglyph of K, the wind-god, is added to this Muluc sign, and K is\nthe patron of the day Muluc. Then the signs _a_ and _o_ follow in 3 and 4.\nThere is no picture belonging to this group; it ought to be the god K. The\nsecond group adds to the Muluc in 6 the glyph of the sun, which is the\nsecond preliminary condition of the harvest. This is followed in 7 by the\nsign _u_ apparently denoting wind and cloud and having the prefix of the\nstorm-god, and in 8 is the sign, which, strange to say, stands also in the\nlast Tonalamatl in the eighth place. I am not very clear in regard to this\nsign. The sun-god G with copal pouch and a vessel containing grains of\nmaize is appropriately represented with this group. With equal fitness the\nthird group contains E, the harvest-god proper, with copal pouch and grains\nof maize, and, as usual, a Kan sign on his head, but also with a parrot,\nprobably as an enemy of the harvest. Sign 10 is E's hieroglyph, to which,\nas is so often the case, sign 11 (Imix-Kan) is added and in 12 the double\nManik (_i_). The last two groups are without figures of deities; the double\nManik (14 and 18), possibly a repeated summons to sacrifice, is common to\nboth groups. There seems here to be a further reference to the _enemies_ of\nthe harvest, for 15 is the hieroglyph of the vulture, 16 that of the\ndeath-bird and 19 that of the night-god, after which this section closes\nwith the quite universal sign a. If space had permitted, the vulture and\nthe night-god would have been represented here.\n\nPage 12b.\n\n  I  13  I  26  I  13  I\n  Ix\n  Cimi\n  Ezanab\n  Oc\n  Ik.\n\nThis is again a regular arrangement, half of the 52 days being in the\nmiddle and a quarter each at the beginning and end.\n\nThe first four days refer to the purport of the prediction, Ix, the tiger,\nCimi, death, Ezanab, the wounding lance point, and Oc, the lightning dog.\nThe 12 hieroglyphs indicate the connection with the foregoing Tonalamatl,\nfor 1, 5 and 9 contain the same Muluc sign which we found there in the same\nplaces.\n\nThe three figures, it seems to me, signify the approach of death, the wound\noccasioning death, and the arrival of death.\n\nThe first picture represents the god probably as feminine, with which the\nillustration on page 9c should be compared. The lock of hair before sign 3,\nthe death hieroglyph, agrees with this as do also the familiar signs 2 and\n4. The god is making sounds, which is indicated by the figure issuing from\nhis mouth. Is the snail in his head-ornament to be understood as the sign\nfor retarded motion?\n\nThe second figure is the wounding serpent deity H, likewise represented\nhere as feminine, with a lock of hair; the copal pouch hangs from her neck,\nher nose-peg resembles a flower as on page 19a. A bird is sitting on her\nhead and is devouring a piece of an animal's body; we have already met this\nrepresentation in the preceding Tonalamatl. Hieroglyph 6 designates the\ndeity H, 7 (Imix-Kan) probably denotes the devouring of the flesh and sign\n8, which is an Ahau with a prefixed knife, may also refer to this.\n\nFinally, the third picture is again the death-god, who is clad in a gala\ncloak and, in contrast to the first picture, where the deity is sitting on\nsome object, is squatting on the ground. The three hieroglyphs 10, 11 and\n12 fit here admirably.\n\nWe will now turn back to page 4 and consider the lowest section (c) of\npages 4 to 12, which like pages 5b-12b (I omit 4b here because its contents\nare of an entirely different nature) contain 7 Tonalamatls, that is, five\nritual years of 364 days. If, however, we add 4b to these and bear in mind\nthat 10c-11c contain a double Tonalamatl, we will have 9 Tonalamatls. We\nfind a group of 7 Tonalamatls also on pages 51a-52a.\n\nPages 4c-5c.\n\n  XII  10  IX  22  V  11  III  9  XII\n  Cauac\n  Chuen\n  Akbal\n  Men\n  Manik.\n\nThe incorrect 10 of the manuscript has been changed to 9. The hieroglyphs\nare as follows:--\n\n  1  2    5  6     9  10    13  14\n  3  4    7  8    11  12    15  16.\n\nand there are four figures of gods.\n\nThe sign of the rising Moan with its usual prefix and superfix (_d_) forms\nthe principal part of this section, the meaning of which, however, is not\nyet very intelligible. This sign appears not merely as the 1st, 5th, 9th\nand 13th hieroglyphs, but all the four gods hold it in their hands. Placed\nafter each of these signs are hieroglyphs 2, 6, 10 and 14, which are the\ndouble Manik or hand sign denoting a sacrifice (_i_).\n\nThe first god portrayed here is G, the sun-god, and the third hieroglyph is\nhis sign, which is rendered yet more unmistakable here by the laterally\nelongated head _q_, the meaning of which is not yet wholly determined.\n\nThe second god is D with his two signs in 7 and 8. 7 designates him rather\nas night and moon-god and 8 more as the old god and lord of the gods.\n\nThe third god is the serpent deity H or Seler's \"young god.\" His sign is\nhieroglyph 11, with which, to be sure, the unusual sign 12 (_v_) appears as\na not very intelligible determinative.\n\nThe fourth god is A and his usual signs are given in 15 and 16.\n\nPages 5c--6c.\n\nThis is the second example in our manuscript of a Tonalamatl divided into\nfour parts:--\n\n  XII  29  II  11  XIII  18  V  7  XII\n  Ezanab\n  Akbal\n  Lamat\n  Ben\n  Ezanab.\n\nThe repetition of the 15th day at the end is superfluous.\n\nHere, then, we have the four days with which the 18 Uinals can begin; in\nthe Tonalamatl on page 9b, the four regents of the year were given instead.\nNow, whether the beginning of these periods of 20 days was celebrated by a\nbanquet or not, at all events, a feast is suggested by the sign Imix-Kan,\nwhich is repeated in hieroglyphs 1, 5, 9 and 13. The four vessels in the\nhands of the four deities, two of whom are sitting and two standing, would\nagree with the idea of a feast. The first vessel is a cup filled apparently\nwith foaming pulque, and the other three are larger vessels meant to be\nhung up. The first deity is D with a snail on his head. Compare page 12b.\nHis hieroglyphs are 2 and 3, and sign _a_ is added as fourth. The next\ndeity is A with his usual signs in 6, 7 and 8. C follows with his\nhieroglyph in 10 and lastly F with the sign 14 which belongs to him.\n\nThere still remain as the 11th and 15th signs, the elongated head _q_ with\nthe Ben-Ik superfix belonging to C and with another superfix belonging to F\n(with which he likewise appeared as sign 4 in the preceding Tonalamatl).\nThe 12th sign (_v_), which occurs in exactly the same place in the\npreceding Tonalamatl, is no more intelligible to me here than there.\n\nPages 6c--7c.\n\n  I  17  V  19  XI  6  IV  10  I\n  Chuen\n  Akbal\n  Men\n  Manik\n  Cauac.\n\nFour sitting gods with the regular 16 hieroglyphs. There is no collective\nsign, however, among these. It seems exactly as if the intention had been\nto represent the _different_ offerings usually presented to the various\ndeities. At all events the sacrifices are designated by hieroglyphs 1, 5, 9\nand 13, and the same objects are also held in the hands of the four gods\nrespectively, although they are clearly recognizable only in the case of\nthe second and third gods.\n\nNow what are these four different sacrificial gifts?\n\nThe principal part of the first looks like the sign of the month Mol. In\nexcellent agreement with its appearance is the fact, that this word\nsignifies egg in the Quecchi language. The god receiving the sacrifice here\nis A. Hieroglyph 2 is his monogram and 3 is that of his companion F and 4\nfits both deities.\n\nThe second figure is D and his signs are hieroglyphs 6 and 7 to which 8 is\nadded quite superfluously. The sacrifice proper is denoted by 5, which, I\nthink, is a sign of multiplicity and which was originally the fin of a\nfish. In the manuscripts and inscriptions, when this sign is added to the\nsign for 360 days, it enhances the value to 20 \u00d7 360 = 7200 days.\n\nThe third picture represents the god with the bird-head of the Moan and his\nsigns are hieroglyphs 10, 11 and 12. One of these, signifying rising birds,\nis also the offering in 9.\n\nLastly, the fourth picture is, according to Schellhas, the serpent deity H,\nand, according to Seler, the \"young god,\" with the snail on his head. His\nsign is hieroglyph 14. Added to this is the sign _a_ in 15, and in 16 it is\n_q_ again with the same superfix as in sign 15 of the preceding Tonalamatl.\nThe sacrifice in 13 is represented by a Kan sign, which is equivalent to\nmaize, maize bread or tortilla.\n\nRepeatedly, as on page 23b or 29b-31b of our manuscript, we see a portion\nof game (deer), a bird, a lizard and a fish represented as sacrifices. With\nthis the fish and bird in our second and third pictures agree very well. I\nshall not venture to explain the other two in the first and fourth\npictures. Perhaps future explanations of the curious head-ornament of the\nfour gods will shed further light on the subject.\n\nPage 8c.\n\n  III  9  XII  9  VIII  9  IV  9  XIII  9  IX  7  III\n  Cib\n  Lamat\n  Ahau\n  Eb\n  Kan.\n\nThe horizontal line should be read in this order; in the manuscript the\nnumbers are in a somewhat unusual order.\n\nAn attempt has been made to divide the 52 days into sections of 9 days\neach, and in doing this the sixth subdivision has fallen short of two days.\nSince this passage has but two pictures, six of the 12 hieroglyphs must\nbelong to each of the figures. I read the hieroglyphs in the following\norder:--\n\n  1  2  5      7   8  11\n  3  4  6      9  10  12.\n\nEach of the two pictures contains a building and a deity in front of it,\neach of whom seems to have placed another deity in the building. In the\nfirst picture D is putting C inside and in the second F is doing the same\nto A or the Moan. I will add also, that the day belonging to C (Chuen) is\nactually 9 days distant from that of D (Ahau). I am uncertain in regard to\nthe other two. In the back of each building we see a cross.\n\nA similar association of two gods appears again elsewhere, as on page 35a,\nwhere D lies on a building in which C is sitting, thus showing an\nassociation of the same two gods as in our first group.\n\nIn both groups the first two hieroglyphs form the common heading, since 1\ncorresponds in general to 7 and 2 to 8. In the first group 3 and 4 are the\nhieroglyphs of D and 5 and 6 are the signs _q_ and _v_; does one of these\nlast signs refer to the god C? In the second group 9 is the sign of F, who\nstands in front of the house and 10 that of the god in the house, as\nperhaps is also 11, when we consider the closed eye; this is one of the\nmany hieroglyphs having an uplifted arm as a prefix. On page 9a we find\nexactly the same sign. The last sign is the hieroglyph _q_, which sometimes\nseems to be used merely to fill space; it corresponds, but with a different\nsuperfix, to the fifth hieroglyph of the first group.\n\nThe last three parts of this section of the manuscript all differ\nappreciably from the usual form (5 \u00d7 52 = 260 days).\n\nPage 9c.\n\nHere for the first time the manuscript contains a Tonalamatl, which is\ndivided into 10 \u00d7 26 days. It is true the position of both the days and\nnumbers is quite irregular. The manuscript presents the following order:--\n\n  III      III          VI    VIII\n                         3       2\n  Cauac    Ben          XI      II\n  Chuen    Chicchan      3       4\n  Akbal    Caban        VI     VII\n  Men      Muluc         4       1\n  Manik    Imix.         I     III\n                         7       2\n\nI read it thus:--\n\n  III  3  VI  2  VIII  3  XI  4  II  4  VI  1  VII  7  I  2  III\n  Cauac\n  Chicchan\n  Chuen\n  Caban\n  Akbal\n  Muluc\n  Men\n  Imix\n  Manik\n  Ben.\n\nTwo figures and eight hieroglyphs are given here. I do not venture to\ndecide whether each of the two figures with its hieroglyphs relates only to\na period of 26 days or to the half of the whole, 130 days. I think the\nlatter is more likely to be the case. The sign Imix-Kan, which I am\ninclined to refer to a sacrificial meal, is common to both groups and\nconnects them. The two gods seem also to have a sign pertaining to a meal\nin their hands; this may be a cup.\n\nThe first deity is D or I, but with a female breast and with a serpent on\nhis head. His signs are 2 and 3. The second god is A with a snail on his\nhead and his signs are 6 and 7.\n\nIn addition to these, sign 4 of the first group is _v_ and sign 8 of the\nsecond group is c.\n\nPages 10c--11c.\n\n  I    3   XIII  1  I  5  VI  10  III  13  III  15  V  8 (in error 9)  XIII\n  Imix     Cimi\n  Ben      Ezanab\n  Chicchan Oc\n  Caban    Ik\n  Muluc    Ix.\n\nHere we have two independent Tonalamatls as on page 12a. There are\nsubdivisions only for the second; the first should be regarded either as\nentirely invalid or else its division has merely been omitted.\n\n6 gods with 4 hieroglyphs each are represented on these pages:--\n\n  1  2    5  6     9  10    13  14    17  18    21  22\n  3  4    7  8    11  12    15  16    19  20    23  24.\n\nHere too Hieroglyphs 1, 5, 9, 13, 17 and 21 are the common factor; they\nhave the form of the month Mol, but here, as on page 6c, they probably\ndesignate the particular object constituting the sacrifice. The following\ndetails are to be noted regarding the six divisions:--\n\n1. The god A with his two signs in 2 and 3.\n\n2. D with the signs 6 and 7.\n\n3. F with the signs 10 and 11 (the latter _c_).\n\n4. E with the signs 14 and 15, having on his head a structure, which is\ncompounded apparently of a Kan sign, a snail and the suggestion of the\nmaize plant.\n\n5. G, clad in the gala cloak and the copal bag. His sign is 18, while 19\nsuggests rather the Moan or K.\n\n6. B, his headdress displays the little circles, which often occur in\nconnection with him, _e.g._, pages 30c, 40a and 41a, and which may suggest\nthe starry sky. His sign is 22; the hieroglyph _m_ is added to it in 23 as\na determinative.\n\nAs usual, the fourth sign of each group is the most puzzling. 4 and 12 are\nImix with the uplifted arm as a prefix, as on page 13a, 8 is the hieroglyph\n_o_, 16 is _a_, 20 is _c_ and the principal part of 24 is _r_. This sign\n_r_ seems to me to suggest the week of 13 days (see above the explanation\nof page 4a); four weeks of this kind end here.\n\nIt is to be noted further that all the six gods are holding one hand\noutstretched:--A downward, B upward and the four in the centre forward.\n\nPage 12c.\n\n  XIII  26  XIII  26  XIII  13  XIII\n  Chuen\n  Cib\n  Imix\n  Cimi\n  Chuen.\n\nThis is another Tonalamatl divided into 4 \u00d7 65, the subdivisions being\ntransferred to the end of the second, fourth and fifth weeks. The Chuen at\nthe bottom is superfluous.\n\nThe twelve hieroglyphs standing here according to rule are grouped together\nin fours by the three pairs of the first row. Of these 1, 5 and 9 are the\nfist, familiar from the inscriptions, and which we also see on page 10b of\nthis manuscript, where, to be sure, it occurs with the sign of B, as often\nhappens, but here it has the closed eye of the death-god A. On the other\nhand, 2, 6 and 10 are the sign Kin = sun, with merely a dotted outline, and\nthe three gods pictured below all hold the same Kin sign in their hands.\nThis passage, may refer to the dying sun, the winter solstice.\n\nThe first god is D, who, however, has B's head on top of his own. An object\nlike a spyglass projects from the eye of B, which one could hardly venture\nto pronounce a nose-peg. The sign 4 (Ahau) refers to D; but what is the\nmeaning of 3, the hieroglyph of the serpent deity H? Is the sun wounded?\n\nThe second god is the baldheaded old deity, whom Schellhas designates as N.\nThe hieroglyph 7, apparently referring to the five Uayeyab days, is his\nsign; we found it on page 4b and shall again find it on page 21c, and this\ntime likewise with the old man. What is the meaning of the grain-goddess E\ndenoted by sign 8? As N is connected with the close of the year, so E seems\nto be in various ways connected with the beginning of the new year.\n\nThe third picture is unmistakably the sun-god G with the copal pouch\nhanging from his neck. His sign is 11, while sign 12, which suggests the\nwind-god K and balled-up clouds, is as difficult to explain here as it was\non page 11c. The signs 8 and 12 seem, therefore, to refer to one another,\nand, if I do not see too much, look like a promise of rain and harvest.\n\nOn page 12 the Tonalamatls of the three sections of the page come to an end\nand a new part of the manuscript begins.\n\nPage 13a.\n\nI shall here group together pages 13 and 14, the top third of 14 encroaches\na little upon page 15. 13a has the following Tonalamatl:--\n\n  Imix\n  Ben\n  Chicchan\n  Caban\n  Muluc.\n\nI have supplied the first day, which is effaced. The week days are wanting.\nThe 52 days are divided into halves of 26 days each.\n\nOf the 8 hieroglyphs the fifth seems to be the same as the destroyed first;\naside from the prefix, it is the sign _s_.\n\nThe two halves of the period have two gods, the first is B with a very\nsingular head-ornament, and the second A, perhaps with the symbol of a\nsnail on his head. Both hold a plant (agave) in their hands, as on pages\n10b and 12a. Hieroglyph 2, which is mostly destroyed, must have been B's\nmonogram, 4 has the Ahau as its determinative, and 3 is the elongated head\n_q_ with Ben-Ik.\n\nIn the second group 6 and 8 are the signs of A, and 7 is an Imix with the\nuplifted arm prefixed, as on page 10c.\n\nPages 14a--15a.\n\n  VIII  13  VIII  13  VIII  13  VIII  13\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThe month days 13 and 5 have changed places in the manuscript. The initial\nday VIII Ahau will prove to be of especial importance in the second part of\nthe manuscript (compare page 70). Here, as in the preceding Tonalamatl, the\nperiod is divided into equal parts.\n\nLittle can be said of the hieroglyphs, 16 in number, since 6, 9, 10, 12,\n13, 14, 15 and 16 are wholly or mostly destroyed. 3, 7 and 11 seem here to\nbe a comprehensive element, as is also probably 15, but I am unable to\nrefer this head to a particular god; 2, 6, 10 and 14 may also be alike, but\nthis is very uncertain. 1, 5, 9 and 13 may have denoted the four cardinal\npoints, at least 1 suggests the south and 5 the north.\n\nThus we have left for the four deities E, H, A and G, only the signs 4, 8,\n12 and 16; 4 surely belongs to E, and 8 to H, but the other two are erased.\n\nPages 13b--14b.\n\n  VI  13  VI  9  II  7  IX  7  III  7  X  9  VI\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThere are 24 hieroglyphs for the 6 divisions:--\n\n  1  2    5  6     9  10    13  14    17  18    21  22\n  3  4    7  8    11  12    15  16    19  20    23  24.\n\nOf these the upper row again contains the comprehensive signs, and the\nlower the discriminating characters. The closed eye in 1, 5, 9, 13, 17 and\n21 suggests A, who also appears below as the first of the six gods, and the\nsuperfix of these signs suggests the south. 2, 6, 10, 14, 18 and 22 are the\nKan sign, and we also find this sign in the hand of each of the six gods.\nThus the subject of this passage seems strictly speaking to be harvest or\nfood.\n\nThe six gods are A, E, C, L, F and D; the second, third fourth and fifth\nhave a bird on their heads. The first and fourth birds are eating, as on\npages 11a and 12b, and thus probably represent enemies of the harvest. The\nfirst is of a different species from the other two. The four gods in the\ncentre have the copal pouch about their necks. Signs 3 and 4 are the common\nhieroglyphs for A; 7 that for E, to which _o_ is added as a determinative;\n11 is C's hieroglyph with an _a_ added to it, and L is undoubtedly denoted\nby sign 15; 16 is _r_ (equal to 13 days; it is meant here for the day III\nCib). F appears quite according to rule in 19, which is appropriately\nfollowed by the sign _c_ in 20. Finally the hieroglyphs for D in 23 and 24\nare the usual ones.\n\nWe come now to the large section extending to page 23, which, owing to the\nnumerous pictures of women, forms a section quite by itself. It is not\nlikely that this contains anything else than oracles relating to pregnancy;\nin fact, the period of 260 days represented here with great frequency is in\nexcellent accord with this subject. In the Codex Tro-Cort. there is also a\nsection devoted to women, which corresponds to this chapter and\nparticularly page 19* of the Troano affords remarkable parallels to the\nDresdensis, even in details.\n\nPages 13c--14c.\n\n  II        II  7  IX  3  XII  3  II  13  II\n  Men       Chicchan\n  Imix      Chuen\n  Manik     Caban\n  Ben       Akbal\n  Cauac     Muluc.\n\nThe second of the two vertical rows on the left should be considered as\nimmediately joined to the first. Thus we have here the second example in\nthis manuscript of a Tonalamatl of ten parts; the first was on page 9c.\n\nThe entire representation on 13c and 14c looks like an introduction to the\nfollowing section, as though treating in general of the relation to one\nanother of pairs of animals, of human beings and of deities. Corresponding\nwith the Tonalamatl, there are four pairs of this kind represented.\n\nThe hieroglyphs belonging to these pictures are distributed among the four\nsections as follows:--\n\n  1  2    5  6     9  10  11    15  16  17\n  3  4    7  8    12  13  14    18  19  20.\n\nApparently, the first two pictures have only 4 signs each, and the other\ntwo 6, but this is equalized by the fact, that hieroglyphs 1, 3, 5, and 7\nare clearly each composed of two signs. The comprehensive sign appearing in\n2, 6, 9 and 16, is, properly speaking, the sign _t_, which may denote\ncoition, and, not unsuitably, contains in its centre two black figures side\nby side.\n\nPassing now to the separate four groups, I think the male figure is always\non the right and the female on the left. In the first and second groups the\ntwo face each other, and in the other two groups the male is behind the\nfemale.\n\n1. The female figure is an animal, perhaps a deer, the male is a black and\nwhite spotted deity having a human form and his head appropriately\nembellished with horns. The hieroglyphs belonging to these are:--1, a\ncombination of Manik and Chuen with a prefixed 4, just as on page 21b; 3,\nlikewise a compound sign, with a prefixed 7, which occurs also on page 46c\non the left, and which I do not venture to explain, but which seems to\ndenote horns, and lastly the hieroglyph c.\n\n2. The female figure is an animal (on page 19a the female is represented\nmore in resemblance to the human form) with a bird-head, to which belongs\nthe compound sign _s_, still unexplained; the male figure is a barking (or\nhowling?) dog, as on page 21b. Hieroglyph 7 is composite and contains first\nthe sign generally belonging to the dog and suggesting a skeleton, which\nalso represents the 14th month, and secondly, a Cimi closely related to it,\nprecisely the same as in the parallel passage 21b. The well-known _q_\nfollows in the 8th place.\n\n3. The god D holds in front of himself an animal, which may be a rabbit.\nHis signs are hieroglyphs 11 and 12, while 13, the principal part of which\nis a grasping hand, clutching a Moan sign, seems to refer to the animal in\nthe picture. 10 is _b_ and 14 is a.\n\n4. Lastly, two beings in human guise, showing thus a closer connection with\nwhat follows. They are the black god L with his hieroglyph in 18 enlarged\nby an Imix, and a woman holding a Kan sign in her hand, hieroglyph 20\nlikewise showing the ordinary combination of Imix-Kan. Sign 15, however,\nrefers to the woman, and lastly 17 and 19 are the signs _m_ and _r_; I note\nthat _r_ ends a period of 13 days.\n\nThe contents of the following seem to suggest that we should first read\npage 15 (including the middle section of 16) from top to bottom, then pages\n16-23, partly from left to right and partly from top to bottom, according\nto the subject.\n\nPage 15a.\n\n  V  34  XIII  18  V\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThere are two pictures with 4 hieroglyphs each.\n\nThe two pictures represent D and A, the latter probably as feminine. Both\nare falling headfirst, and both have leaves about them as if they were\nfalling from a tree and a cry is issuing from A's mouth. The common element\nis given in hieroglyphs 2, 3 and 7, which are all signs of D. Further, 4 is\nthe Chuen sign, the ape (as the animal living on trees?), its prefix is\nhieroglyph _r_, which I regard as denoting the week of 13 days and which\nfalls here exactly on the day XIII. And the same Chuen sign is repeated in\nthe second group as the first part of sign 6, the second part of which is\nillegible. 8 is the sign of A and 1 is effaced.\n\nPages 15b--16b.\n\n  I  13  I  31  VI  8  I  13  I\n  Ik\n  Manik\n  Eb\n  Caban\n  Ik.\n\nThat is 4 \u00d7 65 = 260 days. Hence the sign of Ik repeated at the bottom, as\nis usual in such cases, is superfluous.\n\nThe Tonalamatl contains 4 figures, of which 1 and 2 form one pair and 3 and\n4 another.\n\nAs on page 15a, the pair at the left are falling down and also have leaves\nabout them. They are god B, who holds a Kan sign in his hand, and a woman,\nwhose eyes are closed and who holds the sign of death before her breast. B\nis falling down in a similar fashion in Cort. 17. Hieroglyphs 1-8 belong to\nthis pair. Of these, 1, 5 and 8 and also 7 refer to death, 3 with the\ndeterminative sign, 4, added (which is the sign _q_ with a Ben-Ik), refers\nto B, while signs 2 and 6 belonging to god D, who occurred in the preceding\nTonalamatl, should be noted.\n\nThe pair at the right on the other hand is _seated_, the woman apparently\non the curved handle of a vessel. The head-ornament and hieroglyph of the\nfemale figure prove that she is the serpent deity H, while the male figure\nis the rare black deity M, whom we find again with his sign on page 43a for\nexample; he holds a bone in his hand. Hieroglyphs 9 and 13 agree. The lower\npart of these hieroglyphs is the fist with the thumb unfolded, the sign at\nthe top seeming to be merely an empty outline (Muluc?) and thus, like 1 and\n5 of the preceding group, they seem to refer to a sacrifice offered to the\ndeath-god. 10 and 14 are again, strange to say, like 2 and 6 of the\npreceding group, the sign of D. 11 is the hieroglyph of H, who is\nrepresented below as feminine, and that 12 is a complement of 11 is proved\nby the upper part of this uncommon hieroglyph, which corresponds to the\nobject in H's hand, and which is repeated on page 18a with the same figure;\ncompare also page 8b. 15 is surely the hieroglyph of M, who is pictured\nbelow, as in the Tro. 2a and 22*a where the same M appears with the same\nhieroglyph, and to him belongs in 16 the sign _r_, which I am inclined to\nconsider the week of 13 days, and which here, as on 14c, ends a section of\n13 days.\n\nPage 15c.\n\n  III       III  12  II  14  III\n  Lamat     Ix\n  Ahau      Cimi\n  Eb        Ezanab\n  Kan       Oc\n  Cib       Ik.\n\nThis is a Tonalamatl of ten parts, the days are to be read in the following\norder:--Lamat, Ix, Ahau, Cimi, etc.\n\nThere are two figures, A probably conceived as feminine and D with the same\nhead-ornament as on page 10; both hold in their hands a Kin = sun.\nHieroglyphs 2 and 6 are also the Kin sign, while 1 and 5 have the closed\neye of A, but differ in their secondary parts, the sign suggesting the\nsouth being a suffix in 1 and a superfix in 5; 1, however, has an affix,\nwhile 5 has as a prefix a sign differing from the affix in 1. 3 and 4 are\nthe signs of A, 7 that of D, next to which in 8 one would expect to see an\nAhau, but instead of this there is again the sign of H (borrowed from page\n15b?).\n\nThis seems to end the subject of coition; now, in natural course, follows\nthe subject of pregnancy, to which I believe the following Tonalamatl is\nexclusively devoted.\n\nPage 16a.\n\n  Kan  21  31\n  Cib\n  Lamat\n  Ahau\n  Eb.\n\nThere are no red numerals, hence the Tonalamatl seems to apply to any one\nof the initial week days.\n\nTwo women are portrayed, both of whom are stretching a hand forward and\nupward. There are 8 hieroglyphs of which, however, the top row is almost\nentirely obliterated; 3 and 7 in the lower row are just alike, being the\nusual sign for woman.\n\nThere is a decided contrast between the two figures, which might suggest\nbarrenness and fruitfulness. Observation of their physical differences\nwould give us that idea. Furthermore, the first carries on her back an\nunfamiliar head, perhaps A's, while the second has the Ahau, Imix and Kan\nsigns, from which plants seem to be sprouting. The first is represented in\nthe fourth hieroglyph by the sign _c_, which is closely allied to the death\ndeities, while the second woman is denoted by hieroglyph 8 which is the\nsign of the deity E, the grain-god.\n\nPages 16a--17a.\n\nIn the following I will group together all the pages from page 16-23 as\nfollows:--First, I shall discuss the top thirds, then the middle and lastly\nthe lower thirds. The sense, however, often seems to require that the first\nthird should connect with the second, and the second with the third; but I\nfind it impossible to determine exactly the intended order.\n\nOn pages 16a-17a, we find for the first time in this manuscript not a\nTonalamatl, but in its stead all the twenty days arranged in four columns,\neach of which ends with one of the regents of the year:--\n\n  Men        Ahau      Chicchan     Oc\n  Cib        Imix      Cimi         Chuen\n  Caban      Ik        Manik        Eb\n  Ezanab     Akbal     Lamat        Ben\n  Cauac      Kan       Muluc        Ix.\n\nThis seems to establish the fact that the day of its birth was of\nimportance to a new-born child.\n\nBetween each column and the next there is a picture and above each picture\nfour hieroglyphs, which, however, are mostly destroyed, so that much of the\nmeaning of this passage is lost to us.\n\nThe first is an old man walking, who beyond doubt is N, the Uayeyab god,\nwith a staff in his hand and the signs Imix and Kan on his back. He is\nlooking upward and is also pointing upward with his right hand. Of his\nhieroglyphs only enough of the fourth is visible to enable us to recognize\nin it the regular sign of N, 5 Zac. The second picture is again an old man\nwalking with a stick, he is baldheaded and hence is probably also N, as on\npage 12c. His hieroglyph might be the fourth of those written above him,\nthe other three are entirely unrecognizable. He has a carrying-frame on his\nback, but it is uncertain whether he is carrying anything upon it.\n\nThe third figure is a woman who is pointing upward with one hand and with\nthe other holding the bundle on her back, which I am unable to explain\n(does it refer to the 14th Uinal--the end of pregnancy?) and from which\nrises an object resembling a flame. Her sign is in the fourth place and _q_\nis in the third. 1 and 2 are not legible and perhaps may be supplemented by\nthe third picture on page 19c. Finally, the fourth figure is F, who is\nsitting and has a Cimi sign on his back. His monogram is the second of the\nhieroglyphs above him, the third is very appropriately _b_ and the other\ntwo are not very clear to me.\n\nThe first two pictures might designate a male birth, the first indicating\nwealth and the second poverty, the third might denote a female birth and\nthe fourth a still birth. But who can positively assert this!\n\nPages 18a--19a.\n\n  VIII  12  VII  12  VI  9  II  10  XII  9  VIII\n  Ik\n  Ix\n  Cimi\n  Ezanab\n  Oc.\n\nThis is a Tonalamatl of five parts with 20 hieroglyphs, which unfortunately\nare so much injured that no signs comprehending the whole can be\ndistinguished.\n\nThere are five women in a sitting attitude.\n\nThe first woman corresponds exactly to the third figure on page 15b. She is\nsitting on a bench, the same implement is in her hand and there is also a\nserpent on her head, for which reason she likewise reminds us of H. The\nthird hieroglyph is hers, and the 4th sign is an Ahau.\n\nThe second woman holds in her hand the Kin sign; above it is the Yax sign\nand above this a little cross between two dots (the numeral 18?). Compare\npages 18c, 19c and 27b, and in the second part, 46b and 50c. I shall\nventure no opinion regarding the hieroglyphs.\n\nThe third woman with the copal pouch hanging from her neck has nothing in\nher hand. She is pointing upward with her right hand. Her hair seems to be\nwound in the shape of an 8 in horizontal position and above her is a sign\ndenoting the union of two parts. The hieroglyphs are entirely destroyed.\nDoes this represent the birth of twins?\n\nThe eyes of the fourth woman are closed, she is pointing forward with her\nhand and there is a bird on her head. Nothing is left of the hieroglyphs.\n\nFinally, the fifth is distinguished by a large nose-peg, which, as on 12b,\nresembles a flower. Her hand is extended forward. The fourth of the\nhieroglyphs above her is her sign. There is nothing to be said regarding\nthe three others. Are these five women engaged here in presenting their\nthankofferings and prayers of thanksgiving for the birth which has taken\nplace?\n\nPages 19a--21a.\n\n  XI  13  XI  13  XI  13  XI  13  XI  13  XI\n  Ahau\n  Chicchan\n  Oc\n  Men\n  Ahau.\n\nInstead of Men the Manuscript has incorrectly Eb. Ahau in the fifth place\nis superfluous, since we have here a Tonalamatl divided into four equal\nparts.\n\nThe hieroglyphs are so nearly obliterated that we can no longer distinguish\na common sign. There were in all six signs for the first picture, of which\nthe first two are above the day-signs, while the figures from the second to\nthe fifth have only four signs each, as follows:--\n\n  1  2  5    7   8    11  12    15  16    19  20\n  3  4  6    9  10    13  14    17  18    21  22.\n\nAll that can be distinguished here is that the 4th and 13th have the same\ncross _b_ and that 6 and 10 probably contain the same head.\n\nEach of the five pictures contains a woman sitting. In the first\nrepresentation she sits opposite a male figure, who bends down to her with\nhis bird-head, which we have already seen on page 13c. In the other four\npictures the woman is holding the figure of a god on her lap. I do not\nrecognize the god in the first picture on page 20. In the second and third\npictures he is related to A or the Moan and the first figure on page 21 may\nrepresent the god D. These can only be new-born children represented by the\ngods under whose signs they were born. It should also be noted that the\nsecond woman on page 20 has a serpent on her head and the third a bird. The\nbird's head resembles that on page 16c.\n\nPages 21a--22a.\n\nThe Cimi and Eb of the second column have changed places in the Manuscript.\nInstead of the X there is an erroneous 2 and there is no initial VII.\n\n  VII       VII  3  X  2  XII  7  VI  9  II  3  V  2  VII\n  Oc        Ahau\n  Cib       Cimi\n  Ik        Eb\n  Lamat     Ezanab\n  Ix        Kan.\n\nWe have here a Tonalamatl consisting of 10 \u00d7 26 days, and the 26 days are\nsubdivided into six parts. I have just assumed that the 2 is wrong and the\ninitial VII is wanting over the first column, yet the 2 followed by the\nlaterally elongated head _q_ might here, perhaps, be explained in some\nmanner as the sign of the day VII Oc.\n\nApart from this sign which occupies an entirely exceptional position, we\nhave here 24 hieroglyphs, _i.e._, 4 for each of the six groups.\n\nThe fourth sign in the first five groups is in each case a Chuen combined\nwith the cross _b_ and the suffix, which seems to be a knife, and also with\na numeral, which, however, is not recognizable in the first group; in the\nsecond it is a 3, in the third a 7, in the fourth a 5 and in the fifth a 3.\nWhat can these numbers mean? 3 + 7 + 5 + 3 = 18, and Chuen with the meaning\nof 20 (especially in the inscriptions) would be 18 \u00d7 20 = 360.\n\nIn the fourth place of the sixth group there is a compound character, the\nmain part of which (top, right) seems to be the sign for the thirteenth\nmonth, Mac, and which may also, as we shall see on page 24, denote the\nentire Tonalamatl. It is again compounded with a Chuen, an uplifted arm and\na kind of suffix, and hence might denote the end of a Tonalamatl.\n\nThe remaining 18 signs are in the main destroyed. In the second of the\nfourth group we recognize the lock of hair denoting a woman, in the third\nof the second group the superfix suggesting the south, which we find above\nthe Cimi sign, for example on page 13b. Lastly, the other third signs are\nin the third group Imix-Kan, in the fourth group the head _q_, in the fifth\nthe bird c and in the sixth a Manik sign with prefix and superfix\nresembling the sign _i_; in a few places (24, 39a, 53a, 56b, 58b, 61a, 61c,\n68c) the prefix might have the meaning of 20.\n\nSince the intention was to close this section on the next page, the space\nhad to be used as economically as possible, and instead of the six pictures\nto be expected, there is only one and that is the first. It is a woman in\nwhom I observe nothing characteristic except that she has a kind of cloak,\nwhich has fallen down over the lower part of her body, and who therefore\nremains unexplained.\n\nPages 22a--23a.\n\n  II        II        II        II  2  IV  8  XII  7  VI  10  III  12  II\n  Men       Cib       Caban     Ezanab\n  Chuen     Eb        Ben       Ix\n  Manik     Lamat     Muluc     Oc\n  Akbal     Kan       Chicchan  Cimi\n\nThe Tonalamatl is no doubt to be read in this way after the correction of a\nfew inaccuracies in the Manuscript.\n\nThe 20 days, all of which occur again here as on pages 16a-17a, should be\nread from the right top to the left bottom, since they form but one series.\n\nAs a matter of fact Ezanab is distant 19 days from the future Caban, but 39\ndays distant from the desired weekday of the same name (see my\n\"Erl\u00e4uterungen,\" p. 24). Thus we have here a period of 20 \u00d7 39 days = 780,\n_i.e._, a three-fold Tonalamatl. The three Tonalamatls represented on the\npages between the preceding passage (pages 16a-17a), where all the 20 days\nappear, and this, are of three _different_ kinds (5 \u00d7 52, 4 \u00d7 65, and 10 \u00d7\n26). This in itself is very remarkable. Furthermore a fourth kind of\nTonalamatl seems to be introduced here, which embraces, as it were, these\nthree Tonalamatls.\n\nThe hieroglyphs, which are mostly destroyed, were arranged in groups of\nfour for each subdivision, in the following order:--\n\n         II    II    II    II\n  1  2    5     9    13    17\n  3  4    6    10    14    18\n          7    11    15    19\n          8    12    16    20.\n\nOf the above the third hieroglyph of each group, _i.e._, 7, 11, 15, 19\n(probably also 3) is always the same and is the sign of D, the moon and\nnight-god. In detail we should expect to find five pictures here, but owing\nto lack of space only the first of these is given. It represents a deity\nwith a Kan sign in its hand and a serpent on its head, who is probably E,\nand he is falling down here in exactly the same manner as the four deities\non page 15 at the beginning of this section.\n\nNow, which were the other four deities? Signs 8, 12, 20 refer to A, H and\nC. 16 is the laterally elongated head _q_, to which Seler is inclined to\nrefer the day Men, and Schellhas an undetermined deity I. On account of its\nfrequency this sign must have besides a more general significance. In\naddition, however, we have in 14 and 18 the signs of F and B. 6 is\nuncertain, 10 is probably C, and the top row is entirely illegible. If to\nthese deities is added the D repeated five times in the third row, it will\nbe seen that all the important gods are grouped together here on the last\npage of this section.\n\nPages 16b--17b.\n\nI will now attempt (for it cannot be more than an attempt) to separate into\nthree parts, according to their contents, the middle and lowest thirds of\npages 16 to 23. The first part, 16b to 18b and 16c to 20c, contains six\nTonalamatls with pictures of women, each of whom carries on her back the\nfigure or symbol of a deity. This deity can hardly be any other than the\none to which the horoscope of the child especially refers.\n\nThe first of these Tonalamatls, on pages 16b-17b, runs as follows:--\n\n  Muluc  13  4  35 (or 20  15)\n  Imix\n  Ben\n  Chicchan\n  Caban.\n\nThe red numerals are wanting and were probably forgotten.\n\nThe hieroglyphs stand thus:--\n\n  1  2    5  6     9    13\n  3  4    7  8    10    14\n                  11    15\n                  12    16.\n\nOf these 3, 7, 11 and 15 are the sign for women, 2, 6, 10 and 14 are\nlikewise all the same sign, which is repeated in the same places on pages\n17c to 18c. I do not understand its meaning; it may have reference merely\nto the carrying-frame. Instead of the four women, whom we should expect to\nfind here, only the first two are portrayed. The first carries B, whose\nsign is the first hieroglyph, while the fourth hieroglyph is the sign _q_.\n\nThe second woman carries A to whom hieroglyphs 5 and 8 refer. The third\nwoman would have carried D, which is plainly proved by hieroglyphs 9 and\n12, and the fourth, F, as follows from sign 13 and probably also from 16\n(_q_).\n\nPages 17b--18b.\n\n  Eb  11  7  6  16  8  4.\n  Kan\n  Cib\n  Lamat\n  Ahau.\n\nHere again there are no red numerals.\n\nThe 24 hieroglyphs of the six divisions stand thus:--\n\n  1  2    5   9    13  14    17  18    21  22\n  3  4    6  10    15  16    19  20    23  24.\n          7  11\n          8  12\n\nAgain, six women should be portrayed here, but there are only four; the\nsecond and third are wanting. The signs for the women are given in 3, 7,\n11, 15, 19 and 23, but in 15 and 19 the prefix is different from that of\nthe rest. As from here on the women repeatedly carry a bird, the signs for\nthis are 2, 6, 10, 14, 18 and 22, which are the symbol of a rising bird, as\nin the sign of the 15th Uinal (Moan), which in my opinion generally\ncoincides with the 13th month of 28 days.\n\nThe women pictured here have nothing in their hands, which they hold\nstretched forward, as is usually the case in this section. The first woman\ncarries a vulture on her head. Compare 8a. In regard to it see also\nSchellhas, \"G\u00f6ttergestalten,\" p. 31. The hieroglyph of the vulture, which\nwe find repeated on page 17c, 24, 37b, 46, 50, 65, is here hieroglyph 1,\nusually regarded as the sign of the bat deity, and near it in 4 is _q_.\n\nThe second woman would have carried the black deity L (hieroglyph 5), to\nwhich _q_ is added in 8.\n\nThe third would have had the dog, _i.e._, the lightning dog, which we find\nin hieroglyph 9 and in the month sign Kankin; an _a_ is added to them in\n12.\n\nThe fourth woman carries A, as is proved by his signs in 13 and 16.\n\nThe fifth carries nothing; according to the hieroglyphs 17 and 20 she ought\nto carry D.\n\nLastly the sixth carries the Moan as is proved by signs 21 and 24.\n\nPages 16c--17c.\n\n  Muluc  8  13  13  13  8  10\n  Ix\n  Cauac\n  Kan\n  Muluc.\n\nThis is a Tonalamatl of 4 \u00d7 65 days. The Muluc at the bottom is, therefore,\nsuperfluous. I have been obliged to correct the 12 in the last column of\nthe Manuscript by changing it into a 10. The red numerals are again\nwanting.\n\nThis passage admirably continues the one in the preceding Tonalamatl\ncontaining the women carrying birds, and is also divided into six parts.\n\nThe hieroglyphs stand thus:--\n\n  1  2    5  6     9  10    13    17    21\n  3  4    7  8    11  12    14    18    22\n                            15    19    23\n                            16    20    24.\n\nSigns 3, 7, 11, 14, 19 and 23 (14 and 15 have changed places) denote women.\nOf the six women only the first three are here portrayed.\n\nThe first carries the Moan with which signs 1, 2 and 4 agree perfectly. The\nsecond and third carry two birds, which may be parrots of a different\nspecies. They are very seldom represented elsewhere and hence their\nhieroglyphs, 5 and 9, with the added determinative 10 are unfamiliar. In 8\nand 12 the well-known determinatives _a_ and _c_ are added.\n\nJudging by sign 13 the fourth woman would have carried the same vulture,\nwhich we see in the middle section of this page; 15 and 16 are again signs\n_c_ and _q_.\n\nThe fifth woman would have carried an unknown bird of prey, the signs of\nwhich are 17 and 18, and 18=10; 20 is again _q_, but with a superfix\ndifferent from that in 16.\n\nFinally the sixth woman, like the third in 17b, seems to have carried the\ndog, as is proved by sign 21, but in 22 the symbol of a bird is again\nadded. This passage ends in 24 with the well-known Imix-Kan.\n\nPages 17c--18c.\n\n  IV  15  VI  33  XIII  4  IV\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nHere we again find the regular red numerals (Roman in my transcription of\nthe text), which were wanting in the last three Tonalamatls. That they were\nnot added until after the black script and drawings were completed, is\nevident in several passages of our Manuscript and also in this one, where\nthey have been faintly indicated in black by the scribe (or corrector). The\nabsence of red numbers in the passages 17b-18b and 16c-17c is an evidence\nthat I was right in proceeding directly from the former to the latter.\n\nOf the 12 hieroglyphs, 2, 6 and 10 have again the form which we found on\npages 16b-17b, and which seems to refer to a carrying-frame; compare,\nhowever, the explanation of pages 25-28 below. The women themselves are\ndesignated by hieroglyphs 3, 8 and 12. The first woman carries the god A\nand hieroglyphs 1 and 4 are his regular signs. The second woman has on her\nback a Kin sign, above that a Yax, and this combination overtopped by a\ncross between two dots also forms hieroglyph 5; compare the upper section\nof the same page. That this hieroglyph is nothing else than a designation\nof god D follows from hieroglyph 7. Finally the fourth woman carries a\nfigure, which has a Moan sign for a head and to which hieroglyphs 9 and 11\ncertainly refer.\n\nPages 18c--19c.\n\n  XIII  32  VI  20  XIII\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThe first woman carries the god A, who is denoted by hieroglyphs 4 and 1,\nthough somewhat irregularly by the latter. 2 is the carrying-frame and 3\nthe woman herself.\n\nThe second woman has again the Yax-Kin sign on her back as in the preceding\nTonalamatl, and hieroglyph 5 is also a combination of these signs, but here\nin 7 we find, not the sign of D, but that of E, to which also the Imix-Kan\nin 8 corresponds. 6 is again the carrying-frame, though, as is also the\ncase in 2, more indistinctly drawn than in the earlier Tonalamatls.\n\nPages 19c--20c.\n\n  XIII  11  XI  11  IX  11  VII  10  IV  9  XIII\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThis is a Tonalamatl divided into five parts, to which 20 hieroglyphs\nbelong. The hieroglyphs are in the following order:--\n\n  1  2    5  6     9  10    13  14    17  18\n  3  4    7  8    11  12    15  16    19  20.\n\nAt places 2, 7 (6 and 7 have changed places), 10, 14 and 18 we find again\nthe sign which we think means a carrying-frame, while signs 3, 6, 11, 15\nand 19 are those of the five women.\n\nThe first carries a figure with a Moan head and agreeing with this is the\nsecond death-god F in hieroglyph 1 and his determinative in 4.\n\nThe second woman, who is seated, carries the same object regarding which I\nam still uncertain, which is carried by the standing woman on page 17a.\nThis object is denoted by hieroglyph 5 (_w_). Its determinative is probably\n8. It may perhaps be a step in the right direction to point out that this\nsign suggests the god K.\n\nThe third, like the first, has a figure with a Moan head, with which a\nfemale form of A in 12 and hieroglyph 9 accord.\n\nThe fourth woman carries the maize deity E. 13 is his sign and the food\nhieroglyphs, Imix-Kan in 16, agree with it.\n\nThe fifth woman seems to carry the somewhat indistinct form of D, if this\nmay be inferred from the Ahau of the 17th sign. 20 is the universal sign a.\n\nThis ends the six Tonalamatls, which are represented in what I have called\nthe section of the burden-bearing women. Five other Tonalamatls follow,\nwhich again suggest the idea of conception, which we met once before on\npages 13c-14c.\n\nPage 19b.\n\n  X  29  XIII  23  X\n  Ik\n  Ix\n  Cimi\n  Ezanab\n  Oc\n\nThe most frequent sign in the five Tonalamatls, which I have grouped\ntogether, is the cross _b_, which plays the most important part in all the\nTonalamatls, excepting the third, which differs from the rest also in other\nrespects. It is essentially the sign for union, referring in the case of\nthe stars to their conjunction and here to sexual union.\n\nIn this Tonalamatl we see the cross in hieroglyphs 1 and 5, the sign for\nwoman in 2 and 6, and their determinatives in 3 and 7.\n\nThe first woman has a deity facing her who is devoid of all characteristic\nmarks, and sign 4 is also nothing but the universal a.\n\nThe second woman whose eyes are closed, sits facing A, whose hieroglyph is\nin 8.\n\nPages 19b--20b.\n\n  VI  28  VIII  24  VI\n  Cib\n  Lamat\n  Ahau\n  Eb\n  Kan.\n\nThe arrangement of this Tonalamatl is very similar to that of the\npreceding.\n\nHieroglyphs 1 and 5 are again the cross, and 2 and 6 the signs for woman.\n\nThe first picture is wanting; hieroglyph 3 with the number 7 as a prefix\ndenotes a deity with whom I am not familiar. The same sign is found on page\n50, left, middle; in 4 the usual head _q_ is added.\n\nBeside the woman in the second group--not facing her--is the serpent deity\nH, again, as on pages 11c and 12b, with the nose-peg resembling a flower.\nHis sign is 7 to which in 8 the familiar Ahau is again added.\n\nPage 20b.\n\n  II  20  IX  19  II  13  II\n  Cauac\n  Chuen\n  Akbal\n  Men\n  Manik.\n\nThe hieroglyphs stand thus:--\n\n  1  2    5     9\n  3  4    6    10\n          7    11\n          8    12.\n\nThe subject now passes into the province of astronomy. This is already\nproved by sign 1, which represents the clouds, between which the sun or\nmoon is usually pictured; the sun is probably omitted here merely owing to\nlimited space. Sign 3 suggests the storm-god K (compare pages 7a and 47\nleft) to which in 2 the Ahau might be appropriately added, inasmuch as it\nrules the year here under consideration as on pages 25b to 26c. On account\nof the Ben-Ik sign I see in 4 one of the months of 28 days as a more exact\ndetermination of time. Below the Ben-Ik a head is represented with eyes\napparently closed, and this head is repeated in 6 and 10, though, probably\nfor lack of space, without the Ben-Ik. In each of the three places a sign\nis used as an affix which might readily be the year sign, contracted\nlaterally.\n\nThe two similar hieroglyphs 5 and 9, which have the following form, are\nespecially worthy of consideration:--\n\n[Illustration]\n\nThe part on the right recalls by its trisection the sign _r_, which I\nregard as the week of 13 days and, in fact, the interval between the two\nhieroglyphs is 13 days. On the left is the inverted figure of a person in a\nsquatting attitude, the head surrounded by stars as on pages 57b and 58b\nand a sign on the back which may be a suggestion of the sun-glyph. In this\nfigure, which occurs also in the Tro-Cort. and in the inscriptions, I see\nthe planet Mercury and I believe that that planet's retrogression (which\nlasts 17-18 days) or disappearance into the light of the sun during this\nweek, is the subject of this passage. 7 and 8 are the sign for D with the\nusual Ahau, and 11 and 12 are the hieroglyphs of the death-god A.\n\nInstead of three pictures there is only one here, viz:--a woman with\nnose-peg, sitting on a mat and apparently waiting for something. We also\nfind figures sitting on mats elsewhere, for example on pages 7b and 68b.\n\nPage 21b.\n\n  VII       VII  7  I  7  VIII  7  II  5  VII\n  Oc        Ahau\n  Cib       Cimi\n  Ik        Eb\n  Lamat     Ezanab\n  Ix        Kan.\n\nThis is also a Tonalamatl of 10 parts (10 \u00d7 26). The first column should be\nread first from top to bottom and then the second. The days are exactly the\nsame as on page 21a, and here too Cimi and Eb have changed places.\n\nThe hieroglyphs run thus:--\n\n  1    5  6     9    13\n  2    7  8    10    14\n  3            11    15\n  4            12    16.\n\nThe signs forming the hieroglyphs into groups are, in addition to the cross\nin 2, 6, 10 and 14, the heads in 1, 5, 9 and 13 with an Akbal sign\n(indistinct in 9) which, by the lock of hair in 5, 9 and 13, refer to a\nwoman. This lock of hair is replaced by a hand in 1.\n\nSign 3, with which _m_ in 4 is associated as a determinative, shows that\nthe first group ought to have a picture of the black god L grouped with a\nfemale figure.\n\nThe second group is the only one with a picture. On the right there is a\nfemale figure, which, judging by the headdress, we have already met on page\n19a. Opposite her sits the dog which we saw on page 13c. Here (in sign 7),\nas on page 13c, the hieroglyph of the dog is combined with a Cimi sign, and\nthis hieroglyph is repeated in 8 with the sign _c_, which is so closely\nallied to Cimi.\n\nFor the third group the god A should have been represented with the woman,\nas is proved by sign 11 so peculiarly combined with _r_ as a superfix. To\nthis hieroglyph _a_ is added, doubtless referring to the good days, as if\nmerely to fill space.\n\nThe hieroglyphs of the fourth group do not, I think, convey a clear idea as\nto which deity belongs here. His sign is 15, which is compounded of Manik\nand Chuen with a superfix, nor does the Cimi added in 16 shed light on the\nsubject. As for 15 we have already found it on page 13c with the prefixed\n4, which I find prefixed in this way in at least 12 different signs.\n\nPages 21c--22c.\n\n  Caban  5  21  16  10\n  Muluc\n  Imix\n  Ben\n  Chicchan.\n\nThis is a Tonalamatl of five parts in which the red numerals are wanting.\n\nThe hieroglyphs are in the following order:--\n\n  1  2    5  6     9  11    13\n  3  4    7  8    10  12    14\n                            15\n                            16.\n\nAmong these are hieroglyphs which are common to all the groups:--the cross\nin 1, 5 and 9 and the woman in 3, 7 and 15. In 13 this cross is replaced by\nanother sign, perhaps that for the year of 360 days, and in 12 the sign for\nwoman is replaced by the universal a.\n\nEach of the three pictures contains a woman facing a deity. I will consider\nfirst the second picture in which H is the deity, as is proved by\nhieroglyph 6 to which an Imix is added in 8, with the uplifted arm prefixed\nas in 10c and 13a.\n\nBetween the first and third pictures there is some confusion. The first is\nD, for while his type inclines more to that of N, the other old god of the\nMaya Olympus, comparison with 23c clearly shows that D is intended here.\nBut the year-sign on his head also suggests in some measure the Uayeyab god\nN and moreover this sign does not belong to D and only occurs again with\nhim on page 23c. Further, there is no hieroglyph at all for D and instead\nwe find in 2, 5 Zac, the regular sign of N. Also sign 4 fits N better than\nit does D. Furthermore this passage relates to the day Ik, which might very\nwell be the last day of the year.\n\nOn the other hand the third picture contains, unquestionably, the figure of\nN. I look for his sign in the 11th hieroglyph, which is the head of an old\nman with a prefixed 4, referring to the four different forms of N in the\nKan, Muluc, Ix and Cauac years. The Ahau in 12, however, does not fit N,\nbut D.\n\nThis confusion can only be adjusted by transferring D from the first group\nto the third and also, perhaps, the sign of the woman in 3, which applies\nto all the three groups, and by transferring to the first group N and the\n11th sign of the third group.\n\nThe fourth group has no picture. It should have, as hieroglyph 14 shows,\nthe god F, who represents death by violence in human sacrifice and the\nchase. The hieroglyph Cimi in the 16th place is a suitable sign for this\ndeity.\n\nPages 22c--23c.\n\n  II  10  XII  12  XI  9  VII  6  XIII  7  VII  8  II\n  Oc\n  Ik\n  Ix\n  Cimi\n  Ezanab.\n\nThe hieroglyphs are arranged in the following order:--\n\n  1  2    5  6     9    13  14    17  18    21  22\n  3  4    7  8    10    15  16    19  20    23  24.\n                  11\n                  12\n\nThis Tonalamatl, the fifth and last of this section, presents much that is\nirregular and puzzling.\n\nIt can hardly be said that there are comprehensive hieroglyphs here,\nforming the heading of the six groups. The sign for woman occurs only in 2,\n8 and 24, and the cross _b_ only in 14 and 18, but it is sufficient to make\nit clear that here, too, connection with a woman is the principal theme.\nLet us pass, therefore, directly to the single groups.\n\nThe first group contains A and a woman. The god, however, is not facing the\nwoman but sits beside her. The Cimi sign in 1, the familiar _c_ in 3 and\nthe unknown sign in 4 (=6) hardly explain this particular proceeding.\n\nThe second group contains two persons who sit facing each other, but the\nrepresentation is so obscure and peculiar that it is difficult to determine\nwhich is the male figure and which the female. The hair of the person\nsitting on the right stands up in a manner not found elsewhere. It forms a\nfigure similar to that which is issuing from the mouth of the dog on pages\n13c and 21b. The Cimi sign in 5 and the sign _c_ in 7 are familiar, but the\ninfrequent 6=4 remains a puzzle.\n\nUncertainty regarding the third group is increased by the fact that there\nis no picture belonging to it. The well-known signs, 10 (Cimi) and 12 (_q_)\nafford no explanation, nor does the head with the uplifted arm in 11, which\nwe find with the same hieroglyph on pages 8a and 36a. The most puzzling is\nthe 9th sign, which is composed of two crouching persons leaning back to\nback, and who also appear in the astronomical sections of the Manuscript on\npage 68a, not merely in the form of a hieroglyph, but also carried out in a\npicture. In my article on the Maya chronology published in the Zeitschrift\nf\u00fcr Ethnologie of the year 1891, I attempted to explain this Janus picture\nas meaning the change of the year, but that interpretation would make no\nsense here.\n\nThe fourth group contains the woman opposite D, who is clad in the gala\nmantle and has on his head a bird and apparently the sign for a year, and\nis designated by the Ahau in 16, while Imix-Kan in 13, _b_ in 14 and _a_ in\n15 are rather meaningless.\n\nThe fifth group represents the woman united with A, who is designated by\nthe Cimi sign in 17. 18 with its _b_ and 19 with its _q_ display little\nthat is characteristic, _r_ in 20, which I think is the sign for the week\nof 13 days, invites further study. The sixth picture, which is the last, is\nvery peculiar; it represents three women sitting side by side denoting\nperhaps the virgins who still remain. Sign 21 as Imix-Kan, 23 as _a_ and 24\nas sign of femininity supply nothing in the way of explanation. As 6, 9 and\n20 are the characteristic signs in the preceding groups, so here the\ncharacteristic sign is 22--an open hand holding the day Ben--which perhaps\ndesignates these virgins by referring to the house in which they are held\nfast by the hand. Cf. Tro. 23* d.\n\nNow of the entire woman section closing with page 23 only the two\nTonalamatls on pages 22b-23b remain. These Tonalamatls again display very\nmany peculiarities and seem to be but loosely connected with the five\nTonalamatls last discussed.\n\nPage 22b.\n\n  III  13  III  13  III  13  III  13  III\n  Akbal\n  Men\n  Manik\n  Cauac\n  Chuen.\n\nThis is a regular Tonalamatl, in which the 52 days are divided into four\nequal parts.\n\nThe hieroglyphs are in the following order:--\n\n  1  2    5  6     9  10    13\n  3  4    7  8    11  12    14\n                            15\n                            16.\n\nAn Ahau is added here as the 17th sign, which is very unusual.\n\nWe find elements here forming the hieroglyphs into groups in three\ndifferent ways.\n\n1. The signs 1, 5, 9 and 13 designate the four cardinal points as they so\noften stand together in this Manuscript in the order of East, North, West\nand South, _i.e._, in the sequence of the annual and not of the diurnal\ncourse of the sun.\n\n2. The hieroglyphs 2, 6, 10 and 14 are all alike and are the head with the\nAkbal eye, which in 6 is closed.\n\n3. The three persons pictured here all carry a Kan sign in their hands,\nprobably as the offering they have received. Similarly we found the Kan\nsign held in the hand twice on page 16b.\n\nThe first picture is B; his sign is the third with the _q_ in 4 as a\ndeterminative, which has above it a Ben-Ik sign.\n\nThe second figure is a goddess with a serpent as head-ornament, though we\nfind in the 7th sign, not her hieroglyph, but merely the one generally used\nto denote a woman. 8 is the usual _a_, which in my opinion is the sign for\nthe _good_ days, to which also the Kan sign refers in the hands of the\nthree personages.\n\nThe third picture is that of the sun-god G; his hieroglyph is the 11th, to\nwhich in 12 is added the sign _q_, the sign for the bad days, with a\nsuperfix.\n\nThe fourth picture is wanting. According to the 15th hieroglyph it should\nbe the maize deity E. My theory that 16 is the sign for the week of 13 days\nis supported by the fact that the division into 4 \u00d7 13 days is the\nprevailing one.\n\nPage 23b.\n\n  VIII  12  VII  12  VI  12  V  12  IV  12  III  5  VIII\n  Kan\n  Muluc\n  Ix\n  Cauac\n  Lamat.\n\nThis is a Tonalamatl of 4 \u00d7 65 days divided as evenly as possible into 5 \u00d7\n12 + 5. The 5th day added after the 16th must be a mistake (suggested by\nthe 5th day of the last section) for it is usually the first of the days,\nwhich is repeated superfluously.\n\nThe hieroglyphs are:--\n\n  1  2     7   11    15    19    23\n  3  4     8   12    16    20    24\n  5  6     9   13    17    21    25\n          10   14    18    22    26.\n\nContrary to practice the first section has six hieroglyphs, and the other\nfive but four each.\n\nAs the characteristic hieroglyph we find in 1, 7, 11, 15, 19 and 23 a sign,\nthe meaning of which is still undetermined and which we shall meet again on\npage 60, where it may refer to darkness.\n\nThe groups have in common, furthermore, the head without an underjaw and\nthe hair gathered up in a tuft in 4, 10, 14, 22 and 25 (in 18 perhaps\nrepresented by _q_, the evil days). We shall find this sign on pages 25,\n28, 30-35, 42-44 and 65-69, repeated a number of times in many instances. I\nconsider it the sign for fast-days. It appears also in the Tro-Cort.\nAssociated with this sign here as in other passages are the four sacrifices\nderived from the animal kingdom:--a haunch of venison, a bird, an iguana\nand a fish. The fish is beyond doubt denoted by 3, the mammal by 21 and the\nbird by 13, and I believe, therefore, that the iguana with its spiny back\nis denoted by 9. We find the four animals, though in a different order,\nalso on pages 29b-30b, 30b-31b and 40c-41c, as well as in Cort. 3-6 and 8,\nfor example. They seem to have a certain reference also to the four\ncardinal points.\n\nOnly the first of the six groups has a picture (I?). This represents a\nwoman with a serpent in her hair, holding in her hand a dish containing a\nfish. The woman is denoted by the fifth hieroglyph and the fish by the\nthird. The 6th sign is an Ahau, which is not quite intelligible here. Sign\n2=5 Zac is very remarkable; it is the hieroglyph of the Uayeyab days and of\ntheir god N. If this Ahau refers, as it often does, to the god D, it\nsuggests the relation between D and N, which follows from page 21c.\n\nAccording to the 8th sign, the second group might refer to the serpent\ndeity H, and the 9th sign would not improperly denote the iguana.\n\nIn the same way sign 12 in the third group probably denotes the storm-god\nK, with whom the bird in 13 accords very well.\n\nIn the fourth group both the animal and the sign of fasting, belonging to\nit, are wanting, while 16 and 17 as well as the unlucky day in 18 clearly\nrefer to the death-deity A.\n\nThe fifth passage belongs, as sign 20 shows, to the maize deity E and to\nthis is added the haunch of venison in 21.\n\nIn the sixth group we recognize Imix-Kan, the sign for food derived from\nthe vegetable kingdom. It stands beside the grain-deity E of the fifth\ngroup. I do not understand the vulture-head in 26.\n\nThe five deities specified here may be compared with those on page 24,\nwhich are denoted by hieroglyphs 21-25 of the second column, though the\nagreement is not perfect.\n\nThis ends the first great section of the Manuscript, in which Tonalamatls\nare represented in uninterrupted succession. We come now to a page which\nstands quite alone, being the first which treats of astronomy and which\nends the front of the first part of the Manuscript.\n\nPage 24.\n\nIn my article \"Zur Entzifferung IV\" I discussed this remarkable page in\ndetail and in what follows I shall conform to that treatise, though\nomitting many things which since then have become the established\npossession of science, and shall endeavor to shed a still clearer light\nupon other points.\n\nThis page presents in brief the subject which is more fully treated of on\nthe front of the second part of the Manuscript (pages 46-60).\n\nThe first problem it presents is to find periods in which the solar year\n(365 days) is brought into accord with the apparent Venus year (584 days).\nThis takes place in a term of 2920 days = 8 \u00d7 365 = 5 \u00d7 584. Sequent to\nthis is the still higher aim of bringing the Tonalamatl (260) into harmony\nwith this period, which is accomplished in 37,960 days (= 146 \u00d7 260 = 104 \u00d7\n365 = 65 \u00d7 584).\n\nThe revolution of the moon (28), the ritual year (364 = 28 \u00d7 13) and the\napparent revolution of Mercury (115) come in question as secondary matters.\n\nI will now give an approximate reproduction of the page:--\n\n   Hieroglyphs.\n\n   1   17   29    151,840        113,880         75,920         37,960\n   2   18   30   (4 \u00d7 37,960)   (3 \u00d7 37,960)   (2 \u00d7 37,960)   (13 \u00d7 2920)\n   3   19   31    I Ahau         I Ahau          I Ahau         I Ahau\n\n   4   20   32    185,120         68,900         33,280          9100\n   5   21   33    I Ahau         I Ahau          I Ahau         I Ahau\n\n   6   22   34     35,040         32,120         29,200         26,280\n   7   23   35   (12 \u00d7 2920)    (11 \u00d7 2920)    (10 \u00d7 2920)    (9 \u00d7 2920)\n   8   24   36     VI Ahau       XI Ahau        III Ahau      VIII Ahau\n\n   9   25   37     23,360         20,440         17,520         14,600\n  10   26   38   (8 \u00d7 2920)     (7 \u00d7 2920)     (6 \u00d7 2920)     (5 \u00d7 2920)\n  11   27   39    XIII Ahau       V Ahau        X Ahau         II Ahau\n  12   28   40\n  13               11,680          8,760          5,840          2920\n  14             (4 \u00d7 2920)     (3 \u00d7 2920)     (2 \u00d7 2920)\n                  VII Ahau        XII Ahau      IV Ahau        IX Ahau\n  15\n  16                2,200         1,366,560            1,364,360\n                  IV Ahau          I Ahau               I Ahau\n                  8 Cumhu         18 Kayab              18 Zip.\n\nFirst let me observe that I have restored the four large numbers at the\ntop, which are almost entirely effaced, as follows:--\n\n   1   15   10   5\n   1   16   10   5\n   1    6   16   8\n  14    0    0   0.\n   0\n\nAnd furthermore, at the right, bottom, I have substituted the third month\nfor the second of the Manuscript, which proceeding will be justified later\non.\n\nThe least difficult portion of the contents of this page is the first\nseries consisting of 16 members, each being a multiple of 2920. It begins\nwith the date I Ahau (which is always concealed in these series), regularly\nstops at the month day Ahau (since 2920 = 146 \u00d7 20), but necessarily\nadvances in the week days by 8 days each (since 2920 = 224 \u00d7 13 + 8), until\n37,960 is reached, when the day I Ahau again appears (since 37,960 = 146 \u00d7\n260).\n\nAccording to my method of filling in the numbers, the top row of the page\nconsists only of multiples of 37,960.\n\nOn the other hand, the four numbers of the second row from the top are more\ndifficult. They are, it is true, all divisible without remainder by 260,\nbut otherwise they seem to be without rule, and they give one somewhat the\nimpression of a subsidiary computation such as one might jot down on a slip\nof paper in the course of some important mathematical work.\n\nNevertheless, the following remarkable results are obtained when the first\nand third and the second and fourth numbers are combined by addition or\nsubtraction:--\n\n1) 185,120 + 33,280 = 218,400, which is just 600 years of 13 \u00d7 28 = 364\ndays, 280 Mars years of 780 days, 840 Tonalamatls of 260 days or 7800\nmonths of 28 days.\n\n2) 185,120 - 33,280 = 151,840, _i.e._, precisely the highest number of the\ntop row, = 416 solar years of 365 days each or 260 Venus years of 584 days\neach, _i.e._, the product of the days of the Tonalamatl multiplied by the\nVenus years. We shall again find the 151,840 on page 51, and Seler\n(\"Quetzalcoatl and Kukulcan,\" p. 400) finds this same period on a relief of\nChichen Itza.\n\n3) 68,900 + 9100 = 78,000, _i.e._, 100 Mars years or 300 Tonalamatls. The\nhalf of this number, or 39,000, we shall find again on pages 69-73 by\ncomputation; also the whole 78,000.\n\n4) 68,900 - 9100 = 59,800, _i.e._, 520 Mercury years of 115 days, or 230\nTonalamatls, or five times the period of 11,960 days, in which these two\nperiods are united. By computation again we find the 59,800 on page 58.\nThis period of 11,960 days is, however, to the period of 37,960 in the\nproportion of 23:73, _i.e._, 23 \u00d7 520:73 \u00d7 520. 23 is the fifth part of the\napparent Mercury year, as 73 is of the solar year.\n\nLet us now turn to the numbers, which form the bottom of my transcription,\nbut only the left hand lower corner in the Manuscript. Here, in the latter,\nwe find the following (with the correction already mentioned of the second\nto the third month):--\n\n   2200      1,366,560    1,364,360\n  IV Ahau      I Ahau      I Ahau\n  8 Cumhu     18 Kayab     18 Zip.\n\nThe first thing to be done is to arrange and fill out these numbers to suit\nour purpose.\n\nThe 2200 is clearly nothing more than the difference between the two high\nnumbers. We can therefore dispense with it.\n\nFurther, we find by the usual computation, that the second number belongs\nto the first date and the third to the second. Hence the number\ncorresponding to the third date is wanting from lack of space. This number\ncan be calculated from that date; it is 1,352,400. It would suit this date\nequally well if the number were higher or lower by 18,980 or a multiple of\n18,980; but it will be seen directly that it agrees with the other two\nnumbers only at the value given above.\n\nNow, if we add to this passage the years in which the dates must lie, they\nare in the case of the date on the left, the year 9 Ix, in the case of the\nmiddle date, the year 3 Kan, and of that on the right hand, the year 10\nKan.\n\nThen if we arrange the three numbers with the dates and years belonging to\nthem, according to the value of the first, this part of the page will run\nas follows:--\n\n  1,352,400    1,364,360    1,366,560\n   I Ahau        I Ahau      IV Ahau\n   18 Zip       18 Kayab     8 Cumhu\n   10 Kan        3 Kan         9 Ix.\n\nLet us now consider the properties of the three numbers individually.\n\n1) 1,352,400 = 28 \u00d7 48,300 and = 115 \u00d7 11,760, hence it is divisible by the\nmonth days of the year of 364 days and by the Mercury year. At all events\nthis is the least important of the three numbers.\n\n2) 1,364,360. This looks as if it referred particularly to the moon and to\nMercury; to the latter since it is equal to 115 \u00d7 11,864, and to the former\nif we assume that the lunar revolution has been fixed at 29-2/3 days, in\nwhich case this number is exactly equal to 46,000 such lunations. If this\nlast number be again divided by 115, the number of days required for a\nrevolution of Mercury, the quotient is 400, which is a round number in the\nvigesimal system and which was therefore denoted by a single word, by B\u00e1k\nin the Maya (according to Stoll) and by Huna in the Cakchiquel (according\nto Seler). 1,364,360, therefore, is a Huna of lunar revolutions multiplied\nby the number of days in the Mercury period. Later on we shall find the\nlunar revolution fixed at 29-2/3 days.\n\n3) 1,366,560. This is the most comprehensive number of the entire\nManuscript, for it is divisible into each of the following periods:--Those\nof the Se\u00f1ores de la noche or Lords of the Cycle (9 \u00d7 151,840; this is,\nhowever, the first number of the top row), the Tonalamatls (260 \u00d7 5256),\nthe old official years (360 \u00d7 3796), the solar years (365 \u00d7 3744), the\nVenus years (584 \u00d7 2340), the Mars years (780 \u00d7 1752), the Venus-solar\nperiods (2920 \u00d7 468), the solar year-Tonalamatls (18,980 \u00d7 72), the Venus,\nsolar, Tonalamatl periods (37,960 \u00d7 36), and the periods which are\ngenerally designated Ahau-Katuns (113,880 \u00d7 12).\n\nWe have next to consider the intervals which elapse between the three\ndates.\n\n1) From 1,352,400 to 1,364,360 is 11,960 days, which period we have already\nfound once on this page by computation. 11,960, however, is equal to 104 \u00d7\n115 and 46 \u00d7 260, _i.e._, the Mercury revolution and the Tonalamatl\ncombined. 11,960 is again equal to 32 \u00d7 365 + 280, and from the year 10 Kan\nto 3 Kan it is actually 32 years, and from the date 18 Zip to 18 Kayab it\nis, in fact, 280 days. The day I Ahau must be common to both dates.\n\n2) From 1,364,360 to 1,366,560 is 2200 days, as the Manuscript expressly\nstates. 2200, however, is equal to 8 \u00d7 260+120, and the distance from the\nday I Ahau to IV Ahau is in fact exactly 120 days. Further 2200=6 \u00d7 365+10;\nfrom the year 3 Kan to 9 Ix it is 6 years and from the date 18 Kayab to 8\nCumhu it is 10 days.\n\n3) From these two statements the third follows. The distance from 1,352,400\nto 1,366,560 is 14,160. This contains first the 14040, in which both the\nTonalamatl and the old official year of 360 days meet, and second 120,\nwhich is again the interval between I Ahau and IV Ahau. But 14,160 is also\nequal to 38 \u00d7 365 + 290, and the interval between 10 Kan and 9 Ix is of\ncourse 38 years, and from 18 Zip to 8 Cumhu it is 290 days.\n\nThe numbers with which we have had to do here will again occupy our\nattention further on, especially the 2920 and the 37,960 on pages 46-50,\nthe 11,960 and 115 on pages 51-58, and the 14,040 on page 73.\n\nThat these computations are not confined to the Dresden Manuscript is\nproved by the cross of Palenque, where we find in signs A B 16 precisely\nthe date I Ahau 18 Zotz, a Tonalamatl before 18 Kayab, in D 1 C 2 exactly\nthe difference 2200 and in D 3 C 4 the date IV Ahau 8 Cumhu. This is in\nfavor of the theory that our Manuscript did not originate far from\nPalenque.\n\nNow, the question finally arises as to what may, strictly speaking, be\nconsidered the significance of these numbers, dates and differences.\n\nIn the first place, I would recall the fact that the dates of the monuments\nof Copan and Quirigua, which doubtless refer to present time, are in the\nneighborhood of 1,400,000. The high numbers of our Manuscript, so far as\nthey are in question here, form first a group, which extends from about\n1,200,000 to 1,280,000, and then there is a blank, and next a large group\nextending from about 1,350,000 to 1,480,000, then another blank and lastly\na group extending from about 1,520,000 to 1,580,000. If we assume that our\nManuscript belonged to about the same date as these inscriptions, then the\nthree numbers discussed here would extend over a past period lying about\n160-170 years back, when a new period of importance had begun probably\ndating from the immigration of the Aztecs into Mexico, which they placed in\nthe first half of the 14th century (see \"Weltall,\" Vol. 5. pp. 374-377).\nNow, however, the number 1,366,560 contains the statement that 3744 years\nago (each year having 365 days) an event must have occurred, which can\nhardly be anything other (according to the belief of the Mayas) than the\ncreation of mankind. Hence all the _historical_ dates of the Mayas were\ncomputed from this starting-point. But how did this event come to have the\ndate IV Ahau 8 Cumhu?\n\nIn my opinion this date is to be regarded only as the result of the far\nmore important date I Ahau 18 Kayab, lying 2200 days earlier. Day 17, Ahau,\nbelongs, without doubt, to the chief of the gods, and as the first week day\nit must have been especially sacred. The prophecies of the Tonalamatl\npreferably begin with the Ahau and with the I. The series on the page under\ndiscussion, constructed with the difference 2920 as a basis, begins with I\nAhau, and the three series on pages 46-50 also have the same day as the\nzero point of departure. I Ahau is therefore the starting-point of the\nastronomical computations as IV Ahau is of the historical.\n\nNow, however, all the periods of 260 days end each time with I Ahau. Why is\nprecisely this day chosen here, which is the 18th day of the month Kayab,\ntherefore in the year 3 Kan, and lying 2200 days earlier than the\nhistorical date?\n\nDay 18 Kayab is our June 18th. In my treatise \"Schildkr\u00f6te und Schnecke in\nder Mayaliteratur\" (1892), I have sought to prove that the tortoise served\nas symbol of the summer solstice, that the sign of Kayab was the head of a\ntortoise, and that probably the 18th of June was regarded as the longest\nday. The middle one of the three series on pages 46-50 begins with exactly\nthis date, I Ahau 18 Kayab.\n\nBut whence come the 2200 days? I will offer a suggestion which may serve\nuntil a better theory is propounded. Let us assume that each of the five\nprincipal planets had in succession regulated its time of revolution by\nthis astronomical starting-point, thus:--sun 365, moon 356, Mercury 115,\nVenus 584, and Mars 780 days, these numbers added together give exactly\n2200. It will scarcely excite surprise that I should set down the lunar\nyear at 356 days (and not at the usual 354 days) for there are 12 \u00d7 29-2/3\nlunations in a year and we thought we had already found this period on this\npage, while discussing the number 1,364,360; also on pages 51-58, in\naddition to the half lunar year of 177 days, we shall find one of 178 days.\nWere the planets therefore created 2200 days before the appearance of\nmankind? Jupiter and Saturn, of course, with their 397 and 380 days are\nprobably not considered here, because their periods of revolution so nearly\ncorrespond to that of the sun, and on pages 51-60 they are also treated as\nof secondary importance.\n\nI confess I am quite unable to discover what may have happened 11,960 days\nbefore the creation of the stars--possibly the birth of one of the\nprincipal deities. Perhaps one of my fellow-students may succeed in finding\nan answer in one of the creation myths.\n\nWe come now to the 40 hieroglyphs on the left half of the page. These are\nintended simply to familiarize the reader with those signs which are of\nimportance in the calendrical-astronomical portions of the Manuscript.\nSince no phonetic system of writing existed, we cannot, of course, expect\nthat the scribe should have explained these signs.\n\nSigns 1-4, which are mostly destroyed, can hardly denote anything other\nthan the four quarters of the globe, at least we can still recognize in 4\nthe sign for the east, which has also the fourth place in pages 46-50. They\nstand thus together five times in the middle of the left side of pages\n46-50, which pertain to this subject. 5 to 9 are the sign for Venus\nrepeated 5 times, probably denoting the four parts of its revolution as on\npages 46-50 and also the revolution as a whole. In connection with this\nfirst appearance of the Venus sign, I would mention that the same\nhieroglyph also occurs in the Tro-Cort., _e.g._, Cort. 25c, though this\nManuscript contains little else that is astronomical, yet it also has the\nrectangular heavenly shields.\n\n10. This is a well-known form of the Moan sign. In the Globus, Volume LXV,\n1894, I sought to make it appear probable that the Moan also denoted the\nPleiades, with whose disappearance and reappearance the beginning of the\nyears seems to be connected. Likewise on page 50, where the 2920-period\nends, the Venus and Moan signs appear at the top on the right-hand side.\n\n11 and 12 are the same sign, being that of the 13th Uinal (Mac), with which\n260 days of the year end, and hence this sign is also used as the sign of\nthe Tonalamatl. The repetition seems to show, that not until the 73\nTonalamatls of the period of 18,980 days are doubled--thus obtaining the\nnumber 37,960 of such importance here--are the sun and Venus periods\nbrought into unison (with the whole system).\n\n13. The Kin sign (sun, day) with the superfix, which in all probability\nexpresses conjunction, union, and which, in my opinion, we also see on page\n51, combined with Kin and Imix, as the sign for 18,980 days, is used here\nafter the two Tonalamatls to denote the doubling of this period.\n\n14-18. If the preceding signs led us to the Venus-solar period and to the\ncontinuation of this subject on pages 46-50, these five hieroglyphs bring\nus to the Mercury-lunar period and later, on pages 51-58, which are devoted\nto the same period, we shall find a parallel especially on the last page.\nFirst comes 14, which, as has been acknowledged, is the sign for 20 \u00d7 360 =\n7200 days. 15, a hand holding a rectangle divided by a cross into four\nparts, is, I believe, the sign for the period of 20 days augmented to 21 by\nthe 1 in front of it. The much more distinct form of sign 16 on the middle\nof page 58 and also at the top of page 53, should be compared with the sign\nas given here. The top part is the familiar Ben-Ik sign denoting the 10th\nand 19th days, and the bottom is the sign of the 14th division of 20 days,\nwhich make up the year. Now, however, the 10th day, when it becomes the\n19th of the next 20 days, is distant from the first 29 days. The prefix\nconsists of two parts:--First two small circles joined by a zigzag line,\nwhich I think denotes the division of a day into halves; the sign would\nthen equal 29\u00bd days, _i.e._, very nearly the true lunar month. Second, of\ntwo vertical lines, which might denote a doubling. The whole would then be\nequal to 2 \u00d7 29\u00bd = 59. I admit that this interpretation is very artificial\nand I should be very glad if a better explanation could be found. On the\nother hand the 17th hieroglyph becomes quite clear when it is compared with\nthe parallel passage on page 58; it is 13 \u00d7 360 = 4680 days, a third of the\nremarkable period of 14,040 days.\n\nThus we have\n\n  Hieroglyph 14 = 7200\n      \"      15 =   21\n      \"      16 =   59\n      \"      17 = 4680\n                 -----\n                 11960,\n\nwhich is exactly the lunar-Mercury period.\n\nThe sign Xul = conclusion, end, is fittingly added in 18 to the end of this\nperiod, as also on page 58. This sign is very common on pages 61 and 62 at\nthe end of the long periods.\n\nFrom signs 19 and 20 we see that the four parts of the Venus year are also\nabout to be treated of here, that is, the periods of 236, 90, 250 and 8\ndays respectively, which are discussed on pages 46-50. For 19 is the sign\nfor Venus, and 20 is a hand with a knife as a superfix, which divides the\nVenus revolution. This hand appears 20 times in like manner on the pages\nmentioned above.\n\nSigns 21-25 represent five gods, who in all probability are N, F, H, the\nbat-god and A. These are the same signs which are repeated twice on the\nleft-hand side of pages 46-50, both times at the beginning and end of the\nperiod of 236 days, that is, the period during which Venus is the morning\nstar and which is under the dominion of the east. The fact that there is a\n4 with N has reference to the four forms which this Uayeyab god assumes.\nNow we ought to expect a similar treatment of the periods of the planet,\nwhich are under the rule of the south, west and north, but there is no room\nfor this. Instead, we find in 26, 27 and 28 three different signs plainly\nbelonging together, the first of which is the day Caban, _i.e._, the earth;\nthe second may be Muluc denoting rain and water; the third is Chuen (the\nape) which fittingly denotes the north, for Chuen denotes the little bear,\nas I have proved in my treatise on the day-signs of the Mayas. The Chuen\nsign in 28 also has a prefix, which probably refers to the night-god D. I\nfind exactly the same combination in signs 8 A and 8 B of the inscription\non the Cross of Palenque, but I must leave to others the task of connecting\n26 and 27 likewise with the north, which is very evident in 27 (Muluc).\n\nSign 29 is entirely effaced. Nevertheless, I am positive that it\nrepresented the day IV Ahau, the beginning of Maya chronology, for 30 may\nstill be identified as 8 Cumhu belonging to IV Ahau, and sign 31 is the\nsame sign as 18, _i.e._, the sign Xul = the end, and denoting here the end\nof the long period.\n\nThe comprehensive hieroglyphs, 29-31, stand here in the wrong place. A more\nsuitable position for them would be before 19 or just after 35. For they\nare intended to specify the periods during which Venus is in the west and\nsouth, _i.e._, the time during which it is the evening star and the period\nof its inferior conjunction.\n\nSign 32 is the black deity, L according to Schellhas, here denoting the\nwest, and 33 is the Venus sign with the prefix denoting division. In the\nsame way we find these two signs together on page 46 at the right in the\nmiddle series, where presumably the four Venus periods are specified in\nclose succession. The black deity is also found on page 50 in the middle of\nthe page in the beginning, at the end of a period of 250 days. On page 24\nit has as a prefix the sign Imix with three rows of dots proceeding from\nit. Imix, however, among the Mayas and Aztecs (as Cipactli), under some\ncircumstances often, and under others always, denotes the first of the 20\ndays. Hence this sign may mean:--here begins the Venus period of 250 days.\n\n34-35. The sign for the south still remains to be found. Sign 35 is again\nthe Venus hieroglyph. In 34 we should expect to find one of the five gods\nof the south, which are found on pages 46-50, _e.g._, the Moan, who is\nrepresented on page 47 as the regent of this cardinal point. But there is\nno figure of a god here, and in place of it we find set down here, as on\npage 47, middle, right-hand, an actual date as the beginning of this short\nsouthern period of only eight days. It is the date 10 Zip (third month),\nthe month sign of which does indeed suggest a hieroglyph of the Moan. Now,\nif we recall that in hieroglyph 21 the god N is designated in exactly the\nsame way by an actual date, viz:--4 Zac (11th month), then we see that the\ninterval between 4 Zac and 10 Zip of the second year following, is exactly\n236 + 90 + 250 = 576 days, and this corresponds exactly to the interval of\ntime from the beginning of the period when Venus is in the east to the\nbeginning of the period when she is in the south. If we knew in what years\nthe morning star made its first appearance on February 4th and disappeared\nas the evening star on the 3d of September, we should make some progress in\nthe comprehension of this subject, but not much, since these events fall\napproximately on the same dates after each period of 8 years.\n\n36-40. The last five of the 40 signs appear in the same order again on\npages 46-50, _one_ sign on each page, in the middle group of the right-hand\nhalf of the page at the beginning of the third line, but with this\ndifference, that on page 24 each sign has the same prefix, which is wanting\non pages 46-50, where a similar hieroglyph always _follows_. From their\nposition on pages 46-50 it follows that these are hieroglyphs of five gods,\neach of whom belongs to a whole Venus year of 584 days. I am not very sure\nin regard to these gods. I prefer to call 36 K, 37 F, 38 E and 40 A. Sign\n39 with the person crouching, I am obliged to leave entirely unsettled. We\nshall find this hieroglyph again, _e.g._, on pages 47 and 49 right, middle.\nLet it suffice that in these five signs we have a repetition of the\nVenus-solar period of 2920 days, with which we will end the discussion of\nthis page. Only F and A have already been met with among the five gods\ndenoted by hieroglyphs 21-25.\n\nPages 25--28.\n\nAs these four pages, which are the beginning of the back of the first part\nof the Manuscript, not only belong together, but also display a parallel\narrangement of their separate parts, the corresponding parts will be\nconsidered together as a whole.\n\nThere are seven of these parts on each page, viz:--the column of day-signs\non the left hand; the top, middle and bottom pictures, and lastly the top,\nmiddle and bottom groups of hieroglyphs; but I will consider the pictures\nand hieroglyphs of the same section as belonging together.\n\n1. The Columns of Day-Signs.\n\nOn the left-hand side of each page two days are repeated 13 times. They are\nas follows:--On page 25 Eb and Ben, on page 26 Caban and Ezanab, on page 27\nIk and Akbal, and on page 28 Manik and Lamat. Cyrus Thomas first made the\nimportant discovery that these pages represent the transition from one year\ninto the next, but held the erroneous opinion that the last two days of\neach of the four kinds of years were treated of on each page. While Seler,\non the other hand, found that we have here to do with the last day of one\nyear and the first of the following year, and that, therefore, Ben, Ezanab,\nAkbal and Lamat are the beginnings of the years and thus of the 20-day\nperiods. The years, however, were always named after their second day\n(_i.e._, Kan, Muluc, Ix and Cauac years), since the New Year's Day was\nconsidered unlucky and it was the practice of the Mayas to conceal the real\nstarting-point.\n\nThese four pages, therefore, extend over 13 \u00d7 52 years, that is, over a\nperiod of 18,980 days, after which period all the calendar dates are\nrepeated. A list of all these dates is given in \"The Maya and Tzental\nCalendars\" by William E. Gates (Cleveland, 1900).\n\nThe transition from the Muluc to the Ix years is represented on page 25;\nfrom the Ix to the Cauac years on page 26; from the Cauac to the Kan years\non page 27, and from the Kan to the Muluc years on page 28. The Ix years\nare represented first, because the beginning of the historical chronology\nlies in an Ix year (IV Ahau; 8 Cumhu). This section treats of ceremonies,\nespecially of the setting up of the idols at the changing of the year,\nwhich I can pass over here since they have already been described by Diego\nde Landa and in our own day by Cyrus Thomas in his \"Study of the Manuscript\nTroano,\" and elsewhere.\n\n2. The Top Pictures.\n\nThe principal representation on all the four pages is a priest, but\ndisguised as an animal with the head of a beast of prey as a mask (always\nthe same one) and also with a tail. He is pictured with the same three\narticles in each of the four representations, viz:--First, in his right\nhand, the staff of office with the hand at the top, which, according to\nSeler, \"Mittel-Amerik. Musikinstrum.,\" p. 112, is the rattle-stick, second\nthe incense-pouch, _i.e._, for copal, and third in his left hand a rattle,\nor, according to Schellhas, \"Vergleichende Studien\" (1880), a fan. There is\none point, however, in which the first two pages differ from the other two;\non the first two the priest is walking on dry land and on the second two\nthrough a stream of water. Was the city, to which this calendar especially\nrefers, bordered in two directions by water, so that the road led across\nit?\n\nOn all the four pages, however, the priest carries on his back a different\ndeity, and I cannot find out by what rule these gods are connected with one\nanother, or with the one which is represented below them, or with the\nyears. On page 25 the god is B, on 26 he has the form of a jaguar (Ix), on\n27 he is undoubtedly E, and on page 28 he is the god A, Cimi.\n\nNow to the left of the priest on each page there is one of the familiar\nChuen bundles, such as are also frequently found in the the\nTro-Cortesianus. Here, on pages 25-28, there are always three of these\nChuen signs in a bunch. If Chuen really denotes the eighth day (which, of\ncourse, is only possible when Kan = 1), and at the same time the period of\n8 days, then in this passage these three Chuen signs would properly\ndesignate the 24 days which elapse _before_ the last day of the year, which\nis the last day of the 18th month. In the same way we shall find the Chuen\nbundle appropriately given this meaning on pages 42c-45c. Likewise the\nsimple Chuen sign at the top of page 52 seems to denote 8 days. But what do\nthe Chuen bundles in the Tro-Cortesianus mean, some of which are much\nlarger?\n\nIn close proximity to these Chuen bundles we find numbers as follows:--on\npage 25 numbers 8 and 9, on 26 number 13, on 27 number 2 and on 28 number\n13. I can offer no opinion, which would be even approximately acceptable in\nregard to the meaning of these numerals, but we shall discuss them later.\n\n3. The Top Hieroglyphs.\n\nI shall discuss these glyphs in this place, although each group seems to\nrelate not merely to the top picture, but to the whole page. There are 16\non each page, and arranged as follows:--\n\n  1  2     9  10\n  3  4    11  12\n  5  6    13  14\n  7  8    15  16.\n\nUnfortunately, the writing at the top is obliterated, which makes it\nimpossible to understand not merely this passage, but also those on all the\nrest of these pages. Of the 16 signs in the top line only one is legible,\nand that is the first on page 28. This is the usual cross _b_; as a\ncomprehensive heading it perhaps occupied places 1 and 9 on each page,\nalternating with another sign in 2 and 10.\n\nIn spite of this obliteration there are a few points which can be\nprofitably discussed here.\n\nI would call attention first to signs 7 and 8 on page 25. The first seems\nto contain twice repeated the figure, which is thought to represent eagle\nfeathers, and which we found on pages 10b and 13a, for example. As this\ndouble character is also used to change the 360-sign into a 7200-sign, so\nit may also combine the 52 years of this passage. The 8th sign on page 25\nis the head with the tuft of hair and no underjaw, which I think refers to\nfast-days, such as might properly occur at the transition point of one long\nperiod to another.\n\nThe sign for the year stands five times on the other three pages, which is\nin keeping with their contents. On page 26 it appears three times. This\npage treats of the transition of the Ix to the Cauac years. In the 6th\nplace the Ix sign seems actually to be used as a prefix, in 7 the prefix is\nplainly the Kin-Cauac sign, just as on page 37a, and in 5 the prefix is\nprobably Ezanab, the beginning-day of the Cauac years. At this last place\nthe suffix is the same as that which we often see with the year sign on\npages 13c-14c. On page 27, in the 7th place, the year sign has a prefix and\na suffix, which seem to indicate that here it was intended to represent 365\nas separated into 5 \u00d7 73 or 360 + 5. Lastly, on page 28 the 8th sign can be\nexplained as meaning that the ritual year of 364 days is separated into 4\nBacab periods of 91 days each.\n\nResembling the year sign in form, and placed near it on these pages, is the\nfollowing sign:--\n\n[Illustration]\n\nThis sign frequently appears on pages 8b-9b, 16b-17b, 17c-20c. We find it\nwith slight variations once on each of the four pages 25-28. It is the 6th\non page 25; the 8th on 26; the 6th on 27; the 6th on 28. Its lower part,\nespecially the (phallic?) sign added at the left, suggests the hieroglyphs\nof the Bacabs, as we find them on pages 52, 55, 56, etc.; they might refer\nto the separation of the ritual year of 364 days into 4 \u00d7 91 days. On the\nother hand it has been considered simply as the reproduction of the\ncarrying-frame pictured below it (compare above under page 17c.)\n\nWhile the hieroglyphs, hitherto discussed, demonstrate the connection\nbetween the parts on the left of the four pages, two other signs prove the\nconnection of the portions on the right.\n\nOne of these looks like the Ik sign surrounded by a dotted circle; it\noccurs on page 25 as the 13th sign, on page 26 as the 15th, on page 27 as\nthe 14th and on page 28 as the 15th. To this sign are prefixed successively\nthe numbers 9, 7, 11 and 6.\n\nThe second is unquestionably the hieroglyph for the numeral 20 or for the\nmoon. It is effaced on page 25 and on pages 27 and 28 has a prefix, which\non page 26 is used as a superfix. This sign is the 14th on page 25, the\n16th on page 26, the 15th on page 27 and the 16th on page 28. The prefixed\nnumbers are 7, 16, 5 and 6.\n\nThe meaning of these two signs and that of the apparently irregular numbers\nis still a mystery. The latter will be discussed presently.\n\nThe 4th sign on all the four pages seems to refer to a period like the one\nhitherto discussed. On page 26 the sign resembles that for the 13th Uinal\n(Mac) and hence appears to refer to the Tonalamatl, as in the first column\non page 24. Above it is the sign for the south. The corresponding\nhieroglyphs of the other pages are obliterated, but strange to say the\nvestiges suggest that they too had _below_ them the sign for the south. Now\nthe south and the Bacab of the south preside over the fourth quarter of the\nyear from which ensues the transition to the new year in question here.\n\nAmong the signs on the left side we should expect to find those of the gods\nto whom the expiring year belonged. On page 25 it ought to be B. Sign 5,\nhowever, though it can with difficulty be identified, points rather to god\nK. Sign 3 on page 26 corresponds better; this is the hieroglyph of the\ntiger already known to us, which is carried by the priest in the upper\nsection of page 8a; here its prefix is the sign for the west. On page 27 we\nought to see the grain-god E carried by the priest; his hieroglyph may be\ndestroyed, but sign 5, which is Kan-Imix (food and drink) is his\ndeterminative. Finally the 5th sign on page 28 is, just as we should\nexpect, the hieroglyph of A and, in addition, we find his determinative in\n7.\n\nBut what is to be said of the fact that the tiger appears again on page 28\nin sign 3, and this time with the sign for the east?\n\nThe Ahau on page 27, sign 16, refers to the god D of the middle section.\n\nThere maybe some reference here to sacrifice, thus:--the 11th sign on page\n25 is Kan-Imix, the 12th on page 27 is Kan, which is followed in the 13th\nsign on page 27 by another one with a Yax and a suggestion of a second\nKan-Imix. Also the curious sign in the 8th place on page 27, which we have\nalready discussed under page 8b, is used to denote the sacrifice on pages\n18a and 15b. Here its position with reference to sign 6 is the same as on\npage 8b. On page 26 the prefix of sign 13, which is half destroyed, may be\nrecognized as a serpent. Signs 12 and 15 on page 25 are unintelligible.\nUnfortunately the following signs are entirely effaced:--Sign 1 on pages\n25, 26 and 27, as well as 2 on all the four pages, 3 on page 25, 9 and 10\non all the four pages, 11 on pages 26, 27 and 28, 12 on pages 26 and 28, 13\non page 28, 14 on pages 26 and 28, and 16 on page 27.\n\n4. The Middle Pictures.\n\nOn each page at the right there is a house, the back wall of which is\nalways marked with the cross often met with. In front of the house with his\nback turned towards it, sits a deity. Each of the four deities has the\nfront of his body covered with a gala mantle. Now we know that the god of\nthe new year was set up before the house of the chieftain. On page 25 the\ngod is K with his eyes apparently destroyed, and on page 26 it is B with a\nKin sign on his head covering, hence designated here as a sun or day-god.\nOn page 27 the god is D, and on page 28, A with the cross-bones on his\nrobe, his own hieroglyph on his cheek, and the Akbal sign on his forehead.\nOnly on the last page, therefore, and apparently by mistake, the god in the\ntop picture is the same as in the middle picture.\n\nAt the left of each page, _i.e._, opposite the house and the god, is a\nflaming altar, bearing the sign Ix equivalent to fire.\n\nThe centre, between the gods and the altars, is occupied by vessels of\nwhich there are two on each of the first three pages and but one on the\nfourth; they contain food, without doubt intended for the sacrificial\nfeast. On page 25 the lower vessel contains Kan (maize) and the upper\nprobably a food prepared from Kan. Or are the spines on the back of the\niguana indicated on this vessel? (Compare 40c and Cort. 8 and 12c). The\ncontents of the lower vessel on page 26 are still unknown (birds?). The\nupper vessel contains a Kan, but the sign has a superfix, which corresponds\nto the sign for the west. On page 27 the lower vessel contains a fish and\nthe upper the sign for the south. Lastly, the single vessel on page 28\ncontains the cross-bones (mammal?) and above them the Kan sign repeated\nthree times.\n\nFinally here on the last three pages, we find some numbers, which are still\nundetermined; on page 26 there is a 7 with the lower vessel, and on page 27\nwith the upper vessel two dots with a cross between them (perhaps this may\nmean 20 - 2 = 18, which is used in place of the usual clumsy numeral?). On\npage 28 we see above the vessel a 6, and below it, in place of a second\nvessel, a double Chuen sign, as in the upper section of the page, therefore\nit can hardly be the Akbal sign resembling Chuen.\n\n5. The Middle Hieroglyphs.\n\nOn each page these signs consist of but _one_ line containing 5, 6, 3 and 3\nglyphs respectively. The first of these signs in all of the four places is\nthe same (_o_), which very suitably refers to the change in the year. The\nsecond sign is always the hieroglyph of the god represented in the middle\nsection:--K on page 25, B as the sun-god on page 26, and D on page 27. The\nsecond sign on page 28, which is the head without an underjaw and with the\nprefixed four, probably referring to four fast-days, must, therefore, be an\nuncommon sign for A, who was similarly designated on page 25 in sign 8 of\nthe upper section.\n\nIf the gods in the top thirds are those of the past year and those in the\nmiddle the gods of the year just beginning, we should expect to find in\neach top third the deity who is represented in the middle of the preceding\npage. But this does not hold good. For then we should expect to find K on\npage 26 and not the tiger, on page 27 B or G and not E, on page 28 D and\nnot A, and on page 25 A and not B.\n\nHence there is some confusion here. Yet it seems to be in the nature of a\ncorrection, that on page 26 the third sign, next to that of the sun-god, is\nactually the sign for E who is in the top section on page 27, and that the\nsixth sign is Kan-Imix belonging to this god.\n\nOn pages 25 and 26 this line also refers to the past year, _i.e._, to the\nyear set down in the top third. The fourth sign on page 25 is a Manik,\n_i.e._, originally a grasping hand denoting taking away, disappearance, and\nthe fifth sign on this page is a Muluc, which seems to denote the ending of\nthe Muluc years. The fifth sign on page 26, is, in fact, the tiger pictured\nabove.\n\nThe lunar hieroglyph as the third sign on page 25 and the _a_ as the fourth\non page 26 are strange and unaccountable. Both appear to be almost without\nsignificance here and seem almost like mere points between the names of\ngods in groups of two each.\n\nThe Ahau as the third sign on page 27 is the usual determinative of D,\nwhose hieroglyph stands beside it.\n\nOn page 28 the main part of the third sign corresponds to the sixth of the\nupper section. I do not know, however, how to explain either the upper part\nsuggesting a mat or the familiar leaf-shaped prefix.\n\n6. The Bottom Pictures.\n\nIn the left-hand lower corner of each page we see the sign for the year of\n360 days, which at the same time designates the heap of stones, on which\nthe stelae were erected, the two thick black lines indicating the two\ncolumns of hieroglyphs usually found on them. A tree is growing out of this\nsign, having on its trunk an abbreviated Cauac sign, at least, on pages 26,\n27 and 28, which probably refers to rain as the most desired event of the\nyear. The tree on page 25 has no leaves, but the top is carved into the\nshape of the head of the god B. In the other three cases it has leaves, but\ninstead of ending in the god's head the tree is draped with a mantle and a\nbreech-clout, and a serpent is coiled about it denoting a period of time\n(here, the year). Furthermore there are foot-prints on the trunk or the\ndrapery of the tree, which represent it as the goal of a pilgrimage.\n\nIf the top and middle thirds refer to the mere transportation of the idols,\nthe bottom thirds refer to the feasts connected with this act, or, at any\nrate, to those dedicated to the _new_ god. For we see here on page 25 the\ngod B, on 26 the god K, on 27 A and on 28 D, _i.e._, the same deities as in\nthe middle sections, yet so placed that the first two and the last two have\nchanged places.\n\nEach of the four deities hold in one hand a hen with its head cut off;\n\"degollavan una gallina\" is the statement made by Landa concerning these\nfeasts. Perhaps all four gods, at any rate the last three, are scattering\ngrain; this was one form of divination; we found the other on page 2. There\nare besides, on every page, several small objects between the two pictures,\njust as in the middle section. On page 25 the object is probably an altar,\nbut instead of the flame it has the number 19. Above this is the sign for\nthe west (the Ix days) with that for the sun, and on top of them the sign\nwhich we found in the middle section of page 26 as the contents of the\nlower vessel. On page 26 we see a vessel containing a bird, then another\nwhose contents are indicated by Yax and a double Kan sign. Above it is the\nsign for the moon or for 20 with a prefix, and above this a 9. At the\nbottom of page 27 there is a vessel containing two Kan signs and a fish;\nabove this another vessel the contents of which are the same as we found in\nthe vessel in the middle section of page 26 and in that of the lower\nsection of page 25. Above these is again the sign for the moon or 20 with a\nsuperfix, which is the same as the prefix on page 26, and beside it is a\n16. Page 28 has the usual haunch of venison (Landa:--\"una pierna de\nvenado\"), above this is a vessel with a bird and Kan and above this again\nthe sign for the moon or for 20 with the same superfix and the numeral 15.\nI shall discuss below the numbers scattered over these four pages.\n\n7. The Bottom Hieroglyphs.\n\nThese hieroglyphs also form but _one_ line on each page and each line\ncontains six hieroglyphs. The _first_ of each line is always the same\n(_p_). It consists of a surface divided into four quadrants thus suggesting\nthe four cardinal points, the four Bacabs presiding over them and the four\nkinds of years. The superfix seems to be the abbreviated hieroglyph of the\nnorth; the sign for the north, however, is Muluc and these four pages begin\nwith the Muluc years.\n\nThe _second_ sign is the head of D as the supreme god; to this a Yax is\njoined on pages 26-28 as the symbol of strength, and on page 25, but\nprobably by mistake, the abbreviated sign for the west.\n\nThe _third_ sign always represents one of the four cardinal points:--on\npage 25 the east, on page 26 the south, on page 27 the west and on page 28\nthe north; here then the usual order is reversed and the signs are set down\naccording to the diurnal instead of the annual course of the sun, probably\noccasioned merely by exchanging the sign for the west (Ix), which belongs\non page 25, with that for the east (Kan), which belongs on page 27.\n\nThe other three signs do not stand in the same order on every page.\n\nThe _fifth_ sign on pages 26 and 28 and the _fourth_ on page 27 show\ncorrespondence most clearly. This sign is always a head, undoubtedly that\nof the god pictured in the bottom third. But on page 25 it is the\nhieroglyph of E, who is pictured on the top of page 27, instead of that of\nB.\n\nIn the same way the 6th sign on page 25, the 4th on page 26, the 5th on\npage 27 and the 4th on page 28 have something in common. One element of the\nhieroglyph is always the sign for the year of 360 days, combined on page 25\nwith cross-bones and the Cauac sign, on 26 with Yax and Kan, and on 27 and\n28 simply with Yax.\n\nThe most puzzling and divergent of these hieroglyphs are the remaining\nones. The 4th on page 25 has an oblique cross (or bones?) and the\nabbreviated glyph for the west, the 6th on page 26 is the head of E, the\n6th on page 27 is the 360-day sign combined with Kin and Cauac, and the 6th\non page 28 is the usual Kan-Imix sign. Here, too, there seems to have been\na displacement.\n\nBefore I leave the four pages 25-28, I will glance at the numerals, which\nare scattered over them and which apparently have no connection with one\nanother. I have discussed these numerals in my article \"Die\nMayahieroglyphen\" in Volume LXXI, No. 5, of the Globus, and the following\nis borrowed therefrom.\n\nFirst of all, I believe that I proved there, that the sign composed of two\ndots with a cross between them is an abbreviation for the usual clumsy\nrepresentation of the numeral 18 and designates it like a duodeviginti by\n20 - 2. Next, that in this passage as on pages 18a, 18c, 19c, 46b and 50c,\nthe sign is combined with the hieroglyphs Yax-Kin. Third, that it is\nclosely related to the god D, inasmuch as it stands on page 27b close\nbeside the picture of that god.\n\nAssuming this as a known fact, we find scattered over these four pages the\nfollowing numbers:--\n\n  25:    9,    7,    8,    9,   19,\n  26:    7,   16,   13,    7,    9,\n  27:   11,    5,    2,   18,   16,\n  28:    6,    6,   13,    6,   15.\n\nIt is very remarkable that the sum of the numbers on each of the first\nthree pages is equal to 52, and as an accidental freak it would be most\nsurprising; somewhere on the fourth page six units may have been omitted;\nbut perhaps the 6, which stands above the _two_ Chuen signs in the centre,\nis to be counted twice. The 52, however, designates the very 52 years,\nwhich are treated of on these four pages.\n\nAs yet I know no reason to account for the fact that the 52 is here\nseparated into these apparently very irregular numbers. The discovery of\nthis reason would be an important step in advance. Or does it means 52\n_days_, perhaps those which follow a Tonalamatl coming in the middle of the\nyear?\n\nPage 28 is followed in the Manuscript by three empty pages. The scribe's\nobject in reserving them is beyond our ken; possibly they were intended to\nrepresent the period of 8 years.\n\nPages 29-45 (_i.e._, to the end of the first part of the Manuscript) all\nbelong together. After the Maya manner there is very little system\ndisplayed in their arrangement, and though here and there there may be\noccasion to consider the three parts of each page consecutively, I will\ndiscuss them here as follows:--First, the top thirds, which are most\ndifficult owing to the destruction of a large portion of them; then the\nmiddle, and last the bottom thirds. They all consist in great part, with a\nfew interruptions, of representations of the regular Tonalamatl, such as we\nfind represented from the beginning of the Manuscript to page 23.\n\nThe element which these pages have in common is the fact that the god B,\nwho can hardly be Kukulcan or Quetzalcoatl, occurs on almost all of them.\nHe is the god of wind, fire, breath, _i.e._, the true god of life and is\nhere represented in his relation to the most varied manifestations and\nactivities of a human being, so that this section bears a certain\nresemblance to the Tro-Cortesianus. With this is closely connected his\nrelation to all four cardinal points, which so often occur. He may have\nbeen the local god of the region from whence this Manuscript came; in the\nTro-Cort. It seems rather to be C who lays claim to this office.\n\nPages 29a--30a.\n\n  XI  13  XI  13  XI  13  XI  13  XI  13  XI\n  Lamat\n  Ben\n  Ezanab\n  Akbal.\n\nThis is a Tonalamatl of 4 \u00d7 65 days, each part subdivided into 5 \u00d7 13 days.\nThe four days written on the left are those which may begin the year.\n\nIn each of the five sections B is pictured in a sitting posture, the first\nfour times on a tree (the tree of life rather than the sacrificial tree).\n\nIn the first picture he holds in one hand the haunch of venison, so often\noccurring as an offering, the last time on page 28; the object above it is\nprobably the Kan sign. There is a vessel at the god's feet, probably a\nreceptacle for the venison, bearing the hieroglyph of the 13th day Cib,\nwhich, however, refers rather to a bird.\n\nIn the second picture an animal with a protruding tongue lies on its back\nat the feet of the god, who kneels upon its stomach. This probably\nrepresents the lightning-dog as vanquished. The same animal is pictured on\nthe next page and also on page 40b and perhaps on page 60. There are a\nnumber of small dots around B's head, which on page 11c we attempted to\ninterpret as the starry sky.\n\nI can find nothing of special importance in the third and fourth pictures,\nbut in the fifth, B is sitting in a house, which is marked repeatedly with\nthe sign Caban (ground). Here the god is holding the hatchet (machete) in\nhis hand, as if prepared for some terrestrial activity. Four hieroglyphs in\nthe usual order belong to each of the five pictures. They are almost\nentirely destroyed, but the vestiges show that the fourth sign was always\nthat of B, while the third sign with the first picture had the abbreviated\nhieroglyph of the west as a prefix; with the second picture it had that of\nthe south, and therefore with the third and fourth it must certainly have\nhad the signs of the east and north. We should expect the signs with these\nprefixes to contain references to Ix, Cauac, Kan and Muluc, but they are\nnot distinguishable.\n\nThus B is represented in pictures 1-4 as ruler of the four cardinal points\nand in 5 as the ruler of the earth in general.\n\nPages 30a--31a.\n\nThis passage looks like an amplification of the middle picture on page 29a.\nHere B is represented with the hatchet in his left hand and holding aloft\nby the tail with his right hand the animal, which is spitting out something\nupon a stepped pyramidal structure, probably the pyramid of a teocalli.\nThat this is probably meant to represent lightning is rendered almost a\ncertainty by the picture on page 40b. In this passage there are several red\nand black numerals scattered around the animal in an irregular manner,\nwhich we find nowhere else in our Manuscript, but with which the\nTro-Cortesianus has made us familiar. The sum of the black numbers still\nlegible is 23, probably a 3 is effaced and the sum should be 26, the sum\nwhich so often occurs in the Cod. Troano 8-13 with the animal represented\nthere. The red numbers likewise do not admit of exact determination. This\npassage also contained hieroglyphs, four standing side by side on each of\nthe two pages. The legible portion is limited to the Cimi sign in the third\nplace, perhaps an Imix in the second, and possibly an Ahau in the first.\n\nPages 31a--32a.\n\nIn my article \"Zur Entzifferung, etc., VI,\" published in the year 1897, I\ndiscussed this passage more in detail, and the following will be in\ncontinuation of what I stated there.\n\nThe real aim of the computation on these pages is to find a number in which\nthe following periods of time are united with the Tonalamatl of 260\ndays:--1. The ritual year of 364 days, and consequently also a quarter of\nit, the Bacab period of 91 days. 2. The period of 104 days, being the\nnumber of days which remain after a Tonalamatl has been deducted from a\nritual year. The hypothesis advanced by Mrs. Zelia Nuttall (\"Note on the\nAncient Mexican Calendar System,\" Stockholm, 1894) and also the entirely\ndifferent opinion held by Mr. Charles P. Bowditch (\"The Lords of the Night\nand the Tonalamatl of the Codex Borbonicus\" in the American Anthropologist,\nN. S., Vol. II, New York, 1900) prove the existence not only of merely\narbitrary Tonalamatls for the purpose of prediction, as those in our\nManuscript, but also of Tonalamatls having a fixed position in certain\nyears. But after the manner peculiar to priestcraft, the number sought is\nfound only by an indirect and mysterious process.\n\nIn the first place we find on page 32a all the days set down in the\nfollowing manner:--\n\n  XIII      XIII      XIII         XIII\n  Manik     Cib       Chicchan     Ix\n  Chuen     Ahau      Muluc        Ezanab\n  Men       Kan       Ben          Ik\n  Cauac     Lamat     Caban        Cimi\n  Akbal     Eb        Imix         Oc.\n\nThat is to say, a series counting from the day XIII Akbal, the New Year's\nday of the year I Kan, recurring every 52 years, furthermore a series which\nshows the same difference of 91 from the day XIII Akbal to XIII Ix, XIII\nChicchan, etc., and finally ends with XIII Akbal again, after it has run\nthrough a period of 20 \u00d7 91, _i.e._, 1820 days = 7 Tonalamatls, like a\nsimilar representation of 7 Tonalamatls on page 51. Above these 20 days,\nand to the left of them, numbers are set down rather irregularly, which\nbegin with 91 and are multiples of that number. The signs of the days\ncorresponding to these numbers are joined to them; but they are omitted\nwith the numbers of lowest value. Hence we have:--91, 182, 273, 364 (4),\n455 (5), 546 (6), 637 (7), 728 (8), 819 (9), 910 (10). Then with a bound\nfollow 1456 and 1820; with the last number Akbal is reached in the natural\nway, which day the scribe had erroneously set down again with 1456 in place\nof Cauac.\n\nThe number 728 already united the numbers 91, 104 and 364, but did not\ninclude the number 260. This inclusion is accomplished by the number 3640\non page 32, quite on the left where we find the numbers 10 and 2, under\nwhich only a 0 has been omitted. With the usual hiatuses this series seems\nto end on page 31, where I think the numbers 4, 0, 16 and 0 ought to stand,\nbut they are almost wholly effaced; this would then be 320 \u00d7 91, 280 \u00d7 104,\n112 \u00d7 260, 80 \u00d7 364 = 29,120.\n\nWe have thus gone far in advance of the first problem, but a second always\npresents itself in these series, it is that of using these periods for\nlarger numbers, which refer to a not too remote past or to a future not too\ndistant. The first numbers are, as a rule, in the neighborhood of\n1,252,680, the close of the eleventh Ahau-Katun, and the latter in the\nneighborhood of 1,480,440, the close of the thirteenth Ahau-Katun. The\nManuscript presents the following:--\n\n   1,272,544      1,268,540     1,538,342.\n  XIII Akbal     XIII Akbal     XIII Akbal\n     121             17          51,419\n   IV Ahau        IV Ahau\n   8 Cumhu        8 Cumhu        IV Ahau.\n\nIn connection with this it should be noted first that I have restored the 8\nin the statement of the months, and second that the two numbers on the\nright were found with the aid of page 63 only by an easy conjecture. For\nwith the reading of the Manuscript 10, 13, 3, 13, 2, I do not agree, but\nread instead 10, 13, 13, 3, 2; the number below, however, is given in the\nManuscript as 7, 2 and then a black 14 joined to a red 5; I read this 7, 2,\n14, 19.\n\nThe three numbers nearest the bottom have red circles around them,\nindicating subtraction, or, according to my present point of view,\naddition.\n\nNow let us see how the computer arrived at the large numbers.\n\nDay XIII Akbal, the New Year's day of the 1 Kan years, is given; also the\ndifferences of the series 91 and 104, therefore also in the proportion of 7\nto 8. If we combine these last two numbers by addition and then by\nmultiplication with 260, the result is (7 + 8) \u00d7 260 = 3900. If, however,\n7, 8 and 3900 be combined by multiplication the product is 7 \u00d7 8 \u00d7 3900 =\n218,400 = 2400 \u00d7 91 = 2100 \u00d7 104 = 840 \u00d7 260 = 600 \u00d7 364 = 1120 \u00d7 (91 +\n104). We have already met with the 218,400 on page 24, which was obtained\nby the addition of 33,280 + 185,120.\n\nMy opinion is as follows:--First 11 Ahau-Katuns = 1,252,680, were taken as\na point of departure, and to this sum was added 15,600 = 4 \u00d7 3900, and 243\nas the interval between the normal date IV Ahau and XIII Akbal. The result\nwas 1,268,523. The position of this day, however, is XIII Akbal 11 Xul (1\nIx).\n\nThen the 3900 mentioned above was added to this number and the result was\n1,272,423 = XIII Akbal 16 Pop (12 Muluc).\n\nThen to the 1,268,523 was added the 218,400 and the sum was 1,486,923 =\nXIII Akbal 1 Kankin (1 Kan), the very place in that year where a Tonalamatl\nends.\n\nThe following numbers were thus obtained:--\n\n  1,272,423     1,268,523     1,486,923.\n\nThese numbers are suppressed in the Manuscript. But if the encircled\nnumbers are added to them, viz:--121 (interval between XIII Akbal and IV\nKan), 17 (interval between XIII Akbal and IV Ahau), and 51,419 (= 197 \u00d7 260\n+ 199; 199, however, is the interval between XIII Akbal and IV Ik), the\nresult is the three large numbers set down in the Manuscript, which have\nthe following properties:--\n\n1) 1,272,544 = IV Kan 17 Xul (12 Muluc). This number = 13,984 \u00d7 91 = 12,236\n\u00d7 104 = 3496 \u00d7 364. It also = 4894 \u00d7 260 + 104, the interval between IV\nAhau and IV Kan.\n\n2) 1,268,540 = IV Ahau 8 Mol (1 Ix) = 4879 \u00d7 260 = 3485 \u00d7 364 = 74,620 \u00d7\n17. 17 is the interval between XIII Akbal and IV Ahau.\n\n3) 1,538,342 = IV Ik 15 Zac (12 Muluc). It also = 5916 \u00d7 260 + 182. The\n182, however, the half of the ritual year of 364 days, is the interval\nbetween IV Ahau and IV Ik and between IV Ik and IV Kan. The fact that the\ninterval is the same in each case is clearly the reason for the choice of\nthe days IV Kan and IV Ik, which are otherwise not at all prominent.\n\nIt is remarkable that the third number is obtained by the addition of\n51,419, _i.e._, of 197 \u00d7 260 + 199 (there are 199 days between XIII Akbal\nand IV Ik). But it was evidently desirable to obtain as large a number as\nthis. On page 63 a number of nearly similar value is associated with it,\nviz:--1,535,004. It is set down almost in the middle between the 13th and\n14th Ahau-Katuns, for it is 57,902 days greater than 1,480,440, and 55,978\ndays less than 1,594,320.\n\nNow, however, the Manuscript presents in the last column but one of page 31\na number, 2,804,100, which occupies a very unique position, since it is\nnearly twice as great as all the other large numbers, with the exception of\nthose in the serpents. It must refer to the year 9 Muluc, and to the date\nIV Ahau 13 Mol. It has many remarkable properties, for it is:--\n\n1) = 10,785 \u00d7 260\n\n2) = 17,975 \u00d7 156 (156 = IV Kan - IV Ahau).\n\n3) = 35,950 \u00d7 78 (78 = IV Ik - IV Ahau and IV Kan - IV Ik).\n\n4) = 719 \u00d7 3900. We have already met with this 3900 above. Now, however,\nthe 2,804,100 by virtue of its magnitude creates the suspicion that it may\nbe composed of two ordinary large numbers. It might be\n\n5) 1,308,580 + 1,495,520, therefore 14,380 (91 + 104).\n\n6) 1,380,600 + 1,423,500, therefore 3,900 (354 + 365).\n\nThat is to say, the important 3900 multiplied by the days of the lunar year\nand also by those of the solar year, hence the 719, referred to under 4,\nseparates into these two parts. The lunar year of 354 = 6 \u00d7 29 + 6 \u00d7 30\ndays was not unknown to the Mayas. We shall find its half, 177 days,\nseveral times on pages 51-58.\n\nWe might also use the two important numbers 14,040 and 18,980, the first of\nwhich is divisible by 260 and 360, and the second by 260 and 365, without\nremainder.\n\nThen we have the large number desired:--\n\n7) 147 \u00d7 18,980 + 14,040.\n\n8) 200 \u00d7 14,040 - 3900.\n\nWhat future student will penetrate more deeply into the meaning and purpose\nof these numbers?\n\nWe might now expect to interpret also the upper right-hand corner of page\n31, but here almost everything is in a deplorable state of obliteration. In\nthe first three of the five columns over each of the three large numbers\nthere was a date consisting of a numeral and a hieroglyph, but these admit\nof no certain nor even probable determination.\n\nFour hieroglyphs still remain in the fourth column, respecting which\ncompare my treatise \"Zur Maya-Chronologie\" in the Berliner Zeitschrift f\u00fcr\nEthnologie XXIII, pp. 141-155.\n\nIn the top sign I recognize an Imix with a prefix and probably also a\nsuperfix. I think this denotes the period of 18,980 days.\n\nI am forced to pass over the second entirely, inasmuch as a red 6 inserted\nin it remains a mystery (6 \u00d7 18,980 = 113,880?).\n\nAs I stated in the above-named work, I think the third is three times the\nsacred period of 2920, _i.e._, 8760 days.\n\nFinally, the fourth sign certainly denotes the period of 7200 days.\n\nWhether or not there was a fifth sign above the one now at the top is as\nuncertain as the meaning of the whole.\n\nThe most remarkable thing about it is that in three other passages of this\nManuscript these three signs appear in close proximity to another. On page\n61 we find the third in the 11th place in the second column, the first in\nthe 12th place in the same column, and the fourth in the 14th place in the\nfirst column. Page 70 has the first sign in the middle of the 4th column;\nthe second somewhat lower down in the 3d column and the 4th two places\nbelow. Finally all three signs appear in succession on the top of page 73\nin the same order as on page 31.\n\nThe fifth column on page 31 may have contained another numeral belonging to\nthe series, the loss of which is not so serious a matter, but there may\nhave been one or two hieroglyphs above it, the obliteration of which is\ngreatly to be deplored.\n\nPages 32a--39a.\n\nThis is a large section extending over eight pages, which is difficult of\ninterpretation owing to the prevailing disorder and because a large part of\nthe hieroglyphs are effaced. Here, too, the principal subject is the god B,\nwho is represented in manifold activity. A series of numbers extends\nthrough the entire representation. I read them as follows:--\n\n  I 11 XII 28 I 12 XIII 26 XIII 12 XII 19 V 5 X 1 XI 20 V 12 IV 6 X 8 V 5 X\n      7 IV 12 III 5 VIII 8 III 11 I.\n\nThere are thus 18 divisions, the different lengths of which reveal no rule.\nThey embrace 208 days, _i.e._, 2 \u00d7 104, which may well be considered as a\ncontinuation of the computation in the preceding section, of which the 104\nwas so important a number. The red numbers are entirely lacking in the\nbeginning, then they are very slightly indicated, and finally they are\ndistinctly written out on pages 36-39. I assume that the scribe has set\ndown the 4th, 3d and 2nd numbers from the end, one too little. The last\nnumber has been entirely omitted. I have supplied these omissions though in\na manner somewhat different from that adopted by Cyrus Thomas, \"Aids,\" p.\n28. I would note in addition that a period such as this, consisting of 208\ndays = 16 weeks, might be explained in an entirely different way, if there\nwere a column of five days at the left having a difference of 8 days; then\nthe whole would signify four Tonalamatls. But there is no such series of\ndays.\n\nAnother point of view presents itself, however. If we take cognizance of\nthe fact that a group of four hieroglyphs usually belongs to a picture,\nthen it is evident that here there are such groups not for 18, but for\nabout 22 subdivisions. It may, therefore, be assumed that about four\nsubdivisions averaging 13 days are not specified, in which case this\npassage would extend not over 208, but over 260 days. The very irregularity\nin the arrangement of these numbers is an argument in favor of this\nhypothesis; it may be occasioned by the fact, that the pictures do not\ncorrespond exactly to the subdivisions. For the present, however, we shall\ndiscuss the single pictures assuming that there are 18 subdivisions.\n\n1. Pages 32a-33a. Here at the very beginning it is uncertain whether the\nsigns at the end of page 32 and at the beginning of page 33 are to be\nregarded as a single group of 8 hieroglyphs, as seems to follow from the\nnumbers, or as two groups of 4 hieroglyphs each. At the end of page 32 we\nsee two persons facing one another, one of whom, to be sure, is barely\nvisible. The other wears a head-covering like a man's silk hat, similar to\nthat worn by the priests on the inscriptions of Palenque. It is a\nremarkable fact that of the four hieroglyphs above these figures, 1, 2 and\n4 (the last probably the god C) seem to have the sign for the west as a\nprefix, while the prefix of 3 (Imix) suggests the usual representation of\nthe tortoise head. Below the persons there is a Kan sign, the prefix of\nwhich is also the sign for the west.\n\nOn page 33, B is represented walking and carrying the Caban sign in his\nhand. The first of the four hieroglyphs is the sign for B, the second is\nImix, probably again with the sign for the west as a prefix, the third is\nan Akbal sign with Kin, and the fourth is the cross-hatched sign with Kan.\n\n2. The rest of 33a is occupied by two persons, one of whom is clad in a\ngala mantle, but neither admit of further identification. They are occupied\nin fishing, inasmuch as they are sitting on the shore of a body of water\nand are either casting a net or drawing it in. There is a fish between them\nand above it is a vessel with something apparently cooking in it. Of the 8\nhieroglyphs belonging to this picture, only the following are\ndistinguishable:--the 1st containing an Akbal, the 3d, which is the common\ncross _b_ with a 9, the 4th, an Imix also with 9, and of the 7th only the\nprefix Yax. The 3d and 4th appear again on page 35a, 28 days later.\n\n3. Page 34, like page 3, represents a human sacrifice. The victim, very\nvaguely drawn, lies on a step-shaped sacrificial stone, or on the pyramid\nof a teocalli. There is a Caban (earth) sign between the sacrifice and the\npyramid, and also on the walls of the buildings; the shrieking of the\nvictim is plainly indicated. As on page 3, there are four persons in the\nform of gods surrounding the sacrifice, but here they are different ones.\nThe one at the left above is the black god (L?), holding the rattle-stick\n(Seler, \"Mittelamer. Musikinstrumente,\" p. 111), and at the right, above,\nF, the companion of the death-god, is sitting with a rattle in his hand.\nBelow, the two have changed places, F is on the left and L on the right.\nThe former is beating the drum and the latter blowing a wind-instrument.\nThe sounds emitted by the two instruments are represented by drawings. This\nmay, therefore, be regarded as an instrumental quartette. The following\nobjects are also in this picture:--at the left above is a vessel the\ncontents of which are cooking; at the left below, another vessel with three\nKan signs, and at the right above, a Kan sign with a bird's head and below\nthe food known to us from pages 27b and 29b. These four objects refer to\nthe sacrificial feast. Lastly, at the bottom on the right there is a\nladder, probably intended for scaling the pyramid. Ten hieroglyphs in the\nupper line belong to this picture:--the first, which is effaced, is\nfollowed by a Cauac, then comes the cross _b_, then a Cimi appropriate to\nthe sacrifice, and lastly a head with an Akbal eye, probably D's. The first\nsign in the lower row is likewise destroyed, the second sign is a Kan, the\nnext is the cross _b_, both having a different prefix, then here too is the\nhieroglyph of B with Yax as a prefix, and the last is an unknown sign.\n\n4 and 5. Page 35a. According to the numbers there are two sections here,\nbut neither the pictures nor the hieroglyphs can with certainty be assigned\nto either. On the left is a house in which C sits holding a Kan sign in his\nhand; on the roof, as if guarding him, and also holding a Kan sign, lies\nthe god B. In the Cort. 24b-25b, there are six gods lying on houses, within\nwhich other gods are also represented in a recumbent position. Then follow\ntwo vessels, again denoting the sacrificial feast, the contents of which\nare probably cooking, and which, from the sign on the second, are probably\nliquid. Above these are three others, one with the Cimi sign (human\nflesh?), one with a bird and the third with the haunch of venison. At the\nright of these is an implement, which is unfamiliar to me and is similar to\nthat held in the god's hand on pages 5c and 6c. And quite on the right sits\nB with foot-prints pictured below him and on his clothing.\n\nThe hieroglyphs on page 35, when they were all legible, numbered 14 and\nwere arranged in two rows. 4 of the upper row are preserved, the lower part\nof the first is a year-sign (?), similar to that which often appears on\npages 25-28, the upper element is the cross, and the prefix is the one\nresembling a leaf, which occurs so frequently. The second sign is an Imix\nwith a prefixed 9, the third a cross and the fourth a head (probably D's)\nwith Akbal. In the second row there is a cross with a prefixed 9 (sign of\nthe second or third month?). These two signs with the prefixed 9 are\nperhaps to be read as a calendar date IX Imix 9 Zip (1 Ix), as on page 33a.\nIx, however, belongs to the west, which is the predominant cardinal point\nfrom 32a onward. The second sign is a compound of Kin and Akbal (day and\nnight) which often occurs here, the third is the compound of the Moan and\nCaban signs with the number 1 above each, and the fourth is the hieroglyph\nof B. The fifth sign is unfamiliar to me. The sixth contains an Imix with\nthe sign for the west as a prefix, and the seventh is effaced.\n\nAt this point the representations begin to display a more orderly\narrangement.\n\n6. Page 36a. Here the head of B forms the head of a serpent (cf. pages 61\nand 62) represented in pouring rain, while on page 35b it is emerging from\nthe water. Of the four hieroglyphs 1 and 2 are entirely and 3 for the most\npart destroyed, and 4 is the usual Kan-Imix.\n\n7. The lightning-beast with flames pouring forth from his forepaws and\ntail, is plunging down from the rectangle, which primarily designates stars\nand then the sky in general. This rectangle occurs for the first time here,\nbut will often be met with later. Here it may be a combination of Mars and\nVenus. Of the four hieroglyphs, 1 is effaced, 2 is a compound of Kan and\nKin, 3 a head with Akbal and Kin (D?) with the uplifted arm as a prefix,\nand 4, corresponding with the picture, is the compound of the rain sign\nCauac with the prefix of the storm-god K.\n\n8. Here B himself is the bringer of lightning. In one hand he holds a\nburning torch and flames are bursting from his carrying-frame. The third\nhieroglyph is his sign. It is doubtful whether the fourth is the hatchet\n(machete) or is not rather intended for an ear pierced for the purpose of\nritual blood-letting, as on pages 44b and 45b; the first and second signs\nare rather indistinct.\n\n9. Page 37a. Unless I am entirely mistaken, B is here represented with his\narms bound behind his back. Cf. the pictures on page 2, top, and 60,\nbottom. Are the ends of the rope fluttering in front of the god intended to\nrender this still more plain? Hieroglyph 1 contains the sign _t_, which\nresembles, but is not the same as, the year sign. This sign has already\noccurred frequently, especially on pages 25a-28a, and the last time on page\n35 in the first hieroglyph. As on page 35, hieroglyph 4 is the compound\nKin-Cauac, but here it is joined to the year-sign, _i.e._, it denotes the\nKin-Cauac year, just as it does on page 26a. 3 is again Cauac and 2 is the\nhieroglyph for B.\n\n10. Rain is falling from the heavenly shield, already seen on page 36, here\nhowever designating different planets (Mars and Mercury?) and the figure\nrepresented in the rain is the one which we have already seen on pages 12c,\n17a and 21c. It is that of the old Uayeyab god N with a hatchet in one hand\nand an unfamiliar object in the other like the one on page 39a, and with\nanother unknown object on his back shaped like a shield marked with a Kin.\nThat this figure is really meant to represent N follows from the fourth\nhieroglyph (which, however, is not his regular sign 5 Zac), which is\nrepeated on the head of the figure. The lower part of the hieroglyph is\nreplaced by the year-sign just as it is in the hieroglyph on page 47, left,\nmiddle. The third hieroglyph contains 2 Caban signs, the first and second\ncannot be clearly identified.\n\n11. This is a deity which I hardly think appears elsewhere. It has an\nanimal's head resembling that of a bear, thus recalling page 7a, and it\nalso has the paws of a bear. Of the hieroglyphs only a Kin-Akbal is\nrecognizable.\n\n12. Page 38a. Here we have another heavenly shield (Mars and Venus?) and\nunder this shield B is represented seated and strangely enough facing\nhimself, the figures not being back to back as on page 68a. Hieroglyphs 1\nto 3 are wholly and 4, which is a head, is for the most part destroyed.\n\n13. B is here represented in very close connection with a female figure.\nCf. pages 21c-23c. The representation on page 68b is a still closer\nparallel to this passage. The first hieroglyph is destroyed for the most\npart, the second is B, the third is probably only a determinative of the\nlatter, but has the sign for the west, and the fourth is Kan-Imix.\n\n14. B holding a Kan sign is sitting on an object, which may be meant for\nthe stone on which the idols were set up at the change of the year. Of the\nhieroglyphs the third is again B, and the fourth is probably the frequent\nsign a. The first sign is the most remarkable. In the Zeitschrift f\u00fcr\nEthnologie, Vol. XXIII, p. 147, I stated that this was the sign for the\nchange of the year, which is its meaning on pages 41b, 52b and 68a. The Kan\nyear follows here after the Cauac year of page 37. The prefix of the sign\nis the hieroglyph for the east to which the Kan years belong. The Kan sign\nin B's hand also corresponds to this. The second hieroglyph is destroyed.\n\n15. Page 39. The picture represents the lightning-beast with two flaming\ntorches walking under the heavenly shield (Mercury and Jupiter?). Of the\nhieroglyphs the third belongs to B, the fourth has as a prefix the sign of\nthe storm-god K, but otherwise admits as little of determination as do the\nfirst and second.\n\n16. Here we see B in the rain holding in one hand a machete, and in the\nother a strange implement similar to that on page 37a. Of the hieroglyphs\nthe second was the god's sign, the third is _a_, and the fourth may be an\nAkbal sign with Kin. The first sign somewhat suggests the sign for the\nMoan; its prefix is curious.\n\n17. Here in place of the picture and the superscription, owing perhaps to\nlack of space and in order not to omit the last picture, we have a vertical\nrow of seven hieroglyphs interrupted between the sixth and seventh by the\nred and black numeral belonging here. The top sign is effaced and the\nsecond is B's. I will not venture to determine the third, which contains a\nYax. Could it belong to the serpent deity H? The fourth is probably\nKan-Imix and the fifth is indistinct. And the same is true of the sixth,\nthe prefix of which we have already met with as the sixteenth hieroglyph on\npage 24, and shall meet with again on pages 53, 56, 58, 61, etc. The\nseventh sign, which is quite at the bottom, consists of a vessel with a\nfoot-print beneath it; it seems to be in the place of the picture.\n\n18. The entire section ends with a picture of B, who carries the hatchet\nand probably the copal pouch. The hieroglyphs are wholly obliterated.\n\nPages 40a--41a.\n\nThe following Tonalamatl, one of the form of 10 \u00d7 26, has suffered much\nfrom the carelessness of the scribe and from injury. I have attempted to\nrestore it as follows:--\n\n  X         X  7  IV  4  VIII  4  XII  2  I  1  II  8  X\n  Ahau      Oc\n  Cimi      Cib\n  Eb        Ik\n  Ezanab    Lamat\n  Kan       Ix.\n\nThe first row should be read from top to bottom, and then the second in the\nsame order.\n\nThe six subdivisions all refer to some activity of B. Among the 6 \u00d7 4\nhieroglyphs his sign occurs five times as the fourth and only in the last\ngroup as the third. Let us now examine the six groups individually.\n\n1. B is traversing the water in a canoe, as on pages 29c and 40c, with the\npaddle in his hand. All the hieroglyphs belonging to him are obliterated.\n\n2. B is sitting on the laterally elongated head _q_, which here, as on page\n69, is enlarged and drawn with special care. Seler (\"Charakter der\naztekischen, etc. Handschrift\" in the Zeitschrift f\u00fcr Ethnologie, 1888, p.\n83) discusses this sign in connection with the day Men. It seems to me to\ndenote unlucky days, the influence of which may here be checked by B. B\nholds in his hand a hatchet. The head (_q_) is repeated in the third sign,\nperhaps also in the second, and the superfix of these two signs is probably\nthe same as that of the sign beneath the picture of B. The first sign is\nmostly destroyed.\n\n3. As on pages 30a and 31c, and again just as on page 69a, B is sitting on\nthe tree of life or sacrificial tree. A branch of this, which he grasps in\none hand, ends in a serpent-head, and the root of the tree also represents\nB's head. Around the god's head are again the familiar dots, probably\nsignifying stars. Of the hieroglyphs, the first is probably _f_, the second\nis destroyed, the third may be a variant of _a_, although it recalls the\nsign which, I believe, has the meaning of 73 days on pages 46-50; the\nprefix of 1 also suggests this meaning.\n\n4. B's head is again surrounded by stars and he holds in one hand the\noutline of a hieroglyph. He is sitting on a peculiar ornamented structure\nresembling the crenelations of a wall. This wall displays the spiral which\nwe found also on pages 33b-35b, and which in the treatise, \"Zur\nMaya-Chronologie\" (Zeitschrift f\u00fcr Ethnologie XXIII, p. 147), I regarded as\nan abbreviation for a serpent and hence as a symbol of time. It is further\nto be noted that B is wet with rain and with this the third hieroglyph is\nin keeping, if it is actually intended to denote the rainy season and not\nthe week of 13 days (\"Zur Entzifferung\" V, 6); still the red numeral 13\nbelow is more in keeping with the second meaning. The second sign is an\nAhau with the leaf-shaped prefix, which also appears in the first sign of\nthe third group. The first is effaced.\n\n5. B, represented with a gala mantle hanging down in front and with the\ncopal pouch, is sitting on a head, which looks like his own, especially as\nto the eyes, but which notwithstanding probably belongs to D and is marked\nwith Ik (wind) and Cauac (cumulus clouds). Of the hieroglyphs the first and\nsecond do not admit of positive identification, and the third is Kan-Imix.\n\n6. The god is sitting on a mat in a house. All the hieroglyphs except his\nown are obliterated.\n\nPages 42a--44a.\n\nAnother Tonalamatl of the form of 10 \u00d7 26; I have restored the effaced\nday-signs as follows:--\n\n  XIII     XIII 3 III 2 V 2 VII 6 XIII 2 II 2 IV 2 VI 7 XIII\n  Oc       Cib\n  Ik       Lamat\n  Ix       Ahau\n  Cimi     Eb\n  Ezanab   Kan.\n\nThus the month days are the same as in the preceding Tonalamatl, but should\nbe read in a different order:--Oc, Cib, Ik, Lamat, etc.\n\nHere each of the 8 subdivisions has 6 hieroglyphs, and the order is as\nfollows:--\n\n  1  2\n  3  4\n  5  6.\n\nA few of these signs are common to all the groups. Thus the first sign\n(_v_), as far as what remains is distinguishable, seems to occur in all the\ngroups. It has the leaf-shaped prefix, but I cannot understand the rest of\nit; we shall find it again several times on pages 29c-41c.\n\nAgain the sign in the sixth place, as far as we can see, is always the head\nwithout an underjaw and the tuft of hair tied up on top of it (O, according\nto Schellhas), which we found above on page 25 and which we shall meet\nagain on pages 65-69 no less than 13 times, with regular intervals of 6\nsigns between them. Indeed that passage is a remarkable parallel to this\none.\n\nThat the sign for B, who here too plays the most important part, occurs\noften, is self-evident. It appears in the fourth place, in the 1st, 3d,\n4th, and 7th groups, and in the third of the 8th group; in the 6th group it\nis destroyed. In the 2nd and 5th groups B has neither picture nor sign.\n\nThe hieroglyphs of the cardinal points I shall mention in connection with\nthe separate groups. They are especially conspicuous in this section, being\nsometimes represented in full and sometimes in an abbreviated form as mere\nprefixes.\n\n1. B with arms crossed sits above a serpent denoting time, and holding in\nits coils the cross _b_, which so often refers to astronomical conditions.\nAbove the head of the serpent is the vessel with the three Kan signs, which\nwe have already found several times on pages 25-28. It is remarkable that\nthe flourish, which usually appears as the nose-ornament of the sun-god G\n(_e.g._, pages 11b and c), is added to these Kan signs. As the stars are\nagain indicated on B's head, he plainly denotes a time-god here. The third\nhieroglyph, the sign of the east, corresponds with this meaning, and the\nKan sign, which we see in the fifth hieroglyph probably combined with Ahau,\nalso belongs to the east; the prefix of the fourth hieroglyph is the sign\nfor the west.\n\n2. A deity whom we shall probably have to call F, the god of human\nsacrifice, is sitting on a stepped pyramidal structure (a teocalli as a\nplace of sacrifice?). He holds something in his hands, resembling a long\nand broad scroll, joined to which is the head of the god of the north, C,\nand in the third hieroglyph of this group the sign for the north also\nappears, prefixed to the head of F, who seems to be repeated in the fourth\nhieroglyph. The fifth hieroglyph with an Imix is unintelligible to me.\n\n3. Page 43. B is sitting in the water, the copal pouch hangs from his neck\nand the hatchet is raised as if ready to attack. The second hieroglyph\nclearly denotes water, while the third is the sign for the west and the\nfourth is the sign for B, its prefix being the sign for the east\nabbreviated; the order of the cardinal points is thus exactly the reverse\nof that in the first group. The fifth hieroglyph is not clear to me, but it\nappears to be repeated in the same place in the next group.\n\n4. B is sitting here astride a sort of bench again holding the hatchet in\nhis hand. Belonging to this picture in the third hieroglyph is the sign for\nthe south, which is repeated in an abbreviated form in the fourth\nhieroglyph.\n\nThe fifth is Kan, joined to what appears to be the same sign as the one\nfound in this place in the preceding group. The second sign is indistinct.\n\n5. This is an aged deity, probably M according to Schellhas, seated on an\nindefinite object. In front of the deity is a Cauac sign, which contains\nexactly the same cumulus clouds as those in the sign 5 Zac, which belongs\nto N. Cauac, however, belongs to the south, and therefore corresponds with\nthe north of the second group on page 42. Sign 5, a Kan, corresponds\nexactly with the same sign in the fifth place of the preceding group.\n\n6. Page 44. B seems to be in a state of collapse. Behind him is a second\nperson, who is either trying to support him or to pull him up by some kind\nof a sling. I think the second person is E, the grain-deity, if it is not\nSeler's young god. If the hieroglyphs were not completely effaced, they\nwould probably shed some light on this interesting passage.\n\n7. Here we see B, holding a fish in his hand, and sitting on a hieroglyph,\nwhich is compounded of Imix and a prefix, which resembles the tortoise head\nand which appeared once before in this combination on page 32a. This\npassage recalls page 40a, where B is seated on the laterally elongated head\n_q_. Nothing more can be said of the hieroglyphs, than that 6 is the head\nwithout an underjaw.\n\n8. B is sitting here in a house; his sign in the third place has Yax as a\nprefix. Hieroglyph 5, with the number 4 prefixed, recalls the one which we\nfound on page 21c belonging to the baldheaded old man. Hieroglyph 4 is the\ncommon Kan-Imix.\n\nPage 45a.\n\nThe last page on the front of the first section of this Manuscript is used\nfor a series, which presents itself as a second improved edition of the\nseries which was found on pages 31a-32a. The very fact that the writing is\nso much better proclaims it an amendment. The chief aim of both series is\nthe same, viz:--to bring into unison the numbers 91, 104, 260 and 364. But\nthe two series gain this end by different means. On page 32 the series\nbegins with 91, and at first has only 91 as a difference, until with 728 a\nmultiple of 104 and 364 is obtained, then it returns to the simple\ndifference 91, in 1456 it obtains again the 104 and 364, loses these two\nlast numbers once more in 1820 and finally in 3640 obtains the desired\nmultiple of all four numbers, which is retained in 7280, 14,560, 21,840 and\n29,120. The series on page 45a proceeds much more briefly. It begins at\nonce with 728 (91, 104, 364), loses the 104 in 1092, gains the 260 and\nloses the 104 in 1820, arrives at divisibility by all four numbers in the\n3640, loses the 104 again in 5460, but then comes to a standstill after\nhaving obtained the same multiples (double at that) of 3640, which I\nmentioned just now in the preceding series. Indeed it can be seen from what\nis legible in the third column above, that the series went still further.\nBut so much is obliterated that I have obtained the numbers 14,560 and\n21,840 in both series only by conjecture.\n\nIn the earlier passage the starting-point of the series is the day XIII\nAkbal and in the one before us it is the day XIII Oc. In the former the\ndays specified were 91 days apart from each other, and here they are\nseparated by 104, _i.e._, XIII Ezanab, XIII Ik, XIII Cimi, XIII Oc.\n\nThe initial days of the two series, XIII Oc-XIII Akbal, are separated by 13\ndays, and the reversed series, XIII Akbal-XIII Oc, by 247 days. Hence the\nsubject of both passages is essentially the week of thirteen days, _i.e._,\nthe year of 364 (28 \u00d7 13) days.\n\nNow this series is also accompanied by a number amounting to millions. It\nis in the second column of page 45; only, in order to understand it, we\nmust add a zero as the bottom figure; then it becomes 1,278,420. XIII Oc\nstands below this number as the beginning of the series. The first column\nhas 30 as an encircled number and below it the normal day IV Ahau.\n\nThe large number must have been formed as follows:--\n\nThe point of departure was 230, the interval between IV Ahau and XIII Oc,\nto this was added 98 \u00d7 260 = 25,480, the sum being 25,710. The result of\nthis number added to 11 Ahau-Katuns = 1,252,680, was 1,278,390, which\nnumber is not revealed in the Manuscript. It is concealed in XIII Oc 3 Mol\n(2 Muluc). But 1,278,390 = 42,613 \u00d7 30, _i.e._, it is divisible by the\ninterval XIII Oc-IV Ahau.\n\nNow if we add to this large number the 30 set down in the Manuscript, the\nresult will be the above-mentioned 1,278,420. This number in the Manuscript\nhas the date IV Ahau 13 Chen. (2 Muluc). It is, of course, divisible by 30\nand by 260, hence = 42,614 \u00d7 30 and 4917 \u00d7 260. It corresponds not merely\nin this respect with the largest number on page 31a, viz:--2,804,100, but\nalso with regard to its divisibility by 78, 156, 195, which are all\nmultiples of 13.\n\nOn page 45a, top left, there were doubtless five hieroglyphs, of which the\ntwo topmost ones are effaced. First we see only the sign of the eleventh or\ntwelfth month, Zac or Ceh, with an uncertain number prefixed, then the\nsigns for beginning and end are distinctly legible. Ceh begins and Zac ends\nthe year of 364 days; see page 4 of my treatise \"Zur Entzifferung V.\"\n\nPages 29b--30b.\n\nWe come now to the middle section of pages 29-45, in which we shall not be\nso hampered by obliteration in our attempts at interpretation, as we were\nin the upper section.\n\nWe have here first a Tonalamatl of the usual kind, arranged as follows:--\n\n  III  13  III  13  III  13  III  13  III\n  Ix\n  Cimi\n  Ezanab\n  Oc\n  Ik.\n\nThat is to say, the 52 days divided into four equal parts.\n\nTo these four divisions, as on page 23b, belong the four usual forms of\nanimal food, which are joined in three places to Kan (bread) and probably\ndenote sacrifice. They are, first a mammal, which, however, is erroneously\nrepresented by a fish; second, a fish, third an iguana and lastly a bird. I\nwould add, that in the hieroglyphs above, the east, north, west and south\ncorrespond in turn with these representations of food.\n\nThe hieroglyphs are arranged as follows:--\n\n  1  2    5  6     9  10    13  14\n  3  4    7  8    11  12    15  16.\n\nOf these, 2, 6, 10 and 14 are the cardinal points just mentioned; 4, 8, 12\nand 16 are the sign for B, and 1, 5, 9 and 13 are the head with the tuft of\nhair and the Akbal eye to which I attribute the meaning of _beginning_.\nLikewise the remaining four signs, 3, 7, 11 and 15, although they are not\nexactly alike, have something in common, the 15th being a distinct Imix;\nthey are not yet wholly intelligible to me.\n\nFour pictures of B belong to these hieroglyphs. In the first the god is\nseated with crossed arms on two of the ordinary astronomical signs (Jupiter\nand Mars?). In the second, where he is pointing forward with his hand,\nthere are footprints on his seat, as, for example, on page 35a. In the\nthird the seat contains the usual cumulus clouds in clusters. Finally, in\nthe fourth, he is seated on the tree of life or of sacrifice, the hatchet\nis in his hand and he is clad in the gala mantle; cf. pages 31c, 40a, 69a.\n\nPages 30b--31b.\n\nThis passage is in some respects closely related to the preceding\nTonalamatl, but in other respects it differs significantly from this and\nfrom what is usual, for the Tonalamatl is divided here into only four\nprincipal divisions of 65 days each, which begin very regularly with the\ndays VIII Oc, VIII Men, VIII Ahau and VIII Chicchan. There are neither\nsubdivisions nor the usual pictures belonging to them. But on the other\nhand each of the longer periods of time written down here have eight\nhieroglyphs for each section in the usual order.\n\nB's sign occupies the places 6, 4, 4 and 4; from this it follows that here\ntoo he forms the principal subject.\n\nHere, as in the preceding Tonalamatl, the first place in each group\ncontains the sign denoting beginning, while the eighth sign is invariably\nthe head without an underjaw, which seems to me to refer to _fasting_, as\nif a fast-day fell at the end of every 65 days.\n\nIn the fifth place we see in succession the four animals, which in the\npreceding Tonalamatl are not included in the groups of hieroglyphs. Here\nthey stand in the order of mammal, bird, amphibian and fish, but the bird\nin the second group is replaced by the sign which usually occurs with the\ndog (lightning-beast).\n\nThe signs in the second place are those of the cardinal points, and they\nare given in the same order as in the preceding Tonalamatl, _i.e._, east,\nnorth, west and south, so that they do not belong to the same animals as\nthey do there.\n\nThe third signs are the cardinal points again, but in the abbreviated form\ndiscovered first by Schellhas, and in a different order:--west, north, east\nand south, and always joined to the head of C around which everything\nrevolves as around the polar star. The Kan sign with different accompanying\nsigns occupies the seventh place in the first group, and the sixth in the\nother three.\n\nFour signs still remain:--the fourth of the first group I am inclined to\nconsider the abbreviated sign for the sun; the seventh of the second, rain\nwith the sign for the west as a prefix; the seventh of the third, Caban,\nground, with the sign for the east as a prefix; the seventh of the fourth\nis Kan with the Yax sign above it, probably denoting the vegetable kingdom.\n\nPages 31b--35b.\n\nThis entire passage is devoted to a single Tonalamatl, which is divided and\nwritten out in an unusual manner. Like the preceding it is divided into\nfour parts of 65 days each, but the remarkable thing about it is that these\ndivisions of 65 days are each subdivided into two periods of 46 and 19\ndays, and the 46 days again into eight unequal parts, which are exactly the\nsame each time, while the 19 days run their course without further\nsubdivision. On pages 33, 34 and 35 this 19 is always on the left at the\nbottom, on page 32 it is wanting, probably because it was self-evident and\nthere was no suitable place for it.\n\nWe shall next discuss the division of these four periods of 46 days each.\nThis division is indicated with especial exactness on these pages, since\nnot merely the length of the separate divisions and the week days are\nspecified, but also the month days. This representation has the additional\npeculiarity, that the two columns on each page must be read from bottom to\ntop, and of each group of two days standing side by side, the one on the\nright is to be read first and then the one on the left. If the Tonalamatl\nwere written in the usual manner, it would have the following form:--\n\n  X  9  VI  9  II  9  XI  2  XIII  4  IV  9  XIII  4  IV  19  X\n  Ben\n  Ezanab\n  Akbal\n  Lamat.\n\nInstead of this we read in greater detail as follows (the pages and the\nstated _length_ of time are in parentheses):--\n\n  (31) X Ben (9)     VI Ik (9)     II Chuen (9)  XI Ahau (2)\n         XIII Ik (4)     IV Cimi (9)   XIII Men (4)       IV Cauac (19).\n  (32) X Ezanab (9)  VI Manik (9)  II Cib (9)    XI Chicchan (2)\n         XIII Manik (4)  IV Chuen (9)  XIII Ahau (4)      IV Kan (19).\n  (33) X Akbal (9)   VI Eb (9)     II Imix (9)   XI Oc (2)\n         XIII Eb (4)     IV Cib (9)    XIII Chicchan (4)  IV Muluc (19).\n  (34) X Lamat (9)   VI Caban (9)  II Cimi (9)   XI Men (2)\n         XIII Caban (4)  IV Imix (9)   XIII Oc (4)        IV Ix (19).\n\nIn spite of the seemingly wholly irregular division of time, the following\nrelation, which is certainly not accidental, results from this\narrangement:--the first of the eight members of each row is one of the days\nwhich may begin the year and the months, and the eighth, on the other hand,\none of the four regents of the year. The remaining six members are the\nremaining 12 of the 20 days repeated twice and the second always\ncorresponds with the fifth of its own series, and the third to the sixth\nand the fourth to the seventh of the following series.\n\nTwo pictures of god B belong to each of these periods of 65 days, the first\nof these pictures referring to the divided period of 46 days and the second\nto the undivided one of 19. It is also in agreement with this that on pages\n61 and 62 the fourth, sixth and eighth pictures represent the god as rising\nfrom the jaws of a serpent--the serpent being represented each time as\nlying in water which invariably contains the number 19.\n\nAs the hieroglyphs belonging to the periods of 46 days are allied to one\nanother, and as this is also true of those belonging to the periods of 19\ndays, I will first consider the hieroglyphs of the first period by\nthemselves, then those of the second, and the pictures shall be treated in\nthe same manner.\n\nTherefore, let us first examine the four pictures (1, 3, 5 and 7) on the\nright side of the pages:--\n\n1. The first page shows the god walking with the official staff in his\nright hand, in his left the hatchet raised for a blow and with the copal\npouch hanging from his neck.\n\n2. He is walking and holding a flaming torch reversed in his right hand, in\nhis left the hatchet is raised aloft, the pouch hangs from his neck, the\nmantle is indicated and around his head are the little circles which are so\nfrequently his adjuncts and probably signify stars.\n\n3. He is walking and holding the reversed torch in his left hand and the\nhatchet in his right.\n\n4. He is walking and holding a torch in each hand. He wears on his head the\nhead of K. He seems to be bringing storm and fire.\n\nNow let us examine the hieroglyphs, which I have numbered thus:--\n\n  1  3  5\n  2  4  6.\n\nThe first hieroglyph on each page certainly represents one of the cardinal\npoints. They are in the usual order:--east, north, south and west.\n\n2 is the same sign on each page. I take it to be the sign for Xul = end,\ndenoting, it may be, the end of the period of each cardinal point.\n\nIn each group 3 is the head with tuft of hair and the Akbal eye; probably\nthe sign denoting _beginning_. This beginning and end occur most distinctly\nrepeated on page 63, and the end alone eight times at the bottom of pages\n61-62.\n\nOn page 31, 4 is B's sign, on page 32 B's with the prefix of the north, on\npage 33 it is B's sign again and although quite indistinct its is plainly\njoined with the east. On page 34 there is another indistinct sign which may\nbe that of the serpent deity H.\n\nOwing to indistinctness I do not venture to determine the fifth sign on\npages 31 and 33; on page 32 it is the laterally elongated head _q_ with the\nBen-Ik superfix, and on page 34 the ordinary Kan-Imix.\n\nThe sixth sign varies as much as the fifth; it seems here to denote four\ndifferent gods, perhaps the four given on pages 25-28. On page 31 it is a\nCauac, the prefix of which here, however, suggests K, on 32 it is certainly\nthe hieroglyph of E and on 33 possibly of A, on 34 it most resembles Muluc\nof the day-signs, but also suggests the line crossing F's face from top to\nbottom.\n\nWe come now to the four pictures 2, 4, 6 and 8 and to the hieroglyphs\nbelonging to them, which are on the left side of the pages and belong to\nthe periods of 19 days.\n\n1. B is pictured walking, raising the hatchet in his right hand, and\nholding an uncertain object in his left; the serpent with the 19 set down\nin its coils does not appear here. The 2nd, 3d and 4th pictures belong\ntogether. In each picture on these three pages there is a serpent with\nwater in its coils and the number 19 in the water, denoting the number of\ndays belonging here. As on pages 61 and 62 B is emerging from the open jaws\nof the serpent. In each case he is brandishing the uplifted axe in his left\nhand. The difference in the three pictures consists, first, in the fact\nthat only in the 2nd and 3d B wears the copal pouch, second, that only in\nthe 3d and 4th he has an implement in his right hand (the two implements\ndiffer somewhat but are both, apparently, adapted for hanging up) and\nthird, that only in 3 the whole picture is painted blue, which means that\nthe entire scene is enacted under water.\n\nThe hieroglyphs are as follows:--\n\nThe first in all four cases is a Manik, _i.e._, originally a grasping hand,\nperhaps referring to the chase; on page 32 it has a prefix and on pages\n33-35 a superfix corresponding to the first.\n\nThe second sign on each page is simply B's.\n\nThe Cauac sign in the third refers in all four cases to the water\nrepresented at the bottom of pages 33b-35b. On page 32 it has an Akbal as a\nsuperfix, on 33-35 a prefix, which is familiar and in keeping with the sign\nand probably also the same suffix, though it is indistinct on page 34.\n\nThe fourth sign shows, as do several other things, that the representation\non page 32 differs from that on pages 33-35. On the first of these pages we\nsee an Imix with a puzzling 1 prefixed. If the numbering of the days really\nbegins with Kan, as is probable in this Manuscript, then Imix is the 18th\nday and 1 + 18 might denote the 19, which is not set down here. On pages\n33-35 this sign contains the spiral, which refers to the serpent in the\npicture below (and probably therefore to time). A curious element, however,\nis the numeral 9 prefixed three times to the spiral. This number is rarely\na prefix, but it occurs, for example, on pages 33a and 35a before the cross\n_b_ and on page 60 right, middle, prefixed to Xul (= end). The interval 9\noccurs in this Tonalamatl 16 times, including therefore 117 of the 260\ndays.\n\nThe fifth sign each time contains the head without the under jaw, just as\nit recurs regularly in the preceding passage, pages 30-31.\n\nThe sixth sign in each group is the not uncommon compound of Caban and the\nsign, which resembles Muluc and which we saw before in the sixth place\namong the hieroglyphs on the right side of page 34.\n\nPages 35b--37b.\n\n  I  11  XII  6  V  9  I  4  V  7  XII  9  VIII  6  I\n  Caban\n  Muluc\n  Imix\n  Ben\n  Chicchan.\n\nThat is, a regular Tonalamatl of five parts, 5 \u00d7 52. That the 52 days are\ndivided into two halves (11 + 6 + 9 = 4 + 7 + 9 + 6), may only be\naccidental.\n\nI will designate the hieroglyphs of the seven divisions thus:--\n\n  1  2  |  5  6   9  10  13  14  |  17  18  21  22  25  26\n  3  4  |  7  8  11  12  15  16  |  19  20  23  24  27  28.\n\nI will first consider those signs, which are repeated and by means of which\nthe sections seem to be brought into connection with one another. But I\nshall attend in detail to those hieroglyphs which contain characteristic\nreferences to each picture, when I discuss the latter.\n\nThe first place both among the pictures and among the hieroglyphs again\nbelongs unquestionably to B. He is plainly designated in the 10th, 17th,\n21st and 26th hieroglyphs, but, for an unknown reason, C's sign is joined\nto B's in the 16th, probably also in the 6th and perhaps in the 9th, and in\n20 and 28 C's sign forms an integral part of a hieroglyph. Now in\ndiscussing the great Tonalamatl, pages 4a-10a, I attempted to make it\nappear probable that C belongs to the eighth day (Chuen) and in that case\nthe Chuen sign in the thirteenth hieroglyph may be probably set down here.\nFurther, in discussing pages 25 to 28, I expressed the conjecture that this\nChuen sign might simply mean eight days, if we begin with Kan as the first\nday, for which proceeding there is some warrant in the \"Dresdensis.\" Now,\nin hieroglyphs 8 and 24 we find an 8 inscribed; in hieroglyph 8 it is\njoined to an Imix, exactly as on page 39c; on page 65a it is joined to Kin,\nand on 67a and 68a to a hand. Is it possible that here also the 8 is\nintended as a sign for Chuen = C?\n\nThen the familiar Kin-Akbal sign (day and night) is in the fourth place as\nwell as in the eleventh and nineteenth.\n\nThe other signs which appear but once, I will discuss in connection with\neach of the seven pictures:--\n\n1. A serpent in the water, with B emerging from its head, exactly as on\npages 36a, Tro. 26 and Cort. 10.\n\nThe third sign, that of the serpent-deity H, refers to the serpent. The\nfirst sign is the one which I think may be Caban-Muluc, while the second,\nowing to its indistinctness, eludes interpretation.\n\n2. This also represents a deity sitting in the water, whom we are probably\nsafe in calling H, for the top of his head changes into a serpent, ending,\nhowever, in a bird's bill holding a fish. The deity holds up both hands.\nThe union of serpent and bird should be noted in connection with the fourth\npicture. The deity is represented in the fifth sign; the sixth, seventh and\neighth signs have already been discussed.\n\n3. B is traversing the water in a boat, exactly as on pages 29c, 40a and c,\nand 43c. Here, however, there is a person beside him (probably a woman)\nwhom, from the ninth hieroglyph we recognize as the deity E, unless this\nsign is C's. In 12 we see with Kan a sign which may suggest the usual\nhieroglyph denoting a year.\n\n4. A serpent is pictured here, with a bird sitting upon it. We met with the\nsame bird on page 17b. Schellhas, \"Maya-handschr.,\" p. 51, has already\nexpressed the opinion that this is probably a rebus for the name\nQuetzalcoatl or Kukulcan, and this theory is certainly worthy of\nconsideration. In this connection I would call to mind that it is probably\nalso Kukulcan with serpent and bird who occupies the first place on page\n4a. The bird appears again in the fourteenth sign, while the thirteenth is\na Chuen, which, according to the statement made above, may be connected\nwith the C in the sixteenth. The fifteenth sign is the cross _b_, which\nprobably denotes the connection between the thirteenth and sixteenth or\nelse between the bird and serpent. Or is Chuen intended here to represent\nthe serpent and not the ape?\n\n5. This picture represents B carrying a burning torch, with the copal pouch\nhanging from his neck. His left hand touches a strange object, a kind of\nframe, the top of which ends in the head of a bird of prey.\n\nThe eighteenth sign is obliterated and the twentieth is a curious\ncombination of Caban, C and the front part of K.\n\n6. B is walking, with the hatchet in his left hand and in his right an\nobject which looks like the representation of sounds issuing from musical\ninstruments, as on page 34a. Perhaps B is represented here as the air-god.\n\nThe twenty-second sign is the familiar Kan-Imix. The twenty-third sign\n(_w_) is not intelligible to me; it occurs on pages 19c, 40b, 58, on the\nright, with a superfix suggesting K.\n\n7. Water, in which a small human being seems to be emerging from a snail\n(the symbol of birth). Above the water is B, grasping a serpent which is in\nthe water, as if to protect the new-born being from the serpent. The\ntwenty-fifth (with Kin) is the so-called bat-god, who on page 50 at the\nleft ends the series of twenty gods. The twenty-seventh sign (with Yax) is\nstill undetermined.\n\nPages 38b--41b.\n\n  VI 16 IX 8 IV 11 II 10 XII 1 XIII 12 XII 6 V 12 IV 11 II 11 XIII 6 VI\n  Cauac\n  Akbal\n  Manik\n  Chuen\n  Men.\n\nThe sum of the black numbers is 104, the whole is, therefore, a double\nTonalamatl = 5 \u00d7 104 = 520. While the series on pages 31a-32a primarily\nbrought the 91 and the 104 together, and the series on page 45a\naccomplished the same result with the 104 and the 364, here, though the\nprocess is a different one, the 104 is combined with the 260 in another\nnumber.\n\nIt is characteristic of this part of the Manuscript, that the astronomical\nrectangles, which are very rare in the preceding pages, appear here in no\nless than five of the eleven divisions and six of them represent showers of\nrain. One is very readily, therefore, led to infer that the 104 days have\nreference to the rainy season and to its dependence upon the position of\nthe planets. I will now analyse the eleven sections separately.\n\n1. Rain is streaming down from two astronomical signs (Mars and Jupiter?\nDay and night?) and in the rain stands a black human form, grasping an\nimplement with the right hand held downward and pointing upward with the\nleft. It has the vulture head which occurred on pages 8a and 13c.\n\nHieroglyphs 1 and 2 represent the sun and moon, both surrounded by half\nwhite and half black envelopes, which must denote clouds. The third sign is\nImix, which just here might refer to the rainy season productive of\nnourishment. The fourth sign is the vulture head of the picture.\n\n2. B is walking in the rain and holds in one hand a stick pointed at the\nlower end. This is doubtless a farming implement, likewise occurring\nfrequently in the Tro-Cort., which was used for making furrows or holes in\nthe ground.\n\nThe second hieroglyph is B's, the first is Caban = earth, the fourth might\nbe a compound of Caban and Muluc, referring to the rain, and the third is\nthe familiar Kan-Imix, which, as the designation of food and drink, would\nbe especially appropriate here.\n\n3. B is apparently resting from tilling the soil, since he is sitting on a\nsupport consisting of the signs just spoken of, _i.e._, Caban and Muluc\n(?).\n\nThe latter signs are repeated in the second hieroglyph, while the third is\nB's with the sun-glyph (?) prefixed; the first is the head apparently open\non top with the Akbal eye, probably the sign for beginning, and the fourth\nis the familiar sign _a_, which I think signifies a good, auspicious day.\n\n4. Page 39. This represents a violent shower of rain, which might be\npronounced a cloud-burst. The old red goddess with tiger-claws and a\nserpent on her head is pouring water in a stream from a jug. The same\ngoddess occurs on page 43b and on the last page, 74.\n\nHer hieroglyph is the second; it is more distinct in the two other\npassages. The first part of the third hieroglyph is indistinct, and the\nsecond part is the hieroglyph denoting the year. The first hieroglyph is a\nhead with the Akbal sign, and the fourth is the usual compound of Kin and\nAkbal.\n\n5. The cloud-burst seems to have destroyed the cultivation of the field,\nfor B walks forth again with the implement for tilling the soil, as in the\nsecond picture. The second hieroglyph is B's with the prefix of the west,\ntherefore probably denoting sunshine, the first again contains Caban and\nMuluc and the fourth is Kan-Imix referring again to the produce of the\nfield. I shall not venture to explain the third sign here any more than I\ndid in the previous passages. Compare page 8b.\n\n6. B is again sitting in the rain and under the same astronomical signs as\nbefore on page 38. He is pointing downward (to the sprouting seed?). He has\nthe sun-glyph on his back. The first two hieroglyphs are unfamiliar to me\n(Yax); the third is Imix with the sign for the west, and the fourth is\nagain Muluc.\n\n7. Page 40. B is plunging down headfirst from the same astronomical signs\nand is brandishing the hatchet.\n\nHieroglyph 1 is the cross _b_, 2 is B's sign, 3 probably that of the\ngrain-god E, and 4 being Kan-Imix refers to grain. Favorable weather seems\nto have set in.\n\n8. The astronomical signs are not the same as those in the three preceding\ninstances (Mercury and sun?). Below them is a deity with tortoise-head--in\nmy opinion, the sign for the longest day--holding a torch in each hand and\nthus referring to the heat.\n\nHieroglyph 1 (_w_) with the superfix suggesting K still puzzles me. 2 is\nthe cross _b_, 3 is the tortoise-head with the number 4, which probably\nrefers to the Kan, Muluc, Ix and Cauac years, as the 4 sometimes appears\nprefixed to N's hieroglyph. In exactly the same way the tortoise-head with\nthe tortoise itself occurs frequently in the Cortesianus. 4 is the sign of\nthe year with prefixed Kin and Cauac, _i.e._, day-Cauac-year.\n\n9. A thunder-storm, which is very appropriate after the longest day. The\nlightning-beast, likewise holding a burning torch, is plunging down from\nthe astronomical signs, which are different ones again (Venus and the\nmoon?).\n\nThe second hieroglyph contains the sign of the dog together with the cross\n_b_, while the third is that of the north-god C, and the fourth is Muluc. I\ncannot explain the first sign; its prefix, which rarely occurs, appears\nalso on pages 23b, 25a, 37b, 63a, and possibly on pages 53b, 62-63a, 69b.\n\n10. Page 41. Another representation of rain. There is an old deity in the\nrain, who is N rather than F, denoting the end of the old year. He is\nemerging from a snail (cf. with this page 37b), and is pointing upward; a\npart of the first hieroglyph is on his head.\n\nThis first hieroglyph recalls the sign which, in the Zeitschrift f\u00fcr\nEthnologie, XXIII, p. 145, I ventured to connect with the change of the\nyear; but it also suggests the snail pictured below, hence the birth of the\nnew year. The beginning of the year for the Mayas, although of course not\nfor all parts of the country, is fixed, as a rule, to fall on the 16th of\nJuly. This would agree admirably with the eighth and ninth sections, which\nrepresent the time of the longest day and of thunder-storms.\n\nThe second hieroglyph is B's, the fourth the cross _b_, probably referring\nhere to a union of two years, and the third with its Cauac to the duration\nof the rainy season or to the god N.\n\n11. The rain seems to fall with less violence. B is seated, clad in the\ngala mantle with a Kan on his head, as the sign of grain. His headdress\nalso strongly recalls that of the grain-deity E (which is also the case of\nthe headdress on the preceding picture.)\n\nHieroglyph 1, the upper part of which is very like that of the first sign\nof the preceding group, looks like a plaited mat. Does it not suggest that\nthe name of the first month of the new year is Pop and that this word is\ndenoted by carpet, mat? Hieroglyph 2 is B's, 3 is the sun between a dark\nand a bright sky, and 4 is the common Kin-Akbal, day and night.\n\nIf the seventh picture really refers to the beginning of the year, then the\nentire period of 104 days extends from April 15th to August 2nd, which,\nwith the addition of the five days not counted at the end of the year, does\nindeed make 109 days. All this, however, is only true on the supposition\nthat I have not seen more in these representations than they contain.\n\nPages 41b--43b.\n\n  VI  12  V  7  XII  6  V  21  XIII  6  VI.\n  Caban\n  Muluc\n  Imix\n  Ben\n  Chicchan.\n\nAnother regular Tonalamatl, and like the preceding one apparently referring\nto the change of the year, the tilling of the soil and the rainy season.\nB's sign is regularly repeated in the second place of all five groups of\nhieroglyphs, and moreover each of these groups has six signs. The head with\nthe missing under jaw is in the fourth place of groups 2 and 3, in the\nsixth of group 5 and might perhaps be intended also in the fourth of 1 and\n4. The usual Kan-Imix is in the third sign of group 2, in the fifth of 4,\nand the fourth of 5; possibly also in the fifth of 1; the third hieroglyph\nin group 3, at any rate, contains Imix.\n\nLet us now consider the five groups individually:--\n\n1. The rainy season seems to have been delayed; the beginning of the year\ndraws near. B is kneeling on a kind of footstool, the hatchet is in his\nright hand and his left hand holds a kind of chisel with which he is\ncarving something out of the trunk of a tree. The purpose of the work is\nindicated by the god's own head directly below (probably placed in front of\nthe tree as a model?). No doubt this is intended to represent the making of\nthe statue of the god of the new year destined for the beginning of the\nyear, as we know it from pages 25-28.\n\nCorresponding with this is the first hieroglyph denoting the year with Yax\nas a superfix, and also the sixth being the sign to which in the article in\nthe Zeitschrift f\u00fcr Ethnologie cited above, I attributed the meaning of\nchange of the year. I cannot decide whether the third sign is intended for\nan Imix-Chuen with the sign of the south as a superfix, the fifth for a\nKan-Imix and the fourth for the head without the under jaw.\n\n2. Page 42. Prayer for rain. B (that is to say, his priest) is seated\napparently on the same footstool. He is gazing upward and presenting a\nvessel containing an offering, the nature of which is uncertain. The vessel\nends in a tube; cf. page 67b.\n\nThe first, fifth and sixth hieroglyphs are not finished, and the third is\nKan-Imix.\n\n3. The rain-goddess promises aid. B is seated opposite the old red goddess,\nwho is holding intercourse with him. The god is seated on the Caban sign\n(earth) and the goddess on Muluc (rain?).\n\nThe first, fifth and sixth hieroglyphs are also unfinished; the third is\nImix with its meaning intensified by the prefixed Yax (the luxuriantly\ngrowing grain?).\n\n4. B is again tilling the ground in the manner already familiar to us.\nUnder him lies his own head with the Imix-Kan sign, denoting food and\ndrink, as a superfix. The first hieroglyph is the sign of the eighteenth\nmonth Cumhu, _i.e._, of the end of the year. The third is a Kin-Akbal, the\nfifth a Kan-Imix, the sixth is not finished, and the fourth may be intended\nfor the head without the lower jaw, but it is carelessly drawn.\n\n5. Page 43. The solicited rain begins. The goddess with the serpent on her\nhead is pouring streams of water from her vessel.\n\nThe first hieroglyph repeats the month Cumhu, denoting the beginning of\nrain, before the close of the year; the third is the sign of the goddess\nmet with on page 39b, here also with the sign for the west as a prefix; the\nfifth is her determinative, the serpent, and the fourth is Kan-Imix.\n\nIf the first sign in the first group is not regarded as the sign of the\nyear, but as that of the sixteenth month (Pax) resembling it, and the fact\nis taken into consideration that there is an interval of 34 days between\nthe second and fourth groups and of 40 days between the second and fifth,\nthis would be found to correspond with the interval between the months Pax\nand Cumhu.\n\nPages 43b--44b.\n\nThis is the fourth and last series of the first part of the Manuscript; the\nfirst is on page 24, the second on pages 31a to 32a, and the third on page\n45a. The first series is quite by itself, but the second and third are\nsimilar in form to this fourth, though their initial days are different\nfrom those of the latter:--XIII Akbal, XIII Oc and III Lamat. All three\nbegin with differences which are divisible by 13:--91, 104 and 78, equal to\n7, 8, and 6 \u00d7 13. All three aim and arrive at numbers which are common\nfactors of 260, 104 and 364, and therefore also of 3640, which last number\nis written out in the other two series, while in this series it can only\nappear later on and then, increased by multiplication.\n\nSince this series has the difference 78, the week day numbers remain the\nsame, while those of the month days must advance by 18 each, that is, from\nthe hidden starting-point III Lamat they go on to III Cimi, III Kan, III\nIk, III Ahau, etc., until the tenth member of the series is 10 \u00d7 78,\n_i.e._, 3 \u00d7 260 and thus comes again to the day III Lamat.\n\nFrom 780 onward this number is itself always the difference of the higher\nterms of the present series. At the same time 780 days are the duration of\nthe apparent revolution of Mars, which is here supplementary, as it were,\nsince page 24 treated of the revolutions of the sun and of Venus, and also\nof those of the moon and of Mercury. Hence in the present passage we find\nthe numbers 1560, 2340, 3120 and 3900, always accompanied by the day III\nLamat. The larger numbers require a few corrections; I read them 13,260 (17\n\u00d7 780), 15,600 (20 \u00d7 780), 31,200 (40 \u00d7 780), 62,400 (80 \u00d7 780) and 72,540\n(93 \u00d7 780). The very largest again are correctly set down; first 109,200\nequal to 140 \u00d7 780, but here also equal to 1050 \u00d7 104 and 300 \u00d7 364, so\nthat in this series the goal aimed at is not reached until later than it is\nin the two preceding series. Then follows 131,040 = 168 \u00d7 780, 1260 \u00d7 104,\n360 \u00d7 364, but finally 151,320, which number = 1455 \u00d7 104 and 194 \u00d7 780,\nbut is not divisible by 364.\n\nDetached in the usual way from this series on the left of page 43 is the\nnumber 1,435,980. Above and below it is the day III Lamat, further down IV\nAhau, and between them is 352 in a red circle. This number seems to have\nbeen obtained in the following way:--The writer began with the distance\nbetween III Lamat and IV Ahau, which is 92, added to it 172 \u00d7 260 = 44,720,\nand subtracted the result 44,812 from 13 Ahau-Katuns = 1,480,440. The\nremainder was 1,435,628, which number would correspond to the date III\nLamat 6 Zotz (4 Kan), which, however, is suppressed in the Manuscript. The\n352 = 260 + 92 was added to this sum, and the result was the 1,435,980\nwritten out in the Manuscript, _i.e._, a day IV Ahau 13 Zip (5 Muluc). Now\nthis number is the one sought; it is 5523 \u00d7 260 = 1841 \u00d7 780 = 3945 \u00d7 364,\nand hence must also be equal to 263 \u00d7 5460, since the 780 and 364 are\nunited in 5460. According to our present knowledge, it would seem to lie in\nthe future, but not far from the present; the solar and Mars revolutions\nare united in it. There is but a single hieroglyph here, the hieroglyph of\nthe animal which is the chief subject of the next section; from which it\nappears that the two sections are closely connected.\n\nPages 44b--45b.\n\nThis section supplements the pictures and hieroglyphs belonging to the\nseries just examined. Therefore it likewise extends over 78 days and\ndivides them as follows:--\n\n  III  19  IX  19  II  19  VIII  21  III.\n\nThese five days are plainly intended to be the days III Lamat, IX Manik, II\nCimi, VIII Chicchan, III Cimi.\n\nWith regard to the real purport of this section, it is my opinion that it\nhas reference to the time of the shortest day and also to the four winds\nand that this section therefore forms, in a measure, a contrast to pages\n38-41, where attention was called to the rainy season, the longest day and\nthe thunderstorms.\n\nWe see here in the first place four of the ordinary heavenly shields, with\ntwo astronomical signs each. I cannot decide, at present, whether these are\n1st, the moon and Saturn, 2nd, Mars and Mercury, 3d, the moon and Mars, and\n4th, Jupiter and Venus.\n\nFrom each of these shields hangs a figure not unlike an heraldic beast. It\ncannot be the canine lightning-beast; it has no flames, it is cloven-footed\nand with the upper lip bent upward and the lower lip curved downward\nsuggesting the storm-god K, and therefore probably represents the four\nwinds; this wind-beast repeated four times also occurs on Cort. 2.\n\nSix hieroglyphs belong to each picture. Those in the first place are\npierced ears and refer therefore to the ritual bloodletting, which may have\nbeen performed at this season. In Tro. 5*b we also find the pierced ear; a\npierced _tongue_ (Tro. 17*b), however, does not occur in the Dresdensis.\nThe second place always contains the sign of the beast like the one\ninstance on page 43.\n\nThe third place seems to be devoted to the four cardinal points, _i.e._, to\nthe four winds. First we see Akbal-Kin, _i.e._, the transition from night\nto day, the east. The north-god, C, is here in the second group; in the\nthird we see Kin and beside it in the fourth place Akbal, both enveloped by\nclouds denoting the transition from day to night, the west. The fourth\ngroup, it is true, has the year-sign here, but with the compound Kin-Cauac\nprefixed, and Cauac always belongs to the south. I believe I have found a\ndistinct reference to the season of the year in two other places. The\nfourth hieroglyph of the second group and the sixth of the fourth both have\nthe familiar prefix suggesting K, the storm-god. The first of the two\ncontains the month Mol (December 3d-22nd); the second might very well be\nthe month Yax (January 12th-31st). This is quite in keeping with the\ndistances 19 + 21 = 40 set down below.\n\nIn my \"Tageg\u00f6ttern der Mayas\" (Globus LXXIII, 10) and above in my\ndiscussion of the great Tonalamatl under pages 4a-10a, I have assigned the\nday Chuen to C, and Muluc to K, _i.e._, the first to the dark north and the\nlatter to the wind, which are both under consideration here. In fact, we\nfind the Chuen sign in the fifth place of the fourth group with the same\nprefix that C has in the second group. The Muluc sign, however, seems to\noccur three times:--1st, group 1, sign 6, where it may be joined to the\nmonth Mol belonging here; 2nd, group 3, sign 5, joined to the Akbal, which\nalso belongs here; 3d, group 4, sign 4, with a usual prefix. In the second\ngroup it may be included in the very similar month sign of Mol. Four\nhieroglyphs remain:--1st, Akbal in group 1, sign 5, hence probably denoting\nthe darker time of the year in general; 2nd, A in 2, sign 5; 3d, E in 2,\nsign 6; _i.e._, probably referring to the death of the grain (I do not know\nto what extent this expression may be used in relation to the Maya\ncountry); 4th, Kan-Imix in 3, sign 6, perhaps expressing the hope of new\nharvests.\n\nThis finishes the middle sections of the pages of the first part of the\nManuscript, and we must now turn back again to page 29 in order to examine\nthe lower sections.\n\nPages 29c--30c.\n\n  III  16  VI  16  IX  16  XII  17  III\n  Ix\n  Cauac\n  Kan\n  Muluc.\n\nHere is a Tonalamatl of four quarters, 4 \u00d7 65.\n\nIn the Manuscript 16 is again erroneously set down for 17 and the III\nfollowing it is omitted. The initial day is exactly the same III Ix, as in\nsection 29b above it, to which in other respects the passage now under\nconsideration shows a great likeness, since the four familiar animals occur\nhere as well as there. But in spite of beginning in the same way the days\nhere are different ones, being the four regents of the year, as on page 9b.\n\nThe four parts are grouped together by the sign, which always occupies the\nfirst place in each part; I have denoted this sign by _f_, and I think it\nmust have a very general significance, since from pages 29c to 40c it\nalways begins the groups. The connection between the four parts is further\nshown by the four cardinal points in the second place:--the north in the\nfirst group, the west in the second, the south in the third and the east in\nthe fourth. In the third place these cardinal points are again indicated by\ntheir usual abbreviations; the east is erroneously set down in the second\ngroup. These abbreviations are here invariably joined to the head of C as\nthe representative of the north, the first of the cardinal points occurring\nin this passage; the others revolve about the north pole.\n\nAs B's sign always occurs in the fourth place, there is nothing further to\nbe said concerning the hieroglyphs. We now come to the pictures:--\n\n1. B is rowing a boat, as we have already seen him several times (36b, 40a,\n_c_, and 43c). To the left of his head there is a bird's head and in the\nleft, bottom, corner, a pot in which apparently a soup of fowl is cooking,\nemitting bubbles. The Cib sign on the pot refers to the cooking or\nbubbling.\n\n2. B, with his head surrounded by the familiar stars, is seated in water,\nin which are represented the iguana over a Kan sign, and the familiar\nspiral probably denoting a serpent. He is painted black (perhaps\ncorresponding to the west?) and holds in his hand an implement not yet\ndetermined. Perhaps it may be intended for a tree, _past_ which the water\nis flowing.\n\n3. The god is seated, holding in one hand the spiral with a Kin sign over\nit and a Yax on top of that, and in the other hand something which looks\nlike a bird's feather or a fish's fin. Above him is a fish with a Kan sign,\nas on page 27, where the fish and Kan are also combined.\n\n4. Holding a hunting-spear, he is sitting on an animal slain in the chase,\nas on page 45c.\n\nFinally, I have remarked that pages 42c-45c, the last part of the first\ndivision of the Manuscript, look like an enlargement or amendment of the\nsection just considered.\n\nPages 30c--33c.\n\nTo begin with, the day signs are set down in the following order:--\n\n   XI        XI           XI        XI\n  Ahau      Chicchan     Oc        Men\n  Caban     Ik           Manik     Eb\n  Ix        Cauac        Kan       Muluc\n  Chuen     Cib          Imix      Cimi\n  Lamat     Ben          Ezanab    Akbal.\n\nHere then, as is frequently the case in this Manuscript, all the twenty\ndays are specified. But in order to obtain equal periods of time, the left\ncolumn should first be read from top to bottom and the following ones\nshould be treated in the same way. Then each succeeding day is 17 days\ndistant from the preceding, but in reality the interval is 117 days, since\nthe same week-day is always implied. The hieroglyphs seem to indicate that\nthese 117 days are divided into three distinct parts, 52, 39 and 26.\n\n117 days, however, are equal to 9 \u00d7 13 and hence in what follows we find a\nblack 13 set down 9 times as the interval between the days, and a red XI\nbeing the number of the week-day an equal number of times. Now, since the\nwhole series extends over 20 such sections of 117 days, the duration of\nthis calendar is 2340 days or 9 Tonalamatl.\n\nConsequently we find nine pictures of the same god B. In five of them (in\nGroups 1-4 and 9) he is sitting before or on a sacrificial tree or tree of\nlife; cf. 30b. It is probably not accidental that in these five cases the\nhieroglyphs refer to the cardinal points. In the eighth group the god is\nsurrounded by the suggestion of one or more trees; he is sitting in water\nas if in a forest; or in a cave bordered by trees? In the remaining groups,\n5, 6 and 7 he is seated on various supports, in 5 on an object, which is\nnot completed and which cannot, therefore, be explained, in 6 on\nastronomical figures (Mars and Venus?) and in 7 on agave leaves. In 1 and 3\nhis head is again surrounded by those dots suggesting stars, in 4 there\nseems to be a bird (quetzal?) seated upon it and in 2 it bears what may be\nthe Kin sign. In 1 and 5 he has the pouch for incense in his hand, while in\n3 alone he wears the gala mantle and is painted black, just as he appears\nin connection with the same hieroglyphs on page 29c. He carries a hatchet\nin repose in 2, 6 and 9, and raised for a blow in 1 and 7. In 7 he also\nholds the Imix sign.\n\nThe hieroglyphs form nine groups of four signs each. The first hieroglyph,\nas is always the case in this part of the Manuscript, is the sign which I\nhave denoted by _f_, and the second is always B's hieroglyph. The cardinal\npoints are everywhere specified by two signs each; in places 3 and 4 of\ngroup 1, the west comes first and beside it is the sign for the east,\nerroneously used for that of the west (a like error occurred in the\npreceding Tonalamatl); in group 2 there are two signs for the north; in\ngroup 3 that for the east with the sign for the west beside it erroneously\ngiven for the east, and in group 4 two signs for the south. In groups 5, 6\nand 7 we find in the 4th place the head of C, and the same sign in group 7\nin the 3d place, where it is joined to another head, which may be that of a\nwoman. The 3d sign of group 5 is incomplete and cannot be determined. The\n3d sign of group 6 displays a repetition of the astronomical signs\nrepresented below. There still remain the 3d and 4th signs of groups 8 and\n9. Of these the 3d in group 8 is _w_, which is as yet unexplained. The 4th\nmight be interpreted either as Oc (day 7) or as Xul (end). Its prefix is a\nYax sign. Finally, in group 9 the 3d sign is Manik (day 4), the 4th the\nelongated head _q_ with the Ben-Ik superfix, which Seler assigns to Men\n(day 12).\n\nPages 33c--39c.\n\nThe beginning of this Tonalamatl is indicated by a large red dot on page\n33. It resembles the Tonalamatl almost exactly above it on pages 31b-35b,\ninasmuch as its arrangement is an unusual one. I will here, as I did above,\ngive it the form in which it would present itself if it were set down in\nthe usual order:--\n\n  XIII  9  IX  11  VII  20  I  10  XI  15  XIII\n  Ahau\n  Chicchan\n  Oc\n  Men.\n\nIn this passage as in the earlier one, instead of employing the above\nconcise order, a preference has been shown throughout for carrying out the\nwhole series in such a manner that the week days are set down each time and\nnot merely in the left column. It, therefore, has the following form in the\nManuscript:--\n\n  XIII Ahau (9)     IX Muluc (11) VII Ahau (20)     I Ahau (10)\n                                                           XI Oc (15)\n  XIII Chicchan (9) IX Ix (11)    VII Chicchan (20) I Chicchan (10)\n                                                           XI Men (15)\n  XIII Oc (9)       IX Cauac (11) VII Oc (20)       I Oc (10)\n                                                           XI Ahau (15)\n  XIII Men (9)      IX Kan (11)   VII Men (20)      I Men (10)\n                                                           XI Chicchan (15)\n\nI have arranged the whole series in four parallel periods of 65 days each,\nfor the 65 appears throughout the computation, although the entire\nTonalamatl is written out in _one_ continuous line. On the right of page 35\nthe scribe seems to have wished to erase an entirely incongruous 4, and in\nwriting the last 15, on page 39, he began to use the red paint prematurely,\nso that the top one of the three lines is red.\n\nAttention should also be called to the fact that the second of my vertical\ncolumns contains the year-regents, the others only the days following\nimmediately after them, while 12 month days do not occur at all. Also the\nintervening periods 9 + 11 (= 20), 20, 10, 15 doubtless reveal some design.\n\nIn order to avoid repetition, I think it proper to mention first, that in\nthe twenty groups of four hieroglyphs each, the sign _f_ always stands in\nthe first place, but the hieroglyph of B, who is represented 20 times,\nusually appears in the second place, in the first and second groups in the\nthird place, and in the 18th and 19th his sign does not appear at all. I\nwill discuss the remaining hieroglyphs in their place in each of the 20\ngroups.\n\n1. B is sitting in a house and holding the Kan sign in his hand.\n\nThe second hieroglyph is apparently meant for the Ahau sign (referring to\nthe 17th day), which usually does not belong to B. This hieroglyph, which\ncertainly bears a resemblance to Ahau and with which we have become very\nfamiliar in the inscriptions, occurs again in this Manuscript on pages 46b,\nc, 50b, 54b, 65a and 66a. The fourth sign is a combination of Cauac and\nManik.\n\n2. B is seated on what may be a tree, below him is the cross _b_, and he\nholds the hatchet in his left hand.\n\nThe second sign with an emphasized 6 as a prefix (cf. the same sign with\nthe 6 on page 48, bottom, left, below the gods), has the usual Ben-Ik\nsuperfix, perhaps to denote that a lunar month has now elapsed, for this\npassage extends from the 20th to the 40th day of the Tonalamatl. The rest\nof the hieroglyph is unintelligible. In the 4th place we see a vessel with\nImix, probably denoting pulque.\n\n3. B is sitting in water, the hatchet raised in his right hand and his face\nturned upward.\n\nThe 3d hieroglyph is again Imix and the 4th a compound of Ik and\nMuluc:--wind and clouds.\n\n4. B is seated on a reproduction of his own head or D's, beating a drum\nwith his hand.\n\nThe 3d hieroglyph denotes the serpent-god H with the number 3 as a prefix.\nThe 4th hieroglyph is a Chuen with the sign for the south prefixed,--at any\nrate the upper part of that sign.\n\n5. B is standing in the pouring rain and looking backward.\n\nThe 3d sign here is a Caban apparently in a vessel. Following this in 4 is\nthe hieroglyph which I have proposed to interpret as the sign for\n_beginning_ (Globus, Vol. LXVI, page 79). This sign occurs again in groups\n7, 12, 15, 17 and 19, and must therefore be connected with the principal\nidea embodied in this Tonalamatl.\n\n6. B with folded arms is sitting in a house.\n\nAside from the usual leaflike prefix, the third sign is composed of two\nparts. The upper part looks like a plaited mat and suggests that the word\nfor the first month of the year (Pop) is expressed by mat. The lower part\nis the sign, which occurs frequently especially on pages 25-28, and which\nvery much resembles the familiar sign for a year of 360 days. We shall meet\nit again in the continuation of this Tonalamatl on pages 36 and 38. The\nthree passages refer to the 74th, 139th, and 204th days of the Tonalamatl,\nand hence are 65 days apart.\n\nThe 4th sign is the cross _b_, with possibly the sign of the east as a\nprefix.\n\n7. B is seated on the cross _b_, which is here undoubtedly meant for an\nastronomical sign. He holds a Kan sign in his hand and there is an Ahau\nsign on his back.\n\nThe naked crouching personage, pointing upward, should have especial\nmention here. The same figure recurs above as a prefix to the 4th\nhieroglyph. We have already seen it in the 39th hieroglyph on page 24, and\nshall meet it with especial frequency in the second part of the Manuscript.\nIt is placed sometimes, as in this case, _before_ a sign, sometimes _after_\na sign and again two of these figures are placed back to back as on page\n22c, and one of them is even placed upside down before another sign, where\nit seemed to me to be a sign for Mercury (\"Zur Entzifferung VII,\" p. 11).\nThis figure is represented independently only on the right of page 58. In\nthe passage under present consideration this personage appears again on\npage 38. The two figures are connected one with the 85th and the other with\nthe 215th day, and are, therefore, divided by exactly half a Tonalamatl or\n130 days. Here we find it as a prefix of the supposed sign for _beginning_\nof which mention was made in discussing the 5th group. The 3d sign is the\nsame astronomical one, which we saw below under B. It might refer to the\nMoan and to the change of the year, and thus indicate that a Mercury\nrevolution was coincident here with the beginning of the solar year.\n\n8. B is walking in the rain, both arms are stretched upward, and the pouch\nhangs from his neck. At the left top there is a black spot suggesting those\nwhich usually occur beside the sun and moon.\n\nThe 3rd sign is Manik, with a prefix. The 4th is an indistinct head, which\nmay be C's, with an Imix sign as a prefix.\n\n9. B is walking with the pouch hanging from his neck, and the hatchet in\nhis hand.\n\nThe 3d sign, which is unusual, is very obscure, but suggests the fish on\npage 44c or that on page 36b. The 4th sign with the prefix of the north is\nvery indistinct.\n\n10. B is standing in _water_, his face turned upward while water is pouring\nfrom a cloud. The third sign is very complex. The top, left, suggests a\nserpent, the right a hand, the bottom, left, a Chuen and the element at the\nbottom, right, may be intended for a bird's head. Exactly the same sign,\nwith the 4th part merely indicated, occurs 65 days later on page 38. The\n4th sign is the familiar compound Kin-Akbal.\n\n11. B is sitting in a tent, on the roof of which there is a vessel\ncontaining food of some kind.\n\nThe third sign, which is very complex, is indistinct. The 4th sign likewise\nconsists of four parts, the left, bottom, part is probably the vessel,\nabove it is a spiral (which usually means serpent or time). The right,\nbottom, is again the sign resembling the year-sign which was spoken of in\ndiscussing group 6. The component at the right, top, is indistinct.\n\n12. B is sitting here on no less than four astronomical signs, he has the\nhatchet in his hand and the design on his back may be a shield or the\nelaborately ornamented sun-glyph Kin.\n\nThe third sign (denoting _beginning_?) has already been discussed in\nconnection with group 7, which is 65 days earlier. The fourth is the sign\nof the year of 360 days or the month Pax with the Ben-Ik as a prefix. These\nsigns are here suggestive of the beginning and end of the year.\n\n13. _Above_ B are astronomical signs (Jupiter and Mercury?) and also the\nsun and moon. The rain is pouring down upon the god, and a fish is placed\nbeside him. He seems to have the same chisel in his hand which we saw him\nusing on page 41b in connection with the beginning of the year. This again\nwould correspond to the date indicated in the preceding picture. The shield\n(?) also is the same here as in the preceding group.\n\nThe third sign ought to represent the fish; the drawing seems to have been\nunsuccessful and the sign looks more like a bird and also resembles the\nthird sign in the ninth group on page 36. The fourth sign is a Kin-Akbal.\n\n14. B is seated on the elongated head _q_, which has an ordinary prefix. He\nis pointing upward with his right hand and the left looks as if opened to\nreceive something.\n\nThe third hieroglyph contains a _q_ like the one under the god, the fourth\nis an indistinct head (C's?) with an unintelligible prefix.\n\n15. B is standing in water while rain is again pouring down upon him. He\nholds the hatchet raised in his left hand, while the fingers of the right\nare extended upward in an unusual manner. This is repeated in the third\nhieroglyph.\n\nThe third hieroglyph, however, is the same as the third in the tenth group\n65 days earlier, only here the hand is more distinct, while the element\nbelow it is vague. The fourth sign is again the one denoting beginning.\nCompare the fifth group (130 days earlier).\n\n16. B with arms folded is sitting in a house with the Cauac sign below.\n\nThe third and fourth hieroglyphs contain the sign resembling that for the\nyear, which was mentioned in discussing the sixth group (130 days earlier).\nIn the third a Kin is prefixed to this sign, while the superfix of the\nfourth is what I take to be a mat, which also occurred in the sixth group.\nThe prefix is a figure suggesting the serpent-deity, which we have already\nmet with in the tenth and fifteenth groups.\n\n17. B, holding the hatchet, is seated on a Moan head, and the third sign is\nprobably intended to represent the same Moan head, in front of which we\nfind the same crouching person met with in the seventh group, 130 days\nearlier.\n\nThe fourth hieroglyph is again the sign for beginning, which we have\nalready often met with, as, for example, 65 days earlier in the twelfth\ngroup.\n\n18. B is sitting in the pouring rain under astronomical signs (Mars and\nMercury?) to which those of the sun and moon are added. The god's face is\nupturned and he holds the hatchet in his hand.\n\nThe third hieroglyph may be the vulture head, to which a part of the\nunintelligible second hieroglyph may also refer. This second sign stands in\nthe place of B's hieroglyph, which is wanting here.\n\nThe fourth sign contains the enigmatical numeral 8, which we found on pages\n36b and 37b, and has the Imix sign as a prefix, as in the first of these\ntwo passages. The same compound appears on pages 67a-68a.\n\n19. B is seated here on his own head, as in the fourth group he is sitting\non D's. His hands are empty.\n\nThe second sign is again the vulture head instead of B's hieroglyph. The\nthird is probably the head of the lightning beast, and the fourth is again\nthe sign supposed to denote beginning.\n\n20. B is sitting in water and holding in his hands a vessel with a Kan sign\nupon it.\n\nThe water (with Imix prefixed) is denoted by the third sign, while the\nfourth represents a head (with what is probably a hand pointing to the\nright above it), which I should prefer to consider the grain-deity E.\n\nIn conclusion I would call attention to the remarkable fact that every four\npictures, which are separated from each other by four of the other\npictures, _i.e._, after every 65 days, correspond in certain respects with\none another, _viz_:--\n\n1. Pictures 1, 6, 11 and 16. In all, and _only_ in these, B is sitting in a\nhouse or tent, in 6 and 16 with his arms folded.\n\n2. Pictures 2, 7, 12 and 17. In the first three the god is seated on\nastronomical signs and in the fourth on the Moan head, which I think refers\nto the Pleiades.\n\n3. Pictures 3, 8, 13 and 18. Here in the last two B is sitting _beneath_\nastronomical signs. In all four pictures water, clouds and rain are\nrepresented.\n\n4. Pictures 4, 9, 14 and 19. In the first and fourth the god is seated on\nD's head and on his own, and in the third on the elongated head _q_.\n\n5. Pictures 5, 10, 15 and 20. Like the third of these five classes, these\npictures are likewise distinguished by water, clouds and rain.\n\nNow the first set of pictures is between the week days XIII and IX, the\nsecond between IX and VII, the third between VII and I, the fourth between\nI and XI, the fifth between XI and XIII, while the month days are quite\ndifferent. Hence the conjecture is but natural that the pictures and week\ndays bear some relation to one another, though that relation is still\nshrouded in obscurity.\n\nPages 40c--41c.\n\n  I  10  XI  10  VIII  10  V  10  II  3  V  9  I\n  Ahau\n  Eb\n  Kan\n  Cib\n  Lamat.\n\nThis is a Tonalamatl of the most ordinary kind, in which an unsuccessful\nattempt has been made to divide the subdivisions into equal parts.\n\nIn the groups of four hieroglyphs each, which belong to each of the six\nparts, the sign _f_ always occupies the first place, and B the third. Let\nus now examine the six parts separately.\n\n1. B is sitting in a boat and rowing (as on the top of the same page).\nAround his head there is again the suggestion of what may denote the starry\nsky, and in this picture his nose-peg is unusually large.\n\nThe second sign is an Imix, but it might also denote the thirteenth month\nMac and therefore the Tonalamatl (13 \u00d7 20). The fourth sign is a fish\nforming a connecting link between the water represented below and the rest\nof the group.\n\n2. B is seated on the Caban sign and his arms are apparently resting on an\naltar standing in front of him, on which fire is burning, indicated by the\nIk sign, while the moon is placed below the altar.\n\nThe Caban sign below is repeated in the second hieroglyph, combined here as\nusual with a sign which may be Muluc.\n\nThe fourth sign is a head. I think the scribe meant to set down an 8 before\nit, but as there was not sufficient space for the heavy line _after_ the\nthree small circles, he indicated it by a black dot _below_ the circles.\nNow, if we call the head D's, which of course cannot be asserted\npositively, this would be day VIII Ahau, and this, in fact, is twenty days\nfrom the beginning day I Ahau, as it is meant to be in this passage. There\nis no representation of food; can this have been a fast day?\n\n3. B is seated on four astronomical signs. He wears the gala mantle and\nholds a serpent in his hand.\n\nThe second sign is _b_, and at the same time one of the astronomical signs.\nThe fourth is the iguana prepared as food, recognizable by the spines on\nits back, as on page 25b. It is drawn in precisely the same curious fashion\nin Cort. 8 and 12c; hence it is represented in the picture by the serpent.\n\n4. B is falling down from above headfirst. I believe that the numerous\nfootprints below him are only intended to represent swift motion. The\ndescent from above may only be intended here to bring the god into closer\nrelationship with the head of the bird of prey in the fourth sign. That\nthis head is again as usual joined to Kan, may refer merely to the fact\nthat it was the Maya custom to eat bread with animal food. Compare page\n27b. The second sign might be the abbreviation for the south.\n\n5. B is seated on a mat with his hand extended as if to receive something.\nHe is wet with water.\n\nThe second sign contains the mat, with what may be the sign below it, and\nthe leaf-shaped prefix probably denoting the plant from which the mat is\nplaited. The very same combination is given on page 35c and a similar one\non 38c. The fourth sign has the prefix of the west followed by two Kans, as\nif on this day (V Akbal) it had been the custom to eat tortillas without\nmeat.\n\n6. B is standing holding the hatchet. The fourth sign must denote venison,\nthe fourth article of animal food. The second seems to represent the day\nEb, with which the remaining 52 days begin, and if the prefixed 9 indicates\nnothing more than that the ninth day of the month is here meant, it is\nfurther evidence that the \"Dresdensis\" began the days with Kan and not with\nImix.\n\nIn the discussion of this Tonalamatl I have omitted the mention of a very\npeculiar feature, which as yet does not admit of explanation. I refer to\nthe numbers below the pictures. With the first picture we find 6 + 20, with\nthe second 20, with the third 19 + 20, with the fourth 6 + 20, with the\nfifth 19 + 20, and with the sixth 6 + 20, _i.e._, with the exception of the\nsecond, 26 or 39, two multiples of 13. Now the question arises, should not\none of these multiples have been set down with the second picture? There\nwas no space left for a prefixed 19. Therefore the idea suggests itself\nthat what we took to be an altar with the sign Ik above it, is intended for\nnothing else than this 19, and Ik is the 19th day, if we count from Kan as\nthe starting-point.\n\nPages 42c--45c.\n\nThis is a Tonalamatl consisting of 4 \u00d7 65 days. If written out in the usual\nway it would run as follows:--\n\n  XIII  17  IV  8  XII  8  VII  8  II  8  X  8  V  8  XIII\n  Akbal\n  Lamat\n  Ben\n  Ezanab.\n\nSince, however, the subdivisions are divided and the individual month days\nalso are given for all the parts of the whole Tonalamatl, the\nrepresentation follows the order which we have already found on pages\n31b-35b and 33c-39c. In this place, as in the two former ones, I will\nreproduce in four lines what is set down in the Manuscript in one single\nline extending over all four pages.\n\n  XIII Akbal (17)  IV Ahau (8)     XII Lamat (8)  VII Cib (8)\n                                     II Kan (8)   X Eb (8)    V Ahau (8)\n  XIII Lamat (17)  IV Chicchan (8) XII Ben (8)    VII Imix (8)\n                                     II Muluc (8) X Caban (8) V Chicchan(8)\n  XIII Ben (17)    IV Oc (8)       XII Ezanab (8) VII Cimi (8)\n                                     II Ix (8)    X Ik (8)    V Oc (8)\n  XIII Ezanab (17) IV Men (8)      XII Akbal (8)  VII Chuen (8)\n                                     II Cauac (8) X Manik (8) V Men (8)\n\nThus the days Chicchan, Lamat, Oc, Ben, Men, Ezanab, Ahau, and Akbal are\nrepeated here twice, and the others occur but once. The 4 (17 + 48)\nstrongly recalls the 4 (19 + 46) on pages 31b-35b. The repetition of six\ntimes eight days in each quarter of the Tonalamatl is closely connected\nwith the fact that there are six Chuen signs on each page, two of which,\nhowever, are omitted on page 44. From this it follows, as we have already\nfound on pages 25-28, that Chuen really denotes 8 days and that the count\nof the days in the \"Dresdensis\" begins with Kan. But the numbers 12, 15, 16\nand 17 are entirely unexplained. They show no recognizable order and always\nstand near the bundle of Chuen signs. They recall the numbers on pages\n25-28, which are equally irregular and unintelligible, and upon which, it\nis probable, light will break at the same time as it does upon these now\nunder consideration.\n\nWe come now to the purport of this passage, which seems to be a further\namplification of the contents of pages 29c-30c. The meaning is simply as\nfollows:--every 65 days the god B discards a cardinal point and the deity\npresiding over it and installs another.\n\nFrom this point of view let us now examine the four pictures.\n\n1. Page 42. B is represented here as a warrior with the front of his body\npainted red. He is aiming a blow with his hatchet at a person sunk down\nbefore him, who, from the ornament above his head, seems to be the\ngrain-deity E, the ruler of Kan and of the east, although the contents of\nthis passage really demand a deity of the south, a ruler of Cauac. In a\nvery similar way on page 27, E occurs with the completed Cauac years,\ninstead of with the Kan years just beginning. Behind B's head is the sign\nof the discarded cardinal point, the south, while below it is a vessel with\nfood, clearly a piece of venison with Kan.\n\n2. Page 43 deals not with the removal of the old cardinal point, but with\nthe introduction of the new one. Here B is rowing in a boat, as in other\npassages (29c), and Muluc, the north, has certainly a close relation to\nwater. We see here two kinds of food, while none is represented on page 45.\nThe same bird's head, which we find at the bottom of the corresponding page\n28, is placed in front of the canoe, and on 29c it is combined with the\nrepresentation of rowing a boat. On the left is the picture of a vessel\nwith Kan and the iguana. There is something resembling a net between the\nboat and the bird.\n\n3. Page 44 likewise refers to the introduction of the new cardinal point,\nwest, which is represented on page 26 by the tiger Ix. The two hieroglyphs\nin the middle of this passage must surely refer to an animal; the lower is\nthe skeleton of an animal, which we so often find as the sign of the\nlightning-dog, but also as that of the month Kankin, and the upper I take\nto be a rather vague picture of the day Oc, which certainly denotes the\ndog. Below these two signs the fish is represented as the fourth species of\nanimal food.\n\nThe picture belonging to these hieroglyphs is very remarkable. B stands\nopposite a seated personage wearing an animal's snout, which somewhat\nresembles that of the wind-beast on pages 44b and 45b and also the nose of\nthe storm-god K, who occurs on the corresponding pages 25 and 26 both with\nthe coming and the departing Ix years, as he does here with the coming\nyears. In the picture before us, the two personages seem to be throwing\nsomething resembling a rope at each other, as if these ropes were to be\ntied together. Is this meant to suggest the casting of lots by means of the\nknotting of cords, as it is represented on page 2? Or of hunting with\nsnares?\n\nPage 45 refers to the displacement of the Ix period by the Cauac period,\n_i.e._, of the west by the south. The end of the former is represented\nhere. The lightning-beast, which occurred in the preceding period, here\nlies on his back and B sits astride his body brandishing in each hand a\nburning torch as an appropriate symbol of the south. On pages 29a and 30c\nwe already saw the god riding on the lightning-dog.\n\nFinally the six interesting hieroglyphs set down in a vertical row on the\nleft of each of the four pages are still to be examined. I will give here\nin the following table what I think is a correct interpretation of them:--\n\n                   Page 42.          43.          44.          45.\n                  South (1)     East (7)   North (13)     West (9).\n                It ends (2)          (8)         (14)         (20)\n                      B (3)          (9)         (15)         (21)\n  the time of the Cauac (4),    Kan (10),  Muluc (16),     Ix (22),\n              while Kan (5),  Muluc (11),     Ix (17),  Cauac (23)\n                 begins (6)         (12)         (18)         (24).\n\nIf that which is actually set down in the Manuscript be compared with this,\nit will be seen that in 11 of the 24 places the Manuscript corresponds to\nmy hypothesis:--1, 7 and 19 are the familiar signs for the three cardinal\npoints, 8 and 20 are the sign Xul = end, which I have already frequently\nmentioned, 9 and 21 are the sign for B, 11 is Muluc, 23 is Cauac, where the\nscribe has added to the correct Kin-Cauac the sign for the year, as if the\nCauac _years_ were treated of here as on pages 26 and 27. Finally the two\nagree in 12 and 18, where the Manuscript has the compound Kan-Imix to\ndenote beginning, _i.e._, the two days beginning the series of twenty days,\none of them according to this Manuscript, and the other according to the\nmethod resembling that used by the Aztecs.\n\nThe other cases have the correct signs, but set down in the wrong place,\nthus B is changed from 3 to 2, from 15 to 16, the north from 13 to 14, the\nXul from 2 to 3, 14 to 15, the E (Kan) from 5 to 4 and 6 and Cauac from 4\nto 5, _i.e._, pushed along every time to the next place. This is all in\nfavor of my theory. As one series began at the top, the scribe incorrectly\nplaced the sign for beginning in the thirteenth place.\n\nStrange to say in the tenth place we have the very general sign _a_ in\nplace of Kan. In the 4th, 17th and 22nd, and probably also in the half\ndestroyed 6th sign, the scribe thoughtlessly put down a sign for E, which\nis proper only with Kan and should come after 5 or 10. Finally in the 24th\nplace he put a sign for A, as if it were the intention that this passage\nshould end exactly like its parallel on page 28. For, as a matter of fact,\nthe two principal sections of the first part of the Dresdensis do end in a\nvery similar way.\n\n       *       *       *       *       *\n\nPART II.\n\nPages 46--74.\n\nThe first glance at the form and contents of the second part of the\nManuscript shows that it is very different from the first. The pages are no\nlonger divided into the usual three parts and there are fewer pictures. The\nTonalamatls, which form the principal contents of the first part, disappear\nwholly, and with them both the vertical columns of day-signs and the\nhorizontal lines of numerals alternating between red and black. On the\nother hand, the large number series as well as the high numbers\nsignificantly increase and we note the appearance of the large vertical\ncolumns of hieroglyphs, which were impossible in the triple division of the\nearlier pages. We also find a large number of hieroglyphs which did not\noccur in the first part. The contents are essentially astronomical.\n\nAnd yet the two parts are so closely connected with one another that the\nidea of two independent Manuscripts must be dismissed. Especially the front\nside of the second part as far as page 60 is nothing more than an\namplification of page 24. The contents of pages 61-74 are of a more\nindependent nature, but special attention should be called to the relation\nof 31a-32a to 62-63.\n\nPages 46--50.\n\nThe entire contents of these pages must be represented as a unit, for what\nis in the main true of page 24 is also true of these pages, namely that\nthey treat exclusively of the period of 2920 days, in which five Venus\nyears of 584 days each are brought into accord with eight solar or\nterrestrial years of 365 days each. Each page is a direct continuation of\nthe preceding one. Each period of 2920 days is taken 13 times, the result\nbeing 37,960 days, which are equal to 146 Tonalamatls.\n\nI will give here first a reproduction, as it were, of the left side of the\nfive pages, omitting for greater clearness a few indifferent matters, which\nare intended only to fill the blank spaces, viz:--\n\n1. The twenty hands pointing to the right, with a knife placed over them,\nin the middle of the pages, which mean nothing more than that these parts\nof the Venus year are to be read from left to right.\n\n2. The Venus hieroglyph three lines below, repeated twenty times with the\nsign of the knife, to denote the _division_ of the Venus revolution.\n\n3. The _Akbal_ sign occurring further down, four times on each page, except\non pages 46 and 47. This is the last of the day-signs, again counting\nforward from the day Kan, and means only that henceforth the _close_ of the\nfour periods of the Venus year is indicated below, as the beginning is\nindicated above.\n\n4. The sixteen Venus signs also occurring below, except on page 48. This\nsign likewise occurs in a very similar form on Altar R of Copan.\n\nWith these omissions, the left side of these pages presents the following\nappearance:--\n\n                            Page 46.\n\n     III Cib         II Cimi         V Cib       XIII Kan\n      XI Cib          X Cimi      XIII Cib       VIII Kan\n      VI Cib          V Cimi      VIII Cib        III Kan\n       I Cib       XIII Cimi       III Cib         XI Kan\n      IX Cib       VIII Cimi        XI Cib         VI Kan\n      IV Cib        III Cimi        VI Cib          I Kan\n     XII Cib         XI Cimi         I Cib         IX Kan\n     VII Cib         VI Cimi        IX Cib         IV Kan\n      II Cib          I Cimi        IV Cib        XII Kan\n       X Cib         IX Cimi       XII Cib        VII Kan\n       V Cib         IV Cimi       VII Cib         II Kan\n    XIII Cib        XII Cimi        II Cib          X Kan\n    VIII Cib        VII Cimi         X Cib          V Kan\n\n    4 Yaxkin         14 Zac         19 Zec         7 Xul\n      North.          West           South          East\n      Gods.\n       236            326             576           584\n    9[1] Zac      19[1] Muan         4 Yax        12 Yax\n       Gods\n       East          North            West         South\n    19 Kayab        4 Zotz           14 Pax       2 Kayab\n       236            90              250            8\n\n                            Page 47.\n\n     II Ahau            I Oc       IV Ahau      XII Lamat\n      X Ahau           IX Oc      XII Ahau      VII Lamat\n      V Ahau           IV Oc      VII Ahau       II Lamat\n   XIII Ahau          XII Oc       II Ahau        X Lamat\n   VIII Ahau          VII Oc        X Ahau        V Lamat\n    III Ahau           II Oc        V Ahau     XIII Lamat\n     XI Ahau            X Oc     XIII Ahau     VIII Lamat\n     VI Ahau            V Oc     VIII Ahau      III Lamat\n      I Ahau         XIII Oc      III Ahau       XI Lamat\n     IX Ahau         VIII Oc       XI Ahau       VI Lamat\n     IV Ahau          III Oc       VI Ahau        I Lamat\n    XII Ahau           XI Oc        I Ahau       IX Lamat\n    VII Ahau           VI Oc       IX Ahau       IV Lamat\n\n    3 Cumhu           8 Zotz       18 Pax         6 Kayab\n     North             West         South           East\n     Gods.\n      820               910         1160            1168\n    3 Zotz             13 Mol       18 Uo          6 Zip\n     Gods\n     East              North        West           South\n    13 Yax             3 Pax       8 Chen         16 Chen\n      236               90           250             8\n\n                            Page 48.\n\n       I Kan          XIII Ix       III Kan         XI Eb\n      IX Kan          VIII Ix        XI Kan         VI Eb\n      IV Kan           III Ix        VI Kan          I Eb\n     XII Kan            XI Ix         I Kan         IX Eb\n     VII Kan            VI Ix        IX Kan         IV Eb\n      II Kan             I Ix        IV Kan        XII Eb\n       X Kan            IX Ix       XII Kan        VII Eb\n       V Kan            IV Ix       VII Kan         II Eb\n    XIII Kan           XII Ix        II Kan          X Eb\n    VIII Kan           VII Ix         X Kan          V Eb\n     III Kan            II Ix         V Kan       XIII Eb\n      XI Kan             X Ix      XIII Kan       VIII Eb\n      VI Kan             V Ix      XIII Kan        III Eb\n\n     17 Yax            7 Pax       12 Chen         0 Yax[2]\n      North             West         South          East\n       Gods\n       1404             1494          1744          1752\n      2 Pax            7 Pop        17 Mac      5 Kankin\n       Gods\n       East            North          West         South\n      7 Zip        17 Yaxkin          2 Uo         10 Uo\n       236               90           250             8\n\n                            Page 49.\n\n  XIII Lamat      XII Ezanab       II Lamat         X Cib\n  VIII Lamat      VII Ezanab        X Lamat         V Cib\n   III Lamat       II Ezanab        V Lamat      XIII Cib\n    XI Lamat        X Ezanab     XIII Lamat       VII Cib\n    VI Lamat        V Ezanab     VIII Lamat       III Cib\n     I Lamat     XIII Ezanab      III Lamat        XI Cib\n    IX Lamat     VIII Ezanab       XI Lamat        VI Cib\n    IV Lamat      III Ezanab       VI Lamat         I Cib\n   XII Lamat       XI Ezanab        I Lamat        IX Cib\n   VII Lamat       VI Ezanab       IX Lamat        IV Cib\n    II Lamat        I Ezanab       IV Lamat       XII Cib\n     X Lamat       IX Ezanab      XII Lamat       VII Cib\n     V Lamat       IV Ezanab      VII Lamat        II Cib\n\n     11 Zip          1 Mol            6 Uo         14 Uo\n      North           West           South          East\n       Gods\n       1988           2078            2328          2336\n  16 Yaxkin          6 Ceh          11 Xul        19 Xul\n       Gods\n       East          North            West         South\n   6 Kankin        16 Cumhu           1 Mac         9 Mac\n       236            90             250             8\n\n                            Page 50.\n\n      XII Eb            XI Ik          I Eb       IX Ahau\n      VII Eb            VI Ik         IX Eb       IV Ahau\n       II Eb             I Ik         IV Eb      XII Ahau\n        X Eb            IX Ik        XII Eb      VII Ahau\n        V Eb            IV Ik        VII Eb       II Ahau\n     XIII Eb           XII Ik         II Eb        X Ahau\n     VIII Eb           VII Ik          X Eb        V Ahau\n      III Eb            II Ik          V Eb     XIII Ahau\n       XI Eb             X Ik       XIII Eb     VIII Ahau\n       VI Eb             V Ik       VIII Eb      III Ahau\n        I Eb          XIII Ik        III Eb       XI Ahau\n       IX Eb          VIII Ik         XI Eb       VI Ahau\n       IV Eb           III Ik         VI Eb        I Ahau\n\n  10 Kankin         20 Cumhu[3]      5 Mac        13 Mac\n      North             West         South          East\n       Gods\n       2572             2662          2912          2920\n   15 Cumhu            0 Zec[4]   10 Kayab      18 Kayab\n       Gods\n       East            North          West         South\n     20 Xul           10 Zac        15 Zec         3 Xul\n       236               90           250             8\n\nLet us first examine the numbers which are regularly repeated in the lowest\nline:--236, 90, 250, and 8, and we shall find that the 584 days of the\napparent Venus revolution are divided into these four periods.\n\nThe number 236 denotes the time of the western elongation, when Venus is\nthe morning star, 90 the time of the invisibility of the planet, during its\nsuperior conjunction, 250 that of its eastern elongation, when Venus is the\nevening star, and 8 the time of its invisibility during inferior\nconjunction. The disproportion between 236 and 250 is somewhat striking.\nThese periods which need not of course be exactly equal are usually\ncomputed at 243 days. The short period of eight days is only calculated for\nvery sharp eyes; we actually find in the Anales del Museo Nacional de\nMexico II, 341 (Mex. 1882), that the Aztecs calculated only eight days for\nthe invisibility of Venus, and this period is also mentioned in the Anales\nde Quauhtitlan. The repetition of the cardinal points in the 15th and 20th\nlines of the extract given above refer to these periods; in the upper line\nto their beginning and in the lower to their close. Hence in the lower line\nthe cardinal points must advance one place and the gods belonging to them\nin the 16th and 19th lines must follow the same course.\n\nThe numbers in the 17th line indicate to which day of the period of 2920\ndays the position has advanced.\n\nBut now we see that the indication of days in the lines 1-13, the\nindication of months in lines 14, 18 and 21, and the numbers in line 17 are\nseparated from those directly to the right of them by a number of days\nequal to the numbers given in the lowest line.\n\nFrom this it follows that each day of the thirteen top lines is joined to\neach of the month dates placed just below them, forming a complete calendar\ndate. Therefore from the III Cib on the left upper corner of page 46 a III\nCib 4 Yaxkin, a III Cib 8 Zac, a III Cib 19 Kayab must be formed.\n\nAll the 4 \u00d7 13 \u00d7 5 = 260 day indications combined with three month\nindications each, show therefore that this whole passage is a huge\nabbreviation for 780 calendar dates and that the whole refers to 3 \u00d7 37,960\ndays = 113,880 days. But 37,960 which we already found on page 24, is equal\nto 146 \u00d7 260, 104 \u00d7 365, 65 \u00d7 584, 13 \u00d7 2920. I am inclined to think that I\nalso found 113,880 on page 24.\n\nBut the 3 \u00d7 37,960 = 113,880 days do not form the entire period treated of\nhere. For the three periods begin and end with the days:--\n\n  I Ahau 13 Mac (10 Muluc),\n  I Ahau 18 Kayab (3 Kan),\n  I Ahau 3 Xul (4 Cauac).\n\nHence these three dates, the second of which was found on page 24, prove\nthat the three periods of 37,960 are not consecutive, but that there is an\ninterval between them. Now between the first and second of the three dates\nthe interval is 19 years + 85 days = 7020 days, and between the second and\nthird, the interval is 26 years + 130 days = 9620 days. If these two\nperiods be added to the 113,880 days, the sum is the whole period treated\nof here, viz:-- 130,520 = 502 \u00d7 260 days.\n\nBut a truly surprising result is obtained, if, as must often be the case\nwith series, we begin not with the upper of the three dates, but with the\nlower.\n\nFrom I Ahau 3 Xul (4 Cauac) to I Ahau 18 Kayab (3 Kan) there is a lapse of\n9360 days or 12 apparent Mars years of 780 days, such as we shall find as\nthe principal subject of page 59. 9360, however, equals 25 \u00d7 365 + 235\ndays. We shall meet with this 235 again as a difference on page 63.\n\nBut from I Ahau 18 Kayab (3 Kan) to I Ahau 13 Mac (10 Muluc) there are\n11,960 days, _i.e._, the 104 Mercury years, which we found on page 24, and\nwhich we shall find again as the principal period on pages 51-58. But this\nis equal to 32 years + 280 or 33 years - 85 days. Now if 113,880, 9360,\n11,960 are added together, we have for the entire period under discussion\nhere, 135,200 days, and this is equal to 2 \u00d7 260 \u00d7 260 days. Thus the Mayas\nseem actually to have had an idea of a second power.\n\nFinally I would call attention to a singular double connection between the\nnumbers occurring here:--\n\n  37,960 - 11,960 = 26,000 = 100 Tonalamatls,\n  11,960 -  9,360 =   2600 =  10 Tonalamatls.\n\nBut if we subtract 2 \u00d7 11,960 = 23,920 from 37,960, the remainder is\n14,040, _i.e._, an extraordinary number which often occurs and is equal to\n54 \u00d7 260, 39 \u00d7 360 and 18 \u00d7 780.\n\nIn short, a Mars and a Mercury-lunar period are inserted in the two spaces\nbetween the three solar-Venus periods.\n\nNow, let us try to gain a clearer understanding of this subject by\napproaching from another side.\n\nAs we have seen, the beginning of the middle one of the three equal periods\nof 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24\nfurnished us with a day number for this date, 1,364,360, and from this the\nbeginnings of the other two periods may be computed in the following way:--\n\n  I Ahau  3 Xul  (4 Cauac) = 1,317,040,\n  I Ahau 18 Kayab  (3 Kan) = 1,364,360,\n  I Ahau 13 Mac (10 Muluc) = 1,414,280.\n\nBetween the first number and the second there are 47,320 days = 2^3 \u00d7 5 \u00d7 7\n\u00d7 13^2, and between the second and third 49,920 days = 2^8 \u00d7 3 \u00d7 5 \u00d7 13\ndays.\n\nBut, according to what has been stated above, 47,320 = 37,960 + 9360, and\n49,920 = 37,960 + 11,960.\n\nThe whole period is therefore divided as follows:--\n\nIt begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years,\nthen the great period again followed by 8 \u00d7 13 = 104 Mercury years, and\nlastly, apparently about the present time, comes the third great period,\nwhich, as already stated, ends 135,200 days after the first date.\n\nThe case assumes a different aspect, if we insert between the three dates\nthe other two from page 24:--\n\n  1,317,040 = I Ahau,\n  1,352,400 = I Ahau,\n  1,364,360 = I Ahau,\n  1,366,560 = IV Ahau,\n  1,414,280 = I Ahau.\n\nHere we have again, as examination of page 24 showed, the difference 11,960\nbetween the second and third numbers, while there is no longer any\nconnection with the periods of 37,960 days.\n\nOf the left halves of the pages we have now examined all except the twenty\nhieroglyphs of the gods. I shall mention them according to the upper place\nin line 16; the lower in line 19, where the hieroglyphs move forward only\none place, is only referred to when the two signs differ. They offer many\nproblems still unsolved.\n\nThe first sign on page 46 is an unknown sign, which, however, is repeated\nseveral times on the right side of the pages; the second is probably an\nAhau (_i.e._, D) with a prefix suggesting the snail, the symbol of birth;\nthe third is a head also occurring elsewhere, which I have not yet\ndetermined; the fourth is A; compare page 24, hieroglyph 25.\n\nPage 47. The first sign is probably K; compare the third picture on page 7a\nwith its hieroglyph; the second is C's hieroglyph with an Akbal appropriate\nto it; the third sign is Moan with the 13 belonging to it; the fourth sign\nis N's with a prefixed 4; the year-sign in the lower series is replaced by\nZac, which agrees equally well; compare page 24, hieroglyph 21.\n\nPage 48. The first sign is Kin with the Ben-Ik superfix, perhaps denoting\nG; the second is a figure similar to the year-sign with a prefixed 6. This\nsame sign in the line below has a 6, but is very different in other\nrespects; the third is an Akbal with superfix and prefix, perhaps denoting\nD; the fourth is a head which might easily be F's; compare page 24,\nhieroglyph 22.\n\nPage 49. The first sign is B's; the second, A's; the 3d, K's; compare page\n24, hieroglyph 38; the fourth is H's with a prefixed 1; compare page 24,\nhieroglyphs 23 and perhaps 37.\n\nPage 50. The first sign is E's; compare page 24, hieroglyph 38; the second\nis L, the black deity; compare page 24, hieroglyph 32; the third is an\nunknown hieroglyph with a prefixed 7, which also occurs on page 5a and 19b;\nthe fourth is the bat-god; compare page 24, hieroglyph 24.\n\nI find it impossible to discover any relation between these hieroglyphs and\nthe periods and I have as little success with the hieroglyphs apparently\nbelonging to the same cardinal point. Perhaps we should follow Seler here\n(Quetzalcoatl and Kukulcan, p. 403), who thinks these passages suggest\nconstellations with which Venus is in conjunction; this question, owing to\nthe retrogression of the planet, raises increased difficulties. It is\ncurious that the fourth of these signs on page 46 is like the fourteenth on\npage 49 (A), and perhaps the two following refer to the same god K; the\nfirst two are separated by 1494 days and the latter by 1508 days.\n\nWe come now to the _right_ half of the pages. Interpretation is rendered\nimpossible by the destruction of the top part. For we do not even know\nwhether the upper hieroglyphs occupied three or four rows each, the latter\nbeing the case at least in part, and there may have been a superscription\nover the day signs in the left half.\n\nThese upper signs are always followed by a picture, then three rows of\nhieroglyphs, then a second picture and next two rows of hieroglyphs and\nlastly a third picture.\n\nLet us first examine the pictures:--\n\nAt the top of pages 46-49 there is on each page a deity, who with his right\narm extended is offering or receiving something. He is seated on\nastronomical signs; on page 46 B's head accompanies these signs. On pages\n46 and 48 the deity is undoubtedly the old woman with tiger claws, who\nusually pours streams of water from a jug (compare pages 39, 43 and 74). I\ncannot identify the personage on pages 47 and 49. The object in the deity's\nhand seems invariably to be a cup of foaming pulque. On page 49 another\nobject is placed above the cup, which I am unable to determine. The fifth,\npage 50, differs from the other four and forms the connecting link, as it\nwere, between the upper row of pictures and the middle and lower ones.\nHere, too, a personage is represented sitting on astronomical signs and\nexhibiting symptoms of violent anger toward a second person opposite him\nholding the cup in his hands. Both personages are painted as warriors.\n\nThe middle pictures on all the pages represent a warrior in a\nhalf-kneeling, half-crouching posture, holding spears or a shield in the\nright hand and brandishing a hatchet in the left. The shield on page 46 is\ndoubtless a representation of the sun-glyph; and on 47 the Venus sign is\ncombined with the head ornament. The hieroglyphs of these deities occupy\nthe first place in the middle line of the three lines above the pictures.\n\nThe five lower pictures represent a creature lying on the ground, pierced\nby arrows and spears. On page 47 it is a jaguar; at any rate it is the same\nanimal found on pages 29a, 30c and 45c; a very similar creature pierced by\narrows is given in the Cod. Vat. B.; compare also the pictures in Seler's\n\"Venus-periode,\" page 371. On the other four pages this creature is in\nhuman guise. On page 50 where, differing from the other four pages, this\nfigure is represented lying with the head to the right, it is plainly\nshedding tears. Seler takes this figure to be E on page 48 and the tortoise\non page 49. The varying periods of time occupied by the revolution of the\nplanets is plainly conceived of as contest. But who is the victor in this\ncontest? The planet with the longer or with the shorter period of\nrevolution? Owing to obliteration only a small part of the hieroglyphs of\nthe top section is legible.\n\nOn page 46 we see the Venus sign and E's hieroglyph; on page 47 the sign\n_c_, which occurs frequently on these pages, and is probably always\nconnected with Moan (the Pleiades and thus with the year). The numeral 1,\nprefixed to an obliterated sign on page 47, is still legible, and we find\nit repeated on the lower part of the same page. There is rather more to be\nseen on page 48:--first the elongated head _q_ with the Ben-Ik superfix,\nthen the sign _a_, beside it that for the west with a prefix, in the line\nbelow an Ahau, next, an Akbal sign with the prefix of the north, and lastly\na Moan sign.\n\nOn page 49 we see sign _c_ again occupying the first place, then o with\nBen-Ik, and in the lower line the year sign with that for 20 or the moon as\na superfix, and to the right of it the head with the Akbal eye, probably\ndenoting D.\n\nThis top part of the page is best preserved on page 50. In the third line\nfrom the bottom we see the Venus sign and beside it the Moan sign, below, a\nCauac, then a Kin with the Ben-Ik superfix, then a Kan-Imix. Finally, in\nthe first place in the lowest row there is a Kin sign and in the second\nplace a sign resembling the year-sign, both having the same superfix, the\nnext sign is again _c_ and the last is a half-effaced sign, of which only a\nMuluc is distinguishable.\n\nOur knowledge of the middle section of these pages is somewhat more\ndefinite. There are twelve hieroglyphs on each page, which I will number in\nthe following order:--\n\n  1   2   3   4\n  5   6   7   8\n  9  10  11  12.\n\nUnquestionably these 5 \u00d7 12 signs refer to a Venus year, more exactly to\nthe _beginning_ of it, the period of the east. The first sign, which is a\nhand pointing to the right, merely refers here, as on the left side, to the\ndirection in which this is to be read; the second sign is always the sign\nfor the east, and the sixth invariably that for Venus.\n\nNotice should be taken of the fact that the signs of the Moan and\nscreech-owl or death-bird are recurrent, that of the Moan appearing on page\n46, sign 7; 48, 3; 49, 11; 50, 11; and that of the death-bird on page 47,\nsign 3; 48, 11, 49, 3, 50, 3 and 7, _i.e._, only in places 3, 7 and 11,\nwhich indicates that the 12 signs are divided each time into three times\nfour.\n\nIt is further to be noted that the five gods, who are represented on page\n24 by hieroglyphs 36-40, always recur in the ninth place in the order of\nthe pages:--the god represented on page 24 by sign 36 is the 8th on page\n49; the 38th on the same page is the 11th on page 46 and the 12th on page\n50; the 39th is the 12th on page 47, and the 40th may be the 5th on page\n49, though this is hardly possible. On page 49 the 9th hieroglyph seems to\nbe the 39th on page 24 joined to the sign for the month Kayab.\n\nOf the twenty gods on the left side of these pages, I have already remarked\nthat E, who on page 24 occupies the 38th place, and the 11th on page 46,\nalso occurs as the 9th on page 48 and the 12th on page 50.\n\nIt is doubtless of special significance that the sign of the first of the\ntwenty deities on the left side of page 46 is repeated on the right as the\ntenth sign on all the pages (on page 47 also in the eleventh place where it\nhas a prefixed 3). It seems as if this sign, which is otherwise quite\nunfamiliar, might be connected with the sun and regarded as a contrast to\nthe Venus sign in the sixth place.\n\nAlso the 9th deity of the left side, the 1st of page 48, reappears in the\n4th place on page 49; the 10th deity, the 2nd on page 48, in the 12th on\npage 49; the 15th deity, the 3d on page 49, in the 9th on page 46 and the\n8th on page 49 (as already stated); the 18th, the 2nd on page 50, in the\n5th on page 46.\n\nThe 2nd of these deities is suggested by the 8th on page 47, perhaps also\nby the 5th on page 50; the 3d and 13th seem to be A and to recur in the 3d\nplace on page 46.\n\nOn the other hand C, the god who, as I believe I have proved, is connected\nwith the day-sign Chuen, does not appear on the left side. Now the 4th sign\non page 46 contains a Chuen, which in the 12th sign on page 48 is probably\ncombined with a Muluc, in the 12th on page 49 with Yax and a prefixed 6,\nand in the 4th sign on page 50 with C's sign, _i.e._, as a rule Chuen\nstands in the 4th place in a line.\n\nAs the gods E and K already mentioned also appear on pages 25-28 in\nconnection with the change of the year, so we find the tiger on the top of\npage 26, and I believe this animal occurs again in the 7th sign on page 47.\n\nOf the day-signs I take the 4th on page 47 to be Kan, the 7th on page 48 to\nbe Caban, and the next sign, the 8th on page 48, to be Muluc. Now if we\ntake into consideration the fact, that of the three periods of the month\nsigns on the left side of these pages, the 18th (the middle) line is the\nmost important, owing to its ending, 18 Kayab, alone, if for no other\nreason; furthermore, that in this middle period the second Venus year\nalways ends with a Kan year and the third with a Muluc year, one is\nnaturally led to suppose that the illegible sign 12 on page 46 is an Ix\n(for thus the first Venus year ends) and that the days Cauac and Kan might\nhave been found among the obliterated day-signs on pages 49 and 50.\n\nI shall examine the remaining signs in the order of the pages.\n\nSign 8 on page 46 is the same compound of Yax and Kin having as a superfix\nthe sign assumed by me to be the numeral 18, which occurs again in the\nlower group on page 50 and also on page 27.\n\nIn the number 11 prefixed to the fifth sign on page 47, the 1 seems to be\nindistinct and may not belong here. If we correctly assume that this number\nis 10, then the sign is the same as the 34th on page 24, to the discussion\nof which I beg to refer my readers.\n\nSign 8 on page 47 is an indistinct compound, the first part of which I\nsupposed above to be the sign of the second deity on page 46.\n\nI cannot explain 4 and 5 on page 48.\n\nAs yet I do not understand sign 5 on page 49, which we seem to have met\nbefore on page 22c.\n\nSign 7 on page 49 is the moon, which is very curious here.\n\nI would like to call special attention to signs 5 to 8 on page 50. I\ninterpret the passage thus:--At the time of the summer solstice after the\nreappearance of the Pleiades, the change of the Venus year takes place\n(this time). I have already discussed the Venus sign in the sixth place and\nthe screech-owl so closely connected with the Moan (Pleiades) in the\nseventh place. Sign 5 connects the sun (Kin) with the Ahau (lord) and the\ncross-hatching on the left of it, which I have assigned to the tortoise and\nthus to the summer solstice (Zur Entzifferung III, 3). Sign 8 is recognized\nas very appropriate to the change of year; compare the first sign of the\nmiddle section on pages 25-28. All this points to the day 18 Kayab, of one\nof the Kan years, if, as I stated above, we base our computation on the\nmiddle series of dates.\n\nNow we have yet to examine the eight signs of the lower group, which we\nwill do in the following order:--\n\n  1  2  3  4\n  5  6  7  8.\n\nRegarding the beginnings of these groups, I will venture a bold surmise,\nwhich will, I hope, be improved upon by some one else. It concerns the\nfirst sign of four of these five groups, which seem to me to refer to the\nend of the Venus year, as those above refer to the beginning. This sign has\nthe following form:--\n\n[Illustration]\n\nI see in this the term of 73 days, which is the fifth part of the 365 days\nof the solar year and the eighth part of the 584 days of the Venus year:--\n\nIt is combined with Chuen in all four cases (pages 46, 48, 49 and 50). But\nI attribute the meaning of eight days to this Chuen sign, as I did on pages\n25-28 and 42c-45c, though I am doubtful in these as in other cases.\n\nPage 46 contains the sign for 73 with a Chuen under it, and a 1 prefixed to\neach sign; _i.e._, 1 \u00d7 8 \u00d7 73 = expiration of the first Venus year.\n\nOn page 48 Chuen follows the sign for 73 and each sign has a 3 prefixed to\nit; _i.e._, 3 \u00d7 8 \u00d7 73, expiration of the third Venus year.\n\nOn page 49 the two signs again stand side by side, but the prefix is a 7\ninstead of the expected 4. By an error this 4 has been added to the 3 of\nthe preceding page, but, for a wholly unintelligible reason, prefixed to\nthe crouching person below the Chuen, as if to correct the 7.\n\nPage 50 again has the sign for 73 above and the Chuen below. A prefixed 5\nwould seem to be in order; instead of it, there is a 10, one 5 for the 73\nand another 5 for the 8 days. In this connection let me say that I believe\nI have found on page 27, top left, the year of 365 days divided into 5 \u00d7\n73.\n\nPage 47 differs from the others. Above two oval bodies appears the\ncross-hatched figure resembling a clamp, like the one in the middle group\nof page 50 in the fifth place, which I ventured to refer to the summer\nsolstice. There is a 1 prefixed to it. Is this equivalent to a union of two\nVenus revolutions?\n\nNext we repeatedly meet here, as we did in the middle groups, with the Moan\nsign and that of the screech-owl belonging with it; the former is the 6th\nsign on page 46 and page 50, and the latter is the 3d and 7th on page 47,\nthe 7th on page 49 and finally the 2nd and 4th on page 50.\n\nThe moon is represented in the 5th sign on page 48 and in the 3d on page 49\nand indistinctly in the 4th on page 48.\n\nThe cardinal points occur here several times. The 3d and 7th signs on page\n46 have at least the superfix of the south as a prefix; the 8th on page 47\napparently has the east, but with the familiar cross-hatched sign prefixed;\nthe 7th on page 48 plainly has the east, the 3d on page 50 the prefix of\nthe north prefixed to the cross _b_, and the 8th on page 50 the west, thus\napproximating the usual order and distribution.\n\nOf the gods I note the Akbal head, perhaps intended for D, in the 4th place\non page 46, also in the 3d on page 48, and lastly in the 5th on page 49,\nthe first two times with the Ben-Ik superfix, and in the 2nd place on page\n47 the sign for A.\n\nIn the 4th place on page 47 we have the tortoise as the sign of the month\nKayab or of the summer solstice, in the 6th on page 47 the lightning-beast\nor the month Kankin with a Ben-Ik superfix; the beast itself is pictured\nbelow, and the same hieroglyph also with the Ben-Ik superfix is the 8th\nsign on page 49.\n\nIt is hard to decide whether the sign 4 on page 49 represents the god F\nowing to the line through the eye, or a female by reason of the prefixed\nlock.\n\nSign 7 on page 50 represents the deity whose sign began the series of\ntwenty gods on the left of page 46 and which we have already met with\nseveral times in the centre of the right side. We recognize the prefix as\nhaving occurred in the middle group of the same page.\n\nSign 6 on page 48 is a Kin combined with an unfamiliar sign. Sign 5 on page\n50 contains a Kin with a Yax and probably with 18 as a superfix (as on\npages 27 and 46 middle).\n\nSign 6 on page 49 contains a crouching person with a 4 which is probably\nout of place here and to be regarded as a correction of the 7 above it.\n\nSign 5 on page 46 contains a Mac denoting the thirteenth Uinal or a\nTonalamatl, and having the sign _p_ as a superfix and a double Ik as a\nprefix.\n\nSign 3 on page 46 merits special attention, because it contains the\nduplication of the sign, which, at the end of the first part of the\nManuscript, pages 29-41, always began the groups of hieroglyphs on the\nlower third of the pages.\n\nI do not understand the second hieroglyph on page 46 and the 5th on page\n47.\n\nIn conclusion I would call attention to the fact that the last hieroglyph\non page 48 is very peculiar. As on pages 51, 52, 61 and 69 it has the\nmeaning of 18,980 days and consists of an Imix with a comprehensive\nsuperfix; its prefix is a 7.\n\nBut what is the meaning here of 7 \u00d7 18,980 = 132,860? When we recall the\nstatement made above that the whole section of pages 46-50 embraces 130,520\ndays, or, according to another calculation 135,200 days, it is a striking\nfact that 132,860 is exactly the mean of the two numbers, being separated\nfrom each by 2340 days = 9 \u00d7 260. Can it be an accident that on the next\npage (page 49) the fourth Venus revolution is reached, for 4 \u00d7 584 = 2336,\n_i.e._, almost 2340? The hieroglyph discussed here would not be so\nextraordinary on page 50. I will not venture to assert as to the 511 in\n132,860 = 511 \u00d7 260, that it is connected with the 511 which will appear as\nthe difference on page 58.\n\nBefore leaving these pages, I will give a brief survey of the two signs of\nthe screech-owl and the Moan (hieroglyph _c_ and the lower part of _d_)\nwhich occur on these pages with such marked frequency.\n\nIn spite of obliteration, the first of these two signs is distinguishable\nin the top groups on pages 47, 49 and 50, in the middle groups on pages 47,\n48, 49 and twice on page 50, in the lower groups on page 46, twice on page\n47, once on 49, twice again on 50, making 14 times in all. A few additional\ncases might be added to these where the similar hieroglyph of the moon may\nhave been set down instead of the one in question.\n\nOn the other hand the second sign, always provided with the same prefix and\nsuffix as the first, occurs in the top groups on page 48 and 50, in the\nmiddle of pages 46, 48, 49 and 50, and in the lowest on pages 46 and 50, 8\ntimes in all.\n\nSince the subject here is astronomical, it is suggestive less of a deity or\na sacrifice than of a period of time to which the allied page 24 has\nalready referred (see page 110 of this book). The inner meaning of these\npages is of course still enveloped in mystery.\n\nPages 51a--52a.\n\nI shall begin the discussion of this very peculiar section with the\nremarkable fourth column on page 52, which, very possibly, the scribe ought\nto have placed at the beginning; for it looks like a repetition of the\nsection on pages 46-50, while everything else on the left and right of it,\napparently belongs together.\n\nIf we omit the two hieroglyphs at the top, which I regard as belonging to\nthe two rows of hieroglyphs extending over these two pages, we shall have\nthe following result, according to my point of view:--\n\n    1          5\n  Chuen       360\n    2       18,980.\n\nSince, as is frequently the case, the Chuen will here have the value of 8\ndays and the 5 with the sign for 360 may be regarded as 365, this group\nmight denote 8 \u00d7 365 = 2920, but actually be 2 \u00d7 18,980 = 37,960. Both\nnumbers are the basis of the section included on pages 46-50. And in the\nsame way the 13 repeated 13 times seems to me to refer to the 13 series of\ndays on those pages, which begin with the 13th day of the Uinal.\n\nThe two rows of hieroglyphs are in the main destroyed. We can still\nrecognize in the second and third columns of page 51 the signs for end and\nbeginning, which we often find in the vicinity of numbers; in the second\nand third columns of page 52, the sun and moon; in the fourth column, the 8\ndays of such significance here and in the fifth and sixth, the normal date\nIV Ahau 8 Cumhu repeated twice.\n\nAs the problem on pages 46-50 was to bring into accord the solar year with\nthe Venus year and consequently also the Tonalamatl, _i.e._, to combine\n365, 584 and 260, so the aim here is first of all to bring the Tonalamatl\ninto unison with the Mercury year (115). For this purpose the number 11,960\nis employed. This is equal to 46 \u00d7 260 = 104 \u00d7 115, including, therefore\njust as many Mercury years as there were solar years in the preceding\nsection. 11,960 is also 8 \u00d7 1495, and this 8 is significant here, for, as\nwe shall see directly, the day forming the basis of this calculation is XII\nLamat, which comes 8 days after the normal date IV Ahau.\n\nThe series given here is based, therefore, on 11,960 and consists entirely\nof multiples of this number, which, it is true, are recorded with the usual\nirregularity. The members of this series, representing the greatest values,\nwhich are set down in red numbers among the black, are the 31st and 39th\nmultiples of 11,960, which are separated from each other by 8 \u00d7 11,960,\nviz:--370,760 and 466,440. All these numbers, of course, denote the day IV\nAhau.\n\nThe day XII Lamat as the actual starting-point of the Mercury revolution is\nnot introduced until we come to the dates placed below the series. Here we\nfind the days XII Lamat, I Akbal, III Ezanab, V Ben and VII Lamat written\none below the other, and repeated seven times. Each of these days is\nseparated from the next by 15, and the last of one row and the first of the\nnext on the left are 200 days apart, hence the whole is equal to 7 \u00d7 260 =\n1820 days. From XII Lamat begins also the Peresianus, pages 21-22.\n\nNow these dates are connected with the four large numbers, which we find on\npage 52, but between the third and fourth, one number corresponding to the\nday V Ben is omitted for lack of space.\n\nThese four numbers, to which I have added the corresponding dates, are as\nfollows:--\n\n  1,412,848 = XII Lamat I Muan (6 Muluc).\n  1,412,863 = I Akbal 16 Muan (6 Muluc).\n  1,412,878 = III Ezanab 11 Pax (6 Muluc).\n  1,434,748 = VII Lamat I Muan (1 Muluc).\n\nIt is curious that while the first three are separated from each other by\n15, between the 3d and 4th, or rather between the missing 4th and 5th, 84 \u00d7\n260 days are inserted in excess of the required 15, _i.e._, 21,855. This,\nhowever, is not accidental, but is due to the fact that between the first\nnumber and the last exactly 21,900 = 60 \u00d7 365 days have elapsed. This\nnumber is, however, = 18,980 + 2920, i. e., the sum of two very important\nnumbers, in the first of which the Tonalamatl and the solar year accord,\nwhile both the solar and Venus years occur in the second.\n\nI must here call attention to the fact that the four numbers are not\nobtained without slight corrections, since in the 20-place of the third, I\nhave put a 11 instead of 10, while in the 360-place of the fourth, I have\nomitted the three dots, _i.e._, set down a 5 instead of the 8.\n\nOf these four dates, which were doubtless not far removed from the time of\nthe scribe, the three last are only the result of the first. Day XII Lamat\nis the most important. As the beginning of a Mercury period it should be\nregarded in the same way as I Ahau of the Venus period and IV Ahau of the\nsolar period; and the very next day, XIII Muluc, will subsequently be seen\nto be the beginning day of the Mars period.\n\nThe four dates XII Lamat, I Akbal, III Ezanab and VII Lamat are set down in\nthe Manuscript directly below the numbers.\n\nNow in the first column on page 51 we again find a day XII Lamat, as is\nexpressly stated beneath it. It has the number 1,578,988 and the\ncorresponding date is XII Lamat 6 Cumhu (6 Kan). This day, however, is\nseparated from the same day on page 52 (1,412,848 = XII Lamat I Muan 6\nMuluc) by 166,140 days, that is by 8 \u00d7 18,980 + 14,300 = 639 \u00d7 260, _i.e._,\nby 8 so-called Katuns increased by 55 Tonalamatls. Here 58 \u00d7 260 = 15,080\nseems to have been added to 252 (XII Lamat - IV Ahau) and the sum\nsubtracted from 14 Ahau-Katuns = 1,594, 320. I could obtain this number\nonly by substituting 1 for 0 in the 20-place.\n\nIn the Manuscript the sign XII Lamat is set down above and below this\nnumber. I must leave undetermined whether the 8 directly above the number\nand combined with Kin and the Katun sign refers only to the 8 Katuns or at\nthe same time also to the 8 days from IV Ahau to XII Lamat.\n\nIt is also to be noted here that once before on page 24 of this Manuscript\n(which forms the basis of this section) 8 \u00d7 18,980 = 151,840 days was found\nto be the difference between 185,120 and 33,280, and that there, too, if my\nrestoration is correct, it was the highest term of the series = 4 \u00d7 37,960.\n\nFinally, in the first column of page 51, we have the complete normal date 4\nAhau 8 Cumhu (9 Ix). But below this, between red numerals denoting the\n1,578,988 mentioned above, there is set down in black the number 1,268,800.\nThis corresponds to the date IV Ahau 3 Zip (2 Cauac). It may have been\nformed by adding 16,120 = 62 \u00d7 260 to 11 Ahau-Katuns = 1,252,680. It is,\nhowever, not only equal to 4880 \u00d7 260, but also to 158,600 \u00d7 8, therefore\nalso divisible by the interval between IV Ahau XII Lamat, as well as by 104\n= 8 \u00d7 13, while on the contrary it is not as we should expect, divisible by\n11,960. I have changed the 11, in the 20 \u00d7 11, to 8 by omitting one line\nand adding two dots, for otherwise the result would not be the one\nrequired.\n\nThe magnitude of the number recalls the one on page 31, which is only 260\nless, and that on page 62.\n\nFinally it should be noted that the two large numbers on page 51 are\nseparated from one another by 310,188 days = 849 years and 303 days, which\ncorresponds exactly to the dates given for each. One may be situated as far\nin the future as the other is in the past, but this does not necessarily\nmean that the present coincides exactly with 1,423,894.\n\nPages 51--58.\n\nThus far we have examined only the upper halves of pages 51 and 52 and have\nstill to consider the lower, but not until we have finished the upper parts\nof pages 53-58 of which the former are the continuation. We have first to\nconsider the series, then the pictures and lastly the hieroglyphs.\n\nAs on page 24 we found multiples of the number 2920 (= 8 \u00d7 365 = 5 \u00d7 584),\nwhile on pages 46-50 it was divided into four unequal parts, so on pages\n51-52 we find multiples of the number 11,960 (104 \u00d7 115 = 46 \u00d7 260) while\non pages 53-58 it is divided into 69 unequal parts. On pages 51-52 it was\nthe aim to combine only the Mercury course with the Tonalamatl, but here we\nare confronted with the additional problem of bringing the lunar revolution\ninto accord with these two.\n\nThe lunar revolution, which we assume to be 29.53 days, of course requires\nfractional computation, of which the Mayas either were ignorant or which\nthey timorously avoided; like the ancient Egyptians, who were acquainted\nonly with fractions having 1 as numerator, or beyond these at most with 2/3\n(see Hultsch, \"Die Elemente der \u00e4gyptischen Teilungsrechnung,\" 1895, page\n16).\n\nNow the Mayas had determined the lunar revolution so exactly that they\nperceived the incompatibility of the period of 11,960 days with a multiple\nof lunar revolutions. They found that 405 lunar revolutions amounted\napproximately to 11,958 days, which is, in fact, the largest number on the\nsecond half of page 58. In order not to drop the significant 11,960\naltogether, they made use of a very shrewd artifice. They took as the\nstarting-point the day XII Lamat, corresponding to the number 11,960, and\nset down XI Manik before it and XIII Muluc after it. Now if the count began\nwith XIII Muluc and ended with XI Manik, it actually resulted in 11,958.\n\nTherefore what the Manuscript presents here is, in the first place, the\nseries, which is this time to be read from left to right. Below it are the\nthree days belonging to each member of the series and then a number for\neach member stating the interval between it and the preceding one. The\nmembers, the days and the differences must correspond with one another. It\nis, therefore, no longer necessary to pay especial attention to the two\nlatter. They will serve merely to control and to correct the manifold\nerrors.\n\nThe entire period of 11,958 days was doubtless first divided into three\nequal periods of 3986 days. And in order still further to subdivide these\nshorter periods, the term of 177 days was employed as far as it would go;\n177, however, is the half of a lunar year of 354 days, made up of 6 months\nof 30 days and 6 of 29 days, thus allowing 29.5 days in round numbers for\neach month.\n\nNow 177 is = 3 \u00d7 29 + 3 \u00d7 30. The average, 29.5, however, is too short for\nthe length of the lunar revolution. In order to raise it as nearly as\npossible to the exact time, two other numbers were introduced at certain\npoints of the series, viz:--148 = 2 \u00d7 29 + 3 \u00d7 30, 178 = 2 \u00d7 29 + 4 \u00d7 30.\n148 = 5 months of 29.6 days, while 178 = 6 months of 29-2/3 days. Now let\nus see in what _proportion_ these 148 and 178 days were distributed among\nthe periods of 177.\n\nFirst we see that the period of 3986 days (_i.e._, a third of the whole)\nwas divided into 3 sections of 1742, 1034 and 1210 days, as follows:--\n\n  1742 =  8 \u00d7 177 + 148 + 178\n  1034 =  4 \u00d7 177 + 148 + 178\n  1210 =  6 \u00d7 177 + 148\n  ----------------------------\n  3986 = 18 \u00d7 177 + 3 \u00d7 148 + 2 \u00d7 178.\n\nThis is equal to 135 months of 29.526 days each. Now the question arises\nhow did the Mayas express this fraction?\n\nPerhaps some time in the future it will be found, that following their\nvigesimal system, they designated it approximately thus:--\n\n29 + \u00bd + 1/40 + 1/800.\n\nThe _whole_ period of 11,958 days was divided as follows:--\n\n  3 \u00d7 1742 = 24 \u00d7 177 + 3 \u00d7 148 + 3 \u00d7 178\n  3 \u00d7 1034 = 12 \u00d7 177 + 3 \u00d7 148 + 3 \u00d7 178\n  3 \u00d7 1210 = 18 \u00d7 177 + 3 \u00d7 148\n  ---------------------------------------\n  3 \u00d7 3986 = 54 \u00d7 177 + 9 \u00d7 148 + 6 \u00d7 178.\n\nThus for every 6 parts of 177 days there was consequently 1 of 148 and to\nevery 9 parts of 177, 1 of 178.\n\nSince 177 and 178 include 6 months each, while 148 equals 5 months, the\nentire length of the period is 405 months, which are divided into 69\nperiods.\n\nIt was necessary to discuss all this before I could introduce the entire\nseries itself. In the following table I have set down the numbers and added\nto them the differences between each number and the preceding one (to the\nfirst, the interval between it and the zero point), just as they are given\nin the Manuscript. An asterisk is added to show that the number has been\ncorrected by me and is wrong in the Manuscript, owing to a mistake either\nin writing or in computation. The three columns correspond to the three\ndivisions of 3986 days, and the two horizontal lines divide the periods of\n1742, 1034 and 1210 days.\n\n    Page 53a:      |  24.  4163* 177   |  47.  8149  177\n   1.   177  177   |  25.  4340  177   |  48.  8326  177\n   2.   354* 177   |  26.  4488  148*  |  49.  8474  148\n   3.   502  148   |    Page 58a:      |  50.  8651  177*\n   4.   679* 177   |  27.  4665  177   |    Page 55b:\n   5.   856  177   |  28.  4842  177   |  51.  8828  177\n   6.  1034* 178*  |  29.  5020  178*  |  52.  9006  178*\n    Page 54a:      |  30.  5197  177   |  53.  9183  177\n   7.  1211  177   |    Page 51b:      |  54.  9360  177\n   8.  1388  177   |  31.  5374  177   |  55.  9537  177\n   9.  1565  177   |  32.  5551  177   |  56.  9714  177\n  10.  1742* 177   |  33.  5728  177   |\n  -----------------+-------------------+-----------------\n  11.  1919  177   |  34.  5905  177   |  57.  9891  177\n  12.  2096* 177   |  35.  6082  177   |  58. 10068* 177*\n  13.  2244* 148   |  36.  6230  148   |    Page 56b:\n    Page 55a:      |    Page 52b:      |  59. 10216  148*\n  14.  2422* 178   |  37.  6408  178*  |  60. 10394  178*\n  15.  2599* 177   |  38.  6585  177   |  61. 10571  177\n  16.  2776  177   |  39.  6762  177   |  62. 10748  177\n  -----------------+-------------------+-----------------\n  17.  2953  177   |  40.  6939  177   |    Page 57b:\n  18.  3130  177   |    Page 53b:      |  63. 10925  177\n    Page 56a:      |  41.  7116  177   |  64. 11102  177\n  19.  3278  148   |  42.  7264  148   |  65. 11250  148\n  20.  3455  177   |  43.  7441  177   |  66. 11427  177\n  21.  3632  177   |  44.  7618  177   |  67. 11604  177\n  22.  3809  177   |  45.  7795  177   |    Page 58b:\n    Page 57a:      |    Page 54b:      |  68. 11781  177\n  23.  3986  177*  |  46.  7972  177   |  69. 11958  177\n\nNo one acquainted with the cursoriness of the Maya Manuscripts will be\nsurprised that among 138 numbers I have declared 21 to be wrong.\nFurthermore the 21 errors are lessened by the fact that six of them are\nreally only one, for in all 6 cases where the difference is 178, the scribe\nhas overlooked this and written down the usual 177, although the numbers\nand the days of the series very correctly indicate 178. Again the three\nerrors in groups 58 and 59 are also only one, for the author had confused\nthe differences 177 and 148 and had, therefore, to write down 10,039\ninstead of 10,068. In group 4 the error is merely the omission of a line\nmeaning 5. The scribe must have been at the same time the computer and\ntherefore the actual author of the Manuscript.\n\nFurthermore I must call attention to the regular position of the\ndifferences 178 and 148. In the three periods of 1742 days the 178 always\noccupies the 6th place and in the periods of 1034 it is always in the 4th\nplace. This difference appears, therefore, in groups 6, 14, 29, 37, 52 and\n60, _i.e._, 8, 15, 8, 15 and 8 groups apart; but it is entirely lacking in\nthe periods of 1210 days. And in all nine sections the 148 occupies the\nthird place, _i.e._, directly in front of the pictures, which will be\ndiscussed immediately, therefore in groups 3, 13, 19, 26, 36, 42, 49, 59,\n65, _i.e._, at intervals of 10, 6, 7, 10, 6, 7, 10 and 6 groups. But I must\npoint out an error fraught with consequences. Groups 22 and 23 quite\ncorrectly have the difference 177, but in this single instance the scribe\nhas written down 178 and hence has computed the three days belonging to it\nas VII Ix, VIII Men and IX Cib instead of VI Ben, VII Ix and VIII Men, and\nfrom here on to the close he is always one day in advance, so that on page\n58 group 69 ends with the days X Cimi, XI Manik and XII Lamat, while it\nought to have ended with IX Chicchan, X Cimi and XI Manik.\n\nSo much for the series. Vid. on this series my paper \"Zwei\nHieroglyphenreihen in der Dresdener Mayahandschrift\" (Zeitschrift f\u00fcr\nEthnologie, 1905, numbers 2 and 3). Let us turn next to the ten pictures\nwhich are inserted in this series, three of which appear at the end of each\nperiod of 2920 days as on pages 46-50. Let us attempt to advance a step\nfurther in the darkness which still surrounds us here.\n\nOne of these pictures, the 8th, which is on page 56b, is in the wrong\nplace, owing to the error in computation in Groups 58 and 59 to which I\ncalled attention above. It belongs not _before_ but _after_ group 59, the\nfirst on page 56b. This is indicated in the Manuscript itself. For in group\n59 the two hieroglyphs, usually placed above each group, are missing and we\nfind instead of them the sign resembling a snail, which is doubtless a very\nmuch emphasized zero (compare my \"Erl\u00e4uterungen,\" page 29), which indicates\nthat the section designated by a picture closes with this group.\n\nHaving corrected this error we see that the ten pictures are on the\nfollowing pages and come after the following numbers of the series:--\n\n   1.   53a     502\n   2.   55a    2244\n   3.   56a    3278\n   4.   57a    4488\n   5.   52b    6230\n   6.   53b    7264\n   7.   54b    8474\n   8.   56b   10216\n   9.   57b   11250\n  10.   58b   11958.\n\nFrom this it follows that a picture is assigned to each of the nine\nsections composing the series. They are placed, however, not at the\nbeginning or end of the section, but always after the expiration of 502 (=\n2 \u00d7 177 + 148) days. The pictures are thus separated from one another by\n1742, 1034 and 1210 days, which intervals correspond exactly to the length\nof the nine sections. But the last picture is separated from the preceding\none by 708 days, and as it has a character quite its own, it must be\ndiscussed separately. But these 708 days with the 502 days of the beginning\nquite regularly amount to 1210 days, and the series is therefore to be\nconsidered as a recurring one.\n\nNow these nine pictures might very easily be regarded as forming a new\nseries, which is inserted in the original one and which has the day 502 as\nits zero-point. In that case, we shall have to subtract 502 every time from\nthe days set down in the Manuscript. This new series may be represented\nthus:--\n\n   1.   53a       0\n   2.   55a    1742\n   3.   56a    2776\n   4.   57a    3986\n   5.   52b    5728\n   6.   53b    6762\n   7.   54b    7972\n   8.   56b    9714\n   9.   57b   10748.\n\nIt is certainly remarkable that the last number, 10748, corresponds so\nclosely to the time of the revolution of Saturn, which is computed at 10753\ndays. For owing to the slowness of its progress, the Mayas may have known\nnot only the apparent but also the actual revolution of Saturn. Besides the\napparent revolution of Saturn (378 days from one superior conjunction to\nthe next) could not be made to coincide very well with the length of the\nsolar year. I will immediately present a further confirmation of my theory.\n\nAll these pictures have rectangles above them, of which I have spoken in my\n\"Erl\u00e4uterungen,\" page 16, and which always enclosed two or three\nhieroglyphs in which, with due hesitation, I assumed to be the signs of the\nsun, moon, and planets. This theory has as yet called forth no serious\nopposition.\n\nNow in the passages just mentioned, I indicated the following figures as\nthe signs of Saturn:--\n\n[Illustration]\n\nThese figures actually occur in all the nine pictures with the exception of\nthe first, which has no rectangle at all, and where in true Maya fashion,\nthe zero-point is concealed.\n\nI go still further in my bold hypothesis. The time of the apparent\nrevolution of Jupiter has been placed at 397 days. The Mayas, I think,\ncomputed it at 398 days. In the passage alluded to I regarded the following\nas the sign for Jupiter:--\n\n[Illustration]\n\nWe find these signs in pictures 4, 6, 7 and 9. The corresponding numbers\nreduced for the revolution of Saturn are 3986, 6762, 7972 and 10,748. I\nassume that the third picture, _i.e._, the number 2776, is another\nzero-point, in consequence of which the sign is here suppressed, and that\nstill another is the tenth picture with the number 11,958, which has no\nrelation to the revolution of Saturn.\n\nIf we compare these numbers with the 398, _i.e._, the apparent revolution\nof Jupiter, we have the following:--\n\n   3.     2776 =  7 \u00d7 398 - 10\n   4.     3986 = 10 \u00d7 398 +  6\n   6.     6762 = 17 \u00d7 398 -  4\n   7.     7972 = 20 \u00d7 398 + 12\n   9.    10748 = 27 \u00d7 398 +  2\n  10.    11958 = 30 \u00d7 398 + 18\n\nThe differences 10, 6, 4, 12, 2 and 18 are so small in comparison with 398,\nthat the numbers 2776, etc., might very well have been regarded as\napproximate multiples of the revolution of Jupiter. And the remainders in\nthe seventh and tenth pictures could be still further reduced. In the\nseventh picture, the first sign is very unusual and one which I do not\nremember having met with elsewhere. If it should be possible to regard it\nas the number of the thirteen week days, then it would follow (the Saturn\nsign being regarded as unimportant) that the contents of the rectangle\nmeant:-- 13 + a multiple of 398, by which this remainder would be reduced\nto -1.\n\nThe tenth picture has the cross _b_ as the beginning of the rectangle. This\nis the sign for union, very often denoting especially the union of all the\ntwenty days. Thus we have here (aside from the middle sign to be discussed\nlater) the formula:-- 20 + 30 \u00d7 398 - 2 = 11,958, or even 20 + 30 \u00d7 398 =\n11,960.\n\nThe regular progression from the 7th multiple to the 10th, 17th, 20th,\n27th, and 30th multiples in the above six equations is also somewhat in\nfavor of my theory, while the four rectangles without the Jupiter sign are\nby no means multiples of the Jupiter revolution:--\n\n  1.      502 = 398 + 104\n  2.     1742 =   4 \u00d7 398 + 150\n  5.     5728 =  14 \u00d7 398 + 156\n  8.     9714 =  24 \u00d7 398 + 162.\n\nLet us now try to interpret the meaning of the remaining rectangles (always\nomitting the Saturn sign as a matter of course.)\n\nIn pictures 2 and 8 the rectangle also contains the sign of the moon or of\nthe twenty days. Beside it in picture 2 is the sign, which in my\n\"Erl\u00e4uterungen,\" page 16, I regarded as the sign for Mercury. Hence we have\nhere 20 + 15 \u00d7 115 = 1745, _i.e._, only 3 units more than the required\n1742.\n\nThe rectangle with the eighth picture contains in addition to the moon a\nsign which looks as if it were intended for a whole divided into four\nparts. Until something better (perhaps the the sign of Venus) is proposed,\nI will assume that it is the quarter of the Tonalamatl, _i.e._, 65, and I\ntake the required number to be 9714 in the form of 20 + 149 \u00d7 65 + 9.\n\nAbove the third picture I see a Mercury and a Venus sign and I read 584 +\n19 \u00d7 115 = 2769, which is only 7 units less than the required 2776.\n\nThe fifth picture still remains to be discussed, but I do not know how to\nunite the Mercury revolution here with the 5728. For the present, however,\nI am inclined to believe that there is a mistake in this passage.\n\nWe pass now from the obscure contents of the rectangles to the equally\nmysterious pictures themselves.\n\nAside from the tenth picture, I find human forms in four pictures.\n\nPicture 1, page 53a, is the death-god (A) seated and pointing upward, an\nappropriate representation for the zero-point of the Saturn series, _i.e._,\nfor the end of the preceding revolution.\n\nPicture 2, page 55a, contains the head of a deity, probably D's with the\nsuggestion of a beard and the sun-sign on his forehead. The head is\nsurrounded by a ring striped black and white.\n\nPicture 3, page 56a, is the head of B, again with a beard and with the sign\nKin (sun) above. The head is surrounded by a design, the left part of which\nis black and the right white.\n\nPicture 6, page 53b, represents a hanged woman, which Schellhas,\n\"G\u00f6ttergestalten,\" page 11, takes to be the Maya goddess Ixtab, the goddess\nof the halter, _i.e._, of the hanged.\n\nThe centre of picture 4 on page 57a, contains the suggestion of a face,\nperhaps in place of the Ahau sign, and on either side of it is a black and\nwhite surface.\n\nIt is further important to note that four times in this section Kin (sun)\nforms the centre of the picture, viz:--pictures 5, 7, 8 and 9, pages 52b,\n54b, 56b and 57b. In all four cases there is on either side of Kin a black\nand white surface, such as we have already seen in picture 4 and similar to\nthat in picture 3. Pictures 8 and 9 are vomited up, as it were, by a\nserpent placed below them, in the same way as B is represented on pages 34b\nand 35b. In pictures 5 and 8, four objects suggesting arrows extend from\nthe Kin in four directions and probably denote the four cardinal points or\nthe four Bacabs, of which we shall have more to say presently. Two of these\narrow-like signs also appear in picture 7, page 54b, but only on the black\nand not on the white surface.\n\nI will postpone discussing picture 10 until later and pass on to the\nhieroglyphs above the first nine pictures, about which it is true I have\nnothing satisfactory to say. There are always properly speaking ten of\nthese hieroglyphs, among them the two signs for the sun and moon. But the\nscribe introduced the latter only in pictures 1-4, and also with the more\nelaborate last picture 10. With pictures 5 and 9 he omitted these signs in\norder to represent the other eight larger and with greater distinctness of\ndetail. Among these hieroglyphs are several of gods, especially that of A\nwith pictures 1, 5 and 9, and H with picture 5, and with pictures 1, 3, 5,\n7, 8 and 9 there are other heads, some of them bird-heads, regarding which\nI am uncertain.\n\nThe Ben-Ik sign, to which I have assigned the meaning of a lunar month,\nbelongs with pictures 4, 8 and 9 and occurs twice each with pictures 1 and\n10.\n\nI am inclined to see the sign for Mercury in the crouching figure belonging\nto pictures 9 and 10, which is drawn upside down and combined with the half\nVenus sign (11958 = 104 \u00d7 115 - 2).\n\nHands grasping a hieroglyph (a sign for 20 days?) are represented in\npictures 1, 7, 8 and 10.\n\nThe enigmatical numbers, prefixed to the hieroglyphs, occur several times,\nthus a 1 with pictures 1 and 10, and a 4 twice with picture 8 and a 6 with\npicture 3.\n\nNow let us examine picture 10 somewhat in detail and also the signs\nstanding above it, since both are of special significance here. This\nrepresentation treats of the period of 11,960 days in which the Mercury and\nlunar revolutions meet. And this is proved by the ten hieroglyphs, which I\nwill number as follows:--\n\n  1   6\n  2   7\n  3   8\n  4   9\n  5  10.\n\nI can omit Signs 3 and 8, sun and moon, since they refer to a period of\ntime only in a general way. Sign 1 seems to me, as I have already stated,\nto have reference to the revolutions of Mercury. Then follows sign 2, the\nupper part of which is a mat and the lower the Muluc sign. I believe this\nsign is intended to denote that the beginning of this period is in a Muluc\nyear. Indeed, our examination of pages 51-52 showed that it was the year 6\nMuluc. The mat (Pop) is very properly the symbol of beginning, since the\nfirst month of the year was likewise called Pop. Sign 7, it seems to me,\nindicates that this period should be divided into lunar months (denoted by\nBen-Ik), and, as I have already demonstrated in my examination of page 24,\nthe length of the period is stated here by Signs 4, 5, 6 and 9, but the dot\nbefore the fifth should be placed before the fourth, as is actually the\ncase on page 24. Therefore:--\n\n   4 =   21\n   5 = 7200\n   6 = 4680\n   9 =   59\n      -----\n      11960.\n\nIt is perhaps not accidental that the ninth sign is that of the fourteenth\nmonth, which signifies the expiration of the preceding lunar month, for\nhere the month begins with the first day of the fifteenth month.\n\nSign 10 is doubtless Xul = end, as it so often is, for example, on pages\n61-62 below. But I have not solved the meaning of the two prefixes. The end\nwould be XII Lamat 16 Yax (13 Ix).\n\nThe picture represents a human form, which has in place of a head a design\nsomewhat resembling the head of a lance. It is sitting with legs spread\napart, and in this respect may be compared with god B of Cort. 9, who is\nrepresented in the same way. In the picture before us, the figure holds in\nits upraised hands the sun and moon signs, which are constantly repeated\nthroughout the series. The Venus sign is placed between the outspread legs.\nIn the rectangle above the figure, this sign is repeated in a more concise\nform, while on the left the cross _b_ appears as the sign of union or\nmultiplication, and on the right that of Jupiter, whose period of\nrevolution is here multiplied by 30 (30 \u00d7 398 = 11,940). And the two Venus\nsigns can mean nothing more than that this period of 11,960 also serves the\npurpose of filling up the gap between the two large Venus-solar periods of\n37,960 days, like the similar process which we saw on pages 46-50.\n\nWe have examined first the series and then the pictures with the\nhieroglyphs belonging to them. Let us pass now, as the third step, to the\nexamination of the two rows of hieroglyphs extending above the numbers\nthroughout the whole section. First of all, I will again set down here the\nposition of each of the sixty-nine groups:--\n\n  Page 51.          | 52.        | 53.              | 54.\n  31.32.33.34.35.36.|37.38.39.40.| 1. 2. 3. 4. 5. 6.| 7. 8. 9.10.11.12.13.\n                    |            |41.42. 43.44. 45. |46.47.48.49.50.\n\n  Page 55.             | 56.        | 57.           | 58.\n  14.15.16.17.18.      |19.20.21.22.|23.24.25.26.   |27.28.29.30.\n  51.52.53.54.56.57.58.|59.60.61.62.|63.64.65.66.67.|68.69.\n\nSince each group contains two hieroglyphs, this makes 138. in all. Of\nthese, however, about 24 on the upper halves of the pages, are wholly or\nalmost wholly effaced which very materially hinders the trustworthy\ndetermination of the context.\n\nFurthermore group 59 is entirely lacking or rather group 58, in the place\nof which the 59th has been set down. The eighth picture was probably\nalready drawn, when the artist saw that there was not room enough left for\nthe 58th and 59th groups. Hence he omitted the 58th, setting down in place\nof it the 59th and in the place of the latter he set down the zero\nmentioned above.\n\nThe question now arises:--Are these hieroglyphs dependent upon the days and\nnumbers of the series and upon the pictures, or are they entirely\nindependent of them?\n\nI find but _one_ point in favor of the first possibility, viz:--the Venus\nsign in group 4b (I will designate the upper hieroglyphs by _a_ and the\nlower by _b_). It is placed in the period indicated in which 502-679 days\nelapse, and in which, therefore, Venus has finished a revolution of 584\ndays. It may be, that by way of exception, this significant date was\nintentionally recorded.\n\nOn the other hand, there are many things, which favor an entirely different\ninterpretation of these hieroglyphs. Thus I am of the opinion that the\nritual year of 364 days with its four Bacab periods of 91 days each is\nreferred to here, as we have already found it referred to on pages 31a-32a\nand on page 45a, and shall find it again on pages 65-69 and 71-73. In that\ncase the single groups would be separated from one another by one Maya week\n= 13 days.\n\nI will now arrange the sixty-nine groups in the following order (the reason\nfor which will become clear directly):--\n\n    I   4  11  18  25  32  39  46  53  60  67\n   II   5  12  19  26  33  40  47  54  61  68\n  III   6  13  20  27  34  41  48  55  62  69\n   IV   7  14  21  28  35  42  49  56  63   1\n    V   8  15  22  29  36  43  50  57  64   2\n   VI   9  16  23  30  37  44  51  58  65   3\n  VII  10  17  24  31  38  45  52  59  66.\n\nThe groups in a horizontal row are separated from one another by 7 or a\nmultiple of 7. If now a hieroglyph is repeated in those places, which are\nin the same horizontal row, then this is a confirmation of the supposition\nthat Bacab periods are meant to be represented here. Hence I will examine\neach row in turn. These rows extend over the long period of 69 \u00d7 13 days\nprobably merely for the purpose of filling up the space.\n\nI. In 39b, 46b, 53b and 60b, _i.e._, after every seven groups, perhaps also\nin 18b, we find the following sign, which I identified as that of a Bacab,\nin Globus, Vol. LXXI:--\n\n[Illustration]\n\nHence this denotes the beginning of the Bacab period. In 4b the sign is\nreplaced by that for Venus. In 11b, 25b, 32b and 67b we find other signs,\nit is true, nevertheless the regularity stated above cannot be accidental.\nThe upper signs of groups 39a, 46a, 53a and 60a contain an Imix and\ncorroborate the connection.\n\nII. 5b and 26b (after 3 \u00d7 91 days) contain a head very like the preceding,\nwhich readily suggests the idea that it is merely a Bacab sign pushed one\ngroup ahead, but it also appears in 13b, 50b and 52b.\n\nThen 12b, 54b and 61b correspond, _i.e._, after six groups of 91 days and\none more of the same length, but the same sign appears also in 34b, 48b and\n56b.\n\nIII. 41b and 69a are Xul = end and are therefore separated by 28 \u00d7 13 = 4 \u00d7\n91 days, _i.e._, the length of a year. It is singular that both signs of 41\nare like those of 47; if we assume that 47 was set down one group too soon,\nit would be in excellent keeping with the rest. The Xul also appears in 11b\nand 28b. 34b and 48b correspond after 2 \u00d7 91 days, as already mentioned\nunder II.\n\nIV. 42a and 49b both contain the sign for the sun between clouds.\n\nV. 36b and 57b agree after 3 \u00d7 91 days; the same sign appears again in 10b\nand 20b.\n\n15a and 36a correspond after 3 \u00d7 91 days; we shall continue the examination\nof this sign under pages 71-73.\n\nVI. 37a and 65a agree, _i.e._, after 4 \u00d7 91 days = a year. The sign\ncontains a human figure stretching both arms aloft. The passing of a year\nwas likewise indicated in III, but a year coming 52 days later than this.\n\nVII. 10a and 31a agree, _i.e._, after 3 \u00d7 91 days. The sign is composed of\nthe crouching figure prefixed to the cross, which we also find in 12b, 35a\nand 65b; it is prefixed to a different hieroglyph in 30a. In 38b, 52b and\n59b (58 in the Manuscript) we see bird-like heads resembling the Bacab\nsign. We should expect to find a familiar sign in 45, which is drawn\nbetween these, but a Moan appears there instead. These signs seem to\nindicate the end of the Bacab period. Does the Moan sign here, too, suggest\nthe end of the year?\n\nIn 38a, 52a and 59a we again see an Imix, and I consider it a corroboration\nof my theory that all the four signs of groups 38 and 39 are repeated in 52\nand 53 after 2 \u00d7 91 days.\n\nI believe a further corroboration is the fact that though many of these\nhieroglyphs have no connection with these periods of 7 \u00d7 13, _i.e._, with\nthe divisions of the ritual year, they do correspond with the usual\ndivisions of the Tonalamatl, _i.e._, 4 \u00d7 13 and 5 \u00d7 13 days.\n\nAfter 4 \u00d7 13 or a multiple of it the signs recur in 20b, 24b, 40b, 44b-12b,\n48b, 56b-16b, 32b, 64b-26b, 50b-10a, 30a-37a, 65a-15b, 51b-11b and 47b.\n\nAs examples of 5 \u00d7 13 I would mention 3b, 63b-10a, 20a, 30a-5b, 50b-24b,\n29b-35b, 65b-15b, 20b, 40b.\n\nFinally, I must mention two more hieroglyphs, which are limited almost\nentirely to these pages:--\n\n[Illustration]\n\nIn the first sign, which occurred on page 10a, I thought I recognized the\nlunar month of 28 days. It occurs in this section in connection with the\nthird picture on page 56, and besides in the following groups of\nhieroglyphs:--16b, 32b and 64b, always combined with a Yax. The regularity\nof the intervals is striking, but as yet I can neither explain that, nor\nthe crouching personage (Mercury?) in the 10th, 20th and 30th groups and\nagain in the next, the 31st.\n\nThe second sign is found _only_ on these pages and here not less than\neleven times, possibly with the addition of the effaced sign in 6b and 27b\nwhich may have been the same hieroglyph. The eleven places in which it\noccurs are as follows:--3b, 15b, 17b, 23b, 24b, 29b, 40b, 44b, 49a, 51b and\n63b. Two different prefixes are added to it; one in the first two and the\nlast two places and also in the last but two joined with Kin, and the other\nin the six middle places. Of the eleven groups, 17 and 24, 44 and 51 are 7\ngroups apart, 3 and 17, 15 and 29, 49 and 63 are 14 groups apart, 23 and 44\nare 21 groups apart, and hence 23 and 51 are separated by 28 groups or 1\nyear. Group 40 alone is not concerned with these intervals of seven or\nmultiples of seven.\n\nNow, how far may all these periods of time be due to accident and how far\nto design? Accident _alone_ is quite out of the question. The frequent\nrepetition of the sun-sign in groups 49, 50 and 51 on pages 54b and 55b,\nseems to me to refer to the conjunctions of the sun with certain stars,\nwhich occur at intervals of thirteen days.\n\nPages 58--59.\n\nThis section is also based on a series occupying the whole of page 59,\nwhich contains nothing but number and day signs. This series has the\ndifference 78, which we found once before on page 44. There the\nstarting-point was III Lamat, here it is the day XIII Muluc, probably\ncoming in the year XIII Muluc, as in Cort. 40b, as I shall have occasion to\nsuggest later. The series extends, with the usual errors and variations, in\nfour divisions from top to bottom. The days, which are always two days\nbehindhand, owing to the number 78, in 780 again reach the day XIII Muluc,\nat which point the succeeding members remain stationary, since from here on\nthe difference is always 780 or a multiple of it. 780 days are, however,\nthe apparent time of the revolution of Mars, which is the only planet now\nleft to be discussed, the subject of pages 46-50 having been Venus and the\nsun, and of pages 51-58, Mercury and the moon with incidental treatment of\nSaturn and Jupiter. With 780 as its difference, the series ascends to 19 \u00d7\n780 = 14,820, and then continues with this large number as its difference\nuntil the series is lost in the effaced passages.\n\nCuriously enough, however, directly under the line containing the 14,820,\nthere is a new series composed of nine members, or ten counting the\nsuppressed starting-point. But this starting-point is again the day IX Ik,\nthe difference, as proved by the annexed days, is again 78 and the series\nends with 780. Thus the starting-point is the only difference between the\ntwo series. The principal series contains all the even and the secondary\nseries all the uneven days. Can the starting-point of the revolution of\nMars have been determined according to different principles? Is it possible\nthat in one case the beginning of the planet's retrogression was adopted as\nthe starting-point, and in the other case the date on which the planet,\nafter completing its retrograde course, again reached the degree of right\nascension at which it had begun its retrogression? This is a difficult\nmatter to decide, since the period of the retrogression of Mars fluctuates\nbetween 62 and 81 days. The interval from IX Ik to XIII Muluc is 147 and in\nreversed order 113 days.\n\nIt can hardly be assumed that the 19 of the IX 19 or IX Ik is connected\nwith the 19 \u00d7 780 mentioned above or with the 19 + 19 + 19 + 21 into which\nthe 78 is divided on pages 44-45, or finally with the 19, which four times\nforms the principal part of the sub-divisions of 65 on pages 33-34.\n\nNumbers amounting to millions accompany this series in the usual way. Two\nof these are on page 58, viz:--1,426,360 and 1,386,580; but with the sign\nof the sixth day, which is important here, between them. Below these\nnumbers, however, are two month dates:--first the normal date IV Ahau 8\nCumhu and, if I have correctly restored the effaced number before the month\nsign, which in its turn is indistinct, the second is XIII Muluc 2 Zac,\nwhich would fall in the year VIII Muluc. The encircled numbers also occur\nhere. They are set down beside the lower number of seven figures. We find\nhere a red 12 with a black 1 inserted, below this a black 7 and below this\nagain, enclosed in a red band, a black 11, which I regard as also\nrepresenting the value of a red number. We shall find a similar instance\namong the serpent numerals. Then we have here 1. 7. 11. = 511 and 12. 11. =\n251. But 511 = 260 + 251 and 251 is the interval between XIII Muluc and IV\nAhau.\n\nWith the day XIII Muluc and the interval 9 between IV Ahau and XIII Muluc,\nnumbers for XIII Muluc have been formed amounting to millions, which,\nhowever, have been suppressed in the Manuscript, just as they were on page\n31 where, in like manner, numbers were first formed for day XIII Akbal.\n\nI assume that to begin with, 76 Tonalamatls (= 19,760) were added to this 9\nand then 228 Tonalamatls (= 59,280), the 228 being = 3 \u00d7 76 and the 59,280\nincluding 76 revolutions of Mars.\n\nThe result in one case was 19,769 and in the other 59,289. If the 12\nAhau-Katuns, which are specified as 1,366,560 on page 24b be added here, we\nhave the following numbers:--\n\n  1,386,329 = XIII Muluc 2 Mol (3 Muluc),\n  1,425,849 = XIII Muluc 2 Zip (12 Muluc),\n\nand if the two encircled numbers of the Manuscript:--251 and 511 be added,\nthe sums are 1,386,580 and 1,426,360, _i.e._, the two large numbers of the\nManuscript.\n\nThe dates corresponding to these numbers are as follows:--\n\n  1,386,580 = IV Ahau 13 Muan (12 Muluc),\n  1,426,360 = IV Ahau 8 Muan (4 Ix).\n\nIf we compare the two numbers with the normal date, the curious result\nfollows that:--\n\n1) 1,386,580 - 1,366,560 = 20,020.\n\nThis number is equal to 55 \u00d7 364, including therefore the ritual year of\n364 days.\n\n2) 1,426,360 - 1,366,560 = 59,800.\n\nThis number is five times 11,960 days, which is assumed to be the time in\nwhich the lunar and Mercury revolutions accord. This 59,800 was found once\nbefore on page 24 as the suppressed difference between 68,900 and 9,100.\n\nThus the separate sections (of the book) are very closely connected.\n\nIf the two large numbers be compared with one another their difference will\nbe found to be 39,780. This is equal first to 51 Mars revolutions of 780\ndays, and second to 4420 \u00d7 9, _i.e._, a multiple of the interval between IV\nAhau and XIII Muluc.\n\nNow we must direct our attention to the seventeen hieroglyphs, which we\nfind in the two columns on page 58, apart from the matter-of-course\ncalendar date at the top, which is repeated at the bottom. One column\ncontains 11 hieroglyphs and the other 6. I will here advance the following\ntheory in regard to these hieroglyphs, which may serve until a better is\nfound:--\n\nSince, as a rule, the Tonalamatl is divided into 5 \u00d7 52 days, I believe\nthat each group of three Tonalamatls treated of on page 59, is divided into\n15 of these parts; that each hieroglyph, therefore, denotes 52 days and\nthat the first three parts are separated from the others by the signs of\nbeginning and end in the first and fifth places, so that three of these\nparts, which equal 156 days, always form a separate group. 156 is the 5th\npart of 780. With the omission of the first and fifth signs, the passage, I\nthink, stands thus:--\n\n              0 XIII Muluc       2 Kankin (13 Muluc).\n   1)      0-52 XIII Imix       14 Pax.\n   2)    53-104 XIII Ben         1 Pop (1 Ix).\n   3)   105-156 XIII Chicchan   13 Zip.\n  --------------------------------------\n   4)   157-208 XIII Caban       5 Xul.\n   5)   209-260 XIII Muluc      17 Mol.\n   6)   261-312 XIII Imix        9 Zac.\n  --------------------------------------\n   7)   313-364 XIII Ben         1 Kankin.\n   8)   365-416 XIII Chicchan   13 Pax.\n   9)   417-468 XIII Caban      25 Cumhu.\n  --------------------------------------\n  10)   469-520 XIII Muluc      12 Zip (2 Cauac).\n  11)   521-572 XIII Imix        4 Xul.\n  12)   573-624 XIII Ben        16 Mol.\n  --------------------------------------\n  13)   625-676 XIII Chicchan    8 Zac.\n  14)   677-728 XIII Caban      20 Mac.\n  15)   729-780 XIII Muluc      12 Pax.\n\nIf we adopt this arrangement for the present we cannot fail to see that the\nauthor had an aim in view, when we consider the following:--\n\n1. The zero-point lies 15,609 days later than the normal date IV Ahau 8\nCumhu (9 Ix). This is equal to 20 \u00d7 780 or 60 \u00d7 260 increased by the\ninterval between IV Ahau and XIII Muluc = 9. There are 86 days between 2\nKankin and 8 Cumhu _i.e._, 15,609 = 43 \u00d7 365 - 86, and from 9 Ix to 13\nMuluc it is 43 years.\n\n2. The same zero-point, 13 Muluc, lies in the year with the same name, that\nis, the very point where a Tonalamatl of the year ends.\n\n3. In this arrangement the first as well as the last day of the year 1 Ix\nis exactly reached in the second and ninth groups. While the meaning of the\nsecond is as yet unintelligible to me, the end of the year is appropriately\nindicated by the ninth with its compound of Kin and the year-sign, above\nwhich there may be an Ix as a superfix, but misshapen for want of room.\n\n4. Also the fact that it is the first of the two columns, which closes with\nthis year-end, seems to show a purpose.\n\n5. Several instances of similarity appear among the hieroglyphs in these\ngroups of three:--an Akbal sign in 1 and 4 suggests the god D, the superfix\nand prefix of 2 and 14 the god K and 5 and 11 the screech-owl and therefore\nA.\n\nLittle else is to be said of these hieroglyphs.\n\nC might be denoted by 3 (13 Zip) and 10 (12 Zip). Group 8, the central\npoint of the series, has on the left and right the signs for the north and\nsouth as if the time between the north (Muluc) years and the south (Cauac)\nyears were meant to be indicated here.\n\nI am inclined to consider the crouching personage in 12 as the revolution\nof Mercury, which requires 115 days:--573 is 5 \u00d7 114 + 3 or 5 \u00d7 115 - 2.\n\nIs 7 a sign, as yet unknown, for the year of 364 days?\n\n15 looks like two signs for the month Mac, placed back to back, which here\ndesignates the Tonalamatl as it does on page 24. The superfix of three\nparts might denote three Tonalamatls = 780 days. The familiar sign in the\nfifth place in connection with the expiration of the first Tonalamatl is\nstriking; it is the one usually identified as that of the screech-owl or\ndeath-bird.\n\nPage 60.\n\nThis is the last page of the front of the second part and is divided into\nfour sections:--at the top we find hieroglyphs, below these a picture, then\nhieroglyphs again and in the lowest section another picture.\n\nThe upper picture contains first a rectangular elevation like a platform.\nEnclosed in this rectangle is the picture of the animal resembling a dog\nlying down, which we have often met with, the last time on page 47. In\nfront of the dog is a hieroglyph, which, I regret to say, is still unknown\nand which occurred six times as a heading on page 23b. On the platform two\npersonages are fighting; one is in war-dress holding in his left hand the\nthrowing-stick or atlatl, and in his right probably arrows; the other\nfigure, whose back is somewhat indistinct owing to obliteration, is\napparently unarmed and is making a defensive gesture with one hand. Beside\nthe platform, and therefore on a lower level, is a second person walking\nbehind the armed person as if to help him. He too is in war-dress and\nlikewise holds an atlatl. A black 3 is set down between the two combatants,\nand there may also have been a red 2, which is indistinct owing to the red\nbackground of the picture.\n\nLet us next examine the lower picture. A blindfolded personage is kneeling\non the left. A serpent's head rises from the ground in front of him. A\nsecond serpent rises in several coils on the shoulders of the blindfolded\npersonage and on the serpent's neck sits enthroned another personage, who\nis rather indistinct, holding a spear and a shield. On the right, opposite\nthis group and facing it, is a second. A personage with arms bound and\nbowed head is sitting on the ground. There is a black ring around his eye.\nBehind him stands the victor in war-dress and again equipped with spear and\nshield. There is a red 11 and a black 2 between the two groups.\n\nWe see that the reference here is to combat, just as it was on the right\nside of pages 46-50. And since the subject of these pages like that of\n46-59 is confined to the revolutions of the planets, it is natural that the\npursuit of one by the other, their periodical disappearance, the crossing\nof their orbits and the variation in the length of their revolutions should\nbe looked upon as a contest. Therefore, since the sun, the moon and the\nfive planets have hitherto been treated of on these pages, I look for these\nseven heavenly bodies in the seven personages pictured here on page 60. I\nwill attempt to explain them, hoping that my interpretation may be replaced\nby a better one.\n\nThe sun and moon stand on the platform in the upper picture; their combat\nis equivalent to the eclipses to which they at times succumb. The moon is\nthe assailant and the sun makes only a proud defensive gesture. The person\nbehind the moon must be Mars. The animal under the two persons is the\nembodiment of the eclipses, which the Aztecs interpreted as the act of\nbeing devoured by the jaguar. The hieroglyph in front looks very much like\nthe meeting of two circles. Does it refer to the day Lamat (Aztec tochtli =\nrabbit)?\n\nAt the left, bottom, the powerful Venus triumphs over the weak Mercury. The\ntwo planets are real chronometers by reason of the regular alternation of\ntheir appearance as morning and evening stars, and also by their\ndisappearance twice in each revolution and finally even in the variation in\nthe length of the two periods of invisibility. Hence they are each\naccompanied by a serpent as the usual symbol of time.\n\nOn the right, on the other hand, Jupiter as the stronger has vanquished\nSaturn, whose bound arms symbolize his slowness of motion and the fact that\nhe is confined to the same region of the sky. Should not the ring around\nhis eye have a very special meaning? But we must guard against an excess of\nimagination. Jupiter and Saturn are the last to be represented, as they\nwere of but secondary importance, on pages 51-58 and perhaps also in the\n2200 on page 24.\n\nI will not deny that yet another interpretation of this page is possible.\nThe top picture may be Venus and the moon opposing one another, and the\nbottom picture may represent the sun as victor over Mercury. There are some\nthings in favor of this point of view.\n\nThe correct order of the twenty-four hieroglyphs is the following, in my\nopinion, which is borne out by the different colors of the four groups:--\n\n   1   2  |   7   8\n   3   4  |   9  10\n   5   6  |  11  12\n  -----------------\n  13  14  |  19  20\n  15  16  |  21  22\n  17  18  |  23  24\n\nThese signs can have no relation to mythology. There is not a hieroglyph of\na god among them, for if sign 6 could be taken for B's hieroglyph, the\nresemblance to the sign of the fist, familiar from the inscriptions, as\nwell as the Imix and the cross-hatching as a prefix, makes this doubtful.\nThe latter component would rather suggest the summer solstice. If sign 12\nwere intended to denote the Bacab, then it would refer to chronology rather\nthan to mythology. Also the Cimi in 17 might equally well mean the day as\nthe god. Indeed several things refer here to chronology and astronomy,\namong them the unmistakable union of numbers and month signs, which occur\nhere repeatedly. Thus from what remains of the almost obliterated signs 1\nand 2, they might denote the normal date IV Ahau 8 Cumhu, which always\noccupies the first place. Signs 7 and 20 are plainly the same, 9 Xul (sixth\nmonth) and sign 14 is 10 Yaxkin (seventh month). Sign 5 might be Caban\ncombined with Uo (second month) and a ten. In sign 19 we again see Yaxkin\nwithout a number. Signs 9 and 23 are Zec (fifth month) and signs 21 and 22\nmay be Kankin (fourteenth month). The days occur in the same manner as the\nmonths. It is true that Kin is only a part of hieroglyph 10, the rest of\nwhich is effaced, but the familiar compound of Caban and Muluc appears in\n18 and 24 and Cimi is in 17, as we have seen. In sign 13, Ahau is combined\nwith a red number, which must lie between X and XV. But this should not be\nregarded as forming a calendar date with the 10 Yaxkin near by, for Ahau is\nnever the tenth day of a month. Can 16 be the sign of the twelfth month,\nCeh, combined with that for 7200? Hieroglyphs 3 and 8 are effaced and I do\nnot understand 4, 11 and 15.\n\nThere are no parallels in the kindred passages 46-50, unless it be 7 Zec on\nthe bottom of page 49 and here in signs 9 and 23, but without a number. Cf.\nmy paper on this page 60 in the \"Weltall,\" year 6, pages 251-257.\n\nPage 61--64.\n\nOn examining the reverse of the second part of our Manuscript, _i.e._,\npages 61-74, we find an empty page on the left, the back of which is\noccupied by page 60. This may be explained by assuming that the scribe\nwrote pages 61-64 and possibly even pages 61-74 from right to left, the\ngreat series having occasioned such a proceeding, and that his material\ncame to an end when he had finished page 61. Nevertheless, it is advisable\nto continue with the original numbering in order to avoid confusion.\n\nAside from the concluding (or beginning) page 74, this whole section of\npages 61-74 consists of three parts:--61-64, 65-69 and 70-73. Let us first\nconsider the first section, which I have already discussed in my treatise\n\"Zur Erl\u00e4uterung der Mayahandschriften II.\"\n\nThe basis of this section is a series, the beginning of which is on the\nbottom, right, of page 64. Its primary difference is always that which we\nfound on pages 31-32, viz:--the Bacab period of 91 days, the quarter of the\nritual year of 364 days = 7 weeks of 13 days each. It ascends by 91 until\nit reaches 1820, which number is a multiple of both 364 and 260 and is also\ndivisible by 28, the number of weeks in a year. Just as on page 32 the\nseries continues with the new difference 1820 as far as 7280, its fourth\nmultiple, which then becomes the third difference. Indeed, I believe that\neven the partially effaced numbers could be so restored as to carry the\nseries to the number 36,400 = 400 \u00d7 91, which would then become the fourth\ndifference and the series would close at the top of page 63 with 145,600 =\n1600 \u00d7 91, _i.e._, with the numbers 1. 0. 4. 8. 0. of which the 1 is\nentirely and the 0 half effaced. The series on pages 31-32, however, closed\nwith 29,120 = 320 \u00d7 91, but there is still room for a higher series.\n\nUnder this largest number (1600 \u00d7 91) there is on page 63 a large red\nnumber consisting of 19. 0. 4. 4. which is crowded into a very small space\nbetween the figures of 1820. I can only understand it by replacing the\nfirst 4 by a 3, for then it is 136,864 = 1504 \u00d7 91 or by addition of a\nzero. We shall return to this number in the examination of the serpent\nnumerals.\n\nThe series is accompanied in the regular way by five days. At the beginning\nof this series, page 64, right bottom, are the days III Cib, III Men, III\nChicchan, III Caban and XIII Ix; the III is set down only with the first of\nthese days and is to be supplied with the next three. Hence the actual zero\npoint is to be found 91 days back in the days III Chicchan, III Kan, III\nIx, III Cimi and XIII Akbal, the last of which is also the beginning of the\ncorresponding series on page 32. From 1820 on, these last-named days, of\ncourse unchanged, accompany the numbers. The most important of these days\nare the first and last, but we shall see later in connection with the\nserpent numbers that the other three, which are separated from one another\nby 39, 130 and 52, _i.e._, 3 \u00d7 13, 10 \u00d7 13 and 4 \u00d7 13, are likewise not set\ndown here by mere accident.\n\nWe come now to the five columns, three on page 63 and two on page 62, which\njoin this series on the left. They contain the large numbers, which\ninvariably accompany these series. Here there are six numbers, four of\nwhich, in my opinion, refer to the past and two to the future. Two of these\nnumbers, the two largest, are set down together in the third column on page\n63, one with red numbers and the other with black. Of these black numbers,\nI take the second from the top to be not 8 but 13, assuming that a line is\nomitted. The normal date IV Ahau 8 Cumhu from which, as the starting-point,\nall these numbers are to be computed, is set down below at the end of each\nof the five columns.\n\nI now give the six numbers, first the two highest, then the other four from\nright to left, adding in each case the calendar date and the year in which\nthey should be situated:--\n\n  1,538,342; IV Ik    15 Zac (12 Muluc).\n  1,535,004; VII Kan   2 Chen (3 Kan).\n  1,268,540; IV Ahau   8 Mol (1 Ix).\n  1,234,220; IV Ahau  18 Kayab (11 Kan).\n  1,272,544; IV Kan   17 Yaxkin (12 Muluc).\n  1,272,921; IV Imix   9 Mol (13 Ix).\n\nThe first, third and fifth numbers are already known from page 31a, and\nhence they need no further discussion here.\n\nAs these three numbers depend on the day XIII Akbal, so the other three all\nproceed from the day III Chicchan in the following positions, which are\nagain suppressed in the Manuscript:--\n\n  1,483,585 = III Chicchan   8 Zac (5 Cauac).\n  1,233,985 = III Chicchan   8 Kankin (10 Cauac).\n  1,272,465 = III Chicchan  18 Zip (12 Muluc).\n\nThe second date in the manuscript is 13 Kankin and the third is 13 Zip;\nhence there is one line too many in the former number and one too few in\nthe latter. While on page 31a the origin of the numbers belonging to the\nday XIII Akbal seems to be quite clear, here their relation to one another\nis entirely concealed. I must, therefore, refrain from expressing any\nconjecture in regard to them.\n\nNow the numbers set down in the Manuscript are formed only by the addition\nof the encircled numbers also found there. The encircled number for the\nfirst expressed number is 51,419, which is the same number we found with\nthe corresponding day XIII Akbal; the second has 235 and the third 456 =\n260 + 196. The 51,419 was 197 \u00d7 260 + 199; but 199 is the interval from III\nChicchan to VII Kan, just as it is from XIII Akbal to IV Ik. The 235 is the\ninterval between III Chicchan and IV Ahau and the 196 that from III\nChicchan and IV Imix.\n\nBy the addition of these differences, the numbers written out in the\nManuscript are obtained:--\n\n  1,483,585 + 51,419 = 1,535,004 (VII Kan).\n  1,233,985 + 235 = 1,234,220 (IV Ahau).\n  1,272,465 + 456 = 1,272,921 (IV Imix).\n\nKeeping in mind what was said in reference to page 31a, let us now examine\nthe six numbers and dates collectively.\n\nThe fact that the days IV Ahau and XIII Akbal occur here and consequently\nalso III Chicchan is not surprising. Nor is the choice of VII Kan and IV Ik\nan accident, for the interval between these days is exactly the same as\nthat between III Chicchan and XIII Akbal, viz:--218 days.\n\nHence the distance from III Chicchan to VII Kan is also exactly equal to\nthat between XIII Akbal to IV Ik, viz:--199 days.\n\nFinally, the distance from VII Kan to III Chicchan is exactly equal to that\nbetween IV Ik and XIII Akbal, viz:--61 days.\n\nIV Imix and IV Kan are separated from the normal date IV Ahau by 3 \u00d7 13 =\n39 and 8 \u00d7 13 = 104 days.\n\nRegarding the encircled numbers, so far as they are independent of 260, I\nwould note the following:--\n\n   17 = XIII Akbal to IV Ahau.\n  121 = XIII Akbal to IV Kan.\n  196 = III Chicchan to IV Imix.\n  199 = III Chicchan to VII Kan and XIII Akbal to IV Ik.\n  235 = III Chicchan to IV Ahau.\n\nIn addition let me remark that 36 = VII Kan to IV Ahau, 39 = IV Imix to IV\nAhau and 104 = IV Ahau to IV Kan.\n\nThe following arrangement will prove that these numbers were as usual also\nemployed to form the large numbers by multiplication:--\n\n   17 \u00d7 74,620 = 1,268,540 (IV Ahau),\n  235 \u00d7  5,252 = 1,234,220 (IV Ahau),\n   36 \u00d7 42,639 = 1,535,004 (VII Kan),\n   39 \u00d7 32,639 = 1,272,921 (IV Imix),\n  104 \u00d7 12,236 = 1,272,544 (IV Kan).\n\nBut the highest number, 1,538,342, was formed in a different way; it =\n59,167 \u00d7 26; but the interval from IV Ahau to IV Ik = 182 = 7 \u00d7 26, and\nfrom IV Ik to IV Ahau = 78 = 3 \u00d7 26.\n\nIf in conclusion, we now examine the twelve numbers of seven figures given\nin this section, we will clearly see that by twos and twos they plainly\nbelong together in pairs:--\n\nThe three pairs of numbers found by computation are as follows:--\n\n  1,486,923, XIII Akbal.\n  1,483,585, III Chicchan.\n\nDifference 3338 = 12 \u00d7 260 + 218 (VII Kan to IV Ik, III Chicchan to XIII\nAkbal).\n\n  1,268,523, XIII Akbal.\n  1,233,985, III Chicchan.\n\nDifference 34,538 = 132 \u00d7 260 + 218 (as above).\n\n  1,272,423, XIII Akbal.\n  1,272,465, III Chicchan.\n\nDifference 42 (which is 260 - 218); 42 = IV Kan to IV Imix.\n\nOn the other hand the three pairs specified in the Manuscript are as\nfollows:--\n\n  1,538,342, IV Ik.\n  1,535,004, VII Kan.\n\nDifference 3338 = 12 \u00d7 260 + 218 as above, by reason of the encircled\nnumber 51,419 which is common to both numbers.\n\n  1,268,540, IV Ahau.\n  1,234,220, IV Ahau.\n\nDifference 34,320 = 132 \u00d7 260, on account of the same day.\n\n  1,272,544, IV Kan.\n  1,272,921, IV Imix.\n\nDifference 117 = IV Kan to IV Imix; strictly speaking 377 = 260 + 117.\n\nThe upper part of the five columns just now under discussion still remains\nto be examined. Here are five vertical rows of hieroglyphs, the first four\neach containing seven, and the fifth only six owing to lack of space.\n\nThe two rows at the top are as usual much obliterated, which is the more to\nbe deplored since they consisted of five calendar dates, which would have\ncontributed materially to the comprehension of the entire section.\nFortunately, however, one of these dates is preserved complete, and we are\nable to see in what relation it stands to the rest. Thus we find in the\nthird column of page 63 the date XIII Imix 9 Uo. It comes in the year 12 Ix\nand represents the number 1,523,921 (or a number separated from it by a\nmultiple of 18,980). Now 1,523,921 = 4175 \u00d7 365 + 46 and = 5861 \u00d7 260 + 61.\nThis agrees with the lower number inserted in red:--1,538,342 = IV Ik 15\nZac (12 Muluc), which comes later by 14,421 = 39 \u00d7 365 + 186 and = 55 \u00d7 260\n+ 121. 121, however, is the difference between both XIII Imix and IV Ik and\nthe days XIII Akbal and IV Kan in the last column of page 62. If we set\ndown with these two numbers, those of the normal date just preceding and\nthe normal date next following, we have\n\n  1,518,400 = 80 \u00d7 18980.\n  1,523,921,\n  1,538,342,\n  1,556,360 = 82 \u00d7 18980.\n\nThis is a period of 37,960 = 2 \u00d7 18,980 days. It is possible that at some\nfuture time an indication of such a transition from one Katun to the other\nwill be found in the writings. Now these two top lines contain two dates;\non page 62 we find 13 Ceh, and on page 63, 13 Xul, but nothing further is\nto be learned from this than that one or the other of the day-signs, 2, 7,\n12, 17, must have been set down in the effaced indication of the position\nin the Tonalamatl. All else is obliterated. From the third to the seventh\nrow of these five columns it is all extremely simple. The third row\nconsists only of five signs for beginning, the fourth, of five for end, the\nsixth of B's sign five times and the seventh of the elongated head _q_ four\ntimes. But in the fifth, two deities alternate, one is apparently male and\nthe other female; the god is in columns 1, 3 and 5 and the goddess in 2 and\n4; the god probably belonging to the days III Chicchan and the goddess to\nXIII Akbal.\n\nIf we look upon this series as the first story of a structure and the large\nnumbers just now discussed as the second, then we find the third story\nhere, as we shall find it again on page 69. In the passage on page 31,\nwhich is so closely related to the present one, a timid attempt has already\nbeen made with the number 2,804,100 to erect a third story of this kind,\nwhich however barely attained to a quarter of the height of the one which\nnow engages our attention. If the numbers hitherto examined refer to a time\nnot very far from the present, we now come to numbers which lie in so\nremote a future that they can hardly suggest anything else than the\ndestruction of the world or a sort of twilight of the gods. Nevertheless\nthe starting-point of the whole, the series, which is built up with the\nnumber 91, _i.e._, the Bacab period or the quarter of a ritual year,\ncontinually comes to view. Indeed, the number of serpents is suggestive of\nthis.\n\nThere are four large serpents, which fill most of the space on the left\nhalf of page 62 and the right of page 61. The two outer ones are bluish and\nthe two inner ones white. They rise in several coils, their tails below and\ntheir heads above. A deity is represented above the gaping jaws of each of\nthe four serpents, having apparently been vomited up. Above the first and\nthird serpents B is represented in a fashion very similar to that which we\nhave already seen on pages 33-35. Above the first serpent B has the pouch\nhanging from his neck and his hatchet is held downward; above the third he\nwears the pouch and the gala mantle and his hatchet is raised. Above the\nsecond fourth serpents, on the other hand, there are four-footed animals,\nbut of a species not represented elsewhere. They might suggest a\n(four-footed?) walrus and a bear. We have here a double contrast,\napparently referring to the four cardinal points.\n\nThe veil enveloping this representation would be lifted to a considerable\nextent, if all the eight hieroglyphs written above each serpent, were still\nlegible. But, unfortunately, the second group is wholly and the third\nalmost wholly effaced, while the first is partially effaced and only the\nfourth is preserved in its entirety. I read these groups in the following\norder:--\n\n  1  2\n  3  4\n  5  6\n  7  8.\n\nOf these 7 and 8 in the first and fourth groups form the date IX Kan 12\nKayab, which is in the year 4 Ix; this same date probably occurred also in\nthe other two groups. That it is of special importance here, is shown by\nthe two columns of hieroglyphs on the left side of page 61, where this date\noccurs again in the lowest place. The last three large numbers are not\ncomputed from the normal date IV Ahau 8 Cumhu, but from this very date and\nthe other five from a similar one. The sixth hieroglyph in the first group\nseems to correspond to the fifth in the fourth, since both contain the\nelongated head _q_, though with different accompaniments.\n\nIn the first group the fourth hieroglyph is the Bacab sign familiar to us\nfrom pages 51-58, suggesting that the series here is closely connected with\nthe one which had the difference 91. The fifth sign of the same group is\nthat for _beginning_, probably to confirm the fact that this section begins\nhere. The third sign of the first group is probably an Imix, as it is in\nthe first and fourth of the fourth group, combined here with the woman's\nhead, which we saw repeated on pages 62 and 63 at the top; and over it in\nthe second place of the fourth group is B's hieroglyph, which is also\nrepeated on pages 62 and 63 at the top. The third place of the fourth group\nis occupied by a head, which may be C's and which is distinguished by the\nsame kind of circle which on page 9b surrounded the Ahau.\n\nEight complete dates are set down below the serpents, among which are the\nXIII Akbal already found with the previous large numbers, and III Chicchan\n(repeated three times), and then III Kan (twice), forming the beginning and\nend of the series (page 64), and also III Cimi and III Ix. As we shall see\ndirectly these are the end dates of the large numbers, and Xul = end\nrepeated eight times at the extreme bottom corresponds with this. On the\nother hand, the starting-points must be found by computation, with the\nexception of the date IX Kan 12 Kayab, which is actually written down and\nis the point of departure for three of the numbers.\n\nI will designate the black numbers by _a_ and the red by b. Seven of the\neight numbers are undoubtedly absolutely correct; but I must alter the\nnumber 1b, the red number belonging to the first serpent. I assume that a\nline is wanting in the lowest figure, _i.e._, it should be 8 instead of 3,\nand that the conspicuously large 1 further down on the page serves also as\nthe red number, which belongs here. Only one slight change is necessary in\nthe dates on the bottom of the pages, which were mentioned above. To the 16\nin the date 4b I add a dot, and read it 17.\n\nI will now give a table of the numbers, the starting-points of the periods\nobtained by computation, and the ends of the latter which are indicated\nbelow the serpents:--\n\n  1a: 12,489,781; XI Kan 12 Kankin (1 Ix); III Chicchan 18 Xul (4 Muluc).\n  1b: 12,388,121; XI Kan 12 Muan (7 Ix); III Chicchan 13 Pax (4 Ix).\n  2a: 12,454,761; IX Kan  7 Kankin (4 Cauac); III Chicchan 13 Yaxkin\n           (2 Ix).\n  2b: 12,394,740; IX Kan  2 Chen (5 Kan); III Kan 12 Ceh (7 Ix).\n  3a: 12,438,810; IX Kan 12 Xul (3 Ix); III Ix 7 Zac (9 Muluc).\n  3b: 12,466,942; IX Kan 12 Kayab (4 Ix); III Cimi 14 Kayab (9 Ix).\n  4a: 12,454,459; IX Kan 12 Kayab (4 Ix); XIII Akbal 1 Kankin (1 Kan).\n  4b: 12,394,740; IX Kan 12 Kayab (4 Ix); III Kan 17 Uo (7 Muluc).\n\nSee my treatise, \"Die Schlangenzahlen in der Dresdener Mayahandschrift\"\n(Weltall, year 5, pages 199-203).\n\nSeveral details show how this number-structure forms a definite, closely\nconnected whole.\n\n1. The beginning day in each case is the day Kan, which thereby indicates\nits position as the first.\n\n2. The last three starting-points are the same; the first three end dates,\nat least, are the same in the Tonalamatl, though not in the year.\n\n3. The two numbers 2b and 4b are exactly the same.\n\n4. The first three numbers are each divisible without a remainder by 17,\nthe interval from XIII Akbal to IV Ahau, which was true also of the\n1,268,540 in the second column on page 63, although only this last number\nhas anything to do with these important days, of which the other three\nnumbers are independent.\n\nOn the other hand, a notable difference between the first serpent and the\nother three is, that the day XI Kan is the starting-point of the first and\nIX Kan of the others. There are, however, 80 days between IX Kan and XI\nKan. Hence the numbers 2a and 1b are separated from each other by 66,640 =\n256 \u00d7 260 + 80, although they have the same end III Chicchan.\n\nFurther it is to be noted that the largest of the eight numbers,\n12,489,781, is separated from the lowest, 12,388,121, _i.e._, the black\nnumber from the red one of the first serpent, by only 101,660, _i.e._, by\nnot a full one per cent of the entire magnitude. 101,660 = 5 \u00d7 18,980 + 26\n\u00d7 260 or 391 \u00d7 260 or 7820 \u00d7 13.\n\nIt is to be noted also that the differences between the black and red\nnumbers in the second and third serpents (60,021 and 28,132) are divisible\nby 13 (4617 \u00d7 13 and 2164 \u00d7 13). They _must_ be, since all six numbers\nrefer to the day III.\n\nFinally the question naturally arises, how did the computer obtain these\nvalues, _i.e._, how was the whole structure built up? On page 63 we found a\n136,864 (not 136,884) set down in strikingly small characters and crowded\nbetween the other numbers, which would remain a mystery unless one assumed\nthat it was reserved there for this structure; it is 91 \u00d7 1504. At first I\nthought it possible that this 136,864 had been again multiplied by 91, the\nreal basal number of this section; for we had found a second power once\nbefore (on pages 46-50) by computation, viz:--2 \u00d7 260 \u00d7 260. The result of\nmultiplication in this case would be 12,454,624, and the differences\nbetween the eight numbers in the serpents would be as follows:--1a +\n35,157, 1b - 66,503, 2a + 137, 2b and 4b - 60,884, 3a - 17,814, 3b +\n12,318, 4a - 165. But these differences are doubtful, inasmuch as they bear\nno relation to the dates beginning and ending the serpent numbers.\n\nOn the other hand, another number contains the desired properties. I refer\nto the 12,412,920, _i.e._, it is 109 times the so-called Ahau-Katun of\n113,880 days, and I believe I have found that the Ahau-Katun and its\nmultiples were mostly used in the formation of the large numbers. In the\nfollowing table I have placed this number beside each of the serpent\nnumbers, have then found the difference between the two and have added to\nit the interval between the first and last day of each serpent number:--\n\n  1a) 12,489,781                       1b) 12,388,121\n      12,412,920                           12,412,920\n      ----------                           ----------\n          76,861 = 295 \u00d7 260 + 161            -24,799 = 95 \u00d7 260 + 99\n          XI Kan - III Chicchan = 161.         III Chicchan - XI Kan = 99.\n\n  2a) 12,454,761                       2b) 12,394,740\n      12,412,920                           12,412,920\n      ----------                           ----------\n          41,841 = 160 \u00d7 260 + 241            -18,180 = 69 \u00d7 260 + 240\n          IX Kan - III Chicchan = 241.         III Kan - IX Kan = 240.\n\n  3a) 12,438,810                       3b) 12,466,942\n      12,412,920                           12,412,920\n      ----------                           ----------\n          25,890 = 99 \u00d7 260 + 150              54,022 = 207 \u00d7 260 + 202\n          IX Kan - III Ix = 150.               IX Kan - III Cimi = 202.\n\n  4a) 12,454,459                       4b) = 2b\n      12,412,920\n      ----------\n          41,539 = 159 \u00d7 260 + 199\n          IX Kan - XIII Akbal = 199.\n\nWhere the serpent number is less than 12,412,920, I have had to place the\nlast day before the initial day.\n\nThe work of the Indian computer was, therefore, as follows:--\n\nHe took the days for granted. First he determined the differences between\nthem; then he added to each difference a multiple of 260; and the choice of\nthe multiple seems to have been quite arbitrary. The number thus obtained\nhe added to 12,412,920, unless it was the smaller, in which case he\nsubtracted it from 12,412,920, and the result he wrote down in the\nserpents.\n\nWe shall find the same process, only somewhat amplified, with the serpent\non page 69.\n\nAre the seven numbers intended to denote the destruction of the seven\nplanets? I hope this question will be answered in the near future.\n\nThere now remains of the contents of these pages only the two columns on\nthe left of page 61, which we will now examine and at the same time compare\nthem with the corresponding column of page 69, the upper part of which is\nexactly the same, and the lower very nearly so. Each column consists of 18\nhieroglyphs, which I count from the top downward, designating those of the\nfirst column by _a_ and those of the second by b.\n\nAt the first glance these double columns remind one of the inscriptions in\nthe temples and on the stelae, especially of their beginnings, the\nso-called initial series. Here, in the second column, we find the statement\nof the usual periods:--144,000, 7200, 360, 20, 1, but in the first column\nwe find faces belonging to them. In his work \"The Archaic Maya\nInscriptions,\" 1897, which, on the whole, contains more of imagination than\nof science, J. T. Goodman unqualifiedly declares these faces to be numbers\nby which the periods indicated beside them are to be multiplied, and this\ntheory has already found considerable recognition; we will therefore try to\nfollow where he leads.\n\n1a and 1b are effaced on page 61; they probably contained a sort of\nsuperscription as on the inscriptions. 2a is effaced on page 61, but the\nsign may be recognized from page 69 as that with which on page 46 the\nseries of the twenty deities begins after 236 (4 \u00d7 59) days. On pages 61\nand 69 it takes the place of a face, to which I am inclined to assign the\nnumerical value 4. In 2b, which is C's head, I am inclined to look for the\nvalue 2,880,000 = 20 \u00d7 20 \u00d7 20 \u00d7 360 days, which is not at all\ninappropriate for C, as the sign of the north pole around which everything\nrevolves. I therefore propose to read 2ab as 4 \u00d7 2,880,000 = 11,520,000.\n3b, it seems to me, resembles the sign for 144,000, which I found in the\ninscriptions and which is repeated in 12a. It must, however, be left\nundecided by what this same number in 3a is to be multiplied; 3a is\nrepeated besides in 8a and 13b. 4a contains the head of E, and 4b that of\nthe Moan. 4a seems to refer to 5a, and 4b to 5b. But 5a and 5b are the same\nsign, which, inserted between the 144,000 and the 7200, can scarcely mean\nanything else than the so-called Ahau-Katun of 6 \u00d7 18,980 = 113,880 days.\nHave we two such periods here? Were they designated by consecutive numbers?\nNow comes the 7200 in 6a, and the number 8 with E's head and the inserted\nsign for 360 days in 6b (on page 69 without E's head), therefore 8 \u00d7 360 =\n2880. Seler also thinks 7a has the numerical value 16 (Einiges mehr \u00fcber\ndie Monumente von Copan, etc., page 217); 7b belongs to 7a. 7b, a Kin with\na I and a suffix and a leaf-shaped prefix, is inserted between the 360 and\n20. What can it mean? Hardly the 260, for this is represented elsewhere\n(_e.g._, page 24) by the thirteenth month Mac. Or can it possibly refer to\nthe month Yaxkin (days 120-140)?\n\n8b is a Chuen sign, which, with its prefix (superfix on page 69) always\ndenotes twenty days in the inscriptions. It is multiplied with the same\nunknown head in 8a, which we have already met with in 3a. 9a contains H's\nhead, and 9b is an unknown head with inserted Kin; the two signs must of\nnecessity indicate the single days still to be added to the period, though\nas yet we do not know how.\n\nThe normal date IV Ahau 8 Cumhu then follows in 10ab. If it refers to the\nsigns just now discussed, then they must denote a number of about the same\nmagnitude as the serpent numbers. 653 or 654 times 18,980 seems to suggest\nitself, but we shall have more to say later on this subject. My efforts to\nreach a definite result here have failed.\n\nNor does the lower part of the two columns lead me to the desired goal. As\nit seems to consist of several groups, I will first combine 11ab and 12ab.\nI look upon 11a as denoting 20, and with regard to 11b I have already\nexpressed the surmise in the Zeitschrift f\u00fcr Ethnologie XXIII, page 153,\nthat it may mean 8760 = 24 \u00d7 365, _i.e._, three Venus-solar periods. That\nwould be 20 \u00d7 8760 = 480 \u00d7 365 = 175,200. The Moan in 12a may have the\nvalue 13, for this number is so often combined with the Moan. As we saw\nunder page 51, 12b is = 18,980; 13 \u00d7 18,980 = 246,740. Accordingly the four\nsigns taken together may mean 421,940 = 1156 \u00d7 365.\n\nThe second group, from 13a to 15b, refers, on the other hand, to the year\nof 360 days. First 13a = 144,000, having in 13b the unknown multiplier,\nwhich we have already seen in 3a and 8a. Then follows in 14a, 15 \u00d7 7200 =\n108,000; in 14b, 9 \u00d7 360 = 3240; in 15a, a 20 with a prefixed 1 (21?); and\nin 15b, three days. It would be more correct to place the 1 beside the\nfollowing 3. The whole sum would then end with the number 4, which would\nagree with the day Kan, the date specified below.\n\nIn the third group the 16a = 19 \u00d7 18,980 = 360,620, remains a mystery; an\nempty outline of a sign is added in 16b.\n\n17ab also forms a group by itself. 17a contains a sign, which rather\nsuggests the Bacab, upon whose period of 91 days the series belonging here\nis based. The Imix in 17b with a superfix is still unintelligible.\n\nThe columns end in 18 with the date IX Kan XII Kayab, the starting-point of\nthe serpent numbers.\n\nPages 65--69.\n\nI think it very likely that this section bears the same relation to pages\n61-64 as pages 46-50 do to 24 and as 53-58 to 51-52. For here, too, a\nperiod of time forming the basis of the earlier section seems to be divided\ninto smaller parts. On page 64 we recognize as the basis of the series the\nnumber 91, the quarter of the ritual year of 364 days; here we have to do\nwith the fourfold division of 91 into 13 unequal parts. And the real\nstarting-points on these pages, as on the previous ones, are the days III\nChicchan and XIII Akbal.\n\nThe four series of numbers, the top one of which I have probably correctly\nrestored from what still remains, are as follows:--\n\n  9 XII, 5 IV, 1 V, 10 II, 6 VIII, 2 X, 11 VIII, 7 II, 3 V, 12 IV,\n    8 XII, 4 III, 13 III.\n  11 I, 13 I, 11 XII, 1 XIII, 8 VIII, 6 I, 4 V, 2 VII, 13 VII, 6 XIII,\n    6 VI, 8 I, 2 III.\n  11 XI, 13 XI, 11 IX, 1 X, 8 V, 6 XI, 4 II, 2 IV, 13 IV, 6 X,\n    6 III, 8 XI, 2 XIII.\n  9 IX, 5 I, 1 II, 10 XII, 6 V, 2 VII, 11 V, 7 XII, 3 II, 12 I, 8 IX,\n    4 XIII, 13 XIII.\n\nThe first two lines, forming together a single period of 182 days, refer to\na day III, as we see by the ending, and the last two to XIII, which\nundoubtedly refers to the III Chicchan and XIII Akbal, the days so\nsignificant in the preceding section. Hence an interval of 218 days (III\nChicchan to XIII Akbal) is to be assumed between the second and third\nlines, with the addition of which interval each of the two periods extends\nover 400 days.\n\nThe first and fourth series have the same difference; and the second and\nthird correspond with one another in this respect. In the first and fourth\nthe differences follow a rule, viz:--as if one were walking in a ring\nhaving on its edge the numbers 1 to 13, and kept stepping backward four\nnumbers. The differences of the second and third series apparently do not\nfollow any rule. Hence I think that the fourth series follows the third by\nmistake and ought rightfully to precede it. Only the fifth member in the\nfirst and second series has the same day VIII and the day V in the third\nand fourth series, otherwise the week-days of each series differ from those\nof the others.\n\nAs I regard III Chicchan and XIII Akbal as unquestionably the\nstarting-points, I will here give a table of the days on which each of the\ntwenty-six members of each series must fall and at the same time I will\nindicate for each day its number from the beginning of the series.\nAccordingly the first 182 days present the following appearance:--\n\n     III 2.\n\n   1.      9.    XII Ix\n   2.     14.    IV Cauac\n   3.     15.    V Ahau\n   4.     25.    II Oc\n   5.     31.    VIII Cib\n   6.     33.    X Eznab\n   7.     44.    VIII Muluc\n   8.     51.    II Cib\n   9.     54.    V Cauac\n  10.     66.    IV Chuen\n  11.     74.    XII Cauac\n  12.     78.    III Akbal\n  13.     91.    III Cib\n  14.    102.    I Manik\n  15.    115.    I Ahau\n  16.    126.    XII Chuen\n  17.    127.    XIII Eb.\n  18.    135.    VIII Ahau\n  19.    141.    I Cimi\n  20.    145.    V Oc\n  21.    147.    VII Eb\n  22.    160.    VII Chicchan\n  23.    166.    XIII Chuen\n  24.    172.    V Caban\n  25.    180.    I Chicchan\n  26.    182.    III Manik\n\nIn the same way I will tabulate the second group of 182 days, but in this\ncase I shall place the fourth line before the third, which is probably\ncorrect, and which shows for the first time parallelism of the two rows:--\n\n    XIII 20.\n\n   1.      9.    IX Eb\n   2.     14.    I Caban\n   3.     15.    II Ezanab\n   4.     25.    XII Lamat\n   5.     31.    V Ix\n   6.     33.    VII Cib\n   7.     44.    V Manik\n   8.     51.    XII Ix\n   9.     54.    II Caban\n  10.     66.    I Muluc\n  11.     74.    IX Caban\n  12.     78.    XIII Imix\n  13.     91.    XIII Ix\n  14.    102.    XI Chicchan\n  15.    115.    XI Ezanab\n  16.    126.    IX Muluc\n  17.    127.    X Oc\n  18.    135.    V Ezanab\n  19.    141.    XI Kan\n  20.    145.    II Lamat\n  21.    147.    IV Oc\n  22.    160.    IV Akbal\n  23.    166.    X Muluc\n  24.    172.    III Men\n  25.    180.    XI Akbal\n  26.    182.    XIII Chicchan\n\nIt would be very essential now to know what place these days occupy in the\nyear, and what year is meant; the answer to one of these questions would at\nthe same time solve the other.\n\nNow I think I come nearer to the solution of this problem by assuming that\nthe pictures and hieroglyphs refer here only to the more important of the\ntwo days, XIII Akbal, and that III Chicchan is represented only by the\nnumbers of the series. Thus both the pictures and the hieroglyphs of the\ntwo sections connect without the interval of 218 days, which must be\nassumed in the case of the numbers.\n\nHere, as is usually the case of series, we have to begin at the bottom. Now\nthe first group of the lower half of page 65 contains the sign 9 Kan. If,\nas it seems, this actually denotes the year, then the day XIII Akbal must\nbe the first of the eleventh month, _i.e._, the 201st day of the year.\nHence I will again set down the twenty-six dates, but add to them the\nposition in the year.\n\n   0.            XIII Akbal I Zac (9 Kan)\n   1.      9.    IX Eb 10 Zac\n   2.     14.    I Caban 15 Zac\n   3.     15.    II Ezanab 16 Zac\n   4.     25.    XII Lamat 6 Ceh\n   5.     31.    V Ix 12 Ceh\n   6.     33.    VII Cib 14 Ceh\n   7.     44.    V Manik 5 Mac\n   8.     51.    XII Ix 12 Mac\n   9.     54.    II Caban 15 Mac\n  10.     66.    I Muluc 7 Kankin\n  11.     74.    IX Caban 15 Kankin\n  12.     78.    XIII Imix 19 Kankin\n  13.     91.    XIII Ix 12 Muan\n  14.    102.    XI Chicchan 3 Pax\n  15.    115.    XI Ezanab 16 Pax\n  16.    126.    IX Muluc 7 Kayab\n  17.    127.    X Oc 8 Kayab\n  18.    135.    V Ezanab 16 Kayab\n  19.    141.    XI Kan 2 Cumhu\n  20.    145.    II Lamat 6 Cumhu\n  21.    147.    IV Oc 8 Cumhu\n  22.    160.    IV Akbal 21 Cumhu\n  23.    166.    X Muluc 2 Pop (10 Muluc)\n  24.    172.    III Men 8 Pop\n  25.    180.    XI Akbal 16 Pop\n  26.    182.    XIII Chicchan 18 Pop\n\nLet us now prove the correctness of my theory by an examination of groups\n22 and 23. In 22 the 160th day of this period, the 361st day of the year is\nreached, _i.e._, the first of the five Uayeyab days. The year 9 Kan is\nended and the year 10 Muluc is not yet reached. In the corresponding\npicture we see B occupied in conveying in a bag the image of God K to whom\nbelongs the next year. B is armed with the official staff and the bag also\ncontains water (rain). In the 23d group the 166th day has passed and the\nsecond of the year 10 Muluc is reached, which gives the name to this year.\nThe first hieroglyph shows two personages sitting back to back. This\nrepresentation is repeated on a larger scale below in the Janus picture of\nB who is sitting on signs of planets. The second hieroglyph, with equal\nfitness, represents a clamp, which is intended for fastening two objects\ntogether, and which is repeated twice over the Janus picture, black in one\ncase and white in the other. Rain is pouring over the second half of the\npicture, for it has long been known that Muluc and rain belong together,\nand in our examination of page 7a we saw that K is the ruler of the day\nMuluc (6).\n\nNow, before I begin the examination of the separate pictures and the groups\nof six hieroglyphs belonging to each picture, I wish to mention three\nthings which are often repeated here.\n\nFirst, B's picture, which appears in all the twenty-six pictures with the\nexception of 20, 24 and 25, and represents the god in the most varied\npositions and activities. These pictures are very similar to those on pages\n29-46 and we shall therefore make frequent reference to the section there\nrepresented.\n\nSecond, the first hieroglyph in groups 1 to 13, strange to say, is not\nfound in the second half. It is hieroglyph _f_, which appears in exactly\nthe same way in close combination with B in two sections, which differ from\neach other but are placed side by side on pages 30c-39c. In the present\npassage it has a distinct prefix resembling the beak of a bird or tortoise,\nbut in the former passage it has rather a stunted appearance. It seems to\nrefer to the eagle in B's hands in group 13.\n\nThird, the head with no underjaw, which is the sixth hieroglyph in groups 1\nto 13, but does not occur in groups 14 to 26. It is repeated in a very\nsimilar fashion in the last hieroglyph but one on page 23b. I propose to\nattribute to it the meaning of fasting.\n\nNow for the single groups:--\n\n1. B is seated rowing in a boat, as he is represented also on pages 29c,\n36b, 40c and 43c. A creature is swimming beneath him, which may be a\ncrocodile. The fifth hieroglyph is the important 9 Kan already discussed,\nthe fourth is _a_ and the second the cross _b_ combined with Caban. The day\nis the 210th of the year.\n\n2. B is walking with the atlatl in his hand, and armed with javelins.\nHieroglyph 5, Manik, denotes the chase, but has a prefix, which often seems\nto have the meaning of 20. 2 is the elongated head _q_ with the prefix of\nthe east belonging to the Kan years. 4 is a Moan sign (c) with the\nleaf-shaped prefix. Does this perhaps denote the slaying of game in the\nforest? It is remarkable that B's feet are hidden, as if he were walking in\nsand or in a bog.\n\n3. B is walking, carrying a large stick like that for tilling the field, as\non pages 38b and 39b, and he bears a carrying-frame; there are footprints\nbelow him. Hieroglyph 2 is the compound of the signs for south and east, 4\n(_r_) may denote rain, and 5 is two elongated heads with an unknown prefix.\n\n4. B, is seated on astronomical signs as on page 37c. The copal pouch is\nhanging from his neck and he is brandishing his hatchet. Sign 2 is _b_, 4\nis _a_ and 5 is _r_, but all three signs have unusual prefixes; the first\nof these prefixes appears again in the tenth group, 41 days later.\n\n5. B is seated on a head, probably that of D, which, however, is peculiar\nowing to the ornaments resembling bunches of grapes in place of both the\neye and the ear (compare pages 39c and 41a). I do not venture to decide\nwhat he holds in his hand nor what are the other objects which he carries.\nSign 2 is _r_ with a prefix, 4 is Imix perhaps with a knife as a prefix, 5\nis the skeleton which sometimes belongs to the lightning beast, but also to\nthe 14th month; its prefix is unknown.\n\n6. B is seated on a support, which contains two cross-bones, down to which\nhe points with his right hand, while his left hand holds the hatchet on his\nknee. Sign 2 is the crouching naked personage, with the cross _b_ prefixed,\n4 is the elongated head with a prefixed Yax, and 5 is Kan with a vessel as\na prefix (instead of Imix) from which steam or froth is rising. The day is\nthe 234th of the year, _i.e._, the end of a week of 18 \u00d7 13 days.\n\n7. B is sitting on a tree at the root of which his own head appears\n(compare with this the representations on pages 31c, 33c, and especially\n40a, and also 41b and 42b). The second sign is Yax with a prefix; 4 is Kin\nwithin which there is a 1, as is several times the case, for example, on\npages 61 and 69. The fifth sign is still a mystery to me. The day here is V\nManik. Do the hieroglyphs suggest that the interval from the day IX Kan,\nwhich gives the name to the year, to V Manik is exactly the same as that\nfrom the normal date IV Ahau to the true starting-point of our passage, the\nday XIII Akbal? Both intervals are 243.\n\n8. B is seated in a house, on the roof, wall and floor of which are several\nCaban signs, just as on page 30a; he seems to be pointing forward. Sign 2\nis Caban with a prefix, the 4th and also the 5th is Kan with two unusual\nprefixes.\n\n9. Water is pictured at the bottom of this picture, and in it are a fish, a\nmussel and a snail (possibly page 37b may be compared with this). There\nseems to be a suggestion of footprints on the margin of the water, back of\nwhich B is walking, his legs hidden as far as the knees. He holds the\nhatchet uplifted in his left hand and his right holds what may be a\nlong-stemmed aquatic plant (compare page 42b). Sign 2 is composed of _b_,\nImix, the mouth and nose of C and the object which apparently is a beak,\npreviously met with in sign 1. 4 is Kan-Imix, and 5 is Kan with prefix and\nsuffix.\n\n10. B is seated in an expectant attitude, his hands resting on his knees.\nWe see a very similar representation of him on page 38a, where he faces\nhimself, and in general the remaining pictures of that passage furnish a\nstriking parallel to the present one. Sign 2 is a head (E's?) with a call\nseemingly issuing from its mouth. 4 is the elongated head _q_ with the\nBen-Ik superfix and an unusual prefix, which we found on page 66c prefixed\nto the cross _b_; 5 is Kan with the same prefix, which I regarded as\ndenoting a call in sign 2, and which is probably answered here by an\naffirmative cry.\n\n11. The expectation has been fulfilled. B is seated on a mat holding a\nwoman in the same position as on page 38a. Sign 2 is the cross _b_ with the\nprefixed beak as in 1, and also with another prefix, which seems sometimes\nto denote the number 20. 4 is exactly the same Kin with 1 and the\nleaf-shaped prefix, which occurred in the same place with the seventh\npicture. 5 contains the sign for 73 days; a new period of this length\nbegins here on the 74th day.\n\n12. As in the parallel passage on page 38 B seems to be offering a Kan, so\nhere his gift consists of a kind of wreath, like the one in the fifth\npicture; he is seated on astronomical signs, which contain the cross _b_\ntwice as does also hieroglyph 2. 4 is Kin-Akbal, and 5 is a Kan with the\nprefix which generally belongs to the south as a superfix.\n\n13. B is seated on the elongated head _q_ with a superfix and a prefix,\nexactly as on pages 37c and 40a, and this sign is repeated in the\nhieroglyphs (in 2) just as it is in the two former places. He holds the\neagle on his lap and we see him connected with the same bird in a different\nway on page 43c. Is B represented here as the preventer of evil? Hieroglyph\n4 is _a_, while 5 is Kan, apparently with the sign of the south as a\nprefix. A Bacab period of 91 days ends here. We come now to the upper\nseries of pictures.\n\n14. B is walking in the rain, with the copal pouch around his neck and the\nhatchet uplifted in his left hand. An unknown object, possibly held in his\nright hand, is hanging in front of his legs. Hieroglyphs 1 and 3 are\neffaced, 2 is indistinct, 5 seems to be a Xul (end, close) and 6 is E's\nhead.\n\n15. B is walking, brandishing the hatchet in his left hand, and holding in\nhis right an object resembling a cornucopia filled with fruit; below this\nhangs what appears to be a flower. The god wears the copal pouch.\nHieroglyph 1 is a hand holding K's head; it is curious that this sign\nshould also occur in the next group as an indication of the approaching\nMuluc year. 3 is a sign still undetermined; but the prefix is the crouching\nnaked personage with dots suggesting stars around its head. I have often\nthought that similar figures represented Mercury; it is remarkable that\nexactly the 115th day of this section is reached here, corresponding with\nthe apparent revolution of Mercury = 115 days. Similarly sign 2 invites\ncomputation; it is a face resembling an Ahau sign, with a 3 as a superfix\nand a 9 as a prefix; compare the other places containing the same face,\nwith 33c. After the fashion of the inscriptions this would denote 9 + 3 \u00d7\n20 = 69, which by the way is three fifths of the Mercury revolution. 5 is a\ncompound of Akbal and Imix and 6 a compound of a Moan sign (_c_) with a.\n\n16. B is in a half sitting position and holds a strange object before\nhimself. On top of his own head is K's, which is repeated in sign 2. I do\nnot know how to explain 1, unless it is the bat-god; 3 is a Xul = end (but\nof what?) combined with Imix, and 5 is the usual Kan-Imix. 6 is a Kin with\nan 8 back of it (as 36b, 37b, 67a, 68a) and over it is a hand pointing to\nthe right, just like those in groups 20 and 25. This looks as if we ought\nto count forward 8 days, but what can be the purpose of doing so?\n\n17. B is walking armed with spear and shield. Sign 1 is _b_, 2 the face\nresembling an Ahau, which occupied the second place in group 15, 3 is\nprobably Xul again, but with an effaced prefix; of 5 also only an Imix\nremains; while 6 is the usual compound of Muluc-Caban.\n\n18. We have now reached the day 16 Kayab, a day very close to the day 18\nKayab, which on page 24 we recognized as an especially important day, while\nin my article \"Zur Entzifferung III\" I regarded it as the day of the summer\nsolstice. Computed from the normal date IV Ahau 8 Cumhu it may also have\ndenoted the end of a lunar year, as on pages 51-58 where it is the basis of\nthe series. The picture here agrees with this. B is sitting in the pouring\nrain of the rainy season and gazing upward at the planets, as on page 36c\nand particularly on 39c; the sun and moon are also represented, but below\nthe planets. The hieroglyphs likewise contain the sun and moon in 1 and 2,\nin 3, Ahau and Xul with a prefix, as if this were the end of the increase\nof the sun's power; 5 is Kin-Akbal, day and night, and 6 is Caban with the\ncross b.\n\n19. B is walking armed with hatchet and shield. He holds a serpent in his\nhand as on page 40c, but here with the head downward. Hieroglyphs 1 and 2\nare destroyed, 3 is the cross _b_ with a suffix and the horse-shoe prefix\n_e_, known to us from pages 5 and 6. 5 is Imix combined with Chuen and\nprobably with Yax, and 6 is E's head.\n\n20. This is the old red woman with the tiger claws, whom we saw on pages\n39b and 43b and shall see again on page 74; she reinforces the water\nfalling from the planets by pouring a stream from her jug. The first three\nhieroglyphs are effaced, 4 is the elongated head _q_, 5 is Kin-Akbal, 6, as\nin group 16, is again the enigmatical 8 with a hand pointing to the right.\n\n21. B is walking and bears pouch, spear and shield. Hieroglyph 1 is a hand\nholding the sign of the rising Moan, just as in 15 a hand holds the head of\nK; 2 is again K, whose sign is probably effaced several times in the last\ngroups of this series. 3 is E with the sign of the east; 5 is compounded of\nImix, Chuen and _b_, and 6 is Kin with the sign of the north. Here the day\nof the normal date is reached, but this may be significant only for the\nyear 9 Ix.\n\n22. We come now to the representation of the change of the year, which we\nhave already mentioned. Hieroglyph 1 is curious, consisting of the moon\nwith a stripe running around it like a strap; 3 and 5 are not clear to me\nand are doubtless closely connected with one another; 3 also contains a\ntrace of K and is perhaps a determinative of the same. 6 is again E, and\nsuggests the tilling of the fields.\n\n23. This picture as well as the first two hieroglyphs have already been\ndiscussed above. The crouching personage, repeated again in 3 as a prefix\nto the cross _b_, is curious. 5 is again E and 6 is Imix, referring to\ngrain and honey.\n\n24. The picture and three of the hieroglyphs plainly correspond. The grain\ndeity E holds food and drink in his hand. Rain is pouring from the planets,\nand the wind-beast plunges down, as on pages 44 and 45. Sign 3 is E's\nhieroglyph, 6 is Kan-Imix and 2 is the wind-beast. B is superfluously added\nin 4 and the same is true of the cross _b_ in 1, while Kin-Akbal in 5 seems\nto fit almost everywhere. Pages 29a, 30a and 45c show the lightning-beast\nin a different form.\n\n25. As is usually the case, rain is pouring from the stars and below them\nare the sun and moon as before. This time C is sitting in the rain, clad in\nthe gala mantle and holding Kan. Hieroglyphs 1, 2 and 4, the latter\napparently representing C, are effaced. The other three are enigmatical, 3\nis again Xul with a prefixed 9, 5 a Caban, but with an unintelligible\nprefix, and 6 is again the mysterious 8.\n\n26. B is sitting on a tree or sacrificial stone, which is colored half blue\nand half red, and may denote the ceasing of the rainy season; he is\nbrandishing his hatchet. Hieroglyphs 1, 2 and 3 are effaced; 4 is B's sign,\n5 might be Xul and 6 is _a_ with _c_ added and thus referring to the Moan.\nAnd here the half of the ritual year ends with the 182nd day, which is XIII\nChicchan 18 Pop (10 Muluc); and it is left to the reader to imagine or to\nfind hieroglyphs and pictures for the other two series of numeral signs.\n\nI am troubled about the five naked crouching figures of this section, which\nI am inclined to regard as the sign for Mercury with its apparent\nrevolution of 115 days, which, however, seems sometimes (as on pages 54, 56\nand 58 in the upper sections) to be raised to the value of half a\nTonalamatl = 130 days. This may be explained by the fact that it is\ndifficult to determine exactly the length of the revolution of Mercury. In\ngroup 15 this figure appears exactly on the 115th day of this section, but\nin group 6 on the 234th day of the year, _i.e._, approximately at the\nexpiration of two Mercury periods after the beginning of the year. But now\nfor group 23. Here there are three of these crouching figures. The two\nupper ones leaning back to back must serve the purpose of indicating the\nchange in the year. But they would hardly do so, if the third personage\nwere not added, which may indicate that the solar year consists\napproximately of three Mercury periods. I look upon this view of the matter\nmerely as the first attempt at an explanation.\n\nPages 69--73.\n\nThe chief subject of the last great section of this Manuscript is two of\nthe usual series, from which large numbers are developed in the usual way\nand the largest of all is finally recorded in a serpent. This section thus\nforms a parallel to the contents of pages 61-64, but is somewhat more\ncomposite.\n\nBefore I begin the discussion of these series, I wish to examine two\npassages, which I think are not connected with these series, but are\nindependent, like the instance on pages 51-58, where the hieroglyphs were\nfound to be quite independent of the numerals. The Mayas took advantage of\nspace wherever it presented itself, which is admissible in ideographic\nwriting.\n\nThe first of these two passages is at the top of pages 71-73. Here there\nare four horizontal rows of twelve hieroglyphs each. Since, however, the\ntop row is entirely effaced and none of the other three are perfectly\npreserved, it is quite impossible at present to judge of the\ninterconnection of the whole. But I must point out a certain resemblance to\nthe passage on pages 44b-45b, where a period of 78 days is considered with\nreference to the wind-deities. The first and sixth columns of pages 71-72\nlikewise contain the signs for wind and the pierced ears. The fact that the\nBacab sign occurs in the eighth column, and in no other, must attract\n'attention; if we knew it to be effaced in the first column, then each\ncolumn might refer to 13 days, though 12 \u00d7 13, it is true, does not form a\nnatural whole. C's sign is the only hieroglyph of a god to be found in both\npassages. E also occurs on pages 44b-45b and may be one of the effaced\nsigns on pages 71-72. There is no trace left of the others. The fact that\nsome hieroglyphs occur in both the passages referred to proves nothing with\nregard to signs in frequent use and I can find no cases of correspondence\namong those occurring more rarely. Hence this passage must be left for the\npresent as an almost complete mystery.\n\nI have discussed the second passage in detail in my article \"Zur\nEntzifferung der Mayahandschriften V,\" of the year 1895, and from it I will\nborrow the following. This second passage fills the middle and lower thirds\nof pages 71-73, occupying the same space as the first passage in the upper\nthird, and offering far more reliable material than the latter.\n\nThat these hieroglyphs are not connected with the numerals above and below,\ncan be deduced from the fact that the numbers follow one another from right\nto left and the hieroglyphs in the reversed order. This is proved by the\nhand pointing to the right, which occurs here at least eight times like the\none occurring twenty times on pages 46-50.\n\nBut the scribe, misled by the direction of the numeral series, began on\npage 71 to write the _first_ of these hieroglyphs from the right instead of\nfrom the left, but after the first four groups he corrected his mistake.\nHence I read the groups of three hieroglyphs each, in the following\norder:--\n\n  Page 71.          Page 72.                 Page 73.\n    2  1 |  5   6   7   8   9  10  11 | 19  20  21  22  23\n    4  3 | 12  13  14  15  16  17  18 | 24  25  26  27  28\n\nThe number 28 shows that we have to do here with 28 weeks of 13 days each,\n_i.e._, with a ritual year of 364 days, as was the case on pages 31-32,\n63-64 and 65-69. This year, however, is divided into four parts of 7 x 13 =\n91 days, _i.e._, into four so-called Bacab periods. This is very plainly\nindicated here, for groups 4, 11, 18 and 25, _i.e._, those separated by\nseven groups each, are exactly alike, but in group 4b (I will designate the\nthree hieroglyphs of each group from top to bottom by _a_, _b_ and _c_)\nthere is a prefixed 4 which refers to the four Bacabs as does the same 4\nprefixed to the Bacab sign at the top of page 72.\n\nNow the question arises as to when this ritual year began. Undoubtedly its\nbeginning day was very different from that of the civil year (360 days) and\nfrom that of the astronomical year (365 days).\n\nIn this matter I follow Mrs. Zelia Nuttall, who has rendered such estimable\nservice to Aztec science. At the Congress of Americanists at Stockholm in\n1894, she submitted an article entitled \"Note on the Ancient Mexican\nCalendar System,\" in which with keen discernment she pointed out a year\nbeginning with the spring equinox and including in its centre the sacred\nTonalamatl, _i.e._, 260 days, which were preceded and followed by 52 days.\nI recognize this ritual year also in the present passage of the\n\"Dresdensis,\" as the one current in the Maya country. It probably began\nabout the 10th of March, at that period about the time of the vernal\nequinox, according to the Julian Calendar.\n\nBeginning with this date, I will now attempt to tabulate the chronology of\nthis passage. In the first column I will place the number of the group of\nhieroglyphs in question, in the second I will set down to what day of the\nMaya year each group refers; in the third, the corresponding day of our\nyear, and finally in the fourth, the 20-day periods which agree in general\nwith the dates.\n\n   1.     1-13    March 10-22               Ceh.\n   2.    14-26    March 23-April 5          Mac.\n   3.    27-39    April 6-18              } Kankin.\n   4.    40-52    April 19-May 1          }\n   5.    53-65    May 2-14                  Moan.\n   6.    66-78    May 15-27,                Pax.\n   7.    79-91    May 28-June 9           } Kayab.\n   8.    92-104   June 10-22              }\n   9.   105-117   June 23-July 5          } Cumhu.\n  10.   118-130   July 6-18               }\n  11.   131-143   July 19-31                Pop.\n  12.   144-156   August 1-13             } Uo.\n  13.   157-169   August 14-26            }\n  14.   170-182   August 27-September 8     Zip.\n  15.   183-195   September 9-21          } Zotz.\n  16.   196-208   September 22-October 4  }\n  17.   209-221   October 5-17              Zec.\n  18.   222-234   October 18-30           } Xul.\n  19.   235-247   October 31-November 12  }\n  20.   248-260   November 13-25            Yaxkin.\n  21.   261-273   November 26-December 8  } Mol.\n  22.   274-286   December 9-21           }\n  23.   287-299   December 22-January 3   } Chen.\n  24.   300-312   January 4-16            }\n  25.   313-325   January 17-29             Yax.\n  26.   326-338   January 30-February 11  } Zac.\n  27.   339-351   February 12-24          }\n  28.   352-364   February 25-March 8       Ceh.\n\nIn the following I will call attention to a few points by which this\narrangement is justified.\n\nHieroglyph 1a admits of explanation. It consists of four parts:--the left\ntop is Kin, meaning sun or day, the right top is the sign of the year, the\nright bottom is the knife as symbol of separation or division, and the left\nbottom, which is especially decisive, is the month Ceh. Hence I read 1a\nthus:--the day of the change of year in the month Ceh. The sign 1b is the\nfamiliar Kin-Akbal signifying either the beginning day or the day Akbal. If\nthe year should be named from this sign, then this would mean a Kan year,\nas in the preceding section the beginning lay in the year 9 Kan. If the\nyear in the latter section had been as equally divided as the one in\nquestion here, it would have furnished us with some very remarkable\nparallels.\n\nAgain the four groups:--4, 11, 18 and 25, which are alike, are important.\nThe cross in sign _a_, combined with the three dotted lines passing from\ntop to bottom, may refer to the wind and this meaning is further confirmed\nby the Ik sign (wind) in c. Further the sign _b_ between them is that for\nthe Bacab, the wind deity itself.\n\nThe most important events of the year are obviously the sowing and\nharvesting of the maize together with the beginning and end of the rainy\nseason. Now we find the first two in connection with the god E, the\nmaize-god, who is represented in 6c and 13c, 91 days apart, corresponding\nto the end of May and the beginning of August. Generally speaking, sixty\ndays only were reckoned as the time between sowing and reaping, but here a\nquarter of a year may have been taken as a round number and it may also\nhave reference to a more elevated region.\n\nI am inclined to think that the beginning and end of the rainy season are\nreferred to in signs 8c and 16c, where, as it seems to me, three lines of\ndrops are falling from a rectangle denoting the sky (as is usual) like the\nrepresentation of rain dropping from a cloud at the bottom of page 36\n(second picture). The serpent 8b as symbol of water may also refer to the\nsame thing, especially as it is combined with an Akbal (often denoting\nbeginning). The sign, which I think denotes the rainy season, is very\nsimilar, but not the same as another one, which is common to the Dresdensis\nand Tro-Cortesianus, the significance of which is certainly very close to\nthe idea of the week of 13 days.\n\nI have some other ideas on this subject, which, however, are mere\nconjectures, advanced with some hesitation. If the Chuen sign in 7a is\nactually a serpent's jaw, then it might refer to the beginning of the\nastronomical year in May, since the serpent so often designates that time.\n\nIn 9b we find a crouching figure with the sign which is usually considered\nthat of the death-bird. In another place (Zur Entzifferung IV, 12) I have\nregarded the naked human figure placed upside down on page 58 as the sign\nfor Mercury, and on page 60 at the bottom, left, I also regarded the\ncrouching figure as representing Mercury vanquished by Venus. But in 9b,\nwhich belongs to the 105th-117th days of the year, a 115 day revolution of\nMercury is computed. A crouching figure, like that in 9b, likewise appears\non page 65a in the second series of 91 days after 11 + 13 = 24 days of this\nseries have elapsed, _i.e._, directly after the 115 days of the apparent\nrevolution of Mercury.\n\nIn 10b, and it is the only place in this passage, we find the hieroglyph of\nB, the leading god of this Manuscript. This corresponds with the time of\nthe greatest power of the sun and of the change in the civil year (July\n16th). In Group 12, do _a_ and _c_ mean the year and is _b_ the head with\nthe Akbal eye, thus denoting the beginning of the civil year? It ought\nreally to have formed group 11, but there was no room for it, since it was\nnecessary that the signs for the period of 91 days should be set down\nthere.\n\nSigns 14a and the combined signs 15bc are almost alike and suggest 1a. Is\nit intended to designate here the ritual year, the time of the autumnal\nequinox (September 10th?). In 15a two hooks, turned in opposite directions\nproceed from one side of the sun-glyph. Do they signify two halves of the\nyear and does the 3 in front of them signify the third quarter of the year?\n\n20b is the sign of the death-god A, probably not placed accidentally here\nat the end of the month Xul, which denotes the end; but the end of what?\n\nThe hieroglyph in 23a is a black bird, with two hooks, one pointing up and\nthe other down, projecting from its head. Usually these hooks belong to K,\nand by means of them this bird becomes the storm-bird; the year symbol is\nbelow. Does this hieroglyph signify the time of the shortest day, when\ndarkness predominates?\n\nA peculiarity of this passage is the striking frequency of the sign looked\nupon as that of the death-bird as well as of the cognate sign, which is\ncommonly considered as that of the rising Moan. The first bird is in the\n14th group, in the 9th it is combined with the apparent Mercury sign, and\nin the 17th with the year sign. The second bird with the prefixed Yax is in\nthe 2nd group. But it is especially striking that several times both signs,\nand this is the case nowhere else, are combined into a single sign in\ngroups 9, 13 and 26 and also probably in 19 where, however, the Moan sign\nseems to be effaced.\n\nThis is all I have to say at the present time in reference to this\ncalendar. Some of my statements are positive and some are only conjectures.\nCompare my treatise \"Zwei Hieroglyphenreihen in der Dresdener\nMayahandschrift\" (Zeitschrift f\u00fcr Ethnologie, 1905, 2 and 3).\n\nHaving disposed in this way of the two supplementary subjects of this\nsection, I will now proceed to consider the principal theme, viz:--the two\nseries and whatever is connected with them.\n\n1. The 54-Series of the Day IX Ix.\n\nAs with the other series, we begin here at the right, _i.e._, with page 73.\nThere in the last column we find the superscription as it were. It is true\nthat nothing positive can be gathered from the top part consisting of five\nhieroglyphs, which are mostly destroyed. The third hieroglyph seems to be\nthe sign in group 2a discussed above. The fourth is an Akbal with a\nprefixed arm as on pages 8a, 36a, and the fifth is an Ik with a prefix.\n\nBelow these are three numbers:--14,040, 702 and 54, which are in the\nproportion of 260, 13 and 1, so that the 14,040 is a Tonalamatl, as it\nwere, of 260 periods of 54 days each. The fact that 54 is chosen here as\nthe difference of the following series is curious, because usually only\nparts of 260 or of 364 are selected. But 54 is probably only a secondary\nmatter, while 14,040, with its marvellous property of divisibility into the\nmost varied and important periods, is the chief subject.\n\nThere is a 9 in a red circle under the three numbers. It is meant to denote\nthe starting-point of the series, the day IX Ix. Perhaps these two as well\nas the 54 are connected with the 9 \"se\u00f1ores de las noches.\"\n\nIn passing on to the left, I shall not consider the hieroglyphs and numbers\nin the next two columns in the upper third, since they are only set down\nhere in order to secure space for them. They will be discussed later.\n\nThe series itself begins in the upper third of page 71, in the next to the\nlast column; it is continued on page 72 and on page 73 as far as the third\ncolumn. The first twelve numbers are written from left to right contrary to\nthe usual practice, doubtless occasioned by the passage above the series,\nwhich has already been discussed. And below, again contrary to rule, we\nfind not the week and month days, but only the week days and they are in\nred circles. If written in the usual way, the series would have the\nfollowing form (with the usual omission of the initial day IX Ix):--\n\n     54        108      162      216      270       324        378\n  XI Lamat   XIII Ik   II Cib   IV Oc   VI Kan   VIII Ezanab   X Eb\n    432        486      540      594      648\n  XII Cimi   I Ahau   III Ix   V Lamat   VII Ik.\n\nThe series must now continue with the 702 already specified on page 73,\nwhich it proceeds to do from right to left in the middle of page 71, and\ncontinues from there on with regularly added dates and with the 702 itself\nas the difference. At the same time, since 702 = 54 \u00d7 13, the week-days are\nforced to come to a standstill on the IX, while each of the month days\nascends by two (702 = 35 \u00d7 20 + 2). The 4914 = 7 \u00d7 702 is obtained in the\nnext to the last column of page 70. On page 71 the 702 is incorrectly set\ndown as 1. 15. 2. instead of 1. 17. 2. The series continues on page 71 in\nthe same way beyond the 702, until in 7020 a number is obtained which is\nalso divisible by 260, so that now the accompanying day must be IX Ix. Now\nwe ought to expect to see here the double of 7020, the very 14,040\nabovementioned, but it is omitted just because it was set down on page 73.\nNevertheless this very number forms the new difference with which the\nseries returns from page 70 to the top line of page 71, where the numbers\nare mostly effaced, but enough remains to enable us to assume that the last\nnumber on page 71 is the 10th multiple of 14,040, and this may be followed\nby the 11th and 12th multiples, the last number being 168,480.\n\n2. The 65-Series of the Day IV Eb.\n\nThis series begins in the middle of page 73 with the day IV Caban, the\nzero-point therefore being IV Eb. It then advances to the left across 28\nmembers, until on page 71 it reaches the number 1820 = 5 years of 364 days\n= 7 Tonalamatls. From there on, 1820 itself is the difference, and the\naccompanying day therefore remains IV Eb. Then, in the two lowest sections\nof pages 71 and 70, the fourth multiple of 1820, _i.e._, 7280, is the third\ndifference and thus the series advances to 15 \u00d7 7280 = 109,200 on page 71,\nafter which on page 70 the omitted 8 \u00d7 7280 = 58,240 is written out. Close\nbeside this number are the figures 1. 0. 12. 3. and a 0 below the latter,\nwhich was not successfully erased; this would be the number 7443 of which I\ncan make nothing at all.\n\nThe initial dates of the two series, IX Ix and IV Eb, are 138 days apart\nand reversely 122 days.\n\n3. The Groups of Hieroglyphs.\n\nThe transition, as it were, from the series to the large numbers is formed\nby a few groups of hieroglyphs.\n\nThe first of these groups is at the top of pages 69-70; its first top line\nis completely effaced. The remainder I will designate by the following\nnumbers:--\n\n  1  2    5  6     9  13\n  3  4    7  8    10  14\n                  11  15\n                  12  16.\n\nThe date IX Kan 12 Kayab, set down under 3 and 4 does not belong there but\nto the serpent below and will be discussed later.\n\nI take sign 1 to be that of a Bacab, 2 I do not understand and it is half\nobliterated; it seems to occur again on page 73 in the column to the\nextreme right. 3 and 7 are the elongated head _q_ with an unusual superfix,\n4 and 8 correspond with one another, but I cannot explain them. 5, 10 and\n14 denote the beginning, 6, 11 and 15, the end. 9 and 13 both designate the\n8th day of the month Kayab and over them IV Ahau must have been set down\ntwice. 12 and 16 are two heads of gods, 12 is probably D's with the sign\nfor west and 16, B's with that of the east.\n\nOn page 70, in the middle of the third and fourth columns, the day IX Ix\noccurs twice. In one case it ought to have been IV Eb and the scribe has\nreally changed the IX to IV, but he omitted changing the Ix to Eb. Directly\nbelow these dates we find the second group, consisting of two rows of four\nhieroglyphs.\n\nI think these eight hieroglyphs can be interpreted as follows:--\n\n  1) 13 Pax               2) 20 Pop or 25 Cumhu\n  3) VIII Ahau            4) 13 Yaxkin\n  5) 10 Muan              6) 37,960\n  7) 20                   8) 1 Zec.\n\nThe following is to be noted in this connection:--\n\n3 is really set down X Ahau, but an VIII is written above the Ahau by way\nof correction. The day VIII Ahau will presently prove to be important.\n\n6, a compound of Imix and the superfix denoting multiplication, is the sign\nfor 18,980, and its prefix seems to me to denote duplication. We have long\nknown how important the 37,960 = 146 \u00d7 260 = 104 \u00d7 365 is, and, if my\ntheory is correct, we shall see directly that it occurs again here.\n\n8 seems really to be 1 Zec, but the composite prefixes demand further\nexamination.\n\nImpenetrable darkness still shrouds the meaning of the whole group. Though\nit is clear that in several cases certain days are specified according to\ntheir position in the year, their distance apart does not agree with the\ninterval between days IV Eb, IX Ix and IV Ahau under discussion here.\n\nIf signs 3 and 4 ought to be read together as VIII Ahau 13 Yaxkin, then\nthis date would come in the year 7 Muluc. In the Zeitschrift f\u00fcr Ethnologie\nI explained the five hieroglyphs in the third column at the bottom of page\n70 (the third group) as civil years of 360 and astronomical years of 365\ndays:--\n\n  1)       8,760 = 24 \u00d7 365 = 15 \u00d7 584\n  2)       2,920 =  8 \u00d7 365 =  5 \u00d7 584\n  3)       7,200 = 20 \u00d7 360\n  4)      18,720 = 52 \u00d7 360 = 72 \u00d7 260\n  5)         360\n          ------\n          37,960.\n\nThis, it is true, is a striking explanation and certainly a surprising one!\n\nNow the date IX Ix 12 Kayab is at the very bottom of the fourth column.\nThis, without apparent reason, would refer to the year 4 Kan. Should it not\nbe read IX Kan 12 Kayab (4 Ix), thus indicating that the entire passage is\nonly the preparation for the date from which the serpent numbers proceed?\nThe scribe may have had in mind the IX Ix of the series.\n\nThe fourth and last group on page 73, above the two numbers 83,474 and\n34,732, consists of four hieroglyphs. The two upper hieroglyphs on the left\nare effaced, and the top one on the right. I think it probable that the day\nVIII Ahau, which will be discussed later, may have stood in the top line,\nand possibly with a month date. Of the two remaining signs of the fourth\ngroup, the upper is the moon and the lower Imix, probably with the\nhieroglyph of the east as a prefix; but there is nothing to be done with it\nowing to the obliteration of the sign above it. In the Zeitschrift f\u00fcr\nEthnologie, 1891, page 153, I have endeavored to explain these three signs\non the right above 34,732, by suggesting for them the values\n\n  18,980 = 52 \u00d7 365\n   8,760 = 24 \u00d7 365\n   7,200 = 20 \u00d7 360\n  ------\n  34,940\n\nand calling special attention to the fact that between IV Eb and IV Ahau\nthere are 208 days, and that the 34,732 placed below them in the\nManuscript, increased by 208, is equal to 34,940. This group then seems\nreally to belong to the day IV Eb and to the 65-series, while manifold\nproblems are still to be encountered in interpreting the other groups.\n\n4. The Large Numbers.\n\nThe Manuscript offers material with which to work, beginning on page 70:--\n\n  1,394,120     1,437,020     1,567,332     1,520,654\n    (606)         (1646)        IV Eb         IX Ix\n   IV Ahau       IV Ahau       VIII Ahau; 13 Yaxkin (7 Muluc).\n   8 Cumhu       8 Cumhu\n    IX Ix         IV Eb\n  1,201,200     1,202,240       111,554       101,812\n     (86)         (208)\n   IV Ahau       IV Ahau\n   8 Cumhu       8 Cumhu\n\nThis is followed at the right top of page 73 by\n\n  83,474     34,732\n  IX Ix      IV Eb.\n\nTwo of the numbers and two of the dates are conjectural:--\n\nI read the 1,202,240 as 8. 6. 19. 10. 0. while the Manuscript has 16\ninstead of 6. I read the 101,812 as 14. 2. 14. 12. the Manuscript has 16\ninstead of the second 14. And in two places in the third column of page 70,\nI have restored the day IV Eb, where the Manuscript incorrectly repeats the\nIX Ix, and does the same thing on page 73.\n\nLet us now first consider the construction of those large numbers, which\nare connected with the day IX Ix and thus with the 54-series. These numbers\nare the two upper ones of columns 1 and 2 and the lower one of column 1 on\npage 70.\n\n174 is the starting-point, the number of the day is IX Ix, which seems to\nhave been chosen because it divides the Tonalamatl approximately in the\nproportion of 2 to 1. (IV Ahau - IX Ix = 174.)\n\nThe 5359th, 5520th and 4619th multiples of 260 have been added to 174; why\nprecisely these multiples were chosen remains a mystery. In this way were\nobtained the following numbers, which the Manuscript suppresses. I will\ngive them with their corresponding dates:--\n\n  1,393,514 = IX Ix 12 Muan (5 Kan).\n  1,435,374 = IX Ix 17 Chen (3 Cauac).\n  1,201,114 = IX Ix  7 Mac (11 Muluc).\n\nWhen we add to the above the three encircled numbers 606, 1,646 and 86, the\nresulting sums are the three numbers found in the Manuscript:--\n\n  1,394,120 = IV Ahau  8 Chen (7 Ix).\n  1,437,020 = IV Ahau 23 Cumhu (7 Cauac).\n  1,201,200 = IV Ahau 13 Kayab (11 Muluc).\n\nI am placing the first two not far from the present and the third in the\npast.\n\nAs multiples of 260 these three numbers have the following form:--\n\n  1,394,120 = 5362 \u00d7 260.\n  1,437,020 = 5527 \u00d7 260.\n  1,201,200 = 4620 \u00d7 260.\n\nSome curious facts come to light with regard to their magnitude and their\nmutual relation.\n\nThe two largest numbers are 165 \u00d7 260 = 660 \u00d7 65 apart; this recalls the\n65-series. The third lowest number is 165 \u00d7 7280 and thus contains not only\nthe 65 but = 165 \u00d7 65 \u00d7 112.\n\nThe ritual year (364) and its excess over the Tonalamatl (104) is likewise\ncontained in these numbers, at least in the first and third:--\n\n  1,394,120 = 3830 \u00d7 364 = 13,405 \u00d7 104.\n  1,201,200 = 3300 \u00d7 364 = 11,550 \u00d7 104.\n\nThe three encircled numbers are connected with one another because the\nfirst = 2 \u00d7 260 + 86, the second = 6 \u00d7 260 + 86 and the third is 86 itself.\nThe larger encircled numbers are, therefore, 1040 = 4 \u00d7 260 apart, and this\nis also the interval between the two numbers near the bottom. 1040,\nhowever, also = 5 \u00d7 208, and 208 is the interval from IV Eb to IV Ahau. Now\nit is curious that the two numbers below are 5775 \u00d7 208 and 5780 \u00d7 208,\nthough the third belongs to day IX Ix and the fourth to IV Eb. One result\nof this is that 1,201,200 = 1155 \u00d7 1040 and 1,202,240 = 1156 \u00d7 1040.\n\nAs these three numbers relate to day IX Ix and the 54-series, so the fourth\nrelates to IV Eb and the 65-series.\n\nHere the starting-point is the number 52, which belongs to day IV Eb and\nthis is separated from IV Ahau by 208 days _i.e._, it divides the\nTonalamatl in the proportion of 1 to 4.\n\nTo the number 52 then, for unknown reasons was added 4623 \u00d7 260 =\n1,201,980, and thus the number 1,202,032, suppressed in the Manuscript, was\nobtained for the day IV Eb. To this sum the encircled number 208 was then\nadded and the result was 1,202,240, the number in the Manuscript.\n\nThe number = 23,120 \u00d7 52 = 4624 \u00d7 260, which is self-evident, but it also =\n5780 \u00d7 208, _i.e._, it is a multiple of the encircled number. It\nconsequently also = 11,560 \u00d7 104, and thus it is related to the first and\nthird numbers just now discussed.\n\nThe position of this number is IV Ahau 18 Kankin (1 Kan) and the position\nof the suppressed number is IV Eb 10 Zotz (also 1 Kan).\n\nWe ought now to discuss the last two numbers of this section amounting to\nmillions:--1,567,332 and 1,520,654, which are in the third and fourth\ncolumns at the top of page 70. But before going further, we must examine\nfour other numbers, two of which, 111,554 and (with my correction) 101,812,\nare in column 4 on the lower part of page 70, and the other two, 83,474 and\n34,732, are on the top of page 73. Although these four numbers are not\nornamented with circles, they all have the significance of the numbers\nenclosed in circles and are designations of differences between suppressed\nand specified numbers.\n\nLet us first of all examine their curious relation to one another:--\n\nThe Manuscript should have set down under these numbers the day IX Ix twice\nand IV Eb twice, from which days the numbers in question must be computed;\nbut here the two errors already mentioned were made. 111,554 - 101,812 is\n9742, the very same number which we shall afterward find as the difference\nof the serpent numbers on page 69.\n\n83,474 - 34,732 = 48,742. If 9472 be subtracted from this, the remainder is\nexactly 39,000 = 150 Tonalamatls = 50 revolutions of Mars. I have already\nfound this number on page 31a, and also the double of it, 78,000, on page\n24, and this I found by using 68,900 + 9100 for my computation.\n\n111,554 - 83,474 = 28,080, _i.e._, exactly the double of the important\n14,040, which is recorded on page 73.\n\n101,812 - 34,732 = 67,080, _i.e._, = 258 Tonalamatls or 86 revolutions of\nMars.\n\n111,554 - 34,732 = 76,822; if 122, the interval from IV Eb to IX Ix be\nsubtracted from this, the remainder is 76,700 = 295 Tonalamatls.\n\n101,812 - 83,474 = 18,338; if 138, the interval from IX Ix to IV Eb, be\nsubtracted from 18,338, the remainder is 18,200 = 70 Tonalamatls = 50\nritual years of 364 days each, _i.e._, exactly the double of the 9100\nspecified on page 24.\n\nNow we also have the following equations for the four numbers:--\n\n  111,554 = 429 \u00d7 260 + 14.\n   83,474 = 321 \u00d7 260 + 14.\n  101,812 = 391 \u00d7 260 + 152.\n   34,732 = 133 \u00d7 260 + 152.\n\nA day VIII Ahau is 14 days back of the day IX Ix, and another VIII Ahau is\n152 days back of IV Eb.\n\nThus a day VIII Ahau hitherto unmentioned is introduced into the\ncomputations. This day has no doubt been chosen, because it divides the\nTonalamatl beginning with IV Ahau into two parts of 160 and 100 days, which\nare in the proportion of 8 to 5, _i.e._, the same proportion as the Venus\nyear to the solar year.\n\nThis day VIII Ahau may also figure in the large numbers of the first two\ncolumns on page 70, for 1,394,120 and 1,201,200 are both divisible by 14,\nthe interval between VIII Ahau and IX Ix.\n\nNow I believe that the large numbers were constructed in the following\ntwofold manner (I add the corresponding dates):--\n\n        160\n  1,408,940 = 5419 \u00d7 260\n  ---------\n  1,409,100 = VIII Ahau 3 Yax (9 Cauac).\n    111,554\n  ---------\n  1,520,654 = IX Ix 7 Zip (3 Muluc).\n\n        160\n  1,437,020 = 5527 \u00d7 260\n  ---------\n  1,437,180 = VIII Ahau 18 Mol (8 Kan).\n     83,474\n  ---------\n  1,520,654 = IX Ix 7 Zip (3 Muluc).\n\n        160\n  1,465,360 = 5636 \u00d7 260\n  ---------\n  1,465,520 = VIII Ahau 8 Uo (8 Ix).\n    101,812\n  ---------\n  1,567,332 = IV Eb 5 Pop (1 Muluc).\n\n        160\n  1,532,440 = 5894 \u00d7 260\n  ---------\n  1,532,600 = VIII Ahau 13 Pax (9 Muluc).\n     34,732\n  ---------\n  1,567,332 = IV Eb 5 Pop (1 Muluc).\n\nThe last record of the date of VIII Ahau seems to throw light on the date\n13 Pax (page 70, column 3), which is directly above the date VIII Ahau, and\nwhich I have already mentioned in the discussion of the groups of\nhieroglyphs.\n\nIndeed, it seems as if a day VIII Ahau occurred a fifth time in that\npassage, for in consequence of the correction made by the scribe we read\nhere VIII Ahau 13 Yaxkin. This would point to a year 7 Muluc, the position\nof which between the other four is, of course, undetermined.\n\nIf the two large numbers in the Manuscript were treated in the same way as\nthe other large numbers, they would not be recorded at all, but instead of\nthem there would have been two numbers belonging to the day IV Ahau and\nunder them would have been the encircled numbers 208 and 86, or these\nnumbers increased by a multiple of 260. This passage would then read about\nas follows:--\n\n  1,567,540 (IV Ahau)     1,520,740 (IV Ahau)\n        208 (IV Eb)              86 (IX Ix).\n\nThese two numbers for IV Ahau are equal to 6029 and 5849 Tonalamatls. If\n5549 \u00d7 260 be subtracted from these, the remainders are 480 and 300\nTonalamatls respectively, _i.e._, 124,800 and 78,000, and these are in the\nproportion of 8 to 5.\n\nNow the two large numbers have the difference 46,678 = 179 \u00d7 260 + 138; the\nlatter is the interval from IX Ix to IV Eb.\n\nThe four numbers of the days VIII Ahau seem to stand in very irregular\nrelation to one another and yet they show the following striking results,\nif the first and third and also the second and fourth numbers be combined\n(as I combined them under page 24):--\n\nIn the first case we see the following:--\n\n    1,465,520 - 1,409,100 = 56,420 = 3 \u00d7 18,980 - 520.\n  3 Yax (9 Cauac) to 8 Uo (8 Ix) = 18,460 = 18,980 - 520.\n       56,420 - 18,460 = 37,960 = 2 \u00d7 18,980.\n\nWhile in the second case:--\n\n  1,532,600 - 1,437,180 = 95,420 = 5 \u00d7 18,980 - 520.\n      18 Mol (8 Kan) to 13 Pax (9 Muluc) = 520.\n        95,420 - 520 = 94,900 = 5 \u00d7 18,980.\n\n5. The Serpent.\n\nAs in the section occupying pages 61-64, the single series is crowned by\nfour serpents with eight large numbers, so in this section the two series\nend in a single serpent with two numbers, one for each series, but both\nbear some obscure relation to the day VIII Ahau, which has made its\nappearance here. The two sections also correspond, inasmuch as the numbers\nin both are computed not from the normal date, but from the date IX Kan 12\nKayab (4 Ix).\n\nThe serpent pictured here is different from the previous ones, inasmuch as\nit is partly black. The god B is sitting on its opened jaws, and this time\nhe, too, is painted black (as on page 31c); there is an animal's head upon\nthe god's head, in which we again recognize that of the animal with the\nfourth serpent in the preceding section. The god is armed with spear and\nshield and recalls his picture at the bottom of page 74.\n\nThere are eight hieroglyphs above this picture, just as there are over each\nof the first four serpents. The two top hieroglyphs are obliterated. Of the\nlegible hieroglyphs, the one at the left top is the Bacab sign, which also\noccurs over the first of the four serpents. In the third line are the same\ntwo hieroglyphs, which are in the third line of the first and second\ncolumns on page 70. The first of the two also occupies the same place on\npage 62 above the fourth serpent. But here at the bottom we find the date\nIX Kan 12 Kayab (4 Ix), the same date which we found over the fourth\nserpent, which is thus again brought into closer connection with the single\nserpent.\n\nThere can be no doubt here regarding the two numbers in the serpents, but\nnotice should be taken of the fact that the figure 1 is barely visible in\nthe red number.\n\nThe black number here has the figures 4. 5. 19. 13. 12. 8. and the red 4.\n6. 1. 0. 13. 10. The black is therefore 12,381,728, and the red 12,391,470.\nThe black number is somewhat less than the eight numbers in the four\nserpents, and the red is somewhat larger than the least of them.\n\nThe difference of the two is 9742 = 37 \u00d7 260 + 122; but 122 is the interval\nbetween days IV Eb and IX Ix. Now this is the same 9742 which we found on\npage 70, as the difference between 111,554 and 101,812.\n\nIn order not merely to examine these numbers, but also to understand them,\nwe will again make use of 109 Ahau-Katuns = 12,412,920, as we did in the\nfirst four serpents, and we shall have the following:--\n\n     Black                          Red\n\n  12,381,728                     12,391,470\n  12,412,920                     12,412,920\n  ----------                     ----------\n     -31,192 = 119 \u00d7 260 + 252      -21,450 = 82 \u00d7 260 + 130\n          IV Eb - IX Kan = 252          IX Ix - IX Kan = 130\n\nThe date given for both numbers was the day IX Kan, which was likewise the\nstarting-point for six of the eight numbers in the previous serpents.\n\nBesides this the day IV Eb, the starting-point of the 65-series, is given\nfor the black number, and therefore also the interval between IV Eb and IX\nKan = 252.\n\nTo this 252 was added a multiple of 260, not an arbitrary choice, but one\nwhich combined with 252 resulted in a number divisible by 8, the interval\nfrom IX Kan to IV Eb. 31,192 = 3899 \u00d7 8 = 119 \u00d7 260 + 252 was thus\nobtained.\n\nThe subtraction of this number from 12,412,920 resulted in the serpent\nnumber 12,381,728.\n\nIn addition to all this the day IX Ix, the starting-point of the 54-series,\nis given for the red number; consequently also the interval between IX Ix\nand IX Kan = 130, which, at the same time, is reversely the interval from\nIX Kan to IX Ix.\n\nTo this 130 was added a multiple of 260, which _must_ in every case be a\nmultiple also of 130. Thus we obtain the 21,450 = 82 \u00d7 260 + 130.\n\nThe subtraction of this number from 12,412,920 results in the serpent\nnumber 12,391,470.\n\nReckoned from the starting-point IX Kan 12 Kayab (4 Ix) the black number\ncorresponds to the date IV Eb 5 Chen (10 Muluc) and the red to IX Ix 12 Zip\n(11 Kan), and these two dates must certainly have been under the serpent;\nthe months unfortunately are effaced.\n\nIt is self evident that the black number is exactly divisible by 8 and the\nred by 130.\n\nThe two events indicated by the two numbers must be to some extent\ncoincident with the beginning of the seven events recorded in the previous\nfour serpents. These large numbers pertaining to the destruction of the\nworld are a reminder of the numbers, which on page 24 we believed were\nconnected with the creation of the world. Thus here, too, we have the\ngenesis and the apocalypse of all the mythologies.\n\n6. The Columns of Hieroglyphs.\n\nThe last portion of this section is formed by the two middle columns of\nhieroglyphs on page 69. They bear an extraordinary resemblance to those\ndiscussed under page 61 even in regard to the fact that each column\ncontains 18 signs. Besides, the upper 10 lines, _i.e._, the upper 20 signs,\nare exactly alike on the two pages, aside from slight variations, and\ndiffer only in so far as the passage on page 69 is written on blue ground\nand the one on page 61 on white.\n\nBut also the lower part, with eight signs in each column, shows many points\nin common with page 61. Here as there the whole is divided into several\ngroups.\n\nWith the four signs 11ab and 12ab, which formed the first group there, I\ncan compose only the two signs 11ab here. In the cross 11a, as on pages 24\nand 58 of the Manuscript, I see the sign for 20 with the prefixed 5 making\n25. In 11b we find the sign for 18,980 days, which we have already met with\nseveral times. Hence 11ab would have the value of 25 \u00d7 18,980 = 474,500\ndays, as on page 61 the corresponding four signs seemed to form 421,940.\nAnd as the number there was 1156 \u00d7 365, so on page 69 we have 1300 \u00d7 365.\n\nI believe there is a disarrangement in what follows, inasmuch as I assume\nthat the two signs 12b and 13a ought to be placed _before_ and not _after_\n12a. Assuming that the two little crosses on either side of the 1 are\nmeaningless, we should assign the value of 61 to the 3 Chuen, 1 Kin. Here,\nin the first place, the intention seems to be to establish some connection\nwith the two days VII Kan and IV Ik specified with their numbers on page\n63, column 3, as well as with the days most important there, III Chicchan\nand XIII Akbal, _i.e._, a connection with the previous section of the four\nserpents in general; for the interval from VII Kan to III Chicchan, as well\nas that between IV Ik and XIII Akbal is 61 and on pages 70-73 the two most\nimportant days, IV Eb and IX Ix, are 122 days apart, and 122 is the second\nmultiple of 61. I can now put the 144,000 of 12a in the place of the 13a.\nThen, secondly, the four signs from 13a to 14b in the one section are\nexactly like those in the other section, and therefore need not be\ndiscussed here. Only 15ab differs from the signs in the other passages\ninasmuch as on page 69 we find 4 \u00d7 20 + 4 \u00d7 1. The last 4 agrees even\nbetter than it does there with the distance from IV Ahau to the day Kan\nwith which the serpent numeral begins.\n\nNothing on page 69 corresponds to the signs in 16ab and 17ab of page 61. On\nthe contrary, the initial date of the serpent IX Kan 12 Kayab, which on\npage 61 does not appear until 18ab is set down in 16ab. On the other hand\non page 69 the four signs 17ab and 18ab are added, 17a being a sign as yet\nunknown with 13 as a superfix. I feel inclined, though with many\nmisgivings, to treat 17ab like 5a and b of page 61 and to assign to them\nthe value of an Ahau-Katun of 113,880 days. For then they would denote the\n13th Ahau-Katun, which extends from the day 1,366,560 (page 24) to\n1,480,440 and which contains the two large numbers on page 70, left, top,\nwhile the two lower numbers in the first and second columns of that page\nbelong to the 12th Ahau-Katun, and the two in the third and fourth belong\nto the 14th Ahau-Katun. The 13th would be the present and the 12th and 14th\nthe past and future; but all this could only be confirmed by further\nresearch. At all events, the signs for beginning in 17b and for end in 18a\nrefer to past and future. Unfortunately, 18b is entirely effaced.\n\nPage 74.[5]\n\nBesides the picture, this page contains only 15 hieroglyphs in three\nhorizontal rows. Only about six of these signs are decipherable. The\nsecond, third and fourth of the lower line are three different heads; the\nmiddle is the familiar head of god B, the one on the left has the Akbal eye\nand the abbreviated sign for the south, which is repeated in the affix; the\nhead on the right has the sign for the west as a prefix. Very little more\nis to be said of the other hieroglyphs than that the second and third of\nthe second line have the sign for the east; the first of the second line,\nhowever, was the one which we found on pages 71-73 as the constant\ncompanion of the Bacabs and which suggested the wind. The last sign of the\nsecond line must have contained that for north, so that the four cardinal\npoints all came together here.\n\nThe picture begins below these signs. Astronomical figures, apparently\nVenus, Mars, Mercury and Jupiter, end in the fore part of a crocodile.\nBelow the astronomical signs are the signs for the sun and moon. Streams of\nwater are falling from the jaws of the crocodile and also from the sun and\nmoon. And a fourth stream is being poured from a jug by the old woman with\nthe tiger claws, and with the serpent on her head, whom we saw on pages 39,\n43 and 67 engaged in the same occupation. Cross-bones are represented on\nher skirt as the symbol of death. The sign of the ninth day, Eb, appears on\nthe jug; this is the day which was avoided in the Tonalamatls, for not a\nsingle Tonalamatl begins with Eb in the Dresdensis, nor does one begin with\nthe week-day IX; does Bolon meaning nine suggest Balam, the jaguar?\n\nStill further down on the page sits a black god, who may be the same as the\ngod on pages 7a and 16b, with a bird of prey on his head. There are two\narrows in his right hand and his left hand holds what may be an atlatl, but\nit is very much longer than is usually the case; at the same time it can be\nregarded as a spear.\n\nThis page can denote nothing but the end of the world, for which the\nserpent numbers have prepared the way. Perhaps what looks like a zero above\nthe sign Eb in the stream of water may likewise point to this calamity.\n\n       *       *       *       *       *\n\nINDEX.\n\n------\n\nThe numbers in the first column refer to the pages of the Manuscript, and\nthose in the second column to the pages of the Commentary.\n\n  FIRST PART.\n\n       1   |  55  |      16a  |  90  |  42a-44a  | 146\n       2   |  55  |  16a-17a  |  90  |      45a  | 148\n       3   |  59  |  18a-19a  |  92  |  29b-30b  | 150\n   4a-10a  |  61  |  19a-21a  |  93  |  30b-31b  | 151\n   4b-5b   |  67  |  21a-22a  |  93  |  31b-35b  | 152\n  10a-12a  |  69  |  22a-23a  |  95  |  35b-37b  | 156\n      12a  |  69  |  16b-17b  |  96  |  38b-41b  | 159\n   5b-6b   |  70  |  17b-18b  |  97  |  41b-43b  | 162\n   6b-7b   |  71  |  16c-17c  |  98  |  43b-44b  | 164\n      8b   |  72  |  17c-18c  |  99  |  44b-45b  | 165\n      9b   |  73  |  18c-19c  | 100  |  29c-30c  | 167\n      10b  |  74  |  19c-20c  | 100  |  30c-33c  | 168\n  10b-11b  |  75  |      19b  | 101  |  33c-39c  | 170\n      12b  |  76  |  19b-20b  | 101  |  40c-41c  | 176\n   4c-5c   |  77  |      20b  | 102  |  42c-45c  | 178\n   5c-6c   |  78  |      21b  | 103  |\n   6c-7c   |  79  |  21c-22c  | 104  |  SECOND PART.\n      8c   |  80  |  22c-23c  | 105  |\n      9c   |  81  |      22b  | 107  |   46-50   | 182\n  10c-11c  |  82  |      23b  | 108  |  51a-52a  | 197\n      12c  |  83  |      24   | 110  |   51-58   | 200\n      13a  |  84  |   25-28   | 120  |   58-59   | 215\n  13b-14b  |  85  |  29a-30a  | 132  |      60   | 219\n  13c-14c  |  86  |  30a-31a  | 133  |   61-64   | 222\n  14a-15a  |  85  |  31a-32a  | 133  |   65-69   | 235\n      15a  |  88  |  32a-39a  | 138  |   69-73   | 245\n  15b-16b  |  88  |  40a-41a  | 144  |      74   | 265\n      15c  |  89  |           |      |           |\n\n       *       *       *       *       *\n\n[Illustration: GLYPHS REFERRED TO IN THE TEXT.]\n\n[Illustration: CARDINAL POINTS.]\n\n       *       *       *       *       *\n\nNotes\n\n[1] The Manuscript has incorrectly 8 and 18.\n\n[2] = 20 Chen.\n\n[3] The sign denotes the end of the 360-day year.\n\n[4] = 20 Zotz.\n\n[5] Compare the Peresianus, page 20.","title":"Commentary on the Maya Manuscript in the Royal Public Library of Dresden","tradition":"myth-cosmogony","translated_text":null,"word_count":81667}